LMFDB - Embedded newform 700.2.bj.a.323.43

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [700,2,Mod(127,700)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(700, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 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("700.127");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 700 = 2^{2} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	700.bj (of order $20$, degree $8$, 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:	$5.58952814149$
Analytic rank:	$0$
Dimension:	$720$
Relative dimension:	$90$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			323.43
Character	$\chi$	$=$	700.323
Dual form			700.2.bj.a.687.43

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.126438 + 1.40855i) q^{2} +(-1.45856 - 2.86259i) q^{3} +(-1.96803 - 0.356188i) q^{4} +(1.35907 + 1.77565i) q^{5} +(4.21651 - 1.69252i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(0.750542 - 2.72703i) q^{8} +(-4.30364 + 5.92345i) q^{9} +(-2.67293 + 1.68981i) q^{10} +(2.04399 + 2.81331i) q^{11} +(1.85087 + 6.15317i) q^{12} +(0.0115670 + 0.0730309i) q^{13} +(1.08540 - 0.906590i) q^{14} +(3.10067 - 6.48034i) q^{15} +(3.74626 + 1.40198i) q^{16} +(-2.40861 - 1.22725i) q^{17} +(-7.79934 - 6.81084i) q^{18} +(-0.280546 - 0.863431i) q^{19} +(-2.04222 - 3.97861i) q^{20} +(-0.992796 + 3.05551i) q^{21} +(-4.22112 + 2.52335i) q^{22} +(-0.183083 + 1.15594i) q^{23} +(-8.90106 + 1.82904i) q^{24} +(-1.30587 + 4.82646i) q^{25} +(-0.104330 + 0.00705877i) q^{26} +(13.7139 + 2.17207i) q^{27} +(1.13974 + 1.64347i) q^{28} +(7.67871 + 2.49497i) q^{29} +(8.73584 + 5.18680i) q^{30} +(5.36384 - 1.74282i) q^{31} +(-2.44842 + 5.09953i) q^{32} +(5.07205 - 9.95446i) q^{33} +(2.03318 - 3.23747i) q^{34} +(0.294568 - 2.21658i) q^{35} +(10.5795 - 10.1246i) q^{36} +(3.47004 - 0.549601i) q^{37} +(1.25166 - 0.285992i) q^{38} +(0.192186 - 0.139631i) q^{39} +(5.86229 - 2.37352i) q^{40} +(8.36936 + 6.08070i) q^{41} +(-4.17831 - 1.78473i) q^{42} +(-4.55361 + 4.55361i) q^{43} +(-3.02055 - 6.26471i) q^{44} +(-16.3669 + 0.408618i) q^{45} +(-1.60505 - 0.404036i) q^{46} +(11.8098 - 6.01737i) q^{47} +(-1.45087 - 12.7689i) q^{48} +1.00000i q^{49} +(-6.63320 - 2.44963i) q^{50} +8.68486i q^{51} +(0.00324867 - 0.147847i) q^{52} +(9.84755 - 5.01758i) q^{53} +(-4.79343 + 19.0421i) q^{54} +(-2.21753 + 7.45288i) q^{55} +(-2.45901 + 1.39759i) q^{56} +(-2.06245 + 2.06245i) q^{57} +(-4.48516 + 10.5004i) q^{58} +(1.40535 + 1.02104i) q^{59} +(-8.41042 + 11.6491i) q^{60} +(-3.22028 + 2.33967i) q^{61} +(1.77665 + 7.77560i) q^{62} +(7.23165 - 1.14538i) q^{63} +(-6.87337 - 4.09350i) q^{64} +(-0.113957 + 0.119793i) q^{65} +(13.3801 + 8.40286i) q^{66} +(-3.00737 + 5.90229i) q^{67} +(4.30307 + 3.27317i) q^{68} +(3.57601 - 1.16192i) q^{69} +(3.08492 + 0.695173i) q^{70} +(-12.5751 - 4.08589i) q^{71} +(12.9234 + 16.1820i) q^{72} +(10.3532 + 1.63978i) q^{73} +(0.335395 + 4.95722i) q^{74} +(15.7208 - 3.30153i) q^{75} +(0.244577 + 1.79918i) q^{76} +(0.543991 - 3.43463i) q^{77} +(0.172378 + 0.288359i) q^{78} +(-3.55666 + 10.9463i) q^{79} +(2.60200 + 8.55743i) q^{80} +(-6.99715 - 21.5350i) q^{81} +(-9.62317 + 11.0198i) q^{82} +(-3.82180 - 1.94731i) q^{83} +(3.04219 - 5.65971i) q^{84} +(-1.09430 - 5.94476i) q^{85} +(-5.83824 - 6.98974i) q^{86} +(-4.05781 - 25.6200i) q^{87} +(9.20607 - 3.46251i) q^{88} +(0.877888 + 1.20831i) q^{89} +(1.49384 - 23.1053i) q^{90} +(0.0434616 - 0.0598197i) q^{91} +(0.772043 - 2.20971i) q^{92} +(-12.8125 - 12.8125i) q^{93} +(6.98257 + 17.3955i) q^{94} +(1.15187 - 1.67161i) q^{95} +(18.1690 - 0.429154i) q^{96} +(-6.30893 - 12.3820i) q^{97} +(-1.40855 - 0.126438i) q^{98} -25.4611 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 720 q + 16 q^{10} + 16 q^{12} + 4 q^{13} + 20 q^{17} - 28 q^{18} - 20 q^{20} - 4 q^{22} + 20 q^{25} + 4 q^{30} - 20 q^{37} - 64 q^{40} - 80 q^{42} - 140 q^{44} - 20 q^{45} - 236 q^{48} - 40 q^{50} - 16 q^{52}+ \cdots - 20 q^{97}+O(q^{100}) $ 720 * q + 16 * q^10 + 16 * q^12 + 4 * q^13 + 20 * q^17 - 28 * q^18 - 20 * q^20 - 4 * q^22 + 20 * q^25 + 4 * q^30 - 20 * q^37 - 64 * q^40 - 80 * q^42 - 140 * q^44 - 20 * q^45 - 236 * q^48 - 40 * q^50 - 16 * q^52 + 44 * q^53 - 260 * q^54 + 16 * q^57 - 136 * q^58 - 140 * q^60 - 140 * q^62 - 4 * q^65 - 80 * q^68 - 80 * q^72 - 52 * q^73 + 76 * q^78 + 20 * q^80 + 180 * q^81 + 24 * q^82 - 80 * q^85 + 160 * q^88 - 260 * q^89 + 16 * q^90 + 256 * q^92 - 112 * q^93 + 320 * q^94 - 40 * q^96 - 20 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/700\mathbb{Z}\right)^\times$.

$n$	$101$	$351$	$477$
$\chi(n)$	$1$	$-1$	$e\left(\frac{11}{20}\right)$

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 $

$2$	−0.126438	+	1.40855i	−0.0894051	+	0.995995i
$2$	−0.126438	+	1.40855i	−0.0894051	+	0.995995i
$3$	−1.45856	−	2.86259i	−0.842100	−	1.65271i	−0.754256	−	0.656580i	$-0.772002\pi$
$3$	−1.45856	−	2.86259i	−0.842100	−	1.65271i	−0.0878436	−	0.996134i	$-0.527998\pi$
$4$	−1.96803	−	0.356188i	−0.984013	−	0.178094i
$5$	1.35907	+	1.77565i	0.607794	+	0.794095i
$5$	1.35907	+	1.77565i	0.607794	+	0.794095i
$6$	4.21651	−	1.69252i	1.72138	−	0.690967i
$7$	−0.707107	−	0.707107i	−0.267261	−	0.267261i
$7$	−0.707107	−	0.707107i	−0.267261	−	0.267261i
$8$	0.750542	−	2.72703i	0.265357	−	0.964150i
$9$	−4.30364	+	5.92345i	−1.43455	+	1.97448i
$10$	−2.67293	+	1.68981i	−0.845255	+	0.534364i
$11$	2.04399	+	2.81331i	0.616285	+	0.848244i	0.997076	−	0.0764173i	$-0.0243481\pi$
$11$	2.04399	+	2.81331i	0.616285	+	0.848244i	−0.380791	+	0.924661i	$0.624348\pi$
$12$	1.85087	+	6.15317i	0.534299	+	1.77627i
$13$	0.0115670	+	0.0730309i	0.00320810	+	0.0202551i	0.989240	−	0.146299i	$-0.0467361\pi$
$13$	0.0115670	+	0.0730309i	0.00320810	+	0.0202551i	−0.986032	+	0.166554i	$0.946736\pi$
$14$	1.08540	−	0.906590i	0.290085	−	0.242296i
$15$	3.10067	−	6.48034i	0.800589	−	1.67322i
$16$	3.74626	+	1.40198i	0.936565	+	0.350494i
$17$	−2.40861	−	1.22725i	−0.584173	−	0.297651i	0.136817	−	0.990596i	$-0.456313\pi$
$17$	−2.40861	−	1.22725i	−0.584173	−	0.297651i	−0.720990	+	0.692945i	$0.756313\pi$
$18$	−7.79934	−	6.81084i	−1.83832	−	1.60533i
$19$	−0.280546	−	0.863431i	−0.0643616	−	0.198085i	0.913705	−	0.406379i	$-0.133209\pi$
$19$	−0.280546	−	0.863431i	−0.0643616	−	0.198085i	−0.978066	+	0.208295i	$0.933209\pi$
$20$	−2.04222	−	3.97861i	−0.456654	−	0.889645i
$21$	−0.992796	+	3.05551i	−0.216646	+	0.666767i
$22$	−4.22112	+	2.52335i	−0.899946	+	0.537980i
$23$	−0.183083	+	1.15594i	−0.0381754	+	0.241030i	−0.999396	−	0.0347507i	$-0.988936\pi$
$23$	−0.183083	+	1.15594i	−0.0381754	+	0.241030i	0.961221	+	0.275781i	$0.0889363\pi$
$24$	−8.90106	+	1.82904i	−1.81692	+	0.373352i
$25$	−1.30587	+	4.82646i	−0.261173	+	0.965292i
$26$	−0.104330	+	0.00705877i	−0.0204608	+	0.00138434i
$27$	13.7139	+	2.17207i	2.63924	+	0.418015i
$28$	1.13974	+	1.64347i	0.215391	+	0.310586i
$29$	7.67871	+	2.49497i	1.42590	+	0.463303i	0.917472	−	0.397800i	$-0.130226\pi$
$29$	7.67871	+	2.49497i	1.42590	+	0.463303i	0.508429	+	0.861104i	$0.330226\pi$
$30$	8.73584	+	5.18680i	1.59494	+	0.946977i
$31$	5.36384	−	1.74282i	0.963375	−	0.313019i	0.215236	−	0.976562i	$-0.430948\pi$
$31$	5.36384	−	1.74282i	0.963375	−	0.313019i	0.748138	+	0.663543i	$0.230948\pi$
$32$	−2.44842	+	5.09953i	−0.432824	+	0.901478i
$33$	5.07205	−	9.95446i	0.882931	−	1.73285i
$34$	2.03318	−	3.23747i	0.348687	−	0.555222i
$35$	0.294568	−	2.21658i	0.0497910	−	0.374671i
$36$	10.5795	−	10.1246i	1.76326	−	1.68743i
$37$	3.47004	−	0.549601i	0.570472	−	0.0903538i	0.135467	−	0.990782i	$-0.456747\pi$
$37$	3.47004	−	0.549601i	0.570472	−	0.0903538i	0.435005	+	0.900428i	$0.356747\pi$
$38$	1.25166	−	0.285992i	0.203046	−	0.0463941i
$39$	0.192186	−	0.139631i	0.0307744	−	0.0223589i
$40$	5.86229	−	2.37352i	0.926909	−	0.375286i
$41$	8.36936	+	6.08070i	1.30708	+	0.949646i	0.999998	−	0.00203903i	$-0.000649043\pi$
$41$	8.36936	+	6.08070i	1.30708	+	0.949646i	0.307077	+	0.951685i	$0.400649\pi$
$42$	−4.17831	−	1.78473i	−0.644728	−	0.275391i
$43$	−4.55361	+	4.55361i	−0.694419	+	0.694419i	−0.963201	−	0.268782i	$-0.913379\pi$
$43$	−4.55361	+	4.55361i	−0.694419	+	0.694419i	0.268782	+	0.963201i	$0.413379\pi$
$44$	−3.02055	−	6.26471i	−0.455366	−	0.944440i
$45$	−16.3669	+	0.408618i	−2.43984	+	0.0609132i
$46$	−1.60505	−	0.404036i	−0.236652	−	0.0595718i
$47$	11.8098	−	6.01737i	1.72263	−	0.877724i	0.745093	−	0.666961i	$-0.232405\pi$
$47$	11.8098	−	6.01737i	1.72263	−	0.877724i	0.977537	−	0.210763i	$-0.0675948\pi$
$48$	−1.45087	−	12.7689i	−0.209415	−	1.84303i
$49$			1.00000i			0.142857i
$50$	−6.63320	−	2.44963i	−0.938076	−	0.346429i
$51$			8.68486i			1.21612i
$52$	0.00324867	−	0.147847i	0.000450509	−	0.0205027i
$53$	9.84755	−	5.01758i	1.35267	−	0.689217i	0.380779	−	0.924666i	$-0.375656\pi$
$53$	9.84755	−	5.01758i	1.35267	−	0.689217i	0.971887	+	0.235449i	$0.0756560\pi$
$54$	−4.79343	+	19.0421i	−0.652303	+	2.59130i
$55$	−2.21753	+	7.45288i	−0.299012	+	1.00495i
$56$	−2.45901	+	1.39759i	−0.328600	+	0.186760i
$57$	−2.06245	+	2.06245i	−0.273178	+	0.273178i
$58$	−4.48516	+	10.5004i	−0.588931	+	1.37877i
$59$	1.40535	+	1.02104i	0.182960	+	0.132929i	0.675496	−	0.737364i	$-0.263930\pi$
$59$	1.40535	+	1.02104i	0.182960	+	0.132929i	−0.492535	+	0.870293i	$0.663930\pi$
$60$	−8.41042	+	11.6491i	−1.08578	+	1.50389i
$61$	−3.22028	+	2.33967i	−0.412315	+	0.299564i	−0.774538	−	0.632527i	$-0.782018\pi$
$61$	−3.22028	+	2.33967i	−0.412315	+	0.299564i	0.362223	+	0.932091i	$0.382018\pi$
$62$	1.77665	+	7.77560i	0.225635	+	0.987502i
$63$	7.23165	−	1.14538i	0.911102	−	0.144304i
