LMFDB - Embedded newform 230.2.l.a.53.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [230,2,Mod(7,230)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(230, base_ring=CyclotomicField(44)) chi = DirichletCharacter(H, H._module([11, 38])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("230.7"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	230.l (of order $44$, degree $20$, 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:	$1.83655924649$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			53.1
Character	$\chi$	$=$	230.53
Dual form			230.2.l.a.217.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.0713392 - 0.997452i) q^{2} +(-3.05407 - 0.664372i) q^{3} +(-0.989821 + 0.142315i) q^{4} +(0.783298 - 2.09438i) q^{5} +(-0.444805 + 3.09368i) q^{6} +(-2.28419 - 1.24726i) q^{7} +(0.212565 + 0.977147i) q^{8} +(6.15705 + 2.81183i) q^{9} +(-2.14493 - 0.631890i) q^{10} +(-3.47691 + 3.01276i) q^{11} +(3.11753 + 0.222970i) q^{12} +(1.24765 + 2.28489i) q^{13} +(-1.08113 + 2.36735i) q^{14} +(-3.78370 + 5.87599i) q^{15} +(0.959493 - 0.281733i) q^{16} +(-2.99811 + 2.24436i) q^{17} +(2.36543 - 6.34196i) q^{18} +(0.215083 + 1.49593i) q^{19} +(-0.477263 + 2.18454i) q^{20} +(6.14742 + 5.32677i) q^{21} +(3.25312 + 3.25312i) q^{22} +(0.785478 - 4.73107i) q^{23} -3.12550i q^{24} +(-3.77289 - 3.28105i) q^{25} +(2.19007 - 1.40747i) q^{26} +(-9.42969 - 7.05898i) q^{27} +(2.43844 + 0.909491i) q^{28} +(-6.04466 - 0.869091i) q^{29} +(6.13095 + 3.35487i) q^{30} +(4.50690 + 2.89641i) q^{31} +(-0.349464 - 0.936950i) q^{32} +(12.6203 - 6.89121i) q^{33} +(2.45252 + 2.83036i) q^{34} +(-4.40144 + 3.80699i) q^{35} +(-6.49455 - 1.90697i) q^{36} +(-8.17698 + 3.04986i) q^{37} +(1.47678 - 0.321254i) q^{38} +(-2.29238 - 7.80713i) q^{39} +(2.21302 + 0.320204i) q^{40} +(-4.39226 - 9.61770i) q^{41} +(4.87465 - 6.51176i) q^{42} +(-0.143943 + 0.661697i) q^{43} +(3.01276 - 3.47691i) q^{44} +(10.7119 - 10.6927i) q^{45} +(-4.77505 - 0.445966i) q^{46} +(1.92809 - 1.92809i) q^{47} +(-3.11753 + 0.222970i) q^{48} +(-0.122635 - 0.190823i) q^{49} +(-3.00354 + 3.99734i) q^{50} +(10.6475 - 4.86256i) q^{51} +(-1.56012 - 2.08408i) q^{52} +(-3.01733 + 5.52584i) q^{53} +(-6.36829 + 9.90925i) q^{54} +(3.58642 + 9.64186i) q^{55} +(0.733218 - 2.49711i) q^{56} +(0.336979 - 4.71158i) q^{57} +(-0.435656 + 6.09126i) q^{58} +(1.80006 - 6.13045i) q^{59} +(2.90894 - 6.35466i) q^{60} +(-4.00554 + 6.23274i) q^{61} +(2.56751 - 4.70205i) q^{62} +(-10.5568 - 14.1022i) q^{63} +(-0.909632 + 0.415415i) q^{64} +(5.76272 - 0.823298i) q^{65} +(-7.77397 - 12.0965i) q^{66} +(-7.74682 + 0.554064i) q^{67} +(2.64819 - 2.64819i) q^{68} +(-5.54209 + 13.9272i) q^{69} +(4.11128 + 4.11864i) q^{70} +(-8.49053 + 9.79860i) q^{71} +(-1.43880 + 6.61404i) q^{72} +(-0.891553 + 1.19098i) q^{73} +(3.62542 + 7.93857i) q^{74} +(9.34282 + 12.5272i) q^{75} +(-0.425787 - 1.45010i) q^{76} +(11.6996 - 2.54509i) q^{77} +(-7.62370 + 2.84349i) q^{78} +(-4.18153 - 1.22781i) q^{79} +(0.161513 - 2.23023i) q^{80} +(10.8114 + 12.4770i) q^{81} +(-9.27986 + 5.06719i) q^{82} +(-0.858110 - 2.30068i) q^{83} +(-6.84293 - 4.39768i) q^{84} +(2.35213 + 8.03720i) q^{85} +(0.670280 + 0.0963717i) q^{86} +(17.8834 + 6.67017i) q^{87} +(-3.68298 - 2.75704i) q^{88} +(13.5970 - 8.73826i) q^{89} +(-11.4297 - 9.92176i) q^{90} -6.77526i q^{91} +(-0.104181 + 4.79470i) q^{92} +(-11.8401 - 11.8401i) q^{93} +(-2.06073 - 1.78563i) q^{94} +(3.30154 + 0.721296i) q^{95} +(0.444805 + 3.09368i) q^{96} +(-2.56949 + 6.88907i) q^{97} +(-0.181589 + 0.135936i) q^{98} +(-29.8789 + 8.77322i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 8 q^{3} - 8 q^{6} - 8 q^{12} + 16 q^{13} + 24 q^{16} - 72 q^{18} - 80 q^{23} - 8 q^{26} + 16 q^{27} - 44 q^{28} + 24 q^{31} - 44 q^{33} - 8 q^{35} - 32 q^{36} - 88 q^{37} - 24 q^{41} - 8 q^{46}+ \cdots + 24 q^{98}+O(q^{100}) $ 240 * q - 8 * q^3 - 8 * q^6 - 8 * q^12 + 16 * q^13 + 24 * q^16 - 72 * q^18 - 80 * q^23 - 8 * q^26 + 16 * q^27 - 44 * q^28 + 24 * q^31 - 44 * q^33 - 8 * q^35 - 32 * q^36 - 88 * q^37 - 24 * q^41 - 8 * q^46 - 80 * q^47 + 8 * q^48 + 8 * q^50 + 16 * q^52 - 44 * q^56 - 88 * q^57 - 176 * q^61 - 32 * q^62 - 176 * q^66 + 24 * q^70 - 336 * q^71 + 16 * q^72 - 88 * q^73 - 36 * q^75 - 24 * q^77 + 40 * q^78 - 136 * q^81 + 40 * q^82 - 100 * q^85 - 44 * q^86 + 40 * q^87 + 8 * q^92 + 56 * q^93 + 52 * q^95 + 8 * q^96 + 132 * q^97 + 24 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{19}{22}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.0713392	−	0.997452i	−0.0504444	−	0.705305i
$2$	−0.0713392	−	0.997452i	−0.0504444	−	0.705305i
$3$	−3.05407	−	0.664372i	−1.76327	−	0.383575i	−0.789974	−	0.613140i	$-0.789906\pi$
$3$	−3.05407	−	0.664372i	−1.76327	−	0.383575i	−0.973293	+	0.229565i	$0.926270\pi$
$4$	−0.989821	+	0.142315i	−0.494911	+	0.0711574i
$5$	0.783298	−	2.09438i	0.350301	−	0.936637i
$5$	0.783298	−	2.09438i	0.350301	−	0.936637i
$6$	−0.444805	+	3.09368i	−0.181591	+	1.26299i
$7$	−2.28419	−	1.24726i	−0.863341	−	0.471420i	−0.0143934	−	0.999896i	$-0.504582\pi$
$7$	−2.28419	−	1.24726i	−0.863341	−	0.471420i	−0.848948	+	0.528476i	$0.822764\pi$
$8$	0.212565	+	0.977147i	0.0751532	+	0.345474i
$9$	6.15705	+	2.81183i	2.05235	+	0.937277i
$10$	−2.14493	−	0.631890i	−0.678286	−	0.199821i
$11$	−3.47691	+	3.01276i	−1.04833	+	0.908380i	−0.995920	−	0.0902455i	$-0.971235\pi$
$11$	−3.47691	+	3.01276i	−1.04833	+	0.908380i	−0.0524072	+	0.998626i	$0.516689\pi$
$12$	3.11753	+	0.222970i	0.899954	+	0.0643660i
$13$	1.24765	+	2.28489i	0.346035	+	0.633716i	0.991505	−	0.130070i	$-0.0415203\pi$
$13$	1.24765	+	2.28489i	0.346035	+	0.633716i	−0.645470	+	0.763786i	$0.723338\pi$
$14$	−1.08113	+	2.36735i	−0.288944	+	0.632700i
$15$	−3.78370	+	5.87599i	−0.976946	+	1.51717i
$16$	0.959493	−	0.281733i	0.239873	−	0.0704331i
$17$	−2.99811	+	2.24436i	−0.727149	+	0.544337i	−0.897483	−	0.441050i	$-0.854606\pi$
$17$	−2.99811	+	2.24436i	−0.727149	+	0.544337i	0.170334	+	0.985386i	$0.445515\pi$
$18$	2.36543	−	6.34196i	0.557537	−	1.49481i
$19$	0.215083	+	1.49593i	0.0493434	+	0.343191i	0.999506	+	0.0314355i	$0.0100079\pi$
$19$	0.215083	+	1.49593i	0.0493434	+	0.343191i	−0.950162	+	0.311755i	$0.899083\pi$
$20$	−0.477263	+	2.18454i	−0.106719	+	0.488478i
$21$	6.14742	+	5.32677i	1.34148	+	1.16240i
$22$	3.25312	+	3.25312i	0.693568	+	0.693568i
$23$	0.785478	−	4.73107i	0.163783	−	0.986496i
$23$	0.785478	−	4.73107i	0.163783	−	0.986496i
$24$		−	3.12550i		−	0.637989i
$25$	−3.77289	−	3.28105i	−0.754578	−	0.656211i
$26$	2.19007	−	1.40747i	0.429507	−	0.276028i
$27$	−9.42969	−	7.05898i	−1.81475	−	1.35850i
$28$	2.43844	+	0.909491i	0.460822	+	0.171878i
$29$	−6.04466	−	0.869091i	−1.12247	−	0.161386i	−0.444006	−	0.896024i	$-0.646443\pi$
$29$	−6.04466	−	0.869091i	−1.12247	−	0.161386i	−0.678460	+	0.734638i	$0.737352\pi$
$30$	6.13095	+	3.35487i	1.11935	+	0.612512i
$31$	4.50690	+	2.89641i	0.809464	+	0.520211i	0.878692	−	0.477390i	$-0.158417\pi$
$31$	4.50690	+	2.89641i	0.809464	+	0.520211i	−0.0692275	+	0.997601i	$0.522053\pi$
$32$	−0.349464	−	0.936950i	−0.0617771	−	0.165631i
$33$	12.6203	−	6.89121i	2.19691	−	1.19961i
$34$	2.45252	+	2.83036i	0.420604	+	0.485403i
$35$	−4.40144	+	3.80699i	−0.743979	+	0.643498i
$36$	−6.49455	−	1.90697i	−1.08242	−	0.317829i
$37$	−8.17698	+	3.04986i	−1.34429	+	0.501393i	−0.915611	−	0.402065i	$-0.868293\pi$
$37$	−8.17698	+	3.04986i	−1.34429	+	0.501393i	−0.428676	+	0.903458i	$0.641020\pi$
$38$	1.47678	−	0.321254i	0.239565	−	0.0521142i
$39$	−2.29238	−	7.80713i	−0.367074	−	1.25014i
$40$	2.21302	+	0.320204i	0.349910	+	0.0506286i
$41$	−4.39226	−	9.61770i	−0.685955	−	1.50203i	−0.856207	−	0.516632i	$-0.827186\pi$
$41$	−4.39226	−	9.61770i	−0.685955	−	1.50203i	0.170252	−	0.985401i	$-0.445542\pi$
$42$	4.87465	−	6.51176i	0.752174	−	1.00479i
$43$	−0.143943	+	0.661697i	−0.0219511	+	0.100908i	−0.986819	−	0.161828i	$-0.948261\pi$
$43$	−0.143943	+	0.661697i	−0.0219511	+	0.100908i	0.964868	+	0.262736i	$0.0846247\pi$
$44$	3.01276	−	3.47691i	0.454190	−	0.524163i
$45$	10.7119	−	10.6927i	1.59683	−	1.59398i
$46$	−4.77505	−	0.445966i	−0.704043	−	0.0657540i
$47$	1.92809	−	1.92809i	0.281241	−	0.281241i	−0.552363	−	0.833604i	$-0.686274\pi$
$47$	1.92809	−	1.92809i	0.281241	−	0.281241i	0.833604	+	0.552363i	$0.186274\pi$
$48$	−3.11753	+	0.222970i	−0.449977	+	0.0321830i
$49$	−0.122635	−	0.190823i	−0.0175193	−	0.0272605i
$50$	−3.00354	+	3.99734i	−0.424764	+	0.565310i
$51$	10.6475	−	4.86256i	1.49095	−	0.680895i
$52$	−1.56012	−	2.08408i	−0.216350	−	0.289010i
$53$	−3.01733	+	5.52584i	−0.414463	+	0.759032i	−0.998615	−	0.0526122i	$-0.983245\pi$
$53$	−3.01733	+	5.52584i	−0.414463	+	0.759032i	0.584152	+	0.811644i	$0.301427\pi$
$54$	−6.36829	+	9.90925i	−0.866614	+	1.34848i
$55$	3.58642	+	9.64186i	0.483592	+	1.30011i
$56$	0.733218	−	2.49711i	0.0979803	−	0.333690i
$57$	0.336979	−	4.71158i	0.0446340	−	0.624064i
$58$	−0.435656	+	6.09126i	−0.0572044	+	0.799822i
$59$	1.80006	−	6.13045i	0.234348	−	0.798117i	−0.755396	−	0.655268i	$-0.772556\pi$
$59$	1.80006	−	6.13045i	0.234348	−	0.798117i	0.989745	−	0.142849i	$-0.0456263\pi$
$60$	2.90894	−	6.35466i	0.375543	−	0.820383i
$61$	−4.00554	+	6.23274i	−0.512856	+	0.798020i	−0.997035	−	0.0769490i	$-0.975482\pi$
$61$	−4.00554	+	6.23274i	−0.512856	+	0.798020i	0.484179	+	0.874969i	$0.339118\pi$
$62$	2.56751	−	4.70205i	0.326075	−	0.597161i
$63$	−10.5568	−	14.1022i	−1.33003	−	1.77671i
$64$	−0.909632	+	0.415415i	−0.113704	+	0.0519269i
$65$	5.76272	−	0.823298i	0.714778	−	0.102118i
$66$	−7.77397	−	12.0965i	−0.956910	−	1.48898i
