LMFDB - Embedded newform 64.10.i.a.5.15

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [64,10,Mod(5,64)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("64.5"); S:= CuspForms(chi, 10); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(64, base_ring=CyclotomicField(16)) chi = DirichletCharacter(H, H._module([0, 1])) N = Newforms(chi, 10, names="a")

Level:	$ N $	$=$	$ 64 = 2^{6} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	64.i (of order $16$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$32.9622935145$
Analytic rank:	$0$
Dimension:	$568$
Relative dimension:	$71$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			5.15
Character	$\chi$	$=$	64.5
Dual form			64.10.i.a.13.15

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-18.3262 + 13.2722i) q^{2} +(-96.8286 - 64.6988i) q^{3} +(159.700 - 486.457i) q^{4} +(193.294 + 38.4485i) q^{5} +(2633.19 - 99.4401i) q^{6} +(-1929.06 + 4657.16i) q^{7} +(3529.63 + 11034.5i) q^{8} +(-2342.51 - 5655.33i) q^{9} +(-4052.64 + 1860.81i) q^{10} +(-24497.6 - 36663.3i) q^{11} +(-46936.7 + 36770.5i) q^{12} +(-63224.1 + 12576.1i) q^{13} +(-26458.2 - 110951. i) q^{14} +(-16228.8 - 16228.8i) q^{15} +(-211136. - 155374. i) q^{16} +(110928. - 110928. i) q^{17} +(117988. + 72550.5i) q^{18} +(-88987.9 - 447373. i) q^{19} +(49572.5 - 87888.8i) q^{20} +(488101. - 326139. i) q^{21} +(935549. + 346763. i) q^{22} +(1.27871e6 - 529660. i) q^{23} +(372148. - 1.29682e6i) q^{24} +(-1.76857e6 - 732565. i) q^{25} +(991747. - 1.06959e6i) q^{26} +(-586253. + 2.94729e6i) q^{27} +(1.95744e6 + 1.68215e6i) q^{28} +(-1.47277e6 + 2.20416e6i) q^{29} +(512803. + 82021.3i) q^{30} -4.67830e6i q^{31} +(5.93147e6 + 45192.1i) q^{32} +5.13502e6i q^{33} +(-560637. + 3.50515e6i) q^{34} +(-551937. + 826031. i) q^{35} +(-3.12517e6 + 236375. i) q^{36} +(-327874. + 1.64833e6i) q^{37} +(7.56841e6 + 7.01758e6i) q^{38} +(6.93556e6 + 2.87280e6i) q^{39} +(257997. + 2.26860e6i) q^{40} +(-1.04175e7 + 4.31507e6i) q^{41} +(-4.61648e6 + 1.24550e7i) q^{42} +(-8.82762e6 + 5.89843e6i) q^{43} +(-2.17473e7 + 6.06190e6i) q^{44} +(-235354. - 1.18321e6i) q^{45} +(-1.64042e7 + 2.66779e7i) q^{46} +(-1.62263e7 + 1.62263e7i) q^{47} +(1.03915e7 + 2.87049e7i) q^{48} +(1.05664e7 + 1.05664e7i) q^{49} +(4.21339e7 - 1.00476e7i) q^{50} +(-1.79179e7 + 3.56410e6i) q^{51} +(-3.97918e6 + 3.27642e7i) q^{52} +(5.74460e7 + 8.59739e7i) q^{53} +(-2.83731e7 - 6.17935e7i) q^{54} +(-3.32559e6 - 8.02868e6i) q^{55} +(-5.81982e7 - 4.84809e6i) q^{56} +(-2.03279e7 + 4.90759e7i) q^{57} +(-2.26361e6 - 5.99408e7i) q^{58} +(-1.29342e7 - 2.57278e6i) q^{59} +(-1.04863e7 + 5.30287e6i) q^{60} +(1.53244e8 + 1.02394e8i) q^{61} +(6.20911e7 + 8.57355e7i) q^{62} +3.08566e7 q^{63} +(-1.09301e8 + 7.78952e7i) q^{64} -1.27044e7 q^{65} +(-6.81528e7 - 9.41054e7i) q^{66} +(1.19807e8 + 8.00524e7i) q^{67} +(-3.62465e7 - 7.16769e7i) q^{68} +(-1.58084e8 - 3.14449e7i) q^{69} +(-848310. - 2.24634e7i) q^{70} +(3.94951e7 - 9.53496e7i) q^{71} +(5.41353e7 - 4.58096e7i) q^{72} +(1.19007e8 + 2.87309e8i) q^{73} +(-1.58682e7 - 3.45593e7i) q^{74} +(1.23852e8 + 1.85358e8i) q^{75} +(-2.31839e8 - 2.81566e7i) q^{76} +(2.18004e8 - 4.33637e7i) q^{77} +(-1.65231e8 + 3.94022e7i) q^{78} +(9.73339e7 + 9.73339e7i) q^{79} +(-3.48373e7 - 3.81507e7i) q^{80} +(1.62256e8 - 1.62256e8i) q^{81} +(1.33643e8 - 2.17341e8i) q^{82} +(-9.30536e7 - 4.67812e8i) q^{83} +(-8.07026e7 - 2.89524e8i) q^{84} +(2.57067e7 - 1.71767e7i) q^{85} +(8.34920e7 - 2.25257e8i) q^{86} +(2.85213e8 - 1.18139e8i) q^{87} +(3.18092e8 - 3.99726e8i) q^{88} +(-5.25318e7 - 2.17594e7i) q^{89} +(2.00168e7 + 1.85600e7i) q^{90} +(6.33944e7 - 3.18705e8i) q^{91} +(-5.34463e7 - 7.06625e8i) q^{92} +(-3.02681e8 + 4.52993e8i) q^{93} +(8.20088e7 - 5.12725e8i) q^{94} -8.98958e7i q^{95} +(-5.71412e8 - 3.88135e8i) q^{96} -1.65578e8i q^{97} +(-3.33881e8 - 5.34032e7i) q^{98} +(-1.49957e8 + 2.24426e8i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 568 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 8 q^{8} - 8 q^{9} - 8 q^{10} - 8 q^{11} - 8 q^{12} - 8 q^{13} - 8 q^{14} - 8 q^{15} - 8 q^{16} - 8 q^{17} - 8 q^{18} - 8 q^{19} - 8 q^{20}+ \cdots + 157456 q^{99}+O(q^{100}) $ 568 * q - 8 * q^2 - 8 * q^3 - 8 * q^4 - 8 * q^5 - 8 * q^6 - 8 * q^7 - 8 * q^8 - 8 * q^9 - 8 * q^10 - 8 * q^11 - 8 * q^12 - 8 * q^13 - 8 * q^14 - 8 * q^15 - 8 * q^16 - 8 * q^17 - 8 * q^18 - 8 * q^19 - 8 * q^20 - 8 * q^21 + 3576336 * q^22 - 8 * q^23 + 12096992 * q^24 - 8 * q^25 - 2105968 * q^26 - 8 * q^27 - 21791488 * q^28 - 8 * q^29 + 44263272 * q^30 + 29441312 * q^32 - 38537008 * q^34 - 8 * q^35 - 110500728 * q^36 - 8 * q^37 + 66947312 * q^38 - 8 * q^39 + 97089632 * q^40 - 8 * q^41 - 224559088 * q^42 - 8 * q^43 + 146176992 * q^44 - 8 * q^45 - 8 * q^46 - 8 * q^47 - 8 * q^48 - 8 * q^49 + 182758288 * q^50 - 360057320 * q^51 - 25227512 * q^52 - 8 * q^53 - 646232264 * q^54 + 280217656 * q^55 + 203163008 * q^56 - 8 * q^57 + 855153280 * q^58 - 576150472 * q^59 + 230939416 * q^60 - 8 * q^61 - 597609496 * q^62 + 1260236864 * q^63 - 1364809832 * q^64 - 16 * q^65 + 186013784 * q^66 - 1007094968 * q^67 + 1004327944 * q^68 - 8 * q^69 + 1869092056 * q^70 - 476202952 * q^71 - 714729104 * q^72 - 8 * q^73 - 2182183312 * q^74 + 2309166136 * q^75 - 888710984 * q^76 - 8 * q^77 + 5243787376 * q^78 - 2269128680 * q^79 - 5193915232 * q^80 - 8 * q^81 + 3136405672 * q^82 - 8 * q^83 + 6148771880 * q^84 - 8 * q^85 - 988828368 * q^86 - 8 * q^87 - 4940685368 * q^88 - 8 * q^89 - 7222410008 * q^90 - 8 * q^91 + 1729489584 * q^92 + 157456 * q^93 + 6710490136 * q^94 + 10366581632 * q^96 + 2543861360 * q^98 + 157456 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/64\mathbb{Z}\right)^\times$.

$n$	$5$	$63$
$\chi(n)$	$e\left(\frac{1}{16}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−18.3262	+	13.2722i	−0.809912	+	0.586552i
$2$	−18.3262	+	13.2722i	−0.809912	+	0.586552i
$3$	−96.8286	−	64.6988i	−0.690173	−	0.461159i	0.160375	−	0.987056i	$-0.448730\pi$
$3$	−96.8286	−	64.6988i	−0.690173	−	0.461159i	−0.850548	+	0.525897i	$0.823730\pi$
$4$	159.700	−	486.457i	0.311914	−	0.950110i
$5$	193.294	+	38.4485i	0.138310	+	0.0275115i	0.263760	−	0.964588i	$-0.415037\pi$
$5$	193.294	+	38.4485i	0.138310	+	0.0275115i	−0.125450	+	0.992100i	$0.540037\pi$
$6$	2633.19	−	99.4401i	0.829473	−	0.0313243i
$7$	−1929.06	+	4657.16i	−0.303672	+	0.733129i	0.696211	+	0.717837i	$0.254868\pi$
$7$	−1929.06	+	4657.16i	−0.303672	+	0.733129i	−0.999883	+	0.0152919i	$0.995132\pi$
$8$	3529.63	+	11034.5i	0.304666	+	0.952459i
$9$	−2342.51	−	5655.33i	−0.119012	−	0.287320i
$10$	−4052.64	+	1860.81i	−0.128156	+	0.0588439i
$11$	−24497.6	−	36663.3i	−0.504495	−	0.755030i	0.488579	−	0.872519i	$-0.337515\pi$
$11$	−24497.6	−	36663.3i	−0.504495	−	0.755030i	−0.993074	+	0.117490i	$0.962515\pi$
$12$	−46936.7	+	36770.5i	−0.653427	+	0.511899i
$13$	−63224.1	+	12576.1i	−0.613956	+	0.122124i	−0.492266	−	0.870445i	$-0.663831\pi$
$13$	−63224.1	+	12576.1i	−0.613956	+	0.122124i	−0.121690	+	0.992568i	$0.538831\pi$
$14$	−26458.2	−	110951.i	−0.184071	−	0.771889i
$15$	−16228.8	−	16228.8i	−0.0827705	−	0.0827705i
$16$	−211136.	−	155374.i	−0.805419	−	0.592705i
$17$	110928.	−	110928.i	0.322123	−	0.322123i	−0.527458	−	0.849581i	$-0.676855\pi$
$17$	110928.	−	110928.i	0.322123	−	0.322123i	0.849581	+	0.527458i	$0.176855\pi$
$18$	117988.	+	72550.5i	0.264917	+	0.162897i
$19$	−88987.9	−	447373.i	−0.156653	−	0.787550i	−0.976592	−	0.215099i	$-0.930993\pi$
$19$	−88987.9	−	447373.i	−0.156653	−	0.787550i	0.819939	−	0.572451i	$-0.194007\pi$
$20$	49572.5	−	87888.8i	0.0692797	−	0.122828i
$21$	488101.	−	326139.i	0.547675	−	0.365945i
$22$	935549.	+	346763.i	0.851460	+	0.315595i
$23$	1.27871e6	−	529660.i	0.952791	−	0.394659i	0.148512	−	0.988911i	$-0.452552\pi$
$23$	1.27871e6	−	529660.i	0.952791	−	0.394659i	0.804279	+	0.594252i	$0.202552\pi$
$24$	372148.	−	1.29682e6i	0.228963	−	0.797861i
$25$	−1.76857e6	−	732565.i	−0.905507	−	0.375073i
$26$	991747.	−	1.06959e6i	0.425619	−	0.459027i
$27$	−586253.	+	2.94729e6i	−0.212299	+	1.06730i
$28$	1.95744e6	+	1.68215e6i	0.601834	+	0.517195i
$29$	−1.47277e6	+	2.20416e6i	−0.386674	+	0.578698i	−0.972836	−	0.231496i	$-0.925638\pi$
$29$	−1.47277e6	+	2.20416e6i	−0.386674	+	0.578698i	0.586162	+	0.810194i	$0.300638\pi$
$30$	512803.	+	82021.3i	0.115586	+	0.0184876i
$31$		−	4.67830e6i		−	0.909831i	−0.890535	−	0.454915i	$-0.849670\pi$
$31$		−	4.67830e6i		−	0.909831i	0.890535	−	0.454915i	$-0.150330\pi$
$32$	5.93147e6	+	45192.1i	0.999971	+	0.00761881i
$33$			5.13502e6i			0.753754i
$34$	−560637.	+	3.50515e6i	−0.0719493	+	0.449833i
$35$	−551937.	+	826031.i	−0.0621703	+	0.0930444i
$36$	−3.12517e6	+	236375.i	−0.310108	+	0.0234553i
$37$	−327874.	+	1.64833e6i	−0.0287607	+	0.144590i	−0.992498	−	0.122265i	$-0.960984\pi$
$37$	−327874.	+	1.64833e6i	−0.0287607	+	0.144590i	0.963737	+	0.266854i	$0.0859843\pi$
$38$	7.56841e6	+	7.01758e6i	0.588814	+	0.545961i
$39$	6.93556e6	+	2.87280e6i	0.480055	+	0.198845i
$40$	257997.	+	2.26860e6i	0.0159347	+	0.140116i
$41$	−1.04175e7	+	4.31507e6i	−0.575752	+	0.238484i	−0.651508	−	0.758642i	$-0.725863\pi$
$41$	−1.04175e7	+	4.31507e6i	−0.575752	+	0.238484i	0.0757553	+	0.997126i	$0.475863\pi$
$42$	−4.61648e6	+	1.24550e7i	−0.228923	+	0.617623i
$43$	−8.82762e6	+	5.89843e6i	−0.393764	+	0.263104i	−0.736652	−	0.676272i	$-0.763595\pi$
$43$	−8.82762e6	+	5.89843e6i	−0.393764	+	0.263104i	0.342889	+	0.939376i	$0.388595\pi$
$44$	−2.17473e7	+	6.06190e6i	−0.874720	+	0.243821i
$45$	−235354.	−	1.18321e6i	−0.00855590	−	0.0430134i
$46$	−1.64042e7	+	2.66779e7i	−0.540189	+	0.878500i
$47$	−1.62263e7	+	1.62263e7i	−0.485043	+	0.485043i	−0.906738	−	0.421695i	$-0.861435\pi$
$47$	−1.62263e7	+	1.62263e7i	−0.485043	+	0.485043i	0.421695	+	0.906738i	$0.361435\pi$
$48$	1.03915e7	+	2.87049e7i	0.282547	+	0.780496i
$49$	1.05664e7	+	1.05664e7i	0.261845	+	0.261845i
$50$	4.21339e7	−	1.00476e7i	0.953380	−	0.227350i
$51$	−1.79179e7	+	3.56410e6i	−0.370870	+	0.0737707i
$52$	−3.97918e6	+	3.27642e7i	−0.0754707	+	0.621418i
$53$	5.74460e7	+	8.59739e7i	1.00004	+	1.49667i	0.862427	+	0.506182i	$0.168944\pi$
$53$	5.74460e7	+	8.59739e7i	1.00004	+	1.49667i	0.137615	+	0.990486i	$0.456056\pi$
$54$	−2.83731e7	−	6.17935e7i	−0.454083	−	0.988942i
$55$	−3.32559e6	−	8.02868e6i	−0.0490045	−	0.118307i
$56$	−5.81982e7	−	4.84809e6i	−0.790794	−	0.0658756i
$57$	−2.03279e7	+	4.90759e7i	−0.255068	+	0.615788i
$58$	−2.26361e6	−	5.99408e7i	−0.0262649	−	0.695499i
$59$	−1.29342e7	−	2.57278e6i	−0.138965	−	0.0276419i	0.125117	−	0.992142i	$-0.460069\pi$
