LMFDB - Embedded newform 12.22.b.a.11.22

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [12,22,Mod(11,12)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(12, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 22, names="a")

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

chi := DirichletCharacter("12.11");

S:= CuspForms(chi, 22);

N := Newforms(S);

Level:	$ N $	$=$	$ 12 = 2^{2} \cdot 3 $
Weight:	$ k $	$=$	$ 22 $
Character orbit:	$[\chi]$	$=$	12.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:	$33.5372813144$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			11.22
Character	$\chi$	$=$	12.11
Dual form			12.22.b.a.11.21

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(219.802 + 1431.38i) q^{2} +(101700. - 10835.4i) q^{3} +(-2.00053e6 + 629239. i) q^{4} +7.08257e6i q^{5} +(3.78635e7 + 1.43190e8i) q^{6} -8.25046e8i q^{7} +(-1.34040e9 - 2.72520e9i) q^{8} +(1.02255e10 - 2.20393e9i) q^{9} +O(q^{10})$	\(q+(219.802 + 1431.38i) q^{2} +(101700. - 10835.4i) q^{3} +(-2.00053e6 + 629239. i) q^{4} +7.08257e6i q^{5} +(3.78635e7 + 1.43190e8i) q^{6} -8.25046e8i q^{7} +(-1.34040e9 - 2.72520e9i) q^{8} +(1.02255e10 - 2.20393e9i) q^{9} +(-1.01378e10 + 1.55676e9i) q^{10} -5.64925e10 q^{11} +(-1.96636e11 + 8.56703e10i) q^{12} +7.77040e11 q^{13} +(1.18095e12 - 1.81347e11i) q^{14} +(7.67425e10 + 7.20299e11i) q^{15} +(3.60616e12 - 2.51762e12i) q^{16} +2.14638e12i q^{17} +(5.40224e12 + 1.41522e13i) q^{18} -3.98877e13i q^{19} +(-4.45663e12 - 1.41689e13i) q^{20} +(-8.93970e12 - 8.39074e13i) q^{21} +(-1.24172e13 - 8.08620e13i) q^{22} +1.55135e13 q^{23} +(-1.65847e14 - 2.62630e14i) q^{24} +4.26674e14 q^{25} +(1.70795e14 + 1.11224e15i) q^{26} +(1.01606e15 - 3.34938e14i) q^{27} +(5.19151e14 + 1.65053e15i) q^{28} -2.71758e15i q^{29} +(-1.01415e15 + 2.68171e14i) q^{30} +4.65708e15i q^{31} +(4.39630e15 + 4.60840e15i) q^{32} +(-5.74530e15 + 6.12119e14i) q^{33} +(-3.07228e15 + 4.71778e14i) q^{34} +5.84344e15 q^{35} +(-1.90697e16 + 1.08433e16i) q^{36} +9.19330e15 q^{37} +(5.70943e16 - 8.76739e15i) q^{38} +(7.90251e16 - 8.41954e15i) q^{39} +(1.93014e16 - 9.49346e15i) q^{40} +1.28399e17i q^{41} +(1.18138e17 - 3.12391e16i) q^{42} -6.02134e16i q^{43} +(1.13015e17 - 3.55473e16i) q^{44} +(1.56095e16 + 7.24231e16i) q^{45} +(3.40990e15 + 2.22057e16i) q^{46} +3.86477e17 q^{47} +(3.39468e17 - 2.95117e17i) q^{48} -1.22154e17 q^{49} +(9.37839e16 + 6.10732e17i) q^{50} +(2.32569e16 + 2.18287e17i) q^{51} +(-1.55449e18 + 4.88944e17i) q^{52} +2.81921e17i q^{53} +(7.02754e17 + 1.38074e18i) q^{54} -4.00112e17i q^{55} +(-2.24841e18 + 1.10589e18i) q^{56} +(-4.32199e17 - 4.05659e18i) q^{57} +(3.88988e18 - 5.97329e17i) q^{58} -2.59839e18 q^{59} +(-6.06766e17 - 1.39269e18i) q^{60} +4.21506e18 q^{61} +(-6.66604e18 + 1.02364e18i) q^{62} +(-1.81834e18 - 8.43654e18i) q^{63} +(-5.63004e18 + 7.30570e18i) q^{64} +5.50344e18i q^{65} +(-2.13900e18 - 8.08914e18i) q^{66} -2.12230e19i q^{67} +(-1.35059e18 - 4.29389e18i) q^{68} +(1.57773e18 - 1.68095e17i) q^{69} +(1.28440e18 + 8.36417e18i) q^{70} -3.77073e19 q^{71} +(-1.97124e19 - 2.49125e19i) q^{72} -1.72492e19 q^{73} +(2.02071e18 + 1.31591e19i) q^{74} +(4.33929e19 - 4.62319e18i) q^{75} +(2.50989e19 + 7.97963e19i) q^{76} +4.66089e19i q^{77} +(2.94214e19 + 1.11264e20i) q^{78} -1.33642e20i q^{79} +(1.78312e19 + 2.55409e19i) q^{80} +(9.97044e19 - 4.50727e19i) q^{81} +(-1.83787e20 + 2.82224e19i) q^{82} +2.52005e20 q^{83} +(7.06819e19 + 1.62234e20i) q^{84} -1.52019e19 q^{85} +(8.61881e19 - 1.32350e19i) q^{86} +(-2.94461e19 - 2.76378e20i) q^{87} +(7.57224e19 + 1.53953e20i) q^{88} -3.01861e20i q^{89} +(-1.00234e20 + 3.82618e19i) q^{90} -6.41093e20i q^{91} +(-3.10352e19 + 9.76170e18i) q^{92} +(5.04613e19 + 4.73626e20i) q^{93} +(8.49483e19 + 5.53193e20i) q^{94} +2.82507e20 q^{95} +(4.97039e20 + 4.21040e20i) q^{96} +1.34306e20 q^{97} +(-2.68498e19 - 1.74849e20i) q^{98} +(-5.77666e20 + 1.24505e20i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 1212040 q^{4} - 73477608 q^{6} + 4862757768 q^{9}+O(q^{10}) $ 40 * q + 1212040 * q^4 - 73477608 * q^6 + 4862757768 * q^9	$ 40 q + 1212040 q^{4} - 73477608 q^{6} + 4862757768 q^{9} + 70993722608 q^{10} + 230311800264 q^{12} + 532697931824 q^{13} - 3296861950688 q^{16} - 38138435545488 q^{18} + 6345498814320 q^{21} + 345245332418448 q^{22} + 162733136355360 q^{24} - 28\!\cdots\!08 q^{25}+ \cdots + 19\!\cdots\!68 q^{97}+O(q^{100}) $ 40 * q + 1212040 * q^4 - 73477608 * q^6 + 4862757768 * q^9 + 70993722608 * q^10 + 230311800264 * q^12 + 532697931824 * q^13 - 3296861950688 * q^16 - 38138435545488 * q^18 + 6345498814320 * q^21 + 345245332418448 * q^22 + 162733136355360 * q^24 - 2870634573953208 * q^25 + 3010485857135664 * q^28 + 5225832293639088 * q^30 - 7282205643351936 * q^33 - 11653770049992256 * q^34 - 18580578856893912 * q^36 - 42230886115147792 * q^37 - 89660451263290816 * q^40 - 196777060056297264 * q^42 + 490656937607621376 * q^45 - 24590270471085024 * q^46 - 1070121602451491040 * q^48 - 1521600851011396808 * q^49 + 1474695233111072240 * q^52 - 107978656785090264 * q^54 - 410005705945522032 * q^57 + 9260173307858336144 * q^58 + 6491621502020133696 * q^60 - 5700218795673195856 * q^61 - 2949437838551773568 * q^64 + 1836224451373338192 * q^66 + 25444406037298107648 * q^69 - 24886444039106795232 * q^70 - 27969226308253542336 * q^72 + 101891967257574779024 * q^73 + 22386121373924673552 * q^76 + 76385487692811283152 * q^78 - 476218176140556806040 * q^81 + 1864686882869863520 * q^82 + 311685180307346738352 * q^84 - 605170615993311678464 * q^85 + 15063645347500158144 * q^88 - 159737520743388593232 * q^90 + 682248293569820157360 * q^93 + 242051617770611035200 * q^94 - 1187951481218430818688 * q^96 + 196191301644672463568 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/12\mathbb{Z}\right)^\times$.

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

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 $

$2$	219.802	+	1431.38i	0.151781	+	0.988414i
$2$	219.802	+	1431.38i	0.151781	+	0.988414i
$3$	101700.	−	10835.4i	0.994372	−	0.105943i
$3$	101700.	−	10835.4i	0.994372	−	0.105943i
$4$	−2.00053e6	+	629239.i	−0.953925	+	0.300045i
$5$			7.08257e6i			0.324344i	0.986763	+	0.162172i	$0.0518499\pi$
$5$			7.08257e6i			0.324344i	−0.986763	+	0.162172i	$0.948150\pi$
$6$	3.78635e7	+	1.43190e8i	0.255642	+	0.966772i
$7$		−	8.25046e8i		−	1.10395i	−0.833861	−	0.551974i	$-0.813875\pi$
$7$		−	8.25046e8i		−	1.10395i	0.833861	−	0.551974i	$-0.186125\pi$
$8$	−1.34040e9	−	2.72520e9i	−0.441356	−	0.897332i
$9$	1.02255e10	−	2.20393e9i	0.977552	−	0.210693i
$10$	−1.01378e10	+	1.55676e9i	−0.320586	+	0.0492292i
$11$	−5.64925e10			−0.656700			−0.328350	−	0.944556i	$-0.606493\pi$
$11$	−5.64925e10			−0.656700			−0.328350	+	0.944556i	$0.606493\pi$
$12$	−1.96636e11	+	8.56703e10i	−0.916769	+	0.399418i
$13$	7.77040e11			1.56328			0.781642	−	0.623727i	$-0.214382\pi$
$13$	7.77040e11			1.56328			0.781642	+	0.623727i	$0.214382\pi$
$14$	1.18095e12	−	1.81347e11i	1.09116	−	0.167558i
$15$	7.67425e10	+	7.20299e11i	0.0343619	+	0.322519i
$16$	3.60616e12	−	2.51762e12i	0.819947	−	0.572440i
$17$			2.14638e12i			0.258222i	0.991630	+	0.129111i	$0.0412123\pi$
$17$			2.14638e12i			0.258222i	−0.991630	+	0.129111i	$0.958788\pi$
$18$	5.40224e12	+	1.41522e13i	0.356626	+	0.934247i
$19$		−	3.98877e13i		−	1.49254i	−0.665644	−	0.746270i	$-0.731843\pi$
$19$		−	3.98877e13i		−	1.49254i	0.665644	−	0.746270i	$-0.268157\pi$
$20$	−4.45663e12	−	1.41689e13i	−0.0973176	−	0.309400i
$21$	−8.93970e12	−	8.39074e13i	−0.116955	−	1.09774i
$22$	−1.24172e13	−	8.08620e13i	−0.0996745	−	0.649092i
$23$	1.55135e13			0.0780850			0.0390425	−	0.999238i	$-0.487569\pi$
$23$	1.55135e13			0.0780850			0.0390425	+	0.999238i	$0.487569\pi$
$24$	−1.65847e14	−	2.62630e14i	−0.533938	−	0.845524i
$25$	4.26674e14			0.894801
$26$	1.70795e14	+	1.11224e15i	0.237276	+	1.54517i
$27$	1.01606e15	−	3.34938e14i	0.949729	−	0.313072i
$28$	5.19151e14	+	1.65053e15i	0.331233	+	1.05308i
$29$		−	2.71758e15i		−	1.19951i	−0.800185	−	0.599754i	$-0.795265\pi$
$29$		−	2.71758e15i		−	1.19951i	0.800185	−	0.599754i	$-0.204735\pi$
$30$	−1.01415e15	+	2.68171e14i	−0.313566	+	0.0829160i
$31$			4.65708e15i			1.02051i	0.860024	+	0.510253i	$0.170448\pi$
$31$			4.65708e15i			1.02051i	−0.860024	+	0.510253i	$0.829552\pi$
$32$	4.39630e15	+	4.60840e15i	0.690260	+	0.723561i
$33$	−5.74530e15	+	6.12119e14i	−0.653005	+	0.0695728i
$34$	−3.07228e15	+	4.71778e14i	−0.255230	+	0.0391931i
$35$	5.84344e15			0.358059
$36$	−1.90697e16	+	1.08433e16i	−0.869294	+	0.494295i
$37$	9.19330e15			0.314307			0.157153	−	0.987574i	$-0.449768\pi$
$37$	9.19330e15			0.314307			0.157153	+	0.987574i	$0.449768\pi$
$38$	5.70943e16	−	8.76739e15i	1.47525	−	0.226539i
$39$	7.90251e16	−	8.41954e15i	1.55449	−	0.165619i
$40$	1.93014e16	−	9.49346e15i	0.291044	−	0.143151i
$41$			1.28399e17i			1.49393i	0.664862	+	0.746967i	$0.268491\pi$
$41$			1.28399e17i			1.49393i	−0.664862	+	0.746967i	$0.731509\pi$
$42$	1.18138e17	−	3.12391e16i	1.06727	−	0.282216i
$43$		−	6.02134e16i		−	0.424888i	−0.977173	−	0.212444i	$-0.931858\pi$
$43$		−	6.02134e16i		−	0.424888i	0.977173	−	0.212444i	$-0.0681423\pi$
$44$	1.13015e17	−	3.55473e16i	0.626443	−	0.197039i
$45$	1.56095e16	+	7.24231e16i	0.0683371	+	0.317063i
$46$	3.40990e15	+	2.22057e16i	0.0118518	+	0.0771803i
$47$	3.86477e17			1.07176			0.535878	−	0.844296i	$-0.319981\pi$
$47$	3.86477e17			1.07176			0.535878	+	0.844296i	$0.319981\pi$
