LMFDB - Embedded newform 456.2.bk.a.301.29

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [456,2,Mod(61,456)] 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("456.61"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(456, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 9, 0, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 456 = 2^{3} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	456.bk (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:	$3.64117833217$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$40$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			301.29
Character	$\chi$	$=$	456.301
Dual form			456.2.bk.a.253.29

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.919662 - 1.07435i) q^{2} +(0.342020 + 0.939693i) q^{3} +(-0.308442 - 1.97607i) q^{4} +(-3.60963 - 0.636475i) q^{5} +(1.32410 + 0.496752i) q^{6} +(-0.686638 - 1.18929i) q^{7} +(-2.40665 - 1.48595i) q^{8} +(-0.766044 + 0.642788i) q^{9} +(-4.00344 + 3.29265i) q^{10} +(-1.75591 - 1.01378i) q^{11} +(1.75141 - 0.965698i) q^{12} +(0.0200547 - 0.0551000i) q^{13} +(-1.90919 - 0.356060i) q^{14} +(-0.636475 - 3.60963i) q^{15} +(-3.80973 + 1.21901i) q^{16} +(-0.334054 - 0.280304i) q^{17} +(-0.0139254 + 1.41415i) q^{18} +(-3.22669 + 2.93061i) q^{19} +(-0.144359 + 7.32921i) q^{20} +(0.882725 - 1.05199i) q^{21} +(-2.70399 + 0.954126i) q^{22} +(-1.46664 - 8.31776i) q^{23} +(0.573209 - 2.76973i) q^{24} +(7.92587 + 2.88478i) q^{25} +(-0.0407529 - 0.0722191i) q^{26} +(-0.866025 - 0.500000i) q^{27} +(-2.13834 + 1.72368i) q^{28} +(-1.82717 - 2.17753i) q^{29} +(-4.46334 - 2.63585i) q^{30} +(2.08584 + 3.61278i) q^{31} +(-2.19402 + 5.21404i) q^{32} +(0.352081 - 1.99675i) q^{33} +(-0.608361 + 0.101104i) q^{34} +(1.72156 + 4.72993i) q^{35} +(1.50648 + 1.31550i) q^{36} -9.42746i q^{37} +(0.181036 + 6.16176i) q^{38} +0.0586362 q^{39} +(7.74135 + 6.89549i) q^{40} +(4.55055 - 1.65626i) q^{41} +(-0.318394 - 1.91583i) q^{42} +(3.48899 + 0.615202i) q^{43} +(-1.46170 + 3.78250i) q^{44} +(3.17426 - 1.83266i) q^{45} +(-10.2850 - 6.07384i) q^{46} +(3.66354 - 3.07407i) q^{47} +(-2.44850 - 3.16305i) q^{48} +(2.55706 - 4.42895i) q^{49} +(10.3884 - 5.86211i) q^{50} +(0.149147 - 0.409778i) q^{51} +(-0.115067 - 0.0226345i) q^{52} +(-9.46348 + 1.66867i) q^{53} +(-1.33362 + 0.470580i) q^{54} +(5.69295 + 4.77695i) q^{55} +(-0.114726 + 3.88252i) q^{56} +(-3.85747 - 2.02976i) q^{57} +(-4.01980 - 0.0395839i) q^{58} +(0.840408 - 1.00156i) q^{59} +(-6.93658 + 2.37108i) q^{60} +(9.78309 - 1.72502i) q^{61} +(5.79965 + 1.08162i) q^{62} +(1.29046 + 0.469688i) q^{63} +(3.58393 + 7.15230i) q^{64} +(-0.107460 + 0.186126i) q^{65} +(-1.82140 - 2.21459i) q^{66} +(5.03340 + 5.99857i) q^{67} +(-0.450866 + 0.746572i) q^{68} +(7.31451 - 4.22303i) q^{69} +(6.66484 + 2.50039i) q^{70} +(-2.32739 + 13.1993i) q^{71} +(2.79875 - 0.408665i) q^{72} +(4.37981 - 1.59412i) q^{73} +(-10.1284 - 8.67008i) q^{74} +8.43453i q^{75} +(6.78635 + 5.47224i) q^{76} +2.78439i q^{77} +(0.0539255 - 0.0629956i) q^{78} +(-5.63803 + 2.05207i) q^{79} +(14.5276 - 1.97537i) q^{80} +(0.173648 - 0.984808i) q^{81} +(2.40556 - 6.41207i) q^{82} +(-6.46743 + 3.73397i) q^{83} +(-2.35108 - 1.41985i) q^{84} +(1.02740 + 1.22441i) q^{85} +(3.86963 - 3.18260i) q^{86} +(1.42128 - 2.46174i) q^{87} +(2.71945 + 5.04899i) q^{88} +(-14.5073 - 5.28024i) q^{89} +(0.950334 - 5.09568i) q^{90} +(-0.0793003 + 0.0139828i) q^{91} +(-15.9841 + 5.46374i) q^{92} +(-2.68151 + 3.19570i) q^{93} +(0.0665969 - 6.76302i) q^{94} +(13.5124 - 8.52473i) q^{95} +(-5.65000 - 0.278400i) q^{96} +(-5.92525 - 4.97188i) q^{97} +(-2.40660 - 6.82030i) q^{98} +(1.99675 - 0.352081i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 6 q^{4} + 6 q^{6} - 24 q^{10} + 18 q^{14} - 6 q^{16} + 60 q^{20} - 36 q^{28} - 72 q^{31} - 90 q^{32} + 66 q^{34} - 6 q^{36} + 72 q^{38} - 114 q^{40} - 60 q^{44} + 30 q^{46} + 72 q^{47} + 24 q^{48}+ \cdots - 12 q^{98}+O(q^{100}) $ 240 * q + 6 * q^4 + 6 * q^6 - 24 * q^10 + 18 * q^14 - 6 * q^16 + 60 * q^20 - 36 * q^28 - 72 * q^31 - 90 * q^32 + 66 * q^34 - 6 * q^36 + 72 * q^38 - 114 * q^40 - 60 * q^44 + 30 * q^46 + 72 * q^47 + 24 * q^48 - 120 * q^49 + 18 * q^50 + 6 * q^52 - 6 * q^54 + 72 * q^58 - 12 * q^60 + 12 * q^62 + 30 * q^64 - 48 * q^66 - 78 * q^68 - 108 * q^70 - 36 * q^72 - 24 * q^73 - 96 * q^74 - 48 * q^76 - 96 * q^78 - 114 * q^80 - 66 * q^82 - 36 * q^84 - 24 * q^86 - 24 * q^88 + 6 * q^90 - 108 * q^94 + 120 * q^95 - 12 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/456\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$343$
$\chi(n)$	$e\left(\frac{2}{9}\right)$	$-1$	$1$	$1$

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 $

$2$	0.919662	−	1.07435i	0.650299	−	0.759678i
$2$	0.919662	−	1.07435i	0.650299	−	0.759678i
$3$	0.342020	+	0.939693i	0.197465	+	0.542532i
$3$	0.342020	+	0.939693i	0.197465	+	0.542532i
$4$	−0.308442	−	1.97607i	−0.154221	−	0.988036i
$5$	−3.60963	−	0.636475i	−1.61428	−	0.284640i	−0.707646	−	0.706567i	$-0.750243\pi$
$5$	−3.60963	−	0.636475i	−1.61428	−	0.284640i	−0.906630	+	0.421927i	$0.861354\pi$
$6$	1.32410	+	0.496752i	0.540561	+	0.202798i
$7$	−0.686638	−	1.18929i	−0.259525	−	0.449510i	0.706590	−	0.707623i	$-0.250233\pi$
$7$	−0.686638	−	1.18929i	−0.259525	−	0.449510i	−0.966115	+	0.258113i	$0.916899\pi$
$8$	−2.40665	−	1.48595i	−0.850879	−	0.525361i
$9$	−0.766044	+	0.642788i	−0.255348	+	0.214263i
$10$	−4.00344	+	3.29265i	−1.26600	+	1.04123i
$11$	−1.75591	−	1.01378i	−0.529427	−	0.305665i	0.211356	−	0.977409i	$-0.432212\pi$
$11$	−1.75591	−	1.01378i	−0.529427	−	0.305665i	−0.740783	+	0.671744i	$0.765545\pi$
$12$	1.75141	−	0.965698i	0.505588	−	0.278773i
$13$	0.0200547	−	0.0551000i	0.00556219	−	0.0152820i	−0.936880	−	0.349650i	$-0.886301\pi$
$13$	0.0200547	−	0.0551000i	0.00556219	−	0.0152820i	0.942443	+	0.334368i	$0.108523\pi$
$14$	−1.90919	−	0.356060i	−0.510252	−	0.0951610i
$15$	−0.636475	−	3.60963i	−0.164337	−	0.932003i
$16$	−3.80973	+	1.21901i	−0.952432	+	0.304752i
$17$	−0.334054	−	0.280304i	−0.0810200	−	0.0679838i	0.601378	−	0.798964i	$-0.294619\pi$
$17$	−0.334054	−	0.280304i	−0.0810200	−	0.0679838i	−0.682398	+	0.730981i	$0.739063\pi$
$18$	−0.0139254	+	1.41415i	−0.00328225	+	0.333317i
$19$	−3.22669	+	2.93061i	−0.740252	+	0.672329i
$19$	−3.22669	+	2.93061i	−0.740252	+	0.672329i
$20$	−0.144359	+	7.32921i	−0.0322796	+	1.63886i
$21$	0.882725	−	1.05199i	0.192626	−	0.229563i
$22$	−2.70399	+	0.954126i	−0.576493	+	0.203420i
$23$	−1.46664	−	8.31776i	−0.305817	−	1.73437i	−0.619636	−	0.784889i	$-0.712720\pi$
$23$	−1.46664	−	8.31776i	−0.305817	−	1.73437i	0.313820	−	0.949483i	$-0.398391\pi$
$24$	0.573209	−	2.76973i	0.117006	−	0.565370i
$25$	7.92587	+	2.88478i	1.58517	+	0.576956i
$26$	−0.0407529	−	0.0722191i	−0.00799230	−	0.0141633i
$27$	−0.866025	−	0.500000i	−0.166667	−	0.0962250i
$28$	−2.13834	+	1.72368i	−0.404108	+	0.325744i
$29$	−1.82717	−	2.17753i	−0.339297	−	0.404358i	0.569235	−	0.822175i	$-0.307240\pi$
$29$	−1.82717	−	2.17753i	−0.339297	−	0.404358i	−0.908531	+	0.417817i	$0.862795\pi$
$30$	−4.46334	−	2.63585i	−0.814890	−	0.481237i
$31$	2.08584	+	3.61278i	0.374628	+	0.648875i	0.990271	−	0.139150i	$-0.0444370\pi$
$31$	2.08584	+	3.61278i	0.374628	+	0.648875i	−0.615643	+	0.788025i	$0.711104\pi$
$32$	−2.19402	+	5.21404i	−0.387852	+	0.921722i
$33$	0.352081	−	1.99675i	0.0612894	−	0.347589i
$34$	−0.608361	+	0.101104i	−0.104333	+	0.0173392i
$35$	1.72156	+	4.72993i	0.290996	+	0.799505i
$36$	1.50648	+	1.31550i	0.251079	+	0.219249i
$37$		−	9.42746i		−	1.54987i	−0.632044	−	0.774933i	$-0.717784\pi$
$37$		−	9.42746i		−	1.54987i	0.632044	−	0.774933i	$-0.282216\pi$
$38$	0.181036	+	6.16176i	0.0293679	+	0.999569i
$39$	0.0586362			0.00938930
$40$	7.74135	+	6.89549i	1.22401	+	1.09027i
$41$	4.55055	−	1.65626i	0.710676	−	0.258665i	0.0387136	−	0.999250i	$-0.487674\pi$
$41$	4.55055	−	1.65626i	0.710676	−	0.258665i	0.671962	+	0.740586i	$0.265452\pi$
$42$	−0.318394	−	1.91583i	−0.0491293	−	0.295619i
$43$	3.48899	+	0.615202i	0.532065	+	0.0938175i	0.433225	−	0.901286i	$-0.357376\pi$
$43$	3.48899	+	0.615202i	0.532065	+	0.0938175i	0.0988403	+	0.995103i	$0.468487\pi$
$44$	−1.46170	+	3.78250i	−0.220359	+	0.570233i
$45$	3.17426	−	1.83266i	0.473190	−	0.273196i
$46$	−10.2850	−	6.07384i	−1.51644	−	0.895539i
$47$	3.66354	−	3.07407i	0.534382	−	0.448399i	−0.335230	−	0.942136i	$-0.608814\pi$
$47$	3.66354	−	3.07407i	0.534382	−	0.448399i	0.869611	+	0.493737i	$0.164369\pi$
$48$	−2.44850	−	3.16305i	−0.353410	−	0.456546i
$49$	2.55706	−	4.42895i	0.365294	−	0.632707i
$50$	10.3884	−	5.86211i	1.46914	−	0.829027i
$51$	0.149147	−	0.409778i	0.0208847	−	0.0573804i
$52$	−0.115067	−	0.0226345i	−0.0159570	−	0.00313884i
$53$	−9.46348	+	1.66867i	−1.29991	+	0.229209i	−0.780413	−	0.625264i	$-0.784991\pi$
$53$	−9.46348	+	1.66867i	−1.29991	+	0.229209i	−0.519496	+	0.854473i	$0.673880\pi$
$54$	−1.33362	+	0.470580i	−0.181483	+	0.0640379i
$55$	5.69295	+	4.77695i	0.767637	+	0.644124i
$56$	−0.114726	+	3.88252i	−0.0153309	+	0.518823i
$57$	−3.85747	−	2.02976i	−0.510934	−	0.268849i
$58$	−4.01980	−	0.0395839i	−0.527826	−	0.00519762i
$59$	0.840408	−	1.00156i	0.109412	−	0.130392i	−0.708559	−	0.705651i	$-0.750654\pi$
$59$	0.840408	−	1.00156i	0.109412	−	0.130392i	0.817971	+	0.575259i	$0.195099\pi$
$60$	−6.93658	+	2.37108i	−0.895508	+	0.306106i
$61$	9.78309	−	1.72502i	1.25260	−	0.220867i	0.492290	−	0.870431i	$-0.336160\pi$
$61$	9.78309	−	1.72502i	1.25260	−	0.220867i	0.760306	+	0.649565i	$0.225049\pi$
$62$	5.79965	+	1.08162i	0.736557	+	0.137366i
$63$	1.29046	+	0.469688i	0.162582	+	0.0591752i