$59$	−1.29342e7	−	2.57278e6i	−0.138965	−	0.0276419i	−0.264083	+	0.964500i	$0.585069\pi$
$60$	−1.04863e7	+	5.30287e6i	−0.104458	+	0.0528238i
$61$	1.53244e8	+	1.02394e8i	1.41710	+	0.946873i	0.999264	+	0.0383488i	$0.0122098\pi$
$61$	1.53244e8	+	1.02394e8i	1.41710	+	0.946873i	0.417832	+	0.908525i	$0.362790\pi$
$62$	6.20911e7	+	8.57355e7i	0.533663	+	0.736882i
$63$	3.08566e7			0.246783
$64$	−1.09301e8	+	7.78952e7i	−0.814357	+	0.580364i
$65$	−1.27044e7			−0.0882760
$66$	−6.81528e7	−	9.41054e7i	−0.442116	−	0.610474i
$67$	1.19807e8	+	8.00524e7i	0.726349	+	0.485331i	0.862946	−	0.505296i	$-0.168617\pi$
$67$	1.19807e8	+	8.00524e7i	0.726349	+	0.485331i	−0.136597	+	0.990627i	$0.543617\pi$
$68$	−3.62465e7	−	7.16769e7i	−0.205578	−	0.406527i
$69$	−1.58084e8	−	3.14449e7i	−0.839591	−	0.167005i
$70$	−848310.	−	2.24634e7i	−0.00422292	−	0.111824i
$71$	3.94951e7	−	9.53496e7i	0.184451	−	0.445304i	−0.804424	−	0.594056i	$-0.797526\pi$
$71$	3.94951e7	−	9.53496e7i	0.184451	−	0.445304i	0.988874	+	0.148752i	$0.0475257\pi$
$72$	5.41353e7	−	4.58096e7i	0.237402	−	0.200891i
$73$	1.19007e8	+	2.87309e8i	0.490480	+	1.18412i	0.954477	+	0.298286i	$0.0964150\pi$
$73$	1.19007e8	+	2.87309e8i	0.490480	+	1.18412i	−0.463997	+	0.885837i	$0.653585\pi$
$74$	−1.58682e7	−	3.45593e7i	−0.0615157	−	0.133974i
$75$	1.23852e8	+	1.85358e8i	0.451988	+	0.676448i
$76$	−2.31839e8	−	2.81566e7i	−0.797122	−	0.0968098i
$77$	2.18004e8	−	4.33637e7i	0.706735	−	0.140578i
$78$	−1.65231e8	+	3.94022e7i	−0.505435	+	0.120530i
$79$	9.73339e7	+	9.73339e7i	0.281153	+	0.281153i	0.833569	−	0.552416i	$-0.186294\pi$
$79$	9.73339e7	+	9.73339e7i	0.281153	+	0.281153i	−0.552416	+	0.833569i	$0.686294\pi$
$80$	−3.48373e7	−	3.81507e7i	−0.0950911	−	0.104135i
$81$	1.62256e8	−	1.62256e8i	0.418812	−	0.418812i
$82$	1.33643e8	−	2.17341e8i	0.326425	−	0.530860i
$83$	−9.30536e7	−	4.67812e8i	−0.215220	−	1.08198i	−0.925698	−	0.378263i	$-0.876521\pi$
$83$	−9.30536e7	−	4.67812e8i	−0.215220	−	1.08198i	0.710478	−	0.703719i	$-0.248479\pi$
$84$	−8.07026e7	−	2.89524e8i	−0.176861	−	0.634495i
$85$	2.57067e7	−	1.71767e7i	0.0534148	−	0.0356906i
$86$	8.34920e7	−	2.25257e8i	0.164589	−	0.444054i
$87$	2.85213e8	−	1.18139e8i	0.533744	−	0.221084i
$88$	3.18092e8	−	3.99726e8i	0.565433	−	0.710543i
$89$	−5.25318e7	−	2.17594e7i	−0.0887499	−	0.0367614i	0.337867	−	0.941194i	$-0.390295\pi$
$89$	−5.25318e7	−	2.17594e7i	−0.0887499	−	0.0367614i	−0.426617	+	0.904433i	$0.640295\pi$
$90$	2.00168e7	+	1.85600e7i	0.0321591	+	0.0298186i
$91$	6.33944e7	−	3.18705e8i	0.0969091	−	0.487195i
$92$	−5.34463e7	−	7.06625e8i	−0.0777807	−	1.02836i
$93$	−3.02681e8	+	4.52993e8i	−0.419577	+	0.627941i
$94$	8.20088e7	−	5.12725e8i	0.108339	−	0.677344i
$95$		−	8.98958e7i		−	0.113236i
$96$	−5.71412e8	−	3.88135e8i	−0.686640	−	0.466404i
$97$		−	1.65578e8i		−	0.189903i	−0.995482	−	0.0949513i	$-0.969730\pi$
$97$		−	1.65578e8i		−	0.189903i	0.995482	−	0.0949513i	$-0.0302695\pi$
$98$	−3.33881e8	−	5.34032e7i	−0.365657	−	0.0584857i
$99$	−1.49957e8	+	2.24426e8i	−0.156894	+	0.234809i
$100$	−6.38801e8	+	7.43341e8i	−0.638801	+	0.743341i
$101$	−1.22892e8	+	6.17818e8i	−0.117510	+	0.590764i	0.876493	+	0.481415i	$0.159877\pi$
$101$	−1.22892e8	+	6.17818e8i	−0.117510	+	0.590764i	−0.994003	+	0.109350i	$0.965123\pi$
$102$	2.81065e8	−	3.03126e8i	0.257102	−	0.277282i
$103$	1.86651e8	+	7.73133e7i	0.163404	+	0.0676841i	0.462886	−	0.886418i	$-0.346814\pi$
$103$	1.86651e8	+	7.73133e7i	0.163404	+	0.0676841i	−0.299482	+	0.954102i	$0.596814\pi$
$104$	−3.61928e8	−	6.53255e8i	−0.303369	−	0.547562i
$105$	1.06887e8	−	4.42738e7i	0.0858166	−	0.0355464i
$106$	−2.19383e9	−	8.13145e8i	−1.68782	−	0.625593i
$107$	−1.16746e9	+	7.80071e8i	−0.861022	+	0.575317i	−0.905812	−	0.423680i	$-0.860738\pi$
$107$	−1.16746e9	+	7.80071e8i	−0.861022	+	0.575317i	0.0447896	+	0.998996i	$0.485738\pi$
$108$	1.34010e9	+	7.55869e8i	0.947833	+	0.534613i
$109$	3.29922e8	+	1.65863e9i	0.223868	+	1.12546i	0.915223	+	0.402947i	$0.132014\pi$
$109$	3.29922e8	+	1.65863e9i	0.223868	+	1.12546i	−0.691355	+	0.722515i	$0.742986\pi$
$110$	1.67503e8	+	1.02998e8i	0.109083	+	0.0670749i
$111$	1.38393e8	−	1.38393e8i	0.0865287	−	0.0865287i
$112$	1.13090e9	−	6.83568e8i	0.679113	−	0.410488i
$113$	−1.71167e8	−	1.71167e8i	−0.0987567	−	0.0987567i	0.656002	−	0.754759i	$-0.272246\pi$
$113$	−1.71167e8	−	1.71167e8i	−0.0987567	−	0.0987567i	−0.754759	+	0.656002i	$0.772246\pi$
$114$	−2.78809e8	−	1.16917e9i	−0.154609	−	0.648344i
$115$	2.67532e8	−	5.32154e7i	0.142638	−	0.0283725i
$116$	8.37026e8	+	1.06844e9i	0.429218	+	0.547887i
$117$	2.19225e8	+	3.28093e8i	0.108157	+	0.161868i
$118$	2.71182e8	−	1.24516e8i	0.128763	−	0.0591229i
$119$	3.02623e8	+	7.30598e8i	0.138338	+	0.333977i
$120$	1.21794e8	−	2.36358e8i	0.0536182	−	0.104053i
$121$	1.58285e8	−	3.82135e8i	0.0671285	−	0.162063i
$122$	−4.16738e9	+	1.57377e8i	−1.70311	+	0.0643165i
$123$	1.28789e9	+	2.56177e8i	0.507348	+	0.100918i
$124$	−2.27579e9	−	7.47124e8i	−0.864439	−	0.283789i
$125$	−6.33739e8	−	4.23451e8i	−0.232175	−	0.155134i
$126$	−5.65485e8	+	4.09534e8i	−0.199873	+	0.144751i
$127$	5.45087e9			1.85930			0.929649	−	0.368446i	$-0.120110\pi$
$127$	5.45087e9			1.85930			0.929649	+	0.368446i	$0.120110\pi$
$128$	9.69239e8	−	2.87818e9i	0.319144	−	0.947706i
$129$	1.23639e9			0.393098
$130$	2.32823e8	−	1.68614e8i	0.0714958	−	0.0517784i
$131$	−2.44376e9	−	1.63287e9i	−0.724999	−	0.484429i	0.137491	−	0.990503i	$-0.456096\pi$
$131$	−2.44376e9	−	1.63287e9i	−0.724999	−	0.484429i	−0.862490	+	0.506074i	$0.831096\pi$
$132$	2.49796e9	+	8.20062e8i	0.716149	+	0.235106i
$133$	2.25515e9	+	4.48577e8i	0.624947	+	0.124310i
$134$	−3.25807e9	+	1.23038e8i	−0.872950	+	0.0329662i
$135$	−2.26638e8	+	5.47153e8i	−0.0587261	+	0.141777i
$136$	1.61557e9	+	8.32497e8i	0.404949	+	0.208669i
$137$	1.46815e8	+	3.54443e8i	0.0356064	+	0.0859614i	0.940682	−	0.339288i	$-0.110186\pi$
$137$	1.46815e8	+	3.54443e8i	0.0356064	+	0.0859614i	−0.905076	+	0.425250i	$0.860186\pi$
$138$	3.31443e9	−	1.52185e9i	0.777952	−	0.357204i
$139$	2.12481e9	+	3.18000e9i	0.482784	+	0.722538i	0.990276	−	0.139119i	$-0.0444271\pi$
$139$	2.12481e9	+	3.18000e9i	0.482784	+	0.722538i	−0.507491	+	0.861657i	$0.669427\pi$
$140$	3.13684e8	+	4.00410e8i	0.0690107	+	0.0880905i
$141$	2.62100e9	−	5.21349e8i	0.558445	−	0.111082i
$142$	5.41699e8	+	2.27158e9i	0.111805	+	0.468847i
$143$	2.00992e9	+	2.00992e9i	0.401945	+	0.401945i
$144$	−3.84103e8	+	1.55801e9i	−0.0744417	+	0.301952i
$145$	−3.69424e8	+	3.69424e8i	−0.0694016	+	0.0694016i
$146$	−5.99417e9	−	3.68581e9i	−1.09179	−	0.671343i
$147$	−3.39496e8	−	1.70676e9i	−0.0599663	−	0.301471i
$148$	7.49481e8	+	4.22735e8i	0.128405	+	0.0724253i
$149$	−4.36422e9	+	2.91608e9i	−0.725385	+	0.484687i	−0.862621	−	0.505852i	$-0.831178\pi$
$149$	−4.36422e9	+	2.91608e9i	−0.725385	+	0.484687i	0.137235	+	0.990538i	$0.456178\pi$
$150$	−4.72983e9	−	1.75312e9i	−0.762842	−	0.282749i
$151$	−2.68351e9	+	1.11155e9i	−0.420056	+	0.173993i	−0.582692	−	0.812693i	$-0.698000\pi$
$151$	−2.68351e9	+	1.11155e9i	−0.420056	+	0.173993i	0.162636	+	0.986686i	$0.448000\pi$
$152$	4.62242e9	−	2.56099e9i	0.702382	−	0.389146i
$153$	−8.87185e8	−	3.67484e8i	−0.130889	−	0.0542160i
$154$	−3.41966e9	+	3.68808e9i	−0.489937	+	0.528393i
$155$	1.79874e8	−	9.04287e8i	0.0250308	−	0.125838i
$156$	2.50510e9	−	2.91506e9i	0.338661	−	0.394082i
$157$	−6.71200e9	+	1.00452e10i	−0.881664	+	1.31950i	0.0652007	+	0.997872i	$0.479231\pi$
$157$	−6.71200e9	+	1.00452e10i	−0.881664	+	1.31950i	−0.946865	+	0.321632i	$0.895769\pi$
$158$	−3.07559e9	−	4.91931e8i	−0.392619	−	0.0627982i
$159$		−	1.20414e10i		−	1.49414i
$160$	1.14478e9	+	2.36792e8i	0.138096	+	0.0285645i
$161$			6.97692e9i			0.818365i
$162$	−8.20053e8	+	5.12704e9i	−0.0935459	+	0.584856i
$163$	1.92238e9	−	2.87705e9i	0.213302	−	0.319229i	−0.709354	−	0.704852i	$-0.751013\pi$
$163$	1.92238e9	−	2.87705e9i	0.213302	−	0.319229i	0.922657	+	0.385623i	$0.126013\pi$
$164$	4.35419e8	+	5.75677e9i	0.0470013	+	0.621415i
$165$	−1.97434e8	+	9.92567e8i	−0.0207369	+	0.104251i
$166$	7.91420e9	+	7.33820e9i	0.808948	+	0.750073i
$167$	4.57934e9	+	1.89683e9i	0.455595	+	0.188714i	0.598666	−	0.800999i	$-0.295698\pi$
$167$	4.57934e9	+	1.89683e9i	0.455595	+	0.188714i	−0.143071	+	0.989712i	$0.545698\pi$
$168$	5.32159e9	+	4.23479e9i	0.515406	+	0.410147i
$169$	−5.95815e9	+	2.46795e9i	−0.561851	+	0.232726i
$170$	−2.43135e8	+	6.55967e8i	−0.0223269	+	0.0602368i
$171$	−2.32158e9	+	1.55123e9i	−0.207635	+	0.138738i
$172$	1.45956e9	+	5.23623e9i	0.127158	+	0.456185i
$173$	−8.79970e8	−	4.42391e9i	−0.0746896	−	0.375490i	0.925303	−	0.379228i	$-0.123810\pi$
$173$	−8.79970e8	−	4.42391e9i	−0.0746896	−	0.375490i	−0.999993	+	0.00373754i	$0.998810\pi$
$174$	−3.65891e9	+	5.95043e9i	−0.302608	+	0.492127i
$175$	6.82335e9	−	6.82335e9i	0.549954	−	0.549954i
$176$	−5.24200e8	+	1.15472e10i	−0.0411803	+	0.907132i
$177$	1.08595e9	+	1.08595e9i	0.0831629	+	0.0831629i
$178$	1.25150e9	−	2.98443e8i	0.0934420	−	0.0222829i
$179$	−9.28082e9	+	1.84607e9i	−0.675690	+	0.134403i	−0.520996	−	0.853559i	$-0.674439\pi$
$179$	−9.28082e9	+	1.84607e9i	−0.675690	+	0.134403i	−0.154695	+	0.987962i	$0.549439\pi$
$180$	−6.13164e8	−	7.44683e7i	−0.0435362	−	0.00528743i
$181$	1.06577e10	+	1.59503e10i	0.738089	+	1.10463i	0.990567	+	0.137026i	$0.0437544\pi$
$181$	1.06577e10	+	1.59503e10i	0.738089	+	1.10463i	−0.252478	+	0.967603i	$0.581246\pi$
$182$	3.06812e9	+	6.68203e9i	0.207277	+	0.451427i
$183$	−8.21361e9	−	1.98294e10i	−0.541383	−	1.30701i
$184$	1.03579e10	+	1.22404e10i	0.666180	+	0.787255i
$185$	−1.26752e8	+	3.06006e8i	−0.00795576	+	0.0192069i
$186$	−4.65211e8	−	1.23189e10i	−0.0284998	−	0.754680i
$187$	−6.78446e9	−	1.34951e9i	−0.405722	−	0.0807030i
$188$	5.30206e9	+	1.04847e10i	0.309552	+	0.612135i
$189$	−1.25951e10	−	8.41578e9i	−0.717999	−	0.479751i
$190$	1.19311e9	+	1.64745e9i	0.0664186	+	0.0917109i
$191$	−1.33799e10			−0.727449			−0.363725	−	0.931507i	$-0.618495\pi$
$191$	−1.33799e10			−0.727449			−0.363725	+	0.931507i	$0.618495\pi$
$192$	1.56232e10	−	4.70827e8i	0.829688	−	0.0250038i
$193$	−8.91798e9			−0.462656			−0.231328	−	0.972876i	$-0.574307\pi$
$193$	−8.91798e9			−0.462656			−0.231328	+	0.972876i	$0.574307\pi$
$194$	2.19758e9	+	3.03442e9i	0.111388	+	0.153804i
$195$	1.23015e9	+	8.21957e8i	0.0609257	+	0.0407093i
$196$	6.82755e9	−	3.45264e9i	0.330455	−	0.167109i
$197$	−7.71922e9	−	1.53545e9i	−0.365153	−	0.0726335i	0.00910357	−	0.999959i	$-0.497102\pi$
$197$	−7.71922e9	−	1.53545e9i	−0.365153	−	0.0726335i	−0.374257	+	0.927325i	$0.622102\pi$
