LMFDB - Embedded newform 8.18.b.a.5.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8,18,Mod(5,8)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1]))

N = Newforms(chi, 18, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("8.5");

S:= CuspForms(chi, 18);

N := Newforms(S);

Level:	$ N $	$=$	$ 8 = 2^{3} $
Weight:	$ k $	$=$	$ 18 $
Character orbit:	$[\chi]$	$=$	8.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$14.6577669876$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 7 x^{15} + 4022 x^{14} - 1102776 x^{13} - 373411968 x^{12} + 2100004864 x^{11} + \cdots + 12\!\cdots\!00 $ x^16 - 7x^15 + 4022x^14 - 1102776x^13 - 373411968x^12 + 2100004864x^11 - 3763915816960x^10 + 7317489121656832x^9 - 1108241988138827776x^8 + 163121042717484777472x^7 + 5699397839986467274752x^6 + 1127435088957285706235904x^5 - 217909345031306501735579648x^4 - 78950720850572326734309359616x^3 + 13720647095471028734661620662272x^2 - 5242030267748791654842336509165568*x + 1286374137827816254118965326485913600
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{120}\cdot 3^{14}\cdot 7 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			5.10
Root			$13.1473 - 179.780i$ of defining polynomial
Character	$\chi$	$=$	8.5
Dual form			8.18.b.a.5.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(42.2945 + 359.560i) q^{2} -16002.3i q^{3} +(-127494. + 30414.8i) q^{4} +1.27253e6i q^{5} +(5.75379e6 - 676810. i) q^{6} +5.50569e6 q^{7} +(-1.63282e7 - 4.45555e7i) q^{8} -1.26934e8 q^{9} +O(q^{10})$	\(q+(42.2945 + 359.560i) q^{2} -16002.3i q^{3} +(-127494. + 30414.8i) q^{4} +1.27253e6i q^{5} +(5.75379e6 - 676810. i) q^{6} +5.50569e6 q^{7} +(-1.63282e7 - 4.45555e7i) q^{8} -1.26934e8 q^{9} +(-4.57551e8 + 5.38211e7i) q^{10} -1.09250e9i q^{11} +(4.86707e8 + 2.04020e9i) q^{12} -4.58081e9i q^{13} +(2.32860e8 + 1.97962e9i) q^{14} +2.03635e10 q^{15} +(1.53297e10 - 7.75543e9i) q^{16} -3.61463e10 q^{17} +(-5.36861e9 - 4.56403e10i) q^{18} -2.76727e10i q^{19} +(-3.87038e10 - 1.62241e11i) q^{20} -8.81037e10i q^{21} +(3.92817e11 - 4.62066e10i) q^{22} +2.20613e11 q^{23} +(-7.12990e11 + 2.61290e11i) q^{24} -8.56399e11 q^{25} +(1.64707e12 - 1.93743e11i) q^{26} -3.53044e10i q^{27} +(-7.01944e11 + 1.67454e11i) q^{28} -2.89192e11i q^{29} +(8.61263e11 + 7.32188e12i) q^{30} -6.06840e10 q^{31} +(3.43690e12 + 5.18395e12i) q^{32} -1.74825e13 q^{33} +(-1.52879e12 - 1.29967e13i) q^{34} +7.00616e12i q^{35} +(1.61834e13 - 3.86067e12i) q^{36} +1.88957e12i q^{37} +(9.94998e12 - 1.17040e12i) q^{38} -7.33035e13 q^{39} +(5.66983e13 - 2.07782e13i) q^{40} +6.37984e13 q^{41} +(3.16786e13 - 3.72630e12i) q^{42} -1.04353e14i q^{43} +(3.32280e13 + 1.39287e14i) q^{44} -1.61528e14i q^{45} +(9.33070e12 + 7.93234e13i) q^{46} -1.48111e14 q^{47} +(-1.24105e14 - 2.45311e14i) q^{48} -2.02318e14 q^{49} +(-3.62210e13 - 3.07927e14i) q^{50} +5.78424e14i q^{51} +(1.39324e14 + 5.84027e14i) q^{52} +4.05734e14i q^{53} +(1.26940e13 - 1.49318e12i) q^{54} +1.39024e15 q^{55} +(-8.98982e13 - 2.45308e14i) q^{56} -4.42827e14 q^{57} +(1.03982e14 - 1.22312e13i) q^{58} +7.77037e14i q^{59} +(-2.59623e15 + 6.19351e14i) q^{60} -2.64409e15i q^{61} +(-2.56660e12 - 2.18195e13i) q^{62} -6.98859e14 q^{63} +(-1.71858e15 + 1.45502e15i) q^{64} +5.82922e15 q^{65} +(-7.39412e14 - 6.28599e15i) q^{66} +1.78812e15i q^{67} +(4.60845e15 - 1.09938e15i) q^{68} -3.53031e15i q^{69} +(-2.51913e15 + 2.96322e14i) q^{70} -9.48422e14 q^{71} +(2.07261e15 + 5.65560e15i) q^{72} -6.41511e14 q^{73} +(-6.79414e14 + 7.99185e13i) q^{74} +1.37044e16i q^{75} +(8.41659e14 + 3.52811e15i) q^{76} -6.01494e15i q^{77} +(-3.10034e15 - 2.63570e16i) q^{78} -1.35339e16 q^{79} +(9.86904e15 + 1.95076e16i) q^{80} -1.69572e16 q^{81} +(2.69832e15 + 2.29393e16i) q^{82} +2.30035e16i q^{83} +(2.67966e15 + 1.12327e16i) q^{84} -4.59973e16i q^{85} +(3.75213e16 - 4.41358e15i) q^{86} -4.62775e15 q^{87} +(-4.86766e16 + 1.78385e16i) q^{88} -1.39186e16 q^{89} +(5.80788e16 - 6.83173e15i) q^{90} -2.52205e16i q^{91} +(-2.81269e16 + 6.70989e15i) q^{92} +9.71085e14i q^{93} +(-6.26427e15 - 5.32547e16i) q^{94} +3.52144e16 q^{95} +(8.29552e16 - 5.49984e16i) q^{96} -1.33747e15 q^{97} +(-8.55694e15 - 7.27454e16i) q^{98} +1.38675e17i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 270 q^{2} - 27436 q^{4} + 5839948 q^{6} + 11529600 q^{7} + 24334920 q^{8} - 602654096 q^{9}+O(q^{10}) $ 16 * q + 270 * q^2 - 27436 * q^4 + 5839948 * q^6 + 11529600 * q^7 + 24334920 * q^8 - 602654096 * q^9	$ 16 q + 270 q^{2} - 27436 q^{4} + 5839948 q^{6} + 11529600 q^{7} + 24334920 q^{8} - 602654096 q^{9} + 131002712 q^{10} - 2795125400 q^{12} + 16363788528 q^{14} - 9993282176 q^{15} + 26500434192 q^{16} - 7489125600 q^{17} - 113450563870 q^{18} - 209445719856 q^{20} + 223126527100 q^{22} + 746845345920 q^{23} - 1099415493232 q^{24} - 1809682431664 q^{25} + 2467726531080 q^{26} + 3220542267040 q^{28} - 1188624268048 q^{30} - 318979758592 q^{31} + 1455647316000 q^{32} + 5633526177600 q^{33} - 4461251980292 q^{34} - 33088278002484 q^{36} + 24076283913900 q^{38} - 18457706051456 q^{39} + 60626292962592 q^{40} + 7482251536032 q^{41} - 51630378688160 q^{42} + 193654716236040 q^{44} - 195097141003568 q^{46} - 376698804821760 q^{47} - 329350060416480 q^{48} + 127691292101520 q^{49} + 474997408872102 q^{50} - 272251877663120 q^{52} + 735354219382520 q^{54} + 22\!\cdots\!52 q^{55}+ \cdots + 33\!\cdots\!90 q^{98}+O(q^{100}) $ 16 * q + 270 * q^2 - 27436 * q^4 + 5839948 * q^6 + 11529600 * q^7 + 24334920 * q^8 - 602654096 * q^9 + 131002712 * q^10 - 2795125400 * q^12 + 16363788528 * q^14 - 9993282176 * q^15 + 26500434192 * q^16 - 7489125600 * q^17 - 113450563870 * q^18 - 209445719856 * q^20 + 223126527100 * q^22 + 746845345920 * q^23 - 1099415493232 * q^24 - 1809682431664 * q^25 + 2467726531080 * q^26 + 3220542267040 * q^28 - 1188624268048 * q^30 - 318979758592 * q^31 + 1455647316000 * q^32 + 5633526177600 * q^33 - 4461251980292 * q^34 - 33088278002484 * q^36 + 24076283913900 * q^38 - 18457706051456 * q^39 + 60626292962592 * q^40 + 7482251536032 * q^41 - 51630378688160 * q^42 + 193654716236040 * q^44 - 195097141003568 * q^46 - 376698804821760 * q^47 - 329350060416480 * q^48 + 127691292101520 * q^49 + 474997408872102 * q^50 - 272251877663120 * q^52 + 735354219382520 * q^54 + 2209036687713152 * q^55 - 162767516076480 * q^56 - 190521298294720 * q^57 - 623262610679960 * q^58 - 1973616194963808 * q^60 + 695695648144320 * q^62 - 8131096607338880 * q^63 + 1111931745501248 * q^64 + 2385987975356160 * q^65 + 3598826202828312 * q^66 + 5981109959771880 * q^68 - 10044559836180288 * q^70 + 9025926285576576 * q^71 - 19918679666289160 * q^72 + 11332002046118560 * q^73 + 11098735408189464 * q^74 + 5959440926938280 * q^76 + 4184252259031760 * q^78 - 45299671392008448 * q^79 + 1337342539452480 * q^80 + 20101901999290832 * q^81 + 15639739637081420 * q^82 + 19796542864700224 * q^84 - 14252032276026564 * q^86 + 25965768920837760 * q^87 - 66964872768837680 * q^88 - 69879174608766048 * q^89 + 136151511125051240 * q^90 + 57336249810701280 * q^92 - 192318922166254176 * q^94 + 93790444358203776 * q^95 - 342799224184788928 * q^96 + 95593398602180640 * q^97 + 339641261743253790 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/8\mathbb{Z}\right)^\times$.

