LMFDB - Embedded newform 185.2.v.a.169.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [185,2,Mod(4,185)] 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("185.4"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(185, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([9, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 185 = 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	185.v (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$1.47723243739$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$16$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			169.6
Character	$\chi$	$=$	185.169
Dual form			185.2.v.a.104.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.896403 - 0.326264i) q^{2} +(0.0971484 + 0.266913i) q^{3} +(-0.834998 - 0.700647i) q^{4} +(0.684633 + 2.12868i) q^{5} -0.270958i q^{6} +(-0.0783483 - 0.0138149i) q^{7} +(1.47383 + 2.55275i) q^{8} +(2.23633 - 1.87650i) q^{9} +(0.0808050 - 2.13153i) q^{10} +(2.24001 + 3.87981i) q^{11} +(0.105893 - 0.290938i) q^{12} +(0.642880 + 0.539440i) q^{13} +(0.0657244 + 0.0379460i) q^{14} +(-0.501661 + 0.389535i) q^{15} +(-0.109719 - 0.622249i) q^{16} +(3.63394 - 3.04924i) q^{17} +(-2.61689 + 0.952469i) q^{18} +(0.698848 + 1.92007i) q^{19} +(0.919785 - 2.25713i) q^{20} +(-0.00392403 - 0.0222543i) q^{21} +(-0.742109 - 4.20871i) q^{22} +(0.00227321 - 0.00393731i) q^{23} +(-0.538182 + 0.641381i) q^{24} +(-4.06256 + 2.91473i) q^{25} +(-0.400280 - 0.693304i) q^{26} +(1.45608 + 0.840670i) q^{27} +(0.0557413 + 0.0664299i) q^{28} +(-0.499013 + 0.288105i) q^{29} +(0.576782 - 0.185507i) q^{30} +5.06627i q^{31} +(0.919048 - 5.21218i) q^{32} +(-0.817959 + 0.974805i) q^{33} +(-4.25234 + 1.54772i) q^{34} +(-0.0242322 - 0.176237i) q^{35} -3.18209 q^{36} +(-4.06070 - 4.52888i) q^{37} -1.94917i q^{38} +(-0.0815288 + 0.223999i) q^{39} +(-4.42496 + 4.88501i) q^{40} +(-4.55042 - 3.81825i) q^{41} +(-0.00374326 + 0.0212291i) q^{42} +1.01783 q^{43} +(0.847972 - 4.80909i) q^{44} +(5.52554 + 3.47571i) q^{45} +(-0.00332232 + 0.00278775i) q^{46} +(-6.88975 - 3.97780i) q^{47} +(0.155427 - 0.0897359i) q^{48} +(-6.57190 - 2.39198i) q^{49} +(4.59266 - 1.28730i) q^{50} +(1.16691 + 0.673718i) q^{51} +(-0.158846 - 0.900863i) q^{52} +(-0.788285 + 0.138996i) q^{53} +(-1.03096 - 1.22865i) q^{54} +(-6.72529 + 7.42451i) q^{55} +(-0.0802061 - 0.220365i) q^{56} +(-0.444599 + 0.373063i) q^{57} +(0.541315 - 0.0954485i) q^{58} +(7.84732 - 1.38369i) q^{59} +(0.691813 + 0.0262262i) q^{60} +(-2.86116 + 3.40979i) q^{61} +(1.65294 - 4.54142i) q^{62} +(-0.201136 + 0.116126i) q^{63} +(-3.15623 + 5.46676i) q^{64} +(-0.708159 + 1.73780i) q^{65} +(1.05127 - 0.606948i) q^{66} +(3.19314 + 0.563037i) q^{67} -5.17077 q^{68} +(0.00127176 + 0.000224245i) q^{69} +(-0.0357778 + 0.165885i) q^{70} +(5.63810 - 2.05210i) q^{71} +(8.08622 + 2.94314i) q^{72} -9.38629i q^{73} +(2.16241 + 5.38456i) q^{74} +(-1.17265 - 0.801188i) q^{75} +(0.761753 - 2.09290i) q^{76} +(-0.121902 - 0.334922i) q^{77} +(0.146165 - 0.174193i) q^{78} +(-6.85173 - 1.20814i) q^{79} +(1.24945 - 0.659569i) q^{80} +(1.43787 - 8.15459i) q^{81} +(2.83325 + 4.90733i) q^{82} +(9.01103 + 10.7389i) q^{83} +(-0.0123158 + 0.0213316i) q^{84} +(8.97877 + 5.64789i) q^{85} +(-0.912382 - 0.332080i) q^{86} +(-0.125377 - 0.105204i) q^{87} +(-6.60280 + 11.4364i) q^{88} +(10.5904 - 1.86737i) q^{89} +(-3.81911 - 4.91843i) q^{90} +(-0.0429162 - 0.0511455i) q^{91} +(-0.00465679 + 0.00169493i) q^{92} +(-1.35225 + 0.492180i) q^{93} +(4.87818 + 5.81359i) q^{94} +(-3.60876 + 2.80217i) q^{95} +(1.48048 - 0.261049i) q^{96} +(3.54321 - 6.13702i) q^{97} +(5.11066 + 4.28835i) q^{98} +(12.2899 + 4.47315i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 12 q^{4} - 12 q^{5} - 6 q^{9} - 3 q^{10} - 30 q^{11} - 36 q^{14} - 21 q^{15} - 18 q^{19} - 39 q^{20} - 24 q^{21} + 96 q^{24} + 36 q^{25} + 48 q^{26} - 18 q^{29} - 30 q^{30} - 54 q^{34} + 6 q^{35}+ \cdots - 24 q^{99}+O(q^{100}) $ 96 * q - 12 * q^4 - 12 * q^5 - 6 * q^9 - 3 * q^10 - 30 * q^11 - 36 * q^14 - 21 * q^15 - 18 * q^19 - 39 * q^20 - 24 * q^21 + 96 * q^24 + 36 * q^25 + 48 * q^26 - 18 * q^29 - 30 * q^30 - 54 * q^34 + 6 * q^35 + 24 * q^36 - 36 * q^39 - 63 * q^40 + 72 * q^41 - 84 * q^44 - 36 * q^45 - 18 * q^46 - 6 * q^49 - 27 * q^50 - 18 * q^51 + 24 * q^54 + 6 * q^55 + 90 * q^56 + 18 * q^59 + 108 * q^60 - 144 * q^61 + 66 * q^64 + 27 * q^65 - 36 * q^66 - 6 * q^69 - 66 * q^70 - 30 * q^71 - 6 * q^74 + 96 * q^75 - 54 * q^76 + 60 * q^79 - 18 * q^81 + 48 * q^84 + 21 * q^85 - 72 * q^86 + 108 * q^89 + 165 * q^90 - 54 * q^91 + 6 * q^94 + 57 * q^95 + 24 * q^96 - 24 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/185\mathbb{Z}\right)^\times$.

$n$	$76$	$112$
$\chi(n)$	$e\left(\frac{11}{18}\right)$	$-1$

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 $

$2$	−0.896403	−	0.326264i	−0.633853	−	0.230704i	0.00505447	−	0.999987i	$-0.498391\pi$
$2$	−0.896403	−	0.326264i	−0.633853	−	0.230704i	−0.638907	+	0.769284i	$0.720613\pi$
$3$	0.0971484	+	0.266913i	0.0560886	+	0.154102i	0.964573	−	0.263817i	$-0.0849816\pi$
$3$	0.0971484	+	0.266913i	0.0560886	+	0.154102i	−0.908484	+	0.417920i	$0.862759\pi$
$4$	−0.834998	−	0.700647i	−0.417499	−	0.350323i
$5$	0.684633	+	2.12868i	0.306177	+	0.951975i
$5$	0.684633	+	2.12868i	0.306177	+	0.951975i
$6$		−	0.270958i		−	0.110618i
$7$	−0.0783483	−	0.0138149i	−0.0296129	−	0.00522155i	0.158822	−	0.987307i	$-0.449230\pi$
$7$	−0.0783483	−	0.0138149i	−0.0296129	−	0.00522155i	−0.188435	+	0.982086i	$0.560341\pi$
$8$	1.47383	+	2.55275i	0.521078	+	0.902534i
$9$	2.23633	−	1.87650i	0.745443	−	0.625501i
$10$	0.0808050	−	2.13153i	0.0255528	−	0.674048i
$11$	2.24001	+	3.87981i	0.675389	+	1.16981i	0.976355	+	0.216173i	$0.0693574\pi$
$11$	2.24001	+	3.87981i	0.675389	+	1.16981i	−0.300967	+	0.953635i	$0.597309\pi$
$12$	0.105893	−	0.290938i	0.0305687	−	0.0839867i
$13$	0.642880	+	0.539440i	0.178303	+	0.149614i	0.727571	−	0.686032i	$-0.240649\pi$
$13$	0.642880	+	0.539440i	0.178303	+	0.149614i	−0.549268	+	0.835646i	$0.685094\pi$
$14$	0.0657244	+	0.0379460i	0.0175656	+	0.0101415i
$15$	−0.501661	+	0.389535i	−0.129528	+	0.100578i
$16$	−0.109719	−	0.622249i	−0.0274298	−	0.155562i
$17$	3.63394	−	3.04924i	0.881360	−	0.739549i	−0.0850980	−	0.996373i	$-0.527120\pi$
$17$	3.63394	−	3.04924i	0.881360	−	0.739549i	0.966458	+	0.256823i	$0.0826759\pi$
$18$	−2.61689	+	0.952469i	−0.616806	+	0.224499i
$19$	0.698848	+	1.92007i	0.160327	+	0.440494i	0.993680	−	0.112246i	$-0.0358045\pi$
$19$	0.698848	+	1.92007i	0.160327	+	0.440494i	−0.833354	+	0.552740i	$0.813582\pi$
$20$	0.919785	−	2.25713i	0.205670	−	0.504709i
$21$	−0.00392403	−	0.0222543i	−0.000856293	−	0.00485628i
$22$	−0.742109	−	4.20871i	−0.158218	−	0.897300i
$23$	0.00227321	−	0.00393731i	0.000473997	−	0.000820986i	−0.865788	−	0.500410i	$-0.833182\pi$
$23$	0.00227321	−	0.00393731i	0.000473997	−	0.000820986i	0.866262	+	0.499589i	$0.166516\pi$
$24$	−0.538182	+	0.641381i	−0.109856	+	0.130921i
$25$	−4.06256	+	2.91473i	−0.812511	+	0.582945i
$26$	−0.400280	−	0.693304i	−0.0785013	−	0.135968i
$27$	1.45608	+	0.840670i	0.280223	+	0.161787i
$28$	0.0557413	+	0.0664299i	0.0105341	+	0.0125541i
$29$	−0.499013	+	0.288105i	−0.0926644	+	0.0534998i	−0.545616	−	0.838035i	$-0.683704\pi$
$29$	−0.499013	+	0.288105i	−0.0926644	+	0.0534998i	0.452952	+	0.891535i	$0.350371\pi$
$30$	0.576782	−	0.185507i	0.105306	−	0.0338687i
$31$			5.06627i			0.909929i	0.890510	+	0.454965i	$0.150348\pi$
$31$			5.06627i			0.909929i	−0.890510	+	0.454965i	$0.849652\pi$
$32$	0.919048	−	5.21218i	0.162466	−	0.921392i
$33$	−0.817959	+	0.974805i	−0.142388	+	0.169692i
$34$	−4.25234	+	1.54772i	−0.729270	+	0.265432i
$35$	−0.0242322	−	0.176237i	−0.00409600	−	0.0297894i
$36$	−3.18209			−0.530349
$37$	−4.06070	−	4.52888i	−0.667575	−	0.744543i
$37$	−4.06070	−	4.52888i	−0.667575	−	0.744543i
$38$		−	1.94917i		−	0.316196i
$39$	−0.0815288	+	0.223999i	−0.0130551	+	0.0358685i
$40$	−4.42496	+	4.88501i	−0.699647	+	0.772388i
$41$	−4.55042	−	3.81825i	−0.710656	−	0.596311i	0.214127	−	0.976806i	$-0.431309\pi$
$41$	−4.55042	−	3.81825i	−0.710656	−	0.596311i	−0.924783	+	0.380495i	$0.875754\pi$
$42$	−0.00374326	+	0.0212291i	−0.000577597	+	0.00327572i
$43$	1.01783			0.155217			0.0776084	−	0.996984i	$-0.475272\pi$
$43$	1.01783			0.155217			0.0776084	+	0.996984i	$0.475272\pi$
$44$	0.847972	−	4.80909i	0.127837	−	0.724998i
$45$	5.52554	+	3.47571i	0.823698	+	0.518129i
$46$	−0.00332232	+	0.00278775i	−0.000489849	+	0.000411032i
$47$	−6.88975	−	3.97780i	−1.00497	−	0.580222i	−0.0952574	−	0.995453i	$-0.530367\pi$
$47$	−6.88975	−	3.97780i	−1.00497	−	0.580222i	−0.909716	+	0.415231i	$0.863701\pi$
$48$	0.155427	−	0.0897359i	0.0224340	−	0.0129523i
$49$	−6.57190	−	2.39198i	−0.938843	−	0.341711i
$50$	4.59266	−	1.28730i	0.649500	−	0.182052i
$51$	1.16691	+	0.673718i	0.163401	+	0.0943393i
$52$	−0.158846	−	0.900863i	−0.0220280	−	0.124927i
$53$	−0.788285	+	0.138996i	−0.108279	+	0.0190926i	−0.227525	−	0.973772i	$-0.573063\pi$
$53$	−0.788285	+	0.138996i	−0.108279	+	0.0190926i	0.119246	+	0.992865i	$0.461952\pi$
$54$	−1.03096	−	1.22865i	−0.140296	−	0.167198i
$55$	−6.72529	+	7.42451i	−0.906838	+	1.00112i
$56$	−0.0802061	−	0.220365i	−0.0107180	−	0.0294475i
$57$	−0.444599	+	0.373063i	−0.0588886	+	0.0494134i
$58$	0.541315	−	0.0954485i	0.0710782	−	0.0125330i
$59$	7.84732	−	1.38369i	1.02163	−	0.180142i	0.362355	−	0.932040i	$-0.381973\pi$
$59$	7.84732	−	1.38369i	1.02163	−	0.180142i	0.659279	+	0.751898i	$0.270862\pi$
$60$	0.691813	+	0.0262262i	0.0893126	+	0.00338579i
$61$	−2.86116	+	3.40979i	−0.366333	+	0.436579i	−0.917451	−	0.397848i	$-0.869757\pi$
$61$	−2.86116	+	3.40979i	−0.366333	+	0.436579i	0.551118	+	0.834427i	$0.314201\pi$
