LMFDB - Embedded newform 168.2.ba.c.101.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [168,2,Mod(5,168)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(168, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 3, 5]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("168.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 168 = 2^{3} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	168.ba (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$1.34148675396$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.3
Character	$\chi$	$=$	168.101
Dual form			168.2.ba.c.5.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.33258 + 0.473539i) q^{2} +(-1.52791 + 0.815778i) q^{3} +(1.55152 - 1.26205i) q^{4} +(0.461663 - 0.266541i) q^{5} +(1.64975 - 1.81061i) q^{6} +(0.489180 + 2.60014i) q^{7} +(-1.46989 + 2.41649i) q^{8} +(1.66901 - 2.49287i) q^{9} +O(q^{10})$	\(q+(-1.33258 + 0.473539i) q^{2} +(-1.52791 + 0.815778i) q^{3} +(1.55152 - 1.26205i) q^{4} +(0.461663 - 0.266541i) q^{5} +(1.64975 - 1.81061i) q^{6} +(0.489180 + 2.60014i) q^{7} +(-1.46989 + 2.41649i) q^{8} +(1.66901 - 2.49287i) q^{9} +(-0.488984 + 0.573802i) q^{10} +(-2.28733 + 3.96177i) q^{11} +(-1.34103 + 3.19400i) q^{12} -4.97924 q^{13} +(-1.88313 - 3.23323i) q^{14} +(-0.487941 + 0.783866i) q^{15} +(0.814443 - 3.91621i) q^{16} +(-2.16139 + 3.74363i) q^{17} +(-1.04362 + 4.11228i) q^{18} +(0.921087 + 1.59537i) q^{19} +(0.379891 - 0.996188i) q^{20} +(-2.86856 - 3.57371i) q^{21} +(1.17199 - 6.36250i) q^{22} +(0.103387 - 0.0596907i) q^{23} +(0.274542 - 4.89128i) q^{24} +(-2.35791 + 4.08402i) q^{25} +(6.63522 - 2.35786i) q^{26} +(-0.516471 + 5.17042i) q^{27} +(4.04048 + 3.41680i) q^{28} +7.74542 q^{29} +(0.279028 - 1.27562i) q^{30} +(-1.93668 - 1.11814i) q^{31} +(0.769168 + 5.60432i) q^{32} +(0.262906 - 7.91918i) q^{33} +(1.10746 - 6.01218i) q^{34} +(0.918880 + 1.07000i) q^{35} +(-0.556624 - 5.97413i) q^{36} +(7.02261 - 4.05451i) q^{37} +(-1.98289 - 1.68978i) q^{38} +(7.60783 - 4.06195i) q^{39} +(-0.0345007 + 1.50739i) q^{40} +2.60914 q^{41} +(5.51486 + 3.40387i) q^{42} +1.87217i q^{43} +(1.45112 + 9.03351i) q^{44} +(0.106069 - 1.59573i) q^{45} +(-0.109506 + 0.128500i) q^{46} +(-2.91482 - 5.04861i) q^{47} +(1.95036 + 6.64801i) q^{48} +(-6.52141 + 2.54387i) q^{49} +(1.20816 - 6.55884i) q^{50} +(0.248430 - 7.48314i) q^{51} +(-7.72540 + 6.28407i) q^{52} +(2.29287 - 3.97137i) q^{53} +(-1.76016 - 7.13455i) q^{54} +2.43867i q^{55} +(-7.00224 - 2.63982i) q^{56} +(-2.70880 - 1.68618i) q^{57} +(-10.3214 + 3.66775i) q^{58} +(-5.71492 - 3.29951i) q^{59} +(0.232229 + 1.83199i) q^{60} +(1.07564 + 1.86306i) q^{61} +(3.11026 + 0.572919i) q^{62} +(7.29824 + 3.12020i) q^{63} +(-3.67884 - 7.10395i) q^{64} +(-2.29873 + 1.32717i) q^{65} +(3.39970 + 10.6774i) q^{66} +(10.4812 + 6.05131i) q^{67} +(1.37122 + 8.53611i) q^{68} +(-0.109272 + 0.175543i) q^{69} +(-1.73116 - 0.990732i) q^{70} -6.20627i q^{71} +(3.57072 + 7.69740i) q^{72} +(8.35520 + 4.82388i) q^{73} +(-7.43820 + 8.72842i) q^{74} +(0.271018 - 8.16355i) q^{75} +(3.44253 + 1.31279i) q^{76} +(-11.4201 - 4.00935i) q^{77} +(-8.21452 + 9.01547i) q^{78} +(-0.0228792 - 0.0396280i) q^{79} +(-0.667833 - 2.02505i) q^{80} +(-3.42880 - 8.32126i) q^{81} +(-3.47688 + 1.23553i) q^{82} +3.86459i q^{83} +(-8.96084 - 1.92442i) q^{84} +2.30440i q^{85} +(-0.886545 - 2.49481i) q^{86} +(-11.8343 + 6.31854i) q^{87} +(-6.21145 - 11.3507i) q^{88} +(8.23362 + 14.2610i) q^{89} +(0.614293 + 2.17666i) q^{90} +(-2.43575 - 12.9467i) q^{91} +(0.0850749 - 0.223092i) q^{92} +(3.87123 + 0.128520i) q^{93} +(6.27493 + 5.34738i) q^{94} +(0.850463 + 0.491015i) q^{95} +(-5.74710 - 7.93542i) q^{96} -7.18828i q^{97} +(7.48565 - 6.47804i) q^{98} +(6.05860 + 12.3143i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 6 q^{4} - 4 q^{7} - 14 q^{9}+O(q^{10}) $ 48 * q + 6 * q^4 - 4 * q^7 - 14 * q^9	$ 48 q + 6 q^{4} - 4 q^{7} - 14 q^{9} - 30 q^{10} - 18 q^{12} + 4 q^{15} + 6 q^{16} - 36 q^{22} - 12 q^{24} - 8 q^{25} - 10 q^{28} + 22 q^{30} + 48 q^{31} - 42 q^{33} + 52 q^{36} - 8 q^{39} - 18 q^{40} + 12 q^{42} - 8 q^{46} - 36 q^{49} - 48 q^{52} + 60 q^{54} + 4 q^{57} + 30 q^{58} - 32 q^{60} - 6 q^{63} - 60 q^{64} + 54 q^{66} + 42 q^{70} + 42 q^{72} - 36 q^{73} - 68 q^{78} - 56 q^{79} + 42 q^{81} + 48 q^{82} + 48 q^{84} - 132 q^{87} + 6 q^{88} + 48 q^{94} + 90 q^{96}+O(q^{100}) $ 48 * q + 6 * q^4 - 4 * q^7 - 14 * q^9 - 30 * q^10 - 18 * q^12 + 4 * q^15 + 6 * q^16 - 36 * q^22 - 12 * q^24 - 8 * q^25 - 10 * q^28 + 22 * q^30 + 48 * q^31 - 42 * q^33 + 52 * q^36 - 8 * q^39 - 18 * q^40 + 12 * q^42 - 8 * q^46 - 36 * q^49 - 48 * q^52 + 60 * q^54 + 4 * q^57 + 30 * q^58 - 32 * q^60 - 6 * q^63 - 60 * q^64 + 54 * q^66 + 42 * q^70 + 42 * q^72 - 36 * q^73 - 68 * q^78 - 56 * q^79 + 42 * q^81 + 48 * q^82 + 48 * q^84 - 132 * q^87 + 6 * q^88 + 48 * q^94 + 90 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/168\mathbb{Z}\right)^\times$.

$n$	$73$	$85$	$113$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−1.33258	+	0.473539i	−0.942274	+	0.334842i
$2$	−1.33258	+	0.473539i	−0.942274	+	0.334842i
$3$	−1.52791	+	0.815778i	−0.882139	+	0.470990i
$3$	−1.52791	+	0.815778i	−0.882139	+	0.470990i
$4$	1.55152	−	1.26205i	0.775761	−	0.631027i
$5$	0.461663	−	0.266541i	0.206462	−	0.119201i	−0.393204	−	0.919451i	$-0.628633\pi$
$5$	0.461663	−	0.266541i	0.206462	−	0.119201i	0.599666	+	0.800250i	$0.295300\pi$
$6$	1.64975	−	1.81061i	0.673509	−	0.739179i
$7$	0.489180	+	2.60014i	0.184893	+	0.982759i
$7$	0.489180	+	2.60014i	0.184893	+	0.982759i
$8$	−1.46989	+	2.41649i	−0.519685	+	0.854358i
$9$	1.66901	−	2.49287i	0.556337	−	0.830956i
$10$	−0.488984	+	0.573802i	−0.154630	+	0.181452i
$11$	−2.28733	+	3.96177i	−0.689656	+	1.19452i	0.282293	+	0.959328i	$0.408905\pi$
$11$	−2.28733	+	3.96177i	−0.689656	+	1.19452i	−0.971949	+	0.235191i	$0.924428\pi$
$12$	−1.34103	+	3.19400i	−0.387122	+	0.922029i
$13$	−4.97924			−1.38099			−0.690496	−	0.723336i	$-0.742608\pi$
$13$	−4.97924			−1.38099			−0.690496	+	0.723336i	$0.742608\pi$
$14$	−1.88313	−	3.23323i	−0.503289	−	0.864118i
$15$	−0.487941	+	0.783866i	−0.125986	+	0.202393i
$16$	0.814443	−	3.91621i	0.203611	−	0.979052i
$17$	−2.16139	+	3.74363i	−0.524213	+	0.907964i	0.475389	+	0.879775i	$0.342307\pi$
$17$	−2.16139	+	3.74363i	−0.524213	+	0.907964i	−0.999603	+	0.0281884i	$0.991026\pi$
$18$	−1.04362	+	4.11228i	−0.245983	+	0.969274i
$19$	0.921087	+	1.59537i	0.211312	+	0.366003i	0.952125	−	0.305708i	$-0.0988931\pi$
$19$	0.921087	+	1.59537i	0.211312	+	0.366003i	−0.740814	+	0.671711i	$0.765560\pi$
$20$	0.379891	−	0.996188i	0.0849463	−	0.222754i
$21$	−2.86856	−	3.57371i	−0.625970	−	0.779847i
$22$	1.17199	−	6.36250i	0.249869	−	1.35649i
$23$	0.103387	−	0.0596907i	0.0215577	−	0.0124464i	−0.489182	−	0.872182i	$-0.662705\pi$
$23$	0.103387	−	0.0596907i	0.0215577	−	0.0124464i	0.510740	+	0.859735i	$0.329371\pi$
$24$	0.274542	−	4.89128i	0.0560407	−	0.998428i
$25$	−2.35791	+	4.08402i	−0.471582	+	0.816804i
$26$	6.63522	−	2.35786i	1.30127	−	0.462415i
$27$	−0.516471	+	5.17042i	−0.0993949	+	0.995048i
$28$	4.04048	+	3.41680i	0.763580	+	0.645714i
$29$	7.74542			1.43829			0.719144	−	0.694861i	$-0.244534\pi$
$29$	7.74542			1.43829			0.719144	+	0.694861i	$0.244534\pi$
$30$	0.279028	−	1.27562i	0.0509433	−	0.232895i
$31$	−1.93668	−	1.11814i	−0.347838	−	0.200825i	0.315894	−	0.948794i	$-0.397695\pi$
$31$	−1.93668	−	1.11814i	−0.347838	−	0.200825i	−0.663733	+	0.747970i	$0.731029\pi$
$32$	0.769168	+	5.60432i	0.135971	+	0.990713i
$33$	0.262906	−	7.91918i	0.0457660	−	1.37855i
