LMFDB - Embedded newform 555.2.g.a.184.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [555,2,Mod(184,555)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(555, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 1]))

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

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

chi := DirichletCharacter("555.184");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 555 = 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	555.g (of order $2$, degree $1$, 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:	$40$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			184.12
Character	$\chi$	$=$	555.184
Dual form			555.2.g.a.184.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.47721 q^{2} +1.00000i q^{3} +0.182137 q^{4} +(-0.357763 - 2.20726i) q^{5} -1.47721i q^{6} +1.62051i q^{7} +2.68536 q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-1.47721 q^{2} +1.00000i q^{3} +0.182137 q^{4} +(-0.357763 - 2.20726i) q^{5} -1.47721i q^{6} +1.62051i q^{7} +2.68536 q^{8} -1.00000 q^{9} +(0.528490 + 3.26058i) q^{10} -0.174569 q^{11} +0.182137i q^{12} -4.30618 q^{13} -2.39383i q^{14} +(2.20726 - 0.357763i) q^{15} -4.33110 q^{16} +6.78820 q^{17} +1.47721 q^{18} -3.61639i q^{19} +(-0.0651620 - 0.402024i) q^{20} -1.62051 q^{21} +0.257874 q^{22} -6.61293 q^{23} +2.68536i q^{24} +(-4.74401 + 1.57935i) q^{25} +6.36111 q^{26} -1.00000i q^{27} +0.295155i q^{28} -2.45483i q^{29} +(-3.26058 + 0.528490i) q^{30} -6.18326i q^{31} +1.02721 q^{32} -0.174569i q^{33} -10.0276 q^{34} +(3.57689 - 0.579759i) q^{35} -0.182137 q^{36} +(1.01187 - 5.99801i) q^{37} +5.34215i q^{38} -4.30618i q^{39} +(-0.960723 - 5.92729i) q^{40} +11.5949 q^{41} +2.39383 q^{42} -9.32564 q^{43} -0.0317954 q^{44} +(0.357763 + 2.20726i) q^{45} +9.76866 q^{46} -11.8580i q^{47} -4.33110i q^{48} +4.37395 q^{49} +(7.00788 - 2.33303i) q^{50} +6.78820i q^{51} -0.784314 q^{52} -5.47148i q^{53} +1.47721i q^{54} +(0.0624543 + 0.385319i) q^{55} +4.35165i q^{56} +3.61639 q^{57} +3.62629i q^{58} -3.00991i q^{59} +(0.402024 - 0.0651620i) q^{60} -11.4713i q^{61} +9.13395i q^{62} -1.62051i q^{63} +7.14480 q^{64} +(1.54059 + 9.50486i) q^{65} +0.257874i q^{66} -2.04067i q^{67} +1.23638 q^{68} -6.61293i q^{69} +(-5.28380 + 0.856424i) q^{70} -11.0257 q^{71} -2.68536 q^{72} +7.16903i q^{73} +(-1.49473 + 8.86030i) q^{74} +(-1.57935 - 4.74401i) q^{75} -0.658679i q^{76} -0.282890i q^{77} +6.36111i q^{78} +15.4144i q^{79} +(1.54951 + 9.55987i) q^{80} +1.00000 q^{81} -17.1281 q^{82} -10.8772i q^{83} -0.295155 q^{84} +(-2.42857 - 14.9833i) q^{85} +13.7759 q^{86} +2.45483 q^{87} -0.468779 q^{88} -13.4034i q^{89} +(-0.528490 - 3.26058i) q^{90} -6.97820i q^{91} -1.20446 q^{92} +6.18326 q^{93} +17.5168i q^{94} +(-7.98232 + 1.29381i) q^{95} +1.02721i q^{96} -6.23756 q^{97} -6.46122 q^{98} +0.174569 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 44 q^{4} - 40 q^{9}+O(q^{10}) $ 40 * q + 44 * q^4 - 40 * q^9	$ 40 q + 44 q^{4} - 40 q^{9} + 4 q^{10} + 8 q^{11} + 52 q^{16} - 16 q^{21} + 8 q^{25} - 16 q^{26} + 16 q^{30} - 32 q^{34} - 44 q^{36} - 28 q^{40} + 8 q^{41} + 16 q^{44} - 8 q^{46} - 24 q^{49} + 92 q^{64} - 48 q^{65} - 56 q^{70} + 24 q^{71} - 68 q^{74} + 8 q^{75} + 40 q^{81} - 16 q^{84} - 64 q^{85} + 80 q^{86} - 4 q^{90} + 32 q^{95} - 8 q^{99}+O(q^{100}) $ 40 * q + 44 * q^4 - 40 * q^9 + 4 * q^10 + 8 * q^11 + 52 * q^16 - 16 * q^21 + 8 * q^25 - 16 * q^26 + 16 * q^30 - 32 * q^34 - 44 * q^36 - 28 * q^40 + 8 * q^41 + 16 * q^44 - 8 * q^46 - 24 * q^49 + 92 * q^64 - 48 * q^65 - 56 * q^70 + 24 * q^71 - 68 * q^74 + 8 * q^75 + 40 * q^81 - 16 * q^84 - 64 * q^85 + 80 * q^86 - 4 * q^90 + 32 * q^95 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$76$	$112$	$371$
$\chi(n)$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−1.47721			−1.04454			−0.522271	−	0.852779i	$-0.674915\pi$
$2$	−1.47721			−1.04454			−0.522271	+	0.852779i	$0.674915\pi$
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	0.182137			0.0910685
$5$	−0.357763	−	2.20726i	−0.159997	−	0.987118i
$5$	−0.357763	−	2.20726i	−0.159997	−	0.987118i
$6$		−	1.47721i		−	0.603067i
$7$			1.62051i			0.612495i	0.951952	+	0.306248i	$0.0990736\pi$
$7$			1.62051i			0.612495i	−0.951952	+	0.306248i	$0.900926\pi$
$8$	2.68536			0.949417
$9$	−1.00000			−0.333333
$10$	0.528490	+	3.26058i	0.167123	+	1.03109i
$11$	−0.174569			−0.0526344			−0.0263172	−	0.999654i	$-0.508378\pi$
