LMFDB - Embedded newform 820.2.bv.c.207.40

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [820,2,Mod(103,820)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(820, base_ring=CyclotomicField(20)) chi = DirichletCharacter(H, H._module([10, 15, 7])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("820.103"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 820 = 2^{2} \cdot 5 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	820.bv (of order $20$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [960,-10] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$6.54773296574$
Analytic rank:	$0$
Dimension:	$960$
Relative dimension:	$120$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			207.40
Character	$\chi$	$=$	820.207
Dual form			820.2.bv.c.103.40

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.782514 - 1.17799i) q^{2} -2.23336 q^{3} +(-0.775344 + 1.84359i) q^{4} +(-0.983161 - 2.00833i) q^{5} +(1.74763 + 2.63089i) q^{6} +(3.76737 + 1.22409i) q^{7} +(2.77846 - 0.529286i) q^{8} +1.98789 q^{9} +(-1.59647 + 2.72971i) q^{10} +(-0.259122 - 1.63603i) q^{11} +(1.73162 - 4.11741i) q^{12} +(-5.87435 + 1.90869i) q^{13} +(-1.50604 - 5.39581i) q^{14} +(2.19575 + 4.48532i) q^{15} +(-2.79768 - 2.85884i) q^{16} +(0.889430 - 1.22420i) q^{17} +(-1.55555 - 2.34173i) q^{18} +(-3.09361 + 1.57627i) q^{19} +(4.46484 - 0.255401i) q^{20} +(-8.41388 - 2.73383i) q^{21} +(-1.72447 + 1.58546i) q^{22} +(3.35446 - 6.58351i) q^{23} +(-6.20530 + 1.18209i) q^{24} +(-3.06679 + 3.94902i) q^{25} +(6.84519 + 5.42638i) q^{26} +2.26040 q^{27} +(-5.17773 + 5.99640i) q^{28} +(-8.67047 - 1.37327i) q^{29} +(3.56548 - 6.09641i) q^{30} +(-2.81243 + 3.87098i) q^{31} +(-1.17848 + 5.53274i) q^{32} +(0.578713 + 3.65385i) q^{33} +(-2.13809 - 0.0897944i) q^{34} +(-1.24554 - 8.76960i) q^{35} +(-1.54130 + 3.66486i) q^{36} +(5.76174 + 0.912570i) q^{37} +(4.27763 + 2.41080i) q^{38} +(13.1195 - 4.26279i) q^{39} +(-3.79466 - 5.05970i) q^{40} +(-3.48858 + 5.36934i) q^{41} +(3.36353 + 12.0508i) q^{42} +(4.87565 + 2.48427i) q^{43} +(3.21709 + 0.790773i) q^{44} +(-1.95442 - 3.99234i) q^{45} +(-10.3803 + 1.20014i) q^{46} +(2.80251 + 8.62524i) q^{47} +(6.24823 + 6.38482i) q^{48} +(7.03152 + 5.10870i) q^{49} +(7.05174 + 0.522497i) q^{50} +(-1.98642 + 2.73407i) q^{51} +(1.03579 - 12.3098i) q^{52} +(2.27216 + 3.12736i) q^{53} +(-1.76880 - 2.66274i) q^{54} +(-3.03094 + 2.12889i) q^{55} +(11.1154 + 1.40708i) q^{56} +(6.90913 - 3.52038i) q^{57} +(5.16706 + 11.2884i) q^{58} +(1.23643 + 3.80535i) q^{59} +(-9.97158 + 0.570402i) q^{60} +(1.30986 + 0.425600i) q^{61} +(6.76076 + 0.283935i) q^{62} +(7.48911 + 2.43336i) q^{63} +(7.43971 - 2.94120i) q^{64} +(9.60871 + 9.92109i) q^{65} +(3.85137 - 3.54091i) q^{66} +(-5.15113 + 3.74251i) q^{67} +(1.56731 + 2.58892i) q^{68} +(-7.49172 + 14.7033i) q^{69} +(-9.35588 + 8.32958i) q^{70} +(1.54751 + 9.77059i) q^{71} +(5.52328 - 1.05216i) q^{72} +(1.72464 + 1.72464i) q^{73} +(-3.43364 - 7.50140i) q^{74} +(6.84924 - 8.81959i) q^{75} +(-0.507394 - 6.92551i) q^{76} +(1.02645 - 6.48073i) q^{77} +(-15.2878 - 12.1190i) q^{78} +(1.06927 - 1.06927i) q^{79} +(-2.99093 + 8.42937i) q^{80} -11.0120 q^{81} +(9.05492 - 0.0920563i) q^{82} +(-0.379034 - 0.379034i) q^{83} +(11.5637 - 13.3921i) q^{84} +(-3.33304 - 0.582690i) q^{85} +(-0.888808 - 7.68746i) q^{86} +(19.3643 + 3.06700i) q^{87} +(-1.58589 - 4.40851i) q^{88} +(-0.948782 + 0.483429i) q^{89} +(-3.17360 + 5.42636i) q^{90} -24.4672 q^{91} +(9.53645 + 11.2888i) q^{92} +(6.28117 - 8.64528i) q^{93} +(7.96748 - 10.0507i) q^{94} +(6.20718 + 4.66326i) q^{95} +(2.63196 - 12.3566i) q^{96} +(-2.06341 - 2.84004i) q^{97} +(0.515760 - 12.2807i) q^{98} +(-0.515107 - 3.25226i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 960 q - 10 q^{2} - 20 q^{5} - 16 q^{6} + 2 q^{8} + 960 q^{9} - 60 q^{10} - 40 q^{12} - 20 q^{13} - 8 q^{14} - 28 q^{16} - 20 q^{17} - 48 q^{18} - 34 q^{20} - 40 q^{21} - 10 q^{22} - 48 q^{24} - 4 q^{25}+ \cdots - 38 q^{98}+O(q^{100}) $ 960 * q - 10 * q^2 - 20 * q^5 - 16 * q^6 + 2 * q^8 + 960 * q^9 - 60 * q^10 - 40 * q^12 - 20 * q^13 - 8 * q^14 - 28 * q^16 - 20 * q^17 - 48 * q^18 - 34 * q^20 - 40 * q^21 - 10 * q^22 - 48 * q^24 - 4 * q^25 - 20 * q^26 - 10 * q^28 - 10 * q^30 - 56 * q^33 - 20 * q^34 - 100 * q^36 + 88 * q^37 - 16 * q^40 - 24 * q^41 - 104 * q^42 - 100 * q^45 - 20 * q^46 - 40 * q^48 + 224 * q^49 - 12 * q^50 - 38 * q^52 - 20 * q^53 - 52 * q^54 + 96 * q^56 - 72 * q^57 - 38 * q^58 - 14 * q^60 - 40 * q^61 - 10 * q^62 - 120 * q^64 - 60 * q^65 - 12 * q^66 - 116 * q^68 - 104 * q^69 - 96 * q^70 - 24 * q^72 - 72 * q^73 - 28 * q^74 - 40 * q^76 - 76 * q^77 - 44 * q^78 - 90 * q^80 + 592 * q^81 - 130 * q^82 - 92 * q^84 - 64 * q^85 - 12 * q^86 - 104 * q^88 + 136 * q^89 - 364 * q^90 - 220 * q^92 - 32 * q^94 - 44 * q^96 + 80 * q^97 - 38 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/820\mathbb{Z}\right)^\times$.

$n$	$411$	$621$	$657$
$\chi(n)$	$-1$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−0.782514	−	1.17799i	−0.553321	−	0.832968i
$2$	−0.782514	−	1.17799i	−0.553321	−	0.832968i
$3$	−2.23336			−1.28943			−0.644715	−	0.764423i	$-0.723024\pi$
$3$	−2.23336			−1.28943			−0.644715	+	0.764423i	$0.723024\pi$
$4$	−0.775344	+	1.84359i	−0.387672	+	0.921797i
$5$	−0.983161	−	2.00833i	−0.439683	−	0.898153i
$5$	−0.983161	−	2.00833i	−0.439683	−	0.898153i
$6$	1.74763	+	2.63089i	0.713469	+	1.07405i
$7$	3.76737	+	1.22409i	1.42393	+	0.462663i	0.916849	−	0.399235i	$-0.130724\pi$
$7$	3.76737	+	1.22409i	1.42393	+	0.462663i	0.507082	+	0.861898i	$0.330724\pi$
$8$	2.77846	−	0.529286i	0.982335	−	0.187131i
$9$	1.98789			0.662630
$10$	−1.59647	+	2.72971i	−0.504847	+	0.863209i
$11$	−0.259122	−	1.63603i	−0.0781283	−	0.493283i	−0.995462	−	0.0951628i	$-0.969663\pi$
$11$	−0.259122	−	1.63603i	−0.0781283	−	0.493283i	0.917333	−	0.398120i	$-0.130337\pi$
$12$	1.73162	−	4.11741i	0.499876	−	1.18859i
$13$	−5.87435	+	1.90869i	−1.62925	+	0.529376i	−0.974099	−	0.226121i	$-0.927395\pi$
$13$	−5.87435	+	1.90869i	−1.62925	+	0.529376i	−0.655152	+	0.755497i	$0.727395\pi$
$14$	−1.50604	−	5.39581i	−0.402507	−	1.44209i
$15$	2.19575	+	4.48532i	0.566940	+	1.15811i
$16$	−2.79768	−	2.85884i	−0.699421	−	0.714710i
$17$	0.889430	−	1.22420i	0.215719	−	0.296911i	−0.687420	−	0.726260i	$-0.741257\pi$
$17$	0.889430	−	1.22420i	0.215719	−	0.296911i	0.903139	+	0.429349i	$0.141257\pi$
$18$	−1.55555	−	2.34173i	−0.366647	−	0.551950i
$19$	−3.09361	+	1.57627i	−0.709722	+	0.361621i	−0.771292	−	0.636481i	$-0.780389\pi$
$19$	−3.09361	+	1.57627i	−0.709722	+	0.361621i	0.0615703	+	0.998103i	$0.480389\pi$
$20$	4.46484	−	0.255401i	0.998368	−	0.0571094i
$21$	−8.41388	−	2.73383i	−1.83606	−	0.596572i
$22$	−1.72447	+	1.58546i	−0.367659	+	0.338022i
$23$	3.35446	−	6.58351i	0.699454	−	1.37276i	−0.218409	−	0.975857i	$-0.570087\pi$
$23$	3.35446	−	6.58351i	0.699454	−	1.37276i	0.917863	−	0.396898i	$-0.129913\pi$
$24$	−6.20530	+	1.18209i	−1.26665	+	0.241292i
$25$	−3.06679	+	3.94902i	−0.613358	+	0.789805i
$26$	6.84519	+	5.42638i	1.34245	+	1.06420i
$27$	2.26040			0.435015
$28$	−5.17773	+	5.99640i	−0.978500	+	1.13321i
$29$	−8.67047	−	1.37327i	−1.61007	−	0.255009i	−0.714400	−	0.699738i	$-0.753300\pi$
$29$	−8.67047	−	1.37327i	−1.61007	−	0.255009i	−0.895665	+	0.444729i	$0.853300\pi$
$30$	3.56548	−	6.09641i	0.650965	−	1.11305i
$31$	−2.81243	+	3.87098i	−0.505128	+	0.695248i	−0.983088	−	0.183133i	$-0.941376\pi$
$31$	−2.81243	+	3.87098i	−0.505128	+	0.695248i	0.477961	+	0.878381i	$0.341376\pi$
$32$	−1.17848	+	5.53274i	−0.208327	+	0.978059i
$33$	0.578713	+	3.65385i	0.100741	+	0.636054i
$34$	−2.13809	−	0.0897944i	−0.366679	−	0.0153996i
$35$	−1.24554	−	8.76960i	−0.210535	−	1.48233i
$36$	−1.54130	+	3.66486i	−0.256883	+	0.610811i
$37$	5.76174	+	0.912570i	0.947225	+	0.150026i	0.610889	−	0.791716i	$-0.290812\pi$
$37$	5.76174	+	0.912570i	0.947225	+	0.150026i	0.336336	+	0.941742i	$0.390812\pi$
$38$	4.27763	+	2.41080i	0.693923	+	0.391083i
$39$	13.1195	−	4.26279i	2.10081	−	0.682593i
$40$	−3.79466	−	5.05970i	−0.599988	−	0.800009i
$41$	−3.48858	+	5.36934i	−0.544824	+	0.838550i
$41$	−3.48858	+	5.36934i	−0.544824	+	0.838550i
$42$	3.36353	+	12.0508i	0.519004	+	1.85947i
$43$	4.87565	+	2.48427i	0.743529	+	0.378847i	0.784349	−	0.620319i	$-0.212997\pi$
$43$	4.87565	+	2.48427i	0.743529	+	0.378847i	−0.0408201	+	0.999167i	$0.512997\pi$
$44$	3.21709	+	0.790773i	0.484995	+	0.119214i
$45$	−1.95442	−	3.99234i	−0.291347	−	0.595143i
$46$	−10.3803	+	1.20014i	−1.53048	+	0.176951i
$47$	2.80251	+	8.62524i	0.408788	+	1.25812i	0.917690	+	0.397296i	$0.130051\pi$
$47$	2.80251	+	8.62524i	0.408788	+	1.25812i	−0.508902	+	0.860824i	$0.669949\pi$
$48$	6.24823	+	6.38482i	0.901854	+	0.921569i
$49$	7.03152	+	5.10870i	1.00450	+	0.729814i
$50$	7.05174	+	0.522497i	0.997266	+	0.0738923i
$51$	−1.98642	+	2.73407i	−0.278154	+	0.382846i
$52$	1.03579	−	12.3098i	0.143638	−	1.70706i
$53$	2.27216	+	3.12736i	0.312105	+	0.429576i	0.936036	−	0.351903i	$-0.114465\pi$
$53$	2.27216	+	3.12736i	0.312105	+	0.429576i	−0.623931	+	0.781479i	$0.714465\pi$
$54$	−1.76880	−	2.66274i	−0.240703	−	0.362354i
$55$	−3.03094	+	2.12889i	−0.408692	+	0.287059i
$56$	11.1154	+	1.40708i	1.48536	+	0.188029i
$57$	6.90913	−	3.52038i	0.915137	−	0.466285i
$58$	5.16706	+	11.2884i	0.678468	+	1.48224i
$59$	1.23643	+	3.80535i	0.160970	+	0.495414i	0.998717	−	0.0506448i	$-0.0161276\pi$
$59$	1.23643	+	3.80535i	0.160970	+	0.495414i	−0.837747	+	0.546058i	$0.816128\pi$
$60$	−9.97158	+	0.570402i	−1.28733	+	0.0736386i
$61$	1.30986	+	0.425600i	0.167711	+	0.0544925i	0.391669	−	0.920106i	$-0.371898\pi$