$198$	−2.30479e8	−	6.10313e9i	−0.0106571	−	0.282201i
$199$	1.53822e10	−	3.71360e10i	0.695314	−	1.67864i	−0.0384768	−	0.999259i	$-0.512251\pi$
$199$	1.53822e10	−	3.71360e10i	0.695314	−	1.67864i	0.733790	−	0.679376i	$-0.237749\pi$
$200$	1.84107e9	−	2.21009e10i	0.0813646	−	0.976730i
$201$	−6.42144e9	−	1.55027e10i	−0.277492	−	0.669925i
$202$	−5.94764e9	−	1.29533e10i	−0.251341	−	0.547393i
$203$	−7.42407e9	−	1.11109e10i	−0.306838	−	0.459216i
$204$	−1.12771e9	+	9.28548e9i	−0.0455893	+	0.375378i
$205$	−2.17954e9	+	4.33538e8i	−0.0861933	+	0.0171449i
$206$	−4.44671e9	+	1.06040e9i	−0.172043	+	0.0410267i
$207$	−5.99080e9	−	5.99080e9i	−0.226787	−	0.226787i
$208$	1.53029e10	+	7.16813e9i	0.566876	+	0.265535i
$209$	−1.42221e10	+	1.42221e10i	−0.515593	+	0.515593i
$210$	−1.37122e9	+	2.22999e9i	−0.0486540	+	0.0791253i
$211$	−9.28480e9	−	4.66778e10i	−0.322479	−	1.62121i	−0.713379	−	0.700778i	$-0.752836\pi$
$211$	−9.28480e9	−	4.66778e10i	−0.322479	−	1.62121i	0.390901	−	0.920433i	$-0.372164\pi$
$212$	5.09967e10	−	1.42149e10i	1.73393	−	0.483318i
$213$	−9.99327e9	+	6.67729e9i	−0.332659	+	0.222276i
$214$	1.10419e10	−	2.97904e10i	0.359899	−	0.970990i
$215$	−1.93311e9	+	8.00720e8i	−0.0616997	+	0.0255569i
$216$	−3.45910e10	+	3.93386e9i	−1.08124	+	0.122964i
$217$	2.17876e10	+	9.02473e9i	0.667023	+	0.276290i
$218$	−2.80598e10	−	2.60177e10i	−0.841455	−	0.780215i
$219$	7.06525e9	−	3.55194e10i	0.207553	−	1.04344i
$220$	−4.43670e9	+	3.35574e8i	−0.127690	+	0.00965798i
$221$	−5.61829e9	+	8.40837e9i	−0.158431	+	0.237108i
$222$	−6.99445e8	+	4.37299e9i	−0.0193270	+	0.120834i
$223$		−	3.34370e10i		−	0.905430i	−0.891655	−	0.452715i	$-0.850456\pi$
$223$		−	3.34370e10i		−	0.905430i	0.891655	−	0.452715i	$-0.149544\pi$
$224$	−1.16526e10	+	2.75367e10i	−0.309249	+	0.730794i
$225$			1.17179e10i			0.304809i
$226$	5.40859e9	+	8.65087e8i	0.137910	+	0.0220583i
$227$	3.38019e9	−	5.05882e9i	0.0844938	−	0.126454i	−0.786815	−	0.617189i	$-0.788272\pi$
$227$	3.38019e9	−	5.05882e9i	0.0844938	−	0.126454i	0.871309	+	0.490735i	$0.163272\pi$
$228$	2.06269e10	+	1.77261e10i	0.505507	+	0.434415i
$229$	−5.32350e7	+	2.67630e8i	−0.00127920	+	0.00643096i	−0.981420	−	0.191874i	$-0.938544\pi$
$229$	−5.32350e7	+	2.67630e8i	−0.00127920	+	0.00643096i	0.980140	+	0.198305i	$0.0635436\pi$
$230$	−4.19656e9	+	4.52596e9i	−0.0988822	+	0.106644i
$231$	−2.39146e10	−	9.90577e9i	−0.552599	−	0.228894i
$232$	−2.95201e10	−	8.47139e9i	−0.668993	−	0.191981i
$233$	3.00090e10	−	1.24301e10i	0.667036	−	0.276295i	−0.0233598	−	0.999727i	$-0.507436\pi$
$233$	3.00090e10	−	1.24301e10i	0.667036	−	0.276295i	0.690396	+	0.723432i	$0.257436\pi$
$234$	−8.37207e9	−	3.10312e9i	−0.182541	−	0.0676593i
$235$	−3.76033e9	+	2.51257e9i	−0.0804304	+	0.0537419i
$236$	−3.31714e9	+	5.88107e9i	−0.0696081	+	0.123411i
$237$	−3.12732e9	−	1.57221e10i	−0.0643879	−	0.323700i
$238$	−1.52425e10	−	9.37262e9i	−0.307936	−	0.189350i
$239$	2.45636e10	−	2.45636e10i	0.486970	−	0.486970i	−0.420379	−	0.907349i	$-0.638103\pi$
$239$	2.45636e10	−	2.45636e10i	0.486970	−	0.486970i	0.907349	+	0.420379i	$0.138103\pi$
$240$	9.04945e8	+	5.94802e9i	0.0176065	+	0.115724i
$241$	7.00005e10	+	7.00005e10i	1.33667	+	1.33667i	0.899263	+	0.437408i	$0.144104\pi$
$241$	7.00005e10	+	7.00005e10i	1.33667	+	1.33667i	0.437408	+	0.899263i	$0.355896\pi$
$242$	2.17098e9	+	9.10387e9i	0.0406899	+	0.170631i
$243$	3.18027e10	−	6.32594e9i	0.585107	−	0.116385i
$244$	7.42835e10	−	5.81942e10i	1.34165	−	1.05105i
$245$	1.63616e9	+	2.44868e9i	0.0290120	+	0.0434195i
$246$	−2.70022e10	+	1.23983e10i	−0.470101	+	0.215851i
$247$	1.12524e10	+	2.71656e10i	0.192357	+	0.464390i
$248$	5.16226e10	−	1.65127e10i	0.866576	−	0.277195i
$249$	−2.12566e10	+	5.13181e10i	−0.350427	+	0.846006i
$250$	1.72341e10	−	6.50831e8i	0.279036	−	0.0105375i
$251$	7.86809e10	+	1.56506e10i	1.25123	+	0.248885i	0.775863	−	0.630901i	$-0.217315\pi$
$251$	7.86809e10	+	1.56506e10i	1.25123	+	0.248885i	0.475368	+	0.879787i	$0.342315\pi$
$252$	4.92780e9	−	1.50104e10i	0.0769752	−	0.234472i
$253$	−5.07445e10	−	3.39064e10i	−0.778657	−	0.520282i
$254$	−9.98938e10	+	7.23448e10i	−1.50587	+	1.09057i
$255$	−3.60046e9			−0.0533245
$256$	2.04372e10	+	6.56101e10i	0.297401	+	0.954753i
$257$	−5.58083e10			−0.797995			−0.398997	−	0.916952i	$-0.630642\pi$
$257$	−5.58083e10			−0.797995			−0.398997	+	0.916952i	$0.630642\pi$
$258$	−2.26583e10	+	1.64095e10i	−0.318375	+	0.230572i
$259$	−7.04407e9	−	4.70670e9i	−0.0972691	−	0.0649931i
$260$	−2.02888e9	+	6.18012e9i	−0.0275345	+	0.0838719i
$261$	1.59152e10	+	3.16574e9i	0.212291	+	0.0422272i
$262$	6.64565e10	−	2.50967e9i	0.871328	−	0.0329049i
$263$	−2.06098e10	+	4.97565e10i	−0.265627	+	0.641281i	−0.999268	−	0.0382565i	$-0.987820\pi$
$263$	−2.06098e10	+	4.97565e10i	−0.265627	+	0.641281i	0.733641	+	0.679538i	$0.237820\pi$
$264$	−5.66622e10	+	1.81247e10i	−0.717920	+	0.229643i
$265$	7.79837e9	+	1.88269e10i	0.0971399	+	0.234516i
$266$	−4.72820e10	+	2.17100e10i	−0.579066	+	0.265884i
$267$	3.67878e9	+	5.50568e9i	0.0442999	+	0.0662995i
$268$	5.80752e10	−	4.54965e10i	0.687676	−	0.538730i
$269$	−1.44919e11	+	2.88263e10i	−1.68749	+	0.335663i	−0.943208	−	0.332203i	$-0.892208\pi$
$269$	−1.44919e11	+	2.88263e10i	−1.68749	+	0.335663i	−0.744282	+	0.667866i	$0.767208\pi$
$270$	−3.10848e9	−	1.30352e10i	−0.0355968	−	0.149273i
$271$	3.64479e10	+	3.64479e10i	0.410497	+	0.410497i	0.881912	−	0.471414i	$-0.156256\pi$
$271$	3.64479e10	+	3.64479e10i	0.410497	+	0.410497i	−0.471414	+	0.881912i	$0.656256\pi$
$272$	−4.06563e10	+	6.18554e9i	−0.450368	+	0.0685200i
$273$	−2.67582e10	+	2.67582e10i	−0.291558	+	0.291558i
$274$	−7.39478e9	−	4.54704e9i	−0.0792589	−	0.0487362i
$275$	1.64675e10	+	8.27876e10i	0.173632	+	0.872907i
$276$	−4.05426e10	+	7.18794e10i	−0.420553	+	0.745613i
$277$	4.05801e10	−	2.71148e10i	0.414147	−	0.276724i	−0.330992	−	0.943634i	$-0.607383\pi$
$277$	4.05801e10	−	2.71148e10i	0.414147	−	0.276724i	0.745139	+	0.666910i	$0.232383\pi$
$278$	−8.11451e10	−	3.00766e10i	−0.814818	−	0.302014i
$279$	−2.64573e10	+	1.09590e10i	−0.261413	+	0.108281i
$280$	−1.10629e10	−	3.17474e9i	−0.107562	−	0.0308672i
$281$	9.31202e10	+	3.85716e10i	0.890974	+	0.369054i	0.780743	−	0.624852i	$-0.214841\pi$
$281$	9.31202e10	+	3.85716e10i	0.890974	+	0.369054i	0.110231	+	0.993906i	$0.464841\pi$
$282$	−4.11135e10	+	4.43406e10i	−0.387136	+	0.417523i
$283$	−3.44471e10	+	1.73177e11i	−0.319237	+	1.60491i	0.404299	+	0.914627i	$0.367515\pi$
$283$	−3.44471e10	+	1.73177e11i	−0.319237	+	1.60491i	−0.723536	+	0.690286i	$0.757485\pi$
$284$	−4.00761e10	−	3.44400e10i	−0.365555	−	0.314145i
$285$	−5.81615e9	+	8.70449e9i	−0.0522196	+	0.0781522i
$286$	−6.35101e10	−	1.01582e10i	−0.561301	−	0.0897783i
$287$		−	5.68400e10i		−	0.494522i
$288$	−1.36390e10	−	3.36503e10i	−0.116819	−	0.288219i
$289$			9.39778e10i			0.792474i
$290$	1.86709e9	−	1.16732e10i	0.0155015	−	0.0969168i
$291$	−1.07127e10	+	1.60327e10i	−0.0875753	+	0.131066i
$292$	1.58769e11	−	1.20086e10i	1.27804	−	0.0966655i
$293$	7.08241e9	−	3.56057e10i	0.0561405	−	0.282238i	−0.942510	−	0.334179i	$-0.891541\pi$
$293$	7.08241e9	−	3.56057e10i	0.0561405	−	0.282238i	0.998650	+	0.0519416i	$0.0165410\pi$
$294$	2.88741e10	+	2.67727e10i	0.225396	+	0.208991i
$295$	−2.40119e9	−	9.94604e8i	−0.0184598	−	0.00764630i
$296$	−1.93457e10	+	2.20009e9i	−0.146478	+	0.0166582i
$297$	1.22419e11	−	5.07077e10i	0.912946	−	0.378155i
$298$	4.12770e10	−	1.11363e11i	0.303204	−	0.818030i
$299$	−7.41844e10	+	4.95684e10i	−0.536775	+	0.358662i
$300$	1.09948e11	−	3.06470e10i	0.783682	−	0.218445i
$301$	−1.04409e10	−	5.24901e10i	−0.0733145	−	0.368577i
$302$	3.44259e10	−	5.59864e10i	0.238152	−	0.387303i
$303$	5.18715e10	−	5.18715e10i	0.353539	−	0.353539i
$304$	−5.07216e10	+	1.08283e11i	−0.340613	+	0.727157i
$305$	2.56842e10	+	2.56842e10i	0.169948	+	0.169948i
$306$	2.11360e10	−	5.04027e9i	0.137809	−	0.0328630i
$307$	1.91755e10	−	3.81425e9i	0.123204	−	0.0245068i	−0.133103	−	0.991102i	$-0.542494\pi$
$307$	1.91755e10	−	3.81425e9i	0.123204	−	0.0245068i	0.256307	+	0.966595i	$0.417494\pi$
$308$	1.37207e10	−	1.12975e11i	0.0868756	−	0.715325i
$309$	−1.30711e10	−	1.95622e10i	−0.0815638	−	0.122069i
$310$	8.70542e9	+	1.89595e10i	0.0535380	+	0.116600i
$311$	−1.53534e10	−	3.70663e10i	−0.0930641	−	0.224677i	0.870492	−	0.492182i	$-0.163801\pi$
$311$	−1.53534e10	−	3.70663e10i	−0.0930641	−	0.224677i	−0.963556	+	0.267506i	$0.913801\pi$
$312$	−7.21988e9	+	8.66701e10i	−0.0431355	+	0.517814i
$313$	−1.43833e10	+	3.47243e10i	−0.0847049	+	0.204496i	−0.960557	−	0.278085i	$-0.910300\pi$
$313$	−1.43833e10	+	3.47243e10i	−0.0847049	+	0.204496i	0.875852	+	0.482580i	$0.160300\pi$
$314$	−1.03161e10	−	2.73173e11i	−0.0598871	−	1.58582i
$315$	5.96440e9	+	1.18639e9i	0.0341326	+	0.00678939i
$316$	6.28929e10	−	3.18045e10i	0.354821	−	0.179431i
$317$	−7.40233e9	−	4.94608e9i	−0.0411720	−	0.0275102i	0.534814	−	0.844970i	$-0.320382\pi$
$317$	−7.40233e9	−	4.94608e9i	−0.0411720	−	0.0275102i	−0.575986	+	0.817460i	$0.695382\pi$
$318$	1.59816e11	+	2.20674e11i	0.876389	+	1.21012i
$319$	1.16891e11			0.632009
$320$	−2.41222e10	+	1.08542e10i	−0.128600	+	0.0578658i
$321$	1.63513e11			0.859567
$322$	−9.25987e10	−	1.27860e11i	−0.480014	−	0.662804i
$323$	−5.94975e10	−	3.97549e10i	−0.304149	−	0.203226i
$324$	−5.30184e10	−	1.04843e11i	−0.267284	−	0.528551i
$325$	1.21029e11	+	2.40741e10i	0.601747	+	0.119695i
$326$	2.95464e9	+	7.82395e10i	0.0144886	+	0.383660i
$327$	7.53656e10	−	1.81949e11i	0.364509	−	0.880003i
$328$	−8.43843e10	−	9.97209e10i	−0.402559	−	0.475723i
$329$	−4.42671e10	−	1.06870e11i	−0.208305	−	0.502893i
$330$	−9.55529e9	−	2.08104e10i	−0.0443538	−	0.0965978i
$331$	2.29000e11	+	3.42722e11i	1.04860	+	1.56934i	0.799320	+	0.600906i	$0.205193\pi$
$331$	2.29000e11	+	3.42722e11i	1.04860	+	1.56934i	0.249278	+	0.968432i	$0.419807\pi$
$332$	−2.42431e11	−	2.94430e10i	−1.09513	−	0.133003i
$333$	1.00899e10	−	2.00701e9i	0.0449664	−	0.00894438i
$334$	−1.09097e11	+	2.60161e10i	−0.479682	+	0.114389i
$335$	2.00800e10	+	2.00800e10i	0.0871090	+	0.0871090i
$336$	−1.53729e11	−	6.97872e9i	−0.658006	−	0.0298709i
$337$	1.28983e11	−	1.28983e11i	0.544751	−	0.544751i	−0.380167	−	0.924918i	$-0.624133\pi$
$337$	1.28983e11	−	1.28983e11i	0.544751	−	0.544751i	0.924918	+	0.380167i	$0.124133\pi$
$338$	7.64354e10	−	1.24306e11i	0.318544	−	0.518043i
$339$	5.49956e9	+	2.76481e10i	0.0226167	+	0.113702i
$340$	−4.25035e9	−	1.52483e10i	−0.0172492	−	0.0618824i
$341$	−1.71522e11	+	1.14607e11i	−0.686949	+	0.459005i
$342$	2.19576e10	−	5.92406e10i	0.0867896	−	0.234154i
