LMFDB - Embedded newform 810.2.w.a.23.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [810,2,Mod(23,810)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(810, base_ring=CyclotomicField(108))

chi = DirichletCharacter(H, H._module([22, 81]))

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

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

chi := DirichletCharacter("810.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 810 = 2 \cdot 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	810.w (of order $108$, degree $36$, 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:	$6.46788256372$
Analytic rank:	$0$
Dimension:	$1944$
Relative dimension:	$54$ over $\Q(\zeta_{108})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{108}]$

Embedding invariants

Embedding label			23.13
Character	$\chi$	$=$	810.23
Dual form			810.2.w.a.317.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.989442 + 0.144932i) q^{2} +(-0.107384 - 1.72872i) q^{3} +(0.957990 - 0.286803i) q^{4} +(0.876175 + 2.05726i) q^{5} +(0.356797 + 1.69490i) q^{6} +(-3.77684 - 0.109895i) q^{7} +(-0.906308 + 0.422618i) q^{8} +(-2.97694 + 0.371275i) q^{9} +(-1.16509 - 1.90855i) q^{10} +(1.80592 - 3.59587i) q^{11} +(-0.598675 - 1.62530i) q^{12} +(-1.47285 + 0.585127i) q^{13} +(3.75289 - 0.438650i) q^{14} +(3.46234 - 1.73558i) q^{15} +(0.835488 - 0.549509i) q^{16} +(0.414057 + 4.73269i) q^{17} +(2.89170 - 0.798808i) q^{18} +(4.16730 + 4.96640i) q^{19} +(1.42940 + 1.71954i) q^{20} +(0.215596 + 6.54090i) q^{21} +(-1.26569 + 3.81964i) q^{22} +(-0.0834340 - 2.86744i) q^{23} +(0.827911 + 1.52137i) q^{24} +(-3.46463 + 3.60504i) q^{25} +(1.37250 - 0.792412i) q^{26} +(0.961506 + 5.10642i) q^{27} +(-3.64969 + 0.977932i) q^{28} +(-2.87769 - 0.336354i) q^{29} +(-3.17424 + 2.21906i) q^{30} +(6.28128 + 1.48869i) q^{31} +(-0.747025 + 0.664796i) q^{32} +(-6.41018 - 2.73578i) q^{33} +(-1.09560 - 4.62271i) q^{34} +(-3.08309 - 7.86623i) q^{35} +(-2.74539 + 1.20947i) q^{36} +(5.55298 + 7.93048i) q^{37} +(-4.84309 - 4.30999i) q^{38} +(1.16968 + 2.48331i) q^{39} +(-1.66352 - 1.49422i) q^{40} +(-6.75700 + 5.03040i) q^{41} +(-1.16130 - 6.44059i) q^{42} +(-7.41372 + 8.33073i) q^{43} +(0.698740 - 3.96275i) q^{44} +(-3.37213 - 5.79903i) q^{45} +(0.498137 + 2.82507i) q^{46} +(4.19285 + 2.58619i) q^{47} +(-1.03966 - 1.38531i) q^{48} +(7.26429 + 0.423097i) q^{49} +(2.90557 - 4.06911i) q^{50} +(8.13703 - 1.22400i) q^{51} +(-1.24316 + 0.982964i) q^{52} +(-1.58210 - 5.90450i) q^{53} +(-1.69144 - 4.91315i) q^{54} +(8.97995 + 0.564621i) q^{55} +(3.46942 - 1.49656i) q^{56} +(8.13800 - 7.73741i) q^{57} +(2.89606 - 0.0842667i) q^{58} +(3.98330 - 2.00049i) q^{59} +(2.81911 - 2.65567i) q^{60} +(1.53067 - 5.11279i) q^{61} +(-6.43072 - 0.562615i) q^{62} +(11.2842 - 1.07509i) q^{63} +(0.642788 - 0.766044i) q^{64} +(-2.49424 - 2.51737i) q^{65} +(6.73900 + 1.77786i) q^{66} +(-9.46445 + 11.9698i) q^{67} +(1.75401 + 4.41511i) q^{68} +(-4.94804 + 0.452152i) q^{69} +(4.19061 + 7.33634i) q^{70} +(4.58642 + 12.6011i) q^{71} +(2.54111 - 1.59460i) q^{72} +(3.78500 + 8.11695i) q^{73} +(-6.64373 - 7.04194i) q^{74} +(6.60415 + 5.60225i) q^{75} +(5.41661 + 3.56256i) q^{76} +(-7.21583 + 13.3826i) q^{77} +(-1.51724 - 2.28757i) q^{78} +(2.10128 + 1.56435i) q^{79} +(1.86252 + 1.23735i) q^{80} +(8.72431 - 2.21052i) q^{81} +(5.95659 - 5.95659i) q^{82} +(-1.90257 - 12.9888i) q^{83} +(2.08249 + 6.20428i) q^{84} +(-9.37358 + 4.99849i) q^{85} +(6.12806 - 9.31726i) q^{86} +(-0.272443 + 5.01084i) q^{87} +(-0.117034 + 4.02218i) q^{88} +(4.50971 + 1.64140i) q^{89} +(4.17699 + 5.24907i) q^{90} +(5.62703 - 2.04807i) q^{91} +(-0.902320 - 2.72305i) q^{92} +(1.89902 - 11.0184i) q^{93} +(-4.52341 - 1.95121i) q^{94} +(-6.56588 + 12.9247i) q^{95} +(1.22946 + 1.22001i) q^{96} +(0.122063 - 0.591151i) q^{97} +(-7.24892 + 0.634198i) q^{98} +(-4.04104 + 11.3752i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1944 q + 36 q^{20} + 108 q^{30} + 108 q^{35} + 36 q^{41} + 216 q^{51} + 108 q^{67} - 144 q^{72} - 576 q^{77} - 576 q^{87} - 144 q^{92} + 36 q^{93} + 108 q^{97}+O(q^{100}) $ 1944 * q + 36 * q^20 + 108 * q^30 + 108 * q^35 + 36 * q^41 + 216 * q^51 + 108 * q^67 - 144 * q^72 - 576 * q^77 - 576 * q^87 - 144 * q^92 + 36 * q^93 + 108 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/810\mathbb{Z}\right)^\times$.

$n$	$487$	$731$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{11}{54}\right)$

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 $

$2$	−0.989442	+	0.144932i	−0.699641	+	0.102482i
$2$	−0.989442	+	0.144932i	−0.699641	+	0.102482i
$3$	−0.107384	−	1.72872i	−0.0619984	−	0.998076i
$3$	−0.107384	−	1.72872i	−0.0619984	−	0.998076i
$4$	0.957990	−	0.286803i	0.478995	−	0.143402i
$5$	0.876175	+	2.05726i	0.391838	+	0.920034i
$5$	0.876175	+	2.05726i	0.391838	+	0.920034i
$6$	0.356797	+	1.69490i	0.145662	+	0.691941i
$7$	−3.77684	−	0.109895i	−1.42751	−	0.0415363i	−0.693394	−	0.720559i	$-0.743885\pi$
$7$	−3.77684	−	0.109895i	−1.42751	−	0.0415363i	−0.734118	+	0.679022i	$0.762404\pi$
$8$	−0.906308	+	0.422618i	−0.320428	+	0.149418i
$9$	−2.97694	+	0.371275i	−0.992312	+	0.123758i
$10$	−1.16509	−	1.90855i	−0.368433	−	0.603537i
$11$	1.80592	−	3.59587i	0.544504	−	1.08420i	−0.438176	−	0.898889i	$-0.644375\pi$
$11$	1.80592	−	3.59587i	0.544504	−	1.08420i	0.982681	−	0.185308i	$-0.0593282\pi$
$12$	−0.598675	−	1.62530i	−0.172823	−	0.469183i
$13$	−1.47285	+	0.585127i	−0.408496	+	0.162285i	−0.564427	−	0.825483i	$-0.690903\pi$
$13$	−1.47285	+	0.585127i	−0.408496	+	0.162285i	0.155931	+	0.987768i	$0.450162\pi$
$14$	3.75289	−	0.438650i	1.00300	−	0.117234i
$15$	3.46234	−	1.73558i	0.893971	−	0.448124i
$16$	0.835488	−	0.549509i	0.208872	−	0.137377i
$17$	0.414057	+	4.73269i	0.100423	+	1.14785i	0.864470	+	0.502685i	$0.167654\pi$
$17$	0.414057	+	4.73269i	0.100423	+	1.14785i	−0.764046	+	0.645161i	$0.776790\pi$
$18$	2.89170	−	0.798808i	0.681579	−	0.188281i
$19$	4.16730	+	4.96640i	0.956045	+	1.13937i	0.990158	+	0.139952i	$0.0446947\pi$
$19$	4.16730	+	4.96640i	0.956045	+	1.13937i	−0.0341138	+	0.999418i	$0.510861\pi$
$20$	1.42940	+	1.71954i	0.319623	+	0.384502i
$21$	0.215596	+	6.54090i	0.0470469	+	1.42734i
$22$	−1.26569	+	3.81964i	−0.269846	+	0.814351i
$23$	−0.0834340	−	2.86744i	−0.0173972	−	0.597903i	−0.962524	−	0.271198i	$-0.912580\pi$
$23$	−0.0834340	−	2.86744i	−0.0173972	−	0.597903i	0.945126	−	0.326705i	$-0.105938\pi$
$24$	0.827911	+	1.52137i	0.168997	+	0.310548i
$25$	−3.46463	+	3.60504i	−0.692927	+	0.721008i
$26$	1.37250	−	0.792412i	0.269169	−	0.155405i
$27$	0.961506	+	5.10642i	0.185042	+	0.982731i
$28$	−3.64969	+	0.977932i	−0.689727	+	0.184812i
$29$	−2.87769	−	0.336354i	−0.534374	−	0.0624594i	−0.155374	−	0.987856i	$-0.549658\pi$
$29$	−2.87769	−	0.336354i	−0.534374	−	0.0624594i	−0.379001	+	0.925396i	$0.623732\pi$
$30$	−3.17424	+	2.21906i	−0.579534	+	0.405142i
$31$	6.28128	+	1.48869i	1.12815	+	0.267377i	0.751988	−	0.659176i	$-0.229095\pi$
$31$	6.28128	+	1.48869i	1.12815	+	0.267377i	0.376163	+	0.926553i	$0.377243\pi$
$32$	−0.747025	+	0.664796i	−0.132057	+	0.117520i
$33$	−6.41018	−	2.73578i	−1.11587	−	0.476238i
$34$	−1.09560	−	4.62271i	−0.187894	−	0.792788i
$35$	−3.08309	−	7.86623i	−0.521138	−	1.32964i
$36$	−2.74539	+	1.20947i	−0.457565	+	0.201579i
$37$	5.55298	+	7.93048i	0.912905	+	1.30376i	0.952497	+	0.304547i	$0.0985051\pi$
$37$	5.55298	+	7.93048i	0.912905	+	1.30376i	−0.0395926	+	0.999216i	$0.512606\pi$
$38$	−4.84309	−	4.30999i	−0.785653	−	0.699172i
$39$	1.16968	+	2.48331i	0.187299	+	0.397649i
$40$	−1.66352	−	1.49422i	−0.263026	−	0.236257i
$41$	−6.75700	+	5.03040i	−1.05527	+	0.785616i	−0.977411	−	0.211348i	$-0.932215\pi$
$41$	−6.75700	+	5.03040i	−1.05527	+	0.785616i	−0.0778551	+	0.996965i	$0.524807\pi$
$42$	−1.16130	−	6.44059i	−0.179193	−	0.993804i
$43$	−7.41372	+	8.33073i	−1.13058	+	1.27042i	−0.172161	+	0.985069i	$0.555075\pi$
$43$	−7.41372	+	8.33073i	−1.13058	+	1.27042i	−0.958422	+	0.285356i	$0.907888\pi$
$44$	0.698740	−	3.96275i	0.105339	−	0.597407i
$45$	−3.37213	−	5.79903i	−0.502687	−	0.864468i
$46$	0.498137	+	2.82507i	0.0734462	+	0.416534i
$47$	4.19285	+	2.58619i	0.611591	+	0.377235i	0.795718	−	0.605668i	$-0.207094\pi$
$47$	4.19285	+	2.58619i	0.611591	+	0.377235i	−0.184127	+	0.982902i	$0.558946\pi$
$48$	−1.03966	−	1.38531i	−0.150063	−	0.199953i
$49$	7.26429	+	0.423097i	1.03776	+	0.0604424i
$50$	2.90557	−	4.06911i	0.410909	−	0.575459i
$51$	8.13703	−	1.22400i	1.13941	−	0.171395i
$52$	−1.24316	+	0.982964i	−0.172395	+	0.136313i
$53$	−1.58210	−	5.90450i	−0.217319	−	0.811045i	−0.985337	−	0.170617i	$-0.945424\pi$
$53$	−1.58210	−	5.90450i	−0.217319	−	0.811045i	0.768019	−	0.640428i	$-0.221243\pi$
$54$	−1.69144	−	4.91315i	−0.230175	−	0.668595i
$55$	8.97995	+	0.564621i	1.21086	+	0.0761335i
$56$	3.46942	−	1.49656i	0.463621	−	0.199987i
$57$	8.13800	−	7.73741i	1.07790	−	1.02484i
$58$	2.89606	−	0.0842667i	0.380271	−	0.0110648i
$59$	3.98330	−	2.00049i	0.518582	−	0.260442i	−0.170201	−	0.985409i	$-0.554442\pi$
$59$	3.98330	−	2.00049i	0.518582	−	0.260442i	0.688783	+	0.724968i	$0.258145\pi$
$60$	2.81911	−	2.65567i	0.363946	−	0.342846i
$61$	1.53067	−	5.11279i	0.195982	−	0.654626i	−0.802348	−	0.596857i	$-0.796416\pi$
$61$	1.53067	−	5.11279i	0.195982	−	0.654626i	0.998330	−	0.0577691i	$-0.0183987\pi$
$62$	−6.43072	−	0.562615i	−0.816702	−	0.0714522i
$63$	11.2842	−	1.07509i	1.42168	−	0.135449i
$64$	0.642788	−	0.766044i	0.0803485	−	0.0957556i
$65$	−2.49424	−	2.51737i	−0.309372	−	0.312241i
$66$	6.73900	+	1.77786i	0.829514	+	0.218839i
