LMFDB - Embedded newform 80.12.j.a.67.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [80,12,Mod(43,80)] 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("80.43"); S:= CuspForms(chi, 12); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(80, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 1, 3])) N = Newforms(chi, 12, names="a")

Level:	$ N $	$=$	$ 80 = 2^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	80.j (of order $4$, degree $2$, 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:	$61.4674544448$
Analytic rank:	$0$
Dimension:	$260$
Relative dimension:	$130$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			67.1
Character	$\chi$	$=$	80.67
Dual form			80.12.j.a.43.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-45.2481 - 0.780472i) q^{2} -201.994i q^{3} +(2046.78 + 70.6297i) q^{4} +(-705.591 - 6952.00i) q^{5} +(-157.651 + 9139.85i) q^{6} +(18488.6 + 18488.6i) q^{7} +(-92557.9 - 4793.32i) q^{8} +136345. q^{9} +(26500.8 + 315115. i) q^{10} +(238362. + 238362. i) q^{11} +(14266.8 - 413438. i) q^{12} -1.17648e6 q^{13} +(-822143. - 851003. i) q^{14} +(-1.40426e6 + 142525. i) q^{15} +(4.18433e6 + 289127. i) q^{16} +(-170908. - 170908. i) q^{17} +(-6.16937e6 - 106414. i) q^{18} +(-2.75021e6 - 2.75021e6i) q^{19} +(-953173. - 1.42791e7i) q^{20} +(3.73458e6 - 3.73458e6i) q^{21} +(-1.05994e7 - 1.09715e7i) q^{22} +(-3.92803e7 + 3.92803e7i) q^{23} +(-968221. + 1.86961e7i) q^{24} +(-4.78324e7 + 9.81053e6i) q^{25} +(5.32335e7 + 918209. i) q^{26} -6.33236e7i q^{27} +(3.65362e7 + 3.91479e7i) q^{28} +(3.26727e7 - 3.26727e7i) q^{29} +(6.36514e7 - 5.35301e6i) q^{30} -1.65757e8i q^{31} +(-1.89107e8 - 1.63482e7i) q^{32} +(4.81477e7 - 4.81477e7i) q^{33} +(7.59987e6 + 7.86665e6i) q^{34} +(1.15487e8 - 1.41578e8i) q^{35} +(2.79069e8 + 9.63004e6i) q^{36} +5.33441e8 q^{37} +(1.22295e8 + 1.26588e8i) q^{38} +2.37642e8i q^{39} +(3.19849e7 + 6.46844e8i) q^{40} -7.58275e8i q^{41} +(-1.71897e8 + 1.66068e8i) q^{42} -9.21052e8 q^{43} +(4.71040e8 + 5.04711e8i) q^{44} +(-9.62041e7 - 9.47873e8i) q^{45} +(1.80802e9 - 1.74670e9i) q^{46} +(3.58233e8 - 3.58233e8i) q^{47} +(5.84020e7 - 8.45209e8i) q^{48} -1.29367e9i q^{49} +(2.17198e9 - 4.06576e8i) q^{50} +(-3.45224e7 + 3.45224e7i) q^{51} +(-2.40800e9 - 8.30944e7i) q^{52} +1.15839e9i q^{53} +(-4.94223e7 + 2.86527e9i) q^{54} +(1.48891e9 - 1.82528e9i) q^{55} +(-1.62264e9 - 1.79988e9i) q^{56} +(-5.55526e8 + 5.55526e8i) q^{57} +(-1.50388e9 + 1.45288e9i) q^{58} +(-5.68854e9 + 5.68854e9i) q^{59} +(-2.88428e9 + 1.92535e8i) q^{60} +(1.59207e8 + 1.59207e8i) q^{61} +(-1.29369e8 + 7.50020e9i) q^{62} +(2.52083e9 + 2.52083e9i) q^{63} +(8.54398e9 + 8.87318e8i) q^{64} +(8.30113e8 + 8.17888e9i) q^{65} +(-2.21617e9 + 2.14102e9i) q^{66} -1.27263e10 q^{67} +(-3.37740e8 - 3.61882e8i) q^{68} +(7.93439e9 + 7.93439e9i) q^{69} +(-5.33607e9 + 6.31600e9i) q^{70} -3.29257e9 q^{71} +(-1.26198e10 - 6.53547e8i) q^{72} +(-1.01945e10 - 1.01945e10i) q^{73} +(-2.41372e10 - 4.16335e8i) q^{74} +(1.98167e9 + 9.66186e9i) q^{75} +(-5.43483e9 - 5.82332e9i) q^{76} +8.81395e9i q^{77} +(1.85473e8 - 1.07528e10i) q^{78} -4.22251e10 q^{79} +(-9.42412e8 - 2.92934e10i) q^{80} +1.13622e10 q^{81} +(-5.91812e8 + 3.43105e10i) q^{82} +1.75020e8i q^{83} +(7.90765e9 - 7.38010e9i) q^{84} +(-1.06756e9 + 1.30874e9i) q^{85} +(4.16759e10 + 7.18855e8i) q^{86} +(-6.59969e9 - 6.59969e9i) q^{87} +(-2.09197e10 - 2.32048e10i) q^{88} -8.57989e10 q^{89} +(3.61326e9 + 4.29645e10i) q^{90} +(-2.17514e10 - 2.17514e10i) q^{91} +(-8.31726e10 + 7.76238e10i) q^{92} -3.34820e10 q^{93} +(-1.64890e10 + 1.59298e10i) q^{94} +(-1.71789e10 + 2.10600e10i) q^{95} +(-3.30224e9 + 3.81985e10i) q^{96} +(9.81970e9 + 9.81970e9i) q^{97} +(-1.00967e9 + 5.85362e10i) q^{98} +(3.24996e10 + 3.24996e10i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 260 q - 2 q^{2} - 3956 q^{4} - 2 q^{5} - 4 q^{6} - 4 q^{7} - 74840 q^{8} - 14880348 q^{9} - 4098 q^{10} - 4 q^{11} - 114212 q^{12} - 4 q^{13} + 708588 q^{15} + 5740152 q^{16} - 4 q^{17} - 6791722 q^{18}+ \cdots - 189350900660 q^{99}+O(q^{100}) $ 260 * q - 2 * q^2 - 3956 * q^4 - 2 * q^5 - 4 * q^6 - 4 * q^7 - 74840 * q^8 - 14880348 * q^9 - 4098 * q^10 - 4 * q^11 - 114212 * q^12 - 4 * q^13 + 708588 * q^15 + 5740152 * q^16 - 4 * q^17 - 6791722 * q^18 - 11291288 * q^19 + 27599212 * q^20 - 4 * q^21 + 11921800 * q^22 - 4 * q^23 + 708588 * q^24 - 196875380 * q^26 + 185066800 * q^28 - 534157704 * q^30 - 894200972 * q^32 - 4 * q^33 - 122727336 * q^34 + 434731680 * q^35 + 917614156 * q^36 - 4 * q^37 - 169550316 * q^38 - 1417066568 * q^40 - 1572161236 * q^42 - 4763690660 * q^43 - 1456070840 * q^44 - 97301958 * q^45 - 3653567828 * q^46 + 5707353192 * q^47 - 447163780 * q^48 + 429408694 * q^50 + 112221284 * q^51 - 4957065880 * q^52 - 10995087044 * q^54 - 4 * q^55 - 8945492140 * q^56 + 708588 * q^57 + 33722126388 * q^58 - 11496390224 * q^59 - 6670533420 * q^60 - 2150827028 * q^61 + 15717297108 * q^62 + 708588 * q^63 - 11018267024 * q^64 - 4 * q^65 - 9909115916 * q^66 + 44333852084 * q^67 - 74998571352 * q^68 + 16194123612 * q^69 + 50947270608 * q^70 - 43677902056 * q^71 - 56634399632 * q^72 + 12278087704 * q^73 - 99553151276 * q^74 + 85400572304 * q^75 + 46613107196 * q^76 + 205137826492 * q^78 + 130159671844 * q^80 + 794986843420 * q^81 + 83904972628 * q^82 + 216982878048 * q^84 - 97656252 * q^85 + 56725646132 * q^86 - 50128110092 * q^87 + 346072249440 * q^88 + 174291105374 * q^90 - 46617621428 * q^91 - 51820450984 * q^92 + 708584 * q^93 - 82977932908 * q^94 - 20580862760 * q^95 - 62470624376 * q^96 - 4 * q^97 - 155418407946 * q^98 - 189350900660 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/80\mathbb{Z}\right)^\times$.

$n$	$17$	$21$	$31$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{3}{4}\right)$	$-1$

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 $

$2$	−45.2481	−	0.780472i	−0.999851	−	0.0172461i
$2$	−45.2481	−	0.780472i	−0.999851	−	0.0172461i
$3$		−	201.994i		−	0.479923i	−0.970782	−	0.239962i	$-0.922865\pi$
$3$		−	201.994i		−	0.479923i	0.970782	−	0.239962i	$-0.0771348\pi$
$4$	2046.78	+	70.6297i	0.999405	+	0.0344872i
$5$	−705.591	−	6952.00i	−0.100976	−	0.994889i
$5$	−705.591	−	6952.00i	−0.100976	−	0.994889i
$6$	−157.651	+	9139.85i	−0.00827683	+	0.479852i
$7$	18488.6	+	18488.6i	0.415781	+	0.415781i	0.883746	−	0.467966i	$-0.155013\pi$
$7$	18488.6	+	18488.6i	0.415781	+	0.415781i	−0.467966	+	0.883746i	$0.655013\pi$
$8$	−92557.9	−	4793.32i	−0.998662	−	0.0517179i
$9$	136345.			0.769674
$10$	26500.8	+	315115.i	0.0838030	+	0.996482i
$11$	238362.	+	238362.i	0.446249	+	0.446249i	0.894106	−	0.447856i	$-0.147812\pi$
$11$	238362.	+	238362.i	0.446249	+	0.446249i	−0.447856	+	0.894106i	$0.647812\pi$
$12$	14266.8	−	413438.i	0.0165512	−	0.479638i
$13$	−1.17648e6			−0.878812			−0.439406	−	0.898289i	$-0.644811\pi$
$13$	−1.17648e6			−0.878812			−0.439406	+	0.898289i	$0.644811\pi$
$14$	−822143.	−	851003.i	−0.408548	−	0.422889i
$15$	−1.40426e6	+	142525.i	−0.477470	+	0.0484607i
$16$	4.18433e6	+	289127.i	0.997621	+	0.0689333i
$17$	−170908.	−	170908.i	−0.0291940	−	0.0291940i	0.692359	−	0.721553i	$-0.256571\pi$
$17$	−170908.	−	170908.i	−0.0291940	−	0.0291940i	−0.721553	+	0.692359i	$0.756571\pi$
$18$	−6.16937e6	−	106414.i	−0.769559	−	0.0132739i
$19$	−2.75021e6	−	2.75021e6i	−0.254813	−	0.254813i	0.568128	−	0.822940i	$-0.307668\pi$
$19$	−2.75021e6	−	2.75021e6i	−0.254813	−	0.254813i	−0.822940	+	0.568128i	$0.807668\pi$
$20$	−953173.	−	1.42791e7i	−0.0666050	−	0.997779i
$21$	3.73458e6	−	3.73458e6i	0.199543	−	0.199543i
$22$	−1.05994e7	−	1.09715e7i	−0.438487	−	0.453879i
$23$	−3.92803e7	+	3.92803e7i	−1.27254	+	1.27254i	−0.327790	+	0.944750i	$0.606304\pi$
$23$	−3.92803e7	+	3.92803e7i	−1.27254	+	1.27254i	−0.944750	+	0.327790i	$0.893696\pi$
$24$	−968221.	+	1.86961e7i	−0.0248206	+	0.479281i
$25$	−4.78324e7	+	9.81053e6i	−0.979608	+	0.200920i
$26$	5.32335e7	+	918209.i	0.878681	+	0.0151561i
$27$		−	6.33236e7i		−	0.849307i
$28$	3.65362e7	+	3.91479e7i	0.401194	+	0.429872i
$29$	3.26727e7	−	3.26727e7i	0.295798	−	0.295798i	−0.543567	−	0.839366i	$-0.682927\pi$
$29$	3.26727e7	−	3.26727e7i	0.295798	−	0.295798i	0.839366	+	0.543567i	$0.182927\pi$
$30$	6.36514e7	−	5.35301e6i	0.478235	−	0.0402190i
$31$		−	1.65757e8i		−	1.03988i	−0.854203	−	0.519940i	$-0.825954\pi$
$31$		−	1.65757e8i		−	1.03988i	0.854203	−	0.519940i	$-0.174046\pi$
$32$	−1.89107e8	−	1.63482e7i	−0.996284	−	0.0861282i
$33$	4.81477e7	−	4.81477e7i	0.214165	−	0.214165i
$34$	7.59987e6	+	7.86665e6i	0.0286861	+	0.0296931i
$35$	1.15487e8	−	1.41578e8i	0.371672	−	0.455639i
$36$	2.79069e8	+	9.63004e6i	0.769216	+	0.0265439i
$37$	5.33441e8			1.26467			0.632334	−	0.774696i	$-0.282097\pi$
$37$	5.33441e8			1.26467			0.632334	+	0.774696i	$0.282097\pi$
$38$	1.22295e8	+	1.26588e8i	0.250380	+	0.259169i
$39$			2.37642e8i			0.421762i
$40$	3.19849e7	+	6.46844e8i	0.0493872	+	0.998780i
$41$		−	7.58275e8i		−	1.02215i	−0.859535	−	0.511076i	$-0.829247\pi$
$41$		−	7.58275e8i		−	1.02215i	0.859535	−	0.511076i	$-0.170753\pi$
$42$	−1.71897e8	+	1.66068e8i	−0.202954	+	0.196072i
$43$	−9.21052e8			−0.955450			−0.477725	−	0.878510i	$-0.658538\pi$
$43$	−9.21052e8			−0.955450			−0.477725	+	0.878510i	$0.658538\pi$
$44$	4.71040e8	+	5.04711e8i	0.430594	+	0.461374i
$45$	−9.62041e7	−	9.47873e8i	−0.0777186	−	0.765740i
$46$	1.80802e9	−	1.74670e9i	1.29430	−	1.25041i
$47$	3.58233e8	−	3.58233e8i	0.227839	−	0.227839i	−0.583951	−	0.811789i	$-0.698494\pi$
$47$	3.58233e8	−	3.58233e8i	0.227839	−	0.227839i	0.811789	+	0.583951i	$0.198494\pi$
$48$	5.84020e7	−	8.45209e8i	0.0330827	−	0.478782i
$49$		−	1.29367e9i		−	0.654253i
$50$	2.17198e9	−	4.06576e8i	0.982927	−	0.183995i
$51$	−3.45224e7	+	3.45224e7i	−0.0140109	+	0.0140109i
$52$	−2.40800e9	−	8.30944e7i	−0.878289	−	0.0303077i
$53$			1.15839e9i			0.380486i	0.981737	+	0.190243i	$0.0609276\pi$
$53$			1.15839e9i			0.380486i	−0.981737	+	0.190243i	$0.939072\pi$
$54$	−4.94223e7	+	2.86527e9i	−0.0146473	+	0.849181i
$55$	1.48891e9	−	1.82528e9i	0.398908	−	0.489029i
$56$	−1.62264e9	−	1.79988e9i	−0.393721	−	0.436727i
