LMFDB - Embedded newform 230.2.l.a.17.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [230,2,Mod(7,230)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(230, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([11, 38]))

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

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

chi := DirichletCharacter("230.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	230.l (of order $44$, degree $20$, 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:	$1.83655924649$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			17.1
Character	$\chi$	$=$	230.17
Dual form			230.2.l.a.203.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.936950 + 0.349464i) q^{2} +(-2.43530 + 1.32977i) q^{3} +(0.755750 - 0.654861i) q^{4} +(2.05188 - 0.888703i) q^{5} +(1.81704 - 2.09698i) q^{6} +(-1.58597 - 2.11861i) q^{7} +(-0.479249 + 0.877679i) q^{8} +(2.54045 - 3.95301i) q^{9} +(-1.61194 + 1.54973i) q^{10} +(1.25057 - 0.571117i) q^{11} +(-0.969658 + 2.59975i) q^{12} +(4.76976 + 3.57060i) q^{13} +(2.22635 + 1.43079i) q^{14} +(-3.81516 + 4.89279i) q^{15} +(0.142315 - 0.989821i) q^{16} +(-0.123408 - 1.72547i) q^{17} +(-0.998835 + 4.59157i) q^{18} +(2.57738 + 2.97445i) q^{19} +(0.968730 - 2.01533i) q^{20} +(6.67957 + 3.05046i) q^{21} +(-0.972139 + 0.972139i) q^{22} +(2.48233 + 4.10342i) q^{23} -2.77470i q^{24} +(3.42041 - 3.64702i) q^{25} +(-5.71682 - 1.67861i) q^{26} +(-0.336299 + 4.70208i) q^{27} +(-2.58599 - 0.562548i) q^{28} +(-0.566767 - 0.491106i) q^{29} +(1.86476 - 5.91755i) q^{30} +(8.10734 - 2.38053i) q^{31} +(0.212565 + 0.977147i) q^{32} +(-2.28606 + 3.05382i) q^{33} +(0.718617 + 1.57355i) q^{34} +(-5.13703 - 2.93767i) q^{35} +(-0.668731 - 4.65113i) q^{36} +(5.87592 - 1.27823i) q^{37} +(-3.45434 - 1.88621i) q^{38} +(-16.3639 - 2.35277i) q^{39} +(-0.203365 + 2.22680i) q^{40} +(-7.72122 + 4.96213i) q^{41} +(-7.32445 - 0.523855i) q^{42} +(-5.20194 - 9.52665i) q^{43} +(0.571117 - 1.25057i) q^{44} +(1.69963 - 10.3688i) q^{45} +(-3.75982 - 2.97721i) q^{46} +(-2.78897 - 2.78897i) q^{47} +(0.969658 + 2.59975i) q^{48} +(-0.00107183 + 0.00365032i) q^{49} +(-1.93025 + 4.61239i) q^{50} +(2.59502 + 4.03793i) q^{51} +(5.94299 - 0.425051i) q^{52} +(1.09796 - 0.821926i) q^{53} +(-1.32811 - 4.52314i) q^{54} +(2.05847 - 2.28325i) q^{55} +(2.61953 - 0.376632i) q^{56} +(-10.2320 - 3.81634i) q^{57} +(0.702656 + 0.262077i) q^{58} +(8.33749 - 1.19875i) q^{59} +(0.320789 + 6.19612i) q^{60} +(0.141177 + 0.480803i) q^{61} +(-6.76426 + 5.06366i) q^{62} +(-12.4040 + 0.887149i) q^{63} +(-0.540641 - 0.841254i) q^{64} +(12.9602 + 3.08753i) q^{65} +(1.07472 - 3.66017i) q^{66} +(1.15888 + 3.10707i) q^{67} +(-1.22321 - 1.22321i) q^{68} +(-11.5018 - 6.69210i) q^{69} +(5.83975 + 0.957241i) q^{70} +(-5.61249 + 12.2896i) q^{71} +(2.25197 + 4.12417i) q^{72} +(14.5923 + 1.04366i) q^{73} +(-5.05875 + 3.25106i) q^{74} +(-3.48001 + 13.4299i) q^{75} +(3.89570 + 0.560117i) q^{76} +(-3.19335 - 1.74370i) q^{77} +(16.1543 - 3.51416i) q^{78} +(-0.692476 - 4.81627i) q^{79} +(-0.587645 - 2.15747i) q^{80} +(0.422345 + 0.924807i) q^{81} +(5.50031 - 7.34755i) q^{82} +(0.0505310 + 0.232287i) q^{83} +(7.04571 - 2.06881i) q^{84} +(-1.78665 - 3.43078i) q^{85} +(8.20318 + 7.10810i) q^{86} +(2.03330 + 0.442318i) q^{87} +(-0.0980779 + 1.37131i) q^{88} +(-11.7514 - 3.45054i) q^{89} +(2.03105 + 10.3090i) q^{90} -15.7681i q^{91} +(4.56319 + 1.47558i) q^{92} +(-16.5782 + 16.5782i) q^{93} +(3.58776 + 1.63848i) q^{94} +(7.93187 + 3.81269i) q^{95} +(-1.81704 - 2.09698i) q^{96} +(1.32094 - 6.07227i) q^{97} +(-0.000271405 - 0.00379474i) q^{98} +(0.919379 - 6.39442i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 8 q^{3} - 8 q^{6} - 8 q^{12} + 16 q^{13} + 24 q^{16} - 72 q^{18} - 80 q^{23} - 8 q^{26} + 16 q^{27} - 44 q^{28} + 24 q^{31} - 44 q^{33} - 8 q^{35} - 32 q^{36} - 88 q^{37} - 24 q^{41} - 8 q^{46}+ \cdots + 24 q^{98}+O(q^{100}) $ 240 * q - 8 * q^3 - 8 * q^6 - 8 * q^12 + 16 * q^13 + 24 * q^16 - 72 * q^18 - 80 * q^23 - 8 * q^26 + 16 * q^27 - 44 * q^28 + 24 * q^31 - 44 * q^33 - 8 * q^35 - 32 * q^36 - 88 * q^37 - 24 * q^41 - 8 * q^46 - 80 * q^47 + 8 * q^48 + 8 * q^50 + 16 * q^52 - 44 * q^56 - 88 * q^57 - 176 * q^61 - 32 * q^62 - 176 * q^66 + 24 * q^70 - 336 * q^71 + 16 * q^72 - 88 * q^73 - 36 * q^75 - 24 * q^77 + 40 * q^78 - 136 * q^81 + 40 * q^82 - 100 * q^85 - 44 * q^86 + 40 * q^87 + 8 * q^92 + 56 * q^93 + 52 * q^95 + 8 * q^96 + 132 * q^97 + 24 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{7}{22}\right)$

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 $

$2$	−0.936950	+	0.349464i	−0.662524	+	0.247108i
$2$	−0.936950	+	0.349464i	−0.662524	+	0.247108i
$3$	−2.43530	+	1.32977i	−1.40602	+	0.767744i	−0.989927	−	0.141579i	$-0.954782\pi$
$3$	−2.43530	+	1.32977i	−1.40602	+	0.767744i	−0.416091	+	0.909323i	$0.636600\pi$
$4$	0.755750	−	0.654861i	0.377875	−	0.327430i
$5$	2.05188	−	0.888703i	0.917628	−	0.397440i
$5$	2.05188	−	0.888703i	0.917628	−	0.397440i
$6$	1.81704	−	2.09698i	0.741804	−	0.856088i
$7$	−1.58597	−	2.11861i	−0.599440	−	0.800759i	0.393506	−	0.919322i	$-0.371262\pi$
$7$	−1.58597	−	2.11861i	−0.599440	−	0.800759i	−0.992946	+	0.118563i	$0.962171\pi$
$8$	−0.479249	+	0.877679i	−0.169440	+	0.310306i
$9$	2.54045	−	3.95301i	0.846816	−	1.31767i
$10$	−1.61194	+	1.54973i	−0.509739	+	0.490067i
$11$	1.25057	−	0.571117i	0.377062	−	0.172198i	−0.217864	−	0.975979i	$-0.569909\pi$
$11$	1.25057	−	0.571117i	0.377062	−	0.172198i	0.594926	+	0.803781i	$0.297182\pi$
$12$	−0.969658	+	2.59975i	−0.279916	+	0.750484i
$13$	4.76976	+	3.57060i	1.32289	+	0.990306i	0.999022	+	0.0442052i	$0.0140756\pi$
$13$	4.76976	+	3.57060i	1.32289	+	0.990306i	0.323872	+	0.946101i	$0.395015\pi$
$14$	2.22635	+	1.43079i	0.595018	+	0.382395i
$15$	−3.81516	+	4.89279i	−0.985070	+	1.26331i
$16$	0.142315	−	0.989821i	0.0355787	−	0.247455i
$17$	−0.123408	−	1.72547i	−0.0299309	−	0.418488i	−0.990223	−	0.139492i	$-0.955453\pi$
$17$	−0.123408	−	1.72547i	−0.0299309	−	0.418488i	0.960292	−	0.278996i	$-0.0900016\pi$
$18$	−0.998835	+	4.59157i	−0.235428	+	1.08224i
$19$	2.57738	+	2.97445i	0.591291	+	0.682386i	0.969993	−	0.243133i	$-0.0781750\pi$
$19$	2.57738	+	2.97445i	0.591291	+	0.682386i	−0.378702	+	0.925519i	$0.623630\pi$
$20$	0.968730	−	2.01533i	0.216615	−	0.450642i
$21$	6.67957	+	3.05046i	1.45760	+	0.665665i
$22$	−0.972139	+	0.972139i	−0.207261	+	0.207261i
$23$	2.48233	+	4.10342i	0.517601	+	0.855622i
$23$	2.48233	+	4.10342i	0.517601	+	0.855622i
$24$		−	2.77470i		−	0.566383i
$25$	3.42041	−	3.64702i	0.684083	−	0.729405i
$26$	−5.71682	−	1.67861i	−1.12116	−	0.329203i
$27$	−0.336299	+	4.70208i	−0.0647209	+	0.904916i
$28$	−2.58599	−	0.562548i	−0.488706	−	0.106312i
$29$	−0.566767	−	0.491106i	−0.105246	−	0.0911961i	0.600648	−	0.799513i	$-0.294909\pi$
$29$	−0.566767	−	0.491106i	−0.105246	−	0.0911961i	−0.705894	+	0.708317i	$0.749455\pi$
$30$	1.86476	−	5.91755i	0.340457	−	1.08039i
$31$	8.10734	−	2.38053i	1.45612	−	0.427556i	0.544561	−	0.838721i	$-0.316696\pi$
$31$	8.10734	−	2.38053i	1.45612	−	0.427556i	0.911561	+	0.411165i	$0.134878\pi$
$32$	0.212565	+	0.977147i	0.0375766	+	0.172737i
$33$	−2.28606	+	3.05382i	−0.397952	+	0.531601i
$34$	0.718617	+	1.57355i	0.123242	+	0.269862i
$35$	−5.13703	−	2.93767i	−0.868317	−	0.496557i
$36$	−0.668731	−	4.65113i	−0.111455	−	0.775188i
$37$	5.87592	−	1.27823i	0.965995	−	0.210139i	0.298216	−	0.954499i	$-0.403609\pi$
$37$	5.87592	−	1.27823i	0.965995	−	0.210139i	0.667779	+	0.744359i	$0.267245\pi$
$38$	−3.45434	−	1.88621i	−0.560367	−	0.305984i
$39$	−16.3639	−	2.35277i	−2.62032	−	0.376744i
$40$	−0.203365	+	2.22680i	−0.0321548	+	0.352088i
$41$	−7.72122	+	4.96213i	−1.20585	+	0.774954i	−0.979959	−	0.199199i	$-0.936166\pi$
$41$	−7.72122	+	4.96213i	−1.20585	+	0.774954i	−0.225892	+	0.974152i	$0.572530\pi$
$42$	−7.32445	−	0.523855i	−1.13019	−	0.0808326i
$43$	−5.20194	−	9.52665i	−0.793289	−	1.45280i	−0.889253	−	0.457416i	$-0.848775\pi$
$43$	−5.20194	−	9.52665i	−0.793289	−	1.45280i	0.0959639	−	0.995385i	$-0.469407\pi$
$44$	0.571117	−	1.25057i	0.0860992	−	0.188531i
$45$	1.69963	−	10.3688i	0.253367	−	1.54569i
$46$	−3.75982	−	2.97721i	−0.554355	−	0.438966i
$47$	−2.78897	−	2.78897i	−0.406813	−	0.406813i	0.473813	−	0.880625i	$-0.342877\pi$
$47$	−2.78897	−	2.78897i	−0.406813	−	0.406813i	−0.880625	+	0.473813i	$0.842877\pi$
$48$	0.969658	+	2.59975i	0.139958	+	0.375242i
$49$	−0.00107183	+	0.00365032i	−0.000153119	+	0.000521475i
$50$	−1.93025	+	4.61239i	−0.272979	+	0.652290i
$51$	2.59502	+	4.03793i	0.363375	+	0.565423i
$52$	5.94299	−	0.425051i	0.824145	−	0.0589440i
$53$	1.09796	−	0.821926i	0.150817	−	0.112900i	−0.521205	−	0.853432i	$-0.674517\pi$
$53$	1.09796	−	0.821926i	0.150817	−	0.112900i	0.672022	+	0.740532i	$0.265426\pi$
$54$	−1.32811	−	4.52314i	−0.180733	−	0.615521i
$55$	2.05847	−	2.28325i	0.277564	−	0.307874i
$56$	2.61953	−	0.376632i	0.350050	−	0.0503296i
$57$	−10.2320	−	3.81634i	−1.35526	−	0.505487i
$58$	0.702656	+	0.262077i	0.0922633	+	0.0344124i
$59$	8.33749	−	1.19875i	1.08545	−	0.156064i	0.423710	−	0.905798i	$-0.360728\pi$
$59$	8.33749	−	1.19875i	1.08545	−	0.156064i	0.661739	+	0.749734i	$0.269819\pi$
$60$	0.320789	+	6.19612i	0.0414137	+	0.799915i
$61$	0.141177	+	0.480803i	0.0180758	+	0.0615606i	0.968037	−	0.250807i	$-0.0806960\pi$
$61$	0.141177	+	0.480803i	0.0180758	+	0.0615606i	−0.949961	+	0.312368i	$0.898878\pi$
$62$	−6.76426	+	5.06366i	−0.859062	+	0.643086i
$63$	−12.4040	+	0.887149i	−1.56275	+	0.111770i
$64$	−0.540641	−	0.841254i	−0.0675801	−	0.105157i
$65$	12.9602	+	3.08753i	1.60751	+	0.382962i