$67$	−9.46445	+	11.9698i	−1.15627	+	1.46234i	−0.294056	+	0.955788i	$0.595005\pi$
$67$	−9.46445	+	11.9698i	−1.15627	+	1.46234i	−0.862211	+	0.506550i	$0.830921\pi$
$68$	1.75401	+	4.41511i	0.212705	+	0.535411i
$69$	−4.94804	+	0.452152i	−0.595674	+	0.0544327i
$70$	4.19061	+	7.33634i	0.500873	+	0.876860i
$71$	4.58642	+	12.6011i	0.544308	+	1.49547i	0.841286	+	0.540590i	$0.181799\pi$
$71$	4.58642	+	12.6011i	0.544308	+	1.49547i	−0.296978	+	0.954884i	$0.595979\pi$
$72$	2.54111	−	1.59460i	0.299473	−	0.187925i
$73$	3.78500	+	8.11695i	0.443000	+	0.950017i	0.993355	+	0.115087i	$0.0367146\pi$
$73$	3.78500	+	8.11695i	0.443000	+	0.950017i	−0.550355	+	0.834931i	$0.685508\pi$
$74$	−6.64373	−	7.04194i	−0.772318	−	0.818609i
$75$	6.60415	+	5.60225i	0.762581	+	0.646892i
$76$	5.41661	+	3.56256i	0.621328	+	0.408654i
$77$	−7.21583	+	13.3826i	−0.822320	+	1.52509i
$78$	−1.51724	−	2.28757i	−0.171794	−	0.259016i
$79$	2.10128	+	1.56435i	0.236413	+	0.176003i	0.708845	−	0.705364i	$-0.249217\pi$
$79$	2.10128	+	1.56435i	0.236413	+	0.176003i	−0.472432	+	0.881367i	$0.656624\pi$
$80$	1.86252	+	1.23735i	0.208236	+	0.138340i
$81$	8.72431	−	2.21052i	0.969368	−	0.245614i
$82$	5.95659	−	5.95659i	0.657795	−	0.657795i
$83$	−1.90257	−	12.9888i	−0.208835	−	1.42570i	−0.790594	−	0.612341i	$-0.790228\pi$
$83$	−1.90257	−	12.9888i	−0.208835	−	1.42570i	0.581760	−	0.813361i	$-0.302364\pi$
$84$	2.08249	+	6.20428i	0.227218	+	0.676942i
$85$	−9.37358	+	4.99849i	−1.01671	+	0.542162i
$86$	6.12806	−	9.31726i	0.660805	−	1.00471i
$87$	−0.272443	+	5.01084i	−0.0292089	+	0.537219i
$88$	−0.117034	+	4.02218i	−0.0124758	+	0.428766i
$89$	4.50971	+	1.64140i	0.478028	+	0.173988i	0.569786	−	0.821793i	$-0.307026\pi$
$89$	4.50971	+	1.64140i	0.478028	+	0.173988i	−0.0917575	+	0.995781i	$0.529248\pi$
$90$	4.17699	+	5.24907i	0.440293	+	0.553301i
$91$	5.62703	−	2.04807i	0.589873	−	0.214696i
$92$	−0.902320	−	2.72305i	−0.0940734	−	0.283897i
$93$	1.89902	−	11.0184i	0.196919	−	1.14256i
$94$	−4.52341	−	1.95121i	−0.466554	−	0.201252i
$95$	−6.56588	+	12.9247i	−0.673645	+	1.32604i
$96$	1.22946	+	1.22001i	0.125482	+	0.124517i
$97$	0.122063	−	0.591151i	0.0123936	−	0.0600223i	−0.972684	−	0.232134i	$-0.925429\pi$
$97$	0.122063	−	0.591151i	0.0123936	−	0.0600223i	0.985077	+	0.172111i	$0.0550589\pi$
$98$	−7.24892	+	0.634198i	−0.732251	+	0.0640637i
$99$	−4.04104	+	11.3752i	−0.406140	+	1.14325i
$100$	−2.28514	+	4.44726i	−0.228514	+	0.444726i
$101$	−10.3168	−	3.08864i	−1.02656	−	0.307331i	−0.271115	−	0.962547i	$-0.587393\pi$
$101$	−10.3168	−	3.08864i	−1.02656	−	0.307331i	−0.755442	+	0.655216i	$0.772578\pi$
$102$	−7.87371	+	2.39039i	−0.779614	+	0.236684i
$103$	5.07563	+	1.68188i	0.500117	+	0.165721i	0.553493	−	0.832854i	$-0.313295\pi$
$103$	5.07563	+	1.68188i	0.500117	+	0.165721i	−0.0533761	+	0.998574i	$0.516998\pi$
$104$	1.08757	−	1.15276i	0.106645	−	0.113037i
$105$	−13.2674	+	6.17451i	−1.29477	+	0.602571i
$106$	2.42115	+	5.61286i	0.235163	+	0.545169i
$107$	2.11832	−	7.90568i	0.204786	−	0.764271i	−0.784729	−	0.619839i	$-0.787198\pi$
$107$	2.11832	−	7.90568i	0.204786	−	0.764271i	0.989515	−	0.144432i	$-0.0461355\pi$
$108$	2.38565	+	4.61613i	0.229559	+	0.444188i
$109$	−3.97847	−	2.29697i	−0.381069	−	0.220010i	0.297215	−	0.954811i	$-0.403942\pi$
$109$	−3.97847	−	2.29697i	−0.381069	−	0.220010i	−0.678283	+	0.734801i	$0.737276\pi$
$110$	−8.96696	+	0.742821i	−0.854966	+	0.0708252i
$111$	13.1133	−	10.4512i	1.24466	−	0.991980i
$112$	−3.21589	+	1.98359i	−0.303873	+	0.187432i
$113$	3.69262	+	4.14936i	0.347372	+	0.390339i	0.894765	−	0.446537i	$-0.147343\pi$
$113$	3.69262	+	4.14936i	0.347372	+	0.390339i	−0.547393	+	0.836875i	$0.684380\pi$
$114$	−6.93068	+	8.83517i	−0.649118	+	0.827489i
$115$	5.82597	−	2.68403i	0.543274	−	0.250287i
$116$	−2.85327	+	0.503108i	−0.264919	+	0.0467124i
$117$	4.16735	−	2.28872i	0.385271	−	0.211592i
$118$	−3.65131	+	2.55668i	−0.336131	+	0.235361i
$119$	−1.04373	−	17.9201i	−0.0956784	−	1.64273i
$120$	−2.40445	+	3.03621i	−0.219496	+	0.277167i
$121$	−3.10024	−	4.16434i	−0.281840	−	0.378576i
$122$	−0.773502	+	5.28065i	−0.0700295	+	0.478088i
$123$	9.42174	+	11.1408i	0.849530	+	1.00453i
$124$	6.44436	−	0.375341i	0.578721	−	0.0337067i
$125$	−10.4521	−	3.96900i	−0.934867	−	0.354998i
$126$	−11.0093	+	2.69919i	−0.980783	+	0.240463i
$127$	−13.0229	−	9.11875i	−1.15560	−	0.809159i	−0.171221	−	0.985233i	$-0.554771\pi$
$127$	−13.0229	−	9.11875i	−1.15560	−	0.809159i	−0.984377	+	0.176074i	$0.943660\pi$
$128$	−0.524977	+	0.851117i	−0.0464018	+	0.0752288i
$129$	15.1976	+	11.9217i	1.33808	+	1.04964i
$130$	2.83275	+	2.12929i	0.248448	+	0.186751i
$131$	−1.51796	+	6.40476i	−0.132624	+	0.559586i	0.865638	+	0.500670i	$0.166913\pi$
$131$	−1.51796	+	6.40476i	−0.132624	+	0.559586i	−0.998263	+	0.0589168i	$0.981235\pi$
$132$	−6.92552	−	0.782388i	−0.602789	−	0.0680981i
$133$	−15.1935	−	19.2153i	−1.31744	−	1.66617i
$134$	7.62973	−	13.2151i	0.659108	−	1.14161i
$135$	−9.66278	+	6.45218i	−0.831640	+	0.555316i
$136$	−2.37538	−	4.11429i	−0.203687	−	0.352797i
$137$	−1.93236	+	4.86404i	−0.165093	+	0.415563i	−0.988368	−	0.152079i	$-0.951403\pi$
$137$	−1.93236	+	4.86404i	−0.165093	+	0.415563i	0.823276	+	0.567642i	$0.192144\pi$
$138$	4.83026	−	1.16451i	0.411179	−	0.0991294i
$139$	1.61076	+	1.51968i	0.136623	+	0.128897i	0.751520	−	0.659710i	$-0.229321\pi$
$139$	1.61076	+	1.51968i	0.136623	+	0.128897i	−0.614897	+	0.788607i	$0.710802\pi$
$140$	−5.20963	−	6.65152i	−0.440294	−	0.562156i
$141$	4.02055	−	7.52598i	0.338591	−	0.633802i
$142$	−6.36430	−	11.8033i	−0.534080	−	0.990513i
$143$	−0.555805	+	6.35288i	−0.0464788	+	0.531255i
$144$	−2.28318	+	1.94605i	−0.190265	+	0.162171i
$145$	−1.82940	−	6.21487i	−0.151923	−	0.516117i
$146$	−4.92144	−	7.48268i	−0.407301	−	0.619271i
$147$	−0.0486555	−	12.6034i	−0.00401304	−	1.03951i
$148$	7.59419	+	6.00470i	0.624238	+	0.493584i
$149$	−1.84778	+	4.28362i	−0.151376	+	0.350928i	−0.976983	−	0.213317i	$-0.931573\pi$
$149$	−1.84778	+	4.28362i	−0.151376	+	0.350928i	0.825607	+	0.564245i	$0.190833\pi$
$150$	−7.34636	−	4.58595i	−0.599828	−	0.374441i
$151$	3.93452	+	1.97599i	0.320187	+	0.160804i	0.601632	−	0.798774i	$-0.294517\pi$
$151$	3.93452	+	1.97599i	0.320187	+	0.160804i	−0.281445	+	0.959577i	$0.590814\pi$
$152$	−5.87575	−	2.73991i	−0.476586	−	0.222236i
$153$	−2.98975	−	13.9352i	−0.241707	−	1.12659i
$154$	5.20008	−	14.2871i	0.419034	−	1.15129i
$155$	2.44088	+	14.2266i	0.196056	+	1.14271i
$156$	1.83276	+	2.04352i	0.146739	+	0.163613i
$157$	11.4445	−	2.36311i	0.913373	−	0.188596i	0.277802	−	0.960638i	$-0.410394\pi$
$157$	11.4445	−	2.36311i	0.913373	−	0.188596i	0.635571	+	0.772042i	$0.280765\pi$
$158$	−2.30582	−	1.24329i	−0.183441	−	0.0989106i
$159$	−10.0373	+	3.36906i	−0.796011	+	0.267184i
$160$	−2.02218	−	0.954347i	−0.159868	−	0.0754477i
$161$			10.8390i			0.854236i
$162$	−8.31182	+	3.45161i	−0.653038	+	0.271184i
$163$	−7.26046	−	7.26046i	−0.568683	−	0.568683i	0.363076	−	0.931759i	$-0.381726\pi$
$163$	−7.26046	−	7.26046i	−0.568683	−	0.568683i	−0.931759	+	0.363076i	$0.881726\pi$
$164$	−5.03040	+	6.75700i	−0.392808	+	0.527633i
$165$	0.0117656	−	15.5844i	0.000915948	−	1.21325i
$166$	3.76497	+	12.5759i	0.292218	+	0.976077i
$167$	−4.10933	−	19.9015i	−0.317989	−	1.54002i	−0.764131	−	0.645062i	$-0.776832\pi$
$167$	−4.10933	−	19.9015i	−0.317989	−	1.54002i	0.446141	−	0.894963i	$-0.352798\pi$
$168$	−2.95970	−	5.83695i	−0.228346	−	0.450331i
$169$	−7.62894	+	7.19753i	−0.586841	+	0.553656i
$170$	8.55017	−	6.30424i	0.655768	−	0.483513i
$171$	−14.2497	−	13.2374i	−1.08970	−	1.01229i
$172$	−4.71299	+	10.1070i	−0.359362	+	0.770654i
$173$	23.7716	−	7.87706i	1.80732	−	0.598882i	0.807363	−	0.590055i	$-0.200894\pi$
$173$	23.7716	−	7.87706i	1.80732	−	0.598882i	0.999961	−	0.00882646i	$-0.00280959\pi$
$174$	−0.456665	−	4.99742i	−0.0346197	−	0.378853i
$175$	13.4815	−	13.2349i	1.01911	−	1.00047i
$176$	−0.467144	−	3.99668i	−0.0352123	−	0.301261i
$177$	−3.88603	−	6.67119i	−0.292092	−	0.501437i
$178$	−4.69998	−	0.970469i	−0.352279	−	0.0727397i
$179$	−1.98879	−	1.66879i	−0.148649	−	0.124731i	0.565430	−	0.824796i	$-0.308710\pi$
$179$	−1.98879	−	1.66879i	−0.148649	−	0.124731i	−0.714080	+	0.700065i	$0.753155\pi$
$180$	−4.89364	−	4.58827i	−0.364751	−	0.341990i
$181$	−17.7085	+	14.8592i	−1.31626	+	1.10448i	−0.329181	+	0.944267i	$0.606773\pi$
$181$	−17.7085	+	14.8592i	−1.31626	+	1.10448i	−0.987083	+	0.160210i	$0.948783\pi$
$182$	−5.27079	+	2.84198i	−0.390697	+	0.210662i
$183$	−9.00295	−	2.09706i	−0.665517	−	0.155019i
$184$	1.28745	+	2.56352i	0.0949120	+	0.188985i
$185$	−11.4497	+	18.3724i	−0.841796	+	1.35077i
$186$	−0.282045	+	11.1773i	−0.0206805	+	0.819561i
$187$	17.7659	+	7.05794i	1.29917	+	0.516128i
$188$	4.75844	+	1.27502i	0.347045	+	0.0929904i
$189$	−3.07028	−	19.3918i	−0.223330	−	1.41055i
$190$	4.62336	−	13.7398i	0.335414	−	0.996790i
$191$	2.19480	−	18.7778i	0.158811	−	1.35871i	−0.645163	−	0.764045i	$-0.723210\pi$
$191$	2.19480	−	18.7778i	0.158811	−	1.35871i	0.803973	−	0.594666i	$-0.202716\pi$
$192$	−1.39330	−	1.02894i	−0.100553	−	0.0742572i
$193$	−11.0925	−	17.9836i	−0.798454	−	1.29449i	−0.951923	−	0.306337i	$-0.900897\pi$
$193$	−11.0925	−	17.9836i	−0.798454	−	1.29449i	0.153470	−	0.988153i	$-0.450955\pi$
$194$	−0.0350975	+	0.602600i	−0.00251985	+	0.0432642i
$195$	−4.08398	+	4.58216i	−0.292460	+	0.328135i
$196$	7.08046	−	1.67810i	0.505747	−	0.119864i
$197$	2.01942	−	2.88404i	0.143878	−	0.205479i	−0.740745	−	0.671787i	$-0.765527\pi$
$197$	2.01942	−	2.88404i	0.143878	−	0.205479i	0.884623	+	0.466308i	$0.154416\pi$
$198$	2.34975	−	11.8408i	0.166989	−	0.841486i
