LMFDB - Embedded newform 55.2.j.a.9.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [55,2,Mod(4,55)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(55, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 2]))

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

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

chi := DirichletCharacter("55.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 55 = 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	55.j (of order $10$, degree $4$, 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:	$0.439177211117$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 7x^{14} + 25x^{12} - 57x^{10} + 194x^{8} - 303x^{6} + 235x^{4} - 33x^{2} + 121 $ x^16 - 7x^14 + 25x^12 - 57x^10 + 194x^8 - 303x^6 + 235x^4 - 33*x^2 + 121
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			9.1
Root			$-0.972539 - 1.33858i$ of defining polynomial
Character	$\chi$	$=$	55.9
Dual form			55.2.j.a.49.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.57360 - 0.511294i) q^{2} +(1.16075 + 1.59764i) q^{3} +(0.596764 + 0.433574i) q^{4} +(1.09069 + 1.95203i) q^{5} +(-1.00970 - 3.10753i) q^{6} +(1.31845 - 1.81468i) q^{7} +(1.22769 + 1.68978i) q^{8} +(-0.278050 + 0.855749i) q^{9} +(-0.718246 - 3.62937i) q^{10} +(-3.27115 - 0.547326i) q^{11} +1.45668i q^{12} +(-3.51868 - 1.14329i) q^{13} +(-3.00254 + 2.18148i) q^{14} +(-1.85261 + 4.00834i) q^{15} +(-1.52381 - 4.68982i) q^{16} +(-2.11573 + 0.687441i) q^{17} +(0.875078 - 1.20444i) q^{18} +(4.27714 - 3.10753i) q^{19} +(-0.195466 + 1.63779i) q^{20} +4.42960 q^{21} +(4.86764 + 2.53379i) q^{22} -3.85415i q^{23} +(-1.27460 + 3.92282i) q^{24} +(-2.62081 + 4.25810i) q^{25} +(4.95244 + 3.59816i) q^{26} +(3.94448 - 1.28164i) q^{27} +(1.57360 - 0.511294i) q^{28} +(0.152450 + 0.110762i) q^{29} +(4.96471 - 5.36029i) q^{30} +(0.212253 - 0.653249i) q^{31} +3.98166i q^{32} +(-2.92256 - 5.86142i) q^{33} +3.68079 q^{34} +(4.98032 + 0.594387i) q^{35} +(-0.536960 + 0.390125i) q^{36} +(-1.52422 + 2.09791i) q^{37} +(-8.31938 + 2.70313i) q^{38} +(-2.25775 - 6.94864i) q^{39} +(-1.95946 + 4.23950i) q^{40} +(-6.40421 + 4.65293i) q^{41} +(-6.97041 - 2.26482i) q^{42} +8.41368i q^{43} +(-1.71480 - 1.74491i) q^{44} +(-1.97371 + 0.390594i) q^{45} +(-1.97060 + 6.06490i) q^{46} +(-7.06117 - 9.71886i) q^{47} +(5.72386 - 7.87822i) q^{48} +(0.608337 + 1.87227i) q^{49} +(6.30124 - 5.36054i) q^{50} +(-3.55411 - 2.58222i) q^{51} +(-1.60412 - 2.20788i) q^{52} +(12.0371 + 3.91110i) q^{53} -6.86233 q^{54} +(-2.49941 - 6.98233i) q^{55} +4.68506 q^{56} +(9.92940 + 3.22626i) q^{57} +(-0.183264 - 0.252241i) q^{58} +(-0.278050 - 0.202015i) q^{59} +(-2.84348 + 1.58878i) q^{60} +(0.535643 + 1.64854i) q^{61} +(-0.668004 + 0.919429i) q^{62} +(1.18632 + 1.63283i) q^{63} +(-1.01183 + 3.11409i) q^{64} +(-1.60605 - 8.11552i) q^{65} +(1.60204 + 10.7178i) q^{66} -0.650461i q^{67} +(-1.56065 - 0.507084i) q^{68} +(6.15754 - 4.47371i) q^{69} +(-7.53313 - 3.48174i) q^{70} +(1.43619 + 4.42013i) q^{71} +(-1.78738 + 0.580756i) q^{72} +(-5.20684 + 7.16660i) q^{73} +(3.47116 - 2.52195i) q^{74} +(-9.84499 + 0.755493i) q^{75} +3.89979 q^{76} +(-5.30606 + 5.21449i) q^{77} +12.0888i q^{78} +(2.23551 - 6.88019i) q^{79} +(7.49264 - 8.08965i) q^{80} +(8.80999 + 6.40083i) q^{81} +(12.4567 - 4.04742i) q^{82} +(-3.02593 + 0.983185i) q^{83} +(2.64342 + 1.92056i) q^{84} +(-3.64950 - 3.38017i) q^{85} +(4.30186 - 13.2398i) q^{86} +0.372127i q^{87} +(-3.09111 - 6.19946i) q^{88} -9.92195 q^{89} +(3.30554 + 0.394506i) q^{90} +(-6.71389 + 4.87793i) q^{91} +(1.67106 - 2.30002i) q^{92} +(1.29003 - 0.419156i) q^{93} +(6.14226 + 18.9039i) q^{94} +(10.7310 + 4.95976i) q^{95} +(-6.36125 + 4.62172i) q^{96} +(-2.15710 - 0.700884i) q^{97} -3.25724i q^{98} +(1.37792 - 2.64710i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{4} - 2 q^{5} - 18 q^{6} + 2 q^{9} - 6 q^{11} - 12 q^{14} - 16 q^{15} + 16 q^{16} + 6 q^{19} - 8 q^{20} + 8 q^{21} + 6 q^{24} - 16 q^{25} + 40 q^{26} + 2 q^{29} + 26 q^{30} + 8 q^{31} - 16 q^{34}+ \cdots - 72 q^{99}+O(q^{100}) $ 16 * q - 4 * q^4 - 2 * q^5 - 18 * q^6 + 2 * q^9 - 6 * q^11 - 12 * q^14 - 16 * q^15 + 16 * q^16 + 6 * q^19 - 8 * q^20 + 8 * q^21 + 6 * q^24 - 16 * q^25 + 40 * q^26 + 2 * q^29 + 26 * q^30 + 8 * q^31 - 16 * q^34 + 22 * q^35 + 10 * q^36 + 30 * q^39 + 12 * q^40 - 52 * q^41 + 4 * q^44 + 12 * q^45 - 62 * q^46 - 10 * q^49 + 28 * q^50 - 42 * q^51 - 40 * q^54 - 8 * q^55 - 20 * q^56 + 2 * q^59 - 32 * q^60 - 40 * q^61 - 8 * q^64 - 40 * q^65 + 58 * q^66 + 26 * q^69 - 34 * q^70 + 36 * q^71 + 48 * q^74 - 20 * q^75 + 56 * q^76 + 38 * q^79 + 34 * q^80 + 68 * q^81 + 12 * q^84 + 58 * q^85 + 22 * q^86 + 24 * q^89 + 78 * q^90 - 20 * q^91 + 14 * q^94 + 48 * q^95 - 86 * q^96 - 72 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/55\mathbb{Z}\right)^\times$.

$n$	$12$	$46$
$\chi(n)$	$-1$	$e\left(\frac{3}{5}\right)$

Coefficient data

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

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

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

$2$	−1.57360	−	0.511294i	−1.11270	−	0.361539i	−0.305725	−	0.952120i	$-0.598899\pi$
$2$	−1.57360	−	0.511294i	−1.11270	−	0.361539i	−0.806979	+	0.590581i	$0.798899\pi$
$3$	1.16075	+	1.59764i	0.670160	+	0.922396i	0.999764	−	0.0217231i	$-0.00691523\pi$
$3$	1.16075	+	1.59764i	0.670160	+	0.922396i	−0.329604	+	0.944119i	$0.606915\pi$
$4$	0.596764	+	0.433574i	0.298382	+	0.216787i
$5$	1.09069	+	1.95203i	0.487770	+	0.872972i
$5$	1.09069	+	1.95203i	0.487770	+	0.872972i
$6$	−1.00970	−	3.10753i	−0.412207	−	1.26864i
$7$	1.31845	−	1.81468i	0.498326	−	0.685886i	−0.483571	−	0.875305i	$-0.660660\pi$
$7$	1.31845	−	1.81468i	0.498326	−	0.685886i	0.981896	+	0.189419i	$0.0606604\pi$
$8$	1.22769	+	1.68978i	0.434055	+	0.597426i
$9$	−0.278050	+	0.855749i	−0.0926832	+	0.285250i
$10$	−0.718246	−	3.62937i	−0.227129	−	1.14771i
$11$	−3.27115	−	0.547326i	−0.986289	−	0.165025i
$11$	−3.27115	−	0.547326i	−0.986289	−	0.165025i
$12$			1.45668i			0.420508i
$13$	−3.51868	−	1.14329i	−0.975906	−	0.317091i	−0.222708	−	0.974885i	$-0.571490\pi$
$13$	−3.51868	−	1.14329i	−0.975906	−	0.317091i	−0.753198	+	0.657794i	$0.771490\pi$
$14$	−3.00254	+	2.18148i	−0.802464	+	0.583024i
$15$	−1.85261	+	4.00834i	−0.478342	+	1.03495i
$16$	−1.52381	−	4.68982i	−0.380954	−	1.17245i
$17$	−2.11573	+	0.687441i	−0.513139	+	0.166729i	−0.554129	−	0.832431i	$-0.686949\pi$
$17$	−2.11573	+	0.687441i	−0.513139	+	0.166729i	0.0409903	+	0.999160i	$0.486949\pi$
$18$	0.875078	−	1.20444i	0.206258	−	0.283890i
$19$	4.27714	−	3.10753i	0.981244	−	0.712916i	0.0232580	−	0.999729i	$-0.492596\pi$
$19$	4.27714	−	3.10753i	0.981244	−	0.712916i	0.957986	+	0.286814i	$0.0925961\pi$
$20$	−0.195466	+	1.63779i	−0.0437074	+	0.366221i
$21$	4.42960			0.966617
$22$	4.86764	+	2.53379i	1.03778	+	0.540206i
$23$		−	3.85415i		−	0.803647i	−0.915717	−	0.401823i	$-0.868377\pi$
$23$		−	3.85415i		−	0.803647i	0.915717	−	0.401823i	$-0.131623\pi$
$24$	−1.27460	+	3.92282i	−0.260177	+	0.800742i
$25$	−2.62081	+	4.25810i	−0.524161	+	0.851619i
$26$	4.95244	+	3.59816i	0.971253	+	0.705657i
$27$	3.94448	−	1.28164i	0.759116	−	0.246652i
$28$	1.57360	−	0.511294i	0.297383	−	0.0966255i
$29$	0.152450	+	0.110762i	0.0283093	+	0.0205679i	0.601850	−	0.798609i	$-0.294431\pi$
$29$	0.152450	+	0.110762i	0.0283093	+	0.0205679i	−0.573541	+	0.819177i	$0.694431\pi$
$30$	4.96471	−	5.36029i	0.906428	−	0.978651i
$31$	0.212253	−	0.653249i	0.0381218	−	0.117327i	−0.930185	−	0.367092i	$-0.880353\pi$
$31$	0.212253	−	0.653249i	0.0381218	−	0.117327i	0.968306	+	0.249765i	$0.0803534\pi$
$32$			3.98166i			0.703866i
$33$	−2.92256	−	5.86142i	−0.508753	−	1.02034i
$34$	3.68079			0.631251
$35$	4.98032	+	0.594387i	0.841828	+	0.100470i
$36$	−0.536960	+	0.390125i	−0.0894934	+	0.0650208i
$37$	−1.52422	+	2.09791i	−0.250580	+	0.344894i	−0.915714	−	0.401830i	$-0.868374\pi$
$37$	−1.52422	+	2.09791i	−0.250580	+	0.344894i	0.665134	+	0.746724i	$0.268374\pi$
$38$	−8.31938	+	2.70313i	−1.34958	+	0.438506i
$39$	−2.25775	−	6.94864i	−0.361529	−	1.11267i
$40$	−1.95946	+	4.23950i	−0.309817	+	0.670324i
$41$	−6.40421	+	4.65293i	−1.00017	+	0.726666i	−0.962124	−	0.272611i	$-0.912113\pi$
$41$	−6.40421	+	4.65293i	−1.00017	+	0.726666i	−0.0380448	+	0.999276i	$0.512113\pi$
$42$	−6.97041	−	2.26482i	−1.07556	−	0.349470i
$43$			8.41368i			1.28307i	0.767092	+	0.641537i	$0.221703\pi$
$43$			8.41368i			1.28307i	−0.767092	+	0.641537i	$0.778297\pi$
$44$	−1.71480	−	1.74491i	−0.258515	−	0.263055i
$45$	−1.97371	+	0.390594i	−0.294223	+	0.0582263i
$46$	−1.97060	+	6.06490i	−0.290550	+	0.894220i
$47$	−7.06117	−	9.71886i	−1.02998	−	1.41764i	−0.904965	−	0.425486i	$-0.860103\pi$
$47$	−7.06117	−	9.71886i	−1.02998	−	1.41764i	−0.125012	−	0.992155i	$-0.539897\pi$
$48$	5.72386	−	7.87822i	0.826168	−	1.13712i
$49$	0.608337	+	1.87227i	0.0869053	+	0.267467i
$50$	6.30124	−	5.36054i	0.891130	−	0.758095i
$51$	−3.55411	−	2.58222i	−0.497676	−	0.361582i
$52$	−1.60412	−	2.20788i	−0.222451	−	0.306178i
$53$	12.0371	+	3.91110i	1.65343	+	0.537231i	0.979479	−	0.201549i	$-0.0645974\pi$
$53$	12.0371	+	3.91110i	1.65343	+	0.537231i	0.673947	+	0.738779i	$0.264597\pi$
$54$	−6.86233			−0.933845
$55$	−2.49941	−	6.98233i	−0.337020	−	0.941498i
$56$	4.68506			0.626067
$57$	9.92940	+	3.22626i	1.31518	+	0.427328i
$58$	−0.183264	−	0.252241i	−0.0240638	−	0.0331209i
$59$	−0.278050	−	0.202015i	−0.0361990	−	0.0263001i	0.569539	−	0.821965i	$-0.307122\pi$
$59$	−0.278050	−	0.202015i	−0.0361990	−	0.0263001i	−0.605738	+	0.795664i	$0.707122\pi$