$57$	−5.55526e8	+	5.55526e8i	−0.122290	+	0.122290i
$58$	−1.50388e9	+	1.45288e9i	−0.300856	+	0.290653i
$59$	−5.68854e9	+	5.68854e9i	−1.03589	+	1.03589i	−0.0365612	+	0.999331i	$0.511640\pi$
$59$	−5.68854e9	+	5.68854e9i	−1.03589	+	1.03589i	−0.999331	+	0.0365612i	$0.988360\pi$
$60$	−2.88428e9	+	1.92535e8i	−0.478857	+	0.0319653i
$61$	1.59207e8	+	1.59207e8i	0.0241351	+	0.0241351i	0.719071	−	0.694936i	$-0.244567\pi$
$61$	1.59207e8	+	1.59207e8i	0.0241351	+	0.0241351i	−0.694936	+	0.719071i	$0.744567\pi$
$62$	−1.29369e8	+	7.50020e9i	−0.0179339	+	1.03972i
$63$	2.52083e9	+	2.52083e9i	0.320015	+	0.320015i
$64$	8.54398e9	+	8.87318e8i	0.994651	+	0.103297i
$65$	8.30113e8	+	8.17888e9i	0.0887389	+	0.874320i
$66$	−2.21617e9	+	2.14102e9i	−0.217827	+	0.210440i
$67$	−1.27263e10			−1.15157			−0.575784	−	0.817602i	$-0.695303\pi$
$67$	−1.27263e10			−1.15157			−0.575784	+	0.817602i	$0.695303\pi$
$68$	−3.37740e8	−	3.61882e8i	−0.0281698	−	0.0301834i
$69$	7.93439e9	+	7.93439e9i	0.610722	+	0.610722i
$70$	−5.33607e9	+	6.31600e9i	−0.379474	+	0.449162i
$71$	−3.29257e9			−0.216578			−0.108289	−	0.994119i	$-0.534537\pi$
$71$	−3.29257e9			−0.216578			−0.108289	+	0.994119i	$0.534537\pi$
$72$	−1.26198e10	−	6.53547e8i	−0.768644	−	0.0398059i
$73$	−1.01945e10	−	1.01945e10i	−0.575561	−	0.575561i	0.358116	−	0.933677i	$-0.383419\pi$
$73$	−1.01945e10	−	1.01945e10i	−0.575561	−	0.575561i	−0.933677	+	0.358116i	$0.883419\pi$
$74$	−2.41372e10	−	4.16335e8i	−1.26448	−	0.0218107i
$75$	1.98167e9	+	9.66186e9i	0.0964260	+	0.470136i
$76$	−5.43483e9	−	5.82332e9i	−0.245873	−	0.263449i
$77$			8.81395e9i			0.371083i
$78$	1.85473e8	−	1.07528e10i	0.00727377	−	0.421699i
$79$	−4.22251e10			−1.54391			−0.771955	−	0.635677i	$-0.780721\pi$
$79$	−4.22251e10			−1.54391			−0.771955	+	0.635677i	$0.780721\pi$
$80$	−9.42412e8	−	2.92934e10i	−0.0321548	−	0.999483i
$81$	1.13622e10			0.362071
$82$	−5.91812e8	+	3.43105e10i	−0.0176282	+	1.02200i
$83$			1.75020e8i			0.00487707i	0.999997	+	0.00243854i	$0.000776211\pi$
$83$			1.75020e8i			0.00487707i	−0.999997	+	0.00243854i	$0.999224\pi$
$84$	7.90765e9	−	7.38010e9i	0.206306	−	0.192542i
$85$	−1.06756e9	+	1.30874e9i	−0.0260969	+	0.0319926i
$86$	4.16759e10	+	7.18855e8i	0.955308	+	0.0164778i
$87$	−6.59969e9	−	6.59969e9i	−0.141961	−	0.141961i
$88$	−2.09197e10	−	2.32048e10i	−0.422573	−	0.468731i
$89$	−8.57989e10			−1.62868			−0.814342	−	0.580386i	$-0.802902\pi$
$89$	−8.57989e10			−1.62868			−0.814342	+	0.580386i	$0.802902\pi$
$90$	3.61326e9	+	4.29645e10i	0.0645009	+	0.766966i
$91$	−2.17514e10	−	2.17514e10i	−0.365393	−	0.365393i
$92$	−8.31726e10	+	7.76238e10i	−1.31567	+	1.22790i
$93$	−3.34820e10			−0.499062
$94$	−1.64890e10	+	1.59298e10i	−0.231734	+	0.223875i
$95$	−1.71789e10	+	2.10600e10i	−0.227780	+	0.279240i
$96$	−3.30224e9	+	3.81985e10i	−0.0413349	+	0.478140i
$97$	9.81970e9	+	9.81970e9i	0.116106	+	0.116106i	0.762773	−	0.646667i	$-0.223838\pi$
$97$	9.81970e9	+	9.81970e9i	0.116106	+	0.116106i	−0.646667	+	0.762773i	$0.723838\pi$
$98$	−1.00967e9	+	5.85362e10i	−0.0112833	+	0.654156i
$99$	3.24996e10	+	3.24996e10i	0.343466	+	0.343466i
$100$	−9.85954e10	+	1.67016e10i	−0.985954	+	0.167016i
$101$	−7.98474e10	+	7.98474e10i	−0.755951	+	0.755951i	−0.975583	−	0.219632i	$-0.929514\pi$
$101$	−7.98474e10	+	7.98474e10i	−0.755951	+	0.755951i	0.219632	+	0.975583i	$0.429514\pi$
$102$	1.58902e9	−	1.53513e9i	0.0142504	−	0.0137671i
$103$	−1.20911e10	+	1.20911e10i	−0.102769	+	0.102769i	−0.756622	−	0.653853i	$-0.773151\pi$
$103$	−1.20911e10	+	1.20911e10i	−0.102769	+	0.102769i	0.653853	+	0.756622i	$0.273151\pi$
$104$	1.08892e11	+	5.63924e9i	0.877636	+	0.0454503i
$105$	−2.85979e10	−	2.33277e10i	−0.218672	−	0.178374i
$106$	9.04093e8	−	5.24151e10i	0.00656192	−	0.380429i
$107$			1.62336e11i			1.11893i	0.828853	+	0.559466i	$0.188994\pi$
$107$			1.62336e11i			1.11893i	−0.828853	+	0.559466i	$0.811006\pi$
$108$	4.47253e9	−	1.29610e11i	0.0292902	−	0.848802i
$109$	4.05132e10	−	4.05132e10i	0.252204	−	0.252204i	−0.569670	−	0.821874i	$-0.692929\pi$
$109$	4.05132e10	−	4.05132e10i	0.252204	−	0.252204i	0.821874	+	0.569670i	$0.192929\pi$
$110$	−6.87948e10	+	8.14284e10i	−0.407282	+	0.482076i
$111$		−	1.07752e11i		−	0.606943i
$112$	7.20167e10	+	8.27078e10i	0.386130	+	0.443453i
$113$	−1.12474e11	+	1.12474e11i	−0.574275	+	0.574275i	−0.933320	−	0.359045i	$-0.883102\pi$
$113$	−1.12474e11	+	1.12474e11i	−0.574275	+	0.574275i	0.359045	+	0.933320i	$0.383102\pi$
$114$	2.55701e10	−	2.47029e10i	0.124381	−	0.120163i
$115$	3.00792e11	+	2.45361e11i	1.39453	+	1.13754i
$116$	6.91815e10	−	6.45662e10i	0.305824	−	0.285421i
$117$	−1.60408e11			−0.676399
$118$	2.61835e11	−	2.52956e11i	1.05360	−	1.01787i
$119$		−	6.31968e9i		−	0.0242766i
$120$	1.30659e11	−	6.46076e9i	0.479338	−	0.0237021i
$121$		−	1.71679e11i		−	0.601723i
$122$	−7.07957e9	−	7.32808e9i	−0.0237153	−	0.0245477i
$123$	−1.53167e11			−0.490555
$124$	1.17074e10	−	3.39269e11i	0.0358625	−	1.03926i
$125$	1.01953e11	+	3.25609e11i	0.298810	+	0.954313i
$126$	−1.12095e11	−	1.16030e11i	−0.314449	−	0.325487i
$127$	5.72178e10	−	5.72178e10i	0.153678	−	0.153678i	−0.626081	−	0.779758i	$-0.715342\pi$
$127$	5.72178e10	−	5.72178e10i	0.153678	−	0.153678i	0.779758	+	0.626081i	$0.215342\pi$
$128$	−3.85906e11	−	4.68178e10i	−0.992721	−	0.120436i
$129$			1.86047e11i			0.458542i
$130$	−3.11777e10	−	3.70727e11i	−0.0736470	−	0.875721i
$131$	4.46389e11	−	4.46389e11i	1.01093	−	1.01093i	0.0109903	−	0.999940i	$-0.496502\pi$
$131$	4.46389e11	−	4.46389e11i	1.01093	−	1.01093i	0.999940	−	0.0109903i	$-0.00349840\pi$
$132$	1.01949e11	−	9.51472e10i	0.221424	−	0.206652i
$133$		−	1.01695e11i		−	0.211892i
$134$	5.75839e11	+	9.93249e9i	1.15140	+	0.0198601i
$135$	−4.40226e11	+	4.46806e10i	−0.844966	+	0.0857596i
$136$	1.49997e10	+	1.66381e10i	0.0276450	+	0.0306647i
$137$	−6.43594e11	+	6.43594e11i	−1.13933	+	1.13933i	−0.150757	+	0.988571i	$0.548171\pi$
$137$	−6.43594e11	+	6.43594e11i	−1.13933	+	1.13933i	−0.988571	+	0.150757i	$0.951829\pi$
$138$	−3.52823e11	−	3.65209e11i	−0.600098	−	0.621164i
$139$	3.91558e11	−	3.91558e11i	0.640051	−	0.640051i	−0.310517	−	0.950568i	$-0.600502\pi$
$139$	3.91558e11	−	3.91558e11i	0.640051	−	0.640051i	0.950568	+	0.310517i	$0.100502\pi$
$140$	2.46377e11	−	2.81622e11i	0.387164	−	0.442550i
$141$	−7.23609e10	−	7.23609e10i	−0.109345	−	0.109345i
$142$	1.48983e11	+	2.56976e9i	0.216546	+	0.00373514i
$143$	−2.80428e11	−	2.80428e11i	−0.392169	−	0.392169i
$144$	5.70514e11	+	3.94212e10i	0.767843	+	0.0530562i
$145$	−2.50194e11	−	2.04087e11i	−0.324155	−	0.264418i
$146$	4.53327e11	+	4.69240e11i	0.565550	+	0.585402i
$147$	−2.61314e11			−0.313991
$148$	1.09184e12	+	3.76768e10i	1.26392	+	0.0436148i
$149$	1.05444e12	+	1.05444e12i	1.17625	+	1.17625i	0.980693	+	0.195555i	$0.0626507\pi$
$149$	1.05444e12	+	1.05444e12i	1.17625	+	1.17625i	0.195555	+	0.980693i	$0.437349\pi$
$150$	−8.21260e10	−	4.38728e11i	−0.0883037	−	0.471729i
$151$	−7.29513e10			−0.0756240			−0.0378120	−	0.999285i	$-0.512039\pi$
$151$	−7.29513e10			−0.0756240			−0.0378120	+	0.999285i	$0.512039\pi$
$152$	2.41371e11	+	2.67736e11i	0.241293	+	0.267650i
$153$	−2.33025e10	−	2.33025e10i	−0.0224698	−	0.0224698i
$154$	6.87904e9	−	3.98815e11i	0.00639976	−	0.371028i
$155$	−1.15234e12	+	1.16957e11i	−1.03456	+	0.105003i
$156$	−1.67846e10	+	4.86401e11i	−0.0145454	+	0.421511i
$157$		−	1.79610e12i		−	1.50274i	−0.659882	−	0.751369i	$-0.729394\pi$
$157$		−	1.79610e12i		−	1.50274i	0.659882	−	0.751369i	$-0.270606\pi$
$158$	1.91061e12	+	3.29555e10i	1.54368	+	0.0266265i
$159$	2.33989e11			0.182604
$160$	1.97797e10	+	1.32621e12i	0.0149128	+	0.999889i
$161$	−1.45247e12			−1.05820
$162$	−5.14117e11	−	8.86786e9i	−0.362018	−	0.00624434i
$163$			2.86662e12i			1.95136i	0.219194	+	0.975681i	$0.429657\pi$
$163$			2.86662e12i			1.95136i	−0.219194	+	0.975681i	$0.570343\pi$
$164$	5.35568e10	−	1.55202e12i	0.0352511	−	1.02154i
$165$	−3.68695e11	−	3.00750e11i	−0.234696	−	0.191445i
$166$	1.36598e8	−	7.91934e9i	8.41107e−5	−	0.00487634i
$167$	6.15120e10	+	6.15120e10i	0.0366454	+	0.0366454i	0.725192	−	0.688547i	$-0.241751\pi$
$167$	6.15120e10	+	6.15120e10i	0.0366454	+	0.0366454i	−0.688547	+	0.725192i	$0.741751\pi$
$168$	−3.63566e11	+	3.27764e11i	−0.209596	+	0.188956i
$169$	−4.08056e11			−0.227690
$170$	4.93265e10	−	5.83849e10i	0.0266447	−	0.0315378i
$171$	−3.74978e11	−	3.74978e11i	−0.196123	−	0.196123i
$172$	−1.88519e12	−	6.50537e10i	−0.954881	−	0.0329508i
$173$	−2.66474e12			−1.30738			−0.653689	−	0.756763i	$-0.726780\pi$
$173$	−2.66474e12			−1.30738			−0.653689	+	0.756763i	$0.726780\pi$
$174$	2.93473e11	+	3.03774e11i	0.139491	+	0.144388i
$175$	−1.06574e12	−	7.02970e11i	−0.490840	−	0.323763i
$176$	9.28468e11	+	1.06630e12i	0.414426	+	0.475949i
$177$	1.14905e12	+	1.14905e12i	0.497149	+	0.497149i
$178$	3.88224e12	+	6.69636e10i	1.62844	+	0.0280885i
$179$	6.13530e10	+	6.13530e10i	0.0249542	+	0.0249542i	0.719474	−	0.694520i	$-0.244383\pi$
$179$	6.13530e10	+	6.13530e10i	0.0249542	+	0.0249542i	−0.694520	+	0.719474i	$0.744383\pi$
$180$	−1.29961e11	−	1.94688e12i	−0.0512641	−	0.767965i
$181$	−1.10190e11	+	1.10190e11i	−0.0421610	+	0.0421610i	−0.727873	−	0.685712i	$-0.759491\pi$
$181$	−1.10190e11	+	1.10190e11i	−0.0421610	+	0.0421610i	0.685712	+	0.727873i	$0.259491\pi$
$182$	9.67234e11	+	1.00119e12i	0.359037	+	0.371640i
$183$	3.21589e10	−	3.21589e10i	0.0115830	−	0.0115830i
$184$	3.82398e12	−	3.44742e12i	1.33665	−	1.20502i
$185$	−3.76391e11	−	3.70848e12i	−0.127701	−	1.25820i
$186$	1.51500e12	+	2.61317e10i	0.498988	+	0.00860690i
$187$		−	8.14759e10i		−	0.0260556i
$188$	7.58526e11	−	7.07923e11i	0.235561	−	0.219846i
$189$	1.17076e12	−	1.17076e12i	0.353125	−	0.353125i
$190$	7.93750e11	−	9.39516e11i	0.232562	−	0.275270i
$191$			2.49417e12i			0.709973i	0.934871	+	0.354986i	$0.115515\pi$
$191$			2.49417e12i			0.709973i	−0.934871	+	0.354986i	$0.884485\pi$
$192$	1.79233e11	−	1.72583e12i	0.0495748	−	0.477356i
$193$	−1.95445e12	+	1.95445e12i	−0.525364	+	0.525364i	−0.919186	−	0.393823i	$-0.871152\pi$
$193$	−1.95445e12	+	1.95445e12i	−0.525364	+	0.525364i	0.393823	+	0.919186i	$0.371152\pi$