$64$	3.58393	+	7.15230i	0.447991	+	0.894038i
$65$	−0.107460	+	0.186126i	−0.0133288	+	0.0230861i
$66$	−1.82140	−	2.21459i	−0.224199	−	0.272597i
$67$	5.03340	+	5.99857i	0.614927	+	0.732842i	0.980189	−	0.198063i	$-0.0634650\pi$
$67$	5.03340	+	5.99857i	0.614927	+	0.732842i	−0.365262	+	0.930905i	$0.619021\pi$
$68$	−0.450866	+	0.746572i	−0.0546755	+	0.0905352i
$69$	7.31451	−	4.22303i	0.880564	−	0.508394i
$70$	6.66484	+	2.50039i	0.796601	+	0.298854i
$71$	−2.32739	+	13.1993i	−0.276210	+	1.56646i	0.458882	+	0.888497i	$0.348250\pi$
$71$	−2.32739	+	13.1993i	−0.276210	+	1.56646i	−0.735092	+	0.677967i	$0.762861\pi$
$72$	2.79875	−	0.408665i	0.329836	−	0.0481616i
$73$	4.37981	−	1.59412i	0.512618	−	0.186578i	−0.0727428	−	0.997351i	$-0.523175\pi$
$73$	4.37981	−	1.59412i	0.512618	−	0.186578i	0.585361	+	0.810773i	$0.300953\pi$
$74$	−10.1284	−	8.67008i	−1.17740	−	1.00788i
$75$			8.43453i			0.973936i
$76$	6.78635	+	5.47224i	0.778448	+	0.627709i
$77$			2.78439i			0.317310i
$78$	0.0539255	−	0.0629956i	0.00610586	−	0.00713284i
$79$	−5.63803	+	2.05207i	−0.634328	+	0.230876i	−0.639114	−	0.769112i	$-0.720699\pi$
$79$	−5.63803	+	2.05207i	−0.634328	+	0.230876i	0.00478608	+	0.999989i	$0.498477\pi$
$80$	14.5276	−	1.97537i	1.62423	−	0.220854i
$81$	0.173648	−	0.984808i	0.0192942	−	0.109423i
$82$	2.40556	−	6.41207i	0.265650	−	0.708094i
$83$	−6.46743	+	3.73397i	−0.709893	+	0.409857i	−0.811021	−	0.585017i	$-0.801088\pi$
$83$	−6.46743	+	3.73397i	−0.709893	+	0.409857i	0.101129	+	0.994873i	$0.467755\pi$
$84$	−2.35108	−	1.41985i	−0.256524	−	0.154918i
$85$	1.02740	+	1.22441i	0.111438	+	0.132806i
$86$	3.86963	−	3.18260i	0.417273	−	0.343189i
$87$	1.42128	−	2.46174i	0.152378	−	0.263926i
$88$	2.71945	+	5.04899i	0.289894	+	0.538224i
$89$	−14.5073	−	5.28024i	−1.53777	−	0.559704i	−0.572264	−	0.820070i	$-0.693935\pi$
$89$	−14.5073	−	5.28024i	−1.53777	−	0.559704i	−0.965510	+	0.260366i	$0.916157\pi$
$90$	0.950334	−	5.09568i	0.100174	−	0.537132i
$91$	−0.0793003	+	0.0139828i	−0.00831293	+	0.00146579i
$92$	−15.9841	+	5.46374i	−1.66646	+	0.569635i
$93$	−2.68151	+	3.19570i	−0.278059	+	0.331378i
$94$	0.0665969	−	6.76302i	0.00686894	−	0.697552i
$95$	13.5124	−	8.52473i	1.38634	−	0.874619i
$96$	−5.65000	−	0.278400i	−0.576651	−	0.0284141i
$97$	−5.92525	−	4.97188i	−0.601618	−	0.504818i	0.290347	−	0.956921i	$-0.406229\pi$
$97$	−5.92525	−	4.97188i	−0.601618	−	0.504818i	−0.891965	+	0.452104i	$0.850674\pi$
$98$	−2.40660	−	6.82030i	−0.243103	−	0.688955i
$99$	1.99675	−	0.352081i	0.200681	−	0.0353854i
$100$	3.25586	−	16.5519i	0.325586	−	1.65519i
$101$	1.91713	−	5.26728i	0.190762	−	0.524114i	−0.807031	−	0.590508i	$-0.798927\pi$
$101$	1.91713	−	5.26728i	0.190762	−	0.524114i	0.997793	+	0.0663941i	$0.0211495\pi$
$102$	−0.303079	−	0.537093i	−0.0300093	−	0.0531801i
$103$	−5.98945	+	10.3740i	−0.590158	+	1.02218i	0.404053	+	0.914736i	$0.367601\pi$
$103$	−5.98945	+	10.3740i	−0.590158	+	1.02218i	−0.994211	+	0.107448i	$0.965732\pi$
$104$	−0.130140	+	0.102806i	−0.0127613	+	0.0100810i
$105$	−3.85588	+	3.23547i	−0.376295	+	0.315749i
$106$	−6.91048	+	11.7017i	−0.671205	+	1.13657i
$107$	10.3330	−	5.96577i	0.998931	−	0.576733i	0.0909992	−	0.995851i	$-0.470994\pi$
$107$	10.3330	−	5.96577i	0.998931	−	0.576733i	0.907932	+	0.419118i	$0.137661\pi$
$108$	−0.720917	+	1.86555i	−0.0693703	+	0.179513i
$109$	−7.13908	−	1.25881i	−0.683800	−	0.120572i	−0.179052	−	0.983840i	$-0.557303\pi$
$109$	−7.13908	−	1.25881i	−0.683800	−	0.120572i	−0.504747	+	0.863267i	$0.668414\pi$
$110$	10.3677	−	1.72302i	0.988520	−	0.164283i
$111$	8.85892	−	3.22438i	0.840851	−	0.306045i
$112$	4.06566	+	3.69386i	0.384169	+	0.349037i
$113$	3.68163			0.346339			0.173170	−	0.984892i	$-0.444599\pi$
$113$	3.68163			0.346339			0.173170	+	0.984892i	$0.444599\pi$
$114$	−5.72824	+	2.27756i	−0.536499	+	0.213313i
$115$			30.9575i			2.88680i
$116$	−3.73939	+	4.28226i	−0.347194	+	0.397598i
$117$	0.0200547	+	0.0551000i	0.00185406	+	0.00509399i
$118$	−0.303130	−	1.82399i	−0.0279054	−	0.167912i
$119$	−0.103990	+	0.589755i	−0.00953273	+	0.0540628i
$120$	−3.83194	+	9.63289i	−0.349807	+	0.879358i
$121$	−3.44452	−	5.96608i	−0.313138	−	0.542371i
$122$	7.14387	−	12.0969i	0.646775	−	1.09520i
$123$	3.11276	+	3.70964i	0.280668	+	0.334487i
$124$	6.49576	−	5.23611i	0.583337	−	0.470217i
$125$	−10.9021	−	6.29432i	−0.975112	−	0.562981i
$126$	1.69139	−	0.954445i	0.150681	−	0.0850287i
$127$	−14.2829	−	5.19856i	−1.26740	−	0.461297i	−0.381157	−	0.924510i	$-0.624474\pi$
$127$	−14.2829	−	5.19856i	−1.26740	−	0.461297i	−0.886247	+	0.463213i	$0.846696\pi$
$128$	10.9801	+	2.72732i	0.970509	+	0.241063i
$129$	0.615202	+	3.48899i	0.0541655	+	0.307188i
$130$	0.101137	+	0.286623i	0.00887032	+	0.0251385i
$131$	−4.30581	+	5.13147i	−0.376200	+	0.448338i	−0.920611	−	0.390481i	$-0.872309\pi$
$131$	−4.30581	+	5.13147i	−0.376200	+	0.448338i	0.544411	+	0.838819i	$0.316753\pi$
$132$	−4.05432	−	0.0798552i	−0.352883	−	0.00695050i
$133$	5.70092	+	1.82520i	0.494333	+	0.158265i
$134$	11.0736	+	0.109044i	0.956611	+	0.00941995i
$135$	2.80779	+	2.35602i	0.241656	+	0.202774i
$136$	0.387434	+	1.17098i	0.0332222	+	0.100411i
$137$	−1.67558	−	9.50269i	−0.143154	−	0.811869i	−0.968830	−	0.247725i	$-0.920317\pi$
$137$	−1.67558	−	9.50269i	−0.143154	−	0.811869i	0.825676	−	0.564145i	$-0.190794\pi$
$138$	2.18988	−	11.7421i	0.186415	−	0.999553i
$139$	7.22250	−	19.8436i	0.612604	−	1.68312i	−0.111791	−	0.993732i	$-0.535659\pi$
$139$	7.22250	−	19.8436i	0.612604	−	1.68312i	0.724396	−	0.689384i	$-0.242119\pi$
$140$	8.81569	−	4.86083i	0.745062	−	0.410815i
$141$	4.14169	+	2.39120i	0.348793	+	0.201376i
$142$	12.0402	+	14.6393i	1.01039	+	1.22850i
$143$	−0.0910734	+	0.0764196i	−0.00761594	+	0.00639053i
$144$	2.13486	−	3.38266i	0.177905	−	0.281888i
$145$	5.20945	+	9.02304i	0.432622	+	0.749323i
$146$	2.31531	−	6.17148i	0.191616	−	0.510756i
$147$	5.03642	+	0.888056i	0.415397	+	0.0732456i
$148$	−18.6294	+	2.90783i	−1.53132	+	0.239022i
$149$	−6.38158	−	17.5332i	−0.522799	−	1.43638i	−0.867391	−	0.497626i	$-0.834205\pi$
$149$	−6.38158	−	17.5332i	−0.522799	−	1.43638i	0.344592	−	0.938752i	$-0.388017\pi$
$150$	9.06161	+	7.75692i	0.739878	+	0.633350i
$151$	−7.93770			−0.645961			−0.322980	−	0.946406i	$-0.604685\pi$
$151$	−7.93770			−0.645961			−0.322980	+	0.946406i	$0.604685\pi$
$152$	12.1202	−	2.25829i	0.983081	−	0.183171i
$153$	0.436076			0.0352547
$154$	2.99140	+	2.56070i	0.241054	+	0.206347i
$155$	−5.22967	−	14.3684i	−0.420057	−	1.15410i
$156$	−0.0180859	−	0.115869i	−0.00144803	−	0.00927697i
$157$	17.0370	+	3.00408i	1.35970	+	0.239752i	0.805483	−	0.592620i	$-0.201906\pi$
$157$	17.0370	+	3.00408i	1.35970	+	0.239752i	0.554218	+	0.832371i	$0.313017\pi$
$158$	−2.98044	+	7.94441i	−0.237111	+	0.632024i
$159$	−4.80473	−	8.32204i	−0.381040	−	0.659981i
$160$	11.2382	−	17.4243i	0.888460	−	1.37751i
$161$	−8.88519	+	7.45556i	−0.700251	+	0.587580i
$162$	−0.898327	−	1.09225i	−0.0705793	−	0.0858152i
$163$	−3.50912	−	2.02599i	−0.274855	−	0.158688i	0.356237	−	0.934396i	$-0.384060\pi$
$163$	−3.50912	−	2.02599i	−0.274855	−	0.158688i	−0.631092	+	0.775708i	$0.717393\pi$
$164$	−4.67648	−	8.48135i	−0.365171	−	0.662282i
$165$	−2.54176	+	6.98343i	−0.197876	+	0.543659i
$166$	−1.93627	+	10.3823i	−0.150284	+	0.805819i
$167$	0.366931	+	2.08097i	0.0283940	+	0.161030i	0.995708	−	0.0925518i	$-0.0295024\pi$
$167$	0.366931	+	2.08097i	0.0283940	+	0.161030i	−0.967314	+	0.253582i	$0.918391\pi$
$168$	−3.68761	+	1.22009i	−0.284505	+	0.0941322i
$169$	9.95594	+	8.35403i	0.765842	+	0.642618i
$170$	2.26031	+	0.0222577i	0.173358	+	0.00170709i
$171$	0.588021	−	4.31905i	0.0449671	−	0.330286i
$172$	0.139534	−	7.08424i	0.0106393	−	0.540168i
$173$	8.51700	−	10.1502i	0.647536	−	0.771703i	−0.338005	−	0.941144i	$-0.609752\pi$
$173$	8.51700	−	10.1502i	0.647536	−	0.771703i	0.985540	+	0.169441i	$0.0541964\pi$
$174$	−1.33766	−	3.79092i	−0.101408	−	0.287389i
$175$	−2.01136	−	11.4070i	−0.152044	−	0.862286i
$176$	7.92534	+	1.72174i	0.597395	+	0.129781i
$177$	1.22859	+	0.447172i	0.0923468	+	0.0336115i
$178$	−19.0146	+	10.7299i	−1.42521	+	0.804238i
$179$	−11.7670	−	6.79368i	−0.879506	−	0.507783i	−0.00901080	−	0.999959i	$-0.502868\pi$
$179$	−11.7670	−	6.79368i	−0.879506	−	0.507783i	−0.870496	+	0.492176i	$0.836202\pi$
$180$	−4.60054	−	5.70729i	−0.342904	−	0.425396i
$181$	−12.6242	−	15.0450i	−0.938352	−	1.11828i	−0.992802	−	0.119768i	$-0.961785\pi$
$181$	−12.6242	−	15.0450i	−0.938352	−	1.11828i	0.0544497	−	0.998517i	$-0.482660\pi$
$182$	−0.0579072	+	0.0980555i	−0.00429236	+	0.00726836i
$183$	4.96701	+	8.60311i	0.367172	+	0.635960i
$184$	−8.83003	+	22.1973i	−0.650959	+	1.63641i
$185$	−6.00035	+	34.0297i	−0.441154	+	2.50191i
$186$	0.967205	+	5.81983i	0.0709189	+	0.426731i
$187$	0.302403	+	0.830845i	0.0221139	+	0.0607574i
$188$	−7.20458	−	6.29124i	−0.525448	−	0.458836i
$189$			1.37328i			0.0998912i
$190$	3.26833	−	22.3569i	0.237110	−	1.62194i
$191$	6.61899			0.478933			0.239467	−	0.970905i	$-0.423027\pi$
$191$	6.61899			0.478933			0.239467	+	0.970905i	$0.423027\pi$
$192$	−5.49519	+	5.81403i	−0.396581	+	0.419591i
$193$	−14.4651	+	5.26485i	−1.04122	+	0.378972i	−0.805342	−	0.592811i	$-0.798018\pi$
$193$	−14.4651	+	5.26485i	−1.04122	+	0.378972i	−0.235876	+	0.971783i	$0.575796\pi$
$194$	−10.7907	+	1.79333i	−0.774731	+	0.128753i
$195$	−0.211655	−	0.0373205i	−0.0151569	−	0.00267257i
$196$	−9.54063	−	3.68685i	−0.681474	−	0.263347i
$197$	17.2691	−	9.97031i	1.23037	−	0.710355i	0.263264	−	0.964724i	$-0.415201\pi$
$197$	17.2691	−	9.97031i	1.23037	−	0.710355i	0.967107	+	0.254368i	$0.0818675\pi$