$34$	1.10746	−	6.01218i	0.189928	−	1.03108i
$35$	0.918880	+	1.07000i	0.155319	+	0.180863i
$36$	−0.556624	−	5.97413i	−0.0927707	−	0.995688i
$37$	7.02261	−	4.05451i	1.15451	−	0.666557i	0.204528	−	0.978861i	$-0.434434\pi$
$37$	7.02261	−	4.05451i	1.15451	−	0.666557i	0.949982	+	0.312304i	$0.101101\pi$
$38$	−1.98289	−	1.68978i	−0.321667	−	0.274119i
$39$	7.60783	−	4.06195i	1.21823	−	0.650433i
$40$	−0.0345007	+	1.50739i	−0.00545504	+	0.238339i
$41$	2.60914			0.407479			0.203740	−	0.979025i	$-0.434690\pi$
$41$	2.60914			0.407479			0.203740	+	0.979025i	$0.434690\pi$
$42$	5.51486	+	3.40387i	0.850961	+	0.525228i
$43$			1.87217i			0.285503i	0.989759	+	0.142752i	$0.0455950\pi$
$43$			1.87217i			0.285503i	−0.989759	+	0.142752i	$0.954405\pi$
$44$	1.45112	+	9.03351i	0.218765	+	1.36185i
$45$	0.106069	−	1.59573i	0.0158118	−	0.237877i
$46$	−0.109506	+	0.128500i	−0.0161457	+	0.0189463i
$47$	−2.91482	−	5.04861i	−0.425170	−	0.736415i	0.571267	−	0.820764i	$-0.306452\pi$
$47$	−2.91482	−	5.04861i	−0.425170	−	0.736415i	−0.996436	+	0.0843492i	$0.973119\pi$
$48$	1.95036	+	6.64801i	0.281510	+	0.959558i
$49$	−6.52141	+	2.54387i	−0.931629	+	0.363410i
$50$	1.20816	−	6.55884i	0.170859	−	0.927559i
$51$	0.248430	−	7.48314i	0.0347871	−	1.04785i
$52$	−7.72540	+	6.28407i	−1.07132	+	0.871443i
$53$	2.29287	−	3.97137i	0.314950	−	0.545510i	−0.664476	−	0.747309i	$-0.731345\pi$
$53$	2.29287	−	3.97137i	0.314950	−	0.545510i	0.979427	+	0.201799i	$0.0646788\pi$
$54$	−1.76016	−	7.13455i	−0.239527	−	0.970890i
$55$			2.43867i			0.328830i
$56$	−7.00224	−	2.63982i	−0.935714	−	0.352761i
$57$	−2.70880	−	1.68618i	−0.358790	−	0.223339i
$58$	−10.3214	+	3.66775i	−1.35526	+	0.481600i
$59$	−5.71492	−	3.29951i	−0.744019	−	0.429559i	0.0795100	−	0.996834i	$-0.474664\pi$
$59$	−5.71492	−	3.29951i	−0.744019	−	0.429559i	−0.823529	+	0.567275i	$0.807998\pi$
$60$	0.232229	+	1.83199i	0.0299807	+	0.236509i
$61$	1.07564	+	1.86306i	0.137722	+	0.238541i	0.926634	−	0.375965i	$-0.122689\pi$
$61$	1.07564	+	1.86306i	0.137722	+	0.238541i	−0.788912	+	0.614506i	$0.789355\pi$
$62$	3.11026	+	0.572919i	0.395004	+	0.0727608i
$63$	7.29824	+	3.12020i	0.919492	+	0.393108i
$64$	−3.67884	−	7.10395i	−0.459855	−	0.887994i
$65$	−2.29873	+	1.32717i	−0.285123	+	0.164616i
$66$	3.39970	+	10.6774i	0.418474	+	1.31430i
$67$	10.4812	+	6.05131i	1.28048	+	0.739285i	0.976936	−	0.213532i	$-0.0684968\pi$
$67$	10.4812	+	6.05131i	1.28048	+	0.739285i	0.303544	+	0.952817i	$0.401830\pi$
$68$	1.37122	+	8.53611i	0.166285	+	1.03516i
$69$	−0.109272	+	0.175543i	−0.0131548	+	0.0211329i
$70$	−1.73116	−	0.990732i	−0.206914	−	0.118415i
$71$		−	6.20627i		−	0.736549i	−0.929717	−	0.368275i	$-0.879949\pi$
$71$		−	6.20627i		−	0.736549i	0.929717	−	0.368275i	$-0.120051\pi$
$72$	3.57072	+	7.69740i	0.420814	+	0.907147i
$73$	8.35520	+	4.82388i	0.977902	+	0.564592i	0.901636	−	0.432496i	$-0.142367\pi$
$73$	8.35520	+	4.82388i	0.977902	+	0.564592i	0.0762659	+	0.997088i	$0.475700\pi$
$74$	−7.43820	+	8.72842i	−0.864673	+	1.01466i
$75$	0.271018	−	8.16355i	0.0312945	−	0.942645i
$76$	3.44253	+	1.31279i	0.394885	+	0.150587i
$77$	−11.4201	−	4.00935i	−1.30144	−	0.456908i
$78$	−8.21452	+	9.01547i	−0.930111	+	1.02080i
$79$	−0.0228792	−	0.0396280i	−0.00257411	−	0.00445849i	0.864735	−	0.502228i	$-0.167486\pi$
$79$	−0.0228792	−	0.0396280i	−0.00257411	−	0.00445849i	−0.867310	+	0.497769i	$0.834153\pi$
$80$	−0.667833	−	2.02505i	−0.0746660	−	0.226408i
$81$	−3.42880	−	8.32126i	−0.380977	−	0.924584i
$82$	−3.47688	+	1.23553i	−0.383957	+	0.136441i
$83$			3.86459i			0.424194i	0.977249	+	0.212097i	$0.0680292\pi$
$83$			3.86459i			0.424194i	−0.977249	+	0.212097i	$0.931971\pi$
$84$	−8.96084	−	1.92442i	−0.977708	−	0.209971i
$85$			2.30440i			0.249947i
$86$	−0.886545	−	2.49481i	−0.0955986	−	0.269022i
$87$	−11.8343	+	6.31854i	−1.26877	+	0.677419i
$88$	−6.21145	−	11.3507i	−0.662143	−	1.20999i
$89$	8.23362	+	14.2610i	0.872762	+	1.51167i	0.859128	+	0.511761i	$0.171007\pi$
$89$	8.23362	+	14.2610i	0.872762	+	1.51167i	0.0136336	+	0.999907i	$0.495660\pi$
$90$	0.614293	+	2.17666i	0.0647522	+	0.229440i
$91$	−2.43575	−	12.9467i	−0.255335	−	1.35718i
$92$	0.0850749	−	0.223092i	0.00886967	−	0.0232589i
$93$	3.87123	+	0.128520i	0.401428	+	0.0133269i
$94$	6.27493	+	5.34738i	0.647209	+	0.551540i
$95$	0.850463	+	0.491015i	0.0872557	+	0.0503771i
$96$	−5.74710	−	7.93542i	−0.586561	−	0.809905i
$97$		−	7.18828i		−	0.729859i	−0.931035	−	0.364930i	$-0.881093\pi$
$97$		−	7.18828i		−	0.729859i	0.931035	−	0.364930i	$-0.118907\pi$
$98$	7.48565	−	6.47804i	0.756165	−	0.654381i
$99$	6.05860	+	12.3143i	0.608912	+	1.23763i
$100$	1.49590	+	9.31226i	0.149590	+	0.931226i
$101$	−3.33419	−	1.92499i	−0.331764	−	0.191544i	0.324860	−	0.945762i	$-0.394683\pi$
$101$	−3.33419	−	1.92499i	−0.331764	−	0.191544i	−0.656624	+	0.754218i	$0.728016\pi$
$102$	3.21250	+	10.0895i	0.318085	+	0.999009i
$103$	−4.61020	+	2.66170i	−0.454256	+	0.262265i	−0.709626	−	0.704578i	$-0.751136\pi$
$103$	−4.61020	+	2.66170i	−0.454256	+	0.262265i	0.255370	+	0.966843i	$0.417803\pi$
$104$	7.31894	−	12.0323i	0.717682	−	1.17986i
$105$	−2.27685	−	0.885260i	−0.222198	−	0.0863926i
$106$	−1.17483	+	6.37793i	−0.114110	+	0.619479i
$107$	−4.60634	−	7.97842i	−0.445312	−	0.771303i	0.552762	−	0.833339i	$-0.313574\pi$
$107$	−4.60634	−	7.97842i	−0.445312	−	0.771303i	−0.998074	+	0.0620363i	$0.980241\pi$
$108$	5.72403	+	8.67384i	0.550795	+	0.834640i
$109$	4.24194	+	2.44909i	0.406304	+	0.234580i	0.689201	−	0.724571i	$-0.257962\pi$
$109$	4.24194	+	2.44909i	0.406304	+	0.234580i	−0.282896	+	0.959151i	$0.591295\pi$
$110$	−1.15481	−	3.24972i	−0.110106	−	0.309848i
$111$	−7.42233	+	11.9238i	−0.704497	+	1.13176i
$112$	10.5811	+	0.201931i	0.999818	+	0.0190807i
$113$		−	3.87615i		−	0.364637i	−0.983240	−	0.182319i	$-0.941640\pi$
$113$		−	3.87615i		−	0.364637i	0.983240	−	0.182319i	$-0.0583602\pi$
$114$	4.40816	+	0.964236i	0.412862	+	0.0903090i
$115$	0.0318201	−	0.0551140i	0.00296724	−	0.00513941i
$116$	12.0172	−	9.77513i	1.11577	−	0.907598i
$117$	−8.31041	+	12.4126i	−0.768298	+	1.14754i
$118$	9.17801	+	1.69061i	0.844904	+	0.155634i
$119$	−10.7913	−	3.78859i	−0.989233	−	0.347299i
$120$	−1.17698	−	2.33130i	−0.107443	−	0.212818i
$121$	−4.96376	−	8.59748i	−0.451251	−	0.781589i
$122$	−2.31560	−	1.97332i	−0.209645	−	0.178656i
$123$	−3.98653	+	2.12848i	−0.359453	+	0.191918i
$124$	−4.41596	+	0.709371i	−0.396565	+	0.0637034i
$125$			5.17934i			0.463254i
$126$	−11.2030	−	0.701900i	−0.998043	−	0.0625302i
$127$	8.19005			0.726750			0.363375	−	0.931643i	$-0.381624\pi$
$127$	8.19005			0.726750			0.363375	+	0.931643i	$0.381624\pi$
$128$	8.26633	+	7.72449i	0.730647	+	0.682755i
$129$	−1.52728	−	2.86051i	−0.134469	−	0.251854i
$130$	2.43477	−	2.85710i	0.213543	−	0.250584i
$131$	18.5565	−	10.7136i	1.62129	−	0.936053i	0.634715	−	0.772746i	$-0.281117\pi$
$131$	18.5565	−	10.7136i	1.62129	−	0.936053i	0.986575	−	0.163306i	$-0.0522159\pi$
$132$	−9.58652	−	12.6186i	−0.834400	−	1.09831i
$133$	−3.69760	+	3.17537i	−0.320622	+	0.275340i
$134$	−16.8325	−	3.10059i	−1.45411	−	0.267851i
$135$	1.13970	+	2.52465i	0.0980894	+	0.217288i
$136$	−5.86944	−	10.7257i	−0.503300	−	0.919721i
$137$	3.91533	+	2.26052i	0.334509	+	0.193129i	0.657841	−	0.753157i	$-0.271470\pi$
$137$	3.91533	+	2.26052i	0.334509	+	0.193129i	−0.323332	+	0.946286i	$0.604803\pi$
$138$	0.0624870	−	0.285669i	0.00531925	−	0.0243178i
$139$	−14.8300			−1.25786			−0.628931	−	0.777461i	$-0.716507\pi$
$139$	−14.8300			−1.25786			−0.628931	+	0.777461i	$0.716507\pi$
$140$	2.77606	+	0.500453i	0.234620	+	0.0422960i
$141$	8.57212	+	5.33597i	0.721903	+	0.449370i
