LMFDB - Embedded newform 168.2.ba.c.101.22

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			101.22
Character	$\chi$	$=$	168.101
Dual form			168.2.ba.c.5.22

$q$-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 $\left(\mathbb{Z}/168\mathbb{Z}\right)^\times$.

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

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
$3$	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	−0.599666	−	0.800250i	$-0.704700\pi$
$5$	−0.461663	+	0.266541i	−0.206462	+	0.119201i	0.393204	+	0.919451i	$0.371367\pi$
$6$	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	−0.282293	−	0.959328i	$-0.591095\pi$
$11$	2.28733	−	3.96177i	0.689656	−	1.19452i	0.971949	−	0.235191i	$-0.0755716\pi$
$12$	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	−0.475389	−	0.879775i	$-0.657693\pi$
$17$	2.16139	−	3.74363i	0.524213	−	0.907964i	0.999603	−	0.0281884i	$-0.00897383\pi$
$18$	−3.89471	+	1.68263i	−0.917991	+	0.396601i
$19$	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
$21$	−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	−0.510740	−	0.859735i	$-0.670629\pi$
$23$	−0.103387	+	0.0596907i	−0.0215577	+	0.0124464i	0.489182	+	0.872182i	$0.337295\pi$
$24$	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	0.315894	−	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
$33$	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	0.204528	−	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
$39$	−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	$0.0455950\pi$
$43$			1.87217i			0.285503i	−0.989759	+	0.142752i	$0.954405\pi$
$44$	−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	0.996436	−	0.0843492i	$-0.0268811\pi$
$47$	2.91482	+	5.04861i	0.425170	+	0.736415i	−0.571267	+	0.820764i	$0.693548\pi$
$48$	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	−0.979427	−	0.201799i	$-0.935321\pi$
$53$	−2.29287	+	3.97137i	−0.314950	+	0.545510i	0.664476	+	0.747309i	$0.268655\pi$
$54$	−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	0.823529	−	0.567275i	$-0.192002\pi$
$59$	5.71492	+	3.29951i	0.744019	+	0.429559i	−0.0795100	+	0.996834i	$0.525336\pi$
$60$	−1.74633	−	0.600378i	−0.225450	−	0.0775084i
$61$	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
$63$	−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	0.976936	−	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	$0.120051\pi$
$71$			6.20627i			0.736549i	−0.929717	+	0.368275i	$0.879949\pi$
$72$	−3.91915	+	7.52597i	−0.461876	+	0.886944i
$73$	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
$75$	−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	0.864735	−	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
$81$	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	$-0.931971\pi$
$83$		−	3.86459i		−	0.424194i	0.977249	−	0.212097i	$-0.0680292\pi$
$84$	−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	−0.859128	−	0.511761i	$-0.828993\pi$
$89$	−8.23362	−	14.2610i	−0.872762	−	1.51167i	−0.0136336	−	0.999907i	$-0.504340\pi$
$90$	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	$-0.881093\pi$
$97$		−	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	0.656624	−	0.754218i	$-0.271984\pi$
$101$	3.33419	+	1.92499i	0.331764	+	0.191544i	−0.324860	+	0.945762i	$0.605317\pi$
$102$	10.4713	+	1.57160i	1.03681	+	0.155612i
$103$	−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
$105$	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	0.998074	−	0.0620363i	$-0.0197594\pi$
$107$	4.60634	+	7.97842i	0.445312	+	0.771303i	−0.552762	+	0.833339i	$0.686426\pi$
$108$	−7.32666	−	7.37021i	−0.705009	−	0.709199i
$109$	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	$0.0583602\pi$
$113$			3.87615i			0.364637i	−0.983240	+	0.182319i	$0.941640\pi$
$114$	−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	−0.634715	+	0.772746i	$0.718883\pi$
$131$	−18.5565	+	10.7136i	−1.62129	+	0.936053i	−0.986575	+	0.163306i	$0.947784\pi$
$132$	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	0.323332	−	0.946286i	$-0.395197\pi$
$137$	−3.91533	−	2.26052i	−0.334509	−	0.193129i	−0.657841	+	0.753157i	$0.728530\pi$
