LMFDB - Embedded newform 372.2.p.a.191.14

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [372,2,Mod(191,372)] 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("372.191"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(372, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 372 = 2^{2} \cdot 3 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	372.p (of order $6$, degree $2$, 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:	$2.97043495519$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$60$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			191.14
Character	$\chi$	$=$	372.191
Dual form			372.2.p.a.335.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.979289 + 1.02029i) q^{2} +(1.70357 - 0.312832i) q^{3} +(-0.0819876 - 1.99832i) q^{4} +(-1.50717 + 0.870163i) q^{5} +(-1.34910 + 2.04449i) q^{6} +(2.62156 + 1.51356i) q^{7} +(2.11916 + 1.87328i) q^{8} +(2.80427 - 1.06586i) q^{9} +(0.588131 - 2.38989i) q^{10} +(0.0524986 + 0.0909303i) q^{11} +(-0.764809 - 3.37862i) q^{12} +(-1.25091 - 2.16665i) q^{13} +(-4.11154 + 1.19254i) q^{14} +(-2.29534 + 1.95387i) q^{15} +(-3.98656 + 0.327675i) q^{16} +(0.921869 + 0.532241i) q^{17} +(-1.65870 + 3.90496i) q^{18} +(5.76362 + 3.32763i) q^{19} +(1.86243 + 2.94046i) q^{20} +(4.93949 + 1.75834i) q^{21} +(-0.144187 - 0.0354831i) q^{22} +1.76515 q^{23} +(4.19614 + 2.52832i) q^{24} +(-0.985633 + 1.70717i) q^{25} +(3.43562 + 0.845477i) q^{26} +(4.44383 - 2.69303i) q^{27} +(2.80964 - 5.36281i) q^{28} +5.47454i q^{29} +(0.254287 - 4.25532i) q^{30} +(-0.434039 - 5.55082i) q^{31} +(3.56967 - 4.38834i) q^{32} +(0.117881 + 0.138482i) q^{33} +(-1.44582 + 0.419357i) q^{34} -5.26817 q^{35} +(-2.35984 - 5.51644i) q^{36} +(-2.39418 + 4.14684i) q^{37} +(-9.03939 + 2.62186i) q^{38} +(-2.80881 - 3.29970i) q^{39} +(-4.82398 - 0.979333i) q^{40} +(6.49599 - 3.75046i) q^{41} +(-6.63121 + 3.31780i) q^{42} +(0.710562 + 0.410243i) q^{43} +(0.177403 - 0.112364i) q^{44} +(-3.29903 + 4.04660i) q^{45} +(-1.72859 + 1.80097i) q^{46} +1.57783 q^{47} +(-6.68885 + 1.80534i) q^{48} +(1.08173 + 1.87361i) q^{49} +(-0.776588 - 2.67744i) q^{50} +(1.73697 + 0.618318i) q^{51} +(-4.22709 + 2.67736i) q^{52} +(-8.60561 + 4.96845i) q^{53} +(-1.60412 + 7.17125i) q^{54} +(-0.158248 - 0.0913647i) q^{55} +(2.72018 + 8.11839i) q^{56} +(10.8597 + 3.86579i) q^{57} +(-5.58562 - 5.36116i) q^{58} +(4.59615 - 7.96076i) q^{59} +(4.09264 + 4.42663i) q^{60} -7.64594 q^{61} +(6.08850 + 4.99301i) q^{62} +(8.96482 + 1.45022i) q^{63} +(0.981647 + 7.93954i) q^{64} +(3.77067 + 2.17700i) q^{65} +(-0.256732 - 0.0153416i) q^{66} +(-10.7490 + 6.20592i) q^{67} +(0.988006 - 1.88582i) q^{68} +(3.00705 - 0.552196i) q^{69} +(5.15906 - 5.37507i) q^{70} +(-7.54234 - 13.0637i) q^{71} +(7.93934 + 2.99446i) q^{72} +(-7.30556 - 12.6536i) q^{73} +(-1.88639 - 6.50372i) q^{74} +(-1.14503 + 3.21661i) q^{75} +(6.17711 - 11.7904i) q^{76} +0.317839i q^{77} +(6.11729 + 0.365554i) q^{78} +(-9.00803 - 5.20079i) q^{79} +(5.72327 - 3.96281i) q^{80} +(6.72789 - 5.97792i) q^{81} +(-2.53489 + 10.3006i) q^{82} +(-1.50601 - 2.60849i) q^{83} +(3.10875 - 10.0148i) q^{84} -1.85255 q^{85} +(-1.11441 + 0.323234i) q^{86} +(1.71261 + 9.32624i) q^{87} +(-0.0590851 + 0.291040i) q^{88} +5.45713i q^{89} +(-0.898005 - 7.32876i) q^{90} -7.57334i q^{91} +(-0.144720 - 3.52733i) q^{92} +(-2.47589 - 9.32041i) q^{93} +(-1.54516 + 1.60985i) q^{94} -11.5823 q^{95} +(4.70835 - 8.59252i) q^{96} +5.26914 q^{97} +(-2.97095 - 0.731125i) q^{98} +(0.244139 + 0.199037i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q - 12 q^{4} - 2 q^{9} + 4 q^{10} - 4 q^{12} - 4 q^{16} - 2 q^{18} - 14 q^{21} - 6 q^{22} - 4 q^{24} + 48 q^{25} + 6 q^{28} - 48 q^{30} + 4 q^{33} + 28 q^{34} + 2 q^{36} - 8 q^{37} + 36 q^{40} - 4 q^{42}+ \cdots + 48 q^{96}+O(q^{100}) $ 120 * q - 12 * q^4 - 2 * q^9 + 4 * q^10 - 4 * q^12 - 4 * q^16 - 2 * q^18 - 14 * q^21 - 6 * q^22 - 4 * q^24 + 48 * q^25 + 6 * q^28 - 48 * q^30 + 4 * q^33 + 28 * q^34 + 2 * q^36 - 8 * q^37 + 36 * q^40 - 4 * q^42 - 34 * q^45 - 48 * q^46 + 10 * q^48 + 60 * q^49 + 8 * q^52 - 84 * q^54 - 14 * q^57 - 28 * q^58 - 60 * q^60 - 64 * q^61 + 84 * q^64 - 132 * q^66 - 4 * q^69 - 120 * q^70 + 44 * q^72 + 28 * q^76 + 20 * q^78 - 2 * q^81 + 48 * q^82 - 8 * q^84 + 8 * q^85 - 10 * q^88 + 24 * q^90 - 78 * q^93 - 88 * q^94 + 48 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/372\mathbb{Z}\right)^\times$.

$n$	$125$	$187$	$313$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.979289	+	1.02029i	−0.692462	+	0.721455i
$2$	−0.979289	+	1.02029i	−0.692462	+	0.721455i
$3$	1.70357	−	0.312832i	0.983554	−	0.180614i
$3$	1.70357	−	0.312832i	0.983554	−	0.180614i
$4$	−0.0819876	−	1.99832i	−0.0409938	−	0.999159i
$5$	−1.50717	+	0.870163i	−0.674025	+	0.389149i	−0.797600	−	0.603187i	$-0.793897\pi$
$5$	−1.50717	+	0.870163i	−0.674025	+	0.389149i	0.123575	+	0.992335i	$0.460564\pi$
$6$	−1.34910	+	2.04449i	−0.550769	+	0.834658i
$7$	2.62156	+	1.51356i	0.990858	+	0.572072i	0.905531	−	0.424281i	$-0.139473\pi$
$7$	2.62156	+	1.51356i	0.990858	+	0.572072i	0.0853271	+	0.996353i	$0.472806\pi$
$8$	2.11916	+	1.87328i	0.749235	+	0.662304i
$9$	2.80427	−	1.06586i	0.934757	−	0.355287i
$10$	0.588131	−	2.38989i	0.185983	−	0.755749i
$11$	0.0524986	+	0.0909303i	0.0158289	+	0.0274165i	0.873831	−	0.486229i	$-0.161628\pi$
$11$	0.0524986	+	0.0909303i	0.0158289	+	0.0274165i	−0.858002	+	0.513646i	$0.828295\pi$
$12$	−0.764809	−	3.37862i	−0.220781	−	0.975323i
$13$	−1.25091	−	2.16665i	−0.346941	−	0.600920i	0.638763	−	0.769403i	$-0.279446\pi$
$13$	−1.25091	−	2.16665i	−0.346941	−	0.600920i	−0.985704	+	0.168483i	$0.946113\pi$
$14$	−4.11154	+	1.19254i	−1.09885	+	0.318721i
$15$	−2.29534	+	1.95387i	−0.592655	+	0.504487i
$16$	−3.98656	+	0.327675i	−0.996639	+	0.0819187i
$17$	0.921869	+	0.532241i	0.223586	+	0.129087i	0.607610	−	0.794236i	$-0.292129\pi$
$17$	0.921869	+	0.532241i	0.223586	+	0.129087i	−0.384024	+	0.923323i	$0.625462\pi$
$18$	−1.65870	+	3.90496i	−0.390961	+	0.920407i
$19$	5.76362	+	3.32763i	1.32226	+	0.763410i	0.984090	−	0.177673i	$-0.0568571\pi$
$19$	5.76362	+	3.32763i	1.32226	+	0.763410i	0.338175	+	0.941083i	$0.390190\pi$
$20$	1.86243	+	2.94046i	0.416452	+	0.657506i
$21$	4.93949	+	1.75834i	1.07789	+	0.383701i
$22$	−0.144187	−	0.0354831i	−0.0307407	−	0.00756503i
$23$	1.76515			0.368059			0.184030	−	0.982921i	$-0.441086\pi$
$23$	1.76515			0.368059			0.184030	+	0.982921i	$0.441086\pi$
$24$	4.19614	+	2.52832i	0.856534	+	0.516090i
$25$	−0.985633	+	1.70717i	−0.197127	+	0.341433i
$26$	3.43562	+	0.845477i	0.673780	+	0.165812i
$27$	4.44383	−	2.69303i	0.855215	−	0.518273i
$28$	2.80964	−	5.36281i	0.530972	−	1.01348i
$29$			5.47454i			1.01660i	0.861181	+	0.508298i	$0.169725\pi$
$29$			5.47454i			1.01660i	−0.861181	+	0.508298i	$0.830275\pi$
$30$	0.254287	−	4.25532i	0.0464262	−	0.776911i
$31$	−0.434039	−	5.55082i	−0.0779557	−	0.996957i
$31$	−0.434039	−	5.55082i	−0.0779557	−	0.996957i
$32$	3.56967	−	4.38834i	0.631034	−	0.775755i
$33$	0.117881	+	0.138482i	0.0205204	+	0.0241067i
$34$	−1.44582	+	0.419357i	−0.247955	+	0.0719191i
$35$	−5.26817			−0.890484
$36$	−2.35984	−	5.51644i	−0.393307	−	0.919407i
$37$	−2.39418	+	4.14684i	−0.393601	+	0.681737i	−0.992922	−	0.118772i	$-0.962104\pi$
$37$	−2.39418	+	4.14684i	−0.393601	+	0.681737i	0.599321	+	0.800509i	$0.295437\pi$
$38$	−9.03939	+	2.62186i	−1.46638	+	0.425322i
$39$	−2.80881	−	3.29970i	−0.449770	−	0.528375i
$40$	−4.82398	−	0.979333i	−0.762738	−	0.154846i
$41$	6.49599	−	3.75046i	1.01450	−	0.585724i	0.101997	−	0.994785i	$-0.467477\pi$
$41$	6.49599	−	3.75046i	1.01450	−	0.585724i	0.912507	+	0.409061i	$0.134144\pi$
$42$	−6.63121	+	3.31780i	−1.02322	+	0.511948i
$43$	0.710562	+	0.410243i	0.108360	+	0.0625615i	0.553200	−	0.833048i	$-0.313406\pi$
$43$	0.710562	+	0.410243i	0.108360	+	0.0625615i	−0.444841	+	0.895610i	$0.646740\pi$
$44$	0.177403	−	0.112364i	0.0267446	−	0.0169395i
$45$	−3.29903	+	4.04660i	−0.491791	+	0.603232i
$46$	−1.72859	+	1.80097i	−0.254867	+	0.265538i
$47$	1.57783			0.230151			0.115075	−	0.993357i	$-0.463289\pi$
$47$	1.57783			0.230151			0.115075	+	0.993357i	$0.463289\pi$
$48$	−6.68885	+	1.80534i	−0.965453	+	0.260578i
$49$	1.08173	+	1.87361i	0.154533	+	0.267658i
$50$	−0.776588	−	2.67744i	−0.109826	−	0.378648i
$51$	1.73697	+	0.618318i	0.243224	+	0.0865818i
$52$	−4.22709	+	2.67736i	−0.586192	+	0.371284i
$53$	−8.60561	+	4.96845i	−1.18207	+	0.682469i	−0.956493	−	0.291756i	$-0.905760\pi$
$53$	−8.60561	+	4.96845i	−1.18207	+	0.682469i	−0.225578	+	0.974225i	$0.572427\pi$
$54$	−1.60412	+	7.17125i	−0.218293	+	0.975883i
$55$	−0.158248	−	0.0913647i	−0.0213382	−	0.0123196i
$56$	2.72018	+	8.11839i	0.363499	+	1.08487i
$57$	10.8597	+	3.86579i	1.43840	+	0.512036i
$58$	−5.58562	−	5.36116i	−0.733428	−	0.703954i
$59$	4.59615	−	7.96076i	0.598367	−	1.03640i	−0.394695	−	0.918812i	$-0.629150\pi$
$59$	4.59615	−	7.96076i	0.598367	−	1.03640i	0.993062	−	0.117590i	$-0.0375169\pi$
$60$	4.09264	+	4.42663i	0.528358	+	0.571476i
$61$	−7.64594			−0.978963			−0.489481	−	0.872014i	$-0.662814\pi$
$61$	−7.64594			−0.978963			−0.489481	+	0.872014i	$0.662814\pi$
$62$	6.08850	+	4.99301i	0.773241	+	0.634113i
$63$	8.96482	+	1.45022i	1.12946	+	0.182710i
$64$	0.981647	+	7.93954i	0.122706	+	0.992443i
$65$	3.77067	+	2.17700i	0.467694	+	0.270023i