$194$	−4.36659e11	−	4.51987e11i	−0.114086	−	0.118091i
$195$	1.65209e12	−	1.67678e11i	0.419607	−	0.0425878i
$196$	9.13717e10	−	2.64786e12i	0.0225633	−	0.653864i
$197$	6.00227e12			1.44129			0.720644	−	0.693305i	$-0.243846\pi$
$197$	6.00227e12			1.44129			0.720644	+	0.693305i	$0.243846\pi$
$198$	−1.44518e12	−	1.49591e12i	−0.337492	−	0.349339i
$199$		−	2.75332e10i		−	0.00625409i	−0.999995	−	0.00312704i	$-0.999005\pi$
$199$		−	2.75332e10i		−	0.00625409i	0.999995	−	0.00312704i	$-0.000995371\pi$
$200$	4.47429e12	−	6.78766e11i	0.988688	−	0.149988i
$201$			2.57063e12i			0.552664i
$202$	3.67526e12	−	3.55063e12i	0.768875	−	0.742801i
$203$	1.20814e12			0.245974
$204$	−7.30981e10	+	6.82215e10i	−0.0144857	+	0.0135193i
$205$	−5.27153e12	+	5.35032e11i	−1.01693	+	0.103213i
$206$	5.56536e11	−	5.37662e11i	0.104526	−	0.100981i
$207$	−5.35569e12	+	5.35569e12i	−0.979441	+	0.979441i
$208$	−4.92278e12	−	3.40152e11i	−0.876722	−	0.0605794i
$209$		−	1.31109e12i		−	0.227420i
$210$	1.27579e12	+	1.07785e12i	0.215563	+	0.182119i
$211$	−4.63146e12	+	4.63146e12i	−0.762367	+	0.762367i	−0.976750	−	0.214383i	$-0.931226\pi$
$211$	−4.63146e12	+	4.63146e12i	−0.762367	+	0.762367i	0.214383	+	0.976750i	$0.431226\pi$
$212$	−8.18170e10	+	2.37098e12i	−0.0131219	+	0.380260i
$213$			6.65081e11i			0.103941i
$214$	1.26699e11	−	7.34539e12i	0.0192973	−	1.11877i
$215$	6.49886e11	+	6.40315e12i	0.0964775	+	0.950566i
$216$	−3.03530e11	+	5.86110e12i	−0.0439244	+	0.848171i
$217$	3.06461e12	−	3.06461e12i	0.432362	−	0.432362i
$218$	−1.86477e12	+	1.80153e12i	−0.256516	+	0.247817i
$219$	−2.05924e12	+	2.05924e12i	−0.276225	+	0.276225i
$220$	3.17639e12	−	3.63079e12i	0.415536	−	0.474981i
$221$	2.01070e11	+	2.01070e11i	0.0256560	+	0.0256560i
$222$	−8.40972e10	+	4.87557e12i	−0.0104674	+	0.606853i
$223$	3.66606e11	+	3.66606e11i	0.0445166	+	0.0445166i	0.729015	−	0.684498i	$-0.239979\pi$
$223$	3.66606e11	+	3.66606e11i	0.0445166	+	0.0445166i	−0.684498	+	0.729015i	$0.739979\pi$
$224$	−3.19407e12	−	3.79858e12i	−0.378425	−	0.450046i
$225$	−6.52173e12	+	1.33762e12i	−0.753978	+	0.154643i
$226$	5.17701e12	−	5.00144e12i	0.584094	−	0.564286i
$227$	−4.85092e12			−0.534174			−0.267087	−	0.963672i	$-0.586061\pi$
$227$	−4.85092e12			−0.534174			−0.267087	+	0.963672i	$0.586061\pi$
$228$	−1.17628e12	+	1.09780e12i	−0.126435	+	0.118000i
$229$	5.15336e12	+	5.15336e12i	0.540749	+	0.540749i	0.923749	−	0.383000i	$-0.125109\pi$
$229$	5.15336e12	+	5.15336e12i	0.540749	+	0.540749i	−0.383000	+	0.923749i	$0.625109\pi$
$230$	−1.34188e13	−	1.13369e13i	−1.37471	−	1.16142i
$231$	1.78037e12			0.178092
$232$	−3.18073e12	+	2.86750e12i	−0.310701	+	0.280105i
$233$	−9.23464e12	−	9.23464e12i	−0.880973	−	0.880973i	0.112661	−	0.993634i	$-0.464063\pi$
$233$	−9.23464e12	−	9.23464e12i	−0.880973	−	0.880973i	−0.993634	+	0.112661i	$0.964063\pi$
$234$	7.25814e12	+	1.25194e11i	0.676298	+	0.0116653i
$235$	−2.74320e12	−	2.23767e12i	−0.249680	−	0.203668i
$236$	−1.20450e13	+	1.12414e13i	−1.07100	+	0.999551i
$237$			8.52923e12i			0.740958i
$238$	−4.93233e9	+	2.85954e11i	−0.000418677	+	0.0242729i
$239$	−3.76975e12			−0.312697			−0.156349	−	0.987702i	$-0.549972\pi$
$239$	−3.76975e12			−0.312697			−0.156349	+	0.987702i	$0.549972\pi$
$240$	−5.91710e12	+	1.90362e11i	−0.479675	+	0.0154318i
$241$	1.32255e13			1.04790			0.523948	−	0.851750i	$-0.324459\pi$
$241$	1.32255e13			1.04790			0.523948	+	0.851750i	$0.324459\pi$
$242$	−1.33990e11	+	7.76813e12i	−0.0103774	+	0.601634i
$243$		−	1.35127e13i		−	1.02307i
$244$	3.14618e11	+	3.37107e11i	0.0232884	+	0.0249531i
$245$	−8.99361e12	+	9.12804e11i	−0.650909	+	0.0660638i
$246$	6.93052e12	+	1.19543e11i	0.490482	+	0.00846018i
$247$	3.23556e12	+	3.23556e12i	0.223932	+	0.223932i
$248$	−7.94527e11	+	1.53421e13i	−0.0537804	+	1.03849i
$249$	3.53531e10			0.00234062
$250$	−4.35905e12	−	1.48127e13i	−0.282307	−	0.959324i
$251$	6.96097e12	+	6.96097e12i	0.441026	+	0.441026i	0.892357	−	0.451331i	$-0.149050\pi$
$251$	6.96097e12	+	6.96097e12i	0.441026	+	0.441026i	−0.451331	+	0.892357i	$0.649050\pi$
$252$	4.98155e12	+	5.33764e12i	0.308789	+	0.330861i
$253$	−1.87259e13			−1.13574
$254$	−2.63365e12	+	2.54434e12i	−0.156305	+	0.151004i
$255$	2.64358e11	+	2.15641e11i	0.0153540	+	0.0125245i
$256$	1.74250e13	+	2.41961e12i	0.990496	+	0.137539i
$257$	−2.07493e13	−	2.07493e13i	−1.15444	−	1.15444i	−0.985652	−	0.168788i	$-0.946015\pi$
$257$	−2.07493e13	−	2.07493e13i	−1.15444	−	1.15444i	−0.168788	−	0.985652i	$-0.553985\pi$
$258$	1.45205e11	−	8.41828e12i	0.00790809	−	0.458474i
$259$	9.86255e12	+	9.86255e12i	0.525824	+	0.525824i
$260$	1.12139e12	+	1.67990e13i	0.0585333	+	0.876860i
$261$	4.45477e12	−	4.45477e12i	0.227668	−	0.227668i
$262$	−2.05466e13	+	1.98498e13i	−1.02821	+	0.993345i
$263$	−1.69016e13	+	1.69016e13i	−0.828268	+	0.828268i	−0.987277	−	0.159009i	$-0.949170\pi$
$263$	−1.69016e13	+	1.69016e13i	−0.828268	+	0.828268i	0.159009	+	0.987277i	$0.449170\pi$
$264$	−4.68724e12	+	4.22566e12i	−0.224955	+	0.202803i
$265$	8.05315e12	−	8.17352e11i	0.378541	−	0.0384199i
$266$	−7.93699e10	+	4.60150e12i	−0.00365432	+	0.211861i
$267$			1.73309e13i			0.781643i
$268$	−2.60479e13	−	8.98852e11i	−1.15088	−	0.0397143i
$269$	−1.74089e13	+	1.74089e13i	−0.753586	+	0.753586i	−0.975147	−	0.221560i	$-0.928885\pi$
$269$	−1.74089e13	+	1.74089e13i	−0.753586	+	0.753586i	0.221560	+	0.975147i	$0.428885\pi$
$270$	1.99542e13	−	1.67813e12i	0.846320	−	0.0711745i
$271$			1.52380e13i			0.633282i	0.948545	+	0.316641i	$0.102555\pi$
$271$			1.52380e13i			0.633282i	−0.948545	+	0.316641i	$0.897445\pi$
$272$	−6.65720e11	−	7.64548e11i	−0.0271121	−	0.0311369i
$273$	−4.39366e12	+	4.39366e12i	−0.175361	+	0.175361i
$274$	2.96237e13	−	2.86191e13i	1.15881	−	1.11951i
$275$	−1.37399e13	−	9.06297e12i	−0.526809	−	0.347489i
$276$	1.56796e13	+	1.68004e13i	0.589296	+	0.631421i
$277$	−1.28679e13			−0.474099			−0.237050	−	0.971498i	$-0.576180\pi$
$277$	−1.28679e13			−0.474099			−0.237050	+	0.971498i	$0.576180\pi$
$278$	−1.80228e13	+	1.74116e13i	−0.650994	+	0.628917i
$279$		−	2.26002e13i		−	0.800368i
$280$	−1.13679e13	+	1.25506e13i	−0.394739	+	0.435807i
$281$		−	1.03706e13i		−	0.353116i	−0.984290	−	0.176558i	$-0.943504\pi$
$281$		−	1.03706e13i		−	0.353116i	0.984290	−	0.176558i	$-0.0564963\pi$
$282$	3.21772e12	+	3.33067e12i	0.107443	+	0.111215i
$283$	5.31205e13			1.73955			0.869774	−	0.493450i	$-0.164265\pi$
$283$	5.31205e13			1.73955			0.869774	+	0.493450i	$0.164265\pi$
$284$	−6.73918e12	−	2.32554e11i	−0.216449	−	0.00746917i
$285$	4.25399e12	+	3.47004e12i	0.134014	+	0.109317i
$286$	1.24700e13	+	1.29077e13i	0.385347	+	0.398874i
$287$	1.40194e13	−	1.40194e13i	0.424991	−	0.424991i
$288$	−2.57839e13	−	2.22900e12i	−0.766814	−	0.0662906i
$289$		−	3.42135e13i		−	0.998295i
$290$	1.11615e13	+	9.42982e12i	0.319547	+	0.269969i
$291$	1.98352e12	−	1.98352e12i	0.0557218	−	0.0557218i
$292$	−2.01460e13	−	2.15860e13i	−0.555370	−	0.595069i
$293$		−	2.96157e13i		−	0.801217i	−0.916249	−	0.400609i	$-0.868799\pi$
$293$		−	2.96157e13i		−	0.801217i	0.916249	−	0.400609i	$-0.131201\pi$
$294$	1.18240e13	+	2.03948e11i	0.313945	+	0.00541514i
$295$	4.35605e13	+	3.55329e13i	1.13520	+	0.925998i
$296$	−4.93741e13	−	2.55695e12i	−1.26298	−	0.0654060i
$297$	1.50939e13	−	1.50939e13i	0.379003	−	0.379003i
$298$	−4.68886e13	−	4.85345e13i	−1.15579	−	1.19636i
$299$	4.62125e13	−	4.62125e13i	1.11832	−	1.11832i
$300$	3.37363e12	+	1.99157e13i	0.0801550	+	0.473182i
$301$	−1.70289e13	−	1.70289e13i	−0.397257	−	0.397257i
$302$	3.30091e12	+	5.69364e10i	0.0756128	+	0.00130422i
$303$	1.61287e13	+	1.61287e13i	0.362798	+	0.362798i
$304$	−1.07126e13	−	1.23029e13i	−0.236641	−	0.271771i
$305$	9.94473e11	−	1.21914e12i	0.0215747	−	0.0264488i
$306$	1.03621e12	+	1.07258e12i	0.0220790	+	0.0228540i
$307$	−3.24848e13			−0.679860			−0.339930	−	0.940451i	$-0.610403\pi$
$307$	−3.24848e13			−0.679860			−0.339930	+	0.940451i	$0.610403\pi$
$308$	−6.22527e11	+	1.80402e13i	−0.0127976	+	0.370863i
$309$	2.44233e12	+	2.44233e12i	0.0493211	+	0.0493211i
$310$	5.22326e13	−	4.39270e12i	1.03622	−	0.0871450i
$311$	3.31457e13			0.646018			0.323009	−	0.946396i	$-0.395306\pi$
$311$	3.31457e13			0.646018			0.323009	+	0.946396i	$0.395306\pi$
$312$	1.13909e12	−	2.19956e13i	0.0218127	−	0.421198i
$313$	−1.07303e13	−	1.07303e13i	−0.201891	−	0.201891i	0.598919	−	0.800810i	$-0.295597\pi$
$313$	−1.07303e13	−	1.07303e13i	−0.201891	−	0.201891i	−0.800810	+	0.598919i	$0.795597\pi$
$314$	−1.40181e12	+	8.12703e13i	−0.0259165	+	1.50252i
$315$	1.57461e13	−	1.93035e13i	0.286066	−	0.350694i
$316$	−8.64256e13	−	2.98235e12i	−1.54299	−	0.0532451i
$317$		−	9.68837e13i		−	1.69991i	−0.526859	−	0.849953i	$-0.676630\pi$
$317$		−	9.68837e13i		−	1.69991i	0.526859	−	0.849953i	$-0.323370\pi$
$318$	−1.05875e13	−	1.82621e11i	−0.182577	−	0.00314922i
$319$	1.55759e13			0.264000
$320$	1.40076e11	−	6.00238e13i	0.00233367	−	0.999997i
$321$	3.27909e13			0.537001
$322$	6.57217e13	+	1.13361e12i	1.05804	+	0.0182498i
$323$			9.40064e11i			0.0148780i
$324$	2.32559e13	+	8.02508e11i	0.361856	+	0.0124868i
$325$	5.62739e13	−	1.15419e13i	0.860891	−	0.176571i
$326$	2.23731e12	−	1.29709e14i	0.0336535	−	1.95107i
$327$	−8.18343e12	−	8.18343e12i	−0.121038	−	0.121038i
$328$	−3.63465e12	+	7.01843e13i	−0.0528636	+	1.02078i
$329$	1.32464e13			0.189462
$330$	1.64480e13	+	1.38961e13i	0.231360	+	0.195464i
$331$	8.88934e13	+	8.88934e13i	1.22975	+	1.22975i	0.964059	+	0.265688i	$0.0855990\pi$
$331$	8.88934e13	+	8.88934e13i	1.22975	+	1.22975i	0.265688	+	0.964059i	$0.414401\pi$
$332$	−1.23616e10	+	3.58228e11i	−0.000168196	+	0.00487417i
$333$	7.27322e13			0.973382
$334$	−2.73529e12	−	2.83131e12i	−0.0360080	−	0.0372719i
$335$	8.97954e12	+	8.84729e13i	0.116281	+	1.14568i
$336$	1.67065e13	−	1.45469e13i	0.212823	−	0.185313i
$337$	−2.38830e13	−	2.38830e13i	−0.299313	−	0.299313i	0.541432	−	0.840745i	$-0.317882\pi$
$337$	−2.38830e13	−	2.38830e13i	−0.299313	−	0.299313i	−0.840745	+	0.541432i	$0.817882\pi$
$338$	1.84638e13	+	3.18476e11i	0.227656	+	0.00392677i
$339$	2.27190e13	+	2.27190e13i	0.275608	+	0.275608i