$n$	$5$	$7$
$\chi(n)$	$-1$	$1$

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 $

$2$	42.2945	+	359.560i	0.116823	+	0.993153i
$2$	42.2945	+	359.560i	0.116823	+	0.993153i
$3$		−	16002.3i		−	1.40816i	−0.710120	−	0.704080i	$-0.751360\pi$
$3$		−	16002.3i		−	1.40816i	0.710120	−	0.704080i	$-0.248640\pi$
$4$	−127494.	+	30414.8i	−0.972705	+	0.232046i
$5$			1.27253e6i			1.45688i	0.685110	+	0.728440i	$0.259754\pi$
$5$			1.27253e6i			1.45688i	−0.685110	+	0.728440i	$0.740246\pi$
$6$	5.75379e6	−	676810.i	1.39852	−	0.164506i
$7$	5.50569e6			0.360976			0.180488	−	0.983577i	$-0.442232\pi$
$7$	5.50569e6			0.360976			0.180488	+	0.983577i	$0.442232\pi$
$8$	−1.63282e7	−	4.45555e7i	−0.344092	−	0.938936i
$9$	−1.26934e8			−0.982916
$10$	−4.57551e8	+	5.38211e7i	−1.44690	+	0.170197i
$11$		−	1.09250e9i		−	1.53667i	−0.640045	−	0.768337i	$-0.721084\pi$
$11$		−	1.09250e9i		−	1.53667i	0.640045	−	0.768337i	$-0.278916\pi$
$12$	4.86707e8	+	2.04020e9i	0.326759	+	1.36972i
$13$		−	4.58081e9i		−	1.55748i	−0.627345	−	0.778742i	$-0.715858\pi$
$13$		−	4.58081e9i		−	1.55748i	0.627345	−	0.778742i	$-0.284142\pi$
$14$	2.32860e8	+	1.97962e9i	0.0421703	+	0.358504i
$15$	2.03635e10			2.05152
$16$	1.53297e10	−	7.75543e9i	0.892309	−	0.451425i
$17$	−3.61463e10			−1.25675			−0.628373	−	0.777912i	$-0.716279\pi$
$17$	−3.61463e10			−1.25675			−0.628373	+	0.777912i	$0.716279\pi$
$18$	−5.36861e9	−	4.56403e10i	−0.114827	−	0.976186i
$19$		−	2.76727e10i		−	0.373806i	−0.982378	−	0.186903i	$-0.940155\pi$
$19$		−	2.76727e10i		−	0.373806i	0.982378	−	0.186903i	$-0.0598449\pi$
$20$	−3.87038e10	−	1.62241e11i	−0.338064	−	1.41711i
$21$		−	8.81037e10i		−	0.508312i
$22$	3.92817e11	−	4.62066e10i	1.52615	−	0.179519i
$23$	2.20613e11			0.587413			0.293707	−	0.955896i	$-0.405111\pi$
$23$	2.20613e11			0.587413			0.293707	+	0.955896i	$0.405111\pi$
$24$	−7.12990e11	+	2.61290e11i	−1.32217	+	0.484537i
$25$	−8.56399e11			−1.12250
$26$	1.64707e12	−	1.93743e11i	1.54682	−	0.181950i
$27$		−	3.53044e10i		−	0.0240567i
$28$	−7.01944e11	+	1.67454e11i	−0.351123	+	0.0837632i
$29$		−	2.89192e11i		−	0.107350i	−0.998558	−	0.0536752i	$-0.982906\pi$
$29$		−	2.89192e11i		−	0.107350i	0.998558	−	0.0536752i	$-0.0170936\pi$
$30$	8.61263e11	+	7.32188e12i	0.239665	+	2.03747i
$31$	−6.06840e10			−0.0127791			−0.00638954	−	0.999980i	$-0.502034\pi$
$31$	−6.06840e10			−0.0127791			−0.00638954	+	0.999980i	$0.502034\pi$
$32$	3.43690e12	+	5.18395e12i	0.552577	+	0.833462i
$33$	−1.74825e13			−2.16388
$34$	−1.52879e12	−	1.29967e13i	−0.146817	−	1.24814i
$35$			7.00616e12i			0.525899i
$36$	1.61834e13	−	3.86067e12i	0.956087	−	0.228082i
$37$			1.88957e12i			0.0884400i	0.999022	+	0.0442200i	$0.0140803\pi$
$37$			1.88957e12i			0.0884400i	−0.999022	+	0.0442200i	$0.985920\pi$
$38$	9.94998e12	−	1.17040e12i	0.371246	−	0.0436691i
$39$	−7.33035e13			−2.19319
$40$	5.66983e13	−	2.07782e13i	1.36792	−	0.501301i
$41$	6.37984e13			1.24781			0.623903	−	0.781502i	$-0.285546\pi$
$41$	6.37984e13			1.24781			0.623903	+	0.781502i	$0.285546\pi$
$42$	3.16786e13	−	3.72630e12i	0.504831	−	0.0593826i
$43$		−	1.04353e14i		−	1.36152i	−0.732505	−	0.680761i	$-0.761649\pi$
$43$		−	1.04353e14i		−	1.36152i	0.732505	−	0.680761i	$-0.238351\pi$
$44$	3.32280e13	+	1.39287e14i	0.356580	+	1.49473i
$45$		−	1.61528e14i		−	1.43199i
$46$	9.33070e12	+	7.93234e13i	0.0686235	+	0.583391i
$47$	−1.48111e14			−0.907308			−0.453654	−	0.891178i	$-0.649880\pi$
$47$	−1.48111e14			−0.907308			−0.453654	+	0.891178i	$0.649880\pi$
$48$	−1.24105e14	−	2.45311e14i	−0.635679	−	1.25651i
$49$	−2.02318e14			−0.869696
$50$	−3.62210e13	−	3.07927e14i	−0.131134	−	1.11481i
$51$			5.78424e14i			1.76970i
$52$	1.39324e14	+	5.84027e14i	0.361409	+	1.51497i
$53$			4.05734e14i			0.895151i	0.894246	+	0.447575i	$0.147712\pi$
$53$			4.05734e14i			0.895151i	−0.894246	+	0.447575i	$0.852288\pi$
$54$	1.26940e13	−	1.49318e12i	0.0238920	−	0.00281038i
$55$	1.39024e15			2.23875
$56$	−8.98982e13	−	2.45308e14i	−0.124209	−	0.338933i
$57$	−4.42827e14			−0.526378
$58$	1.03982e14	−	1.22312e13i	0.106615	−	0.0125410i
$59$			7.77037e14i			0.688969i	0.938792	+	0.344484i	$0.111946\pi$
$59$			7.77037e14i			0.688969i	−0.938792	+	0.344484i	$0.888054\pi$
$60$	−2.59623e15	+	6.19351e14i	−1.99552	+	0.476048i
$61$		−	2.64409e15i		−	1.76592i	−0.469445	−	0.882962i	$-0.655546\pi$
$61$		−	2.64409e15i		−	1.76592i	0.469445	−	0.882962i	$-0.344454\pi$
$62$	−2.56660e12	−	2.18195e13i	−0.00149289	−	0.0126916i
$63$	−6.98859e14			−0.354809
$64$	−1.71858e15	+	1.45502e15i	−0.763201	+	0.646161i
$65$	5.82922e15			2.26907
$66$	−7.39412e14	−	6.28599e15i	−0.252792	−	2.14907i
$67$			1.78812e15i			0.537973i	0.963144	+	0.268987i	$0.0866887\pi$
$67$			1.78812e15i			0.537973i	−0.963144	+	0.268987i	$0.913311\pi$
$68$	4.60845e15	−	1.09938e15i	1.22244	−	0.291624i
$69$		−	3.53031e15i		−	0.827172i
$70$	−2.51913e15	+	2.96322e14i	−0.522298	+	0.0614371i
$71$	−9.48422e14			−0.174303			−0.0871516	−	0.996195i	$-0.527776\pi$
$71$	−9.48422e14			−0.174303			−0.0871516	+	0.996195i	$0.527776\pi$
$72$	2.07261e15	+	5.65560e15i	0.338214	+	0.922895i
$73$	−6.41511e14			−0.0931021			−0.0465511	−	0.998916i	$-0.514823\pi$
$73$	−6.41511e14			−0.0931021			−0.0465511	+	0.998916i	$0.514823\pi$
$74$	−6.79414e14	+	7.99185e13i	−0.0878344	+	0.0103318i
$75$			1.37044e16i			1.58066i
$76$	8.41659e14	+	3.52811e15i	0.0867403	+	0.363602i
$77$		−	6.01494e15i		−	0.554702i
$78$	−3.10034e15	−	2.63570e16i	−0.256215	−	2.17817i
$79$	−1.35339e16			−1.00367			−0.501836	−	0.864963i	$-0.667342\pi$
$79$	−1.35339e16			−1.00367			−0.501836	+	0.864963i	$0.667342\pi$
$80$	9.86904e15	+	1.95076e16i	0.657673	+	1.29999i
$81$	−1.69572e16			−1.01679
$82$	2.69832e15	+	2.29393e16i	0.145773	+	1.23926i
$83$			2.30035e16i			1.12106i	0.828133	+	0.560532i	$0.189403\pi$
$83$			2.30035e16i			1.12106i	−0.828133	+	0.560532i	$0.810597\pi$
$84$	2.67966e15	+	1.12327e16i	0.117952	+	0.494437i
$85$		−	4.59973e16i		−	1.83093i
$86$	3.75213e16	−	4.41358e15i	1.35220	−	0.159057i
$87$	−4.62775e15			−0.151167
$88$	−4.86766e16	+	1.78385e16i	−1.44284	+	0.528757i
$89$	−1.39186e16			−0.374785			−0.187392	−	0.982285i	$-0.560004\pi$
$89$	−1.39186e16			−0.374785			−0.187392	+	0.982285i	$0.560004\pi$
$90$	5.80788e16	−	6.83173e15i	1.42219	−	0.167290i
$91$		−	2.52205e16i		−	0.562214i
$92$	−2.81269e16	+	6.70989e15i	−0.571380	+	0.136307i
$93$			9.71085e14i			0.0179950i
$94$	−6.26427e15	−	5.32547e16i	−0.105995	−	0.901096i
$95$	3.52144e16			0.544590
$96$	8.29552e16	−	5.49984e16i	1.17365	−	0.778117i
$97$	−1.33747e15			−0.0173270			−0.00866350	−	0.999962i	$-0.502758\pi$
$97$	−1.33747e15			−0.0173270			−0.00866350	+	0.999962i	$0.502758\pi$
$98$	−8.55694e15	−	7.27454e16i	−0.101601	−	0.863741i
$99$			1.38675e17i			1.51042i
$100$	1.09186e17	−	2.60472e16i	1.09186	−	0.260472i
$101$		−	2.99972e16i		−	0.275645i	−0.990457	−	0.137822i	$-0.955990\pi$
$101$		−	2.99972e16i		−	0.275645i	0.990457	−	0.137822i	$-0.0440103\pi$
$102$	−2.07978e17	+	2.44642e16i	−1.75758	+	0.206742i
$103$	5.73300e15			0.0445929			0.0222965	−	0.999751i	$-0.492902\pi$
$103$	5.73300e15			0.0445929			0.0222965	+	0.999751i	$0.492902\pi$
$104$	−2.04100e17	+	7.47965e16i	−1.46238	+	0.535918i
$105$	1.12115e17			0.740550
$106$	−1.45885e17	+	1.71603e16i	−0.889021	+	0.104574i
$107$		−	3.35465e17i		−	1.88749i	−0.330670	−	0.943747i	$-0.607275\pi$
$107$		−	3.35465e17i		−	1.88749i	0.330670	−	0.943747i	$-0.392725\pi$
$108$	1.07378e15	+	4.50111e15i	0.00558228	+	0.0234001i
$109$			2.00351e17i			0.963091i	0.876421	+	0.481545i	$0.159924\pi$
$109$			2.00351e17i			0.963091i	−0.876421	+	0.481545i	$0.840076\pi$
$110$	5.87993e16	+	4.99873e17i	0.261538	+	2.22342i
$111$	3.02375e16			0.124538
$112$	8.44008e16	−	4.26990e16i	0.322102	−	0.162954i
$113$	4.77266e17			1.68886			0.844430	−	0.535665i	$-0.179939\pi$
$113$	4.77266e17			1.68886			0.844430	+	0.535665i	$0.179939\pi$
$114$	−1.87292e16	−	1.59223e17i	−0.0614932	−	0.522774i
$115$			2.80737e17i			0.855791i
$116$	8.79573e15	+	3.68704e16i	0.0249103	+	0.104420i
$117$			5.81460e17i			1.53088i
$118$	−2.79391e17	+	3.28644e16i	−0.684251	+	0.0804875i
$119$	−1.99010e17			−0.453655
$120$	−3.32500e17	−	9.07303e17i	−0.705912	−	1.92625i
$121$	−6.88100e17			−1.36137
$122$	9.50707e17	−	1.11830e17i	1.75383	−	0.206301i
$123$		−	1.02092e18i		−	1.75711i
$124$	7.73687e15	−	1.84569e15i	0.0124303	−	0.00296534i
$125$		−	1.18931e17i		−	0.178467i
$126$	−2.95579e16	−	2.51281e17i	−0.0414499	−	0.352380i
$127$	1.01392e18			1.32945			0.664723	−	0.747090i	$-0.268549\pi$
$127$	1.01392e18			1.32945			0.664723	+	0.747090i	$0.268549\pi$
$128$	−5.95855e17	−	5.56391e17i	−0.730896	−	0.682489i
$129$	−1.66990e18			−1.91724
$130$	2.46544e17	+	2.09595e18i	0.265080	+	2.25353i
$131$		−	7.50169e17i		−	0.755706i	−0.925866	−	0.377853i	$-0.876662\pi$
$131$		−	7.50169e17i		−	0.755706i	0.925866	−	0.377853i	$-0.123338\pi$
$132$	2.22891e18	−	5.31725e17i	2.10482	−	0.502122i
$133$		−	1.52357e17i		−	0.134935i
$134$	−6.42936e17	+	7.56276e16i	−0.534290	+	0.0628477i
$135$	4.49260e16			0.0350478
$136$	5.90205e17	+	1.61051e18i	0.432437	+	1.18000i
$137$	1.03661e18			0.713659			0.356830	−	0.934170i	$-0.383858\pi$
$137$	1.03661e18			0.713659			0.356830	+	0.934170i	$0.383858\pi$
$138$	1.26936e18	−	1.49313e17i	0.821508	−	0.0966329i
$139$		−	8.10539e17i		−	0.493342i	−0.969099	−	0.246671i	$-0.920663\pi$
$139$		−	8.10539e17i		−	0.493342i	0.969099	−	0.246671i	$-0.0793367\pi$
$140$	−2.13091e17	−	8.93246e17i	−0.122033	−	0.511544i
$141$			2.37012e18i			1.27764i
$142$	−4.01130e16	−	3.41014e17i	−0.0203627	−	0.173110i
$143$	−5.00451e18			−2.39335