$66$	−0.256732	−	0.0153416i	−0.0316015	−	0.00188842i
$67$	−10.7490	+	6.20592i	−1.31320	+	0.758174i	−0.982624	−	0.185606i	$-0.940575\pi$
$67$	−10.7490	+	6.20592i	−1.31320	+	0.758174i	−0.330572	+	0.943781i	$0.607242\pi$
$68$	0.988006	−	1.88582i	0.119813	−	0.228690i
$69$	3.00705	−	0.552196i	0.362006	−	0.0664765i
$70$	5.15906	−	5.37507i	0.616626	−	0.642444i
$71$	−7.54234	−	13.0637i	−0.895111	−	1.55038i	−0.833667	−	0.552267i	$-0.813763\pi$
$71$	−7.54234	−	13.0637i	−0.895111	−	1.55038i	−0.0614435	−	0.998111i	$-0.519570\pi$
$72$	7.93934	+	2.99446i	0.935661	+	0.352901i
$73$	−7.30556	−	12.6536i	−0.855051	−	1.48099i	−0.876598	−	0.481224i	$-0.840192\pi$
$73$	−7.30556	−	12.6536i	−0.855051	−	1.48099i	0.0215470	−	0.999768i	$-0.493141\pi$
$74$	−1.88639	−	6.50372i	−0.219289	−	0.756042i
$75$	−1.14503	+	3.21661i	−0.132217	+	0.371422i
$76$	6.17711	−	11.7904i	0.708563	−	1.35245i
$77$			0.317839i			0.0362211i
$78$	6.11729	+	0.365554i	0.692647	+	0.0413908i
$79$	−9.00803	−	5.20079i	−1.01348	−	0.585135i	−0.101273	−	0.994859i	$-0.532292\pi$
$79$	−9.00803	−	5.20079i	−1.01348	−	0.585135i	−0.912210	+	0.409724i	$0.865625\pi$
$80$	5.72327	−	3.96281i	0.639881	−	0.443056i
$81$	6.72789	−	5.97792i	0.747543	−	0.664213i
$82$	−2.53489	+	10.3006i	−0.279932	+	1.13751i
$83$	−1.50601	−	2.60849i	−0.165307	−	0.286319i	0.771458	−	0.636281i	$-0.219528\pi$
$83$	−1.50601	−	2.60849i	−0.165307	−	0.286319i	−0.936764	+	0.349961i	$0.886195\pi$
$84$	3.10875	−	10.0148i	0.339192	−	1.09271i
$85$	−1.85255			−0.200937
$86$	−1.11441	+	0.323234i	−0.120170	+	0.0348552i
$87$	1.71261	+	9.32624i	0.183611	+	0.999878i
$88$	−0.0590851	+	0.291040i	−0.00629849	+	0.0310250i
$89$			5.45713i			0.578454i	0.957260	+	0.289227i	$0.0933983\pi$
$89$			5.45713i			0.578454i	−0.957260	+	0.289227i	$0.906602\pi$
$90$	−0.898005	−	7.32876i	−0.0946581	−	0.772520i
$91$		−	7.57334i		−	0.793902i
$92$	−0.144720	−	3.52733i	−0.0150882	−	0.367750i
$93$	−2.47589	−	9.32041i	−0.256738	−	0.966481i
$94$	−1.54516	+	1.60985i	−0.159371	+	0.166043i
$95$	−11.5823			−1.18832
$96$	4.70835	−	8.59252i	0.480544	−	0.876971i
$97$	5.26914			0.535000			0.267500	−	0.963558i	$-0.413802\pi$
$97$	5.26914			0.535000			0.267500	+	0.963558i	$0.413802\pi$
$98$	−2.97095	−	0.731125i	−0.300111	−	0.0738548i
$99$	0.244139	+	0.199037i	0.0245369	+	0.0200040i
$100$	3.49227	+	1.82964i	0.349227	+	0.182964i
$101$		−	7.26469i		−	0.722864i	−0.932398	−	0.361432i	$-0.882288\pi$
$101$		−	7.26469i		−	0.722864i	0.932398	−	0.361432i	$-0.117712\pi$
$102$	−2.33185	+	1.16670i	−0.230888	+	0.115520i
$103$	2.17281	−	1.25447i	0.214093	−	0.123607i	−0.389119	−	0.921187i	$-0.627221\pi$
$103$	2.17281	−	1.25447i	0.214093	−	0.123607i	0.603212	+	0.797581i	$0.293887\pi$
$104$	1.40785	−	6.93478i	0.138051	−	0.680011i
$105$	−8.97468	+	1.64805i	−0.875839	+	0.160834i
$106$	3.35811	−	13.6458i	0.326168	−	1.32539i
$107$	6.92842	−	12.0004i	0.669796	−	1.16012i	−0.308166	−	0.951333i	$-0.599715\pi$
$107$	6.92842	−	12.0004i	0.669796	−	1.16012i	0.977961	−	0.208787i	$-0.0669516\pi$
$108$	−5.74587	−	8.65939i	−0.552896	−	0.833250i
$109$	0.640695			0.0613674			0.0306837	−	0.999529i	$-0.490232\pi$
$109$	0.640695			0.0613674			0.0306837	+	0.999529i	$0.490232\pi$
$110$	0.248189	−	0.0719869i	0.0236639	−	0.00686368i
$111$	−2.78138	+	7.81339i	−0.263997	+	0.741615i
$112$	−10.9470	−	5.17487i	−1.03439	−	0.488979i
$113$	−5.75383	+	3.32198i	−0.541275	+	0.312505i	−0.745596	−	0.666399i	$-0.767835\pi$
$113$	−5.75383	+	3.32198i	−0.541275	+	0.312505i	0.204321	+	0.978904i	$0.434502\pi$
$114$	−14.5790	+	7.29432i	−1.36545	+	0.683176i
$115$	−2.66038	+	1.53597i	−0.248081	+	0.143230i
$116$	10.9399	−	0.448844i	1.01574	−	0.0416742i
$117$	−5.81725	−	4.74257i	−0.537805	−	0.438451i
$118$	3.62134	+	12.4853i	0.333371	+	1.14936i
$119$	1.61116	+	2.79061i	0.147695	+	0.255815i
$120$	−8.52433	−	0.159263i	−0.778161	−	0.0145386i
$121$	5.49449	−	9.51673i	0.499499	−	0.865157i
$122$	7.48758	−	7.80109i	0.677894	−	0.706277i
$123$	9.89309	−	8.42132i	0.892030	−	0.759325i
$124$	−11.0567	+	1.32245i	−0.992923	+	0.118759i
$125$		−	12.1323i		−	1.08514i
$126$	−10.2588	+	7.72654i	−0.913925	+	0.688335i
$127$	14.8389	+	8.56722i	1.31674	+	0.760218i	0.983202	−	0.182520i	$-0.0584256\pi$
$127$	14.8389	+	8.56722i	1.31674	+	0.760218i	0.333534	+	0.942738i	$0.391759\pi$
$128$	−9.06196	−	6.77354i	−0.800972	−	0.598702i
$129$	1.33883	+	0.476590i	0.117877	+	0.0419614i
$130$	−5.91375	+	1.71527i	−0.518670	+	0.150439i
$131$	−8.30013	+	14.3763i	−0.725186	+	1.25606i	0.233711	+	0.972306i	$0.424913\pi$
$131$	−8.30013	+	14.3763i	−0.725186	+	1.25606i	−0.958897	+	0.283753i	$0.908420\pi$
$132$	0.267067	−	0.246917i	0.0232452	−	0.0214914i
$133$	10.0731	+	17.4472i	0.873451	+	1.51286i
$134$	4.19450	−	17.0445i	0.362350	−	1.47242i
$135$	−4.35421	+	7.92569i	−0.374751	+	0.682135i
$136$	0.956547	+	2.85482i	0.0820232	+	0.244799i
$137$	−13.4377	+	7.75827i	−1.14806	+	0.662834i	−0.948414	−	0.317034i	$-0.897313\pi$
$137$	−13.4377	+	7.75827i	−1.14806	+	0.662834i	−0.199648	+	0.979868i	$0.563980\pi$
$138$	−2.38137	+	3.60883i	−0.202716	+	0.307204i
$139$			2.37109i			0.201114i	0.994931	+	0.100557i	$0.0320624\pi$
$139$			2.37109i			0.201114i	−0.994931	+	0.100557i	$0.967938\pi$
$140$	0.431925	+	10.5275i	0.0365043	+	0.889735i
$141$	2.68795	−	0.493597i	0.226366	−	0.0415684i
$142$	20.7149	+	5.09777i	1.73836	+	0.427795i
$143$	0.131343	−	0.227492i	0.0109834	−	0.0190238i
$144$	−10.8301	+	5.16800i	−0.902511	+	0.430667i
$145$	−4.76374	−	8.25104i	−0.395607	−	0.685212i
$146$	20.0646	+	4.93773i	1.66056	+	0.408649i
$147$	2.42892	+	2.85341i	0.200334	+	0.235346i
$148$	8.48301	+	4.44435i	0.697299	+	0.365323i
$149$	−2.80208	−	1.61778i	−0.229555	−	0.132534i	0.380812	−	0.924653i	$-0.375645\pi$
$149$	−2.80208	−	1.61778i	−0.229555	−	0.132534i	−0.610367	+	0.792119i	$0.708978\pi$
$150$	−2.16056	−	4.31826i	−0.176409	−	0.352584i
$151$		−	4.01599i		−	0.326816i	−0.986559	−	0.163408i	$-0.947751\pi$
$151$		−	4.01599i		−	0.326816i	0.986559	−	0.163408i	$-0.0522488\pi$
$152$	5.98043	+	17.8486i	0.485077	+	1.44771i
$153$	3.15246	+	0.509966i	0.254862	+	0.0412283i
$154$	−0.324289	−	0.311256i	−0.0261319	−	0.0250818i
$155$	5.48429	+	7.98832i	0.440508	+	0.641638i
$156$	−6.36357	+	5.88344i	−0.509493	+	0.471052i
$157$	1.54160			0.123033			0.0615167	−	0.998106i	$-0.480406\pi$
$157$	1.54160			0.123033			0.0615167	+	0.998106i	$0.480406\pi$
$158$	14.1278	−	4.09774i	1.12395	−	0.325999i
$159$	−13.1059	+	11.1562i	−1.03937	+	0.884743i
$160$	−1.56151	+	9.72014i	−0.123448	+	0.768445i
$161$	4.62745	+	2.67166i	0.364694	+	0.210556i
$162$	−0.489323	+	12.7185i	−0.0384449	+	0.999261i
$163$		−	8.14608i		−	0.638050i	−0.947746	−	0.319025i	$-0.896645\pi$
$163$		−	8.14608i		−	0.638050i	0.947746	−	0.319025i	$-0.103355\pi$
$164$	−8.02721	−	12.6736i	−0.626820	−	0.989640i
$165$	−0.298168	−	0.106141i	−0.0232124	−	0.00826304i
$166$	4.13624	+	1.01789i	0.321035	+	0.0790040i
$167$	−11.0137	+	19.0763i	−0.852268	+	1.47617i	0.0268885	+	0.999638i	$0.491440\pi$
$167$	−11.0137	+	19.0763i	−0.852268	+	1.47617i	−0.879157	+	0.476533i	$0.841893\pi$
$168$	7.17370	+	12.9793i	0.553463	+	1.00137i
$169$	3.37042	−	5.83775i	0.259263	−	0.449057i
$170$	1.81418	−	1.89014i	0.139141	−	0.144967i
$171$	19.7095	+	3.18836i	1.50723	+	0.243820i
$172$	0.761539	−	1.45356i	0.0580668	−	0.110833i
$173$	−21.6076	+	12.4752i	−1.64280	+	0.948470i	−0.662965	+	0.748650i	$0.730702\pi$
$173$	−21.6076	+	12.4752i	−1.64280	+	0.948470i	−0.979833	+	0.199820i	$0.935964\pi$
$174$	−11.1926	−	7.38572i	−0.848510	−	0.559910i
$175$	−5.16780	+	2.98363i	−0.390649	+	0.225541i
$176$	−0.239084	−	0.345296i	−0.0180217	−	0.0260277i
$177$	5.33946	−	14.9995i	0.401338	−	1.12743i
$178$	−5.56786	−	5.34410i	−0.417329	−	0.400557i
$179$	−1.64214	+	2.84427i	−0.122739	+	0.212590i	−0.920847	−	0.389924i	$-0.872501\pi$
$179$	−1.64214	+	2.84427i	−0.122739	+	0.212590i	0.798108	+	0.602515i	$0.205835\pi$
$180$	8.35688	+	6.26075i	0.622885	+	0.466649i
$181$	6.21366	+	10.7624i	0.461858	+	0.799961i	0.999054	−	0.0434965i	$-0.0138497\pi$
$181$	6.21366	+	10.7624i	0.461858	+	0.799961i	−0.537196	+	0.843458i	$0.680516\pi$
$182$	7.72701	+	7.41648i	0.572764	+	0.549746i
$183$	−13.0254	+	2.39190i	−0.962863	+	0.176814i
$184$	3.74063	+	3.30662i	0.275763	+	0.243767i
$185$		−	8.33331i		−	0.612677i
$186$	11.9341	+	6.60124i	0.875053	+	0.484027i
$187$			0.111768i			0.00817326i
$188$	−0.129363	−	3.15302i	−0.00943476	−	0.229957i
$189$	15.7258	−	0.333943i	1.14389	−	0.0242908i
$190$	11.3424	−	11.8173i	0.822866	−	0.857319i
$191$	−0.216766	−	0.375450i	−0.0156846	−	0.0271666i	0.858077	−	0.513522i	$-0.171659\pi$
$191$	−0.216766	−	0.375450i	−0.0156846	−	0.0271666i	−0.873761	+	0.486355i	$0.838326\pi$
$192$	4.15604	+	13.2184i	0.299937	+	0.953959i
$193$	10.4816	−	18.1547i	0.754483	−	1.30680i	−0.191149	−	0.981561i	$-0.561221\pi$
$193$	10.4816	−	18.1547i	0.754483	−	1.30680i	0.945631	−	0.325241i	$-0.105445\pi$
$194$	−5.16001	+	5.37606i	−0.370467	+	0.385978i
$195$	7.10462	+	2.52907i	0.508773	+	0.181111i
$196$	3.65538	−	2.31525i	0.261098	−	0.165375i
$197$	10.1308	−	5.84900i	0.721787	−	0.416724i	−0.0936229	−	0.995608i	$-0.529845\pi$
$197$	10.1308	−	5.84900i	0.721787	−	0.416724i	0.815410	+	0.578884i	$0.196511\pi$
$198$	−0.442159	+	0.0541784i	−0.0314228	+	0.00385029i
$199$	−6.79422	+	3.92264i	−0.481629	+	0.278069i	−0.721095	−	0.692836i	$-0.756361\pi$
