LMFDB - Embedded newform 507.2.m.b.40.15

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [507,2,Mod(40,507)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("507.40"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(507, base_ring=CyclotomicField(26)) chi = DirichletCharacter(H, H._module([0, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.m (of order $13$, degree $12$, minimal)

Newform invariants

comment:select newform

sage:traces = [204] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$204$
Relative dimension:	$17$ over $\Q(\zeta_{13})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{13}]$

Embedding invariants

Embedding label			40.15
Character	$\chi$	$=$	507.40
Dual form			507.2.m.b.469.15

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.11067 + 0.520234i) q^{2} +(0.120537 - 0.992709i) q^{3} +(2.41339 + 1.26664i) q^{4} +(1.14528 - 1.65922i) q^{5} +(0.770855 - 2.03258i) q^{6} +(-0.139189 - 0.123310i) q^{7} +(1.18063 + 1.04595i) q^{8} +(-0.970942 - 0.239316i) q^{9} +(3.28049 - 2.90626i) q^{10} +(-1.09442 + 0.269750i) q^{11} +(1.54831 - 2.24311i) q^{12} +(3.58095 - 0.420472i) q^{13} +(-0.229631 - 0.332679i) q^{14} +(-1.50908 - 1.33693i) q^{15} +(-1.14883 - 1.66437i) q^{16} +(4.76457 + 4.22104i) q^{17} +(-1.92484 - 1.01023i) q^{18} -5.05597 q^{19} +(4.86564 - 2.55369i) q^{20} +(-0.139189 + 0.123310i) q^{21} -2.45030 q^{22} -0.336172 q^{23} +(1.18063 - 1.04595i) q^{24} +(0.331667 + 0.874535i) q^{25} +(7.77696 + 0.975453i) q^{26} +(-0.354605 + 0.935016i) q^{27} +(-0.179726 - 0.473898i) q^{28} +(-1.76677 - 0.435471i) q^{29} +(-2.48965 - 3.60689i) q^{30} +(-0.895206 + 2.36046i) q^{31} +(-2.67758 - 7.06021i) q^{32} +(0.135866 + 1.11896i) q^{33} +(7.86052 + 11.3879i) q^{34} +(-0.364009 + 0.0897202i) q^{35} +(-2.04013 - 1.80740i) q^{36} +(-2.36603 + 6.23870i) q^{37} +(-10.6715 - 2.63029i) q^{38} +(0.0142292 - 3.60552i) q^{39} +(3.08761 - 0.761028i) q^{40} +(-0.477741 + 3.93455i) q^{41} +(-0.357932 + 0.187857i) q^{42} +(-0.677727 - 1.78702i) q^{43} +(-2.98294 - 0.735228i) q^{44} +(-1.50908 + 1.33693i) q^{45} +(-0.709550 - 0.174888i) q^{46} +(-3.37119 + 1.76934i) q^{47} +(-1.79071 + 0.939836i) q^{48} +(-0.839589 - 6.91464i) q^{49} +(0.245078 + 2.01840i) q^{50} +(4.76457 - 4.22104i) q^{51} +(9.17480 + 3.52102i) q^{52} +(8.31313 + 7.36479i) q^{53} +(-1.23488 + 1.78904i) q^{54} +(-0.805841 + 2.12483i) q^{55} +(-0.0353542 - 0.291168i) q^{56} +(-0.609430 + 5.01911i) q^{57} +(-3.50253 - 1.83827i) q^{58} +(-4.41089 + 6.39028i) q^{59} +(-1.94858 - 5.13798i) q^{60} +(-2.09642 + 1.85727i) q^{61} +(-3.11748 + 4.51645i) q^{62} +(0.105634 + 0.153037i) q^{63} +(-1.49101 - 12.2795i) q^{64} +(3.40353 - 6.42315i) q^{65} +(-0.295351 + 2.43243i) q^{66} +(5.98271 - 3.13997i) q^{67} +(6.15220 + 16.2220i) q^{68} +(-0.0405211 + 0.333721i) q^{69} -0.814980 q^{70} +(1.06597 - 8.77902i) q^{71} +(-0.896012 - 1.29810i) q^{72} +(-0.352506 + 0.0868848i) q^{73} +(-8.23950 + 11.9370i) q^{74} +(0.908136 - 0.223835i) q^{75} +(-12.2020 - 6.40411i) q^{76} +(0.185594 + 0.0974072i) q^{77} +(1.90575 - 7.60268i) q^{78} +(-1.90983 + 1.00236i) q^{79} -4.07729 q^{80} +(0.885456 + 0.464723i) q^{81} +(-3.05524 + 8.05601i) q^{82} +(0.780625 + 6.42902i) q^{83} +(-0.492106 + 0.121293i) q^{84} +(12.4604 - 3.07122i) q^{85} +(-0.500792 - 4.12439i) q^{86} +(-0.645256 + 1.70140i) q^{87} +(-1.57425 - 0.826230i) q^{88} -16.5976 q^{89} +(-3.88068 + 2.03674i) q^{90} +(-0.550276 - 0.383043i) q^{91} +(-0.811314 - 0.425810i) q^{92} +(2.23535 + 1.17320i) q^{93} +(-8.03595 + 1.98068i) q^{94} +(-5.79050 + 8.38899i) q^{95} +(-7.33148 + 1.80705i) q^{96} +(-1.23550 - 1.78994i) q^{97} +(1.82513 - 15.0313i) q^{98} +1.12717 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 204 q - q^{2} - 17 q^{3} - 21 q^{4} - 6 q^{5} - q^{6} - 8 q^{7} - 9 q^{8} - 17 q^{9} - 6 q^{10} - 8 q^{11} - 21 q^{12} + 54 q^{13} - 30 q^{14} - 6 q^{15} - 45 q^{16} - 18 q^{17} - q^{18} - 20 q^{19}+ \cdots + 18 q^{99}+O(q^{100}) $ 204 * q - q^2 - 17 * q^3 - 21 * q^4 - 6 * q^5 - q^6 - 8 * q^7 - 9 * q^8 - 17 * q^9 - 6 * q^10 - 8 * q^11 - 21 * q^12 + 54 * q^13 - 30 * q^14 - 6 * q^15 - 45 * q^16 - 18 * q^17 - q^18 - 20 * q^19 - 58 * q^20 - 8 * q^21 + 44 * q^22 + 40 * q^23 - 9 * q^24 + 7 * q^25 - 2 * q^26 - 17 * q^27 - 40 * q^28 + 11 * q^29 - 6 * q^30 + 2 * q^31 + 61 * q^32 + 5 * q^33 - q^34 + 11 * q^35 - 21 * q^36 - 34 * q^37 + 17 * q^38 - 11 * q^39 - 31 * q^40 - 58 * q^41 + 35 * q^42 + 32 * q^43 - 41 * q^44 - 6 * q^45 + 76 * q^46 - 36 * q^47 - 45 * q^48 + 9 * q^49 - 35 * q^50 - 18 * q^51 - 24 * q^52 + 66 * q^53 - q^54 + 7 * q^55 - 114 * q^56 - 7 * q^57 - 60 * q^58 + 40 * q^59 + 59 * q^60 - 54 * q^61 - 31 * q^62 - 8 * q^63 + 75 * q^64 - 26 * q^65 + 18 * q^66 + 2 * q^67 + 26 * q^68 - 12 * q^69 - 56 * q^70 - 37 * q^71 - 9 * q^72 + 70 * q^73 + 174 * q^74 - 45 * q^75 - 26 * q^76 + 24 * q^78 - 66 * q^79 + 126 * q^80 - 17 * q^81 - 17 * q^82 - 2 * q^83 - 40 * q^84 + 54 * q^85 + 61 * q^86 + 24 * q^87 + 94 * q^88 - 114 * q^89 - 6 * q^90 + 104 * q^91 - 78 * q^92 + 67 * q^93 - 63 * q^94 - 70 * q^95 - 4 * q^96 + 36 * q^97 - 65 * q^98 + 18 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{1}{13}\right)$

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 $

$2$	2.11067	+	0.520234i	1.49247	+	0.367861i	0.899342	−	0.437246i	$-0.144046\pi$
$2$	2.11067	+	0.520234i	1.49247	+	0.367861i	0.593129	+	0.805107i	$0.297892\pi$
$3$	0.120537	−	0.992709i	0.0695919	−	0.573141i
$3$	0.120537	−	0.992709i	0.0695919	−	0.573141i
$4$	2.41339	+	1.26664i	1.20669	+	0.633321i
$5$	1.14528	−	1.65922i	0.512184	−	0.742027i	−0.478518	−	0.878078i	$-0.658826\pi$
$5$	1.14528	−	1.65922i	0.512184	−	0.742027i	0.990702	+	0.136051i	$0.0434411\pi$
$6$	0.770855	−	2.03258i	0.314700	−	0.829796i
$7$	−0.139189	−	0.123310i	−0.0526084	−	0.0466069i	0.636409	−	0.771352i	$-0.280419\pi$
$7$	−0.139189	−	0.123310i	−0.0526084	−	0.0466069i	−0.689017	+	0.724745i	$0.741958\pi$
$8$	1.18063	+	1.04595i	0.417416	+	0.369798i
$9$	−0.970942	−	0.239316i	−0.323647	−	0.0797719i
$10$	3.28049	−	2.90626i	1.03738	−	0.919041i
$11$	−1.09442	+	0.269750i	−0.329980	+	0.0813328i	−0.400825	−	0.916155i	$-0.631277\pi$
$11$	−1.09442	+	0.269750i	−0.329980	+	0.0813328i	0.0708451	+	0.997487i	$0.477430\pi$
$12$	1.54831	−	2.24311i	0.446958	−	0.647531i
$13$	3.58095	−	0.420472i	0.993177	−	0.116618i
$13$	3.58095	−	0.420472i	0.993177	−	0.116618i
$14$	−0.229631	−	0.332679i	−0.0613716	−	0.0889121i
$15$	−1.50908	−	1.33693i	−0.389642	−	0.345193i
$16$	−1.14883	−	1.66437i	−0.287208	−	0.416092i
$17$	4.76457	+	4.22104i	1.15558	+	1.02375i	0.999351	+	0.0360320i	$0.0114718\pi$
$17$	4.76457	+	4.22104i	1.15558	+	1.02375i	0.156228	+	0.987721i	$0.450067\pi$
$18$	−1.92484	−	1.01023i	−0.453689	−	0.238115i
$19$	−5.05597			−1.15992			−0.579960	−	0.814645i	$-0.696932\pi$
$19$	−5.05597			−1.15992			−0.579960	+	0.814645i	$0.696932\pi$
$20$	4.86564	−	2.55369i	1.08799	−	0.571021i
$21$	−0.139189	+	0.123310i	−0.0303734	+	0.0269085i
$22$	−2.45030			−0.522405
$23$	−0.336172			−0.0700968			−0.0350484	−	0.999386i	$-0.511159\pi$
$23$	−0.336172			−0.0700968			−0.0350484	+	0.999386i	$0.511159\pi$
$24$	1.18063	−	1.04595i	0.240995	−	0.213503i
$25$	0.331667	+	0.874535i	0.0663334	+	0.174907i
$26$	7.77696	+	0.975453i	1.52519	+	0.191302i
$27$	−0.354605	+	0.935016i	−0.0682437	+	0.179944i
$28$	−0.179726	−	0.473898i	−0.0339650	−	0.0895582i
$29$	−1.76677	−	0.435471i	−0.328082	−	0.0808649i	0.0718346	−	0.997417i	$-0.477115\pi$
$29$	−1.76677	−	0.435471i	−0.328082	−	0.0808649i	−0.399916	+	0.916552i	$0.630961\pi$
$30$	−2.48965	−	3.60689i	−0.454547	−	0.658524i
$31$	−0.895206	+	2.36046i	−0.160784	+	0.423952i	−0.991063	−	0.133396i	$-0.957412\pi$
$31$	−0.895206	+	2.36046i	−0.160784	+	0.423952i	0.830279	+	0.557348i	$0.188181\pi$
$32$	−2.67758	−	7.06021i	−0.473335	−	1.24808i
$33$	0.135866	+	1.11896i	0.0236512	+	0.194785i
$34$	7.86052	+	11.3879i	1.34807	+	1.95301i
$35$	−0.364009	+	0.0897202i	−0.0615288	+	0.0151655i
$36$	−2.04013	−	1.80740i	−0.340022	−	0.301233i
$37$	−2.36603	+	6.23870i	−0.388973	+	1.02564i	0.587353	+	0.809331i	$0.300170\pi$
$37$	−2.36603	+	6.23870i	−0.388973	+	1.02564i	−0.976326	+	0.216306i	$0.930599\pi$
$38$	−10.6715	−	2.63029i	−1.73115	−	0.426689i
$39$	0.0142292	−	3.60552i	0.00227850	−	0.577346i
$40$	3.08761	−	0.761028i	0.488194	−	0.120329i
$41$	−0.477741	+	3.93455i	−0.0746106	+	0.614474i	0.906663	+	0.421855i	$0.138621\pi$
$41$	−0.477741	+	3.93455i	−0.0746106	+	0.614474i	−0.981274	+	0.192618i	$0.938302\pi$
$42$	−0.357932	+	0.187857i	−0.0552301	+	0.0289870i
$43$	−0.677727	−	1.78702i	−0.103352	−	0.272518i	0.873358	−	0.487078i	$-0.161937\pi$
$43$	−0.677727	−	1.78702i	−0.103352	−	0.272518i	−0.976711	+	0.214560i	$0.931168\pi$
$44$	−2.98294	−	0.735228i	−0.449694	−	0.110840i
$45$	−1.50908	+	1.33693i	−0.224960	+	0.199297i
$46$	−0.709550	−	0.174888i	−0.104617	−	0.0257859i
$47$	−3.37119	+	1.76934i	−0.491738	+	0.258084i	−0.692317	−	0.721593i	$-0.743410\pi$
$47$	−3.37119	+	1.76934i	−0.491738	+	0.258084i	0.200579	+	0.979678i	$0.435718\pi$
$48$	−1.79071	+	0.939836i	−0.258467	+	0.135654i
$49$	−0.839589	−	6.91464i	−0.119941	−	0.987805i
$50$	0.245078	+	2.01840i	0.0346593	+	0.285445i
$51$	4.76457	−	4.22104i	0.667173	−	0.591064i
$52$	9.17480	+	3.52102i	1.27232	+	0.488278i
$53$	8.31313	+	7.36479i	1.14190	+	1.01163i	0.999763	+	0.0217846i	$0.00693480\pi$
$53$	8.31313	+	7.36479i	1.14190	+	1.01163i	0.142134	+	0.989847i	$0.454604\pi$
$54$	−1.23488	+	1.78904i	−0.168046	+	0.243457i
$55$	−0.805841	+	2.12483i	−0.108660	+	0.286512i
$56$	−0.0353542	−	0.291168i	−0.00472440	−	0.0389089i
$57$	−0.609430	+	5.01911i	−0.0807210	+	0.664797i