$64$	−6.87337	−	4.09350i	−0.859172	−	0.511688i
$65$	−0.113957	+	0.119793i	−0.0141346	+	0.0148585i
$66$	13.3801	+	8.40286i	1.64697	+	1.03432i
$67$	−3.00737	+	5.90229i	−0.367408	+	0.721079i	−0.998507	−	0.0546231i	$-0.982604\pi$
$67$	−3.00737	+	5.90229i	−0.367408	+	0.721079i	0.631099	+	0.775703i	$0.282604\pi$
$68$	4.30307	+	3.27317i	0.521824	+	0.396930i
$69$	3.57601	−	1.16192i	0.430501	−	0.139878i
$70$	3.08492	+	0.695173i	0.368719	+	0.0830891i
$71$	−12.5751	−	4.08589i	−1.49239	−	0.484906i	−0.554599	−	0.832118i	$-0.687128\pi$
$71$	−12.5751	−	4.08589i	−1.49239	−	0.484906i	−0.937787	+	0.347212i	$0.887128\pi$
$72$	12.9234	+	16.1820i	1.52303	+	1.90706i
$73$	10.3532	+	1.63978i	1.21175	+	0.191922i	0.729418	−	0.684069i	$-0.239791\pi$
$73$	10.3532	+	1.63978i	1.21175	+	0.191922i	0.482329	+	0.875990i	$0.339791\pi$
$74$	0.335395	+	4.95722i	0.0389889	+	0.576265i
$75$	15.7208	−	3.30153i	1.81529	−	0.381228i
$76$	0.244577	+	1.79918i	0.0280550	+	0.206380i
$77$	0.543991	−	3.43463i	0.0619936	−	0.391412i
$78$	0.172378	+	0.288359i	0.0195180	+	0.0326502i
$79$	−3.55666	+	10.9463i	−0.400155	+	1.23155i	0.524718	+	0.851276i	$0.324171\pi$
$79$	−3.55666	+	10.9463i	−0.400155	+	1.23155i	−0.924873	+	0.380275i	$0.875829\pi$
$80$	2.60200	+	8.55743i	0.290913	+	0.956750i
$81$	−6.99715	−	21.5350i	−0.777461	−	2.39278i
$82$	−9.62317	+	11.0198i	−1.06270	+	1.21694i
$83$	−3.82180	−	1.94731i	−0.419497	−	0.213745i	0.231483	−	0.972839i	$-0.425642\pi$
$83$	−3.82180	−	1.94731i	−0.419497	−	0.213745i	−0.650981	+	0.759094i	$0.725642\pi$
$84$	3.04219	−	5.65971i	0.331930	−	0.617525i
$85$	−1.09430	−	5.94476i	−0.118694	−	0.644799i
$86$	−5.83824	−	6.98974i	−0.629553	−	0.753723i
$87$	−4.05781	−	25.6200i	−0.435043	−	2.74676i
$88$	9.20607	−	3.46251i	0.981370	−	0.369104i
$89$	0.877888	+	1.20831i	0.0930559	+	0.128080i	0.853006	−	0.521901i	$-0.174777\pi$
$89$	0.877888	+	1.20831i	0.0930559	+	0.128080i	−0.759950	+	0.649981i	$0.774777\pi$
$90$	1.49384	−	23.1053i	0.157465	−	2.43551i
$91$	0.0434616	−	0.0598197i	0.00455601	−	0.00627081i
$92$	0.772043	−	2.20971i	0.0804911	−	0.230378i
$93$	−12.8125	−	12.8125i	−1.32859	−	1.32859i
$94$	6.98257	+	17.3955i	0.720197	+	1.79420i
$95$	1.15187	−	1.67161i	0.118179	−	0.171504i
$96$	18.1690	−	0.429154i	1.85437	−	0.0438003i
$97$	−6.30893	−	12.3820i	−0.640575	−	1.25720i	−0.951758	−	0.306850i	$-0.900725\pi$
$97$	−6.30893	−	12.3820i	−0.640575	−	1.25720i	0.311183	−	0.950350i	$-0.399275\pi$
$98$	−1.40855	−	0.126438i	−0.142285	−	0.0127722i
$99$	−25.4611			−2.55893
$100$	4.28911	−	9.03347i	0.428911	−	0.903347i
$101$	−7.70466			−0.766642			−0.383321	−	0.923615i	$-0.625220\pi$
$101$	−7.70466			−0.766642			−0.383321	+	0.923615i	$0.625220\pi$
$102$	−12.2331	−	1.09810i	−1.21125	−	0.108728i
$103$	5.33809	+	10.4766i	0.525978	+	1.03229i	0.989272	+	0.146085i	$0.0466673\pi$
$103$	5.33809	+	10.4766i	0.525978	+	1.03229i	−0.463294	+	0.886204i	$0.653333\pi$
$104$	0.207839	+	0.0232694i	0.0203803	+	0.00228175i
$105$	−6.77480	+	2.38979i	−0.661152	+	0.233220i
$106$	5.82241	+	14.5052i	0.565522	+	1.40887i
$107$	−9.53214	−	9.53214i	−0.921507	−	0.921507i	0.0756292	−	0.997136i	$-0.475903\pi$
$107$	−9.53214	−	9.53214i	−0.921507	−	0.921507i	−0.997136	+	0.0756292i	$0.975903\pi$
$108$	−26.2157	−	9.15942i	−2.52260	−	0.881366i
$109$	−2.58581	+	3.55906i	−0.247676	+	0.340896i	−0.914696	−	0.404144i	$-0.867570\pi$
$109$	−2.58581	+	3.55906i	−0.247676	+	0.340896i	0.667020	+	0.745040i	$0.267570\pi$
$110$	−10.2174	−	4.06583i	−0.974189	−	0.387662i
$111$	−6.63454	−	9.13167i	−0.629723	−	0.866739i
$112$	−1.65766	−	3.64035i	−0.156634	−	0.343981i
$113$	2.75325	+	17.3833i	0.259004	+	1.63529i	0.683567	+	0.729888i	$0.260428\pi$
$113$	2.75325	+	17.3833i	0.259004	+	1.63529i	−0.424563	+	0.905398i	$0.639572\pi$
$114$	−2.64429	−	3.16584i	−0.247661	−	0.296508i
$115$	−2.30136	+	1.24591i	−0.214603	+	0.116182i
$116$	−14.2232	−	7.64523i	−1.32059	−	0.709841i
$117$	−0.482375	−	0.245782i	−0.0445956	−	0.0227226i
$118$	−1.61588	+	1.85040i	−0.148754	+	0.170343i
$119$	0.835348	+	2.57094i	0.0765762	+	0.235677i
$120$	−15.3449	−	13.3194i	−1.40079	−	1.21589i
$121$	−0.337626	+	1.03911i	−0.0306933	+	0.0944642i
$122$	−2.88838	−	4.83175i	−0.261502	−	0.437447i
$123$	5.19930	−	32.8271i	0.468805	−	2.95992i
$124$	−11.1770	+	1.51938i	−1.00372	+	0.136444i
$125$	−10.3449	+	4.24073i	−0.925273	+	0.379302i
$126$	0.698971	+	10.3310i	0.0622693	+	0.920355i
$127$	16.1188	+	2.55297i	1.43031	+	0.226539i	0.823053	−	0.567965i	$-0.192269\pi$
$127$	16.1188	+	2.55297i	1.43031	+	0.226539i	0.607259	+	0.794504i	$0.292269\pi$
$128$	6.63496	−	9.16392i	0.586453	−	0.809983i
$129$	19.6768	+	6.39338i	1.73245	+	0.562906i
$130$	−0.154326	−	0.175661i	−0.0135353	−	0.0154065i
$131$	7.97167	−	2.59015i	0.696488	−	0.226303i	0.0606885	−	0.998157i	$-0.480670\pi$
$131$	7.97167	−	2.59015i	0.696488	−	0.226303i	0.635800	+	0.771854i	$0.280670\pi$
$132$	−13.5276	+	17.7840i	−1.17743	+	1.54790i
$133$	−0.412162	+	0.808913i	−0.0357390	+	0.0701417i
$134$	−7.93342	−	4.98230i	−0.685344	−	0.430405i
$135$	14.7813	+	27.3031i	1.27217	+	2.34988i
$136$	−5.15450	+	5.64724i	−0.441995	+	0.484247i
$137$	−0.924680	+	0.146455i	−0.0790007	+	0.0125125i	−0.195810	−	0.980642i	$-0.562733\pi$
$137$	−0.924680	+	0.146455i	−0.0790007	+	0.0125125i	0.116809	+	0.993154i	$0.462733\pi$
$138$	1.18447	+	5.18390i	0.100829	+	0.441283i
$139$	0.360612	−	0.262000i	0.0305867	−	0.0222225i	−0.572387	−	0.819984i	$-0.693982\pi$
$139$	0.360612	−	0.262000i	0.0305867	−	0.0222225i	0.602974	+	0.797761i	$0.293982\pi$
$140$	−1.36924	+	4.25737i	−0.115722	+	0.359813i
$141$	−34.4505	−	25.0297i	−2.90125	−	2.10788i
$142$	7.34514	−	17.1960i	0.616391	−	1.44306i
$143$	−0.181816	+	0.181816i	−0.0152042	+	0.0152042i
$144$	−24.4271	+	16.1572i	−2.03559	+	1.34643i
$145$	6.00571	+	17.0255i	0.498747	+	1.41389i
$146$	−3.61875	+	14.3756i	−0.299490	+	1.18973i
$147$	2.86259	−	1.45856i	0.236102	−	0.120300i
$148$	−7.02490	−	0.154359i	−0.577443	−	0.0126883i
$149$			10.4736i			0.858031i	0.903297	+	0.429015i	$0.141139\pi$
$149$			10.4736i			0.858031i	−0.903297	+	0.429015i	$0.858861\pi$
$150$	2.66266	+	22.5610i	0.217405	+	1.84210i
$151$		−	12.9663i		−	1.05518i	−0.849498	−	0.527591i	$-0.823095\pi$
$151$		−	12.9663i		−	1.05518i	0.849498	−	0.527591i	$-0.176905\pi$
$152$	−2.56516	+	0.117015i	−0.208062	+	0.00949116i
$153$	17.6353	−	8.98564i	1.42573	−	0.726446i
$154$	4.76906	+	1.20051i	0.384302	+	0.0967395i
$155$	10.3845	+	7.15570i	0.834100	+	0.574760i
$156$	−0.427963	+	0.206344i	−0.0342644	+	0.0165207i
$157$	−5.75202	+	5.75202i	−0.459061	+	0.459061i	−0.898347	−	0.439286i	$-0.855231\pi$
$157$	−5.75202	+	5.75202i	−0.459061	+	0.459061i	0.439286	+	0.898347i	$0.355231\pi$
$158$	−14.9687	−	6.39375i	−1.19084	−	0.508660i
$159$	−28.7265	−	20.8710i	−2.27816	−	1.65518i
$160$	−12.3826	+	2.58307i	−0.978927	+	0.204210i
$161$	0.946831	−	0.687913i	0.0746207	−	0.0542151i
$162$	31.2178	−	7.13299i	2.45270	−	0.560421i
$163$	−4.11379	+	0.651560i	−0.322217	+	0.0510341i	−0.315448	−	0.948943i	$-0.602155\pi$
$163$	−4.11379	+	0.651560i	−0.322217	+	0.0510341i	−0.00676903	+	0.999977i	$0.502155\pi$
$164$	−14.3053	−	14.9480i	−1.11705	−	1.16725i
$165$	24.5689	−	4.52261i	1.91269	−	0.352084i
$166$	3.22610	−	5.13699i	0.250394	−	0.398708i
$167$	−9.32486	+	18.3011i	−0.721579	+	1.41618i	0.180045	+	0.983658i	$0.442376\pi$
$167$	−9.32486	+	18.3011i	−0.721579	+	1.41618i	−0.901624	+	0.432521i	$0.857624\pi$
$168$	7.58733	+	5.00067i	0.585375	+	0.385810i
$169$	12.3585	−	4.01553i	0.950657	−	0.308887i
$170$	8.51185	−	0.789736i	0.652829	−	0.0605700i
$171$	6.32186	+	2.05410i	0.483445	+	0.157081i
$172$	10.5836	−	7.33968i	0.806989	−	0.559646i
$173$	−4.92119	−	0.779440i	−0.374151	−	0.0592597i	−0.0334727	−	0.999440i	$-0.510657\pi$
$173$	−4.92119	−	0.779440i	−0.374151	−	0.0592597i	−0.340678	+	0.940180i	$0.610657\pi$
$174$	36.6002	−	2.47629i	2.77465	−	0.187727i
$175$	4.33621	−	2.48944i	0.327787	−	0.188184i
$176$	3.71312	+	13.4050i	0.279887	+	1.01044i
$177$	0.873043	−	5.51217i	0.0656219	−	0.414320i
$178$	−1.81296	+	1.08377i	−0.135887	+	0.0812322i
$179$	5.29692	−	16.3023i	0.395911	−	1.21849i	−0.532339	−	0.846531i	$-0.678687\pi$
$179$	5.29692	−	16.3023i	0.395911	−	1.21849i	0.928250	−	0.371957i	$-0.121313\pi$
$180$	32.3561	+	5.02553i	2.41168	+	0.374581i
$181$	0.931407	+	2.86658i	0.0692309	+	0.213071i	0.979686	−	0.200537i	$-0.0642686\pi$
$181$	0.931407	+	2.86658i	0.0692309	+	0.213071i	−0.910455	+	0.413608i	$0.864269\pi$
$182$	0.0787639	+	0.0687813i	0.00583837	+	0.00509841i
$183$	11.3945	+	5.80578i	0.842305	+	0.429176i
$184$	3.01487	+	1.36685i	0.222259	+	0.100766i
$185$	5.69192	+	5.41464i	0.418479	+	0.398092i
$186$	19.6670	−	16.4270i	1.44205	−	1.20449i
$187$	−1.47054	−	9.28463i	−0.107537	−	0.678959i
$188$	−25.3852	+	7.63585i	−1.85141	+	0.556902i
$189$	−8.16131	−	11.2331i	−0.593648	−	0.817086i
$190$	2.20891	+	1.83382i	0.160251	+	0.133039i
$191$	−10.8384	+	14.9178i	−0.784238	+	1.07941i	0.210563	+	0.977580i	$0.432470\pi$
$191$	−10.8384	+	14.9178i	−0.784238	+	1.07941i	−0.994802	+	0.101831i	$0.967530\pi$
$192$	−1.69277	+	25.6462i	−0.122165	+	1.85086i
$193$	−3.65543	−	3.65543i	−0.263123	−	0.263123i	0.563198	−	0.826322i	$-0.309571\pi$
$193$	−3.65543	−	3.65543i	−0.263123	−	0.263123i	−0.826322	+	0.563198i	$0.809571\pi$
$194$	18.2383	−	7.32090i	1.30944	−	0.525610i
$195$	0.509131	+	0.151487i	0.0364596	+	0.0108482i
$196$	0.356188	−	1.96803i	0.0254420	−	0.140573i
$197$	−0.372579	−	0.731228i	−0.0265452	−	0.0520978i	0.877353	−	0.479845i	$-0.159307\pi$
$197$	−0.372579	−	0.731228i	−0.0265452	−	0.0520978i	−0.903898	+	0.427748i	$0.859307\pi$