$199$	−6.79422	+	3.92264i	−0.481629	+	0.278069i	0.239466	+	0.970905i	$0.423028\pi$
$200$	−5.28671	+	1.77139i	−0.373827	+	0.125256i
$201$	−16.3702	+	13.9348i	−1.15466	+	0.982887i
$202$	7.41210	+	7.11423i	0.521514	+	0.500556i
$203$	−8.28605	+	14.3519i	−0.581566	+	1.00730i
$204$	1.09319	−	3.52171i	0.0765383	−	0.246569i
$205$	−6.52703	+	11.3051i	−0.455867	+	0.789586i
$206$	−0.847880	+	3.44538i	−0.0590746	+	0.240051i
$207$	4.94996	−	1.88140i	0.344046	−	0.130767i
$208$	5.69680	+	8.22757i	0.395002	+	0.570479i
$209$			0.698783i			0.0483358i
$210$	7.10731	−	10.7707i	0.490451	−	0.743249i
$211$	−6.44387	−	3.72037i	−0.443615	−	0.256121i	0.261515	−	0.965199i	$-0.415778\pi$
$211$	−6.44387	−	3.72037i	−0.443615	−	0.256121i	−0.705130	+	0.709078i	$0.749111\pi$
$212$	10.6341	+	16.7894i	0.730353	+	1.15310i
$213$	−16.9356	−	19.8954i	−1.16041	−	1.36321i
$214$	5.45895	+	18.8208i	0.373166	+	1.28657i
$215$	−1.42791			−0.0973829
$216$	14.4620	+	2.61758i	0.984012	+	0.178104i
$217$	7.26364	−	15.2088i	0.493088	−	1.03244i
$218$	−0.627425	+	0.653695i	−0.0424946	+	0.0442738i
$219$	−16.4039	−	19.2708i	−1.10848	−	1.30220i
$220$	−0.169601	+	0.323721i	−0.0114345	+	0.0218253i
$221$		−	2.66315i		−	0.179143i
$222$	−5.24816	−	10.4894i	−0.352234	−	0.704001i
$223$	18.0626	+	10.4285i	1.20956	+	0.698342i	0.962664	−	0.270699i	$-0.0872547\pi$
$223$	18.0626	+	10.4285i	1.20956	+	0.698342i	0.246900	+	0.969041i	$0.420588\pi$
$224$	16.0001	−	6.10139i	1.06905	−	0.407667i
$225$	−0.944384	+	5.83791i	−0.0629589	+	0.389194i
$226$	2.24528	−	9.12376i	0.149354	−	0.606903i
$227$	−6.10966	−	10.5822i	−0.405512	−	0.702368i	0.588869	−	0.808229i	$-0.299574\pi$
$227$	−6.10966	−	10.5822i	−0.405512	−	0.702368i	−0.994381	+	0.105861i	$0.966240\pi$
$228$	6.83471	−	22.0181i	0.452640	−	1.45818i
$229$	−10.8143	+	18.7309i	−0.714630	+	1.23778i	0.248472	+	0.968639i	$0.420072\pi$
$229$	−10.8143	+	18.7309i	−0.714630	+	1.23778i	−0.963102	+	0.269136i	$0.913262\pi$
$230$	1.03814	−	4.21851i	0.0684530	−	0.278161i
$231$	0.0994303	+	0.541460i	0.00654203	+	0.0356255i
$232$	−10.2553	+	11.6014i	−0.673296	+	0.761670i
$233$			14.1410i			0.926410i	0.886251	+	0.463205i	$0.153301\pi$
$233$			14.1410i			0.926410i	−0.886251	+	0.463205i	$0.846699\pi$
$234$	10.5356	−	1.29094i	0.688732	−	0.0843914i
$235$	−2.37806	+	1.37297i	−0.155127	+	0.0895629i
$236$	−16.2850	−	8.53188i	−1.06006	−	0.555378i
$237$	−16.9727	−	6.04189i	−1.10250	−	0.392463i
$238$	−4.42502	−	1.08896i	−0.286831	−	0.0705868i
$239$	−1.26305	−	2.18767i	−0.0816998	−	0.141508i	0.822280	−	0.569083i	$-0.192702\pi$
$239$	−1.26305	−	2.18767i	−0.0816998	−	0.141508i	−0.903980	+	0.427574i	$0.859368\pi$
$240$	8.51028	−	8.54133i	0.549336	−	0.551341i
$241$	−14.3163	+	24.7966i	−0.922197	+	1.59729i	−0.126189	+	0.992006i	$0.540274\pi$
$241$	−14.3163	+	24.7966i	−0.922197	+	1.59729i	−0.796008	+	0.605286i	$0.793059\pi$
$242$	4.32915	+	14.9256i	0.278288	+	0.959454i
$243$	9.59131	−	12.2885i	0.615283	−	0.788306i
$244$	0.626872	+	15.2790i	0.0401314	+	0.978140i
$245$	−3.26069	−	1.88256i	−0.208318	−	0.120272i
$246$	−1.09599	+	18.3407i	−0.0698781	+	1.16936i
$247$		−	16.6503i		−	1.05943i
$248$	9.47844	−	12.5761i	0.601882	−	0.798585i
$249$	−3.38161	−	3.97261i	−0.214301	−	0.251754i
$250$	12.3785	+	11.8810i	0.782882	+	0.751420i
$251$	6.03366	−	10.4506i	0.380841	−	0.659636i	−0.610342	−	0.792138i	$-0.708968\pi$
$251$	6.03366	−	10.4506i	0.380841	−	0.659636i	0.991183	+	0.132502i	$0.0423012\pi$
$252$	2.16299	−	18.0335i	0.136256	−	1.13600i
$253$	0.0926680	+	0.160506i	0.00582599	+	0.0100909i
$254$	−23.2726	+	6.75017i	−1.46025	+	0.423544i
$255$	−3.15593	+	0.579535i	−0.197632	+	0.0362919i
$256$	15.7853	−	2.61259i	0.986579	−	0.163287i
$257$	16.1976	−	9.35168i	1.01038	−	0.583342i	0.0990753	−	0.995080i	$-0.468412\pi$
$257$	16.1976	−	9.35168i	1.01038	−	0.583342i	0.911302	+	0.411738i	$0.135078\pi$
$258$	−1.79736	+	0.899273i	−0.111899	+	0.0559863i
$259$	−12.5530	+	7.24747i	−0.780005	+	0.450336i
$260$	4.04119	−	7.71349i	0.250624	−	0.478371i
$261$	5.83509	+	15.3521i	0.361183	+	0.950271i
$262$	−6.53974	−	22.5471i	−0.404026	−	1.39296i
$263$	15.2767			0.942003			0.471002	−	0.882132i	$-0.343893\pi$
$263$	15.2767			0.942003			0.471002	+	0.882132i	$0.343893\pi$
$264$	−0.00960864	+	0.514290i	−0.000591371	+	0.0316523i
$265$	8.64672	−	14.9766i	0.531164	−	0.920003i
$266$	−27.6657	−	6.80829i	−1.69629	−	0.417443i
$267$	1.70716	+	9.29658i	0.104477	+	0.568941i
$268$	13.2827	+	20.9711i	0.811370	+	1.28101i
$269$	−18.6520	+	10.7688i	−1.13723	+	0.656583i	−0.945744	−	0.324912i	$-0.894665\pi$
$269$	−18.6520	+	10.7688i	−1.13723	+	0.656583i	−0.191491	+	0.981494i	$0.561332\pi$
$270$	−3.82248	−	12.2041i	−0.232629	−	0.742718i
$271$		−	14.6833i		−	0.891947i	−0.895046	−	0.445974i	$-0.852857\pi$
$271$		−	14.6833i		−	0.891947i	0.895046	−	0.445974i	$-0.147143\pi$
$272$	−3.84948	−	1.81974i	−0.233409	−	0.110338i
$273$	−2.36918	−	12.9017i	−0.143389	−	0.780845i
$274$	5.24371	−	21.3080i	0.316784	−	1.28726i
$275$	−0.206978			−0.0124812
$276$	−1.35000	−	5.96377i	−0.0812607	−	0.358977i
$277$	24.9436			1.49871			0.749356	−	0.662167i	$-0.230363\pi$
$277$	24.9436			1.49871			0.749356	+	0.662167i	$0.230363\pi$
$278$	−2.41921	−	2.32199i	−0.145094	−	0.139263i
$279$	−7.13356	−	15.1034i	−0.427075	−	0.904216i
$280$	−11.1641	−	9.86876i	−0.667182	−	0.589771i
$281$		−	9.15500i		−	0.546141i	−0.961994	−	0.273071i	$-0.911961\pi$
$281$		−	9.15500i		−	0.546141i	0.961994	−	0.273071i	$-0.0880393\pi$
$282$	−2.12866	+	3.22586i	−0.126760	+	0.192097i
$283$			19.3192i			1.14841i	0.818712	+	0.574205i	$0.194689\pi$
$283$			19.3192i			1.14841i	−0.818712	+	0.574205i	$0.805311\pi$
$284$	−25.4871	+	16.1431i	−1.51238	+	0.957914i
$285$	−19.7312	+	3.62332i	−1.16878	+	0.214627i
$286$	0.103486	+	0.356788i	0.00611924	+	0.0210973i
$287$	22.7062			1.34031
$288$	5.33296	−	16.1109i	0.314248	−	0.949341i
$289$	−7.93344	−	13.7411i	−0.466673	−	0.808301i
$290$	13.0835	+	3.21975i	0.768292	+	0.189070i
$291$	8.97633	−	1.64836i	0.526201	−	0.0966283i
$292$	−24.6870	+	15.6363i	−1.44469	+	0.915044i
$293$	−7.13768	−	4.12094i	−0.416988	−	0.240748i	0.276800	−	0.960928i	$-0.410726\pi$
$293$	−7.13768	−	4.12094i	−0.416988	−	0.240748i	−0.693788	+	0.720180i	$0.744059\pi$
$294$	−5.28993	−	0.316112i	−0.308515	−	0.0184360i
$295$			15.9976i			0.931415i
$296$	−12.8418	+	4.30284i	−0.746417	+	0.250097i
$297$	0.478173	+	0.262698i	0.0277464	+	0.0152433i
$298$	4.39465	−	1.27466i	0.254575	−	0.0738391i
$299$	−2.20805	−	3.82446i	−0.127695	−	0.221174i
$300$	6.52169	+	2.02442i	0.376530	+	0.116880i
$301$	1.24186	+	2.15096i	0.0715793	+	0.123979i
$302$	4.09748	+	3.93281i	0.235783	+	0.226308i
$303$	−2.27263	−	12.3759i	−0.130559	−	0.710976i
$304$	−24.0674	−	11.3772i	−1.38036	−	0.652526i
$305$	11.5237	−	6.65321i	0.659845	−	0.380962i
$306$	−3.60749	+	2.71703i	−0.206226	+	0.155322i
$307$	−0.258088	−	0.149007i	−0.0147299	−	0.00850430i	0.492617	−	0.870246i	$-0.336040\pi$
$307$	−0.258088	−	0.149007i	−0.0147299	−	0.00850430i	−0.507347	+	0.861742i	$0.669374\pi$
$308$	0.635144	−	0.0260589i	0.0361907	−	0.00148484i
$309$	3.30908	−	2.81680i	0.188247	−	0.160242i
$310$	−13.5211	−	2.22731i	−0.767948	−	0.126503i
$311$	15.1251			0.857663			0.428832	−	0.903384i	$-0.358925\pi$
$311$	15.1251			0.857663			0.428832	+	0.903384i	$0.358925\pi$
$312$	0.228951	−	12.2543i	0.0129618	−	0.693762i
$313$	−12.0183	+	20.8163i	−0.679313	+	1.17660i	0.295876	+	0.955226i	$0.404389\pi$
$313$	−12.0183	+	20.8163i	−0.679313	+	1.17660i	−0.975188	+	0.221378i	$0.928945\pi$
$314$	−1.50967	+	1.57288i	−0.0851958	+	0.0887630i
$315$	−14.7734	+	5.61513i	−0.832387	+	0.316377i
$316$	−9.65429	+	18.4273i	−0.543096	+	1.03662i
$317$	4.85711	+	2.80425i	0.272802	+	0.157503i	0.630160	−	0.776465i	$-0.282989\pi$
$317$	4.85711	+	2.80425i	0.272802	+	0.157503i	−0.357358	+	0.933967i	$0.616322\pi$
$318$	1.45193	−	24.2970i	0.0814199	−	1.36251i
$319$	−0.497802	+	0.287406i	−0.0278715	+	0.0160916i
$320$	−8.38820	−	11.1120i	−0.468915	−	0.621181i
$321$	8.04892	−	22.6109i	0.449247	−	1.26201i
$322$	−7.25748	+	2.10502i	−0.404444	+	0.117308i
$323$	3.54220	+	6.13527i	0.197093	+	0.341375i
$324$	−12.4974	−	12.9543i	−0.694300	−	0.719686i
$325$	4.93177			0.273566
$326$	8.31137	+	7.97736i	0.460324	+	0.441825i
$327$	1.09147	−	0.200430i	0.0603582	−	0.0110838i
$328$	20.7917	+	4.22099i	1.14803	+	0.233065i
$329$	4.13639	+	2.38815i	0.228047	+	0.131663i
$330$	0.400287	−	0.200276i	0.0220351	−	0.0110248i
$331$	7.48363	−	4.32068i	0.411337	−	0.237486i	−0.280027	−	0.959992i	$-0.590343\pi$
$331$	7.48363	−	4.32068i	0.411337	−	0.237486i	0.691364	+	0.722506i	$0.257010\pi$
$332$	−5.08913	+	3.22336i	−0.279302	+	0.176905i
$333$	−2.29398	+	14.1807i	−0.125709	+	0.777099i
$334$	−8.67780	−	29.9185i	−0.474828	−	1.63706i
$335$	10.8003	−	18.7067i	0.590085	−	1.02206i
$336$	−20.2677	−	5.39117i	−1.10570	−	0.294113i
$337$	24.5094			1.33511			0.667557	−	0.744559i	$-0.267340\pi$
$337$	24.5094			1.33511			0.667557	+	0.744559i	$0.267340\pi$
$338$	2.65558	+	9.15565i	0.144445	+	0.498002i
$339$	−8.76281	+	7.45919i	−0.475931	+	0.405127i
$340$	0.151886	+	3.70198i	0.00823716	+	0.200768i
$341$	0.481951	−	0.330878i	0.0260991	−	0.0179180i
$342$	−22.5544	+	16.9871i	−1.21960	+	0.918559i
$343$		−	14.6408i		−	0.790529i
$344$	0.737292	+	2.20045i	0.0397521	+	0.118640i
