LMFDB - Embedded newform 336.3.bv.a.325.21

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [336,3,Mod(61,336)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(336, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([0, 9, 0, 10])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("336.61"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	336.bv (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$9.15533688251$
Analytic rank:	$0$
Dimension:	$256$
Relative dimension:	$64$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			325.21
Character	$\chi$	$=$	336.325
Dual form			336.3.bv.a.61.21

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.823038 + 1.82280i) q^{2} +(1.67303 - 0.448288i) q^{3} +(-2.64522 - 3.00047i) q^{4} +(-9.06845 - 2.42988i) q^{5} +(-0.559829 + 3.41857i) q^{6} +(-6.77691 + 1.75315i) q^{7} +(7.64638 - 2.35221i) q^{8} +(2.59808 - 1.50000i) q^{9} +(11.8929 - 14.5301i) q^{10} +(15.0619 - 4.03581i) q^{11} +(-5.77061 - 3.83407i) q^{12} +(8.68701 + 8.68701i) q^{13} +(2.38200 - 13.7959i) q^{14} -16.2611 q^{15} +(-2.00564 + 15.8738i) q^{16} +(12.8308 + 7.40787i) q^{17} +(0.595889 + 5.97034i) q^{18} +(-4.71384 + 17.5923i) q^{19} +(16.6972 + 33.6372i) q^{20} +(-10.5521 + 5.97108i) q^{21} +(-5.03998 + 30.7764i) q^{22} +(-8.25787 + 4.76768i) q^{23} +(11.7382 - 7.36310i) q^{24} +(54.6819 + 31.5706i) q^{25} +(-22.9844 + 8.68497i) q^{26} +(3.67423 - 3.67423i) q^{27} +(23.1867 + 15.6964i) q^{28} +(28.7528 - 28.7528i) q^{29} +(13.3835 - 29.6408i) q^{30} +(-3.46843 - 2.00250i) q^{31} +(-27.2841 - 16.7206i) q^{32} +(23.3898 - 13.5041i) q^{33} +(-24.0633 + 17.2911i) q^{34} +(65.7160 + 0.568726i) q^{35} +(-11.3732 - 3.82762i) q^{36} +(0.253408 - 0.945732i) q^{37} +(-28.1876 - 23.0715i) q^{38} +(18.4279 + 10.6394i) q^{39} +(-75.0564 + 2.75109i) q^{40} -23.1289 q^{41} +(-2.19936 - 24.1488i) q^{42} +(21.1443 + 21.1443i) q^{43} +(-51.9512 - 34.5170i) q^{44} +(-27.2054 + 7.28965i) q^{45} +(-1.89401 - 18.9764i) q^{46} +(72.7787 - 42.0188i) q^{47} +(3.76052 + 27.4565i) q^{48} +(42.8529 - 23.7619i) q^{49} +(-102.552 + 73.6905i) q^{50} +(24.7872 + 6.64171i) q^{51} +(3.08608 - 49.0442i) q^{52} +(20.9412 - 5.61117i) q^{53} +(3.67337 + 9.72144i) q^{54} -146.394 q^{55} +(-47.6950 + 29.3460i) q^{56} +31.5456i q^{57} +(28.7460 + 76.0752i) q^{58} +(4.88238 + 18.2213i) q^{59} +(43.0142 + 48.7910i) q^{60} +(-28.6078 + 106.766i) q^{61} +(6.50481 - 4.67413i) q^{62} +(-14.9772 + 14.7202i) q^{63} +(52.9342 - 35.9718i) q^{64} +(-57.6693 - 99.8862i) q^{65} +(5.36463 + 53.7493i) q^{66} +(-2.12221 - 7.92019i) q^{67} +(-11.7132 - 58.0939i) q^{68} +(-11.6784 + 11.6784i) q^{69} +(-55.1234 + 119.319i) q^{70} -22.4919i q^{71} +(16.3376 - 17.5808i) q^{72} +(-16.6746 + 28.8813i) q^{73} +(1.51532 + 1.24029i) q^{74} +(105.637 + 28.3054i) q^{75} +(65.2543 - 32.3917i) q^{76} +(-94.9974 + 53.7560i) q^{77} +(-34.5604 + 24.8339i) q^{78} +(10.9701 + 19.0007i) q^{79} +(56.7596 - 139.077i) q^{80} +(4.50000 - 7.79423i) q^{81} +(19.0360 - 42.1594i) q^{82} +(98.1751 + 98.1751i) q^{83} +(45.8286 + 15.8663i) q^{84} +(-98.3553 - 98.3553i) q^{85} +(-55.9443 + 21.1393i) q^{86} +(35.2148 - 60.9938i) q^{87} +(105.676 - 66.2880i) q^{88} +(-46.7566 - 80.9847i) q^{89} +(9.10344 - 55.5897i) q^{90} +(-74.1007 - 43.6414i) q^{91} +(36.1491 + 12.1659i) q^{92} +(-6.70049 - 1.79539i) q^{93} +(16.6924 + 167.244i) q^{94} +(85.4945 - 148.081i) q^{95} +(-53.1428 - 15.7430i) q^{96} -114.643i q^{97} +(8.04367 + 97.6693i) q^{98} +(33.0781 - 33.0781i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 256 q - 12 q^{4} - 24 q^{8} + 108 q^{10} + 32 q^{11} + 32 q^{14} - 4 q^{16} + 12 q^{18} + 48 q^{22} - 64 q^{29} - 96 q^{35} - 96 q^{37} + 60 q^{40} - 60 q^{42} - 192 q^{43} + 228 q^{44} + 180 q^{46} - 32 q^{50}+ \cdots + 192 q^{99}+O(q^{100}) $ 256 * q - 12 * q^4 - 24 * q^8 + 108 * q^10 + 32 * q^11 + 32 * q^14 - 4 * q^16 + 12 * q^18 + 48 * q^22 - 64 * q^29 - 96 * q^35 - 96 * q^37 + 60 * q^40 - 60 * q^42 - 192 * q^43 + 228 * q^44 + 180 * q^46 - 32 * q^50 + 720 * q^52 + 160 * q^53 - 56 * q^56 - 312 * q^58 + 384 * q^59 + 72 * q^60 - 96 * q^64 - 216 * q^66 - 320 * q^67 - 780 * q^68 - 828 * q^70 + 60 * q^72 - 88 * q^74 - 72 * q^78 - 612 * q^80 + 1152 * q^81 + 780 * q^82 - 72 * q^84 - 212 * q^86 - 464 * q^88 - 480 * q^91 - 488 * q^92 - 612 * q^94 + 768 * q^95 - 900 * q^96 - 196 * q^98 + 192 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.823038	+	1.82280i	−0.411519	+	0.911401i
$2$	−0.823038	+	1.82280i	−0.411519	+	0.911401i
$3$	1.67303	−	0.448288i	0.557678	−	0.149429i
$3$	1.67303	−	0.448288i	0.557678	−	0.149429i
$4$	−2.64522	−	3.00047i	−0.661305	−	0.750118i
$5$	−9.06845	−	2.42988i	−1.81369	−	0.485977i	−0.817717	−	0.575621i	$-0.804761\pi$
$5$	−9.06845	−	2.42988i	−1.81369	−	0.485977i	−0.995974	+	0.0896436i	$0.971427\pi$
$6$	−0.559829	+	3.41857i	−0.0933048	+	0.569761i
$7$	−6.77691	+	1.75315i	−0.968129	+	0.250450i
$7$	−6.77691	+	1.75315i	−0.968129	+	0.250450i
$8$	7.64638	−	2.35221i	0.955797	−	0.294026i
$9$	2.59808	−	1.50000i	0.288675	−	0.166667i
$10$	11.8929	−	14.5301i	1.18929	−	1.45301i
$11$	15.0619	−	4.03581i	1.36926	−	0.366892i	0.502051	−	0.864838i	$-0.332579\pi$
$11$	15.0619	−	4.03581i	1.36926	−	0.366892i	0.867208	+	0.497946i	$0.165912\pi$
$12$	−5.77061	−	3.83407i	−0.480884	−	0.319505i
$13$	8.68701	+	8.68701i	0.668232	+	0.668232i	0.957306	−	0.289075i	$-0.0933477\pi$
$13$	8.68701	+	8.68701i	0.668232	+	0.668232i	−0.289075	+	0.957306i	$0.593348\pi$
$14$	2.38200	−	13.7959i	0.170143	−	0.985419i
$15$	−16.2611			−1.08407
$16$	−2.00564	+	15.8738i	−0.125353	+	0.992112i
$17$	12.8308	+	7.40787i	0.754753	+	0.435757i	0.827409	−	0.561600i	$-0.189814\pi$
$17$	12.8308	+	7.40787i	0.754753	+	0.435757i	−0.0726556	+	0.997357i	$0.523147\pi$
$18$	0.595889	+	5.97034i	0.0331050	+	0.331685i
$19$	−4.71384	+	17.5923i	−0.248097	+	0.925910i	0.723705	+	0.690110i	$0.242438\pi$
$19$	−4.71384	+	17.5923i	−0.248097	+	0.925910i	−0.971802	+	0.235800i	$0.924229\pi$
$20$	16.6972	+	33.6372i	0.834862	+	1.68186i
$21$	−10.5521	+	5.97108i	−0.502479	+	0.284337i
$22$	−5.03998	+	30.7764i	−0.229090	+	1.39893i
$23$	−8.25787	+	4.76768i	−0.359038	+	0.207290i	−0.668659	−	0.743570i	$-0.733131\pi$
$23$	−8.25787	+	4.76768i	−0.359038	+	0.207290i	0.309621	+	0.950860i	$0.399798\pi$
$24$	11.7382	−	7.36310i	0.489091	−	0.306796i
$25$	54.6819	+	31.5706i	2.18728	+	1.26282i
$26$	−22.9844	+	8.68497i	−0.884017	+	0.334037i
$27$	3.67423	−	3.67423i	0.136083	−	0.136083i
$28$	23.1867	+	15.6964i	0.828096	+	0.560587i
$29$	28.7528	−	28.7528i	0.991474	−	0.991474i	−0.00848949	−	0.999964i	$-0.502702\pi$
$29$	28.7528	−	28.7528i	0.991474	−	0.991474i	0.999964	+	0.00848949i	$0.00270232\pi$
$30$	13.3835	−	29.6408i	0.446117	−	0.988026i
$31$	−3.46843	−	2.00250i	−0.111885	−	0.0645967i	0.443013	−	0.896515i	$-0.353909\pi$
$31$	−3.46843	−	2.00250i	−0.111885	−	0.0645967i	−0.554898	+	0.831918i	$0.687243\pi$
$32$	−27.2841	−	16.7206i	−0.852627	−	0.522519i
$33$	23.3898	−	13.5041i	0.708781	−	0.409215i
$34$	−24.0633	+	17.2911i	−0.707744	+	0.508561i
$35$	65.7160	+	0.568726i	1.87760	+	0.0162493i
$36$	−11.3732	−	3.82762i	−0.315922	−	0.106323i
$37$	0.253408	−	0.945732i	0.00684887	−	0.0255603i	−0.962417	−	0.271577i	$-0.912455\pi$
$37$	0.253408	−	0.945732i	0.00684887	−	0.0255603i	0.969266	+	0.246016i	$0.0791217\pi$
$38$	−28.1876	−	23.0715i	−0.741779	−	0.607145i
$39$	18.4279	+	10.6394i	0.472511	+	0.272804i
$40$	−75.0564	+	2.75109i	−1.87641	+	0.0687773i
$41$	−23.1289			−0.564120			−0.282060	−	0.959397i	$-0.591018\pi$
$41$	−23.1289			−0.564120			−0.282060	+	0.959397i	$0.591018\pi$
$42$	−2.19936	−	24.1488i	−0.0523657	−	0.574971i
$43$	21.1443	+	21.1443i	0.491727	+	0.491727i	0.908850	−	0.417123i	$-0.136962\pi$
$43$	21.1443	+	21.1443i	0.491727	+	0.491727i	−0.417123	+	0.908850i	$0.636962\pi$
$44$	−51.9512	−	34.5170i	−1.18071	−	0.784478i
$45$	−27.2054	+	7.28965i	−0.604564	+	0.161992i
$46$	−1.89401	−	18.9764i	−0.0411741	−	0.412531i
$47$	72.7787	−	42.0188i	1.54848	−	0.894017i	0.550224	−	0.835017i	$-0.314542\pi$
$47$	72.7787	−	42.0188i	1.54848	−	0.894017i	0.998258	−	0.0589997i	$-0.0187911\pi$
$48$	3.76052	+	27.4565i	0.0783442	+	0.572010i
$49$	42.8529	−	23.7619i	0.874549	−	0.484937i
$50$	−102.552	+	73.6905i	−2.05104	+	1.47381i
$51$	24.7872	+	6.64171i	0.486024	+	0.130230i
$52$	3.08608	−	49.0442i	0.0593477	−	0.943157i
$53$	20.9412	−	5.61117i	0.395117	−	0.105871i	−0.0557896	−	0.998443i	$-0.517768\pi$
$53$	20.9412	−	5.61117i	0.395117	−	0.105871i	0.450906	+	0.892571i	$0.351101\pi$
$54$	3.67337	+	9.72144i	0.0680254	+	0.180027i
$55$	−146.394			−2.66171
$56$	−47.6950	+	29.3460i	−0.851697	+	0.524035i
$57$			31.5456i			0.553432i
$58$	28.7460	+	76.0752i	0.495621	+	1.31164i
$59$	4.88238	+	18.2213i	0.0827523	+	0.308836i	0.994879	−	0.101073i	$-0.0322274\pi$
$59$	4.88238	+	18.2213i	0.0827523	+	0.308836i	−0.912127	+	0.409908i	$0.865561\pi$
$60$	43.0142	+	48.7910i	0.716903	+	0.813183i
$61$	−28.6078	+	106.766i	−0.468980	+	1.75026i	0.174366	+	0.984681i	$0.444212\pi$
$61$	−28.6078	+	106.766i	−0.468980	+	1.75026i	−0.643346	+	0.765575i	$0.722454\pi$
$62$	6.50481	−	4.67413i	0.104916	−	0.0753892i
$63$	−14.9772	+	14.7202i	−0.237733	+	0.233654i
$64$	52.9342	−	35.9718i	0.827097	−	0.562059i
$65$	−57.6693	−	99.8862i	−0.887220	−	1.53671i
$66$	5.36463	+	53.7493i	0.0812822	+	0.814383i
