LMFDB - Embedded newform 140.2.o.a.131.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [140,2,Mod(31,140)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(140, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 1]))

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

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

chi := DirichletCharacter("140.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 140 = 2^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	140.o (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$1.11790562830$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			131.12
Character	$\chi$	$=$	140.131
Dual form			140.2.o.a.31.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.906567 + 1.08542i) q^{2} +(0.406021 + 0.703249i) q^{3} +(-0.356272 + 1.96801i) q^{4} +(0.866025 + 0.500000i) q^{5} +(-0.395235 + 1.07825i) q^{6} +(-0.336411 - 2.62428i) q^{7} +(-2.45910 + 1.39743i) q^{8} +(1.17029 - 2.02701i) q^{9} +O(q^{10})$	\(q+(0.906567 + 1.08542i) q^{2} +(0.406021 + 0.703249i) q^{3} +(-0.356272 + 1.96801i) q^{4} +(0.866025 + 0.500000i) q^{5} +(-0.395235 + 1.07825i) q^{6} +(-0.336411 - 2.62428i) q^{7} +(-2.45910 + 1.39743i) q^{8} +(1.17029 - 2.02701i) q^{9} +(0.242400 + 1.39328i) q^{10} +(-4.20925 + 2.43021i) q^{11} +(-1.52866 + 0.548506i) q^{12} +0.895933i q^{13} +(2.54346 - 2.74423i) q^{14} +0.812042i q^{15} +(-3.74614 - 1.40230i) q^{16} +(5.10231 - 2.94582i) q^{17} +(3.26111 - 0.567359i) q^{18} +(1.45818 - 2.52565i) q^{19} +(-1.29255 + 1.52621i) q^{20} +(1.70893 - 1.30209i) q^{21} +(-6.45377 - 2.36566i) q^{22} +(1.35231 + 0.780755i) q^{23} +(-1.98119 - 1.16198i) q^{24} +(0.500000 + 0.866025i) q^{25} +(-0.972464 + 0.812224i) q^{26} +4.33678 q^{27} +(5.28446 + 0.272896i) q^{28} -9.73084 q^{29} +(-0.881406 + 0.736170i) q^{30} +(-2.20757 - 3.82363i) q^{31} +(-1.87405 - 5.33741i) q^{32} +(-3.41809 - 1.97344i) q^{33} +(7.82304 + 2.86757i) q^{34} +(1.02080 - 2.44090i) q^{35} +(3.57223 + 3.02532i) q^{36} +(0.910682 - 1.57735i) q^{37} +(4.06333 - 0.706927i) q^{38} +(-0.630064 + 0.363768i) q^{39} +(-2.82836 - 0.0193421i) q^{40} +10.4920i q^{41} +(2.96258 + 0.674472i) q^{42} +3.04581i q^{43} +(-3.28305 - 9.14968i) q^{44} +(2.02701 - 1.17029i) q^{45} +(0.378510 + 2.17563i) q^{46} +(2.60966 - 4.52006i) q^{47} +(-0.534848 - 3.20383i) q^{48} +(-6.77366 + 1.76567i) q^{49} +(-0.486718 + 1.32782i) q^{50} +(4.14329 + 2.39213i) q^{51} +(-1.76321 - 0.319196i) q^{52} +(-0.0898619 - 0.155645i) q^{53} +(3.93158 + 4.70723i) q^{54} -4.86043 q^{55} +(4.49451 + 5.98326i) q^{56} +2.36821 q^{57} +(-8.82166 - 10.5620i) q^{58} +(5.68287 + 9.84302i) q^{59} +(-1.59811 - 0.289308i) q^{60} +(-5.33107 - 3.07789i) q^{61} +(2.14893 - 5.86252i) q^{62} +(-5.71313 - 2.38927i) q^{63} +(4.09438 - 6.87285i) q^{64} +(-0.447967 + 0.775901i) q^{65} +(-0.956722 - 5.49911i) q^{66} +(-6.75417 + 3.89952i) q^{67} +(3.97960 + 11.0909i) q^{68} +1.26801i q^{69} +(3.57482 - 1.10484i) q^{70} +8.38078i q^{71} +(-0.0452719 + 6.62003i) q^{72} +(-7.60453 + 4.39048i) q^{73} +(2.53768 - 0.441499i) q^{74} +(-0.406021 + 0.703249i) q^{75} +(4.45099 + 3.76954i) q^{76} +(7.79359 + 10.2287i) q^{77} +(-0.966036 - 0.354104i) q^{78} +(-3.14686 - 1.81684i) q^{79} +(-2.54310 - 3.08749i) q^{80} +(-1.75006 - 3.03119i) q^{81} +(-11.3882 + 9.51172i) q^{82} +2.03796 q^{83} +(1.95369 + 3.82709i) q^{84} +5.89164 q^{85} +(-3.30598 + 2.76123i) q^{86} +(-3.95092 - 6.84320i) q^{87} +(6.95494 - 11.8583i) q^{88} +(1.52812 + 0.882262i) q^{89} +(3.10788 + 1.13921i) q^{90} +(2.35118 - 0.301402i) q^{91} +(-2.01832 + 2.38320i) q^{92} +(1.79264 - 3.10495i) q^{93} +(7.27200 - 1.26516i) q^{94} +(2.52565 - 1.45818i) q^{95} +(2.99262 - 3.48502i) q^{96} -7.83641i q^{97} +(-8.05727 - 5.75156i) q^{98} +11.3763i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{2} - 2 q^{4} - 4 q^{8} - 16 q^{9}+O(q^{10}) $ 32 * q + 2 * q^2 - 2 * q^4 - 4 * q^8 - 16 * q^9	$ 32 q + 2 q^{2} - 2 q^{4} - 4 q^{8} - 16 q^{9} - 30 q^{12} + 2 q^{14} - 14 q^{16} - 12 q^{21} - 8 q^{22} + 36 q^{24} + 16 q^{25} + 30 q^{26} + 2 q^{28} - 40 q^{29} + 2 q^{32} + 60 q^{36} + 8 q^{37} - 60 q^{38} - 62 q^{42} - 18 q^{44} + 12 q^{45} + 2 q^{46} - 16 q^{49} + 4 q^{50} - 36 q^{52} - 8 q^{53} + 12 q^{54} - 4 q^{56} + 48 q^{57} + 2 q^{58} + 14 q^{60} + 24 q^{61} + 4 q^{64} + 4 q^{65} + 24 q^{66} + 60 q^{68} - 4 q^{70} + 4 q^{72} - 72 q^{73} + 38 q^{74} - 40 q^{77} + 120 q^{78} - 36 q^{81} + 42 q^{82} - 20 q^{84} + 28 q^{86} + 4 q^{88} - 60 q^{89} - 4 q^{92} - 8 q^{93} + 18 q^{94} - 60 q^{96} + 78 q^{98}+O(q^{100}) $ 32 * q + 2 * q^2 - 2 * q^4 - 4 * q^8 - 16 * q^9 - 30 * q^12 + 2 * q^14 - 14 * q^16 - 12 * q^21 - 8 * q^22 + 36 * q^24 + 16 * q^25 + 30 * q^26 + 2 * q^28 - 40 * q^29 + 2 * q^32 + 60 * q^36 + 8 * q^37 - 60 * q^38 - 62 * q^42 - 18 * q^44 + 12 * q^45 + 2 * q^46 - 16 * q^49 + 4 * q^50 - 36 * q^52 - 8 * q^53 + 12 * q^54 - 4 * q^56 + 48 * q^57 + 2 * q^58 + 14 * q^60 + 24 * q^61 + 4 * q^64 + 4 * q^65 + 24 * q^66 + 60 * q^68 - 4 * q^70 + 4 * q^72 - 72 * q^73 + 38 * q^74 - 40 * q^77 + 120 * q^78 - 36 * q^81 + 42 * q^82 - 20 * q^84 + 28 * q^86 + 4 * q^88 - 60 * q^89 - 4 * q^92 - 8 * q^93 + 18 * q^94 - 60 * q^96 + 78 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/140\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$101$
$\chi(n)$	$1$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	0.906567	+	1.08542i	0.641040	+	0.767508i
$2$	0.906567	+	1.08542i	0.641040	+	0.767508i
$3$	0.406021	+	0.703249i	0.234416	+	0.406021i	0.959103	−	0.283058i	$-0.0913488\pi$
$3$	0.406021	+	0.703249i	0.234416	+	0.406021i	−0.724687	+	0.689079i	$0.758015\pi$
$4$	−0.356272	+	1.96801i	−0.178136	+	0.984006i
$5$	0.866025	+	0.500000i	0.387298	+	0.223607i
$5$	0.866025	+	0.500000i	0.387298	+	0.223607i
$6$	−0.395235	+	1.07825i	−0.161354	+	0.440192i
$7$	−0.336411	−	2.62428i	−0.127151	−	0.991883i
$7$	−0.336411	−	2.62428i	−0.127151	−	0.991883i
$8$	−2.45910	+	1.39743i	−0.869424	+	0.494066i
$9$	1.17029	−	2.02701i	0.390098	−	0.675670i
$10$	0.242400	+	1.39328i	0.0766537	+	0.440595i
$11$	−4.20925	+	2.43021i	−1.26914	+	0.732737i	−0.974825	−	0.222972i	$-0.928424\pi$
$11$	−4.20925	+	2.43021i	−1.26914	+	0.732737i	−0.294313	+	0.955709i	$0.595091\pi$
$12$	−1.52866	+	0.548506i	−0.441285	+	0.158340i
$13$			0.895933i			0.248487i	0.992252	+	0.124244i	$0.0396504\pi$
$13$			0.895933i			0.248487i	−0.992252	+	0.124244i	$0.960350\pi$
$14$	2.54346	−	2.74423i	0.679769	−	0.733426i
$15$			0.812042i			0.209668i
$16$	−3.74614	−	1.40230i	−0.936535	−	0.350574i
$17$	5.10231	−	2.94582i	1.23749	−	0.714467i	0.268911	−	0.963165i	$-0.413336\pi$
$17$	5.10231	−	2.94582i	1.23749	−	0.714467i	0.968581	+	0.248698i	$0.0800028\pi$
$18$	3.26111	−	0.567359i	0.768650	−	0.133728i
$19$	1.45818	−	2.52565i	0.334530	−	0.579423i	−0.648865	−	0.760904i	$-0.724756\pi$
$19$	1.45818	−	2.52565i	0.334530	−	0.579423i	0.983394	+	0.181481i	$0.0580891\pi$
$20$	−1.29255	+	1.52621i	−0.289022	+	0.341271i
$21$	1.70893	−	1.30209i	0.372919	−	0.284140i
$22$	−6.45377	−	2.36566i	−1.37595	−	0.504359i
$23$	1.35231	+	0.780755i	0.281976	+	0.162799i	0.634317	−	0.773073i	$-0.281281\pi$
$23$	1.35231	+	0.780755i	0.281976	+	0.162799i	−0.352342	+	0.935871i	$0.614615\pi$
$24$	−1.98119	−	1.16198i	−0.404408	−	0.237187i
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$	−0.972464	+	0.812224i	−0.190716	+	0.159290i
$27$	4.33678			0.834614
$28$	5.28446	+	0.272896i	0.998669	+	0.0515724i
$29$	−9.73084			−1.80697			−0.903486	−	0.428618i	$-0.859001\pi$
$29$	−9.73084			−1.80697			−0.903486	+	0.428618i	$0.859001\pi$
$30$	−0.881406	+	0.736170i	−0.160922	+	0.134406i
$31$	−2.20757	−	3.82363i	−0.396492	−	0.686744i	0.596798	−	0.802391i	$-0.296439\pi$
$31$	−2.20757	−	3.82363i	−0.396492	−	0.686744i	−0.993290	+	0.115647i	$0.963106\pi$
$32$	−1.87405	−	5.33741i	−0.331288	−	0.943530i
$33$	−3.41809	−	1.97344i	−0.595013	−	0.343531i
$34$	7.82304	+	2.86757i	1.34164	+	0.491783i
$35$	1.02080	−	2.44090i	0.172546	−	0.412587i
$36$	3.57223	+	3.02532i	0.595372	+	0.504220i
$37$	0.910682	−	1.57735i	0.149715	−	0.259314i	−0.781407	−	0.624022i	$-0.785498\pi$
$37$	0.910682	−	1.57735i	0.149715	−	0.259314i	0.931122	+	0.364707i	$0.118831\pi$
$38$	4.06333	−	0.706927i	0.659158	−	0.114679i
$39$	−0.630064	+	0.363768i	−0.100891	+	0.0582494i
$40$	−2.82836	−	0.0193421i	−0.447203	−	0.00305826i
$41$			10.4920i			1.63858i	0.573381	+	0.819289i	$0.305632\pi$
$41$			10.4920i			1.63858i	−0.573381	+	0.819289i	$0.694368\pi$
$42$	2.96258	+	0.674472i	0.457135	+	0.104073i
$43$			3.04581i			0.464481i	0.972658	+	0.232240i	$0.0746056\pi$
$43$			3.04581i			0.464481i	−0.972658	+	0.232240i	$0.925394\pi$
$44$	−3.28305	−	9.14968i	−0.494938	−	1.37937i
$45$	2.02701	−	1.17029i	0.302169	−	0.174457i
$46$	0.378510	+	2.17563i	0.0558083	+	0.320779i
$47$	2.60966	−	4.52006i	0.380658	−	0.659319i	−0.610498	−	0.792017i	$-0.709031\pi$
$47$	2.60966	−	4.52006i	0.380658	−	0.659319i	0.991156	+	0.132698i	$0.0423642\pi$
$48$	−0.534848	−	3.20383i	−0.0771987	−	0.462433i
$49$	−6.77366	+	1.76567i	−0.967665	+	0.252239i
$50$	−0.486718	+	1.32782i	−0.0688323	+	0.187782i
$51$	4.14329	+	2.39213i	0.580177	+	0.334965i
$52$	−1.76321	−	0.319196i	−0.244513	−	0.0442645i
$53$	−0.0898619	−	0.155645i	−0.0123435	−	0.0213795i	0.859788	−	0.510652i	$-0.170596\pi$
$53$	−0.0898619	−	0.155645i	−0.0123435	−	0.0213795i	−0.872131	+	0.489272i	$0.837262\pi$
$54$	3.93158	+	4.70723i	0.535021	+	0.640573i
$55$	−4.86043			−0.655380
$56$	4.49451	+	5.98326i	0.600604	+	0.799546i
$57$	2.36821			0.313677
$58$	−8.82166	−	10.5620i	−1.15834	−	1.38686i