$340$	−2.27750e12	+	2.60331e12i	−0.0271847	+	0.0310736i
$341$	3.95102e13	−	3.95102e13i	0.464045	−	0.464045i
$342$	1.66744e13	+	1.72597e13i	0.192711	+	0.199476i
$343$	6.04761e13	−	6.04761e13i	0.687806	−	0.687806i
$344$	8.52506e13	+	4.41490e12i	0.954171	+	0.0494139i
$345$	4.95614e13	−	6.07583e13i	0.545932	−	0.669269i
$346$	1.20574e14	+	2.07975e12i	1.30718	+	0.0225472i
$347$		−	6.48567e12i		−	0.0692058i	−0.999401	−	0.0346029i	$-0.988983\pi$
$347$		−	6.48567e12i		−	0.0692058i	0.999401	−	0.0346029i	$-0.0110166\pi$
$348$	−1.30420e13	−	1.39743e13i	−0.136980	−	0.146772i
$349$	3.60040e13	−	3.60040e13i	0.372230	−	0.372230i	−0.496059	−	0.868289i	$-0.665220\pi$
$349$	3.60040e13	−	3.60040e13i	0.372230	−	0.372230i	0.868289	+	0.496059i	$0.165220\pi$
$350$	4.76739e13	+	3.26398e13i	0.485184	+	0.332180i
$351$			7.44989e13i			0.746382i
$352$	−4.11792e13	−	4.89728e13i	−0.406156	−	0.483026i
$353$	−8.05151e13	+	8.05151e13i	−0.781838	+	0.781838i	−0.980141	−	0.198303i	$-0.936457\pi$
$353$	−8.05151e13	+	8.05151e13i	−0.781838	+	0.781838i	0.198303	+	0.980141i	$0.436457\pi$
$354$	−5.10956e13	−	5.28892e13i	−0.488501	−	0.505649i
$355$	2.32321e12	+	2.28900e13i	0.0218692	+	0.215471i
$356$	−1.75612e14	−	6.05995e12i	−1.62771	−	0.0561687i
$357$	−1.27654e12			−0.0116509
$358$	−2.72822e12	−	2.82399e12i	−0.0245202	−	0.0253809i
$359$		−	2.00497e14i		−	1.77455i	−0.461242	−	0.887274i	$-0.652596\pi$
$359$		−	2.00497e14i		−	1.77455i	0.461242	−	0.887274i	$-0.347404\pi$
$360$	4.36099e12	+	8.81942e13i	0.0380121	+	0.768735i
$361$		−	1.01363e14i		−	0.870141i
$362$	5.07189e12	−	4.89989e12i	0.0428818	−	0.0414276i
$363$	−3.46781e13			−0.288781
$364$	−4.29841e13	−	4.60567e13i	−0.352574	−	0.377777i
$365$	−6.36792e13	+	7.80656e13i	−0.514502	+	0.630738i
$366$	−1.48023e12	+	1.43003e12i	−0.0117810	+	0.0113815i
$367$	2.34865e13	−	2.34865e13i	0.184143	−	0.184143i	−0.609016	−	0.793158i	$-0.708435\pi$
$367$	2.34865e13	−	2.34865e13i	0.184143	−	0.184143i	0.793158	+	0.609016i	$0.208435\pi$
$368$	−1.75719e14	+	1.53005e14i	−1.35723	+	1.18179i
$369$		−	1.03387e14i		−	0.786724i
$370$	1.41366e13	+	1.68095e14i	0.105983	+	1.26022i
$371$	−2.14170e13	+	2.14170e13i	−0.158199	+	0.158199i
$372$	−6.85303e13	−	2.36482e12i	−0.498765	−	0.0172112i
$373$			4.43355e13i			0.317946i	0.987283	+	0.158973i	$0.0508182\pi$
$373$			4.43355e13i			0.317946i	−0.987283	+	0.158973i	$0.949182\pi$
$374$	−6.35896e10	+	3.68663e12i	−0.000449358	+	0.0260517i
$375$	6.57710e13	−	2.05939e13i	0.457997	−	0.143406i
$376$	−3.48744e13	+	3.14402e13i	−0.239317	+	0.215750i
$377$	−3.84388e13	+	3.84388e13i	−0.259951	+	0.259951i
$378$	−5.38886e13	+	5.20611e13i	−0.359163	+	0.346983i
$379$	−6.79500e13	+	6.79500e13i	−0.446349	+	0.446349i	−0.894139	−	0.447790i	$-0.852211\pi$
$379$	−6.79500e13	+	6.79500e13i	−0.446349	+	0.446349i	0.447790	+	0.894139i	$0.352211\pi$
$380$	−3.66490e13	+	4.18918e13i	−0.237275	+	0.271219i
$381$	−1.15577e13	−	1.15577e13i	−0.0737534	−	0.0737534i
$382$	1.94663e12	−	1.12856e14i	0.0122443	−	0.709867i
$383$	6.25260e13	+	6.25260e13i	0.387675	+	0.387675i	0.873857	−	0.486182i	$-0.161611\pi$
$383$	6.25260e13	+	6.25260e13i	0.387675	+	0.387675i	−0.486182	+	0.873857i	$0.661611\pi$
$384$	−9.45692e12	+	7.79508e13i	−0.0578000	+	0.476430i
$385$	6.12746e13	−	6.21904e12i	0.369187	−	0.0374705i
$386$	8.99607e13	−	8.69099e13i	0.534346	−	0.516225i
$387$	−1.25581e14			−0.735385
$388$	1.94052e13	+	2.07923e13i	0.112032	+	0.120041i
$389$	−3.70031e13	−	3.70031e13i	−0.210627	−	0.210627i	0.593907	−	0.804534i	$-0.297585\pi$
$389$	−3.70031e13	−	3.70031e13i	−0.210627	−	0.210627i	−0.804534	+	0.593907i	$0.797585\pi$
$390$	−7.48846e13	+	6.29771e12i	−0.420279	+	0.0353449i
$391$	1.34266e13			0.0743010
$392$	−6.20098e12	+	1.19740e14i	−0.0338366	+	0.653378i
$393$	−9.01679e13	−	9.01679e13i	−0.485169	−	0.485169i
$394$	−2.71591e14	−	4.68460e12i	−1.44107	−	0.0248567i
$395$	2.97937e13	+	2.93549e14i	0.155898	+	1.53602i
$396$	6.42241e13	+	6.88150e13i	0.331417	+	0.355107i
$397$		−	2.07816e14i		−	1.05763i	−0.848739	−	0.528813i	$-0.822637\pi$
$397$		−	2.07816e14i		−	1.05763i	0.848739	−	0.528813i	$-0.177363\pi$
$398$	−2.14888e10	+	1.24582e12i	−0.000107859	+	0.00625316i
$399$	−2.05418e13			−0.101692
$400$	−2.02983e14	+	2.72208e13i	−0.991128	+	0.132914i
$401$	−1.85476e14			−0.893294			−0.446647	−	0.894710i	$-0.647382\pi$
$401$	−1.85476e14			−0.893294			−0.446647	+	0.894710i	$0.647382\pi$
$402$	2.00630e12	−	1.16316e14i	0.00953133	−	0.552582i
$403$			1.95010e14i			0.913859i
$404$	−1.69070e14	+	1.57791e14i	−0.781571	+	0.729430i
$405$	−8.01706e12	−	7.89899e13i	−0.0365605	−	0.360221i
$406$	−5.46662e13	−	9.42921e11i	−0.245938	−	0.00424211i
$407$	1.27152e14	+	1.27152e14i	0.564357	+	0.564357i
$408$	3.36079e12	−	3.02984e12i	0.0147167	−	0.0132675i
$409$	−3.42135e14			−1.47815			−0.739077	−	0.673621i	$-0.764738\pi$
$409$	−3.42135e14			−1.47815			−0.739077	+	0.673621i	$0.764738\pi$
$410$	2.38944e14	−	2.00949e13i	1.01856	−	0.0856594i
$411$	1.30002e14	+	1.30002e14i	0.546790	+	0.546790i
$412$	−2.56018e13	+	2.38938e13i	−0.106252	+	0.0991633i
$413$	−2.10346e14			−0.861408
$414$	2.46515e14	−	2.38155e14i	0.996187	−	0.962404i
$415$	1.21674e12	−	1.23493e11i	0.00485214	−	0.000492467i
$416$	2.22481e14	+	1.92333e13i	0.875546	+	0.0756905i
$417$	−7.90923e13	−	7.90923e13i	−0.307175	−	0.307175i
$418$	−1.02327e12	+	5.93244e13i	−0.00392212	+	0.227386i
$419$	2.25671e13	+	2.25671e13i	0.0853686	+	0.0853686i	0.748502	−	0.663133i	$-0.230774\pi$
$419$	2.25671e13	+	2.25671e13i	0.0853686	+	0.0853686i	−0.663133	+	0.748502i	$0.730774\pi$
$420$	−5.68860e13	−	4.97666e13i	−0.212390	−	0.185809i
$421$	3.06654e13	−	3.06654e13i	0.113005	−	0.113005i	−0.648343	−	0.761348i	$-0.724538\pi$
$421$	3.06654e13	−	3.06654e13i	0.113005	−	0.113005i	0.761348	+	0.648343i	$0.224538\pi$
$422$	2.13179e14	−	2.05950e14i	0.775402	−	0.749106i
$423$	4.88434e13	−	4.88434e13i	0.175361	−	0.175361i
$424$	5.55254e12	−	1.07218e14i	0.0196779	−	0.379977i
$425$	9.85163e12	+	6.49824e12i	0.0344643	+	0.0227330i
$426$	5.19077e11	−	3.00936e13i	0.00179258	−	0.103925i
$427$			5.88703e12i			0.0200698i
$428$	−1.14657e13	+	3.32266e14i	−0.0385888	+	1.11827i
$429$	−5.66448e13	+	5.66448e13i	−0.188211	+	0.188211i
$430$	−2.44086e13	−	2.90238e14i	−0.0800695	−	0.952089i
$431$			1.86723e14i			0.604746i	0.953190	+	0.302373i	$0.0977788\pi$
$431$			1.86723e14i			0.604746i	−0.953190	+	0.302373i	$0.902221\pi$
$432$	1.83086e13	−	2.64967e14i	0.0585456	−	0.847287i
$433$	−1.23480e14	+	1.23480e14i	−0.389863	+	0.389863i	−0.874639	−	0.484776i	$-0.838901\pi$
$433$	−1.23480e14	+	1.23480e14i	−0.389863	+	0.389863i	0.484776	+	0.874639i	$0.338901\pi$
$434$	−1.41060e14	+	1.36276e14i	−0.439754	+	0.424841i
$435$	−4.12243e13	+	5.05377e13i	−0.126900	+	0.155570i
$436$	8.57832e13	−	8.00603e13i	0.260751	−	0.243356i
$437$	2.16058e14			0.648519
$438$	9.47837e13	−	9.15693e13i	0.280948	−	0.271420i
$439$			1.33224e14i			0.389965i	0.980807	+	0.194983i	$0.0624651\pi$
$439$			1.33224e14i			0.389965i	−0.980807	+	0.194983i	$0.937535\pi$
$440$	−1.46559e14	+	1.61807e14i	−0.423666	+	0.467744i
$441$		−	1.76386e14i		−	0.503561i
$442$	−8.94109e12	−	9.25495e12i	−0.0252097	−	0.0260947i
$443$	−3.01550e14			−0.839728			−0.419864	−	0.907587i	$-0.637922\pi$
$443$	−3.01550e14			−0.839728			−0.419864	+	0.907587i	$0.637922\pi$
$444$	7.61048e12	−	2.20544e14i	0.0209318	−	0.606582i
$445$	6.05389e13	+	5.96474e14i	0.164458	+	1.62036i
$446$	−1.63021e13	−	1.68743e13i	−0.0437423	−	0.0452778i
$447$	2.12991e14	−	2.12991e14i	0.564508	−	0.564508i
$448$	1.41561e14	+	1.74371e14i	0.370607	+	0.456505i
$449$			4.81493e14i			1.24519i	0.782544	+	0.622595i	$0.213921\pi$
$449$			4.81493e14i			1.24519i	−0.782544	+	0.622595i	$0.786079\pi$
$450$	2.96140e14	−	5.54348e13i	0.756533	−	0.141616i
$451$	1.80744e14	−	1.80744e14i	0.456135	−	0.456135i
$452$	−2.38153e14	+	2.22265e14i	−0.593739	+	0.554128i
$453$			1.47357e13i			0.0362937i
$454$	2.19495e14	+	3.78601e12i	0.534094	+	0.00921244i
$455$	−1.35868e14	+	1.66563e14i	−0.326629	+	0.400421i
$456$	5.40811e13	−	4.87555e13i	0.128451	−	0.115802i
$457$	5.22442e14	−	5.22442e14i	1.22602	−	1.22602i	0.260570	−	0.965455i	$-0.416090\pi$
$457$	5.22442e14	−	5.22442e14i	1.22602	−	1.22602i	0.965455	−	0.260570i	$-0.0839105\pi$
$458$	−2.29158e14	−	2.37202e14i	−0.531343	−	0.549994i
$459$	−1.08225e13	+	1.08225e13i	−0.0247946	+	0.0247946i
$460$	5.98327e14	+	5.23445e14i	1.35447	+	1.18496i
$461$	−5.33271e14	−	5.33271e14i	−1.19287	−	1.19287i	−0.976258	−	0.216611i	$-0.930500\pi$
$461$	−5.33271e14	−	5.33271e14i	−1.19287	−	1.19287i	−0.216611	−	0.976258i	$-0.569500\pi$
$462$	−8.05582e13	−	1.38952e12i	−0.178065	−	0.00307139i
$463$	−2.04336e14	−	2.04336e14i	−0.446324	−	0.446324i	0.447807	−	0.894130i	$-0.352205\pi$
$463$	−2.04336e14	−	2.04336e14i	−0.446324	−	0.446324i	−0.894130	+	0.447807i	$0.852205\pi$
$464$	1.46160e14	−	1.27267e14i	0.315485	−	0.274704i
$465$	2.36246e13	+	2.32767e14i	0.0503933	+	0.496511i
$466$	4.10643e14	+	4.25057e14i	0.865648	+	0.896035i
$467$	−8.57582e14			−1.78662			−0.893311	−	0.449438i	$-0.851624\pi$
$467$	−8.57582e14			−1.78662			−0.893311	+	0.449438i	$0.851624\pi$
$468$	−3.28319e14	−	1.13295e13i	−0.675996	−	0.0233271i
$469$	−2.35290e14	−	2.35290e14i	−0.478799	−	0.478799i
$470$	1.22378e14	+	1.03391e14i	0.246131	+	0.207944i
$471$	−3.62802e14			−0.721199
$472$	5.53786e14	−	4.99252e14i	1.08808	−	0.980932i
$473$	−2.19544e14	−	2.19544e14i	−0.426369	−	0.426369i
$474$	6.65682e12	−	3.85931e14i	0.0127787	−	0.740848i
$475$	1.58530e14	+	1.04568e14i	0.300813	+	0.198419i
$476$	4.46358e11	−	1.29350e13i	0.000837230	−	0.0242621i
$477$			1.57942e14i			0.292850i
$478$	1.70574e14	+	2.94218e12i	0.312651	+	0.00539283i
$479$	3.94898e14			0.715550			0.357775	−	0.933808i	$-0.383535\pi$
$479$	3.94898e14			0.715550			0.357775	+	0.933808i	$0.383535\pi$
$480$	2.67886e14	−	3.99537e12i	0.479870	−	0.00715699i
$481$	−6.27582e14			−1.11141
$482$	−5.98429e14	−	1.03221e13i	−1.04774	−	0.0180722i
$483$			2.93391e14i			0.507852i
$484$	1.21256e13	−	3.51389e14i	0.0207517	−	0.601365i
