LMFDB - Embedded newform 252.2.bi.c.223.25

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [252,2,Mod(139,252)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(252, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 2, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("252.139"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	252.bi (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [80,-6,0,-2,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$2.01223013094$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			223.25
Character	$\chi$	$=$	252.223
Dual form			252.2.bi.c.139.25

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.325239 - 1.37631i) q^{2} +(-0.844480 - 1.51223i) q^{3} +(-1.78844 - 0.895257i) q^{4} +(3.45303 - 1.99361i) q^{5} +(-2.35596 + 0.670425i) q^{6} +(2.03435 - 1.69157i) q^{7} +(-1.81382 + 2.17027i) q^{8} +(-1.57371 + 2.55410i) q^{9} +(-1.62076 - 5.40083i) q^{10} +(1.72816 + 0.997755i) q^{11} +(0.156462 + 3.46057i) q^{12} +(-2.38515 + 1.37707i) q^{13} +(-1.66647 - 3.35006i) q^{14} +(-5.93082 - 3.53823i) q^{15} +(2.39703 + 3.20222i) q^{16} +2.88632i q^{17} +(3.00340 + 2.99660i) q^{18} -0.0855521 q^{19} +(-7.96033 + 0.474099i) q^{20} +(-4.27602 - 1.64792i) q^{21} +(1.93528 - 2.05397i) q^{22} +(-5.06735 + 2.92564i) q^{23} +(4.81369 + 0.910170i) q^{24} +(5.44896 - 9.43788i) q^{25} +(1.11952 + 3.73057i) q^{26} +(5.19137 + 0.222928i) q^{27} +(-5.15271 + 1.20400i) q^{28} +(-2.39499 + 4.14825i) q^{29} +(-6.79863 + 7.01186i) q^{30} +(-0.893108 - 1.54691i) q^{31} +(5.18685 - 2.25756i) q^{32} +(0.0494419 - 3.45597i) q^{33} +(3.97246 + 0.938743i) q^{34} +(3.65236 - 9.89675i) q^{35} +(5.10106 - 3.15899i) q^{36} +6.22828 q^{37} +(-0.0278249 + 0.117746i) q^{38} +(4.09666 + 2.44400i) q^{39} +(-1.93650 + 11.1101i) q^{40} +(-3.94059 + 2.27510i) q^{41} +(-3.65877 + 5.34915i) q^{42} +(9.28817 + 5.36253i) q^{43} +(-2.19747 - 3.33157i) q^{44} +(-0.342182 + 11.9568i) q^{45} +(2.37847 + 7.92576i) q^{46} +(2.22398 - 3.85205i) q^{47} +(2.81827 - 6.32909i) q^{48} +(1.27718 - 6.88250i) q^{49} +(-11.2172 - 10.5690i) q^{50} +(4.36479 - 2.43744i) q^{51} +(5.49852 - 0.327479i) q^{52} +2.30892 q^{53} +(1.99525 - 7.07241i) q^{54} +7.95654 q^{55} +(-0.0187828 + 7.48329i) q^{56} +(0.0722470 + 0.129375i) q^{57} +(4.93031 + 4.64541i) q^{58} +(-2.41588 - 4.18443i) q^{59} +(7.43929 + 11.6375i) q^{60} +(-7.08218 - 4.08890i) q^{61} +(-2.41949 + 0.726076i) q^{62} +(1.11897 + 7.85798i) q^{63} +(-1.42013 - 7.87294i) q^{64} +(-5.49066 + 9.51011i) q^{65} +(-4.74040 - 1.19206i) q^{66} +(-1.76145 + 1.01697i) q^{67} +(2.58400 - 5.16201i) q^{68} +(8.70352 + 5.19238i) q^{69} +(-12.4331 - 8.24557i) q^{70} -3.57003i q^{71} +(-2.68867 - 8.04805i) q^{72} -11.4000i q^{73} +(2.02568 - 8.57202i) q^{74} +(-18.8738 - 0.270013i) q^{75} +(0.153005 + 0.0765911i) q^{76} +(5.20346 - 0.893522i) q^{77} +(4.69608 - 4.84337i) q^{78} +(-11.4989 - 6.63892i) q^{79} +(14.6610 + 6.27865i) q^{80} +(-4.04688 - 8.03883i) q^{81} +(1.84960 + 6.16341i) q^{82} +(-8.56210 + 14.8300i) q^{83} +(6.17209 + 6.77534i) q^{84} +(5.75420 + 9.96656i) q^{85} +(10.4014 - 11.0393i) q^{86} +(8.29564 + 0.118679i) q^{87} +(-5.29997 + 1.94083i) q^{88} +7.76882i q^{89} +(16.3449 + 4.35975i) q^{90} +(-2.52283 + 6.83608i) q^{91} +(11.6818 - 0.695744i) q^{92} +(-1.58508 + 2.65692i) q^{93} +(-4.57827 - 4.31372i) q^{94} +(-0.295414 + 0.170557i) q^{95} +(-7.79415 - 5.93727i) q^{96} +(4.07462 + 2.35248i) q^{97} +(-9.05704 - 3.99625i) q^{98} +(-5.26799 + 2.84373i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 6 q^{2} - 2 q^{4} - 24 q^{8} - 32 q^{9} + 10 q^{14} - 18 q^{16} - 22 q^{18} + 4 q^{21} - 14 q^{22} + 32 q^{25} + 28 q^{28} + 8 q^{29} - 16 q^{30} - 16 q^{32} + 34 q^{36} - 16 q^{37} - 8 q^{42} - 84 q^{44}+ \cdots + 20 q^{98}+O(q^{100}) $ 80 * q - 6 * q^2 - 2 * q^4 - 24 * q^8 - 32 * q^9 + 10 * q^14 - 18 * q^16 - 22 * q^18 + 4 * q^21 - 14 * q^22 + 32 * q^25 + 28 * q^28 + 8 * q^29 - 16 * q^30 - 16 * q^32 + 34 * q^36 - 16 * q^37 - 8 * q^42 - 84 * q^44 + 24 * q^46 - 24 * q^49 - 12 * q^50 - 48 * q^53 + 32 * q^56 + 72 * q^57 - 14 * q^58 + 56 * q^60 - 8 * q^64 - 40 * q^65 - 22 * q^70 - 100 * q^72 + 64 * q^74 - 12 * q^77 - 24 * q^78 - 104 * q^81 + 62 * q^84 + 40 * q^85 - 52 * q^86 + 6 * q^88 + 30 * q^92 + 48 * q^93 + 20 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.325239	−	1.37631i	0.229979	−	0.973196i
$2$	0.325239	−	1.37631i	0.229979	−	0.973196i
$3$	−0.844480	−	1.51223i	−0.487561	−	0.873089i
$3$	−0.844480	−	1.51223i	−0.487561	−	0.873089i
$4$	−1.78844	−	0.895257i	−0.894220	−	0.447628i
$5$	3.45303	−	1.99361i	1.54424	−	0.891570i	0.545680	−	0.837994i	$-0.316271\pi$
$5$	3.45303	−	1.99361i	1.54424	−	0.891570i	0.998564	−	0.0535758i	$-0.0170619\pi$
$6$	−2.35596	+	0.670425i	−0.961815	+	0.273700i
$7$	2.03435	−	1.69157i	0.768913	−	0.639353i
$7$	2.03435	−	1.69157i	0.768913	−	0.639353i
$8$	−1.81382	+	2.17027i	−0.641281	+	0.767306i
$9$	−1.57371	+	2.55410i	−0.524569	+	0.851368i
$10$	−1.62076	−	5.40083i	−0.512529	−	1.70789i
$11$	1.72816	+	0.997755i	0.521061	+	0.300834i	0.737368	−	0.675491i	$-0.236068\pi$
$11$	1.72816	+	0.997755i	0.521061	+	0.300834i	−0.216308	+	0.976325i	$0.569402\pi$
$12$	0.156462	+	3.46057i	0.0451668	+	0.998979i
$13$	−2.38515	+	1.37707i	−0.661521	+	0.381929i	−0.792856	−	0.609409i	$-0.791407\pi$
$13$	−2.38515	+	1.37707i	−0.661521	+	0.381929i	0.131335	+	0.991338i	$0.458074\pi$
$14$	−1.66647	−	3.35006i	−0.445382	−	0.895340i
$15$	−5.93082	−	3.53823i	−1.53133	−	0.913568i
$16$	2.39703	+	3.20222i	0.599258	+	0.800556i
$17$			2.88632i			0.700035i	0.936743	+	0.350018i	$0.113824\pi$
$17$			2.88632i			0.700035i	−0.936743	+	0.350018i	$0.886176\pi$
$18$	3.00340	+	2.99660i	0.707908	+	0.706305i
$19$	−0.0855521			−0.0196270			−0.00981349	−	0.999952i	$-0.503124\pi$
$19$	−0.0855521			−0.0196270			−0.00981349	+	0.999952i	$0.503124\pi$
$20$	−7.96033	+	0.474099i	−1.77998	+	0.106012i
$21$	−4.27602	−	1.64792i	−0.933104	−	0.359606i
$22$	1.93528	−	2.05397i	0.412604	−	0.437908i
$23$	−5.06735	+	2.92564i	−1.05662	+	0.610037i	−0.924494	−	0.381196i	$-0.875512\pi$
$23$	−5.06735	+	2.92564i	−1.05662	+	0.610037i	−0.132122	+	0.991234i	$0.542179\pi$
$24$	4.81369	+	0.910170i	0.982590	+	0.185788i
$25$	5.44896	−	9.43788i	1.08979	−	1.88758i
$26$	1.11952	+	3.73057i	0.219556	+	0.731625i
$27$	5.19137	+	0.222928i	0.999079	+	0.0429026i
$28$	−5.15271	+	1.20400i	−0.973770	+	0.227535i
$29$	−2.39499	+	4.14825i	−0.444739	+	0.770310i	−0.998034	−	0.0626752i	$-0.980037\pi$
$29$	−2.39499	+	4.14825i	−0.444739	+	0.770310i	0.553295	+	0.832985i	$0.313370\pi$
$30$	−6.79863	+	7.01186i	−1.24125	+	1.28018i
$31$	−0.893108	−	1.54691i	−0.160407	−	0.277833i	0.774608	−	0.632442i	$-0.217947\pi$
$31$	−0.893108	−	1.54691i	−0.160407	−	0.277833i	−0.935015	+	0.354609i	$0.884614\pi$
$32$	5.18685	−	2.25756i	0.916914	−	0.399084i
$33$	0.0494419	−	3.45597i	0.00860673	−	0.601607i
$34$	3.97246	+	0.938743i	0.681271	+	0.160993i
$35$	3.65236	−	9.89675i	0.617361	−	1.67286i
$36$	5.10106	−	3.15899i	0.850177	−	0.526498i
$37$	6.22828			1.02392			0.511961	−	0.859009i	$-0.328919\pi$
$37$	6.22828			1.02392			0.511961	+	0.859009i	$0.328919\pi$
$38$	−0.0278249	+	0.117746i	−0.00451379	+	0.0191009i
$39$	4.09666	+	2.44400i	0.655990	+	0.391353i
$40$	−1.93650	+	11.1101i	−0.306188	+	1.75665i
$41$	−3.94059	+	2.27510i	−0.615417	+	0.355311i	−0.775083	−	0.631860i	$-0.782292\pi$
$41$	−3.94059	+	2.27510i	−0.615417	+	0.355311i	0.159666	+	0.987171i	$0.448958\pi$
$42$	−3.65877	+	5.34915i	−0.564561	+	0.825391i
$43$	9.28817	+	5.36253i	1.41643	+	0.817777i	0.995983	−	0.0895388i	$-0.0285393\pi$
$43$	9.28817	+	5.36253i	1.41643	+	0.817777i	0.420449	+	0.907316i	$0.361873\pi$
$44$	−2.19747	−	3.33157i	−0.331281	−	0.502254i
$45$	−0.342182	+	11.9568i	−0.0510095	+	1.78241i
$46$	2.37847	+	7.92576i	0.350687	+	1.16859i
$47$	2.22398	−	3.85205i	0.324401	−	0.561879i	−0.656990	−	0.753899i	$-0.728171\pi$
$47$	2.22398	−	3.85205i	0.324401	−	0.561879i	0.981391	+	0.192020i	$0.0615039\pi$
$48$	2.81827	−	6.32909i	0.406782	−	0.913525i
$49$	1.27718	−	6.88250i	0.182454	−	0.983214i
$50$	−11.2172	−	10.5690i	−1.58635	−	1.49468i
$51$	4.36479	−	2.43744i	0.611193	−	0.341310i
$52$	5.49852	−	0.327479i	0.762508	−	0.0454132i
$53$	2.30892			0.317154			0.158577	−	0.987347i	$-0.449309\pi$
$53$	2.30892			0.317154			0.158577	+	0.987347i	$0.449309\pi$
$54$	1.99525	−	7.07241i	0.271519	−	0.962433i
$55$	7.95654			1.07286
$56$	−0.0187828	+	7.48329i	−0.00250996	+	0.999997i
$57$	0.0722470	+	0.129375i	0.00956935	+	0.0171361i
$58$	4.93031	+	4.64541i	0.647382	+	0.609973i
$59$	−2.41588	−	4.18443i	−0.314521	−	0.544767i	0.664814	−	0.747009i	$-0.268511\pi$
$59$	−2.41588	−	4.18443i	−0.314521	−	0.544767i	−0.979336	+	0.202242i	$0.935177\pi$
$60$	7.43929	+	11.6375i	0.960408	+	1.50240i
$61$	−7.08218	−	4.08890i	−0.906780	−	0.523530i	−0.0273862	−	0.999625i	$-0.508718\pi$
$61$	−7.08218	−	4.08890i	−0.906780	−	0.523530i	−0.879394	+	0.476095i	$0.842052\pi$
$62$	−2.41949	+	0.726076i	−0.307276	+	0.0922117i
$63$	1.11897	+	7.85798i	0.140977	+	0.990013i
$64$	−1.42013	−	7.87294i	−0.177516	−	0.984118i
$65$	−5.49066	+	9.51011i	−0.681033	+	1.17958i
$66$	−4.74040	−	1.19206i	−0.583502	−	0.146733i
$67$	−1.76145	+	1.01697i	−0.215195	+	0.124243i	−0.603724	−	0.797194i	$-0.706317\pi$
$67$	−1.76145	+	1.01697i	−0.215195	+	0.124243i	0.388528	+	0.921437i	$0.372984\pi$