$11$	−0.174569			−0.0526344			−0.0263172	+	0.999654i	$0.508378\pi$
$12$			0.182137i			0.0525784i
$13$	−4.30618			−1.19432			−0.597159	−	0.802123i	$-0.703704\pi$
$13$	−4.30618			−1.19432			−0.597159	+	0.802123i	$0.703704\pi$
$14$		−	2.39383i		−	0.639777i
$15$	2.20726	−	0.357763i	0.569913	−	0.0923741i
$16$	−4.33110			−1.08278
$17$	6.78820			1.64638			0.823190	−	0.567766i	$-0.192192\pi$
$17$	6.78820			1.64638			0.823190	+	0.567766i	$0.192192\pi$
$18$	1.47721			0.348181
$19$		−	3.61639i		−	0.829657i	−0.909900	−	0.414828i	$-0.863842\pi$
$19$		−	3.61639i		−	0.829657i	0.909900	−	0.414828i	$-0.136158\pi$
$20$	−0.0651620	−	0.402024i	−0.0145707	−	0.0898954i
$21$	−1.62051			−0.353624
$22$	0.257874			0.0549789
$23$	−6.61293			−1.37889			−0.689446	−	0.724337i	$-0.742146\pi$
$23$	−6.61293			−1.37889			−0.689446	+	0.724337i	$0.742146\pi$
$24$			2.68536i			0.548146i
$25$	−4.74401	+	1.57935i	−0.948802	+	0.315871i
$26$	6.36111			1.24752
$27$		−	1.00000i		−	0.192450i
$28$			0.295155i			0.0557791i
$29$		−	2.45483i		−	0.455851i	−0.973679	−	0.227925i	$-0.926806\pi$
$29$		−	2.45483i		−	0.455851i	0.973679	−	0.227925i	$-0.0731942\pi$
$30$	−3.26058	+	0.528490i	−0.595298	+	0.0964887i
$31$		−	6.18326i		−	1.11055i	−0.831668	−	0.555273i	$-0.812614\pi$
$31$		−	6.18326i		−	1.11055i	0.831668	−	0.555273i	$-0.187386\pi$
$32$	1.02721			0.181587
$33$		−	0.174569i		−	0.0303885i
$34$	−10.0276			−1.71971
$35$	3.57689	−	0.579759i	0.604605	−	0.0979972i
$36$	−0.182137			−0.0303562
$37$	1.01187	−	5.99801i	0.166350	−	0.986067i
$37$	1.01187	−	5.99801i	0.166350	−	0.986067i
$38$			5.34215i			0.866611i
$39$		−	4.30618i		−	0.689540i
$40$	−0.960723	−	5.92729i	−0.151904	−	0.937187i
$41$	11.5949			1.81082			0.905412	−	0.424533i	$-0.139562\pi$
$41$	11.5949			1.81082			0.905412	+	0.424533i	$0.139562\pi$
$42$	2.39383			0.369376
$43$	−9.32564			−1.42215			−0.711073	−	0.703118i	$-0.751791\pi$
$43$	−9.32564			−1.42215			−0.711073	+	0.703118i	$0.751791\pi$
$44$	−0.0317954			−0.00479334
$45$	0.357763	+	2.20726i	0.0533322	+	0.329039i
$46$	9.76866			1.44031
$47$		−	11.8580i		−	1.72967i	−0.502054	−	0.864836i	$-0.667422\pi$
$47$		−	11.8580i		−	1.72967i	0.502054	−	0.864836i	$-0.332578\pi$
$48$		−	4.33110i		−	0.625140i
$49$	4.37395			0.624849
$50$	7.00788	−	2.33303i	0.991064	−	0.329941i
$51$			6.78820i			0.950538i
$52$	−0.784314			−0.108765
$53$		−	5.47148i		−	0.751566i	−0.926708	−	0.375783i	$-0.877374\pi$
$53$		−	5.47148i		−	0.751566i	0.926708	−	0.375783i	$-0.122626\pi$
$54$			1.47721i			0.201022i
$55$	0.0624543	+	0.385319i	0.00842133	+	0.0519564i
$56$			4.35165i			0.581514i
$57$	3.61639			0.479002
$58$			3.62629i			0.476155i
$59$		−	3.00991i		−	0.391857i	−0.980618	−	0.195928i	$-0.937228\pi$
$59$		−	3.00991i		−	0.391857i	0.980618	−	0.195928i	$-0.0627720\pi$
$60$	0.402024	−	0.0651620i	0.0519011	−	0.00841237i
$61$		−	11.4713i		−	1.46875i	−0.678745	−	0.734374i	$-0.737476\pi$
$61$		−	11.4713i		−	1.46875i	0.678745	−	0.734374i	$-0.262524\pi$
$62$			9.13395i			1.16001i
$63$		−	1.62051i		−	0.204165i
$64$	7.14480			0.893100
$65$	1.54059	+	9.50486i	0.191087	+	1.17893i
$66$			0.257874i			0.0317421i
$67$		−	2.04067i		−	0.249307i	−0.992200	−	0.124654i	$-0.960218\pi$
$67$		−	2.04067i		−	0.249307i	0.992200	−	0.124654i	$-0.0397820\pi$
$68$	1.23638			0.149933
$69$		−	6.61293i		−	0.796103i
$70$	−5.28380	+	0.856424i	−0.631535	+	0.102362i
$71$	−11.0257			−1.30851			−0.654253	−	0.756276i	$-0.727017\pi$
$71$	−11.0257			−1.30851			−0.654253	+	0.756276i	$0.727017\pi$
$72$	−2.68536			−0.316472
$73$			7.16903i			0.839071i	0.907739	+	0.419535i	$0.137807\pi$
$73$			7.16903i			0.839071i	−0.907739	+	0.419535i	$0.862193\pi$
$74$	−1.49473	+	8.86030i	−0.173759	+	1.02999i
$75$	−1.57935	−	4.74401i	−0.182368	−	0.547791i
$76$		−	0.658679i		−	0.0755556i
$77$		−	0.282890i		−	0.0322383i
$78$			6.36111i			0.720254i
$79$			15.4144i			1.73425i	0.498089	+	0.867126i	$0.334035\pi$
$79$			15.4144i			1.73425i	−0.498089	+	0.867126i	$0.665965\pi$
$80$	1.54951	+	9.55987i	0.173240	+	1.06883i
$81$	1.00000			0.111111
$82$	−17.1281			−1.89148
$83$		−	10.8772i		−	1.19393i	−0.802267	−	0.596965i	$-0.796373\pi$
$83$		−	10.8772i		−	1.19393i	0.802267	−	0.596965i	$-0.203627\pi$
$84$	−0.295155			−0.0322041
$85$	−2.42857	−	14.9833i	−0.263415	−	1.62517i
$86$	13.7759			1.48549
$87$	2.45483			0.263185
$88$	−0.468779			−0.0499720
$89$		−	13.4034i		−	1.42075i	−0.703821	−	0.710377i	$-0.748524\pi$
$89$		−	13.4034i		−	1.42075i	0.703821	−	0.710377i	$-0.251476\pi$