$66$	1.07472	−	3.66017i	0.132289	−	0.450535i
$67$	1.15888	+	3.10707i	0.141579	+	0.379589i	0.988315	−	0.152425i	$-0.0487082\pi$
$67$	1.15888	+	3.10707i	0.141579	+	0.379589i	−0.846736	+	0.532014i	$0.821435\pi$
$68$	−1.22321	−	1.22321i	−0.148336	−	0.148336i
$69$	−11.5018	−	6.69210i	−1.38466	−	0.805635i
$70$	5.83975	+	0.957241i	0.697984	+	0.114412i
$71$	−5.61249	+	12.2896i	−0.666080	+	1.45851i	0.210667	+	0.977558i	$0.432436\pi$
$71$	−5.61249	+	12.2896i	−0.666080	+	1.45851i	−0.876746	+	0.480953i	$0.840291\pi$
$72$	2.25197	+	4.12417i	0.265397	+	0.486039i
$73$	14.5923	+	1.04366i	1.70789	+	0.122151i	0.890812	−	0.454371i	$-0.150136\pi$
$73$	14.5923	+	1.04366i	1.70789	+	0.122151i	0.817081	+	0.576522i	$0.195591\pi$
$74$	−5.05875	+	3.25106i	−0.588067	+	0.377928i
$75$	−3.48001	+	13.4299i	−0.401837	+	1.55076i
$76$	3.89570	+	0.560117i	0.446868	+	0.0642499i
$77$	−3.19335	−	1.74370i	−0.363916	−	0.198713i
$78$	16.1543	−	3.51416i	1.82912	−	0.397900i
$79$	−0.692476	−	4.81627i	−0.0779096	−	0.541873i	−0.990974	−	0.134057i	$-0.957199\pi$
$79$	−0.692476	−	4.81627i	−0.0779096	−	0.541873i	0.913064	−	0.407816i	$-0.133710\pi$
$80$	−0.587645	−	2.15747i	−0.0657007	−	0.241212i
$81$	0.422345	+	0.924807i	0.0469272	+	0.102756i
$82$	5.50031	−	7.34755i	0.607407	−	0.811401i
$83$	0.0505310	+	0.232287i	0.00554650	+	0.0254968i	0.979837	−	0.199799i	$-0.0640288\pi$
$83$	0.0505310	+	0.232287i	0.00554650	+	0.0254968i	−0.974290	+	0.225296i	$0.927665\pi$
$84$	7.04571	−	2.06881i	0.768750	−	0.225725i
$85$	−1.78665	−	3.43078i	−0.193789	−	0.372121i
$86$	8.20318	+	7.10810i	0.884572	+	0.766486i
$87$	2.03330	+	0.442318i	0.217993	+	0.0474215i
$88$	−0.0980779	+	1.37131i	−0.0104551	+	0.146182i
$89$	−11.7514	−	3.45054i	−1.24565	−	0.365756i	−0.408515	−	0.912752i	$-0.633953\pi$
$89$	−11.7514	−	3.45054i	−1.24565	−	0.365756i	−0.837136	+	0.546995i	$0.815771\pi$
$90$	2.03105	+	10.3090i	0.214092	+	1.08667i
$91$		−	15.7681i		−	1.65295i
$92$	4.56319	+	1.47558i	0.475745	+	0.153839i
$93$	−16.5782	+	16.5782i	−1.71908	+	1.71908i
$94$	3.58776	+	1.63848i	0.370050	+	0.168996i
$95$	7.93187	+	3.81269i	0.813793	+	0.391174i
$96$	−1.81704	−	2.09698i	−0.185451	−	0.214022i
$97$	1.32094	−	6.07227i	0.134121	−	0.616546i	−0.860185	−	0.509983i	$-0.829652\pi$
$97$	1.32094	−	6.07227i	0.134121	−	0.616546i	0.994306	−	0.106563i	$-0.0339845\pi$
$98$	−0.000271405	−	0.00379474i	−2.74160e−5	−	0.000383326i
$99$	0.919379	−	6.39442i	0.0924011	−	0.642664i
$100$	0.196684	−	4.99613i	0.0196684	−	0.499613i
$101$	−10.1269	−	6.50814i	−1.00766	−	0.647584i	−0.0708740	−	0.997485i	$-0.522579\pi$
$101$	−10.1269	−	6.50814i	−1.00766	−	0.647584i	−0.936787	+	0.349901i	$0.886215\pi$
$102$	−3.84251	−	2.87647i	−0.380465	−	0.284813i
$103$	−1.04915	+	2.81288i	−0.103376	+	0.277162i	−0.978333	−	0.207040i	$-0.933617\pi$
$103$	−1.04915	+	2.81288i	−0.103376	+	0.277162i	0.874957	+	0.484201i	$0.160890\pi$
$104$	−5.41974	+	2.47511i	−0.531450	+	0.242705i
$105$	16.4166	+	0.323014i	1.60210	+	0.0315229i
$106$	−0.741504	+	1.15380i	−0.0720212	+	0.112067i
$107$	6.65557	−	12.1888i	0.643418	−	1.17833i	−0.328832	−	0.944388i	$-0.606655\pi$
$107$	6.65557	−	12.1888i	0.643418	−	1.17833i	0.972250	−	0.233944i	$-0.0751632\pi$
$108$	2.82505	+	3.77382i	0.271841	+	0.363136i
$109$	−6.76218	+	7.80397i	−0.647699	+	0.747484i	−0.980716	−	0.195436i	$-0.937388\pi$
$109$	−6.76218	+	7.80397i	−0.647699	+	0.747484i	0.333017	+	0.942921i	$0.391933\pi$
$110$	−1.13077	+	2.85865i	−0.107815	+	0.272562i
$111$	−12.6098	+	10.9265i	−1.19687	+	1.03710i
$112$	−2.32275	+	1.26832i	−0.219479	+	0.119845i
$113$	−13.0823	+	4.87945i	−1.23068	+	0.459020i	−0.878875	−	0.477053i	$-0.841705\pi$
$113$	−13.0823	+	4.87945i	−1.23068	+	0.459020i	−0.351806	+	0.936073i	$0.614432\pi$
$114$	10.9206			1.02280
$115$	8.74016	+	6.21366i	0.815024	+	0.579427i
$116$	−0.749940			−0.0696302
$117$	26.2320	−	9.78402i	2.42515	−	0.904533i
$118$	−7.39289	+	4.03683i	−0.680571	+	0.371620i
$119$	−3.45988	+	2.99800i	−0.317166	+	0.274826i
$120$	−2.46588	−	5.69335i	−0.225103	−	0.519729i
$121$	−5.96571	+	6.88480i	−0.542337	+	0.625891i
$122$	−0.300299	−	0.401152i	−0.0271878	−	0.0363186i
$123$	12.2049	−	22.3517i	1.10048	−	2.01538i
$124$	4.56821	−	7.10827i	0.410237	−	0.638341i
$125$	3.77715	−	10.5230i	0.337839	−	0.941204i
$126$	11.3119	−	5.16595i	1.00774	−	0.460220i
$127$	−5.48421	+	14.7037i	−0.486645	+	1.30474i	0.429199	+	0.903210i	$0.358796\pi$
$127$	−5.48421	+	14.7037i	−0.486645	+	1.30474i	−0.915844	+	0.401535i	$0.868477\pi$
$128$	0.800541	+	0.599278i	0.0707585	+	0.0529692i
$129$	25.3365	+	16.2828i	2.23076	+	1.43362i
$130$	−13.2220	+	1.63625i	−1.15965	+	0.143509i
$131$	−0.695018	+	4.83395i	−0.0607240	+	0.422345i	0.936671	+	0.350211i	$0.113890\pi$
$131$	−0.695018	+	4.83395i	−0.0607240	+	0.422345i	−0.997395	+	0.0721340i	$0.977019\pi$
$132$	0.272137	+	3.80497i	0.0236865	+	0.331180i
$133$	2.21405	−	10.1778i	0.191983	−	0.882531i
$134$	−2.17162	−	2.50618i	−0.187599	−	0.216501i
$135$	3.48871	+	9.94697i	0.300260	+	0.856099i
$136$	1.57355	+	0.718617i	0.134931	+	0.0616209i
$137$	−5.35840	+	5.35840i	−0.457799	+	0.457799i	−0.897932	−	0.440134i	$-0.854931\pi$
$137$	−5.35840	+	5.35840i	−0.457799	+	0.457799i	0.440134	+	0.897932i	$0.354931\pi$
$138$	13.1153	+	2.25069i	1.11645	+	0.191592i
$139$			15.1640i			1.28620i	0.765783	+	0.643099i	$0.222352\pi$
$139$			15.1640i			1.28620i	−0.765783	+	0.643099i	$0.777648\pi$
$140$	−5.80608	+	1.14390i	−0.490703	+	0.0966770i
$141$	10.5006	+	3.08327i	0.884314	+	0.259658i
$142$	0.963832	−	13.4761i	0.0808830	−	1.13089i
$143$	8.00417	+	1.74120i	0.669342	+	0.145606i
$144$	−3.55123	−	3.07716i	−0.295936	−	0.256430i
$145$	−1.59938	−	0.504003i	−0.132822	−	0.0418552i
$146$	−14.0369	+	4.12161i	−1.16170	+	0.341107i
$147$	−0.00224387	−	0.0103149i	−0.000185071	−	0.000850760i
$148$	3.60366	−	4.81393i	0.296219	−	0.395702i
$149$	−6.54971	−	14.3419i	−0.536573	−	1.17493i	−0.962775	−	0.270303i	$-0.912876\pi$
$149$	−6.54971	−	14.3419i	−0.536573	−	1.17493i	0.426202	−	0.904628i	$-0.359851\pi$
$150$	−1.43269	−	13.7993i	−0.116979	−	1.12671i
$151$	0.405528	+	2.82051i	0.0330014	+	0.229530i	0.999646	−	0.0265900i	$-0.00846487\pi$
$151$	0.405528	+	2.82051i	0.0330014	+	0.229530i	−0.966645	+	0.256120i	$0.917556\pi$
$152$	−3.84582	+	0.836607i	−0.311937	+	0.0678578i
$153$	−7.13432	−	3.89563i	−0.576776	−	0.314943i
$154$	3.60136	+	0.517798i	0.290206	+	0.0417254i
$155$	14.5197	−	12.0896i	1.16625	−	0.971059i
$156$	−13.9077	+	8.93795i	−1.11351	+	0.715609i
$157$	−19.8516	−	1.41981i	−1.58433	−	0.113313i	−0.748813	−	0.662781i	$-0.769376\pi$
$157$	−19.8516	−	1.41981i	−1.58433	−	0.113313i	−0.835515	+	0.549468i	$0.814831\pi$
$158$	2.33193	+	4.27061i	0.185518	+	0.339752i
$159$	−1.58089	+	3.46167i	−0.125373	+	0.274529i
$160$	1.30455	+	1.81608i	0.103134	+	0.143574i
$161$	4.75664	−	11.7670i	0.374875	−	0.927368i
$162$	−0.718903	−	0.718903i	−0.0564823	−	0.0564823i
$163$	−0.0220215	−	0.0590420i	−0.00172486	−	0.00462452i	0.936084	−	0.351775i	$-0.114422\pi$
$163$	−0.0220215	−	0.0590420i	−0.00172486	−	0.00462452i	−0.937809	+	0.347151i	$0.887149\pi$
$164$	−2.58581	+	8.80645i	−0.201918	+	0.687668i
$165$	−1.97678	+	8.29769i	−0.153892	+	0.645974i
$166$	−0.128521	−	0.199983i	−0.00997517	−	0.0155217i
$167$	1.69553	−	0.121267i	0.131204	−	0.00938389i	−0.00558276	−	0.999984i	$-0.501777\pi$
$167$	1.69553	−	0.121267i	0.131204	−	0.00938389i	0.136787	+	0.990601i	$0.456323\pi$
$168$	−5.87850	+	4.40059i	−0.453536	+	0.339513i
$169$	6.33893	+	21.5884i	0.487610	+	1.66065i
$170$	2.87294	+	2.59010i	0.220344	+	0.198652i
$171$	18.3057	−	2.63197i	1.39987	−	0.201272i
$172$	−10.1700	−	3.79321i	−0.775455	−	0.289230i
$173$	8.78296	+	3.27587i	0.667756	+	0.249060i	0.660401	−	0.750913i	$-0.270386\pi$
$173$	8.78296	+	3.27587i	0.667756	+	0.249060i	0.00735456	+	0.999973i	$0.497659\pi$
$174$	−2.05968	+	0.296137i	−0.156144	+	0.0224501i
$175$	−13.1513	−	1.46245i	−0.994144	−	0.110551i
$176$	−0.387329	−	1.31912i	−0.0291960	−	0.0994326i
$177$	−18.7102	+	14.0063i	−1.40634	+	1.05278i
$178$	12.2164	−	0.873731i	0.915654	−	0.0654889i
$179$	−1.20944	−	1.88192i	−0.0903975	−	0.140661i	0.793110	−	0.609079i	$-0.208461\pi$
$179$	−1.20944	−	1.88192i	−0.0903975	−	0.140661i	−0.883507	+	0.468417i	$0.844824\pi$
$180$	−5.50563	−	8.94925i	−0.410365	−	0.667037i
$181$	3.49917	−	11.9171i	0.260091	−	0.885789i	−0.721113	−	0.692817i	$-0.756369\pi$
$181$	3.49917	−	11.9171i	0.260091	−	0.885789i	0.981204	−	0.192972i	$-0.0618126\pi$
$182$	5.51040	+	14.7739i	0.408458	+	1.09512i
$183$	−0.983166	−	0.983166i	−0.0726777	−	0.0726777i
$184$	−4.79114	+	0.212129i	−0.353207	+	0.0156384i
$185$	10.9207	−	7.84472i	0.802906	−	0.576755i
$186$	9.73946	−	21.3264i	0.714132	−	1.56373i
$187$	−1.13978	−	2.08735i	−0.0833488	−	0.152642i
$188$	−3.93414	−	0.281376i	−0.286927	−	0.0205214i
$189$	10.4952	−	6.74487i	0.763416	−	0.490617i
$190$	−8.76416	−	0.800395i	−0.635819	−	0.0580668i
$191$	−12.0591	−	1.73384i	−0.872566	−	0.125456i	−0.308538	−	0.951212i	$-0.599840\pi$
$191$	−12.0591	−	1.73384i	−0.872566	−	0.125456i	−0.564028	+	0.825756i	$0.690749\pi$
$192$	2.43530	+	1.32977i	0.175752	+	0.0959680i
$193$	−3.23525	+	0.703786i	−0.232879	+	0.0506596i	−0.327490	−	0.944855i	$-0.606203\pi$
$193$	−3.23525	+	0.703786i	−0.232879	+	0.0506596i	0.0946114	+	0.995514i	$0.469839\pi$
$194$	0.884385	+	6.15103i	0.0634951	+	0.441618i
$195$	−35.6676	+	9.71502i	−2.55421	+	0.695707i
$196$	0.00158042	+	0.00346063i	0.000112887	+	0.000247188i
$197$	−10.7201	+	14.3204i	−0.763779	+	1.02029i	0.235054	+	0.971982i	$0.424473\pi$
$197$	−10.7201	+	14.3204i	−0.763779	+	1.02029i	−0.998833	+	0.0483064i	$0.984618\pi$