$48$	3.39468e17	−	2.95117e17i	0.754686	−	0.656086i
$49$	−1.22154e17			−0.218701
$50$	9.37839e16	+	6.10732e17i	0.135814	+	0.884434i
$51$	2.32569e16	+	2.18287e17i	0.0273568	+	0.256768i
$52$	−1.55449e18	+	4.88944e17i	−1.49126	+	0.469055i
$53$			2.81921e17i			0.221427i	0.993852	+	0.110714i	$0.0353136\pi$
$53$			2.81921e17i			0.221427i	−0.993852	+	0.110714i	$0.964686\pi$
$54$	7.02754e17	+	1.38074e18i	0.453596	+	0.891208i
$55$		−	4.00112e17i		−	0.212997i
$56$	−2.24841e18	+	1.10589e18i	−0.990608	+	0.487234i
$57$	−4.32199e17	−	4.05659e18i	−0.158124	−	1.48414i
$58$	3.88988e18	−	5.97329e17i	1.18561	−	0.182062i
$59$	−2.59839e18			−0.661849			−0.330924	−	0.943657i	$-0.607360\pi$
$59$	−2.59839e18			−0.661849			−0.330924	+	0.943657i	$0.607360\pi$
$60$	−6.06766e17	−	1.39269e18i	−0.129549	−	0.297349i
$61$	4.21506e18			0.756555			0.378278	−	0.925692i	$-0.376517\pi$
$61$	4.21506e18			0.756555			0.378278	+	0.925692i	$0.376517\pi$
$62$	−6.66604e18	+	1.02364e18i	−1.00868	+	0.154893i
$63$	−1.81834e18	−	8.43654e18i	−0.232595	−	1.07917i
$64$	−5.63004e18	+	7.30570e18i	−0.610410	+	0.792085i
$65$			5.50344e18i			0.507042i
$66$	−2.13900e18	−	8.08914e18i	−0.167880	−	0.634879i
$67$		−	2.12230e19i		−	1.42240i	−0.702989	−	0.711200i	$-0.748152\pi$
$67$		−	2.12230e19i		−	1.42240i	0.702989	−	0.711200i	$-0.251848\pi$
$68$	−1.35059e18	−	4.29389e18i	−0.0774780	−	0.246324i
$69$	1.57773e18	−	1.68095e17i	0.0776455	−	0.00827255i
$70$	1.28440e18	+	8.36417e18i	0.0543464	+	0.353910i
$71$	−3.77073e19			−1.37472			−0.687358	−	0.726318i	$-0.741230\pi$
$71$	−3.77073e19			−1.37472			−0.687358	+	0.726318i	$0.741230\pi$
$72$	−1.97124e19	−	2.49125e19i	−0.620510	−	0.784198i
$73$	−1.72492e19			−0.469763			−0.234881	−	0.972024i	$-0.575470\pi$
$73$	−1.72492e19			−0.469763			−0.234881	+	0.972024i	$0.575470\pi$
$74$	2.02071e18	+	1.31591e19i	0.0477057	+	0.310665i
$75$	4.33929e19	−	4.62319e18i	0.889765	−	0.0947978i
$76$	2.50989e19	+	7.97963e19i	0.447828	+	1.42377i
$77$			4.66089e19i			0.724963i
$78$	2.94214e19	+	1.11264e20i	0.399641	+	1.51134i
$79$		−	1.33642e20i		−	1.58803i	−0.607898	−	0.794015i	$-0.707987\pi$
$79$		−	1.33642e20i		−	1.58803i	0.607898	−	0.794015i	$-0.292013\pi$
$80$	1.78312e19	+	2.55409e19i	0.185667	+	0.265945i
$81$	9.97044e19	−	4.50727e19i	0.911217	−	0.411928i
$82$	−1.83787e20	+	2.82224e19i	−1.47662	+	0.226750i
$83$	2.52005e20			1.78275			0.891373	−	0.453271i	$-0.149743\pi$
$83$	2.52005e20			1.78275			0.891373	+	0.453271i	$0.149743\pi$
$84$	7.06819e19	+	1.62234e20i	0.440936	+	1.01207i
$85$	−1.52019e19			−0.0837526
$86$	8.61881e19	−	1.32350e19i	0.419966	−	0.0644899i
$87$	−2.94461e19	−	2.76378e20i	−0.127079	−	1.19276i
$88$	7.57224e19	+	1.53953e20i	0.289838	+	0.589278i
$89$		−	3.01861e20i		−	1.02615i	−0.858343	−	0.513076i	$-0.828506\pi$
$89$		−	3.01861e20i		−	1.02615i	0.858343	−	0.513076i	$-0.171494\pi$
$90$	−1.00234e20	+	3.82618e19i	−0.303017	+	0.115669i
$91$		−	6.41093e20i		−	1.72578i
$92$	−3.10352e19	+	9.76170e18i	−0.0744872	+	0.0234290i
$93$	5.04613e19	+	4.73626e20i	0.108115	+	1.01476i
$94$	8.49483e19	+	5.53193e20i	0.162672	+	1.05934i
$95$	2.82507e20			0.484096
$96$	4.97039e20	+	4.21040e20i	0.763032	+	0.646361i
$97$	1.34306e20			0.184924			0.0924620	−	0.995716i	$-0.470526\pi$
$97$	1.34306e20			0.184924			0.0924620	+	0.995716i	$0.470526\pi$
$98$	−2.68498e19	−	1.74849e20i	−0.0331946	−	0.216167i
$99$	−5.77666e20	+	1.24505e20i	−0.641959	+	0.138362i
$100$	−8.53573e20	+	2.68480e20i	−0.853573	+	0.268480i
$101$			3.90163e20i			0.351457i	0.984439	+	0.175728i	$0.0562280\pi$
$101$			3.90163e20i			0.351457i	−0.984439	+	0.175728i	$0.943772\pi$
$102$	−3.07340e20	+	8.12694e19i	−0.249641	+	0.0660123i
$103$		−	3.18006e20i		−	0.233155i	−0.993182	−	0.116578i	$-0.962808\pi$
$103$		−	3.18006e20i		−	0.233155i	0.993182	−	0.116578i	$-0.0371923\pi$
$104$	−1.04154e21	−	2.11759e21i	−0.689964	−	1.40279i
$105$	5.94280e20	−	6.33161e19i	0.356044	−	0.0379338i
$106$	−4.03535e20	+	6.19668e19i	−0.218862	+	0.0336084i
$107$	−2.80906e21			−1.38048			−0.690241	−	0.723579i	$-0.742496\pi$
$107$	−2.80906e21			−1.38048			−0.690241	+	0.723579i	$0.742496\pi$
$108$	−1.82190e21	+	1.30940e21i	−0.812035	+	0.583609i
$109$	−3.01755e21			−1.22089			−0.610444	−	0.792059i	$-0.709009\pi$
$109$	−3.01755e21			−1.22089			−0.610444	+	0.792059i	$0.709009\pi$
$110$	5.72711e20	−	8.79454e19i	0.210529	−	0.0323288i
$111$	9.34962e20	−	9.96132e19i	0.312538	−	0.0332986i
$112$	−2.07715e21	−	2.97525e21i	−0.631944	−	0.905178i
$113$		−	2.48707e21i		−	0.689230i	−0.938744	−	0.344615i	$-0.888009\pi$
$113$		−	2.48707e21i		−	0.689230i	0.938744	−	0.344615i	$-0.111991\pi$
$114$	5.71151e21	−	1.51029e21i	1.44294	−	0.381556i
$115$			1.09875e20i			0.0253264i
$116$	1.71001e21	+	5.43659e21i	0.359906	+	1.14424i
$117$	7.94565e21	−	1.71254e21i	1.52819	−	0.329374i
$118$	−5.71132e20	−	3.71928e21i	−0.100456	−	0.654181i
$119$	1.77086e21			0.285063
$120$	1.86009e21	−	1.17463e21i	0.274240	−	0.173180i
$121$	−4.20885e21			−0.568745
$122$	9.26479e20	+	6.03334e21i	0.114830	+	0.747790i
$123$	1.39126e21	+	1.30582e22i	0.158272	+	1.48553i
$124$	−2.93042e21	−	9.31661e21i	−0.306197	−	0.973487i
$125$			6.39918e21i			0.614567i
$126$	1.16762e22	−	4.45710e21i	1.03136	−	0.393696i
$127$			1.61658e22i			1.31419i	0.753806	+	0.657097i	$0.228216\pi$
$127$			1.61658e22i			1.31419i	−0.753806	+	0.657097i	$0.771784\pi$
$128$	−1.16947e22	−	6.45290e21i	−0.875557	−	0.483115i
$129$	−6.52437e20	−	6.12372e21i	−0.0450139	−	0.422497i
$130$	−7.87749e21	+	1.20967e21i	−0.501167	+	0.0769592i
$131$	1.46273e22			0.858647			0.429323	−	0.903151i	$-0.358752\pi$
$131$	1.46273e22			0.858647			0.429323	+	0.903151i	$0.358752\pi$
$132$	1.11085e22	−	4.83973e21i	0.602043	−	0.262298i
$133$	−3.29092e22			−1.64769
$134$	3.03781e22	−	4.66486e21i	1.40592	−	0.215893i
$135$	2.37222e21	+	7.19632e21i	0.101543	+	0.308039i
$136$	5.84931e21	−	2.87700e21i	0.231711	−	0.113968i
$137$			4.08347e22i			1.49783i	0.662664	+	0.748917i	$0.269426\pi$
$137$			4.08347e22i			1.49783i	−0.662664	+	0.748917i	$0.730574\pi$
$138$	5.87395e20	+	2.22137e21i	0.0199618	+	0.0754903i
$139$			2.84738e22i			0.896994i	0.893784	+	0.448497i	$0.148041\pi$
$139$			2.84738e22i			0.896994i	−0.893784	+	0.448497i	$0.851959\pi$
$140$	−1.16900e22	+	3.67692e21i	−0.341561	+	0.107434i
$141$	3.93048e22	−	4.18763e21i	1.06572	−	0.113545i
$142$	−8.28815e21	−	5.39734e22i	−0.208656	−	1.35879i
$143$	−4.38969e22			−1.02661
$144$	3.13263e22	−	3.36917e22i	0.680931	−	0.732347i
$145$	1.92474e22			0.389053
$146$	−3.79141e21	−	2.46901e22i	−0.0713010	−	0.464320i
$147$	−1.24231e22	+	1.32359e21i	−0.217470	+	0.0231698i
$148$	−1.83914e22	+	5.78479e21i	−0.299825	+	0.0943060i
$149$		−	1.13609e23i		−	1.72566i	−0.505493	−	0.862830i	$-0.668690\pi$
$149$		−	1.13609e23i		−	1.72566i	0.505493	−	0.862830i	$-0.331310\pi$
$150$	1.61554e22	+	6.10954e22i	0.228749	+	0.865068i
$151$		−	1.10674e23i		−	1.46146i	−0.682666	−	0.730731i	$-0.739179\pi$
$151$		−	1.10674e23i		−	1.46146i	0.682666	−	0.730731i	$-0.260821\pi$
$152$	−1.08702e23	+	5.34653e22i	−1.33930	+	0.658741i
$153$	4.73046e21	+	2.19479e22i	0.0544056	+	0.252425i
$154$	−6.67148e22	+	1.02447e22i	−0.716564	+	0.110035i
$155$	−3.29841e22			−0.330995
$156$	−1.52794e23	+	6.65692e22i	−1.43317	+	0.624403i
$157$	−1.01622e23			−0.891336			−0.445668	−	0.895198i	$-0.647034\pi$
$157$	−1.01622e23			−0.891336			−0.445668	+	0.895198i	$0.647034\pi$
$158$	1.91292e23	−	2.93748e22i	1.56963	−	0.241032i
$159$	3.05473e21	+	2.86714e22i	0.0234586	+	0.220181i
$160$	−3.26393e22	+	3.11371e22i	−0.234683	+	0.223882i
$161$		−	1.27993e22i		−	0.0862018i
$162$	8.64312e22	+	1.32807e23i	0.545460	+	0.838137i
$163$		−	2.75185e22i		−	0.162800i	−0.996682	−	0.0814000i	$-0.974061\pi$
$163$		−	2.75185e22i		−	0.162800i	0.996682	−	0.0814000i	$-0.0259391\pi$
$164$	−8.07937e22	−	2.56866e23i	−0.448246	−	1.42510i
$165$	−4.33537e21	−	4.06915e22i	−0.0225655	−	0.211798i
$166$	5.53912e22	+	3.60714e23i	0.270586	+	1.76209i
$167$	1.29525e23			0.594062			0.297031	−	0.954868i	$-0.404004\pi$
$167$	1.29525e23			0.594062			0.297031	+	0.954868i	$0.404004\pi$
$168$	−2.16681e23	+	1.36832e23i	−0.933414	+	0.589440i
$169$	3.56726e23			1.44386
$170$	−3.34140e21	−	2.17596e22i	−0.0127120	−	0.0827823i
$171$	−8.79095e22	−	4.07873e23i	−0.314468	−	1.45904i
$172$	3.78886e22	+	1.20459e23i	0.127485	+	0.405312i
$173$			4.84401e23i			1.53363i	0.641867	+	0.766816i	$0.278160\pi$
$173$			4.84401e23i			1.53363i	−0.641867	+	0.766816i	$0.721840\pi$
$174$	3.89129e23	−	1.02897e23i	1.15965	−	0.306645i
$175$		−	3.52026e23i		−	0.987814i
$176$	−2.03721e23	+	1.42226e23i	−0.538459	+	0.375922i
$177$	−2.64257e23	+	2.81546e22i	−0.658124	+	0.0701182i
$178$	4.32076e23	−	6.63496e22i	1.01426	−	0.155750i
$179$	5.07130e23			1.12244			0.561219	−	0.827667i	$-0.310332\pi$
$179$	5.07130e23			1.12244			0.561219	+	0.827667i	$0.310332\pi$
$180$	−7.67986e22	−	1.35062e23i	−0.160322	−	0.281950i
$181$	−1.30045e23			−0.256135			−0.128068	−	0.991765i	$-0.540877\pi$
$181$	−1.30045e23			−0.256135			−0.128068	+	0.991765i	$0.540877\pi$
$182$	9.17646e23	−	1.40914e23i	1.70579	−	0.261941i
$183$	4.28673e23	−	4.56719e22i	0.752297	−	0.0801517i
$184$	−2.07943e22	−	4.22774e22i	−0.0344633	−	0.0700682i
$185$			6.51122e22i			0.101943i
$186$	−6.66846e23	+	1.76333e23i	−0.986597	+	0.260884i
$187$		−	1.21254e23i		−	0.169574i
$188$	−7.73156e23	+	2.43186e23i	−1.02237	+	0.321574i
$189$	−2.76339e23	−	8.38296e23i	−0.345616	−	1.04845i
$190$	6.20957e22	+	4.04374e23i	0.0734765	+	0.478488i