$138$	−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	−0.848636	−	0.528977i	$-0.822576\pi$
$149$	−10.7714	−	18.6566i	−0.882425	−	1.52841i	−0.0337890	−	0.999429i	$-0.510757\pi$
$150$	−11.4234	−	1.71450i	−0.932718	−	0.139988i
$151$	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
$156$	−11.3223	−	13.0123i	−0.906510	−	1.04182i
$157$	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
$159$	−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	−0.704429	−	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
$165$	−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	0.167737	−	0.985832i	$-0.446354\pi$
$173$	14.5387	−	8.39395i	1.10536	−	0.638180i	0.937624	+	0.347652i	$0.113021\pi$
$174$	−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	−0.931309	−	0.364231i	$-0.881332\pi$
$179$	−2.00982	+	3.48110i	−0.150221	+	0.260190i	0.781088	+	0.624421i	$0.214665\pi$
$180$	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	0.269655	−	0.962957i	$-0.413090\pi$
$191$	17.1154	−	9.88159i	1.23843	−	0.715006i	0.968773	+	0.247951i	$0.0797570\pi$
$192$	12.0862	−	6.77669i	0.872247	−	0.489065i
$193$	−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	$-0.403053\pi$
$197$	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	0.870287	−	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
$201$	−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	$0.107468\pi$
$211$			9.62315i			0.662485i	−0.943546	+	0.331243i	$0.892532\pi$
$212$	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	$-0.763794\pi$
$223$		−	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	0.533923	−	0.845533i	$-0.320717\pi$
$227$	1.03403	+	0.597000i	0.0686313	+	0.0396243i	−0.465292	+	0.885157i	$0.654051\pi$
$228$	−2.07472	+	6.03479i	−0.137402	+	0.399664i
$229$	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
$231$	−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	0.0392607	−	0.999229i	$-0.487500\pi$
$233$	14.1080	−	8.14528i	0.924249	−	0.533615i	0.884988	+	0.465614i	$0.154166\pi$
$234$	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	$-0.772810\pi$
$239$		−	20.2417i		−	1.30933i	0.755920	−	0.654664i	$-0.227190\pi$
$240$	−3.46718	+	1.27246i	−0.223806	+	0.0821372i
$241$	−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
$243$	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	$-0.916452\pi$
$251$		−	8.22152i		−	0.518938i	0.965751	−	0.259469i	$-0.0835475\pi$
$252$	−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	0.576974	−	0.816763i	$-0.304233\pi$
$257$	−6.71468	−	11.6302i	−0.418850	−	0.725470i	−0.995824	+	0.0912928i	$0.970900\pi$
$258$	−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	0.844927	−	0.534881i	$-0.179644\pi$
$263$	13.0415	+	7.52949i	0.804170	+	0.464288i	−0.0407569	+	0.999169i	$0.512977\pi$
$264$	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	0.106560	−	0.994306i	$-0.466016\pi$
$269$	−11.5014	−	6.64035i	−0.701254	−	0.404869i	−0.807814	+	0.589437i	$0.799350\pi$
$270$	3.21934	+	2.23190i	0.195923	+	0.135829i
$271$	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
$273$	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	−0.247052	−	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	$0.218810\pi$
$281$			21.2736i			1.26908i	−0.772892	+	0.634538i	$0.781190\pi$
$282$	−8.89622	+	11.1698i	−0.529762	+	0.665153i
$283$	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
$285$	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	$0.231297\pi$
$293$			22.7441i			1.32872i	−0.747411	+	0.664362i	$0.768703\pi$
$294$	−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	−0.295339	−	0.955393i	$-0.595433\pi$
$311$	11.9871	−	20.7622i	0.679725	−	1.17732i	0.975064	−	0.221925i	$-0.0712341\pi$
$312$	−21.2497	−	11.9783i	−1.20303	−	0.678138i
$313$	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
$315$	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	0.834699	−	0.550706i	$-0.185642\pi$
$317$	−1.06072	−	1.83723i	−0.0595762	−	0.103189i	−0.894275	+	0.447517i	$0.852308\pi$
$318$	−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	−0.534088	−	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
