LMFDB - Embedded newform 555.2.bb.a.454.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [555,2,Mod(454,555)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(555, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("555.454");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 555 = 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	555.bb (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:	$4.43169731218$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			454.14
Character	$\chi$	$=$	555.454
Dual form			555.2.bb.a.544.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.931961 - 0.538068i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.420965 - 0.729134i) q^{4} +(-0.374645 + 2.20446i) q^{5} +1.07614 q^{6} +(-3.54514 + 2.04679i) q^{7} +3.05830i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.931961 - 0.538068i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.420965 - 0.729134i) q^{4} +(-0.374645 + 2.20446i) q^{5} +1.07614 q^{6} +(-3.54514 + 2.04679i) q^{7} +3.05830i q^{8} +(0.500000 - 0.866025i) q^{9} +(1.53530 - 1.85289i) q^{10} -2.24295 q^{11} +(0.729134 + 0.420965i) q^{12} +(4.79584 - 2.76888i) q^{13} +4.40525 q^{14} +(-0.777777 - 2.09644i) q^{15} +(0.803645 - 1.39195i) q^{16} +(0.535580 + 0.309217i) q^{17} +(-0.931961 + 0.538068i) q^{18} +(-2.08675 - 3.61436i) q^{19} +(1.76506 - 0.654835i) q^{20} +(2.04679 - 3.54514i) q^{21} +(2.09034 + 1.20686i) q^{22} -5.65188i q^{23} +(-1.52915 - 2.64857i) q^{24} +(-4.71928 - 1.65178i) q^{25} -5.95938 q^{26} +1.00000i q^{27} +(2.98477 + 1.72326i) q^{28} +8.34715 q^{29} +(-0.403169 + 2.37230i) q^{30} -4.71376 q^{31} +(3.79921 - 2.19347i) q^{32} +(1.94245 - 1.12147i) q^{33} +(-0.332760 - 0.576357i) q^{34} +(-3.18389 - 8.58195i) q^{35} -0.841931 q^{36} +(-5.75555 + 1.96817i) q^{37} +4.49126i q^{38} +(-2.76888 + 4.79584i) q^{39} +(-6.74191 - 1.14578i) q^{40} +(4.08344 + 7.07273i) q^{41} +(-3.81506 + 2.20262i) q^{42} -10.8405i q^{43} +(0.944203 + 1.63541i) q^{44} +(1.72180 + 1.42668i) q^{45} +(-3.04110 + 5.26734i) q^{46} -1.43023i q^{47} +1.60729i q^{48} +(4.87870 - 8.45015i) q^{49} +(3.50942 + 4.07869i) q^{50} -0.618434 q^{51} +(-4.03777 - 2.33121i) q^{52} +(-5.03741 - 2.90835i) q^{53} +(0.538068 - 0.931961i) q^{54} +(0.840310 - 4.94448i) q^{55} +(-6.25971 - 10.8421i) q^{56} +(3.61436 + 2.08675i) q^{57} +(-7.77922 - 4.49134i) q^{58} +(0.603982 - 1.04613i) q^{59} +(-1.20117 + 1.44963i) q^{60} +(-4.13777 - 7.16683i) q^{61} +(4.39304 + 2.53632i) q^{62} +4.09358i q^{63} -7.93553 q^{64} +(4.30714 + 11.6096i) q^{65} -2.41372 q^{66} +(12.1932 - 7.03977i) q^{67} -0.520679i q^{68} +(2.82594 + 4.89467i) q^{69} +(-1.65041 + 9.71119i) q^{70} +(-4.15262 - 7.19255i) q^{71} +(2.64857 + 1.52915i) q^{72} -0.356372i q^{73} +(6.42296 + 1.26262i) q^{74} +(4.91291 - 0.929156i) q^{75} +(-1.75690 + 3.04304i) q^{76} +(7.95157 - 4.59084i) q^{77} +(5.16098 - 2.97969i) q^{78} +(0.0130972 + 0.0226850i) q^{79} +(2.76743 + 2.29309i) q^{80} +(-0.500000 - 0.866025i) q^{81} -8.78868i q^{82} +(9.81892 + 5.66896i) q^{83} -3.44651 q^{84} +(-0.882309 + 1.06482i) q^{85} +(-5.83293 + 10.1029i) q^{86} +(-7.22885 + 4.17358i) q^{87} -6.85961i q^{88} +(2.40898 - 4.17247i) q^{89} +(-0.836994 - 2.25606i) q^{90} +(-11.3346 + 19.6322i) q^{91} +(-4.12098 + 2.37925i) q^{92} +(4.08224 - 2.35688i) q^{93} +(-0.769560 + 1.33292i) q^{94} +(8.74951 - 3.24606i) q^{95} +(-2.19347 + 3.79921i) q^{96} -5.17187i q^{97} +(-9.09351 + 5.25014i) q^{98} +(-1.12147 + 1.94245i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 32 q^{4} - 2 q^{5} + 36 q^{9}+O(q^{10}) $ 72 * q + 32 * q^4 - 2 * q^5 + 36 * q^9	$ 72 q + 32 q^{4} - 2 q^{5} + 36 q^{9} - 8 q^{11} - 16 q^{14} - 24 q^{16} + 4 q^{19} + 4 q^{20} + 12 q^{21} + 10 q^{25} + 24 q^{26} + 16 q^{29} + 12 q^{30} + 24 q^{31} - 44 q^{34} - 2 q^{35} + 64 q^{36} - 8 q^{39} + 46 q^{40} - 48 q^{41} - 8 q^{44} - 4 q^{45} - 64 q^{46} + 32 q^{49} - 46 q^{50} - 8 q^{51} - 12 q^{55} - 72 q^{56} + 32 q^{59} - 68 q^{60} - 8 q^{61} - 136 q^{64} - 42 q^{65} - 32 q^{66} - 4 q^{69} + 4 q^{70} + 12 q^{71} - 96 q^{74} - 8 q^{75} + 8 q^{76} - 8 q^{79} - 44 q^{80} - 36 q^{81} + 136 q^{84} + 4 q^{85} + 8 q^{86} + 8 q^{91} - 28 q^{94} + 18 q^{95} - 20 q^{96} - 4 q^{99}+O(q^{100}) $ 72 * q + 32 * q^4 - 2 * q^5 + 36 * q^9 - 8 * q^11 - 16 * q^14 - 24 * q^16 + 4 * q^19 + 4 * q^20 + 12 * q^21 + 10 * q^25 + 24 * q^26 + 16 * q^29 + 12 * q^30 + 24 * q^31 - 44 * q^34 - 2 * q^35 + 64 * q^36 - 8 * q^39 + 46 * q^40 - 48 * q^41 - 8 * q^44 - 4 * q^45 - 64 * q^46 + 32 * q^49 - 46 * q^50 - 8 * q^51 - 12 * q^55 - 72 * q^56 + 32 * q^59 - 68 * q^60 - 8 * q^61 - 136 * q^64 - 42 * q^65 - 32 * q^66 - 4 * q^69 + 4 * q^70 + 12 * q^71 - 96 * q^74 - 8 * q^75 + 8 * q^76 - 8 * q^79 - 44 * q^80 - 36 * q^81 + 136 * q^84 + 4 * q^85 + 8 * q^86 + 8 * q^91 - 28 * q^94 + 18 * q^95 - 20 * q^96 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/555\mathbb{Z}\right)^\times$.

$n$	$76$	$112$	$371$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$1$

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 $

$2$	−0.931961	−	0.538068i	−0.658996	−	0.380472i	0.132898	−	0.991130i	$-0.457572\pi$
$2$	−0.931961	−	0.538068i	−0.658996	−	0.380472i	−0.791894	+	0.610658i	$0.790905\pi$
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$4$	−0.420965	−	0.729134i	−0.210483	−	0.364567i
$5$	−0.374645	+	2.20446i	−0.167547	+	0.985864i
$5$	−0.374645	+	2.20446i	−0.167547	+	0.985864i
$6$	1.07614			0.439331
$7$	−3.54514	+	2.04679i	−1.33994	+	0.773614i	−0.986798	−	0.161956i	$-0.948220\pi$
$7$	−3.54514	+	2.04679i	−1.33994	+	0.773614i	−0.353141	+	0.935570i	$0.614886\pi$
$8$			3.05830i			1.08127i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	1.53530	−	1.85289i	0.485506	−	0.585934i
$11$	−2.24295			−0.676274			−0.338137	−	0.941097i	$-0.609797\pi$
$11$	−2.24295			−0.676274			−0.338137	+	0.941097i	$0.609797\pi$
$12$	0.729134	+	0.420965i	0.210483	+	0.121522i
$13$	4.79584	−	2.76888i	1.33013	−	0.767949i	0.344808	−	0.938673i	$-0.387944\pi$
$13$	4.79584	−	2.76888i	1.33013	−	0.767949i	0.985319	+	0.170724i	$0.0546106\pi$
$14$	4.40525			1.17735
$15$	−0.777777	−	2.09644i	−0.200821	−	0.541299i
$16$	0.803645	−	1.39195i	0.200911	−	0.347989i
$17$	0.535580	+	0.309217i	0.129897	+	0.0749961i	0.563540	−	0.826088i	$-0.309439\pi$
$17$	0.535580	+	0.309217i	0.129897	+	0.0749961i	−0.433643	+	0.901085i	$0.642772\pi$
$18$	−0.931961	+	0.538068i	−0.219665	+	0.126824i
$19$	−2.08675	−	3.61436i	−0.478734	−	0.829192i	0.520969	−	0.853576i	$-0.325571\pi$
$19$	−2.08675	−	3.61436i	−0.478734	−	0.829192i	−0.999703	+	0.0243840i	$0.992238\pi$
$20$	1.76506	−	0.654835i	0.394679	−	0.146425i
$21$	2.04679	−	3.54514i	0.446646	−	0.773614i
$22$	2.09034	+	1.20686i	0.445662	+	0.257303i
$23$		−	5.65188i		−	1.17850i	−0.807951	−	0.589249i	$-0.799424\pi$
$23$		−	5.65188i		−	1.17850i	0.807951	−	0.589249i	$-0.200576\pi$
$24$	−1.52915	−	2.64857i	−0.312137	−	0.540637i
$25$	−4.71928	−	1.65178i	−0.943856	−	0.330356i
$26$	−5.95938			−1.16873
$27$			1.00000i			0.192450i
$28$	2.98477	+	1.72326i	0.564068	+	0.325665i
$29$	8.34715			1.55003			0.775014	−	0.631944i	$-0.217743\pi$
$29$	8.34715			1.55003			0.775014	+	0.631944i	$0.217743\pi$
$30$	−0.403169	+	2.37230i	−0.0736083	+	0.433120i
$31$	−4.71376			−0.846616			−0.423308	−	0.905986i	$-0.639131\pi$
$31$	−4.71376			−0.846616			−0.423308	+	0.905986i	$0.639131\pi$
$32$	3.79921	−	2.19347i	0.671611	−	0.387755i
$33$	1.94245	−	1.12147i	0.338137	−	0.195223i
$34$	−0.332760	−	0.576357i	−0.0570678	−	0.0988443i
$35$	−3.18389	−	8.58195i	−0.538176	−	1.45061i
$36$	−0.841931			−0.140322
$37$	−5.75555	+	1.96817i	−0.946206	+	0.323565i
$37$	−5.75555	+	1.96817i	−0.946206	+	0.323565i
$38$			4.49126i			0.728579i
$39$	−2.76888	+	4.79584i	−0.443376	+	0.767949i
$40$	−6.74191	−	1.14578i	−1.06599	−	0.181164i
$41$	4.08344	+	7.07273i	0.637726	+	1.10457i	0.985931	+	0.167156i	$0.0534582\pi$
$41$	4.08344	+	7.07273i	0.637726	+	1.10457i	−0.348204	+	0.937419i	$0.613208\pi$
$42$	−3.81506	+	2.20262i	−0.588676	+	0.339872i
$43$		−	10.8405i		−	1.65316i	−0.562819	−	0.826580i	$-0.690283\pi$
$43$		−	10.8405i		−	1.65316i	0.562819	−	0.826580i	$-0.309717\pi$
$44$	0.944203	+	1.63541i	0.142344	+	0.246547i
$45$	1.72180	+	1.42668i	0.256670	+	0.212677i
$46$	−3.04110	+	5.26734i	−0.448385	+	0.776626i
$47$		−	1.43023i		−	0.208620i	−0.994545	−	0.104310i	$-0.966737\pi$
$47$		−	1.43023i		−	0.208620i	0.994545	−	0.104310i	$-0.0332634\pi$
$48$			1.60729i			0.231992i
$49$	4.87870	−	8.45015i	0.696957	−	1.20716i
$50$	3.50942	+	4.07869i	0.496307	+	0.576814i
$51$	−0.618434			−0.0865981
$52$	−4.03777	−	2.33121i	−0.559938	−	0.323280i
$53$	−5.03741	−	2.90835i	−0.691941	−	0.399493i	0.112397	−	0.993663i	$-0.464147\pi$
$53$	−5.03741	−	2.90835i	−0.691941	−	0.399493i	−0.804339	+	0.594171i	$0.797480\pi$
$54$	0.538068	−	0.931961i	0.0732218	−	0.126824i
$55$	0.840310	−	4.94448i	0.113307	−	0.666714i
$56$	−6.25971	−	10.8421i	−0.836489	−	1.44884i
$57$	3.61436	+	2.08675i	0.478734	+	0.276397i
$58$	−7.77922	−	4.49134i	−1.02146	−	0.589741i