$90$	−0.528490	−	3.26058i	−0.0557078	−	0.343695i
$91$		−	6.97820i		−	0.731514i
$92$	−1.20446			−0.125574
$93$	6.18326			0.641174
$94$			17.5168i			1.80672i
$95$	−7.98232	+	1.29381i	−0.818969	+	0.132742i
$96$			1.02721i			0.104839i
$97$	−6.23756			−0.633328			−0.316664	−	0.948538i	$-0.602563\pi$
$97$	−6.23756			−0.633328			−0.316664	+	0.948538i	$0.602563\pi$
$98$	−6.46122			−0.652682
$99$	0.174569			0.0175448
$100$	−0.864060	+	0.287659i	−0.0864060	+	0.0287659i
$101$	1.63491			0.162680			0.0813400	−	0.996686i	$-0.474080\pi$
$101$	1.63491			0.162680			0.0813400	+	0.996686i	$0.474080\pi$
$102$		−	10.0276i		−	0.992877i
$103$	−14.8032			−1.45861			−0.729304	−	0.684190i	$-0.760156\pi$
$103$	−14.8032			−1.45861			−0.729304	+	0.684190i	$0.760156\pi$
$104$	−11.5636			−1.13391
$105$	0.579759	+	3.57689i	0.0565787	+	0.349069i
$106$			8.08250i			0.785042i
$107$		−	3.70555i		−	0.358229i	−0.983828	−	0.179114i	$-0.942677\pi$
$107$		−	3.70555i		−	0.358229i	0.983828	−	0.179114i	$-0.0573232\pi$
$108$		−	0.182137i		−	0.0175261i
$109$			9.02932i			0.864852i	0.901669	+	0.432426i	$0.142342\pi$
$109$			9.02932i			0.864852i	−0.901669	+	0.432426i	$0.857658\pi$
$110$	−0.0922578	−	0.569195i	−0.00879644	−	0.0542706i
$111$	5.99801	+	1.01187i	0.569306	+	0.0960420i
$112$		−	7.01859i		−	0.663195i
$113$	12.4027			1.16675			0.583375	−	0.812203i	$-0.301732\pi$
$113$	12.4027			1.16675			0.583375	+	0.812203i	$0.301732\pi$
$114$	−5.34215			−0.500338
$115$	2.36586	+	14.5965i	0.220618	+	1.36113i
$116$		−	0.447116i		−	0.0415136i
$117$	4.30618			0.398106
$118$			4.44626i			0.409311i
$119$			11.0003i			1.00840i
$120$	5.92729	−	0.960723i	0.541085	−	0.0877016i
$121$	−10.9695			−0.997230
$122$			16.9455i			1.53417i
$123$			11.5949i			1.04548i
$124$		−	1.12620i		−	0.101136i
$125$	5.18328	+	9.90624i	0.463607	+	0.886041i
$126$			2.39383i			0.213259i
$127$			10.2955i			0.913574i	0.889576	+	0.456787i	$0.151000\pi$
$127$			10.2955i			0.913574i	−0.889576	+	0.456787i	$0.849000\pi$
$128$	−12.6088			−1.11447
$129$		−	9.32564i		−	0.821076i
$130$	−2.27577	−	14.0406i	−0.199598	−	1.23144i
$131$			15.1552i			1.32411i	0.749454	+	0.662056i	$0.230316\pi$
$131$			15.1552i			1.32411i	−0.749454	+	0.662056i	$0.769684\pi$
$132$		−	0.0317954i		−	0.00276744i
$133$	5.86040			0.508161
$134$			3.01449i			0.260412i
$135$	−2.20726	+	0.357763i	−0.189971	+	0.0307914i
$136$	18.2287			1.56310
$137$			14.4532i			1.23482i	0.786642	+	0.617410i	$0.211818\pi$
$137$			14.4532i			1.23482i	−0.786642	+	0.617410i	$0.788182\pi$
$138$			9.76866i			0.831564i
$139$	−1.59000			−0.134862			−0.0674312	−	0.997724i	$-0.521480\pi$
$139$	−1.59000			−0.134862			−0.0674312	+	0.997724i	$0.521480\pi$
$140$	0.651484	−	0.105596i	0.0550605	−	0.00892446i
$141$	11.8580			0.998627
$142$	16.2872			1.36679
$143$	0.751723			0.0628623
$144$	4.33110			0.360925
$145$	−5.41845	+	0.878248i	−0.449978	+	0.0729346i
$146$		−	10.5901i		−	0.876445i
$147$			4.37395i			0.360757i
$148$	0.184298	−	1.09246i	0.0151492	−	0.0897997i
$149$	−12.7220			−1.04223			−0.521113	−	0.853488i	$-0.674483\pi$
$149$	−12.7220			−1.04223			−0.521113	+	0.853488i	$0.674483\pi$
$150$	2.33303	+	7.00788i	0.190491	+	0.572191i
$151$	16.8436			1.37071			0.685357	−	0.728207i	$-0.259646\pi$
$151$	16.8436			1.37071			0.685357	+	0.728207i	$0.259646\pi$
$152$		−	9.71130i		−	0.787690i
$153$	−6.78820			−0.548793
$154$			0.417887i			0.0336743i
$155$	−13.6481	+	2.21214i	−1.09624	+	0.177684i
$156$		−	0.784314i		−	0.0627954i
$157$			11.9808i			0.956172i	0.878313	+	0.478086i	$0.158669\pi$
$157$			11.9808i			0.956172i	−0.878313	+	0.478086i	$0.841331\pi$
$158$		−	22.7702i		−	1.81150i
$159$	5.47148			0.433917
$160$	−0.367499	−	2.26732i	−0.0290533	−	0.179248i
$161$		−	10.7163i		−	0.844565i
$162$	−1.47721			−0.116060
$163$	−5.71059			−0.447288			−0.223644	−	0.974671i	$-0.571795\pi$
$163$	−5.71059			−0.447288			−0.223644	+	0.974671i	$0.571795\pi$
$164$	2.11187			0.164909
$165$	−0.385319	+	0.0624543i	−0.0299970	+	0.00486206i
$166$			16.0679i			1.24711i
$167$	11.3389			0.877429			0.438714	−	0.898627i	$-0.355434\pi$
$167$	11.3389			0.877429			0.438714	+	0.898627i	$0.355434\pi$
$168$	−4.35165			−0.335737
$169$	5.54314			0.426396
$170$	3.58750	+	22.1335i	0.275148	+	1.69756i
$171$			3.61639i			0.276552i
$172$	−1.69854			−0.129513
$173$		−	1.44520i		−	0.109876i	−0.998490	−	0.0549382i	$-0.982504\pi$
$173$		−	1.44520i		−	0.109876i	0.998490	−	0.0549382i	$-0.0174962\pi$
$174$	−3.62629			−0.274908