$142$	2.93891	+	8.27034i	0.246628	+	0.694031i
$143$	11.3892	−	19.7266i	0.952410	−	1.64962i
$144$	−8.40328	−	8.56650i	−0.700273	−	0.713875i
$145$	3.57577	−	2.06447i	0.296952	−	0.171445i
$146$	−13.4182	−	2.47168i	−1.11050	−	0.204557i
$147$	7.88888	−	9.20682i	0.650664	−	0.759366i
$148$	5.77873	−	15.1536i	0.475009	−	1.24562i
$149$	10.7714	+	18.6566i	0.882425	+	1.52841i	0.848636	+	0.528977i	$0.177424\pi$
$149$	10.7714	+	18.6566i	0.882425	+	1.52841i	0.0337890	+	0.999429i	$0.489243\pi$
$150$	3.50460	+	11.0069i	0.286150	+	0.898709i
$151$	1.40767	−	2.43816i	0.114555	−	0.198415i	−0.803047	−	0.595916i	$-0.796789\pi$
$151$	1.40767	−	2.43816i	0.114555	−	0.198415i	0.917602	+	0.397501i	$0.130122\pi$
$152$	−5.20909	−	0.119224i	−0.422513	−	0.00967034i
$153$	5.72500	+	11.6362i	0.462839	+	0.940733i
$154$	17.1167	−	0.0650753i	1.37930	−	0.00524392i
$155$	−1.19213			−0.0957539
$156$	6.67731	−	15.9037i	0.534613	−	1.27331i
$157$	3.54427	−	6.13885i	0.282863	−	0.489933i	−0.689226	−	0.724547i	$-0.742049\pi$
$157$	3.54427	−	6.13885i	0.282863	−	0.489933i	0.972089	+	0.234613i	$0.0753824\pi$
$158$	0.0492537	+	0.0419731i	0.00391841	+	0.00333920i
$159$	−0.263543	+	7.93838i	−0.0209003	+	0.629554i
$160$	1.84888	+	2.38229i	0.146167	+	0.188337i
$161$	0.205779	+	0.239622i	0.0162176	+	0.0188848i
$162$	8.50957	+	9.46505i	0.668575	+	0.743645i
$163$	−5.64257	+	3.25774i	−0.441960	+	0.255166i	−0.704429	−	0.709775i	$-0.748797\pi$
$163$	−5.64257	+	3.25774i	−0.441960	+	0.255166i	0.262469	+	0.964941i	$0.415463\pi$
$164$	4.04814	−	3.29287i	0.316106	−	0.257130i
$165$	−1.98942	−	3.72607i	−0.154876	−	0.290074i
$166$	−1.83003	−	5.14986i	−0.142038	−	0.399707i
$167$	17.2470			1.33462			0.667308	−	0.744782i	$-0.267447\pi$
$167$	17.2470			1.33462			0.667308	+	0.744782i	$0.267447\pi$
$168$	12.8523	−	1.67887i	0.991576	−	0.129528i
$169$	11.7928			0.907141
$170$	−1.09122	−	3.07078i	−0.0836928	−	0.235518i
$171$	5.51435	+	0.366542i	0.421693	+	0.0280301i
$172$	2.36278	+	2.90471i	0.180160	+	0.221482i
$173$	−14.5387	+	8.39395i	−1.10536	+	0.638180i	−0.937624	−	0.347652i	$-0.886979\pi$
$173$	−14.5387	+	8.39395i	−1.10536	+	0.638180i	−0.167737	+	0.985832i	$0.553646\pi$
$174$	12.7780	−	14.0239i	0.968700	−	1.06315i
$175$	−11.7725	−	4.13307i	−0.889914	−	0.312430i
$176$	13.6522	+	12.1843i	1.02907	+	0.918426i
$177$	11.4235	+	0.379246i	0.858646	+	0.0285058i
$178$	−17.7251	−	15.1050i	−1.32855	−	1.13217i
$179$	2.00982	−	3.48110i	0.150221	−	0.260190i	−0.781088	−	0.624421i	$-0.785335\pi$
$179$	2.00982	−	3.48110i	0.150221	−	0.260190i	0.931309	+	0.364231i	$0.118668\pi$
$180$	−1.84932	−	2.60967i	−0.137840	−	0.194513i
$181$	−14.8596			−1.10451			−0.552253	−	0.833676i	$-0.686232\pi$
$181$	−14.8596			−1.10451			−0.552253	+	0.833676i	$0.686232\pi$
$182$	9.37658	+	16.0991i	0.695038	+	1.19334i
$183$	−3.16332	−	1.96911i	−0.233840	−	0.145561i
$184$	−0.00772627	+	0.337573i	−0.000569588	+	0.0248862i
$185$	2.16139	−	3.74363i	0.158908	−	0.275237i
$186$	−5.21957	+	1.66192i	−0.382718	+	0.121858i
$187$	−9.88761	−	17.1258i	−0.723053	−	1.25237i
$188$	−10.8940	−	4.15438i	−0.794528	−	0.302989i
$189$	−13.6964	+	1.18637i	−0.996270	+	0.0862959i
$190$	−1.36582	−	0.251588i	−0.0990872	−	0.0182521i
$191$	−17.1154	+	9.88159i	−1.23843	+	0.715006i	−0.968773	−	0.247951i	$-0.920243\pi$
$191$	−17.1154	+	9.88159i	−1.23843	+	0.715006i	−0.269655	+	0.962957i	$0.586910\pi$
$192$	11.4162	+	7.85308i	0.823892	+	0.566747i
$193$	−6.29229	+	10.8986i	−0.452929	+	0.784496i	−0.998566	−	0.0535255i	$-0.982954\pi$
$193$	−6.29229	+	10.8986i	−0.452929	+	0.784496i	0.545638	+	0.838021i	$0.316287\pi$
$194$	3.40393	+	9.57894i	0.244388	+	0.687728i
$195$	2.42957	−	3.90305i	0.173985	−	0.279504i
$196$	−6.90761	+	12.1772i	−0.493401	+	0.869802i
$197$	−8.41804			−0.599761			−0.299880	−	0.953977i	$-0.596947\pi$
$197$	−8.41804			−0.599761			−0.299880	+	0.953977i	$0.596947\pi$
$198$	−13.9048	−	13.5407i	−0.988173	−	0.962297i
$199$	12.3980	+	7.15800i	0.878873	+	0.507417i	0.870287	−	0.492546i	$-0.163934\pi$
$199$	12.3980	+	7.15800i	0.878873	+	0.507417i	0.00858618	+	0.999963i	$0.497267\pi$
$200$	−6.40312	−	11.7009i	−0.452769	−	0.827381i
$201$	−20.9508	−	0.695538i	−1.47776	−	0.0490595i
$202$	5.35462	+	0.986336i	0.376750	+	0.0693983i
$203$	3.78890	+	20.1391i	0.265929	+	1.41349i
$204$	−9.05868	−	11.9238i	−0.634234	−	0.834832i
$205$	1.20454	−	0.695443i	0.0841290	−	0.0485719i
$206$	4.88303	−	5.73003i	0.340217	−	0.399230i
$207$	0.0237536	−	0.357356i	0.00165099	−	0.0248379i
$208$	−4.05531	+	19.4997i	−0.281185	+	1.35206i
$209$	−8.42732			−0.582930
$210$	3.45328	+	0.101502i	0.238299	+	0.00700433i
$211$			9.62315i			0.662485i	0.943546	+	0.331243i	$0.107468\pi$
$211$			9.62315i			0.662485i	−0.943546	+	0.331243i	$0.892532\pi$
$212$	−1.45464	−	9.05541i	−0.0999051	−	0.621928i
$213$	5.06294	+	9.48262i	0.346907	+	0.649739i
$214$	9.91640	+	8.45058i	0.677871	+	0.577669i
$215$	0.499011	+	0.864312i	0.0340323	+	0.0589456i
$216$	−11.7351	−	8.84801i	−0.798473	−	0.602031i
$217$	1.95994	−	5.58261i	0.133049	−	0.378972i
$218$	−6.81245	−	1.25487i	−0.461397	−	0.0849907i
$219$	−16.7012	−	0.554457i	−1.12856	−	0.0374667i
$220$	3.07773	+	3.78365i	0.207501	+	0.255094i
$221$	10.7621	−	18.6404i	0.723935	−	1.25389i
$222$	4.24444	−	19.4041i	0.284868	−	1.30232i
$223$		−	20.1840i		−	1.35162i	−0.737076	−	0.675810i	$-0.763794\pi$
$223$		−	20.1840i		−	1.35162i	0.737076	−	0.675810i	$-0.236206\pi$
$224$	−14.1957	+	4.74146i	−0.948492	+	0.316802i
$225$	6.24555	+	12.6942i	0.416370	+	0.846283i
$226$	1.83551	+	5.16526i	0.122096	+	0.343588i
$227$	−1.03403	−	0.597000i	−0.0686313	−	0.0396243i	0.465292	−	0.885157i	$-0.345949\pi$
$227$	−1.03403	−	0.597000i	−0.0686313	−	0.0396243i	−0.533923	+	0.845533i	$0.679283\pi$
$228$	−6.33081	+	0.802514i	−0.419268	+	0.0531478i
$229$	11.4021	+	19.7490i	0.753472	+	1.30505i	0.946130	+	0.323786i	$0.104956\pi$
$229$	11.4021	+	19.7490i	0.753472	+	1.30505i	−0.192658	+	0.981266i	$0.561711\pi$
$230$	−0.0163041	+	0.0885117i	−0.00107506	+	0.00583629i
$231$	20.7195	−	3.19031i	1.36325	−	0.209907i
$232$	−11.3849	+	18.7167i	−0.747457	+	1.22881i
$233$	−14.1080	+	8.14528i	−0.924249	+	0.533615i	−0.884988	−	0.465614i	$-0.845834\pi$
$233$	−14.1080	+	8.14528i	−0.924249	+	0.533615i	−0.0392607	+	0.999229i	$0.512500\pi$
$234$	5.19642	−	20.4760i	0.339701	−	1.33856i
$235$	−2.69133	−	1.55384i	−0.175563	−	0.101361i
$236$	−13.0310	+	2.09327i	−0.848244	+	0.136260i
$237$	0.0672850	+	0.0418836i	0.00437063	+	0.00272063i
$238$	16.1742	−	0.0614922i	1.04842	−	0.00398594i
$239$			20.2417i			1.30933i	0.755920	+	0.654664i	$0.227190\pi$
$239$			20.2417i			1.30933i	−0.755920	+	0.654664i	$0.772810\pi$
$240$	2.67238	+	2.54929i	0.172501	+	0.164556i
$241$	−7.99312	−	4.61483i	−0.514882	−	0.297267i	0.219956	−	0.975510i	$-0.429409\pi$
$241$	−7.99312	−	4.61483i	−0.514882	−	0.297267i	−0.734838	+	0.678242i	$0.762742\pi$
$242$	10.6858	+	9.10627i	0.686911	+	0.585373i
$243$	12.0272	+	9.91699i	0.771545	+	0.636175i
$244$	4.02016	+	1.53307i	0.257365	+	0.0981446i
$245$	−2.33265	+	2.91263i	−0.149027	+	0.186081i
$246$	4.30444	−	4.72414i	0.274441	−	0.301200i
$247$	−4.58631	−	7.94372i	−0.291820	−	0.505447i
$248$	5.54869	−	3.03642i	0.352342	−	0.192813i
$249$	−3.15265	−	5.90474i	−0.199791	−	0.374198i
$250$	−2.45262	−	6.90186i	−0.155117	−	0.436512i
$251$			8.22152i			0.518938i	0.965751	+	0.259469i	$0.0835475\pi$
$251$			8.22152i			0.518938i	−0.965751	+	0.259469i	$0.916452\pi$
$252$	15.2612	−	4.36972i	0.961368	−	0.275267i
$253$			0.546129i			0.0343349i
$254$	−10.9139	+	3.87831i	−0.684797	+	0.243347i