$59$	0.603982	−	1.04613i	0.0786318	−	0.136194i	−0.824028	−	0.566549i	$-0.808278\pi$
$59$	0.603982	−	1.04613i	0.0786318	−	0.136194i	0.902660	+	0.430355i	$0.141612\pi$
$60$	−1.20117	+	1.44963i	−0.155070	+	0.187147i
$61$	−4.13777	−	7.16683i	−0.529787	−	0.917619i	−0.999396	−	0.0347442i	$-0.988938\pi$
$61$	−4.13777	−	7.16683i	−0.529787	−	0.917619i	0.469609	−	0.882875i	$-0.344395\pi$
$62$	4.39304	+	2.53632i	0.557917	+	0.322113i
$63$			4.09358i			0.515743i
$64$	−7.93553			−0.991942
$65$	4.30714	+	11.6096i	0.534235	+	1.43999i
$66$	−2.41372			−0.297108
$67$	12.1932	−	7.03977i	1.48964	−	0.860045i	0.489711	−	0.871885i	$-0.337102\pi$
$67$	12.1932	−	7.03977i	1.48964	−	0.860045i	0.999930	+	0.0118400i	$0.00376889\pi$
$68$		−	0.520679i		−	0.0631416i
$69$	2.82594	+	4.89467i	0.340203	+	0.589249i
$70$	−1.65041	+	9.71119i	−0.197261	+	1.16071i
$71$	−4.15262	−	7.19255i	−0.492825	−	0.853598i	0.507141	−	0.861863i	$-0.330702\pi$
$71$	−4.15262	−	7.19255i	−0.492825	−	0.853598i	−0.999966	+	0.00826502i	$0.997369\pi$
$72$	2.64857	+	1.52915i	0.312137	+	0.180212i
$73$		−	0.356372i		−	0.0417102i	−0.999783	−	0.0208551i	$-0.993361\pi$
$73$		−	0.356372i		−	0.0417102i	0.999783	−	0.0208551i	$-0.00663887\pi$
$74$	6.42296	+	1.26262i	0.746653	+	0.146776i
$75$	4.91291	−	0.929156i	0.567294	−	0.107290i
$76$	−1.75690	+	3.04304i	−0.201531	+	0.349061i
$77$	7.95157	−	4.59084i	0.906165	−	0.523175i
$78$	5.16098	−	2.97969i	0.584366	−	0.337384i
$79$	0.0130972	+	0.0226850i	0.00147355	+	0.00255226i	0.866761	−	0.498723i	$-0.166198\pi$
$79$	0.0130972	+	0.0226850i	0.00147355	+	0.00255226i	−0.865288	+	0.501276i	$0.832864\pi$
$80$	2.76743	+	2.29309i	0.309408	+	0.256376i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		−	8.78868i		−	0.970547i
$83$	9.81892	+	5.66896i	1.07777	+	0.622249i	0.930293	−	0.366817i	$-0.119553\pi$
$83$	9.81892	+	5.66896i	1.07777	+	0.622249i	0.147473	+	0.989066i	$0.452886\pi$
$84$	−3.44651			−0.376045
$85$	−0.882309	+	1.06482i	−0.0956998	+	0.115496i
$86$	−5.83293	+	10.1029i	−0.628981	+	1.08943i
$87$	−7.22885	+	4.17358i	−0.775014	+	0.447454i
$88$		−	6.85961i		−	0.731237i
$89$	2.40898	−	4.17247i	0.255351	−	0.442281i	−0.709640	−	0.704565i	$-0.751142\pi$
$89$	2.40898	−	4.17247i	0.255351	−	0.442281i	0.964991	+	0.262284i	$0.0844756\pi$
$90$	−0.836994	−	2.25606i	−0.0882269	−	0.237809i
$91$	−11.3346	+	19.6322i	−1.18819	+	2.05801i
$92$	−4.12098	+	2.37925i	−0.429642	+	0.248054i
$93$	4.08224	−	2.35688i	0.423308	−	0.244397i
$94$	−0.769560	+	1.33292i	−0.0793740	+	0.137480i
$95$	8.74951	−	3.24606i	0.897681	−	0.333039i
$96$	−2.19347	+	3.79921i	−0.223870	+	0.387755i
$97$		−	5.17187i		−	0.525124i	−0.964915	−	0.262562i	$-0.915433\pi$
$97$		−	5.17187i		−	0.525124i	0.964915	−	0.262562i	$-0.0845674\pi$
$98$	−9.09351	+	5.25014i	−0.918584	+	0.530345i
$99$	−1.12147	+	1.94245i	−0.112712	+	0.195223i
$100$	0.782285	+	4.13633i	0.0782285	+	0.413633i
$101$	5.60267			0.557487			0.278743	−	0.960366i	$-0.410082\pi$
$101$	5.60267			0.557487			0.278743	+	0.960366i	$0.410082\pi$
$102$	0.576357	+	0.332760i	0.0570678	+	0.0329481i
$103$		−	0.232525i		−	0.0229114i	−0.999934	−	0.0114557i	$-0.996353\pi$
$103$		−	0.232525i		−	0.0229114i	0.999934	−	0.0114557i	$-0.00364654\pi$
$104$	8.46808	+	14.6671i	0.830364	+	1.43823i
$105$	7.04831	+	5.84024i	0.687844	+	0.569949i
$106$	3.12978	+	5.42094i	0.303991	+	0.526528i
$107$	−15.0845	+	8.70907i	−1.45828	+	0.841937i	−0.998927	−	0.0463171i	$-0.985252\pi$
$107$	−15.0845	+	8.70907i	−1.45828	+	0.841937i	−0.459352	+	0.888255i	$0.651918\pi$
$108$	0.729134	−	0.420965i	0.0701609	−	0.0405074i
$109$	−6.57599	+	11.3900i	−0.629866	+	1.09096i	0.357712	+	0.933832i	$0.383557\pi$
$109$	−6.57599	+	11.3900i	−0.629866	+	1.09096i	−0.987578	+	0.157128i	$0.949777\pi$
$110$	−3.44361	+	4.15592i	−0.328335	+	0.396252i
$111$	4.00037	−	4.58226i	0.379698	−	0.434929i
$112$			6.57957i			0.621711i
$113$	4.68413	+	2.70438i	0.440646	+	0.254407i	0.703872	−	0.710327i	$-0.251453\pi$
$113$	4.68413	+	2.70438i	0.440646	+	0.254407i	−0.263226	+	0.964734i	$0.584786\pi$
$114$	−2.24563	−	3.88955i	−0.210323	−	0.364289i
$115$	12.4593	+	2.11745i	1.16184	+	0.197453i
$116$	−3.51386	−	6.08619i	−0.326254	−	0.565089i
$117$		−	5.53776i		−	0.511966i
$118$	−1.12578	+	0.649967i	−0.103636	+	0.0598343i
$119$	−2.53161			−0.232072
$120$	6.41155	−	2.37868i	0.585292	−	0.217143i
$121$	−5.96919			−0.542654
$122$			8.90561i			0.806276i
$123$	−7.07273	−	4.08344i	−0.637726	−	0.368191i
$124$	1.98433	+	3.43696i	0.178198	+	0.308648i
$125$	5.40934	−	9.78463i	0.483826	−	0.875164i
$126$	2.20262	−	3.81506i	0.196225	−	0.339872i
$127$	5.35862	+	3.09380i	0.475500	+	0.274530i	0.718539	−	0.695486i	$-0.244811\pi$
$127$	5.35862	+	3.09380i	0.475500	+	0.274530i	−0.243039	+	0.970016i	$0.578144\pi$
$128$	−0.202804	−	0.117089i	−0.0179255	−	0.0103493i
$129$	5.42025	+	9.38815i	0.477226	+	0.826580i
$130$	2.23266	−	13.1372i	0.195817	−	1.15221i
$131$	3.59915	−	6.23392i	0.314460	−	0.544660i	−0.664863	−	0.746965i	$-0.731510\pi$
$131$	3.59915	−	6.23392i	0.314460	−	0.544660i	0.979322	+	0.202305i	$0.0648434\pi$
$132$	−1.63541	−	0.944203i	−0.142344	−	0.0821823i
$133$	14.7957	+	8.54229i	1.28295	+	0.740711i
$134$	−15.1515			−1.30889
$135$	−2.20446	−	0.374645i	−0.189730	−	0.0322443i
$136$	−0.945680	+	1.63797i	−0.0810914	+	0.140454i
$137$		−	4.99942i		−	0.427129i	−0.976929	−	0.213565i	$-0.931493\pi$
$137$		−	4.99942i		−	0.427129i	0.976929	−	0.213565i	$-0.0685074\pi$
$138$		−	6.08220i		−	0.517751i
$139$	3.04464	−	5.27347i	0.258243	−	0.447290i	−0.707528	−	0.706685i	$-0.750190\pi$
$139$	3.04464	−	5.27347i	0.258243	−	0.447290i	0.965771	+	0.259395i	$0.0835232\pi$
$140$	−4.91708	+	5.93419i	−0.415569	+	0.501530i
$141$	0.715114	+	1.23861i	0.0602234	+	0.104310i
$142$			8.93757i			0.750024i
$143$	−10.7568	+	6.21045i	−0.899530	+	0.519344i
$144$	−0.803645	−	1.39195i	−0.0669704	−	0.115996i
$145$	−3.12722	+	18.4010i	−0.259702	+	1.52812i
$146$	−0.191753	+	0.332125i	−0.0158696	+	0.0274869i
$147$			9.75739i			0.804776i
$148$	3.85794	+	3.36803i	0.317121	+	0.276850i
$149$	−10.7498			−0.880660			−0.440330	−	0.897836i	$-0.645139\pi$
$149$	−10.7498			−0.880660			−0.440330	+	0.897836i	$0.645139\pi$
$150$	−5.07859	−	1.77754i	−0.414665	−	0.145136i
$151$	0.973389	+	1.68596i	0.0792132	+	0.137201i	0.902911	−	0.429828i	$-0.141426\pi$
$151$	0.973389	+	1.68596i	0.0792132	+	0.137201i	−0.823697	+	0.567030i	$0.808093\pi$
$152$	11.0538	−	6.38193i	0.896584	−	0.517643i
$153$	0.535580	−	0.309217i	0.0432990	−	0.0249987i
$154$	−9.88074			−0.796213
$155$	1.76599	−	10.3913i	0.141848	−	0.834649i
$156$	4.66241			0.373292
$157$	−2.38309	−	1.37588i	−0.190191	−	0.109807i	0.401881	−	0.915692i	$-0.368357\pi$
$157$	−2.38309	−	1.37588i	−0.190191	−	0.109807i	−0.592072	+	0.805885i	$0.701690\pi$
$158$		−	0.0281887i		−	0.00224257i
$159$	5.81670			0.461294
$160$	3.41207	+	9.19697i	0.269748	+	0.727084i
$161$	11.5682	+	20.0367i	0.911703	+	1.57912i
$162$			1.07614i			0.0845492i
$163$	13.1461	+	7.58991i	1.02968	+	0.594488i	0.916894	−	0.399131i	$-0.130688\pi$
$163$	13.1461	+	7.58991i	1.02968	+	0.594488i	0.112789	+	0.993619i	$0.464022\pi$
$164$	3.43797	−	5.95475i	0.268461	−	0.464988i
$165$	1.74451	+	4.70220i	0.135810	+	0.366066i
$166$	−6.10057	−	10.5665i	−0.473496	−	0.820119i
$167$	−11.4715	+	6.62309i	−0.887693	+	0.512510i	−0.873187	−	0.487385i	$-0.837951\pi$
$167$	−11.4715	+	6.62309i	−0.887693	+	0.512510i	−0.0145057	+	0.999895i	$0.504617\pi$
$168$	10.8421	+	6.25971i	0.836489	+	0.482947i
$169$	8.83340	−	15.2999i	0.679492	−	1.17691i
$170$	1.39522	−	0.517626i	0.107009	−	0.0397001i
$171$	−4.17351			−0.319156
$172$	−7.90417	+	4.56347i	−0.602687	+	0.347962i
$173$	2.68593	+	1.55072i	0.204207	+	0.117899i	0.598616	−	0.801036i	$-0.295717\pi$
$173$	2.68593	+	1.55072i	0.204207	+	0.117899i	−0.394409	+	0.918935i	$0.629051\pi$
$174$	8.98267			0.680975
$175$	20.1114	−	3.80358i	1.52028	−	0.287523i
$176$	−1.80253	+	3.12208i	−0.135871	+	0.235336i
$177$			1.20796i			0.0907961i
$178$	−4.49015	+	2.59239i	−0.336551	+	0.194308i
$179$	−14.0525			−1.05033			−0.525165	−	0.851000i	$-0.675996\pi$
$179$	−14.0525			−1.05033			−0.525165	+	0.851000i	$0.675996\pi$
$180$	0.315426	−	1.85600i	0.0235104	−	0.138338i
$181$	−11.4278	−	19.7935i	−0.849422	−	1.47124i	−0.881724	−	0.471765i	$-0.843617\pi$
$181$	−11.4278	−	19.7935i	−0.849422	−	1.47124i	0.0323020	−	0.999478i	$-0.489716\pi$
$182$	21.1269	−	12.1976i	1.56603	−	0.904147i
$183$	7.16683	+	4.13777i	0.529787	+	0.305873i
$184$	17.2852			1.27428
$185$	−2.18246	−	13.4252i	−0.160458	−	0.987043i
$186$	−5.07265			−0.371945
$187$	−1.20128	−	0.693557i	−0.0878460	−	0.0507179i
$188$	−1.04283	+	0.602076i	−0.0760560	+	0.0439109i
$189$	−2.04679	−	3.54514i	−0.148882	−	0.257871i
$190$	−9.90081	−	1.68263i	−0.718280	−	0.122071i
$191$	−13.0541			−0.944562			−0.472281	−	0.881448i	$-0.656569\pi$
$191$	−13.0541			−0.944562			−0.472281	+	0.881448i	$0.656569\pi$
$192$	6.87237	−	3.96777i	0.495971	−	0.286349i
$193$		−	23.8887i		−	1.71955i	−0.510677	−	0.859773i	$-0.670605\pi$