$199$	−1.21563	−	0.214348i	−0.0861735	−	0.0151947i	0.130395	−	0.991462i	$-0.458375\pi$
$199$	−1.21563	−	0.214348i	−0.0861735	−	0.0151947i	−0.216569	+	0.976267i	$0.569487\pi$
$200$	1.61647	−	4.73149i	0.114302	−	0.334567i
$201$	21.7087	+	15.0760i	1.53121	+	1.06338i
$202$	10.6555	+	1.56080i	0.749717	+	0.109817i
$203$	10.8316	+	1.58660i	0.760231	+	0.111357i
$204$	7.44414	−	3.50631i	0.521194	−	0.245491i
$205$	−16.2692	−	9.49339i	−1.13629	−	0.663047i
$206$	−5.26580	−	0.928503i	−0.366886	−	0.0646919i
$207$	1.31299	+	8.50521i	0.0912588	+	0.591153i
$208$	−0.909018	+	1.29821i	−0.0630290	+	0.0900148i
$209$	25.3843	−	6.01620i	1.75587	−	0.416149i
$210$	12.2325	−	8.03219i	0.844120	−	0.554274i
$211$	−1.54643	+	26.5512i	−0.106461	+	1.82786i	0.348454	+	0.937326i	$0.386707\pi$
$211$	−1.54643	+	26.5512i	−0.106461	+	1.82786i	−0.454914	+	0.890535i	$0.650330\pi$
$212$	−3.20907	−	5.20269i	−0.220400	−	0.357322i
$213$	21.2912	−	9.28179i	1.45885	−	0.635978i
$214$	−0.950170	+	8.12922i	−0.0649523	+	0.555702i
$215$	−23.6342	−	7.95277i	−1.61184	−	0.542374i
$216$	−3.02949	−	4.22164i	−0.206130	−	0.287246i
$217$	−23.5598	−	6.31283i	−1.59934	−	0.428543i
$218$	4.26937	+	1.69611i	0.289158	+	0.114875i
$219$	13.6255	−	7.41483i	0.920725	−	0.501048i
$220$	8.76463	−	2.03458i	0.590911	−	0.137171i
$221$	−3.37907	−	6.72828i	−0.227301	−	0.452593i
$222$	−11.4601	+	12.2413i	−0.769152	+	0.821585i
$223$	−1.92167	+	1.03616i	−0.128685	+	0.0693862i	−0.537673	−	0.843153i	$-0.680697\pi$
$223$	−1.92167	+	1.03616i	−0.128685	+	0.0693862i	0.408988	+	0.912540i	$0.365882\pi$
$224$	2.89445	−	2.42873i	0.193394	−	0.162277i
$225$	8.97554	−	12.0183i	0.598369	−	0.801221i
$226$	−4.25500	−	3.57037i	−0.283038	−	0.237497i
$227$	4.38122	+	0.904650i	0.290792	+	0.0600437i	0.345373	−	0.938466i	$-0.387753\pi$
$227$	4.38122	+	0.904650i	0.290792	+	0.0600437i	−0.0545806	+	0.998509i	$0.517382\pi$
$228$	5.57701	−	9.74636i	0.369346	−	0.645468i
$229$	0.362917	+	3.10496i	0.0239822	+	0.205181i	0.999917	−	0.0128814i	$-0.00410038\pi$
$229$	0.362917	+	3.10496i	0.0239822	+	0.205181i	−0.975935	+	0.218063i	$0.930026\pi$
$230$	−5.37545	+	3.50006i	−0.354447	+	0.230787i
$231$	23.9096	+	11.0371i	1.57314	+	0.726185i
$232$	2.75023	−	0.911325i	0.180561	−	0.0598314i
$233$	−5.27741	+	11.3174i	−0.345734	+	0.741430i	−0.999889	−	0.0149314i	$-0.995247\pi$
$233$	−5.27741	+	11.3174i	−0.345734	+	0.741430i	0.654154	+	0.756361i	$0.273025\pi$
$234$	−3.79164	+	2.86853i	−0.247867	+	0.187522i
$235$	−1.64679	+	10.8917i	−0.107425	+	0.710499i
$236$	3.24222	−	3.05887i	0.211050	−	0.199116i
$237$	2.47867	−	3.80051i	0.161007	−	0.246870i
$238$	3.62990	+	17.5796i	0.235292	+	1.13952i
$239$	1.16922	+	3.90546i	0.0756304	+	0.252623i	0.987441	−	0.157988i	$-0.0505007\pi$
$239$	1.16922	+	3.90546i	0.0756304	+	0.252623i	−0.911811	+	0.410611i	$0.865315\pi$
$240$	1.93902	−	3.35264i	0.125163	−	0.216412i
$241$	−9.91020	+	13.3117i	−0.638372	+	0.857483i	−0.997111	−	0.0759553i	$-0.975799\pi$
$241$	−9.91020	+	13.3117i	−0.638372	+	0.857483i	0.358739	+	0.933438i	$0.383207\pi$
$242$	3.67105	+	3.67105i	0.235984	+	0.235984i
$243$	−4.75822	−	14.8445i	−0.305240	−	0.952275i
$244$		−	5.33700i		−	0.341666i
$245$	5.49438	+	15.3152i	0.351023	+	0.978455i
$246$	−10.9369	−	9.65763i	−0.697312	−	0.615748i
$247$	−9.04379	−	4.87637i	−0.575443	−	0.310276i
$248$	−6.32192	+	1.30537i	−0.401443	+	0.0828912i
$249$	−22.2496	+	4.68380i	−1.41001	+	0.296824i
$250$	10.9170	+	2.41225i	0.690452	+	0.152564i
$251$	1.12935	−	3.10287i	0.0712840	−	0.195851i	−0.898934	−	0.438084i	$-0.855657\pi$
$251$	1.12935	−	3.10287i	0.0712840	−	0.195851i	0.970218	+	0.242232i	$0.0778796\pi$
$252$	10.5018	−	4.26628i	0.661553	−	0.268750i
$253$	−10.4616	−	4.87834i	−0.657717	−	0.306699i
$254$	14.2070	+	7.13504i	0.891428	+	0.447692i
$255$	9.64756	+	15.6675i	0.604153	+	0.981139i
$256$	0.396080	−	0.918216i	0.0247550	−	0.0573885i
$257$	10.9150	+	8.63048i	0.680860	+	0.538354i	0.899211	−	0.437516i	$-0.144142\pi$
$257$	10.9150	+	8.63048i	0.680860	+	0.538354i	−0.218351	+	0.975870i	$0.570068\pi$
$258$	−16.7650	−	9.59316i	−1.04374	−	0.597244i
$259$	−20.1012	−	30.5624i	−1.24903	−	1.89906i
$260$	−3.11144	−	1.69626i	−0.192963	−	0.105197i
$261$	8.69159	−	0.0671092i	0.537996	−	0.00415395i
$262$	0.573675	−	6.55714i	0.0354418	−	0.405101i
$263$	−0.611428	−	1.13396i	−0.0377023	−	0.0699233i	0.860656	−	0.509187i	$-0.170054\pi$
$263$	−0.611428	−	1.13396i	−0.0377023	−	0.0699233i	−0.898358	+	0.439264i	$0.855239\pi$
$264$	6.96579	−	0.229601i	0.428715	−	0.0141310i
$265$	10.7609	−	8.42817i	0.661035	−	0.517739i
$266$	17.8179	+	16.8104i	1.09249	+	1.03071i
$267$	2.35325	−	7.97228i	0.144016	−	0.487895i
$268$	−5.63388	+	14.1813i	−0.344144	+	0.866263i
$269$	−5.63059	−	9.75246i	−0.343303	−	0.594618i	0.641741	−	0.766921i	$-0.278212\pi$
$269$	−5.63059	−	9.75246i	−0.343303	−	0.594618i	−0.985044	+	0.172303i	$0.944879\pi$
$270$	8.62563	−	7.78450i	0.524939	−	0.473750i
$271$	10.2047	−	17.6750i	0.619891	−	1.07368i	−0.369614	−	0.929185i	$-0.620510\pi$
$271$	10.2047	−	17.6750i	0.619891	−	1.07368i	0.989505	−	0.144497i	$-0.0461566\pi$
$272$	2.94659	+	3.72658i	0.178664	+	0.225957i
$273$	−4.14480	−	9.50763i	−0.250854	−	0.575428i
$274$	1.20700	−	5.09275i	0.0729177	−	0.307664i
$275$	6.70644	+	18.9688i	0.404413	+	1.14386i
$276$	−4.61049	+	1.85227i	−0.277519	+	0.111494i
$277$	−11.1037	+	18.0018i	−0.667155	+	1.08162i	0.323631	+	0.946183i	$0.395096\pi$
$277$	−11.1037	+	18.0018i	−0.667155	+	1.08162i	−0.990786	+	0.135439i	$0.956756\pi$
$278$	−1.81400	−	1.27018i	−0.108797	−	0.0761803i
$279$	−19.2517	−	2.09966i	−1.15257	−	0.125703i
$280$	6.11864	+	5.82625i	0.365659	+	0.348185i
$281$	−23.9991	+	1.39779i	−1.43166	+	0.0833850i	−0.756361	−	0.654155i	$-0.773025\pi$
$281$	−23.9991	+	1.39779i	−1.43166	+	0.0833850i	−0.675304	+	0.737540i	$0.735988\pi$
$282$	−2.88734	+	8.02923i	−0.171939	+	0.478133i
$283$	2.36049	−	16.1149i	0.140316	−	0.957932i	−0.795628	−	0.605785i	$-0.792859\pi$
$283$	2.36049	−	16.1149i	0.140316	−	0.957932i	0.935945	−	0.352147i	$-0.114548\pi$
$284$	8.00778	+	10.7563i	0.475174	+	0.638270i
$285$	23.0482	+	9.96265i	1.36526	+	0.590137i
$286$	−0.370798	−	6.36636i	−0.0219258	−	0.376451i
$287$	26.0729	−	18.2565i	1.53904	−	1.07764i
$288$	1.97702	−	2.25641i	0.116497	−	0.132960i
$289$	−5.48517	+	0.967184i	−0.322657	+	0.0568932i
$290$	2.71081	+	5.88411i	0.159184	+	0.345527i
$291$	−1.03504	−	0.147532i	−0.0606752	−	0.00864848i
$292$	5.95396	+	6.69041i	0.348429	+	0.391526i
$293$	−2.20875	+	1.36238i	−0.129036	+	0.0795908i	−0.587984	−	0.808872i	$-0.700078\pi$
$293$	−2.20875	+	1.36238i	−0.129036	+	0.0795908i	0.458948	+	0.888463i	$0.348226\pi$
$294$	1.87477	+	12.4632i	0.109339	+	0.726871i
$295$	7.60560	+	6.44191i	0.442815	+	0.375062i
$296$	−8.38428	−	4.84066i	−0.487326	−	0.281358i
$297$	20.0984	+	5.76431i	1.16623	+	0.334479i
$298$	1.20743	−	4.50620i	0.0699447	−	0.261037i
$299$	1.80070	+	4.17450i	0.104137	+	0.241417i
$300$	7.93345	+	3.47281i	0.458038	+	0.200503i
$301$	28.9160	−	30.6491i	1.66669	−	1.76659i
$302$	−4.17936	−	1.38489i	−0.240495	−	0.0796914i
$303$	−4.23153	+	18.1665i	−0.243095	+	1.04364i
$304$	6.21081	+	1.85939i	0.356214	+	0.106644i
$305$	11.8595	−	1.33072i	0.679071	−	0.0761967i
$306$	4.97783	+	13.3547i	0.284564	+	0.763440i
$307$	−20.4838	+	1.79210i	−1.16907	+	0.102281i	−0.655111	−	0.755532i	$-0.727378\pi$
$307$	−20.4838	+	1.79210i	−1.16907	+	0.102281i	−0.513962	+	0.857813i	$0.671823\pi$
$308$	−3.07452	+	14.8899i	−0.175187	+	0.848431i
$309$	2.36246	−	8.95495i	0.134395	−	0.509429i
$310$	−4.47699	−	13.7226i	−0.254276	−	0.779392i
$311$	−23.8467	−	10.2865i	−1.35222	−	0.583293i	−0.408117	−	0.912930i	$-0.633814\pi$
$311$	−23.8467	−	10.2865i	−1.35222	−	0.583293i	−0.944108	+	0.329637i	$0.893074\pi$
$312$	−2.10959	−	1.75632i	−0.119432	−	0.0994320i
$313$	0.252929	+	0.763298i	0.0142964	+	0.0431441i	0.956146	−	0.292891i	$-0.0946175\pi$
$313$	0.252929	+	0.763298i	0.0142964	+	0.0431441i	−0.941849	+	0.336036i	$0.890914\pi$
$314$	−10.9812	+	3.99683i	−0.619705	+	0.225554i
$315$	12.0987	+	22.2726i	0.681685	+	1.25492i
$316$	2.46167	+	0.895973i	0.138480	+	0.0504024i
$317$	−0.196761	+	6.76223i	−0.0110512	+	0.379805i	0.975846	+	0.218457i	$0.0701025\pi$
$317$	−0.196761	+	6.76223i	−0.0110512	+	0.379805i	−0.986898	+	0.161347i	$0.948416\pi$
$318$	9.44306	−	4.78822i	0.529540	−	0.268510i
$319$	−6.40636	+	9.74040i	−0.358687	+	0.545357i
$320$	2.13915	+	0.651192i	0.119582	+	0.0364027i
$321$	−13.8942	−	2.81304i	−0.775497	−	0.157008i
$322$	−1.57092	−	10.7246i	−0.0875440	−	0.597658i
$323$	−21.7789	+	21.7789i	−1.21181	+	1.21181i
$324$	7.72381	−	4.61982i	0.429101	−	0.256657i
$325$	2.99349	−	7.33694i	0.166049	−	0.406980i
$326$	8.23608	+	6.13153i	0.456154	+	0.339594i
$327$	−3.54359	+	7.12432i	−0.195961	+	0.393976i
$328$	3.99798	−	7.41472i	0.220752	−	0.409409i
$329$	−15.5515	−	10.2284i	−0.857384	−	0.563910i
$330$	2.24704	+	15.4216i	0.123695	+	0.848931i
$331$	−7.23978	−	7.67372i	−0.397934	−	0.421786i	0.497163	−	0.867657i	$-0.334375\pi$
$331$	−7.23978	−	7.67372i	−0.397934	−	0.421786i	−0.895097	+	0.445872i	$0.852894\pi$
$332$	−5.54786	−	11.8974i	−0.304479	−	0.652956i
$333$	−19.4753	−	21.5469i	−1.06724	−	1.18076i
$334$	6.95030	+	19.0958i	0.380304	+	1.04488i
$335$	−32.9174	−	8.98323i	−1.79847	−	0.490806i
$336$	3.77441	+	5.34637i	0.205911	+	0.291668i
$337$	11.8839	+	29.9135i	0.647355	+	1.62949i	0.770754	+	0.637133i	$0.219880\pi$
$337$	11.8839	+	29.9135i	0.647355	+	1.62949i	−0.123400	+	0.992357i	$0.539380\pi$
$338$	6.50524	−	8.22721i	0.353838	−	0.447501i
$339$	6.77654	−	6.82907i	0.368051	−	0.370904i
$340$	−7.54621	+	7.47687i	−0.409251	+	0.405490i