$60$	−2.84348	+	1.58878i	−0.367092	+	0.205111i
$61$	0.535643	+	1.64854i	0.0685821	+	0.211074i	0.979474	−	0.201572i	$-0.0646049\pi$
$61$	0.535643	+	1.64854i	0.0685821	+	0.211074i	−0.910892	+	0.412645i	$0.864605\pi$
$62$	−0.668004	+	0.919429i	−0.0848366	+	0.116768i
$63$	1.18632	+	1.63283i	0.149462	+	0.205717i
$64$	−1.01183	+	3.11409i	−0.126479	+	0.389261i
$65$	−1.60605	−	8.11552i	−0.199206	−	1.00661i
$66$	1.60204	+	10.7178i	0.197197	+	1.31927i
$67$		−	0.650461i		−	0.0794664i	−0.999210	−	0.0397332i	$-0.987349\pi$
$67$		−	0.650461i		−	0.0794664i	0.999210	−	0.0397332i	$-0.0126508\pi$
$68$	−1.56065	−	0.507084i	−0.189256	−	0.0614930i
$69$	6.15754	−	4.47371i	0.741281	−	0.538572i
$70$	−7.53313	−	3.48174i	−0.900381	−	0.416147i
$71$	1.43619	+	4.42013i	0.170444	+	0.524573i	0.999396	−	0.0347464i	$-0.0110624\pi$
$71$	1.43619	+	4.42013i	0.170444	+	0.524573i	−0.828952	+	0.559320i	$0.811062\pi$
$72$	−1.78738	+	0.580756i	−0.210645	+	0.0684427i
$73$	−5.20684	+	7.16660i	−0.609415	+	0.838787i	−0.996529	−	0.0832444i	$-0.973472\pi$
$73$	−5.20684	+	7.16660i	−0.609415	+	0.838787i	0.387115	+	0.922032i	$0.373472\pi$
$74$	3.47116	−	2.52195i	0.403515	−	0.293171i
$75$	−9.84499	+	0.755493i	−1.13680	+	0.0872368i
$76$	3.89979			0.447336
$77$	−5.30606	+	5.21449i	−0.604682	+	0.594246i
$78$			12.0888i			1.36878i
$79$	2.23551	−	6.88019i	0.251514	−	0.774082i	−0.742982	−	0.669311i	$-0.766589\pi$
$79$	2.23551	−	6.88019i	0.251514	−	0.774082i	0.994496	−	0.104770i	$-0.0334108\pi$
$80$	7.49264	−	8.08965i	0.837703	−	0.904450i
$81$	8.80999	+	6.40083i	0.978888	+	0.711203i
$82$	12.4567	−	4.04742i	1.37561	−	0.446963i
$83$	−3.02593	+	0.983185i	−0.332139	+	0.107919i	−0.470339	−	0.882486i	$-0.655868\pi$
$83$	−3.02593	+	0.983185i	−0.332139	+	0.107919i	0.138200	+	0.990404i	$0.455868\pi$
$84$	2.64342	+	1.92056i	0.288421	+	0.209550i
$85$	−3.64950	−	3.38017i	−0.395844	−	0.366631i
$86$	4.30186	−	13.2398i	0.463882	−	1.42768i
$87$			0.372127i			0.0398962i
$88$	−3.09111	−	6.19946i	−0.329514	−	0.660865i
$89$	−9.92195			−1.05172			−0.525862	−	0.850570i	$-0.676257\pi$
$89$	−9.92195			−1.05172			−0.525862	+	0.850570i	$0.676257\pi$
$90$	3.30554	+	0.394506i	0.348434	+	0.0415846i
$91$	−6.71389	+	4.87793i	−0.703807	+	0.511346i
$92$	1.67106	−	2.30002i	0.174220	−	0.239793i
$93$	1.29003	−	0.419156i	0.133770	−	0.0434644i
$94$	6.14226	+	18.9039i	0.633526	+	1.94979i
$95$	10.7310	+	4.95976i	1.10098	+	0.508860i
$96$	−6.36125	+	4.62172i	−0.649243	+	0.471703i
$97$	−2.15710	−	0.700884i	−0.219020	−	0.0711640i	0.197451	−	0.980313i	$-0.436734\pi$
$97$	−2.15710	−	0.700884i	−0.219020	−	0.0711640i	−0.416472	+	0.909149i	$0.636734\pi$
$98$		−	3.25724i		−	0.329031i
$99$	1.37792	−	2.64710i	0.138486	−	0.266044i
$100$	−3.41020	+	1.40476i	−0.341020	+	0.140476i
$101$	3.05830	−	9.41247i	0.304312	−	0.936576i	−0.675621	−	0.737249i	$-0.736124\pi$
$101$	3.05830	−	9.41247i	0.304312	−	0.936576i	0.979933	−	0.199327i	$-0.0638756\pi$
$102$	4.27249	+	5.88057i	0.423039	+	0.582263i
$103$	6.01958	−	8.28525i	0.593127	−	0.816370i	−0.401930	−	0.915670i	$-0.631661\pi$
$103$	6.01958	−	8.28525i	0.593127	−	0.816370i	0.995057	+	0.0993007i	$0.0316606\pi$
$104$	−2.38796	−	7.34938i	−0.234159	−	0.720666i
$105$	4.83130	+	8.64668i	0.471487	+	0.843830i
$106$	−16.9419	−	12.3090i	−1.64554	−	1.19556i
$107$	5.90536	+	8.12803i	0.570893	+	0.785767i	0.992660	−	0.120937i	$-0.0385900\pi$
$107$	5.90536	+	8.12803i	0.570893	+	0.785767i	−0.421767	+	0.906704i	$0.638590\pi$
$108$	2.90961	+	0.945389i	0.279977	+	0.0909701i
$109$	8.80173			0.843053			0.421527	−	0.906816i	$-0.361494\pi$
$109$	8.80173			0.843053			0.421527	+	0.906816i	$0.361494\pi$
$110$	0.363043	+	12.2653i	0.0346148	+	1.16945i
$111$	−5.12094			−0.486058
$112$	−10.5196	−	3.41803i	−0.994010	−	0.322973i
$113$	−0.135985	−	0.187168i	−0.0127924	−	0.0176073i	0.802573	−	0.596554i	$-0.203464\pi$
$113$	−0.135985	−	0.187168i	−0.0127924	−	0.0176073i	−0.815365	+	0.578947i	$0.803464\pi$
$114$	−13.9753	−	10.1537i	−1.30891	−	0.950980i
$115$	7.52341	−	4.20367i	0.701561	−	0.391995i
$116$	0.0429534	+	0.132197i	0.00398812	+	0.0122742i
$117$	1.95673	−	2.69321i	0.180900	−	0.248988i
$118$	0.334250	+	0.460056i	0.0307702	+	0.0423516i
$119$	−1.54198	+	4.74573i	−0.141353	+	0.435040i
$120$	−9.04763	+	1.79051i	−0.825932	+	0.163451i
$121$	10.4009	+	3.58078i	0.945533	+	0.325525i
$122$		−	2.86801i		−	0.259658i
$123$	−14.8674	−	4.83071i	−1.34055	−	0.435570i
$124$	0.409897	−	0.297808i	0.0368098	−	0.0267439i
$125$	−11.1704	−	0.471632i	−0.999110	−	0.0421840i
$126$	−1.03194	−	3.17598i	−0.0919324	−	0.282939i
$127$	−2.31140	+	0.751018i	−0.205103	+	0.0666421i	−0.409767	−	0.912190i	$-0.634390\pi$
$127$	−2.31140	+	0.751018i	−0.205103	+	0.0666421i	0.204664	+	0.978832i	$0.434390\pi$
$128$	7.86516	−	10.8255i	0.695188	−	0.956844i
$129$	−13.4420	+	9.76619i	−1.18350	+	0.859865i
$130$	−1.62214	+	13.5917i	−0.142271	+	1.19207i
$131$	1.58846			0.138785			0.0693924	−	0.997589i	$-0.477894\pi$
$131$	1.58846			0.138785			0.0693924	+	0.997589i	$0.477894\pi$
$132$	0.797281	−	4.76503i	0.0693944	−	0.414743i
$133$		−	11.8588i		−	1.02829i
$134$	−0.332577	+	1.02357i	−0.0287302	+	0.0884226i
$135$	6.80399	+	6.30186i	0.585594	+	0.542378i
$136$	−3.75909	−	2.73114i	−0.322339	−	0.234193i
$137$	−17.7866	+	5.77920i	−1.51961	+	0.493750i	−0.945664	−	0.325145i	$-0.894587\pi$
$137$	−17.7866	+	5.77920i	−1.51961	+	0.493750i	−0.573943	+	0.818895i	$0.694587\pi$
$138$	−11.9769	+	3.89153i	−1.01954	+	0.331269i
$139$	9.40675	+	6.83441i	0.797870	+	0.579687i	0.910289	−	0.413974i	$-0.135860\pi$
$139$	9.40675	+	6.83441i	0.797870	+	0.579687i	−0.112418	+	0.993661i	$0.535860\pi$
$140$	2.71436	+	2.51405i	0.229406	+	0.212476i
$141$	7.33095	−	22.5624i	0.617378	−	1.90009i
$142$		−	7.68984i		−	0.645317i
$143$	10.8844	+	5.66573i	0.910197	+	0.473792i
$144$	4.43700			0.369750
$145$	−0.0499340	+	0.418393i	−0.00414679	+	0.0347457i
$146$	11.8577	−	8.61514i	0.981352	−	0.712994i
$147$	−2.28508	+	3.14514i	−0.188470	+	0.259407i
$148$	−1.81920	+	0.591094i	−0.149537	+	0.0485876i
$149$	−1.82800	−	5.62600i	−0.149755	−	0.460900i	0.847836	−	0.530258i	$-0.177905\pi$
$149$	−1.82800	−	5.62600i	−0.149755	−	0.460900i	−0.997592	+	0.0693580i	$0.977905\pi$
$150$	15.8784	+	3.84484i	1.29646	+	0.313930i
$151$	−10.3375	+	7.51064i	−0.841254	+	0.611207i	−0.922721	−	0.385469i	$-0.874040\pi$
$151$	−10.3375	+	7.51064i	−0.841254	+	0.611207i	0.0814664	+	0.996676i	$0.474040\pi$
$152$	10.5020	+	3.41232i	0.851828	+	0.276776i
$153$		−	2.00167i		−	0.161826i
$154$	11.0158	−	5.49257i	0.887675	−	0.442604i
$155$	1.50666	−	0.298166i	0.121018	−	0.0239492i
$156$	1.66541	−	5.12560i	0.133339	−	0.410376i
$157$	8.43394	+	11.6083i	0.673102	+	0.926445i	0.999826	−	0.0186749i	$-0.00594475\pi$
$157$	8.43394	+	11.6083i	0.673102	+	0.926445i	−0.326724	+	0.945120i	$0.605945\pi$
$158$	−7.03560	+	9.68367i	−0.559722	+	0.770391i
$159$	7.72359	+	23.7708i	0.612520	+	1.88514i
$160$	−7.77231	+	4.34275i	−0.614455	+	0.343324i
$161$	−6.99407	−	5.08149i	−0.551210	−	0.400478i
$162$	−10.5907	−	14.5768i	−0.832084	−	1.14527i
$163$	−3.44963	−	1.12085i	−0.270196	−	0.0877921i	0.170785	−	0.985308i	$-0.445370\pi$
$163$	−3.44963	−	1.12085i	−0.270196	−	0.0877921i	−0.440982	+	0.897516i	$0.645370\pi$
$164$	−5.83919			−0.455964
$165$	8.25404	−	12.0979i	0.642576	−	0.941820i
$166$	5.26430			0.408589
$167$	3.63370	+	1.18066i	0.281184	+	0.0913623i	0.446214	−	0.894926i	$-0.352772\pi$
$167$	3.63370	+	1.18066i	0.281184	+	0.0913623i	−0.165030	+	0.986289i	$0.552772\pi$
$168$	5.43819	+	7.48502i	0.419565	+	0.577482i
$169$	0.556767	+	0.404515i	0.0428282	+	0.0311165i
$170$	4.01459	+	7.18500i	0.307905	+	0.551065i
$171$	1.47000	+	4.52421i	0.112414	+	0.345975i
$172$	−3.64795	+	5.02098i	−0.278154	+	0.382846i
$173$	−1.23855	−	1.70472i	−0.0941651	−	0.129607i	0.759335	−	0.650700i	$-0.225524\pi$
$173$	−1.23855	−	1.70472i	−0.0941651	−	0.129607i	−0.853500	+	0.521093i	$0.825524\pi$
$174$	0.190266	−	0.585579i	0.0144240	−	0.0443926i
$175$	4.27171	+	10.3700i	0.322911	+	0.783899i
$176$	2.41777	+	16.1751i	0.182246	+	1.21925i
$177$		−	0.678711i		−	0.0510151i
$178$	15.6132	+	5.07303i	1.17026	+	0.380240i
$179$	4.06448	−	2.95302i	0.303793	−	0.220719i	−0.425435	−	0.904989i	$-0.639879\pi$
$179$	4.06448	−	2.95302i	0.303793	−	0.220719i	0.729229	+	0.684270i	$0.239879\pi$
$180$	−1.34719	−	0.622657i	−0.100413	−	0.0464101i
$181$	−4.83538	−	14.8818i	−0.359411	−	1.10615i	−0.953408	−	0.301685i	$-0.902451\pi$
$181$	−4.83538	−	14.8818i	−0.359411	−	1.10615i	0.593997	−	0.804467i	$-0.297549\pi$
$182$	13.0590	−	4.24314i	0.968000	−	0.314522i
$183$	−2.01202	+	2.76931i	−0.148733	+	0.204713i
$184$	6.51265	−	4.73172i	0.480119	−	0.348827i
$185$	−5.75762	−	0.687156i	−0.423309	−	0.0505207i
$186$	−2.24430			−0.164560
$187$	7.29712	−	1.09073i	0.533618	−	0.0797622i
$188$		−	8.86140i		−	0.646284i
$189$	2.87481	−	8.84777i	0.209112	−	0.643580i
$190$	−14.3504	−	13.2914i	−1.04109	−	0.964257i
$191$	−2.52078	−	1.83145i	−0.182397	−	0.132519i	0.492840	−	0.870120i	$-0.335959\pi$
$191$	−2.52078	−	1.83145i	−0.182397	−	0.132519i	−0.675237	+	0.737601i	$0.735959\pi$
$192$	−6.14966	+	1.99815i	−0.443814	+	0.144204i
$193$	9.16474	−	2.97780i	0.659692	−	0.214347i	0.0400095	−	0.999199i	$-0.487261\pi$
$193$	9.16474	−	2.97780i	0.659692	−	0.214347i	0.619683	+	0.784852i	$0.287261\pi$
$194$	3.03606	+	2.20582i	0.217976	+	0.158369i
$195$	11.1014	−	11.9860i	0.794990	−	0.858334i
$196$	−0.448734	+	1.38106i	−0.0320524	+	0.0986472i
$197$		−	14.3974i		−	1.02577i	−0.858457	−	0.512885i	$-0.828577\pi$
$197$		−	14.3974i		−	1.02577i	0.858457	−	0.512885i	$-0.171423\pi$