$59$	5.68287	+	9.84302i	0.739846	+	1.28145i	0.952564	+	0.304338i	$0.0984352\pi$
$59$	5.68287	+	9.84302i	0.739846	+	1.28145i	−0.212718	+	0.977114i	$0.568232\pi$
$60$	−1.59811	−	0.289308i	−0.206315	−	0.0373495i
$61$	−5.33107	−	3.07789i	−0.682573	−	0.394084i	0.118251	−	0.992984i	$-0.462271\pi$
$61$	−5.33107	−	3.07789i	−0.682573	−	0.394084i	−0.800824	+	0.598900i	$0.795605\pi$
$62$	2.14893	−	5.86252i	0.272914	−	0.744541i
$63$	−5.71313	−	2.38927i	−0.719787	−	0.301019i
$64$	4.09438	−	6.87285i	0.511798	−	0.859106i
$65$	−0.447967	+	0.775901i	−0.0555634	+	0.0962387i
$66$	−0.956722	−	5.49911i	−0.117764	−	0.676894i
$67$	−6.75417	+	3.89952i	−0.825154	+	0.476403i	−0.852190	−	0.523232i	$-0.824726\pi$
$67$	−6.75417	+	3.89952i	−0.825154	+	0.476403i	0.0270367	+	0.999634i	$0.491393\pi$
$68$	3.97960	+	11.0909i	0.482597	+	1.34497i
$69$			1.26801i			0.152651i
$70$	3.57482	−	1.10484i	0.427272	−	0.132054i
$71$			8.38078i			0.994616i	0.867574	+	0.497308i	$0.165678\pi$
$71$			8.38078i			0.994616i	−0.867574	+	0.497308i	$0.834322\pi$
$72$	−0.0452719	+	6.62003i	−0.00533535	+	0.780178i
$73$	−7.60453	+	4.39048i	−0.890043	+	0.513866i	−0.873956	−	0.486004i	$-0.838454\pi$
$73$	−7.60453	+	4.39048i	−0.890043	+	0.513866i	−0.0160862	+	0.999871i	$0.505121\pi$
$74$	2.53768	−	0.441499i	0.294999	−	0.0513232i
$75$	−0.406021	+	0.703249i	−0.0468833	+	0.0812042i
$76$	4.45099	+	3.76954i	0.510564	+	0.432396i
$77$	7.79359	+	10.2287i	0.888162	+	1.16567i
$78$	−0.966036	−	0.354104i	−0.109382	−	0.0400944i
$79$	−3.14686	−	1.81684i	−0.354049	−	0.204410i	0.312418	−	0.949945i	$-0.398861\pi$
$79$	−3.14686	−	1.81684i	−0.354049	−	0.204410i	−0.666467	+	0.745534i	$0.732194\pi$
$80$	−2.54310	−	3.08749i	−0.284328	−	0.345192i
$81$	−1.75006	−	3.03119i	−0.194451	−	0.336799i
$82$	−11.3882	+	9.51172i	−1.25762	+	1.05039i
$83$	2.03796			0.223695			0.111847	−	0.993725i	$-0.464323\pi$
$83$	2.03796			0.223695			0.111847	+	0.993725i	$0.464323\pi$
$84$	1.95369	+	3.82709i	0.213165	+	0.417570i
$85$	5.89164			0.639038
$86$	−3.30598	+	2.76123i	−0.356493	+	0.297751i
$87$	−3.95092	−	6.84320i	−0.423584	−	0.733668i
$88$	6.95494	−	11.8583i	0.741399	−	1.26410i
$89$	1.52812	+	0.882262i	0.161981	+	0.0935195i	0.578799	−	0.815470i	$-0.303522\pi$
$89$	1.52812	+	0.882262i	0.161981	+	0.0935195i	−0.416818	+	0.908990i	$0.636855\pi$
$90$	3.10788	+	1.13921i	0.327599	+	0.120083i
$91$	2.35118	−	0.301402i	0.246470	−	0.0315955i
$92$	−2.01832	+	2.38320i	−0.210425	+	0.248465i
$93$	1.79264	−	3.10495i	0.185888	−	0.321968i
$94$	7.27200	−	1.26516i	0.750049	−	0.130492i
$95$	2.52565	−	1.45818i	0.259126	−	0.149606i
$96$	2.99262	−	3.48502i	0.305433	−	0.355689i
$97$		−	7.83641i		−	0.795667i	−0.917458	−	0.397834i	$-0.869762\pi$
$97$		−	7.83641i		−	0.795667i	0.917458	−	0.397834i	$-0.130238\pi$
$98$	−8.05727	−	5.75156i	−0.813907	−	0.580995i
$99$			11.3763i			1.14336i
$100$	−1.88248	+	0.675465i	−0.188248	+	0.0675465i
$101$	−6.30931	+	3.64268i	−0.627799	+	0.362460i	−0.779899	−	0.625905i	$-0.784730\pi$
$101$	−6.30931	+	3.64268i	−0.627799	+	0.362460i	0.152100	+	0.988365i	$0.451396\pi$
$102$	1.15971	+	6.66584i	0.114828	+	0.660016i
$103$	4.60525	−	7.97652i	0.453768	−	0.785950i	−0.544848	−	0.838535i	$-0.683413\pi$
$103$	4.60525	−	7.97652i	0.453768	−	0.785950i	0.998616	+	0.0525850i	$0.0167460\pi$
$104$	−1.25200	−	2.20319i	−0.122769	−	0.216041i
$105$	2.13102	−	0.273180i	0.207966	−	0.0266596i
$106$	0.0874748	−	0.238641i	0.00849630	−	0.0231789i
$107$	12.9808	+	7.49445i	1.25490	+	0.724516i	0.972078	−	0.234657i	$-0.0753968\pi$
$107$	12.9808	+	7.49445i	1.25490	+	0.724516i	0.282820	+	0.959173i	$0.408730\pi$
$108$	−1.54507	+	8.53484i	−0.148675	+	0.821265i
$109$	−0.795610	−	1.37804i	−0.0762056	−	0.131992i	0.825404	−	0.564542i	$-0.190947\pi$
$109$	−0.795610	−	1.37804i	−0.0762056	−	0.131992i	−0.901610	+	0.432550i	$0.857614\pi$
$110$	−4.40630	−	5.27560i	−0.420125	−	0.503009i
$111$	1.47902			0.140383
$112$	−2.41977	+	10.3027i	−0.228647	+	0.973509i
$113$	3.57866			0.336652			0.168326	−	0.985731i	$-0.446164\pi$
$113$	3.57866			0.336652			0.168326	+	0.985731i	$0.446164\pi$
$114$	2.14694	+	2.57050i	0.201079	+	0.240750i
$115$	0.780755	+	1.35231i	0.0728058	+	0.126103i
$116$	3.46683	−	19.1504i	0.321887	−	1.77807i
$117$	1.81606	+	1.04851i	0.167895	+	0.0969344i
$118$	−5.53190	+	15.0917i	−0.509253	+	1.38930i
$119$	−9.44712	−	12.3989i	−0.866016	−	1.13660i
$120$	−1.13477	−	1.99689i	−0.103590	−	0.182291i
$121$	6.31188	−	10.9325i	0.573807	−	0.993863i
$122$	−1.49216	−	8.57676i	−0.135094	−	0.776503i
$123$	−7.37850	+	4.25998i	−0.665297	+	0.384109i
$124$	8.31145	−	2.98228i	0.746390	−	0.267816i
$125$			1.00000i			0.0894427i
$126$	−2.58598	−	8.36718i	−0.230377	−	0.745407i
$127$		−	7.67404i		−	0.680961i	−0.940252	−	0.340481i	$-0.889410\pi$
$127$		−	7.67404i		−	0.680961i	0.940252	−	0.340481i	$-0.110590\pi$
$128$	11.1718	−	1.78658i	0.987453	−	0.157913i
$129$	−2.14196	+	1.23666i	−0.188589	+	0.108882i
$130$	−1.24829	+	0.217174i	−0.109482	+	0.0190475i
$131$	9.95404	−	17.2409i	0.869689	−	1.50635i	0.00737416	−	0.999973i	$-0.497653\pi$
$131$	9.95404	−	17.2409i	0.869689	−	1.50635i	0.862315	−	0.506373i	$-0.169014\pi$
$132$	5.10151	−	6.02376i	0.444030	−	0.524301i
$133$	−7.11854	−	2.97702i	−0.617256	−	0.258140i
$134$	−10.3557	−	3.79593i	−0.894599	−	0.327919i
$135$	3.75576	+	2.16839i	0.323245	+	0.186625i
$136$	−8.43053	+	14.3742i	−0.722912	+	1.23258i
$137$	4.41809	+	7.65236i	0.377463	+	0.653785i	0.990692	−	0.136120i	$-0.0434632\pi$
$137$	4.41809	+	7.65236i	0.377463	+	0.653785i	−0.613229	+	0.789905i	$0.710130\pi$
$138$	−1.37632	+	1.14954i	−0.117161	+	0.0978551i
$139$	−7.91285			−0.671159			−0.335580	−	0.942012i	$-0.608932\pi$
$139$	−7.91285			−0.671159			−0.335580	+	0.942012i	$0.608932\pi$
$140$	4.44003	+	2.87857i	0.375251	+	0.243283i
$141$	4.23831			0.356930
$142$	−9.09667	+	7.59774i	−0.763375	+	0.637588i
$143$	−2.17731	−	3.77121i	−0.182076	−	0.315364i
$144$	−7.22655	+	5.95236i	−0.602213	+	0.496030i
$145$	−8.42715	−	4.86542i	−0.699837	−	0.404051i
$146$	−11.6595	−	4.27384i	−0.964949	−	0.353706i
$147$	−3.99195	−	4.04667i	−0.329251	−	0.333763i
$148$	2.77979	+	2.35420i	0.228497	+	0.193514i
$149$	0.861502	−	1.49217i	0.0705770	−	0.122243i	−0.828577	−	0.559875i	$-0.810849\pi$
$149$	0.861502	−	1.49217i	0.0705770	−	0.122243i	0.899154	+	0.437632i	$0.144183\pi$
$150$	−1.13141	+	0.196839i	−0.0923789	+	0.0160718i
$151$	−0.705057	+	0.407065i	−0.0573767	+	0.0331265i	−0.528414	−	0.848987i	$-0.677213\pi$
$151$	−0.705057	+	0.407065i	−0.0573767	+	0.0331265i	0.471037	+	0.882113i	$0.343880\pi$
$152$	−0.0564087	+	8.24853i	−0.00457535	+	0.669044i
$153$		−	13.7899i		−	1.11485i
$154$	−4.03701	+	17.7323i	−0.325312	+	1.42891i
$155$		−	4.41515i		−	0.354633i
$156$	−0.491425	−	1.36957i	−0.0393455	−	0.109654i
$157$	11.5660	−	6.67764i	0.923068	−	0.532934i	0.0384557	−	0.999260i	$-0.487756\pi$
$157$	11.5660	−	6.67764i	0.923068	−	0.532934i	0.884613	+	0.466327i	$0.154423\pi$
$158$	−0.880805	−	5.06275i	−0.0700730	−	0.402771i
$159$	0.0729717	−	0.126391i	0.00578703	−	0.0100234i
$160$	1.04573	−	5.55936i	0.0826724	−	0.439506i
$161$	1.59399	−	3.81148i	0.125624	−	0.300387i
$162$	1.70357	−	4.64753i	0.133845	−	0.365144i
$163$	7.77441	+	4.48856i	0.608939	+	0.351571i	0.772550	−	0.634954i	$-0.218981\pi$
$163$	7.77441	+	4.48856i	0.608939	+	0.351571i	−0.163611	+	0.986525i	$0.552314\pi$
$164$	−20.6484	−	3.73802i	−1.61237	−	0.291890i
$165$	−1.97344	−	3.41809i	−0.153632	−	0.266098i
$166$	1.84754	+	2.21204i	0.143397	+	0.171688i
$167$	−17.0324			−1.31801			−0.659003	−	0.752140i	$-0.729022\pi$
$167$	−17.0324			−1.31801			−0.659003	+	0.752140i	$0.729022\pi$
$168$	−2.38285	+	5.59009i	−0.183841	+	0.431285i
$169$	12.1973			0.938254
$170$	5.34117	+	6.39490i	0.409649	+	0.490467i
$171$	−3.41300	−	5.91150i	−0.260999	−	0.452063i
$172$	−5.99418	−	1.08514i	−0.457052	−	0.0827408i
$173$	14.2599	+	8.23299i	1.08416	+	0.625942i	0.932017	−	0.362416i	$-0.118048\pi$
$173$	14.2599	+	8.23299i	1.08416	+	0.625942i	0.152147	+	0.988358i	$0.451381\pi$
$174$	3.84597	−	10.4922i	0.291562	−	0.795414i
$175$	2.10448	−	1.60348i	0.159084	−	0.121212i
$176$	19.1763	−	3.20130i	1.44547	−	0.241307i
$177$	−4.61473	+	7.99294i	−0.346864	+	0.600786i
$178$	0.427721	+	2.45848i	0.0320590	+	0.184271i
$179$	9.26501	−	5.34916i	0.692499	−	0.399815i	−0.112048	−	0.993703i	$-0.535741\pi$
$179$	9.26501	−	5.34916i	0.692499	−	0.399815i	0.804548	+	0.593888i	$0.202408\pi$
$180$	1.58099	+	4.40612i	0.117840	+	0.328413i
$181$		−	10.8661i		−	0.807672i	−0.914831	−	0.403836i	$-0.867677\pi$
$181$		−	10.8661i		−	0.807672i	0.914831	−	0.403836i	$-0.132323\pi$
$182$	2.45865	+	2.27877i	0.182247	+	0.168914i
$183$		−	4.99875i		−	0.369519i
$184$	−4.41651	−	0.0302029i	−0.325590	−	0.00222659i
$185$	1.57735	−	0.910682i	0.115969	−	0.0669547i
$186$	4.99532	−	0.869074i	0.366275	−	0.0637236i
$187$	−14.3179	+	24.7994i	−1.04703	+	1.81351i
$188$	7.96579	+	6.74622i	0.580965	+	0.492018i
$189$	−1.45894	−	11.3809i	−0.106122	−	0.827840i
$190$	3.87241	+	1.41945i	0.280934	+	0.102977i
$191$	−0.439231	−	0.253590i	−0.0317816	−	0.0183491i	0.484025	−	0.875054i	$-0.339174\pi$
$191$	−0.439231	−	0.253590i	−0.0317816	−	0.0183491i	−0.515807	+	0.856705i	$0.672508\pi$
$192$	6.49573	+	0.0888479i	0.468789	+	0.00641205i
$193$	10.4098	+	18.0302i	0.749311	+	1.29784i	0.948153	+	0.317813i	$0.102949\pi$
$193$	10.4098	+	18.0302i	0.749311	+	1.29784i	−0.198842	+	0.980031i	$0.563718\pi$
$194$	8.50580	−	7.10424i	0.610681	−	0.510054i
$195$	−0.727535			−0.0520999
$196$	−1.06160	−	13.9597i	−0.0758284	−	0.997121i
$197$	−8.86095			−0.631317			−0.315658	−	0.948873i	$-0.602225\pi$
