LMFDB - Embedded newform 168.2.ba.c.5.22

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			5.22
Character	$\chi$	$=$	168.5
Dual form			168.2.ba.c.101.22

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.33258 + 0.473539i) q^{2} +(0.0574700 - 1.73110i) q^{3} +(1.55152 + 1.26205i) q^{4} +(-0.461663 - 0.266541i) q^{5} +(0.896325 - 2.27961i) q^{6} +(0.489180 - 2.60014i) q^{7} +(1.46989 + 2.41649i) q^{8} +(-2.99339 - 0.198972i) q^{9} +O(q^{10})$	\(q+(1.33258 + 0.473539i) q^{2} +(0.0574700 - 1.73110i) q^{3} +(1.55152 + 1.26205i) q^{4} +(-0.461663 - 0.266541i) q^{5} +(0.896325 - 2.27961i) q^{6} +(0.489180 - 2.60014i) q^{7} +(1.46989 + 2.41649i) q^{8} +(-2.99339 - 0.198972i) q^{9} +(-0.488984 - 0.573802i) q^{10} +(2.28733 + 3.96177i) q^{11} +(2.27390 - 2.61331i) 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} +(-3.89471 - 1.68263i) q^{18} +(0.921087 - 1.59537i) q^{19} +(-0.379891 - 0.996188i) q^{20} +(-4.47297 - 0.996248i) q^{21} +(1.17199 + 6.36250i) q^{22} +(-0.103387 - 0.0596907i) q^{23} +(4.26765 - 2.40565i) 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} +(-1.02141 + 0.813502i) q^{30} +(-1.93668 + 1.11814i) q^{31} +(-0.769168 + 5.60432i) q^{32} +(6.98966 - 3.73191i) q^{33} +(1.10746 + 6.01218i) q^{34} +(-0.918880 + 1.07000i) q^{35} +(-4.39320 - 4.08653i) q^{36} +(7.02261 + 4.05451i) q^{37} +(1.98289 - 1.68978i) q^{38} +(-0.286157 + 8.61955i) q^{39} +(-0.0345007 - 1.50739i) q^{40} -2.60914 q^{41} +(-5.48882 - 3.44570i) q^{42} -1.87217i q^{43} +(-1.45112 + 9.03351i) q^{44} +(1.32891 + 0.889722i) q^{45} +(-0.109506 - 0.128500i) q^{46} +(2.91482 - 5.04861i) q^{47} +(6.82614 - 1.18482i) q^{48} +(-6.52141 - 2.54387i) q^{49} +(-1.20816 - 6.55884i) q^{50} +(6.60480 - 3.52642i) q^{51} +(-7.72540 - 6.28407i) q^{52} +(-2.29287 - 3.97137i) q^{53} +(-3.13663 + 6.64542i) 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} +(-1.74633 + 0.600378i) q^{60} +(1.07564 - 1.86306i) q^{61} +(-3.11026 + 0.572919i) q^{62} +(-1.98166 + 7.68590i) q^{63} +(-3.67884 + 7.10395i) q^{64} +(2.29873 + 1.32717i) q^{65} +(11.0815 - 1.66318i) 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} +(-3.91915 - 7.52597i) q^{72} +(8.35520 - 4.82388i) q^{73} +(7.43820 + 8.72842i) q^{74} +(-7.20535 + 3.84706i) q^{75} +(3.44253 - 1.31279i) q^{76} +(11.4201 - 4.00935i) q^{77} +(-4.46302 + 11.3507i) q^{78} +(-0.0228792 + 0.0396280i) q^{79} +(0.667833 - 2.02505i) q^{80} +(8.92082 + 1.19121i) q^{81} +(-3.47688 - 1.23553i) q^{82} +3.86459i q^{83} +(-5.68260 - 7.19083i) q^{84} -2.30440i q^{85} +(0.886545 - 2.49481i) q^{86} +(-0.445129 + 13.4081i) q^{87} +(-6.21145 + 11.3507i) q^{88} +(-8.23362 + 14.2610i) q^{89} +(1.34955 + 1.81491i) q^{90} +(-2.43575 + 12.9467i) q^{91} +(-0.0850749 - 0.223092i) q^{92} +(1.82431 + 3.41684i) q^{93} +(6.27493 - 5.34738i) q^{94} +(-0.850463 + 0.491015i) q^{95} +(9.65741 + 1.65358i) 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 $\left(\mathbb{Z}/168\mathbb{Z}\right)^\times$.

$n$	$73$	$85$	$113$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$-1$	$1$

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
$3$	0.0574700	−	1.73110i	0.0331803	−	0.999449i
$3$	0.0574700	−	1.73110i	0.0331803	−	0.999449i
$4$	1.55152	+	1.26205i	0.775761	+	0.631027i
$5$	−0.461663	−	0.266541i	−0.206462	−	0.119201i	0.393204	−	0.919451i	$-0.371367\pi$
$5$	−0.461663	−	0.266541i	−0.206462	−	0.119201i	−0.599666	+	0.800250i	$0.704700\pi$
$6$	0.896325	−	2.27961i	0.365923	−	0.930645i
$7$	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
$9$	−2.99339	−	0.198972i	−0.997798	−	0.0663241i
$10$	−0.488984	−	0.573802i	−0.154630	−	0.181452i
$11$	2.28733	+	3.96177i	0.689656	+	1.19452i	0.971949	+	0.235191i	$0.0755716\pi$
$11$	2.28733	+	3.96177i	0.689656	+	1.19452i	−0.282293	+	0.959328i	$0.591095\pi$
$12$	2.27390	−	2.61331i	0.656419	−	0.754396i
$13$	−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	0.999603	+	0.0281884i	$0.00897383\pi$
$17$	2.16139	+	3.74363i	0.524213	+	0.907964i	−0.475389	+	0.879775i	$0.657693\pi$
$18$	−3.89471	−	1.68263i	−0.917991	−	0.396601i
$19$	0.921087	−	1.59537i	0.211312	−	0.366003i	−0.740814	−	0.671711i	$-0.765560\pi$
$19$	0.921087	−	1.59537i	0.211312	−	0.366003i	0.952125	+	0.305708i	$0.0988931\pi$
$20$	−0.379891	−	0.996188i	−0.0849463	−	0.222754i
$21$	−4.47297	−	0.996248i	−0.976083	−	0.217399i
$22$	1.17199	+	6.36250i	0.249869	+	1.35649i
$23$	−0.103387	−	0.0596907i	−0.0215577	−	0.0124464i	0.489182	−	0.872182i	$-0.337295\pi$
$23$	−0.103387	−	0.0596907i	−0.0215577	−	0.0124464i	−0.510740	+	0.859735i	$0.670629\pi$
$24$	4.26765	−	2.40565i	0.871131	−	0.491051i
$25$	−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	$-0.755466\pi$
$29$	−7.74542			−1.43829			−0.719144	+	0.694861i	$0.755466\pi$
$30$	−1.02141	+	0.813502i	−0.186483	+	0.148525i
$31$	−1.93668	+	1.11814i	−0.347838	+	0.200825i	−0.663733	−	0.747970i	$-0.731029\pi$
$31$	−1.93668	+	1.11814i	−0.347838	+	0.200825i	0.315894	+	0.948794i	$0.397695\pi$
$32$	−0.769168	+	5.60432i	−0.135971	+	0.990713i
$33$	6.98966	−	3.73191i	1.21674	−	0.649642i
$34$	1.10746	+	6.01218i	0.189928	+	1.03108i
$35$	−0.918880	+	1.07000i	−0.155319	+	0.180863i
$36$	−4.39320	−	4.08653i	−0.732201	−	0.681089i
$37$	7.02261	+	4.05451i	1.15451	+	0.666557i	0.949982	−	0.312304i	$-0.101101\pi$
$37$	7.02261	+	4.05451i	1.15451	+	0.666557i	0.204528	+	0.978861i	$0.434434\pi$
$38$	1.98289	−	1.68978i	0.321667	−	0.274119i
$39$	−0.286157	+	8.61955i	−0.0458218	+	1.38023i
$40$	−0.0345007	−	1.50739i	−0.00545504	−	0.238339i
$41$	−2.60914			−0.407479			−0.203740	−	0.979025i	$-0.565310\pi$
$41$	−2.60914			−0.407479			−0.203740	+	0.979025i	$0.565310\pi$
$42$	−5.48882	−	3.44570i	−0.846943	−	0.531683i
$43$		−	1.87217i		−	0.285503i	−0.989759	−	0.142752i	$-0.954405\pi$
$43$		−	1.87217i		−	0.285503i	0.989759	−	0.142752i	$-0.0455950\pi$
$44$	−1.45112	+	9.03351i	−0.218765	+	1.36185i
$45$	1.32891	+	0.889722i	0.198102	+	0.132632i
$46$	−0.109506	−	0.128500i	−0.0161457	−	0.0189463i
$47$	2.91482	−	5.04861i	0.425170	−	0.736415i	−0.571267	−	0.820764i	$-0.693548\pi$
$47$	2.91482	−	5.04861i	0.425170	−	0.736415i	0.996436	+	0.0843492i	$0.0268811\pi$