$61$	1.30986	+	0.425600i	0.167711	+	0.0544925i	−0.223958	+	0.974599i	$0.571898\pi$
$62$	6.76076	+	0.283935i	0.858617	+	0.0360598i
$63$	7.48911	+	2.43336i	0.943539	+	0.306574i
$64$	7.43971	−	2.94120i	0.929964	−	0.367651i
$65$	9.60871	+	9.92109i	1.19181	+	1.23056i
$66$	3.85137	−	3.54091i	0.474070	−	0.435856i
$67$	−5.15113	+	3.74251i	−0.629310	+	0.457221i	−0.856161	−	0.516709i	$-0.827157\pi$
$67$	−5.15113	+	3.74251i	−0.629310	+	0.457221i	0.226851	+	0.973929i	$0.427157\pi$
$68$	1.56731	+	2.58892i	0.190064	+	0.313953i
$69$	−7.49172	+	14.7033i	−0.901897	+	1.77007i
$70$	−9.35588	+	8.32958i	−1.11824	+	0.995575i
$71$	1.54751	+	9.77059i	0.183656	+	1.15956i	0.891444	+	0.453131i	$0.149693\pi$
$71$	1.54751	+	9.77059i	0.183656	+	1.15956i	−0.707788	+	0.706425i	$0.750307\pi$
$72$	5.52328	−	1.05216i	0.650925	−	0.123999i
$73$	1.72464	+	1.72464i	0.201854	+	0.201854i	0.800794	−	0.598940i	$-0.204411\pi$
$73$	1.72464	+	1.72464i	0.201854	+	0.201854i	−0.598940	+	0.800794i	$0.704411\pi$
$74$	−3.43364	−	7.50140i	−0.399153	−	0.872020i
$75$	6.84924	−	8.81959i	0.790882	−	1.01840i
$76$	−0.507394	−	6.92551i	−0.0582021	−	0.794410i
$77$	1.02645	−	6.48073i	0.116974	−	0.738547i
$78$	−15.2878	−	12.1190i	−1.73100	−	1.37221i
$79$	1.06927	−	1.06927i	0.120302	−	0.120302i	−0.644393	−	0.764695i	$-0.722890\pi$
$79$	1.06927	−	1.06927i	0.120302	−	0.120302i	0.764695	+	0.644393i	$0.222890\pi$
$80$	−2.99093	+	8.42937i	−0.334396	+	0.942433i
$81$	−11.0120			−1.22355
$82$	9.05492	−	0.0920563i	0.999948	−	0.0101659i
$83$	−0.379034	−	0.379034i	−0.0416044	−	0.0416044i	0.685999	−	0.727603i	$-0.259366\pi$
$83$	−0.379034	−	0.379034i	−0.0416044	−	0.0416044i	−0.727603	+	0.685999i	$0.759366\pi$
$84$	11.5637	−	13.3921i	1.26171	−	1.46120i
$85$	−3.33304	−	0.582690i	−0.361519	−	0.0632016i
$86$	−0.888808	−	7.68746i	−0.0958426	−	0.828960i
$87$	19.3643	+	3.06700i	2.07607	+	0.328817i
$88$	−1.58589	−	4.40851i	−0.169057	−	0.469949i
$89$	−0.948782	+	0.483429i	−0.100571	+	0.0512433i	−0.503552	−	0.863965i	$-0.667974\pi$
$89$	−0.948782	+	0.483429i	−0.100571	+	0.0512433i	0.402982	+	0.915208i	$0.367974\pi$
$90$	−3.17360	+	5.42636i	−0.334527	+	0.571988i
$91$	−24.4672			−2.56486
$92$	9.53645	+	11.2888i	0.994244	+	1.17693i
$93$	6.28117	−	8.64528i	0.651327	−	0.896474i
$94$	7.96748	−	10.0507i	0.821783	−	1.03665i
$95$	6.20718	+	4.66326i	0.636844	+	0.478440i
$96$	2.63196	−	12.3566i	0.268623	−	1.26114i
$97$	−2.06341	−	2.84004i	−0.209508	−	0.288363i	0.691312	−	0.722557i	$-0.257033\pi$
$97$	−2.06341	−	2.84004i	−0.209508	−	0.288363i	−0.900819	+	0.434194i	$0.857033\pi$
$98$	0.515760	−	12.2807i	0.0520996	−	1.24054i
$99$	−0.515107	−	3.25226i	−0.0517702	−	0.326864i
$100$	−4.90258	−	8.71577i	−0.490258	−	0.871577i
$101$	−13.1878	+	6.71950i	−1.31223	+	0.668615i	−0.963273	−	0.268523i	$-0.913465\pi$
$101$	−13.1878	+	6.71950i	−1.31223	+	0.668615i	−0.348958	+	0.937138i	$0.613465\pi$
$102$	4.77512	+	0.200543i	0.472807	+	0.0198567i
$103$	−4.71668	−	9.25700i	−0.464748	−	0.912120i	−0.997816	−	0.0660475i	$-0.978961\pi$
$103$	−4.71668	−	9.25700i	−0.464748	−	0.912120i	0.533068	−	0.846072i	$-0.321039\pi$
$104$	−15.3114	+	8.41244i	−1.50141	+	0.824908i
$105$	2.78175	+	19.5857i	0.271471	+	1.91136i
$106$	1.90602	−	5.12380i	0.185129	−	0.497667i
$107$	4.02915	+	7.90764i	0.389512	+	0.764461i	0.999612	−	0.0278640i	$-0.00887054\pi$
$107$	4.02915	+	7.90764i	0.389512	+	0.764461i	−0.610099	+	0.792325i	$0.708871\pi$
$108$	−1.75259	+	4.16727i	−0.168643	+	0.400995i
$109$	3.92313	−	3.92313i	0.375768	−	0.375768i	−0.493805	−	0.869573i	$-0.664394\pi$
$109$	3.92313	−	3.92313i	0.375768	−	0.375768i	0.869573	+	0.493805i	$0.164394\pi$
$110$	4.87957	+	1.90455i	0.465249	+	0.181591i
$111$	−12.8680	−	2.03810i	−1.22138	−	0.193448i
$112$	−7.04041	−	14.1949i	−0.665256	−	1.34129i
$113$	−18.4352	+	2.91985i	−1.73424	+	0.274676i	−0.942019	−	0.335560i	$-0.891074\pi$
$113$	−18.4352	+	2.91985i	−1.73424	+	0.274676i	−0.792219	+	0.610237i	$0.791074\pi$
$114$	−9.55348	−	5.38418i	−0.894765	−	0.504274i
$115$	−16.5198	−	0.264231i	−1.54048	−	0.0246397i
$116$	9.25434	−	14.9201i	0.859244	−	1.38529i
$117$	−11.6776	+	3.79427i	−1.07959	+	0.350780i
$118$	3.51515	−	4.43425i	0.323596	−	0.408205i
$119$	4.84934	−	3.52325i	0.444538	−	0.322976i
$120$	8.47483	+	11.3001i	0.773643	+	1.03156i
$121$	7.85216	−	2.55132i	0.713833	−	0.231938i
$122$	−0.523630	−	1.87605i	−0.0474073	−	0.169849i
$123$	7.79125	−	11.9917i	0.702513	−	1.08125i
$124$	−4.95591	−	8.18632i	−0.445054	−	0.735154i
$125$	10.9461	+	2.27661i	0.979049	+	0.203626i
$126$	−2.99385	−	10.7263i	−0.266713	−	0.955572i
$127$	−3.23429	+	20.4205i	−0.286997	+	1.81203i	0.249778	+	0.968303i	$0.419642\pi$
$127$	−3.23429	+	20.4205i	−0.286997	+	1.81203i	−0.536775	+	0.843726i	$0.680358\pi$
$128$	−9.28640	−	6.46241i	−0.820810	−	0.571202i
$129$	−10.8891	−	5.54826i	−0.958729	−	0.488497i
$130$	4.16804	−	19.0824i	0.365561	−	1.67364i
$131$	11.0511	+	8.02907i	0.965536	+	0.701503i	0.954430	−	0.298435i	$-0.0964648\pi$
$131$	11.0511	+	8.02907i	0.965536	+	0.701503i	0.0111061	+	0.999938i	$0.496465\pi$
$132$	−7.18492	−	1.76608i	−0.625367	−	0.153718i
$133$	−13.5842	+	2.15153i	−1.17790	+	0.186561i
$134$	8.43949	+	3.13943i	0.729061	+	0.271206i
$135$	−2.22234	−	4.53964i	−0.191269	−	0.390710i
$136$	1.82330	−	3.87215i	0.156347	−	0.332034i
$137$		−	10.4655i		−	0.894124i	−0.894503	−	0.447062i	$-0.852470\pi$
$137$		−	10.4655i		−	0.894124i	0.894503	−	0.447062i	$-0.147530\pi$
$138$	23.1828	−	2.68035i	1.97345	−	0.228166i
$139$	−3.83827	+	11.8130i	−0.325558	+	1.00197i	0.645630	+	0.763650i	$0.276595\pi$
$139$	−3.83827	+	11.8130i	−0.325558	+	1.00197i	−0.971188	+	0.238315i	$0.923405\pi$
$140$	17.1333	+	4.50318i	1.44803	+	0.380588i
$141$	−6.25901	−	19.2632i	−0.527104	−	1.62226i
$142$	10.2988	−	9.46858i	0.864253	−	0.794585i
$143$	4.64486	+	9.11605i	0.388423	+	0.762322i
$144$	−5.56149	−	5.68306i	−0.463457	−	0.473589i
$145$	5.76649	+	18.7633i	0.478881	+	1.55821i
$146$	0.682065	−	3.38118i	0.0564481	−	0.279829i
$147$	−15.7039	−	11.4096i	−1.29524	−	0.941045i
$148$	−6.14975	+	9.91476i	−0.505506	+	0.814988i
$149$	0.893586	−	5.64188i	0.0732054	−	0.462201i	−0.923669	−	0.383192i	$-0.874825\pi$
$149$	0.893586	−	5.64188i	0.0732054	−	0.462201i	0.996874	−	0.0790084i	$-0.0251754\pi$
$150$	−15.7491	−	1.16692i	−1.28591	−	0.0952789i
$151$	2.00594	−	3.93687i	0.163241	−	0.320378i	−0.794868	−	0.606782i	$-0.792460\pi$
$151$	2.00594	−	3.93687i	0.163241	−	0.320378i	0.958109	+	0.286404i	$0.0924600\pi$
$152$	−7.76117	+	6.01701i	−0.629514	+	0.488044i
$153$	1.76809	−	2.43357i	0.142942	−	0.196742i
$154$	−8.43747	+	3.86211i	−0.679911	+	0.311218i
$155$	10.5393	+	1.84250i	0.846535	+	0.147993i
$156$	−2.31329	+	27.4922i	−0.185211	+	2.20114i
$157$	−5.92134	+	18.2240i	−0.472574	+	1.45443i	0.376627	+	0.926365i	$0.377084\pi$
$157$	−5.92134	+	18.2240i	−0.472574	+	1.45443i	−0.849201	+	0.528070i	$0.822916\pi$
$158$	−2.09631	−	0.422876i	−0.166774	−	0.0336422i
$159$	−5.07455	−	6.98452i	−0.402438	−	0.553908i
$160$	12.2702	−	3.07280i	0.970045	−	0.242926i
$161$	20.6963	−	20.6963i	1.63110	−	1.63110i
$162$	8.61701	+	12.9720i	0.677016	+	1.01918i
$163$	11.3720	+	11.3720i	0.890721	+	0.890721i	0.994591	−	0.103870i	$-0.0331225\pi$
$163$	11.3720	+	11.3720i	0.890721	+	0.890721i	−0.103870	+	0.994591i	$0.533123\pi$
$164$	−7.19404	−	10.5946i	−0.561760	−	0.827300i
$165$	6.76917	−	4.75457i	0.526979	−	0.370143i
$166$	−0.149901	+	0.743099i	−0.0116346	+	0.0576757i
$167$		−	5.70105i		−	0.441161i	−0.975369	−	0.220580i	$-0.929205\pi$
$167$		−	5.70105i		−	0.441161i	0.975369	−	0.220580i	$-0.0707951\pi$
$168$	−24.8246	−	3.14251i	−1.91526	−	0.242450i
$169$	20.3476	−	14.7834i	1.56520	−	1.13719i
$170$	1.92175	+	4.38227i	0.147391	+	0.336105i
$171$	−6.14975	+	3.13345i	−0.470283	+	0.239621i
$172$	−8.36028	+	7.06255i	−0.637466	+	0.538515i
$173$	14.2852	+	14.2852i	1.08608	+	1.08608i	0.995928	+	0.0901547i	$0.0287361\pi$
$173$	14.2852	+	14.2852i	1.08608	+	1.08608i	0.0901547	+	0.995928i	$0.471264\pi$
$174$	−11.5399	−	25.2110i	−0.874837	−	1.91124i
$175$	−16.3877	+	11.1234i	−1.23879	+	0.840849i
$176$	−3.95222	+	5.31789i	−0.297910	+	0.400851i
$177$	−2.76140	−	8.49870i	−0.207559	−	0.638801i
$178$	1.31191	+	0.739371i	0.0983319	+	0.0554182i
$179$	−15.7353	−	2.49223i	−1.17611	−	0.186278i	−0.462370	−	0.886687i	$-0.653001\pi$
$179$	−15.7353	−	2.49223i	−1.17611	−	0.186278i	−0.713742	+	0.700409i	$0.753001\pi$
$180$	8.87561	−	0.507709i	0.661549	−	0.0378424i
$181$	1.55046	+	9.78922i	0.115245	+	0.727627i	0.975864	+	0.218378i	$0.0700767\pi$
$181$	1.55046	+	9.78922i	0.115245	+	0.727627i	−0.860619	+	0.509249i	$0.829923\pi$
$182$	19.1459	+	28.8223i	1.41919	+	2.13645i
$183$	−2.92539	−	0.950517i	−0.216251	−	0.0702643i
$184$	5.83569	−	20.0675i	0.430213	−	1.47940i
$185$	−3.83198	−	12.4687i	−0.281732	−	0.916717i
$186$	−15.0992	−	0.634129i	−1.10713	−	0.0464966i
$187$	−2.23330	−	1.13792i	−0.163315	−	0.0832131i
$188$	−18.0744	−	1.52084i	−1.31821	−	0.110919i
$189$	8.51576	+	2.76694i	0.619431	+	0.201265i
$190$	0.636086	−	10.9611i	0.0461466	−	0.795201i
$191$	−6.07782	+	6.07782i	−0.439776	+	0.439776i	−0.891936	−	0.452161i	$-0.850653\pi$
$191$	−6.07782	+	6.07782i	−0.439776	+	0.439776i	0.452161	+	0.891936i	$0.350653\pi$
$192$	−16.6155	+	6.56877i	−1.19912	+	0.474060i
$193$	−8.80629	−	12.1208i	−0.633891	−	0.872476i	0.364380	−	0.931250i	$-0.381281\pi$
$193$	−8.80629	−	12.1208i	−0.633891	−	0.872476i	−0.998271	+	0.0587742i	$0.981281\pi$
$194$	−1.73091	+	4.65306i	−0.124272	+	0.334070i
$195$	−21.4597	−	22.1573i	−1.53676	−	1.58672i
$196$	−14.8702	+	9.00228i	−1.06216	+	0.643020i