$198$	1.37321	+	6.31254i	0.0975898	+	0.448613i
$199$	21.3398	−	6.26592i	1.51274	−	0.444179i	0.583020	−	0.812458i	$-0.301871\pi$
$199$	21.3398	−	6.26592i	1.51274	−	0.444179i	0.929715	+	0.368279i	$0.120053\pi$
$200$	1.56169	+	4.74986i	0.110428	+	0.335866i
$201$	−6.95390	−	6.02559i	−0.490491	−	0.425012i
$202$	11.7627	+	2.55882i	0.827622	+	0.180038i
$203$	−0.141586	+	1.97964i	−0.00993742	+	0.138943i
$204$	4.60546	+	1.35229i	0.322447	+	0.0946789i
$205$	−11.4331	+	17.0435i	−0.798526	+	1.19037i
$206$		−	3.00217i		−	0.209171i
$207$	22.5271	+	0.611837i	1.56574	+	0.0425256i
$208$	4.21306	−	4.21306i	0.292123	−	0.292123i
$209$	4.92196	+	2.24778i	0.340459	+	0.155482i
$210$	−15.4944	+	5.43437i	−1.06922	+	0.375007i
$211$	−5.39990	−	6.23182i	−0.371745	−	0.429016i	0.538796	−	0.842436i	$-0.318879\pi$
$211$	−5.39990	−	6.23182i	−0.371745	−	0.429016i	−0.910540	+	0.413420i	$0.864334\pi$
$212$	0.291539	−	1.34018i	0.0200230	−	0.0920442i
$213$	−2.67434	−	37.3922i	−0.183243	−	2.56207i
$214$	−1.97640	+	13.7461i	−0.135104	+	0.939667i
$215$	−19.1401	−	14.9245i	−1.30535	−	1.01785i
$216$	−3.96575	−	2.54863i	−0.269835	−	0.173412i
$217$	−17.9014	−	13.4008i	−1.21523	−	0.909708i
$218$	3.60861	−	9.67506i	0.244406	−	0.655278i
$219$	−36.9243	+	16.8627i	−2.49511	+	1.13948i
$220$	0.0604757	−	3.07358i	0.00407727	−	0.207221i
$221$	5.57234	−	8.67073i	0.374836	−	0.583256i
$222$	7.99637	−	14.6443i	0.536681	−	0.982859i
$223$	−9.51627	−	12.7123i	−0.637257	−	0.851276i	0.359382	−	0.933190i	$-0.382987\pi$
$223$	−9.51627	−	12.7123i	−0.637257	−	0.851276i	−0.996639	+	0.0819148i	$0.973896\pi$
$224$	1.73307	−	2.00007i	0.115796	−	0.133635i
$225$	−5.72735	−	22.7860i	−0.381823	−	1.51907i
$226$	10.5523	−	9.14360i	0.701927	−	0.608223i
$227$	19.4321	−	10.6108i	1.28976	−	0.704260i	0.319788	−	0.947489i	$-0.396388\pi$
$227$	19.4321	−	10.6108i	1.28976	−	0.704260i	0.969969	+	0.243229i	$0.0782066\pi$
$228$	−10.2320	+	3.81634i	−0.677632	+	0.252744i
$229$	11.3129			0.747578			0.373789	−	0.927514i	$-0.378058\pi$
$229$	11.3129			0.747578			0.373789	+	0.927514i	$0.378058\pi$
$230$	−10.3605	−	2.76752i	−0.683154	−	0.182485i
$231$	10.0955			0.664233
$232$	0.702656	−	0.262077i	0.0461316	−	0.0172062i
$233$	4.23642	−	2.31326i	0.277537	−	0.151547i	−0.334452	−	0.942413i	$-0.608551\pi$
$233$	4.23642	−	2.31326i	0.277537	−	0.151547i	0.611990	+	0.790866i	$0.290369\pi$
$234$	−21.1589	+	18.3343i	−1.38320	+	1.19855i
$235$	−8.20118	−	3.24406i	−0.534986	−	0.211619i
$236$	5.51604	−	6.36585i	0.359064	−	0.414382i
$237$	8.09093	+	10.8082i	0.525562	+	0.702069i
$238$	2.19404	−	4.01808i	0.142218	−	0.260453i
$239$	4.00693	−	6.23490i	0.259187	−	0.403302i	−0.687134	−	0.726530i	$-0.741132\pi$
$239$	4.00693	−	6.23490i	0.259187	−	0.403302i	0.946321	+	0.323228i	$0.104768\pi$
$240$	4.30003	+	4.47264i	0.277566	+	0.288708i
$241$	−5.82788	+	2.66150i	−0.375407	+	0.171442i	−0.594178	−	0.804334i	$-0.702522\pi$
$241$	−5.82788	+	2.66150i	−0.375407	+	0.171442i	0.218771	+	0.975776i	$0.429795\pi$
$242$	3.18358	−	8.53551i	0.204648	−	0.548683i
$243$	−13.5798	−	10.1657i	−0.871144	−	0.652130i
$244$	0.421553	+	0.270916i	0.0269872	+	0.0173436i
$245$	0.00104479	+	0.00844257i	6.67489e−5	+	0.000539376i
$246$	−3.62431	+	25.2076i	−0.231077	+	1.60718i
$247$	1.67290	+	23.3902i	0.106444	+	1.48828i
$248$	−1.79609	+	8.25651i	−0.114052	+	0.524289i
$249$	−0.431947	−	0.498493i	−0.0273735	−	0.0315907i
$250$	0.138403	+	11.1795i	0.00875335	+	0.707053i
$251$	16.0945	+	7.35010i	1.01587	+	0.463934i	0.852554	−	0.522639i	$-0.175052\pi$
$251$	16.0945	+	7.35010i	1.01587	+	0.463934i	0.163320	+	0.986573i	$0.447780\pi$
$252$	−8.79333	+	8.79333i	−0.553928	+	0.553928i
$253$	5.44787	+	3.71392i	0.342504	+	0.233492i
$254$		−	15.6932i		−	0.984678i
$255$	8.91318	+	5.97913i	0.558165	+	0.374428i
$256$	−0.959493	−	0.281733i	−0.0599683	−	0.0176083i
$257$	−0.895787	+	12.5247i	−0.0558777	+	0.781272i	0.889838	+	0.456277i	$0.150817\pi$
$257$	−0.895787	+	12.5247i	−0.0558777	+	0.781272i	−0.945716	+	0.324995i	$0.894637\pi$
$258$	−29.4293	−	6.40196i	−1.83219	−	0.398568i
$259$	−12.0271	−	10.4215i	−0.747327	−	0.647563i
$260$	11.8166	−	6.15371i	0.732832	−	0.381637i
$261$	−3.38119	+	0.992807i	−0.209290	+	0.0614532i
$262$	−1.03810	−	4.77206i	−0.0641339	−	0.294819i
$263$	−15.5565	+	20.7811i	−0.959257	+	1.28142i	0.000328105		1.00000i	$0.499896\pi$
$263$	−15.5565	+	20.7811i	−0.959257	+	1.28142i	−0.959585	+	0.281418i	$0.909195\pi$
$264$	−1.58468	−	3.46996i	−0.0975303	−	0.213561i
$265$	1.52244	−	2.66226i	0.0935229	−	0.163541i
$266$	1.48233	+	10.3099i	0.0908877	+	0.632138i
$267$	33.2067	−	7.22367i	2.03221	−	0.442081i
$268$	2.91052	+	1.58926i	0.177788	+	0.0970798i
$269$	10.0983	+	1.45191i	0.615702	+	0.0885245i	0.443108	−	0.896468i	$-0.353876\pi$
$269$	10.0983	+	1.45191i	0.615702	+	0.0885245i	0.172594	+	0.984993i	$0.444785\pi$
$270$	−6.74485	−	8.10063i	−0.410479	−	0.492989i
$271$	−2.21069	+	1.42072i	−0.134290	+	0.0863028i	−0.606061	−	0.795418i	$-0.707251\pi$
$271$	−2.21069	+	1.42072i	−0.134290	+	0.0863028i	0.471771	+	0.881721i	$0.343615\pi$
$272$	−1.72547	−	0.123408i	−0.104622	−	0.00748271i
$273$	20.9680	+	38.4000i	1.26904	+	2.32408i
$274$	3.14798	−	6.89312i	0.190176	−	0.416428i
$275$	2.19460	−	6.51432i	0.132339	−	0.392829i
$276$	−13.0749	+	2.47453i	−0.787016	+	0.148949i
$277$	−2.04506	−	2.04506i	−0.122876	−	0.122876i	0.642995	−	0.765871i	$-0.277692\pi$
$277$	−2.04506	−	2.04506i	−0.122876	−	0.122876i	−0.765871	+	0.642995i	$0.777692\pi$
$278$	−5.29929	−	14.2079i	−0.317830	−	0.852136i
$279$	11.1860	−	38.0961i	0.669689	−	2.28075i
$280$	5.04025	−	3.10079i	0.301213	−	0.185308i
$281$	11.0785	+	17.2385i	0.660890	+	1.02836i	0.996271	+	0.0862818i	$0.0274986\pi$
$281$	11.0785	+	17.2385i	0.660890	+	1.02836i	−0.335381	+	0.942083i	$0.608865\pi$
$282$	−10.9161	+	0.780733i	−0.650042	+	0.0464919i
$283$	−3.37738	+	2.52827i	−0.200764	+	0.150290i	−0.694930	−	0.719078i	$-0.744565\pi$
$283$	−3.37738	+	2.52827i	−0.200764	+	0.150290i	0.494166	+	0.869368i	$0.335474\pi$
$284$	3.80636	+	12.9633i	0.225866	+	0.769229i
$285$	−24.3865	+	1.26255i	−1.44453	+	0.0747869i
$286$	−8.10799	+	1.16575i	−0.479435	+	0.0689324i
$287$	22.7584	+	8.48845i	1.34339	+	0.501058i
$288$	4.40269	+	1.64212i	0.259431	+	0.0967627i
$289$	13.8649	−	1.99348i	0.815585	−	0.117263i
$290$	1.67467	−	0.0867021i	0.0983402	−	0.00509132i
$291$	4.85785	+	16.5443i	0.284772	+	0.969845i
$292$	11.7115	−	8.76715i	0.685366	−	0.513059i
$293$	7.45052	−	0.532871i	0.435264	−	0.0311307i	0.148012	−	0.988986i	$-0.452713\pi$
$293$	7.45052	−	0.532871i	0.435264	−	0.0311307i	0.287252	+	0.957855i	$0.407258\pi$
$294$	0.00570709	+	0.00888040i	0.000332844	+	0.000517915i
$295$	16.0422	−	9.86925i	0.934013	−	0.574610i
$296$	−1.69415	+	5.76976i	−0.0984707	+	0.335360i
$297$	2.26487	+	6.07236i	0.131421	+	0.352354i
$298$	11.1487	+	11.1487i	0.645828	+	0.645828i
$299$	−2.81154	+	28.4357i	−0.162596	+	1.64448i
$300$	6.16473	+	12.4286i	0.355921	+	0.717565i
$301$	−11.9331	+	26.1299i	−0.687813	+	1.50610i
$302$	−1.36563	−	2.50096i	−0.0785830	−	0.143914i
$303$	33.3162	+	2.38282i	1.91397	+	0.136890i
$304$	3.31097	−	2.12783i	0.189897	−	0.122040i
$305$	0.716969	+	0.861086i	0.0410535	+	0.0493057i
$306$	8.04588	+	1.15682i	0.459953	+	0.0661312i
$307$	−18.7623	−	10.2450i	−1.07082	−	0.584712i	−0.155663	−	0.987810i	$-0.549752\pi$
$307$	−18.7623	−	10.2450i	−1.07082	−	0.584712i	−0.915157	+	0.403098i	$0.867933\pi$
$308$	−3.55525	+	0.773397i	−0.202579	+	0.0440684i
$309$	−1.18550	−	8.24533i	−0.0674407	−	0.469060i
$310$	−9.37936	+	16.4014i	−0.532712	+	0.931540i
$311$	−11.6819	−	25.5797i	−0.662418	−	1.45049i	−0.880251	−	0.474508i	$-0.842626\pi$
$311$	−11.6819	−	25.5797i	−0.662418	−	1.45049i	0.217833	−	0.975986i	$-0.430101\pi$
$312$	9.90734	−	13.2347i	0.560893	−	0.749265i
$313$	−4.18920	−	19.2574i	−0.236787	−	1.08849i	−0.929942	−	0.367705i	$-0.880144\pi$
$313$	−4.18920	−	19.2574i	−0.236787	−	1.08849i	0.693155	−	0.720789i	$-0.256220\pi$
$314$	19.0961	−	5.60712i	1.07766	−	0.316428i
$315$	−24.6630	+	12.8438i	−1.38960	+	0.723664i
$316$	−3.67733	−	3.18642i	−0.206866	−	0.179250i
$317$	10.5080	+	2.28588i	0.590188	+	0.128388i	0.497735	−	0.867329i	$-0.334165\pi$
$317$	10.5080	+	2.28588i	0.590188	+	0.128388i	0.0924537	+	0.995717i	$0.470529\pi$
$318$	0.271487	−	3.79588i	0.0152242	−	0.212862i
$319$	−0.989263	−	0.290474i	−0.0553881	−	0.0162634i
$320$	−1.85695	−	1.24568i	−0.103807	−	0.0696357i
$321$			38.5336i			2.15074i
$322$	−0.344589	+	12.6873i	−0.0192032	+	0.707038i
$323$	4.81426	−	4.81426i	0.267873	−	0.267873i
$324$	0.924807	+	0.422345i	0.0513782	+	0.0234636i
$325$	29.3366	−	5.18251i	1.62730	−	0.287474i
$326$	0.0412661	+	0.0476236i	0.00228552	+	0.00263763i
$327$	6.09040	−	27.9971i	0.336800	−	1.54824i
$328$	−0.654767	−	9.15484i	−0.0361535	−	0.505492i
$329$	−1.48551	+	10.3319i	−0.0818988	+	0.569619i
$330$	−1.04760	−	8.46533i	−0.0576686	−	0.466001i
$331$	−3.02903	−	1.94664i	−0.166491	−	0.106997i	0.454742	−	0.890623i	$-0.349731\pi$
$331$	−3.02903	−	1.94664i	−0.166491	−	0.106997i	−0.621233	+	0.783626i	$0.713368\pi$
$332$	0.190305	+	0.142460i	0.0104443	+	0.00781852i
$333$	9.87461	−	26.4749i	0.541125	−	1.45081i
$334$	−1.54625	+	0.706147i	−0.0846068	+	0.0386387i
$335$	5.13914	+	5.34543i	0.280781	+	0.292052i
$336$	3.97001	−	6.17746i	0.216582	−	0.337008i
$337$	−10.8121	+	19.8009i	−0.588972	+	1.07862i	0.397947	+	0.917408i	$0.369723\pi$
$337$	−10.8121	+	19.8009i	−0.588972	+	1.07862i	−0.986919	+	0.161214i	$0.948459\pi$
$338$	−13.4836	−	18.0120i	−0.733413	−	0.979726i
$339$	25.3707	−	29.2794i	1.37795	−	1.59024i
$340$	−3.59695	−	1.42281i	−0.195072	−	0.0771625i