$485$	6.13378e13	−	7.51952e13i	0.103788	−	0.127236i
$486$	−1.05463e13	+	6.11423e14i	−0.0176441	+	1.02292i
$487$	1.93818e14	+	1.93818e14i	0.320616	+	0.320616i	0.849003	−	0.528387i	$-0.177203\pi$
$487$	1.93818e14	+	1.93818e14i	0.320616	+	0.320616i	−0.528387	+	0.849003i	$0.677203\pi$
$488$	−1.39728e13	−	1.54990e13i	−0.0228546	−	0.0253510i
$489$	5.79040e14			0.936504
$490$	4.07656e14	−	3.42834e13i	0.651952	−	0.0548283i
$491$	3.96028e14	+	3.96028e14i	0.626294	+	0.626294i	0.947133	−	0.320840i	$-0.103965\pi$
$491$	3.96028e14	+	3.96028e14i	0.626294	+	0.626294i	−0.320840	+	0.947133i	$0.603965\pi$
$492$	−3.13500e14	−	1.08182e13i	−0.490263	−	0.0169178i
$493$	−1.11680e13			−0.0172711
$494$	−1.43878e14	−	1.48928e14i	−0.220037	−	0.227761i
$495$	2.03006e14	−	2.48868e14i	0.307029	−	0.376393i
$496$	4.79249e13	−	6.93582e14i	0.0716823	−	1.03741i
$497$	−6.08750e13	−	6.08750e13i	−0.0900490	−	0.0900490i
$498$	−1.59966e12	−	2.75921e10i	−0.00234027	−	4.03667e-5i
$499$	−6.42463e14	−	6.42463e14i	−0.929597	−	0.929597i	0.0680825	−	0.997680i	$-0.478312\pi$
$499$	−6.42463e14	−	6.42463e14i	−0.929597	−	0.929597i	−0.997680	+	0.0680825i	$0.978312\pi$
$500$	1.85678e14	+	6.73651e14i	0.265720	+	0.964050i
$501$	1.24251e13	−	1.24251e13i	0.0175870	−	0.0175870i
$502$	−3.09538e14	−	3.20404e14i	−0.433355	−	0.448567i
$503$	−5.74225e14	+	5.74225e14i	−0.795167	+	0.795167i	−0.982329	−	0.187162i	$-0.940071\pi$
$503$	−5.74225e14	+	5.74225e14i	−0.795167	+	0.795167i	0.187162	+	0.982329i	$0.440071\pi$
$504$	−2.21240e14	−	2.45406e14i	−0.303037	−	0.336138i
$505$	6.11439e14	+	4.98759e14i	0.828420	+	0.675754i
$506$	8.47310e14	+	1.46150e13i	1.13557	+	0.0195872i
$507$			8.24249e13i			0.109273i
$508$	1.21154e14	−	1.13071e14i	0.158886	−	0.148286i
$509$	−2.69625e14	+	2.69625e14i	−0.349794	+	0.349794i	−0.860033	−	0.510239i	$-0.829557\pi$
$509$	−2.69625e14	+	2.69625e14i	−0.349794	+	0.349794i	0.510239	+	0.860033i	$0.329557\pi$
$510$	−1.17934e13	−	9.96366e12i	−0.0151357	−	0.0127874i
$511$		−	3.76965e14i		−	0.478614i
$512$	−7.86560e14	−	1.23082e14i	−0.987977	−	0.154600i
$513$	−1.74153e14	+	1.74153e14i	−0.216414	+	0.216414i
$514$	9.22673e14	+	9.55061e14i	1.13436	+	1.17418i
$515$	9.25886e13	+	7.55258e13i	0.112621	+	0.0918662i
$516$	−1.31405e13	+	3.80798e14i	−0.0158138	+	0.458270i
$517$	1.70778e14			0.203346
$518$	−4.38564e14	−	4.53959e14i	−0.516678	−	0.534815i
$519$			5.38262e14i			0.627441i
$520$	−3.76296e13	−	7.60999e14i	−0.0434021	−	0.877740i
$521$			2.10320e13i			0.0240034i	0.999928	+	0.0120017i	$0.00382035\pi$
$521$			2.10320e13i			0.0240034i	−0.999928	+	0.0120017i	$0.996180\pi$
$522$	−2.05047e14	+	1.98093e14i	−0.231561	+	0.223708i
$523$	−4.46844e14			−0.499340			−0.249670	−	0.968331i	$-0.580322\pi$
$523$	−4.46844e14			−0.499340			−0.249670	+	0.968331i	$0.580322\pi$
$524$	9.45189e14	−	8.82132e14i	1.04519	−	0.975464i
$525$	−1.41996e14	+	2.15272e14i	−0.155381	+	0.235566i
$526$	7.77956e14	−	7.51573e14i	0.842429	−	0.813860i
$527$	−2.83292e13	+	2.83292e13i	−0.0303582	+	0.0303582i
$528$	2.15387e14	−	1.87545e14i	0.228419	−	0.198893i
$529$		−	2.13307e15i		−	2.23872i
$530$	−3.65027e14	+	3.06984e13i	−0.379148	+	0.0318858i
$531$	−7.75606e14	+	7.75606e14i	−0.797299	+	0.797299i
$532$	7.18268e12	−	2.08147e14i	0.00730756	−	0.211766i
$533$			8.92095e14i			0.898280i
$534$	1.35263e13	−	7.84189e14i	0.0134803	−	0.781527i
$535$	1.12856e15	−	1.14543e14i	1.11321	−	0.112985i
$536$	1.17792e15	+	6.10010e13i	1.15003	+	0.0595567i
$537$	1.23929e13	−	1.23929e13i	0.0119761	−	0.0119761i
$538$	8.01305e14	−	7.74131e14i	0.766471	−	0.740478i
$539$	3.08362e14	−	3.08362e14i	0.291960	−	0.291960i
$540$	−9.04201e14	+	6.03584e13i	−0.847421	+	0.0565681i
$541$	1.38476e15	+	1.38476e15i	1.28467	+	1.28467i	0.937981	+	0.346688i	$0.112694\pi$
$541$	1.38476e15	+	1.38476e15i	1.28467	+	1.28467i	0.346688	+	0.937981i	$0.387306\pi$
$542$	1.18928e13	−	6.89491e14i	0.0109217	−	0.633188i
$543$	2.22577e13	+	2.22577e13i	0.0202340	+	0.0202340i
$544$	2.95259e13	+	3.51139e13i	0.0265711	+	0.0315999i
$545$	−3.10234e14	−	2.53062e14i	−0.276381	−	0.225448i
$546$	2.02234e14	−	1.95376e14i	0.178359	−	0.172310i
$547$	−3.23530e14			−0.282478			−0.141239	−	0.989976i	$-0.545109\pi$
$547$	−3.23530e14			−0.282478			−0.141239	+	0.989976i	$0.545109\pi$
$548$	−1.36275e15	+	1.27184e15i	−1.17794	+	1.09936i
$549$	2.17072e13	+	2.17072e13i	0.0185761	+	0.0185761i
$550$	6.14631e14	+	4.20806e14i	0.520738	+	0.356523i
$551$	−1.79713e14			−0.150746
$552$	−6.96358e14	−	7.72422e14i	−0.578319	−	0.641490i
$553$	−7.80682e14	−	7.80682e14i	−0.641928	−	0.641928i
$554$	5.82248e14	+	1.00430e13i	0.474029	+	0.00817638i
$555$	−7.49090e14	+	7.60287e13i	−0.603841	+	0.0612867i
$556$	8.29089e14	−	7.73778e14i	0.661744	−	0.617596i
$557$			1.68783e15i			1.33390i	0.745101	+	0.666951i	$0.232401\pi$
$557$			1.68783e15i			1.33390i	−0.745101	+	0.666951i	$0.767599\pi$
$558$	−1.76388e13	+	1.02262e15i	−0.0138033	+	0.800249i
$559$	1.08360e15			0.839661
$560$	5.24170e14	−	5.59018e14i	0.402196	−	0.428935i
$561$	−1.64577e13			−0.0125047
$562$	−8.09392e12	+	4.69248e14i	−0.00608989	+	0.353063i
$563$		−	1.02305e15i		−	0.762257i	−0.924522	−	0.381129i	$-0.875536\pi$
$563$		−	1.02305e15i		−	0.762257i	0.924522	−	0.381129i	$-0.124464\pi$
$564$	−1.42996e14	−	1.53218e14i	−0.105509	−	0.113051i
$565$	8.61278e14	+	7.02557e14i	0.629328	+	0.513352i
$566$	−2.40360e15	−	4.14590e13i	−1.73929	−	0.0300005i
$567$	2.10071e14	+	2.10071e14i	0.150542	+	0.150542i
$568$	3.04754e14	+	1.57824e13i	0.216288	+	0.0112010i
$569$	1.17876e15			0.828531			0.414265	−	0.910156i	$-0.364039\pi$
$569$	1.17876e15			0.828531			0.414265	+	0.910156i	$0.364039\pi$
$570$	−1.89777e14	−	1.60333e14i	−0.132109	−	0.111612i
$571$	−4.53035e14	−	4.53035e14i	−0.312344	−	0.312344i	0.533473	−	0.845817i	$-0.320887\pi$
$571$	−4.53035e14	−	4.53035e14i	−0.312344	−	0.312344i	−0.845817	+	0.533473i	$0.820887\pi$
$572$	−5.54169e14	−	5.93782e14i	−0.378411	−	0.405461i
$573$	5.03807e14			0.340732
$574$	−6.45294e14	+	6.23411e14i	−0.432257	+	0.417598i
$575$	1.49351e15	−	2.26423e15i	0.990912	−	1.50227i
$576$	1.16493e15	+	1.20982e14i	0.765556	+	0.0795053i
$577$	−1.14003e15	−	1.14003e15i	−0.742076	−	0.742076i	0.230901	−	0.972977i	$-0.425833\pi$
$577$	−1.14003e15	−	1.14003e15i	−0.742076	−	0.742076i	−0.972977	+	0.230901i	$0.925833\pi$
$578$	−2.67026e13	+	1.54809e15i	−0.0172168	+	0.998147i
$579$	3.94788e14	+	3.94788e14i	0.252134	+	0.252134i
$580$	−4.97678e14	−	4.35392e14i	−0.314843	−	0.275440i
$581$	−3.23588e12	+	3.23588e12i	−0.00202779	+	0.00202779i
$582$	−9.12986e13	+	8.82025e13i	−0.0566745	+	0.0547525i
$583$	−2.76117e14	+	2.76117e14i	−0.169792	+	0.169792i
$584$	8.94719e14	+	9.92450e14i	0.545024	+	0.604558i
$585$	1.13182e14	+	1.11515e15i	0.0683000	+	0.672941i
$586$	−2.31142e13	+	1.34005e15i	−0.0138179	+	0.801098i
$587$			1.10460e14i			0.0654175i	0.999465	+	0.0327087i	$0.0104134\pi$
$587$			1.10460e14i			0.0654175i	−0.999465	+	0.0327087i	$0.989587\pi$
$588$	−5.34853e14	−	1.84565e13i	−0.313804	−	0.0108287i
$589$	−4.55867e14	+	4.55867e14i	−0.264974	+	0.264974i
$590$	−1.94330e15	−	1.64180e15i	−1.11906	−	0.945438i
$591$		−	1.21242e15i		−	0.691708i
$592$	2.23209e15	+	1.54232e14i	1.26166	+	0.0871778i
$593$	−1.63227e14	+	1.63227e14i	−0.0914095	+	0.0914095i	−0.751333	−	0.659923i	$-0.770589\pi$
$593$	−1.63227e14	+	1.63227e14i	−0.0914095	+	0.0914095i	0.659923	+	0.751333i	$0.270589\pi$
$594$	−6.94753e14	+	6.71192e14i	−0.385483	+	0.372410i
$595$	−4.39344e13	+	4.45911e12i	−0.0241525	+	0.00245135i
$596$	2.08374e15	+	2.23269e15i	1.13498	+	1.21611i
$597$	−5.56153e12			−0.00300148
$598$	−2.12709e15	+	2.05496e15i	−1.13744	+	1.09887i
$599$		−	3.06282e15i		−	1.62283i	−0.584469	−	0.811416i	$-0.698697\pi$
$599$		−	3.06282e15i		−	1.62283i	0.584469	−	0.811416i	$-0.301303\pi$
$600$	−1.37107e14	−	9.03780e14i	−0.0719825	−	0.474494i
$601$			6.87551e14i			0.357681i	0.983878	+	0.178840i	$0.0572345\pi$
$601$			6.87551e14i			0.357681i	−0.983878	+	0.178840i	$0.942765\pi$
$602$	7.57237e14	+	7.83818e14i	0.390347	+	0.404049i
$603$	−1.73517e15			−0.886331
$604$	−1.49315e14	−	5.15253e12i	−0.0755790	−	0.00260806i
$605$	−1.19351e15	+	1.21135e14i	−0.598648	+	0.0607596i
$606$	−7.17205e14	−	7.42381e14i	−0.356487	−	0.369001i
$607$	1.54006e15	−	1.54006e15i	0.758575	−	0.758575i	−0.217488	−	0.976063i	$-0.569786\pi$
$607$	1.54006e15	−	1.54006e15i	0.758575	−	0.758575i	0.976063	+	0.217488i	$0.0697863\pi$
$608$	4.75123e14	+	5.65045e14i	0.231919	+	0.275812i
$609$		−	2.44038e14i		−	0.118049i
$610$	−4.59495e13	+	5.43878e13i	−0.0220276	+	0.0260728i
$611$	−4.21454e14	+	4.21454e14i	−0.200227	+	0.200227i
$612$	−4.60493e13	−	4.93410e13i	−0.0216815	−	0.0232314i
$613$		−	2.33280e15i		−	1.08854i	−0.838910	−	0.544270i	$-0.816807\pi$
$613$		−	2.33280e15i		−	1.08854i	0.838910	−	0.544270i	$-0.183193\pi$
$614$	1.46988e15	+	2.53535e13i	0.679759	+	0.0117250i
$615$	1.08073e14	+	1.06482e15i	0.0495342	+	0.488047i
$616$	4.22480e13	−	8.15800e14i	0.0191917	−	0.370587i
$617$	−1.03812e15	+	1.03812e15i	−0.467388	+	0.467388i	−0.901067	−	0.433680i	$-0.857215\pi$
$617$	−1.03812e15	+	1.03812e15i	−0.467388	+	0.467388i	0.433680	+	0.901067i	$0.357215\pi$
$618$	−1.08605e14	−	1.12417e14i	−0.0484631	−	0.0501643i
$619$	1.98843e15	−	1.98843e15i	0.879452	−	0.879452i	−0.114026	−	0.993478i	$-0.536375\pi$
$619$	1.98843e15	−	1.98843e15i	0.879452	−	0.879452i	0.993478	+	0.114026i	$0.0363747\pi$
$620$	−2.36686e15	+	1.57995e14i	−1.03757	+	0.0692612i
$621$	2.48737e15	+	2.48737e15i	1.08078	+	1.08078i
$622$	−1.49978e15	−	2.58692e13i	−0.645922	−	0.0111413i
$623$	−1.58630e15	−	1.58630e15i	−0.677175	−	0.677175i
$624$	−6.87087e13	+	9.94371e14i	−0.0290735	+	0.420759i
$625$	2.19169e15	−	9.38523e14i	0.919263	−	0.393645i
$626$	4.77150e14	+	4.93900e14i	0.198379	+	0.205343i
$627$	−2.64833e14			−0.109144
$628$	1.26858e14	−	3.67623e15i	0.0518252	−	1.50184i
$629$	−9.11692e13	−	9.11692e13i	−0.0369207	−	0.0369207i
$630$	−7.27549e14	+	8.61157e14i	−0.292071	+	0.345708i
$631$	1.32176e15			0.526005			0.263002	−	0.964795i	$-0.415287\pi$
$631$	1.32176e15			0.526005			0.263002	+	0.964795i	$0.415287\pi$
