LMFDB - Embedded newform 372.2.p.a.191.48

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			191.48
Character	$\chi$	$=$	372.191
Dual form			372.2.p.a.335.47

$q$-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} +(-1.98746 - 1.43178i) q^{6} +(-2.62156 - 1.51356i) q^{7} +(-2.11916 + 1.87328i) q^{8} +(2.80427 - 1.06586i) q^{9} +(-2.36377 - 0.685608i) q^{10} +(-0.0524986 - 0.0909303i) q^{11} +(-0.485467 - 3.42992i) q^{12} +(-1.25091 - 2.16665i) q^{13} +(-1.02299 - 4.15697i) q^{14} +(2.29534 - 1.95387i) q^{15} +(-3.98656 - 0.327675i) q^{16} +(0.921869 + 0.532241i) q^{17} +(3.83368 + 1.81739i) q^{18} +(-5.76362 - 3.32763i) q^{19} +(-1.61529 - 3.08314i) q^{20} +(4.93949 + 1.75834i) q^{21} +(0.0413640 - 0.142611i) q^{22} -1.76515 q^{23} +(3.02410 - 3.85419i) q^{24} +(-0.985633 + 1.70717i) q^{25} +(0.985605 - 3.39807i) q^{26} +(-4.44383 + 2.69303i) q^{27} +(3.23951 - 5.11463i) q^{28} +5.47454i q^{29} +(4.24132 + 0.428515i) q^{30} +(0.434039 + 5.55082i) q^{31} +(-3.56967 - 4.38834i) q^{32} +(0.117881 + 0.138482i) q^{33} +(0.359735 + 1.46179i) q^{34} +5.26817 q^{35} +(1.90001 + 5.69122i) q^{36} +(-2.39418 + 4.14684i) q^{37} +(-2.24910 - 9.13927i) q^{38} +(2.80881 + 3.29970i) q^{39} +(1.56386 - 4.66735i) q^{40} +(6.49599 - 3.75046i) q^{41} +(3.04317 + 6.76164i) q^{42} +(-0.710562 - 0.410243i) q^{43} +(0.186012 - 0.0974538i) q^{44} +(-3.29903 + 4.04660i) q^{45} +(-1.72859 - 1.80097i) q^{46} -1.57783 q^{47} +(6.89387 - 0.688907i) q^{48} +(1.08173 + 1.87361i) q^{49} +(-2.70703 + 0.666176i) q^{50} +(-1.73697 - 0.618318i) q^{51} +(4.43221 - 2.32209i) q^{52} +(-8.60561 + 4.96845i) q^{53} +(-7.09946 - 1.89675i) q^{54} +(0.158248 + 0.0913647i) q^{55} +(8.39082 - 1.70345i) q^{56} +(10.8597 + 3.86579i) q^{57} +(-5.58562 + 5.36116i) q^{58} +(-4.59615 + 7.96076i) q^{59} +(3.71626 + 4.74702i) q^{60} -7.64594 q^{61} +(-5.23840 + 5.87870i) q^{62} +(-8.96482 - 1.45022i) q^{63} +(0.981647 - 7.93954i) q^{64} +(3.77067 + 2.17700i) q^{65} +(-0.0258531 + 0.255887i) q^{66} +(10.7490 - 6.20592i) q^{67} +(-1.13917 + 1.79855i) q^{68} +(3.00705 - 0.552196i) q^{69} +(5.15906 + 5.37507i) q^{70} +(7.54234 + 13.0637i) q^{71} +(-3.94604 + 7.51191i) q^{72} +(-7.30556 - 12.6536i) q^{73} +(-6.57558 + 1.61819i) q^{74} +(1.14503 - 3.21661i) q^{75} +(7.12220 - 11.2447i) q^{76} +0.317839i q^{77} +(-0.616018 + 6.09717i) q^{78} +(9.00803 + 5.20079i) q^{79} +(6.29353 - 2.97509i) q^{80} +(6.72789 - 5.97792i) q^{81} +(10.1880 + 2.95502i) q^{82} +(1.50601 + 2.60849i) q^{83} +(-3.91870 + 9.72652i) q^{84} -1.85255 q^{85} +(-0.277278 - 1.12673i) q^{86} +(-1.71261 - 9.32624i) q^{87} +(0.281591 + 0.0943509i) q^{88} +5.45713i q^{89} +(-7.35942 + 0.596817i) 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} +(7.45397 + 6.35911i) q^{96} +5.26914 q^{97} +(-0.852301 + 2.93848i) 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	$0.460564\pi$
$6$	−1.98746	−	1.43178i	−0.811378	−	0.584522i
$7$	−2.62156	−	1.51356i	−0.990858	−	0.572072i	−0.0853271	−	0.996353i	$-0.527194\pi$
$7$	−2.62156	−	1.51356i	−0.990858	−	0.572072i	−0.905531	+	0.424281i	$0.860527\pi$
$8$	−2.11916	+	1.87328i	−0.749235	+	0.662304i
$9$	2.80427	−	1.06586i	0.934757	−	0.355287i
$10$	−2.36377	−	0.685608i	−0.747490	−	0.216808i
$11$	−0.0524986	−	0.0909303i	−0.0158289	−	0.0274165i	0.858002	−	0.513646i	$-0.171705\pi$
$11$	−0.0524986	−	0.0909303i	−0.0158289	−	0.0274165i	−0.873831	+	0.486229i	$0.838372\pi$
$12$	−0.485467	−	3.42992i	−0.140142	−	0.990131i
$13$	−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	$0.946113\pi$
$14$	−1.02299	−	4.15697i	−0.273407	−	1.11100i
$15$	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	$0.625462\pi$
$18$	3.83368	+	1.81739i	0.903607	+	0.428363i
$19$	−5.76362	−	3.32763i	−1.32226	−	0.763410i	−0.338175	−	0.941083i	$-0.609810\pi$
$19$	−5.76362	−	3.32763i	−1.32226	−	0.763410i	−0.984090	+	0.177673i	$0.943143\pi$
$20$	−1.61529	−	3.08314i	−0.361191	−	0.689411i
$21$	4.93949	+	1.75834i	1.07789	+	0.383701i
$22$	0.0413640	−	0.142611i	0.00881884	−	0.0304047i
$23$	−1.76515			−0.368059			−0.184030	−	0.982921i	$-0.558914\pi$
$23$	−1.76515			−0.368059			−0.184030	+	0.982921i	$0.558914\pi$
$24$	3.02410	−	3.85419i	0.617292	−	0.786734i
$25$	−0.985633	+	1.70717i	−0.197127	+	0.341433i
$26$	0.985605	−	3.39807i	0.193293	−	0.666416i
$27$	−4.44383	+	2.69303i	−0.855215	+	0.518273i
$28$	3.23951	−	5.11463i	0.612210	−	0.966573i
$29$			5.47454i			1.01660i	0.861181	+	0.508298i	$0.169725\pi$
$29$			5.47454i			1.01660i	−0.861181	+	0.508298i	$0.830275\pi$
$30$	4.24132	+	0.428515i	0.774355	+	0.0782357i
$31$	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
$34$	0.359735	+	1.46179i	0.0616940	+	0.250695i
$35$	5.26817			0.890484
$36$	1.90001	+	5.69122i	0.316669	+	0.948536i
$37$	−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	$0.295437\pi$
$38$	−2.24910	−	9.13927i	−0.364852	−	1.48259i
$39$	2.80881	+	3.29970i	0.449770	+	0.528375i
$40$	1.56386	−	4.66735i	0.247268	−	0.737974i
$41$	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	$0.134144\pi$
$42$	3.04317	+	6.76164i	0.469572	+	1.04334i
$43$	−0.710562	−	0.410243i	−0.108360	−	0.0625615i	0.444841	−	0.895610i	$-0.353260\pi$
$43$	−0.710562	−	0.410243i	−0.108360	−	0.0625615i	−0.553200	+	0.833048i	$0.686594\pi$
$44$	0.186012	−	0.0974538i	0.0280424	−	0.0146917i
$45$	−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	$-0.536711\pi$
$47$	−1.57783			−0.230151			−0.115075	+	0.993357i	$0.536711\pi$
$48$	6.89387	−	0.688907i	0.995044	−	0.0994351i
$49$	1.08173	+	1.87361i	0.154533	+	0.267658i
$50$	−2.70703	+	0.666176i	−0.382831	+	0.0942116i
$51$	−1.73697	−	0.618318i	−0.243224	−	0.0865818i
$52$	4.43221	−	2.32209i	0.614637	−	0.322016i
$53$	−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	$0.572427\pi$
$54$	−7.09946	−	1.89675i	−0.966114	−	0.258114i
$55$	0.158248	+	0.0913647i	0.0213382	+	0.0123196i
$56$	8.39082	−	1.70345i	1.12127	−	0.227633i
$57$	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	$0.370850\pi$
$59$	−4.59615	+	7.96076i	−0.598367	+	1.03640i	−0.993062	+	0.117590i	$0.962483\pi$
$60$	3.71626	+	4.74702i	0.479768	+	0.612837i
$61$	−7.64594			−0.978963			−0.489481	−	0.872014i	$-0.662814\pi$
$61$	−7.64594			−0.978963			−0.489481	+	0.872014i	$0.662814\pi$
$62$	−5.23840	+	5.87870i	−0.665278	+	0.746596i
$63$	−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
$66$	−0.0258531	+	0.255887i	−0.00318230	+	0.0314975i
$67$	10.7490	−	6.20592i	1.31320	−	0.758174i	0.330572	−	0.943781i	$-0.392758\pi$
$67$	10.7490	−	6.20592i	1.31320	−	0.758174i	0.982624	+	0.185606i	$0.0594249\pi$
$68$	−1.13917	+	1.79855i	−0.138145	+	0.218106i
$69$	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	$0.186237\pi$
$71$	7.54234	+	13.0637i	0.895111	+	1.55038i	0.0614435	+	0.998111i	$0.480430\pi$
$72$	−3.94604	+	7.51191i	−0.465045	+	0.885287i
$73$	−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	$-0.493141\pi$
$74$	−6.57558	+	1.61819i	−0.764396	+	0.188111i
$75$	1.14503	−	3.21661i	0.132217	−	0.371422i
$76$	7.12220	−	11.2447i	0.816973	−	1.28986i
$77$			0.317839i			0.0362211i
$78$	−0.616018	+	6.09717i	−0.0697502	+	0.690368i
$79$	9.00803	+	5.20079i	1.01348	+	0.585135i	0.912210	−	0.409724i	$-0.134375\pi$
$79$	9.00803	+	5.20079i	1.01348	+	0.585135i	0.101273	+	0.994859i	$0.467708\pi$
