LMFDB - Embedded newform 252.2.bi.c.223.26

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			223.26
Character	$\chi$	$=$	252.223
Dual form			252.2.bi.c.139.26

$q$-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} +(-0.447766 + 2.60759i) 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} +(3.44321 + 1.46435i) 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} +(-4.32141 + 1.52493i) 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} +(3.13526 - 4.26264i) 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} +(0.693274 + 6.44355i) 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} +(-6.59901 - 2.33518i) 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} +(-4.84700 - 5.70146i) 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} +(-5.95539 - 5.24722i) 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} +(-14.8089 + 1.80795i) 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} +(-3.37555 + 4.05957i) 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} +(9.09378 + 1.14154i) 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} +(-5.36018 + 8.32277i) 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	$0.683729\pi$
$5$	−3.45303	+	1.99361i	−1.54424	+	0.891570i	−0.998564	+	0.0535758i	$0.982938\pi$
$6$	2.35596	−	0.670425i	0.961815	−	0.273700i
$7$	−0.447766	+	2.60759i	−0.169240	+	0.985575i
$7$	−0.447766	+	2.60759i	−0.169240	+	0.985575i
$8$	−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	−0.131335	−	0.991338i	$-0.541926\pi$
$13$	2.38515	−	1.37707i	0.661521	−	0.381929i	0.792856	+	0.609409i	$0.208593\pi$
$14$	3.44321	+	1.46435i	0.920236	+	0.391365i
$15$	−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	$-0.886176\pi$
$17$		−	2.88632i		−	0.700035i	0.936743	−	0.350018i	$-0.113824\pi$
$18$	3.00340	+	2.99660i	0.707908	+	0.706305i
$19$	0.0855521			0.0196270			0.00981349	−	0.999952i	$-0.496876\pi$
$19$	0.0855521			0.0196270			0.00981349	+	0.999952i	$0.496876\pi$
$20$	7.96033	−	0.474099i	1.77998	−	0.106012i
$21$	−4.32141	+	1.52493i	−0.943009	+	0.332766i
$22$	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
$28$	3.13526	−	4.26264i	0.592509	−	0.805564i
$29$	−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	0.935015	−	0.354609i	$-0.115386\pi$
$31$	0.893108	+	1.54691i	0.160407	+	0.277833i	−0.774608	+	0.632442i	$0.782053\pi$
$32$	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	−0.159666	−	0.987171i	$-0.551042\pi$
$41$	3.94059	−	2.27510i	0.615417	−	0.355311i	0.775083	+	0.631860i	$0.217708\pi$
$42$	0.693274	+	6.44355i	0.106974	+	0.994262i
$43$	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	−0.981391	−	0.192020i	$-0.938496\pi$
$47$	−2.22398	+	3.85205i	−0.324401	+	0.561879i	0.656990	+	0.753899i	$0.271829\pi$
$48$	−2.81827	+	6.32909i	−0.406782	+	0.913525i
$49$	−6.59901	−	2.33518i	−0.942716	−	0.333597i
$50$	−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
$56$	−4.84700	−	5.70146i	−0.647707	−	0.761890i
$57$	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	0.979336	−	0.202242i	$-0.0648227\pi$
$59$	2.41588	+	4.18443i	0.314521	+	0.544767i	−0.664814	+	0.747009i	$0.731489\pi$
$60$	7.43929	+	11.6375i	0.960408	+	1.50240i
$61$	7.08218	+	4.08890i	0.906780	+	0.523530i	0.879394	−	0.476095i	$-0.157948\pi$
$61$	7.08218	+	4.08890i	0.906780	+	0.523530i	0.0273862	+	0.999625i	$0.491282\pi$
$62$	2.41949	−	0.726076i	0.307276	−	0.0922117i
$63$	−5.95539	−	5.24722i	−0.750309	−	0.661088i
$64$	−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
$70$	−14.8089	+	1.80795i	−1.77000	+	0.216092i
$71$		−	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	$0.232478\pi$
$73$			11.4000i			1.33426i	−0.744940	+	0.667132i	$0.767522\pi$
$74$	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