$341$	8.77926	−	7.60727i	0.475424	−	0.411957i
$342$	−16.2318	+	8.86322i	−0.877714	+	0.479268i
$343$	−17.3478	+	6.47041i	−0.936695	+	0.349369i
$344$	10.8544			0.585228
$345$	−29.5476	−	3.50969i	−1.59079	−	0.188955i
$346$	−9.37399			−0.503949
$347$	−7.50174	+	2.79801i	−0.402715	+	0.150205i	−0.542656	−	0.839955i	$-0.682581\pi$
$347$	−7.50174	+	2.79801i	−0.402715	+	0.150205i	0.139941	+	0.990160i	$0.455309\pi$
$348$	1.82633	−	0.997249i	0.0979013	−	0.0534582i
$349$	−13.6277	+	11.8085i	−0.729474	+	0.632092i	−0.938285	−	0.345864i	$-0.887586\pi$
$349$	−13.6277	+	11.8085i	−0.729474	+	0.632092i	0.208811	+	0.977956i	$0.433041\pi$
$350$	12.8332	−	3.22567i	0.685962	−	0.172419i
$351$	−18.3933	+	21.2270i	−0.981763	+	1.13301i
$352$	0.823894	+	1.10059i	0.0439137	+	0.0586618i
$353$	−2.83415	+	5.19035i	−0.150846	+	0.276255i	−0.942165	−	0.335149i	$-0.891213\pi$
$353$	−2.83415	+	5.19035i	−0.150846	+	0.276255i	0.791319	+	0.611404i	$0.209395\pi$
$354$	12.6358	−	19.6617i	0.671586	−	1.04501i
$355$	−0.594307	+	30.2047i	−0.0315426	+	1.60310i
$356$	−11.1408	+	5.08782i	−0.590460	+	0.269654i
$357$	4.43916	−	11.9019i	0.234945	−	0.629913i
$358$	1.79084	+	1.34061i	0.0946491	+	0.0708534i
$359$	−20.9720	−	13.4779i	−1.10686	−	0.711336i	−0.146253	−	0.989247i	$-0.546721\pi$
$359$	−20.9720	−	13.4779i	−1.10686	−	0.711336i	−0.960607	+	0.277912i	$0.910358\pi$
$360$	8.28594	+	6.46097i	0.436707	+	0.340523i
$361$	0.499492	−	3.47404i	0.0262891	−	0.182844i
$362$	0.886045	+	12.3885i	0.0465695	+	0.651127i
$363$	5.37306	−	24.6995i	0.282012	−	1.29639i
$364$	−10.3259	−	11.9168i	−0.541226	−	0.624608i
$365$	30.8690	−	10.8267i	1.61576	−	0.566696i
$366$	1.26476	+	0.577596i	0.0661100	+	0.0301914i
$367$	13.6622	−	13.6622i	0.713159	−	0.713159i	−0.254036	−	0.967195i	$-0.581758\pi$
$367$	13.6622	−	13.6622i	0.713159	−	0.713159i	0.967195	+	0.254036i	$0.0817581\pi$
$368$	4.41492	−	1.87309i	0.230144	−	0.0976413i
$369$			43.1281i			2.24516i
$370$	−7.49071	+	11.1665i	−0.389423	+	0.580519i
$371$	−3.48268	−	1.02261i	−0.180812	−	0.0530911i
$372$	−1.67256	+	23.3854i	−0.0867180	+	1.21248i
$373$	28.1127	+	6.11554i	1.45562	+	0.316651i	0.869644	−	0.493679i	$-0.164348\pi$
$373$	28.1127	+	6.11554i	1.45562	+	0.316651i	0.585975	+	0.810329i	$0.300712\pi$
$374$	1.79737	+	1.55743i	0.0929396	+	0.0805326i
$375$	4.79468	+	30.6493i	0.247596	+	1.58272i
$376$	3.78443	−	1.11121i	0.195167	−	0.0573062i
$377$	−0.949800	−	4.36616i	−0.0489172	−	0.224869i
$378$	−7.47641	+	9.98731i	−0.384545	+	0.513692i
$379$	4.91280	+	10.7575i	0.252354	+	0.552577i	0.992834	−	0.119500i	$-0.0381293\pi$
$379$	4.91280	+	10.7575i	0.252354	+	0.552577i	−0.740481	+	0.672078i	$0.765402\pi$
$380$	8.49129	−	2.31283i	0.435594	−	0.118646i
$381$	−6.19694	−	43.1007i	−0.317479	−	2.20811i
$382$	11.9047	−	2.58971i	0.609097	−	0.132501i
$383$	−13.2317	−	7.22506i	−0.676108	−	0.369183i	0.104219	−	0.994554i	$-0.466766\pi$
$383$	−13.2317	−	7.22506i	−0.676108	−	0.369183i	−0.780327	+	0.625371i	$0.784948\pi$
$384$	−2.74646	−	0.394881i	−0.140155	−	0.0201512i
$385$	−8.10199	−	0.739922i	−0.412916	−	0.0377099i
$386$	2.78532	−	1.79002i	0.141769	−	0.0911095i
$387$	−50.8742	−	3.63860i	−2.58608	−	0.184960i
$388$	−2.97819	−	5.45415i	−0.151195	−	0.276892i
$389$	3.34366	−	7.32159i	0.169530	−	0.371219i	−0.805729	−	0.592285i	$-0.798226\pi$
$389$	3.34366	−	7.32159i	0.169530	−	0.371219i	0.975259	+	0.221065i	$0.0709534\pi$
$390$	30.0237	−	21.5670i	1.52031	−	1.09209i
$391$	6.77399	−	4.78958i	0.342575	−	0.242220i
$392$	−0.00269014	−	0.00269014i	−0.000135873	−	0.000135873i
$393$	−4.73548	−	12.6963i	−0.238874	−	0.640445i
$394$	5.03976	−	17.1638i	0.253899	−	0.864701i
$395$	−5.70112	−	9.26701i	−0.286854	−	0.466274i
$396$	−3.49264	−	5.43465i	−0.175512	−	0.273101i
$397$	20.5946	−	1.47296i	1.03361	−	0.0739256i	0.455790	−	0.890087i	$-0.349357\pi$
$397$	20.5946	−	1.47296i	1.03361	−	0.0739256i	0.577824	+	0.816162i	$0.303902\pi$
$398$	−17.8046	+	13.3283i	−0.892462	+	0.668089i
$399$	8.14233	+	27.7302i	0.407627	+	1.38825i
$400$	−3.12313	−	3.90462i	−0.156156	−	0.195231i
$401$	−19.4357	+	2.79444i	−0.970574	+	0.139547i	−0.609324	−	0.792921i	$-0.708559\pi$
$401$	−19.4357	+	2.79444i	−0.970574	+	0.139547i	−0.361250	+	0.932469i	$0.617650\pi$
$402$	8.62119	+	3.21554i	0.429986	+	0.160376i
$403$	47.1700	+	17.5935i	2.34971	+	0.876395i
$404$	−11.9153	+	1.71316i	−0.592808	+	0.0852330i
$405$	1.68848	+	1.52225i	0.0839012	+	0.0756413i
$406$	−0.559153	−	1.90430i	−0.0277503	−	0.0945088i
$407$	6.61825	−	4.95436i	0.328054	−	0.245578i
$408$	−4.78766	+	0.342420i	−0.237025	+	0.0169523i
$409$	−8.65689	−	13.4704i	−0.428056	−	0.666068i	0.558498	−	0.829506i	$-0.311378\pi$
$409$	−8.65689	−	13.4704i	−0.428056	−	0.666068i	−0.986554	+	0.163438i	$0.947742\pi$
$410$	4.75617	−	19.9644i	0.234891	−	0.985973i
$411$	5.92383	−	20.1747i	0.292201	−	0.995146i
$412$	1.04915	+	2.81288i	0.0516880	+	0.138581i
$413$	−15.7627	−	15.7627i	−0.775632	−	0.775632i
$414$	−21.3206	+	7.29915i	−1.04785	+	0.358734i
$415$	0.310118	+	0.431718i	0.0152231	+	0.0211922i
$416$	−2.47511	+	5.41974i	−0.121352	+	0.265725i
$417$	−20.1647	−	36.9289i	−0.987470	−	1.80842i
$418$	−5.39715	−	0.386012i	−0.263983	−	0.0188804i
$419$	18.4843	−	11.8791i	0.903016	−	0.580333i	−0.00466696	−	0.999989i	$-0.501486\pi$
$419$	18.4843	−	11.8791i	0.903016	−	0.580333i	0.907683	+	0.419656i	$0.137849\pi$
$420$	12.6184	−	10.5065i	0.615714	−	0.512664i
$421$	−23.0779	−	3.31809i	−1.12475	−	0.161714i	−0.445259	−	0.895402i	$-0.646888\pi$
$421$	−23.0779	−	3.31809i	−1.12475	−	0.161714i	−0.679487	+	0.733688i	$0.737798\pi$
$422$	7.23723	+	3.95183i	0.352303	+	0.192372i
$423$	−18.1100	+	3.93960i	−0.880540	+	0.191550i
$424$	0.195189	+	1.35757i	0.00947920	+	0.0659293i
$425$	−6.71494	−	5.45175i	−0.325722	−	0.264449i
$426$	15.5730	+	34.1000i	0.754512	+	1.65215i
$427$	0.794732	−	1.06164i	0.0384598	−	0.0513763i
$428$	−2.95200	−	13.5701i	−0.142690	−	0.655937i
$429$	−21.8079	+	6.40338i	−1.05290	+	0.309158i
$430$	23.1489	+	7.29476i	1.11634	+	0.351785i
$431$	−0.824252	−	0.714218i	−0.0397028	−	0.0344027i	0.634783	−	0.772690i	$-0.281089\pi$
$431$	−0.824252	−	0.714218i	−0.0397028	−	0.0344027i	−0.674486	+	0.738287i	$0.735635\pi$
$432$	4.60636	+	1.00205i	0.221624	+	0.0482113i
$433$	−1.46639	+	20.5028i	−0.0704702	+	0.985302i	0.832063	+	0.554682i	$0.187160\pi$
$433$	−1.46639	+	20.5028i	−0.0704702	+	0.985302i	−0.902533	+	0.430621i	$0.858295\pi$
$434$	21.4558	+	6.30001i	1.02991	+	0.302410i
$435$	4.56518	−	0.899420i	0.218884	−	0.0431239i
$436$			10.3261i			0.494532i
$437$	−5.80752	+	17.9596i	−0.277811	+	0.859125i
$438$	28.7033	−	28.7033i	1.37149	−	1.37149i
$439$	−16.3568	−	7.46989i	−0.780666	−	0.356518i	−0.0151087	−	0.999886i	$-0.504809\pi$
$439$	−16.3568	−	7.46989i	−0.780666	−	0.356518i	−0.765557	+	0.643368i	$0.777537\pi$
$440$	1.01744	+	2.90092i	0.0485047	+	0.138296i
$441$	0.0117068	+	0.0135104i	0.000557469	+	0.000643354i
$442$	−2.19089	+	10.0714i	−0.104210	+	0.479046i
$443$	1.98757	+	27.7898i	0.0944322	+	1.32033i	0.794939	+	0.606689i	$0.207503\pi$
$443$	1.98757	+	27.7898i	0.0944322	+	1.32033i	−0.700507	+	0.713646i	$0.747043\pi$
$444$	−2.37455	+	16.5154i	−0.112691	+	0.783785i
$445$	−27.1790	+	3.36347i	−1.28841	+	0.159444i
$446$	13.3587	+	8.58515i	0.632555	+	0.406518i
$447$	35.0219	+	26.2170i	1.65648	+	1.24002i
$448$	−0.924847	+	2.47961i	−0.0436949	+	0.117151i
$449$	−6.54884	+	2.99076i	−0.309059	+	0.141142i	−0.563906	−	0.825839i	$-0.690702\pi$
$449$	−6.54884	+	2.99076i	−0.309059	+	0.141142i	0.254847	+	0.966981i	$0.417975\pi$
$450$	13.3291	+	19.3478i	0.628341	+	0.912066i
$451$	−6.82199	+	10.6152i	−0.321235	+	0.499851i
$452$	−6.69159	+	12.2547i	−0.314746	+	0.576414i
$453$	−4.73822	−	6.32952i	−0.222621	−	0.297387i
$454$	−14.4989	+	16.7326i	−0.680465	+	0.785299i
$455$	−14.0132	−	32.3543i	−0.656948	−	1.51679i
$456$	8.25321	−	7.15145i	0.386492	−	0.334897i
$457$	−30.8748	+	16.8589i	−1.44426	+	0.788627i	−0.994521	−	0.104533i	$-0.966665\pi$
$457$	−30.8748	+	16.8589i	−1.44426	+	0.788627i	−0.449740	+	0.893159i	$0.648483\pi$
$458$	−10.5996	+	3.95346i	−0.495288	+	0.184733i
$459$	8.15480			0.380634
$460$	10.6745	−	1.02761i	0.497699	−	0.0479128i
$461$	−13.1694			−0.613361			−0.306681	−	0.951813i	$-0.599218\pi$
$461$	−13.1694			−0.613361			−0.306681	+	0.951813i	$0.599218\pi$
$462$	−9.45894	+	3.52800i	−0.440070	+	0.164138i
$463$	−6.77715	+	3.70060i	−0.314961	+	0.171982i	−0.628952	−	0.777444i	$-0.716516\pi$
$463$	−6.77715	+	3.70060i	−0.314961	+	0.171982i	0.313991	+	0.949426i	$0.398334\pi$
$464$	−0.566767	+	0.491106i	−0.0263115	+	0.0227990i
$465$	−19.2834	+	48.7496i	−0.894245	+	2.26071i
$466$	−3.16091	+	3.64789i	−0.146427	+	0.168985i
$467$	22.0057	+	29.3961i	1.01830	+	1.36029i	0.931369	+	0.364077i	$0.118615\pi$
$467$	22.0057	+	29.3961i	1.01830	+	1.36029i	0.0869321	+	0.996214i	$0.472294\pi$
$468$	13.4176	−	24.5725i	0.620230	−	1.13587i
$469$	4.74472	−	7.38293i	0.219091	−	0.340912i
$470$	8.81778	+	0.173499i	0.406734	+	0.00800290i
$471$	50.2325	−	22.9404i	2.31459	−	1.05704i
$472$	−2.94362	+	7.89214i	−0.135491	+	0.363265i
$473$	−11.9462	−	8.94285i	−0.549289	−	0.411193i
$474$	−11.3579	−	7.29927i	−0.521685	−	0.335266i
$475$	19.6636	+	0.774101i	0.902227	+	0.0355182i
$476$	−0.651527	+	4.53147i	−0.0298627	+	0.207700i
$477$	−0.459763	−	6.42833i	−0.0210511	−	0.294333i
$478$	−1.57542	+	7.24207i	−0.0720579	+	0.331245i
$479$	0.844566	+	0.974681i	0.0385892	+	0.0445343i	0.774716	−	0.632309i	$-0.217893\pi$
$479$	0.844566	+	0.974681i	0.0385892	+	0.0445343i	−0.736127	+	0.676844i	$0.763347\pi$
$480$	−5.59194	−	2.68793i	−0.255236	−	0.122687i
$481$	32.5908	+	14.8837i	1.48601	+	0.678639i