$80$	6.29353	−	2.97509i	0.703638	−	0.332625i
$81$	6.72789	−	5.97792i	0.747543	−	0.664213i
$82$	10.1880	+	2.95502i	1.12508	+	0.326327i
$83$	1.50601	+	2.60849i	0.165307	+	0.286319i	0.936764	−	0.349961i	$-0.113805\pi$
$83$	1.50601	+	2.60849i	0.165307	+	0.286319i	−0.771458	+	0.636281i	$0.780472\pi$
$84$	−3.91870	+	9.72652i	−0.427565	+	1.06125i
$85$	−1.85255			−0.200937
$86$	−0.277278	−	1.12673i	−0.0298996	−	0.121498i
$87$	−1.71261	−	9.32624i	−0.183611	−	0.999878i
$88$	0.281591	+	0.0943509i	0.0300177	+	0.0100578i
$89$			5.45713i			0.578454i	0.957260	+	0.289227i	$0.0933983\pi$
$89$			5.45713i			0.578454i	−0.957260	+	0.289227i	$0.906602\pi$
$90$	−7.35942	+	0.596817i	−0.775751	+	0.0629100i
$91$			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
$96$	7.45397	+	6.35911i	0.760768	+	0.649024i
$97$	5.26914			0.535000			0.267500	−	0.963558i	$-0.413802\pi$
$97$	5.26914			0.535000			0.267500	+	0.963558i	$0.413802\pi$
$98$	−0.852301	+	2.93848i	−0.0860954	+	0.296831i
$99$	−0.244139	−	0.199037i	−0.0245369	−	0.0200040i
$100$	−3.33065	−	2.10958i	−0.333065	−	0.210958i
$101$		−	7.26469i		−	0.722864i	−0.932398	−	0.361432i	$-0.882288\pi$
$101$		−	7.26469i		−	0.722864i	0.932398	−	0.361432i	$-0.117712\pi$
$102$	−1.07013	−	2.37772i	−0.105958	−	0.235430i
$103$	−2.17281	+	1.25447i	−0.214093	+	0.123607i	−0.603212	−	0.797581i	$-0.706113\pi$
$103$	−2.17281	+	1.25447i	−0.214093	+	0.123607i	0.389119	+	0.921187i	$0.372779\pi$
$104$	6.70962	+	2.24815i	0.657932	+	0.220449i
$105$	−8.97468	+	1.64805i	−0.875839	+	0.160834i
$106$	−13.4966	−	3.91468i	−1.31091	−	0.380227i
$107$	−6.92842	+	12.0004i	−0.669796	+	1.16012i	0.308166	+	0.951333i	$0.400285\pi$
$107$	−6.92842	+	12.0004i	−0.669796	+	1.16012i	−0.977961	+	0.208787i	$0.933048\pi$
$108$	−5.01719	−	9.10098i	−0.482779	−	0.875742i
$109$	0.640695			0.0613674			0.0306837	−	0.999529i	$-0.490232\pi$
$109$	0.640695			0.0613674			0.0306837	+	0.999529i	$0.490232\pi$
$110$	0.0617522	+	0.250932i	0.00588784	+	0.0239254i
$111$	2.78138	−	7.81339i	0.263997	−	0.741615i
$112$	9.95505	+	6.89291i	0.940664	+	0.651319i
$113$	−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	$0.434502\pi$
$114$	6.69054	+	14.8658i	0.626627	+	1.39231i
$115$	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
$118$	−12.6232	+	3.10647i	−1.16206	+	0.285974i
$119$	−1.61116	−	2.79061i	−0.147695	−	0.255815i
$120$	−1.20404	+	8.44037i	−0.109914	+	0.770497i
$121$	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
$124$	−11.1279	+	0.412250i	−0.999314	+	0.0370211i
$125$		−	12.1323i		−	1.08514i
$126$	−7.29950	−	10.5669i	−0.650291	−	0.941375i
$127$	−14.8389	−	8.56722i	−1.31674	−	0.760218i	−0.333534	−	0.942738i	$-0.608241\pi$
$127$	−14.8389	−	8.56722i	−1.31674	−	0.760218i	−0.983202	+	0.182520i	$0.941574\pi$
$128$	9.06196	−	6.77354i	0.800972	−	0.598702i
$129$	1.33883	+	0.476590i	0.117877	+	0.0419614i
$130$	1.47140	+	5.97909i	0.129051	+	0.524401i
$131$	8.30013	−	14.3763i	0.725186	−	1.25606i	−0.233711	−	0.972306i	$-0.575087\pi$
$131$	8.30013	−	14.3763i	0.725186	−	1.25606i	0.958897	−	0.283753i	$-0.0915796\pi$
$132$	−0.286397	+	0.224209i	−0.0249276	+	0.0195149i
$133$	10.0731	+	17.4472i	0.873451	+	1.51286i
$134$	16.8582	+	4.88969i	1.45633	+	0.422405i
$135$	4.35421	−	7.92569i	0.374751	−	0.682135i
$136$	−2.95062	+	0.599016i	−0.253014	+	0.0513652i
$137$	−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	$0.563980\pi$
$138$	3.50817	+	2.52731i	0.298635	+	0.215139i
$139$		−	2.37109i		−	0.201114i	−0.994931	−	0.100557i	$-0.967938\pi$
$139$		−	2.37109i		−	0.201114i	0.994931	−	0.100557i	$-0.0320624\pi$
$140$	−0.431925	+	10.5275i	−0.0365043	+	0.889735i
$141$	2.68795	−	0.493597i	0.226366	−	0.0415684i
$142$	−5.94266	+	20.4885i	−0.498697	+	1.71936i
$143$	−0.131343	+	0.227492i	−0.0109834	+	0.0190238i
$144$	−11.5286	+	3.33022i	−0.960720	+	0.277518i
$145$	−4.76374	−	8.25104i	−0.395607	−	0.685212i
$146$	5.75610	−	19.8453i	0.476378	−	1.64241i
$147$	−2.42892	−	2.85341i	−0.200334	−	0.235346i
$148$	−8.09042	−	5.12432i	−0.665028	−	0.421217i
$149$	−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	$0.708978\pi$
$150$	4.40320	−	1.98172i	0.359520	−	0.161807i
$151$			4.01599i			0.326816i	0.986559	+	0.163408i	$0.0522488\pi$
$151$			4.01599i			0.326816i	−0.986559	+	0.163408i	$0.947751\pi$
$152$	18.4476	−	3.74511i	1.49630	−	0.303768i
$153$	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
$156$	−6.82414	+	5.34237i	−0.546369	+	0.427732i
$157$	1.54160			0.123033			0.0615167	−	0.998106i	$-0.480406\pi$
$157$	1.54160			0.123033			0.0615167	+	0.998106i	$0.480406\pi$
$158$	3.51514	+	14.2839i	0.279650	+	1.13637i
$159$	13.1059	−	11.1562i	1.03937	−	0.884743i
$160$	9.19865	+	3.50776i	0.727217	+	0.277313i
$161$	4.62745	+	2.67166i	0.364694	+	0.210556i
$162$	12.6878	+	1.01029i	0.996845	+	0.0793760i
$163$			8.14608i			0.638050i	0.947746	+	0.319025i	$0.103355\pi$
$163$			8.14608i			0.638050i	−0.947746	+	0.319025i	$0.896645\pi$
$164$	6.96203	+	13.2886i	0.543643	+	1.03766i
$165$	−0.298168	−	0.106141i	−0.0232124	−	0.00826304i
$166$	−1.18660	+	4.09104i	−0.0920980	+	0.317526i
$167$	11.0137	−	19.0763i	0.852268	−	1.47617i	−0.0268885	−	0.999638i	$-0.508560\pi$
$167$	11.0137	−	19.0763i	0.852268	−	1.47617i	0.879157	−	0.476533i	$-0.158107\pi$
$168$	−13.7614	+	5.52686i	−1.06172	+	0.426406i
$169$	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
$172$	0.878054	−	1.38629i	0.0669510	−	0.105704i
$173$	−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	$0.935964\pi$
$174$	7.83834	−	10.8804i	0.594223	−	0.824844i
$175$	5.16780	−	2.98363i	0.390649	−	0.225541i
$176$	0.179493	+	0.379701i	0.0135298	+	0.0286211i
$177$	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	−0.798108	−	0.602515i	$-0.794165\pi$
$179$	1.64214	−	2.84427i	0.122739	−	0.212590i	0.920847	+	0.389924i	$0.127499\pi$
$180$	−7.81592	−	6.92429i	−0.582564	−	0.516106i
$181$	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
$186$	7.08492	−	11.6535i	0.519491	−	0.854476i
$187$		−	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	0.873761	−	0.486355i	$-0.161674\pi$
$191$	0.216766	+	0.375450i	0.0156846	+	0.0271666i	−0.858077	+	0.513522i	$0.828341\pi$
$192$	0.811444	+	13.8326i	0.0585609	+	0.998284i
$193$	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
$196$	−3.83275	+	2.00802i	−0.273768	+	0.143430i
$197$	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	$0.196511\pi$
$198$	−0.0360071	−	0.444008i	−0.00255891	−	0.0315543i
$199$	6.79422	−	3.92264i	0.481629	−	0.278069i	−0.239466	−	0.970905i	$-0.576972\pi$
$199$	6.79422	−	3.92264i	0.481629	−	0.278069i	0.721095	+	0.692836i	$0.243639\pi$
$200$	−1.10929	−	5.46412i	−0.0784387	−	0.386372i
$201$	−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
$204$	1.37801	−	3.42032i	0.0964797	−	0.239470i
$205$	−6.52703	+	11.3051i	−0.455867	+	0.789586i
$206$	−3.40773	−	0.988406i	−0.237428	−	0.0688655i
$207$	−4.94996	+	1.88140i	−0.344046	+	0.130767i
$208$	4.27689	+	9.04736i	0.296549	+	0.627321i
$209$			0.698783i			0.0483358i
$210$	−10.4703	−	7.54287i	−0.722519	−	0.520507i
$211$	6.44387	+	3.72037i	0.443615	+	0.256121i	0.705130	−	0.709078i	$-0.250889\pi$
$211$	6.44387	+	3.72037i	0.443615	+	0.256121i	−0.261515	+	0.965199i	$0.584222\pi$
$212$	−9.22299	−	17.6041i	−0.633438	−	1.20905i