$345$	−4.05162	+	3.44887i	−0.218132	+	0.185681i
$346$	8.43180	−	34.2629i	0.453296	−	1.84198i
$347$	5.23744	−	9.07151i	0.281161	−	0.486984i	−0.690510	−	0.723323i	$-0.742614\pi$
$347$	5.23744	−	9.07151i	0.281161	−	0.486984i	0.971671	+	0.236338i	$0.0759473\pi$
$348$	18.4964	−	4.18698i	0.991510	−	0.224446i
$349$	8.14721			0.436110			0.218055	−	0.975936i	$-0.430029\pi$
$349$	8.14721			0.436110			0.218055	+	0.975936i	$0.430029\pi$
$350$	2.01660	−	8.19450i	0.107792	−	0.438014i
$351$	−11.3937	−	6.25946i	−0.608150	−	0.334105i
$352$	0.586435	+	0.0942091i	0.0312571	+	0.00502136i
$353$	25.2979	+	14.6058i	1.34647	+	0.777386i	0.987748	−	0.156057i	$-0.0498785\pi$
$353$	25.2979	+	14.6058i	1.34647	+	0.777386i	0.358724	+	0.933444i	$0.383212\pi$
$354$	10.0750	+	20.1366i	0.535479	+	1.07025i
$355$	22.7351	+	13.1261i	1.20665	+	0.696662i
$356$	10.9051	−	0.447417i	0.577968	−	0.0237130i
$357$	3.61770	+	4.24996i	0.191469	+	0.224932i
$358$	−1.29385	−	4.46081i	−0.0683822	−	0.235761i
$359$	−13.0064	−	22.5277i	−0.686449	−	1.18897i	−0.972979	−	0.230894i	$-0.925835\pi$
$359$	−13.0064	−	22.5277i	−0.686449	−	1.18897i	0.286530	−	0.958071i	$-0.407498\pi$
$360$	−14.5716	+	2.39537i	−0.767990	+	0.126247i
$361$	12.6462	+	21.9039i	0.665589	+	1.15283i
$362$	−17.0657	−	4.19973i	−0.896954	−	0.220733i
$363$	6.38308	−	17.9312i	0.335025	−	0.941145i
$364$	−15.1339	+	0.620920i	−0.793234	+	0.0325450i
$365$	22.0214	+	12.7140i	1.15265	+	0.665484i
$366$	10.3152	−	15.6320i	0.539182	−	0.817099i
$367$	8.43271	−	4.86863i	0.440184	−	0.254140i	−0.263492	−	0.964662i	$-0.584874\pi$
$367$	8.43271	−	4.86863i	0.440184	−	0.254140i	0.703676	+	0.710521i	$0.251541\pi$
$368$	−7.03687	+	0.578395i	−0.366822	+	0.0301509i
$369$	14.2191	−	17.4411i	0.740215	−	0.907950i
$370$	8.50240	+	8.16071i	0.442019	+	0.424255i
$371$	−30.0802			−1.56169
$372$	−18.4222	+	5.71177i	−0.955144	+	0.296142i
$373$	−37.3504			−1.93393			−0.966966	−	0.254904i	$-0.917956\pi$
$373$	−37.3504			−1.93393			−0.966966	+	0.254904i	$0.917956\pi$
$374$	−0.114036	−	0.109453i	−0.00589664	−	0.00565967i
$375$	−3.79536	−	20.6681i	−0.195992	−	1.06730i
$376$	3.34368	+	2.95573i	0.172437	+	0.152430i
$377$	11.8614	−	6.84818i	0.610893	−	0.352699i
$378$	−15.0594	+	16.3720i	−0.774572	+	0.842082i
$379$	−12.8153	−	7.39889i	−0.658275	−	0.380055i	0.133344	−	0.991070i	$-0.457428\pi$
$379$	−12.8153	−	7.39889i	−0.658275	−	0.380055i	−0.791620	+	0.611014i	$0.790762\pi$
$380$	0.949606	+	23.1451i	0.0487137	+	1.18732i
$381$	27.9591	+	9.95275i	1.43239	+	0.509895i
$382$	0.595344	+	0.146509i	0.0304605	+	0.00749606i
$383$	13.4838	+	23.3547i	0.688992	+	1.19337i	0.972164	+	0.234301i	$0.0752800\pi$
$383$	13.4838	+	23.3547i	0.688992	+	1.19337i	−0.283172	+	0.959069i	$0.591387\pi$
$384$	−17.5566	−	8.70430i	−0.895933	−	0.444189i
$385$	−0.276572	−	0.479037i	−0.0140954	−	0.0244140i
$386$	8.25854	+	28.4730i	0.420348	+	1.44924i
$387$	2.42987	+	0.393074i	0.123517	+	0.0199811i
$388$	−0.432004	−	10.5294i	−0.0219317	−	0.534550i
$389$	−19.6604	−	11.3510i	−0.996824	−	0.575517i	−0.0895170	−	0.995985i	$-0.528532\pi$
$389$	−19.6604	−	11.3510i	−0.996824	−	0.575517i	−0.907307	+	0.420469i	$0.861866\pi$
$390$	−9.53787	+	4.77209i	−0.482969	+	0.241644i
$391$	1.62724	+	0.939486i	0.0822929	+	0.0475118i
$392$	−1.21744	+	5.99685i	−0.0614900	+	0.302886i
$393$	−9.64247	+	27.0874i	−0.486398	+	1.36638i
$394$	−3.95326	+	16.0642i	−0.199162	+	0.809302i
$395$	18.1021			0.910817
$396$	0.377723	−	0.504187i	0.0189813	−	0.0253363i
$397$	3.91358	−	6.77852i	0.196417	−	0.340204i	−0.750947	−	0.660362i	$-0.770403\pi$
$397$	3.91358	−	6.77852i	0.196417	−	0.340204i	0.947364	+	0.320158i	$0.103736\pi$
$398$	2.65126	−	10.7735i	0.132896	−	0.540026i
$399$	22.6183	+	26.5712i	1.13233	+	1.33022i
$400$	3.36989	−	7.12869i	0.168494	−	0.356434i
$401$			34.0123i			1.69849i	0.527998	+	0.849246i	$0.322943\pi$
$401$			34.0123i			1.69849i	−0.527998	+	0.849246i	$0.677057\pi$
$402$	1.81355	−	30.3486i	0.0904517	−	1.51365i
$403$	−11.4837	+	7.88401i	−0.572045	+	0.392731i
$404$	−14.5172	+	0.595615i	−0.722256	+	0.0296329i
$405$	−4.93828	+	14.8641i	−0.245385	+	0.738602i
$406$	−6.52864	−	22.5088i	−0.324011	−	1.11709i
$407$	−0.502765			−0.0249211
$408$	2.52262	+	4.56413i	0.124888	+	0.225958i
$409$	−0.760643	+	1.31747i	−0.0376114	+	0.0651448i	−0.884218	−	0.467074i	$-0.845308\pi$
$409$	−0.760643	+	1.31747i	−0.0376114	+	0.0651448i	0.846607	+	0.532219i	$0.178642\pi$
$410$	−5.14269	−	17.7305i	−0.253980	−	0.875645i
$411$	−20.4650	+	17.4205i	−1.00946	+	0.859289i
$412$	−2.68498	−	4.23911i	−0.132279	−	0.208846i
$413$	24.0982	−	13.9131i	1.18579	−	0.684618i
$414$	−2.92786	+	6.89284i	−0.143897	+	0.338765i
$415$	4.53963	+	2.62096i	0.222842	+	0.128658i
$416$	−13.9733	−	2.24477i	−0.685099	−	0.110059i
$417$	0.741754	+	4.03932i	0.0363239	+	0.197806i
$418$	−0.712962	−	0.684310i	−0.0348721	−	0.0334707i
$419$	−10.1055			−0.493684			−0.246842	−	0.969056i	$-0.579393\pi$
$419$	−10.1055			−0.493684			−0.246842	+	0.969056i	$0.579393\pi$
$420$	4.02915	+	17.7992i	0.196602	+	0.868510i
$421$	6.67942	+	11.5691i	0.325535	+	0.563843i	0.981621	−	0.190843i	$-0.0611222\pi$
$421$	6.67942	+	11.5691i	0.325535	+	0.563843i	−0.656085	+	0.754687i	$0.727789\pi$
$422$	10.1063	−	2.93131i	0.491966	−	0.142694i
$423$	4.42468	−	1.68175i	0.215135	−	0.0817695i
$424$	−27.5439	−	5.59179i	−1.33765	−	0.271561i
$425$	−1.81725	+	1.04919i	−0.0881495	+	0.0508932i
$426$	36.8840	+	2.20409i	1.78703	+	0.106789i
$427$	−20.0443	−	11.5726i	−0.970013	−	0.560037i
$428$	−24.5486	−	12.8613i	−1.18660	−	0.621675i
$429$	0.152584	−	0.428636i	0.00736682	−	0.0206947i
$430$	1.39834	−	1.45689i	0.0674339	−	0.0702573i
$431$	−2.22699	+	3.85727i	−0.107270	+	0.185798i	−0.914664	−	0.404216i	$-0.867544\pi$
$431$	−2.22699	+	3.85727i	−0.107270	+	0.185798i	0.807393	+	0.590014i	$0.200878\pi$
$432$	−16.8331	+	12.1920i	−0.809884	+	0.586590i
$433$	−7.76496			−0.373160			−0.186580	−	0.982440i	$-0.559740\pi$
$433$	−7.76496			−0.373160			−0.186580	+	0.982440i	$0.559740\pi$
$434$	8.40417	+	22.3048i	0.403413	+	1.07066i
$435$	−10.6965	−	12.5659i	−0.512860	−	0.602491i
$436$	−0.0525290	−	1.28031i	−0.00251568	−	0.0613158i
$437$	10.1737	+	5.87376i	0.486672	+	0.280980i
$438$	35.7260	+	2.13490i	1.70706	+	0.102009i
$439$	3.75921	−	2.17038i	0.179417	−	0.103587i	−0.407602	−	0.913160i	$-0.633635\pi$
$439$	3.75921	−	2.17038i	0.179417	−	0.103587i	0.587019	+	0.809573i	$0.300301\pi$
$440$	−0.164201	−	0.490059i	−0.00782799	−	0.0233627i
$441$	5.03046	+	4.10114i	0.239546	+	0.195292i
$442$	2.71719	+	2.60800i	0.129244	+	0.124050i
$443$	12.5847	+	21.7973i	0.597915	+	1.03562i	0.993128	+	0.117030i	$0.0373375\pi$
$443$	12.5847	+	21.7973i	0.597915	+	1.03562i	−0.395213	+	0.918590i	$0.629329\pi$
$444$	15.8417	+	4.91748i	0.751813	+	0.233373i
$445$	−4.74859	−	8.22480i	−0.225105	−	0.389893i
$446$	−28.3286	+	8.21667i	−1.34140	+	0.389071i
$447$	−5.27961	−	1.87941i	−0.249717	−	0.0888932i
$448$	−9.44353	+	22.2998i	−0.446165	+	1.05357i
$449$		−	31.2110i		−	1.47294i	−0.676472	−	0.736468i	$-0.736492\pi$
$449$		−	31.2110i		−	1.47294i	0.676472	−	0.736468i	$-0.263508\pi$
$450$	−5.03154	−	6.68054i	−0.237189	−	0.314924i
$451$	0.682062	+	0.393788i	0.0321170	+	0.0185428i
$452$	7.11011	+	11.2256i	0.334431	+	0.528009i
$453$	−1.25633	−	6.84150i	−0.0590275	−	0.321442i
$454$	16.7801	+	4.12944i	0.787528	+	0.193804i
$455$	6.59004	+	11.4143i	0.308946	+	0.535110i
$456$	15.7717	+	28.5354i	0.738577	+	1.33629i
$457$	−22.3663			−1.04625			−0.523126	−	0.852256i	$-0.675234\pi$
$457$	−22.3663			−1.04625			−0.523126	+	0.852256i	$0.675234\pi$
$458$	−8.52068	−	29.3767i	−0.398145	−	1.37269i
$459$	5.52996	−	0.117430i	0.258117	−	0.00548119i
$460$	3.28747	+	5.19035i	0.153279	+	0.242001i
$461$		−	27.4939i		−	1.28052i	−0.768158	−	0.640260i	$-0.778827\pi$
$461$		−	27.4939i		−	1.28052i	0.768158	−	0.640260i	$-0.221173\pi$
$462$	−0.649818	−	0.428798i	−0.0302323	−	0.0199495i
$463$		−	17.1957i		−	0.799153i	−0.916700	−	0.399577i	$-0.869157\pi$
$463$		−	17.1957i		−	0.799153i	0.916700	−	0.399577i	$-0.130843\pi$
$464$	−1.79387	−	21.8246i	−0.0832783	−	1.01318i
$465$	11.8418	+	11.8930i	0.549152	+	0.551524i
$466$	−14.4280	−	13.8481i	−0.668363	−	0.641503i
$467$	−18.3465			−0.848976			−0.424488	−	0.905434i	$-0.639546\pi$
$467$	−18.3465			−0.848976			−0.424488	+	0.905434i	$0.639546\pi$
$468$	−9.00023	+	12.0135i	−0.416036	+	0.555326i
$469$	−37.5722			−1.73492
$470$	0.927974	−	3.77085i	0.0428043	−	0.173936i
$471$	2.62622	−	0.482263i	0.121010	−	0.0222215i
$472$	24.6527	−	8.26022i	1.13473	−	0.380208i
$473$			0.0861488i			0.00396113i
$474$	22.7857	−	11.4004i	1.04658	−	0.523637i
$475$	−11.3616	+	6.55964i	−0.521307	+	0.300977i
$476$	5.44443	−	3.44840i	0.249545	−	0.158057i
$477$	−18.8368	+	23.1053i	−0.862478	+	1.05792i
$478$	3.46894	+	0.853678i	0.158666	+	0.0390463i
$479$	11.7946	−	20.4288i	0.538908	−	0.933416i	−0.460055	−	0.887890i	$-0.652170\pi$
$479$	11.7946	−	20.4288i	0.538908	−	0.933416i	0.998963	−	0.0455254i	$-0.0144962\pi$
$480$	0.380632	+	17.0474i	0.0173734	+	0.778103i
$481$	11.9797			0.546226
$482$	−11.2800	−	38.8899i	−0.513788	−	1.77139i
$483$	8.71895	+	3.10374i	0.396726	+	0.141225i
$484$	−19.4679	−	10.1995i	−0.884907	−	0.463613i
$485$	−7.94147	+	4.58501i	−0.360604	+	0.208195i
$486$	3.14516	+	21.8199i	0.142667	+	0.989771i
$487$	17.3158	−	9.99730i	0.784655	−	0.453021i	−0.0534226	−	0.998572i	$-0.517013\pi$