$68$	2.58400	−	5.16201i	0.313356	−	0.625985i
$69$	8.70352	+	5.19238i	1.04778	+	0.625090i
$70$	−12.4331	−	8.24557i	−1.48604	−	0.985534i
$71$		−	3.57003i		−	0.423685i	−0.977304	−	0.211842i	$-0.932054\pi$
$71$		−	3.57003i		−	0.423685i	0.977304	−	0.211842i	$-0.0679464\pi$
$72$	−2.68867	−	8.04805i	−0.316863	−	0.948471i
$73$		−	11.4000i		−	1.33426i	−0.744940	−	0.667132i	$-0.767522\pi$
$73$		−	11.4000i		−	1.33426i	0.744940	−	0.667132i	$-0.232478\pi$
$74$	2.02568	−	8.57202i	0.235480	−	0.996477i
$75$	−18.8738	−	0.270013i	−2.17936	−	0.0311784i
$76$	0.153005	+	0.0765911i	0.0175508	+	0.00878560i
$77$	5.20346	−	0.893522i	0.592990	−	0.101826i
$78$	4.69608	−	4.84337i	0.531727	−	0.548404i
$79$	−11.4989	−	6.63892i	−1.29373	−	0.746936i	−0.314418	−	0.949285i	$-0.601809\pi$
$79$	−11.4989	−	6.63892i	−1.29373	−	0.746936i	−0.979314	+	0.202348i	$0.935143\pi$
$80$	14.6610	+	6.27865i	1.63915	+	0.701974i
$81$	−4.04688	−	8.03883i	−0.449654	−	0.893203i
$82$	1.84960	+	6.16341i	0.204255	+	0.680635i
$83$	−8.56210	+	14.8300i	−0.939812	+	1.62780i	−0.173993	+	0.984747i	$0.555667\pi$
$83$	−8.56210	+	14.8300i	−0.939812	+	1.62780i	−0.765820	+	0.643056i	$0.777666\pi$
$84$	6.17209	+	6.77534i	0.673430	+	0.739251i
$85$	5.75420	+	9.96656i	0.624130	+	1.08103i
$86$	10.4014	−	11.0393i	1.12161	−	1.19039i
$87$	8.29564	+	0.118679i	0.889386	+	0.0127238i
$88$	−5.29997	+	1.94083i	−0.564978	+	0.206893i
$89$			7.76882i			0.823493i	0.911298	+	0.411746i	$0.135081\pi$
$89$			7.76882i			0.823493i	−0.911298	+	0.411746i	$0.864919\pi$
$90$	16.3449	+	4.35975i	1.72290	+	0.459558i
$91$	−2.52283	+	6.83608i	−0.264464	+	0.716616i
$92$	11.6818	−	0.695744i	1.21792	−	0.0725363i
$93$	−1.58508	+	2.65692i	−0.164365	+	0.275510i
$94$	−4.57827	−	4.31372i	−0.472213	−	0.444926i
$95$	−0.295414	+	0.170557i	−0.0303089	+	0.0174988i
$96$	−7.79415	−	5.93727i	−0.795487	−	0.605970i
$97$	4.07462	+	2.35248i	0.413715	+	0.238859i	0.692385	−	0.721528i	$-0.256560\pi$
$97$	4.07462	+	2.35248i	0.413715	+	0.238859i	−0.278670	+	0.960387i	$0.589893\pi$
$98$	−9.05704	−	3.99625i	−0.914899	−	0.403682i
$99$	−5.26799	+	2.84373i	−0.529453	+	0.285806i
$100$	−18.1945	+	12.0009i	−1.81945	+	1.20009i
$101$	−2.46857	−	1.42523i	−0.245631	−	0.141815i	0.372131	−	0.928180i	$-0.378627\pi$
$101$	−2.46857	−	1.42523i	−0.245631	−	0.141815i	−0.617762	+	0.786365i	$0.711961\pi$
$102$	−1.93506	−	6.80004i	−0.191600	−	0.673305i
$103$	1.02846	+	1.78135i	0.101337	+	0.175521i	0.912236	−	0.409665i	$-0.134355\pi$
$103$	1.02846	+	1.78135i	0.101337	+	0.175521i	−0.810899	+	0.585187i	$0.801021\pi$
$104$	1.33762	−	7.67416i	0.131164	−	0.752513i
$105$	−18.0506	+	2.83439i	−1.76155	+	0.276608i
$106$	0.750949	−	3.17778i	0.0729387	−	0.308653i
$107$			15.5534i			1.50361i	0.659387	+	0.751803i	$0.270816\pi$
$107$			15.5534i			1.50361i	−0.659387	+	0.751803i	$0.729184\pi$
$108$	−9.08487	−	5.04630i	−0.874192	−	0.485581i
$109$	1.28192			0.122786			0.0613930	−	0.998114i	$-0.480446\pi$
$109$	1.28192			0.122786			0.0613930	+	0.998114i	$0.480446\pi$
$110$	2.58778	−	10.9506i	0.246735	−	1.04410i
$111$	−5.25965	−	9.41862i	−0.499224	−	0.893976i
$112$	10.2932	+	2.45971i	0.972615	+	0.232421i
$113$	7.39267	+	12.8045i	0.695444	+	1.20454i	0.970031	+	0.242982i	$0.0781257\pi$
$113$	7.39267	+	12.8045i	0.695444	+	1.20454i	−0.274586	+	0.961562i	$0.588541\pi$
$114$	0.201557	−	0.0573563i	0.0188775	−	0.00537191i
$115$	−11.6652	+	20.2046i	−1.08778	+	1.88409i
$116$	7.99704	−	5.27475i	0.742507	−	0.489749i
$117$	0.236359	−	8.25901i	0.0218514	−	0.763546i
$118$	−6.54480	+	1.96406i	−0.602498	+	0.180806i
$119$	4.88241	+	5.87179i	0.447570	+	0.538266i
$120$	18.4364	−	6.45377i	1.68300	−	0.589146i
$121$	−3.50897	−	6.07771i	−0.318997	−	0.552519i
$122$	−7.93097	+	8.41738i	−0.718037	+	0.762074i
$123$	6.76824	+	4.03782i	0.610271	+	0.364078i
$124$	0.212389	+	3.56611i	0.0190731	+	0.320246i
$125$		−	23.5163i		−	2.10336i
$126$	11.1789	+	1.01568i	0.995898	+	0.0904839i
$127$			0.327377i			0.0290500i	0.999895	+	0.0145250i	$0.00462361\pi$
$127$			0.327377i			0.0290500i	−0.999895	+	0.0145250i	$0.995376\pi$
$128$	−11.2975	−	0.606051i	−0.998564	−	0.0535678i
$129$	0.265730	−	18.5744i	0.0233962	−	1.63539i
$130$	11.3030	+	10.6499i	0.991343	+	0.934058i
$131$	1.15307	+	1.99717i	0.100744	+	0.174494i	0.911991	−	0.410209i	$-0.134544\pi$
$131$	1.15307	+	1.99717i	0.100744	+	0.174494i	−0.811247	+	0.584703i	$0.801211\pi$
$132$	−3.18241	+	6.13653i	−0.276993	+	0.534117i
$133$	−0.174043	+	0.144717i	−0.0150914	+	0.0125486i
$134$	0.826776	+	2.75506i	0.0714226	+	0.238001i
$135$	18.3704	−	9.57978i	1.58107	−	0.824497i
$136$	−6.26409	−	5.23526i	−0.537141	−	0.448920i
$137$	6.07413	−	10.5207i	0.518948	−	0.898844i	−0.480810	−	0.876825i	$-0.659657\pi$
$137$	6.07413	−	10.5207i	0.518948	−	0.898844i	0.999758	−	0.0220190i	$-0.00700942\pi$
$138$	9.97704	−	10.2900i	0.849302	−	0.875939i
$139$	−4.45697	−	7.71970i	−0.378035	−	0.654776i	0.612741	−	0.790284i	$-0.290067\pi$
$139$	−4.45697	−	7.71970i	−0.378035	−	0.654776i	−0.990776	+	0.135507i	$0.956734\pi$
$140$	−15.3922	+	14.4299i	−1.30087	+	1.21955i
$141$	−7.70331	−	0.110205i	−0.648736	−	0.00928096i
$142$	−4.91346	−	1.16111i	−0.412328	−	0.0974384i
$143$	−5.49590			−0.459590
$144$	−11.9510	+	1.08290i	−0.995920	+	0.0902414i
$145$			19.0987i			1.58606i
$146$	−15.6898	−	3.70771i	−1.29850	−	0.306852i
$147$	−11.4865	+	3.88073i	−0.947391	+	0.320078i
$148$	−11.1389	−	5.57591i	−0.915612	−	0.458337i
$149$	−1.02048	−	1.76752i	−0.0836008	−	0.144801i	0.821193	−	0.570650i	$-0.193309\pi$
$149$	−1.02048	−	1.76752i	−0.0836008	−	0.144801i	−0.904794	+	0.425849i	$0.859975\pi$
$150$	−6.51012	+	25.8884i	−0.531549	+	2.11378i
$151$	9.32355	+	5.38296i	0.758740	+	0.438059i	0.828843	−	0.559481i	$-0.189000\pi$
$151$	9.32355	+	5.38296i	0.758740	+	0.438059i	−0.0701032	+	0.997540i	$0.522333\pi$
$152$	0.155176	−	0.185671i	0.0125864	−	0.0150599i
$153$	−7.37196	−	4.54223i	−0.595988	−	0.367217i
$154$	0.462608	−	7.45217i	0.0372780	−	0.600513i
$155$	−6.16786	−	3.56102i	−0.495415	−	0.286028i
$156$	−5.13861	−	8.03850i	−0.411418	−	0.643595i
$157$	−6.83827	+	3.94808i	−0.545753	+	0.315091i	−0.747407	−	0.664366i	$-0.768702\pi$
$157$	−6.83827	+	3.94808i	−0.545753	+	0.315091i	0.201654	+	0.979457i	$0.435368\pi$
$158$	−12.8771	+	13.6668i	−1.02445	+	1.08727i
$159$	−1.94983	−	3.49162i	−0.154632	−	0.276904i
$160$	13.4097	−	18.1360i	1.06013	−	1.43378i
$161$	−5.35986	+	14.5236i	−0.422416	+	1.14462i
$162$	−12.3801	+	2.95522i	−0.972672	+	0.232184i
$163$		−	13.3844i		−	1.04835i	−0.851611	−	0.524175i	$-0.824374\pi$
$163$		−	13.3844i		−	1.04835i	0.851611	−	0.524175i	$-0.175626\pi$
$164$	9.08431	−	0.541040i	0.709365	−	0.0422481i
$165$	−6.71913	−	12.0322i	−0.523084	−	0.936702i
$166$	17.6259	+	16.6074i	1.36803	+	1.28898i
$167$	−6.33117	−	10.9659i	−0.489921	−	0.848568i	0.510012	−	0.860167i	$-0.329641\pi$
$167$	−6.33117	−	10.9659i	−0.489921	−	0.848568i	−0.999933	+	0.0115994i	$0.996308\pi$
$168$	11.3324	−	6.29108i	0.874310	−	0.485368i
$169$	−2.70738	+	4.68932i	−0.208260	+	0.360717i
$170$	15.5885	−	4.67803i	1.19559	−	0.358788i
$171$	0.134634	−	0.218509i	0.0102957	−	0.0167098i
$172$	−11.8105	−	17.9058i	−0.900541	−	1.36531i
$173$	6.59908	+	3.80998i	0.501719	+	0.289668i	0.729423	−	0.684063i	$-0.239789\pi$
$173$	6.59908	+	3.80998i	0.501719	+	0.289668i	−0.227704	+	0.973730i	$0.573122\pi$
$174$	2.86140	−	11.3787i	0.216923	−	0.862621i
$175$	−4.87973	−	28.4173i	−0.368873	−	2.14814i
$176$	0.947423	+	7.92561i	0.0714147	+	0.597416i
$177$	−4.28768	+	7.18705i	−0.322282	+	0.540212i
$178$	10.6923	+	2.52672i	0.801420	+	0.189386i
$179$			8.19202i			0.612300i	0.951983	+	0.306150i	$0.0990410\pi$
$179$			8.19202i			0.612300i	−0.951983	+	0.306150i	$0.900959\pi$
$180$	11.3163	−	21.0776i	0.843471	−	1.57103i
$181$			3.68997i			0.274274i	0.990552	+	0.137137i	$0.0437900\pi$
$181$			3.68997i			0.274274i	−0.990552	+	0.137137i	$0.956210\pi$
$182$	8.58802	+	5.69554i	0.636587	+	0.422182i
$183$	−0.202618	+	14.1629i	−0.0149779	+	1.04695i
$184$	2.84183	−	16.3041i	0.209503	−	1.20195i
$185$	21.5065	−	12.4168i	1.58119	−	0.912898i
$186$	3.14121	+	3.04569i	0.230325	+	0.223321i
$187$	−2.87984	+	4.98803i	−0.210595	+	0.364761i
$188$	−7.42603	+	4.89812i	−0.541599	+	0.357232i
$189$	10.9382	−	8.32805i	0.795635	−	0.605776i
$190$	0.138659	+	0.462052i	0.0100594	+	0.0335208i
$191$	−8.72331	−	5.03641i	−0.631197	−	0.364422i	0.150019	−	0.988683i	$-0.452067\pi$
$191$	−8.72331	−	5.03641i	−0.631197	−	0.364422i	−0.781215	+	0.624262i	$0.785400\pi$
$192$	−10.7065	+	8.79611i	−0.772673	+	0.634805i
$193$	−5.87003	−	10.1672i	−0.422534	−	0.731851i	0.573652	−	0.819099i	$-0.305526\pi$
$193$	−5.87003	−	10.1672i	−0.422534	−	0.731851i	−0.996187	+	0.0872481i	$0.972193\pi$
$194$	4.56296	−	4.84281i	0.327602	−	0.347693i
$195$	19.0183	+	0.272080i	1.36193	+	0.0194840i
$196$	−8.44576	+	11.1655i	−0.603269	+	0.797538i
$197$	20.3333			1.44869			0.724343	−	0.689440i	$-0.242143\pi$
$197$	20.3333			1.44869			0.724343	+	0.689440i	$0.242143\pi$
$198$	2.20049	+	8.17526i	0.156382	+	0.580991i
$199$	22.7777			1.61467			0.807335	−	0.590093i	$-0.200909\pi$
$199$	22.7777			1.61467			0.807335	+	0.590093i	$0.200909\pi$
$200$	10.5993	+	28.9443i	0.749484	+	2.04667i
$201$	3.02541	+	1.80491i	0.213396	+	0.127309i
$202$	−2.76442	+	2.93396i	−0.194504	+	0.206433i
$203$	2.14479	+	12.4903i	0.150535	+	0.876646i