$77$	−3.37555	+	4.05957i	−0.384679	+	0.462631i
$78$	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	$-0.444333\pi$
$83$	8.56210	−	14.8300i	0.939812	−	1.62780i	0.765820	−	0.643056i	$-0.222334\pi$
$84$	9.09378	+	1.14154i	0.992213	+	0.124552i
$85$	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	$-0.864919\pi$
$89$		−	7.76882i		−	0.823493i	0.911298	−	0.411746i	$-0.135081\pi$
$90$	−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	0.278670	−	0.960387i	$-0.410107\pi$
$97$	−4.07462	−	2.35248i	−0.413715	−	0.238859i	−0.692385	+	0.721528i	$0.743440\pi$
$98$	−5.36018	+	8.32277i	−0.541460	+	0.840727i
$99$	−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	0.617762	−	0.786365i	$-0.288039\pi$
$101$	2.46857	+	1.42523i	0.245631	+	0.141815i	−0.372131	+	0.928180i	$0.621373\pi$
$102$	−1.93506	−	6.80004i	−0.191600	−	0.673305i
$103$	−1.02846	−	1.78135i	−0.101337	−	0.175521i	0.810899	−	0.585187i	$-0.198979\pi$
$103$	−1.02846	−	1.78135i	−0.101337	−	0.175521i	−0.912236	+	0.409665i	$0.865645\pi$
$104$	−1.33762	+	7.67416i	−0.131164	+	0.752513i
$105$	11.8819	−	13.8808i	1.15955	−	1.35463i
$106$	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
$112$	−9.42339	+	4.81662i	−0.890426	+	0.455127i
$113$	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
$119$	7.52633	+	1.29240i	0.689937	+	0.118474i
$120$	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
$126$	−9.15871	+	6.48984i	−0.815923	+	0.578161i
$127$			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	0.811247	−	0.584703i	$-0.198789\pi$
$131$	−1.15307	−	1.99717i	−0.100744	−	0.174494i	−0.911991	+	0.410209i	$0.865456\pi$
$132$	3.18241	−	6.13653i	0.276993	−	0.534117i
$133$	−0.0383073	+	0.223084i	−0.00332167	+	0.0193439i
$134$	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	0.990776	−	0.135507i	$-0.0432665\pi$
$139$	4.45697	+	7.71970i	0.378035	+	0.654776i	−0.612741	+	0.790284i	$0.709933\pi$
$140$	−2.32812	+	20.9695i	−0.196762	+	1.77225i
$141$	−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
$147$	−2.04139	−	11.9513i	−0.168371	−	0.985724i
$148$	−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
$154$	4.48936	+	5.96612i	0.361763	+	0.480763i
$155$	−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	−0.201654	−	0.979457i	$-0.564632\pi$
$157$	6.83827	−	3.94808i	0.545753	−	0.315091i	0.747407	+	0.664366i	$0.231298\pi$
$158$	−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	0.999933	−	0.0115994i	$-0.00369227\pi$
$167$	6.33117	+	10.9659i	0.489921	+	0.848568i	−0.510012	+	0.860167i	$0.670359\pi$
$168$	4.52876	−	12.1446i	0.349401	−	0.936973i
$169$	−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	0.227704	−	0.973730i	$-0.426878\pi$
$173$	−6.59908	−	3.80998i	−0.501719	−	0.289668i	−0.729423	+	0.684063i	$0.760211\pi$
$174$	−2.86140	+	11.3787i	−0.216923	+	0.862621i
$175$	22.1702	+	18.4346i	1.67591	+	1.39353i
$176$	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	$-0.956210\pi$
$181$		−	3.68997i		−	0.274274i	0.990552	−	0.137137i	$-0.0437900\pi$
$182$	10.2291	−	1.24883i	0.758229	−	0.0925691i
$183$	−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
$189$	2.90583	−	13.4371i	0.211368	−	0.977407i
$190$	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
$196$	9.71135	+	10.0841i	0.693668	+	0.720295i
$197$	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	$-0.799091\pi$
$199$	−22.7777			−1.61467			−0.807335	+	0.590093i	$0.799091\pi$
$200$	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
$203$	−9.74451	−	8.10259i	−0.683931	−	0.568690i
$204$	−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
$210$	−15.2398	−	20.8677i	−1.05165	−	1.44001i
$211$	−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	−0.691734	−	0.722152i	$-0.743153\pi$