$487$	17.3158	−	9.99730i	0.784655	−	0.453021i	0.838077	+	0.545551i	$0.183680\pi$
$488$	−16.2029	−	14.3230i	−0.733473	−	0.648371i
$489$	−2.54835	−	13.8774i	−0.115241	−	0.627557i
$490$	5.11391	−	1.48328i	0.231023	−	0.0670078i
$491$	−2.17592	−	3.76881i	−0.0981981	−	0.170084i	0.812741	−	0.582625i	$-0.197975\pi$
$491$	−2.17592	−	3.76881i	−0.0981981	−	0.170084i	−0.910939	+	0.412541i	$0.864641\pi$
$492$	−17.6396	−	19.0791i	−0.795254	−	0.860152i
$493$	−2.91378	+	5.04681i	−0.131230	+	0.227297i
$494$	16.9882	+	16.3055i	0.764333	+	0.733617i
$495$	−0.541153	−	0.0875410i	−0.0243230	−	0.00393468i
$496$	3.54918	+	21.9864i	0.159363	+	0.987220i
$497$		−	45.6631i		−	2.04827i
$498$	7.36479	+	0.440101i	0.330024	+	0.0197214i
$499$	33.0539	+	19.0837i	1.47969	+	0.854302i	0.999736	−	0.0229890i	$-0.00731828\pi$
$499$	33.0539	+	19.0837i	1.47969	+	0.854302i	0.479959	+	0.877291i	$0.340652\pi$
$500$	−24.2442	+	0.994696i	−1.08423	+	0.0444842i
$501$	−12.7949	+	35.9432i	−0.571635	+	1.60583i
$502$	4.75396	+	16.3902i	0.212180	+	0.731532i
$503$	12.0923	−	20.9444i	0.539167	−	0.933865i	−0.459782	−	0.888032i	$-0.652072\pi$
$503$	12.0923	−	20.9444i	0.539167	−	0.933865i	0.998949	−	0.0458331i	$-0.0145942\pi$
$504$	16.2812	+	19.8668i	0.725222	+	0.884940i
$505$	6.32147	+	10.9491i	0.281302	+	0.487229i
$506$	−0.254511	−	0.0626330i	−0.0113144	−	0.00278438i
$507$	3.91551	−	10.9994i	0.173894	−	0.488499i
$508$	15.9034	−	30.3552i	0.705601	−	1.34679i
$509$	17.1839	−	9.92114i	0.761664	−	0.439747i	−0.0682288	−	0.997670i	$-0.521735\pi$
$509$	17.1839	−	9.92114i	0.761664	−	0.439747i	0.829893	+	0.557923i	$0.188401\pi$
$510$	2.49927	−	3.78750i	0.110670	−	0.167713i
$511$		−	44.2296i		−	1.95660i
$512$	−12.7927	+	18.6640i	−0.565364	+	0.824842i
$513$	34.5739	−	0.734187i	1.52648	−	0.0324152i
$514$	−6.32067	+	25.6842i	−0.278793	+	1.13288i
$515$	−2.18319	+	3.78139i	−0.0962027	+	0.166628i
$516$	0.842611	−	2.71448i	0.0370939	−	0.119498i
$517$	0.0828342	+	0.143473i	0.00364304	+	0.00630993i
$518$	4.89847	−	19.9051i	0.215226	−	0.874578i
$519$	−32.9074	+	28.0118i	−1.44447	+	1.22958i
$520$	3.91252	+	11.6769i	0.171575	+	0.512067i
$521$	−10.9374	−	6.31471i	−0.479176	−	0.276652i	0.240897	−	0.970551i	$-0.422558\pi$
$521$	−10.9374	−	6.31471i	−0.479176	−	0.276652i	−0.720073	+	0.693898i	$0.755892\pi$
$522$	−21.3779	−	9.08065i	−0.935683	−	0.397449i
$523$			26.0346i			1.13841i	0.822195	+	0.569206i	$0.192749\pi$
$523$			26.0346i			1.13841i	−0.822195	+	0.569206i	$0.807251\pi$
$524$	29.4088	+	15.4076i	1.28473	+	0.673086i
$525$	−7.87031	+	6.69946i	−0.343489	+	0.292389i
$526$	−14.9603	+	15.5867i	−0.652301	+	0.679613i
$527$	2.55425	−	5.34814i	0.111265	−	0.232969i
$528$	−0.515315	−	0.513442i	−0.0224262	−	0.0223447i
$529$	−19.8842			−0.864532
$530$	6.81281	+	23.4885i	0.295930	+	1.02028i
$531$	4.40379	−	27.2230i	0.191108	−	1.18138i
$532$	34.0391	−	21.5598i	1.47578	−	0.934734i
$533$	−16.2519	−	9.38302i	−0.703947	−	0.406424i
$534$	−11.1570	−	7.36223i	−0.482811	−	0.318595i
$535$			24.1154i			1.04260i
$536$	−34.4042	−	6.98452i	−1.48603	−	0.301685i
$537$	−1.90771	+	5.35911i	−0.0823238	+	0.231262i
$538$	7.27846	−	29.5762i	0.313797	−	1.27512i
$539$	−0.113578	+	0.196724i	−0.00489217	+	0.00847349i
$540$	16.1951	+	8.05130i	0.696924	+	0.346473i
$541$	19.3775	−	33.5628i	0.833103	−	1.44298i	−0.0624628	−	0.998047i	$-0.519895\pi$
$541$	19.3775	−	33.5628i	0.833103	−	1.44298i	0.895566	−	0.444929i	$-0.146771\pi$
$542$	14.9812	+	14.3792i	0.643500	+	0.617639i
$543$	13.9522	+	16.3906i	0.598746	+	0.703387i
$544$	5.62641	−	2.14555i	0.241231	−	0.0919895i
$545$	−0.965633	+	0.557509i	−0.0413632	+	0.0238810i
$546$	15.4836	+	10.2172i	0.662636	+	0.437256i
$547$	−16.6021	+	9.58523i	−0.709855	+	0.409835i	−0.811007	−	0.585036i	$-0.801080\pi$
$547$	−16.6021	+	9.58523i	−0.709855	+	0.409835i	0.101153	+	0.994871i	$0.467747\pi$
$548$	16.6052	+	26.2168i	0.709340	+	1.11992i
$549$	−21.4413	+	8.14950i	−0.915093	+	0.347812i
$550$	0.202691	−	0.211177i	0.00864277	−	0.00900463i
$551$	−18.2172	+	31.5532i	−0.776080	+	1.34421i
$552$	7.40683	+	4.46286i	0.315255	+	0.189952i
$553$	−15.7434	−	27.2684i	−0.669478	−	1.15957i
$554$	−24.4269	+	25.4497i	−1.03780	+	1.08125i
$555$	−2.60692	−	14.1963i	−0.110658	−	0.602601i
$556$	4.73820	−	0.194400i	0.200945	−	0.00824441i
$557$			5.51682i			0.233755i	0.993146	+	0.116878i	$0.0372885\pi$
$557$			5.51682i			0.233755i	−0.993146	+	0.116878i	$0.962711\pi$
$558$	22.3957	+	7.51227i	0.948084	+	0.318020i
$559$		−	2.05272i		−	0.0868207i
$560$	21.0019	−	1.72625i	0.887491	−	0.0729473i
$561$	0.0349645	+	0.190404i	0.00147620	+	0.00803885i
$562$	9.34076	+	8.96539i	0.394016	+	0.378182i
$563$	22.8558	+	39.5875i	0.963258	+	1.66841i	0.714223	+	0.699918i	$0.246780\pi$
$563$	22.8558	+	39.5875i	0.963258	+	1.66841i	0.249035	+	0.968494i	$0.419886\pi$
$564$	−1.20674	−	5.33090i	−0.0508130	−	0.224471i
$565$	5.78132	−	10.0135i	0.243222	−	0.421273i
$566$	−19.7112	−	18.9191i	−0.828525	−	0.795229i
$567$	26.6855	−	5.48844i	1.12069	−	0.230493i
$568$	8.48859	−	41.8130i	0.356173	−	1.75443i
$569$	−9.46792	+	5.46630i	−0.396916	+	0.229159i	−0.685152	−	0.728400i	$-0.740264\pi$
$569$	−9.46792	+	5.46630i	−0.396916	+	0.229159i	0.288237	+	0.957559i	$0.406931\pi$
$570$	15.6257	−	23.6799i	0.654489	−	0.991840i
$571$	27.6439	−	15.9602i	1.15686	−	0.667914i	0.206311	−	0.978486i	$-0.433854\pi$
$571$	27.6439	−	15.9602i	1.15686	−	0.667914i	0.950550	+	0.310572i	$0.100521\pi$
$572$	−0.465370	−	0.243813i	−0.0194581	−	0.0101943i
$573$	−0.486728	−	0.571792i	−0.0203333	−	0.0238870i
$574$	−22.2359	+	23.1669i	−0.928110	+	0.966970i
$575$	−1.73979	+	3.01341i	−0.0725543	+	0.125668i
$576$	11.2152	+	21.2183i	0.467302	+	0.884098i
$577$	4.08595	−	7.07707i	0.170100	−	0.294622i	−0.768355	−	0.640024i	$-0.778924\pi$
$577$	4.08595	−	7.07707i	0.170100	−	0.294622i	0.938455	+	0.345402i	$0.112258\pi$
$578$	21.7891	+	5.36211i	0.906306	+	0.223034i
$579$	12.1767	−	34.2067i	0.506048	−	1.42158i
$580$	−16.0976	+	10.1960i	−0.668418	+	0.423364i
$581$		−	9.11777i		−	0.378269i
$582$	−7.10861	+	10.7727i	−0.294661	+	0.446542i
$583$	−0.903565	−	0.521674i	−0.0374218	−	0.0216055i
$584$	8.22211	−	40.5003i	0.340233	−	1.67591i
$585$	12.8944	+	2.08589i	0.533117	+	0.0862409i
$586$	11.1944	−	3.24692i	0.462437	−	0.134129i
$587$	7.64917			0.315715			0.157857	−	0.987462i	$-0.449541\pi$
$587$	7.64917			0.315715			0.157857	+	0.987462i	$0.449541\pi$
$588$	5.50289	−	5.08770i	0.226935	−	0.209813i
$589$	15.9694	−	33.4371i	0.658009	−	1.37775i
$590$	−16.3222	−	15.6662i	−0.671974	−	0.644969i
$591$	15.4287	−	13.1334i	0.634651	−	0.540235i
$592$	8.18572	−	17.3161i	0.336431	−	0.711689i
$593$			17.5137i			0.719200i	0.933107	+	0.359600i	$0.117087\pi$
$593$			17.5137i			0.719200i	−0.933107	+	0.359600i	$0.882913\pi$
$594$	−0.736298	+	0.230618i	−0.0302107	+	0.00946237i
$595$	−4.85656	−	2.80394i	−0.199100	−	0.114950i
$596$	−3.00310	+	5.73208i	−0.123012	+	0.234795i
$597$	−10.3473	+	8.80793i	−0.423485	+	0.360484i
$598$	6.06438	+	1.49239i	0.247991	+	0.0610285i
$599$	13.7906	+	23.8860i	0.563469	+	0.975957i	0.997190	+	0.0749098i	$0.0238669\pi$
$599$	13.7906	+	23.8860i	0.563469	+	0.975957i	−0.433721	+	0.901047i	$0.642800\pi$
$600$	−8.45212	+	4.67153i	−0.345056	+	0.190714i
$601$	−15.5871	+	26.9977i	−0.635812	+	1.10126i	0.350531	+	0.936551i	$0.386001\pi$
$601$	−15.5871	+	26.9977i	−0.635812	+	1.10126i	−0.986343	+	0.164707i	$0.947332\pi$
$602$	−3.41074	−	0.839353i	−0.139011	−	0.0342095i
$603$	−23.5284	+	28.8600i	−0.958151	+	1.17527i
$604$	−8.02522	+	0.329261i	−0.326542	+	0.0133974i
$605$			19.1244i			0.777517i
$606$	14.8526	+	9.80082i	0.603344	+	0.398131i
$607$	20.8450	−	12.0349i	0.846072	−	0.488480i	−0.0132518	−	0.999912i	$-0.504218\pi$
$607$	20.8450	−	12.0349i	0.846072	−	0.488480i	0.859323	+	0.511432i	$0.170885\pi$
$608$	35.1769	−	13.4142i	1.42661	−	0.544017i
$609$	−9.62611	+	27.0415i	−0.390069	+	1.09578i
$610$	−4.49682	+	18.2729i	−0.182071	+	0.739850i
$611$	−1.97374	−	3.41861i	−0.0798488	−	0.138302i
$612$	0.760612	−	6.34144i	0.0307459	−	0.256338i
$613$	−9.06702	+	15.7045i	−0.366213	+	0.634300i	−0.988970	−	0.148115i	$-0.952679\pi$
$613$	−9.06702	+	15.7045i	−0.366213	+	0.634300i	0.622757	+	0.782416i	$0.286013\pi$
$614$	0.404774	−	0.117404i	0.0163353	−	0.00473804i
$615$	−7.58261	+	21.3009i	−0.305760	+	0.858936i
$616$	−0.595402	+	0.673551i	−0.0239894	+	0.0271381i
$617$	31.9964	+	18.4731i	1.28813	+	0.743700i	0.978320	−	0.207100i	$-0.0664025\pi$
$617$	31.9964	+	18.4731i	1.28813	+	0.743700i	0.309806	+	0.950800i	$0.399736\pi$
$618$	−0.366593	+	6.13468i	−0.0147465	+	0.246773i
$619$			6.23686i			0.250681i	0.992114	+	0.125340i	$0.0400023\pi$
$619$			6.23686i			0.250681i	−0.992114	+	0.125340i	$0.959998\pi$
$620$	15.5136	−	11.6143i	0.623040	−	0.466441i
$621$	7.84402	−	4.75360i	0.314770	−	0.190755i
$622$	−14.8118	+	15.4320i	−0.593899	+	0.618765i
$623$	−8.25969	+	14.3062i	−0.330918	+	0.573166i
$624$	12.2787	+	12.2341i	0.491542	+	0.489755i
$625$	5.62889	+	9.74952i	0.225155	+	0.389981i
$626$	−9.46928	−	32.6472i	−0.378469	−	1.30485i
$627$	0.218602	+	1.19042i	0.00873011	+	0.0475409i
$628$	−0.126392	−	3.08061i	−0.00504360	−	0.122930i
$629$	−4.41424	+	2.54856i	−0.176007	+	0.101618i
$630$	8.73835	−	20.5720i	0.348144	−	0.819608i
$631$	−28.4535	+	16.4277i	−1.13272	+	0.653975i	−0.944617	−	0.328175i	$-0.893566\pi$