$144$	−1.94587e18	+	9.84427e17i	−0.877065	+	0.443713i
$145$	3.68007e17			0.156397
$146$	−2.71324e16	−	2.30661e17i	−0.0108765	−	0.0924646i
$147$			3.23756e18i			1.22467i
$148$	−5.74709e16	−	2.40910e17i	−0.0205222	−	0.0860260i
$149$		−	2.43823e18i		−	0.822228i	−0.911584	−	0.411114i	$-0.865140\pi$
$149$		−	2.43823e18i		−	0.822228i	0.911584	−	0.411114i	$-0.134860\pi$
$150$	−4.92754e18	+	5.79620e17i	−1.56984	+	0.184658i
$151$	1.09271e18			0.329004			0.164502	−	0.986377i	$-0.447398\pi$
$151$	1.09271e18			0.329004			0.164502	+	0.986377i	$0.447398\pi$
$152$	−1.23297e18	+	4.51846e17i	−0.350979	+	0.128624i
$153$	4.58819e18			1.23528
$154$	2.16273e18	−	2.54399e17i	0.550904	−	0.0648021i
$155$		−	7.72224e16i		−	0.0186176i
$156$	9.34578e18	−	2.22951e18i	2.13332	−	0.508921i
$157$			3.20208e18i			0.692286i	0.938182	+	0.346143i	$0.112509\pi$
$157$			3.20208e18i			0.692286i	−0.938182	+	0.346143i	$0.887491\pi$
$158$	−5.72408e17	−	4.86623e18i	−0.117252	−	0.996799i
$159$	6.49268e18			1.26052
$160$	−6.59674e18	+	4.37357e18i	−1.21425	+	0.805038i
$161$	1.21462e18			0.212042
$162$	−7.17197e17	−	6.09713e18i	−0.118785	−	1.00983i
$163$			5.19837e18i			0.817094i	0.912737	+	0.408547i	$0.133964\pi$
$163$			5.19837e18i			0.817094i	−0.912737	+	0.408547i	$0.866036\pi$
$164$	−8.13394e18	+	1.94042e18i	−1.21375	+	0.289549i
$165$		−	2.22470e19i		−	3.15252i
$166$	−8.27114e18	+	9.72922e17i	−1.11339	+	0.130966i
$167$	1.13255e19			1.44866			0.724329	−	0.689455i	$-0.242150\pi$
$167$	1.13255e19			1.44866			0.724329	+	0.689455i	$0.242150\pi$
$168$	−3.92550e18	+	1.43858e18i	−0.477272	+	0.174906i
$169$	−1.23334e19			−1.42576
$170$	1.65388e19	−	1.94543e18i	1.81839	−	0.213895i
$171$			3.51260e18i			0.367420i
$172$	3.17389e18	+	1.33045e19i	0.315937	+	1.32436i
$173$			6.41050e18i			0.607435i	0.952762	+	0.303717i	$0.0982279\pi$
$173$			6.41050e18i			0.607435i	−0.952762	+	0.303717i	$0.901772\pi$
$174$	−1.95728e17	−	1.66395e18i	−0.0176598	−	0.150132i
$175$	−4.71507e18			−0.405195
$176$	−8.47277e18	−	1.67477e19i	−0.693694	−	1.37119i
$177$	1.24344e19			0.970179
$178$	−5.88682e17	−	5.00459e18i	−0.0437836	−	0.372219i
$179$			7.04159e18i			0.499367i	0.968327	+	0.249684i	$0.0803266\pi$
$179$			7.04159e18i			0.499367i	−0.968327	+	0.249684i	$0.919673\pi$
$180$	4.91283e18	+	2.05939e19i	0.332288	+	1.39290i
$181$			6.07746e18i			0.392152i	0.980589	+	0.196076i	$0.0628199\pi$
$181$			6.07746e18i			0.392152i	−0.980589	+	0.196076i	$0.937180\pi$
$182$	9.06827e18	−	1.06669e18i	0.558364	−	0.0656796i
$183$	−4.23115e19			−2.48670
$184$	−3.60222e18	−	9.82949e18i	−0.202124	−	0.551543i
$185$	−2.40454e18			−0.128846
$186$	−3.49163e17	+	4.10715e16i	−0.0178718	+	0.00210223i
$187$			3.94896e19i			1.93121i
$188$	1.88833e19	−	4.50476e18i	0.882543	−	0.210538i
$189$		−	1.94375e17i		−	0.00868390i
$190$	1.48938e18	+	1.26617e19i	0.0636207	+	0.540861i
$191$	1.49750e19			0.611762			0.305881	−	0.952070i	$-0.401049\pi$
$191$	1.49750e19			0.611762			0.305881	+	0.952070i	$0.401049\pi$
$192$	2.32838e19	+	2.75012e19i	0.909898	+	1.07471i
$193$	−2.19206e19			−0.819625			−0.409812	−	0.912170i	$-0.634406\pi$
$193$	−2.19206e19			−0.819625			−0.409812	+	0.912170i	$0.634406\pi$
$194$	−5.65675e16	−	4.80899e17i	−0.00202420	−	0.0172084i
$195$		−	9.32811e19i		−	3.19521i
$196$	2.57944e19	−	6.15346e18i	0.845958	−	0.201810i
$197$		−	4.49841e19i		−	1.41285i	−0.707788	−	0.706425i	$-0.750307\pi$
$197$		−	4.49841e19i		−	1.41285i	0.707788	−	0.706425i	$-0.249693\pi$
$198$	−4.98619e19	+	5.86518e18i	−1.50008	+	0.176452i
$199$	6.77221e17			0.0195200			0.00975999	−	0.999952i	$-0.496893\pi$
$199$	6.77221e17			0.0195200			0.00975999	+	0.999952i	$0.496893\pi$
$200$	1.39835e19	+	3.81573e19i	0.386243	+	1.05396i
$201$	2.86141e19			0.757553
$202$	1.07858e19	−	1.26872e18i	0.273757	−	0.0322017i
$203$		−	1.59220e18i		−	0.0387509i
$204$	−1.75927e19	−	7.37458e19i	−0.410653	−	1.72140i
$205$			8.11855e19i			1.81790i
$206$	2.42475e17	+	2.06136e18i	0.00520948	+	0.0442876i
$207$	−2.80032e19			−0.577378
$208$	−3.55261e19	−	7.02226e19i	−0.703088	−	1.38976i
$209$	−3.02323e19			−0.574417
$210$	4.74184e18	+	4.03120e19i	0.0865133	+	0.735479i
$211$		−	1.50647e18i		−	0.0263974i	−0.999913	−	0.0131987i	$-0.995799\pi$
$211$		−	1.50647e18i		−	0.0263974i	0.999913	−	0.0131987i	$-0.00420139\pi$
$212$	−1.23403e19	−	5.17287e19i	−0.207717	−	0.870717i
$213$			1.51769e19i			0.245447i
$214$	1.20620e20	−	1.41883e19i	1.87457	−	0.220503i
$215$	1.32793e20			1.98358
$216$	−1.57300e18	+	5.76459e17i	−0.0225877	+	0.00827773i
$217$	−3.34107e17			−0.00461294
$218$	−7.20383e19	+	8.47377e18i	−0.956496	+	0.112511i
$219$			1.02657e19i			0.131103i
$220$	−1.77247e20	+	4.22837e19i	−2.17764	+	0.519494i
$221$			1.65579e20i			1.95736i
$222$	1.27888e18	+	1.08722e19i	0.0145489	+	0.123685i
$223$	4.18501e19			0.458252			0.229126	−	0.973397i	$-0.426413\pi$
$223$	4.18501e19			0.458252			0.229126	+	0.973397i	$0.426413\pi$
$224$	1.89225e19	+	2.85412e19i	0.199467	+	0.300860i
$225$	1.08706e20			1.10332
$226$	2.01857e19	+	1.71606e20i	0.197298	+	1.67730i
$227$		−	5.35510e19i		−	0.504137i	−0.967709	−	0.252068i	$-0.918889\pi$
$227$		−	5.35510e19i		−	0.504137i	0.967709	−	0.252068i	$-0.0811108\pi$
$228$	5.64580e19	−	1.34685e19i	0.512011	−	0.122144i
$229$		−	1.59891e20i		−	1.39708i	−0.715571	−	0.698540i	$-0.753834\pi$
$229$		−	1.59891e20i		−	1.39708i	0.715571	−	0.698540i	$-0.246166\pi$
$230$	−1.00942e20	+	1.18736e19i	−0.849931	+	0.0999762i
$231$	−9.62529e19			−0.781110
$232$	−1.28851e19	+	4.72200e18i	−0.100795	+	0.0369384i
$233$	−1.58383e20			−1.19449			−0.597246	−	0.802058i	$-0.703738\pi$
$233$	−1.58383e20			−1.19449			−0.597246	+	0.802058i	$0.703738\pi$
$234$	−2.09070e20	+	2.45926e19i	−1.52039	+	0.178842i
$235$		−	1.88476e20i		−	1.32184i
$236$	−2.36334e19	−	9.90678e19i	−0.159873	−	0.670163i
$237$			2.16573e20i			1.41333i
$238$	−8.41703e18	−	7.15560e19i	−0.0529974	−	0.450549i
$239$	8.94881e19			0.543730			0.271865	−	0.962335i	$-0.412360\pi$
$239$	8.94881e19			0.543730			0.271865	+	0.962335i	$0.412360\pi$
$240$	3.12167e20	−	1.57927e20i	1.83059	−	0.926109i
$241$	1.21178e19			0.0685926			0.0342963	−	0.999412i	$-0.489081\pi$
$241$	1.21178e19			0.0685926			0.0342963	+	0.999412i	$0.489081\pi$
$242$	−2.91028e19	−	2.47413e20i	−0.159039	−	1.35205i
$243$			2.66796e20i			1.40775i
$244$	8.04193e19	+	3.37106e20i	0.409776	+	1.71772i
$245$		−	2.57456e20i		−	1.26704i
$246$	3.67082e20	−	4.31794e19i	1.74508	−	0.205271i
$247$	−1.26763e20			−0.582196
$248$	9.90863e17	+	2.70380e18i	0.00439718	+	0.0119987i
$249$	3.68110e20			1.57864
$250$	4.27626e19	−	5.03011e18i	0.177245	−	0.0208491i
$251$			1.61721e19i			0.0647948i	0.999475	+	0.0323974i	$0.0103142\pi$
$251$			1.61721e19i			0.0647948i	−0.999475	+	0.0323974i	$0.989686\pi$
$252$	8.91005e19	−	2.12556e19i	0.345124	−	0.0823322i
$253$		−	2.41018e20i		−	0.902663i
$254$	4.28831e19	+	3.64564e20i	0.155310	+	1.32034i
$255$	−7.36063e20			−2.57824
$256$	1.74855e20	−	2.37778e20i	0.592430	−	0.805622i
$257$	−2.29544e20			−0.752376			−0.376188	−	0.926543i	$-0.622765\pi$
$257$	−2.29544e20			−0.752376			−0.376188	+	0.926543i	$0.622765\pi$
$258$	−7.06274e19	−	6.00427e20i	−0.223978	−	1.90411i
$259$			1.04034e19i			0.0319247i
$260$	−7.43193e20	+	1.77295e20i	−2.20713	+	0.526529i
$261$			3.67083e19i			0.105516i
$262$	2.69731e20	−	3.17280e19i	0.750532	−	0.0882840i
$263$	3.30068e20			0.889159			0.444579	−	0.895739i	$-0.353353\pi$
$263$	3.30068e20			0.889159			0.444579	+	0.895739i	$0.353353\pi$
$264$	2.85458e20	+	7.78939e20i	0.744575	+	2.03175i
$265$	−5.16309e20			−1.30413
$266$	5.47815e19	−	6.44387e18i	0.134011	−	0.0157635i
$267$			2.22731e20i			0.527757i
$268$	−5.43853e19	−	2.27975e20i	−0.124835	−	0.523289i
$269$		−	3.65029e20i		−	0.811770i	−0.913924	−	0.405885i	$-0.866963\pi$
$269$		−	3.65029e20i		−	0.811770i	0.913924	−	0.405885i	$-0.133037\pi$
$270$	1.90012e18	+	1.61536e19i	0.00409439	+	0.0348078i
$271$	8.51437e20			1.77792			0.888962	−	0.457980i	$-0.151427\pi$
$271$	8.51437e20			1.77792			0.888962	+	0.457980i	$0.151427\pi$
$272$	−5.54113e20	+	2.80330e20i	−1.12141	+	0.567327i
$273$	−4.03586e20			−0.791688
$274$	4.38429e19	+	3.72723e20i	0.0833719	+	0.708773i
$275$			9.35612e20i			1.72492i
$276$	1.07374e20	+	4.50095e20i	0.191942	+	0.804594i
$277$		−	1.55690e20i		−	0.269888i	−0.990853	−	0.134944i	$-0.956915\pi$
$277$		−	1.55690e20i		−	0.269888i	0.990853	−	0.134944i	$-0.0430854\pi$
$278$	2.91437e20	−	3.42814e19i	0.489964	−	0.0576338i
$279$	7.70286e18			0.0125608
$280$	3.12163e20	−	1.14398e20i	0.493785	−	0.180957i
$281$	9.25634e20			1.42048			0.710241	−	0.703959i	$-0.248586\pi$
$281$	9.25634e20			1.42048			0.710241	+	0.703959i	$0.248586\pi$
$282$	−8.52198e20	+	1.00243e20i	−1.26889	+	0.149257i
$283$		−	1.32593e20i		−	0.191574i	−0.995402	−	0.0957869i	$-0.969463\pi$
$283$		−	1.32593e20i		−	0.191574i	0.995402	−	0.0957869i	$-0.0305367\pi$
$284$	1.20918e20	−	2.88461e19i	0.169546	−	0.0404465i
$285$		−	5.63512e20i		−	0.766870i
$286$	−2.11663e20	−	1.79942e21i	−0.279598	−	2.37696i
$287$	3.51254e20			0.450428
$288$	−4.36260e20	−	6.58019e20i	−0.543137	−	0.819223i
$289$	4.79313e20			0.579412
$290$	1.55647e19	+	1.32320e20i	0.0182708	+	0.155326i
$291$			2.14026e19i			0.0243992i
$292$	8.17890e19	−	1.95114e19i	0.0905609	−	0.0216040i
$293$			1.61233e21i			1.73412i	0.498207	+	0.867058i	$0.333992\pi$
$293$			1.61233e21i			1.73412i	−0.498207	+	0.867058i	$0.666008\pi$
$294$	−1.16409e21	+	1.36931e20i	−1.21629	+	0.143070i
$295$	−9.88805e20			−1.00375
$296$	8.41907e19	−	3.08534e19i	0.0830395	−	0.0304315i
$297$	−3.85699e19			−0.0369674
$298$	8.76691e20	−	1.03124e20i	0.816598	−	0.0960553i