$632$	3.90827e15	+	2.02398e14i	1.54184	+	0.0798478i
$633$	9.35527e14	+	9.35527e14i	0.365878	+	0.365878i
$634$	−7.56150e13	+	4.38380e15i	−0.0293168	+	1.69965i
$635$	−4.38150e14	−	3.57406e14i	−0.168410	−	0.137374i
$636$	4.78923e14	+	1.65265e13i	0.182495	+	0.00629750i
$637$			1.52198e15i			0.574965i
$638$	−7.04778e14	−	1.21565e13i	−0.263960	−	0.00455298i
$639$	−4.48927e14			−0.166695
$640$	−5.31851e13	+	2.71586e15i	−0.0195794	+	0.999808i
$641$	−4.43778e15			−1.61974			−0.809872	−	0.586607i	$-0.800463\pi$
$641$	−4.43778e15			−1.61974			−0.809872	+	0.586607i	$0.800463\pi$
$642$	−1.48373e15	−	2.55924e13i	−0.536922	−	0.00926121i
$643$		−	7.85312e14i		−	0.281762i	−0.990027	−	0.140881i	$-0.955007\pi$
$643$		−	7.85312e14i		−	0.281762i	0.990027	−	0.140881i	$-0.0449934\pi$
$644$	−2.97290e15	−	1.02588e14i	−1.05757	−	0.0364942i
$645$	1.29340e15	−	1.31273e14i	0.456199	−	0.0463018i
$646$	7.33694e11	−	4.25361e13i	0.000256588	−	0.0148758i
$647$	3.46645e15	+	3.46645e15i	1.20202	+	1.20202i	0.973551	+	0.228470i	$0.0733722\pi$
$647$	3.46645e15	+	3.46645e15i	1.20202	+	1.20202i	0.228470	+	0.973551i	$0.426628\pi$
$648$	−1.05166e15	−	5.44626e13i	−0.361587	−	0.0187256i
$649$	−2.71186e15			−0.924533
$650$	−2.55529e15	+	4.78329e14i	−0.863808	+	0.161697i
$651$	−6.19034e14	−	6.19034e14i	−0.207500	−	0.207500i
$652$	−2.02468e14	+	5.86734e15i	−0.0672970	+	1.95020i
$653$	3.96721e15			1.30756			0.653781	−	0.756684i	$-0.273182\pi$
$653$	3.96721e15			1.30756			0.653781	+	0.756684i	$0.273182\pi$
$654$	3.63898e14	+	3.76672e14i	0.118933	+	0.123108i
$655$	−3.41826e15	−	2.78833e15i	−1.10784	−	0.903683i
$656$	2.19238e14	−	3.17287e15i	0.0704604	−	1.01972i
$657$	−1.38998e15	−	1.38998e15i	−0.442995	−	0.442995i
$658$	−5.99376e14	−	1.03385e13i	−0.189434	−	0.00326748i
$659$	−3.57762e15	−	3.57762e15i	−1.12131	−	1.12131i	−0.991545	−	0.129760i	$-0.958579\pi$
$659$	−3.57762e15	−	3.57762e15i	−1.12131	−	1.12131i	−0.129760	−	0.991545i	$-0.541421\pi$
$660$	−7.33397e14	−	6.41611e14i	−0.227954	−	0.199425i
$661$	−1.49264e15	+	1.49264e15i	−0.460094	+	0.460094i	−0.898686	−	0.438592i	$-0.855477\pi$
$661$	−1.49264e15	+	1.49264e15i	−0.460094	+	0.460094i	0.438592	+	0.898686i	$0.355477\pi$
$662$	−3.95288e15	−	4.09164e15i	−1.20836	−	1.25077i
$663$	4.06149e13	−	4.06149e13i	0.0123129	−	0.0123129i
$664$	8.38928e11	−	1.61995e13i	0.000252232	−	0.00487054i
$665$	−7.06982e14	+	7.17550e13i	−0.210809	+	0.0213960i
$666$	−3.29099e15	−	5.67654e13i	−0.973237	−	0.0167871i
$667$			2.56679e15i			0.752831i
$668$	1.21557e14	+	1.30246e14i	0.0353598	+	0.0378874i
$669$	7.40522e13	−	7.40522e13i	0.0213646	−	0.0213646i
$670$	−3.37256e14	−	4.01024e15i	−0.0965048	−	1.14752i
$671$			7.58980e13i			0.0215405i
$672$	−7.67290e14	+	6.45183e14i	−0.215987	+	0.181615i
$673$	3.97071e15	−	3.97071e15i	1.10863	−	1.10863i	0.115294	−	0.993331i	$-0.463219\pi$
$673$	3.97071e15	−	3.97071e15i	1.10863	−	1.10863i	0.993331	−	0.115294i	$-0.0367811\pi$
$674$	1.06202e15	+	1.09930e15i	0.294106	+	0.304430i
$675$	6.21238e14	+	3.02892e15i	0.170643	+	0.831988i
$676$	−8.35202e14	−	2.88209e13i	−0.227554	−	0.00785237i
$677$	4.90867e15			1.32656			0.663279	−	0.748372i	$-0.269164\pi$
$677$	4.90867e15			1.32656			0.663279	+	0.748372i	$0.269164\pi$
$678$	−1.01026e15	−	1.04573e15i	−0.270814	−	0.280320i
$679$			3.63104e14i			0.0965490i
$680$	1.05084e14	−	1.16017e14i	0.0277165	−	0.0306001i
$681$			9.79858e14i			0.256362i
$682$	−1.81860e15	+	1.75693e15i	−0.471979	+	0.455973i
$683$	4.22613e15			1.08800			0.544000	−	0.839085i	$-0.316909\pi$
$683$	4.22613e15			1.08800			0.544000	+	0.839085i	$0.316909\pi$
$684$	−7.41014e14	−	7.93983e14i	−0.189242	−	0.202770i
$685$	4.92838e15	+	4.02015e15i	1.24855	+	1.01846i
$686$	−2.78363e15	+	2.68923e15i	−0.699566	+	0.675842i
$687$	1.04095e15	−	1.04095e15i	0.259518	−	0.259518i
$688$	−3.85398e15	−	2.66301e14i	−0.953177	−	0.0658623i
$689$		−	1.36283e15i		−	0.334376i
$690$	−2.28998e15	+	2.71052e15i	−0.557393	+	0.659754i
$691$	−3.91684e15	+	3.91684e15i	−0.945816	+	0.945816i	−0.998606	−	0.0527894i	$-0.983189\pi$
$691$	−3.91684e15	+	3.91684e15i	−0.945816	+	0.945816i	0.0527894	+	0.998606i	$0.483189\pi$
$692$	−5.45414e15	−	1.88210e14i	−1.30660	−	0.0450878i
$693$			1.20174e15i			0.285613i
$694$	−5.06188e12	+	2.93464e14i	−0.00119353	+	0.0691955i
$695$	−2.99839e15	−	2.44583e15i	−0.701409	−	0.572150i
$696$	5.79219e14	+	6.42488e14i	0.134429	+	0.149112i
$697$	−1.29595e14	+	1.29595e14i	−0.0298407	+	0.0298407i
$698$	−1.65721e15	+	1.60101e15i	−0.378594	+	0.365755i
$699$	−1.86534e15	+	1.86534e15i	−0.422799	+	0.422799i
$700$	−2.13168e15	−	1.51410e15i	−0.479383	−	0.340498i
$701$	4.11187e15	+	4.11187e15i	0.917466	+	0.917466i	0.996845	−	0.0793787i	$-0.0252936\pi$
$701$	4.11187e15	+	4.11187e15i	0.917466	+	0.917466i	−0.0793787	+	0.996845i	$0.525294\pi$
$702$	5.81443e13	−	3.37094e15i	0.0128722	−	0.746271i
$703$	−1.46707e15	−	1.46707e15i	−0.322253	−	0.322253i
$704$	1.82506e15	+	2.24806e15i	0.397766	+	0.489958i
$705$	−4.51996e14	+	5.54110e14i	−0.0977449	+	0.119827i
$706$	3.70600e15	−	3.58032e15i	0.795205	−	0.768238i
$707$	−2.95253e15			−0.628619
$708$	2.27070e15	+	2.43301e15i	0.479708	+	0.513998i
$709$	7.31520e14	+	7.31520e14i	0.153346	+	0.153346i	0.779611	−	0.626265i	$-0.215417\pi$
$709$	7.31520e14	+	7.31520e14i	0.153346	+	0.153346i	−0.626265	+	0.779611i	$0.715417\pi$
$710$	−8.72559e13	−	1.03754e15i	−0.0181499	−	0.215816i
$711$	−5.75720e15			−1.18831
$712$	7.94136e15	+	4.11261e14i	1.62650	+	0.0842321i
$713$	6.51099e15	+	6.51099e15i	1.32329	+	1.32329i
$714$	5.77610e13	+	9.96302e11i	0.0116491	+	0.000200933i
$715$	−1.75167e15	+	2.14740e15i	−0.350565	+	0.429764i
$716$	1.21243e14	+	1.29910e14i	0.0240788	+	0.0258000i
$717$			7.61467e14i			0.150071i
$718$	−1.56482e14	+	9.07210e15i	−0.0306041	+	1.77428i
$719$	7.04990e15			1.36828			0.684139	−	0.729352i	$-0.260178\pi$
$719$	7.04990e15			1.36828			0.684139	+	0.729352i	$0.260178\pi$
$720$	−1.28494e14	−	3.99403e15i	−0.0247487	−	0.769276i
$721$	−4.47094e14			−0.0854584
$722$	−7.91109e13	+	4.58648e15i	−0.0150066	+	0.870012i
$723$		−	2.67147e15i		−	0.502910i
$724$	−2.33318e14	+	2.17752e14i	−0.0435899	+	0.0406819i
$725$	−1.24228e15	+	1.88335e15i	−0.230335	+	0.349198i
$726$	1.56912e15	+	2.70653e13i	0.288738	+	0.00498036i
$727$	−2.02430e15	−	2.02430e15i	−0.369688	−	0.369688i	0.497675	−	0.867363i	$-0.334187\pi$
$727$	−2.02430e15	−	2.02430e15i	−0.369688	−	0.369688i	−0.867363	+	0.497675i	$0.834187\pi$
$728$	1.90900e15	+	2.11753e15i	0.346007	+	0.383801i
$729$	−7.16704e14			−0.128925
$730$	2.94229e15	−	3.48262e15i	0.525303	−	0.621771i
$731$	1.57415e14	+	1.57415e14i	0.0278934	+	0.0278934i
$732$	6.80937e13	−	6.35509e13i	0.0119756	−	0.0111766i
$733$	−1.20123e15			−0.209678			−0.104839	−	0.994489i	$-0.533433\pi$
$733$	−1.20123e15			−0.209678			−0.104839	+	0.994489i	$0.533433\pi$
$734$	−1.08105e15	+	1.04439e15i	−0.187291	+	0.180939i
$735$	1.84381e14	+	1.81665e15i	0.0317056	+	0.312386i
$736$	8.07035e15	−	6.78603e15i	1.37741	−	1.15821i
$737$	−3.03346e15	−	3.03346e15i	−0.513886	−	0.513886i
$738$	−8.06909e13	+	4.67808e15i	−0.0135680	+	0.786607i
$739$	−1.74161e15	−	1.74161e15i	−0.290674	−	0.290674i	0.546673	−	0.837347i	$-0.315894\pi$
$739$	−1.74161e15	−	1.74161e15i	−0.290674	−	0.290674i	−0.837347	+	0.546673i	$0.815894\pi$
$740$	−5.08461e14	−	7.61703e15i	−0.0842332	−	1.26186i
$741$	6.53565e14	−	6.53565e14i	0.107470	−	0.107470i
$742$	9.85796e14	−	9.52365e14i	0.160903	−	0.155447i
$743$	8.21939e15	−	8.21939e15i	1.33168	−	1.33168i	0.427820	−	0.903864i	$-0.359282\pi$
$743$	8.21939e15	−	8.21939e15i	1.33168	−	1.33168i	0.903864	−	0.427820i	$-0.140718\pi$
$744$	3.09902e15	+	1.60490e14i	0.498394	+	0.0258105i
$745$	6.58648e15	−	8.07449e15i	1.05146	−	1.28901i
$746$	3.46026e13	−	2.00610e15i	0.00548334	−	0.317898i
$747$			2.38632e13i			0.00375375i
$748$	5.75462e12	−	1.66763e14i	0.000898583	−	0.0260401i
$749$	−3.00136e15	+	3.00136e15i	−0.465230	+	0.465230i
$750$	−2.99209e15	+	8.80502e14i	−0.460402	+	0.135486i
$751$		−	1.13252e16i		−	1.72992i	−0.501842	−	0.864960i	$-0.667344\pi$
$751$		−	1.13252e16i		−	1.72992i	0.501842	−	0.864960i	$-0.332656\pi$
$752$	1.60254e15	−	1.39539e15i	0.243002	−	0.211591i
$753$	1.40608e15	−	1.40608e15i	0.211659	−	0.211659i
$754$	1.76928e15	−	1.70928e15i	0.264396	−	0.255429i
$755$	5.14738e13	+	5.07157e14i	0.00763621	+	0.0752375i
$756$	2.47899e15	−	2.31361e15i	0.365094	−	0.340737i
$757$	8.45933e15			1.23683			0.618413	−	0.785853i	$-0.287776\pi$
$757$	8.45933e15			1.23683			0.618413	+	0.785853i	$0.287776\pi$
$758$	3.12764e15	−	3.02158e15i	0.453980	−	0.438584i
$759$			3.78251e15i			0.545068i
$760$	1.69099e15	−	1.86692e15i	0.241917	−	0.267086i
$761$		−	1.23615e16i		−	1.75572i	−0.478920	−	0.877859i	$-0.658972\pi$
$761$		−	1.23615e16i		−	1.75572i	0.478920	−	0.877859i	$-0.341028\pi$
$762$	5.13941e14	+	5.31982e14i	0.0724705	+	0.0750144i
$763$	1.49806e15			0.209723
$764$	−1.76162e14	+	5.10501e15i	−0.0244850	+	0.709551i
$765$	−1.45557e14	+	1.78441e14i	−0.0200861	+	0.0246239i
$766$	−2.78038e15	−	2.87798e15i	−0.380931	−	0.394303i
$767$	6.69245e15	−	6.69245e15i	0.910355	−	0.910355i
$768$	4.88746e14	−	3.51975e15i	0.0660080	−	0.475362i
$769$		−	4.79021e15i		−	0.642332i	−0.947023	−	0.321166i	$-0.895925\pi$
$769$		−	4.79021e15i		−	0.642332i	0.947023	−	0.321166i	$-0.104075\pi$
$770$	−2.77741e15	+	2.33577e14i	−0.369778	+	0.0310979i
$771$	−4.19124e15	+	4.19124e15i	−0.554043	+	0.554043i
$772$	−4.13838e15	+	3.86230e15i	−0.543169	+	0.506933i
$773$		−	7.70523e15i		−	1.00415i	−0.864824	−	0.502075i	$-0.832570\pi$
$773$		−	7.70523e15i		−	1.00415i	0.864824	−	0.502075i	$-0.167430\pi$
$774$	5.68231e15	+	9.80126e13i	0.735275	+	0.0126826i
$775$	1.62617e15	+	7.92856e15i	0.208932	+	1.01867i
$776$	−8.61821e14	−	9.55959e14i	−0.109946	−	0.121955i
$777$	1.99218e15	−	1.99218e15i	0.252355	−	0.252355i
$778$	1.64544e15	+	1.70320e15i	0.206964	+	0.214229i
$779$	−2.08542e15	+	2.08542e15i	−0.260457	+	0.260457i
$780$	3.39330e15	−	2.26514e14i	0.420826	−	0.0280915i
$781$	−7.84825e14	−	7.84825e14i	−0.0966478	−	0.0966478i