$198$	−3.52174	+	3.46096i	−0.250279	+	0.245960i
$199$	−14.7978			−1.04899			−0.524493	−	0.851415i	$-0.675745\pi$
$199$	−14.7978			−1.04899			−0.524493	+	0.851415i	$0.675745\pi$
$200$	−10.4128	+	0.799064i	−0.736294	+	0.0565023i
$201$	1.03920	−	0.755023i	0.0732995	−	0.0532552i
$202$	−9.62508	+	13.2478i	−0.677218	+	0.932111i
$203$	0.401995	−	0.130616i	0.0282145	−	0.00916745i
$204$	−1.00138	−	3.08194i	−0.0701109	−	0.215779i
$205$	−16.0676	−	7.42629i	−1.12221	−	0.518675i
$206$	−13.7086	+	9.95989i	−0.955125	+	0.693939i
$207$	3.29819	+	1.07165i	0.229240	+	0.0744845i
$208$			18.2441i			1.26500i
$209$	−15.6920	+	7.82420i	−1.08544	+	0.541211i
$210$	−3.18154	−	16.0766i	−0.219547	−	1.10939i
$211$	−2.09250	+	6.44005i	−0.144054	+	0.443352i	−0.996888	−	0.0788298i	$-0.974882\pi$
$211$	−2.09250	+	6.44005i	−0.144054	+	0.443352i	0.852834	+	0.522181i	$0.174882\pi$
$212$	5.48756	+	7.55299i	0.376888	+	0.518741i
$213$	−5.39471	+	7.42518i	−0.369640	+	0.508765i
$214$	−5.13687	−	15.8097i	−0.351149	−	1.08073i
$215$	−16.4237	+	9.17669i	−1.12009	+	0.625845i
$216$	7.00830	+	5.09183i	0.476854	+	0.346455i
$217$	−0.905596	−	1.24645i	−0.0614759	−	0.0846143i
$218$	−13.8504	−	4.50027i	−0.938069	−	0.304797i
$219$	−17.4935			−1.18210
$220$	1.53580	−	5.25048i	0.103544	−	0.353987i
$221$	8.23051			0.553644
$222$	8.05832	+	2.61831i	0.540839	+	0.175729i
$223$	−5.12388	−	7.05242i	−0.343121	−	0.472265i	0.602229	−	0.798323i	$-0.294279\pi$
$223$	−5.12388	−	7.05242i	−0.343121	−	0.472265i	−0.945350	+	0.326058i	$0.894279\pi$
$224$	7.22547	+	5.24961i	0.482772	+	0.350754i
$225$	−2.91515	−	3.42671i	−0.194343	−	0.228448i
$226$	0.118289	+	0.364056i	0.00786846	+	0.0242166i
$227$	2.23795	−	3.08028i	0.148538	−	0.204445i	−0.728264	−	0.685297i	$-0.759672\pi$
$227$	2.23795	−	3.08028i	0.148538	−	0.204445i	0.876802	+	0.480852i	$0.159672\pi$
$228$	4.52668	+	6.23044i	0.299787	+	0.412621i
$229$	0.838570	−	2.58085i	0.0554142	−	0.170547i	−0.919519	−	0.393046i	$-0.871421\pi$
$229$	0.838570	−	2.58085i	0.0554142	−	0.170547i	0.974933	+	0.222499i	$0.0714213\pi$
$230$	−13.9881	+	2.76823i	−0.922351	+	0.182532i
$231$	−14.4899	−	2.42443i	−0.953364	−	0.159516i
$232$			0.393588i			0.0258403i
$233$	9.99634	+	3.24801i	0.654882	+	0.212784i	0.617566	−	0.786519i	$-0.288119\pi$
$233$	9.99634	+	3.24801i	0.654882	+	0.212784i	0.0373166	+	0.999303i	$0.488119\pi$
$234$	−4.45614	+	3.23758i	−0.291307	+	0.211647i
$235$	11.2699	−	24.3838i	0.735170	−	1.59062i
$236$	−0.0783415	−	0.241110i	−0.00509959	−	0.0156949i
$237$	13.5869	−	4.41466i	0.882565	−	0.286763i
$238$	4.85293	−	6.67948i	0.314569	−	0.432966i
$239$	16.2124	−	11.7790i	1.04869	−	0.761919i	0.0767288	−	0.997052i	$-0.475552\pi$
$239$	16.2124	−	11.7790i	1.04869	−	0.761919i	0.971963	+	0.235133i	$0.0755524\pi$
$240$	21.6214	+	2.58045i	1.39566	+	0.166568i
$241$	28.4450			1.83230			0.916152	−	0.400832i	$-0.131279\pi$
$241$	28.4450			1.83230			0.916152	+	0.400832i	$0.131279\pi$
$242$	−14.5360	−	10.9526i	−0.934408	−	0.704060i
$243$			9.06251i			0.581361i
$244$	−0.395112	+	1.21603i	−0.0252944	+	0.0778483i
$245$	−2.99121	+	3.22955i	−0.191101	+	0.206328i
$246$	20.9254	+	15.2032i	1.33416	+	0.969321i
$247$	−18.6027	+	6.04438i	−1.18366	+	0.384595i
$248$	1.36443	−	0.443329i	0.0866411	−	0.0281514i
$249$	−5.08313	−	3.69311i	−0.322130	−	0.234041i
$250$	17.3366	+	6.45351i	1.09646	+	0.408156i
$251$	−7.36604	+	22.6703i	−0.464940	+	1.43094i	0.394117	+	0.919060i	$0.371050\pi$
$251$	−7.36604	+	22.6703i	−0.464940	+	1.43094i	−0.859058	+	0.511879i	$0.828950\pi$
$252$			1.48877i			0.0937838i
$253$	−2.10948	+	12.6075i	−0.132622	+	0.792628i
$254$	4.02120			0.252313
$255$	1.16412	−	9.75411i	0.0729003	−	0.610826i
$256$	−12.6136	+	9.16432i	−0.788350	+	0.572770i
$257$	14.5044	−	19.9636i	0.904758	−	1.24529i	−0.0641671	−	0.997939i	$-0.520439\pi$
$257$	14.5044	−	19.9636i	0.904758	−	1.24529i	0.968925	−	0.247354i	$-0.0795609\pi$
$258$	26.1458	−	8.49527i	1.62776	−	0.528892i
$259$	1.79744	+	5.53196i	0.111688	+	0.343739i
$260$	2.56025	−	5.53939i	0.158780	−	0.343538i
$261$	−0.137173	+	0.0996619i	−0.00849079	+	0.00616892i
$262$	−2.49961	−	0.812172i	−0.154426	−	0.0501761i
$263$		−	5.44098i		−	0.335505i	−0.985829	−	0.167753i	$-0.946349\pi$
$263$		−	5.44098i		−	0.335505i	0.985829	−	0.167753i	$-0.0536510\pi$
$264$	6.31647	−	12.1345i	0.388752	−	0.746827i
$265$	5.49416	+	27.7625i	0.337504	+	1.70544i
$266$	−6.06332	+	18.6610i	−0.371766	+	1.14418i
$267$	−11.5169	−	15.8517i	−0.704824	−	0.970107i
$268$	0.282023	−	0.388171i	0.0172273	−	0.0237113i
$269$	2.07213	+	6.37738i	0.126340	+	0.388835i	0.994143	−	0.108074i	$-0.0344682\pi$
$269$	2.07213	+	6.37738i	0.126340	+	0.388835i	−0.867803	+	0.496909i	$0.834468\pi$
$270$	−7.48466	−	13.3955i	−0.455502	−	0.815221i
$271$	4.09349	+	2.97409i	0.248662	+	0.180663i	0.705134	−	0.709075i	$-0.250887\pi$
$271$	4.09349	+	2.97409i	0.248662	+	0.180663i	−0.456472	+	0.889738i	$0.650887\pi$
$272$	6.44795	+	8.87484i	0.390964	+	0.538116i
$273$	−15.5863	−	5.06430i	−0.943327	−	0.306505i
$274$	30.9438			1.86938
$275$	10.9036	−	12.4944i	0.657513	−	0.753443i
$276$	5.61428			0.337940
$277$	−10.1703	−	3.30453i	−0.611074	−	0.198550i	−0.0129009	−	0.999917i	$-0.504107\pi$
$277$	−10.1703	−	3.30453i	−0.611074	−	0.198550i	−0.598173	+	0.801367i	$0.704107\pi$
$278$	−11.3081	−	15.5642i	−0.678214	−	0.933481i
$279$	0.500000	+	0.363271i	0.0299342	+	0.0217485i
$280$	5.10993	+	9.14535i	0.305377	+	0.546539i
$281$	−4.23963	−	13.0482i	−0.252915	−	0.778392i	−0.994233	−	0.107238i	$-0.965799\pi$
$281$	−4.23963	−	13.0482i	−0.252915	−	0.778392i	0.741319	−	0.671153i	$-0.234201\pi$
$282$	−23.0720	+	31.7559i	−1.37392	+	1.89103i
$283$	−12.9132	−	17.7735i	−0.767611	−	1.05653i	−0.996543	−	0.0830832i	$-0.973523\pi$
$283$	−12.9132	−	17.7735i	−0.767611	−	1.05653i	0.228932	−	0.973442i	$-0.426477\pi$
$284$	−1.05939	+	3.26047i	−0.0628633	+	0.193473i
$285$	4.53213	+	22.9013i	0.268460	+	1.35655i
$286$	−14.2308	−	14.4807i	−0.841485	−	0.856263i
$287$			17.7563i			1.04812i
$288$	−3.40730	−	1.10710i	−0.200777	−	0.0652365i
$289$	−9.74956	+	7.08347i	−0.573504	+	0.416675i
$290$	0.292498	−	0.632853i	0.0171761	−	0.0371624i
$291$	−1.38410	−	4.25981i	−0.0811372	−	0.249715i
$292$	−6.21450	+	2.01922i	−0.363676	+	0.118166i
$293$	−8.25135	+	11.3570i	−0.482049	+	0.663483i	−0.978897	−	0.204354i	$-0.934491\pi$
$293$	−8.25135	+	11.3570i	−0.482049	+	0.663483i	0.496848	+	0.867837i	$0.334491\pi$
$294$	5.20389	−	3.78085i	0.303497	−	0.220504i
$295$	0.0910732	−	0.763095i	0.00530249	−	0.0444291i
$296$	−5.41627			−0.314815
$297$	−13.6045	+	2.03352i	−0.789412	+	0.117997i
$298$			9.78772i			0.566988i
$299$	−4.40641	+	13.5615i	−0.254829	+	0.784283i
$300$	−6.20270	−	3.81768i	−0.358113	−	0.220414i
$301$	15.2682	+	11.0930i	0.880043	+	0.639389i
$302$	20.1073	−	6.53324i	1.15704	−	0.375946i
$303$	18.5876	−	6.03949i	1.06783	−	0.346960i
$304$	−21.0913	−	15.3237i	−1.20967	−	0.878877i
$305$	−2.63377	+	2.84363i	−0.150809	+	0.162826i
$306$	−1.02344	+	3.14983i	−0.0585064	+	0.180064i
$307$		−	6.86951i		−	0.392064i	−0.980598	−	0.196032i	$-0.937194\pi$
$307$		−	6.86951i		−	0.392064i	0.980598	−	0.196032i	$-0.0628056\pi$
$308$	−5.42733	+	0.811246i	−0.309251	+	0.0462251i
$309$	20.2241			1.15051
$310$	−2.52333	−	0.301152i	−0.143316	−	0.0171043i
$311$	4.45087	−	3.23374i	0.252385	−	0.183369i	−0.454398	−	0.890799i	$-0.650146\pi$
$311$	4.45087	−	3.23374i	0.252385	−	0.183369i	0.706783	+	0.707430i	$0.250146\pi$
$312$	8.96982	−	12.3459i	0.507816	−	0.698949i
$313$	13.5354	−	4.39793i	0.765068	−	0.248586i	0.0996156	−	0.995026i	$-0.468239\pi$
$313$	13.5354	−	4.39793i	0.765068	−	0.248586i	0.665452	+	0.746440i	$0.268239\pi$
$314$	−7.33639	−	22.5791i	−0.414016	−	1.27421i
$315$	−1.89342	+	4.09664i	−0.106682	+	0.230819i
$316$	4.31714	−	3.13659i	0.242858	−	0.176447i
$317$	17.7718	+	5.77442i	0.998166	+	0.324324i	0.762132	−	0.647421i	$-0.224153\pi$
$317$	17.7718	+	5.77442i	0.998166	+	0.324324i	0.236033	+	0.971745i	$0.424153\pi$
$318$		−	41.3547i		−	2.31906i
$319$	−0.438065	−	0.445758i	−0.0245269	−	0.0249577i
$320$	−7.18237	+	1.42138i	−0.401506	+	0.0794575i
$321$	−6.13099	+	18.8693i	−0.342199	+	1.05318i
$322$	8.40774	+	11.5723i	0.468545	+	0.644897i
$323$	−6.91303	+	9.51497i	−0.384651	+	0.529427i
$324$	2.48225	+	7.63957i	0.137903	+	0.424420i
$325$	14.0900	−	11.9865i	0.781573	−	0.664893i
$326$	4.85526	+	3.52755i	0.268908	+	0.195373i
$327$	10.2166	+	14.0620i	0.564981	+	0.777629i
$328$	−15.7248	−	5.10930i	−0.868257	−	0.282114i
$329$	−26.9464			−1.48560
$330$	−19.1741	+	14.8170i	−1.05550	+	0.815650i
$331$	0.468249			0.0257373			0.0128686	−	0.999917i	$-0.495904\pi$
$331$	0.468249			0.0257373			0.0128686	+	0.999917i	$0.495904\pi$
$332$	−2.23205	−	0.725237i	−0.122500	−	0.0398025i
$333$	−1.37148	−	1.88767i	−0.0751564	−	0.103444i
$334$	−5.11433	−	3.71578i	−0.279844	−	0.203318i
$335$	1.26972	−	0.709449i	0.0693720	−	0.0387613i
$336$	−6.74988	−	20.7740i	−0.368236	−	1.13331i
$337$	20.0360	−	27.5771i	1.09143	−	1.50222i	0.245146	−	0.969486i	$-0.421164\pi$
$337$	20.0360	−	27.5771i	1.09143	−	1.50222i	0.846282	−	0.532735i	$-0.178836\pi$
$338$	−0.669303	−	0.921216i	−0.0364053	−	0.0501075i
$339$	0.141181	−	0.434511i	0.00766790	−	0.0235994i
$340$	−0.712333	−	3.59949i	−0.0386317	−	0.195210i
$341$	−1.05185	+	2.02070i	−0.0569611	+	0.109427i
$342$		−	7.87090i		−	0.425610i
$343$	19.1327	+	6.21658i	1.03307	+	0.335664i
$344$	−14.2172	+	10.3294i	−0.766542	+	0.556925i
$345$	15.4487	+	7.14025i	0.831733	+	0.384418i
$346$	1.07737	+	3.31580i	0.0579198	+	0.178259i
$347$	−3.41707	+	1.11027i	−0.183438	+	0.0596026i	−0.399296	−	0.916822i	$-0.630745\pi$