$299$		−	1.01058e21i		−	0.914886i
$300$	−4.16816e20	−	1.74723e21i	−0.366787	−	1.53752i
$301$		−	5.74537e20i		−	0.491477i
$302$	4.62157e19	+	3.92895e20i	0.0384353	+	0.326751i
$303$	−4.80025e20			−0.388152
$304$	−2.14614e20	−	4.24215e20i	−0.168745	−	0.333550i
$305$	3.36469e21			2.57274
$306$	1.94055e20	+	1.64973e21i	0.144309	+	1.22682i
$307$		−	1.25031e21i		−	0.904357i	−0.891927	−	0.452178i	$-0.850647\pi$
$307$		−	1.25031e21i		−	0.904357i	0.891927	−	0.452178i	$-0.149353\pi$
$308$	1.82943e20	+	7.66871e20i	0.128717	+	0.539562i
$309$		−	9.17413e19i		−	0.0627940i
$310$	2.77660e19	−	3.26608e18i	0.0184901	−	0.00217497i
$311$	2.50382e20			0.162234			0.0811168	−	0.996705i	$-0.474151\pi$
$311$	2.50382e20			0.162234			0.0811168	+	0.996705i	$0.474151\pi$
$312$	1.19692e21	+	3.26607e21i	0.754658	+	2.05926i
$313$	−2.54935e21			−1.56423			−0.782117	−	0.623131i	$-0.785860\pi$
$313$	−2.54935e21			−1.56423			−0.782117	+	0.623131i	$0.785860\pi$
$314$	−1.15134e21	+	1.35431e20i	−0.687546	+	0.0808751i
$315$		−	8.89320e20i		−	0.516914i
$316$	1.72549e21	−	4.11630e20i	0.976276	−	0.232898i
$317$			1.11353e21i			0.613337i	0.951816	+	0.306668i	$0.0992143\pi$
$317$			1.11353e21i			0.613337i	−0.951816	+	0.306668i	$0.900786\pi$
$318$	2.74605e20	+	2.33451e21i	0.147257	+	1.25188i
$319$	−3.15941e20			−0.164963
$320$	−1.85157e21	−	2.18694e21i	−0.941379	−	1.11189i
$321$	−5.36822e21			−2.65789
$322$	5.13719e19	+	4.36730e20i	0.0247714	+	0.210590i
$323$			1.00026e21i			0.469779i
$324$	2.16195e21	−	5.15751e20i	0.989038	−	0.235943i
$325$			3.92300e21i			1.74827i
$326$	−1.86912e21	+	2.19862e20i	−0.811499	+	0.0954555i
$327$	3.20609e21			1.35619
$328$	−1.04172e21	−	2.84257e21i	−0.429360	−	1.17161i
$329$	−8.15452e20			−0.327516
$330$	7.99912e21	−	9.40926e20i	3.13093	−	0.368287i
$331$			1.36776e21i			0.521761i	0.965371	+	0.260880i	$0.0840128\pi$
$331$			1.36776e21i			0.521761i	−0.965371	+	0.260880i	$0.915987\pi$
$332$	−6.99647e20	−	2.93282e21i	−0.260139	−	1.09046i
$333$		−	2.39851e20i		−	0.0869291i
$334$	4.79004e20	+	4.07218e21i	0.169237	+	1.43874i
$335$	−2.27544e21			−0.783762
$336$	−6.83282e20	−	1.35061e21i	−0.229465	−	0.453571i
$337$	−1.13951e21			−0.373133			−0.186567	−	0.982442i	$-0.559736\pi$
$337$	−1.13951e21			−0.373133			−0.186567	+	0.982442i	$0.559736\pi$
$338$	−5.21634e20	−	4.43458e21i	−0.166561	−	1.41599i
$339$		−	7.63736e21i		−	2.37819i
$340$	1.39900e21	+	5.86440e21i	0.424861	+	1.78095i
$341$			6.62970e19i			0.0196373i
$342$	−1.26299e21	+	1.48564e20i	−0.364904	+	0.0429231i
$343$	−2.39469e21			−0.674915
$344$	−4.64951e21	+	1.70391e21i	−1.27838	+	0.468489i
$345$	4.49244e21			1.20509
$346$	−2.30496e21	+	2.71129e20i	−0.603276	+	0.0709625i
$347$			1.78923e21i			0.456946i	0.973550	+	0.228473i	$0.0733732\pi$
$347$			1.78923e21i			0.456946i	−0.973550	+	0.228473i	$0.926627\pi$
$348$	5.90012e20	−	1.40752e20i	0.147041	−	0.0350777i
$349$		−	7.51876e21i		−	1.82865i	−0.404984	−	0.914324i	$-0.632723\pi$
$349$		−	7.51876e21i		−	1.82865i	0.404984	−	0.914324i	$-0.367277\pi$
$350$	−1.99421e20	−	1.69535e21i	−0.0473362	−	0.402421i
$351$	−1.61723e20			−0.0374680
$352$	5.66344e21	−	3.75480e21i	1.28076	−	0.849131i
$353$	6.92424e21			1.52858			0.764288	−	0.644875i	$-0.223091\pi$
$353$	6.92424e21			1.52858			0.764288	+	0.644875i	$0.223091\pi$
$354$	5.25906e20	+	4.47091e21i	0.113339	+	0.963536i
$355$		−	1.20690e21i		−	0.253939i
$356$	1.77455e21	−	4.23333e20i	0.364555	−	0.0869675i
$357$			3.18462e21i			0.638819i
$358$	−2.53187e21	+	2.97821e20i	−0.495948	+	0.0583377i
$359$	6.83078e21			1.30667			0.653337	−	0.757067i	$-0.273368\pi$
$359$	6.83078e21			1.30667			0.653337	+	0.757067i	$0.273368\pi$
$360$	−7.19693e21	+	2.63746e21i	−1.34455	+	0.492737i
$361$	4.71461e21			0.860269
$362$	−2.18521e21	+	2.57043e20i	−0.389467	+	0.0458124i
$363$			1.10112e22i			1.91703i
$364$	7.67076e20	+	3.21547e21i	0.130460	+	0.546868i
$365$		−	8.16343e20i		−	0.135639i
$366$	−1.78954e21	−	1.52135e22i	−0.290505	−	2.46968i
$367$	−5.85117e21			−0.928071			−0.464036	−	0.885817i	$-0.653599\pi$
$367$	−5.85117e21			−0.928071			−0.464036	+	0.885817i	$0.653599\pi$
$368$	3.38194e21	−	1.71095e21i	0.524154	−	0.265173i
$369$	−8.09818e21			−1.22649
$370$	−1.01699e20	−	8.64576e20i	−0.0150523	−	0.127964i
$371$			2.23384e21i			0.323128i
$372$	−2.95353e19	−	1.23808e20i	−0.00417568	−	0.0175038i
$373$			8.31710e21i			1.14933i	0.818387	+	0.574667i	$0.194869\pi$
$373$			8.31710e21i			1.14933i	−0.818387	+	0.574667i	$0.805131\pi$
$374$	−1.41989e22	+	1.67019e21i	−1.91799	+	0.225610i
$375$	−1.90316e21			−0.251310
$376$	2.41839e21	+	6.59914e21i	0.312198	+	0.851904i
$377$	−1.32473e21			−0.167197
$378$	6.98894e19	−	8.22099e18i	0.00862444	−	0.00101448i
$379$			5.50827e21i			0.664633i	0.943168	+	0.332317i	$0.107830\pi$
$379$			5.50827e21i			0.664633i	−0.943168	+	0.332317i	$0.892170\pi$
$380$	−4.48964e21	+	1.07104e21i	−0.529725	+	0.126370i
$381$		−	1.62250e22i		−	1.87207i
$382$	6.33360e20	+	5.38440e21i	0.0714680	+	0.607574i
$383$	1.37047e22			1.51244			0.756222	−	0.654315i	$-0.227043\pi$
$383$	1.37047e22			1.51244			0.756222	+	0.654315i	$0.227043\pi$
$384$	−8.90355e21	+	9.53505e21i	−0.961054	+	1.02922i
$385$	7.65420e21			0.808135
$386$	−9.27120e20	−	7.88176e21i	−0.0957512	−	0.814013i
$387$			1.32460e22i			1.33826i
$388$	1.70520e20	−	4.06788e19i	0.0168541	−	0.00402067i
$389$		−	1.27957e22i		−	1.23735i	−0.785649	−	0.618673i	$-0.787671\pi$
$389$		−	1.27957e22i		−	1.23735i	0.785649	−	0.618673i	$-0.212329\pi$
$390$	3.35401e22	−	3.94528e21i	3.17333	−	0.373275i
$391$	−7.97432e21			−0.738230
$392$	3.30350e21	+	9.01437e21i	0.299256	+	0.816589i
$393$	−1.20044e22			−1.06416
$394$	1.61745e22	−	1.90258e21i	1.40318	−	0.165054i
$395$		−	1.72223e22i		−	1.46223i
$396$	−4.21777e21	−	1.76803e22i	−0.350488	−	1.46919i
$397$			1.34055e22i			1.09035i	0.838324	+	0.545173i	$0.183536\pi$
$397$			1.34055e22i			1.09035i	−0.838324	+	0.545173i	$0.816464\pi$
$398$	2.86427e19	+	2.43501e20i	0.00228039	+	0.0193863i
$399$	−2.43807e21			−0.190010
$400$	−1.31284e22	+	6.64174e21i	−1.00162	+	0.506725i
$401$	3.18862e21			0.238164			0.119082	−	0.992884i	$-0.462005\pi$
$401$	3.18862e21			0.238164			0.119082	+	0.992884i	$0.462005\pi$
$402$	1.21022e21	+	1.02885e22i	0.0884997	+	0.752366i
$403$			2.77982e20i			0.0199032i
$404$	9.12360e20	+	3.82448e21i	0.0639624	+	0.268121i
$405$		−	2.15786e22i		−	1.48134i
$406$	5.72492e20	−	6.73414e19i	0.0384856	−	0.00452700i
$407$	2.06435e21			0.135903
$408$	2.57719e22	−	9.44465e21i	1.66164	−	0.608940i
$409$	−1.47757e22			−0.933036			−0.466518	−	0.884512i	$-0.654492\pi$
$409$	−1.47757e22			−0.933036			−0.466518	+	0.884512i	$0.654492\pi$
$410$	−2.91910e22	+	3.43370e21i	−1.80546	+	0.212373i
$411$		−	1.65882e22i		−	1.00495i
$412$	−7.30926e20	+	1.74368e20i	−0.0433757	+	0.0103476i
$413$			4.27812e21i			0.248701i
$414$	−1.18438e21	−	1.00688e22i	−0.0674511	−	0.573425i
$415$	−2.92727e22			−1.63326
$416$	2.37467e22	−	1.57438e22i	1.29810	−	0.860629i
$417$	−1.29705e22			−0.694705
$418$	−1.27866e21	−	1.08703e22i	−0.0671053	−	0.570484i
$419$			2.32213e22i			1.19418i	0.802176	+	0.597088i	$0.203676\pi$
$419$			2.32213e22i			1.19418i	−0.802176	+	0.597088i	$0.796324\pi$
$420$	−1.42940e22	+	3.40995e21i	−0.720336	+	0.171842i
$421$			9.61252e19i			0.00474722i	0.999997	+	0.00237361i	$0.000755544\pi$
$421$			9.61252e19i			0.00474722i	−0.999997	+	0.00237361i	$0.999244\pi$
$422$	5.41667e20	−	6.37156e19i	0.0262166	−	0.00308383i
$423$	1.88003e22			0.891808
$424$	1.80776e22	−	6.62492e21i	0.840489	−	0.308014i
$425$	3.09556e22			1.41070
$426$	−5.45702e21	+	6.41901e20i	−0.243766	+	0.0286739i
$427$		−	1.45575e22i		−	0.637456i
$428$	1.02031e22	+	4.27699e22i	0.437986	+	1.83597i
$429$			8.00838e22i			3.37021i
$430$	5.61642e21	+	4.77471e22i	0.231728	+	1.96999i
$431$	−8.67397e21			−0.350882			−0.175441	−	0.984490i	$-0.556135\pi$
$431$	−8.67397e21			−0.350882			−0.175441	+	0.984490i	$0.556135\pi$
$432$	−2.73801e20	−	5.41207e20i	−0.0108598	−	0.0214660i
$433$	−5.54728e21			−0.215741			−0.107871	−	0.994165i	$-0.534403\pi$
$433$	−5.54728e21			−0.215741			−0.107871	+	0.994165i	$0.534403\pi$
$434$	−1.41309e19	−	1.20131e20i	−0.000538898	−	0.00458136i
$435$		−	5.88896e21i		−	0.220232i
$436$	−6.09365e21	−	2.55437e22i	−0.223482	−	0.936803i
$437$		−	6.10494e21i		−	0.219578i
$438$	−3.69112e21	+	4.34181e20i	−0.130205	+	0.0153158i
$439$	2.90117e22			1.00375			0.501875	−	0.864940i	$-0.332644\pi$
$439$	2.90117e22			1.00375			0.501875	+	0.864940i	$0.332644\pi$
$440$	−2.27001e22	−	6.19426e22i	−0.770336	−	2.10204i
$441$	2.56810e22			0.854839
$442$	−5.95356e22	+	7.00309e21i	−1.94396	+	0.228665i
$443$		−	1.05398e22i		−	0.337600i	−0.985650	−	0.168800i	$-0.946011\pi$
$443$		−	1.05398e22i		−	0.337600i	0.985650	−	0.168800i	$-0.0539892\pi$
$444$	−3.85511e21	+	9.19668e20i	−0.121138	+	0.0288985i
$445$		−	1.77119e22i		−	0.546017i
$446$	1.77003e21	+	1.50476e22i	0.0535345	+	0.455115i
$447$	−3.90174e22			−1.15783
$448$	−9.46194e21	+	8.01091e21i	−0.275497	+	0.233248i
$449$	2.19051e22			0.625824			0.312912	−	0.949782i	$-0.398696\pi$
$449$	2.19051e22			0.625824			0.312912	+	0.949782i	$0.398696\pi$
$450$	4.59767e21	+	3.90863e22i	0.128894	+	1.09577i
$451$		−	6.96995e22i		−	1.91747i
$452$	−6.08487e22	+	1.45160e22i	−1.64276	+	0.391894i
$453$		−	1.74859e22i		−	0.463291i
$454$	1.92548e22	−	2.26491e21i	0.500685	−	0.0588948i
$455$	3.20939e22			0.819078
$456$	7.23059e21	+	1.97304e22i	0.181123	+	0.494235i
$457$	−1.81055e22			−0.445168			−0.222584	−	0.974914i	$-0.571449\pi$
$457$	−1.81055e22			−0.445168			−0.222584	+	0.974914i	$0.571449\pi$