$58$	−3.50253	−	1.83827i	−0.459905	−	0.241377i
$59$	−4.41089	+	6.39028i	−0.574249	+	0.831944i	−0.997244	−	0.0741883i	$-0.976363\pi$
$59$	−4.41089	+	6.39028i	−0.574249	+	0.831944i	0.422995	+	0.906132i	$0.360979\pi$
$60$	−1.94858	−	5.13798i	−0.251560	−	0.663310i
$61$	−2.09642	+	1.85727i	−0.268420	+	0.237799i	−0.786586	−	0.617481i	$-0.788153\pi$
$61$	−2.09642	+	1.85727i	−0.268420	+	0.237799i	0.518166	+	0.855280i	$0.326615\pi$
$62$	−3.11748	+	4.51645i	−0.395920	+	0.573590i
$63$	0.105634	+	0.153037i	0.0133086	+	0.0192809i
$64$	−1.49101	−	12.2795i	−0.186376	−	1.53494i
$65$	3.40353	−	6.42315i	0.422156	−	0.796694i
$66$	−0.295351	+	2.43243i	−0.0363552	+	0.299412i
$67$	5.98271	−	3.13997i	0.730904	−	0.383608i	−0.0578432	−	0.998326i	$-0.518422\pi$
$67$	5.98271	−	3.13997i	0.730904	−	0.383608i	0.788747	+	0.614718i	$0.210730\pi$
$68$	6.15220	+	16.2220i	0.746063	+	1.96721i
$69$	−0.0405211	+	0.333721i	−0.00487817	+	0.0401753i
$70$	−0.814980			−0.0974087
$71$	1.06597	−	8.77902i	0.126507	−	1.04188i	−0.781787	−	0.623546i	$-0.785692\pi$
$71$	1.06597	−	8.77902i	0.126507	−	1.04188i	0.908294	−	0.418333i	$-0.137385\pi$
$72$	−0.896012	−	1.29810i	−0.105596	−	0.152982i
$73$	−0.352506	+	0.0868848i	−0.0412577	+	0.0101691i	−0.259890	−	0.965638i	$-0.583686\pi$
$73$	−0.352506	+	0.0868848i	−0.0412577	+	0.0101691i	0.218633	+	0.975807i	$0.429840\pi$
$74$	−8.23950	+	11.9370i	−0.957822	+	1.38765i
$75$	0.908136	−	0.223835i	0.104863	−	0.0258463i
$76$	−12.2020	−	6.40411i	−1.39967	−	0.734602i
$77$	0.185594	+	0.0974072i	0.0211504	+	0.0111006i
$78$	1.90575	−	7.60268i	0.215784	−	0.860834i
$79$	−1.90983	+	1.00236i	−0.214873	+	0.112774i	−0.568726	−	0.822527i	$-0.692564\pi$
$79$	−1.90983	+	1.00236i	−0.214873	+	0.112774i	0.353853	+	0.935301i	$0.384871\pi$
$80$	−4.07729			−0.455855
$81$	0.885456	+	0.464723i	0.0983840	+	0.0516359i
$82$	−3.05524	+	8.05601i	−0.337395	+	0.889638i
$83$	0.780625	+	6.42902i	0.0856847	+	0.705677i	0.970730	+	0.240172i	$0.0772040\pi$
$83$	0.780625	+	6.42902i	0.0856847	+	0.705677i	−0.885046	+	0.465504i	$0.845873\pi$
$84$	−0.492106	+	0.121293i	−0.0536932	+	0.0132342i
$85$	12.4604	−	3.07122i	1.35152	−	0.333120i
$86$	−0.500792	−	4.12439i	−0.0540018	−	0.444745i
$87$	−0.645256	+	1.70140i	−0.0691788	+	0.182409i
$88$	−1.57425	−	0.826230i	−0.167816	−	0.0880765i
$89$	−16.5976			−1.75935			−0.879673	−	0.475579i	$-0.842239\pi$
$89$	−16.5976			−1.75935			−0.879673	+	0.475579i	$0.842239\pi$
$90$	−3.88068	+	2.03674i	−0.409060	+	0.214691i
$91$	−0.550276	−	0.383043i	−0.0576846	−	0.0401538i
$92$	−0.811314	−	0.425810i	−0.0845853	−	0.0443938i
$93$	2.23535	+	1.17320i	0.231795	+	0.121655i
$94$	−8.03595	+	1.98068i	−0.828845	+	0.204292i
$95$	−5.79050	+	8.38899i	−0.594093	+	0.860692i
$96$	−7.33148	+	1.80705i	−0.748266	+	0.184431i
$97$	−1.23550	−	1.78994i	−0.125446	−	0.181741i	0.755229	−	0.655462i	$-0.227526\pi$
$97$	−1.23550	−	1.78994i	−0.125446	−	0.181741i	−0.880675	+	0.473721i	$0.842910\pi$
$98$	1.82513	−	15.0313i	0.184366	−	1.51839i
$99$	1.12717			0.113285
$100$	−0.307282	+	2.53069i	−0.0307282	+	0.253069i
$101$	−4.89915	−	12.9180i	−0.487484	−	1.28539i	−0.922858	−	0.385140i	$-0.874153\pi$
$101$	−4.89915	−	12.9180i	−0.487484	−	1.28539i	0.435374	−	0.900250i	$-0.356616\pi$
$102$	12.2524	−	6.43055i	1.21317	−	0.636719i
$103$	2.13569	−	17.5890i	0.210436	−	1.73309i	−0.379103	−	0.925354i	$-0.623767\pi$
$103$	2.13569	−	17.5890i	0.210436	−	1.73309i	0.589539	−	0.807740i	$-0.299310\pi$
$104$	4.66757	+	3.24906i	0.457693	+	0.318597i
$105$	0.0451896	+	0.372170i	0.00441005	+	0.0363200i
$106$	13.7149	+	19.8694i	1.33211	+	1.92989i
$107$	−2.83141	+	4.10200i	−0.273723	+	0.396556i	−0.935603	−	0.353054i	$-0.885143\pi$
$107$	−2.83141	+	4.10200i	−0.273723	+	0.396556i	0.661880	+	0.749609i	$0.269759\pi$
$108$	−2.04013	+	1.80740i	−0.196312	+	0.173917i
$109$	−3.51105	−	9.25787i	−0.336297	−	0.886743i	−0.991360	−	0.131169i	$-0.958127\pi$
$109$	−3.51105	−	9.25787i	−0.336297	−	0.886743i	0.655063	−	0.755574i	$-0.272642\pi$
$110$	−2.80627	+	4.06559i	−0.267568	+	0.387639i
$111$	5.90802	+	3.10077i	0.560765	+	0.294312i
$112$	−0.0453297	+	0.373324i	−0.00428325	+	0.0352758i
$113$	0.663193	+	5.46188i	0.0623879	+	0.513811i	0.990084	+	0.140475i	$0.0448630\pi$
$113$	0.663193	+	5.46188i	0.0623879	+	0.513811i	−0.927696	+	0.373336i	$0.878214\pi$
$114$	−3.89742	+	10.2767i	−0.365027	+	0.962497i
$115$	−0.385011	+	0.557785i	−0.0359025	+	0.0520137i
$116$	−3.71232	−	3.28883i	−0.344680	−	0.305360i
$117$	−3.57752	−	0.448723i	−0.330742	−	0.0414845i
$118$	−12.6344	+	11.1931i	−1.16309	+	1.03041i
$119$	−0.142676	−	1.17504i	−0.0130791	−	0.107716i
$120$	−0.383309	−	3.15683i	−0.0349911	−	0.288178i
$121$	−8.61503	+	4.52151i	−0.783184	+	0.411047i
$122$	−5.39108	+	2.82946i	−0.488086	+	0.256167i
$123$	3.84828	+	0.948515i	0.346988	+	0.0855247i
$124$	−5.15034	+	4.56280i	−0.462514	+	0.409752i
$125$	11.6185	+	2.86371i	1.03919	+	0.256138i
$126$	0.143344	+	0.377966i	0.0127701	+	0.0336719i
$127$	−2.31201	+	1.21344i	−0.205158	+	0.107675i	−0.564173	−	0.825657i	$-0.690805\pi$
$127$	−2.31201	+	1.21344i	−0.205158	+	0.107675i	0.359015	+	0.933332i	$0.383113\pi$
$128$	1.42089	−	11.7021i	0.125590	−	1.03433i
$129$	−1.85568	+	0.457384i	−0.163384	+	0.0402705i
$130$	10.5253	−	11.7865i	0.923128	−	1.03375i
$131$	18.8795	+	4.65338i	1.64951	+	0.406568i	0.951039	−	0.309071i	$-0.100018\pi$
$131$	18.8795	+	4.65338i	1.64951	+	0.406568i	0.698470	+	0.715639i	$0.253864\pi$
$132$	−1.08942	+	2.87256i	−0.0948218	+	0.250025i
$133$	0.703734	+	0.623454i	0.0610215	+	0.0540603i
$134$	14.2611	−	3.51504i	1.23197	−	0.303653i
$135$	1.14528	+	1.65922i	0.0985699	+	0.142803i
$136$	1.21021	+	9.96698i	0.103775	+	0.854661i
$137$	3.96785	+	10.4624i	0.338997	+	0.893861i	0.990783	+	0.135458i	$0.0432506\pi$
$137$	3.96785	+	10.4624i	0.338997	+	0.893861i	−0.651786	+	0.758403i	$0.725980\pi$
$138$	−0.259140	+	0.683296i	−0.0220595	+	0.0581660i
$139$	−6.81409	−	9.87191i	−0.577964	−	0.837325i	0.419555	−	0.907730i	$-0.362186\pi$
$139$	−6.81409	−	9.87191i	−0.577964	−	0.837325i	−0.997518	+	0.0704052i	$0.977571\pi$
$140$	−0.992138	−	0.244540i	−0.0838509	−	0.0206674i
$141$	1.35008	+	3.55988i	0.113698	+	0.299796i
$142$	6.81706	−	17.9751i	0.572075	−	1.50844i
$143$	−3.80564	+	1.42614i	−0.318244	+	0.119260i
$144$	0.717138	+	1.89094i	0.0597615	+	0.157578i
$145$	−2.74599	+	2.43274i	−0.228042	+	0.202028i
$146$	−0.789224			−0.0653167
$147$	−6.96542			−0.574498
$148$	−13.6123	+	12.0595i	−1.11893	+	0.991284i
$149$	11.7741	−	6.17955i	0.964576	−	0.506248i	0.0925499	−	0.995708i	$-0.470498\pi$
$149$	11.7741	−	6.17955i	0.964576	−	0.506248i	0.872026	+	0.489460i	$0.162806\pi$
$150$	2.03323			0.166012
$151$	1.04771	+	0.549883i	0.0852618	+	0.0447488i	0.506815	−	0.862055i	$-0.330823\pi$
$151$	1.04771	+	0.549883i	0.0852618	+	0.0447488i	−0.421553	+	0.906804i	$0.638515\pi$
$152$	−5.96923	−	5.28828i	−0.484169	−	0.428936i
$153$	−3.61596	−	5.23862i	−0.292333	−	0.423518i
$154$	0.341053	+	0.302147i	0.0274829	+	0.0243477i
$155$	2.89128	+	4.18874i	0.232233	+	0.336447i
$156$	4.60125	−	8.68349i	0.368395	−	0.695236i
$157$	7.24879	−	10.5017i	0.578516	−	0.838125i	−0.419042	−	0.907967i	$-0.637634\pi$
$157$	7.24879	−	10.5017i	0.578516	−	0.838125i	0.997558	+	0.0698415i	$0.0222494\pi$
$158$	−4.55250	+	1.12209i	−0.362177	+	0.0892686i
$159$	8.31313	−	7.36479i	0.659274	−	0.584066i
$160$	−14.7810	−	3.64320i	−1.16854	−	0.288020i
$161$	0.0467914	+	0.0414535i	0.00368768	+	0.00326700i
$162$	1.62714	+	1.44152i	0.127840	+	0.113257i
$163$	8.78666	−	23.1685i	0.688224	−	1.81470i	0.118340	−	0.992973i	$-0.462243\pi$
$163$	8.78666	−	23.1685i	0.688224	−	1.81470i	0.569884	−	0.821725i	$-0.306988\pi$
$164$	−6.13664	+	8.89046i	−0.479191	+	0.694228i
$165$	2.01220	+	1.05608i	0.156650	+	0.0822161i
$166$	−1.69695	+	13.9757i	−0.131709	+	1.08472i
$167$	−4.13444	−	1.01905i	−0.319932	−	0.0788562i	0.0760792	−	0.997102i	$-0.475760\pi$
$167$	−4.13444	−	1.01905i	−0.319932	−	0.0788562i	−0.396011	+	0.918246i	$0.629606\pi$
$168$	−0.293306			−0.0226291
$169$	12.6464	−	3.01138i	0.972800	−	0.231645i
$170$	27.8976			2.13965
$171$	4.90906	+	1.20997i	0.375405	+	0.0925290i
$172$	0.627898	−	5.17121i	0.0478768	−	0.394301i
$173$	−3.24259	−	1.70184i	−0.246530	−	0.129389i	0.336933	−	0.941529i	$-0.390610\pi$
$173$	−3.24259	−	1.70184i	−0.246530	−	0.129389i	−0.583463	+	0.812140i	$0.698303\pi$
$174$	−2.24705	+	3.25542i	−0.170349	+	0.246793i
$175$	0.0616749	−	0.162623i	0.00466218	−	0.0122932i
$176$	1.70627	+	1.51162i	0.128615	+	0.113943i
$177$	5.81201	+	5.14900i	0.436858	+	0.387022i
$178$	−35.0322	−	8.63466i	−2.62577	−	0.647195i
$179$	−12.3028	+	10.8994i	−0.919557	+	0.814656i	−0.983052	−	0.183326i	$-0.941314\pi$
$179$	−12.3028	+	10.8994i	−0.919557	+	0.814656i	0.0634953	+	0.997982i	$0.479775\pi$
$180$	−5.33539	+	1.31506i	−0.397677	+	0.0980185i
$181$	12.4053	−	17.9721i	0.922076	−	1.33586i	−0.0197675	−	0.999805i	$-0.506293\pi$
$181$	12.4053	−	17.9721i	0.922076	−	1.33586i	0.941843	−	0.336053i	$-0.109092\pi$
$182$	−0.962181	−	1.09475i	−0.0713216	−	0.0811484i
$183$	1.59103	+	2.30501i	0.117612	+	0.170391i
$184$	−0.396895	−	0.351619i	−0.0292595	−	0.0259217i
$185$	7.64164	+	11.0708i	0.561824	+	0.813943i
$186$	4.10775	+	3.63915i	0.301195	+	0.266835i
$187$	−6.35307	−	3.33435i	−0.464583	−	0.243832i
$188$	−10.3771			−0.756827
$189$	0.164654	−	0.0864172i	0.0119768	−	0.00628592i
$190$	−16.5861	+	14.6940i	−1.20328	+	1.06601i
$191$	17.2361			1.24716			0.623580	−	0.781759i	$-0.285677\pi$
$191$	17.2361			1.24716			0.623580	+	0.781759i	$0.285677\pi$
$192$	−12.3697			−0.892708
$193$	5.45341	−	4.83130i	0.392545	−	0.347765i	−0.443647	−	0.896202i	$-0.646315\pi$