$175$	−2.55936	−	7.68772i	−0.193470	−	0.581137i
$176$	0.756074			0.0569913
$177$	3.00991			0.226239
$178$			19.7995i			1.48404i
$179$		−	5.34851i		−	0.399766i	−0.979820	−	0.199883i	$-0.935944\pi$
$179$		−	5.34851i		−	0.399766i	0.979820	−	0.199883i	$-0.0640562\pi$
$180$	0.0651620	+	0.402024i	0.00485689	+	0.0299651i
$181$	20.3928			1.51578			0.757892	−	0.652380i	$-0.226229\pi$
$181$	20.3928			1.51578			0.757892	+	0.652380i	$0.226229\pi$
$182$			10.3082i			0.764098i
$183$	11.4713			0.847982
$184$	−17.7581			−1.30914
$185$	−13.6012	−	0.0875839i	−0.999979	−	0.00643930i
$186$	−9.13395			−0.669734
$187$	−1.18501			−0.0866563
$188$		−	2.15979i		−	0.157519i
$189$	1.62051			0.117875
$190$	11.7915	−	1.91123i	0.855447	−	0.138655i
$191$		−	8.41729i		−	0.609053i	−0.952504	−	0.304527i	$-0.901502\pi$
$191$		−	8.41729i		−	0.609053i	0.952504	−	0.304527i	$-0.0984983\pi$
$192$			7.14480i			0.515631i
$193$	7.63343			0.549466			0.274733	−	0.961521i	$-0.411411\pi$
$193$	7.63343			0.549466			0.274733	+	0.961521i	$0.411411\pi$
$194$	9.21416			0.661538
$195$	−9.50486	+	1.54059i	−0.680657	+	0.110324i
$196$	0.796658			0.0569041
$197$		−	20.4107i		−	1.45420i	−0.686530	−	0.727101i	$-0.740867\pi$
$197$		−	20.4107i		−	1.45420i	0.686530	−	0.727101i	$-0.259133\pi$
$198$	−0.257874			−0.0183263
$199$		−	9.37755i		−	0.664757i	−0.943146	−	0.332378i	$-0.892149\pi$
$199$		−	9.37755i		−	0.664757i	0.943146	−	0.332378i	$-0.107851\pi$
$200$	−12.7394	+	4.24113i	−0.900809	+	0.299893i
$201$	2.04067			0.143938
$202$	−2.41510			−0.169926
$203$	3.97808			0.279206
$204$			1.23638i			0.0865641i
$205$	−4.14824	−	25.5931i	−0.289726	−	1.78750i
$206$	21.8674			1.52358
$207$	6.61293			0.459631
$208$	18.6505			1.29318
$209$			0.631308i			0.0436685i
$210$	−0.856424	−	5.28380i	−0.0590989	−	0.364617i
$211$	−2.19686			−0.151238			−0.0756189	−	0.997137i	$-0.524093\pi$
$211$	−2.19686			−0.151238			−0.0756189	+	0.997137i	$0.524093\pi$
$212$		−	0.996560i		−	0.0684440i
$213$		−	11.0257i		−	0.755466i
$214$			5.47385i			0.374185i
$215$	3.33637	+	20.5841i	0.227539	+	1.40383i
$216$		−	2.68536i		−	0.182715i
$217$	10.0200			0.680204
$218$		−	13.3382i		−	0.903375i
$219$	−7.16903			−0.484438
$220$	0.0113752	+	0.0701808i	0.000766918	+	0.00473159i
$221$	−29.2312			−1.96630
$222$	−8.86030	−	1.49473i	−0.594664	−	0.100320i
$223$		−	12.3815i		−	0.829127i	−0.910020	−	0.414564i	$-0.863934\pi$
$223$		−	12.3815i		−	0.829127i	0.910020	−	0.414564i	$-0.136066\pi$
$224$			1.66461i			0.111221i
$225$	4.74401	−	1.57935i	0.316267	−	0.105290i
$226$	−18.3214			−1.21872
$227$	1.90018			0.126119			0.0630597	−	0.998010i	$-0.479914\pi$
$227$	1.90018			0.126119			0.0630597	+	0.998010i	$0.479914\pi$
$228$	0.658679			0.0436221
$229$	−5.07678			−0.335483			−0.167741	−	0.985831i	$-0.553647\pi$
$229$	−5.07678			−0.335483			−0.167741	+	0.985831i	$0.553647\pi$
$230$	−3.49487	−	21.5620i	−0.230445	−	1.42176i
$231$	0.282890			0.0186128
$232$		−	6.59210i		−	0.432792i
$233$		−	0.381223i		−	0.0249747i	−0.999922	−	0.0124874i	$-0.996025\pi$
$233$		−	0.381223i		−	0.0249747i	0.999922	−	0.0124874i	$-0.00397495\pi$
$234$	−6.36111			−0.415839
$235$	−26.1738	+	4.24237i	−1.70739	+	0.276742i
$236$		−	0.548216i		−	0.0356858i
$237$	−15.4144			−1.00127
$238$		−	16.2498i		−	1.05332i
$239$		−	2.59160i		−	0.167637i	−0.996481	−	0.0838183i	$-0.973288\pi$
$239$		−	2.59160i		−	0.167637i	0.996481	−	0.0838183i	$-0.0267115\pi$
$240$	−9.55987	+	1.54951i	−0.617087	+	0.100020i
$241$			1.08953i			0.0701826i	0.999384	+	0.0350913i	$0.0111722\pi$
$241$			1.08953i			0.0701826i	−0.999384	+	0.0350913i	$0.988828\pi$
$242$	16.2042			1.04165
$243$			1.00000i			0.0641500i
$244$		−	2.08935i		−	0.133757i
$245$	−1.56484	−	9.65445i	−0.0999738	−	0.616800i
$246$		−	17.1281i		−	1.09205i
$247$			15.5728i			0.990874i
$248$		−	16.6043i		−	1.05437i
$249$	10.8772			0.689316
$250$	−7.65678	−	14.6336i	−0.484257	−	0.925507i
$251$			17.5464i			1.10752i	0.832676	+	0.553761i	$0.186808\pi$
$251$			17.5464i			1.10752i	−0.832676	+	0.553761i	$0.813192\pi$
$252$		−	0.295155i		−	0.0185930i
$253$	1.15441			0.0725772
$254$		−	15.2085i		−	0.954267i
$255$	14.9833	−	2.42857i	0.938292	−	0.152083i
$256$	4.33614			0.271009
$257$	0.704289			0.0439323			0.0219662	−	0.999759i	$-0.493007\pi$
$257$	0.704289			0.0439323			0.0219662	+	0.999759i	$0.493007\pi$
$258$			13.7759i			0.857649i
$259$	9.71984	+	1.63974i	0.603961	+	0.101888i
$260$	0.280599	+	1.73119i	0.0174020	+	0.107364i
$261$			2.45483i			0.151950i