$191$	−8.90233e23			−0.996904			−0.498452	−	0.866917i	$-0.666098\pi$
$191$	−8.90233e23			−0.996904			−0.498452	+	0.866917i	$0.666098\pi$
$192$	−4.93417e23	+	8.03995e23i	−0.523059	+	0.852296i
$193$	1.13067e24			1.13496			0.567482	−	0.823386i	$-0.307918\pi$
$193$	1.13067e24			1.13496			0.567482	+	0.823386i	$0.307918\pi$
$194$	2.95208e22	+	1.92243e23i	0.0280679	+	0.182782i
$195$	5.96320e22	+	5.59701e23i	0.0537175	+	0.504188i
$196$	2.44373e23	−	7.68644e22i	0.208624	−	0.0656200i
$197$			5.57410e23i			0.451107i	0.974231	+	0.225553i	$0.0724190\pi$
$197$			5.57410e23i			0.451107i	−0.974231	+	0.225553i	$0.927581\pi$
$198$	−3.05186e23	−	7.99491e23i	−0.234196	−	0.613521i
$199$			1.95310e24i			1.42157i	0.703410	+	0.710784i	$0.251660\pi$
$199$			1.95310e24i			1.42157i	−0.703410	+	0.710784i	$0.748340\pi$
$200$	−5.71913e23	−	1.16277e24i	−0.394926	−	0.802934i
$201$	−2.29960e23	−	2.15839e24i	−0.150693	−	1.41440i
$202$	−5.58470e23	+	8.57586e22i	−0.347385	+	0.0533443i
$203$	−2.24213e24			−1.32419
$204$	−1.83881e23	−	4.22055e23i	−0.103138	−	0.236730i
$205$	−9.09395e23			−0.484548
$206$	4.55187e23	−	6.98984e22i	0.230454	−	0.0353884i
$207$	1.58634e23	−	3.41906e22i	0.0763321	−	0.0164520i
$208$	2.80213e24	−	1.95629e24i	1.28181	−	0.894886i
$209$			2.25335e24i			0.980151i
$210$	2.21253e23	+	8.36721e23i	0.0915349	+	0.346161i
$211$			1.50499e24i			0.592334i	0.955136	+	0.296167i	$0.0957085\pi$
$211$			1.50499e24i			0.592334i	−0.955136	+	0.296167i	$0.904292\pi$
$212$	−1.77396e23	−	5.63990e23i	−0.0664380	−	0.211225i
$213$	−3.83485e24	+	4.08574e23i	−1.36698	+	0.145642i
$214$	−6.17437e23	−	4.02082e24i	−0.209531	−	1.36449i
$215$	4.26466e23			0.137810
$216$	−2.27470e24	−	2.32002e24i	−0.700098	−	0.714046i
$217$	3.84230e24			1.12659
$218$	−6.63263e23	−	4.31925e24i	−0.185307	−	1.20674i
$219$	−1.75425e24	+	1.86902e23i	−0.467119	+	0.0497680i
$220$	2.51766e23	+	8.00434e23i	0.0639085	+	0.203183i
$221$			1.66782e24i			0.403674i
$222$	3.48090e23	+	1.31639e24i	0.0803500	+	0.303863i
$223$			2.97297e24i			0.654621i	0.944917	+	0.327310i	$0.106142\pi$
$223$			2.97297e24i			0.654621i	−0.944917	+	0.327310i	$0.893858\pi$
$224$	3.80214e24	−	3.62715e24i	0.798774	−	0.762011i
$225$	4.36298e24	−	9.40359e23i	0.874715	−	0.188529i
$226$	3.55993e24	−	5.46663e23i	0.681245	−	0.104612i
$227$	7.84324e24			1.43293			0.716463	−	0.697625i	$-0.245760\pi$
$227$	7.84324e24			1.43293			0.716463	+	0.697625i	$0.245760\pi$
$228$	3.41719e24	+	7.84335e24i	0.596147	+	1.36831i
$229$	−4.90891e24			−0.817923			−0.408962	−	0.912552i	$-0.634109\pi$
$229$	−4.90891e24			−0.817923			−0.408962	+	0.912552i	$0.634109\pi$
$230$	−1.57273e23	+	2.41508e22i	−0.0250330	+	0.00384406i
$231$	5.05026e23	+	4.74013e24i	0.0768047	+	0.720883i
$232$	−7.40594e24	+	3.64263e24i	−1.07636	+	0.529410i
$233$			6.69583e24i			0.930181i	0.885263	+	0.465090i	$0.153978\pi$
$233$			6.69583e24i			0.930181i	−0.885263	+	0.465090i	$0.846022\pi$
$234$	4.19776e24	+	1.09968e25i	0.557508	+	1.46049i
$235$			2.73725e24i			0.347617i
$236$	5.19815e24	−	1.63501e24i	0.631354	−	0.198584i
$237$	−1.44807e24	−	1.35914e25i	−0.168240	−	1.57909i
$238$	3.89239e23	+	2.53477e24i	0.0432671	+	0.281761i
$239$	−2.59957e24			−0.276518			−0.138259	−	0.990396i	$-0.544151\pi$
$239$	−2.59957e24			−0.276518			−0.138259	+	0.990396i	$0.544151\pi$
$240$	2.09018e24	+	2.40431e24i	0.212798	+	0.244778i
$241$	−8.46372e24			−0.824863			−0.412432	−	0.910989i	$-0.635320\pi$
$241$	−8.46372e24			−0.824863			−0.412432	+	0.910989i	$0.635320\pi$
$242$	−9.25114e23	−	6.02445e24i	−0.0863245	−	0.562155i
$243$	9.65158e24	−	5.66424e24i	0.862448	−	0.506146i
$244$	−8.43234e24	+	2.65228e24i	−0.721697	+	0.227000i
$245$		−	8.65168e23i		−	0.0709343i
$246$	−1.83854e25	+	4.86163e24i	−1.44429	+	0.381912i
$247$		−	3.09943e25i		−	2.33326i
$248$	1.26915e25	−	6.24234e24i	0.915734	−	0.450407i
$249$	2.56290e25	−	2.73058e24i	1.77271	−	0.188869i
$250$	−9.15964e24	+	1.40655e24i	−0.607447	+	0.0932795i
$251$	−1.47321e25			−0.936892			−0.468446	−	0.883492i	$-0.655186\pi$
$251$	−1.47321e25			−0.936892			−0.468446	+	0.883492i	$0.655186\pi$
$252$	8.94624e24	+	1.57333e25i	0.545676	+	0.959656i
$253$	−8.76396e23			−0.0512784
$254$	−2.31394e25	+	3.55328e24i	−1.29897	+	0.199469i
$255$	−1.54604e24	+	1.64718e23i	−0.0832813	+	0.00887300i
$256$	6.66601e24	−	1.81579e25i	0.344625	−	0.938741i
$257$			3.39279e25i			1.68368i	0.539729	+	0.841839i	$0.318527\pi$
$257$			3.39279e25i			1.68368i	−0.539729	+	0.841839i	$0.681473\pi$
$258$	8.62195e24	−	2.27989e24i	0.410770	−	0.108619i
$259$		−	7.58490e24i		−	0.346978i
$260$	−3.46298e24	−	1.10098e25i	−0.152135	−	0.483680i
$261$	−5.98934e24	−	2.77887e25i	−0.252728	−	1.17258i
$262$	3.21510e24	+	2.09371e25i	0.130326	+	0.848699i
$263$	−1.02804e25			−0.400382			−0.200191	−	0.979757i	$-0.564156\pi$
$263$	−1.02804e25			−0.400382			−0.200191	+	0.979757i	$0.564156\pi$
$264$	9.36913e24	+	1.48366e25i	0.350637	+	0.555256i
$265$	−1.99672e24			−0.0718185
$266$	−7.23350e24	−	4.71054e25i	−0.250087	−	1.62860i
$267$	−3.27078e24	−	3.06993e25i	−0.108714	−	1.02038i
$268$	1.33544e25	+	4.24572e25i	0.426783	+	1.35686i
$269$			5.57243e25i			1.71256i	0.516511	+	0.856280i	$0.327230\pi$
$269$			5.57243e25i			1.71256i	−0.516511	+	0.856280i	$0.672770\pi$
$270$	−9.77922e24	+	4.97731e24i	−0.289058	+	0.147121i
$271$		−	1.60338e25i		−	0.455890i	−0.973674	−	0.227945i	$-0.926799\pi$
$271$		−	1.60338e25i		−	0.455890i	0.973674	−	0.227945i	$-0.0732006\pi$
$272$	5.40376e24	+	7.74019e24i	0.147816	+	0.211728i
$273$	−6.94650e24	−	6.51993e25i	−0.182835	−	1.71607i
$274$	−5.84499e25	+	8.97555e24i	−1.48048	+	0.227342i
$275$	−2.41039e25			−0.587616
$276$	−3.05051e24	+	1.32905e24i	−0.0715859	+	0.0311885i
$277$	−2.63776e25			−0.595933			−0.297967	−	0.954576i	$-0.596308\pi$
$277$	−2.63776e25			−0.595933			−0.297967	+	0.954576i	$0.596308\pi$
$278$	−4.07567e25	+	6.25859e24i	−0.886602	+	0.136146i
$279$	1.02639e25	+	4.76212e25i	0.215014	+	0.997599i
$280$	−7.83254e24	−	1.59245e25i	−0.158031	−	0.321298i
$281$		−	9.91101e24i		−	0.192620i	−0.995351	−	0.0963101i	$-0.969296\pi$
$281$		−	9.91101e24i		−	0.192620i	0.995351	−	0.0963101i	$-0.0307040\pi$
$282$	1.46333e25	+	5.53395e25i	0.273986	+	1.03614i
$283$			5.06088e25i			0.912995i	0.889725	+	0.456498i	$0.150896\pi$
$283$			5.06088e25i			0.912995i	−0.889725	+	0.456498i	$0.849104\pi$
$284$	7.54345e25	−	2.37269e25i	1.31138	−	0.412476i
$285$	2.87311e25	−	3.06108e24i	0.481372	−	0.0512866i
$286$	−9.64862e24	−	6.28330e25i	−0.155820	−	1.01472i
$287$	1.05935e26			1.64922
$288$	5.51111e25	+	3.74343e25i	0.827215	+	0.561886i
$289$	6.44850e25			0.933322
$290$	4.23062e24	+	2.75503e25i	0.0590508	+	0.384546i
$291$	1.36590e25	−	1.45526e24i	0.183883	−	0.0195914i
$292$	3.45075e25	−	1.08539e25i	0.448119	−	0.140950i
$293$			1.30739e25i			0.163793i	0.996641	+	0.0818964i	$0.0260977\pi$
$293$			1.30739e25i			0.163793i	−0.996641	+	0.0818964i	$0.973902\pi$
$294$	−4.62519e24	−	1.74913e25i	−0.0559092	−	0.211434i
$295$		−	1.84033e25i		−	0.214667i
$296$	−1.23227e25	−	2.50536e25i	−0.138721	−	0.282037i
$297$	−5.73997e25	+	1.89215e25i	−0.623688	+	0.205595i
$298$	1.62617e26	−	2.49714e25i	1.70567	−	0.261922i
$299$	1.20546e25			0.122069
$300$	−8.38995e25	+	3.65533e25i	−0.820326	+	0.357399i
$301$	−4.96788e25			−0.469054
$302$	1.58416e26	−	2.43264e25i	1.44453	−	0.221822i
$303$	4.22757e24	+	3.96797e25i	0.0372343	+	0.349479i
$304$	−1.00422e26	−	1.43841e26i	−0.854389	−	1.22380i
$305$			2.98535e25i			0.245384i
$306$	−3.03759e25	+	1.15953e25i	−0.241243	+	0.0920886i
$307$			2.26517e26i			1.73839i	0.494467	+	0.869197i	$0.335363\pi$
$307$			2.26517e26i			1.73839i	−0.494467	+	0.869197i	$0.664637\pi$
$308$	−2.93281e25	−	9.32422e25i	−0.217521	−	0.691560i
$309$	−3.44573e24	−	3.23413e25i	−0.0247011	−	0.231843i
$310$	−7.24997e24	−	4.72127e25i	−0.0502387	−	0.327160i
$311$	−2.70840e26			−1.81438			−0.907189	−	0.420722i	$-0.861777\pi$
$311$	−2.70840e26			−1.81438			−0.907189	+	0.420722i	$0.861777\pi$
$312$	−1.28870e26	−	2.04074e26i	−0.834697	−	1.32179i
$313$	2.08831e24			0.0130791			0.00653957	−	0.999979i	$-0.497918\pi$
$313$	2.08831e24			0.0130791			0.00653957	+	0.999979i	$0.497918\pi$
$314$	−2.23367e25	−	1.45459e26i	−0.135288	−	0.881010i
$315$	5.97524e25	−	1.28785e25i	0.350021	−	0.0754406i
$316$	8.40928e25	+	2.67354e26i	0.476480	+	1.51486i
$317$			1.33494e26i			0.731713i	0.930671	+	0.365856i	$0.119224\pi$
$317$			1.33494e26i			0.731713i	−0.930671	+	0.365856i	$0.880776\pi$
$318$	−4.03682e25	+	1.06745e25i	−0.214069	+	0.0566061i
$319$			1.53523e26i			0.787717i
$320$	−5.17431e25	−	3.98752e25i	−0.256908	−	0.197983i
$321$	−2.85682e26	+	3.04373e25i	−1.37271	+	0.146252i
$322$	1.83207e25	−	2.81332e24i	0.0852030	−	0.0130838i
$323$	8.56141e25			0.385406
$324$	−1.71100e26	+	1.52907e26i	−0.745636	+	0.666354i
$325$	3.31543e26			1.39883
$326$	3.93893e25	−	6.04861e24i	0.160914	−	0.0247099i
$327$	−3.06886e26	+	3.26964e25i	−1.21402	+	0.129345i
$328$	3.49913e26	−	1.72106e26i	1.34055	−	0.659356i
$329$		−	3.18861e26i		−	1.18316i
$330$	5.72919e25	−	1.51496e25i	0.205919	−	0.0544509i
$331$		−	2.67105e26i		−	0.930011i	−0.885308	−	0.465005i	$-0.846052\pi$
$331$		−	2.67105e26i		−	0.930011i	0.885308	−	0.465005i	$-0.153948\pi$
$332$	−5.04143e26	+	1.58571e26i	−1.70061	+	0.534903i
$333$	9.40065e25	−	2.02614e25i	0.307251	−	0.0662223i
$334$	2.84699e25	+	1.85399e26i	0.0901671	+	0.587179i
$335$	1.50314e26			0.461347
$336$	−2.43485e26	−	2.80077e26i	−0.724285	−	0.833134i