$193$	5.45341	−	4.83130i	0.392545	−	0.347765i	0.836192	+	0.548437i	$0.184777\pi$
$194$	−1.67656	−	4.42072i	−0.120370	−	0.317389i
$195$	−5.96607	−	4.15294i	−0.427239	−	0.297398i
$196$	6.73212	−	17.7511i	0.480866	−	1.26794i
$197$	1.55044	+	4.08818i	0.110464	+	0.291270i	0.978837	−	0.204642i	$-0.0656030\pi$
$197$	1.55044	+	4.08818i	0.110464	+	0.291270i	−0.868373	+	0.495912i	$0.834834\pi$
$198$	2.37910	+	0.586395i	0.169075	+	0.0416732i
$199$	−3.01449	−	4.36724i	−0.213691	−	0.309585i	0.701450	−	0.712719i	$-0.252536\pi$
$199$	−3.01449	−	4.36724i	−0.213691	−	0.309585i	−0.915141	+	0.403134i	$0.867921\pi$
$200$	−0.523141	+	1.37941i	−0.0369916	+	0.0975389i
$201$	−2.39594	−	6.31757i	−0.168996	−	0.445607i
$202$	−3.62012	−	29.8144i	−0.254711	−	2.09773i
$203$	0.192217	+	0.278474i	0.0134910	+	0.0195450i
$204$	16.8453	−	4.15199i	1.17941	−	0.290698i
$205$	5.98115	+	5.29884i	0.417742	+	0.370087i
$206$	13.6581	−	36.0135i	0.951607	−	2.50918i
$207$	0.326404	+	0.0804513i	0.0226866	+	0.00559175i
$208$	−4.81372	−	5.47697i	−0.333772	−	0.379759i
$209$	5.53336	−	1.36385i	0.382751	−	0.0943395i
$210$	−0.0982350	+	0.809038i	−0.00677886	+	0.0558289i
$211$	−2.28097	+	1.19714i	−0.157028	+	0.0824149i	−0.541407	−	0.840761i	$-0.682108\pi$
$211$	−2.28097	+	1.19714i	−0.157028	+	0.0824149i	0.384378	+	0.923176i	$0.374416\pi$
$212$	10.7342	+	28.3038i	0.737230	+	1.94392i
$213$	−8.58653	−	2.11639i	−0.588339	−	0.145013i
$214$	−8.11018	+	7.18499i	−0.554400	+	0.491156i
$215$	−3.74125	−	0.922136i	−0.255151	−	0.0628891i
$216$	−1.39663	+	0.733010i	−0.0950290	+	0.0498750i
$217$	0.415672	−	0.218162i	0.0282177	−	0.0148098i
$218$	−2.59441	−	21.3669i	−0.175716	−	1.44715i
$219$	0.0437615	+	0.360408i	0.00295713	+	0.0243541i
$220$	−4.63620	+	4.10731i	−0.312573	+	0.276915i
$221$	18.8365	+	13.1120i	1.26708	+	0.882007i
$222$	10.8568	+	9.61827i	0.728659	+	0.645536i
$223$	−2.55986	+	3.70860i	−0.171421	+	0.248346i	−0.899273	−	0.437388i	$-0.855903\pi$
$223$	−2.55986	+	3.70860i	−0.171421	+	0.248346i	0.727852	+	0.685734i	$0.240519\pi$
$224$	−0.497908	+	1.31287i	−0.0332679	+	0.0877201i
$225$	−0.112740	−	0.928495i	−0.00751598	−	0.0618997i
$226$	−1.44168	+	11.8733i	−0.0958988	+	0.789798i
$227$	−8.53639	−	4.48024i	−0.566580	−	0.297364i	0.157007	−	0.987598i	$-0.449816\pi$
$227$	−8.53639	−	4.48024i	−0.566580	−	0.297364i	−0.723587	+	0.690233i	$0.757508\pi$
$228$	−7.82821	+	11.3411i	−0.518436	+	0.751084i
$229$	4.03326	+	10.6348i	0.266525	+	0.702769i	0.999741	+	0.0227728i	$0.00724945\pi$
$229$	4.03326	+	10.6348i	0.266525	+	0.702769i	−0.733215	+	0.679996i	$0.761981\pi$
$230$	−1.10281	+	0.977006i	−0.0727173	+	0.0644219i
$231$	0.119068	−	0.172500i	0.00783409	−	0.0113496i
$232$	−1.63043	−	2.36208i	−0.107043	−	0.155078i
$233$	2.28727	+	18.8374i	0.149844	+	1.23408i	0.852569	+	0.522614i	$0.175043\pi$
$233$	2.28727	+	18.8374i	0.149844	+	1.23408i	−0.702725	+	0.711461i	$0.748034\pi$
$234$	−7.31753	−	2.80826i	−0.478362	−	0.183581i
$235$	−0.925228	+	7.61994i	−0.0603552	+	0.497070i
$236$	−18.7394	+	9.83519i	−1.21983	+	0.640216i
$237$	0.764845	+	2.01673i	0.0496820	+	0.131001i
$238$	0.310155	−	2.55435i	0.0201043	−	0.165574i
$239$	2.67424			0.172982			0.0864911	−	0.996253i	$-0.472435\pi$
$239$	2.67424			0.172982			0.0864911	+	0.996253i	$0.472435\pi$
$240$	−0.491463	+	4.04756i	−0.0317238	+	0.261269i
$241$	6.18592	+	8.96185i	0.398470	+	0.577284i	0.969941	−	0.243338i	$-0.0782426\pi$
$241$	6.18592	+	8.96185i	0.398470	+	0.577284i	−0.571471	+	0.820622i	$0.693627\pi$
$242$	−20.5357	+	5.06161i	−1.32009	+	0.325372i
$243$	0.568065	−	0.822984i	0.0364414	−	0.0527944i
$244$	−7.41198	+	1.82689i	−0.474503	+	0.116955i
$245$	−12.4345	−	6.52612i	−0.794410	−	0.416939i
$246$	7.62901	+	4.00401i	0.486408	+	0.255286i
$247$	−18.1052	+	2.12590i	−1.15201	+	0.135268i
$248$	−3.52583	+	1.85050i	−0.223890	+	0.117507i
$249$	6.47624			0.410415
$250$	23.0331	+	12.0887i	1.45674	+	0.764556i
$251$	−2.09296	+	5.51869i	−0.132107	+	0.348337i	−0.984705	−	0.174230i	$-0.944256\pi$
$251$	−2.09296	+	5.51869i	−0.132107	+	0.348337i	0.852598	+	0.522567i	$0.175026\pi$
$252$	0.0610920	+	0.503138i	0.00384844	+	0.0316947i
$253$	0.367914	−	0.0906827i	0.0231306	−	0.00570117i
$254$	−5.51117	+	1.35838i	−0.345801	+	0.0852324i
$255$	−1.54689	−	12.7398i	−0.0968698	−	0.797795i
$256$	0.314129	−	0.828289i	0.0196330	−	0.0517681i
$257$	5.75798	+	3.02202i	0.359173	+	0.188509i	0.634651	−	0.772799i	$-0.281144\pi$
$257$	5.75798	+	3.02202i	0.359173	+	0.188509i	−0.275478	+	0.961307i	$0.588836\pi$
$258$	−4.15468			−0.258659
$259$	1.09862	−	0.576601i	0.0682650	−	0.0358282i
$260$	16.3499	−	11.1905i	1.01398	−	0.694005i
$261$	1.61122	+	0.845633i	0.0997320	+	0.0523434i
$262$	37.4276	+	19.6435i	2.31228	+	1.21358i
$263$	−15.4979	+	3.81989i	−0.955641	+	0.235544i	−0.686151	−	0.727459i	$-0.740701\pi$
$263$	−15.4979	+	3.81989i	−0.955641	+	0.235544i	−0.269490	+	0.963003i	$0.586855\pi$
$264$	−1.00996	+	1.46318i	−0.0621588	+	0.0900526i
$265$	21.7407	−	5.35860i	1.33552	−	0.329176i
$266$	1.16101	+	1.68201i	0.0711861	+	0.103131i
$267$	−2.00062	+	16.4766i	−0.122436	+	1.00835i
$268$	18.4158			1.12492
$269$	−0.556526	+	4.58341i	−0.0339320	+	0.279455i	0.965860	+	0.259064i	$0.0834142\pi$
$269$	−0.556526	+	4.58341i	−0.0339320	+	0.279455i	−0.999792	+	0.0203909i	$0.993509\pi$
$270$	1.55412	+	4.09789i	0.0945810	+	0.249390i
$271$	−20.4937	+	10.7559i	−1.24490	+	0.653375i	−0.952970	−	0.303064i	$-0.901990\pi$
$271$	−20.4937	+	10.7559i	−1.24490	+	0.653375i	−0.291932	+	0.956439i	$0.594298\pi$
$272$	1.55168	−	12.7793i	0.0940846	−	0.774856i
$273$	−0.446579	+	0.500093i	−0.0270282	+	0.0302670i
$274$	2.93196	+	24.1469i	0.177126	+	1.45877i
$275$	−0.598889	−	0.867641i	−0.0361144	−	0.0523207i
$276$	−0.520499	+	0.754073i	−0.0313303	+	0.0453898i
$277$	10.3377	−	9.15839i	0.621131	−	0.550274i	−0.292784	−	0.956178i	$-0.594582\pi$
$277$	10.3377	−	9.15839i	0.621131	−	0.550274i	0.913916	+	0.405904i	$0.133043\pi$
$278$	−9.24661	−	24.3813i	−0.554575	−	1.46229i
$279$	1.43409	−	2.07764i	0.0858566	−	0.124385i
$280$	−0.523603	−	0.274808i	−0.0312913	−	0.0164229i
$281$	2.58784	−	21.3128i	0.154378	−	1.27142i	−0.685272	−	0.728287i	$-0.740317\pi$
$281$	2.58784	−	21.3128i	0.154378	−	1.27142i	0.839650	−	0.543128i	$-0.182760\pi$
$282$	0.997615	+	8.21610i	0.0594071	+	0.489262i
$283$	3.56087	−	9.38924i	0.211672	−	0.558133i	−0.786564	−	0.617509i	$-0.788142\pi$
$283$	3.56087	−	9.38924i	0.211672	−	0.558133i	0.998236	+	0.0593763i	$0.0189112\pi$
$284$	13.6925	−	19.8370i	0.812499	−	1.17711i
$285$	7.62986	+	6.75946i	0.451954	+	0.400396i
$286$	−8.77439	+	1.03028i	−0.518841	+	0.0609219i
$287$	0.551667	−	0.488734i	0.0325639	−	0.0288491i
$288$	0.910160	+	7.49584i	0.0536317	+	0.441697i
$289$	2.83482	+	23.3469i	0.166754	+	1.37334i
$290$	−7.06148	+	3.70615i	−0.414665	+	0.217633i
$291$	−1.92581	+	1.01074i	−0.112893	+	0.0592508i
$292$	−0.960784	−	0.236812i	−0.0562256	−	0.0138584i
$293$	−23.5072	+	20.8256i	−1.37331	+	1.21664i	−0.422689	+	0.906275i	$0.638914\pi$
$293$	−23.5072	+	20.8256i	−1.37331	+	1.21664i	−0.950617	+	0.310368i	$0.899548\pi$
$294$	−14.7017	−	3.62365i	−0.857422	−	0.211336i
$295$	5.55120	+	14.6373i	0.323203	+	0.852217i
$296$	−9.31876	+	4.89086i	−0.541642	+	0.284276i
$297$	0.135866	−	1.11896i	0.00788373	−	0.0649284i
$298$	28.0662	−	6.91770i	1.62583	−	0.400731i
$299$	−1.20382	+	0.141351i	−0.0696185	+	0.00817455i
$300$	2.47520	+	0.610083i	0.142906	+	0.0352231i
$301$	−0.126026	+	0.332304i	−0.00726403	+	0.0191537i
$302$	1.92531	+	1.70568i	0.110789	+	0.0981509i
$303$	−13.4143	+	3.30634i	−0.770634	+	0.189944i
$304$	5.80845	+	8.41500i	0.333138	+	0.482633i
$305$	0.680634	+	5.60553i	0.0389730	+	0.320972i
$306$	−4.90680	−	12.9382i	−0.280503	−	0.739626i
$307$	5.87226	−	15.4839i	0.335148	−	0.883712i	−0.656452	−	0.754368i	$-0.727944\pi$
$307$	5.87226	−	15.4839i	0.335148	−	0.883712i	0.991600	−	0.129344i	$-0.0412872\pi$
$308$	0.324529	+	0.470162i	0.0184918	+	0.0267900i
$309$	−17.2033	−	4.24024i	−0.978662	−	0.241219i
$310$	3.92341	+	10.3452i	0.222835	+	0.587567i
$311$	−7.71306	+	20.3377i	−0.437368	+	1.15324i	0.517361	+	0.855767i	$0.326914\pi$
$311$	−7.71306	+	20.3377i	−0.437368	+	1.15324i	−0.954729	+	0.297477i	$0.903855\pi$
$312$	3.78799	−	4.24191i	0.214452	−	0.240151i
$313$	−9.29994	−	24.5219i	−0.525664	−	1.38606i	−0.890497	−	0.454989i	$-0.849643\pi$
$313$	−9.29994	−	24.5219i	−0.525664	−	1.38606i	0.364833	−	0.931073i	$-0.381126\pi$
$314$	20.7632	−	18.3945i	1.17173	−	1.03806i
$315$	0.374903			0.0211234
$316$	−5.87879			−0.330708
$317$	24.6656	−	21.8518i	1.38536	−	1.22732i	0.441374	−	0.897323i	$-0.354491\pi$
$317$	24.6656	−	21.8518i	1.38536	−	1.22732i	0.943982	−	0.329996i	$-0.107047\pi$
$318$	21.3777	−	11.2199i	1.19880	−	0.629180i
$319$	2.05106			0.114837
$320$	−22.0821	−	11.5896i	−1.23443	−	0.647878i
$321$	3.73081	+	3.30521i	0.208233	+	0.184479i
$322$	0.0771958	+	0.111837i	0.00430195	+	0.00623245i
$323$	−24.0895	−	21.3415i	−1.34038	−	1.18747i
$324$	1.54831	+	2.24311i	0.0860171	+	0.124617i
$325$	1.55540	+	2.99221i	0.0862781	+	0.165978i
$326$	30.5988	−	44.3300i	1.69471	−	2.45521i
$327$	−9.61358	+	2.36953i	−0.531632	+	0.131036i
$328$	−4.67937	+	4.14556i	−0.258375	+	0.228900i
$329$	0.687409	+	0.169431i	0.0378981	+	0.00934103i
$330$	3.69769	+	3.27587i	0.203551	+	0.180330i
$331$	−10.3914	−	9.20595i	−0.571161	−	0.506005i	0.327381	−	0.944893i	$-0.393834\pi$
$331$	−10.3914	−	9.20595i	−0.571161	−	0.506005i	−0.898542	+	0.438888i	$0.855373\pi$
$332$	−6.25932	+	16.5045i	−0.343525	+	0.905801i
$333$	3.79030	−	5.49119i	0.207707	−	0.300915i
$334$	−8.19630	−	4.30175i	−0.448482	−	0.235381i
$335$	1.64196	−	13.5228i	0.0897100	−	0.738829i
