LMFDB - Embedded newform 804.2.c.b.671.101

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(671,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("804.671");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.c (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:	$6.41997232251$
Analytic rank:	$0$
Dimension:	$128$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			671.101
Character	$\chi$	$=$	804.671
Dual form			804.2.c.b.671.102

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.11601 - 0.868635i) q^{2} +(-1.72876 + 0.106712i) q^{3} +(0.490945 - 1.93881i) q^{4} +3.33937i q^{5} +(-1.83662 + 1.62075i) q^{6} +0.598149i q^{7} +(-1.13622 - 2.59018i) q^{8} +(2.97723 - 0.368959i) q^{9} +O(q^{10})$	\(q+(1.11601 - 0.868635i) q^{2} +(-1.72876 + 0.106712i) q^{3} +(0.490945 - 1.93881i) q^{4} +3.33937i q^{5} +(-1.83662 + 1.62075i) q^{6} +0.598149i q^{7} +(-1.13622 - 2.59018i) q^{8} +(2.97723 - 0.368959i) q^{9} +(2.90070 + 3.72676i) q^{10} -6.25726 q^{11} +(-0.641832 + 3.40412i) q^{12} -3.61246 q^{13} +(0.519573 + 0.667538i) q^{14} +(-0.356351 - 5.77297i) q^{15} +(-3.51795 - 1.90370i) q^{16} -5.84110i q^{17} +(3.00211 - 2.99788i) q^{18} -3.83853i q^{19} +(6.47440 + 1.63945i) q^{20} +(-0.0638297 - 1.03406i) q^{21} +(-6.98315 + 5.43527i) q^{22} -2.28203 q^{23} +(2.24065 + 4.35654i) q^{24} -6.15141 q^{25} +(-4.03153 + 3.13791i) q^{26} +(-5.10754 + 0.955548i) q^{27} +(1.15970 + 0.293658i) q^{28} +0.970928i q^{29} +(-5.41230 - 6.13314i) q^{30} -8.10842i q^{31} +(-5.57967 + 0.931273i) q^{32} +(10.8173 - 0.667725i) q^{33} +(-5.07379 - 6.51871i) q^{34} -1.99744 q^{35} +(0.746313 - 5.95340i) q^{36} -2.41368 q^{37} +(-3.33429 - 4.28383i) q^{38} +(6.24508 - 0.385493i) q^{39} +(8.64956 - 3.79425i) q^{40} +7.82589i q^{41} +(-0.969452 - 1.09857i) q^{42} +6.30778i q^{43} +(-3.07197 + 12.1316i) q^{44} +(1.23209 + 9.94206i) q^{45} +(-2.54676 + 1.98225i) q^{46} -8.81601 q^{47} +(6.28483 + 2.91563i) q^{48} +6.64222 q^{49} +(-6.86501 + 5.34333i) q^{50} +(0.623316 + 10.0979i) q^{51} +(-1.77352 + 7.00387i) q^{52} +6.57802i q^{53} +(-4.87003 + 5.50299i) q^{54} -20.8953i q^{55} +(1.54931 - 0.679627i) q^{56} +(0.409618 + 6.63591i) q^{57} +(0.843382 + 1.08356i) q^{58} +14.0688 q^{59} +(-11.3676 - 2.14332i) q^{60} -13.9587 q^{61} +(-7.04326 - 9.04906i) q^{62} +(0.220693 + 1.78082i) q^{63} +(-5.41802 + 5.88601i) q^{64} -12.0634i q^{65} +(11.4922 - 10.1415i) q^{66} -1.00000i q^{67} +(-11.3248 - 2.86766i) q^{68} +(3.94508 - 0.243520i) q^{69} +(-2.22916 + 1.73505i) q^{70} -8.83049 q^{71} +(-4.33845 - 7.29232i) q^{72} -0.0844839 q^{73} +(-2.69368 + 2.09661i) q^{74} +(10.6343 - 0.656429i) q^{75} +(-7.44218 - 1.88451i) q^{76} -3.74277i q^{77} +(6.63470 - 5.85491i) q^{78} +12.8855i q^{79} +(6.35715 - 11.7477i) q^{80} +(8.72774 - 2.19695i) q^{81} +(6.79785 + 8.73375i) q^{82} +2.46521 q^{83} +(-2.03617 - 0.383911i) q^{84} +19.5056 q^{85} +(5.47916 + 7.03953i) q^{86} +(-0.103610 - 1.67850i) q^{87} +(7.10961 + 16.2074i) q^{88} -1.95347i q^{89} +(10.0111 + 10.0252i) q^{90} -2.16079i q^{91} +(-1.12035 + 4.42441i) q^{92} +(0.865266 + 14.0175i) q^{93} +(-9.83873 + 7.65789i) q^{94} +12.8183 q^{95} +(9.54654 - 2.20537i) q^{96} +4.36011 q^{97} +(7.41276 - 5.76967i) q^{98} +(-18.6293 + 2.30867i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q + 4 q^{4} - 6 q^{6} - 4 q^{9}+O(q^{10}) $ 128 * q + 4 * q^4 - 6 * q^6 - 4 * q^9	$ 128 q + 4 q^{4} - 6 q^{6} - 4 q^{9} - 4 q^{10} + 4 q^{12} - 8 q^{13} - 4 q^{16} + 18 q^{18} - 8 q^{21} - 8 q^{22} - 24 q^{24} - 136 q^{25} + 14 q^{30} - 32 q^{33} + 34 q^{36} - 48 q^{37} + 16 q^{40} - 28 q^{42} - 16 q^{45} - 28 q^{46} - 22 q^{48} - 152 q^{49} + 8 q^{52} - 16 q^{54} - 32 q^{57} - 20 q^{58} - 14 q^{60} + 8 q^{61} + 16 q^{64} + 14 q^{66} + 56 q^{69} - 4 q^{70} - 8 q^{72} - 48 q^{73} - 36 q^{76} + 40 q^{78} + 44 q^{81} + 60 q^{82} + 46 q^{84} + 64 q^{85} - 28 q^{88} - 14 q^{90} + 32 q^{93} - 8 q^{96} + 64 q^{97}+O(q^{100}) $ 128 * q + 4 * q^4 - 6 * q^6 - 4 * q^9 - 4 * q^10 + 4 * q^12 - 8 * q^13 - 4 * q^16 + 18 * q^18 - 8 * q^21 - 8 * q^22 - 24 * q^24 - 136 * q^25 + 14 * q^30 - 32 * q^33 + 34 * q^36 - 48 * q^37 + 16 * q^40 - 28 * q^42 - 16 * q^45 - 28 * q^46 - 22 * q^48 - 152 * q^49 + 8 * q^52 - 16 * q^54 - 32 * q^57 - 20 * q^58 - 14 * q^60 + 8 * q^61 + 16 * q^64 + 14 * q^66 + 56 * q^69 - 4 * q^70 - 8 * q^72 - 48 * q^73 - 36 * q^76 + 40 * q^78 + 44 * q^81 + 60 * q^82 + 46 * q^84 + 64 * q^85 - 28 * q^88 - 14 * q^90 + 32 * q^93 - 8 * q^96 + 64 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/804\mathbb{Z}\right)^\times$.

$n$	$269$	$337$	$403$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$	1.11601	−	0.868635i	0.789136	−	0.614218i
$2$	1.11601	−	0.868635i	0.789136	−	0.614218i
$3$	−1.72876	+	0.106712i	−0.998100	+	0.0616103i
$3$	−1.72876	+	0.106712i	−0.998100	+	0.0616103i
$4$	0.490945	−	1.93881i	0.245473	−	0.969404i
$5$			3.33937i			1.49341i	0.665154	+	0.746706i	$0.268366\pi$
$5$			3.33937i			1.49341i	−0.665154	+	0.746706i	$0.731634\pi$
$6$	−1.83662	+	1.62075i	−0.749795	+	0.661670i
$7$			0.598149i			0.226079i	0.993590	+	0.113039i	$0.0360587\pi$
$7$			0.598149i			0.226079i	−0.993590	+	0.113039i	$0.963941\pi$
$8$	−1.13622	−	2.59018i	−0.401714	−	0.915765i
$9$	2.97723	−	0.368959i	0.992408	−	0.122986i
$10$	2.90070	+	3.72676i	0.917281	+	1.17851i
$11$	−6.25726			−1.88663			−0.943317	−	0.331893i	$-0.892313\pi$
$11$	−6.25726			−1.88663			−0.943317	+	0.331893i	$0.892313\pi$
$12$	−0.641832	+	3.40412i	−0.185281	+	0.982686i
$13$	−3.61246			−1.00192			−0.500958	−	0.865471i	$-0.667019\pi$
$13$	−3.61246			−1.00192			−0.500958	+	0.865471i	$0.667019\pi$
$14$	0.519573	+	0.667538i	0.138862	+	0.178407i
$15$	−0.356351	−	5.77297i	−0.0920095	−	1.49058i
$16$	−3.51795	−	1.90370i	−0.879486	−	0.475924i
$17$		−	5.84110i		−	1.41667i	−0.705874	−	0.708337i	$-0.749446\pi$
$17$		−	5.84110i		−	1.41667i	0.705874	−	0.708337i	$-0.250554\pi$
$18$	3.00211	−	2.99788i	0.707605	−	0.706608i
$19$		−	3.83853i		−	0.880620i	−0.897846	−	0.440310i	$-0.854869\pi$
$19$		−	3.83853i		−	0.880620i	0.897846	−	0.440310i	$-0.145131\pi$
$20$	6.47440	+	1.63945i	1.44772	+	0.366592i
$21$	−0.0638297	−	1.03406i	−0.0139288	−	0.225649i
$22$	−6.98315	+	5.43527i	−1.48881	+	1.15880i
$23$	−2.28203			−0.475836			−0.237918	−	0.971285i	$-0.576465\pi$
$23$	−2.28203			−0.475836			−0.237918	+	0.971285i	$0.576465\pi$
$24$	2.24065	+	4.35654i	0.457371	+	0.889276i
$25$	−6.15141			−1.23028
$26$	−4.03153	+	3.13791i	−0.790649	+	0.615395i
$27$	−5.10754	+	0.955548i	−0.982946	+	0.183895i
$28$	1.15970	+	0.293658i	0.219162	+	0.0554962i
$29$			0.970928i			0.180297i	0.995928	+	0.0901484i	$0.0287341\pi$
$29$			0.970928i			0.180297i	−0.995928	+	0.0901484i	$0.971266\pi$
$30$	−5.41230	−	6.13314i	−0.988146	−	1.11975i
$31$		−	8.10842i		−	1.45632i	−0.685410	−	0.728158i	$-0.740377\pi$
$31$		−	8.10842i		−	1.45632i	0.685410	−	0.728158i	$-0.259623\pi$
$32$	−5.57967	+	0.931273i	−0.986356	+	0.164627i
$33$	10.8173	−	0.667725i	1.88305	−	0.116236i
$34$	−5.07379	−	6.51871i	−0.870147	−	1.11795i
$35$	−1.99744			−0.337629
$36$	0.746313	−	5.95340i	0.124386	−	0.992234i
$37$	−2.41368			−0.396806			−0.198403	−	0.980121i	$-0.563576\pi$
$37$	−2.41368			−0.396806			−0.198403	+	0.980121i	$0.563576\pi$
$38$	−3.33429	−	4.28383i	−0.540893	−	0.694929i
$39$	6.24508	−	0.385493i	1.00001	−	0.0617284i
$40$	8.64956	−	3.79425i	1.36762	−	0.599924i
$41$			7.82589i			1.22220i	0.791554	+	0.611099i	$0.209272\pi$
$41$			7.82589i			1.22220i	−0.791554	+	0.611099i	$0.790728\pi$
$42$	−0.969452	−	1.09857i	−0.149590	−	0.169513i
$43$			6.30778i			0.961927i	0.876741	+	0.480964i	$0.159713\pi$
$43$			6.30778i			0.961927i	−0.876741	+	0.480964i	$0.840287\pi$
$44$	−3.07197	+	12.1316i	−0.463117	+	1.82891i
$45$	1.23209	+	9.94206i	0.183670	+	1.48208i
$46$	−2.54676	+	1.98225i	−0.375499	+	0.292267i
$47$	−8.81601			−1.28595			−0.642973	−	0.765889i	$-0.722299\pi$
$47$	−8.81601			−1.28595			−0.642973	+	0.765889i	$0.722299\pi$
$48$	6.28483	+	2.91563i	0.907137	+	0.420834i
$49$	6.64222			0.948888
$50$	−6.86501	+	5.34333i	−0.970860	+	0.755661i
$51$	0.623316	+	10.0979i	0.0872817	+	1.41398i
$52$	−1.77352	+	7.00387i	−0.245943	+	0.971262i
$53$			6.57802i			0.903560i	0.892129	+	0.451780i	$0.149211\pi$
$53$			6.57802i			0.903560i	−0.892129	+	0.451780i	$0.850789\pi$
$54$	−4.87003	+	5.50299i	−0.662727	+	0.748862i
$55$		−	20.8953i		−	2.81752i
$56$	1.54931	−	0.679627i	0.207035	−	0.0908190i
$57$	0.409618	+	6.63591i	0.0542552	+	0.878947i