$341$	16.6966	−	19.8983i	0.904172	−	1.07755i
$342$	16.0178	+	11.0324i	0.866142	+	0.596566i
$343$	−1.04116	−	0.0910897i	−0.0562174	−	0.00491838i
$344$	3.19840	−	10.6834i	0.172446	−	0.576009i
$345$	−5.26554	−	9.78324i	−0.283487	−	0.526712i
$346$	−22.3790	+	11.2392i	−1.20310	+	0.604221i
$347$	−17.4835	+	0.508718i	−0.938563	+	0.0273094i	−0.494962	−	0.868915i	$-0.664818\pi$
$347$	−17.4835	+	0.508718i	−0.938563	+	0.0273094i	−0.443601	+	0.896224i	$0.646299\pi$
$348$	1.17613	+	4.87847i	0.0630471	+	0.261513i
$349$	−6.57758	+	2.83729i	−0.352090	+	0.151877i	−0.564777	−	0.825244i	$-0.691038\pi$
$349$	−6.57758	+	2.83729i	−0.352090	+	0.151877i	0.212687	+	0.977120i	$0.431779\pi$
$350$	−11.4210	+	15.0491i	−0.610480	+	0.804407i
$351$	−4.40406	−	6.95840i	−0.235071	−	0.371412i
$352$	1.04146	+	3.88677i	0.0555099	+	0.207166i
$353$	−1.28083	+	1.01275i	−0.0681716	+	0.0539031i	−0.653735	−	0.756723i	$-0.726799\pi$
$353$	−1.28083	+	1.01275i	−0.0681716	+	0.0539031i	0.585564	+	0.810626i	$0.300873\pi$
$354$	4.81187	+	6.03754i	0.255748	+	0.320892i
$355$	−21.9052	+	20.4762i	−1.16261	+	1.08677i
$356$	4.79101	+	0.279045i	0.253923	+	0.0147893i
$357$	−30.8668	+	3.72865i	−1.63364	+	0.197341i
$358$	2.20965	+	1.36293i	0.116784	+	0.0720333i
$359$	2.58567	+	14.6641i	0.136466	+	0.773939i	0.973827	+	0.227289i	$0.0729861\pi$
$359$	2.58567	+	14.6641i	0.136466	+	0.773939i	−0.837361	+	0.546650i	$0.815903\pi$
$360$	5.50696	+	3.83058i	0.290242	+	0.201890i
$361$	−3.99938	+	22.6816i	−0.210494	+	1.19377i
$362$	15.3680	−	17.2689i	0.807723	−	0.907631i
$363$	−6.86605	+	5.80662i	−0.360374	+	0.304768i
$364$	4.80324	−	3.57588i	0.251758	−	0.187427i
$365$	−13.3824	+	14.8986i	−0.700465	+	0.779828i
$366$	9.21182	+	0.770108i	0.481510	+	0.0402542i
$367$	5.41468	+	4.81865i	0.282644	+	0.251532i	0.794113	−	0.607770i	$-0.207936\pi$
$367$	5.41468	+	4.81865i	0.282644	+	0.251532i	−0.511469	+	0.859302i	$0.670899\pi$
$368$	−1.64539	−	2.34986i	−0.0857720	−	0.122495i
$369$	18.2475	−	17.4839i	0.949927	−	0.910175i
$370$	8.66603	−	19.8379i	0.450526	−	1.03132i
$371$	5.32648	+	22.4742i	0.276537	+	1.16680i
$372$	−1.34088	−	11.1002i	−0.0695216	−	0.575518i
$373$	15.5327	−	13.8229i	0.804251	−	0.715722i	−0.158133	−	0.987418i	$-0.550547\pi$
$373$	15.5327	−	13.8229i	0.804251	−	0.715722i	0.962383	+	0.271696i	$0.0875844\pi$
$374$	−18.6012	−	4.40858i	−0.961848	−	0.227962i
$375$	−5.73889	+	18.4950i	−0.296355	+	0.955078i
$376$	−4.89299	−	0.571908i	−0.252337	−	0.0294939i
$377$	4.43523	−	1.18842i	0.228426	−	0.0612065i
$378$	5.84836	+	18.7421i	0.300807	+	0.963988i
$379$	20.8555	−	12.0409i	1.07127	−	0.618500i	0.142745	−	0.989760i	$-0.454407\pi$
$379$	20.8555	−	12.0409i	1.07127	−	0.618500i	0.928529	+	0.371259i	$0.121074\pi$
$380$	−2.58321	+	14.2648i	−0.132516	+	0.731769i
$381$	−14.3653	+	23.4922i	−0.735957	+	1.20354i
$382$	0.549864	+	18.8976i	0.0281335	+	0.966885i
$383$	−3.26647	+	9.85764i	−0.166909	+	0.503702i	−0.998677	−	0.0514209i	$-0.983625\pi$
$383$	−3.26647	+	9.85764i	−0.166909	+	0.503702i	0.831768	+	0.555123i	$0.187329\pi$
$384$	1.52772	+	0.816140i	0.0779609	+	0.0416485i
$385$	−33.8538	−	3.11933i	−1.72535	−	0.158976i
$386$	13.5818	+	16.1861i	0.691293	+	0.823851i
$387$	18.9772	−	27.5526i	0.964665	−	1.40058i
$388$	−0.0526091	−	0.601324i	−0.00267082	−	0.0305276i
$389$	−1.36605	+	0.898464i	−0.0692614	+	0.0455539i	−0.583667	−	0.811993i	$-0.698383\pi$
$389$	−1.36605	+	0.898464i	−0.0692614	+	0.0455539i	0.514406	+	0.857547i	$0.328012\pi$
$390$	3.37676	−	5.12567i	0.170989	−	0.259549i
$391$	13.5362	−	1.58215i	0.684553	−	0.0800128i
$392$	−6.76250	+	2.68657i	−0.341558	+	0.135692i
$393$	11.2350	+	1.93635i	0.566732	+	0.0976758i
$394$	−1.58011	+	3.14627i	−0.0796050	+	0.158507i
$395$	−1.37718	+	5.69353i	−0.0692932	+	0.286472i
$396$	−0.608837	+	12.0563i	−0.0305952	+	0.605851i
$397$	−0.714150	+	0.333013i	−0.0358421	+	0.0167135i	−0.440457	−	0.897774i	$-0.645183\pi$
$397$	−0.714150	+	0.333013i	−0.0358421	+	0.0167135i	0.404615	+	0.914487i	$0.367406\pi$
$398$	1.23386	+	0.0359016i	0.0618477	+	0.00179958i
$399$	−31.5862	+	28.3286i	−1.58129	+	1.41821i
$400$	−0.913657	+	4.91581i	−0.0456828	+	0.245791i
$401$	24.3617	−	7.29341i	1.21656	−	0.364215i	0.386713	−	0.922200i	$-0.373610\pi$
$401$	24.3617	−	7.29341i	1.21656	−	0.364215i	0.829851	+	0.557985i	$0.188425\pi$
$402$	−23.6645	−	11.7706i	−1.18028	−	0.587062i
$403$	−10.1225	+	1.48272i	−0.504236	+	0.0738598i
$404$	−10.7692			−0.535787
$405$	12.1916	+	16.0114i	0.605808	+	0.795611i
$406$	−10.9472			−0.543301
$407$	38.5452	−	5.64604i	1.91062	−	0.279864i
$408$	−6.85736	+	4.54818i	−0.339490	+	0.225168i
$409$	−18.3478	+	5.49297i	−0.907240	+	0.271610i	−0.706233	−	0.707980i	$-0.749607\pi$
$409$	−18.3478	+	5.49297i	−0.907240	+	0.271610i	−0.201007	+	0.979590i	$0.564422\pi$
$410$	17.4733	+	7.03523i	0.862943	+	0.347445i
$411$	8.61607	+	2.81819i	0.424999	+	0.139011i
$412$	5.34477	+	0.155517i	0.263318	+	0.00766177i
$413$	−15.2641	+	7.11779i	−0.751100	+	0.350244i
$414$	−2.53180	−	8.22512i	−0.124431	−	0.404243i
$415$	25.0543	−	15.2945i	1.22987	−	0.750778i
$416$	0.711268	−	1.41625i	0.0348728	−	0.0694374i
$417$	2.45412	−	2.94774i	0.120179	−	0.144352i
$418$	−24.2444	+	9.63168i	−1.18583	+	0.471101i
$419$	15.9411	−	1.86325i	0.778773	−	0.0910255i	0.282587	−	0.959242i	$-0.408807\pi$
$419$	15.9411	−	1.86325i	0.778773	−	0.0910255i	0.496186	+	0.868216i	$0.334733\pi$
$420$	−10.9392	+	9.72026i	−0.533777	+	0.474300i
$421$	25.2702	−	16.6205i	1.23160	−	0.810033i	0.244420	−	0.969670i	$-0.421403\pi$
$421$	25.2702	−	16.6205i	1.23160	−	0.810033i	0.987176	+	0.159636i	$0.0510322\pi$
$422$	−2.31801	−	26.4950i	−0.112839	−	1.28976i
$423$	−13.4420	−	6.14223i	−0.653575	−	0.298645i
$424$	3.92922	+	4.68266i	0.190820	+	0.227410i
$425$	−18.4961	−	14.9043i	−0.897192	−	0.722967i
$426$	−19.7212	+	12.2696i	−0.955496	+	0.594463i
$427$	−6.34296	+	19.1420i	−0.306958	+	0.926346i
$428$	−0.238046	−	8.18110i	−0.0115064	−	0.395448i
$429$	11.0420	+	0.278631i	0.533114	+	0.0134524i
$430$	24.5373	+	4.44345i	1.18329	+	0.214282i
$431$	14.9703	−	8.64311i	0.721094	−	0.416324i	−0.0940611	−	0.995566i	$-0.529985\pi$
$431$	14.9703	−	8.64311i	0.721094	−	0.416324i	0.815155	+	0.579243i	$0.196652\pi$
$432$	3.60935	+	3.73799i	0.173655	+	0.179844i
$433$	−11.1314	+	2.98265i	−0.534940	+	0.143337i	−0.516169	−	0.856487i	$-0.672642\pi$
$433$	−11.1314	+	2.98265i	−0.534940	+	0.143337i	−0.0187717	+	0.999824i	$0.505976\pi$
$434$	24.2260	+	2.83161i	1.16288	+	0.135922i
$435$	−10.5473	+	3.82989i	−0.505705	+	0.183629i
$436$	−4.47011	−	1.05944i	−0.214080	−	0.0507378i
$437$	13.8932	−	12.3639i	0.664600	−	0.591443i
$438$	−12.4070	+	9.31131i	−0.592828	+	0.444911i
$439$	2.50394	+	10.5649i	0.119506	+	0.504237i	0.999568	+	0.0293782i	$0.00935270\pi$
$439$	2.50394	+	10.5649i	0.119506	+	0.504237i	−0.880062	+	0.474859i	$0.842499\pi$
$440$	−8.37721	+	3.28337i	−0.399368	+	0.156528i
$441$	−21.7824	+	1.43751i	−1.03726	+	0.0684531i
$442$	4.31853	+	6.16750i	0.205412	+	0.293358i
$443$	24.9707	+	22.2220i	1.18639	+	1.05580i	0.997270	+	0.0738464i	$0.0235275\pi$
$443$	24.9707	+	22.2220i	1.18639	+	1.05580i	0.189123	+	0.981953i	$0.439436\pi$
$444$	9.56495	−	13.7730i	0.453932	−	0.653639i
$445$	0.574511	+	10.7158i	0.0272344	+	0.507977i
$446$	1.75121	−	1.30373i	0.0829223	−	0.0617333i
$447$	7.60360	+	2.73429i	0.359638	+	0.129327i
$448$	−2.51189	+	2.82259i	−0.118676	+	0.133355i
$449$	−4.03438	+	22.8801i	−0.190394	+	1.07978i	0.728433	+	0.685117i	$0.240249\pi$
$449$	−4.03438	+	22.8801i	−0.190394	+	1.07978i	−0.918827	+	0.394661i	$0.870862\pi$
$450$	−7.13893	+	13.1923i	−0.336533	+	0.621889i
$451$	5.88611	+	33.3818i	0.277166	+	1.57189i
$452$	4.72754	+	2.91599i	0.222365	+	0.137157i
$453$	2.99343	−	7.01387i	0.140643	−	0.329540i
$454$	−4.46608	−	0.260119i	−0.209603	−	0.0122080i
$455$	9.14368	+	9.78180i	0.428663	+	0.458578i
$456$	−4.10556	+	10.4517i	−0.192261	+	0.489448i
$457$	23.6747	−	18.7195i	1.10745	−	0.875661i	0.114413	−	0.993433i	$-0.463501\pi$
$457$	23.6747	−	18.7195i	1.10745	−	0.875661i	0.993041	+	0.117773i	$0.0375754\pi$
$458$	−0.809092	−	3.01957i	−0.0378064	−	0.141095i
$459$	−23.7690	+	6.66485i	−1.10944	+	0.311089i
$460$	4.81143	−	4.24218i	0.224334	−	0.197792i
$461$	3.99434	−	1.72299i	0.186035	−	0.0802477i	−0.301025	−	0.953616i	$-0.597329\pi$
$461$	3.99434	−	1.72299i	0.186035	−	0.0802477i	0.487060	+	0.873369i	$0.338069\pi$
$462$	−25.2568	−	7.45526i	−1.17505	−	0.346850i
$463$	40.4482	−	1.17692i	1.87979	−	0.0546963i	0.929995	−	0.367572i	$-0.119811\pi$
$463$	40.4482	−	1.17692i	1.87979	−	0.0546963i	0.949794	+	0.312876i	$0.101292\pi$
$464$	−2.58911	+	1.30030i	−0.120196	+	0.0603648i
$465$	24.3316	−	5.74731i	1.12835	−	0.266525i
$466$	3.58143	−	11.9628i	0.165907	−	0.554166i
$467$	2.92945	+	0.256294i	0.135559	+	0.0118599i	0.154733	−	0.987956i	$-0.450548\pi$
$467$	2.92945	+	0.256294i	0.135559	+	0.0118599i	−0.0191743	+	0.999816i	$0.506104\pi$
$468$	3.33586	−	3.38778i	0.154200	−	0.156600i
$469$	37.0611	−	44.1678i	1.71132	−	2.03948i
$470$	0.0508416	−	11.0154i	0.00234515	−	0.508103i
$471$	−5.31411	−	19.5306i	−0.244861	−	0.899923i
$472$	−2.76466	+	3.49648i	−0.127254	+	0.160938i
$473$	16.5677	+	41.7034i	0.761784	+	1.91753i
$474$	−1.90168	+	4.11962i	−0.0873473	+	0.189221i
$475$	−32.3422	−	2.18345i	−1.48396	−	0.100184i
$476$	−6.13943	−	16.8679i	−0.281400	−	0.773141i
$477$	6.90202	+	16.9899i	0.316022	+	0.777915i
$478$	−1.72290	−	3.69477i	−0.0788035	−	0.168995i
$479$	27.7533	+	29.4168i	1.26808	+	1.34409i	0.912304	+	0.409514i	$0.134302\pi$
$479$	27.7533	+	29.4168i	1.26808	+	1.34409i	0.355776	+	0.934571i	$0.384217\pi$