$62$	1.65294	−	4.54142i	0.209924	−	0.576761i
$63$	−0.201136	+	0.116126i	−0.0253408	+	0.0146305i
$64$	−3.15623	+	5.46676i	−0.394529	+	0.683345i
$65$	−0.708159	+	1.73780i	−0.0878363	+	0.215548i
$66$	1.05127	−	0.606948i	0.129402	−	0.0747102i
$67$	3.19314	+	0.563037i	0.390104	+	0.0687859i	0.365260	−	0.930905i	$-0.380980\pi$
$67$	3.19314	+	0.563037i	0.390104	+	0.0687859i	0.0248440	+	0.999691i	$0.492091\pi$
$68$	−5.17077			−0.627048
$69$	0.00127176		0.000224245i	0.000153102		2.69960e-5i
$70$	−0.0357778	+	0.165885i	−0.00427627	+	0.0198271i
$71$	5.63810	−	2.05210i	0.669119	−	0.243539i	0.0149505	−	0.999888i	$-0.495241\pi$
$71$	5.63810	−	2.05210i	0.669119	−	0.243539i	0.654168	+	0.756349i	$0.273019\pi$
$72$	8.08622	+	2.94314i	0.952970	+	0.346853i
$73$		−	9.38629i		−	1.09858i	−0.835631	−	0.549291i	$-0.814898\pi$
$73$		−	9.38629i		−	1.09858i	0.835631	−	0.549291i	$-0.185102\pi$
$74$	2.16241	+	5.38456i	0.251376	+	0.625943i
$75$	−1.17265	−	0.801188i	−0.135406	−	0.0925132i
$76$	0.761753	−	2.09290i	0.0873791	−	0.240072i
$77$	−0.121902	−	0.334922i	−0.0138920	−	0.0381679i
$78$	0.146165	−	0.174193i	0.0165500	−	0.0197235i
$79$	−6.85173	−	1.20814i	−0.770879	−	0.135927i	−0.225644	−	0.974210i	$-0.572449\pi$
$79$	−6.85173	−	1.20814i	−0.770879	−	0.135927i	−0.545235	+	0.838283i	$0.683560\pi$
$80$	1.24945	−	0.659569i	0.139693	−	0.0737420i
$81$	1.43787	−	8.15459i	0.159764	−	0.906065i
$82$	2.83325	+	4.90733i	0.312880	+	0.541924i
$83$	9.01103	+	10.7389i	0.989089	+	1.17875i	0.983892	+	0.178764i	$0.0572099\pi$
$83$	9.01103	+	10.7389i	0.989089	+	1.17875i	0.00519711	+	0.999986i	$0.498346\pi$
$84$	−0.0123158	+	0.0213316i	−0.00134377	+	0.00232747i
$85$	8.97877	+	5.64789i	0.973884	+	0.612600i
$86$	−0.912382	−	0.332080i	−0.0983847	−	0.0358091i
$87$	−0.125377	−	0.105204i	−0.0134419	−	0.0112791i
$88$	−6.60280	+	11.4364i	−0.703861	+	1.21912i
$89$	10.5904	−	1.86737i	1.12258	−	0.197941i	0.418607	−	0.908167i	$-0.362518\pi$
$89$	10.5904	−	1.86737i	1.12258	−	0.197941i	0.703974	+	0.710226i	$0.251407\pi$
$90$	−3.81911	−	4.91843i	−0.402569	−	0.518448i
$91$	−0.0429162	−	0.0511455i	−0.00449884	−	0.00536151i
$92$	−0.00465679	+	0.00169493i	−0.000485504	+	0.000176709i
$93$	−1.35225	+	0.492180i	−0.140222	+	0.0510367i
$94$	4.87818	+	5.81359i	0.503146	+	0.599626i
$95$	−3.60876	+	2.80217i	−0.370251	+	0.287496i
$96$	1.48048	−	0.261049i	0.151101	−	0.0266432i
$97$	3.54321	−	6.13702i	0.359759	−	0.623120i	−0.628162	−	0.778083i	$-0.716192\pi$
$97$	3.54321	−	6.13702i	0.359759	−	0.623120i	0.987920	+	0.154962i	$0.0495257\pi$
$98$	5.11066	+	4.28835i	0.516254	+	0.433189i
$99$	12.2899	+	4.47315i	1.23518	+	0.449568i
$100$	5.43442	+	0.412625i	0.543442	+	0.0412625i
$101$	3.69395	−	6.39812i	0.367562	−	0.636636i	−0.621622	−	0.783318i	$-0.713526\pi$
$101$	3.69395	−	6.39812i	0.367562	−	0.636636i	0.989184	+	0.146681i	$0.0468592\pi$
$102$	−0.826215	−	0.984645i	−0.0818075	−	0.0974944i
$103$	−5.31788	−	9.21085i	−0.523987	−	0.907572i	−0.999610	−	0.0279226i	$-0.991111\pi$
$103$	−5.31788	−	9.21085i	−0.523987	−	0.907572i	0.475623	−	0.879649i	$-0.342223\pi$
$104$	−0.429560	+	2.43616i	−0.0421218	+	0.238885i
$105$	0.0446857	−	0.0235890i	0.00436088	−	0.00230205i
$106$	0.751971	+	0.132593i	0.0730379	+	0.0128785i
$107$	−7.41377	+	8.83539i	−0.716716	+	0.854149i	−0.994307	−	0.106550i	$-0.966020\pi$
$107$	−7.41377	+	8.83539i	−0.716716	+	0.854149i	0.277591	+	0.960699i	$0.410464\pi$
$108$	−0.626814	−	1.72216i	−0.0603152	−	0.165715i
$109$	3.70141	−	10.1695i	0.354531	−	0.974066i	−0.626365	−	0.779530i	$-0.715458\pi$
$109$	3.70141	−	10.1695i	0.354531	−	0.974066i	0.980895	−	0.194535i	$-0.0623199\pi$
$110$	8.45093	−	4.46113i	0.805764	−	0.425352i
$111$	0.814326	−	1.52383i	0.0772924	−	0.144635i
$112$			0.0502679i			0.00474987i
$113$	17.0050	+	6.18933i	1.59970	+	0.582243i	0.979366	−	0.202095i	$-0.0647750\pi$
$113$	17.0050	+	6.18933i	1.59970	+	0.582243i	0.620334	+	0.784338i	$0.286997\pi$
$114$	0.520258	−	0.189358i	0.0487266	−	0.0177350i
$115$	0.00993759	+	0.00214332i	0.000926685	+	0.000199866i
$116$	0.618535	+	0.109064i	0.0574295	+	0.0101264i
$117$	2.44995			0.226498
$118$	−7.48582	−	1.31995i	−0.689125	−	0.121511i
$119$	−0.326838	+	0.188700i	−0.0299612	+	0.0172981i
$120$	−1.73375	−	0.706508i	−0.158269	−	0.0644950i
$121$	−4.53529	+	7.85536i	−0.412299	+	0.714123i
$122$	3.67724	−	2.12306i	0.332922	−	0.192213i
$123$	0.577076	−	1.58550i	0.0520332	−	0.142960i
$124$	3.54967	−	4.23033i	0.318769	−	0.379895i
$125$	−8.98588	−	6.65237i	−0.803721	−	0.595006i
$126$	0.218187	−	0.0384723i	0.0194376	−	0.00342738i
$127$	−8.76576	+	1.54564i	−0.777835	+	0.137153i	−0.548451	−	0.836183i	$-0.684782\pi$
$127$	−8.76576	+	1.54564i	−0.777835	+	0.137153i	−0.229384	+	0.973336i	$0.573671\pi$
$128$	−3.49585	+	2.93336i	−0.308992	+	0.259275i
$129$	0.0988801	+	0.271671i	0.00870591	+	0.0239193i
$130$	1.20178	−	1.32673i	0.105403	−	0.116362i
$131$	−13.7521	−	16.3891i	−1.20152	−	1.43192i	−0.873206	−	0.487352i	$-0.837963\pi$
$131$	−13.7521	−	16.3891i	−1.20152	−	1.43192i	−0.328317	−	0.944567i	$-0.606482\pi$
$132$	1.36599	−	0.240860i	0.118894	−	0.0209642i
$133$	−0.0282279	−	0.160089i	−0.00244767	−	0.0138814i
$134$	−2.67864	−	1.54652i	−0.231400	−	0.133599i
$135$	−0.792636	+	3.67509i	−0.0682192	+	0.316301i
$136$	13.1398	+	4.78249i	1.12673	+	0.410095i
$137$	−17.7659	+	10.2571i	−1.51784	+	0.876327i	−0.518063	+	0.855343i	$0.673347\pi$
$137$	−17.7659	+	10.2571i	−1.51784	+	0.876327i	−0.999780	+	0.0209840i	$0.993320\pi$
$138$	−0.00106685		0.000615943i	−9.08159e−5		5.24326e-5i
$139$	−16.1848	+	13.5807i	−1.37278	+	1.15190i	−0.400979	+	0.916087i	$0.631330\pi$
$139$	−16.1848	+	13.5807i	−1.37278	+	1.15190i	−0.971799	+	0.235810i	$0.924226\pi$
$140$	−0.103246	+	0.164135i	−0.00872585	+	0.0138720i
$141$	0.392398	−	2.22540i	0.0330459	−	0.187413i
$142$	−5.72354			−0.480308
$143$	−0.652869	+	3.70260i	−0.0545956	+	0.309627i
$144$	−1.41302	−	1.18566i	−0.117752	−	0.0988054i
$145$	−0.954924	−	0.864992i	−0.0793021	−	0.0718337i
$146$	−3.06241	+	8.41391i	−0.253447	+	0.696340i
$147$		−	1.98650i		−	0.163844i
$148$	0.217533	+	6.62672i	0.0178811	+	0.544713i
$149$	−15.0751			−1.23500			−0.617501	−	0.786570i	$-0.711855\pi$
$149$	−15.0751			−1.23500			−0.617501	+	0.786570i	$0.711855\pi$
$150$	0.789768	+	1.10078i	0.0644843	+	0.0898784i
$151$	−9.99530	+	3.63799i	−0.813406	+	0.296056i	−0.715030	−	0.699094i	$-0.753587\pi$
$151$	−9.99530	+	3.63799i	−0.813406	+	0.296056i	−0.0983759	+	0.995149i	$0.531365\pi$
$152$	−3.87148	+	4.61384i	−0.314018	+	0.374232i
$153$	2.40478	−	13.6382i	0.194415	−	1.10258i
$154$			0.339997i			0.0273978i
$155$	−10.7845	+	3.46853i	−0.866230	+	0.278599i
$156$	0.225020	−	0.129916i	0.0180160	−	0.0104016i
$157$	11.5580	+	13.7743i	0.922432	+	1.09931i	0.994791	+	0.101933i	$0.0325028\pi$
$157$	11.5580	+	13.7743i	0.922432	+	1.09931i	−0.0723591	+	0.997379i	$0.523053\pi$
$158$	5.74774	+	3.31846i	0.457265	+	0.264002i
$159$	−0.113680	−	0.196900i	−0.00901545	−	0.0156152i
$160$	11.7243	−	1.61207i	0.926885	−	0.127445i
$161$	−0.000232496	0	0.000277077i	−1.83232e−5	0	2.18368e-5i
$162$	−3.94947	+	6.84067i	−0.310299	+	0.537454i
$163$	−3.94850	−	22.3930i	−0.309270	−	1.75396i	−0.602690	−	0.797975i	$-0.705905\pi$
$163$	−3.94850	−	22.3930i	−0.309270	−	1.75396i	0.293420	−	0.955984i	$-0.405207\pi$
$164$	1.12434	+	6.37647i	0.0877965	+	0.497918i
$165$	−2.63505	−	1.07379i	−0.205138	−	0.0835944i
$166$	−4.57379	−	12.5664i	−0.354995	−	0.975341i
$167$	13.9313	−	5.07057i	1.07803	−	0.392372i	0.258859	−	0.965915i	$-0.416654\pi$
$167$	13.9313	−	5.07057i	1.07803	−	0.392372i	0.819176	+	0.573543i	$0.194431\pi$
$168$	0.0510263	−	0.0428161i	0.00393676	−	0.00330334i
$169$	−2.13513	−	12.1089i	−0.164241	−	0.931455i
$170$	−6.20590	−	7.99224i	−0.475970	−	0.612977i
$171$	5.16587	+	2.98252i	0.395044	+	0.228079i
$172$	−0.849882	−	0.713136i	−0.0648029	−	0.0543761i
$173$	7.69707	−	21.1475i	0.585198	−	1.60782i	−0.193974	−	0.981007i	$-0.562138\pi$
$173$	7.69707	−	21.1475i	0.585198	−	1.60782i	0.779171	−	0.626811i	$-0.215640\pi$
$174$	0.0780643	+	0.135211i	0.00591804	+	0.0102503i
$175$	0.358561	−	0.172240i	0.0271047	−	0.0130201i
$176$	2.16844	−	1.81953i	0.163452	−	0.137153i
$177$	1.13168	+	1.96013i	0.0850623	+	0.147332i
$178$	−10.1025	−	1.78135i	−0.757217	−	0.133518i
$179$		−	10.0280i		−	0.749526i	−0.927121	−	0.374763i	$-0.877724\pi$
$179$		−	10.0280i		−	0.749526i	0.927121	−	0.374763i	$-0.122276\pi$
$180$	−2.17857	−	6.77366i	−0.162381	−	0.504879i
$181$	−6.29551	−	5.28256i	−0.467942	−	0.392650i	0.378101	−	0.925764i	$-0.376577\pi$
$181$	−6.29551	−	5.28256i	−0.467942	−	0.392650i	−0.846043	+	0.533114i	$0.821022\pi$
$182$	0.0217833	+	0.0598490i	0.00161468	+	0.00443631i
$183$	−1.18807	−	0.432424i	−0.0878250	−	0.0319657i
$184$	0.0134013			0.000987958
$185$	6.86044	−	11.7445i	0.504390	−	0.863476i
$186$	1.37275			0.100655
$187$	19.9705	+	7.26868i	1.46039	+	0.531539i
$188$	2.96590	+	8.14873i	0.216310	+	0.594308i
$189$	−0.102468	−	0.0859807i	−0.00745344	−	0.00625418i
$190$	4.14915	−	1.33446i	0.301011	−	0.0968121i
$191$			22.0191i			1.59324i	0.604478	+	0.796622i	$0.293382\pi$
$191$			22.0191i			1.59324i	−0.604478	+	0.796622i	$0.706618\pi$
$192$	−1.76577	−	0.311353i	−0.127434	−	0.0224700i
$193$	2.94581	+	5.10229i	0.212044	+	0.367271i	0.952354	−	0.304995i	$-0.0986547\pi$
$193$	2.94581	+	5.10229i	0.212044	+	0.367271i	−0.740310	+	0.672265i	$0.765321\pi$
$194$	−5.17844	+	4.34523i	−0.371790	+	0.311969i
$195$	−0.532639	−	0.0201920i	−0.0381430	−	0.00144598i
$196$	3.81159	+	6.60187i	0.272257	+	0.471562i
$197$	−2.28577	+	6.28009i	−0.162854	+	0.447438i	−0.994100	−	0.108467i	$-0.965406\pi$
$197$	−2.28577	+	6.28009i	−0.162854	+	0.447438i	0.831246	+	0.555905i	$0.187628\pi$