$336$	0.365138	+	0.0899984i	0.0199199	+	0.00490982i
$337$	14.4084			0.784877			0.392439	−	0.919778i	$-0.371632\pi$
$337$	14.4084			0.784877			0.392439	+	0.919778i	$0.371632\pi$
$338$	28.2591	+	0.223053i	1.53709	+	0.0121325i
$339$	5.50200			0.298828
$340$	33.9619	+	8.37086i	1.84184	+	0.453974i
$341$	0.342995	−	2.82482i	0.0185742	−	0.152973i
$342$	9.73194	+	5.10772i	0.526243	+	0.276194i
$343$	−1.47522	+	2.13723i	−0.0796545	+	0.115400i
$344$	1.06898	−	2.81868i	0.0576357	−	0.151973i
$345$	0.507310	+	0.449438i	0.0273127	+	0.0241969i
$346$	−5.95869	−	5.27894i	−0.320341	−	0.283798i
$347$	22.3781	+	5.51572i	1.20132	+	0.296099i	0.788686	−	0.614797i	$-0.210762\pi$
$347$	22.3781	+	5.51572i	1.20132	+	0.296099i	0.412636	+	0.910896i	$0.364608\pi$
$348$	−3.71232	+	3.28883i	−0.199001	+	0.176300i
$349$	−4.80107	+	1.18336i	−0.256996	+	0.0633437i	−0.365708	−	0.930729i	$-0.619173\pi$
$349$	−4.80107	+	1.18336i	−0.256996	+	0.0633437i	0.108713	+	0.994073i	$0.465327\pi$
$350$	0.214778	−	0.311159i	0.0114803	−	0.0166322i
$351$	−0.876674	+	3.49735i	−0.0467934	+	0.186675i
$352$	4.83490	+	7.00456i	0.257701	+	0.373344i
$353$	−26.3274	−	23.3241i	−1.40127	−	1.24141i	−0.933988	−	0.357305i	$-0.883696\pi$
$353$	−26.3274	−	23.3241i	−1.40127	−	1.24141i	−0.467279	−	0.884110i	$-0.654766\pi$
$354$	9.58858	+	13.8915i	0.509627	+	0.738322i
$355$	−13.3455	−	11.8231i	−0.708307	−	0.627505i
$356$	−40.0565	−	21.0233i	−2.12299	−	1.11423i
$357$	−1.18367			−0.0626466
$358$	−31.6375	+	16.6046i	−1.67209	+	0.877582i
$359$	2.80267	−	2.48295i	0.147919	−	0.131045i	−0.585918	−	0.810370i	$-0.699266\pi$
$359$	2.80267	−	2.48295i	0.147919	−	0.131045i	0.733837	+	0.679325i	$0.237727\pi$
$360$	−3.18002			−0.167602
$361$	6.56287			0.345414
$362$	35.5332	−	31.4796i	1.86758	−	1.65453i
$363$	3.45012	+	9.09722i	0.181084	+	0.477480i
$364$	−0.842849	−	1.62143i	−0.0441773	−	0.0849862i
$365$	−0.259556	+	0.684393i	−0.0135858	+	0.0358228i
$366$	2.15900	+	5.69283i	0.112853	+	0.297569i
$367$	23.7492	+	5.85366i	1.23970	+	0.305558i	0.804052	−	0.594559i	$-0.202673\pi$
$367$	23.7492	+	5.85366i	1.23970	+	0.305558i	0.435647	+	0.900117i	$0.356519\pi$
$368$	0.386205	+	0.559515i	0.0201323	+	0.0291667i
$369$	1.40546	−	3.70589i	0.0731652	−	0.192921i
$370$	10.3696	+	27.3423i	0.539089	+	1.42146i
$371$	−0.248938	−	2.05019i	−0.0129242	−	0.106441i
$372$	3.90873	+	5.66277i	0.202658	+	0.293601i
$373$	−6.34961	+	1.56504i	−0.328771	+	0.0810347i	−0.400246	−	0.916408i	$-0.631075\pi$
$373$	−6.34961	+	1.56504i	−0.328771	+	0.0810347i	0.0714756	+	0.997442i	$0.477229\pi$
$374$	−11.6746	−	10.3428i	−0.603680	−	0.534814i
$375$	4.24328	−	11.1886i	0.219122	−	0.577778i
$376$	−5.83076	−	1.43715i	−0.300698	−	0.0741155i
$377$	−6.50983	−	0.816519i	−0.335273	−	0.0420529i
$378$	0.392488	−	0.0967397i	0.0201874	−	0.00497575i
$379$	3.91520	−	32.2446i	0.201110	−	1.65629i	−0.446843	−	0.894612i	$-0.647452\pi$
$379$	3.91520	−	32.2446i	0.201110	−	1.65629i	0.647954	−	0.761680i	$-0.275625\pi$
$380$	−24.6006	+	12.9114i	−1.26198	+	0.662339i
$381$	0.925907	+	2.44142i	0.0474356	+	0.125078i
$382$	36.3798	+	8.96681i	1.86135	+	0.458782i
$383$	−18.9433	+	16.7823i	−0.967958	+	0.857536i	−0.989834	−	0.142225i	$-0.954574\pi$
$383$	−18.9433	+	16.7823i	−0.967958	+	0.857536i	0.0218763	+	0.999761i	$0.493036\pi$
$384$	−11.4455	−	2.82106i	−0.584076	−	0.143962i
$385$	0.374177	−	0.196383i	0.0190698	−	0.0100086i
$386$	14.0238	−	7.36025i	0.713792	−	0.374627i
$387$	0.230372	+	1.89728i	0.0117105	+	0.0964443i
$388$	−0.714538	−	5.88475i	−0.0362752	−	0.298753i
$389$	13.1510	−	11.6508i	0.666785	−	0.590720i	−0.260320	−	0.965522i	$-0.583828\pi$
$389$	13.1510	−	11.6508i	0.666785	−	0.590720i	0.927105	+	0.374803i	$0.122290\pi$
$390$	−10.4319	−	11.8693i	−0.528241	−	0.601023i
$391$	−1.60172	−	1.41900i	−0.0810024	−	0.0717618i
$392$	6.24110	−	9.04179i	0.315223	−	0.456679i
$393$	6.89512	−	18.1809i	0.347813	−	0.917107i
$394$	1.14566	+	9.43539i	0.0577177	+	0.475348i
$395$	−0.524157	+	4.31682i	−0.0263732	+	0.217203i
$396$	2.72031	+	1.42773i	0.136700	+	0.0717460i
$397$	−19.9783	+	28.9436i	−1.00268	+	1.45264i	−0.114350	+	0.993441i	$0.536478\pi$
$397$	−19.9783	+	28.9436i	−1.00268	+	1.45264i	−0.888334	+	0.459198i	$0.848137\pi$
$398$	−4.09061	−	10.7860i	−0.205044	−	0.540656i
$399$	0.703734	−	0.623454i	0.0352308	−	0.0312117i
$400$	1.07452	−	1.55671i	0.0537259	−	0.0778354i
$401$	−0.311935	−	0.451915i	−0.0155773	−	0.0225676i	0.815118	−	0.579295i	$-0.196672\pi$
$401$	−0.311935	−	0.451915i	−0.0155773	−	0.0225676i	−0.830695	+	0.556728i	$0.812057\pi$
$402$	−1.77043	−	14.5808i	−0.0883008	−	0.727223i
$403$	−2.21318	+	8.82911i	−0.110246	+	0.439809i
$404$	4.53895	−	37.3816i	0.225821	−	1.85980i
$405$	1.78517	−	0.936931i	0.0887060	−	0.0465565i
$406$	0.260835	+	0.687765i	0.0129450	+	0.0341332i
$407$	0.906537	−	7.46600i	0.0449354	−	0.370076i
$408$	10.0402			0.497063
$409$	−1.83671	+	15.1267i	−0.0908197	+	0.747967i	0.874159	+	0.485640i	$0.161413\pi$
$409$	−1.83671	+	15.1267i	−0.0908197	+	0.747967i	−0.964979	+	0.262328i	$0.915510\pi$
$410$	9.86762	+	14.2957i	0.487327	+	0.706015i
$411$	10.8644	−	2.67782i	0.535899	−	0.132087i
$412$	27.4332	−	39.7439i	1.35154	−	1.95804i
$413$	1.40193	−	0.345546i	0.0689847	−	0.0170032i
$414$	0.647078	+	0.339613i	0.0318022	+	0.0166911i
$415$	11.5612	+	6.06779i	0.567518	+	0.297856i
$416$	−12.5569	−	24.1564i	−0.615654	−	1.18437i
$417$	−10.6213	+	5.57448i	−0.520127	+	0.272983i
$418$	12.3886			0.605948
$419$	−9.13416	−	4.79398i	−0.446233	−	0.234201i	0.226611	−	0.973985i	$-0.427235\pi$
$419$	−9.13416	−	4.79398i	−0.446233	−	0.234201i	−0.672844	+	0.739784i	$0.734928\pi$
$420$	−0.362346	+	0.955428i	−0.0176807	+	0.0466201i
$421$	2.14367	+	17.6548i	0.104476	+	0.860440i	0.946879	+	0.321591i	$0.104218\pi$
$421$	2.14367	+	17.6548i	0.104476	+	0.860440i	−0.842402	+	0.538849i	$0.818859\pi$
$422$	−5.43718	+	1.34014i	−0.264678	+	0.0652372i
$423$	3.69666	−	0.911144i	0.179738	−	0.0443014i
$424$	2.11155	+	17.3902i	0.102546	+	0.844542i
$425$	−2.11119	+	5.56676i	−0.102408	+	0.270028i
$426$	−17.0223	−	8.93401i	−0.824735	−	0.432854i
$427$	0.520819			0.0252042
$428$	−12.0290	+	6.31333i	−0.581446	+	0.305166i
$429$	0.957019	+	3.94980i	0.0462053	+	0.190698i
$430$	−7.41683	−	3.89265i	−0.357671	−	0.187720i
$431$	−1.02713	−	0.539078i	−0.0494750	−	0.0259665i	0.439804	−	0.898094i	$-0.355048\pi$
$431$	−1.02713	−	0.539078i	−0.0494750	−	0.0259665i	−0.489279	+	0.872127i	$0.662740\pi$
$432$	1.96359	−	0.483982i	0.0944733	−	0.0232856i
$433$	−3.35057	+	4.85413i	−0.161018	+	0.233275i	−0.895186	−	0.445693i	$-0.852957\pi$
$433$	−3.35057	+	4.85413i	−0.161018	+	0.233275i	0.734168	+	0.678968i	$0.237573\pi$
$434$	0.990843	−	0.244221i	0.0475620	−	0.0117230i
$435$	2.08401	+	3.01920i	0.0999204	+	0.144760i
$436$	3.25290	−	26.7900i	0.155786	−	1.28301i
$437$	1.69968			0.0813067
$438$	−0.0951305	+	0.783470i	−0.00454551	+	0.0374357i
$439$	−0.531654	−	1.40186i	−0.0253745	−	0.0669069i	0.921730	−	0.387831i	$-0.126776\pi$
$439$	−0.531654	−	1.40186i	−0.0253745	−	0.0669069i	−0.947105	+	0.320924i	$0.896006\pi$
$440$	−3.17386	+	1.66577i	−0.151308	+	0.0794124i
$441$	−0.839589	+	6.91464i	−0.0399804	+	0.329268i
$442$	32.9364	+	37.4745i	1.56663	+	1.78248i
$443$	−0.628925	−	5.17966i	−0.0298811	−	0.246093i	−0.999994	−	0.00343943i	$-0.998905\pi$
$443$	−0.628925	−	5.17966i	−0.0298811	−	0.246093i	0.970113	−	0.242654i	$-0.0780179\pi$
$444$	10.3308	+	14.9667i	0.490277	+	0.710288i
$445$	−19.0089	+	27.5392i	−0.901110	+	1.30548i
$446$	−7.33236	+	6.49591i	−0.347197	+	0.307590i
$447$	−4.71528	−	12.4332i	−0.223025	−	0.588069i
$448$	−1.30666	+	1.89303i	−0.0617340	+	0.0894372i
$449$	−15.4862	−	8.12779i	−0.730840	−	0.383574i	0.0578830	−	0.998323i	$-0.481565\pi$
$449$	−15.4862	−	8.12779i	−0.730840	−	0.383574i	−0.788723	+	0.614749i	$0.789257\pi$
$450$	0.245078	−	2.01840i	0.0115531	−	0.0951483i
$451$	−0.538497	−	4.43492i	−0.0253568	−	0.208832i
$452$	−5.31771	+	14.0217i	−0.250124	+	0.659523i
$453$	0.672162	−	0.973794i	0.0315809	−	0.0457529i
$454$	−15.6868	−	13.8972i	−0.736216	−	0.652230i
$455$	−1.26577	+	0.474339i	−0.0593404	+	0.0222374i
$456$	−5.96923	+	5.28828i	−0.279535	+	0.247646i
$457$	1.61595	+	13.3086i	0.0755911	+	0.622549i	0.980440	+	0.196817i	$0.0630604\pi$
$457$	1.61595	+	13.3086i	0.0755911	+	0.622549i	−0.904849	+	0.425732i	$0.860017\pi$
$458$	2.98029	+	24.5449i	0.139260	+	1.14691i
$459$	−5.63628	+	2.95815i	−0.263079	+	0.138075i
$460$	−1.63569	+	0.858479i	−0.0762647	+	0.0400268i
$461$	−8.35979	−	2.06050i	−0.389354	−	0.0959671i	0.0397789	−	0.999209i	$-0.487335\pi$
$461$	−8.35979	−	2.06050i	−0.389354	−	0.0959671i	−0.429133	+	0.903241i	$0.641181\pi$
$462$	0.341053	−	0.302147i	0.0158672	−	0.0140572i
$463$	−30.5627	−	7.53303i	−1.42037	−	0.350089i	−0.546993	−	0.837137i	$-0.684228\pi$
$463$	−30.5627	−	7.53303i	−1.42037	−	0.350089i	−0.873376	+	0.487047i	$0.838074\pi$
$464$	1.30494	+	3.44084i	0.0605803	+	0.159737i
$465$	4.50670	−	2.36530i	0.208993	−	0.109688i
$466$	−4.97216	+	40.9494i	−0.230331	+	1.89694i
$467$	−8.26059	+	2.03605i	−0.382255	+	0.0942173i	−0.425761	−	0.904836i	$-0.639993\pi$
$467$	−8.26059	+	2.03605i	−0.382255	+	0.0942173i	0.0435059	+	0.999053i	$0.486147\pi$
$468$	−8.06556	−	5.61438i	−0.372831	−	0.259525i
$469$	−1.21992	−	0.300682i	−0.0563304	−	0.0138842i
$470$	−5.91701	+	15.6019i	−0.272931	+	0.719660i
$471$	−9.55137	−	8.46177i	−0.440104	−	0.389898i
$472$	−11.8915	+	2.93100i	−0.547352	+	0.134910i
$473$	1.22377	+	1.77293i	0.0562689	+	0.0815196i
$474$	0.565165	+	4.65456i	0.0259589	+	0.213791i
$475$	−1.67690	−	4.42162i	−0.0769415	−	0.202878i
$476$	1.14403	−	3.01655i	0.0524363	−	0.138263i
$477$	−6.30906	−	9.14025i	−0.288872	−	0.418503i