$333$	−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	−0.216171	−	0.976356i	$-0.569357\pi$
$347$	13.7374	−	23.7939i	0.737463	−	1.27732i	0.953634	−	0.300969i	$-0.0973099\pi$
$348$	−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	−0.987626	−	0.156828i	$-0.949873\pi$
$353$	−6.72613	+	11.6500i	−0.357996	+	0.620067i	0.629630	+	0.776895i	$0.283207\pi$
$354$	−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	−0.923930	−	0.382561i	$-0.875042\pi$
$359$	−19.9816	+	11.5364i	−1.05459	+	0.608867i	−0.130658	+	0.991428i	$0.541709\pi$
$360$	−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	0.900931	−	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
$369$	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	−0.495881	−	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
$375$	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	$0.0240055\pi$
$379$			2.93359i			0.150688i	−0.997158	+	0.0753441i	$0.975994\pi$
$380$	−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	0.992735	−	0.120319i	$-0.0383918\pi$
$383$	7.67488	+	13.2933i	0.392168	+	0.679255i	−0.600567	+	0.799574i	$0.705058\pi$
$384$	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	−0.810842	−	0.585266i	$-0.800990\pi$
$389$	2.00060	−	3.46513i	0.101434	−	0.175689i	0.912276	+	0.409577i	$0.134324\pi$
$390$	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	−0.994470	−	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
$399$	−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	−0.817066	−	0.576544i	$-0.804401\pi$
$401$	−14.5441	+	8.39703i	−0.726297	+	0.419328i	0.0907689	+	0.995872i	$0.471068\pi$
$402$	−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	0.765936	−	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
$411$	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	$0.141086\pi$
$419$			17.5573i			0.857728i	−0.903369	+	0.428864i	$0.858914\pi$
$420$	0.706793	−	4.83439i	0.0344880	−	0.235894i
$421$		−	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
$423$	−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	−0.257139	−	0.966374i	$-0.582780\pi$
$431$	−25.3821	−	14.6544i	−1.22261	−	0.705876i	−0.965474	+	0.260498i	$0.916113\pi$
$432$	−20.6691	−	2.18841i	−0.994442	−	0.105290i
$433$			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
$438$	−3.50757	+	23.3703i	−0.167598	+	1.11668i
$439$	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
$441$	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	0.660984	−	0.750400i	$-0.270139\pi$
$443$	−6.72205	−	11.6429i	−0.319374	−	0.553172i	−0.980358	+	0.197228i	$0.936806\pi$
$444$	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	$0.126017\pi$
$449$			16.3428i			0.771266i	−0.922652	+	0.385633i	$0.873983\pi$
$450$	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	0.973497	+	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
$459$	−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	$-0.954856\pi$
$461$		−	6.06975i		−	0.282696i	0.989960	−	0.141348i	$-0.0451437\pi$
$462$	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	−0.328217	−	0.944602i	$-0.606448\pi$
$467$	7.03895	−	4.06394i	0.325724	−	0.188057i	0.653941	+	0.756546i	$0.273114\pi$
$468$	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	−0.856132	−	0.516757i	$-0.827139\pi$
$479$	0.425876	−	0.737638i	0.0194588	−	0.0337035i	0.875591	+	0.483054i	$0.160472\pi$
$480$	−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	−0.916329	−	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	$-0.463473\pi$
$491$	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	−0.840388	−	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
$501$	−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	0.169697	−	0.985496i	$-0.445721\pi$
$509$	24.9978	−	14.4325i	1.10801	−	0.639710i	0.938313	+	0.345787i	$0.112388\pi$
$510$	−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	−0.448161	−	0.893953i	$-0.647921\pi$
$521$	12.5564	−	21.7483i	0.550105	−	0.952811i	0.998266	−	0.0588577i	$-0.0187458\pi$
$522$	30.1661	−	13.0327i	1.32034	−	0.570426i