$347$	−3.41707	+	1.11027i	−0.183438	+	0.0596026i	0.215858	+	0.976425i	$0.430745\pi$
$348$	−0.161345	+	0.222072i	−0.00864898	+	0.0119043i
$349$	−5.15433	+	3.74484i	−0.275905	+	0.200457i	−0.717129	−	0.696940i	$-0.754544\pi$
$349$	−5.15433	+	3.74484i	−0.275905	+	0.200457i	0.441224	+	0.897397i	$0.354544\pi$
$350$	−1.41985	−	18.5023i	−0.0758941	−	0.988992i
$351$	−15.3446			−0.819037
$352$	2.17927	−	13.0246i	0.116156	−	0.694215i
$353$			12.1971i			0.649186i	0.945854	+	0.324593i	$0.105227\pi$
$353$			12.1971i			0.649186i	−0.945854	+	0.324593i	$0.894773\pi$
$354$	−0.347021	+	1.06802i	−0.0184440	+	0.0567647i
$355$	−7.06178	+	7.62446i	−0.374800	+	0.404664i
$356$	−5.92106	−	4.30190i	−0.313815	−	0.228000i
$357$	−9.37181	+	3.04509i	−0.496009	+	0.161163i
$358$	−7.90573	+	2.56873i	−0.417831	+	0.135761i
$359$	19.5093	+	14.1744i	1.02966	+	0.748094i	0.968241	−	0.250018i	$-0.0804364\pi$
$359$	19.5093	+	14.1744i	1.02966	+	0.748094i	0.0614222	+	0.998112i	$0.480436\pi$
$360$	−3.08312	−	2.85559i	−0.162495	−	0.150503i
$361$	2.76592	−	8.51262i	0.145575	−	0.448032i
$362$			25.8902i			1.36076i
$363$	6.35204	+	20.7732i	0.333396	+	1.09031i
$364$	−6.12155			−0.320856
$365$	−19.6684	−	2.34737i	−1.02949	−	0.122867i
$366$	4.58205	−	3.32905i	0.239507	−	0.174012i
$367$	−11.9849	+	16.4958i	−0.625606	+	0.861073i	−0.997746	−	0.0671034i	$-0.978624\pi$
$367$	−11.9849	+	16.4958i	−0.625606	+	0.861073i	0.372140	+	0.928177i	$0.378624\pi$
$368$	−18.0753	+	5.87302i	−0.942239	+	0.306152i
$369$	−2.20105	−	6.77414i	−0.114582	−	0.352648i
$370$	8.70886	+	4.02515i	0.452752	+	0.209257i
$371$	22.9677	−	16.6870i	1.19242	−	0.866347i
$372$	0.951577	+	0.309186i	0.0493370	+	0.0160305i
$373$		−	7.51997i		−	0.389369i	−0.980866	−	0.194685i	$-0.937632\pi$
$373$		−	7.51997i		−	0.389369i	0.980866	−	0.194685i	$-0.0623684\pi$
$374$	−12.0404	−	2.01460i	−0.622596	−	0.104172i
$375$	−12.2125	−	18.3937i	−0.630653	−	0.949845i
$376$	7.75374	−	23.8636i	0.399869	−	1.23067i
$377$	−0.409791	−	0.564029i	−0.0211053	−	0.0290490i
$378$	−9.04762	+	12.4530i	−0.465359	+	0.640512i
$379$	−7.16649	−	22.0562i	−0.368118	−	1.13295i	−0.948006	−	0.318254i	$-0.896904\pi$
$379$	−7.16649	−	22.0562i	−0.368118	−	1.13295i	0.579888	−	0.814696i	$-0.303096\pi$
$380$	4.25345	+	7.61248i	0.218197	+	0.390512i
$381$	−3.88281	−	2.82103i	−0.198922	−	0.144526i
$382$	3.03029	+	4.17083i	0.155043	+	0.213398i
$383$	−2.32095	−	0.754123i	−0.118595	−	0.0385339i	0.249118	−	0.968473i	$-0.419859\pi$
$383$	−2.32095	−	0.754123i	−0.118595	−	0.0385339i	−0.367713	+	0.929939i	$0.619859\pi$
$384$	26.4246			1.34848
$385$	−15.9661	−	4.67019i	−0.813706	−	0.238015i
$386$	−15.9442			−0.811537
$387$	−7.20000	−	2.33942i	−0.365997	−	0.118919i
$388$	−0.983393	−	1.35352i	−0.0499242	−	0.0687148i
$389$	27.4849	+	19.9689i	1.39354	+	1.01246i	0.995467	+	0.0951096i	$0.0303201\pi$
$389$	27.4849	+	19.9689i	1.39354	+	1.01246i	0.398071	+	0.917355i	$0.369680\pi$
$390$	−23.5976	+	13.1851i	−1.19491	+	0.667651i
$391$	2.64950	+	8.15434i	0.133991	+	0.412383i
$392$	−2.41686	+	3.32653i	−0.122070	+	0.168015i
$393$	1.84381	+	2.53779i	0.0930080	+	0.128015i
$394$	−7.36129	+	22.6557i	−0.370856	+	1.14138i
$395$	15.8685	−	3.14036i	0.798433	−	0.158009i
$396$	1.97000	−	0.982264i	0.0989964	−	0.0493606i
$397$		−	27.4961i		−	1.37999i	−0.723814	−	0.689995i	$-0.757613\pi$
$397$		−	27.4961i		−	1.37999i	0.723814	−	0.689995i	$-0.242387\pi$
$398$	23.2858	+	7.56601i	1.16721	+	0.379250i
$399$	18.9460	−	13.7651i	0.948487	−	0.689116i
$400$	23.9633	+	5.80256i	1.19817	+	0.290128i
$401$	−0.583247	−	1.79505i	−0.0291259	−	0.0896404i	0.935437	−	0.353494i	$-0.115006\pi$
$401$	−0.583247	−	1.79505i	−0.0291259	−	0.0896404i	−0.964563	+	0.263853i	$0.915006\pi$
$402$	−2.02132	+	0.656768i	−0.100815	+	0.0327566i
$403$	−1.49370	+	2.05591i	−0.0744067	+	0.102412i
$404$	5.90608	−	4.29102i	0.293839	−	0.213486i
$405$	−2.88565	+	24.1786i	−0.143389	+	1.20145i
$406$	−0.699363			−0.0347088
$407$	6.13420	−	6.02834i	0.304061	−	0.298814i
$408$		−	9.17582i		−	0.454271i
$409$	−4.18949	+	12.8939i	−0.207157	+	0.637563i	0.792461	+	0.609923i	$0.208799\pi$
$409$	−4.18949	+	12.8939i	−0.207157	+	0.637563i	−0.999618	+	0.0276408i	$0.991201\pi$
$410$	21.4870	+	19.9013i	1.06117	+	0.982855i
$411$	−29.8788	−	21.7082i	−1.47381	−	1.07079i
$412$	7.18454	−	2.33440i	0.353957	−	0.115008i
$413$	−0.733187	+	0.238227i	−0.0360778	+	0.0117224i
$414$	−4.64210	−	3.37269i	−0.228147	−	0.165758i
$415$	−5.21954	−	4.83435i	−0.256217	−	0.237309i
$416$	4.55219	−	14.0102i	0.223189	−	0.686906i
$417$			22.9616i			1.12444i
$418$	28.6934	−	4.28893i	1.40344	−	0.209779i
$419$	22.1368			1.08145			0.540727	−	0.841198i	$-0.318149\pi$
$419$	22.1368			1.08145			0.540727	+	0.841198i	$0.318149\pi$
$420$	−0.865834	+	7.25475i	−0.0422484	+	0.353996i
$421$	−14.4835	+	10.5229i	−0.705881	+	0.512853i	−0.881842	−	0.471544i	$-0.843697\pi$
$421$	−14.4835	+	10.5229i	−0.705881	+	0.512853i	0.175961	+	0.984397i	$0.443697\pi$
$422$	6.58552	−	9.06419i	0.320578	−	0.441238i
$423$	10.2803	−	3.34026i	0.499843	−	0.162409i
$424$	8.16902	+	25.1417i	0.396723	+	1.22099i
$425$	2.61772	−	10.8106i	0.126978	−	0.524392i
$426$	12.2856	−	8.92599i	0.595238	−	0.432466i
$427$	3.69780	+	1.20149i	0.178949	+	0.0581440i
$428$			7.41093i			0.358221i
$429$	3.58227	+	23.9658i	0.172954	+	1.15708i
$430$	30.5364	−	6.04310i	1.47259	−	0.291424i
$431$	10.3353	−	31.8087i	0.497833	−	1.53217i	−0.314662	−	0.949204i	$-0.601891\pi$
$431$	10.3353	−	31.8087i	0.497833	−	1.53217i	0.812495	−	0.582968i	$-0.198109\pi$
$432$	−12.0213	−	16.5459i	−0.578376	−	0.796066i
$433$	−18.5102	+	25.4771i	−0.889543	+	1.22435i	0.0841428	+	0.996454i	$0.473185\pi$
$433$	−18.5102	+	25.4771i	−0.889543	+	1.22435i	−0.973685	+	0.227897i	$0.926815\pi$
$434$	0.787747	+	2.42443i	0.0378130	+	0.116377i
$435$	−0.726401	+	0.405874i	−0.0348283	+	0.0194602i
$436$	5.25255	+	3.81620i	0.251552	+	0.182763i
$437$	−11.9769	−	16.4848i	−0.572932	−	0.788574i
$438$	27.5277	+	8.94431i	1.31533	+	0.427375i
$439$	−35.6208			−1.70009			−0.850045	−	0.526710i	$-0.823425\pi$
$439$	−35.6208			−1.70009			−0.850045	+	0.526710i	$0.823425\pi$
$440$	8.73007	−	12.7956i	0.416190	−	0.610006i
$441$	−1.77134			−0.0843495
$442$	−12.9515	−	4.20821i	−0.616041	−	0.200164i
$443$	13.8056	+	19.0018i	0.655926	+	0.902805i	0.999338	−	0.0363802i	$-0.0115827\pi$
$443$	13.8056	+	19.0018i	0.655926	+	0.902805i	−0.343412	+	0.939185i	$0.611583\pi$
$444$	−3.05599	−	2.22031i	−0.145031	−	0.105371i
$445$	−10.8217	−	19.3679i	−0.513000	−	0.918126i
$446$	4.45709	+	13.7175i	0.211049	+	0.649543i
$447$	6.86646	−	9.45086i	0.324772	−	0.447011i
$448$	4.31705	+	5.94191i	0.203961	+	0.280729i
$449$	9.70066	−	29.8555i	0.457802	−	1.40897i	−0.410011	−	0.912080i	$-0.634475\pi$
$449$	9.70066	−	29.8555i	0.457802	−	1.40897i	0.867814	−	0.496890i	$-0.165525\pi$
$450$	2.83522	+	6.88277i	0.133653	+	0.324457i
$451$	23.4958	−	11.7152i	1.10637	−	0.551649i
$452$		−	0.170655i		−	0.00802692i
$453$	−23.9985	−	7.79760i	−1.12755	−	0.366363i
$454$	−5.09658	+	3.70288i	−0.239194	+	0.173785i
$455$	−16.8446	−	7.78540i	−0.789687	−	0.364985i
$456$	6.73861	+	20.7393i	0.315564	+	0.971207i
$457$	−37.1964	+	12.0859i	−1.73998	+	0.565352i	−0.994830	−	0.101550i	$-0.967620\pi$
$457$	−37.1964	+	12.0859i	−1.73998	+	0.565352i	−0.745145	+	0.666903i	$0.767620\pi$
$458$	−2.63915	+	3.63247i	−0.123319	+	0.169734i
$459$	−7.46440	+	5.42320i	−0.348408	+	0.253133i
$460$	6.31230	+	0.753355i	0.294312	+	0.0351253i
$461$	−8.88399			−0.413769			−0.206884	−	0.978365i	$-0.566332\pi$
$461$	−8.88399			−0.413769			−0.206884	+	0.978365i	$0.566332\pi$
$462$	21.5617	+	11.2237i	1.00314	+	0.522173i
$463$		−	4.21081i		−	0.195693i	−0.995202	−	0.0978464i	$-0.968805\pi$
$463$		−	4.21081i		−	0.195693i	0.995202	−	0.0978464i	$-0.0311954\pi$
$464$	0.287146	−	0.883744i	0.0133304	−	0.0410268i
$465$	2.22522	+	2.06100i	0.103192	+	0.0955766i
$466$	−14.0696	−	10.2221i	−0.651760	−	0.473531i
$467$	6.39912	−	2.07920i	0.296116	−	0.0962139i	−0.157191	−	0.987568i	$-0.550244\pi$
$467$	6.39912	−	2.07920i	0.296116	−	0.0962139i	0.453307	+	0.891354i	$0.350244\pi$
$468$	2.33542	−	0.758822i	0.107955	−	0.0350766i
$469$	−1.18038	−	0.857597i	−0.0545049	−	0.0396002i
$470$	−30.2017	+	32.6081i	−1.39310	+	1.50410i
$471$	−8.75618	+	26.9487i	−0.403463	+	1.24173i
$472$		−	0.717854i		−	0.0330419i
$473$	4.60503	−	27.5224i	0.211740	−	1.26548i
$474$	−23.6376			−1.08571
$475$	2.02258	+	26.3567i	0.0928025	+	1.20933i
$476$	−2.97782	+	2.16352i	−0.136488	+	0.0991646i
$477$	−6.69383	+	9.21327i	−0.306490	+	0.421847i
$478$	−31.5343	+	10.2461i	−1.44235	+	0.468647i
$479$	−6.43046	−	19.7909i	−0.293815	−	0.904270i	−0.983617	−	0.180272i	$-0.942302\pi$
$479$	−6.43046	−	19.7909i	−0.293815	−	0.904270i	0.689802	−	0.723998i	$-0.257698\pi$
$480$	−15.9599	−	7.37648i	−0.728464	−	0.336689i
$481$	7.76176	−	5.63925i	0.353906	−	0.257128i
$482$	−44.7611	−	14.5437i	−2.03881	−	0.662450i
$483$		−	17.0723i		−	0.776818i
$484$	4.65433	+	6.64642i	0.211560	+	0.302110i
$485$	−0.984576	−	4.97516i	−0.0447073	−	0.225910i
$486$	4.63361	−	14.2608i	0.210185	−	0.646882i
$487$	9.27489	+	12.7658i	0.420285	+	0.578473i	0.965689	−	0.259700i	$-0.0836237\pi$
$487$	9.27489	+	12.7658i	0.420285	+	0.578473i	−0.545404	+	0.838173i	$0.683624\pi$
$488$	−2.12806	+	2.92902i	−0.0963326	+	0.132590i
$489$	−2.21345	−	6.81230i	−0.100096	−	0.308063i
$490$	6.35822	−	3.55263i	0.287235	−	0.160491i
$491$	−15.6386	−	11.3621i	−0.705759	−	0.512764i	0.176044	−	0.984382i	$-0.443670\pi$
$491$	−15.6386	−	11.3621i	−0.705759	−	0.512764i	−0.881803	+	0.471618i	$0.843670\pi$
$492$	−6.77784	−	9.32890i	−0.305569	−	0.420579i