$198$	−9.55726	−	8.01949i	−0.679205	−	0.569921i
$199$	−9.14409	−	5.27934i	−0.648207	−	0.374243i	0.139562	−	0.990213i	$-0.455431\pi$
$199$	−9.14409	−	5.27934i	−0.648207	−	0.374243i	−0.787769	+	0.615971i	$0.788764\pi$
$200$	−13.4281	−	6.07488i	−0.949510	−	0.429559i
$201$	0.159927	+	0.906989i	0.0112804	+	0.0639741i
$202$	−5.39875	+	4.53009i	−0.379855	+	0.318736i
$203$	0.0430769	−	0.0156787i	0.00302341	−	0.00110043i
$204$	−0.502332	−	1.38015i	−0.0351703	−	0.0966296i
$205$	5.01248	−	12.3005i	0.350086	−	0.859103i
$206$	1.76180	+	9.99167i	0.122750	+	0.696153i
$207$	−0.00230474	−	0.0130708i	−0.000160190	−	0.000908484i
$208$	0.265130	−	0.459218i	0.0183834	−	0.0318410i
$209$	−5.88408	+	7.01237i	−0.407010	+	0.485056i
$210$	−0.0477527	+	0.00656592i	−0.00329525	+	0.000453091i
$211$	5.33976	+	9.24874i	0.367605	+	0.636710i	0.989190	−	0.146636i	$-0.0468447\pi$
$211$	5.33976	+	9.24874i	0.367605	+	0.636710i	−0.621586	+	0.783346i	$0.713511\pi$
$212$	0.755604	+	0.436248i	0.0518951	+	0.0299616i
$213$	1.09546	+	1.30552i	0.0750600	+	0.0894530i
$214$	9.52840	−	5.50122i	0.651348	−	0.376056i
$215$	0.696836	+	2.16662i	0.0475238	+	0.147763i
$216$			4.95603i			0.337215i
$217$	0.0699901	−	0.396934i	0.00475124	−	0.0269456i
$218$	−6.63592	+	7.90838i	−0.449441	+	0.535623i
$219$	2.50532	−	0.911863i	0.169294	−	0.0616180i
$220$	10.8176	−	1.48740i	0.729320	−	0.100280i
$221$	3.98107			0.267796
$222$	−1.22713	+	1.10028i	−0.0823599	+	0.0738458i
$223$		−	14.5288i		−	0.972917i	−0.873704	−	0.486459i	$-0.838288\pi$
$223$		−	14.5288i		−	0.972917i	0.873704	−	0.486459i	$-0.161712\pi$
$224$	−0.144012	+	0.395669i	−0.00962218	+	0.0264367i
$225$	−3.61572	+	14.1417i	−0.241048	+	0.942779i
$226$	−13.2240	−	11.0963i	−0.879649	−	0.738113i
$227$	−3.94753	+	22.3876i	−0.262007	+	1.48591i	0.515418	+	0.856939i	$0.327637\pi$
$227$	−3.94753	+	22.3876i	−0.262007	+	1.48591i	−0.777425	+	0.628976i	$0.783474\pi$
$228$	0.632625			0.0418966
$229$	0.748417	−	4.24448i	0.0494568	−	0.280483i	−0.950043	−	0.312120i	$-0.898961\pi$
$229$	0.748417	−	4.24448i	0.0494568	−	0.280483i	0.999499	+	0.0316367i	$0.0100720\pi$
$230$	−0.00820880	−	0.00516356i	−0.000541272	−	0.000340475i
$231$	0.0775525	−	0.0650743i	0.00510258	−	0.00428157i
$232$	−1.47092	−	0.849237i	−0.0965708	−	0.0557552i
$233$	4.84592	−	2.79779i	0.317467	−	0.183289i	−0.332796	−	0.942999i	$-0.607992\pi$
$233$	4.84592	−	2.79779i	0.317467	−	0.183289i	0.650263	+	0.759709i	$0.274659\pi$
$234$	−2.19614	−	0.799331i	−0.143566	−	0.0522539i
$235$	3.75051	−	17.3894i	0.244657	−	1.13436i
$236$	−7.52198	−	4.34282i	−0.489639	−	0.282693i
$237$	−0.343165	−	1.94618i	−0.0222909	−	0.126418i
$238$	0.354545	−	0.0625158i	0.0229817	−	0.00405230i
$239$	13.5730	+	16.1757i	0.877966	+	1.04632i	0.998562	+	0.0536175i	$0.0170752\pi$
$239$	13.5730	+	16.1757i	0.877966	+	1.04632i	−0.120595	+	0.992702i	$0.538480\pi$
$240$	0.297430	+	0.269419i	0.0191990	+	0.0173909i
$241$	2.32326	+	6.38312i	0.149655	+	0.411173i	0.991755	−	0.128148i	$-0.0409033\pi$
$241$	2.32326	+	6.38312i	0.149655	+	0.411173i	−0.842100	+	0.539321i	$0.818681\pi$
$242$	6.62837	−	5.56187i	0.426088	−	0.357530i
$243$	7.28364	−	1.28430i	0.467246	−	0.0823881i
$244$	4.77812	−	0.842511i	0.305888	−	0.0539362i
$245$	0.592415	−	15.6271i	0.0378480	−	0.998379i
$246$	−1.03459	+	1.23297i	−0.0659628	+	0.0786114i
$247$	−0.586487	+	1.61136i	−0.0373173	+	0.102528i
$248$	−12.9329	+	7.46683i	−0.821242	+	0.474144i
$249$	−1.99095	+	3.44843i	−0.126171	+	0.218535i
$250$	5.88455	+	8.89497i	0.372171	+	0.562568i
$251$	4.04419	−	2.33491i	0.255267	−	0.147379i	−0.366907	−	0.930258i	$-0.619583\pi$
$251$	4.04419	−	2.33491i	0.255267	−	0.147379i	0.622174	+	0.782879i	$0.286250\pi$
$252$	0.249312	+	0.0439604i	0.0157052	+	0.00276924i
$253$	0.0203680			0.00128053
$254$	8.36194	+	1.47444i	0.524675	+	0.0925144i
$255$	−0.635222	+	2.94523i	−0.0397792	+	0.184438i
$256$	15.9543	−	5.80689i	0.997144	−	0.362931i
$257$	−15.8124	−	5.75524i	−0.986350	−	0.359002i	−0.202044	−	0.979376i	$-0.564759\pi$
$257$	−15.8124	−	5.75524i	−0.986350	−	0.359002i	−0.784306	+	0.620374i	$0.786981\pi$
$258$		−	0.275788i		−	0.0171698i
$259$	0.255583	+	0.410928i	0.0158811	+	0.0255338i
$260$	1.80890	−	0.954893i	0.112183	−	0.0592199i
$261$	−0.575327	+	1.58070i	−0.0356118	+	0.0978427i
$262$	6.98023	+	19.1780i	0.431240	+	1.18482i
$263$	−16.2226	+	19.3334i	−1.00033	+	1.19215i	−0.0190003	+	0.999819i	$0.506048\pi$
$263$	−16.2226	+	19.3334i	−1.00033	+	1.19215i	−0.981331	+	0.192329i	$0.938396\pi$
$264$	−3.69397	−	0.651346i	−0.227348	−	0.0400876i
$265$	−0.835564	−	1.58285i	−0.0513283	−	0.0972334i
$266$	−0.0269276	+	0.152714i	−0.00165103	+	0.00936348i
$267$	1.52727	+	2.64530i	0.0934672	+	0.161890i
$268$	−2.27178	−	2.70740i	−0.138771	−	0.165381i
$269$	8.30018	−	14.3763i	0.506071	−	0.876541i	−0.493904	−	0.869516i	$-0.664431\pi$
$269$	8.30018	−	14.3763i	0.506071	−	0.876541i	0.999975	−	0.00702440i	$-0.00223596\pi$
$270$	1.90957	−	3.03575i	0.116213	−	0.184750i
$271$	3.10033	+	1.12843i	0.188331	+	0.0685470i	0.434464	−	0.900689i	$-0.356938\pi$
$271$	3.10033	+	1.12843i	0.188331	+	0.0685470i	−0.246133	+	0.969236i	$0.579160\pi$
$272$	−2.29610	−	1.92666i	−0.139221	−	0.116821i
$273$	0.00948217	−	0.0164236i	0.000573887	−	0.000994001i
$274$	19.2719	−	3.39816i	1.16426	−	0.205291i
$275$	−20.4088	−	9.23294i	−1.23069	−	0.556767i
$276$	−0.000904799	−	0.00107830i	−5.44625e−5	−	6.49059e-5i
$277$	−16.2940	+	5.93054i	−0.979013	+	0.356332i	−0.781456	−	0.623960i	$-0.785523\pi$
$277$	−16.2940	+	5.93054i	−0.979013	+	0.356332i	−0.197557	+	0.980291i	$0.563301\pi$
$278$	18.9390	−	6.89323i	1.13589	−	0.413429i
$279$	9.50687	+	11.3298i	0.569162	+	0.678300i
$280$	0.414174	−	0.321602i	0.0247516	−	0.0192194i
$281$	18.8706	−	3.32740i	1.12573	−	0.198496i	0.420374	−	0.907351i	$-0.361899\pi$
$281$	18.8706	−	3.32740i	1.12573	−	0.198496i	0.705354	+	0.708855i	$0.250788\pi$
$282$	−1.07782	+	1.86683i	−0.0641830	+	0.111168i
$283$	0.463488	+	0.388913i	0.0275515	+	0.0231185i	0.656459	−	0.754361i	$-0.272053\pi$
$283$	0.463488	+	0.388913i	0.0275515	+	0.0231185i	−0.628908	+	0.777480i	$0.716498\pi$
$284$	−6.14560	−	2.23681i	−0.364674	−	0.132730i
$285$	−1.09852	−	0.690999i	−0.0650707	−	0.0409312i
$286$	1.79326	−	3.10602i	0.106038	−	0.183663i
$287$	0.303768	+	0.362017i	0.0179309	+	0.0213692i
$288$	−7.72538	−	13.3807i	−0.455222	−	0.788468i
$289$	0.955655	−	5.41979i	0.0562150	−	0.318811i
$290$	0.573781	+	1.08694i	0.0336936	+	0.0638273i
$291$	1.98227	+	0.349527i	0.116203	+	0.0204897i
$292$	−6.57647	+	7.83754i	−0.384859	+	0.458657i
$293$	5.25445	+	14.4365i	0.306968	+	0.843388i	0.993244	+	0.116046i	$0.0370221\pi$
$293$	5.25445	+	14.4365i	0.306968	+	0.843388i	−0.686276	+	0.727341i	$0.740756\pi$
$294$	−0.648125	+	1.78071i	−0.0377994	+	0.103853i
$295$	8.31798	+	15.7571i	0.484291	+	0.917415i
$296$	5.57631	−	17.0408i	0.324117	−	0.990474i
$297$			7.53244i			0.437076i
$298$	13.5134	+	4.91847i	0.782809	+	0.284919i
$299$	0.00358534	−	0.00130496i	0.000207346	−	7.54677e-5i
$300$	0.417810	+	1.49060i	0.0241223	+	0.0860600i
$301$	−0.0797449	−	0.0140612i	−0.00459642	−	0.000810472i
$302$	10.1468			0.583881
$303$	2.06660	+	0.364398i	0.118723	+	0.0209341i
$304$	1.11808	−	0.645526i	0.0641265	−	0.0370234i
$305$	−9.21720	−	3.75603i	−0.527775	−	0.215070i
$306$	−6.60531	+	11.4407i	−0.377601	+	0.654023i
$307$	25.5038	−	14.7246i	1.45558	−	0.840378i	0.456788	−	0.889575i	$-0.349000\pi$
$307$	25.5038	−	14.7246i	1.45558	−	0.840378i	0.998789	+	0.0491975i	$0.0156664\pi$
$308$	−0.132874	+	0.365069i	−0.00757122	+	0.0208018i
$309$	1.94187	−	2.31423i	0.110469	−	0.131652i
$310$	10.7989	+	0.409380i	0.613336	+	0.0232512i
$311$	2.29988	−	0.405531i	0.130414	−	0.0229956i	−0.108060	−	0.994144i	$-0.534464\pi$
$311$	2.29988	−	0.405531i	0.130414	−	0.0229956i	0.238474	+	0.971149i	$0.423353\pi$
$312$	−0.691973	+	0.122013i	−0.0391752	+	0.00690765i
$313$	2.61953	−	2.19805i	0.148065	−	0.124241i	−0.565746	−	0.824579i	$-0.691412\pi$
$313$	2.61953	−	2.19805i	0.148065	−	0.124241i	0.713811	+	0.700338i	$0.246967\pi$
$314$	−5.86660	−	16.1183i	−0.331071	−	0.909611i
$315$	−0.384900	−	0.348651i	−0.0216866	−	0.0196443i
$316$	4.87469	+	5.80944i	0.274223	+	0.326806i
$317$	−9.50445	+	1.67589i	−0.533823	+	0.0941274i	−0.434060	−	0.900884i	$-0.642920\pi$
$317$	−9.50445	+	1.67589i	−0.533823	+	0.0941274i	−0.0997628	+	0.995011i	$0.531808\pi$
$318$	0.0376620	+	0.213592i	0.00211198	+	0.0119776i
$319$	−2.23559	−	1.29072i	−0.125169	−	0.0722663i
$320$	−13.7978	−	2.97589i	−0.771323	−	0.166357i
$321$	−3.07852	−	1.12049i	−0.171826	−	0.0625395i
$322$	0.000298810	0	0.000172518i	1.66520e−5	0	9.61406e-6i
$323$	8.39432	+	4.84646i	0.467073	+	0.269665i
$324$	−6.91411	+	5.80162i	−0.384117	+	0.322312i
$325$	−4.18405	−	0.317687i	−0.232090	−	0.0176221i
$326$	−3.76660	+	21.3615i	−0.208613	+	1.18310i
$327$	3.07397			0.169991
$328$	3.04050	−	17.2435i	0.167884	−	0.952116i
$329$	0.484847	+	0.406835i	0.0267305	+	0.0224295i
$330$	2.01173	+	1.82227i	0.110742	+	0.100313i
$331$	3.72850	−	10.2440i	0.204937	−	0.563059i	−0.794060	−	0.607839i	$-0.792037\pi$
$331$	3.72850	−	10.2440i	0.204937	−	0.563059i	0.998997	+	0.0447803i	$0.0142588\pi$
$332$		−	15.2805i		−	0.838628i
$333$	−17.5795	−	2.50815i	−0.963351	−	0.137446i
$334$	−14.1424			−0.773837
$335$	0.987603	+	7.18265i	0.0539585	+	0.392430i
$336$	−0.0134171	+	0.00488344i	−0.000731965	+	0.000266414i
$337$	−19.1085	+	22.7726i	−1.04091	+	1.24050i	−0.0708850	+	0.997484i	$0.522582\pi$
$337$	−19.1085	+	22.7726i	−1.04091	+	1.24050i	−0.970021	+	0.243019i	$0.921862\pi$
$338$	−2.03677	+	11.5511i	−0.110786	+	0.628296i
$339$			5.14015i			0.279175i
$340$	−3.54008	−	11.0069i	−0.191988	−	0.596934i
$341$	−19.6562	+	11.3485i	−1.06444	+	0.614556i