$198$	1.45808	−	2.46900i	0.103621	−	0.175464i
$199$	−12.0578	+	10.1177i	−0.854758	+	0.717227i	−0.960832	−	0.277131i	$-0.910616\pi$
$199$	−12.0578	+	10.1177i	−0.854758	+	0.717227i	0.106074	+	0.994358i	$0.466172\pi$
$200$	−14.7882	−	18.7201i	−1.04568	−	1.32371i
$201$	−3.91529	+	6.78148i	−0.276163	+	0.478329i
$202$	−3.89577	−	6.90379i	−0.274106	−	0.485749i
$203$	−1.33512	+	3.66821i	−0.0937071	+	0.257458i
$204$	−0.855754	−	0.168332i	−0.0599147	−	0.0117856i
$205$	−17.4800	+	3.08219i	−1.22085	+	0.215269i
$206$	5.63704	+	15.9754i	0.392751	+	1.11306i
$207$	6.47006	+	5.42903i	0.449701	+	0.377344i
$208$	−0.00923576	+	0.234363i	−0.000640385	+	0.0162501i
$209$	8.63676	−	1.87476i	0.597417	−	0.129680i
$210$	−0.0700933	+	7.11809i	−0.00483690	+	0.491195i
$211$	15.5936	−	18.5837i	1.07351	−	1.27936i	0.115286	−	0.993332i	$-0.463222\pi$
$211$	15.5936	−	18.5837i	1.07351	−	1.27936i	0.958222	−	0.286025i	$-0.0923340\pi$
$212$	6.21634	+	18.1858i	0.426940	+	1.24901i
$213$	−13.1993	+	2.32739i	−0.904399	+	0.159470i
$214$	3.09358	−	16.5877i	0.211473	−	1.13392i
$215$	−12.2024	−	4.44131i	−0.832196	−	0.302895i
$216$	1.34125	+	2.49019i	0.0912603	+	0.169436i
$217$	2.86444	−	4.96135i	0.194451	−	0.336799i
$218$	−7.91794	+	6.51216i	−0.536271	+	0.441059i
$219$	2.99597	+	3.57045i	0.202449	+	0.241269i
$220$	7.68365	−	12.7231i	0.518032	−	0.857790i
$221$	−0.0221441	+	0.0127849i	−0.00148958	+	0.000860007i
$222$	4.68311	−	12.4829i	0.314310	−	0.837797i
$223$	−0.287032	+	1.62784i	−0.0192211	+	0.109008i	−0.992909	−	0.118878i	$-0.962070\pi$
$223$	−0.287032	+	1.62784i	−0.0192211	+	0.109008i	0.973688	+	0.227886i	$0.0731814\pi$
$224$	7.70752	−	0.970827i	0.514981	−	0.0648661i
$225$	−7.92587	+	2.88478i	−0.528391	+	0.192319i
$226$	3.38586	−	3.95535i	0.225224	−	0.263106i
$227$			27.8353i			1.84749i	0.383003	+	0.923747i	$0.374890\pi$
$227$			27.8353i			1.84749i	−0.383003	+	0.923747i	$0.625110\pi$
$228$	−2.82115	+	8.24870i	−0.186835	+	0.546284i
$229$			24.5496i			1.62228i	0.584851	+	0.811141i	$0.301153\pi$
$229$			24.5496i			1.62228i	−0.584851	+	0.811141i	$0.698847\pi$
$230$	33.2591	+	28.4705i	2.19304	+	1.87729i
$231$	−2.61647	+	0.952317i	−0.172151	+	0.0626579i
$232$	1.16166	+	7.95563i	0.0762665	+	0.522313i
$233$	−3.81443	+	21.6327i	−0.249891	+	1.41720i	0.558962	+	0.829193i	$0.311200\pi$
$233$	−3.81443	+	21.6327i	−0.249891	+	1.41720i	−0.808853	+	0.588011i	$0.799911\pi$
$234$	0.0776401	+	0.0291276i	0.00507549	+	0.00190413i
$235$	−15.1806	+	8.76451i	−0.990272	+	0.571734i
$236$	−2.23837	−	1.35178i	−0.145706	−	0.0879936i
$237$	−3.85664	−	4.59616i	−0.250516	−	0.298553i
$238$	0.537966	+	0.654097i	0.0348712	+	0.0423988i
$239$	−5.79538	+	10.0379i	−0.374872	+	0.649298i	−0.990308	−	0.138890i	$-0.955647\pi$
$239$	−5.79538	+	10.0379i	−0.374872	+	0.649298i	0.615436	+	0.788187i	$0.288980\pi$
$240$	6.82497	+	12.9758i	0.440550	+	0.837587i
$241$	−3.66437	−	1.33372i	−0.236043	−	0.0859127i	0.221290	−	0.975208i	$-0.428973\pi$
$241$	−3.66437	−	1.33372i	−0.236043	−	0.0859127i	−0.457333	+	0.889295i	$0.651195\pi$
$242$	−9.57743	−	1.78617i	−0.615661	−	0.114820i
$243$	0.984808	−	0.173648i	0.0631754	−	0.0111395i
$244$	−6.42629	−	18.8000i	−0.411401	−	1.20355i
$245$	−12.0489	+	14.3594i	−0.769779	+	0.917387i
$246$	6.84812	+	0.0674349i	0.436620	+	0.00429949i
$247$	0.0967664	+	0.236563i	0.00615710	+	0.0150521i
$248$	0.348509	−	11.7942i	0.0221303	−	0.748930i
$249$	−5.72078	−	4.80030i	−0.362540	−	0.304207i
$250$	−16.7885	+	5.92397i	−1.06180	+	0.374665i
$251$	−25.3595	+	4.47156i	−1.60068	+	0.282242i	−0.901524	−	0.432730i	$-0.857550\pi$
$251$	−25.3595	+	4.47156i	−1.60068	+	0.282242i	−0.699153	+	0.714972i	$0.746439\pi$
$252$	0.530106	−	2.69491i	0.0333936	−	0.169763i
$253$	−5.85704	+	16.0921i	−0.368229	+	1.01170i
$254$	−18.7205	+	10.5639i	−1.17463	+	0.662837i
$255$	−0.799178	+	1.38422i	−0.0500465	+	0.0866831i
$256$	13.0280	−	9.28818i	0.814252	−	0.580511i
$257$	10.0402	−	8.42470i	0.626288	−	0.525518i	−0.273485	−	0.961876i	$-0.588176\pi$
$257$	10.0402	−	8.42470i	0.626288	−	0.525518i	0.899773	+	0.436358i	$0.143732\pi$
$258$	4.31416	+	2.54775i	0.268588	+	0.158616i
$259$	−11.2120	+	6.47326i	−0.696680	+	0.402229i
$260$	0.400944	+	0.154940i	0.0248655	+	0.00960895i
$261$	2.79938	+	0.493607i	0.173277	+	0.0305535i
$262$	1.55308	+	9.34515i	0.0959497	+	0.577345i
$263$	7.89503	−	2.87355i	0.486828	−	0.177191i	−0.0869322	−	0.996214i	$-0.527706\pi$
$263$	7.89503	−	2.87355i	0.486828	−	0.177191i	0.573760	+	0.819023i	$0.305484\pi$
$264$	−3.81439	+	4.28230i	−0.234760	+	0.263557i
$265$	35.2217			2.16365
$266$	7.20382	−	4.44620i	0.441695	−	0.272614i
$267$		−	15.4384i		−	0.944813i
$268$	10.3011	−	11.7966i	0.629240	−	0.720590i
$269$	6.43389	+	17.6770i	0.392281	+	1.07778i	0.965957	+	0.258702i	$0.0832946\pi$
$269$	6.43389	+	17.6770i	0.392281	+	1.07778i	−0.573676	+	0.819082i	$0.694483\pi$
$270$	5.11340	−	0.849803i	0.311192	−	0.0517173i
$271$	−0.234529	+	1.33008i	−0.0142466	+	0.0807967i	−0.991102	−	0.133104i	$-0.957506\pi$
$271$	−0.234529	+	1.33008i	−0.0142466	+	0.0807967i	0.976855	+	0.213900i	$0.0686168\pi$
$272$	1.61435	+	0.660669i	0.0978842	+	0.0400589i
$273$	−0.0402618	−	0.0697355i	−0.00243676	−	0.00422059i
$274$	−11.7501	−	6.93911i	−0.709852	−	0.419207i
$275$	−10.9926	−	13.1005i	−0.662879	−	0.789988i
$276$	−10.6011	−	13.1514i	−0.638113	−	0.791624i
$277$	−0.690127	−	0.398445i	−0.0414657	−	0.0239403i	0.479124	−	0.877747i	$-0.340954\pi$
$277$	−0.690127	−	0.398445i	−0.0414657	−	0.0239403i	−0.520590	+	0.853807i	$0.674288\pi$
$278$	−14.6767	−	26.0089i	−0.880250	−	1.55991i
$279$	−3.92010	−	1.42680i	−0.234690	−	0.0854203i
$280$	2.88524	−	13.9414i	0.172426	−	0.833160i
$281$	−2.58001	−	14.6320i	−0.153911	−	0.872871i	−0.959775	−	0.280771i	$-0.909410\pi$
$281$	−2.58001	−	14.6320i	−0.153911	−	0.872871i	0.805864	−	0.592100i	$-0.201701\pi$
$282$	6.37793	−	2.25051i	0.379800	−	0.134016i
$283$	5.49662	−	6.55061i	0.326740	−	0.389394i	−0.577520	−	0.816377i	$-0.695979\pi$
$283$	5.49662	−	6.55061i	0.326740	−	0.389394i	0.904259	+	0.426983i	$0.140424\pi$
$284$	26.8006	+	0.527873i	1.59032	+	0.0313235i
$285$	12.6321	+	9.78188i	0.748264	+	0.579428i
$286$	−0.00165556	+	0.168125i	−9.78953e−5	+	0.00994142i
$287$	−5.09436	−	4.27468i	−0.300711	−	0.252326i
$288$	−1.67080	−	5.40448i	−0.0984530	−	0.318462i
$289$	−2.91900	−	16.5545i	−0.171706	−	0.973792i
$290$	14.4848	+	2.70139i	0.850578	+	0.158631i
$291$	2.64548	−	7.26840i	0.155081	−	0.426081i
$292$	−4.50101	−	8.16312i	−0.263402	−	0.477711i
$293$	20.0878	+	11.5977i	1.17354	+	0.677546i	0.954512	−	0.298172i	$-0.0963769\pi$
$293$	20.0878	+	11.5977i	1.17354	+	0.677546i	0.219032	+	0.975718i	$0.429710\pi$
$294$	5.58588	−	4.59415i	0.325775	−	0.267936i
$295$	−3.67103	+	3.08036i	−0.213736	+	0.179345i
$296$	−14.0087	+	22.6886i	−0.814239	+	1.31875i
$297$	1.01378	+	1.75591i	0.0588252	+	0.101888i
$298$	−24.7057	−	9.26863i	−1.43116	−	0.536917i
$299$	−0.487721	−	0.0859984i	−0.0282056	−	0.00497342i
$300$	16.6673	−	2.60157i	0.962284	−	0.150202i
$301$	−1.66402	−	4.57184i	−0.0959123	−	0.263517i
$302$	−7.30000	+	8.52784i	−0.420068	+	0.490722i
$303$	5.60533			0.322018
$304$	8.72034	−	15.0982i	0.500146	−	0.865941i
$305$	−36.4113			−2.08490
$306$	0.401043	−	0.468497i	0.0229261	−	0.0267822i
$307$	−4.77810	−	13.1277i	−0.272701	−	0.749239i	−0.998141	−	0.0609537i	$-0.980586\pi$
$307$	−4.77810	−	13.1277i	−0.272701	−	0.749239i	0.725440	−	0.688286i	$-0.241636\pi$
$308$	5.50215	−	0.858823i	0.313514	−	0.0489360i
$309$	−11.7969	−	2.08011i	−0.671103	−	0.118334i
$310$	−20.2462	−	7.59560i	−1.14991	−	0.431401i
$311$	16.7255	+	28.9695i	0.948418	+	1.64271i	0.748759	+	0.662843i	$0.230650\pi$
$311$	16.7255	+	28.9695i	0.948418	+	1.64271i	0.199659	+	0.979865i	$0.436016\pi$
$312$	−0.141117	−	0.0871302i	−0.00798916	−	0.00493277i
$313$	25.9771	−	21.7974i	1.46831	−	1.23206i	0.550631	−	0.834749i	$-0.314387\pi$
$313$	25.9771	−	21.7974i	1.46831	−	1.23206i	0.917683	−	0.397313i	$-0.130057\pi$
$314$	18.8957	−	15.5409i	1.06635	−	0.877024i
$315$	−4.35913	−	2.51675i	−0.245609	−	0.141803i
$316$	5.79406	+	10.5082i	0.325941	+	0.591133i
$317$	−3.38914	+	9.31160i	−0.190353	+	0.522992i	−0.997752	−	0.0670148i	$-0.978653\pi$
$317$	−3.38914	+	9.31160i	−0.190353	+	0.522992i	0.807399	+	0.590006i	$0.200875\pi$
$318$	−13.3595	−	2.49152i	−0.749163	−	0.139717i
$319$	1.00081	+	5.67589i	0.0560348	+	0.317789i
$320$	−8.38440	−	28.0983i	−0.468702	−	1.57074i
$321$	9.14009	+	7.66945i	0.510150	+	0.428067i
$322$	−0.161518	+	16.4024i	−0.00900103	+	0.914068i
$323$	1.89935	−	0.0745289i	0.105683	−	0.00414690i
$324$	−1.99961	−	0.0393850i	−0.111090	−	0.00218806i
$325$	0.317903	−	0.378862i	0.0176341	−	0.0210155i
$326$	−5.40382	+	1.90678i	−0.299290	+	0.105607i
$327$	−1.25881	−	7.13908i	−0.0696125	−	0.394792i
$328$	−13.4127	−	2.77582i	−0.740592	−	0.153269i
$329$	−6.17149	−	2.24624i	−0.340245	−	0.123839i
$330$	5.16507	+	9.15313i	0.284328	+	0.503863i
$331$	18.8554	+	10.8862i	1.03639	+	0.598359i	0.918808	−	0.394704i	$-0.129153\pi$
$331$	18.8554	+	10.8862i	1.03639	+	0.598359i	0.117581	+	0.993063i	$0.462486\pi$
$332$	9.37343	+	11.6284i	0.514434	+	0.638191i
$333$	6.05986	+	7.22186i	0.332078	+	0.395755i
$334$	2.57313	+	1.51958i	0.140796	+	0.0831476i
$335$	−14.3508	−	24.8563i	−0.784066	−	1.35804i
$336$	−2.08056	+	5.08385i	−0.113504	+	0.277347i
$337$	−0.651565	+	3.69521i	−0.0354930	+	0.201291i	−0.997398	−	0.0720936i	$-0.977032\pi$
$337$	−0.651565	+	3.69521i	−0.0354930	+	0.201291i	0.961905	+	0.273384i	$0.0881431\pi$
$338$	18.1312	−	3.01325i	0.986209	−	0.163899i
$339$	1.25919	+	3.45961i	0.0683900	+	0.187900i