$58$	0.843382	+	1.08356i	0.110742	+	0.142279i
$59$	14.0688			1.83161			0.915803	−	0.401629i	$-0.131556\pi$
$59$	14.0688			1.83161			0.915803	+	0.401629i	$0.131556\pi$
$60$	−11.3676	−	2.14332i	−1.46756	−	0.276701i
$61$	−13.9587			−1.78723			−0.893617	−	0.448831i	$-0.851841\pi$
$61$	−13.9587			−1.78723			−0.893617	+	0.448831i	$0.851841\pi$
$62$	−7.04326	−	9.04906i	−0.894495	−	1.14923i
$63$	0.220693	+	1.78082i	0.0278046	+	0.224363i
$64$	−5.41802	+	5.88601i	−0.677252	+	0.735751i
$65$		−	12.0634i		−	1.49627i
$66$	11.4922	−	10.1415i	1.41459	−	1.24833i
$67$		−	1.00000i		−	0.122169i
$67$		−	1.00000i		−	0.122169i
$68$	−11.3248	−	2.86766i	−1.37333	−	0.347755i
$69$	3.94508	−	0.243520i	0.474932	−	0.0293164i
$70$	−2.22916	+	1.73505i	−0.266435	+	0.207378i
$71$	−8.83049			−1.04799			−0.523993	−	0.851722i	$-0.675558\pi$
$71$	−8.83049			−1.04799			−0.523993	+	0.851722i	$0.675558\pi$
$72$	−4.33845	−	7.29232i	−0.511291	−	0.859408i
$73$	−0.0844839			−0.00988809			−0.00494405	−	0.999988i	$-0.501574\pi$
$73$	−0.0844839			−0.00988809			−0.00494405	+	0.999988i	$0.501574\pi$
$74$	−2.69368	+	2.09661i	−0.313134	+	0.243726i
$75$	10.6343	−	0.656429i	1.22794	−	0.0757979i
$76$	−7.44218	−	1.88451i	−0.853676	−	0.216168i
$77$		−	3.74277i		−	0.426528i
$78$	6.63470	−	5.85491i	0.751232	−	0.662938i
$79$			12.8855i			1.44974i	0.688888	+	0.724868i	$0.258099\pi$
$79$			12.8855i			1.44974i	−0.688888	+	0.724868i	$0.741901\pi$
$80$	6.35715	−	11.7477i	0.710751	−	1.31344i
$81$	8.72774	−	2.19695i	0.969749	−	0.244106i
$82$	6.79785	+	8.73375i	0.750696	+	0.964482i
$83$	2.46521			0.270592			0.135296	−	0.990805i	$-0.456801\pi$
$83$	2.46521			0.270592			0.135296	+	0.990805i	$0.456801\pi$
$84$	−2.03617	−	0.383911i	−0.222165	−	0.0418881i
$85$	19.5056			2.11568
$86$	5.47916	+	7.03953i	0.590833	+	0.759092i
$87$	−0.103610	−	1.67850i	−0.0111081	−	0.179954i
$88$	7.10961	+	16.2074i	0.757887	+	1.72771i
$89$		−	1.95347i		−	0.207068i	−0.994626	−	0.103534i	$-0.966985\pi$
$89$		−	1.95347i		−	0.207068i	0.994626	−	0.103534i	$-0.0330150\pi$
$90$	10.0111	+	10.0252i	1.05526	+	1.05675i
$91$		−	2.16079i		−	0.226512i
$92$	−1.12035	+	4.42441i	−0.116805	+	0.461277i
$93$	0.865266	+	14.0175i	0.0897240	+	1.45355i
$94$	−9.83873	+	7.65789i	−1.01479	+	0.789852i
$95$	12.8183			1.31513
$96$	9.54654	−	2.20537i	0.974339	−	0.225084i
$97$	4.36011			0.442702			0.221351	−	0.975194i	$-0.428953\pi$
$97$	4.36011			0.442702			0.221351	+	0.975194i	$0.428953\pi$
$98$	7.41276	−	5.76967i	0.748802	−	0.582824i
$99$	−18.6293	+	2.30867i	−1.87231	+	0.232030i
$100$	−3.02000	+	11.9264i	−0.302000	+	1.19264i
$101$		−	14.9169i		−	1.48428i	−0.670243	−	0.742142i	$-0.733810\pi$
$101$		−	14.9169i		−	1.48428i	0.670243	−	0.742142i	$-0.266190\pi$
$102$	9.46699	+	10.7279i	0.937371	+	1.06222i
$103$		−	5.86917i		−	0.578307i	−0.957283	−	0.289153i	$-0.906626\pi$
$103$		−	5.86917i		−	0.578307i	0.957283	−	0.289153i	$-0.0933738\pi$
$104$	4.10454	+	9.35691i	0.402484	+	0.917520i
$105$	3.45310	−	0.213151i	0.336988	−	0.0208014i
$106$	5.71390	+	7.34111i	0.554983	+	0.713032i
$107$	5.85257			0.565790			0.282895	−	0.959151i	$-0.408705\pi$
$107$	5.85257			0.565790			0.282895	+	0.959151i	$0.408705\pi$
$108$	−0.654896	+	10.3716i	−0.0630174	+	0.998012i
$109$	−11.4937			−1.10090			−0.550450	−	0.834868i	$-0.685544\pi$
$109$	−11.4937			−1.10090			−0.550450	+	0.834868i	$0.685544\pi$
$110$	−18.1504	−	23.3193i	−1.73057	−	2.22341i
$111$	4.17267	−	0.257569i	0.396052	−	0.0244473i
$112$	1.13869	−	2.10425i	0.107596	−	0.198833i
$113$		−	1.57684i		−	0.148337i	−0.997246	−	0.0741684i	$-0.976370\pi$
$113$		−	1.57684i		−	0.148337i	0.997246	−	0.0741684i	$-0.0236302\pi$
$114$	6.22132	+	7.04991i	0.582680	+	0.660285i
$115$		−	7.62054i		−	0.710619i
$116$	1.88244	+	0.476672i	0.174780	+	0.0442579i
$117$	−10.7551	+	1.33285i	−0.994310	+	0.123222i
$118$	15.7009	−	12.2207i	1.44539	−	1.12500i
$119$	3.49385			0.320280
$120$	−14.5481	+	7.48237i	−1.32806	+	0.683044i
$121$	28.1533			2.55939
$122$	−15.5781	+	12.1251i	−1.41037	+	1.09775i
$123$	−0.835117	−	13.5291i	−0.0753000	−	1.21988i
$124$	−15.7207	−	3.98079i	−1.41176	−	0.357485i
$125$		−	3.84497i		−	0.343905i
$126$	1.79318	+	1.79571i	0.159749	+	0.159975i
$127$			10.4675i			0.928841i	0.885615	+	0.464420i	$0.153737\pi$
$127$			10.4675i			0.928841i	−0.885615	+	0.464420i	$0.846263\pi$
$128$	−0.933753	+	11.2751i	−0.0825329	+	0.996588i
$129$	−0.673116	−	10.9046i	−0.0592646	−	0.960100i
$130$	−10.4787	−	13.4628i	−0.919039	−	1.18077i
$131$	−1.74480			−0.152444			−0.0762220	−	0.997091i	$-0.524286\pi$
$131$	−1.74480			−0.152444			−0.0762220	+	0.997091i	$0.524286\pi$
$132$	4.01611	−	21.3005i	0.349557	−	1.85397i
$133$	2.29601			0.199090
$134$	−0.868635	−	1.11601i	−0.0750387	−	0.0964084i
$135$	−3.19093	−	17.0560i	−0.274632	−	1.46794i
$136$	−15.1295	+	6.63676i	−1.29734	+	0.569098i
$137$		−	17.8625i		−	1.52609i	−0.646343	−	0.763047i	$-0.723703\pi$
$137$		−	17.8625i		−	1.52609i	0.646343	−	0.763047i	$-0.276297\pi$
$138$	4.19121	−	3.69860i	0.356779	−	0.314846i
$139$		−	5.16904i		−	0.438432i	−0.975676	−	0.219216i	$-0.929650\pi$
$139$		−	5.16904i		−	0.438432i	0.975676	−	0.219216i	$-0.0703500\pi$
$140$	−0.980634	+	3.87265i	−0.0828787	+	0.327299i
$141$	15.2408	−	0.940775i	1.28350	−	0.0792275i
$142$	−9.85489	+	7.67048i	−0.827004	+	0.643692i
$143$	22.6041			1.89025
$144$	−11.1761	−	4.36975i	−0.931342	−	0.364146i
$145$	−3.24229			−0.269257
$146$	−0.0942847	+	0.0733857i	−0.00780305	+	0.00607344i
$147$	−11.4828	+	0.708805i	−0.947086	+	0.0584613i
$148$	−1.18498	+	4.67966i	−0.0974051	+	0.384665i
$149$		−	6.09864i		−	0.499620i	−0.968295	−	0.249810i	$-0.919632\pi$
$149$		−	6.09864i		−	0.499620i	0.968295	−	0.249810i	$-0.0803682\pi$
$150$	11.2978	−	9.96992i	0.922459	−	0.814040i
$151$		−	2.76310i		−	0.224858i	−0.993660	−	0.112429i	$-0.964137\pi$
$151$		−	2.76310i		−	0.224858i	0.993660	−	0.112429i	$-0.0358631\pi$
$152$	−9.94248	+	4.36141i	−0.806441	+	0.353757i
$153$	−2.15513	−	17.3903i	−0.174232	−	1.40592i
$154$	−3.25110	−	4.17696i	−0.261981	−	0.336589i
$155$	27.0770			2.17488
$156$	2.31859	−	12.2973i	0.185636	−	0.984569i
$157$	−1.36591			−0.109011			−0.0545056	−	0.998513i	$-0.517358\pi$
$157$	−1.36591			−0.109011			−0.0545056	+	0.998513i	$0.517358\pi$
$158$	11.1928	+	14.3804i	0.890454	+	1.14404i
$159$	−0.701954	−	11.3718i	−0.0556686	−	0.901843i
$160$	−3.10987	−	18.6326i	−0.245857	−	1.47304i
$161$		−	1.36499i		−	0.107576i
$162$	7.83187	−	10.0330i	0.615330	−	0.788270i
$163$			21.0239i			1.64672i	0.567519	+	0.823360i	$0.307903\pi$
$163$			21.0239i			1.64672i	−0.567519	+	0.823360i	$0.692097\pi$
$164$	15.1729	+	3.84208i	1.18480	+	0.300016i
$165$	2.22978	+	36.1230i	0.173588	+	2.81217i
$166$	2.75120	−	2.14137i	0.213534	−	0.166203i
$167$	−18.9558			−1.46684			−0.733422	−	0.679773i	$-0.762078\pi$
$167$	−18.9558			−1.46684			−0.733422	+	0.679773i	$0.762078\pi$
$168$	−2.60586	+	1.34024i	−0.201047	+	0.103402i
$169$	0.0498803			0.00383695
$170$	21.7684	−	16.9433i	1.66956	−	1.29949i
$171$	−1.41626	−	11.4282i	−0.108304	−	0.873935i
$172$	12.2296	+	3.09677i	0.932496	+	0.236127i
$173$		−	7.51671i		−	0.571485i	−0.958306	−	0.285742i	$-0.907760\pi$
$173$		−	7.51671i		−	0.571485i	0.958306	−	0.285742i	$-0.0922402\pi$
$174$	−1.57364	−	1.78322i	−0.119297	−	0.135186i
$175$		−	3.67946i		−	0.278141i
$176$	22.0127	+	11.9119i	1.65927	+	0.897894i
$177$	−24.3216	+	1.50131i	−1.82813	+	0.112846i
$178$	−1.69685	−	2.18009i	−0.127185	−	0.163405i
$179$	−4.01865			−0.300368			−0.150184	−	0.988658i	$-0.547987\pi$
$179$	−4.01865			−0.300368			−0.150184	+	0.988658i	$0.547987\pi$
$180$	19.8806	+	2.49222i	1.48181	+	0.185759i
$181$	−12.0756			−0.897574			−0.448787	−	0.893639i	$-0.648144\pi$
$181$	−12.0756			−0.897574			−0.448787	+	0.893639i	$0.648144\pi$
$182$	−1.87694	−	2.41146i	−0.139128	−	0.178749i
$183$	24.1313	−	1.48957i	1.78384	−	0.110112i
$184$	2.59288	+	5.91085i	0.191150	+	0.435754i
$185$		−	8.06017i		−	0.592595i
$186$	13.1418	+	14.8920i	0.963600	+	1.09194i
$187$			36.5493i			2.67275i
$188$	−4.32818	+	17.0925i	−0.315665	+	1.24660i
$189$	−0.571560	−	3.05507i	−0.0415749	−	0.222223i
$190$	14.3053	−	11.1344i	1.03782	−	0.807776i
$191$	0.00767385			0.000555260			0.000277630	−	1.00000i	$-0.499912\pi$
$191$	0.00767385			0.000555260			0.000277630		1.00000i	$0.499912\pi$
$192$	8.73835	−	10.7537i	0.630636	−	0.776079i
$193$	−14.3237			−1.03104			−0.515521	−	0.856877i	$-0.672402\pi$
$193$	−14.3237			−1.03104			−0.515521	+	0.856877i	$0.672402\pi$
$194$	4.86591	−	3.78734i	0.349352	−	0.271915i