$342$	−3.65761	−	4.35897i	−0.197781	−	0.235706i
$343$	0.964140	+	0.556647i	0.0520587	+	0.0300561i
$344$	1.50010	+	2.59826i	0.0808802	+	0.140089i
$345$	0.000393341		0.00286069i	2.11767e−5		0.000154014i
$346$	−13.7994	+	16.4454i	−0.741859	+	0.884113i
$347$	10.6888	−	18.5136i	0.573807	−	0.993863i	−0.422363	−	0.906427i	$-0.638799\pi$
$347$	10.6888	−	18.5136i	0.573807	−	0.993863i	0.996170	−	0.0874362i	$-0.0278674\pi$
$348$	0.0309789	+	0.175690i	0.00166065	+	0.00941799i
$349$	1.56915	+	8.89911i	0.0839948	+	0.476358i	0.997569	+	0.0696862i	$0.0221998\pi$
$349$	1.56915	+	8.89911i	0.0839948	+	0.476358i	−0.913574	+	0.406672i	$0.866689\pi$
$350$	−0.377611	+	0.0374109i	−0.0201842	+	0.00199970i
$351$	0.482595	+	1.32592i	0.0257590	+	0.0707723i
$352$	22.2810	−	8.10961i	1.18758	−	0.432243i
$353$	16.0232	−	13.4451i	0.852830	−	0.715609i	−0.107581	−	0.994196i	$-0.534310\pi$
$353$	16.0232	−	13.4451i	0.852830	−	0.715609i	0.960411	+	0.278587i	$0.0898660\pi$
$354$	−0.374923	−	2.12629i	−0.0199269	−	0.113011i
$355$	8.22829	+	10.5968i	0.436712	+	0.562418i
$356$	−10.1513	−	5.86088i	−0.538020	−	0.310626i
$357$	−0.0821183	−	0.0689054i	−0.00434616	−	0.00364686i
$358$	−3.27177	+	8.98911i	−0.172918	+	0.475089i
$359$	−1.20188	−	2.08172i	−0.0634328	−	0.109869i	0.832565	−	0.553927i	$-0.186872\pi$
$359$	−1.20188	−	2.08172i	−0.0634328	−	0.109869i	−0.895998	+	0.444059i	$0.853538\pi$
$360$	−0.728921	+	19.2279i	−0.0384175	+	1.01340i
$361$	11.3566	−	9.52929i	0.597714	−	0.501542i
$362$	3.91981	+	6.78931i	0.206021	+	0.356838i
$363$	−2.53729	−	0.447393i	−0.133173	−	0.0234821i
$364$			0.0727755i			0.00381447i
$365$	19.9804	−	6.42616i	1.04582	−	0.336361i
$366$	0.923910	+	0.775252i	0.0482935	+	0.0405231i
$367$	−4.96213	−	13.6333i	−0.259021	−	0.711655i	−0.999228	−	0.0392761i	$-0.987495\pi$
$367$	−4.96213	−	13.6333i	−0.259021	−	0.711655i	0.740207	−	0.672379i	$-0.234727\pi$
$368$	−0.00269940		0.000982502i	−0.000140716		5.12165e-5i
$369$	−17.3412			−0.902746
$370$	−9.98155	+	8.28953i	−0.518916	+	0.430952i
$371$	0.0636810			0.00330615
$372$	1.47397	+	0.536482i	0.0764220	+	0.0278153i
$373$	11.1702	+	30.6899i	0.578372	+	1.58907i	0.790923	+	0.611915i	$0.209601\pi$
$373$	11.1702	+	30.6899i	0.578372	+	1.58907i	−0.212551	+	0.977150i	$0.568177\pi$
$374$	−15.5302	−	13.0313i	−0.803045	−	0.673835i
$375$	0.902639	−	3.04471i	0.0466121	−	0.157228i
$376$		−	23.4504i		−	1.20936i
$377$	−0.476221	−	0.0839705i	−0.0245266	−	0.00432470i
$378$	0.0638001	+	0.110505i	0.00328152	+	0.00568377i
$379$	5.35493	−	4.49332i	0.275064	−	0.230806i	−0.494811	−	0.869001i	$-0.664763\pi$
$379$	5.35493	−	4.49332i	0.275064	−	0.230806i	0.769875	+	0.638194i	$0.220318\pi$
$380$	4.97663	+	0.188661i	0.255296	+	0.00967813i
$381$	−1.26413	−	2.18954i	−0.0647634	−	0.112173i
$382$	7.18403	−	19.7380i	0.367567	−	1.00988i
$383$	−16.9250	−	14.2017i	−0.864826	−	0.725675i	0.0981762	−	0.995169i	$-0.468699\pi$
$383$	−16.9250	−	14.2017i	−0.864826	−	0.725675i	−0.963002	+	0.269494i	$0.913144\pi$
$384$	−1.12257	−	0.648116i	−0.0572859	−	0.0330740i
$385$	0.629484	−	0.488788i	0.0320815	−	0.0249110i
$386$	−0.975938	−	5.53482i	−0.0496739	−	0.281715i
$387$	2.27619	−	1.90995i	0.115705	−	0.0970883i
$388$	−7.25846	+	2.64186i	−0.368492	+	0.134120i
$389$	11.8837	+	32.6501i	0.602525	+	1.65542i	0.746139	+	0.665790i	$0.231906\pi$
$389$	11.8837	+	32.6501i	0.602525	+	1.65542i	−0.143614	+	0.989634i	$0.545872\pi$
$390$	0.470871	+	0.191881i	0.0238435	+	0.00971628i
$391$	−0.00374510	−	0.0212395i	−0.000189398	−	0.00107413i
$392$	−3.57976	−	20.3018i	−0.180805	−	1.02540i
$393$	3.03846	−	5.26277i	0.153270	−	0.265472i
$394$	4.09794	−	4.88373i	0.206451	−	0.246039i
$395$	−2.11916	−	15.4123i	−0.106627	−	0.775475i
$396$	−7.12793	−	12.3459i	−0.358192	−	0.620406i
$397$	−28.6683	−	16.5516i	−1.43882	−	0.830702i	−0.441051	−	0.897482i	$-0.645394\pi$
$397$	−28.6683	−	16.5516i	−1.43882	−	0.830702i	−0.997768	+	0.0667799i	$0.978727\pi$
$398$	6.47433	+	7.71581i	0.324529	+	0.386759i
$399$	0.0399874	−	0.0230868i	0.00200188	−	0.00115578i
$400$	2.25943	+	2.20812i	0.112971	+	0.110406i
$401$		−	9.52924i		−	0.475868i	−0.971281	−	0.237934i	$-0.923530\pi$
$401$		−	9.52924i		−	0.475868i	0.971281	−	0.237934i	$-0.0764701\pi$
$402$	0.152559	−	0.865206i	0.00760896	−	0.0431526i
$403$	−2.73295	+	3.25700i	−0.136138	+	0.162243i
$404$	−7.56726	+	2.75426i	−0.376485	+	0.137029i
$405$	18.3429	−	2.52212i	0.911467	−	0.125325i
$406$	−0.0437297			−0.00217027
$407$	8.47518	−	25.8995i	0.420099	−	1.28379i
$408$			3.97179i			0.196633i
$409$	−5.48437	+	15.0682i	−0.271185	+	0.745074i	0.727100	+	0.686531i	$0.240868\pi$
$409$	−5.48437	+	15.0682i	−0.271185	+	0.745074i	−0.998285	+	0.0585427i	$0.981355\pi$
$410$	−8.50641	+	9.39080i	−0.420102	+	0.463779i
$411$	−4.46369	−	3.74548i	−0.220178	−	0.184751i
$412$	−2.01312	+	11.4170i	−0.0991795	+	0.562475i
$413$	−0.633940			−0.0311941
$414$	−0.00219856	+	0.0124687i	−0.000108053	+	0.000612802i
$415$	−16.6905	+	26.5338i	−0.819304	+	1.30249i
$416$	3.40250	−	2.85503i	0.166821	−	0.139980i
$417$	−5.19719	−	3.00060i	−0.254507	−	0.146940i
$418$	7.56240	−	4.36615i	0.369889	−	0.213555i
$419$	−4.35092	−	1.58361i	−0.212557	−	0.0773643i	0.233547	−	0.972345i	$-0.424967\pi$
$419$	−4.35092	−	1.58361i	−0.212557	−	0.0773643i	−0.446104	+	0.894981i	$0.647189\pi$
$420$	−0.0538400	−	0.0116121i	−0.00262712	−	0.000566613i
$421$	7.17774	+	4.14407i	0.349822	+	0.201970i	0.664607	−	0.747193i	$-0.268599\pi$
$421$	7.17774	+	4.14407i	0.349822	+	0.201970i	−0.314785	+	0.949163i	$0.601932\pi$
$422$	−1.76905	−	10.0328i	−0.0861160	−	0.488388i
$423$	−22.8721	+	4.03297i	−1.11208	+	0.196090i
$424$	−1.51662	−	1.80744i	−0.0736537	−	0.0877770i
$425$	−5.87539	+	22.9797i	−0.284998	+	1.11468i
$426$	−0.556032	−	1.52769i	−0.0269399	−	0.0740166i
$427$	0.271273	−	0.227625i	0.0131278	−	0.0110155i
$428$	12.3810	−	2.18310i	0.598457	−	0.105524i
$429$	−1.05170	+	0.185443i	−0.0507765	+	0.00895326i
$430$	0.0822454	−	2.16952i	0.00396623	−	0.104624i
$431$	−0.202710	+	0.241581i	−0.00976422	+	0.0116365i	−0.770904	−	0.636951i	$-0.780195\pi$
$431$	−0.202710	+	0.241581i	−0.00976422	+	0.0116365i	0.761140	+	0.648587i	$0.224640\pi$
$432$	0.363346	−	0.998284i	0.0174815	−	0.0480300i
$433$	7.90137	−	4.56186i	0.379716	−	0.219229i	−0.297979	−	0.954572i	$-0.596312\pi$
$433$	7.90137	−	4.56186i	0.379716	−	0.219229i	0.677695	+	0.735343i	$0.262979\pi$
$434$	−0.192245	+	0.332977i	−0.00922804	+	0.0159834i
$435$	0.138108	−	0.338914i	0.00662179	−	0.0162497i
$436$	−10.2159	+	5.89817i	−0.489254	+	0.282471i
$437$	0.00914854	+	0.00161313i	0.000437634	+	7.71667e-5i
$438$	−2.54329			−0.121523
$439$	−19.7260	−	3.47823i	−0.941473	−	0.166007i	−0.318211	−	0.948020i	$-0.603082\pi$
$439$	−19.7260	−	3.47823i	−0.941473	−	0.166007i	−0.623262	+	0.782013i	$0.714193\pi$
$440$	−28.8649	−	6.22552i	−1.37608	−	0.296790i
$441$	−19.1855	+	6.98294i	−0.913594	+	0.332521i
$442$	−3.56864	−	1.29888i	−0.169743	−	0.0617814i
$443$			25.8163i			1.22657i	0.789862	+	0.613284i	$0.210152\pi$
$443$			25.8163i			1.22657i	−0.789862	+	0.613284i	$0.789848\pi$
$444$	−1.74762	+	0.701837i	−0.0829386	+	0.0333077i
$445$	11.2256	+	21.2651i	0.532143	+	1.00806i
$446$	−4.74021	+	13.0236i	−0.224456	+	0.616686i
$447$	−1.46452	−	4.02374i	−0.0692695	−	0.190317i
$448$	0.322808	−	0.384708i	0.0152513	−	0.0181757i
$449$	25.1893	+	4.44155i	1.18876	+	0.209610i	0.732832	−	0.680409i	$-0.238198\pi$
$449$	25.1893	+	4.44155i	1.18876	+	0.209610i	0.455923	+	0.890019i	$0.349309\pi$
$450$	7.85507	−	11.4970i	0.370291	−	0.541973i
$451$	4.62112	−	26.2077i	0.217600	−	1.23407i
$452$	−9.86264	−	17.0826i	−0.463900	−	0.803498i
$453$	−1.94205	−	2.31445i	−0.0912457	−	0.108742i
$454$	10.8428	−	18.7803i	0.508880	−	0.881405i
$455$	0.0794906	−	0.126371i	0.00372658	−	0.00592435i
$456$	−1.60760	−	0.585119i	−0.0752829	−	0.0274007i
$457$	−2.69802	−	2.26391i	−0.126208	−	0.105901i	0.577499	−	0.816391i	$-0.304029\pi$
$457$	−2.69802	−	2.26391i	−0.126208	−	0.105901i	−0.703707	+	0.710490i	$0.748473\pi$
$458$	−2.05571	+	3.56059i	−0.0960569	+	0.166375i
$459$	7.85473	−	1.38500i	0.366627	−	0.0646463i
$460$	−0.00679616	−	0.00875241i	−0.000316872	−	0.000408083i
$461$	−6.74610	−	8.03969i	−0.314197	−	0.374446i	0.585715	−	0.810517i	$-0.300814\pi$
$461$	−6.74610	−	8.03969i	−0.314197	−	0.374446i	−0.899912	+	0.436072i	$0.856369\pi$
$462$	−0.0907497	+	0.0330302i	−0.00422206	+	0.00153670i
$463$	−11.2011	+	4.07686i	−0.520558	+	0.189468i	−0.588918	−	0.808193i	$-0.700446\pi$
$463$	−11.2011	+	4.07686i	−0.520558	+	0.189468i	0.0683595	+	0.997661i	$0.478224\pi$
$464$	0.234024	+	0.278899i	0.0108643	+	0.0129476i
$465$	−1.97349	−	2.54155i	−0.0915184	−	0.117862i
$466$	−5.25672	+	0.926901i	−0.243513	+	0.0429379i
$467$	0.664094	−	1.15024i	0.0307306	−	0.0532270i	−0.850251	−	0.526377i	$-0.823550\pi$
$467$	0.664094	−	1.15024i	0.0307306	−	0.0532270i	0.880982	+	0.473150i	$0.156883\pi$
$468$	−2.04570	−	1.71655i	−0.0945627	−	0.0793475i
$469$	−0.242399	−	0.0882259i	−0.0111929	−	0.00407390i
$470$	−9.03551	+	14.3643i	−0.416777	+	0.662574i
$471$	−2.55370	+	4.42315i	−0.117668	+	0.203808i
$472$	15.0979	+	17.9929i	0.694936	+	0.828192i
$473$	2.27994	+	3.94897i	0.104832	+	0.181574i
$474$	−0.327356	+	1.85653i	−0.0150360	+	0.0852732i
$475$	−8.43559	−	5.76344i	−0.387051	−	0.264445i
$476$	0.405121	+	0.0714338i	0.0185687	+	0.00327416i
$477$	−1.50204	+	1.79006i	−0.0687736	+	0.0819612i
$478$	−6.88936	−	18.9283i	−0.315112	−	0.865763i
$479$	−13.6672	+	37.5504i	−0.624472	+	1.71572i	0.0712949	+	0.997455i	$0.477287\pi$
$479$	−13.6672	+	37.5504i	−0.624472	+	1.71572i	−0.695767	+	0.718268i	$0.744935\pi$
$480$	1.56928	+	2.97275i	0.0716273	+	0.135687i
$481$	−0.167483	−	5.10203i	−0.00763655	−	0.232632i
$482$		−	6.47985i		−	0.295149i