$197$	7.53066	−	1.19274i	0.536537	−	0.0849792i	0.117715	−	0.993047i	$-0.462443\pi$
$197$	7.53066	−	1.19274i	0.536537	−	0.0849792i	0.418822	+	0.908068i	$0.362443\pi$
$198$	−3.42806	+	3.15173i	−0.243622	+	0.223984i
$199$	−3.96890	+	7.78941i	−0.281348	+	0.552176i	−0.987827	−	0.155558i	$-0.950283\pi$
$199$	−3.96890	+	7.78941i	−0.281348	+	0.552176i	0.706479	+	0.707734i	$0.250283\pi$
$200$	−6.43080	+	12.5954i	−0.454726	+	0.890631i
$201$	11.5043	−	8.35837i	0.811452	−	0.589554i
$202$	18.2351	+	10.2770i	1.28302	+	0.723088i
$203$	−30.9838	−	15.7870i	−2.17464	−	1.10803i
$204$	−3.50036	−	5.78199i	−0.245074	−	0.404820i
$205$	14.2132	+	1.72730i	0.992696	+	0.120640i
$206$	−7.21384	+	12.8000i	−0.502612	+	0.891815i
$207$	6.66831	−	13.0873i	0.463479	−	0.909629i
$208$	21.8912	+	11.4539i	1.51788	+	0.794186i
$209$	3.38045	+	4.65279i	0.233831	+	0.321841i
$210$	20.8950	−	18.6029i	1.44190	−	1.28372i
$211$	−8.75002	−	4.45836i	−0.602376	−	0.306926i	0.126078	−	0.992020i	$-0.459761\pi$
$211$	−8.75002	−	4.45836i	−0.602376	−	0.306926i	−0.728454	+	0.685094i	$0.759761\pi$
$212$	−7.52729	+	1.76416i	−0.516977	+	0.121163i
$213$	−3.45614	−	21.8212i	−0.236811	−	1.49517i
$214$	6.16230	−	10.9342i	0.421246	−	0.747443i
$215$	0.195686	−	12.2343i	0.0133457	−	0.834376i
$216$	6.28045	−	1.19640i	0.427330	−	0.0814047i
$217$	−15.3339	+	11.1407i	−1.04093	+	0.756281i
$218$	−7.69133	−	1.55152i	−0.520922	−	0.105082i
$219$	−3.85175	−	3.85175i	−0.260277	−	0.260277i
$220$	−1.57478	−	7.23844i	−0.106172	−	0.488016i
$221$	−2.88821	+	8.88900i	−0.194282	+	0.597939i
$222$	7.66855	+	16.7533i	0.514679	+	1.12441i
$223$	−3.27544	+	6.42842i	−0.219340	+	0.430479i	−0.974288	−	0.225306i	$-0.927662\pi$
$223$	−3.27544	+	6.42842i	−0.219340	+	0.430479i	0.754948	+	0.655784i	$0.227662\pi$
$224$	−11.2123	+	19.4013i	−0.749155	+	1.29630i
$225$	−6.09644	+	7.85023i	−0.406430	+	0.523349i
$226$	17.8654	+	19.4318i	1.18839	+	1.29258i
$227$	1.91469	−	5.89281i	0.127082	−	0.391119i	−0.867192	−	0.497973i	$-0.834078\pi$
$227$	1.91469	−	5.89281i	0.127082	−	0.391119i	0.994275	+	0.106854i	$0.0340777\pi$
$228$	1.13319	+	15.4671i	0.0750476	+	1.02434i
$229$	−22.3754	+	3.54392i	−1.47861	+	0.234189i	−0.843038	−	0.537854i	$-0.819235\pi$
$229$	−22.3754	+	3.54392i	−1.47861	+	0.234189i	−0.635571	+	0.772043i	$0.719235\pi$
$230$	12.6157	+	19.6671i	0.831857	+	1.29681i
$231$	−2.29242	+	14.4738i	−0.150830	+	0.952305i
$232$	−24.8174	+	0.773588i	−1.62934	+	0.0507885i
$233$	8.19907	−	2.66404i	0.537139	−	0.174527i	−0.0278705	−	0.999612i	$-0.508873\pi$
$233$	8.19907	−	2.66404i	0.537139	−	0.174527i	0.565009	+	0.825085i	$0.308873\pi$
$234$	13.6075	+	10.7870i	0.889549	+	0.705171i
$235$	14.5670	−	14.1084i	0.950248	−	0.920328i
$236$	−7.97417	−	0.670974i	−0.519075	−	0.0436767i
$237$	−2.38806	+	2.38806i	−0.155121	+	0.155121i
$238$	−7.94504	−	2.95550i	−0.515001	−	0.191577i
$239$	−7.26553	−	14.2594i	−0.469968	−	0.922365i	−0.997351	−	0.0727369i	$-0.976827\pi$
$239$	−7.26553	−	14.2594i	−0.469968	−	0.922365i	0.527383	−	0.849628i	$-0.323173\pi$
$240$	6.67982	−	18.8258i	0.431181	−	1.21520i
$241$	−3.27172	−	4.50313i	−0.210750	−	0.290072i	0.690535	−	0.723299i	$-0.257375\pi$
$241$	−3.27172	−	4.50313i	−0.210750	−	0.290072i	−0.901285	+	0.433227i	$0.857375\pi$
$242$	−9.14987	−	7.25336i	−0.588176	−	0.466264i
$243$	17.8125			1.14267
$244$	−1.80023	+	2.08487i	−0.115248	+	0.133470i
$245$	3.34685	−	19.1443i	0.213822	−	1.22308i
$246$	−20.2229	+	0.205595i	−1.28936	+	0.0131082i
$247$	15.1643	−	15.1643i	0.964881	−	0.964881i
$248$	−5.76538	+	12.2440i	−0.366102	+	0.777492i
$249$	0.846519	+	0.846519i	0.0536459	+	0.0536459i
$250$	−5.88364	−	14.6759i	−0.372114	−	0.928187i
$251$	21.4300	−	15.5698i	1.35265	−	0.982757i	0.353774	−	0.935331i	$-0.384898\pi$
$251$	21.4300	−	15.5698i	1.35265	−	0.982757i	0.998875	−	0.0474255i	$-0.0151017\pi$
$252$	−10.2928	+	11.9202i	−0.648383	+	0.750901i
$253$	−11.6401	−	3.78208i	−0.731804	−	0.237777i
$254$	26.5862	−	12.1694i	1.66816	−	0.763574i
$255$	7.44388	+	1.30136i	0.466154	+	0.0814940i
$256$	−0.345950	+	15.9963i	−0.0216218	+	0.999766i
$257$	−14.4166	−	10.4743i	−0.899286	−	0.653369i	0.0389968	−	0.999239i	$-0.487584\pi$
$257$	−14.4166	−	10.4743i	−0.899286	−	0.653369i	−0.938282	+	0.345870i	$0.887584\pi$
$258$	1.98503	+	17.1689i	0.123582	+	1.06889i
$259$	20.5895	+	10.4909i	1.27937	+	0.651872i
$260$	−25.7405	+	10.0223i	−1.59636	+	0.621557i
$261$	−17.2359	−	2.72990i	−1.06688	−	0.168977i
$262$	0.810592	−	19.3010i	0.0500785	−	1.19242i
$263$	−2.42900	+	3.34323i	−0.149779	+	0.206152i	−0.877313	−	0.479919i	$-0.840666\pi$
$263$	−2.42900	+	3.34323i	−0.149779	+	0.206152i	0.727534	+	0.686071i	$0.240666\pi$
$264$	3.54187	+	9.84578i	0.217987	+	0.605966i
$265$	4.04688	−	7.63795i	0.248598	−	0.469196i
$266$	13.1643	+	14.3186i	0.807158	+	0.877927i
$267$	2.11897	−	1.07967i	0.129679	−	0.0660747i
$268$	−2.90578	−	12.3983i	−0.177499	−	0.757348i
$269$	−1.56932	+	0.509904i	−0.0956833	+	0.0310894i	−0.356467	−	0.934308i	$-0.616019\pi$
$269$	−1.56932	+	0.509904i	−0.0956833	+	0.0310894i	0.260784	+	0.965397i	$0.416019\pi$
$270$	−3.60866	+	6.17023i	−0.219616	+	0.375509i
$271$	−4.93651	−	1.60397i	−0.299872	−	0.0974343i	0.155217	−	0.987880i	$-0.450392\pi$
$271$	−4.93651	−	1.60397i	−0.299872	−	0.0974343i	−0.455089	+	0.890446i	$0.650392\pi$
$272$	−5.98813	+	0.882171i	−0.363083	+	0.0534894i
$273$	54.6441			3.30721
$274$	−12.3283	+	8.18936i	−0.744777	+	0.494737i
$275$	7.25541	+	3.99409i	0.437518	+	0.240853i
$276$	−21.2983	−	25.2118i	−1.28201	−	1.51757i
$277$	−0.799831	−	5.04993i	−0.0480572	−	0.303421i	0.951939	−	0.306289i	$-0.0990873\pi$
$277$	−0.799831	−	5.04993i	−0.0480572	−	0.303421i	−0.999996	+	0.00286747i	$0.999087\pi$
$278$	16.9191	−	4.72236i	1.01474	−	0.283228i
$279$	−5.59081	+	7.69508i	−0.334713	+	0.460693i
$280$	−8.10233	−	23.7067i	−0.484207	−	1.41675i
$281$	−9.35562	+	18.3614i	−0.558110	+	1.09535i	0.423757	+	0.905776i	$0.360711\pi$
$281$	−9.35562	+	18.3614i	−0.558110	+	1.09535i	−0.981866	+	0.189576i	$0.939289\pi$
$282$	−17.7943	+	22.4468i	−1.05963	+	1.33669i
$283$	−24.3190	−	3.85175i	−1.44562	−	0.228963i	−0.616198	−	0.787591i	$-0.711328\pi$
$283$	−24.3190	−	3.85175i	−1.44562	−	0.228963i	−0.829418	+	0.558628i	$0.811328\pi$
$284$	−19.2129	−	4.72259i	−1.14007	−	0.280234i
$285$	−13.8629	−	10.4147i	−0.821165	−	0.616915i
$286$	7.10399	−	12.6051i	0.420068	−	0.745352i
$287$	−19.7153	+	15.9579i	−1.16376	+	0.941967i
$288$	−2.34268	+	10.9985i	−0.138044	+	0.648092i
$289$	4.54572	+	13.9903i	0.267395	+	0.822958i
$290$	17.5907	−	21.4754i	1.03296	−	1.26108i
$291$	4.60834	+	6.34284i	0.270146	+	0.371824i
$292$	−4.51674	+	1.84235i	−0.264322	+	0.107816i
$293$	−5.82625	−	17.9314i	−0.340373	−	1.04756i	−0.964014	−	0.265850i	$-0.914347\pi$
$293$	−5.82625	−	17.9314i	−0.340373	−	1.04756i	0.623641	−	0.781711i	$-0.285653\pi$
$294$	−1.15188	+	27.4273i	−0.0671788	+	1.59959i
$295$	6.42678	−	6.22443i	0.374182	−	0.362400i
$296$	16.4918	−	0.514069i	0.958566	−	0.0298796i
$297$	−0.585721	−	3.69810i	−0.0339870	−	0.214585i
$298$	−7.34535	+	3.36221i	−0.425505	+	0.194768i
$299$	−7.13941	+	45.0764i	−0.412883	+	2.60684i
$300$	10.9492	+	19.4654i	0.632154	+	1.12384i
$301$	15.3274	+	15.3274i	0.883455	+	0.883455i
$302$	−6.20729	+	0.717673i	−0.357189	+	0.0412974i
$303$	29.4530	−	15.0071i	1.69203	−	0.862133i
$304$	13.1612	+	4.43422i	0.754848	+	0.254320i
$305$	−0.433059	−	3.04907i	−0.0247969	−	0.174589i
$306$	−4.25029	−	0.178501i	−0.242973	−	0.0102042i
$307$	17.4188	−	8.87530i	0.994141	−	0.506540i	0.120292	−	0.992739i	$-0.461617\pi$
$307$	17.4188	−	8.87530i	0.994141	−	0.506540i	0.873848	+	0.486199i	$0.161617\pi$
$308$	11.1520	+	6.91714i	0.635443	+	0.394141i
$309$	10.5340	+	20.6742i	0.599260	+	1.17611i
$310$	−6.07668	−	13.8570i	−0.345132	−	0.787025i
$311$	5.98001	−	0.947141i	0.339095	−	0.0537074i	0.0154353	−	0.999881i	$-0.495087\pi$
$311$	5.98001	−	0.947141i	0.339095	−	0.0537074i	0.323660	+	0.946173i	$0.395087\pi$
$312$	34.1959	−	18.7880i	1.93596	−	1.06366i
$313$	−8.21177	+	5.96620i	−0.464157	+	0.337230i	−0.795160	−	0.606400i	$-0.792613\pi$
$313$	−8.21177	+	5.96620i	−0.464157	+	0.337230i	0.331003	+	0.943630i	$0.392613\pi$
$314$	26.1013	−	7.28523i	1.47298	−	0.411129i
$315$	−2.47601	−	17.4330i	−0.139507	−	0.982238i
$316$	1.14225	+	2.80035i	0.0642564	+	0.157532i
$317$	−1.13401	−	0.823905i	−0.0636923	−	0.0462751i	0.555484	−	0.831528i	$-0.312533\pi$
$317$	−1.13401	−	0.823905i	−0.0636923	−	0.0462751i	−0.619176	+	0.785252i	$0.712533\pi$
$318$	−4.25682	+	11.4433i	−0.238711	+	0.641707i
$319$			14.5410i			0.814141i
$320$	−13.2213	−	12.0497i	−0.739096	−	0.673600i
$321$	−8.99853	−	17.6606i	−0.502249	−	0.985719i
$322$	−40.5753	−	8.18500i	−2.26117	−	0.456132i
$323$	−0.821883	+	5.18916i	−0.0457308	+	0.288733i
$324$	8.53806	−	20.3016i	0.474337	−	1.12787i
$325$	10.4779	−	29.0515i	0.581211	−	1.61149i
$326$	4.49740	−	22.2948i	0.249088	−	1.23480i
$327$	−8.76175	+	8.76175i	−0.484526	+	0.484526i
$328$	−6.85096	+	16.7650i	−0.378281	+	0.925691i
$329$			35.9250i			1.98061i
$330$	−10.8978	−	4.25354i	−0.599906	−	0.234149i
$331$	−7.43942	−	7.43942i	−0.408908	−	0.408908i	0.472450	−	0.881358i	$-0.343370\pi$
$331$	−7.43942	−	7.43942i	−0.408908	−	0.408908i	−0.881358	+	0.472450i	$0.843370\pi$
$332$	0.992667	−	0.404903i	0.0544797	−	0.0222219i
$333$	11.4537	+	1.81409i	0.627660	+	0.0994115i
$334$	−6.71581	+	4.46115i	−0.367473	+	0.244103i
$335$	12.5806	+	6.66568i	0.687351	+	0.364185i
$336$	15.7238	+	31.7023i	0.857801	+	1.72950i
$337$	0.213185	−	0.213185i	0.0116129	−	0.0116129i	−0.701276	−	0.712889i	$-0.747386\pi$
$337$	0.213185	−	0.213185i	0.0116129	−	0.0116129i	0.712889	+	0.701276i	$0.247386\pi$