$478$	5.64445	+	1.39123i	0.258171	+	0.0636334i
$479$	7.27246	+	19.1759i	0.332287	+	0.876170i	0.992181	+	0.124810i	$0.0398322\pi$
$479$	7.27246	+	19.1759i	0.332287	+	0.876170i	−0.659893	+	0.751359i	$0.729399\pi$
$480$	−5.39830	+	14.2341i	−0.246397	+	0.649696i
$481$	−5.84943	+	23.3353i	−0.266711	+	1.06400i
$482$	8.39419	+	22.1337i	0.382345	+	1.00816i
$483$	0.0467914	−	0.0414535i	0.00212908	−	0.00188620i
$484$	−26.5185			−1.20539
$485$	−4.38490			−0.199108
$486$	1.62714	−	1.44152i	0.0738087	−	0.0653888i
$487$	−2.55510	+	1.34102i	−0.115782	+	0.0607673i	−0.521620	−	0.853178i	$-0.674672\pi$
$487$	−2.55510	+	1.34102i	−0.115782	+	0.0607673i	0.405838	+	0.913945i	$0.366980\pi$
$488$	−4.41771			−0.199980
$489$	−21.9405	−	11.5153i	−0.992183	−	0.520738i
$490$	−22.8500	−	20.2434i	−1.03226	−	0.914502i
$491$	9.05872	+	13.1238i	0.408814	+	0.592270i	0.972266	−	0.233879i	$-0.0751421\pi$
$491$	9.05872	+	13.1238i	0.408814	+	0.592270i	−0.563451	+	0.826149i	$0.690527\pi$
$492$	8.08595	+	7.16352i	0.364543	+	0.322957i
$493$	−6.57978	−	9.53246i	−0.296338	−	0.429320i
$494$	−39.3201	−	4.93186i	−1.76909	−	0.221895i
$495$	1.29093	−	1.87023i	0.0580229	−	0.0840607i
$496$	4.95712	−	1.22182i	0.222581	−	0.0548613i
$497$	−1.23092	+	1.09050i	−0.0552141	+	0.0489154i
$498$	13.6692	+	3.36916i	0.612533	+	0.150976i
$499$	13.5172	+	11.9752i	0.605112	+	0.536083i	0.909092	−	0.416596i	$-0.136777\pi$
$499$	13.5172	+	11.9752i	0.605112	+	0.536083i	−0.303979	+	0.952679i	$0.598315\pi$
$500$	24.4127	+	21.6277i	1.09177	+	0.967221i
$501$	−1.50997	+	3.98146i	−0.0674604	+	0.177878i
$502$	−7.28858	+	10.5593i	−0.325305	+	0.471286i
$503$	−14.5694	−	7.64664i	−0.649620	−	0.340947i	0.107517	−	0.994203i	$-0.465710\pi$
$503$	−14.5694	−	7.64664i	−0.649620	−	0.340947i	−0.757137	+	0.653257i	$0.773402\pi$
$504$	−0.0353542	+	0.291168i	−0.00157480	+	0.0129696i
$505$	−27.0448	−	6.66593i	−1.20348	−	0.296630i
$506$	0.823723			0.0366189
$507$	−1.46507	−	12.9172i	−0.0650660	−	0.573672i
$508$	−7.11676			−0.315755
$509$	4.20198	+	1.03570i	0.186250	+	0.0459064i	0.331337	−	0.943512i	$-0.392500\pi$
$509$	4.20198	+	1.03570i	0.186250	+	0.0459064i	−0.145088	+	0.989419i	$0.546346\pi$
$510$	3.36269	−	27.6942i	0.148902	−	1.22632i
$511$	0.0597786	+	0.0313742i	0.00264445	+	0.00138791i
$512$	−12.2988	+	17.8179i	−0.543536	+	0.787447i
$513$	1.79287	−	4.72742i	0.0791573	−	0.208721i
$514$	10.5811	+	9.37400i	0.466711	+	0.413469i
$515$	−26.7381	−	23.6879i	−1.17822	−	1.04381i
$516$	−5.05782	−	1.24664i	−0.222658	−	0.0548803i
$517$	3.21222	−	2.84578i	0.141273	−	0.125157i
$518$	2.61880	−	0.645476i	0.115063	−	0.0283606i
$519$	−2.08028	+	3.01381i	−0.0913144	+	0.132292i
$520$	10.7366	−	4.02346i	0.470831	−	0.176440i
$521$	−11.1549	−	16.1607i	−0.488706	−	0.708013i	0.498602	−	0.866831i	$-0.333847\pi$
$521$	−11.1549	−	16.1607i	−0.488706	−	0.708013i	−0.987308	+	0.158818i	$0.949232\pi$
$522$	2.96083	+	2.62307i	0.129592	+	0.114809i
$523$	18.8946	+	27.3736i	0.826204	+	1.19696i	0.978011	+	0.208553i	$0.0668752\pi$
$523$	18.8946	+	27.3736i	0.826204	+	1.19696i	−0.151808	+	0.988410i	$0.548509\pi$
$524$	39.6693	+	35.1440i	1.73296	+	1.53527i
$525$	−0.154003	−	0.0808273i	−0.00672126	−	0.00352759i
$526$	−34.6982			−1.51291
$527$	−14.2289	+	7.46790i	−0.619820	+	0.325307i
$528$	1.70627	−	1.51162i	0.0742557	−	0.0657848i
$529$	−22.8870			−0.995086
$530$	48.6752			2.11432
$531$	5.81201	−	5.14900i	0.252220	−	0.223447i
$532$	0.908688	+	2.39601i	0.0393966	+	0.103880i
$533$	−0.0563968	+	14.2903i	−0.00244282	+	0.618982i
$534$	−12.7944	+	33.7360i	−0.553667	+	1.45990i
$535$	3.56339	+	9.39587i	0.154059	+	0.406219i
$536$	10.3476	+	2.55046i	0.446948	+	0.110163i
$537$	9.33695	+	13.5269i	0.402919	+	0.583729i
$538$	−3.55909	+	9.38455i	−0.153443	+	0.404597i
$539$	2.78409	+	7.34104i	0.119919	+	0.316201i
$540$	0.662357	+	5.45500i	0.0285033	+	0.234746i
$541$	12.1530	+	17.6066i	0.522496	+	0.756967i	0.992037	−	0.125944i	$-0.0401960\pi$
$541$	12.1530	+	17.6066i	0.522496	+	0.756967i	−0.469541	+	0.882911i	$0.655581\pi$
$542$	−48.8510	+	12.0407i	−2.09833	+	0.517192i
$543$	−16.3458	−	14.4811i	−0.701465	−	0.621444i
$544$	17.0439	−	44.9411i	0.730751	−	1.92683i
$545$	−19.3820	−	4.77723i	−0.830234	−	0.204634i
$546$	−1.20275	+	0.823208i	−0.0514728	+	0.0352300i
$547$	−28.1037	+	6.92694i	−1.20163	+	0.296174i	−0.788809	−	0.614639i	$-0.789302\pi$
$547$	−28.1037	+	6.92694i	−1.20163	+	0.296174i	−0.412818	+	0.910813i	$0.635456\pi$
$548$	−3.67612	+	30.2756i	−0.157036	+	1.29331i
$549$	2.47998	−	1.30159i	0.105843	−	0.0555507i
$550$	−0.812683	−	2.14287i	−0.0346529	−	0.0913723i
$551$	8.93276	+	2.20173i	0.380548	+	0.0937967i
$552$	−0.396895	+	0.351619i	−0.0168930	+	0.0149659i
$553$	0.389428	+	0.0959854i	0.0165602	+	0.00408172i
$554$	26.5840	−	13.9523i	1.12944	−	0.592778i
$555$	11.9112	−	6.25148i	0.505602	−	0.265361i
$556$	−3.94084	−	32.4557i	−0.167129	−	1.37643i
$557$	3.67881	+	30.2977i	0.155876	+	1.28376i	0.835212	+	0.549928i	$0.185345\pi$
$557$	3.67881	+	30.2977i	0.155876	+	1.28376i	−0.679336	+	0.733827i	$0.737732\pi$
$558$	4.10775	−	3.63915i	0.173895	−	0.154057i
$559$	−3.17830	−	6.11426i	−0.134428	−	0.258606i
$560$	0.567512	+	0.502772i	0.0239818	+	0.0212460i
$561$	−4.07582	+	5.90484i	−0.172081	+	0.249303i
$562$	16.5497	−	43.6381i	0.698109	−	1.84076i
$563$	−2.57341	−	21.1940i	−0.108456	−	0.893219i	−0.940801	−	0.338960i	$-0.889925\pi$
$563$	−2.57341	−	21.1940i	−0.108456	−	0.893219i	0.832344	−	0.554259i	$-0.186998\pi$
$564$	−1.25082	+	10.3014i	−0.0526690	+	0.433769i
$565$	9.82203	+	5.15500i	0.413216	+	0.216872i
$566$	12.4004	−	17.9651i	0.521229	−	0.755131i
$567$	−0.0659402	−	0.173870i	−0.00276923	−	0.00730186i
$568$	10.4409	−	9.24984i	0.438091	−	0.388115i
$569$	22.5300	−	32.6404i	0.944508	−	1.36836i	0.0148663	−	0.999889i	$-0.495268\pi$
$569$	22.5300	−	32.6404i	0.944508	−	1.36836i	0.929641	−	0.368466i	$-0.120117\pi$
$570$	12.5876	+	18.2363i	0.527238	+	0.763836i
$571$	1.62228	+	13.3606i	0.0678901	+	0.559126i	0.986476	+	0.163905i	$0.0524089\pi$
$571$	1.62228	+	13.3606i	0.0678901	+	0.559126i	−0.918586	+	0.395221i	$0.870668\pi$
$572$	−10.9909	−	1.37857i	−0.459552	−	0.0576410i
$573$	2.07758	−	17.1104i	0.0867923	−	0.714799i
$574$	1.41864	−	0.744562i	0.0592131	−	0.0310774i
$575$	−0.111497	−	0.293994i	−0.00464976	−	0.0122604i
$576$	−1.49101	+	12.2795i	−0.0621253	+	0.511648i
$577$	−17.3518			−0.722366			−0.361183	−	0.932495i	$-0.617627\pi$
$577$	−17.3518			−0.722366			−0.361183	+	0.932495i	$0.617627\pi$
$578$	−6.16245	+	50.7524i	−0.256324	+	2.11102i
$579$	−4.13874	−	5.99600i	−0.172000	−	0.249185i
$580$	−9.70854	+	2.39294i	−0.403125	+	0.0993615i
$581$	0.684111	−	0.991106i	0.0283817	−	0.0411180i
$582$	−4.59058	+	1.13148i	−0.190286	+	0.0469012i
$583$	−11.0847	−	5.81771i	−0.459082	−	0.240945i
$584$	−0.507056	−	0.266123i	−0.0209821	−	0.0110123i
$585$	−4.84179	+	5.42199i	−0.200183	+	0.224172i
$586$	−60.4502	+	31.7267i	−2.49717	+	1.31062i
$587$	−8.95690			−0.369691			−0.184845	−	0.982768i	$-0.559178\pi$
$587$	−8.95690			−0.369691			−0.184845	+	0.982768i	$0.559178\pi$
$588$	−16.8102	−	8.82270i	−0.693243	−	0.363842i
$589$	4.52614	−	11.9344i	0.186496	−	0.491750i
$590$	4.10194	+	33.7825i	0.168874	+	1.39080i
$591$	4.24525	−	1.04636i	0.174626	−	0.0430415i
$592$	13.1017	−	3.22927i	0.538475	−	0.132722i
$593$	−2.17654	−	17.9254i	−0.0893796	−	0.736107i	−0.966648	−	0.256108i	$-0.917560\pi$
$593$	−2.17654	−	17.9254i	−0.0893796	−	0.736107i	0.877269	−	0.480000i	$-0.159363\pi$
$594$	0.868887	−	2.29107i	0.0356509	−	0.0940036i
$595$	−2.11306	−	1.10902i	−0.0866270	−	0.0454654i
$596$	36.2428			1.48456
$597$	−4.69875	+	2.46609i	−0.192307	+	0.100931i
$598$	−2.61440	−	0.327920i	−0.106911	−	0.0134097i
$599$	−14.0952	−	7.39771i	−0.575913	−	0.302262i	0.151506	−	0.988456i	$-0.451588\pi$
$599$	−14.0952	−	7.39771i	−0.575913	−	0.302262i	−0.727419	+	0.686194i	$0.759280\pi$
$600$	1.30629	+	0.685596i	0.0533292	+	0.0279893i
$601$	−23.2059	+	5.71975i	−0.946589	+	0.233313i	−0.682252	−	0.731117i	$-0.738999\pi$
$601$	−23.2059	+	5.71975i	−0.946589	+	0.233313i	−0.264337	+	0.964430i	$0.585153\pi$
$602$	−0.438876	+	0.635821i	−0.0178872	+	0.0259141i
$603$	−6.56030	+	1.61697i	−0.267156	+	0.0658481i
$604$	1.83203	+	2.65416i	0.0745444	+	0.107996i
$605$	−2.36441	+	19.4726i	−0.0961268	+	0.791676i
$606$	−30.0334			−1.22002
$607$	−3.88567	+	32.0014i	−0.157714	+	1.29890i	0.671935	+	0.740610i	$0.265464\pi$
$607$	−3.88567	+	32.0014i	−0.157714	+	1.29890i	−0.829649	+	0.558285i	$0.811460\pi$
$608$	13.5378	+	35.6962i	0.549030	+	1.44767i
$609$	0.299613	−	0.157249i	0.0121409	−	0.00637205i
$610$	−1.47959	+	12.1855i	−0.0599069	+	0.493377i
$611$	−11.3281	+	7.75340i	−0.458286	+	0.313669i
$612$	−2.09124	−	17.2229i	−0.0845335	−	0.696196i
$613$	−11.4990	−	16.6591i	−0.464439	−	0.672855i	0.518859	−	0.854860i	$-0.326357\pi$
$613$	−11.4990	−	16.6591i	−0.464439	−	0.672855i	−0.983298	+	0.182004i	$0.941742\pi$
$614$	20.4497	−	29.6265i	0.825282	−	1.19563i
$615$	5.98115	−	5.29884i	0.241183	−	0.213670i
$616$	0.117235	+	0.309123i	0.00472353	+	0.0124549i
$617$	−2.11048	+	3.05756i	−0.0849647	+	0.123093i	−0.863162	−	0.504928i	$-0.831519\pi$
$617$	−2.11048	+	3.05756i	−0.0849647	+	0.123093i	0.778197	+	0.628020i	$0.216135\pi$
$618$	−34.1047	−	17.8995i	−1.37189	−	0.720024i
$619$	−0.366646	+	3.01960i	−0.0147367	+	0.121368i	−0.998221	−	0.0596273i	$-0.981009\pi$
$619$	−0.366646	+	3.01960i	−0.0147367	+	0.121368i	0.983484	+	0.180995i	$0.0579319\pi$
$620$	1.67213	+	13.7712i	0.0671544	+	0.553066i
$621$	0.119208	−	0.314327i	0.00478367	−	0.0126135i
$622$	−26.8601	+	38.9136i	−1.07699	+	1.56029i
$623$	2.31020	+	2.04666i	0.0925563	+	0.0819977i
$624$	−6.01726	+	4.11845i	−0.240883	+	0.164870i