$193$		−	23.8887i		−	1.71955i	0.510677	−	0.859773i	$-0.329395\pi$
$194$	−2.78282	+	4.81998i	−0.199795	+	0.346054i
$195$	−9.53489	−	7.90062i	−0.682808	−	0.565775i
$196$	−8.21505			−0.586789
$197$	−14.2838	−	8.24676i	−1.01768	−	0.587557i	−0.104248	−	0.994551i	$-0.533244\pi$
$197$	−14.2838	−	8.24676i	−1.01768	−	0.587557i	−0.913431	+	0.406994i	$0.866577\pi$
$198$	2.09034	−	1.20686i	0.148554	−	0.0857677i
$199$	24.4453			1.73288			0.866442	−	0.499277i	$-0.166401\pi$
$199$	24.4453			1.73288			0.866442	+	0.499277i	$0.166401\pi$
$200$	5.05165	−	14.4330i	0.357206	−	1.02057i
$201$	−7.03977	+	12.1932i	−0.496547	+	0.860045i
$202$	−5.22148	−	3.01462i	−0.367382	−	0.212108i
$203$	−29.5919	+	17.0849i	−2.07694	+	1.19912i
$204$	0.260339	+	0.450921i	0.0182274	+	0.0315708i
$205$	−17.1214	+	6.35201i	−1.19581	+	0.443644i
$206$	−0.125114	+	0.216705i	−0.00871713	+	0.0150985i
$207$	−4.89467	−	2.82594i	−0.340203	−	0.196416i
$208$		−	8.90079i		−	0.617159i
$209$	4.68048	+	8.10682i	0.323755	+	0.560761i
$210$	−3.42630	−	9.23534i	−0.236437	−	0.637299i
$211$	−19.3383			−1.33130			−0.665652	−	0.746263i	$-0.731846\pi$
$211$	−19.3383			−1.33130			−0.665652	+	0.746263i	$0.731846\pi$
$212$			4.89726i			0.336345i
$213$	7.19255	+	4.15262i	0.492825	+	0.284533i
$214$	18.7443			1.28133
$215$	23.8974	+	4.06134i	1.62979	+	0.276981i
$216$	−3.05830			−0.208091
$217$	16.7110	−	9.64808i	1.13441	−	0.654954i
$218$	12.2571	−	7.07666i	0.830158	−	0.479292i
$219$	0.178186	+	0.308627i	0.0120407	+	0.0208551i
$220$	−3.95893	+	1.46876i	−0.266911	+	0.0990237i
$221$	3.42474			0.230373
$222$	−6.19375	+	2.11802i	−0.415697	+	0.142152i
$223$			6.02272i			0.403311i	0.979456	+	0.201656i	$0.0646322\pi$
$223$			6.02272i			0.403311i	−0.979456	+	0.201656i	$0.935368\pi$
$224$	−8.97916	+	15.5524i	−0.599945	+	1.03914i
$225$	−3.79013	+	3.26113i	−0.252675	+	0.217408i
$226$	−2.91028	−	5.04076i	−0.193589	−	0.335306i
$227$	11.6760	−	6.74115i	0.774965	−	0.447426i	−0.0596782	−	0.998218i	$-0.519007\pi$
$227$	11.6760	−	6.74115i	0.774965	−	0.447426i	0.834643	+	0.550792i	$0.185674\pi$
$228$		−	3.51380i		−	0.232707i
$229$	−0.372456	−	0.645114i	−0.0246126	−	0.0426303i	0.853457	−	0.521164i	$-0.174502\pi$
$229$	−0.372456	−	0.645114i	−0.0246126	−	0.0426303i	−0.878069	+	0.478533i	$0.841169\pi$
$230$	−10.4723	−	8.67736i	−0.690523	−	0.572168i
$231$	−4.59084	+	7.95157i	−0.302055	+	0.523175i
$232$			25.5281i			1.67600i
$233$			14.2975i			0.936663i	0.883553	+	0.468332i	$0.155145\pi$
$233$			14.2975i			0.936663i	−0.883553	+	0.468332i	$0.844855\pi$
$234$	−2.97969	+	5.16098i	−0.194789	+	0.337384i
$235$	3.15288	+	0.535828i	0.205671	+	0.0349536i
$236$	−1.01702			−0.0662025
$237$	−0.0226850	−	0.0130972i	−0.00147355	−	0.000850753i
$238$	2.35936	+	1.36218i	0.152935	+	0.0882969i
$239$	10.5386	−	18.2534i	0.681685	−	1.18071i	−0.292781	−	0.956179i	$-0.594581\pi$
$239$	10.5386	−	18.2534i	0.681685	−	1.18071i	0.974466	−	0.224534i	$-0.0720859\pi$
$240$	−3.54321	−	0.602164i	−0.228713	−	0.0388695i
$241$	−5.42285	−	9.39265i	−0.349316	−	0.605033i	0.636812	−	0.771019i	$-0.280253\pi$
$241$	−5.42285	−	9.39265i	−0.349316	−	0.605033i	−0.986128	+	0.165986i	$0.946919\pi$
$242$	5.56306	+	3.21183i	0.357607	+	0.206464i
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$	−3.48372	+	6.03398i	−0.223022	+	0.386286i
$245$	16.8002	+	13.9207i	1.07333	+	0.889361i
$246$	4.39434	+	7.61122i	0.280173	+	0.485273i
$247$	−20.0155	−	11.5559i	−1.27355	−	0.735287i
$248$		−	14.4161i		−	0.915424i
$249$	−11.3379			−0.718511
$250$	−10.3061	+	6.20830i	−0.651815	+	0.392648i
$251$	−0.510438			−0.0322185			−0.0161093	−	0.999870i	$-0.505128\pi$
$251$	−0.510438			−0.0322185			−0.0161093	+	0.999870i	$0.505128\pi$
$252$	2.98477	−	1.72326i	0.188023	−	0.108555i
$253$			12.6769i			0.796988i
$254$	−3.32935	−	5.76660i	−0.208902	−	0.361829i
$255$	0.231693	−	1.36331i	0.0145092	−	0.0853740i
$256$	8.06154	+	13.9630i	0.503846	+	0.872687i
$257$	−15.7039	−	9.06666i	−0.979584	−	0.565563i	−0.0774392	−	0.996997i	$-0.524674\pi$
$257$	−15.7039	−	9.06666i	−0.979584	−	0.565563i	−0.902144	+	0.431434i	$0.858008\pi$
$258$		−	11.6659i		−	0.726284i
$259$	16.3758	−	18.7578i	1.01754	−	1.16556i
$260$	6.65178	−	8.02772i	0.412526	−	0.497858i
$261$	4.17358	−	7.22885i	0.258338	−	0.447454i
$262$	−6.70854	+	3.87318i	−0.414455	+	0.239286i
$263$	−23.1792	+	13.3825i	−1.42929	+	0.825203i	−0.997065	−	0.0765609i	$-0.975606\pi$
$263$	−23.1792	+	13.3825i	−1.42929	+	0.825203i	−0.432229	+	0.901764i	$0.642273\pi$
$264$	3.42981	+	5.94060i	0.211090	+	0.365619i
$265$	8.29858	−	10.0152i	0.509778	−	0.615227i
$266$	−9.19267	−	15.9222i	−0.563639	−	0.976251i
$267$			4.81795i			0.294854i
$268$	−10.2659	−	5.92700i	−0.627087	−	0.362049i
$269$	−17.8445			−1.08800			−0.543999	−	0.839086i	$-0.683091\pi$
$269$	−17.8445			−1.08800			−0.543999	+	0.839086i	$0.683091\pi$
$270$	1.85289	+	1.53530i	0.112763	+	0.0934356i
$271$	15.2784	−	26.4629i	0.928095	−	1.60751i	0.141590	−	0.989925i	$-0.454779\pi$
$271$	15.2784	−	26.4629i	0.928095	−	1.60751i	0.786506	−	0.617583i	$-0.211888\pi$
$272$	0.860832	−	0.497002i	0.0521956	−	0.0301352i
$273$		−	22.6693i		−	1.37201i
$274$	−2.69003	+	4.65927i	−0.162511	+	0.281477i
$275$	10.5851	+	3.70486i	0.638305	+	0.223411i
$276$	2.37925	−	4.12098i	0.143214	−	0.248054i
$277$	10.8786	−	6.28076i	0.653632	−	0.377374i	−0.136214	−	0.990679i	$-0.543494\pi$
$277$	10.8786	−	6.28076i	0.653632	−	0.377374i	0.789846	+	0.613305i	$0.210160\pi$
$278$	−5.67497	+	3.27645i	−0.340362	+	0.196508i
$279$	−2.35688	+	4.08224i	−0.141103	+	0.244397i
$280$	26.2462	−	9.73731i	1.56851	−	0.581916i
$281$	5.25393	−	9.10007i	0.313423	−	0.542865i	−0.665678	−	0.746239i	$-0.731858\pi$
$281$	5.25393	−	9.10007i	0.313423	−	0.542865i	0.979101	+	0.203374i	$0.0651908\pi$
$282$		−	1.53912i		−	0.0916532i
$283$	−5.32033	+	3.07169i	−0.316261	+	0.182593i	−0.649725	−	0.760170i	$-0.725116\pi$
$283$	−5.32033	+	3.07169i	−0.316261	+	0.182593i	0.333464	+	0.942763i	$0.391782\pi$
$284$	−3.49622	+	6.05563i	−0.207462	+	0.359335i
$285$	−5.95427	+	7.18592i	−0.352700	+	0.425657i
$286$	13.3666			0.790382
$287$	−28.9528	−	16.7159i	−1.70903	−	0.986708i
$288$		−	4.38695i		−	0.258503i
$289$	−8.30877	−	14.3912i	−0.488751	−	0.846542i
$290$	12.8154	−	15.4663i	0.752547	−	0.908214i
$291$	2.58593	+	4.47897i	0.151590	+	0.262562i
$292$	−0.259843	+	0.150020i	−0.0152062	+	0.00877928i
$293$	−6.90458	+	3.98636i	−0.403370	+	0.232886i	−0.687937	−	0.725770i	$-0.741483\pi$
$293$	−6.90458	+	3.98636i	−0.403370	+	0.232886i	0.284567	+	0.958656i	$0.408150\pi$
$294$	5.25014	−	9.09351i	0.306195	−	0.530345i
$295$	2.07987	+	1.72338i	0.121095	+	0.100339i
$296$	−6.01926	−	17.6022i	−0.349862	−	1.02311i
$297$		−	2.24295i		−	0.130149i
$298$	10.0184	+	5.78414i	0.580352	+	0.335066i
$299$	−15.6494	−	27.1055i	−0.905027	−	1.56755i
$300$	−2.74564	−	3.19102i	−0.158520	−	0.184234i
$301$	22.1882	+	38.4311i	1.27891	+	2.21513i
$302$		−	2.09500i		−	0.120554i
$303$	−4.85206	+	2.80134i	−0.278743	+	0.160933i
$304$	−6.70804			−0.384732
$305$	17.3492	−	6.43653i	0.993412	−	0.368555i
$306$	−0.665519			−0.0380452
$307$		−	3.14284i		−	0.179371i	−0.995970	−	0.0896857i	$-0.971414\pi$
$307$		−	3.14284i		−	0.179371i	0.995970	−	0.0896857i	$-0.0285863\pi$
$308$	−6.69467	−	3.86517i	−0.381464	−	0.220238i
$309$	0.116263	+	0.201373i	0.00661395	+	0.0114557i
$310$	−7.23706	+	8.73406i	−0.411037	+	0.496061i
$311$	−8.66656	+	15.0109i	−0.491436	+	0.851191i	−0.999951	−	0.00986123i	$-0.996861\pi$
$311$	−8.66656	+	15.0109i	−0.491436	+	0.851191i	0.508516	+	0.861053i	$0.330194\pi$
$312$	−14.6671	−	8.46808i	−0.830364	−	0.479411i
$313$	3.53469	+	2.04075i	0.199792	+	0.115350i	0.596559	−	0.802570i	$-0.296534\pi$
$313$	3.53469	+	2.04075i	0.199792	+	0.115350i	−0.396766	+	0.917920i	$0.629868\pi$
$314$	1.48063	+	2.56453i	0.0835569	+	0.144725i
$315$	−9.02413	−	1.53364i	−0.508452	−	0.0864109i
$316$	0.0110269	−	0.0190992i	0.000620312	−	0.00107441i
$317$	19.1194	+	11.0386i	1.07385	+	0.619990i	0.929232	−	0.369497i	$-0.120470\pi$
$317$	19.1194	+	11.0386i	1.07385	+	0.619990i	0.144623	+	0.989487i	$0.453803\pi$
$318$	−5.42094	−	3.12978i	−0.303991	−	0.175509i
$319$	−18.7222			−1.04824
$320$	2.97301	−	17.4936i	0.166196	−	0.977920i
$321$	8.70907	−	15.0845i	0.486093	−	0.841937i
$322$		−	24.8980i		−	1.38751i
$323$		−	2.58104i		−	0.143613i
$324$	−0.420965	+	0.729134i	−0.0233870	+	0.0405074i
$325$	−27.2065	+	5.14545i	−1.50915	+	0.285418i
$326$	−8.16778	−	14.1470i	−0.452371	−	0.783530i
$327$		−	13.1520i		−	0.727306i
$328$	−21.6306	+	12.4884i	−1.19435	+	0.689557i
$329$	2.92738	+	5.07036i	0.161391	+	0.279538i
$330$	0.904288	−	5.32094i	0.0497794	−	0.292908i
$331$	−6.22276	+	10.7781i	−0.342034	+	0.592420i	−0.984810	−	0.173634i	$-0.944449\pi$
$331$	−6.22276	+	10.7781i	−0.342034	+	0.592420i	0.642777	+	0.766054i	$0.277782\pi$
$332$		−	9.54574i		−	0.523890i
$333$	−1.17329	+	5.96853i	−0.0642959	+	0.327074i
$334$	14.2547			0.779982
$335$	10.9507	+	29.5169i	0.598303	+	1.61268i
$336$	−3.28979	−	5.69808i	−0.179473	−	0.310856i
$337$	−16.9374	+	9.77882i	−0.922640	+	0.532686i	−0.884476	−	0.466585i	$-0.845484\pi$