$213$	−16.9356	−	19.8954i	−1.16041	−	1.36321i
$214$	−19.0288	+	4.68283i	−1.30078	+	0.320111i
$215$	1.42791			0.0973829
$216$	4.37237	−	14.0315i	0.297502	−	0.954721i
$217$	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
$220$	−0.195550	+	0.308740i	−0.0131840	+	0.0208152i
$221$		−	2.66315i		−	0.179143i
$222$	10.6957	−	4.81375i	0.717849	−	0.323078i
$223$	−18.0626	−	10.4285i	−1.20956	−	0.698342i	−0.246900	−	0.969041i	$-0.579412\pi$
$223$	−18.0626	−	10.4285i	−1.20956	−	0.698342i	−0.962664	+	0.270699i	$0.912745\pi$
$224$	2.71609	+	16.9072i	0.181477	+	1.12966i
$225$	−0.944384	+	5.83791i	−0.0629589	+	0.389194i
$226$	−9.02405	−	2.61741i	−0.600271	−	0.174107i
$227$	6.10966	+	10.5822i	0.405512	+	0.702368i	0.994381	−	0.105861i	$-0.0337598\pi$
$227$	6.10966	+	10.5822i	0.405512	+	0.702368i	−0.588869	+	0.808229i	$0.700426\pi$
$228$	−8.61543	+	21.3842i	−0.570571	+	1.41620i
$229$	−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	$0.913262\pi$
$230$	4.17241	+	1.21020i	0.275121	+	0.0797983i
$231$	−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	$0.846699\pi$
$234$	−0.857962	−	10.5796i	−0.0560867	−	0.691612i
$235$	2.37806	−	1.37297i	0.155127	−	0.0895629i
$236$	−15.5313	−	9.83725i	−1.01100	−	0.640350i
$237$	−16.9727	−	6.04189i	−1.10250	−	0.392463i
$238$	1.26944	−	4.37666i	0.0822858	−	0.283697i
$239$	1.26305	+	2.18767i	0.0816998	+	0.141508i	0.903980	−	0.427574i	$-0.140632\pi$
$239$	1.26305	+	2.18767i	0.0816998	+	0.141508i	−0.822280	+	0.569083i	$0.807298\pi$
$240$	−9.79074	+	7.03708i	−0.631990	+	0.454242i
$241$	−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	$0.793059\pi$
$242$	15.0905	−	3.71365i	0.970056	−	0.238723i
$243$	−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
$246$	−18.2804	−	1.84693i	−1.16551	−	0.117756i
$247$			16.6503i			1.05943i
$248$	−11.3180	−	10.9500i	−0.718696	−	0.695324i
$249$	−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	−0.991183	−	0.132502i	$-0.957699\pi$
$251$	−6.03366	+	10.4506i	−0.380841	+	0.659636i	0.610342	+	0.792138i	$0.291032\pi$
$252$	3.63300	−	17.7957i	0.228857	−	1.12102i
$253$	0.0926680	+	0.160506i	0.00582599	+	0.0100909i
$254$	−5.79047	−	23.5297i	−0.363326	−	1.47639i
$255$	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	$0.135078\pi$
$258$	0.824837	+	1.83271i	0.0513521	+	0.114100i
$259$	12.5530	−	7.24747i	0.780005	−	0.450336i
$260$	−4.65949	+	7.35652i	−0.288969	+	0.456232i
$261$	5.83509	+	15.3521i	0.361183	+	0.950271i
$262$	22.7962	−	5.60995i	1.40835	−	0.346584i
$263$	−15.2767			−0.942003			−0.471002	−	0.882132i	$-0.656107\pi$
$263$	−15.2767			−0.942003			−0.471002	+	0.882132i	$0.656107\pi$
$264$	−0.509224	−	0.0726424i	−0.0313406	−	0.00447083i
$265$	8.64672	−	14.9766i	0.531164	−	0.920003i
$266$	−7.93669	+	27.3633i	−0.486630	+	1.67775i
$267$	−1.70716	−	9.29658i	−0.104477	−	0.568941i
$268$	11.5201	+	21.9887i	0.703704	+	1.34317i
$269$	−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	$0.561332\pi$
$270$	12.3505	−	3.31898i	0.751630	−	0.201986i
$271$			14.6833i			0.891947i	0.895046	+	0.445974i	$0.147143\pi$
$271$			14.6833i			0.891947i	−0.895046	+	0.445974i	$0.852857\pi$
$272$	−3.50068	−	2.42388i	−0.212260	−	0.146969i
$273$	−2.36918	−	12.9017i	−0.143389	−	0.780845i
$274$	−21.0751	−	6.11280i	−1.27319	−	0.369288i
$275$	0.206978			0.0124812
$276$	0.856922	+	6.05432i	0.0515806	+	0.364427i
$277$	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	$-0.0880393\pi$
$282$	3.13589	+	2.25911i	0.186739	+	0.134528i
$283$		−	19.3192i		−	1.14841i	−0.818712	−	0.574205i	$-0.805311\pi$
$283$		−	19.3192i		−	1.14841i	0.818712	−	0.574205i	$-0.194689\pi$
$284$	−26.7238	+	14.0009i	−1.58577	+	0.830803i
$285$	−19.7312	+	3.62332i	−1.16878	+	0.214627i
$286$	−0.360730	+	0.0887727i	−0.0213304	+	0.00524924i
$287$	−22.7062			−1.34031
$288$	−14.6877	−	8.50133i	−0.865479	−	0.500945i
$289$	−7.93344	−	13.7411i	−0.466673	−	0.808301i
$290$	3.75339	−	12.9406i	0.220406	−	0.759896i
$291$	−8.97633	+	1.64836i	−0.526201	+	0.0966283i
$292$	25.8849	−	13.5614i	1.51480	−	0.793621i
$293$	−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	$0.744059\pi$
$294$	0.532701	−	5.27252i	0.0310677	−	0.307500i
$295$		−	15.9976i		−	0.931415i
$296$	−2.69455	−	13.2728i	−0.156618	−	0.771464i
$297$	0.478173	+	0.262698i	0.0277464	+	0.0152433i
$298$	−1.09344	−	4.44320i	−0.0633410	−	0.257388i
$299$	2.20805	+	3.82446i	0.127695	+	0.221174i
$300$	6.33393	+	2.55187i	0.365690	+	0.147332i
$301$	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
$304$	21.8866	+	15.1544i	1.25528	+	0.869162i
$305$	11.5237	−	6.65321i	0.659845	−	0.380962i
$306$	2.56686	+	3.71584i	0.146738	+	0.212420i
$307$	0.258088	+	0.149007i	0.0147299	+	0.00850430i	0.507347	−	0.861742i	$-0.330626\pi$
$307$	0.258088	+	0.149007i	0.0147299	+	0.00850430i	−0.492617	+	0.870246i	$0.663960\pi$
$308$	−0.635144	−	0.0260589i	−0.0361907	−	0.00148484i
$309$	3.30908	−	2.81680i	0.188247	−	0.160242i
$310$	2.77972	−	13.4184i	0.157877	−	0.762116i
$311$	−15.1251			−0.857663			−0.428832	−	0.903384i	$-0.641075\pi$
$311$	−15.1251			−0.857663			−0.428832	+	0.903384i	$0.641075\pi$
$312$	−12.1336	−	1.73089i	−0.686928	−	0.0979924i
$313$	−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
$316$	−11.1314	+	17.5745i	−0.626189	+	0.988644i
$317$	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	$0.616322\pi$
$318$	24.2170	+	2.44673i	1.35802	+	0.137206i
$319$	0.497802	−	0.287406i	0.0278715	−	0.0160916i
$320$	5.42919	+	12.8204i	0.303501	+	0.716682i
$321$	8.04892	−	22.6109i	0.449247	−	1.26201i
$322$	1.80574	+	7.33768i	0.100630	+	0.408913i
$323$	−3.54220	−	6.13527i	−0.197093	−	0.341375i
$324$	11.3942	+	13.9346i	0.633011	+	0.774143i
$325$	4.93177			0.273566
$326$	−8.31137	+	7.97736i	−0.460324	+	0.441825i
$327$	−1.09147	+	0.200430i	−0.0603582	+	0.0110838i
$328$	−6.74036	+	20.1166i	−0.372174	+	1.11076i
$329$	4.13639	+	2.38815i	0.228047	+	0.131663i
$330$	−0.183698	−	0.408161i	−0.0101123	−	0.0224685i
$331$	−7.48363	+	4.32068i	−0.411337	+	0.237486i	−0.691364	−	0.722506i	$-0.742990\pi$
$331$	−7.48363	+	4.32068i	−0.411337	+	0.237486i	0.280027	+	0.959992i	$0.409657\pi$
$332$	−5.33608	+	2.79563i	−0.292855	+	0.153430i
$333$	−2.29398	+	14.1807i	−0.125709	+	0.777099i
$334$	30.2490	−	7.44403i	1.65515	−	0.407319i
$335$	−10.8003	+	18.7067i	−0.590085	+	1.02206i
$336$	−19.1154	−	8.62827i	−1.04283	−	0.470711i
$337$	24.5094			1.33511			0.667557	−	0.744559i	$-0.267340\pi$
$337$	24.5094			1.33511			0.667557	+	0.744559i	$0.267340\pi$
$338$	9.25682	−	2.27802i	0.503505	−	0.123908i
$339$	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
$342$	−16.0483	−	23.2318i	−0.867791	−	1.25623i
$343$			14.6408i			0.790529i
$344$	2.27429	−	0.461712i	0.122622	−	0.0248938i
$345$	−4.05162	+	3.44887i	−0.218132	+	0.185681i
$346$	−33.8884	−	9.82928i	−1.82185	−	0.528425i
$347$	−5.23744	+	9.07151i	−0.281161	+	0.486984i	−0.971671	−	0.236338i	$-0.924053\pi$
$347$	−5.23744	+	9.07151i	−0.281161	+	0.486984i	0.690510	+	0.723323i	$0.257386\pi$
$348$	18.7772	−	2.65771i	1.00656	−	0.142468i
$349$	8.14721			0.436110			0.218055	−	0.975936i	$-0.430029\pi$
$349$	8.14721			0.436110			0.218055	+	0.975936i	$0.430029\pi$
$350$	8.10494	+	2.35082i	0.433227	+	0.125657i
$351$	11.3937	+	6.25946i	0.608150	+	0.334105i
$352$	−0.211630	+	0.554972i	−0.0112799	+	0.0295801i