$337$	−8.49335e25			−0.244887			−0.122443	−	0.992476i	$-0.539073\pi$
$337$	−8.49335e25			−0.244887			−0.122443	+	0.992476i	$0.539073\pi$
$338$	7.84091e25	+	5.10609e26i	0.219150	+	1.42713i
$339$	−2.69484e25	−	2.52936e26i	−0.0730190	−	0.685351i
$340$	3.04118e25	−	9.56561e24i	0.0798938	−	0.0251295i
$341$		−	2.63090e26i		−	0.670167i
$342$	5.64497e26	−	2.15483e26i	1.39440	−	0.532278i
$343$		−	3.60043e26i		−	0.862513i
$344$	−1.64094e26	+	8.07100e25i	−0.381266	+	0.187527i
$345$	1.19054e24	+	1.11744e25i	0.00268315	+	0.0251839i
$346$	−6.93361e26	+	1.06472e26i	−1.51586	+	0.232776i
$347$	−6.33127e25			−0.134286			−0.0671431	−	0.997743i	$-0.521388\pi$
$347$	−6.33127e25			−0.134286			−0.0671431	+	0.997743i	$0.521388\pi$
$348$	2.32816e26	+	5.34374e26i	0.479104	+	1.09967i
$349$	3.23551e26			0.646064			0.323032	−	0.946388i	$-0.395298\pi$
$349$	3.23551e26			0.646064			0.323032	+	0.946388i	$0.395298\pi$
$350$	5.03882e26	−	7.73760e25i	0.976369	−	0.149931i
$351$	7.89519e26	−	2.60260e26i	1.48470	−	0.489421i
$352$	−2.48358e26	−	2.60340e26i	−0.453294	−	0.475163i
$353$			6.85861e26i			1.21507i	0.794293	+	0.607535i	$0.207842\pi$
$353$			6.85861e26i			1.21507i	−0.794293	+	0.607535i	$0.792158\pi$
$354$	−9.83842e25	−	3.72063e26i	−0.169196	−	0.639856i
$355$		−	2.67065e26i		−	0.445881i
$356$	1.89943e26	+	6.03880e26i	0.307891	+	0.978872i
$357$	1.80097e26	−	1.91880e25i	0.283459	−	0.0302004i
$358$	1.11468e26	+	7.25894e26i	0.170365	+	1.10943i
$359$	4.19281e26			0.622320			0.311160	−	0.950358i	$-0.399282\pi$
$359$	4.19281e26			0.622320			0.311160	+	0.950358i	$0.399282\pi$
$360$	1.76444e26	−	1.39615e26i	0.254350	−	0.201259i
$361$	−8.76817e26			−1.22767
$362$	−2.85842e25	−	1.86144e26i	−0.0388764	−	0.253168i
$363$	−4.28041e26	+	4.56046e25i	−0.565544	+	0.0602545i
$364$	4.03401e26	+	1.28252e27i	0.517812	+	1.64627i
$365$		−	1.22169e26i		−	0.152365i
$366$	1.59597e26	+	6.03553e26i	0.193407	+	0.731416i
$367$		−	3.00713e26i		−	0.354127i	−0.984199	−	0.177063i	$-0.943340\pi$
$367$		−	3.00713e26i		−	0.354127i	0.984199	−	0.177063i	$-0.0566597\pi$
$368$	5.59442e25	−	3.90571e25i	0.0640255	−	0.0446990i
$369$	2.82982e26	+	1.31295e27i	0.314762	+	1.46040i
$370$	−9.32001e25	+	1.43118e25i	−0.100762	+	0.0154731i
$371$	2.32598e26			0.244444
$372$	−3.98973e26	−	9.15750e26i	−0.407608	−	0.935569i
$373$	1.98315e26			0.196976			0.0984880	−	0.995138i	$-0.468599\pi$
$373$	1.98315e26			0.196976			0.0984880	+	0.995138i	$0.468599\pi$
$374$	1.73560e26	−	2.66519e25i	0.167610	−	0.0257381i
$375$	6.93377e25	+	6.50799e26i	0.0651090	+	0.611109i
$376$	−5.18032e26	−	1.05323e27i	−0.473025	−	0.961721i
$377$		−	2.11167e27i		−	1.87517i
$378$	1.13918e27	−	5.79804e26i	0.983847	−	0.500746i
$379$		−	2.83826e26i		−	0.238419i	−0.992869	−	0.119210i	$-0.961964\pi$
$379$		−	2.83826e26i		−	0.238419i	0.992869	−	0.119210i	$-0.0380360\pi$
$380$	−5.65163e26	+	1.77765e26i	−0.461792	+	0.145250i
$381$	1.75163e26	+	1.64407e27i	0.139229	+	1.30680i
$382$	−1.95675e26	−	1.27426e27i	−0.151311	−	0.985354i
$383$	−1.11513e27			−0.838957			−0.419478	−	0.907765i	$-0.637787\pi$
$383$	−1.11513e27			−0.838957			−0.419478	+	0.907765i	$0.637787\pi$
$384$	−1.25927e27	−	5.29545e26i	−0.921812	−	0.387637i
$385$	−3.30110e26			−0.235137
$386$	2.48522e26	+	1.61841e27i	0.172266	+	1.12181i
$387$	−1.32706e26	−	6.15715e26i	−0.0895211	−	0.415350i
$388$	−2.68683e26	+	8.45108e25i	−0.176404	+	0.0554854i
$389$		−	1.71658e27i		−	1.09696i	−0.836163	−	0.548482i	$-0.815206\pi$
$389$		−	1.71658e27i		−	1.09696i	0.836163	−	0.548482i	$-0.184794\pi$
$390$	−7.88036e26	+	2.08379e26i	−0.490193	+	0.129621i
$391$			3.32979e25i			0.0201632i
$392$	1.63736e26	+	3.32895e26i	0.0965249	+	0.196247i
$393$	1.48760e27	−	1.58492e26i	0.853815	−	0.0909676i
$394$	−7.97864e26	+	1.22520e26i	−0.445881	+	0.0684694i
$395$	9.46529e26			0.515068
$396$	1.07729e27	−	6.12566e26i	0.570866	−	0.324604i
$397$	−1.36489e27			−0.704365			−0.352183	−	0.935931i	$-0.614560\pi$
$397$	−1.36489e27			−0.704365			−0.352183	+	0.935931i	$0.614560\pi$
$398$	−2.79562e27	+	4.29296e26i	−1.40510	+	0.215767i
$399$	−3.34687e27	+	3.56584e26i	−1.63841	+	0.174561i
$400$	1.53866e27	−	1.07420e27i	0.733689	−	0.512220i
$401$		−	2.73211e27i		−	1.26906i	−0.772898	−	0.634531i	$-0.781193\pi$
$401$		−	2.73211e27i		−	1.26906i	0.772898	−	0.634531i	$-0.218807\pi$
$402$	3.03892e27	−	8.03578e26i	1.37514	−	0.363625i
$403$			3.61874e27i			1.59534i
$404$	−2.45506e26	−	7.80531e26i	−0.105453	−	0.335263i
$405$	3.19231e26	+	7.06163e26i	0.133606	+	0.295548i
$406$	−4.92824e26	−	3.20933e27i	−0.200987	−	1.30885i
$407$	−5.19352e26			−0.206405
$408$	5.63703e26	−	3.55971e26i	0.218333	−	0.137874i
$409$	−1.60190e27			−0.604700			−0.302350	−	0.953197i	$-0.597771\pi$
$409$	−1.60190e27			−0.604700			−0.302350	+	0.953197i	$0.597771\pi$
$410$	−1.99887e26	−	1.30169e27i	−0.0735451	−	0.478934i
$411$	4.42461e26	+	4.15290e27i	0.158685	+	1.48940i
$412$	2.00102e26	+	6.36180e26i	0.0699569	+	0.222412i
$413$			2.14379e27i			0.730646i
$414$	8.38077e25	+	2.19550e26i	0.0278471	+	0.0729507i
$415$			1.78484e27i			0.578223i
$416$	3.41610e27	+	3.58091e27i	1.07907	+	1.13113i
$417$	3.08525e26	+	2.89579e27i	0.0950302	+	0.891946i
$418$	−3.22540e27	+	4.95291e26i	−0.968796	+	0.148768i
$419$	2.21973e27			0.650208			0.325104	−	0.945678i	$-0.394601\pi$
$419$	2.21973e27			0.650208			0.325104	+	0.945678i	$0.394601\pi$
$420$	−1.14903e27	+	5.00609e26i	−0.328257	+	0.143015i
$421$	4.60896e26			0.128423			0.0642113	−	0.997936i	$-0.479547\pi$
$421$	4.60896e26			0.128423			0.0642113	+	0.997936i	$0.479547\pi$
$422$	−2.15420e27	+	3.30799e26i	−0.585471	+	0.0899049i
$423$	3.95193e27	−	8.51766e26i	1.04770	−	0.225812i
$424$	7.68290e26	−	3.77886e26i	0.198694	−	0.0977281i
$425$			9.15805e26i			0.231057i
$426$	−1.42773e27	−	5.39931e27i	−0.351435	−	1.32904i
$427$		−	3.47762e27i		−	0.835197i
$428$	5.61959e27	−	1.76757e27i	1.31688	−	0.414206i
$429$	−4.46432e27	+	4.75640e26i	−1.02083	+	0.108762i
$430$	9.37381e25	+	6.10433e26i	0.0209169	+	0.136213i
$431$	−7.69227e26			−0.167511			−0.0837555	−	0.996486i	$-0.526691\pi$
$431$	−7.69227e26			−0.167511			−0.0837555	+	0.996486i	$0.526691\pi$
$432$	2.82083e27	−	3.76589e27i	0.599512	−	0.800366i
$433$	3.52973e27			0.732182			0.366091	−	0.930579i	$-0.380696\pi$
$433$	3.52973e27			0.732182			0.366091	+	0.930579i	$0.380696\pi$
$434$	8.44546e26	+	5.49978e27i	0.170994	+	1.11353i
$435$	1.95747e27	−	2.08554e26i	0.386864	−	0.0412174i
$436$	6.03668e27	−	1.89876e27i	1.16464	−	0.366321i
$437$		−	6.18797e26i		−	0.116545i
$438$	−6.53114e26	−	2.46991e27i	−0.120091	−	0.454153i
$439$			3.79075e27i			0.680530i	0.940329	+	0.340265i	$0.110517\pi$
$439$			3.79075e27i			0.680530i	−0.940329	+	0.340265i	$0.889483\pi$
$440$	−1.09038e27	+	5.36309e26i	−0.191129	+	0.0940074i
$441$	−1.24910e27	+	2.69220e26i	−0.213792	+	0.0460788i
$442$	−2.38728e27	+	3.66591e26i	−0.398997	+	0.0612699i
$443$	−2.82606e27			−0.461256			−0.230628	−	0.973042i	$-0.574078\pi$
$443$	−2.82606e27			−0.461256			−0.230628	+	0.973042i	$0.574078\pi$
$444$	−1.80773e27	+	7.87593e26i	−0.288147	+	0.125540i
$445$	2.13795e27			0.332826
$446$	−4.25544e27	+	6.53465e26i	−0.647037	+	0.0993589i
$447$	−1.23100e27	−	1.15540e28i	−0.182822	−	1.71595i
$448$	6.02754e27	+	4.64504e27i	0.874421	+	0.673861i
$449$			1.56228e27i			0.221397i	0.993854	+	0.110698i	$0.0353088\pi$
$449$			1.56228e27i			0.221397i	−0.993854	+	0.110698i	$0.964691\pi$
$450$	2.30500e27	+	6.03837e27i	0.319109	+	0.835965i
$451$		−	7.25358e27i		−	0.981066i
$452$	1.56496e27	+	4.97545e27i	0.206800	+	0.657474i
$453$	−1.19920e27	−	1.12556e28i	−0.154831	−	1.45324i
$454$	1.72396e27	+	1.12266e28i	0.217491	+	1.41633i
$455$	4.54059e27			0.559748
$456$	−1.04757e28	+	6.61527e27i	−1.26198	+	0.796923i
$457$	1.49778e28			1.76330			0.881652	−	0.471900i	$-0.156432\pi$
$457$	1.49778e28			1.76330			0.881652	+	0.471900i	$0.156432\pi$
$458$	−1.07899e27	−	7.02650e27i	−0.124145	−	0.808447i
$459$	7.18904e26	+	2.18085e27i	0.0808421	+	0.245241i
$460$	−6.91379e25	−	2.19809e26i	−0.00759904	−	0.0241595i
$461$		−	1.14804e27i		−	0.123338i	−0.998097	−	0.0616691i	$-0.980358\pi$
$461$		−	1.14804e27i		−	0.123338i	0.998097	−	0.0616691i	$-0.0196423\pi$
$462$	−6.67391e27	+	1.76477e27i	−0.700874	+	0.185331i
$463$			9.71055e26i			0.0996881i	0.998757	+	0.0498440i	$0.0158724\pi$
$463$			9.71055e26i			0.0996881i	−0.998757	+	0.0498440i	$0.984128\pi$
$464$	−6.84182e27	−	9.80003e27i	−0.686646	−	0.983532i
$465$	−3.35449e27	+	3.57396e26i	−0.329132	+	0.0350666i
$466$	−9.58426e27	+	1.47176e27i	−0.919404	+	0.141184i
$467$	−4.98538e27			−0.467596			−0.233798	−	0.972285i	$-0.575115\pi$
$467$	−4.98538e27			−0.467596			−0.233798	+	0.972285i	$0.575115\pi$
$468$	−1.48179e28	+	8.42569e27i	−1.35895	+	0.772723i
$469$	−1.75100e28			−1.57026
$470$	−3.91803e27	+	6.01652e26i	−0.343590	+	0.0527616i
$471$	−1.03350e28	+	1.10112e27i	−0.886320	+	0.0944308i
$472$	3.48288e27	+	7.08114e27i	0.292111	+	0.593898i
$473$			3.40161e27i			0.279024i
$474$	1.91362e28	−	5.06015e27i	1.53526	−	0.405967i
$475$		−	1.70190e28i		−	1.33553i
$476$	−3.54265e27	+	1.11429e27i	−0.271929	+	0.0855317i
$477$	6.21333e26	+	2.88279e27i	0.0466532	+	0.216457i
$478$	−5.71391e26	−	3.72097e27i	−0.0419702	−	0.273315i
$479$	−1.07280e28			−0.770895			−0.385447	−	0.922730i	$-0.625953\pi$
$479$	−1.07280e28			−0.770895			−0.385447	+	0.922730i	$0.625953\pi$
$480$	−2.98204e27	+	3.52031e27i	−0.209643	+	0.247485i
$481$	7.14356e27			0.491351
$482$	−1.86034e27	−	1.21148e28i	−0.125198	−	0.815307i