$67$	−7.74682	+	0.554064i	−0.946425	+	0.0676897i	−0.536012	−	0.844210i	$-0.680070\pi$
$67$	−7.74682	+	0.554064i	−0.946425	+	0.0676897i	−0.410413	+	0.911900i	$0.634615\pi$
$68$	2.64819	−	2.64819i	0.321140	−	0.321140i
$69$	−5.54209	+	13.9272i	−0.667190	+	1.67663i
$70$	4.11128	+	4.11864i	0.491392	+	0.492272i
$71$	−8.49053	+	9.79860i	−1.00764	+	1.16288i	−0.0210313	+	0.999779i	$0.506695\pi$
$71$	−8.49053	+	9.79860i	−1.00764	+	1.16288i	−0.986609	+	0.163101i	$0.947851\pi$
$72$	−1.43880	+	6.61404i	−0.169564	+	0.779472i
$73$	−0.891553	+	1.19098i	−0.104348	+	0.139393i	−0.849676	−	0.527306i	$-0.823202\pi$
$73$	−0.891553	+	1.19098i	−0.104348	+	0.139393i	0.745327	+	0.666699i	$0.232293\pi$
$74$	3.62542	+	7.93857i	0.421447	+	0.922840i
$75$	9.34282	+	12.5272i	1.07882	+	1.44651i
$76$	−0.425787	−	1.45010i	−0.0488412	−	0.166338i
$77$	11.6996	−	2.54509i	1.33329	−	0.290040i
$78$	−7.62370	+	2.84349i	−0.863214	+	0.321962i
$79$	−4.18153	−	1.22781i	−0.470459	−	0.138139i	0.0379052	−	0.999281i	$-0.487932\pi$
$79$	−4.18153	−	1.22781i	−0.470459	−	0.138139i	−0.508364	+	0.861142i	$0.669750\pi$
$80$	0.161513	−	2.23023i	0.0180577	−	0.249347i
$81$	10.8114	+	12.4770i	1.20127	+	1.38634i
$82$	−9.27986	+	5.06719i	−1.02479	+	0.559577i
$83$	−0.858110	−	2.30068i	−0.0941898	−	0.252533i	0.881308	−	0.472543i	$-0.156664\pi$
$83$	−0.858110	−	2.30068i	−0.0941898	−	0.252533i	−0.975498	+	0.220010i	$0.929391\pi$
$84$	−6.84293	−	4.39768i	−0.746624	−	0.479826i
$85$	2.35213	+	8.03720i	0.255125	+	0.871757i
$86$	0.670280	+	0.0963717i	0.0722781	+	0.0103920i
$87$	17.8834	+	6.67017i	1.91730	+	0.715117i
$88$	−3.68298	−	2.75704i	−0.392606	−	0.293902i
$89$	13.5970	−	8.73826i	1.44128	−	0.926254i	0.441703	−	0.897161i	$-0.354374\pi$
$89$	13.5970	−	8.73826i	1.44128	−	0.926254i	0.999577	−	0.0290929i	$-0.00926187\pi$
$90$	−11.4297	−	9.92176i	−1.20479	−	1.04584i
$91$		−	6.77526i		−	0.710241i
$92$	−0.104181	+	4.79470i	−0.0108616	+	0.499882i
$93$	−11.8401	−	11.8401i	−1.22776	−	1.22776i
$94$	−2.06073	−	1.78563i	−0.212548	−	0.184174i
$95$	3.30154	+	0.721296i	0.338730	+	0.0740034i
$96$	0.444805	+	3.09368i	0.0453977	+	0.315748i
$97$	−2.56949	+	6.88907i	−0.260892	+	0.699479i	0.738782	+	0.673945i	$0.235401\pi$
$97$	−2.56949	+	6.88907i	−0.260892	+	0.699479i	−0.999674	+	0.0255342i	$0.991871\pi$
$98$	−0.181589	+	0.135936i	−0.0183432	+	0.0137316i
$99$	−29.8789	+	8.77322i	−3.00294	+	0.881742i
$100$	4.20143	+	2.71072i	0.420143	+	0.271072i
$101$	5.86240	−	12.8369i	0.583330	−	1.27732i	−0.356059	−	0.934463i	$-0.615880\pi$
$101$	5.86240	−	12.8369i	0.583330	−	1.27732i	0.939389	−	0.342852i	$-0.111393\pi$
$102$	−5.60976	−	10.2735i	−0.555449	−	1.01723i
$103$	13.1808	+	0.942711i	1.29874	+	0.0928881i	0.703522	−	0.710673i	$-0.251609\pi$
$103$	13.1808	+	0.942711i	1.29874	+	0.0928881i	0.595222	+	0.803561i	$0.297064\pi$
$104$	−1.96747	+	1.70482i	−0.192926	+	0.167172i
$105$	15.9716	−	8.70261i	1.55866	−	0.849288i
$106$	5.72701	+	2.61544i	0.556256	+	0.254034i
$107$	−1.26668	−	5.82282i	−0.122454	−	0.562913i	−0.996961	−	0.0778999i	$-0.975179\pi$
$107$	−1.26668	−	5.82282i	−0.122454	−	0.562913i	0.874507	−	0.485013i	$-0.161185\pi$
$108$	10.3383	+	5.64514i	0.994804	+	0.543204i
$109$	0.132276	−	0.919999i	0.0126697	−	0.0881199i	−0.982505	−	0.186234i	$-0.940372\pi$
$109$	0.132276	−	0.919999i	0.0126697	−	0.0881199i	0.995175	+	0.0981138i	$0.0312809\pi$
$110$	9.36144	−	4.26512i	0.892579	−	0.406663i
$111$	26.9993	−	3.88191i	2.56266	−	0.368455i
$112$	−2.54306	−	0.553208i	−0.240296	−	0.0522732i
$113$	−0.0449236	−	0.628113i	−0.00422605	−	0.0590879i	0.994901	−	0.100852i	$-0.0321568\pi$
$113$	−0.0449236	−	0.628113i	−0.00422605	−	0.0590879i	−0.999128	+	0.0417639i	$0.986702\pi$
$114$	−4.72362			−0.442407
$115$	−9.29341	−	5.35093i	−0.866615	−	0.498977i
$116$	6.10682			0.567004
$117$	1.25709	+	17.5764i	0.116218	+	1.62494i
$118$	−6.24325	−	1.35814i	−0.574738	−	0.125027i
$119$	9.64755	−	1.38711i	0.884389	−	0.127156i
$120$	−6.54599	−	2.44819i	−0.597564	−	0.223489i
$121$	1.44671	−	10.0621i	0.131519	−	0.914737i
$122$	6.50261	+	3.55069i	0.588718	+	0.321465i
$123$	7.02452	+	32.2912i	0.633380	+	2.91160i
$124$	−4.87323	−	2.22553i	−0.437629	−	0.199859i
$125$	−9.82708	+	5.33184i	−0.878961	+	0.476894i
$126$	−13.3132	+	11.5359i	−1.18603	+	1.02770i
$127$	2.58455	+	0.184850i	0.229341	+	0.0164028i	0.185537	−	0.982637i	$-0.440598\pi$
$127$	2.58455	+	0.184850i	0.229341	+	0.0164028i	0.0438045	+	0.999040i	$0.486052\pi$
$128$	0.479249	+	0.877679i	0.0423600	+	0.0775766i
$129$	0.879226	−	1.92524i	0.0774115	−	0.169508i
$130$	−1.23231	−	5.68931i	−0.108081	−	0.498985i
$131$	−20.2225	+	5.93786i	−1.76685	+	0.518794i	−0.993363	−	0.115021i	$-0.963307\pi$
$131$	−20.2225	+	5.93786i	−1.76685	+	0.518794i	−0.773485	+	0.633814i	$0.781488\pi$
$132$	−11.5111	+	8.61712i	−1.00191	+	0.750024i
$133$	1.37453	−	3.68526i	0.119187	−	0.319552i
$134$	1.10530	+	7.68756i	0.0954837	+	0.664104i
$135$	−22.1705	+	14.2201i	−1.90813	+	1.22387i
$136$	−2.83036	−	2.45252i	−0.242702	−	0.210302i
$137$	3.47894	+	3.47894i	0.297226	+	0.297226i	0.839926	−	0.542701i	$-0.182598\pi$
$137$	3.47894	+	3.47894i	0.297226	+	0.297226i	−0.542701	+	0.839926i	$0.682598\pi$
$138$	14.2870	+	4.53442i	1.21619	+	0.385996i
$139$		−	9.56448i		−	0.811249i	−0.914040	−	0.405624i	$-0.867054\pi$
$139$		−	9.56448i		−	0.811249i	0.914040	−	0.405624i	$-0.132946\pi$
$140$	3.81485	−	4.39463i	0.322414	−	0.371414i
$141$	−7.16949	+	4.60755i	−0.603780	+	0.388026i
$142$	10.3793	+	7.76987i	0.871015	+	0.652033i
$143$	−11.2218	−	4.18551i	−0.938412	−	0.350010i
$144$	6.69983	+	0.963290i	0.558319	+	0.0802742i
$145$	−6.55498	+	11.9791i	−0.544362	+	0.994809i
$146$	1.25154	+	0.804318i	0.103579	+	0.0665659i
$147$	0.247757	+	0.664263i	0.0204347	+	0.0547875i
$148$	7.65971	−	4.18252i	0.629624	−	0.343801i
$149$	−8.43804	−	9.73802i	−0.691271	−	0.797770i	0.296274	−	0.955103i	$-0.404256\pi$
$149$	−8.43804	−	9.73802i	−0.691271	−	0.797770i	−0.987546	+	0.157333i	$0.949710\pi$
$150$	11.8287	−	10.2127i	0.965812	−	0.833863i
$151$	−6.62240	−	1.94451i	−0.538924	−	0.158242i	0.000932510	−	1.00000i	$-0.499703\pi$
$151$	−6.62240	−	1.94451i	−0.538924	−	0.158242i	−0.539856	+	0.841757i	$0.681521\pi$
$152$	−1.41603	+	0.528151i	−0.114855	+	0.0428387i
$153$	−24.7703	+	5.38845i	−2.00256	+	0.435630i
$154$	−3.37325	−	11.4882i	−0.271824	−	0.925747i
$155$	9.59645	−	7.17044i	0.770805	−	0.575943i
$156$	3.38012	+	7.40142i	0.270626	+	0.592588i
$157$	−8.34427	+	11.1466i	−0.665946	+	0.889599i	−0.998570	−	0.0534602i	$-0.982975\pi$
$157$	−8.34427	+	11.1466i	−0.665946	+	0.889599i	0.332624	+	0.943059i	$0.392066\pi$
$158$	−0.926374	+	4.25847i	−0.0736983	+	0.338786i
$159$	12.8864	−	14.8717i	1.02195	−	1.17940i
$160$	−2.23607	−	0.00199849i	−0.176777	−	0.000157994i
$161$	−7.69505	+	9.82695i	−0.606455	+	0.774472i
$162$	11.6740	−	11.6740i	0.917194	−	0.917194i
$163$	12.0572	−	0.862351i	0.944396	−	0.0675445i	0.409359	−	0.912373i	$-0.365752\pi$
$163$	12.0572	−	0.862351i	0.944396	−	0.0675445i	0.535037	+	0.844829i	$0.320298\pi$
$164$	5.71629	+	8.89472i	0.446367	+	0.694561i
$165$	−4.54738	−	31.8296i	−0.354013	−	2.47793i
$166$	−2.23360	+	1.02005i	−0.173361	+	0.0791714i
$167$	−6.24220	−	8.33860i	−0.483036	−	0.645260i	0.491132	−	0.871085i	$-0.336583\pi$
$167$	−6.24220	−	8.33860i	−0.483036	−	0.645260i	−0.974168	+	0.225825i	$0.927492\pi$
$168$	−3.89831	+	7.13922i	−0.300761	+	0.550803i
$169$	3.36421	−	5.23482i	0.258786	−	0.402678i
$170$	7.84892	−	2.91951i	0.601985	−	0.223916i
$171$	−2.88204	+	9.81532i	−0.220395	+	0.750596i
$172$	0.0483089	−	0.675447i	0.00368352	−	0.0515023i
$173$	0.904460	−	12.6460i	0.0687649	−	0.961458i	−0.839580	−	0.543236i	$-0.817199\pi$
$173$	0.904460	−	12.6460i	0.0687649	−	0.961458i	0.908345	−	0.418222i	$-0.137347\pi$
$174$	5.37739	−	18.3137i	0.407659	−	1.38836i
$175$	4.52566	+	12.2003i	0.342107	+	0.922257i
$176$	−2.48728	+	3.87028i	−0.187485	+	0.291733i
$177$	−9.57042	+	17.5269i	−0.719357	+	1.31740i
$178$	−9.68600	−	12.9390i	−0.725996	−	0.969818i
$179$	−0.654216	+	0.298770i	−0.0488984	+	0.0223311i	−0.439714	−	0.898138i	$-0.644920\pi$
$179$	−0.654216	+	0.298770i	−0.0488984	+	0.0223311i	0.390816	+	0.920469i	$0.372193\pi$
$180$	−9.08109	+	12.1083i	−0.676865	+	0.902503i
$181$	7.33618	+	11.4153i	0.545294	+	0.848494i	0.999092	−	0.0426108i	$-0.0135675\pi$
$181$	7.33618	+	11.4153i	0.545294	+	0.848494i	−0.453798	+	0.891105i	$0.649931\pi$
$182$	−6.75800	+	0.483342i	−0.500936	+	0.0358277i
$183$	16.3740	−	16.3740i	1.21040	−	1.21040i
$184$	4.78992	−	0.238134i	0.353117	−	0.0175555i
$185$	−0.0174413	+	19.5147i	−0.00128231	+	1.43475i
$186$	−10.9653	+	12.6546i	−0.804013	+	0.927880i
$187$	3.66245	−	16.8360i	0.267825	−	1.23117i
$188$	−1.63407	+	2.18286i	−0.119177	+	0.159201i
$189$	12.7348	+	27.8853i	0.926320	+	2.02836i
$190$	0.483929	−	3.34458i	0.0351079	−	0.242641i
$191$	−4.97822	−	16.9543i	−0.360211	−	1.22677i	−0.917932	−	0.396738i	$-0.870142\pi$
$191$	−4.97822	−	16.9543i	−0.360211	−	1.22677i	0.557720	−	0.830029i	$-0.311676\pi$
$192$	3.05407	−	0.664372i	0.220408	−	0.0479469i
$193$	−12.8226	+	4.78257i	−0.922989	+	0.344257i	−0.765628	−	0.643284i	$-0.777571\pi$
$193$	−12.8226	+	4.78257i	−0.922989	+	0.344257i	−0.157361	+	0.987541i	$0.550299\pi$
$194$	7.05482	+	2.07148i	0.506507	+	0.148724i
$195$	−18.1467	−	1.31418i	−1.29951	−	0.0941106i
$196$	0.148544	+	0.171428i	0.0106103	+	0.0122449i
$197$	15.4396	−	8.43065i	1.10003	−	0.600659i	0.176540	−	0.984293i	$-0.443510\pi$
$197$	15.4396	−	8.43065i	1.10003	−	0.600659i	0.923485	+	0.383634i	$0.125328\pi$
$198$	10.8824	+	29.1769i	0.773379	+	2.07351i