$353$	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	$0.383212\pi$
$354$	20.5327	−	9.24104i	1.09130	−	0.491156i
$355$	−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
$358$	4.51010	−	1.10990i	0.238366	−	0.0586600i
$359$	13.0064	+	22.5277i	0.686449	+	1.18897i	0.972979	+	0.230894i	$0.0741650\pi$
$359$	13.0064	+	22.5277i	0.686449	+	1.18897i	−0.286530	+	0.958071i	$0.592502\pi$
$360$	−0.589249	−	14.7554i	−0.0310561	−	0.777677i
$361$	12.6462	+	21.9039i	0.665589	+	1.15283i
$362$	−4.89579	+	16.8792i	−0.257317	+	0.887152i
$363$	−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
$366$	15.1960	+	10.9473i	0.794309	+	0.572225i
$367$	−8.43271	+	4.86863i	−0.440184	+	0.254140i	−0.703676	−	0.710521i	$-0.748459\pi$
$367$	−8.43271	+	4.86863i	−0.440184	+	0.254140i	0.263492	+	0.964662i	$0.415126\pi$
$368$	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
$372$	18.8281	−	4.18346i	0.976193	−	0.216902i
$373$	−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
$378$	15.7408	+	15.7179i	0.809622	+	0.808441i
$379$	12.8153	+	7.39889i	0.658275	+	0.380055i	0.791620	−	0.611014i	$-0.209238\pi$
$379$	12.8153	+	7.39889i	0.658275	+	0.380055i	−0.133344	+	0.991070i	$0.542572\pi$
$380$	−0.949606	+	23.1451i	−0.0487137	+	1.18732i
$381$	27.9591	+	9.95275i	1.43239	+	0.509895i
$382$	−0.170792	+	0.588838i	−0.00873845	+	0.0301276i
$383$	−13.4838	−	23.3547i	−0.688992	−	1.19337i	−0.972164	−	0.234301i	$-0.924720\pi$
$383$	−13.4838	−	23.3547i	−0.688992	−	1.19337i	0.283172	−	0.959069i	$-0.408613\pi$
$384$	−13.3187	+	14.3740i	−0.679665	+	0.733522i
$385$	−0.276572	−	0.479037i	−0.0140954	−	0.0244140i
$386$	28.7876	−	7.08438i	1.46525	−	0.360585i
$387$	−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	$0.861866\pi$
$390$	−4.37709	−	9.72548i	−0.221642	−	0.492469i
$391$	−1.62724	−	0.939486i	−0.0822929	−	0.0475118i
$392$	−5.80214	−	1.94409i	−0.293052	−	0.0981913i
$393$	−9.64247	+	27.0874i	−0.486398	+	1.36638i
$394$	15.8886	+	4.60847i	0.800458	+	0.232171i
$395$	−18.1021			−0.910817
$396$	0.417756	−	0.471550i	0.0209930	−	0.0236963i
$397$	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	$0.103736\pi$
$398$	10.6557	+	3.09068i	0.534124	+	0.154922i
$399$	−22.6183	−	26.5712i	−1.13233	−	1.33022i
$400$	4.48868	−	6.48275i	0.224434	−	0.324138i
$401$			34.0123i			1.69849i	0.527998	+	0.849246i	$0.322943\pi$
$401$			34.0123i			1.69849i	−0.527998	+	0.849246i	$0.677057\pi$
$402$	−30.2487	−	3.05613i	−1.50867	−	0.152426i
$403$	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
$406$	22.7575	−	5.60043i	1.12944	−	0.277945i
$407$	0.502765			0.0249211
$408$	4.83918	−	1.94351i	0.239575	−	0.0962181i
$409$	−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	$0.178642\pi$
$410$	−17.9264	+	4.41153i	−0.885321	+	0.217870i
$411$	20.4650	−	17.4205i	1.00946	−	0.859289i
$412$	−2.32869	−	4.44481i	−0.114726	−	0.218980i
$413$	24.0982	−	13.9131i	1.18579	−	0.684618i
$414$	−6.76702	−	3.20797i	−0.332581	−	0.157663i
$415$	−4.53963	−	2.62096i	−0.222842	−	0.128658i
$416$	−5.04263	+	13.2236i	−0.247235	+	0.648342i
$417$	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	$-0.420607\pi$
$419$	10.1055			0.493684			0.246842	+	0.969056i	$0.420607\pi$
$420$	−2.55752	−	18.0694i	−0.124794	−	0.881696i
$421$	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	$0.727789\pi$
$422$	2.51455	+	10.2179i	0.122406	+	0.497402i
$423$	−4.42468	+	1.68175i	−0.215135	+	0.0817695i
$424$	8.92933	−	26.6496i	0.433647	−	1.29422i
$425$	−1.81725	+	1.04919i	−0.0881495	+	0.0508932i
$426$	3.71425	−	36.7626i	0.179956	−	1.78115i
$427$	20.0443	+	11.5726i	0.970013	+	0.560037i
$428$	−23.4125	−	14.8291i	−1.13169	−	0.716790i
$429$	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	−0.807393	−	0.590014i	$-0.799122\pi$
$431$	2.22699	−	3.85727i	0.107270	−	0.185798i	0.914664	+	0.404216i	$0.132456\pi$
$432$	18.5980	−	9.27978i	0.894797	−	0.446473i
$433$	−7.76496			−0.373160			−0.186580	−	0.982440i	$-0.559740\pi$
$433$	−7.76496			−0.373160			−0.186580	+	0.982440i	$0.559740\pi$
$434$	22.6306	−	7.48275i	1.08630	−	0.359183i
$435$	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
$438$	−3.59765	+	35.6085i	−0.171902	+	1.70144i
$439$	−3.75921	+	2.17038i	−0.179417	+	0.103587i	−0.587019	−	0.809573i	$-0.699699\pi$
$439$	−3.75921	+	2.17038i	−0.179417	+	0.103587i	0.407602	+	0.913160i	$0.366365\pi$
$440$	−0.506505	+	0.102827i	−0.0241467	+	0.00490210i
$441$	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	$-0.962663\pi$
$443$	−12.5847	−	21.7973i	−0.597915	−	1.03562i	0.395213	−	0.918590i	$-0.370671\pi$
$444$	15.3856	+	6.19868i	0.730169	+	0.294176i
$445$	−4.74859	−	8.22480i	−0.225105	−	0.389893i
$446$	−7.04846	−	28.6416i	−0.333754	−	1.35622i
$447$	5.27961	+	1.87941i	0.249717	+	0.0888932i
$448$	−14.5904	+	19.3282i	−0.689333	+	0.913173i
$449$		−	31.2110i		−	1.47294i	−0.676472	−	0.736468i	$-0.736492\pi$
$449$		−	31.2110i		−	1.47294i	0.676472	−	0.736468i	$-0.263508\pi$
$450$	−6.88119	+	4.75345i	−0.324382	+	0.224080i
$451$	−0.682062	−	0.393788i	−0.0321170	−	0.0185428i
$452$	−6.16663	−	11.7704i	−0.290054	−	0.553631i
$453$	−1.25633	−	6.84150i	−0.0590275	−	0.321442i
$454$	−4.81385	+	16.5967i	−0.225925	+	0.778922i
$455$	−6.59004	−	11.4143i	−0.308946	−	0.535110i
$456$	−30.2551	+	12.1510i	−1.41682	+	0.569024i
$457$	−22.3663			−1.04625			−0.523126	−	0.852256i	$-0.675234\pi$
$457$	−22.3663			−1.04625			−0.523126	+	0.852256i	$0.675234\pi$
$458$	−29.7013	+	7.30925i	−1.38785	+	0.341539i
$459$	−5.52996	+	0.117430i	−0.258117	+	0.00548119i
$460$	2.85124	+	5.44221i	0.132940	+	0.253744i
$461$		−	27.4939i		−	1.28052i	−0.768158	−	0.640260i	$-0.778827\pi$
$461$		−	27.4939i		−	1.28052i	0.768158	−	0.640260i	$-0.221173\pi$
$462$	0.455076	−	0.631694i	0.0211720	−	0.0293890i
$463$			17.1957i			0.799153i	0.916700	+	0.399577i	$0.130843\pi$
$463$			17.1957i			0.799153i	−0.916700	+	0.399577i	$0.869157\pi$
$464$	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	$-0.360454\pi$
$467$	18.3465			0.848976			0.424488	+	0.905434i	$0.360454\pi$
$468$	9.95411	−	11.2359i	0.460129	−	0.519379i
$469$	−37.5722			−1.73492
$470$	3.72964	+	1.08178i	0.172035	+	0.0498986i
$471$	−2.62622	+	0.482263i	−0.121010	+	0.0222215i
$472$	−5.17277	−	25.4800i	−0.238096	−	1.17281i
$473$			0.0861488i			0.00396113i
$474$	−10.4567	−	23.2339i	−0.480294	−	1.06717i
$475$	11.3616	−	6.55964i	0.521307	−	0.300977i
$476$	5.70862	−	2.99081i	0.261654	−	0.137084i
$477$	−18.8368	+	23.1053i	−0.862478	+	1.05792i
$478$	−0.995166	+	3.43103i	−0.0455178	+	0.156932i
$479$	−11.7946	+	20.4288i	−0.538908	+	0.933416i	0.460055	+	0.887890i	$0.347830\pi$
$479$	−11.7946	+	20.4288i	−0.538908	+	0.933416i	−0.998963	+	0.0455254i	$0.985504\pi$
$480$	−16.7678	−	3.09807i	−0.765344	−	0.141407i
$481$	11.9797			0.546226
$482$	−39.3196	+	9.67623i	−1.79096	+	0.440740i
$483$	−8.71895	−	3.10374i	−0.396726	−	0.141225i
$484$	18.5670	+	11.7600i	0.843954	+	0.534545i
$485$	−7.94147	+	4.58501i	−0.360604	+	0.208195i
$486$	−21.9305	+	2.24804i	−0.994787	+	0.101973i
$487$	−17.3158	+	9.99730i	−0.784655	+	0.453021i	−0.838077	−	0.545551i	$-0.816320\pi$
$487$	−17.3158	+	9.99730i	−0.784655	+	0.453021i	0.0534226	+	0.998572i	$0.482987\pi$
$488$	16.2029	−	14.3230i	0.733473	−	0.648371i
$489$	−2.54835	−	13.8774i	−0.115241	−	0.627557i
$490$	−1.27240	−	5.17042i	−0.0574810	−	0.233576i