$483$	−1.38686e26	−	1.30170e27i	−0.00913247	−	0.0857166i
$484$	8.41992e27	−	2.64837e27i	0.542540	−	0.170649i
$485$			9.51234e26i			0.0599790i
$486$	1.02291e28	+	1.25700e28i	0.631185	+	0.775632i
$487$		−	6.09274e27i		−	0.367924i	−0.982933	−	0.183962i	$-0.941108\pi$
$487$		−	6.09274e27i		−	0.367924i	0.982933	−	0.183962i	$-0.0588924\pi$
$488$	−5.64986e27	−	1.14869e28i	−0.333910	−	0.678881i
$489$	−2.98174e26	−	2.79863e27i	−0.0172475	−	0.161884i
$490$	1.23838e27	−	1.90166e26i	0.0701125	−	0.0107665i
$491$	2.82299e28			1.56442			0.782212	−	0.623013i	$-0.214092\pi$
$491$	2.82299e28			1.56442			0.782212	+	0.623013i	$0.214092\pi$
$492$	−1.10000e28	−	2.52479e28i	−0.596703	−	1.36959i
$493$	5.83295e27			0.309739
$494$	4.43645e28	−	6.81261e27i	2.30623	−	0.354145i
$495$	−8.81817e26	−	4.09136e27i	−0.0448770	−	0.208215i
$496$	1.17247e28	+	1.67942e28i	0.584179	+	0.836761i
$497$			3.11103e28i			1.51762i
$498$	9.54179e27	+	3.60845e28i	0.455745	+	1.72351i
$499$			2.89085e28i			1.35198i	0.736912	+	0.675989i	$0.236283\pi$
$499$			2.89085e28i			1.35198i	−0.736912	+	0.675989i	$0.763717\pi$
$500$	−4.02662e27	−	1.28017e28i	−0.184398	−	0.586251i
$501$	1.31728e28	−	1.40346e27i	0.590718	−	0.0629366i
$502$	−3.23814e27	−	2.10871e28i	−0.142202	−	0.926037i
$503$	−1.66225e28			−0.714878			−0.357439	−	0.933936i	$-0.616350\pi$
$503$	−1.66225e28			−0.714878			−0.357439	+	0.933936i	$0.616350\pi$
$504$	−2.05539e28	+	1.62637e28i	−0.865714	+	0.685011i
$505$	−2.76336e27			−0.113993
$506$	−1.92634e26	−	1.25445e27i	−0.00778308	−	0.0506843i
$507$	3.62791e28	−	3.86527e27i	1.43573	−	0.152966i
$508$	−1.01722e28	−	3.23402e28i	−0.394316	−	1.25364i
$509$			3.70662e27i			0.140748i	0.997521	+	0.0703738i	$0.0224192\pi$
$509$			3.70662e27i			0.140748i	−0.997521	+	0.0703738i	$0.977581\pi$
$510$	−5.75596e26	−	2.17675e27i	−0.0214107	−	0.0809697i
$511$			1.42314e28i			0.518594i
$512$	2.74560e28	+	5.55044e27i	0.980172	+	0.198149i
$513$	−1.33599e28	−	4.05283e28i	−0.467273	−	1.41751i
$514$	−4.85636e28	+	7.45742e27i	−1.66417	+	0.255550i
$515$	2.25230e27			0.0756224
$516$	5.15850e27	+	1.18401e28i	0.169708	+	0.389524i
$517$	−2.18330e28			−0.703822
$518$	1.08568e28	−	1.66718e27i	0.342958	−	0.0526646i
$519$	5.24869e27	+	4.92638e28i	0.162478	+	1.52500i
$520$	1.49980e28	−	7.37679e27i	0.454985	−	0.223786i
$521$		−	2.10125e28i		−	0.624713i	−0.949965	−	0.312357i	$-0.898882\pi$
$521$		−	2.10125e28i		−	0.624713i	0.949965	−	0.312357i	$-0.101118\pi$
$522$	3.84596e28	−	1.46810e28i	1.12064	−	0.427776i
$523$			4.06782e28i			1.16170i	0.814011	+	0.580850i	$0.197280\pi$
$523$			4.06782e28i			1.16170i	−0.814011	+	0.580850i	$0.802720\pi$
$524$	−2.92622e28	+	9.20405e27i	−0.819085	+	0.257632i
$525$	−3.81434e27	−	3.58011e28i	−0.104652	−	0.982254i
$526$	−2.25965e27	−	1.47151e28i	−0.0607704	−	0.395744i
$527$	−9.99586e27			−0.263517
$528$	−1.91774e28	+	1.66719e28i	−0.495603	+	0.430852i
$529$	−3.92309e28			−0.993903
$530$	−4.38884e26	−	2.85806e27i	−0.0109007	−	0.0709864i
$531$	−2.65700e28	+	5.72667e27i	−0.646992	+	0.139447i
$532$	6.58356e28	−	2.07077e28i	1.57177	−	0.494379i
$533$			9.97711e28i			2.33544i
$534$	4.32234e28	−	1.14295e28i	0.992054	−	0.262328i
$535$		−	1.98953e28i		−	0.447751i
$536$	−5.78370e28	+	2.84473e28i	−1.27637	+	0.627785i
$537$	5.15753e28	−	5.49496e27i	1.11612	−	0.118914i
$538$	−7.97625e28	+	1.22483e28i	−1.69272	+	0.259934i
$539$	6.90081e27			0.143621
$540$	−9.27389e27	−	1.29037e28i	−0.189290	−	0.263379i
$541$	5.26752e28			1.05447			0.527235	−	0.849719i	$-0.323229\pi$
$541$	5.26752e28			1.05447			0.527235	+	0.849719i	$0.323229\pi$
$542$	2.29505e28	−	3.52427e27i	0.450608	−	0.0691953i
$543$	−1.32256e28	+	1.40909e27i	−0.254694	+	0.0271357i
$544$	−9.89137e27	+	9.43613e27i	−0.186839	+	0.178240i
$545$		−	2.13720e28i		−	0.395988i
$546$	9.17980e28	−	2.42740e28i	1.66844	−	0.441183i
$547$		−	2.23858e28i		−	0.399122i	−0.979885	−	0.199561i	$-0.936048\pi$
$547$		−	2.23858e28i		−	0.399122i	0.979885	−	0.199561i	$-0.0639517\pi$
$548$	−2.56948e28	−	8.16909e28i	−0.449417	−	1.42882i
$549$	4.31013e28	−	9.28969e27i	0.739572	−	0.159401i
$550$	−5.29808e27	−	3.45017e28i	−0.0891888	−	0.580808i
$551$	−1.08398e29			−1.79031
$552$	−2.57287e27	−	4.07431e27i	−0.0416925	−	0.0660227i
$553$	−1.10261e29			−1.75310
$554$	−5.79785e27	−	3.77563e28i	−0.0904512	−	0.589029i
$555$	7.05517e26	+	6.62193e27i	0.0108002	+	0.101370i
$556$	−1.79168e28	−	5.69625e28i	−0.269138	−	0.855665i
$557$			1.86435e26i			0.00274820i	0.999999	+	0.00137410i	$0.000437389\pi$
$557$			1.86435e26i			0.00274820i	−0.999999	+	0.00137410i	$0.999563\pi$
$558$	−6.59078e28	+	2.51587e28i	−0.953406	+	0.363939i
$559$		−	4.67882e28i		−	0.664221i
$560$	2.10724e28	−	1.47116e28i	0.293589	−	0.204967i
$561$	−1.31384e27	−	1.23316e28i	−0.0179652	−	0.168620i
$562$	1.41864e28	−	2.17846e27i	0.190388	−	0.0292360i
$563$	9.06814e28			1.19448			0.597241	−	0.802062i	$-0.296263\pi$
$563$	9.06814e28			1.19448			0.597241	+	0.802062i	$0.296263\pi$
$564$	−7.59952e28	+	3.31096e28i	−0.982552	+	0.428078i
$565$	1.76148e28			0.223548
$566$	−7.24402e28	+	1.11239e28i	−0.902417	+	0.138575i
$567$	−3.71870e28	−	8.22607e28i	−0.454747	−	1.00594i
$568$	5.05428e28	+	1.02760e29i	0.606739	+	1.23358i
$569$			9.32949e28i			1.09946i	0.835343	+	0.549729i	$0.185269\pi$
$569$			9.32949e28i			1.09946i	−0.835343	+	0.549729i	$0.814731\pi$
$570$	1.06967e28	+	4.04521e28i	0.123755	+	0.468010i
$571$		−	2.63549e28i		−	0.299352i	−0.988735	−	0.149676i	$-0.952177\pi$
$571$		−	2.63549e28i		−	0.299352i	0.988735	−	0.149676i	$-0.0478230\pi$
$572$	8.78168e28	−	2.76216e28i	0.979309	−	0.308028i
$573$	−9.05370e28	+	9.64604e27i	−0.991294	+	0.105615i
$574$	2.32847e28	+	1.51633e29i	0.250321	+	1.63012i
$575$	6.61921e27			0.0698705
$576$	−4.14690e28	+	8.71129e28i	−0.429821	+	0.902914i
$577$	5.69382e28			0.579506			0.289753	−	0.957102i	$-0.406427\pi$
$577$	5.69382e28			0.579506			0.289753	+	0.957102i	$0.406427\pi$
$578$	1.41739e28	+	9.23023e28i	0.141660	+	0.922508i
$579$	1.14989e29	−	1.22512e28i	1.12858	−	0.120241i
$580$	−3.85050e28	+	1.21112e28i	−0.371128	+	0.116733i
$581$		−	2.07916e29i		−	1.96806i
$582$	5.08530e27	+	1.92313e28i	0.0472744	+	0.178779i
$583$		−	1.59264e28i		−	0.145411i
$584$	2.31208e28	+	4.70075e28i	0.207333	+	0.421533i
$585$	1.21292e28	+	5.62756e28i	0.106830	+	0.495660i
$586$	−1.87137e28	+	2.87367e27i	−0.161895	+	0.0248606i
$587$	7.91865e28			0.672901			0.336450	−	0.941701i	$-0.390774\pi$
$587$	7.91865e28			0.672901			0.336450	+	0.941701i	$0.390774\pi$
$588$	2.40200e28	−	1.04650e28i	0.200498	−	0.0873530i
$589$	1.85760e29			1.52315
$590$	2.63421e28	−	4.04508e27i	0.212180	−	0.0325823i
$591$	6.03976e27	+	5.66888e28i	0.0477916	+	0.448568i
$592$	3.31526e28	−	2.31452e28i	0.257715	−	0.179922i
$593$		−	1.13767e29i		−	0.868847i	−0.900709	−	0.434423i	$-0.856952\pi$
$593$		−	1.13767e29i		−	0.868847i	0.900709	−	0.434423i	$-0.143048\pi$
$594$	−3.97003e28	−	7.80017e28i	−0.297877	−	0.585256i
$595$			1.25422e28i			0.0924586i
$596$	7.14870e28	+	2.27277e29i	0.517775	+	1.64615i
$597$	2.11626e28	+	1.98631e29i	0.150605	+	1.41357i
$598$	2.64963e27	+	1.72547e28i	0.0185277	+	0.120655i
$599$	−5.88550e28			−0.404391			−0.202196	−	0.979345i	$-0.564808\pi$
$599$	−5.88550e28			−0.404391			−0.202196	+	0.979345i	$0.564808\pi$
$600$	−7.07629e28	−	1.12057e29i	−0.477768	−	0.756575i
$601$	−3.99979e28			−0.265372			−0.132686	−	0.991158i	$-0.542360\pi$
$601$	−3.99979e28			−0.265372			−0.132686	+	0.991158i	$0.542360\pi$
$602$	−1.09195e28	−	7.11091e28i	−0.0711934	−	0.463620i
$603$	−4.67740e28	−	2.17017e29i	−0.299690	−	1.39047i
$604$	6.96403e28	+	2.21406e29i	0.438503	+	1.39412i
$605$		−	2.98095e28i		−	0.184469i
$606$	−5.58673e28	+	1.47729e28i	−0.339778	+	0.0898471i
$607$		−	2.03938e29i		−	1.21903i	−0.792773	−	0.609517i	$-0.791363\pi$
$607$		−	2.03938e29i		−	1.21903i	0.792773	−	0.609517i	$-0.208637\pi$
$608$	1.83818e29	−	1.75358e29i	1.07994	−	1.03024i
$609$	−2.28025e29	+	2.42943e28i	−1.31674	+	0.140289i
$610$	−4.27315e28	+	6.56185e27i	−0.242541	+	0.0372446i
$611$	3.00308e29			1.67546
$612$	−2.32739e28	−	4.09307e28i	−0.127638	−	0.224471i
$613$	−2.81653e28			−0.151838			−0.0759188	−	0.997114i	$-0.524189\pi$
$613$	−2.81653e28			−0.151838			−0.0759188	+	0.997114i	$0.524189\pi$
$614$	−3.24231e29	+	4.97889e28i	−1.71825	+	0.263855i
$615$	−9.24857e28	+	9.85366e27i	−0.481821	+	0.0513344i
$616$	1.27018e29	−	6.24744e28i	0.650533	−	0.319967i
$617$			8.95713e28i			0.450998i	0.974243	+	0.225499i	$0.0724012\pi$
$617$			8.95713e28i			0.450998i	−0.974243	+	0.225499i	$0.927599\pi$
$618$	4.55352e28	−	1.20408e28i	0.225408	−	0.0596042i
$619$			1.23512e29i			0.601113i	0.953764	+	0.300556i	$0.0971723\pi$
$619$			1.23512e29i			0.601113i	−0.953764	+	0.300556i	$0.902828\pi$
$620$	6.59855e28	−	2.07549e28i	0.315745	−	0.0993133i
$621$	1.57626e28	−	5.19606e27i	0.0741596	−	0.0244463i
$622$	−5.95311e28	−	3.87673e29i	−0.275388	−	1.79336i
$623$	−2.49049e29			−1.13282
$624$	2.63780e29	−	2.29317e29i	1.17979	−	1.02565i
$625$	1.58132e29			0.695470
$626$	4.59015e26	+	2.98916e27i	0.00198516	+	0.0129276i
$627$	2.44160e28	+	2.29167e29i	0.103840	+	0.974635i
$628$	2.03298e29	−	6.39446e28i	0.850268	−	0.267441i
$629$			1.97323e28i			0.0811608i
$630$	3.15677e28	+	8.26974e28i	0.127693	+	0.334515i
$631$			2.59842e29i			1.03372i	0.856071	+	0.516858i	$0.172898\pi$
$631$			2.59842e29i			1.03372i	−0.856071	+	0.516858i	$0.827102\pi$
$632$	−3.64201e29	+	1.79133e29i	−1.42499	+	0.700886i
$633$	1.63071e28	+	1.53057e29i	0.0627536	+	0.589000i