$67$	−2.12221	−	7.92019i	−0.0316748	−	0.118212i	0.948278	−	0.317440i	$-0.102823\pi$
$67$	−2.12221	−	7.92019i	−0.0316748	−	0.118212i	−0.979953	+	0.199228i	$0.936157\pi$
$68$	−11.7132	−	58.0939i	−0.172253	−	0.854322i
$69$	−11.6784	+	11.6784i	−0.169252	+	0.169252i
$70$	−55.1234	+	119.319i	−0.787478	+	1.70456i
$71$		−	22.4919i		−	0.316787i	−0.987376	−	0.158394i	$-0.949369\pi$
$71$		−	22.4919i		−	0.316787i	0.987376	−	0.158394i	$-0.0506315\pi$
$72$	16.3376	−	17.5808i	0.226911	−	0.244178i
$73$	−16.6746	+	28.8813i	−0.228419	+	0.395634i	−0.957340	−	0.288964i	$-0.906689\pi$
$73$	−16.6746	+	28.8813i	−0.228419	+	0.395634i	0.728920	+	0.684598i	$0.240022\pi$
$74$	1.51532	+	1.24029i	0.0204773	+	0.0167606i
$75$	105.637	+	28.3054i	1.40850	+	0.377406i
$76$	65.2543	−	32.3917i	0.858609	−	0.426207i
$77$	−94.9974	+	53.7560i	−1.23373	+	0.698130i
$78$	−34.5604	+	24.8339i	−0.443082	+	0.318383i
$79$	10.9701	+	19.0007i	0.138862	+	0.240515i	0.927066	−	0.374898i	$-0.122322\pi$
$79$	10.9701	+	19.0007i	0.138862	+	0.240515i	−0.788204	+	0.615414i	$0.788989\pi$
$80$	56.7596	−	139.077i	0.709495	−	1.73847i
$81$	4.50000	−	7.79423i	0.0555556	−	0.0962250i
$82$	19.0360	−	42.1594i	0.232146	−	0.514139i
$83$	98.1751	+	98.1751i	1.18283	+	1.18283i	0.979007	+	0.203825i	$0.0653375\pi$
$83$	98.1751	+	98.1751i	1.18283	+	1.18283i	0.203825	+	0.979007i	$0.434663\pi$
$84$	45.8286	+	15.8663i	0.545578	+	0.188885i
$85$	−98.3553	−	98.3553i	−1.15712	−	1.15712i
$86$	−55.9443	+	21.1393i	−0.650516	+	0.245806i
$87$	35.2148	−	60.9938i	0.404768	−	0.701078i
$88$	105.676	−	66.2880i	1.20086	−	0.753273i
$89$	−46.7566	−	80.9847i	−0.525354	−	0.909941i	−0.999564	−	0.0295286i	$-0.990599\pi$
$89$	−46.7566	−	80.9847i	−0.525354	−	0.909941i	0.474209	−	0.880412i	$-0.342734\pi$
$90$	9.10344	−	55.5897i	0.101149	−	0.617663i
$91$	−74.1007	−	43.6414i	−0.814294	−	0.479576i
$92$	36.1491	+	12.1659i	0.392925	+	0.132238i
$93$	−6.70049	−	1.79539i	−0.0720483	−	0.0193053i
$94$	16.6924	+	167.244i	0.177578	+	1.77919i
$95$	85.4945	−	148.081i	0.899942	−	1.55875i
$96$	−53.1428	−	15.7430i	−0.553571	−	0.163990i
$97$		−	114.643i		−	1.18188i	−0.806714	−	0.590942i	$-0.798756\pi$
$97$		−	114.643i		−	1.18188i	0.806714	−	0.590942i	$-0.201244\pi$
$98$	8.04367	+	97.6693i	0.0820783	+	0.996626i
$99$	33.0781	−	33.0781i	0.334122	−	0.334122i
$100$	−49.9189	−	247.582i	−0.499189	−	2.47582i
$101$	45.2263	+	168.787i	0.447785	+	1.67116i	0.708475	+	0.705735i	$0.249383\pi$
$101$	45.2263	+	168.787i	0.447785	+	1.67116i	−0.260690	+	0.965423i	$0.583950\pi$
$102$	−32.5073	+	39.7158i	−0.318699	+	0.389371i
$103$	96.0431	+	166.352i	0.932457	+	1.61506i	0.779106	+	0.626892i	$0.215673\pi$
$103$	96.0431	+	166.352i	0.932457	+	1.61506i	0.153351	+	0.988172i	$0.450993\pi$
$104$	86.8579	+	45.9905i	0.835172	+	0.442216i
$105$	110.200	−	28.5082i	1.04952	−	0.271507i
$106$	−7.00732	+	42.7898i	−0.0661068	+	0.403678i
$107$	−7.74731	+	28.9133i	−0.0724048	+	0.270218i	−0.992632	−	0.121166i	$-0.961337\pi$
$107$	−7.74731	+	28.9133i	−0.0724048	+	0.270218i	0.920228	+	0.391384i	$0.128003\pi$
$108$	−20.7436	−	1.30528i	−0.192070	−	0.0120859i
$109$	−9.24491	−	34.5025i	−0.0848157	−	0.316537i	0.910464	−	0.413589i	$-0.135725\pi$
$109$	−9.24491	−	34.5025i	−0.0848157	−	0.316537i	−0.995279	+	0.0970528i	$0.969058\pi$
$110$	120.488	−	266.848i	1.09535	−	2.42589i
$111$		−	1.69584i		−	0.0152778i
$112$	−14.2371	−	111.091i	−0.127117	−	0.991888i
$113$	−165.343			−1.46321			−0.731605	−	0.681729i	$-0.761228\pi$
$113$	−165.343			−1.46321			−0.731605	+	0.681729i	$0.761228\pi$
$114$	−57.5015	−	25.9632i	−0.504399	−	0.227748i
$115$	86.4710	−	23.1698i	0.751922	−	0.201477i
$116$	−162.329	−	10.2145i	−1.39939	−	0.0880558i
$117$	35.6000	+	9.53900i	0.304274	+	0.0815299i
$118$	−37.2322	−	6.09720i	−0.315527	−	0.0516712i
$119$	−99.9403	−	27.7081i	−0.839834	−	0.232841i
$120$	−124.339	+	38.2495i	−1.03615	+	0.318746i
$121$	105.783	−	61.0736i	0.874236	−	0.504740i
$122$	−171.067	−	140.018i	−1.40219	−	1.14769i
$123$	−38.6954	+	10.3684i	−0.314597	+	0.0842960i
$124$	3.16632	+	15.7040i	0.0255348	+	0.126645i
$125$	−253.203	−	253.203i	−2.02562	−	2.02562i
$126$	−14.5052	−	39.4157i	−0.115121	−	0.312823i
$127$	149.192			1.17474			0.587371	−	0.809318i	$-0.300163\pi$
$127$	149.192			1.17474			0.587371	+	0.809318i	$0.300163\pi$
$128$	22.0026	+	126.095i	0.171895	+	0.985115i
$129$	44.8538	+	25.8963i	0.347704	+	0.200747i
$130$	229.537	−	22.9097i	1.76567	−	0.176228i
$131$	−20.9611	+	78.2278i	−0.160008	+	0.597159i	0.838616	+	0.544723i	$0.183365\pi$
$131$	−20.9611	+	78.2278i	−0.160008	+	0.597159i	−0.998624	+	0.0524358i	$0.983302\pi$
$132$	−102.390	−	34.4590i	−0.775679	−	0.261053i
$133$	1.10330	−	127.485i	0.00829546	−	0.958537i
$134$	16.1836	+	2.65025i	0.120773	+	0.0197780i
$135$	−42.2476	+	24.3917i	−0.312945	+	0.180679i
$136$	115.534	+	26.4626i	0.849515	+	0.194578i
$137$	−6.24491	−	3.60550i	−0.0455833	−	0.0263175i	0.477035	−	0.878884i	$-0.341711\pi$
$137$	−6.24491	−	3.60550i	−0.0455833	−	0.0263175i	−0.522618	+	0.852567i	$0.675045\pi$
$138$	−11.6756	−	30.8991i	−0.0846061	−	0.223907i
$139$	−0.896461	+	0.896461i	−0.00644936	+	0.00644936i	−0.710324	−	0.703875i	$-0.751452\pi$
$139$	−0.896461	+	0.896461i	−0.00644936	+	0.00644936i	0.703875	+	0.710324i	$0.251452\pi$
$140$	−172.127	−	198.683i	−1.22948	−	1.41917i
$141$	102.925	−	102.925i	0.729962	−	0.729962i
$142$	40.9983	+	18.5117i	0.288720	+	0.130364i
$143$	165.902	+	95.7833i	1.16015	+	0.669814i
$144$	18.5999	+	44.2498i	0.129166	+	0.307290i
$145$	−330.609	+	190.877i	−2.28006	+	1.31639i
$146$	−38.9210	−	54.1649i	−0.266582	−	0.370993i
$147$	61.0422	−	58.9649i	0.415253	−	0.401121i
$148$	−3.50796	+	1.74132i	−0.0237024	+	0.0117657i
$149$	61.0940	−	228.006i	0.410027	−	1.53024i	−0.384566	−	0.923098i	$-0.625649\pi$
$149$	61.0940	−	228.006i	0.410027	−	1.53024i	0.794592	−	0.607143i	$-0.207685\pi$
$150$	−138.539	+	169.259i	−0.923591	+	1.12840i
$151$	99.6326	+	57.5229i	0.659818	+	0.380946i	0.792208	−	0.610251i	$-0.208932\pi$
$151$	99.6326	+	57.5229i	0.659818	+	0.380946i	−0.132389	+	0.991198i	$0.542265\pi$
$152$	5.33696	+	145.605i	0.0351116	+	0.957929i
$153$	44.4472			0.290505
$154$	−19.8002	−	217.405i	−0.128573	−	1.41172i
$155$	26.5875	+	26.5875i	0.171532	+	0.171532i
$156$	−16.8228	−	83.4359i	−0.107838	−	0.534846i
$157$	42.2217	−	11.3133i	0.268928	−	0.0720590i	−0.121835	−	0.992550i	$-0.538878\pi$
$157$	42.2217	−	11.3133i	0.268928	−	0.0720590i	0.390763	+	0.920491i	$0.372211\pi$
$158$	−43.6633	+	4.35796i	−0.276350	+	0.0275820i
$159$	32.5198	−	18.7753i	0.204527	−	0.118084i
$160$	206.795	+	217.927i	1.29247	+	1.36205i
$161$	47.6043	−	46.7874i	0.295679	−	0.290605i
$162$	10.5037	+	14.6176i	0.0648375	+	0.0902318i
$163$	37.7822	+	10.1237i	0.231793	+	0.0621086i	0.372846	−	0.927893i	$-0.378382\pi$
$163$	37.7822	+	10.1237i	0.231793	+	0.0621086i	−0.141053	+	0.990002i	$0.545049\pi$
$164$	61.1810	+	69.3976i	0.373055	+	0.423156i
$165$	−244.922	+	65.6268i	−1.48438	+	0.397738i
$166$	−259.756	+	98.1520i	−1.56479	+	0.591277i
$167$	−36.7194			−0.219877			−0.109938	−	0.993938i	$-0.535065\pi$
$167$	−36.7194			−0.219877			−0.109938	+	0.993938i	$0.535065\pi$
$168$	−66.6399	+	70.4779i	−0.396666	+	0.419511i
$169$		−	18.0717i		−	0.106933i
$170$	260.232	−	98.3322i	1.53078	−	0.578424i
$171$	14.1415	+	52.7769i	0.0826990	+	0.308637i
$172$	7.51154	−	119.374i	0.0436718	−	0.694035i
$173$	−23.1969	+	86.5719i	−0.134086	+	0.500416i	0.865914	+	0.500193i	$0.166738\pi$
$173$	−23.1969	+	86.5719i	−0.134086	+	0.500416i	−1.00000		0.000222833i	$0.999929\pi$
$174$	82.1966	+	114.390i	0.472394	+	0.657413i
$175$	−425.922	−	118.085i	−2.43384	−	0.674773i
$176$	33.8549	+	247.183i	0.192358	+	1.40445i
$177$	16.3368	+	28.2961i	0.0922982	+	0.159865i
$178$	186.102	−	18.5745i	1.04551	−	0.104351i
$179$	−22.4121	−	83.6432i	−0.125207	−	0.467281i	0.874640	−	0.484774i	$-0.161098\pi$
$179$	−22.4121	−	83.6432i	−0.125207	−	0.467281i	−0.999847	+	0.0174933i	$0.994431\pi$
$180$	93.8365	+	62.3462i	0.521314	+	0.346368i
$181$	−160.895	+	160.895i	−0.888925	+	0.888925i	−0.994420	−	0.105495i	$-0.966357\pi$
$181$	−160.895	+	160.895i	−0.888925	+	0.888925i	0.105495	+	0.994420i	$0.466357\pi$
$182$	140.537	−	99.1524i	0.772183	−	0.544794i
$183$			191.447i			1.04616i
$184$	−51.9282	+	55.8797i	−0.282218	+	0.303694i
$185$	−4.59604	+	7.96057i	−0.0248435	+	0.0430301i
$186$	8.78740	−	10.7360i	0.0472441	−	0.0577204i
$187$	223.152	+	59.7935i	1.19333	+	0.319751i
$188$	−318.592	−	107.221i	−1.69464	−	0.570326i
$189$	−18.4585	+	31.3414i	−0.0976638	+	0.165828i
$190$	199.557	+	277.716i	1.05030	+	1.46166i
$191$	48.2319	+	83.5401i	0.252523	+	0.437383i	0.964220	−	0.265104i	$-0.0854063\pi$
$191$	48.2319	+	83.5401i	0.252523	+	0.437383i	−0.711697	+	0.702487i	$0.752073\pi$
$192$	72.4350	−	83.9117i	0.377265	−	0.437040i
$193$	22.2068	−	38.4632i	0.115061	−	0.199291i	−0.802743	−	0.596325i	$-0.796627\pi$
$193$	22.2068	−	38.4632i	0.115061	−	0.199291i	0.917804	+	0.397034i	$0.129960\pi$
$194$	208.971	+	94.3553i	1.07717	+	0.486367i
$195$	−141.260	−	141.260i	−0.724412	−	0.724412i
$196$	−184.652	−	65.7235i	−0.942103	−	0.335324i
$197$	229.119	+	229.119i	1.16304	+	1.16304i	0.983807	+	0.179232i	$0.0573613\pi$
$197$	229.119	+	229.119i	1.16304	+	1.16304i	0.179232	+	0.983807i	$0.442639\pi$
$198$	33.0703	+	87.5194i	0.167022	+	0.442017i
$199$	131.929	−	228.507i	0.662959	−	1.14828i	−0.316876	−	0.948467i	$-0.602634\pi$