$340$	2.10263	−	2.40789i	0.114031	−	0.130586i
$341$		−	8.45830i		−	0.458043i
$342$	−4.09938	−	4.60381i	−0.221669	−	0.248946i
$343$	−16.6360			−0.898261
$344$	−7.48261	−	6.66502i	−0.403435	−	0.359354i
$345$	−29.0905	+	10.5881i	−1.56618	+	0.570044i
$346$	−3.07203	−	18.4849i	−0.165154	−	0.993757i
$347$	4.01644	+	0.708206i	0.215614	+	0.0380185i	0.280411	−	0.959880i	$-0.409529\pi$
$347$	4.01644	+	0.708206i	0.215614	+	0.0380185i	−0.0647978	+	0.997898i	$0.520640\pi$
$348$	−5.30295	−	2.04926i	−0.284268	−	0.109852i
$349$	22.2504	−	12.8463i	1.19103	−	0.687644i	0.232493	−	0.972598i	$-0.425312\pi$
$349$	22.2504	−	12.8463i	1.19103	−	0.687644i	0.958541	+	0.284954i	$0.0919782\pi$
$350$	−14.1048	−	8.32967i	−0.753934	−	0.445240i
$351$	−0.0449179	+	0.0376906i	−0.00239754	+	0.00201178i
$352$	9.13838	−	6.93115i	0.487077	−	0.369431i
$353$	11.6943	−	20.2552i	0.622427	−	1.07807i	−0.366606	−	0.930376i	$-0.619480\pi$
$353$	11.6943	−	20.2552i	0.622427	−	1.07807i	0.989032	−	0.147698i	$-0.0471864\pi$
$354$	1.61031	−	0.908689i	0.0855870	−	0.0482963i
$355$	16.8020	−	46.1631i	0.891758	−	2.45008i
$356$	−5.95946	+	30.2962i	−0.315850	+	1.60569i
$357$	−0.589755	+	0.103990i	−0.0312132	+	0.00550372i
$358$	−18.1204	+	6.39394i	−0.957694	+	0.337930i
$359$	−4.93607	−	4.14186i	−0.260516	−	0.218599i	0.503169	−	0.864188i	$-0.332167\pi$
$359$	−4.93607	−	4.14186i	−0.260516	−	0.218599i	−0.763685	+	0.645589i	$0.776612\pi$
$360$	−10.3626	−	0.306206i	−0.546154	−	0.0161385i
$361$	1.82299	−	18.9123i	0.0959470	−	0.995386i
$362$	−27.7736	−	0.273492i	−1.45975	−	0.0143744i
$363$	4.42819	−	5.27731i	0.232420	−	0.276987i
$364$	0.0520906	+	0.152390i	0.00273029	+	0.00798742i
$365$	−16.8241	+	2.96654i	−0.880614	+	0.155276i
$366$	13.8107	+	2.57567i	0.721896	+	0.134632i
$367$	−10.3959	−	3.78380i	−0.542662	−	0.197513i	0.0561213	−	0.998424i	$-0.482127\pi$
$367$	−10.3959	−	3.78380i	−0.542662	−	0.197513i	−0.598783	+	0.800911i	$0.704349\pi$
$368$	15.7269	+	29.9005i	0.819823	+	1.55867i
$369$	−2.42129	+	4.19381i	−0.126048	+	0.218321i
$370$	31.0414	+	37.7423i	1.61376	+	1.96213i
$371$	8.48252	+	10.1091i	0.440390	+	0.524837i
$372$	7.14202	+	4.31317i	0.370296	+	0.223627i
$373$	−24.7097	+	14.2661i	−1.27942	+	0.738672i	−0.976741	−	0.214421i	$-0.931213\pi$
$373$	−24.7097	+	14.2661i	−1.27942	+	0.738672i	−0.302676	+	0.953093i	$0.597880\pi$
$374$	1.17072	+	0.439211i	0.0605367	+	0.0227111i
$375$	2.18600	−	12.3974i	0.112884	−	0.640199i
$376$	−13.3848	+	1.95440i	−0.690266	+	0.100790i
$377$	−0.156625	+	0.0570070i	−0.00806662	+	0.00293601i
$378$	1.47538	+	1.26295i	0.0758851	+	0.0649592i
$379$			4.94280i			0.253895i	0.991909	+	0.126947i	$0.0405179\pi$
$379$			4.94280i			0.253895i	−0.991909	+	0.126947i	$0.959482\pi$
$380$	−21.0133	−	24.0721i	−1.07796	−	1.23487i
$381$		−	15.1996i		−	0.778697i
$382$	6.08724	−	7.11109i	0.311450	−	0.363835i
$383$	18.2846	−	6.65506i	0.934301	−	0.340058i	0.170388	−	0.985377i	$-0.445498\pi$
$383$	18.2846	−	6.65506i	0.934301	−	0.340058i	0.763913	+	0.645319i	$0.223276\pi$
$384$	1.19256	+	11.2507i	0.0608576	+	0.574134i
$385$	1.77219	−	10.0506i	0.0903194	−	0.512227i
$386$	−7.64669	+	20.3824i	−0.389206	+	1.03744i
$387$	−3.06816	+	1.77140i	−0.155963	+	0.0900455i
$388$	−7.99719	+	13.2423i	−0.405996	+	0.672274i
$389$	2.46268	+	2.93491i	0.124863	+	0.148806i	0.824854	−	0.565346i	$-0.191257\pi$
$389$	2.46268	+	2.93491i	0.124863	+	0.148806i	−0.699991	+	0.714151i	$0.746813\pi$
$390$	−0.234746	+	0.193069i	−0.0118868	+	0.00977641i
$391$	−1.84157	+	3.18968i	−0.0931320	+	0.161309i
$392$	−12.7351	+	6.85929i	−0.643221	+	0.346446i
$393$	−6.29467	−	2.29107i	−0.317524	−	0.115569i
$394$	5.17016	−	27.7223i	0.260469	−	1.39663i
$395$	21.6573	−	3.81877i	1.08970	−	0.192143i
$396$	−1.31162	−	3.83712i	−0.0659113	−	0.192823i
$397$	2.88731	−	3.44096i	0.144910	−	0.172697i	−0.688707	−	0.725040i	$-0.741821\pi$
$397$	2.88731	−	3.44096i	0.144910	−	0.172697i	0.833617	+	0.552342i	$0.186266\pi$
$398$	−0.219191	+	22.2592i	−0.0109871	+	1.11575i
$399$	0.234704	+	5.98137i	0.0117499	+	0.299443i
$400$	−33.7120	−	1.32852i	−1.68560	−	0.0664260i
$401$	12.4383	+	10.4370i	0.621141	+	0.521199i	0.898162	−	0.439665i	$-0.144903\pi$
$401$	12.4383	+	10.4370i	0.621141	+	0.521199i	−0.277021	+	0.960864i	$0.589347\pi$
$402$	3.68492	+	10.4430i	0.183787	+	0.520852i
$403$	0.240895	−	0.0424764i	0.0119999	−	0.00211590i
$404$	−10.9999	−	2.16374i	−0.547264	−	0.107650i
$405$	−1.25361	+	3.44427i	−0.0622925	+	0.171147i
$406$	2.71307	+	4.80790i	0.134648	+	0.238612i
$407$	−9.55733	+	16.5538i	−0.473739	+	0.820541i
$408$	−0.967852	+	0.764567i	−0.0479158	+	0.0378517i
$409$	14.0032	−	11.7501i	0.692413	−	0.581004i	−0.227191	−	0.973850i	$-0.572954\pi$
$409$	14.0032	−	11.7501i	0.692413	−	0.581004i	0.919604	+	0.392847i	$0.128510\pi$
$410$	−12.7643	+	21.6141i	−0.630385	+	1.06744i
$411$	8.35652	−	4.82464i	0.412197	−	0.237982i
$412$	22.3472	+	8.63580i	1.10097	+	0.425455i
$413$	−1.76820	−	0.311782i	−0.0870076	−	0.0153418i
$414$	11.7829	−	1.95822i	0.579100	−	0.0962413i
$415$	25.7216	−	9.36190i	1.26262	−	0.459558i
$416$	0.243293	+	0.225457i	0.0119284	+	0.0110539i
$417$	21.1172			1.03411
$418$	5.92875	−	11.0030i	0.289985	−	0.538175i
$419$		−	21.6852i		−	1.05939i	−0.848188	−	0.529696i	$-0.822306\pi$
$419$		−	21.6852i		−	1.05939i	0.848188	−	0.529696i	$-0.177694\pi$
$420$	7.58283	+	6.62154i	0.370004	+	0.323098i
$421$	−0.683080	−	1.87675i	−0.0332913	−	0.0914670i	0.921933	−	0.387348i	$-0.126609\pi$
$421$	−0.683080	−	1.87675i	−0.0332913	−	0.0914670i	−0.955225	+	0.295881i	$0.904387\pi$
$422$	−5.62453	−	33.8437i	−0.273798	−	1.64749i
$423$	−0.830456	+	4.70975i	−0.0403782	+	0.228996i
$424$	25.2548	+	10.0463i	1.22648	+	0.487892i
$425$	−1.83905	−	3.18533i	−0.0892070	−	0.154511i
$426$	−9.63844	+	16.3210i	−0.466984	+	0.790755i
$427$	−8.76900	−	10.4505i	−0.424362	−	0.505735i
$428$	−14.9759	−	18.5787i	−0.723890	−	0.898036i
$429$	−0.102960	−	0.0594439i	−0.00497095	−	0.00286998i
$430$	−15.9936	+	9.02509i	−0.771279	+	0.435229i
$431$	27.0992	+	9.86330i	1.30532	+	0.475098i	0.898726	−	0.438510i	$-0.144494\pi$
$431$	27.0992	+	9.86330i	1.30532	+	0.475098i	0.406596	+	0.913608i	$0.366716\pi$
$432$	3.90882	+	0.849171i	0.188063	+	0.0408557i
$433$	−1.13668	−	6.44643i	−0.0546253	−	0.309796i	0.945237	−	0.326385i	$-0.105830\pi$
$433$	−1.13668	−	6.44643i	−0.0546253	−	0.309796i	−0.999862	+	0.0165889i	$0.994719\pi$
$434$	−2.69590	−	7.64017i	−0.129407	−	0.366740i
$435$	−6.69715	+	7.98135i	−0.321104	+	0.382676i
$436$	−0.285510	+	14.4956i	−0.0136735	+	0.694214i
$437$	29.1085	+	22.5406i	1.39245	+	1.07826i
$438$	6.59118	+	0.0649048i	0.314939	+	0.00310127i
$439$	18.2069	+	15.2774i	0.868967	+	0.729150i	0.963880	−	0.266336i	$-0.0858130\pi$
$439$	18.2069	+	15.2774i	0.868967	+	0.729150i	−0.0949135	+	0.995486i	$0.530257\pi$
$440$	−6.60264	−	19.9559i	−0.314769	−	0.951358i
$441$	0.888056	+	5.03642i	0.0422884	+	0.239829i
$442$	−0.00662969	+	0.0355483i	−0.000315342	+	0.00169086i
$443$	11.7259	−	32.2168i	0.557116	−	1.53066i	−0.266684	−	0.963784i	$-0.585928\pi$
$443$	11.7259	−	32.2168i	0.557116	−	1.53066i	0.823800	−	0.566880i	$-0.191850\pi$
$444$	−9.10408	−	16.5113i	−0.432060	−	0.783593i
$445$	49.0054	+	28.2933i	2.32308	+	1.34123i
$446$	1.48489	+	1.80544i	0.0703117	+	0.0854899i
$447$	14.2932	−	11.9934i	0.676046	−	0.567270i
$448$	6.04532	−	9.17339i	0.285614	−	0.433402i
$449$	17.0193	+	29.4783i	0.803191	+	1.39117i	0.917506	+	0.397723i	$0.130199\pi$
$449$	17.0193	+	29.4783i	0.803191	+	1.39117i	−0.114315	+	0.993445i	$0.536467\pi$
$450$	−4.18987	+	11.1682i	−0.197512	+	0.526472i
$451$	−9.66943	−	1.70498i	−0.455316	−	0.0802844i
$452$	−1.13557	−	7.27518i	−0.0534128	−	0.342196i
$453$	−2.71485	−	7.45900i	−0.127555	−	0.350454i
$454$	29.9048	+	25.5991i	1.40350	+	1.20142i
$455$	0.295145			0.0138366
$456$	6.26746	+	10.6169i	0.293501	+	0.497183i
$457$	−9.12554			−0.426875			−0.213437	−	0.976957i	$-0.568466\pi$
$457$	−9.12554			−0.426875			−0.213437	+	0.976957i	$0.568466\pi$
$458$	26.3748	+	22.5773i	1.23241	+	1.05497i
$459$	0.149147	+	0.409778i	0.00696158	+	0.0191268i
$460$	61.1743	−	9.54860i	2.85227	−	0.445206i
$461$	−10.8009	−	1.90449i	−0.503049	−	0.0887010i	−0.0836352	−	0.996496i	$-0.526653\pi$
$461$	−10.8009	−	1.90449i	−0.503049	−	0.0887010i	−0.419413	+	0.907795i	$0.637764\pi$
$462$	−1.38315	+	3.68681i	−0.0643499	+	0.171526i
$463$	−15.9834	−	27.6840i	−0.742811	−	1.28659i	−0.951211	−	0.308542i	$-0.900159\pi$
$463$	−15.9834	−	27.6840i	−0.742811	−	1.28659i	0.208400	−	0.978044i	$-0.433174\pi$
$464$	9.61544	+	6.06847i	0.446386	+	0.281722i
$465$	11.7132	−	9.82857i	0.543188	−	0.455789i
$466$	19.7330	+	23.9928i	0.914115	+	1.11144i
$467$	10.5167	+	6.07183i	0.486656	+	0.280971i	0.723186	−	0.690653i	$-0.242677\pi$
$467$	10.5167	+	6.07183i	0.486656	+	0.280971i	−0.236530	+	0.971624i	$0.576010\pi$
$468$	0.102696	−	0.0566248i	0.00474712	−	0.00261748i
$469$	3.67793	−	10.1050i	0.169831	−	0.466607i
$470$	−4.54488	+	24.3696i	−0.209640	+	1.12409i
$471$	3.00408	+	17.0370i	0.138421	+	0.785024i
$472$	−3.51083	+	1.16160i	−0.161599	+	0.0534671i
$473$	−5.50267	−	4.61729i	−0.253013	−	0.212303i
$474$	−8.48468	−	0.0835505i	−0.389714	−	0.00383760i
$475$	−34.0285	+	13.9194i	−1.56133	+	0.638665i
$476$	1.19747	+	0.0235859i	0.0548861	+	0.00108106i
$477$	6.17685	−	7.36128i	0.282818	−	0.337050i
$478$	5.45439	+	15.4577i	0.249478	+	0.707020i
$479$	−4.03772	−	22.8991i	−0.184488	−	1.04629i	−0.926611	−	0.376021i	$-0.877292\pi$
$479$	−4.03772	−	22.8991i	−0.184488	−	1.04629i	0.742123	−	0.670264i	$-0.233819\pi$
$480$	20.2172	+	4.60101i	0.922785	+	0.210006i