$483$	−9.65421e−5	0	3.51385e-5i	−4.39282e−6	0	1.59886e-6i
$484$	9.29079	−	3.38157i	0.422309	−	0.153708i
$485$	15.4896	+	3.34076i	0.703345	+	0.151696i
$486$	−6.94811	−	1.22514i	−0.315172	−	0.0555734i
$487$	23.3742			1.05919			0.529593	−	0.848252i	$-0.322345\pi$
$487$	23.3742			1.05919			0.529593	+	0.848252i	$0.322345\pi$
$488$	−12.9212	−	2.27836i	−0.584916	−	0.103136i
$489$	5.59340	−	3.22935i	0.252943	−	0.146036i
$490$	−5.62961	+	13.8149i	−0.254320	+	0.624094i
$491$	1.94286	−	3.36513i	0.0876800	−	0.151866i	−0.818850	−	0.574007i	$-0.805388\pi$
$491$	1.94286	−	3.36513i	0.0876800	−	0.151866i	0.906530	+	0.422141i	$0.138721\pi$
$492$	−1.59273	+	0.919565i	−0.0718060	+	0.0414572i
$493$	−0.934882	+	2.56857i	−0.0421050	+	0.115682i
$494$	1.05146	−	1.25308i	0.0473073	−	0.0563787i
$495$	−1.10785	+	29.2237i	−0.0497943	+	1.31351i
$496$	3.15248	−	0.555867i	0.141551	−	0.0249592i
$497$	−0.470085	+	0.0828886i	−0.0210862	+	0.00371806i
$498$	2.90980	−	2.44161i	0.130391	−	0.109411i
$499$	−9.60639	−	26.3933i	−0.430041	−	1.18153i	−0.945787	−	0.324787i	$-0.894707\pi$
$499$	−9.60639	−	26.3933i	−0.430041	−	1.18153i	0.515746	−	0.856741i	$-0.327515\pi$
$500$	2.84223	+	11.8506i	0.127109	+	0.529977i
$501$	2.70680	+	3.22584i	0.120931	+	0.144120i
$502$	−4.38703	+	0.773551i	−0.195803	+	0.0345253i
$503$	−2.06975	−	11.7381i	−0.0922856	−	0.523378i	−0.995545	−	0.0942836i	$-0.969944\pi$
$503$	−2.06975	−	11.7381i	−0.0922856	−	0.523378i	0.903260	−	0.429094i	$-0.141167\pi$
$504$	−0.592882	−	0.342301i	−0.0264091	−	0.0152473i
$505$	16.1485	+	3.48289i	0.718601	+	0.154986i
$506$	−0.0182580	−	0.00664536i	−0.000811666	−	0.000295422i
$507$	3.02460	−	1.74625i	0.134327	−	0.0775539i
$508$	8.40234	+	4.85109i	0.372793	+	0.215232i
$509$	12.1400	−	10.1867i	0.538097	−	0.451517i	−0.332790	−	0.943001i	$-0.607990\pi$
$509$	12.1400	−	10.1867i	0.538097	−	0.451517i	0.870886	+	0.491484i	$0.163546\pi$
$510$	1.53034	−	2.43287i	0.0677646	−	0.107729i
$511$	−0.129671	+	0.735400i	−0.00573630	+	0.0325322i
$512$	−7.06906			−0.312411
$513$	−0.596564	+	3.38328i	−0.0263389	+	0.149376i
$514$	12.2966	+	10.3180i	0.542378	+	0.455109i
$515$	15.9661	−	17.6261i	0.703552	−	0.776700i
$516$	0.107781	−	0.296125i	0.00474477	−	0.0130362i
$517$		−	35.6412i		−	1.56750i
$518$	−0.0950341	−	0.451745i	−0.00417556	−	0.0198485i
$519$	6.39231			0.280591
$520$	−5.47989	+	0.753476i	−0.240309	+	0.0330421i
$521$	−2.75061	+	1.00114i	−0.120507	+	0.0438608i	−0.401570	−	0.915829i	$-0.631535\pi$
$521$	−2.75061	+	1.00114i	−0.120507	+	0.0438608i	0.281063	+	0.959689i	$0.409313\pi$
$522$	1.03145	−	1.22923i	0.0451453	−	0.0538021i
$523$	2.54875	−	14.4547i	0.111449	−	0.632060i	−0.876998	−	0.480494i	$-0.840457\pi$
$523$	2.54875	−	14.4547i	0.111449	−	0.632060i	0.988447	−	0.151566i	$-0.0484316\pi$
$524$			23.3202i			1.01875i
$525$	0.0808067	+	0.0789718i	0.00352669	+	0.00344661i
$526$	20.8498	−	12.0377i	0.909096	−	0.524867i
$527$	15.4483	+	18.4105i	0.672937	+	0.801976i
$528$	0.696317	+	0.402019i	0.0303033	+	0.0174956i
$529$	11.5000	+	19.9186i	0.500000	+	0.866025i
$530$	0.232576	+	1.69148i	0.0101025	+	0.0734733i
$531$	14.9527	−	17.8199i	0.648891	−	0.773319i
$532$	−0.0885953	+	0.153451i	−0.00384109	+	0.00665297i
$533$	−0.865652	−	4.90935i	−0.0374955	−	0.212648i
$534$	−0.505980	−	2.86955i	−0.0218959	−	0.124178i
$535$	−23.8834	−	9.73255i	−1.03257	−	0.420775i
$536$	3.26886	+	8.98112i	0.141193	+	0.387925i
$537$	2.67660	−	0.974201i	0.115504	−	0.0420399i
$538$	−12.1308	+	10.1789i	−0.522996	+	0.438846i
$539$	−5.44071	−	30.8558i	−0.234348	−	1.32905i
$540$	3.23679	−	2.51333i	0.139289	−	0.108157i
$541$	35.5976	+	20.5523i	1.53046	+	0.883611i	0.999340	+	0.0363140i	$0.0115617\pi$
$541$	35.5976	+	20.5523i	1.53046	+	0.883611i	0.531119	+	0.847297i	$0.321772\pi$
$542$	−2.41098	−	2.02305i	−0.103560	−	0.0868974i
$543$	0.798386	−	2.19355i	0.0342620	−	0.0941341i
$544$	−12.5534	−	21.7432i	−0.538223	−	0.932230i
$545$	24.1818	+	0.916719i	1.03583	+	0.0392679i
$546$	−0.0138583	+	0.0116285i	−0.000593079	+	0.000497653i
$547$	3.94634	+	6.83527i	0.168734	+	0.292255i	0.937975	−	0.346703i	$-0.112699\pi$
$547$	3.94634	+	6.83527i	0.168734	+	0.292255i	−0.769241	+	0.638958i	$0.779366\pi$
$548$	22.0211	+	3.88292i	0.940695	+	0.165870i
$549$			12.9944i			0.554587i
$550$	15.2821	+	14.9351i	0.651631	+	0.636834i
$551$	−0.901916	−	0.756797i	−0.0384229	−	0.0322406i
$552$	0.00130192	+	0.00357698i	5.54132e−5	+	0.000152247i
$553$	0.520130	+	0.189312i	0.0221182	+	0.00805037i
$554$	16.5409			0.702757
$555$	3.80125	+	0.690178i	0.161354	+	0.0292964i
$556$	23.0295			0.976670
$557$	22.7781	+	8.29054i	0.965137	+	0.351281i	0.776045	−	0.630678i	$-0.217223\pi$
$557$	22.7781	+	8.29054i	0.965137	+	0.351281i	0.189093	+	0.981959i	$0.439445\pi$
$558$	−4.82547	−	13.2579i	−0.204278	−	0.561250i
$559$	0.654339	+	0.549056i	0.0276756	+	0.0232226i
$560$	−0.107004	+	0.0344150i	−0.00452175	+	0.00145430i
$561$			6.03654i			0.254863i
$562$	−18.0013	−	3.17412i	−0.759340	−	0.133892i
$563$	17.5915	+	30.4693i	0.741391	+	1.28413i	0.951862	+	0.306527i	$0.0991670\pi$
$563$	17.5915	+	30.4693i	0.741391	+	1.28413i	−0.210471	+	0.977600i	$0.567500\pi$
$564$	−1.88687	+	1.58327i	−0.0794516	+	0.0666678i
$565$	−1.53290	+	40.4357i	−0.0644894	+	1.70114i
$566$	−0.288584	−	0.499842i	−0.0121301	−	0.0210099i
$567$	−0.225310	+	0.619034i	−0.00946213	+	0.0259970i
$568$	13.5481	+	11.3682i	0.568466	+	0.477000i
$569$	−27.2904	−	15.7561i	−1.14407	−	0.660531i	−0.196638	−	0.980476i	$-0.563002\pi$
$569$	−27.2904	−	15.7561i	−1.14407	−	0.660531i	−0.947436	+	0.319945i	$0.896336\pi$
$570$	0.759268	+	0.977821i	0.0318023	+	0.0409564i
$571$	−2.32777	−	13.2014i	−0.0974141	−	0.552463i	−0.993981	−	0.109554i	$-0.965058\pi$
$571$	−2.32777	−	13.2014i	−0.0974141	−	0.552463i	0.896567	−	0.442909i	$-0.146053\pi$
$572$	3.13936	−	2.63424i	0.131263	−	0.110143i
$573$	−5.87718	+	2.13912i	−0.245523	+	0.0893629i
$574$	−0.154186	−	0.423622i	−0.00643559	−	0.0176817i
$575$	0.00224115	+	0.0226213i	9.34626e−5	+	0.000943375i
$576$	3.20001	+	18.1481i	0.133334	+	0.756173i
$577$	−0.183282	−	1.03944i	−0.00763013	−	0.0432726i	0.980755	−	0.195243i	$-0.0625494\pi$
$577$	−0.183282	−	1.03944i	−0.00763013	−	0.0432726i	−0.988385	+	0.151970i	$0.951438\pi$
$578$	−2.62493	+	4.54652i	−0.109183	+	0.189110i
$579$	−1.07569	+	1.28195i	−0.0447040	+	0.0532761i
$580$	0.191306	+	1.39133i	0.00794354	+	0.0577719i
$581$	−0.557641	−	0.965863i	−0.0231349	−	0.0400708i
$582$	−1.66287	−	0.960061i	−0.0689284	−	0.0397958i
$583$	−2.30505	−	2.74705i	−0.0954652	−	0.113771i
$584$	23.9609	−	13.8338i	0.991508	−	0.572447i
$585$	1.67732	+	5.21516i	0.0693485	+	0.215620i
$586$		−	14.6552i		−	0.605402i
$587$	−1.36532	+	7.74311i	−0.0563528	+	0.319592i	−0.999933	−	0.0115508i	$-0.996323\pi$
$587$	−1.36532	+	7.74311i	−0.0563528	+	0.319592i	0.943581	+	0.331143i	$0.107434\pi$
$588$	−1.39184	+	1.65873i	−0.0573983	+	0.0684047i
$589$	−9.72759	+	3.54055i	−0.400818	+	0.145886i
$590$	−2.31528	−	16.8386i	−0.0953186	−	0.693234i
$591$	−1.89830			−0.0780855
$592$	−2.37255	+	3.02367i	−0.0975113	+	0.124272i
$593$			28.8879i			1.18628i	0.805098	+	0.593142i	$0.202113\pi$
$593$			28.8879i			1.18628i	−0.805098	+	0.593142i	$0.797887\pi$
$594$	2.45757	−	6.75211i	0.100835	−	0.277042i
$595$	−0.625446	−	0.566543i	−0.0256408	−	0.0232260i
$596$	12.5877	+	10.5623i	0.515612	+	0.432650i
$597$	0.520792	−	2.95356i	0.0213146	−	0.120881i
$598$	−0.00363968			−0.000148837
$599$	−7.63439	+	43.2968i	−0.311933	+	1.76906i	0.276994	+	0.960872i	$0.410662\pi$
$599$	−7.63439	+	43.2968i	−0.311933	+	1.76906i	−0.588927	+	0.808187i	$0.700449\pi$
$600$	0.316946	−	4.17430i	0.0129393	−	0.170415i
$601$	−16.3655	+	13.7323i	−0.667563	+	0.560152i	−0.912343	−	0.409427i	$-0.865729\pi$
$601$	−16.3655	+	13.7323i	−0.667563	+	0.560152i	0.244780	+	0.969579i	$0.421284\pi$
$602$	0.0668959	+	0.0386224i	0.00272647	+	0.00157413i
$603$	8.19745	−	4.73280i	0.333826	−	0.192735i
$604$	10.8950	+	3.96546i	0.443311	+	0.161352i
$605$	−19.8265	−	4.27615i	−0.806064	−	0.173850i
$606$	−1.73362	−	1.00091i	−0.0704235	−	0.0406590i
$607$	−3.68445	−	20.8955i	−0.149547	−	0.848124i	−0.963603	−	0.267337i	$-0.913856\pi$
$607$	−3.68445	−	20.8955i	−0.149547	−	0.848124i	0.814056	−	0.580787i	$-0.197255\pi$
$608$	10.6500	−	1.87789i	0.431915	−	0.0761583i
$609$	0.00836971	+	0.00997463i	0.000339158	+	0.000404192i
$610$	7.03687	+	6.37416i	0.284915	+	0.258082i
$611$	−2.28350	−	6.27385i	−0.0923803	−	0.253813i
$612$	−11.5635	+	9.70297i	−0.467429	+	0.392219i
$613$	−28.5303	+	5.03066i	−1.15233	+	0.203187i	−0.716992	−	0.697081i	$-0.754482\pi$
$613$	−28.5303	+	5.03066i	−1.15233	+	0.203187i	−0.435336	+	0.900268i	$0.643370\pi$
$614$	−27.6658	+	4.87822i	−1.11650	+	0.196869i
$615$	3.77011	+	0.142923i	0.152026	+	0.00576321i
$616$	0.675310	−	0.804804i	0.0272090	−	0.0324265i
$617$	8.89630	−	24.4424i	0.358152	−	0.984014i	−0.621519	−	0.783399i	$-0.713484\pi$
$617$	8.89630	−	24.4424i	0.358152	−	0.984014i	0.979670	−	0.200614i	$-0.0642938\pi$
$618$	−2.49575	+	1.44092i	−0.100394	+	0.0579624i
$619$	20.5919	−	35.6662i	0.827658	−	1.43355i	−0.0722132	−	0.997389i	$-0.523006\pi$
$619$	20.5919	−	35.6662i	0.827658	−	1.43355i	0.899871	−	0.436156i	$-0.143660\pi$
$620$	11.4352	+	4.65988i	0.459250	+	0.187145i
$621$	0.00661996	−	0.00382204i	0.000265650	−	0.000153373i
$622$	−2.19393	−	0.386849i	−0.0879686	−	0.0155112i
$623$	−0.855538			−0.0342764
$624$	0.148328	+	0.0261543i	0.00593788	+	0.00104701i
$625$	8.00873	−	23.6825i	0.320349	−	0.947299i
$626$	−3.06530	+	1.11568i	−0.122514	+	0.0445915i
$627$	−2.44332	−	0.889296i	−0.0975769	−	0.0355151i
$628$		−	19.5996i		−	0.782111i
$629$	−28.5660	−	4.07563i	−1.13900	−	0.162506i
$630$	0.231273	+	0.438111i	0.00921414	+	0.0174548i