$199$	131.929	−	228.507i	0.662959	−	1.14828i	0.979834	−	0.199811i	$-0.0640328\pi$
$200$	492.379	+	112.777i	2.46190	+	0.563887i
$201$	−7.10105	−	12.2994i	−0.0353286	−	0.0611909i
$202$	−344.888	−	56.4794i	−1.70737	−	0.279601i
$203$	−144.447	+	245.263i	−0.711561	+	1.20819i
$204$	−45.6393	−	91.9421i	−0.223722	−	0.450696i
$205$	209.743	+	56.2006i	1.02314	+	0.274149i
$206$	−382.273	+	38.1540i	−1.85569	+	0.185214i
$207$	−14.3030	+	24.7736i	−0.0690968	+	0.119679i
$208$	−155.319	+	120.473i	−0.746725	+	0.579196i
$209$			283.997i			1.35884i
$210$	−38.7339	+	224.336i	−0.184447	+	1.06827i
$211$	−162.315	+	162.315i	−0.769267	+	0.769267i	−0.977977	−	0.208710i	$-0.933073\pi$
$211$	−162.315	+	162.315i	−0.769267	+	0.769267i	0.208710	+	0.977977i	$0.433073\pi$
$212$	−72.2301	−	47.9906i	−0.340708	−	0.226371i
$213$	−10.0828	−	37.6297i	−0.0473373	−	0.176665i
$214$	−46.3270	−	37.9186i	−0.216481	−	0.177190i
$215$	−140.368	−	243.124i	−0.652873	−	1.13081i
$216$	19.4520	−	36.7372i	0.0900556	−	0.170079i
$217$	27.0159	+	7.49006i	0.124497	+	0.0345164i
$218$	70.5001	+	11.5452i	0.323395	+	0.0529596i
$219$	−14.9501	+	55.7943i	−0.0682651	+	0.254769i
$220$	387.245	+	439.252i	1.76020	+	1.99660i
$221$	47.1091	+	175.814i	0.213163	+	0.795536i
$222$	3.09118	+	1.39574i	0.0139242	+	0.00628712i
$223$		−	200.991i		−	0.901304i	−0.892700	−	0.450652i	$-0.851192\pi$
$223$		−	200.991i		−	0.901304i	0.892700	−	0.450652i	$-0.148808\pi$
$224$	214.215	+	65.4810i	0.956319	+	0.292326i
$225$	189.424			0.841883
$226$	136.083	−	301.387i	0.602138	−	1.33357i
$227$	93.5464	−	25.0657i	0.412099	−	0.110421i	−0.0468125	−	0.998904i	$-0.514906\pi$
$227$	93.5464	−	25.0657i	0.412099	−	0.110421i	0.458911	+	0.888482i	$0.348240\pi$
$228$	94.6517	−	83.4451i	0.415139	−	0.365987i
$229$	−36.8500	−	9.87393i	−0.160917	−	0.0431176i	0.177461	−	0.984128i	$-0.443212\pi$
$229$	−36.8500	−	9.87393i	−0.160917	−	0.0431176i	−0.338378	+	0.941010i	$0.609878\pi$
$230$	−28.9349	+	176.689i	−0.125804	+	0.768214i
$231$	−134.836	+	132.522i	−0.583704	+	0.573687i
$232$	152.222	−	287.487i	0.656129	−	1.23917i
$233$	361.752	−	208.857i	1.55258	−	0.896384i	0.554652	−	0.832083i	$-0.312851\pi$
$233$	361.752	−	208.857i	1.55258	−	0.896384i	0.997931	−	0.0643012i	$-0.0204818\pi$
$234$	−46.6879	+	57.0409i	−0.199521	+	0.243764i
$235$	−762.091	+	204.202i	−3.24294	+	0.868943i
$236$	41.7575	−	62.8488i	0.176939	−	0.266308i
$237$	26.8711	+	26.8711i	0.113380	+	0.113380i
$238$	132.761	−	159.367i	0.557819	−	0.669607i
$239$	−243.100			−1.01716			−0.508578	−	0.861016i	$-0.669829\pi$
$239$	−243.100			−1.01716			−0.508578	+	0.861016i	$0.669829\pi$
$240$	32.6140	−	258.125i	0.135892	−	1.07552i
$241$	−261.466	−	150.958i	−1.08492	−	0.626380i	−0.152702	−	0.988272i	$-0.548798\pi$
$241$	−261.466	−	150.958i	−1.08492	−	0.626380i	−0.932220	+	0.361892i	$0.882131\pi$
$242$	24.2621	+	243.087i	0.100256	+	1.00449i
$243$	4.03459	−	15.0573i	0.0166032	−	0.0619642i
$244$	396.021	−	196.582i	1.62304	−	0.805662i
$245$	−446.348	+	111.356i	−1.82183	+	0.454514i
$246$	12.9482	−	79.0677i	0.0526351	−	0.321413i
$247$	−193.774	+	111.875i	−0.784509	+	0.452936i
$248$	−31.2312	−	7.15339i	−0.125932	−	0.0288443i
$249$	208.261	+	120.239i	0.836389	+	0.482889i
$250$	669.935	−	253.143i	2.67974	−	1.01257i
$251$	77.3684	−	77.3684i	0.308241	−	0.308241i	−0.535986	−	0.844227i	$-0.680060\pi$
$251$	77.3684	−	77.3684i	0.308241	−	0.308241i	0.844227	+	0.535986i	$0.180060\pi$
$252$	83.7854	+	6.00053i	0.332482	+	0.0238116i
$253$	−105.137	+	105.137i	−0.415562	+	0.415562i
$254$	−122.791	+	271.948i	−0.483429	+	1.07066i
$255$	−208.643	−	120.460i	−0.818208	−	0.472393i
$256$	−247.955	−	63.6743i	−0.968573	−	0.248728i
$257$	−146.253	+	84.4390i	−0.569076	+	0.328556i	−0.756780	−	0.653669i	$-0.773229\pi$
$257$	−146.253	+	84.4390i	−0.569076	+	0.328556i	0.187704	+	0.982226i	$0.439895\pi$
$258$	−84.1202	+	60.4459i	−0.326047	+	0.234286i
$259$	−0.0593114	+	6.85340i	−0.000229001	+	0.0264610i
$260$	−147.158	+	437.256i	−0.565991	+	1.68175i
$261$	31.5727	−	117.831i	0.120968	−	0.451460i
$262$	−125.342	−	102.592i	−0.478405	−	0.391574i
$263$	181.799	+	104.962i	0.691251	+	0.399094i	0.804081	−	0.594520i	$-0.202658\pi$
$263$	181.799	+	104.962i	0.691251	+	0.399094i	−0.112829	+	0.993614i	$0.535991\pi$
$264$	147.083	−	158.275i	0.557131	−	0.599527i
$265$	−203.539			−0.768070
$266$	231.473	+	106.936i	0.870198	+	0.402016i
$267$	−114.530	−	114.530i	−0.428950	−	0.428950i
$268$	−18.1506	+	27.3183i	−0.0677261	+	0.101934i
$269$	−197.643	+	52.9582i	−0.734732	+	0.196871i	−0.606735	−	0.794904i	$-0.707521\pi$
$269$	−197.643	+	52.9582i	−0.734732	+	0.196871i	−0.127996	+	0.991775i	$0.540855\pi$
$270$	−9.68982	−	97.0843i	−0.0358882	−	0.359571i
$271$	−167.861	+	96.9144i	−0.619412	+	0.357618i	−0.776640	−	0.629945i	$-0.783078\pi$
$271$	−167.861	+	96.9144i	−0.619412	+	0.357618i	0.157228	+	0.987562i	$0.449744\pi$
$272$	−143.325	+	188.816i	−0.526930	+	0.694177i
$273$	−143.537	−	39.7951i	−0.525776	−	0.145769i
$274$	11.7119	−	8.41577i	0.0427442	−	0.0307145i
$275$	951.023	+	254.826i	3.45827	+	0.926640i
$276$	65.9325	+	4.14877i	0.238886	+	0.0150318i
$277$	−328.648	+	88.0610i	−1.18646	+	0.317910i	−0.797484	−	0.603340i	$-0.793836\pi$
$277$	−328.648	+	88.0610i	−1.18646	+	0.317910i	−0.388971	+	0.921250i	$0.627169\pi$
$278$	−0.896250	−	2.37189i	−0.00322392	−	0.00853199i
$279$	−12.0150			−0.0430645
$280$	503.827	−	150.229i	1.79938	−	0.536533i
$281$		−	82.2196i		−	0.292597i	−0.989241	−	0.146298i	$-0.953264\pi$
$281$		−	82.2196i		−	0.292597i	0.989241	−	0.146298i	$-0.0467359\pi$
$282$	102.900	+	272.322i	0.364895	+	0.965681i
$283$	−41.6541	−	155.455i	−0.147188	−	0.549312i	−0.999648	−	0.0265203i	$-0.991557\pi$
$283$	−41.6541	−	155.455i	−0.147188	−	0.549312i	0.852461	−	0.522791i	$-0.175109\pi$
$284$	−67.4862	+	59.4960i	−0.237628	+	0.209493i
$285$	76.6523	−	286.070i	0.268955	−	1.00375i
$286$	−311.137	+	223.573i	−1.08789	+	0.781722i
$287$	156.742	−	40.5485i	0.546141	−	0.141284i
$288$	−95.9670	−	2.51534i	−0.333219	−	0.00873381i
$289$	−34.7470	−	60.1836i	−0.120232	−	0.208248i
$290$	−75.8278	−	759.734i	−0.261475	−	2.61977i
$291$	−51.3929	−	191.801i	−0.176608	−	0.659110i
$292$	130.765	−	26.3656i	0.447827	−	0.0902931i
$293$	−79.5362	+	79.5362i	−0.271455	+	0.271455i	−0.829686	−	0.558231i	$-0.811480\pi$
$293$	−79.5362	+	79.5362i	−0.271455	+	0.271455i	0.558231	+	0.829686i	$0.311480\pi$
$294$	57.2413	+	159.798i	0.194698	+	0.543531i
$295$		−	177.103i		−	0.600348i
$296$	−0.286906	−	7.82749i	−0.000969277	−	0.0264442i
$297$	40.5123	−	70.1693i	0.136405	−	0.236260i
$298$	365.327	+	299.020i	1.22593	+	1.00342i
$299$	−113.153	−	30.3193i	−0.378438	−	0.101402i
$300$	−194.504	−	391.836i	−0.648347	−	1.30612i
$301$	−180.362	−	106.224i	−0.599209	−	0.352902i
$302$	−186.854	+	134.267i	−0.618723	+	0.444593i
$303$	151.330	+	262.112i	0.499440	+	0.865055i
$304$	−269.802	−	110.110i	−0.887507	−	0.362205i
$305$	518.856	−	898.686i	1.70117	−	2.94651i
$306$	−36.5817	+	81.0185i	−0.119548	+	0.264766i
$307$	417.110	+	417.110i	1.35866	+	1.35866i	0.875568	+	0.483095i	$0.160488\pi$
$307$	417.110	+	417.110i	1.35866	+	1.35866i	0.483095	+	0.875568i	$0.339512\pi$
$308$	412.582	+	142.840i	1.33955	+	0.463767i
$309$	235.257	+	235.257i	0.761348	+	0.761348i
$310$	−70.3462	+	26.5812i	−0.226923	+	0.0857458i
$311$	295.949	−	512.598i	0.951604	−	1.64823i	0.209649	−	0.977777i	$-0.432768\pi$
$311$	295.949	−	512.598i	0.951604	−	1.64823i	0.741955	−	0.670450i	$-0.233899\pi$
$312$	165.933	+	38.0063i	0.531837	+	0.121815i
$313$	−61.4458	−	106.427i	−0.196312	−	0.340023i	0.751018	−	0.660282i	$-0.229563\pi$
$313$	−61.4458	−	106.427i	−0.196312	−	0.340023i	−0.947330	+	0.320259i	$0.896230\pi$
$314$	−14.1282	+	86.2730i	−0.0449942	+	0.274755i
$315$	171.588	−	97.0964i	0.544725	−	0.308243i
$316$	27.9928	−	83.1763i	0.0885849	−	0.263216i
$317$	112.684	+	30.1936i	0.355470	+	0.0952478i	0.432135	−	0.901809i	$-0.357760\pi$
$317$	112.684	+	30.1936i	0.355470	+	0.0952478i	−0.0766649	+	0.997057i	$0.524427\pi$
$318$	7.45868	+	74.7301i	0.0234550	+	0.235000i
$319$	317.029	−	549.111i	0.993822	−	1.72135i
$320$	−567.439	+	197.584i	−1.77325	+	0.617451i
$321$			51.8460i			0.161514i
$322$	46.1041	+	125.281i	0.143180	+	0.389072i
$323$	−190.804	+	190.804i	−0.590724	+	0.590724i
$324$	−35.2898	+	7.11532i	−0.108919	+	0.0219609i
$325$	200.768	+	749.276i	0.617748	+	2.30547i
$326$	−49.5497	+	60.5373i	−0.151993	+	0.185697i
$327$	−30.9341	−	53.5794i	−0.0945996	−	0.163851i
$328$	−176.852	+	54.4041i	−0.539184	+	0.165866i
$329$	−419.549	+	412.349i	−1.27522	+	1.25334i
$330$	81.9557	−	500.458i	0.248351	−	1.51654i
$331$	38.3200	−	143.012i	0.115771	−	0.432062i	−0.883573	−	0.468294i	$-0.844869\pi$
$331$	38.3200	−	143.012i	0.115771	−	0.432062i	0.999343	+	0.0362322i	$0.0115356\pi$
$332$	34.8769	−	554.266i	0.105051	−	1.66948i
$333$	−0.760224	−	2.83720i	−0.00228296	−	0.00852011i
$334$	30.2215	−	66.9323i	0.0904835	−	0.200396i
$335$			76.9806i			0.229793i
$336$	−73.6201	−	179.477i	−0.219107	−	0.534158i
$337$	337.879			1.00261			0.501304	−	0.865271i	$-0.332854\pi$
$337$	337.879			1.00261			0.501304	+	0.865271i	$0.332854\pi$
$338$	32.9411	+	14.8737i	0.0974589	+	0.0440049i
$339$	−276.624	+	74.1211i	−0.815999	+	0.218646i
$340$	−34.9409	+	555.283i	−0.102767	+	1.63319i
$341$	−60.3227	−	16.1634i	−0.176899	−	0.0474000i
$342$	−107.841	−	17.6602i	−0.315324	−	0.0516379i
$343$	−248.752	+	236.160i	−0.725225	+	0.688512i