$481$	−0.519453	−	0.189065i	−0.0236850	−	0.00862064i
$482$	−4.80287	+	2.71023i	−0.218765	+	0.123448i
$483$	−10.0448	−	5.79939i	−0.457056	−	0.263882i
$484$	−10.7270	+	8.64681i	−0.487590	+	0.393037i
$485$	18.2235	+	21.7179i	0.827486	+	0.986160i
$486$	0.719132	−	1.21772i	0.0326205	−	0.0552370i
$487$	−0.603863	−	1.04592i	−0.0273637	−	0.0473952i	0.852019	−	0.523510i	$-0.175378\pi$
$487$	−0.603863	−	1.04592i	−0.0273637	−	0.0473952i	−0.879383	+	0.476115i	$0.842045\pi$
$488$	−26.1078	−	10.3856i	−1.18184	−	0.470135i
$489$	0.703619	−	3.99042i	0.0318188	−	0.180453i
$490$	4.34599	+	26.1505i	0.196332	+	1.18136i
$491$	4.45502	+	12.2401i	0.201052	+	0.552386i	0.998713	−	0.0507201i	$-0.0161516\pi$
$491$	4.45502	+	12.2401i	0.201052	+	0.552386i	−0.797661	+	0.603106i	$0.793929\pi$
$492$	6.37041	−	7.29524i	0.287200	−	0.328895i
$493$			1.23958i			0.0558277i
$494$	0.343143	+	0.113597i	0.0154387	+	0.00511099i
$495$	−7.43161			−0.334026
$496$	−12.3505	−	11.2211i	−0.554554	−	0.503841i
$497$	17.2959	−	6.29518i	0.775825	−	0.282377i
$498$	−10.4184	+	1.73144i	−0.466858	+	0.0775878i
$499$	−20.6357	−	3.63863i	−0.923781	−	0.162887i	−0.308526	−	0.951216i	$-0.599836\pi$
$499$	−20.6357	−	3.63863i	−0.923781	−	0.162887i	−0.615255	+	0.788328i	$0.710947\pi$
$500$	−9.07537	+	23.4847i	−0.405863	+	1.05027i
$501$	−1.82997	+	1.05654i	−0.0817572	+	0.0472025i
$502$	−18.5182	+	31.3572i	−0.826506	+	1.39954i
$503$	14.9252	−	12.5238i	0.665483	−	0.558407i	−0.246242	−	0.969208i	$-0.579196\pi$
$503$	14.9252	−	12.5238i	0.665483	−	0.558407i	0.911725	+	0.410802i	$0.134751\pi$
$504$	−2.40775	−	3.04793i	−0.107250	−	0.135765i
$505$	−10.2726	+	17.7927i	−0.457127	+	0.791766i
$506$	11.9020	+	21.0918i	0.529108	+	0.937644i
$507$	−4.44509	+	12.2128i	−0.197413	+	0.542388i
$508$	−5.86727	+	29.8275i	−0.260318	+	1.32338i
$509$	−25.9811	+	4.58117i	−1.15159	+	0.203057i	−0.716671	−	0.697411i	$-0.754335\pi$
$509$	−25.9811	+	4.58117i	−1.15159	+	0.203057i	−0.434922	+	0.900468i	$0.643224\pi$
$510$	0.752156	+	2.13161i	0.0333060	+	0.0943892i
$511$	−4.90322	−	4.11429i	−0.216906	−	0.182005i
$512$	2.00266	−	22.5386i	0.0885061	−	0.996076i
$513$	4.25970	−	0.924644i	0.188070	−	0.0408240i
$514$	0.182513	−	18.5345i	0.00805031	−	0.817522i
$515$	28.2225	−	33.6343i	1.24363	−	1.48210i
$516$	6.70473	−	2.29184i	0.295159	−	0.100892i
$517$	−9.54926	+	1.68379i	−0.419976	+	0.0740531i
$518$	−3.35674	+	17.9988i	−0.147487	+	0.790822i
$519$	12.4510	+	4.53180i	0.546539	+	0.198924i
$520$	0.535192	−	0.288261i	0.0234697	−	0.0126411i
$521$	11.0907	−	19.2097i	0.485893	−	0.841591i	−0.513976	−	0.857805i	$-0.671828\pi$
$521$	11.0907	−	19.2097i	0.485893	−	0.841591i	0.999869	+	0.0162136i	$0.00516119\pi$
$522$	3.10479	−	2.55356i	0.135893	−	0.111766i
$523$	3.19064	+	3.80245i	0.139517	+	0.166270i	0.831278	−	0.555856i	$-0.187610\pi$
$523$	3.19064	+	3.80245i	0.139517	+	0.166270i	−0.691762	+	0.722126i	$0.743165\pi$
$524$	11.4682	+	6.92583i	0.500993	+	0.302556i
$525$	10.0311	−	5.79147i	0.437794	−	0.252761i
$526$	4.17356	−	11.1247i	0.181976	−	0.485060i
$527$	0.315896	−	1.79154i	0.0137606	−	0.0780405i
$528$	1.09272	+	8.03625i	0.0475547	+	0.349733i
$529$	−45.4211	+	16.5319i	−1.97483	+	0.718779i
$530$	32.3921	−	37.8403i	1.40702	−	1.64368i
$531$			1.30744i			0.0567382i
$532$	1.84832	−	11.8284i	0.0801349	−	0.512827i
$533$		−	0.283951i		−	0.0122993i
$534$	−16.5862	−	14.1981i	−0.717754	−	0.614412i
$535$	−41.0955	+	14.9575i	−1.77671	+	0.646670i
$536$	−3.20008	−	21.9158i	−0.138222	−	0.946619i
$537$	2.35942	−	13.3809i	0.101816	−	0.577430i
$538$	24.9082	+	9.34461i	1.07387	+	0.402875i
$539$	−8.97992	+	5.18456i	−0.386793	+	0.223315i
$540$	3.78962	−	6.27510i	0.163079	−	0.270037i
$541$	−14.0331	−	16.7240i	−0.603332	−	0.719023i	0.374777	−	0.927115i	$-0.377719\pi$
$541$	−14.0331	−	16.7240i	−0.603332	−	0.719023i	−0.978109	+	0.208092i	$0.933275\pi$
$542$	1.21328	+	1.47519i	0.0521149	+	0.0633649i
$543$	9.81991	−	17.0086i	0.421413	−	0.729908i
$544$	2.19444	−	1.12678i	0.0940859	−	0.0483102i
$545$	24.9682	+	9.08769i	1.06952	+	0.389274i
$546$	−0.111947	−	0.0208780i	−0.00479091	−	0.000893495i
$547$	20.7434	−	3.65762i	0.886923	−	0.156388i	0.288415	−	0.957506i	$-0.406872\pi$
$547$	20.7434	−	3.65762i	0.886923	−	0.156388i	0.598508	+	0.801117i	$0.295761\pi$
$548$	−18.2612	+	6.24210i	−0.780079	+	0.266649i
$549$	−6.38546	+	7.60989i	−0.272525	+	0.324782i
$550$	−24.1839	−	0.238144i	−1.03121	−	0.0101545i
$551$	12.2772	+	1.67149i	0.523027	+	0.0712079i
$552$	−23.8787	−	0.705598i	−1.01634	−	0.0300322i
$553$	6.31180	+	5.29623i	0.268405	+	0.225219i
$554$	−1.06275	+	0.375001i	−0.0451520	+	0.0159323i
$555$	−34.0297	+	6.00035i	−1.44448	+	0.254701i
$556$	−41.4402	−	8.15156i	−1.75746	−	0.345703i
$557$	−6.81979	+	18.7372i	−0.288964	+	0.793922i	0.707248	+	0.706965i	$0.249936\pi$
$557$	−6.81979	+	18.7372i	−0.288964	+	0.793922i	−0.996212	+	0.0869564i	$0.972286\pi$
$558$	−5.13805	+	2.89937i	−0.217511	+	0.122740i
$559$	0.103868	−	0.179905i	0.00439316	−	0.00760918i
$560$	−12.3245	−	15.9212i	−0.520805	−	0.672792i
$561$	−0.677311	+	0.568332i	−0.0285961	+	0.0239950i
$562$	−18.0926	−	10.6847i	−0.763189	−	0.450705i
$563$	19.1810	−	11.0742i	0.808384	−	0.466721i	−0.0380103	−	0.999277i	$-0.512102\pi$
$563$	19.1810	−	11.0742i	0.808384	−	0.466721i	0.846394	+	0.532557i	$0.178769\pi$
$564$	3.44772	−	8.92182i	0.145175	−	0.375676i
$565$	−13.2893	−	2.34327i	−0.559087	−	0.0985821i
$566$	−1.98260	−	11.9296i	−0.0833348	−	0.501440i
$567$	−1.29046	+	0.469688i	−0.0541941	+	0.0197251i
$568$	25.2146	−	28.3076i	1.05798	−	1.18776i
$569$	−40.1025			−1.68118			−0.840592	−	0.541669i	$-0.817793\pi$
$569$	−40.1025			−1.68118			−0.840592	+	0.541669i	$0.817793\pi$
$570$	22.1264	−	4.57528i	0.926774	−	0.191637i
$571$			25.1495i			1.05247i	0.850338	+	0.526237i	$0.176398\pi$
$571$			25.1495i			1.05247i	−0.850338	+	0.526237i	$0.823602\pi$
$572$	0.179102	+	0.156397i	0.00748861	+	0.00653927i
$573$	2.26383	+	6.21982i	0.0945728	+	0.259837i
$574$	−9.27757	+	1.54185i	−0.387238	+	0.0643556i
$575$	12.3705	−	70.1564i	0.515884	−	2.92572i
$576$	−7.34286	−	3.17528i	−0.305953	−	0.132303i
$577$	16.4947	+	28.5697i	0.686683	+	1.18937i	0.972905	+	0.231207i	$0.0742675\pi$
$577$	16.4947	+	28.5697i	0.686683	+	1.18937i	−0.286221	+	0.958164i	$0.592399\pi$
$578$	−20.4697	−	12.0885i	−0.851428	−	0.502815i
$579$	−9.89468	−	11.7920i	−0.411209	−	0.490060i
$580$	16.2234	−	13.0773i	0.673639	−	0.543007i
$581$	8.88157	+	5.12778i	0.368470	+	0.212736i
$582$	−5.37583	−	9.52663i	−0.222835	−	0.394892i
$583$	18.3087	+	6.66381i	0.758268	+	0.275987i
$584$	−12.9094	−	2.67167i	−0.534196	−	0.110554i
$585$	−0.0373205	−	0.211655i	−0.00154301	−	0.00875085i
$586$	30.9340	−	10.9153i	1.27787	−	0.450908i
$587$	−8.05095	+	9.59475i	−0.332298	+	0.396018i	−0.906160	−	0.422934i	$-0.861000\pi$
$587$	−8.05095	+	9.59475i	−0.332298	+	0.396018i	0.573862	+	0.818952i	$0.305445\pi$
$588$	0.201419	−	10.2262i	0.00830640	−	0.421723i
$589$	−17.3180	−	5.54452i	−0.713577	−	0.228458i
$590$	−0.0667331	+	6.77685i	−0.00274736	+	0.278999i
$591$	15.2754	+	12.8176i	0.628346	+	0.527245i
$592$	11.4922	+	35.9161i	0.472325	+	1.47614i
$593$	2.11950	+	12.0203i	0.0870376	+	0.493615i	0.996898	+	0.0787009i	$0.0250772\pi$
$593$	2.11950	+	12.0203i	0.0870376	+	0.493615i	−0.909861	+	0.414914i	$0.863812\pi$
$594$	2.81879	+	0.525698i	0.115656	+	0.0215697i
$595$	0.750729	−	2.06261i	0.0307769	−	0.0845589i
$596$	−32.6786	+	18.0185i	−1.33857	+	0.738065i
$597$	−13.6316	−	7.87020i	−0.557904	−	0.322106i
$598$	−0.540931	+	0.444892i	−0.0221203	+	0.0181930i
$599$	−10.2192	+	8.57489i	−0.417544	+	0.350361i	−0.827228	−	0.561867i	$-0.810083\pi$
$599$	−10.2192	+	8.57489i	−0.417544	+	0.350361i	0.409684	+	0.912227i	$0.365639\pi$
$600$	12.5333	−	20.2990i	0.511668	−	0.828702i
$601$	−7.06611	−	12.2389i	−0.288232	−	0.499233i	0.685155	−	0.728397i	$-0.259734\pi$
$601$	−7.06611	−	12.2389i	−0.288232	−	0.499233i	−0.973388	+	0.229164i	$0.926401\pi$
$602$	−6.44208	−	2.41682i	−0.262560	−	0.0985024i
$603$	−7.71161	−	1.35977i	−0.314041	−	0.0553739i
$604$	2.44832	+	15.6855i	0.0996208	+	0.638233i
$605$	8.63618	+	23.7277i	0.351110	+	0.964668i
$606$	5.15501	−	6.02206i	0.209408	−	0.244630i
$607$	4.05081			0.164417			0.0822086	−	0.996615i	$-0.473803\pi$
$607$	4.05081			0.164417			0.0822086	+	0.996615i	$0.473803\pi$
$608$	−8.20093	−	23.2539i	−0.332592	−	0.943071i
$609$	−3.90363			−0.158183
$610$	−33.4861	+	39.1183i	−1.35581	+	1.58386i
$611$	−0.0959100	−	0.263510i	−0.00388010	−	0.0106605i
$612$	−0.134504	−	0.861718i	−0.00543702	−	0.0348329i
$613$	0.547387	+	0.0965190i	0.0221087	+	0.00389837i	0.184692	−	0.982797i	$-0.440871\pi$
$613$	0.547387	+	0.0965190i	0.0221087	+	0.00389837i	−0.162583	+	0.986695i	$0.551982\pi$
$614$	−18.4980	−	6.93974i	−0.746518	−	0.280065i
$615$	−8.87481	−	15.3716i	−0.357867	−	0.619843i
$616$	4.13745	−	6.70105i	0.166703	−	0.269993i
$617$	1.74834	−	1.46703i	0.0703856	−	0.0590605i	−0.606916	−	0.794766i	$-0.707594\pi$
$617$	1.74834	−	1.46703i	0.0703856	−	0.0590605i	0.677302	+	0.735705i	$0.263149\pi$
$618$	−13.0839	+	10.7610i	−0.526313	+	0.432870i
$619$	−14.6114	−	8.43592i	−0.587283	−	0.339068i	0.176739	−	0.984258i	$-0.443445\pi$
$619$	−14.6114	−	8.43592i	−0.587283	−	0.339068i	−0.764023	+	0.645190i	$0.776778\pi$
$620$	−26.7800	+	14.7660i	−1.07551	+	0.593018i
$621$	−2.88873	+	7.93671i	−0.115921	+	0.318489i
$622$	46.5051	+	8.67311i	1.86468	+	0.347760i
$623$	3.68154	+	20.8791i	0.147498	+	0.836502i
$624$	−0.223388	+	0.0714780i	−0.00894267	+	0.00286141i
$625$	3.04019	+	2.55102i	0.121607	+	0.102041i
$626$	0.472220	−	47.9547i	0.0188737	−	1.91666i