$204$	−9.98830	+	0.451600i	−0.699321	+	0.0316184i
$205$	−9.07133	+	15.7120i	−0.633569	+	1.09737i
$206$	2.78618	−	0.836115i	0.194122	−	0.0582549i
$207$	0.502155	−	17.5466i	0.0349022	−	1.21958i
$208$	−10.1269	−	4.33691i	−0.702177	−	0.300711i
$209$	−0.147848	−	0.0853600i	−0.0102269	−	0.00590447i
$210$	−1.96976	+	25.7650i	−0.135926	+	1.77795i
$211$	−20.1250	+	11.6191i	−1.38546	+	0.799895i	−0.992799	−	0.119789i	$-0.961778\pi$
$211$	−20.1250	+	11.6191i	−1.38546	+	0.799895i	−0.392659	+	0.919684i	$0.628445\pi$
$212$	−4.12936	−	2.06707i	−0.283605	−	0.141967i
$213$	−5.39873	+	3.01482i	−0.369915	+	0.206572i
$214$	21.4063	+	5.05858i	1.46330	+	0.345797i
$215$	42.7631			2.91642
$216$	−9.90001	+	10.8623i	−0.673610	+	0.739087i
$217$	−4.43360	−	1.63620i	−0.300972	−	0.111073i
$218$	0.416932	−	1.76432i	0.0282382	−	0.119495i
$219$	−17.2394	+	9.62703i	−1.16493	+	0.650534i
$220$	−14.2298	−	7.12314i	−0.959372	−	0.480242i
$221$	−3.97465	−	6.88430i	−0.267364	−	0.463088i
$222$	−14.6735	+	4.17560i	−0.984824	+	0.280248i
$223$	−4.17435	+	7.23018i	−0.279535	+	0.484169i	−0.971269	−	0.237984i	$-0.923514\pi$
$223$	−4.17435	+	7.23018i	−0.279535	+	0.484169i	0.691734	+	0.722152i	$0.256847\pi$
$224$	6.73306	−	13.3666i	0.449871	−	0.893093i
$225$	15.5302	+	28.7697i	1.03535	+	1.91798i
$226$	20.0273	−	6.01007i	1.33220	−	0.399784i
$227$	3.33734	−	5.78045i	0.221507	−	0.383662i	−0.733759	−	0.679410i	$-0.762236\pi$
$227$	3.33734	−	5.78045i	0.221507	−	0.383662i	0.955266	+	0.295748i	$0.0955690\pi$
$228$	−0.0133857	−	0.296059i	−0.000886488	−	0.0196070i
$229$	8.63009	−	4.98258i	0.570292	−	0.329258i	−0.186974	−	0.982365i	$-0.559868\pi$
$229$	8.63009	−	4.98258i	0.570292	−	0.329258i	0.757266	+	0.653107i	$0.226535\pi$
$230$	24.0138	+	22.6262i	1.58342	+	1.49193i
$231$	−5.74544	−	7.11430i	−0.378022	−	0.468086i
$232$	−4.65873	−	12.7219i	−0.305861	−	0.835236i
$233$	3.55156			0.232670			0.116335	−	0.993210i	$-0.462885\pi$
$233$	3.55156			0.232670			0.116335	+	0.993210i	$0.462885\pi$
$234$	−11.2901	−	3.01145i	−0.738054	−	0.196865i
$235$		−	17.7350i		−	1.15690i
$236$	0.574520	+	9.64644i	0.0373981	+	0.627930i
$237$	−0.328979	+	22.9955i	−0.0213695	+	1.49372i
$238$	9.66934	−	4.80996i	0.626770	−	0.311784i
$239$	5.01808	−	2.89719i	0.324592	−	0.187403i	−0.328845	−	0.944384i	$-0.606659\pi$
$239$	5.01808	−	2.89719i	0.324592	−	0.187403i	0.653438	+	0.756980i	$0.273326\pi$
$240$	−2.88614	−	27.4731i	−0.186300	−	1.77338i
$241$	−2.63364	−	1.52053i	−0.169648	−	0.0979461i	0.412772	−	0.910834i	$-0.364561\pi$
$241$	−2.63364	−	1.52053i	−0.169648	−	0.0979461i	−0.582420	+	0.812888i	$0.697894\pi$
$242$	−9.50605	+	2.85271i	−0.611072	+	0.183379i
$243$	−8.73908	+	12.9085i	−0.560612	+	0.828078i
$244$	9.00543	+	13.6531i	0.576514	+	0.874051i
$245$	−9.31087	−	26.3117i	−0.594850	−	1.68099i
$246$	7.75857	−	8.00191i	0.494669	−	0.510183i
$247$	0.204054	−	0.117811i	0.0129837	−	0.00749612i
$248$	4.97714	+	0.867525i	0.316049	+	0.0550879i
$249$	29.6569	+	0.424279i	1.87943	+	0.0268876i
$250$	−32.3657	−	7.64842i	−2.04698	−	0.483729i
$251$	−15.9355			−1.00584			−0.502920	−	0.864333i	$-0.667741\pi$
$251$	−15.9355			−1.00584			−0.502920	+	0.864333i	$0.667741\pi$
$252$	5.03371	−	15.0553i	0.317094	−	0.948394i
$253$	−11.6763			−0.734081
$254$	0.450571	+	0.106476i	0.0282713	+	0.00668087i
$255$	10.2125	−	17.1183i	0.639530	−	1.07199i
$256$	−4.50849	+	15.3517i	−0.281780	+	0.959479i
$257$	−17.9529	+	10.3651i	−1.11987	+	0.646559i	−0.941369	−	0.337380i	$-0.890459\pi$
$257$	−17.9529	+	10.3651i	−1.11987	+	0.646559i	−0.178505	+	0.983939i	$0.557126\pi$
$258$	−25.4777	−	6.40685i	−1.58617	−	0.398873i
$259$	12.6705	−	10.5356i	0.787307	−	0.654648i
$260$	18.3337	−	12.0927i	1.13701	−	0.749957i
$261$	−6.82603	−	12.6452i	−0.422521	−	0.782717i
$262$	3.12375	−	0.937417i	0.192986	−	0.0579138i
$263$	−1.29122	−	0.745488i	−0.0796202	−	0.0459687i	0.459661	−	0.888094i	$-0.347971\pi$
$263$	−1.29122	−	0.745488i	−0.0796202	−	0.0459687i	−0.539282	+	0.842126i	$0.681304\pi$
$264$	7.41071	+	6.37580i	0.456097	+	0.392404i
$265$	7.97277	−	4.60308i	0.489763	−	0.282765i
$266$	0.142570	+	0.286604i	0.00874152	+	0.0175728i
$267$	11.7483	−	6.56061i	0.718983	−	0.401503i
$268$	4.06070	−	0.241846i	0.248047	−	0.0147731i
$269$			18.2450i			1.11242i	0.831043	+	0.556209i	$0.187745\pi$
$269$			18.2450i			1.11242i	−0.831043	+	0.556209i	$0.812255\pi$
$270$	−7.20995	−	28.3990i	−0.438784	−	1.72831i
$271$	15.4908			0.940998			0.470499	−	0.882400i	$-0.344074\pi$
$271$	15.4908			0.940998			0.470499	+	0.882400i	$0.344074\pi$
$272$	−9.24264	+	6.91860i	−0.560418	+	0.419502i
$273$	12.4682	−	1.95782i	0.754612	−	0.118493i
$274$	−12.5042	−	11.7816i	−0.755404	−	0.711753i
$275$	18.8334	−	10.8735i	1.13570	−	0.655694i
$276$	−10.9172	−	17.0782i	−0.657139	−	1.02798i
$277$	−9.29870	+	16.1058i	−0.558705	+	0.967705i	0.438900	+	0.898536i	$0.355368\pi$
$277$	−9.29870	+	16.1058i	−0.558705	+	0.967705i	−0.997605	+	0.0691691i	$0.977965\pi$
$278$	−12.0743	+	3.62341i	−0.724165	+	0.217318i
$279$	5.35645	+	0.153293i	0.320683	+	0.00917739i
$280$	14.8539	+	25.8775i	0.887691	+	1.54648i
$281$	−9.87259	+	17.0998i	−0.588950	+	1.02009i	0.405421	+	0.914130i	$0.367125\pi$
$281$	−9.87259	+	17.0998i	−0.588950	+	1.02009i	−0.994370	+	0.105960i	$0.966208\pi$
$282$	−2.65709	+	10.5663i	−0.158227	+	0.629212i
$283$	8.53005	+	14.7745i	0.507059	+	0.878252i	0.999967	+	0.00817031i	$0.00260072\pi$
$283$	8.53005	+	14.7745i	0.507059	+	0.878252i	−0.492908	+	0.870082i	$0.664066\pi$
$284$	−3.19609	+	6.38479i	−0.189653	+	0.378867i
$285$	0.507394	+	0.302703i	0.0300554	+	0.0179306i
$286$	−1.78748	+	7.56404i	−0.105696	+	0.447271i
$287$	−4.16806	+	11.2941i	−0.246033	+	0.666672i
$288$	−2.39654	+	16.8005i	−0.141218	+	0.989979i
$289$	8.66916			0.509950
$290$	26.2857	+	6.21164i	1.54355	+	0.364760i
$291$	0.116573	−	8.14841i	0.00683363	−	0.477668i
$292$	−10.2059	+	20.3881i	−0.597254	+	1.19312i
$293$	−22.2955	+	12.8723i	−1.30252	+	0.752009i	−0.980835	−	0.194838i	$-0.937582\pi$
$293$	−22.2955	+	12.8723i	−1.30252	+	0.752009i	−0.321683	+	0.946847i	$0.604249\pi$
$294$	1.60522	+	17.0711i	0.0936184	+	0.995608i
$295$	−16.6843	−	9.63266i	−0.971395	−	0.560835i
$296$	−11.2970	+	13.5170i	−0.656622	+	0.785662i
$297$	8.74910	+	5.56497i	0.507674	+	0.322912i
$298$	−2.76455	+	0.829624i	−0.160146	+	0.0480588i
$299$	8.05759	−	13.9562i	0.465982	−	0.807105i
$300$	33.5130	+	17.3798i	1.93487	+	1.00342i
$301$	27.9665	−	4.80232i	1.61196	−	0.276801i
$302$	10.4410	−	11.0813i	0.600811	−	0.637658i
$303$	−0.0706245	+	4.93663i	−0.00405727	+	0.283602i
$304$	−0.205071	−	0.273957i	−0.0117616	−	0.0157125i
$305$	−32.6067			−1.86705
$306$	−8.64914	+	8.66877i	−0.494439	+	0.495560i
$307$	7.34083			0.418963			0.209482	−	0.977813i	$-0.432822\pi$
$307$	7.34083			0.418963			0.209482	+	0.977813i	$0.432822\pi$
$308$	−10.1060	−	3.06043i	−0.575843	−	0.174384i
$309$	1.82530	−	3.05959i	0.103838	−	0.174054i
$310$	−6.90708	+	7.33069i	−0.392296	+	0.416355i
$311$	−14.2106	−	24.6135i	−0.805809	−	1.39570i	−0.915744	−	0.401763i	$-0.868398\pi$
$311$	−14.2106	−	24.6135i	−0.805809	−	1.39570i	0.109935	−	0.993939i	$-0.464936\pi$
$312$	−12.7347	+	4.45787i	−0.720962	+	0.252377i
$313$	−12.8704	−	7.43074i	−0.727479	−	0.420010i	0.0900203	−	0.995940i	$-0.471307\pi$
$313$	−12.8704	−	7.43074i	−0.727479	−	0.420010i	−0.817499	+	0.575930i	$0.804640\pi$
$314$	3.20969	+	10.6956i	0.181133	+	0.603589i
$315$	19.5296	+	24.9031i	1.10037	+	1.40313i
$316$	14.6216	+	22.1678i	0.822530	+	1.24704i
$317$	10.7056	−	18.5426i	0.601284	−	1.04145i	−0.391343	−	0.920245i	$-0.627990\pi$
$317$	10.7056	−	18.5426i	0.601284	−	1.04145i	0.992627	−	0.121209i	$-0.0386771\pi$
$318$	−5.43971	+	1.54796i	−0.305044	+	0.0868051i
$319$	−8.27787	+	4.77923i	−0.463472	+	0.267585i
$320$	−20.5993	−	24.3543i	−1.15154	−	1.36145i
$321$	23.5204	−	13.1346i	1.31278	−	0.733099i
$322$	18.2456	+	12.1004i	1.01679	+	0.674331i
$323$		−	0.246931i		−	0.0137396i
$324$	0.0407957	+	18.0000i	0.00226643	+	0.999997i
$325$			30.0143i			1.66489i
$326$	−18.4211	−	4.35314i	−1.02025	−	0.241098i
$327$	−1.08256	−	1.93857i	−0.0598656	−	0.107203i
$328$	2.20993	−	12.6788i	0.122023	−	0.700067i
$329$	−1.99165	−	11.5984i	−0.109803	−	0.639443i
$330$	−18.7453	+	5.33426i	−1.03189	+	0.293642i
$331$	14.7097	+	8.49262i	0.808515	+	0.466797i	0.846440	−	0.532484i	$-0.178741\pi$
$331$	14.7097	+	8.49262i	0.808515	+	0.466797i	−0.0379246	+	0.999281i	$0.512075\pi$
$332$	28.5894	−	18.8573i	1.56905	−	1.03493i
$333$	−9.80149	+	15.9077i	−0.537118	+	0.871735i
$334$	−17.1516	+	5.14710i	−0.938494	+	0.281637i
$335$	−4.05490	+	7.02329i	−0.221543	+	0.383723i
$336$	−4.97274	−	17.6429i	−0.271285	−	0.962499i
$337$	4.90546	+	8.49651i	0.267217	+	0.462834i	0.968142	−	0.250401i	$-0.0805625\pi$
$337$	4.90546	+	8.49651i	0.267217	+	0.462834i	−0.700925	+	0.713235i	$0.747229\pi$
$338$	5.57340	+	5.25133i	0.303153	+	0.285635i
$339$	13.1204	−	21.9926i	0.712604	−	1.19447i
$340$	−1.36840	−	22.9761i	−0.0742120	−	1.24605i
$341$		−	3.56441i		−	0.193024i
$342$	−0.256947	−	0.256365i	−0.0138941	−	0.0138626i
$343$	−9.04400	−	16.1619i	−0.488330	−	0.872659i
$344$	−28.4852	+	10.4312i	−1.53582	+	0.562411i
$345$	40.4052	+	0.578045i	2.17534	+	0.0311209i
$346$	7.38998	−	7.84321i	0.397288	−	0.421653i
$347$	3.21012	−	1.85336i	0.172328	−	0.0994937i	−0.411355	−	0.911475i	$-0.634944\pi$
$347$	3.21012	−	1.85336i	0.172328	−	0.0994937i	0.583683	+	0.811982i	$0.301611\pi$