$344$	211.413	+	111.941i	0.614572	+	0.325411i
$345$	134.282	−	77.5278i	0.389223	−	0.224718i
$346$	−138.712	−	113.535i	−0.400901	−	0.328137i
$347$	416.688	−	111.651i	1.20083	−	0.321762i	0.397673	−	0.917527i	$-0.369818\pi$
$347$	416.688	−	111.651i	1.20083	−	0.321762i	0.803158	+	0.595766i	$0.203151\pi$
$348$	−276.161	+	55.6810i	−0.793566	+	0.160003i
$349$	−77.9645	−	77.9645i	−0.223394	−	0.223394i	0.586532	−	0.809926i	$-0.300493\pi$
$349$	−77.9645	−	77.9645i	−0.223394	−	0.223394i	−0.809926	+	0.586532i	$0.800493\pi$
$350$	565.796	−	679.183i	1.61656	−	1.94052i
$351$	63.8362			0.181870
$352$	−478.430	−	141.730i	−1.35918	−	0.402642i
$353$	−484.225	−	279.568i	−1.37174	−	0.791976i	−0.380595	−	0.924742i	$-0.624281\pi$
$353$	−484.225	−	279.568i	−1.37174	−	0.791976i	−0.991147	+	0.132766i	$0.957614\pi$
$354$	−65.0240	+	6.48994i	−0.183684	+	0.0183332i
$355$	−54.6527	+	203.967i	−0.153951	+	0.574554i
$356$	−119.311	+	354.514i	−0.335143	+	0.995826i
$357$	−179.625	−	1.55452i	−0.503150	−	0.00435441i
$358$	170.911	+	27.9886i	0.477405	+	0.0781805i
$359$	−318.844	+	184.085i	−0.888146	+	0.512771i	−0.873336	−	0.487119i	$-0.838048\pi$
$359$	−318.844	+	184.085i	−0.888146	+	0.512771i	−0.0148102	+	0.999890i	$0.504714\pi$
$360$	−190.876	+	119.732i	−0.530210	+	0.332589i
$361$	25.3667	+	14.6455i	0.0702678	+	0.0405692i
$362$	−160.858	−	425.704i	−0.444358	−	1.17598i
$363$	149.599	−	149.599i	0.412119	−	0.412119i
$364$	65.0678	+	337.778i	0.178758	+	0.927962i
$365$	221.391	−	221.391i	0.606551	−	0.606551i
$366$	−348.970	−	157.568i	−0.953470	−	0.430514i
$367$	−87.5912	−	50.5708i	−0.238668	−	0.137795i	0.375896	−	0.926662i	$-0.377335\pi$
$367$	−87.5912	−	50.5708i	−0.238668	−	0.137795i	−0.614564	+	0.788867i	$0.710668\pi$
$368$	−59.1189	−	140.646i	−0.160649	−	0.382190i
$369$	−60.0907	+	34.6934i	−0.162847	+	0.0940200i
$370$	−10.7278	−	14.9295i	−0.0289942	−	0.0403501i
$371$	−132.079	+	74.7394i	−0.356008	+	0.201454i
$372$	12.3372	+	24.8538i	0.0331646	+	0.0668114i
$373$	−2.11033	+	7.87584i	−0.00565771	+	0.0211149i	−0.968697	−	0.248246i	$-0.920146\pi$
$373$	−2.11033	+	7.87584i	−0.00565771	+	0.0211149i	0.963039	+	0.269361i	$0.0868125\pi$
$374$	−292.655	+	357.550i	−0.782499	+	0.956017i
$375$	−537.125	−	310.109i	−1.43233	−	0.826958i
$376$	457.656	−	492.482i	1.21717	−	1.30979i
$377$	499.551			1.32507
$378$	−41.9372	−	59.4413i	−0.110945	−	0.157252i
$379$	401.529	+	401.529i	1.05944	+	1.05944i	0.998118	+	0.0613258i	$0.0195329\pi$
$379$	401.529	+	401.529i	1.05944	+	1.05944i	0.0613258	+	0.998118i	$0.480467\pi$
$380$	−670.464	+	135.182i	−1.76438	+	0.355743i
$381$	249.604	−	66.8811i	0.655127	−	0.175541i
$382$	−191.974	+	19.1606i	−0.502549	+	0.0501586i
$383$	49.5231	−	28.5922i	0.129303	−	0.0746531i	−0.433953	−	0.900935i	$-0.642882\pi$
$383$	49.5231	−	28.5922i	0.129303	−	0.0746531i	0.563256	+	0.826282i	$0.309548\pi$
$384$	93.3378	+	201.097i	0.243067	+	0.523690i
$385$	992.100	−	256.651i	2.57688	−	0.666627i
$386$	51.8339	+	72.1352i	0.134285	+	0.186879i
$387$	86.6508	+	23.2180i	0.223904	+	0.0599949i
$388$	−343.982	+	303.255i	−0.886552	+	0.781585i
$389$	1.13034	−	0.302874i	0.00290576	−	0.000778595i	−0.257366	−	0.966314i	$-0.582855\pi$
$389$	1.13034	−	0.302874i	0.00290576	−	0.000778595i	0.260272	+	0.965535i	$0.416188\pi$
$390$	373.752	−	141.227i	0.958340	−	0.362121i
$391$	−141.273			−0.361313
$392$	271.777	−	282.491i	0.693308	−	0.720642i
$393$			140.274i			0.356932i
$394$	−606.211	+	229.065i	−1.53861	+	0.581383i
$395$	−53.3120	−	198.963i	−0.134967	−	0.503704i
$396$	−186.749	−	11.7511i	−0.471588	−	0.0296744i
$397$	−48.8099	+	182.161i	−0.122947	+	0.458844i	−0.999758	−	0.0219905i	$-0.993000\pi$
$397$	−48.8099	+	182.161i	−0.122947	+	0.458844i	0.876811	+	0.480835i	$0.159666\pi$
$398$	307.941	+	428.550i	0.773722	+	1.07676i
$399$	−55.3043	−	213.782i	−0.138607	−	0.535794i
$400$	−610.818	+	804.690i	−1.52704	+	2.01172i
$401$	43.4263	+	75.2165i	0.108295	+	0.187572i	0.915080	−	0.403273i	$-0.132128\pi$
$401$	43.4263	+	75.2165i	0.108295	+	0.187572i	−0.806785	+	0.590846i	$0.798794\pi$
$402$	28.2638	−	2.82096i	0.0703079	−	0.00701731i
$403$	−12.7346	−	47.5260i	−0.0315994	−	0.117931i
$404$	386.807	−	582.179i	0.957442	−	1.44104i
$405$	−59.7471	+	59.7471i	−0.147524	+	0.147524i
$406$	−328.180	−	465.158i	−0.808326	−	1.14571i
$407$		−	15.2672i		−	0.0375115i
$408$	205.155	−	7.51968i	0.502831	−	0.0184306i
$409$	73.8086	−	127.840i	0.180461	−	0.312568i	−0.761577	−	0.648075i	$-0.775574\pi$
$409$	73.8086	−	127.840i	0.180461	−	0.312568i	0.942038	+	0.335507i	$0.108908\pi$
$410$	−275.069	+	336.066i	−0.670901	+	0.819672i
$411$	−12.0642	−	3.23260i	−0.0293534	−	0.00786521i
$412$	245.078	−	728.211i	0.594849	−	1.76750i
$413$	−65.0322	−	114.925i	−0.157463	−	0.278268i
$414$	−33.3854	−	46.4612i	−0.0806411	−	0.112225i
$415$	−651.742	−	1128.85i	−1.57046	−	2.72012i
$416$	−91.7648	−	382.269i	−0.220589	−	0.918917i
$417$	−1.09794	+	1.90168i	−0.00263294	+	0.00456039i
$418$	−517.670	−	233.740i	−1.23844	−	0.559186i
$419$	−132.535	−	132.535i	−0.316312	−	0.316312i	0.531037	−	0.847349i	$-0.321803\pi$
$419$	−132.535	−	132.535i	−0.316312	−	0.316312i	−0.847349	+	0.531037i	$0.821803\pi$
$420$	−377.041	−	255.241i	−0.897717	−	0.607718i
$421$	132.979	+	132.979i	0.315865	+	0.315865i	0.847177	−	0.531311i	$-0.178301\pi$
$421$	132.979	+	132.979i	0.315865	+	0.315865i	−0.531311	+	0.847177i	$0.678301\pi$
$422$	−162.277	−	429.460i	−0.384543	−	1.01768i
$423$	126.056	−	218.336i	0.298006	−	0.516161i
$424$	146.926	−	92.1632i	0.346522	−	0.217366i
$425$	467.742	+	810.152i	1.10057	+	1.90624i
$426$	76.8900	+	12.5916i	0.180493	+	0.0295578i
$427$	6.69578	−	773.694i	0.0156810	−	1.81193i
$428$	107.247	−	53.2365i	0.250577	−	0.124384i
$429$	320.497	+	85.8770i	0.747080	+	0.200179i
$430$	558.695	−	55.7624i	1.29929	−	0.129680i
$431$	−375.701	+	650.734i	−0.871697	+	1.50982i	−0.0114569	+	0.999934i	$0.503647\pi$
$431$	−375.701	+	650.734i	−0.871697	+	1.50982i	−0.860240	+	0.509889i	$0.829686\pi$
$432$	50.9548	+	65.6933i	0.117951	+	0.152068i
$433$		−	127.109i		−	0.293555i	−0.989170	−	0.146777i	$-0.953110\pi$
$433$		−	127.109i		−	0.293555i	0.989170	−	0.146777i	$-0.0468901\pi$
$434$	−35.8880	+	43.0801i	−0.0826913	+	0.0992628i
$435$	−467.552	+	467.552i	−1.07483	+	1.07483i
$436$	−79.0689	+	119.006i	−0.181351	+	0.272949i
$437$	−44.9482	−	167.749i	−0.102856	−	0.383865i
$438$	−89.3976	−	73.1718i	−0.204104	−	0.167059i
$439$	198.342	+	343.539i	0.451804	+	0.782548i	0.998498	−	0.0547844i	$-0.0174472\pi$
$439$	198.342	+	343.539i	0.451804	+	0.782548i	−0.546694	+	0.837333i	$0.684114\pi$
$440$	−1119.39	+	344.350i	−2.54406	+	0.782614i
$441$	75.6923	−	126.015i	0.171638	−	0.285747i
$442$	−359.246	−	58.8306i	−0.812774	−	0.133101i
$443$	58.0185	−	216.528i	0.130967	−	0.488776i	−0.869015	−	0.494786i	$-0.835246\pi$
$443$	58.0185	−	216.528i	0.130967	−	0.488776i	0.999982	+	0.00600999i	$0.00191305\pi$
$444$	−5.08832	+	4.48587i	−0.0114602	+	0.0101033i
$445$	227.226	+	848.019i	0.510620	+	1.90566i
$446$	366.366	+	165.423i	0.821449	+	0.370903i
$447$		−	408.849i		−	0.914651i
$448$	−295.666	+	336.579i	−0.659969	+	0.751293i
$449$	−105.243			−0.234395			−0.117197	−	0.993109i	$-0.537391\pi$
$449$	−105.243			−0.234395			−0.117197	+	0.993109i	$0.537391\pi$
$450$	−155.903	+	345.282i	−0.346451	+	0.767293i
$451$	−348.364	+	93.3439i	−0.772426	+	0.206971i
$452$	437.368	+	496.106i	0.967627	+	1.09758i
$453$	192.475	+	51.5736i	0.424890	+	0.113849i
$454$	−31.3024	+	191.147i	−0.0689480	+	0.421028i
$455$	565.935	+	575.816i	1.24381	+	1.26553i
$456$	74.2020	+	241.210i	0.162724	+	0.528969i
$457$	−78.1493	+	45.1195i	−0.171005	+	0.0987297i	−0.583060	−	0.812429i	$-0.698145\pi$
$457$	−78.1493	+	45.1195i	−0.171005	+	0.0987297i	0.412055	+	0.911159i	$0.364811\pi$
$458$	48.3272	−	59.0437i	0.105518	−	0.128916i
$459$	74.3616	−	19.9251i	0.162008	−	0.0434099i
$460$	−298.255	−	198.164i	−0.648380	−	0.430792i
$461$	−274.248	−	274.248i	−0.594897	−	0.594897i	0.344053	−	0.938950i	$-0.388200\pi$
$461$	−274.248	−	274.248i	−0.594897	−	0.594897i	−0.938950	+	0.344053i	$0.888200\pi$
$462$	−130.586	−	354.849i	−0.282654	−	0.768071i
$463$	763.416			1.64885			0.824423	−	0.565974i	$-0.191500\pi$
$463$	763.416			1.64885			0.824423	+	0.565974i	$0.191500\pi$
$464$	398.748	+	514.083i	0.859370	+	1.10794i
$465$	56.4005	+	32.5629i	0.121291	+	0.0700276i
$466$	82.9706	+	831.299i	0.178048	+	1.78390i
$467$	−147.772	+	551.494i	−0.316429	+	1.18093i	0.606223	+	0.795295i	$0.292684\pi$
$467$	−147.772	+	551.494i	−0.316429	+	1.18093i	−0.922652	+	0.385634i	$0.873983\pi$
$468$	−65.5484	−	132.050i	−0.140061	−	0.282157i
$469$	28.2673	+	49.9538i	0.0602714	+	0.106511i
$470$	255.010	−	1557.21i	0.542575	−	3.31321i
$471$	65.5666	−	37.8549i	0.139207	−	0.0803713i
$472$	80.1929	+	127.843i	0.169900	+	0.270853i
$473$	403.806	+	233.138i	0.853713	+	0.492891i
$474$	−71.0965	+	26.8647i	−0.149993	+	0.0566767i
$475$	−813.161	+	813.161i	−1.71192	+	1.71192i
$476$	181.227	+	373.162i	0.380728	+	0.783953i
$477$	45.9900	−	45.9900i	0.0964151	−	0.0964151i
$478$	200.081	−	443.124i	0.418579	−	0.927037i
$479$	−176.451	−	101.874i	−0.368375	−	0.212681i	0.304373	−	0.952553i	$-0.401553\pi$
$479$	−176.451	−	101.874i	−0.368375	−	0.212681i	−0.672748	+	0.739872i	$0.734886\pi$
$480$	443.669	+	271.896i	0.924311	+	0.566450i
$481$	10.4169	−	6.01422i	0.0216568	−	0.0125036i
$482$	490.362	−	352.358i	1.01735	−	0.731032i