$223$	4.17435	−	7.23018i	0.279535	−	0.484169i	0.971269	+	0.237984i	$0.0764864\pi$
$224$	3.56429	+	14.5360i	0.238149	+	0.971229i
$225$	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	−0.955266	−	0.295748i	$-0.904431\pi$
$227$	−3.33734	+	5.78045i	−0.221507	+	0.383662i	0.733759	+	0.679410i	$0.237764\pi$
$228$	−0.0133857	−	0.296059i	−0.000886488	−	0.0196070i
$229$	−8.63009	+	4.98258i	−0.570292	+	0.329258i	−0.757266	−	0.653107i	$-0.773465\pi$
$229$	−8.63009	+	4.98258i	−0.570292	+	0.329258i	0.186974	+	0.982365i	$0.440132\pi$
$230$	−24.0138	−	22.6262i	−1.58342	−	1.49193i
$231$	−8.98960	−	1.67639i	−0.591473	−	0.110298i
$232$	−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
$238$	4.22659	−	9.93820i	0.273969	−	0.644198i
$239$	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	0.582420	−	0.812888i	$-0.302106\pi$
$241$	2.63364	+	1.52053i	0.169648	+	0.0979461i	−0.412772	+	0.910834i	$0.635439\pi$
$242$	−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
$245$	27.4420	−	5.09240i	1.75321	−	0.325342i
$246$	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	$-0.332259\pi$
$251$	15.9355			1.00584			0.502920	+	0.864333i	$0.332259\pi$
$252$	5.95324	+	14.7159i	0.375019	+	0.927017i
$253$	−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	0.178505	−	0.983939i	$-0.442874\pi$
$257$	17.9529	−	10.3651i	1.11987	−	0.646559i	0.941369	+	0.337380i	$0.109541\pi$
$258$	25.4777	+	6.40685i	1.58617	+	0.398873i
$259$	−2.78881	+	16.2408i	−0.173288	+	1.00915i
$260$	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
$266$	0.294573	+	0.125278i	0.0180615	+	0.00768131i
$267$	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	$-0.812255\pi$
$269$		−	18.2450i		−	1.11242i	0.831043	−	0.556209i	$-0.187745\pi$
$270$	−7.20995	−	28.3990i	−0.438784	−	1.72831i
$271$	−15.4908			−0.940998			−0.470499	−	0.882400i	$-0.655926\pi$
$271$	−15.4908			−0.940998			−0.470499	+	0.882400i	$0.655926\pi$
$272$	9.24264	−	6.91860i	0.560418	−	0.419502i
$273$	−8.20728	+	9.58804i	−0.496727	+	0.580295i
$274$	−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
$280$	28.1033	+	10.0243i	1.67949	+	0.599067i
$281$	−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	$-0.997399\pi$
$283$	−8.53005	−	14.7745i	−0.507059	−	0.878252i	0.492908	−	0.870082i	$-0.335934\pi$
$284$	−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	0.321683	−	0.946847i	$-0.395751\pi$
$293$	22.2955	−	12.8723i	1.30252	−	0.752009i	0.980835	+	0.194838i	$0.0624181\pi$
$294$	−17.1125	−	1.07744i	−0.998024	−	0.0628373i
$295$	−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
$301$	−18.1422	+	21.8185i	−1.04570	+	1.25760i
$302$	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	$-0.567178\pi$
$307$	−7.34083			−0.418963			−0.209482	+	0.977813i	$0.567178\pi$
$308$	9.67132	−	4.23832i	0.551074	−	0.241501i
$309$	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	$0.131602\pi$
$311$	14.2106	+	24.6135i	0.805809	+	1.39570i	−0.109935	+	0.993939i	$0.535064\pi$
$312$	−12.7347	+	4.45787i	−0.720962	+	0.252377i
$313$	12.8704	+	7.43074i	0.727479	+	0.420010i	0.817499	−	0.575930i	$-0.195360\pi$
$313$	12.8704	+	7.43074i	0.727479	+	0.420010i	−0.0900203	+	0.995940i	$0.528693\pi$
$314$	−3.20969	−	10.6956i	−0.181133	−	0.603589i
$315$	31.0251	+	6.24611i	1.74807	+	0.351928i
$316$	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
$322$	−21.7321	+	2.65318i	−1.21108	+	0.147856i
$323$		−	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
$329$	−9.04872	−	7.52404i	−0.498872	−	0.414814i
$330$	−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
$336$	−15.2417	−	10.1828i	−0.831504	−	0.555519i
$337$	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	0.380069	−	0.924958i	$-0.375900\pi$
$349$	−4.31419	−	2.49080i	−0.230933	−	0.133329i	−0.611003	+	0.791629i	$0.709233\pi$