$634$	−1.91081e29	+	2.93423e28i	−0.723235	+	0.111060i
$635$	−1.14496e29			−0.426251
$636$	−2.41522e28	−	5.54358e28i	−0.0884418	−	0.202997i
$637$	−9.49189e28			−0.341892
$638$	−2.19749e29	+	3.37446e28i	−0.778591	+	0.119560i
$639$	−3.85578e29	+	8.31042e28i	−1.34386	+	0.289644i
$640$	4.57031e28	−	8.28285e28i	0.156695	−	0.283982i
$641$		−	2.91364e29i		−	0.982713i	−0.870958	−	0.491357i	$-0.836501\pi$
$641$		−	2.91364e29i		−	0.982713i	0.870958	−	0.491357i	$-0.163499\pi$
$642$	−1.06361e29	−	4.02228e29i	−0.352909	−	1.33461i
$643$			3.53401e29i			1.15359i	0.816888	+	0.576796i	$0.195697\pi$
$643$			3.53401e29i			1.15359i	−0.816888	+	0.576796i	$0.804303\pi$
$644$	8.05385e27	+	2.56054e28i	0.0258644	+	0.0822300i
$645$	4.33717e28	−	4.62093e27i	0.137034	−	0.0146000i
$646$	1.88181e28	+	1.22546e29i	0.0584972	+	0.380941i
$647$	−4.11541e29			−1.25869			−0.629344	−	0.777127i	$-0.716676\pi$
$647$	−4.11541e29			−1.25869			−0.629344	+	0.777127i	$0.716676\pi$
$648$	−2.56476e29	−	2.11299e29i	−0.771807	−	0.635857i
$649$	1.46790e29			0.434636
$650$	7.28738e28	+	4.74563e29i	0.212315	+	1.38262i
$651$	3.90763e29	−	4.16329e28i	1.12025	−	0.119354i
$652$	1.73157e28	+	5.50514e28i	0.0488472	+	0.155299i
$653$		−	4.01524e29i		−	1.11461i	−0.830307	−	0.557306i	$-0.811835\pi$
$653$		−	4.01524e29i		−	1.11461i	0.830307	−	0.557306i	$-0.188165\pi$
$654$	−1.14255e29	−	4.32082e29i	−0.312110	−	1.18032i
$655$			1.03599e29i			0.278497i
$656$	3.23260e29	+	4.63028e29i	0.855187	+	1.22495i
$657$	−1.76382e29	+	3.80160e28i	−0.459218	+	0.0989759i
$658$	4.56410e29	−	7.00862e28i	1.16945	−	0.179581i
$659$	5.03843e29			1.27057			0.635285	−	0.772278i	$-0.280883\pi$
$659$	5.03843e29			1.27057			0.635285	+	0.772278i	$0.280883\pi$
$660$	3.42777e28	+	7.86764e28i	0.0850747	+	0.195269i
$661$	−5.89699e29			−1.44051			−0.720253	−	0.693711i	$-0.755974\pi$
$661$	−5.89699e29			−1.44051			−0.720253	+	0.693711i	$0.755974\pi$
$662$	3.82328e29	−	5.87102e28i	0.919236	−	0.141158i
$663$	1.80715e28	+	1.69618e29i	0.0427664	+	0.401402i
$664$	−3.37787e29	−	6.86764e29i	−0.786825	−	1.59971i
$665$		−	2.33081e29i		−	0.534417i
$666$	4.96645e28	+	1.30105e29i	0.112090	+	0.293640i
$667$		−	4.21591e28i		−	0.0936635i
$668$	−2.59119e29	+	8.15023e28i	−0.566690	+	0.178245i
$669$	3.22134e28	+	3.02352e29i	0.0693525	+	0.650937i
$670$	3.30392e28	+	2.15155e29i	0.0700236	+	0.456002i
$671$	−2.38119e29			−0.496830
$672$	3.47377e29	−	4.10080e29i	0.713549	−	0.842347i
$673$	3.97013e29			0.802873			0.401436	−	0.915887i	$-0.368511\pi$
$673$	3.97013e29			0.802873			0.401436	+	0.915887i	$0.368511\pi$
$674$	−1.86686e28	−	1.21572e29i	−0.0371691	−	0.242049i
$675$	4.33527e29	−	1.42909e29i	0.849819	−	0.280137i
$676$	−7.13640e29	+	2.24466e29i	−1.37733	+	0.433221i
$677$			4.54844e29i			0.864334i	0.901794	+	0.432167i	$0.142251\pi$
$677$			4.54844e29i			0.864334i	−0.901794	+	0.432167i	$0.857749\pi$
$678$	3.56123e29	−	9.41691e28i	0.666328	−	0.176196i
$679$		−	1.10809e29i		−	0.204146i
$680$	2.03766e28	+	4.14281e28i	0.0369647	+	0.0751539i
$681$	7.97660e29	−	8.49847e28i	1.42486	−	0.151808i
$682$	3.76581e29	−	5.78277e28i	0.662403	−	0.101718i
$683$	7.95324e29			1.37761			0.688805	−	0.724946i	$-0.258136\pi$
$683$	7.95324e29			1.37761			0.688805	+	0.724946i	$0.258136\pi$
$684$	4.32515e29	+	7.60645e29i	0.737755	+	1.29746i
$685$	−2.89215e29			−0.485813
$686$	5.15357e29	−	7.91381e28i	0.852521	−	0.130913i
$687$	−4.99237e29	+	5.31900e28i	−0.813320	+	0.0866532i
$688$	−1.51594e29	−	2.17140e29i	−0.243223	−	0.348386i
$689$			2.19064e29i			0.346153i
$690$	−1.57330e28	+	4.16027e27i	−0.0244848	+	0.00647449i
$691$		−	6.47344e29i		−	0.992238i	−0.868255	−	0.496119i	$-0.834758\pi$
$691$		−	6.47344e29i		−	0.992238i	0.868255	−	0.496119i	$-0.165242\pi$
$692$	−3.04804e29	−	9.69058e29i	−0.460158	−	1.46297i
$693$	1.02723e29	+	4.76601e29i	0.152745	+	0.708689i
$694$	−1.39163e28	−	9.06244e28i	−0.0203821	−	0.132730i
$695$	−2.01667e29			−0.290935
$696$	−7.13717e29	+	4.50703e29i	−1.01421	+	0.640463i
$697$	−2.75593e29			−0.385766
$698$	7.11171e28	+	4.63123e29i	0.0980601	+	0.638579i
$699$	7.25521e28	+	6.80968e29i	0.0985461	+	0.924946i
$700$	2.21508e29	+	7.04237e29i	0.296388	+	0.942300i
$701$		−	3.81304e29i		−	0.502611i	−0.967908	−	0.251306i	$-0.919140\pi$
$701$		−	3.81304e29i		−	0.502611i	0.967908	−	0.251306i	$-0.0808599\pi$
$702$	5.46068e29	+	1.07289e30i	0.709099	+	1.39321i
$703$		−	3.66700e29i		−	0.469115i
$704$	3.18055e29	−	4.12717e29i	0.400857	−	0.520163i
$705$	2.96592e28	+	2.78379e29i	0.0368276	+	0.345661i
$706$	−9.81725e29	+	1.50754e29i	−1.20099	+	0.184424i
$707$	3.21902e29			0.387990
$708$	5.10938e29	−	2.22605e29i	0.606762	−	0.264354i
$709$	−8.39004e29			−0.981700			−0.490850	−	0.871244i	$-0.663314\pi$
$709$	−8.39004e29			−0.981700			−0.490850	+	0.871244i	$0.663314\pi$
$710$	3.82270e29	−	5.87014e28i	0.440715	−	0.0676762i
$711$	−2.94537e29	−	1.36656e30i	−0.334587	−	1.55238i
$712$	−8.22630e29	+	4.04613e29i	−0.920799	+	0.452898i
$713$			7.22476e28i			0.0796863i
$714$	6.70509e28	+	2.53569e29i	0.0728742	+	0.275591i
$715$		−	3.10903e29i		−	0.332975i
$716$	−1.01453e30	+	3.19106e29i	−1.07072	+	0.336781i
$717$	−2.64377e29	+	2.81674e28i	−0.274962	+	0.0292952i
$718$	9.21589e28	+	6.00150e29i	0.0944562	+	0.615110i
$719$	−2.84602e29			−0.287464			−0.143732	−	0.989617i	$-0.545910\pi$
$719$	−2.84602e29			−0.287464			−0.143732	+	0.989617i	$0.545910\pi$
$720$	2.38624e29	+	2.21871e29i	0.237532	+	0.220856i
$721$	−2.62370e29			−0.257391
$722$	−1.92726e29	−	1.25506e30i	−0.186337	−	1.21345i
$723$	−8.60762e29	+	9.17078e28i	−0.820221	+	0.0873884i
$724$	2.60159e29	−	8.18295e28i	0.244334	−	0.0768520i
$725$		−	1.15952e30i		−	1.07332i
$726$	−1.59362e29	−	6.02665e29i	−0.145395	−	0.549846i
$727$		−	3.61004e29i		−	0.324639i	−0.986738	−	0.162319i	$-0.948102\pi$
$727$		−	3.61004e29i		−	0.324639i	0.986738	−	0.162319i	$-0.0518975\pi$
$728$	−1.74711e30	+	8.59320e29i	−1.54860	+	0.761685i
$729$	9.20194e29	−	6.80634e29i	0.803971	−	0.594668i
$730$	1.74869e29	−	2.68529e28i	0.150599	−	0.0231260i
$731$	1.29241e29			0.109715
$732$	−8.28833e29	+	3.61105e29i	−0.693586	+	0.302181i
$733$	2.21437e30			1.82666			0.913331	−	0.407217i	$-0.133501\pi$
$733$	2.21437e30			1.82666			0.913331	+	0.407217i	$0.133501\pi$
$734$	4.30434e29	−	6.60973e28i	0.350024	−	0.0537496i
$735$	−9.37444e27	−	8.79878e28i	−0.00751499	−	0.0705351i
$736$	6.82020e28	+	7.14924e28i	0.0538989	+	0.0564993i
$737$			1.19894e30i			0.934091i
$738$	−1.81712e30	+	6.93643e29i	−1.39570	+	0.532775i
$739$		−	1.59257e30i		−	1.20596i	−0.797756	−	0.602980i	$-0.793980\pi$
$739$		−	1.59257e30i		−	1.20596i	0.797756	−	0.602980i	$-0.206020\pi$
$740$	−4.09711e28	−	1.30259e29i	−0.0305876	−	0.0972464i
$741$	−3.35836e29	−	3.15213e30i	−0.247193	−	2.32013i
$742$	5.11254e28	+	3.32935e29i	0.0371019	+	0.241612i
$743$	−2.25578e30			−1.61404			−0.807021	−	0.590523i	$-0.798921\pi$
$743$	−2.25578e30			−1.61404			−0.807021	+	0.590523i	$0.798921\pi$
$744$	1.22309e30	−	7.72365e29i	0.862863	−	0.544887i
$745$	8.04641e29			0.559708
$746$	4.35901e28	+	2.83864e29i	0.0298972	+	0.194694i
$747$	2.57689e30	−	5.55401e29i	1.74273	−	0.375613i
$748$	7.62979e28	+	2.42572e29i	0.0508798	+	0.161761i
$749$			2.31760e30i			1.52398i
$750$	−9.16297e29	+	2.42295e29i	−0.594146	+	0.157109i
$751$			9.45189e29i			0.604365i	0.953250	+	0.302182i	$0.0977152\pi$
$751$			9.45189e29i			0.604365i	−0.953250	+	0.302182i	$0.902285\pi$
$752$	1.39370e30	−	9.73000e29i	0.878782	−	0.613516i
$753$	−1.49825e30	+	1.59628e29i	−0.931619	+	0.0992571i
$754$	3.02259e30	−	4.64148e29i	1.85345	−	0.284615i
$755$	7.83856e29			0.474016
$756$	1.08031e30	+	1.50315e30i	0.644274	+	0.896444i
$757$	−6.67117e29			−0.392369			−0.196185	−	0.980567i	$-0.562855\pi$
$757$	−6.67117e29			−0.392369			−0.196185	+	0.980567i	$0.562855\pi$
$758$	4.06263e29	−	6.23856e28i	0.235657	−	0.0361874i
$759$	−8.91297e28	+	9.49610e27i	−0.0509899	+	0.00543259i
$760$	−3.78672e29	−	7.69888e29i	−0.213659	−	0.434395i
$761$			1.23141e30i			0.685275i	0.939468	+	0.342637i	$0.111320\pi$
$761$			1.23141e30i			0.685275i	−0.939468	+	0.342637i	$0.888680\pi$
$762$	−2.31478e30	+	6.12095e29i	−1.27052	+	0.335963i
$763$			2.48962e30i			1.34780i
$764$	1.78094e30	−	5.60169e29i	0.950972	−	0.299116i
$765$	−1.55447e29	+	3.35038e28i	−0.0818726	+	0.0176461i
$766$	−2.45109e29	−	1.59618e30i	−0.127338	−	0.829237i
$767$	−2.01905e30			−1.03466
$768$	4.81187e29	−	1.91889e30i	0.243232	−	0.969968i
$769$	−3.15321e30			−1.57227			−0.786133	−	0.618058i	$-0.787920\pi$
$769$	−3.15321e30			−1.57227			−0.786133	+	0.618058i	$0.787920\pi$
$770$	−7.25589e28	−	4.72512e29i	−0.0356893	−	0.232413i
$771$	3.67622e29	+	3.45048e30i	0.178374	+	1.67420i
$772$	−2.26192e30	+	7.11458e29i	−1.08267	+	0.340540i
$773$			1.51154e30i			0.713730i	0.934156	+	0.356865i	$0.116154\pi$
$773$			1.51154e30i			0.713730i	−0.934156	+	0.356865i	$0.883846\pi$
$774$	8.52151e29	−	3.25288e29i	0.396951	−	0.151526i
$775$			1.98706e30i			0.913151i
$776$	−1.80024e29	−	3.66011e29i	−0.0816173	−	0.165938i
$777$	−8.21854e28	−	7.71386e29i	−0.0367599	−	0.345025i
$778$	2.45707e30	−	3.77307e29i	1.08425	−	0.166498i
$779$	5.12154e30			2.22975
$780$	−4.71481e29	−	1.08217e30i	−0.202521	−	0.464840i
$781$	2.13018e30			0.902777
$782$	−4.76618e28	+	7.31894e27i	−0.0199296	+	0.00306039i
$783$	−9.10220e29	−	2.76122e30i	−0.375533	−	1.13921i
$784$	−4.40509e29	+	3.07538e29i	−0.179323	+	0.125193i
$785$		−	7.19745e29i		−	0.289100i
$786$	5.53839e29	+	2.09447e30i	0.219506	+	0.830115i