$480$	−1.43265	+	3.59827i	−0.0653911	+	0.164238i
$481$	−12.8191	−	8.43123i	−0.584499	−	0.384431i
$482$	7.87627	−	14.6075i	0.358754	−	0.665352i
$483$	18.7376	−	1.16394i	0.852592	−	0.0529612i
$484$	−4.16434	−	3.10024i	−0.189288	−	0.140920i
$485$	1.32310	−	0.266837i	0.0600789	−	0.0121164i
$486$	6.85943	+	13.9982i	0.311150	+	0.634969i
$487$	13.3051	−	13.3051i	0.602910	−	0.602910i	−0.338174	−	0.941084i	$-0.609809\pi$
$487$	13.3051	−	13.3051i	0.602910	−	0.602910i	0.941084	+	0.338174i	$0.109809\pi$
$488$	0.773502	+	5.28065i	0.0350148	+	0.239044i
$489$	−11.7716	+	13.3310i	−0.532332	+	0.602847i
$490$	−7.65603	−	14.3572i	−0.345864	−	0.648594i
$491$	−7.89481	+	12.0035i	−0.356288	+	0.541709i	−0.968509	−	0.248977i	$-0.919906\pi$
$491$	−7.89481	+	12.0035i	−0.356288	+	0.541709i	0.612222	+	0.790686i	$0.290276\pi$
$492$	12.2211	+	7.97055i	0.550971	+	0.359340i
$493$	0.400331	−	13.7585i	0.0180300	−	0.619652i
$494$	9.65505	+	3.51415i	0.434401	+	0.158109i
$495$	−26.9424	+	1.65318i	−1.21097	+	0.0743051i
$496$	6.06598	−	2.20784i	0.272371	−	0.0991348i
$497$	−15.9374	−	48.0963i	−0.714890	−	2.15742i
$498$	21.3359	−	7.85903i	0.956082	−	0.352171i
$499$	23.8185	+	10.2743i	1.06626	+	0.459940i	0.855610	−	0.517621i	$-0.173182\pi$
$499$	23.8185	+	10.2743i	1.06626	+	0.459940i	0.210651	+	0.977561i	$0.432442\pi$
$500$	−11.1514	−	0.804557i	−0.498704	−	0.0359809i
$501$	−33.9628	+	9.24098i	−1.51735	+	0.412857i
$502$	−0.667723	+	3.23378i	−0.0298019	+	0.144331i
$503$	−23.4061	+	2.04777i	−1.04363	+	0.0913056i	−0.596056	−	0.802943i	$-0.703266\pi$
$503$	−23.4061	+	2.04777i	−1.04363	+	0.0913056i	−0.447571	+	0.894248i	$0.647711\pi$
$504$	−9.77262	+	5.74328i	−0.435307	+	0.255826i
$505$	−2.68517	−	23.9305i	−0.119489	−	1.06489i
$506$	11.0582	+	3.31061i	0.491597	+	0.147174i
$507$	13.2617	+	12.4154i	0.588974	+	0.551387i
$508$	−15.0911	−	5.00065i	−0.669560	−	0.221868i
$509$	12.0009	−	12.7202i	0.531929	−	0.563812i	−0.404559	−	0.914512i	$-0.632575\pi$
$509$	12.0009	−	12.7202i	0.531929	−	0.563812i	0.936488	+	0.350700i	$0.114056\pi$
$510$	−11.8164	−	14.1039i	−0.523240	−	0.624530i
$511$	−13.4033	−	31.0724i	−0.592928	−	1.37456i
$512$	−0.258819	+	0.965926i	−0.0114383	+	0.0426883i
$513$	−21.3536	+	26.0552i	−0.942785	+	1.15037i
$514$	−12.0506	−	6.95742i	−0.531529	−	0.306879i
$515$	0.987078	+	11.9155i	0.0434959	+	0.525060i
$516$	17.9783	+	7.06209i	0.791452	+	0.310891i
$517$	16.8716	−	10.4065i	0.742010	−	0.457679i
$518$	24.3184	+	27.3264i	1.06849	+	1.20065i
$519$	−16.1699	−	40.2486i	−0.709781	−	1.76672i
$520$	3.32443	+	1.22740i	0.145786	+	0.0538250i
$521$	−24.5689	+	4.33216i	−1.07638	+	0.189795i	−0.683615	−	0.729843i	$-0.739593\pi$
$521$	−24.5689	+	4.33216i	−1.07638	+	0.189795i	−0.392767	+	0.919638i	$0.628482\pi$
$522$	−8.59010	+	1.32609i	−0.375978	+	0.0580413i
$523$	18.3279	−	12.8333i	0.801423	−	0.561163i	−0.0995522	−	0.995032i	$-0.531741\pi$
$523$	18.3279	−	12.8333i	0.801423	−	0.561163i	0.900976	+	0.433870i	$0.142852\pi$
$524$	0.382720	+	6.57105i	0.0167192	+	0.287058i
$525$	−24.3272	−	21.8846i	−1.06172	−	0.955121i
$526$	0.769320	+	1.03338i	0.0335440	+	0.0450574i
$527$	−4.44471	+	30.3438i	−0.193614	+	1.32180i
$528$	−6.85897	+	1.23674i	−0.298498	+	0.0538223i
$529$	14.7458	−	0.858847i	0.641123	−	0.0373412i
$530$	−9.42575	+	9.89878i	−0.409428	+	0.429976i
$531$	−11.1153	+	7.43423i	−0.482364	+	0.322618i
$532$	−20.0662	−	14.0505i	−0.869979	−	0.609166i
$533$	7.00864	−	11.3627i	0.303578	−	0.492175i
$534$	−1.17296	+	8.22916i	−0.0507591	+	0.356111i
$535$	18.1201	−	2.56883i	0.783398	−	0.111060i
$536$	3.51907	−	14.8481i	0.152001	−	0.641342i
$537$	−2.67131	+	3.61726i	−0.115275	+	0.156096i
$538$	6.98458	+	8.83344i	0.301127	+	0.380837i
$539$	14.6401	−	25.3574i	0.630594	−	1.09222i
$540$	−7.40633	+	8.95244i	−0.318718	+	0.385252i
$541$	−4.65039	−	8.05471i	−0.199936	−	0.346299i	0.748572	−	0.663054i	$-0.230740\pi$
$541$	−4.65039	−	8.05471i	−0.199936	−	0.346299i	−0.948507	+	0.316755i	$0.897407\pi$
$542$	−7.53527	+	18.9674i	−0.323668	+	0.814720i
$543$	27.5890	+	29.0174i	1.18396	+	1.24526i
$544$	−3.45558	−	3.26017i	−0.148157	−	0.139779i
$545$	1.23963	−	10.1973i	0.0530998	−	0.436804i
$546$	5.47899	+	8.80653i	0.234479	+	0.376885i
$547$	16.7642	+	31.0912i	0.716787	+	1.32936i	0.935413	+	0.353556i	$0.115028\pi$
$547$	16.7642	+	31.0912i	0.716787	+	1.32936i	−0.218626	+	0.975809i	$0.570157\pi$
$548$	−0.456158	+	5.21391i	−0.0194861	+	0.222727i
$549$	−2.65846	+	15.7888i	−0.113460	+	0.673848i
$550$	−9.38481	−	17.7965i	−0.400170	−	0.758847i
$551$	−10.3217	−	15.6935i	−0.439721	−	0.668564i
$552$	4.29336	−	2.50092i	0.182737	−	0.106446i
$553$	−7.76430	−	6.13921i	−0.330171	−	0.261066i
$554$	8.37740	−	19.4210i	0.355921	−	0.825119i
$555$	32.9903	+	17.8203i	1.40036	+	0.756432i
$556$	1.97894	+	0.993861i	0.0839258	+	0.0421491i
$557$	−14.7477	−	6.87695i	−0.624878	−	0.291386i	0.0842720	−	0.996443i	$-0.473144\pi$
$557$	−14.7477	−	6.87695i	−0.624878	−	0.291386i	−0.709150	+	0.705057i	$0.750921\pi$
$558$	19.3527	−	0.712693i	0.819267	−	0.0301707i
$559$	6.04479	−	16.6079i	0.255667	−	0.702440i
$560$	−6.89845	−	4.87795i	−0.291513	−	0.206131i
$561$	10.2934	−	31.4702i	0.434589	−	1.32867i
$562$	23.5431	−	4.86126i	0.993106	−	0.205060i
$563$	29.3835	+	15.8435i	1.23837	+	0.667722i	0.956500	−	0.291731i	$-0.0942314\pi$
$563$	29.3835	+	15.8435i	1.23837	+	0.667722i	0.281867	+	0.959453i	$0.409046\pi$
$564$	1.69317	−	8.36292i	0.0712953	−	0.352142i
$565$	−5.30093	+	11.2322i	−0.223012	+	0.472544i
$566$			16.2869i			0.684589i
$567$	−33.1933	+	7.39003i	−1.39399	+	0.310352i
$568$	−9.48216	−	9.48216i	−0.397863	−	0.397863i
$569$	13.2114	−	17.7460i	0.553852	−	0.743952i	−0.433733	−	0.901042i	$-0.642804\pi$
$569$	13.2114	−	17.7460i	0.553852	−	0.743952i	0.987584	+	0.157090i	$0.0502112\pi$
$570$	−24.2487	−	6.51705i	−1.01567	−	0.272969i
$571$	−1.85571	−	6.19852i	−0.0776592	−	0.259400i	0.910339	−	0.413862i	$-0.135821\pi$
$571$	−1.85571	−	6.19852i	−0.0776592	−	0.259400i	−0.987999	+	0.154463i	$0.950635\pi$
$572$	1.28957	+	6.24540i	0.0539197	+	0.261133i
$573$	−32.6971	−	1.77776i	−1.36594	−	0.0742672i
$574$	−23.1517	+	21.8425i	−0.966333	+	0.911688i
$575$	10.6263	+	9.63385i	0.443148	+	0.401759i
$576$	−1.62913	+	2.51912i	−0.0678802	+	0.104963i
$577$	−7.27317	+	15.5974i	−0.302786	+	0.649327i	−0.997553	−	0.0699075i	$-0.977730\pi$
$577$	−7.27317	+	15.5974i	−0.302786	+	0.649327i	0.694767	+	0.719235i	$0.255507\pi$
$578$	5.28708	−	1.75195i	0.219914	−	0.0728715i
$579$	−29.8975	+	21.1069i	−1.24250	+	0.877174i
$580$	−3.53499	−	5.42910i	−0.146782	−	0.225431i
$581$	5.75832	+	49.2656i	0.238895	+	2.04388i
$582$	1.04550	−	0.00403616i	0.0433372	−	0.000167304i
$583$	−24.0890	−	4.97397i	−0.997663	−	0.206001i
$584$	−6.86074	−	5.75685i	−0.283900	−	0.238220i
$585$	8.35982	+	6.56799i	0.345636	+	0.271553i
$586$	1.98797	−	1.66811i	0.0821225	−	0.0689089i
$587$	12.8088	−	6.90644i	0.528675	−	0.285059i	−0.188355	−	0.982101i	$-0.560316\pi$
$587$	12.8088	−	6.90644i	0.528675	−	0.285059i	0.717031	+	0.697042i	$0.245501\pi$
$588$	−3.66129	−	12.0599i	−0.150989	−	0.497343i
$589$	18.7826	+	37.3992i	0.773922	+	1.54101i
$590$	−8.45894	−	5.27160i	−0.348249	−	0.217028i
$591$	−5.20254	−	3.18132i	−0.214004	−	0.130862i
$592$	8.99732	+	3.57441i	0.369788	+	0.146907i
$593$	40.0822	+	10.7400i	1.64598	+	0.441039i	0.958483	−	0.285149i	$-0.0920429\pi$
$593$	40.0822	+	10.7400i	1.64598	+	0.441039i	0.687497	+	0.726188i	$0.258710\pi$
$594$	−20.7217	−	2.79054i	−0.850220	−	0.114497i
$595$	35.9518	−	17.8484i	1.47388	−	0.731713i
$596$	−0.541592	+	4.63362i	−0.0221845	+	0.189800i
$597$	−0.240008	+	2.12449i	−0.00982286	+	0.0869498i
$598$	−2.38671	−	3.86944i	−0.0975997	−	0.158233i
$599$	1.78696	−	30.6809i	0.0730132	−	1.25359i	−0.740506	−	0.672050i	$-0.765414\pi$
$599$	1.78696	−	30.6809i	0.0730132	−	1.25359i	0.813519	−	0.581539i	$-0.197549\pi$
$600$	−8.35301	−	2.28633i	−0.341010	−	0.0933391i
$601$	−28.5504	+	6.76657i	−1.16459	+	0.276014i	−0.767061	−	0.641574i	$-0.778282\pi$
$601$	−28.5504	+	6.76657i	−1.16459	+	0.276014i	−0.397533	+	0.917588i	$0.630134\pi$
$602$	−24.1686	+	34.5164i	−0.985039	+	1.40678i
$603$	23.7310	−	39.1471i	0.966402	−	1.59419i
$604$	4.33595	+	0.764545i	0.176427	+	0.0311089i
$605$	5.85078	−	10.0267i	0.237868	−	0.407642i
$606$	1.55395	−	18.5879i	0.0631249	−	0.755084i
$607$	13.8994	+	2.03596i	0.564158	+	0.0826369i	0.420996	−	0.907062i	$-0.361681\pi$
$607$	13.8994	+	2.03596i	0.564158	+	0.0826369i	0.143161	+	0.989699i	$0.454273\pi$
$608$	−6.41472	−	0.939618i	−0.260151	−	0.0381065i
$609$	1.57964	−	18.8952i	0.0640102	−	0.765673i
$610$	−11.5414	+	3.03548i	−0.467297	+	0.122903i
$611$	−7.68871	−	1.35573i	−0.311052	−	0.0548468i
$612$	−6.86080	−	12.4923i	−0.277332	−	0.504971i
$613$	6.18452	−	8.83241i	0.249790	−	0.356738i	−0.674601	−	0.738182i	$-0.735684\pi$
$613$	6.18452	−	8.83241i	0.249790	−	0.356738i	0.924392	+	0.381445i	$0.124573\pi$
$614$	20.0078	−	4.74194i	0.807450	−	0.191369i
$615$	−14.6643	+	29.1442i	−0.591323	+	1.17521i
$616$	0.884034	−	15.1783i	0.0356188	−	0.611550i
$617$	−6.36057	−	10.3120i	−0.256067	−	0.415147i	0.697383	−	0.716698i	$-0.254348\pi$
$617$	−6.36057	−	10.3120i	−0.256067	−	0.415147i	−0.953450	+	0.301551i	$0.902496\pi$
$618$	−1.03966	+	9.20280i	−0.0418211	+	0.370191i
$619$	−0.222926	+	1.90726i	−0.00896016	+	0.0766591i	−0.996979	−	0.0776769i	$-0.975250\pi$
$619$	−0.222926	+	1.90726i	−0.00896016	+	0.0766591i	0.988018	+	0.154336i	$0.0493238\pi$
$620$	6.41857	+	12.9289i	0.257776	+	0.519236i
$621$	14.5621	−	3.18311i	0.584358	−	0.127734i
$622$	25.0858	+	6.72172i	1.00585	+	0.269516i
$623$	−16.8521	−	6.69490i	−0.675164	−	0.268225i