$350$	32.5823	−	24.5174i	1.74160	−	1.31051i
$351$	−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	0.750674	−	0.660672i	$-0.229729\pi$
$353$	10.4059	+	6.00788i	0.553853	+	0.319767i	−0.196822	+	0.980439i	$0.563062\pi$
$354$	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
$357$	4.40142	+	12.4730i	0.232948	+	0.660140i
$358$	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
$364$	1.60812	−	14.4845i	0.0842885	−	0.759194i
$365$	−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	$-0.553192\pi$
$367$	14.7663	−	25.5760i	0.770796	−	1.33506i	0.937127	−	0.348988i	$-0.113475\pi$
$368$	−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
$371$	−1.03386	+	6.02070i	−0.0536751	+	0.312579i
$372$	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
$378$	−17.5485	−	8.36958i	−0.902598	−	0.430485i
$379$		−	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	0.557724	−	0.830026i	$-0.311675\pi$
$383$	−8.61022	−	14.9133i	−0.439962	−	0.762036i	−0.997686	+	0.0679904i	$0.978341\pi$
$384$	−8.62399	−	17.5962i	−0.440091	−	0.897953i
$385$	3.56267	−	20.7474i	0.181571	−	1.05738i
$386$	−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
$392$	17.0374	−	10.0860i	0.860517	−	0.509422i
$393$	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	$0.254755\pi$
$397$			28.5958i			1.43518i	−0.696466	+	0.717590i	$0.745245\pi$
$398$	−7.40820	+	31.3491i	−0.371340	+	1.57139i
$399$	−0.369706	+	0.130461i	−0.0185084	+	0.00653119i
$400$	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
$406$	−14.3209	+	10.7762i	−0.710736	+	0.534812i
$407$	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	0.0789208	−	0.996881i	$-0.474853\pi$
$409$	19.8538	−	11.4626i	0.981705	−	0.566788i	0.902785	+	0.430093i	$0.141519\pi$
$410$	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	0.687136	−	0.726528i	$-0.258867\pi$
$419$	−5.84657	−	10.1266i	−0.285624	−	0.494715i	−0.972760	+	0.231813i	$0.925534\pi$
$420$	−33.6769	+	14.1877i	−1.64327	+	0.692289i
$421$	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
$427$	−13.8333	+	16.6365i	−0.669441	+	0.805097i
$428$	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	$-0.947948\pi$
$433$		−	6.77529i		−	0.325600i	0.986659	−	0.162800i	$-0.0520525\pi$
$434$	0.809937	+	6.63415i	0.0388782	+	0.318449i
$435$	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	−0.866454	−	0.499257i	$-0.833606\pi$
$439$	−0.0179749	+	0.0311334i	−0.000857895	+	0.00148592i	0.865596	+	0.500743i	$0.166940\pi$
$440$	14.4317	−	17.2678i	0.688005	−	0.823211i
$441$	16.3492	−	13.1797i	0.778534	−	0.627603i
$442$	−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
$448$	21.1653	−	0.177875i	0.999965	−	0.00840381i
$449$	−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
$455$	−22.3399	−	18.5757i	−1.04731	−	0.870842i
$456$	−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	−0.391025	−	0.920380i	$-0.627879\pi$
$461$	−29.7074	−	17.1515i	−1.38361	−	0.798827i	−0.992585	+	0.121553i	$0.961213\pi$
$462$	−5.23100	+	11.8272i	−0.243368	+	0.550252i
$463$	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	$-0.515529\pi$
$467$	−2.10775			−0.0975348			−0.0487674	+	0.998810i	$0.515529\pi$
$468$	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
$476$	−12.3034	−	9.04937i	−0.563923	−	0.414777i
$477$	−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	−0.879445	−	0.476001i	$-0.842086\pi$
$479$	−0.601718	+	1.04221i	−0.0274932	+	0.0476196i	0.851951	+	0.523621i	$0.175419\pi$
$480$	−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
$483$	17.4367	−	20.3702i	0.793399	−	0.926877i
$484$	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
$490$	1.91651	−	39.4249i	0.0865793	−	1.78104i
$491$	−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