$458$	5.74902e22	−	6.76249e21i	1.38751	−	0.163211i
$459$			1.27612e21i			0.0302332i
$460$	−8.53855e21	−	3.57923e22i	−0.198583	−	0.832432i
$461$			5.23537e22i			1.19534i	0.801744	+	0.597668i	$0.203906\pi$
$461$			5.23537e22i			1.19534i	−0.801744	+	0.597668i	$0.796094\pi$
$462$	−4.07097e21	−	3.46087e22i	−0.0912517	−	0.775761i
$463$	8.11473e22			1.78581			0.892906	−	0.450244i	$-0.148663\pi$
$463$	8.11473e22			1.78581			0.892906	+	0.450244i	$0.148663\pi$
$464$	−2.24281e21	−	4.43325e21i	−0.0484607	−	0.0957897i
$465$	−1.23574e21			−0.0262166
$466$	−6.69873e21	−	5.69481e22i	−0.139544	−	1.18631i
$467$			6.19948e22i			1.26812i	0.773282	+	0.634062i	$0.218614\pi$
$467$			6.19948e22i			1.26812i	−0.773282	+	0.634062i	$0.781386\pi$
$468$	−1.76850e22	−	7.41329e22i	−0.355234	−	1.48909i
$469$			9.84482e21i			0.194195i
$470$	6.77683e22	−	7.97149e21i	1.31279	−	0.154421i
$471$	5.12408e22			0.974850
$472$	3.46212e22	−	1.26877e22i	0.646898	−	0.237069i
$473$	−1.14006e23			−2.09222
$474$	−7.78710e22	+	9.15985e21i	−1.40365	+	0.165110i
$475$			2.36989e22i			0.419597i
$476$	2.53727e22	−	6.05285e21i	0.441273	−	0.105269i
$477$		−	5.15014e22i		−	0.879858i
$478$	3.78485e21	+	3.21763e22i	0.0635202	+	0.540007i
$479$	−9.58348e22			−1.58005			−0.790026	−	0.613073i	$-0.789933\pi$
$479$	−9.58348e22			−1.58005			−0.790026	+	0.613073i	$0.789933\pi$
$480$	6.99873e22	+	1.05563e23i	1.13362	+	1.70986i
$481$	8.65576e21			0.137744
$482$	5.12514e20	+	4.35705e21i	0.00801320	+	0.0681229i
$483$		−	1.94368e22i		−	0.298589i
$484$	8.77288e22	−	2.09284e22i	1.32421	−	0.315901i
$485$		−	1.70197e21i		−	0.0252434i
$486$	−9.59290e22	+	1.12840e22i	−1.39811	+	0.164458i
$487$	−1.77480e22			−0.254187			−0.127094	−	0.991891i	$-0.540565\pi$
$487$	−1.77480e22			−0.254187			−0.127094	+	0.991891i	$0.540565\pi$
$488$	−1.17808e23	+	4.31733e22i	−1.65809	+	0.607640i
$489$	8.31859e22			1.15060
$490$	9.25708e22	−	1.08890e22i	1.25837	−	0.148020i
$491$		−	2.79794e22i		−	0.373805i	−0.982378	−	0.186903i	$-0.940155\pi$
$491$		−	2.79794e22i		−	0.373805i	0.982378	−	0.186903i	$-0.0598449\pi$
$492$	3.10511e22	+	1.30162e23i	0.407731	+	1.70915i
$493$			1.04532e22i			0.134912i
$494$	−5.36139e21	−	4.55790e22i	−0.0680140	−	0.578210i
$495$	−1.76468e23			−2.20050
$496$	−9.30271e20	+	4.70631e20i	−0.0114029	+	0.00576880i
$497$	−5.22171e21			−0.0629193
$498$	1.55690e22	+	1.32357e23i	0.184422	+	1.56783i
$499$			2.93207e22i			0.341444i	0.985319	+	0.170722i	$0.0546100\pi$
$499$			2.93207e22i			0.341444i	−0.985319	+	0.170722i	$0.945390\pi$
$500$	3.61725e21	+	1.51630e22i	0.0414127	+	0.173596i
$501$		−	1.81233e23i		−	2.03994i
$502$	−5.81484e21	+	6.83992e20i	−0.0643511	+	0.00756953i
$503$	−5.05003e22			−0.549498			−0.274749	−	0.961516i	$-0.588595\pi$
$503$	−5.05003e22			−0.549498			−0.274749	+	0.961516i	$0.588595\pi$
$504$	1.14111e22	+	3.11380e22i	0.122087	+	0.333143i
$505$	3.81725e22			0.401581
$506$	8.66605e22	−	1.01937e22i	0.896482	−	0.105452i
$507$			1.97363e23i			2.00769i
$508$	−1.29269e23	+	3.08381e22i	−1.29316	+	0.308493i
$509$		−	6.53584e22i		−	0.642984i	−0.946912	−	0.321492i	$-0.895816\pi$
$509$		−	6.53584e22i		−	0.642984i	0.946912	−	0.321492i	$-0.104184\pi$
$510$	−3.11314e22	−	2.64659e23i	−0.301198	−	2.56059i
$511$	−3.53196e21			−0.0336076
$512$	9.28906e22	+	5.28140e22i	0.869315	+	0.494258i
$513$	−9.76967e20			−0.00899254
$514$	−9.70846e21	−	8.25349e22i	−0.0878949	−	0.747224i
$515$			7.29543e21i			0.0649665i
$516$	2.12902e23	−	5.07896e22i	1.86491	−	0.444889i
$517$			1.61810e23i			1.39424i
$518$	−3.74064e21	+	4.40006e20i	−0.0317061	+	0.00372954i
$519$	1.02583e23			0.855366
$520$	−9.51810e22	−	2.59724e23i	−0.780768	−	2.13051i
$521$	2.48515e22			0.200555			0.100277	−	0.994960i	$-0.468027\pi$
$521$	2.48515e22			0.200555			0.100277	+	0.994960i	$0.468027\pi$
$522$	−1.31988e22	+	1.55256e21i	−0.104794	+	0.0123268i
$523$		−	4.03025e22i		−	0.314824i	−0.987533	−	0.157412i	$-0.949685\pi$
$523$		−	4.03025e22i		−	0.314824i	0.987533	−	0.157412i	$-0.0503151\pi$
$524$	2.28162e22	+	9.56423e22i	0.175359	+	0.735079i
$525$			7.54520e22i			0.570580i
$526$	1.39601e22	+	1.18679e23i	0.103874	+	0.883070i
$527$	2.19350e21			0.0160601
$528$	−2.68002e23	+	1.35584e23i	−1.93085	+	0.976832i
$529$	−9.23801e22			−0.654946
$530$	−2.18370e22	−	1.85644e23i	−0.152352	−	1.29520i
$531$		−	9.86324e22i		−	0.677199i
$532$	4.63391e21	+	1.94247e22i	0.0313111	+	0.131252i
$533$		−	2.92248e23i		−	1.94344i
$534$	−8.00850e22	+	9.42028e21i	−0.524144	+	0.0616543i
$535$	4.26890e23			2.74985
$536$	7.96705e22	−	2.91969e22i	0.505122	−	0.185112i
$537$	1.12682e23			0.703189
$538$	1.31250e23	−	1.54387e22i	0.806211	−	0.0948335i
$539$			2.21031e23i			1.33644i
$540$	−5.72781e21	+	1.36641e21i	−0.0340911	+	0.00813271i
$541$		−	2.15571e23i		−	1.26303i	−0.775365	−	0.631514i	$-0.782434\pi$
$541$		−	2.15571e23i		−	1.26303i	0.775365	−	0.631514i	$-0.217566\pi$
$542$	3.60111e22	+	3.06142e23i	0.207703	+	1.76575i
$543$	9.72535e22			0.552213
$544$	−1.24231e23	−	1.87380e23i	−0.694449	−	1.04745i
$545$	−2.54954e23			−1.40311
$546$	−1.70695e22	−	1.45113e23i	−0.0924874	−	0.786267i
$547$		−	1.65986e23i		−	0.885483i	−0.896649	−	0.442742i	$-0.854006\pi$
$547$		−	1.65986e23i		−	0.885483i	0.896649	−	0.442742i	$-0.145994\pi$
$548$	−1.32162e23	+	3.15283e22i	−0.694180	+	0.165602i
$549$			3.35624e23i			1.73576i
$550$	−3.36408e23	+	3.95713e22i	−1.71311	+	0.201510i
$551$	−8.00273e21			−0.0401282
$552$	−1.57295e23	+	5.76438e22i	−0.776662	+	0.284623i
$553$	−7.45132e22			−0.362301
$554$	5.59799e22	−	6.58483e21i	0.268040	−	0.0315291i
$555$			3.84782e22i			0.181437i
$556$	2.46524e22	+	1.03339e23i	0.114478	+	0.479876i
$557$			1.22488e23i			0.560177i	0.959974	+	0.280089i	$0.0903639\pi$
$557$			1.22488e23i			0.560177i	−0.959974	+	0.280089i	$0.909636\pi$
$558$	3.25789e20	+	2.76964e21i	0.00146739	+	0.0124748i
$559$	−4.78023e23			−2.12055
$560$	5.43358e22	+	1.07403e23i	0.237404	+	0.469264i
$561$	6.31926e23			2.71945
$562$	3.91492e22	+	3.32821e23i	0.165945	+	1.41075i
$563$		−	1.24421e23i		−	0.519484i	−0.965678	−	0.259742i	$-0.916362\pi$
$563$		−	1.24421e23i		−	0.519484i	0.965678	−	0.259742i	$-0.0836376\pi$
$564$	−7.20866e22	−	3.02176e23i	−0.296471	−	1.24276i
$565$			6.07337e23i			2.46047i
$566$	4.76751e22	−	5.60796e21i	0.190262	−	0.0223803i
$567$	−9.33612e22			−0.367037
$568$	1.54861e22	+	4.22574e22i	0.0599764	+	0.163660i
$569$	−4.42193e22			−0.168716			−0.0843582	−	0.996435i	$-0.526884\pi$
$569$	−4.42193e22			−0.168716			−0.0843582	+	0.996435i	$0.526884\pi$
$570$	2.02616e23	−	2.38335e22i	0.761619	−	0.0895882i
$571$		−	3.40211e23i		−	1.25992i	−0.776629	−	0.629958i	$-0.783072\pi$
$571$		−	3.40211e23i		−	1.25992i	0.776629	−	0.629958i	$-0.216928\pi$
$572$	6.38047e23	−	1.52211e23i	2.32802	−	0.555367i
$573$		−	2.39634e23i		−	0.861460i
$574$	1.48561e22	+	1.26297e23i	0.0526204	+	0.447344i
$575$	−1.88932e23			−0.659371
$576$	2.18146e23	−	1.84692e23i	0.750163	−	0.635122i
$577$	2.03213e23			0.688584			0.344292	−	0.938863i	$-0.388119\pi$
$577$	2.03213e23			0.688584			0.344292	+	0.938863i	$0.388119\pi$
$578$	2.02723e22	+	1.72342e23i	0.0676887	+	0.575445i
$579$			3.50780e23i			1.15416i
$580$	−4.69188e22	+	1.11928e22i	−0.152128	+	0.0362913i
$581$			1.26650e23i			0.404677i
$582$	−7.69551e21	+	9.05212e20i	−0.0242321	+	0.00285039i
$583$	4.43262e23			1.37555
$584$	1.04747e22	+	2.85828e22i	0.0320357	+	0.0874169i
$585$	−7.39927e23			−2.23030
$586$	−5.79728e23	+	6.81925e22i	−1.72224	+	0.202585i
$587$		−	5.86095e23i		−	1.71611i	−0.513561	−	0.858053i	$-0.671674\pi$
$587$		−	5.86095e23i		−	1.71611i	0.513561	−	0.858053i	$-0.328326\pi$
$588$	−9.84696e22	−	4.12770e23i	−0.284181	−	1.19124i
$589$			1.67929e21i			0.00477689i
$590$	−4.18210e22	−	3.55534e23i	−0.117261	−	0.996872i
$591$	−7.19850e23			−1.98952
$592$	1.46544e22	+	2.89667e22i	0.0399241	+	0.0789158i
$593$	−6.25760e23			−1.68052			−0.840259	−	0.542185i	$-0.817597\pi$
$593$	−6.25760e23			−1.68052			−0.840259	+	0.542185i	$0.817597\pi$
$594$	−1.63129e21	−	1.38682e22i	−0.00431864	−	0.0367142i
$595$		−	2.53247e23i		−	0.660921i
$596$	7.41584e22	+	3.10861e23i	0.190795	+	0.799785i
$597$		−	1.08371e22i		−	0.0274873i
$598$	3.63365e23	−	4.27421e22i	0.908622	−	0.106880i
$599$	5.45652e23			1.34520			0.672601	−	0.740005i	$-0.265177\pi$
$599$	5.45652e23			1.34520			0.672601	+	0.740005i	$0.265177\pi$
$600$	6.10604e23	−	2.23768e23i	1.48414	−	0.543892i
$601$	5.66889e23			1.35852			0.679259	−	0.733899i	$-0.262301\pi$
$601$	5.66889e23			1.35852			0.679259	+	0.733899i	$0.262301\pi$
$602$	2.06580e23	−	2.42998e22i	0.488111	−	0.0574159i
$603$		−	2.26973e23i		−	0.528783i
$604$	−1.39314e23	+	3.32346e22i	−0.320024	+	0.0763442i
$605$		−	8.75629e23i		−	1.98335i
$606$	−2.03024e22	−	1.72598e23i	−0.0453451	−	0.385494i
$607$	−4.77180e23			−1.05094			−0.525470	−	0.850812i	$-0.676111\pi$
$607$	−4.77180e23			−1.05094			−0.525470	+	0.850812i	$0.676111\pi$
$608$	1.43454e23	−	9.51084e22i	0.311553	−	0.206556i
$609$	−2.54789e22			−0.0545675
$610$	1.42308e23	+	1.20981e24i	0.300556	+	2.55512i
$611$			6.78467e23i			1.41312i
$612$	−5.84968e23	+	1.39549e23i	−1.20156	+	0.286642i
$613$			7.99469e23i			1.61952i	0.586758	+	0.809762i	$0.300404\pi$
$613$			7.99469e23i			1.61952i	−0.586758	+	0.809762i	$0.699596\pi$
$614$	4.49559e23	−	5.28810e22i	0.898165	−	0.105650i
$615$	1.29916e24			2.55990
$616$	−2.67998e23	+	9.82134e22i	−0.520830	+	0.190869i
$617$	1.83317e23			0.351381			0.175691	−	0.984445i	$-0.443784\pi$
$617$	1.83317e23			0.351381			0.175691	+	0.984445i	$0.443784\pi$
$618$	3.29865e22	−	3.88015e21i	0.0623640	−	0.00733579i