$198$	3.21925	−	35.8632i	0.228782	−	2.54869i
$199$	−1.64864			−0.116869			−0.0584344	−	0.998291i	$-0.518611\pi$
$199$	−1.64864			−0.116869			−0.0584344	+	0.998291i	$0.518611\pi$
$200$	12.1818	+	7.18360i	0.861382	+	0.507957i
$201$	21.2822			1.50113
$202$	0.974161	−	10.8524i	0.0685417	−	0.763572i
$203$	−3.66546	−	7.19388i	−0.257265	−	0.504911i
$204$	3.09344	−	17.0920i	0.216584	−	1.19668i
$205$	0.577345	+	23.1251i	0.0403235	+	1.61513i
$206$	−15.4317	+	6.19433i	−1.07518	+	0.431579i
$207$	−6.05923	−	6.05923i	−0.421145	−	0.421145i
$208$	−0.0590548	+	0.289809i	−0.00409471	+	0.0200947i
$209$	1.85566	−	2.55410i	0.128359	−	0.176671i
$210$	−2.50955	−	9.84480i	−0.173175	−	0.679356i
$211$	4.58436	+	6.30983i	0.315600	+	0.434387i	0.937118	−	0.349014i	$-0.113483\pi$
$211$	4.58436	+	6.30983i	0.315600	+	0.434387i	−0.621517	+	0.783400i	$0.713483\pi$
$212$	−21.1675	+	6.36715i	−1.45379	+	0.437297i
$213$	6.64529	+	41.9567i	0.455328	+	2.87483i
$214$	14.6317	−	12.2213i	1.00020	−	0.835429i
$215$	−14.2743	−	1.89695i	−0.973498	−	0.129371i
$216$	16.2162	−	35.7680i	1.10337	−	2.43370i
$217$	−5.02517	−	2.56045i	−0.341131	−	0.173815i
$218$	−4.68617	−	4.09224i	−0.317388	−	0.277162i
$219$	−10.4067	−	32.0285i	−0.703220	−	2.16429i
$220$	7.01879	−	13.8776i	0.473207	−	0.935629i
$221$	0.0617667	−	0.190098i	0.00415488	−	0.0127874i
$222$	13.7013	−	8.19050i	0.919569	−	0.549710i
$223$	−1.61889	+	10.2213i	−0.108409	+	0.684466i	0.872297	+	0.488976i	$0.162630\pi$
$223$	−1.61889	+	10.2213i	−0.108409	+	0.684466i	−0.980706	+	0.195490i	$0.937370\pi$
$224$	5.33721	−	1.87462i	0.356607	−	0.125253i
$225$	−22.9693	−	28.5066i	−1.53129	−	1.90044i
$226$	−24.8334	+	1.68018i	−1.65189	+	0.111764i
$227$	−2.27030	−	0.359580i	−0.150685	−	0.0238661i	0.0806362	−	0.996744i	$-0.474305\pi$
$227$	−2.27030	−	0.359580i	−0.150685	−	0.0238661i	−0.231321	+	0.972877i	$0.574305\pi$
$228$	4.79358	−	3.32434i	0.317463	−	0.220160i
$229$	−18.5308	−	6.02103i	−1.22455	−	0.397881i	−0.375813	−	0.926695i	$-0.622637\pi$
$229$	−18.5308	−	6.02103i	−1.22455	−	0.397881i	−0.848737	+	0.528815i	$0.822637\pi$
$230$	−1.46395	−	3.39912i	−0.0965297	−	0.224131i
$231$	−10.6254	+	3.45239i	−0.699097	+	0.227150i
$232$	12.5670	−	19.0675i	0.825067	−	1.25184i
$233$	4.85860	−	9.53553i	0.318297	−	0.624693i	−0.675317	−	0.737528i	$-0.735993\pi$
$233$	4.85860	−	9.53553i	0.318297	−	0.624693i	0.993614	+	0.112835i	$0.0359930\pi$
$234$	0.407187	−	0.648374i	0.0266187	−	0.0423855i
$235$	26.7350	+	12.7920i	1.74400	+	0.834456i
$236$	−2.40207	−	2.51001i	−0.156362	−	0.163388i
$237$	36.5222	−	5.78455i	2.37237	−	0.375747i
$238$	−3.72691	+	0.851566i	−0.241580	+	0.0551988i
$239$	−6.60885	+	4.80161i	−0.427491	+	0.310590i	−0.780645	−	0.624975i	$-0.785109\pi$
$239$	−6.60885	+	4.80161i	−0.427491	+	0.310590i	0.353154	+	0.935565i	$0.385109\pi$
$240$	20.7012	−	19.9300i	1.33626	−	1.28647i
$241$	24.5254	+	17.8188i	1.57982	+	1.14781i	0.916897	+	0.399123i	$0.130685\pi$
$241$	24.5254	+	17.8188i	1.57982	+	1.14781i	0.662926	+	0.748685i	$0.269315\pi$
$242$	−1.42094	−	0.606945i	−0.0913417	−	0.0390159i
$243$	−21.9858	+	21.9858i	−1.41039	+	1.41039i
$244$	7.17097	−	3.45751i	0.459074	−	0.221345i
$245$	−1.77565	+	1.35907i	−0.113442	+	0.0868277i
$246$	45.5812	+	11.4741i	2.90615	+	0.731559i
$247$	0.0598121	−	0.0304758i	0.00380575	−	0.00193913i
$248$	−0.726925	−	15.9354i	−0.0461598	−	1.01190i
$249$			13.7805i			0.873304i
$250$	−4.66529	−	15.1074i	−0.295059	−	0.955479i
$251$		−	8.24256i		−	0.520266i	−0.965573	−	0.260133i	$-0.916234\pi$
$251$		−	8.24256i		−	0.520266i	0.965573	−	0.260133i	$-0.0837664\pi$
$252$	−14.6400	−	0.321688i	−0.922236	−	0.0202645i
$253$	−3.62623	+	1.84766i	−0.227979	+	0.116161i
$254$	−5.63401	+	22.3813i	−0.353509	+	1.40433i
$255$	−15.4213	+	11.8033i	−0.965717	+	0.739152i
$256$	12.0689	+	10.5043i	0.754308	+	0.656521i
$257$	19.7861	−	19.7861i	1.23422	−	1.23422i	0.271899	−	0.962326i	$-0.412348\pi$
$257$	19.7861	−	19.7861i	1.23422	−	1.23422i	0.962326	−	0.271899i	$-0.0876516\pi$
$258$	−11.4933	+	26.9074i	−0.715541	+	1.67518i
$259$	−2.84232	−	2.06506i	−0.176613	−	0.128317i
$260$	0.266939	−	0.195165i	0.0165549	−	0.0121036i
$261$	−47.8252	+	34.7471i	−2.96031	+	2.15079i
$262$	2.64044	+	11.5560i	0.163127	+	0.713932i
$263$	−16.9344	+	2.68214i	−1.04422	+	0.165388i	−0.654900	−	0.755715i	$-0.727289\pi$
$263$	−16.9344	+	2.68214i	−1.04422	+	0.165388i	−0.389318	+	0.921103i	$0.627289\pi$
$264$	−23.3393	−	21.3029i	−1.43644	−	1.31110i
$265$	22.2930	+	10.6666i	1.36945	+	0.655242i
$266$	−1.08728	−	0.682828i	−0.0666655	−	0.0418669i
$267$	2.17843	−	4.27542i	0.133318	−	0.261651i
$268$	8.02090	−	10.5447i	0.489955	−	0.644119i
$269$	−0.336795	+	0.109431i	−0.0205347	+	0.00667214i	−0.319266	−	0.947665i	$-0.603436\pi$
$269$	−0.336795	+	0.109431i	−0.0205347	+	0.00667214i	0.298732	+	0.954337i	$0.403436\pi$
$270$	−40.3267	+	17.3681i	−2.45420	+	1.05699i
$271$	22.7533	+	7.39300i	1.38217	+	0.449093i	0.903381	−	0.428839i	$-0.141077\pi$
$271$	22.7533	+	7.39300i	1.38217	+	0.449093i	0.478785	+	0.877932i	$0.341077\pi$
$272$	−7.30270	−	7.97440i	−0.442791	−	0.483519i
$273$	−0.234630	−	0.0371618i	−0.0142005	−	0.00224914i
$274$	−0.0893745	−	1.32098i	−0.00539931	−	0.0798030i
$275$	−16.2475	+	6.19142i	−0.979760	+	0.373357i
$276$	−7.45154	+	1.01295i	−0.448530	+	0.0609724i
$277$	2.13994	−	13.5111i	0.128577	−	0.811801i	−0.836141	−	0.548515i	$-0.815194\pi$
$277$	2.13994	−	13.5111i	0.128577	−	0.811801i	0.964718	−	0.263287i	$-0.0848065\pi$
$278$	0.323445	+	0.541066i	0.0193989	+	0.0324510i
$279$	−12.7605	+	39.2729i	−0.763954	+	2.35121i
$280$	−5.82359	−	2.46693i	−0.348026	−	0.147427i
$281$	−1.93437	−	5.95338i	−0.115395	−	0.355149i	0.876634	−	0.481157i	$-0.159783\pi$
$281$	−1.93437	−	5.95338i	−0.115395	−	0.355149i	−0.992029	+	0.126008i	$0.959783\pi$
$282$	39.6115	−	45.3605i	2.35883	−	2.70118i
$283$	1.86390	+	0.949703i	0.110797	+	0.0564540i	0.508511	−	0.861056i	$-0.330196\pi$
$283$	1.86390	+	0.949703i	0.110797	+	0.0564540i	−0.397714	+	0.917510i	$0.630196\pi$
$284$	23.2927	+	12.5202i	1.38217	+	0.742939i
$285$	−6.46520	−	0.859179i	−0.382966	−	0.0508934i
$286$	−0.233108	−	0.279085i	−0.0137840	−	0.0165026i
$287$	−1.61833	−	10.2177i	−0.0955270	−	0.603134i
$288$	−19.6697	−	36.4497i	−1.15905	−	2.14782i
$289$	−5.69709	−	7.84138i	−0.335123	−	0.461257i
$290$	−24.7407	+	6.30667i	−1.45282	+	0.370341i
$291$	−26.2425	+	36.1197i	−1.53836	+	2.11738i
$292$	−19.7912	−	6.91481i	−1.15819	−	0.404659i
$293$	−12.9723	−	12.9723i	−0.757849	−	0.757849i	0.218081	−	0.975931i	$-0.430020\pi$
$293$	−12.9723	−	12.9723i	−0.757849	−	0.757849i	−0.975931	+	0.218081i	$0.930020\pi$
$294$	1.69252	+	4.21651i	0.0987095	+	0.245912i
$295$	0.0969451	+	3.88307i	0.00564436	+	0.226081i
$296$	1.10564	−	9.87541i	0.0642638	−	0.573996i
$297$	21.9203	+	43.0211i	1.27195	+	2.49634i
$298$	−14.7526	−	1.32426i	−0.854595	−	0.0767123i
$299$	−0.0865370			−0.00500456
$300$	−32.1150	+	0.897919i	−1.85416	+	0.0518414i
$301$	6.43978			0.371182
$302$	18.2637	+	1.63943i	1.05096	+	0.0943387i
$303$	11.2377	+	22.0552i	0.645589	+	1.26704i
$304$	0.159512	−	3.62795i	0.00914866	−	0.208077i
$305$	−8.53103	−	2.53832i	−0.488485	−	0.145344i
$306$	10.4270	+	25.9764i	0.596069	+	1.48497i
$307$	1.19164	+	1.19164i	0.0680107	+	0.0680107i	0.740294	−	0.672283i	$-0.234686\pi$
$307$	1.19164	+	1.19164i	0.0680107	+	0.0680107i	−0.672283	+	0.740294i	$0.734686\pi$
$308$	−2.29396	+	6.56567i	−0.130711	+	0.374114i
$309$	22.2042	−	30.5615i	1.26315	−	1.73858i
$310$	−11.3922	+	13.7223i	−0.647031	+	0.779374i
$311$	6.14312	+	8.45528i	0.348344	+	0.479455i	0.946855	−	0.321660i	$-0.104241\pi$
$311$	6.14312	+	8.45528i	0.348344	+	0.479455i	−0.598511	+	0.801115i	$0.704241\pi$
$312$	−0.236535	−	0.628896i	−0.0133912	−	0.0356042i
$313$	2.38138	+	15.0354i	0.134603	+	0.849853i	0.958910	+	0.283710i	$0.0915652\pi$
$313$	2.38138	+	15.0354i	0.134603	+	0.849853i	−0.824307	+	0.566143i	$0.808435\pi$
$314$	−7.37474	−	8.82928i	−0.416180	−	0.498265i
$315$	11.8621	+	11.2842i	0.668353	+	0.635794i
$316$	10.8985	−	20.2757i	0.613090	−	1.14060i
$317$	−21.3863	−	10.8968i	−1.20117	−	0.612028i	−0.265231	−	0.964185i	$-0.585448\pi$
$317$	−21.3863	−	10.8968i	−1.20117	−	0.612028i	−0.935941	+	0.352157i	$0.885448\pi$
$318$	33.0300	−	37.8238i	1.85223	−	2.12105i
$319$	8.67609	+	26.7023i	0.485768	+	1.49504i
$320$	−2.07276	−	17.7681i	−0.115871	−	0.993264i
$321$	−13.3834	+	41.1898i	−0.746987	+	2.29899i
$322$	0.849245	+	1.42064i	0.0473266	+	0.0791690i
$323$	−0.383918	+	2.42396i	−0.0213618	+	0.134873i
$324$	6.10006	+	44.8738i	0.338892	+	2.49299i
$325$	−0.367586	−	0.0395411i	−0.0203900	−	0.00219335i
$326$	−0.397616	−	5.87686i	−0.0220219	−	0.325489i
$327$	13.9597	+	2.21100i	0.771972	+	0.122268i
$328$	22.8638	−	18.2597i	1.26244	−	1.00822i
$329$	−12.6057	−	4.09583i	−0.694974	−	0.225811i
$330$	3.26388	+	35.1784i	0.179671	+	1.93651i
$331$	−23.4978	+	7.63489i	−1.29156	+	0.419652i	−0.872636	−	0.488372i	$-0.837591\pi$
$331$	−23.4978	+	7.63489i	−1.29156	+	0.419652i	−0.418920	+	0.908023i	$0.637591\pi$
$332$	6.82780	+	5.19363i	0.374724	+	0.285038i
$333$	−11.6783	+	22.9199i	−0.639966	+	1.25600i
$334$	−24.5990	−	15.4485i	−1.34599	−	0.845303i
$335$	−14.5676	+	2.68158i	−0.795914	+	0.146511i
$336$	−8.00302	+	10.0549i	−0.436601	+	0.548538i
$337$	−27.8023	+	4.40345i	−1.51449	+	0.239871i	−0.857679	−	0.514185i	$-0.828094\pi$
$337$	−27.8023	+	4.40345i	−1.51449	+	0.239871i	−0.656810	+	0.754056i	$0.728094\pi$
$338$	4.09349	+	17.9153i	0.222657	+	0.974466i
$339$	45.7455	−	33.2360i	2.48455	−	1.80513i
$340$	0.0361624	+	12.0892i	0.00196118	+	0.655630i