$491$	2.17592	+	3.76881i	0.0981981	+	0.170084i	0.910939	−	0.412541i	$-0.135359\pi$
$491$	2.17592	+	3.76881i	0.0981981	+	0.170084i	−0.812741	+	0.582625i	$0.802025\pi$
$492$	−16.0174	−	20.4600i	−0.722119	−	0.922408i
$493$	−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
$496$	0.0885427	−	22.2709i	0.00397568	−	0.999992i
$497$		−	45.6631i		−	2.04827i
$498$	0.741642	−	7.34056i	0.0332338	−	0.328938i
$499$	−33.0539	−	19.0837i	−1.47969	−	0.854302i	−0.479959	−	0.877291i	$-0.659348\pi$
$499$	−33.0539	−	19.0837i	−1.47969	−	0.854302i	−0.999736	+	0.0229890i	$0.992682\pi$
$500$	24.2442	+	0.994696i	1.08423	+	0.0444842i
$501$	−12.7949	+	35.9432i	−0.571635	+	1.60583i
$502$	−16.5713	+	4.07807i	−0.739615	+	0.182013i
$503$	−12.0923	+	20.9444i	−0.539167	+	0.933865i	0.459782	+	0.888032i	$0.347928\pi$
$503$	−12.0923	+	20.9444i	−0.539167	+	0.933865i	−0.998949	+	0.0458331i	$0.985406\pi$
$504$	21.7145	−	13.7204i	0.967241	−	0.611154i
$505$	6.32147	+	10.9491i	0.281302	+	0.487229i
$506$	−0.0730138	+	0.251730i	−0.00324586	+	0.0111907i
$507$	−3.91551	+	10.9994i	−0.173894	+	0.488499i
$508$	18.3366	−	28.9504i	0.813557	−	1.28446i
$509$	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	$0.188401\pi$
$510$	3.68186	+	2.65244i	0.163036	+	0.117452i
$511$			44.2296i			1.95660i
$512$	12.7927	+	18.6640i	0.565364	+	0.824842i
$513$	34.5739	−	0.734187i	1.52648	−	0.0324152i
$514$	25.4035	+	7.36826i	1.12050	+	0.325000i
$515$	2.18319	−	3.78139i	0.0962027	−	0.166628i
$516$	−1.06215	+	2.63633i	−0.0467583	+	0.116058i
$517$	0.0828342	+	0.143473i	0.00364304	+	0.00630993i
$518$	19.6875	+	5.71034i	0.865020	+	0.250898i
$519$	32.9074	−	28.0118i	1.44447	−	1.22958i
$520$	−12.0688	+	2.45012i	−0.529251	+	0.107445i
$521$	−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	$0.755892\pi$
$522$	−9.94937	+	20.9876i	−0.435472	+	0.918604i
$523$		−	26.0346i		−	1.13841i	−0.822195	−	0.569206i	$-0.807251\pi$
$523$		−	26.0346i		−	1.13841i	0.822195	−	0.569206i	$-0.192749\pi$
$524$	28.0478	+	17.7650i	1.22528	+	0.776067i
$525$	−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
$528$	−0.424561	−	0.590695i	−0.0184766	−	0.0257067i
$529$	−19.8842			−0.864532
$530$	23.7481	−	5.84420i	1.03155	−	0.253856i
$531$	−4.40379	+	27.2230i	−0.191108	+	1.18138i
$532$	−35.6909	+	18.6989i	−1.54740	+	0.810699i
$533$	−16.2519	−	9.38302i	−0.703947	−	0.406424i
$534$	7.81341	−	10.8458i	0.338119	−	0.469345i
$535$		−	24.1154i		−	1.04260i
$536$	−11.1533	+	33.2872i	−0.481750	+	1.43779i
$537$	−1.90771	+	5.35911i	−0.0823238	+	0.231262i
$538$	−29.2530	−	8.48478i	−1.26119	−	0.365805i
$539$	0.113578	−	0.196724i	0.00489217	−	0.00847349i
$540$	15.4811	+	9.35091i	0.666199	+	0.402399i
$541$	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
$544$	−0.955110	−	5.94539i	−0.0409500	−	0.254907i
$545$	−0.965633	+	0.557509i	−0.0413632	+	0.0238810i
$546$	10.8434	−	15.0517i	0.464053	−	0.644154i
$547$	16.6021	−	9.58523i	0.709855	−	0.409835i	−0.101153	−	0.994871i	$-0.532253\pi$
$547$	16.6021	−	9.58523i	0.709855	−	0.409835i	0.811007	+	0.585036i	$0.198920\pi$
$548$	−14.4018	−	27.4889i	−0.615213	−	1.17427i
$549$	−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
$552$	−5.33799	+	6.80323i	−0.227200	+	0.289565i
$553$	−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	$0.962711\pi$
$558$	−8.42404	+	22.0689i	−0.356618	+	0.934250i
$559$			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	$-0.753220\pi$
$563$	−22.8558	−	39.5875i	−0.963258	−	1.66841i	−0.249035	−	0.968494i	$-0.580114\pi$
$564$	0.765986	+	5.41184i	0.0322538	+	0.227880i
$565$	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
$568$	−40.4554	−	13.5551i	−1.69747	−	0.568761i
$569$	−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	$0.406931\pi$
$570$	−23.0194	−	16.5833i	−0.964176	−	0.694599i
$571$	−27.6439	+	15.9602i	−1.15686	+	0.667914i	−0.950550	−	0.310572i	$-0.899479\pi$
$571$	−27.6439	+	15.9602i	−1.15686	+	0.667914i	−0.206311	+	0.978486i	$0.566146\pi$
$572$	−0.443833	−	0.281116i	−0.0185576	−	0.0117540i
$573$	−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
$576$	−5.70964	−	23.3109i	−0.237901	−	0.971289i
$577$	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	$0.112258\pi$
$578$	6.25081	−	21.5509i	0.260000	−	0.896401i
$579$	−12.1767	+	34.2067i	−0.506048	+	1.42158i
$580$	16.8788	−	8.84299i	0.700853	−	0.367185i
$581$		−	9.11777i		−	0.378269i
$582$	−10.4722	−	7.54425i	−0.434087	−	0.312719i
$583$	0.903565	+	0.521674i	0.0374218	+	0.0216055i
$584$	39.1853	+	13.1296i	1.62150	+	0.543307i
$585$	12.8944	+	2.08589i	0.533117	+	0.0862409i
$586$	−2.78529	−	11.3181i	−0.115059	−	0.467546i
$587$	−7.64917			−0.315715			−0.157857	−	0.987462i	$-0.550459\pi$
$587$	−7.64917			−0.315715			−0.157857	+	0.987462i	$0.550459\pi$
$588$	5.90117	−	4.61981i	0.243360	−	0.190518i
$589$	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
$592$	10.9033	−	15.7471i	0.448125	−	0.647202i
$593$			17.5137i			0.719200i	0.933107	+	0.359600i	$0.117087\pi$
$593$			17.5137i			0.719200i	−0.933107	+	0.359600i	$0.882913\pi$
$594$	0.200240	+	0.745133i	0.00821596	+	0.0305732i
$595$	4.85656	+	2.80394i	0.199100	+	0.114950i
$596$	3.46257	−	5.46680i	0.141833	−	0.223929i
$597$	−10.3473	+	8.80793i	−0.423485	+	0.360484i
$598$	−1.73974	+	5.99811i	−0.0711433	+	0.245281i
$599$	−13.7906	−	23.8860i	−0.563469	−	0.975957i	−0.997190	−	0.0749098i	$-0.976133\pi$
$599$	−13.7906	−	23.8860i	−0.563469	−	0.975957i	0.433721	−	0.901047i	$-0.357200\pi$
$600$	3.59910	+	8.96147i	0.146933	+	0.365850i
$601$	−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	$0.947332\pi$
$602$	−0.978467	+	3.37346i	−0.0398793	+	0.137492i
$603$	23.5284	−	28.8600i	0.958151	−	1.17527i
$604$	−8.02522	−	0.329261i	−0.326542	−	0.0133974i
$605$			19.1244i			0.777517i
$606$	−10.4014	+	14.4383i	−0.422530	+	0.586516i
$607$	−20.8450	+	12.0349i	−0.846072	+	0.488480i	−0.859323	−	0.511432i	$-0.829115\pi$
$607$	−20.8450	+	12.0349i	−0.846072	+	0.488480i	0.0132518	+	0.999912i	$0.495782\pi$
$608$	5.97145	+	37.1712i	0.242174	+	1.50749i
$609$	−9.62611	+	27.0415i	−0.390069	+	1.09578i
$610$	18.0732	+	5.24212i	0.731764	+	0.212247i
$611$	1.97374	+	3.41861i	0.0798488	+	0.138302i
$612$	−1.27754	+	6.25782i	−0.0516414	+	0.252957i
$613$	−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	$0.286013\pi$
$614$	0.100712	+	0.409246i	0.00406441	+	0.0165158i
$615$	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	$0.399736\pi$
$618$	6.11450	+	0.617769i	0.245961	+	0.0248503i
$619$		−	6.23686i		−	0.250681i	−0.992114	−	0.125340i	$-0.959998\pi$
$619$		−	6.23686i		−	0.250681i	0.992114	−	0.125340i	$-0.0400023\pi$
$620$	16.4129	−	10.3044i	0.659156	−	0.413835i
$621$	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
$624$	−10.1163	−	14.0748i	−0.404974	−	0.563444i
$625$	5.62889	+	9.74952i	0.225155	+	0.389981i
$626$	−33.0080	+	8.12299i	−1.31926	+	0.324660i
$627$	−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
$630$	20.1965	+	9.57433i	0.804647	+	0.381450i
$631$	28.4535	−	16.4277i	1.13272	−	0.653975i	0.188100	−	0.982150i	$-0.439767\pi$
$631$	28.4535	−	16.4277i	1.13272	−	0.653975i	0.944617	+	0.328175i	$0.106434\pi$
$632$	−28.8320	+	5.85328i	−1.14687	+	0.232831i
$633$	−12.1414	−	4.32205i	−0.482578	−	0.171786i
$634$	1.89536	+	7.70184i	0.0752742	+	0.305879i