$619$		−	5.31085e23i		−	0.990361i	−0.868790	−	0.495181i	$-0.835102\pi$
$619$		−	5.31085e23i		−	0.990361i	0.868790	−	0.495181i	$-0.164898\pi$
$620$	2.34870e21	+	9.84541e21i	0.00432015	+	0.0181094i
$621$		−	7.78859e21i		−	0.0141312i
$622$	1.05898e22	+	9.00275e22i	0.0189526	+	0.161123i
$623$	−7.66317e22			−0.135288
$624$	−1.12372e24	+	5.68500e23i	−1.95700	+	0.990060i
$625$	−5.02038e23			−0.862494
$626$	−1.07823e23	−	9.16642e23i	−0.182739	−	1.55352i
$627$			4.83787e23i			0.808872i
$628$	−9.73907e22	−	4.08248e23i	−0.160643	−	0.673390i
$629$		−	6.83010e22i		−	0.111147i
$630$	3.19764e23	−	3.76134e22i	0.513375	−	0.0603875i
$631$	−5.48119e23			−0.868211			−0.434105	−	0.900862i	$-0.642935\pi$
$631$	−5.48119e23			−0.868211			−0.434105	+	0.900862i	$0.642935\pi$
$632$	2.20984e23	+	6.03007e23i	0.345355	+	0.942383i
$633$	−2.41071e22			−0.0371717
$634$	−4.00381e23	+	4.70963e22i	−0.609137	+	0.0716520i
$635$			1.29024e24i			1.93684i
$636$	−8.27780e23	+	1.97473e23i	−1.22611	+	0.292498i
$637$			9.26779e23i			1.35454i
$638$	−1.33626e22	−	1.13600e23i	−0.0192715	−	0.163833i
$639$	1.20387e23			0.171326
$640$	7.08026e23	−	7.58244e23i	0.994305	−	1.06483i
$641$	9.52772e23			1.32037			0.660185	−	0.751103i	$-0.270478\pi$
$641$	9.52772e23			1.32037			0.660185	+	0.751103i	$0.270478\pi$
$642$	−2.27046e23	−	1.93020e24i	−0.310504	−	2.63969i
$643$			1.01291e24i			1.36703i	0.729935	+	0.683517i	$0.239551\pi$
$643$			1.01291e24i			1.36703i	−0.729935	+	0.683517i	$0.760449\pi$
$644$	−1.54858e23	+	3.69425e22i	−0.206254	+	0.0492036i
$645$		−	2.12500e24i		−	2.79319i
$646$	−3.59655e23	+	4.23057e22i	−0.466562	+	0.0548811i
$647$	−1.18216e24			−1.51352			−0.756762	−	0.653690i	$-0.773220\pi$
$647$	−1.18216e24			−1.51352			−0.756762	+	0.653690i	$0.773220\pi$
$648$	2.76882e23	+	7.55537e23i	0.349870	+	0.954702i
$649$	8.48910e23			1.05872
$650$	−1.41055e24	+	1.65921e23i	−1.73630	+	0.204239i
$651$			5.34649e21i			0.00649576i
$652$	−1.58107e23	−	6.62762e23i	−0.189604	−	0.794792i
$653$		−	1.00840e23i		−	0.119363i	−0.998217	−	0.0596815i	$-0.980992\pi$
$653$		−	1.00840e23i		−	0.119363i	0.998217	−	0.0596815i	$-0.0190085\pi$
$654$	1.35600e23	+	1.15278e24i	0.158434	+	1.34690i
$655$	9.54614e23			1.10097
$656$	9.78013e23	−	4.94784e23i	1.11343	−	0.563291i
$657$	8.14295e22			0.0915116
$658$	−3.44891e22	−	2.93204e23i	−0.0382615	−	0.325274i
$659$		−	1.65436e24i		−	1.81177i	−0.423523	−	0.905885i	$-0.639207\pi$
$659$		−	1.65436e24i		−	1.81177i	0.423523	−	0.905885i	$-0.360793\pi$
$660$	6.76638e23	+	2.83637e24i	0.731531	+	3.06647i
$661$		−	6.63378e22i		−	0.0708025i	−0.999373	−	0.0354012i	$-0.988729\pi$
$661$		−	6.63378e22i		−	0.0708025i	0.999373	−	0.0354012i	$-0.0112709\pi$
$662$	−4.91791e23	+	5.78486e22i	−0.518188	+	0.0609537i
$663$	2.64965e24			2.75628
$664$	1.02493e24	−	3.75607e23i	1.05261	−	0.385749i
$665$	1.93879e23			0.196584
$666$	8.62407e22	−	1.01444e22i	0.0863339	−	0.0101553i
$667$		−	6.37995e22i		−	0.0630591i
$668$	−1.44393e24	+	3.44461e23i	−1.40912	+	0.336156i
$669$		−	6.69698e23i		−	0.645293i
$670$	−9.62386e22	−	8.18156e23i	−0.0915616	−	0.778396i
$671$	−2.88865e24			−2.71365
$672$	4.56725e23	−	3.02804e23i	0.423659	−	0.280881i
$673$	−7.36498e23			−0.674595			−0.337298	−	0.941398i	$-0.609513\pi$
$673$	−7.36498e23			−0.674595			−0.337298	+	0.941398i	$0.609513\pi$
$674$	−4.81950e22	−	4.09722e23i	−0.0435906	−	0.370578i
$675$			3.02346e22i			0.0270037i
$676$	1.57244e24	−	3.75117e23i	1.38684	−	0.330841i
$677$		−	1.40187e24i		−	1.22097i	−0.792029	−	0.610483i	$-0.790975\pi$
$677$		−	1.40187e24i		−	1.22097i	0.792029	−	0.610483i	$-0.209025\pi$
$678$	2.74609e24	−	3.23019e23i	2.36190	−	0.277827i
$679$	−7.36368e21			−0.00625463
$680$	−2.04943e24	+	7.51055e23i	−1.71913	+	0.630008i
$681$	−8.56941e23			−0.709905
$682$	−2.38377e22	+	2.80400e21i	−0.0195028	+	0.00229409i
$683$			1.74717e24i			1.41175i	0.708334	+	0.705877i	$0.249447\pi$
$683$			1.74717e24i			1.41175i	−0.708334	+	0.705877i	$0.750553\pi$
$684$	−1.06835e23	−	4.47837e23i	−0.0852584	−	0.357391i
$685$			1.31912e24i			1.03972i
$686$	−1.01282e23	−	8.61034e23i	−0.0788457	−	0.670294i
$687$	−2.55862e24			−1.96731
$688$	−8.09306e23	−	1.59971e24i	−0.614626	−	1.21490i
$689$	1.85859e24			1.39418
$690$	1.90005e23	+	1.61530e24i	0.140783	+	1.19684i
$691$		−	1.43755e24i		−	1.05211i	−0.850451	−	0.526053i	$-0.823671\pi$
$691$		−	1.43755e24i		−	1.05211i	0.850451	−	0.526053i	$-0.176329\pi$
$692$	−1.94974e23	−	8.17302e23i	−0.140953	−	0.590855i
$693$			7.63500e23i			0.545226i
$694$	−6.43334e23	+	7.56744e22i	−0.453817	+	0.0533818i
$695$	1.03144e24			0.718740
$696$	7.55630e22	+	2.06191e23i	0.0520152	+	0.141936i
$697$	−2.30607e24			−1.56818
$698$	2.70344e24	−	3.18002e23i	1.81613	−	0.213628i
$699$			2.53449e24i			1.68204i
$700$	6.01144e23	−	1.43408e23i	0.394135	−	0.0940241i
$701$			2.46688e24i			1.59788i	0.601411	+	0.798940i	$0.294605\pi$
$701$			2.46688e24i			1.59788i	−0.601411	+	0.798940i	$0.705395\pi$
$702$	−6.83997e21	−	5.81489e22i	−0.00437713	−	0.0372114i
$703$	5.22895e22			0.0330594
$704$	1.58961e24	+	1.87754e24i	0.992939	+	1.17279i
$705$	−3.01605e24			−1.86136
$706$	2.92857e23	+	2.48968e24i	0.178573	+	1.51811i
$707$		−	1.65155e23i		−	0.0995011i
$708$	−1.58531e24	+	3.78190e23i	−0.943698	+	0.225127i
$709$		−	4.96755e23i		−	0.292179i	−0.989271	−	0.146090i	$-0.953331\pi$
$709$		−	4.96755e23i		−	0.292179i	0.989271	−	0.146090i	$-0.0466688\pi$
$710$	4.33952e23	−	5.10451e22i	0.252200	−	0.0296660i
$711$	1.71791e24			0.986525
$712$	2.27267e23	+	6.20152e23i	0.128960	+	0.351899i
$713$	−1.33877e22			−0.00750660
$714$	−1.14506e24	+	1.34692e23i	−0.634445	+	0.0746289i
$715$		−	6.36840e24i		−	3.48682i
$716$	−2.14169e23	−	8.97763e23i	−0.115876	−	0.485737i
$717$		−	1.43202e24i		−	0.765659i
$718$	2.88904e23	+	2.45607e24i	0.152650	+	1.29773i
$719$	2.19102e24			1.14407			0.572033	−	0.820231i	$-0.306155\pi$
$719$	2.19102e24			1.14407			0.572033	+	0.820231i	$0.306155\pi$
$720$	−1.25272e24	−	2.47618e24i	−0.646437	−	1.27778i
$721$	3.15641e22			0.0160970
$722$	1.99402e23	+	1.69518e24i	0.100499	+	0.854379i
$723$		−	1.93912e23i		−	0.0965894i
$724$	−1.84845e23	−	7.74842e23i	−0.0909975	−	0.381448i
$725$			2.47664e23i			0.120501i
$726$	−3.95918e24	+	4.65713e23i	−1.90390	+	0.223953i
$727$	5.04345e23			0.239710			0.119855	−	0.992791i	$-0.461757\pi$
$727$	5.04345e23			0.239710			0.119855	+	0.992791i	$0.461757\pi$
$728$	−1.12371e24	+	4.11806e23i	−0.527883	+	0.193453i
$729$	2.07949e24			0.965546
$730$	2.93524e23	−	3.45268e22i	0.134710	−	0.0158457i
$731$			3.77199e24i			1.71109i
$732$	5.39448e24	−	1.28690e24i	2.41883	−	0.577031i
$733$			3.20975e24i			1.42261i	0.702882	+	0.711307i	$0.251896\pi$
$733$			3.20975e24i			1.42261i	−0.702882	+	0.711307i	$0.748104\pi$
$734$	−2.47472e23	−	2.10385e24i	−0.108420	−	0.921716i
$735$	−4.11989e24			−1.78420
$736$	7.58224e23	+	1.14364e24i	0.324591	+	0.489587i
$737$	1.95351e24			0.826690
$738$	−3.42509e23	−	2.91178e24i	−0.143282	−	1.21809i
$739$		−	3.55163e24i		−	1.46876i	−0.678741	−	0.734378i	$-0.737474\pi$
$739$		−	3.55163e24i		−	1.46876i	0.678741	−	0.734378i	$-0.262526\pi$
$740$	3.06565e23	−	7.31336e22i	0.125330	−	0.0298984i
$741$			2.02851e24i			0.819825i
$742$	−8.03200e23	+	9.44792e22i	−0.320915	+	0.0377488i
$743$	4.55330e24			1.79854			0.899272	−	0.437389i	$-0.144097\pi$
$743$	4.55330e24			1.79854			0.899272	+	0.437389i	$0.144097\pi$
$744$	4.32671e22	−	1.58561e22i	0.0168962	−	0.00619194i
$745$	3.10273e24			1.19789
$746$	−2.99049e24	+	3.51767e23i	−1.14147	+	0.134269i
$747$		−	2.91993e24i		−	1.10191i
$748$	−1.20107e24	−	5.03471e24i	−0.448131	−	1.87850i
$749$		−	1.84697e24i		−	0.681339i
$750$	−8.04934e22	−	6.84301e23i	−0.0293589	−	0.249590i
$751$	−2.50774e24			−0.904362			−0.452181	−	0.891926i	$-0.649354\pi$
$751$	−2.50774e24			−0.904362			−0.452181	+	0.891926i	$0.649354\pi$
$752$	−2.27050e24	+	1.14866e24i	−0.809599	+	0.409582i
$753$	2.58791e23			0.0912415
$754$	−5.60290e22	−	4.76321e23i	−0.0195324	−	0.166052i
$755$			1.39051e24i			0.479319i
$756$	5.91187e21	+	2.47817e22i	0.00201507	+	0.00844687i
$757$		−	1.69510e24i		−	0.571323i	−0.958331	−	0.285661i	$-0.907787\pi$
$757$		−	1.69510e24i		−	0.571323i	0.958331	−	0.285661i	$-0.0922133\pi$
$758$	−1.98055e24	+	2.32970e23i	−0.660083	+	0.0776446i
$759$	−3.85685e24			−1.27109
$760$	−5.74989e23	−	1.56899e24i	−0.187389	−	0.511335i
$761$	1.92045e23			0.0618919			0.0309459	−	0.999521i	$-0.490148\pi$
$761$	1.92045e23			0.0618919			0.0309459	+	0.999521i	$0.490148\pi$
$762$	5.83386e24	−	6.86229e23i	1.85926	−	0.218702i
$763$			1.10307e24i			0.347653i
$764$	−1.90923e24	+	4.55461e23i	−0.595064	+	0.141957i
$765$			5.83862e24i			1.79965i
$766$	5.79633e23	+	4.92765e24i	0.176689	+	1.50209i
$767$	3.55946e24			1.07306
$768$	−3.80499e24	−	2.79808e24i	−1.13444	−	0.834237i
$769$	1.94625e24			0.573884			0.286942	−	0.957948i	$-0.407361\pi$
$769$	1.94625e24			0.573884			0.286942	+	0.957948i	$0.407361\pi$
$770$	3.23731e23	+	2.75214e24i	0.0944089	+	0.802601i
$771$			3.67324e24i			1.05947i
$772$	2.79475e24	−	6.66710e23i	0.797253	−	0.190191i
$773$		−	2.45731e24i		−	0.693320i	−0.937991	−	0.346660i	$-0.887316\pi$
$773$		−	2.45731e24i		−	0.693320i	0.937991	−	0.346660i	$-0.112684\pi$
$774$	−4.76273e24	+	5.60233e23i	−1.32910	+	0.156340i
$775$	5.19697e22			0.0143445
$776$	2.18385e22	+	5.95915e22i	0.00596209	+	0.0162689i
$777$	1.66478e23			0.0449551
$778$	4.60080e24	−	5.41186e23i	1.22887	−	0.144551i
$779$		−	1.76547e24i		−	0.466437i
$780$	2.83713e24	+	1.18928e25i	0.741437	+	3.10800i
$781$			1.03615e24i			0.267847i
$782$	−3.37270e23	−	2.86725e24i	−0.0862423	−	0.733175i
$783$	−1.02098e22			−0.00258250