$343$	−2.57526e11	+	1.06671e11i	−1.00461	+	0.416123i
$344$	−9.62442e10	−	7.65888e10i	−0.370563	−	0.294885i
$345$	−2.93477e10	−	1.21562e10i	−0.111529	−	0.0461969i
$346$	7.48413e10	+	6.93944e10i	0.280736	+	0.260305i
$347$	−5.11012e10	+	2.56903e11i	−0.189212	+	0.951233i	0.763140	+	0.646233i	$0.223656\pi$
$347$	−5.11012e10	+	2.56903e11i	−0.189212	+	0.951233i	−0.952352	+	0.305000i	$0.901344\pi$
$348$	−1.19210e10	−	1.57611e11i	−0.0435720	−	0.576075i
$349$	8.25606e10	−	1.23561e11i	0.297892	−	0.445827i	−0.652086	−	0.758145i	$-0.726106\pi$
$349$	8.25606e10	−	1.23561e11i	0.297892	−	0.445827i	0.949977	+	0.312319i	$0.101106\pi$
$350$	−3.44856e10	+	2.15607e11i	−0.122838	+	0.767991i
$351$		−	1.93713e11i		−	0.681202i
$352$	−1.43650e11	−	2.18574e11i	−0.498728	−	0.758851i
$353$			1.24227e11i			0.425823i	0.977071	+	0.212912i	$0.0682947\pi$
$353$			1.24227e11i			0.425823i	−0.977071	+	0.212912i	$0.931705\pi$
$354$	−3.43142e10	−	5.48845e9i	−0.116134	−	0.0185752i
$355$	1.13002e10	−	1.69120e10i	0.0377623	−	0.0565153i
$356$	−1.89743e10	+	2.20795e10i	−0.0626097	+	0.0728558i
$357$	1.79662e10	−	9.03221e10i	0.0585395	−	0.294298i
$358$	1.45581e11	−	1.57008e11i	0.468415	−	0.505182i
$359$	1.96726e11	+	8.14867e10i	0.625083	+	0.258918i	0.672662	−	0.739950i	$-0.265151\pi$
$359$	1.96726e11	+	8.14867e10i	0.625083	+	0.258918i	−0.0475795	+	0.998867i	$0.515151\pi$
$360$	1.22253e10	−	6.77329e9i	0.0383618	−	0.0212539i
$361$	1.05901e11	−	4.38657e10i	0.328185	−	0.135939i
$362$	−4.07010e11	−	1.50859e11i	−1.24571	−	0.461724i
$363$	−4.00502e10	+	2.67607e10i	−0.121067	+	0.0808943i
$364$	−1.44912e11	−	8.17358e10i	−0.432662	−	0.244037i
$365$	1.19568e10	+	6.01108e10i	0.0352611	+	0.177270i
$366$	4.13703e11	+	2.54386e11i	1.20510	+	0.741016i
$367$	3.40532e11	−	3.40532e11i	0.979853	−	0.979853i	−0.0199479	−	0.999801i	$-0.506350\pi$
$367$	3.40532e11	−	3.40532e11i	0.979853	−	0.979853i	0.999801	+	0.0199479i	$0.00635003\pi$
$368$	−3.52277e11	−	8.68486e10i	−1.00131	−	0.246858i
$369$	4.88062e10	+	4.88062e10i	0.137043	+	0.137043i
$370$	−1.73848e9	−	7.29021e9i	−0.00482238	−	0.0202224i
$371$	−5.11212e11	+	1.01686e11i	−1.40094	+	0.278663i
$372$	1.72024e11	+	2.19584e11i	0.465741	+	0.594508i
$373$	−1.95272e11	−	2.92246e11i	−0.522338	−	0.781734i	0.472701	−	0.881223i	$-0.343279\pi$
$373$	−1.95272e11	−	2.92246e11i	−0.522338	−	0.781734i	−0.995039	+	0.0994894i	$0.968279\pi$
$374$	1.42244e11	−	6.53129e10i	0.375935	−	0.172614i
$375$	3.39673e10	+	8.20043e10i	0.0886993	+	0.214139i
$376$	−2.36322e11	−	1.21776e11i	−0.609759	−	0.314207i
$377$	6.53951e10	−	1.57878e11i	0.166728	−	0.402517i
$378$	3.42516e11	−	1.29348e10i	0.862915	−	0.0325872i
$379$	−5.30225e11	−	1.05468e11i	−1.32003	−	0.262570i	−0.515708	−	0.856764i	$-0.672471\pi$
$379$	−5.30225e11	−	1.05468e11i	−1.32003	−	0.262570i	−0.804322	+	0.594194i	$0.797471\pi$
$380$	−4.37304e10	−	1.43564e10i	−0.107586	−	0.0353198i
$381$	−5.27800e11	−	3.52665e11i	−1.28324	−	0.857432i
$382$	2.45203e11	−	1.77580e11i	0.589170	−	0.426687i
$383$	2.16086e9			0.00513136			0.00256568	−	0.999997i	$-0.499183\pi$
$383$	2.16086e9			0.00513136			0.00256568	+	0.999997i	$0.499183\pi$
$384$	−2.80065e11	+	2.15982e11i	−0.657308	+	0.506906i
$385$	4.38061e10			0.101616
$386$	1.63433e11	−	1.18361e11i	0.374711	−	0.271372i
$387$	5.40363e10	+	3.61059e10i	0.122458	+	0.0818237i
$388$	−8.05467e10	−	2.64429e10i	−0.180428	−	0.0592333i
$389$	−2.26037e11	−	4.49615e10i	−0.500502	−	0.0995561i	−0.0616182	−	0.998100i	$-0.519626\pi$
$389$	−2.26037e11	−	4.49615e10i	−0.500502	−	0.0995561i	−0.438884	+	0.898544i	$0.644626\pi$
$390$	−3.34530e10	+	1.26332e9i	−0.0732225	+	0.00276518i
$391$	8.30910e10	−	2.00599e11i	0.179787	−	0.434044i
$392$	−7.92991e10	+	1.53890e11i	−0.169622	+	0.329172i
$393$	1.30981e11	+	3.16216e11i	0.276976	+	0.668679i
$394$	1.61843e11	−	7.43117e10i	0.338345	−	0.155355i
$395$	1.50717e10	+	2.25564e10i	0.0311512	+	0.0466211i
$396$	8.52255e10	+	1.08788e11i	0.174157	+	0.222307i
$397$	−3.22490e11	+	6.41473e10i	−0.651568	+	0.129605i	−0.509797	−	0.860295i	$-0.670280\pi$
$397$	−3.22490e11	+	6.41473e10i	−0.651568	+	0.129605i	−0.141771	+	0.989900i	$0.545280\pi$
$398$	2.10977e11	+	8.84718e11i	0.421464	+	1.76738i
$399$	−1.89341e11	−	1.89341e11i	−0.373995	−	0.373995i
$400$	2.59586e11	+	4.29460e11i	0.507005	+	0.838790i
$401$	6.89936e11	−	6.89936e11i	1.33247	−	1.33247i	0.429324	−	0.903150i	$-0.358752\pi$
$401$	6.89936e11	−	6.89936e11i	1.33247	−	1.33247i	0.903150	−	0.429324i	$-0.141248\pi$
$402$	3.23435e11	+	1.98880e11i	0.617690	+	0.379817i
$403$	5.88346e10	+	2.95781e11i	0.111112	+	0.558596i
$404$	2.80916e11	+	1.58447e11i	0.524638	+	0.295915i
$405$	3.76017e10	−	2.51246e10i	0.0694480	−	0.0464037i
$406$	2.83521e11	+	1.05087e11i	0.517866	+	0.191948i
$407$	6.84654e10	−	2.83593e10i	0.123679	−	0.0512296i
$408$	−1.02572e11	−	1.85135e11i	−0.183255	−	0.330763i
$409$	6.82821e11	+	2.82834e11i	1.20657	+	0.499777i	0.893116	−	0.449827i	$-0.148514\pi$
$409$	6.82821e11	+	2.82834e11i	1.20657	+	0.499777i	0.313452	+	0.949604i	$0.398514\pi$
$410$	3.41888e10	−	3.68724e10i	0.0597526	−	0.0644427i
$411$	8.71613e9	−	4.38190e10i	0.0150673	−	0.0757485i
$412$	6.74177e10	−	7.84505e10i	0.115275	−	0.134140i
$413$	3.69328e10	−	5.52738e10i	0.0624650	−	0.0934855i
$414$	1.89299e11	+	3.02778e10i	0.316700	+	0.0506551i
$415$		−	9.40030e10i		−	0.155570i
$416$	−3.75580e11	+	7.17373e10i	−0.614869	+	0.117442i
$417$		−	4.45388e11i		−	0.721316i
$418$	7.18795e10	−	4.49397e11i	0.115163	−	0.720007i
$419$	−2.11565e11	+	3.16630e11i	−0.335337	+	0.501867i	−0.960369	−	0.278732i	$-0.910086\pi$
$419$	−2.11565e11	+	3.16630e11i	−0.335337	+	0.501867i	0.625032	+	0.780599i	$0.285086\pi$
$420$	−4.46753e9	−	5.90662e10i	−0.00700560	−	0.0926226i
$421$	1.10900e10	−	5.57532e10i	0.0172053	−	0.0864969i	−0.971229	−	0.238149i	$-0.923459\pi$
$421$	1.10900e10	−	5.57532e10i	0.0172053	−	0.0864969i	0.988434	+	0.151652i	$0.0484593\pi$
$422$	7.89670e11	+	7.32198e11i	1.21210	+	1.12389i
$423$	1.29776e11	+	5.37548e10i	0.197088	+	0.0816367i
$424$	−7.45914e11	+	9.37342e11i	−1.12084	+	1.40848i
$425$	−2.77446e11	+	1.14922e11i	−0.412504	+	0.170865i
$426$	9.45167e10	−	2.55001e11i	0.139048	−	0.375145i
$427$	−7.72485e11	+	5.16158e11i	−1.12451	+	0.751375i
$428$	1.93027e11	+	6.92495e11i	0.278050	+	0.997516i
$429$	−6.45783e10	−	3.24657e11i	−0.0920510	−	0.462772i
$430$	2.47993e10	−	4.03307e10i	0.0349809	−	0.0568889i
$431$	−7.83920e11	+	7.83920e11i	−1.09427	+	1.09427i	−0.0992018	+	0.995067i	$0.531629\pi$
$431$	−7.83920e11	+	7.83920e11i	−1.09427	+	1.09427i	−0.995067	+	0.0992018i	$0.968371\pi$
$432$	5.81712e11	−	5.31190e11i	0.803584	−	0.733793i
$433$	−5.04351e11	−	5.04351e11i	−0.689505	−	0.689505i	0.272617	−	0.962123i	$-0.412111\pi$
$433$	−5.04351e11	−	5.04351e11i	−0.689505	−	0.689505i	−0.962123	+	0.272617i	$0.912111\pi$
$434$	−5.19062e11	+	1.23780e11i	−0.702288	+	0.167473i
$435$	5.96722e10	−	1.18695e10i	0.0799043	−	0.0158940i
$436$	8.59541e11	+	1.04391e11i	1.13914	+	0.138348i
$437$	−3.50745e11	−	5.24927e11i	−0.460072	−	0.688546i
$438$	3.41940e11	+	7.44707e11i	0.443932	+	0.966834i
$439$	−1.01233e11	−	2.44397e11i	−0.130086	−	0.314055i	0.845394	−	0.534143i	$-0.179366\pi$
$439$	−1.01233e11	−	2.44397e11i	−0.130086	−	0.314055i	−0.975480	+	0.220088i	$0.929366\pi$
$440$	7.68541e10	−	6.50343e10i	0.0977530	−	0.0827191i
$441$	3.50045e10	−	8.45084e10i	0.0440707	−	0.106396i
$442$	−8.63514e9	−	2.28660e11i	−0.0107614	−	0.284964i
$443$	−1.24245e12	−	2.47138e11i	−1.53272	−	0.304876i	−0.644609	−	0.764513i	$-0.722980\pi$
$443$	−1.24245e12	−	2.47138e11i	−1.53272	−	0.304876i	−0.888107	+	0.459636i	$0.847980\pi$
$444$	−4.52207e10	−	8.94234e10i	−0.0552223	−	0.109201i
$445$	−9.31746e9	−	6.22573e9i	−0.0112636	−	0.00752610i
$446$	4.43780e11	+	6.12773e11i	0.531082	+	0.733318i
$447$	6.11249e11			0.724159
$448$	−1.51922e11	−	6.59298e11i	−0.178184	−	0.773269i
$449$	2.76370e11			0.320910			0.160455	−	0.987043i	$-0.448704\pi$
$449$	2.76370e11			0.320910			0.160455	+	0.987043i	$0.448704\pi$
$450$	−1.55521e11	−	2.14744e11i	−0.178786	−	0.246868i
$451$	4.13408e11	+	2.76230e11i	0.470527	+	0.314396i
$452$	−1.10601e11	+	5.59299e10i	−0.124633	+	0.0630262i
$453$	3.31756e11	+	6.59904e10i	0.370149	+	0.0736273i
$454$	5.19525e9	+	1.37571e11i	0.00573925	+	0.151977i
$455$	2.45075e10	−	5.91663e10i	0.0268069	−	0.0647177i
$456$	−6.13276e11	−	5.10878e10i	−0.664224	−	0.0553318i
$457$	−3.50001e11	−	8.44977e11i	−0.375359	−	0.906196i	−0.992823	−	0.119597i	$-0.961840\pi$
$457$	−3.50001e11	−	8.44977e11i	−0.375359	−	0.906196i	0.617464	−	0.786599i	$-0.288160\pi$
$458$	−2.57643e9	−	5.61119e9i	−0.00273605	−	0.00595882i
$459$	2.61906e11	+	3.91969e11i	0.275415	+	0.412188i
$460$	1.68378e10	−	1.38641e11i	0.0175338	−	0.144372i
$461$	−6.11911e11	+	1.21717e11i	−0.631007	+	0.125515i	−0.500224	−	0.865896i	$-0.666749\pi$
$461$	−6.11911e11	+	1.21717e11i	−0.631007	+	0.125515i	−0.130783	+	0.991411i	$0.541749\pi$
$462$	5.69735e11	−	1.35864e11i	0.581814	−	0.138744i
$463$	−2.26076e11	−	2.26076e11i	−0.228634	−	0.228634i	0.583488	−	0.812122i	$-0.301688\pi$
$463$	−2.26076e11	−	2.26076e11i	−0.228634	−	0.228634i	−0.812122	+	0.583488i	$0.801688\pi$
$464$	6.53425e11	−	2.36546e11i	0.654432	−	0.236911i
$465$	−7.59232e10	+	7.59232e10i	−0.0753071	+	0.0753071i
$466$	−3.84976e11	+	6.26080e11i	−0.378179	+	0.615026i
$467$	3.85846e11	+	1.93978e12i	0.375394	+	1.88724i	0.455139	+	0.890420i	$0.349589\pi$
$467$	3.85846e11	+	1.93978e12i	0.375394	+	1.88724i	−0.0797448	+	0.996815i	$0.525411\pi$
$468$	1.94613e11	−	5.42469e10i	0.187528	−	0.0522719i
$469$	−6.03932e11	+	4.03535e11i	−0.576382	+	0.385126i
$470$	3.55653e10	−	9.59535e10i	0.0336191	−	0.0907028i
$471$	1.29983e12	−	5.38406e11i	1.21700	−	0.504099i
$472$	−1.72638e10	−	1.51803e11i	−0.0160102	−	0.140780i
$473$	4.32511e11	+	1.79152e11i	0.397303	+	0.164568i
$474$	2.65978e11	+	2.46620e11i	0.242015	+	0.224402i
$475$	−1.70348e11	+	8.56398e11i	−0.153538	+	0.771888i
$476$	4.03733e11	−	3.05367e10i	0.360465	−	0.0272641i
$477$	3.51643e11	−	5.26271e11i	0.311006	−	0.465454i
$478$	−1.24146e11	+	7.76170e11i	−0.108770	+	0.680035i
$479$		−	1.18114e12i		−	1.02516i	−0.858640	−	0.512580i	$-0.828690\pi$
$479$		−	1.18114e12i		−	1.02516i	0.858640	−	0.512580i	$-0.171310\pi$
$480$	−9.55272e10	−	9.69940e10i	−0.0821375	−	0.0833987i
$481$		−	1.08338e11i		−	0.0922841i
$482$	−2.21190e12	−	3.53787e11i	−1.86661	−	0.298559i
$483$	4.51398e11	−	6.75566e11i	0.377397	−	0.564814i
$484$	−1.60614e11	−	1.38026e11i	−0.133039	−	0.114329i
$485$	6.36624e9	−	3.20053e10i	0.00522451	−	0.0262654i