$338$	−33.3371	−	12.4012i	−1.81330	−	0.674536i
$339$	41.1724	−	6.52107i	2.23618	−	0.354176i
$340$	3.65850	−	5.69300i	0.198410	−	0.308746i
$341$	7.06182	+	3.59817i	0.382419	+	0.194852i
$342$	8.50345	+	4.79240i	0.459814	+	0.259143i
$343$	3.93828	+	5.42058i	0.212647	+	0.292684i
$344$	14.8617	+	4.32183i	0.801289	+	0.233017i
$345$	36.8947	+	0.590123i	1.98635	+	0.0317712i
$346$	5.64952	−	28.0062i	0.303720	−	1.50562i
$347$	10.1089	−	31.1119i	0.542673	−	1.67017i	−0.183788	−	0.982966i	$-0.558836\pi$
$347$	10.1089	−	31.1119i	0.542673	−	1.67017i	0.726460	−	0.687209i	$-0.241164\pi$
$348$	−20.6683	+	33.3219i	−1.10794	+	1.78624i
$349$	−9.61091	+	29.5793i	−0.514460	+	1.58335i	0.269801	+	0.962916i	$0.413042\pi$
$349$	−9.61091	+	29.5793i	−0.514460	+	1.58335i	−0.784262	+	0.620430i	$0.786958\pi$
$350$	25.9269	+	10.6004i	1.38585	+	0.566616i
$351$	−13.2784	+	4.31441i	−0.708748	+	0.230286i
$352$	9.35712	+	0.494371i	0.498736	+	0.0263501i
$353$	15.3466	+	30.1193i	0.816815	+	1.60309i	0.797533	+	0.603276i	$0.206138\pi$
$353$	15.3466	+	30.1193i	0.816815	+	1.60309i	0.0192826	+	0.999814i	$0.493862\pi$
$354$	−7.85060	+	9.90326i	−0.417254	+	0.526352i
$355$	18.1011	−	12.7140i	0.960708	−	0.674787i
$356$	−0.155614	−	2.12399i	−0.00824750	−	0.112571i
$357$	−10.8303	+	7.86868i	−0.573201	+	0.416455i
$358$	9.37726	+	20.4863i	0.495604	+	1.08274i
$359$	−19.5221	−	14.1836i	−1.03034	−	0.748583i	−0.0619600	−	0.998079i	$-0.519735\pi$
$359$	−19.5221	−	14.1836i	−1.03034	−	0.748583i	−0.968376	+	0.249496i	$0.919735\pi$
$360$	−7.54336	−	10.0581i	−0.397570	−	0.530110i
$361$	−4.08216	+	5.61861i	−0.214850	+	0.295716i
$362$	10.3184	−	9.48664i	0.542323	−	0.498607i
$363$	−17.5367	+	5.69802i	−0.920437	+	0.299068i
$364$	18.9705	−	45.1076i	0.994326	−	2.36428i
$365$	1.76806	−	5.15926i	0.0925443	−	0.270048i
$366$	1.16945	+	4.18989i	0.0611284	+	0.219009i
$367$	3.74499	−	7.34995i	0.195487	−	0.383664i	−0.772368	−	0.635176i	$-0.780928\pi$
$367$	3.74499	−	7.34995i	0.195487	−	0.383664i	0.967854	+	0.251511i	$0.0809276\pi$
$368$	−28.2059	+	8.82868i	−1.47034	+	0.460227i
$369$	−6.93491	+	10.6737i	−0.361017	+	0.555649i
$370$	−11.6895	+	14.2710i	−0.607707	+	0.741913i
$371$	4.73188	+	14.5632i	0.245667	+	0.756086i
$372$	11.0683	+	18.2830i	0.573866	+	0.947929i
$373$	4.88412	−	30.8371i	0.252890	−	1.59669i	−0.455084	−	0.890448i	$-0.650391\pi$
$373$	4.88412	−	30.8371i	0.252890	−	1.59669i	0.707974	−	0.706238i	$-0.249609\pi$
$374$	0.407120	+	3.52125i	0.0210517	+	0.182080i
$375$	−24.4466	−	5.08448i	−1.26242	−	0.262561i
$376$	12.3519	+	22.4816i	0.637000	+	1.15940i
$377$	53.5545	−	8.48220i	2.75820	−	0.436855i
$378$	−3.40426	−	12.1967i	−0.175096	−	0.627330i
$379$	4.43841	+	3.22469i	0.227986	+	0.165641i	0.695914	−	0.718125i	$-0.254999\pi$
$379$	4.43841	+	3.22469i	0.227986	+	0.165641i	−0.467928	+	0.883766i	$0.654999\pi$
$380$	−13.4099	+	7.82790i	−0.687911	+	0.401563i
$381$	7.22334	−	45.6064i	0.370063	−	2.33648i
$382$	11.9156	+	2.40366i	0.609656	+	0.122982i
$383$			12.4495i			0.636140i	0.948067	+	0.318070i	$0.103035\pi$
$383$			12.4495i			0.636140i	−0.948067	+	0.318070i	$0.896965\pi$
$384$	20.7399	+	14.4329i	1.05838	+	0.736525i
$385$	−14.0246	+	4.31015i	−0.714760	+	0.219666i
$386$	−7.38722	+	19.8585i	−0.376000	+	1.01077i
$387$	9.69225	+	4.93845i	0.492685	+	0.251035i
$388$	6.83574	−	1.60208i	0.347032	−	0.0813335i
$389$	10.4674	−	32.2154i	0.530719	−	1.63339i	−0.222003	−	0.975046i	$-0.571259\pi$
$389$	10.4674	−	32.2154i	0.530719	−	1.63339i	0.752722	−	0.658339i	$-0.228741\pi$
$390$	−9.30873	+	42.6178i	−0.471366	+	2.15804i
$391$	−5.07594	−	9.96209i	−0.256701	−	0.503805i
$392$	22.2408	+	10.4726i	1.12333	+	0.528948i
$393$	−24.6810	−	17.9318i	−1.24499	−	0.904539i
$394$	−7.29789	−	7.93774i	−0.367662	−	0.399898i
$395$	−3.19871	−	1.09618i	−0.160945	−	0.0551550i
$396$	6.39523	+	1.57197i	0.321372	+	0.0789945i
$397$	−8.16720	−	25.1361i	−0.409900	−	1.26154i	−0.916734	−	0.399499i	$-0.869184\pi$
$397$	−8.16720	−	25.1361i	−0.409900	−	1.26154i	0.506833	−	0.862044i	$-0.330816\pi$
$398$	12.2816	−	1.41997i	0.615621	−	0.0711768i
$399$	30.3385	−	4.80514i	1.51882	−	0.240558i
$400$	19.8695	−	2.28065i	0.993477	−	0.114032i
$401$		−	9.53530i		−	0.476170i	−0.971244	−	0.238085i	$-0.923480\pi$
$401$		−	9.53530i		−	0.476170i	0.971244	−	0.238085i	$-0.0765197\pi$
$402$	−18.8484	−	7.01148i	−0.940073	−	0.349701i
$403$	9.13269	−	28.1075i	0.454932	−	1.40014i
$404$	−2.16298	−	29.5228i	−0.107612	−	1.46882i
$405$	10.8265	+	22.1157i	0.537975	+	1.09894i
$406$	5.64820	+	48.8523i	0.280316	+	2.42450i
$407$		−	9.66287i		−	0.478971i
$408$	−4.07208	+	8.64789i	−0.201598	+	0.428134i
$409$			5.01149i			0.247802i	0.992295	+	0.123901i	$0.0395406\pi$
$409$			5.01149i			0.247802i	−0.992295	+	0.123901i	$0.960459\pi$
$410$	−9.08732	−	18.0948i	−0.448791	−	0.893637i
$411$			23.3731i			1.15291i
$412$	20.7232	−	1.51828i	1.02096	−	0.0748002i
$413$			15.8496i			0.779909i
$414$	−20.6348	+	2.38575i	−1.01415	+	0.117253i
$415$	−0.388575	+	1.13388i	−0.0190744	+	0.0556598i
$416$	−3.63751	−	34.7506i	−0.178344	−	1.70379i
$417$	8.57224	−	26.3827i	0.419785	−	1.29196i
$418$	2.83572	−	7.62303i	0.138699	−	0.372855i
$419$		−	3.64669i		−	0.178152i	−0.996025	−	0.0890762i	$-0.971609\pi$
$419$		−	3.64669i		−	0.178152i	0.996025	−	0.0890762i	$-0.0283915\pi$
$420$	−38.2648	−	10.0572i	−1.86713	−	0.490742i
$421$	3.12265	−	0.494580i	0.152189	−	0.0241043i	−0.0798751	−	0.996805i	$-0.525452\pi$
$421$	3.12265	−	0.494580i	0.152189	−	0.0241043i	0.232064	+	0.972701i	$0.425452\pi$
$422$	1.59509	+	13.7962i	0.0776477	+	0.671589i
$423$	5.57108	+	17.1460i	0.270875	+	0.833668i
$424$	7.96838	+	7.48663i	0.386979	+	0.363583i
$425$	2.10668	+	7.26674i	0.102189	+	0.352488i
$426$	−23.0008	+	21.1467i	−1.11439	+	1.02456i
$427$	4.41376	+	3.20678i	0.213597	+	0.155187i
$428$	−17.7025	+	1.29696i	−0.855681	+	0.0626911i
$429$	−10.3736	−	20.3594i	−0.500844	−	0.982961i
$430$	−14.5651	+	9.34303i	−0.702393	+	0.450561i
$431$	7.06433	−	21.7418i	0.340277	−	1.04726i	−0.623787	−	0.781594i	$-0.714407\pi$
$431$	7.06433	−	21.7418i	0.340277	−	1.04726i	0.964064	−	0.265670i	$-0.0855933\pi$
$432$	−6.32389	−	6.46213i	−0.304258	−	0.310910i
$433$	15.0326	+	7.65951i	0.722422	+	0.368093i	0.776222	−	0.630459i	$-0.217133\pi$
$433$	15.0326	+	7.65951i	0.722422	+	0.368093i	−0.0538001	+	0.998552i	$0.517133\pi$
$434$	25.1227	+	9.34547i	1.20593	+	0.448597i
$435$	−12.8786	−	41.9052i	−0.617483	−	2.00920i
$436$	4.19088	+	10.2744i	0.200707	+	0.492056i
$437$			25.6543i			1.22721i
$438$	−1.52330	+	7.55139i	−0.0727859	+	0.360819i
$439$	0.622671	−	3.93139i	0.0297185	−	0.187635i	−0.968363	−	0.249545i	$-0.919719\pi$
$439$	0.622671	−	3.93139i	0.0297185	−	0.187635i	0.998082	+	0.0619096i	$0.0197190\pi$
$440$	−7.29456	+	7.51927i	−0.347755	+	0.358467i
$441$	13.9779	+	10.1555i	0.665614	+	0.483597i
$442$	12.7313	−	3.55347i	0.605565	−	0.169021i
$443$	−29.4982	+	4.67205i	−1.40150	+	0.221976i	−0.810993	−	0.585056i	$-0.801072\pi$
$443$	−29.4982	+	4.67205i	−1.40150	+	0.221976i	−0.590507	+	0.807032i	$0.701072\pi$
$444$	13.7346	−	22.1432i	0.651815	−	1.05087i
$445$	1.90369	+	1.43018i	0.0902436	+	0.0677971i
$446$	10.1357	−	1.17187i	0.479940	−	0.0554897i
$447$	−1.99570	+	12.6003i	−0.0943933	+	0.595976i
$448$	31.6284	−	1.97371i	1.49430	−	0.0932489i
$449$	−1.22197	−	3.76083i	−0.0576682	−	0.177485i	0.918073	−	0.396411i	$-0.129744\pi$
$449$	−1.22197	−	3.76083i	−0.0576682	−	0.177485i	−0.975741	+	0.218927i	$0.929744\pi$
$450$	14.0181	+	1.03867i	0.660819	+	0.0489633i
$451$	9.68839	+	4.31611i	0.456208	+	0.203238i
$452$	8.91061	−	36.2509i	0.419120	−	1.70510i
$453$	−4.47997	+	8.79244i	−0.210488	+	0.413105i
$454$	−8.43997	+	2.35571i	−0.396107	+	0.110559i
$455$	24.0552	+	49.1383i	1.12773	+	2.30364i
$456$	17.3335	−	13.4381i	0.811714	−	0.629299i
$457$	−19.3008	+	6.27120i	−0.902852	+	0.293354i	−0.723414	−	0.690415i	$-0.757428\pi$
$457$	−19.3008	+	6.27120i	−0.902852	+	0.293354i	−0.179438	+	0.983769i	$0.557428\pi$
$458$	21.6838	+	23.5850i	1.01322	+	1.10205i
$459$	2.01047	−	2.76718i	0.0938408	−	0.129161i
$460$	13.2957	−	30.2510i	0.619915	−	1.41046i
$461$	−13.7082	−	9.95962i	−0.638457	−	0.463866i	0.220863	−	0.975305i	$-0.429113\pi$
$461$	−13.7082	−	9.95962i	−0.638457	−	0.463866i	−0.859320	+	0.511439i	$0.829113\pi$
$462$	18.8439	−	8.62547i	0.876697	−	0.401293i
$463$	1.29514	−	0.940973i	0.0601902	−	0.0437307i	−0.557283	−	0.830322i	$-0.688156\pi$
$463$	1.29514	−	0.940973i	0.0601902	−	0.0437307i	0.617473	+	0.786592i	$0.288156\pi$
$464$	20.3313	+	28.6295i	0.943855	+	1.32909i
$465$	−23.5380	−	4.11496i	−1.09155	−	0.190827i
$466$	−9.55411	−	7.57381i	−0.442585	−	0.350850i
$467$	−9.28740	−	18.2275i	−0.429770	−	0.843470i	−0.999762	−	0.0218203i	$-0.993054\pi$
$467$	−9.28740	−	18.2275i	−0.429770	−	0.843470i	0.569992	−	0.821650i	$-0.306946\pi$
$468$	2.05904	−	24.4706i	0.0951790	−	1.13115i
$469$	−23.9874	+	7.79396i	−1.10763	+	0.359892i
$470$	−28.0185	−	6.11989i	−1.29240	−	0.282289i
$471$	13.2245	−	40.7008i	0.609352	−	1.87539i
$472$	5.44950	+	9.91858i	0.250833	+	0.456540i
$473$	2.80095	−	8.62045i	0.128788	−	0.396369i
$474$	4.68182	+	0.944434i	0.215043	+	0.0433793i
$475$	3.26271	−	17.0508i	0.149703	−	0.782345i
$476$	2.73554	+	11.6719i	0.125383	+	0.534983i
$477$	4.51681	+	6.21685i	0.206810	+	0.284650i
$478$	−11.1121	+	19.7169i	−0.508257	+	0.901832i
$479$	11.9433	+	6.08544i	0.545705	+	0.278051i	0.705032	−	0.709175i	$-0.250932\pi$
$479$	11.9433	+	6.08544i	0.545705	+	0.278051i	−0.159327	+	0.987226i	$0.550932\pi$
$480$	−27.4038	+	6.86266i	−1.25081	+	0.313236i
$481$	−35.5883	+	5.63663i	−1.62269	+	0.257008i