$784$	−3.10148e24	+	1.56906e24i	−0.776038	+	0.392603i
$785$	−4.07475e24			−1.00858
$786$	−5.07722e23	−	4.31631e24i	−0.124318	−	1.05687i
$787$		−	1.09863e23i		−	0.0266113i	−0.999911	−	0.0133056i	$-0.995765\pi$
$787$		−	1.09863e23i		−	0.0266113i	0.999911	−	0.0133056i	$-0.00423544\pi$
$788$	1.36818e24	+	5.73522e24i	0.327847	+	1.37429i
$789$		−	5.28185e24i		−	1.25208i
$790$	6.19244e24	−	7.28408e23i	1.45222	−	0.170822i
$791$	2.62768e24			0.609638
$792$	6.17872e24	−	2.26432e24i	1.41819	−	0.519724i
$793$	−1.21120e25			−2.75040
$794$	−4.82009e24	+	5.66980e23i	−1.08288	+	0.127378i
$795$			8.26214e24i			1.83642i
$796$	−8.63419e22	+	2.05975e22i	−0.0189872	+	0.00452954i
$797$		−	5.01970e24i		−	1.09215i	−0.837737	−	0.546075i	$-0.816121\pi$
$797$		−	5.01970e24i		−	1.09215i	0.837737	−	0.546075i	$-0.183879\pi$
$798$	−1.03117e23	−	8.76631e23i	−0.0221976	−	0.188709i
$799$	5.35365e24			1.14026
$800$	−2.94336e24	−	4.43953e24i	−0.620267	−	0.935561i
$801$	1.76675e24			0.368382
$802$	1.34861e23	+	1.14650e24i	0.0278231	+	0.236533i
$803$			7.00848e23i			0.143068i
$804$	−3.64813e24	+	8.70291e23i	−0.736875	+	0.175787i
$805$			1.54565e24i			0.308920i
$806$	−9.99510e22	+	1.17571e22i	−0.0197669	+	0.00232516i
$807$	−5.84131e24			−1.14310
$808$	−1.33654e24	+	4.89802e23i	−0.258813	+	0.0948471i
$809$	−3.24682e24			−0.622151			−0.311076	−	0.950385i	$-0.600689\pi$
$809$	−3.24682e24			−0.622151			−0.311076	+	0.950385i	$0.600689\pi$
$810$	7.75880e24	−	9.12657e23i	1.47120	−	0.173055i
$811$		−	7.41408e24i		−	1.39117i	−0.718444	−	0.695585i	$-0.755145\pi$
$811$		−	7.41408e24i		−	1.39117i	0.718444	−	0.695585i	$-0.244855\pi$
$812$	4.84265e22	+	2.02997e23i	0.00899201	+	0.0376932i
$813$		−	1.36250e25i		−	2.50360i
$814$	8.73106e22	+	7.42257e23i	0.0158767	+	0.134973i
$815$	−6.61509e24			−1.19041
$816$	4.48593e24	+	8.86710e24i	0.798888	+	1.57912i
$817$	−2.88774e24			−0.508945
$818$	−6.24929e23	−	5.31273e24i	−0.109000	−	0.926647i
$819$			3.20134e24i			0.552609i
$820$	−2.46924e24	−	1.03507e25i	−0.421838	−	1.76828i
$821$			5.46829e24i			0.924560i	0.886734	+	0.462280i	$0.152968\pi$
$821$			5.46829e24i			0.924560i	−0.886734	+	0.462280i	$0.847032\pi$
$822$	5.96444e24	−	7.01588e23i	0.998066	−	0.117401i
$823$	−3.24572e24			−0.537542			−0.268771	−	0.963204i	$-0.586617\pi$
$823$	−3.24572e24			−0.537542			−0.268771	+	0.963204i	$0.586617\pi$
$824$	−9.36099e22	−	2.55437e23i	−0.0153441	−	0.0418699i
$825$	1.49720e25			2.42896
$826$	−1.53824e24	+	1.80941e23i	−0.246998	+	0.0290541i
$827$			2.96432e24i			0.471116i	0.971860	+	0.235558i	$0.0756918\pi$
$827$			2.96432e24i			0.471116i	−0.971860	+	0.235558i	$0.924308\pi$
$828$	3.57025e24	−	8.51713e23i	0.561618	−	0.133979i
$829$			7.49941e24i			1.16765i	0.811879	+	0.583826i	$0.198445\pi$
$829$			7.49941e24i			1.16765i	−0.811879	+	0.583826i	$0.801555\pi$
$830$	−1.23808e24	−	1.05253e25i	−0.190802	−	1.62207i
$831$	−2.49140e24			−0.380045
$832$	6.66519e24	+	7.87247e24i	1.00638	+	1.18867i
$833$	7.31304e24			1.09299
$834$	−5.48581e23	−	4.66367e24i	−0.0811576	−	0.689948i
$835$			1.44120e25i			2.11052i
$836$	3.85445e24	−	9.19509e23i	0.558739	−	0.133292i
$837$			2.14241e21i			0.000307423i
$838$	−8.34946e24	+	9.82135e23i	−1.18600	+	0.139507i
$839$	4.17137e24			0.586546			0.293273	−	0.956029i	$-0.405256\pi$
$839$	4.17137e24			0.586546			0.293273	+	0.956029i	$0.405256\pi$
$840$	−1.83064e24	−	4.99533e24i	−0.254817	−	0.695329i
$841$	7.17352e24			0.988476
$842$	−3.45627e22	+	4.06557e21i	−0.00471472	+	0.000554585i
$843$		−	1.48123e25i		−	2.00027i
$844$	4.58191e22	+	1.92067e23i	0.00612542	+	0.0256769i
$845$		−	1.56946e25i		−	2.07715i
$846$	7.95149e23	+	6.75983e24i	0.104184	+	0.885702i
$847$	−3.78846e24			−0.491421
$848$	3.14664e24	+	6.21979e24i	0.404094	+	0.798751i
$849$	−2.12180e24			−0.269767
$850$	1.30925e24	+	1.11304e25i	0.164802	+	1.40104i
$851$			4.16863e23i			0.0519508i
$852$	−4.61604e23	−	1.93497e24i	−0.0569551	−	0.238747i
$853$			1.13957e25i			1.39211i	0.717986	+	0.696057i	$0.245064\pi$
$853$			1.13957e25i			1.39211i	−0.717986	+	0.696057i	$0.754936\pi$
$854$	5.23429e24	−	6.15703e23i	0.633091	−	0.0744696i
$855$	−4.46990e24			−0.535286
$856$	−1.49468e25	+	5.47756e24i	−1.77224	+	0.649471i
$857$	−5.05880e24			−0.593896			−0.296948	−	0.954894i	$-0.595969\pi$
$857$	−5.05880e24			−0.593896			−0.296948	+	0.954894i	$0.595969\pi$
$858$	−2.87949e25	+	3.38710e24i	−3.34714	+	0.393719i
$859$			2.76471e24i			0.318205i	0.987262	+	0.159103i	$0.0508601\pi$
$859$			2.76471e24i			0.318205i	−0.987262	+	0.159103i	$0.949140\pi$
$860$	−1.69304e25	+	4.03888e24i	−1.92943	+	0.460282i
$861$		−	5.62088e24i		−	0.634275i
$862$	−3.66861e23	−	3.11881e24i	−0.0409912	−	0.348479i
$863$	1.17975e25			1.30526			0.652631	−	0.757676i	$-0.273665\pi$
$863$	1.17975e25			1.30526			0.652631	+	0.757676i	$0.273665\pi$
$864$	1.83016e23	−	1.21338e23i	0.0200504	−	0.0132932i
$865$	−8.15756e24			−0.884960
$866$	−2.34620e23	−	1.99458e24i	−0.0252036	−	0.214264i
$867$		−	7.67012e24i		−	0.815905i
$868$	4.25968e22	−	1.01618e22i	0.00448703	−	0.00107042i
$869$			1.47857e25i			1.54232i
$870$	2.11743e24	−	2.49071e23i	0.218724	−	0.0257282i
$871$	8.19103e24			0.837884
$872$	8.92675e24	−	3.27139e24i	0.904281	−	0.331392i
$873$	1.69770e23			0.0170310
$874$	2.19509e24	−	2.58206e23i	0.218075	−	0.0256518i
$875$		−	6.54794e23i		−	0.0644223i
$876$	−3.12228e23	−	1.30881e24i	−0.0304219	−	0.127524i
$877$			3.77610e24i			0.364373i	0.983264	+	0.182187i	$0.0583175\pi$
$877$			3.77610e24i			0.364373i	−0.983264	+	0.182187i	$0.941683\pi$
$878$	1.22704e24	+	1.04314e25i	0.117261	+	0.996876i
$879$	2.58010e25			2.44191
$880$	2.13120e25	−	1.07819e25i	1.99766	−	1.01063i
$881$	1.38554e24			0.128624			0.0643121	−	0.997930i	$-0.479515\pi$
$881$	1.38554e24			0.128624			0.0643121	+	0.997930i	$0.479515\pi$
$882$	1.08617e24	+	9.23386e24i	0.0998650	+	0.848985i
$883$		−	6.59564e24i		−	0.600608i	−0.953844	−	0.300304i	$-0.902912\pi$
$883$		−	6.59564e24i		−	0.600608i	0.953844	−	0.300304i	$-0.0970882\pi$
$884$	−5.03605e24	−	2.11104e25i	−0.454199	−	1.90394i
$885$			1.58232e25i			1.41343i
$886$	3.78970e24	−	4.45777e23i	0.335288	−	0.0394395i
$887$	−9.01867e24			−0.790300			−0.395150	−	0.918617i	$-0.629307\pi$
$887$	−9.01867e24			−0.790300			−0.395150	+	0.918617i	$0.629307\pi$
$888$	−4.93726e23	−	1.34725e24i	−0.0428524	−	0.116933i
$889$	5.58231e24			0.479898
$890$	6.36850e24	−	7.49117e23i	0.542278	−	0.0637874i
$891$			1.85257e25i			1.56248i
$892$	−5.33565e24	+	1.27286e24i	−0.445744	+	0.106336i
$893$			4.09862e24i			0.339157i
$894$	−1.65022e24	−	1.40291e25i	−0.135261	−	1.14990i
$895$	−8.96065e24			−0.727518
$896$	−3.28059e24	−	3.06332e24i	−0.263836	−	0.246362i
$897$	−1.61717e25			−1.28831
$898$	9.26467e23	+	7.87621e24i	0.0731107	+	0.621539i
$899$			1.75493e22i			0.00137184i
$900$	−1.38594e25	+	3.30628e24i	−1.07321	+	0.256022i
$901$		−	1.46658e25i		−	1.12498i
$902$	2.50611e25	−	2.94790e24i	1.90434	−	0.224005i
$903$	−9.19393e24			−0.692078
$904$	−7.79292e24	−	2.12648e25i	−0.581124	−	1.58573i
$905$	−7.73377e24			−0.571318
$906$	6.28723e24	−	7.39558e23i	0.460118	−	0.0541231i
$907$		−	1.92455e25i		−	1.39530i	−0.716440	−	0.697648i	$-0.754230\pi$
$907$		−	1.92455e25i		−	1.39530i	0.716440	−	0.697648i	$-0.245770\pi$
$908$	1.62874e24	+	6.82746e24i	0.116983	+	0.490376i
$909$			3.80767e24i			0.270936i
$910$	1.35739e24	+	1.15397e25i	0.0956873	+	0.813470i
$911$	−4.68353e24			−0.327090			−0.163545	−	0.986536i	$-0.552293\pi$
$911$	−4.68353e24			−0.327090			−0.163545	+	0.986536i	$0.552293\pi$
$912$	−6.78843e24	+	3.43431e24i	−0.469692	+	0.237621i
$913$	2.51312e25			1.72271
$914$	−7.65765e23	−	6.51002e24i	−0.0520059	−	0.442120i
$915$		−	5.38428e25i		−	3.62283i
$916$	4.86304e24	+	2.03851e25i	0.324187	+	1.35895i
$917$		−	4.13020e24i		−	0.272792i
$918$	−4.58842e23	+	5.39729e22i	−0.0300262	+	0.00353194i
$919$	5.15384e24			0.334156			0.167078	−	0.985944i	$-0.446567\pi$
$919$	5.15384e24			0.334156			0.167078	+	0.985944i	$0.446567\pi$
$920$	1.25083e25	−	4.58394e24i	0.803533	−	0.294471i
$921$	−2.00078e25			−1.27348
$922$	−1.88243e25	+	2.21427e24i	−1.18715	+	0.139643i
$923$			4.34454e24i			0.271474i
$924$	1.22717e25	−	2.92751e24i	0.759789	−	0.181254i
$925$		−	1.61823e24i		−	0.0992739i
$926$	3.43208e24	+	2.91773e25i	0.208624	+	1.77358i
$927$	−7.27713e23			−0.0438311
$928$	1.49916e24	−	9.93926e23i	0.0894725	−	0.0593194i
$929$	1.88112e25			1.11246			0.556228	−	0.831030i	$-0.312248\pi$
$929$	1.88112e25			1.11246			0.556228	+	0.831030i	$0.312248\pi$
$930$	−5.22649e22	−	4.44321e23i	−0.00306270	−	0.0260371i
$931$			5.59868e24i			0.325097i
$932$	2.01929e25	−	4.81719e24i	1.16189	−	0.277178i
$933$		−	4.00670e24i		−	0.228451i
$934$	−2.22908e25	+	2.62204e24i	−1.25944	+	0.148146i
$935$	−5.02519e25			−2.81354
$936$	2.59072e25	−	9.49422e24i	1.43739	−	0.526762i
$937$	−2.64879e25			−1.45633			−0.728166	−	0.685401i	$-0.759627\pi$
$937$	−2.64879e25			−1.45633			−0.728166	+	0.685401i	$0.759627\pi$
$938$	−3.53980e24	+	4.16382e23i	−0.192866	+	0.0226865i
$939$			4.07954e25i			2.20269i
$940$	5.73245e24	+	2.40296e25i	0.306728	+	1.28576i
$941$			2.10548e25i			1.11645i	0.829690	+	0.558224i	$0.188517\pi$
$941$			2.10548e25i			1.11645i	−0.829690	+	0.558224i	$0.811483\pi$
$942$	2.16720e24	+	1.84241e25i	0.113885	+	0.968175i
$943$	1.40747e25			0.732978
$944$	6.02626e24	+	1.19118e25i	0.311018	+	0.614773i
$945$	2.47348e23			0.0126514
$946$	−4.82181e24	−	4.09918e25i	−0.244419	−	2.07789i
$947$		−	4.55382e24i		−	0.228771i	−0.993436	−	0.114385i	$-0.963510\pi$
$947$		−	4.55382e24i		−	0.228771i	0.993436	−	0.114385i	$-0.0364899\pi$