$497$	9.30917	+	1.59854i	0.417573	+	0.0717043i
$498$	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	$-0.433235\pi$
$503$	9.33949			0.416427			0.208214	+	0.978083i	$0.433235\pi$
$504$	22.1899	−	3.40729i	0.988415	−	0.151773i
$505$	−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	−0.262625	−	0.964898i	$-0.584588\pi$
$509$	9.96494	−	5.75326i	0.441688	−	0.255009i	0.704313	+	0.709889i	$0.251255\pi$
$510$	20.2385	+	19.6230i	0.896175	+	0.868922i
$511$	−29.7264	−	5.10452i	−1.31502	−	0.225811i
$512$	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
$518$	21.4452	+	9.12039i	0.942250	+	0.400727i
$519$	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	$0.216668\pi$
$521$			28.7291i			1.25865i	−0.777144	+	0.629323i	$0.783332\pi$
$522$	−19.6237	+	5.28201i	−0.858908	+	0.231187i
$523$	20.1932			0.882986			0.441493	−	0.897265i	$-0.354449\pi$
$523$	20.1932			0.882986			0.441493	+	0.897265i	$0.354449\pi$
$524$	0.274210	+	4.60412i	0.0119789	+	0.201132i
$525$	−9.15515	+	49.0942i	−0.399563	+	2.14265i
$526$	−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
$532$	0.268228	−	0.364678i	0.0116292	−	0.0158108i
$533$	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
$546$	10.5268	+	14.4141i	0.450504	+	0.616868i
$547$	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
$553$	22.4604	−	27.0118i	0.955113	−	1.14866i
$554$	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
$560$	22.9368	−	35.4185i	0.969258	−	1.49670i
$561$	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	$-0.994389\pi$
$563$	−12.2242	−	21.1729i	−0.515187	−	0.892331i	0.484657	−	0.874704i	$-0.338944\pi$
$564$	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
$567$	22.7740	−	6.95308i	0.956418	−	0.292002i
$568$	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
$574$	16.8998	−	2.06323i	0.705385	−	0.0861176i
$575$			63.7667i			2.65926i
$576$	22.3432	+	8.76255i	0.930966	+	0.365106i
$577$			13.5843i			0.565523i	0.959190	+	0.282762i	$0.0912505\pi$
$577$			13.5843i			0.565523i	−0.959190	+	0.282762i	$0.908749\pi$
$578$	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
$581$	34.8366	+	28.9668i	1.44527	+	1.20174i
$582$	−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	$0.596865\pi$
$587$	−23.6479	+	40.9593i	−0.976052	+	1.69057i	−0.676418	+	0.736518i	$0.736469\pi$
$588$	−7.04855	+	23.2017i	−0.290677	+	0.956821i
$589$	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	$0.00572261\pi$
$593$			0.875544i			0.0359543i	−0.999838	+	0.0179772i	$0.994277\pi$
$594$	−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	0.968797	−	0.247854i	$-0.0797252\pi$
$601$	30.3634	+	17.5303i	1.23855	+	0.715076i	0.269751	+	0.962930i	$0.413059\pi$
$602$	24.1285	+	32.0654i	0.983402	+	1.30689i
$603$	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	$0.108865\pi$
$607$	18.7611	+	32.4951i	0.761489	+	1.31894i	−0.180594	+	0.983558i	$0.557802\pi$
$608$	0.443746	−	0.193139i	0.0179963	−	0.00783282i
$609$	4.02398	−	21.5785i	0.163060	−	0.874403i
$610$	−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
$616$	−2.68774	−	14.6892i	−0.108292	−	0.591843i
$617$	−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	−0.994780	−	0.102045i	$-0.967461\pi$
$619$	−10.1762	+	17.6257i	−0.409016	+	0.708436i	0.585764	+	0.810482i	$0.300795\pi$
$620$	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
$623$	20.2579	+	3.47862i	0.811614	+	0.139368i
$624$	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
$630$	18.6871	−	40.6685i	0.744513	−	1.62027i
$631$		−	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
$637$	−18.9553	+	3.51752i	−0.751037	+	0.139369i
$638$	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	$-0.869446\pi$