$199$	16.9934	+	10.9210i	1.20463	+	0.774170i	0.979752	−	0.200216i	$-0.0641643\pi$
$199$	16.9934	+	10.9210i	1.20463	+	0.774170i	0.224881	+	0.974386i	$0.427801\pi$
$200$	2.40409	−	4.38410i	0.169995	−	0.310003i
$201$	24.0274	+	3.45462i	1.69476	+	0.243670i
$202$	−13.2224	−	4.93169i	−0.930323	−	0.346993i
$203$	12.7232	+	9.52443i	0.892990	+	0.668484i
$204$	−9.84714	+	6.32837i	−0.689438	+	0.443075i
$205$	−23.5836	+	1.66555i	−1.64715	+	0.116327i
$206$		−	13.2145i		−	0.920697i
$207$	18.1392	−	26.9208i	1.26076	−	1.87113i
$208$	1.84084	+	1.84084i	0.127639	+	0.127639i
$209$	−5.25471	−	4.55323i	−0.363476	−	0.314954i
$210$	−9.81984	−	15.3100i	−0.677633	−	1.05649i
$211$	0.469737	+	3.26709i	0.0323380	+	0.224916i	0.999581	−	0.0289354i	$-0.00921170\pi$
$211$	0.469737	+	3.26709i	0.0323380	+	0.224916i	−0.967243	+	0.253851i	$0.918303\pi$
$212$	2.20021	−	5.89900i	0.151111	−	0.405145i
$213$	32.4406	−	24.2847i	2.22279	−	1.66396i
$214$	−5.71762	+	1.67884i	−0.390848	+	0.114763i
$215$	1.27310	+	0.819778i	0.0868245	+	0.0559084i
$216$	4.89323	−	10.7147i	0.332942	−	0.729042i
$217$	−6.68203	−	12.2372i	−0.453606	−	0.830717i
$218$	−0.927091	−	0.0663069i	−0.0627905	−	0.00449087i
$219$	3.51412	−	3.04500i	0.237462	−	0.205762i
$220$	−4.92209	−	9.03332i	−0.331847	−	0.609026i
$221$	−8.86870	−	4.05020i	−0.596574	−	0.272446i
$222$	−5.79813	−	26.6536i	−0.389145	−	1.78887i
$223$	6.18260	+	3.37595i	0.414017	+	0.226070i	0.672737	−	0.739882i	$-0.265119\pi$
$223$	6.18260	+	3.37595i	0.414017	+	0.226070i	−0.258719	+	0.965953i	$0.583301\pi$
$224$	−0.370379	+	2.57604i	−0.0247470	+	0.172119i
$225$	−14.0041	−	30.8103i	−0.933607	−	2.05402i
$226$	−0.623308	+	0.0896182i	−0.0414618	+	0.00596131i
$227$	6.23564	+	1.35648i	0.413874	+	0.0900327i	0.414681	−	0.909967i	$-0.363893\pi$
$227$	6.23564	+	1.35648i	0.413874	+	0.0900327i	−0.000807034		1.00000i	$0.500257\pi$
$228$	0.336979	+	4.71158i	0.0223170	+	0.312032i
$229$	−0.740462			−0.0489311			−0.0244655	−	0.999701i	$-0.507788\pi$
$229$	−0.740462			−0.0489311			−0.0244655	+	0.999701i	$0.507788\pi$
$230$	−4.67431	+	9.65147i	−0.308215	+	0.636399i
$231$	−37.4223			−2.46220
$232$	−0.435656	−	6.09126i	−0.0286022	−	0.399911i
$233$	−23.3081	−	5.07036i	−1.52696	−	0.332171i	−0.630818	−	0.775931i	$-0.717281\pi$
$233$	−23.3081	−	5.07036i	−1.52696	−	0.332171i	−0.896146	+	0.443760i	$0.853644\pi$
$234$	17.4419	−	2.50777i	1.14021	−	0.163938i
$235$	−2.52789	−	5.54843i	−0.164901	−	0.361940i
$236$	−0.909287	+	6.32423i	−0.0591895	+	0.411672i
$237$	11.9550	+	6.52791i	0.776559	+	0.424033i
$238$	−2.07182	−	9.52401i	−0.134296	−	0.617350i
$239$	−14.8082	−	6.76267i	−0.957861	−	0.437440i	−0.125758	−	0.992061i	$-0.540136\pi$
$239$	−14.8082	−	6.76267i	−0.957861	−	0.437440i	−0.832103	+	0.554621i	$0.812863\pi$
$240$	−1.97497	+	6.70396i	−0.127484	+	0.432739i
$241$	14.7073	−	12.7439i	0.947378	−	0.820908i	−0.0365754	−	0.999331i	$-0.511645\pi$
$241$	14.7073	−	12.7439i	0.947378	−	0.820908i	0.983954	+	0.178423i	$0.0570995\pi$
$242$	−10.1397	−	0.725204i	−0.651803	−	0.0466179i
$243$	−7.79399	−	14.2736i	−0.499985	−	0.915654i
$244$	3.07776	−	6.73934i	0.197033	−	0.431442i
$245$	−0.495717	+	0.107373i	−0.0316702	+	0.00685979i
$246$	31.7078	−	9.31026i	2.02162	−	0.593600i
$247$	−3.14970	+	2.35784i	−0.200411	+	0.150026i
$248$	−1.87221	+	5.01958i	−0.118885	+	0.318744i
$249$	1.09222	+	7.59655i	0.0692165	+	0.481412i
$250$	6.01931	+	9.42167i	0.380694	+	0.595879i
$251$	9.70871	+	8.41265i	0.612808	+	0.531002i	0.905029	−	0.425349i	$-0.139849\pi$
$251$	9.70871	+	8.41265i	0.612808	+	0.531002i	−0.292221	+	0.956351i	$0.594394\pi$
$252$	12.4563	+	12.4563i	0.784671	+	0.784671i
$253$	11.5225	+	18.8159i	0.724415	+	1.18295i
$254$		−	2.59115i		−	0.162583i
$255$	−1.84389	−	26.1089i	−0.115469	−	1.63500i
$256$	0.841254	−	0.540641i	0.0525783	−	0.0337901i
$257$	3.03881	+	2.27483i	0.189556	+	0.141900i	0.689841	−	0.723961i	$-0.257680\pi$
$257$	3.03881	+	2.27483i	0.189556	+	0.141900i	−0.500285	+	0.865861i	$0.666771\pi$
$258$	−1.98305	−	0.739641i	−0.123460	−	0.0460480i
$259$	22.4817	+	3.23238i	1.39695	+	0.200850i
$260$	−5.58690	+	1.63504i	−0.346485	+	0.101401i
$261$	−34.7736	−	22.3476i	−2.15243	−	1.38328i
$262$	7.36539	+	19.7474i	0.455035	+	1.22000i
$263$	−8.94562	+	4.88468i	−0.551610	+	0.301202i	−0.730777	−	0.682617i	$-0.760842\pi$
$263$	−8.94562	+	4.88468i	−0.551610	+	0.301202i	0.179166	+	0.983819i	$0.442660\pi$
$264$	9.41636	+	10.8671i	0.579537	+	0.668821i
$265$	9.20975	+	10.6478i	0.565750	+	0.654091i
$266$	−3.77393	−	1.10812i	−0.231394	−	0.0679435i
$267$	−47.3317	+	17.6538i	−2.89665	+	1.08039i
$268$	7.58912	−	1.65091i	0.463579	−	0.100845i
$269$	−0.0847081	−	0.288489i	−0.00516474	−	0.0175895i	0.956870	−	0.290515i	$-0.0938268\pi$
$269$	−0.0847081	−	0.288489i	−0.00516474	−	0.0175895i	−0.962035	+	0.272926i	$0.912009\pi$
$270$	15.7655	+	21.0995i	0.959458	+	1.28408i
$271$	−0.124734	−	0.273130i	−0.00757706	−	0.0165915i	0.905806	−	0.423693i	$-0.139267\pi$
$271$	−0.124734	−	0.273130i	−0.00757706	−	0.0165915i	−0.913383	+	0.407102i	$0.866539\pi$
$272$	−2.24436	+	2.99811i	−0.136084	+	0.181787i
$273$	−4.50130	+	20.6921i	−0.272431	+	1.25234i
$274$	3.22189	−	3.71826i	0.194641	−	0.224628i
$275$	23.0030	+	0.0411179i	1.38713	+	0.00247950i
$276$	3.50364	−	14.5741i	0.210894	−	0.877260i
$277$	4.35669	−	4.35669i	0.261768	−	0.261768i	−0.564004	−	0.825772i	$-0.690740\pi$
$277$	4.35669	−	4.35669i	0.261768	−	0.261768i	0.825772	+	0.564004i	$0.190740\pi$
$278$	−9.54011	+	0.682322i	−0.572178	+	0.0409230i
$279$	19.6050	+	30.5060i	1.17372	+	1.82635i
$280$	−4.65558	−	3.49162i	−0.278224	−	0.208664i
$281$	25.5276	−	11.6581i	1.52285	−	0.695463i	0.534154	−	0.845387i	$-0.320630\pi$
$281$	25.5276	−	11.6581i	1.52285	−	0.695463i	0.988698	+	0.149924i	$0.0479029\pi$
$282$	5.10728	+	6.82252i	0.304134	+	0.406275i
$283$	2.99164	−	5.47879i	0.177835	−	0.325680i	−0.773523	−	0.633768i	$-0.781507\pi$
$283$	2.99164	−	5.47879i	0.177835	−	0.325680i	0.951358	+	0.308088i	$0.0996891\pi$
$284$	7.00962	−	10.9072i	0.415945	−	0.647223i
$285$	−9.60391	−	4.39634i	−0.568886	−	0.260416i
$286$	−3.37429	+	11.4918i	−0.199526	+	0.679523i
$287$	−1.96304	+	27.4469i	−0.115875	+	1.62014i
$288$	0.482876	−	6.75148i	0.0284537	−	0.397835i
$289$	−0.837923	+	2.85370i	−0.0492896	+	0.167865i
$290$	12.4162	+	5.68370i	0.729104	+	0.333758i
$291$	12.4243	−	19.3326i	0.728326	−	1.13330i
$292$	0.712985	−	1.30573i	0.0417243	−	0.0764123i
$293$	10.2353	+	13.6728i	0.597953	+	0.798772i	0.992776	−	0.119986i	$-0.0382849\pi$
$293$	10.2353	+	13.6728i	0.597953	+	0.798772i	−0.394823	+	0.918757i	$0.629194\pi$
$294$	0.644896	−	0.294514i	0.0376111	−	0.0171764i
$295$	−11.4295	−	8.57200i	−0.665453	−	0.499081i
$296$	−4.71830	−	7.34182i	−0.274246	−	0.426734i
$297$	54.0531	−	3.86596i	3.13648	−	0.224326i
$298$	−9.11124	+	9.11124i	−0.527800	+	0.527800i
$299$	11.7900	−	4.10797i	0.681833	−	0.237570i
$300$	−11.0305	−	11.0700i	−0.636848	−	0.639129i
$301$	1.15410	−	1.33190i	0.0665213	−	0.0767697i
$302$	−1.46712	+	6.74425i	−0.0844234	+	0.388088i
$303$	−26.4326	+	35.3099i	−1.51851	+	2.02850i
$304$	0.627824	+	1.37474i	0.0360082	+	0.0788469i
$305$	9.91622	+	13.2712i	0.567801	+	0.759908i
$306$	7.14181	+	24.3228i	0.408270	+	1.39044i
$307$	−13.6666	+	2.97299i	−0.779996	+	0.169678i	−0.584899	−	0.811106i	$-0.698866\pi$
$307$	−13.6666	+	2.97299i	−0.779996	+	0.169678i	−0.195097	+	0.980784i	$0.562502\pi$
$308$	−11.2183	+	4.18421i	−0.639222	+	0.238418i
$309$	−39.6288	−	11.6361i	−2.25440	−	0.661953i
$310$	−7.83677	−	9.06046i	−0.445099	−	0.514600i
$311$	−2.93544	−	3.38768i	−0.166454	−	0.192098i	0.666394	−	0.745599i	$-0.267837\pi$
$311$	−2.93544	−	3.38768i	−0.166454	−	0.192098i	−0.832848	+	0.553502i	$0.813291\pi$
$312$	7.14143	−	3.89951i	0.404304	−	0.220767i
$313$	−5.04980	−	13.5390i	−0.285432	−	0.765272i	−0.997973	−	0.0636414i	$-0.979729\pi$
$313$	−5.04980	−	13.5390i	−0.285432	−	0.765272i	0.712541	−	0.701630i	$-0.247544\pi$
$314$	11.7135	+	7.52782i	0.661032	+	0.424820i
$315$	−37.8045	+	11.0637i	−2.13004	+	0.623370i
$316$	4.31371	+	0.620217i	0.242665	+	0.0348900i
$317$	12.1053	+	4.51505i	0.679902	+	0.253591i	0.665602	−	0.746307i	$-0.268175\pi$
$317$	12.1053	+	4.51505i	0.679902	+	0.253591i	0.0143009	+	0.999898i	$0.495448\pi$
$318$	−15.7531	−	11.7926i	−0.883388	−	0.661296i
$319$	23.6351	−	15.1893i	1.32331	−	0.850440i
$320$	0.157526	+	2.23051i	0.00880596	+	0.124689i
$321$			18.6248i			1.03954i
$322$	10.3509	+	6.97440i	0.576832	+	0.388668i
$323$	−4.00226	−	4.00226i	−0.222691	−	0.222691i
$324$	−12.4770	−	10.8114i	−0.693169	−	0.600635i
$325$	2.78963	−	12.7142i	0.154741	−	0.705259i
$326$	−1.72031	−	11.9650i	−0.0952790	−	0.662680i
$327$	−1.01520	+	2.72186i	−0.0561407	+	0.150519i
$328$	8.46427	−	6.33627i	0.467361	−	0.349862i
$329$	−6.80895	+	1.99929i	−0.375389	+	0.110224i
$330$	−31.4241	+	6.80649i	−1.72984	+	0.374685i
$331$	−6.24039	+	13.6646i	−0.343003	+	0.751072i	−0.999996	−	0.00282474i	$-0.999101\pi$
$331$	−6.24039	+	13.6646i	−0.343003	+	0.751072i	0.656993	+	0.753897i	$0.271828\pi$
$332$	1.17680	+	2.15514i	0.0645851	+	0.118279i
$333$	−58.9218	−	4.21417i	−3.22889	−	0.230935i
$334$	−7.87204	+	6.82116i	−0.430739	+	0.373237i
$335$	−4.90765	+	16.6588i	−0.268133	+	0.910168i
$336$	7.39913	+	3.37907i	0.403656	+	0.184343i
$337$	−0.930715	−	4.27843i	−0.0506993	−	0.233061i	0.944824	−	0.327579i	$-0.106233\pi$
$337$	−0.930715	−	4.27843i	−0.0506993	−	0.233061i	−0.995523	+	0.0945180i	$0.969869\pi$
$338$	−5.46148	−	2.98219i	−0.297065	−	0.162210i
$339$	−0.280101	+	1.94815i	−0.0152130	+	0.105809i
$340$	−3.47201	−	7.62065i	−0.188296	−	0.413288i