$197$	−8.86095			−0.631317			−0.315658	+	0.948873i	$0.602225\pi$
$198$	−12.3480	+	10.3133i	−0.877535	+	0.732937i
$199$	11.6081	+	20.1059i	0.822878	+	1.42527i	0.903530	+	0.428524i	$0.140966\pi$
$199$	11.6081	+	20.1059i	0.822878	+	1.42527i	−0.0806522	+	0.996742i	$0.525700\pi$
$200$	−2.43976	−	1.43093i	−0.172517	−	0.101182i
$201$	−5.48467	−	3.16658i	−0.386859	−	0.223353i
$202$	−9.67365	−	3.54591i	−0.680635	−	0.249490i
$203$	3.27356	+	25.5364i	0.229759	+	1.79231i
$204$	−6.18388	+	7.30179i	−0.432958	+	0.511228i
$205$	−5.24601	+	9.08636i	−0.366397	+	0.634619i
$206$	12.8328	−	2.23262i	0.894106	−	0.155554i
$207$	3.16519	−	1.82743i	0.219996	−	0.127015i
$208$	1.25636	−	3.35629i	0.0871131	−	0.232717i
$209$			14.1748i			0.980490i
$210$	2.22843	+	2.06540i	0.153776	+	0.142526i
$211$		−	6.21092i		−	0.427578i	−0.976880	−	0.213789i	$-0.931420\pi$
$211$		−	6.21092i		−	0.427578i	0.976880	−	0.213789i	$-0.0685804\pi$
$212$	0.338327	−	0.121397i	0.0232364	−	0.00833759i
$213$	−5.89378	+	3.40277i	−0.403835	+	0.233154i
$214$	3.63331	+	20.8838i	0.248368	+	1.42759i
$215$	−1.52290	+	2.63774i	−0.103861	+	0.179893i
$216$	−10.6646	+	6.06035i	−0.725634	+	0.412354i
$217$	−9.29161	+	7.07960i	−0.630756	+	0.480594i
$218$	0.774475	−	2.11285i	0.0524541	−	0.143101i
$219$	−6.17519	−	3.56525i	−0.417281	−	0.240917i
$220$	1.73164	−	9.56538i	0.116747	−	0.644898i
$221$	2.63926	+	4.57133i	0.177536	+	0.307501i
$222$	1.34083	+	1.60536i	0.0899909	+	0.107745i
$223$	12.8221			0.858632			0.429316	−	0.903154i	$-0.358755\pi$
$223$	12.8221			0.858632			0.429316	+	0.903154i	$0.358755\pi$
$224$	−13.3764	+	6.71358i	−0.893748	+	0.448570i
$225$	2.34059			0.156039
$226$	3.24430	+	3.88435i	0.215807	+	0.258383i
$227$	1.80332	+	3.12345i	0.119691	+	0.207310i	0.919645	−	0.392750i	$-0.128476\pi$
$227$	1.80332	+	3.12345i	0.119691	+	0.207310i	−0.799954	+	0.600061i	$0.795143\pi$
$228$	−0.843727	+	4.66066i	−0.0558772	+	0.308660i
$229$	15.4049	+	8.89400i	1.01798	+	0.587732i	0.913519	−	0.406796i	$-0.133354\pi$
$229$	15.4049	+	8.89400i	1.01798	+	0.587732i	0.104463	+	0.994529i	$0.466687\pi$
$230$	−0.760014	+	2.07340i	−0.0501139	+	0.136716i
$231$	−4.02896	+	9.63390i	−0.265086	+	0.633864i
$232$	23.9291	−	13.5982i	1.57103	−	0.892763i
$233$	−0.137037	+	0.237354i	−0.00897756	+	0.0155496i	−0.870479	−	0.492205i	$-0.836191\pi$
$233$	−0.137037	+	0.237354i	−0.00897756	+	0.0155496i	0.861502	+	0.507755i	$0.169524\pi$
$234$	0.508316	+	2.92173i	0.0332297	+	0.191000i
$235$	4.52006	−	2.60966i	0.294856	−	0.170235i
$236$	−21.3958	+	7.67716i	−1.39275	+	0.499740i
$237$		−	2.95070i		−	0.191668i
$238$	4.89353	−	21.4945i	0.317200	−	1.39328i
$239$		−	23.0254i		−	1.48939i	−0.667406	−	0.744694i	$-0.732595\pi$
$239$		−	23.0254i		−	1.48939i	0.667406	−	0.744694i	$-0.267405\pi$
$240$	1.13872	−	3.04202i	0.0735042	−	0.196362i
$241$	3.25210	−	1.87760i	0.209486	−	0.120947i	−0.391587	−	0.920141i	$-0.628074\pi$
$241$	3.25210	−	1.87760i	0.209486	−	0.120947i	0.601072	+	0.799195i	$0.294740\pi$
$242$	17.5885	−	3.06000i	1.13063	−	0.196704i
$243$	7.92629	−	13.7287i	0.508472	−	0.880699i
$244$	7.95664	−	9.39503i	0.509372	−	0.601455i
$245$	−6.74899	−	1.85771i	−0.431177	−	0.118685i
$246$	−11.3130	−	4.14681i	−0.721289	−	0.264391i
$247$	2.26281	+	1.30643i	0.143979	+	0.0831264i
$248$	10.7719	+	6.31777i	0.684017	+	0.401179i
$249$	0.827453	+	1.43319i	0.0524377	+	0.0908248i
$250$	−1.08542	+	0.906567i	−0.0686480	+	0.0573363i
$251$	−0.268218			−0.0169298			−0.00846489	−	0.999964i	$-0.502694\pi$
$251$	−0.268218			−0.0169298			−0.00846489	+	0.999964i	$0.502694\pi$
$252$	6.73754	−	10.3923i	0.424425	−	0.654652i
$253$	−7.58961			−0.477155
$254$	8.32956	−	6.95703i	0.522643	−	0.436523i
$255$	2.39213	+	4.14329i	0.149801	+	0.259463i
$256$	12.0671	+	10.5064i	0.754196	+	0.656650i
$257$	−26.9207	−	15.5426i	−1.67926	−	0.969524i	−0.962131	−	0.272588i	$-0.912120\pi$
$257$	−26.9207	−	15.5426i	−1.67926	−	0.969524i	−0.717134	−	0.696936i	$-0.754546\pi$
$258$	−3.28413	−	1.20381i	−0.204461	−	0.0749459i
$259$	−4.44576	−	1.85924i	−0.276246	−	0.115528i
$260$	−1.36738	−	1.15804i	−0.0848016	−	0.0718183i
$261$	−11.3879	+	19.7245i	−0.704896	+	1.22092i
$262$	27.7376	−	4.82573i	1.71364	−	0.298134i
$263$	−24.1154	+	13.9230i	−1.48702	+	0.858532i	−0.999891	−	0.0147973i	$-0.995290\pi$
$263$	−24.1154	+	13.9230i	−1.48702	+	0.858532i	−0.487130	+	0.873329i	$0.661956\pi$
$264$	11.1632	+	0.0763408i	0.687046	+	0.00469845i
$265$		−	0.179724i		−	0.0110404i
$266$	−3.22212	−	10.4255i	−0.197561	−	0.639227i
$267$			1.43287i			0.0876900i
$268$	−5.26799	−	14.6816i	−0.321793	−	0.896821i
$269$	−1.25127	+	0.722424i	−0.0762916	+	0.0440470i	−0.537661	−	0.843161i	$-0.680692\pi$
$269$	−1.25127	+	0.722424i	−0.0762916	+	0.0440470i	0.461369	+	0.887208i	$0.347358\pi$
$270$	1.05124	+	6.04237i	0.0639762	+	0.367727i
$271$	−6.99708	+	12.1193i	−0.425042	+	0.736195i	−0.996424	−	0.0844893i	$-0.973074\pi$
$271$	−6.99708	+	12.1193i	−0.425042	+	0.736195i	0.571382	+	0.820684i	$0.306407\pi$
$272$	−23.2449	+	3.88051i	−1.40943	+	0.235290i
$273$	1.16659	+	1.53109i	0.0706051	+	0.0926656i
$274$	−4.30072	+	11.7329i	−0.259816	+	0.708808i
$275$	−4.20925	−	2.43021i	−0.253828	−	0.146547i
$276$	−2.49546	−	0.451757i	−0.150209	−	0.0271926i
$277$	−9.25674	−	16.0332i	−0.556184	−	0.963339i	−0.997810	−	0.0661397i	$-0.978932\pi$
$277$	−9.25674	−	16.0332i	−0.556184	−	0.963339i	0.441627	−	0.897199i	$-0.354402\pi$
$278$	−7.17353	−	8.58877i	−0.430240	−	0.515120i
$279$	−10.3340			−0.618683
$280$	0.900733	+	7.42891i	0.0538291	+	0.443962i
$281$	−9.00853			−0.537404			−0.268702	−	0.963223i	$-0.586595\pi$
$281$	−9.00853			−0.537404			−0.268702	+	0.963223i	$0.586595\pi$
$282$	3.84231	+	4.60034i	0.228806	+	0.273946i
$283$	−13.6475	−	23.6382i	−0.811261	−	1.40515i	−0.911982	−	0.410231i	$-0.865448\pi$
$283$	−13.6475	−	23.6382i	−0.811261	−	1.40515i	0.100720	−	0.994915i	$-0.467885\pi$
$284$	−16.4935	−	2.98584i	−0.978708	−	0.177177i
$285$	2.05093	+	1.18410i	0.121487	+	0.0701403i
$286$	2.11947	−	5.78215i	0.125327	−	0.341906i
$287$	27.5340	−	3.52963i	1.62528	−	0.208348i
$288$	−13.0122	−	2.44763i	−0.766749	−	0.144228i
$289$	8.85572	−	15.3386i	0.520925	−	0.902268i
$290$	−2.35876	−	13.5578i	−0.138511	−	0.796143i
$291$	5.51095	−	3.18175i	0.323058	−	0.186517i
$292$	−5.93123	−	16.5300i	−0.347099	−	0.967345i
$293$		−	10.6330i		−	0.621188i	−0.950543	−	0.310594i	$-0.899472\pi$
$293$		−	10.6330i		−	0.621188i	0.950543	−	0.310594i	$-0.100528\pi$
$294$	0.773358	−	8.00152i	0.0451032	−	0.466658i
$295$			11.3657i			0.661739i
$296$	−0.0352290	+	5.15148i	−0.00204765	+	0.299424i
$297$	−18.2546	+	10.5393i	−1.05924	+	0.611552i
$298$	2.40064	−	0.417657i	0.139065	−	0.0241942i
$299$	−0.699505	+	1.21158i	−0.0404534	+	0.0700673i
$300$	−1.23935	−	1.04960i	−0.0715538	−	0.0605988i
$301$	7.99304	−	1.02464i	0.460711	−	0.0590594i
$302$	−1.08102	−	0.396251i	−0.0622056	−	0.0228017i
$303$	−5.12342	−	2.95801i	−0.294333	−	0.169933i
$304$	−9.00426	+	7.41662i	−0.516430	+	0.425372i
$305$	−3.07789	−	5.33107i	−0.176240	−	0.305256i
$306$	14.9678	−	12.5015i	0.855654	−	0.714662i
$307$	17.9812			1.02624			0.513120	−	0.858317i	$-0.328490\pi$
$307$	17.9812			1.02624			0.513120	+	0.858317i	$0.328490\pi$
$308$	−22.9068	+	11.6937i	−1.30524	+	0.666309i
$309$	7.47930			0.425483
$310$	4.79229	−	4.00263i	0.272184	−	0.227334i
$311$	14.1579	+	24.5222i	0.802821	+	1.39053i	0.917752	+	0.397153i	$0.130002\pi$
$311$	14.1579	+	24.5222i	0.802821	+	1.39053i	−0.114931	+	0.993373i	$0.536665\pi$
$312$	1.04105	−	1.77501i	0.0589380	−	0.100490i
$313$	−4.84537	−	2.79748i	−0.273877	−	0.158123i	0.356771	−	0.934192i	$-0.383878\pi$
$313$	−4.84537	−	2.79748i	−0.273877	−	0.158123i	−0.630648	+	0.776069i	$0.717211\pi$
$314$	17.7334	+	6.50025i	1.00075	+	0.366830i
$315$	−3.75308	−	4.92573i	−0.211462	−	0.277534i
$316$	4.69670	−	5.54576i	0.264210	−	0.311974i
$317$	−15.6736	+	27.1475i	−0.880318	+	1.52476i	−0.0293312	+	0.999570i	$0.509338\pi$
$317$	−15.6736	+	27.1475i	−0.880318	+	1.52476i	−0.850987	+	0.525186i	$0.823996\pi$
$318$	0.203341	−	0.0353767i	0.0114028	−	0.00198383i
$319$	40.9596	−	23.6480i	2.29330	−	1.32404i
$320$	6.98226	−	3.90487i	0.390320	−	0.218289i
$321$			12.1716i			0.679353i
$322$	5.58211	−	1.72522i	0.311079	−	0.0961428i
$323$		−	17.1822i		−	0.956042i
$324$	6.58892	−	2.36421i	0.366051	−	0.131345i
$325$	−0.775901	+	0.447967i	−0.0430392	+	0.0248487i
$326$	2.17605	+	12.5077i	0.120520	+	0.692736i
$327$	0.646069	−	1.11902i	0.0357277	−	0.0618822i
$328$	−14.6619	−	25.8010i	−0.809566	−	1.42462i
$329$	−12.7398	−	5.32787i	−0.702369	−	0.293735i
$330$	1.92101	−	5.24073i	0.105748	−	0.288493i
$331$	−18.6312	−	10.7567i	−1.02406	−	0.591244i	−0.108786	−	0.994065i	$-0.534696\pi$
$331$	−18.6312	−	10.7567i	−1.02406	−	0.591244i	−0.915279	+	0.402821i	$0.868030\pi$
$332$	−0.726068	+	4.01072i	−0.0398481	+	0.220117i
$333$	−2.13153	−	3.69192i	−0.116807	−	0.202316i
$334$	−15.4410	−	18.4873i	−0.844895	−	1.01158i
$335$	−7.79905			−0.426108
$336$	−8.22781	+	2.48139i	−0.448864	+	0.135371i
$337$	−0.0584151			−0.00318207			−0.00159104	−	0.999999i	$-0.500506\pi$
$337$	−0.0584151			−0.00318207			−0.00159104	+	0.999999i	$0.500506\pi$
$338$	11.0577	+	13.2392i	0.601458	+	0.720117i
$339$	1.45301	+	2.51669i	0.0789167	+	0.136688i
$340$	−2.09903	+	11.5948i	−0.113836	+	0.628817i
$341$	18.5845	+	10.7298i	1.00641	+	0.581049i
$342$	3.32234	−	9.06371i	0.179651	−	0.490109i
$343$	6.91235	+	17.1820i	0.373232	+	0.927738i
$344$	−4.25630	−	7.48995i	−0.229484	−	0.403831i
$345$	−0.634006	+	1.09813i	−0.0341337	+	0.0591213i
$346$	3.99136	+	22.9418i	0.214577	+	1.23336i