$627$	4.71565	+	7.47469i	0.188325	+	0.298510i
$628$	0.681354	−	34.5929i	0.0271890	−	1.38041i
$629$	−2.64256	+	3.14928i	−0.105366	+	0.125570i
$630$	−6.71279	+	2.36866i	−0.267444	+	0.0943698i
$631$	−4.11266	−	23.3241i	−0.163723	−	0.928517i	−0.950372	−	0.311117i	$-0.899297\pi$
$631$	−4.11266	−	23.3241i	−0.163723	−	0.928517i	0.786649	−	0.617400i	$-0.211814\pi$
$632$	16.6180	+	3.43918i	0.661030	+	0.136803i
$633$	22.7963	+	8.29718i	0.906073	+	0.329783i
$634$	6.88702	+	12.2046i	0.273518	+	0.484708i
$635$	48.2473	+	27.8556i	1.91464	+	1.10542i
$636$	−14.9630	+	12.0614i	−0.593321	+	0.478265i
$637$	−0.192754	−	0.229715i	−0.00763719	−	0.00910165i
$638$	7.01829	+	4.14468i	0.277857	+	0.164090i
$639$	−6.70144	−	11.6072i	−0.265105	−	0.459175i
$640$	−37.8981	−	16.8331i	−1.49805	−	0.665389i
$641$	0.332931	−	1.88815i	0.0131500	−	0.0745773i	−0.977527	−	0.210812i	$-0.932389\pi$
$641$	0.332931	−	1.88815i	0.0131500	−	0.0745773i	0.990677	+	0.136235i	$0.0435002\pi$
$642$	16.6455	−	2.76633i	0.656944	−	0.109178i
$643$	−9.07407	−	24.9308i	−0.357846	−	0.983175i	−0.979775	−	0.200101i	$-0.935873\pi$
$643$	−9.07407	−	24.9308i	−0.357846	−	0.983175i	0.621929	−	0.783074i	$-0.286349\pi$
$644$	17.4733	+	15.2582i	0.688544	+	0.601256i
$645$		−	12.9855i		−	0.511304i
$646$	1.66669	−	2.10910i	0.0655751	−	0.0829815i
$647$	12.5679			0.494094			0.247047	−	0.969004i	$-0.420540\pi$
$647$	12.5679			0.494094			0.247047	+	0.969004i	$0.420540\pi$
$648$	−1.88128	+	2.11206i	−0.0739037	+	0.0829694i
$649$	−2.49104	+	0.906664i	−0.0977818	+	0.0355897i
$650$	−0.114666	−	0.689962i	−0.00449756	−	0.0270626i
$651$	5.64184	+	0.994809i	0.221121	+	0.0389896i
$652$	−2.92114	+	7.55917i	−0.114401	+	0.296040i
$653$	7.43086	−	4.29021i	0.290792	−	0.167889i	−0.347507	−	0.937677i	$-0.612972\pi$
$653$	7.43086	−	4.29021i	0.290792	−	0.167889i	0.638299	+	0.769789i	$0.279638\pi$
$654$	−8.82753	−	5.21314i	−0.345184	−	0.203850i
$655$	18.8084	−	15.7822i	0.734906	−	0.616660i
$656$	−15.3173	+	11.8571i	−0.598041	+	0.462941i
$657$	−2.33045	+	4.03645i	−0.0909194	+	0.157477i
$658$	−8.08893	+	4.56454i	−0.315339	+	0.177944i
$659$	0.406103	−	1.11576i	0.0158195	−	0.0434638i	−0.931532	−	0.363661i	$-0.881527\pi$
$659$	0.406103	−	1.11576i	0.0158195	−	0.0434638i	0.947351	+	0.320197i	$0.103749\pi$
$660$	14.5838	+	2.86872i	0.567672	+	0.111665i
$661$	−18.9611	+	3.34335i	−0.737500	+	0.130041i	−0.529766	−	0.848144i	$-0.677720\pi$
$661$	−18.9611	+	3.34335i	−0.737500	+	0.130041i	−0.207735	+	0.978185i	$0.566609\pi$
$662$	29.0362	−	10.2457i	1.12852	−	0.398209i
$663$	−0.0195876	−	0.0164360i	−0.000760721	−	0.000638320i
$664$	21.1133	+	0.623884i	0.819356	+	0.0242114i
$665$	−19.4165	−	10.2168i	−0.752941	−	0.396190i
$666$	13.3318	+	0.131281i	0.516597	+	0.00508704i
$667$	−15.4324	+	18.3916i	−0.597544	+	0.712126i
$668$	3.99897	−	1.36694i	0.154725	−	0.0528885i
$669$	−1.62784	+	0.287032i	−0.0629360	+	0.0110973i
$670$	−39.9021	−	7.44166i	−1.54155	−	0.287496i
$671$	−18.9270	−	6.88887i	−0.730669	−	0.265942i
$672$	3.54841	+	6.91066i	0.136883	+	0.266585i
$673$	20.7172	−	35.8833i	0.798591	−	1.38320i	−0.121943	−	0.992537i	$-0.538913\pi$
$673$	20.7172	−	35.8833i	0.798591	−	1.38320i	0.920534	−	0.390663i	$-0.127754\pi$
$674$	3.37072	+	4.09835i	0.129835	+	0.157863i
$675$	−5.42161	−	6.46123i	−0.208678	−	0.248693i
$676$	13.4373	−	22.2504i	0.516821	−	0.855785i
$677$	33.0040	−	19.0549i	1.26845	−	0.732339i	0.293754	−	0.955881i	$-0.405095\pi$
$677$	33.0040	−	19.0549i	1.26845	−	0.732339i	0.974694	+	0.223542i	$0.0717621\pi$
$678$	4.87485	+	1.82886i	0.187217	+	0.0702369i
$679$	−1.84451	+	10.4607i	−0.0707858	+	0.401446i
$680$	−0.653192	−	4.47340i	−0.0250488	−	0.171547i
$681$	−26.1566	+	9.52024i	−1.00232	+	0.364816i
$682$	−9.08715	−	7.77878i	−0.347965	−	0.297865i
$683$		−	11.1589i		−	0.426984i	−0.976945	−	0.213492i	$-0.931516\pi$
$683$		−	11.1589i		−	0.426984i	0.976945	−	0.213492i	$-0.0684837\pi$
$684$	−8.71614	+	0.170206i	−0.333270	+	0.00650800i
$685$			35.3676i			1.35133i
$686$	−15.2995	+	17.8729i	−0.584139	+	0.682389i
$687$	−23.0691	+	8.39645i	−0.880139	+	0.320345i
$688$	−14.0420	+	1.90935i	−0.535347	+	0.0727934i
$689$	−0.0978442	+	0.554902i	−0.00372757	+	0.0211401i
$690$	−15.3782	+	40.9908i	−0.585438	+	1.56049i
$691$	−7.36097	+	4.24986i	−0.280024	+	0.161672i	−0.633434	−	0.773796i	$-0.718355\pi$
$691$	−7.36097	+	4.24986i	−0.280024	+	0.161672i	0.353410	+	0.935468i	$0.385022\pi$
$692$	−22.6845	−	13.6995i	−0.862334	−	0.520776i
$693$	−1.78977	−	2.13297i	−0.0679878	−	0.0810246i
$694$	4.45462	−	3.66374i	0.169095	−	0.139073i
$695$	−38.7005	+	67.0313i	−1.46799	+	2.54264i
$696$	−7.07854	+	3.81259i	−0.268311	+	0.144516i
$697$	−1.98438	−	0.722257i	−0.0751639	−	0.0273574i
$698$	6.66149	−	35.7188i	0.252141	−	1.35198i
$699$	−21.6327	+	3.81443i	−0.818223	+	0.144275i
$700$	−21.9206	+	7.49298i	−0.828522	+	0.283208i
$701$	11.5969	−	13.8207i	0.438011	−	0.522001i	−0.501205	−	0.865329i	$-0.667110\pi$
$701$	11.5969	−	13.8207i	0.438011	−	0.522001i	0.939216	+	0.343328i	$0.111554\pi$
$702$	−0.000816531		0.0829200i	−3.08180e−5		0.00312962i
$703$	27.6283	+	30.4195i	1.04202	+	1.14729i
$704$	0.957767	−	16.1921i	0.0360972	−	0.610263i
$705$	−13.4280	−	11.2674i	−0.505728	−	0.424356i
$706$	−11.0063	−	31.1917i	−0.414226	−	1.17392i
$707$	−7.58072	+	1.33669i	−0.285102	+	0.0502712i
$708$	0.504693	−	2.56572i	0.0189675	−	0.0964256i
$709$	14.1577	−	38.8980i	0.531704	−	1.46084i	−0.325338	−	0.945598i	$-0.605478\pi$
$709$	14.1577	−	38.8980i	0.531704	−	1.46084i	0.857042	−	0.515247i	$-0.172300\pi$
$710$	−34.1430	−	60.5057i	−1.28137	−	2.27074i
$711$	2.99993	−	5.19604i	0.112506	−	0.194867i
$712$	27.0679	+	34.2648i	1.01441	+	1.28413i
$713$	26.9911	−	22.6482i	1.01082	−	0.848182i
$714$	−0.430655	+	0.729237i	−0.0161168	+	0.0272910i
$715$	0.377380	−	0.217881i	0.0141132	−	0.00814827i
$716$	−9.79536	+	25.3479i	−0.366070	+	0.947295i
$717$	−11.4147	−	2.01271i	−0.426289	−	0.0751662i
$718$	−8.98931	+	1.49394i	−0.335478	+	0.0557535i
$719$	−12.3924	+	4.51046i	−0.462158	+	0.168212i	−0.562597	−	0.826732i	$-0.690198\pi$
$719$	−12.3924	+	4.51046i	−0.462158	+	0.168212i	0.100439	+	0.994943i	$0.467975\pi$
$720$	−9.85902	+	10.8514i	−0.367424	+	0.404407i
$721$	16.4503			0.612643
$722$	−18.6419	−	19.3515i	−0.693779	−	0.720188i
$723$		−	3.89955i		−	0.145026i
$724$	−25.8361	+	29.5869i	−0.960192	+	1.09959i
$725$	−8.20019	−	22.5298i	−0.304547	−	0.836737i
$726$	−1.59722	−	9.61075i	−0.0592785	−	0.356688i
$727$	−4.31118	+	24.4499i	−0.159893	+	0.906797i	0.794283	+	0.607549i	$0.207847\pi$
$727$	−4.31118	+	24.4499i	−0.159893	+	0.906797i	−0.954175	+	0.299248i	$0.903264\pi$
$728$	0.211626	+	0.0841843i	0.00784338	+	0.00312008i
$729$	0.500000	+	0.866025i	0.0185185	+	0.0320750i
$730$	−12.2854	+	20.8031i	−0.454703	+	0.769959i
$731$	−0.993065	−	1.18349i	−0.0367298	−	0.0437729i
$732$	15.4683	−	12.4687i	0.571726	−	0.460857i
$733$	−26.3284	−	15.2007i	−0.972463	−	0.561452i	−0.0724766	−	0.997370i	$-0.523090\pi$
$733$	−26.3284	−	15.2007i	−0.972463	−	0.561452i	−0.899986	+	0.435919i	$0.856424\pi$
$734$	−13.6258	+	7.68899i	−0.502939	+	0.283806i
$735$	−17.6144	−	6.41111i	−0.649716	−	0.236477i
$736$	46.5870	+	10.6022i	1.71722	+	0.390802i
$737$	−2.75699	−	15.6357i	−0.101555	−	0.575948i
$738$	2.27883	+	6.45819i	0.0838848	+	0.237729i
$739$	−12.0448	+	14.3544i	−0.443074	+	0.528035i	−0.940647	−	0.339387i	$-0.889780\pi$
$739$	−12.0448	+	14.3544i	−0.443074	+	0.528035i	0.497573	+	0.867422i	$0.334225\pi$
$740$	69.0958	+	1.36094i	2.54001	+	0.0500290i
$741$	−0.189200	+	0.171840i	−0.00695045	+	0.00631270i
$742$	18.6617	+	0.183766i	0.685093	+	0.00674625i
$743$	−3.58226	−	3.00587i	−0.131420	−	0.110275i	0.574708	−	0.818358i	$-0.305116\pi$
$743$	−3.58226	−	3.00587i	−0.131420	−	0.110275i	−0.706129	+	0.708084i	$0.749560\pi$
$744$	11.2021	−	3.70635i	0.410688	−	0.135881i
$745$	11.8757	+	67.3502i	0.435091	+	2.46752i
$746$	−7.39777	+	39.6668i	−0.270852	+	1.45230i
$747$	2.55419	−	7.01757i	0.0934528	−	0.256760i
$748$	1.54854	−	0.853838i	0.0566201	−	0.0312194i
$749$	−14.1901	−	8.19266i	−0.518495	−	0.299353i
$750$	−11.3087	−	13.7499i	−0.412936	−	0.502077i
$751$	34.4023	−	28.8669i	1.25536	−	1.05337i	0.259195	−	0.965825i	$-0.416543\pi$
$751$	34.4023	−	28.8669i	1.25536	−	1.05337i	0.996161	−	0.0875439i	$-0.0279018\pi$
$752$	−10.2097	+	16.1773i	−0.372311	+	0.589924i
$753$	−12.8753	−	22.3008i	−0.469204	−	0.812685i
$754$	−0.0827972	+	0.220697i	−0.00301530	+	0.00803732i
$755$	28.6522	+	5.05215i	1.04276	+	0.183867i
$756$	2.71369	−	0.423577i	0.0986961	−	0.0154053i
$757$	2.88932	+	7.93835i	0.105014	+	0.288524i	0.981060	−	0.193703i	$-0.0620500\pi$
$757$	2.88932	+	7.93835i	0.105014	+	0.288524i	−0.876046	+	0.482228i	$0.839828\pi$
$758$	5.31028	+	4.54571i	0.192878	+	0.165107i
$759$	−17.1248			−0.621592
$760$	−45.1869	+	0.437349i	−1.63910	+	0.0158643i
$761$	−32.6120			−1.18218			−0.591092	−	0.806604i	$-0.701303\pi$
$761$	−32.6120			−1.18218			−0.591092	+	0.806604i	$0.701303\pi$
$762$	−16.3296	−	13.9785i	−0.591559	−	0.506386i
$763$	3.40487	+	9.35480i	0.123264	+	0.338666i
$764$	−2.04158	−	13.0796i	−0.0738617	−	0.473204i
$765$	−1.57407	−	0.277552i	−0.0569108	−	0.0100349i
$766$	9.66584	−	25.7644i	0.349241	−	0.930907i
$767$	−0.0383317	−	0.0663925i	−0.00138408	−	0.00239729i
$768$	13.1839	+	9.06560i	0.475733	+	0.327127i
$769$	−30.9106	+	25.9370i	−1.11466	+	0.935314i	−0.998323	−	0.0578959i	$-0.981561\pi$
$769$	−30.9106	+	25.9370i	−1.11466	+	0.935314i	−0.116341	+	0.993209i	$0.537116\pi$
$770$	−9.16802	−	11.1471i	−0.330393	−	0.401714i
$771$	11.3506	+	6.55325i	0.408781	+	0.236010i