$48$	6.82614	−	1.18482i	0.985269	−	0.171013i
$49$	−6.52141	−	2.54387i	−0.931629	−	0.363410i
$50$	−1.20816	−	6.55884i	−0.170859	−	0.927559i
$51$	6.60480	−	3.52642i	0.924857	−	0.493798i
$52$	−7.72540	−	6.28407i	−1.07132	−	0.871443i
$53$	−2.29287	−	3.97137i	−0.314950	−	0.545510i	0.664476	−	0.747309i	$-0.268655\pi$
$53$	−2.29287	−	3.97137i	−0.314950	−	0.545510i	−0.979427	+	0.201799i	$0.935321\pi$
$54$	−3.13663	+	6.64542i	−0.426842	+	0.904326i
$55$		−	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	$-0.525336\pi$
$59$	5.71492	−	3.29951i	0.744019	−	0.429559i	0.823529	+	0.567275i	$0.192002\pi$
$60$	−1.74633	+	0.600378i	−0.225450	+	0.0775084i
$61$	1.07564	−	1.86306i	0.137722	−	0.238541i	−0.788912	−	0.614506i	$-0.789355\pi$
$61$	1.07564	−	1.86306i	0.137722	−	0.238541i	0.926634	+	0.375965i	$0.122689\pi$
$62$	−3.11026	+	0.572919i	−0.395004	+	0.0727608i
$63$	−1.98166	+	7.68590i	−0.249666	+	0.968332i
$64$	−3.67884	+	7.10395i	−0.459855	+	0.887994i
$65$	2.29873	+	1.32717i	0.285123	+	0.164616i
$66$	11.0815	−	1.66318i	1.36403	−	0.204723i
$67$	10.4812	−	6.05131i	1.28048	−	0.739285i	0.303544	−	0.952817i	$-0.401830\pi$
$67$	10.4812	−	6.05131i	1.28048	−	0.739285i	0.976936	+	0.213532i	$0.0684968\pi$
$68$	−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	$-0.120051\pi$
$72$	−3.91915	−	7.52597i	−0.461876	−	0.886944i
$73$	8.35520	−	4.82388i	0.977902	−	0.564592i	0.0762659	−	0.997088i	$-0.475700\pi$
$73$	8.35520	−	4.82388i	0.977902	−	0.564592i	0.901636	+	0.432496i	$0.142367\pi$
$74$	7.43820	+	8.72842i	0.864673	+	1.01466i
$75$	−7.20535	+	3.84706i	−0.832002	+	0.444221i
$76$	3.44253	−	1.31279i	0.394885	−	0.150587i
$77$	11.4201	−	4.00935i	1.30144	−	0.456908i
$78$	−4.46302	+	11.3507i	−0.505337	+	1.28521i
$79$	−0.0228792	+	0.0396280i	−0.00257411	+	0.00445849i	−0.867310	−	0.497769i	$-0.834153\pi$
$79$	−0.0228792	+	0.0396280i	−0.00257411	+	0.00445849i	0.864735	+	0.502228i	$0.167486\pi$
$80$	0.667833	−	2.02505i	0.0746660	−	0.226408i
$81$	8.92082	+	1.19121i	0.991202	+	0.132356i
$82$	−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	$0.931971\pi$
$84$	−5.68260	−	7.19083i	−0.620022	−	0.784584i
$85$		−	2.30440i		−	0.249947i
$86$	0.886545	−	2.49481i	0.0955986	−	0.269022i
$87$	−0.445129	+	13.4081i	−0.0477229	+	1.43750i
$88$	−6.21145	+	11.3507i	−0.662143	+	1.20999i
$89$	−8.23362	+	14.2610i	−0.872762	+	1.51167i	−0.0136336	+	0.999907i	$0.504340\pi$
$89$	−8.23362	+	14.2610i	−0.872762	+	1.51167i	−0.859128	+	0.511761i	$0.828993\pi$
$90$	1.34955	+	1.81491i	0.142255	+	0.191308i
$91$	−2.43575	+	12.9467i	−0.255335	+	1.35718i
$92$	−0.0850749	−	0.223092i	−0.00886967	−	0.0232589i
$93$	1.82431	+	3.41684i	0.189173	+	0.354310i
$94$	6.27493	−	5.34738i	0.647209	−	0.551540i
$95$	−0.850463	+	0.491015i	−0.0872557	+	0.0503771i
$96$	9.65741	+	1.65358i	0.985656	+	0.168768i
$97$			7.18828i			0.729859i	0.931035	+	0.364930i	$0.118907\pi$
$97$			7.18828i			0.729859i	−0.931035	+	0.364930i	$0.881093\pi$
$98$	−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	$-0.605317\pi$
$101$	3.33419	−	1.92499i	0.331764	−	0.191544i	0.656624	+	0.754218i	$0.271984\pi$
$102$	10.4713	−	1.57160i	1.03681	−	0.155612i
$103$	−4.61020	−	2.66170i	−0.454256	−	0.262265i	0.255370	−	0.966843i	$-0.417803\pi$
$103$	−4.61020	−	2.66170i	−0.454256	−	0.262265i	−0.709626	+	0.704578i	$0.751136\pi$
$104$	−7.31894	−	12.0323i	−0.717682	−	1.17986i
$105$	1.79947	+	1.65216i	0.175610	+	0.161235i
$106$	−1.17483	−	6.37793i	−0.114110	−	0.619479i
$107$	4.60634	−	7.97842i	0.445312	−	0.771303i	−0.552762	−	0.833339i	$-0.686426\pi$
$107$	4.60634	−	7.97842i	0.445312	−	0.771303i	0.998074	+	0.0620363i	$0.0197594\pi$
$108$	−7.32666	+	7.37021i	−0.705009	+	0.709199i
$109$	4.24194	−	2.44909i	0.406304	−	0.234580i	−0.282896	−	0.959151i	$-0.591295\pi$
$109$	4.24194	−	2.44909i	0.406304	−	0.234580i	0.689201	+	0.724571i	$0.257962\pi$
$110$	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	$-0.0583602\pi$
$114$	−2.81122	−	3.52968i	−0.263295	−	0.330585i
$115$	0.0318201	+	0.0551140i	0.00296724	+	0.00513941i
$116$	−12.0172	−	9.77513i	−1.11577	−	0.907598i
$117$	14.9048	+	0.990731i	1.37795	+	0.0915932i
$118$	9.17801	−	1.69061i	0.844904	−	0.155634i
$119$	10.7913	−	3.78859i	0.989233	−	0.347299i
$120$	−2.61142	−	0.0269057i	−0.238389	−	0.00245615i
$121$	−4.96376	+	8.59748i	−0.451251	+	0.781589i
$122$	2.31560	−	1.97332i	0.209645	−	0.178656i
$123$	−0.149947	+	4.51667i	−0.0135203	+	0.407255i
$124$	−4.41596	−	0.709371i	−0.396565	−	0.0637034i
$125$			5.17934i			0.463254i
$126$	−6.28029	+	9.30365i	−0.559493	+	0.828835i
$127$	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
$129$	−3.24091	−	0.107594i	−0.285346	−	0.00947310i
$130$	2.43477	+	2.85710i	0.213543	+	0.250584i
$131$	−18.5565	−	10.7136i	−1.62129	−	0.936053i	−0.986575	−	0.163306i	$-0.947784\pi$
$131$	−18.5565	−	10.7136i	−1.62129	−	0.936053i	−0.634715	−	0.772746i	$-0.718883\pi$
$132$	15.5545	+	3.03119i	1.35384	+	0.263831i
$133$	−3.69760	−	3.17537i	−0.320622	−	0.275340i
$134$	16.8325	−	3.10059i	1.45411	−	0.267851i
$135$	1.61657	−	2.24933i	0.139132	−	0.193592i
$136$	−5.86944	+	10.7257i	−0.503300	+	0.919721i
$137$	−3.91533	+	2.26052i	−0.334509	+	0.193129i	−0.657841	−	0.753157i	$-0.728530\pi$
$137$	−3.91533	+	2.26052i	−0.334509	+	0.193129i	0.323332	+	0.946286i	$0.395197\pi$
$138$	−0.228740	+	0.182180i	−0.0194716	+	0.0155082i
$139$	−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
$144$	−1.65873	−	11.8848i	−0.138228	−	0.990400i
$145$	3.57577	+	2.06447i	0.296952	+	0.171445i
$146$	13.4182	−	2.47168i	1.11050	−	0.204557i
$147$	−4.77847	+	11.1430i	−0.394121	+	0.919058i
$148$	5.77873	+	15.1536i	0.475009	+	1.24562i
$149$	−10.7714	+	18.6566i	−0.882425	+	1.52841i	−0.0337890	+	0.999429i	$0.510757\pi$
$149$	−10.7714	+	18.6566i	−0.882425	+	1.52841i	−0.848636	+	0.528977i	$0.822576\pi$
$150$	−11.4234	+	1.71450i	−0.932718	+	0.139988i
$151$	1.40767	+	2.43816i	0.114555	+	0.198415i	0.917602	−	0.397501i	$-0.130122\pi$
$151$	1.40767	+	2.43816i	0.114555	+	0.198415i	−0.803047	+	0.595916i	$0.796789\pi$
$152$	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