$625$	14.5575	−	12.8968i	0.582300	−	0.515873i
$626$	−6.87199	−	56.5959i	−0.274660	−	2.26203i
$627$	−0.686934	−	5.65741i	−0.0274335	−	0.225935i
$628$	30.7960	−	16.1630i	1.22889	−	0.644973i
$629$	−37.6069	+	19.7376i	−1.49949	+	0.786991i
$630$	0.791298	+	0.195037i	0.0315261	+	0.00777048i
$631$	−24.6502	+	21.8381i	−0.981307	+	0.869362i	−0.991437	−	0.130586i	$-0.958314\pi$
$631$	−24.6502	+	21.8381i	−0.981307	+	0.869362i	0.0101298	+	0.999949i	$0.496776\pi$
$632$	−3.30322	−	0.814171i	−0.131395	−	0.0323860i
$633$	0.913476	+	2.40864i	0.0363074	+	0.0957348i
$634$	63.4290	−	33.2901i	2.51909	−	1.32212i
$635$	−0.634534	+	5.22586i	−0.0251807	+	0.207382i
$636$	29.3913	−	7.24432i	1.16544	−	0.287256i
$637$	−5.91394	−	24.4079i	−0.234319	−	0.967078i
$638$	4.32912	+	1.06703i	0.171392	+	0.0422442i
$639$	−3.13595	+	8.26882i	−0.124056	+	0.327109i
$640$	−17.7891	−	15.7597i	−0.703174	−	0.622958i
$641$	16.7074	−	4.11801i	0.659904	−	0.162652i	0.104879	−	0.994485i	$-0.466555\pi$
$641$	16.7074	−	4.11801i	0.659904	−	0.162652i	0.555026	+	0.831833i	$0.312708\pi$
$642$	6.15503	+	8.91710i	0.242920	+	0.351930i
$643$	−5.74845	−	47.3427i	−0.226697	−	1.86701i	−0.451039	−	0.892504i	$-0.648946\pi$
$643$	−5.74845	−	47.3427i	−0.226697	−	1.86701i	0.224342	−	0.974510i	$-0.427977\pi$
$644$	0.0604188	+	0.159311i	0.00238083	+	0.00627775i
$645$	−1.36637	+	3.60282i	−0.0538008	+	0.141861i
$646$	−39.7426	−	57.5771i	−1.56365	−	2.26534i
$647$	−8.73765	−	2.15364i	−0.343513	−	0.0846683i	0.0637852	−	0.997964i	$-0.479683\pi$
$647$	−8.73765	−	2.15364i	−0.343513	−	0.0846683i	−0.407298	+	0.913295i	$0.633529\pi$
$648$	0.559320	+	1.47481i	0.0219722	+	0.0579359i
$649$	3.10359	−	8.18349i	0.121827	−	0.321230i
$650$	1.72629	+	7.12475i	0.0677109	+	0.279455i
$651$	−0.166467	−	0.438938i	−0.00652436	−	0.0172033i
$652$	50.5518	−	44.7850i	1.97976	−	1.75392i
$653$	36.4382			1.42594			0.712969	−	0.701196i	$-0.247350\pi$
$653$	36.4382			1.42594			0.712969	+	0.701196i	$0.247350\pi$
$654$	−21.5238			−0.841649
$655$	29.3433	−	25.9959i	1.14654	−	1.01574i
$656$	7.09738	−	3.72499i	0.277106	−	0.145437i
$657$	0.363055			0.0141641
$658$	1.36275	+	0.715227i	0.0531256	+	0.0278824i
$659$	−7.40854	−	6.56339i	−0.288596	−	0.255673i	0.506386	−	0.862307i	$-0.330981\pi$
$659$	−7.40854	−	6.56339i	−0.288596	−	0.255673i	−0.794982	+	0.606634i	$0.792520\pi$
$660$	3.51854	+	5.09748i	0.136959	+	0.198419i
$661$	21.1906	+	18.7732i	0.824217	+	0.730193i	0.965676	−	0.259751i	$-0.0836406\pi$
$661$	21.1906	+	18.7732i	0.824217	+	0.730193i	−0.141458	+	0.989944i	$0.545179\pi$
$662$	−17.1435	−	24.8367i	−0.666302	−	0.965305i
$663$	15.2869	−	17.1187i	0.593692	−	0.664836i
$664$	−5.80279	+	8.40679i	−0.225192	+	0.326247i
$665$	1.84042	−	0.453623i	0.0713685	−	0.0175907i
$666$	10.8568	−	9.61827i	0.420692	−	0.372700i
$667$	0.593941	+	0.146393i	0.0229975	+	0.00566837i
$668$	−8.68722	−	7.69621i	−0.336119	−	0.297775i
$669$	3.37300	+	2.98822i	0.130408	+	0.115531i
$670$	10.5007	−	27.6880i	0.405676	−	1.06968i
$671$	1.79337	−	2.59815i	0.0692323	−	0.100300i
$672$	1.24329	+	0.652527i	0.0479608	+	0.0251718i
$673$	4.71999	−	38.8726i	0.181942	−	1.49843i	−0.560295	−	0.828293i	$-0.689312\pi$
$673$	4.71999	−	38.8726i	0.181942	−	1.49843i	0.742238	−	0.670137i	$-0.233765\pi$
$674$	30.4115	+	7.49576i	1.17141	+	0.288726i
$675$	−0.935315			−0.0360003
$676$	34.3350	+	8.75085i	1.32058	+	0.336571i
$677$	49.2614			1.89327			0.946634	−	0.322310i	$-0.104459\pi$
$677$	49.2614			1.89327			0.946634	+	0.322310i	$0.104459\pi$
$678$	11.6129	+	2.86233i	0.445992	+	0.109927i
$679$	−0.0487496	+	0.401489i	−0.00187084	+	0.0154077i
$680$	17.9235	+	9.40696i	0.687334	+	0.360741i
$681$	−5.47652	+	7.93412i	−0.209861	+	0.304036i
$682$	2.19352	−	5.78384i	0.0839942	−	0.221475i
$683$	38.3759	+	33.9981i	1.46841	+	1.30090i	0.863228	+	0.504815i	$0.168439\pi$
$683$	38.3759	+	33.9981i	1.46841	+	1.30090i	0.605185	+	0.796085i	$0.293099\pi$
$684$	10.3148	+	9.13815i	0.394398	+	0.349406i
$685$	21.9037	+	5.39878i	0.836898	+	0.206277i
$686$	−4.22557	+	3.74353i	−0.161333	+	0.142929i
$687$	11.0434	−	2.72196i	0.421334	−	0.103849i
$688$	−2.19567	+	3.18097i	−0.0837089	+	0.121273i
$689$	32.8656	+	22.8775i	1.25208	+	0.871564i
$690$	0.836953	+	1.21254i	0.0318623	+	0.0461605i
$691$	−37.2316	−	32.9843i	−1.41636	−	1.25478i	−0.922915	−	0.385003i	$-0.874200\pi$
$691$	−37.2316	−	32.9843i	−1.41636	−	1.25478i	−0.493441	−	0.869779i	$-0.664261\pi$
$692$	−5.66999	−	8.21440i	−0.215541	−	0.312265i
$693$	−0.156890	−	0.138992i	−0.00595975	−	0.00527988i
$694$	44.3635	+	23.2837i	1.68401	+	0.883839i
$695$	−24.1837			−0.917342
$696$	−2.54139	+	1.33382i	−0.0963310	+	0.0505584i
$697$	−18.8841	+	16.7299i	−0.715288	+	0.633689i
$698$	−10.7491			−0.406860
$699$	18.9757			0.717727
$700$	0.354831	−	0.314353i	0.0134113	−	0.0118814i
$701$	2.77826	+	7.32568i	0.104934	+	0.276687i	0.977192	−	0.212358i	$-0.0681144\pi$
$701$	2.77826	+	7.32568i	0.104934	+	0.276687i	−0.872258	+	0.489046i	$0.837345\pi$
$702$	−3.66981	+	6.92568i	−0.138508	+	0.261393i
$703$	11.9626	−	31.5427i	0.451177	−	1.18966i
$704$	4.94420	+	13.0368i	0.186342	+	0.491342i
$705$	7.45286	+	1.83696i	0.280691	+	0.0691841i
$706$	−43.4346	−	62.9259i	−1.63468	−	2.36825i
$707$	−0.911018	+	2.40216i	−0.0342623	+	0.0903424i
$708$	7.50469	+	19.7883i	0.282044	+	0.743688i
$709$	−1.97245	−	16.2446i	−0.0740768	−	0.610078i	−0.981719	−	0.190334i	$-0.939043\pi$
$709$	−1.97245	−	16.2446i	−0.0740768	−	0.610078i	0.907643	−	0.419744i	$-0.137880\pi$
$710$	−22.0173	−	31.8975i	−0.826293	−	1.19709i
$711$	2.09422	−	0.516178i	0.0785393	−	0.0193582i
$712$	−19.5957	−	17.3603i	−0.734379	−	0.650603i
$713$	0.300944	−	0.793523i	0.0112704	−	0.0297177i
$714$	−2.49835	−	0.615787i	−0.0934982	−	0.0230452i
$715$	−1.99224	+	7.94773i	−0.0745057	+	0.297228i
$716$	−43.4971	+	10.7211i	−1.62556	+	0.400665i
$717$	0.322344	−	2.65474i	0.0120382	−	0.0991431i
$718$	7.20723	−	3.78265i	0.268971	−	0.141167i
$719$	8.21224	+	21.6539i	0.306265	+	0.807554i	0.996471	+	0.0839410i	$0.0267507\pi$
$719$	8.21224	+	21.6539i	0.306265	+	0.807554i	−0.690206	+	0.723613i	$0.742480\pi$
$720$	3.95881	+	0.975759i	0.147536	+	0.0363644i
$721$	−2.46617	+	2.18483i	−0.0918449	+	0.0813675i
$722$	13.8521	+	3.41423i	0.515521	+	0.127064i
$723$	9.64214	−	5.06059i	0.358595	−	0.188205i
$724$	52.7029	−	27.6606i	1.95869	−	1.02800i
$725$	−0.205147	−	1.68954i	−0.00761896	−	0.0627478i
$726$	2.54939	+	20.9961i	0.0946168	+	0.779239i
$727$	28.6733	−	25.4023i	1.06343	−	0.942120i	0.0649898	−	0.997886i	$-0.479299\pi$
$727$	28.6733	−	25.4023i	1.06343	−	0.942120i	0.998444	+	0.0557659i	$0.0177600\pi$
$728$	−0.249030	−	1.02779i	−0.00922965	−	0.0380925i
$729$	−0.748511	−	0.663123i	−0.0277226	−	0.0245601i
$730$	−0.903882	+	1.30950i	−0.0334542	+	0.0484668i
$731$	4.31401	−	11.3751i	0.159559	−	0.420723i
$732$	0.920153	+	7.57814i	0.0340098	+	0.280096i
$733$	−6.07515	+	50.0334i	−0.224391	+	1.84802i	0.250671	+	0.968072i	$0.419349\pi$
$733$	−6.07515	+	50.0334i	−0.224391	+	1.84802i	−0.475062	+	0.879952i	$0.657574\pi$
$734$	47.0816	+	24.7103i	1.73781	+	0.912074i
$735$	−7.97735	+	11.5572i	−0.294249	+	0.426293i
$736$	0.900130	+	2.37345i	0.0331792	+	0.0874865i
$737$	−5.70059	+	5.05028i	−0.209984	+	0.186030i
$738$	4.89439	−	7.09075i	0.180165	−	0.261014i
$739$	28.0855	+	40.6889i	1.03314	+	1.49676i	0.858954	+	0.512052i	$0.171115\pi$
$739$	28.0855	+	40.6889i	1.03314	+	1.49676i	0.174188	+	0.984712i	$0.444270\pi$
$740$	4.41944	+	36.3974i	0.162462	+	1.33799i
$741$	−0.0719426	+	18.2294i	−0.00264288	+	0.669675i
$742$	0.541152	−	4.45679i	0.0198663	−	0.163614i
$743$	−28.8614	+	15.1476i	−1.05882	+	0.555712i	−0.901920	−	0.431902i	$-0.857843\pi$
$743$	−28.8614	+	15.1476i	−1.05882	+	0.555712i	−0.156901	+	0.987614i	$0.550150\pi$
$744$	1.41201	+	3.72317i	0.0517669	+	0.136498i
$745$	3.23143	−	26.6132i	0.118391	−	0.975034i
$746$	−14.2161			−0.520490
$747$	0.780625	−	6.42902i	0.0285616	−	0.235226i
$748$	−11.1090	−	16.0941i	−0.406185	−	0.588460i
$749$	0.899919	−	0.221810i	0.0328823	−	0.00810477i
$750$	14.7769	−	21.4080i	0.539575	−	0.781710i
$751$	−7.88455	+	1.94337i	−0.287711	+	0.0709145i	−0.380530	−	0.924769i	$-0.624258\pi$
$751$	−7.88455	+	1.94337i	−0.287711	+	0.0709145i	0.0928187	+	0.995683i	$0.470412\pi$
$752$	6.81775	+	3.57823i	0.248618	+	0.130485i
$753$	5.22618	+	2.74291i	0.190453	+	0.0999572i
$754$	−13.3153	−	5.11004i	−0.484916	−	0.186097i
$755$	2.11230	−	1.10862i	0.0768746	−	0.0403469i
$756$	0.506834			0.0184334
$757$	31.6764	+	16.6251i	1.15130	+	0.604249i	0.928763	−	0.370675i	$-0.120874\pi$
$757$	31.6764	+	16.6251i	1.15130	+	0.604249i	0.222537	+	0.974924i	$0.428566\pi$
$758$	25.0384	−	66.0209i	0.909437	−	2.39799i
$759$	−0.0456744	−	0.376162i	−0.00165787	−	0.0136538i
$760$	−15.6109	+	3.84774i	−0.566266	+	0.139572i
$761$	18.2544	−	4.49931i	0.661723	−	0.163100i	0.105869	−	0.994380i	$-0.466238\pi$
$761$	18.2544	−	4.49931i	0.661723	−	0.163100i	0.555854	+	0.831280i	$0.312391\pi$
$762$	0.684179	+	5.63472i	0.0247852	+	0.204124i
$763$	−0.652893	+	1.72154i	−0.0236363	+	0.0623239i
$764$	41.5974	+	21.8320i	1.50494	+	0.789853i
$765$	−12.8333			−0.463990
$766$	−48.7139	+	25.5670i	−1.76010	+	0.923774i
$767$	−13.1082	+	24.7379i	−0.473311	+	0.893235i
$768$	−0.784386	−	0.411677i	−0.0283041	−	0.0148551i
$769$	−26.3344	−	13.8213i	−0.949642	−	0.498410i	−0.0825653	−	0.996586i	$-0.526311\pi$
$769$	−26.3344	−	13.8213i	−0.949642	−	0.498410i	−0.867076	+	0.498175i	$0.834004\pi$
$770$	0.891931	−	0.219841i	0.0321430	−	0.00792253i
$771$	3.69404	−	5.35174i	0.133037	−	0.192738i
$772$	19.2807	−	4.75227i	0.693928	−	0.171038i
$773$	4.99650	+	7.23869i	0.179712	+	0.260357i	0.902479	−	0.430734i	$-0.141745\pi$