$348$	−14.7300	−	7.63898i	−0.789611	−	0.409492i
$349$	4.31419	+	2.49080i	0.230933	+	0.133329i	0.611003	−	0.791629i	$-0.290767\pi$
$349$	4.31419	+	2.49080i	0.230933	+	0.133329i	−0.380069	+	0.924958i	$0.624100\pi$
$350$	−40.6980	−	2.52640i	−2.17540	−	0.135042i
$351$	−12.6892	+	6.61714i	−0.677298	+	0.353197i
$352$	11.2162	+	1.27377i	0.597826	+	0.0678923i
$353$	−10.4059	−	6.00788i	−0.553853	−	0.319767i	0.196822	−	0.980439i	$-0.436938\pi$
$353$	−10.4059	−	6.00788i	−0.553853	−	0.319767i	−0.750674	+	0.660672i	$0.770271\pi$
$354$	8.49707	+	8.23867i	0.451614	+	0.437881i
$355$	−7.11725	−	12.3274i	−0.377744	−	0.654273i
$356$	6.95508	−	13.8941i	0.368619	−	0.736384i
$357$	4.75643	−	12.3420i	0.251737	−	0.653206i
$358$	11.2747	+	2.66436i	0.595888	+	0.140816i
$359$		−	27.6368i		−	1.45861i	−0.684187	−	0.729307i	$-0.739843\pi$
$359$		−	27.6368i		−	1.45861i	0.684187	−	0.729307i	$-0.260157\pi$
$360$	−25.3287	−	22.4300i	−1.33494	−	1.18217i
$361$	−18.9927			−0.999615
$362$	5.07853	+	1.20012i	0.266922	+	0.0630770i
$363$	−6.22768	+	10.4389i	−0.326868	+	0.547900i
$364$	10.6320	−	9.96734i	0.557267	−	0.522431i
$365$	−22.7271	−	39.3644i	−1.18959	−	2.06043i
$366$	19.4266	+	4.88519i	1.01544	+	0.255353i
$367$	−14.7663	+	25.5760i	−0.770796	+	1.33506i	0.166331	+	0.986070i	$0.446808\pi$
$367$	−14.7663	+	25.5760i	−0.770796	+	1.33506i	−0.937127	+	0.348988i	$0.886525\pi$
$368$	−21.5151	−	9.21395i	−1.12155	−	0.480311i
$369$	0.390497	−	13.6450i	0.0203285	−	0.710331i
$370$	−10.0945	−	33.6379i	−0.524790	−	1.74875i
$371$	4.69715	−	3.90570i	0.243864	−	0.202774i
$372$	5.21344	−	3.33269i	0.270304	−	0.172792i
$373$	−6.89959	−	11.9504i	−0.357247	−	0.618770i	0.630253	−	0.776390i	$-0.282951\pi$
$373$	−6.89959	−	11.9504i	−0.357247	−	0.618770i	−0.987500	+	0.157620i	$0.949618\pi$
$374$	5.92842	+	5.58584i	0.306551	+	0.288837i
$375$	−35.5622	+	19.8591i	−1.83642	+	1.02552i
$376$	4.32608	+	11.8136i	0.223101	+	0.609237i
$377$		−	13.1922i		−	0.679435i
$378$	−7.90443	−	17.7629i	−0.406560	−	0.913624i
$379$		−	16.1019i		−	0.827099i	−0.910482	−	0.413549i	$-0.864289\pi$
$379$		−	16.1019i		−	0.827099i	0.910482	−	0.413549i	$-0.135711\pi$
$380$	0.681023	−	0.0405602i	0.0349357	−	0.00208069i
$381$	0.495070	−	0.276463i	0.0253632	−	0.0141636i
$382$	−9.76880	+	10.3679i	−0.499815	+	0.530469i
$383$	8.61022	+	14.9133i	0.439962	+	0.762036i	0.997686	−	0.0679904i	$-0.0216587\pi$
$383$	8.61022	+	14.9133i	0.439962	+	0.762036i	−0.557724	+	0.830026i	$0.688325\pi$
$384$	8.62399	+	17.5962i	0.440091	+	0.897953i
$385$	16.1864	−	13.4590i	0.824935	−	0.685936i
$386$	−15.9023	+	4.77220i	−0.809408	+	0.242898i
$387$	−28.3133	+	15.2839i	−1.43925	+	0.776924i
$388$	−5.18114	−	7.85511i	−0.263032	−	0.398783i
$389$	2.16557	−	3.75088i	0.109799	−	0.190177i	−0.805890	−	0.592066i	$-0.798313\pi$
$389$	2.16557	−	3.75088i	0.109799	−	0.190177i	0.915689	+	0.401888i	$0.131646\pi$
$390$	6.55995	−	26.0865i	0.332176	−	1.32094i
$391$	−8.44432	−	14.6260i	−0.427048	−	0.739668i
$392$	12.6203	+	15.2554i	0.637421	+	0.770515i
$393$	2.04645	−	3.43028i	0.103230	−	0.173035i
$394$	6.61317	−	27.9848i	0.333167	−	1.40985i
$395$	−52.9416			−2.66378
$396$	11.9674	−	0.369632i	0.601382	−	0.0185747i
$397$		−	28.5958i		−	1.43518i	−0.696466	−	0.717590i	$-0.745245\pi$
$397$		−	28.5958i		−	1.43518i	0.696466	−	0.717590i	$-0.254755\pi$
$398$	7.40820	−	31.3491i	0.371340	−	1.57139i
$399$	0.365822	+	0.140983i	0.0183140	+	0.00705799i
$400$	43.2835	−	5.17409i	2.16418	−	0.258704i
$401$	−6.03293	−	10.4493i	−0.301270	−	0.521815i	0.675154	−	0.737677i	$-0.264077\pi$
$401$	−6.03293	−	10.4493i	−0.301270	−	0.521815i	−0.976424	+	0.215862i	$0.930744\pi$
$402$	3.46810	−	3.57687i	0.172973	−	0.178398i
$403$	4.26039	+	2.45974i	0.212225	+	0.122528i
$404$	3.13894	+	4.75893i	0.156168	+	0.236766i
$405$	−30.0003	−	19.6904i	−1.49073	−	0.978425i
$406$	17.8880	+	1.11043i	0.887768	+	0.0551099i
$407$	10.7635	+	6.21430i	0.533526	+	0.308031i
$408$	−2.62704	+	13.8938i	−0.130058	+	0.687848i
$409$	−19.8538	+	11.4626i	−0.981705	+	0.566788i	−0.902785	−	0.430093i	$-0.858481\pi$
$409$	−19.8538	+	11.4626i	−0.981705	+	0.566788i	−0.0789208	+	0.996881i	$0.525147\pi$
$410$	18.6742	+	17.5951i	0.922252	+	0.868959i
$411$	−21.0392	−	0.300992i	−1.03779	−	0.0148468i
$412$	−0.244578	−	4.10657i	−0.0120495	−	0.202316i
$413$	−11.9930	−	4.42598i	−0.590138	−	0.217788i
$414$	−23.9862	−	6.39797i	−1.17886	−	0.314443i
$415$			68.2779i			3.35163i
$416$	−9.26259	+	12.5273i	−0.454136	+	0.614199i
$417$	−7.91018	+	13.2591i	−0.387363	+	0.649302i
$418$	−0.165567	+	0.175722i	−0.00809817	+	0.00859482i
$419$	5.84657	+	10.1266i	0.285624	+	0.494715i	0.972760	−	0.231813i	$-0.0744659\pi$
$419$	5.84657	+	10.1266i	0.285624	+	0.494715i	−0.687136	+	0.726528i	$0.741133\pi$
$420$	34.8198	+	11.0908i	1.69903	+	0.541173i
$421$	5.56174	−	9.63321i	0.271063	−	0.469494i	−0.698072	−	0.716028i	$-0.745958\pi$
$421$	5.56174	−	9.63321i	0.271063	−	0.469494i	0.969134	+	0.246534i	$0.0792916\pi$
$422$	9.44609	+	31.4771i	0.459828	+	1.53228i
$423$	6.33863	+	11.7423i	0.308195	+	0.570929i
$424$	−4.18795	+	5.01097i	−0.203385	+	0.243354i
$425$	27.2407	+	15.7274i	1.32137	+	0.762893i
$426$	2.39344	+	8.41084i	0.115963	+	0.407506i
$427$	−21.3243	+	3.66174i	−1.03196	+	0.177204i
$428$	13.9243	−	27.8164i	0.673057	−	1.34455i
$429$	4.64117	+	8.31109i	0.224078	+	0.401263i
$430$	13.9082	−	58.8552i	0.670715	−	2.83825i
$431$		−	33.5046i		−	1.61386i	−0.590647	−	0.806930i	$-0.701127\pi$
$431$		−	33.5046i		−	1.61386i	0.590647	−	0.806930i	$-0.298873\pi$
$432$	11.7300	+	17.1583i	0.564360	+	0.825529i
$433$			6.77529i			0.325600i	0.986659	+	0.162800i	$0.0520525\pi$
$433$			6.77529i			0.325600i	−0.986659	+	0.162800i	$0.947948\pi$
$434$	−3.69389	+	5.56984i	−0.177313	+	0.267361i
$435$	28.8817	−	16.1285i	1.38477	−	0.773301i
$436$	−2.29264	−	1.14765i	−0.109798	−	0.0549625i
$437$	0.433522	−	0.250294i	0.0207382	−	0.0119732i
$438$	7.64282	+	26.8578i	0.365188	+	1.28331i
$439$	0.0179749	−	0.0311334i	0.000857895	−	0.00148592i	−0.865596	−	0.500743i	$-0.833060\pi$
$439$	0.0179749	−	0.0311334i	0.000857895	−	0.00148592i	0.866454	+	0.499257i	$0.166394\pi$
$440$	−14.4317	+	17.2678i	−0.688005	+	0.823211i
$441$	15.5687	+	14.0931i	0.741367	+	0.671100i
$442$	−10.7676	+	3.23130i	−0.512163	+	0.153697i
$443$	13.0209	+	7.51761i	0.618641	+	0.357172i	0.776340	−	0.630315i	$-0.217074\pi$
$443$	13.0209	+	7.51761i	0.618641	+	0.357172i	−0.157699	+	0.987487i	$0.550408\pi$
$444$	0.974491	+	21.5534i	0.0462473	+	1.02288i
$445$	15.4880	+	26.8260i	0.734201	+	1.27167i
$446$	8.59328	+	8.09671i	0.406904	+	0.383390i
$447$	−1.81113	+	3.03584i	−0.0856636	+	0.143590i
$448$	−16.2067	−	13.6141i	−0.765694	−	0.643205i
$449$	−22.0365			−1.03997			−0.519983	−	0.854177i	$-0.674062\pi$
$449$	−22.0365			−1.03997			−0.519983	+	0.854177i	$0.674062\pi$
$450$	44.6469	−	12.0174i	2.10468	−	0.566503i
$451$	−9.07998			−0.427559
$452$	−1.75805	−	29.5184i	−0.0826916	−	1.38843i
$453$	0.266742	−	18.6452i	0.0125326	−	0.876028i
$454$	−6.87024	−	6.47323i	−0.322436	−	0.303804i
$455$	4.91707	+	28.6348i	0.230516	+	1.34242i
$456$	−0.411821	−	0.0778670i	−0.0192853	−	0.00364645i
$457$	−8.88558	+	15.3903i	−0.415650	+	0.719927i	−0.995496	−	0.0947989i	$-0.969779\pi$
$457$	−8.88558	+	15.3903i	−0.415650	+	0.719927i	0.579846	+	0.814726i	$0.303113\pi$
$458$	−4.05072	−	13.4982i	−0.189278	−	0.630728i
$459$	−0.643442	+	14.9839i	−0.0300333	+	0.699391i
$460$	38.9508	−	25.6915i	1.81609	−	1.19787i
$461$	29.7074	+	17.1515i	1.38361	+	0.798827i	0.992585	−	0.121553i	$-0.0387874\pi$
$461$	29.7074	+	17.1515i	1.38361	+	0.798827i	0.391025	+	0.920380i	$0.372121\pi$
$462$	−11.6601	+	5.59363i	−0.542477	+	0.260239i
$463$	30.4583	−	17.5851i	1.41552	−	0.817248i	0.419615	−	0.907702i	$-0.362165\pi$
$463$	30.4583	−	17.5851i	1.41552	−	0.817248i	0.995901	+	0.0904537i	$0.0288317\pi$
$464$	−19.0245	+	2.27417i	−0.883189	+	0.105576i
$465$	−0.176460	+	12.3345i	−0.00818312	+	0.571997i
$466$	1.15510	−	4.88803i	0.0535092	−	0.226434i
$467$	2.10775			0.0975348			0.0487674	−	0.998810i	$-0.484471\pi$
$467$	2.10775			0.0975348			0.0487674	+	0.998810i	$0.484471\pi$
$468$	−7.81665	+	14.5591i	−0.361325	+	0.672997i
$469$	−1.86313	+	5.04850i	−0.0860313	+	0.233118i
$470$	−24.4088	−	5.76811i	−1.12589	−	0.266063i
$471$	11.7452	+	7.00700i	0.541190	+	0.322865i
$472$	13.4633	+	2.34668i	0.619700	+	0.108015i
$473$	10.7010	+	18.5346i	0.492031	+	0.852223i
$474$	31.5419	+	7.93181i	1.44877	+	0.364320i
$475$	−0.466170	+	0.807430i	−0.0213893	+	0.0370474i
$476$	−3.47514	−	14.8724i	−0.159283	−	0.681673i
$477$	−3.63356	+	5.89721i	−0.166369	+	0.270015i
$478$	−2.35534	−	7.84869i	−0.107731	−	0.358991i
$479$	0.601718	−	1.04221i	0.0274932	−	0.0476196i	−0.851951	−	0.523621i	$-0.824581\pi$
$479$	0.601718	−	1.04221i	0.0274932	−	0.0476196i	0.879445	+	0.476001i	$0.157914\pi$
$480$	−38.7501	−	4.96310i	−1.76869	−	0.226533i
$481$	−14.8554	+	8.57675i	−0.677346	+	0.391066i
$482$	−2.94928	+	3.13016i	−0.134336	+	0.142575i
$483$	26.4893	−	4.15948i	1.20531	−	0.189263i
$484$	0.834466	+	14.0111i	0.0379303	+	0.636866i
$485$	18.7597			0.851836
$486$	14.9237	+	16.2260i	0.676954	+	0.736026i
$487$		−	4.23920i		−	0.192097i	−0.995377	−	0.0960483i	$-0.969380\pi$
$487$		−	4.23920i		−	0.192097i	0.995377	−	0.0960483i	$-0.0306203\pi$
$488$	21.7198	−	7.95371i	0.983208	−	0.360048i
$489$	−20.2404	+	11.3029i	−0.915302	+	0.511134i