$156$	−11.3223	+	13.0123i	−0.906510	+	1.04182i
$157$	3.54427	+	6.13885i	0.282863	+	0.489933i	0.972089	−	0.234613i	$-0.0753824\pi$
$157$	3.54427	+	6.13885i	0.282863	+	0.489933i	−0.689226	+	0.724547i	$0.742049\pi$
$158$	−0.0492537	+	0.0419731i	−0.00391841	+	0.00333920i
$159$	−7.00661	+	3.74095i	−0.555660	+	0.296677i
$160$	1.84888	−	2.38229i	0.146167	−	0.188337i
$161$	−0.205779	+	0.239622i	−0.0162176	+	0.0188848i
$162$	11.3236	+	5.81173i	0.889666	+	0.456612i
$163$	−5.64257	−	3.25774i	−0.441960	−	0.255166i	0.262469	−	0.964941i	$-0.415463\pi$
$163$	−5.64257	−	3.25774i	−0.441960	−	0.255166i	−0.704429	+	0.709775i	$0.748797\pi$
$164$	−4.04814	−	3.29287i	−0.316106	−	0.257130i
$165$	−4.22158	−	0.140151i	−0.328649	−	0.0109107i
$166$	−1.83003	+	5.14986i	−0.142038	+	0.399707i
$167$	−17.2470			−1.33462			−0.667308	−	0.744782i	$-0.732553\pi$
$167$	−17.2470			−1.33462			−0.667308	+	0.744782i	$0.732553\pi$
$168$	−4.16736	−	12.2733i	−0.321519	−	0.946903i
$169$	11.7928			0.907141
$170$	1.09122	−	3.07078i	0.0836928	−	0.235518i
$171$	−3.07461	+	4.59230i	−0.235121	+	0.351182i
$172$	2.36278	−	2.90471i	0.180160	−	0.221482i
$173$	14.5387	+	8.39395i	1.10536	+	0.638180i	0.937624	−	0.347652i	$-0.113021\pi$
$173$	14.5387	+	8.39395i	1.10536	+	0.638180i	0.167737	+	0.985832i	$0.446354\pi$
$174$	−6.94241	+	17.6565i	−0.526303	+	1.33854i
$175$	−11.7725	+	4.13307i	−0.889914	+	0.312430i
$176$	−13.6522	+	12.1843i	−1.02907	+	0.918426i
$177$	−5.38333	−	10.0827i	−0.404636	−	0.757862i
$178$	−17.7251	+	15.1050i	−1.32855	+	1.13217i
$179$	−2.00982	−	3.48110i	−0.150221	−	0.260190i	0.781088	−	0.624421i	$-0.214665\pi$
$179$	−2.00982	−	3.48110i	−0.150221	−	0.260190i	−0.931309	+	0.364231i	$0.881332\pi$
$180$	0.938950	+	3.05757i	0.0699852	+	0.227898i
$181$	−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
$186$	0.813031	+	5.41709i	0.0596143	+	0.397200i
$187$	−9.88761	+	17.1258i	−0.723053	+	1.25237i
$188$	10.8940	−	4.15438i	0.794528	−	0.302989i
$189$	13.1911	+	3.87216i	0.959515	+	0.281658i
$190$	−1.36582	+	0.251588i	−0.0990872	+	0.0182521i
$191$	17.1154	+	9.88159i	1.23843	+	0.715006i	0.968773	−	0.247951i	$-0.0797570\pi$
$191$	17.1154	+	9.88159i	1.23843	+	0.715006i	0.269655	+	0.962957i	$0.413090\pi$
$192$	12.0862	+	6.77669i	0.872247	+	0.489065i
$193$	−6.29229	−	10.8986i	−0.452929	−	0.784496i	0.545638	−	0.838021i	$-0.316287\pi$
$193$	−6.29229	−	10.8986i	−0.452929	−	0.784496i	−0.998566	+	0.0535255i	$0.982954\pi$
$194$	−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	$-0.403053\pi$
$197$	8.41804			0.599761			0.299880	+	0.953977i	$0.403053\pi$
$198$	−2.24227	−	19.2787i	−0.159351	−	1.37008i
$199$	12.3980	−	7.15800i	0.878873	−	0.507417i	0.00858618	−	0.999963i	$-0.497267\pi$
$199$	12.3980	−	7.15800i	0.878873	−	0.507417i	0.870287	+	0.492546i	$0.163934\pi$
$200$	6.40312	−	11.7009i	0.452769	−	0.827381i
$201$	−9.87305	−	18.4917i	−0.696392	−	1.30430i
$202$	5.35462	−	0.986336i	0.376750	−	0.0693983i
$203$	−3.78890	+	20.1391i	−0.265929	+	1.41349i
$204$	14.6980	+	2.86429i	1.02907	+	0.200540i
$205$	1.20454	+	0.695443i	0.0841290	+	0.0485719i
$206$	−4.88303	−	5.73003i	−0.340217	−	0.399230i
$207$	0.297602	+	0.199249i	0.0206848	+	0.0138488i
$208$	−4.05531	−	19.4997i	−0.281185	−	1.35206i
$209$	8.42732			0.582930
$210$	1.61556	+	3.05375i	0.111484	+	0.210729i
$211$		−	9.62315i		−	0.662485i	−0.943546	−	0.331243i	$-0.892532\pi$
$211$		−	9.62315i		−	0.662485i	0.943546	−	0.331243i	$-0.107468\pi$
$212$	1.45464	−	9.05541i	0.0999051	−	0.621928i
$213$	−10.7437	−	0.356675i	−0.736144	−	0.0244390i
$214$	9.91640	−	8.45058i	0.677871	−	0.577669i
$215$	−0.499011	+	0.864312i	−0.0340323	+	0.0589456i
$216$	−13.2534	+	6.35191i	−0.901781	+	0.432193i
$217$	1.95994	+	5.58261i	0.133049	+	0.378972i
$218$	6.81245	−	1.25487i	0.461397	−	0.0849907i
$219$	−7.87042	−	14.7409i	−0.531834	−	0.996097i
$220$	3.07773	−	3.78365i	0.207501	−	0.255094i
$221$	−10.7621	−	18.6404i	−0.723935	−	1.25389i
$222$	15.5372	−	12.3746i	1.04279	−	0.830531i
$223$			20.1840i			1.35162i	0.737076	+	0.675810i	$0.236206\pi$
$223$			20.1840i			1.35162i	−0.737076	+	0.675810i	$0.763794\pi$
$224$	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	$-0.654051\pi$
$227$	1.03403	−	0.597000i	0.0686313	−	0.0396243i	0.533923	+	0.845533i	$0.320717\pi$
$228$	−2.07472	−	6.03479i	−0.137402	−	0.399664i
$229$	11.4021	−	19.7490i	0.753472	−	1.30505i	−0.192658	−	0.981266i	$-0.561711\pi$
$229$	11.4021	−	19.7490i	0.753472	−	1.30505i	0.946130	−	0.323786i	$-0.104956\pi$
$230$	0.0163041	+	0.0885117i	0.00107506	+	0.00583629i
$231$	−6.28426	−	19.9996i	−0.413474	−	1.31588i
$232$	−11.3849	−	18.7167i	−0.747457	−	1.22881i
$233$	14.1080	+	8.14528i	0.924249	+	0.533615i	0.884988	−	0.465614i	$-0.154166\pi$
$233$	14.1080	+	8.14528i	0.924249	+	0.533615i	0.0392607	+	0.999229i	$0.487500\pi$
$234$	19.3927	+	8.37824i	1.26774	+	0.547703i
$235$	−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	$0.772810\pi$
$240$	−3.46718	−	1.27246i	−0.223806	−	0.0821372i
$241$	−7.99312	+	4.61483i	−0.514882	+	0.297267i	−0.734838	−	0.678242i	$-0.762742\pi$
$241$	−7.99312	+	4.61483i	−0.514882	+	0.297267i	0.219956	+	0.975510i	$0.429409\pi$
$242$	−10.6858	+	9.10627i	−0.686911	+	0.585373i
$243$	2.57477	−	15.3743i	0.165172	−	0.986265i
$244$	4.02016	−	1.53307i	0.257365	−	0.0981446i
$245$	2.33265	+	2.91263i	0.149027	+	0.186081i
$246$	−2.33864	+	5.94781i	−0.149106	+	0.379218i
$247$	−4.58631	+	7.94372i	−0.291820	+	0.505447i
$248$	−5.54869	−	3.03642i	−0.352342	−	0.192813i
$249$	6.68998	+	0.222098i	0.423960	+	0.0140749i
$250$	−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	$0.916452\pi$
$252$	−12.7746	+	9.42387i	−0.804725	+	0.593648i
$253$		−	0.546129i		−	0.0343349i
$254$	10.9139	+	3.87831i	0.684797	+	0.243347i
$255$	−3.98913	−	0.132434i	−0.249809	−	0.00829332i
$256$	−14.6734	+	6.37906i	−0.917085	+	0.398691i
$257$	−6.71468	+	11.6302i	−0.418850	+	0.725470i	−0.995824	−	0.0912928i	$-0.970900\pi$
$257$	−6.71468	+	11.6302i	−0.418850	+	0.725470i	0.576974	+	0.816763i	$0.304233\pi$
$258$	−4.26781	−	1.67807i	−0.265702	−	0.104472i
$259$	13.9776	−	16.2763i	0.868525	−	1.01136i