$483$	58.6693	−	99.6173i	0.121469	−	0.206247i
$484$	−463.067	−	155.844i	−0.956751	−	0.321993i
$485$	−278.569	+	1039.63i	−0.574368	+	2.14357i
$486$	24.1259	+	19.7470i	0.0496417	+	0.0406316i
$487$	−528.022	−	304.854i	−1.08423	−	0.625983i	−0.152199	−	0.988350i	$-0.548635\pi$
$487$	−528.022	−	304.854i	−1.08423	−	0.625983i	−0.932036	+	0.362367i	$0.881969\pi$
$488$	32.3894	+	883.662i	0.0663718	+	1.81078i
$489$	67.7492			0.138546
$490$	164.382	−	905.255i	0.335473	−	1.84746i
$491$	372.226	+	372.226i	0.758098	+	0.758098i	0.975976	−	0.217878i	$-0.0699135\pi$
$491$	372.226	+	372.226i	0.758098	+	0.758098i	−0.217878	+	0.975976i	$0.569913\pi$
$492$	133.468	+	88.6778i	0.271276	+	0.180239i
$493$	581.918	−	155.924i	1.18036	−	0.316277i
$494$	−44.4435	−	445.289i	−0.0899666	−	0.901394i
$495$	−380.343	+	219.591i	−0.768371	+	0.443619i
$496$	38.7437	−	51.0409i	0.0781123	−	0.102905i
$497$	39.4317	+	152.425i	0.0793394	+	0.306691i
$498$	−390.579	+	280.657i	−0.784296	+	0.563568i
$499$	−299.327	−	80.2044i	−0.599853	−	0.160730i	−0.0539008	−	0.998546i	$-0.517165\pi$
$499$	−299.327	−	80.2044i	−0.599853	−	0.160730i	−0.545953	+	0.837816i	$0.683832\pi$
$500$	−89.9509	+	1429.51i	−0.179902	+	2.85901i
$501$	−61.4328	+	16.4609i	−0.122620	+	0.0328560i
$502$	77.3502	+	204.705i	0.154084	+	0.407778i
$503$	−298.261			−0.592964			−0.296482	−	0.955038i	$-0.595813\pi$
$503$	−298.261			−0.592964			−0.296482	+	0.955038i	$0.595813\pi$
$504$	−79.8963	+	147.786i	−0.158524	+	0.293225i
$505$		−	1640.53i		−	3.24858i
$506$	−105.113	−	278.176i	−0.207732	−	0.549756i
$507$	−8.10131	−	30.2345i	−0.0159789	−	0.0596341i
$508$	−394.646	−	447.647i	−0.776863	−	0.881195i
$509$	98.4583	−	367.451i	0.193435	−	0.721908i	−0.799232	−	0.601023i	$-0.794760\pi$
$509$	98.4583	−	367.451i	0.193435	−	0.721908i	0.992666	−	0.120885i	$-0.0385733\pi$
$510$	391.296	−	281.172i	0.767247	−	0.551317i
$511$	62.3690	−	224.959i	0.122053	−	0.440233i
$512$	320.142	−	399.566i	0.625277	−	0.780403i
$513$	47.3185	+	81.9580i	0.0922387	+	0.159762i
$514$	−33.5442	−	336.086i	−0.0652611	−	0.653864i
$515$	−466.747	−	1741.93i	−0.906306	−	3.38238i
$516$	−40.9468	−	203.084i	−0.0793543	−	0.393573i
$517$	926.602	−	926.602i	1.79227	−	1.79227i
$518$	−12.4436	−	5.74872i	−0.0240223	−	0.0110979i
$519$			155.237i			0.299107i
$520$	−675.915	−	628.117i	−1.29984	−	1.20792i
$521$	−177.915	+	308.158i	−0.341487	+	0.591473i	−0.984709	−	0.174207i	$-0.944264\pi$
$521$	−177.915	+	308.158i	−0.341487	+	0.591473i	0.643222	+	0.765680i	$0.277597\pi$
$522$	188.797	+	154.530i	0.361680	+	0.296035i
$523$	−107.507	−	28.8064i	−0.205558	−	0.0550792i	0.154570	−	0.987982i	$-0.450601\pi$
$523$	−107.507	−	28.8064i	−0.205558	−	0.0550792i	−0.360129	+	0.932903i	$0.617267\pi$
$524$	290.167	−	144.036i	0.553753	−	0.274879i
$525$	−765.518	−	6.62502i	−1.45813	−	0.0126191i
$526$	−340.952	+	244.996i	−0.648198	+	0.465773i
$527$	−29.6685	−	51.3873i	−0.0562970	−	0.0975092i
$528$	167.450	+	398.369i	0.317139	+	0.754486i
$529$	−219.038	+	379.386i	−0.414061	+	0.717175i
$530$	167.520	−	371.011i	0.316075	−	0.700020i
$531$	40.0168	+	40.0168i	0.0753611	+	0.0753611i
$532$	−385.435	+	333.916i	−0.724501	+	0.627662i
$533$	−200.921	−	200.921i	−0.376963	−	0.376963i
$534$	303.027	−	114.503i	0.567467	−	0.214425i
$535$	140.512	−	243.374i	0.262640	−	0.454905i
$536$	−34.8572	−	55.5689i	−0.0650320	−	0.103673i
$537$	−74.9925	−	129.891i	−0.139651	−	0.241882i
$538$	66.1351	−	403.850i	0.122928	−	0.750651i
$539$	549.546	−	530.844i	1.01957	−	0.984869i
$540$	184.941	+	62.2414i	0.342483	+	0.115262i
$541$	721.561	+	193.342i	1.33375	+	0.357378i	0.854114	−	0.520087i	$-0.174100\pi$
$541$	721.561	+	193.342i	1.33375	+	0.357378i	0.479641	+	0.877465i	$0.340767\pi$
$542$	−38.5002	−	385.741i	−0.0710335	−	0.711700i
$543$	−197.056	+	341.311i	−0.362902	+	0.628565i
$544$	−226.212	−	416.656i	−0.415832	−	0.765911i
$545$			335.348i			0.615318i
$546$	190.675	−	228.886i	0.349221	−	0.419206i
$547$	−97.8219	+	97.8219i	−0.178833	+	0.178833i	−0.790847	−	0.612014i	$-0.790360\pi$
$547$	−97.8219	+	97.8219i	−0.178833	+	0.178833i	0.612014	+	0.790847i	$0.290360\pi$
$548$	5.70095	+	28.2750i	0.0104032	+	0.0515967i
$549$	85.8233	+	320.297i	0.156327	+	0.583419i
$550$	−1247.23	+	1523.80i	−2.26768	+	2.77054i
$551$	370.291	+	641.363i	0.672035	+	1.16400i
$552$	−61.8273	+	116.767i	−0.112006	+	0.211535i
$553$	−107.654	−	109.534i	−0.194673	−	0.198072i
$554$	109.972	−	671.538i	0.198505	−	1.21216i
$555$	−4.12070	+	15.3786i	−0.00742468	+	0.0277093i
$556$	5.06114	+	0.318470i	0.00910277	+	0.000572787i
$557$	−155.604	−	580.720i	−0.279360	−	1.04259i	−0.952863	−	0.303401i	$-0.901878\pi$
$557$	−155.604	−	580.720i	−0.279360	−	1.04259i	0.673503	−	0.739185i	$-0.264789\pi$
$558$	9.88879	−	21.9010i	0.0177219	−	0.0392490i
$559$			367.361i			0.657175i
$560$	−140.831	+	1042.02i	−0.251483	+	1.86075i
$561$	400.146			0.713273
$562$	149.870	+	67.6699i	0.266673	+	0.120409i
$563$	345.845	−	92.6690i	0.614290	−	0.164599i	0.0617594	−	0.998091i	$-0.480329\pi$
$563$	345.845	−	92.6690i	0.614290	−	0.164599i	0.552531	+	0.833493i	$0.313662\pi$
$564$	−581.080	−	36.5642i	−1.03028	−	0.0648301i
$565$	1499.40	+	401.764i	2.65381	+	0.711086i
$566$	317.647	+	52.0183i	0.561214	+	0.0919051i
$567$	−16.8316	+	60.7099i	−0.0296854	+	0.107072i
$568$	−52.9057	−	171.982i	−0.0931438	−	0.302784i
$569$	−638.798	+	368.810i	−1.12267	+	0.648172i	−0.942081	−	0.335387i	$-0.891133\pi$
$569$	−638.798	+	368.810i	−1.12267	+	0.648172i	−0.180587	+	0.983559i	$0.557800\pi$
$570$	458.362	+	375.168i	0.804143	+	0.658190i
$571$	65.6940	−	17.6027i	0.115051	−	0.0308278i	−0.200834	−	0.979625i	$-0.564365\pi$
$571$	65.6940	−	17.6027i	0.115051	−	0.0308278i	0.315885	+	0.948797i	$0.397699\pi$
$572$	−151.451	−	751.151i	−0.264774	−	1.31320i
$573$	118.144	+	118.144i	0.206184	+	0.206184i
$574$	−55.0930	+	319.083i	−0.0959809	+	0.555895i
$575$	−602.074			−1.04709
$576$	83.5694	−	172.859i	0.145086	−	0.300102i
$577$	442.753	+	255.624i	0.767337	+	0.443022i	0.831924	−	0.554890i	$-0.187240\pi$
$577$	442.753	+	255.624i	0.767337	+	0.443022i	−0.0645869	+	0.997912i	$0.520573\pi$
$578$	138.301	−	13.8036i	0.239275	−	0.0238816i
$579$	19.9100	−	74.3053i	0.0343869	−	0.128334i
$580$	1447.25	+	487.071i	2.49527	+	0.839777i
$581$	−837.439	−	493.208i	−1.44138	−	0.848894i
$582$	391.914	+	64.1803i	0.673391	+	0.110275i
$583$	292.767	−	169.029i	0.502174	−	0.289930i
$584$	−59.5656	+	260.059i	−0.101996	+	0.445307i
$585$	−299.659	−	173.008i	−0.512237	−	0.295740i
$586$	−79.5175	−	210.440i	−0.135695	−	0.359113i
$587$	426.246	−	426.246i	0.726143	−	0.726143i	−0.243706	−	0.969849i	$-0.578363\pi$
$587$	426.246	−	426.246i	0.726143	−	0.726143i	0.969849	+	0.243706i	$0.0783633\pi$
$588$	−338.392	−	27.1803i	−0.575497	−	0.0462250i
$589$	51.5782	−	51.5782i	0.0875691	−	0.0875691i
$590$	322.823	+	145.762i	0.547158	+	0.247055i
$591$	486.034	+	280.612i	0.822393	+	0.474809i
$592$	14.5041	+	5.91935i	0.0245002	+	0.00999890i
$593$	459.114	−	265.070i	0.774222	−	0.446997i	−0.0601564	−	0.998189i	$-0.519160\pi$
$593$	459.114	−	265.070i	0.774222	−	0.446997i	0.834379	+	0.551191i	$0.185827\pi$
$594$	94.5616	+	131.598i	0.159195	+	0.221545i
$595$	838.976	+	494.113i	1.41004	+	0.830442i
$596$	−845.732	+	419.815i	−1.41901	+	0.704387i
$597$	118.284	−	441.442i	0.198131	−	0.739434i
$598$	148.395	−	181.302i	0.248153	−	0.303180i
$599$	157.423	+	90.8882i	0.262810	+	0.151733i	0.625616	−	0.780131i	$-0.284848\pi$
$599$	157.423	+	90.8882i	0.262810	+	0.151733i	−0.362806	+	0.931865i	$0.618181\pi$
$600$	874.323	−	32.0471i	1.45721	−	0.0534119i
$601$	−522.041			−0.868621			−0.434311	−	0.900763i	$-0.643008\pi$
$601$	−522.041			−0.868621			−0.434311	+	0.900763i	$0.643008\pi$
$602$	342.069	−	241.338i	0.568221	−	0.400894i
$603$	−17.3939	−	17.3939i	−0.0288457	−	0.0288457i
$604$	−90.9542	−	451.105i	−0.150586	−	0.746863i
$605$	−1107.69	+	296.804i	−1.83089	+	0.490584i
$606$	−602.328	+	60.1174i	−0.993941	+	0.0992036i
$607$	538.593	−	310.957i	0.887303	−	0.512285i	0.0142438	−	0.999899i	$-0.495466\pi$
$607$	538.593	−	310.957i	0.887303	−	0.512285i	0.873059	+	0.487614i	$0.162133\pi$
$608$	422.767	−	401.171i	0.695340	−	0.659821i
$609$	−131.716	+	475.086i	−0.216282	+	0.780109i
$610$	1211.09	+	1685.42i	1.98539	+	2.76299i
$611$	997.247	+	267.211i	1.63215	+	0.437335i
$612$	−117.573	−	133.363i	−0.192112	−	0.217913i
$613$	704.987	−	188.901i	1.15006	−	0.308158i	0.367071	−	0.930193i	$-0.380361\pi$
$613$	704.987	−	188.901i	1.15006	−	0.308158i	0.782989	+	0.622036i	$0.213694\pi$
$614$	−1103.61	+	417.012i	−1.79740	+	0.679172i
$615$	376.102			0.611547
$616$	−599.940	+	634.493i	−0.973929	+	1.03002i
$617$		−	1060.66i		−	1.71906i	−0.511082	−	0.859532i	$-0.670755\pi$
$617$		−	1060.66i		−	1.71906i	0.511082	−	0.859532i	$-0.329245\pi$
$618$	−622.451	+	235.201i	−1.00720	+	0.380585i
$619$	272.287	+	1016.19i	0.439882	+	1.64166i	0.729106	+	0.684401i	$0.239936\pi$
$619$	272.287	+	1016.19i	0.439882	+	1.64166i	−0.289224	+	0.957261i	$0.593397\pi$
$620$	9.44525	−	150.104i	0.0152343	−	0.242104i
$621$	−12.8238	+	47.8589i	−0.0206502	+	0.0770675i
$622$	690.789	+	961.344i	1.11059	+	1.54557i
$623$	458.843	+	466.855i	0.736506	+	0.749365i
$624$	−205.847	+	271.182i	−0.329883	+	0.434587i
$625$	891.641	+	1544.37i	1.42662	+	2.47099i
$626$	244.568	−	24.4099i	0.390684	−	0.0389935i
$627$	127.312	+	475.136i	0.203050	+	0.757792i