$341$	15.8667	+	11.5278i	0.859230	+	0.624267i
$342$	−3.69262	+	8.64494i	−0.199674	+	0.467465i
$343$	0.707107	−	0.707107i	0.0381802	−	0.0381802i
$344$	9.00015	+	15.8355i	0.485255	+	0.853793i
$345$	6.92320	+	4.77062i	0.372732	+	0.256841i
$346$	1.72010	−	6.83319i	0.0924734	−	0.367354i
$347$	17.4031	−	8.86734i	0.934250	−	0.476024i	0.0805273	−	0.996752i	$-0.474340\pi$
$347$	17.4031	−	8.86734i	0.934250	−	0.476024i	0.853722	+	0.520728i	$0.174340\pi$
$348$	−1.13967	+	51.8662i	−0.0610925	+	2.78032i
$349$		−	16.2156i		−	0.868000i	−0.900913	−	0.434000i	$-0.857102\pi$
$349$		−	16.2156i		−	0.868000i	0.900913	−	0.434000i	$-0.142898\pi$
$350$	2.95823	+	6.42253i	0.158124	+	0.343299i
$351$			1.02666i			0.0547992i
$352$	−19.3511	+	3.53521i	−1.03142	+	0.188427i
$353$	−4.70626	+	2.39796i	−0.250489	+	0.127631i	−0.574728	−	0.818345i	$-0.694892\pi$
$353$	−4.70626	+	2.39796i	−0.250489	+	0.127631i	0.324239	+	0.945975i	$0.394892\pi$
$354$	7.65379	+	1.92667i	0.406794	+	0.102401i
$355$	−9.83527	−	27.8819i	−0.522002	−	1.47982i
$356$	−1.29732	−	2.69068i	−0.0687579	−	0.142606i
$357$	6.14112	−	6.14112i	0.325023	−	0.325023i
$358$	22.2928	+	9.52221i	1.17821	+	0.503264i
$359$	12.1034	+	8.79360i	0.638791	+	0.464109i	0.859434	−	0.511246i	$-0.170816\pi$
$359$	12.1034	+	8.79360i	0.638791	+	0.464109i	−0.220644	+	0.975354i	$0.570816\pi$
$360$	−11.1698	+	44.9398i	−0.588698	+	2.36853i
$361$	14.7045	−	10.6835i	0.773922	−	0.562287i
$362$	−4.15548	+	0.949490i	−0.218407	+	0.0499041i
$363$	3.46698	−	0.549115i	0.181969	−	0.0288211i
$364$	−0.106841	+	0.102246i	−0.00559997	+	0.00535917i
$365$	11.1590	+	20.6122i	0.584088	+	1.07889i
$366$	−9.61843	+	15.3156i	−0.502764	+	0.800561i
$367$	9.55671	−	18.7561i	0.498856	−	0.979060i	−0.495054	−	0.868862i	$-0.664852\pi$
$367$	9.55671	−	18.7561i	0.498856	−	0.979060i	0.993910	−	0.110198i	$-0.0351484\pi$
$368$	−2.30647	+	4.07377i	−0.120233	+	0.212360i
$369$	−72.0375	+	23.4064i	−3.75012	+	1.21849i
$370$	−8.34646	+	7.33275i	−0.433912	+	0.381211i
$371$	−10.5112	−	3.41531i	−0.545716	−	0.177314i
$372$	20.6516	+	29.7789i	1.07074	+	1.54396i
$373$	−5.67504	−	0.898838i	−0.293842	−	0.0465401i	0.00777285	−	0.999970i	$-0.497526\pi$
$373$	−5.67504	−	0.898838i	−0.293842	−	0.0465401i	−0.301615	+	0.953430i	$0.597526\pi$
$374$	13.2638	−	0.897401i	0.685855	−	0.0464035i
$375$	27.2280	+	23.4277i	1.40605	+	1.20980i
$376$	−7.54582	−	36.7218i	−0.389146	−	1.89378i
$377$	−0.0933902	+	0.589643i	−0.00480984	+	0.0303681i
$378$	16.8543	−	10.0753i	0.866889	−	0.518219i
$379$	−7.79517	+	23.9911i	−0.400411	+	1.23234i	0.524256	+	0.851561i	$0.324344\pi$
$379$	−7.79517	+	23.9911i	−0.400411	+	1.23234i	−0.924667	+	0.380777i	$0.875656\pi$
$380$	−2.86232	+	2.87949i	−0.146834	+	0.147715i
$381$	−16.2021	−	49.8651i	−0.830061	−	2.55467i
$382$	−19.6420	−	17.1526i	−1.00497	−	0.877603i
$383$	3.66081	+	1.86527i	0.187058	+	0.0953110i	0.545012	−	0.838429i	$-0.316525\pi$
$383$	3.66081	+	1.86527i	0.187058	+	0.0953110i	−0.357953	+	0.933740i	$0.616525\pi$
$384$	−35.9100	−	5.62700i	−1.83252	−	0.287152i
$385$	6.83801	−	3.70195i	0.348497	−	0.188669i
$386$	5.61103	−	4.68667i	0.285594	−	0.238545i
$387$	−7.37599	−	46.5702i	−0.374943	−	2.36730i
$388$	8.00584	+	26.6152i	0.406435	+	1.35118i
$389$	−4.93507	−	6.79254i	−0.250218	−	0.344395i	0.665370	−	0.746514i	$-0.268274\pi$
$389$	−4.93507	−	6.79254i	−0.250218	−	0.344395i	−0.915588	+	0.402119i	$0.868274\pi$
$390$	−0.277750	+	0.697982i	−0.0140644	+	0.0353437i
$391$	1.85960	−	2.55951i	0.0940438	−	0.129440i
$392$	2.72703	+	0.750542i	0.137736	+	0.0379081i
$393$	−19.0417	−	19.0417i	−0.960527	−	0.960527i
$394$	1.07708	−	0.432342i	0.0542625	−	0.0217811i
$395$	−24.2705	+	8.56134i	−1.22118	+	0.430768i
$396$	50.1081	+	9.06894i	2.51803	+	0.455731i
$397$	−6.28936	−	12.3436i	−0.315654	−	0.619506i	0.677604	−	0.735427i	$-0.263018\pi$
$397$	−6.28936	−	12.3436i	−0.315654	−	0.619506i	−0.993258	+	0.115921i	$0.963018\pi$
$398$	0.208450	−	2.32219i	0.0104487	−	0.116401i
$399$	2.91675			0.146020
$400$	−11.6587	+	16.2504i	−0.582935	+	0.812519i
$401$	22.2413			1.11068			0.555340	−	0.831624i	$-0.312588\pi$
$401$	22.2413			1.11068			0.555340	+	0.831624i	$0.312588\pi$
$402$	−2.69088	+	29.9771i	−0.134209	+	1.49512i
$403$	0.189323	+	0.371567i	0.00943085	+	0.0185091i
$404$	15.1630	+	2.74431i	0.754386	+	0.136534i
$405$	28.7290	−	41.6920i	1.42756	−	2.07169i
$406$	10.5964	−	4.25341i	0.525890	−	0.211093i
$407$	8.63892	+	8.63892i	0.428215	+	0.428215i
$408$	23.6839	+	6.51835i	1.17253	+	0.322706i
$409$	2.36032	−	3.24871i	0.116711	−	0.160638i	−0.746665	−	0.665200i	$-0.768346\pi$
$409$	2.36032	−	3.24871i	0.116711	−	0.160638i	0.863375	+	0.504562i	$0.168346\pi$
$410$	−32.6459	−	2.11068i	−1.61227	−	0.104239i
$411$	1.76794	+	2.43336i	0.0872061	+	0.120029i
$412$	−6.77387	−	22.5196i	−0.333724	−	1.10946i
$413$	−0.271743	−	1.71572i	−0.0133716	−	0.0844249i
$414$	9.30084	−	7.76861i	0.457111	−	0.381806i
$415$	−1.73636	−	9.43271i	−0.0852345	−	0.463033i
$416$	−0.400744	−	0.119825i	−0.0196481	−	0.00587488i
$417$	−1.27597	−	0.650139i	−0.0624845	−	0.0318374i
$418$	3.36295	+	2.93673i	0.164487	+	0.143640i
$419$	−10.7343	−	33.0366i	−0.524403	−	1.61394i	−0.765494	−	0.643443i	$-0.777505\pi$
$419$	−10.7343	−	33.0366i	−0.524403	−	1.61394i	0.241092	−	0.970502i	$-0.422495\pi$
$420$	14.1842	−	2.29007i	0.692118	−	0.111744i
$421$	4.16899	−	12.8308i	0.203184	−	0.625336i	−0.796599	−	0.604508i	$-0.793370\pi$
$421$	4.16899	−	12.8308i	0.203184	−	0.625336i	0.999783	−	0.0208281i	$-0.00663028\pi$
$422$	−9.46735	+	5.65950i	−0.460863	+	0.275500i
$423$	−15.1813	+	95.8511i	−0.738141	+	4.66044i
$424$	−6.29208	−	30.6205i	−0.305570	−	1.48706i
$425$	9.06858	−	10.0224i	0.439891	−	0.486159i
$426$	−59.9383	+	4.05531i	−2.90402	+	0.196480i
$427$	3.93148	+	0.622686i	0.190258	+	0.0301339i
$428$	15.3643	+	22.1547i	0.742660	+	1.07089i
$429$	0.785652	+	0.255274i	0.0379316	+	0.0123247i
$430$	4.47676	−	19.8662i	0.215888	−	0.958033i
$431$	−23.8875	+	7.76153i	−1.15062	+	0.373860i	−0.821378	−	0.570385i	$-0.806794\pi$
$431$	−23.8875	+	7.76153i	−1.15062	+	0.373860i	−0.329245	+	0.944245i	$0.606794\pi$
$432$	48.3307	+	27.3637i	2.32531	+	1.31654i
$433$	12.9235	−	25.3638i	0.621064	−	1.21891i	−0.339436	−	0.940629i	$-0.610236\pi$
$433$	12.9235	−	25.3638i	0.621064	−	1.21891i	0.960501	−	0.278278i	$-0.0897637\pi$
$434$	4.24190	−	6.75446i	0.203618	−	0.324225i
$435$	39.9774	−	42.0246i	1.91677	−	2.01493i
$436$	6.35664	−	6.08330i	0.304428	−	0.291337i
$437$	1.04944	−	0.166214i	0.0502013	−	0.00795111i
$438$	46.4296	−	10.6087i	2.21849	−	0.506905i
$439$	−6.80972	+	4.94755i	−0.325010	+	0.236134i	−0.738310	−	0.674461i	$-0.764376\pi$
$439$	−6.80972	+	4.94755i	−0.325010	+	0.236134i	0.413300	+	0.910595i	$0.364376\pi$
$440$	18.6599	+	11.6410i	0.889575	+	0.554962i
$441$	−5.92345	−	4.30364i	−0.282069	−	0.204935i
$442$	0.259953	+	0.111037i	0.0123647	+	0.00528150i
$443$	−12.1953	+	12.1953i	−0.579416	+	0.579416i	−0.934742	−	0.355327i	$-0.884370\pi$
$443$	−12.1953	+	12.1953i	−0.579416	+	0.579416i	0.355327	+	0.934742i	$0.384370\pi$
$444$	9.80437	+	20.3345i	0.465295	+	0.965033i
$445$	−0.952424	+	3.20100i	−0.0451492	+	0.151742i
$446$	−14.1925	−	3.57264i	−0.672033	−	0.169169i
$447$	29.9816	−	15.2764i	1.41808	−	0.722548i
$448$	1.96567	+	7.75475i	0.0928690	+	0.366378i
$449$			4.10992i			0.193959i	0.995286	+	0.0969795i	$0.0309181\pi$
$449$			4.10992i			0.193959i	−0.995286	+	0.0969795i	$0.969082\pi$
$450$	43.0571	−	28.7491i	2.02973	−	1.35525i
$451$			35.9745i			1.69397i
$452$	0.773270	−	35.1915i	0.0363716	−	1.65527i
$453$	−37.1171	+	18.9121i	−1.74392	+	0.888569i
$454$	0.793537	−	3.15236i	0.0372426	−	0.147948i
$455$	0.165286	−	0.00412655i	0.00774874	−	0.000193456i
$456$	4.07641	+	7.17232i	0.190895	+	0.335875i
$457$	5.36234	−	5.36234i	0.250840	−	0.250840i	−0.570475	−	0.821315i	$-0.693241\pi$
$457$	5.36234	−	5.36234i	0.250840	−	0.250840i	0.821315	+	0.570475i	$0.193241\pi$
$458$	10.8239	−	25.3403i	0.505768	−	1.18407i
$459$	−30.3657	−	22.0620i	−1.41735	−	1.02977i
$460$	4.97292	−	1.63226i	0.231864	−	0.0761047i
$461$	12.7411	−	9.25695i	0.593412	−	0.431139i	−0.250122	−	0.968214i	$-0.580471\pi$
$461$	12.7411	−	9.25695i	0.593412	−	0.431139i	0.843535	+	0.537075i	$0.180471\pi$
$462$	−3.51941	−	15.4029i	−0.163738	−	0.716606i
$463$	14.5845	−	2.30995i	0.677798	−	0.107353i	0.191961	−	0.981402i	$-0.438515\pi$
$463$	14.5845	−	2.30995i	0.677798	−	0.107353i	0.485836	+	0.874050i	$0.338515\pi$
$464$	25.2686	+	20.1122i	1.17306	+	0.933684i
$465$	5.33743	−	40.1634i	0.247517	−	1.86253i
$466$	12.8170	+	8.04923i	0.593734	+	0.372873i
$467$	−11.3942	+	22.3624i	−0.527262	+	1.03481i	0.461755	+	0.887008i	$0.347220\pi$
$467$	−11.3942	+	22.3624i	−0.527262	+	1.03481i	−0.989017	+	0.147803i	$0.952780\pi$
$468$	0.861783	+	0.655523i	0.0398359	+	0.0303016i
$469$	6.30008	−	2.04702i	0.290911	−	0.0945226i
$470$	−21.3985	+	36.0402i	−0.987037	+	1.66241i
$471$	24.8553	+	8.07598i	1.14527	+	0.372122i
$472$	3.83919	−	3.06608i	0.176713	−	0.141128i
$473$	−22.1182	−	3.50318i	−1.01700	−	0.161076i
$474$	3.53004	+	52.1748i	0.162140	+	2.39647i
$475$	4.53367	−	0.226517i	0.208019	−	0.0103933i
$476$	−0.728250	−	5.35721i	−0.0333793	−	0.245548i
$477$	−12.6589	+	79.9254i	−0.579613	+	3.65953i
$478$	−5.92770	−	9.91599i	−0.271126	−	0.453547i
$479$	11.5392	−	35.5139i	0.527238	−	1.62267i	−0.232609	−	0.972570i	$-0.574726\pi$
$479$	11.5392	−	35.5139i	0.527238	−	1.62267i	0.759847	−	0.650102i	$-0.225274\pi$
$480$	25.4550	+	31.6786i	1.16185	+	1.44592i
$481$	0.0802757	+	0.247063i	0.00366026	+	0.0112651i