$482$	4.53033	−	4.53033i	0.206351	−	0.206351i
$483$	4.06359	+	34.9813i	0.184900	+	1.59171i
$484$			9.10989i			0.414086i
$485$	−2.68603	−	13.6335i	−0.121967	−	0.619065i
$486$	16.2761	+	4.77910i	0.738300	+	0.216785i
$487$	1.67381	−	23.4030i	0.0758477	−	1.06049i	−0.806914	−	0.590669i	$-0.798864\pi$
$487$	1.67381	−	23.4030i	0.0758477	−	1.06049i	0.882762	−	0.469821i	$-0.155682\pi$
$488$	−0.489650	−	0.106517i	−0.0221654	−	0.00482179i
$489$	0.132141	+	0.114501i	0.00597563	+	0.00517792i
$490$	−0.00392929	−	0.00754514i	−0.000177507	−	0.000340855i
$491$	−21.4094	+	6.28635i	−0.966191	+	0.283699i	−0.726512	−	0.687153i	$-0.758860\pi$
$491$	−21.4094	+	6.28635i	−0.966191	+	0.283699i	−0.239678	+	0.970852i	$0.577042\pi$
$492$	−5.41336	−	24.8848i	−0.244053	−	1.12189i
$493$	−0.777446	+	1.03855i	−0.0350144	+	0.0467738i
$494$	−9.74146	−	21.3308i	−0.438289	−	0.959719i
$495$	−3.79629	−	13.9376i	−0.170631	−	0.626450i
$496$	−1.20251	−	8.36361i	−0.0539941	−	0.375537i
$497$	34.9382	−	7.60033i	1.56719	−	0.340921i
$498$	0.578918	+	0.316113i	0.0259419	+	0.0141654i
$499$	−8.79665	−	1.26477i	−0.393792	−	0.0566187i	−0.0574253	−	0.998350i	$-0.518289\pi$
$499$	−8.79665	−	1.26477i	−0.393792	−	0.0566187i	−0.336367	+	0.941731i	$0.609198\pi$
$500$	−4.03651	−	10.4262i	−0.180518	−	0.466276i
$501$	−3.96786	+	2.54999i	−0.177271	+	0.113925i
$502$	−17.6483	−	1.26223i	−0.787683	−	0.0563362i
$503$	11.8162	+	21.6397i	0.526856	+	0.964865i	0.996626	+	0.0820762i	$0.0261551\pi$
$503$	11.8162	+	21.6397i	0.526856	+	0.964865i	−0.469770	+	0.882789i	$0.655663\pi$
$504$	5.16595	−	11.3119i	0.230110	−	0.503870i
$505$	−26.5629	−	4.35414i	−1.18203	−	0.193757i
$506$	−6.40226	−	1.57592i	−0.284615	−	0.0700583i
$507$	−44.1448	−	44.1448i	−1.96054	−	1.96054i
$508$	5.48421	+	14.7037i	0.243322	+	0.652372i
$509$	5.02208	−	17.1036i	0.222600	−	0.758104i	−0.770146	−	0.637868i	$-0.779817\pi$
$509$	5.02208	−	17.1036i	0.222600	−	0.758104i	0.992745	−	0.120236i	$-0.0383653\pi$
$510$	−10.4407	−	2.48731i	−0.462322	−	0.110140i
$511$	−20.9318	−	32.5705i	−0.925967	−	1.44083i
$512$	0.997452	−	0.0713392i	0.0440816	−	0.00315278i
$513$	−14.8529	+	11.1187i	−0.655771	+	0.490904i
$514$	−3.53764	−	12.0481i	−0.156039	−	0.531419i
$515$	0.347087	+	6.70408i	0.0152945	+	0.295417i
$516$	29.8110	−	4.28618i	1.31236	−	0.188689i
$517$	−5.08063	−	1.89498i	−0.223446	−	0.0833410i
$518$	14.9107	+	5.56142i	0.655140	+	0.244355i
$519$	−25.7453	+	3.70161i	−1.13009	+	0.162483i
$520$	−8.92102	+	9.89518i	−0.391212	+	0.433932i
$521$	−2.58096	−	8.78993i	−0.113074	−	0.385094i	0.883438	−	0.468548i	$-0.155223\pi$
$521$	−2.58096	−	8.78993i	−0.113074	−	0.385094i	−0.996512	+	0.0834546i	$0.973405\pi$
$522$	2.82106	−	2.11182i	0.123474	−	0.0924317i
$523$	1.30052	−	0.0930148i	0.0568676	−	0.00406725i	−0.0428764	−	0.999080i	$-0.513652\pi$
$523$	1.30052	−	0.0930148i	0.0568676	−	0.00406725i	0.0997440	+	0.995013i	$0.468198\pi$
$524$	2.64031	+	4.10840i	0.115342	+	0.179476i
$525$	33.9720	−	13.9267i	1.48266	−	0.607812i
$526$	7.31344	−	24.9073i	0.318881	−	1.08601i
$527$	−5.10805	−	13.6952i	−0.222510	−	0.596573i
$528$	2.69739	+	2.69739i	0.117389	+	0.117389i
$529$	−10.6761	+	20.3721i	−0.464177	+	0.885742i
$530$	−0.496088	+	3.02644i	−0.0215487	+	0.131460i
$531$	16.4423	−	36.0036i	0.713535	−	1.56242i
$532$	−4.99180	−	9.14180i	−0.216422	−	0.396347i
$533$	−54.5461	−	3.90122i	−2.36266	−	0.168980i
$534$	−28.5886	+	18.3728i	−1.23715	+	0.795067i
$535$	2.82423	−	30.9247i	0.122102	−	1.33699i
$536$	−3.28240	−	0.471938i	−0.141778	−	0.0203846i
$537$	5.44786	+	2.97476i	0.235092	+	0.128370i
$538$	−9.96895	+	2.16861i	−0.429792	+	0.0934955i
$539$	0.000744360		0.00517714i	3.20619e−5		0.000222995i
$540$	9.15047	+	5.23280i	0.393773	+	0.225184i
$541$	4.91854	+	10.7701i	0.211464	+	0.463042i	0.985407	−	0.170213i	$-0.0544456\pi$
$541$	4.91854	+	10.7701i	0.211464	+	0.463042i	−0.773943	+	0.633255i	$0.781718\pi$
$542$	1.57481	−	2.10370i	0.0676440	−	0.0903618i
$543$	7.32548	+	33.6747i	0.314366	+	1.44512i
$544$	1.65981	−	0.487363i	0.0711636	−	0.0208955i
$545$	−6.93975	+	22.0224i	−0.297266	+	0.943334i
$546$	−33.0654	−	28.6513i	−1.41507	−	1.22616i
$547$	−29.7265	−	6.46661i	−1.27101	−	0.276492i	−0.474038	−	0.880504i	$-0.657204\pi$
$547$	−29.7265	−	6.46661i	−1.27101	−	0.276492i	−0.796975	+	0.604012i	$0.793568\pi$
$548$	−0.540603	+	7.55861i	−0.0230934	+	0.322888i
$549$	2.25927	+	0.663383i	0.0964235	+	0.0283125i
$550$	0.220296	+	6.87053i	0.00939344	+	0.292960i
$551$		−	2.95159i		−	0.125742i
$552$	11.3858	−	6.88772i	0.484610	−	0.293161i
$553$	−9.10555	+	9.10555i	−0.387208	+	0.387208i
$554$	2.63080	+	1.20144i	0.111772	+	0.0510445i
$555$	−16.1635	+	33.6262i	−0.686101	+	1.42735i
$556$	9.93034	+	11.4602i	0.421140	+	0.486022i
$557$	1.83775	−	8.44802i	0.0778681	−	0.357954i	−0.921682	−	0.387946i	$-0.873185\pi$
$557$	1.83775	−	8.44802i	0.0778681	−	0.357954i	0.999550	+	0.0299923i	$0.00954826\pi$
$558$	2.83248	+	39.6032i	0.119908	+	1.67654i
$559$	9.20381	−	64.0139i	0.389280	−	2.70750i
$560$	−3.63885	+	4.66667i	−0.153769	+	0.197203i
$561$	5.55139	+	3.56766i	0.234380	+	0.150627i
$562$	−16.4043	−	12.2801i	−0.691973	−	0.518004i
$563$	1.57398	−	4.21999i	0.0663352	−	0.177851i	−0.899553	−	0.436812i	$-0.856107\pi$
$563$	1.57398	−	4.21999i	0.0663352	−	0.177851i	0.965888	+	0.258961i	$0.0833801\pi$
$564$	9.95497	−	4.54628i	0.419180	−	0.191433i
$565$	−22.5069	+	21.6383i	−0.946874	+	0.910332i
$566$	2.28089	−	3.54914i	0.0958730	−	0.149181i
$567$	1.28948	−	2.36150i	0.0541529	−	0.0991737i
$568$	−8.09657	−	10.8158i	−0.339725	−	0.453819i
$569$	−3.67330	+	4.23922i	−0.153993	+	0.177717i	−0.827504	−	0.561460i	$-0.810240\pi$
$569$	−3.67330	+	4.23922i	−0.153993	+	0.177717i	0.673511	+	0.739177i	$0.264785\pi$
$570$	22.4077	−	9.70514i	0.938554	−	0.406503i
$571$	3.34028	−	2.89437i	0.139786	−	0.121125i	−0.582161	−	0.813073i	$-0.697793\pi$
$571$	3.34028	−	2.89437i	0.139786	−	0.121125i	0.721947	+	0.691948i	$0.243247\pi$
$572$	7.18939	−	3.92570i	0.300603	−	0.164142i
$573$	31.6731	−	11.8134i	1.32316	−	0.493514i
$574$	−24.2899			−1.01384
$575$	23.4559	+	4.98227i	0.978177	+	0.207775i
$576$	−4.69896			−0.195790
$577$	−30.5917	+	11.4101i	−1.27355	+	0.475009i	−0.893127	−	0.449804i	$-0.851494\pi$
$577$	−30.5917	+	11.4101i	−1.27355	+	0.475009i	−0.380422	+	0.924813i	$0.624221\pi$
$578$	−12.2941	+	6.71309i	−0.511367	+	0.279228i
$579$	6.94292	−	6.01608i	0.288538	−	0.250020i
$580$	−1.53879	+	0.666474i	−0.0638946	+	0.0276738i
$581$	0.411985	−	0.475456i	0.0170920	−	0.0197252i
$582$	−10.3332	−	13.8036i	−0.428325	−	0.572176i
$583$	0.903668	−	1.65494i	0.0374261	−	0.0685408i
$584$	−7.90932	+	12.3071i	−0.327290	+	0.509273i
$585$	45.1297	−	43.3880i	1.86588	−	1.79387i
$586$	−6.79454	+	3.10296i	−0.280680	+	0.128182i
$587$	−11.1852	+	29.9887i	−0.461662	+	1.23776i	0.472631	+	0.881260i	$0.343304\pi$
$587$	−11.1852	+	29.9887i	−0.461662	+	1.23776i	−0.934294	+	0.356504i	$0.883968\pi$
$588$	−0.00845064	−	0.00632607i	−0.000348498	−	0.000260883i
$589$	27.9765	+	17.9794i	1.15275	+	0.740827i
$590$	−11.5818	+	14.8532i	−0.476814	+	0.611495i
$591$	7.06380	−	49.1298i	0.290566	−	2.02093i
$592$	−0.428987	−	5.99802i	−0.0176313	−	0.246517i
$593$	−0.274726	+	1.26290i	−0.0112817	+	0.0518610i	−0.982444	−	0.186560i	$-0.940266\pi$
$593$	−0.274726	+	1.26290i	−0.0112817	+	0.0518610i	0.971162	+	0.238421i	$0.0766298\pi$
$594$	−4.24414	−	4.89800i	−0.174139	−	0.200968i
$595$	−4.43491	+	9.22633i	−0.181814	+	0.378243i
$596$	−14.3419	−	6.54971i	−0.587466	−	0.268287i
$597$	−43.6364	+	43.6364i	−1.78592	+	1.78592i
$598$	−7.30300	−	27.6254i	−0.298642	−	1.12969i
$599$		−	28.2374i		−	1.15375i	−0.816832	−	0.576875i	$-0.804272\pi$
$599$		−	28.2374i		−	1.15375i	0.816832	−	0.576875i	$-0.195728\pi$
$600$	−10.1194	−	9.49062i	−0.413122	−	0.387453i
$601$	25.7171	+	7.55122i	1.04902	+	0.308021i	0.760422	−	0.649429i	$-0.224992\pi$
$601$	25.7171	+	7.55122i	1.04902	+	0.308021i	0.288600	+	0.957450i	$0.406810\pi$
$602$	2.04927	−	28.6526i	0.0835221	−	1.16779i
$603$	15.2264	+	3.31229i	0.620065	+	0.134887i
$604$	2.15352	+	1.86604i	0.0876255	+	0.0759279i
$605$	−6.12237	+	19.4285i	−0.248910	+	0.789882i
$606$	−32.0484	+	9.41025i	−1.30188	+	0.382265i
$607$	5.74499	+	26.4093i	0.233182	+	1.07192i	0.933636	+	0.358222i	$0.116617\pi$
$607$	5.74499	+	26.4093i	0.233182	+	1.07192i	−0.700454	+	0.713697i	$0.747019\pi$
$608$	−2.35861	+	3.15074i	−0.0956545	+	0.127779i
$609$	−2.28766	−	5.00928i	−0.0927007	−	0.202986i
$610$	−0.972683	−	0.556240i	−0.0393828	−	0.0225215i
$611$	−3.34443	−	23.2610i	−0.135301	−	0.941039i
$612$	−7.94286	+	1.72786i	−0.321071	+	0.0698447i
$613$	−33.1121	−	18.0806i	−1.33739	−	0.730269i	−0.358280	−	0.933614i	$-0.616637\pi$
$613$	−33.1121	−	18.0806i	−1.33739	−	0.730269i	−0.979107	+	0.203346i	$0.934819\pi$
$614$	21.1596	+	3.04229i	0.853931	+	0.122777i
$615$	5.17905	−	56.7095i	0.208840	−	2.28675i
$616$	3.06082	−	1.96707i	0.123324	−	0.0792554i
$617$	19.5082	+	1.39525i	0.785369	+	0.0561707i	0.458263	−	0.888817i	$-0.348472\pi$
$617$	19.5082	+	1.39525i	0.785369	+	0.0561707i	0.327106	+	0.944988i	$0.393926\pi$
$618$	3.99220	+	7.31117i	0.160590	+	0.294098i
$619$	−3.87216	+	8.47884i	−0.155635	+	0.340793i	−0.971347	−	0.237665i	$-0.923618\pi$
$619$	−3.87216	+	8.47884i	−0.155635	+	0.340793i	0.815712	+	0.578458i	$0.196345\pi$
$620$	3.05627	−	18.6451i	0.122743	−	0.748805i
$621$	−20.1294	+	10.2921i	−0.807765	+	0.413009i
$622$	19.8845	+	19.8845i	0.797297	+	0.797297i
$623$	11.3271	+	30.3692i	0.453811	+	1.21671i
$624$	−4.65764	+	15.8625i	−0.186455	+	0.635007i
$625$	−1.60155	−	24.9486i	−0.0640619	−	0.997946i
$626$	10.6548	+	16.5793i	0.425853	+	0.662641i