$773$	4.99650	+	7.23869i	0.179712	+	0.260357i	−0.722767	+	0.691092i	$0.757130\pi$
$774$	−0.500792	+	4.12439i	−0.0180006	+	0.148248i
$775$	−2.36122			−0.0848174
$776$	0.413506	−	3.40552i	0.0148440	−	0.122251i
$777$	−0.439973	−	1.16011i	−0.0157839	−	0.0416188i
$778$	33.8187	−	17.7494i	1.21246	−	0.636348i
$779$	2.41545	−	19.8930i	0.0865423	−	0.712740i
$780$	−9.13814	−	17.5795i	−0.327198	−	0.629448i
$781$	1.20153	+	9.89549i	0.0429941	+	0.354088i
$782$	−2.64249	−	3.82831i	−0.0944953	−	0.136900i
$783$	1.03368	−	1.49754i	0.0369407	−	0.0535178i
$784$	−10.5440	+	9.34113i	−0.376570	+	0.333612i
$785$	−9.12275	−	24.0547i	−0.325605	−	0.858549i
$786$	24.0117	−	34.7869i	0.856469	−	1.24081i
$787$	−34.8352	−	18.2829i	−1.24174	−	0.651717i	−0.289534	−	0.957168i	$-0.593500\pi$
$787$	−34.8352	−	18.2829i	−1.24174	−	0.651717i	−0.952208	+	0.305451i	$0.901193\pi$
$788$	−1.43645	+	11.8302i	−0.0511713	+	0.421433i
$789$	1.92397	+	15.8453i	0.0684952	+	0.564109i
$790$	−3.35208	+	8.83871i	−0.119262	+	0.314467i
$791$	0.581198	−	0.842011i	0.0206650	−	0.0299385i
$792$	1.33078	+	1.17896i	0.0472871	+	0.0418927i
$793$	−6.72626	+	7.53228i	−0.238856	+	0.267479i
$794$	−57.2252	+	50.6971i	−2.03085	+	1.79917i
$795$	−2.69898	−	22.2281i	−0.0957229	−	0.788349i
$796$	−1.74339	−	14.3581i	−0.0617928	−	0.508909i
$797$	6.35963	−	3.33779i	0.225269	−	0.118231i	−0.348313	−	0.937378i	$-0.613245\pi$
$797$	6.35963	−	3.33779i	0.225269	−	0.118231i	0.573583	+	0.819148i	$0.305553\pi$
$798$	1.80969	−	0.949801i	0.0640625	−	0.0336226i
$799$	−23.5307	−	5.79980i	−0.832457	−	0.205182i
$800$	5.28633	−	4.68328i	0.186900	−	0.165579i
$801$	16.1153	+	3.97208i	0.569408	+	0.140346i
$802$	−0.423290	−	1.11612i	−0.0149469	−	0.0394117i
$803$	0.362352	−	0.190177i	0.0127871	−	0.00671120i
$804$	2.21978	−	18.2815i	0.0782856	−	0.644740i
$805$	0.122370	−	0.0301615i	0.00431297	−	0.00106305i
$806$	−9.26450	+	17.4840i	−0.326328	+	0.615847i
$807$	4.48291	+	1.10494i	0.157806	+	0.0388956i
$808$	7.72746	−	20.3756i	0.271851	−	0.716813i
$809$	37.4014	+	33.1348i	1.31496	+	1.16496i	0.974422	+	0.224727i	$0.0721489\pi$
$809$	37.4014	+	33.1348i	1.31496	+	1.16496i	0.340542	+	0.940229i	$0.389390\pi$
$810$	4.25534	−	1.04885i	0.149517	−	0.0368527i
$811$	18.5988	+	26.9450i	0.653093	+	0.946168i	0.999966	+	0.00825593i	$0.00262797\pi$
$811$	18.5988	+	26.9450i	0.653093	+	0.946168i	−0.346873	+	0.937912i	$0.612757\pi$
$812$	0.111166	+	0.915535i	0.00390116	+	0.0321290i
$813$	8.20725	+	21.6407i	0.287841	+	0.758974i
$814$	5.79747	−	15.2867i	0.203201	−	0.535798i
$815$	−28.3786	−	41.1134i	−0.994058	−	1.44014i
$816$	−12.4990	−	3.08074i	−0.437554	−	0.107847i
$817$	3.42657	+	9.03513i	0.119881	+	0.316099i
$818$	−11.7461	+	30.9720i	−0.410694	+	1.08291i
$819$	0.442618	+	0.503602i	0.0154663	+	0.0175973i
$820$	7.72309	+	20.3641i	0.269702	+	0.711146i
$821$	−2.22771	+	1.97358i	−0.0777475	+	0.0688783i	−0.701102	−	0.713061i	$-0.747308\pi$
$821$	−2.22771	+	1.97358i	−0.0777475	+	0.0688783i	0.623354	+	0.781940i	$0.285770\pi$
$822$	24.3242			0.848404
$823$	41.9867			1.46356			0.731781	−	0.681539i	$-0.238689\pi$
$823$	41.9867			1.46356			0.731781	+	0.681539i	$0.238689\pi$
$824$	20.9186	−	18.5323i	0.728734	−	0.645602i
$825$	−0.933503	+	0.489940i	−0.0325004	+	0.0170575i
$826$	3.13879			0.109212
$827$	20.6325	+	10.8288i	0.717461	+	0.376553i	0.783607	−	0.621257i	$-0.213378\pi$
$827$	20.6325	+	10.8288i	0.717461	+	0.376553i	−0.0661455	+	0.997810i	$0.521070\pi$
$828$	0.685835	+	0.607597i	0.0238344	+	0.0211155i
$829$	25.6112	+	37.1042i	0.889513	+	1.28868i	0.956740	+	0.290944i	$0.0939693\pi$
$829$	25.6112	+	37.1042i	0.889513	+	1.28868i	−0.0672276	+	0.997738i	$0.521415\pi$
$830$	21.2453	+	18.8217i	0.737434	+	0.653310i
$831$	−7.84554	−	11.3662i	−0.272159	−	0.394290i
$832$	−10.5024	−	43.3455i	−0.364106	−	1.50273i
$833$	25.1867	−	36.4892i	0.872667	−	1.26428i
$834$	−25.3181	+	6.24035i	−0.876694	+	0.216086i
$835$	−6.42591	+	5.69286i	−0.222378	+	0.197010i
$836$	15.0816	+	3.71729i	0.521610	+	0.128565i
$837$	−1.88963	−	1.67406i	−0.0653151	−	0.0578641i
$838$	−16.7852	−	14.8704i	−0.579837	−	0.513690i
$839$	13.8817	−	36.6032i	0.479251	−	1.26368i	−0.449600	−	0.893230i	$-0.648434\pi$
$839$	13.8817	−	36.6032i	0.479251	−	1.26368i	0.928852	−	0.370452i	$-0.120797\pi$
$840$	−0.335918	+	0.486661i	−0.0115903	+	0.0167914i
$841$	−22.7464	−	11.9382i	−0.784358	−	0.411663i
$842$	−4.66001	+	38.3786i	−0.160594	+	1.32261i
$843$	−20.8455	−	5.13795i	−0.717957	−	0.176960i
$844$	−7.02121			−0.241680
$845$	9.48711	−	24.4321i	0.326367	−	0.840489i
$846$	8.27645			0.284550
$847$	1.75666	+	0.432979i	0.0603597	+	0.0148773i
$848$	2.70735	−	22.2970i	0.0929707	−	0.765682i
$849$	−8.89157	−	4.66666i	−0.305158	−	0.160159i
$850$	−7.35206	+	10.6513i	−0.252174	+	0.365337i
$851$	0.795394	−	2.09728i	0.0272657	−	0.0718939i
$852$	−18.0419	−	15.9837i	−0.618105	−	0.547593i
$853$	−2.04500	−	1.81171i	−0.0700194	−	0.0620317i	0.627387	−	0.778707i	$-0.284124\pi$
$853$	−2.04500	−	1.81171i	−0.0700194	−	0.0620317i	−0.697407	+	0.716676i	$0.745663\pi$
$854$	1.09928	+	0.270948i	0.0376165	+	0.00927164i
$855$	7.62986	−	6.75946i	0.260936	−	0.231169i
$856$	−7.63332	+	1.88145i	−0.260902	+	0.0643065i
$857$	−6.81857	+	9.87840i	−0.232918	+	0.337440i	−0.921962	−	0.387279i	$-0.873415\pi$
$857$	−6.81857	+	9.87840i	−0.232918	+	0.337440i	0.689045	+	0.724719i	$0.258030\pi$
$858$	−0.0348658	+	8.83460i	−0.00119030	+	0.301608i
$859$	25.5382	+	36.9985i	0.871354	+	1.26237i	0.963792	+	0.266655i	$0.0859185\pi$
$859$	25.5382	+	36.9985i	0.871354	+	1.26237i	−0.0924383	+	0.995718i	$0.529466\pi$
$860$	−7.86107	−	6.96430i	−0.268060	−	0.237481i
$861$	−0.418675	−	0.606555i	−0.0142684	−	0.0206713i
$862$	−1.88748	−	1.67216i	−0.0642879	−	0.0569541i
$863$	−5.56462	−	2.92054i	−0.189422	−	0.0994164i	0.367346	−	0.930084i	$-0.380266\pi$
$863$	−5.56462	−	2.92054i	−0.189422	−	0.0994164i	−0.556768	+	0.830668i	$0.687959\pi$
$864$	7.55090			0.256887
$865$	−6.53741	+	3.43110i	−0.222278	+	0.116661i
$866$	−9.59724	+	8.50241i	−0.326127	+	0.288924i
$867$	23.5183			0.798725
$868$	1.27951			0.0434294
$869$	1.81977	−	1.61218i	0.0617316	−	0.0546895i
$870$	2.82796	+	7.45672i	0.0958769	+	0.252807i
$871$	20.1035	−	13.7596i	0.681181	−	0.466227i
$872$	5.53799	−	14.6025i	0.187540	−	0.494503i
$873$	0.771243	+	2.03360i	0.0261026	+	0.0688269i
$874$	3.58747	+	0.884231i	0.121348	+	0.0299096i
$875$	−1.26404	−	1.83128i	−0.0427323	−	0.0619085i
$876$	−0.350895	+	0.925234i	−0.0118556	+	0.0312608i
$877$	−9.01626	−	23.7739i	−0.304458	−	0.802788i	−0.996704	−	0.0811271i	$-0.974148\pi$
$877$	−9.01626	−	23.7739i	−0.304458	−	0.802788i	0.692246	−	0.721661i	$-0.256621\pi$
$878$	−0.392854	−	3.23544i	−0.0132582	−	0.109191i
$879$	17.8402	+	25.8461i	0.601737	+	0.871766i
$880$	4.46227	−	1.09985i	0.150423	−	0.0370759i
$881$	−21.7594	−	19.2771i	−0.733092	−	0.649463i	0.211624	−	0.977351i	$-0.432125\pi$
$881$	−21.7594	−	19.2771i	−0.733092	−	0.649463i	−0.944717	+	0.327888i	$0.893663\pi$
$882$	−5.36933	+	14.1578i	−0.180795	+	0.476716i
$883$	10.1913	+	2.51193i	0.342965	+	0.0845333i	0.407036	−	0.913412i	$-0.366562\pi$
$883$	10.1913	+	2.51193i	0.342965	+	0.0845333i	−0.0640712	+	0.997945i	$0.520408\pi$
$884$	28.8516	+	55.5034i	0.970385	+	1.86678i
$885$	15.1997	−	3.74639i	0.510933	−	0.125934i
$886$	1.36718	−	11.2598i	0.0459314	−	0.378279i
$887$	31.7433	−	16.6602i	1.06584	−	0.559394i	0.161788	−	0.986825i	$-0.448274\pi$
$887$	31.7433	−	16.6602i	1.06584	−	0.559394i	0.904048	+	0.427432i	$0.140582\pi$
$888$	3.73195	+	9.84034i	0.125236	+	0.330220i
$889$	0.471435	+	0.116198i	0.0158114	+	0.00389716i
$890$	−54.4485	+	48.2371i	−1.82512	+	1.61691i
$891$	−1.09442	−	0.269750i	−0.0366645	−	0.00903698i
$892$	−10.8754	+	5.70785i	−0.364135	+	0.191113i
$893$	17.0446	−	8.94572i	0.570377	−	0.299357i
$894$	−3.48425	−	28.6954i	−0.116531	−	0.959718i
$895$	3.99429	+	32.8960i	0.133514	+	1.09959i
$896$	−1.64076	+	1.45359i	−0.0548140	+	0.0485609i
$897$	−0.00478348	+	1.21208i	−0.000159716	+	0.0404701i
$898$	−28.4580	−	25.2116i	−0.949655	−	0.841321i
$899$	2.60954	−	3.78057i	0.0870330	−	0.126089i
$900$	0.903987	−	2.38362i	0.0301329	−	0.0794539i
$901$	8.52141	+	70.1802i	0.283889	+	2.33804i
$902$	1.17061	−	9.64082i	0.0389770	−	0.321004i
$903$	0.314690	+	0.165162i	0.0104722	+	0.00549625i
$904$	−4.92986	+	7.14213i	−0.163965	+	0.237544i
$905$	−15.6123	−	41.1662i	−0.518970	−	1.36841i
$906$	1.92531	−	1.70568i	0.0639643	−	0.0566674i
$907$	24.8747	−	36.0372i	0.825951	−	1.19660i	−0.152128	−	0.988361i	$-0.548612\pi$
$907$	24.8747	−	36.0372i	0.825951	−	1.19660i	0.978079	−	0.208236i	$-0.0667721\pi$
$908$	−14.9267	−	21.6251i	−0.495361	−	0.717654i
$909$	1.66531	+	13.7151i	0.0552349	+	0.454900i
$910$	−2.91840	+	0.342676i	−0.0967441	+	0.0113596i
$911$	−5.53827	+	45.6117i	−0.183491	+	1.51118i	0.552112	+	0.833770i	$0.313822\pi$
$911$	−5.53827	+	45.6117i	−0.183491	+	1.51118i	−0.735602	+	0.677413i	$0.763101\pi$
$912$	9.05378	−	4.75179i	0.299800	−	0.157347i
$913$	−2.58856	−	6.82548i	−0.0856689	−	0.225890i
$914$	−3.51283	+	28.9307i	−0.116194	+	0.956944i
$915$	5.64670			0.186674
$916$	−3.73672	+	30.7746i	−0.123465	+	1.01682i
$917$	−2.05400	−	2.97573i	−0.0678291	−	0.0982674i
$918$	−13.4353	+	3.31150i	−0.443430	+	0.109296i
$919$	34.2627	−	49.6381i	1.13022	−	1.63741i	0.481305	−	0.876553i	$-0.340163\pi$
$919$	34.2627	−	49.6381i	1.13022	−	1.63741i	0.648919	−	0.760858i	$-0.275221\pi$
$920$	−1.03797	+	0.255837i	−0.0342208	+	0.00843468i
$921$	−14.6632	−	7.69582i	−0.483168	−	0.253586i
$922$	−16.5728	−	8.69809i	−0.545797	−	0.286456i
$923$	0.125836	−	31.8855i	0.00414195	−	1.04952i
$924$	0.505852	−	0.265492i	0.0166413	−	0.00873403i