$787$			1.45905e30i			0.570605i	0.958438	+	0.285302i	$0.0920940\pi$
$787$			1.45905e30i			0.570605i	−0.958438	+	0.285302i	$0.907906\pi$
$788$	−3.50744e29	−	1.11511e30i	−0.135352	−	0.430322i
$789$	−1.04552e30	+	1.11392e29i	−0.398129	+	0.0424177i
$790$	2.08049e29	+	1.35484e30i	0.0781774	+	0.509100i
$791$	−2.05195e30			−0.760874
$792$	1.11360e30	+	1.40737e30i	0.407489	+	0.514983i
$793$	3.27527e30			1.18271
$794$	−3.00006e29	−	1.95367e30i	−0.106909	−	0.696205i
$795$	−2.03067e29	+	2.16353e28i	−0.0714143	+	0.00760866i
$796$	−1.22897e30	−	3.90723e30i	−0.426534	−	1.35607i
$797$			4.63961e30i			1.58916i	0.607156	+	0.794582i	$0.292310\pi$
$797$			4.63961e30i			1.58916i	−0.607156	+	0.794582i	$0.707690\pi$
$798$	−1.24605e30	−	4.71225e30i	−0.421218	−	1.59294i
$799$			8.29525e29i			0.276750i
$800$	1.87579e30	+	1.96629e30i	0.617645	+	0.647444i
$801$	−6.65279e29	−	3.08669e30i	−0.216203	−	1.00312i
$802$	3.91068e30	−	6.00524e29i	1.25436	−	0.192619i
$803$	9.74449e29			0.308493
$804$	1.81818e30	+	4.17321e30i	0.568132	+	1.30401i
$805$	9.06523e28			0.0279590
$806$	−5.17977e30	+	7.95405e29i	−1.57686	+	0.242142i
$807$	6.03796e29	+	5.66718e30i	0.181434	+	1.70292i
$808$	1.06327e30	−	5.22974e29i	0.315373	−	0.155117i
$809$		−	1.43073e30i		−	0.418887i	−0.977821	−	0.209444i	$-0.932835\pi$
$809$		−	1.43073e30i		−	0.418887i	0.977821	−	0.209444i	$-0.0671653\pi$
$810$	−9.40618e29	+	6.12155e29i	−0.271845	+	0.176917i
$811$			2.54044e29i			0.0724752i	0.999343	+	0.0362376i	$0.0115373\pi$
$811$			2.54044e29i			0.0724752i	−0.999343	+	0.0362376i	$0.988463\pi$
$812$	4.48543e30	−	1.41083e30i	1.26318	−	0.397317i
$813$	−1.73733e29	−	1.63065e30i	−0.0482983	−	0.453324i
$814$	−1.14155e29	−	7.43389e29i	−0.0313284	−	0.204014i
$815$	1.94901e29			0.0528032
$816$	6.33432e29	+	7.28628e29i	0.169416	+	0.194876i
$817$	−2.40177e30			−0.634162
$818$	−3.52100e29	−	2.29292e30i	−0.0917818	−	0.597694i
$819$	−1.41292e30	−	6.55552e30i	−0.363611	−	1.68704i
$820$	1.81927e30	−	5.72227e29i	0.462223	−	0.145386i
$821$		−	6.81124e30i		−	1.70853i	−0.519836	−	0.854266i	$-0.674007\pi$
$821$		−	6.81124e30i		−	1.70853i	0.519836	−	0.854266i	$-0.325993\pi$
$822$	−5.84711e30	+	1.54614e30i	−1.44806	+	0.382909i
$823$		−	5.29973e30i		−	1.29585i	−0.761703	−	0.647926i	$-0.775637\pi$
$823$		−	5.29973e30i		−	1.29585i	0.761703	−	0.647926i	$-0.224363\pi$
$824$	−8.66630e29	+	4.26255e29i	−0.209217	+	0.102904i
$825$	−2.45137e30	+	2.61175e29i	−0.584309	+	0.0622538i
$826$	−3.06858e30	+	4.71210e29i	−0.722181	+	0.110898i
$827$	−7.40038e30			−1.71967			−0.859837	−	0.510568i	$-0.829435\pi$
$827$	−7.40038e30			−1.71967			−0.859837	+	0.510568i	$0.829435\pi$
$828$	−2.95837e29	+	1.68218e29i	−0.0678788	+	0.0385970i
$829$	5.29022e30			1.19854			0.599269	−	0.800548i	$-0.295458\pi$
$829$	5.29022e30			1.19854			0.599269	+	0.800548i	$0.295458\pi$
$830$	−2.55478e30	+	3.92312e29i	−0.571523	+	0.0877631i
$831$	−2.68261e30	+	2.85812e29i	−0.592579	+	0.0631349i
$832$	−4.37476e30	+	5.67682e30i	−0.954245	+	1.23825i
$833$		−	2.62190e29i		−	0.0564733i
$834$	−4.07715e30	+	1.07812e30i	−0.867188	+	0.229309i
$835$			9.17372e29i			0.192680i
$836$	−1.41790e30	−	4.50789e30i	−0.294089	−	0.934991i
$837$	1.55983e30	+	4.73187e30i	0.319493	+	0.969205i
$838$	4.87901e29	+	3.17727e30i	0.0986891	+	0.642675i
$839$	3.60873e30			0.720865			0.360433	−	0.932785i	$-0.382629\pi$
$839$	3.60873e30			0.720865			0.360433	+	0.932785i	$0.382629\pi$
$840$	−9.69120e29	−	1.53466e30i	−0.191181	−	0.302747i
$841$	−2.25239e30			−0.438819
$842$	1.01306e29	+	6.59716e29i	0.0194921	+	0.126935i
$843$	−1.07390e29	−	1.00795e30i	−0.0204067	−	0.191536i
$844$	−9.46996e29	−	3.01076e30i	−0.177727	−	0.565042i
$845$			2.52654e30i			0.468306i
$846$	2.08784e30	+	5.46948e30i	0.382216	+	1.00128i
$847$			3.47250e30i			0.627864i
$848$	7.09769e29	+	1.01665e30i	0.126754	+	0.181558i
$849$	5.48367e29	+	5.14693e30i	0.0967254	+	0.907857i
$850$	−1.31086e30	+	2.01296e29i	−0.228380	+	0.0350700i
$851$	1.42620e29			0.0245426
$852$	7.41462e30	−	3.23040e30i	1.26030	−	0.549086i
$853$	−4.83126e30			−0.811140			−0.405570	−	0.914064i	$-0.632927\pi$
$853$	−4.83126e30			−0.811140			−0.405570	+	0.914064i	$0.632927\pi$
$854$	4.97778e30	−	7.64387e29i	0.825521	−	0.126767i
$855$	2.88879e30	−	6.22625e29i	0.473229	−	0.101996i
$856$	3.76525e30	+	7.65524e30i	0.609284	+	1.23875i
$857$		−	3.28335e30i		−	0.524829i	−0.964955	−	0.262415i	$-0.915481\pi$
$857$		−	3.28335e30i		−	0.524829i	0.964955	−	0.262415i	$-0.0845188\pi$
$858$	−1.66209e30	−	6.28558e30i	−0.262445	−	0.992497i
$859$		−	6.08036e30i		−	0.948420i	−0.880412	−	0.474210i	$-0.842734\pi$
$859$		−	6.08036e30i		−	0.948420i	0.880412	−	0.474210i	$-0.157266\pi$
$860$	−8.53156e29	+	2.68349e29i	−0.131460	+	0.0413491i
$861$	1.07736e31	−	1.14785e30i	1.63994	−	0.174724i
$862$	−1.69078e29	−	1.10105e30i	−0.0254249	−	0.165570i
$863$	2.96453e29			0.0440396			0.0220198	−	0.999758i	$-0.492990\pi$
$863$	2.96453e29			0.0440396			0.0220198	+	0.999758i	$0.492990\pi$
$864$	6.01043e30	+	3.20992e30i	0.882087	+	0.471086i
$865$	−3.43081e30			−0.497424
$866$	7.75843e29	+	5.05238e30i	0.111131	+	0.723699i
$867$	6.55814e30	−	6.98721e29i	0.928069	−	0.0988788i
$868$	−7.68663e30	+	2.41773e30i	−1.07468	+	0.338026i
$869$			7.54977e30i			1.04286i
$870$	7.28775e29	+	2.75604e30i	0.0994583	+	0.376125i
$871$		−	1.64911e31i		−	2.22362i
$872$	4.04471e30	+	8.22342e30i	0.538846	+	1.09554i
$873$	1.37336e30	−	2.96001e29i	0.180773	−	0.0389623i
$874$	8.85732e29	−	1.36013e29i	0.115195	−	0.0176893i
$875$	5.27962e30			0.678450
$876$	3.39181e30	−	1.47774e30i	0.430664	−	0.187632i
$877$	−1.00412e31			−1.25977			−0.629883	−	0.776690i	$-0.716897\pi$
$877$	−1.00412e31			−1.25977			−0.629883	+	0.776690i	$0.716897\pi$
$878$	−5.42599e30	+	8.33214e29i	−0.672646	+	0.103291i
$879$	1.41661e29	+	1.32962e30i	0.0173527	+	0.162871i
$880$	−1.00733e30	−	1.44287e30i	−0.121928	−	0.174646i
$881$			1.67305e30i			0.200107i	0.994982	+	0.100054i	$0.0319014\pi$
$881$			1.67305e30i			0.200107i	−0.994982	+	0.100054i	$0.968099\pi$
$882$	−6.59908e29	−	1.72875e30i	−0.0779944	−	0.204321i
$883$		−	2.92750e30i		−	0.341908i	−0.985279	−	0.170954i	$-0.945315\pi$
$883$		−	2.92750e30i		−	0.341908i	0.985279	−	0.170954i	$-0.0546850\pi$
$884$	−1.04946e30	−	3.33652e30i	−0.121120	−	0.385075i
$885$	−1.99407e29	−	1.87162e30i	−0.0227424	−	0.213459i
$886$	−6.21174e29	−	4.04516e30i	−0.0700098	−	0.455912i
$887$	−3.76931e29			−0.0419821			−0.0209910	−	0.999780i	$-0.506682\pi$
$887$	−3.76931e29			−0.0419821			−0.0209910	+	0.999780i	$0.506682\pi$
$888$	−1.52469e30	−	2.41443e30i	−0.167820	−	0.265754i
$889$	1.33376e31			1.45080
$890$	4.69926e29	+	3.06021e30i	0.0505166	+	0.328970i
$891$	−5.63255e30	+	2.54627e30i	−0.598396	+	0.270513i
$892$	−1.87071e30	−	5.94751e30i	−0.196415	−	0.624459i
$893$		−	1.54156e31i		−	1.59964i
$894$	1.62676e31	−	4.30162e30i	1.66832	−	0.441152i
$895$			3.59178e30i			0.364056i
$896$	−5.32394e30	+	9.64866e30i	−0.533334	+	0.966569i
$897$	1.22596e30	−	1.30616e29i	0.121382	−	0.0129323i
$898$	−2.23621e30	+	3.43392e29i	−0.218832	+	0.0336038i
$899$	1.26560e31			1.22411
$900$	−8.13654e30	+	4.62657e30i	−0.777845	+	0.442296i
$901$	−6.05109e29			−0.0571773
$902$	1.03826e31	−	1.59435e30i	0.969700	−	0.148907i
$903$	−5.05235e30	+	5.38290e29i	−0.466415	+	0.0496930i
$904$	−6.77776e30	+	3.33366e30i	−0.618468	+	0.304196i
$905$		−	9.21054e29i		−	0.0830759i
$906$	1.58474e31	−	4.19050e30i	1.41290	−	0.373611i
$907$			1.44056e31i			1.26956i	0.772692	+	0.634781i	$0.218909\pi$
$907$			1.44056e31i			1.26956i	−0.772692	+	0.634781i	$0.781091\pi$
$908$	−1.56906e31	+	4.93527e30i	−1.36690	+	0.429942i
$909$	8.59891e29	+	3.98963e30i	0.0740496	+	0.343567i
$910$	9.98030e29	+	6.49929e30i	0.0849589	+	0.553263i
$911$	2.07629e30			0.174721			0.0873603	−	0.996177i	$-0.472157\pi$
$911$	2.07629e30			0.174721			0.0873603	+	0.996177i	$0.472157\pi$
$912$	−1.17715e31	−	1.35406e31i	−0.979234	−	1.12640i
$913$	−1.42364e31			−1.17073
$914$	3.29215e30	+	2.14388e31i	0.267636	+	1.74288i
$915$	3.23474e29	+	3.03610e30i	0.0259967	+	0.244003i
$916$	9.82040e30	−	3.08888e30i	0.780237	−	0.245413i
$917$		−	1.20682e31i		−	0.947901i
$918$	−2.96360e30	+	1.50838e30i	−0.230129	+	0.117128i
$919$			1.88208e31i			1.44486i	0.691443	+	0.722431i	$0.256975\pi$
$919$			1.88208e31i			1.44486i	−0.691443	+	0.722431i	$0.743025\pi$
$920$	2.99432e29	−	1.47277e29i	0.0227262	−	0.0111779i
$921$	2.45440e30	+	2.30368e31i	0.184170	+	1.72861i
$922$	1.64328e30	−	2.52342e29i	0.121909	−	0.0187204i
$923$	−2.93001e31			−2.14907
$924$	−3.99299e30	−	9.16498e30i	−0.289563	−	0.664624i
$925$	3.92255e30			0.281242
$926$	−1.38994e30	+	2.13440e29i	−0.0985331	+	0.0151307i
$927$	−7.00863e29	−	3.25179e30i	−0.0491242	−	0.227921i
$928$	1.25237e31	−	1.19473e31i	0.867918	−	0.827972i
$929$		−	8.29721e30i		−	0.568548i	−0.958743	−	0.284274i	$-0.908247\pi$
$929$		−	8.29721e30i		−	0.568548i	0.958743	−	0.284274i	$-0.0917526\pi$
$930$	−1.24889e30	−	4.72298e30i	−0.0846163	−	0.319997i
$931$			4.87246e30i			0.326420i
$932$	−4.21328e30	−	1.33952e31i	−0.279096	−	0.887323i
$933$	−2.75445e31	+	2.93466e30i	−1.80417	+	0.192221i
$934$	−1.09580e30	−	7.13595e30i	−0.0709721	−	0.462179i
$935$	8.58792e29			0.0550004
$936$	−1.53173e31	−	1.93580e31i	−0.970034	−	1.22592i
$937$	2.26767e31			1.42008			0.710042	−	0.704159i	$-0.248676\pi$
$937$	2.26767e31			1.42008			0.710042	+	0.704159i	$0.248676\pi$
$938$	−3.84873e30	−	2.50634e31i	−0.238335	−	1.55206i
$939$	2.12382e29	−	2.26277e28i	0.0130055	−	0.00138564i