$260$	1.89157	+	4.96026i	0.117310	+	0.307622i
$261$	23.1851	+	1.54112i	1.43512	+	0.0953932i
$262$	−19.6547	−	23.0639i	−1.21427	−	1.42489i
$263$	13.0415	−	7.52949i	0.804170	−	0.464288i	−0.0407569	−	0.999169i	$-0.512977\pi$
$263$	13.0415	−	7.52949i	0.804170	−	0.464288i	0.844927	+	0.534881i	$0.179644\pi$
$264$	19.2922	+	11.4049i	1.18735	+	0.701926i
$265$			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	$-0.799350\pi$
$269$	−11.5014	+	6.64035i	−0.701254	+	0.404869i	0.106560	+	0.994306i	$0.466016\pi$
$270$	3.21934	−	2.23190i	0.195923	−	0.135829i
$271$	16.2954	+	9.40818i	0.989878	+	0.571506i	0.905238	−	0.424905i	$-0.139693\pi$
$271$	16.2954	+	9.40818i	0.989878	+	0.571506i	0.0846401	+	0.996412i	$0.473026\pi$
$272$	−12.9005	+	11.5134i	−0.782208	+	0.698103i
$273$	22.2720	+	4.96056i	1.34796	+	0.300227i
$274$	−6.28792	+	1.15825i	−0.379867	+	0.0699726i
$275$	10.7866	−	18.6830i	0.650459	−	1.12663i
$276$	−0.391083	+	0.134452i	−0.0235404	+	0.00809305i
$277$	−20.1344	+	11.6246i	−1.20976	+	0.698454i	−0.962706	−	0.270548i	$-0.912795\pi$
$277$	−20.1344	+	11.6246i	−1.20976	+	0.698454i	−0.247052	+	0.969002i	$0.579462\pi$
$278$	−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	$-0.218810\pi$
$282$	−8.89622	−	11.1698i	−0.529762	−	0.665153i
$283$	4.31186	+	7.46836i	0.256314	+	0.443948i	0.965251	−	0.261323i	$-0.0841587\pi$
$283$	4.31186	+	7.46836i	0.256314	+	0.443948i	−0.708938	+	0.705271i	$0.750825\pi$
$284$	7.83265	−	9.62917i	0.464782	−	0.571386i
$285$	0.801119	+	1.50045i	0.0474542	+	0.0888792i
$286$	−5.83563	−	31.6804i	−0.345068	−	1.87330i
$287$	−1.27634	+	6.78411i	−0.0753399	+	0.400454i
$288$	3.41753	−	16.6229i	0.201380	−	0.979513i
$289$	−0.843181	+	1.46043i	−0.0495989	+	0.0859078i
$290$	3.78739	+	4.44434i	0.222403	+	0.260980i
$291$	12.4436	+	0.413111i	0.729457	+	0.0242170i
$292$	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	$-0.231297\pi$
$294$	−11.6443	+	12.5861i	−0.679110	+	0.734036i
$295$	−3.51782			−0.204815
$296$	0.524809	+	22.9297i	0.0305039	+	1.33276i
$297$	−21.6654	+	9.78032i	−1.25715	+	0.567512i
$298$	−23.1883	+	19.7606i	−1.34326	+	1.14470i
$299$	0.514790	+	0.297214i	0.0297711	+	0.0171883i
$300$	−16.0345	−	3.12473i	−0.925750	−	0.180406i
$301$	−4.86790	−	0.915828i	−0.280581	−	0.0527875i
$302$	0.721270	+	3.91563i	0.0415044	+	0.225319i
$303$	−3.14074	−	5.88243i	−0.180431	−	0.337937i
$304$	6.99797	+	2.30783i	0.401361	+	0.132363i
$305$	−0.993166	+	0.573405i	−0.0568685	+	0.0328331i
$306$	−2.11881	−	18.2172i	−0.121124	−	1.04141i
$307$	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	0.975064	+	0.221925i	$0.0712341\pi$
$311$	11.9871	+	20.7622i	0.679725	+	1.17732i	−0.295339	+	0.955393i	$0.595433\pi$
$312$	−21.2497	+	11.9783i	−1.20303	+	0.678138i
$313$	19.4419	+	11.2248i	1.09892	+	0.634463i	0.935938	−	0.352166i	$-0.114555\pi$
$313$	19.4419	+	11.2248i	1.09892	+	0.634463i	0.162984	+	0.986629i	$0.447888\pi$
$314$	1.81602	+	9.85883i	0.102484	+	0.556366i
$315$	2.96347	−	3.02010i	0.166973	−	0.170163i
$316$	−0.0855102	+	0.0326089i	−0.00481032	+	0.00183439i
$317$	−1.06072	+	1.83723i	−0.0595762	+	0.103189i	−0.894275	−	0.447517i	$-0.852308\pi$
$317$	−1.06072	+	1.83723i	−0.0595762	+	0.103189i	0.834699	+	0.550706i	$0.185642\pi$
$318$	−11.1083	+	1.66721i	−0.622924	+	0.0934924i
$319$	−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
$324$	12.3375	+	13.1067i	0.685416	+	0.728152i
$325$	11.7406	+	20.3353i	0.651252	+	1.12800i
$326$	−5.97649	−	7.01316i	−0.331007	−	0.388423i
$327$	−3.99582	−	7.48396i	−0.220969	−	0.413864i
$328$	−3.83515	−	6.30496i	−0.211761	−	0.348133i
$329$	−11.7012	−	10.0486i	−0.645108	−	0.553997i
$330$	−5.55921	−	2.18584i	−0.306024	−	0.120327i
$331$	−1.25478	−	0.724448i	−0.0689689	−	0.0398192i	0.465119	−	0.885248i	$-0.346012\pi$
$331$	−1.25478	−	0.724448i	−0.0689689	−	0.0398192i	−0.534088	+	0.845429i	$0.679345\pi$
$332$	−4.87732	+	5.99599i	−0.267677	+	0.329073i
$333$	−20.2147	−	13.5340i	−1.10776	−	0.741661i
$334$	−22.9830	−	8.16713i	−1.25757	−	0.446886i
$335$	−6.45170			−0.352494
$336$	0.258533	−	18.3285i	0.0141041	−	0.999901i
$337$	−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
$339$	−6.70999	−	0.222762i	−0.364436	−	0.0120988i
$340$	2.90827	−	3.57532i	0.157723	−	0.193899i
$341$	−8.85966	−	5.11513i	−0.479778	−	0.277000i
$342$	−6.27178	+	4.66364i	−0.339139	+	0.252181i
$343$	−9.80454	+	15.7121i	−0.529396	+	0.848375i
$344$	4.52408	−	2.75189i	0.243922	−	0.148372i
$345$	0.0972364	−	0.0519162i	0.00523503	−	0.00279508i
$346$	15.3991	+	18.0702i	0.827863	+	0.971462i
$347$	13.7374	+	23.7939i	0.737463	+	1.27732i	0.953634	+	0.300969i	$0.0973099\pi$
$347$	13.7374	+	23.7939i	0.737463	+	1.27732i	−0.216171	+	0.976356i	$0.569357\pi$
$348$	−17.6123	+	20.2411i	−0.944120	+	1.08504i
$349$	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	$-0.283207\pi$
$353$	−6.72613	−	11.6500i	−0.357996	−	0.620067i	−0.987626	+	0.156828i	$0.949873\pi$
$354$	−2.39916	−	15.9852i	−0.127514	−	0.849603i
$355$	−1.65423	+	2.86521i	−0.0877973	+	0.152069i
$356$	−30.7728	+	11.7351i	−1.63096	+	0.621957i
$357$	−5.93824	−	18.8984i	−0.314285	−	1.00021i
$358$	−1.02980	−	5.59056i	−0.0544265	−	0.295470i
$359$	−19.9816	−	11.5364i	−1.05459	−	0.608867i	−0.130658	−	0.991428i	$-0.541709\pi$
$359$	−19.9816	−	11.5364i	−1.05459	−	0.608867i	−0.923930	+	0.382561i	$0.875042\pi$
$360$	−0.196655	+	4.51908i	−0.0103646	+	0.238176i
$361$	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
$366$	−3.28293	−	4.12194i	−0.171601	−	0.215457i
$367$	18.6893	−	10.7903i	0.975574	−	0.563248i	0.0746427	−	0.997210i	$-0.476218\pi$
$367$	18.6893	−	10.7903i	0.975574	−	0.563248i	0.900931	+	0.433963i	$0.142885\pi$
$368$	0.149558	−	0.453501i	0.00779625	−	0.0236404i
$369$	7.81018	+	0.519147i	0.406582	+	0.0270257i
$370$	−1.10746	−	6.01218i	−0.0575741	−	0.312558i
$371$	−11.4477	+	4.01907i	−0.594337	+	0.208659i
$372$	−1.48177	+	7.60369i	−0.0768264	+	0.394233i
$373$	0.158888	+	0.0917338i	0.00822689	+	0.00474980i	0.504108	−	0.863641i	$-0.331821\pi$
$373$	0.158888	+	0.0917338i	0.00822689	+	0.00474980i	−0.495881	+	0.868391i	$0.665155\pi$
$374$	−21.2857	+	18.1393i	−1.10066	+	0.937963i