$631$	−12.7116	+	34.9248i	−0.506040	+	1.39033i	0.379251	+	0.925294i	$0.376182\pi$
$631$	−12.7116	+	34.9248i	−0.506040	+	1.39033i	−0.885290	+	0.465039i	$0.846040\pi$
$632$	−7.01420	−	19.2714i	−0.279010	−	0.766573i
$633$	−1.94986	+	2.32375i	−0.0775000	+	0.0923609i
$634$	9.06660	+	1.59869i	0.360081	+	0.0634920i
$635$	−9.29150	−	17.6013i	−0.368722	−	0.698486i
$636$	−0.0430346	+	0.244061i	−0.00170643	+	0.00967766i
$637$	−2.93461	−	5.08290i	−0.116274	−	0.201392i
$638$	1.58287	+	1.88640i	0.0626666	+	0.0746831i
$639$	8.75787	−	15.1691i	0.346456	−	0.600079i
$640$	−8.63757	−	5.43326i	−0.341430	−	0.214769i
$641$	17.7377	+	6.45598i	0.700595	+	0.254996i	0.667665	−	0.744462i	$-0.267294\pi$
$641$	17.7377	+	6.45598i	0.700595	+	0.254996i	0.0329303	+	0.999458i	$0.489516\pi$
$642$	2.39402	+	2.00882i	0.0944843	+	0.0792817i
$643$	−7.90467	+	13.6913i	−0.311730	+	0.539932i	−0.978737	−	0.205119i	$-0.934242\pi$
$643$	−7.90467	+	13.6913i	−0.311730	+	0.539932i	0.667007	+	0.745051i	$0.267575\pi$
$644$	0.000388267	0	6.84619e-5i	1.52999e−5	0	2.69778e-6i
$645$	−0.510604	+	0.396479i	−0.0201050	+	0.0156113i
$646$	−5.94347	−	7.08315i	−0.233843	−	0.278683i
$647$	20.8004	−	7.57072i	0.817747	−	0.297636i	0.100927	−	0.994894i	$-0.467819\pi$
$647$	20.8004	−	7.57072i	0.817747	−	0.297636i	0.716820	+	0.697258i	$0.245597\pi$
$648$	22.9358	−	8.34796i	0.901004	−	0.327939i
$649$	22.9466	+	27.3466i	0.900731	+	1.07345i
$650$	3.64695	+	1.64988i	0.143045	+	0.0647137i
$651$	0.112746	−	0.0198802i	0.00441887	−	0.000779166i
$652$	−12.3926	+	21.4647i	−0.485333	+	0.840621i
$653$	9.48480	+	7.95869i	0.371169	+	0.311448i	0.809224	−	0.587501i	$-0.199888\pi$
$653$	9.48480	+	7.95869i	0.371169	+	0.311448i	−0.438055	+	0.898948i	$0.644332\pi$
$654$	−2.75552	−	1.00293i	−0.107749	−	0.0392175i
$655$	25.4720	−	40.4942i	0.995272	−	1.58224i
$656$	−1.87663	+	3.25043i	−0.0732703	+	0.126908i
$657$	−17.6134	−	20.9908i	−0.687164	−	0.818931i
$658$	−0.301883	−	0.522877i	−0.0117686	−	0.0203839i
$659$	8.18785	−	46.4356i	0.318953	−	1.80887i	−0.230190	−	0.973146i	$-0.573935\pi$
$659$	8.18785	−	46.4356i	0.318953	−	1.80887i	0.549143	−	0.835728i	$-0.314954\pi$
$660$	1.44791	+	2.74285i	0.0563600	+	0.106765i
$661$	−16.8898	−	2.97813i	−0.656937	−	0.115836i	−0.164764	−	0.986333i	$-0.552686\pi$
$661$	−16.8898	−	2.97813i	−0.656937	−	0.115836i	−0.492173	+	0.870497i	$0.663797\pi$
$662$	−6.68447	+	7.96624i	−0.259799	+	0.309617i
$663$	0.386754	+	1.06260i	0.0150203	+	0.0412679i
$664$	−14.1331	+	38.8303i	−0.548470	+	1.50691i
$665$	0.321452	−	0.169690i	0.0124654	−	0.00658030i
$666$	14.9400	+	7.98387i	0.578914	+	0.309369i
$667$			0.00261969i			0.000101435i
$668$	−15.1853	−	5.52698i	−0.587535	−	0.213845i
$669$	3.87791	−	1.41144i	0.149929	−	0.0545696i
$670$	1.45815	−	6.76077i	0.0563333	−	0.261191i
$671$	−19.6384	−	3.46277i	−0.758131	−	0.133679i
$672$	−0.119600			−0.00461366
$673$	−19.9313	−	3.51443i	−0.768297	−	0.135471i	−0.224256	−	0.974530i	$-0.571995\pi$
$673$	−19.9313	−	3.51443i	−0.768297	−	0.135471i	−0.544041	+	0.839059i	$0.683106\pi$
$674$	24.5588	−	14.1790i	0.945970	−	0.546156i
$675$	−8.36575	+	0.828816i	−0.321998	+	0.0319011i
$676$	−6.70124	+	11.6069i	−0.257740	+	0.446419i
$677$	−21.5559	+	12.4453i	−0.828461	+	0.478312i	−0.853326	−	0.521379i	$-0.825418\pi$
$677$	−21.5559	+	12.4453i	−0.828461	+	0.478312i	0.0248643	+	0.999691i	$0.492085\pi$
$678$	1.67705	−	4.60765i	0.0644066	−	0.176956i
$679$	−0.362387	+	0.431876i	−0.0139071	+	0.0165739i
$680$	−1.18447	+	31.2446i	−0.0454222	+	1.19818i
$681$	−6.35903	+	1.12127i	−0.243678	+	0.0429671i
$682$	21.3225	−	3.75973i	0.816480	−	0.143967i
$683$	−8.87476	+	7.44681i	−0.339583	+	0.284944i	−0.796591	−	0.604518i	$-0.793366\pi$
$683$	−8.87476	+	7.44681i	−0.339583	+	0.284944i	0.457008	+	0.889463i	$0.348921\pi$
$684$	−2.22380	−	6.10984i	−0.0850291	−	0.233616i
$685$	−33.9973	−	30.7955i	−1.29897	−	1.17664i
$686$	−0.682645	−	0.813545i	−0.0260635	−	0.0310613i
$687$	1.20562	−	0.212583i	0.0459971	−	0.00811053i
$688$	−0.111675	−	0.633340i	−0.00425757	−	0.0241459i
$689$	−0.581752	−	0.335875i	−0.0221630	−	0.0127958i
$690$	0.000580749	−	0.00269267i	2.21088e−5	−	0.000102508i
$691$	0.0158943	+	0.00578507i	0.000604649	+	0.000220074i	0.342322	−	0.939583i	$-0.388786\pi$
$691$	0.0158943	+	0.00578507i	0.000604649	+	0.000220074i	−0.341718	+	0.939803i	$0.611009\pi$
$692$	−21.2440	+	12.2652i	−0.807575	+	0.466254i
$693$	−0.901094	−	0.520247i	−0.0342297	−	0.0197626i
$694$	−15.6218	+	13.1083i	−0.592997	+	0.497584i
$695$	−39.9895	−	25.1545i	−1.51689	−	0.954165i
$696$	0.0837747	−	0.475110i	0.00317547	−	0.0180090i
$697$	−28.1787			−1.06735
$698$	1.49687	−	8.48915i	0.0566572	−	0.321319i
$699$	1.21754	+	1.02164i	0.0460516	+	0.0386419i
$700$	−0.420077	−	0.107404i	−0.0158774	−	0.00405951i
$701$	1.50535	−	4.13593i	0.0568565	−	0.156212i	−0.908013	−	0.418943i	$-0.862401\pi$
$701$	1.50535	−	4.13593i	0.0568565	−	0.156212i	0.964869	+	0.262731i	$0.0846231\pi$
$702$		−	1.34601i		−	0.0508020i
$703$	5.85795	−	10.9618i	0.220937	−	0.413433i
$704$	−28.2800			−1.06584
$705$	5.00581	−	0.688292i	0.188530	−	0.0259226i
$706$	−18.7499	+	6.82441i	−0.705663	+	0.256840i
$707$	−0.377804	+	0.450250i	−0.0142088	+	0.0169334i
$708$	0.428406	−	2.42961i	0.0161005	−	0.0913104i
$709$			32.9793i			1.23856i	0.785169	+	0.619281i	$0.212576\pi$
$709$			32.9793i			1.23856i	−0.785169	+	0.619281i	$0.787424\pi$
$710$	−3.91852	−	12.1836i	−0.147059	−	0.457241i
$711$	−17.5898	+	10.1555i	−0.659669	+	0.380860i
$712$	20.3754	+	24.2825i	0.763601	+	0.910024i
$713$	0.0199475	+	0.0115167i	0.000747040	+	0.000431303i
$714$	0.0511297	+	0.0885593i	0.00191348	+	0.00331425i
$715$	−8.32863	+	1.14517i	−0.311473	+	0.0428271i
$716$	−7.02606	+	8.37333i	−0.262576	+	0.312926i
$717$	−2.99891	+	5.19426i	−0.111996	+	0.193983i
$718$	0.398180	+	2.25819i	0.0148599	+	0.0842749i
$719$	−2.37186	−	13.4515i	−0.0884554	−	0.501655i	−0.996557	−	0.0829063i	$-0.973580\pi$
$719$	−2.37186	−	13.4515i	−0.0884554	−	0.501655i	0.908102	−	0.418749i	$-0.137531\pi$
$720$	1.55650	−	3.81961i	0.0580073	−	0.142348i
$721$	0.289400	+	0.795120i	0.0107778	+	0.0296118i
$722$	−13.2891	+	4.83685i	−0.494570	+	0.180009i
$723$	−1.47804	+	1.24022i	−0.0549687	+	0.0461242i
$724$	1.55553	+	8.82186i	0.0578109	+	0.327862i
$725$	1.18752	−	2.62493i	0.0441034	−	0.0974874i
$726$	2.12847	+	1.22887i	0.0789949	+	0.0456077i
$727$	31.8057	+	26.6882i	1.17961	+	0.989809i	0.999982	+	0.00607473i	$0.00193366\pi$
$727$	31.8057	+	26.6882i	1.17961	+	0.989809i	0.179627	+	0.983735i	$0.442511\pi$
$728$	0.0673106	−	0.184934i	0.00249470	−	0.00685412i
$729$	−11.3702	−	19.6937i	−0.421118	−	0.729398i
$730$	−20.0071	−	0.758460i	−0.740497	−	0.0280719i
$731$	3.69872	−	3.10359i	0.136802	−	0.114791i
$732$	0.689064	+	1.19349i	0.0254685	+	0.0441128i
$733$	14.8531	+	2.61901i	0.548613	+	0.0967353i	0.441083	−	0.897466i	$-0.354595\pi$
$733$	14.8531	+	2.61901i	0.548613	+	0.0967353i	0.107531	+	0.994202i	$0.465706\pi$
$734$			13.8399i			0.510842i
$735$	4.22863	−	1.36002i	0.155975	−	0.0501652i
$736$	−0.0184328	−	0.0154670i	−0.000679442	−	0.000570119i
$737$	4.96819	+	13.6500i	0.183006	+	0.502804i
$738$	15.5447	+	5.65781i	0.572208	+	0.208267i
$739$	−21.3018			−0.783601			−0.391801	−	0.920050i	$-0.628148\pi$
$739$	−21.3018			−0.783601			−0.391801	+	0.920050i	$0.628148\pi$
$740$	−13.9572	+	4.99993i	−0.513078	+	0.183801i
$741$	−0.487069			−0.0178929
$742$	−0.0570839	−	0.0207768i	−0.00209561	−	0.000762741i
$743$	−3.19381	−	8.77491i	−0.117169	−	0.321920i	0.867220	−	0.497925i	$-0.165905\pi$
$743$	−3.19381	−	8.77491i	−0.117169	−	0.321920i	−0.984389	+	0.176005i	$0.943682\pi$
$744$	−3.24941	−	2.72658i	−0.119129	−	0.0999612i
$745$	−10.3209	−	32.0901i	−0.378129	−	1.17569i
$746$		−	31.1550i		−	1.14067i
$747$	40.3033	+	7.10655i	1.47462	+	0.260015i
$748$	−11.5826	−	20.0616i	−0.423501	−	0.733526i
$749$	0.702916	−	0.589817i	0.0256840	−	0.0215514i
$750$	−1.80251	+	2.43479i	−0.0658184	+	0.0889061i
$751$	−18.5706	−	32.1652i	−0.677651	−	1.17373i	−0.975687	−	0.219171i	$-0.929665\pi$
$751$	−18.5706	−	32.1652i	−0.677651	−	1.17373i	0.298036	−	0.954555i	$-0.403669\pi$
$752$	−1.71924	+	4.72358i	−0.0626943	+	0.172251i
$753$	1.01611	+	0.852614i	0.0370290	+	0.0310710i
$754$	0.399489	+	0.230645i	0.0145485	+	0.00839960i
$755$	−14.5872	−	18.7861i	−0.530883	−	0.683696i
$756$	0.0253183	+	0.143587i	0.000920819	+	0.00522223i
$757$	25.5138	−	21.4087i	0.927317	−	0.778111i	−0.0480171	−	0.998847i	$-0.515290\pi$
$757$	25.5138	−	21.4087i	0.927317	−	0.778111i	0.975334	+	0.220736i	$0.0708458\pi$
$758$	−6.26619	+	2.28071i	−0.227598	+	0.0828390i
$759$	0.00197872	+	0.00543649i	7.18231e−5	+	0.000197332i
$760$	−12.4719	−	5.08234i	−0.452405	−	0.184356i
$761$	3.84248	+	21.7918i	0.139290	+	0.789951i	0.971776	+	0.235905i	$0.0758055\pi$
$761$	3.84248	+	21.7918i	0.139290	+	0.789951i	−0.832486	+	0.554045i	$0.813083\pi$
$762$	0.418803	+	2.37515i	0.0151716	+	0.0860426i
$763$	−0.430491	+	0.745632i	−0.0155848	+	0.0269937i
$764$	15.4276	−	18.3859i	0.558150	−	0.665178i
$765$	30.6778	−	4.21814i	1.10916	−	0.152507i
$766$	10.5381	+	18.2525i	0.380757	+	0.659490i
$767$	5.79130	+	3.34361i	0.209112	+	0.120731i
$768$	3.09987	+	3.69428i	0.111857	+	0.133306i
$769$	0.919212	−	0.530707i	0.0331476	−	0.0191378i	−0.483335	−	0.875436i	$-0.660575\pi$
$769$	0.919212	−	0.530707i	0.0331476	−	0.0191378i	0.516482	+	0.856298i	$0.327241\pi$
$770$	−0.723746	+	0.232773i	−0.0260820	+	0.00838857i
$771$		−	4.77965i		−	0.172135i
$772$	1.11516	−	6.32437i	0.0401354	−	0.227619i
$773$	7.16366	−	8.53732i	0.257659	−	0.307066i	−0.621672	−	0.783278i	$-0.713546\pi$
$773$	7.16366	−	8.53732i	0.257659	−	0.307066i	0.879330	+	0.476212i	$0.157991\pi$
$774$	−2.66354	+	0.969447i	−0.0957388	+	0.0348461i