$940$	−1.72238e30	−	5.47593e30i	−0.104301	−	0.331601i
$941$		−	5.62964e30i		−	0.337124i	−0.985691	−	0.168562i	$-0.946088\pi$
$941$		−	5.62964e30i		−	0.337124i	0.985691	−	0.168562i	$-0.0539123\pi$
$942$	−3.84776e30	−	1.45512e31i	−0.227863	−	0.861719i
$943$			1.99192e30i			0.116654i
$944$	−9.37023e30	+	6.54176e30i	−0.542681	+	0.378869i
$945$	5.93729e30	−	1.95719e30i	0.340059	−	0.112098i
$946$	−4.86898e30	+	7.47680e29i	−0.275792	+	0.0423505i
$947$	−1.84904e31			−1.03579			−0.517896	−	0.855444i	$-0.673284\pi$
$947$	−1.84904e31			−1.03579			−0.517896	+	0.855444i	$0.673284\pi$
$948$	1.14492e31	+	2.62788e31i	0.634287	+	1.45586i
$949$	−1.34033e31			−0.734373
$950$	2.43607e31	−	3.74082e30i	1.32005	−	0.202707i
$951$	1.44647e30	+	1.35764e31i	0.0775198	+	0.727595i
$952$	−2.37366e30	−	4.82595e30i	−0.125814	−	0.255796i
$953$			6.23953e30i			0.327097i	0.986535	+	0.163548i	$0.0522940\pi$
$953$			6.23953e30i			0.327097i	−0.986535	+	0.163548i	$0.947706\pi$
$954$	−3.98979e30	+	1.52301e30i	−0.206868	+	0.0789666i
$955$		−	6.30514e30i		−	0.323340i
$956$	5.20051e30	−	1.63575e30i	0.263778	−	0.0829678i
$957$	1.66348e30	+	1.56133e31i	0.0834531	+	0.783284i
$958$	−2.35803e30	−	1.53558e31i	−0.117007	−	0.761963i
$959$	3.36905e31			1.65353
$960$	−5.69435e30	−	3.49466e30i	−0.276437	−	0.169651i
$961$	−8.62890e29			−0.0414343
$962$	1.57017e30	+	1.02251e31i	0.0745776	+	0.485658i
$963$	−2.87241e31	+	6.19096e30i	−1.34949	+	0.290859i
$964$	1.69319e31	−	5.32570e30i	0.786858	−	0.247496i
$965$			8.00801e30i			0.368119i
$966$	1.83274e30	−	4.84628e29i	0.0833374	−	0.0220368i
$967$		−	1.26100e31i		−	0.567200i	−0.958943	−	0.283600i	$-0.908471\pi$
$967$		−	1.26100e31i		−	0.567200i	0.958943	−	0.283600i	$-0.0915287\pi$
$968$	5.64154e30	+	1.14700e31i	0.251019	+	0.510353i
$969$	8.70697e30	−	9.27663e29i	0.383237	−	0.0408311i
$970$	−1.36157e30	+	2.09083e29i	−0.0592841	+	0.00910366i
$971$	7.20387e28			0.00310287			0.00155144	−	0.999999i	$-0.499506\pi$
$971$	7.20387e28			0.00310287			0.00155144	+	0.999999i	$0.499506\pi$
$972$	−1.57441e31	+	1.74046e31i	−0.670844	+	0.741598i
$973$	2.34922e31			0.990235
$974$	8.72100e30	−	1.33920e30i	0.363661	−	0.0558438i
$975$	3.37180e31	−	3.59240e30i	1.39096	−	0.148196i
$976$	1.52002e31	−	1.06119e31i	0.620335	−	0.433082i
$977$		−	3.99307e31i		−	1.61218i	−0.591790	−	0.806092i	$-0.701579\pi$
$977$		−	3.99307e31i		−	1.61218i	0.591790	−	0.806092i	$-0.298421\pi$
$978$	3.94036e30	−	1.04194e30i	0.157390	−	0.0416185i
$979$			1.70529e31i			0.673874i
$980$	5.44397e29	+	1.73079e30i	0.0212835	+	0.0676660i
$981$	−3.08561e31	+	6.65046e30i	−1.19348	+	0.257233i
$982$	6.20500e30	+	4.04077e31i	0.237449	+	1.54630i
$983$	3.07325e31			1.16355			0.581776	−	0.813349i	$-0.302358\pi$
$983$	3.07325e31			1.16355			0.581776	+	0.813349i	$0.302358\pi$
$984$	3.37214e31	−	2.12946e31i	1.26316	−	0.797667i
$985$	−3.94790e30			−0.146314
$986$	1.28209e30	+	8.34915e30i	0.0470124	+	0.306150i
$987$	−3.45499e30	−	3.24282e31i	−0.125348	−	1.17650i
$988$	1.95028e31	+	6.20049e31i	0.700083	+	2.22576i
$989$		−	9.34121e29i		−	0.0331774i
$990$	5.66245e30	−	2.16150e30i	0.198992	−	0.0759602i
$991$			7.59153e30i			0.263971i	0.991252	+	0.131985i	$0.0421352\pi$
$991$			7.59153e30i			0.263971i	−0.991252	+	0.131985i	$0.957865\pi$
$992$	−2.14617e31	+	2.04739e31i	−0.738399	+	0.704415i
$993$	−2.89419e30	−	2.71646e31i	−0.0985281	−	0.924777i
$994$	−4.45305e31	+	6.83810e30i	−1.50003	+	0.230345i
$995$	−1.38330e31			−0.461077
$996$	−4.95533e31	+	2.15893e31i	−1.63437	+	0.712060i
$997$	2.02301e31			0.660234			0.330117	−	0.943940i	$-0.392912\pi$
$997$	2.02301e31			0.660234			0.330117	+	0.943940i	$0.392912\pi$
$998$	−4.13789e31	+	6.35414e30i	−1.33631	+	0.205204i
$999$	9.34095e30	−	3.07919e30i	0.298506	−	0.0984007i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	12.22.b.a.11.22	yes	40
3.2	odd	2	inner	12.22.b.a.11.19	✓	40
4.3	odd	2	inner	12.22.b.a.11.20	yes	40
12.11	even	2	inner	12.22.b.a.11.21	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
12.22.b.a.11.19	✓	40	3.2	odd	2	inner
12.22.b.a.11.20	yes	40	4.3	odd	2	inner
12.22.b.a.11.21	yes	40	12.11	even	2	inner
12.22.b.a.11.22	yes	40	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 12 = 2^{2} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 22 \)
Character orbit:	\([\chi]\)	\(=\)	12.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(219.802 + 1431.38i) q^{2} +(101700. - 10835.4i) q^{3} +(-2.00053e6 + 629239. i) q^{4} +7.08257e6i q^{5} +(3.78635e7 + 1.43190e8i) q^{6} -8.25046e8i q^{7} +(-1.34040e9 - 2.72520e9i) q^{8} +(1.02255e10 - 2.20393e9i) q^{9} +O(q^{10})\)	\(q+(219.802 + 1431.38i) q^{2} +(101700. - 10835.4i) q^{3} +(-2.00053e6 + 629239. i) q^{4} +7.08257e6i q^{5} +(3.78635e7 + 1.43190e8i) q^{6} -8.25046e8i q^{7} +(-1.34040e9 - 2.72520e9i) q^{8} +(1.02255e10 - 2.20393e9i) q^{9} +(-1.01378e10 + 1.55676e9i) q^{10} -5.64925e10 q^{11} +(-1.96636e11 + 8.56703e10i) q^{12} +7.77040e11 q^{13} +(1.18095e12 - 1.81347e11i) q^{14} +(7.67425e10 + 7.20299e11i) q^{15} +(3.60616e12 - 2.51762e12i) q^{16} +2.14638e12i q^{17} +(5.40224e12 + 1.41522e13i) q^{18} -3.98877e13i q^{19} +(-4.45663e12 - 1.41689e13i) q^{20} +(-8.93970e12 - 8.39074e13i) q^{21} +(-1.24172e13 - 8.08620e13i) q^{22} +1.55135e13 q^{23} +(-1.65847e14 - 2.62630e14i) q^{24} +4.26674e14 q^{25} +(1.70795e14 + 1.11224e15i) q^{26} +(1.01606e15 - 3.34938e14i) q^{27} +(5.19151e14 + 1.65053e15i) q^{28} -2.71758e15i q^{29} +(-1.01415e15 + 2.68171e14i) q^{30} +4.65708e15i q^{31} +(4.39630e15 + 4.60840e15i) q^{32} +(-5.74530e15 + 6.12119e14i) q^{33} +(-3.07228e15 + 4.71778e14i) q^{34} +5.84344e15 q^{35} +(-1.90697e16 + 1.08433e16i) q^{36} +9.19330e15 q^{37} +(5.70943e16 - 8.76739e15i) q^{38} +(7.90251e16 - 8.41954e15i) q^{39} +(1.93014e16 - 9.49346e15i) q^{40} +1.28399e17i q^{41} +(1.18138e17 - 3.12391e16i) q^{42} -6.02134e16i q^{43} +(1.13015e17 - 3.55473e16i) q^{44} +(1.56095e16 + 7.24231e16i) q^{45} +(3.40990e15 + 2.22057e16i) q^{46} +3.86477e17 q^{47} +(3.39468e17 - 2.95117e17i) q^{48} -1.22154e17 q^{49} +(9.37839e16 + 6.10732e17i) q^{50} +(2.32569e16 + 2.18287e17i) q^{51} +(-1.55449e18 + 4.88944e17i) q^{52} +2.81921e17i q^{53} +(7.02754e17 + 1.38074e18i) q^{54} -4.00112e17i q^{55} +(-2.24841e18 + 1.10589e18i) q^{56} +(-4.32199e17 - 4.05659e18i) q^{57} +(3.88988e18 - 5.97329e17i) q^{58} -2.59839e18 q^{59} +(-6.06766e17 - 1.39269e18i) q^{60} +4.21506e18 q^{61} +(-6.66604e18 + 1.02364e18i) q^{62} +(-1.81834e18 - 8.43654e18i) q^{63} +(-5.63004e18 + 7.30570e18i) q^{64} +5.50344e18i q^{65} +(-2.13900e18 - 8.08914e18i) q^{66} -2.12230e19i q^{67} +(-1.35059e18 - 4.29389e18i) q^{68} +(1.57773e18 - 1.68095e17i) q^{69} +(1.28440e18 + 8.36417e18i) q^{70} -3.77073e19 q^{71} +(-1.97124e19 - 2.49125e19i) q^{72} -1.72492e19 q^{73} +(2.02071e18 + 1.31591e19i) q^{74} +(4.33929e19 - 4.62319e18i) q^{75} +(2.50989e19 + 7.97963e19i) q^{76} +4.66089e19i q^{77} +(2.94214e19 + 1.11264e20i) q^{78} -1.33642e20i q^{79} +(1.78312e19 + 2.55409e19i) q^{80} +(9.97044e19 - 4.50727e19i) q^{81} +(-1.83787e20 + 2.82224e19i) q^{82} +2.52005e20 q^{83} +(7.06819e19 + 1.62234e20i) q^{84} -1.52019e19 q^{85} +(8.61881e19 - 1.32350e19i) q^{86} +(-2.94461e19 - 2.76378e20i) q^{87} +(7.57224e19 + 1.53953e20i) q^{88} -3.01861e20i q^{89} +(-1.00234e20 + 3.82618e19i) q^{90} -6.41093e20i q^{91} +(-3.10352e19 + 9.76170e18i) q^{92} +(5.04613e19 + 4.73626e20i) q^{93} +(8.49483e19 + 5.53193e20i) q^{94} +2.82507e20 q^{95} +(4.97039e20 + 4.21040e20i) q^{96} +1.34306e20 q^{97} +(-2.68498e19 - 1.74849e20i) q^{98} +(-5.77666e20 + 1.24505e20i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 1212040 q^{4} - 73477608 q^{6} + 4862757768 q^{9}+O(q^{10}) \) 40 * q + 1212040 * q^4 - 73477608 * q^6 + 4862757768 * q^9	\( 40 q + 1212040 q^{4} - 73477608 q^{6} + 4862757768 q^{9} + 70993722608 q^{10} + 230311800264 q^{12} + 532697931824 q^{13} - 3296861950688 q^{16} - 38138435545488 q^{18} + 6345498814320 q^{21} + 345245332418448 q^{22} + 162733136355360 q^{24} - 28\!\cdots\!08 q^{25}+ \cdots + 19\!\cdots\!68 q^{97}+O(q^{100}) \) 40 * q + 1212040 * q^4 - 73477608 * q^6 + 4862757768 * q^9 + 70993722608 * q^10 + 230311800264 * q^12 + 532697931824 * q^13 - 3296861950688 * q^16 - 38138435545488 * q^18 + 6345498814320 * q^21 + 345245332418448 * q^22 + 162733136355360 * q^24 - 2870634573953208 * q^25 + 3010485857135664 * q^28 + 5225832293639088 * q^30 - 7282205643351936 * q^33 - 11653770049992256 * q^34 - 18580578856893912 * q^36 - 42230886115147792 * q^37 - 89660451263290816 * q^40 - 196777060056297264 * q^42 + 490656937607621376 * q^45 - 24590270471085024 * q^46 - 1070121602451491040 * q^48 - 1521600851011396808 * q^49 + 1474695233111072240 * q^52 - 107978656785090264 * q^54 - 410005705945522032 * q^57 + 9260173307858336144 * q^58 + 6491621502020133696 * q^60 - 5700218795673195856 * q^61 - 2949437838551773568 * q^64 + 1836224451373338192 * q^66 + 25444406037298107648 * q^69 - 24886444039106795232 * q^70 - 27969226308253542336 * q^72 + 101891967257574779024 * q^73 + 22386121373924673552 * q^76 + 76385487692811283152 * q^78 - 476218176140556806040 * q^81 + 1864686882869863520 * q^82 + 311685180307346738352 * q^84 - 605170615993311678464 * q^85 + 15063645347500158144 * q^88 - 159737520743388593232 * q^90 + 682248293569820157360 * q^93 + 242051617770611035200 * q^94 - 1187951481218430818688 * q^96 + 196191301644672463568 * q^97

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