$195$	1.28731	+	20.8546i	0.0921859	+	1.49343i
$196$	3.26096	−	12.8780i	0.232926	−	0.919856i
$197$		−	16.9545i		−	1.20796i	−0.797000	−	0.603980i	$-0.793581\pi$
$197$		−	16.9545i		−	1.20796i	0.797000	−	0.603980i	$-0.206419\pi$
$198$	−18.7850	+	18.7585i	−1.33499	+	1.33311i
$199$			9.25186i			0.655847i	0.944704	+	0.327923i	$0.106349\pi$
$199$			9.25186i			0.655847i	−0.944704	+	0.327923i	$0.893651\pi$
$200$	6.98934	+	15.9332i	0.494221	+	1.12665i
$201$	0.106712	+	1.72876i	0.00752689	+	0.121937i
$202$	−12.9573	−	16.6473i	−0.911673	−	1.17130i
$203$	−0.580759			−0.0407613
$204$	19.8838	+	3.74901i	1.39215	+	0.262483i
$205$	−26.1336			−1.82525
$206$	−5.09817	−	6.55004i	−0.355206	−	0.456363i
$207$	−6.79411	+	0.841975i	−0.472223	+	0.0585213i
$208$	12.7084	+	6.87703i	0.881172	+	0.476836i
$209$			24.0187i			1.66141i
$210$	3.66853	−	3.23736i	0.253153	−	0.223399i
$211$		−	5.47152i		−	0.376675i	−0.982104	−	0.188338i	$-0.939690\pi$
$211$		−	5.47152i		−	0.376675i	0.982104	−	0.188338i	$-0.0603099\pi$
$212$	12.7535	+	3.22944i	0.875914	+	0.221799i
$213$	15.2658	−	0.942320i	1.04600	−	0.0645667i
$214$	6.53152	−	5.08375i	0.446485	−	0.347518i
$215$	−21.0640			−1.43655
$216$	8.27831	+	12.1437i	0.563268	+	0.826274i
$217$	4.85004			0.329242
$218$	−12.8271	+	9.98386i	−0.868760	+	0.676192i
$219$	0.146052	−	0.00901545i	0.00986931	−	0.000609208i
$220$	−40.5120	−	10.2585i	−2.73132	−	0.691625i
$221$			21.1007i			1.41939i
$222$	4.43300	−	3.91198i	0.297523	−	0.262555i
$223$		−	8.98820i		−	0.601894i	−0.953641	−	0.300947i	$-0.902697\pi$
$223$		−	8.98820i		−	0.601894i	0.953641	−	0.300947i	$-0.0973028\pi$
$224$	−0.557040	−	3.33747i	−0.0372188	−	0.222994i
$225$	−18.3141	+	2.26962i	−1.22094	+	0.151308i
$226$	−1.36970	−	1.75977i	−0.0911111	−	0.117058i
$227$	11.9681			0.794351			0.397176	−	0.917743i	$-0.369990\pi$
$227$	11.9681			0.794351			0.397176	+	0.917743i	$0.369990\pi$
$228$	13.0668	+	2.46370i	0.865373	+	0.163162i
$229$	−6.00263			−0.396665			−0.198332	−	0.980135i	$-0.563553\pi$
$229$	−6.00263			−0.396665			−0.198332	+	0.980135i	$0.563553\pi$
$230$	−6.61947	−	8.50458i	−0.436475	−	0.560775i
$231$	0.399399	+	6.47035i	0.0262785	+	0.425718i
$232$	2.51487	−	1.10319i	0.165110	−	0.0724277i
$233$			19.5574i			1.28125i	0.767855	+	0.640623i	$0.221324\pi$
$233$			19.5574i			1.28125i	−0.767855	+	0.640623i	$0.778676\pi$
$234$	−10.8450	+	10.8297i	−0.708961	+	0.707962i
$235$		−	29.4399i		−	1.92045i
$236$	6.90702	−	27.2767i	0.449609	−	1.77556i
$237$	−1.37504	−	22.2760i	−0.0893186	−	1.44698i
$238$	3.89916	−	3.03488i	0.252745	−	0.196722i
$239$	20.5538			1.32951			0.664757	−	0.747060i	$-0.268535\pi$
$239$	20.5538			1.32951			0.664757	+	0.747060i	$0.268535\pi$
$240$	−9.73636	+	20.9874i	−0.628479	+	1.35473i
$241$	28.9376			1.86403			0.932016	−	0.362417i	$-0.118048\pi$
$241$	28.9376			1.86403			0.932016	+	0.362417i	$0.118048\pi$
$242$	31.4193	−	24.4549i	2.01971	−	1.57202i
$243$	−14.8537	+	4.72936i	−0.952867	+	0.303388i
$244$	−6.85298	+	27.0633i	−0.438717	+	1.73255i
$245$			22.1808i			1.41708i
$246$	−12.6838	−	14.3732i	−0.808692	−	0.916399i
$247$			13.8666i			0.882308i
$248$	−21.0022	+	9.21293i	−1.33364	+	0.585022i
$249$	−4.26176	+	0.263068i	−0.270078	+	0.0166713i
$250$	−3.33988	−	4.29102i	−0.211232	−	0.271388i
$251$	−0.558609			−0.0352591			−0.0176296	−	0.999845i	$-0.505612\pi$
$251$	−0.558609			−0.0352591			−0.0176296	+	0.999845i	$0.505612\pi$
$252$	3.56102	+	0.446406i	0.224323	+	0.0281210i
$253$	14.2792			0.897727
$254$	9.09244	+	11.6818i	0.570511	+	0.732982i
$255$	−33.7205	+	2.08148i	−2.11166	+	0.130348i
$256$	8.75188	+	13.3942i	0.546993	+	0.837137i
$257$			18.1040i			1.12930i	0.825332	+	0.564648i	$0.190988\pi$
$257$			18.1040i			1.12930i	−0.825332	+	0.564648i	$0.809012\pi$
$258$	−10.2234	−	11.5850i	−0.636478	−	0.721248i
$259$		−	1.44374i		−	0.0897096i
$260$	−23.3885	−	5.92245i	−1.45049	−	0.367294i
$261$	0.358233	+	2.89067i	0.0221741	+	0.178928i
$262$	−1.94721	+	1.51560i	−0.120299	+	0.0936339i
$263$	−4.22946			−0.260800			−0.130400	−	0.991461i	$-0.541626\pi$
$263$	−4.22946			−0.260800			−0.130400	+	0.991461i	$0.541626\pi$
$264$	−14.0203	−	27.2600i	−0.862892	−	1.67774i
$265$	−21.9664			−1.34939
$266$	2.56237	−	1.99440i	0.157109	−	0.122284i
$267$	0.208459	+	3.37708i	0.0127575	+	0.206674i
$268$	−1.93881	−	0.490945i	−0.118431	−	0.0299892i
$269$		−	24.1197i		−	1.47060i	−0.677740	−	0.735302i	$-0.737040\pi$
$269$		−	24.1197i		−	1.47060i	0.677740	−	0.735302i	$-0.262960\pi$
$270$	−18.3765	−	16.2628i	−1.11836	−	0.989724i
$271$		−	0.784908i		−	0.0476798i	−0.999716	−	0.0238399i	$-0.992411\pi$
$271$		−	0.784908i		−	0.0476798i	0.999716	−	0.0238399i	$-0.00758919\pi$
$272$	−11.1197	+	20.5487i	−0.674229	+	1.24595i
$273$	0.230582	+	3.73549i	0.0139555	+	0.226082i
$274$	−15.5160	−	19.9346i	−0.937354	−	1.20430i
$275$	38.4909			2.32109
$276$	1.46468	−	7.76830i	0.0881633	−	0.467597i
$277$	−17.9222			−1.07684			−0.538420	−	0.842677i	$-0.680979\pi$
$277$	−17.9222			−1.07684			−0.538420	+	0.842677i	$0.680979\pi$
$278$	−4.49001	−	5.76869i	−0.269293	−	0.345983i
$279$	−2.99168	−	24.1406i	−0.179107	−	1.44526i
$280$	2.26953	+	5.17372i	0.135630	+	0.309189i
$281$			10.1535i			0.605710i	0.953037	+	0.302855i	$0.0979397\pi$
$281$			10.1535i			0.605710i	−0.953037	+	0.302855i	$0.902060\pi$
$282$	16.1916	−	14.2886i	0.964197	−	0.850872i
$283$			0.405787i			0.0241215i	0.999927	+	0.0120608i	$0.00383915\pi$
$283$			0.405787i			0.0241215i	−0.999927	+	0.0120608i	$0.996161\pi$
$284$	−4.33529	+	17.1206i	−0.257252	+	1.01592i
$285$	−22.1598	+	1.36787i	−1.31263	+	0.0810255i
$286$	25.2263	−	19.6347i	1.49167	−	1.16103i
$287$	−4.68105			−0.276313
$288$	−16.2683	+	4.83128i	−0.958621	+	0.284686i
$289$	−17.1184			−1.00697
$290$	−3.61842	+	2.81637i	−0.212481	+	0.165383i
$291$	−7.53758	+	0.465276i	−0.441861	+	0.0272750i
$292$	−0.0414770	+	0.163798i	−0.00242726	+	0.00958555i
$293$		−	8.09874i		−	0.473134i	−0.971615	−	0.236567i	$-0.923978\pi$
$293$		−	8.09874i		−	0.473134i	0.971615	−	0.236567i	$-0.0760222\pi$
$294$	−12.1992	+	10.7654i	−0.711472	+	0.627851i
$295$			46.9810i			2.73534i
$296$	2.74246	+	6.25185i	0.159403	+	0.363381i
$297$	31.9592	−	5.97911i	1.85446	−	0.346943i
$298$	−5.29749	−	6.80613i	−0.306876	−	0.394268i
$299$	8.24374			0.476748
$300$	3.94817	−	20.9401i	0.227948	−	1.20898i
$301$	−3.77299			−0.217472
$302$	−2.40013	−	3.08364i	−0.138112	−	0.177444i
$303$	1.59181	+	25.7877i	0.0914471	+	1.48146i
$304$	−7.30740	+	13.5038i	−0.419108	+	0.774493i
$305$		−	46.6134i		−	2.66908i
$306$	−17.5109	−	17.5356i	−1.00103	−	1.00245i
$307$		−	1.93555i		−	0.110468i	−0.998473	−	0.0552340i	$-0.982410\pi$
$307$		−	1.93555i		−	0.110468i	0.998473	−	0.0552340i	$-0.0175905\pi$
$308$	−7.25651	−	1.83749i	−0.413478	−	0.104701i
$309$	0.626312	+	10.1464i	0.0356296	+	0.577208i
$310$	30.2182	−	23.5201i	1.71628	−	1.33585i
$311$	−6.09017			−0.345342			−0.172671	−	0.984980i	$-0.555240\pi$
$311$	−6.09017			−0.345342			−0.172671	+	0.984980i	$0.555240\pi$
$312$	−8.09427	−	15.7379i	−0.458248	−	0.890980i
$313$	−10.5675			−0.597308			−0.298654	−	0.954362i	$-0.596538\pi$
$313$	−10.5675			−0.597308			−0.298654	+	0.954362i	$0.596538\pi$
$314$	−1.52436	+	1.18647i	−0.0860247	+	0.0669567i
$315$	−5.94683	+	0.736975i	−0.335066	+	0.0415238i
$316$	24.9826	+	6.32609i	1.40538	+	0.355871i
$317$			6.14032i			0.344875i	0.985020	+	0.172437i	$0.0551643\pi$
$317$			6.14032i			0.344875i	−0.985020	+	0.172437i	$0.944836\pi$
$318$	−10.6613	−	12.0813i	−0.597859	−	0.677485i
$319$		−	6.07535i		−	0.340154i
$320$	−19.6556	−	18.0928i	−1.09878	−	1.01142i
$321$	−10.1177	+	0.624541i	−0.564715	+	0.0348585i
$322$	−1.18568	−	1.52334i	−0.0660754	−	0.0848925i
$323$	−22.4213			−1.24755
$324$	0.0253783	−	18.0000i	0.00140991	−	0.999999i
$325$	22.2217			1.23264
$326$	18.2621	+	23.4629i	1.01145	+	1.29949i
$327$	19.8699	−	1.22652i	1.09881	−	0.0678267i
$328$	20.2704	−	8.89192i	1.11925	−	0.490974i
$329$		−	5.27328i		−	0.290725i
$330$	33.8662	+	38.3766i	1.86427	+	2.11256i
$331$		−	0.345630i		−	0.0189975i	−0.999955	−	0.00949877i	$-0.996976\pi$
$331$		−	0.345630i		−	0.0189975i	0.999955	−	0.00949877i	$-0.00302360\pi$
$332$	1.21028	−	4.77957i	0.0664230	−	0.262313i
$333$	−7.18606	+	0.890549i	−0.393794	+	0.0488018i
$334$	−21.1548	+	16.4657i	−1.15754	+	0.900962i
$335$	3.33937			0.182449
$336$	−1.74398	+	3.75926i	−0.0951418	+	0.205085i
$337$	−11.0625			−0.602615			−0.301308	−	0.953527i	$-0.597423\pi$
$337$	−11.0625			−0.602615			−0.301308	+	0.953527i	$0.597423\pi$