$347$	−7.63282	+	4.40681i	−0.409751	+	0.236570i	−0.690683	−	0.723158i	$-0.742690\pi$
$347$	−7.63282	+	4.40681i	−0.409751	+	0.236570i	0.280932	+	0.959728i	$0.409357\pi$
$348$	14.8751	−	5.33742i	0.797389	−	0.286116i
$349$			1.78555i			0.0955784i	0.998857	+	0.0477892i	$0.0152176\pi$
$349$			1.78555i			0.0955784i	−0.998857	+	0.0477892i	$0.984782\pi$
$350$	3.64830	+	0.830588i	0.195010	+	0.0443968i
$351$			3.88547i			0.207391i
$352$	20.8594	+	17.9122i	1.11181	+	0.954722i
$353$	23.8096	−	13.7465i	1.26726	−	0.731651i	0.292789	−	0.956177i	$-0.405417\pi$
$353$	23.8096	−	13.7465i	1.26726	−	0.731651i	0.974468	+	0.224526i	$0.0720835\pi$
$354$	−12.8593	+	2.23722i	−0.683462	+	0.118907i
$355$	−4.19039	+	7.25797i	−0.222403	+	0.385213i
$356$	−2.28073	+	2.69304i	−0.120878	+	0.142731i
$357$	4.88376	−	11.6779i	0.258476	−	0.618059i
$358$	14.2054	+	5.20706i	0.750780	+	0.275201i
$359$	−16.1118	−	9.30213i	−0.850346	−	0.490948i	0.0104213	−	0.999946i	$-0.496683\pi$
$359$	−16.1118	−	9.30213i	−0.850346	−	0.490948i	−0.860768	+	0.508998i	$0.830016\pi$
$360$	−3.34922	+	5.71048i	−0.176519	+	0.300969i
$361$	5.24741	+	9.08878i	0.276179	+	0.478357i
$362$	11.7943	−	9.85087i	0.619895	−	0.517750i
$363$	10.2510			0.538039
$364$	−0.244496	+	4.73452i	−0.0128151	+	0.248157i
$365$	−8.78095			−0.459616
$366$	5.42575	−	4.53171i	0.283608	−	0.236876i
$367$	−10.9922	−	19.0390i	−0.573788	−	0.993829i	−0.996172	−	0.0874124i	$-0.972140\pi$
$367$	−10.9922	−	19.0390i	−0.573788	−	0.993829i	0.422385	−	0.906417i	$-0.361193\pi$
$368$	−3.97108	−	4.82115i	−0.207007	−	0.251320i
$369$	21.2674	+	12.2787i	1.10714	+	0.639206i
$370$	2.41844	+	0.886490i	0.125729	+	0.0460864i
$371$	−0.378226	+	0.288183i	−0.0196365	+	0.0149617i
$372$	5.47190	+	4.63415i	0.283705	+	0.240269i
$373$	−0.282808	+	0.489838i	−0.0146433	+	0.0253629i	−0.873254	−	0.487265i	$-0.837995\pi$
$373$	−0.282808	+	0.489838i	−0.0146433	+	0.0253629i	0.858611	+	0.512628i	$0.171328\pi$
$374$	−39.8980	+	6.94135i	−2.06307	+	0.358929i
$375$	−0.703249	+	0.406021i	−0.0363156	+	0.0209668i
$376$	−0.100953	+	14.7621i	−0.00520624	+	0.761298i
$377$		−	8.71818i		−	0.449009i
$378$	11.0304	−	11.9011i	0.567345	−	0.612128i
$379$			28.3294i			1.45518i	0.686010	+	0.727592i	$0.259361\pi$
$379$			28.3294i			1.45518i	−0.686010	+	0.727592i	$0.740639\pi$
$380$	1.96990	+	5.49001i	0.101054	+	0.281632i
$381$	5.39676	−	3.11582i	0.276484	−	0.159628i
$382$	−0.122941	−	0.706647i	−0.00629019	−	0.0361552i
$383$	−1.54300	+	2.67256i	−0.0788438	+	0.136561i	−0.902751	−	0.430163i	$-0.858456\pi$
$383$	−1.54300	+	2.67256i	−0.0788438	+	0.136561i	0.823908	+	0.566724i	$0.191790\pi$
$384$	5.79237	+	7.13114i	0.295591	+	0.363909i
$385$	1.63510	+	12.7551i	0.0833325	+	0.650060i
$386$	−10.1332	+	27.6446i	−0.515768	+	1.40707i
$387$	6.17387	+	3.56449i	0.313836	+	0.181193i
$388$	15.4222	+	2.79190i	0.782941	+	0.141737i
$389$	−8.17685	−	14.1627i	−0.414583	−	0.718078i	0.580802	−	0.814045i	$-0.302739\pi$
$389$	−8.17685	−	14.1627i	−0.414583	−	0.718078i	−0.995385	+	0.0959669i	$0.969406\pi$
$390$	−0.659560	−	0.789681i	−0.0333981	−	0.0399871i
$391$	9.19986			0.465257
$392$	14.1897	−	13.8077i	0.716689	−	0.697393i
$393$	16.1662			0.815477
$394$	−8.03305	−	9.61786i	−0.404699	−	0.484541i
$395$	−1.81684	−	3.14686i	−0.0914151	−	0.158336i
$396$	−22.3886	−	4.05305i	−1.12507	−	0.203673i
$397$	−6.77631	−	3.91230i	−0.340093	−	0.196353i	0.320220	−	0.947343i	$-0.396243\pi$
$397$	−6.77631	−	3.91230i	−0.340093	−	0.196353i	−0.660313	+	0.750990i	$0.729576\pi$
$398$	−11.2998	+	30.8270i	−0.566406	+	1.54522i
$399$	−0.796692	−	6.21484i	−0.0398845	−	0.311131i
$400$	−0.658646	−	3.94540i	−0.0329323	−	0.197270i
$401$	9.89379	−	17.1366i	0.494072	−	0.855758i	−0.505904	−	0.862590i	$-0.668841\pi$
$401$	9.89379	−	17.1366i	0.494072	−	0.855758i	0.999977	+	0.00683114i	$0.00217444\pi$
$402$	−1.53516	−	8.82389i	−0.0765667	−	0.440095i
$403$	3.42572	−	1.97784i	0.170647	−	0.0985232i
$404$	−4.92101	−	13.7146i	−0.244829	−	0.682326i
$405$		−	3.50012i		−	0.173922i
$406$	−24.7500	+	26.7037i	−1.22832	+	1.32528i
$407$			8.85261i			0.438808i
$408$	−13.5316	−	0.0925377i	−0.669915	−	0.00458130i
$409$	21.9116	−	12.6507i	1.08346	−	0.625536i	0.151633	−	0.988437i	$-0.451547\pi$
$409$	21.9116	−	12.6507i	1.08346	−	0.625536i	0.931828	+	0.362900i	$0.118214\pi$
$410$	−14.6184	+	2.54327i	−0.721950	+	0.125603i
$411$	−3.58767	+	6.21403i	−0.176967	+	0.306516i
$412$	14.0572	+	11.9050i	0.692547	+	0.586517i
$413$	23.9190	−	18.2247i	1.17698	−	0.896780i
$414$	4.85299	+	1.77888i	0.238511	+	0.0874272i
$415$	1.76492	+	1.01898i	0.0866366	+	0.0500197i
$416$	4.78196	−	1.67902i	0.234455	−	0.0823208i
$417$	−3.21278	−	5.56470i	−0.157331	−	0.272505i
$418$	−15.3856	+	12.8504i	−0.752533	+	0.628533i
$419$	−16.6804			−0.814889			−0.407445	−	0.913230i	$-0.633580\pi$
$419$	−16.6804			−0.814889			−0.407445	+	0.913230i	$0.633580\pi$
$420$	−0.221603	+	4.29120i	−0.0108131	+	0.209389i
$421$	3.13305			0.152695			0.0763477	−	0.997081i	$-0.475674\pi$
$421$	3.13305			0.152695			0.0763477	+	0.997081i	$0.475674\pi$
$422$	6.74146	−	5.63062i	0.328169	−	0.274094i
$423$	−6.10814	−	10.5796i	−0.296988	−	0.514398i
$424$	0.438483	+	0.257173i	0.0212946	+	0.0124894i
$425$	5.10231	+	2.94582i	0.247498	+	0.142893i
$426$	−9.03654	−	3.31238i	−0.437822	−	0.160485i
$427$	−6.28381	+	15.0256i	−0.304095	+	0.727141i
$428$	−19.3739	+	22.8762i	−0.936470	+	1.10576i
$429$	1.76807	−	3.06238i	0.0853630	−	0.147853i
$430$	−4.24367	+	0.738304i	−0.204648	+	0.0356042i
$431$	−23.5490	+	13.5960i	−1.13432	+	0.654898i	−0.945017	−	0.327021i	$-0.893955\pi$
$431$	−23.5490	+	13.5960i	−1.13432	+	0.654898i	−0.189300	+	0.981919i	$0.560622\pi$
$432$	−16.2462	−	6.08145i	−0.781645	−	0.292594i
$433$			32.0204i			1.53880i	0.638766	+	0.769401i	$0.279445\pi$
$433$			32.0204i			1.53880i	−0.638766	+	0.769401i	$0.720555\pi$
$434$	−16.1078	−	3.66717i	−0.773199	−	0.176030i
$435$		−	7.90185i		−	0.378865i
$436$	2.99545	−	1.07481i	0.143456	−	0.0514743i
$437$	3.94382	−	2.27697i	0.188659	−	0.108922i
$438$	−1.72843	−	9.93482i	−0.0825878	−	0.474704i
$439$	−10.0502	+	17.4074i	−0.479668	+	0.830809i	−0.999728	−	0.0233207i	$-0.992576\pi$
$439$	−10.0502	+	17.4074i	−0.479668	+	0.830809i	0.520060	+	0.854130i	$0.325909\pi$
$440$	11.9523	−	6.79211i	0.569803	−	0.323801i
$441$	−4.34814	+	15.7966i	−0.207054	+	0.752220i
$442$	−2.56915	+	7.00892i	−0.122202	+	0.333380i
$443$	−12.9010	−	7.44839i	−0.612945	−	0.353884i	0.161172	−	0.986926i	$-0.448473\pi$
$443$	−12.9010	−	7.44839i	−0.612945	−	0.353884i	−0.774117	+	0.633042i	$0.781806\pi$
$444$	−0.526935	+	2.91074i	−0.0250072	+	0.138137i
$445$	0.882262	+	1.52812i	0.0418232	+	0.0724399i
$446$	11.6241	+	13.9174i	0.550417	+	0.659006i
$447$	1.39915			0.0661776
$448$	−19.4137	−	8.43268i	−0.917209	−	0.398407i
$449$	−6.18602			−0.291936			−0.145968	−	0.989289i	$-0.546630\pi$
$449$	−6.18602			−0.291936			−0.145968	+	0.989289i	$0.546630\pi$
$450$	2.12190	+	2.54052i	0.100027	+	0.119761i
$451$	−25.4979	−	44.1636i	−1.20065	−	2.07958i
$452$	−1.27498	+	7.04285i	−0.0599699	+	0.331268i
$453$	−0.572536	−	0.330554i	−0.0269001	−	0.0155308i
$454$	−1.75542	+	4.78898i	−0.0823858	+	0.224758i
$455$	2.18688	+	0.914567i	0.102523	+	0.0428755i
$456$	−5.82367	+	3.30941i	−0.272718	+	0.154977i
$457$	11.6751	−	20.2219i	0.546140	−	0.945943i	−0.452394	−	0.891818i	$-0.649430\pi$
$457$	11.6751	−	20.2219i	0.546140	−	0.945943i	0.998534	−	0.0541246i	$-0.0172368\pi$
$458$	4.31182	+	24.7838i	0.201478	+	1.15807i
$459$	22.1276	−	12.7754i	1.03283	−	0.596304i
$460$	−2.93952	+	1.05475i	−0.137056	+	0.0491778i
$461$		−	17.4080i		−	0.810772i	−0.914146	−	0.405386i	$-0.867137\pi$
$461$		−	17.4080i		−	0.810772i	0.914146	−	0.405386i	$-0.132863\pi$
$462$	−14.1093	+	4.36067i	−0.656426	+	0.202877i
$463$			0.962509i			0.0447316i	0.999750	+	0.0223658i	$0.00711985\pi$
$463$			0.962509i			0.0447316i	−0.999750	+	0.0223658i	$0.992880\pi$
$464$	36.4531	+	13.6455i	1.69229	+	0.633477i
$465$	3.10495	−	1.79264i	0.143988	−	0.0831318i
$466$	−0.381862	+	0.0664354i	−0.0176894	+	0.00307756i
$467$	−0.145490	+	0.251997i	−0.00673249	+	0.0116610i	−0.869372	−	0.494158i	$-0.835476\pi$
$467$	−0.145490	+	0.251997i	−0.00673249	+	0.0116610i	0.862640	+	0.505819i	$0.168810\pi$
$468$	−2.71048	+	3.20048i	−0.125292	+	0.147942i
$469$	12.5056	+	16.4130i	0.577455	+	0.757881i
$470$	6.93032	+	2.54034i	0.319672	+	0.117177i
$471$	9.39209	+	5.42252i	0.432764	+	0.249857i
$472$	−27.7297	−	16.2636i	−1.27636	−	0.748592i
$473$	−7.40196	−	12.8206i	−0.340342	−	0.589490i
$474$	3.20275	−	2.67501i	0.147107	−	0.122867i
$475$	2.91636			0.133812
$476$	27.7669	−	14.1747i	1.27269	−	0.649695i
$477$	−0.420660			−0.0192607
$478$	24.9922	−	20.8741i	1.14312	−	0.954757i
$479$	9.89481	+	17.1383i	0.452106	+	0.783070i	0.998517	−	0.0544474i	$-0.0173397\pi$
$479$	9.89481	+	17.1383i	0.452106	+	0.783070i	−0.546411	+	0.837517i	$0.684006\pi$
$480$	4.33420	−	1.52181i	0.197828	−	0.0694606i
$481$	1.41320	+	0.815911i	0.0644363	+	0.0372023i
$482$	4.98623	+	1.82772i	0.227116	+	0.0832504i
$483$	3.32761	−	0.426573i	0.151412	−	0.0194098i
$484$	19.2665	+	16.3168i	0.875751	+	0.741672i
$485$	3.91821	−	6.78653i	0.177917	−	0.308161i
$486$	22.0872	−	3.84267i	1.00189	−	0.174307i
$487$	19.5908	−	11.3108i	0.887745	−	0.512540i	0.0145405	−	0.999894i	$-0.495371\pi$
$487$	19.5908	−	11.3108i	0.887745	−	0.512540i	0.873204	+	0.487355i	$0.162038\pi$
$488$	17.4108	+	0.119066i	0.788149	+	0.00538986i
$489$			7.28979i			0.329656i
$490$	−4.10202	−	9.00963i	−0.185310	−	0.407014i
$491$		−	38.9565i		−	1.75808i	−0.476745	−	0.879042i	$-0.658184\pi$