$631$	−28.4535	+	16.4277i	−1.13272	+	0.653975i	−0.188100	+	0.982150i	$0.560233\pi$
$632$	−9.34690	−	27.8959i	−0.371800	−	1.10964i
$633$	−12.1414	−	4.32205i	−0.482578	−	0.171786i
$634$	−7.61766	+	2.20949i	−0.302536	+	0.0877501i
$635$	−29.8195			−1.18335
$636$	23.3681	+	25.2752i	0.926607	+	1.00223i
$637$	2.70630	−	4.68745i	0.107227	−	0.185723i
$638$	0.194254	−	0.789356i	0.00769058	−	0.0312509i
$639$	−35.0749	−	28.5951i	−1.38754	−	1.13121i
$640$	19.5520	+	2.32347i	0.772859	+	0.0918432i
$641$	17.8120	−	10.2838i	0.703533	−	0.406185i	−0.105129	−	0.994459i	$-0.533525\pi$
$641$	17.8120	−	10.2838i	0.703533	−	0.406185i	0.808662	+	0.588273i	$0.200192\pi$
$642$	15.1874	+	30.3548i	0.599401	+	1.19801i
$643$			0.298201i			0.0117599i	0.999983	+	0.00587994i	$0.00187165\pi$
$643$			0.298201i			0.0117599i	−0.999983	+	0.00587994i	$0.998128\pi$
$644$	4.95944	−	9.46617i	0.195429	−	0.373019i
$645$	−2.43254	+	0.446697i	−0.0957813	+	0.0175887i
$646$	−9.72859	−	2.39412i	−0.382766	−	0.0941956i
$647$	−6.10709			−0.240095			−0.120047	−	0.992768i	$-0.538305\pi$
$647$	−6.10709			−0.240095			−0.120047	+	0.992768i	$0.538305\pi$
$648$	25.4558	−	0.0649367i	0.999997	−	0.00255095i
$649$	0.965165			0.0378861
$650$	−4.82963	+	5.03184i	−0.189434	+	0.197365i
$651$	7.61630	−	28.1814i	0.298506	−	1.10452i
$652$	−16.2785	+	0.667877i	−0.637514	+	0.0261561i
$653$			29.2706i			1.14545i	0.819749	+	0.572723i	$0.194113\pi$
$653$			29.2706i			1.14545i	−0.819749	+	0.572723i	$0.805887\pi$
$654$	−0.864363	+	1.30989i	−0.0337993	+	0.0512208i
$655$		−	28.8899i		−	1.12882i
$656$	−24.6677	+	17.0800i	−0.963112	+	0.666862i
$657$	−33.9737	−	27.6974i	−1.32544	−	1.08058i
$658$	−6.48733	+	1.88164i	−0.252902	+	0.0733539i
$659$	−19.1942			−0.747698			−0.373849	−	0.927490i	$-0.621962\pi$
$659$	−19.1942			−0.747698			−0.373849	+	0.927490i	$0.621962\pi$
$660$	−0.187657	+	0.604537i	−0.00730453	+	0.0235316i
$661$	6.19503	+	10.7301i	0.240959	+	0.417353i	0.960988	−	0.276591i	$-0.0892048\pi$
$661$	6.19503	+	10.7301i	0.240959	+	0.417353i	−0.720029	+	0.693944i	$0.755871\pi$
$662$	−2.92029	+	11.8667i	−0.113500	+	0.461211i
$663$	−0.833119	−	4.53686i	−0.0323557	−	0.176197i
$664$	1.69496	−	8.34899i	0.0657771	−	0.324004i
$665$	−30.3637	−	17.5305i	−1.17746	−	0.679804i
$666$	−12.2220	−	16.2276i	−0.473593	−	0.628805i
$667$			9.66339i			0.374168i
$668$	39.0236	+	20.4449i	1.50987	+	0.791038i
$669$	34.0333	+	12.1150i	1.31580	+	0.468394i
$670$	8.50966	+	29.3388i	0.328757	+	1.13346i
$671$	−0.401401	−	0.695248i	−0.0154959	−	0.0268397i
$672$	25.3485	−	15.3995i	0.977841	−	0.594048i
$673$	−14.4698	−	25.0625i	−0.557771	−	0.966088i	−0.997682	−	0.0680468i	$-0.978323\pi$
$673$	−14.4698	−	25.0625i	−0.557771	−	0.966088i	0.439911	−	0.898041i	$-0.355010\pi$
$674$	−24.0018	+	25.0068i	−0.924515	+	0.963225i
$675$	0.217464	+	10.2407i	0.00837020	+	0.394165i
$676$	−11.9420	−	6.25656i	−0.459308	−	0.240637i
$677$	−9.88999	+	5.70999i	−0.380103	+	0.219453i	−0.677863	−	0.735188i	$-0.737094\pi$
$677$	−9.88999	+	5.70999i	−0.380103	+	0.219453i	0.297760	+	0.954641i	$0.403760\pi$
$678$	0.970778	−	16.2453i	0.0372825	−	0.623898i
$679$	13.8134	+	7.97516i	0.530109	+	0.306059i
$680$	−3.92583	−	3.47034i	−0.150549	−	0.133081i
$681$	−13.7187	−	16.1162i	−0.525701	−	0.617576i
$682$	−0.134378	+	0.815755i	−0.00514559	+	0.0312369i
$683$	34.1169			1.30545			0.652723	−	0.757597i	$-0.273627\pi$
$683$	34.1169			1.30545			0.652723	+	0.757597i	$0.273627\pi$
$684$	4.75543	−	39.6473i	0.181828	−	1.51595i
$685$	13.5019	−	23.3860i	0.515882	−	0.893533i
$686$	14.9379	+	14.3376i	0.570331	+	0.547411i
$687$	−12.5633	+	35.2925i	−0.479318	+	1.34649i
$688$	−2.96712	−	1.40262i	−0.113120	−	0.0534745i
$689$	21.5298	+	12.4302i	0.820219	+	0.473553i
$690$	0.448855	−	7.51128i	0.0170876	−	0.285949i
$691$	−31.8937	+	18.4138i	−1.21329	+	0.700494i	−0.963475	−	0.267799i	$-0.913704\pi$
$691$	−31.8937	+	18.4138i	−1.21329	+	0.700494i	−0.249817	+	0.968293i	$0.580370\pi$
$692$	26.7009	+	42.1561i	1.01502	+	1.60254i
$693$	0.338772	+	0.891308i	0.0128689	+	0.0338580i
$694$	4.12662	+	14.2273i	0.156644	+	0.540063i
$695$	−2.06324	−	3.57363i	−0.0782631	−	0.135556i
$696$	−13.8414	+	22.9720i	−0.524656	+	0.870750i
$697$	7.98460			0.302438
$698$	−7.97847	+	8.31252i	−0.301990	+	0.314634i
$699$	4.42377	+	24.0902i	0.167322	+	0.911174i
$700$	6.38594	+	10.0823i	0.241366	+	0.381075i
$701$	−34.2922	−	19.7986i	−1.29520	−	0.747783i	−0.315628	−	0.948883i	$-0.602215\pi$
$701$	−34.2922	−	19.7986i	−1.29520	−	0.747783i	−0.979571	+	0.201100i	$0.935549\pi$
$702$	17.5442	−	5.49506i	0.662163	−	0.207398i
$703$	−27.5983	+	15.9339i	−1.04089	+	0.600957i
$704$	−0.670410	+	0.506077i	−0.0252670	+	0.0190735i
$705$	−3.62167	+	3.08288i	−0.136400	+	0.116108i
$706$	−39.6761	+	11.5080i	−1.49323	+	0.433109i
$707$	10.9955	−	19.0449i	0.413530	−	0.716255i
$708$	−30.4115	−	9.44016i	−1.14294	−	0.354783i
$709$	−11.9309			−0.448073			−0.224036	−	0.974581i	$-0.571923\pi$
$709$	−11.9309			−0.448073			−0.224036	+	0.974581i	$0.571923\pi$
$710$	−35.6567	+	10.3422i	−1.33817	+	0.388135i
$711$	−30.8043	−	4.98313i	−1.15525	−	0.186882i
$712$	−10.2227	+	11.5645i	−0.383113	+	0.433398i
$713$	−0.766144	−	9.79803i	−0.0286923	−	0.366939i
$714$	−7.87897	−	0.470827i	−0.294863	−	0.0176203i
$715$			0.457158i			0.0170967i
$716$	5.81838	+	3.04832i	0.217443	+	0.113921i
$717$	−2.83606	−	3.33171i	−0.105915	−	0.124425i
$718$	35.7218	+	8.79082i	1.33312	+	0.328071i
$719$	9.23931	−	16.0030i	0.344568	−	0.596809i	−0.640707	−	0.767785i	$-0.721359\pi$
$719$	9.23931	−	16.0030i	0.344568	−	0.596809i	0.985275	+	0.170976i	$0.0546920\pi$
$720$	11.8258	−	17.2130i	0.440722	−	0.641491i
$721$	7.59487			0.282848
$722$	−34.7326	−	8.54739i	−1.29261	−	0.318101i
$723$	−16.6317	+	46.7213i	−0.618538	+	1.73758i
$724$	20.9972	−	13.2993i	0.780355	−	0.494263i
$725$	−9.34596	−	5.39589i	−0.347100	−	0.200398i
$726$	12.0442	+	24.0725i	0.447002	+	0.893412i
$727$	17.8837	+	10.3251i	0.663268	+	0.382938i	0.793521	−	0.608543i	$-0.208246\pi$
$727$	17.8837	+	10.3251i	0.663268	+	0.382938i	−0.130253	+	0.991481i	$0.541579\pi$
$728$	14.1870	−	16.0491i	0.525804	−	0.594819i
$729$	12.4952	−	23.9347i	0.462785	−	0.886470i
$730$	−34.5373	+	10.0175i	−1.27828	+	0.370764i
$731$	0.436696	+	0.756380i	0.0161518	+	0.0279757i
$732$	5.84769	+	25.8327i	0.216137	+	0.954805i
$733$	−11.6308	−	20.1451i	−0.429594	−	0.744078i	0.567244	−	0.823550i	$-0.308010\pi$
$733$	−11.6308	−	20.1451i	−0.429594	−	0.744078i	−0.996837	+	0.0794723i	$0.974676\pi$
$734$	−3.29064	+	13.3716i	−0.121460	+	0.493555i
$735$	−6.14372	−	2.18702i	−0.226615	−	0.0806693i
$736$	6.30100	−	7.74607i	0.232258	−	0.285524i
$737$	−1.12861	−	0.651605i	−0.0415730	−	0.0240022i
$738$	3.87047	+	31.5875i	0.142474	+	1.16275i
$739$	−39.0165	+	22.5262i	−1.43525	+	0.828640i	−0.997514	−	0.0704662i	$-0.977551\pi$
$739$	−39.0165	+	22.5262i	−1.43525	+	0.828640i	−0.437732	+	0.899106i	$0.644218\pi$
$740$	−16.6526	+	0.683228i	−0.612162	+	0.0251160i
$741$	−5.20875	−	28.3649i	−0.191348	−	1.04201i
$742$	29.4572	−	30.6905i	1.08141	−	1.12669i
$743$	−31.5549			−1.15764			−0.578819	−	0.815456i	$-0.696486\pi$
$743$	−31.5549			−1.15764			−0.578819	+	0.815456i	$0.696486\pi$
$744$	12.2129	−	24.3894i	0.447748	−	0.894160i
$745$	5.63092			0.206301
$746$	36.5769	−	38.1083i	1.33917	−	1.39524i
$747$	−7.00356	−	5.70973i	−0.256247	−	0.208908i
$748$	0.223347	−	0.00916357i	0.00816639	−	0.000335053i
$749$	36.3266	−	20.9732i	1.32734	−	0.766342i
$750$	24.8043	+	16.3677i	0.905724	+	0.597663i
$751$	−9.12874	−	5.27048i	−0.333112	−	0.192323i	0.324110	−	0.946020i	$-0.394935\pi$
$751$	−9.12874	−	5.27048i	−0.333112	−	0.192323i	−0.657222	+	0.753697i	$0.728269\pi$
$752$	−6.29013	+	0.517017i	−0.229377	+	0.0188537i
$753$	7.00945	−	19.6908i	0.255438	−	0.717573i
$754$	−4.62860	+	18.8084i	−0.168564	+	0.684963i
$755$	3.49456	+	6.05276i	0.127180	+	0.220283i
$756$	−1.95665	−	31.3978i	−0.0711626	−	1.14193i
$757$	3.42573	+	5.93354i	0.124510	+	0.215658i	0.921541	−	0.388280i	$-0.126931\pi$
$757$	3.42573	+	5.93354i	0.124510	+	0.215658i	−0.797031	+	0.603938i	$0.793597\pi$
$758$	20.0989	−	5.82964i	0.730023	−	0.211742i
$759$	0.208077	+	0.244442i	0.00755273	+	0.00887270i
$760$	−24.5447	−	21.6969i	−0.890330	−	0.787029i
$761$	0.872667	+	0.503834i	0.0316341	+	0.0182640i	0.515734	−	0.856749i	$-0.327519\pi$
$761$	0.872667	+	0.503834i	0.0316341	+	0.0182640i	−0.484100	+	0.875013i	$0.660853\pi$
$762$	−37.5347	+	18.7798i	−1.35974	+	0.680319i
$763$	1.67962	+	0.969730i	0.0608064	+	0.0351066i
$764$	−0.732496	+	0.463950i	−0.0265008	+	0.0167851i
$765$	−5.19504	+	1.97455i	−0.187827	+	0.0713901i
$766$	−37.0332	−	9.11355i	−1.33806	−	0.329286i
$767$	−22.9975			−0.830393
$768$	26.0739	−	9.38885i	0.940862	−	0.338791i
$769$	10.4957	−	18.1790i	0.378483	−	0.655552i	−0.612359	−	0.790580i	$-0.709779\pi$
$769$	10.4957	−	18.1790i	0.378483	−	0.655552i	0.990842	+	0.135028i	$0.0431125\pi$
$770$	0.759600	+	0.186931i	0.0273741	+	0.00673653i
$771$	24.6681	−	20.9983i	0.888401	−	0.756236i
$772$	−37.1382	−	19.4571i	−1.33663	−	0.700278i
$773$			30.3010i			1.08985i	0.838484	+	0.544926i	$0.183442\pi$
$773$			30.3010i			1.08985i	−0.838484	+	0.544926i	$0.816558\pi$
$774$	−2.78059	+	2.09424i	−0.0999464	+	0.0752760i
$775$	9.90398	+	4.73010i	0.355762	+	0.169910i
$776$	11.1661	+	9.87057i	0.400841	+	0.354333i