$262$		−	22.3873i		−	1.38309i
$263$			2.40942i			0.148571i	0.997237	+	0.0742857i	$0.0236677\pi$
$263$			2.40942i			0.148571i	−0.997237	+	0.0742857i	$0.976332\pi$
$264$		−	0.468779i		−	0.0288514i
$265$	−12.0770	+	1.95750i	−0.741884	+	0.120248i
$266$	−8.65701			−0.530795
$267$	13.4034			0.820273
$268$		−	0.371681i		−	0.0227040i
$269$	−31.2880			−1.90766			−0.953831	−	0.300345i	$-0.902898\pi$
$269$	−31.2880			−1.90766			−0.953831	+	0.300345i	$0.902898\pi$
$270$	3.26058	−	0.528490i	0.198433	−	0.0321629i
$271$	−1.13176			−0.0687498			−0.0343749	−	0.999409i	$-0.510944\pi$
$271$	−1.13176			−0.0687498			−0.0343749	+	0.999409i	$0.510944\pi$
$272$	−29.4004			−1.78266
$273$	6.97820			0.422340
$274$		−	21.3503i		−	1.28982i
$275$	0.828156	−	0.275706i	0.0499397	−	0.0166257i
$276$		−	1.20446i		−	0.0725000i
$277$	−1.15138			−0.0691799			−0.0345900	−	0.999402i	$-0.511013\pi$
$277$	−1.15138			−0.0691799			−0.0345900	+	0.999402i	$0.511013\pi$
$278$	2.34876			0.140869
$279$			6.18326i			0.370182i
$280$	9.60523	−	1.55686i	0.574022	−	0.0930402i
$281$		−	15.7460i		−	0.939325i	−0.882846	−	0.469663i	$-0.844376\pi$
$281$		−	15.7460i		−	0.939325i	0.882846	−	0.469663i	$-0.155624\pi$
$282$	−17.5168			−1.04311
$283$	8.55489			0.508535			0.254268	−	0.967134i	$-0.418166\pi$
$283$	8.55489			0.508535			0.254268	+	0.967134i	$0.418166\pi$
$284$	−2.00818			−0.119164
$285$	−1.29381	−	7.98232i	−0.0766388	−	0.472832i
$286$	−1.11045			−0.0656623
$287$			18.7897i			1.10912i
$288$	−1.02721			−0.0605290
$289$	29.0796			1.71057
$290$	8.00417	−	1.29735i	0.470021	−	0.0761832i
$291$		−	6.23756i		−	0.365652i
$292$			1.30575i			0.0764130i
$293$			8.87914i			0.518725i	0.965780	+	0.259363i	$0.0835124\pi$
$293$			8.87914i			0.518725i	−0.965780	+	0.259363i	$0.916488\pi$
$294$		−	6.46122i		−	0.376826i
$295$	−6.64366	+	1.07684i	−0.386809	+	0.0626958i
$296$	2.71722	−	16.1068i	0.157935	−	0.936189i
$297$			0.174569i			0.0101295i
$298$	18.7930			1.08865
$299$	28.4764			1.64684
$300$	−0.287659	−	0.864060i	−0.0166080	−	0.0498865i
$301$		−	15.1123i		−	0.871058i
$302$	−24.8815			−1.43177
$303$			1.63491i			0.0939233i
$304$			15.6629i			0.898331i
$305$	−25.3201	+	4.10401i	−1.44983	+	0.234995i
$306$	10.0276			0.573238
$307$		−	9.27241i		−	0.529204i	−0.964358	−	0.264602i	$-0.914759\pi$
$307$		−	9.27241i		−	0.529204i	0.964358	−	0.264602i	$-0.0852407\pi$
$308$		−	0.0515248i		−	0.00293590i
$309$		−	14.8032i		−	0.842127i
$310$	20.1610	−	3.26779i	1.14507	−	0.185598i
$311$			30.4567i			1.72704i	0.504316	+	0.863519i	$0.331745\pi$
$311$			30.4567i			1.72704i	−0.504316	+	0.863519i	$0.668255\pi$
$312$		−	11.5636i		−	0.654661i
$313$	9.88196			0.558562			0.279281	−	0.960209i	$-0.409904\pi$
$313$	9.88196			0.558562			0.279281	+	0.960209i	$0.409904\pi$
$314$		−	17.6981i		−	0.998762i
$315$	−3.57689	+	0.579759i	−0.201535	+	0.0326657i
$316$			2.80753i			0.157936i
$317$			20.6863i			1.16186i	0.813955	+	0.580929i	$0.197310\pi$
$317$			20.6863i			1.16186i	−0.813955	+	0.580929i	$0.802690\pi$
$318$	−8.08250			−0.453244
$319$			0.428537i			0.0239934i
$320$	−2.55615	−	15.7704i	−0.142893	−	0.881594i
$321$	3.70555			0.206823
$322$			15.8302i			0.882183i
$323$		−	24.5488i		−	1.36593i
$324$	0.182137			0.0101187
$325$	20.4285	−	6.80098i	1.13317	−	0.377250i
$326$	8.43571			0.467211
$327$	−9.02932			−0.499323
$328$	31.1366			1.71923
$329$	19.2161			1.05942
$330$	0.569195	−	0.0922578i	0.0313332	−	0.00507863i
$331$		−	12.1462i		−	0.667616i	−0.942641	−	0.333808i	$-0.891666\pi$
$331$		−	12.1462i		−	0.667616i	0.942641	−	0.333808i	$-0.108334\pi$
$332$		−	1.98115i		−	0.108729i
$333$	−1.01187	+	5.99801i	−0.0554499	+	0.328689i
$334$	−16.7499			−0.916511
$335$	−4.50429	+	0.730076i	−0.246096	+	0.0398883i
$336$	7.01859			0.382896
$337$		−	14.3720i		−	0.782892i	−0.920201	−	0.391446i	$-0.871975\pi$
$337$		−	14.3720i		−	0.782892i	0.920201	−	0.391446i	$-0.128025\pi$
$338$	−8.18837			−0.445388
$339$			12.4027i			0.673623i
$340$	−0.442332	−	2.72902i	−0.0239888	−	0.148002i
$341$			1.07940i			0.0584530i
$342$		−	5.34215i		−	0.288870i
$343$			18.4316i			0.995213i
$344$	−25.0427			−1.35021
$345$	−14.5965	+	2.36586i	−0.785848	+	0.127374i
$346$			2.13486i			0.114771i
$347$	8.00478			0.429719			0.214860	−	0.976645i	$-0.431071\pi$
$347$	8.00478			0.429719			0.214860	+	0.976645i	$0.431071\pi$
$348$	0.447116			0.0239679
$349$	−16.6323			−0.890308			−0.445154	−	0.895454i	$-0.646851\pi$
$349$	−16.6323			−0.890308			−0.445154	+	0.895454i	$0.646851\pi$