$375$	8.96593	+	0.297657i	0.462999	+	0.0153709i
$376$	16.4844	−	0.377289i	0.850116	−	0.0194572i
$377$	38.5663			1.98627
$378$	15.7446	+	11.4065i	0.809815	+	0.586686i
$379$		−	2.93359i		−	0.150688i	−0.997158	−	0.0753441i	$-0.975994\pi$
$379$		−	2.93359i		−	0.150688i	0.997158	−	0.0753441i	$-0.0240055\pi$
$380$	−1.93920	−	0.311509i	−0.0994789	−	0.0159801i
$381$	0.470683	−	14.1778i	0.0241138	−	0.726349i
$382$	18.1283	+	21.2728i	0.927524	+	1.08841i
$383$	7.67488	−	13.2933i	0.392168	−	0.679255i	−0.600567	−	0.799574i	$-0.705058\pi$
$383$	7.67488	−	13.2933i	0.392168	−	0.679255i	0.992735	+	0.120319i	$0.0383918\pi$
$384$	12.8968	+	14.7537i	0.658136	+	0.752899i
$385$	−6.34088	−	1.19295i	−0.323161	−	0.0607983i
$386$	−3.22407	−	17.5028i	−0.164101	−	0.890870i
$387$	−0.372510	+	5.60414i	−0.0189358	+	0.284875i
$388$	−9.07199	+	11.1528i	−0.460561	+	0.566197i
$389$	2.00060	+	3.46513i	0.101434	+	0.175689i	0.912276	−	0.409577i	$-0.134324\pi$
$389$	2.00060	+	3.46513i	0.101434	+	0.175689i	−0.810842	+	0.585266i	$0.800990\pi$
$390$	5.08584	−	4.05062i	0.257532	−	0.205111i
$391$		−	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
$396$	6.14120	−	26.7521i	0.308607	−	1.34434i
$397$	−11.7195	+	20.2987i	−0.588183	+	1.01876i	0.406288	+	0.913745i	$0.366823\pi$
$397$	−11.7195	+	20.2987i	−0.588183	+	1.01876i	−0.994470	+	0.105017i	$0.966510\pi$
$398$	19.9109	−	3.66765i	0.998044	−	0.183842i
$399$	−5.70938	+	6.21841i	−0.285826	+	0.311310i
$400$	14.0735	−	12.5603i	0.703675	−	0.628014i
$401$	−14.5441	−	8.39703i	−0.726297	−	0.419328i	0.0907689	−	0.995872i	$-0.471068\pi$
$401$	−14.5441	−	8.39703i	−0.726297	−	0.419328i	−0.817066	+	0.576544i	$0.804401\pi$
$402$	−4.40007	−	29.3169i	−0.219455	−	1.46219i
$403$	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
$408$	18.2299	+	10.7770i	0.902515	+	0.533540i
$409$	11.9749	−	6.91372i	0.592121	−	0.341861i	−0.173815	−	0.984778i	$-0.555609\pi$
$409$	11.9749	−	6.91372i	0.592121	−	0.341861i	0.765936	+	0.642917i	$0.222276\pi$
$410$	1.27583	+	1.49713i	0.0630086	+	0.0739380i
$411$	3.68816	+	6.90773i	0.181924	+	0.340733i
$412$	−3.79362	−	9.94800i	−0.186898	−	0.490103i
$413$	−5.78354	−	16.4736i	−0.284590	−	0.810613i
$414$	0.302226	+	0.406441i	0.0148536	+	0.0199755i
$415$	1.03007	−	1.78414i	0.0505643	−	0.0875799i
$416$	3.82987	−	27.9052i	0.187775	−	1.36817i
$417$	−0.852279	+	25.6721i	−0.0417363	+	1.25717i
$418$	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	$-0.141086\pi$
$420$	0.706793	+	4.83439i	0.0344880	+	0.235894i
$421$			19.8896i			0.969362i	0.874691	+	0.484681i	$0.161064\pi$
$421$			19.8896i			0.969362i	−0.874691	+	0.484681i	$0.838936\pi$
$422$	4.55694	−	12.8236i	0.221828	−	0.624243i
$423$	−9.72973	+	14.5325i	−0.473075	+	0.706595i
$424$	6.22650	−	11.3782i	0.302386	−	0.552574i
$425$	10.1927	−	17.6543i	0.494419	−	0.856359i
$426$	−14.1479	−	5.56284i	−0.685466	−	0.269520i
$427$	−4.31803	−	3.70818i	−0.208964	−	0.179451i
$428$	17.2160	−	6.56525i	0.832168	−	0.317343i
$429$	−34.8032	+	18.5821i	−1.68032	+	0.897150i
$430$	−1.07426	+	0.915461i	−0.0518052	+	0.0441475i
$431$	−25.3821	+	14.6544i	−1.22261	+	0.705876i	−0.965474	−	0.260498i	$-0.916113\pi$
$431$	−25.3821	+	14.6544i	−1.22261	+	0.705876i	−0.257139	+	0.966374i	$0.582780\pi$
$432$	−20.6691	+	2.18841i	−0.994442	+	0.105290i
$433$		−	12.5427i		−	0.602763i	−0.953504	−	0.301381i	$-0.902552\pi$
$433$		−	12.5427i		−	0.602763i	0.953504	−	0.301381i	$-0.0974477\pi$
$434$	−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
$438$	−3.50757	−	23.3703i	−0.167598	−	1.11668i
$439$	11.7921	+	6.80818i	0.562807	+	0.324937i	0.754271	−	0.656563i	$-0.227990\pi$
$439$	11.7921	+	6.80818i	0.562807	+	0.324937i	−0.191464	+	0.981500i	$0.561324\pi$
$440$	5.89302	−	3.58458i	0.280939	−	0.170888i
$441$	19.0150	+	8.91238i	0.905475	+	0.424399i
$442$	−5.51431	−	29.9361i	−0.262289	−	1.42391i
$443$	−6.72205	+	11.6429i	−0.319374	+	0.553172i	−0.980358	−	0.197228i	$-0.936806\pi$
$443$	−6.72205	+	11.6429i	−0.319374	+	0.553172i	0.660984	+	0.750400i	$0.270139\pi$
$444$	26.5644	−	9.13267i	1.26069	−	0.433417i
$445$	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	$-0.126017\pi$
$450$	2.31146	+	19.8736i	0.108963	+	0.936849i
$451$	−5.96796	−	10.3368i	−0.281020	−	0.486742i
$452$	4.89190	−	6.01393i	0.230096	−	0.282871i
$453$	4.30160	−	2.29670i	0.202107	−	0.107908i
$454$	1.66063	−	0.305893i	0.0779374	−	0.0143563i
$455$	4.57532	−	5.32779i	0.214494	−	0.249770i
$456$	0.0929782	−	9.02429i	0.00435410	−	0.422601i
$457$	14.6395	−	25.3564i	0.684808	−	1.18612i	−0.288689	−	0.957423i	$-0.593219\pi$
$457$	14.6395	−	25.3564i	0.684808	−	1.18612i	0.973497	−	0.228699i	$-0.0734472\pi$
$458$	24.5461	−	20.9178i	1.14696	−	0.977423i
$459$	−20.4724	+	9.24180i	−0.955572	+	0.431370i
$460$	−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	$0.954856\pi$
$462$	1.09635	−	29.6269i	0.0510067	−	1.37837i
$463$	−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
$465$	0.0685115	−	2.06369i	0.00317715	−	0.0957011i
$466$	14.9429	+	17.5349i	0.692219	+	0.812290i
$467$	7.03895	+	4.06394i	0.325724	+	0.188057i	0.653941	−	0.756546i	$-0.273114\pi$
$467$	7.03895	+	4.06394i	0.325724	+	0.188057i	−0.328217	+	0.944602i	$0.606448\pi$
$468$	21.8748	+	20.3478i	1.01116	+	0.940579i
$469$	−10.6070	−	30.2127i	−0.489788	−	1.39509i
$470$	−4.32220	+	0.796161i	−0.199368	+	0.0367242i
$471$	10.8306	−	5.78267i	0.499049	−	0.266451i
$472$	16.3735	+	8.96011i	0.753653	+	0.412422i
$473$	7.41711	−	4.28227i	0.341039	−	0.196899i
$474$	0.0698289	+	0.0876751i	0.00320735	+	0.00402705i
$475$	−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	$-0.160472\pi$
$479$	0.425876	+	0.737638i	0.0194588	+	0.0337035i	−0.856132	+	0.516757i	$0.827139\pi$
$480$	−4.01772	−	3.33750i	−0.183383	−	0.152335i
$481$	−34.9673	−	20.1884i	−1.59437	−	0.920510i
$482$	−12.8368	+	2.36457i	−0.584698	+	0.107703i
$483$	0.402982	+	0.369994i	0.0183363	+	0.0168353i
$484$	−18.5519	+	7.07466i	−0.843266	+	0.321575i
$485$	1.91597	−	3.31856i	0.0869999	−	0.150688i
$486$	10.7114	−	19.2682i	0.485880	−	0.874025i
$487$	−2.45804	−	4.25745i	−0.111384	−	0.192923i	0.804944	−	0.593350i	$-0.202195\pi$