$490$	−39.2412	+	4.25703i	−1.77274	+	0.192313i
$491$	−14.4458	+	8.34027i	−0.651928	+	0.376391i	−0.789195	−	0.614143i	$-0.789502\pi$
$491$	−14.4458	+	8.34027i	−0.651928	+	0.376391i	0.137266	+	0.990534i	$0.456168\pi$
$492$	−8.48969	−	13.2807i	−0.382745	−	0.598741i
$493$	−11.9732	−	6.91271i	−0.539244	−	0.311333i
$494$	−0.0957774	−	0.319158i	−0.00430923	−	0.0143596i
$495$	−12.5213	+	20.3218i	−0.562789	+	0.913398i
$496$	2.81274	−	6.56792i	0.126296	−	0.294908i
$497$	−6.03896	−	7.26270i	−0.270884	−	0.325777i
$498$	10.2295	−	40.6790i	0.458396	−	1.82287i
$499$	26.1648	−	15.1063i	1.17130	−	0.676249i	0.217312	−	0.976102i	$-0.430271\pi$
$499$	26.1648	−	15.1063i	1.17130	−	0.676249i	0.953985	+	0.299853i	$0.0969378\pi$
$500$	−21.0531	+	42.0575i	−0.941525	+	1.88087i
$501$	−11.2365	+	18.8347i	−0.502009	+	0.841473i
$502$	−5.18284	+	21.9321i	−0.231322	+	0.978879i
$503$	−9.33949			−0.416427			−0.208214	−	0.978083i	$-0.566765\pi$
$503$	−9.33949			−0.416427			−0.208214	+	0.978083i	$0.566765\pi$
$504$	−19.0835	−	11.8245i	−0.850048	−	0.526705i
$505$	−11.3654			−0.505753
$506$	−3.79758	+	16.0701i	−0.168823	+	0.714404i
$507$	9.37768	+	0.134159i	0.416477	+	0.00595822i
$508$	0.293086	−	0.585493i	0.0130036	−	0.0259771i
$509$	−9.96494	+	5.75326i	−0.441688	+	0.255009i	−0.704313	−	0.709889i	$-0.748745\pi$
$509$	−9.96494	+	5.75326i	−0.441688	+	0.255009i	0.262625	+	0.964898i	$0.415412\pi$
$510$	−20.2385	−	19.6230i	−0.896175	−	0.868922i
$511$	−19.2838	−	23.1915i	−0.853066	−	1.02593i
$512$	19.6623	+	11.1980i	0.868957	+	0.494887i
$513$	−0.444132	−	0.0190720i	−0.0196089	−	0.000842048i
$514$	8.42661	+	28.0799i	0.371682	+	1.23855i
$515$	7.10263	+	4.10070i	0.312979	+	0.180699i
$516$	−17.1041	+	32.9814i	−0.752967	+	1.45192i
$517$	7.68680	−	4.43798i	0.338065	−	0.195182i
$518$	−10.3792	−	20.8651i	−0.456037	−	0.916759i
$519$	0.188797	−	13.1968i	0.00828725	−	0.579276i
$520$	−10.6804	−	29.1658i	−0.468368	−	1.27901i
$521$		−	28.7291i		−	1.25865i	−0.777144	−	0.629323i	$-0.783332\pi$
$521$		−	28.7291i		−	1.25865i	0.777144	−	0.629323i	$-0.216668\pi$
$522$	−19.6237	+	5.28201i	−0.858908	+	0.231187i
$523$	−20.1932			−0.882986			−0.441493	−	0.897265i	$-0.645551\pi$
$523$	−20.1932			−0.882986			−0.441493	+	0.897265i	$0.645551\pi$
$524$	−0.274210	−	4.60412i	−0.0119789	−	0.201132i
$525$	−38.8528	+	31.3771i	−1.69567	+	1.36941i
$526$	−1.44598	+	1.53466i	−0.0630475	+	0.0669142i
$527$	4.46487	−	2.57779i	0.194493	−	0.112291i
$528$	11.1853	−	8.12575i	0.486778	−	0.353628i
$529$	5.61870	−	9.73187i	0.244291	−	0.423125i
$530$	−3.74220	−	12.4701i	−0.162551	−	0.541665i
$531$	14.4894	+	0.414661i	0.628785	+	0.0179948i
$532$	0.440825	−	0.103005i	0.0191122	−	0.00446583i
$533$	6.26593	−	10.8529i	0.271408	−	0.470092i
$534$	−5.20841	−	18.3030i	−0.225390	−	0.792048i
$535$	31.0075	+	53.7065i	1.34057	+	2.32193i
$536$	0.987843	−	5.66743i	0.0426683	−	0.244796i
$537$	12.3883	−	6.91800i	0.534593	−	0.298534i
$538$	25.1107	+	5.93398i	1.08260	+	0.255832i
$539$	9.07422	−	10.6198i	0.390855	−	0.457426i
$540$	−41.4307	+	0.686639i	−1.78289	+	0.0295482i
$541$	31.7977			1.36709			0.683545	−	0.729908i	$-0.260437\pi$
$541$	31.7977			1.36709			0.683545	+	0.729908i	$0.260437\pi$
$542$	5.03821	−	21.3201i	0.216409	−	0.915775i
$543$	5.58011	−	3.11611i	0.239465	−	0.133725i
$544$	6.51604	+	14.9709i	0.279373	+	0.641872i
$545$	4.42653	−	2.55566i	0.189612	−	0.109472i
$546$	1.36059	−	17.7969i	0.0582279	−	0.761636i
$547$	6.72258	+	3.88128i	0.287437	+	0.165952i	0.636785	−	0.771041i	$-0.280264\pi$
$547$	6.72258	+	3.88128i	0.287437	+	0.165952i	−0.349349	+	0.936993i	$0.613597\pi$
$548$	−20.2819	+	13.3777i	−0.866401	+	0.571468i
$549$	21.5887	−	11.6539i	0.921385	−	0.497375i
$550$	−8.83986	−	29.4570i	−0.376933	−	1.25605i
$551$	0.204896	−	0.354891i	0.00872888	−	0.0151189i
$552$	−27.0555	+	9.47095i	−1.15156	+	0.403110i
$553$	−34.6231	+	5.94537i	−1.47232	+	0.252823i
$554$	19.1422	+	18.0361i	0.813276	+	0.766280i
$555$	−36.9388	−	22.0371i	−1.56797	−	0.935423i
$556$	1.05991	+	17.7963i	0.0449501	+	0.754733i
$557$	28.2834			1.19841			0.599203	−	0.800597i	$-0.295484\pi$
$557$	28.2834			1.19841			0.599203	+	0.800597i	$0.295484\pi$
$558$	1.95310	−	7.32227i	0.0826815	−	0.309976i
$559$	−29.5382			−1.24933
$560$	40.4464	−	12.0272i	1.70917	−	0.508240i
$561$	9.97504	+	0.142705i	0.421146	+	0.00602501i
$562$	20.3237	+	19.1492i	0.857302	+	0.807762i
$563$	12.2242	+	21.1729i	0.515187	+	0.892331i	0.999845	+	0.0176266i	$0.00561102\pi$
$563$	12.2242	+	21.1729i	0.515187	+	0.892331i	−0.484657	+	0.874704i	$0.661056\pi$
$564$	13.6782	+	7.09353i	0.575958	+	0.298692i
$565$	51.0543	+	29.4762i	2.14787	+	1.24007i
$566$	23.1085	−	6.93473i	0.971324	−	0.291488i
$567$	−21.8310	−	9.50822i	−0.916817	−	0.399308i
$568$	7.74793	+	6.47539i	0.325096	+	0.271701i
$569$	−12.6476	+	21.9063i	−0.530215	+	0.918360i	0.469163	+	0.883111i	$0.344556\pi$
$569$	−12.6476	+	21.9063i	−0.530215	+	0.918360i	−0.999379	+	0.0352483i	$0.988778\pi$
$570$	0.581637	−	0.599879i	0.0243621	−	0.0251262i
$571$	−15.5735	+	8.99137i	−0.651731	+	0.376277i	−0.789119	−	0.614240i	$-0.789463\pi$
$571$	−15.5735	+	8.99137i	−0.651731	+	0.376277i	0.137388	+	0.990517i	$0.456129\pi$
$572$	9.82908	+	4.92024i	0.410974	+	0.205726i
$573$	−0.249570	+	17.4448i	−0.0104259	+	0.728769i
$574$	14.1886	+	9.40982i	0.592220	+	0.392758i
$575$			63.7667i			2.65926i
$576$	22.3432	+	8.76255i	0.930966	+	0.365106i
$577$		−	13.5843i		−	0.565523i	−0.959190	−	0.282762i	$-0.908749\pi$
$577$		−	13.5843i		−	0.565523i	0.959190	−	0.282762i	$-0.0912505\pi$
$578$	2.81955	−	11.9314i	0.117278	−	0.496282i
$579$	−10.4181	+	17.4629i	−0.432960	+	0.725732i
$580$	17.0982	−	34.1569i	0.709966	−	1.41829i
$581$	7.66764	+	44.6528i	0.318107	+	1.85251i
$582$	−11.1768	−	2.81062i	−0.463293	−	0.116504i
$583$	3.99018	+	2.30373i	0.165257	+	0.0954109i
$584$	24.7410	+	20.6774i	1.02379	+	0.855638i
$585$	−15.6491	−	28.9899i	−0.647011	−	1.19858i
$586$	10.4649	+	34.8721i	0.432301	+	1.44055i
$587$	23.6479	−	40.9593i	0.976052	−	1.69057i	0.299634	−	0.954054i	$-0.403135\pi$
$587$	23.6479	−	40.9593i	0.976052	−	1.69057i	0.676418	−	0.736518i	$-0.263531\pi$
$588$	24.0172	+	3.34292i	0.990452	+	0.137860i
$589$	0.0764072	+	0.132341i	0.00314830	+	0.00545302i
$590$	−18.6839	+	19.8297i	−0.769203	+	0.816378i
$591$	−17.1710	−	30.7487i	−0.706322	−	1.26483i
$592$	14.9294	+	19.9443i	0.613593	+	0.819707i
$593$		−	0.875544i		−	0.0359543i	−0.999838	−	0.0179772i	$-0.994277\pi$
$593$		−	0.875544i		−	0.0359543i	0.999838	−	0.0179772i	$-0.00572261\pi$
$594$	10.5047	−	10.2315i	0.431011	−	0.419803i
$595$	28.5652	+	10.5419i	1.17106	+	0.432175i
$596$	0.242679	+	4.07469i	0.00994052	+	0.166906i
$597$	−19.2353	−	34.4453i	−0.787250	−	1.40975i
$598$	−16.5873	−	15.6288i	−0.678305	−	0.639109i
$599$	−12.3931	+	7.15518i	−0.506370	+	0.292353i	−0.731340	−	0.682013i	$-0.761105\pi$
$599$	−12.3931	+	7.15518i	−0.506370	+	0.292353i	0.224970	+	0.974366i	$0.427771\pi$
$600$	34.8197	−	40.4715i	1.42151	−	1.65224i
$601$	−30.3634	−	17.5303i	−1.23855	−	0.715076i	−0.269751	−	0.962930i	$-0.586941\pi$
$601$	−30.3634	−	17.5303i	−1.23855	−	0.715076i	−0.968797	+	0.247854i	$0.920275\pi$
$602$	2.48633	−	40.0524i	0.101335	−	1.63241i
$603$	0.174553	−	6.09935i	0.00710834	−	0.248385i
$604$	−11.8555	−	17.9741i	−0.482393	−	0.731354i
$605$	−24.2332	−	13.9910i	−0.985219	−	0.568816i
$606$	6.77134	+	1.70278i	0.275067	+	0.0691708i
$607$	−18.7611	−	32.4951i	−0.761489	−	1.31894i	−0.942083	−	0.335380i	$-0.891135\pi$
$607$	−18.7611	−	32.4951i	−0.761489	−	1.31894i	0.180594	−	0.983558i	$-0.442198\pi$
$608$	−0.443746	+	0.193139i	−0.0179963	+	0.00783282i
$609$	17.0770	−	13.7912i	0.691996	−	0.558849i
$610$	−10.6050	+	44.8768i	−0.429382	+	1.81701i
$611$			12.2503i			0.495593i
$612$	9.11784	+	14.7233i	0.368567	+	0.595154i
$613$	−0.149504			−0.00603840			−0.00301920	−	0.999995i	$-0.500961\pi$
$613$	−0.149504			−0.00603840			−0.00301920	+	0.999995i	$0.500961\pi$
$614$	2.38752	−	10.1032i	0.0963526	−	0.407733i
$615$	31.4208	+	0.449513i	1.26701	+	0.0181261i
$616$	−7.49895	+	12.9136i	−0.302141	+	0.520304i
$617$	−3.41249	−	5.91061i	−0.137382	−	0.237952i	0.789123	−	0.614235i	$-0.210535\pi$
$617$	−3.41249	−	5.91061i	−0.137382	−	0.237952i	−0.926505	+	0.376283i	$0.877202\pi$
$618$	−3.61727	−	3.50727i	−0.145508	−	0.141083i
$619$	10.1762	−	17.6257i	0.409016	−	0.708436i	−0.585764	−	0.810482i	$-0.699205\pi$
$619$	10.1762	−	17.6257i	0.409016	−	0.708436i	0.994780	+	0.102045i	$0.0325387\pi$
$620$	7.84282	+	11.8905i	0.314975	+	0.477533i
$621$	−26.9587	+	14.0584i	−1.08181	+	0.564144i
$622$	−38.4975	+	11.5529i	−1.54361	+	0.463228i
$623$	13.1415	+	15.8045i	0.526503	+	0.633194i
$624$	1.99357	+	18.9768i	0.0798069	+	0.759678i
$625$	−19.6376	−	34.0133i	−0.785503	−	1.36053i
$626$	−14.4129	+	15.2969i	−0.576057	+	0.611386i
$627$	−0.00422986	+	0.295665i	−0.000168924	+	0.0118077i
$628$	15.7644	−	0.938889i	0.629067	−	0.0374658i
$629$			17.9768i			0.716782i
$630$	40.6261	−	18.7792i	1.61858	−	0.748183i
$631$		−	21.2923i		−	0.847634i	−0.905748	−	0.423817i	$-0.860690\pi$
$631$		−	21.2923i		−	0.847634i	0.905748	−	0.423817i	$-0.139310\pi$
$632$	35.2652	−	12.9140i	1.40277	−	0.513691i
$633$	34.5660	+	20.6215i	1.37387	+	0.819632i
$634$	−22.0384	−	20.7649i	−0.875256	−	0.824679i
$635$	0.652661	+	1.13044i	0.0259001	+	0.0448603i
$636$	0.361259	+	7.99016i	0.0143248	+	0.316830i