$948$	−6.58703e24	−	2.76119e25i	−0.327958	−	1.37475i
$949$			2.93864e24i			0.145005i
$950$	−8.52116e24	+	1.00233e24i	−0.416723	+	0.0490186i
$951$	1.78191e25			0.863677
$952$	3.24949e24	+	8.86698e24i	0.156099	+	0.425953i
$953$	2.89554e25			1.37860			0.689302	−	0.724474i	$-0.257917\pi$
$953$	2.89554e25			1.37860			0.689302	+	0.724474i	$0.257917\pi$
$954$	1.85178e25	−	2.17822e24i	0.873833	−	0.102788i
$955$			1.90562e25i			0.891265i
$956$	−1.14092e25	+	2.72176e24i	−0.528888	+	0.126171i
$957$			5.05579e24i			0.232294i
$958$	−4.05329e24	−	3.44583e25i	−0.184587	−	1.56923i
$959$	5.70725e24			0.257614
$960$	−3.49962e25	+	2.96293e25i	−1.56572	+	1.32561i
$961$	−2.25464e25			−0.999837
$962$	3.66091e23	+	3.11226e24i	0.0160917	+	0.136801i
$963$			4.25819e25i			1.85525i
$964$	−1.54494e24	+	3.68559e23i	−0.0667203	+	0.0159167i
$965$		−	2.78947e25i		−	1.19409i
$966$	6.98869e24	−	8.22070e23i	0.296545	−	0.0348821i
$967$	−2.54959e25			−1.07237			−0.536186	−	0.844100i	$-0.680136\pi$
$967$	−2.54959e25			−1.07237			−0.536186	+	0.844100i	$0.680136\pi$
$968$	1.12355e25	+	3.06586e25i	0.468436	+	1.27824i
$969$	1.60066e25			0.661524
$970$	6.11960e23	−	7.19840e22i	0.0250705	−	0.00294901i
$971$		−	4.33990e25i		−	1.76245i	−0.472699	−	0.881224i	$-0.656720\pi$
$971$		−	4.33990e25i		−	1.76245i	0.472699	−	0.881224i	$-0.343280\pi$
$972$	−8.11454e24	−	3.40149e25i	−0.326663	−	1.36932i
$973$		−	4.46257e24i		−	0.178085i
$974$	−7.50644e23	−	6.38147e24i	−0.0296950	−	0.252447i
$975$	6.27771e25			2.46185
$976$	−2.05060e25	−	4.05332e25i	−0.797183	−	1.57575i
$977$	−3.34009e25			−1.28723			−0.643613	−	0.765352i	$-0.722565\pi$
$977$	−3.34009e25			−1.28723			−0.643613	+	0.765352i	$0.722565\pi$
$978$	3.51831e24	+	2.99103e25i	0.134417	+	1.14272i
$979$			1.52061e25i			0.575922i
$980$	7.83048e24	+	3.28242e25i	0.294013	+	1.23246i
$981$		−	2.54314e25i		−	0.946638i
$982$	1.00603e25	−	1.18337e24i	0.371246	−	0.0436691i
$983$	−4.27909e25			−1.56548			−0.782738	−	0.622351i	$-0.786177\pi$
$983$	−4.27909e25			−1.56548			−0.782738	+	0.622351i	$0.786177\pi$
$984$	−4.54876e25	+	1.66699e25i	−1.64981	+	0.604608i
$985$	5.72437e25			2.05835
$986$	−3.75856e24	+	4.42114e23i	−0.133989	+	0.0157609i
$987$			1.30491e25i			0.461196i
$988$	1.61616e25	−	3.85548e24i	0.566305	−	0.135097i
$989$		−	2.30217e25i		−	0.799776i
$990$	−7.46363e24	−	6.34508e25i	−0.257070	−	2.18544i
$991$	4.65952e25			1.59117			0.795583	−	0.605845i	$-0.207165\pi$
$991$	4.65952e25			1.59117			0.795583	+	0.605845i	$0.207165\pi$
$992$	−2.08565e23	−	3.14583e23i	−0.00706143	−	0.0106509i
$993$	2.18873e25			0.734723
$994$	−2.20850e23	−	1.87752e24i	−0.00735043	−	0.0624884i
$995$			8.61786e23i			0.0284383i
$996$	−4.69319e25	+	1.11960e25i	−1.53555	+	0.366317i
$997$		−	2.19776e25i		−	0.712971i	−0.934301	−	0.356485i	$-0.883975\pi$
$997$		−	2.19776e25i		−	0.712971i	0.934301	−	0.356485i	$-0.116025\pi$
$998$	−1.05425e25	+	1.24010e24i	−0.339106	+	0.0398886i
$999$	6.67101e22			0.00212758

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8.18.b.a.5.10	yes	16
3.2	odd	2		72.18.d.b.37.7		16
4.3	odd	2		32.18.b.a.17.15		16
8.3	odd	2		32.18.b.a.17.2		16
8.5	even	2	inner	8.18.b.a.5.9	✓	16
24.5	odd	2		72.18.d.b.37.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8.18.b.a.5.9	✓	16	8.5	even	2	inner
8.18.b.a.5.10	yes	16	1.1	even	1	trivial
32.18.b.a.17.2		16	8.3	odd	2
32.18.b.a.17.15		16	4.3	odd	2
72.18.d.b.37.7		16	3.2	odd	2
72.18.d.b.37.8		16	24.5	odd	2

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 8 = 2^{3} \)
Weight:	\( k \)	\(=\)	\( 18 \)
Character orbit:	\([\chi]\)	\(=\)	8.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(42.2945 + 359.560i) q^{2} -16002.3i q^{3} +(-127494. + 30414.8i) q^{4} +1.27253e6i q^{5} +(5.75379e6 - 676810. i) q^{6} +5.50569e6 q^{7} +(-1.63282e7 - 4.45555e7i) q^{8} -1.26934e8 q^{9} +O(q^{10})\)	\(q+(42.2945 + 359.560i) q^{2} -16002.3i q^{3} +(-127494. + 30414.8i) q^{4} +1.27253e6i q^{5} +(5.75379e6 - 676810. i) q^{6} +5.50569e6 q^{7} +(-1.63282e7 - 4.45555e7i) q^{8} -1.26934e8 q^{9} +(-4.57551e8 + 5.38211e7i) q^{10} -1.09250e9i q^{11} +(4.86707e8 + 2.04020e9i) q^{12} -4.58081e9i q^{13} +(2.32860e8 + 1.97962e9i) q^{14} +2.03635e10 q^{15} +(1.53297e10 - 7.75543e9i) q^{16} -3.61463e10 q^{17} +(-5.36861e9 - 4.56403e10i) q^{18} -2.76727e10i q^{19} +(-3.87038e10 - 1.62241e11i) q^{20} -8.81037e10i q^{21} +(3.92817e11 - 4.62066e10i) q^{22} +2.20613e11 q^{23} +(-7.12990e11 + 2.61290e11i) q^{24} -8.56399e11 q^{25} +(1.64707e12 - 1.93743e11i) q^{26} -3.53044e10i q^{27} +(-7.01944e11 + 1.67454e11i) q^{28} -2.89192e11i q^{29} +(8.61263e11 + 7.32188e12i) q^{30} -6.06840e10 q^{31} +(3.43690e12 + 5.18395e12i) q^{32} -1.74825e13 q^{33} +(-1.52879e12 - 1.29967e13i) q^{34} +7.00616e12i q^{35} +(1.61834e13 - 3.86067e12i) q^{36} +1.88957e12i q^{37} +(9.94998e12 - 1.17040e12i) q^{38} -7.33035e13 q^{39} +(5.66983e13 - 2.07782e13i) q^{40} +6.37984e13 q^{41} +(3.16786e13 - 3.72630e12i) q^{42} -1.04353e14i q^{43} +(3.32280e13 + 1.39287e14i) q^{44} -1.61528e14i q^{45} +(9.33070e12 + 7.93234e13i) q^{46} -1.48111e14 q^{47} +(-1.24105e14 - 2.45311e14i) q^{48} -2.02318e14 q^{49} +(-3.62210e13 - 3.07927e14i) q^{50} +5.78424e14i q^{51} +(1.39324e14 + 5.84027e14i) q^{52} +4.05734e14i q^{53} +(1.26940e13 - 1.49318e12i) q^{54} +1.39024e15 q^{55} +(-8.98982e13 - 2.45308e14i) q^{56} -4.42827e14 q^{57} +(1.03982e14 - 1.22312e13i) q^{58} +7.77037e14i q^{59} +(-2.59623e15 + 6.19351e14i) q^{60} -2.64409e15i q^{61} +(-2.56660e12 - 2.18195e13i) q^{62} -6.98859e14 q^{63} +(-1.71858e15 + 1.45502e15i) q^{64} +5.82922e15 q^{65} +(-7.39412e14 - 6.28599e15i) q^{66} +1.78812e15i q^{67} +(4.60845e15 - 1.09938e15i) q^{68} -3.53031e15i q^{69} +(-2.51913e15 + 2.96322e14i) q^{70} -9.48422e14 q^{71} +(2.07261e15 + 5.65560e15i) q^{72} -6.41511e14 q^{73} +(-6.79414e14 + 7.99185e13i) q^{74} +1.37044e16i q^{75} +(8.41659e14 + 3.52811e15i) q^{76} -6.01494e15i q^{77} +(-3.10034e15 - 2.63570e16i) q^{78} -1.35339e16 q^{79} +(9.86904e15 + 1.95076e16i) q^{80} -1.69572e16 q^{81} +(2.69832e15 + 2.29393e16i) q^{82} +2.30035e16i q^{83} +(2.67966e15 + 1.12327e16i) q^{84} -4.59973e16i q^{85} +(3.75213e16 - 4.41358e15i) q^{86} -4.62775e15 q^{87} +(-4.86766e16 + 1.78385e16i) q^{88} -1.39186e16 q^{89} +(5.80788e16 - 6.83173e15i) q^{90} -2.52205e16i q^{91} +(-2.81269e16 + 6.70989e15i) q^{92} +9.71085e14i q^{93} +(-6.26427e15 - 5.32547e16i) q^{94} +3.52144e16 q^{95} +(8.29552e16 - 5.49984e16i) q^{96} -1.33747e15 q^{97} +(-8.55694e15 - 7.27454e16i) q^{98} +1.38675e17i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 270 q^{2} - 27436 q^{4} + 5839948 q^{6} + 11529600 q^{7} + 24334920 q^{8} - 602654096 q^{9}+O(q^{10}) \) 16 * q + 270 * q^2 - 27436 * q^4 + 5839948 * q^6 + 11529600 * q^7 + 24334920 * q^8 - 602654096 * q^9	\( 16 q + 270 q^{2} - 27436 q^{4} + 5839948 q^{6} + 11529600 q^{7} + 24334920 q^{8} - 602654096 q^{9} + 131002712 q^{10} - 2795125400 q^{12} + 16363788528 q^{14} - 9993282176 q^{15} + 26500434192 q^{16} - 7489125600 q^{17} - 113450563870 q^{18} - 209445719856 q^{20} + 223126527100 q^{22} + 746845345920 q^{23} - 1099415493232 q^{24} - 1809682431664 q^{25} + 2467726531080 q^{26} + 3220542267040 q^{28} - 1188624268048 q^{30} - 318979758592 q^{31} + 1455647316000 q^{32} + 5633526177600 q^{33} - 4461251980292 q^{34} - 33088278002484 q^{36} + 24076283913900 q^{38} - 18457706051456 q^{39} + 60626292962592 q^{40} + 7482251536032 q^{41} - 51630378688160 q^{42} + 193654716236040 q^{44} - 195097141003568 q^{46} - 376698804821760 q^{47} - 329350060416480 q^{48} + 127691292101520 q^{49} + 474997408872102 q^{50} - 272251877663120 q^{52} + 735354219382520 q^{54} + 22\!\cdots\!52 q^{55}+ \cdots + 33\!\cdots\!90 q^{98}+O(q^{100}) \) 16 * q + 270 * q^2 - 27436 * q^4 + 5839948 * q^6 + 11529600 * q^7 + 24334920 * q^8 - 602654096 * q^9 + 131002712 * q^10 - 2795125400 * q^12 + 16363788528 * q^14 - 9993282176 * q^15 + 26500434192 * q^16 - 7489125600 * q^17 - 113450563870 * q^18 - 209445719856 * q^20 + 223126527100 * q^22 + 746845345920 * q^23 - 1099415493232 * q^24 - 1809682431664 * q^25 + 2467726531080 * q^26 + 3220542267040 * q^28 - 1188624268048 * q^30 - 318979758592 * q^31 + 1455647316000 * q^32 + 5633526177600 * q^33 - 4461251980292 * q^34 - 33088278002484 * q^36 + 24076283913900 * q^38 - 18457706051456 * q^39 + 60626292962592 * q^40 + 7482251536032 * q^41 - 51630378688160 * q^42 + 193654716236040 * q^44 - 195097141003568 * q^46 - 376698804821760 * q^47 - 329350060416480 * q^48 + 127691292101520 * q^49 + 474997408872102 * q^50 - 272251877663120 * q^52 + 735354219382520 * q^54 + 2209036687713152 * q^55 - 162767516076480 * q^56 - 190521298294720 * q^57 - 623262610679960 * q^58 - 1973616194963808 * q^60 + 695695648144320 * q^62 - 8131096607338880 * q^63 + 1111931745501248 * q^64 + 2385987975356160 * q^65 + 3598826202828312 * q^66 + 5981109959771880 * q^68 - 10044559836180288 * q^70 + 9025926285576576 * q^71 - 19918679666289160 * q^72 + 11332002046118560 * q^73 + 11098735408189464 * q^74 + 5959440926938280 * q^76 + 4184252259031760 * q^78 - 45299671392008448 * q^79 + 1337342539452480 * q^80 + 20101901999290832 * q^81 + 15639739637081420 * q^82 + 19796542864700224 * q^84 - 14252032276026564 * q^86 + 25965768920837760 * q^87 - 66964872768837680 * q^88 - 69879174608766048 * q^89 + 136151511125051240 * q^90 + 57336249810701280 * q^92 - 192318922166254176 * q^94 + 93790444358203776 * q^95 - 342799224184788928 * q^96 + 95593398602180640 * q^97 + 339641261743253790 * q^98

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