$628$	−145.631	−	96.7588i	−0.231896	−	0.154074i
$629$	10.2573	−	10.2573i	0.0163073	−	0.0163073i
$630$	35.7640	+	392.686i	0.0567682	+	0.623311i
$631$		−	36.5138i		−	0.0578666i	−0.999581	−	0.0289333i	$-0.990789\pi$
$631$		−	36.5138i		−	0.0578666i	0.999581	−	0.0289333i	$-0.00921103\pi$
$632$	128.575	+	119.483i	0.203441	+	0.189055i
$633$	−198.795	+	344.323i	−0.314052	+	0.543954i
$634$	−147.780	+	180.550i	−0.233092	+	0.284779i
$635$	−1352.94	−	362.520i	−2.13062	−	0.570898i
$636$	−142.357	−	47.9100i	−0.223832	−	0.0753301i
$637$	578.684	+	165.844i	0.908451	+	0.260352i
$638$	739.993	+	1029.82i	1.15986	+	1.61414i
$639$	−33.7378	−	58.4356i	−0.0527979	−	0.0914486i
$640$	106.866	−	1196.95i	0.166978	−	1.87023i
$641$	−371.141	+	642.835i	−0.579003	+	1.00286i	0.416591	+	0.909094i	$0.363225\pi$
$641$	−371.141	+	642.835i	−0.579003	+	1.00286i	−0.995594	+	0.0937683i	$0.970109\pi$
$642$	−94.5050	−	42.6712i	−0.147204	−	0.0664661i
$643$	−777.060	−	777.060i	−1.20849	−	1.20849i	−0.971516	−	0.236976i	$-0.923844\pi$
$643$	−777.060	−	777.060i	−1.20849	−	1.20849i	−0.236976	−	0.971516i	$-0.576156\pi$
$644$	−266.308	−	19.0724i	−0.413522	−	0.0296155i
$645$	−343.829	−	343.829i	−0.533068	−	0.533068i
$646$	−190.759	−	504.836i	−0.295292	−	0.781480i
$647$	184.073	−	318.823i	0.284502	−	0.492772i	−0.687986	−	0.725724i	$-0.741505\pi$
$647$	184.073	−	318.823i	0.284502	−	0.492772i	0.972488	+	0.232952i	$0.0748385\pi$
$648$	16.0750	−	70.1826i	0.0248072	−	0.108306i
$649$	147.075	+	254.742i	0.226619	+	0.392515i
$650$	−1531.02	−	250.722i	−2.35542	−	0.385726i
$651$	48.5562	+	0.420220i	0.0745871	+	0.000645499i
$652$	−69.5663	−	140.144i	−0.106697	−	0.214944i
$653$	−543.679	−	145.678i	−0.832586	−	0.223091i	−0.182745	−	0.983160i	$-0.558498\pi$
$653$	−543.679	−	145.678i	−0.832586	−	0.223091i	−0.649842	+	0.760070i	$0.725165\pi$
$654$	123.125	−	12.2889i	0.188264	−	0.0187903i
$655$	380.169	−	658.472i	0.580411	−	1.00530i
$656$	46.3883	−	367.144i	0.0707139	−	0.559670i
$657$			100.048i			0.152280i
$658$	−406.327	−	1104.13i	−0.617518	−	1.67801i
$659$	266.102	−	266.102i	0.403797	−	0.403797i	−0.475772	−	0.879569i	$-0.657831\pi$
$659$	266.102	−	266.102i	0.403797	−	0.403797i	0.879569	+	0.475772i	$0.157831\pi$
$660$	844.784	+	561.285i	1.27998	+	0.850432i
$661$	−184.051	−	686.887i	−0.278443	−	1.03916i	−0.953499	−	0.301397i	$-0.902547\pi$
$661$	−184.051	−	686.887i	−0.278443	−	1.03916i	0.675056	−	0.737767i	$-0.264120\pi$
$662$	229.144	+	187.554i	0.346140	+	0.283315i
$663$	157.630	+	273.023i	0.237753	+	0.411800i
$664$	981.613	+	519.756i	1.47833	+	0.782764i
$665$	−319.780	+	1153.41i	−0.480872	+	1.73446i
$666$	5.79734	+	0.949380i	0.00870472	+	0.00142550i
$667$	−100.352	+	374.520i	−0.150453	+	0.561500i
$668$	97.1309	+	110.176i	0.145406	+	0.164933i
$669$	−90.1017	−	336.264i	−0.134681	−	0.502637i
$670$	−140.320	−	63.3579i	−0.209433	−	0.0945641i
$671$			1723.54i			2.56862i
$672$	387.744	+	13.5216i	0.577000	+	0.0201215i
$673$	−840.334			−1.24864			−0.624320	−	0.781169i	$-0.714624\pi$
$673$	−840.334			−1.24864			−0.624320	+	0.781169i	$0.714624\pi$
$674$	−278.087	+	615.886i	−0.412592	+	0.913778i
$675$	316.912	−	84.9163i	0.469499	−	0.125802i
$676$	−54.2235	+	47.8035i	−0.0802123	+	0.0707153i
$677$	−1059.56	−	283.907i	−1.56508	−	0.419361i	−0.630810	−	0.775937i	$-0.717277\pi$
$677$	−1059.56	−	283.907i	−1.56508	−	0.419361i	−0.934266	+	0.356576i	$0.883944\pi$
$678$	92.5636	−	565.235i	0.136525	−	0.833680i
$679$	200.986	+	776.923i	0.296003	+	1.14422i
$680$	−983.414	−	520.709i	−1.44620	−	0.765749i
$681$	145.270	−	83.8714i	0.213318	−	0.123159i
$682$	79.1106	−	96.6532i	0.115998	−	0.141720i
$683$	−940.272	+	251.945i	−1.37668	+	0.368880i	−0.869914	−	0.493204i	$-0.835826\pi$
$683$	−940.272	+	251.945i	−1.37668	+	0.368880i	−0.506765	+	0.862084i	$0.669159\pi$
$684$	120.948	−	182.038i	0.176825	−	0.266137i
$685$	47.8707	+	47.8707i	0.0698843	+	0.0698843i
$686$	−225.740	−	647.794i	−0.329068	−	0.944306i
$687$	−66.0776			−0.0961829
$688$	−378.048	+	293.232i	−0.549488	+	0.426209i
$689$	230.661	+	133.172i	0.334776	+	0.193283i
$690$	30.7986	+	308.578i	0.0446357	+	0.447214i
$691$	−94.8048	+	353.816i	−0.137199	+	0.512035i	0.862780	+	0.505580i	$0.168721\pi$
$691$	−94.8048	+	353.816i	−0.137199	+	0.512035i	−0.999979	+	0.00645530i	$0.997945\pi$
$692$	321.117	−	159.400i	0.464042	−	0.230347i
$693$	−166.176	+	282.158i	−0.239793	+	0.407155i
$694$	−139.432	+	851.434i	−0.200911	+	1.22685i
$695$	10.3078	−	5.95122i	0.0148314	−	0.00856290i
$696$	125.795	−	549.214i	0.180740	−	0.789101i
$697$	−296.762	−	171.336i	−0.425771	−	0.245819i
$698$	206.282	−	77.9462i	0.295533	−	0.111671i
$699$	511.594	−	511.594i	0.731894	−	0.731894i
$700$	772.345	+	1590.33i	1.10335	+	2.27190i
$701$	491.476	−	491.476i	0.701106	−	0.701106i	−0.263542	−	0.964648i	$-0.584891\pi$
$701$	491.476	−	491.476i	0.701106	−	0.701106i	0.964648	+	0.263542i	$0.0848907\pi$
$702$	−52.5396	+	116.361i	−0.0748428	+	0.165756i
$703$	15.4431	+	8.91606i	0.0219674	+	0.0126829i
$704$	652.112	−	755.434i	0.926295	−	1.07306i
$705$	−1183.46	+	683.272i	−1.67867	+	0.969180i
$706$	908.132	−	652.552i	1.28631	−	0.924295i
$707$	−602.404	−	1064.56i	−0.852056	−	1.50575i
$708$	41.6873	−	123.867i	0.0588804	−	0.174954i
$709$	174.558	−	651.459i	0.246203	−	0.918842i	−0.726572	−	0.687090i	$-0.758888\pi$
$709$	174.558	−	651.459i	0.246203	−	0.918842i	0.972775	−	0.231752i	$-0.0744457\pi$
$710$	−326.810	−	267.493i	−0.460295	−	0.376751i
$711$	57.0021	+	32.9102i	0.0801717	+	0.0462872i
$712$	−548.011	−	509.259i	−0.769679	−	0.715251i
$713$	38.1891			0.0535612
$714$	150.671	−	326.141i	0.211024	−	0.456780i
$715$	−1271.73	−	1271.73i	−1.77864	−	1.77864i
$716$	−191.684	+	288.501i	−0.267715	+	0.402935i
$717$	−406.715	+	108.979i	−0.567245	+	0.151993i
$718$	−73.1295	−	732.699i	−0.101852	−	1.02047i
$719$	−722.269	+	417.002i	−1.00455	+	0.579975i	−0.909590	−	0.415506i	$-0.863604\pi$
$719$	−722.269	+	417.002i	−1.00455	+	0.579975i	−0.0949562	+	0.995481i	$0.530271\pi$
$720$	−61.1503	−	446.473i	−0.0849309	−	0.620101i
$721$	−942.515	−	958.971i	−1.30723	−	1.33006i
$722$	−47.5735	+	34.1847i	−0.0658913	+	0.0473472i
$723$	−505.114	−	135.345i	−0.698636	−	0.187199i
$724$	908.366	+	57.1585i	1.25465	+	0.0789481i
$725$	2480.00	−	664.513i	3.42069	−	0.916570i
$726$	149.564	+	395.815i	0.206011	+	0.545200i
$727$	479.467			0.659515			0.329758	−	0.944066i	$-0.393033\pi$
$727$	479.467			0.659515			0.329758	+	0.944066i	$0.393033\pi$
$728$	−669.256	−	159.398i	−0.919307	−	0.218954i
$729$		−	27.0000i		−	0.0370370i
$730$	221.339	+	585.766i	0.303204	+	0.802419i
$731$	114.664	+	427.932i	0.156859	+	0.585406i
$732$	574.431	−	506.419i	0.784741	−	0.691829i
$733$	−173.230	+	646.502i	−0.236330	+	0.881995i	0.741215	+	0.671267i	$0.234250\pi$
$733$	−173.230	+	646.502i	−0.236330	+	0.881995i	−0.977545	+	0.210727i	$0.932417\pi$
$734$	164.271	−	118.040i	0.223803	−	0.160817i
$735$	−696.836	+	386.395i	−0.948076	+	0.525707i
$736$	305.027	+	7.99488i	0.414439	+	0.0108626i
$737$	−63.9288	−	110.728i	−0.0867419	−	0.150241i
$738$	−13.7823	−	138.087i	−0.0186752	−	0.187110i
$739$	−98.6111	−	368.021i	−0.133439	−	0.497999i	0.866561	−	0.499071i	$-0.166325\pi$
$739$	−98.6111	−	368.021i	−0.133439	−	0.497999i	−0.999999	+	0.00107204i	$0.999659\pi$
$740$	36.0430	−	7.26717i	0.0487067	−	0.00982051i
$741$	−274.037	+	274.037i	−0.369821	+	0.369821i
$742$	−27.5291	−	302.268i	−0.0371013	−	0.407369i
$743$		−	517.706i		−	0.696777i	−0.937350	−	0.348389i	$-0.886729\pi$
$743$		−	517.706i		−	0.696777i	0.937350	−	0.348389i	$-0.113271\pi$
$744$	−55.4576	+	2.03272i	−0.0745398	+	0.00273216i
$745$	−1108.06	+	1919.21i	−1.48732	+	2.57612i
$746$	−12.6192	−	10.3288i	−0.0169159	−	0.0138456i
$747$	402.329	+	107.804i	0.538593	+	0.144316i
$748$	−410.878	−	827.729i	−0.549302	−	1.10659i
$749$	1.81329	−	209.525i	0.00242095	−	0.279740i
$750$	1007.34	−	723.841i	1.34312	−	0.965121i
$751$	378.094	+	654.879i	0.503454	+	0.872009i	0.999992	+	0.00399348i	$0.00127117\pi$
$751$	378.094	+	654.879i	0.503454	+	0.872009i	−0.496538	+	0.868015i	$0.665396\pi$
$752$	521.030	+	1239.55i	0.692858	+	1.64834i
$753$	94.7566	−	164.123i	0.125839	−	0.217959i
$754$	−411.149	+	910.583i	−0.545291	+	1.20767i
$755$	−763.739	−	763.739i	−1.01158	−	1.01158i
$756$	142.866	−	27.5209i	0.188976	−	0.0364033i
$757$	−890.330	−	890.330i	−1.17613	−	1.17613i	−0.980722	−	0.195408i	$-0.937397\pi$
$757$	−890.330	−	890.330i	−1.17613	−	1.17613i	−0.195408	−	0.980722i	$-0.562603\pi$
$758$	−1062.38	+	401.435i	−1.40156	+	0.529597i
$759$	−128.766	+	223.030i	−0.169653	+	0.293847i
$760$	305.406	−	1333.38i	0.401850	−	1.75445i
$761$	75.3853	+	130.571i	0.0990609	+	0.171578i	0.911296	−	0.411751i	$-0.135083\pi$
$761$	75.3853	+	130.571i	0.0990609	+	0.171578i	−0.812235	+	0.583330i	$0.801749\pi$
$762$	−83.5221	+	510.024i	−0.109609	+	0.669322i
$763$	123.140	+	217.612i	0.161389	+	0.285206i
$764$	123.076	−	365.700i	0.161094	−	0.478665i
$765$	−403.067	−	108.002i	−0.526886	−	0.141179i
$766$	11.3585	+	113.803i	0.0148283	+	0.148568i
$767$	−115.875	+	200.702i	−0.151076	+	0.261671i
$768$	−443.381	+	4.62588i	−0.577319	+	0.00602328i
$769$		−	835.155i		−	1.08603i	−0.839724	−	0.543014i	$-0.817283\pi$
$769$		−	835.155i		−	1.08603i	0.839724	−	0.543014i	$-0.182717\pi$
$770$	−348.711	+	2019.64i	−0.452872	+	2.62290i
$771$	−206.832	+	206.832i	−0.268265	+	0.268265i
$772$	−174.149	+	35.1129i	−0.225582	+	0.0454831i