$523$	−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
$525$	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	−0.916187	−	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
$543$	−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	$-0.759483\pi$
$547$		−	32.0757i		−	1.37146i	0.727856	−	0.685730i	$-0.240517\pi$
$548$	−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	−0.637104	−	0.770777i	$-0.719868\pi$
$557$	8.23577	−	14.2648i	0.348961	−	0.604417i	0.986065	+	0.166360i	$0.0532014\pi$
$558$	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	0.160902	−	0.986970i	$-0.448560\pi$
$563$	−14.5542	−	8.40290i	−0.613388	−	0.354140i	−0.774290	+	0.632830i	$0.781893\pi$
$564$	−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	−0.988203	−	0.153149i	$-0.951059\pi$
$569$	−32.1947	+	18.5876i	−1.34967	+	0.779235i	−0.361471	+	0.932383i	$0.617725\pi$
$570$	0.357030	−	2.37883i	0.0149543	−	0.0996382i
$571$	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
$576$	12.4257	+	20.5329i	0.517737	+	0.855540i
$577$	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
$579$	−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	$0.167782\pi$
$587$			24.3750i			1.00606i	−0.864268	+	0.503032i	$0.832218\pi$
$588$	−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	0.866612	−	0.498983i	$-0.166293\pi$
$593$	0.0286004	+	0.0495374i	0.00117448	+	0.00203426i	−0.865438	+	0.501017i	$0.832959\pi$
$594$	−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	0.999247	−	0.0387877i	$-0.0123496\pi$
$599$	35.8620	+	20.7049i	1.46528	+	0.845980i	0.466033	+	0.884768i	$0.345683\pi$
$600$	−19.8875	+	11.7569i	−0.811903	+	0.479972i
$601$		−	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
$606$	−1.39971	+	9.32605i	−0.0568594	+	0.378845i
$607$	−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
$609$	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	0.800450	−	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	$0.143049\pi$
$617$			21.5819i			0.868854i	−0.900707	+	0.434427i	$0.856951\pi$
$618$	−10.1999	−	8.12369i	−0.410299	−	0.326783i
$619$	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
$621$	0.362023	+	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	0.268107	−	0.963389i	$-0.413602\pi$
$641$	−10.9414	−	6.31703i	−0.432160	−	0.249508i	−0.700266	+	0.713882i	$0.746935\pi$
$642$	−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	−0.981759	−	0.190131i	$-0.939109\pi$
$647$	−8.29783	+	14.3723i	−0.326221	+	0.565032i	0.655538	+	0.755163i	$0.272442\pi$
$648$	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	0.811247	−	0.584704i	$-0.198789\pi$
$653$	−2.57443	−	4.45904i	−0.100745	−	0.174496i	−0.911992	+	0.410208i	$0.865456\pi$
$654$	−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	−0.999786	−	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
$663$	−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	−0.989169	−	0.146779i	$-0.953109\pi$
$677$	−35.2987	+	20.3797i	−1.35664	+	0.783256i	−0.367471	+	0.930035i	$0.619776\pi$
$678$	−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	0.428936	+	0.903335i	$0.358888\pi$
$683$	−14.8402	+	25.7039i	−0.567843	+	0.983532i	−0.996779	+	0.0801976i	$0.974445\pi$
$684$	−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	0.929650	−	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
$693$	−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	0.366339	−	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
$711$	0.0763714	+	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	0.863904	+	0.503656i	$0.168012\pi$
$719$	23.2782	+	40.3190i	0.868131	+	1.50365i	0.00422645	+	0.999991i	$0.498655\pi$
$720$	−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	$0.0637127\pi$
$727$			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
$732$	−2.42285	+	7.04740i	−0.0895512	+	0.260479i
$733$	−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
$735$	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	−0.974538	−	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	$-0.838686\pi$
$743$		−	26.4603i		−	0.970735i	0.874310	−	0.485367i	$-0.161314\pi$