$643$	−20.3837	−	35.3055i	−0.803853	−	1.39231i	0.113209	−	0.993571i	$-0.463887\pi$
$644$	−3.41653	+	30.7729i	−0.134630	+	1.21262i
$645$	−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	$-0.386172\pi$
$647$	17.8067			0.700054			0.350027	+	0.936740i	$0.386172\pi$
$648$	24.7867	+	5.79814i	0.973714	+	0.227772i
$649$			9.64184i			0.378475i
$650$	−41.3089	−	9.76182i	−1.62027	−	0.382890i
$651$	−6.21841	−	5.32290i	−0.243719	−	0.208621i
$652$	−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
$658$	−13.2984	+	10.0067i	−0.518425	+	0.390102i
$659$	−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	−0.999260	−	0.0384716i	$-0.987751\pi$
$661$	−37.6797	+	21.7544i	−1.46557	+	0.846148i	−0.466312	+	0.884620i	$0.654418\pi$
$662$	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
$672$	−18.9719	+	17.6654i	−0.731857	+	0.681458i
$673$	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	0.804628	−	0.593779i	$-0.202365\pi$
$677$	18.0239	+	10.4061i	0.692714	+	0.399939i	−0.111914	+	0.993718i	$0.535698\pi$
$678$	26.0013	+	25.2106i	0.998573	+	0.968206i
$679$	7.95878	−	9.57156i	0.305430	−	0.367323i
$680$	−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
$686$	−19.3022	−	17.7038i	−0.736963	−	0.675933i
$687$	−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	$0.398469\pi$
$691$	−17.4952	+	30.3025i	−0.665548	+	1.15276i	−0.979136	+	0.203204i	$0.934864\pi$
$692$	8.39115	+	12.7218i	0.318984	+	0.483610i
$693$	−5.05644	−	15.0101i	−0.192078	−	0.570185i
$694$	−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
$700$	−23.1464	−	52.8172i	−0.874851	−	1.99630i
$701$	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
$707$	−4.82174	+	5.79883i	−0.181340	+	0.218087i
$708$	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
$714$	18.5982	−	2.00101i	0.696018	−	0.0748859i
$715$	−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	$-0.426334\pi$
$719$	12.3006			0.458734			0.229367	+	0.973340i	$0.426334\pi$
$720$	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	−0.990132	−	0.140140i	$-0.955245\pi$
$727$	−10.0761	+	17.4523i	−0.373701	+	0.647269i	0.616431	+	0.787409i	$0.288578\pi$
$728$	−19.4121	−	6.92419i	−0.719460	−	0.256628i
$729$	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	0.0473190	−	0.998880i	$-0.484932\pi$
$733$	25.3422	−	14.6313i	0.936034	−	0.540419i	0.888715	+	0.458460i	$0.151599\pi$
$734$	−30.3979	−	28.6413i	−1.12201	−	1.05717i
$735$	30.8752	+	37.1984i	1.13885	+	1.37208i
$736$	−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
$742$	7.95008	+	3.38107i	0.291857	+	0.124123i
$743$	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
$749$	−40.5569	−	6.96430i	−1.48192	−	0.254470i
$750$	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
$756$	−17.2266	+	21.4300i	−0.626524	+	0.779402i
$757$	−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	−0.877777	−	0.479069i	$-0.840975\pi$
$761$	−24.8767	+	14.3626i	−0.901781	+	0.520643i	−0.0240032	+	0.999712i	$0.507641\pi$
$762$	0.219482	+	0.771285i	0.00795098	+	0.0279407i
$763$	−0.574003	+	3.34273i	−0.0207803	+	0.121015i
$764$	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	−0.591065	−	0.806624i	$-0.701292\pi$
$769$	−5.21450	+	3.01059i	−0.188040	+	0.108565i	0.403025	+	0.915189i	$0.367959\pi$
$770$	−27.3960	−	11.6512i	−0.987283	−	0.419879i
$771$	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	$0.200833\pi$
$773$			32.8018i			1.17980i	−0.807476	+	0.589900i	$0.799167\pi$
$774$	11.8267	+	43.9387i	0.425103	+	1.57934i
$775$	19.4660			0.699241
$776$	12.4961	−	4.57605i	0.448585	−	0.164271i
$777$	−26.9150	+	9.49766i	−0.965569	+	0.340727i
$778$	−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
$784$	−8.34026	−	26.7290i	−0.297867	−	0.954608i
$785$	−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	0.881891	−	0.471454i	$-0.156270\pi$