$350$	3.78070	+	11.3563i	0.202087	+	0.607022i
$351$			4.30618i			0.229847i
$352$	−0.179319			−0.00955773
$353$	−0.896749			−0.0477291			−0.0238646	−	0.999715i	$-0.507597\pi$
$353$	−0.896749			−0.0477291			−0.0238646	+	0.999715i	$0.507597\pi$
$354$	−4.44626			−0.236316
$355$	3.94458	+	24.3365i	0.209356	+	1.29165i
$356$		−	2.44125i		−	0.129386i
$357$	−11.0003			−0.582200
$358$			7.90085i			0.417573i
$359$	30.7362			1.62219			0.811096	−	0.584913i	$-0.198871\pi$
$359$	30.7362			1.62219			0.811096	+	0.584913i	$0.198871\pi$
$360$	0.960723	+	5.92729i	0.0506345	+	0.312396i
$361$	5.92173			0.311670
$362$	−30.1243			−1.58330
$363$		−	10.9695i		−	0.575751i
$364$		−	1.27099i		−	0.0666179i
$365$	15.8239	−	2.56481i	0.828262	−	0.134249i
$366$	−16.9455			−0.885753
$367$		−	36.6361i		−	1.91239i	−0.292731	−	0.956195i	$-0.594564\pi$
$367$		−	36.6361i		−	1.91239i	0.292731	−	0.956195i	$-0.405436\pi$
$368$	28.6413			1.49303
$369$	−11.5949			−0.603608
$370$	20.0918	+	0.129379i	1.04452	+	0.00672612i
$371$	8.86659			0.460331
$372$	1.12620			0.0583908
$373$			1.76921i			0.0916061i	0.998950	+	0.0458030i	$0.0145847\pi$
$373$			1.76921i			0.0916061i	−0.998950	+	0.0458030i	$0.985415\pi$
$374$	1.75050			0.0905161
$375$	−9.90624	+	5.18328i	−0.511556	+	0.267664i
$376$		−	31.8431i		−	1.64218i
$377$			10.5709i			0.544431i
$378$	−2.39383			−0.123125
$379$	0.0747528			0.00383979			0.00191990	−	0.999998i	$-0.499389\pi$
$379$	0.0747528			0.00383979			0.00191990	+	0.999998i	$0.499389\pi$
$380$	−1.45388	+	0.235651i	−0.0745823	+	0.0120886i
$381$	−10.2955			−0.527452
$382$			12.4341i			0.636182i
$383$	−8.19560			−0.418776			−0.209388	−	0.977833i	$-0.567147\pi$
$383$	−8.19560			−0.418776			−0.209388	+	0.977833i	$0.567147\pi$
$384$		−	12.6088i		−	0.643438i
$385$	−0.624413	+	0.101208i	−0.0318230	+	0.00515803i
$386$	−11.2761			−0.573941
$387$	9.32564			0.474049
$388$	−1.13609			−0.0576763
$389$		−	31.3597i		−	1.59000i	−0.606610	−	0.795000i	$-0.707471\pi$
$389$		−	31.3597i		−	1.59000i	0.606610	−	0.795000i	$-0.292529\pi$
$390$	14.0406	−	2.27577i	0.710975	−	0.115238i
$391$	−44.8899			−2.27018
$392$	11.7456			0.593243
$393$	−15.1552			−0.764476
$394$			30.1508i			1.51898i
$395$	34.0235	−	5.51470i	1.71191	−	0.277474i
$396$	0.0317954			0.00159778
$397$			11.5467i			0.579513i	0.957100	+	0.289757i	$0.0935743\pi$
$397$			11.5467i			0.579513i	−0.957100	+	0.289757i	$0.906426\pi$
$398$			13.8526i			0.694366i
$399$			5.86040i			0.293387i
$400$	20.5468	−	6.84034i	1.02734	−	0.342017i
$401$			11.4067i			0.569622i	0.958584	+	0.284811i	$0.0919309\pi$
$401$			11.4067i			0.569622i	−0.958584	+	0.284811i	$0.908069\pi$
$402$	−3.01449			−0.150349
$403$			26.6262i			1.32635i
$404$	0.297778			0.0148150
$405$	−0.357763	−	2.20726i	−0.0177774	−	0.109680i
$406$	−5.87644			−0.291643
$407$	−0.176640	+	1.04706i	−0.00875572	+	0.0519011i
$408$			18.2287i			0.902457i
$409$			11.6247i			0.574805i	0.957810	+	0.287403i	$0.0927918\pi$
$409$			11.6247i			0.574805i	−0.957810	+	0.287403i	$0.907208\pi$
$410$	6.12781	+	37.8062i	0.302631	+	1.86712i
$411$	−14.4532			−0.712923
$412$	−2.69622			−0.132833
$413$	4.87759			0.240011
$414$	−9.76866			−0.480104
$415$	−24.0089	+	3.89147i	−1.17855	+	0.191025i
$416$	−4.42335			−0.216873
$417$		−	1.59000i		−	0.0778628i
$418$		−	0.932572i		−	0.0456136i
$419$	23.3160			1.13906			0.569532	−	0.821969i	$-0.307125\pi$
$419$	23.3160			1.13906			0.569532	+	0.821969i	$0.307125\pi$
$420$	0.105596	+	0.651484i	0.00515254	+	0.0317892i
$421$			12.1803i			0.593633i	0.954935	+	0.296816i	$0.0959249\pi$
$421$			12.1803i			0.593633i	−0.954935	+	0.296816i	$0.904075\pi$
$422$	3.24521			0.157974
$423$			11.8580i			0.576558i
$424$		−	14.6929i		−	0.713550i
$425$	−32.2033	+	10.7210i	−1.56209	+	0.520044i
$426$			16.2872i			0.789116i
$427$	18.5893			0.899601
$428$		−	0.674917i		−	0.0326234i
$429$			0.751723i			0.0362935i
$430$	−4.92851	−	30.4070i	−0.237674	−	1.46636i
$431$		−	13.7069i		−	0.660238i	−0.943939	−	0.330119i	$-0.892911\pi$
$431$		−	13.7069i		−	0.660238i	0.943939	−	0.330119i	$-0.107089\pi$
$432$			4.33110i			0.208380i
$433$			0.286467i			0.0137667i	0.999976	+	0.00688337i	$0.00219106\pi$
$433$			0.286467i			0.0137667i	−0.999976	+	0.00688337i	$0.997809\pi$
$434$	−14.8017			−0.710502
$435$	−0.878248	−	5.41845i	−0.0421088	−	0.259795i
$436$			1.64457i			0.0787609i
$437$			23.9149i			1.14401i
$438$	10.5901			0.506016
$439$			20.9601i			1.00037i	0.865918	+	0.500186i	$0.166735\pi$