$482$	−28.1996	+	32.2924i	−1.28446	+	1.47088i
$483$	−3.35022	−	1.70702i	−0.152440	−	0.0776722i
$484$	1.03457	−	1.92473i	0.0470261	−	0.0874877i
$485$	13.4118	−	28.0304i	0.608998	−	1.27280i
$486$	−28.1883	−	33.7479i	−1.27865	−	1.53084i
$487$	1.19605	+	7.55156i	0.0541981	+	0.342194i	0.999855	+	0.0170274i	$0.00542026\pi$
$487$	1.19605	+	7.55156i	0.0541981	+	0.342194i	−0.945657	+	0.325166i	$0.894580\pi$
$488$	3.96340	+	10.5378i	0.179415	+	0.477025i
$489$	7.86535	+	10.8257i	0.355683	+	0.489556i
$490$	−1.68981	−	2.67293i	−0.0763377	−	0.120751i
$491$	23.1233	−	31.8264i	1.04354	−	1.43631i	0.149259	−	0.988798i	$-0.452311\pi$
$491$	23.1233	−	31.8264i	1.04354	−	1.43631i	0.894279	−	0.447509i	$-0.147689\pi$
$492$	−21.9250	+	62.7526i	−0.988454	+	2.82911i
$493$	−15.4331	−	15.4331i	−0.695070	−	0.695070i
$494$	0.0353641	+	0.0881016i	0.00159111	+	0.00396388i
$495$	−34.6033	−	45.2100i	−1.55530	−	2.03204i
$496$	22.5377	+	0.990930i	1.01197	+	0.0444941i
$497$	6.00276	+	11.7811i	0.269260	+	0.528453i
$498$	−19.4105	−	1.74238i	−0.869806	−	0.0780778i
$499$	−4.55336			−0.203837			−0.101918	−	0.994793i	$-0.532498\pi$
$499$	−4.55336			−0.203837			−0.101918	+	0.994793i	$0.532498\pi$
$500$	21.8695	−	4.66115i	0.978032	−	0.208453i
$501$	65.9892			2.94818
$502$	11.6101	+	1.04217i	0.518182	+	0.0465144i
$503$	−16.6882	−	32.7524i	−0.744088	−	1.46036i	−0.882665	−	0.470003i	$-0.844253\pi$
$503$	−16.6882	−	32.7524i	−0.744088	−	1.46036i	0.138576	−	0.990352i	$-0.455747\pi$
$504$	2.30417	−	20.5806i	0.102636	−	0.916731i
$505$	−10.4712	−	13.6808i	−0.465960	−	0.608787i
$506$	−2.14402	−	5.34134i	−0.0953135	−	0.237451i
$507$	−29.5205	−	29.5205i	−1.31105	−	1.31105i
$508$	−30.8129	−	10.7656i	−1.36710	−	0.477648i
$509$	21.9125	−	30.1599i	0.971253	−	1.33682i	0.0298416	−	0.999555i	$-0.490500\pi$
$509$	21.9125	−	30.1599i	0.971253	−	1.33682i	0.941411	−	0.337260i	$-0.109500\pi$
$510$	−14.6757	−	23.2140i	−0.649852	−	1.02793i
$511$	−6.16129	−	8.48029i	−0.272560	−	0.375146i
$512$	−16.3219	+	15.6715i	−0.721331	+	0.692591i
$513$	−1.97194	−	12.4504i	−0.0870635	−	0.549697i
$514$	25.3680	+	30.3715i	1.11894	+	1.33963i
$515$	−11.3479	+	23.7170i	−0.500050	+	1.04510i
$516$	−36.4472	−	19.5910i	−1.60450	−	0.862445i
$517$	41.0677	+	20.9250i	1.80616	+	0.920282i
$518$	3.26812	−	3.74244i	0.143593	−	0.164434i
$519$	4.94664	+	15.2242i	0.217133	+	0.668267i
$520$	0.241149	+	0.400674i	0.0105751	+	0.0175707i
$521$	1.78358	−	5.48931i	0.0781402	−	0.240491i	−0.904354	−	0.426783i	$-0.859647\pi$
$521$	1.78358	−	5.48931i	0.0781402	−	0.240491i	0.982494	+	0.186292i	$0.0596470\pi$
$522$	−42.8961	−	71.7576i	−1.87751	−	3.14074i
$523$	−4.36444	+	27.5560i	−0.190844	+	1.20494i	0.687239	+	0.726431i	$0.258823\pi$
$523$	−4.36444	+	27.5560i	−0.190844	+	1.20494i	−0.878083	+	0.478509i	$0.841177\pi$
$524$	−16.6111	+	2.25808i	−0.725657	+	0.0986445i
$525$	−13.4508	−	8.78178i	−0.587043	−	0.383268i
$526$	−1.63678	−	24.1920i	−0.0713672	−	1.05482i
$527$	−15.0583	−	2.38499i	−0.655948	−	0.103892i
$528$	32.9571	−	30.1811i	1.43428	−	1.31346i
$529$	20.5716	+	6.68413i	0.894418	+	0.290614i
$530$	−17.8431	+	30.0521i	−0.775054	+	1.30538i
$531$	−12.0962	+	3.93029i	−0.524931	+	0.170560i
$532$	1.09927	−	1.44516i	0.0476594	−	0.0626555i
$533$	−0.347271	+	0.681558i	−0.0150420	+	0.0295215i
$534$	5.74671	+	3.60901i	0.248684	+	0.156177i
$535$	3.97091	−	29.8806i	0.171678	−	1.29185i
$536$	13.8386	+	12.6311i	0.597735	+	0.545580i
$537$	−54.3925	+	8.61492i	−2.34721	+	0.371761i
$538$	−0.111556	−	0.488229i	−0.00480951	−	0.0210490i
$539$	−2.81331	+	2.04399i	−0.121178	+	0.0880408i
$540$	−19.3650	−	58.9981i	−0.833335	−	2.53888i
$541$	8.86180	+	6.43847i	0.380998	+	0.276812i	0.761757	−	0.647863i	$-0.224337\pi$
$541$	8.86180	+	6.43847i	0.380998	+	0.276812i	−0.380758	+	0.924675i	$0.624337\pi$
$542$	−13.2903	+	31.1144i	−0.570867	+	1.33648i
$543$	6.84730	−	6.84730i	0.293846	−	0.293846i
$544$	12.1557	−	9.27795i	0.521170	−	0.397789i
$545$	−9.83394	+	0.245515i	−0.421240	+	0.0105167i
$546$	0.0820105	−	0.325790i	0.00350972	−	0.0139425i
$547$	−0.739673	+	0.376882i	−0.0316261	+	0.0161143i	−0.469732	−	0.882809i	$-0.655649\pi$
$547$	−0.739673	+	0.376882i	−0.0316261	+	0.0161143i	0.438106	+	0.898923i	$0.355649\pi$
$548$	1.87196	+	0.0411329i	0.0799662	+	0.00175711i
$549$		−	29.1443i		−	1.24385i
$550$	−6.66663	−	23.6682i	−0.284266	−	1.00922i
$551$		−	7.32999i		−	0.312268i
$552$	−0.484632	−	10.6239i	−0.0206273	−	0.452185i
$553$	10.2551	−	5.22524i	0.436092	−	0.222200i
$554$	18.7604	+	4.72253i	0.797055	+	0.200641i
$555$	7.19784	−	24.1912i	0.305532	−	1.02686i
$556$	−0.803014	+	0.387177i	−0.0340554	+	0.0164199i
$557$	−9.05930	+	9.05930i	−0.383855	+	0.383855i	−0.872489	−	0.488634i	$-0.837495\pi$
$557$	−9.05930	+	9.05930i	−0.383855	+	0.383855i	0.488634	+	0.872489i	$0.337495\pi$
$558$	−53.7045	−	22.9395i	−2.27349	−	0.971105i
$559$	−0.385226	−	0.279883i	−0.0162933	−	0.0118378i
$560$	4.21112	−	7.89091i	0.177952	−	0.333452i
$561$	−24.4332	+	17.7517i	−1.03157	+	0.749479i
$562$	8.63021	−	1.97193i	0.364044	−	0.0831806i
$563$	25.8539	−	4.09486i	1.08961	−	0.172578i	0.414323	−	0.910130i	$-0.364018\pi$
$563$	25.8539	−	4.09486i	1.08961	−	0.172578i	0.675291	+	0.737552i	$0.264018\pi$
$564$	58.8842	+	61.5300i	2.47947	+	2.59088i
$565$	−27.1249	+	28.5139i	−1.14115	+	1.19959i
$566$	−1.57337	+	2.50531i	−0.0661338	+	0.105306i
$567$	−10.2798	+	20.1753i	−0.431712	+	0.847282i
$568$	−20.5805	+	31.2259i	−0.863537	+	1.31021i
$569$	17.5782	−	5.71150i	0.736917	−	0.239439i	0.0835745	−	0.996502i	$-0.473366\pi$
$569$	17.5782	−	5.71150i	0.736917	−	0.239439i	0.653342	+	0.757063i	$0.273366\pi$
$570$	2.02764	−	8.99793i	0.0849286	−	0.376882i
$571$	15.1743	+	4.93042i	0.635024	+	0.206332i	0.608799	−	0.793324i	$-0.291651\pi$
$571$	15.1743	+	4.93042i	0.635024	+	0.206332i	0.0262248	+	0.999656i	$0.491651\pi$
$572$	0.422579	−	0.293058i	0.0176689	−	0.0122534i
$573$	58.5118	+	9.26736i	2.44437	+	0.387150i
$574$	14.5968	−	0.987590i	0.609259	−	0.0412212i
$575$	−5.34001	−	2.39314i	−0.222694	−	0.0998009i
$576$	53.8282	−	23.0971i	2.24284	−	0.962381i
$577$	1.74314	−	11.0058i	0.0725679	−	0.458176i	−0.924469	−	0.381256i	$-0.875492\pi$
$577$	1.74314	−	11.0058i	0.0725679	−	0.458176i	0.997037	−	0.0769195i	$-0.0245084\pi$
$578$	11.7653	−	7.03320i	0.489372	−	0.292542i
$579$	−5.13231	+	15.7956i	−0.213291	+	0.656444i
$580$	−5.75511	−	35.6459i	−0.238968	−	1.48011i
$581$	1.32547	+	4.07938i	0.0549897	+	0.169241i
$582$	−47.5584	−	41.5308i	−1.97136	−	1.72151i
$583$	34.2443	+	17.4483i	1.41825	+	0.722636i
$584$	12.2422	−	27.0027i	0.506587	−	1.11738i
$585$	−0.219157	−	1.19056i	−0.00906104	−	0.0492238i
$586$	19.9123	−	16.6319i	0.822570	−	0.687059i
$587$	−0.0310454	−	0.196013i	−0.00128138	−	0.00809031i	0.987039	−	0.160478i	$-0.0513037\pi$
$587$	−0.0310454	−	0.196013i	−0.00128138	−	0.00809031i	−0.988321	+	0.152388i	$0.951304\pi$
$588$	−6.15317	+	1.85087i	−0.253752	+	0.0763284i
$589$	−3.00961	−	4.14237i	−0.124009	−	0.170683i
$590$	−5.48176	−	0.354415i	−0.225680	−	0.0145910i
$591$	−1.54977	+	2.13308i	−0.0637492	+	0.0877432i
$592$	13.7702	+	2.80597i	0.565952	+	0.115325i
$593$	−14.3735	−	14.3735i	−0.590249	−	0.590249i	0.347449	−	0.937699i	$-0.387048\pi$
$593$	−14.3735	−	14.3735i	−0.590249	−	0.590249i	−0.937699	+	0.347449i	$0.887048\pi$
$594$	−63.3689	+	25.4364i	−2.60006	+	1.04367i
$595$	−3.42979	+	4.97737i	−0.140608	+	0.204052i
$596$	3.73057	−	20.6123i	0.152810	−	0.844314i
$597$	2.40464	+	4.71937i	0.0984152	+	0.193151i
$598$	0.0109416	−	0.121892i	0.000447433	−	0.00498452i
$599$	27.4145			1.12013			0.560064	−	0.828449i	$-0.310777\pi$
$599$	27.4145			1.12013			0.560064	+	0.828449i	$0.310777\pi$
$600$	2.79579	−	45.3491i	0.114138	−	1.85137i
$601$	11.9310			0.486674			0.243337	−	0.969942i	$-0.421758\pi$
$601$	11.9310			0.486674			0.243337	+	0.969942i	$0.421758\pi$
$602$	−0.814232	+	9.07075i	−0.0331856	+	0.369696i
$603$	−22.0193	−	43.2153i	−0.896695	−	1.75986i
$604$	−4.61844	+	25.5180i	−0.187922	+	1.03831i
$605$	−2.30394	+	0.812710i	−0.0936687	+	0.0330414i
$606$	−32.4868	+	13.0403i	−1.31969	+	0.529724i
$607$	11.2316	+	11.2316i	0.455878	+	0.455878i	0.897300	−	0.441422i	$-0.145526\pi$
$607$	11.2316	+	11.2316i	0.455878	+	0.455878i	−0.441422	+	0.897300i	$0.645526\pi$
$608$	5.08999	+	0.683392i	0.206426	+	0.0277152i
$609$	−15.2468	+	20.9854i	−0.617831	+	0.850371i
$610$	4.65400	−	11.6954i	0.188435	−	0.473535i
$611$	0.576057	+	0.792875i	0.0233048	+	0.0320763i
$612$	−37.9074	+	11.4025i	−1.53231	+	0.460919i
$613$	4.39303	+	27.7365i	0.177433	+	1.12027i	0.902214	+	0.431288i	$0.141941\pi$
$613$	4.39303	+	27.7365i	0.177433	+	1.12027i	−0.724781	+	0.688979i	$0.758059\pi$
$614$	−1.82916	+	1.52782i	−0.0738189	+	0.0616579i
$615$	65.3556	−	35.3821i	2.63539	−	1.42674i
$616$	−8.95804	−	4.06131i	−0.360930	−	0.163635i
$617$	22.4401	+	11.4338i	0.903403	+	0.460307i	0.843028	−	0.537869i	$-0.180771\pi$
$617$	22.4401	+	11.4338i	0.903403	+	0.460307i	0.0603744	+	0.998176i	$0.480771\pi$
$618$	40.2399	+	35.1399i	1.61869	+	1.41353i
$619$	−2.06731	−	6.36252i	−0.0830921	−	0.255731i	0.900876	−	0.434077i	$-0.142925\pi$
$619$	−2.06731	−	6.36252i	−0.0830921	−	0.255731i	−0.983968	+	0.178346i	$0.942925\pi$
$620$	−17.8881	−	17.7814i	−0.718405	−	0.714120i
$621$	−5.02156	+	15.4548i	−0.201508	+	0.620178i
$622$	−12.6864	+	7.58382i	−0.508678	+	0.304084i
$623$	0.233643	−	1.47516i	0.00936071	−	0.0591012i
$624$	0.915739	−	0.253655i	0.0366589	−	0.0101543i
$625$	−21.5894	−	12.6054i	−0.863577	−	0.504217i
$626$	−21.4793	+	1.45324i	−0.858484	+	0.0580833i
$627$	−10.0179	−	1.58668i	−0.400078	−	0.0633661i