$491$		−	38.9565i		−	1.75808i	0.476745	−	0.879042i	$-0.341816\pi$
$492$	−5.75493	−	16.0387i	−0.259452	−	0.723080i
$493$	−49.6498	+	28.6653i	−2.23611	+	1.29102i
$494$	0.633360	+	3.64047i	0.0284962	+	0.163792i
$495$	−5.68813	+	9.85213i	−0.255662	+	0.442820i
$496$	2.90802	+	17.4195i	0.130574	+	0.782160i
$497$	21.9935	−	2.81939i	0.986543	−	0.126467i
$498$	−0.805472	+	2.19742i	−0.0360941	+	0.0984686i
$499$	−32.6131	−	18.8292i	−1.45996	−	0.842909i	−0.460953	−	0.887425i	$-0.652492\pi$
$499$	−32.6131	−	18.8292i	−1.45996	−	0.842909i	−0.999009	+	0.0445156i	$0.985826\pi$
$500$	−1.96801	−	0.356272i	−0.0880122	−	0.0159330i
$501$	−6.91551	−	11.9780i	−0.308962	−	0.535138i
$502$	−0.243158	−	0.291129i	−0.0108527	−	0.0129937i
$503$	42.9688			1.91589			0.957943	−	0.286959i	$-0.0926442\pi$
$503$	42.9688			1.91589			0.957943	+	0.286959i	$0.0926442\pi$
$504$	17.3880	−	2.10825i	0.774524	−	0.0939087i
$505$	−7.28536			−0.324194
$506$	−6.88049	−	8.23791i	−0.305875	−	0.366220i
$507$	4.95236	+	8.57774i	0.219942	+	0.380951i
$508$	15.1026	+	2.73405i	0.670070	+	0.121304i
$509$	4.13736	+	2.38870i	0.183385	+	0.105877i	0.588882	−	0.808219i	$-0.299568\pi$
$509$	4.13736	+	2.38870i	0.183385	+	0.105877i	−0.405497	+	0.914096i	$0.632902\pi$
$510$	−2.32858	+	6.35264i	−0.103111	+	0.281299i
$511$	14.0801	+	18.4794i	0.622866	+	0.817480i
$512$	−0.464182	+	22.6227i	−0.0205141	+	0.999790i
$513$	6.32382	−	10.9532i	0.279203	−	0.483594i
$514$	−7.53508	−	43.3107i	−0.332358	−	1.91035i
$515$	7.97652	−	4.60525i	0.351487	−	0.202931i
$516$	−1.67064	−	4.65599i	−0.0735459	−	0.204968i
$517$			25.3681i			1.11569i
$518$	−2.01232	−	6.51105i	−0.0884163	−	0.286079i
$519$			13.3711i			0.586924i
$520$	0.0173292	−	2.53402i	0.000759938	−	0.111124i
$521$	−15.8425	+	9.14670i	−0.694075	+	0.400724i	−0.805137	−	0.593089i	$-0.797908\pi$
$521$	−15.8425	+	9.14670i	−0.694075	+	0.400724i	0.111062	+	0.993813i	$0.464575\pi$
$522$	−31.7333	+	5.52088i	−1.38893	+	0.241642i
$523$	−9.25624	+	16.0323i	−0.404747	+	0.701043i	−0.994292	−	0.106693i	$-0.965974\pi$
$523$	−9.25624	+	16.0323i	−0.404747	+	0.701043i	0.589545	+	0.807736i	$0.299307\pi$
$524$	30.3840	+	25.7321i	1.32733	+	1.12411i
$525$	1.98211	+	0.828930i	0.0865063	+	0.0361775i
$526$	−36.9746	−	13.5532i	−1.61217	−	0.590947i
$527$	−22.5275	−	13.0062i	−0.981311	−	0.566560i
$528$	10.0373	+	12.1859i	0.436818	+	0.530325i
$529$	−10.2808	−	17.8069i	−0.446993	−	0.774215i
$530$	0.195076	−	0.162932i	0.00847355	−	0.00707730i
$531$	26.6025			1.15445
$532$	8.39494	−	12.9487i	0.363967	−	0.561399i
$533$	−9.40015			−0.407166
$534$	−1.55526	+	1.29899i	−0.0673028	+	0.0562128i
$535$	7.49445	+	12.9808i	0.324013	+	0.561207i
$536$	11.1599	−	19.0278i	0.482034	−	0.821877i
$537$	7.52358	+	4.34374i	0.324666	+	0.187446i
$538$	−1.91850	−	0.703233i	−0.0827123	−	0.0303185i
$539$	24.2211	−	23.8936i	1.04328	−	1.02917i
$540$	−5.60549	+	6.61885i	−0.241222	+	0.284830i
$541$	1.99811	−	3.46083i	0.0859055	−	0.148793i	−0.819871	−	0.572548i	$-0.805955\pi$
$541$	1.99811	−	3.46083i	0.0859055	−	0.148793i	0.905777	+	0.423755i	$0.139288\pi$
$542$	−19.4978	+	3.39219i	−0.837504	+	0.145707i
$543$	7.64159	−	4.41187i	0.327932	−	0.189332i
$544$	−25.2850	−	21.7125i	−1.08409	−	0.930917i
$545$		−	1.59122i		−	0.0681604i
$546$	−0.604282	+	2.65427i	−0.0258609	+	0.113592i
$547$		−	13.3961i		−	0.572774i	−0.958114	−	0.286387i	$-0.907546\pi$
$547$		−	13.3961i		−	0.572774i	0.958114	−	0.286387i	$-0.0924543\pi$
$548$	−16.6340	+	5.96853i	−0.710568	+	0.254963i
$549$	−12.4778	+	7.20408i	−0.532541	+	0.307463i
$550$	−1.17817	−	6.77196i	−0.0502373	−	0.288757i
$551$	−14.1893	+	24.5767i	−0.604486	+	1.04700i
$552$	−1.77196	−	3.11817i	−0.0754195	−	0.132718i
$553$	−3.70925	+	8.86943i	−0.157733	+	0.377167i
$554$	9.01084	−	24.5826i	0.382834	−	1.04441i
$555$	1.28087	+	0.739512i	0.0543700	+	0.0313905i
$556$	2.81913	−	15.5726i	0.119558	−	0.660425i
$557$	−7.20598	−	12.4811i	−0.305327	−	0.528842i	0.672007	−	0.740545i	$-0.265432\pi$
$557$	−7.20598	−	12.4811i	−0.305327	−	0.528842i	−0.977334	+	0.211703i	$0.932099\pi$
$558$	−9.36850	−	11.2168i	−0.396600	−	0.474844i
$559$	−2.72884			−0.115418
$560$	−7.24691	+	7.71248i	−0.306238	+	0.325912i
$561$	−23.2535			−0.981766
$562$	−8.16684	−	9.77804i	−0.344497	−	0.412462i
$563$	3.33957	+	5.78430i	0.140746	+	0.243779i	0.927778	−	0.373133i	$-0.121717\pi$
$563$	3.33957	+	5.78430i	0.140746	+	0.243779i	−0.787032	+	0.616912i	$0.788383\pi$
$564$	−1.50999	+	8.34104i	−0.0635821	+	0.351221i
$565$	3.09921	+	1.78933i	0.130385	+	0.0752777i
$566$	13.2850	−	36.2429i	0.558410	−	1.52340i
$567$	−7.36594	+	5.61236i	−0.309341	+	0.235697i
$568$	−11.7116	−	20.6092i	−0.491406	−	0.864743i
$569$	−10.4511	+	18.1019i	−0.438134	+	0.758871i	−0.997546	−	0.0700192i	$-0.977694\pi$
$569$	−10.4511	+	18.1019i	−0.438134	+	0.758871i	0.559411	+	0.828890i	$0.311027\pi$
$570$	0.574055	+	3.29959i	0.0240445	+	0.138205i
$571$	4.83991	−	2.79432i	0.202544	−	0.116939i	−0.395298	−	0.918553i	$-0.629359\pi$
$571$	4.83991	−	2.79432i	0.202544	−	0.116939i	0.597841	+	0.801614i	$0.296025\pi$
$572$	8.19750	−	2.94139i	0.342755	−	0.122986i
$573$		−	0.411852i		−	0.0172053i
$574$	28.7925	+	26.6861i	1.20178	+	1.11385i
$575$			1.56151i			0.0651195i
$576$	−9.13970	−	16.3426i	−0.380821	−	0.680942i
$577$	−1.57544	+	0.909582i	−0.0655865	+	0.0378664i	−0.532435	−	0.846471i	$-0.678723\pi$
$577$	−1.57544	+	0.909582i	−0.0655865	+	0.0378664i	0.466848	+	0.884337i	$0.345389\pi$
$578$	24.6771	−	4.29326i	1.02643	−	0.178576i
$579$	−8.45316	+	14.6413i	−0.351301	+	0.608472i
$580$	12.5776	−	14.8513i	0.522255	−	0.616668i
$581$	−0.685592	−	5.34816i	−0.0284431	−	0.221879i
$582$	8.44958	+	3.09723i	0.350246	+	0.128384i
$583$	0.756503	+	0.436767i	0.0313312	+	0.0180891i
$584$	12.5649	−	21.4234i	0.519941	−	0.886508i
$585$	1.04851	+	1.81606i	0.0433504	+	0.0750850i
$586$	11.5413	−	9.63956i	0.476767	−	0.398207i
$587$	−26.1792			−1.08053			−0.540265	−	0.841495i	$-0.681676\pi$
$587$	−26.1792			−1.08053			−0.540265	+	0.841495i	$0.681676\pi$
$588$	9.38611	−	6.41449i	0.387076	−	0.264529i
$589$	−12.8762			−0.530554
$590$	−12.3366	+	10.3038i	−0.507890	+	0.424201i
$591$	−3.59773	−	6.23146i	−0.147991	−	0.256328i
$592$	−5.62345	+	4.63192i	−0.231122	+	0.190371i
$593$	−23.9296	−	13.8158i	−0.982671	−	0.567345i	−0.0795955	−	0.996827i	$-0.525363\pi$
$593$	−23.9296	−	13.8158i	−0.982671	−	0.567345i	−0.903075	+	0.429482i	$0.858696\pi$
$594$	−27.9886	−	10.2593i	−1.14839	−	0.420945i
$595$	−1.98201	−	15.4613i	−0.0812547	−	0.633851i
$596$	2.62967	+	2.22706i	0.107716	+	0.0912241i
$597$	−9.42628	+	16.3268i	−0.385792	+	0.668211i
$598$	−1.94922	+	0.339120i	−0.0797094	+	0.0138677i
$599$	−4.82336	+	2.78477i	−0.197077	+	0.113783i	−0.595291	−	0.803510i	$-0.702963\pi$
$599$	−4.82336	+	2.78477i	−0.197077	+	0.113783i	0.398214	+	0.917292i	$0.369630\pi$
$600$	0.0157066	−	2.29675i	0.000641220	−	0.0937643i
$601$		−	30.5902i		−	1.24780i	−0.781504	−	0.623901i	$-0.785547\pi$
$601$		−	30.5902i		−	1.24780i	0.781504	−	0.623901i	$-0.214453\pi$
$602$	8.35839	+	7.74689i	0.340663	+	0.315740i
$603$			18.2544i			0.743375i
$604$	−0.549916	−	1.53259i	−0.0223758	−	0.0623600i
$605$	10.9325	−	6.31188i	0.444469	−	0.256614i
$606$	−1.43404	−	8.24270i	−0.0582541	−	0.334837i
$607$	10.1110	−	17.5127i	0.410391	−	0.710818i	−0.584541	−	0.811364i	$-0.698725\pi$
$607$	10.1110	−	17.5127i	0.410391	−	0.710818i	0.994932	+	0.100546i	$0.0320588\pi$
$608$	−16.2131	−	3.04974i	−0.657528	−	0.123683i
$609$	−16.6293	+	12.6704i	−0.673854	+	0.513432i
$610$	2.99613	−	8.17377i	0.121310	−	0.330946i
$611$	4.04968	+	2.33808i	0.163832	+	0.0945887i
$612$	27.1387	+	4.91296i	1.09702	+	0.198595i
$613$	11.2510	+	19.4874i	0.454425	+	0.787087i	0.998655	−	0.0518488i	$-0.0165114\pi$
$613$	11.2510	+	19.4874i	0.454425	+	0.787087i	−0.544230	+	0.838936i	$0.683178\pi$
$614$	16.3011	+	19.5171i	0.657860	+	0.787647i
$615$	−8.51996			−0.343558
$616$	−33.4591	−	14.2624i	−1.34811	−	0.574649i
$617$	22.5772			0.908922			0.454461	−	0.890767i	$-0.349832\pi$
$617$	22.5772			0.908922			0.454461	+	0.890767i	$0.349832\pi$
$618$	6.78049	+	8.11818i	0.272751	+	0.326561i
$619$	6.15713	+	10.6645i	0.247476	+	0.428641i	0.962825	−	0.270126i	$-0.0870655\pi$
$619$	6.15713	+	10.6645i	0.247476	+	0.428641i	−0.715349	+	0.698768i	$0.753732\pi$
$620$	8.68906	+	1.57299i	0.348961	+	0.0631730i
$621$	5.86466	+	3.38596i	0.235341	+	0.135874i
$622$	−13.7818	+	37.5983i	−0.552600	+	1.50755i
$623$	1.80122	−	4.30702i	0.0721644	−	0.172557i
$624$	2.87042	−	0.479188i	0.114909	−	0.0191829i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−1.35622	−	7.79537i	−0.0542054	−	0.311565i
$627$	−9.96839	+	5.75526i	−0.398099	+	0.229843i
$628$	9.02103	+	25.1411i	0.359978	+	1.00324i
$629$		−	10.7308i		−	0.427866i
$630$	1.94406	−	8.53918i	0.0774534	−	0.340209i
$631$			22.9961i			0.915459i	0.889091	+	0.457730i	$0.151337\pi$
$631$			22.9961i			0.915459i	−0.889091	+	0.457730i	$0.848663\pi$
$632$	10.2774	+	0.0702830i	0.408811	+	0.00279571i
$633$	4.36782	−	2.52176i	0.173605	−	0.100231i
$634$	−43.6756	+	7.59858i	−1.73458	+	0.301778i
$635$	3.83702	−	6.64592i	0.152268	−	0.263735i
$636$	0.222740	+	0.188639i	0.00883223	+	0.00748000i
$637$	−1.58192	−	6.06874i	−0.0626781	−	0.240452i
$638$	62.8006	+	23.0198i	2.48630	+	0.911363i
$639$	16.9879	+	9.80798i	0.672032	+	0.387998i
$640$	10.5683	+	4.03866i	0.417749	+	0.159642i
$641$	17.7377	+	30.7226i	0.700598	+	1.21347i	0.968257	+	0.249957i	$0.0804165\pi$
$641$	17.7377	+	30.7226i	0.700598	+	1.21347i	−0.267659	+	0.963514i	$0.586250\pi$
$642$	−13.2113	+	11.0344i	−0.521409	+	0.435492i