$635$	29.8195			1.18335
$636$	21.2191	+	27.1045i	0.841392	+	1.07476i
$637$	2.70630	−	4.68745i	0.107227	−	0.185723i
$638$	0.780729	+	0.226449i	0.0309094	+	0.00896521i
$639$	35.0749	+	28.5951i	1.38754	+	1.13121i
$640$	−7.76380	+	18.0942i	−0.306891	+	0.715237i
$641$	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	$0.200192\pi$
$642$	30.9519	−	13.9303i	1.22157	−	0.549786i
$643$		−	0.298201i		−	0.0117599i	−0.999983	−	0.00587994i	$-0.998128\pi$
$643$		−	0.298201i		−	0.0117599i	0.999983	−	0.00587994i	$-0.00187165\pi$
$644$	−5.71823	+	9.02808i	−0.225330	+	0.355756i
$645$	−2.43254	+	0.446697i	−0.0957813	+	0.0175887i
$646$	2.79092	−	9.62227i	0.109807	−	0.378583i
$647$	6.10709			0.240095			0.120047	−	0.992768i	$-0.461695\pi$
$647$	6.10709			0.240095			0.120047	+	0.992768i	$0.461695\pi$
$648$	−3.05912	+	25.2714i	−0.120174	+	0.992753i
$649$	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	$0.805887\pi$
$654$	−1.27336	−	0.917334i	−0.0497922	−	0.0358706i
$655$			28.8899i			1.12882i
$656$	−27.1256	+	12.8229i	−1.05908	+	0.500649i
$657$	−33.9737	−	27.6974i	−1.32544	−	1.08058i
$658$	1.61412	+	6.55901i	0.0629248	+	0.255697i
$659$	19.1942			0.747698			0.373849	−	0.927490i	$-0.378038\pi$
$659$	19.1942			0.747698			0.373849	+	0.927490i	$0.378038\pi$
$660$	0.236549	−	0.587133i	0.00920765	−	0.0228541i
$661$	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	$0.755871\pi$
$662$	−11.7370	−	3.40429i	−0.456171	−	0.132312i
$663$	0.833119	+	4.53686i	0.0323557	+	0.176197i
$664$	−8.07792	−	2.70662i	−0.313484	−	0.105037i
$665$	−30.3637	−	17.5305i	−1.17746	−	0.679804i
$666$	−16.7149	+	11.5465i	−0.647691	+	0.447418i
$667$		−	9.66339i		−	0.374168i
$668$	37.2176	+	23.5730i	1.43999	+	0.912065i
$669$	34.0333	+	12.1150i	1.31580	+	0.468394i
$670$	−29.6629	+	7.29980i	−1.14598	+	0.282016i
$671$	0.401401	+	0.695248i	0.0154959	+	0.0268397i
$672$	−9.91616	−	27.9528i	−0.382524	−	1.07830i
$673$	−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
$676$	11.3893	+	7.21381i	0.438052	+	0.277454i
$677$	−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	$0.403760\pi$
$678$	16.1919	+	1.63592i	0.621845	+	0.0628271i
$679$	−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
$682$	0.809561	+	0.167706i	0.0309997	+	0.00642178i
$683$	−34.1169			−1.30545			−0.652723	−	0.757597i	$-0.726373\pi$
$683$	−34.1169			−1.30545			−0.652723	+	0.757597i	$0.726373\pi$
$684$	7.98730	−	39.1245i	0.305402	−	1.49596i
$685$	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
$688$	2.69827	+	1.86829i	0.102871	+	0.0712279i
$689$	21.5298	+	12.4302i	0.820219	+	0.473553i
$690$	−7.48656	−	0.756393i	−0.285009	−	0.0287954i
$691$	31.8937	−	18.4138i	1.21329	−	0.700494i	0.249817	−	0.968293i	$-0.419630\pi$
$691$	31.8937	−	18.4138i	1.21329	−	0.700494i	0.963475	+	0.267799i	$0.0862962\pi$
$692$	−23.1578	−	44.2017i	−0.880328	−	1.68030i
$693$	0.338772	+	0.891308i	0.0128689	+	0.0338580i
$694$	−14.3846	+	3.53992i	−0.546030	+	0.134373i
$695$	2.06324	+	3.57363i	0.0782631	+	0.135556i
$696$	21.0999	+	16.5556i	0.799791	+	0.627537i
$697$	7.98460			0.302438
$698$	7.97847	+	8.31252i	0.301990	+	0.314634i
$699$	−4.42377	−	24.0902i	−0.167322	−	0.911174i
$700$	5.53855	+	10.5715i	0.209338	+	0.399566i
$701$	−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	$0.935549\pi$
$702$	4.77124	+	17.7547i	0.180079	+	0.670108i
$703$	27.5983	−	15.9339i	1.04089	−	0.600957i
$704$	−0.773480	+	0.327554i	−0.0291516	+	0.0123451i
$705$	−3.62167	+	3.08288i	−0.136400	+	0.116108i
$706$	9.87184	+	40.1145i	0.371532	+	1.50973i
$707$	−10.9955	+	19.0449i	−0.413530	+	0.716255i
$708$	29.5360	+	11.8997i	1.11003	+	0.447218i
$709$	−11.9309			−0.448073			−0.224036	−	0.974581i	$-0.571923\pi$
$709$	−11.9309			−0.448073			−0.224036	+	0.974581i	$0.571923\pi$
$710$	−8.87177	−	36.0507i	−0.332952	−	1.35296i
$711$	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
$714$	−0.793420	+	7.85305i	−0.0296930	+	0.293893i
$715$		−	0.457158i		−	0.0170967i
$716$	5.54911	+	3.51471i	0.207380	+	0.131351i
$717$	−2.83606	−	3.33171i	−0.105915	−	0.124425i
$718$	−10.2478	+	35.3314i	−0.382445	+	1.31855i
$719$	−9.23931	+	16.0030i	−0.344568	+	0.596809i	−0.985275	−	0.170976i	$-0.945308\pi$
$719$	−9.23931	+	16.0030i	−0.344568	+	0.596809i	0.640707	+	0.767785i	$0.278641\pi$
$720$	14.4777	−	15.0510i	0.539554	−	0.560917i
$721$	7.59487			0.282848
$722$	−9.96403	+	34.3530i	−0.370823	+	1.27849i
$723$	16.6317	−	46.7213i	0.618538	−	1.73758i
$724$	−22.0161	+	11.5345i	−0.818222	+	0.428676i
$725$	−9.34596	−	5.39589i	−0.347100	−	0.200398i
$726$	−24.5460	+	11.0472i	−0.910986	+	0.410002i
$727$	−17.8837	−	10.3251i	−0.663268	−	0.382938i	0.130253	−	0.991481i	$-0.458421\pi$
$727$	−17.8837	−	10.3251i	−0.663268	−	0.382938i	−0.793521	+	0.608543i	$0.791754\pi$
$728$	−14.1870	−	16.0491i	−0.525804	−	0.594819i
$729$	12.4952	−	23.9347i	0.462785	−	0.886470i
$730$	8.59325	+	34.9189i	0.318051	+	1.29241i
$731$	−0.436696	−	0.756380i	−0.0161518	−	0.0279757i
$732$	3.71185	+	26.2249i	0.137194	+	0.969302i
$733$	−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	$0.974676\pi$
$734$	−13.2255	−	3.83603i	−0.488161	−	0.141590i
$735$	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
$738$	31.7196	−	2.57232i	1.16762	−	0.0946885i
$739$	39.0165	−	22.5262i	1.43525	−	0.828640i	0.437732	−	0.899106i	$-0.355782\pi$
$739$	39.0165	−	22.5262i	1.43525	−	0.828640i	0.997514	+	0.0704662i	$0.0224487\pi$
$740$	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	$-0.303514\pi$
$743$	31.5549			1.15764			0.578819	+	0.815456i	$0.303514\pi$
$744$	22.7065	+	15.1134i	0.832461	+	0.554083i
$745$	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
$750$	−17.3707	+	24.1124i	−0.634290	+	0.880462i
$751$	9.12874	+	5.27048i	0.333112	+	0.192323i	0.657222	−	0.753697i	$-0.271731\pi$
$751$	9.12874	+	5.27048i	0.333112	+	0.192323i	−0.324110	+	0.946020i	$0.605065\pi$
$752$	6.29013	+	0.517017i	0.229377	+	0.0188537i
$753$	7.00945	−	19.6908i	0.255438	−	0.717573i
$754$	18.6029	+	5.39573i	0.677477	+	0.196501i
$755$	−3.49456	−	6.05276i	−0.127180	−	0.220283i
$756$	−0.621999	+	31.4526i	−0.0226219	+	1.14392i
$757$	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	$0.793597\pi$
$758$	5.00081	+	20.3209i	0.181638	+	0.738090i
$759$	−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	$0.660853\pi$
$762$	17.2253	+	38.2730i	0.624007	+	1.38648i
$763$	−1.67962	−	0.969730i	−0.0608064	−	0.0351066i
$764$	−0.768040	+	0.402385i	−0.0277867	+	0.0145578i
$765$	−5.19504	+	1.97455i	−0.187827	+	0.0713901i
$766$	10.6240	−	36.6285i	0.383862	−	1.32344i
$767$	22.9975			0.830393
$768$	−27.7085	+	0.487419i	−0.999845	+	0.0175882i
$769$	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	$0.0431125\pi$
$770$	0.217913	−	0.751299i	0.00785304	−	0.0270749i
$771$	−24.6681	+	20.9983i	−0.888401	+	0.756236i
$772$	35.4195	+	22.4341i	1.27477	+	0.807419i
$773$			30.3010i			1.08985i	0.838484	+	0.544926i	$0.183442\pi$
$773$			30.3010i			1.08985i	−0.838484	+	0.544926i	$0.816558\pi$
$774$	−1.97849	−	2.86411i	−0.0711155	−	0.102948i
$775$	−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
$778$	−7.67196	−	31.1752i	−0.275053	−	1.11769i
$779$	−49.9206			−1.78859
$780$	5.63639	−	13.9900i	0.201815	−	0.500921i
$781$	0.791925	−	1.37165i	0.0283373	−	0.0490816i