$787$	0.916080	+	1.58670i	0.0326547	+	0.0565597i	−0.849236	+	0.528013i	$0.822937\pi$
$788$	−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	−0.864186	−	0.503172i	$-0.832166\pi$
$797$	−24.2935	+	14.0259i	−0.860520	+	0.496822i	0.00366627	+	0.999993i	$0.498833\pi$
$798$	0.0593110	+	0.551259i	0.00209959	+	0.0195144i
$799$	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
$805$	47.4621	+	39.4649i	1.67282	+	1.39095i
$806$	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	$-0.456848\pi$
$811$	7.69767			0.270302			0.135151	+	0.990825i	$0.456848\pi$
$812$	10.1736	+	23.2148i	0.357022	+	0.814681i
$813$	−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
$819$	−21.4303	−	4.31444i	−0.748834	−	0.150759i
$820$	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
$826$	2.19090	+	17.9456i	0.0762313	+	0.624407i
$827$		−	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	$-0.965626\pi$
$829$		−	6.20652i		−	0.215561i	0.994175	−	0.107781i	$-0.0343744\pi$
$830$	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
$833$	−6.74007	+	19.0469i	−0.233530	+	0.659934i
$834$	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	$-0.590936\pi$
$839$	19.9867	−	34.6180i	0.690017	−	1.19514i	0.971832	−	0.235676i	$-0.0757304\pi$
$840$	8.57357	+	50.9642i	0.295816	+	1.75843i
$841$	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	0.000915480	−	1.00000i	$-0.499709\pi$
$853$	−25.2532	−	14.5799i	−0.864652	−	0.499207i	−0.865567	+	0.500793i	$0.833042\pi$
$854$	18.3978	+	24.4497i	0.629560	+	0.836652i
$855$	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	−0.130139	−	0.991496i	$-0.541542\pi$
$857$	−30.8516	−	17.8122i	−1.05387	−	0.608452i	−0.923730	+	0.383044i	$0.874876\pi$
$858$	12.9481	−	3.68459i	0.442041	−	0.125790i
$859$	−0.414494	−	0.717924i	−0.0141423	−	0.0244953i	0.858868	−	0.512198i	$-0.171168\pi$
$859$	−0.414494	−	0.717924i	−0.0141423	−	0.0244953i	−0.873010	+	0.487702i	$0.837835\pi$
$860$	76.4793	+	38.2840i	2.60792	+	1.30547i
$861$	−13.5596	+	15.8408i	−0.462109	+	0.539852i
$862$	−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
$868$	9.39405	+	1.04296i	0.318855	+	0.0354004i
$869$	−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
$875$	−61.3208	−	10.5298i	−2.07302	−	0.355973i
$876$	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	$-0.913387\pi$
$881$		−	15.9543i		−	0.537513i	0.963208	−	0.268756i	$-0.0866126\pi$
$882$	−12.8219	−	26.7881i	−0.431734	−	0.902001i
$883$			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	$-0.949438\pi$
$887$	−18.7836	−	32.5342i	−0.630692	−	1.09239i	0.356719	−	0.934212i	$-0.383895\pi$
$888$	−29.9810	−	5.66879i	−1.00610	−	0.190232i
$889$	−0.853663	−	0.146588i	−0.0286309	−	0.00491641i
$890$	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
$896$	6.63895	−	29.1877i	0.221792	−	0.975094i
$897$	−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
$903$	−48.3154	−	9.00992i	−1.60784	−	0.299831i
$904$	−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
$910$	−32.8316	+	24.7050i	−1.08836	+	0.818963i
$911$	−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
$924$	14.5766	+	11.0461i	0.479534	+	0.363391i
$925$	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	0.772768	−	0.634688i	$-0.218871\pi$
$929$	18.5771	+	10.7255i	0.609496	+	0.351893i	−0.163272	+	0.986581i	$0.552205\pi$
$930$	−16.9186	−	4.25451i	−0.554783	−	0.139511i
$931$	−0.564559	−	0.199779i	−0.0185027	−	0.00654751i
$932$	−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	$-0.615813\pi$
$937$		−	57.2133i		−	1.86908i	0.355863	−	0.934538i	$-0.384187\pi$
$938$	−7.55425	+	0.922268i	−0.246655	+	0.0301131i
$939$	−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	−0.626870	−	0.779124i	$-0.715664\pi$