$775$	−14.7668	−	20.5820i	−0.530439	−	0.739328i
$776$	20.8884			0.749850
$777$	−0.0848526	+	0.108139i	−0.00304407	+	0.00387948i
$778$		−	33.1448i		−	1.18830i
$779$	4.15126	−	11.4055i	0.148734	−	0.408644i
$780$	0.430605	+	0.390052i	0.0154181	+	0.0139661i
$781$	20.5912	+	17.2780i	0.736809	+	0.618257i
$782$	−0.00357257	+	0.0202611i	−0.000127755	+	0.000724534i
$783$	−0.968806			−0.0346223
$784$	−0.767340	+	4.35180i	−0.0274050	+	0.155422i
$785$	−21.4081	+	34.0337i	−0.764089	+	1.21472i
$786$	−4.44074	+	3.72623i	−0.158396	+	0.132910i
$787$	−31.9760	−	18.4614i	−1.13982	−	0.658077i	−0.193436	−	0.981113i	$-0.561963\pi$
$787$	−31.9760	−	18.4614i	−1.13982	−	0.658077i	−0.946387	+	0.323036i	$0.895296\pi$
$788$	6.30873	−	3.64235i	0.224739	−	0.129753i
$789$	−6.73634	−	2.45183i	−0.239820	−	0.0872873i
$790$	−3.12885	+	14.5070i	−0.111319	+	0.516136i
$791$	−1.24681	−	0.719846i	−0.0443315	−	0.0255948i
$792$	6.69437	+	37.9657i	0.237874	+	1.34905i
$793$	−3.67876	+	0.648664i	−0.130636	+	0.0230347i
$794$	20.2981	+	24.1904i	0.720353	+	0.858484i
$795$	0.341308	−	0.376794i	0.0121050	−	0.0133635i
$796$	3.93634	+	10.8150i	0.139520	+	0.383328i
$797$	−38.9751	+	32.7040i	−1.38057	+	1.15843i	−0.411565	+	0.911380i	$0.635018\pi$
$797$	−38.9751	+	32.7040i	−1.38057	+	1.15843i	−0.969002	+	0.247053i	$0.920538\pi$
$798$	−0.0433773	+	0.00764858i	−0.00153554	+	0.000270757i
$799$	−37.1662	+	6.55341i	−1.31485	+	0.231843i
$800$	11.4584	+	23.8536i	0.405116	+	0.843351i
$801$	20.1795	−	24.0490i	0.713007	−	0.849729i
$802$	−3.10905	+	8.54205i	−0.109784	+	0.301630i
$803$	36.4171	−	21.0254i	1.28513	−	0.741970i
$804$	0.501940	−	0.869386i	0.0177021	−	0.0306609i
$805$	−0.000748983	0	0.000305212i	−2.63982e−5	0	1.07573e-5i
$806$	3.51247	−	2.02792i	0.123721	−	0.0714306i
$807$	4.64358	+	0.818788i	0.163462	+	0.0288227i
$808$	21.7771			0.766115
$809$	−12.0988	−	2.13335i	−0.425373	−	0.0750047i	−0.0431362	−	0.999069i	$-0.513735\pi$
$809$	−12.0988	−	2.13335i	−0.425373	−	0.0750047i	−0.382237	+	0.924064i	$0.624846\pi$
$810$	−17.2655	−	3.72380i	−0.606649	−	0.130841i
$811$	−17.9533	+	6.53447i	−0.630426	+	0.229456i	−0.637417	−	0.770519i	$-0.719997\pi$
$811$	−17.9533	+	6.53447i	−0.630426	+	0.229456i	0.00699079	+	0.999976i	$0.497775\pi$
$812$	−0.0469544	−	0.0170900i	−0.00164778	−	0.000599742i
$813$			0.937142i			0.0328670i
$814$	−16.0473	+	20.4512i	−0.562456	+	0.716815i
$815$	44.9644	−	23.7361i	1.57503	−	0.831439i
$816$	0.291187	−	0.800030i	0.0101936	−	0.0280067i
$817$	0.711305	+	1.95429i	0.0248854	+	0.0683721i
$818$	9.83242	−	11.7178i	0.343783	−	0.409704i
$819$	−0.191949	−	0.0338459i	−0.00670725	−	0.00118267i
$820$	−12.8037	+	6.75890i	−0.447124	+	0.236031i
$821$	−5.18433	+	29.4018i	−0.180934	+	1.02613i	0.750134	+	0.661286i	$0.229989\pi$
$821$	−5.18433	+	29.4018i	−0.180934	+	1.02613i	−0.931069	+	0.364844i	$0.881122\pi$
$822$	2.77925	+	4.81381i	0.0969375	+	0.167901i
$823$	−23.2766	−	27.7400i	−0.811371	−	0.966955i	0.188514	−	0.982070i	$-0.439633\pi$
$823$	−23.2766	−	27.7400i	−0.811371	−	0.966955i	−0.999886	+	0.0151157i	$0.995188\pi$
$824$	15.6753	−	27.1505i	0.546076	−	0.945832i
$825$	0.481712	−	6.34433i	0.0167711	−	0.220881i
$826$	0.568266	+	0.206832i	0.0197725	+	0.00719660i
$827$	11.9890	+	10.0600i	0.416898	+	0.349819i	0.826982	−	0.562229i	$-0.190056\pi$
$827$	11.9890	+	10.0600i	0.416898	+	0.349819i	−0.410084	+	0.912048i	$0.634500\pi$
$828$	−0.00723356	+	0.0125289i	−0.000251384	+	0.000435409i
$829$	35.2290	−	6.21182i	1.22355	−	0.215745i	0.475699	−	0.879608i	$-0.342195\pi$
$829$	35.2290	−	6.21182i	1.22355	−	0.215745i	0.747854	+	0.663863i	$0.231084\pi$
$830$	23.6185	−	18.3395i	0.819808	−	0.636573i
$831$	−3.16588	−	3.77294i	−0.109823	−	0.130882i
$832$	−4.97807	+	1.81187i	−0.172583	+	0.0628152i
$833$	−31.1756	+	11.3470i	−1.08017	+	0.393150i
$834$	3.67979	+	4.38540i	0.127421	+	0.151854i
$835$	20.3314	+	26.1837i	0.703598	+	0.906126i
$836$	9.82639	−	1.73266i	0.339853	−	0.0599252i
$837$	−4.25906	+	7.37692i	−0.147215	+	0.254983i
$838$	3.38351	+	2.83910i	0.116881	+	0.0980752i
$839$	11.7973	+	4.29388i	0.407289	+	0.148241i	0.537537	−	0.843240i	$-0.319355\pi$
$839$	11.7973	+	4.29388i	0.407289	+	0.148241i	−0.130248	+	0.991482i	$0.541577\pi$
$840$	0.126076	+	0.0793053i	0.00435004	+	0.00273629i
$841$	−14.3340	+	24.8272i	−0.494276	+	0.856110i
$842$	−5.08209	−	6.05660i	−0.175140	−	0.208724i
$843$	2.72138	+	4.71357i	0.0937293	+	0.162344i
$844$	2.02141	−	11.4640i	0.0695797	−	0.394606i
$845$	24.3142	−	12.8352i	0.836435	−	0.441543i
$846$	21.8184	+	3.84718i	0.750133	+	0.132269i
$847$	0.463853	−	0.552799i	0.0159382	−	0.0189944i
$848$	0.172980	+	0.475259i	0.00594016	+	0.0163205i
$849$	−0.0587787	+	0.161493i	−0.00201728	+	0.00554243i
$850$	12.7642	−	18.6821i	0.437807	−	0.640791i
$851$	−0.0270624	+	0.00569316i	−0.000927688	+	0.000195159i
$852$		−	1.85764i		−	0.0636418i
$853$	−19.9764	−	7.27082i	−0.683979	−	0.248948i	−0.0234241	−	0.999726i	$-0.507457\pi$
$853$	−19.9764	−	7.27082i	−0.683979	−	0.248948i	−0.660555	+	0.750778i	$0.729679\pi$
$854$	−0.317435	+	0.115537i	−0.0108624	+	0.00395360i
$855$	−2.81210	+	13.0384i	−0.0961718	+	0.445904i
$856$	−33.4812	−	5.90364i	−1.14436	−	0.201782i
$857$	−11.6284			−0.397217			−0.198609	−	0.980079i	$-0.563642\pi$
$857$	−11.6284			−0.397217			−0.198609	+	0.980079i	$0.563642\pi$
$858$	1.00325	+	0.176900i	0.0342504	+	0.00603926i
$859$	5.34045	−	3.08331i	0.182214	−	0.105201i	−0.406119	−	0.913820i	$-0.633118\pi$
$859$	5.34045	−	3.08331i	0.182214	−	0.105201i	0.588332	+	0.808619i	$0.299785\pi$
$860$	0.936181	−	2.29736i	0.0319235	−	0.0783394i
$861$	−0.0671165	+	0.116249i	−0.00228732	+	0.00396176i
$862$	0.260530	−	0.150417i	0.00887367	−	0.00512322i
$863$	−10.6340	+	29.2167i	−0.361986	+	0.994548i	0.616341	+	0.787480i	$0.288614\pi$
$863$	−10.6340	+	29.2167i	−0.361986	+	0.994548i	−0.978327	+	0.207068i	$0.933608\pi$
$864$	5.71994	−	6.81675i	0.194596	−	0.231911i
$865$	50.2860	+	1.90632i	1.70978	+	0.0648167i
$866$	−8.57119	+	1.51133i	−0.291261	+	0.0513571i
$867$	1.53945	−	0.271447i	0.0522825	−	0.00921882i
$868$	−0.336552	+	0.282400i	−0.0114233	+	0.00958530i
$869$	−10.6606	−	29.2897i	−0.361635	−	0.993584i
$870$	−0.234376	+	0.258744i	−0.00794610	+	0.00877225i
$871$	1.74908	+	2.08447i	0.0592653	+	0.0706297i
$872$	31.4156	−	5.53941i	1.06387	−	0.187588i
$873$	−3.59235	−	20.3733i	−0.121583	−	0.689530i
$874$	−0.00767447	−	0.00443086i	−0.000259593	−	0.000149876i
$875$	0.612126	+	0.645341i	0.0206936	+	0.0218165i
$876$	−2.73083	−	0.993942i	−0.0922663	−	0.0335822i
$877$	−12.5309	+	7.23472i	−0.423138	+	0.244299i	−0.696419	−	0.717635i	$-0.745224\pi$
$877$	−12.5309	+	7.23472i	−0.423138	+	0.244299i	0.273281	+	0.961934i	$0.411891\pi$
$878$	16.5477	+	9.55380i	0.558457	+	0.322425i
$879$	−3.34282	+	2.80496i	−0.112751	+	0.0946089i
$880$	5.35779	+	3.37019i	0.180611	+	0.113609i
$881$	6.21884	−	35.2688i	0.209518	−	1.18824i	−0.680652	−	0.732607i	$-0.738303\pi$
$881$	6.21884	−	35.2688i	0.209518	−	1.18824i	0.890170	−	0.455629i	$-0.150585\pi$
$882$	19.4762			0.655798
$883$	−3.08352	+	17.4875i	−0.103769	+	0.588502i	0.887936	+	0.459967i	$0.152139\pi$
$883$	−3.08352	+	17.4875i	−0.103769	+	0.588502i	−0.991705	+	0.128535i	$0.958972\pi$
$884$	−3.32418	−	2.78932i	−0.111804	−	0.0938150i
$885$	−3.39770	+	3.75095i	−0.114212	+	0.126087i
$886$	8.42293	−	23.1418i	0.282974	−	0.777464i
$887$			33.9486i			1.13988i	0.821685	+	0.569942i	$0.193034\pi$
$887$			33.9486i			1.13988i	−0.821685	+	0.569942i	$0.806966\pi$
$888$	5.09013	−	0.167092i	0.170814	−	0.00560725i
$889$	0.708135			0.0237501
$890$	−3.12460	−	22.7246i	−0.104737	−	0.761731i
$891$	34.8591	−	12.6877i	1.16782	−	0.425053i
$892$	−10.1795	+	12.1315i	−0.340836	+	0.406192i
$893$	2.82276	−	16.0087i	0.0944601	−	0.535710i
$894$			4.08472i			0.136613i
$895$	21.3463	−	6.86547i	0.713529	−	0.229487i
$896$	0.314418	−	0.181529i	0.0105040	−	0.00606447i
$897$	0.000696621	0	0.000830200i	2.32595e−5	0	2.77196e-5i
$898$	−21.1306	−	12.1998i	−0.705138	−	0.407112i
$899$	−1.45962	−	2.52813i	−0.0486810	−	0.0843180i
$900$	12.9274	−	9.27494i	0.430915	−	0.309165i
$901$	−2.44075	+	2.90877i	−0.0813132	+	0.0969053i
$902$	−12.6930	+	21.9850i	−0.422631	+	0.732019i
$903$	−0.00399397	−	0.0226510i	−0.000132911	−	0.000753777i
$904$	9.26275	+	52.5317i	0.308075	+	1.74718i
$905$	6.93477	−	17.0177i	0.230520	−	0.565689i
$906$	0.985742	+	2.70830i	0.0327491	+	0.0899774i
$907$	24.1970	−	8.80699i	0.803449	−	0.292431i	0.0925339	−	0.995710i	$-0.470503\pi$
$907$	24.1970	−	8.80699i	0.803449	−	0.292431i	0.710915	+	0.703278i	$0.248281\pi$
$908$	18.9819	−	15.9277i	0.629938	−	0.528581i
$909$	−3.74519	−	21.2400i	−0.124220	−	0.704486i
$910$	−0.112486	+	0.0873442i	−0.00372887	+	0.00289543i
$911$	20.1765	+	11.6489i	0.668477	+	0.385946i	0.795499	−	0.605954i	$-0.207209\pi$
$911$	20.1765	+	11.6489i	0.668477	+	0.385946i	−0.127022	+	0.991900i	$0.540542\pi$
$912$	0.280919	+	0.235719i	0.00930216	+	0.00780544i
$913$	−21.4802	+	59.0164i	−0.710891	+	1.95316i
$914$	1.67988	+	2.90964i	0.0555656	+	0.0962424i
$915$	0.107097	−	2.82508i	0.00354053	−	0.0933943i
$916$	−3.59881	+	3.01976i	−0.118908	+	0.0997757i
$917$	0.851037	+	1.47404i	0.0281037	+	0.0486770i
$918$	−7.49288	−	1.32120i	−0.247302	−	0.0436060i
$919$			5.85605i			0.193173i	0.995325	+	0.0965866i	$0.0307925\pi$
$919$			5.85605i			0.193173i	−0.995325	+	0.0965866i	$0.969208\pi$
$920$	0.00917497	+	0.0285271i	0.000302490	+	0.000940510i
$921$	6.40784	+	5.37682i	0.211146	+	0.177172i
$922$	3.42417	+	9.40782i	0.112769	+	0.309830i
$923$	4.73160	+	1.72216i	0.155743	+	0.0566857i
$924$	−0.110350			−0.00363026
$925$	29.6973	+	6.56299i	0.976440	+	0.215790i
$926$	11.3708			0.373668
$927$	−29.1767	−	10.6195i	−0.958289	−	0.348789i