$782$	−0.634986	−	2.58028i	−0.0227070	−	0.0922707i
$783$	−14.7431	−	24.3279i	−0.526875	−	0.869409i
$784$	−3.69844	−	7.82370i	−0.132087	−	0.279418i
$785$	−2.32345	+	1.34145i	−0.0829276	+	0.0478782i
$786$	−37.0798	+	16.6883i	−1.32259	+	0.595252i
$787$	32.5190	+	18.7748i	1.15918	+	0.669250i	0.951106	−	0.308864i	$-0.0999487\pi$
$787$	32.5190	+	18.7748i	1.15918	+	0.669250i	0.208069	+	0.978114i	$0.433282\pi$
$788$	10.8576	+	20.7240i	0.386785	+	0.738264i
$789$	26.0249	−	4.77905i	0.926511	−	0.170139i
$790$	−17.7272	−	18.4694i	−0.630706	−	0.657113i
$791$	20.1120			0.715102
$792$	0.890222	−	0.0355505i	0.0316326	−	0.00126323i
$793$	9.56442	+	16.5661i	0.339643	+	0.588278i
$794$	10.7486	−	2.64514i	0.381453	−	0.0938724i
$795$	−10.0451	+	28.2185i	−0.356263	+	1.00081i
$796$	7.28165	+	13.8986i	0.258091	+	0.492623i
$797$	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	$0.213421\pi$
$798$	4.96055	−	49.0981i	0.175601	−	1.73805i
$799$	−1.45456	−	0.839788i	−0.0514585	−	0.0297096i
$800$	11.0100	−	1.76873i	0.389262	−	0.0625339i
$801$	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
$804$	−26.5041	−	33.8553i	−0.934726	−	1.19398i
$805$	−9.29912			−0.327751
$806$	19.2899	+	3.99602i	0.679457	+	0.140754i
$807$	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	$-0.679008\pi$
$810$	−20.0017	+	9.51774i	−0.702788	+	0.334419i
$811$	0.441552	−	0.254930i	0.0155050	−	0.00895181i	−0.492227	−	0.870467i	$-0.663817\pi$
$811$	0.441552	−	0.254930i	0.0155050	−	0.00895181i	0.507732	+	0.861515i	$0.330484\pi$
$812$	28.0002	+	17.7348i	0.982615	+	0.622371i
$813$	−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
$816$	6.72190	+	3.03412i	0.235314	+	0.106215i
$817$	2.73027	+	4.72897i	0.0955201	+	0.165446i
$818$	−2.08909	+	0.514108i	−0.0730435	+	0.0179754i
$819$	8.07212	+	21.2377i	0.282063	+	0.742105i
$820$	−22.0561	−	13.9700i	−0.770234	−	0.487852i
$821$		−	21.6746i		−	0.756449i	−0.925714	−	0.378224i	$-0.876535\pi$
$821$		−	21.6746i		−	0.756449i	0.925714	−	0.378224i	$-0.123465\pi$
$822$	37.8151	+	3.82059i	1.31895	+	0.133258i
$823$	28.0907	+	16.2182i	0.979179	+	0.565329i	0.902022	−	0.431690i	$-0.142082\pi$
$823$	28.0907	+	16.2182i	0.979179	+	0.565329i	0.0771569	+	0.997019i	$0.475416\pi$
$824$	2.25454	−	6.72869i	0.0785407	−	0.234405i
$825$	−0.352600	+	0.0647492i	−0.0122760	+	0.00225428i
$826$	37.7945	+	10.9622i	1.31504	+	0.381424i
$827$	3.47956	+	6.02677i	0.120996	+	0.209571i	0.920161	−	0.391541i	$-0.128058\pi$
$827$	3.47956	+	6.02677i	0.120996	+	0.209571i	−0.799165	+	0.601112i	$0.794724\pi$
$828$	−3.35381	−	10.0459i	−0.116553	−	0.349118i
$829$	−2.74093			−0.0951965			−0.0475982	−	0.998867i	$-0.515157\pi$
$829$	−2.74093			−0.0951965			−0.0475982	+	0.998867i	$0.515157\pi$
$830$	−1.77147	−	7.19841i	−0.0614886	−	0.249861i
$831$	−42.4930	+	7.80314i	−1.47407	+	0.270688i
$832$	−18.4302	+	7.80481i	−0.638951	+	0.270583i
$833$			2.30296i			0.0797928i
$834$	−3.39489	+	4.71246i	−0.117555	+	0.163179i
$835$			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	$-0.669352\pi$
$839$	−29.3877			−1.01457			−0.507287	+	0.861777i	$0.669352\pi$
$840$	15.9315	−	20.3046i	0.549689	−	0.700574i
$841$	−0.970596			−0.0334688
$842$	−5.26277	+	18.1444i	−0.181367	+	0.625299i
$843$	2.86398	+	15.5961i	0.0986406	+	0.537160i
$844$	−7.96281	+	12.5719i	−0.274091	+	0.432742i
$845$			11.7313i			0.403568i
$846$	−6.04891	−	2.86754i	−0.207966	−	0.0985881i
$847$	−28.8083	+	16.6325i	−0.989865	+	0.571499i
$848$	35.9348	−	16.9872i	1.23401	−	0.583342i
$849$	6.04367	+	32.9116i	0.207418	+	1.12952i
$850$	−2.85009	−	0.826664i	−0.0977573	−	0.0283543i
$851$	4.22609	−	7.31980i	0.144868	−	0.250920i
$852$	41.1459	−	32.2116i	1.40963	−	1.10355i
$853$	29.0315			0.994020			0.497010	−	0.867745i	$-0.334431\pi$
$853$	29.0315			0.994020			0.497010	+	0.867745i	$0.334431\pi$
$854$	7.82176	+	31.7839i	0.267655	+	1.08762i
$855$	32.4799	−	12.3451i	1.11079	−	0.422194i
$856$	−7.79765	−	38.4095i	−0.266518	−	1.31281i
$857$	−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	$0.665964\pi$
$858$	0.586757	−	0.264078i	0.0200316	−	0.00901548i
$859$	20.2493	−	11.6909i	0.690897	−	0.398890i	−0.113051	−	0.993589i	$-0.536062\pi$
$859$	20.2493	−	11.6909i	0.690897	−	0.398890i	0.803948	+	0.594700i	$0.202729\pi$
$860$	−0.117071	+	2.85343i	−0.00399209	+	0.0973010i
$861$	38.6815	−	7.10323i	1.31826	−	0.242077i
$862$	6.11640	−	1.50519i	0.208325	−	0.0512671i
$863$	−1.54349	−	2.67340i	−0.0525409	−	0.0910035i	0.838559	−	0.544811i	$-0.183399\pi$
$863$	−1.54349	−	2.67340i	−0.0525409	−	0.0910035i	−0.891100	+	0.453808i	$0.850065\pi$
$864$	27.6809	+	9.88780i	0.941723	+	0.336390i
$865$	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
$868$	29.7964	+	15.7620i	1.01136	+	0.534997i
$869$		−	1.09214i		−	0.0370482i
$870$	−2.34592	+	23.2193i	−0.0795342	+	0.787207i
$871$	−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
$874$	3.97000	+	16.1322i	0.134287	+	0.545680i
$875$	−18.3629	+	31.8055i	−0.620780	+	1.07522i
$876$	−39.8542	+	31.2003i	−1.34655	+	1.05416i
$877$	−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	$0.859688\pi$
$878$	−5.89577	−	1.71006i	−0.198973	−	0.0577117i
$879$	13.4487	+	4.78740i	0.453612	+	0.161475i
$880$	−0.600928	−	0.416084i	−0.0202573	−	0.0140262i
$881$	−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	$0.458299\pi$
$882$	0.741922	+	9.14873i	0.0249818	+	0.308054i
$883$			12.9691i			0.436444i	0.975899	+	0.218222i	$0.0700257\pi$
$883$			12.9691i			0.436444i	−0.975899	+	0.218222i	$0.929974\pi$
$884$	5.32183	+	0.218346i	0.178992	+	0.00734375i
$885$	5.00455	+	27.2529i	0.168226	+	0.916097i
$886$	9.91555	−	34.1858i	0.333119	−	1.14850i
$887$	9.35908	−	16.2104i	0.314247	−	0.544292i	−0.665030	−	0.746817i	$-0.731581\pi$
$887$	9.35908	−	16.2104i	0.314247	−	0.544292i	0.979277	+	0.202524i	$0.0649146\pi$
$888$	8.74250	+	21.7681i	0.293379	+	0.730490i
$889$	25.9340	+	44.9190i	0.869798	+	1.50654i
$890$	3.74145	−	12.8994i	0.125414	−	0.432389i
$891$	−0.896779	−	0.297936i	−0.0300432	−	0.00998123i
$892$	22.3203	−	35.2399i	0.747340	−	1.17992i
$893$	9.09404	+	5.25044i	0.304320	+	0.175699i
$894$	3.25272	+	7.22723i	0.108787	+	0.241715i
$895$			5.71571i			0.191055i
$896$	−34.0087	+	4.04144i	−1.13615	+	0.135015i
$897$	−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
$900$	−11.5886	−	2.36582i	−0.386286	−	0.0788606i
$901$	−10.5777			−0.352393
$902$	−0.266156	−	1.08153i	−0.00886204	−	0.0360111i
$903$	−2.78847	−	3.27580i	−0.0927945	−	0.109012i
$904$	5.97028	−	17.8183i	0.198569	−	0.592629i
$905$	−18.7300	−	10.8138i	−0.622607	−	0.359463i
$906$	5.75001	−	7.98162i	0.191031	−	0.265172i
$907$			23.5720i			0.782696i	0.920243	+	0.391348i	$0.127991\pi$
$907$			23.5720i			0.782696i	−0.920243	+	0.391348i	$0.872009\pi$
$908$	−21.6476	+	11.3414i	−0.718401	+	0.376379i
$909$	−7.74314	−	20.3722i	−0.256824	−	0.675703i
$910$	5.19234	−	17.9016i	0.172124	−	0.593433i
$911$	11.8822	−	20.5805i	0.393674	−	0.681864i	−0.599257	−	0.800557i	$-0.704537\pi$
$911$	11.8822	−	20.5805i	0.393674	−	0.681864i	0.992931	+	0.118693i	$0.0378704\pi$
$912$	−42.0260	−	18.9696i	−1.39162	−	0.628147i
$913$	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
$916$	−36.5438	−	23.1462i	−1.20744	−	0.764770i
$917$	−43.5187	+	25.1255i	−1.43711	+	0.829717i
$918$	−5.53524	−	5.52718i	−0.182690	−	0.182424i