$338$	0.0556668	−	0.0433278i	0.00302788	−	0.00235672i
$339$	0.168268	+	2.72598i	0.00913907	+	0.148055i
$340$	9.57618	−	37.8176i	0.519341	−	2.05095i
$341$			50.7365i			2.74753i
$342$	−11.5075	−	11.5237i	−0.622253	−	0.623131i
$343$			8.16008i			0.440603i
$344$	16.3383	−	7.16701i	0.880900	−	0.386419i
$345$	0.813204	+	13.1741i	0.0437814	+	0.709269i
$346$	−6.52928	−	8.38871i	−0.351016	−	0.450980i
$347$	20.8420			1.11886			0.559429	−	0.828878i	$-0.311020\pi$
$347$	20.8420			1.11886			0.559429	+	0.828878i	$0.311020\pi$
$348$	−3.30516	−	0.623173i	−0.177175	−	0.0334056i
$349$	20.9068			1.11912			0.559559	−	0.828791i	$-0.310971\pi$
$349$	20.9068			1.11912			0.559559	+	0.828791i	$0.310971\pi$
$350$	−3.19611	−	4.10630i	−0.170839	−	0.219491i
$351$	18.4508	−	3.45188i	0.984830	−	0.184248i
$352$	34.9134	−	5.82722i	1.86089	−	0.310592i
$353$		−	15.1319i		−	0.805389i	−0.915335	−	0.402694i	$-0.868074\pi$
$353$		−	15.1319i		−	0.805389i	0.915335	−	0.402694i	$-0.131926\pi$
$354$	−25.8390	+	22.8021i	−1.37333	+	1.21192i
$355$		−	29.4883i		−	1.56508i
$356$	−3.78740	−	0.959047i	−0.200732	−	0.0508294i
$357$	−6.04002	+	0.372836i	−0.319672	+	0.0197326i
$358$	−4.48484	+	3.49074i	−0.237031	+	0.184491i
$359$	4.84209			0.255556			0.127778	−	0.991803i	$-0.459216\pi$
$359$	4.84209			0.255556			0.127778	+	0.991803i	$0.459216\pi$
$360$	24.3518	−	14.4877i	1.28345	−	0.763568i
$361$	4.26566			0.224508
$362$	−13.4765	+	10.4893i	−0.708308	+	0.551306i
$363$	−48.6702	+	3.00429i	−2.55453	+	0.157685i
$364$	−4.18935	−	1.06083i	−0.219582	−	0.0556026i
$365$		−	0.282123i		−	0.0147670i
$366$	25.6368	−	22.6237i	1.34006	−	1.18256i
$367$		−	9.60111i		−	0.501174i	−0.968094	−	0.250587i	$-0.919376\pi$
$367$		−	9.60111i		−	0.501174i	0.968094	−	0.250587i	$-0.0806236\pi$
$368$	8.02805	+	4.34429i	0.418491	+	0.226462i
$369$	2.88744	+	23.2994i	0.150314	+	1.21292i
$370$	−7.00135	−	8.99521i	−0.363983	−	0.467639i
$371$	−3.93463			−0.204276
$372$	27.6021	+	5.20425i	1.43110	+	0.269828i
$373$	3.59873			0.186335			0.0931676	−	0.995650i	$-0.470301\pi$
$373$	3.59873			0.186335			0.0931676	+	0.995650i	$0.470301\pi$
$374$	31.7480	+	40.7892i	1.64165	+	2.10916i
$375$	0.410305	+	6.64704i	0.0211881	+	0.343251i
$376$	10.0169	+	22.8350i	0.516582	+	1.17763i
$377$		−	3.50744i		−	0.180642i
$378$	−3.29160	−	2.91300i	−0.169302	−	0.149829i
$379$			4.01187i			0.206076i	0.994677	+	0.103038i	$0.0328563\pi$
$379$			4.01187i			0.206076i	−0.994677	+	0.103038i	$0.967144\pi$
$380$	6.29308	−	24.8522i	0.322828	−	1.27489i
$381$	−1.11701	−	18.0958i	−0.0572261	−	0.927076i
$382$	0.00856408	−	0.00666578i	0.000438176	−	0.000341051i
$383$	−4.97921			−0.254426			−0.127213	−	0.991875i	$-0.540603\pi$
$383$	−4.97921			−0.254426			−0.127213	+	0.991875i	$0.540603\pi$
$384$	0.411044	−	19.5916i	0.0209760	−	0.999780i
$385$	12.4985			0.636983
$386$	−15.9853	+	12.4421i	−0.813633	+	0.633285i
$387$	2.32731	+	18.7797i	0.118304	+	0.954625i
$388$	2.14057	−	8.45341i	0.108671	−	0.429157i
$389$		−	29.4427i		−	1.49280i	−0.665496	−	0.746402i	$-0.731780\pi$
$389$		−	29.4427i		−	1.49280i	0.665496	−	0.746402i	$-0.268220\pi$
$390$	19.5517	+	22.1557i	0.990040	+	1.12190i
$391$			13.3295i			0.674104i
$392$	−7.54701	−	17.2045i	−0.381181	−	0.868959i
$393$	3.01634	−	0.186191i	0.152154	−	0.00939212i
$394$	−14.7273	−	18.9214i	−0.741950	−	0.953245i
$395$	−43.0296			−2.16505
$396$	−4.66987	+	37.2520i	−0.234670	+	1.87198i
$397$	−12.0725			−0.605902			−0.302951	−	0.953006i	$-0.597972\pi$
$397$	−12.0725			−0.605902			−0.302951	+	0.953006i	$0.597972\pi$
$398$	8.03649	+	10.3251i	0.402833	+	0.517553i
$399$	−3.96926	+	0.245013i	−0.198711	+	0.0122660i
$400$	21.6403	+	11.7104i	1.08202	+	0.585520i
$401$		−	27.4454i		−	1.37056i	−0.728282	−	0.685278i	$-0.759681\pi$
$401$		−	27.4454i		−	1.37056i	0.728282	−	0.685278i	$-0.240319\pi$
$402$	1.62075	+	1.83662i	0.0808359	+	0.0916021i
$403$			29.2914i			1.45911i
$404$	−28.9209	−	7.32336i	−1.43887	−	0.364351i
$405$	7.33643	+	29.1452i	0.364550	+	1.44823i
$406$	−0.648132	+	0.504468i	−0.0321662	+	0.0250363i
$407$	15.1030			0.748628
$408$	25.4470	−	13.0879i	1.25981	−	0.647946i
$409$	13.4515			0.665136			0.332568	−	0.943079i	$-0.392085\pi$
$409$	13.4515			0.665136			0.332568	+	0.943079i	$0.392085\pi$
$410$	−29.1652	+	22.7005i	−1.44037	+	1.12110i
$411$	1.90614	+	30.8799i	0.0940230	+	1.52319i
$412$	−11.3792	−	2.88144i	−0.560613	−	0.141958i
$413$			8.41525i			0.414087i
$414$	−6.85091	+	6.84125i	−0.336704	+	0.336229i
$415$			8.23227i			0.404106i
$416$	20.1563	−	3.36419i	0.988246	−	0.164943i
$417$	0.551599	+	8.93603i	0.0270119	+	0.437599i
$418$	20.8635	+	26.8050i	1.02047	+	1.31108i
$419$	17.8929			0.874124			0.437062	−	0.899431i	$-0.356019\pi$
$419$	17.8929			0.874124			0.437062	+	0.899431i	$0.356019\pi$
$420$	1.28202	−	6.79953i	0.0625563	−	0.331783i
$421$	13.4521			0.655617			0.327808	−	0.944744i	$-0.393690\pi$
$421$	13.4521			0.655617			0.327808	+	0.944744i	$0.393690\pi$
$422$	−4.75276	−	6.10626i	−0.231361	−	0.297248i
$423$	−26.2472	+	3.25275i	−1.27618	+	0.158154i
$424$	17.0382	−	7.47406i	0.827449	−	0.362972i
$425$			35.9310i			1.74291i
$426$	16.2182	−	14.3121i	0.785775	−	0.693421i
$427$		−	8.34940i		−	0.404056i
$428$	2.87329	−	11.3470i	0.138886	−	0.548479i
$429$	−39.0771	+	2.41213i	−1.88666	+	0.116459i
$430$	−23.5076	+	18.2970i	−1.13364	+	0.882358i
$431$	−31.3545			−1.51029			−0.755145	−	0.655557i	$-0.772434\pi$
$431$	−31.3545			−1.51029			−0.755145	+	0.655557i	$0.772434\pi$
$432$	19.7871	+	6.36163i	0.952008	+	0.306074i
$433$	−19.4130			−0.932928			−0.466464	−	0.884540i	$-0.654472\pi$
$433$	−19.4130			−0.932928			−0.466464	+	0.884540i	$0.654472\pi$
$434$	5.41268	−	4.21292i	0.259817	−	0.202226i
$435$	5.60514	−	0.345992i	0.268746	−	0.0165890i
$436$	−5.64279	+	22.2841i	−0.270241	+	1.06722i
$437$			8.75964i			0.419030i
$438$	0.155164	−	0.136928i	0.00741404	−	0.00654265i
$439$		−	10.0523i		−	0.479770i	−0.970801	−	0.239885i	$-0.922890\pi$
$439$		−	10.0523i		−	0.479770i	0.970801	−	0.239885i	$-0.0771097\pi$
$440$	−54.1225	+	23.7416i	−2.58019	+	1.13184i
$441$	19.7754	−	2.45071i	0.941685	−	0.116700i
$442$	18.3289	+	23.5486i	0.871815	+	1.12009i
$443$	−25.4860			−1.21088			−0.605439	−	0.795892i	$-0.707002\pi$
$443$	−25.4860			−1.21088			−0.605439	+	0.795892i	$0.707002\pi$
$444$	1.54918	−	8.21646i	0.0735207	−	0.389936i
$445$	6.52337			0.309237
$446$	−7.80747	−	10.0309i	−0.369694	−	0.474977i
$447$	0.650799	+	10.5431i	0.0307817	+	0.498671i
$448$	−3.52071	−	3.24078i	−0.166338	−	0.153112i
$449$		−	5.59916i		−	0.264241i	−0.991234	−	0.132120i	$-0.957821\pi$
$449$		−	5.59916i		−	0.264241i	0.991234	−	0.132120i	$-0.0421785\pi$
$450$	−18.4672	+	18.4412i	−0.870553	+	0.869327i
$451$		−	48.9686i		−	2.30584i
$452$	−3.05719	−	0.774143i	−0.143798	−	0.0364126i
$453$	0.294857	+	4.77674i	0.0138536	+	0.224431i
$454$	13.3565	−	10.3959i	0.626852	−	0.487905i
$455$	7.21568			0.338276
$456$	16.7227	−	8.60082i	0.783114	−	0.402770i
$457$	−31.9360			−1.49390			−0.746952	−	0.664878i	$-0.768483\pi$
$457$	−31.9360			−1.49390			−0.746952	+	0.664878i	$0.768483\pi$
$458$	−6.69898	+	5.21410i	−0.313023	+	0.243639i
$459$	5.58145	+	29.8336i	0.260520	+	1.39251i
$460$	−14.7748	−	3.74127i	−0.688876	−	0.174437i
$461$		−	9.81767i		−	0.457255i	−0.973514	−	0.228627i	$-0.926576\pi$
$461$		−	9.81767i		−	0.457255i	0.973514	−	0.228627i	$-0.0734237\pi$
$462$	6.06611	+	6.87403i	0.282221	+	0.319809i
$463$			6.01481i			0.279532i	0.990185	+	0.139766i	$0.0446350\pi$
$463$			6.01481i			0.279532i	−0.990185	+	0.139766i	$0.955365\pi$
$464$	1.84835	−	3.41567i	0.0858076	−	0.158569i
$465$	−46.8097	+	2.88945i	−2.17075	+	0.133995i
$466$	16.9882	+	21.8262i	0.786965	+	1.01108i
$467$	−20.3748			−0.942834			−0.471417	−	0.881910i	$-0.656257\pi$
$467$	−20.3748			−0.942834			−0.471417	+	0.881910i	$0.656257\pi$
$468$	−2.69603	+	21.5064i	−0.124624	+	0.994136i
$469$	0.598149			0.0276199
$470$	−25.5726	−	32.8552i	−1.17957	−	1.51550i
$471$	2.36133	−	0.145759i	0.108804	−	0.00671621i
$472$	−15.9853	−	36.4407i	−0.735781	−	1.67732i
$473$		−	39.4694i		−	1.81480i
$474$	−20.8843	−	23.6658i	−0.959247	−	1.08701i
$475$			23.6124i			1.08341i
$476$	1.71529	−	6.77389i	0.0786200	−	0.310481i
$477$	2.42702	+	19.5842i	0.111126	+	0.896700i
$478$	22.9382	−	17.8537i	1.04917	−	0.816611i
$479$	24.6296			1.12536			0.562678	−	0.826676i	$-0.309771\pi$
$479$	24.6296			1.12536			0.562678	+	0.826676i	$0.309771\pi$
$480$	7.36454	+	31.8794i	0.336144	+	1.45509i
$481$	8.71932			0.397567
$482$	32.2945	−	25.1362i	1.47098	−	1.14492i