$777$	−19.1176	+	16.2735i	−0.685840	+	0.583809i
$778$	30.8345	−	8.94351i	1.10547	−	0.320640i
$779$	49.9206			1.78859
$780$	4.47140	−	14.4047i	0.160102	−	0.515769i
$781$	0.791925	−	1.37165i	0.0283373	−	0.0490816i
$782$	−2.55208	+	0.740228i	−0.0912623	+	0.0264705i
$783$	14.7431	+	24.3279i	0.526875	+	0.869409i
$784$	−4.92630	−	7.11479i	−0.175939	−	0.254100i
$785$	−2.32345	+	1.34145i	−0.0829276	+	0.0478782i
$786$	−18.1943	−	36.3646i	−0.648970	−	1.29708i
$787$	−32.5190	−	18.7748i	−1.15918	−	0.669250i	−0.208069	−	0.978114i	$-0.566718\pi$
$787$	−32.5190	−	18.7748i	−1.15918	−	0.669250i	−0.951106	+	0.308864i	$0.900051\pi$
$788$	−12.5188	−	19.7650i	−0.445963	−	0.704097i
$789$	26.0249	−	4.77905i	0.926511	−	0.170139i
$790$	−17.7272	+	18.4694i	−0.630706	+	0.657113i
$791$	−20.1120			−0.715102
$792$	0.144517	+	0.879132i	0.00513520	+	0.0312386i
$793$	9.56442	+	16.5661i	0.339643	+	0.588278i
$794$	3.08354	+	10.6311i	0.109431	+	0.377285i
$795$	10.0451	−	28.2185i	0.356263	−	1.00081i
$796$	8.39573	+	13.2554i	0.297579	+	0.469825i
$797$	17.9880	−	10.3854i	0.637168	−	0.367869i	−0.146355	−	0.989232i	$-0.546754\pi$
$797$	17.9880	−	10.3854i	0.637168	−	0.367869i	0.783523	+	0.621363i	$0.213421\pi$
$798$	−49.2602	−	2.94366i	−1.74379	−	0.104204i
$799$	1.45456	+	0.839788i	0.0514585	+	0.0297096i
$800$	3.97324	+	10.4193i	0.140475	+	0.368378i
$801$	5.81653	+	15.3033i	0.205517	+	0.540715i
$802$	−34.7024	−	33.3078i	−1.22538	−	1.17614i
$803$	0.767063	−	1.32859i	0.0270691	−	0.0468850i
$804$	29.1884	+	31.5703i	1.02939	+	1.11340i
$805$	−9.29912			−0.327751
$806$	3.20190	−	19.4375i	0.112782	−	0.684656i
$807$	−28.4062	+	24.1802i	−0.999944	+	0.851185i
$808$	13.6088	−	15.3950i	0.478756	−	0.541595i
$809$	−43.5871	−	25.1651i	−1.53244	−	0.884756i	−0.999248	−	0.0387631i	$-0.987658\pi$
$809$	−43.5871	−	25.1651i	−1.53244	−	0.884756i	−0.533194	−	0.845993i	$-0.679008\pi$
$810$	−10.3297	−	19.5947i	−0.362948	−	0.688488i
$811$	−0.441552	+	0.254930i	−0.0155050	+	0.00895181i	−0.507732	−	0.861515i	$-0.669516\pi$
$811$	−0.441552	+	0.254930i	−0.0155050	+	0.00895181i	0.492227	+	0.870467i	$0.336183\pi$
$812$	29.3589	+	15.3815i	1.03030	+	0.539784i
$813$	−4.59341	−	25.0140i	−0.161098	−	0.877279i
$814$	0.492352	−	0.512966i	0.0172569	−	0.0179795i
$815$	7.08841	+	12.2775i	0.248296	+	0.430062i
$816$	−7.12712	−	1.89580i	−0.249499	−	0.0663662i
$817$	2.73027	+	4.72897i	0.0955201	+	0.165446i
$818$	−0.599316	−	2.06626i	−0.0209546	−	0.0722452i
$819$	−8.07212	−	21.2377i	−0.282063	−	0.742105i
$820$	23.1264	+	12.1162i	0.807610	+	0.423116i
$821$		−	21.6746i		−	0.756449i	−0.925714	−	0.378224i	$-0.876535\pi$
$821$		−	21.6746i		−	0.756449i	0.925714	−	0.378224i	$-0.123465\pi$
$822$	2.26719	−	37.9399i	0.0790774	−	1.32331i
$823$	−28.0907	−	16.2182i	−0.979179	−	0.565329i	−0.0771569	−	0.997019i	$-0.524584\pi$
$823$	−28.0907	−	16.2182i	−0.979179	−	0.565329i	−0.902022	+	0.431690i	$0.857918\pi$
$824$	6.95449	+	1.41186i	0.242271	+	0.0491843i
$825$	−0.352600	+	0.0647492i	−0.0122760	+	0.00225428i
$826$	−9.40367	+	38.2121i	−0.327195	+	1.32957i
$827$	−3.47956	−	6.02677i	−0.120996	−	0.209571i	0.799165	−	0.601112i	$-0.205276\pi$
$827$	−3.47956	−	6.02677i	−0.120996	−	0.209571i	−0.920161	+	0.391541i	$0.871942\pi$
$828$	−4.16548	−	9.73735i	−0.144760	−	0.338396i
$829$	−2.74093			−0.0951965			−0.0475982	−	0.998867i	$-0.515157\pi$
$829$	−2.74093			−0.0951965			−0.0475982	+	0.998867i	$0.515157\pi$
$830$	−7.11974	+	2.06507i	−0.247130	+	0.0716796i
$831$	42.4930	−	7.80314i	1.47407	−	0.270688i
$832$	15.9742	−	12.0586i	0.553807	−	0.418056i
$833$			2.30296i			0.0797928i
$834$	−4.84767	−	3.19885i	−0.167861	−	0.110767i
$835$		−	38.3350i		−	1.32664i
$836$	1.39639	−	0.0572916i	0.0482952	−	0.00198147i
$837$	−16.8773	−	23.4980i	−0.583365	−	0.812210i
$838$	9.89616	−	10.3105i	0.341857	−	0.356171i
$839$	29.3877			1.01457			0.507287	−	0.861777i	$-0.330648\pi$
$839$	29.3877			1.01457			0.507287	+	0.861777i	$0.330648\pi$
$840$	−22.1060	−	13.3196i	−0.762730	−	0.459570i
$841$	−0.970596			−0.0334688
$842$	−18.3449	−	4.51453i	−0.632208	−	0.155581i
$843$	−2.86398	−	15.5961i	−0.0986406	−	0.537160i
$844$	−6.90617	+	13.1819i	−0.237720	+	0.453741i
$845$			11.7313i			0.403568i
$846$	−2.61716	+	6.16138i	−0.0899799	+	0.211833i
$847$	28.8083	−	16.6325i	0.989865	−	0.571499i
$848$	32.6787	−	22.6268i	1.12219	−	0.777009i
$849$	6.04367	+	32.9116i	0.207418	+	1.12952i
$850$	0.709133	−	2.88158i	0.0243231	−	0.0988374i
$851$	−4.22609	+	7.31980i	−0.144868	+	0.250920i
$852$	−38.3689	+	35.4739i	−1.31450	+	1.21532i
$853$	29.0315			0.994020			0.497010	−	0.867745i	$-0.334431\pi$
$853$	29.0315			0.994020			0.497010	+	0.867745i	$0.334431\pi$
$854$	31.4366	−	9.11813i	1.07574	−	0.312016i
$855$	−32.4799	+	12.3451i	−1.11079	+	0.422194i
$856$	37.1625	−	12.4518i	1.27019	−	0.425594i
$857$	−43.8558	+	25.3201i	−1.49808	+	0.864920i	−0.999998	−	0.00220746i	$-0.999297\pi$
$857$	−43.8558	+	25.3201i	−1.49808	+	0.864920i	−0.498087	+	0.867127i	$0.665964\pi$
$858$	0.287910	+	0.575438i	0.00982907	+	0.0196451i
$859$	−20.2493	+	11.6909i	−0.690897	+	0.398890i	−0.803948	−	0.594700i	$-0.797271\pi$
$859$	−20.2493	+	11.6909i	−0.690897	+	0.398890i	0.113051	+	0.993589i	$0.463938\pi$
$860$	0.117071	+	2.85343i	0.00399209	+	0.0973010i
$861$	38.6815	−	7.10323i	1.31826	−	0.242077i
$862$	−1.75466	−	6.04956i	−0.0597641	−	0.206049i
$863$	1.54349	+	2.67340i	0.0525409	+	0.0910035i	0.891100	−	0.453808i	$-0.149935\pi$
$863$	1.54349	+	2.67340i	0.0525409	+	0.0910035i	−0.838559	+	0.544811i	$0.816601\pi$
$864$	4.04507	−	29.1142i	0.137616	−	0.990486i
$865$	21.7109	−	37.6043i	0.738191	−	1.27859i
$866$	7.60414	−	7.92252i	0.258399	−	0.269218i
$867$	−17.8138	−	20.9271i	−0.604988	−	0.710720i
$868$	−30.9875	−	13.2681i	−1.05178	−	0.450350i
$869$		−	1.09214i		−	0.0370482i
$870$	23.2959	+	1.39210i	0.789805	+	0.0471967i
$871$	26.8921	+	15.5262i	0.911204	+	0.526084i
$872$	1.35773	+	1.20020i	0.0459786	+	0.0406439i
$873$	14.7761	−	5.61616i	0.500095	−	0.190078i
$874$	−15.9559	+	4.62798i	−0.539716	+	0.156544i
$875$	18.3629	−	31.8055i	0.620780	−	1.07522i
$876$	−37.1643	+	34.3603i	−1.25567	+	1.16093i
$877$	−2.44909	−	4.24194i	−0.0826998	−	0.143240i	0.821709	−	0.569907i	$-0.193021\pi$
$877$	−2.44909	−	4.24194i	−0.0826998	−	0.143240i	−0.904409	+	0.426667i	$0.859688\pi$
$878$	−1.46693	+	5.96091i	−0.0495065	+	0.201171i
$879$	−13.4487	−	4.78740i	−0.453612	−	0.161475i
$880$	0.660804	+	0.312377i	0.0222757	+	0.0105302i
$881$	−19.6687	+	11.3557i	−0.662654	+	0.382584i	−0.793288	−	0.608847i	$-0.791632\pi$
$881$	−19.6687	+	11.3557i	−0.662654	+	0.382584i	0.130633	+	0.991431i	$0.458299\pi$
$882$	−9.11063	+	1.11634i	−0.306771	+	0.0375891i
$883$		−	12.9691i		−	0.436444i	−0.975899	−	0.218222i	$-0.929974\pi$
$883$		−	12.9691i		−	0.436444i	0.975899	−	0.218222i	$-0.0700257\pi$
$884$	−5.32183	+	0.218346i	−0.178992	+	0.00734375i
$885$	5.00455	+	27.2529i	0.168226	+	0.916097i
$886$	−34.5636	−	8.50581i	−1.16119	−	0.285758i
$887$	−9.35908	+	16.2104i	−0.314247	+	0.544292i	−0.979277	−	0.202524i	$-0.935085\pi$
$887$	−9.35908	+	16.2104i	−0.314247	+	0.544292i	0.665030	+	0.746817i	$0.268419\pi$
$888$	−20.5308	+	11.3475i	−0.688970	+	0.380797i
$889$	25.9340	+	44.9190i	0.869798	+	1.50654i
$890$	13.0419	+	3.20951i	0.437166	+	0.107583i
$891$	0.896779	+	0.297936i	0.0300432	+	0.00998123i
$892$	19.3585	−	36.9499i	0.648171	−	1.23718i
$893$	9.09404	+	5.25044i	0.304320	+	0.175699i
$894$	7.08781	−	3.54625i	0.237052	−	0.118604i
$895$		−	5.71571i		−	0.191055i
$896$	−13.5043	−	31.4731i	−0.451148	−	1.05144i
$897$	−4.95798	−	5.82447i	−0.165542	−	0.194473i
$898$	31.8443	+	30.5645i	1.06266	+	1.01995i
$899$	30.3882	−	2.37616i	1.01350	−	0.0792495i
$900$	11.7434	+	1.40854i	0.391448	+	0.0469515i
$901$	−10.5777			−0.352393
$902$	−1.06971	+	0.310269i	−0.0356176	+	0.0103308i
$903$	2.78847	+	3.27580i	0.0927945	+	0.109012i
$904$	−18.4163	−	3.73875i	−0.612516	−	0.124349i
$905$	−18.7300	−	10.8138i	−0.622607	−	0.359463i
$906$	8.21063	+	5.41798i	0.272780	+	0.180000i
$907$		−	23.5720i		−	0.782696i	−0.920243	−	0.391348i	$-0.872009\pi$
$907$		−	23.5720i		−	0.782696i	0.920243	−	0.391348i	$-0.127991\pi$
$908$	−20.6458	+	13.0767i	−0.685154	+	0.433964i
$909$	−7.74314	−	20.3722i	−0.256824	−	0.675703i
$910$	−18.0994	−	4.45412i	−0.599990	−	0.147653i
$911$	−11.8822	+	20.5805i	−0.393674	+	0.681864i	−0.992931	−	0.118693i	$-0.962130\pi$
$911$	−11.8822	+	20.5805i	−0.393674	+	0.681864i	0.599257	+	0.800557i	$0.295463\pi$
$912$	−44.5595	−	11.8527i	−1.47551	−	0.392483i
$913$	0.158127	−	0.273885i	0.00523325	−	0.00906426i
$914$	21.9031	−	22.8201i	0.724489	−	0.754823i
$915$	17.5501	−	14.9392i	0.580187	−	0.493874i
$916$	38.3170	+	20.0747i	1.26603	+	0.663288i
$917$	−43.5187	+	25.1255i	−1.43711	+	0.829717i
$918$	−5.29562	+	5.75717i	−0.174781	+	0.190015i
$919$	37.6711	−	21.7494i	1.24266	−	0.717448i	0.273022	−	0.962008i	$-0.411977\pi$
$919$	37.6711	−	21.7494i	1.24266	−	0.717448i	0.969634	+	0.244560i	$0.0786434\pi$
$920$	−8.51505	−	1.72867i	−0.280733	−	0.0569926i
$921$	−0.486285	−	0.173106i	−0.0160236	−	0.00570402i
$922$	28.0518	+	26.9245i	0.923837	+	0.886711i
$923$	−18.8696	+	32.6832i	−0.621102	+	1.07578i
$924$	1.07386	−	0.243086i	0.0353273	−	0.00799696i
$925$	−4.71957	−	8.17453i	−0.155178	−	0.268777i
$926$	17.5446	+	16.8396i	0.576553	+	0.553383i
$927$	4.75605	−	5.83378i	0.156209	−	0.191607i