$772$	14.8654	+	26.9601i	0.535016	+	0.970315i
$773$	1.28158	−	3.52112i	0.0460953	−	0.126646i	−0.914509	−	0.404566i	$-0.867423\pi$
$773$	1.28158	−	3.52112i	0.0460953	−	0.126646i	0.960604	+	0.277920i	$0.0896449\pi$
$774$	−0.918571	+	4.92536i	−0.0330173	+	0.177039i
$775$	6.11002	+	34.6517i	0.219478	+	1.24472i
$776$	6.87207	+	20.7702i	0.246693	+	0.745606i
$777$	−9.91761	−	8.32186i	−0.355792	−	0.298545i
$778$	5.41794	+	0.0533516i	0.194243	+	0.00191275i
$779$	−9.82931	+	18.6801i	−0.352171	+	0.669285i
$780$	−0.00846463	+	0.429757i	−0.000303082	+	0.0153878i
$781$	17.4678	−	20.8173i	0.625046	−	0.744901i
$782$	1.73321	+	4.91191i	0.0619794	+	0.175650i
$783$	0.493607	+	2.79938i	0.0176401	+	0.100042i
$784$	−4.34275	+	19.9902i	−0.155098	+	0.713934i
$785$	−59.5853	−	21.6873i	−2.12669	−	0.774051i
$786$	−8.25038	+	4.65565i	−0.294281	+	0.166062i
$787$	11.6622	+	6.73318i	0.415713	+	0.240012i	0.693241	−	0.720706i	$-0.256182\pi$
$787$	11.6622	+	6.73318i	0.415713	+	0.240012i	−0.277529	+	0.960717i	$0.589515\pi$
$788$	−25.0286	−	31.0497i	−0.891606	−	1.10610i
$789$	5.40052	+	6.43608i	0.192263	+	0.229131i
$790$	15.8147	−	26.7794i	0.562663	−	0.952769i
$791$	−2.52795	−	4.37854i	−0.0898836	−	0.155683i
$792$	−5.32865	−	2.11972i	−0.189345	−	0.0753211i
$793$	0.101149	−	0.573643i	0.00359190	−	0.0203707i
$794$	−1.04144	−	6.26650i	−0.0369592	−	0.222390i
$795$	12.0465	+	33.0976i	0.427247	+	1.17385i
$796$	23.7125	+	20.7064i	0.840468	+	0.733921i
$797$		−	30.6309i		−	1.08500i	−0.840056	−	0.542500i	$-0.817478\pi$
$797$		−	30.6309i		−	1.08500i	0.840056	−	0.542500i	$-0.182522\pi$
$798$	6.64192	+	5.24869i	0.235121	+	0.185802i
$799$	−2.08549			−0.0737795
$800$	−32.4309	+	34.9966i	−1.14661	+	1.23732i
$801$	14.5073	−	5.28024i	0.512591	−	0.186568i
$802$	22.6520	−	3.76457i	0.799871	−	0.132931i
$803$	−9.30663	−	1.64101i	−0.328424	−	0.0579100i
$804$	14.6083	+	5.64520i	0.515196	+	0.199091i
$805$	36.8175	−	21.2566i	1.29765	−	0.749197i
$806$	0.175908	−	0.297869i	0.00619610	−	0.0104920i
$807$	−14.4104	+	12.0918i	−0.507270	+	0.425650i
$808$	−12.4408	+	9.82775i	−0.437665	+	0.345739i
$809$	13.1578	−	22.7900i	0.462605	−	0.801255i	−0.536485	−	0.843910i	$-0.680248\pi$
$809$	13.1578	−	22.7900i	0.462605	−	0.801255i	0.999090	+	0.0426547i	$0.0135815\pi$
$810$	2.54744	+	4.51438i	0.0895079	+	0.158619i
$811$	−5.32655	+	14.6346i	−0.187041	+	0.513890i	−0.997402	−	0.0720411i	$-0.977049\pi$
$811$	−5.32655	+	14.6346i	−0.187041	+	0.513890i	0.810361	+	0.585931i	$0.199271\pi$
$812$	7.66047	+	1.50686i	0.268830	+	0.0528805i
$813$	−1.33008	+	0.234529i	−0.0466480	+	0.00822530i
$814$	8.99499	+	25.4918i	0.315274	+	0.893487i
$815$	11.3771	+	9.54654i	0.398523	+	0.334401i
$816$	−0.0686862	+	1.74295i	−0.00240450	+	0.0610155i
$817$	−13.0608	+	8.23981i	−0.456939	+	0.288274i
$818$	0.254554	−	25.8504i	0.00890028	−	0.903837i
$819$	0.0517596	−	0.0616847i	0.00180863	−	0.00215544i
$820$	11.4822	+	33.5910i	0.400975	+	1.17305i
$821$	−24.4095	+	4.30405i	−0.851897	+	0.150213i	−0.582514	−	0.812821i	$-0.697931\pi$
$821$	−24.4095	+	4.30405i	−0.851897	+	0.150213i	−0.269383	+	0.963033i	$0.586820\pi$
$822$	2.50184	−	13.4148i	0.0872617	−	0.467896i
$823$	20.6795	+	7.52673i	0.720843	+	0.262365i	0.676283	−	0.736641i	$-0.263589\pi$
$823$	20.6795	+	7.52673i	0.720843	+	0.262365i	0.0445592	+	0.999007i	$0.485812\pi$
$824$	29.8298	−	16.0667i	1.03917	−	0.559709i
$825$	8.55072	−	14.8103i	0.297698	−	0.515628i
$826$	−1.96111	+	1.61293i	−0.0682358	+	0.0561210i
$827$	9.78752	+	11.6643i	0.340345	+	0.405608i	0.908884	−	0.417049i	$-0.136936\pi$
$827$	9.78752	+	11.6643i	0.340345	+	0.405608i	−0.568539	+	0.822656i	$0.692491\pi$
$828$	8.73251	−	14.4599i	0.303476	−	0.502515i
$829$	−37.0502	+	21.3909i	−1.28681	+	0.742938i	−0.978083	−	0.208215i	$-0.933235\pi$
$829$	−37.0502	+	21.3909i	−1.28681	+	0.742938i	−0.308722	+	0.951152i	$0.599901\pi$
$830$	13.5973	−	36.2437i	0.471968	−	1.25804i
$831$	0.138379	−	0.784784i	0.00480030	−	0.0272239i
$832$	0.465967	−	0.0540369i	0.0161545	−	0.00187339i
$833$	−2.09565	+	0.762754i	−0.0726099	+	0.0264279i
$834$	19.4207	−	22.6872i	0.672483	−	0.785592i
$835$		−	7.74507i		−	0.268029i
$836$	−6.36861	−	16.4886i	−0.220263	−	0.570270i
$837$		−	4.17168i		−	0.144195i
$838$	−23.2974	−	19.9431i	−0.804797	−	0.688922i
$839$	−52.1532	+	18.9822i	−1.80053	+	0.655338i	−0.802230	+	0.597016i	$0.796353\pi$
$839$	−52.1532	+	18.9822i	−1.80053	+	0.655338i	−0.998298	+	0.0583228i	$0.981425\pi$
$840$	14.0875	−	2.05701i	0.486064	−	0.0709736i
$841$	3.63269	−	20.6020i	0.125265	−	0.710413i
$842$	−2.64448	−	0.992108i	−0.0911348	−	0.0341903i
$843$	12.8672	−	7.42885i	0.443168	−	0.255863i
$844$	−41.5325	−	25.0821i	−1.42961	−	0.863361i
$845$	−30.6201	−	36.4917i	−1.05337	−	1.25535i
$846$	4.29617	+	5.22358i	0.147705	+	0.179590i
$847$	−4.73028	+	8.19308i	−0.162534	+	0.281518i
$848$	34.0191	−	17.8932i	1.16822	−	0.614456i
$849$	8.03552	+	2.92469i	0.275778	+	0.100375i
$850$	−5.11345	−	0.953649i	−0.175390	−	0.0327099i
$851$	−78.4153	+	13.8267i	−2.68804	+	0.473975i
$852$	8.67029	+	25.3648i	0.297039	+	0.868985i
$853$	−15.4823	+	18.4511i	−0.530103	+	0.631753i	−0.962939	−	0.269720i	$-0.913069\pi$
$853$	−15.4823	+	18.4511i	−0.530103	+	0.631753i	0.432835	+	0.901473i	$0.357513\pi$
$854$	−19.2920	−	0.189972i	−0.660158	−	0.00650071i
$855$	−4.87151	+	15.2159i	−0.166602	+	0.520374i
$856$	−33.7328	−	0.996780i	−1.15296	−	0.0340692i
$857$	18.5121	+	15.5335i	0.632361	+	0.530614i	0.901662	−	0.432442i	$-0.142348\pi$
$857$	18.5121	+	15.5335i	0.632361	+	0.530614i	−0.269300	+	0.963056i	$0.586792\pi$
$858$	−0.158552	+	0.0559463i	−0.00541287	+	0.00190997i
$859$	54.3335	−	9.58046i	1.85383	−	0.326881i	0.868258	−	0.496113i	$-0.165240\pi$
$859$	54.3335	−	9.58046i	1.85383	−	0.326881i	0.985576	+	0.169232i	$0.0541288\pi$
$860$	−5.01261	+	25.4827i	−0.170929	+	0.868952i
$861$	2.27451	−	6.24916i	0.0775150	−	0.212971i
$862$	35.5187	−	20.0430i	1.20977	−	0.682668i
$863$	−1.45648	+	2.52270i	−0.0495793	+	0.0858738i	−0.889750	−	0.456448i	$-0.849121\pi$
$863$	−1.45648	+	2.52270i	−0.0495793	+	0.0858738i	0.840171	+	0.542322i	$0.182455\pi$
$864$	4.50710	−	3.41848i	0.153335	−	0.116299i
$865$	−37.2036	+	31.2175i	−1.26496	+	1.06143i
$866$	−7.97106	−	4.70735i	−0.270868	−	0.159962i
$867$	14.5577	−	8.40492i	0.494407	−	0.285446i
$868$	−10.6875	−	4.13005i	−0.362758	−	0.140183i
$869$	11.9802	+	2.11244i	0.406401	+	0.0716595i
$870$	2.41562	+	14.5352i	0.0818973	+	0.492789i
$871$	0.431465	−	0.157040i	0.0146196	−	0.00532111i
$872$	15.3107	+	13.6378i	0.518487	+	0.461834i
$873$	7.73487			0.261786
$874$	50.9865	−	10.5429i	1.72464	−	0.356620i
$875$			17.2877i			0.584431i
$876$	6.13139	−	7.02152i	0.207160	−	0.237235i
$877$	1.48916	+	4.09142i	0.0502852	+	0.138158i	0.962293	−	0.272016i	$-0.0876904\pi$
$877$	1.48916	+	4.09142i	0.0502852	+	0.138158i	−0.912007	+	0.410174i	$0.865468\pi$
$878$	33.1574	−	5.51047i	1.11901	−	0.185969i
$879$	−4.02784	+	22.8430i	−0.135856	+	0.770477i
$880$	−27.5117	−	11.2591i	−0.927420	−	0.379545i
$881$	7.15927	+	12.4002i	0.241202	+	0.417774i	0.961057	−	0.276350i	$-0.0891250\pi$
$881$	7.15927	+	12.4002i	0.241202	+	0.417774i	−0.719855	+	0.694125i	$0.755792\pi$
$882$	6.22757	+	3.67772i	0.209693	+	0.123835i
$883$	−3.38302	−	4.03173i	−0.113848	−	0.135678i	0.706111	−	0.708101i	$-0.250448\pi$
$883$	−3.38302	−	4.03173i	−0.113848	−	0.135678i	−0.819959	+	0.572423i	$0.806004\pi$
$884$	0.0320941	+	0.0398150i	0.00107944	+	0.00133912i
$885$	−4.15016	−	2.39609i	−0.139506	−	0.0805438i
$886$	−23.8281	−	42.2263i	−0.800520	−	1.41862i
$887$	14.0321	+	5.10728i	0.471153	+	0.171486i	0.566674	−	0.823942i	$-0.308230\pi$
$887$	14.0321	+	5.10728i	0.471153	+	0.171486i	−0.0955217	+	0.995427i	$0.530452\pi$
$888$	−26.1116	−	5.40391i	−0.876247	−	0.181343i
$889$	3.62459	+	20.5561i	0.121565	+	0.689429i
$890$	75.4651	−	26.6285i	2.52960	−	0.892590i
$891$	−1.30328	+	1.55319i	−0.0436617	+	0.0520340i
$892$	3.30526	+	0.0651016i	0.110668	+	0.00217976i
$893$	−2.81216	+	20.6555i	−0.0941052	+	0.691209i
$894$	0.259827	−	26.3858i	0.00868990	−	0.882473i
$895$	38.1505	+	32.0121i	1.27523	+	1.07005i
$896$	−4.29575	−	14.9312i	−0.143511	−	0.498816i
$897$	−0.0859984	−	0.487721i	−0.00287140	−	0.0162845i
$898$	47.3219	+	8.82545i	1.57915	+	0.294509i
$899$	4.05578	−	11.1432i	0.135268	−	0.371645i
$900$	8.14521	+	14.7723i	0.271507	+	0.492410i
$901$	3.62905	+	2.09523i	0.120901	+	0.0698022i
$902$	−10.7244	+	8.82031i	−0.357082	+	0.293684i
$903$	3.72700	−	3.12733i	0.124027	−	0.104071i
$904$	−8.86041	−	5.47071i	−0.294693	−	0.181953i
$905$	35.9931	+	62.3418i	1.19645	+	2.07231i
$906$	−10.5103	−	3.94307i	−0.349181	−	0.131000i
$907$	3.86208	+	0.680989i	0.128238	+	0.0226119i	0.237399	−	0.971412i	$-0.423705\pi$
$907$	3.86208	+	0.680989i	0.128238	+	0.0226119i	−0.109161	+	0.994024i	$0.534816\pi$
$908$	55.0046	−	8.58559i	1.82539	−	0.284923i
$909$	1.91713	+	5.26728i	0.0635873	+	0.174705i
$910$	0.271433	−	0.317088i	0.00899793	−	0.0105114i
$911$	−24.5914			−0.814750			−0.407375	−	0.913261i	$-0.633556\pi$
$911$	−24.5914			−0.814750			−0.407375	+	0.913261i	$0.633556\pi$
$912$	17.1702	+	3.03055i	0.568562	+	0.100352i
$913$	15.1416			0.501115
$914$	−8.39241	+	9.80399i	−0.277596	+	0.324287i
$915$	−12.4534	−	34.2154i	−0.411696	−	1.13113i
$916$	48.5117	−	7.57213i	1.60287	−	0.250190i
$917$	9.05935	+	1.59741i	0.299166	+	0.0527510i
$918$	0.577408	+	0.216622i	0.0190573	+	0.00714958i
$919$	−8.52050	−	14.7579i	−0.281065	−	0.486820i	0.690582	−	0.723254i	$-0.257354\pi$
$919$	−8.52050	−	14.7579i	−0.281065	−	0.486820i	−0.971647	+	0.236435i	$0.924021\pi$
$920$	46.0012	−	74.5039i	1.51661	−	2.45632i