$624$	2.34186	+	1.43203i	0.0937493	+	0.0573270i
$625$	−0.992634	−	24.9803i	−0.0397054	−	0.999211i
$626$	−0.360885	−	0.718581i	−0.0144239	−	0.0287203i
$627$	−13.1262	−	43.2363i	−0.524210	−	1.72669i
$628$	10.2860	−	5.54616i	0.410456	−	0.221316i
$629$	−35.2333	+	29.5642i	−1.40484	+	1.17880i
$630$	−15.1990	−	20.2839i	−0.605542	−	0.808132i
$631$	−33.1568	−	27.8218i	−1.31995	−	1.10757i	−0.986316	−	0.164866i	$-0.947281\pi$
$631$	−33.1568	−	27.8218i	−1.31995	−	1.10757i	−0.333634	−	0.942703i	$-0.608275\pi$
$632$	−2.56553	−	0.529739i	−0.102051	−	0.0210719i
$633$	46.0657	−	0.177837i	1.83095	−	0.00706841i
$634$	−0.785380	−	6.71935i	−0.0311914	−	0.266860i
$635$	7.34927	−	34.7812i	0.291647	−	1.38025i
$636$	−8.64939	+	6.10626i	−0.342971	+	0.242129i
$637$	−10.9468	+	3.62737i	−0.433728	+	0.143722i
$638$	4.92702	−	10.5660i	0.195063	−	0.418313i
$639$	−18.3320	−	35.8098i	−0.725201	−	1.41662i
$640$	−2.21094	−	0.334286i	−0.0873951	−	0.0132138i
$641$	14.9497	−	14.1043i	0.590478	−	0.557087i	−0.331930	−	0.943304i	$-0.607700\pi$
$641$	14.9497	−	14.1043i	0.590478	−	0.557087i	0.922408	+	0.386217i	$0.126218\pi$
$642$	14.1552	+	0.769626i	0.558660	+	0.0303747i
$643$	1.87862	+	9.09818i	0.0740856	+	0.358797i	0.999812	−	0.0193973i	$-0.00617473\pi$
$643$	1.87862	+	9.09818i	0.0740856	+	0.358797i	−0.925726	+	0.378194i	$0.876545\pi$
$644$	3.10867	+	10.3837i	0.122499	+	0.409174i
$645$	−11.2102	+	41.7109i	−0.441400	+	1.64236i
$646$	18.3925	−	24.7054i	0.723643	−	0.972022i
$647$	−3.03952	−	3.03952i	−0.119496	−	0.119496i	0.644830	−	0.764326i	$-0.276928\pi$
$647$	−3.03952	−	3.03952i	−0.119496	−	0.119496i	−0.764326	+	0.644830i	$0.776928\pi$
$648$	−6.97270	+	5.69047i	−0.273914	+	0.223543i
$649$		−	17.9362i		−	0.704057i
$650$	−1.89852	+	7.69333i	−0.0744663	+	0.301757i
$651$	−8.38316	+	41.4062i	−0.328562	+	1.62284i
$652$	−9.03777	−	4.87312i	−0.353946	−	0.190846i
$653$	−18.5206	+	3.82419i	−0.724766	+	0.149652i	−0.550247	−	0.835002i	$-0.685467\pi$
$653$	−18.5206	+	3.82419i	−0.724766	+	0.149652i	−0.174519	+	0.984654i	$0.555837\pi$
$654$	2.47364	−	7.56268i	0.0967269	−	0.295724i
$655$	−14.5062	+	2.48886i	−0.566806	+	0.0972480i
$656$	−2.88114	+	7.91587i	−0.112490	+	0.309063i
$657$	−14.2813	−	22.7584i	−0.557167	−	0.887889i
$658$	16.8698	+	7.86650i	0.657652	+	0.306668i
$659$	−6.63044	−	3.32993i	−0.258285	−	0.129716i	0.314945	−	0.949110i	$-0.398014\pi$
$659$	−6.63044	−	3.32993i	−0.258285	−	0.129716i	−0.573231	+	0.819394i	$0.694310\pi$
$660$	−4.45839	−	14.9331i	−0.173543	−	0.581270i
$661$	13.4699	−	31.2267i	0.523917	−	1.21458i	−0.426752	−	0.904369i	$-0.640342\pi$
$661$	13.4699	−	31.2267i	0.523917	−	1.21458i	0.950669	−	0.310207i	$-0.100399\pi$
$662$	8.27550	+	6.54342i	0.321637	+	0.254317i
$663$	−11.2684	+	6.56397i	−0.437630	+	0.254923i
$664$	7.21360	+	10.9678i	0.279942	+	0.425631i
$665$	26.2186	−	48.0928i	1.01672	−	1.86496i
$666$	22.3925	+	18.4968i	0.867690	+	0.716736i
$667$	−0.724378	+	8.27968i	−0.0280480	+	0.320590i
$668$	−9.64451	−	17.8869i	−0.373157	−	0.692063i
$669$	1.99758	+	3.21077i	0.0772310	+	0.124135i
$670$	33.8718	+	4.11760i	1.30858	+	0.159077i
$671$	−15.6207	−	14.7374i	−0.603030	−	0.568930i
$672$	−4.50942	−	4.74289i	−0.173955	−	0.182961i
$673$	1.65351	−	4.16212i	0.0637380	−	0.160438i	−0.894010	−	0.448047i	$-0.852120\pi$
$673$	1.65351	−	4.16212i	0.0637380	−	0.160438i	0.957748	+	0.287609i	$0.0928604\pi$
$674$	−16.0938	−	27.8753i	−0.619910	−	1.07372i
$675$	−21.7401	−	14.2256i	−0.836777	−	0.547544i
$676$	−5.24417	+	9.08316i	−0.201699	+	0.349352i
$677$	−10.0988	−	12.7720i	−0.388129	−	0.490870i	0.550965	−	0.834528i	$-0.314260\pi$
$677$	−10.0988	−	12.7720i	−0.388129	−	0.490870i	−0.939095	+	0.343658i	$0.888334\pi$
$678$	−5.71525	+	7.73910i	−0.219493	+	0.297218i
$679$	−0.525976	+	2.21927i	−0.0201851	+	0.0851677i
$680$	6.38290	−	8.49162i	0.244773	−	0.325639i
$681$	1.09341	−	7.67105i	0.0418996	−	0.293955i
$682$	−13.6364	+	22.1080i	−0.522166	+	0.846560i
$683$	22.7849	+	15.9542i	0.871841	+	0.610469i	0.921535	−	0.388295i	$-0.126936\pi$
$683$	22.7849	+	15.9542i	0.871841	+	0.610469i	−0.0496945	+	0.998764i	$0.515825\pi$
$684$	−17.4476	−	8.59447i	−0.667126	−	0.328618i
$685$	−11.6997	+	0.286388i	−0.447022	+	0.0109423i
$686$	1.04337	−	0.0607693i	0.0398360	−	0.00232018i
$687$	5.32862	−	0.960805i	0.203300	−	0.0366570i
$688$	−1.61626	+	11.0341i	−0.0616194	+	0.420672i
$689$	5.78509	+	7.77072i	0.220394	+	0.296041i
$690$	6.62785	+	8.91680i	0.252318	+	0.339457i
$691$	0.00327520	+	0.0562330i	0.000124594	+	0.00213920i	0.998370	−	0.0570752i	$-0.0181775\pi$
$691$	0.00327520	+	0.0562330i	0.000124594	+	0.00213920i	−0.998245	+	0.0592144i	$0.981140\pi$
$692$	20.5138	−	14.3639i	0.779818	−	0.546034i
$693$	16.5124	−	42.5182i	0.627256	−	1.61513i
$694$	17.2252	−	3.03726i	0.653858	−	0.115293i
$695$	−1.71506	+	4.64526i	−0.0650558	+	0.176205i
$696$	−1.87076	−	4.65650i	−0.0709108	−	0.176504i
$697$	−26.6051	−	29.8959i	−1.00774	−	1.13239i
$698$	6.09692	−	3.76064i	0.230772	−	0.142342i
$699$	20.1314	+	7.90784i	0.761439	+	0.299102i
$700$	9.11936	−	16.5455i	0.344679	−	0.625360i
$701$	17.1925	+	9.92609i	0.649352	+	0.374903i	0.788208	−	0.615409i	$-0.211009\pi$
$701$	17.1925	+	9.92609i	0.649352	+	0.374903i	−0.138856	+	0.990313i	$0.544343\pi$
$702$	5.36605	+	6.24664i	0.202529	+	0.235764i
$703$	−16.2450	+	60.6270i	−0.612690	+	2.28659i
$704$	−1.59378	−	3.69480i	−0.0600678	−	0.139253i
$705$	19.0056	+	1.67723i	0.715792	+	0.0631683i
$706$	1.12053	−	1.18769i	0.0421715	−	0.0446992i
$707$	38.6254	+	12.7991i	1.45266	+	0.481358i
$708$	−5.63609	−	5.27641i	−0.211817	−	0.198299i
$709$	1.80222	+	0.539548i	0.0676837	+	0.0202632i	0.320466	−	0.947260i	$-0.396160\pi$
$709$	1.80222	+	0.539548i	0.0676837	+	0.0202632i	−0.252782	+	0.967523i	$0.581346\pi$
$710$	18.7063	−	23.4348i	0.702034	−	0.879492i
$711$	−6.83619	−	3.87681i	−0.256377	−	0.145392i
$712$	−4.78087	+	0.418272i	−0.179171	+	0.0156754i
$713$	3.74466	−	18.1354i	0.140239	−	0.679177i
$714$	30.0005	−	8.16286i	1.12274	−	0.305487i
$715$	−13.5565	+	4.42280i	−0.506985	+	0.165404i
$716$	−2.38385	−	1.02829i	−0.0890888	−	0.0384292i
$717$	6.62588	−	2.44063i	0.247448	−	0.0911471i
$718$	−4.68366	−	14.1345i	−0.174792	−	0.527494i
$719$	−25.5188	+	9.28807i	−0.951689	+	0.346387i	−0.770772	−	0.637112i	$-0.780129\pi$
$719$	−25.5188	+	9.28807i	−0.951689	+	0.346387i	−0.180918	+	0.983498i	$0.557907\pi$
$720$	−6.00399	−	2.99201i	−0.223756	−	0.111505i
$721$	−18.9850	−	6.90999i	−0.707039	−	0.257341i
$722$	0.669865	−	23.0218i	0.0249298	−	0.856781i
$723$	24.0764	+	15.7025i	0.895411	+	0.583981i
$724$	−12.7029	+	19.3138i	−0.472100	+	0.717793i
$725$	11.1827	−	9.20886i	0.415316	−	0.342008i
$726$	5.95200	−	6.74042i	0.220899	−	0.250160i
$727$	−1.19475	−	8.15649i	−0.0443108	−	0.302507i	−0.999968	−	0.00802532i	$-0.997445\pi$
$727$	−1.19475	−	8.15649i	−0.0443108	−	0.302507i	0.955657	−	0.294482i	$-0.0951472\pi$
$728$	−4.23427	+	4.23427i	−0.156933	+	0.156933i
$729$	−25.1510	+	9.81970i	−0.931519	+	0.363693i
$730$	11.0818	−	16.6808i	0.410155	−	0.617385i
$731$	−42.4965	−	31.6375i	−1.57179	−	1.17015i
$732$	−9.22617	+	0.573110i	−0.341009	+	0.0211828i
$733$	−16.1929	+	30.0315i	−0.598097	+	1.10924i	0.384436	+	0.923152i	$0.374396\pi$
$733$	−16.1929	+	30.0315i	−0.598097	+	1.10924i	−0.982533	+	0.186089i	$0.940419\pi$
$734$	−6.05588	−	3.98302i	−0.223527	−	0.147016i
$735$	25.8857	−	11.1428i	0.954810	−	0.411010i
$736$	1.96859	+	2.08658i	0.0725632	+	0.0769125i
$737$	25.9497	+	55.6493i	0.955870	+	2.04987i
$738$	−15.5209	+	19.9439i	−0.571331	+	0.734146i
$739$	2.29616	+	6.30865i	0.0844656	+	0.232067i	0.974734	−	0.223369i	$-0.0717055\pi$
$739$	2.29616	+	6.30865i	0.0844656	+	0.232067i	−0.890268	+	0.455436i	$0.849483\pi$
$740$	−5.69939	+	20.8844i	−0.209514	+	0.767725i
$741$	−7.45871	+	16.1578i	−0.274003	+	0.593572i
$742$	−8.52747	−	21.4649i	−0.313053	−	0.788003i
$743$	9.48244	−	11.9925i	0.347877	−	0.439962i	−0.579000	−	0.815328i	$-0.696557\pi$
$743$	9.48244	−	11.9925i	0.347877	−	0.439962i	0.926877	+	0.375365i	$0.122483\pi$
$744$	2.93550	+	10.7887i	0.107621	+	0.395531i
$745$	−10.4315	−	0.0481465i	−0.382181	−	0.00176395i
$746$	−13.3653	+	15.9281i	−0.489338	+	0.583170i
$747$	10.4862	+	37.9603i	0.383671	+	1.38890i
$748$	19.0438	+	1.66612i	0.696310	+	0.0609192i
$749$	−8.86936	+	29.6257i	−0.324079	+	1.08250i
$750$	2.99778	−	19.1315i	0.109464	−	0.698583i
$751$	−35.1852	+	17.6707i	−1.28393	+	0.644813i	−0.954174	−	0.299254i	$-0.903262\pi$
$751$	−35.1852	+	17.6707i	−1.28393	+	0.644813i	−0.329754	+	0.944067i	$0.606966\pi$
$752$	4.92421	−	0.143280i	0.179568	−	0.00522488i
$753$	−5.48526	−	1.61913i	−0.199894	−	0.0590044i
$754$	−4.21616	+	1.81867i	−0.153543	+	0.0662322i
$755$	−0.617795	+	9.82564i	−0.0224839	+	0.357592i
$756$	−8.50293	−	17.6966i	−0.309249	−	0.643618i
$757$	10.1392	+	37.8401i	0.368516	+	1.37532i	0.862591	+	0.505902i	$0.168840\pi$
$757$	10.1392	+	37.8401i	0.368516	+	1.37532i	−0.494074	+	0.869420i	$0.664493\pi$
$758$	−18.8902	+	14.9364i	−0.686122	+	0.542515i
$759$	−7.30986	+	18.6091i	−0.265331	+	0.675467i
$760$	0.488512	−	14.4886i	0.0177202	−	0.525556i
$761$	−38.1383	−	2.22130i	−1.38251	−	0.0805222i	−0.649305	−	0.760528i	$-0.724940\pi$
$761$	−38.1383	−	2.22130i	−1.38251	−	0.0805222i	−0.733207	+	0.680006i	$0.761977\pi$
$762$	10.8089	−	25.3261i	0.391564	−	0.917469i
$763$	14.7736	+	9.11251i	0.534841	+	0.329895i
$764$	−3.28292	−	18.6184i	−0.118772	−	0.673589i
$765$	26.0488	−	18.3604i	0.941795	−	0.663820i
$766$	1.80329	−	10.2270i	0.0651556	−	0.369516i
$767$	−4.69628	+	5.27717i	−0.169573	+	0.190547i
$768$	−1.62987	−	0.586109i	−0.0588129	−	0.0211494i