$482$	−2.74450	+	7.37783i	−0.125009	+	0.336051i
$483$	−46.2223	+	46.2223i	−2.10319	+	2.10319i
$484$	−1.38453	+	16.4544i	−0.0629330	+	0.747925i
$485$	−3.67508	+	6.93623i	−0.166877	+	0.314958i
$486$	−13.9385	−	20.9830i	−0.632263	−	0.951807i
$487$	−29.9558	−	4.74454i	−1.35743	−	0.214995i	−0.565065	−	0.825046i	$-0.691149\pi$
$487$	−29.9558	−	4.74454i	−1.35743	−	0.214995i	−0.792362	+	0.610051i	$0.791149\pi$
$488$	3.86467	+	0.489222i	0.174945	+	0.0221460i
$489$	−25.3977	−	25.3977i	−1.14852	−	1.14852i
$490$	−25.1708	+	11.0381i	−1.13710	+	0.498651i
$491$			21.1626i			0.955056i	0.878617	+	0.477528i	$0.158467\pi$
$491$			21.1626i			0.955056i	−0.878617	+	0.477528i	$0.841533\pi$
$492$	16.0669	+	23.6616i	0.724350	+	1.06675i
$493$	−9.39292	+	9.39292i	−0.423036	+	0.423036i
$494$	−29.7297	−	5.99720i	−1.33760	−	0.269827i
$495$	−6.02517	+	4.23199i	−0.270811	+	0.190214i
$496$	18.9348	−	2.78947i	0.850198	−	0.125251i
$497$	−6.13006	+	38.7037i	−0.274971	+	1.73610i
$498$	0.334782	−	1.65961i	0.0150020	−	0.0743688i
$499$	10.7065	+	21.0128i	0.479290	+	0.940661i	0.996403	+	0.0847430i	$0.0270069\pi$
$499$	10.7065	+	21.0128i	0.479290	+	0.940661i	−0.517112	+	0.855918i	$0.672993\pi$
$500$	−12.6841	+	18.4150i	−0.567252	+	0.823544i
$501$			12.7325i			0.568846i
$502$	−35.1104	−	13.0608i	−1.56705	−	0.582934i
$503$	12.5925	+	9.14895i	0.561470	+	0.407932i	0.831997	−	0.554781i	$-0.187198\pi$
$503$	12.5925	+	9.14895i	0.561470	+	0.407932i	−0.270527	+	0.962712i	$0.587198\pi$
$504$	22.0962	+	2.79711i	0.984241	+	0.124593i
$505$	26.4607	+	19.8791i	1.17748	+	0.884606i
$506$	4.65323	+	16.6715i	0.206861	+	0.741137i
$507$	−45.4436	+	33.0167i	−2.01822	+	1.46632i
$508$	−35.1395	−	21.7957i	−1.55906	−	0.967026i
$509$	−38.5231	+	6.10146i	−1.70751	+	0.270442i	−0.932410	−	0.361402i	$-0.882298\pi$
$509$	−38.5231	+	6.10146i	−1.70751	+	0.270442i	−0.775095	+	0.631844i	$0.782298\pi$
$510$	−4.29195	−	9.78719i	−0.190051	−	0.433384i
$511$	4.38624	+	8.60849i	0.194036	+	0.380817i
$512$	19.1142	−	12.1098i	0.844737	−	0.535181i
$513$	−6.99280	+	3.56301i	−0.308739	+	0.157311i
$514$	−1.05746	+	25.1790i	−0.0466424	+	1.11060i
$515$	−13.9539	+	18.5738i	−0.614881	+	0.818458i
$516$	18.6715	−	15.7732i	0.821968	−	0.694377i
$517$	13.3850	−	6.81999i	0.588671	−	0.299943i
$518$	−3.75337	−	32.4636i	−0.164914	−	1.42637i
$519$	−31.9039	−	31.9039i	−1.40043	−	1.40043i
$520$	31.9485	+	22.4796i	1.40104	+	0.985796i
$521$	−6.95049	+	43.8837i	−0.304507	+	1.92258i	0.0745728	+	0.997216i	$0.476241\pi$
$521$	−6.95049	+	43.8837i	−0.304507	+	1.92258i	−0.379080	+	0.925364i	$0.623759\pi$
$522$	10.2715	+	22.4400i	0.449573	+	0.982174i
$523$	1.91926	+	12.1177i	0.0839235	+	0.529872i	0.993454	+	0.114235i	$0.0364415\pi$
$523$	1.91926	+	12.1177i	0.0839235	+	0.529872i	−0.909530	+	0.415638i	$0.863558\pi$
$524$	−23.3707	+	14.1484i	−1.02095	+	0.618075i
$525$	36.5996	−	24.8425i	1.59734	−	1.08422i
$526$	5.83903	+	0.245225i	0.254594	+	0.0106923i
$527$	2.23738	+	6.88593i	0.0974616	+	0.299956i
$528$	8.82672	−	11.8768i	0.384134	−	0.516870i
$529$	−18.5711	−	25.5609i	−0.807437	−	1.11134i
$530$	−12.1642	+	1.20960i	−0.528379	+	0.0525416i
$531$	2.45789	+	7.56461i	0.106663	+	0.328276i
$532$	6.56591	−	26.7120i	0.284668	−	1.15811i
$533$	10.2447	−	38.2000i	0.443747	−	1.65463i
$534$	−2.92997	−	1.65128i	−0.126792	−	0.0714579i
$535$	11.9199	−	15.8663i	0.515341	−	0.685962i
$536$	−12.3314	+	13.1249i	−0.532633	+	0.566907i
$537$	35.1426	+	5.56604i	1.51651	+	0.240192i
$538$	1.82868	+	1.44965i	0.0788400	+	0.0624988i
$539$	6.53598	−	12.8276i	0.281525	−	0.552523i
$540$	10.0923	−	0.577309i	0.434305	−	0.0248434i
$541$	13.9504	−	19.2011i	0.599776	−	0.825520i	−0.395912	−	0.918288i	$-0.629572\pi$
$541$	13.9504	−	19.2011i	0.599776	−	0.825520i	0.995688	+	0.0927682i	$0.0295715\pi$
$542$	1.97342	+	7.07032i	0.0847657	+	0.303696i
$543$	−3.46273	−	21.8628i	−0.148600	−	0.938225i
$544$	5.72498	+	6.36367i	0.245457	+	0.272840i
$545$	−11.7360	−	4.02188i	−0.502715	−	0.172278i
$546$	−42.7598	−	64.3705i	−1.82995	−	2.75480i
$547$	11.6484			0.498050			0.249025	−	0.968497i	$-0.419890\pi$
$547$	11.6484			0.498050			0.249025	+	0.968497i	$0.419890\pi$
$548$	19.2941	+	8.11433i	0.824201	+	0.346627i
$549$	2.60386	+	0.846046i	0.111130	+	0.0361084i
$550$	−0.972439	−	11.6723i	−0.0414649	−	0.497707i
$551$	28.9876	−	9.41865i	1.23491	−	0.401248i
$552$	−13.0332	+	44.8179i	−0.554730	+	1.90758i
$553$	5.33721	−	2.71945i	0.226961	−	0.115643i
$554$	−5.32292	+	4.89384i	−0.226149	+	0.207919i
$555$	8.55817	+	27.8471i	0.363274	+	1.18204i
$556$	−18.8024	−	16.2354i	−0.797399	−	0.688533i
$557$	14.2703	−	19.6414i	0.604652	−	0.832233i	−0.391472	−	0.920190i	$-0.628034\pi$
$557$	14.2703	−	19.6414i	0.604652	−	0.832233i	0.996124	+	0.0879575i	$0.0280340\pi$
$558$	13.4397	+	0.564432i	0.568946	+	0.0238943i
$559$	−33.3829	−	5.28734i	−1.41195	−	0.223631i
$560$	−21.5862	+	28.0954i	−0.912186	+	1.18725i
$561$	4.98775	+	2.54139i	0.210583	+	0.107297i
$562$	28.9506	−	3.34721i	1.22121	−	0.141193i
$563$	14.1297	+	10.2659i	0.595498	+	0.432654i	0.844278	−	0.535906i	$-0.180030\pi$
$563$	14.1297	+	10.2659i	0.595498	+	0.432654i	−0.248780	+	0.968560i	$0.580030\pi$
$564$	40.3665	+	3.39658i	1.69974	+	0.143022i
$565$	23.9888	+	34.1533i	1.00922	+	1.43684i
$566$	14.4926	+	31.6617i	0.609170	+	1.33084i
$567$	−41.4861	−	13.4796i	−1.74225	−	0.566092i
$568$	9.47114	+	26.3281i	0.397400	+	1.10470i
$569$	−22.1717	+	16.1087i	−0.929487	+	0.675312i	−0.945867	−	0.324554i	$-0.894786\pi$
$569$	−22.1717	+	16.1087i	−0.929487	+	0.675312i	0.0163802	+	0.999866i	$0.494786\pi$
$570$	−1.42061	+	24.4801i	−0.0595028	+	1.02536i
$571$	27.6858	+	27.6858i	1.15861	+	1.15861i	0.984774	+	0.173839i	$0.0556171\pi$
$571$	27.6858	+	27.6858i	1.15861	+	1.15861i	0.173839	+	0.984774i	$0.444383\pi$
$572$	−20.4077	+	1.49516i	−0.853287	+	0.0625157i
$573$	13.5740	−	13.5740i	0.567060	−	0.567060i
$574$	34.2259	+	10.7372i	1.42856	+	0.448164i
$575$	15.7110	+	33.4371i	0.655194	+	1.39442i
$576$	14.7893	−	5.84679i	0.616222	−	0.243616i
$577$	6.29920			0.262239			0.131120	−	0.991367i	$-0.458143\pi$
$577$	6.29920			0.262239			0.131120	+	0.991367i	$0.458143\pi$
$578$	12.9234	−	16.3024i	0.537543	−	0.678092i
$579$	19.6676	+	27.0701i	0.817358	+	1.12500i
$580$	−39.0630	−	3.91697i	−1.62200	−	0.162643i
$581$	−0.963987	−	1.89193i	−0.0399929	−	0.0784905i
$582$	3.86574	−	10.3920i	0.160240	−	0.430760i
$583$	4.52770	−	4.52770i	0.187518	−	0.187518i
$584$	5.70469	+	3.87903i	0.236062	+	0.160515i
$585$	19.1011	+	19.7220i	0.789732	+	0.815406i
$586$	−16.5639	+	20.8948i	−0.684249	+	0.863157i
$587$	−16.1134	+	5.23556i	−0.665071	+	0.216095i	−0.622048	−	0.782979i	$-0.713699\pi$
$587$	−16.1134	+	5.23556i	−0.665071	+	0.216095i	−0.0430233	+	0.999074i	$0.513699\pi$
$588$	33.2105	−	20.1053i	1.36958	−	0.829129i
$589$	2.59884	−	16.4084i	0.107083	−	0.676098i
$590$	−12.3614	−	2.70002i	−0.508911	−	0.111158i
$591$	−16.8187	+	2.66381i	−0.691827	+	0.109575i
$592$	−13.5106	−	19.0250i	−0.555284	−	0.781922i
$593$	−1.58365	+	4.87396i	−0.0650325	+	0.200150i	−0.978293	−	0.207227i	$-0.933556\pi$
$593$	−1.58365	+	4.87396i	−0.0650325	+	0.200150i	0.913260	+	0.407376i	$0.133556\pi$
$594$	−3.89800	+	3.58379i	−0.159937	+	0.147045i
$595$	−11.8435	−	6.27516i	−0.485537	−	0.257256i
$596$	9.70850	+	6.02181i	0.397676	+	0.246663i
$597$	8.86398	−	17.3965i	0.362778	−	0.711993i
$598$	58.6865	−	26.8628i	2.39987	−	1.09850i
$599$	6.83087	−	21.0232i	0.279102	−	0.858986i	−0.709003	−	0.705205i	$-0.750855\pi$
$599$	6.83087	−	21.0232i	0.279102	−	0.858986i	0.988105	−	0.153781i	$-0.0491451\pi$
$600$	14.3623	−	28.1301i	0.586338	−	1.14841i
$601$	−11.9766	−	11.9766i	−0.488535	−	0.488535i	0.419309	−	0.907844i	$-0.362273\pi$
$601$	−11.9766	−	11.9766i	−0.488535	−	0.488535i	−0.907844	+	0.419309i	$0.862273\pi$
$602$	6.06169	−	30.0495i	0.247056	−	1.22472i
$603$	−10.2399	+	7.43971i	−0.417000	+	0.302968i
$604$	5.70270	+	6.75056i	0.232040	+	0.274676i
$605$	−12.8438	−	13.2614i	−0.522176	−	0.539152i
$606$	−40.7256	−	22.9523i	−1.65437	−	0.932372i
$607$	2.01432	+	12.7179i	0.0817589	+	0.516205i	0.994248	+	0.107104i	$0.0341577\pi$
$607$	2.01432	+	12.7179i	0.0817589	+	0.516205i	−0.912489	+	0.409101i	$0.865842\pi$
$608$	−5.07535	−	18.9737i	−0.205833	−	0.769485i
$609$	69.1980	+	35.2581i	2.80404	+	1.42873i
$610$	−3.25291	+	2.89608i	−0.131707	+	0.117259i
$611$	−32.9258	−	45.3185i	−1.33204	−	1.83339i
$612$	3.11563	+	5.14650i	0.125942	+	0.208035i
$613$	−14.4031	+	28.2677i	−0.581737	+	1.14172i	0.393244	+	0.919434i	$0.371353\pi$
$613$	−14.4031	+	28.2677i	−0.581737	+	1.14172i	−0.974981	+	0.222288i	$0.928647\pi$
$614$	−24.0855	−	13.5742i	−0.972010	−	0.547809i
$615$	−31.7433	−	3.85767i	−1.28001	−	0.155556i
$616$	−0.578217	−	18.5497i	−0.0232970	−	0.747390i
$617$	−18.1514	−	9.24862i	−0.730749	−	0.372335i	0.0486893	−	0.998814i	$-0.484496\pi$
$617$	−18.1514	−	9.24862i	−0.730749	−	0.372335i	−0.779439	+	0.626479i	$0.784496\pi$
$618$	16.1111	−	28.5869i	0.648083	−	1.14993i
$619$	16.4029	−	11.9174i	0.659287	−	0.479000i	−0.207135	−	0.978312i	$-0.566414\pi$
$619$	16.4029	−	11.9174i	0.659287	−	0.479000i	0.866422	+	0.499313i	$0.166414\pi$
$620$	−11.5684	+	18.0016i	−0.464598	+	0.722961i
$621$	7.58244	−	14.8814i	0.304273	−	0.597169i
$622$	−5.79517	−	6.30327i	−0.232365	−	0.252738i
$623$	−4.16617	+	0.659856i	−0.166914	+	0.0264366i
$624$	−48.8909	−	25.5807i	−1.95720	−	1.02405i
$625$	−6.18959	−	24.2217i	−0.247584	−	0.968866i
$626$	13.4540	+	5.00479i	0.537729	+	0.200032i
$627$	−7.54976	−	10.3914i	−0.301509	−	0.414991i
$628$	−29.0066	−	25.0464i	−1.15749	−	0.999462i
$629$	6.24184	−	6.24184i	0.248878	−	0.248878i
$630$	−18.5985	+	16.5583i	−0.740981	+	0.659698i