$921$	10.7018	−	8.97990i	0.352637	−	0.295898i
$922$	−11.9793	+	9.85243i	−0.394516	+	0.324473i
$923$	0.680604	+	0.392947i	0.0224023	+	0.0129340i
$924$	2.68888	+	4.87660i	0.0884576	+	0.160428i
$925$	27.1962	−	74.7208i	0.894204	−	2.45681i
$926$	−44.4416	−	8.28826i	−1.46044	−	0.272369i
$927$	−2.08011	−	11.7969i	−0.0683199	−	0.387461i
$928$	15.3626	−	4.74937i	0.504302	−	0.155906i
$929$	−16.4499	−	13.8031i	−0.539705	−	0.452866i	0.331732	−	0.943374i	$-0.392367\pi$
$929$	−16.4499	−	13.8031i	−0.539705	−	0.452866i	−0.871437	+	0.490507i	$0.836811\pi$
$930$	0.212927	−	21.6230i	0.00698214	−	0.709047i
$931$	4.72873	+	21.7846i	0.154978	+	0.713961i
$932$	43.9243	+	0.865148i	1.43879	+	0.0283389i
$933$	−21.5019	+	25.6250i	−0.703942	+	0.838925i
$934$	16.1951	−	5.71457i	0.529919	−	0.186986i
$935$	−0.562750	−	3.19152i	−0.0184039	−	0.104374i
$936$	0.0336108	−	0.162407i	0.00109860	−	0.00530843i
$937$	31.6434	+	11.5173i	1.03375	+	0.376252i	0.802506	−	0.596644i	$-0.203500\pi$
$937$	31.6434	+	11.5173i	1.03375	+	0.376252i	0.231239	+	0.972897i	$0.425722\pi$
$938$	−7.47385	−	13.2446i	−0.244030	−	0.432451i
$939$	29.3676	+	16.9554i	0.958374	+	0.553318i
$940$	22.0016	+	27.2946i	0.717615	+	0.890251i
$941$	11.0964	+	13.2242i	0.361732	+	0.431096i	0.915960	−	0.401269i	$-0.131431\pi$
$941$	11.0964	+	13.2242i	0.361732	+	0.431096i	−0.554228	+	0.832365i	$0.686986\pi$
$942$	21.0664	+	12.4409i	0.686380	+	0.405345i
$943$	−20.4504	−	35.4212i	−0.665957	−	1.15347i
$944$	−1.98082	+	4.84013i	−0.0644700	+	0.157533i
$945$	0.874057	−	4.95702i	0.0284331	−	0.161252i
$946$	−10.0212	+	1.66543i	−0.325816	+	0.0541478i
$947$	20.1580	+	55.3836i	0.655047	+	1.79973i	0.598206	+	0.801343i	$0.295881\pi$
$947$	20.1580	+	55.3836i	0.655047	+	1.79973i	0.0568409	+	0.998383i	$0.481897\pi$
$948$	−7.89280	+	9.03865i	−0.256346	+	0.293562i
$949$		−	0.273297i		−	0.00887159i
$950$	−16.3404	+	49.3595i	−0.530154	+	1.60143i
$951$	−9.90920			−0.321328
$952$	1.12661	−	1.26481i	0.0365137	−	0.0409928i
$953$	24.1958	−	8.80655i	0.783779	−	0.285272i	0.0810313	−	0.996712i	$-0.474179\pi$
$953$	24.1958	−	8.80655i	0.783779	−	0.285272i	0.702747	+	0.711439i	$0.251956\pi$
$954$	−2.22795	−	13.4060i	−0.0721327	−	0.434034i
$955$	−23.8921	−	4.21282i	−0.773131	−	0.136324i
$956$	21.6232	+	8.35598i	0.699343	+	0.270252i
$957$	−4.99130	+	2.88173i	−0.161346	+	0.0931530i
$958$	−28.3149	−	16.7215i	−0.914812	−	0.540247i
$959$	−10.1510	+	8.51766i	−0.327791	+	0.275050i
$960$	23.5361	−	17.4889i	0.759624	−	0.564453i
$961$	6.79852	−	11.7754i	0.219307	−	0.379851i
$962$	−0.680843	+	0.384196i	−0.0219513	+	0.0123870i
$963$	−4.08083	+	11.2120i	−0.131503	+	0.361301i
$964$	−1.50529	+	7.65245i	−0.0484820	+	0.246469i
$965$	55.5644	−	9.79751i	1.78868	−	0.315393i
$966$	−15.4684	+	5.45816i	−0.497689	+	0.175614i
$967$	2.22404	+	1.86619i	0.0715202	+	0.0600126i	0.677847	−	0.735203i	$-0.262913\pi$
$967$	2.22404	+	1.86619i	0.0715202	+	0.0600126i	−0.606327	+	0.795216i	$0.707358\pi$
$968$	−0.575521	+	19.4766i	−0.0184979	+	0.626003i
$969$	0.719651	+	1.75932i	0.0231185	+	0.0565174i
$970$	40.0920	+	0.394795i	1.28728	+	0.0126761i
$971$	−25.2809	+	30.1286i	−0.811304	+	0.966874i	−0.999885	−	0.0151836i	$-0.995167\pi$
$971$	−25.2809	+	30.1286i	−0.811304	+	0.966874i	0.188581	+	0.982058i	$0.439611\pi$
$972$	−0.646898	−	1.89249i	−0.0207493	−	0.0607017i
$973$	−28.5591	+	5.03575i	−0.915564	+	0.161439i
$974$	−1.67903	−	0.313136i	−0.0537997	−	0.0100335i
$975$	0.464743	+	0.169152i	0.0148837	+	0.00541721i
$976$	−35.1681	+	18.4975i	−1.12570	+	0.592092i
$977$	15.3343	−	26.5598i	0.490587	−	0.849722i	−0.509354	−	0.860557i	$-0.670116\pi$
$977$	15.3343	−	26.5598i	0.490587	−	0.849722i	0.999941	+	0.0108350i	$0.00344896\pi$
$978$	−3.64000	−	4.42577i	−0.116395	−	0.141521i
$979$	20.1206	+	23.9788i	0.643057	+	0.766366i
$980$	32.0916	+	19.3806i	1.02513	+	0.619089i
$981$	6.27800	−	3.62460i	0.200441	−	0.115725i
$982$	17.2472	+	6.47049i	0.550380	+	0.206482i
$983$	0.466892	−	2.64787i	0.0148915	−	0.0844540i	−0.976456	−	0.215715i	$-0.930792\pi$
$983$	0.466892	−	2.64787i	0.0148915	−	0.0844540i	0.991348	+	0.131261i	$0.0419027\pi$
$984$	−1.97899	−	13.5532i	−0.0630880	−	0.432060i
$985$	−68.6809	+	24.9978i	−2.18836	+	0.796496i
$986$	1.33174	+	1.13999i	0.0424111	+	0.0363047i
$987$		−	6.56757i		−	0.209048i
$988$	0.437619	−	0.264184i	0.0139225	−	0.00840480i
$989$		−	29.9228i		−	0.951490i
$990$	−6.83457	+	7.98413i	−0.217217	+	0.253752i
$991$	13.9247	−	5.06819i	0.442334	−	0.160996i	−0.111245	−	0.993793i	$-0.535484\pi$
$991$	13.9247	−	5.06819i	0.442334	−	0.160996i	0.553579	+	0.832797i	$0.313262\pi$
$992$	−23.4136	+	2.94914i	−0.743383	+	0.0936352i
$993$	−3.78074	+	21.4416i	−0.119978	+	0.680429i
$994$	9.14314	−	24.3712i	0.290003	−	0.773007i
$995$	49.9641	−	28.8468i	1.58397	−	0.914504i
$996$	−7.72122	+	12.7853i	−0.244656	+	0.405117i
$997$	−1.02010	−	1.21571i	−0.0323070	−	0.0385020i	0.749649	−	0.661836i	$-0.230222\pi$
$997$	−1.02010	−	1.21571i	−0.0323070	−	0.0385020i	−0.781956	+	0.623334i	$0.785778\pi$
$998$	−22.8870	+	18.8236i	−0.724476	+	0.595850i
$999$	−4.71373	+	8.16442i	−0.149136	+	0.258311i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	456.2.bk.a.301.29	yes	240
8.5	even	2	inner	456.2.bk.a.301.12	yes	240
19.6	even	9	inner	456.2.bk.a.253.12	✓	240
152.101	even	18	inner	456.2.bk.a.253.29	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
456.2.bk.a.253.12	✓	240	19.6	even	9	inner
456.2.bk.a.253.29	yes	240	152.101	even	18	inner
456.2.bk.a.301.12	yes	240	8.5	even	2	inner
456.2.bk.a.301.29	yes	240	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 456 = 2^{3} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	456.bk (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.919662 - 1.07435i) q^{2} +(0.342020 + 0.939693i) q^{3} +(-0.308442 - 1.97607i) q^{4} +(-3.60963 - 0.636475i) q^{5} +(1.32410 + 0.496752i) q^{6} +(-0.686638 - 1.18929i) q^{7} +(-2.40665 - 1.48595i) q^{8} +(-0.766044 + 0.642788i) q^{9} +(-4.00344 + 3.29265i) q^{10} +(-1.75591 - 1.01378i) q^{11} +(1.75141 - 0.965698i) q^{12} +(0.0200547 - 0.0551000i) q^{13} +(-1.90919 - 0.356060i) q^{14} +(-0.636475 - 3.60963i) q^{15} +(-3.80973 + 1.21901i) q^{16} +(-0.334054 - 0.280304i) q^{17} +(-0.0139254 + 1.41415i) q^{18} +(-3.22669 + 2.93061i) q^{19} +(-0.144359 + 7.32921i) q^{20} +(0.882725 - 1.05199i) q^{21} +(-2.70399 + 0.954126i) q^{22} +(-1.46664 - 8.31776i) q^{23} +(0.573209 - 2.76973i) q^{24} +(7.92587 + 2.88478i) q^{25} +(-0.0407529 - 0.0722191i) q^{26} +(-0.866025 - 0.500000i) q^{27} +(-2.13834 + 1.72368i) q^{28} +(-1.82717 - 2.17753i) q^{29} +(-4.46334 - 2.63585i) q^{30} +(2.08584 + 3.61278i) q^{31} +(-2.19402 + 5.21404i) q^{32} +(0.352081 - 1.99675i) q^{33} +(-0.608361 + 0.101104i) q^{34} +(1.72156 + 4.72993i) q^{35} +(1.50648 + 1.31550i) q^{36} -9.42746i q^{37} +(0.181036 + 6.16176i) q^{38} +0.0586362 q^{39} +(7.74135 + 6.89549i) q^{40} +(4.55055 - 1.65626i) q^{41} +(-0.318394 - 1.91583i) q^{42} +(3.48899 + 0.615202i) q^{43} +(-1.46170 + 3.78250i) q^{44} +(3.17426 - 1.83266i) q^{45} +(-10.2850 - 6.07384i) q^{46} +(3.66354 - 3.07407i) q^{47} +(-2.44850 - 3.16305i) q^{48} +(2.55706 - 4.42895i) q^{49} +(10.3884 - 5.86211i) q^{50} +(0.149147 - 0.409778i) q^{51} +(-0.115067 - 0.0226345i) q^{52} +(-9.46348 + 1.66867i) q^{53} +(-1.33362 + 0.470580i) q^{54} +(5.69295 + 4.77695i) q^{55} +(-0.114726 + 3.88252i) q^{56} +(-3.85747 - 2.02976i) q^{57} +(-4.01980 - 0.0395839i) q^{58} +(0.840408 - 1.00156i) q^{59} +(-6.93658 + 2.37108i) q^{60} +(9.78309 - 1.72502i) q^{61} +(5.79965 + 1.08162i) q^{62} +(1.29046 + 0.469688i) q^{63} +(3.58393 + 7.15230i) q^{64} +(-0.107460 + 0.186126i) q^{65} +(-1.82140 - 2.21459i) q^{66} +(5.03340 + 5.99857i) q^{67} +(-0.450866 + 0.746572i) q^{68} +(7.31451 - 4.22303i) q^{69} +(6.66484 + 2.50039i) q^{70} +(-2.32739 + 13.1993i) q^{71} +(2.79875 - 0.408665i) q^{72} +(4.37981 - 1.59412i) q^{73} +(-10.1284 - 8.67008i) q^{74} +8.43453i q^{75} +(6.78635 + 5.47224i) q^{76} +2.78439i q^{77} +(0.0539255 - 0.0629956i) q^{78} +(-5.63803 + 2.05207i) q^{79} +(14.5276 - 1.97537i) q^{80} +(0.173648 - 0.984808i) q^{81} +(2.40556 - 6.41207i) q^{82} +(-6.46743 + 3.73397i) q^{83} +(-2.35108 - 1.41985i) q^{84} +(1.02740 + 1.22441i) q^{85} +(3.86963 - 3.18260i) q^{86} +(1.42128 - 2.46174i) q^{87} +(2.71945 + 5.04899i) q^{88} +(-14.5073 - 5.28024i) q^{89} +(0.950334 - 5.09568i) q^{90} +(-0.0793003 + 0.0139828i) q^{91} +(-15.9841 + 5.46374i) q^{92} +(-2.68151 + 3.19570i) q^{93} +(0.0665969 - 6.76302i) q^{94} +(13.5124 - 8.52473i) q^{95} +(-5.65000 - 0.278400i) q^{96} +(-5.92525 - 4.97188i) q^{97} +(-2.40660 - 6.82030i) q^{98} +(1.99675 - 0.352081i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 6 q^{4} + 6 q^{6} - 24 q^{10} + 18 q^{14} - 6 q^{16} + 60 q^{20} - 36 q^{28} - 72 q^{31} - 90 q^{32} + 66 q^{34} - 6 q^{36} + 72 q^{38} - 114 q^{40} - 60 q^{44} + 30 q^{46} + 72 q^{47} + 24 q^{48}+ \cdots - 12 q^{98}+O(q^{100}) \) 240 * q + 6 * q^4 + 6 * q^6 - 24 * q^10 + 18 * q^14 - 6 * q^16 + 60 * q^20 - 36 * q^28 - 72 * q^31 - 90 * q^32 + 66 * q^34 - 6 * q^36 + 72 * q^38 - 114 * q^40 - 60 * q^44 + 30 * q^46 + 72 * q^47 + 24 * q^48 - 120 * q^49 + 18 * q^50 + 6 * q^52 - 6 * q^54 + 72 * q^58 - 12 * q^60 + 12 * q^62 + 30 * q^64 - 48 * q^66 - 78 * q^68 - 108 * q^70 - 36 * q^72 - 24 * q^73 - 96 * q^74 - 48 * q^76 - 96 * q^78 - 114 * q^80 - 66 * q^82 - 36 * q^84 - 24 * q^86 - 24 * q^88 + 6 * q^90 - 108 * q^94 + 120 * q^95 - 12 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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