$493$	−0.398685	−	0.129541i	−0.0179559	−	0.00583422i
$494$	32.3637			1.45611
$495$	6.67008	−	0.197429i	0.299798	−	0.00887376i
$496$	−3.38705			−0.152083
$497$	9.91469	+	3.22148i	0.444734	+	0.144503i
$498$	6.11055	+	8.41045i	0.273820	+	0.376881i
$499$	−33.5416	−	24.3694i	−1.50153	−	1.09092i	−0.969769	−	0.244026i	$-0.921532\pi$
$499$	−33.5416	−	24.3694i	−1.50153	−	1.09092i	−0.531758	−	0.846896i	$-0.678468\pi$
$500$	−6.46159	−	5.12464i	−0.288971	−	0.229181i
$501$	2.33156	+	7.17579i	0.104166	+	0.320591i
$502$	23.1824	−	31.9078i	1.03468	−	1.42412i
$503$	−19.1978	−	26.4236i	−0.855990	−	1.17817i	−0.982511	−	0.186205i	$-0.940381\pi$
$503$	−19.1978	−	26.4236i	−0.855990	−	1.17817i	0.126521	−	0.991964i	$-0.459619\pi$
$504$	−1.30268	+	4.00923i	−0.0580259	+	0.178585i
$505$	21.7090	−	4.29618i	0.966039	−	0.191178i
$506$	9.76563	−	18.7606i	0.434135	−	0.834012i
$507$			1.35905i			0.0603576i
$508$	−1.70498	−	0.553981i	−0.0756462	−	0.0245789i
$509$	13.4662	−	9.78379i	0.596881	−	0.433659i	−0.247890	−	0.968788i	$-0.579737\pi$
$509$	13.4662	−	9.78379i	0.596881	−	0.433659i	0.844770	+	0.535129i	$0.179737\pi$
$510$	−6.81908	+	14.7539i	−0.301954	+	0.653312i
$511$	6.14019	+	18.8975i	0.271626	+	0.835978i
$512$	−0.917749	+	0.298195i	−0.0405592	+	0.0131785i
$513$	12.8884	−	17.7393i	0.569036	−	0.783211i
$514$	−33.0313	+	23.9987i	−1.45695	+	1.05854i
$515$	22.7385	+	2.71377i	1.00198	+	0.119583i
$516$	−12.2561			−0.539543
$517$	17.7788	+	35.6566i	0.781909	+	1.56818i
$518$		−	9.62412i		−	0.422860i
$519$	1.28587	−	3.95750i	0.0564434	−	0.173715i
$520$	11.7417	−	12.6772i	0.514906	−	0.555933i
$521$	−11.3717	−	8.26206i	−0.498205	−	0.361967i	0.310126	−	0.950696i	$-0.399629\pi$
$521$	−11.3717	−	8.26206i	−0.498205	−	0.361967i	−0.808331	+	0.588728i	$0.799629\pi$
$522$	0.266812	−	0.0866924i	0.0116780	−	0.00379442i
$523$	−14.9009	+	4.84159i	−0.651570	+	0.211708i	−0.616106	−	0.787663i	$-0.711291\pi$
$523$	−14.9009	+	4.84159i	−0.651570	+	0.211708i	−0.0354635	+	0.999371i	$0.511291\pi$
$524$	0.947937	+	0.688717i	0.0414108	+	0.0300867i
$525$	−11.6091	+	18.8616i	−0.506663	+	0.823189i
$526$	−2.78194	+	8.56194i	−0.121298	+	0.373318i
$527$			1.52801i			0.0665611i
$528$	−23.0356	+	22.6380i	−1.00249	+	0.985193i
$529$	8.14550			0.354152
$530$	5.54920	−	46.4963i	0.241042	−	2.01967i
$531$	0.250186	−	0.181770i	0.0108571	−	0.00788817i
$532$	5.14166	−	7.07689i	0.222919	−	0.306822i
$533$	27.8540	−	9.05031i	1.20649	−	0.392012i
$534$	10.0182	+	30.8327i	0.433528	+	1.33426i
$535$	−9.42523	+	20.3926i	−0.407488	+	0.881647i
$536$	1.09913	−	0.798567i	0.0474753	−	0.0344928i
$537$	9.43570	+	3.06584i	0.407180	+	0.132301i
$538$		−	11.0949i		−	0.478336i
$539$	−0.965221	−	6.45743i	−0.0415750	−	0.278141i
$540$	1.32805	+	6.71075i	0.0571501	+	0.288785i
$541$	−12.2489	+	37.6983i	−0.526623	+	1.62078i	0.234461	+	0.972125i	$0.424667\pi$
$541$	−12.2489	+	37.6983i	−0.526623	+	1.62078i	−0.761084	+	0.648653i	$0.775333\pi$
$542$	−4.92088	−	6.77301i	−0.211370	−	0.290926i
$543$	18.1630	−	24.9992i	0.779448	−	1.07282i
$544$	−2.73716	−	8.42412i	−0.117355	−	0.361181i
$545$	9.59993	+	17.1812i	0.411216	+	0.735962i
$546$	21.9373	+	15.9384i	0.938830	+	0.682100i
$547$	24.1970	+	33.3043i	1.03459	+	1.42399i	0.901445	+	0.432895i	$0.142508\pi$
$547$	24.1970	+	33.3043i	1.03459	+	1.42399i	0.133145	+	0.991097i	$0.457492\pi$
$548$	−13.1201	−	4.26297i	−0.560462	−	0.182105i
$549$	−1.55967			−0.0665651
$550$	−23.5463	+	14.0863i	−1.00402	+	0.600642i
$551$	0.996247			0.0424415
$552$	15.1191	+	4.91251i	0.643513	+	0.209090i
$553$	−9.53798	−	13.1279i	−0.405596	−	0.558255i
$554$	14.3144	+	10.4000i	0.608161	+	0.441855i
$555$	−5.58534	−	9.99621i	−0.237085	−	0.424315i
$556$	2.65039	+	8.15705i	0.112401	+	0.345936i
$557$	−17.5606	+	24.1702i	−0.744069	+	1.02412i	0.254306	+	0.967124i	$0.418153\pi$
$557$	−17.5606	+	24.1702i	−0.744069	+	1.02412i	−0.998374	+	0.0569987i	$0.981847\pi$
$558$	−0.601062	−	0.827291i	−0.0254450	−	0.0350220i
$559$	9.61926	−	29.6050i	0.406851	−	1.25216i
$560$	−4.80152	−	24.2625i	−0.202901	−	1.02528i
$561$	10.2127	+	10.3921i	0.431182	+	0.438754i
$562$			22.7004i			0.957558i
$563$	2.05218	+	0.666795i	0.0864892	+	0.0281021i	0.351942	−	0.936022i	$-0.385521\pi$
$563$	2.05218	+	0.666795i	0.0864892	+	0.0281021i	−0.265453	+	0.964124i	$0.585521\pi$
$564$	14.1573	−	10.2859i	0.596130	−	0.433114i
$565$	0.217039	−	0.469588i	0.00913090	−	0.0197557i
$566$	11.2328	+	34.5709i	0.472148	+	1.45312i
$567$	23.2310	−	7.54820i	0.975610	−	0.316995i
$568$	−5.70583	+	7.85341i	−0.239411	+	0.329522i
$569$	0.580298	−	0.421611i	0.0243274	−	0.0176749i	−0.575555	−	0.817763i	$-0.695214\pi$
$569$	0.580298	−	0.421611i	0.0243274	−	0.0176749i	0.599882	+	0.800088i	$0.295214\pi$
$570$	4.57753	−	38.3547i	0.191731	−	1.60650i
$571$	−21.6311			−0.905235			−0.452617	−	0.891705i	$-0.649510\pi$
$571$	−21.6311			−0.905235			−0.452617	+	0.891705i	$0.649510\pi$
$572$	4.03888	+	8.10029i	0.168874	+	0.338690i
$573$		−	6.15315i		−	0.257051i
$574$	9.07866	−	27.9413i	0.378936	−	1.16625i
$575$	16.4114	+	10.1010i	0.684401	+	0.421240i
$576$	−2.38354	−	1.73174i	−0.0993141	−	0.0721559i
$577$	22.2810	−	7.23952i	0.927568	−	0.301385i	0.194000	−	0.981001i	$-0.437854\pi$
$577$	22.2810	−	7.23952i	0.927568	−	0.301385i	0.733568	+	0.679616i	$0.237854\pi$
$578$	18.9637	−	6.16167i	0.788784	−	0.256291i
$579$	15.3954	+	11.1854i	0.639812	+	0.464851i
$580$	−0.211203	+	0.228032i	−0.00876973	+	0.00946850i
$581$	−2.20536	+	6.78739i	−0.0914936	+	0.281588i
$582$			7.41093i			0.307193i
$583$	−37.2346	−	19.3820i	−1.54210	−	0.802722i
$584$	−18.5023			−0.765633
$585$	7.39140	+	0.882143i	0.305597	+	0.0364721i
$586$	18.7911	−	13.6525i	0.776253	−	0.563981i
$587$	1.32095	−	1.81814i	0.0545216	−	0.0750425i	−0.780886	−	0.624674i	$-0.785232\pi$
$587$	1.32095	−	1.81814i	0.0545216	−	0.0750425i	0.835407	+	0.549632i	$0.185232\pi$
$588$	−2.72730	+	0.886154i	−0.112472	+	0.0365444i
$589$	−1.12215	−	3.45362i	−0.0462374	−	0.142304i
$590$	−0.533479	+	1.15424i	−0.0219630	+	0.0475194i
$591$	23.0018	−	16.7118i	0.946167	−	0.687431i
$592$	12.1615	+	3.95149i	0.499833	+	0.162405i
$593$			25.4034i			1.04319i	0.853193	+	0.521596i	$0.174663\pi$
$593$			25.4034i			1.04319i	−0.853193	+	0.521596i	$0.825337\pi$
$594$	22.4477	+	3.75594i	0.921042	+	0.154108i
$595$	−10.9456	+	2.16612i	−0.448726	+	0.0888022i
$596$	1.34841	−	4.14996i	0.0552328	−	0.169989i
$597$	−17.1765	−	23.6415i	−0.702988	−	0.967580i
$598$	13.8678	−	19.0875i	0.567098	−	0.780544i
$599$	5.63194	+	17.3333i	0.230115	+	0.708220i	0.997732	+	0.0673118i	$0.0214422\pi$
$599$	5.63194	+	17.3333i	0.230115	+	0.708220i	−0.767617	+	0.640909i	$0.778558\pi$
$600$	−13.3633	−	15.7083i	−0.545552	−	0.641289i
$601$	28.0242	+	20.3608i	1.14313	+	0.830533i	0.987552	−	0.157290i	$-0.0502758\pi$
$601$	28.0242	+	20.3608i	1.14313	+	0.830533i	0.155579	+	0.987824i	$0.450276\pi$
$602$	−18.3542	−	25.2625i	−0.748063	−	1.02962i
$603$	0.556631	+	0.180860i	0.0226678	+	0.00736520i
$604$	−9.42547			−0.383517
$605$	4.35432	+	24.2083i	0.177028	+	0.984206i
$606$	−32.3375			−1.31362
$607$	−24.2027	−	7.86394i	−0.982358	−	0.319187i	−0.226564	−	0.973996i	$-0.572749\pi$
$607$	−24.2027	−	7.86394i	−0.982358	−	0.319187i	−0.755794	+	0.654809i	$0.772749\pi$
$608$	12.3731	+	17.0302i	0.501797	+	0.690664i
$609$	0.675293	+	0.490629i	0.0273643	+	0.0198813i
$610$	5.59844	−	3.12810i	0.226674	−	0.126653i
$611$	13.7345	+	42.2705i	0.555639	+	1.71008i
$612$	0.867874	−	1.19453i	0.0350817	−	0.0482858i
$613$	21.7843	+	29.9835i	0.879859	+	1.21102i	0.976460	+	0.215698i	$0.0692027\pi$
$613$	21.7843	+	29.9835i	0.879859	+	1.21102i	−0.0966016	+	0.995323i	$0.530797\pi$
$614$	−3.51234	+	10.8099i	−0.141746	+	0.436251i
$615$	−6.78600	−	34.2903i	−0.273638	−	1.38272i
$616$	−15.3255	−	2.56426i	−0.617483	−	0.103317i
$617$			27.5937i			1.11088i	0.831557	+	0.555439i	$0.187450\pi$
$617$			27.5937i			1.11088i	−0.831557	+	0.555439i	$0.812550\pi$
$618$	−31.8246	−	10.3404i	−1.28017	−	0.415953i
$619$	16.5391	−	12.0164i	0.664764	−	0.482979i	−0.203504	−	0.979074i	$-0.565233\pi$
$619$	16.5391	−	12.0164i	0.664764	−	0.482979i	0.868268	+	0.496095i	$0.165233\pi$
$620$	1.02840	+	0.475315i	0.0413014	+	0.0190891i
$621$	−4.93964	−	15.2026i	−0.198221	−	0.610061i
$622$	−8.65728	+	2.81292i	−0.347125	+	0.112788i
$623$	−13.0816	+	18.0052i	−0.524101	+	0.721364i
$624$	−29.1475	+	21.1769i	−1.16683	+	0.847754i
$625$	−11.2628	−	22.3193i	−0.450510	−	0.892771i
$626$	−23.5480			−0.941167
$627$	−30.7148	−	15.9882i	−1.22663	−	0.638507i
$628$			10.5842i			0.422354i
$629$	1.78265	−	5.48642i	0.0710787	−	0.218758i
$630$	5.07408	−	5.47837i	0.202156	−	0.218264i
$631$	−0.614155	−	0.446210i	−0.0244491	−	0.0177633i	0.575494	−	0.817806i	$-0.304810\pi$
$631$	−0.614155	−	0.446210i	−0.0244491	−	0.0177633i	−0.599943	+	0.800043i	$0.704810\pi$
$632$	14.3705	−	4.66926i	0.571627	−	0.185733i
$633$	−12.7177	+	4.13224i	−0.505485	+	0.164242i
$634$	−25.0133	−	18.1733i	−0.993407	−	0.721752i
$635$	−3.98701	−	3.69278i	−0.158220	−	0.146543i
$636$	−5.69723	+	17.5343i	−0.225910	+	0.695279i
$637$		−	7.28342i		−	0.288579i
$638$	0.461426	+	0.925425i	0.0182680	+	0.0366379i
$639$	−4.18186			−0.165432
$640$	29.7100	+	3.54580i	1.17439	+	0.140160i
$641$	12.0584	−	8.76094i	0.476278	−	0.346037i	−0.323605	−	0.946192i	$-0.604895\pi$
$641$	12.0584	−	8.76094i	0.476278	−	0.346037i	0.799883	+	0.600156i	$0.204895\pi$
$642$	19.2955	−	26.5579i	0.761531	−	1.04816i
$643$	−26.2820	+	8.53955i	−1.03646	+	0.336767i	−0.777342	−	0.629078i	$-0.783432\pi$
$643$	−26.2820	+	8.53955i	−1.03646	+	0.336767i	−0.259120	+	0.965845i	$0.583432\pi$