$337$	−16.9374	+	9.77882i	−0.922640	+	0.532686i	−0.0381636	+	0.999272i	$0.512151\pi$
$338$	−16.4648	+	9.50594i	−0.895565	+	0.517055i
$339$	−5.40877			−0.293764
$340$	1.14782	+	0.195070i	0.0622490	+	0.0105791i
$341$	10.5727			0.572544
$342$	3.88955	+	2.24563i	0.210323	+	0.121430i
$343$			11.2876i			0.609474i
$344$	33.1535			1.78752
$345$	−11.8488	+	4.39591i	−0.637920	+	0.236668i
$346$	−1.66879	−	2.89042i	−0.0897146	−	0.155390i
$347$		−	28.7352i		−	1.54258i	−0.636481	−	0.771292i	$-0.719611\pi$
$347$		−	28.7352i		−	1.54258i	0.636481	−	0.771292i	$-0.280389\pi$
$348$	6.08619	+	3.51386i	0.326254	+	0.188363i
$349$	−2.67899	+	4.64015i	−0.143403	+	0.248382i	−0.928776	−	0.370641i	$-0.879138\pi$
$349$	−2.67899	+	4.64015i	−0.143403	+	0.248382i	0.785373	+	0.619023i	$0.212471\pi$
$350$	−20.7896	−	7.27651i	−1.11125	−	0.388946i
$351$	2.76888	+	4.79584i	0.147792	+	0.255983i
$352$	−8.52142	+	4.91984i	−0.454193	+	0.262228i
$353$	−19.8502	−	11.4605i	−1.05652	−	0.609983i	−0.132054	−	0.991243i	$-0.542157\pi$
$353$	−19.8502	−	11.4605i	−1.05652	−	0.609983i	−0.924468	+	0.381259i	$0.875490\pi$
$354$	0.649967	−	1.12578i	0.0345454	−	0.0598343i
$355$	17.4114	−	6.45962i	0.924103	−	0.342841i
$356$	−4.05638			−0.214988
$357$	2.19244	−	1.26580i	0.116036	−	0.0669935i
$358$	13.0963	+	7.56118i	0.692163	+	0.399621i
$359$	−20.5580			−1.08501			−0.542504	−	0.840053i	$-0.682524\pi$
$359$	−20.5580			−1.08501			−0.542504	+	0.840053i	$0.682524\pi$
$360$	−4.36323	+	5.26577i	−0.229962	+	0.277531i
$361$	0.790918	−	1.36991i	0.0416273	−	0.0721005i
$362$			24.5958i			1.29272i
$363$	5.16947	−	2.98460i	0.271327	−	0.156651i
$364$	19.0860			1.00038
$365$	0.785608	+	0.133513i	0.0411206	+	0.00698840i
$366$	−4.45281	−	7.71249i	−0.232752	−	0.403138i
$367$	−21.3119	+	12.3044i	−1.11247	+	0.642286i	−0.939469	−	0.342635i	$-0.888681\pi$
$367$	−21.3119	+	12.3044i	−1.11247	+	0.642286i	−0.173004	+	0.984921i	$0.555347\pi$
$368$	−7.86716	−	4.54211i	−0.410104	−	0.236774i
$369$	8.16688			0.425151
$370$	−5.18972	+	13.6861i	−0.269801	+	0.711507i
$371$	23.8111			1.23621
$372$	−3.43696	−	1.98433i	−0.178198	−	0.102883i
$373$	3.81939	−	2.20513i	0.197761	−	0.114177i	−0.397850	−	0.917451i	$-0.630244\pi$
$373$	3.81939	−	2.20513i	0.197761	−	0.114177i	0.595610	+	0.803273i	$0.296910\pi$
$374$	0.746362	+	1.29274i	0.0385935	+	0.0668458i
$375$	0.207689	+	11.1784i	0.0107250	+	0.577251i
$376$	4.37407			0.225576
$377$	40.0316	−	23.1123i	2.06173	−	1.19034i
$378$			4.40525i			0.226582i
$379$	−8.78871	+	15.2225i	−0.451446	+	0.781927i	−0.998476	−	0.0551856i	$-0.982425\pi$
$379$	−8.78871	+	15.2225i	−0.451446	+	0.781927i	0.547030	+	0.837113i	$0.315758\pi$
$380$	−6.05005	−	5.01308i	−0.310361	−	0.257166i
$381$	−6.18760			−0.317000
$382$	12.1659	+	7.02399i	0.622462	+	0.359379i
$383$	−0.423938	+	0.244761i	−0.0216622	+	0.0125067i	−0.510792	−	0.859704i	$-0.670648\pi$
$383$	−0.423938	+	0.244761i	−0.0216622	+	0.0125067i	0.489130	+	0.872211i	$0.337314\pi$
$384$	0.234177			0.0119503
$385$	7.14130	+	19.2488i	0.363954	+	0.981012i
$386$	−12.8537	+	22.2633i	−0.654238	+	1.13317i
$387$	−9.38815	−	5.42025i	−0.477226	−	0.275527i
$388$	−3.77098	+	2.17718i	−0.191443	+	0.110529i
$389$	9.92186	+	17.1852i	0.503058	+	0.871322i	0.999994	+	0.00353474i	$0.00112515\pi$
$389$	9.92186	+	17.1852i	0.503058	+	0.871322i	−0.496936	+	0.867787i	$0.665542\pi$
$390$	4.63507	+	12.4935i	0.234706	+	0.632633i
$391$	1.74766	−	3.02703i	0.0883829	−	0.153084i
$392$	25.8431	+	14.9205i	1.30528	+	0.753601i
$393$			7.19831i			0.363107i
$394$	8.87464	+	15.3713i	0.447098	+	0.774396i
$395$	−0.0549149	+	0.0203734i	−0.00276307	+	0.00102510i
$396$	1.88841			0.0948960
$397$			32.5662i			1.63445i	0.576320	+	0.817224i	$0.304488\pi$
$397$			32.5662i			1.63445i	−0.576320	+	0.817224i	$0.695512\pi$
$398$	−22.7821	−	13.1533i	−1.14196	−	0.659313i
$399$	−17.0846			−0.855299
$400$	−6.09183	+	5.24158i	−0.304592	+	0.262079i
$401$	−0.286240			−0.0142941			−0.00714707	−	0.999974i	$-0.502275\pi$
$401$	−0.286240			−0.0142941			−0.00714707	+	0.999974i	$0.502275\pi$
$402$	13.1216	−	7.57575i	0.654445	−	0.377844i
$403$	−22.6064	+	13.0518i	−1.12611	+	0.650158i
$404$	−2.35853	−	4.08510i	−0.117341	−	0.203241i
$405$	2.09644	−	0.777777i	0.104173	−	0.0386481i
$406$	36.7713			1.82493
$407$	12.9094	−	4.41450i	0.639894	−	0.218818i
$408$		−	1.89136i		−	0.0936363i
$409$	17.1016	−	29.6208i	0.845619	−	1.46465i	−0.0394645	−	0.999221i	$-0.512565\pi$
$409$	17.1016	−	29.6208i	0.845619	−	1.46465i	0.885083	−	0.465433i	$-0.154101\pi$
$410$	19.3743	+	3.29264i	0.956827	+	0.162612i
$411$	2.49971	+	4.32963i	0.123302	+	0.213565i
$412$	−0.169542	+	0.0978851i	−0.00835273	+	0.00482245i
$413$			4.94490i			0.243323i
$414$	3.04110	+	5.26734i	0.149462	+	0.258875i
$415$	−16.1756	+	19.5216i	−0.794029	+	0.958276i
$416$	12.1469	−	21.0391i	0.595552	−	1.03153i
$417$			6.08928i			0.298193i
$418$		−	10.0737i		−	0.492719i
$419$	16.8538	−	29.1916i	0.823361	−	1.42610i	−0.0798045	−	0.996811i	$-0.525430\pi$
$419$	16.8538	−	29.1916i	0.823361	−	1.42610i	0.903166	−	0.429293i	$-0.141237\pi$
$420$	1.29122	−	7.59769i	0.0630051	−	0.370729i
$421$	22.1401			1.07904			0.539522	−	0.841972i	$-0.318605\pi$
$421$	22.1401			1.07904			0.539522	+	0.841972i	$0.318605\pi$
$422$	18.0225	+	10.4053i	0.877324	+	0.506523i
$423$	−1.23861	−	0.715114i	−0.0602234	−	0.0347700i
$424$	8.89462	−	15.4059i	0.431961	−	0.748178i
$425$	−2.01679	−	2.34394i	−0.0978288	−	0.113698i
$426$	−4.46878	−	7.74016i	−0.216513	−	0.375012i
$427$	29.3380	+	16.9383i	1.41977	+	0.819702i
$428$	12.7001	+	7.33243i	0.613885	+	0.354427i
$429$	6.21045	−	10.7568i	0.299843	−	0.519344i
$430$	−20.0862	−	16.6435i	−0.968643	−	0.802619i
$431$	17.8482	+	30.9141i	0.859720	+	1.48908i	0.872196	+	0.489156i	$0.162695\pi$
$431$	17.8482	+	30.9141i	0.859720	+	1.48908i	−0.0124770	+	0.999922i	$0.503972\pi$
$432$	1.39195	+	0.803645i	0.0669704	+	0.0386654i
$433$		−	23.6986i		−	1.13888i	−0.822032	−	0.569441i	$-0.807160\pi$
$433$		−	23.6986i		−	1.13888i	0.822032	−	0.569441i	$-0.192840\pi$
$434$	−20.7653			−0.996766
$435$	−6.49223	−	17.4993i	−0.311278	−	0.839028i
$436$	11.0731			0.530303
$437$	−20.4280	+	11.7941i	−0.977202	+	0.564188i
$438$		−	0.383505i		−	0.0183246i
$439$	−20.3201	−	35.1955i	−0.969828	−	1.67979i	−0.696044	−	0.717999i	$-0.745058\pi$
$439$	−20.3201	−	35.1955i	−0.969828	−	1.67979i	−0.273784	−	0.961791i	$-0.588275\pi$
$440$	15.1217	+	2.56992i	0.720901	+	0.122516i
$441$	−4.87870	−	8.45015i	−0.232319	−	0.402388i
$442$	−3.19173	−	1.84274i	−0.151815	−	0.0876504i
$443$		−	5.83133i		−	0.277055i	−0.990359	−	0.138527i	$-0.955763\pi$
$443$		−	5.83133i		−	0.277055i	0.990359	−	0.138527i	$-0.0442369\pi$
$444$	−5.02509	−	0.987828i	−0.238480	−	0.0468803i
$445$	8.29553	+	6.87369i	0.393246	+	0.325844i
$446$	3.24063	−	5.61294i	0.153448	−	0.265780i
$447$	9.30962	−	5.37491i	0.440330	−	0.254225i
$448$	28.1326	−	16.2424i	1.32914	−	0.767380i
$449$	13.0634	+	22.6265i	0.616500	+	1.06781i	0.990119	+	0.140227i	$0.0447833\pi$
$449$	13.0634	+	22.6265i	0.616500	+	1.06781i	−0.373619	+	0.927582i	$0.621883\pi$
$450$	5.28696	−	0.999899i	0.249230	−	0.0471357i
$451$	−9.15894	−	15.8637i	−0.431278	−	0.746995i
$452$		−	4.55381i		−	0.214193i
$453$	−1.68596	−	0.973389i	−0.0792132	−	0.0457338i
$454$	−14.5088			−0.680932
$455$	−39.0318	−	32.3418i	−1.82984	−	1.51621i
$456$	−6.38193	+	11.0538i	−0.298861	+	0.517643i
$457$	18.8479	−	10.8818i	0.881666	−	0.509030i	0.0104586	−	0.999945i	$-0.496671\pi$
$457$	18.8479	−	10.8818i	0.881666	−	0.509030i	0.871207	+	0.490915i	$0.163338\pi$
$458$			0.801628i			0.0374576i
$459$	−0.309217	+	0.535580i	−0.0144330	+	0.0249987i
$460$	−3.70105	−	9.97590i	−0.172562	−	0.465129i
$461$	−17.2023	+	29.7952i	−0.801190	+	1.38770i	0.117643	+	0.993056i	$0.462466\pi$
$461$	−17.2023	+	29.7952i	−0.801190	+	1.38770i	−0.918833	+	0.394646i	$0.870867\pi$
$462$	8.55697	−	4.94037i	0.398106	−	0.229847i
$463$	34.0064	−	19.6336i	1.58041	−	0.912452i	0.585615	−	0.810589i	$-0.300853\pi$
$463$	34.0064	−	19.6336i	1.58041	−	0.912452i	0.994798	−	0.101863i	$-0.0324803\pi$
$464$	6.70815	−	11.6189i	0.311418	−	0.539392i
$465$	3.66626	+	9.88212i	0.170019	+	0.458272i
$466$	7.69305	−	13.3248i	0.356374	−	0.617257i
$467$			23.1693i			1.07215i	0.844172	+	0.536073i	$0.180093\pi$
$467$			23.1693i			1.07215i	−0.844172	+	0.536073i	$0.819907\pi$
$468$	−4.03777	+	2.33121i	−0.186646	+	0.107760i
$469$	−28.8179	+	49.9140i	−1.33068	+	2.30481i
$470$	−2.65005	−	2.19583i	−0.122238	−	0.101286i
$471$	2.75176			0.126794
$472$	3.19938	+	1.84716i	0.147263	+	0.0850225i
$473$			24.3147i			1.11799i
$474$	0.0140943	+	0.0244121i	0.000647374	+	0.00112129i
$475$	3.87784	+	20.5041i	0.177928	+	0.940791i
$476$	1.06572	+	1.84588i	0.0488472	+	0.0846058i
$477$	−5.03741	+	2.90835i	−0.230647	+	0.133164i
$478$	−19.6431	+	11.3410i	−0.898456	+	0.518724i
$479$	−2.59012	+	4.48622i	−0.118346	+	0.204980i	−0.919112	−	0.393996i	$-0.871092\pi$
$479$	−2.59012	+	4.48622i	−0.118346	+	0.204980i	0.800767	+	0.598976i	$0.204426\pi$
$480$	−7.55342	−	6.25878i	−0.344765	−	0.285673i