$486$	−4.98864e11	+	5.38020e11i	−0.405619	+	0.437457i
$487$	1.61766e12	+	6.70055e11i	1.30318	+	0.539797i	0.922888	−	0.385068i	$-0.125822\pi$
$487$	1.61766e12	+	6.70055e11i	1.30318	+	0.539797i	0.380296	+	0.924865i	$0.375822\pi$
$488$	−5.88973e11	+	2.05238e12i	−0.470117	+	1.63821i
$489$	−3.72283e11	+	1.54205e11i	−0.294431	+	0.121957i
$490$	−6.24838e10	−	2.31597e10i	−0.0489650	−	0.0181489i
$491$	4.72854e11	−	3.15951e11i	0.367164	−	0.245331i	−0.358277	−	0.933615i	$-0.616636\pi$
$491$	4.72854e11	−	3.15951e11i	0.367164	−	0.245331i	0.725441	+	0.688284i	$0.241636\pi$
$492$	3.30295e11	−	5.85591e11i	0.254132	−	0.450559i
$493$	8.11314e10	+	4.07875e11i	0.0618554	+	0.310968i
$494$	−5.66759e11	−	3.48500e11i	−0.428181	−	0.263288i
$495$	−3.76146e10	+	3.76146e10i	−0.0281600	+	0.0281600i
$496$	−7.26887e11	+	9.87757e11i	−0.539261	+	0.732795i
$497$	3.67870e11	+	3.67870e11i	0.270453	+	0.270453i
$498$	−2.91548e11	−	1.22259e12i	−0.212411	−	0.890734i
$499$	−1.46297e12	+	2.91002e11i	−1.05629	+	0.210109i	−0.692533	−	0.721386i	$-0.743505\pi$
$499$	−1.46297e12	+	2.91002e11i	−1.05629	+	0.210109i	−0.363755	+	0.931495i	$0.618505\pi$
$500$	−3.07199e11	+	2.40661e11i	−0.219813	+	0.172203i
$501$	−3.20689e11	−	4.79945e11i	−0.227413	−	0.340347i
$502$	−1.64964e12	+	7.57449e11i	−1.15937	+	0.532337i
$503$	−3.41650e11	−	8.24816e11i	−0.237972	−	0.574515i	0.759101	−	0.650973i	$-0.225639\pi$
$503$	−3.41650e11	−	8.24816e11i	−0.237972	−	0.574515i	−0.997073	+	0.0764581i	$0.975639\pi$
$504$	1.08913e11	+	3.40486e11i	0.0751866	+	0.235051i
$505$	−4.75084e10	+	1.14695e11i	−0.0325057	+	0.0784756i
$506$	1.37996e12	−	5.21131e10i	0.935816	−	0.0353402i
$507$	7.36593e11	+	1.46517e11i	0.495099	+	0.0984812i
$508$	8.70504e11	−	2.65161e12i	0.579941	−	1.76654i
$509$	−1.53661e12	−	1.02673e12i	−1.01469	−	0.677993i	−0.0671859	−	0.997740i	$-0.521402\pi$
$509$	−1.53661e12	−	1.02673e12i	−1.01469	−	0.677993i	−0.947503	+	0.319747i	$0.896402\pi$
$510$	6.59828e10	−	4.77859e10i	0.0431882	−	0.0312776i
$511$	−1.56762e12			−1.01706
$512$	−1.24532e12	−	9.31139e11i	−0.800880	−	0.598824i
$513$	1.37071e12			0.873809
$514$	1.02276e12	−	7.40697e11i	0.646305	−	0.468065i
$515$	3.31058e10	+	2.21206e10i	0.0207383	+	0.0138569i
$516$	1.97451e11	−	6.01449e11i	0.122613	−	0.373486i
$517$	9.92416e11	+	1.97404e11i	0.610923	+	0.121520i
$518$	1.91559e11	−	7.23405e9i	0.116901	−	0.00441466i
$519$	−2.01015e11	+	4.85294e11i	−0.121612	+	0.293597i
$520$	−4.48417e10	−	1.40186e11i	−0.0268947	−	0.0840793i
$521$	1.08903e12	+	2.62914e12i	0.647543	+	1.56331i	0.816286	+	0.577648i	$0.196029\pi$
$521$	1.08903e12	+	2.62914e12i	0.647543	+	1.56331i	−0.168743	+	0.985660i	$0.553971\pi$
$522$	−3.33682e11	+	1.53213e11i	−0.196705	+	0.0903191i
$523$	7.39107e11	+	1.10615e12i	0.431966	+	0.646483i	0.982049	−	0.188627i	$-0.0604038\pi$
$523$	7.39107e11	+	1.10615e12i	0.431966	+	0.646483i	−0.550083	+	0.835110i	$0.685404\pi$
$524$	−1.18459e12	+	9.28013e11i	−0.686398	+	0.537729i
$525$	−1.10216e12	+	2.19233e11i	−0.633180	+	0.125947i
$526$	−2.82676e11	−	1.18538e12i	−0.161010	−	0.675185i
$527$	−5.18955e11	−	5.18955e11i	−0.293077	−	0.293077i
$528$	7.97849e11	−	1.08419e12i	0.446754	−	0.607088i
$529$	8.09581e10	−	8.09581e10i	0.0449479	−	0.0449479i
$530$	−3.92789e11	−	2.41525e11i	−0.216231	−	0.132960i
$531$	1.57487e10	+	7.91741e10i	0.00859646	+	0.0432173i
$532$	5.78361e11	−	1.02540e12i	0.313038	−	0.554995i
$533$	6.04370e11	−	4.03827e11i	0.324362	−	0.216732i
$534$	−1.40490e11	−	5.20730e10i	−0.0747671	−	0.0277126i
$535$	−2.55655e11	+	1.05896e11i	−0.134916	+	0.0558839i
$536$	−4.60462e11	+	1.60456e12i	−0.240964	+	0.839682i
$537$	1.01809e12	+	4.21706e11i	0.528325	+	0.218839i
$538$	2.27324e12	−	2.45167e12i	1.16983	−	1.26166i
$539$	1.28547e11	−	6.46250e11i	0.0656014	−	0.329801i
$540$	2.29972e11	+	1.97630e11i	0.116387	+	0.100019i
$541$	1.54749e11	−	2.31598e11i	0.0776674	−	0.116238i	−0.790602	−	0.612330i	$-0.790232\pi$
$541$	1.54749e11	−	2.31598e11i	0.0776674	−	0.116238i	0.868270	+	0.496093i	$0.165232\pi$
$542$	−1.15169e12	−	1.84210e11i	−0.573245	−	0.0916887i
$543$		−	2.23399e12i		−	1.10276i
$544$	6.62980e11	−	6.52954e11i	0.324568	−	0.319659i
$545$			3.33288e11i			0.161821i
$546$	1.35238e11	−	8.45516e11i	0.0651224	−	0.407151i
$547$	1.49565e12	−	2.23840e12i	0.714310	−	1.06904i	−0.279736	−	0.960077i	$-0.590247\pi$
$547$	1.49565e12	−	2.23840e12i	0.714310	−	1.06904i	0.994046	−	0.108963i	$-0.0347531\pi$
$548$	1.95867e11	−	1.48146e10i	0.0927790	−	0.00701743i
$549$	2.20098e11	−	1.10650e12i	0.103405	−	0.519850i
$550$	−1.40056e12	−	1.29862e12i	−0.652632	−	0.605133i
$551$	1.11714e12	+	4.62734e11i	0.516327	+	0.213870i
$552$	−2.11001e11	−	1.85537e12i	−0.0967295	−	0.850557i
$553$	−6.41063e11	+	2.65537e11i	−0.291499	+	0.120743i
$554$	−3.83808e11	+	1.03550e12i	−0.173109	+	0.467041i
$555$	3.20715e10	−	2.14295e10i	0.0143483	−	0.00958723i
$556$	1.88626e12	−	5.25781e11i	0.837078	−	0.233329i
$557$	3.11721e10	+	1.56713e11i	0.0137220	+	0.0689851i	0.987040	−	0.160477i	$-0.0513033\pi$
$557$	3.11721e10	+	1.56713e11i	0.0137220	+	0.0689851i	−0.973318	+	0.229462i	$0.926303\pi$
$558$	3.39413e11	−	5.51982e11i	0.148209	−	0.241030i
$559$	4.83939e11	−	4.83939e11i	0.209622	−	0.209622i
$560$	2.44878e11	−	8.86482e10i	0.105221	−	0.0380911i
$561$	5.69618e11	+	5.69618e11i	0.242801	+	0.242801i
$562$	−2.21847e12	+	5.29033e11i	−0.938080	+	0.223702i
$563$	2.86580e12	−	5.70042e11i	1.20215	−	0.239122i	0.446913	−	0.894577i	$-0.352523\pi$
$563$	2.86580e12	−	5.70042e11i	1.20215	−	0.239122i	0.755234	+	0.655456i	$0.227523\pi$
$564$	1.64960e11	−	1.35826e12i	0.0686470	−	0.565232i
$565$	−2.65044e10	−	3.96666e10i	−0.0109421	−	0.0163760i
$566$	−1.66715e12	−	3.63087e12i	−0.682811	−	1.48709i
$567$	4.42652e11	+	1.06866e12i	0.179862	+	0.434225i
$568$	1.19154e12	+	9.92585e10i	0.480330	+	0.0400129i
$569$	−1.89919e12	+	4.58506e12i	−0.759563	+	1.83375i	−0.266223	+	0.963911i	$0.585776\pi$
$569$	−1.89919e12	+	4.58506e12i	−0.759563	+	1.83375i	−0.493340	+	0.869836i	$0.664224\pi$
$570$	−8.93925e9	−	2.36713e11i	−0.00354702	−	0.0939259i
$571$	−3.65815e12	−	7.27651e11i	−1.44012	−	0.286458i	−0.587600	−	0.809152i	$-0.699927\pi$
$571$	−3.65815e12	−	7.27651e11i	−1.44012	−	0.286458i	−0.852520	+	0.522694i	$0.824927\pi$
$572$	1.29872e12	−	6.56754e11i	0.507264	−	0.256520i
$573$	1.29556e12	+	8.65664e11i	0.502066	+	0.335470i
$574$	7.54389e11	+	1.04166e12i	0.290063	+	0.400519i
$575$	−2.64950e12			−1.01078
$576$	6.96562e11	+	4.35663e11i	0.263669	+	0.164911i
$577$	−1.62719e12			−0.611150			−0.305575	−	0.952168i	$-0.598849\pi$
$577$	−1.62719e12			−0.611150			−0.305575	+	0.952168i	$0.598849\pi$
$578$	−1.24729e12	−	1.72226e12i	−0.464827	−	0.641834i
$579$	8.63516e11	+	5.76983e11i	0.319313	+	0.213358i
$580$	1.20712e11	+	2.38706e11i	0.0442919	+	0.0875865i
$581$	2.35818e12	+	4.69072e11i	0.858589	+	0.170784i
$582$	−1.64651e10	−	4.36000e11i	−0.00594856	−	0.157519i
$583$	1.74480e12	−	4.21231e12i	0.625513	−	1.51012i
$584$	−2.75025e12	+	2.32728e12i	−0.978396	+	0.827924i
$585$	2.97601e10	+	7.18473e10i	0.0105059	+	0.0253635i
$586$	3.42770e11	+	7.46516e11i	0.120078	+	0.261517i
$587$	−8.04830e11	−	1.20451e12i	−0.279790	−	0.418736i	0.664783	−	0.747037i	$-0.268524\pi$
$587$	−8.04830e11	−	1.20451e12i	−0.279790	−	0.418736i	−0.944573	+	0.328301i	$0.893524\pi$
$588$	−8.84484e11	−	1.07420e11i	−0.305135	−	0.0370584i
$589$	−2.09294e12	+	4.16312e11i	−0.716537	+	0.142528i
$590$	5.72052e10	−	1.36416e10i	0.0194358	−	0.00463480i
$591$	6.48100e11	+	6.48100e11i	0.218523	+	0.218523i
$592$	3.25334e11	−	2.97079e11i	0.108863	−	0.0994087i
$593$	4.03399e12	−	4.03399e12i	1.33964	−	1.33964i	0.443241	−	0.896403i	$-0.353829\pi$
$593$	4.03399e12	−	4.03399e12i	1.33964	−	1.33964i	0.896403	−	0.443241i	$-0.146171\pi$
$594$	−1.57048e12	+	2.55404e12i	−0.517599	+	0.841762i
$595$	3.04048e10	+	1.52855e11i	0.00994526	+	0.0499982i
$596$	7.21580e11	+	2.58870e12i	0.234248	+	0.840377i
$597$	−3.89210e12	+	2.60062e12i	−1.25400	+	0.837899i
$598$	7.01639e11	−	1.89299e12i	0.224367	−	0.605330i
$599$	−2.21368e12	+	9.16937e11i	−0.702578	+	0.291017i	−0.705229	−	0.708979i	$-0.749156\pi$
$599$	−2.21368e12	+	9.16937e11i	−0.702578	+	0.291017i	0.00265155	+	0.999996i	$0.499156\pi$
$600$	−1.60817e12	+	2.02088e12i	−0.506584	+	0.636591i
$601$	3.66174e12	+	1.51674e12i	1.14486	+	0.474216i	0.872806	−	0.488066i	$-0.162298\pi$
$601$	3.66174e12	+	1.51674e12i	1.14486	+	0.474216i	0.272052	+	0.962282i	$0.412298\pi$
$602$	8.87999e11	+	8.23371e11i	0.275568	+	0.255512i
$603$	1.72073e11	−	8.65071e11i	0.0530012	−	0.266455i
$604$	1.12162e11	+	1.48292e12i	0.0342911	+	0.453370i
$605$	4.52881e10	−	6.77785e10i	0.0137431	−	0.0205680i
$606$	−2.62162e11	+	1.63905e12i	−0.0789664	+	0.493704i
$607$			5.64832e11i			0.168877i	0.996429	+	0.0844385i	$0.0269096\pi$
$607$			5.64832e11i			0.168877i	−0.996429	+	0.0844385i	$0.973090\pi$
$608$	−5.07612e11	−	2.65760e12i	−0.150649	−	0.788721i
$609$			1.55618e12i			0.458440i
$610$	−8.11579e11	−	1.29809e11i	−0.237327	−	0.0379596i
$611$	8.21832e11	−	1.22996e12i	0.238560	−	0.357030i
$612$	−3.20448e11	+	3.72890e11i	−0.0923372	+	0.107448i
$613$	−8.74971e11	+	4.39877e12i	−0.250277	+	1.25823i	0.627294	+	0.778782i	$0.284162\pi$
$613$	−8.74971e11	+	4.39877e12i	−0.250277	+	1.25823i	−0.877571	+	0.479446i	$0.840838\pi$
$614$	−3.00791e11	+	3.24401e11i	−0.0854098	+	0.0921138i
$615$	2.39092e11	+	9.90350e10i	0.0673948	+	0.0279158i
$616$	1.24797e12	+	2.25250e12i	0.349213	+	0.630307i
$617$	−4.01574e12	+	1.66337e12i	−1.11553	+	0.462069i	−0.862840	−	0.505477i	$-0.831316\pi$
$617$	−4.01574e12	+	1.66337e12i	−1.11553	+	0.462069i	−0.252693	+	0.967546i	$0.581316\pi$
$618$	4.99176e11	+	1.85020e11i	0.137659	+	0.0510236i
$619$	1.73256e11	−	1.15766e11i	0.0474329	−	0.0316936i	−0.531628	−	0.846978i	$-0.678419\pi$
$619$	1.73256e11	−	1.15766e11i	0.0474329	−	0.0316936i	0.579061	+	0.815284i	$0.303419\pi$
$620$	−4.11170e11	−	2.31915e11i	−0.111753	−	0.0630328i
$621$	8.11414e11	+	4.07925e12i	0.218943	+	1.10070i
$622$	7.73320e11	+	4.75513e11i	0.207158	+	0.127381i
$623$	2.02674e11	−	2.02674e11i	0.0539017	−	0.0539017i
$624$	−1.01799e12	−	1.68416e12i	−0.268789	−	0.444685i
$625$	2.53754e12	+	2.53754e12i	0.665201	+	0.665201i
$626$	−1.97275e11	−	8.27262e11i	−0.0513438	−	0.215307i
$627$	2.29727e12	−	4.56955e11i	0.593619	−	0.118078i
$628$	3.81465e12	+	4.86931e12i	0.978671	+	1.24925i
$629$	1.46476e11	+	2.19217e11i	0.0373112	+	0.0558401i
$630$	−1.25051e11	+	5.74183e10i	−0.0316267	+	0.0145217i
$631$	2.07133e12	+	5.00064e12i	0.520138	+	1.25572i	0.937817	+	0.347129i	$0.112843\pi$