$782$	−6.07529e14	−	1.04791e13i	−0.0742900	−	0.00128141i
$783$	−2.06895e15	−	2.06895e15i	−0.251224	−	0.251224i
$784$	3.74036e14	−	5.41315e15i	0.0450998	−	0.652697i
$785$	−1.24865e16	+	1.26732e15i	−1.49506	+	0.151740i
$786$	4.00955e15	+	4.15030e15i	0.476729	+	0.493464i
$787$	1.85503e14			0.0219024			0.0109512	−	0.999940i	$-0.496514\pi$
$787$	1.85503e14			0.0219024			0.0109512	+	0.999940i	$0.496514\pi$
$788$	1.22853e16	+	4.23938e14i	1.44043	+	0.0497060i
$789$	3.41402e15	+	3.41402e15i	0.397505	+	0.397505i
$790$	−1.11900e15	−	1.33058e16i	−0.129384	−	1.53848i
$791$	−4.15896e15			−0.477545
$792$	−2.85231e15	−	3.16387e15i	−0.325243	−	0.360770i
$793$	−1.87304e14	−	1.87304e14i	−0.0212102	−	0.0212102i
$794$	−1.62195e14	+	9.40329e15i	−0.0182400	+	1.05747i
$795$	−1.65100e14	−	1.62669e15i	−0.0184386	−	0.181671i
$796$	1.94466e12	−	5.63544e13i	0.000215686	−	0.00625037i
$797$			8.87635e15i			0.977719i	0.872363	+	0.488859i	$0.162587\pi$
$797$			8.87635e15i			0.977719i	−0.872363	+	0.488859i	$0.837413\pi$
$798$	9.29475e14	+	1.60323e13i	0.101677	+	0.00175379i
$799$	−1.22450e14			−0.0133030
$800$	9.20584e15	−	1.07327e15i	0.993272	−	0.115801i
$801$	−1.16983e16			−1.25355
$802$	8.39245e15	+	1.44759e14i	0.893161	+	0.0154059i
$803$		−	4.85998e15i		−	0.513688i
$804$	−1.81563e14	+	5.26152e15i	−0.0190598	+	0.552335i
$805$	1.02485e15	+	1.00976e16i	0.106852	+	1.05279i
$806$	1.52200e14	−	8.82383e15i	0.0157605	−	0.913723i
$807$	3.51649e15	+	3.51649e15i	0.361664	+	0.361664i
$808$	7.77324e15	−	7.00777e15i	0.794035	−	0.715843i
$809$	−6.16800e15			−0.625788			−0.312894	−	0.949788i	$-0.601298\pi$
$809$	−6.16800e15			−0.625788			−0.312894	+	0.949788i	$0.601298\pi$
$810$	3.01107e14	+	3.58040e15i	0.0303427	+	0.360798i
$811$	−5.41240e15	−	5.41240e15i	−0.541720	−	0.541720i	0.382313	−	0.924033i	$-0.375128\pi$
$811$	−5.41240e15	−	5.41240e15i	−0.541720	−	0.541720i	−0.924033	+	0.382313i	$0.875128\pi$
$812$	2.47280e15	+	8.53308e13i	0.245828	+	0.00848296i
$813$	3.07799e15			0.303927
$814$	−5.65415e15	−	5.85263e15i	−0.554540	−	0.574006i
$815$	1.99287e16	−	2.02266e15i	1.94139	−	0.197041i
$816$	−1.54434e14	+	1.34472e14i	−0.0149433	+	0.0130117i
$817$	2.53309e15	+	2.53309e15i	0.243461	+	0.243461i
$818$	1.54810e16	+	2.67027e14i	1.47793	+	0.0254925i
$819$	−2.96571e15	−	2.96571e15i	−0.281233	−	0.281233i
$820$	−1.08275e16	+	7.22768e14i	−1.01988	+	0.0680805i
$821$	−8.84513e15	+	8.84513e15i	−0.827593	+	0.827593i	−0.987183	−	0.159590i	$-0.948983\pi$
$821$	−8.84513e15	+	8.84513e15i	−0.827593	+	0.827593i	0.159590	+	0.987183i	$0.448983\pi$
$822$	−5.78089e15	−	5.98381e15i	−0.537279	−	0.556139i
$823$	1.19484e13	−	1.19484e13i	0.00110309	−	0.00110309i	−0.706555	−	0.707658i	$-0.749752\pi$
$823$	1.19484e13	−	1.19484e13i	0.00110309	−	0.00110309i	0.707658	+	0.706555i	$0.249752\pi$
$824$	1.17708e15	−	1.06117e15i	0.107946	−	0.0973161i
$825$	−1.83067e15	+	2.77538e15i	−0.166768	+	0.252828i
$826$	9.51776e15	+	1.64169e14i	0.861280	+	0.0148560i
$827$			4.75097e15i			0.427073i	0.976935	+	0.213537i	$0.0684983\pi$
$827$			4.75097e15i			0.427073i	−0.976935	+	0.213537i	$0.931502\pi$
$828$	−1.13402e16	+	1.05837e16i	−1.01264	+	0.945081i
$829$	−1.32128e16	+	1.32128e16i	−1.17205	+	1.17205i	−0.190330	+	0.981720i	$0.560956\pi$
$829$	−1.32128e16	+	1.32128e16i	−1.17205	+	1.17205i	−0.981720	+	0.190330i	$0.939044\pi$
$830$	−5.51516e13	+	4.63818e12i	−0.00485991	+	0.000408713i
$831$			2.59924e15i			0.227531i
$832$	−1.00518e16	−	1.04391e15i	−0.874111	−	0.0907790i
$833$	−2.21099e14	+	2.21099e14i	−0.0191002	+	0.0191002i
$834$	3.51705e15	+	3.64051e15i	0.301832	+	0.312427i
$835$	3.84229e14	−	4.71034e14i	0.0327578	−	0.0401584i
$836$	9.26020e13	−	2.68352e15i	0.00784306	−	0.227285i
$837$	−1.04963e16			−0.883177
$838$	−1.00350e15	−	1.03873e15i	−0.0838836	−	0.0868282i
$839$			1.86125e16i			1.54566i	0.634613	+	0.772830i	$0.281160\pi$
$839$			1.86125e16i			1.54566i	−0.634613	+	0.772830i	$0.718840\pi$
$840$	2.53514e15	+	2.29624e15i	0.209154	+	0.189444i
$841$			1.00655e16i			0.825007i
$842$	−1.41148e15	+	1.36362e15i	−0.114937	+	0.111039i
$843$	−2.09479e15			−0.169468
$844$	−9.80670e15	+	9.15246e15i	−0.788205	+	0.735622i
$845$	2.87921e14	+	2.83681e15i	0.0229912	+	0.226526i
$846$	−2.24819e15	+	2.17195e15i	−0.178360	+	0.172311i
$847$	3.17409e15	−	3.17409e15i	0.250185	−	0.250185i
$848$	−3.34923e14	+	4.84710e15i	−0.0262282	+	0.379581i
$849$		−	1.07300e16i		−	0.834849i
$850$	−4.40696e14	−	3.01722e14i	−0.0340671	−	0.0233240i
$851$	−2.09537e16	+	2.09537e16i	−1.60934	+	1.60934i
$852$	−4.69745e13	+	1.36127e15i	−0.00358463	+	0.103879i
$853$		−	2.00149e16i		−	1.51751i	−0.651373	−	0.758757i	$-0.725807\pi$
$853$		−	2.00149e16i		−	1.51751i	0.651373	−	0.758757i	$-0.274193\pi$
$854$	4.59466e12	−	2.66377e14i	0.000346127	−	0.0200668i
$855$	−2.34227e15	+	2.87143e15i	−0.175316	+	0.214924i
$856$	7.78127e14	−	1.50255e16i	0.0578689	−	1.11743i
$857$	3.65149e15	−	3.65149e15i	0.269821	−	0.269821i	−0.559207	−	0.829028i	$-0.688894\pi$
$857$	3.65149e15	−	3.65149e15i	0.269821	−	0.269821i	0.829028	+	0.559207i	$0.188894\pi$
$858$	2.60728e15	−	2.51886e15i	0.191429	−	0.184937i
$859$	−3.43573e15	+	3.43573e15i	−0.250643	+	0.250643i	−0.821234	−	0.570591i	$-0.806714\pi$
$859$	−3.43573e15	+	3.43573e15i	−0.250643	+	0.250643i	0.570591	+	0.821234i	$0.306714\pi$
$860$	8.77923e14	+	1.31518e16i	0.0636377	+	0.953328i
$861$	−2.83184e15	−	2.83184e15i	−0.203963	−	0.203963i
$862$	1.45732e14	−	8.44886e15i	0.0104295	−	0.604656i
$863$	1.72527e14	+	1.72527e14i	0.0122687	+	0.0122687i	0.713215	−	0.700946i	$-0.247239\pi$
$863$	1.72527e14	+	1.72527e14i	0.0122687	+	0.0122687i	−0.700946	+	0.713215i	$0.747239\pi$
$864$	−1.03523e15	+	1.19749e16i	−0.0731493	+	0.846151i
$865$	1.88022e15	+	1.85253e16i	0.132014	+	1.30070i
$866$	5.68359e15	−	5.49085e15i	0.396529	−	0.383081i
$867$	−6.91092e15			−0.479105
$868$	6.48905e15	−	6.05614e15i	0.447015	−	0.417194i
$869$	−1.00649e16	−	1.00649e16i	−0.688969	−	0.688969i
$870$	1.90477e15	−	2.25456e15i	0.129564	−	0.153358i
$871$	1.49722e16			1.01201
$872$	−3.94401e15	+	3.55563e15i	−0.264909	+	0.238823i
$873$	1.33887e15	+	1.33887e15i	0.0893635	+	0.0893635i
$874$	−9.77622e15	−	1.68627e14i	−0.648422	−	0.0111845i
$875$	−4.13507e15	+	7.90500e15i	−0.272545	+	0.521024i
$876$	−4.36025e15	+	4.06936e15i	−0.285587	+	0.266535i
$877$			4.37519e15i			0.284773i	0.989811	+	0.142387i	$0.0454776\pi$
$877$			4.37519e15i			0.284773i	−0.989811	+	0.142387i	$0.954522\pi$
$878$	1.03977e14	−	6.02811e15i	0.00672540	−	0.389907i
$879$	−5.98220e15			−0.384523
$880$	6.75781e15	−	7.20708e15i	0.431669	−	0.460367i
$881$	−1.85863e16			−1.17985			−0.589923	−	0.807460i	$-0.700842\pi$
$881$	−1.85863e16			−1.17985			−0.589923	+	0.807460i	$0.700842\pi$
$882$	−1.37664e14	+	7.98114e15i	−0.00868450	+	0.503487i
$883$		−	1.00594e16i		−	0.630650i	−0.948984	−	0.315325i	$-0.897887\pi$
$883$		−	1.00594e16i		−	0.630650i	0.948984	−	0.315325i	$-0.102113\pi$
$884$	3.97344e14	+	4.25747e14i	0.0247559	+	0.0265255i
$885$	7.17744e15	−	8.79896e15i	0.444408	−	0.544808i
$886$	1.36446e16	+	2.35351e14i	0.839603	+	0.0144821i
$887$	8.79320e15	+	8.79320e15i	0.537733	+	0.537733i	0.922863	−	0.385129i	$-0.125843\pi$
$887$	8.79320e15	+	8.79320e15i	0.537733	+	0.537733i	−0.385129	+	0.922863i	$0.625843\pi$
$888$	−5.16489e14	+	9.97328e15i	−0.0313899	+	0.606131i
$889$	2.11575e15			0.127792
$890$	−2.27374e15	−	2.70366e16i	−0.136488	−	1.62295i
$891$	2.70831e15	+	2.70831e15i	0.161574	+	0.161574i
$892$	7.24469e14	+	7.76255e14i	0.0429549	+	0.0460254i
$893$	−1.97043e15			−0.116112
$894$	−9.80368e15	+	9.47122e15i	−0.574160	+	0.554689i
$895$	3.83236e14	−	4.69816e14i	0.0223069	−	0.0273465i
$896$	−6.26927e15	−	8.00045e15i	−0.362679	−	0.462829i
$897$	−9.33465e15	−	9.33465e15i	−0.536710	−	0.536710i
$898$	3.75792e14	−	2.17867e16i	0.0214747	−	1.24500i
$899$	−5.41573e15	−	5.41573e15i	−0.307595	−	0.307595i
$900$	−1.34430e16	+	2.27719e15i	−0.758863	+	0.128548i
$901$	1.97978e14	−	1.97978e14i	0.0111079	−	0.0111079i
$902$	−8.31939e15	+	8.03726e15i	−0.463933	+	0.448200i
$903$	−3.43975e15	+	3.43975e15i	−0.190653	+	0.190653i
$904$	1.09495e16	−	9.87121e15i	0.603207	−	0.543806i
$905$	8.43791e14	+	6.88292e14i	0.0462027	+	0.0376882i
$906$	1.15008e13	−	6.66764e14i	0.000625927	−	0.0362883i
$907$			2.64762e16i			1.43224i	0.697979	+	0.716118i	$0.254083\pi$
$907$			2.64762e16i			1.43224i	−0.697979	+	0.716118i	$0.745917\pi$
$908$	−9.92878e15	−	3.42619e14i	−0.533856	−	0.0184221i
$909$	−1.08868e16	+	1.08868e16i	−0.581835	+	0.581835i
$910$	6.27778e15	−	7.43064e15i	0.333487	−	0.394729i
$911$		−	1.09198e16i		−	0.576585i	−0.957542	−	0.288293i	$-0.906912\pi$
$911$		−	1.09198e16i		−	0.576585i	0.957542	−	0.288293i	$-0.0930876\pi$
$912$	−2.48512e15	+	2.16388e15i	−0.130429	+	0.113570i
$913$	−4.17182e13	+	4.17182e13i	−0.00217639	+	0.00217639i
$914$	−2.40473e16	+	2.32318e16i	−1.24699	+	1.20470i
$915$	−2.46260e14	−	2.00878e14i	−0.0126934	−	0.0103542i
$916$	1.01838e16	+	1.09118e16i	0.521778	+	0.559076i
$917$	1.65062e16			0.840650
$918$	4.98144e14	−	4.81251e14i	0.0252186	−	0.0243633i
$919$		−	1.59105e16i		−	0.800660i	−0.916371	−	0.400330i	$-0.868895\pi$
$919$		−	1.59105e16i		−	0.800660i	0.916371	−	0.400330i	$-0.131105\pi$
$920$	−2.66646e16	−	2.41519e16i	−1.33384	−	1.20814i
$921$			6.56174e15i			0.326281i
$922$	2.37133e16	+	2.45457e16i	1.17212	+	1.21326i
$923$	3.87365e15			0.190332
$924$	3.64402e15	+	1.25747e14i	0.177986	+	0.00614187i
$925$	−2.55157e16	+	5.23334e15i	−1.23888	+	0.254097i
$926$	9.08635e15	+	9.40530e15i	0.438560	+	0.453955i
$927$	−1.64856e15	+	1.64856e15i	−0.0790983	+	0.0790983i
$928$	−6.71278e15	+	5.64450e15i	−0.320176	+	0.269223i
$929$			2.00886e16i			0.952494i	0.879312	+	0.476247i	$0.158003\pi$
$929$			2.00886e16i			0.952494i	−0.879312	+	0.476247i	$0.841997\pi$
$930$	−8.87300e14	−	1.05507e16i	−0.0418229	−	0.497307i
$931$	−3.55787e15	+	3.55787e15i	−0.166712	+	0.166712i
$932$	−1.82491e16	−	1.95535e16i	−0.850066	−	0.910831i
$933$		−	6.69523e15i		−	0.310039i
$934$	3.88040e16	+	6.69319e14i	1.78636	+	0.0308124i
$935$	−5.66420e14	+	5.74887e13i	−0.0259224	+	0.00263099i