$341$	−24.3963	+	3.50765i	−1.32113	+	0.189950i
$342$	9.99592	+	2.17448i	0.540517	+	0.117582i
$343$	1.34175	+	18.7601i	0.0724478	+	1.01295i
$344$	−0.677172			−0.0365107
$345$	24.8277	+	22.5164i	1.33668	+	1.21224i
$346$	−12.6783			−0.681590
$347$	−0.959472	−	13.4152i	−0.0515072	−	0.720164i	−0.955943	−	0.293554i	$-0.905162\pi$
$347$	−0.959472	−	13.4152i	−0.0515072	−	0.720164i	0.904435	−	0.426611i	$-0.140293\pi$
$348$	−18.6507	−	4.05720i	−0.999780	−	0.217489i
$349$	−20.0416	+	2.88155i	−1.07280	+	0.154246i	−0.656007	−	0.754755i	$-0.727756\pi$
$349$	−20.0416	+	2.88155i	−1.07280	+	0.154246i	−0.416795	+	0.909001i	$0.636847\pi$
$350$	11.8464	−	5.38449i	0.633215	−	0.287813i
$351$	4.36410	−	30.3530i	0.232938	−	1.62012i
$352$	4.03786	+	2.20484i	0.215218	+	0.117518i
$353$	7.15039	+	32.8698i	0.380577	+	1.74948i	0.625767	+	0.780010i	$0.284786\pi$
$353$	7.15039	+	32.8698i	0.380577	+	1.74948i	−0.245190	+	0.969475i	$0.578850\pi$
$354$	18.1650	+	8.29568i	0.965459	+	0.440910i
$355$	13.8714	+	25.4577i	0.736218	+	1.35115i
$356$	−12.2150	+	10.5844i	−0.647395	+	0.560971i
$357$	−30.3858	−	2.17324i	−1.60819	−	0.115020i
$358$	0.344680	+	0.631235i	0.0182169	+	0.0333618i
$359$	−7.61976	+	16.6849i	−0.402155	+	0.880598i	0.594892	+	0.803806i	$0.297195\pi$
$359$	−7.61976	+	16.6849i	−0.402155	+	0.880598i	−0.997047	+	0.0767917i	$0.975532\pi$
$360$	12.7253	+	8.19416i	0.670684	+	0.431870i
$361$	16.0388	−	4.70942i	0.844148	−	0.247864i
$362$	10.8629	−	8.13185i	0.570940	−	0.427400i
$363$	−11.1033	+	29.7692i	−0.582775	+	1.56248i
$364$	0.964221	+	6.70630i	0.0505389	+	0.351506i
$365$	1.79601	+	2.80014i	0.0940074	+	0.146566i
$366$	−17.5004	−	15.1642i	−0.914762	−	0.792646i
$367$	−8.88352	−	8.88352i	−0.463716	−	0.463716i	0.436155	−	0.899871i	$-0.356340\pi$
$367$	−8.88352	−	8.88352i	−0.463716	−	0.463716i	−0.899871	+	0.436155i	$0.856340\pi$
$368$	−0.579236	−	4.76072i	−0.0301948	−	0.248170i
$369$		−	71.5670i		−	3.72563i
$370$	19.4662	−	1.37476i	1.01200	−	0.0714706i
$371$	13.7843	−	8.85864i	0.715646	−	0.459918i
$372$	13.4046	+	10.0346i	0.694997	+	0.520268i
$373$	−8.37203	−	3.12260i	−0.433487	−	0.161682i	0.123242	−	0.992377i	$-0.460671\pi$
$373$	−8.37203	−	3.12260i	−0.433487	−	0.161682i	−0.556729	+	0.830694i	$0.687944\pi$
$374$	−17.0544	−	2.45205i	−0.881861	−	0.126793i
$375$	33.5549	−	9.75496i	1.73277	−	0.503744i
$376$	2.29387	+	1.47418i	0.118297	+	0.0760251i
$377$	−5.55582	−	14.8957i	−0.286139	−	0.767169i
$378$	26.9058	−	14.6917i	1.38388	−	0.755658i
$379$	−8.15891	−	9.41588i	−0.419095	−	0.483661i	0.506466	−	0.862260i	$-0.330952\pi$
$379$	−8.15891	−	9.41588i	−0.419095	−	0.483661i	−0.925561	+	0.378599i	$0.876406\pi$
$380$	−3.37058	−	0.244097i	−0.172907	−	0.0125219i
$381$	−7.77058	−	2.28165i	−0.398099	−	0.116892i
$382$	−16.5559	+	6.17504i	−0.847075	+	0.315942i
$383$	−8.69015	+	1.89043i	−0.444046	+	0.0965963i	−0.429029	−	0.903291i	$-0.641144\pi$
$383$	−8.69015	+	1.89043i	−0.444046	+	0.0965963i	−0.0150175	+	0.999887i	$0.504780\pi$
$384$	−0.880554	−	2.99889i	−0.0449356	−	0.153037i
$385$	3.83387	−	26.4970i	0.195392	−	1.35041i
$386$	5.68514	+	12.4487i	0.289366	+	0.633623i
$387$	−2.74685	+	3.66936i	−0.139630	+	0.186524i
$388$	1.56292	−	7.18462i	0.0793452	−	0.364744i
$389$	−18.6433	+	21.5155i	−0.945253	+	1.09088i	0.0504916	+	0.998724i	$0.483921\pi$
$389$	−18.6433	+	21.5155i	−0.945253	+	1.09088i	−0.995745	+	0.0921556i	$0.970624\pi$
$390$	−0.0162611	+	18.1943i	−0.000823414	+	0.921302i
$391$	8.26327	+	15.9472i	0.417891	+	0.806483i
$392$	0.160395	−	0.160395i	0.00810115	−	0.00810115i
$393$	65.7059	−	4.69938i	3.31442	−	0.237052i
$394$	−9.51062	−	14.7988i	−0.479138	−	0.745553i
$395$	−5.84689	+	7.79600i	−0.294189	+	0.392259i
$396$	28.3262	−	12.9361i	1.42344	−	0.650065i
$397$	−10.8551	−	14.5007i	−0.544800	−	0.727767i	0.440660	−	0.897674i	$-0.354744\pi$
$397$	−10.8551	−	14.5007i	−0.544800	−	0.727767i	−0.985460	+	0.169907i	$0.945653\pi$
$398$	9.68089	−	17.7292i	0.485259	−	0.888686i
$399$	−6.64629	+	10.3418i	−0.332731	+	0.517739i
$400$	−4.54444	−	2.08520i	−0.227222	−	0.104260i
$401$	−9.50070	+	32.3564i	−0.474442	+	1.61580i	0.280392	+	0.959886i	$0.409536\pi$
$401$	−9.50070	+	32.3564i	−0.474442	+	1.61580i	−0.754834	+	0.655916i	$0.772283\pi$
$402$	1.73172	−	24.2127i	0.0863705	−	1.20762i
$403$	−0.994970	+	13.9115i	−0.0495630	+	0.692981i
$404$	−3.97585	+	13.5405i	−0.197806	+	0.673665i
$405$	34.6003	−	12.8700i	1.71930	−	0.639517i
$406$	8.59251	−	13.3702i	0.426439	−	0.663552i
$407$	19.2421	−	35.2393i	0.953796	−	1.74675i
$408$	7.01473	+	9.37059i	0.347281	+	0.463913i
$409$	24.1954	−	11.0497i	1.19639	−	0.546372i	0.285241	−	0.958456i	$-0.407926\pi$
$409$	24.1954	−	11.0497i	1.19639	−	0.546372i	0.911146	+	0.412084i	$0.135199\pi$
$410$	3.34374	+	23.4047i	0.165136	+	1.15588i
$411$	−8.31361	−	12.9362i	−0.410080	−	0.638097i
$412$	−13.1808	+	0.942711i	−0.649372	+	0.0464440i
$413$	−11.7580	+	11.7580i	−0.578571	+	0.578571i
$414$	−28.1463	−	16.1725i	−1.38331	−	0.794834i
$415$	−5.49067	−	0.00490729i	−0.269526	−	0.000240889i
$416$	1.70482	−	1.96747i	0.0835858	−	0.0964632i
$417$	−6.35437	+	29.2106i	−0.311175	+	1.43045i
$418$	−4.16676	+	5.56614i	−0.203803	+	0.272249i
$419$	6.02766	+	13.1987i	0.294470	+	0.644800i	0.997816	−	0.0660475i	$-0.0210389\pi$
$419$	6.02766	+	13.1987i	0.294470	+	0.644800i	−0.703346	+	0.710847i	$0.748312\pi$
$420$	−14.5705	+	10.8870i	−0.710967	+	0.531232i
$421$	2.59875	+	8.85054i	0.126656	+	0.431349i	0.998267	−	0.0588484i	$-0.0187428\pi$
$421$	2.59875	+	8.85054i	0.126656	+	0.431349i	−0.871611	+	0.490197i	$0.836925\pi$
$422$	3.22526	−	0.701612i	0.157003	−	0.0341539i
$423$	17.2928	−	6.44988i	0.840805	−	0.313604i
$424$	−6.04093	−	1.77378i	−0.293374	−	0.0861423i
$425$	18.6754	+	1.36925i	0.905890	+	0.0664183i
$426$	−26.5371	−	30.6255i	−1.28573	−	1.48381i
$427$	16.9232	−	9.24079i	0.818973	−	0.447193i
$428$	2.08246	+	5.58328i	0.100659	+	0.269878i
$429$	31.4914	+	20.2383i	1.52042	+	0.977113i
$430$	0.726868	−	1.32834i	0.0350527	−	0.0640580i
$431$	−23.2189	−	3.33838i	−1.11842	−	0.160804i	−0.441782	−	0.897123i	$-0.645653\pi$
$431$	−23.2189	−	3.33838i	−1.11842	−	0.160804i	−0.676635	+	0.736319i	$0.736562\pi$
$432$	−11.0365	−	4.11639i	−0.530992	−	0.198050i
$433$	−12.0033	−	8.98558i	−0.576843	−	0.431820i	0.270610	−	0.962689i	$-0.412775\pi$
$433$	−12.0033	−	8.98558i	−0.576843	−	0.431820i	−0.847454	+	0.530869i	$0.821865\pi$
$434$	−11.7294	+	7.53800i	−0.563027	+	0.361836i
$435$	27.9779	−	32.2300i	1.34144	−	1.54531i
$436$			0.929459i			0.0445130i
$437$	7.24631	+	0.157451i	0.346638	+	0.00753189i
$438$	−3.28794	−	3.28794i	−0.157104	−	0.157104i
$439$	3.74540	+	3.24541i	0.178758	+	0.154895i	0.739644	−	0.672998i	$-0.234994\pi$
$439$	3.74540	+	3.24541i	0.178758	+	0.154895i	−0.560886	+	0.827893i	$0.689539\pi$
$440$	−8.65917	+	5.55398i	−0.412810	+	0.264776i
$441$	−0.218505	−	1.51974i	−0.0104050	−	0.0723685i
$442$	−3.40720	+	9.13505i	−0.162064	+	0.434510i
$443$	26.4865	−	19.8275i	1.25841	−	0.942034i	0.258696	−	0.965959i	$-0.416707\pi$
$443$	26.4865	−	19.8275i	1.25841	−	0.942034i	0.999714	+	0.0239248i	$0.00761624\pi$
$444$	−26.1720	+	7.68480i	−1.24207	+	0.364705i
$445$	−7.65078	−	35.3220i	−0.362682	−	1.67442i
$446$	2.92629	−	6.40768i	0.138564	−	0.303412i
$447$	19.3007	+	35.3466i	0.912891	+	1.67184i
$448$	2.59590	+	0.185662i	0.122645	+	0.00877173i
$449$	−7.55683	+	6.54803i	−0.356629	+	0.309021i	−0.814686	−	0.579902i	$-0.803091\pi$
$449$	−7.55683	+	6.54803i	−0.356629	+	0.309021i	0.458057	+	0.888923i	$0.348545\pi$
$450$	−29.7328	+	16.1664i	−1.40162	+	0.762092i
$451$	44.2473	+	20.2070i	2.08352	+	0.951513i
$452$	0.133856	+	0.615327i	0.00629606	+	0.0289425i
$453$	18.9334	+	10.3384i	0.889569	+	0.485741i
$454$	0.908178	−	6.31652i	0.0426229	−	0.296449i
$455$	−14.1900	−	5.30705i	−0.665238	−	0.248798i
$456$	4.67554	−	0.672241i	0.218952	−	0.0314806i
$457$	−4.38274	−	0.953406i	−0.205016	−	0.0445985i	0.108884	−	0.994054i	$-0.465272\pi$
$457$	−4.38274	−	0.953406i	−0.205016	−	0.0445985i	−0.313900	+	0.949456i	$0.601636\pi$
$458$	0.0528239	+	0.738575i	0.00246830	+	0.0345113i
$459$	44.1142			2.05907
$460$	9.96034	+	3.97387i	0.464403	+	0.185283i
$461$	−34.9162			−1.62621			−0.813106	−	0.582116i	$-0.802225\pi$
$461$	−34.9162			−1.62621			−0.813106	+	0.582116i	$0.802225\pi$
$462$	2.66967	+	37.3269i	0.124204	+	1.73661i
$463$	−23.5886	−	5.13139i	−1.09626	−	0.238476i	−0.372155	−	0.928170i	$-0.621381\pi$
$463$	−23.5886	−	5.13139i	−1.09626	−	0.238476i	−0.724100	+	0.689695i	$0.757745\pi$
$464$	−6.04466	+	0.869091i	−0.280616	+	0.0403465i
$465$	−34.0721	+	15.5234i	−1.58005	+	0.719880i
$466$	−3.39467	+	23.6104i	−0.157255	+	1.09373i
$467$	−27.9510	−	15.2624i	−1.29342	−	0.706260i	−0.322706	−	0.946499i	$-0.604592\pi$
$467$	−27.9510	−	15.2624i	−1.29342	−	0.706260i	−0.970714	+	0.240239i	$0.922774\pi$
$468$	−3.74567	−	17.2186i	−0.173144	−	0.795929i
$469$	18.3863	+	8.39672i	0.848998	+	0.387724i
$470$	−5.35395	+	2.91727i	−0.246959	+	0.134564i
$471$	32.8895	−	28.4989i	1.51547	−	1.31316i
$472$	6.37298	+	0.455805i	0.293340	+	0.0209801i
$473$	−1.49305	−	2.73432i	−0.0686507	−	0.125724i
$474$	5.65842	−	12.3902i	0.259900	−	0.569101i
$475$	4.09676	−	6.34969i	0.187972	−	0.291344i
$476$	−9.35194	+	2.74598i	−0.428646	+	0.125862i
$477$	−34.1156	+	25.5386i	−1.56205	+	1.16933i
$478$	−5.68903	+	15.2529i	−0.260210	+	0.697651i
$479$	0.570408	+	3.96728i	0.0260626	+	0.181269i	0.998694	−	0.0510823i	$-0.0162671\pi$
$479$	0.570408	+	3.96728i	0.0260626	+	0.181269i	−0.972632	+	0.232352i	$0.925358\pi$
$480$	6.82778	+	1.49168i	0.311644	+	0.0680857i
$481$	−17.1706	−	14.8784i	−0.782911	−	0.678396i