$643$	−8.46366			−0.333774			−0.166887	−	0.985976i	$-0.553372\pi$
$643$	−8.46366			−0.333774			−0.166887	+	0.985976i	$0.553372\pi$
$644$	6.93315	+	4.49491i	0.273204	+	0.177124i
$645$	−2.47332			−0.0973869
$646$	18.6499	−	15.5768i	0.733769	−	0.612861i
$647$	−2.47704	−	4.29036i	−0.0973826	−	0.168672i	0.813218	−	0.581959i	$-0.197714\pi$
$647$	−2.47704	−	4.29036i	−0.0973826	−	0.168672i	−0.910600	+	0.413288i	$0.864380\pi$
$648$	8.53945	+	5.00843i	0.335461	+	0.196750i
$649$	−47.8413	−	27.6212i	−1.87793	−	1.08423i
$650$	−1.18964	−	0.436066i	−0.0466615	−	0.0171039i
$651$	−8.75130	−	3.65985i	−0.342991	−	0.143441i
$652$	−11.6033	+	13.7010i	−0.454422	+	0.536572i
$653$	0.945688	−	1.63798i	0.0370076	−	0.0640991i	−0.846928	−	0.531707i	$-0.821551\pi$
$653$	0.945688	−	1.63798i	0.0370076	−	0.0640991i	0.883936	+	0.467608i	$0.154884\pi$
$654$	1.80032	−	0.313214i	0.0703979	−	0.0122477i
$655$	17.2409	−	9.95404i	0.673658	−	0.388937i
$656$	14.7129	−	39.3046i	0.574443	−	1.53459i
$657$			20.5526i			0.801833i
$658$	−5.76652	−	18.6581i	−0.224802	−	0.727369i
$659$			4.20598i			0.163842i	0.996639	+	0.0819209i	$0.0261055\pi$
$659$			4.20598i			0.163842i	−0.996639	+	0.0819209i	$0.973895\pi$
$660$	7.42992	−	2.66597i	0.289209	−	0.103773i
$661$	9.78997	−	5.65224i	0.380786	−	0.219847i	−0.297374	−	0.954761i	$-0.596111\pi$
$661$	9.78997	−	5.65224i	0.380786	−	0.219847i	0.678160	+	0.734914i	$0.262778\pi$
$662$	−5.21487	−	29.9744i	−0.202682	−	1.16499i
$663$	−2.14319	+	3.71211i	−0.0832346	+	0.144166i
$664$	−5.01155	+	2.84790i	−0.194486	+	0.110520i
$665$	−4.67633	−	6.13744i	−0.181340	−	0.238000i
$666$	2.07491	−	5.66058i	0.0804011	−	0.219343i
$667$	−13.1591	−	7.59740i	−0.509522	−	0.294173i
$668$	6.06817	−	33.5200i	0.234785	−	1.29693i
$669$	5.20604	+	9.01713i	0.201277	+	0.348622i
$670$	−7.07036	−	8.46524i	−0.273152	−	0.327041i
$671$	29.9197			1.15504
$672$	−10.1524	−	6.68107i	−0.391638	−	0.257728i
$673$	−36.8435			−1.42021			−0.710106	−	0.704095i	$-0.751353\pi$
$673$	−36.8435			−1.42021			−0.710106	+	0.704095i	$0.751353\pi$
$674$	−0.0529572	−	0.0634049i	−0.00203983	−	0.00244226i
$675$	2.16839	+	3.75576i	0.0834614	+	0.144559i
$676$	−4.34556	+	24.0044i	−0.167137	+	0.923248i
$677$	24.0708	+	13.8973i	0.925115	+	0.534115i	0.885263	−	0.465090i	$-0.153978\pi$
$677$	24.0708	+	13.8973i	0.925115	+	0.534115i	0.0398518	+	0.999206i	$0.487311\pi$
$678$	−1.41441	+	3.85867i	−0.0543202	+	0.148191i
$679$	−20.5649	+	2.63626i	−0.789209	+	0.101170i
$680$	−14.4882	+	8.23316i	−0.555595	+	0.315727i
$681$	−1.46437	+	2.53637i	−0.0561149	+	0.0971939i
$682$	5.20179	+	29.8992i	0.199187	+	1.14490i
$683$	−40.9116	+	23.6203i	−1.56544	+	0.903806i	−0.568748	+	0.822512i	$0.692572\pi$
$683$	−40.9116	+	23.6203i	−1.56544	+	0.903806i	−0.996690	+	0.0812945i	$0.974095\pi$
$684$	12.8499	−	4.61073i	0.491326	−	0.176296i
$685$			8.83618i			0.337613i
$686$	−12.3831	+	23.0794i	−0.472790	+	0.881175i
$687$			14.4446i			0.551096i
$688$	4.27112	−	11.4100i	0.162835	−	0.435003i
$689$	0.139448	−	0.0805103i	0.00531254	−	0.00306720i
$690$	−1.76670	+	0.307366i	−0.0672572	+	0.0117012i
$691$	17.2216	−	29.8286i	0.655139	−	1.13473i	−0.326720	−	0.945121i	$-0.605943\pi$
$691$	17.2216	−	29.8286i	0.655139	−	1.13473i	0.981859	−	0.189613i	$-0.0607233\pi$
$692$	−21.2830	+	25.1306i	−0.809060	+	0.955321i
$693$	29.8544	−	3.82710i	1.13408	−	0.145380i
$694$	−11.7029	−	4.28974i	−0.444236	−	0.162836i
$695$	−6.85273	−	3.95643i	−0.259939	−	0.150076i
$696$	19.2786	+	11.3070i	0.730754	+	0.428591i
$697$	30.9076	+	53.5336i	1.17071	+	2.02773i
$698$	−1.93807	+	1.61872i	−0.0733572	+	0.0612695i
$699$	−0.222559			−0.00841795
$700$	2.40590	+	4.71293i	0.0909343	+	0.178132i
$701$	−28.7191			−1.08470			−0.542352	−	0.840151i	$-0.682466\pi$
$701$	−28.7191			−1.08470			−0.542352	+	0.840151i	$0.682466\pi$
$702$	−4.21736	+	3.52244i	−0.159174	+	0.132946i
$703$	−2.65588	−	4.60012i	−0.100168	−	0.173497i
$704$	−0.531794	+	38.8798i	−0.0200427	+	1.46534i
$705$	3.67048	+	2.11915i	0.138238	+	0.0798119i
$706$	36.5057	+	13.3813i	1.37391	+	0.503612i
$707$	11.6819	+	15.3319i	0.439344	+	0.576616i
$708$	−14.0861	−	11.9295i	−0.529388	−	0.448338i
$709$	−24.7310	+	42.8354i	−0.928794	+	1.60872i	−0.143450	+	0.989658i	$0.545820\pi$
$709$	−24.7310	+	42.8354i	−0.928794	+	1.60872i	−0.785344	+	0.619060i	$0.787514\pi$
$710$	−11.6768	+	2.03150i	−0.438223	+	0.0762410i
$711$	−7.36550	+	4.25247i	−0.276228	+	0.159480i
$712$	−4.99071	−	0.0341296i	−0.187035	−	0.00127906i
$713$		−	6.89430i		−	0.258193i
$714$	17.1029	−	5.28585i	0.640058	−	0.197818i
$715$		−	4.35462i		−	0.162854i
$716$	7.22634	+	20.1394i	0.270061	+	0.752645i
$717$	16.1926	−	9.34879i	0.604723	−	0.349137i
$718$	−4.50968	−	25.9210i	−0.168300	−	0.967364i
$719$	2.38663	−	4.13376i	0.0890061	−	0.154163i	−0.818085	−	0.575097i	$-0.804964\pi$
$719$	2.38663	−	4.13376i	0.0890061	−	0.154163i	0.907091	+	0.420934i	$0.138298\pi$
$720$	−9.23456	+	1.54162i	−0.344152	+	0.0574528i
$721$	−22.4818	−	9.40205i	−0.837268	−	0.350151i
$722$	−5.10801	+	13.9352i	−0.190101	+	0.518616i
$723$	2.64084	+	1.52469i	0.0982138	+	0.0567038i
$724$	21.3846	+	3.87130i	0.794754	+	0.143876i
$725$	−4.86542	−	8.42715i	−0.180697	−	0.312977i
$726$	9.29323	+	11.1267i	0.344904	+	0.412949i
$727$	20.9881			0.778405			0.389202	−	0.921152i	$-0.372751\pi$
$727$	20.9881			0.778405			0.389202	+	0.921152i	$0.372751\pi$
$728$	−5.36060	+	4.02678i	−0.198677	+	0.149243i
$729$	2.37261			0.0878744
$730$	−7.96052	−	9.53102i	−0.294632	−	0.352759i
$731$	8.97240	+	15.5406i	0.331856	+	0.574792i
$732$	9.83761	+	1.78092i	0.363608	+	0.0658246i
$733$	16.4524	+	9.49880i	0.607684	+	0.350846i	0.772058	−	0.635552i	$-0.219227\pi$
$733$	16.4524	+	9.49880i	0.607684	+	0.350846i	−0.164375	+	0.986398i	$0.552561\pi$
$734$	10.7002	−	29.1913i	0.394951	−	1.07747i
$735$	−1.43380	−	5.50049i	−0.0528865	−	0.202889i
$736$	1.63292	−	8.68099i	0.0601903	−	0.319986i
$737$	18.9534	−	32.8282i	0.698156	−	1.20924i
$738$	5.95274	+	34.2156i	0.219123	+	1.25949i
$739$	−15.2226	+	8.78874i	−0.559971	+	0.323299i	−0.753134	−	0.657867i	$-0.771459\pi$
$739$	−15.2226	+	8.78874i	−0.559971	+	0.323299i	0.193163	+	0.981167i	$0.438125\pi$
$740$	1.23027	+	3.42869i	0.0452256	+	0.126041i
$741$			2.12176i			0.0779447i
$742$	−0.655687	−	0.149276i	−0.0240710	−	0.00548011i
$743$		−	0.624385i		−	0.0229065i	−0.999934	−	0.0114532i	$-0.996354\pi$
$743$		−	0.624385i		−	0.0229065i	0.999934	−	0.0114532i	$-0.00364575\pi$
$744$	−0.0693470	+	10.1405i	−0.00254238	+	0.371768i
$745$	1.49217	−	0.861502i	0.0546687	−	0.0315630i
$746$	−0.788065	+	0.137106i	−0.0288531	+	0.00501979i
$747$	2.38501	−	4.13096i	0.0872629	−	0.151144i
$748$	−43.7045	−	37.0132i	−1.59799	−	1.35334i
$749$	15.3006	−	36.5863i	0.559073	−	1.33684i
$750$	−1.07825	−	0.395235i	−0.0393720	−	0.0144319i
$751$	28.7011	+	16.5706i	1.04732	+	0.604670i	0.921898	−	0.387433i	$-0.126638\pi$
$751$	28.7011	+	16.5706i	1.04732	+	0.604670i	0.125422	+	0.992103i	$0.459972\pi$
$752$	−16.1146	+	13.2733i	−0.587640	+	0.484027i
$753$	−0.108902	−	0.188624i	−0.00396862	−	0.00687384i
$754$	9.46289	−	7.90362i	0.344618	−	0.287833i
$755$	−0.814130			−0.0296292
$756$	22.9175	+	1.18349i	0.833503	+	0.0430431i
$757$	43.9649			1.59793			0.798966	−	0.601376i	$-0.205380\pi$
$757$	43.9649			1.59793			0.798966	+	0.601376i	$0.205380\pi$
$758$	−30.7493	+	25.6825i	−1.11686	+	0.932831i
$759$	−3.08154	−	5.33738i	−0.111853	−	0.193735i
$760$	−4.17312	+	7.11523i	−0.151375	+	0.258097i
$761$	−6.43253	−	3.71382i	−0.233179	−	0.134626i	0.378859	−	0.925455i	$-0.376317\pi$
$761$	−6.43253	−	3.71382i	−0.233179	−	0.134626i	−0.612038	+	0.790829i	$0.709650\pi$
$762$	8.27450	+	3.03305i	0.299754	+	0.109876i
$763$	−3.34870	+	2.55149i	−0.121231	+	0.0923701i
$764$	0.655554	−	0.774065i	0.0237171	−	0.0280047i
$765$	6.89495	−	11.9424i	0.249288	−	0.431779i
$766$	−4.29969	+	0.748049i	−0.155354	+	0.0270281i
$767$	−8.81869	+	5.09147i	−0.318424	+	0.183842i
$768$	−2.48910	+	12.7520i	−0.0898177	+	0.460149i
$769$			17.2607i			0.622438i	0.950338	+	0.311219i	$0.100737\pi$
$769$			17.2607i			0.622438i	−0.950338	+	0.311219i	$0.899263\pi$
$770$	−12.3623	+	13.3381i	−0.445507	+	0.480673i
$771$		−	25.2426i		−	0.909089i
$772$	−39.1924	+	14.0629i	−1.41057	+	0.506133i
$773$	30.6272	−	17.6826i	1.10158	−	0.636000i	0.164948	−	0.986302i	$-0.447254\pi$
$773$	30.6272	−	17.6826i	1.10158	−	0.636000i	0.936637	+	0.350302i	$0.113921\pi$
$774$	1.72807	+	9.93269i	0.0621140	+	0.357023i
$775$	2.20757	−	3.82363i	0.0792984	−	0.137349i
$776$	10.9508	+	19.2706i	0.393112	+	0.691773i
$777$	−0.497560	−	3.88137i	−0.0178499	−	0.139243i
$778$	7.95963	−	21.7148i	0.285367	−	0.778512i
$779$	26.4991	+	15.2993i	0.949430	+	0.548153i
$780$	0.259201	−	1.43180i	0.00928087	−	0.0512666i
$781$	−20.3671	−	35.2768i	−0.728792	−	1.26230i
$782$	8.34029	+	9.98571i	0.298248	+	0.357088i
$783$	−42.2005			−1.50812
$784$	27.8511	+	2.88421i	0.994681	+	0.103008i
$785$	13.3553			0.476670
$786$	14.6557	+	17.5471i	0.522753	+	0.625885i
$787$	5.59512	+	9.69103i	0.199444	+	0.345448i	0.948348	−	0.317231i	$-0.102753\pi$
$787$	5.59512	+	9.69103i	0.199444	+	0.345448i	−0.748904	+	0.662678i	$0.769420\pi$
$788$	3.15691	−	17.4385i	0.112460	−	0.621220i
$789$	−19.5827	−	11.3061i	−0.697164	−	0.402508i
$790$	1.76858	−	4.82487i	0.0629231	−	0.171661i
$791$	−1.20390	−	9.39140i	−0.0428058	−	0.333920i
$792$	−15.8975	−	27.9754i	−0.564894	−	0.994062i
$793$	2.75759	−	4.77628i	0.0979248	−	0.169611i
$794$	−1.89669	−	10.9019i	−0.0673109	−	0.386894i
$795$	0.126391	−	0.0729717i	0.00448261	−	0.00258804i
$796$	−43.7042	+	15.6818i	−1.54906	+	0.555825i