$631$	−27.6967	−	8.99919i	−1.10259	−	0.358252i	−0.299489	−	0.954100i	$-0.596816\pi$
$631$	−27.6967	−	8.99919i	−1.10259	−	0.358252i	−0.803097	+	0.595848i	$0.796816\pi$
$632$	2.40498	−	3.53688i	0.0956648	−	0.140689i
$633$	19.5419	+	9.95711i	0.776722	+	0.395760i
$634$	−0.0831792	+	1.98057i	−0.00330347	+	0.0786586i
$635$	44.1910	−	13.5811i	1.75367	−	0.538951i
$636$	16.8111	−	3.94001i	0.666605	−	0.156231i
$637$	−51.0565	−	16.5893i	−2.02293	−	0.657291i
$638$	17.1292	−	11.3785i	0.678153	−	0.450481i
$639$	3.07628	+	19.4229i	0.121696	+	0.768357i
$640$	−3.84864	+	25.0038i	−0.152131	+	0.988360i
$641$	43.0787	+	6.82299i	1.70151	+	0.269492i	0.930222	−	0.366998i	$-0.119615\pi$
$641$	43.0787	+	6.82299i	1.70151	+	0.269492i	0.771284	+	0.636491i	$0.219615\pi$
$642$	−13.7626	+	24.4199i	−0.543168	+	0.963776i
$643$	−4.31112	−	13.2683i	−0.170014	−	0.523250i	0.829357	−	0.558720i	$-0.188707\pi$
$643$	−4.31112	−	13.2683i	−0.170014	−	0.523250i	−0.999371	+	0.0354699i	$0.988707\pi$
$644$	22.1088	+	54.2024i	0.871210	+	2.13587i
$645$	−0.437036	+	27.3237i	−0.0172083	+	1.07587i
$646$	6.75594	−	3.09242i	0.265809	−	0.121670i
$647$	0.786636	+	0.786636i	0.0309259	+	0.0309259i	0.722401	−	0.691475i	$-0.243039\pi$
$647$	0.786636	+	0.786636i	0.0309259	+	0.0309259i	−0.691475	+	0.722401i	$0.743039\pi$
$648$	−30.5963	+	5.82848i	−1.20194	+	0.228964i
$649$	5.90529	−	3.00889i	0.231803	−	0.118109i
$650$	−42.4216	+	10.3903i	−1.66391	+	0.407539i
$651$	34.2461	−	24.8812i	1.34221	−	0.975172i
$652$	−29.7825	+	12.1481i	−1.16637	+	0.475756i
$653$			25.4645i			0.996503i	0.867032	+	0.498252i	$0.166024\pi$
$653$			25.4645i			0.996503i	−0.867032	+	0.498252i	$0.833976\pi$
$654$	17.1775	+	3.46511i	0.671693	+	0.135496i
$655$	5.26006	−	30.0881i	0.205527	−	1.17564i
$656$	25.1100	−	5.04842i	0.980382	−	0.197108i
$657$	3.42841	+	3.42841i	0.133755	+	0.133755i
$658$	42.3194	−	28.1118i	1.64978	−	1.09591i
$659$	1.22147	−	1.22147i	0.0475819	−	0.0475819i	−0.682915	−	0.730497i	$-0.739288\pi$
$659$	1.22147	−	1.22147i	0.0475819	−	0.0475819i	0.730497	+	0.682915i	$0.239288\pi$
$660$	3.51706	+	16.1660i	0.136901	+	0.629262i
$661$	−9.71777	−	13.3754i	−0.377977	−	0.520241i	0.577070	−	0.816695i	$-0.304196\pi$
$661$	−9.71777	−	13.3754i	−0.377977	−	0.520241i	−0.955047	+	0.296454i	$0.904196\pi$
$662$	−2.94215	+	14.5851i	−0.114350	+	0.566864i
$663$	6.45041	−	19.8523i	0.250513	−	0.771001i
$664$	−1.25375	−	0.852514i	−0.0486549	−	0.0330840i
$665$	17.6765	+	25.1664i	0.685464	+	0.975909i
$666$	−6.82570	−	14.9120i	−0.264491	−	0.577827i
$667$	−38.1257	+	52.4755i	−1.47623	+	2.03186i
$668$	10.5104	+	4.42028i	0.406661	+	0.171026i
$669$	7.31524	−	14.3570i	0.282823	−	0.555072i
$670$	−1.99235	−	20.0359i	−0.0769712	−	0.774053i
$671$	0.356881	−	2.25326i	0.0137773	−	0.0869862i
$672$	25.0411	−	43.3300i	0.965983	−	1.67149i
$673$	11.0962	+	8.06186i	0.427727	+	0.310762i	0.780739	−	0.624857i	$-0.214843\pi$
$673$	11.0962	+	8.06186i	0.427727	+	0.310762i	−0.353012	+	0.935619i	$0.614843\pi$
$674$	−0.417950	−	0.0843105i	−0.0160988	−	0.00324752i
$675$	−6.93218	+	8.92639i	−0.266820	+	0.343577i
$676$	11.4782	+	48.9751i	0.441470	+	1.88366i
$677$	−11.7685	−	23.0970i	−0.452300	−	0.887689i	−0.998740	−	0.0501903i	$-0.984017\pi$
$677$	−11.7685	−	23.0970i	−0.452300	−	0.887689i	0.546440	−	0.837498i	$-0.315983\pi$
$678$	−39.8998	−	43.3981i	−1.53234	−	1.66669i
$679$	−4.29716	−	13.2253i	−0.164910	−	0.507540i
$680$	−9.56915	+	0.145153i	−0.366960	+	0.00556635i
$681$	−4.27619	+	13.1608i	−0.163864	+	0.504321i
$682$	−1.28734	−	11.1344i	−0.0492946	−	0.426358i
$683$		−	9.05126i		−	0.346337i	−0.984892	−	0.173168i	$-0.944599\pi$
$683$		−	9.05126i		−	0.346337i	0.984892	−	0.173168i	$-0.0554005\pi$
$684$	−1.00864	−	13.7671i	−0.0385665	−	0.526400i
$685$	−21.0181	+	10.2892i	−0.803060	+	0.393131i
$686$	3.30366	−	8.88095i	0.126134	−	0.339076i
$687$	49.9723	−	7.91484i	1.90656	−	0.301970i
$688$	−6.53839	−	20.8889i	−0.249274	−	0.796381i
$689$	−19.3166	−	14.0344i	−0.735905	−	0.534666i
$690$	−28.1755	−	43.9236i	−1.07262	−	1.67214i
$691$	29.3587	+	14.9590i	1.11686	+	0.569067i	0.912191	−	0.409765i	$-0.134389\pi$
$691$	29.3587	+	14.9590i	1.11686	+	0.569067i	0.204666	+	0.978832i	$0.434389\pi$
$692$	−37.4120	+	15.2602i	−1.42219	+	0.580104i
$693$	2.04046	−	12.8830i	0.0775108	−	0.489384i
$694$	−44.5600	+	12.4373i	−1.69147	+	0.472113i
$695$	27.4980	−	3.90554i	1.04306	−	0.148146i
$696$	55.4262	−	1.72770i	2.10092	−	0.0654883i
$697$	3.47028	+	9.04636i	0.131446	+	0.342655i
$698$	42.3650	−	11.8246i	1.60354	−	0.447569i
$699$	−18.3115	+	5.94975i	−0.692603	+	0.225040i
$700$	−7.80092	−	38.8367i	−0.294847	−	1.46789i
$701$	−24.2490	+	17.6179i	−0.915871	+	0.665419i	−0.942493	−	0.334226i	$-0.891525\pi$
$701$	−24.2490	+	17.6179i	−0.915871	+	0.665419i	0.0266220	+	0.999646i	$0.491525\pi$
$702$	15.4729	+	12.2658i	0.583986	+	0.462943i
$703$	−19.2630	+	6.25893i	−0.726518	+	0.236060i
$704$	−6.73970	−	11.4095i	−0.254012	−	0.430011i
$705$	−32.5334	+	31.5090i	−1.22528	+	1.18670i
$706$	23.4715	−	41.6470i	0.883362	−	1.56740i
$707$	−57.9084	+	9.17179i	−2.17787	+	0.344941i
$708$	17.8092	+	1.49853i	0.669310	+	0.0563181i
$709$	−18.4549	−	2.92297i	−0.693089	−	0.109775i	−0.200055	−	0.979785i	$-0.564112\pi$
$709$	−18.4549	−	2.92297i	−0.693089	−	0.109775i	−0.493034	+	0.870010i	$0.664112\pi$
$710$	−29.1414	−	11.3742i	−1.09366	−	0.426866i
$711$	2.12559	−	2.12559i	0.0797159	−	0.0797159i
$712$	−2.38028	+	1.84537i	−0.0892049	+	0.0691580i
$713$	16.0504	+	31.5007i	0.601093	+	1.17971i
$714$	17.7441	+	6.60070i	0.664057	+	0.247025i
$715$	13.7414	−	18.2910i	0.513899	−	0.684043i
$716$	16.7949	−	27.0772i	0.627656	−	1.01192i
$717$	16.2265	+	31.8464i	0.605991	+	1.18932i
$718$	−1.43194	+	34.0958i	−0.0534395	+	1.27244i
$719$	−31.6023	+	16.1022i	−1.17857	+	0.600511i	−0.929805	−	0.368053i	$-0.880024\pi$
$719$	−31.6023	+	16.1022i	−1.17857	+	0.600511i	−0.248764	+	0.968564i	$0.580024\pi$
$720$	−5.94564	+	16.7567i	−0.221581	+	0.624484i
$721$	−6.43804	−	40.6482i	−0.239765	−	1.51382i
$722$	9.81303	+	0.412123i	0.365203	+	0.0153376i
$723$	7.30692	+	10.0571i	0.271747	+	0.374028i
$724$	−19.2495	−	4.73160i	−0.715402	−	0.175848i
$725$	32.0136	−	30.0284i	1.18895	−	1.11523i
$726$	20.4349	+	16.1994i	0.758412	+	0.601215i
$727$	2.56881	−	3.53566i	0.0952718	−	0.131130i	−0.758720	−	0.651417i	$-0.774175\pi$
$727$	2.56881	−	3.53566i	0.0952718	−	0.131130i	0.853992	+	0.520287i	$0.174175\pi$
$728$	−67.9813	+	12.9502i	−2.51955	+	0.479965i
$729$	−6.74570			−0.249841
$730$	−7.46111	+	1.95443i	−0.276148	+	0.0723368i
$731$	7.37778	−	3.75917i	0.272877	−	0.139038i
$732$	4.02055	−	4.65626i	0.148604	−	0.172100i
$733$	33.7221	+	5.34106i	1.24555	+	0.197276i	0.744195	−	0.667963i	$-0.232833\pi$
$733$	33.7221	+	5.34106i	1.24555	+	0.197276i	0.501360	+	0.865239i	$0.332833\pi$
$734$	−11.5887	+	1.33986i	−0.427747	+	0.0494552i
$735$	−7.47471	+	42.7561i	−0.275709	+	1.57708i
$736$	32.4717	+	26.3179i	1.19692	+	0.970090i
$737$	7.45765	+	7.45765i	0.274706	+	0.274706i
$738$	18.0002	−	0.182998i	0.662596	−	0.00673624i
$739$	25.2086			0.927315			0.463658	−	0.886014i	$-0.346537\pi$
$739$	25.2086			0.927315			0.463658	+	0.886014i	$0.346537\pi$
$740$	25.9583	+	2.60292i	0.954247	+	0.0956854i
$741$	−33.8673	+	33.8673i	−1.24415	+	1.24415i
$742$	13.4527	−	16.9701i	0.493863	−	0.622991i
$743$	−0.758139	+	4.78670i	−0.0278134	+	0.175607i	−0.997685	−	0.0680116i	$-0.978335\pi$
$743$	−0.758139	+	4.78670i	−0.0278134	+	0.175607i	0.969871	+	0.243619i	$0.0783345\pi$
$744$	12.8762	−	27.3451i	0.472063	−	1.00252i
$745$	−12.2093	+	3.75226i	−0.447314	+	0.137472i
$746$	−40.1479	+	18.3770i	−1.46992	+	0.672830i
$747$	−0.753478	−	0.753478i	−0.0275683	−	0.0275683i
$748$	3.82944	−	3.23501i	0.140018	−	0.118284i
$749$	5.49959	+	34.7230i	0.200951	+	1.26875i
$750$	13.1403	+	32.7766i	0.479815	+	1.19683i
$751$	−8.92059	+	17.5076i	−0.325517	+	0.638863i	−0.994537	−	0.104381i	$-0.966714\pi$
$751$	−8.92059	+	17.5076i	−0.325517	+	0.638863i	0.669020	+	0.743244i	$0.266714\pi$
$752$	16.8177	−	32.1426i	0.613277	−	1.17212i
$753$	−47.8608	+	34.7729i	−1.74415	+	1.26720i
$754$	−51.8991	−	56.4495i	−1.89005	−	2.05577i
$755$	−9.87870	−	0.158008i	−0.359523	−	0.00575049i
$756$	−11.7038	+	13.5543i	−0.425662	+	0.492965i
$757$	−19.5045	−	6.33740i	−0.708903	−	0.230337i	−0.0676977	−	0.997706i	$-0.521565\pi$
$757$	−19.5045	−	6.33740i	−0.708903	−	0.230337i	−0.641205	+	0.767369i	$0.721565\pi$
$758$	0.325556	−	7.75179i	0.0118247	−	0.281558i
$759$	25.9964	+	8.44675i	0.943610	+	0.306597i
$760$	19.7146	+	9.67131i	0.715125	+	0.350815i
$761$	−13.8231	−	42.5431i	−0.501087	−	1.54219i	−0.807251	−	0.590209i	$-0.799045\pi$
$761$	−13.8231	−	42.5431i	−0.501087	−	1.54219i	0.306164	−	0.951979i	$-0.400955\pi$
$762$	−59.3764	+	27.1785i	−2.15098	+	0.984575i
$763$	19.5821	−	9.97759i	0.708921	−	0.361213i
$764$	−6.49263	−	15.9174i	−0.234895	−	0.575873i
$765$	−6.62573	−	1.15832i	−0.239554	−	0.0418793i
$766$	14.6655	−	9.74191i	0.529884	−	0.351990i
$767$	−14.5265	−	19.9940i	−0.524520	−	0.721940i
$768$	0.772629	−	35.7254i	0.0278799	−	1.28913i
$769$	−4.26338	+	5.86804i	−0.153741	+	0.211607i	−0.878939	−	0.476934i	$-0.841748\pi$
$769$	−4.26338	+	5.86804i	−0.153741	+	0.211607i	0.725198	+	0.688540i	$0.241748\pi$
$770$	16.0518	+	13.1482i	0.578466	+	0.473827i
$771$	32.1975	+	23.3929i	1.15957	+	0.842474i
$772$	29.1738	−	6.83742i	1.04999	−	0.246084i
$773$	−7.33245	−	22.5669i	−0.263730	−	0.811677i	−0.991983	−	0.126369i	$-0.959668\pi$
$773$	−7.33245	−	22.5669i	−0.263730	−	0.811677i	0.728254	−	0.685308i	$-0.240332\pi$
$774$	−1.76685	−	15.2818i	−0.0635082	−	0.549294i