$487$	−2.45804	−	4.25745i	−0.111384	−	0.192923i	−0.916329	+	0.400427i	$0.868862\pi$
$488$	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	$-0.463473\pi$
$491$	5.07434			0.229002			0.114501	+	0.993423i	$0.463473\pi$
$492$	−5.93293	+	6.81848i	−0.267477	+	0.307401i
$493$	−16.7408	−	28.9960i	−0.753970	−	1.30591i
$494$	−9.87327	+	8.41383i	−0.444220	+	0.378556i
$495$	−0.485228	+	7.29991i	−0.0218094	+	0.328106i
$496$	−5.95620	−	6.67378i	−0.267441	−	0.299662i
$497$	−16.1372	−	3.03599i	−0.723850	−	0.136183i
$498$	8.80974	+	3.46392i	0.394774	+	0.155222i
$499$	−17.6743	−	10.2042i	−0.791209	−	0.456805i	0.0491790	−	0.998790i	$-0.484340\pi$
$499$	−17.6743	−	10.2042i	−0.791209	−	0.456805i	−0.840388	+	0.541985i	$0.817673\pi$
$500$	−6.53660	+	8.03586i	−0.292326	+	0.359374i
$501$	−0.991187	+	29.8563i	−0.0442830	+	1.33388i
$502$	−3.89321	+	10.9558i	−0.173762	+	0.488982i
$503$	−26.6102			−1.18649			−0.593245	−	0.805022i	$-0.702153\pi$
$503$	−26.6102			−1.18649			−0.593245	+	0.805022i	$0.702153\pi$
$504$	−21.4857	+	6.50877i	−0.957050	+	0.289924i
$505$	−2.05236			−0.0913289
$506$	0.258613	−	0.727759i	0.0114968	−	0.0323528i
$507$	0.677734	−	20.4145i	0.0300992	−	0.906641i
$508$	12.7070	+	10.3363i	0.563784	+	0.458598i
$509$	24.9978	+	14.4325i	1.10801	+	0.639710i	0.938313	−	0.345787i	$-0.112388\pi$
$509$	24.9978	+	14.4325i	1.10801	+	0.639710i	0.169697	+	0.985496i	$0.445721\pi$
$510$	−5.25311	−	2.06549i	−0.232612	−	0.0914613i
$511$	−8.45553	−	24.0844i	−0.374051	−	1.06543i
$512$	−22.5741	+	1.55218i	−0.997644	+	0.0685972i
$513$	7.77301	+	5.58637i	0.343187	+	0.246644i
$514$	−14.4552	+	12.3184i	−0.637590	+	0.543343i
$515$	1.41891	+	2.45762i	0.0625245	+	0.108296i
$516$	−4.89255	−	4.25713i	−0.215383	−	0.187410i
$517$	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	0.998266	+	0.0588577i	$0.0187458\pi$
$521$	12.5564	+	21.7483i	0.550105	+	0.952811i	−0.448161	+	0.893953i	$0.647921\pi$
$522$	30.1661	+	13.0327i	1.32034	+	0.570426i
$523$	−1.54754	+	2.68042i	−0.0676692	+	0.117206i	−0.897875	−	0.440251i	$-0.854890\pi$
$523$	−1.54754	+	2.68042i	−0.0676692	+	0.117206i	0.830206	+	0.557457i	$0.188223\pi$
$524$	−15.2697	−	40.0417i	−0.667060	−	1.74923i
$525$	6.47818	+	20.6168i	0.282731	+	0.899790i
$526$	20.9442	−	3.85799i	0.913212	−	0.168216i
$527$	−8.37183	−	4.83348i	−0.364683	−	0.210550i
$528$	20.3076	+	24.3336i	0.883775	+	1.05898i
$529$	−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
$534$	25.1296	+	31.5519i	1.08746	+	1.36539i
$535$	−4.25316	+	2.45556i	−0.183880	+	0.106163i
$536$	30.0291	+	16.4329i	1.29706	+	0.709792i
$537$	−6.14163	+	3.27913i	−0.265031	+	0.141505i
$538$	−18.4710	+	3.40241i	−0.796341	+	0.146688i
$539$	−4.83838	−	31.6550i	−0.208404	−	1.36348i
$540$	5.34692	−	1.44970i	0.230095	−	0.0623850i
$541$	−23.8925	−	13.7944i	−1.02722	−	0.593066i	−0.111033	−	0.993817i	$-0.535416\pi$
$541$	−23.8925	−	13.7944i	−1.02722	−	0.593066i	−0.916187	+	0.400751i	$0.868749\pi$
$542$	17.2598	+	20.2536i	0.741372	+	0.869969i
$543$	−0.853983	+	25.7234i	−0.0366479	+	1.10390i
$544$	−22.6430	+	9.23362i	−0.970809	+	0.395888i
$545$	−2.61113			−0.111849
$546$	27.3301	+	17.1570i	1.16962	+	0.734251i
$547$			32.0757i			1.37146i	0.727856	+	0.685730i	$0.240517\pi$
$547$			32.0757i			1.37146i	−0.727856	+	0.685730i	$0.759483\pi$
$548$	−8.92762	−	1.43411i	−0.381369	−	0.0612623i
$549$	−3.59051	+	5.36286i	−0.153239	+	0.228881i
$550$	23.2212	−	19.7887i	0.990154	−	0.843791i
$551$	−7.13420	+	12.3568i	−0.303927	+	0.526417i
$552$	−0.584816	−	0.00602542i	−0.0248914	−	0.000256459i
$553$	0.0918460	+	0.0788743i	0.00390569	+	0.00335407i
$554$	−32.3353	+	5.95626i	−1.37380	+	0.253057i
$555$	−6.60480	+	3.52642i	−0.280358	+	0.149688i
$556$	−23.0090	−	18.7162i	−0.975800	−	0.793744i
$557$	8.23577	+	14.2648i	0.348961	+	0.604417i	0.986065	−	0.166360i	$-0.0532014\pi$
$557$	8.23577	+	14.2648i	0.348961	+	0.604417i	−0.637104	+	0.770777i	$0.719868\pi$
$558$	9.42423	−	1.09612i	0.398960	−	0.0464023i
$559$			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	$-0.781893\pi$
$563$	−14.5542	+	8.40290i	−0.613388	+	0.354140i	0.160902	+	0.986970i	$0.448560\pi$
$564$	−6.56555	−	19.0973i	−0.276460	−	0.804143i
$565$	−1.03315	+	1.78947i	−0.0434651	+	0.0752837i
$566$	2.20933	+	11.9940i	0.0928650	+	0.504145i
$567$	7.46118	−	22.6126i	0.313340	−	0.949641i
$568$	14.9974	−	9.12255i	0.629277	−	0.382774i
$569$	−32.1947	−	18.5876i	−1.34967	−	0.779235i	−0.361471	−	0.932383i	$-0.617725\pi$
$569$	−32.1947	−	18.5876i	−1.34967	−	0.779235i	−0.988203	+	0.153149i	$0.951059\pi$
$570$	0.357030	+	2.37883i	0.0149543	+	0.0996382i
$571$	6.80801	−	3.93061i	0.284906	−	0.164491i	−0.350736	−	0.936474i	$-0.614069\pi$
$571$	6.80801	−	3.93061i	0.284906	−	0.164491i	0.635642	+	0.771984i	$0.280735\pi$
$572$	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
$576$	12.4257	−	20.5329i	0.517737	−	0.855540i
$577$	14.7236	−	8.50067i	0.612951	−	0.353888i	−0.161168	−	0.986927i	$-0.551526\pi$
$577$	14.7236	−	8.50067i	0.612951	−	0.353888i	0.774120	+	0.633039i	$0.218193\pi$
$578$	−1.81518	+	1.54686i	−0.0755013	+	0.0643409i
$579$	−19.2281	+	10.2662i	−0.799092	+	0.426650i
$580$	2.94242	+	7.71589i	0.122177	+	0.320385i
$581$	10.0484	+	1.89048i	0.416880	+	0.0784303i
$582$	16.3864	+	6.44303i	0.679240	+	0.267072i
$583$	10.4891	−	18.1677i	0.434415	−	0.752429i
$584$	23.9381	+	13.0997i	0.990565	+	0.542068i
$585$	−6.61694	−	4.43014i	−0.273577	−	0.183164i
$586$	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	$-0.167782\pi$
$588$	−21.4769	+	11.2579i	−0.885694	+	0.464269i
$589$			4.11963i			0.169746i
$590$	−4.68777	−	1.66582i	−0.192992	−	0.0685809i
$591$	0.483785	−	14.5724i	0.0199003	−	0.599430i
$592$	−10.1588	+	30.8042i	−0.417523	+	1.26604i
$593$	0.0286004	−	0.0495374i	0.00117448	−	0.00203426i	−0.865438	−	0.501017i	$-0.832959\pi$
$593$	0.0286004	−	0.0495374i	0.00117448	−	0.00203426i	0.866612	+	0.498983i	$0.166293\pi$
$594$	−33.5021	+	2.77364i	−1.37461	+	0.113804i
$595$	−5.99174	−	1.12726i	−0.245637	−	0.0462133i
$596$	−40.2576	+	15.3520i	−1.64902	+	0.628844i
$597$	−11.6787	−	21.8736i	−0.477977	−	0.895225i
$598$	0.545255	+	0.639834i	0.0222971	+	0.0261648i