$936$	1.48470e16	+	7.68884e14i	0.675493	+	0.0349819i
$937$	2.63183e16	−	2.63183e16i	1.19039	−	1.19039i	0.213437	−	0.976957i	$-0.431534\pi$
$937$	2.63183e16	−	2.63183e16i	1.19039	−	1.19039i	0.976957	−	0.213437i	$-0.0684658\pi$
$938$	1.04628e16	+	1.08301e16i	0.470471	+	0.486986i
$939$	−2.16745e15	+	2.16745e15i	−0.0968923	+	0.0968923i
$940$	−5.45669e15	−	4.77377e15i	−0.242508	−	0.212157i
$941$	−2.19134e16	−	2.19134e16i	−0.968202	−	0.968202i	0.0313077	−	0.999510i	$-0.490033\pi$
$941$	−2.19134e16	−	2.19134e16i	−0.968202	−	0.968202i	−0.999510	+	0.0313077i	$0.990033\pi$
$942$	1.64161e16	+	2.83157e14i	0.721092	+	0.0124379i
$943$	2.97853e16	+	2.97853e16i	1.30073	+	1.30073i
$944$	−2.54474e16	+	2.21580e16i	−1.10484	+	0.962021i
$945$	−8.96522e15	−	7.31306e15i	−0.386978	−	0.315663i
$946$	9.76260e15	+	1.01053e16i	0.418952	+	0.433658i
$947$	−3.71691e15			−0.158583			−0.0792916	−	0.996851i	$-0.525266\pi$
$947$	−3.71691e15			−0.158583			−0.0792916	+	0.996851i	$0.525266\pi$
$948$	−6.02417e14	+	1.74575e16i	−0.0255536	+	0.740518i
$949$	1.19937e16	+	1.19937e16i	0.505810	+	0.505810i
$950$	−7.09157e15	−	4.85524e15i	−0.297346	−	0.203578i
$951$	−1.95699e16			−0.815824
$952$	−3.02922e13	+	5.84937e14i	−0.00125553	+	0.0242441i
$953$	−2.60029e16	−	2.60029e16i	−1.07155	−	1.07155i	−0.997235	−	0.0743114i	$-0.976324\pi$
$953$	−2.60029e16	−	2.60029e16i	−1.07155	−	1.07155i	−0.0743114	−	0.997235i	$-0.523676\pi$
$954$	1.23269e14	−	7.14656e15i	0.00505054	−	0.292807i
$955$	1.73394e16	−	1.75986e15i	0.706344	−	0.0716902i
$956$	−7.71586e15	−	2.66257e14i	−0.312511	−	0.0107840i
$957$		−	3.14623e15i		−	0.126700i
$958$	−1.78684e16	−	3.08207e14i	−0.715444	−	0.0123405i
$959$	−2.37983e16			−0.947421
$960$	−1.21245e16	−	2.82945e13i	−0.479922	−	0.00111998i
$961$	−2.06697e15			−0.0813495
$962$	2.83969e16	+	4.89810e14i	1.11124	+	0.0191675i
$963$			2.21338e16i			0.861213i
$964$	2.70697e16	+	9.34113e14i	1.04727	+	0.0361390i
$965$	1.49664e16	+	1.22083e16i	0.575727	+	0.469629i
$966$	2.28983e14	−	1.32754e16i	0.00875850	−	0.507777i
$967$	1.58000e16	+	1.58000e16i	0.600914	+	0.600914i	0.940555	−	0.339641i	$-0.110306\pi$
$967$	1.58000e16	+	1.58000e16i	0.600914	+	0.600914i	−0.339641	+	0.940555i	$0.610306\pi$
$968$	−8.22910e14	+	1.58902e16i	−0.0311199	+	0.600918i
$969$	1.89887e14			0.00714028
$970$	−2.83411e15	+	3.35457e15i	−0.105967	+	0.125427i
$971$	2.23973e16	+	2.23973e16i	0.832703	+	0.832703i	0.987886	−	0.155183i	$-0.0495966\pi$
$971$	2.23973e16	+	2.23973e16i	0.832703	+	0.832703i	−0.155183	+	0.987886i	$0.549597\pi$
$972$	9.54397e14	−	2.76575e16i	0.0352829	−	1.02247i
$973$	1.44787e16			0.532241
$974$	−8.61863e15	−	8.92117e15i	−0.315039	−	0.326098i
$975$	−2.33139e15	−	1.13670e16i	−0.0847404	−	0.413162i
$976$	6.20144e14	+	7.12206e14i	0.0224140	+	0.0257414i
$977$	−1.96105e14	−	1.96105e14i	−0.00704806	−	0.00704806i	0.703574	−	0.710622i	$-0.251586\pi$
$977$	−1.96105e14	−	1.96105e14i	−0.00704806	−	0.00704806i	−0.710622	+	0.703574i	$0.751586\pi$
$978$	−2.62005e16	−	4.51924e14i	−0.936365	−	0.0161511i
$979$	−2.04512e16	−	2.04512e16i	−0.726799	−	0.726799i
$980$	−1.84724e16	+	1.23309e15i	−0.652800	+	0.0435765i
$981$	5.52379e15	−	5.52379e15i	0.194114	−	0.194114i
$982$	−1.76104e16	−	1.82286e16i	−0.615399	−	0.637002i
$983$	2.25436e16	−	2.25436e16i	0.783392	−	0.783392i	−0.197010	−	0.980402i	$-0.563123\pi$
$983$	2.25436e16	−	2.25436e16i	0.783392	−	0.783392i	0.980402	+	0.197010i	$0.0631230\pi$
$984$	1.41768e16	+	7.34178e14i	0.489898	+	0.0253705i
$985$	−4.23515e15	−	4.17277e16i	−0.145536	−	1.43392i
$986$	5.05333e14	+	8.71634e12i	0.0172685	+	0.000297859i
$987$		−	2.67570e15i		−	0.0909271i
$988$	6.39397e15	+	6.85102e15i	0.216076	+	0.231522i
$989$	3.61792e16	−	3.61792e16i	1.21585	−	1.21585i
$990$	−9.37985e15	+	1.11024e16i	−0.313475	+	0.371042i
$991$			5.10302e16i			1.69599i	0.530008	+	0.847993i	$0.322189\pi$
$991$			5.10302e16i			1.69599i	−0.530008	+	0.847993i	$0.677811\pi$
$992$	−2.70983e15	+	3.13459e16i	−0.0895629	+	1.03602i
$993$	1.79559e16	−	1.79559e16i	0.590184	−	0.590184i
$994$	2.70697e15	+	2.80199e15i	0.0884826	+	0.0915886i
$995$	−1.91410e14	+	1.94271e13i	−0.00622212	+	0.000631513i
$996$	7.23600e13	+	2.49698e12i	0.00233923	+	8.07213e-5i
$997$	1.03213e16			0.331826			0.165913	−	0.986140i	$-0.446943\pi$
$997$	1.03213e16			0.331826			0.165913	+	0.986140i	$0.446943\pi$
$998$	2.85688e16	+	2.95716e16i	0.913427	+	0.945491i
$999$		−	3.37794e16i		−	1.07409i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	80.12.j.a.67.1	yes	260
5.3	odd	4		80.12.s.a.3.65	yes	260
16.11	odd	4		80.12.s.a.27.65	yes	260
80.43	even	4	inner	80.12.j.a.43.1	✓	260

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.12.j.a.43.1	✓	260	80.43	even	4	inner
80.12.j.a.67.1	yes	260	1.1	even	1	trivial
80.12.s.a.3.65	yes	260	5.3	odd	4
80.12.s.a.27.65	yes	260	16.11	odd	4

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:	\( N \)	\(=\)	\( 80 = 2^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	80.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-45.2481 - 0.780472i) q^{2} -201.994i q^{3} +(2046.78 + 70.6297i) q^{4} +(-705.591 - 6952.00i) q^{5} +(-157.651 + 9139.85i) q^{6} +(18488.6 + 18488.6i) q^{7} +(-92557.9 - 4793.32i) q^{8} +136345. q^{9} +(26500.8 + 315115. i) q^{10} +(238362. + 238362. i) q^{11} +(14266.8 - 413438. i) q^{12} -1.17648e6 q^{13} +(-822143. - 851003. i) q^{14} +(-1.40426e6 + 142525. i) q^{15} +(4.18433e6 + 289127. i) q^{16} +(-170908. - 170908. i) q^{17} +(-6.16937e6 - 106414. i) q^{18} +(-2.75021e6 - 2.75021e6i) q^{19} +(-953173. - 1.42791e7i) q^{20} +(3.73458e6 - 3.73458e6i) q^{21} +(-1.05994e7 - 1.09715e7i) q^{22} +(-3.92803e7 + 3.92803e7i) q^{23} +(-968221. + 1.86961e7i) q^{24} +(-4.78324e7 + 9.81053e6i) q^{25} +(5.32335e7 + 918209. i) q^{26} -6.33236e7i q^{27} +(3.65362e7 + 3.91479e7i) q^{28} +(3.26727e7 - 3.26727e7i) q^{29} +(6.36514e7 - 5.35301e6i) q^{30} -1.65757e8i q^{31} +(-1.89107e8 - 1.63482e7i) q^{32} +(4.81477e7 - 4.81477e7i) q^{33} +(7.59987e6 + 7.86665e6i) q^{34} +(1.15487e8 - 1.41578e8i) q^{35} +(2.79069e8 + 9.63004e6i) q^{36} +5.33441e8 q^{37} +(1.22295e8 + 1.26588e8i) q^{38} +2.37642e8i q^{39} +(3.19849e7 + 6.46844e8i) q^{40} -7.58275e8i q^{41} +(-1.71897e8 + 1.66068e8i) q^{42} -9.21052e8 q^{43} +(4.71040e8 + 5.04711e8i) q^{44} +(-9.62041e7 - 9.47873e8i) q^{45} +(1.80802e9 - 1.74670e9i) q^{46} +(3.58233e8 - 3.58233e8i) q^{47} +(5.84020e7 - 8.45209e8i) q^{48} -1.29367e9i q^{49} +(2.17198e9 - 4.06576e8i) q^{50} +(-3.45224e7 + 3.45224e7i) q^{51} +(-2.40800e9 - 8.30944e7i) q^{52} +1.15839e9i q^{53} +(-4.94223e7 + 2.86527e9i) q^{54} +(1.48891e9 - 1.82528e9i) q^{55} +(-1.62264e9 - 1.79988e9i) q^{56} +(-5.55526e8 + 5.55526e8i) q^{57} +(-1.50388e9 + 1.45288e9i) q^{58} +(-5.68854e9 + 5.68854e9i) q^{59} +(-2.88428e9 + 1.92535e8i) q^{60} +(1.59207e8 + 1.59207e8i) q^{61} +(-1.29369e8 + 7.50020e9i) q^{62} +(2.52083e9 + 2.52083e9i) q^{63} +(8.54398e9 + 8.87318e8i) q^{64} +(8.30113e8 + 8.17888e9i) q^{65} +(-2.21617e9 + 2.14102e9i) q^{66} -1.27263e10 q^{67} +(-3.37740e8 - 3.61882e8i) q^{68} +(7.93439e9 + 7.93439e9i) q^{69} +(-5.33607e9 + 6.31600e9i) q^{70} -3.29257e9 q^{71} +(-1.26198e10 - 6.53547e8i) q^{72} +(-1.01945e10 - 1.01945e10i) q^{73} +(-2.41372e10 - 4.16335e8i) q^{74} +(1.98167e9 + 9.66186e9i) q^{75} +(-5.43483e9 - 5.82332e9i) q^{76} +8.81395e9i q^{77} +(1.85473e8 - 1.07528e10i) q^{78} -4.22251e10 q^{79} +(-9.42412e8 - 2.92934e10i) q^{80} +1.13622e10 q^{81} +(-5.91812e8 + 3.43105e10i) q^{82} +1.75020e8i q^{83} +(7.90765e9 - 7.38010e9i) q^{84} +(-1.06756e9 + 1.30874e9i) q^{85} +(4.16759e10 + 7.18855e8i) q^{86} +(-6.59969e9 - 6.59969e9i) q^{87} +(-2.09197e10 - 2.32048e10i) q^{88} -8.57989e10 q^{89} +(3.61326e9 + 4.29645e10i) q^{90} +(-2.17514e10 - 2.17514e10i) q^{91} +(-8.31726e10 + 7.76238e10i) q^{92} -3.34820e10 q^{93} +(-1.64890e10 + 1.59298e10i) q^{94} +(-1.71789e10 + 2.10600e10i) q^{95} +(-3.30224e9 + 3.81985e10i) q^{96} +(9.81970e9 + 9.81970e9i) q^{97} +(-1.00967e9 + 5.85362e10i) q^{98} +(3.24996e10 + 3.24996e10i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 260 q - 2 q^{2} - 3956 q^{4} - 2 q^{5} - 4 q^{6} - 4 q^{7} - 74840 q^{8} - 14880348 q^{9} - 4098 q^{10} - 4 q^{11} - 114212 q^{12} - 4 q^{13} + 708588 q^{15} + 5740152 q^{16} - 4 q^{17} - 6791722 q^{18}+ \cdots - 189350900660 q^{99}+O(q^{100}) \) 260 * q - 2 * q^2 - 3956 * q^4 - 2 * q^5 - 4 * q^6 - 4 * q^7 - 74840 * q^8 - 14880348 * q^9 - 4098 * q^10 - 4 * q^11 - 114212 * q^12 - 4 * q^13 + 708588 * q^15 + 5740152 * q^16 - 4 * q^17 - 6791722 * q^18 - 11291288 * q^19 + 27599212 * q^20 - 4 * q^21 + 11921800 * q^22 - 4 * q^23 + 708588 * q^24 - 196875380 * q^26 + 185066800 * q^28 - 534157704 * q^30 - 894200972 * q^32 - 4 * q^33 - 122727336 * q^34 + 434731680 * q^35 + 917614156 * q^36 - 4 * q^37 - 169550316 * q^38 - 1417066568 * q^40 - 1572161236 * q^42 - 4763690660 * q^43 - 1456070840 * q^44 - 97301958 * q^45 - 3653567828 * q^46 + 5707353192 * q^47 - 447163780 * q^48 + 429408694 * q^50 + 112221284 * q^51 - 4957065880 * q^52 - 10995087044 * q^54 - 4 * q^55 - 8945492140 * q^56 + 708588 * q^57 + 33722126388 * q^58 - 11496390224 * q^59 - 6670533420 * q^60 - 2150827028 * q^61 + 15717297108 * q^62 + 708588 * q^63 - 11018267024 * q^64 - 4 * q^65 - 9909115916 * q^66 + 44333852084 * q^67 - 74998571352 * q^68 + 16194123612 * q^69 + 50947270608 * q^70 - 43677902056 * q^71 - 56634399632 * q^72 + 12278087704 * q^73 - 99553151276 * q^74 + 85400572304 * q^75 + 46613107196 * q^76 + 205137826492 * q^78 + 130159671844 * q^80 + 794986843420 * q^81 + 83904972628 * q^82 + 216982878048 * q^84 - 97656252 * q^85 + 56725646132 * q^86 - 50128110092 * q^87 + 346072249440 * q^88 + 174291105374 * q^90 - 46617621428 * q^91 - 51820450984 * q^92 + 708584 * q^93 - 82977932908 * q^94 - 20580862760 * q^95 - 62470624376 * q^96 - 4 * q^97 - 155418407946 * q^98 - 189350900660 * q^99

Introduction

L-functions

Modular forms

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Database

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