$797$		−	9.18543i		−	0.325365i	−0.986679	−	0.162682i	$-0.947985\pi$
$797$		−	9.18543i		−	0.325365i	0.986679	−	0.162682i	$-0.0520146\pi$
$798$	6.02345	−	6.49891i	0.213228	−	0.230059i
$799$		−	30.7504i		−	1.08787i
$800$	3.68531	−	4.29168i	0.130295	−	0.151734i
$801$	3.57670	−	2.06501i	0.126377	−	0.0729636i
$802$	27.5697	−	4.79652i	0.973521	−	0.169371i
$803$	21.3396	−	36.9613i	0.753058	−	1.30433i
$804$	8.18590	−	9.66574i	0.288694	−	0.340884i
$805$	3.28617	−	2.50385i	0.115822	−	0.0882491i
$806$	5.25243	+	1.92530i	0.185009	+	0.0678157i
$807$	−1.01609	−	0.586638i	−0.0357680	−	0.0206506i
$808$	10.4248	−	17.7745i	0.366745	−	0.625306i
$809$	0.0848856	+	0.147026i	0.00298442	+	0.00516917i	0.867514	−	0.497413i	$-0.165717\pi$
$809$	0.0848856	+	0.147026i	0.00298442	+	0.00516917i	−0.864529	+	0.502582i	$0.832383\pi$
$810$	3.79910	−	3.17309i	0.133487	−	0.111491i
$811$	−38.6906			−1.35861			−0.679306	−	0.733855i	$-0.737719\pi$
$811$	−38.6906			−1.35861			−0.679306	+	0.733855i	$0.737719\pi$
$812$	−51.4222	−	2.65550i	−1.80457	−	0.0931899i
$813$	−11.3638			−0.398547
$814$	−9.60880	+	8.02549i	−0.336788	+	0.281293i
$815$	4.48856	+	7.77441i	0.157227	+	0.272326i
$816$	−12.1669	−	14.7714i	−0.425926	−	0.517101i
$817$	7.69262	+	4.44134i	0.269131	+	0.155383i
$818$	33.5957	+	12.3146i	1.17465	+	0.430571i
$819$	2.14062	−	5.11859i	0.0747995	−	0.178858i
$820$	−16.0130	−	13.5614i	−0.559200	−	0.473585i
$821$	−16.9114	+	29.2914i	−0.590213	+	1.02228i	0.403991	+	0.914763i	$0.367623\pi$
$821$	−16.9114	+	29.2914i	−0.590213	+	1.02228i	−0.994203	+	0.107515i	$0.965710\pi$
$822$	−9.99730	+	1.73931i	−0.348696	+	0.0606653i
$823$	9.03275	−	5.21506i	0.314862	−	0.181786i	−0.334238	−	0.942489i	$-0.608479\pi$
$823$	9.03275	−	5.21506i	0.314862	−	0.181786i	0.649100	+	0.760703i	$0.275146\pi$
$824$	−0.178150	+	26.0506i	−0.00620616	+	0.907515i
$825$		−	3.94687i		−	0.137412i
$826$	41.4657	+	9.44024i	1.44277	+	0.328468i
$827$			10.1110i			0.351594i	0.984426	+	0.175797i	$0.0562502\pi$
$827$			10.1110i			0.351594i	−0.984426	+	0.175797i	$0.943750\pi$
$828$	2.46872	+	6.88020i	0.0857941	+	0.239104i
$829$	6.66205	−	3.84634i	0.231383	−	0.133589i	−0.379827	−	0.925058i	$-0.624017\pi$
$829$	6.66205	−	3.84634i	0.231383	−	0.133589i	0.611210	+	0.791469i	$0.290683\pi$
$830$	0.494001	+	2.83945i	0.0171470	+	0.0985589i
$831$	7.51686	−	13.0196i	0.260757	−	0.451645i
$832$	6.15761	+	3.66829i	0.213477	+	0.127175i
$833$	−29.3599	+	28.9630i	−1.01726	+	1.00351i
$834$	3.12744	−	8.53200i	0.108294	−	0.295439i
$835$	−14.7505	−	8.51620i	−0.510462	−	0.294715i
$836$	−27.8961	−	5.05008i	−0.964808	−	0.174661i
$837$	−9.57376	−	16.5822i	−0.330918	−	0.573166i
$838$	−15.1219	−	18.1052i	−0.522376	−	0.625434i
$839$	−46.1347			−1.59275			−0.796373	−	0.604806i	$-0.793251\pi$
$839$	−46.1347			−1.59275			−0.796373	+	0.604806i	$0.793251\pi$
$840$	−4.85865	+	3.64973i	−0.167640	+	0.125928i
$841$	65.6893			2.26515
$842$	2.84032	+	3.40067i	0.0978838	+	0.117195i
$843$	−3.65765	−	6.33524i	−0.125976	−	0.218197i
$844$	12.2232	+	2.21278i	0.420739	+	0.0761670i
$845$	10.5632	+	6.09865i	0.363384	+	0.209800i
$846$	5.94588	−	16.2210i	0.204423	−	0.557690i
$847$	−30.8133	−	12.8863i	−1.05876	−	0.442778i
$848$	0.118374	+	0.709083i	0.00406500	+	0.0243500i
$849$	11.0824	−	19.1952i	0.380346	−	0.658778i
$850$	1.42814	+	8.20873i	0.0489846	+	0.281557i
$851$	2.46305	−	1.42204i	0.0844321	−	0.0487469i
$852$	−4.59691	−	12.8113i	−0.157487	−	0.438909i
$853$		−	29.1420i		−	0.997804i	−0.866658	−	0.498902i	$-0.833737\pi$
$853$		−	29.1420i		−	0.997804i	0.866658	−	0.498902i	$-0.166263\pi$
$854$	−22.0058	+	6.80117i	−0.753023	+	0.232731i
$855$		−	6.82601i		−	0.233445i
$856$	−42.3940	−	0.289917i	−1.44900	−	0.00990916i
$857$	−10.5403	+	6.08543i	−0.360049	+	0.207874i	−0.669102	−	0.743170i	$-0.733321\pi$
$857$	−10.5403	+	6.08543i	−0.360049	+	0.207874i	0.309053	+	0.951045i	$0.399988\pi$
$858$	4.92684	−	0.857159i	0.168200	−	0.0292629i
$859$	−2.45770	+	4.25686i	−0.0838555	+	0.145242i	−0.904903	−	0.425618i	$-0.860057\pi$
$859$	−2.45770	+	4.25686i	−0.0838555	+	0.145242i	0.821047	+	0.570860i	$0.193390\pi$
$860$	−4.64854	−	3.93685i	−0.158514	−	0.134245i
$861$	13.6616	+	17.9301i	0.465585	+	0.611057i
$862$	−36.1062	−	13.2349i	−1.22978	−	0.450781i
$863$	18.5564	+	10.7135i	0.631666	+	0.364692i	0.781397	−	0.624034i	$-0.214507\pi$
$863$	18.5564	+	10.7135i	0.631666	+	0.364692i	−0.149731	+	0.988727i	$0.547841\pi$
$864$	−8.12733	−	23.1472i	−0.276498	−	0.787483i
$865$	8.23299	+	14.2599i	0.279930	+	0.484853i
$866$	−34.7556	+	29.0286i	−1.18104	+	0.986433i
$867$	14.3824			0.488453
$868$	−10.6224	−	20.8083i	−0.360547	−	0.706278i
$869$	17.6612			0.599116
$870$	8.57682	−	7.16356i	0.290782	−	0.242867i
$871$	−3.49371	−	6.05129i	−0.118380	−	0.205040i
$872$	3.88220	+	2.27693i	0.131468	+	0.0771065i
$873$	−15.8845	−	9.17091i	−0.537608	−	0.310388i
$874$	6.04680	+	2.21648i	0.204536	+	0.0749735i
$875$	2.62428	−	0.336411i	0.0887167	−	0.0113728i
$876$	9.21650	−	10.8827i	0.311397	−	0.367691i
$877$	12.1125	−	20.9794i	0.409009	−	0.708424i	−0.585770	−	0.810477i	$-0.699208\pi$
$877$	12.1125	−	20.9794i	0.409009	−	0.708424i	0.994779	+	0.102053i	$0.0325412\pi$
$878$	−28.0055	+	4.87232i	−0.945138	+	0.164433i
$879$	7.47767	−	4.31723i	0.252216	−	0.145617i
$880$	18.2078	+	6.81576i	0.613786	+	0.229759i
$881$		−	30.4932i		−	1.02734i	−0.857987	−	0.513671i	$-0.828285\pi$
$881$		−	30.4932i		−	1.02734i	0.857987	−	0.513671i	$-0.171715\pi$
$882$	−21.0878	+	9.60114i	−0.710064	+	0.323287i
$883$		−	0.362622i		−	0.0122032i	−0.999981	−	0.00610160i	$-0.998058\pi$
$883$		−	0.362622i		−	0.0122032i	0.999981	−	0.00610160i	$-0.00194221\pi$
$884$	−9.93673	+	3.56545i	−0.334208	+	0.119919i
$885$	−7.99294	+	4.61473i	−0.268680	+	0.155122i
$886$	−3.61099	−	20.7555i	−0.121313	−	0.697294i
$887$	18.8687	−	32.6816i	0.633550	−	1.09734i	−0.353270	−	0.935521i	$-0.614930\pi$
$887$	18.8687	−	32.6816i	0.633550	−	1.09734i	0.986820	−	0.161820i	$-0.0517363\pi$
$888$	−3.63707	+	2.06683i	−0.122052	+	0.0693584i
$889$	−20.1388	+	2.58163i	−0.675434	+	0.0865852i
$890$	−0.858824	+	2.34297i	−0.0287879	+	0.0785365i
$891$	14.7329	+	8.50603i	0.493570	+	0.284963i
$892$	−4.56816	+	25.2341i	−0.152953	+	0.844899i
$893$	−7.61072	−	13.1822i	−0.254683	−	0.441124i
$894$	1.26843	+	1.51867i	0.0424225	+	0.0507918i
$895$	10.6983			0.357605
$896$	−8.44678	−	28.7168i	−0.282187	−	0.959359i
$897$	−1.13605			−0.0379317
$898$	−5.60804	−	6.71442i	−0.187143	−	0.224063i
$899$	21.4815	+	37.2071i	0.716450	+	1.24093i
$900$	−0.833887	+	4.60630i	−0.0277962	+	0.153543i
$901$	−0.917007	−	0.529434i	−0.0305499	−	0.0176380i
$902$	24.8205	−	67.7131i	0.826432	−	2.25460i
$903$	3.96592	+	5.20507i	0.131978	+	0.173214i
$904$	−8.80030	+	5.00093i	−0.292694	+	0.166328i
$905$	5.43306	−	9.41034i	0.180601	−	0.312810i
$906$	−0.160253	−	0.921111i	−0.00532403	−	0.0306018i
$907$	4.41171	−	2.54710i	0.146489	−	0.0845752i	−0.424964	−	0.905210i	$-0.639713\pi$
$907$	4.41171	−	2.54710i	0.146489	−	0.0845752i	0.571453	+	0.820635i	$0.306380\pi$
$908$	−6.78945	+	2.43616i	−0.225316	+	0.0808469i
$909$			17.0520i			0.565580i
$910$	0.989865	+	3.20280i	0.0328137	+	0.106172i
$911$			4.73127i			0.156754i	0.996924	+	0.0783769i	$0.0249738\pi$
$911$			4.73127i			0.156754i	−0.996924	+	0.0783769i	$0.975026\pi$
$912$	−8.87164	−	3.32093i	−0.293770	−	0.109967i
$913$	−8.57828	+	4.95267i	−0.283900	+	0.163910i
$914$	32.5336	−	5.66012i	1.07612	−	0.187220i
$915$	2.49938	−	4.32905i	0.0826269	−	0.143114i
$916$	−22.9918	+	27.1483i	−0.759671	+	0.897004i
$917$	−48.5936	−	20.3221i	−1.60470	−	0.671096i
$918$	33.9268	+	12.4360i	1.11975	+	0.410449i
$919$	25.6239	+	14.7939i	0.845254	+	0.488007i	0.859047	−	0.511898i	$-0.171057\pi$
$919$	25.6239	+	14.7939i	0.845254	+	0.488007i	−0.0137930	+	0.999905i	$0.504391\pi$
$920$	−3.80971	−	2.23441i	−0.125602	−	0.0736664i
$921$	7.30073	+	12.6452i	0.240567	+	0.416675i
$922$	18.8950	−	15.7815i	0.622273	−	0.519737i
$923$	−7.50862			−0.247149
$924$	−17.5242	−	11.3613i	−0.576505	−	0.373760i
$925$	1.82136			0.0598861
$926$	−1.04473	+	0.872579i	−0.0343318	+	0.0286747i
$927$	−10.7790	−	18.6697i	−0.354028	−	0.613195i
$928$	18.2361	+	51.9375i	0.598628	+	1.70493i
$929$	0.232942	+	0.134489i	0.00764257	+	0.00441244i	0.503816	−	0.863811i	$-0.331929\pi$
$929$	0.232942	+	0.134489i	0.00764257	+	0.00441244i	−0.496174	+	0.868223i	$0.665262\pi$
$930$	4.76061	+	1.74502i	0.156107	+	0.0572215i
$931$	−5.41776	+	19.6825i	−0.177560	+	0.645069i
$932$	−0.418294	−	0.354252i	−0.0137017	−	0.0116039i
$933$	−11.4968	+	19.9131i	−0.376389	+	0.651924i
$934$	−0.405419	+	0.0705338i	−0.0132657	+	0.00230794i
$935$	−24.7994	+	14.3179i	−0.811028	+	0.468247i
$936$	−5.93110	−	0.0405606i	−0.193864	−	0.00132577i
$937$		−	32.3858i		−	1.05800i	−0.848623	−	0.528999i	$-0.822568\pi$
$937$		−	32.3858i		−	1.05800i	0.848623	−	0.528999i	$-0.177432\pi$
$938$	−6.47780	+	28.4533i	−0.211508	+	0.929033i
$939$		−	4.54334i		−	0.148266i
$940$	3.52547	+	9.82529i	0.114988	+	0.320466i
$941$	−14.7440	+	8.51248i	−0.480642	+	0.277499i	−0.720684	−	0.693264i	$-0.756172\pi$
$941$	−14.7440	+	8.51248i	−0.480642	+	0.277499i	0.240042	+	0.970763i	$0.422839\pi$
$942$	2.62884	+	15.1102i	0.0856523	+	0.492318i
$943$	−8.19170	+	14.1884i	−0.266758	+	0.462039i
$944$	−7.48600	−	44.8424i	−0.243649	−	1.45950i
$945$	4.42698	−	10.5856i	0.144010	−	0.344351i
$946$	7.20533	−	19.6569i	0.234265	−	0.639102i
$947$	−0.317117	−	0.183088i	−0.0103049	−	0.00594955i	0.494839	−	0.868985i	$-0.335227\pi$
$947$	−0.317117	−	0.183088i	−0.0103049	−	0.00594955i	−0.505144	+	0.863035i	$0.668560\pi$
$948$	5.80701	+	1.05125i	0.188603	+	0.0341431i