$483$	0.145661	+	2.35974i	0.00662781	+	0.107372i
$484$	13.8217	−	54.5837i	0.628259	−	2.48108i
$485$			14.5600i			0.661137i
$486$	−12.4688	+	18.1805i	−0.565596	+	0.824683i
$487$			2.64350i			0.119788i	0.998205	+	0.0598941i	$0.0190763\pi$
$487$			2.64350i			0.119788i	−0.998205	+	0.0598941i	$0.980924\pi$
$488$	15.8602	+	36.1556i	0.717956	+	1.63669i
$489$	−2.24351	−	36.3453i	−0.101455	−	1.64359i
$490$	19.2671	+	24.7540i	0.870397	+	1.11827i
$491$	15.9249			0.718679			0.359339	−	0.933207i	$-0.383002\pi$
$491$	15.9249			0.718679			0.359339	+	0.933207i	$0.383002\pi$
$492$	−26.6403	−	5.02291i	−1.20104	−	0.226450i
$493$	5.67129			0.255422
$494$	12.0450	+	15.4752i	0.541929	+	0.696261i
$495$	−7.70952	−	62.2100i	−0.346517	−	2.79613i
$496$	−15.4360	+	28.5250i	−0.693095	+	1.28081i
$497$		−	5.28195i		−	0.236928i
$498$	−4.52765	+	3.99551i	−0.202889	+	0.179043i
$499$		−	4.55108i		−	0.203735i	−0.994798	−	0.101867i	$-0.967518\pi$
$499$		−	4.55108i		−	0.203735i	0.994798	−	0.101867i	$-0.0324817\pi$
$500$	−7.45466	−	1.88767i	−0.333383	−	0.0844192i
$501$	32.7701	−	2.02281i	1.46406	−	0.0903727i
$502$	−0.623412	+	0.485228i	−0.0278242	+	0.0216568i
$503$	−14.3865			−0.641463			−0.320731	−	0.947170i	$-0.603929\pi$
$503$	−14.3865			−0.641463			−0.320731	+	0.947170i	$0.603929\pi$
$504$	4.36189	−	2.59504i	0.194294	−	0.115592i
$505$	49.8130			2.21665
$506$	15.9357	−	12.4034i	0.708429	−	0.551400i
$507$	−0.0862312	+	0.00532284i	−0.00382966	+	0.000236395i
$508$	20.2945	+	5.13897i	0.900421	+	0.228005i
$509$			8.55828i			0.379339i	0.981848	+	0.189670i	$0.0607417\pi$
$509$			8.55828i			0.379339i	−0.981848	+	0.189670i	$0.939258\pi$
$510$	−35.8243	+	31.6138i	−1.58633	+	1.39988i
$511$		−	0.0505339i		−	0.00223549i
$512$	21.4018	+	7.34583i	0.945837	+	0.324643i
$513$	3.66790	+	19.6055i	0.161942	+	0.865602i
$514$	15.7258	+	20.2042i	0.693634	+	0.891169i
$515$	19.5994			0.863651
$516$	−21.4725	−	4.04854i	−0.945272	−	0.178227i
$517$	55.1640			2.42611
$518$	−1.25408	−	1.61122i	−0.0551012	−	0.0707931i
$519$	0.802124	+	12.9946i	0.0352093	+	0.570399i
$520$	−31.2462	+	13.7066i	−1.37024	+	0.601074i
$521$		−	40.8185i		−	1.78829i	−0.447774	−	0.894147i	$-0.647783\pi$
$521$		−	40.8185i		−	1.78829i	0.447774	−	0.894147i	$-0.352217\pi$
$522$	2.91073	+	2.91484i	0.127399	+	0.127579i
$523$			7.70325i			0.336840i	0.985715	+	0.168420i	$0.0538664\pi$
$523$			7.70325i			0.336840i	−0.985715	+	0.168420i	$0.946134\pi$
$524$	−0.856602	+	3.38283i	−0.0374208	+	0.147780i
$525$	0.392642	+	6.36090i	0.0171363	+	0.277612i
$526$	−4.72011	+	3.67386i	−0.205807	+	0.160188i
$527$	−47.3621			−2.06312
$528$	−39.3258	−	18.2438i	−1.71144	−	0.793961i
$529$	−17.7924			−0.773581
$530$	−24.5147	+	19.0808i	−1.06485	+	0.828818i
$531$	41.8861	−	5.19083i	1.81770	−	0.225263i
$532$	1.12722	−	4.45153i	0.0488711	−	0.192998i
$533$		−	28.2707i		−	1.22454i
$534$	3.16610	+	3.58778i	0.137010	+	0.155258i
$535$			19.5439i			0.844957i
$536$	−2.59018	+	1.13622i	−0.111879	+	0.0490771i
$537$	6.94728	−	0.428838i	0.299797	−	0.0185057i
$538$	−20.9512	−	26.9178i	−0.903271	−	1.16051i
$539$	−41.5621			−1.79020
$540$	−34.6348	−	2.18694i	−1.49044	−	0.0941110i
$541$	14.0075			0.602229			0.301115	−	0.953588i	$-0.402641\pi$
$541$	14.0075			0.602229			0.301115	+	0.953588i	$0.402641\pi$
$542$	−0.681799	−	0.875963i	−0.0292858	−	0.0376258i
$543$	20.8758	−	1.28861i	0.895868	−	0.0552997i
$544$	5.43966	+	32.5914i	0.233224	+	1.39735i
$545$		−	38.3818i		−	1.64410i
$546$	3.50211	+	3.96854i	0.149876	+	0.169838i
$547$		−	23.2754i		−	0.995186i	−0.867411	−	0.497593i	$-0.834217\pi$
$547$		−	23.2754i		−	0.995186i	0.867411	−	0.497593i	$-0.165783\pi$
$548$	−34.6319	−	8.76949i	−1.47940	−	0.374614i
$549$	−41.5583	+	5.15021i	−1.77367	+	0.219806i
$550$	42.9562	−	33.4346i	1.83166	−	1.42566i
$551$	3.72694			0.158773
$552$	−5.11323	−	9.94175i	−0.217633	−	0.423149i
$553$	−7.70747			−0.327755
$554$	−20.0013	+	15.5679i	−0.849774	+	0.661415i
$555$	0.860118	+	13.9341i	0.0365100	+	0.591470i
$556$	−10.0218	−	2.53772i	−0.425018	−	0.107623i
$557$			21.4875i			0.910456i	0.890375	+	0.455228i	$0.150442\pi$
$557$			21.4875i			0.910456i	−0.890375	+	0.455228i	$0.849558\pi$
$558$	−24.3081	−	24.3424i	−1.02904	−	1.03050i
$559$		−	22.7866i		−	0.963771i
$560$	7.02689	+	3.80252i	0.296940	+	0.160686i
$561$	−3.90025	−	63.1849i	−0.164669	−	2.66767i
$562$	8.81973	+	11.3314i	0.372038	+	0.477988i
$563$	−22.2547			−0.937923			−0.468962	−	0.883218i	$-0.655372\pi$
$563$	−22.2547			−0.937923			−0.468962	+	0.883218i	$0.655372\pi$
$564$	5.65840	−	30.0108i	0.238262	−	1.26368i
$565$	5.26566			0.221528
$566$	0.352481	+	0.452861i	0.0148159	+	0.0190352i
$567$	1.31410	+	5.22049i	0.0551871	+	0.219240i
$568$	10.0334	+	22.8725i	0.420991	+	0.959710i
$569$		−	28.0722i		−	1.17685i	−0.808553	−	0.588424i	$-0.799749\pi$
$569$		−	28.0722i		−	1.17685i	0.808553	−	0.588424i	$-0.200251\pi$
$570$	−23.5423	+	20.7753i	−0.986077	+	0.870182i
$571$			13.2790i			0.555709i	0.960623	+	0.277855i	$0.0896234\pi$
$571$			13.2790i			0.555709i	−0.960623	+	0.277855i	$0.910377\pi$
$572$	11.0974	−	43.8250i	0.464005	−	1.83241i
$573$	−0.0132663		0.000818893i	−0.000554206		3.42097e-5i
$574$	−5.22408	+	4.06612i	−0.218049	+	0.169717i
$575$	14.0377			0.585411
$576$	−13.9590	+	19.5230i	−0.581623	+	0.813458i
$577$	−39.8971			−1.66094			−0.830469	−	0.557064i	$-0.811928\pi$
$577$	−39.8971			−1.66094			−0.830469	+	0.557064i	$0.811928\pi$
$578$	−19.1043	+	14.8697i	−0.794635	+	0.618497i
$579$	24.7622	−	1.52851i	1.02908	−	0.0635228i
$580$	−1.59179	+	6.28617i	−0.0660953	+	0.261019i
$581$			1.47456i			0.0611752i
$582$	−8.00784	+	7.06666i	−0.331936	+	0.292923i
$583$		−	41.1603i		−	1.70469i
$584$	0.0959921	+	0.218828i	0.00397218	+	0.00905517i
$585$	−4.45089	−	35.9153i	−0.184022	−	1.48492i
$586$	−7.03486	−	9.03826i	−0.290607	−	0.373367i
$587$	−6.92062			−0.285645			−0.142822	−	0.989748i	$-0.545618\pi$
$587$	−6.92062			−0.285645			−0.142822	+	0.989748i	$0.545618\pi$
$588$	−4.26319	+	22.6109i	−0.175811	+	0.932459i
$589$	−31.1244			−1.28246
$590$	40.8094	+	52.4312i	1.68010	+	2.15856i
$591$	1.80925	+	29.3103i	0.0744227	+	1.20566i
$592$	8.49119	+	4.59491i	0.348986	+	0.188850i
$593$		−	12.3344i		−	0.506512i	−0.967399	−	0.253256i	$-0.918499\pi$
$593$		−	12.3344i		−	0.506512i	0.967399	−	0.253256i	$-0.0815015\pi$
$594$	30.4730	−	34.4336i	1.25032	−	1.41283i
$595$			11.6673i			0.478311i
$596$	−11.8241	−	2.99410i	−0.484333	−	0.122643i
$597$	−0.987286	−	15.9942i	−0.0404069	−	0.654601i
$598$	9.20007	−	7.16080i	0.376219	−	0.292827i
$599$	1.34554			0.0549773			0.0274886	−	0.999622i	$-0.491249\pi$
$599$	1.34554			0.0549773			0.0274886	+	0.999622i	$0.491249\pi$
$600$	−13.7832	−	26.7989i	−0.562695	−	1.09406i
$601$	−3.14701			−0.128369			−0.0641846	−	0.997938i	$-0.520445\pi$
$601$	−3.14701			−0.128369			−0.0641846	+	0.997938i	$0.520445\pi$
$602$	−4.21069	+	3.27735i	−0.171615	+	0.133575i
$603$	−0.368959	−	2.97723i	−0.0150252	−	0.121242i
$604$	−5.35713	−	1.35653i	−0.217978	−	0.0551965i
$605$			94.0142i			3.82222i
$606$	24.1766	+	27.3965i	0.982106	+	1.11291i
$607$		−	7.16055i		−	0.290638i	−0.989385	−	0.145319i	$-0.953579\pi$
$607$		−	7.16055i		−	0.290638i	0.989385	−	0.145319i	$-0.0464208\pi$
$608$	3.57473	+	21.4178i	0.144974	+	0.868605i
$609$	1.00399	−	0.0619741i	0.0406839	−	0.00251132i
$610$	−40.4901	−	52.0209i	−1.63940	−	2.10627i
$611$	31.8475			1.28841
$612$	−34.7744	−	4.35929i	−1.40567	−	0.176214i
$613$	−19.1912			−0.775126			−0.387563	−	0.921843i	$-0.626683\pi$
$613$	−19.1912			−0.775126			−0.387563	+	0.921843i	$0.626683\pi$
$614$	−1.68129	−	2.16009i	−0.0678514	−	0.0871742i
$615$	45.1787	−	2.78877i	1.82178	−	0.112454i
$616$	−9.69443	+	4.25260i	−0.390600	+	0.171342i
$617$			22.8012i			0.917943i	0.888451	+	0.458971i	$0.151782\pi$
$617$			22.8012i			0.917943i	−0.888451	+	0.458971i	$0.848218\pi$
$618$	9.51249	+	10.7794i	0.382648	+	0.433612i
$619$		−	1.95964i		−	0.0787646i	−0.999224	−	0.0393823i	$-0.987461\pi$
$619$		−	1.95964i		−	0.0787646i	0.999224	−	0.0393823i	$-0.0125390\pi$
$620$	13.2933	−	52.4971i	0.533873	−	2.10834i
$621$	11.6555	−	2.18059i	0.467721	−	0.0875039i
$622$	−6.79667	+	5.29013i	−0.272522	+	0.212115i
$623$	1.16847			0.0468136
$624$	−22.7037	−	10.5326i	−0.908876	−	0.421641i
$625$	−17.9172			−0.716689
$626$	−11.7934	+	9.17926i	−0.471357	+	0.366877i
$627$	−2.56309	−	41.5226i	−0.102360	−	1.65825i
$628$	−0.670585	+	2.64823i	−0.0267593	+	0.105676i
$629$			14.0985i			0.562145i
$630$	−5.99655	+	5.98810i	−0.238908	+	0.238572i