$628$	13.3689	−	9.27133i	0.533479	−	0.369966i
$629$	−9.03247	−	2.93483i	−0.360148	−	0.117019i
$630$	−17.3942	+	15.2816i	−0.693002	+	0.608834i
$631$	−3.25306	+	1.05698i	−0.129502	+	0.0420779i	−0.373051	−	0.927811i	$-0.621688\pi$
$631$	−3.25306	+	1.05698i	−0.129502	+	0.0420779i	0.243549	+	0.969889i	$0.421688\pi$
$632$	27.1814	+	17.9147i	1.08122	+	0.712610i
$633$	11.3759	−	22.3264i	0.452150	−	0.887394i
$634$	18.0528	−	28.7458i	0.716968	−	1.14164i
$635$	17.3734	+	32.0910i	0.689441	+	1.27349i
$636$	49.1005	+	51.3068i	1.94696	+	2.03445i
$637$	−0.0730309	+	0.0115670i	−0.00289359	+	0.000458300i
$638$	−38.7085	+	8.84453i	−1.53248	+	0.350158i
$639$	78.3211	−	56.9036i	3.09834	−	2.25107i
$640$	25.2893	−	0.673030i	0.999646	−	0.0266038i
$641$	26.0128	+	18.8994i	1.02745	+	0.746483i	0.967796	−	0.251736i	$-0.0810016\pi$
$641$	26.0128	+	18.8994i	1.02745	+	0.746483i	0.0596497	+	0.998219i	$0.481002\pi$
$642$	−56.3257	−	24.0591i	−2.22300	−	0.949536i
$643$	−6.34830	+	6.34830i	−0.250352	+	0.250352i	−0.821115	−	0.570763i	$-0.806648\pi$
$643$	−6.34830	+	6.34830i	−0.250352	+	0.250352i	0.570763	+	0.821115i	$0.306648\pi$
$644$	−2.10842	+	1.01658i	−0.0830832	+	0.0400589i
$645$	15.3897	+	43.6282i	0.605969	+	1.71786i
$646$	−3.36573	−	0.847249i	−0.132423	−	0.0333346i
$647$	−27.2070	+	13.8627i	−1.06962	+	0.544998i	−0.897923	−	0.440152i	$-0.854925\pi$
$647$	−27.2070	+	13.8627i	−1.06962	+	0.544998i	−0.171696	+	0.985150i	$0.554925\pi$
$648$	−63.9782	+	2.91849i	−2.51330	+	0.114649i
$649$			6.04067i			0.237117i
$650$	0.102172	−	0.512763i	0.00400753	−	0.0201122i
$651$			18.1195i			0.710161i
$652$	8.32812	+	0.182995i	0.326154	+	0.00716665i
$653$	−30.3741	+	15.4764i	−1.18863	+	0.605638i	−0.932558	−	0.361020i	$-0.882429\pi$
$653$	−30.3741	+	15.4764i	−1.18863	+	0.605638i	−0.256073	+	0.966658i	$0.582429\pi$
$654$	−4.87933	+	19.3834i	−0.190797	+	0.757949i
$655$	15.4333	+	10.6347i	0.603027	+	0.415532i
$656$	22.8288	+	34.5135i	0.891316	+	1.34753i
$657$	−54.2695	+	54.2695i	−2.11725	+	2.11725i
$658$	7.36302	−	17.2379i	0.287041	−	0.672002i
$659$	−11.1781	−	8.12136i	−0.435437	−	0.316363i	0.348382	−	0.937352i	$-0.386731\pi$
$659$	−11.1781	−	8.12136i	−0.435437	−	0.316363i	−0.783819	+	0.620989i	$0.786731\pi$
$660$	−49.9632	+	0.149454i	−1.94481	+	0.00581751i
$661$	1.26178	−	0.916736i	0.0490775	−	0.0356569i	−0.562976	−	0.826473i	$-0.690344\pi$
$661$	1.26178	−	0.916736i	0.0490775	−	0.0356569i	0.612054	+	0.790816i	$0.290344\pi$
$662$	−7.78312	−	34.0632i	−0.302500	−	1.32390i
$663$	−0.634263	+	0.100457i	−0.0246327	+	0.00390144i
$664$	−8.17878	+	8.96063i	−0.317398	+	0.347740i
$665$	−1.99650	+	0.367513i	−0.0774211	+	0.0142516i
$666$	−30.8073	−	19.3474i	−1.19376	−	0.749696i
$667$	−4.28987	+	8.41934i	−0.166104	+	0.325998i
$668$	24.8702	−	32.6956i	0.962257	−	1.26503i
$669$	31.6205	−	10.2741i	1.22252	−	0.397220i
$670$	−1.93525	−	20.8583i	−0.0747651	−	0.805825i
$671$	−13.1644	−	4.27739i	−0.508208	−	0.165127i
$672$	−13.1509	−	12.5440i	−0.507307	−	0.483894i
$673$	−35.4888	−	5.62087i	−1.36799	−	0.216669i	−0.571145	−	0.820849i	$-0.693501\pi$
$673$	−35.4888	−	5.62087i	−1.36799	−	0.216669i	−0.796847	+	0.604181i	$0.793501\pi$
$674$	−2.68722	−	39.7177i	−0.103508	−	1.52987i
$675$	−28.3919	+	63.3532i	−1.09281	+	2.43846i
$676$	−25.7522	+	3.50071i	−0.990470	+	0.134643i
$677$	−1.45609	+	9.19341i	−0.0559622	+	0.353331i	0.943779	+	0.330577i	$0.107243\pi$
$677$	−1.45609	+	9.19341i	−0.0559622	+	0.353331i	−0.999741	+	0.0227541i	$0.992757\pi$
$678$	41.0307	+	68.6371i	1.57577	+	2.63599i
$679$	−4.29429	+	13.2165i	−0.164800	+	0.507202i
$680$	−17.0328	−	1.47760i	−0.653180	−	0.0566633i
$681$	2.28204	+	7.02338i	0.0874478	+	0.269137i
$682$	−18.2437	+	20.8915i	−0.698587	+	0.799977i
$683$	1.07479	+	0.547633i	0.0411257	+	0.0209546i	0.474432	−	0.880292i	$-0.342653\pi$
$683$	1.07479	+	0.547633i	0.0411257	+	0.0209546i	−0.433307	+	0.901247i	$0.642653\pi$
$684$	−11.7099	−	6.29429i	−0.447741	−	0.240668i
$685$	−1.51676	−	1.44287i	−0.0579523	−	0.0551291i
$686$	0.906590	+	1.08540i	0.0346138	+	0.0414408i
$687$	9.79260	+	61.8281i	0.373611	+	2.35889i
$688$	−23.4431	+	10.6750i	−0.893758	+	0.406979i
$689$	0.480345	+	0.661138i	0.0182997	+	0.0251873i
$690$	−7.59501	+	9.14848i	−0.289137	+	0.348277i
$691$	15.8698	−	21.8430i	0.603717	−	0.830945i	−0.392325	−	0.919827i	$-0.628329\pi$
$691$	15.8698	−	21.8430i	0.603717	−	0.830945i	0.996042	+	0.0888812i	$0.0283291\pi$
$692$	9.40740	+	3.28683i	0.357616	+	0.124946i
$693$	18.0037	+	18.0037i	0.683904	+	0.683904i
$694$	10.2897	+	25.6344i	0.390591	+	0.973067i
$695$	0.955315	+	0.284244i	0.0362372	+	0.0107820i
$696$	−72.9121	−	8.16314i	−2.76373	−	0.309423i
$697$	−12.6960	−	24.9173i	−0.480895	−	0.943810i
$698$	22.8404	+	2.05026i	0.864524	+	0.0776036i
$699$	−34.3828			−1.30048
$700$	−9.42048	+	3.35477i	−0.356061	+	0.126798i
$701$	24.4885			0.924917			0.462458	−	0.886641i	$-0.346967\pi$
$701$	24.4885			0.924917			0.462458	+	0.886641i	$0.346967\pi$
$702$	−1.44611	−	0.129809i	−0.0545798	−	0.00489933i
$703$	−1.44805	−	2.84195i	−0.0546141	−	0.107186i
$704$	−2.53281	−	27.7040i	−0.0954589	−	1.04413i
$705$	−2.37650	−	95.1891i	−0.0895042	−	3.58503i
$706$	−2.78260	−	6.93220i	−0.104724	−	0.260897i
$707$	5.44802	+	5.44802i	0.204894	+	0.204894i
$708$	−3.68154	+	10.5371i	−0.138361	+	0.396010i
$709$	−13.7222	+	18.8871i	−0.515350	+	0.709318i	−0.984810	−	0.173635i	$-0.944449\pi$
$709$	−13.7222	+	18.8871i	−0.515350	+	0.709318i	0.469460	+	0.882954i	$0.344449\pi$
$710$	40.5166	−	10.3281i	1.52056	−	0.387608i
$711$	−49.5331	−	68.1765i	−1.85764	−	2.55682i
$712$	3.95399	−	1.48714i	0.148182	−	0.0557329i
$713$	1.03256	+	6.51935i	0.0386698	+	0.244152i
$714$	7.87361	+	9.42655i	0.294662	+	0.352780i
$715$	−0.569941	−	0.0757411i	−0.0213146	−	0.00283256i
$716$	−16.2312	+	30.1966i	−0.606587	+	1.12850i
$717$	23.3844	+	11.9149i	0.873307	+	0.444972i
$718$	−13.9166	+	15.9363i	−0.519361	+	0.594739i
$719$	−13.2468	−	40.7695i	−0.494023	−	1.52045i	−0.818474	−	0.574544i	$-0.805180\pi$
$719$	−13.2468	−	40.7695i	−0.494023	−	1.52045i	0.324451	−	0.945902i	$-0.394820\pi$
$720$	−61.8876	−	21.4152i	−2.30642	−	0.798099i
$721$	3.63347	−	11.1827i	0.135317	−	0.416464i
$722$	13.1890	+	22.0628i	0.490843	+	0.821094i
$723$	15.2359	−	96.1959i	0.566631	−	3.57757i
$724$	−0.811993	−	5.97326i	−0.0301775	−	0.221994i
$725$	−22.0692	+	33.8029i	−0.819630	+	1.25541i
$726$	0.335099	+	4.95284i	0.0124367	+	0.183817i
$727$	−16.0731	−	2.54573i	−0.596119	−	0.0944160i	−0.148918	−	0.988850i	$-0.547579\pi$
$727$	−16.0731	−	2.54573i	−0.596119	−	0.0944160i	−0.447201	+	0.894434i	$0.647579\pi$
$728$	−0.130510	−	0.163418i	−0.00483704	−	0.00605668i
$729$	30.3988	+	9.87718i	1.12588	+	0.365822i
$730$	−30.4442	+	13.1118i	−1.12679	+	0.485291i
$731$	16.5563	−	5.37945i	0.612355	−	0.198966i
$732$	−20.3567	−	15.4845i	−0.752406	−	0.572324i
$733$	−16.9005	+	33.1691i	−0.624234	+	1.22513i	0.334921	+	0.942246i	$0.391290\pi$
$733$	−16.9005	+	33.1691i	−0.624234	+	1.22513i	−0.959155	+	0.282882i	$0.908710\pi$
$734$	25.2106	+	15.8326i	0.930539	+	0.584391i
$735$	6.48034	+	3.10067i	0.239031	+	0.114370i
$736$	−5.44648	−	3.76386i	−0.200760	−	0.138738i
$737$	−22.7520	+	3.60356i	−0.838080	+	0.132739i
$738$	−23.8608	−	104.428i	−0.878329	−	3.84404i
$739$	−37.8883	+	27.5275i	−1.39374	+	1.01261i	−0.398301	+	0.917255i	$0.630400\pi$
$739$	−37.8883	+	27.5275i	−1.39374	+	1.01261i	−0.995443	+	0.0953592i	$0.969600\pi$
$740$	−9.27323	−	12.6835i	−0.340891	−	0.466256i
$741$	−0.174479	−	0.126766i	−0.00640965	−	0.00465688i
$742$	6.13965	−	14.3738i	0.225394	−	0.527678i
$743$	1.74948	−	1.74948i	0.0641820	−	0.0641820i	−0.674287	−	0.738469i	$-0.735549\pi$
$743$	1.74948	−	1.74948i	0.0641820	−	0.0641820i	0.738469	+	0.674287i	$0.235549\pi$
$744$	−44.5562	+	25.3236i	−1.63351	+	0.928410i
$745$	−18.5974	+	14.2343i	−0.681358	+	0.521506i
$746$	1.98360	−	7.87993i	0.0726247	−	0.288505i
$747$	27.9824	−	14.2578i	1.02382	−	0.521664i
$748$	−0.413012	+	18.7962i	−0.0151012	+	0.687257i
$749$			13.4805i			0.492566i
$750$	−36.4417	+	35.3899i	−1.33066	+	1.29226i
$751$		−	1.87197i		−	0.0683093i	−0.999417	−	0.0341547i	$-0.989126\pi$
$751$		−	1.87197i		−	0.0683093i	0.999417	−	0.0341547i	$-0.0108739\pi$
$752$	52.6786	−	5.98564i	1.92099	−	0.218274i
$753$	−23.5950	+	12.0223i	−0.859851	+	0.438116i
$754$	−0.818733	−	0.206098i	−0.0298165	−	0.00750565i
$755$	23.0236	−	17.6221i	0.837915	−	0.641334i
$756$	12.0606	+	25.0140i	0.438639	+	0.909749i
$757$	10.6552	−	10.6552i	0.387271	−	0.387271i	−0.486442	−	0.873713i	$-0.661705\pi$
$757$	10.6552	−	10.6552i	0.387271	−	0.387271i	0.873713	+	0.486442i	$0.161705\pi$
$758$	−32.8070	−	14.0133i	−1.19160	−	0.508985i
$759$	10.5781	+	7.68547i	0.383962	+	0.278965i
$760$	−3.69401	−	4.39580i	−0.133996	−	0.159452i
$761$	19.8929	−	14.4530i	0.721115	−	0.523921i	−0.165625	−	0.986189i	$-0.552964\pi$
$761$	19.8929	−	14.4530i	0.721115	−	0.523921i	0.886740	+	0.462268i	$0.152964\pi$
$762$	72.2860	−	16.5167i	2.61865	−	0.598337i
$763$	4.34508	−	0.688193i	0.157303	−	0.0249143i
$764$	26.6438	−	25.4981i	0.963938	−	0.922487i
$765$	39.9230	+	19.1020i	1.44342	+	0.690636i
$766$	−3.09020	+	4.92059i	−0.111653	+	0.177788i
$767$	−0.0583122	+	0.114444i	−0.00210553	+	0.00413234i
$768$	12.4663	−	49.8695i	0.449839	−	1.79951i
$769$	−26.2801	+	8.53892i	−0.947685	+	0.307921i	−0.741774	−	0.670650i	$-0.766015\pi$
$769$	−26.2801	+	8.53892i	−0.947685	+	0.307921i	−0.205910	+	0.978571i	$0.566015\pi$
$770$	4.34980	+	10.0998i	0.156756	+	0.363970i
$771$	−85.4987	−	27.7802i	−3.07916	−	1.00048i
$772$	5.89196	+	8.49599i	0.212056	+	0.305778i