$925$	−6.24070			−0.205193
$926$	−60.5889	−	31.7995i	−1.99108	−	1.04500i
$927$	−6.28295	+	16.5668i	−0.206359	+	0.544124i
$928$	1.65617	+	13.6398i	0.0543665	+	0.447748i
$929$	15.2736	−	3.76461i	0.501112	−	0.123513i	0.0193457	−	0.999813i	$-0.493842\pi$
$929$	15.2736	−	3.76461i	0.501112	−	0.123513i	0.481766	+	0.876300i	$0.339996\pi$
$930$	10.7427	−	2.64783i	0.352266	−	0.0868258i
$931$	4.24494	+	34.9602i	0.139122	+	1.14577i
$932$	−18.3401	+	48.3589i	−0.600751	+	1.58405i
$933$	19.2597	+	10.1083i	0.630534	+	0.330930i
$934$	−18.4946			−0.605163
$935$	−12.8085	+	6.72240i	−0.418882	+	0.219846i
$936$	−3.75439	−	4.27167i	−0.122716	−	0.139624i
$937$	−44.3726	−	23.2885i	−1.44959	−	0.760803i	−0.457844	−	0.889033i	$-0.651378\pi$
$937$	−44.3726	−	23.2885i	−1.44959	−	0.760803i	−0.991744	+	0.128230i	$0.959070\pi$
$938$	−2.41842	−	1.26928i	−0.0789641	−	0.0414436i
$939$	−25.4641	+	6.27634i	−0.830990	+	0.204821i
$940$	−11.8847	+	17.2179i	−0.387635	+	0.561586i
$941$	45.4288	−	11.1972i	1.48094	−	0.365018i	0.585671	−	0.810549i	$-0.300831\pi$
$941$	45.4288	−	11.1972i	1.48094	−	0.365018i	0.895267	+	0.445530i	$0.146985\pi$
$942$	−15.7577	−	22.8290i	−0.513414	−	0.743809i
$943$	0.160603	−	1.32269i	0.00522996	−	0.0430726i
$944$	15.7031			0.511094
$945$	0.0451896	−	0.372170i	0.00147002	−	0.0121067i
$946$	1.66063	+	4.37873i	0.0539918	+	0.142365i
$947$	10.5880	−	5.55702i	0.344064	−	0.180579i	−0.283836	−	0.958873i	$-0.591607\pi$
$947$	10.5880	−	5.55702i	0.344064	−	0.180579i	0.627900	+	0.778294i	$0.283915\pi$
$948$	−0.708610	+	5.83593i	−0.0230146	+	0.189542i
$949$	−1.22577	+	0.459349i	−0.0397902	+	0.0149111i
$950$	−1.23911	−	10.2050i	−0.0402020	−	0.331093i
$951$	−18.7194	−	27.1197i	−0.607017	−	0.879416i
$952$	1.06058	−	1.53652i	0.0343737	−	0.0497989i
$953$	43.7144	−	38.7276i	1.41605	−	1.25451i	0.492889	−	0.870092i	$-0.335941\pi$
$953$	43.7144	−	38.7276i	1.41605	−	1.25451i	0.923160	−	0.384417i	$-0.125597\pi$
$954$	−8.56129	−	22.5743i	−0.277182	−	0.730869i
$955$	19.7402	−	28.5985i	0.638776	−	0.925427i
$956$	6.45397	+	3.38731i	0.208736	+	0.109553i
$957$	0.247228	−	2.03611i	0.00799175	−	0.0658180i
$958$	5.37383	+	44.2575i	0.173621	+	1.42989i
$959$	0.737839	−	1.94552i	0.0238261	−	0.0628241i
$960$	−14.1668	+	20.5241i	−0.457231	+	0.662414i
$961$	18.4334	+	16.3306i	0.594627	+	0.526794i
$962$	−24.4861	+	46.2102i	−0.789462	+	1.48988i
$963$	3.73081	−	3.30521i	0.120224	−	0.106509i
$964$	3.57755	+	29.4637i	0.115225	+	0.948963i
$965$	−1.77053	−	14.5816i	−0.0569953	−	0.469399i
$966$	0.120327	−	0.0631524i	0.00387145	−	0.00203190i
$967$	37.8404	−	19.8602i	1.21686	−	0.638660i	0.270799	−	0.962636i	$-0.412712\pi$
$967$	37.8404	−	19.8602i	1.21686	−	0.638660i	0.946065	+	0.323976i	$0.105020\pi$
$968$	−14.9004	−	3.67262i	−0.478918	−	0.118043i
$969$	−24.0895	+	21.3415i	−0.773868	+	0.685587i
$970$	−9.25509	−	2.28118i	−0.297163	−	0.0732441i
$971$	4.13413	+	10.9008i	0.132671	+	0.349823i	0.984846	−	0.173433i	$-0.0554861\pi$
$971$	4.13413	+	10.9008i	0.132671	+	0.349823i	−0.852175	+	0.523257i	$0.824717\pi$
$972$	2.41339	−	1.26664i	0.0774094	−	0.0406276i
$973$	−0.268865	+	2.21431i	−0.00861943	+	0.0709874i
$974$	−6.09061	+	1.50120i	−0.195156	+	0.0481016i
$975$	3.15787	−	1.18339i	0.101133	−	0.0378988i
$976$	5.49961	+	1.35553i	0.176038	+	0.0433896i
$977$	−8.25417	+	21.7645i	−0.264074	+	0.696307i	0.735744	+	0.677260i	$0.236833\pi$
$977$	−8.25417	+	21.7645i	−0.264074	+	0.696307i	−0.999819	+	0.0190474i	$0.993937\pi$
$978$	−40.3185	−	35.7191i	−1.28924	−	1.14217i
$979$	18.1648	−	4.47722i	0.580549	−	0.143093i
$980$	−21.7429	−	31.5001i	−0.694553	−	1.00623i
$981$	1.19347	+	9.82910i	0.0381045	+	0.313819i
$982$	12.2925	+	32.4128i	0.392271	+	1.03433i
$983$	−7.91169	+	20.8614i	−0.252344	+	0.665376i	0.747655	+	0.664087i	$0.231179\pi$
$983$	−7.91169	+	20.8614i	−0.252344	+	0.665376i	−0.999999	+	0.00128880i	$0.999590\pi$
$984$	3.55130	+	5.14494i	0.113211	+	0.164015i
$985$	8.55888	+	2.10957i	0.272709	+	0.0672166i
$986$	−8.92865	−	23.5429i	−0.284346	−	0.749759i
$987$	0.251054	−	0.661974i	0.00799112	−	0.0210709i
$988$	−46.3875	−	17.8022i	−1.47578	−	0.566363i
$989$	0.227833	+	0.600747i	0.00724468	+	0.0191026i
$990$	3.69769	−	3.27587i	0.117520	−	0.104114i
$991$	−1.05670			−0.0335672			−0.0167836	−	0.999859i	$-0.505343\pi$
$991$	−1.05670			−0.0335672			−0.0167836	+	0.999859i	$0.505343\pi$
$992$	19.0624			0.605230
$993$	−10.3914	+	9.20595i	−0.329760	+	0.292142i
$994$	−3.16537	+	1.66132i	−0.100400	+	0.0526937i
$995$	−10.6986			−0.339170
$996$	15.6297	+	8.20308i	0.495245	+	0.259925i
$997$	16.8101	+	14.8924i	0.532380	+	0.471648i	0.885963	−	0.463755i	$-0.153498\pi$
$997$	16.8101	+	14.8924i	0.532380	+	0.471648i	−0.353583	+	0.935403i	$0.615037\pi$
$998$	22.3005	+	32.3078i	0.705909	+	1.02269i
$999$	−4.99428	−	4.42455i	−0.158012	−	0.139987i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.m.b.40.15	✓	204
169.131	even	13	inner	507.2.m.b.469.15	yes	204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.m.b.40.15	✓	204	1.1	even	1	trivial
507.2.m.b.469.15	yes	204	169.131	even	13	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.m (of order \(13\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(2.11067 + 0.520234i) q^{2} +(0.120537 - 0.992709i) q^{3} +(2.41339 + 1.26664i) q^{4} +(1.14528 - 1.65922i) q^{5} +(0.770855 - 2.03258i) q^{6} +(-0.139189 - 0.123310i) q^{7} +(1.18063 + 1.04595i) q^{8} +(-0.970942 - 0.239316i) q^{9} +(3.28049 - 2.90626i) q^{10} +(-1.09442 + 0.269750i) q^{11} +(1.54831 - 2.24311i) q^{12} +(3.58095 - 0.420472i) q^{13} +(-0.229631 - 0.332679i) q^{14} +(-1.50908 - 1.33693i) q^{15} +(-1.14883 - 1.66437i) q^{16} +(4.76457 + 4.22104i) q^{17} +(-1.92484 - 1.01023i) q^{18} -5.05597 q^{19} +(4.86564 - 2.55369i) q^{20} +(-0.139189 + 0.123310i) q^{21} -2.45030 q^{22} -0.336172 q^{23} +(1.18063 - 1.04595i) q^{24} +(0.331667 + 0.874535i) q^{25} +(7.77696 + 0.975453i) q^{26} +(-0.354605 + 0.935016i) q^{27} +(-0.179726 - 0.473898i) q^{28} +(-1.76677 - 0.435471i) q^{29} +(-2.48965 - 3.60689i) q^{30} +(-0.895206 + 2.36046i) q^{31} +(-2.67758 - 7.06021i) q^{32} +(0.135866 + 1.11896i) q^{33} +(7.86052 + 11.3879i) q^{34} +(-0.364009 + 0.0897202i) q^{35} +(-2.04013 - 1.80740i) q^{36} +(-2.36603 + 6.23870i) q^{37} +(-10.6715 - 2.63029i) q^{38} +(0.0142292 - 3.60552i) q^{39} +(3.08761 - 0.761028i) q^{40} +(-0.477741 + 3.93455i) q^{41} +(-0.357932 + 0.187857i) q^{42} +(-0.677727 - 1.78702i) q^{43} +(-2.98294 - 0.735228i) q^{44} +(-1.50908 + 1.33693i) q^{45} +(-0.709550 - 0.174888i) q^{46} +(-3.37119 + 1.76934i) q^{47} +(-1.79071 + 0.939836i) q^{48} +(-0.839589 - 6.91464i) q^{49} +(0.245078 + 2.01840i) q^{50} +(4.76457 - 4.22104i) q^{51} +(9.17480 + 3.52102i) q^{52} +(8.31313 + 7.36479i) q^{53} +(-1.23488 + 1.78904i) q^{54} +(-0.805841 + 2.12483i) q^{55} +(-0.0353542 - 0.291168i) q^{56} +(-0.609430 + 5.01911i) q^{57} +(-3.50253 - 1.83827i) q^{58} +(-4.41089 + 6.39028i) q^{59} +(-1.94858 - 5.13798i) q^{60} +(-2.09642 + 1.85727i) q^{61} +(-3.11748 + 4.51645i) q^{62} +(0.105634 + 0.153037i) q^{63} +(-1.49101 - 12.2795i) q^{64} +(3.40353 - 6.42315i) q^{65} +(-0.295351 + 2.43243i) q^{66} +(5.98271 - 3.13997i) q^{67} +(6.15220 + 16.2220i) q^{68} +(-0.0405211 + 0.333721i) q^{69} -0.814980 q^{70} +(1.06597 - 8.77902i) q^{71} +(-0.896012 - 1.29810i) q^{72} +(-0.352506 + 0.0868848i) q^{73} +(-8.23950 + 11.9370i) q^{74} +(0.908136 - 0.223835i) q^{75} +(-12.2020 - 6.40411i) q^{76} +(0.185594 + 0.0974072i) q^{77} +(1.90575 - 7.60268i) q^{78} +(-1.90983 + 1.00236i) q^{79} -4.07729 q^{80} +(0.885456 + 0.464723i) q^{81} +(-3.05524 + 8.05601i) q^{82} +(0.780625 + 6.42902i) q^{83} +(-0.492106 + 0.121293i) q^{84} +(12.4604 - 3.07122i) q^{85} +(-0.500792 - 4.12439i) q^{86} +(-0.645256 + 1.70140i) q^{87} +(-1.57425 - 0.826230i) q^{88} -16.5976 q^{89} +(-3.88068 + 2.03674i) q^{90} +(-0.550276 - 0.383043i) q^{91} +(-0.811314 - 0.425810i) q^{92} +(2.23535 + 1.17320i) q^{93} +(-8.03595 + 1.98068i) q^{94} +(-5.79050 + 8.38899i) q^{95} +(-7.33148 + 1.80705i) q^{96} +(-1.23550 - 1.78994i) q^{97} +(1.82513 - 15.0313i) q^{98} +1.12717 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q - q^{2} - 17 q^{3} - 21 q^{4} - 6 q^{5} - q^{6} - 8 q^{7} - 9 q^{8} - 17 q^{9} - 6 q^{10} - 8 q^{11} - 21 q^{12} + 54 q^{13} - 30 q^{14} - 6 q^{15} - 45 q^{16} - 18 q^{17} - q^{18} - 20 q^{19}+ \cdots + 18 q^{99}+O(q^{100}) \) 204 * q - q^2 - 17 * q^3 - 21 * q^4 - 6 * q^5 - q^6 - 8 * q^7 - 9 * q^8 - 17 * q^9 - 6 * q^10 - 8 * q^11 - 21 * q^12 + 54 * q^13 - 30 * q^14 - 6 * q^15 - 45 * q^16 - 18 * q^17 - q^18 - 20 * q^19 - 58 * q^20 - 8 * q^21 + 44 * q^22 + 40 * q^23 - 9 * q^24 + 7 * q^25 - 2 * q^26 - 17 * q^27 - 40 * q^28 + 11 * q^29 - 6 * q^30 + 2 * q^31 + 61 * q^32 + 5 * q^33 - q^34 + 11 * q^35 - 21 * q^36 - 34 * q^37 + 17 * q^38 - 11 * q^39 - 31 * q^40 - 58 * q^41 + 35 * q^42 + 32 * q^43 - 41 * q^44 - 6 * q^45 + 76 * q^46 - 36 * q^47 - 45 * q^48 + 9 * q^49 - 35 * q^50 - 18 * q^51 - 24 * q^52 + 66 * q^53 - q^54 + 7 * q^55 - 114 * q^56 - 7 * q^57 - 60 * q^58 + 40 * q^59 + 59 * q^60 - 54 * q^61 - 31 * q^62 - 8 * q^63 + 75 * q^64 - 26 * q^65 + 18 * q^66 + 2 * q^67 + 26 * q^68 - 12 * q^69 - 56 * q^70 - 37 * q^71 - 9 * q^72 + 70 * q^73 + 174 * q^74 - 45 * q^75 - 26 * q^76 + 24 * q^78 - 66 * q^79 + 126 * q^80 - 17 * q^81 - 17 * q^82 - 2 * q^83 - 40 * q^84 + 54 * q^85 + 61 * q^86 + 24 * q^87 + 94 * q^88 - 114 * q^89 - 6 * q^90 + 104 * q^91 - 78 * q^92 + 67 * q^93 - 63 * q^94 - 70 * q^95 - 4 * q^96 + 36 * q^97 - 65 * q^98 + 18 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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