$631$		−	19.2726i		−	0.767230i	−0.923493	−	0.383615i	$-0.874679\pi$
$631$		−	19.2726i		−	0.767230i	0.923493	−	0.383615i	$-0.125321\pi$
$632$	33.3758	−	14.6408i	1.32762	−	0.582379i
$633$	0.583878	+	9.45895i	0.0232071	+	0.375960i
$634$	5.33370	+	6.85264i	0.211828	+	0.272153i
$635$	−34.9549			−1.38714
$636$	−22.3924	−	4.22198i	−0.887915	−	0.167413i
$637$	−23.9948			−0.950707
$638$	−5.27726	−	6.78013i	−0.208929	−	0.268428i
$639$	−26.2904	+	3.25809i	−1.04003	+	0.128888i
$640$	−37.6518	−	3.11815i	−1.48832	−	0.123256i
$641$			13.0752i			0.516439i	0.966086	+	0.258219i	$0.0831357\pi$
$641$			13.0752i			0.516439i	−0.966086	+	0.258219i	$0.916864\pi$
$642$	−10.7489	+	9.48558i	−0.424226	+	0.374366i
$643$			28.6398i			1.12944i	0.825281	+	0.564722i	$0.191017\pi$
$643$			28.6398i			1.12944i	−0.825281	+	0.564722i	$0.808983\pi$
$644$	−2.64646	−	0.670136i	−0.104285	−	0.0264071i
$645$	36.4146	−	2.24779i	1.43383	−	0.0885065i
$646$	−25.0223	+	19.4759i	−0.984489	+	0.766269i
$647$	14.1737			0.557226			0.278613	−	0.960404i	$-0.410125\pi$
$647$	14.1737			0.557226			0.278613	+	0.960404i	$0.410125\pi$
$648$	−15.6071	−	20.1102i	−0.613105	−	0.790002i
$649$	−88.0323			−3.45557
$650$	24.7996	−	19.3026i	0.972720	−	0.757109i
$651$	−8.38456	+	0.517558i	−0.328617	+	0.0202847i
$652$	40.7613	+	10.3216i	1.59634	+	0.404225i
$653$		−	1.17910i		−	0.0461417i	−0.999734	−	0.0230708i	$-0.992656\pi$
$653$		−	1.17910i		−	0.0461417i	0.999734	−	0.0230708i	$-0.00734433\pi$
$654$	21.1096	−	18.6285i	0.825449	−	0.728432i
$655$		−	5.82654i		−	0.227662i
$656$	14.8981	−	27.5311i	0.581674	−	1.07491i
$657$	−0.251528	+	0.0311711i	−0.00981302	+	0.00121610i
$658$	−4.58056	−	5.88502i	−0.178569	−	0.229422i
$659$	−41.8999			−1.63219			−0.816094	−	0.577919i	$-0.803865\pi$
$659$	−41.8999			−1.63219			−0.816094	+	0.577919i	$0.803865\pi$
$660$	71.1302	+	13.4113i	2.76874	+	0.522034i
$661$	−13.5722			−0.527899			−0.263949	−	0.964537i	$-0.585025\pi$
$661$	−13.5722			−0.527899			−0.263949	+	0.964537i	$0.585025\pi$
$662$	−0.300226	−	0.385725i	−0.0116686	−	0.0149916i
$663$	−2.25171	−	36.4781i	−0.0874490	−	1.41669i
$664$	−2.80102	−	6.38534i	−0.108701	−	0.247799i
$665$			7.66725i			0.297323i
$666$	−7.24614	+	7.23593i	−0.280782	+	0.280387i
$667$		−	2.21568i		−	0.0857916i
$668$	−9.30626	+	36.7517i	−0.360070	+	1.42196i
$669$	0.959150	+	15.5384i	0.0370829	+	0.600751i
$670$	3.72676	−	2.90070i	0.143977	−	0.112064i
$671$	87.3434			3.37186
$672$	1.31914	+	5.71025i	0.0508868	+	0.220278i
$673$	12.0864			0.465896			0.232948	−	0.972489i	$-0.425163\pi$
$673$	12.0864			0.465896			0.232948	+	0.972489i	$0.425163\pi$
$674$	−12.3459	+	9.60932i	−0.475545	+	0.370137i
$675$	31.4185	−	5.87797i	1.20930	−	0.226243i
$676$	0.0244885	−	0.0967083i	0.000941866	−	0.00371955i
$677$		−	13.3115i		−	0.511602i	−0.966729	−	0.255801i	$-0.917661\pi$
$677$		−	13.3115i		−	0.511602i	0.966729	−	0.255801i	$-0.0823392\pi$
$678$	2.55567	+	2.89605i	0.0981500	+	0.111222i
$679$			2.60799i			0.100086i
$680$	−22.1626	−	50.5229i	−0.849898	−	1.93747i
$681$	−20.6900	+	1.27714i	−0.792842	+	0.0489402i
$682$	44.0715	+	56.6223i	1.68758	+	2.16818i
$683$	32.6777			1.25038			0.625190	−	0.780473i	$-0.285022\pi$
$683$	32.6777			1.25038			0.625190	+	0.780473i	$0.285022\pi$
$684$	−22.8523	−	2.86475i	−0.873781	−	0.109536i
$685$	59.6494			2.27909
$686$	7.08813	+	9.10670i	0.270626	+	0.347696i
$687$	10.3771	−	0.640553i	0.395911	−	0.0244386i
$688$	12.0081	−	22.1904i	0.457804	−	0.846002i
$689$		−	23.7628i		−	0.905292i
$690$	12.3510	+	13.9960i	0.470195	+	0.532819i
$691$		−	26.2009i		−	0.996728i	−0.866968	−	0.498364i	$-0.833934\pi$
$691$		−	26.2009i		−	0.996728i	0.866968	−	0.498364i	$-0.166066\pi$
$692$	−14.5735	−	3.69029i	−0.554000	−	0.140284i
$693$	−1.38093	−	11.1431i	−0.0524572	−	0.423290i
$694$	23.2599	−	18.1041i	0.882932	−	0.687223i
$695$	17.2614			0.654760
$696$	−4.22989	+	2.17551i	−0.160334	+	0.0824625i
$697$	45.7118			1.73146
$698$	23.3322	−	18.1604i	0.883136	−	0.687382i
$699$	−2.08701	−	33.8100i	−0.0789379	−	1.27881i
$700$	−7.13375	−	1.80641i	−0.269631	−	0.0682759i
$701$			40.4817i			1.52897i	0.644639	+	0.764487i	$0.277008\pi$
$701$			40.4817i			1.52897i	−0.644639	+	0.764487i	$0.722992\pi$
$702$	17.5928	−	19.8793i	0.663997	−	0.750297i
$703$			9.26499i			0.349436i
$704$	33.9019	−	36.8303i	1.27773	−	1.38809i
$705$	3.14160	+	50.8946i	0.118319	+	1.91680i
$706$	−13.1441	−	16.8873i	−0.494684	−	0.635561i
$707$	8.92250			0.335565
$708$	−9.02983	+	47.8920i	−0.339362	+	1.79989i
$709$	−16.1878			−0.607947			−0.303973	−	0.952681i	$-0.598313\pi$
$709$	−16.1878			−0.607947			−0.303973	+	0.952681i	$0.598313\pi$
$710$	−25.6146	−	32.9092i	−0.961298	−	1.23506i
$711$	4.75424	+	38.3631i	0.178298	+	1.43873i
$712$	−5.05983	+	2.21957i	−0.189625	+	0.0831819i
$713$			18.5036i			0.692966i
$714$	−6.41685	+	5.66267i	−0.240145	+	0.211920i
$715$			75.4835i			2.82292i
$716$	−1.97294	+	7.79138i	−0.0737320	+	0.291178i
$717$	−35.5326	+	2.19334i	−1.32699	+	0.0819117i
$718$	5.40381	−	4.20601i	0.201668	−	0.156967i
$719$	36.7071			1.36894			0.684471	−	0.729040i	$-0.260033\pi$
$719$	36.7071			1.36894			0.684471	+	0.729040i	$0.260033\pi$
$720$	14.5922	−	37.3212i	0.543820	−	1.39088i
$721$	3.51064			0.130743
$722$	4.76050	−	3.70530i	0.177168	−	0.137897i
$723$	−50.0261	+	3.08799i	−1.86049	+	0.114844i
$724$	−5.92847	+	23.4123i	−0.220330	+	0.870111i
$725$		−	5.97257i		−	0.221816i
$726$	−51.7067	+	45.6295i	−1.91902	+	1.69347i
$727$		−	38.3268i		−	1.42146i	−0.703464	−	0.710731i	$-0.748364\pi$
$727$		−	38.3268i		−	1.42146i	0.703464	−	0.710731i	$-0.251636\pi$
$728$	−5.59682	+	2.45513i	−0.207432	+	0.0909931i
$729$	25.1739	−	9.76100i	0.932365	−	0.361518i
$730$	−0.245062	−	0.314852i	−0.00907016	−	0.0116532i
$731$	36.8444			1.36274
$732$	8.95917	−	47.5173i	0.331140	−	1.75629i
$733$	27.1165			1.00157			0.500785	−	0.865572i	$-0.333045\pi$
$733$	27.1165			1.00157			0.500785	+	0.865572i	$0.333045\pi$
$734$	−8.33986	−	10.7149i	−0.307830	−	0.395494i
$735$	−2.36696	−	38.3454i	−0.0873068	−	1.41439i
$736$	12.7330	−	2.12519i	0.469343	−	0.0783356i
$737$			6.25726i			0.230489i
$738$	23.4611	+	23.4942i	0.863616	+	0.864834i
$739$			12.7223i			0.467999i	0.972237	+	0.234000i	$0.0751814\pi$
$739$			12.7223i			0.467999i	−0.972237	+	0.234000i	$0.924819\pi$
$740$	−15.6271	−	3.95710i	−0.574464	−	0.145466i
$741$	−1.47973	−	23.9720i	−0.0543592	−	0.880632i
$742$	−4.39108	+	3.41776i	−0.161202	+	0.125470i
$743$	−29.7567			−1.09167			−0.545834	−	0.837893i	$-0.683787\pi$
$743$	−29.7567			−1.09167			−0.545834	+	0.837893i	$0.683787\pi$
$744$	35.3247	−	18.1681i	1.29507	−	0.666076i
$745$	20.3656			0.746139
$746$	4.01621	−	3.12598i	0.147044	−	0.114450i
$747$	7.33950	−	0.909564i	0.268538	−	0.0332792i
$748$	70.8620	+	17.9437i	2.59097	+	0.656086i
$749$			3.50071i			0.127913i
$750$	6.23175	+	7.06174i	0.227551	+	0.257858i
$751$		−	39.4462i		−	1.43941i	−0.694279	−	0.719706i	$-0.744277\pi$
$751$		−	39.4462i		−	1.43941i	0.694279	−	0.719706i	$-0.255723\pi$
$752$	31.0142	+	16.7830i	1.13097	+	0.612013i
$753$	0.965702	−	0.0596104i	0.0351921	−	0.00217232i
$754$	−3.04669	−	3.91433i	−0.110954	−	0.142551i
$755$	9.22703			0.335806
$756$	−6.20379	−	0.391725i	−0.225630	−	0.0142469i
$757$	−7.34671			−0.267021			−0.133510	−	0.991047i	$-0.542625\pi$
$757$	−7.34671			−0.267021			−0.133510	+	0.991047i	$0.542625\pi$
$758$	3.48485	+	4.47728i	0.126576	+	0.162622i
$759$	−24.6854	+	1.52377i	−0.896022	+	0.0553092i
$760$	−14.5644	−	33.2016i	−0.528305	−	1.20435i
$761$			8.41587i			0.305075i	0.988298	+	0.152537i	$0.0487445\pi$
$761$			8.41587i			0.305075i	−0.988298	+	0.152537i	$0.951256\pi$
$762$	−16.9652	−	19.2248i	−0.614586	−	0.696440i
$763$		−	6.87496i		−	0.248890i
$764$	0.00376744	−	0.0148781i	0.000136301	−	0.000538271i
$765$	58.0726	−	7.19678i	2.09962	−	0.260200i
$766$	−5.55683	+	4.32512i	−0.200777	+	0.156273i
$767$	−50.8231			−1.83512
$768$	−16.5592	−	22.2214i	−0.597530	−	0.801847i
$769$	23.7113			0.855052			0.427526	−	0.904003i	$-0.359385\pi$
$769$	23.7113			0.855052			0.427526	+	0.904003i	$0.359385\pi$
$770$	13.9484	−	10.8566i	0.502666	−	0.391246i
$771$	−1.93192	−	31.2975i	−0.0695763	−	1.12715i
$772$	−7.03215	+	27.7709i	−0.253093	+	0.999496i
$773$			30.9181i			1.11205i	0.831166	+	0.556024i	$0.187674\pi$
$773$			30.9181i			1.11205i	−0.831166	+	0.556024i	$0.812326\pi$
$774$	18.9100	+	18.9367i	0.679706	+	0.680665i
$775$			49.8782i			1.79168i
$776$	−4.95403	−	11.2934i	−0.177839	−	0.405411i
$777$	0.154064	+	2.49588i	0.00552703	+	0.0895391i