$631$	2.07133e12	+	5.00064e12i	0.520138	+	1.25572i	−0.417680	+	0.908594i	$0.637157\pi$
$632$	−7.30475e11	+	1.41758e12i	−0.182129	+	0.353444i
$633$	−2.12097e12	+	5.12046e12i	−0.525070	+	1.26763i
$634$	2.01302e11	−	7.60197e9i	0.0494819	−	0.00186864i
$635$	1.05362e12	+	2.09578e11i	0.257159	+	0.0511521i
$636$	−5.85763e12	−	1.92301e12i	−1.41960	−	0.466043i
$637$	−8.00935e11	−	5.35168e11i	−0.192739	−	0.128784i
$638$	−2.14217e12	+	1.55140e12i	−0.511872	+	0.370706i
$639$	−6.31751e11			−0.149897
$640$	2.98010e11	−	5.19069e11i	0.0702135	−	0.122297i
$641$	−6.39627e12			−1.49646			−0.748231	−	0.663438i	$-0.769097\pi$
$641$	−6.39627e12			−1.49646			−0.748231	+	0.663438i	$0.769097\pi$
$642$	−2.99657e12	+	2.17017e12i	−0.696174	+	0.504181i
$643$	1.83311e12	+	1.22484e12i	0.422900	+	0.282573i	0.748755	−	0.662847i	$-0.230652\pi$
$643$	1.83311e12	+	1.22484e12i	0.422900	+	0.282573i	−0.325855	+	0.945420i	$0.605652\pi$
$644$	3.39397e12	+	1.11421e12i	0.777538	+	0.255260i
$645$	2.38986e11	+	4.75373e10i	0.0543693	+	0.0108147i
$646$	1.61800e12	−	6.11021e10i	0.365537	−	0.0138042i
$647$	−7.90671e11	+	1.90885e12i	−0.177389	+	0.428255i	−0.987417	−	0.158136i	$-0.949452\pi$
$647$	−7.90671e11	+	1.90885e12i	−0.177389	+	0.428255i	0.810029	+	0.586390i	$0.199452\pi$
$648$	2.36312e12	+	1.21771e12i	0.526499	+	0.271304i
$649$	2.22531e11	+	5.37238e11i	0.0492368	+	0.118868i
$650$	−2.53752e12	+	1.16513e12i	−0.557569	+	0.256013i
$651$	−1.52578e12	−	2.28348e12i	−0.332948	−	0.498292i
$652$	−1.09255e12	−	1.39462e12i	−0.236771	−	0.302233i
$653$	3.79528e12	−	7.54927e11i	0.816834	−	0.162478i	0.231046	−	0.972943i	$-0.425785\pi$
$653$	3.79528e12	−	7.54927e11i	0.816834	−	0.162478i	0.585788	+	0.810464i	$0.300785\pi$
$654$	1.03368e12	+	4.33469e12i	0.220947	+	0.926528i
$655$	−4.09582e11	−	4.09582e11i	−0.0869471	−	0.0869471i
$656$	2.86996e12	+	7.07544e11i	0.605073	+	0.149172i
$657$	1.34605e12	−	1.34605e12i	0.281850	−	0.281850i
$658$	2.22965e12	+	1.37101e12i	0.463681	+	0.285117i
$659$	−5.52367e11	−	2.77693e12i	−0.114089	−	0.573563i	−0.994966	−	0.100217i	$-0.968046\pi$
$659$	−5.52367e11	−	2.77693e12i	−0.114089	−	0.573563i	0.880877	−	0.473346i	$-0.156954\pi$
$660$	4.51311e11	+	2.54556e11i	0.0925823	+	0.0522198i
$661$	4.20211e12	−	2.80776e12i	0.856171	−	0.572075i	−0.0481923	−	0.998838i	$-0.515346\pi$
$661$	4.20211e12	−	2.80776e12i	0.856171	−	0.572075i	0.904364	+	0.426763i	$0.140346\pi$
$662$	−8.74536e12	−	3.24148e12i	−1.76977	−	0.655968i
$663$	1.08802e12	−	4.50674e11i	0.218689	−	0.0905840i
$664$	4.83361e12	−	2.67800e12i	0.964974	−	0.534631i
$665$	4.18660e11	+	1.73414e11i	0.0830163	+	0.0343865i
$666$	−1.58272e11	+	1.70696e11i	−0.0311725	+	0.0336193i
$667$	−7.15797e11	+	3.59855e12i	−0.140031	+	0.703982i
$668$	1.65404e12	−	1.92473e12i	0.321405	−	0.374003i
$669$	−2.16333e12	+	3.23765e12i	−0.417547	+	0.624903i
$670$	−6.34496e11	−	1.01486e11i	−0.121645	−	0.0194567i
$671$		−	8.12684e12i		−	1.54764i
$672$	2.90990e12	−	1.91242e12i	0.550448	−	0.361762i
$673$		−	9.47453e12i		−	1.78029i	−0.455680	−	0.890143i	$-0.650604\pi$
$673$		−	9.47453e12i		−	1.78029i	0.455680	−	0.890143i	$-0.349396\pi$
$674$	−6.51888e11	+	4.07566e12i	−0.121676	+	0.760725i
$675$	3.19591e12	−	4.78302e12i	0.592553	−	0.886819i
$676$	2.49032e11	+	3.29251e12i	0.0458665	+	0.606411i
$677$	2.95722e11	−	1.48670e12i	0.0541047	−	0.272003i	−0.944258	−	0.329207i	$-0.893219\pi$
$677$	2.95722e11	−	1.48670e12i	0.0541047	−	0.272003i	0.998362	+	0.0572042i	$0.0182186\pi$
$678$	−4.67736e11	−	4.33695e11i	−0.0850095	−	0.0788225i
$679$	7.71126e11	+	3.19411e11i	0.139223	+	0.0576681i
$680$	2.80271e11	+	2.23033e11i	0.0502676	+	0.0400017i
$681$	−6.54599e11	+	2.71144e11i	−0.116631	+	0.0483100i
$682$	1.62226e12	−	4.37678e12i	0.287138	−	0.774685i
$683$	−6.53856e11	+	4.36893e11i	−0.114971	+	0.0768213i	−0.611726	−	0.791069i	$-0.709525\pi$
$683$	−6.53856e11	+	4.36893e11i	−0.114971	+	0.0768213i	0.496755	+	0.867891i	$0.334525\pi$
$684$	3.83850e11	+	1.37708e12i	0.0670516	+	0.240551i
$685$	1.47506e10	+	7.41564e10i	0.00255978	+	0.0128689i
$686$	3.30373e12	−	5.37280e12i	0.569568	−	0.926279i
$687$	2.24700e10	−	2.24700e10i	0.00384856	−	0.00384856i
$688$	2.78029e12	+	1.26214e11i	0.473088	+	0.0214764i
$689$	−4.71318e12	−	4.71318e12i	−0.796760	−	0.796760i
$690$	6.99171e11	−	1.66730e11i	0.117426	−	0.0280022i
$691$	3.84385e11	−	7.64590e10i	0.0641380	−	0.0127578i	−0.162917	−	0.986640i	$-0.552090\pi$
$691$	3.84385e11	−	7.64590e10i	0.0641380	−	0.0127578i	0.227055	+	0.973882i	$0.427090\pi$
$692$	−2.29257e12	−	2.78431e11i	−0.380054	−	0.0461572i
$693$	−7.55914e11	−	1.13130e12i	−0.124501	−	0.186329i
$694$	−2.47317e12	−	5.38628e12i	−0.404702	−	0.881397i
$695$	2.88446e11	+	6.96370e11i	0.0468957	+	0.113216i
$696$	2.31030e12	+	2.73019e12i	0.373187	+	0.441012i
$697$	−6.76930e11	+	1.63425e12i	−0.108642	+	0.262284i
$698$	1.26893e11	+	3.36016e12i	0.0202343	+	0.535809i
$699$	−3.70994e12	−	7.37953e11i	−0.587787	−	0.116918i
$700$	−2.22957e12	−	4.40895e12i	−0.350979	−	0.694055i
$701$	−6.13632e12	−	4.10016e12i	−0.959791	−	0.641312i	−0.0262019	−	0.999657i	$-0.508341\pi$
$701$	−6.13632e12	−	4.10016e12i	−0.959791	−	0.641312i	−0.933589	+	0.358345i	$0.883341\pi$
$702$	2.57098e12	+	3.55002e12i	0.399560	+	0.551713i
$703$	7.66596e11			0.118377
$704$	5.53351e12	+	2.09909e12i	0.849031	+	0.322073i
$705$	5.26668e11			0.0802944
$706$	−1.64876e12	−	2.27661e12i	−0.249767	−	0.344879i
$707$	−2.64021e12	−	1.76413e12i	−0.397422	−	0.265549i
$708$	7.01692e11	−	3.54841e11i	0.104954	−	0.0530742i
$709$	9.01437e12	+	1.79307e12i	1.33976	+	0.266495i	0.812377	−	0.583132i	$-0.198173\pi$
$709$	9.01437e12	+	1.79307e12i	1.33976	+	0.266495i	0.527384	+	0.849627i	$0.323173\pi$
$710$	1.73681e10	+	4.59910e11i	0.00256501	+	0.0679220i
$711$	3.22449e11	−	7.78460e11i	0.0473203	−	0.114241i
$712$	5.46854e10	−	6.56464e11i	0.00797465	−	0.0957306i
$713$	−2.47791e12	−	5.98220e12i	−0.359073	−	0.866878i
$714$	8.69517e11	+	1.89371e12i	0.125209	+	0.272692i
$715$	3.11226e11	+	4.65783e11i	0.0445348	+	0.0666510i
$716$	−5.84114e11	+	4.80953e12i	−0.0830594	+	0.683903i
$717$	−3.96770e12	+	7.89225e11i	−0.560664	+	0.111523i
$718$	−4.68675e12	+	1.11764e12i	−0.658130	+	0.156943i
$719$	−2.61157e12	−	2.61157e12i	−0.364436	−	0.364436i	0.501007	−	0.865443i	$-0.332963\pi$
$719$	−2.61157e12	−	2.61157e12i	−0.364436	−	0.364436i	−0.865443	+	0.501007i	$0.832963\pi$
$720$	−1.34148e11	+	2.86385e11i	−0.0186032	+	0.0397150i
$721$	−7.20121e11	+	7.20121e11i	−0.0992423	+	0.0992423i
$722$	−1.35858e12	+	2.20943e12i	−0.186066	+	0.302596i
$723$	−2.24910e12	−	1.13070e13i	−0.306117	−	1.53895i
$724$	9.46118e12	−	2.63723e12i	1.27974	−	0.356717i
$725$	4.21939e12	−	2.81931e12i	0.567190	−	0.378984i
$726$	3.78797e11	−	1.02198e12i	0.0506048	−	0.136529i
$727$	−1.18228e13	+	4.89717e12i	−1.56970	+	0.650190i	−0.986740	−	0.162311i	$-0.948105\pi$
$727$	−1.18228e13	+	4.89717e12i	−1.56970	+	0.650190i	−0.582959	+	0.812502i	$0.698105\pi$
$728$	3.74050e12	−	4.25388e11i	0.493558	−	0.0561298i
$729$	−7.66145e12	−	3.17348e12i	−1.00470	−	0.416161i
$730$	−1.01692e12	−	9.42910e11i	−0.132536	−	0.122890i
$731$	−3.24930e11	+	1.63353e12i	−0.0420883	+	0.211592i
$732$	−1.09579e13	+	8.28809e11i	−1.41067	+	0.106698i
$733$	−4.43745e11	+	6.64112e11i	−0.0567761	+	0.0849715i	−0.858772	−	0.512359i	$-0.828772\pi$
$733$	−4.43745e11	+	6.64112e11i	−0.0567761	+	0.0849715i	0.801995	+	0.597330i	$0.203772\pi$
$734$	−1.72107e12	+	1.07603e13i	−0.218860	+	1.36833i
$735$		−	3.42960e11i		−	0.0433461i
$736$	7.60858e12	−	3.08387e12i	0.955770	−	0.387388i
$737$		−	6.35361e12i		−	0.793262i
$738$	−1.54220e12	−	2.46669e11i	−0.191375	−	0.0306099i
$739$	1.81661e12	−	2.71875e12i	0.224058	−	0.335327i	−0.702360	−	0.711821i	$-0.747871\pi$
$739$	1.81661e12	−	2.71875e12i	0.224058	−	0.335327i	0.926419	+	0.376494i	$0.122871\pi$
$740$	1.28616e11	+	1.10529e11i	0.0157672	+	0.0135498i
$741$	6.68032e11	−	3.35842e12i	0.0813983	−	0.409217i
$742$	8.01897e12	−	8.64840e12i	0.971183	−	1.04741i
$743$	7.29018e12	+	3.01969e12i	0.877584	+	0.363507i	0.775559	−	0.631275i	$-0.217468\pi$
$743$	7.29018e12	+	3.01969e12i	0.877584	+	0.363507i	0.102025	+	0.994782i	$0.467468\pi$
$744$	−6.06689e12	−	1.74102e12i	−0.725919	−	0.208317i
$745$	−9.55696e11	+	3.95862e11i	−0.113662	+	0.0470805i
$746$	7.45734e12	+	2.76407e12i	0.881575	+	0.326757i
$747$	−2.42765e12	+	1.62210e12i	−0.285262	+	0.190606i
$748$	−1.73996e12	+	3.08483e12i	−0.203227	+	0.360308i
$749$	−1.38082e12	−	6.94185e12i	−0.160313	−	0.805948i
$750$	−1.71087e12	−	1.05201e12i	−0.197442	−	0.121407i
$751$	−3.49410e12	+	3.49410e12i	−0.400826	+	0.400826i	−0.878524	−	0.477698i	$-0.841471\pi$
$751$	−3.49410e12	+	3.49410e12i	−0.400826	+	0.400826i	0.477698	+	0.878524i	$0.341471\pi$
$752$	5.94711e12	−	9.04808e11i	0.678150	−	0.103175i
$753$	−6.60599e12	−	6.60599e12i	−0.748791	−	0.748791i
$754$	8.96933e11	+	3.76123e12i	0.101062	+	0.423798i
$755$	−5.61443e11	+	1.11678e11i	−0.0628846	+	0.0125085i
$756$	−6.10535e12	+	4.78297e12i	−0.679771	+	0.532537i
$757$	8.23471e12	+	1.23241e13i	0.911417	+	1.36403i	0.931309	+	0.364229i	$0.118667\pi$
$757$	8.23471e12	+	1.23241e13i	0.911417	+	1.36403i	−0.0198929	+	0.999802i	$0.506333\pi$
$758$	1.11168e13	−	5.10439e12i	1.22312	−	0.561607i
$759$	2.71981e12	+	6.56621e12i	0.297476	+	0.718169i
$760$	9.91952e11	−	3.17299e11i	0.107852	−	0.0344991i
$761$	3.11162e12	−	7.51211e12i	0.336322	−	0.811953i	−0.661741	−	0.749733i	$-0.730182\pi$
$761$	3.11162e12	−	7.51211e12i	0.336322	−	0.811953i	0.998062	−	0.0622200i	$-0.0198181\pi$
$762$	1.43532e13	−	5.42035e11i	1.54224	−	0.0582412i
$763$	−8.36096e12	−	1.66310e12i	−0.893091	−	0.177647i
$764$	−2.13677e12	+	6.50874e12i	−0.226902	+	0.691157i
$765$	−1.57358e11	−	1.05143e11i	−0.0166117	−	0.0110996i
$766$	−3.96004e10	+	2.86793e10i	−0.00415595	+	0.00300981i
$767$	8.50111e11			0.0886944
$768$	2.26599e12	−	7.67520e12i	0.235035	−	0.796094i
$769$	−8.40525e12			−0.866726			−0.433363	−	0.901219i	$-0.642673\pi$
$769$	−8.40525e12			−0.866726			−0.433363	+	0.901219i	$0.642673\pi$
$770$	−8.02800e11	+	5.81402e11i	−0.0822999	+	0.0596030i
$771$	5.40384e12	+	3.61073e12i	0.550755	+	0.368002i
$772$	−1.42420e12	+	4.33821e12i	−0.144309	+	0.439575i
$773$	1.37728e13	+	2.73958e12i	1.38744	+	0.275979i	0.831631	−	0.555329i	$-0.187408\pi$
$773$	1.37728e13	+	2.73958e12i	1.38744	+	0.275979i	0.555811	+	0.831308i	$0.312408\pi$
$774$	−1.46948e12	+	5.54937e10i	−0.147174	+	0.00555788i
$775$	−3.42716e12	+	8.27389e12i	−0.341253	+	0.823858i
$776$	1.82707e12	−	5.84430e11i	0.180874	−	0.0578569i