$627$	−14.9755	+	1.07107i	−0.598062	+	0.0427743i
$628$	−15.9326	+	11.9270i	−0.635780	+	0.475939i
$629$	−2.93068	−	9.98098i	−0.116854	−	0.397968i
$630$	18.6196	−	20.6528i	0.741821	−	0.822827i
$631$	6.50840	−	0.935767i	0.259095	−	0.0372523i	−0.0115430	−	0.999933i	$-0.503674\pi$
$631$	6.50840	−	0.935767i	0.259095	−	0.0372523i	0.270638	+	0.962681i	$0.412765\pi$
$632$	4.55901	+	1.70042i	0.181348	+	0.0676392i
$633$	21.4373	+	7.99568i	0.852054	+	0.317800i
$634$	−10.6443	+	1.53042i	−0.422739	+	0.0607807i
$635$	1.81432	+	35.0441i	0.0719992	+	1.39068i
$636$	1.07215	+	3.65142i	0.0425137	+	0.144788i
$637$	−0.0181462	+	0.0135841i	−0.000718980	+	0.000538222i
$638$	1.02840	−	0.0735526i	0.0407147	−	0.00291197i
$639$	34.3228	+	53.4074i	1.35779	+	2.11276i
$640$	2.17519	+	0.518202i	0.0859821	+	0.0204837i
$641$	7.31588	−	24.9156i	0.288960	−	0.984107i	−0.679237	−	0.733919i	$-0.737689\pi$
$641$	7.31588	−	24.9156i	0.288960	−	0.984107i	0.968197	−	0.250188i	$-0.0804926\pi$
$642$	−13.4661	−	36.1041i	−0.531466	−	1.42491i
$643$	5.77968	+	5.77968i	0.227928	+	0.227928i	0.811827	−	0.583898i	$-0.198473\pi$
$643$	5.77968	+	5.77968i	0.227928	+	0.227928i	−0.583898	+	0.811827i	$0.698473\pi$
$644$	−4.11091	−	12.0078i	−0.161993	−	0.473175i
$645$	66.4581	+	10.8937i	2.61678	+	0.428938i
$646$	−2.82831	+	6.19313i	−0.111278	+	0.243665i
$647$	−3.50627	−	6.42125i	−0.137846	−	0.252445i	0.799632	−	0.600490i	$-0.205028\pi$
$647$	−3.50627	−	6.42125i	−0.137846	−	0.252445i	−0.937478	+	0.348044i	$0.886846\pi$
$648$	−1.01409	−	0.0725293i	−0.0398373	−	0.00284922i
$649$	9.74202	−	6.26081i	0.382408	−	0.245758i
$650$	−25.6758	+	15.1078i	−1.00709	+	0.592578i
$651$	61.4153	+	8.83019i	2.40706	+	0.346082i
$652$	−0.0553070	−	0.0301999i	−0.00216599	−	0.00118272i
$653$	32.0502	−	6.97209i	1.25422	−	0.272839i	0.464095	−	0.885785i	$-0.346380\pi$
$653$	32.0502	−	6.97209i	1.25422	−	0.272839i	0.790124	+	0.612946i	$0.210016\pi$
$654$	4.07759	+	28.3603i	0.159446	+	1.10897i
$655$	2.86986	+	10.5364i	0.112135	+	0.411689i
$656$	3.81277	+	8.34881i	0.148864	+	0.325966i
$657$	41.1964	−	55.0320i	1.60723	−	2.14700i
$658$	−2.21880	−	10.1996i	−0.0864977	−	0.397624i
$659$	−8.88229	+	2.60807i	−0.346005	+	0.101596i	−0.450117	−	0.892969i	$-0.648618\pi$
$659$	−8.88229	+	2.60807i	−0.346005	+	0.101596i	0.104113	+	0.994565i	$0.466800\pi$
$660$	3.93988	+	7.56549i	0.153360	+	0.294486i
$661$	34.6672	+	30.0393i	1.34840	+	1.16839i	0.970099	+	0.242709i	$0.0780360\pi$
$661$	34.6672	+	30.0393i	1.34840	+	1.16839i	0.378298	+	0.925684i	$0.376509\pi$
$662$	3.51833	+	0.765366i	0.136744	+	0.0297468i
$663$	−2.04020	+	28.5257i	−0.0792348	+	1.10785i
$664$	−0.228090	−	0.0669734i	−0.00885163	−	0.00259907i
$665$	−4.50211	−	22.8513i	−0.174584	−	0.886137i
$666$			28.2564i			1.09491i
$667$	0.608312	−	3.54477i	0.0235540	−	0.137254i
$668$	1.20198	−	1.20198i	0.0465061	−	0.0465061i
$669$	40.0793	+	18.3036i	1.54956	+	0.707659i
$670$	−6.68315	−	3.21246i	−0.258193	−	0.124108i
$671$	0.451147	+	0.520651i	0.0174163	+	0.0200995i
$672$	−1.56090	+	7.17534i	−0.0602131	+	0.276795i
$673$	−0.231468	−	3.23635i	−0.00892243	−	0.124752i	0.991039	−	0.133576i	$-0.0426459\pi$
$673$	−0.231468	−	3.23635i	−0.00892243	−	0.124752i	−0.999961	+	0.00882359i	$0.997191\pi$
$674$	3.21069	−	22.3309i	0.123671	−	0.860153i
$675$	15.9983	+	17.3095i	0.615775	+	0.666245i
$676$	18.9281	+	12.1643i	0.728002	+	0.467859i
$677$	−24.8613	−	18.6109i	−0.955496	−	0.715275i	0.00311468	−	0.999995i	$-0.499009\pi$
$677$	−24.8613	−	18.6109i	−0.955496	−	0.715275i	−0.958611	+	0.284720i	$0.908099\pi$
$678$	−13.5390	+	36.2995i	−0.519962	+	1.39407i
$679$	−14.9597	+	6.83188i	−0.574102	+	0.262184i
$680$	3.86738	+	0.0760945i	0.148307	+	0.00291809i
$681$	−33.2131	+	51.6806i	−1.27273	+	1.98041i
$682$	−5.56726	+	10.1957i	−0.213181	+	0.390412i
$683$	6.31157	+	8.43127i	0.241505	+	0.322614i	0.904874	−	0.425679i	$-0.139965\pi$
$683$	6.31157	+	8.43127i	0.241505	+	0.322614i	−0.663369	+	0.748293i	$0.730874\pi$
$684$	12.1110	−	13.9768i	0.463075	−	0.534417i
$685$	−6.23276	+	15.7568i	−0.238141	+	0.602037i
$686$	13.9929	−	12.1249i	0.534250	−	0.462931i
$687$	−27.5503	+	15.0436i	−1.05111	+	0.573949i
$688$	−10.1700	+	3.79321i	−0.387727	+	0.144615i
$689$	8.17180			0.311321
$690$	28.9111	−	7.03744i	1.10063	−	0.267911i
$691$	10.0464			0.382184			0.191092	−	0.981572i	$-0.438797\pi$
$691$	10.0464			0.382184			0.191092	+	0.981572i	$0.438797\pi$
$692$	8.78296	−	3.27587i	0.333878	−	0.124530i
$693$	−15.0054	+	8.19356i	−0.570008	+	0.311248i
$694$	6.05095	−	5.24318i	0.229691	−	0.199028i
$695$	13.4763	+	31.1148i	0.511187	+	1.18025i
$696$	−1.36267	+	1.57261i	−0.0516520	+	0.0596095i
$697$	9.51486	+	12.7104i	0.360401	+	0.481439i
$698$	8.64183	−	15.8263i	0.327098	−	0.599035i
$699$	−7.24083	+	11.2670i	−0.273873	+	0.426155i
$700$	−10.8968	+	7.50702i	−0.411860	+	0.283739i
$701$	−12.4545	+	5.68778i	−0.470400	+	0.214824i	−0.636488	−	0.771287i	$-0.719614\pi$
$701$	−12.4545	+	5.68778i	−0.470400	+	0.214824i	0.166088	+	0.986111i	$0.446886\pi$
$702$	9.81553	−	26.3165i	0.370463	−	0.993251i
$703$	18.9465	+	14.1832i	0.714580	+	0.534928i
$704$	−1.15657	−	0.743279i	−0.0435897	−	0.0280134i
$705$	24.2862	−	3.00547i	0.914670	−	0.113192i
$706$	0.841611	−	5.85353i	0.0316745	−	0.220301i
$707$	2.27271	+	31.7766i	0.0854739	+	1.19508i
$708$	−4.96806	+	22.8378i	−0.186711	+	0.858298i
$709$	17.4233	+	20.1075i	0.654344	+	0.755154i	0.981842	−	0.189698i	$-0.0607510\pi$
$709$	17.4233	+	20.1075i	0.654344	+	0.755154i	−0.327498	+	0.944852i	$0.606206\pi$
$710$	−9.99861	−	28.5079i	−0.375241	−	1.06988i
$711$	−20.7980	−	9.49813i	−0.779986	−	0.356208i
$712$	8.66033	−	8.66033i	0.324560	−	0.324560i
$713$	29.8934	+	27.3586i	1.11952	+	1.02459i
$714$			12.7028i			0.475389i
$715$	17.9710	−	3.54060i	0.672077	−	0.132411i
$716$	−2.14643	−	0.630248i	−0.0802157	−	0.0235535i
$717$	−1.46706	+	20.5121i	−0.0547882	+	0.766040i
$718$	24.3597	+	5.29914i	0.909098	+	0.197762i
$719$	−18.6160	−	16.1309i	−0.694260	−	0.601580i	0.234564	−	0.972101i	$-0.424634\pi$
$719$	−18.6160	−	16.1309i	−0.694260	−	0.601580i	−0.928824	+	0.370521i	$0.879179\pi$
$720$	−10.0214	−	3.15797i	−0.373475	−	0.117691i
$721$	7.62332	−	2.23841i	0.283907	−	0.0833627i
$722$	0.746055	+	3.42956i	0.0277653	+	0.127635i
$723$	10.6534	−	14.2313i	0.396205	−	0.529267i
$724$	−5.15953	−	11.2978i	−0.191752	−	0.419879i
$725$	−3.72965	+	0.387225i	−0.138516	+	0.0143812i
$726$	3.59732	+	25.0199i	0.133509	+	0.928577i
$727$	−7.83078	+	1.70348i	−0.290428	+	0.0631786i	−0.355419	−	0.934707i	$-0.615662\pi$
$727$	−7.83078	+	1.70348i	−0.290428	+	0.0631786i	0.0649912	+	0.997886i	$0.479298\pi$
$728$	13.8394	+	7.55686i	0.512921	+	0.280076i
$729$	43.5699	+	6.26440i	1.61370	+	0.232015i
$730$	−25.1392	+	20.9317i	−0.930443	+	0.774718i
$731$	−15.7960	+	10.1515i	−0.584236	+	0.375466i
$732$	−1.38686	−	0.0991904i	−0.0512600	−	0.00366618i
$733$	−7.40959	−	13.5697i	−0.273679	−	0.501207i	0.704301	−	0.709901i	$-0.251260\pi$
$733$	−7.40959	−	13.5697i	−0.273679	−	0.501207i	−0.977981	+	0.208695i	$0.933079\pi$
$734$	−8.02632	+	17.5752i	−0.296257	+	0.648712i
$735$	−0.0137710	−	0.0191708i	−0.000507953	−	0.000707126i
$736$	−3.48199	+	3.29784i	−0.128348	+	0.121560i
$737$	3.22376	+	3.22376i	0.118749	+	0.118749i
$738$	−15.0717	−	40.4089i	−0.554798	−	1.48747i
$739$	7.79624	−	26.5515i	0.286789	−	0.976714i	−0.682520	−	0.730867i	$-0.739116\pi$
$739$	7.79624	−	26.5515i	0.286789	−	0.976714i	0.969309	−	0.245847i	$-0.0790660\pi$
$740$	3.11612	−	13.0802i	0.114551	−	0.480837i
$741$	−35.1776	−	54.7375i	−1.29228	−	2.01083i
$742$	3.62046	−	0.258940i	0.132911	−	0.00950600i
$743$	7.72104	−	5.77990i	0.283258	−	0.212044i	−0.448196	−	0.893935i	$-0.647933\pi$
$743$	7.72104	−	5.77990i	0.283258	−	0.212044i	0.731453	+	0.681891i	$0.238842\pi$
$744$	−6.60526	−	22.4954i	−0.242161	−	0.824723i
$745$	−26.1849	−	23.6070i	−0.959339	−	0.864894i
$746$	−28.4773	+	4.09442i	−1.04263	+	0.149907i
$747$	1.04661	+	0.390364i	0.0382933	+	0.0142827i
$748$	−2.22831	−	0.831116i	−0.0814750	−	0.0303886i
$749$	−36.3788	+	5.23048i	−1.32925	+	0.191117i
$750$	−15.2032	−	27.0413i	−0.555143	−	0.987409i
$751$	0.475411	+	1.61910i	0.0173480	+	0.0590818i	0.967712	−	0.252058i	$-0.0811074\pi$
$751$	0.475411	+	1.61910i	0.0173480	+	0.0590818i	−0.950364	+	0.311140i	$0.899289\pi$
$752$	−3.15749	+	2.36367i	−0.115142	+	0.0861941i
$753$	−48.9688	+	3.50232i	−1.78452	+	0.127631i
$754$	2.41573	+	3.75895i	0.0879757	+	0.136893i
$755$	3.33869	+	5.42695i	0.121507	+	0.197507i
$756$	3.51481	−	11.9703i	0.127832	−	0.435357i
$757$	−13.4679	−	36.1088i	−0.489499	−	1.31240i	−0.913538	−	0.406754i	$-0.866661\pi$
$757$	−13.4679	−	36.1088i	−0.489499	−	1.31240i	0.424039	−	0.905644i	$-0.360612\pi$
$758$	−8.36242	−	8.36242i	−0.303737	−	0.303737i
$759$	−18.2058	−	1.80008i	−0.660830	−	0.0653386i
$760$	−7.14766	+	5.13441i	−0.259273	+	0.186245i
$761$	9.29182	−	20.3462i	0.336828	−	0.737551i	−0.663112	−	0.748520i	$-0.730765\pi$
$761$	9.29182	−	20.3462i	0.336828	−	0.737551i	0.999940	+	0.0109698i	$0.00349187\pi$
$762$	20.8684	+	38.2175i	0.755981	+	1.38448i
$763$	27.2582	+	1.94954i	0.986812	+	0.0705782i
$764$	−10.2491	+	6.58668i	−0.370799	+	0.238298i
$765$	−18.1008	−	1.65307i	−0.654437	−	0.0597670i
$766$	14.9223	+	2.14551i	0.539166	+	0.0775204i
$767$	44.0481	+	24.0521i	1.59049	+	0.868471i
$768$	2.71129	−	0.589805i	0.0978352	−	0.0212827i
$769$	−4.94990	−	34.4273i	−0.178498	−	1.24148i	−0.860240	−	0.509889i	$-0.829686\pi$
$769$	−4.94990	−	34.4273i	−0.178498	−	1.24148i	0.681742	−	0.731593i	$-0.261223\pi$
$770$	7.84973	−	2.13809i	0.282885	−	0.0770513i
$771$	−14.4735	−	31.6926i	−0.521252	−	1.14138i