$949$	−3.93357	−	6.81315i	−0.127689	−	0.221164i
$950$	2.64388	+	3.16548i	0.0857788	+	0.102702i
$951$	−25.4553			−0.825444
$952$	40.5580	+	17.2884i	1.31449	+	0.560321i
$953$	28.7452			0.931148			0.465574	−	0.885009i	$-0.345848\pi$
$953$	28.7452			0.931148			0.465574	+	0.885009i	$0.345848\pi$
$954$	−0.381356	−	0.456592i	−0.0123469	−	0.0147827i
$955$	−0.253590	−	0.439231i	−0.00820599	−	0.0142132i
$956$	45.3142	+	8.20330i	1.46557	+	0.265314i
$957$	33.2609	+	19.2032i	1.07517	+	0.620751i
$958$	−9.63196	+	26.2771i	−0.311194	+	0.848973i
$959$	18.5956	−	14.1686i	0.600483	−	0.457529i
$960$	5.58104	+	3.32481i	0.180127	+	0.107308i
$961$	5.75324	−	9.96490i	0.185588	−	0.321448i
$962$	0.395554	+	2.27359i	0.0127532	+	0.0733035i
$963$	30.3826	−	17.5414i	0.979067	−	0.565264i
$964$	2.53650	+	7.06910i	0.0816953	+	0.227680i
$965$			20.8195i			0.670204i
$966$	3.47972	+	3.22514i	0.111958	+	0.103767i
$967$		−	38.1396i		−	1.22649i	−0.789895	−	0.613243i	$-0.789865\pi$
$967$		−	38.1396i		−	1.22649i	0.789895	−	0.613243i	$-0.210135\pi$
$968$	−0.244170	+	35.7045i	−0.00784793	+	1.14759i
$969$	12.0833	−	6.97632i	0.388173	−	0.224112i
$970$	10.9184	−	1.89955i	0.350567	−	0.0609908i
$971$	−2.80103	+	4.85153i	−0.0898895	+	0.155693i	−0.907464	−	0.420129i	$-0.861985\pi$
$971$	−2.80103	+	4.85153i	−0.0898895	+	0.155693i	0.817575	+	0.575822i	$0.195318\pi$
$972$	24.1944	+	20.4902i	0.776036	+	0.657224i
$973$	2.66197	+	20.7655i	0.0853389	+	0.665712i
$974$	30.0373	+	11.0103i	0.962458	+	0.352793i
$975$	−0.630064	−	0.363768i	−0.0201782	−	0.0116499i
$976$	15.6548	+	19.0059i	0.501098	+	0.608366i
$977$	20.7850	+	36.0007i	0.664972	+	1.15176i	0.979293	+	0.202448i	$0.0648898\pi$
$977$	20.7850	+	36.0007i	0.664972	+	1.15176i	−0.314321	+	0.949317i	$0.601777\pi$
$978$	−7.91248	+	6.60868i	−0.253013	+	0.211322i
$979$	−8.57634			−0.274101
$980$	6.06048	−	12.6202i	0.193595	−	0.403139i
$981$	−3.72439			−0.118911
$982$	42.2842	−	35.3167i	1.34934	−	1.12700i
$983$	−22.5595	−	39.0742i	−0.719536	−	1.24627i	−0.961184	−	0.275909i	$-0.911021\pi$
$983$	−22.5595	−	39.0742i	−0.719536	−	1.24627i	0.241647	−	0.970364i	$-0.422312\pi$
$984$	12.1915	−	20.7867i	0.388650	−	0.662655i
$985$	−7.67381	−	4.43048i	−0.244508	−	0.141167i
$986$	−76.1248	−	27.9038i	−2.42431	−	0.888639i
$987$	−1.42581	−	11.1225i	−0.0453842	−	0.354033i
$988$	−3.37725	+	3.98779i	−0.107445	+	0.126869i
$989$	−2.37803	+	4.11887i	−0.0756169	+	0.130972i
$990$	−15.8504	+	2.75761i	−0.503758	+	0.0876425i
$991$	−22.2587	+	12.8510i	−0.707069	+	0.408227i	−0.809975	−	0.586464i	$-0.800519\pi$
$991$	−22.2587	+	12.8510i	−0.707069	+	0.408227i	0.102906	+	0.994691i	$0.467186\pi$
$992$	−16.2712	+	18.9484i	−0.516611	+	0.601612i
$993$		−	17.4699i		−	0.554389i
$994$	22.9988	+	21.3162i	0.729478	+	0.676109i
$995$			23.2162i			0.736005i
$996$	−3.11534	+	1.11783i	−0.0987132	+	0.0354198i
$997$	−25.9069	+	14.9574i	−0.820481	+	0.473705i	−0.850582	−	0.525842i	$-0.823750\pi$
$997$	−25.9069	+	14.9574i	−0.820481	+	0.473705i	0.0301015	+	0.999547i	$0.490417\pi$
$998$	−9.12839	−	52.4688i	−0.288954	−	1.66087i
$999$	3.94943	−	6.84061i	0.124954	−	0.216427i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	140.2.o.a.131.12	yes	32
4.3	odd	2	inner	140.2.o.a.131.1	yes	32
5.2	odd	4		700.2.t.c.299.4		32
5.3	odd	4		700.2.t.d.299.13		32
5.4	even	2		700.2.p.c.551.5		32
7.2	even	3		980.2.g.a.391.21		32
7.3	odd	6	inner	140.2.o.a.31.1	✓	32
7.4	even	3		980.2.o.f.31.1		32
7.5	odd	6		980.2.g.a.391.22		32
7.6	odd	2		980.2.o.f.411.12		32
20.3	even	4		700.2.t.d.299.9		32
20.7	even	4		700.2.t.c.299.8		32
20.19	odd	2		700.2.p.c.551.16		32
28.3	even	6	inner	140.2.o.a.31.12	yes	32
28.11	odd	6		980.2.o.f.31.12		32
28.19	even	6		980.2.g.a.391.23		32
28.23	odd	6		980.2.g.a.391.24		32
28.27	even	2		980.2.o.f.411.1		32
35.3	even	12		700.2.t.c.199.8		32
35.17	even	12		700.2.t.d.199.9		32
35.24	odd	6		700.2.p.c.451.16		32
140.3	odd	12		700.2.t.c.199.4		32
140.59	even	6		700.2.p.c.451.5		32
140.87	odd	12		700.2.t.d.199.13		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.o.a.31.1	✓	32	7.3	odd	6	inner
140.2.o.a.31.12	yes	32	28.3	even	6	inner
140.2.o.a.131.1	yes	32	4.3	odd	2	inner
140.2.o.a.131.12	yes	32	1.1	even	1	trivial
700.2.p.c.451.5		32	140.59	even	6
700.2.p.c.451.16		32	35.24	odd	6
700.2.p.c.551.5		32	5.4	even	2
700.2.p.c.551.16		32	20.19	odd	2
700.2.t.c.199.4		32	140.3	odd	12
700.2.t.c.199.8		32	35.3	even	12
700.2.t.c.299.4		32	5.2	odd	4
700.2.t.c.299.8		32	20.7	even	4
700.2.t.d.199.9		32	35.17	even	12
700.2.t.d.199.13		32	140.87	odd	12
700.2.t.d.299.9		32	20.3	even	4
700.2.t.d.299.13		32	5.3	odd	4
980.2.g.a.391.21		32	7.2	even	3
980.2.g.a.391.22		32	7.5	odd	6
980.2.g.a.391.23		32	28.19	even	6
980.2.g.a.391.24		32	28.23	odd	6
980.2.o.f.31.1		32	7.4	even	3
980.2.o.f.31.12		32	28.11	odd	6
980.2.o.f.411.1		32	28.27	even	2
980.2.o.f.411.12		32	7.6	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 140 = 2^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	140.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.906567 + 1.08542i) q^{2} +(0.406021 + 0.703249i) q^{3} +(-0.356272 + 1.96801i) q^{4} +(0.866025 + 0.500000i) q^{5} +(-0.395235 + 1.07825i) q^{6} +(-0.336411 - 2.62428i) q^{7} +(-2.45910 + 1.39743i) q^{8} +(1.17029 - 2.02701i) q^{9} +O(q^{10})\)	\(q+(0.906567 + 1.08542i) q^{2} +(0.406021 + 0.703249i) q^{3} +(-0.356272 + 1.96801i) q^{4} +(0.866025 + 0.500000i) q^{5} +(-0.395235 + 1.07825i) q^{6} +(-0.336411 - 2.62428i) q^{7} +(-2.45910 + 1.39743i) q^{8} +(1.17029 - 2.02701i) q^{9} +(0.242400 + 1.39328i) q^{10} +(-4.20925 + 2.43021i) q^{11} +(-1.52866 + 0.548506i) q^{12} +0.895933i q^{13} +(2.54346 - 2.74423i) q^{14} +0.812042i q^{15} +(-3.74614 - 1.40230i) q^{16} +(5.10231 - 2.94582i) q^{17} +(3.26111 - 0.567359i) q^{18} +(1.45818 - 2.52565i) q^{19} +(-1.29255 + 1.52621i) q^{20} +(1.70893 - 1.30209i) q^{21} +(-6.45377 - 2.36566i) q^{22} +(1.35231 + 0.780755i) q^{23} +(-1.98119 - 1.16198i) q^{24} +(0.500000 + 0.866025i) q^{25} +(-0.972464 + 0.812224i) q^{26} +4.33678 q^{27} +(5.28446 + 0.272896i) q^{28} -9.73084 q^{29} +(-0.881406 + 0.736170i) q^{30} +(-2.20757 - 3.82363i) q^{31} +(-1.87405 - 5.33741i) q^{32} +(-3.41809 - 1.97344i) q^{33} +(7.82304 + 2.86757i) q^{34} +(1.02080 - 2.44090i) q^{35} +(3.57223 + 3.02532i) q^{36} +(0.910682 - 1.57735i) q^{37} +(4.06333 - 0.706927i) q^{38} +(-0.630064 + 0.363768i) q^{39} +(-2.82836 - 0.0193421i) q^{40} +10.4920i q^{41} +(2.96258 + 0.674472i) q^{42} +3.04581i q^{43} +(-3.28305 - 9.14968i) q^{44} +(2.02701 - 1.17029i) q^{45} +(0.378510 + 2.17563i) q^{46} +(2.60966 - 4.52006i) q^{47} +(-0.534848 - 3.20383i) q^{48} +(-6.77366 + 1.76567i) q^{49} +(-0.486718 + 1.32782i) q^{50} +(4.14329 + 2.39213i) q^{51} +(-1.76321 - 0.319196i) q^{52} +(-0.0898619 - 0.155645i) q^{53} +(3.93158 + 4.70723i) q^{54} -4.86043 q^{55} +(4.49451 + 5.98326i) q^{56} +2.36821 q^{57} +(-8.82166 - 10.5620i) q^{58} +(5.68287 + 9.84302i) q^{59} +(-1.59811 - 0.289308i) q^{60} +(-5.33107 - 3.07789i) q^{61} +(2.14893 - 5.86252i) q^{62} +(-5.71313 - 2.38927i) q^{63} +(4.09438 - 6.87285i) q^{64} +(-0.447967 + 0.775901i) q^{65} +(-0.956722 - 5.49911i) q^{66} +(-6.75417 + 3.89952i) q^{67} +(3.97960 + 11.0909i) q^{68} +1.26801i q^{69} +(3.57482 - 1.10484i) q^{70} +8.38078i q^{71} +(-0.0452719 + 6.62003i) q^{72} +(-7.60453 + 4.39048i) q^{73} +(2.53768 - 0.441499i) q^{74} +(-0.406021 + 0.703249i) q^{75} +(4.45099 + 3.76954i) q^{76} +(7.79359 + 10.2287i) q^{77} +(-0.966036 - 0.354104i) q^{78} +(-3.14686 - 1.81684i) q^{79} +(-2.54310 - 3.08749i) q^{80} +(-1.75006 - 3.03119i) q^{81} +(-11.3882 + 9.51172i) q^{82} +2.03796 q^{83} +(1.95369 + 3.82709i) q^{84} +5.89164 q^{85} +(-3.30598 + 2.76123i) q^{86} +(-3.95092 - 6.84320i) q^{87} +(6.95494 - 11.8583i) q^{88} +(1.52812 + 0.882262i) q^{89} +(3.10788 + 1.13921i) q^{90} +(2.35118 - 0.301402i) q^{91} +(-2.01832 + 2.38320i) q^{92} +(1.79264 - 3.10495i) q^{93} +(7.27200 - 1.26516i) q^{94} +(2.52565 - 1.45818i) q^{95} +(2.99262 - 3.48502i) q^{96} -7.83641i q^{97} +(-8.05727 - 5.75156i) q^{98} +11.3763i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{2} - 2 q^{4} - 4 q^{8} - 16 q^{9}+O(q^{10}) \) 32 * q + 2 * q^2 - 2 * q^4 - 4 * q^8 - 16 * q^9	\( 32 q + 2 q^{2} - 2 q^{4} - 4 q^{8} - 16 q^{9} - 30 q^{12} + 2 q^{14} - 14 q^{16} - 12 q^{21} - 8 q^{22} + 36 q^{24} + 16 q^{25} + 30 q^{26} + 2 q^{28} - 40 q^{29} + 2 q^{32} + 60 q^{36} + 8 q^{37} - 60 q^{38} - 62 q^{42} - 18 q^{44} + 12 q^{45} + 2 q^{46} - 16 q^{49} + 4 q^{50} - 36 q^{52} - 8 q^{53} + 12 q^{54} - 4 q^{56} + 48 q^{57} + 2 q^{58} + 14 q^{60} + 24 q^{61} + 4 q^{64} + 4 q^{65} + 24 q^{66} + 60 q^{68} - 4 q^{70} + 4 q^{72} - 72 q^{73} + 38 q^{74} - 40 q^{77} + 120 q^{78} - 36 q^{81} + 42 q^{82} - 20 q^{84} + 28 q^{86} + 4 q^{88} - 60 q^{89} - 4 q^{92} - 8 q^{93} + 18 q^{94} - 60 q^{96} + 78 q^{98}+O(q^{100}) \) 32 * q + 2 * q^2 - 2 * q^4 - 4 * q^8 - 16 * q^9 - 30 * q^12 + 2 * q^14 - 14 * q^16 - 12 * q^21 - 8 * q^22 + 36 * q^24 + 16 * q^25 + 30 * q^26 + 2 * q^28 - 40 * q^29 + 2 * q^32 + 60 * q^36 + 8 * q^37 - 60 * q^38 - 62 * q^42 - 18 * q^44 + 12 * q^45 + 2 * q^46 - 16 * q^49 + 4 * q^50 - 36 * q^52 - 8 * q^53 + 12 * q^54 - 4 * q^56 + 48 * q^57 + 2 * q^58 + 14 * q^60 + 24 * q^61 + 4 * q^64 + 4 * q^65 + 24 * q^66 + 60 * q^68 - 4 * q^70 + 4 * q^72 - 72 * q^73 + 38 * q^74 - 40 * q^77 + 120 * q^78 - 36 * q^81 + 42 * q^82 - 20 * q^84 + 28 * q^86 + 4 * q^88 - 60 * q^89 - 4 * q^92 - 8 * q^93 + 18 * q^94 - 60 * q^96 + 78 * q^98

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