$481$	−22.1531	+	25.3754i	−1.01009	+	1.15702i
$482$			11.6714i			0.531620i
$483$	−20.0367	−	11.5682i	−0.911703	−	0.526372i
$484$	2.51282	+	4.35234i	0.114219	+	0.197834i
$485$	11.4012	+	1.93762i	0.517701	+	0.0879826i
$486$	−0.538068	−	0.931961i	−0.0244073	−	0.0422746i
$487$			4.02936i			0.182588i	0.995824	+	0.0912938i	$0.0291002\pi$
$487$			4.02936i			0.182588i	−0.995824	+	0.0912938i	$0.970900\pi$
$488$	21.9184	−	12.6546i	0.992197	−	0.572845i
$489$	−15.1798			−0.686455
$490$	−8.16688	−	22.0132i	−0.368942	−	0.994456i
$491$	26.8350			1.21105			0.605523	−	0.795828i	$-0.292964\pi$
$491$	26.8350			1.21105			0.605523	+	0.795828i	$0.292964\pi$
$492$			6.87595i			0.309992i
$493$	4.47057	+	2.58108i	0.201344	+	0.116246i
$494$	12.4358	+	21.5394i	0.559512	+	0.969103i
$495$	−3.86189	−	3.19997i	−0.173579	−	0.143828i
$496$	−3.78819	+	6.56134i	−0.170095	+	0.294613i
$497$	29.4433	+	16.9991i	1.32071	+	0.762513i
$498$	10.5665	+	6.10057i	0.473496	+	0.273373i
$499$	−2.31611	−	4.01163i	−0.103684	−	0.179585i	0.809516	−	0.587098i	$-0.199730\pi$
$499$	−2.31611	−	4.01163i	−0.103684	−	0.179585i	−0.913200	+	0.407513i	$0.866396\pi$
$500$	−9.41145	+	0.174860i	−0.420893	+	0.00781997i
$501$	6.62309	−	11.4715i	0.295898	−	0.512510i
$502$	0.475708	+	0.274650i	0.0212319	+	0.0122582i
$503$	−5.47482	−	3.16089i	−0.244110	−	0.140937i	0.372954	−	0.927850i	$-0.378345\pi$
$503$	−5.47482	−	3.16089i	−0.244110	−	0.140937i	−0.617064	+	0.786913i	$0.711678\pi$
$504$	−12.5194			−0.557659
$505$	−2.09902	+	12.3509i	−0.0934050	+	0.549606i
$506$	6.82102	−	11.8144i	0.303231	−	0.525212i
$507$			17.6668i			0.784610i
$508$		−	5.20953i		−	0.231135i
$509$	−8.88206	+	15.3842i	−0.393690	+	0.681892i	−0.992933	−	0.118676i	$-0.962135\pi$
$509$	−8.88206	+	15.3842i	−0.393690	+	0.681892i	0.599243	+	0.800567i	$0.295468\pi$
$510$	−0.949484	+	1.14589i	−0.0420439	+	0.0507408i
$511$	0.729419	+	1.26339i	0.0322676	+	0.0558891i
$512$		−	16.8823i		−	0.746098i
$513$	3.61436	−	2.08675i	0.159578	−	0.0921324i
$514$	9.75696	+	16.8996i	0.430361	+	0.745408i
$515$	0.512592	+	0.0871145i	0.0225875	+	0.00383872i
$516$	4.56347	−	7.90417i	0.200896	−	0.347962i
$517$			3.20792i			0.141084i
$518$	−25.3546	+	8.67027i	−1.11402	+	0.380950i
$519$	−3.10144			−0.136138
$520$	−35.5057	+	13.1726i	−1.55703	+	0.577655i
$521$	4.12558	+	7.14571i	0.180745	+	0.313059i	0.942134	−	0.335235i	$-0.108816\pi$
$521$	4.12558	+	7.14571i	0.180745	+	0.313059i	−0.761390	+	0.648295i	$0.775483\pi$
$522$	−7.77922	+	4.49134i	−0.340487	+	0.196580i
$523$	−15.1040	+	8.72028i	−0.660450	+	0.381311i	−0.792449	−	0.609939i	$-0.791194\pi$
$523$	−15.1040	+	8.72028i	−0.660450	+	0.381311i	0.131998	+	0.991250i	$0.457861\pi$
$524$	−6.06048			−0.264753
$525$	−15.5152	+	13.3497i	−0.677138	+	0.582628i
$526$	28.8029			1.25587
$527$	−2.52459	−	1.45757i	−0.109973	−	0.0634930i
$528$		−	3.60507i		−	0.156890i
$529$	−8.94378			−0.388860
$530$	−13.1228	+	4.86854i	−0.570018	+	0.211476i
$531$	−0.603982	−	1.04613i	−0.0262106	−	0.0453981i
$532$		−	14.3840i		−	0.623627i
$533$	39.1671	+	22.6131i	1.69651	+	0.979483i
$534$	2.59239	−	4.49015i	0.112184	−	0.194308i
$535$	−13.5474	−	36.5161i	−0.585706	−	1.57873i
$536$	21.5298	+	37.2906i	0.929944	+	1.61071i
$537$	12.1698	−	7.02623i	0.525165	−	0.303204i
$538$	16.6304	+	9.60156i	0.716987	+	0.413953i
$539$	−10.9427	+	18.9532i	−0.471334	+	0.816374i
$540$	0.654835	+	1.76506i	0.0281796	+	0.0759560i
$541$	−5.82173			−0.250296			−0.125148	−	0.992138i	$-0.539941\pi$
$541$	−5.82173			−0.250296			−0.125148	+	0.992138i	$0.539941\pi$
$542$	−28.4777	+	16.4416i	−1.22322	+	0.706228i
$543$	19.7935	+	11.4278i	0.849422	+	0.490414i
$544$	2.71304			0.116320
$545$	−22.6450	−	18.7637i	−0.970006	−	0.803749i
$546$	−12.1976	+	21.1269i	−0.522009	+	0.904147i
$547$			30.6835i			1.31193i	0.754791	+	0.655965i	$0.227738\pi$
$547$			30.6835i			1.31193i	−0.754791	+	0.655965i	$0.772262\pi$
$548$	−3.64525	+	2.10458i	−0.155717	+	0.0899034i
$549$	−8.27555			−0.353192
$550$	−7.87143	−	9.14829i	−0.335639	−	0.390084i
$551$	−17.4185	−	30.1696i	−0.742051	−	1.28527i
$552$	−14.9694	+	8.64259i	−0.637140	+	0.367853i
$553$	−0.0928627	−	0.0536143i	−0.00394892	−	0.00227991i
$554$	−13.5179			−0.574321
$555$	8.60268	+	10.5354i	0.365163	+	0.447201i
$556$	−5.12675			−0.217423
$557$	−22.6978	−	13.1046i	−0.961736	−	0.555258i	−0.0650289	−	0.997883i	$-0.520714\pi$
$557$	−22.6978	−	13.1046i	−0.961736	−	0.555258i	−0.896707	+	0.442625i	$0.854047\pi$
$558$	4.39304	−	2.53632i	0.185972	−	0.107371i
$559$	−30.0160	−	51.9893i	−1.26954	−	2.19891i
$560$	−14.5044	−	2.46501i	−0.612923	−	0.104166i
$561$	1.38711			0.0585640
$562$	−9.79292	+	5.65394i	−0.413089	+	0.238497i
$563$		−	16.9377i		−	0.713840i	−0.934135	−	0.356920i	$-0.883827\pi$
$563$		−	16.9377i		−	0.713840i	0.934135	−	0.356920i	$-0.116173\pi$
$564$	0.602076	−	1.04283i	0.0253520	−	0.0439109i
$565$	−7.71659	+	9.31279i	−0.324639	+	0.391792i
$566$	6.61112			0.277886
$567$	3.54514	+	2.04679i	0.148882	+	0.0859571i
$568$	21.9970	−	12.7000i	0.922974	−	0.532879i
$569$	−20.5786			−0.862698			−0.431349	−	0.902185i	$-0.641962\pi$
$569$	−20.5786			−0.862698			−0.431349	+	0.902185i	$0.641962\pi$
$570$	9.41566	−	3.49320i	0.394379	−	0.146314i
$571$	−2.48711	+	4.30780i	−0.104082	+	0.180276i	−0.913363	−	0.407146i	$-0.866524\pi$
$571$	−2.48711	+	4.30780i	−0.104082	+	0.180276i	0.809281	+	0.587422i	$0.199857\pi$
$572$	9.05649	+	5.22877i	0.378671	+	0.218626i
$573$	11.3052	−	6.52705i	0.472281	−	0.272671i
$574$	17.9886	+	31.1571i	0.750829	+	1.30047i
$575$	−9.33567	+	26.6728i	−0.389324	+	1.11233i
$576$	−3.96777	+	6.87237i	−0.165324	+	0.286349i
$577$	−19.7025	−	11.3752i	−0.820224	−	0.473557i	0.0302695	−	0.999542i	$-0.490363\pi$
$577$	−19.7025	−	11.3752i	−0.820224	−	0.473557i	−0.850494	+	0.525985i	$0.823697\pi$
$578$			17.8827i			0.743824i
$579$	11.9443	+	20.6882i	0.496390	+	0.859773i
$580$	14.7332	−	5.46601i	0.611763	−	0.226964i
$581$	−46.4126			−1.92552
$582$		−	5.56563i		−	0.230703i
$583$	11.2986	+	6.52327i	0.467942	+	0.270166i
$584$	1.08990			0.0451002
$585$	12.2078	+	2.07470i	0.504729	+	0.0857781i
$586$	8.57973			0.354426
$587$	−14.0752	+	8.12631i	−0.580945	+	0.335409i	−0.761509	−	0.648155i	$-0.775541\pi$
$587$	−14.0752	+	8.12631i	−0.580945	+	0.335409i	0.180564	+	0.983563i	$0.442208\pi$
$588$	7.11444	−	4.10753i	0.293395	−	0.169392i
$589$	9.83646	+	17.0372i	0.405304	+	0.702007i
$590$	−1.01106	−	2.72523i	−0.0416246	−	0.112196i
$591$	16.4935			0.678453
$592$	−1.88582	+	9.59317i	−0.0775066	+	0.394277i
$593$		−	22.6512i		−	0.930174i	−0.885265	−	0.465087i	$-0.846023\pi$
$593$		−	22.6512i		−	0.930174i	0.885265	−	0.465087i	$-0.153977\pi$
$594$	−1.20686	+	2.09034i	−0.0495180	+	0.0857677i
$595$	0.948456	−	5.58083i	0.0388829	−	0.228792i
$596$	4.52531	+	7.83806i	0.185364	+	0.321059i
$597$	−21.1703	+	12.2227i	−0.866442	+	0.500241i
$598$			33.6817i			1.37735i
$599$	11.7227	+	20.3043i	0.478977	+	0.829612i	0.999709	−	0.0241080i	$-0.00767455\pi$
$599$	11.7227	+	20.3043i	0.478977	+	0.829612i	−0.520733	+	0.853720i	$0.674341\pi$
$600$	2.84164	+	15.0252i	0.116010	+	0.613400i
$601$	23.1669	−	40.1262i	0.944996	−	1.63678i	0.189237	−	0.981931i	$-0.439399\pi$
$601$	23.1669	−	40.1262i	0.944996	−	1.63678i	0.755759	−	0.654850i	$-0.227268\pi$
$602$		−	47.7551i		−	1.94635i
$603$		−	14.0795i		−	0.573363i
$604$	0.819526	−	1.41946i	0.0333460	−	0.0577570i
$605$	2.23633	−	13.1588i	0.0909198	−	0.534983i
$606$	6.02924			0.244921
$607$	24.3040	+	14.0319i	0.986469	+	0.569538i	0.904217	−	0.427073i	$-0.140455\pi$
$607$	24.3040	+	14.0319i	0.986469	+	0.569538i	0.0822522	+	0.996612i	$0.473789\pi$
$608$	−15.8560	−	9.15448i	−0.643046	−	0.371263i
$609$	17.0849	−	29.5919i	0.692314	−	1.19912i
$610$	−19.6321	−	3.33645i	−0.794879	−	0.135089i
$611$	−3.96013	−	6.85914i	−0.160210	−	0.277491i
$612$	−0.450921	−	0.260339i	−0.0182274	−	0.0105236i
$613$	−11.1051	−	6.41151i	−0.448529	−	0.258958i	0.258680	−	0.965963i	$-0.416713\pi$
$613$	−11.1051	−	6.41151i	−0.448529	−	0.258958i	−0.707209	+	0.707005i	$0.750046\pi$
$614$	−1.69106	+	2.92901i	−0.0682458	+	0.118205i
$615$	11.6515	−	14.0617i	0.469836	−	0.567022i
$616$	14.0402	+	24.3183i	0.565695	+	0.979813i
$617$	17.6656	+	10.1992i	0.711188	+	0.410605i	0.811501	−	0.584351i	$-0.198651\pi$
$617$	17.6656	+	10.1992i	0.711188	+	0.410605i	−0.100313	+	0.994956i	$0.531984\pi$
$618$		−	0.250229i		−	0.0100657i
$619$	−30.2391			−1.21541			−0.607705	−	0.794163i	$-0.707910\pi$
$619$	−30.2391			−1.21541			−0.607705	+	0.794163i	$0.707910\pi$
$620$	−8.32006	+	3.08673i	−0.334142	+	0.123966i
$621$	5.65188			0.226802
$622$	16.1538	−	9.32640i	0.647708	−	0.373955i
$623$			19.7227i			0.790172i
$624$	4.45040	+	7.70831i	0.178158	+	0.308579i
$625$	19.5432	+	15.5904i	0.781730	+	0.623618i
$626$	−2.19613	−	3.80380i	−0.0877749	−	0.152031i
$627$	−8.10682	−	4.68048i	−0.323755	−	0.186920i
$628$			2.31679i			0.0924500i
$629$	−3.69114	−	0.725602i	−0.147176	−	0.0289316i
$630$	7.58494	+	6.28489i	0.302191	+	0.250396i
$631$	−8.52832	+	14.7715i	−0.339507	+	0.588043i	−0.984340	−	0.176280i	$-0.943594\pi$