$744$	−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	0.633129	−	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
$753$	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	$-0.969888\pi$
$757$		−	5.19772i		−	0.188914i	0.995529	−	0.0944572i	$-0.0301115\pi$
$758$	1.38917	+	3.90923i	0.0504568	+	0.141990i
$759$	−0.945403	+	0.0313861i	−0.0343160	+	0.00113924i
$760$	−2.43662	+	1.33340i	−0.0883856	+	0.0483674i
$761$	−18.8681	−	32.6805i	−0.683969	−	1.18467i	−0.973760	−	0.227578i	$-0.926919\pi$
$761$	−18.8681	−	32.6805i	−0.683969	−	1.18467i	0.289791	−	0.957090i	$-0.406414\pi$
$762$	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	$-0.919058\pi$
$769$		−	13.9517i		−	0.503110i	0.967843	−	0.251555i	$-0.0809419\pi$
$770$	−7.88480	+	4.59235i	−0.284148	+	0.165497i
$771$	19.7471	−	12.2921i	0.711173	−	0.442691i
$772$	3.99194	+	24.8506i	0.143673	+	0.894391i
$773$	21.5519	+	12.4430i	0.775169	+	0.447544i	0.834715	−	0.550682i	$-0.185632\pi$
$773$	21.5519	+	12.4430i	0.775169	+	0.447544i	−0.0595465	+	0.998226i	$0.518965\pi$
$774$	−3.15018	−	7.29156i	−0.113231	−	0.262090i
$775$	9.13305	−	5.27297i	0.328069	−	0.189411i
$776$	−17.3704	−	10.5660i	−0.623561	−	0.379297i
$777$	−27.3726	+	25.1320i	−0.981988	+	0.901604i
$778$	1.02507	−	5.56492i	0.0367506	−	0.199512i
$779$	−2.40324	−	4.16254i	−0.0861051	−	0.149138i
$780$	8.69540	+	2.98942i	0.311345	+	0.107039i
$781$	24.5878	+	14.1958i	0.879822	+	0.507966i
$782$	0.244374	+	0.687688i	0.00873879	+	0.0245917i
$783$	4.00028	+	40.0471i	0.142958	+	1.43117i
$784$	4.65100	+	27.6110i	0.166107	+	0.986108i
$785$			3.77877i			0.134870i
$786$	−41.0555	−	32.6987i	−1.46440	−	1.16632i
$787$	4.90837	−	8.50154i	0.174964	−	0.303047i	−0.765185	−	0.643811i	$-0.777352\pi$
$787$	4.90837	−	8.50154i	0.174964	−	0.303047i	0.940149	+	0.340764i	$0.110686\pi$
$788$	13.0608	−	10.6240i	0.465271	−	0.378465i
$789$	−12.2848	+	23.0087i	−0.437350	+	0.819133i
$790$	0.0339262	+	0.00624930i	0.00120704	+	0.000222340i
$791$	−10.0785	+	1.89613i	−0.358350	+	0.0674188i
$792$	20.8518	+	32.7412i	0.740936	+	1.16341i
$793$	−5.35587	−	9.27663i	−0.190192	−	0.329423i
$794$	−25.2293	−	21.4999i	−0.895354	−	0.763005i
$795$	4.23181	−	0.140490i	0.150087	−	0.00498268i
$796$	28.2696	−	4.54117i	1.00199	−	0.160957i
$797$			11.3322i			0.401406i	0.979652	+	0.200703i	$0.0643226\pi$
$797$			11.3322i			0.401406i	−0.979652	+	0.200703i	$0.935677\pi$
$798$	−10.5528	−	5.58290i	−0.373567	−	0.197632i
$799$	25.2002			0.891518
$800$	24.7018	+	10.0732i	0.873340	+	0.356141i
$801$	27.4840	+	41.0507i	0.971100	+	1.45045i
$802$	−15.4048	+	18.0769i	−0.543962	+	0.638317i
$803$	38.2222	−	22.0676i	1.34883	−	0.778748i
$804$	8.01926	+	41.1506i	0.282817	+	1.45127i
$805$	0.158870	+	0.0557758i	0.00559942	+	0.00196584i
$806$	15.4867	+	2.85270i	0.545497	+	0.100482i
$807$	10.8341	−	20.2917i	0.381378	−	0.714301i
$808$	9.55262	−	5.22749i	0.336060	−	0.183903i
$809$	−19.0031	−	10.9714i	−0.668113	−	0.385735i	0.127248	−	0.991871i	$-0.459385\pi$
$809$	−19.0031	−	10.9714i	−0.668113	−	0.385735i	−0.795361	+	0.606136i	$0.792719\pi$
$810$	−3.67862	+	5.70127i	−0.129254	+	0.200322i
$811$	12.2220			0.429171			0.214586	−	0.976705i	$-0.431160\pi$
$811$	12.2220			0.429171			0.214586	+	0.976705i	$0.431160\pi$
$812$	−31.2952	−	26.4645i	−1.09825	−	0.928723i
$813$	17.2230	+	27.6683i	0.604036	+	0.970370i
$814$	−17.5664	−	49.4332i	−0.615701	−	1.73263i
$815$	1.73664	−	3.00796i	0.0608320	−	0.105364i
$816$	19.1894	−	22.9937i	0.671765	−	0.804941i
$817$	−2.98680	+	1.72443i	−0.104495	+	0.0603302i
$818$	19.2314	+	3.54248i	0.672410	+	0.123860i
$819$	9.86718	+	38.2699i	0.344787	+	1.33726i
$820$	0.991189	−	2.59919i	0.0346138	−	0.0907678i
$821$	22.2720	+	38.5763i	0.777299	+	1.34632i	0.933493	+	0.358595i	$0.116744\pi$
$821$	22.2720	+	38.5763i	0.777299	+	1.34632i	−0.156195	+	0.987726i	$0.549923\pi$
$822$	1.64368	−	10.9516i	0.0573299	−	0.381980i
$823$	13.6219	−	23.5938i	0.474830	−	0.822429i	−0.524755	−	0.851254i	$-0.675843\pi$
$823$	13.6219	−	23.5938i	0.474830	−	0.822429i	0.999584	+	0.0288241i	$0.00917627\pi$
$824$	−0.344526	+	15.0529i	−0.0120021	+	0.524393i
$825$	−31.7222	+	19.7464i	−1.10443	+	0.687483i