$775$	−6.66146	−	22.9778i	−0.239287	−	0.825388i
$776$	−7.23631	−	6.79882i	−0.259768	−	0.244063i
$777$	−45.9838	−	23.4299i	−1.64966	−	0.840543i
$778$	−46.1405	+	12.8784i	−1.65422	+	0.461714i
$779$	2.32875	−	22.1096i	0.0834360	−	0.792157i
$780$	57.4878	−	22.3834i	2.05839	−	0.801455i
$781$	15.5840	−	5.06355i	0.557640	−	0.181188i
$782$	−7.76330	+	13.7749i	−0.277615	+	0.492590i
$783$	−19.5988	−	3.10414i	−0.700402	−	0.110933i
$784$	−5.06700	−	34.3945i	−0.180964	−	1.22838i
$785$	42.4215	−	6.02512i	1.51409	−	0.215046i
$786$	−1.81034	+	43.1059i	−0.0645728	+	1.53754i
$787$	4.71778	+	29.7869i	0.168171	+	1.06179i	0.916960	+	0.398980i	$0.130636\pi$
$787$	4.71778	+	29.7869i	0.168171	+	1.06179i	−0.748789	+	0.662809i	$0.769364\pi$
$788$	−3.63993	+	14.8083i	−0.129667	+	0.527523i
$789$	5.42483	−	7.46663i	0.193129	−	0.265819i
$790$	1.21174	+	4.62584i	0.0431117	+	0.164580i
$791$	−73.0263	−	11.5662i	−2.59652	−	0.411248i
$792$	−3.15258	−	8.76363i	−0.112022	−	0.311402i
$793$	−8.50692			−0.302090
$794$	−23.2192	+	29.2902i	−0.824019	+	1.03947i
$795$	−9.03813	+	17.0583i	−0.320549	+	0.604995i
$796$	−11.2832	−	13.3565i	−0.399924	−	0.473409i
$797$	15.0442	−	29.5260i	0.532894	−	1.04586i	−0.454965	−	0.890509i	$-0.650348\pi$
$797$	15.0442	−	29.5260i	0.532894	−	1.04586i	0.987859	−	0.155354i	$-0.0496518\pi$
$798$	−29.4007	−	31.9785i	−1.04077	−	1.13203i
$799$	13.0516	+	4.24073i	0.461733	+	0.150026i
$800$	−18.2348	−	21.6216i	−0.644697	−	0.764438i
$801$	−1.88608	+	0.961003i	−0.0666412	+	0.0339554i
$802$	−11.2325	+	7.46150i	−0.396635	+	0.263475i
$803$	2.37468	−	3.26847i	0.0838007	−	0.115342i
$804$	6.48965	+	27.6899i	0.228872	+	0.976548i
$805$	−61.9128	−	21.2172i	−2.18214	−	0.747810i
$806$	−40.2570	+	11.2363i	−1.41799	+	0.395781i
$807$	3.50486	−	1.13880i	0.123377	−	0.0400876i
$808$	−33.0852	+	25.6500i	−1.16393	+	0.902363i
$809$	2.64134	+	16.6767i	0.0928645	+	0.586323i	0.989610	+	0.143777i	$0.0459248\pi$
$809$	2.64134	+	16.6767i	0.0928645	+	0.586323i	−0.896746	+	0.442546i	$0.854075\pi$
$810$	17.5802	−	30.0594i	0.617707	−	1.05618i
$811$	−0.301743			−0.0105956			−0.00529781	−	0.999986i	$-0.501686\pi$
$811$	−0.301743			−0.0105956			−0.00529781	+	0.999986i	$0.501686\pi$
$812$	53.1280	−	44.8812i	1.86443	−	1.57502i
$813$	11.0250	+	3.58224i	0.386664	+	0.125635i
$814$	−11.3828	+	7.56133i	−0.398967	+	0.265025i
$815$	11.6582	−	34.0191i	0.408369	−	1.19164i
$816$	13.3736	−	1.97020i	0.468171	−	0.0689709i
$817$	−18.9992			−0.664698
$818$	5.90352	−	3.92156i	0.206412	−	0.137114i
$819$	−48.6382			−1.69956
$820$	−14.2046	+	24.8642i	−0.496046	+	0.868296i
$821$	−34.6624			−1.20972			−0.604862	−	0.796330i	$-0.706772\pi$
$821$	−34.6624			−1.20972			−0.604862	+	0.796330i	$0.706772\pi$
$822$	27.5334	−	18.2898i	0.960338	−	0.637929i
$823$	−20.6558			−0.720017			−0.360008	−	0.932949i	$-0.617226\pi$
$823$	−20.6558			−0.720017			−0.360008	+	0.932949i	$0.617226\pi$
$824$	−18.0047	−	23.2238i	−0.627224	−	0.809038i
$825$	−16.2039	−	8.92024i	−0.564149	−	0.310563i
$826$	18.6708	−	12.4026i	0.649640	−	0.431540i
$827$	30.8935	+	10.0379i	1.07427	+	0.349052i	0.792150	−	0.610327i	$-0.208962\pi$
$827$	30.8935	+	10.0379i	1.07427	+	0.349052i	0.282122	+	0.959379i	$0.408962\pi$
$828$	18.9574	+	22.4408i	0.658816	+	0.779872i
$829$	−47.7823			−1.65955			−0.829774	−	0.558100i	$-0.811531\pi$
$829$	−47.7823			−1.65955			−0.829774	+	0.558100i	$0.811531\pi$
$830$	1.63977	−	0.429536i	0.0569171	−	0.0149094i
$831$	1.78631	+	11.2783i	0.0619664	+	0.391240i
$832$	−38.0896	+	31.4778i	−1.32052	+	1.09130i
$833$	12.5081	−	4.06413i	0.433380	−	0.140814i
$834$	−37.7865	+	10.5467i	−1.30844	+	0.365203i
$835$	−11.4496	+	5.60505i	−0.396230	+	0.193971i
$836$	−11.1989	+	2.62467i	−0.387321	+	0.0907760i
$837$	−6.35723	+	8.74997i	−0.219738	+	0.302443i
$838$	−4.29578	+	2.85358i	−0.148395	+	0.0985754i
$839$	−14.6508	+	7.46495i	−0.505802	+	0.257719i	−0.688220	−	0.725502i	$-0.741608\pi$
$839$	−14.6508	+	7.46495i	−0.505802	+	0.257719i	0.182418	+	0.983221i	$0.441608\pi$
$840$	18.0954	+	52.9457i	0.624351	+	1.82680i
$841$	45.7105	+	14.8522i	1.57622	+	0.512146i
$842$	−3.02613	−	3.29146i	−0.104287	−	0.113431i
$843$	20.8945	−	41.0077i	0.719643	−	1.41238i
$844$	15.0037	−	12.6747i	0.516448	−	0.436282i
$845$	−49.6950	−	26.3303i	−1.70956	−	0.905791i
$846$	15.8385	−	19.9797i	0.544538	−	0.686917i
$847$	32.7050			1.12376
$848$	2.58385	−	15.2451i	0.0887296	−	0.523519i
$849$	54.3131	+	8.60235i	1.86402	+	0.295232i
$850$	6.91167	−	8.16798i	0.237068	−	0.280160i
$851$	25.3355	−	34.8713i	0.868489	−	1.19537i
$852$	42.9092	+	10.5472i	1.47005	+	0.361343i
$853$	8.45724	+	53.3969i	0.289570	+	1.82828i	0.518791	+	0.854901i	$0.326382\pi$
$853$	8.45724	+	53.3969i	0.289570	+	1.82828i	−0.229221	+	0.973374i	$0.573618\pi$
$854$	0.323748	−	7.70873i	0.0110784	−	0.263787i
$855$	12.3392	+	9.27004i	0.421992	+	0.317029i
$856$	15.3802	+	19.8385i	0.525686	+	0.678067i
$857$	−27.3063	−	4.32489i	−0.932766	−	0.147736i	−0.328487	−	0.944509i	$-0.606539\pi$
$857$	−27.3063	−	4.32489i	−0.932766	−	0.147736i	−0.604279	+	0.796773i	$0.706539\pi$
$858$	−15.8658	+	28.1516i	−0.541648	+	0.961080i
$859$	40.3542	−	13.1119i	1.37687	−	0.447372i	0.475230	−	0.879861i	$-0.342365\pi$
$859$	40.3542	−	13.1119i	1.37687	−	0.447372i	0.901639	+	0.432490i	$0.142365\pi$
$860$	22.4035	+	9.84660i	0.763951	+	0.335766i
$861$	44.0314	−	35.6398i	1.50058	−	1.21460i
$862$	−31.1396	+	8.69149i	−1.06062	+	0.296033i
$863$	−2.69083	−	1.37105i	−0.0915970	−	0.0466710i	0.407592	−	0.913164i	$-0.366369\pi$
$863$	−2.69083	−	1.37105i	−0.0915970	−	0.0466710i	−0.499189	+	0.866493i	$0.666369\pi$
$864$	−2.66383	+	12.5062i	−0.0906254	+	0.425470i
$865$	14.6448	−	42.7340i	0.497937	−	1.45300i
$866$	−2.74038	−	23.7020i	−0.0931219	−	0.805428i
$867$	−10.1522	−	31.2453i	−0.344788	−	1.06115i
$868$	−8.64993	−	36.9074i	−0.293598	−	1.25272i
$869$	−2.02643	−	1.47229i	−0.0687420	−	0.0499440i
$870$	−39.2864	+	47.9624i	−1.33193	+	1.62608i
$871$	23.1162	−	31.8167i	0.783263	−	1.07807i
$872$	8.82381	−	12.9767i	0.298812	−	0.439447i
$873$	−4.10184	−	5.64570i	−0.138826	−	0.191078i
$874$	30.2206	−	20.0748i	1.02223	−	0.679042i
$875$	38.4512	+	21.9758i	1.29989	+	0.742919i
$876$	10.0875	−	4.11463i	0.340825	−	0.139021i
$877$	14.1804	−	7.22525i	0.478837	−	0.243979i	−0.197876	−	0.980227i	$-0.563404\pi$
$877$	14.1804	−	7.22525i	0.478837	−	0.243979i	0.676712	+	0.736248i	$0.263404\pi$
$878$	−5.11841	+	2.34287i	−0.172738	+	0.0790679i
$879$	13.0121	+	40.0471i	0.438887	+	1.35076i
$880$	14.5658	+	2.70902i	0.491011	+	0.0913212i
$881$	−27.5857	−	8.96315i	−0.929387	−	0.301976i	−0.195075	−	0.980788i	$-0.562495\pi$
$881$	−27.5857	−	8.96315i	−0.929387	−	0.301976i	−0.734312	+	0.678812i	$0.762495\pi$
$882$	1.02527	−	24.4127i	0.0345228	−	0.822020i
$883$	52.2101	+	16.9641i	1.75701	+	0.570887i	0.996883	−	0.0788887i	$-0.0251372\pi$
$883$	52.2101	+	16.9641i	1.75701	+	0.570887i	0.760126	+	0.649776i	$0.225137\pi$
$884$	−14.1484	−	12.2167i	−0.475861	−	0.410893i
$885$	−14.3533	+	13.9014i	−0.482481	+	0.467290i
$886$	28.5864	+	31.0927i	0.960378	+	1.04458i
$887$	−1.95260	+	1.41865i	−0.0655619	+	0.0476335i	−0.620083	−	0.784536i	$-0.712901\pi$
$887$	−1.95260	+	1.41865i	−0.0655619	+	0.0476335i	0.554522	+	0.832169i	$0.312901\pi$
$888$	−36.8321	+	1.14810i	−1.23600	+	0.0385277i
$889$	−37.1814	+	72.9725i	−1.24702	+	2.44742i
$890$	0.195082	−	3.36167i	0.00653917	−	0.112684i
$891$	2.85344	+	18.0159i	0.0955940	+	0.603557i
$892$	−9.31180	−	11.0228i	−0.311782	−	0.369071i
$893$	−22.2656	−	22.2656i	−0.745089	−	0.745089i
$894$	16.4048	−	7.50902i	0.548659	−	0.251139i
$895$	10.4651	+	34.0520i	0.349810	+	1.13823i
$896$	−27.0747	−	35.7137i	−0.904502	−	1.19311i
$897$	15.9449	−	100.672i	0.532383	−	3.36134i
$898$	−3.47403	+	4.38237i	−0.115930	+	0.146242i
$899$	29.7010	−	29.7010i	0.990583	−	0.990583i
$900$	−9.74580	−	17.3260i	−0.324860	−	0.577533i
$901$	5.84943			0.194873
$902$	−2.49694	−	14.7903i	−0.0831389	−	0.492463i
$903$	−34.2315	−	34.2315i	−1.13915	−	1.13915i
$904$	−49.6761	+	17.8702i	−1.65220	+	0.594354i
$905$	18.1357	−	12.7382i	0.602850	−	0.423433i
$906$	13.8631	−	1.60282i	0.460570	−	0.0532502i
$907$	−17.6639	−	2.79769i	−0.586521	−	0.0928959i	−0.143881	−	0.989595i	$-0.545958\pi$
$907$	−17.6639	−	2.79769i	−0.586521	−	0.0928959i	−0.442640	+	0.896699i	$0.645958\pi$
$908$	9.37940	+	8.09887i	0.311266	+	0.268770i
$909$	−26.2158	+	13.3576i	−0.869524	+	0.443045i
$910$	39.0611	−	66.7883i	1.29486	−	2.21401i
$911$	44.5912			1.47737			0.738685	−	0.674050i	$-0.235447\pi$
$911$	44.5912			1.47737			0.738685	+	0.674050i	$0.235447\pi$
$912$	−29.3937	−	9.90321i	−0.973324	−	0.327928i
$913$	−0.521896	+	0.718328i	−0.0172722	+	0.0237732i
$914$	22.4906	+	17.8289i	0.743922	+	0.589728i
$915$	0.967176	+	6.80967i	0.0319739	+	0.225121i
$916$	10.8151	−	43.9989i	0.357341	−	1.45377i
$917$	31.8051	+	43.7759i	1.05030	+	1.44561i
$918$	−4.83294	−	0.202972i	−0.159511	−	0.00669906i
$919$	−4.05637	−	25.6109i	−0.133807	−	0.844826i	−0.959706	−	0.281007i	$-0.909332\pi$
$919$	−4.05637	−	25.6109i	−0.133807	−	0.844826i	0.825898	−	0.563819i	$-0.190668\pi$
$920$	−46.0396	+	8.00957i	−1.51788	+	0.264068i
$921$	−38.9023	+	19.8217i	−1.28188	+	0.653148i
$922$	−1.00550	+	23.9418i	−0.0331142	+	0.788481i
$923$	−27.7396	−	54.4421i	−0.913062	−	1.79198i
$924$	−24.9064	−	15.4485i	−0.819359	−	0.508217i
$925$	−21.2738	+	19.9546i	−0.699479	+	0.656103i
$926$	−2.12192	−	0.789342i	−0.0697307	−	0.0259394i
$927$	−9.37624	−	18.4019i	−0.307956	−	0.604398i
$928$	17.8159	−	46.3531i	0.584834	−	1.52161i
$929$	−4.66996	+	4.66996i	−0.153216	+	0.153216i	−0.779553	−	0.626336i	$-0.784554\pi$