$769$	−18.6289	+	13.8687i	−0.671774	+	0.500117i	−0.878168	−	0.478352i	$-0.841234\pi$
$769$	−18.6289	+	13.8687i	−0.671774	+	0.500117i	0.206395	+	0.978469i	$0.433827\pi$
$770$	33.9484	−	1.82009i	1.22342	−	0.0655916i
$771$	13.7476	−	19.7958i	0.495106	−	0.712927i
$772$	−15.7842	−	14.0468i	−0.568087	−	0.505555i
$773$	4.33759	+	6.19471i	0.156012	+	0.222808i	0.889547	−	0.456843i	$-0.151020\pi$
$773$	4.33759	+	6.19471i	0.156012	+	0.222808i	−0.733535	+	0.679651i	$0.762131\pi$
$774$	−14.7836	+	30.0121i	−0.531385	+	1.07876i
$775$	−27.1291	+	17.4865i	−0.974507	+	0.628134i
$776$	0.139205	+	0.587351i	0.00499716	+	0.0210847i
$777$	−50.6753	+	38.0313i	−1.81796	+	1.36436i
$778$	1.22141	−	1.08696i	0.0437896	−	0.0389695i
$779$	−53.1414	−	12.5947i	−1.90399	−	0.451254i
$780$	−2.59823	+	5.56096i	−0.0930315	+	0.199114i
$781$	53.5946	+	6.26431i	1.91777	+	0.224155i
$782$	−13.1639	+	3.52727i	−0.470741	+	0.126135i
$783$	−1.04935	−	15.0181i	−0.0375008	−	0.536704i
$784$	6.30173	−	3.63830i	0.225062	−	0.129939i
$785$	14.8889	+	21.4739i	0.531409	+	0.766435i
$786$	−11.3970	−	0.287589i	−0.406519	−	0.0102580i
$787$	−1.46060	−	50.1977i	−0.0520649	−	1.78936i	−0.471797	−	0.881707i	$-0.656394\pi$
$787$	−1.46060	−	50.1977i	−0.0520649	−	1.78936i	0.419732	−	0.907648i	$-0.362124\pi$
$788$	1.10744	−	3.34205i	0.0394508	−	0.119056i
$789$	−1.89465	+	1.17876i	−0.0674513	+	0.0419649i
$790$	0.537461	−	5.83301i	0.0191220	−	0.207529i
$791$	−13.4904	−	16.0773i	−0.479664	−	0.571642i
$792$	−1.14493	−	12.0172i	−0.0406834	−	0.427014i
$793$	0.737182	+	8.42602i	0.0261781	+	0.299217i
$794$	0.658345	−	0.433000i	0.0233638	−	0.0153666i
$795$	−15.7255	−	17.6975i	−0.557726	−	0.627665i
$796$	−1.22603	+	0.143303i	−0.0434556	+	0.00507923i
$797$	−18.7476	+	7.44795i	−0.664074	+	0.263820i	−0.676875	−	0.736098i	$-0.736666\pi$
$797$	−18.7476	+	7.44795i	−0.664074	+	0.263820i	0.0128004	+	0.999918i	$0.495925\pi$
$798$	27.1470	−	32.6074i	0.960994	−	1.15429i
$799$	−10.5036	+	20.9143i	−0.371589	+	0.739895i
$800$	0.191552	−	4.99633i	0.00677238	−	0.176647i
$801$	−14.0345	−	3.21200i	−0.495886	−	0.113491i
$802$	−23.0474	+	10.7472i	−0.813833	+	0.379496i
$803$	36.0229	+	1.04816i	1.27122	+	0.0369888i
$804$	25.1205	+	8.21655i	0.885933	+	0.289775i
$805$	−22.2987	+	9.49690i	−0.785926	+	0.334722i
$806$	9.80071	−	2.93414i	0.345215	−	0.103351i
$807$	−16.2546	+	10.7810i	−0.572190	+	0.379508i
$808$	10.6555	−	1.56080i	0.374859	−	0.0549087i
$809$	31.8396			1.11942			0.559710	−	0.828688i	$-0.310912\pi$
$809$	31.8396			1.11942			0.559710	+	0.828688i	$0.310912\pi$
$810$	−14.3835	−	14.0754i	−0.505384	−	0.494558i
$811$	33.1968			1.16570			0.582849	−	0.812580i	$-0.301938\pi$
$811$	33.1968			1.16570			0.582849	+	0.812580i	$0.301938\pi$
$812$	10.8316	−	1.58660i	0.380116	−	0.0556787i
$813$	−31.6510	−	15.7430i	−1.11005	−	0.552132i
$814$	−37.3200	+	11.1729i	−1.30806	+	0.391609i
$815$	8.57522	−	21.2981i	0.300377	−	0.746040i
$816$	6.12578	−	5.49401i	0.214445	−	0.192329i
$817$	−72.2690	−	2.10281i	−2.52837	−	0.0735681i
$818$	17.3580	−	8.09415i	0.606907	−	0.283005i
$819$	−15.9909	+	8.18616i	−0.558768	+	0.286047i
$820$	−18.3084	−	4.42852i	−0.639357	−	0.154651i
$821$	6.34445	−	12.6328i	0.221423	−	0.440889i	−0.755304	−	0.655374i	$-0.772511\pi$
$821$	6.34445	−	12.6328i	0.221423	−	0.440889i	0.976727	+	0.214485i	$0.0688072\pi$
$822$	−8.93354	−	1.53969i	−0.311593	−	0.0537028i
$823$	29.8704	−	11.8667i	1.04122	−	0.413649i	0.214770	−	0.976665i	$-0.431100\pi$
$823$	29.8704	−	11.8667i	1.04122	−	0.413649i	0.826446	+	0.563016i	$0.190359\pi$
$824$	−5.31088	+	0.620753i	−0.185013	+	0.0216250i
$825$	32.0715	−	13.6305i	1.11659	−	0.474553i
$826$	14.0714	−	9.25490i	0.489606	−	0.322019i
$827$	−4.82430	−	55.1420i	−0.167757	−	1.91748i	−0.354480	−	0.935063i	$-0.615342\pi$
$827$	−4.82430	−	55.1420i	−0.167757	−	1.91748i	0.186723	−	0.982413i	$-0.440213\pi$
$828$	3.69715	+	7.77134i	0.128485	+	0.270073i
$829$	12.6345	+	15.0572i	0.438815	+	0.522960i	0.939444	−	0.342702i	$-0.111342\pi$
$829$	12.6345	+	15.0572i	0.438815	+	0.522960i	−0.500629	+	0.865662i	$0.666898\pi$
$830$	−22.5731	+	18.7642i	−0.783522	+	0.651315i
$831$	32.3124	+	17.2620i	1.12090	+	0.598812i
$832$	−0.498498	+	1.50438i	−0.0172823	+	0.0521551i
$833$	1.00544	+	34.5548i	0.0348365	+	1.19725i
$834$	−2.00099	+	3.27230i	−0.0692885	+	0.113311i
$835$	37.3421	−	25.8912i	1.29228	−	0.896001i
$836$	22.5925	−	13.0438i	0.781377	−	0.451128i
$837$	−1.56239	+	33.5062i	−0.0540042	+	1.15815i
$838$	−15.5027	+	4.15395i	−0.535533	+	0.143496i
$839$	−12.4232	−	1.45206i	−0.428895	−	0.0501306i	−0.101093	−	0.994877i	$-0.532234\pi$
$839$	−12.4232	−	1.45206i	−0.428895	−	0.0501306i	−0.327802	+	0.944746i	$0.606308\pi$
$840$	9.41491	−	11.2031i	0.324845	−	0.386542i
$841$	−20.0503	−	4.75201i	−0.691390	−	0.163863i
$842$	−22.5946	+	20.1075i	−0.778661	+	0.692949i
$843$	4.99350	+	41.3376i	0.171985	+	1.42374i
$844$	6.13351	+	25.8793i	0.211124	+	0.890803i
$845$	−21.4915	−	9.38840i	−0.739329	−	0.322971i
$846$	14.1903	+	4.12919i	0.487874	+	0.141965i
$847$	11.2515	+	16.0687i	0.386605	+	0.552129i
$848$	−4.56640	−	4.06375i	−0.156811	−	0.139550i
$849$	−28.1116	−	2.35013i	−0.964789	−	0.0806563i
$850$	20.4609	+	12.0663i	0.701804	+	0.413871i
$851$	22.2769	−	16.5845i	0.763641	−	0.568510i
$852$	17.7347	−	14.9983i	0.607582	−	0.513832i
$853$	−29.0070	+	32.5949i	−0.993182	+	1.11603i	6.37364e−5		1.00000i	$0.499980\pi$
$853$	−29.0070	+	32.5949i	−0.993182	+	1.11603i	−0.993246	+	0.116030i	$0.962983\pi$
$854$	3.50171	−	19.8592i	0.119826	−	0.679567i
$855$	14.7476	−	40.9136i	0.504358	−	1.39922i
$856$	1.42123	+	8.06022i	0.0485768	+	0.275493i
$857$	7.32627	+	4.51891i	0.250260	+	0.154363i	0.644402	−	0.764687i	$-0.277106\pi$
$857$	7.32627	+	4.51891i	0.250260	+	0.154363i	−0.394142	+	0.919050i	$0.628958\pi$
$858$	−10.9658	+	1.32465i	−0.374367	+	0.0452229i
$859$	27.2265	+	1.58576i	0.928957	+	0.0541056i	0.515947	−	0.856621i	$-0.327440\pi$
$859$	27.2265	+	1.58576i	0.928957	+	0.0541056i	0.413010	+	0.910726i	$0.364477\pi$
$860$	−24.9222	−	0.840303i	−0.849840	−	0.0286541i
$861$	−34.3601	−	43.1123i	−1.17099	−	1.46926i
$862$	−13.5596	+	10.7215i	−0.461841	+	0.365177i
$863$	−12.7266	−	47.4962i	−0.433218	−	1.61679i	−0.745295	−	0.666734i	$-0.767692\pi$
$863$	−12.7266	−	47.4962i	−0.433218	−	1.61679i	0.312078	−	0.950057i	$-0.398975\pi$
$864$	−4.11299	−	3.17542i	−0.139927	−	0.108030i
$865$	37.0333	+	42.0027i	1.25917	+	1.42814i
$866$	10.5816	−	4.56445i	0.359577	−	0.155106i
$867$	2.26101	+	9.37846i	0.0767880	+	0.318509i
$868$	−24.3806	+	0.709403i	−0.827531	+	0.0240787i
$869$	9.41993	−	4.73087i	0.319549	−	0.160484i
$870$	9.88087	−	5.31809i	0.334993	−	0.180300i
$871$	6.93592	−	23.1676i	0.235015	−	0.785004i
$872$	4.57646	+	0.400389i	0.154979	+	0.0135589i
$873$	−0.143894	+	1.80514i	−0.00487008	+	0.0610947i
$874$	−11.9545	+	14.2469i	−0.404369	+	0.481908i
$875$	39.0399	+	16.1389i	1.31979	+	0.545595i
$876$	10.9265	−	11.0112i	0.369171	−	0.372033i
$877$	35.0494	−	44.3271i	1.18353	−	1.49682i	0.356842	−	0.934165i	$-0.383854\pi$
$877$	35.0494	−	44.3271i	1.18353	−	1.49682i	0.826691	−	0.562656i	$-0.190220\pi$
$878$	−4.00869	−	10.0905i	−0.135287	−	0.340537i
$879$	2.59235	+	3.67200i	0.0874377	+	0.123854i
$880$	7.81290	−	4.46283i	0.263373	−	0.150442i
$881$	3.23585	+	8.89044i	0.109019	+	0.299526i	0.982191	−	0.187885i	$-0.0601633\pi$
$881$	3.23585	+	8.89044i	0.109019	+	0.299526i	−0.873172	+	0.487412i	$0.837941\pi$
$882$	21.3441	−	4.57931i	0.718693	−	0.154193i
$883$	−13.9121	−	29.8345i	−0.468178	−	1.00401i	−0.988665	−	0.150141i	$-0.952027\pi$
$883$	−13.9121	−	29.8345i	−0.468178	−	1.00401i	0.520487	−	0.853870i	$-0.325751\pi$
$884$	−5.16680	−	5.47649i	−0.173778	−	0.184194i
$885$	10.3195	−	13.8397i	0.346887	−	0.465217i
$886$	−27.9277	−	18.3683i	−0.938250	−	0.617096i
$887$	−5.89465	+	10.9323i	−0.197923	+	0.367071i	−0.959815	−	0.280633i	$-0.909456\pi$
$887$	−5.89465	+	10.9323i	−0.197923	+	0.367071i	0.761892	+	0.647704i	$0.224271\pi$
$888$	−7.46781	+	15.0139i	−0.250603	+	0.503832i
$889$	48.1834	+	35.8712i	1.61602	+	1.20308i
$890$	−2.12150	−	10.5194i	−0.0711130	−	0.352611i
$891$	7.80661	−	35.3635i	0.261531	−	1.18472i
$892$	−1.54377	+	1.54377i	−0.0516892	+	0.0516892i
$893$	4.62884	+	31.6008i	0.154898	+	1.05748i
$894$	−7.91961	−	1.60342i	−0.264871	−	0.0536262i
$895$	1.69061	−	5.55361i	0.0565109	−	0.185637i
$896$	2.07629	−	3.15684i	0.0693639	−	0.105463i
$897$	7.02317	−	3.56118i	0.234497	−	0.118904i
$898$	0.675726	−	23.2232i	0.0225493	−	0.774969i
$899$	−17.5749	−	6.39673i	−0.586155	−	0.213343i
$900$	5.15158	−	14.0876i	0.171719	−	0.469588i
$901$	27.2891	−	9.93241i	0.909130	−	0.330896i
$902$	−10.6620	−	32.1763i	−0.355007	−	1.07135i
$903$	−56.0888	−	46.6963i	−1.86652	−	1.55396i
$904$	−5.10024	−	2.20003i	−0.169631	−	0.0731719i
$905$	−46.0850	−	23.4117i	−1.53192	−	0.778233i
$906$	−1.94529	+	7.37366i	−0.0646278	+	0.244973i
$907$	−4.98875	+	24.1605i	−0.165649	+	0.802237i	0.810603	+	0.585596i	$0.199140\pi$
$907$	−4.98875	+	24.1605i	−0.165649	+	0.802237i	−0.976251	+	0.216641i	$0.930490\pi$
$908$	4.45662	−	0.389904i	0.147898	−	0.0129394i
$909$	31.8591	+	5.36433i	1.05670	+	0.177924i
$910$	−10.4648	−	8.35330i	−0.346906	−	0.276909i
$911$	−37.3911	−	11.1941i	−1.23882	−	0.370879i	−0.400622	−	0.916243i	$-0.631206\pi$
$911$	−37.3911	−	11.1941i	−1.23882	−	0.370879i	−0.838199	+	0.545365i	$0.816391\pi$
$912$	2.54743	−	10.9364i	0.0843537	−	0.362141i
$913$	−50.1418	−	16.6152i	−1.65945	−	0.549883i
$914$	−20.7116	+	21.9531i	−0.685080	+	0.726142i
$915$	−3.57396	−	20.3588i	−0.118151	−	0.673041i
$916$	1.23818	+	2.87043i	0.0409107	+	0.0948416i