$826$	0.0938721	+	24.6911i	0.00326623	+	0.859112i
$827$	−10.2913			−0.357864			−0.178932	−	0.983861i	$-0.557264\pi$
$827$	−10.2913			−0.357864			−0.178932	+	0.983861i	$0.557264\pi$
$828$	0.210274	−	0.684729i	0.00730751	−	0.0237960i
$829$	16.2859	−	28.2081i	0.565634	−	0.979707i	−0.431356	−	0.902182i	$-0.641965\pi$
$829$	16.2859	−	28.2081i	0.565634	−	0.979707i	0.996990	−	0.0775252i	$-0.0247018\pi$
$830$	2.21751	+	1.88972i	0.0769708	+	0.0655932i
$831$	18.9662	−	35.5226i	0.657929	−	1.23227i
$832$	18.3178	+	35.3723i	0.635056	+	1.22631i
$833$	−4.57197	+	29.9120i	−0.158409	+	1.03639i
$834$	−13.2925	−	33.8065i	−0.460281	−	1.17062i
$835$	7.96232	−	4.59705i	0.275547	−	0.159087i
$836$	13.0752	−	10.6357i	0.452214	−	0.367844i
$837$	−4.78103	+	10.5909i	−0.165257	+	0.366077i
$838$	8.31404	+	23.3964i	0.287204	+	0.808215i
$839$	4.55619			0.157297			0.0786486	−	0.996902i	$-0.474939\pi$
$839$	4.55619			0.157297			0.0786486	+	0.996902i	$0.474939\pi$
$840$	−1.34741	−	6.77689i	−0.0464902	−	0.233825i
$841$	30.9915			1.06867
$842$	−9.41851	−	26.5045i	−0.324583	−	0.913404i
$843$	−36.8266	+	1.22259i	−1.26838	+	0.0421084i
$844$	12.1449	+	14.9305i	0.418046	+	0.513930i
$845$	−5.44432	+	3.14328i	−0.187290	+	0.108132i
$846$	−19.8473	−	14.7583i	−0.682365	−	0.507400i
$847$	19.9264	−	17.1122i	0.684681	−	0.587981i
$848$	13.6853	+	12.2138i	0.469956	+	0.419425i
$849$	13.1763	+	7.03504i	0.452208	+	0.241442i
$850$	21.9426	+	18.6991i	0.752624	+	0.641373i
$851$	−0.484032	+	0.838369i	−0.0165924	+	0.0287389i
$852$	−16.2189	+	14.1125i	−0.555650	+	0.483485i
$853$	−50.6930			−1.73570			−0.867848	−	0.496830i	$-0.834497\pi$
$853$	−50.6930			−1.73570			−0.867848	+	0.496830i	$0.834497\pi$
$854$	−3.99814	+	6.98619i	−0.136814	+	0.239063i
$855$	2.64347	+	1.30058i	0.0904048	+	0.0444790i
$856$	26.0506	+	0.596238i	0.890391	+	0.0203790i
$857$	3.66887	−	6.35467i	0.125326	−	0.217071i	−0.796534	−	0.604594i	$-0.793336\pi$
$857$	3.66887	−	6.35467i	0.125326	−	0.217071i	0.921860	+	0.387522i	$0.126669\pi$
$858$	−55.1773	−	8.28136i	−1.88372	−	0.282721i
$859$	28.8455	+	49.9619i	0.984195	+	1.70468i	0.645458	+	0.763795i	$0.276666\pi$
$859$	28.8455	+	49.9619i	0.984195	+	1.70468i	0.338737	+	0.940881i	$0.390000\pi$
$860$	−1.86503	−	0.711221i	−0.0635971	−	0.0242524i
$861$	11.6706	−	2.59935i	0.397733	−	0.0885856i
$862$	−40.7630	−	7.50866i	−1.38839	−	0.255746i
$863$	−31.1345	+	17.9755i	−1.05983	+	0.611894i	−0.925385	−	0.379027i	$-0.876259\pi$
$863$	−31.1345	+	17.9755i	−1.05983	+	0.611894i	−0.134445	+	0.990921i	$0.542925\pi$
$864$	−28.5794	+	6.87139i	−0.972292	+	0.233769i
$865$	−4.47467	+	7.75035i	−0.152143	+	0.263520i
$866$	5.93945	+	16.7141i	0.201831	+	0.567968i
$867$	2.47969	−	1.54356i	0.0842148	−	0.0524220i
$868$	−4.00466	−	11.1351i	−0.135927	−	0.377950i
$869$	−0.209329			−0.00710101
$870$	7.91124	+	6.30092i	0.268216	+	0.213621i
$871$	−52.1883	−	30.1309i	−1.76833	−	1.02095i
$872$	12.1534	−	6.65071i	0.411566	−	0.225222i
$873$	1.43027	+	21.5174i	0.0484073	+	0.728252i
$874$	−0.305870	−	0.0563420i	−0.0103462	−	0.00190580i
$875$	13.4670	−	2.53363i	0.455267	−	0.0856523i
$876$	6.39265	+	32.8037i	0.215988	+	1.10833i
$877$	−43.3964	+	25.0550i	−1.46539	+	0.846046i	−0.999252	−	0.0386646i	$-0.987690\pi$
$877$	−43.3964	+	25.0550i	−1.46539	+	0.846046i	−0.466142	+	0.884710i	$0.654356\pi$
$878$	12.4900	−	14.6565i	0.421516	−	0.494631i
$879$	−39.3722	+	1.30710i	−1.32799	+	0.0440875i
$880$	9.55035	+	1.98616i	0.321942	+	0.0669534i
$881$	47.9585			1.61576			0.807882	−	0.589344i	$-0.200614\pi$
$881$	47.9585			1.61576			0.807882	+	0.589344i	$0.200614\pi$
$882$	21.1186	−	20.8808i	0.711099	−	0.703092i
$883$		−	0.345258i		−	0.0116188i	−0.999983	−	0.00580942i	$-0.998151\pi$
$883$		−	0.345258i		−	0.0116188i	0.999983	−	0.00580942i	$-0.00184921\pi$
$884$	6.82765	+	42.5033i	0.229639	+	1.42954i
$885$	−0.202169	−	6.08969i	−0.00679585	−	0.204703i
$886$	−14.4710	−	12.3319i	−0.486163	−	0.414300i
$887$	13.7032	+	23.7346i	0.460109	+	0.796931i	0.998966	−	0.0454656i	$-0.0144771\pi$
$887$	13.7032	+	23.7346i	0.460109	+	0.796931i	−0.538857	+	0.842397i	$0.681144\pi$