$631$	−8.52832	+	14.7715i	−0.339507	+	0.588043i	0.644833	+	0.764323i	$0.276927\pi$
$632$	−0.0693775	+	0.0400551i	−0.00275969	+	0.00159331i
$633$	16.7475	−	9.66915i	0.665652	−	0.384314i
$634$	−11.8791	−	20.5751i	−0.471777	−	0.817142i
$635$	−8.82773	+	10.6538i	−0.350318	+	0.422782i
$636$	−2.44863	−	4.24115i	−0.0970945	−	0.168173i
$637$		−	54.0341i		−	2.14091i
$638$	17.4484	+	10.0738i	0.690788	+	0.398827i
$639$	−8.30524			−0.328550
$640$	0.334097	−	0.403206i	0.0132063	−	0.0159381i
$641$	22.0279	−	38.1535i	0.870050	−	1.50697i	0.00810680	−	0.999967i	$-0.497419\pi$
$641$	22.0279	−	38.1535i	0.870050	−	1.50697i	0.861944	−	0.507004i	$-0.169247\pi$
$642$	−16.2330	+	9.37214i	−0.640667	+	0.369889i
$643$		−	5.67025i		−	0.223613i	−0.993730	−	0.111806i	$-0.964336\pi$
$643$		−	5.67025i		−	0.223613i	0.993730	−	0.111806i	$-0.0356636\pi$
$644$	9.73964	−	16.8695i	0.383795	−	0.664753i
$645$	−22.7265	+	8.43149i	−0.894853	+	0.331990i
$646$	−1.38877	+	2.40543i	−0.0546406	+	0.0946403i
$647$	−16.0588	+	9.27153i	−0.631335	+	0.364501i	−0.781269	−	0.624195i	$-0.785427\pi$
$647$	−16.0588	+	9.27153i	−0.631335	+	0.364501i	0.149934	+	0.988696i	$0.452094\pi$
$648$	2.64857	−	1.52915i	0.104046	−	0.0600708i
$649$	−1.35470	+	2.34641i	−0.0531766	+	0.0921046i
$650$	28.1240	+	9.84360i	1.10311	+	0.386098i
$651$	−9.64808	+	16.7110i	−0.378138	+	0.654954i
$652$		−	12.7804i		−	0.500517i
$653$	28.8009	−	16.6282i	1.12707	−	0.650711i	0.183870	−	0.982951i	$-0.441137\pi$
$653$	28.8009	−	16.6282i	1.12707	−	0.650711i	0.943195	+	0.332239i	$0.107804\pi$
$654$	−7.07666	+	12.2571i	−0.276719	+	0.479292i
$655$	12.3940	+	10.2697i	0.484274	+	0.401270i
$656$	13.1266			0.512506
$657$	−0.308627	−	0.178186i	−0.0120407	−	0.00695170i
$658$		−	6.30051i		−	0.245619i
$659$	−5.43366	−	9.41138i	−0.211665	−	0.366615i	0.740570	−	0.671979i	$-0.234555\pi$
$659$	−5.43366	−	9.41138i	−0.211665	−	0.366615i	−0.952236	+	0.305363i	$0.901222\pi$
$660$	2.69415	−	3.25145i	0.104870	−	0.126562i
$661$	4.91486	+	8.51279i	0.191166	+	0.331109i	0.945637	−	0.325224i	$-0.105440\pi$
$661$	4.91486	+	8.51279i	0.191166	+	0.331109i	−0.754471	+	0.656333i	$0.772106\pi$
$662$	11.5987	−	6.69653i	0.450798	−	0.260268i
$663$	−2.96591	+	1.71237i	−0.115186	+	0.0665029i
$664$	−17.3374	+	30.0292i	−0.672821	+	1.16536i
$665$	−24.3743	+	29.4162i	−0.945194	+	1.14071i
$666$	4.30494	−	4.93113i	0.166813	−	0.191078i
$667$		−	47.1771i		−	1.82671i
$668$	9.65823	+	5.57618i	0.373688	+	0.215749i
$669$	−3.01136	−	5.21583i	−0.116426	−	0.201656i
$670$	5.67644	−	33.4009i	0.219300	−	1.29039i
$671$	9.28080	+	16.0748i	0.358281	+	0.620562i
$672$		−	17.9583i		−	0.692757i
$673$	5.79102	−	3.34345i	0.223227	−	0.128880i	−0.384216	−	0.923243i	$-0.625528\pi$
$673$	5.79102	−	3.34345i	0.223227	−	0.128880i	0.607444	+	0.794363i	$0.292195\pi$
$674$	21.0467			0.810688
$675$	1.65178	−	4.71928i	0.0635771	−	0.181645i
$676$	−14.8742			−0.572085
$677$		−	16.9879i		−	0.652899i	−0.945215	−	0.326449i	$-0.894148\pi$
$677$		−	16.9879i		−	0.652899i	0.945215	−	0.326449i	$-0.105852\pi$
$678$	5.04076	+	2.91028i	0.193589	+	0.111769i
$679$	10.5857	+	18.3350i	0.406243	+	0.703633i
$680$	−3.25653	−	2.69837i	−0.124882	−	0.103478i
$681$	−6.74115	+	11.6760i	−0.258322	+	0.447426i
$682$	−9.85336	−	5.68884i	−0.377305	−	0.217837i
$683$	0.0912701	+	0.0526948i	0.00349235	+	0.00201631i	0.501745	−	0.865015i	$-0.332692\pi$
$683$	0.0912701	+	0.0526948i	0.00349235	+	0.00201631i	−0.498253	+	0.867032i	$0.666025\pi$
$684$	1.75690	+	3.04304i	0.0671768	+	0.116354i
$685$	11.0210	+	1.87301i	0.421092	+	0.0715641i
$686$	6.07350	−	10.5196i	0.231887	−	0.401641i
$687$	0.645114	+	0.372456i	0.0246126	+	0.0142101i
$688$	−15.0895	−	8.71191i	−0.575281	−	0.332139i
$689$	−32.2115			−1.22716
$690$	13.4080	+	2.27867i	0.510432	+	0.0867474i
$691$	4.18037	−	7.24062i	0.159029	−	0.275446i	−0.775490	−	0.631360i	$-0.782497\pi$
$691$	4.18037	−	7.24062i	0.159029	−	0.275446i	0.934519	+	0.355914i	$0.115830\pi$
$692$		−	2.61120i		−	0.0992630i
$693$		−	9.18168i		−	0.348783i
$694$	−15.4615	+	26.7801i	−0.586910	+	1.01656i
$695$	10.4845	+	8.68747i	0.397699	+	0.329534i
$696$	−12.7641	−	22.1080i	−0.483821	−	0.838002i
$697$			5.05068i			0.191308i
$698$	4.99344	−	2.88296i	0.189004	−	0.109122i
$699$	−7.14877	−	12.3820i	−0.270391	−	0.468332i
$700$	−11.2395	−	13.0627i	−0.424814	−	0.493724i
$701$	21.1257	−	36.5908i	0.797907	−	1.38202i	−0.123069	−	0.992398i	$-0.539274\pi$
$701$	21.1257	−	36.5908i	0.797907	−	1.38202i	0.920977	−	0.389618i	$-0.127393\pi$
$702$		−	5.95938i		−	0.224922i
$703$	19.1241	+	16.6956i	0.721278	+	0.629685i
$704$	17.7990			0.670824
$705$	−2.99839	+	1.11240i	−0.112926	+	0.0418953i
$706$	12.3331	+	21.3616i	0.464163	+	0.803953i
$707$	−19.8623	+	11.4675i	−0.746998	+	0.431280i
$708$	0.880767	−	0.508511i	0.0331013	−	0.0191110i
$709$	0.316027			0.0118686			0.00593431	−	0.999982i	$-0.498111\pi$
$709$	0.316027			0.0118686			0.00593431	+	0.999982i	$0.498111\pi$
$710$	−19.7025	−	3.34842i	−0.739422	−	0.125664i
$711$	0.0261943			0.000982365
$712$	12.7607	+	7.36738i	0.478227	+	0.276104i
$713$			26.6416i			0.997737i
$714$	−2.72436			−0.101956
$715$	−9.66069	−	26.0397i	−0.361289	−	0.973829i
$716$	5.91560	+	10.2461i	0.221076	+	0.382915i
$717$			21.0772i			0.787142i
$718$	19.1592	+	11.0616i	0.715016	+	0.412815i
$719$	15.4657	−	26.7874i	0.576774	−	0.999001i	−0.419073	−	0.907953i	$-0.637645\pi$
$719$	15.4657	−	26.7874i	0.576774	−	0.999001i	0.995846	−	0.0910487i	$-0.0290219\pi$
$720$	3.36959	−	1.25011i	0.125577	−	0.0465890i
$721$	0.475930	+	0.824336i	0.0177246	+	0.0306999i
$722$	−1.47421	+	0.851135i	−0.0548644	+	0.0316760i
$723$	9.39265	+	5.42285i	0.349316	+	0.201678i
$724$	−9.62143	+	16.6648i	−0.357577	+	0.619342i
$725$	−39.3926	−	13.7877i	−1.46300	−	0.512061i
$726$	−6.42366			−0.238405
$727$	15.2146	−	8.78414i	0.564277	−	0.325786i	−0.190583	−	0.981671i	$-0.561038\pi$
$727$	15.2146	−	8.78414i	0.564277	−	0.325786i	0.754860	+	0.655885i	$0.227705\pi$
$728$	−60.0411	−	34.6648i	−2.22527	−	1.28476i
$729$	−1.00000			−0.0370370
$730$	−0.660317	−	0.547140i	−0.0244394	−	0.0202506i
$731$	3.35207	−	5.80595i	0.123981	−	0.214741i
$732$		−	6.96744i		−	0.257524i
$733$	37.0075	−	21.3663i	1.36691	−	0.789183i	0.376373	−	0.926468i	$-0.377171\pi$
$733$	37.0075	−	21.3663i	1.36691	−	0.789183i	0.990532	+	0.137285i	$0.0438376\pi$
$734$	26.4825			0.977487
$735$	−21.5098	−	3.65556i	−0.793400	−	0.134837i
$736$	−12.3973	−	21.4727i	−0.456969	−	0.791493i
$737$	−27.3488	+	15.7898i	−1.00741	+	0.581626i
$738$	−7.61122	−	4.39434i	−0.280173	−	0.161758i
$739$	−12.9872			−0.477741			−0.238871	−	0.971051i	$-0.576777\pi$
$739$	−12.9872			−0.477741			−0.238871	+	0.971051i	$0.576777\pi$
$740$	−8.87005	+	7.24286i	−0.326069	+	0.266253i
$741$	23.1119			0.849036
$742$	−22.1910	−	12.8120i	−0.814659	−	0.470344i
$743$	9.18309	−	5.30186i	0.336895	−	0.194506i	−0.322003	−	0.946739i	$-0.604356\pi$
$743$	9.18309	−	5.30186i	0.336895	−	0.194506i	0.658898	+	0.752232i	$0.271023\pi$
$744$	7.20806	+	12.4847i	0.264260	+	0.457712i
$745$	4.02737	−	23.6976i	0.147552	−	0.868211i
$746$	−4.74603			−0.173765
$747$	9.81892	−	5.66896i	0.359255	−	0.207416i
$748$			1.16785i			0.0427010i
$749$	35.6513	−	61.7498i	1.30267	−	2.25629i
$750$	5.82119	−	10.5296i	0.212560	−	0.384487i
$751$	−13.0352			−0.475660			−0.237830	−	0.971307i	$-0.576436\pi$
$751$	−13.0352			−0.475660			−0.237830	+	0.971307i	$0.576436\pi$
$752$	−1.99081	−	1.14940i	−0.0725974	−	0.0419141i
$753$	0.442052	−	0.255219i	0.0161093	−	0.00930069i
$754$	−49.7439			−1.81157
$755$	−4.08130	+	1.51416i	−0.148534	+	0.0551059i
$756$	−1.72326	+	2.98477i	−0.0626742	+	0.108555i
$757$	15.2295	+	8.79274i	0.553525	+	0.319578i	0.750542	−	0.660822i	$-0.229792\pi$
$757$	15.2295	+	8.79274i	0.553525	+	0.319578i	−0.197018	+	0.980400i	$0.563126\pi$
$758$	16.3815	−	9.45785i	0.595002	−	0.343525i
$759$	−6.33843	−	10.9785i	−0.230071	−	0.398494i
$760$	9.92744	+	26.7587i	0.360106	+	0.970639i
$761$	14.9523	−	25.8982i	0.542022	−	0.938809i	−0.456766	−	0.889587i	$-0.650992\pi$
$761$	14.9523	−	25.8982i	0.542022	−	0.938809i	0.998788	−	0.0492225i	$-0.0156743\pi$
$762$	5.76660	+	3.32935i	0.208902	+	0.120610i
$763$		−	53.8387i		−	1.94909i
$764$	5.49532	+	9.51818i	0.198814	+	0.344356i
$765$	0.481004	+	1.29651i	0.0173907	+	0.0468754i
$766$	0.526792			0.0190338
$767$		−	6.68942i		−	0.241541i
$768$	−13.9630	−	8.06154i	−0.503846	−	0.290896i
$769$	15.3250			0.552635			0.276317	−	0.961066i	$-0.410886\pi$
$769$	15.3250			0.552635			0.276317	+	0.961066i	$0.410886\pi$
$770$	3.70177	−	21.7817i	0.133403	−	0.784957i
$771$	18.1333			0.653056
$772$	−17.4180	+	10.0563i	−0.626889	+	0.361935i
$773$	−8.72041	+	5.03473i	−0.313651	+	0.181087i	−0.648559	−	0.761164i	$-0.724628\pi$
$773$	−8.72041	+	5.03473i	−0.313651	+	0.181087i	0.334908	+	0.942251i	$0.391295\pi$
$774$	5.83293	+	10.1029i	0.209660	+	0.363142i
$775$	22.2456	+	7.78610i	0.799084	+	0.279685i
$776$	15.8171			0.567802
$777$	−4.80295	+	24.4327i	−0.172305	+	0.876517i
$778$		−	21.3545i		−	0.765597i
$779$	17.0423	−	29.5181i	0.610603	−	1.05759i