$773$	−367.991	−	1373.36i	−0.476056	−	1.77666i	−0.617341	−	0.786695i	$-0.711790\pi$
$773$	−367.991	−	1373.36i	−0.476056	−	1.77666i	0.141285	−	0.989969i	$-0.454876\pi$
$774$	−113.639	+	138.838i	−0.146820	+	0.179377i
$775$	−126.440	−	219.001i	−0.163149	−	0.282582i
$776$	−269.664	−	876.602i	−0.347505	−	1.12964i
$777$	2.97306	+	11.4925i	0.00382634	+	0.0147909i
$778$	−0.378233	+	2.30966i	−0.000486161	+	0.00296872i
$779$	109.026	−	406.891i	0.139956	−	0.522324i
$780$	−50.1831	+	797.512i	−0.0643373	+	1.02245i
$781$	−90.7730	−	338.770i	−0.116227	−	0.433764i
$782$	116.273	−	257.513i	0.148687	−	0.329301i
$783$		−	211.289i		−	0.269845i
$784$	291.244	+	727.896i	0.371484	+	0.928439i
$785$	−410.375			−0.522771
$786$	−255.692	−	115.451i	−0.325308	−	0.146884i
$787$	329.683	−	88.3383i	0.418911	−	0.112247i	−0.0432053	−	0.999066i	$-0.513757\pi$
$787$	329.683	−	88.3383i	0.418911	−	0.112247i	0.462116	+	0.886819i	$0.347090\pi$
$788$	81.3949	−	1293.53i	0.103293	−	1.64154i
$789$	351.209	+	94.1061i	0.445132	+	0.119273i
$790$	406.548	+	66.5768i	0.514618	+	0.0842745i
$791$	1120.51	−	289.871i	1.41658	−	0.366461i
$792$	175.121	−	330.735i	0.221113	−	0.417594i
$793$	−1175.99	+	678.958i	−1.48296	+	0.856189i
$794$	−291.871	−	238.896i	−0.367596	−	0.300877i
$795$	−340.527	+	91.2439i	−0.428335	+	0.114772i
$796$	−1034.61	+	208.603i	−1.29976	+	0.262065i
$797$	257.753	+	257.753i	0.323404	+	0.323404i	0.850071	−	0.526668i	$-0.176559\pi$
$797$	257.753	+	257.753i	0.323404	+	0.323404i	−0.526668	+	0.850071i	$0.676559\pi$
$798$	435.200	+	75.1417i	0.545363	+	0.0941625i
$799$	1245.08			1.55830
$800$	−964.065	−	1775.69i	−1.20508	−	2.21961i
$801$	−242.954	−	140.270i	−0.303314	−	0.175118i
$802$	−172.846	+	17.2515i	−0.215519	+	0.0215106i
$803$	−134.591	+	502.301i	−0.167610	+	0.625531i
$804$	−18.1201	+	53.8410i	−0.0225374	+	0.0669664i
$805$	−545.386	+	308.617i	−0.677498	+	0.383375i
$806$	97.1116	+	15.9031i	0.120486	+	0.0197309i
$807$	−306.922	+	177.202i	−0.380325	+	0.219581i
$808$	742.840	+	1184.23i	0.919357	+	1.46563i
$809$	−1208.30	−	697.611i	−1.49357	−	0.862313i	−0.493597	−	0.869691i	$-0.664318\pi$
$809$	−1208.30	−	697.611i	−1.49357	−	0.862313i	−0.999973	+	0.00737735i	$0.997652\pi$
$810$	−59.7331	−	158.081i	−0.0737445	−	0.195162i
$811$	−115.420	+	115.420i	−0.142318	+	0.142318i	−0.774676	−	0.632358i	$-0.782087\pi$
$811$	−115.420	+	115.420i	−0.142318	+	0.142318i	0.632358	+	0.774676i	$0.282087\pi$
$812$	1118.00	−	215.365i	1.37684	−	0.265228i
$813$	−237.391	+	237.391i	−0.291994	+	0.291994i
$814$	27.8291	+	12.5655i	0.0341880	+	0.0154367i
$815$	−318.027	−	183.613i	−0.390217	−	0.225292i
$816$	−155.143	+	380.146i	−0.190127	+	0.465865i
$817$	−471.647	+	272.305i	−0.577291	+	0.333299i
$818$	172.280	+	239.756i	0.210612	+	0.293100i
$819$	−257.981	−	2.23265i	−0.314996	−	0.00272607i
$820$	−386.189	−	777.992i	−0.470962	−	0.948770i
$821$	−278.156	+	1038.09i	−0.338801	+	1.26442i	0.560888	+	0.827892i	$0.310460\pi$
$821$	−278.156	+	1038.09i	−0.338801	+	1.26442i	−0.899689	+	0.436531i	$0.856207\pi$
$822$	15.8217	−	19.3302i	0.0192478	−	0.0235160i
$823$	371.294	+	214.367i	0.451147	+	0.260470i	0.708315	−	0.705897i	$-0.249456\pi$
$823$	371.294	+	214.367i	0.451147	+	0.260470i	−0.257167	+	0.966367i	$0.582789\pi$
$824$	1125.68	+	1046.07i	1.36611	+	1.26951i
$825$	1705.33			2.06706
$826$	263.009	−	23.9536i	0.318412	−	0.0289995i
$827$	222.327	+	222.327i	0.268835	+	0.268835i	0.828631	−	0.559796i	$-0.189120\pi$
$827$	222.327	+	222.327i	0.268835	+	0.268835i	−0.559796	+	0.828631i	$0.689120\pi$
$828$	112.167	−	22.6157i	0.135468	−	0.0273137i
$829$	−368.602	+	98.7667i	−0.444635	+	0.119140i	−0.474188	−	0.880424i	$-0.657258\pi$
$829$	−368.602	+	98.7667i	−0.444635	+	0.119140i	0.0295531	+	0.999563i	$0.490592\pi$
$830$	2594.08	−	258.911i	3.12540	−	0.311941i
$831$	−510.362	+	294.658i	−0.614154	+	0.354582i
$832$	772.327	+	147.353i	0.928278	+	0.177107i
$833$	725.862	+	12.5646i	0.871383	+	0.0150836i
$834$	−2.56275	−	3.56648i	−0.00307284	−	0.00427635i
$835$	332.989	+	89.2240i	0.398789	+	0.106855i
$836$	852.124	−	751.233i	1.01929	−	0.898604i
$837$	−20.1015	+	5.38617i	−0.0240161	+	0.00643509i
$838$	350.666	−	132.504i	0.418455	−	0.158119i
$839$	−899.004			−1.07152			−0.535759	−	0.844371i	$-0.679975\pi$
$839$	−899.004			−1.07152			−0.535759	+	0.844371i	$0.679975\pi$
$840$	775.574	−	477.198i	0.923302	−	0.568093i
$841$		−	812.442i		−	0.966043i
$842$	−351.842	+	132.948i	−0.417865	+	0.157896i
$843$	−36.8581	−	137.556i	−0.0437225	−	0.163175i
$844$	916.382	+	57.6629i	1.08576	+	0.0683209i
$845$	−43.9121	+	163.882i	−0.0519670	+	0.193943i
$846$	294.234	+	409.475i	0.347795	+	0.484012i
$847$	−609.807	+	599.343i	−0.719961	+	0.707606i
$848$	47.0701	+	343.670i	0.0555072	+	0.405271i
$849$	−139.377	−	241.409i	−0.164166	−	0.284345i
$850$	−1861.72	+	185.815i	−2.19025	+	0.218606i
$851$	2.41634	+	9.01789i	0.00283941	+	0.0105968i
$852$	−86.2354	+	129.792i	−0.101215	+	0.152338i
$853$	−370.003	+	370.003i	−0.433766	+	0.433766i	−0.889907	−	0.456141i	$-0.849231\pi$
$853$	−370.003	+	370.003i	−0.433766	+	0.433766i	0.456141	+	0.889907i	$0.349231\pi$
$854$	1404.78	+	648.985i	1.64494	+	0.759935i
$855$		−	512.967i		−	0.599961i
$856$	8.77142	+	239.306i	0.0102470	+	0.279563i
$857$	568.661	−	984.951i	0.663549	−	1.14930i	−0.316128	−	0.948717i	$-0.602383\pi$
$857$	568.661	−	984.951i	0.663549	−	1.14930i	0.979677	−	0.200584i	$-0.0642839\pi$
$858$	−420.318	+	513.523i	−0.489881	+	0.598512i
$859$	67.8283	+	18.1745i	0.0789619	+	0.0211578i	0.298084	−	0.954540i	$-0.403653\pi$
$859$	67.8283	+	18.1745i	0.0789619	+	0.0211578i	−0.219122	+	0.975698i	$0.570319\pi$
$860$	−358.183	+	1064.28i	−0.416492	+	1.23754i
$861$	244.058	−	138.105i	0.283459	−	0.160400i
$862$	−876.943	−	1220.41i	−1.01734	−	1.41579i
$863$	−719.174	−	1245.65i	−0.833341	−	1.44339i	−0.895374	−	0.445315i	$-0.853092\pi$
$863$	−719.174	−	1245.65i	−0.833341	−	1.44339i	0.0620324	−	0.998074i	$-0.480242\pi$
$864$	−161.684	+	38.8126i	−0.187134	+	0.0449220i
$865$	420.720	−	728.708i	0.486381	−	0.842437i
$866$	231.695	+	104.616i	0.267546	+	0.120803i
$867$	−85.1124	−	85.1124i	−0.0981689	−	0.0981689i
$868$	−48.9893	−	100.873i	−0.0564392	−	0.116213i
$869$	241.913	+	241.913i	0.278381	+	0.278381i
$870$	−467.442	−	1237.07i	−0.537289	−	1.42192i
$871$	50.3671	−	87.2384i	0.0578268	−	0.100159i
$872$	−151.847	−	242.073i	−0.174137	−	0.277607i
$873$	−171.964	−	297.850i	−0.196981	−	0.341180i
$874$	342.767	+	56.1320i	0.392182	+	0.0642242i
$875$	2159.84	+	1272.03i	2.46838	+	1.45375i
$876$	206.955	−	102.731i	0.236250	−	0.117273i
$877$	587.192	+	157.338i	0.669546	+	0.179404i	0.577550	−	0.816355i	$-0.304009\pi$
$877$	587.192	+	157.338i	0.669546	+	0.179404i	0.0919958	+	0.995759i	$0.470675\pi$
$878$	−789.446	+	78.7933i	−0.899141	+	0.0897418i
$879$	−97.4115	+	168.722i	−0.110821	+	0.191947i
$880$	293.615	−	2323.83i	0.333653	−	2.64072i
$881$		−	238.416i		−	0.270620i	−0.990803	−	0.135310i	$-0.956797\pi$
$881$		−	238.416i		−	0.270620i	0.990803	−	0.135310i	$-0.0432030\pi$
$882$	167.402	+	241.687i	0.189798	+	0.274021i
$883$	468.315	−	468.315i	0.530368	−	0.530368i	−0.390314	−	0.920682i	$-0.627634\pi$
$883$	468.315	−	468.315i	0.530368	−	0.530368i	0.920682	+	0.390314i	$0.127634\pi$
$884$	402.909	−	606.415i	0.455780	−	0.685989i
$885$	−79.3930	−	296.299i	−0.0897096	−	0.334801i
$886$	346.936	+	283.967i	0.391576	+	0.320504i
$887$	−695.397	−	1204.46i	−0.783988	−	1.35791i	−0.929602	−	0.368565i	$-0.879849\pi$
$887$	−695.397	−	1204.46i	−0.783988	−	1.35791i	0.145614	−	0.989341i	$-0.453484\pi$
$888$	−3.98897	−	12.9670i	−0.00449209	−	0.0146025i
$889$	−1011.06	+	261.557i	−1.13730	+	0.294215i
$890$	−1732.79	−	283.764i	−1.94695	−	0.318835i
$891$	36.3223	−	135.557i	0.0407658	−	0.152140i
$892$	−603.067	+	531.664i	−0.676084	+	0.596036i
$893$	396.140	+	1478.41i	0.443605	+	1.65556i
$894$	745.251	+	336.498i	0.833614	+	0.376396i
$895$			812.974i			0.908350i
$896$	−370.173	−	815.958i	−0.413139	−	0.910668i
$897$	−202.901			−0.226199
$898$	86.6192	−	191.838i	0.0964579	−	0.213628i
$899$	−157.304	+	42.1496i	−0.174977	+	0.0468849i
$900$	−501.067	−	568.360i	−0.556741	−	0.631511i
$901$	310.259	+	83.1336i	0.344349	+	0.0922682i
$902$	116.569	−	711.825i	0.129234	−	0.789163i
$903$	−349.370	−	96.8616i	−0.386899	−	0.107266i
$904$	−1264.27	+	388.921i	−1.39853	+	0.430222i
$905$	1850.03	−	1068.12i	2.04423	−	1.18024i
$906$	−252.423	+	308.398i	−0.278613	+	0.340395i
$907$	368.034	−	98.6144i	0.405771	−	0.108726i	−0.0501601	−	0.998741i	$-0.515973\pi$
$907$	368.034	−	98.6144i	0.405771	−	0.108726i	0.455931	+	0.890015i	$0.349306\pi$
$908$	−322.659	−	214.379i	−0.355352	−	0.236100i
$909$	370.682	+	370.682i	0.407791	+	0.407791i
$910$	−1515.39	+	557.670i	−1.66526	+	0.612824i
$911$	1296.80			1.42349			0.711745	−	0.702438i	$-0.247905\pi$
$911$	1296.80			1.42349			0.711745	+	0.702438i	$0.247905\pi$
$912$	−500.749	−	63.2693i	−0.549067	−	0.0693742i
$913$	1874.92	+	1082.48i	2.05358	+	1.18563i
$914$	−17.9241	−	179.586i	−0.0196107	−	0.196483i
$915$	465.194	−	1736.13i	0.508409	−	1.89741i
$916$	67.8499	+	136.686i	0.0740719	+	0.149221i
$917$	4.90604	−	566.890i	0.00535010	−	0.618201i
$918$	−24.8828	+	151.946i	−0.0271055	+	0.165518i
$919$	−647.051	+	373.575i	−0.704082	+	0.406502i	−0.808866	−	0.587993i	$-0.799918\pi$
$919$	−647.051	+	373.575i	−0.704082	+	0.406502i	0.104784	+	0.994495i	$0.466585\pi$