$888$	39.7238	−	0.409278i	1.33304	−	0.0137345i
$889$	4.00641	+	21.2952i	0.134371	+	0.714220i
$890$	12.2091	+	2.24895i	0.409251	+	0.0753851i
$891$	15.6856	−	38.0669i	0.525487	−	1.27529i
$892$	−25.4733	−	31.3159i	−0.852908	−	1.04853i
$893$	−5.36959	+	9.30041i	−0.179687	+	0.311226i
$894$	32.8750	−	41.2768i	1.09950	−	1.38050i
$895$		−	2.14280i		−	0.0716258i
$896$	16.0410	−	25.2722i	0.535892	−	0.844286i
$897$	0.544092	+	0.874071i	0.0181667	+	0.0291844i
$898$	7.73897	+	21.7781i	0.258253	+	0.726744i
$899$	15.0004	+	8.66049i	0.500292	+	0.288844i
$900$	−6.33071	−	27.5776i	−0.211024	−	0.919254i
$901$	9.91157	+	17.1673i	0.330202	+	0.571927i
$902$	−3.05789	+	16.6007i	−0.101817	+	0.552742i
$903$	−1.86515	−	8.37417i	−0.0620682	−	0.278675i
$904$	9.36666	+	5.69752i	0.311531	+	0.189497i
$905$	6.86014	−	3.96070i	0.228039	−	0.131658i
$906$	6.81979	+	1.02356i	0.226572	+	0.0340054i
$907$	7.67380	+	4.43047i	0.254804	+	0.147111i	0.621962	−	0.783047i	$-0.286336\pi$
$907$	7.67380	+	4.43047i	0.254804	+	0.147111i	−0.367158	+	0.930159i	$0.619669\pi$
$908$	2.35777	−	0.378748i	0.0782454	−	0.0125692i
$909$	−10.3636	−	5.09885i	−0.343737	−	0.169118i
$910$	8.61988	+	4.93309i	0.285746	+	0.163530i
$911$			17.2124i			0.570272i	0.958487	+	0.285136i	$0.0920388\pi$
$911$			17.2124i			0.570272i	−0.958487	+	0.285136i	$0.907961\pi$
$912$	4.39725	+	11.9815i	0.145608	+	0.396748i
$913$	−15.3106	−	8.83959i	−0.506707	−	0.292548i
$914$	31.5155	+	26.8570i	1.04244	+	0.888349i
$915$	0.935542	−	1.75222i	0.0309281	−	0.0579266i
$916$	42.6149	+	16.2510i	1.40804	+	0.536948i
$917$	−36.9343	−	43.0086i	−1.21968	−	1.42027i
$918$	−31.6575	−	2.62092i	−1.04485	−	0.0865032i
$919$	2.91012	+	5.04048i	0.0959961	+	0.166270i	0.910024	−	0.414556i	$-0.136063\pi$
$919$	2.91012	+	5.04048i	0.0959961	+	0.166270i	−0.814028	+	0.580826i	$0.802730\pi$
$920$	−0.0864103	−	0.157904i	−0.00284886	−	0.00520596i
$921$	1.31129	+	39.4982i	0.0432084	+	1.30151i
$922$	−2.87426	−	8.08841i	−0.0946587	−	0.266378i
$923$		−	30.9025i		−	1.01717i
$924$	15.4905	+	38.9610i	0.509599	+	1.28172i
$925$			38.2407i			1.25734i
$926$	−4.40284	+	1.56457i	−0.144686	+	0.0514151i
$927$	13.2705	−	8.88482i	0.435862	−	0.291816i
$928$	5.95753	+	43.4078i	0.195565	+	1.42493i
$929$	−3.36170	−	5.82263i	−0.110294	−	0.191034i	0.805595	−	0.592467i	$-0.201846\pi$
$929$	−3.36170	−	5.82263i	−0.110294	−	0.191034i	−0.915889	+	0.401432i	$0.868512\pi$
$930$	1.06853	+	2.71758i	0.0350385	+	0.0891129i
$931$	−10.0652	−	8.06092i	−0.329873	−	0.264186i
$932$	11.6092	−	30.4427i	0.380271	−	0.997184i
$933$	36.6303	+	19.5576i	1.19922	+	0.640287i
$934$	7.45551	−	8.74872i	0.243952	−	0.286267i
$935$	9.12949	+	5.27091i	0.298566	+	0.172377i
$936$	19.5144	−	37.4736i	0.637848	−	1.22486i
$937$			5.64519i			0.184420i	0.995740	+	0.0922102i	$0.0293932\pi$
$937$			5.64519i			0.184420i	−0.995740	+	0.0922102i	$0.970607\pi$
$938$	0.172162	+	45.2835i	0.00562128	+	1.47856i
$939$	20.5485	+	33.0107i	0.670576	+	1.07726i
$940$	−6.13668	+	0.985783i	−0.200156	+	0.0321527i
$941$	−39.2739	−	22.6748i	−1.28029	−	0.739177i	−0.303391	−	0.952866i	$-0.598119\pi$
$941$	−39.2739	−	22.6748i	−1.28029	−	0.739177i	−0.976902	+	0.213689i	$0.931452\pi$
$942$	17.1710	+	2.57713i	0.559460	+	0.0839674i
$943$	0.269752	−	0.155741i	0.00878433	−	0.00507164i
$944$	17.5760	−	19.6935i	0.572051	−	0.640970i
$945$	−5.05778	+	5.30362i	−0.164529	+	0.172527i
$946$	11.9117	+	2.19417i	0.387283	+	0.0713385i
$947$	−0.0324938	−	0.0562810i	−0.00105591	−	0.00182889i	0.865497	−	0.500914i	$-0.167003\pi$
$947$	−0.0324938	−	0.0562810i	−0.00105591	−	0.00182889i	−0.866553	+	0.499085i	$0.833669\pi$
$948$	0.0515349	−	0.149901i	0.00167377	−	0.00486854i
$949$	−41.6025	−	24.0192i	−1.35048	−	0.779697i
$950$	−11.5766	+	4.11380i	−0.375594	+	0.133469i
$951$	3.11946	−	1.94180i	0.101155	−	0.0629672i
$952$	25.0171	−	20.5081i	0.810807	−	0.664672i
$953$		−	33.3269i		−	1.07956i	−0.841805	−	0.539781i	$-0.818507\pi$
$953$		−	33.3269i		−	1.07956i	0.841805	−	0.539781i	$-0.181493\pi$
$954$	2.24770	−	19.3254i	0.0727721	−	0.625683i
$955$	−5.26770	+	9.12393i	−0.170459	+	0.295243i
$956$	−25.5461	−	31.4055i	−0.826220	−	1.01573i