$773$	0.686778	+	0.108775i	0.0247017	+	0.00391236i	0.168773	−	0.985655i	$-0.446019\pi$
$773$	0.686778	+	0.108775i	0.0247017	+	0.00391236i	−0.144071	+	0.989567i	$0.546019\pi$
$774$	66.5290	−	4.50122i	2.39134	−	0.161793i
$775$	1.40718	+	28.1643i	0.0505474	+	1.01169i
$776$	−38.5011	+	7.91145i	−1.38211	+	0.284004i
$777$	−1.76573	+	11.1484i	−0.0633453	+	0.399946i
$778$	10.1916	−	6.09245i	0.365387	−	0.218425i
$779$	2.90227	−	8.93228i	0.103985	−	0.320032i
$780$	−0.948025	−	0.479476i	−0.0339447	−	0.0171680i
$781$	−14.2084	−	43.7290i	−0.508417	−	1.56475i
$782$	3.37008	+	2.94295i	0.120514	+	0.105240i
$783$	99.8859	+	50.8944i	3.56963	+	1.81882i
$784$	−1.40198	+	3.74626i	−0.0500706	+	0.133795i
$785$	−18.0310	−	2.39619i	−0.643553	−	0.0855236i
$786$	29.2288	−	24.4136i	1.04256	−	0.870804i
$787$	−0.937263	−	5.91764i	−0.0334098	−	0.210941i	0.965336	−	0.261011i	$-0.0840558\pi$
$787$	−0.937263	−	5.91764i	−0.0334098	−	0.210941i	−0.998746	+	0.0500694i	$0.984056\pi$
$788$	0.472791	+	1.57179i	0.0168425	+	0.0559925i
$789$	32.3777	+	44.5640i	1.15268	+	1.58652i
$790$	−8.99038	−	35.2687i	−0.319863	−	1.25480i
$791$	10.3450	−	14.2387i	0.367827	−	0.506270i
$792$	−19.1096	+	69.4331i	−0.679031	+	2.46720i
$793$	−0.208117	−	0.208117i	−0.00739047	−	0.00739047i
$794$	18.1818	−	7.29819i	0.645246	−	0.259003i
$795$	−1.98164	−	79.3733i	−0.0702817	−	2.81508i
$796$	3.24456	+	0.587225i	0.115000	+	0.0208136i
$797$	−24.2883	−	47.6685i	−0.860336	−	1.68851i	−0.715002	−	0.699123i	$-0.753574\pi$
$797$	−24.2883	−	47.6685i	−0.860336	−	1.68851i	−0.145335	−	0.989383i	$-0.546426\pi$
$798$	−0.368787	+	4.10838i	−0.0130549	+	0.145435i
$799$	−35.8299			−1.26757
$800$	−21.4154	−	18.4765i	−0.757148	−	0.653244i
$801$	−10.9355			−0.386386
$802$	−2.81215	+	31.3280i	−0.0993004	+	1.10623i
$803$	16.5485	+	32.4783i	0.583985	+	1.14614i
$804$	−41.8840	−	7.58048i	−1.47713	−	0.267343i
$805$	2.50830	+	0.746320i	0.0884060	+	0.0263043i
$806$	−0.547309	+	0.219691i	−0.0192781	+	0.00773828i
$807$	0.804492	+	0.804492i	0.0283195	+	0.0283195i
$808$	−5.78267	+	21.0108i	−0.203434	+	0.739158i
$809$	−23.5924	+	32.4721i	−0.829464	+	1.14166i	0.158559	+	0.987350i	$0.449315\pi$
$809$	−23.5924	+	32.4721i	−0.829464	+	1.14166i	−0.988023	+	0.154309i	$0.950685\pi$
$810$	55.0929	+	45.7377i	1.93577	+	1.60706i
$811$	−24.4958	−	33.7156i	−0.860165	−	1.18392i	−0.981530	−	0.191308i	$-0.938727\pi$
$811$	−24.4958	−	33.7156i	−0.860165	−	1.18392i	0.121365	−	0.992608i	$-0.461273\pi$
$812$	4.65136	+	15.4633i	0.163231	+	0.542657i
$813$	−12.0240	−	75.9165i	−0.421700	−	2.66251i
$814$	−13.2606	+	11.0761i	−0.464785	+	0.388216i
$815$	−6.74786	−	6.41913i	−0.236367	−	0.224852i
$816$	−12.1760	+	32.5357i	−0.426244	+	1.13898i
$817$	5.20922	+	2.65423i	0.182248	+	0.0928598i
$818$	4.27753	+	3.73539i	0.149560	+	0.130605i
$819$	0.167296	+	0.514885i	0.00584581	+	0.0179915i
$820$	7.10068	−	45.7166i	0.247966	−	1.59649i
$821$	−4.05554	+	12.4817i	−0.141539	+	0.435614i	−0.996550	−	0.0829973i	$-0.973551\pi$
$821$	−4.05554	+	12.4817i	−0.141539	+	0.435614i	0.855010	+	0.518611i	$0.173551\pi$
$822$	−3.65105	+	2.18256i	−0.127345	+	0.0761256i
$823$	4.54237	−	28.6794i	0.158337	−	0.999702i	−0.772698	−	0.634773i	$-0.781093\pi$
$823$	4.54237	−	28.6794i	0.158337	−	0.999702i	0.931036	−	0.364928i	$-0.118907\pi$
$824$	32.5764	−	6.69400i	1.13485	−	0.233197i
$825$	41.4214	+	37.4793i	1.44211	+	1.30486i
$826$	2.45103	−	0.165832i	0.0852823	−	0.00577002i
$827$	−50.3119	−	7.96862i	−1.74952	−	0.277096i	−0.802121	−	0.597162i	$-0.796295\pi$
$827$	−50.3119	−	7.96862i	−1.74952	−	0.277096i	−0.947395	+	0.320066i	$0.896295\pi$
$828$	9.76649	+	14.0829i	0.339409	+	0.489416i
$829$	−31.6985	−	10.2995i	−1.10093	−	0.357715i	−0.298472	−	0.954418i	$-0.596477\pi$
$829$	−31.6985	−	10.2995i	−1.10093	−	0.357715i	−0.802462	+	0.596703i	$0.796477\pi$
$830$	13.5060	−	1.25310i	0.468799	−	0.0434956i
$831$	−41.7978	+	13.5809i	−1.44995	+	0.471117i
$832$	0.219448	−	0.549318i	0.00760799	−	0.0190442i
$833$	1.22725	−	2.40861i	0.0425216	−	0.0834533i
$834$	1.07708	−	1.71507i	0.0372964	−	0.0593878i
$835$	−45.1694	+	8.31472i	−1.56315	+	0.287743i
$836$	−4.56174	+	4.36558i	−0.157771	+	0.150987i
$837$	77.3448	−	12.2502i	2.67343	−	0.423429i
$838$	47.8910	−	10.9426i	1.65437	−	0.378008i
$839$	23.3666	−	16.9768i	0.806705	−	0.586105i	−0.106169	−	0.994348i	$-0.533858\pi$
$839$	23.3666	−	16.9768i	0.806705	−	0.586105i	0.912873	+	0.408243i	$0.133858\pi$
$840$	1.43226	+	20.2687i	0.0494176	+	0.699337i
$841$	29.2763	+	21.2705i	1.00953	+	0.733464i
$842$	17.5457	+	7.49453i	0.604666	+	0.258279i
$843$	−14.2207	+	14.2207i	−0.489786	+	0.489786i
$844$	−6.77465	−	14.0508i	−0.233193	−	0.483649i
$845$	23.9263	+	16.4871i	0.823089	+	0.567172i
$846$	−133.092	−	33.5029i	−4.57578	−	1.15185i
$847$	0.973496	−	0.496021i	0.0334497	−	0.0170435i
$848$	43.9260	−	4.99112i	1.50843	−	0.171396i
$849$		−	6.72076i		−	0.230656i
$850$	12.9705	+	14.0408i	0.444884	+	0.481594i
$851$			4.11178i			0.140950i
$852$	1.86638	−	84.9389i	0.0639411	−	2.90996i
$853$	−12.7662	+	6.50472i	−0.437108	+	0.222717i	−0.658675	−	0.752428i	$-0.728883\pi$
$853$	−12.7662	+	6.50472i	−0.437108	+	0.222717i	0.221567	+	0.975145i	$0.428883\pi$
$854$	−1.37417	+	5.45896i	−0.0470232	+	0.186802i
$855$	4.94448	+	14.0171i	0.169098	+	0.479373i
$856$	−33.1487	+	18.8401i	−1.13300	+	0.643943i
$857$	5.50998	−	5.50998i	0.188217	−	0.188217i	−0.606708	−	0.794925i	$-0.707510\pi$
$857$	5.50998	−	5.50998i	0.188217	−	0.188217i	0.794925	+	0.606708i	$0.207510\pi$
$858$	−0.458902	+	1.07435i	−0.0156667	+	0.0366778i
$859$	16.4136	+	11.9252i	0.560026	+	0.406883i	0.831469	−	0.555572i	$-0.187501\pi$
$859$	16.4136	+	11.9252i	0.560026	+	0.406883i	−0.271442	+	0.962455i	$0.587501\pi$
$860$	27.4165	+	8.81758i	0.934895	+	0.300677i
$861$	−26.8887	+	19.5358i	−0.916365	+	0.665778i
$862$	−7.91222	−	34.6281i	−0.269491	−	1.17944i
$863$	−16.2307	+	2.57070i	−0.552501	+	0.0875076i	−0.426442	−	0.904515i	$-0.640233\pi$
$863$	−16.2307	+	2.57070i	−0.552501	+	0.0875076i	−0.126059	+	0.992023i	$0.540233\pi$
$864$	−44.6540	+	64.6164i	−1.51916	+	2.19829i
$865$	−5.30422	−	9.79762i	−0.180349	−	0.333129i
$866$	34.0922	+	21.4104i	1.15850	+	0.727553i
$867$	−14.1371	+	27.7455i	−0.480120	+	0.942288i
$868$	8.97766	+	6.82894i	0.304722	+	0.231789i
$869$	−38.0650	+	12.3681i	−1.29127	+	0.419558i
$870$	54.1391	+	61.6236i	1.83549	+	2.08924i
$871$	−0.465836	−	0.151359i	−0.0157842	−	0.00512861i
$872$	7.76491	+	9.72281i	0.262953	+	0.329256i
$873$	100.495	+	15.9169i	3.40126	+	0.538706i
$874$	0.101433	+	1.49920i	0.00343101	+	0.0507112i
$875$	10.3136	+	4.31628i	0.348662	+	0.145917i
$876$	9.07248	+	66.7398i	0.306531	+	2.25493i
$877$	4.82044	−	30.4351i	0.162775	−	1.02772i	−0.762104	−	0.647455i	$-0.775833\pi$
$877$	4.82044	−	30.4351i	0.162775	−	1.02772i	0.924878	−	0.380264i	$-0.124167\pi$
$878$	−6.10786	−	10.2174i	−0.206130	−	0.344820i
$879$	−18.2134	+	56.0551i	−0.614323	+	1.89069i
$880$	−18.7562	+	24.8115i	−0.632272	+	0.836396i
$881$	−8.65880	−	26.6490i	−0.291722	−	0.897829i	−0.984303	−	0.176488i	$-0.943526\pi$
$881$	−8.65880	−	26.6490i	−0.291722	−	0.897829i	0.692580	−	0.721341i	$-0.256474\pi$
$882$	6.81084	−	7.79934i	0.229333	−	0.262617i
$883$	13.2849	+	6.76898i	0.447072	+	0.227794i	0.663007	−	0.748613i	$-0.269280\pi$
$883$	13.2849	+	6.76898i	0.447072	+	0.227794i	−0.215935	+	0.976408i	$0.569280\pi$
$884$	−0.189269	+	0.352118i	−0.00636582	+	0.0118430i
$885$	10.9742	−	5.94120i	0.368894	−	0.199711i
$886$	−15.6357	−	18.7196i	−0.525293	−	0.628898i
$887$	−0.354375	−	2.23744i	−0.0118988	−	0.0751258i	0.981024	−	0.193884i	$-0.0621086\pi$
$887$	−0.354375	−	2.23744i	−0.0118988	−	0.0751258i	−0.992923	+	0.118758i	$0.962109\pi$
$888$	−29.8818	+	11.2389i	−1.00277	+	0.377153i
$889$	−9.59249	−	13.2029i	−0.321722	−	0.442812i
$890$	−4.38834	−	1.74626i	−0.147098	−	0.0585349i
$891$	46.2825	−	63.7024i	1.55052	−	2.13411i
$892$	6.82671	−	19.5391i	0.228575	−	0.654217i
$893$	−8.50876	−	8.50876i	−0.284735	−	0.284735i
$894$	17.7267	+	44.1621i	0.592870	+	1.47700i
$895$	36.1460	−	12.7504i	1.20823	−	0.426199i
$896$	−11.1715	+	1.78825i	−0.373213	+	0.0597411i
$897$	0.126219	+	0.247719i	0.00421434	+	0.00827111i
$898$	−5.78903	−	0.519650i	−0.193182	−	0.0173409i
$899$	45.5357			1.51870
$900$	35.0505	+	64.2831i	1.16835	+	2.14277i
$901$	−29.8767			−0.995337
$902$	−50.6718	−	4.54854i	−1.68719	−	0.151450i
$903$	−9.39280	−	18.4344i	−0.312573	−	0.613459i
$904$	49.4713	+	5.53873i	1.64539	+	0.184216i
$905$	−3.82419	+	5.54973i	−0.127120	+	0.184479i
$906$	−21.9457	−	54.6726i	−0.729096	−	1.81637i
$907$	39.9891	+	39.9891i	1.32782	+	1.32782i	0.907271	+	0.420547i	$0.138162\pi$
$907$	39.9891	+	39.9891i	1.32782	+	1.32782i	0.420547	+	0.907271i	$0.361838\pi$
$908$	4.33993	+	1.51632i	0.144026	+	0.0503207i
$909$	33.1581	−	45.6382i	1.09978	−	1.51372i
$910$	−0.0150860	+	0.233336i	−0.000500095	+	0.00773500i
$911$	−4.96295	−	6.83092i	−0.164430	−	0.226318i	0.718849	−	0.695166i	$-0.244669\pi$
$911$	−4.96295	−	6.83092i	−0.164430	−	0.226318i	−0.883279	+	0.468848i	$0.844669\pi$
$912$	−10.6180	+	4.83497i	−0.351597	+	0.160102i
$913$	−2.33335	−	14.7322i	−0.0772225	−	0.487564i
$914$	6.87512	+	8.23113i	0.227409	+	0.272261i
$915$	5.17685	+	28.1231i	0.171142	+	0.929721i
$916$	34.3245	+	18.4500i	1.13411	+	0.609605i
$917$	−7.46834	−	3.80531i	−0.246626	−	0.125662i
$918$	34.9148	−	39.9822i	1.15236	−	1.31961i
$919$	10.6086	+	32.6500i	0.349946	+	1.07702i	0.958882	+	0.283804i	$0.0915964\pi$
$919$	10.6086	+	32.6500i	0.349946	+	1.07702i	−0.608937	+	0.793219i	$0.708404\pi$
$920$	1.67036	+	7.21099i	0.0550701	+	0.237739i