$772$	−1.98416	+	2.65053i	−0.0714115	+	0.0953945i
$773$	−9.81004	−	45.0960i	−0.352843	−	1.62199i	−0.721492	−	0.692423i	$-0.756543\pi$
$773$	−9.81004	−	45.0960i	−0.352843	−	1.62199i	0.368649	−	0.929569i	$-0.379820\pi$
$774$	48.9382	−	14.3695i	1.75905	−	0.516502i
$775$	19.0486	−	37.7101i	0.684247	−	1.35459i
$776$	4.69644	+	4.06949i	0.168592	+	0.146086i
$777$	43.1478	+	9.38623i	1.54792	+	0.336729i
$778$	−0.574206	+	8.02845i	−0.0205863	+	0.287834i
$779$	−34.6601	−	10.1771i	−1.24183	−	0.364633i
$780$	−20.5938	+	30.6994i	−0.737375	+	1.09922i
$781$			18.5745i			0.664647i
$782$	−4.67310	+	6.85486i	−0.167110	+	0.245129i
$783$	2.49982	−	2.49982i	0.0893364	−	0.0893364i
$784$	0.00346063	+	0.00158042i	0.000123594	+	5.64435e-5i
$785$	−41.9948	+	14.7289i	−1.49886	+	0.525696i
$786$	8.87382	+	10.2409i	0.316519	+	0.365282i
$787$	5.83546	−	26.8252i	0.208012	−	0.956214i	−0.748185	−	0.663490i	$-0.769075\pi$
$787$	5.83546	−	26.8252i	0.208012	−	0.956214i	0.956197	−	0.292724i	$-0.0945617\pi$
$788$	1.27615	+	17.8429i	0.0454608	+	0.635626i
$789$	10.2506	−	71.2948i	0.364932	−	2.53816i
$790$	8.58015	+	6.69038i	0.305268	+	0.238033i
$791$	31.0858	+	19.9776i	1.10528	+	0.710323i
$792$	5.17164	+	3.87144i	0.183766	+	0.137566i
$793$	−1.04338	+	2.79740i	−0.0370514	+	0.0993387i
$794$	−18.7814	+	8.57717i	−0.666526	+	0.304392i
$795$	−0.167401	+	8.50788i	−0.00593711	+	0.301743i
$796$	12.0242	−	18.7100i	0.426187	−	0.663160i
$797$	−2.83557	+	5.19296i	−0.100441	+	0.183944i	−0.923067	−	0.384638i	$-0.874326\pi$
$797$	−2.83557	+	5.19296i	−0.100441	+	0.183944i	0.822626	+	0.568582i	$0.192508\pi$
$798$	−17.3197	−	23.1364i	−0.613110	−	0.819019i
$799$	−4.46810	+	5.15646i	−0.158070	+	0.182422i
$800$	4.29074	+	2.56702i	0.151700	+	0.0907577i
$801$	−43.4939	+	37.6877i	−1.53678	+	1.33163i
$802$	17.2337	−	9.41034i	0.608545	−	0.332291i
$803$	18.8447	−	7.02872i	0.665016	−	0.248038i
$804$	−9.20133			−0.324506
$805$	−0.697316	−	28.3717i	−0.0245772	−	0.999970i
$806$	−50.3443			−1.77330
$807$	−26.5230	+	9.89255i	−0.933652	+	0.348234i
$808$	10.5653	−	5.76912i	0.371688	−	0.202957i
$809$	3.48741	−	3.02186i	0.122611	−	0.106243i	−0.591397	−	0.806380i	$-0.701423\pi$
$809$	3.48741	−	3.02186i	0.122611	−	0.106243i	0.714008	+	0.700138i	$0.246878\pi$
$810$	−2.11399	−	0.836210i	−0.0742781	−	0.0293814i
$811$	−18.6058	+	21.4722i	−0.653337	+	0.753991i	−0.981674	−	0.190570i	$-0.938966\pi$
$811$	−18.6058	+	21.4722i	−0.653337	+	0.753991i	0.328337	+	0.944561i	$0.393512\pi$
$812$	1.18938	+	1.58883i	0.0417392	+	0.0557570i
$813$	3.49444	−	6.39959i	0.122555	−	0.224444i
$814$	−4.46959	+	6.95482i	−0.156659	+	0.243766i
$815$	−0.0976563	−	0.101576i	−0.00342075	−	0.00355807i
$816$	4.36613	−	1.99395i	0.152845	−	0.0698021i
$817$	14.9292	−	40.0267i	0.522306	−	1.40036i
$818$	12.8185	+	9.59580i	0.448188	+	0.335509i
$819$	−62.3316	−	40.0581i	−2.17804	−	1.39974i
$820$	2.52056	+	20.3678i	0.0880217	+	0.711274i
$821$	4.82637	−	33.5681i	0.168441	−	1.17154i	−0.713666	−	0.700487i	$-0.752966\pi$
$821$	4.82637	−	33.5681i	0.168441	−	1.17154i	0.882107	−	0.471049i	$-0.156125\pi$
$822$	1.50001	+	20.9729i	0.0523188	+	0.731513i
$823$	−0.614569	+	2.82513i	−0.0214225	+	0.0984777i	−0.986617	−	0.163056i	$-0.947865\pi$
$823$	−0.614569	+	2.82513i	−0.0214225	+	0.0984777i	0.965194	+	0.261534i	$0.0842284\pi$
$824$	−1.96600	−	2.26889i	−0.0684890	−	0.0790405i
$825$	3.31807	+	18.7826i	0.115520	+	0.653927i
$826$	20.2774	+	9.26036i	0.705540	+	0.322209i
$827$	−17.3894	+	17.3894i	−0.604688	+	0.604688i	−0.941553	−	0.336865i	$-0.890633\pi$
$827$	−17.3894	+	17.3894i	−0.604688	+	0.604688i	0.336865	+	0.941553i	$0.390633\pi$
$828$	17.4255	−	14.2897i	0.605578	−	0.496602i
$829$			48.0785i			1.66983i	0.550376	+	0.834917i	$0.314484\pi$
$829$			48.0785i			1.66983i	−0.550376	+	0.834917i	$0.685516\pi$
$830$	−0.441435	−	0.296123i	−0.0153224	−	0.0102786i
$831$	7.69979	+	2.26086i	0.267103	+	0.0784285i
$832$	0.425051	−	5.94299i	0.0147360	−	0.206036i
$833$	0.00643080	+	0.00139894i	0.000222814	+	4.84702e-5i
$834$	31.7987	+	27.5537i	1.10110	+	0.954107i
$835$	3.37125	−	1.75565i	0.116667	−	0.0607566i
$836$	5.19175	−	1.52444i	0.179561	−	0.0527237i
$837$	8.46695	+	38.9220i	0.292661	+	1.34534i
$838$	−13.1675	+	17.5897i	−0.454864	+	0.607628i
$839$	−1.77280	−	3.88190i	−0.0612040	−	0.134018i	0.876558	−	0.481295i	$-0.159834\pi$
$839$	−1.77280	−	3.88190i	−0.0612040	−	0.134018i	−0.937762	+	0.347277i	$0.887106\pi$
$840$	−8.15115	+	14.2537i	−0.281241	+	0.491800i
$841$	−4.04709	−	28.1481i	−0.139555	−	0.970625i
$842$	22.7823	−	4.95600i	0.785132	−	0.170795i
$843$	−49.9028	−	27.2490i	−1.71874	−	0.938505i
$844$	−8.16195	−	1.17351i	−0.280946	−	0.0403939i
$845$	32.1924	+	38.6634i	1.10745	+	1.33006i
$846$	15.5914	−	10.0200i	0.536045	−	0.344495i
$847$	24.0476	+	1.71992i	0.826286	+	0.0590972i
$848$	−0.657303	−	1.20376i	−0.0225719	−	0.0413373i
$849$	4.86288	−	10.6482i	0.166894	−	0.365446i
$850$	8.19675	+	2.76139i	0.281146	+	0.0947148i
$851$	19.8311	+	20.9384i	0.679800	+	0.717758i
$852$	−26.5078	−	26.5078i	−0.908143	−	0.908143i
$853$	1.18753	+	3.18390i	0.0406604	+	0.109015i	0.955693	−	0.294365i	$-0.0951081\pi$
$853$	1.18753	+	3.18390i	0.0406604	+	0.109015i	−0.915033	+	0.403380i	$0.867835\pi$
$854$	−0.373620	+	1.27243i	−0.0127850	+	0.0435417i
$855$	35.2221	−	21.6688i	1.20457	−	0.741059i
$856$	7.50815	+	11.6829i	0.256623	+	0.399314i
$857$	11.1531	−	0.797684i	0.380982	−	0.0272484i	0.120465	−	0.992718i	$-0.461561\pi$
$857$	11.1531	−	0.797684i	0.380982	−	0.0272484i	0.260517	+	0.965469i	$0.416107\pi$
$858$	18.1952	−	13.6207i	0.621173	−	0.465004i
$859$	−3.08930	−	10.5212i	−0.105406	−	0.358979i	0.889852	−	0.456248i	$-0.150807\pi$
$859$	−3.08930	−	10.5212i	−0.105406	−	0.358979i	−0.995258	+	0.0972699i	$0.968989\pi$
$860$	−24.2386	+	1.25490i	−0.826531	+	0.0427916i
$861$	−66.7112	+	9.59162i	−2.27351	+	0.326882i
$862$	1.02188	+	0.381140i	0.0348052	+	0.0129817i
$863$	−44.7119	−	16.6767i	−1.52201	−	0.567680i	−0.557143	−	0.830417i	$-0.688102\pi$
$863$	−44.7119	−	16.6767i	−1.52201	−	0.567680i	−0.964868	+	0.262736i	$0.915375\pi$
$864$	−4.66611	+	0.670885i	−0.158744	+	0.0228240i
$865$	20.9328	−	1.08375i	0.711738	−	0.0368485i
$866$	−5.79107	−	19.7226i	−0.196788	−	0.670200i
$867$	−31.1144	+	23.2919i	−1.05670	+	0.791035i
$868$	−22.3047	+	1.59526i	−0.757070	+	0.0541467i
$869$	−3.61665	−	5.62762i	−0.122686	−	0.190904i
$870$	−3.96303	+	2.43808i	−0.134359	+	0.0826586i
$871$	−5.56654	+	18.9579i	−0.188615	+	0.642363i
$872$	−3.60861	−	9.67506i	−0.122203	−	0.327639i
$873$	−20.6480	−	20.6480i	−0.698828	−	0.698828i
$874$	−0.834890	−	18.8568i	−0.0282406	−	0.637840i
$875$	−28.2845	+	8.68683i	−0.956192	+	0.293668i
$876$	−16.8627	+	36.9243i	−0.569739	+	1.24756i
$877$	26.3488	+	48.2542i	0.889736	+	1.62943i	0.771304	+	0.636467i	$0.219605\pi$
$877$	26.3488	+	48.2542i	0.889736	+	1.62943i	0.118432	+	0.992962i	$0.462213\pi$
$878$	17.9359	+	1.28280i	0.605308	+	0.0432925i
$879$	−17.4356	+	11.2052i	−0.588089	+	0.377942i
$880$	−1.96706	−	2.36246i	−0.0663096	−	0.0796384i
$881$	0.244909	+	0.0352126i	0.00825120	+	0.00118634i	0.146439	−	0.989220i	$-0.453219\pi$
$881$	0.244909	+	0.0352126i	0.00825120	+	0.00118634i	−0.138188	+	0.990406i	$0.544128\pi$
$882$	−0.0156901	−	0.00856746i	−0.000528314	−	0.000288482i
$883$	−19.8870	+	4.32616i	−0.669252	+	0.145587i	−0.534339	−	0.845270i	$-0.679439\pi$
$883$	−19.8870	+	4.32616i	−0.669252	+	0.145587i	−0.134914	+	0.990857i	$0.543076\pi$
$884$	−1.46683	−	10.2020i	−0.0493347	−	0.343131i
$885$	−25.9436	+	45.3670i	−0.872086	+	1.52499i
$886$	−11.5738	−	25.3431i	−0.388830	−	0.851418i
$887$	−28.4018	+	37.9404i	−0.953641	+	1.27391i	0.00810398	+	0.999967i	$0.497420\pi$
$887$	−28.4018	+	37.9404i	−0.953641	+	1.27391i	−0.961745	+	0.273948i	$0.911671\pi$
$888$	−3.54670	−	16.3039i	−0.119019	−	0.547123i
$889$	39.8492	−	11.7008i	1.33650	−	0.392432i
$890$	24.2900	−	12.6495i	0.814202	−	0.424012i
$891$	1.05635	+	0.915329i	0.0353889	+	0.0306647i
$892$	−15.5167	−	3.37545i	−0.519537	−	0.113018i
$893$	1.10743	−	15.4839i	0.0370587	−	0.518148i
$894$	−41.9757	−	12.3252i	−1.40388	−	0.412215i
$895$	−4.15409	−	2.78664i	−0.138856	−	0.0931472i
$896$		−	2.64647i		−	0.0884124i
$897$	−30.9661	−	72.9881i	−1.03393	−	2.43700i
$898$	5.09077	−	5.09077i	0.169881	−	0.169881i
$899$	−5.76407	−	2.63236i	−0.192242	−	0.0877942i
$900$	−19.2501	−	13.4699i	−0.641670	−	0.448997i
$901$	−1.55371	−	1.79307i	−0.0517615	−	0.0597359i
$902$	2.68222	−	12.3300i	0.0893082	−	0.410543i
$903$	−5.68611	−	79.5023i	−0.189222	−	2.64567i
$904$	1.98709	−	13.8205i	0.0660898	−	0.459664i
$905$	−3.41087	−	27.5621i	−0.113381	−	0.916196i
$906$	6.65141	+	4.27460i	0.220978	+	0.142014i
$907$	27.7337	+	20.7612i	0.920882	+	0.689364i	0.950674	−	0.310192i	$-0.100393\pi$
$907$	27.7337	+	20.7612i	0.920882	+	0.689364i	−0.0297917	+	0.999556i	$0.509484\pi$
$908$	7.73727	−	20.7444i	0.256770	−	0.688428i
$909$	−51.4535	+	23.4980i	−1.70661	+	0.779381i
$910$	24.4363	+	25.4172i	0.810056	+	0.842573i
$911$	−17.4886	+	27.2128i	−0.579424	+	0.901602i	−0.999984	−	0.00566312i	$-0.998197\pi$
$911$	−17.4886	+	27.2128i	−0.579424	+	0.901602i	0.420560	+	0.907265i	$0.361834\pi$
$912$	−5.23367	+	9.58475i	−0.173304	+	0.317383i
$913$	0.195856	+	0.261633i	0.00648188	+	0.00865878i
$914$	23.0365	−	26.5856i	0.761981	−	0.879373i
$915$	−2.89108	−	1.14359i	−0.0955761	−	0.0378061i
$916$	8.54973	−	7.40838i	0.282491	−	0.244780i
$917$	11.3435	−	6.19404i	0.374597	−	0.204545i
$918$	−7.64064	+	2.84981i	−0.252179	+	0.0940578i
$919$	−3.16084			−0.104266			−0.0521332	−	0.998640i	$-0.516602\pi$
$919$	−3.16084			−0.104266			−0.0521332	+	0.998640i	$0.516602\pi$