$777$	3.77550e11	+	9.11486e11i	0.0371603	+	0.0897130i
$778$	4.73913e12	−	2.17602e12i	0.463757	−	0.212939i
$779$	2.85747e12	+	4.27651e12i	0.278012	+	0.416074i
$780$	5.96300e11	−	4.67146e11i	0.0576819	−	0.0451884i
$781$	−4.46336e12	+	8.87818e11i	−0.429272	+	0.0853875i
$782$	1.13964e12	+	4.77902e12i	0.108978	+	0.456992i
$783$	−5.63288e12	−	5.63288e12i	−0.535554	−	0.535554i
$784$	−5.89201e11	−	3.87269e12i	−0.0556982	−	0.366092i
$785$	−1.68361e12	+	1.68361e12i	−0.158244	+	0.158244i
$786$	−6.59726e12	−	4.05665e12i	−0.616541	−	0.379111i
$787$	−7.73874e11	−	3.89053e12i	−0.0719091	−	0.361512i	0.928030	−	0.372504i	$-0.121501\pi$
$787$	−7.73874e11	−	3.89053e12i	−0.0719091	−	0.361512i	−0.999940	+	0.0109928i	$0.996501\pi$
$788$	−1.97969e12	+	3.50985e12i	−0.182906	+	0.324281i
$789$	5.21480e12	−	3.48442e12i	0.479062	−	0.320099i
$790$	−5.75579e11	−	2.13339e11i	−0.0525754	−	0.0194872i
$791$	1.12734e12	−	4.66961e11i	0.102391	−	0.0424118i
$792$	−3.00571e12	−	8.62551e11i	−0.271447	−	0.0778972i
$793$	−1.09764e13	−	4.54659e12i	−0.985671	−	0.408278i
$794$	5.05865e12	−	5.45572e12i	0.451692	−	0.487147i
$795$	4.62975e11	−	2.32753e12i	0.0411060	−	0.206654i
$796$	−1.56085e13	−	1.34134e13i	−1.37801	−	1.18421i
$797$	−3.04720e12	+	4.56046e12i	−0.267509	+	0.400356i	−0.940768	−	0.339051i	$-0.889894\pi$
$797$	−3.04720e12	+	4.56046e12i	−0.267509	+	0.400356i	0.673259	+	0.739407i	$0.264894\pi$
$798$	5.98286e12	+	9.56939e11i	0.522271	+	0.0835355i
$799$			3.59991e12i			0.312487i
$800$	−1.04571e13	−	4.42511e12i	−0.902623	−	0.381961i
$801$			3.48056e11i			0.0298747i
$802$	−3.48697e12	+	2.18008e13i	−0.297621	+	1.86075i
$803$	7.61830e12	−	1.14016e13i	0.646604	−	0.967711i
$804$	−8.56691e12	+	6.47967e11i	−0.723056	+	0.0546891i
$805$	−2.68252e11	+	1.34860e12i	−0.0225145	+	0.113188i
$806$	−5.00387e12	−	4.63969e12i	−0.417636	−	0.387241i
$807$	1.58974e13	+	6.58491e12i	1.31945	+	0.546536i
$808$	−7.25105e12	+	8.24625e11i	−0.598480	+	0.0680621i
$809$	−3.60299e12	+	1.49241e12i	−0.295729	+	0.122495i	−0.525615	−	0.850723i	$-0.676165\pi$
$809$	−3.60299e12	+	1.49241e12i	−0.295729	+	0.122495i	0.229886	+	0.973218i	$0.426165\pi$
$810$	−3.55638e11	+	9.59495e11i	−0.0290286	+	0.0783177i
$811$	−1.25546e13	+	8.38872e12i	−1.01908	+	0.680929i	−0.948565	−	0.316581i	$-0.897465\pi$
$811$	−1.25546e13	+	8.38872e12i	−1.01908	+	0.680929i	−0.0705174	+	0.997511i	$0.522465\pi$
$812$	−6.59059e12	+	1.83708e12i	−0.532013	+	0.148294i
$813$	−1.17106e12	−	5.88733e12i	−0.0940097	−	0.472619i
$814$	−8.78322e11	+	1.42840e12i	−0.0701204	+	0.114036i
$815$	4.82203e11	−	4.82203e11i	0.0382843	−	0.0382843i
$816$	4.33689e12	+	2.03147e12i	0.342430	+	0.160401i
$817$	3.42435e12	+	3.42435e12i	0.268892	+	0.268892i
$818$	−1.62673e13	+	3.87923e12i	−1.27036	+	0.302939i
$819$	−1.95088e12	+	3.88055e11i	−0.151514	+	0.0301381i
$820$	−1.37176e11	+	1.12949e12i	−0.0105953	+	0.0872408i
$821$	1.14769e13	+	1.71764e13i	0.881617	+	1.31943i	0.946887	+	0.321566i	$0.104209\pi$
$821$	1.14769e13	+	1.71764e13i	0.881617	+	1.31943i	−0.0652701	+	0.997868i	$0.520791\pi$
$822$	4.21838e11	+	9.18717e11i	0.0322272	+	0.0701873i
$823$	4.12271e12	+	9.95310e12i	0.313244	+	0.756239i	0.999581	+	0.0289545i	$0.00921779\pi$
$823$	4.12271e12	+	9.95310e12i	0.313244	+	0.756239i	−0.686336	+	0.727284i	$0.740782\pi$
$824$	−1.94303e11	+	2.33248e12i	−0.0146827	+	0.176257i
$825$	3.76173e12	−	9.08163e12i	0.282713	−	0.682529i
$826$	5.67646e10	+	1.50314e12i	0.00424294	+	0.112354i
$827$	1.83714e13	+	3.65429e12i	1.36573	+	0.271662i	0.822904	−	0.568180i	$-0.192352\pi$
$827$	1.83714e13	+	3.65429e12i	1.36573	+	0.271662i	0.542831	+	0.839842i	$0.317352\pi$
$828$	−3.87099e12	+	1.95753e12i	−0.286211	+	0.144735i
$829$	−7.84066e12	−	5.23896e12i	−0.576577	−	0.385256i	0.232819	−	0.972520i	$-0.425205\pi$
$829$	−7.84066e12	−	5.23896e12i	−0.576577	−	0.385256i	−0.809396	+	0.587264i	$0.800205\pi$
$830$	1.24762e12	+	1.72272e12i	0.0912497	+	0.125998i
$831$	−5.68361e12			−0.413447
$832$	5.93085e12	−	6.29943e12i	0.429104	−	0.455770i
$833$	2.34422e12			0.168693
$834$	5.91125e12	+	8.16227e12i	0.423089	+	0.584203i
$835$	8.12228e11	+	5.42714e11i	0.0578215	+	0.0386351i
$836$	4.64718e12	+	9.18973e12i	0.329049	+	0.650691i
$837$	1.37883e13	+	2.74267e12i	0.971061	+	0.193156i
$838$	−3.25169e11	−	8.61055e12i	−0.0227778	−	0.603161i
$839$	−6.34754e12	+	1.53243e13i	−0.442259	+	1.06771i	0.532895	+	0.846181i	$0.321104\pi$
$839$	−6.34754e12	+	1.53243e13i	−0.442259	+	1.06771i	−0.975154	+	0.221526i	$0.928896\pi$
$840$	8.65808e11	+	1.02317e12i	0.0600019	+	0.0709070i
$841$	2.86238e12	+	6.91040e12i	0.197308	+	0.476345i
$842$	5.36727e11	+	1.16893e12i	0.0368001	+	0.0801466i
$843$	−6.52116e12	−	9.75960e12i	−0.444734	−	0.665592i
$844$	−2.41895e13	−	2.93780e12i	−1.64091	−	0.199288i
$845$	−1.24656e12	+	2.47957e11i	−0.0841122	+	0.0167310i
$846$	−3.09174e12	+	7.37279e11i	−0.207508	+	0.0494841i
$847$	1.47432e12	+	1.47432e12i	0.0984277	+	0.0984277i
$848$	1.22923e12	−	2.70778e13i	0.0816303	−	1.79818i
$849$	1.45398e13	−	1.45398e13i	0.960449	−	0.960449i
$850$	3.55927e12	−	5.78839e12i	0.233871	−	0.380340i
$851$	4.53800e11	+	2.28141e12i	0.0296607	+	0.149114i
$852$	1.65229e12	+	5.92765e12i	0.107425	+	0.385394i
$853$	3.44059e12	−	2.29893e12i	0.222516	−	0.148681i	−0.439316	−	0.898333i	$-0.644779\pi$
$853$	3.44059e12	−	2.29893e12i	0.222516	−	0.148681i	0.661832	+	0.749652i	$0.269779\pi$
$854$	7.30619e12	−	1.97117e13i	0.470035	−	1.26813i
$855$	−5.08390e11	+	2.10582e11i	−0.0325349	+	0.0134764i
$856$	−1.27284e13	−	1.01289e13i	−0.810290	−	0.644809i
$857$	2.70743e13	+	1.12145e13i	1.71452	+	0.710178i	0.999944	+	0.0106219i	$0.00338113\pi$
$857$	2.70743e13	+	1.12145e13i	1.71452	+	0.710178i	0.714578	+	0.699556i	$0.246619\pi$
$858$	5.49237e12	+	5.09264e12i	0.345993	+	0.320812i
$859$	−4.56097e12	+	2.29296e13i	−0.285817	+	1.43690i	0.524752	+	0.851255i	$0.324158\pi$
$859$	−4.56097e12	+	2.29296e13i	−0.285817	+	1.43690i	−0.810569	+	0.585644i	$0.800842\pi$
$860$	8.07981e10	+	1.06825e12i	0.00503684	+	0.0665931i
$861$	−3.67748e12	+	5.50374e12i	−0.228053	+	0.341306i
$862$	3.96198e12	−	2.47706e13i	0.244416	−	1.52811i
$863$			1.34682e13i			0.826533i	0.910610	+	0.413267i	$0.135612\pi$
$863$			1.34682e13i			0.826533i	−0.910610	+	0.413267i	$0.864388\pi$
$864$	−3.61053e12	+	1.74553e13i	−0.220424	+	1.06565i
$865$		−	8.88947e11i		−	0.0539888i
$866$	1.59367e13	+	2.54902e12i	0.962869	+	0.154008i
$867$	6.08025e12	−	9.09974e12i	0.365456	−	0.546944i
$868$	7.86962e12	−	9.15748e12i	0.470560	−	0.547567i
$869$	1.18413e12	−	5.95302e12i	0.0704385	−	0.354118i
$870$	−9.36031e11	+	1.00950e12i	−0.0553928	+	0.0597407i
$871$	−8.58143e12	−	3.55454e12i	−0.505217	−	0.209268i
$872$	−1.71376e13	+	9.49488e12i	−1.00375	+	0.556116i
$873$	−9.36400e11	+	3.87869e11i	−0.0545629	+	0.0226007i
$874$	1.33947e13	+	4.96479e12i	0.776485	+	0.287805i
$875$	3.19460e12	−	2.13456e12i	0.184239	−	0.123104i
$876$	−1.61503e13	−	9.10938e12i	−0.926644	−	0.522661i
$877$	2.11623e11	+	1.06390e12i	0.0120799	+	0.0607299i	0.986355	−	0.164632i	$-0.0526436\pi$
$877$	2.11623e11	+	1.06390e12i	0.0120799	+	0.0607299i	−0.974275	+	0.225362i	$0.927644\pi$
$878$	5.09889e12	+	3.13530e12i	0.289568	+	0.178055i
$879$	−2.98942e12	+	2.98942e12i	−0.168903	+	0.168903i
$880$	−5.45298e11	+	2.21185e12i	−0.0306522	+	0.124332i
$881$	−8.89921e12	−	8.89921e12i	−0.497691	−	0.497691i	0.413028	−	0.910719i	$-0.364471\pi$
$881$	−8.89921e12	−	8.89921e12i	−0.497691	−	0.497691i	−0.910719	+	0.413028i	$0.864471\pi$
$882$	4.80108e11	+	2.01330e12i	0.0267135	+	0.112021i
$883$	1.17456e13	−	2.33634e12i	0.650206	−	0.129334i	0.141042	−	0.990004i	$-0.454955\pi$
$883$	1.17456e13	−	2.33634e12i	0.650206	−	0.129334i	0.509164	+	0.860669i	$0.329955\pi$
$884$	3.19306e12	+	4.07587e12i	0.175862	+	0.224484i
$885$	1.68154e11	+	2.51660e11i	0.00921430	+	0.0137902i
$886$	2.60494e13	−	1.19609e13i	1.42019	−	0.652095i
$887$	9.43847e12	+	2.27865e13i	0.511971	+	1.23601i	0.942735	+	0.333543i	$0.108244\pi$
$887$	9.43847e12	+	2.27865e13i	0.511971	+	1.23601i	−0.430764	+	0.902465i	$0.641756\pi$
$888$	2.01557e12	+	1.03862e12i	0.108777	+	0.0560527i
$889$	−1.05151e13	+	2.53856e13i	−0.564617	+	1.36311i
$890$	2.53383e11	−	9.56876e9i	0.0135370	−	0.000511211i
$891$	−9.92374e12	−	1.97396e12i	−0.527504	−	0.104927i
$892$	−1.62656e13	−	5.33988e12i	−0.860258	−	0.282416i
$893$	8.70316e12	+	5.81527e12i	0.457979	+	0.306012i
$894$	−1.12019e13	+	8.11258e12i	−0.586505	+	0.424757i
$895$	−1.86490e12			−0.0971522
$896$	1.15345e13	+	1.00661e13i	0.597876	+	0.521765i
$897$	1.03902e13			0.535868
$898$	−5.06482e12	+	3.66803e12i	−0.259909	+	0.188230i
$899$	1.03117e13	+	6.89007e12i	0.526517	+	0.351808i
$900$	5.70023e12	+	1.87134e12i	0.289602	+	0.0950741i
$901$	1.59093e13	+	3.16456e12i	0.804247	+	0.159975i
$902$	−1.12424e13	+	4.24558e11i	−0.565495	+	0.0213554i
$903$	−2.38507e12	+	5.75806e12i	−0.119373	+	0.288192i
$904$	1.28458e12	−	2.49289e12i	0.0639739	−	0.124150i
$905$	1.44680e12	+	3.49287e12i	0.0716949	+	0.173087i
$906$	−6.95567e12	+	3.19376e12i	−0.342975	+	0.157480i
$907$	5.09680e12	+	7.62789e12i	0.250072	+	0.374259i	0.935174	−	0.354188i	$-0.115243\pi$
$907$	5.09680e12	+	7.62789e12i	0.250072	+	0.374259i	−0.685103	+	0.728447i	$0.740243\pi$
$908$	−1.92108e12	−	2.45221e12i	−0.0937904	−	0.119721i
$909$	3.78184e12	−	7.52254e11i	0.183724	−	0.0365449i
$910$	3.36135e11	+	1.40956e12i	0.0162490	+	0.0681393i
$911$	−1.46271e13	−	1.46271e13i	−0.703602	−	0.703602i	0.261580	−	0.965182i	$-0.415756\pi$
$911$	−1.46271e13	−	1.46271e13i	−0.703602	−	0.703602i	−0.965182	+	0.261580i	$0.915756\pi$
$912$	1.19171e13	−	7.20325e12i	0.570417	−	0.344788i
$913$	−1.48719e13	+	1.48719e13i	−0.708352	+	0.708352i
$914$	1.76289e13	+	1.08400e13i	0.835538	+	0.513772i
$915$	−8.25228e11	−	4.14870e12i	−0.0389206	−	0.195667i
$916$	1.21689e11	+	6.86370e10i	0.00571112	+	0.00322128i
$917$	1.23187e13	−	8.23108e12i	0.575311	−	0.384410i
$918$	−1.00020e13	−	3.70726e12i	−0.464831	−	0.172290i
$919$	−2.27495e13	+	9.42317e12i	−1.05209	+	0.435790i	−0.840637	−	0.541598i	$-0.817819\pi$
$919$	−2.27495e13	+	9.42317e12i	−1.05209	+	0.435790i	−0.211453	+	0.977388i	$0.567819\pi$
$920$	1.53149e12	+	2.76424e12i	0.0704806	+	0.127213i
$921$	−2.10352e12	−	8.71305e11i	−0.0963336	−	0.0399027i
$922$	9.59857e12	−	1.03520e13i	0.437439	−	0.471774i
$923$	−1.29792e12	+	6.52509e12i	−0.0588627	+	0.295923i
$924$	−8.63789e12	+	1.00515e13i	−0.389838	+	0.453634i
$925$	1.78738e12	−	2.67500e12i	0.0802747	−	0.120140i
$926$	7.14364e12	+	1.14260e12i	0.319279	+	0.0510677i
$927$		−	1.23668e12i		−	0.0550045i