$482$	−13.7607	−	13.7607i	−0.626781	−	0.626781i
$483$	30.0300	−	24.8998i	1.36641	−	1.13298i
$484$			10.1656i			0.462072i
$485$	12.4157	+	10.7777i	0.563767	+	0.489390i
$486$	−13.6813	+	8.79241i	−0.620594	+	0.398832i
$487$	24.2327	+	18.1404i	1.09809	+	0.822019i	0.985169	−	0.171585i	$-0.0548888\pi$
$487$	24.2327	+	18.1404i	1.09809	+	0.822019i	0.112920	+	0.993604i	$0.463980\pi$
$488$	−6.94174	−	2.58913i	−0.314238	−	0.117205i
$489$	−37.3966	−	5.37682i	−1.69113	−	0.243148i
$490$	0.142463	+	0.486794i	0.00643583	+	0.0219911i
$491$	4.91636	+	3.15956i	0.221872	+	0.142589i	0.646856	−	0.762613i	$-0.276084\pi$
$491$	4.91636	+	3.15956i	0.221872	+	0.142589i	−0.424983	+	0.905201i	$0.639720\pi$
$492$	−11.5485	−	30.9628i	−0.520649	−	1.39591i
$493$	20.0731	−	10.9608i	0.904048	−	0.493648i
$494$	2.57653	+	2.97347i	0.115923	+	0.133783i
$495$	−5.02954	+	69.4498i	−0.226061	+	3.12154i
$496$	5.14036	+	1.50935i	0.230809	+	0.0677716i
$497$	31.6154	−	11.7919i	1.41814	−	0.528940i
$498$	7.49927	−	1.63137i	0.336050	−	0.0731033i
$499$	−10.4192	−	35.4845i	−0.466427	−	1.58851i	−0.771535	−	0.636187i	$-0.780511\pi$
$499$	−10.4192	−	35.4845i	−0.466427	−	1.58851i	0.305108	−	0.952318i	$-0.401308\pi$
$500$	8.96826	−	6.67611i	0.401073	−	0.298565i
$501$	13.5242	+	29.6138i	0.604215	+	1.32305i
$502$	7.69860	−	10.2841i	0.343605	−	0.459003i
$503$	1.17057	−	5.38101i	0.0521930	−	0.239928i	−0.943658	−	0.330921i	$-0.892641\pi$
$503$	1.17057	−	5.38101i	0.0521930	−	0.239928i	0.995851	+	0.0909935i	$0.0290043\pi$
$504$	11.5359	−	13.3132i	0.513850	−	0.593015i
$505$	−22.2933	−	22.3332i	−0.992040	−	0.993814i
$506$	17.9460	−	12.8355i	0.797797	−	0.570607i
$507$	−13.7524	+	13.7524i	−0.610766	+	0.610766i
$508$	−2.58455	+	0.184850i	−0.114671	+	0.00820141i
$509$	−19.3176	−	30.0587i	−0.856237	−	1.33233i	−0.941861	−	0.336003i	$-0.890925\pi$
$509$	−19.3176	−	30.0587i	−0.856237	−	1.33233i	0.0856244	−	0.996327i	$-0.472711\pi$
$510$	−25.9108	+	3.70178i	−1.14735	+	0.163917i
$511$	3.52193	−	1.60841i	0.155801	−	0.0711520i
$512$	−0.599278	−	0.800541i	−0.0264846	−	0.0353793i
$513$	8.53160	−	15.6245i	0.376680	−	0.689837i
$514$	2.05225	−	3.19336i	0.0905207	−	0.140853i
$515$	12.2989	−	26.8673i	0.541955	−	1.18391i
$516$	−0.596287	+	2.03077i	−0.0262501	+	0.0893995i
$517$	−0.894923	+	12.5127i	−0.0393586	+	0.550306i
$518$	1.62032	−	22.6550i	0.0711928	−	0.995405i
$519$	−11.1639	+	38.0209i	−0.490043	+	1.66893i
$520$	2.02944	+	5.45602i	0.0889968	+	0.239262i
$521$	−10.7141	+	16.6715i	−0.469394	+	0.730391i	−0.992549	−	0.121846i	$-0.961118\pi$
$521$	−10.7141	+	16.6715i	−0.469394	+	0.730391i	0.523155	+	0.852238i	$0.324755\pi$
$522$	−19.8100	+	36.2792i	−0.867058	+	1.58790i
$523$	6.78495	+	9.06364i	0.296685	+	0.396325i	0.923970	−	0.382465i	$-0.124925\pi$
$523$	6.78495	+	9.06364i	0.296685	+	0.396325i	−0.627285	+	0.778790i	$0.715834\pi$
$524$	19.1716	−	8.75539i	0.837516	−	0.382481i
$525$	−5.71612	−	40.2673i	−0.249472	−	1.75741i
$526$	5.51040	+	8.57436i	0.240265	+	0.373860i
$527$	−20.0128	+	1.43134i	−0.871771	+	0.0623503i
$528$	10.1676	−	10.1676i	0.442489	−	0.442489i
$529$	−21.7660	−	7.43230i	−0.946350	−	0.323143i
$530$	9.96369	−	9.94589i	0.432795	−	0.432022i
$531$	28.3209	−	32.6840i	1.22902	−	1.41837i
$532$	−0.836073	+	3.84336i	−0.0362483	+	0.166631i
$533$	16.4954	−	22.0353i	0.714497	−	0.954456i
$534$	20.9854	+	45.9517i	0.908128	+	1.98852i
$535$	−13.1874	−	1.90809i	−0.570141	−	0.0824940i
$536$	−2.18811	−	7.45201i	−0.0945118	−	0.321878i
$537$	2.19651	−	0.477822i	0.0947866	−	0.0206196i
$538$	−0.281711	+	0.105073i	−0.0121454	+	0.00453001i
$539$	1.00129	+	0.294007i	0.0431288	+	0.0126638i
$540$	19.9211	−	17.2306i	0.857267	−	0.741485i
$541$	10.8010	+	12.4650i	0.464372	+	0.535914i	0.938838	−	0.344360i	$-0.111904\pi$
$541$	10.8010	+	12.4650i	0.464372	+	0.535914i	−0.474466	+	0.880274i	$0.657359\pi$
$542$	−0.263535	+	0.143901i	−0.0113198	+	0.00618109i
$543$	−14.8212	−	39.7371i	−0.636038	−	1.70528i
$544$	3.15058	+	2.02476i	0.135080	+	0.0868108i
$545$	−1.82322	−	0.997669i	−0.0780981	−	0.0427355i
$546$	20.9605	+	3.01367i	0.897028	+	0.128973i
$547$	42.3431	+	15.7931i	1.81046	+	0.675266i	0.995391	+	0.0959013i	$0.0305733\pi$
$547$	42.3431	+	15.7931i	1.81046	+	0.675266i	0.815068	+	0.579365i	$0.196699\pi$
$548$	−3.93863	−	2.94842i	−0.168250	−	0.125950i
$549$	−42.1877	+	27.1124i	−1.80053	+	1.15713i
$550$	−1.60000	−	22.9473i	−0.0682243	−	0.978477i
$551$		−	9.22935i		−	0.393183i
$552$	−14.7869	−	2.45501i	−0.629374	−	0.104492i
$553$	8.02001	+	8.02001i	0.341045	+	0.341045i
$554$	−4.65639	−	4.03479i	−0.197831	−	0.171422i
$555$	13.0183	−	59.5876i	0.552595	−	2.52935i
$556$	1.36117	+	9.46713i	0.0577264	+	0.401496i
$557$	2.21642	−	5.94246i	0.0939128	−	0.251790i	−0.881497	−	0.472190i	$-0.843464\pi$
$557$	2.21642	−	5.94246i	0.0939128	−	0.251790i	0.975410	+	0.220400i	$0.0707363\pi$
$558$	29.0297	−	21.7313i	1.22892	−	0.919961i
$559$	−1.69150	+	0.496668i	−0.0715427	+	0.0210068i
$560$	−3.15060	+	4.89281i	−0.133137	+	0.206759i
$561$	−22.3707	+	48.9851i	−0.944494	+	2.06815i
$562$	−13.4495	−	24.6309i	−0.567333	−	1.03899i
$563$	3.92544	+	0.280753i	0.165438	+	0.0118323i	0.153812	−	0.988100i	$-0.450845\pi$
$563$	3.92544	+	0.280753i	0.165438	+	0.0118323i	0.0116254	+	0.999932i	$0.496299\pi$
$564$	6.44079	−	5.58098i	0.271206	−	0.235002i
$565$	−1.35070	−	0.397913i	−0.0568243	−	0.0167403i
$566$	−5.67825	−	2.59317i	−0.238675	−	0.108999i
$567$	−9.13318	−	41.9846i	−0.383558	−	1.76319i
$568$	−11.3795	−	6.21365i	−0.477472	−	0.260719i
$569$	−5.74397	+	39.9502i	−0.240800	+	1.67480i	0.407340	+	0.913277i	$0.366457\pi$
$569$	−5.74397	+	39.9502i	−0.240800	+	1.67480i	−0.648139	+	0.761522i	$0.724453\pi$
$570$	−3.70000	+	9.89307i	−0.154976	+	0.414375i
$571$	−17.5505	+	2.52338i	−0.734466	+	0.105600i	−0.499391	−	0.866377i	$-0.666443\pi$
$571$	−17.5505	+	2.52338i	−0.734466	+	0.105600i	−0.235075	+	0.971977i	$0.575534\pi$
$572$	11.7032	+	2.54588i	0.489336	+	0.106449i
$573$	3.93989	+	55.0869i	0.164591	+	2.30129i
$574$	27.5170			1.14854
$575$	−18.4864	+	15.2726i	−0.770937	+	0.636912i
$576$	−6.76873			−0.282030
$577$	−0.677143	−	9.46769i	−0.0281898	−	0.394145i	−0.991885	−	0.127140i	$-0.959420\pi$
$577$	−0.677143	−	9.46769i	−0.0281898	−	0.394145i	0.963695	−	0.267006i	$-0.0860342\pi$
$578$	2.90621	+	0.632207i	0.120882	+	0.0262964i
$579$	42.3384	−	6.08735i	1.75952	−	0.252981i
$580$	4.78346	−	12.7900i	0.198622	−	0.531077i
$581$	−0.909466	+	6.32547i	−0.0377310	+	0.262425i
$582$	−20.1697	−	11.0135i	−0.836060	−	0.456523i
$583$	−6.15701	−	28.3033i	−0.254997	−	1.17220i
$584$	−1.35327	−	0.618018i	−0.0559988	−	0.0255738i
$585$	37.7964	+	11.1347i	1.56269	+	0.460364i
$586$	12.9078	−	11.1846i	0.533214	−	0.462033i
$587$	−19.3865	−	1.38655i	−0.800168	−	0.0572291i	−0.334735	−	0.942312i	$-0.608647\pi$
$587$	−19.3865	−	1.38655i	−0.800168	−	0.0572291i	−0.465433	+	0.885083i	$0.654101\pi$
$588$	−0.339770	−	0.622242i	−0.0140119	−	0.0256608i
$589$	−3.36348	+	7.36500i	−0.138590	+	0.303470i
$590$	−7.73478	+	12.0119i	−0.318436	+	0.494524i
$591$	−52.7547	+	15.4902i	−2.17004	+	0.637180i
$592$	−6.98651	+	5.23004i	−0.287144	+	0.214953i
$593$	14.5226	−	38.9367i	0.596373	−	1.59894i	−0.190408	−	0.981705i	$-0.560981\pi$
$593$	14.5226	−	38.9367i	0.596373	−	1.59894i	0.786781	−	0.617232i	$-0.211746\pi$
$594$	−7.71221	−	53.6396i	−0.316436	−	2.20086i
$595$	4.65177	−	21.2922i	0.190704	−	0.872895i
$596$	9.73802	+	8.43804i	0.398885	+	0.345636i
$597$	−44.6435	−	44.6435i	−1.82714	−	1.82714i
$598$	−4.93859	−	11.4669i	−0.201954	−	0.468916i
$599$			38.9627i			1.59197i	0.605315	+	0.795986i	$0.293047\pi$
$599$			38.9627i			1.59197i	−0.605315	+	0.795986i	$0.706953\pi$
$600$	−10.2549	+	11.7922i	−0.418655	+	0.481413i
$601$	−1.12932	+	0.725767i	−0.0460658	+	0.0296047i	−0.563471	−	0.826136i	$-0.690534\pi$
$601$	−1.12932	+	0.725767i	−0.0460658	+	0.0296047i	0.517405	+	0.855740i	$0.326898\pi$
$602$	−1.41084	−	1.05614i	−0.0575017	−	0.0430452i
$603$	−49.2555	−	18.3714i	−2.00584	−	0.748140i
$604$	6.83173	+	0.982255i	0.277979	+	0.0399674i
$605$	−19.9407	−	10.9116i	−0.810705	−	0.443620i
$606$	37.1056	+	23.8463i	1.50731	+	0.968690i
$607$	−10.1159	−	27.1219i	−0.410593	−	1.10084i	−0.963526	−	0.267616i	$-0.913764\pi$
$607$	−10.1159	−	27.1219i	−0.410593	−	1.10084i	0.552933	−	0.833226i	$-0.313509\pi$
$608$	1.32645	−	0.724297i	0.0537947	−	0.0293741i
$609$	−32.5296	−	37.5412i	−1.31817	−	1.52125i
$610$	12.5300	−	10.8377i	0.507325	−	0.438806i
$611$	6.81105	+	1.99991i	0.275546	+	0.0809075i
$612$	23.7513	−	8.85878i	0.960090	−	0.358095i
$613$	9.55639	−	2.07887i	0.385979	−	0.0839646i	−0.0153887	−	0.999882i	$-0.504899\pi$
$613$	9.55639	−	2.07887i	0.385979	−	0.0839646i	0.401368	+	0.915917i	$0.368535\pi$
$614$	3.94038	+	13.4197i	0.159021	+	0.541576i
$615$	73.1325	+	10.5816i	2.94899	+	0.426691i
$616$	4.97386	+	10.8912i	0.200402	+	0.438820i
$617$	8.05106	−	10.7550i	0.324124	−	0.432978i	−0.608651	−	0.793438i	$-0.708289\pi$
$617$	8.05106	−	10.7550i	0.324124	−	0.432978i	0.932775	+	0.360459i	$0.117380\pi$
$618$	−8.77934	+	40.3580i	−0.353157	+	1.62344i
$619$	2.29681	−	2.65066i	0.0923165	−	0.106539i	−0.707712	−	0.706501i	$-0.750272\pi$
$619$	2.29681	−	2.65066i	0.0923165	−	0.106539i	0.800028	+	0.599962i	$0.204818\pi$
$620$	−8.47831	+	8.46317i	−0.340497	+	0.339889i
$621$	−40.8033	+	39.0679i	−1.63738	+	1.56774i
$622$	−3.16964	+	3.16964i	−0.127091	+	0.127091i
$623$	−41.9570	+	3.00082i	−1.68097	+	0.120225i
$624$	−4.39904	−	6.84504i	−0.176103	−	0.274021i
$625$	3.46938	+	24.7581i	0.138775	+	0.990324i
$626$	−13.1443	+	6.00280i	−0.525352	+	0.239920i