$644$	−1.97060	−	6.06490i	−0.0776527	−	0.238990i
$645$	−33.7249	−	15.5873i	−1.32792	−	0.613749i
$646$	15.7433	−	11.4382i	0.619411	−	0.450029i
$647$	−23.7560	−	7.71879i	−0.933945	−	0.303457i	−0.197770	−	0.980248i	$-0.563370\pi$
$647$	−23.7560	−	7.71879i	−0.933945	−	0.303457i	−0.736175	+	0.676791i	$0.763370\pi$
$648$			22.7452i			0.893514i
$649$	0.798974	+	0.813005i	0.0313625	+	0.0319132i
$650$	−28.3007	+	11.6579i	−1.11004	+	0.457260i
$651$	0.940197	−	2.89363i	0.0368492	−	0.113410i
$652$	−1.57264	−	2.16456i	−0.0615895	−	0.0847706i
$653$	16.3187	−	22.4607i	0.638599	−	0.878956i	−0.359941	−	0.932975i	$-0.617203\pi$
$653$	16.3187	−	22.4607i	0.638599	−	0.878956i	0.998540	+	0.0540191i	$0.0172032\pi$
$654$	−8.88708	−	27.3516i	−0.347513	−	1.06953i
$655$	1.73252	+	3.10072i	0.0676950	+	0.121155i
$656$	31.5802	+	22.9444i	1.23300	+	0.895827i
$657$	−4.68505	−	6.44842i	−0.182781	−	0.251577i
$658$	42.4029	+	13.7775i	1.65304	+	0.537105i
$659$	21.5863			0.840883			0.420442	−	0.907320i	$-0.361875\pi$
$659$	21.5863			0.840883			0.420442	+	0.907320i	$0.361875\pi$
$660$	10.1710	−	3.64084i	0.395907	−	0.141720i
$661$	−16.0174			−0.623003			−0.311502	−	0.950246i	$-0.600832\pi$
$661$	−16.0174			−0.623003			−0.311502	+	0.950246i	$0.600832\pi$
$662$	−0.736837	−	0.239413i	−0.0286380	−	0.00930504i
$663$	9.55357	+	13.1494i	0.371030	+	0.510679i
$664$	−5.37628	−	3.90609i	−0.208640	−	0.151586i
$665$	23.1486	−	12.9342i	0.897665	−	0.501567i
$666$	1.19300	+	3.67167i	0.0462277	+	0.142274i
$667$	0.426892	−	0.587567i	0.0165293	−	0.0227507i
$668$	1.65656	+	2.28005i	0.0640941	+	0.0882180i
$669$	5.31966	−	16.3722i	0.205670	−	0.632986i
$670$	−2.36076	+	0.467191i	−0.0912042	+	0.0180492i
$671$	−0.849880	−	5.68579i	−0.0328093	−	0.219498i
$672$			17.6372i			0.680368i
$673$	29.8127	+	9.68673i	1.14920	+	0.373396i	0.820840	−	0.571158i	$-0.193506\pi$
$673$	29.8127	+	9.68673i	1.14920	+	0.373396i	0.328355	+	0.944554i	$0.393506\pi$
$674$	−45.6286	+	33.1511i	−1.75755	+	1.27693i
$675$	−4.88038	+	20.1549i	−0.187846	+	0.775763i
$676$	0.156871	+	0.482799i	0.00603350	+	0.0185692i
$677$	−29.1654	+	9.47642i	−1.12092	+	0.364209i	−0.810118	−	0.586267i	$-0.800597\pi$
$677$	−29.1654	+	9.47642i	−1.12092	+	0.364209i	−0.310801	+	0.950475i	$0.600597\pi$
$678$	−0.444325	+	0.611561i	−0.0170642	+	0.0234869i
$679$	−4.11590	+	2.99038i	−0.157954	+	0.114760i
$680$	1.23126	−	10.3166i	0.0472167	−	0.395625i
$681$	7.51888			0.288124
$682$	2.68837	−	2.64198i	0.102943	−	0.101166i
$683$		−	3.27236i		−	0.125213i	−0.998038	−	0.0626066i	$-0.980059\pi$
$683$		−	3.27236i		−	0.125213i	0.998038	−	0.0626066i	$-0.0199414\pi$
$684$	−1.08433	+	3.33724i	−0.0414606	+	0.127602i
$685$	−30.6807	−	28.4165i	−1.17225	−	1.08574i
$686$	−26.9287	−	19.5648i	−1.02814	−	0.746989i
$687$	5.09664	−	1.65600i	0.194449	−	0.0631802i
$688$	39.4586	−	12.8209i	1.50435	−	0.488792i
$689$	−37.8832	−	27.5238i	−1.44324	−	1.04857i
$690$	−20.6594	−	19.1348i	−0.786490	−	0.728448i
$691$	−11.2774	+	34.7084i	−0.429014	+	1.32037i	0.470083	+	0.882622i	$0.344224\pi$
$691$	−11.2774	+	34.7084i	−0.429014	+	1.32037i	−0.899098	+	0.437748i	$0.855776\pi$
$692$		−	1.55431i		−	0.0590862i
$693$	−2.98694	−	5.99054i	−0.113465	−	0.227562i
$694$	5.94478			0.225661
$695$	−3.08111	+	25.8164i	−0.116873	+	0.979272i
$696$	−0.628811	+	0.456858i	−0.0238350	+	0.0173172i
$697$	10.3509	−	14.2468i	0.392070	−	0.539638i
$698$	10.0256	−	3.25750i	0.379473	−	0.123298i
$699$	6.41413	+	19.7407i	0.242605	+	0.746660i
$700$	−1.94696	+	8.04054i	−0.0735883	+	0.303904i
$701$	−37.6684	+	27.3677i	−1.42272	+	1.03366i	−0.431399	+	0.902161i	$0.641980\pi$
$701$	−37.6684	+	27.3677i	−1.42272	+	1.03366i	−0.991316	+	0.131502i	$0.958020\pi$
$702$	24.1463	+	7.84562i	0.911345	+	0.296114i
$703$			13.7096i			0.517068i
$704$	5.01427	−	9.63285i	0.188982	−	0.363052i
$705$	52.0381	−	10.2983i	1.95987	−	0.387855i
$706$	6.23630	−	19.1933i	0.234706	−	0.722351i
$707$	−13.0485	−	17.9597i	−0.490738	−	0.675443i
$708$	0.294272	−	0.405030i	0.0110594	−	0.0152220i
$709$	11.0000	+	33.8544i	0.413112	+	1.27143i	0.913929	+	0.405874i	$0.133033\pi$
$709$	11.0000	+	33.8544i	0.413112	+	1.27143i	−0.500817	+	0.865553i	$0.666967\pi$
$710$	15.0108	−	8.38721i	0.563344	−	0.314766i
$711$	5.26613	+	3.82607i	0.197495	+	0.143489i
$712$	−12.1811	−	16.7659i	−0.456507	−	0.628327i
$713$	−2.51772	−	0.818057i	−0.0942894	−	0.0306365i
$714$	16.3044			0.610178
$715$	0.811789	+	27.4261i	0.0303592	+	1.02568i
$716$	3.70588			0.138495
$717$	37.6371	+	12.2290i	1.40558	+	0.456702i
$718$	−23.4526	−	32.2798i	−0.875245	−	1.20467i
$719$	17.8722	+	12.9849i	0.666522	+	0.484256i	0.868859	−	0.495060i	$-0.164854\pi$
$719$	17.8722	+	12.9849i	0.666522	+	0.484256i	−0.202337	+	0.979316i	$0.564854\pi$
$720$	4.83938	+	8.66114i	0.180353	+	0.322782i
$721$	−7.09862	−	21.8473i	−0.264366	−	0.813636i
$722$	−8.70490	+	11.9813i	−0.323963	+	0.445896i
$723$	33.0176	+	45.4448i	1.22794	+	1.69011i
$724$	3.56677	−	10.9774i	0.132558	−	0.407971i
$725$	−0.871176	+	0.358863i	−0.0323547	+	0.0133278i
$726$	0.625636	−	35.9365i	0.0232195	−	1.33373i
$727$		−	45.5415i		−	1.68904i	−0.535522	−	0.844521i	$-0.679885\pi$
$727$		−	45.5415i		−	1.68904i	0.535522	−	0.844521i	$-0.320115\pi$
$728$	−16.4852	−	5.35637i	−0.610982	−	0.198520i
$729$	11.9514	−	8.68317i	0.442643	−	0.321599i
$730$	29.7500	+	13.7502i	1.10110	+	0.508916i
$731$	−5.78391	−	17.8011i	−0.213926	−	0.658396i
$732$	−2.40140	+	0.780262i	−0.0887583	+	0.0288393i
$733$	6.68835	−	9.20572i	0.247040	−	0.340021i	−0.667432	−	0.744671i	$-0.732607\pi$
$733$	6.68835	−	9.20572i	0.247040	−	0.340021i	0.914472	+	0.404650i	$0.132607\pi$
$734$	27.2936	−	19.8300i	1.00743	−	0.731938i
$735$	−8.63170	−	1.03017i	−0.318385	−	0.0379983i
$736$	15.3459			0.565659
$737$	−0.356014	+	2.12776i	−0.0131140	+	0.0783769i
$738$			11.7852i			0.433818i
$739$	1.34045	−	4.12547i	0.0493091	−	0.151758i	−0.923370	−	0.383911i	$-0.874577\pi$
$739$	1.34045	−	4.12547i	0.0493091	−	0.151758i	0.972679	+	0.232153i	$0.0745770\pi$
$740$	−3.13801	−	2.90643i	−0.115355	−	0.106842i
$741$	−31.2498	−	22.7043i	−1.14799	−	0.834064i
$742$	−44.6740	+	14.5154i	−1.64003	+	0.532879i
$743$	−16.4480	+	5.34429i	−0.603420	+	0.196063i	−0.594765	−	0.803900i	$-0.702755\pi$
$743$	−16.4480	+	5.34429i	−0.603420	+	0.196063i	−0.00865478	+	0.999963i	$0.502755\pi$
$744$	2.29204	+	1.66526i	0.0840302	+	0.0610515i
$745$	8.98832	−	9.70450i	0.329307	−	0.355545i
$746$	−3.84491	+	11.8334i	−0.140772	+	0.433253i
$747$		−	2.86281i		−	0.104745i
$748$	4.82757	+	2.51293i	0.176513	+	0.0918819i
$749$	22.5357			0.823437
$750$	9.81310	+	35.1885i	0.358324	+	1.28490i
$751$	25.4946	−	18.5229i	0.930310	−	0.675910i	−0.0157586	−	0.999876i	$-0.505016\pi$
$751$	25.4946	−	18.5229i	0.930310	−	0.675910i	0.946069	+	0.323966i	$0.105016\pi$
$752$	−34.8198	+	47.9253i	−1.26975	+	1.74766i
$753$	−44.7691	+	14.5464i	−1.63148	+	0.530099i
$754$	0.356463	+	1.09708i	0.0129816	+	0.0399533i
$755$	−25.9359	−	11.9873i	−0.943905	−	0.436263i
$756$	5.55175	−	4.03358i	0.201915	−	0.146700i
$757$	−8.82332	−	2.86687i	−0.320689	−	0.104198i	0.144249	−	0.989541i	$-0.453923\pi$
$757$	−8.82332	−	2.86687i	−0.320689	−	0.104198i	−0.464938	+	0.885343i	$0.653923\pi$
$758$			38.3718i			1.39373i
$759$	−22.5908	+	11.2640i	−0.819995	+	0.408858i
$760$	4.79350	+	24.2220i	0.173879	+	0.878626i
$761$	−1.28492	+	3.95459i	−0.0465784	+	0.143354i	−0.971641	−	0.236461i	$-0.924012\pi$
$761$	−1.28492	+	3.95459i	−0.0465784	+	0.143354i	0.925062	+	0.379815i	$0.124012\pi$
$762$	4.66762	+	6.42442i	0.169090	+	0.232732i
$763$	11.6046	−	15.9724i	0.420115	−	0.578239i
$764$	−0.710238	−	2.18589i	−0.0256955	−	0.0790827i
$765$	3.90732	−	2.18320i	0.141269	−	0.0789337i
$766$	3.26667	+	2.37338i	0.118030	+	0.0857536i
$767$	0.747406	+	1.02872i	0.0269873	+	0.0371448i
$768$	−29.2825	−	9.51446i	−1.05664	−	0.343324i
$769$	−16.8800			−0.608709			−0.304355	−	0.952559i	$-0.598441\pi$
$769$	−16.8800			−0.608709			−0.304355	+	0.952559i	$0.598441\pi$
$770$	22.7364	+	15.5124i	0.819362	+	0.559027i
$771$	48.7305			1.75499
$772$	6.76028	+	2.19655i	0.243308	+	0.0790555i
$773$	4.98301	+	6.85852i	0.179226	+	0.246684i	0.889173	−	0.457572i	$-0.151281\pi$
$773$	4.98301	+	6.85852i	0.179226	+	0.246684i	−0.709946	+	0.704256i	$0.751281\pi$
$774$	10.1338	+	7.36263i	0.364252	+	0.264644i
$775$	2.22532	+	2.61583i	0.0799359	+	0.0939635i
$776$	−1.46392	−	4.50548i	−0.0525517	−	0.161737i
$777$	−6.75168	+	9.29289i	−0.242215	+	0.333381i
$778$	−33.0402	−	45.4759i	−1.18455	−	1.63039i
$779$	−12.9326	+	39.8025i	−0.463359	+	1.42607i
$780$	11.8217	−	2.33950i	0.423286	−	0.0837676i
$781$	−2.27873	−	15.2450i	−0.0815395	−	0.545509i
$782$		−	14.1863i		−	0.507303i
$783$	0.743294	+	0.241511i	0.0265632	+	0.00863089i
$784$	7.85361	−	5.70598i	0.280486	−	0.203785i
$785$	−13.4610	+	29.1243i	−0.480442	+	1.03949i
$786$	−1.60387	−	4.93620i	−0.0572080	−	0.176068i
$787$	50.9924	−	16.5684i	1.81768	−	0.590601i	0.817796	−	0.575508i	$-0.195196\pi$
$787$	50.9924	−	16.5684i	1.81768	−	0.590601i	0.999886	−	0.0150924i	$-0.00480424\pi$
$788$	6.24233	−	8.59183i	0.222374	−	0.306071i
$789$	8.69272	−	6.31563i	0.309469	−	0.224842i
$790$	−26.5764	−	3.17182i	−0.945546	−	0.112848i
$791$	−0.518940			−0.0184514
$792$	6.16466	−	0.921459i	0.219052	−	0.0327426i
$793$		−	6.41307i		−	0.227735i
$794$	−14.0586	+	43.2679i	−0.498921	+	1.53552i
$795$	−37.9771	+	41.0031i	−1.34691	+	1.45423i
$796$	−8.83077	−	6.41593i	−0.312998	−	0.227407i
$797$	27.1477	−	8.82082i	0.961621	−	0.312450i	0.214192	−	0.976792i	$-0.431288\pi$
$797$	27.1477	−	8.82082i	0.961621	−	0.312450i	0.747429	+	0.664342i	$0.231288\pi$