$917$	6.43693	−	24.0229i	0.212566	−	0.793307i
$918$	22.5521	−	10.0394i	0.744329	−	0.331348i
$919$	−25.0784	−	14.4790i	−0.827261	−	0.477619i	0.0256532	−	0.999671i	$-0.491833\pi$
$919$	−25.0784	−	14.4790i	−0.827261	−	0.477619i	−0.852914	+	0.522052i	$0.825167\pi$
$920$	−4.14580	+	4.89471i	−0.136683	+	0.161374i
$921$	5.29768	+	35.2183i	0.174565	+	1.16048i
$922$	−3.70245	+	2.28371i	−0.121934	+	0.0752098i
$923$	−14.1284	−	15.8759i	−0.465041	−	0.522562i
$924$	26.0706	+	3.71603i	0.857660	+	0.122249i
$925$	−47.8287	−	7.45748i	−1.57260	−	0.245200i
$926$	−39.8506	+	7.02674i	−1.30957	+	0.230913i
$927$	−15.7343	−	3.12240i	−0.516782	−	0.102553i
$928$	2.37332	−	1.66181i	0.0779079	−	0.0545517i
$929$	−0.611485	−	10.4988i	−0.0200622	−	0.344454i	−0.993371	−	0.114954i	$-0.963328\pi$
$929$	−0.611485	−	10.4988i	−0.0200622	−	0.344454i	0.973309	−	0.229500i	$-0.0737091\pi$
$930$	−23.2418	+	9.21306i	−0.762128	+	0.302108i
$931$	28.1712	+	37.8405i	0.923275	+	1.24017i
$932$	−1.80982	+	12.3556i	−0.0592827	+	0.404720i
$933$	−15.2217	+	42.3289i	−0.498335	+	1.38579i
$934$	−2.93567	+	0.170983i	−0.0960580	+	0.00559474i
$935$	1.04603	+	42.7331i	0.0342089	+	1.39752i
$936$	−2.80964	+	3.83548i	−0.0918361	+	0.125367i
$937$	29.1415	+	20.4051i	0.952012	+	0.666606i	0.942803	−	0.333351i	$-0.108180\pi$
$937$	29.1415	+	20.4051i	0.952012	+	0.666606i	0.00920959	+	0.999958i	$0.497068\pi$
$938$	−30.2685	+	49.0728i	−0.988302	+	1.60228i
$939$	1.29237	−	0.519210i	0.0421748	−	0.0169438i
$940$	1.54618	+	10.9065i	0.0504308	+	0.355730i
$941$	−0.0919764	+	0.388079i	−0.00299834	+	0.0126510i	−0.974523	−	0.224285i	$-0.927995\pi$
$941$	−0.0919764	+	0.388079i	−0.00299834	+	0.0126510i	0.971525	+	0.236937i	$0.0761433\pi$
$942$	8.08861	+	18.5542i	0.263541	+	0.604529i
$943$	14.9881	+	18.9556i	0.488081	+	0.617279i
$944$	2.22871	−	3.86025i	0.0725385	−	0.125640i
$945$	37.2038	−	23.3070i	1.21024	−	0.758176i
$946$	−22.4369	−	38.8619i	−0.729488	−	1.26351i
$947$	−17.6703	+	44.4789i	−0.574209	+	1.44537i	0.297200	+	0.954815i	$0.403947\pi$
$947$	−17.6703	+	44.4789i	−0.574209	+	1.44537i	−0.871410	+	0.490556i	$0.836794\pi$
$948$	1.28454	−	4.35174i	0.0417200	−	0.141338i
$949$	−10.3242	−	9.74037i	−0.335137	−	0.316186i
$950$	32.3172	−	2.52702i	1.04851	−	0.0819874i
$951$	11.7111	−	0.386014i	0.379759	−	0.0125173i
$952$	8.51931	+	15.8000i	0.276112	+	0.512082i
$953$	−4.13420	+	47.2541i	−0.133920	+	1.53071i	0.570719	+	0.821146i	$0.306665\pi$
$953$	−4.13420	+	47.2541i	−0.133920	+	1.53071i	−0.704639	+	0.709566i	$0.748891\pi$
$954$	−9.29152	−	15.8102i	−0.300824	−	0.511874i
$955$	40.5538	−	11.9373i	1.31229	−	0.386283i
$956$	2.24020	+	3.40605i	0.0724531	+	0.110160i
$957$	17.5263	+	10.0288i	0.566546	+	0.324186i
$958$	−31.7237	−	25.0838i	−1.02495	−	0.810422i
$959$	7.83275	−	18.1584i	0.252933	−	0.586364i
$960$	0.896016	−	3.76791i	0.0289188	−	0.121609i
$961$	9.53570	+	4.78901i	0.307603	+	0.154484i
$962$	13.9057	+	6.48432i	0.448337	+	0.209063i
$963$	−3.37093	+	24.3212i	−0.108627	+	0.783740i
$964$	−5.67603	+	15.5948i	−0.182812	+	0.502273i
$965$	27.2781	−	38.5769i	0.878112	−	1.24183i
$966$	−18.3711	+	3.86733i	−0.591081	+	0.124429i
$967$	21.3253	−	4.40332i	0.685776	−	0.141601i	0.153470	−	0.988153i	$-0.450955\pi$
$967$	21.3253	−	4.40332i	0.685776	−	0.141601i	0.532306	+	0.846552i	$0.321326\pi$
$968$	4.56969	+	2.46396i	0.146875	+	0.0791946i
$969$	39.9883	+	35.3109i	1.28461	+	1.13435i
$970$	−1.27046	+	0.455779i	−0.0407919	+	0.0146342i
$971$			29.4457i			0.944959i	0.881342	+	0.472479i	$0.156641\pi$
$971$			29.4457i			0.944959i	−0.881342	+	0.472479i	$0.843359\pi$
$972$	−8.81578	−	12.8562i	−0.282766	−	0.412363i
$973$	−5.91659	−	5.91659i	−0.189677	−	0.189677i
$974$	−11.2363	+	15.0929i	−0.360033	+	0.483608i
$975$	−13.0050	−	4.38703i	−0.416492	−	0.140497i
$976$	−1.53067	−	5.11279i	−0.0489955	−	0.163656i
$977$	4.38837	+	21.2529i	0.140396	+	0.679941i	0.988636	+	0.150328i	$0.0480331\pi$
$977$	4.38837	+	21.2529i	0.140396	+	0.679941i	−0.848240	+	0.529613i	$0.822337\pi$
$978$	9.71527	−	14.8963i	0.310660	−	0.476331i
$979$	14.0464	−	13.2521i	0.448926	−	0.423539i
$980$	9.65602	+	13.0960i	0.308450	+	0.418338i
$981$	12.6965	+	5.36084i	0.405367	+	0.171158i
$982$	6.07176	−	13.0209i	0.193758	−	0.415515i
$983$	−38.0567	+	12.6106i	−1.21382	+	0.402216i	−0.848765	−	0.528770i	$-0.822654\pi$
$983$	−38.0567	+	12.6106i	−1.21382	+	0.402216i	−0.365055	+	0.930986i	$0.618950\pi$
$984$	−13.2473	−	6.11516i	−0.422308	−	0.194944i
$985$	7.70258	+	1.62756i	0.245425	+	0.0518583i
$986$	1.59794	+	13.6713i	0.0508888	+	0.435381i
$987$	−16.0120	+	27.9826i	−0.509669	+	0.890696i
$988$	−10.0624	−	2.07772i	−0.320128	−	0.0661011i
$989$	24.5064	+	20.5633i	0.779259	+	0.653876i
$990$	26.4183	−	5.54054i	0.839629	−	0.176090i
$991$	−5.73537	+	4.81255i	−0.182190	+	0.152876i	−0.729322	−	0.684171i	$-0.760164\pi$
$991$	−5.73537	+	4.81255i	−0.182190	+	0.152876i	0.547132	+	0.837047i	$0.315720\pi$
$992$	−5.68195	+	3.06368i	−0.180402	+	0.0972720i
$993$	−12.4883	+	13.3396i	−0.396303	+	0.423319i
$994$	22.7398	+	45.2787i	0.721263	+	1.43615i
$995$	−0.624133	−	2.68867i	−0.0197864	−	0.0852364i
$996$	−19.9716	+	10.8683i	−0.632823	+	0.344375i
$997$	35.8372	+	14.2372i	1.13498	+	0.450897i	0.859868	−	0.510517i	$-0.170546\pi$
$997$	35.8372	+	14.2372i	1.13498	+	0.450897i	0.275108	+	0.961413i	$0.411287\pi$
$998$	−25.0560	−	6.71375i	−0.793135	−	0.212520i
$999$	−35.1571	+	35.9811i	−1.11232	+	1.13839i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	810.2.w.a.23.13	✓	1944
5.2	odd	4	inner	810.2.w.a.347.1	yes	1944
81.74	odd	54	inner	810.2.w.a.803.1	yes	1944
405.317	even	108	inner	810.2.w.a.317.13	yes	1944

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
810.2.w.a.23.13	✓	1944	1.1	even	1	trivial
810.2.w.a.317.13	yes	1944	405.317	even	108	inner
810.2.w.a.347.1	yes	1944	5.2	odd	4	inner
810.2.w.a.803.1	yes	1944	81.74	odd	54	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:	\( N \)	\(=\)	\( 810 = 2 \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	810.w (of order \(108\), degree \(36\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.989442 + 0.144932i) q^{2} +(-0.107384 - 1.72872i) q^{3} +(0.957990 - 0.286803i) q^{4} +(0.876175 + 2.05726i) q^{5} +(0.356797 + 1.69490i) q^{6} +(-3.77684 - 0.109895i) q^{7} +(-0.906308 + 0.422618i) q^{8} +(-2.97694 + 0.371275i) q^{9} +(-1.16509 - 1.90855i) q^{10} +(1.80592 - 3.59587i) q^{11} +(-0.598675 - 1.62530i) q^{12} +(-1.47285 + 0.585127i) q^{13} +(3.75289 - 0.438650i) q^{14} +(3.46234 - 1.73558i) q^{15} +(0.835488 - 0.549509i) q^{16} +(0.414057 + 4.73269i) q^{17} +(2.89170 - 0.798808i) q^{18} +(4.16730 + 4.96640i) q^{19} +(1.42940 + 1.71954i) q^{20} +(0.215596 + 6.54090i) q^{21} +(-1.26569 + 3.81964i) q^{22} +(-0.0834340 - 2.86744i) q^{23} +(0.827911 + 1.52137i) q^{24} +(-3.46463 + 3.60504i) q^{25} +(1.37250 - 0.792412i) q^{26} +(0.961506 + 5.10642i) q^{27} +(-3.64969 + 0.977932i) q^{28} +(-2.87769 - 0.336354i) q^{29} +(-3.17424 + 2.21906i) q^{30} +(6.28128 + 1.48869i) q^{31} +(-0.747025 + 0.664796i) q^{32} +(-6.41018 - 2.73578i) q^{33} +(-1.09560 - 4.62271i) q^{34} +(-3.08309 - 7.86623i) q^{35} +(-2.74539 + 1.20947i) q^{36} +(5.55298 + 7.93048i) q^{37} +(-4.84309 - 4.30999i) q^{38} +(1.16968 + 2.48331i) q^{39} +(-1.66352 - 1.49422i) q^{40} +(-6.75700 + 5.03040i) q^{41} +(-1.16130 - 6.44059i) q^{42} +(-7.41372 + 8.33073i) q^{43} +(0.698740 - 3.96275i) q^{44} +(-3.37213 - 5.79903i) q^{45} +(0.498137 + 2.82507i) q^{46} +(4.19285 + 2.58619i) q^{47} +(-1.03966 - 1.38531i) q^{48} +(7.26429 + 0.423097i) q^{49} +(2.90557 - 4.06911i) q^{50} +(8.13703 - 1.22400i) q^{51} +(-1.24316 + 0.982964i) q^{52} +(-1.58210 - 5.90450i) q^{53} +(-1.69144 - 4.91315i) q^{54} +(8.97995 + 0.564621i) q^{55} +(3.46942 - 1.49656i) q^{56} +(8.13800 - 7.73741i) q^{57} +(2.89606 - 0.0842667i) q^{58} +(3.98330 - 2.00049i) q^{59} +(2.81911 - 2.65567i) q^{60} +(1.53067 - 5.11279i) q^{61} +(-6.43072 - 0.562615i) q^{62} +(11.2842 - 1.07509i) q^{63} +(0.642788 - 0.766044i) q^{64} +(-2.49424 - 2.51737i) q^{65} +(6.73900 + 1.77786i) q^{66} +(-9.46445 + 11.9698i) q^{67} +(1.75401 + 4.41511i) q^{68} +(-4.94804 + 0.452152i) q^{69} +(4.19061 + 7.33634i) q^{70} +(4.58642 + 12.6011i) q^{71} +(2.54111 - 1.59460i) q^{72} +(3.78500 + 8.11695i) q^{73} +(-6.64373 - 7.04194i) q^{74} +(6.60415 + 5.60225i) q^{75} +(5.41661 + 3.56256i) q^{76} +(-7.21583 + 13.3826i) q^{77} +(-1.51724 - 2.28757i) q^{78} +(2.10128 + 1.56435i) q^{79} +(1.86252 + 1.23735i) q^{80} +(8.72431 - 2.21052i) q^{81} +(5.95659 - 5.95659i) q^{82} +(-1.90257 - 12.9888i) q^{83} +(2.08249 + 6.20428i) q^{84} +(-9.37358 + 4.99849i) q^{85} +(6.12806 - 9.31726i) q^{86} +(-0.272443 + 5.01084i) q^{87} +(-0.117034 + 4.02218i) q^{88} +(4.50971 + 1.64140i) q^{89} +(4.17699 + 5.24907i) q^{90} +(5.62703 - 2.04807i) q^{91} +(-0.902320 - 2.72305i) q^{92} +(1.89902 - 11.0184i) q^{93} +(-4.52341 - 1.95121i) q^{94} +(-6.56588 + 12.9247i) q^{95} +(1.22946 + 1.22001i) q^{96} +(0.122063 - 0.591151i) q^{97} +(-7.24892 + 0.634198i) q^{98} +(-4.04104 + 11.3752i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1944 q + 36 q^{20} + 108 q^{30} + 108 q^{35} + 36 q^{41} + 216 q^{51} + 108 q^{67} - 144 q^{72} - 576 q^{77} - 576 q^{87} - 144 q^{92} + 36 q^{93} + 108 q^{97}+O(q^{100}) \) 1944 * q + 36 * q^20 + 108 * q^30 + 108 * q^35 + 36 * q^41 + 216 * q^51 + 108 * q^67 - 144 * q^72 - 576 * q^77 - 576 * q^87 - 144 * q^92 + 36 * q^93 + 108 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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