$627$	13.0232	+	17.3970i	0.520097	+	0.694768i
$628$	6.67301	−	12.2207i	0.266282	−	0.487659i
$629$	17.6705	−	27.4959i	0.704570	−	1.09633i
$630$	13.7325	+	36.9189i	0.547115	+	1.47088i
$631$	3.84888	−	13.1081i	0.153222	−	0.521825i	−0.846726	−	0.532029i	$-0.821430\pi$
$631$	3.84888	−	13.1081i	0.153222	−	0.521825i	0.999948	+	0.0102039i	$0.00324805\pi$
$632$	0.310901	−	4.34696i	0.0123670	−	0.172913i
$633$	0.735956	−	10.2900i	0.0292516	−	0.408991i
$634$	3.63996	−	12.3966i	0.144561	−	0.492331i
$635$	2.41162	−	5.26824i	0.0957021	−	0.209064i
$636$	−10.6387	+	16.5542i	−0.421853	+	0.656417i
$637$	0.283007	−	0.518288i	0.0112131	−	0.0205353i
$638$	−16.8368	−	22.4913i	−0.666574	−	0.890438i
$639$	−79.8286	+	36.4565i	−3.15797	+	1.44220i
$640$	2.21359	−	0.316247i	0.0874999	−	0.0125008i
$641$	4.47438	+	6.96227i	0.176727	+	0.274993i	0.918305	−	0.395874i	$-0.129558\pi$
$641$	4.47438	+	6.96227i	0.176727	+	0.274993i	−0.741577	+	0.670867i	$0.765922\pi$
$642$	18.5774	−	1.32868i	0.733190	−	0.0524388i
$643$	−3.79292	+	3.79292i	−0.149578	+	0.149578i	−0.777930	−	0.628351i	$-0.783730\pi$
$643$	−3.79292	+	3.79292i	−0.149578	+	0.149578i	0.628351	+	0.777930i	$0.283730\pi$
$644$	6.21821	−	10.8220i	0.245032	−	0.426448i
$645$	−3.34349	−	3.34947i	−0.131650	−	0.131885i
$646$	−3.70654	+	4.27758i	−0.145832	+	0.168299i
$647$	1.35172	−	6.21375i	0.0531415	−	0.244288i	−0.942912	−	0.333042i	$-0.891925\pi$
$647$	1.35172	−	6.21375i	0.0531415	−	0.244288i	0.996054	+	0.0887542i	$0.0282886\pi$
$648$	−9.89377	+	13.2165i	−0.388664	+	0.519194i
$649$	12.2109	+	26.7382i	0.479320	+	1.04956i
$650$	−12.8809	−	1.87549i	−0.505229	−	0.0735630i
$651$	12.2773	+	41.8127i	0.481186	+	1.63877i
$652$	−11.8118	+	2.56950i	−0.462585	+	0.100629i
$653$	−5.03508	+	1.87799i	−0.197038	+	0.0734913i	−0.446046	−	0.895010i	$-0.647168\pi$
$653$	−5.03508	+	1.87799i	−0.197038	+	0.0734913i	0.249008	+	0.968501i	$0.419895\pi$
$654$	2.78735	+	0.818439i	0.108994	+	0.0320035i
$655$	−3.40408	+	47.0048i	−0.133008	+	1.83663i
$656$	−6.92396	−	7.99068i	−0.270335	−	0.311983i
$657$	−8.83816	+	4.82600i	−0.344810	+	0.188280i
$658$	2.47994	+	6.64897i	0.0966780	+	0.259204i
$659$	4.73466	+	3.04278i	0.184436	+	0.118530i	0.629601	−	0.776919i	$-0.283218\pi$
$659$	4.73466	+	3.04278i	0.184436	+	0.118530i	−0.445165	+	0.895449i	$0.646855\pi$
$660$	9.03092	+	30.8585i	0.351528	+	1.20117i
$661$	−31.5886	−	4.54176i	−1.22865	−	0.176654i	−0.502739	−	0.864438i	$-0.667674\pi$
$661$	−31.5886	−	4.54176i	−1.22865	−	0.176654i	−0.725915	+	0.687784i	$0.758584\pi$
$662$	14.0749	+	5.24968i	0.547038	+	0.204034i
$663$	24.3948	+	18.2617i	0.947415	+	0.709226i
$664$	2.06570	−	1.32754i	0.0801647	−	0.0515187i
$665$	−6.64168	−	5.76545i	−0.257553	−	0.223575i
$666$			59.0723i			2.28900i
$667$	−8.85968	+	27.9151i	−0.343048	+	1.08088i
$668$	7.36537	+	7.36537i	0.284975	+	0.284975i
$669$	−16.6392	−	14.4179i	−0.643308	−	0.557430i
$670$	16.9665	+	3.70672i	0.655472	+	0.143203i
$671$	−4.85084	−	33.7383i	−0.187265	−	1.30245i
$672$	2.84261	−	7.62134i	0.109656	−	0.293999i
$673$	2.60877	−	1.95290i	0.100561	−	0.0752789i	−0.547814	−	0.836600i	$-0.684540\pi$
$673$	2.60877	−	1.95290i	0.100561	−	0.0752789i	0.648375	+	0.761321i	$0.275449\pi$
$674$	−4.20113	+	1.23356i	−0.161821	+	0.0475151i
$675$	12.4163	+	57.5721i	0.477904	+	2.21595i
$676$	−2.58498	+	5.66031i	−0.0994222	+	0.217704i
$677$	−0.101291	−	0.185501i	−0.00389293	−	0.00712938i	0.875725	−	0.482810i	$-0.160384\pi$
$677$	−0.101291	−	0.185501i	−0.00389293	−	0.00712938i	−0.879618	+	0.475680i	$0.842202\pi$
$678$	1.96317	+	0.140408i	0.0753949	+	0.00539235i
$679$	14.4617	−	12.5311i	0.554987	−	0.480899i
$680$	−7.35354	+	4.00681i	−0.281995	+	0.153654i
$681$	−18.1429	−	8.28557i	−0.695236	−	0.317504i
$682$	5.23913	+	24.0839i	0.200617	+	0.922219i
$683$	30.7247	+	16.7769i	1.17565	+	0.641952i	0.943709	−	0.330778i	$-0.107311\pi$
$683$	30.7247	+	16.7769i	1.17565	+	0.641952i	0.231939	+	0.972730i	$0.425493\pi$
$684$	1.45584	−	10.1256i	0.0556653	−	0.387161i
$685$	10.0113	−	4.56119i	0.382511	−	0.174274i
$686$	18.6166	−	2.67667i	0.710786	−	0.102196i
$687$	2.26142	+	0.491942i	0.0862786	+	0.0187688i
$688$	0.0483089	+	0.675447i	0.00184176	+	0.0257512i
$689$	−16.3905			−0.624429
$690$	20.6878	−	26.3708i	0.787572	−	1.00392i
$691$	27.6793			1.05297			0.526485	−	0.850185i	$-0.323510\pi$
$691$	27.6793			1.05297			0.526485	+	0.850185i	$0.323510\pi$
$692$	0.904460	+	12.6460i	0.0343824	+	0.480729i
$693$	79.1914	+	17.2270i	3.00823	+	0.654401i
$694$	−13.3125	+	1.91406i	−0.505337	+	0.0726566i
$695$	−20.0317	−	7.49184i	−0.759846	−	0.284182i
$696$	−2.71634	+	18.8926i	−0.102963	+	0.716121i
$697$	34.7540	+	18.9771i	1.31640	+	0.718811i
$698$	4.30396	+	19.7850i	0.162907	+	0.748872i
$699$	67.8159	+	30.9705i	2.56503	+	1.17141i
$700$	−6.21588	−	11.4321i	−0.234938	−	0.432091i
$701$	−14.5899	+	12.6422i	−0.551051	+	0.477489i	−0.885316	−	0.464991i	$-0.846058\pi$
$701$	−14.5899	+	12.6422i	−0.551051	+	0.477489i	0.334264	+	0.942479i	$0.391512\pi$
$702$	−30.5870	−	2.18762i	−1.15443	−	0.0825665i
$703$	−6.32111	−	11.5763i	−0.238405	−	0.436607i
$704$	1.91116	−	4.18486i	0.0720296	−	0.157723i
$705$	4.03414	+	18.6247i	0.151934	+	0.701448i
$706$	32.2760	−	9.47708i	1.21472	−	0.356675i
$707$	−29.4017	+	22.0099i	−1.10577	+	0.827766i
$708$	6.97867	−	18.7105i	0.262274	−	0.703185i
$709$	1.99572	+	13.8805i	0.0749509	+	0.521295i	0.992363	+	0.123355i	$0.0393655\pi$
$709$	1.99572	+	13.8805i	0.0749509	+	0.521295i	−0.917412	+	0.397939i	$0.869725\pi$
$710$	24.4032	−	15.6522i	0.915836	−	0.587416i
$711$	−22.2935	−	19.3175i	−0.836073	−	0.724461i
$712$	11.4288	+	11.4288i	0.428313	+	0.428313i
$713$	17.2432	−	19.0474i	0.645763	−	0.713331i
$714$			30.4634i			1.14007i
$715$	−17.5561	+	20.2242i	−0.656559	+	0.756343i
$716$	0.605037	−	0.388834i	0.0226113	−	0.0145314i
$717$	40.7323	+	30.4918i	1.52117	+	1.13874i
$718$	17.1860	+	6.41005i	0.641376	+	0.239221i
$719$	−21.8991	−	3.14862i	−0.816699	−	0.117424i	−0.278710	−	0.960375i	$-0.589907\pi$
$719$	−21.8991	−	3.14862i	−0.816699	−	0.117424i	−0.537989	+	0.842952i	$0.680816\pi$
$720$	7.26546	−	13.2775i	0.270768	−	0.494822i
$721$	−28.9316	−	18.5932i	−1.07747	−	0.692448i
$722$	−5.84162	−	15.6620i	−0.217402	−	0.582878i
$723$	−53.3837	+	29.1497i	−1.98536	+	1.08409i
$724$	−8.88608	−	10.2551i	−0.330248	−	0.381127i
$725$	19.9543	+	23.1118i	0.741084	+	0.858352i
$726$	30.4855	+	8.95134i	1.13142	+	0.332216i
$727$	−16.5824	+	6.18491i	−0.615006	+	0.229385i	−0.637610	−	0.770359i	$-0.720077\pi$
$727$	−16.5824	+	6.18491i	−0.615006	+	0.229385i	0.0226041	+	0.999744i	$0.492804\pi$
$728$	6.62043	−	1.44019i	0.245369	−	0.0533768i
$729$	0.366606	+	1.24854i	0.0135780	+	0.0462424i
$730$	2.66488	−	1.99119i	0.0986318	−	0.0736974i
$731$	−1.05353	−	2.30690i	−0.0389661	−	0.0853238i
$732$	−13.8771	+	18.5376i	−0.512913	+	0.685171i
$733$	4.09955	−	18.8453i	0.151420	−	0.696068i	−0.837355	−	0.546659i	$-0.815899\pi$
$733$	4.09955	−	18.8453i	0.151420	−	0.696068i	0.988776	−	0.149409i	$-0.0477371\pi$
$734$	−8.22714	+	9.49463i	−0.303669	+	0.350453i
$735$	1.58529	+	0.00141685i	0.0584743	+	5.22615e-5i
$736$	−4.70727	+	0.917387i	−0.173512	+	0.0338153i
$737$	25.2657	−	25.2657i	0.930675	−	0.930675i
$738$	−71.3846	+	5.10553i	−2.62770	+	0.187937i
$739$	−4.25075	−	6.61429i	−0.156366	−	0.243311i	0.754228	−	0.656613i	$-0.228012\pi$
$739$	−4.25075	−	6.61429i	−0.156366	−	0.243311i	−0.910594	+	0.413303i	$0.864375\pi$
$740$	−2.75996	−	19.3185i	−0.101458	−	0.710163i
$741$	11.1859	−	5.10843i	0.410924	−	0.187663i
$742$	−9.81943	−	13.1172i	−0.360483	−	0.481548i
$743$	7.22835	−	13.2377i	0.265183	−	0.485646i	−0.710829	−	0.703365i	$-0.751680\pi$
$743$	7.22835	−	13.2377i	0.265183	−	0.485646i	0.976011	+	0.217719i	$0.0698618\pi$
$744$	9.05273	−	14.0863i	0.331889	−	0.516429i
$745$	−27.0046	+	10.0447i	−0.989374	+	0.368010i
$746$	−2.51739	+	8.57346i	−0.0921684	+	0.313897i
$747$	1.18570	−	16.5783i	0.0433826	−	0.606567i
$748$	−1.22916	+	17.1859i	−0.0449424	+	0.628377i
$749$	−4.36924	+	14.8803i	−0.159649	+	0.543713i
$750$	−12.1239	−	32.7735i	−0.442702	−	1.19672i
$751$	8.20525	−	12.7676i	0.299414	−	0.465897i	−0.658651	−	0.752448i	$-0.728873\pi$
$751$	8.20525	−	12.7676i	0.299414	−	0.465897i	0.958065	+	0.286552i	$0.0925090\pi$
$752$	1.30678	−	2.39319i	0.0476535	−	0.0872708i
$753$	−24.0619	−	32.1430i	−0.876866	−	1.17136i
$754$	−14.4614	+	6.60431i	−0.526654	+	0.240515i
$755$	−9.25987	+	12.3467i	−0.337001	+	0.449343i
$756$	−16.5737	−	25.7891i	−0.602778	−	0.937941i
$757$	26.9491	−	1.92744i	0.979483	−	0.0700540i	0.427593	−	0.903971i	$-0.359361\pi$
$757$	26.9491	−	1.92744i	0.979483	−	0.0700540i	0.551890	+	0.833917i	$0.313907\pi$
$758$	−8.80984	+	8.80984i	−0.319988	+	0.319988i
$759$	−22.6898	−	65.1204i	−0.823588	−	2.36372i
$760$	−0.00302035	+	3.37941i	−0.000109560	+	0.122584i
$761$	16.6650	−	19.2325i	0.604106	−	0.697176i	−0.368502	−	0.929627i	$-0.620129\pi$
$761$	16.6650	−	19.2325i	0.604106	−	0.697176i	0.972608	+	0.232451i	$0.0746746\pi$
$762$	−1.72149	+	7.91355i	−0.0623629	+	0.286678i
$763$	−1.44962	+	1.93647i	−0.0524798	+	0.0701048i
$764$	7.34039	+	16.0732i	0.265566	+	0.581509i
$765$	−8.11704	+	56.0993i	−0.293472	+	2.02827i
$766$	2.50556	+	8.53315i	0.0905295	+	0.308315i
$767$	16.2533	−	3.53568i	0.586872	−	0.127666i
$768$	−2.92843	+	1.09225i	−0.105671	+	0.0394131i
$769$	−30.6638	−	9.00371i	−1.10577	−	0.324682i	−0.322625	−	0.946527i	$-0.604565\pi$
$769$	−30.6638	−	9.00371i	−1.10577	−	0.324682i	−0.783140	+	0.621845i	$0.786383\pi$
$770$	−26.7030	−	1.93383i	−0.962309	−	0.0696903i