$255$	−1.87987	−	3.52091i	−0.117722	−	0.220488i
$256$	−14.6734	−	6.37906i	−0.917085	−	0.398691i
$257$	6.71468	+	11.6302i	0.418850	+	0.725470i	0.995824	−	0.0912928i	$-0.0290999\pi$
$257$	6.71468	+	11.6302i	0.418850	+	0.725470i	−0.576974	+	0.816763i	$0.695767\pi$
$258$	3.38977	+	3.08862i	0.211038	+	0.192289i
$259$	13.9776	+	16.2763i	0.868525	+	1.01136i
$260$	−1.89157	+	4.96026i	−0.117310	+	0.307622i
$261$	12.9272	−	19.3083i	0.800174	−	1.19515i
$262$	−19.6547	+	23.0639i	−1.21427	+	1.42489i
$263$	−13.0415	−	7.52949i	−0.804170	−	0.464288i	0.0407569	−	0.999169i	$-0.487023\pi$
$263$	−13.0415	−	7.52949i	−0.804170	−	0.464288i	−0.844927	+	0.534881i	$0.820356\pi$
$264$	18.7502	+	12.2756i	1.15399	+	0.755514i
$265$		−	2.44458i		−	0.150170i
$266$	3.42367	−	5.98238i	0.209919	−	0.366803i
$267$	−24.2141	−	15.0728i	−1.48188	−	0.922439i
$268$	23.8989	−	3.83906i	1.45986	−	0.234508i
$269$	11.5014	+	6.64035i	0.701254	+	0.404869i	0.807814	−	0.589437i	$-0.200650\pi$
$269$	11.5014	+	6.64035i	0.701254	+	0.404869i	−0.106560	+	0.994306i	$0.533984\pi$
$270$	−2.71425	−	2.82461i	−0.165184	−	0.171900i
$271$	16.2954	−	9.40818i	0.989878	−	0.571506i	0.0846401	−	0.996412i	$-0.473026\pi$
$271$	16.2954	−	9.40818i	0.989878	−	0.571506i	0.905238	+	0.424905i	$0.139693\pi$
$272$	12.9005	+	11.5134i	0.782208	+	0.698103i
$273$	14.2832	+	17.7943i	0.864460	+	1.07696i
$274$	−6.28792	−	1.15825i	−0.379867	−	0.0699726i
$275$	−10.7866	−	18.6830i	−0.650459	−	1.12663i
$276$	0.0520067	+	0.410266i	0.00313043	+	0.0246951i
$277$	−20.1344	−	11.6246i	−1.20976	−	0.698454i	−0.247052	−	0.969002i	$-0.579462\pi$
$277$	−20.1344	−	11.6246i	−1.20976	−	0.698454i	−0.962706	+	0.270548i	$0.912795\pi$
$278$	19.7621	−	7.02256i	1.18525	−	0.421185i
$279$	−6.01973	+	2.96170i	−0.360392	+	0.177312i
$280$	−3.93630	+	0.647679i	−0.235239	+	0.0387062i
$281$		−	21.2736i		−	1.26908i	−0.772892	−	0.634538i	$-0.781190\pi$
$281$		−	21.2736i		−	1.26908i	0.772892	−	0.634538i	$-0.218810\pi$
$282$	−13.9498	−	3.05136i	−0.830698	−	0.181706i
$283$	4.31186	−	7.46836i	0.256314	−	0.443948i	−0.708938	−	0.705271i	$-0.750825\pi$
$283$	4.31186	−	7.46836i	0.256314	−	0.443948i	0.965251	+	0.261323i	$0.0841587\pi$
$284$	−7.83265	−	9.62917i	−0.464782	−	0.571386i
$285$	−1.69999	−	0.0564373i	−0.100699	−	0.00334306i
$286$	−5.83563	+	31.6804i	−0.345068	+	1.87330i
$287$	1.27634	+	6.78411i	0.0753399	+	0.400454i
$288$	15.2546	+	7.43624i	0.898885	+	0.438185i
$289$	−0.843181	−	1.46043i	−0.0495989	−	0.0859078i
$290$	−3.78739	+	4.44434i	−0.222403	+	0.260980i
$291$	5.86404	+	10.9830i	0.343756	+	0.643837i
$292$	19.0513	−	3.06035i	1.11489	−	0.179094i
$293$		−	22.7441i		−	1.32872i	−0.747411	−	0.664362i	$-0.768703\pi$
$293$		−	22.7441i		−	1.32872i	0.747411	−	0.664362i	$-0.231297\pi$
$294$	−6.15276	+	16.0045i	−0.358836	+	0.933401i
$295$	−3.51782			−0.204815
$296$	−0.524809	+	22.9297i	−0.0305039	+	1.33276i
$297$	−19.3027	−	13.8726i	−1.12006	−	0.804970i
$298$	−23.1883	−	19.7606i	−1.34326	−	1.14470i
$299$	−0.514790	+	0.297214i	−0.0297711	+	0.0171883i
$300$	−9.88234	−	13.0080i	−0.570557	−	0.751015i
$301$	−4.86790	+	0.915828i	−0.280581	+	0.0527875i
$302$	−0.721270	+	3.91563i	−0.0415044	+	0.225319i
$303$	6.66470	+	0.221259i	0.382877	+	0.0127110i
$304$	6.99797	−	2.30783i	0.401361	−	0.132363i
$305$	0.993166	+	0.573405i	0.0568685	+	0.0328331i
$306$	−13.1392	−	12.7951i	−0.751118	−	0.731450i
$307$	22.8169			1.30223			0.651114	−	0.758980i	$-0.274302\pi$
$307$	22.8169			1.30223			0.651114	+	0.758980i	$0.274302\pi$
$308$	−22.7785	+	8.19213i	−1.29792	+	0.466790i
$309$	4.87261	−	7.82773i	0.277193	−	0.445304i
$310$	1.58860	−	0.564518i	0.0902264	−	0.0320625i
$311$	−11.9871	+	20.7622i	−0.679725	+	1.17732i	0.295339	+	0.955393i	$0.404567\pi$
$311$	−11.9871	+	20.7622i	−0.679725	+	1.17732i	−0.975064	+	0.221925i	$0.928766\pi$
$312$	−1.36701	+	24.3549i	−0.0773919	+	1.37882i
$313$	19.4419	−	11.2248i	1.09892	−	0.634463i	0.162984	−	0.986629i	$-0.447888\pi$
$313$	19.4419	−	11.2248i	1.09892	−	0.634463i	0.935938	+	0.352166i	$0.114555\pi$
$314$	−1.81602	+	9.85883i	−0.102484	+	0.556366i
$315$	4.20099	−	0.504805i	0.236699	−	0.0284425i
$316$	−0.0855102	−	0.0326089i	−0.00481032	−	0.00183439i
$317$	1.06072	+	1.83723i	0.0595762	+	0.103189i	0.894275	−	0.447517i	$-0.147692\pi$
$317$	1.06072	+	1.83723i	0.0595762	+	0.103189i	−0.834699	+	0.550706i	$0.814358\pi$
$318$	−3.40794	−	10.7033i	−0.191108	−	0.600211i
$319$	−17.7163	+	30.6856i	−0.991924	+	1.71806i
$320$	−3.59188	−	2.29907i	−0.200792	−	0.128522i
$321$	13.5467	+	8.43255i	0.756103	+	0.470659i
$322$	−0.387686	−	0.221870i	−0.0216049	−	0.0123643i
$323$	−7.96330			−0.443090
$324$	−15.8217	−	8.58330i	−0.878985	−	0.476850i
$325$	11.7406	−	20.3353i	0.651252	−	1.12800i
$326$	5.97649	−	7.01316i	0.331007	−	0.388423i
$327$	−8.47921	−	0.281498i	−0.468902	−	0.0155669i
$328$	−3.83515	+	6.30496i	−0.211761	+	0.348133i
$329$	11.7012	−	10.0486i	0.645108	−	0.553997i
$330$	4.41549	+	4.02321i	0.243065	+	0.221470i
$331$	−1.25478	+	0.724448i	−0.0689689	+	0.0398192i	−0.534088	−	0.845429i	$-0.679345\pi$
$331$	−1.25478	+	0.724448i	−0.0689689	+	0.0398192i	0.465119	+	0.885248i	$0.346012\pi$
$332$	4.87732	+	5.99599i	0.267677	+	0.329073i
$333$	1.61347	−	24.2735i	0.0884176	−	1.33018i
$334$	−22.9830	+	8.16713i	−1.25757	+	0.446886i
$335$	6.45170			0.352494
$336$	−16.3317	+	8.32328i	−0.890965	+	0.454072i
$337$	−21.6680			−1.18033			−0.590165	−	0.807282i	$-0.700937\pi$
$337$	−21.6680			−1.18033			−0.590165	+	0.807282i	$0.700937\pi$
$338$	−15.7149	+	5.58436i	−0.854775	+	0.303749i
$339$	3.16208	+	5.92240i	0.171740	+	0.321661i
$340$	2.90827	+	3.57532i	0.157723	+	0.193899i
$341$	8.85966	−	5.11513i	0.479778	−	0.277000i
$342$	−7.52187	+	2.12281i	−0.406736	+	0.114789i
$343$	−9.80454	−	15.7121i	−0.529396	−	0.848375i
$344$	−4.52408	−	2.75189i	−0.243922	−	0.148372i
$345$	−0.00365740	+	0.110167i	−0.000196908	+	0.00593121i
$346$	15.3991	−	18.0702i	0.827863	−	0.971462i
$347$	−13.7374	+	23.7939i	−0.737463	+	1.27732i	0.216171	+	0.976356i	$0.430643\pi$
$347$	−13.7374	+	23.7939i	−0.737463	+	1.27732i	−0.953634	+	0.300969i	$0.902690\pi$
$348$	−10.3868	+	24.7389i	−0.556793	+	1.32614i
$349$	15.6203			0.836134			0.418067	−	0.908416i	$-0.362708\pi$
$349$	15.6203			0.836134			0.418067	+	0.908416i	$0.362708\pi$
$350$	17.6449	−	0.0670834i	0.943158	−	0.00358576i
$351$	2.57163	−	25.7448i	0.137264	−	1.37415i
$352$	−23.9624	−	9.77166i	−1.27720	−	0.520831i
$353$	6.72613	−	11.6500i	0.357996	−	0.620067i	−0.629630	−	0.776895i	$-0.716793\pi$
$353$	6.72613	−	11.6500i	0.357996	−	0.620067i	0.987626	+	0.156828i	$0.0501268\pi$
$354$	−15.4023	+	4.90411i	−0.818625	+	0.260651i
$355$	−1.65423	−	2.86521i	−0.0877973	−	0.152069i
$356$	30.7728	+	11.7351i	1.63096	+	0.621957i
$357$	19.5787	−	3.01465i	1.03621	−	0.159552i
$358$	−1.02980	+	5.59056i	−0.0544265	+	0.295470i
$359$	19.9816	−	11.5364i	1.05459	−	0.608867i	0.130658	−	0.991428i	$-0.458291\pi$
$359$	19.9816	−	11.5364i	1.05459	−	0.608867i	0.923930	+	0.382561i	$0.124958\pi$
$360$	3.70015	+	2.60186i	0.195015	+	0.137130i
$361$	7.80320	−	13.5155i	0.410695	−	0.711344i
$362$	19.8016	−	7.03660i	1.04075	−	0.369836i
$363$	14.5978	+	9.08684i	0.766186	+	0.476936i
$364$	−20.1185	−	17.0130i	−1.05450	−	0.891726i
$365$	5.14305			0.269200
$366$	5.14782	+	1.12603i	0.269081	+	0.0588585i
$367$	18.6893	+	10.7903i	0.975574	+	0.563248i	0.900931	−	0.433963i	$-0.142885\pi$
$367$	18.6893	+	10.7903i	0.975574	+	0.563248i	0.0746427	+	0.997210i	$0.476218\pi$
$368$	−0.149558	−	0.453501i	−0.00779625	−	0.0236404i
$369$	4.35469	−	6.50424i	0.226696	−	0.338597i
$370$	−1.10746	+	6.01218i	−0.0575741	+	0.312558i