$798$	−36.8515	+	11.9738i	−1.30453	+	0.423867i
$799$	21.6206	+	15.7083i	0.764883	+	0.555720i
$800$	−16.9543	−	10.4352i	−0.599425	−	0.368939i
$801$	2.75879	−	8.49070i	0.0974772	−	0.300004i
$802$			3.12290i			0.110273i
$803$	20.9548	−	20.5932i	0.739480	−	0.726718i
$804$	0.947515			0.0334163
$805$	2.29086	−	19.1949i	0.0807422	−	0.676532i
$806$	3.40166	−	2.47145i	0.119819	−	0.0870532i
$807$	−7.78350	+	10.7131i	−0.273992	+	0.377118i
$808$	19.6596	−	6.38780i	0.691623	−	0.224722i
$809$	−11.4170	−	35.1378i	−0.401399	−	1.23538i	−0.923865	−	0.382718i	$-0.874988\pi$
$809$	−11.4170	−	35.1378i	−0.401399	−	1.23538i	0.522466	−	0.852660i	$-0.325012\pi$
$810$	16.9032	−	36.5721i	0.593919	−	1.28501i
$811$	31.0475	−	22.5573i	1.09022	−	0.792094i	0.110787	−	0.993844i	$-0.464663\pi$
$811$	31.0475	−	22.5573i	1.09022	−	0.792094i	0.979437	+	0.201750i	$0.0646629\pi$
$812$	0.296528	+	0.0963477i	0.0104061	+	0.00338114i
$813$			9.99209i			0.350438i
$814$	−12.7350	+	6.34982i	−0.446363	+	0.222561i
$815$	−1.57453	−	7.95628i	−0.0551535	−	0.278696i
$816$	−6.69431	+	20.6030i	−0.234348	+	0.721248i
$817$	26.1458	+	35.9865i	0.914724	+	1.25901i
$818$	13.1852	−	18.1478i	0.461008	−	0.634524i
$819$	−2.30749	−	7.10171i	−0.0806301	−	0.248154i
$820$	−6.36872	−	11.3982i	−0.222405	−	0.398044i
$821$	8.29214	+	6.02459i	0.289398	+	0.210260i	0.723006	−	0.690842i	$-0.242760\pi$
$821$	8.29214	+	6.02459i	0.289398	+	0.210260i	−0.433608	+	0.901101i	$0.642760\pi$
$822$	35.9181	+	49.4370i	1.25279	+	1.72431i
$823$	23.9948	+	7.79637i	0.836405	+	0.271764i	0.695741	−	0.718293i	$-0.255076\pi$
$823$	23.9948	+	7.79637i	0.836405	+	0.271764i	0.140664	+	0.990057i	$0.455076\pi$
$824$	21.3904			0.745170
$825$	32.6180	+	2.91709i	1.13561	+	0.101560i
$826$	1.27555			0.0443820
$827$	17.4505	+	5.67001i	0.606813	+	0.197165i	0.596277	−	0.802779i	$-0.296646\pi$
$827$	17.4505	+	5.67001i	0.606813	+	0.197165i	0.0105362	+	0.999944i	$0.496646\pi$
$828$	1.50360	+	2.06953i	0.0522537	+	0.0719211i
$829$	19.7259	+	14.3317i	0.685110	+	0.497761i	0.875049	−	0.484035i	$-0.160829\pi$
$829$	19.7259	+	14.3317i	0.685110	+	0.497761i	−0.189939	+	0.981796i	$0.560829\pi$
$830$	5.74170	+	10.2761i	0.199297	+	0.356687i
$831$	−6.52575	−	20.0842i	−0.226376	−	0.696713i
$832$	7.12060	−	9.80066i	0.246862	−	0.339777i
$833$	−2.57415	−	3.54301i	−0.0891890	−	0.122758i
$834$	11.7401	−	36.1324i	0.406528	−	1.25116i
$835$	1.65855	+	8.38081i	0.0573964	+	0.290030i
$836$	−12.7568	−	2.13446i	−0.441203	−	0.0738217i
$837$		−	2.84876i		−	0.0984676i
$838$	−34.8345	−	11.3184i	−1.20334	−	0.390988i
$839$	−34.2059	+	24.8520i	−1.18092	+	0.857988i	−0.992275	−	0.124058i	$-0.960409\pi$
$839$	−34.2059	+	24.8520i	−1.18092	+	0.857988i	−0.188644	+	0.982046i	$0.560409\pi$
$840$	−8.67959	+	18.7793i	−0.299474	+	0.647947i
$841$	−8.95052	−	27.5469i	−0.308639	−	0.949892i
$842$	28.1715	−	9.15347i	0.970853	−	0.315449i
$843$	15.9252	−	21.9191i	0.548492	−	0.754935i
$844$	−4.04097	+	2.93594i	−0.139096	+	0.101059i
$845$	−0.182365	+	1.52802i	−0.00627355	+	0.0525655i
$846$	−17.8849			−0.614895
$847$	20.2110	−	14.1532i	0.694457	−	0.486311i
$848$		−	62.4117i		−	2.14323i
$849$	13.4066	−	41.2613i	0.460113	−	1.41608i
$850$	−9.64665	+	15.6732i	−0.330877	+	0.537585i
$851$	8.08567	+	5.87458i	0.277173	+	0.201378i
$852$	−6.43874	+	2.09207i	−0.220587	+	0.0716732i
$853$	−14.6353	+	4.75529i	−0.501103	+	0.162818i	−0.548652	−	0.836051i	$-0.684859\pi$
$853$	−14.6353	+	4.75529i	−0.501103	+	0.162818i	0.0475493	+	0.998869i	$0.484859\pi$
$854$	−5.20454	−	3.78132i	−0.178096	−	0.129394i
$855$	−7.22806	+	7.80398i	−0.247194	+	0.266890i
$856$	−6.48458	+	19.9575i	−0.221638	+	0.682132i
$857$		−	36.1038i		−	1.23328i	−0.787245	−	0.616641i	$-0.788493\pi$
$857$		−	36.1038i		−	1.23328i	0.787245	−	0.616641i	$-0.211507\pi$
$858$	6.61650	−	39.5442i	0.225884	−	1.35002i
$859$	−48.3509			−1.64971			−0.824855	−	0.565344i	$-0.808743\pi$
$859$	−48.3509			−1.64971			−0.824855	+	0.565344i	$0.808743\pi$
$860$	−13.7799	−	1.64459i	−0.469889	−	0.0560799i
$861$	−28.3680	+	20.6106i	−0.966781	+	0.702407i
$862$	−32.5272	+	44.7699i	−1.10788	+	1.52487i
$863$	−35.3685	+	11.4919i	−1.20396	+	0.391190i	−0.841216	−	0.540699i	$-0.818160\pi$
$863$	−35.3685	+	11.4919i	−1.20396	+	0.391190i	−0.362743	+	0.931889i	$0.618160\pi$
$864$	5.10306	+	15.7056i	0.173610	+	0.534316i
$865$	1.97678	−	4.27699i	0.0672125	−	0.145422i
$866$	42.1539	−	30.6266i	1.43245	−	1.04073i
$867$	−22.6336	−	7.35411i	−0.768679	−	0.249759i
$868$		−	1.13648i		−	0.0385745i
$869$	−11.0784	+	21.2826i	−0.375809	+	0.721962i
$870$	1.35059	−	0.267279i	0.0457892	−	0.00906160i
$871$	−0.743664	+	2.28876i	−0.0251981	+	0.0775517i
$872$	10.8058	+	14.8730i	0.365932	+	0.503662i
$873$	1.19956	−	1.65105i	0.0405990	−	0.0558797i
$874$	10.4183	+	32.0642i	0.352403	+	1.08459i
$875$	−15.5834	+	19.6489i	−0.526816	+	0.664254i
$876$	−10.4395	−	7.58472i	−0.352717	−	0.256264i
$877$	−15.1609	−	20.8672i	−0.511947	−	0.704634i	0.472299	−	0.881438i	$-0.343424\pi$
$877$	−15.1609	−	20.8672i	−0.511947	−	0.704634i	−0.984246	+	0.176804i	$0.943424\pi$
$878$	56.0530	+	18.2127i	1.89170	+	0.614649i
$879$	−27.7221			−0.935044
$880$	−28.9372	+	22.3615i	−0.975474	+	0.753807i
$881$	−45.6820			−1.53906			−0.769532	−	0.638608i	$-0.779511\pi$
$881$	−45.6820			−1.53906			−0.769532	+	0.638608i	$0.779511\pi$
$882$	2.78738	+	0.905675i	0.0938560	+	0.0304957i
$883$	2.91912	+	4.01783i	0.0982364	+	0.135211i	0.855306	−	0.518124i	$-0.173369\pi$
$883$	2.91912	+	4.01783i	0.0982364	+	0.135211i	−0.757069	+	0.653335i	$0.773369\pi$
$884$	4.91167	+	3.56853i	0.165197	+	0.120023i
$885$	1.32486	−	0.740261i	0.0445347	−	0.0248836i
$886$	−12.0090	−	36.9600i	−0.403452	−	1.24170i
$887$	−17.0006	+	23.3994i	−0.570826	+	0.785674i	−0.992652	−	0.121002i	$-0.961389\pi$
$887$	−17.0006	+	23.3994i	−0.570826	+	0.785674i	0.421827	+	0.906677i	$0.361389\pi$
$888$	−6.28695	−	8.65324i	−0.210976	−	0.290384i
$889$	−1.68459	+	5.18463i	−0.0564993	+	0.173887i
$890$	7.12641	+	36.0104i	0.238878	+	1.20707i
$891$	−25.3155	−	25.7600i	−0.848100	−	0.862994i
$892$		−	6.43021i		−	0.215299i
$893$	−60.4033	−	19.6262i	−2.02132	−	0.656766i
$894$	−15.6372	+	11.3611i	−0.522987	+	0.379972i
$895$	10.1974	+	4.71315i	0.340863	+	0.157543i
$896$	−9.27501	−	28.5456i	−0.309856	−	0.953640i
$897$	−26.7811	+	8.70172i	−0.894196	+	0.290542i
$898$	−30.5299	+	42.0208i	−1.01880	+	1.40225i
$899$	0.104713	−	0.0760785i	0.00349237	−	0.00253736i
$900$	−0.253919	−	3.30887i	−0.00846396	−	0.110296i
$901$	−28.1559			−0.938010
$902$	−42.9630	+	6.42186i	−1.43051	+	0.213824i
$903$			37.2692i			1.24024i
$904$	0.149323	−	0.459570i	0.00496642	−	0.0152851i
$905$	23.7757	−	25.6701i	0.790331	−	0.853303i
$906$	33.7773	+	24.5406i	1.12217	+	0.815307i
$907$	−12.6041	+	4.09531i	−0.418511	+	0.135983i	−0.510700	−	0.859759i	$-0.670614\pi$
$907$	−12.6041	+	4.09531i	−0.418511	+	0.135983i	0.0921887	+	0.995742i	$0.470614\pi$
$908$	2.67106	−	0.867880i	0.0886422	−	0.0288016i
$909$	7.20435	+	5.23427i	0.238953	+	0.173610i
$910$	22.5260	+	20.8636i	0.746731	+	0.691623i
$911$	4.24361	−	13.0605i	0.140597	−	0.432713i	−0.855822	−	0.517271i	$-0.826948\pi$
$911$	4.24361	−	13.0605i	0.140597	−	0.432713i	0.996419	+	0.0845580i	$0.0269478\pi$
$912$		−	51.4833i		−	1.70478i
$913$	10.4364	−	1.55997i	0.345395	−	0.0516276i
$914$	64.7117			2.14047
$915$	−7.60024	−	0.907067i	−0.251256	−	0.0299867i
$916$	1.61942	−	1.17658i	0.0535071	−	0.0388752i
$917$	2.09430	−	2.88256i	0.0691600	−	0.0951906i
$918$	14.5188	−	4.71745i	0.479193	−	0.155699i
$919$	−18.3494	−	56.4737i	−0.605292	−	1.86290i	−0.494774	−	0.869022i	$-0.664749\pi$
$919$	−18.3494	−	56.4737i	−0.605292	−	1.86290i	−0.110517	−	0.993874i	$-0.535251\pi$
$920$	16.3397	+	7.55204i	0.538704	+	0.248983i
$921$	10.9750	−	7.97379i	0.361638	−	0.262745i
$922$	13.9798	+	4.54233i	0.460402	+	0.149594i
$923$		−	17.1950i		−	0.565981i
$924$	−7.59586	−	7.72925i	−0.249885	−	0.254274i
$925$	−4.93842	−	11.9885i	−0.162374	−	0.394179i
$926$	−2.15296	+	6.62613i	−0.0707507	+	0.217748i
$927$	5.41635	+	7.45496i	0.177896	+	0.244853i
$928$	−0.441016	+	0.607006i	−0.0144770	+	0.0199259i
$929$	−6.05305	−	18.6294i	−0.198594	−	0.611210i	−0.999916	−	0.0129763i	$-0.995869\pi$
$929$	−6.05305	−	18.6294i	−0.198594	−	0.611210i	0.801322	−	0.598234i	$-0.204131\pi$
$930$	−2.44783	−	4.38093i	−0.0802675	−	0.143656i
$931$	8.42007	+	6.11754i	0.275957	+	0.200494i
$932$	4.55720	+	6.27245i	0.149276	+	0.205461i
$933$	10.3327	+	3.35730i	0.338277	+	0.109913i
$934$	−11.1327			−0.364275
$935$	10.0880	+	13.0545i	0.329913	+	0.426928i
$936$	6.95320			0.227272
$937$	−38.5608	−	12.5292i	−1.25973	−	0.409310i	−0.398329	−	0.917242i	$-0.630410\pi$
$937$	−38.5608	−	12.5292i	−1.25973	−	0.409310i	−0.861397	+	0.507933i	$0.830410\pi$
$938$	1.41896	+	1.95304i	0.0463308	+	0.0637689i
$939$	22.7376	+	16.5198i	0.742012	+	0.539104i
$940$	17.2977	−	9.66501i	0.564188	−	0.315238i
$941$	−0.126602	−	0.389640i	−0.00412709	−	0.0127019i	0.948972	−	0.315361i	$-0.102126\pi$
$941$	−0.126602	−	0.389640i	−0.00412709	−	0.0127019i	−0.953099	+	0.302659i	$0.902126\pi$
$942$	27.5575	−	37.9296i	0.897870	−	1.23581i
$943$	17.9331	+	24.6828i	0.583982	+	0.803783i
$944$	−0.523717	+	1.61184i	−0.0170455	+	0.0524608i
$945$	20.4066	−	4.03843i	0.663826	−	0.131370i
$946$	−21.3185	+	40.9548i	−0.693125	+	1.33156i
$947$		−	2.45729i		−	0.0798511i	−0.999203	−	0.0399256i	$-0.987288\pi$
$947$		−	2.45729i		−	0.0798511i	0.999203	−	0.0399256i	$-0.0127121\pi$
$948$	10.0223	+	3.25643i	0.325508	+	0.105764i
$949$	26.5147	−	19.2640i	0.860703	−	0.625337i
$950$	10.2933	−	42.5091i	0.333958	−	1.37918i