$439$			20.9601i			1.00037i	−0.865918	+	0.500186i	$0.833265\pi$
$440$	0.167712	+	1.03472i	0.00799536	+	0.0493283i
$441$	−4.37395			−0.208283
$442$	43.1804			2.05388
$443$		−	26.4686i		−	1.25756i	−0.777583	−	0.628781i	$-0.783554\pi$
$443$		−	26.4686i		−	1.25756i	0.777583	−	0.628781i	$-0.216446\pi$
$444$	1.09246	+	0.184298i	0.0518459	+	0.00874641i
$445$	−29.5847	+	4.79523i	−1.40245	+	0.227316i
$446$			18.2900i			0.866059i
$447$		−	12.7220i		−	0.601730i
$448$			11.5782i			0.547019i
$449$			29.1827i			1.37722i	0.725133	+	0.688609i	$0.241778\pi$
$449$			29.1827i			1.37722i	−0.725133	+	0.688609i	$0.758222\pi$
$450$	−7.00788	+	2.33303i	−0.330355	+	0.109980i
$451$	−2.02411			−0.0953117
$452$	2.25899			0.106254
$453$			16.8436i			0.791383i
$454$	−2.80696			−0.131737
$455$	−15.4027	+	2.49654i	−0.722091	+	0.117040i
$456$	9.71130			0.454773
$457$	17.4278			0.815238			0.407619	−	0.913152i	$-0.366359\pi$
$457$	17.4278			0.815238			0.407619	+	0.913152i	$0.366359\pi$
$458$	7.49944			0.350426
$459$		−	6.78820i		−	0.316846i
$460$	0.430912	+	2.65856i	0.0200914	+	0.123956i
$461$		−	11.4065i		−	0.531256i	−0.964076	−	0.265628i	$-0.914421\pi$
$461$		−	11.4065i		−	0.531256i	0.964076	−	0.265628i	$-0.0855793\pi$
$462$	−0.417887			−0.0194419
$463$	−13.0363			−0.605847			−0.302923	−	0.953015i	$-0.597963\pi$
$463$	−13.0363			−0.605847			−0.302923	+	0.953015i	$0.597963\pi$
$464$			10.6321i			0.493584i
$465$	−2.21214	−	13.6481i	−0.102586	−	0.632914i
$466$			0.563144i			0.0260872i
$467$	−14.2125			−0.657677			−0.328839	−	0.944386i	$-0.606657\pi$
$467$	−14.2125			−0.657677			−0.328839	+	0.944386i	$0.606657\pi$
$468$	0.784314			0.0362549
$469$	3.30692			0.152700
$470$	38.6641	−	6.26686i	1.78344	−	0.289069i
$471$	−11.9808			−0.552046
$472$		−	8.08269i		−	0.372036i
$473$	1.62796			0.0748539
$474$	22.7702			1.04587
$475$	5.71156	+	17.1562i	0.262064	+	0.787180i
$476$			2.00357i			0.0918335i
$477$			5.47148i			0.250522i
$478$			3.82833i			0.175104i
$479$			24.8239i			1.13423i	0.823638	+	0.567116i	$0.191941\pi$
$479$			24.8239i			1.13423i	−0.823638	+	0.567116i	$0.808059\pi$
$480$	2.26732	−	0.367499i	0.103489	−	0.0167739i
$481$	−4.35727	+	25.8285i	−0.198674	+	1.17768i
$482$		−	1.60946i		−	0.0733087i
$483$	10.7163			0.487610
$484$	−1.99796			−0.0908162
$485$	2.23157	+	13.7679i	0.101330	+	0.625169i
$486$		−	1.47721i		−	0.0670074i
$487$	−11.1773			−0.506490			−0.253245	−	0.967402i	$-0.581498\pi$
$487$	−11.1773			−0.506490			−0.253245	+	0.967402i	$0.581498\pi$
$488$		−	30.8045i		−	1.39445i
$489$		−	5.71059i		−	0.258242i
$490$	2.31159	+	14.2616i	0.104427	+	0.644274i
$491$	3.03944			0.137168			0.0685840	−	0.997645i	$-0.478152\pi$
$491$	3.03944			0.137168			0.0685840	+	0.997645i	$0.478152\pi$
$492$			2.11187i			0.0952104i
$493$		−	16.6639i		−	0.750503i
$494$		−	23.0042i		−	1.03501i
$495$	−0.0624543	−	0.385319i	−0.00280711	−	0.0173188i
$496$			26.7803i			1.20247i
$497$		−	17.8672i		−	0.801453i
$498$	−16.0679			−0.720020
$499$			20.1551i			0.902265i	0.892457	+	0.451132i	$0.148980\pi$
$499$			20.1551i			0.902265i	−0.892457	+	0.451132i	$0.851020\pi$
$500$	0.944068	+	1.80429i	0.0422200	+	0.0806905i
$501$			11.3389i			0.506584i
$502$		−	25.9197i		−	1.15685i
$503$	−0.743522			−0.0331520			−0.0165760	−	0.999863i	$-0.505277\pi$
$503$	−0.743522			−0.0331520			−0.0165760	+	0.999863i	$0.505277\pi$
$504$		−	4.35165i		−	0.193838i
$505$	−0.584912	−	3.60868i	−0.0260283	−	0.160584i
$506$	−1.70530			−0.0758099
$507$			5.54314i			0.246180i
$508$			1.87518i			0.0831979i
$509$	19.9428			0.883949			0.441974	−	0.897028i	$-0.354278\pi$
$509$	19.9428			0.883949			0.441974	+	0.897028i	$0.354278\pi$
$510$	−22.1335	+	3.58750i	−0.980086	+	0.158857i
$511$	−11.6175			−0.513927
$512$	18.8122			0.831388
$513$	−3.61639			−0.159667
$514$	−1.04038			−0.0458892
$515$	5.29606	+	32.6746i	0.233372	+	1.43982i
$516$		−	1.69854i		−	0.0747742i
$517$			2.07004i			0.0910404i
$518$	−14.3582	−	2.42223i	−0.630863	−	0.106427i
$519$	1.44520			0.0634372
$520$	4.13704	+	25.5239i	0.181421	+	1.11930i
$521$	3.97783			0.174272			0.0871359	−	0.996196i	$-0.472229\pi$
$521$	3.97783			0.174272			0.0871359	+	0.996196i	$0.472229\pi$
$522$		−	3.62629i		−	0.158718i
$523$	24.7110			1.08054			0.540268	−	0.841493i	$-0.318323\pi$
$523$	24.7110			1.08054			0.540268	+	0.841493i	$0.318323\pi$
$524$			2.76032i			0.120585i
$525$	7.68772	−	2.55936i	0.335520	−	0.111700i
$526$		−	3.55921i		−	0.155189i
$527$		−	41.9732i		−	1.82838i
$528$			0.756074i			0.0329039i