$371$	11.4477	+	4.01907i	0.594337	+	0.208659i
$372$	6.16850	−	4.68630i	0.319822	−	0.242973i
$373$	0.158888	−	0.0917338i	0.00822689	−	0.00474980i	−0.495881	−	0.868391i	$-0.665155\pi$
$373$	0.158888	−	0.0917338i	0.00822689	−	0.00474980i	0.504108	+	0.863641i	$0.331821\pi$
$374$	21.2857	+	18.1393i	1.10066	+	0.937963i
$375$	−4.22519	−	7.91356i	−0.218188	−	0.408654i
$376$	16.4844	+	0.377289i	0.850116	+	0.0194572i
$377$	−38.5663			−1.98627
$378$	17.6898	−	8.06673i	0.909864	−	0.414908i
$379$			2.93359i			0.150688i	0.997158	+	0.0753441i	$0.0240055\pi$
$379$			2.93359i			0.150688i	−0.997158	+	0.0753441i	$0.975994\pi$
$380$	1.93920	−	0.311509i	0.0994789	−	0.0159801i
$381$	−12.5137	+	6.68127i	−0.641094	+	0.342292i
$382$	18.1283	−	21.2728i	0.927524	−	1.08841i
$383$	−7.67488	−	13.2933i	−0.392168	−	0.679255i	0.600567	−	0.799574i	$-0.294942\pi$
$383$	−7.67488	−	13.2933i	−0.392168	−	0.679255i	−0.992735	+	0.120319i	$0.961608\pi$
$384$	−18.9317	−	5.05883i	−0.966103	−	0.258158i
$385$	−6.34088	+	1.19295i	−0.323161	+	0.0607983i
$386$	3.22407	−	17.5028i	0.164101	−	0.890870i
$387$	4.66708	+	3.12468i	0.237241	+	0.158836i
$388$	−9.07199	−	11.1528i	−0.460561	−	0.566197i
$389$	−2.00060	+	3.46513i	−0.101434	+	0.175689i	−0.912276	−	0.409577i	$-0.865676\pi$
$389$	−2.00060	+	3.46513i	−0.101434	+	0.175689i	0.810842	+	0.585266i	$0.199010\pi$
$390$	−1.38935	+	6.35162i	−0.0703523	+	0.321627i
$391$			0.516059i			0.0260982i
$392$	3.43853	−	19.4981i	0.173672	−	0.984804i
$393$	−19.6127	+	31.5074i	−0.989332	+	1.58934i
$394$	11.2177	−	3.98627i	0.565139	−	0.200825i
$395$	−0.0211250	−	0.0121965i	−0.00106291	−	0.000613673i
$396$	24.9413	+	11.4596i	1.25335	+	0.575865i
$397$	−11.7195	−	20.2987i	−0.588183	−	1.01876i	−0.994470	−	0.105017i	$-0.966510\pi$
$397$	−11.7195	−	20.2987i	−0.588183	−	1.01876i	0.406288	−	0.913745i	$-0.366823\pi$
$398$	−19.9109	−	3.66765i	−0.998044	−	0.183842i
$399$	3.05919	−	7.86810i	0.153151	−	0.393898i
$400$	14.0735	+	12.5603i	0.703675	+	0.628014i
$401$	14.5441	−	8.39703i	0.726297	−	0.419328i	−0.0907689	−	0.995872i	$-0.528932\pi$
$401$	14.5441	−	8.39703i	0.726297	−	0.419328i	0.817066	+	0.576544i	$0.195599\pi$
$402$	28.2479	−	8.99416i	1.40888	−	0.448588i
$403$	9.64320	+	5.56751i	0.480362	+	0.277337i
$404$	−7.60251	+	1.22125i	−0.378239	+	0.0607595i
$405$	−3.80091	−	2.92770i	−0.188869	−	0.145479i
$406$	−14.5857	−	25.0428i	−0.723874	−	1.24285i
$407$			37.0960i			1.83878i
$408$	17.7178	+	11.5997i	0.877160	+	0.574272i
$409$	11.9749	+	6.91372i	0.592121	+	0.341861i	0.765936	−	0.642917i	$-0.222276\pi$
$409$	11.9749	+	6.91372i	0.592121	+	0.341861i	−0.173815	+	0.984778i	$0.555609\pi$
$410$	−1.27583	+	1.49713i	−0.0630086	+	0.0739380i
$411$	−7.82635	−	0.259824i	−0.386045	−	0.0128162i
$412$	−3.79362	+	9.94800i	−0.186898	+	0.490103i
$413$	5.78354	−	16.4736i	0.284590	−	0.810613i
$414$	0.137568	+	0.487452i	0.00676111	+	0.0239570i
$415$	1.03007	+	1.78414i	0.0505643	+	0.0875799i
$416$	−3.82987	−	27.9052i	−0.187775	−	1.36817i
$417$	22.6588	−	12.0980i	1.10961	−	0.592440i
$418$	11.2300	−	3.99066i	0.549280	−	0.195190i
$419$		−	17.5573i		−	0.857728i	−0.903369	−	0.428864i	$-0.858914\pi$
$419$		−	17.5573i		−	0.857728i	0.903369	−	0.428864i	$-0.141086\pi$
$420$	−4.64983	+	1.50000i	−0.226888	+	0.0731926i
$421$		−	19.8896i		−	0.969362i	−0.874691	−	0.484681i	$-0.838936\pi$
$421$		−	19.8896i		−	0.969362i	0.874691	−	0.484681i	$-0.161064\pi$
$422$	−4.55694	−	12.8236i	−0.221828	−	0.624243i
$423$	−17.4504	−	1.15994i	−0.848467	−	0.0563980i
$424$	6.22650	+	11.3782i	0.302386	+	0.552574i
$425$	−10.1927	−	17.6543i	−0.494419	−	0.856359i
$426$	−11.2371	−	10.2388i	−0.544442	−	0.496073i
$427$	−4.31803	+	3.70818i	−0.208964	+	0.179451i
$428$	−17.2160	−	6.56525i	−0.832168	−	0.317343i
$429$	−1.30907	+	39.4315i	−0.0632026	+	1.90377i
$430$	−1.07426	−	0.915461i	−0.0518052	−	0.0441475i
$431$	25.3821	+	14.6544i	1.22261	+	0.705876i	0.965474	−	0.260498i	$-0.0838868\pi$
$431$	25.3821	+	14.6544i	1.22261	+	0.705876i	0.257139	+	0.966374i	$0.417220\pi$
$432$	19.8278	+	6.23362i	0.953966	+	0.299915i
$433$			12.5427i			0.602763i	0.953504	+	0.301381i	$0.0974477\pi$
$433$			12.5427i			0.602763i	−0.953504	+	0.301381i	$0.902552\pi$
$434$	0.0318116	+	8.36736i	0.00152700	+	0.401646i
$435$	−3.77930	+	6.07137i	−0.181204	+	0.291100i
$436$	9.67234	−	1.55374i	0.463221	−	0.0744109i
$437$	0.190457	+	0.109961i	0.00911081	+	0.00526013i
$438$	22.5182	−	7.16981i	1.07596	−	0.342587i
$439$	11.7921	−	6.80818i	0.562807	−	0.324937i	−0.191464	−	0.981500i	$-0.561324\pi$
$439$	11.7921	−	6.80818i	0.562807	−	0.324937i	0.754271	+	0.656563i	$0.227990\pi$
$440$	−5.89302	−	3.58458i	−0.280939	−	0.170888i
$441$	−4.54277	+	20.5028i	−0.216323	+	0.976322i
$442$	−5.51431	+	29.9361i	−0.262289	+	1.42391i
$443$	6.72205	+	11.6429i	0.319374	+	0.553172i	0.980358	−	0.197228i	$-0.0631940\pi$
$443$	6.72205	+	11.6429i	0.319374	+	0.553172i	−0.660984	+	0.750400i	$0.729861\pi$
$444$	3.53256	+	27.8674i	0.167648	+	1.32253i
$445$	7.60232	+	4.38920i	0.360384	+	0.208068i
$446$	9.55790	+	26.8967i	0.452580	+	1.27360i
$447$	−31.6773	−	19.7185i	−1.49828	−	0.932653i
$448$	16.6716	−	13.0406i	0.787660	−	0.616110i
$449$		−	16.3428i		−	0.771266i	−0.922652	−	0.385633i	$-0.873983\pi$
$449$		−	16.3428i		−	0.771266i	0.922652	−	0.385633i	$-0.126017\pi$
$450$	−14.3339	−	13.9586i	−0.675706	−	0.658013i
$451$	−5.96796	+	10.3368i	−0.281020	+	0.486742i
$452$	−4.89190	−	6.01393i	−0.230096	−	0.282871i
$453$	−0.161798	+	4.87364i	−0.00760194	+	0.228984i
$454$	1.66063	+	0.305893i	0.0779374	+	0.0143563i
$455$	−4.57532	−	5.32779i	−0.214494	−	0.249770i
$456$	8.05627	−	4.06730i	0.377270	−	0.190469i
$457$	14.6395	+	25.3564i	0.684808	+	1.18612i	0.973497	+	0.228699i	$0.0734472\pi$
$457$	14.6395	+	25.3564i	0.684808	+	1.18612i	−0.288689	+	0.957423i	$0.593219\pi$
$458$	−24.5461	−	20.9178i	−1.14696	−	0.977423i
$459$	−18.2399	−	13.1088i	−0.851364	−	0.611864i
$460$	−0.0201872	−	0.125669i	−0.000941235	−	0.00585936i
$461$			6.06975i			0.282696i	0.989960	+	0.141348i	$0.0451437\pi$
$461$			6.06975i			0.282696i	−0.989960	+	0.141348i	$0.954856\pi$
$462$	−26.0997	+	14.0628i	−1.21427	+	0.654263i
$463$	−3.30400			−0.153550			−0.0767750	−	0.997048i	$-0.524462\pi$
$463$	−3.30400			−0.153550			−0.0767750	+	0.997048i	$0.524462\pi$
$464$	6.30820	−	30.3327i	0.292851	−	1.40816i
$465$	1.82146	−	0.972510i	0.0844682	−	0.0450991i
$466$	14.9429	−	17.5349i	0.692219	−	0.812290i
$467$	−7.03895	+	4.06394i	−0.325724	+	0.188057i	−0.653941	−	0.756546i	$-0.726886\pi$
$467$	−7.03895	+	4.06394i	−0.325724	+	0.188057i	0.328217	+	0.944602i	$0.393552\pi$
$468$	2.77156	+	29.7466i	0.128116	+	1.37504i
$469$	−10.6070	+	30.2127i	−0.489788	+	1.39509i
$470$	4.32220	+	0.796161i	0.199368	+	0.0367242i
$471$	−0.407378	+	12.2709i	−0.0187710	+	0.565415i
$472$	16.3735	−	8.96011i	0.753653	−	0.412422i
$473$	−7.41711	−	4.28227i	−0.341039	−	0.196899i
$474$	−0.109496	−	0.0239510i	−0.00502931	−	0.00110011i
$475$	−8.68736			−0.398604
$476$	−21.5243	+	7.74106i	−0.986563	+	0.354811i
$477$	−6.07328	−	12.3441i	−0.278076	−	0.565198i
$478$	−9.58523	−	26.9736i	−0.438418	−	1.23375i
$479$	−0.425876	+	0.737638i	−0.0194588	+	0.0337035i	−0.875591	−	0.483054i	$-0.839528\pi$
$479$	−0.425876	+	0.737638i	−0.0194588	+	0.0337035i	0.856132	+	0.516757i	$0.172861\pi$
$480$	−4.76834	−	2.13165i	−0.217644	−	0.0972961i
$481$	−34.9673	+	20.1884i	−1.59437	+	0.920510i
$482$	12.8368	+	2.36457i	0.584698	+	0.107703i
$483$	−0.509889	−	0.198250i	−0.0232008	−	0.00902069i
$484$	−18.5519	−	7.07466i	−0.843266	−	0.321575i
$485$	−1.91597	−	3.31856i	−0.0869999	−	0.150688i