$928$	−8.83532e12	+	1.30073e13i	−0.391071	+	0.575735i
$929$		−	3.27990e13i		−	1.44474i	−0.691507	−	0.722370i	$-0.743053\pi$
$929$		−	3.27990e13i		−	1.44474i	0.691507	−	0.722370i	$-0.256947\pi$
$930$	3.83720e11	−	2.39905e12i	0.0168206	−	0.105164i
$931$	3.78684e12	−	5.66740e12i	0.165197	−	0.247235i
$932$	−1.25428e12	−	1.65831e13i	−0.0544533	−	0.719938i
$933$	−9.11502e11	+	4.58243e12i	−0.0393813	+	0.197983i
$934$	−3.28161e13	−	3.04278e13i	−1.41100	−	1.30831i
$935$	−1.25951e12	−	5.21705e11i	−0.0538950	−	0.0223240i
$936$	−2.84655e12	+	3.57708e12i	−0.121221	+	0.152331i
$937$	−3.78257e13	+	1.56679e13i	−1.60310	+	0.664024i	−0.991849	−	0.127417i	$-0.959331\pi$
$937$	−3.78257e13	+	1.56679e13i	−1.60310	+	0.664024i	−0.611246	+	0.791441i	$0.709331\pi$
$938$	5.71202e12	−	1.54107e13i	0.240922	−	0.649996i
$939$	3.63933e12	−	2.43173e12i	0.152766	−	0.102075i
$940$	6.21732e11	+	2.23049e12i	0.0259733	+	0.0931806i
$941$	−7.25495e12	−	3.64731e13i	−0.301634	−	1.51642i	−0.772957	−	0.634458i	$-0.781223\pi$
$941$	−7.25495e12	−	3.64731e13i	−0.301634	−	1.51642i	0.471323	−	0.881961i	$-0.343777\pi$
$942$	−1.66751e13	+	2.71184e13i	−0.689984	+	1.12211i
$943$	−1.10355e13	+	1.10355e13i	−0.454452	+	0.454452i
$944$	2.33114e12	+	2.55285e12i	0.0955419	+	0.104629i
$945$	−2.11098e12	−	2.11098e12i	−0.0861075	−	0.0861075i
$946$	−1.03040e13	+	2.45718e12i	−0.418308	+	0.0997531i
$947$	2.59797e13	−	5.16768e12i	1.04969	−	0.208795i	0.360036	−	0.932939i	$-0.382765\pi$
$947$	2.59797e13	−	5.16768e12i	1.04969	−	0.208795i	0.689650	+	0.724143i	$0.257765\pi$
$948$	−8.14754e12	−	9.89513e11i	−0.327634	−	0.0397909i
$949$	−1.11374e13	−	1.66682e13i	−0.445743	−	0.667101i
$950$	−8.24441e12	−	1.79554e13i	−0.328400	−	0.715220i
$951$	3.96752e11	+	9.57844e11i	0.0157292	+	0.0379737i
$952$	−6.99361e12	+	5.91803e12i	−0.275953	+	0.233513i
$953$	1.05000e13	−	2.53492e13i	0.412354	−	0.995510i	−0.572151	−	0.820149i	$-0.693891\pi$
$953$	1.05000e13	−	2.53492e13i	0.412354	−	0.995510i	0.984504	−	0.175361i	$-0.0561093\pi$
$954$	5.40464e11	+	1.43116e13i	0.0211251	+	0.559398i
$955$	−2.58625e12	−	5.14437e11i	−0.100613	−	0.0200132i
$956$	−8.02633e12	−	1.58719e13i	−0.310782	−	0.614568i
$957$	−1.13184e13	−	7.56272e12i	−0.436196	−	0.291457i
$958$	1.56763e13	+	2.16458e13i	0.601309	+	0.830288i
$959$	−1.93391e12			−0.0738335
$960$	3.03797e12	+	5.09681e11i	0.115442	+	0.0193677i
$961$	4.55312e12			0.172208
$962$	1.43787e12	+	1.98542e12i	0.0541294	+	0.0747420i
$963$	7.14634e12	+	4.77503e12i	0.267772	+	0.178920i
$964$	4.52313e13	−	2.28731e13i	1.68691	−	0.853059i
$965$	−1.72379e12	−	3.42883e11i	−0.0639899	−	0.0127284i
$966$	6.93786e11	+	1.83716e13i	0.0256347	+	0.678812i
$967$	−9.28681e12	+	2.24203e13i	−0.341545	+	0.824561i	0.656016	+	0.754747i	$0.272241\pi$
$967$	−9.28681e12	+	2.24203e13i	−0.341545	+	0.824561i	−0.997560	+	0.0698140i	$0.977759\pi$
$968$	4.77534e12	+	3.97801e11i	0.174810	+	0.0145622i
$969$	3.18896e12	+	7.69883e12i	0.116196	+	0.280523i
$970$	3.08110e11	+	6.71029e11i	0.0111746	+	0.0243371i
$971$	−1.30063e13	−	1.94653e13i	−0.469535	−	0.702709i	0.518819	−	0.854884i	$-0.326372\pi$
$971$	−1.30063e13	−	1.94653e13i	−0.469535	−	0.702709i	−0.988353	+	0.152176i	$0.951372\pi$
$972$	2.00159e12	−	1.64809e13i	0.0719244	−	0.592218i
$973$	−1.89087e13	+	3.76117e12i	−0.676321	+	0.134529i
$974$	−3.85386e13	+	9.19021e12i	−1.37208	+	0.327198i
$975$	−1.01615e13	−	1.01615e13i	−0.360111	−	0.360111i
$976$	−1.64459e13	−	4.54293e13i	−0.580140	−	1.60255i
$977$	−2.03004e13	+	2.03004e13i	−0.712819	+	0.712819i	−0.967124	−	0.254305i	$-0.918153\pi$
$977$	−2.03004e13	+	2.03004e13i	−0.712819	+	0.712819i	0.254305	+	0.967124i	$0.418153\pi$
$978$	4.77591e12	−	7.76698e12i	0.166929	−	0.271474i
$979$	4.89134e11	+	2.45904e12i	0.0170179	+	0.0855547i
$980$	1.45247e12	−	4.04865e11i	0.0503026	−	0.0140214i
$981$	8.60726e12	−	5.75119e12i	0.296725	−	0.198265i
$982$	−4.47227e12	+	1.20660e13i	−0.153471	+	0.414057i
$983$	4.38604e13	−	1.81676e13i	1.49824	−	0.620592i	0.525151	−	0.851009i	$-0.324009\pi$
$983$	4.38604e13	−	1.81676e13i	1.49824	−	0.620592i	0.973092	+	0.230417i	$0.0740089\pi$
$984$	1.71900e12	+	1.51154e13i	0.0584517	+	0.513975i
$985$	−1.43304e12	−	5.93585e11i	−0.0485060	−	0.0200919i
$986$	−6.90021e12	−	6.39802e12i	−0.232496	−	0.215575i
$987$	−2.62806e12	+	1.32121e13i	−0.0881470	+	0.443145i
$988$	1.50119e13	−	1.13544e12i	0.501221	−	0.0379103i
$989$	−8.16382e12	+	1.22180e13i	−0.271338	+	0.406086i
$990$	1.90106e11	−	1.18856e12i	0.00628981	−	0.0393244i
$991$			1.61495e13i			0.531895i	0.963987	+	0.265948i	$0.0856849\pi$
$991$			1.61495e13i			0.531895i	−0.963987	+	0.265948i	$0.914315\pi$
$992$	2.11422e11	−	2.77492e13i	0.00693183	−	0.909804i
$993$		−	4.80013e13i		−	1.56669i
$994$	−1.16241e13	−	1.85924e12i	−0.377677	−	0.0604083i
$995$	4.40112e12	−	6.58674e12i	0.142350	−	0.213043i
$996$	2.15693e13	+	1.85359e13i	0.694496	+	0.596825i
$997$	1.08823e12	−	5.47090e12i	0.0348813	−	0.175360i	−0.959418	−	0.281989i	$-0.909006\pi$
$997$	1.08823e12	−	5.47090e12i	0.0348813	−	0.175360i	0.994299	+	0.106629i	$0.0340058\pi$
$998$	2.29484e13	−	2.47497e13i	0.732260	−	0.789737i
$999$	−4.66590e12	−	1.93268e12i	−0.148215	−	0.0613925i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	64.10.i.a.5.15	✓	568
64.13	even	16	inner	64.10.i.a.13.15	yes	568

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
64.10.i.a.5.15	✓	568	1.1	even	1	trivial
64.10.i.a.13.15	yes	568	64.13	even	16	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 64 = 2^{6} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	64.i (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-18.3262 + 13.2722i) q^{2} +(-96.8286 - 64.6988i) q^{3} +(159.700 - 486.457i) q^{4} +(193.294 + 38.4485i) q^{5} +(2633.19 - 99.4401i) q^{6} +(-1929.06 + 4657.16i) q^{7} +(3529.63 + 11034.5i) q^{8} +(-2342.51 - 5655.33i) q^{9} +(-4052.64 + 1860.81i) q^{10} +(-24497.6 - 36663.3i) q^{11} +(-46936.7 + 36770.5i) q^{12} +(-63224.1 + 12576.1i) q^{13} +(-26458.2 - 110951. i) q^{14} +(-16228.8 - 16228.8i) q^{15} +(-211136. - 155374. i) q^{16} +(110928. - 110928. i) q^{17} +(117988. + 72550.5i) q^{18} +(-88987.9 - 447373. i) q^{19} +(49572.5 - 87888.8i) q^{20} +(488101. - 326139. i) q^{21} +(935549. + 346763. i) q^{22} +(1.27871e6 - 529660. i) q^{23} +(372148. - 1.29682e6i) q^{24} +(-1.76857e6 - 732565. i) q^{25} +(991747. - 1.06959e6i) q^{26} +(-586253. + 2.94729e6i) q^{27} +(1.95744e6 + 1.68215e6i) q^{28} +(-1.47277e6 + 2.20416e6i) q^{29} +(512803. + 82021.3i) q^{30} -4.67830e6i q^{31} +(5.93147e6 + 45192.1i) q^{32} +5.13502e6i q^{33} +(-560637. + 3.50515e6i) q^{34} +(-551937. + 826031. i) q^{35} +(-3.12517e6 + 236375. i) q^{36} +(-327874. + 1.64833e6i) q^{37} +(7.56841e6 + 7.01758e6i) q^{38} +(6.93556e6 + 2.87280e6i) q^{39} +(257997. + 2.26860e6i) q^{40} +(-1.04175e7 + 4.31507e6i) q^{41} +(-4.61648e6 + 1.24550e7i) q^{42} +(-8.82762e6 + 5.89843e6i) q^{43} +(-2.17473e7 + 6.06190e6i) q^{44} +(-235354. - 1.18321e6i) q^{45} +(-1.64042e7 + 2.66779e7i) q^{46} +(-1.62263e7 + 1.62263e7i) q^{47} +(1.03915e7 + 2.87049e7i) q^{48} +(1.05664e7 + 1.05664e7i) q^{49} +(4.21339e7 - 1.00476e7i) q^{50} +(-1.79179e7 + 3.56410e6i) q^{51} +(-3.97918e6 + 3.27642e7i) q^{52} +(5.74460e7 + 8.59739e7i) q^{53} +(-2.83731e7 - 6.17935e7i) q^{54} +(-3.32559e6 - 8.02868e6i) q^{55} +(-5.81982e7 - 4.84809e6i) q^{56} +(-2.03279e7 + 4.90759e7i) q^{57} +(-2.26361e6 - 5.99408e7i) q^{58} +(-1.29342e7 - 2.57278e6i) q^{59} +(-1.04863e7 + 5.30287e6i) q^{60} +(1.53244e8 + 1.02394e8i) q^{61} +(6.20911e7 + 8.57355e7i) q^{62} +3.08566e7 q^{63} +(-1.09301e8 + 7.78952e7i) q^{64} -1.27044e7 q^{65} +(-6.81528e7 - 9.41054e7i) q^{66} +(1.19807e8 + 8.00524e7i) q^{67} +(-3.62465e7 - 7.16769e7i) q^{68} +(-1.58084e8 - 3.14449e7i) q^{69} +(-848310. - 2.24634e7i) q^{70} +(3.94951e7 - 9.53496e7i) q^{71} +(5.41353e7 - 4.58096e7i) q^{72} +(1.19007e8 + 2.87309e8i) q^{73} +(-1.58682e7 - 3.45593e7i) q^{74} +(1.23852e8 + 1.85358e8i) q^{75} +(-2.31839e8 - 2.81566e7i) q^{76} +(2.18004e8 - 4.33637e7i) q^{77} +(-1.65231e8 + 3.94022e7i) q^{78} +(9.73339e7 + 9.73339e7i) q^{79} +(-3.48373e7 - 3.81507e7i) q^{80} +(1.62256e8 - 1.62256e8i) q^{81} +(1.33643e8 - 2.17341e8i) q^{82} +(-9.30536e7 - 4.67812e8i) q^{83} +(-8.07026e7 - 2.89524e8i) q^{84} +(2.57067e7 - 1.71767e7i) q^{85} +(8.34920e7 - 2.25257e8i) q^{86} +(2.85213e8 - 1.18139e8i) q^{87} +(3.18092e8 - 3.99726e8i) q^{88} +(-5.25318e7 - 2.17594e7i) q^{89} +(2.00168e7 + 1.85600e7i) q^{90} +(6.33944e7 - 3.18705e8i) q^{91} +(-5.34463e7 - 7.06625e8i) q^{92} +(-3.02681e8 + 4.52993e8i) q^{93} +(8.20088e7 - 5.12725e8i) q^{94} -8.98958e7i q^{95} +(-5.71412e8 - 3.88135e8i) q^{96} -1.65578e8i q^{97} +(-3.33881e8 - 5.34032e7i) q^{98} +(-1.49957e8 + 2.24426e8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 568 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 8 q^{8} - 8 q^{9} - 8 q^{10} - 8 q^{11} - 8 q^{12} - 8 q^{13} - 8 q^{14} - 8 q^{15} - 8 q^{16} - 8 q^{17} - 8 q^{18} - 8 q^{19} - 8 q^{20}+ \cdots + 157456 q^{99}+O(q^{100}) \) 568 * q - 8 * q^2 - 8 * q^3 - 8 * q^4 - 8 * q^5 - 8 * q^6 - 8 * q^7 - 8 * q^8 - 8 * q^9 - 8 * q^10 - 8 * q^11 - 8 * q^12 - 8 * q^13 - 8 * q^14 - 8 * q^15 - 8 * q^16 - 8 * q^17 - 8 * q^18 - 8 * q^19 - 8 * q^20 - 8 * q^21 + 3576336 * q^22 - 8 * q^23 + 12096992 * q^24 - 8 * q^25 - 2105968 * q^26 - 8 * q^27 - 21791488 * q^28 - 8 * q^29 + 44263272 * q^30 + 29441312 * q^32 - 38537008 * q^34 - 8 * q^35 - 110500728 * q^36 - 8 * q^37 + 66947312 * q^38 - 8 * q^39 + 97089632 * q^40 - 8 * q^41 - 224559088 * q^42 - 8 * q^43 + 146176992 * q^44 - 8 * q^45 - 8 * q^46 - 8 * q^47 - 8 * q^48 - 8 * q^49 + 182758288 * q^50 - 360057320 * q^51 - 25227512 * q^52 - 8 * q^53 - 646232264 * q^54 + 280217656 * q^55 + 203163008 * q^56 - 8 * q^57 + 855153280 * q^58 - 576150472 * q^59 + 230939416 * q^60 - 8 * q^61 - 597609496 * q^62 + 1260236864 * q^63 - 1364809832 * q^64 - 16 * q^65 + 186013784 * q^66 - 1007094968 * q^67 + 1004327944 * q^68 - 8 * q^69 + 1869092056 * q^70 - 476202952 * q^71 - 714729104 * q^72 - 8 * q^73 - 2182183312 * q^74 + 2309166136 * q^75 - 888710984 * q^76 - 8 * q^77 + 5243787376 * q^78 - 2269128680 * q^79 - 5193915232 * q^80 - 8 * q^81 + 3136405672 * q^82 - 8 * q^83 + 6148771880 * q^84 - 8 * q^85 - 988828368 * q^86 - 8 * q^87 - 4940685368 * q^88 - 8 * q^89 - 7222410008 * q^90 - 8 * q^91 + 1729489584 * q^92 + 157456 * q^93 + 6710490136 * q^94 + 10366581632 * q^96 + 2543861360 * q^98 + 157456 * q^99

Introduction

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