$637$	6.43139	+	18.1745i	0.254821	+	0.720102i
$638$	3.88540	+	12.9473i	0.153824	+	0.512587i
$639$	9.11823	+	5.61819i	0.360712	+	0.222252i
$640$	−40.2188	+	20.4300i	−1.58979	+	0.807568i
$641$	−3.95191	+	6.84490i	−0.156091	+	0.270357i	−0.933456	−	0.358693i	$-0.883223\pi$
$641$	−3.95191	+	6.84490i	−0.156091	+	0.270357i	0.777365	+	0.629050i	$0.216556\pi$
$642$	−10.4274	−	36.6432i	−0.411537	−	1.44619i
$643$	20.3837	+	35.3055i	0.803853	+	1.39231i	0.917062	+	0.398744i	$0.130554\pi$
$643$	20.3837	+	35.3055i	0.803853	+	1.39231i	−0.113209	+	0.993571i	$0.536113\pi$
$644$	22.5881	−	21.1760i	0.890096	−	0.834453i
$645$	−36.1126	−	64.6679i	−1.42193	−	2.54630i
$646$	−0.339852	−	0.0803114i	−0.0133713	−	0.00315981i
$647$	−17.8067			−0.700054			−0.350027	−	0.936740i	$-0.613828\pi$
$647$	−17.8067			−0.700054			−0.350027	+	0.936740i	$0.613828\pi$
$648$	24.7867	+	5.79814i	0.973714	+	0.227772i
$649$		−	9.64184i		−	0.378475i
$650$	41.3089	+	9.76182i	1.62027	+	0.382890i
$651$	1.26976	+	8.08638i	0.0497660	+	0.316930i
$652$	−11.9825	+	23.9372i	−0.469271	+	0.937454i
$653$	6.78123	+	11.7454i	0.265370	+	0.459635i	0.967661	−	0.252256i	$-0.0811725\pi$
$653$	6.78123	+	11.7454i	0.265370	+	0.459635i	−0.702290	+	0.711891i	$0.747839\pi$
$654$	−3.02016	+	0.859435i	−0.118097	+	0.0336065i
$655$	7.96317	+	4.59754i	0.311147	+	0.179641i
$656$	−16.7311	−	7.16517i	−0.653240	−	0.279753i
$657$	29.1167	+	17.9402i	1.13595	+	0.699914i
$658$	−16.6108	−	1.03115i	−0.647556	−	0.0401983i
$659$	−37.2494	−	21.5060i	−1.45103	−	0.837754i	−0.452492	−	0.891768i	$-0.649465\pi$
$659$	−37.2494	−	21.5060i	−1.45103	−	0.837754i	−0.998540	+	0.0540142i	$0.982798\pi$
$660$	1.24490	+	27.5341i	0.0484576	+	1.07176i
$661$	37.6797	−	21.7544i	1.46557	−	0.846148i	0.466312	−	0.884620i	$-0.345582\pi$
$661$	37.6797	−	21.7544i	1.46557	−	0.846148i	0.999260	+	0.0384716i	$0.0122489\pi$
$662$	16.4726	−	17.4829i	0.640226	−	0.679491i
$663$	−7.05417	+	11.8243i	−0.273961	+	0.459216i
$664$	−16.6550	−	45.4809i	−0.646338	−	1.76500i
$665$	−0.312467	+	0.846688i	−0.0121169	+	0.0328331i
$666$	18.7060	+	18.6636i	0.724843	+	0.723202i
$667$		−	28.0275i		−	1.08523i
$668$	1.50561	+	25.2799i	0.0582539	+	0.978109i
$669$	14.4589	+	0.206852i	0.559012	+	0.00799736i
$670$	8.34739	+	7.86503i	0.322488	+	0.303853i
$671$	−8.15943	−	14.1326i	−0.314991	−	0.545581i
$672$	−25.8994	+	1.10585i	−0.999090	+	0.0426592i
$673$	21.6667	−	37.5278i	0.835189	−	1.44659i	−0.0586878	−	0.998276i	$-0.518692\pi$
$673$	21.6667	−	37.5278i	0.835189	−	1.44659i	0.893877	−	0.448313i	$-0.147975\pi$
$674$	13.2892	−	3.98802i	0.511882	−	0.153613i
$675$	30.3915	−	47.7808i	1.16977	−	1.83908i
$676$	9.04013	−	5.96276i	0.347697	−	0.229337i
$677$	−18.0239	−	10.4061i	−0.692714	−	0.399939i	0.111914	−	0.993718i	$-0.464302\pi$
$677$	−18.0239	−	10.4061i	−0.692714	−	0.399939i	−0.804628	+	0.593779i	$0.797635\pi$
$678$	−26.0013	−	25.2106i	−0.998573	−	0.968206i
$679$	12.2686	−	2.10673i	0.470826	−	0.0808488i
$680$	−32.0672	−	5.58937i	−1.22972	−	0.214343i
$681$	−11.5597	−	0.165376i	−0.442969	−	0.00633722i
$682$	−4.90572	−	1.15929i	−0.187850	−	0.0443913i
$683$		−	10.0088i		−	0.382976i	−0.981495	−	0.191488i	$-0.938669\pi$
$683$		−	10.0088i		−	0.382976i	0.981495	−	0.191488i	$-0.0613313\pi$
$684$	−0.436406	+	0.270258i	−0.0166864	+	0.0103336i
$685$		−	48.4378i		−	1.85071i
$686$	−25.1851	+	7.19084i	−0.961573	+	0.274548i
$687$	−14.8228	−	8.84303i	−0.565524	−	0.337383i
$688$	5.09201	+	42.5969i	0.194131	+	1.62399i
$689$	−5.50711	+	3.17953i	−0.209804	+	0.121130i
$690$	13.9369	−	55.4219i	0.530568	−	2.10987i
$691$	17.4952	−	30.3025i	0.665548	−	1.15276i	−0.313588	−	0.949559i	$-0.601531\pi$
$691$	17.4952	−	30.3025i	0.665548	−	1.15276i	0.979136	−	0.203204i	$-0.0651355\pi$
$692$	−8.39115	−	12.7218i	−0.318984	−	0.483610i
$693$	−5.90659	+	14.6963i	−0.224373	+	0.558267i
$694$	−1.50674	−	5.02089i	−0.0571950	−	0.190590i
$695$	−30.7801	−	17.7709i	−1.16756	−	0.674089i
$696$	−15.3043	+	17.7885i	−0.580110	+	0.674272i
$697$	−6.56667	−	11.3738i	−0.248730	−	0.430814i
$698$	4.83124	−	5.12754i	0.182865	−	0.194080i
$699$	−2.99922	−	5.37079i	−0.113441	−	0.203142i
$700$	−16.7137	+	55.1912i	−0.631717	+	2.08603i
$701$	30.2491			1.14249			0.571246	−	0.820779i	$-0.306460\pi$
$701$	30.2491			1.14249			0.571246	+	0.820779i	$0.306460\pi$
$702$	4.98020	+	19.6163i	0.187966	+	0.740371i
$703$	−0.532842			−0.0200965
$704$	5.40105	−	15.0227i	0.203560	−	0.566188i
$705$	−26.8195	+	14.9769i	−1.01008	+	0.564061i
$706$	−11.6531	+	12.3678i	−0.438570	+	0.465468i
$707$	−7.43280	+	1.27634i	−0.279539	+	0.0480016i
$708$	14.1025	−	9.01503i	0.530005	−	0.338806i
$709$	−19.3696	+	33.5492i	−0.727441	+	1.25997i	0.230520	+	0.973068i	$0.425957\pi$
$709$	−19.3696	+	33.5492i	−0.727441	+	1.25997i	−0.957961	+	0.286897i	$0.907376\pi$
$710$	−19.2811	+	5.78616i	−0.723608	+	0.217151i
$711$	35.0524	−	18.9218i	1.31457	−	0.709621i
$712$	−16.8604	−	14.0912i	−0.631871	−	0.528091i
$713$	9.05138	+	5.22582i	0.338977	+	0.195708i
$714$	−15.4393	−	10.5604i	−0.577803	−	0.395213i
$715$	−18.9775	+	10.9567i	−0.709719	+	0.409756i
$716$	7.33396	−	14.6509i	0.274083	−	0.547531i
$717$	−8.61889	−	5.14189i	−0.321878	−	0.192028i
$718$	−38.0367	−	8.98855i	−1.41952	−	0.335450i
$719$	−12.3006			−0.458734			−0.229367	−	0.973340i	$-0.573666\pi$
$719$	−12.3006			−0.458734			−0.229367	+	0.973340i	$0.573666\pi$
$720$	−39.1085	+	27.5650i	−1.45749	+	1.02729i
$721$	5.10553	+	1.88417i	0.190140	+	0.0701703i
$722$	−6.17716	+	26.1398i	−0.229890	+	0.972821i
$723$	−0.0753472	+	5.26674i	−0.00280219	+	0.195872i
$724$	3.30347	−	6.59929i	0.122773	−	0.245261i
$725$	26.1004	+	45.2073i	0.969346	+	1.67896i
$726$	12.3416	+	11.9663i	0.458041	+	0.444112i
$727$	10.0761	−	17.4523i	0.373701	−	0.647269i	−0.616431	−	0.787409i	$-0.711422\pi$
$727$	10.0761	−	17.4523i	0.373701	−	0.647269i	0.990132	+	0.140140i	$0.0447552\pi$
$728$	−10.2602	−	17.8746i	−0.380268	−	0.662478i
$729$	26.9006	+	2.31461i	0.996319	+	0.0857261i
$730$	−61.5692	+	18.4766i	−2.27878	+	0.683848i
$731$	−15.4780	+	26.8086i	−0.572473	+	0.991553i
$732$	13.0418	−	25.1481i	0.482039	−	0.929501i
$733$	−25.3422	+	14.6313i	−0.936034	+	0.540419i	−0.888715	−	0.458460i	$-0.848401\pi$
$733$	−25.3422	+	14.6313i	−0.936034	+	0.540419i	−0.0473190	+	0.998880i	$0.515068\pi$
$734$	30.3979	+	28.6413i	1.12201	+	1.05717i
$735$	−31.9266	+	36.2999i	−1.17763	+	1.33894i
$736$	−19.6788	+	26.6147i	−0.725370	+	0.981031i
$737$	−4.05876			−0.149506
$738$	−18.6527	−	4.97534i	−0.686616	−	0.183145i
$739$			11.9818i			0.440757i	0.975414	+	0.220378i	$0.0707292\pi$
$739$			11.9818i			0.440757i	−0.975414	+	0.220378i	$0.929271\pi$
$740$	−49.5792	+	2.95282i	−1.82257	+	0.108548i
$741$	−0.350477	−	0.209089i	−0.0128751	−	0.00768108i
$742$	−3.84774	−	7.73500i	−0.141255	−	0.283961i
$743$	30.9885	−	17.8912i	1.13686	−	0.656365i	0.191207	−	0.981550i	$-0.438760\pi$
$743$	30.9885	−	17.8912i	1.13686	−	0.656365i	0.945651	+	0.325184i	$0.105426\pi$
$744$	−2.89119	−	8.25921i	−0.105996	−	0.302797i
$745$	−7.04749	−	4.06887i	−0.258200	−	0.149072i
$746$	−18.6915	+	5.60920i	−0.684343	+	0.205367i
$747$	−24.4031	−	45.2065i	−0.892862	−	1.65402i
$748$	9.61599	−	6.34259i	0.351595	−	0.231908i
$749$	26.3097	+	31.6412i	0.961336	+	1.15614i
$750$	15.7659	+	55.4034i	0.575691	+	2.02305i
$751$	5.11442	−	2.95281i	0.186628	−	0.107750i	−0.403775	−	0.914858i	$-0.632302\pi$
$751$	5.11442	−	2.95281i	0.186628	−	0.107750i	0.590403	+	0.807109i	$0.298969\pi$
$752$	17.6661	−	2.11179i	0.644216	−	0.0770091i
$753$	13.4572	+	24.0982i	0.490408	+	0.878188i
$754$	−18.1566	−	4.29063i	−0.661223	−	0.156255i
$755$	42.9261			1.56224
$756$	−27.0180	+	5.10174i	−0.982635	+	0.185548i
$757$	−14.4509			−0.525226			−0.262613	−	0.964901i	$-0.584584\pi$
$757$	−14.4509			−0.525226			−0.262613	+	0.964901i	$0.584584\pi$
$758$	−22.1611	−	5.23696i	−0.804929	−	0.190215i
$759$	9.86038	+	17.6573i	0.357909	+	0.640918i
$760$	0.165672	−	0.950488i	0.00600955	−	0.0344778i
$761$	24.8767	−	14.3626i	0.901781	−	0.520643i	0.0240032	−	0.999712i	$-0.492359\pi$
$761$	24.8767	−	14.3626i	0.901781	−	0.520643i	0.877777	+	0.479069i	$0.159025\pi$
$762$	−0.219482	−	0.771285i	−0.00795098	−	0.0279407i
$763$	2.60789	−	2.16846i	0.0944118	−	0.0785037i
$764$	11.0922	+	16.8169i	0.401303	+	0.608415i
$765$	−34.5110	−	0.987648i	−1.24775	−	0.0357085i
$766$	23.3257	−	6.99990i	0.842792	−	0.252917i
$767$	11.5245	+	6.65366i	0.416125	+	0.240250i
$768$	27.0226	−	6.14628i	0.975096	−	0.221785i
$769$	5.21450	−	3.01059i	0.188040	−	0.108565i	−0.403025	−	0.915189i	$-0.632041\pi$
$769$	5.21450	−	3.01059i	0.188040	−	0.108565i	0.591065	+	0.806624i	$0.298708\pi$
$770$	−13.2593	−	26.6549i	−0.477833	−	0.960574i
$771$	30.8354	+	18.3959i	1.11051	+	0.662513i
$772$	1.39595	+	23.4386i	0.0502413	+	0.843574i
$773$		−	32.8018i		−	1.17980i	−0.807476	−	0.589900i	$-0.799167\pi$
$773$		−	32.8018i		−	1.17980i	0.807476	−	0.589900i	$-0.200833\pi$
$774$	11.8267	+	43.9387i	0.425103	+	1.57934i
$775$	−19.4660			−0.699241
$776$	−12.4961	+	4.57605i	−0.448585	+	0.164271i
$777$	−26.6322	−	10.2637i	−0.955426	−	0.368209i
$778$	−4.45804	−	4.20043i	−0.159828	−	0.150593i
$779$	0.337126	−	0.194640i	0.0120788	−	0.00697369i
$780$	−33.7694	−	17.5128i	−1.20914	−	0.627060i
$781$	3.56202	−	6.16959i	0.127459	−	0.220765i
$782$	−22.8763	+	6.86503i	−0.818054	+	0.245493i
$783$	−13.3580	+	21.0012i	−0.477377	+	0.750520i