$771$	−7.76942	−	8.96639i	−0.279809	−	0.322917i
$772$	12.0114	−	6.55873i	0.432301	−	0.236054i
$773$	−9.43955	−	25.3084i	−0.339517	−	0.910281i	−0.988735	−	0.149678i	$-0.952176\pi$
$773$	−9.43955	−	25.3084i	−0.339517	−	0.910281i	0.649218	−	0.760603i	$-0.275096\pi$
$774$	3.85597	+	2.47808i	0.138600	+	0.0890727i
$775$	−7.50077	−	25.7152i	−0.269436	−	0.923718i
$776$	−7.27782	−	1.04639i	−0.261258	−	0.0375633i
$777$	−66.5132	−	24.8081i	−2.38615	−	0.889987i
$778$	22.7907	+	17.0609i	0.817086	+	0.611663i
$779$	13.4428	−	8.63913i	0.481637	−	0.309529i
$780$	18.1491	−	1.28174i	0.649840	−	0.0458938i
$781$		−	59.6487i		−	2.13440i
$782$	15.3170	−	9.37987i	0.547736	−	0.335424i
$783$	50.8644	+	50.8644i	1.81775	+	1.81775i
$784$	−0.171428	−	0.148544i	−0.00612244	−	0.00530513i
$785$	16.8093	+	26.2073i	0.599950	+	0.935377i
$786$	−9.37481	−	65.2032i	−0.334388	−	2.32572i
$787$	6.93542	−	18.5946i	0.247221	−	0.662825i	−0.752769	−	0.658285i	$-0.771282\pi$
$787$	6.93542	−	18.5946i	0.247221	−	0.662825i	0.999990	−	0.00453983i	$-0.00144508\pi$
$788$	−14.0826	+	10.5421i	−0.501673	+	0.375548i
$789$	30.5658	−	8.97492i	1.08817	−	0.319516i
$790$	8.19325	+	5.27583i	0.291503	+	0.187706i
$791$	−0.680807	+	1.49076i	−0.0242067	+	0.0530053i
$792$	−14.9239	−	27.3311i	−0.530299	−	0.971170i
$793$	−19.2386	−	1.37597i	−0.683184	−	0.0488623i
$794$	−13.6893	+	11.8619i	−0.485816	+	0.420962i
$795$	−21.0531	−	38.6379i	−0.746676	−	1.37035i
$796$	−18.3747	−	8.39144i	−0.651274	−	0.297427i
$797$	5.11790	+	23.5266i	0.181285	+	0.833356i	0.974495	+	0.224407i	$0.0720446\pi$
$797$	5.11790	+	23.5266i	0.181285	+	0.833356i	−0.793210	+	0.608948i	$0.791592\pi$
$798$	10.7896	+	5.89158i	0.381949	+	0.208560i
$799$	−1.45330	+	10.1080i	−0.0514142	+	0.357594i
$800$	−1.75569	+	4.68162i	−0.0620731	+	0.165520i
$801$	108.288	−	15.5695i	3.82617	−	0.550120i
$802$	32.9517	+	7.16821i	1.16357	+	0.253118i
$803$	−0.488273	−	6.82694i	−0.0172308	−	0.240918i
$804$	−24.2745			−0.856096
$805$	14.5539	+	23.8138i	0.512957	+	0.839327i
$806$	13.9470			0.491263
$807$	0.0670402	+	0.937344i	0.00235993	+	0.0329961i
$808$	13.7896	+	2.99975i	0.485118	+	0.105531i
$809$	2.16520	−	0.311308i	0.0761242	−	0.0109450i	−0.104147	−	0.994562i	$-0.533211\pi$
$809$	2.16520	−	0.311308i	0.0761242	−	0.0109450i	0.180272	+	0.983617i	$0.442302\pi$
$810$	−15.3056	−	33.5940i	−0.537784	−	1.18037i
$811$	1.89548	−	13.1833i	0.0665592	−	0.462929i	−0.929098	−	0.369834i	$-0.879415\pi$
$811$	1.89548	−	13.1833i	0.0665592	−	0.462929i	0.995657	−	0.0930956i	$-0.0296762\pi$
$812$	−13.9491	−	7.61680i	−0.489518	−	0.267297i
$813$	0.199487	+	0.917027i	0.00699632	+	0.0321615i
$814$	−36.5222	−	16.6791i	−1.28010	−	0.584604i
$815$	7.63832	−	25.9280i	0.267559	−	0.908217i
$816$	8.84629	−	7.66535i	0.309682	−	0.268341i
$817$	−1.02081	−	0.0730101i	−0.0357138	−	0.00255430i
$818$	−12.7476	−	23.3455i	−0.445710	−	0.816257i
$819$	19.0509	−	41.7157i	0.665692	−	1.45766i
$820$	23.1065	−	5.00489i	0.806915	−	0.174778i
$821$	20.1128	−	5.90566i	0.701943	−	0.206109i	0.0887634	−	0.996053i	$-0.471709\pi$
$821$	20.1128	−	5.90566i	0.701943	−	0.206109i	0.613179	+	0.789944i	$0.289890\pi$
$822$	−12.3102	+	9.21529i	−0.429367	+	0.321420i
$823$	4.96012	−	13.2986i	0.172899	−	0.463560i	−0.821379	−	0.570383i	$-0.806795\pi$
$823$	4.96012	−	13.2986i	0.172899	−	0.463560i	0.994278	+	0.106823i	$0.0340677\pi$
$824$	1.88062	+	13.0800i	0.0655144	+	0.455663i
$825$	−70.2254	−	15.4081i	−2.44494	−	0.536442i
$826$	12.5668	+	10.8892i	0.437255	+	0.378883i
$827$	39.1807	+	39.1807i	1.36245	+	1.36245i	0.870790	+	0.491656i	$0.163608\pi$
$827$	39.1807	+	39.1807i	1.36245	+	1.36245i	0.491656	+	0.870790i	$0.336392\pi$
$828$	−14.1233	+	29.2283i	−0.490820	+	1.01575i
$829$			45.0301i			1.56396i	0.623303	+	0.781980i	$0.285790\pi$
$829$			45.0301i			1.56396i	−0.623303	+	0.781980i	$0.714210\pi$
$830$	0.386805	+	5.47703i	0.0134262	+	0.190110i
$831$	−16.2001	+	10.4112i	−0.561975	+	0.361159i
$832$	−2.08408	−	1.56012i	−0.0722524	−	0.0540875i
$833$	0.795949	+	0.296874i	0.0275780	+	0.0102861i
$834$	29.5895	+	4.25432i	1.02460	+	0.147315i
$835$	−22.3537	+	6.54195i	−0.773583	+	0.226394i
$836$	5.84922	+	3.75906i	0.202299	+	0.130010i
$837$	−22.0530	−	59.1264i	−0.762264	−	2.04371i
$838$	12.7351	−	6.95388i	0.439926	−	0.240218i
$839$	30.7170	+	35.4493i	1.06047	+	1.22385i	0.973751	+	0.227614i	$0.0730924\pi$
$839$	30.7170	+	35.4493i	1.06047	+	1.22385i	0.0867177	+	0.996233i	$0.472362\pi$
$840$	11.8987	+	13.7567i	0.410545	+	0.474651i
$841$	7.95733	+	2.33648i	0.274391	+	0.0805684i
$842$	8.64260	−	3.22352i	0.297844	−	0.111090i
$843$	−85.7085	+	18.6447i	−2.95196	+	0.642159i
$844$	−0.929912	−	3.16699i	−0.0320089	−	0.109012i
$845$	−8.32854	−	11.1464i	−0.286510	−	0.383447i
$846$	−7.66711	−	16.7886i	−0.263601	−	0.577205i
$847$	−15.8546	+	21.1793i	−0.544772	+	0.727730i
$848$	−1.33830	+	6.15208i	−0.0459575	+	0.211263i
$849$	−12.7766	+	14.7450i	−0.438493	+	0.506048i
$850$	0.0334719	−	18.7255i	0.00114808	−	0.642279i
$851$	8.00625	+	41.0815i	0.274451	+	1.40825i
$852$	−28.6543	+	28.6543i	−0.981680	+	0.981680i
$853$	12.1649	−	0.870050i	0.416518	−	0.0297899i	0.138492	−	0.990364i	$-0.455774\pi$
$853$	12.1649	−	0.870050i	0.416518	−	0.0297899i	0.278026	+	0.960574i	$0.410320\pi$
$854$	−10.4245	−	16.2209i	−0.356720	−	0.555067i
$855$	18.2996	+	13.7244i	0.625832	+	0.469365i
$856$	5.42049	−	2.47546i	0.185269	−	0.0846094i
$857$	21.0873	+	28.1693i	0.720328	+	0.962246i	0.999998	+	0.00214954i	$0.000684222\pi$
$857$	21.0873	+	28.1693i	0.720328	+	0.962246i	−0.279669	+	0.960096i	$0.590225\pi$
$858$	17.9401	−	32.8549i	0.612466	−	1.12165i
$859$	−20.5494	+	31.9755i	−0.701136	+	1.09099i	0.289856	+	0.957070i	$0.406392\pi$
$859$	−20.5494	+	31.9755i	−0.701136	+	1.09099i	−0.990992	+	0.133919i	$0.957244\pi$
$860$	−1.37680	−	0.630253i	−0.0469487	−	0.0214915i
$861$	24.2302	−	82.5206i	0.825764	−	2.81229i
$862$	−1.67345	+	23.3979i	−0.0569980	+	0.796937i
$863$	0.555924	−	7.77284i	0.0189239	−	0.264590i	−0.979178	−	0.203004i	$-0.934930\pi$
$863$	0.555924	−	7.77284i	0.0189239	−	0.264590i	0.998102	−	0.0615863i	$-0.0196159\pi$
$864$	−3.31857	+	11.3020i	−0.112900	+	0.384502i
$865$	−25.7771	−	11.7999i	−0.876449	−	0.401208i
$866$	−8.10638	+	12.6138i	−0.275466	+	0.428634i
$867$	4.45500	−	8.15872i	0.151300	−	0.277085i
$868$	8.35556	+	11.1617i	0.283606	+	0.378853i
$869$	18.2379	−	8.32897i	0.618678	−	0.282541i
$870$	−34.1438	−	25.6074i	−1.15758	−	0.868172i
$871$	−10.9313	−	17.0094i	−0.370392	−	0.576341i
$872$	0.927091	−	0.0663069i	0.0313953	−	0.00224543i
$873$	−35.1914	+	35.1914i	−1.19105	+	1.19105i
$874$	−0.359897	−	7.23908i	−0.0121737	−	0.244866i
$875$	29.0971	+	0.0780168i	0.983661	+	0.00263745i
$876$	−3.04500	+	3.51412i	−0.102881	+	0.118731i
$877$	4.89744	−	22.5132i	0.165375	−	0.760216i	−0.817498	−	0.575931i	$-0.804640\pi$
$877$	4.89744	−	22.5132i	0.165375	−	0.760216i	0.982873	−	0.184285i	$-0.0589968\pi$
$878$	2.96995	−	3.96739i	0.100231	−	0.133893i
$879$	−22.1755	−	48.5576i	−0.747962	−	1.63781i
$880$	6.15757	+	8.24089i	0.207572	+	0.277800i
$881$	4.09163	+	13.9348i	0.137851	+	0.469476i	0.999261	−	0.0384331i	$-0.0122366\pi$
$881$	4.09163	+	13.9348i	0.137851	+	0.469476i	−0.861410	+	0.507909i	$0.830418\pi$
$882$	−1.50028	+	0.326366i	−0.0505170	+	0.0109893i
$883$	−7.99675	+	2.98263i	−0.269112	+	0.100374i	−0.480398	−	0.877051i	$-0.659508\pi$
$883$	−7.99675	+	2.98263i	−0.269112	+	0.100374i	0.211286	+	0.977424i	$0.432235\pi$
$884$	9.35484	+	2.74683i	0.314637	+	0.0923858i
$885$	29.2116	+	33.7729i	0.981937	+	1.13526i
$886$	−21.6665	−	25.0045i	−0.727901	−	0.840043i
$887$	3.43719	−	1.87685i	0.115410	−	0.0630184i	−0.420507	−	0.907289i	$-0.638148\pi$
$887$	3.43719	−	1.87685i	0.115410	−	0.0630184i	0.535917	+	0.844271i	$0.319966\pi$
$888$	9.53231	+	25.5571i	0.319883	+	0.857641i
$889$	−5.67303	−	3.64584i	−0.190267	−	0.122277i
$890$	−34.6862	+	10.1511i	−1.16268	+	0.340267i
$891$	−75.1806	−	10.8093i	−2.51864	−	0.362126i
$892$	−6.60011	−	2.46172i	−0.220988	−	0.0824243i
$893$	3.29899	+	2.46960i	0.110397	+	0.0826419i
$894$	33.8796	−	21.7731i	1.13310	−	0.728202i
$895$	0.113294	+	1.60420i	0.00378700	+	0.0536227i
$896$		−	2.60253i		−	0.0869445i
$897$	−38.7367	+	4.71308i	−1.29338	+	0.157365i
$898$	7.07044	+	7.07044i	0.235944	+	0.235944i
$899$	−24.7255	−	21.4247i	−0.824641	−	0.714555i
$900$	18.2463	+	28.5037i	0.608211	+	0.950125i
$901$	−3.35565	−	23.3391i	−0.111793	−	0.777537i
$902$	16.9990	−	45.5761i	0.566005	−	1.51752i
$903$	−4.40959	+	3.30097i	−0.146742	+	0.109850i
$904$	0.604210	−	0.177412i	0.0200957	−	0.00590064i
$905$	29.6545	−	6.42318i	0.985748	−	0.213514i
$906$	8.96138	−	19.6227i	0.297722	−	0.651920i
$907$	−23.3341	−	42.7332i	−0.774795	−	1.41893i	−0.904098	−	0.427326i	$-0.859456\pi$
$907$	−23.3341	−	42.7332i	−0.774795	−	1.41893i	0.129303	−	0.991605i	$-0.458726\pi$
$908$	−6.36521	−	0.455249i	−0.211237	−	0.0151080i
$909$	72.1902	−	62.5531i	2.39440	−	2.07476i
$910$	−4.28122	+	14.5325i	−0.141921	+	0.481746i
$911$	25.3691	+	11.5857i	0.840517	+	0.383851i	0.788680	−	0.614804i	$-0.210765\pi$
$911$	25.3691	+	11.5857i	0.840517	+	0.383851i	0.0518375	+	0.998656i	$0.483492\pi$
$912$	−1.00408	−	4.61567i	−0.0332483	−	0.152840i
$913$	9.91496	+	5.41398i	0.328137	+	0.179177i
$914$	−0.638316	+	4.43959i	−0.0211136	+	0.146848i
$915$	−21.4678	−	47.1193i	−0.709703	−	1.55772i
$916$	0.732925	−	0.105379i	0.0242165	−	0.00348181i
$917$	53.5980	+	11.6595i	1.76996	+	0.385032i
$918$	−3.14707	−	44.0018i	−0.103869	−	1.45227i
$919$	−25.1171			−0.828537			−0.414269	−	0.910155i	$-0.635963\pi$
$919$	−25.1171			−0.828537			−0.414269	+	0.910155i	$0.635963\pi$