$957$	−54.1379	−	28.9052i	−1.75003	−	0.934372i
$958$	0.218212	−	1.18463i	0.00705010	−	0.0382736i
$959$	3.96235	−	11.2862i	0.127951	−	0.364450i
$960$	−3.77349	+	6.35002i	−0.121789	+	0.204946i
$961$	−12.9995	−	22.5158i	−0.419339	−	0.726316i
$962$	−37.0366	+	43.4609i	−1.19411	+	1.40124i
$963$	−15.3761	−	22.9660i	−0.495487	−	0.740070i
$964$	−18.2257	+	2.92773i	−0.587009	+	0.0942959i
$965$		−	6.70862i		−	0.215958i
$966$	0.361798	−	0.683873i	0.0116407	−	0.0220033i
$967$	8.68323			0.279234			0.139617	−	0.990206i	$-0.455413\pi$
$967$	8.68323			0.279234			0.139617	+	0.990206i	$0.455413\pi$
$968$	−28.0719	−	0.642501i	−0.902265	−	0.0206508i
$969$	0.457651	+	13.7852i	0.0147019	+	0.442846i
$970$	4.12465	+	3.51495i	0.132435	+	0.112858i
$971$	37.7352	−	21.7864i	1.21098	−	0.699159i	0.248007	−	0.968758i	$-0.420225\pi$
$971$	37.7352	−	21.7864i	1.21098	−	0.699159i	0.962973	+	0.269599i	$0.0868912\pi$
$972$	23.3981	+	20.6041i	0.750493	+	0.660878i
$973$	−7.25453	−	38.5599i	−0.232569	−	1.23617i
$974$	−1.25946	+	6.83735i	−0.0403557	+	0.219083i
$975$	35.8772	+	19.1555i	1.14899	+	0.613466i
$976$	8.17219	−	2.69507i	0.261585	−	0.0862671i
$977$	16.6770	+	9.62846i	0.533544	+	0.308042i	0.742458	−	0.669892i	$-0.233660\pi$
$977$	16.6770	+	9.62846i	0.533544	+	0.308042i	−0.208914	+	0.977934i	$0.566993\pi$
$978$	−12.4839	−	9.94284i	−0.399192	−	0.317937i
$979$	−75.3320			−2.40762
$980$	−0.0567470	−	7.46294i	−0.00181272	−	0.238395i
$981$	−13.1851	−	6.48705i	−0.420968	−	0.207116i
$982$	6.76195	−	2.40290i	0.215782	−	0.0766795i
$983$	−12.6512	+	21.9125i	−0.403510	+	0.698900i	−0.994147	−	0.108037i	$-0.965543\pi$
$983$	−12.6512	+	21.9125i	−0.403510	+	0.698900i	0.590637	+	0.806938i	$0.298877\pi$
$984$	−11.1349	−	6.27668i	−0.354968	−	0.200093i
$985$	−3.88630	+	2.24376i	−0.123828	+	0.0714920i
$986$	−8.57774	+	46.5668i	−0.273171	+	1.48299i
$987$	−18.0676	−	19.6784i	−0.575097	−	0.626371i
$988$	−17.1412	−	6.53670i	−0.545333	−	0.207960i
$989$	−0.111751	−	0.193559i	−0.00355348	−	0.00615481i
$990$	−4.10339	−	9.49791i	−0.130414	−	0.301863i
$991$	6.86308	−	11.8872i	0.218013	−	0.377609i	−0.736187	−	0.676778i	$-0.763376\pi$
$991$	6.86308	−	11.8872i	0.218013	−	0.377609i	0.954200	+	0.299168i	$0.0967092\pi$
$992$	−4.77680	+	11.7138i	−0.151664	+	0.371914i
$993$	−1.32620	−	2.13051i	−0.0420857	−	0.0676098i
$994$	−20.0663	+	11.6872i	−0.636466	+	0.370697i
$995$	−7.63161			−0.241938
$996$	10.0993	−	8.78770i	0.320010	−	0.278449i
$997$	1.12122	−	1.94201i	0.0355094	−	0.0615041i	−0.847725	−	0.530437i	$-0.822028\pi$
$997$	1.12122	−	1.94201i	0.0355094	−	0.0615041i	0.883234	+	0.468933i	$0.155361\pi$
$998$	−18.7202	+	21.9674i	−0.592578	+	0.695366i
$999$	−24.5905	−	34.2158i	−0.778008	−	1.08254i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	168.2.ba.c.101.22	yes	48
3.2	odd	2	inner	168.2.ba.c.101.3	yes	48
4.3	odd	2		672.2.bi.c.17.12		48
7.5	odd	6	inner	168.2.ba.c.5.6	yes	48
8.3	odd	2		672.2.bi.c.17.13		48
8.5	even	2	inner	168.2.ba.c.101.19	yes	48
12.11	even	2		672.2.bi.c.17.21		48
21.5	even	6	inner	168.2.ba.c.5.19	yes	48
24.5	odd	2	inner	168.2.ba.c.101.6	yes	48
24.11	even	2		672.2.bi.c.17.4		48
28.19	even	6		672.2.bi.c.593.4		48
56.5	odd	6	inner	168.2.ba.c.5.3	✓	48
56.19	even	6		672.2.bi.c.593.21		48
84.47	odd	6		672.2.bi.c.593.13		48
168.5	even	6	inner	168.2.ba.c.5.22	yes	48
168.131	odd	6		672.2.bi.c.593.12		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.ba.c.5.3	✓	48	56.5	odd	6	inner
168.2.ba.c.5.6	yes	48	7.5	odd	6	inner
168.2.ba.c.5.19	yes	48	21.5	even	6	inner
168.2.ba.c.5.22	yes	48	168.5	even	6	inner
168.2.ba.c.101.3	yes	48	3.2	odd	2	inner
168.2.ba.c.101.6	yes	48	24.5	odd	2	inner
168.2.ba.c.101.19	yes	48	8.5	even	2	inner
168.2.ba.c.101.22	yes	48	1.1	even	1	trivial
672.2.bi.c.17.4		48	24.11	even	2
672.2.bi.c.17.12		48	4.3	odd	2
672.2.bi.c.17.13		48	8.3	odd	2
672.2.bi.c.17.21		48	12.11	even	2
672.2.bi.c.593.4		48	28.19	even	6
672.2.bi.c.593.12		48	168.131	odd	6
672.2.bi.c.593.13		48	84.47	odd	6
672.2.bi.c.593.21		48	56.19	even	6

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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