$784$	25.1008	−	12.4077i	0.896455	−	0.443134i
$785$	−15.7418	+	27.2657i	−0.561851	+	0.973154i
$786$	−4.05553	−	3.93221i	−0.144656	−	0.140257i
$787$	−0.916080	−	1.58670i	−0.0326547	−	0.0565597i	0.849236	−	0.528013i	$-0.177063\pi$
$787$	−0.916080	−	1.58670i	−0.0326547	−	0.0565597i	−0.881891	+	0.471454i	$0.843730\pi$
$788$	−36.3648	−	18.2035i	−1.29544	−	0.648473i
$789$	−0.0369413	+	2.58218i	−0.00131514	+	0.0919281i
$790$	−17.2187	+	72.8639i	−0.612613	+	2.59238i
$791$	36.6990	+	13.5436i	1.30487	+	0.481556i
$792$	3.38352	−	16.5910i	0.120228	−	0.589534i
$793$	22.5227			0.799805
$794$	−39.3565	−	9.30045i	−1.39671	−	0.330061i
$795$	−13.6938	−	8.16949i	−0.485668	−	0.289742i
$796$	−40.7366	−	20.3919i	−1.44387	−	0.722772i
$797$	24.2935	−	14.0259i	0.860520	−	0.496822i	−0.00366627	−	0.999993i	$-0.501167\pi$
$797$	24.2935	−	14.0259i	0.860520	−	0.496822i	0.864186	+	0.503172i	$0.167834\pi$
$798$	0.313016	−	0.457631i	0.0110806	−	0.0161999i
$799$	11.1182	+	6.41912i	0.393335	+	0.227092i
$800$	6.95636	−	61.2542i	0.245944	−	2.16566i
$801$	−19.8424	−	12.2258i	−0.701095	−	0.431979i
$802$	−16.3436	+	4.90463i	−0.577114	+	0.173188i
$803$	11.3744	−	19.7010i	0.401392	−	0.695232i
$804$	−3.79491	−	5.93650i	−0.133836	−	0.209364i
$805$	10.4465	+	60.8358i	0.368192	+	2.14418i
$806$	4.77100	−	5.06360i	0.168051	−	0.178358i
$807$	27.5907	−	15.4075i	0.971240	−	0.542371i
$808$	7.57065	−	2.77235i	0.266335	−	0.0975309i
$809$	−21.3196			−0.749557			−0.374779	−	0.927114i	$-0.622281\pi$
$809$	−21.3196			−0.749557			−0.374779	+	0.927114i	$0.622281\pi$
$810$	−36.8573	+	34.8855i	−1.29503	+	1.22575i
$811$	−7.69767			−0.270302			−0.135151	−	0.990825i	$-0.543152\pi$
$811$	−7.69767			−0.270302			−0.135151	+	0.990825i	$0.543152\pi$
$812$	7.34618	−	24.2583i	0.257800	−	0.851298i
$813$	−13.0817	−	23.4257i	−0.458794	−	0.821575i
$814$	12.0535	−	12.7927i	0.422474	−	0.448384i
$815$	−26.6833	−	46.2169i	−0.934676	−	1.61891i
$816$	18.2678	+	8.13443i	0.639500	+	0.284762i
$817$	−0.794622	−	0.458775i	−0.0278003	−	0.0160505i
$818$	9.31880	+	31.0529i	0.325824	+	1.08574i
$819$	−13.4899	−	17.2016i	−0.471374	−	0.601071i
$820$	30.2898	−	19.9788i	1.05777	−	0.697690i
$821$	9.17336	−	15.8887i	0.320152	−	0.554520i	−0.660367	−	0.750943i	$-0.729599\pi$
$821$	9.17336	−	15.8887i	0.320152	−	0.554520i	0.980519	+	0.196423i	$0.0629325\pi$
$822$	−7.25704	+	28.8586i	−0.253118	+	1.00656i
$823$	−10.2067	+	5.89282i	−0.355782	+	0.205411i	−0.667229	−	0.744853i	$-0.732520\pi$
$823$	−10.2067	+	5.89282i	−0.355782	+	0.205411i	0.311447	+	0.950264i	$0.399186\pi$
$824$	−5.73144	−	0.999002i	−0.199664	−	0.0348019i
$825$	−32.3476	−	19.2981i	−1.12620	−	0.671873i
$826$	−9.99210	+	15.0666i	−0.347670	+	0.524233i
$827$		−	6.80800i		−	0.236737i	−0.992970	−	0.118369i	$-0.962234\pi$
$827$		−	6.80800i		−	0.236737i	0.992970	−	0.118369i	$-0.0377665\pi$
$828$	−16.6068	+	30.9315i	−0.577127	+	1.07495i
$829$			6.20652i			0.215561i	0.994175	+	0.107781i	$0.0343744\pi$
$829$			6.20652i			0.215561i	−0.994175	+	0.107781i	$0.965626\pi$
$830$	93.9714	+	22.2066i	3.26179	+	0.770804i
$831$	32.2083	+	0.460780i	1.11730	+	0.0159843i
$832$	14.2288	+	16.8225i	0.493294	+	0.583216i
$833$	19.8651	+	3.68635i	0.688285	+	0.127725i
$834$	15.6759	+	15.1992i	0.542812	+	0.526305i
$835$	−43.7235	−	25.2438i	−1.51311	−	0.873597i
$836$	0.187998	+	0.285023i	0.00650204	+	0.00985773i
$837$	−4.29160	−	8.22967i	−0.148339	−	0.284459i
$838$	15.8388	−	4.75313i	0.547142	−	0.164194i
$839$	−19.9867	+	34.6180i	−0.690017	+	1.19514i	0.281815	+	0.959469i	$0.409064\pi$
$839$	−19.9867	+	34.6180i	−0.690017	+	1.19514i	−0.971832	+	0.235676i	$0.924270\pi$
$840$	26.5890	−	44.3156i	0.917409	−	1.52903i
$841$	3.02804	+	5.24471i	0.104415	+	0.180852i
$842$	−11.4494	−	10.7878i	−0.394571	−	0.371770i
$843$	34.1962	+	0.489218i	1.17778	+	0.0168496i
$844$	46.3944	−	2.76314i	1.59696	−	0.0951112i
$845$			21.5898i			0.742713i
$846$	18.2225	−	4.90486i	0.626504	−	0.168632i
$847$	−17.4194	−	6.42854i	−0.598536	−	0.220887i
$848$	5.53455	+	7.39367i	0.190057	+	0.253900i
$849$	15.1390	−	25.3762i	0.519570	−	0.870909i
$850$	30.5055	−	32.3764i	1.04633	−	1.11050i
$851$	−31.5609	+	18.2217i	−1.08189	+	0.624631i
$852$	12.3543	−	0.558576i	0.423252	−	0.0191365i
$853$	25.2532	+	14.5799i	0.864652	+	0.499207i	0.865567	−	0.500793i	$-0.166958\pi$
$853$	25.2532	+	14.5799i	0.864652	+	0.499207i	−0.000915480		1.00000i	$0.500291\pi$
$854$	−1.89581	+	30.5397i	−0.0648733	+	1.04505i
$855$	0.0292744	−	1.02293i	0.00100116	−	0.0349833i
$856$	−33.7551	−	28.2111i	−1.15373	−	0.964235i
$857$	30.8516	+	17.8122i	1.05387	+	0.608452i	0.923730	−	0.383044i	$-0.125124\pi$
$857$	30.8516	+	17.8122i	1.05387	+	0.608452i	0.130139	+	0.991496i	$0.458458\pi$
$858$	12.9481	−	3.68459i	0.442041	−	0.125790i
$859$	0.414494	+	0.717924i	0.0141423	+	0.0244953i	0.873010	−	0.487702i	$-0.162165\pi$
$859$	0.414494	+	0.717924i	0.0141423	+	0.0244953i	−0.858868	+	0.512198i	$0.828832\pi$
$860$	−76.4793	−	38.2840i	−2.60792	−	1.30547i
$861$	20.5992	−	3.23459i	0.702020	−	0.110235i
$862$	−46.1126	−	10.8970i	−1.57060	−	0.371153i
$863$		−	7.37519i		−	0.251054i	−0.992090	−	0.125527i	$-0.959938\pi$
$863$		−	7.37519i		−	0.251054i	0.992090	−	0.125527i	$-0.0400622\pi$
$864$	27.4301	−	10.5635i	0.933192	−	0.359379i
$865$	30.3825			1.03304
$866$	9.32488	+	2.20359i	0.316872	+	0.0748810i
$867$	−7.32093	−	13.1098i	−0.248632	−	0.445232i
$868$	6.46440	+	6.89546i	0.219416	+	0.234047i
$869$	−13.2480	−	22.9462i	−0.449408	−	0.778398i
$870$	−12.8043	−	44.9957i	−0.434105	−	1.52550i
$871$	2.80088	−	4.85127i	0.0949042	−	0.164379i
$872$	−2.32518	+	2.78212i	−0.0787404	+	0.0942145i
$873$	−12.4208	+	6.70488i	−0.420379	+	0.226926i
$874$	−0.203483	−	0.678065i	−0.00688292	−	0.0229359i
$875$	−39.7795	−	47.8405i	−1.34479	−	1.61730i
$876$	39.4503	−	1.78366i	1.33290	−	0.0602644i
$877$	−10.0813	−	17.4613i	−0.340420	−	0.589625i	0.644091	−	0.764949i	$-0.277236\pi$
$877$	−10.0813	−	17.4613i	−0.340420	−	0.589625i	−0.984511	+	0.175324i	$0.943903\pi$
$878$	−0.0370030	−	0.0348648i	−0.00124879	−	0.00117663i
$879$	38.2941	+	22.8457i	1.29163	+	0.770565i
$880$	19.0721	+	25.4786i	0.642919	+	0.858884i
$881$			15.9543i			0.537513i	0.963208	+	0.268756i	$0.0866126\pi$
$881$			15.9543i			0.537513i	−0.963208	+	0.268756i	$0.913387\pi$
$882$	24.4600	−	16.8437i	0.823610	−	0.567156i
$883$			53.4055i			1.79724i	0.438731	+	0.898619i	$0.355428\pi$
$883$			53.4055i			1.79724i	−0.438731	+	0.898619i	$0.644572\pi$
$884$	0.945209	+	15.8705i	0.0317908	+	0.533782i
$885$	−0.477329	+	33.3651i	−0.0160452	+	1.12156i
$886$	14.5814	−	15.4757i	0.489873	−	0.519917i
$887$	18.7836	+	32.5342i	0.630692	+	1.09239i	0.987411	+	0.158178i	$0.0505621\pi$
$887$	18.7836	+	32.5342i	0.630692	+	1.09239i	−0.356719	+	0.934212i	$0.616105\pi$
$888$	29.9810	+	5.66879i	1.00610	+	0.190232i
$889$	0.553781	+	0.666000i	0.0185732	+	0.0223369i
$890$	41.9581	−	12.5914i	1.40644	−	0.422064i
$891$	1.02710	−	17.9302i	0.0344093	−	0.600684i
$892$	13.9384	−	9.19362i	0.466693	−	0.307825i
$893$	−0.190266	+	0.329551i	−0.00636702	+	0.0110280i
$894$	3.58919	+	3.48004i	0.120040	+	0.116390i
$895$	16.3317	+	28.2873i	0.545908	+	0.945541i
$896$	−24.0082	+	17.8775i	−0.802058	+	0.597246i
$897$	−27.9094	−	0.399279i	−0.931869	−	0.0133315i
$898$	−7.16712	+	30.3289i	−0.239170	+	1.01209i
$899$	8.55594			0.285357
$900$	−2.01865	−	65.3564i	−0.0672882	−	2.17855i
$901$			6.66427i			0.222019i
$902$	−2.95316	+	12.4968i	−0.0983295	+	0.416099i
$903$	−30.8794	−	38.2364i	−1.02760	−	1.27243i
$904$	−41.1981	−	7.18092i	−1.37023	−	0.238834i
$905$	7.35637	+	12.7416i	0.244534	+	0.423545i
$906$	−25.5748	−	6.43126i	−0.849664	−	0.213664i
$907$	−24.9768	−	14.4203i	−0.829340	−	0.478819i	0.0242869	−	0.999705i	$-0.492268\pi$
$907$	−24.9768	−	14.4203i	−0.829340	−	0.478819i	−0.853627	+	0.520886i	$0.825602\pi$
$908$	−11.1436	+	7.35020i	−0.369814	+	0.243925i
$909$	7.52498	−	4.06208i	0.249588	−	0.134731i
$910$	41.0094	+	2.54574i	1.35945	+	0.0843904i
$911$	−3.53596	−	2.04149i	−0.117152	−	0.0676376i	0.440279	−	0.897861i	$-0.354879\pi$
$911$	−3.53596	−	2.04149i	−0.117152	−	0.0676376i	−0.557431	+	0.830223i	$0.688213\pi$
$912$	−0.241109	+	0.541466i	−0.00798392	+	0.0179297i
$913$	−29.5934	+	17.0857i	−0.979398	+	0.565456i
$914$	18.2918	+	17.2348i	0.605039	+	0.570077i
$915$	27.5357	+	49.3089i	0.910301	+	1.63010i
$916$	−19.8951	+	1.18490i	−0.657352	+	0.0391504i
$917$	5.72411	+	2.11246i	0.189027	+	0.0697595i
$918$	20.4132	+	5.75894i	0.673737	+	0.190073i
$919$		−	0.244050i		−	0.00805047i	−0.999992	−	0.00402523i	$-0.998719\pi$
$919$		−	0.244050i		−	0.00805047i	0.999992	−	0.00402523i	$-0.00128128\pi$
$920$	−22.6910	−	61.9641i	−0.748101	−	2.04289i
$921$	−6.19918	−	11.1011i	−0.204270	−	0.365792i
$922$	33.2678	−	35.3081i	1.09562	−	1.16281i
$923$	4.91617	+	8.51505i	0.161818	+	0.280276i
$924$	3.90624	+	17.8671i	0.128506	+	0.587785i
$925$	33.9376	−	58.7817i	1.11586	−	1.93273i
$926$	−14.2963	−	47.6393i	−0.469804	−	1.56552i
$927$	−6.16824	−	0.176525i	−0.202592	−	0.00579783i
$928$	−3.05754	+	26.9232i	−0.100369	+	0.883796i
$929$	−18.5771	−	10.7255i	−0.609496	−	0.351893i	0.163272	−	0.986581i	$-0.447795\pi$
$929$	−18.5771	−	10.7255i	−0.609496	−	0.351893i	−0.772768	+	0.634688i	$0.781129\pi$
$930$	16.9186	+	4.25451i	0.554783	+	0.139511i
$931$	−0.109265	+	0.588812i	−0.00358103	+	0.0192975i
$932$	−6.35174	−	3.17956i	−0.208058	−	0.104150i