$486$	−20.7232	−	7.51982i	−0.940025	−	0.341106i
$487$	−2.45804	+	4.25745i	−0.111384	+	0.192923i	−0.916329	−	0.400427i	$-0.868862\pi$
$487$	−2.45804	+	4.25745i	−0.111384	+	0.192923i	0.804944	+	0.593350i	$0.202195\pi$
$488$	−6.08314	−	0.139229i	−0.275371	−	0.00630260i
$489$	5.96374	−	9.58062i	0.269690	−	0.433250i
$490$	1.72919	−	4.98591i	0.0781166	−	0.225240i
$491$	−5.07434			−0.229002			−0.114501	−	0.993423i	$-0.536527\pi$
$491$	−5.07434			−0.229002			−0.114501	+	0.993423i	$0.536527\pi$
$492$	−3.49893	+	8.33359i	−0.157744	+	0.375707i
$493$	−16.7408	+	28.9960i	−0.753970	+	1.30591i
$494$	9.87327	+	8.41383i	0.444220	+	0.378556i
$495$	6.07929	+	4.07017i	0.273244	+	0.182941i
$496$	−5.95620	+	6.67378i	−0.267441	+	0.299662i
$497$	16.1372	−	3.03599i	0.723850	−	0.136183i
$498$	6.99726	+	6.37562i	0.313555	+	0.285698i
$499$	−17.6743	+	10.2042i	−0.791209	+	0.456805i	−0.840388	−	0.541985i	$-0.817673\pi$
$499$	−17.6743	+	10.2042i	−0.791209	+	0.456805i	0.0491790	+	0.998790i	$0.484340\pi$
$500$	6.53660	+	8.03586i	0.292326	+	0.359374i
$501$	−26.3519	+	14.0697i	−1.17732	+	0.628590i
$502$	−3.89321	−	10.9558i	−0.173762	−	0.488982i
$503$	26.6102			1.18649			0.593245	−	0.805022i	$-0.297847\pi$
$503$	26.6102			1.18649			0.593245	+	0.805022i	$0.297847\pi$
$504$	−18.2675	+	13.0498i	−0.813701	+	0.581283i
$505$	−2.05236			−0.0913289
$506$	−0.258613	−	0.727759i	−0.0114968	−	0.0323528i
$507$	−18.0184	+	9.62033i	−0.800224	+	0.427254i
$508$	12.7070	−	10.3363i	0.563784	−	0.458598i
$509$	−24.9978	+	14.4325i	−1.10801	+	0.639710i	−0.938313	−	0.345787i	$-0.887612\pi$
$509$	−24.9978	+	14.4325i	−1.10801	+	0.639710i	−0.169697	+	0.985496i	$0.554279\pi$
$510$	4.17236	+	3.80168i	0.184755	+	0.168341i
$511$	−8.45553	+	24.0844i	−0.374051	+	1.06543i
$512$	22.5741	+	1.55218i	0.997644	+	0.0685972i
$513$	−8.72444	+	3.93844i	−0.385194	+	0.173887i
$514$	−14.4552	−	12.3184i	−0.637590	−	0.543343i
$515$	−1.41891	+	2.45762i	−0.0625245	+	0.108296i
$516$	−5.97971	−	2.51064i	−0.263242	−	0.110525i
$517$	26.6686			1.17288
$518$	−26.3337	−	15.0706i	−1.15704	−	0.662162i
$519$	15.3663	−	24.6856i	0.674505	−	1.08358i
$520$	0.171787	−	7.50566i	0.00753337	−	0.329145i
$521$	−12.5564	+	21.7483i	−0.550105	+	0.952811i	0.448161	+	0.893953i	$0.352079\pi$
$521$	−12.5564	+	21.7483i	−0.550105	+	0.952811i	−0.998266	+	0.0588577i	$0.981254\pi$
$522$	−8.08325	+	31.8513i	−0.353794	+	1.39410i
$523$	−1.54754	−	2.68042i	−0.0676692	−	0.117206i	0.830206	−	0.557457i	$-0.188223\pi$
$523$	−1.54754	−	2.68042i	−0.0676692	−	0.117206i	−0.897875	+	0.440251i	$0.854890\pi$
$524$	15.2697	−	40.0417i	0.667060	−	1.74923i
$525$	21.3589	−	3.28876i	0.932179	−	0.143533i
$526$	20.9442	+	3.85799i	0.913212	+	0.168216i
$527$	8.37183	−	4.83348i	0.364683	−	0.210550i
$528$	−30.7990	−	7.47932i	−1.34036	−	0.325495i
$529$	−11.4929	+	19.9062i	−0.499690	+	0.865489i
$530$	1.15760	+	3.25759i	0.0502831	+	0.141501i
$531$	−17.7635	+	8.73962i	−0.770871	+	0.379267i
$532$	−1.72942	+	9.59323i	−0.0749797	+	0.415919i
$533$	−12.9915			−0.562726
$534$	39.4046	+	8.61933i	1.70521	+	0.372995i
$535$	−4.25316	−	2.45556i	−0.183880	−	0.106163i
$536$	−30.0291	+	16.4329i	−1.29706	+	0.709792i
$537$	−0.231008	+	6.95837i	−0.00996875	+	0.300276i
$538$	−18.4710	−	3.40241i	−0.796341	−	0.146688i
$539$	4.83838	−	31.6550i	0.208404	−	1.36348i
$540$	4.95451	+	2.47870i	0.213208	+	0.106666i
$541$	−23.8925	+	13.7944i	−1.02722	+	0.593066i	−0.916187	−	0.400751i	$-0.868749\pi$
$541$	−23.8925	+	13.7944i	−1.02722	+	0.593066i	−0.111033	+	0.993817i	$0.535416\pi$
$542$	−17.2598	+	20.2536i	−0.741372	+	0.869969i
$543$	22.7041	−	12.1221i	0.974328	−	0.520211i
$544$	−22.6430	−	9.23362i	−0.970809	−	0.395888i
$545$	2.61113			0.111849
$546$	−27.4598	−	16.9487i	−1.17517	−	0.725336i
$547$		−	32.0757i		−	1.37146i	−0.727856	−	0.685730i	$-0.759483\pi$
$547$		−	32.0757i		−	1.37146i	0.727856	−	0.685730i	$-0.240517\pi$
$548$	8.92762	−	1.43411i	0.381369	−	0.0612623i
$549$	6.43963	+	0.428045i	0.274837	+	0.0182685i
$550$	23.2212	+	19.7887i	0.990154	+	0.843791i
$551$	7.13420	+	12.3568i	0.303927	+	0.526417i
$552$	−0.263580	−	0.522084i	−0.0112187	−	0.0222214i
$553$	0.0918460	−	0.0788743i	0.00390569	−	0.00335407i
$554$	32.3353	+	5.95626i	1.37380	+	0.253057i
$555$	−0.248430	+	7.48314i	−0.0105453	+	0.317642i
$556$	−23.0090	+	18.7162i	−0.975800	+	0.793744i
$557$	−8.23577	+	14.2648i	−0.348961	+	0.604417i	−0.986065	−	0.166360i	$-0.946799\pi$
$557$	−8.23577	+	14.2648i	−0.348961	+	0.604417i	0.637104	+	0.770777i	$0.280132\pi$
$558$	6.61928	−	6.79727i	0.280216	−	0.287751i
$559$		−	9.32199i		−	0.394278i
$560$	4.93872	−	2.72707i	0.208699	−	0.115240i
$561$	29.0782	+	18.1006i	1.22768	+	0.764209i
$562$	10.0739	+	28.3487i	0.424940	+	1.19582i
$563$	14.5542	+	8.40290i	0.613388	+	0.354140i	0.774290	−	0.632830i	$-0.218107\pi$
$563$	14.5542	+	8.40290i	0.613388	+	0.354140i	−0.160902	+	0.986970i	$0.551440\pi$
$564$	20.0341	−	2.53959i	0.843588	−	0.106936i
$565$	−1.03315	−	1.78947i	−0.0434651	−	0.0752837i
$566$	−2.20933	+	11.9940i	−0.0928650	+	0.504145i
$567$	19.9591	−	12.9859i	0.838203	−	0.545358i
$568$	14.9974	+	9.12255i	0.629277	+	0.382774i
$569$	32.1947	−	18.5876i	1.34967	−	0.779235i	0.361471	−	0.932383i	$-0.382275\pi$
$569$	32.1947	−	18.5876i	1.34967	−	0.779235i	0.988203	+	0.153149i	$0.0489414\pi$
$570$	2.29209	−	0.729804i	0.0960052	−	0.0305681i
$571$	6.80801	+	3.93061i	0.284906	+	0.164491i	0.635642	−	0.771984i	$-0.280735\pi$
$571$	6.80801	+	3.93061i	0.284906	+	0.164491i	−0.350736	+	0.936474i	$0.614069\pi$
$572$	−7.22549	−	44.9800i	−0.302113	−	1.88071i
$573$	18.0896	−	29.0605i	0.755704	−	1.21402i
$574$	−4.91336	−	8.43596i	−0.205080	−	0.352110i
$575$			0.562982i			0.0234780i
$576$	−23.8493	−	2.68573i	−0.993719	−	0.111905i
$577$	14.7236	+	8.50067i	0.612951	+	0.353888i	0.774120	−	0.633039i	$-0.218193\pi$
$577$	14.7236	+	8.50067i	0.612951	+	0.353888i	−0.161168	+	0.986927i	$0.551526\pi$
$578$	1.81518	+	1.54686i	0.0755013	+	0.0643409i
$579$	0.723236	−	21.7851i	0.0300567	−	0.905359i
$580$	2.94242	−	7.71589i	0.122177	−	0.320385i
$581$	−10.0484	+	1.89048i	−0.416880	+	0.0784303i
$582$	−13.0152	−	11.8589i	−0.539497	−	0.491567i
$583$	10.4891	+	18.1677i	0.434415	+	0.752429i
$584$	−23.9381	+	13.0997i	−0.990565	+	0.542068i
$585$	−0.528142	+	7.94551i	−0.0218360	+	0.328506i
$586$	10.7702	+	30.3082i	0.444913	+	1.25202i
$587$		−	24.3750i		−	1.00606i	−0.864268	−	0.503032i	$-0.832218\pi$
$587$		−	24.3750i		−	1.00606i	0.864268	−	0.503032i	$-0.167782\pi$
$588$	0.620281	−	24.2408i	0.0255799	−	0.999673i
$589$		−	4.11963i		−	0.169746i
$590$	4.68777	−	1.66582i	0.192992	−	0.0685809i
$591$	12.8620	−	6.86725i	0.529072	−	0.282481i
$592$	−10.1588	−	30.8042i	−0.417523	−	1.26604i
$593$	−0.0286004	−	0.0495374i	−0.00117448	−	0.00203426i	0.865438	−	0.501017i	$-0.167041\pi$
$593$	−0.0286004	−	0.0495374i	−0.00117448	−	0.00203426i	−0.866612	+	0.498983i	$0.833707\pi$
$594$	32.2915	+	9.34574i	1.32494	+	0.383460i
$595$	−5.99174	+	1.12726i	−0.245637	+	0.0462133i
$596$	40.2576	+	15.3520i	1.64902	+	0.628844i
$597$	−24.7824	−	0.822741i	−1.01428	−	0.0336726i
$598$	0.545255	−	0.639834i	0.0222971	−	0.0261648i
$599$	−35.8620	−	20.7049i	−1.46528	−	0.845980i	−0.466033	−	0.884768i	$-0.654317\pi$
$599$	−35.8620	−	20.7049i	−1.46528	−	0.845980i	−0.999247	+	0.0387877i	$0.987650\pi$
$600$	19.3288	+	12.6544i	0.789093	+	0.516616i
$601$		−	23.8559i		−	0.973104i	−0.873652	−	0.486552i	$-0.838254\pi$
$601$		−	23.8559i		−	0.973104i	0.873652	−	0.486552i	$-0.161746\pi$
$602$	6.05317	−	3.52555i	0.246709	−	0.143691i
$603$	32.5783	−	16.0285i	1.32669	−	0.652731i