$599$	35.8620	−	20.7049i	1.46528	−	0.845980i	0.466033	−	0.884768i	$-0.345683\pi$
$599$	35.8620	−	20.7049i	1.46528	−	0.845980i	0.999247	+	0.0387877i	$0.0123496\pi$
$600$	−19.8875	−	11.7569i	−0.811903	−	0.479972i
$601$			23.8559i			0.973104i	0.873652	+	0.486552i	$0.161746\pi$
$601$			23.8559i			0.973104i	−0.873652	+	0.486552i	$0.838254\pi$
$602$	−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
$606$	−1.39971	−	9.32605i	−0.0568594	−	0.378845i
$607$	−33.6542	−	19.4303i	−1.36598	−	0.788650i	−0.375570	−	0.926794i	$-0.622553\pi$
$607$	−33.6542	−	19.4303i	−1.36598	−	0.788650i	−0.990412	+	0.138144i	$0.955886\pi$
$608$	8.23248	+	6.38917i	0.333871	+	0.259115i
$609$	34.6450	+	7.71636i	1.40389	+	0.312683i
$610$	−1.59500	+	0.293803i	−0.0645796	+	0.0118958i
$611$	−14.5136	+	25.1382i	−0.587156	+	1.01698i
$612$	5.80306	−	25.2791i	0.234575	−	1.02185i
$613$	16.8751	−	9.74286i	0.681580	−	0.393510i	−0.118870	−	0.992910i	$-0.537927\pi$
$613$	16.8751	−	9.74286i	0.681580	−	0.393510i	0.800450	+	0.599400i	$0.204594\pi$
$614$	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	$-0.143049\pi$
$618$	−10.1999	+	8.12369i	−0.410299	+	0.326783i
$619$	5.60757	+	9.71259i	0.225387	+	0.390382i	0.956436	−	0.291944i	$-0.0943020\pi$
$619$	5.60757	+	9.71259i	0.225387	+	0.390382i	−0.731048	+	0.682326i	$0.760969\pi$
$620$	1.84961	+	1.50453i	0.0742821	+	0.0604232i
$621$	0.362023	−	0.503728i	0.0145275	−	0.0202139i
$622$	6.14199	+	33.3436i	0.246271	+	1.33696i
$623$	33.0529	+	28.3847i	1.32424	+	1.13721i
$624$	−33.9890	+	5.89948i	−1.36065	+	0.236168i
$625$	−10.4090	+	18.0290i	−0.416362	+	0.721160i
$626$	20.5925	+	24.1644i	0.823040	+	0.965803i
$627$	0.484318	−	14.5885i	0.0193418	−	0.582609i
$628$	−2.24855	+	13.9976i	−0.0897268	+	0.558566i
$629$			35.0534i			1.39767i
$630$	5.37919	−	2.62120i	0.214312	−	0.104431i
$631$	−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
$633$	−16.6586	−	0.553043i	−0.662121	−	0.0219815i
$634$	−2.28350	+	1.94595i	−0.0906892	+	0.0772837i
$635$	−3.78105	−	2.18299i	−0.150046	−	0.0866292i
$636$	−15.5922	−	3.03854i	−0.618270	−	0.120486i
$637$	32.4716	+	12.6665i	1.28657	+	0.501866i
$638$	−9.07756	−	49.2803i	−0.359384	−	1.95102i
$639$	−1.23488	+	18.5778i	−0.0488510	+	0.734927i
$640$	5.87516	−	1.36280i	0.232236	−	0.0538692i
$641$	−10.9414	+	6.31703i	−0.432160	+	0.249508i	−0.700266	−	0.713882i	$-0.746935\pi$
$641$	−10.9414	+	6.31703i	−0.432160	+	0.249508i	0.268107	+	0.963389i	$0.413602\pi$
$642$	−14.0589	−	17.6519i	−0.554859	−	0.696665i
$643$	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	$-0.272442\pi$
$647$	−8.29783	−	14.3723i	−0.326221	−	0.565032i	−0.981759	+	0.190131i	$0.939109\pi$
$648$	10.2341	+	23.3080i	0.402034	+	0.915625i
$649$	26.1438	+	15.0941i	1.02623	+	0.592496i
$650$	6.01570	+	32.6580i	0.235955	+	1.28095i
$651$	9.77667	−	3.07201i	0.383178	−	0.120402i
$652$	−4.64313	−	12.1757i	−0.181839	−	0.476836i
$653$	−2.57443	+	4.45904i	−0.100745	+	0.174496i	−0.911992	−	0.410208i	$-0.865456\pi$
$653$	−2.57443	+	4.45904i	−0.100745	+	0.174496i	0.811247	+	0.584704i	$0.198789\pi$
$654$	−1.78079	−	11.8651i	−0.0696346	−	0.463963i
$655$	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	$-0.632021\pi$
$659$	−20.6891			−0.805934			−0.402967	+	0.915214i	$0.632021\pi$
$660$	−6.37299	−	5.54530i	−0.248068	−	0.215851i
$661$	−12.3911	−	21.4621i	−0.481960	−	0.834779i	0.517826	−	0.855486i	$-0.326742\pi$
$661$	−12.3911	−	21.4621i	−0.481960	−	0.834779i	−0.999786	+	0.0207072i	$0.993408\pi$
$662$	−1.32904	−	1.55957i	−0.0516545	−	0.0606144i
$663$	−32.8869	+	17.5589i	−1.27722	+	0.681931i
$664$	−9.33873	+	5.68053i	−0.362413	+	0.220447i
$665$	0.860676	+	2.45151i	0.0333756	+	0.0950657i
$666$	−20.5288	−	27.6076i	−0.795473	−	1.06977i
$667$	0.800778	+	0.462329i	0.0310063	+	0.0179015i
$668$	−26.7591	−	21.7667i	−1.03534	−	0.842178i
$669$	34.9404	+	1.15997i	1.35088	+	0.0448472i
$670$	−8.59738	−	3.05513i	−0.332146	−	0.118030i
$671$	9.84137			0.379922
$672$	9.02376	−	24.3017i	0.348099	−	0.937458i
$673$	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
$675$	22.3339	−	10.0821i	0.859633	−	0.388061i
$676$	18.2968	+	14.8832i	0.703725	+	0.572430i
$677$	−35.2987	−	20.3797i	−1.35664	−	0.783256i	−0.367471	−	0.930035i	$-0.619776\pi$
$677$	−35.2987	−	20.3797i	−1.35664	−	0.783256i	−0.989169	+	0.146779i	$0.953109\pi$
$678$	−8.83609	−	3.47429i	−0.339348	−	0.133429i
$679$	18.6905	+	3.51636i	0.717276	+	0.134946i
$680$	5.56854	−	3.38721i	0.213544	−	0.129894i
$681$	−0.974039	−	1.82432i	−0.0373253	−	0.0699082i
$682$	−9.38397	−	11.0117i	−0.359331	−	0.421659i
$683$	−14.8402	−	25.7039i	−0.567843	−	0.983532i	−0.996779	−	0.0801976i	$-0.974445\pi$
$683$	−14.8402	−	25.7039i	−0.567843	−	0.983532i	0.428936	−	0.903335i	$-0.358888\pi$
$684$	−10.5660	+	3.24473i	−0.404003	+	0.124065i
$685$	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
$690$	0.154159	−	0.0231372i	0.00586874	−	0.000880818i
$691$	3.83116	−	6.63576i	0.145744	−	0.252436i	−0.783906	−	0.620879i	$-0.786776\pi$
$691$	3.83116	−	6.63576i	0.145744	−	0.252436i	0.929650	+	0.368443i	$0.120109\pi$
$692$	11.9636	+	31.3721i	0.454787	+	1.19259i
$693$	−34.9825	+	9.72928i	−1.32887	+	0.369585i
$694$	7.03883	+	38.2124i	0.267190	+	1.45052i
$695$	6.84645	+	3.95280i	0.259701	+	0.149938i
$696$	−33.0547	+	18.6328i	−1.25294	+	0.706273i
$697$	−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	$-0.459283\pi$
$701$	6.75507			0.255136			0.127568	+	0.991830i	$0.459283\pi$
$702$	15.6180	−	33.0891i	0.589465	−	1.24887i
$703$	12.9369	−	7.46910i	0.487923	−	0.281702i
$704$	−36.5590	+	1.67438i	−1.37787	+	0.0631055i
$705$	2.53517	+	4.74825i	0.0954801	+	0.178829i
$706$	−3.44636	−	18.7096i	−0.129706	−	0.704145i
$707$	−3.37423	−	9.61100i	−0.126901	−	0.361459i
$708$	4.37254	−	22.4376i	0.164330	−	0.843256i
$709$	36.0884	+	20.8357i	1.35533	+	0.782499i	0.988990	−	0.147982i	$-0.0472778\pi$
$709$	36.0884	+	20.8357i	1.35533	+	0.782499i	0.366339	+	0.930482i	$0.380611\pi$
$710$	−3.56117	+	3.03477i	−0.133648	+	0.113893i
$711$	0.0763714	−	0.114070i	0.00286415	−	0.00427795i
$712$	−46.5642	+	1.06575i	−1.74507	+	0.0399405i
$713$	0.266971			0.00999815