$933$	−25.2208	+	42.2753i	−0.825692	+	1.38403i
$934$	0.685521	−	2.90090i	0.0224309	−	0.0949205i
$935$			22.9651i			0.751040i
$936$	17.4956	+	15.4933i	0.571860	+	0.506415i
$937$			57.2133i			1.86908i	0.355863	+	0.934538i	$0.384187\pi$
$937$			57.2133i			1.86908i	−0.355863	+	0.934538i	$0.615813\pi$
$938$	6.34232	+	4.20620i	0.207084	+	0.137337i
$939$	−0.368216	+	25.7382i	−0.0120163	+	0.839934i
$940$	−15.8774	+	31.7180i	−0.517863	+	1.03453i
$941$	8.14635	−	4.70330i	0.265564	−	0.153323i	−0.361306	−	0.932447i	$-0.617669\pi$
$941$	8.14635	−	4.70330i	0.265564	−	0.153323i	0.626870	+	0.779124i	$0.284336\pi$
$942$	13.4638	−	13.8860i	0.438673	−	0.452432i
$943$	13.3122	−	23.0575i	0.433506	−	0.750855i
$944$	7.60855	−	17.7664i	0.247637	−	0.578248i
$945$	21.1670	−	50.5635i	0.688562	−	1.64483i
$946$	28.9897	−	8.69964i	0.942537	−	0.282850i
$947$	33.4447	+	19.3093i	1.08681	+	0.627469i	0.932725	−	0.360589i	$-0.117424\pi$
$947$	33.4447	+	19.3093i	1.08681	+	0.627469i	0.154083	+	0.988058i	$0.450758\pi$
$948$	21.1753	−	40.8316i	0.687740	−	1.32615i
$949$	15.6985	+	27.1906i	0.509594	+	0.882643i
$950$	0.959655	+	0.904200i	0.0311353	+	0.0293361i
$951$	−37.0813	−	0.530494i	−1.20244	−	0.0172024i
$952$	−21.5992	−	0.0542133i	−0.700033	−	0.00175706i
$953$	52.7991			1.71033			0.855166	−	0.518355i	$-0.173455\pi$
$953$	52.7991			1.71033			0.855166	+	0.518355i	$0.173455\pi$
$954$	6.93460	+	6.91890i	0.224516	+	0.224008i
$955$	−40.1625			−1.29963
$956$	−11.5683	+	0.688978i	−0.374144	+	0.0222831i
$957$	14.2178	+	8.48212i	0.459596	+	0.274188i
$958$	−1.23869	−	1.16711i	−0.0400203	−	0.0377077i
$959$	−5.43958	−	31.6776i	−0.175653	−	1.02292i
$960$	−19.4338	+	51.7178i	−0.627222	+	1.66918i
$961$	13.9047	−	24.0837i	0.448539	−	0.776893i
$962$	6.97269	+	23.2350i	0.224809	+	0.749127i
$963$	−39.7251	−	24.4766i	−1.28012	−	0.788746i
$964$	3.34884	+	5.07716i	0.107859	+	0.163524i
$965$	−40.5388	−	23.4051i	−1.30499	−	0.753437i
$966$	2.89063	−	37.8102i	0.0930046	−	1.21652i
$967$	−9.22794	+	5.32776i	−0.296751	+	0.171329i	−0.640982	−	0.767556i	$-0.721473\pi$
$967$	−9.22794	+	5.32776i	−0.296751	+	0.171329i	0.344232	+	0.938885i	$0.388139\pi$
$968$	19.5549	+	3.40846i	0.628518	+	0.109552i
$969$	−0.373417	+	0.208528i	−0.0119959	+	0.00669888i
$970$	6.10140	−	25.8192i	0.195904	−	0.829003i
$971$	−9.00425			−0.288960			−0.144480	−	0.989508i	$-0.546151\pi$
$971$	−9.00425			−0.288960			−0.144480	+	0.989508i	$0.546151\pi$
$972$	27.1857	−	15.2623i	0.871982	−	0.489538i
$973$	−22.1255	−	8.16531i	−0.709310	−	0.261768i
$974$	−5.83444	−	1.37875i	−0.186948	−	0.0441781i
$975$	45.3887	−	25.3465i	1.45360	−	0.811737i
$976$	−3.88263	−	32.4799i	−0.124280	−	1.03966i
$977$	−4.49955	−	7.79345i	−0.143953	−	0.249334i	0.785029	−	0.619459i	$-0.212648\pi$
$977$	−4.49955	−	7.79345i	−0.143953	−	0.249334i	−0.928982	+	0.370125i	$0.879315\pi$
$978$	8.97326	+	31.5331i	0.286933	+	1.00832i
$979$	−7.75137	+	13.4258i	−0.247735	+	0.429090i
$980$	−6.90380	+	55.3925i	−0.220534	+	1.76945i
$981$	−2.01737	+	3.27417i	−0.0644098	+	0.104536i
$982$	6.78044	+	22.5944i	0.216373	+	0.721016i
$983$	−2.02127	+	3.50095i	−0.0644686	+	0.111663i	−0.896458	−	0.443128i	$-0.853869\pi$
$983$	−2.02127	+	3.50095i	−0.0644686	+	0.111663i	0.831990	+	0.554791i	$0.187202\pi$
$984$	−21.0395	+	7.36502i	−0.670715	+	0.234788i
$985$	70.2115	−	40.5366i	2.23712	−	1.29160i
$986$	−13.4081	+	14.2305i	−0.427002	+	0.453190i
$987$	−15.8577	+	12.8065i	−0.504755	+	0.407635i
$988$	−0.470410	+	0.0280165i	−0.0149657	+	0.000891324i
$989$	−62.7552			−1.99550
$990$	23.8966	+	23.8425i	0.759485	+	0.757766i
$991$			27.3007i			0.867235i	0.901097	+	0.433617i	$0.142763\pi$
$991$			27.3007i			0.867235i	−0.901097	+	0.433617i	$0.857237\pi$
$992$	−8.12466	−	6.00734i	−0.257958	−	0.190733i
$993$	0.420836	−	29.4163i	0.0133548	−	0.933498i
$994$	−11.9598	+	5.94935i	−0.379342	+	0.188702i
$995$	78.6523	−	45.4099i	2.49344	−	1.43959i
$996$	−52.6598	−	27.3094i	−1.66859	−	0.865330i
$997$	−28.4727	−	16.4387i	−0.901740	−	0.520620i	−0.0239754	−	0.999713i	$-0.507632\pi$
$997$	−28.4727	−	16.4387i	−0.901740	−	0.520620i	−0.877764	+	0.479093i	$0.840966\pi$
$998$	−12.2810	−	40.9239i	−0.388749	−	1.29542i
$999$	32.3333	+	1.38846i	1.02298	+	0.0439289i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.2.bi.c.223.25	yes	80
3.2	odd	2		756.2.bi.c.559.15		80
4.3	odd	2	inner	252.2.bi.c.223.32	yes	80
7.6	odd	2	inner	252.2.bi.c.223.26	yes	80
9.4	even	3	inner	252.2.bi.c.139.31	yes	80
9.5	odd	6		756.2.bi.c.307.10		80
12.11	even	2		756.2.bi.c.559.9		80
21.20	even	2		756.2.bi.c.559.16		80
28.27	even	2	inner	252.2.bi.c.223.31	yes	80
36.23	even	6		756.2.bi.c.307.16		80
36.31	odd	6	inner	252.2.bi.c.139.26	yes	80
63.13	odd	6	inner	252.2.bi.c.139.32	yes	80
63.41	even	6		756.2.bi.c.307.9		80
84.83	odd	2		756.2.bi.c.559.10		80
252.139	even	6	inner	252.2.bi.c.139.25	✓	80
252.167	odd	6		756.2.bi.c.307.15		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.bi.c.139.25	✓	80	252.139	even	6	inner
252.2.bi.c.139.26	yes	80	36.31	odd	6	inner
252.2.bi.c.139.31	yes	80	9.4	even	3	inner
252.2.bi.c.139.32	yes	80	63.13	odd	6	inner
252.2.bi.c.223.25	yes	80	1.1	even	1	trivial
252.2.bi.c.223.26	yes	80	7.6	odd	2	inner
252.2.bi.c.223.31	yes	80	28.27	even	2	inner
252.2.bi.c.223.32	yes	80	4.3	odd	2	inner
756.2.bi.c.307.9		80	63.41	even	6
756.2.bi.c.307.10		80	9.5	odd	6
756.2.bi.c.307.15		80	252.167	odd	6
756.2.bi.c.307.16		80	36.23	even	6
756.2.bi.c.559.9		80	12.11	even	2
756.2.bi.c.559.10		80	84.83	odd	2
756.2.bi.c.559.15		80	3.2	odd	2
756.2.bi.c.559.16		80	21.20	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	252.bi (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.325239 - 1.37631i) q^{2} +(-0.844480 - 1.51223i) q^{3} +(-1.78844 - 0.895257i) q^{4} +(3.45303 - 1.99361i) q^{5} +(-2.35596 + 0.670425i) q^{6} +(2.03435 - 1.69157i) q^{7} +(-1.81382 + 2.17027i) q^{8} +(-1.57371 + 2.55410i) q^{9} +(-1.62076 - 5.40083i) q^{10} +(1.72816 + 0.997755i) q^{11} +(0.156462 + 3.46057i) q^{12} +(-2.38515 + 1.37707i) q^{13} +(-1.66647 - 3.35006i) q^{14} +(-5.93082 - 3.53823i) q^{15} +(2.39703 + 3.20222i) q^{16} +2.88632i q^{17} +(3.00340 + 2.99660i) q^{18} -0.0855521 q^{19} +(-7.96033 + 0.474099i) q^{20} +(-4.27602 - 1.64792i) q^{21} +(1.93528 - 2.05397i) q^{22} +(-5.06735 + 2.92564i) q^{23} +(4.81369 + 0.910170i) q^{24} +(5.44896 - 9.43788i) q^{25} +(1.11952 + 3.73057i) q^{26} +(5.19137 + 0.222928i) q^{27} +(-5.15271 + 1.20400i) q^{28} +(-2.39499 + 4.14825i) q^{29} +(-6.79863 + 7.01186i) q^{30} +(-0.893108 - 1.54691i) q^{31} +(5.18685 - 2.25756i) q^{32} +(0.0494419 - 3.45597i) q^{33} +(3.97246 + 0.938743i) q^{34} +(3.65236 - 9.89675i) q^{35} +(5.10106 - 3.15899i) q^{36} +6.22828 q^{37} +(-0.0278249 + 0.117746i) q^{38} +(4.09666 + 2.44400i) q^{39} +(-1.93650 + 11.1101i) q^{40} +(-3.94059 + 2.27510i) q^{41} +(-3.65877 + 5.34915i) q^{42} +(9.28817 + 5.36253i) q^{43} +(-2.19747 - 3.33157i) q^{44} +(-0.342182 + 11.9568i) q^{45} +(2.37847 + 7.92576i) q^{46} +(2.22398 - 3.85205i) q^{47} +(2.81827 - 6.32909i) q^{48} +(1.27718 - 6.88250i) q^{49} +(-11.2172 - 10.5690i) q^{50} +(4.36479 - 2.43744i) q^{51} +(5.49852 - 0.327479i) q^{52} +2.30892 q^{53} +(1.99525 - 7.07241i) q^{54} +7.95654 q^{55} +(-0.0187828 + 7.48329i) q^{56} +(0.0722470 + 0.129375i) q^{57} +(4.93031 + 4.64541i) q^{58} +(-2.41588 - 4.18443i) q^{59} +(7.43929 + 11.6375i) q^{60} +(-7.08218 - 4.08890i) q^{61} +(-2.41949 + 0.726076i) q^{62} +(1.11897 + 7.85798i) q^{63} +(-1.42013 - 7.87294i) q^{64} +(-5.49066 + 9.51011i) q^{65} +(-4.74040 - 1.19206i) q^{66} +(-1.76145 + 1.01697i) q^{67} +(2.58400 - 5.16201i) q^{68} +(8.70352 + 5.19238i) q^{69} +(-12.4331 - 8.24557i) q^{70} -3.57003i q^{71} +(-2.68867 - 8.04805i) q^{72} -11.4000i q^{73} +(2.02568 - 8.57202i) q^{74} +(-18.8738 - 0.270013i) q^{75} +(0.153005 + 0.0765911i) q^{76} +(5.20346 - 0.893522i) q^{77} +(4.69608 - 4.84337i) q^{78} +(-11.4989 - 6.63892i) q^{79} +(14.6610 + 6.27865i) q^{80} +(-4.04688 - 8.03883i) q^{81} +(1.84960 + 6.16341i) q^{82} +(-8.56210 + 14.8300i) q^{83} +(6.17209 + 6.77534i) q^{84} +(5.75420 + 9.96656i) q^{85} +(10.4014 - 11.0393i) q^{86} +(8.29564 + 0.118679i) q^{87} +(-5.29997 + 1.94083i) q^{88} +7.76882i q^{89} +(16.3449 + 4.35975i) q^{90} +(-2.52283 + 6.83608i) q^{91} +(11.6818 - 0.695744i) q^{92} +(-1.58508 + 2.65692i) q^{93} +(-4.57827 - 4.31372i) q^{94} +(-0.295414 + 0.170557i) q^{95} +(-7.79415 - 5.93727i) q^{96} +(4.07462 + 2.35248i) q^{97} +(-9.05704 - 3.99625i) q^{98} +(-5.26799 + 2.84373i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 6 q^{2} - 2 q^{4} - 24 q^{8} - 32 q^{9} + 10 q^{14} - 18 q^{16} - 22 q^{18} + 4 q^{21} - 14 q^{22} + 32 q^{25} + 28 q^{28} + 8 q^{29} - 16 q^{30} - 16 q^{32} + 34 q^{36} - 16 q^{37} - 8 q^{42} - 84 q^{44}+ \cdots + 20 q^{98}+O(q^{100}) \) 80 * q - 6 * q^2 - 2 * q^4 - 24 * q^8 - 32 * q^9 + 10 * q^14 - 18 * q^16 - 22 * q^18 + 4 * q^21 - 14 * q^22 + 32 * q^25 + 28 * q^28 + 8 * q^29 - 16 * q^30 - 16 * q^32 + 34 * q^36 - 16 * q^37 - 8 * q^42 - 84 * q^44 + 24 * q^46 - 24 * q^49 - 12 * q^50 - 48 * q^53 + 32 * q^56 + 72 * q^57 - 14 * q^58 + 56 * q^60 - 8 * q^64 - 40 * q^65 - 22 * q^70 - 100 * q^72 + 64 * q^74 - 12 * q^77 - 24 * q^78 - 104 * q^81 + 62 * q^84 + 40 * q^85 - 52 * q^86 + 6 * q^88 + 30 * q^92 + 48 * q^93 + 20 * q^98

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