$604$	−0.893054	−	5.55943i	−0.0363379	−	0.226210i
$605$	−4.58317	−	2.64609i	−0.186332	−	0.107579i
$606$	−8.98600	+	2.86115i	−0.365031	+	0.116226i
$607$	−33.6542	+	19.4303i	−1.36598	+	0.788650i	−0.990412	−	0.138144i	$-0.955886\pi$
$607$	−33.6542	+	19.4303i	−1.36598	+	0.788650i	−0.375570	+	0.926794i	$0.622553\pi$
$608$	−8.23248	+	6.38917i	−0.333871	+	0.259115i
$609$	−22.2182	−	27.6799i	−0.900325	−	1.12164i
$610$	−1.59500	−	0.293803i	−0.0645796	−	0.0118958i
$611$	14.5136	+	25.1382i	0.587156	+	1.01698i
$612$	23.5680	+	10.8286i	0.952680	+	0.437720i
$613$	16.8751	+	9.74286i	0.681580	+	0.393510i	0.800450	−	0.599400i	$-0.204594\pi$
$613$	16.8751	+	9.74286i	0.681580	+	0.393510i	−0.118870	+	0.992910i	$0.537927\pi$
$614$	−30.4052	+	10.8047i	−1.22706	+	0.436041i
$615$	−1.27311	+	2.04521i	−0.0513366	+	0.0824710i
$616$	26.4748	−	21.7031i	1.06670	−	0.874444i
$617$		−	21.5819i		−	0.868854i	−0.900707	−	0.434427i	$-0.856951\pi$
$617$		−	21.5819i		−	0.868854i	0.900707	−	0.434427i	$-0.143049\pi$
$618$	−2.78639	+	12.7384i	−0.112085	+	0.512415i
$619$	5.60757	−	9.71259i	0.225387	−	0.390382i	−0.731048	−	0.682326i	$-0.760969\pi$
$619$	5.60757	−	9.71259i	0.225387	−	0.390382i	0.956436	+	0.291944i	$0.0943020\pi$
$620$	−1.84961	+	1.50453i	−0.0742821	+	0.0604232i
$621$	0.255230	+	0.565385i	0.0102420	+	0.0226881i
$622$	6.14199	−	33.3436i	0.246271	−	1.33696i
$623$	−33.0529	+	28.3847i	−1.32424	+	1.13721i
$624$	−9.71132	−	33.1021i	−0.388764	−	1.32514i
$625$	−10.4090	−	18.0290i	−0.416362	−	0.721160i
$626$	−20.5925	+	24.1644i	−0.823040	+	0.965803i
$627$	12.8762	−	6.87482i	0.514225	−	0.274554i
$628$	−2.24855	−	13.9976i	−0.0897268	−	0.558566i
$629$			35.0534i			1.39767i
$630$	−5.35910	+	2.66202i	−0.213512	+	0.106058i
$631$	−22.3220			−0.888626			−0.444313	−	0.895872i	$-0.646552\pi$
$631$	−22.3220			−0.888626			−0.444313	+	0.895872i	$0.646552\pi$
$632$	0.129390	+	0.00296145i	0.00514688	+	0.000117800i
$633$	−7.85036	−	14.7033i	−0.312024	−	0.584404i
$634$	−2.28350	−	1.94595i	−0.0906892	−	0.0772837i
$635$	3.78105	−	2.18299i	0.150046	−	0.0866292i
$636$	9.60976	+	12.6492i	0.381052	+	0.501572i
$637$	32.4716	−	12.6665i	1.28657	−	0.501866i
$638$	9.07756	−	49.2803i	0.359384	−	1.95102i
$639$	−15.4714	−	10.3583i	−0.612040	−	0.409770i
$640$	5.87516	+	1.36280i	0.232236	+	0.0538692i
$641$	10.9414	+	6.31703i	0.432160	+	0.249508i	0.700266	−	0.713882i	$-0.253065\pi$
$641$	10.9414	+	6.31703i	0.432160	+	0.249508i	−0.268107	+	0.963389i	$0.586398\pi$
$642$	−22.0451	−	4.82213i	−0.870052	−	0.190314i
$643$	25.9092			1.02176			0.510879	−	0.859652i	$-0.329320\pi$
$643$	25.9092			1.02176			0.510879	+	0.859652i	$0.329320\pi$
$644$	0.621686	+	0.112074i	0.0244978	+	0.00441634i
$645$	−1.46753	−	0.913508i	−0.0577839	−	0.0359693i
$646$	10.6117	−	3.77093i	0.417512	−	0.148365i
$647$	8.29783	−	14.3723i	0.326221	−	0.565032i	−0.655538	−	0.755163i	$-0.727558\pi$
$647$	8.29783	−	14.3723i	0.326221	−	0.565032i	0.981759	+	0.190131i	$0.0608912\pi$
$648$	25.1482	+	3.94571i	0.987914	+	0.155002i
$649$	26.1438	−	15.0941i	1.02623	−	0.592496i
$650$	−6.01570	+	32.6580i	−0.235955	+	1.28095i
$651$	1.55956	+	10.1286i	0.0611240	+	0.396971i
$652$	−4.64313	+	12.1757i	−0.181839	+	0.476836i
$653$	2.57443	+	4.45904i	0.100745	+	0.174496i	0.911992	−	0.410208i	$-0.134544\pi$
$653$	2.57443	+	4.45904i	0.100745	+	0.174496i	−0.811247	+	0.584704i	$0.801211\pi$
$654$	11.4325	−	3.64012i	0.447046	−	0.142340i
$655$	5.71124	−	9.89216i	0.223157	−	0.386519i
$656$	2.12500	−	10.2179i	0.0829671	−	0.398943i
$657$	25.9702	−	12.7773i	1.01319	−	0.498490i
$658$	−10.8343	+	18.9315i	−0.422367	+	0.738026i
$659$	20.6891			0.805934			0.402967	−	0.915214i	$-0.367979\pi$
$659$	20.6891			0.805934			0.402967	+	0.915214i	$0.367979\pi$
$660$	−7.78912	−	3.27033i	−0.303191	−	0.127297i
$661$	−12.3911	+	21.4621i	−0.481960	+	0.834779i	−0.999786	−	0.0207072i	$-0.993408\pi$
$661$	−12.3911	+	21.4621i	−0.481960	+	0.834779i	0.517826	+	0.855486i	$0.326742\pi$
$662$	1.32904	−	1.55957i	0.0516545	−	0.0606144i
$663$	−1.23699	+	37.2603i	−0.0480408	+	1.44707i
$664$	−9.33873	−	5.68053i	−0.362413	−	0.220447i
$665$	−0.860676	+	2.45151i	−0.0333756	+	0.0950657i
$666$	9.34435	+	33.1103i	0.362086	+	1.28300i
$667$	0.800778	−	0.462329i	0.0310063	−	0.0179015i
$668$	26.7591	−	21.7667i	1.03534	−	0.842178i
$669$	16.4657	+	30.8393i	0.636599	+	1.19232i
$670$	−8.59738	+	3.05513i	−0.332146	+	0.118030i
$671$	−9.84137			−0.379922
$672$	17.8218	−	18.8251i	0.687491	−	0.726193i
$673$	0.492833			0.0189973			0.00949866	−	0.999955i	$-0.496976\pi$
$673$	0.492833			0.0189973			0.00949866	+	0.999955i	$0.496976\pi$
$674$	28.8743	−	10.2606i	1.11219	−	0.395225i
$675$	−19.8983	−	14.3007i	−0.765887	−	0.550433i
$676$	18.2968	−	14.8832i	0.703725	−	0.572430i
$677$	35.2987	−	20.3797i	1.35664	−	0.783256i	0.367471	−	0.930035i	$-0.380224\pi$
$677$	35.2987	−	20.3797i	1.35664	−	0.783256i	0.989169	+	0.146779i	$0.0468905\pi$
$678$	−7.01819	−	6.39469i	−0.269532	−	0.245587i
$679$	18.6905	−	3.51636i	0.717276	−	0.134946i
$680$	−5.56854	−	3.38721i	−0.213544	−	0.129894i
$681$	2.06693	+	0.0686192i	0.0792049	+	0.00262949i
$682$	−9.38397	+	11.0117i	−0.359331	+	0.421659i
$683$	14.8402	−	25.7039i	0.567843	−	0.983532i	−0.428936	−	0.903335i	$-0.641112\pi$
$683$	14.8402	−	25.7039i	0.567843	−	0.983532i	0.996779	−	0.0801976i	$-0.0255551\pi$
$684$	9.01823	−	6.39071i	0.344821	−	0.244355i
$685$	2.41009			0.0920846
$686$	20.5056	+	16.2948i	0.782908	+	0.622138i
$687$	−33.5322	−	20.8731i	−1.27933	−	0.796360i
$688$	7.33181	+	1.52478i	0.279523	+	0.0581315i
$689$	−11.4168	+	19.7744i	−0.434944	+	0.753346i
$690$	−0.0472947	−	0.148538i	−0.00180048	−	0.00565476i
$691$	3.83116	+	6.63576i	0.145744	+	0.252436i	0.929650	−	0.368443i	$-0.120109\pi$
$691$	3.83116	+	6.63576i	0.145744	+	0.252436i	−0.783906	+	0.620879i	$0.786776\pi$
$692$	−11.9636	+	31.3721i	−0.454787	+	1.19259i
$693$	−29.0550	+	21.7771i	−1.10371	+	0.827242i
$694$	7.03883	−	38.2124i	0.267190	−	1.45052i
$695$	−6.84645	+	3.95280i	−0.259701	+	0.149938i
$696$	2.12645	−	37.8850i	0.0806027	−	1.43603i
$697$	−5.63936	+	9.76765i	−0.213606	+	0.369976i
$698$	−20.8152	+	7.39680i	−0.787867	+	0.279973i
$699$	14.9111	−	23.9543i	0.563988	−	0.906034i
$700$	−23.4814	+	8.44492i	−0.887513	+	0.319188i
$701$	−6.75507			−0.255136			−0.127568	−	0.991830i	$-0.540717\pi$
$701$	−6.75507			−0.255136			−0.127568	+	0.991830i	$0.540717\pi$
$702$	8.76424	+	35.5247i	0.330785	+	1.34079i
$703$	12.9369	+	7.46910i	0.487923	+	0.281702i
$704$	36.5590	+	1.67438i	1.37787	+	0.0631055i
$705$	5.37969	+	0.178598i	0.202611	+	0.00672640i
$706$	−3.44636	+	18.7096i	−0.129706	+	0.704145i
$707$	3.37423	−	9.61100i	0.126901	−	0.361459i
$708$	18.2025	−	13.8287i	0.684092	−	0.519715i
$709$	36.0884	−	20.8357i	1.35533	−	0.782499i	0.366339	−	0.930482i	$-0.380611\pi$
$709$	36.0884	−	20.8357i	1.35533	−	0.782499i	0.988990	+	0.147982i	$0.0472778\pi$
$710$	3.56117	+	3.03477i	0.133648	+	0.113893i
$711$	−0.136973	−	0.00910466i	−0.00513689	−	0.000341452i
$712$	−46.5642	−	1.06575i	−1.74507	−	0.0399405i
$713$	−0.266971			−0.00999815
$714$	−24.6626	+	13.2885i	−0.922973	+	0.497311i
$715$		−	12.1427i		−	0.454112i
$716$	−1.27506	−	7.93750i	−0.0476514	−	0.296638i
$717$	−16.5127	−	30.9275i	−0.616680	−	1.15501i
$718$	−21.1641	+	24.8352i	−0.789836	+	0.926840i
$719$	−23.2782	−	40.3190i	−0.868131	−	1.50365i	−0.863904	−	0.503656i	$-0.831988\pi$
$719$	−23.2782	−	40.3190i	−0.868131	−	1.50365i	−0.00422645	−	0.999991i	$-0.501345\pi$
$720$	−6.16281	−	1.71502i	−0.229674	−	0.0639149i
$721$	−9.17600	−	10.6851i	−0.341732	−	0.397934i