$780$	−1.74675	+	10.2781i	−0.0625437	+	0.368015i
$781$	9.31410	+	16.1325i	0.333285	+	0.577266i
$782$	−3.25750	+	1.88072i	−0.116488	+	0.0672544i
$783$			8.34715i			0.298303i
$784$	−7.84148	−	13.5819i	−0.280053	−	0.485066i
$785$	3.92588	−	4.73796i	0.140121	−	0.169105i
$786$	3.87318	−	6.70854i	0.138152	−	0.239286i
$787$			39.1632i			1.39602i	0.716090	+	0.698008i	$0.245930\pi$
$787$			39.1632i			1.39602i	−0.716090	+	0.698008i	$0.754070\pi$
$788$			13.8864i			0.494683i
$789$	13.3825	−	23.1792i	0.476431	−	0.825203i
$790$	0.0621408	+	0.0105608i	0.00221087	+	0.000375735i
$791$	−22.1412			−0.787251
$792$	−5.94060	−	3.42981i	−0.211090	−	0.121873i
$793$	−39.6882	−	22.9140i	−1.40937	−	0.813700i
$794$	17.5228	−	30.3504i	0.621861	−	1.07710i
$795$	−2.17920	+	12.8227i	−0.0772883	+	0.454774i
$796$	−10.2906	−	17.8239i	−0.364742	−	0.631752i
$797$	33.2325	+	19.1868i	1.17715	+	0.679631i	0.955355	−	0.295461i	$-0.0954734\pi$
$797$	33.2325	+	19.1868i	1.17715	+	0.679631i	0.221800	+	0.975092i	$0.428807\pi$
$798$	15.9222	+	9.19267i	0.563639	+	0.325417i
$799$	0.442251	−	0.766001i	0.0156457	−	0.0270992i
$800$	−21.5527	+	4.07616i	−0.762002	+	0.144114i
$801$	−2.40898	−	4.17247i	−0.0851170	−	0.147427i
$802$	0.266764	+	0.154016i	0.00941978	+	0.00543851i
$803$			0.799324i			0.0282075i
$804$	11.8540			0.418058
$805$	−48.5042	+	17.9950i	−1.70955	+	0.634240i
$806$	28.0911			0.989467
$807$	15.4538	−	8.92225i	0.543999	−	0.314078i
$808$			17.1347i			0.602796i
$809$	18.1379	+	31.4158i	0.637696	+	1.10452i	0.985937	+	0.167117i	$0.0534456\pi$
$809$	18.1379	+	31.4158i	0.637696	+	1.10452i	−0.348241	+	0.937405i	$0.613221\pi$
$810$	−2.37230	−	0.403169i	−0.0833541	−	0.0141659i
$811$	19.2140	+	33.2795i	0.674693	+	1.16860i	0.976558	+	0.215252i	$0.0690574\pi$
$811$	19.2140	+	33.2795i	0.674693	+	1.16860i	−0.301865	+	0.953351i	$0.597609\pi$
$812$	24.9143	+	14.3843i	0.874321	+	0.504789i
$813$			30.5568i			1.07167i
$814$	−14.4063	−	2.83199i	−0.504942	−	0.0992611i
$815$	−21.6568	+	26.1365i	−0.758604	+	0.915523i
$816$	−0.497002	+	0.860832i	−0.0173985	+	0.0301352i
$817$	−39.1815	+	22.6214i	−1.37079	+	0.791424i
$818$	−31.8760	+	18.4036i	−1.11452	+	0.643468i
$819$	11.3346	+	19.6322i	0.396064	+	0.686003i
$820$	11.8390	+	9.80979i	0.413435	+	0.342573i
$821$	5.29020	+	9.16289i	0.184629	+	0.319787i	0.943452	−	0.331511i	$-0.107558\pi$
$821$	5.29020	+	9.16289i	0.184629	+	0.319787i	−0.758822	+	0.651298i	$0.774225\pi$
$822$		−	5.38006i		−	0.187651i
$823$	−0.771074	−	0.445180i	−0.0268780	−	0.0155180i	0.486501	−	0.873680i	$-0.338273\pi$
$823$	−0.771074	−	0.445180i	−0.0268780	−	0.0155180i	−0.513379	+	0.858162i	$0.671606\pi$
$824$	0.711133			0.0247735
$825$	−11.0194	+	2.08405i	−0.383646	+	0.0725572i
$826$	2.66069	−	4.60845i	0.0925773	−	0.160349i
$827$	−25.1856	+	14.5409i	−0.875791	+	0.505638i	−0.869268	−	0.494341i	$-0.835410\pi$
$827$	−25.1856	+	14.5409i	−0.875791	+	0.505638i	−0.00652256	+	0.999979i	$0.502076\pi$
$828$			4.75849i			0.165369i
$829$	−2.79876	+	4.84760i	−0.0972051	+	0.168364i	−0.910527	−	0.413450i	$-0.864324\pi$
$829$	−2.79876	+	4.84760i	−0.0972051	+	0.168364i	0.813322	+	0.581814i	$0.197657\pi$
$830$	25.5790	−	9.48977i	0.887858	−	0.329395i
$831$	−6.28076	+	10.8786i	−0.217877	+	0.377374i
$832$	−38.0576	+	21.9725i	−1.31941	+	0.761761i
$833$	5.22586	−	3.01715i	0.181065	−	0.104538i
$834$	3.27645	−	5.67497i	0.113454	−	0.196508i
$835$	−10.3026	−	27.7698i	−0.356535	−	0.961014i
$836$	3.94064	−	6.82538i	0.136290	−	0.236061i
$837$		−	4.71376i		−	0.162931i
$838$	−31.4141	+	18.1370i	−1.08518	+	0.626531i
$839$	−4.45316	+	7.71309i	−0.153740	+	0.266286i	−0.932600	−	0.360913i	$-0.882465\pi$
$839$	−4.45316	+	7.71309i	−0.153740	+	0.266286i	0.778859	+	0.627198i	$0.215798\pi$
$840$	−17.8612	+	21.5559i	−0.616271	+	0.743748i
$841$	40.6750			1.40259
$842$	−20.6337	−	11.9129i	−0.711085	−	0.410545i
$843$			10.5079i			0.361910i
$844$	8.14076	+	14.1002i	0.280216	+	0.485349i
$845$	30.4186	+	25.2049i	1.04643	+	0.867075i
$846$	0.769560	+	1.33292i	0.0264580	+	0.0458266i
$847$	21.1616	−	12.2177i	0.727123	−	0.419804i
$848$	−8.09658	+	4.67456i	−0.278038	+	0.160525i
$849$	3.07169	−	5.32033i	0.105420	−	0.182593i
$850$	0.618372	+	3.26964i	0.0212100	+	0.112148i
$851$	11.1239	+	32.5297i	0.381321	+	1.11510i
$852$		−	6.99244i		−	0.239557i
$853$	−22.8830	−	13.2115i	−0.783499	−	0.452353i	0.0541701	−	0.998532i	$-0.482749\pi$
$853$	−22.8830	−	13.2115i	−0.783499	−	0.452353i	−0.837669	+	0.546179i	$0.816082\pi$
$854$	−18.2279	−	31.5717i	−0.623747	−	1.08036i
$855$	1.56359	−	9.20033i	0.0534735	−	0.314645i
$856$	−26.6350	−	46.1331i	−0.910365	−	1.57680i
$857$		−	42.4278i		−	1.44931i	−0.689114	−	0.724653i	$-0.742000\pi$
$857$		−	42.4278i		−	1.44931i	0.689114	−	0.724653i	$-0.258000\pi$
$858$	−11.5758	+	6.68329i	−0.395191	+	0.228164i
$859$	19.1231			0.652471			0.326235	−	0.945289i	$-0.394220\pi$
$859$	19.1231			0.652471			0.326235	+	0.945289i	$0.394220\pi$
$860$	−7.09873	−	19.1341i	−0.242065	−	0.652468i
$861$	33.4318			1.13935
$862$		−	38.4143i		−	1.30840i
$863$	6.06966	+	3.50432i	0.206614	+	0.119288i	0.599737	−	0.800197i	$-0.295272\pi$
$863$	6.06966	+	3.50432i	0.206614	+	0.119288i	−0.393123	+	0.919486i	$0.628605\pi$
$864$	2.19347	+	3.79921i	0.0746235	+	0.129252i
$865$	−4.42477	+	5.34005i	−0.150447	+	0.181567i
$866$	−12.7515	+	22.0862i	−0.433313	+	0.750519i
$867$	14.3912	+	8.30877i	0.488751	+	0.282181i
$868$	−14.0695	−	8.12301i	−0.477549	−	0.275713i
$869$	−0.0293763	−	0.0508812i	−0.000996521	−	0.00172603i
$870$	−3.36532	+	19.8019i	−0.114095	+	0.671349i
$871$	38.9846	−	67.5232i	1.32094	−	2.28794i
$872$	−34.8339	−	20.1114i	−1.17963	−	0.681058i
$873$	−4.47897	−	2.58593i	−0.151590	−	0.0875206i
$874$	25.3841			0.858630
$875$	0.850192	+	45.7597i	0.0287417	+	1.54696i
$876$	0.150020	−	0.259843i	0.00506872	−	0.00877928i
$877$		−	18.3238i		−	0.618750i	−0.950940	−	0.309375i	$-0.899880\pi$
$877$		−	18.3238i		−	0.618750i	0.950940	−	0.309375i	$-0.100120\pi$
$878$			43.7345i			1.47597i
$879$	3.98636	−	6.90458i	0.134457	−	0.232886i
$880$	−6.20719	−	5.14328i	−0.209244	−	0.173380i
$881$	−0.520865	−	0.902164i	−0.0175484	−	0.0303947i	0.857118	−	0.515120i	$-0.172253\pi$
$881$	−0.520865	−	0.902164i	−0.0175484	−	0.0303947i	−0.874666	+	0.484726i	$0.838919\pi$
$882$			10.5003i			0.353563i
$883$	−18.2586	+	10.5416i	−0.614450	+	0.354753i	−0.774705	−	0.632323i	$-0.782102\pi$
$883$	−18.2586	+	10.5416i	−0.614450	+	0.354753i	0.160255	+	0.987076i	$0.448768\pi$
$884$	−1.44170	−	2.49709i	−0.0484895	−	0.0839863i
$885$	−2.66291	−	0.452558i	−0.0895127	−	0.0152126i
$886$	−3.13765	+	5.43457i	−0.105411	+	0.182578i
$887$		−	17.9848i		−	0.603870i	−0.953328	−	0.301935i	$-0.902367\pi$
$887$		−	17.9848i		−	0.603870i	0.953328	−	0.301935i	$-0.0976326\pi$
$888$	14.0139	+	12.2343i	0.470277	+	0.410557i
$889$	−25.3294			−0.849521
$890$	−4.03260	−	10.8696i	−0.135173	−	0.364349i
$891$	1.12147	+	1.94245i	0.0375708	+	0.0650745i
$892$	4.39137	−	2.53536i	0.147034	−	0.0848900i
$893$	−5.16936	+	2.98453i	−0.172986	+	0.0998736i
$894$	−11.5683			−0.386901
$895$	5.26469	−	30.9781i	0.175979	−	1.03548i
$896$	0.958624			0.0320254
$897$	27.1055	+	15.6494i	0.905027	+	0.522518i
$898$		−	28.1160i		−	0.938243i
$899$	−39.3465			−1.31228
$900$	3.97331	+	1.39069i	0.132444	+	0.0463562i
$901$	−1.79862	−	3.11531i	−0.0599208	−	0.103786i
$902$			19.7125i			0.656355i
$903$	−38.4311	−	22.1882i	−1.27891	−	0.738378i
$904$	−8.27083	+	14.3255i	−0.275084	+	0.476459i
$905$	47.9154	−	17.7766i	1.59276	−	0.590914i
$906$	1.04750	+	1.81432i	0.0348008	+	0.0602768i
$907$	−21.0231	+	12.1377i	−0.698061	+	0.403026i	−0.806625	−	0.591064i	$-0.798708\pi$
$907$	−21.0231	+	12.1377i	−0.698061	+	0.403026i	0.108564	+	0.994089i	$0.465375\pi$
$908$	−9.83040	−	5.67558i	−0.326233	−	0.188351i
$909$	2.80134	−	4.85206i	0.0929145	−	0.160933i
$910$	18.9740	+	51.1431i	0.628983	+	1.69538i
$911$	−35.2786			−1.16883			−0.584417	−	0.811454i	$-0.698677\pi$
$911$	−35.2786			−1.16883			−0.584417	+	0.811454i	$0.698677\pi$
$912$	5.80933	−	3.35402i	0.192366	−	0.111063i
$913$	−22.0233	−	12.7152i	−0.728865	−	0.420810i
$914$	−23.4206			−0.774686
$915$	−11.8066	+	14.2488i	−0.390313	+	0.471051i
$916$	−0.313583	+	0.543141i	−0.0103611	+	0.0179459i
$917$			29.4668i			0.973081i
$918$	0.576357	−	0.332760i	0.0190226	−	0.0109827i
$919$	49.6621			1.63820			0.819101	−	0.573650i	$-0.194473\pi$
$919$	49.6621			1.63820			0.819101	+	0.573650i	$0.194473\pi$
$920$	−6.47581	+	38.1045i	−0.213501	+	1.25627i
$921$	1.57142	+	2.72178i	0.0517801	+	0.0896857i
$922$	32.0637	−	18.5120i	1.05596	−	0.609660i
$923$	−39.8306	−	22.9962i	−1.31104	−	0.756930i
$924$	7.73034			0.254309
$925$	30.4130	+	0.218561i	0.999974	+	0.00718625i
$926$	−42.2569			−1.38865
$927$	−0.201373	−	0.116263i	−0.00661395	−	0.00381857i
$928$	31.7126	−	18.3093i	1.04102	−	0.601031i
$929$	7.08063	+	12.2640i	0.232308	+	0.402369i	0.958487	−	0.285136i	$-0.0920389\pi$
$929$	7.08063	+	12.2640i	0.232308	+	0.402369i	−0.726179	+	0.687506i	$0.758706\pi$
$930$	1.90044	−	11.1824i	0.0623180	−	0.366687i
$931$	−40.7226			−1.33463