$941$	−8.14635	+	4.70330i	−0.265564	+	0.153323i	0.361306	+	0.932447i	$0.382331\pi$
$942$	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
$945$	16.7545	+	52.1919i	0.545023	+	1.69780i
$946$	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
$952$	−16.4562	+	13.9900i	−0.533350	+	0.453418i
$953$	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
$959$	24.7138	+	20.5496i	0.798051	+	0.663582i
$960$	−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
$966$	−22.3646	−	30.6235i	−0.719568	−	0.985294i
$967$	−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	$-0.453849\pi$
$971$	9.00425			0.288960			0.144480	+	0.989508i	$0.453849\pi$
$972$	−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
$980$	−53.6374	−	15.4602i	−1.71339	−	0.493859i
$981$	−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	−0.831990	−	0.554791i	$-0.812798\pi$
$983$	2.02127	−	3.50095i	0.0644686	−	0.111663i	0.896458	+	0.443128i	$0.146131\pi$
$984$	−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
$987$	3.73665	−	20.0377i	0.118939	−	0.637807i
$988$	−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
$994$	5.22778	−	12.2924i	0.165815	−	0.389890i
$995$	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	0.877764	−	0.479093i	$-0.159034\pi$
$997$	28.4727	+	16.4387i	0.901740	+	0.520620i	0.0239754	+	0.999713i	$0.492368\pi$
$998$	−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.223.26	yes	80
3.2	odd	2		756.2.bi.c.559.16		80
4.3	odd	2	inner	252.2.bi.c.223.31	yes	80
7.6	odd	2	inner	252.2.bi.c.223.25	yes	80
9.4	even	3	inner	252.2.bi.c.139.32	yes	80
9.5	odd	6		756.2.bi.c.307.9		80
12.11	even	2		756.2.bi.c.559.10		80
21.20	even	2		756.2.bi.c.559.15		80
28.27	even	2	inner	252.2.bi.c.223.32	yes	80
36.23	even	6		756.2.bi.c.307.15		80
36.31	odd	6	inner	252.2.bi.c.139.25	✓	80
63.13	odd	6	inner	252.2.bi.c.139.31	yes	80
63.41	even	6		756.2.bi.c.307.10		80
84.83	odd	2		756.2.bi.c.559.9		80
252.139	even	6	inner	252.2.bi.c.139.26	yes	80
252.167	odd	6		756.2.bi.c.307.16		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.bi.c.139.25	✓	80	36.31	odd	6	inner
252.2.bi.c.139.26	yes	80	252.139	even	6	inner
252.2.bi.c.139.31	yes	80	63.13	odd	6	inner
252.2.bi.c.139.32	yes	80	9.4	even	3	inner
252.2.bi.c.223.25	yes	80	7.6	odd	2	inner
252.2.bi.c.223.26	yes	80	1.1	even	1	trivial
252.2.bi.c.223.31	yes	80	4.3	odd	2	inner
252.2.bi.c.223.32	yes	80	28.27	even	2	inner
756.2.bi.c.307.9		80	9.5	odd	6
756.2.bi.c.307.10		80	63.41	even	6
756.2.bi.c.307.15		80	36.23	even	6
756.2.bi.c.307.16		80	252.167	odd	6
756.2.bi.c.559.9		80	84.83	odd	2
756.2.bi.c.559.10		80	12.11	even	2
756.2.bi.c.559.15		80	21.20	even	2
756.2.bi.c.559.16		80	3.2	odd	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} +(-0.447766 + 2.60759i) 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} +(3.44321 + 1.46435i) 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} +(-4.32141 + 1.52493i) 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} +(3.13526 - 4.26264i) 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} +(0.693274 + 6.44355i) 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} +(-6.59901 - 2.33518i) 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} +(-4.84700 - 5.70146i) 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} +(-5.95539 - 5.24722i) 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} +(-14.8089 + 1.80795i) 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} +(-3.37555 + 4.05957i) 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} +(9.09378 + 1.14154i) 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} +(-5.36018 + 8.32277i) 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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