$928$	24.0241	+	19.5423i	0.788630	+	0.641507i
$929$			34.2935i			1.12513i	0.826751	+	0.562567i	$0.190186\pi$
$929$			34.2935i			1.12513i	−0.826751	+	0.562567i	$0.809814\pi$
$930$	−23.7309	+	0.435474i	−0.778166	+	0.0142797i
$931$			14.3983i			0.471887i
$932$	28.2583	−	1.15939i	0.925631	−	0.0379771i
$933$	25.7665	−	4.73160i	0.843558	−	0.154906i
$934$	17.9665	−	18.7188i	0.587883	−	0.612498i
$935$	−0.0972561	−	0.168452i	−0.00318061	−	0.00550899i
$936$	−3.44350	−	20.9476i	−0.112554	−	0.684693i
$937$	−18.0975	+	31.3458i	−0.591221	+	1.02402i	0.402848	+	0.915267i	$0.368020\pi$
$937$	−18.0975	+	31.3458i	−0.591221	+	1.02402i	−0.994068	+	0.108757i	$0.965313\pi$
$938$	36.7940	−	38.3345i	1.20137	−	1.25167i
$939$	−13.9619	+	39.2215i	−0.455630	+	1.27995i
$940$	2.93861	+	4.63955i	0.0958469	+	0.151326i
$941$	34.3766	−	19.8473i	1.12064	−	0.647004i	0.179079	−	0.983835i	$-0.442688\pi$
$941$	34.3766	−	19.8473i	1.12064	−	0.647004i	0.941565	+	0.336830i	$0.109355\pi$
$942$	−2.07978	+	3.15179i	−0.0677629	+	0.102691i
$943$	11.4664	−	6.62013i	0.373398	−	0.215581i
$944$	−15.7143	+	33.2421i	−0.511455	+	1.08194i
$945$	−23.4109	+	14.1873i	−0.761555	+	0.461514i
$946$	−0.0878968	−	0.0843645i	−0.00285777	−	0.00274293i
$947$	26.7627	−	46.3543i	0.869670	−	1.50631i	0.00733489	−	0.999973i	$-0.497665\pi$
$947$	26.7627	−	46.3543i	0.869670	−	1.50631i	0.862335	−	0.506339i	$-0.169001\pi$
$948$	−10.6821	+	34.4123i	−0.346937	+	1.11766i
$949$	−18.2773	+	31.6571i	−0.593305	+	1.02763i
$950$	4.43357	−	18.0159i	0.143844	−	0.584515i
$951$	9.15166	+	3.25777i	0.296763	+	0.105640i
$952$	−1.81329	+	8.93188i	−0.0587691	+	0.289484i
$953$			19.3680i			0.627391i	0.949524	+	0.313696i	$0.101567\pi$
$953$			19.3680i			0.627391i	−0.949524	+	0.313696i	$0.898433\pi$
$954$	−5.12742	−	41.8457i	−0.166007	−	1.35481i
$955$	0.653405	+	0.377243i	0.0211437	+	0.0122073i
$956$	−4.26810	+	2.70334i	−0.138040	+	0.0874321i
$957$	−0.758128	+	0.645343i	−0.0245068	+	0.0208610i
$958$	9.29303	+	32.0396i	0.300244	+	1.03515i
$959$	−46.9704			−1.51675
$960$	−17.7660	−	16.3060i	−0.573397	−	0.526273i
$961$	−30.6232	+	4.81855i	−0.987846	+	0.155437i
$962$	−11.7315	+	12.2227i	−0.378240	+	0.394077i
$963$	6.63846	−	41.0370i	0.213921	−	1.32240i
$964$	50.7254	+	26.5756i	1.63375	+	0.855943i
$965$			36.4828i			1.17442i
$966$	−11.7051	+	5.85642i	−0.376605	+	0.188427i
$967$	2.37692	+	1.37232i	0.0764366	+	0.0441307i	0.537731	−	0.843116i	$-0.319282\pi$
$967$	2.37692	+	1.37232i	0.0764366	+	0.0441307i	−0.461295	+	0.887247i	$0.652615\pi$
$968$	29.4712	−	9.87473i	0.947240	−	0.317386i
$969$	7.95368	+	9.34372i	0.255509	+	0.300164i
$970$	3.09895	−	12.5927i	0.0995012	−	0.404326i
$971$	−3.34005	−	5.78514i	−0.107187	−	0.185654i	0.807442	−	0.589946i	$-0.200851\pi$
$971$	−3.34005	−	5.78514i	−0.107187	−	0.185654i	−0.914630	+	0.404292i	$0.867518\pi$
$972$	−25.3427	−	18.1590i	−0.812866	−	0.582450i
$973$	−3.58879	+	6.21597i	−0.115051	+	0.199275i
$974$	−6.75704	+	27.4574i	−0.216509	+	0.879792i
$975$	8.40160	−	1.54282i	0.269067	−	0.0494097i
$976$	30.4810	−	2.50538i	0.975672	−	0.0801953i
$977$		−	13.1119i		−	0.419488i	−0.977756	−	0.209744i	$-0.932737\pi$
$977$		−	13.1119i		−	0.419488i	0.977756	−	0.209744i	$-0.0672630\pi$
$978$	16.6545	+	10.9899i	0.532553	+	0.351418i
$979$	−0.496218	+	0.286492i	−0.0158592	+	0.00915632i
$980$	−3.49462	+	6.67024i	−0.111631	+	0.213073i
$981$	1.79668	−	0.682891i	0.0573637	−	0.0218030i
$982$	5.97614	+	1.47068i	0.190706	+	0.0469312i
$983$	−21.1039	−	36.5529i	−0.673108	−	1.16586i	−0.977018	−	0.213157i	$-0.931625\pi$
$983$	−21.1039	−	36.5529i	−0.673108	−	1.16586i	0.303910	−	0.952701i	$-0.401708\pi$
$984$	36.7405	+	0.686434i	1.17124	+	0.0218827i
$985$	−10.1792	+	17.6308i	−0.324335	+	0.561765i
$986$	−2.29578	−	7.91518i	−0.0731127	−	0.252071i
$987$	7.79371	+	2.77437i	0.248076	+	0.0883092i
$988$	−33.2726	+	1.36512i	−1.05854	+	0.0434302i
$989$	1.25425	+	0.724141i	0.0398828	+	0.0230263i
$990$	0.619263	−	0.466406i	0.0196815	−	0.0148234i
$991$			18.8936i			0.600174i	0.953912	+	0.300087i	$0.0970157\pi$
$991$			18.8936i			0.600174i	−0.953912	+	0.300087i	$0.902984\pi$
$992$	−25.9082	−	17.9099i	−0.822587	−	0.568639i
$993$	11.3972	−	9.70167i	0.361679	−	0.307873i
$994$	46.5897	+	44.7174i	1.47773	+	1.41835i
$995$	6.82668	−	11.8241i	0.216420	−	0.374851i
$996$	−7.66129	+	7.08325i	−0.242757	+	0.224441i
$997$	13.5419	+	23.4553i	0.428877	+	0.742836i	0.996774	−	0.0802632i	$-0.0255761\pi$
$997$	13.5419	+	23.4553i	0.428877	+	0.742836i	−0.567897	+	0.823100i	$0.692243\pi$
$998$	−51.8402	+	15.0362i	−1.64097	+	0.475961i
$999$	0.528238	+	24.8754i	0.0167127	+	0.787024i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	372.2.p.a.191.14	yes	120
3.2	odd	2	inner	372.2.p.a.191.47	yes	120
4.3	odd	2	inner	372.2.p.a.191.48	yes	120
12.11	even	2	inner	372.2.p.a.191.13	✓	120
31.25	even	3	inner	372.2.p.a.335.14	yes	120
93.56	odd	6	inner	372.2.p.a.335.47	yes	120
124.87	odd	6	inner	372.2.p.a.335.48	yes	120
372.335	even	6	inner	372.2.p.a.335.13	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
372.2.p.a.191.13	✓	120	12.11	even	2	inner
372.2.p.a.191.14	yes	120	1.1	even	1	trivial
372.2.p.a.191.47	yes	120	3.2	odd	2	inner
372.2.p.a.191.48	yes	120	4.3	odd	2	inner
372.2.p.a.335.13	yes	120	372.335	even	6	inner
372.2.p.a.335.14	yes	120	31.25	even	3	inner
372.2.p.a.335.47	yes	120	93.56	odd	6	inner
372.2.p.a.335.48	yes	120	124.87	odd	6	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:	\( N \)	\(=\)	\( 372 = 2^{2} \cdot 3 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	372.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.979289 + 1.02029i) q^{2} +(1.70357 - 0.312832i) q^{3} +(-0.0819876 - 1.99832i) q^{4} +(-1.50717 + 0.870163i) q^{5} +(-1.34910 + 2.04449i) q^{6} +(2.62156 + 1.51356i) q^{7} +(2.11916 + 1.87328i) q^{8} +(2.80427 - 1.06586i) q^{9} +(0.588131 - 2.38989i) q^{10} +(0.0524986 + 0.0909303i) q^{11} +(-0.764809 - 3.37862i) q^{12} +(-1.25091 - 2.16665i) q^{13} +(-4.11154 + 1.19254i) q^{14} +(-2.29534 + 1.95387i) q^{15} +(-3.98656 + 0.327675i) q^{16} +(0.921869 + 0.532241i) q^{17} +(-1.65870 + 3.90496i) q^{18} +(5.76362 + 3.32763i) q^{19} +(1.86243 + 2.94046i) q^{20} +(4.93949 + 1.75834i) q^{21} +(-0.144187 - 0.0354831i) q^{22} +1.76515 q^{23} +(4.19614 + 2.52832i) q^{24} +(-0.985633 + 1.70717i) q^{25} +(3.43562 + 0.845477i) q^{26} +(4.44383 - 2.69303i) q^{27} +(2.80964 - 5.36281i) q^{28} +5.47454i q^{29} +(0.254287 - 4.25532i) q^{30} +(-0.434039 - 5.55082i) q^{31} +(3.56967 - 4.38834i) q^{32} +(0.117881 + 0.138482i) q^{33} +(-1.44582 + 0.419357i) q^{34} -5.26817 q^{35} +(-2.35984 - 5.51644i) q^{36} +(-2.39418 + 4.14684i) q^{37} +(-9.03939 + 2.62186i) q^{38} +(-2.80881 - 3.29970i) q^{39} +(-4.82398 - 0.979333i) q^{40} +(6.49599 - 3.75046i) q^{41} +(-6.63121 + 3.31780i) q^{42} +(0.710562 + 0.410243i) q^{43} +(0.177403 - 0.112364i) q^{44} +(-3.29903 + 4.04660i) q^{45} +(-1.72859 + 1.80097i) q^{46} +1.57783 q^{47} +(-6.68885 + 1.80534i) q^{48} +(1.08173 + 1.87361i) q^{49} +(-0.776588 - 2.67744i) q^{50} +(1.73697 + 0.618318i) q^{51} +(-4.22709 + 2.67736i) q^{52} +(-8.60561 + 4.96845i) q^{53} +(-1.60412 + 7.17125i) q^{54} +(-0.158248 - 0.0913647i) q^{55} +(2.72018 + 8.11839i) q^{56} +(10.8597 + 3.86579i) q^{57} +(-5.58562 - 5.36116i) q^{58} +(4.59615 - 7.96076i) q^{59} +(4.09264 + 4.42663i) q^{60} -7.64594 q^{61} +(6.08850 + 4.99301i) q^{62} +(8.96482 + 1.45022i) q^{63} +(0.981647 + 7.93954i) q^{64} +(3.77067 + 2.17700i) q^{65} +(-0.256732 - 0.0153416i) q^{66} +(-10.7490 + 6.20592i) q^{67} +(0.988006 - 1.88582i) q^{68} +(3.00705 - 0.552196i) q^{69} +(5.15906 - 5.37507i) q^{70} +(-7.54234 - 13.0637i) q^{71} +(7.93934 + 2.99446i) q^{72} +(-7.30556 - 12.6536i) q^{73} +(-1.88639 - 6.50372i) q^{74} +(-1.14503 + 3.21661i) q^{75} +(6.17711 - 11.7904i) q^{76} +0.317839i q^{77} +(6.11729 + 0.365554i) q^{78} +(-9.00803 - 5.20079i) q^{79} +(5.72327 - 3.96281i) q^{80} +(6.72789 - 5.97792i) q^{81} +(-2.53489 + 10.3006i) q^{82} +(-1.50601 - 2.60849i) q^{83} +(3.10875 - 10.0148i) q^{84} -1.85255 q^{85} +(-1.11441 + 0.323234i) q^{86} +(1.71261 + 9.32624i) q^{87} +(-0.0590851 + 0.291040i) q^{88} +5.45713i q^{89} +(-0.898005 - 7.32876i) q^{90} -7.57334i q^{91} +(-0.144720 - 3.52733i) q^{92} +(-2.47589 - 9.32041i) q^{93} +(-1.54516 + 1.60985i) q^{94} -11.5823 q^{95} +(4.70835 - 8.59252i) q^{96} +5.26914 q^{97} +(-2.97095 - 0.731125i) q^{98} +(0.244139 + 0.199037i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q - 12 q^{4} - 2 q^{9} + 4 q^{10} - 4 q^{12} - 4 q^{16} - 2 q^{18} - 14 q^{21} - 6 q^{22} - 4 q^{24} + 48 q^{25} + 6 q^{28} - 48 q^{30} + 4 q^{33} + 28 q^{34} + 2 q^{36} - 8 q^{37} + 36 q^{40} - 4 q^{42}+ \cdots + 48 q^{96}+O(q^{100}) \) 120 * q - 12 * q^4 - 2 * q^9 + 4 * q^10 - 4 * q^12 - 4 * q^16 - 2 * q^18 - 14 * q^21 - 6 * q^22 - 4 * q^24 + 48 * q^25 + 6 * q^28 - 48 * q^30 + 4 * q^33 + 28 * q^34 + 2 * q^36 - 8 * q^37 + 36 * q^40 - 4 * q^42 - 34 * q^45 - 48 * q^46 + 10 * q^48 + 60 * q^49 + 8 * q^52 - 84 * q^54 - 14 * q^57 - 28 * q^58 - 60 * q^60 - 64 * q^61 + 84 * q^64 - 132 * q^66 - 4 * q^69 - 120 * q^70 + 44 * q^72 + 28 * q^76 + 20 * q^78 - 2 * q^81 + 48 * q^82 - 8 * q^84 + 8 * q^85 - 10 * q^88 + 24 * q^90 - 78 * q^93 - 88 * q^94 + 48 * q^96

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