$932$	10.4248	−	6.01877i	0.341476	−	0.197151i
$933$		−	17.3331i		−	0.567461i
$934$	12.4666	−	21.5929i	0.407921	−	0.706540i
$935$	1.97897	−	2.38833i	0.0647193	−	0.0781066i
$936$	16.9362			0.553576
$937$	−40.5876	−	23.4333i	−1.32594	−	0.765531i	−0.341270	−	0.939965i	$-0.610857\pi$
$937$	−40.5876	−	23.4333i	−1.32594	−	0.765531i	−0.984669	+	0.174434i	$0.944190\pi$
$938$	53.7143	−	31.0119i	1.75383	−	1.01258i
$939$	−4.08150			−0.133195
$940$	−0.936563	−	2.52443i	−0.0305473	−	0.0823380i
$941$	0.0755042	−	0.130777i	0.00246137	−	0.00426321i	−0.864792	−	0.502130i	$-0.832550\pi$
$941$	0.0755042	−	0.130777i	0.00246137	−	0.00426321i	0.867253	+	0.497867i	$0.165883\pi$
$942$	−2.56453	−	1.48063i	−0.0835569	−	0.0482416i
$943$	39.9742	−	23.0791i	1.30174	−	0.751560i
$944$	−0.970775	−	1.68143i	−0.0315960	−	0.0547259i
$945$	8.58195	−	3.18389i	0.279171	−	0.103572i
$946$	13.0829	−	22.6603i	0.425363	−	0.736750i
$947$	41.6303	+	24.0353i	1.35280	+	0.781042i	0.988641	−	0.150294i	$-0.0480219\pi$
$947$	41.6303	+	24.0353i	1.35280	+	0.781042i	0.364163	+	0.931335i	$0.381355\pi$
$948$			0.0220538i			0.000716275i
$949$	−0.986752	−	1.70910i	−0.0320313	−	0.0554799i
$950$	7.41858	−	21.1955i	0.240691	−	0.687674i
$951$	−22.0772			−0.715903
$952$		−	7.74243i		−	0.250934i
$953$	−16.5917	−	9.57922i	−0.537458	−	0.310301i	0.206590	−	0.978428i	$-0.433763\pi$
$953$	−16.5917	−	9.57922i	−0.537458	−	0.310301i	−0.744048	+	0.668126i	$0.767097\pi$
$954$	6.25956			0.202661
$955$	4.89066	−	28.7772i	0.158258	−	0.931209i
$956$	−17.7455			−0.573932
$957$	16.2139	−	9.36111i	0.524122	−	0.302602i
$958$	4.82778	−	2.78732i	0.155979	−	0.0900542i
$959$	10.2328	+	17.7237i	0.330433	+	0.572327i
$960$	6.17208	+	16.6364i	0.199203	+	0.536937i
$961$	−8.78046			−0.283241
$962$	34.2995	−	11.7291i	1.10586	−	0.378161i
$963$			17.4181i			0.561292i
$964$	−4.56566	+	7.90796i	−0.147050	+	0.254698i
$965$	52.6616	+	8.94979i	1.69524	+	0.288104i
$966$	12.4490	+	21.5623i	0.400539	+	0.693754i
$967$	−50.8665	+	29.3678i	−1.63576	+	0.944405i	−0.653486	+	0.756939i	$0.726694\pi$
$967$	−50.8665	+	29.3678i	−1.63576	+	0.944405i	−0.982271	+	0.187466i	$0.939973\pi$
$968$		−	18.2556i		−	0.586757i
$969$	1.29052	+	2.23525i	0.0414575	+	0.0718064i
$970$	−9.58288	−	7.94039i	−0.307688	−	0.254951i
$971$	−4.88491	+	8.46092i	−0.156764	+	0.271524i	−0.933700	−	0.358056i	$-0.883440\pi$
$971$	−4.88491	+	8.46092i	−0.156764	+	0.271524i	0.776936	+	0.629580i	$0.216773\pi$
$972$		−	0.841931i		−	0.0270049i
$973$			24.9270i			0.799121i
$974$	2.16807	−	3.75521i	0.0694694	−	0.120325i
$975$	20.9888	−	18.0593i	0.672180	−	0.578362i
$976$	−13.3012			−0.425761
$977$	−26.7956	−	15.4705i	−0.857269	−	0.494944i	0.00582801	−	0.999983i	$-0.498145\pi$
$977$	−26.7956	−	15.4705i	−0.857269	−	0.494944i	−0.863097	+	0.505039i	$0.831478\pi$
$978$	14.1470	+	8.16778i	0.452371	+	0.261177i
$979$	−5.40320	+	9.35862i	−0.172687	+	0.299103i
$980$	3.07773	−	18.1097i	0.0983145	−	0.578495i
$981$	6.57599	+	11.3900i	0.209955	+	0.363653i
$982$	−25.0092	−	14.4390i	−0.798074	−	0.460768i
$983$	22.4959	+	12.9880i	0.717506	+	0.414252i	0.813834	−	0.581097i	$-0.197376\pi$
$983$	22.4959	+	12.9880i	0.717506	+	0.414252i	−0.0963278	+	0.995350i	$0.530710\pi$
$984$	12.4884	−	21.6306i	0.398116	−	0.689557i
$985$	23.5310	−	28.3985i	0.749760	−	0.904850i
$986$	−2.77760	−	4.81094i	−0.0884567	−	0.153211i
$987$	−5.07036	−	2.92738i	−0.161391	−	0.0931794i
$988$			19.4586i			0.619061i
$989$	−61.2692			−1.94825
$990$	1.87733	+	5.06021i	0.0596656	+	0.160824i
$991$	4.90155			0.155703			0.0778514	−	0.996965i	$-0.475194\pi$
$991$	4.90155			0.155703			0.0778514	+	0.996965i	$0.475194\pi$
$992$	−17.9085	+	10.3395i	−0.568597	+	0.328280i
$993$		−	12.4455i		−	0.394946i
$994$	−18.2933	−	31.6850i	−0.580229	−	1.00499i
$995$	−9.15834	+	53.8888i	−0.290339	+	1.70839i
$996$	4.77287	+	8.26685i	0.151234	+	0.261945i
$997$	20.9005	+	12.0669i	0.661927	+	0.382164i	0.793011	−	0.609208i	$-0.208512\pi$
$997$	20.9005	+	12.0669i	0.661927	+	0.382164i	−0.131084	+	0.991371i	$0.541846\pi$
$998$			4.98491i			0.157795i
$999$	−1.96817	−	5.75555i	−0.0622701	−	0.182097i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	555.2.bb.a.454.14	✓	72
5.4	even	2	inner	555.2.bb.a.454.23	yes	72
37.26	even	3	inner	555.2.bb.a.544.23	yes	72
185.174	even	6	inner	555.2.bb.a.544.14	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
555.2.bb.a.454.14	✓	72	1.1	even	1	trivial
555.2.bb.a.454.23	yes	72	5.4	even	2	inner
555.2.bb.a.544.14	yes	72	185.174	even	6	inner
555.2.bb.a.544.23	yes	72	37.26	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 555 = 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	555.bb (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.931961 - 0.538068i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.420965 - 0.729134i) q^{4} +(-0.374645 + 2.20446i) q^{5} +1.07614 q^{6} +(-3.54514 + 2.04679i) q^{7} +3.05830i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.931961 - 0.538068i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.420965 - 0.729134i) q^{4} +(-0.374645 + 2.20446i) q^{5} +1.07614 q^{6} +(-3.54514 + 2.04679i) q^{7} +3.05830i q^{8} +(0.500000 - 0.866025i) q^{9} +(1.53530 - 1.85289i) q^{10} -2.24295 q^{11} +(0.729134 + 0.420965i) q^{12} +(4.79584 - 2.76888i) q^{13} +4.40525 q^{14} +(-0.777777 - 2.09644i) q^{15} +(0.803645 - 1.39195i) q^{16} +(0.535580 + 0.309217i) q^{17} +(-0.931961 + 0.538068i) q^{18} +(-2.08675 - 3.61436i) q^{19} +(1.76506 - 0.654835i) q^{20} +(2.04679 - 3.54514i) q^{21} +(2.09034 + 1.20686i) q^{22} -5.65188i q^{23} +(-1.52915 - 2.64857i) q^{24} +(-4.71928 - 1.65178i) q^{25} -5.95938 q^{26} +1.00000i q^{27} +(2.98477 + 1.72326i) q^{28} +8.34715 q^{29} +(-0.403169 + 2.37230i) q^{30} -4.71376 q^{31} +(3.79921 - 2.19347i) q^{32} +(1.94245 - 1.12147i) q^{33} +(-0.332760 - 0.576357i) q^{34} +(-3.18389 - 8.58195i) q^{35} -0.841931 q^{36} +(-5.75555 + 1.96817i) q^{37} +4.49126i q^{38} +(-2.76888 + 4.79584i) q^{39} +(-6.74191 - 1.14578i) q^{40} +(4.08344 + 7.07273i) q^{41} +(-3.81506 + 2.20262i) q^{42} -10.8405i q^{43} +(0.944203 + 1.63541i) q^{44} +(1.72180 + 1.42668i) q^{45} +(-3.04110 + 5.26734i) q^{46} -1.43023i q^{47} +1.60729i q^{48} +(4.87870 - 8.45015i) q^{49} +(3.50942 + 4.07869i) q^{50} -0.618434 q^{51} +(-4.03777 - 2.33121i) q^{52} +(-5.03741 - 2.90835i) q^{53} +(0.538068 - 0.931961i) q^{54} +(0.840310 - 4.94448i) q^{55} +(-6.25971 - 10.8421i) q^{56} +(3.61436 + 2.08675i) q^{57} +(-7.77922 - 4.49134i) q^{58} +(0.603982 - 1.04613i) q^{59} +(-1.20117 + 1.44963i) q^{60} +(-4.13777 - 7.16683i) q^{61} +(4.39304 + 2.53632i) q^{62} +4.09358i q^{63} -7.93553 q^{64} +(4.30714 + 11.6096i) q^{65} -2.41372 q^{66} +(12.1932 - 7.03977i) q^{67} -0.520679i q^{68} +(2.82594 + 4.89467i) q^{69} +(-1.65041 + 9.71119i) q^{70} +(-4.15262 - 7.19255i) q^{71} +(2.64857 + 1.52915i) q^{72} -0.356372i q^{73} +(6.42296 + 1.26262i) q^{74} +(4.91291 - 0.929156i) q^{75} +(-1.75690 + 3.04304i) q^{76} +(7.95157 - 4.59084i) q^{77} +(5.16098 - 2.97969i) q^{78} +(0.0130972 + 0.0226850i) q^{79} +(2.76743 + 2.29309i) q^{80} +(-0.500000 - 0.866025i) q^{81} -8.78868i q^{82} +(9.81892 + 5.66896i) q^{83} -3.44651 q^{84} +(-0.882309 + 1.06482i) q^{85} +(-5.83293 + 10.1029i) q^{86} +(-7.22885 + 4.17358i) q^{87} -6.85961i q^{88} +(2.40898 - 4.17247i) q^{89} +(-0.836994 - 2.25606i) q^{90} +(-11.3346 + 19.6322i) q^{91} +(-4.12098 + 2.37925i) q^{92} +(4.08224 - 2.35688i) q^{93} +(-0.769560 + 1.33292i) q^{94} +(8.74951 - 3.24606i) q^{95} +(-2.19347 + 3.79921i) q^{96} -5.17187i q^{97} +(-9.09351 + 5.25014i) q^{98} +(-1.12147 + 1.94245i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 32 q^{4} - 2 q^{5} + 36 q^{9}+O(q^{10}) \) 72 * q + 32 * q^4 - 2 * q^5 + 36 * q^9	\( 72 q + 32 q^{4} - 2 q^{5} + 36 q^{9} - 8 q^{11} - 16 q^{14} - 24 q^{16} + 4 q^{19} + 4 q^{20} + 12 q^{21} + 10 q^{25} + 24 q^{26} + 16 q^{29} + 12 q^{30} + 24 q^{31} - 44 q^{34} - 2 q^{35} + 64 q^{36} - 8 q^{39} + 46 q^{40} - 48 q^{41} - 8 q^{44} - 4 q^{45} - 64 q^{46} + 32 q^{49} - 46 q^{50} - 8 q^{51} - 12 q^{55} - 72 q^{56} + 32 q^{59} - 68 q^{60} - 8 q^{61} - 136 q^{64} - 42 q^{65} - 32 q^{66} - 4 q^{69} + 4 q^{70} + 12 q^{71} - 96 q^{74} - 8 q^{75} + 8 q^{76} - 8 q^{79} - 44 q^{80} - 36 q^{81} + 136 q^{84} + 4 q^{85} + 8 q^{86} + 8 q^{91} - 28 q^{94} + 18 q^{95} - 20 q^{96} - 4 q^{99}+O(q^{100}) \) 72 * q + 32 * q^4 - 2 * q^5 + 36 * q^9 - 8 * q^11 - 16 * q^14 - 24 * q^16 + 4 * q^19 + 4 * q^20 + 12 * q^21 + 10 * q^25 + 24 * q^26 + 16 * q^29 + 12 * q^30 + 24 * q^31 - 44 * q^34 - 2 * q^35 + 64 * q^36 - 8 * q^39 + 46 * q^40 - 48 * q^41 - 8 * q^44 - 4 * q^45 - 64 * q^46 + 32 * q^49 - 46 * q^50 - 8 * q^51 - 12 * q^55 - 72 * q^56 + 32 * q^59 - 68 * q^60 - 8 * q^61 - 136 * q^64 - 42 * q^65 - 32 * q^66 - 4 * q^69 + 4 * q^70 + 12 * q^71 - 96 * q^74 - 8 * q^75 + 8 * q^76 - 8 * q^79 - 44 * q^80 - 36 * q^81 + 136 * q^84 + 4 * q^85 + 8 * q^86 + 8 * q^91 - 28 * q^94 + 18 * q^95 - 20 * q^96 - 4 * q^99

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