$919$	−37.6711	+	21.7494i	−1.24266	+	0.717448i	−0.969634	−	0.244560i	$-0.921357\pi$
$919$	−37.6711	+	21.7494i	−1.24266	+	0.717448i	−0.273022	+	0.962008i	$0.588023\pi$
$920$	−2.76045	+	8.23858i	−0.0910094	+	0.271618i
$921$	−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
$924$	1.09016	−	0.154300i	0.0358637	−	0.00507611i
$925$	−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	$0.809814\pi$
$930$	−0.537711	+	23.7288i	−0.0176323	+	0.778097i
$931$		−	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
$936$	21.2118	−	0.847083i	0.693330	−	0.0276878i
$937$	−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
$940$	2.54867	+	4.86469i	0.0831283	+	0.158669i
$941$	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	$0.109355\pi$
$942$	−3.06388	−	2.20724i	−0.0998265	−	0.0719156i
$943$	−11.4664	+	6.62013i	−0.373398	+	0.215581i
$944$	20.9313	−	30.2300i	0.681257	−	0.983902i
$945$	−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	$0.502335\pi$
$947$	−26.7627	+	46.3543i	−0.869670	+	1.50631i	−0.862335	+	0.506339i	$0.830999\pi$
$948$	13.4652	−	33.4216i	0.437328	−	1.08548i
$949$	−18.2773	+	31.6571i	−0.593305	+	1.02763i
$950$	17.8191	+	5.16839i	0.578127	+	0.167685i
$951$	−9.15166	−	3.25777i	−0.296763	−	0.105640i
$952$	8.64188	+	2.89558i	0.280085	+	0.0938464i
$953$			19.3680i			0.627391i	0.949524	+	0.313696i	$0.101567\pi$
$953$			19.3680i			0.627391i	−0.949524	+	0.313696i	$0.898433\pi$
$954$	−42.0207	+	3.40770i	−1.36047	+	0.110328i
$955$	−0.653405	−	0.377243i	−0.0211437	−	0.0122073i
$956$	−4.47521	+	2.34461i	−0.144739	+	0.0758302i
$957$	−0.758128	+	0.645343i	−0.0245068	+	0.0208610i
$958$	−32.3936	+	7.97179i	−1.04659	+	0.257557i
$959$	46.9704			1.51675
$960$	−13.2596	−	20.1420i	−0.427952	−	0.650080i
$961$	−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
$964$	−48.3778	−	30.6416i	−1.55814	−	0.986901i
$965$			36.4828i			1.17442i
$966$	−5.37166	−	11.9353i	−0.172830	−	0.384013i
$967$	−2.37692	−	1.37232i	−0.0764366	−	0.0441307i	0.461295	−	0.887247i	$-0.347385\pi$
$967$	−2.37692	−	1.37232i	−0.0764366	−	0.0441307i	−0.537731	+	0.843116i	$0.680718\pi$
$968$	6.18382	+	30.4602i	0.198756	+	0.979026i
$969$	7.95368	+	9.34372i	0.255509	+	0.300164i
$970$	−12.4550	−	3.61256i	−0.399907	−	0.115992i
$971$	3.34005	+	5.78514i	0.107187	+	0.185654i	0.914630	−	0.404292i	$-0.132482\pi$
$971$	3.34005	+	5.78514i	0.107187	+	0.185654i	−0.807442	+	0.589946i	$0.799149\pi$
$972$	−23.7699	−	20.1740i	−0.762421	−	0.647081i
$973$	−3.58879	+	6.21597i	−0.115051	+	0.199275i
$974$	−27.1573	−	7.87694i	−0.870177	−	0.252393i
$975$	−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	$-0.0672630\pi$
$978$	11.6634	−	16.1900i	0.372954	−	0.517700i
$979$	0.496218	−	0.286492i	0.0158592	−	0.00915632i
$980$	4.02929	−	6.36155i	0.128711	−	0.203212i
$981$	1.79668	−	0.682891i	0.0573637	−	0.0218030i
$982$	−1.71443	+	5.91083i	−0.0547095	+	0.188622i
$983$	21.1039	+	36.5529i	0.673108	+	1.16586i	0.977018	+	0.213157i	$0.0683746\pi$
$983$	21.1039	+	36.5529i	0.673108	+	1.16586i	−0.303910	+	0.952701i	$0.598292\pi$
$984$	5.18952	−	36.3786i	0.165436	−	1.15971i
$985$	−10.1792	+	17.6308i	−0.324335	+	0.561765i
$986$	−8.00264	+	1.96938i	−0.254856	+	0.0627179i
$987$	−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
$990$	0.440628	+	0.637862i	0.0140041	+	0.0202726i
$991$		−	18.8936i		−	0.600174i	−0.953912	−	0.300087i	$-0.902984\pi$
$991$		−	18.8936i		−	0.600174i	0.953912	−	0.300087i	$-0.0970157\pi$
$992$	22.8095	−	21.7193i	0.724202	−	0.689588i
$993$	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
$996$	8.21579	−	6.43184i	0.260327	−	0.203801i
$997$	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	$0.692243\pi$
$998$	−12.8984	−	52.4130i	−0.408291	−	1.65910i
$999$	−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.191.48	yes	120
3.2	odd	2	inner	372.2.p.a.191.13	✓	120
4.3	odd	2	inner	372.2.p.a.191.14	yes	120
12.11	even	2	inner	372.2.p.a.191.47	yes	120
31.25	even	3	inner	372.2.p.a.335.48	yes	120
93.56	odd	6	inner	372.2.p.a.335.13	yes	120
124.87	odd	6	inner	372.2.p.a.335.14	yes	120
372.335	even	6	inner	372.2.p.a.335.47	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
372.2.p.a.191.13	✓	120	3.2	odd	2	inner
372.2.p.a.191.14	yes	120	4.3	odd	2	inner
372.2.p.a.191.47	yes	120	12.11	even	2	inner
372.2.p.a.191.48	yes	120	1.1	even	1	trivial
372.2.p.a.335.13	yes	120	93.56	odd	6	inner
372.2.p.a.335.14	yes	120	124.87	odd	6	inner
372.2.p.a.335.47	yes	120	372.335	even	6	inner
372.2.p.a.335.48	yes	120	31.25	even	3	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} +(-1.98746 - 1.43178i) q^{6} +(-2.62156 - 1.51356i) q^{7} +(-2.11916 + 1.87328i) q^{8} +(2.80427 - 1.06586i) q^{9} +(-2.36377 - 0.685608i) q^{10} +(-0.0524986 - 0.0909303i) q^{11} +(-0.485467 - 3.42992i) q^{12} +(-1.25091 - 2.16665i) q^{13} +(-1.02299 - 4.15697i) q^{14} +(2.29534 - 1.95387i) q^{15} +(-3.98656 - 0.327675i) q^{16} +(0.921869 + 0.532241i) q^{17} +(3.83368 + 1.81739i) q^{18} +(-5.76362 - 3.32763i) q^{19} +(-1.61529 - 3.08314i) q^{20} +(4.93949 + 1.75834i) q^{21} +(0.0413640 - 0.142611i) q^{22} -1.76515 q^{23} +(3.02410 - 3.85419i) q^{24} +(-0.985633 + 1.70717i) q^{25} +(0.985605 - 3.39807i) q^{26} +(-4.44383 + 2.69303i) q^{27} +(3.23951 - 5.11463i) q^{28} +5.47454i q^{29} +(4.24132 + 0.428515i) q^{30} +(0.434039 + 5.55082i) q^{31} +(-3.56967 - 4.38834i) q^{32} +(0.117881 + 0.138482i) q^{33} +(0.359735 + 1.46179i) q^{34} +5.26817 q^{35} +(1.90001 + 5.69122i) q^{36} +(-2.39418 + 4.14684i) q^{37} +(-2.24910 - 9.13927i) q^{38} +(2.80881 + 3.29970i) q^{39} +(1.56386 - 4.66735i) q^{40} +(6.49599 - 3.75046i) q^{41} +(3.04317 + 6.76164i) q^{42} +(-0.710562 - 0.410243i) q^{43} +(0.186012 - 0.0974538i) q^{44} +(-3.29903 + 4.04660i) q^{45} +(-1.72859 - 1.80097i) q^{46} -1.57783 q^{47} +(6.89387 - 0.688907i) q^{48} +(1.08173 + 1.87361i) q^{49} +(-2.70703 + 0.666176i) q^{50} +(-1.73697 - 0.618318i) q^{51} +(4.43221 - 2.32209i) q^{52} +(-8.60561 + 4.96845i) q^{53} +(-7.09946 - 1.89675i) q^{54} +(0.158248 + 0.0913647i) q^{55} +(8.39082 - 1.70345i) q^{56} +(10.8597 + 3.86579i) q^{57} +(-5.58562 + 5.36116i) q^{58} +(-4.59615 + 7.96076i) q^{59} +(3.71626 + 4.74702i) q^{60} -7.64594 q^{61} +(-5.23840 + 5.87870i) q^{62} +(-8.96482 - 1.45022i) q^{63} +(0.981647 - 7.93954i) q^{64} +(3.77067 + 2.17700i) q^{65} +(-0.0258531 + 0.255887i) q^{66} +(10.7490 - 6.20592i) q^{67} +(-1.13917 + 1.79855i) q^{68} +(3.00705 - 0.552196i) q^{69} +(5.15906 + 5.37507i) q^{70} +(7.54234 + 13.0637i) q^{71} +(-3.94604 + 7.51191i) q^{72} +(-7.30556 - 12.6536i) q^{73} +(-6.57558 + 1.61819i) q^{74} +(1.14503 - 3.21661i) q^{75} +(7.12220 - 11.2447i) q^{76} +0.317839i q^{77} +(-0.616018 + 6.09717i) q^{78} +(9.00803 + 5.20079i) q^{79} +(6.29353 - 2.97509i) q^{80} +(6.72789 - 5.97792i) q^{81} +(10.1880 + 2.95502i) q^{82} +(1.50601 + 2.60849i) q^{83} +(-3.91870 + 9.72652i) q^{84} -1.85255 q^{85} +(-0.277278 - 1.12673i) q^{86} +(-1.71261 - 9.32624i) q^{87} +(0.281591 + 0.0943509i) q^{88} +5.45713i q^{89} +(-7.35942 + 0.596817i) 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} +(7.45397 + 6.35911i) q^{96} +5.26914 q^{97} +(-0.852301 + 2.93848i) 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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