$920$	3.25319	−	10.2185i	0.107254	−	0.336892i
$921$	43.7140			1.44043
$922$	2.49090	+	34.8273i	0.0820333	+	1.14698i
$923$	−32.9819	−	7.17478i	−1.08561	−	0.236161i
$924$	37.0414	−	5.32574i	1.21857	−	0.175204i
$925$	40.8576	+	15.3223i	1.34339	+	0.503795i
$926$	−3.43552	+	23.8946i	−0.112898	+	0.785224i
$927$	78.5042	+	42.8666i	2.57842	+	1.40792i
$928$	1.29810	+	5.96726i	0.0426122	+	0.195885i
$929$	32.9625	+	15.0535i	1.08146	+	0.493888i	0.874780	−	0.484520i	$-0.161006\pi$
$929$	32.9625	+	15.0535i	1.08146	+	0.493888i	0.206684	+	0.978408i	$0.433733\pi$
$930$	17.9145	+	32.8778i	0.587440	+	1.07811i
$931$	0.259083	−	0.224496i	0.00849109	−	0.00735758i
$932$	23.7924	+	1.70167i	0.779347	+	0.0557400i
$933$	6.71436	+	12.2964i	0.219818	+	0.402567i
$934$	−13.2295	+	28.9686i	−0.432883	+	0.947882i
$935$	−32.3923	−	20.8582i	−1.05934	−	0.682135i
$936$	−16.9075	+	4.96449i	−0.552639	+	0.162269i
$937$	−7.10587	+	5.31939i	−0.232139	+	0.173777i	−0.709015	−	0.705194i	$-0.750860\pi$
$937$	−7.10587	+	5.31939i	−0.232139	+	0.173777i	0.476876	+	0.878971i	$0.341769\pi$
$938$	7.06367	−	18.9384i	0.230637	−	0.618361i
$939$	6.42748	+	44.7041i	0.209753	+	1.45886i
$940$	3.29179	+	5.13220i	0.107366	+	0.167394i
$941$	23.4217	+	20.2950i	0.763526	+	0.661599i	0.946930	−	0.321439i	$-0.104166\pi$
$941$	23.4217	+	20.2950i	0.763526	+	0.661599i	−0.183405	+	0.983038i	$0.558712\pi$
$942$	−30.7726	−	30.7726i	−1.00263	−	1.00263i
$943$	−48.9520	+	13.2256i	−1.59410	+	0.430684i
$944$		−	6.38926i		−	0.207953i
$945$	68.3777	−	4.82905i	2.22433	−	0.157089i
$946$	−2.62084	+	1.68431i	−0.0852110	+	0.0547618i
$947$	−37.2350	−	27.8737i	−1.20997	−	0.905775i	−0.212525	−	0.977156i	$-0.568169\pi$
$947$	−37.2350	−	27.8737i	−1.20997	−	0.905775i	−0.997449	+	0.0713807i	$0.977259\pi$
$948$	−12.7623	−	4.76009i	−0.414500	−	0.154601i
$949$	−3.83360	−	0.551188i	−0.124444	−	0.0178923i
$950$	−6.62577	−	3.63334i	−0.214968	−	0.117881i
$951$	−33.9708	−	21.8317i	−1.10158	−	0.707942i
$952$	3.40614	+	9.13222i	0.110394	+	0.295977i
$953$	−3.37390	+	1.84229i	−0.109291	+	0.0596775i	−0.532965	−	0.846137i	$-0.678922\pi$
$953$	−3.37390	+	1.84229i	−0.109291	+	0.0596775i	0.423674	+	0.905815i	$0.360740\pi$
$954$	27.9073	+	32.2068i	0.903533	+	1.04273i
$955$	−39.4082	−	2.85393i	−1.27522	−	0.0923510i
$956$	15.6199	+	4.58641i	0.505183	+	0.148335i
$957$	−82.2746	+	30.6868i	−2.65956	+	0.991964i
$958$	3.91647	−	0.851977i	0.126536	−	0.0275261i
$959$	−3.60740	−	12.2857i	−0.116489	−	0.396725i
$960$	1.00080	−	6.91679i	0.0323005	−	0.223239i
$961$	−0.954875	−	2.09088i	−0.0308024	−	0.0674479i
$962$	−13.6155	+	18.1882i	−0.438983	+	0.586412i
$963$	8.57379	−	39.4131i	0.276286	−	1.27007i
$964$	−12.7439	+	14.7073i	−0.410454	+	0.473689i
$965$	−0.0273502	+	30.6016i	−0.000880433	+	0.985099i
$966$	−26.9787	−	28.1771i	−0.868025	−	0.906584i
$967$	−11.4499	+	11.4499i	−0.368205	+	0.368205i	−0.866822	−	0.498617i	$-0.833841\pi$
$967$	−11.4499	+	11.4499i	−0.368205	+	0.368205i	0.498617	+	0.866822i	$0.333841\pi$
$968$	10.1397	−	0.725204i	0.325902	−	0.0233089i
$969$	9.56418	+	14.8822i	0.307246	+	0.478084i
$970$	9.86451	−	13.1529i	0.316730	−	0.422315i
$971$	−24.6330	+	11.2495i	−0.790511	+	0.361015i	−0.769404	−	0.638763i	$-0.779447\pi$
$971$	−24.6330	+	11.2495i	−0.790511	+	0.361015i	−0.0211077	+	0.999777i	$0.506719\pi$
$972$	9.74601	+	13.0191i	0.312604	+	0.417589i
$973$	−11.9294	+	21.8471i	−0.382439	+	0.700385i
$974$	16.3654	−	25.4651i	0.524382	−	0.815954i
$975$	−16.9667	+	36.9768i	−0.543369	+	1.18421i
$976$	−2.08732	+	7.10876i	−0.0668135	+	0.227546i
$977$	−1.36073	+	19.0254i	−0.0435335	+	0.608678i	0.928122	+	0.372276i	$0.121423\pi$
$977$	−1.36073	+	19.0254i	−0.0435335	+	0.608678i	−0.971655	+	0.236401i	$0.924032\pi$
$978$	−2.69528	+	37.6849i	−0.0861854	+	1.20503i
$979$	−20.9493	+	71.3466i	−0.669541	+	2.28025i
$980$	0.475391	−	0.176828i	0.0151858	−	0.00564856i
$981$	3.40131	−	5.29254i	0.108595	−	0.168978i
$982$	2.80078	−	5.12924i	0.0893763	−	0.163681i
$983$	−16.3604	−	21.8549i	−0.521815	−	0.697063i	0.459781	−	0.888032i	$-0.347928\pi$
$983$	−16.3604	−	21.8549i	−0.521815	−	0.697063i	−0.981596	+	0.190969i	$0.938837\pi$
$984$	−30.0601	+	13.7280i	−0.958281	+	0.437632i
$985$	−5.56323	−	38.9401i	−0.177259	−	1.24074i
$986$	−12.3648	−	19.2401i	−0.393776	−	0.612728i
$987$	22.1233	−	1.58229i	0.704191	−	0.0503648i
$988$	2.78209	−	2.78209i	0.0885100	−	0.0885100i
$989$	3.01747	+	1.20075i	0.0959499	+	0.0381817i
$990$	69.6317	+	0.0622334i	2.21304	+	0.00197791i
$991$	−30.9827	+	35.7559i	−0.984198	+	1.13582i	0.00653234	+	0.999979i	$0.497921\pi$
$991$	−30.9827	+	35.7559i	−0.984198	+	1.13582i	−0.990730	+	0.135846i	$0.956625\pi$
$992$	1.13879	−	5.23494i	0.0361566	−	0.166209i
$993$	28.1369	−	37.5866i	0.892899	−	1.19277i
$994$	−14.0173	−	30.6936i	−0.444601	−	0.973541i
$995$	36.1837	−	27.0364i	1.14710	−	0.857111i
$996$	−2.16220	−	7.36379i	−0.0685120	−	0.233330i
$997$	26.2370	−	5.70752i	0.830935	−	0.180759i	0.223073	−	0.974802i	$-0.428391\pi$
$997$	26.2370	−	5.70752i	0.830935	−	0.180759i	0.607862	+	0.794043i	$0.292027\pi$
$998$	−34.6508	+	12.9241i	−1.09685	+	0.409105i
$999$	98.6353	+	28.9619i	3.12068	+	0.916315i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.2.l.a.53.1	yes	240
5.2	odd	4	inner	230.2.l.a.7.7	✓	240
23.10	odd	22	inner	230.2.l.a.33.7	yes	240
115.102	even	44	inner	230.2.l.a.217.1	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.l.a.7.7	✓	240	5.2	odd	4	inner
230.2.l.a.33.7	yes	240	23.10	odd	22	inner
230.2.l.a.53.1	yes	240	1.1	even	1	trivial
230.2.l.a.217.1	yes	240	115.102	even	44	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	230.l (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0713392 - 0.997452i) q^{2} +(-3.05407 - 0.664372i) q^{3} +(-0.989821 + 0.142315i) q^{4} +(0.783298 - 2.09438i) q^{5} +(-0.444805 + 3.09368i) q^{6} +(-2.28419 - 1.24726i) q^{7} +(0.212565 + 0.977147i) q^{8} +(6.15705 + 2.81183i) q^{9} +(-2.14493 - 0.631890i) q^{10} +(-3.47691 + 3.01276i) q^{11} +(3.11753 + 0.222970i) q^{12} +(1.24765 + 2.28489i) q^{13} +(-1.08113 + 2.36735i) q^{14} +(-3.78370 + 5.87599i) q^{15} +(0.959493 - 0.281733i) q^{16} +(-2.99811 + 2.24436i) q^{17} +(2.36543 - 6.34196i) q^{18} +(0.215083 + 1.49593i) q^{19} +(-0.477263 + 2.18454i) q^{20} +(6.14742 + 5.32677i) q^{21} +(3.25312 + 3.25312i) q^{22} +(0.785478 - 4.73107i) q^{23} -3.12550i q^{24} +(-3.77289 - 3.28105i) q^{25} +(2.19007 - 1.40747i) q^{26} +(-9.42969 - 7.05898i) q^{27} +(2.43844 + 0.909491i) q^{28} +(-6.04466 - 0.869091i) q^{29} +(6.13095 + 3.35487i) q^{30} +(4.50690 + 2.89641i) q^{31} +(-0.349464 - 0.936950i) q^{32} +(12.6203 - 6.89121i) q^{33} +(2.45252 + 2.83036i) q^{34} +(-4.40144 + 3.80699i) q^{35} +(-6.49455 - 1.90697i) q^{36} +(-8.17698 + 3.04986i) q^{37} +(1.47678 - 0.321254i) q^{38} +(-2.29238 - 7.80713i) q^{39} +(2.21302 + 0.320204i) q^{40} +(-4.39226 - 9.61770i) q^{41} +(4.87465 - 6.51176i) q^{42} +(-0.143943 + 0.661697i) q^{43} +(3.01276 - 3.47691i) q^{44} +(10.7119 - 10.6927i) q^{45} +(-4.77505 - 0.445966i) q^{46} +(1.92809 - 1.92809i) q^{47} +(-3.11753 + 0.222970i) q^{48} +(-0.122635 - 0.190823i) q^{49} +(-3.00354 + 3.99734i) q^{50} +(10.6475 - 4.86256i) q^{51} +(-1.56012 - 2.08408i) q^{52} +(-3.01733 + 5.52584i) q^{53} +(-6.36829 + 9.90925i) q^{54} +(3.58642 + 9.64186i) q^{55} +(0.733218 - 2.49711i) q^{56} +(0.336979 - 4.71158i) q^{57} +(-0.435656 + 6.09126i) q^{58} +(1.80006 - 6.13045i) q^{59} +(2.90894 - 6.35466i) q^{60} +(-4.00554 + 6.23274i) q^{61} +(2.56751 - 4.70205i) q^{62} +(-10.5568 - 14.1022i) q^{63} +(-0.909632 + 0.415415i) q^{64} +(5.76272 - 0.823298i) q^{65} +(-7.77397 - 12.0965i) q^{66} +(-7.74682 + 0.554064i) q^{67} +(2.64819 - 2.64819i) q^{68} +(-5.54209 + 13.9272i) q^{69} +(4.11128 + 4.11864i) q^{70} +(-8.49053 + 9.79860i) q^{71} +(-1.43880 + 6.61404i) q^{72} +(-0.891553 + 1.19098i) q^{73} +(3.62542 + 7.93857i) q^{74} +(9.34282 + 12.5272i) q^{75} +(-0.425787 - 1.45010i) q^{76} +(11.6996 - 2.54509i) q^{77} +(-7.62370 + 2.84349i) q^{78} +(-4.18153 - 1.22781i) q^{79} +(0.161513 - 2.23023i) q^{80} +(10.8114 + 12.4770i) q^{81} +(-9.27986 + 5.06719i) q^{82} +(-0.858110 - 2.30068i) q^{83} +(-6.84293 - 4.39768i) q^{84} +(2.35213 + 8.03720i) q^{85} +(0.670280 + 0.0963717i) q^{86} +(17.8834 + 6.67017i) q^{87} +(-3.68298 - 2.75704i) q^{88} +(13.5970 - 8.73826i) q^{89} +(-11.4297 - 9.92176i) q^{90} -6.77526i q^{91} +(-0.104181 + 4.79470i) q^{92} +(-11.8401 - 11.8401i) q^{93} +(-2.06073 - 1.78563i) q^{94} +(3.30154 + 0.721296i) q^{95} +(0.444805 + 3.09368i) q^{96} +(-2.56949 + 6.88907i) q^{97} +(-0.181589 + 0.135936i) q^{98} +(-29.8789 + 8.77322i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 8 q^{3} - 8 q^{6} - 8 q^{12} + 16 q^{13} + 24 q^{16} - 72 q^{18} - 80 q^{23} - 8 q^{26} + 16 q^{27} - 44 q^{28} + 24 q^{31} - 44 q^{33} - 8 q^{35} - 32 q^{36} - 88 q^{37} - 24 q^{41} - 8 q^{46}+ \cdots + 24 q^{98}+O(q^{100}) \) 240 * q - 8 * q^3 - 8 * q^6 - 8 * q^12 + 16 * q^13 + 24 * q^16 - 72 * q^18 - 80 * q^23 - 8 * q^26 + 16 * q^27 - 44 * q^28 + 24 * q^31 - 44 * q^33 - 8 * q^35 - 32 * q^36 - 88 * q^37 - 24 * q^41 - 8 * q^46 - 80 * q^47 + 8 * q^48 + 8 * q^50 + 16 * q^52 - 44 * q^56 - 88 * q^57 - 176 * q^61 - 32 * q^62 - 176 * q^66 + 24 * q^70 - 336 * q^71 + 16 * q^72 - 88 * q^73 - 36 * q^75 - 24 * q^77 + 40 * q^78 - 136 * q^81 + 40 * q^82 - 100 * q^85 - 44 * q^86 + 40 * q^87 + 8 * q^92 + 56 * q^93 + 52 * q^95 + 8 * q^96 + 132 * q^97 + 24 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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