$722$	−3.99823	+	21.7056i	−0.148799	+	0.807799i
$723$	15.9774	+	0.530429i	0.594208	+	0.0197269i
$724$	−23.0550	+	18.7536i	−0.856833	+	0.696973i
$725$	−18.2630	+	31.6325i	−0.678271	+	1.17480i
$726$	−23.7557	−	5.19629i	−0.881656	−	0.192853i
$727$			10.7218i			0.397651i	0.980035	+	0.198825i	$0.0637127\pi$
$727$			10.7218i			0.397651i	−0.980035	+	0.198825i	$0.936287\pi$
$728$	34.8658	+	13.1443i	1.29221	+	0.487160i
$729$	−26.4665	−	5.34075i	−0.980241	−	0.197805i
$730$	−6.85351	+	2.43543i	−0.253660	+	0.0901394i
$731$	−7.00871	−	4.04648i	−0.259227	−	0.149665i
$732$	−7.39309	+	0.937171i	−0.273256	+	0.0346388i
$733$	−12.5202	−	21.6857i	−0.462445	−	0.800979i	0.536637	−	0.843813i	$-0.319695\pi$
$733$	−12.5202	−	21.6857i	−0.462445	−	0.800979i	−0.999082	+	0.0428345i	$0.986361\pi$
$734$	−30.0145	−	5.52876i	−1.10786	−	0.204070i
$735$	1.18801	−	6.35316i	0.0438203	−	0.234340i
$736$	0.414048	+	0.533503i	0.0152620	+	0.0196652i
$737$	−47.9478	+	27.6827i	−1.76618	+	1.01971i
$738$	−2.72294	+	10.7295i	−0.100233	+	0.394959i
$739$	−45.0173	−	25.9908i	−1.65599	−	0.956086i	−0.974538	−	0.224224i	$-0.928015\pi$
$739$	−45.0173	−	25.9908i	−1.65599	−	0.956086i	−0.681452	−	0.731863i	$-0.738651\pi$
$740$	−1.37122	−	8.53611i	−0.0504071	−	0.313794i
$741$	13.4878	+	8.39588i	0.495486	+	0.308430i
$742$	−17.1582	+	0.0652330i	−0.629896	+	0.00239478i
$743$			26.4603i			0.970735i	0.874310	+	0.485367i	$0.161314\pi$
$743$			26.4603i			0.970735i	−0.874310	+	0.485367i	$0.838686\pi$
$744$	−6.00086	+	9.16588i	−0.220002	+	0.336037i
$745$	9.94549	+	5.74203i	0.364375	+	0.210372i
$746$	−0.168290	+	0.197482i	−0.00616155	+	0.00723032i
$747$	9.63391	+	6.45004i	0.352486	+	0.235995i
$748$	−36.9546	−	14.0924i	−1.35119	−	0.515270i
$749$	18.4916	−	15.8800i	0.675670	−	0.580242i
$750$	9.37776	+	8.54463i	0.342428	+	0.312006i
$751$	−9.69510	−	16.7924i	−0.353779	−	0.612763i	0.633129	−	0.774046i	$-0.281770\pi$
$751$	−9.69510	−	16.7924i	−0.353779	−	0.612763i	−0.986908	+	0.161283i	$0.948437\pi$
$752$	−22.1454	+	7.30322i	−0.807558	+	0.266321i
$753$	−6.70694	−	12.5617i	−0.244414	−	0.457775i
$754$	51.3926	−	18.2626i	1.87161	−	0.665086i
$755$		−	1.50081i		−	0.0546202i
$756$	−19.7531	+	19.1263i	−0.718412	+	0.695618i
$757$		−	5.19772i		−	0.188914i	−0.995529	−	0.0944572i	$-0.969888\pi$
$757$		−	5.19772i		−	0.188914i	0.995529	−	0.0944572i	$-0.0301115\pi$
$758$	−1.38917	−	3.90923i	−0.0504568	−	0.141990i
$759$	−0.445520	−	0.834436i	−0.0161714	−	0.0302881i
$760$	−2.43662	+	1.33340i	−0.0883856	+	0.0483674i
$761$	18.8681	+	32.6805i	0.683969	+	1.18467i	0.973760	+	0.227578i	$0.0730808\pi$
$761$	18.8681	+	32.6805i	0.683969	+	1.18467i	−0.289791	+	0.957090i	$0.593586\pi$
$762$	13.5116	−	14.8290i	0.489473	−	0.537198i
$763$	−4.29288	+	12.2277i	−0.155413	+	0.442671i
$764$	−14.0839	+	36.9321i	−0.509536	+	1.33616i
$765$	5.74456	+	3.84606i	0.207695	+	0.139055i
$766$	16.5223	+	14.0800i	0.596973	+	0.508730i
$767$	28.4559	+	16.4290i	1.02748	+	0.593218i
$768$	27.6235	−	2.22359i	0.996776	−	0.0802370i
$769$		−	13.9517i		−	0.503110i	−0.967843	−	0.251555i	$-0.919058\pi$
$769$		−	13.9517i		−	0.503110i

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 168 = 2^{3} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	168.ba (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.33258 + 0.473539i) q^{2} +(-1.52791 + 0.815778i) q^{3} +(1.55152 - 1.26205i) q^{4} +(0.461663 - 0.266541i) q^{5} +(1.64975 - 1.81061i) q^{6} +(0.489180 + 2.60014i) q^{7} +(-1.46989 + 2.41649i) q^{8} +(1.66901 - 2.49287i) q^{9} +O(q^{10})\)	\(q+(-1.33258 + 0.473539i) q^{2} +(-1.52791 + 0.815778i) q^{3} +(1.55152 - 1.26205i) q^{4} +(0.461663 - 0.266541i) q^{5} +(1.64975 - 1.81061i) q^{6} +(0.489180 + 2.60014i) q^{7} +(-1.46989 + 2.41649i) q^{8} +(1.66901 - 2.49287i) q^{9} +(-0.488984 + 0.573802i) q^{10} +(-2.28733 + 3.96177i) q^{11} +(-1.34103 + 3.19400i) q^{12} -4.97924 q^{13} +(-1.88313 - 3.23323i) q^{14} +(-0.487941 + 0.783866i) q^{15} +(0.814443 - 3.91621i) q^{16} +(-2.16139 + 3.74363i) q^{17} +(-1.04362 + 4.11228i) q^{18} +(0.921087 + 1.59537i) q^{19} +(0.379891 - 0.996188i) q^{20} +(-2.86856 - 3.57371i) q^{21} +(1.17199 - 6.36250i) q^{22} +(0.103387 - 0.0596907i) q^{23} +(0.274542 - 4.89128i) q^{24} +(-2.35791 + 4.08402i) q^{25} +(6.63522 - 2.35786i) q^{26} +(-0.516471 + 5.17042i) q^{27} +(4.04048 + 3.41680i) q^{28} +7.74542 q^{29} +(0.279028 - 1.27562i) q^{30} +(-1.93668 - 1.11814i) q^{31} +(0.769168 + 5.60432i) q^{32} +(0.262906 - 7.91918i) q^{33} +(1.10746 - 6.01218i) q^{34} +(0.918880 + 1.07000i) q^{35} +(-0.556624 - 5.97413i) q^{36} +(7.02261 - 4.05451i) q^{37} +(-1.98289 - 1.68978i) q^{38} +(7.60783 - 4.06195i) q^{39} +(-0.0345007 + 1.50739i) q^{40} +2.60914 q^{41} +(5.51486 + 3.40387i) q^{42} +1.87217i q^{43} +(1.45112 + 9.03351i) q^{44} +(0.106069 - 1.59573i) q^{45} +(-0.109506 + 0.128500i) q^{46} +(-2.91482 - 5.04861i) q^{47} +(1.95036 + 6.64801i) q^{48} +(-6.52141 + 2.54387i) q^{49} +(1.20816 - 6.55884i) q^{50} +(0.248430 - 7.48314i) q^{51} +(-7.72540 + 6.28407i) q^{52} +(2.29287 - 3.97137i) q^{53} +(-1.76016 - 7.13455i) q^{54} +2.43867i q^{55} +(-7.00224 - 2.63982i) q^{56} +(-2.70880 - 1.68618i) q^{57} +(-10.3214 + 3.66775i) q^{58} +(-5.71492 - 3.29951i) q^{59} +(0.232229 + 1.83199i) q^{60} +(1.07564 + 1.86306i) q^{61} +(3.11026 + 0.572919i) q^{62} +(7.29824 + 3.12020i) q^{63} +(-3.67884 - 7.10395i) q^{64} +(-2.29873 + 1.32717i) q^{65} +(3.39970 + 10.6774i) q^{66} +(10.4812 + 6.05131i) q^{67} +(1.37122 + 8.53611i) q^{68} +(-0.109272 + 0.175543i) q^{69} +(-1.73116 - 0.990732i) q^{70} -6.20627i q^{71} +(3.57072 + 7.69740i) q^{72} +(8.35520 + 4.82388i) q^{73} +(-7.43820 + 8.72842i) q^{74} +(0.271018 - 8.16355i) q^{75} +(3.44253 + 1.31279i) q^{76} +(-11.4201 - 4.00935i) q^{77} +(-8.21452 + 9.01547i) q^{78} +(-0.0228792 - 0.0396280i) q^{79} +(-0.667833 - 2.02505i) q^{80} +(-3.42880 - 8.32126i) q^{81} +(-3.47688 + 1.23553i) q^{82} +3.86459i q^{83} +(-8.96084 - 1.92442i) q^{84} +2.30440i q^{85} +(-0.886545 - 2.49481i) q^{86} +(-11.8343 + 6.31854i) q^{87} +(-6.21145 - 11.3507i) q^{88} +(8.23362 + 14.2610i) q^{89} +(0.614293 + 2.17666i) q^{90} +(-2.43575 - 12.9467i) q^{91} +(0.0850749 - 0.223092i) q^{92} +(3.87123 + 0.128520i) q^{93} +(6.27493 + 5.34738i) q^{94} +(0.850463 + 0.491015i) q^{95} +(-5.74710 - 7.93542i) q^{96} -7.18828i q^{97} +(7.48565 - 6.47804i) q^{98} +(6.05860 + 12.3143i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 6 q^{4} - 4 q^{7} - 14 q^{9}+O(q^{10}) \) 48 * q + 6 * q^4 - 4 * q^7 - 14 * q^9	\( 48 q + 6 q^{4} - 4 q^{7} - 14 q^{9} - 30 q^{10} - 18 q^{12} + 4 q^{15} + 6 q^{16} - 36 q^{22} - 12 q^{24} - 8 q^{25} - 10 q^{28} + 22 q^{30} + 48 q^{31} - 42 q^{33} + 52 q^{36} - 8 q^{39} - 18 q^{40} + 12 q^{42} - 8 q^{46} - 36 q^{49} - 48 q^{52} + 60 q^{54} + 4 q^{57} + 30 q^{58} - 32 q^{60} - 6 q^{63} - 60 q^{64} + 54 q^{66} + 42 q^{70} + 42 q^{72} - 36 q^{73} - 68 q^{78} - 56 q^{79} + 42 q^{81} + 48 q^{82} + 48 q^{84} - 132 q^{87} + 6 q^{88} + 48 q^{94} + 90 q^{96}+O(q^{100}) \) 48 * q + 6 * q^4 - 4 * q^7 - 14 * q^9 - 30 * q^10 - 18 * q^12 + 4 * q^15 + 6 * q^16 - 36 * q^22 - 12 * q^24 - 8 * q^25 - 10 * q^28 + 22 * q^30 + 48 * q^31 - 42 * q^33 + 52 * q^36 - 8 * q^39 - 18 * q^40 + 12 * q^42 - 8 * q^46 - 36 * q^49 - 48 * q^52 + 60 * q^54 + 4 * q^57 + 30 * q^58 - 32 * q^60 - 6 * q^63 - 60 * q^64 + 54 * q^66 + 42 * q^70 + 42 * q^72 - 36 * q^73 - 68 * q^78 - 56 * q^79 + 42 * q^81 + 48 * q^82 + 48 * q^84 - 132 * q^87 + 6 * q^88 + 48 * q^94 + 90 * q^96

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