$778$	−25.5750	−	32.8583i	−0.916907	−	1.17803i
$779$	30.0399			1.07629
$780$	41.0651	+	7.74265i	1.47037	+	0.277231i
$781$	55.2547			1.97717
$782$	11.5785	+	14.8759i	0.414047	+	0.531960i
$783$	−0.927769	−	4.95905i	−0.0331557	−	0.177222i
$784$	−23.3670	−	12.6448i	−0.834534	−	0.451599i
$785$		−	4.56127i		−	0.162799i
$786$	3.20453	−	2.82789i	0.114302	−	0.100868i
$787$		−	39.5304i		−	1.40911i	−0.709651	−	0.704554i	$-0.751147\pi$
$787$		−	39.5304i		−	1.40911i	0.709651	−	0.704554i	$-0.248853\pi$
$788$	−32.8715	−	8.32374i	−1.17100	−	0.296521i
$789$	7.31173	−	0.451335i	0.260304	−	0.0160679i
$790$	−48.0214	+	37.3770i	−1.70852	+	1.32982i
$791$	0.943186			0.0335358
$792$	27.1468	+	45.6299i	0.964619	+	1.62139i
$793$	50.4254			1.79066
$794$	−13.4730	+	10.4866i	−0.478140	+	0.372156i
$795$	37.9747	−	2.34409i	1.34682	−	0.0831361i
$796$	17.9376	+	4.54216i	0.635780	+	0.160992i
$797$			45.6869i			1.61831i	0.587592	+	0.809157i	$0.300076\pi$
$797$			45.6869i			1.61831i	−0.587592	+	0.809157i	$0.699924\pi$
$798$	−4.21690	+	3.72127i	−0.149276	+	0.131732i
$799$			51.4952i			1.82177i
$800$	34.3228	−	5.72864i	1.21349	−	0.202538i
$801$	−0.720752	−	5.81593i	−0.0254665	−	0.205496i
$802$	−23.8400	−	30.6292i	−0.841820	−	1.08156i
$803$	0.528637			0.0186552
$804$	3.40412	+	0.641832i	0.120054	+	0.0226357i
$805$	4.55821			0.160656
$806$	25.4435	+	32.6894i	0.896209	+	1.15143i
$807$	2.57386	+	41.6972i	0.0906043	+	1.46781i
$808$	−38.6373	+	16.9488i	−1.35926	+	0.596257i
$809$			54.5763i			1.91880i	0.282049	+	0.959400i	$0.408986\pi$
$809$			54.5763i			1.91880i	−0.282049	+	0.959400i	$0.591014\pi$
$810$	33.5040	+	26.1535i	1.17721	+	0.918942i
$811$		−	35.1158i		−	1.23308i	−0.787323	−	0.616541i	$-0.788534\pi$
$811$		−	35.1158i		−	1.23308i	0.787323	−	0.616541i	$-0.211466\pi$
$812$	−0.285121	+	1.12598i	−0.0100058	+	0.0395142i
$813$	0.0837592	+	1.35692i	0.00293756	+	0.0475892i
$814$	16.8551	−	13.1190i	0.590770	−	0.459821i
$815$	−70.2067			−2.45923
$816$	17.0305	−	36.7103i	0.596186	−	1.28512i
$817$	24.2126			0.847093
$818$	15.0120	−	11.6845i	0.524883	−	0.408538i
$819$	−0.797243	−	6.43316i	−0.0278579	−	0.224793i
$820$	−12.8301	+	50.6679i	−0.448048	+	1.76940i
$821$			12.1496i			0.424024i	0.977267	+	0.212012i	$0.0680016\pi$
$821$			12.1496i			0.424024i	−0.977267	+	0.212012i	$0.931998\pi$
$822$	28.9507	+	32.8065i	1.00977	+	1.14426i
$823$			20.0109i			0.697537i	0.937209	+	0.348769i	$0.113400\pi$
$823$			20.0109i			0.697537i	−0.937209	+	0.348769i	$0.886600\pi$
$824$	−15.2022	+	6.66866i	−0.529593	+	0.232314i
$825$	−66.5416	+	4.10745i	−2.31668	+	0.143003i
$826$	7.30979	+	9.39148i	0.254340	+	0.326771i
$827$	17.1962			0.597970			0.298985	−	0.954258i	$-0.403352\pi$
$827$	17.1962			0.597970			0.298985	+	0.954258i	$0.403352\pi$
$828$	−1.70311	+	13.5858i	−0.0591871	+	0.472140i
$829$	−3.65158			−0.126825			−0.0634124	−	0.997987i	$-0.520198\pi$
$829$	−3.65158			−0.126825			−0.0634124	+	0.997987i	$0.520198\pi$
$830$	7.15084	+	9.18727i	0.248209	+	0.318895i
$831$	30.9832	−	1.91252i	1.07479	−	0.0663444i
$832$	19.5724	−	21.2630i	0.678550	−	0.737161i
$833$		−	38.7979i		−	1.34427i
$834$	8.37774	+	9.49354i	0.290098	+	0.328734i
$835$		−	63.3005i		−	2.19060i
$836$	46.5676	+	11.7919i	1.61057	+	0.407830i
$837$	7.74799	+	41.4140i	0.267810	+	1.43148i
$838$	19.9686	−	15.5424i	0.689803	−	0.536902i
$839$	−40.0741			−1.38351			−0.691755	−	0.722132i	$-0.743162\pi$
$839$	−40.0741			−1.38351			−0.691755	+	0.722132i	$0.743162\pi$
$840$	−4.47557	−	8.70194i	−0.154422	−	0.300245i
$841$	28.0573			0.967493
$842$	15.0127	−	11.6850i	0.517371	−	0.402691i
$843$	−1.08351	−	17.5530i	−0.0373179	−	0.604559i
$844$	−10.6082	−	2.68622i	−0.365150	−	0.0924634i
$845$			0.166569i			0.00573015i
$846$	−26.4667	+	26.4294i	−0.909942	+	0.908660i
$847$			16.8398i			0.578624i
$848$	12.5225	−	23.1411i	0.430026	−	0.794669i
$849$	−0.0433024	−	0.701508i	−0.00148613	−	0.0240757i
$850$	31.2109	+	40.0992i	1.07053	+	1.37539i
$851$	5.50808			0.188815
$852$	5.66769	−	30.0601i	0.194172	−	1.02984i
$853$	23.6523			0.809838			0.404919	−	0.914353i	$-0.367300\pi$
$853$	23.6523			0.809838			0.404919	+	0.914353i	$0.367300\pi$
$854$	−7.25259	−	9.31800i	−0.248178	−	0.318855i
$855$	38.1629	−	4.72943i	1.30515	−	0.161743i
$856$	−6.64980	−	15.1592i	−0.227285	−	0.518131i
$857$			46.1460i			1.57632i	0.615473	+	0.788158i	$0.288965\pi$
$857$			46.1460i			1.57632i	−0.615473	+	0.788158i	$0.711035\pi$
$858$	−41.5150	+	36.6357i	−1.41730	+	1.25072i
$859$		−	22.6923i		−	0.774250i	−0.922027	−	0.387125i	$-0.873468\pi$
$859$		−	22.6923i		−	0.774250i	0.922027	−	0.387125i	$-0.126532\pi$
$860$	−10.3413	+	40.8391i	−0.352635	+	1.39260i
$861$	8.09241	−	0.499524i	0.275789	−	0.0170237i
$862$	−34.9918	+	27.2356i	−1.19183	+	0.927648i
$863$	−16.5485			−0.563319			−0.281660	−	0.959514i	$-0.590885\pi$
$863$	−16.5485			−0.563319			−0.281660	+	0.959514i	$0.590885\pi$
$864$	27.6085	−	10.0882i	0.939260	−	0.343206i
$865$	25.1011			0.853463
$866$	−21.6650	+	16.8628i	−0.736208	+	0.573021i
$867$	29.5937	−	1.82675i	1.00505	−	0.0620395i
$868$	2.38110	−	9.40329i	0.0808199	−	0.319169i
$869$		−	80.6281i		−	2.73512i
$870$	5.95484	−	5.25495i	0.201888	−	0.178160i
$871$			3.61246i			0.122404i
$872$	13.0594	+	29.7708i	0.442246	+	1.00817i
$873$	12.9810	−	1.60870i	0.439341	−	0.0544463i
$874$	7.60893	+	9.77582i	0.257376	+	0.330672i
$875$	2.29987			0.0777496
$876$	0.0542245	−	0.287594i	0.00183208	−	0.00971689i
$877$	−37.4660			−1.26514			−0.632568	−	0.774505i	$-0.717999\pi$
$877$	−37.4660			−1.26514			−0.632568	+	0.774505i	$0.717999\pi$
$878$	−8.73178	−	11.2184i	−0.294683	−	0.378604i
$879$	0.864234	+	14.0008i	0.0291499	+	0.472235i
$880$	−39.7783	+	73.5086i	−1.34093	+	2.47797i
$881$		−	47.1581i		−	1.58880i	−0.607396	−	0.794399i	$-0.707786\pi$
$881$		−	47.1581i		−	1.58880i	0.607396	−	0.794399i	$-0.292214\pi$
$882$	19.9407	−	19.9126i	0.671438	−	0.670492i
$883$		−	41.7487i		−	1.40496i	−0.711705	−	0.702478i	$-0.752077\pi$
$883$		−	41.7487i		−	1.40496i	0.711705	−	0.702478i	$-0.247923\pi$
$884$	40.9103	+	10.3593i	1.37596	+	0.348421i
$885$	−5.01345	−	81.2190i	−0.168525	−	2.73015i
$886$	−28.4426	+	22.1381i	−0.955548	+	0.743743i
$887$	17.5246			0.588418			0.294209	−	0.955741i	$-0.404944\pi$
$887$	17.5246			0.588418			0.294209	+	0.955741i	$0.404944\pi$
$888$	−5.40821	−	10.5153i	−0.181488	−	0.352870i
$889$	−6.26112			−0.209991
$890$	7.28013	−	5.66643i	0.244030	−	0.189939i
$891$	−54.6117	+	13.7469i	−1.82956	+	0.460538i
$892$	−17.4264	−	4.41271i	−0.583479	−	0.147749i
$893$			33.8405i			1.13243i
$894$	9.88439	+	11.2009i	0.330584	+	0.374613i
$895$		−	13.4198i		−	0.448573i
$896$	−6.74419	−	0.558523i	−0.225308	−	0.0186589i
$897$	−14.2514	+	0.879706i	−0.475842	+	0.0293725i
$898$	−4.86363	−	6.24870i	−0.162301	−	0.208522i
$899$	7.87269			0.262569
$900$	−4.59088	+	36.6218i	−0.153029	+	1.22073i
$901$	38.4228			1.28005
$902$	−42.5359	−	54.6493i	−1.41629	−	1.81962i
$903$	6.52260	−	0.402624i	0.217058	−	0.0133985i
$904$	−4.08430	+	1.79164i	−0.135842	+	0.0595889i
$905$		−	40.3250i		−	1.34045i
$906$	4.47831	+	5.07476i	0.148782	+	0.168598i
$907$			48.4959i			1.61028i	0.593084	+	0.805140i	$0.297910\pi$
$907$			48.4959i			1.61028i	−0.593084	+	0.805140i	$0.702090\pi$
$908$	5.87568	−	23.2039i	0.194991	−	0.770047i
$909$	−5.50372	−	44.4109i	−0.182547	−	1.47302i
$910$	8.05275	−	6.26779i	0.266946	−	0.207775i
$911$	0.318752			0.0105607			0.00528036	−	0.999986i	$-0.498319\pi$
$911$	0.318752			0.0105607			0.00528036	+	0.999986i	$0.498319\pi$
$912$	11.1917	−	24.1245i	0.370595	−	0.798843i
$913$	−15.4255			−0.510509
$914$	−35.6408	+	27.7407i	−1.17889	+	0.917582i
$915$	4.97422	+	80.5835i	0.164443	+	2.66401i
$916$	−2.94696	+	11.6379i	−0.0973703	+	0.384528i
$917$		−	1.04365i		−	0.0344644i
$918$	32.1435	+	28.4463i	1.06089	+	0.938868i
$919$			1.06146i			0.0350145i	0.999847	+	0.0175072i	$0.00557301\pi$
$919$			1.06146i			0.0350145i	−0.999847	+	0.0175072i	$0.994427\pi$
$920$	−19.7385	+	8.65859i	−0.650760	+	0.285465i
$921$	0.206547	+	3.34611i	0.00680596	+	0.110258i
$922$	−8.52798	−	10.9566i	−0.280854	−	0.360836i
$923$	31.8998			1.05000
$924$	12.7408	+	2.40223i	0.419143	+	0.0790276i
$925$	14.8475			0.488183
$926$	5.22468	+	6.71258i	0.171694	+	0.220589i
$927$	−2.16549	−	17.4739i	−0.0711239	−	0.573917i
$928$	−0.904199	−	5.41746i	−0.0296818	−	0.177837i
$929$			16.6628i			0.546688i	0.961916	+	0.273344i	$0.0881297\pi$
$929$			16.6628i			0.546688i	−0.961916	+	0.273344i	$0.911870\pi$
$930$	−49.7301	+	43.8852i	−1.63071	+	1.43905i