$928$	1.04304	+	2.86573i	0.0342395	+	0.0940721i
$929$	7.91261	+	6.63947i	0.259604	+	0.217834i	0.763295	−	0.646050i	$-0.223580\pi$
$929$	7.91261	+	6.63947i	0.259604	+	0.217834i	−0.503690	+	0.863884i	$0.668025\pi$
$930$	0.939826	+	2.92214i	0.0308181	+	0.0958206i
$931$		−	14.2901i		−	0.468340i
$932$	−6.00660	−	1.05912i	−0.196753	−	0.0346928i
$933$	0.331671	+	0.574471i	0.0108584	+	0.0188074i
$934$	−0.970580	+	0.814413i	−0.0317583	+	0.0266484i
$935$	−1.80022	+	47.4873i	−0.0588734	+	1.55300i
$936$	3.61082	+	6.25412i	0.118023	+	0.204422i
$937$	−16.5873	+	45.5732i	−0.541884	+	1.48881i	0.302540	+	0.953137i	$0.402165\pi$
$937$	−16.5873	+	45.5732i	−0.541884	+	1.48881i	−0.844424	+	0.535676i	$0.820057\pi$
$938$	0.188502	+	0.158172i	0.00615481	+	0.00516450i
$939$	0.841171	+	0.485650i	0.0274506	+	0.0158486i
$940$	−15.3155	+	11.8923i	−0.499536	+	0.387885i
$941$	−3.34738	−	18.9839i	−0.109122	−	0.618859i	−0.989494	−	0.144576i	$-0.953818\pi$
$941$	−3.34738	−	18.9839i	−0.109122	−	0.618859i	0.880372	−	0.474283i	$-0.157293\pi$
$942$	3.73226	−	3.13174i	0.121604	−	0.102038i
$943$	−0.0253777	+	0.00923673i	−0.000826412	+	0.000300789i
$944$	−1.72200	−	4.73117i	−0.0560465	−	0.153986i
$945$	0.112873	−	0.276986i	0.00367175	−	0.00901037i
$946$	−0.755338	−	4.28373i	−0.0245581	−	0.139276i
$947$	1.99999	+	11.3425i	0.0649910	+	0.368582i	0.999906	+	0.0137104i	$0.00436430\pi$
$947$	1.99999	+	11.3425i	0.0649910	+	0.368582i	−0.934915	+	0.354872i	$0.884525\pi$
$948$	−1.07704	+	1.86550i	−0.0349808	+	0.0605885i
$949$	5.06334	−	6.03426i	0.164363	−	0.195880i
$950$	5.68129	+	7.91860i	0.184325	+	0.256913i
$951$	−1.37066	−	2.37405i	−0.0444467	−	0.0769839i
$952$	−0.963409	−	0.556224i	−0.0312243	−	0.0180273i
$953$	−13.4126	−	15.9845i	−0.434477	−	0.517790i	0.503731	−	0.863860i	$-0.331960\pi$
$953$	−13.4126	−	15.9845i	−0.434477	−	0.517790i	−0.938208	+	0.346071i	$0.887516\pi$
$954$	1.93046	−	1.11455i	0.0625011	−	0.0360850i
$955$	−46.8716	+	15.0750i	−1.51673	+	0.487815i
$956$		−	23.0166i		−	0.744409i
$957$	0.127325	−	0.722098i	0.00411585	−	0.0233421i
$958$	24.5027	−	29.2012i	0.791647	−	0.943448i
$959$	1.53363	−	0.558195i	0.0495234	−	0.0180251i
$960$	−0.546133	−	3.97192i	−0.0176264	−	0.128193i
$961$	5.33289			0.172029
$962$	−1.51448	+	4.62812i	−0.0488287	+	0.149216i
$963$			33.6708i			1.08503i
$964$	2.53239	−	6.95768i	0.0815627	−	0.224092i
$965$	−8.84434	+	9.76387i	−0.284709	+	0.314310i
$966$	7.50763e−5	0	6.29965e-5i	2.41554e−6	0	2.02688e-6i
$967$	−4.95322	+	28.0911i	−0.159285	+	0.903349i	0.795479	+	0.605982i	$0.207220\pi$
$967$	−4.95322	+	28.0911i	−0.159285	+	0.903349i	−0.954763	+	0.297367i	$0.903892\pi$
$968$	−26.7370			−0.859361
$969$	−0.478089	+	2.71138i	−0.0153584	+	0.0871021i
$970$	−12.7949	−	8.04836i	−0.410820	−	0.258417i
$971$	32.7310	−	27.4646i	1.05039	−	0.881380i	0.0572532	−	0.998360i	$-0.481766\pi$
$971$	32.7310	−	27.4646i	1.05039	−	0.881380i	0.993134	+	0.116980i	$0.0373213\pi$
$972$	−6.98167	−	4.03087i	−0.223937	−	0.129290i
$973$	1.45567	−	0.840430i	0.0466666	−	0.0269430i
$974$	−20.9527	−	7.62617i	−0.671369	−	0.244358i
$975$	−0.321679	−	1.14764i	−0.0103020	−	0.0367539i
$976$	2.43566	+	1.40623i	0.0779637	+	0.0450123i
$977$	6.88994	+	39.0748i	0.220429	+	1.25011i	0.871234	+	0.490869i	$0.163321\pi$
$977$	6.88994	+	39.0748i	0.220429	+	1.25011i	−0.650805	+	0.759245i	$0.725568\pi$
$978$	−6.06757	+	1.06988i	−0.194019	+	0.0342109i
$979$	30.9677	+	36.9058i	0.989731	+	1.17952i
$980$	−11.4437	+	12.6335i	−0.365557	+	0.403563i
$981$	−10.8056	−	29.6881i	−0.344996	−	0.947870i
$982$	−2.83951	+	2.38263i	−0.0906123	+	0.0760327i
$983$	−26.3723	+	4.65015i	−0.841146	+	0.148317i	−0.577590	−	0.816327i	$-0.696007\pi$
$983$	−26.3723	+	4.65015i	−0.841146	+	0.148317i	−0.263556	+	0.964644i	$0.584896\pi$
$984$	4.89791	−	0.863633i	0.156140	−	0.0275316i
$985$	−14.9332	−	0.566110i	−0.475812	−	0.0180378i
$986$	1.67606	−	1.99745i	0.0533767	−	0.0636119i
$987$	−0.0614874	+	0.168935i	−0.00195717	+	0.00537727i
$988$	1.61871	−	0.934562i	0.0514980	−	0.0297324i
$989$	0.00231373	−	0.00400750i	7.35723e−5	−	0.000127431i
$990$	10.5277	−	25.8348i	0.334593	−	0.821082i
$991$	−21.3558	+	12.3298i	−0.678390	+	0.391669i	−0.799248	−	0.601001i	$-0.794769\pi$
$991$	−21.3558	+	12.3298i	−0.678390	+	0.391669i	0.120858	+	0.992670i	$0.461435\pi$
$992$	26.4063	+	4.65615i	0.838402	+	0.147833i
$993$	3.09646			0.0982633
$994$	0.448429	+	0.0790702i	0.0142233	+	0.00250795i
$995$	4.97769	−	23.0792i	0.157803	−	0.731661i
$996$	4.07857	−	1.48448i	0.129234	−	0.0470375i
$997$	−35.0601	−	12.7608i	−1.11036	−	0.404140i	−0.279237	−	0.960222i	$-0.590082\pi$
$997$	−35.0601	−	12.7608i	−1.11036	−	0.404140i	−0.831127	+	0.556083i	$0.812304\pi$
$998$			26.7933i			0.848127i
$999$	−2.10542	−	10.0081i	−0.0666127	−	0.316643i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	185.2.v.a.169.6	yes	96
5.2	odd	4		925.2.bb.e.576.11		96
5.3	odd	4		925.2.bb.e.576.6		96
5.4	even	2	inner	185.2.v.a.169.11	yes	96
37.30	even	18	inner	185.2.v.a.104.11	yes	96
185.67	odd	36		925.2.bb.e.326.11		96
185.104	even	18	inner	185.2.v.a.104.6	✓	96
185.178	odd	36		925.2.bb.e.326.6		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
185.2.v.a.104.6	✓	96	185.104	even	18	inner
185.2.v.a.104.11	yes	96	37.30	even	18	inner
185.2.v.a.169.6	yes	96	1.1	even	1	trivial
185.2.v.a.169.11	yes	96	5.4	even	2	inner
925.2.bb.e.326.6		96	185.178	odd	36
925.2.bb.e.326.11		96	185.67	odd	36
925.2.bb.e.576.6		96	5.3	odd	4
925.2.bb.e.576.11		96	5.2	odd	4

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:	\( N \)	\(=\)	\( 185 = 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	185.v (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.896403 - 0.326264i) q^{2} +(0.0971484 + 0.266913i) q^{3} +(-0.834998 - 0.700647i) q^{4} +(0.684633 + 2.12868i) q^{5} -0.270958i q^{6} +(-0.0783483 - 0.0138149i) q^{7} +(1.47383 + 2.55275i) q^{8} +(2.23633 - 1.87650i) q^{9} +(0.0808050 - 2.13153i) q^{10} +(2.24001 + 3.87981i) q^{11} +(0.105893 - 0.290938i) q^{12} +(0.642880 + 0.539440i) q^{13} +(0.0657244 + 0.0379460i) q^{14} +(-0.501661 + 0.389535i) q^{15} +(-0.109719 - 0.622249i) q^{16} +(3.63394 - 3.04924i) q^{17} +(-2.61689 + 0.952469i) q^{18} +(0.698848 + 1.92007i) q^{19} +(0.919785 - 2.25713i) q^{20} +(-0.00392403 - 0.0222543i) q^{21} +(-0.742109 - 4.20871i) q^{22} +(0.00227321 - 0.00393731i) q^{23} +(-0.538182 + 0.641381i) q^{24} +(-4.06256 + 2.91473i) q^{25} +(-0.400280 - 0.693304i) q^{26} +(1.45608 + 0.840670i) q^{27} +(0.0557413 + 0.0664299i) q^{28} +(-0.499013 + 0.288105i) q^{29} +(0.576782 - 0.185507i) q^{30} +5.06627i q^{31} +(0.919048 - 5.21218i) q^{32} +(-0.817959 + 0.974805i) q^{33} +(-4.25234 + 1.54772i) q^{34} +(-0.0242322 - 0.176237i) q^{35} -3.18209 q^{36} +(-4.06070 - 4.52888i) q^{37} -1.94917i q^{38} +(-0.0815288 + 0.223999i) q^{39} +(-4.42496 + 4.88501i) q^{40} +(-4.55042 - 3.81825i) q^{41} +(-0.00374326 + 0.0212291i) q^{42} +1.01783 q^{43} +(0.847972 - 4.80909i) q^{44} +(5.52554 + 3.47571i) q^{45} +(-0.00332232 + 0.00278775i) q^{46} +(-6.88975 - 3.97780i) q^{47} +(0.155427 - 0.0897359i) q^{48} +(-6.57190 - 2.39198i) q^{49} +(4.59266 - 1.28730i) q^{50} +(1.16691 + 0.673718i) q^{51} +(-0.158846 - 0.900863i) q^{52} +(-0.788285 + 0.138996i) q^{53} +(-1.03096 - 1.22865i) q^{54} +(-6.72529 + 7.42451i) q^{55} +(-0.0802061 - 0.220365i) q^{56} +(-0.444599 + 0.373063i) q^{57} +(0.541315 - 0.0954485i) q^{58} +(7.84732 - 1.38369i) q^{59} +(0.691813 + 0.0262262i) q^{60} +(-2.86116 + 3.40979i) q^{61} +(1.65294 - 4.54142i) q^{62} +(-0.201136 + 0.116126i) q^{63} +(-3.15623 + 5.46676i) q^{64} +(-0.708159 + 1.73780i) q^{65} +(1.05127 - 0.606948i) q^{66} +(3.19314 + 0.563037i) q^{67} -5.17077 q^{68} +(0.00127176 + 0.000224245i) q^{69} +(-0.0357778 + 0.165885i) q^{70} +(5.63810 - 2.05210i) q^{71} +(8.08622 + 2.94314i) q^{72} -9.38629i q^{73} +(2.16241 + 5.38456i) q^{74} +(-1.17265 - 0.801188i) q^{75} +(0.761753 - 2.09290i) q^{76} +(-0.121902 - 0.334922i) q^{77} +(0.146165 - 0.174193i) q^{78} +(-6.85173 - 1.20814i) q^{79} +(1.24945 - 0.659569i) q^{80} +(1.43787 - 8.15459i) q^{81} +(2.83325 + 4.90733i) q^{82} +(9.01103 + 10.7389i) q^{83} +(-0.0123158 + 0.0213316i) q^{84} +(8.97877 + 5.64789i) q^{85} +(-0.912382 - 0.332080i) q^{86} +(-0.125377 - 0.105204i) q^{87} +(-6.60280 + 11.4364i) q^{88} +(10.5904 - 1.86737i) q^{89} +(-3.81911 - 4.91843i) q^{90} +(-0.0429162 - 0.0511455i) q^{91} +(-0.00465679 + 0.00169493i) q^{92} +(-1.35225 + 0.492180i) q^{93} +(4.87818 + 5.81359i) q^{94} +(-3.60876 + 2.80217i) q^{95} +(1.48048 - 0.261049i) q^{96} +(3.54321 - 6.13702i) q^{97} +(5.11066 + 4.28835i) q^{98} +(12.2899 + 4.47315i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 12 q^{4} - 12 q^{5} - 6 q^{9} - 3 q^{10} - 30 q^{11} - 36 q^{14} - 21 q^{15} - 18 q^{19} - 39 q^{20} - 24 q^{21} + 96 q^{24} + 36 q^{25} + 48 q^{26} - 18 q^{29} - 30 q^{30} - 54 q^{34} + 6 q^{35}+ \cdots - 24 q^{99}+O(q^{100}) \) 96 * q - 12 * q^4 - 12 * q^5 - 6 * q^9 - 3 * q^10 - 30 * q^11 - 36 * q^14 - 21 * q^15 - 18 * q^19 - 39 * q^20 - 24 * q^21 + 96 * q^24 + 36 * q^25 + 48 * q^26 - 18 * q^29 - 30 * q^30 - 54 * q^34 + 6 * q^35 + 24 * q^36 - 36 * q^39 - 63 * q^40 + 72 * q^41 - 84 * q^44 - 36 * q^45 - 18 * q^46 - 6 * q^49 - 27 * q^50 - 18 * q^51 + 24 * q^54 + 6 * q^55 + 90 * q^56 + 18 * q^59 + 108 * q^60 - 144 * q^61 + 66 * q^64 + 27 * q^65 - 36 * q^66 - 6 * q^69 - 66 * q^70 - 30 * q^71 - 6 * q^74 + 96 * q^75 - 54 * q^76 + 60 * q^79 - 18 * q^81 + 48 * q^84 + 21 * q^85 - 72 * q^86 + 108 * q^89 + 165 * q^90 - 54 * q^91 + 6 * q^94 + 57 * q^95 + 24 * q^96 - 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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