$921$	1.67310	−	5.14927i	0.0551305	−	0.169674i
$922$	11.4279	+	19.1169i	0.376359	+	0.629582i
$923$	0.152941	−	0.965630i	0.00503411	−	0.0317841i
$924$	22.1407	−	3.00976i	0.728375	−	0.0990139i
$925$	−1.87879	+	17.4657i	−0.0617741	+	0.574270i
$926$	1.40965	+	20.8350i	0.0463241	+	0.684681i
$927$	−85.0308	−	13.4676i	−2.79278	−	0.442333i
$928$	−31.5239	+	33.0491i	−1.03482	+	1.08489i
$929$	−23.7048	−	7.70215i	−0.777729	−	0.252699i	−0.106859	−	0.994274i	$-0.534079\pi$
$929$	−23.7048	−	7.70215i	−0.777729	−	0.252699i	−0.670870	+	0.741575i	$0.734079\pi$
$930$	55.8974	+	12.5962i	1.83295	+	0.413046i
$931$	0.863431	−	0.280546i	0.0282978	−	0.00919451i
$932$	−12.9583	+	17.0356i	−0.424463	+	0.558020i
$933$	15.2438	−	29.9177i	0.499061	−	0.979462i
$934$	−30.0580	−	18.8768i	−0.983527	−	0.617668i
$935$	14.4877	−	15.2296i	0.473798	−	0.498062i
$936$	−1.03230	+	1.13098i	−0.0337417	+	0.0369673i
$937$	−32.2481	+	5.10759i	−1.05350	+	0.166858i	−0.659079	−	0.752073i	$-0.729054\pi$
$937$	−32.2481	+	5.10759i	−1.05350	+	0.166858i	−0.394418	+	0.918931i	$0.629054\pi$
$938$	2.08676	+	9.13280i	0.0681352	+	0.298196i
$939$	39.5668	−	28.7470i	1.29121	−	0.938122i
$940$	−48.0589	−	34.6976i	−1.56751	−	1.13171i
$941$	1.36533	+	0.991974i	0.0445086	+	0.0323374i	0.609817	−	0.792542i	$-0.291243\pi$
$941$	1.36533	+	0.991974i	0.0445086	+	0.0323374i	−0.565309	+	0.824880i	$0.691243\pi$
$942$	−14.5181	+	33.9889i	−0.473025	+	1.10742i
$943$	−8.56120	+	8.56120i	−0.278791	+	0.278791i
$944$	3.83331	+	5.79535i	0.124764	+	0.188623i
$945$	8.85424	−	29.7582i	0.288028	−	0.968033i
$946$	7.73099	−	30.7117i	0.251356	−	0.998523i
$947$	49.1101	−	25.0228i	1.59586	−	0.813133i	0.595915	−	0.803048i	$-0.296790\pi$
$947$	49.1101	−	25.0228i	1.59586	−	0.813133i	0.999949	−	0.0100855i	$-0.00321038\pi$
$948$	−73.9371	−	1.62463i	−2.40136	−	0.0527656i
$949$			0.775069i			0.0251598i
$950$	−0.254166	+	6.41454i	−0.00824625	+	0.208115i
$951$			77.1137i			2.50058i
$952$	7.63798	−	0.348422i	0.247548	−	0.0112924i
$953$	−6.62266	+	3.37442i	−0.214529	+	0.109308i	−0.557953	−	0.829872i	$-0.688413\pi$
$953$	−6.62266	+	3.37442i	−0.214529	+	0.109308i	0.343424	+	0.939180i	$0.388413\pi$
$954$	−110.978	−	27.9363i	−3.59306	−	0.904472i
$955$	−41.2188	+	1.02907i	−1.33381	+	0.0333001i
$956$	14.7167	−	7.09570i	0.475971	−	0.229491i
$957$	63.7829	−	63.7829i	2.06181	−	2.06181i
$958$	48.5641	+	20.7438i	1.56904	+	0.670202i
$959$	0.757407	+	0.550288i	0.0244579	+	0.0177697i
$960$	−47.8393	+	31.8492i	−1.54401	+	1.02793i
$961$	0.653870	−	0.475064i	0.0210926	−	0.0153247i
$962$	−0.358151	+	0.0818342i	−0.0115472	+	0.00263844i
$963$	97.4861	−	15.4403i	3.14145	−	0.497556i
$964$	−41.9199	−	43.8035i	−1.35015	−	1.41082i
$965$	1.52278	−	11.4587i	0.0490201	−	0.368870i
$966$	2.82802	−	4.50312i	0.0909901	−	0.144885i
$967$	17.6622	−	34.6640i	0.567977	−	1.11472i	−0.411169	−	0.911559i	$-0.634879\pi$
$967$	17.6622	−	34.6640i	0.567977	−	1.11472i	0.979146	−	0.203159i	$-0.0651207\pi$
$968$	2.58027	+	1.70061i	0.0829330	+	0.0546596i
$969$	7.49877	−	2.43650i	0.240895	−	0.0782716i
$970$	37.7865	+	22.4353i	1.21325	+	0.720354i
$971$	32.7371	+	10.6369i	1.05058	+	0.341356i	0.782898	−	0.622150i	$-0.213741\pi$
$971$	32.7371	+	10.6369i	1.05058	+	0.341356i	0.267687	+	0.963506i	$0.413741\pi$
$972$	51.0997	−	35.4376i	1.63902	−	1.13666i
$973$	−0.440253	−	0.0697292i	−0.0141138	−	0.00223541i
$974$	−10.7880	+	0.729892i	−0.345669	+	0.0233872i
$975$	0.422956	+	1.10992i	0.0135454	+	0.0355458i
$976$	−15.3442	+	4.25026i	−0.491155	+	0.136048i
$977$	4.19255	−	26.4707i	0.134131	−	0.846873i	−0.825251	−	0.564765i	$-0.808967\pi$
$977$	4.19255	−	26.4707i	0.134131	−	0.846873i	0.959383	−	0.282107i	$-0.0910334\pi$
$978$	−16.2431	+	9.70996i	−0.519396	+	0.310490i
$979$	−1.60495	+	4.93954i	−0.0512945	+	0.157868i
$980$	3.97861	−	2.04222i	0.127092	−	0.0652362i
$981$	−9.95354	−	30.6339i	−0.317792	−	0.978064i
$982$	41.9055	+	36.5944i	1.33726	+	1.16777i
$983$	−9.48402	−	4.83235i	−0.302493	−	0.154128i	0.296155	−	0.955140i	$-0.404295\pi$
$983$	−9.48402	−	4.83235i	−0.302493	−	0.154128i	−0.598649	+	0.801012i	$0.704295\pi$
$984$	−85.6181	−	38.8167i	−2.72941	−	1.23743i
$985$	0.792044	−	1.65536i	0.0252366	−	0.0527441i
$986$	23.6896	−	19.7869i	0.754430	−	0.630144i
$987$	6.66147	+	42.0589i	0.212037	+	1.33875i
$988$	−0.128567	+	0.0386728i	−0.00409026	+	0.00123035i
$989$	−4.43001	−	6.09738i	−0.140866	−	0.193885i
$990$	68.0557	−	43.0243i	2.16295	−	1.36740i
$991$	−22.9259	+	31.5548i	−0.728266	+	1.00237i	0.270942	+	0.962596i	$0.412665\pi$
$991$	−22.9259	+	31.5548i	−0.728266	+	1.00237i	−0.999209	+	0.0397771i	$0.987335\pi$
$992$	−4.24540	+	31.6202i	−0.134792	+	1.00394i
$993$	56.1285	+	56.1285i	1.78118	+	1.78118i
$994$	−17.3532	+	6.96561i	−0.550410	+	0.220936i
$995$	−2.24061	−	2.92740i	−0.0710321	−	0.0928049i
$996$	4.90845	−	27.1204i	0.155530	−	0.859342i
$997$	17.8211	+	34.9759i	0.564400	+	1.10770i	0.980157	+	0.198222i	$0.0635168\pi$
$997$	17.8211	+	34.9759i	0.564400	+	1.10770i	−0.415757	+	0.909476i	$0.636483\pi$
$998$	0.575718	−	6.41364i	0.0182240	−	0.203020i
$999$	48.7816			1.54338

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	700.2.bj.a.323.43	yes	720
4.3	odd	2	inner	700.2.bj.a.323.39	✓	720
25.12	odd	20	inner	700.2.bj.a.687.39	yes	720
100.87	even	20	inner	700.2.bj.a.687.43	yes	720

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
700.2.bj.a.323.39	✓	720	4.3	odd	2	inner
700.2.bj.a.323.43	yes	720	1.1	even	1	trivial
700.2.bj.a.687.39	yes	720	25.12	odd	20	inner
700.2.bj.a.687.43	yes	720	100.87	even	20	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:	\( N \)	\(=\)	\( 700 = 2^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	700.bj (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.126438 + 1.40855i) q^{2} +(-1.45856 - 2.86259i) q^{3} +(-1.96803 - 0.356188i) q^{4} +(1.35907 + 1.77565i) q^{5} +(4.21651 - 1.69252i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(0.750542 - 2.72703i) q^{8} +(-4.30364 + 5.92345i) q^{9} +(-2.67293 + 1.68981i) q^{10} +(2.04399 + 2.81331i) q^{11} +(1.85087 + 6.15317i) q^{12} +(0.0115670 + 0.0730309i) q^{13} +(1.08540 - 0.906590i) q^{14} +(3.10067 - 6.48034i) q^{15} +(3.74626 + 1.40198i) q^{16} +(-2.40861 - 1.22725i) q^{17} +(-7.79934 - 6.81084i) q^{18} +(-0.280546 - 0.863431i) q^{19} +(-2.04222 - 3.97861i) q^{20} +(-0.992796 + 3.05551i) q^{21} +(-4.22112 + 2.52335i) q^{22} +(-0.183083 + 1.15594i) q^{23} +(-8.90106 + 1.82904i) q^{24} +(-1.30587 + 4.82646i) q^{25} +(-0.104330 + 0.00705877i) q^{26} +(13.7139 + 2.17207i) q^{27} +(1.13974 + 1.64347i) q^{28} +(7.67871 + 2.49497i) q^{29} +(8.73584 + 5.18680i) q^{30} +(5.36384 - 1.74282i) q^{31} +(-2.44842 + 5.09953i) q^{32} +(5.07205 - 9.95446i) q^{33} +(2.03318 - 3.23747i) q^{34} +(0.294568 - 2.21658i) q^{35} +(10.5795 - 10.1246i) q^{36} +(3.47004 - 0.549601i) q^{37} +(1.25166 - 0.285992i) q^{38} +(0.192186 - 0.139631i) q^{39} +(5.86229 - 2.37352i) q^{40} +(8.36936 + 6.08070i) q^{41} +(-4.17831 - 1.78473i) q^{42} +(-4.55361 + 4.55361i) q^{43} +(-3.02055 - 6.26471i) q^{44} +(-16.3669 + 0.408618i) q^{45} +(-1.60505 - 0.404036i) q^{46} +(11.8098 - 6.01737i) q^{47} +(-1.45087 - 12.7689i) q^{48} +1.00000i q^{49} +(-6.63320 - 2.44963i) q^{50} +8.68486i q^{51} +(0.00324867 - 0.147847i) q^{52} +(9.84755 - 5.01758i) q^{53} +(-4.79343 + 19.0421i) q^{54} +(-2.21753 + 7.45288i) q^{55} +(-2.45901 + 1.39759i) q^{56} +(-2.06245 + 2.06245i) q^{57} +(-4.48516 + 10.5004i) q^{58} +(1.40535 + 1.02104i) q^{59} +(-8.41042 + 11.6491i) q^{60} +(-3.22028 + 2.33967i) q^{61} +(1.77665 + 7.77560i) q^{62} +(7.23165 - 1.14538i) q^{63} +(-6.87337 - 4.09350i) q^{64} +(-0.113957 + 0.119793i) q^{65} +(13.3801 + 8.40286i) q^{66} +(-3.00737 + 5.90229i) q^{67} +(4.30307 + 3.27317i) q^{68} +(3.57601 - 1.16192i) q^{69} +(3.08492 + 0.695173i) q^{70} +(-12.5751 - 4.08589i) q^{71} +(12.9234 + 16.1820i) q^{72} +(10.3532 + 1.63978i) q^{73} +(0.335395 + 4.95722i) q^{74} +(15.7208 - 3.30153i) q^{75} +(0.244577 + 1.79918i) q^{76} +(0.543991 - 3.43463i) q^{77} +(0.172378 + 0.288359i) q^{78} +(-3.55666 + 10.9463i) q^{79} +(2.60200 + 8.55743i) q^{80} +(-6.99715 - 21.5350i) q^{81} +(-9.62317 + 11.0198i) q^{82} +(-3.82180 - 1.94731i) q^{83} +(3.04219 - 5.65971i) q^{84} +(-1.09430 - 5.94476i) q^{85} +(-5.83824 - 6.98974i) q^{86} +(-4.05781 - 25.6200i) q^{87} +(9.20607 - 3.46251i) q^{88} +(0.877888 + 1.20831i) q^{89} +(1.49384 - 23.1053i) q^{90} +(0.0434616 - 0.0598197i) q^{91} +(0.772043 - 2.20971i) q^{92} +(-12.8125 - 12.8125i) q^{93} +(6.98257 + 17.3955i) q^{94} +(1.15187 - 1.67161i) q^{95} +(18.1690 - 0.429154i) q^{96} +(-6.30893 - 12.3820i) q^{97} +(-1.40855 - 0.126438i) q^{98} -25.4611 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 720 q + 16 q^{10} + 16 q^{12} + 4 q^{13} + 20 q^{17} - 28 q^{18} - 20 q^{20} - 4 q^{22} + 20 q^{25} + 4 q^{30} - 20 q^{37} - 64 q^{40} - 80 q^{42} - 140 q^{44} - 20 q^{45} - 236 q^{48} - 40 q^{50} - 16 q^{52}+ \cdots - 20 q^{97}+O(q^{100}) \) 720 * q + 16 * q^10 + 16 * q^12 + 4 * q^13 + 20 * q^17 - 28 * q^18 - 20 * q^20 - 4 * q^22 + 20 * q^25 + 4 * q^30 - 20 * q^37 - 64 * q^40 - 80 * q^42 - 140 * q^44 - 20 * q^45 - 236 * q^48 - 40 * q^50 - 16 * q^52 + 44 * q^53 - 260 * q^54 + 16 * q^57 - 136 * q^58 - 140 * q^60 - 140 * q^62 - 4 * q^65 - 80 * q^68 - 80 * q^72 - 52 * q^73 + 76 * q^78 + 20 * q^80 + 180 * q^81 + 24 * q^82 - 80 * q^85 + 160 * q^88 - 260 * q^89 + 16 * q^90 + 256 * q^92 - 112 * q^93 + 320 * q^94 - 40 * q^96 - 20 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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