$929$	−4.66996	+	4.66996i	−0.153216	+	0.153216i	0.626336	+	0.779553i	$0.284554\pi$
$930$	13.5714	+	30.9477i	0.445024	+	1.01481i
$931$	−29.8054	−	4.72072i	−0.976834	−	0.154715i
$932$	−1.44569	+	17.1813i	−0.0473553	+	0.562792i
$933$	−13.3555	+	2.11530i	−0.437240	+	0.0692520i
$934$	−14.2044	+	25.2038i	−0.464784	+	0.824694i
$935$	−0.0896341	+	5.60396i	−0.00293135	+	0.183269i
$936$	−30.4374	+	16.7230i	−0.994878	+	0.546609i
$937$	11.1325	−	3.61718i	0.363684	−	0.118168i	−0.121474	−	0.992595i	$-0.538762\pi$
$937$	11.1325	−	3.61718i	0.363684	−	0.118168i	0.485158	+	0.874426i	$0.338762\pi$
$938$	27.9517	+	22.1581i	0.912655	+	0.723488i
$939$	18.3398	−	13.3247i	0.598498	−	0.434834i
$940$	14.7156	+	37.7945i	0.479971	+	1.23272i
$941$	21.4728	−	6.97694i	0.699994	−	0.227442i	0.0626659	−	0.998035i	$-0.480040\pi$
$941$	21.4728	−	6.97694i	0.699994	−	0.227442i	0.637328	+	0.770593i	$0.280040\pi$
$942$	−58.2936	+	16.2705i	−1.89931	+	0.530123i
$943$	23.6468	+	40.9783i	0.770045	+	1.33444i
$944$	7.41974	−	14.1809i	0.241492	−	0.461549i
$945$	−2.81543	−	19.8228i	−0.0915860	−	0.644837i
$946$	−12.3466	+	3.44611i	−0.401424	+	0.112043i
$947$	−1.04784	+	6.61581i	−0.0340503	+	0.214985i	−0.998847	−	0.0480128i	$-0.984711\pi$
$947$	−1.04784	+	6.61581i	−0.0340503	+	0.214985i	0.964796	+	0.262998i	$0.0847112\pi$
$948$	−2.55105	−	6.25419i	−0.0828542	−	0.203127i
$949$	−13.4230	−	6.83935i	−0.435728	−	0.222015i
$950$	−22.6389	+	9.49904i	−0.734502	+	0.308190i
$951$	2.53265	+	1.84008i	0.0821267	+	0.0596686i
$952$	11.6089	−	12.3559i	0.376246	−	0.400457i
$953$	50.9146	−	8.06408i	1.64929	−	0.261221i	0.738546	−	0.674203i	$-0.235513\pi$
$953$	50.9146	−	8.06408i	1.64929	−	0.261221i	0.910739	+	0.412982i	$0.135513\pi$
$954$	3.78896	−	10.1855i	0.122672	−	0.329769i
$955$	18.1818	+	6.23080i	0.588348	+	0.201624i
$956$	31.9219	−	2.33874i	1.03243	−	0.0756403i
$957$		−	32.4753i		−	1.04978i
$958$	−2.17722	−	18.8311i	−0.0703427	−	0.608407i
$959$	12.8107	−	39.4272i	0.413678	−	1.27317i
$960$	29.5280	+	26.9114i	0.953012	+	0.868561i
$961$	2.50482	+	7.70903i	0.0808005	+	0.248678i
$962$	34.4883	+	37.5121i	1.11195	+	1.20944i
$963$	8.00950	+	15.7195i	0.258103	+	0.506555i
$964$	10.8387	−	2.54024i	0.349090	−	0.0818157i
$965$	−15.6846	+	29.6027i	−0.504906	+	0.952944i
$966$	90.6192	+	18.2800i	2.91562	+	0.588151i
$967$	32.8911	+	23.8968i	1.05771	+	0.768470i	0.973663	−	0.227992i	$-0.0732161\pi$
$967$	32.8911	+	23.8968i	1.05771	+	0.768470i	0.0840448	+	0.996462i	$0.473216\pi$
$968$	20.4666	−	11.2448i	0.657820	−	0.361421i
$969$	1.83556	−	11.5893i	0.0589666	−	0.372301i
$970$	11.0467	−	1.09847i	0.354687	−	0.0352698i
$971$	−12.9470	+	25.4100i	−0.415490	+	0.815444i	0.584502	+	0.811392i	$0.301290\pi$
$971$	−12.9470	+	25.4100i	−0.415490	+	0.815444i	−0.999992	+	0.00405211i	$0.998710\pi$
$972$	−13.8108	+	32.8389i	−0.442981	+	1.05331i
$973$	−28.9204	+	39.8055i	−0.927144	+	1.27610i
$974$	17.8518	+	39.0005i	0.572009	+	1.24966i
$975$	−23.4010	+	64.8824i	−0.749431	+	2.07790i
$976$	−2.44785	−	4.93538i	−0.0783539	−	0.157978i
$977$	−0.251011	+	0.772532i	−0.00803055	+	0.0247155i	−0.954992	−	0.296633i	$-0.904136\pi$
$977$	−0.251011	+	0.772532i	−0.00803055	+	0.0247155i	0.946961	+	0.321349i	$0.104136\pi$
$978$	−10.0443	+	49.7924i	−0.321181	+	1.59218i
$979$	1.03676	+	1.42697i	0.0331349	+	0.0456062i
$980$	32.6994	+	21.0137i	1.04454	+	0.671257i
$981$	7.79875	−	7.79875i	0.248995	−	0.248995i
$982$	24.9295	−	16.5600i	0.795531	−	0.528452i
$983$	13.2573	+	13.2573i	0.422843	+	0.422843i	0.886181	−	0.463339i	$-0.153349\pi$
$983$	13.2573	+	13.2573i	0.422843	+	0.422843i	−0.463339	+	0.886181i	$0.653349\pi$
$984$	15.3007	−	37.4422i	0.487767	−	1.19361i
$985$	−9.79926	−	13.9514i	−0.312231	−	0.444529i
$986$	18.4149	+	3.71473i	0.586450	+	0.118301i
$987$		−	80.2333i		−	2.55385i
$988$	16.1993	+	39.7144i	0.515367	+	1.26348i
$989$	32.7104	−	23.7655i	1.04013	−	0.755698i
$990$	9.70005	+	3.78603i	0.308288	+	0.120328i
$991$	16.1283	−	8.21780i	0.512334	−	0.261047i	−0.178656	−	0.983912i	$-0.557175\pi$
$991$	16.1283	−	8.21780i	0.512334	−	0.261047i	0.690990	+	0.722865i	$0.257175\pi$
$992$	−18.1027	−	20.1223i	−0.574762	−	0.638884i
$993$	16.6149	+	16.6149i	0.527258	+	0.527258i
$994$	50.3896	−	23.0650i	1.59826	−	0.731577i
$995$	19.5458	+	0.312630i	0.619643	+	0.00991105i
$996$	−2.21698	+	0.904294i	−0.0702477	+	0.0286536i
$997$	15.7453	+	48.4590i	0.498658	+	1.53471i	0.811178	+	0.584800i	$0.198827\pi$
$997$	15.7453	+	48.4590i	0.498658	+	1.53471i	−0.312520	+	0.949911i	$0.601173\pi$
$998$	16.3749	−	29.0550i	0.518339	−	0.919721i
$999$	13.0239	+	2.06278i	0.412057	+	0.0652634i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	820.2.bv.c.207.40	yes	960
4.3	odd	2	inner	820.2.bv.c.207.4	yes	960
5.3	odd	4		820.2.bk.c.43.22	✓	960
20.3	even	4		820.2.bk.c.43.64	yes	960
41.21	even	20		820.2.bk.c.267.64	yes	960
164.103	odd	20		820.2.bk.c.267.22	yes	960
205.103	odd	20	inner	820.2.bv.c.103.4	yes	960
820.103	even	20	inner	820.2.bv.c.103.40	yes	960

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.bk.c.43.22	✓	960	5.3	odd	4
820.2.bk.c.43.64	yes	960	20.3	even	4
820.2.bk.c.267.22	yes	960	164.103	odd	20
820.2.bk.c.267.64	yes	960	41.21	even	20
820.2.bv.c.103.4	yes	960	205.103	odd	20	inner
820.2.bv.c.103.40	yes	960	820.103	even	20	inner
820.2.bv.c.207.4	yes	960	4.3	odd	2	inner
820.2.bv.c.207.40	yes	960	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 820 = 2^{2} \cdot 5 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	820.bv (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.782514 - 1.17799i) q^{2} -2.23336 q^{3} +(-0.775344 + 1.84359i) q^{4} +(-0.983161 - 2.00833i) q^{5} +(1.74763 + 2.63089i) q^{6} +(3.76737 + 1.22409i) q^{7} +(2.77846 - 0.529286i) q^{8} +1.98789 q^{9} +(-1.59647 + 2.72971i) q^{10} +(-0.259122 - 1.63603i) q^{11} +(1.73162 - 4.11741i) q^{12} +(-5.87435 + 1.90869i) q^{13} +(-1.50604 - 5.39581i) q^{14} +(2.19575 + 4.48532i) q^{15} +(-2.79768 - 2.85884i) q^{16} +(0.889430 - 1.22420i) q^{17} +(-1.55555 - 2.34173i) q^{18} +(-3.09361 + 1.57627i) q^{19} +(4.46484 - 0.255401i) q^{20} +(-8.41388 - 2.73383i) q^{21} +(-1.72447 + 1.58546i) q^{22} +(3.35446 - 6.58351i) q^{23} +(-6.20530 + 1.18209i) q^{24} +(-3.06679 + 3.94902i) q^{25} +(6.84519 + 5.42638i) q^{26} +2.26040 q^{27} +(-5.17773 + 5.99640i) q^{28} +(-8.67047 - 1.37327i) q^{29} +(3.56548 - 6.09641i) q^{30} +(-2.81243 + 3.87098i) q^{31} +(-1.17848 + 5.53274i) q^{32} +(0.578713 + 3.65385i) q^{33} +(-2.13809 - 0.0897944i) q^{34} +(-1.24554 - 8.76960i) q^{35} +(-1.54130 + 3.66486i) q^{36} +(5.76174 + 0.912570i) q^{37} +(4.27763 + 2.41080i) q^{38} +(13.1195 - 4.26279i) q^{39} +(-3.79466 - 5.05970i) q^{40} +(-3.48858 + 5.36934i) q^{41} +(3.36353 + 12.0508i) q^{42} +(4.87565 + 2.48427i) q^{43} +(3.21709 + 0.790773i) q^{44} +(-1.95442 - 3.99234i) q^{45} +(-10.3803 + 1.20014i) q^{46} +(2.80251 + 8.62524i) q^{47} +(6.24823 + 6.38482i) q^{48} +(7.03152 + 5.10870i) q^{49} +(7.05174 + 0.522497i) q^{50} +(-1.98642 + 2.73407i) q^{51} +(1.03579 - 12.3098i) q^{52} +(2.27216 + 3.12736i) q^{53} +(-1.76880 - 2.66274i) q^{54} +(-3.03094 + 2.12889i) q^{55} +(11.1154 + 1.40708i) q^{56} +(6.90913 - 3.52038i) q^{57} +(5.16706 + 11.2884i) q^{58} +(1.23643 + 3.80535i) q^{59} +(-9.97158 + 0.570402i) q^{60} +(1.30986 + 0.425600i) q^{61} +(6.76076 + 0.283935i) q^{62} +(7.48911 + 2.43336i) q^{63} +(7.43971 - 2.94120i) q^{64} +(9.60871 + 9.92109i) q^{65} +(3.85137 - 3.54091i) q^{66} +(-5.15113 + 3.74251i) q^{67} +(1.56731 + 2.58892i) q^{68} +(-7.49172 + 14.7033i) q^{69} +(-9.35588 + 8.32958i) q^{70} +(1.54751 + 9.77059i) q^{71} +(5.52328 - 1.05216i) q^{72} +(1.72464 + 1.72464i) q^{73} +(-3.43364 - 7.50140i) q^{74} +(6.84924 - 8.81959i) q^{75} +(-0.507394 - 6.92551i) q^{76} +(1.02645 - 6.48073i) q^{77} +(-15.2878 - 12.1190i) q^{78} +(1.06927 - 1.06927i) q^{79} +(-2.99093 + 8.42937i) q^{80} -11.0120 q^{81} +(9.05492 - 0.0920563i) q^{82} +(-0.379034 - 0.379034i) q^{83} +(11.5637 - 13.3921i) q^{84} +(-3.33304 - 0.582690i) q^{85} +(-0.888808 - 7.68746i) q^{86} +(19.3643 + 3.06700i) q^{87} +(-1.58589 - 4.40851i) q^{88} +(-0.948782 + 0.483429i) q^{89} +(-3.17360 + 5.42636i) q^{90} -24.4672 q^{91} +(9.53645 + 11.2888i) q^{92} +(6.28117 - 8.64528i) q^{93} +(7.96748 - 10.0507i) q^{94} +(6.20718 + 4.66326i) q^{95} +(2.63196 - 12.3566i) q^{96} +(-2.06341 - 2.84004i) q^{97} +(0.515760 - 12.2807i) q^{98} +(-0.515107 - 3.25226i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 960 q - 10 q^{2} - 20 q^{5} - 16 q^{6} + 2 q^{8} + 960 q^{9} - 60 q^{10} - 40 q^{12} - 20 q^{13} - 8 q^{14} - 28 q^{16} - 20 q^{17} - 48 q^{18} - 34 q^{20} - 40 q^{21} - 10 q^{22} - 48 q^{24} - 4 q^{25}+ \cdots - 38 q^{98}+O(q^{100}) \) 960 * q - 10 * q^2 - 20 * q^5 - 16 * q^6 + 2 * q^8 + 960 * q^9 - 60 * q^10 - 40 * q^12 - 20 * q^13 - 8 * q^14 - 28 * q^16 - 20 * q^17 - 48 * q^18 - 34 * q^20 - 40 * q^21 - 10 * q^22 - 48 * q^24 - 4 * q^25 - 20 * q^26 - 10 * q^28 - 10 * q^30 - 56 * q^33 - 20 * q^34 - 100 * q^36 + 88 * q^37 - 16 * q^40 - 24 * q^41 - 104 * q^42 - 100 * q^45 - 20 * q^46 - 40 * q^48 + 224 * q^49 - 12 * q^50 - 38 * q^52 - 20 * q^53 - 52 * q^54 + 96 * q^56 - 72 * q^57 - 38 * q^58 - 14 * q^60 - 40 * q^61 - 10 * q^62 - 120 * q^64 - 60 * q^65 - 12 * q^66 - 116 * q^68 - 104 * q^69 - 96 * q^70 - 24 * q^72 - 72 * q^73 - 28 * q^74 - 40 * q^76 - 76 * q^77 - 44 * q^78 - 90 * q^80 + 592 * q^81 - 130 * q^82 - 92 * q^84 - 64 * q^85 - 12 * q^86 - 104 * q^88 + 136 * q^89 - 364 * q^90 - 220 * q^92 - 32 * q^94 - 44 * q^96 + 80 * q^97 - 38 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more