$920$	606.690	−	380.563i	0.659445	−	0.413656i
$921$	884.823	+	510.853i	0.960720	+	0.554672i
$922$	725.615	−	274.183i	0.787002	−	0.297379i
$923$	195.387	−	195.387i	0.211687	−	0.211687i
$924$	754.297	+	54.0211i	0.816339	+	0.0584644i
$925$	43.7142	−	43.7142i	0.0472585	−	0.0472585i
$926$	−628.320	+	1391.56i	−0.678531	+	1.50276i
$927$	499.055	+	288.129i	0.538355	+	0.310819i
$928$	−1265.26	+	303.728i	−1.36342	+	0.327294i
$929$	−16.9566	+	9.78992i	−0.0182526	+	0.0105381i	−0.509099	−	0.860708i	$-0.670021\pi$
$929$	−16.9566	+	9.78992i	−0.0182526	+	0.0105381i	0.490846	+	0.871246i	$0.336688\pi$
$930$	−105.775	+	76.0065i	−0.113737	+	0.0817275i
$931$	216.024	+	865.891i	0.232035	+	0.930065i
$932$	−1583.58	−	532.952i	−1.69912	−	0.571837i
$933$	265.340	−	990.264i	0.284395	−	1.06138i
$934$	−883.643	−	723.260i	−0.946084	−	0.774369i
$935$	−1878.36	−	1084.47i	−2.00894	−	1.15986i
$936$	294.649	−	10.8000i	0.314796	−	0.0115384i
$937$	−1.52100			−0.00162327			−0.000811634	−	1.00000i	$-0.500258\pi$
$937$	−1.52100			−0.00162327			−0.000811634		1.00000i	$0.500258\pi$
$938$	−114.321	+	10.4118i	−0.121877	+	0.0111000i
$939$	−150.511	−	150.511i	−0.160288	−	0.160288i
$940$	2628.60	+	1746.47i	2.79638	+	1.85795i
$941$	334.864	−	89.7265i	0.355860	−	0.0953523i	−0.0764602	−	0.997073i	$-0.524362\pi$
$941$	334.864	−	89.7265i	0.355860	−	0.0953523i	0.432320	+	0.901720i	$0.357695\pi$
$942$	15.0382	+	150.671i	0.0159641	+	0.159948i
$943$	190.995	−	110.271i	0.202540	−	0.116937i
$944$	−299.034	+	40.9565i	−0.316773	+	0.0433862i
$945$	243.546	−	239.366i	0.257720	−	0.253298i
$946$	−757.311	+	544.178i	−0.800540	+	0.575241i
$947$	−769.710	−	206.243i	−0.812788	−	0.217786i	−0.171597	−	0.985167i	$-0.554893\pi$
$947$	−769.710	−	206.243i	−0.812788	−	0.217786i	−0.641191	+	0.767382i	$0.721559\pi$
$948$	9.54600	−	151.706i	0.0100696	−	0.160027i
$949$	−395.745	+	106.039i	−0.417012	+	0.111738i
$950$	−812.970	−	2151.49i	−0.855758	−	2.26473i
$951$	202.059			0.212470
$952$	−829.356	+	23.2141i	−0.871173	+	0.0243845i
$953$			632.383i			0.663571i	0.943355	+	0.331785i	$0.107651\pi$
$953$			632.383i			0.663571i	−0.943355	+	0.331785i	$0.892349\pi$
$954$	45.9792	+	121.682i	0.0481962	+	0.127549i
$955$	−234.396	−	874.778i	−0.245441	−	0.915998i
$956$	643.053	+	729.415i	0.672650	+	0.762987i
$957$	284.241	−	1060.80i	0.297012	−	1.10846i
$958$	330.923	−	237.790i	0.345431	−	0.248215i
$959$	48.6422	+	13.4859i	0.0507217	+	0.0140624i
$960$	−860.769	+	584.941i	−0.896634	+	0.609314i
$961$	−472.480	−	818.359i	−0.491655	−	0.851571i
$962$	2.38921	+	23.9380i	0.00248358	+	0.0248835i
$963$	23.2419	+	86.7400i	0.0241349	+	0.0900727i
$964$	238.691	+	1183.84i	0.247605	+	1.22805i
$965$	−294.842	+	294.842i	−0.305536	+	0.305536i
$966$	133.296	+	188.931i	0.137987	+	0.195581i
$967$		−	90.6873i		−	0.0937821i	−0.998900	−	0.0468911i	$-0.985069\pi$
$967$		−	90.6873i		−	0.0937821i	0.998900	−	0.0468911i	$-0.0149314\pi$
$968$	665.195	−	715.814i	0.687185	−	0.739478i
$969$	−233.686	+	404.756i	−0.241162	+	0.417705i
$970$	−1665.77	−	1363.43i	−1.71729	−	1.40560i
$971$	499.413	+	133.817i	0.514328	+	0.137814i	0.506642	−	0.862157i	$-0.330887\pi$
$971$	499.413	+	133.817i	0.514328	+	0.137814i	0.00768637	+	0.999970i	$0.497553\pi$
$972$	−55.8513	+	27.7242i	−0.0574602	+	0.0285228i
$973$	4.50360	−	7.64686i	0.00462857	−	0.00785906i
$974$	990.270	−	711.574i	1.01670	−	0.730569i
$975$	671.783	+	1163.56i	0.689008	+	1.19340i
$976$	−1637.40	−	668.248i	−1.67766	−	0.684680i
$977$	−953.270	+	1651.11i	−0.975711	+	1.68998i	−0.298144	+	0.954521i	$0.596368\pi$
$977$	−953.270	+	1651.11i	−0.975711	+	1.68998i	−0.677567	+	0.735461i	$0.736966\pi$
$978$	−55.7601	+	123.493i	−0.0570144	+	0.126271i
$979$	−1031.08	−	1031.08i	−1.05320	−	1.05320i
$980$	1514.81	+	1044.69i	1.54572	+	1.06601i
$981$	−75.7727	−	75.7727i	−0.0772403	−	0.0772403i
$982$	−984.851	+	372.139i	−1.00290	+	0.378960i
$983$	−190.952	+	330.739i	−0.194255	+	0.336459i	−0.946656	−	0.322246i	$-0.895562\pi$
$983$	−190.952	+	330.739i	−0.194255	+	0.336459i	0.752401	+	0.658705i	$0.228896\pi$
$984$	−271.491	+	170.301i	−0.275906	+	0.173070i
$985$	−1521.02	−	2634.48i	−1.54418	−	2.67460i
$986$	−194.721	+	1189.05i	−0.197486	+	1.20594i
$987$	−517.068	+	877.953i	−0.523878	+	0.889516i
$988$	848.252	+	285.478i	0.858555	+	0.288945i
$989$	−275.416	−	73.7974i	−0.278479	−	0.0746182i
$990$	−87.2348	−	874.023i	−0.0881159	−	0.882852i
$991$	733.510	−	1270.48i	0.740172	−	1.28202i	−0.212245	−	0.977217i	$-0.568077\pi$
$991$	733.510	−	1270.48i	0.740172	−	1.28202i	0.952417	−	0.304799i	$-0.0985893\pi$
$992$	61.1499	+	112.631i	0.0616430	+	0.113539i
$993$		−	256.443i		−	0.258251i
$994$	−310.295	−	53.5757i	−0.312168	−	0.0538991i
$995$	−1751.64	+	1751.64i	−1.76044	+	1.76044i
$996$	−190.120	−	942.940i	−0.190884	−	0.946727i
$997$	354.432	+	1322.76i	0.355499	+	1.32674i	0.879855	+	0.475241i	$0.157639\pi$
$997$	354.432	+	1322.76i	0.355499	+	1.32674i	−0.524356	+	0.851499i	$0.675694\pi$
$998$	392.554	−	479.602i	0.393341	−	0.480564i
$999$	−2.54376	−	4.40592i	−0.00254631	−	0.00441033i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.3.bv.a.325.21	yes	256
7.5	odd	6	inner	336.3.bv.a.229.63	yes	256
16.13	even	4	inner	336.3.bv.a.157.63	yes	256
112.61	odd	12	inner	336.3.bv.a.61.21	✓	256

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.3.bv.a.61.21	✓	256	112.61	odd	12	inner
336.3.bv.a.157.63	yes	256	16.13	even	4	inner
336.3.bv.a.229.63	yes	256	7.5	odd	6	inner
336.3.bv.a.325.21	yes	256	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	336.bv (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.823038 + 1.82280i) q^{2} +(1.67303 - 0.448288i) q^{3} +(-2.64522 - 3.00047i) q^{4} +(-9.06845 - 2.42988i) q^{5} +(-0.559829 + 3.41857i) q^{6} +(-6.77691 + 1.75315i) q^{7} +(7.64638 - 2.35221i) q^{8} +(2.59808 - 1.50000i) q^{9} +(11.8929 - 14.5301i) q^{10} +(15.0619 - 4.03581i) q^{11} +(-5.77061 - 3.83407i) q^{12} +(8.68701 + 8.68701i) q^{13} +(2.38200 - 13.7959i) q^{14} -16.2611 q^{15} +(-2.00564 + 15.8738i) q^{16} +(12.8308 + 7.40787i) q^{17} +(0.595889 + 5.97034i) q^{18} +(-4.71384 + 17.5923i) q^{19} +(16.6972 + 33.6372i) q^{20} +(-10.5521 + 5.97108i) q^{21} +(-5.03998 + 30.7764i) q^{22} +(-8.25787 + 4.76768i) q^{23} +(11.7382 - 7.36310i) q^{24} +(54.6819 + 31.5706i) q^{25} +(-22.9844 + 8.68497i) q^{26} +(3.67423 - 3.67423i) q^{27} +(23.1867 + 15.6964i) q^{28} +(28.7528 - 28.7528i) q^{29} +(13.3835 - 29.6408i) q^{30} +(-3.46843 - 2.00250i) q^{31} +(-27.2841 - 16.7206i) q^{32} +(23.3898 - 13.5041i) q^{33} +(-24.0633 + 17.2911i) q^{34} +(65.7160 + 0.568726i) q^{35} +(-11.3732 - 3.82762i) q^{36} +(0.253408 - 0.945732i) q^{37} +(-28.1876 - 23.0715i) q^{38} +(18.4279 + 10.6394i) q^{39} +(-75.0564 + 2.75109i) q^{40} -23.1289 q^{41} +(-2.19936 - 24.1488i) q^{42} +(21.1443 + 21.1443i) q^{43} +(-51.9512 - 34.5170i) q^{44} +(-27.2054 + 7.28965i) q^{45} +(-1.89401 - 18.9764i) q^{46} +(72.7787 - 42.0188i) q^{47} +(3.76052 + 27.4565i) q^{48} +(42.8529 - 23.7619i) q^{49} +(-102.552 + 73.6905i) q^{50} +(24.7872 + 6.64171i) q^{51} +(3.08608 - 49.0442i) q^{52} +(20.9412 - 5.61117i) q^{53} +(3.67337 + 9.72144i) q^{54} -146.394 q^{55} +(-47.6950 + 29.3460i) q^{56} +31.5456i q^{57} +(28.7460 + 76.0752i) q^{58} +(4.88238 + 18.2213i) q^{59} +(43.0142 + 48.7910i) q^{60} +(-28.6078 + 106.766i) q^{61} +(6.50481 - 4.67413i) q^{62} +(-14.9772 + 14.7202i) q^{63} +(52.9342 - 35.9718i) q^{64} +(-57.6693 - 99.8862i) q^{65} +(5.36463 + 53.7493i) q^{66} +(-2.12221 - 7.92019i) q^{67} +(-11.7132 - 58.0939i) q^{68} +(-11.6784 + 11.6784i) q^{69} +(-55.1234 + 119.319i) q^{70} -22.4919i q^{71} +(16.3376 - 17.5808i) q^{72} +(-16.6746 + 28.8813i) q^{73} +(1.51532 + 1.24029i) q^{74} +(105.637 + 28.3054i) q^{75} +(65.2543 - 32.3917i) q^{76} +(-94.9974 + 53.7560i) q^{77} +(-34.5604 + 24.8339i) q^{78} +(10.9701 + 19.0007i) q^{79} +(56.7596 - 139.077i) q^{80} +(4.50000 - 7.79423i) q^{81} +(19.0360 - 42.1594i) q^{82} +(98.1751 + 98.1751i) q^{83} +(45.8286 + 15.8663i) q^{84} +(-98.3553 - 98.3553i) q^{85} +(-55.9443 + 21.1393i) q^{86} +(35.2148 - 60.9938i) q^{87} +(105.676 - 66.2880i) q^{88} +(-46.7566 - 80.9847i) q^{89} +(9.10344 - 55.5897i) q^{90} +(-74.1007 - 43.6414i) q^{91} +(36.1491 + 12.1659i) q^{92} +(-6.70049 - 1.79539i) q^{93} +(16.6924 + 167.244i) q^{94} +(85.4945 - 148.081i) q^{95} +(-53.1428 - 15.7430i) q^{96} -114.643i q^{97} +(8.04367 + 97.6693i) q^{98} +(33.0781 - 33.0781i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 256 q - 12 q^{4} - 24 q^{8} + 108 q^{10} + 32 q^{11} + 32 q^{14} - 4 q^{16} + 12 q^{18} + 48 q^{22} - 64 q^{29} - 96 q^{35} - 96 q^{37} + 60 q^{40} - 60 q^{42} - 192 q^{43} + 228 q^{44} + 180 q^{46} - 32 q^{50}+ \cdots + 192 q^{99}+O(q^{100}) \) 256 * q - 12 * q^4 - 24 * q^8 + 108 * q^10 + 32 * q^11 + 32 * q^14 - 4 * q^16 + 12 * q^18 + 48 * q^22 - 64 * q^29 - 96 * q^35 - 96 * q^37 + 60 * q^40 - 60 * q^42 - 192 * q^43 + 228 * q^44 + 180 * q^46 - 32 * q^50 + 720 * q^52 + 160 * q^53 - 56 * q^56 - 312 * q^58 + 384 * q^59 + 72 * q^60 - 96 * q^64 - 216 * q^66 - 320 * q^67 - 780 * q^68 - 828 * q^70 + 60 * q^72 - 88 * q^74 - 72 * q^78 - 612 * q^80 + 1152 * q^81 + 780 * q^82 - 72 * q^84 - 212 * q^86 - 464 * q^88 - 480 * q^91 - 488 * q^92 - 612 * q^94 + 768 * q^95 - 900 * q^96 - 196 * q^98 + 192 * q^99

Introduction

L-functions

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