$714$	1.03598	−	27.9956i	0.0387706	−	1.04771i
$715$			12.1427i			0.454112i
$716$	1.27506	−	7.93750i	0.0476514	−	0.296638i
$717$	35.0404	+	1.16329i	1.30861	+	0.0434439i
$718$	−21.1641	−	24.8352i	−0.789836	−	0.926840i
$719$	23.2782	−	40.3190i	0.868131	−	1.50365i	0.00422645	−	0.999991i	$-0.498655\pi$
$719$	23.2782	−	40.3190i	0.868131	−	1.50365i	0.863904	−	0.503656i	$-0.168012\pi$
$720$	−2.40202	+	5.92890i	−0.0895179	+	0.220957i
$721$	−9.17600	+	10.6851i	−0.341732	+	0.397934i
$722$	3.99823	+	21.7056i	0.148799	+	0.807799i
$723$	7.52936	+	14.1021i	0.280020	+	0.524462i
$724$	−23.0550	−	18.7536i	−0.856833	−	0.696973i
$725$	18.2630	+	31.6325i	0.678271	+	1.17480i
$726$	15.1497	+	19.0215i	0.562259	+	0.705956i
$727$		−	10.7218i		−	0.397651i	−0.980035	−	0.198825i	$-0.936287\pi$
$727$		−	10.7218i		−	0.397651i	0.980035	−	0.198825i	$-0.0637127\pi$
$728$	−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
$732$	−2.42285	−	7.04740i	−0.0895512	−	0.260479i
$733$	−12.5202	+	21.6857i	−0.462445	+	0.800979i	−0.999082	−	0.0428345i	$-0.986361\pi$
$733$	−12.5202	+	21.6857i	−0.462445	+	0.800979i	0.536637	+	0.843813i	$0.319695\pi$
$734$	30.0145	−	5.52876i	1.10786	−	0.204070i
$735$	5.17611	−	3.87065i	0.190924	−	0.142771i
$736$	0.414048	−	0.533503i	0.0152620	−	0.0196652i
$737$	47.9478	+	27.6827i	1.76618	+	1.01971i
$738$	10.1618	+	4.39023i	0.374062	+	0.161606i
$739$	−45.0173	+	25.9908i	−1.65599	+	0.956086i	−0.681452	+	0.731863i	$0.738651\pi$
$739$	−45.0173	+	25.9908i	−1.65599	+	0.956086i	−0.974538	+	0.224224i	$0.928015\pi$
$740$	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	$0.838686\pi$
$744$	−5.57522	+	9.43083i	−0.204398	+	0.345751i
$745$	9.94549	−	5.74203i	0.364375	−	0.210372i
$746$	0.168290	+	0.197482i	0.00616155	+	0.00723032i
$747$	0.768946	−	11.5682i	0.0281343	−	0.423260i
$748$	−36.9546	+	14.0924i	−1.35119	+	0.515270i
$749$	−18.4916	−	15.8800i	−0.675670	−	0.580242i
$750$	11.8068	+	4.64237i	0.431125	+	0.169515i
$751$	−9.69510	+	16.7924i	−0.353779	+	0.612763i	−0.986908	−	0.161283i	$-0.948437\pi$
$751$	−9.69510	+	16.7924i	−0.353779	+	0.612763i	0.633129	+	0.774046i	$0.281770\pi$
$752$	22.1454	+	7.30322i	0.807558	+	0.266321i
$753$	14.2323	+	0.472491i	0.518652	+	0.0172185i
$754$	51.3926	+	18.2626i	1.87161	+	0.665086i
$755$		−	1.50081i		−	0.0546202i
$756$	15.5795	+	22.6557i	0.566620	+	0.823979i
$757$			5.19772i			0.188914i	0.995529	+	0.0944572i	$0.0301115\pi$
$757$			5.19772i			0.188914i	−0.995529	+	0.0944572i	$0.969888\pi$
$758$	1.38917	−	3.90923i	0.0504568	−	0.141990i
$759$	−0.945403	−	0.0313861i	−0.0343160	−	0.00113924i
$760$	−2.43662	−	1.33340i	−0.0883856	−	0.0483674i
$761$	−18.8681	+	32.6805i	−0.683969	+	1.18467i	0.289791	+	0.957090i	$0.406414\pi$
$761$	−18.8681	+	32.6805i	−0.683969	+	1.18467i	−0.973760	+	0.227578i	$0.926919\pi$
$762$	7.34095	−	18.6701i	0.265934	−	0.676346i
$763$	−4.29288	−	12.2277i	−0.155413	−	0.442671i
$764$	14.0839	+	36.9321i	0.509536	+	1.33616i
$765$	−0.458511	+	6.89796i	−0.0165775	+	0.249396i
$766$	16.5223	−	14.0800i	0.596973	−	0.508730i
$767$	−28.4559	+	16.4290i	−1.02748	+	0.593218i
$768$	10.1995	+	25.7676i	0.368042	+	0.929809i
$769$			13.9517i			0.503110i	0.967843	+	0.251555i	$0.0809419\pi$
$769$			13.9517i			0.503110i	−0.967843	+

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)

\(f(q)\)	\(=\)	\(q+(1.33258 + 0.473539i) q^{2} +(0.0574700 - 1.73110i) q^{3} +(1.55152 + 1.26205i) q^{4} +(-0.461663 - 0.266541i) q^{5} +(0.896325 - 2.27961i) q^{6} +(0.489180 - 2.60014i) q^{7} +(1.46989 + 2.41649i) q^{8} +(-2.99339 - 0.198972i) q^{9} +O(q^{10})\)	\(q+(1.33258 + 0.473539i) q^{2} +(0.0574700 - 1.73110i) q^{3} +(1.55152 + 1.26205i) q^{4} +(-0.461663 - 0.266541i) q^{5} +(0.896325 - 2.27961i) q^{6} +(0.489180 - 2.60014i) q^{7} +(1.46989 + 2.41649i) q^{8} +(-2.99339 - 0.198972i) q^{9} +(-0.488984 - 0.573802i) q^{10} +(2.28733 + 3.96177i) q^{11} +(2.27390 - 2.61331i) 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} +(-3.89471 - 1.68263i) q^{18} +(0.921087 - 1.59537i) q^{19} +(-0.379891 - 0.996188i) q^{20} +(-4.47297 - 0.996248i) q^{21} +(1.17199 + 6.36250i) q^{22} +(-0.103387 - 0.0596907i) q^{23} +(4.26765 - 2.40565i) 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} +(-1.02141 + 0.813502i) q^{30} +(-1.93668 + 1.11814i) q^{31} +(-0.769168 + 5.60432i) q^{32} +(6.98966 - 3.73191i) q^{33} +(1.10746 + 6.01218i) q^{34} +(-0.918880 + 1.07000i) q^{35} +(-4.39320 - 4.08653i) q^{36} +(7.02261 + 4.05451i) q^{37} +(1.98289 - 1.68978i) q^{38} +(-0.286157 + 8.61955i) q^{39} +(-0.0345007 - 1.50739i) q^{40} -2.60914 q^{41} +(-5.48882 - 3.44570i) q^{42} -1.87217i q^{43} +(-1.45112 + 9.03351i) q^{44} +(1.32891 + 0.889722i) q^{45} +(-0.109506 - 0.128500i) q^{46} +(2.91482 - 5.04861i) q^{47} +(6.82614 - 1.18482i) q^{48} +(-6.52141 - 2.54387i) q^{49} +(-1.20816 - 6.55884i) q^{50} +(6.60480 - 3.52642i) q^{51} +(-7.72540 - 6.28407i) q^{52} +(-2.29287 - 3.97137i) q^{53} +(-3.13663 + 6.64542i) 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} +(-1.74633 + 0.600378i) q^{60} +(1.07564 - 1.86306i) q^{61} +(-3.11026 + 0.572919i) q^{62} +(-1.98166 + 7.68590i) q^{63} +(-3.67884 + 7.10395i) q^{64} +(2.29873 + 1.32717i) q^{65} +(11.0815 - 1.66318i) 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} +(-3.91915 - 7.52597i) q^{72} +(8.35520 - 4.82388i) q^{73} +(7.43820 + 8.72842i) q^{74} +(-7.20535 + 3.84706i) q^{75} +(3.44253 - 1.31279i) q^{76} +(11.4201 - 4.00935i) q^{77} +(-4.46302 + 11.3507i) q^{78} +(-0.0228792 + 0.0396280i) q^{79} +(0.667833 - 2.02505i) q^{80} +(8.92082 + 1.19121i) q^{81} +(-3.47688 - 1.23553i) q^{82} +3.86459i q^{83} +(-5.68260 - 7.19083i) q^{84} -2.30440i q^{85} +(0.886545 - 2.49481i) q^{86} +(-0.445129 + 13.4081i) q^{87} +(-6.21145 + 11.3507i) q^{88} +(-8.23362 + 14.2610i) q^{89} +(1.34955 + 1.81491i) q^{90} +(-2.43575 + 12.9467i) q^{91} +(-0.0850749 - 0.223092i) q^{92} +(1.82431 + 3.41684i) q^{93} +(6.27493 - 5.34738i) q^{94} +(-0.850463 + 0.491015i) q^{95} +(9.65741 + 1.65358i) 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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