$931$		−	25.4964i		−	0.835610i
$932$	37.9180	+	9.60160i	1.24204	+	0.314511i
$933$	10.5284	−	0.649894i	0.344686	−	0.0212766i
$934$	−22.7385	+	17.6983i	−0.744025	+	0.579106i
$935$	−122.052			−3.99151
$936$	15.6725	+	26.3432i	0.512271	+	0.861055i
$937$	−5.82716			−0.190365			−0.0951825	−	0.995460i	$-0.530343\pi$
$937$	−5.82716			−0.190365			−0.0951825	+	0.995460i	$0.530343\pi$
$938$	0.667538	−	0.519573i	0.0217959	−	0.0169647i
$939$	18.2686	−	1.12768i	0.596173	−	0.0368003i
$940$	−57.0783	−	14.4534i	−1.86169	−	0.471418i
$941$			57.1062i			1.86161i	0.365518	+	0.930804i	$0.380892\pi$
$941$			57.1062i			1.86161i	−0.365518	+	0.930804i	$0.619108\pi$
$942$	2.50865	−	2.21380i	0.0817361	−	0.0721295i
$943$		−	17.8589i		−	0.581566i
$944$	−49.4934	−	26.7828i	−1.61087	−	0.871705i
$945$	10.2020	−	1.90865i	0.331871	−	0.0620884i
$946$	−34.2845	−	44.0481i	−1.11469	−	1.43213i
$947$	−24.9903			−0.812075			−0.406037	−	0.913856i	$-0.633090\pi$
$947$	−24.9903			−0.812075			−0.406037	+	0.913856i	$0.633090\pi$
$948$	−43.8640	−	8.27036i	−1.42464	−	0.268609i
$949$	0.305195			0.00990704
$950$	20.5105	+	26.3516i	0.665450	+	0.854959i
$951$	−0.655247	−	10.6151i	−0.0212478	−	0.344220i
$952$	−3.96977	−	9.04968i	−0.128661	−	0.293302i
$953$			14.5583i			0.471591i	0.971803	+	0.235795i	$0.0757695\pi$
$953$			14.5583i			0.471591i	−0.971803	+	0.235795i	$0.924230\pi$
$954$	19.7201	+	19.7480i	0.638463	+	0.639364i
$955$			0.0256258i			0.000829233i
$956$	10.0908	−	39.8498i	0.326359	−	1.28884i
$957$	0.648313	+	10.5028i	0.0209570	+	0.339508i
$958$	27.4868	−	21.3941i	0.888059	−	0.691213i
$959$	10.6844			0.345018
$960$	35.9105	+	29.1806i	1.15901	+	0.941799i
$961$	−34.7465			−1.12085
$962$	9.73083	−	7.57391i	0.313734	−	0.244193i
$963$	17.4244	−	2.15936i	0.561494	−	0.0695845i
$964$	14.2068	−	56.1044i	0.457569	−	1.80700i
$965$		−	47.8321i		−	1.53977i
$966$	2.21232	+	2.50696i	0.0711801	+	0.0806603i
$967$			49.7884i			1.60109i	0.599275	+	0.800543i	$0.295456\pi$
$967$			49.7884i			1.60109i	−0.599275	+	0.800543i	$0.704544\pi$
$968$	−31.9882	−	72.9219i	−1.02814	−	2.34380i
$969$	38.7610	−	2.39262i	1.24518	−	0.0768620i
$970$	12.6474	+	16.2491i	0.406082	+	0.521727i
$971$	52.3436			1.67979			0.839893	−	0.542751i	$-0.182617\pi$
$971$	52.3436			1.67979			0.839893	+	0.542751i	$0.182617\pi$
$972$	1.87694	+	31.1204i	0.0602030	+	0.998186i
$973$	3.09186			0.0991203
$974$	2.29623	+	2.95016i	0.0735761	+	0.0945293i
$975$	−38.4160	+	2.37133i	−1.23030	+	0.0759432i
$976$	49.1061	+	26.5732i	1.57185	+	0.850587i
$977$		−	57.0863i		−	1.82635i	−0.407565	−	0.913176i	$-0.633622\pi$
$977$		−	57.0863i		−	1.82635i	0.407565	−	0.913176i	$-0.366378\pi$
$978$	−34.0746	−	38.6129i	−1.08959	−	1.23470i
$979$			12.2234i			0.390661i
$980$	43.0044	+	10.8896i	1.37372	+	0.347855i
$981$	−34.2194	+	4.24072i	−1.09254	+	0.135396i
$982$	17.7723	−	13.8329i	0.567136	−	0.441425i
$983$	−17.1695			−0.547622			−0.273811	−	0.961784i	$-0.588284\pi$
$983$	−17.1695			−0.547622			−0.273811	+	0.961784i	$0.588284\pi$
$984$	−34.0938	+	17.5351i	−1.08687	+	0.558998i
$985$	56.6174			1.80398
$986$	6.32920	−	4.92628i	0.201563	−	0.156885i
$987$	0.562723	+	9.11624i	0.0179117	+	0.290173i
$988$	26.8846	+	6.80772i	0.855312	+	0.216582i
$989$		−	14.3945i		−	0.457719i
$990$	−62.6417	−	62.7301i	−1.99088	−	1.99369i
$991$		−	47.7738i		−	1.51758i	−0.651333	−	0.758792i	$-0.725790\pi$
$991$		−	47.7738i		−	1.51758i	0.651333	−	0.758792i	$-0.274210\pi$
$992$	7.55116	+	45.2423i	0.239749	+	1.43644i
$993$	0.0368829	+	0.597511i	0.00117044	+	0.0189614i
$994$	−4.58809	−	5.89469i	−0.145525	−	0.186968i
$995$	−30.8954			−0.979450
$996$	−1.58225	+	8.39189i	−0.0501356	+	0.265907i
$997$	19.1191			0.605507			0.302754	−	0.953069i	$-0.402094\pi$
$997$	19.1191			0.605507			0.302754	+	0.953069i	$0.402094\pi$
$998$	−3.95323	−	5.07904i	−0.125137	−	0.160774i
$999$	12.3279	−	2.30639i	0.390039	−	0.0729708i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.c.b.671.101	yes	128
3.2	odd	2	inner	804.2.c.b.671.28	yes	128
4.3	odd	2	inner	804.2.c.b.671.27	✓	128
12.11	even	2	inner	804.2.c.b.671.102	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.c.b.671.27	✓	128	4.3	odd	2	inner
804.2.c.b.671.28	yes	128	3.2	odd	2	inner
804.2.c.b.671.101	yes	128	1.1	even	1	trivial
804.2.c.b.671.102	yes	128	12.11	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	804.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.11601 - 0.868635i) q^{2} +(-1.72876 + 0.106712i) q^{3} +(0.490945 - 1.93881i) q^{4} +3.33937i q^{5} +(-1.83662 + 1.62075i) q^{6} +0.598149i q^{7} +(-1.13622 - 2.59018i) q^{8} +(2.97723 - 0.368959i) q^{9} +O(q^{10})\)	\(q+(1.11601 - 0.868635i) q^{2} +(-1.72876 + 0.106712i) q^{3} +(0.490945 - 1.93881i) q^{4} +3.33937i q^{5} +(-1.83662 + 1.62075i) q^{6} +0.598149i q^{7} +(-1.13622 - 2.59018i) q^{8} +(2.97723 - 0.368959i) q^{9} +(2.90070 + 3.72676i) q^{10} -6.25726 q^{11} +(-0.641832 + 3.40412i) q^{12} -3.61246 q^{13} +(0.519573 + 0.667538i) q^{14} +(-0.356351 - 5.77297i) q^{15} +(-3.51795 - 1.90370i) q^{16} -5.84110i q^{17} +(3.00211 - 2.99788i) q^{18} -3.83853i q^{19} +(6.47440 + 1.63945i) q^{20} +(-0.0638297 - 1.03406i) q^{21} +(-6.98315 + 5.43527i) q^{22} -2.28203 q^{23} +(2.24065 + 4.35654i) q^{24} -6.15141 q^{25} +(-4.03153 + 3.13791i) q^{26} +(-5.10754 + 0.955548i) q^{27} +(1.15970 + 0.293658i) q^{28} +0.970928i q^{29} +(-5.41230 - 6.13314i) q^{30} -8.10842i q^{31} +(-5.57967 + 0.931273i) q^{32} +(10.8173 - 0.667725i) q^{33} +(-5.07379 - 6.51871i) q^{34} -1.99744 q^{35} +(0.746313 - 5.95340i) q^{36} -2.41368 q^{37} +(-3.33429 - 4.28383i) q^{38} +(6.24508 - 0.385493i) q^{39} +(8.64956 - 3.79425i) q^{40} +7.82589i q^{41} +(-0.969452 - 1.09857i) q^{42} +6.30778i q^{43} +(-3.07197 + 12.1316i) q^{44} +(1.23209 + 9.94206i) q^{45} +(-2.54676 + 1.98225i) q^{46} -8.81601 q^{47} +(6.28483 + 2.91563i) q^{48} +6.64222 q^{49} +(-6.86501 + 5.34333i) q^{50} +(0.623316 + 10.0979i) q^{51} +(-1.77352 + 7.00387i) q^{52} +6.57802i q^{53} +(-4.87003 + 5.50299i) q^{54} -20.8953i q^{55} +(1.54931 - 0.679627i) q^{56} +(0.409618 + 6.63591i) q^{57} +(0.843382 + 1.08356i) q^{58} +14.0688 q^{59} +(-11.3676 - 2.14332i) q^{60} -13.9587 q^{61} +(-7.04326 - 9.04906i) q^{62} +(0.220693 + 1.78082i) q^{63} +(-5.41802 + 5.88601i) q^{64} -12.0634i q^{65} +(11.4922 - 10.1415i) q^{66} -1.00000i q^{67} +(-11.3248 - 2.86766i) q^{68} +(3.94508 - 0.243520i) q^{69} +(-2.22916 + 1.73505i) q^{70} -8.83049 q^{71} +(-4.33845 - 7.29232i) q^{72} -0.0844839 q^{73} +(-2.69368 + 2.09661i) q^{74} +(10.6343 - 0.656429i) q^{75} +(-7.44218 - 1.88451i) q^{76} -3.74277i q^{77} +(6.63470 - 5.85491i) q^{78} +12.8855i q^{79} +(6.35715 - 11.7477i) q^{80} +(8.72774 - 2.19695i) q^{81} +(6.79785 + 8.73375i) q^{82} +2.46521 q^{83} +(-2.03617 - 0.383911i) q^{84} +19.5056 q^{85} +(5.47916 + 7.03953i) q^{86} +(-0.103610 - 1.67850i) q^{87} +(7.10961 + 16.2074i) q^{88} -1.95347i q^{89} +(10.0111 + 10.0252i) q^{90} -2.16079i q^{91} +(-1.12035 + 4.42441i) q^{92} +(0.865266 + 14.0175i) q^{93} +(-9.83873 + 7.65789i) q^{94} +12.8183 q^{95} +(9.54654 - 2.20537i) q^{96} +4.36011 q^{97} +(7.41276 - 5.76967i) q^{98} +(-18.6293 + 2.30867i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q + 4 q^{4} - 6 q^{6} - 4 q^{9}+O(q^{10}) \) 128 * q + 4 * q^4 - 6 * q^6 - 4 * q^9	\( 128 q + 4 q^{4} - 6 q^{6} - 4 q^{9} - 4 q^{10} + 4 q^{12} - 8 q^{13} - 4 q^{16} + 18 q^{18} - 8 q^{21} - 8 q^{22} - 24 q^{24} - 136 q^{25} + 14 q^{30} - 32 q^{33} + 34 q^{36} - 48 q^{37} + 16 q^{40} - 28 q^{42} - 16 q^{45} - 28 q^{46} - 22 q^{48} - 152 q^{49} + 8 q^{52} - 16 q^{54} - 32 q^{57} - 20 q^{58} - 14 q^{60} + 8 q^{61} + 16 q^{64} + 14 q^{66} + 56 q^{69} - 4 q^{70} - 8 q^{72} - 48 q^{73} - 36 q^{76} + 40 q^{78} + 44 q^{81} + 60 q^{82} + 46 q^{84} + 64 q^{85} - 28 q^{88} - 14 q^{90} + 32 q^{93} - 8 q^{96} + 64 q^{97}+O(q^{100}) \) 128 * q + 4 * q^4 - 6 * q^6 - 4 * q^9 - 4 * q^10 + 4 * q^12 - 8 * q^13 - 4 * q^16 + 18 * q^18 - 8 * q^21 - 8 * q^22 - 24 * q^24 - 136 * q^25 + 14 * q^30 - 32 * q^33 + 34 * q^36 - 48 * q^37 + 16 * q^40 - 28 * q^42 - 16 * q^45 - 28 * q^46 - 22 * q^48 - 152 * q^49 + 8 * q^52 - 16 * q^54 - 32 * q^57 - 20 * q^58 - 14 * q^60 + 8 * q^61 + 16 * q^64 + 14 * q^66 + 56 * q^69 - 4 * q^70 - 8 * q^72 - 48 * q^73 - 36 * q^76 + 40 * q^78 + 44 * q^81 + 60 * q^82 + 46 * q^84 + 64 * q^85 - 28 * q^88 - 14 * q^90 + 32 * q^93 - 8 * q^96 + 64 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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