$951$	11.4033	+	35.0956i	0.369776	+	1.13805i
$952$	−9.91230	+	3.22070i	−0.321260	+	0.104384i
$953$	35.8704	−	49.3714i	1.16196	−	1.59930i	0.458215	−	0.888841i	$-0.348489\pi$
$953$	35.8704	−	49.3714i	1.16196	−	1.59930i	0.703742	−	0.710456i	$-0.251511\pi$
$954$	15.2441	−	11.0755i	0.493546	−	0.358582i
$955$	0.825663	−	6.91816i	0.0267178	−	0.223867i
$956$	14.7820			0.478085
$957$	0.203675	−	1.21728i	0.00658387	−	0.0393492i
$958$			34.4309i			1.11241i
$959$	−12.9632	+	39.8965i	−0.418603	+	1.28833i
$960$	−10.6078	−	9.82495i	−0.342365	−	0.317099i
$961$	24.6978	+	17.9440i	0.796705	+	0.578840i
$962$	−15.0972	+	4.90538i	−0.486754	+	0.158156i
$963$	−8.59754	+	2.79351i	−0.277052	+	0.0900196i
$964$	16.9749	+	12.3330i	0.546726	+	0.397220i
$965$	15.8086	+	14.6420i	0.508897	+	0.471341i
$966$	−8.72898	+	26.8650i	−0.280850	+	0.864369i
$967$		−	17.1997i		−	0.553106i	−0.960999	−	0.276553i	$-0.910808\pi$
$967$		−	17.1997i		−	0.553106i	0.960999	−	0.276553i	$-0.0891921\pi$
$968$	6.71837	+	21.9712i	0.215937	+	0.706182i
$969$	−23.2258			−0.746119
$970$	−0.994438	+	8.33232i	−0.0319295	+	0.267535i
$971$	−22.0125	+	15.9930i	−0.706415	+	0.513241i	−0.882015	−	0.471221i	$-0.843813\pi$
$971$	−22.0125	+	15.9930i	−0.706415	+	0.513241i	0.175600	+	0.984462i	$0.443813\pi$
$972$	−3.92927	+	5.40818i	−0.126031	+	0.173467i
$973$	24.8046	−	8.05950i	0.795198	−	0.258376i
$974$	−8.06790	−	24.8304i	−0.258512	−	0.795619i
$975$	35.5051	+	8.59732i	1.13707	+	0.275335i
$976$	6.91513	−	5.02414i	0.221348	−	0.160819i
$977$	18.2339	+	5.92454i	0.583353	+	0.189543i	0.585802	−	0.810454i	$-0.300780\pi$
$977$	18.2339	+	5.92454i	0.583353	+	0.189543i	−0.00244904	+	0.999997i	$0.500780\pi$
$978$			11.8516i			0.378971i
$979$	32.4562	+	5.43055i	1.03730	+	0.173561i
$980$	−3.18529	+	0.630365i	−0.101750	+	0.0201363i
$981$	−2.44732	+	7.53207i	−0.0781369	+	0.240481i
$982$	18.7995	+	25.8753i	0.599916	+	0.825714i
$983$	−14.1835	+	19.5219i	−0.452384	+	0.622653i	−0.972908	−	0.231194i	$-0.925737\pi$
$983$	−14.1835	+	19.5219i	−0.452384	+	0.622653i	0.520524	+	0.853847i	$0.325737\pi$
$984$	−10.0898	−	31.0532i	−0.321651	−	0.989939i
$985$	28.1040	−	15.7030i	0.895469	−	0.500340i
$986$	0.561138	+	0.407691i	0.0178703	+	0.0129835i
$987$	−31.2781	−	43.0506i	−0.995593	−	1.37032i
$988$	−13.7221	−	4.45858i	−0.436558	−	0.141846i
$989$	32.4276			1.03114
$990$	−10.5970	−	3.09970i	−0.336794	−	0.0985149i
$991$	27.7081			0.880177			0.440089	−	0.897954i	$-0.354947\pi$
$991$	27.7081			0.880177			0.440089	+	0.897954i	$0.354947\pi$
$992$	2.60102	+	0.845122i	0.0825824	+	0.0268327i
$993$	0.543521	+	0.748092i	0.0172481	+	0.0237400i
$994$	−13.9546	−	10.1386i	−0.442614	−	0.321578i
$995$	−16.1397	−	28.8856i	−0.511664	−	0.915735i
$996$	−1.43219	−	4.40782i	−0.0453806	−	0.139667i
$997$	−19.6856	+	27.0950i	−0.623451	+	0.858106i	−0.997598	−	0.0692628i	$-0.977935\pi$
$997$	−19.6856	+	27.0950i	−0.623451	+	0.858106i	0.374148	+	0.927369i	$0.377935\pi$
$998$	40.3211	+	55.4972i	1.27634	+	1.75673i
$999$	−3.32350	+	10.2287i	−0.105151	+	0.323621i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	55.2.j.a.9.1	✓	16
3.2	odd	2		495.2.ba.a.64.4		16
4.3	odd	2		880.2.cd.c.449.1		16
5.2	odd	4		275.2.h.d.251.4		16
5.3	odd	4		275.2.h.d.251.1		16
5.4	even	2	inner	55.2.j.a.9.4	yes	16
11.2	odd	10		605.2.j.g.124.1		16
11.3	even	5		605.2.j.h.444.1		16
11.4	even	5		605.2.b.g.364.2		8
11.5	even	5	inner	55.2.j.a.49.4	yes	16
11.6	odd	10		605.2.j.d.269.1		16
11.7	odd	10		605.2.b.f.364.7		8
11.8	odd	10		605.2.j.g.444.4		16
11.9	even	5		605.2.j.h.124.4		16
11.10	odd	2		605.2.j.d.9.4		16
15.14	odd	2		495.2.ba.a.64.1		16
20.19	odd	2		880.2.cd.c.449.4		16
33.5	odd	10		495.2.ba.a.379.1		16
44.27	odd	10		880.2.cd.c.49.4		16
55.4	even	10		605.2.b.g.364.7		8
55.7	even	20		3025.2.a.bk.1.2		8
55.9	even	10		605.2.j.h.124.1		16
55.14	even	10		605.2.j.h.444.4		16
55.18	even	20		3025.2.a.bk.1.7		8
55.19	odd	10		605.2.j.g.444.1		16
55.24	odd	10		605.2.j.g.124.4		16
55.27	odd	20		275.2.h.d.126.4		16
55.29	odd	10		605.2.b.f.364.2		8
55.37	odd	20		3025.2.a.bl.1.7		8
55.38	odd	20		275.2.h.d.126.1		16
55.39	odd	10		605.2.j.d.269.4		16
55.48	odd	20		3025.2.a.bl.1.2		8
55.49	even	10	inner	55.2.j.a.49.1	yes	16
55.54	odd	2		605.2.j.d.9.1		16
165.104	odd	10		495.2.ba.a.379.4		16
220.159	odd	10		880.2.cd.c.49.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.j.a.9.1	✓	16	1.1	even	1	trivial
55.2.j.a.9.4	yes	16	5.4	even	2	inner
55.2.j.a.49.1	yes	16	55.49	even	10	inner
55.2.j.a.49.4	yes	16	11.5	even	5	inner
275.2.h.d.126.1		16	55.38	odd	20
275.2.h.d.126.4		16	55.27	odd	20
275.2.h.d.251.1		16	5.3	odd	4
275.2.h.d.251.4		16	5.2	odd	4
495.2.ba.a.64.1		16	15.14	odd	2
495.2.ba.a.64.4		16	3.2	odd	2
495.2.ba.a.379.1		16	33.5	odd	10
495.2.ba.a.379.4		16	165.104	odd	10
605.2.b.f.364.2		8	55.29	odd	10
605.2.b.f.364.7		8	11.7	odd	10
605.2.b.g.364.2		8	11.4	even	5
605.2.b.g.364.7		8	55.4	even	10
605.2.j.d.9.1		16	55.54	odd	2
605.2.j.d.9.4		16	11.10	odd	2
605.2.j.d.269.1		16	11.6	odd	10
605.2.j.d.269.4		16	55.39	odd	10
605.2.j.g.124.1		16	11.2	odd	10
605.2.j.g.124.4		16	55.24	odd	10
605.2.j.g.444.1		16	55.19	odd	10
605.2.j.g.444.4		16	11.8	odd	10
605.2.j.h.124.1		16	55.9	even	10
605.2.j.h.124.4		16	11.9	even	5
605.2.j.h.444.1		16	11.3	even	5
605.2.j.h.444.4		16	55.14	even	10
880.2.cd.c.49.1		16	220.159	odd	10
880.2.cd.c.49.4		16	44.27	odd	10
880.2.cd.c.449.1		16	4.3	odd	2
880.2.cd.c.449.4		16	20.19	odd	2
3025.2.a.bk.1.2		8	55.7	even	20
3025.2.a.bk.1.7		8	55.18	even	20
3025.2.a.bl.1.2		8	55.48	odd	20
3025.2.a.bl.1.7		8	55.37	odd	20

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:	\( N \)	\(=\)	\( 55 = 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	55.j (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.57360 - 0.511294i) q^{2} +(1.16075 + 1.59764i) q^{3} +(0.596764 + 0.433574i) q^{4} +(1.09069 + 1.95203i) q^{5} +(-1.00970 - 3.10753i) q^{6} +(1.31845 - 1.81468i) q^{7} +(1.22769 + 1.68978i) q^{8} +(-0.278050 + 0.855749i) q^{9} +(-0.718246 - 3.62937i) q^{10} +(-3.27115 - 0.547326i) q^{11} +1.45668i q^{12} +(-3.51868 - 1.14329i) q^{13} +(-3.00254 + 2.18148i) q^{14} +(-1.85261 + 4.00834i) q^{15} +(-1.52381 - 4.68982i) q^{16} +(-2.11573 + 0.687441i) q^{17} +(0.875078 - 1.20444i) q^{18} +(4.27714 - 3.10753i) q^{19} +(-0.195466 + 1.63779i) q^{20} +4.42960 q^{21} +(4.86764 + 2.53379i) q^{22} -3.85415i q^{23} +(-1.27460 + 3.92282i) q^{24} +(-2.62081 + 4.25810i) q^{25} +(4.95244 + 3.59816i) q^{26} +(3.94448 - 1.28164i) q^{27} +(1.57360 - 0.511294i) q^{28} +(0.152450 + 0.110762i) q^{29} +(4.96471 - 5.36029i) q^{30} +(0.212253 - 0.653249i) q^{31} +3.98166i q^{32} +(-2.92256 - 5.86142i) q^{33} +3.68079 q^{34} +(4.98032 + 0.594387i) q^{35} +(-0.536960 + 0.390125i) q^{36} +(-1.52422 + 2.09791i) q^{37} +(-8.31938 + 2.70313i) q^{38} +(-2.25775 - 6.94864i) q^{39} +(-1.95946 + 4.23950i) q^{40} +(-6.40421 + 4.65293i) q^{41} +(-6.97041 - 2.26482i) q^{42} +8.41368i q^{43} +(-1.71480 - 1.74491i) q^{44} +(-1.97371 + 0.390594i) q^{45} +(-1.97060 + 6.06490i) q^{46} +(-7.06117 - 9.71886i) q^{47} +(5.72386 - 7.87822i) q^{48} +(0.608337 + 1.87227i) q^{49} +(6.30124 - 5.36054i) q^{50} +(-3.55411 - 2.58222i) q^{51} +(-1.60412 - 2.20788i) q^{52} +(12.0371 + 3.91110i) q^{53} -6.86233 q^{54} +(-2.49941 - 6.98233i) q^{55} +4.68506 q^{56} +(9.92940 + 3.22626i) q^{57} +(-0.183264 - 0.252241i) q^{58} +(-0.278050 - 0.202015i) q^{59} +(-2.84348 + 1.58878i) q^{60} +(0.535643 + 1.64854i) q^{61} +(-0.668004 + 0.919429i) q^{62} +(1.18632 + 1.63283i) q^{63} +(-1.01183 + 3.11409i) q^{64} +(-1.60605 - 8.11552i) q^{65} +(1.60204 + 10.7178i) q^{66} -0.650461i q^{67} +(-1.56065 - 0.507084i) q^{68} +(6.15754 - 4.47371i) q^{69} +(-7.53313 - 3.48174i) q^{70} +(1.43619 + 4.42013i) q^{71} +(-1.78738 + 0.580756i) q^{72} +(-5.20684 + 7.16660i) q^{73} +(3.47116 - 2.52195i) q^{74} +(-9.84499 + 0.755493i) q^{75} +3.89979 q^{76} +(-5.30606 + 5.21449i) q^{77} +12.0888i q^{78} +(2.23551 - 6.88019i) q^{79} +(7.49264 - 8.08965i) q^{80} +(8.80999 + 6.40083i) q^{81} +(12.4567 - 4.04742i) q^{82} +(-3.02593 + 0.983185i) q^{83} +(2.64342 + 1.92056i) q^{84} +(-3.64950 - 3.38017i) q^{85} +(4.30186 - 13.2398i) q^{86} +0.372127i q^{87} +(-3.09111 - 6.19946i) q^{88} -9.92195 q^{89} +(3.30554 + 0.394506i) q^{90} +(-6.71389 + 4.87793i) q^{91} +(1.67106 - 2.30002i) q^{92} +(1.29003 - 0.419156i) q^{93} +(6.14226 + 18.9039i) q^{94} +(10.7310 + 4.95976i) q^{95} +(-6.36125 + 4.62172i) q^{96} +(-2.15710 - 0.700884i) q^{97} -3.25724i q^{98} +(1.37792 - 2.64710i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{4} - 2 q^{5} - 18 q^{6} + 2 q^{9} - 6 q^{11} - 12 q^{14} - 16 q^{15} + 16 q^{16} + 6 q^{19} - 8 q^{20} + 8 q^{21} + 6 q^{24} - 16 q^{25} + 40 q^{26} + 2 q^{29} + 26 q^{30} + 8 q^{31} - 16 q^{34}+ \cdots - 72 q^{99}+O(q^{100}) \) 16 * q - 4 * q^4 - 2 * q^5 - 18 * q^6 + 2 * q^9 - 6 * q^11 - 12 * q^14 - 16 * q^15 + 16 * q^16 + 6 * q^19 - 8 * q^20 + 8 * q^21 + 6 * q^24 - 16 * q^25 + 40 * q^26 + 2 * q^29 + 26 * q^30 + 8 * q^31 - 16 * q^34 + 22 * q^35 + 10 * q^36 + 30 * q^39 + 12 * q^40 - 52 * q^41 + 4 * q^44 + 12 * q^45 - 62 * q^46 - 10 * q^49 + 28 * q^50 - 42 * q^51 - 40 * q^54 - 8 * q^55 - 20 * q^56 + 2 * q^59 - 32 * q^60 - 40 * q^61 - 8 * q^64 - 40 * q^65 + 58 * q^66 + 26 * q^69 - 34 * q^70 + 36 * q^71 + 48 * q^74 - 20 * q^75 + 56 * q^76 + 38 * q^79 + 34 * q^80 + 68 * q^81 + 12 * q^84 + 58 * q^85 + 22 * q^86 + 24 * q^89 + 78 * q^90 - 20 * q^91 + 14 * q^94 + 48 * q^95 - 86 * q^96 - 72 * q^99

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