$920$	−9.64231	+	4.69316i	−0.317898	+	0.154729i
$921$	59.3152			1.95450
$922$	12.3391	−	4.60224i	0.406366	−	0.151567i
$923$	−70.6516	+	38.5787i	−2.32552	+	1.26983i
$924$	7.62964	−	6.61112i	0.250997	−	0.217490i
$925$	15.4363	−	25.8017i	0.507544	−	0.848354i
$926$	5.05662	−	5.83565i	0.166171	−	0.191771i
$927$	8.45405	+	11.2933i	0.277667	+	0.370920i
$928$	0.359408	−	0.658207i	0.0117981	−	0.0216067i
$929$	13.0029	−	20.2330i	0.426612	−	0.663822i	−0.559703	−	0.828694i	$-0.689085\pi$
$929$	13.0029	−	20.2330i	0.426612	−	0.663822i	0.986315	+	0.164872i	$0.0527210\pi$
$930$	1.03131	−	52.4148i	0.0338181	−	1.71875i
$931$	−0.0136202	+	0.00622015i	−0.000446385	+	0.000203857i
$932$	1.68681	−	4.52252i	0.0552533	−	0.148140i
$933$	62.4640	+	46.7600i	2.04498	+	1.53085i
$934$	−30.8911	−	19.8525i	−1.01079	−	0.649594i
$935$	−4.19372	−	3.27006i	−0.137149	−	0.106942i
$936$	−3.98442	+	27.7122i	−0.130235	+	0.905802i
$937$	−0.396973	−	5.55041i	−0.0129686	−	0.181324i	−0.999808	−	0.0196182i	$-0.993755\pi$
$937$	−0.396973	−	5.55041i	−0.0129686	−	0.181324i	0.986839	−	0.161706i	$-0.0516996\pi$
$938$	−1.86550	+	8.57554i	−0.0609106	+	0.280001i
$939$	35.8099	+	41.3268i	1.16861	+	1.34865i
$940$	−8.32245	+	2.91894i	−0.271448	+	0.0952053i
$941$	21.2346	+	9.69751i	0.692228	+	0.316130i	0.730282	−	0.683146i	$-0.239389\pi$
$941$	21.2346	+	9.69751i	0.692228	+	0.316130i	−0.0380541	+	0.999276i	$0.512116\pi$
$942$	−39.0485	+	39.0485i	−1.27227	+	1.27227i
$943$	−39.5283	−	19.3658i	−1.28722	−	0.630636i
$944$		−	8.42323i		−	0.274153i
$945$	15.5407	−	23.1668i	0.505540	−	0.753616i
$946$	14.3182	+	4.20421i	0.465526	+	0.136691i
$947$	1.32637	−	18.5450i	0.0431012	−	0.602633i	−0.929301	−	0.369323i	$-0.879590\pi$
$947$	1.32637	−	18.5450i	0.0431012	−	0.602633i	0.972402	−	0.233310i	$-0.0749558\pi$
$948$	13.1926	+	2.86987i	0.428475	+	0.0932091i
$949$	65.8751	+	57.0811i	2.13840	+	1.85293i
$950$	−18.6943	+	6.14642i	−0.606524	+	0.199416i
$951$	−28.6298	+	8.40646i	−0.928384	+	0.272598i
$952$	−0.973139	−	4.47345i	−0.0315396	−	0.144985i
$953$	18.9550	−	25.3209i	0.614013	−	0.820226i	−0.380506	−	0.924778i	$-0.624250\pi$
$953$	18.9550	−	25.3209i	0.614013	−	0.820226i	0.994519	+	0.104553i	$0.0333411\pi$
$954$	2.67724	+	5.86235i	0.0866790	+	0.189801i
$955$	−26.2847	+	7.15934i	−0.850552	+	0.231671i
$956$	−1.05476	−	7.33601i	−0.0341133	−	0.237263i
$957$	2.79541	−	0.608104i	0.0903628	−	0.0196572i
$958$	−1.13193	−	0.618082i	−0.0365711	−	0.0199693i
$959$	19.8506	+	2.85409i	0.641010	+	0.0921633i
$960$	6.17870	+	0.564276i	0.199417	+	0.0182119i
$961$	33.9833	−	21.8397i	1.09623	−	0.704507i
$962$	−35.7372	−	2.55598i	−1.15221	−	0.0824080i
$963$	−31.2742	−	57.2745i	−1.00780	−	1.84564i
$964$	−2.66150	+	5.82788i	−0.0857212	+	0.187703i
$965$	−6.01289	+	4.31926i	−0.193562	+	0.139042i
$966$	−16.0321	−	31.3557i	−0.515824	−	1.00885i
$967$	−5.16362	−	5.16362i	−0.166051	−	0.166051i	0.619190	−	0.785241i	$-0.287461\pi$
$967$	−5.16362	−	5.16362i	−0.166051	−	0.166051i	−0.785241	+	0.619190i	$0.787461\pi$
$968$	−3.18358	−	8.53551i	−0.102324	−	0.274342i
$969$	−5.32228	+	18.1260i	−0.170976	+	0.582291i
$970$	7.28109	+	11.8352i	0.233782	+	0.380006i
$971$	31.0161	+	48.2620i	0.995353	+	1.54880i	0.826329	+	0.563188i	$0.190425\pi$
$971$	31.0161	+	48.2620i	0.995353	+	1.54880i	0.169025	+	0.985612i	$0.445938\pi$
$972$	−16.9200	+	1.21015i	−0.542711	+	0.0388154i
$973$	32.1267	−	24.0497i	1.02993	−	0.770999i
$974$	6.61022	+	22.5123i	0.211805	+	0.721342i
$975$	−64.5518	+	51.6319i	−2.06731	+	1.65355i
$976$	0.496001	−	0.0713142i	0.0158766	−	0.00228271i
$977$	27.7922	+	10.3660i	0.889152	+	0.331637i	0.752195	−	0.658940i	$-0.228995\pi$
$977$	27.7922	+	10.3660i	0.889152	+	0.331637i	0.136957	+	0.990577i	$0.456268\pi$
$978$	−0.163824	−	0.0611031i	−0.00523850	−	0.00195386i
$979$	−16.6667	+	2.39631i	−0.532670	+	0.0765864i
$980$	0.00631830	+	0.00569628i	0.000201831	+	0.000181961i
$981$	13.6702	+	46.5565i	0.436457	+	1.48644i
$982$	17.8626	−	13.3718i	0.570019	−	0.426711i
$983$	28.1815	−	2.01558i	0.898852	−	0.0642871i	0.385739	−	0.922608i	$-0.373947\pi$
$983$	28.1815	−	2.01558i	0.898852	−	0.0642871i	0.513113	+	0.858321i	$0.328492\pi$
$984$	13.7684	+	21.4241i	0.438921	+	0.682974i
$985$	−9.26982	+	38.9108i	−0.295361	+	1.23980i
$986$	0.365493	−	1.24475i	0.0116397	−	0.0396411i
$987$	−10.1215	−	27.1367i	−0.322170	−	0.863772i
$988$	16.5816	+	16.5816i	0.527532	+	0.527532i
$989$	26.1789	−	44.9940i	0.832440	−	1.43073i
$990$	8.42764	+	11.7322i	0.267848	+	0.372874i
$991$	−23.1313	+	50.6504i	−0.734789	+	1.60896i	0.0571516	+	0.998366i	$0.481798\pi$
$991$	−23.1313	+	50.6504i	−0.734789	+	1.60896i	−0.791941	+	0.610598i	$0.790929\pi$
$992$	4.04947	+	7.41605i	0.128571	+	0.235460i
$993$	9.96517	+	0.712723i	0.316235	+	0.0226176i
$994$	−30.0792	+	19.3308i	−0.954056	+	0.613134i
$995$	38.2181	−	31.8216i	1.21159	−	1.00881i
$996$	−0.652887	−	0.0938710i	−0.0206875	−	0.00297442i
$997$	−32.7850	−	17.9019i	−1.03831	−	0.566960i	−0.132738	−	0.991151i	$-0.542377\pi$
$997$	−32.7850	−	17.9019i	−1.03831	−	0.566960i	−0.905573	+	0.424191i	$0.860559\pi$
$998$	8.68401	−	1.88909i	0.274887	−	0.0597981i
$999$	4.03426	+	28.0589i	0.127638	+	0.887744i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.2.l.a.17.1	✓	240
5.3	odd	4	inner	230.2.l.a.63.7	yes	240
23.19	odd	22	inner	230.2.l.a.157.7	yes	240
115.88	even	44	inner	230.2.l.a.203.1	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.l.a.17.1	✓	240	1.1	even	1	trivial
230.2.l.a.63.7	yes	240	5.3	odd	4	inner
230.2.l.a.157.7	yes	240	23.19	odd	22	inner
230.2.l.a.203.1	yes	240	115.88	even	44	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	230.l (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.936950 + 0.349464i) q^{2} +(-2.43530 + 1.32977i) q^{3} +(0.755750 - 0.654861i) q^{4} +(2.05188 - 0.888703i) q^{5} +(1.81704 - 2.09698i) q^{6} +(-1.58597 - 2.11861i) q^{7} +(-0.479249 + 0.877679i) q^{8} +(2.54045 - 3.95301i) q^{9} +(-1.61194 + 1.54973i) q^{10} +(1.25057 - 0.571117i) q^{11} +(-0.969658 + 2.59975i) q^{12} +(4.76976 + 3.57060i) q^{13} +(2.22635 + 1.43079i) q^{14} +(-3.81516 + 4.89279i) q^{15} +(0.142315 - 0.989821i) q^{16} +(-0.123408 - 1.72547i) q^{17} +(-0.998835 + 4.59157i) q^{18} +(2.57738 + 2.97445i) q^{19} +(0.968730 - 2.01533i) q^{20} +(6.67957 + 3.05046i) q^{21} +(-0.972139 + 0.972139i) q^{22} +(2.48233 + 4.10342i) q^{23} -2.77470i q^{24} +(3.42041 - 3.64702i) q^{25} +(-5.71682 - 1.67861i) q^{26} +(-0.336299 + 4.70208i) q^{27} +(-2.58599 - 0.562548i) q^{28} +(-0.566767 - 0.491106i) q^{29} +(1.86476 - 5.91755i) q^{30} +(8.10734 - 2.38053i) q^{31} +(0.212565 + 0.977147i) q^{32} +(-2.28606 + 3.05382i) q^{33} +(0.718617 + 1.57355i) q^{34} +(-5.13703 - 2.93767i) q^{35} +(-0.668731 - 4.65113i) q^{36} +(5.87592 - 1.27823i) q^{37} +(-3.45434 - 1.88621i) q^{38} +(-16.3639 - 2.35277i) q^{39} +(-0.203365 + 2.22680i) q^{40} +(-7.72122 + 4.96213i) q^{41} +(-7.32445 - 0.523855i) q^{42} +(-5.20194 - 9.52665i) q^{43} +(0.571117 - 1.25057i) q^{44} +(1.69963 - 10.3688i) q^{45} +(-3.75982 - 2.97721i) q^{46} +(-2.78897 - 2.78897i) q^{47} +(0.969658 + 2.59975i) q^{48} +(-0.00107183 + 0.00365032i) q^{49} +(-1.93025 + 4.61239i) q^{50} +(2.59502 + 4.03793i) q^{51} +(5.94299 - 0.425051i) q^{52} +(1.09796 - 0.821926i) q^{53} +(-1.32811 - 4.52314i) q^{54} +(2.05847 - 2.28325i) q^{55} +(2.61953 - 0.376632i) q^{56} +(-10.2320 - 3.81634i) q^{57} +(0.702656 + 0.262077i) q^{58} +(8.33749 - 1.19875i) q^{59} +(0.320789 + 6.19612i) q^{60} +(0.141177 + 0.480803i) q^{61} +(-6.76426 + 5.06366i) q^{62} +(-12.4040 + 0.887149i) q^{63} +(-0.540641 - 0.841254i) q^{64} +(12.9602 + 3.08753i) q^{65} +(1.07472 - 3.66017i) q^{66} +(1.15888 + 3.10707i) q^{67} +(-1.22321 - 1.22321i) q^{68} +(-11.5018 - 6.69210i) q^{69} +(5.83975 + 0.957241i) q^{70} +(-5.61249 + 12.2896i) q^{71} +(2.25197 + 4.12417i) q^{72} +(14.5923 + 1.04366i) q^{73} +(-5.05875 + 3.25106i) q^{74} +(-3.48001 + 13.4299i) q^{75} +(3.89570 + 0.560117i) q^{76} +(-3.19335 - 1.74370i) q^{77} +(16.1543 - 3.51416i) q^{78} +(-0.692476 - 4.81627i) q^{79} +(-0.587645 - 2.15747i) q^{80} +(0.422345 + 0.924807i) q^{81} +(5.50031 - 7.34755i) q^{82} +(0.0505310 + 0.232287i) q^{83} +(7.04571 - 2.06881i) q^{84} +(-1.78665 - 3.43078i) q^{85} +(8.20318 + 7.10810i) q^{86} +(2.03330 + 0.442318i) q^{87} +(-0.0980779 + 1.37131i) q^{88} +(-11.7514 - 3.45054i) q^{89} +(2.03105 + 10.3090i) q^{90} -15.7681i q^{91} +(4.56319 + 1.47558i) q^{92} +(-16.5782 + 16.5782i) q^{93} +(3.58776 + 1.63848i) q^{94} +(7.93187 + 3.81269i) q^{95} +(-1.81704 - 2.09698i) q^{96} +(1.32094 - 6.07227i) q^{97} +(-0.000271405 - 0.00379474i) q^{98} +(0.919379 - 6.39442i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 8 q^{3} - 8 q^{6} - 8 q^{12} + 16 q^{13} + 24 q^{16} - 72 q^{18} - 80 q^{23} - 8 q^{26} + 16 q^{27} - 44 q^{28} + 24 q^{31} - 44 q^{33} - 8 q^{35} - 32 q^{36} - 88 q^{37} - 24 q^{41} - 8 q^{46}+ \cdots + 24 q^{98}+O(q^{100}) \) 240 * q - 8 * q^3 - 8 * q^6 - 8 * q^12 + 16 * q^13 + 24 * q^16 - 72 * q^18 - 80 * q^23 - 8 * q^26 + 16 * q^27 - 44 * q^28 + 24 * q^31 - 44 * q^33 - 8 * q^35 - 32 * q^36 - 88 * q^37 - 24 * q^41 - 8 * q^46 - 80 * q^47 + 8 * q^48 + 8 * q^50 + 16 * q^52 - 44 * q^56 - 88 * q^57 - 176 * q^61 - 32 * q^62 - 176 * q^66 + 24 * q^70 - 336 * q^71 + 16 * q^72 - 88 * q^73 - 36 * q^75 - 24 * q^77 + 40 * q^78 - 136 * q^81 + 40 * q^82 - 100 * q^85 - 44 * q^86 + 40 * q^87 + 8 * q^92 + 56 * q^93 + 52 * q^95 + 8 * q^96 + 132 * q^97 + 24 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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