$529$	20.7309			0.901342
$530$	17.8402	−	2.89162i	0.774929	−	0.125604i
$531$			3.00991i			0.130619i
$532$	1.06740			0.0462775
$533$	−49.9298			−2.16270
$534$	−19.7995			−0.856810
$535$	−8.17911	+	1.32571i	−0.353614	+	0.0573154i
$536$		−	5.47992i		−	0.236697i
$537$	5.34851			0.230805
$538$	46.2188			1.99263
$539$	−0.763554			−0.0328886
$540$	−0.402024	+	0.0651620i	−0.0173004	+	0.00280412i
$541$		−	20.7204i		−	0.890840i	−0.895322	−	0.445420i	$-0.853054\pi$
$541$		−	20.7204i		−	0.890840i	0.895322	−	0.445420i	$-0.146946\pi$
$542$	1.67185			0.0718121
$543$			20.3928i			0.875138i
$544$	6.97291			0.298961
$545$	19.9301	−	3.23036i	0.853711	−	0.138373i
$546$	−10.3082			−0.441152
$547$	−24.9724			−1.06774			−0.533872	−	0.845565i	$-0.679264\pi$
$547$	−24.9724			−1.06774			−0.533872	+	0.845565i	$0.679264\pi$
$548$			2.63246i			0.112453i
$549$			11.4713i			0.489583i
$550$	−1.22336	+	0.407274i	−0.0521641	+	0.0173662i
$551$	−8.87762			−0.378199
$552$		−	17.7581i		−	0.755834i
$553$	−24.9791			−1.06222
$554$	1.70083			0.0722613
$555$	0.0875839	−	13.6012i	0.00371773	−	0.577338i
$556$	−0.289599			−0.0122817
$557$	26.3241			1.11539			0.557694	−	0.830047i	$-0.311686\pi$
$557$	26.3241			1.11539			0.557694	+	0.830047i	$0.311686\pi$
$558$		−	9.13395i		−	0.386671i
$559$	40.1578			1.69849
$560$	−15.4919	+	2.51100i	−0.654651	+	0.106109i
$561$		−	1.18501i		−	0.0500310i
$562$			23.2600i			0.981165i
$563$	−4.99738			−0.210615			−0.105307	−	0.994440i	$-0.533583\pi$
$563$	−4.99738			−0.210615			−0.105307	+	0.994440i	$0.533583\pi$
$564$	2.15979			0.0909435
$565$	−4.43724	−	27.3760i	−0.186676	−	1.15172i
$566$	−12.6373			−0.531187
$567$			1.62051i			0.0680550i
$568$	−29.6078			−1.24232
$569$			10.2365i			0.429138i	0.976709	+	0.214569i	$0.0688347\pi$
$569$			10.2365i			0.429138i	−0.976709	+	0.214569i	$0.931165\pi$
$570$	1.91123	+	11.7915i	0.0800524	+	0.493893i
$571$	−36.3617			−1.52169			−0.760845	−	0.648933i	$-0.775215\pi$
$571$	−36.3617			−1.52169			−0.760845	+	0.648933i	$0.775215\pi$
$572$	0.136917			0.00572477
$573$	8.41729			0.351637
$574$		−	27.7563i		−	1.15852i
$575$	31.3718	−	10.4442i	1.30830	−	0.435552i
$576$	−7.14480			−0.297700
$577$	−32.0573			−1.33456			−0.667281	−	0.744806i	$-0.732542\pi$
$577$	−32.0573			−1.33456			−0.667281	+	0.744806i	$0.732542\pi$
$578$	−42.9566			−1.78676
$579$			7.63343i			0.317234i
$580$	−0.986901	+	0.159962i	−0.0409789	+	0.00664204i
$581$	17.6267			0.731277
$582$			9.21416i			0.381939i
$583$			0.955149i			0.0395582i
$584$			19.2514i			0.796628i
$585$	−1.54059	−	9.50486i	−0.0636956	−	0.392977i
$586$		−	13.1163i		−	0.541830i
$587$	−16.8055			−0.693637			−0.346818	−	0.937932i	$-0.612738\pi$
$587$	−16.8055			−0.693637			−0.346818	+	0.937932i	$0.612738\pi$
$588$			0.796658i			0.0328536i
$589$	−22.3611			−0.921372
$590$	9.81405	−	1.59071i	0.404038	−	0.0654884i
$591$	20.4107			0.839584
$592$	−4.38249	+	25.9780i	−0.180119	+	1.06769i
$593$		−	43.2235i		−	1.77498i	−0.460832	−	0.887488i	$-0.652449\pi$
$593$		−	43.2235i		−	1.77498i	0.460832	−	0.887488i	$-0.347551\pi$
$594$		−	0.257874i		−	0.0105807i
$595$	24.2806	−	3.93552i	0.995409	−	0.161341i
$596$	−2.31715			−0.0949141
$597$	9.37755			0.383797
$598$	−42.0656			−1.72019
$599$	−19.8867			−0.812549			−0.406274	−	0.913751i	$-0.633172\pi$
$599$	−19.8867			−0.812549			−0.406274	+	0.913751i	$0.633172\pi$
$600$	−4.24113	−	12.7394i	−0.173144	−	0.520082i
$601$	−12.5839			−0.513309			−0.256655	−	0.966503i	$-0.582620\pi$
$601$	−12.5839			−0.513309			−0.256655	+	0.966503i	$0.582620\pi$
$602$			22.3240i			0.909857i
$603$			2.04067i			0.0831024i
$604$	3.06785			0.124829
$605$	3.92449	+	24.2126i	0.159553	+	0.984383i
$606$		−	2.41510i		−	0.0981069i
$607$	−23.2592			−0.944062			−0.472031	−	0.881582i	$-0.656479\pi$
$607$	−23.2592			−0.944062			−0.472031	+	0.881582i	$0.656479\pi$
$608$		−	3.71479i		−	0.150655i
$609$			3.97808i			0.161200i
$610$	37.4031	−	6.06246i	1.51441	−	0.245462i
$611$			51.0628i			2.06578i
$612$	−1.23638			−0.0499778
$613$			11.0844i			0.447696i	0.974624	+	0.223848i	$0.0718619\pi$
$613$			11.0844i			0.447696i	−0.974624	+	0.223848i	$0.928138\pi$
$614$			13.6973i			0.552776i
$615$	25.5931	−	4.14824i	1.03201	−	0.167273i
$616$		−	0.759662i		−	0.0306076i
$617$		−	41.4784i		−	1.66986i	−0.550358	−	0.834929i	$-0.685509\pi$
$617$		−	41.4784i		−	1.66986i	0.550358	−	0.834929i	$-0.314491\pi$
$618$			21.8674i			0.879638i
$619$	−0.380216			−0.0152822			−0.00764109	−	0.999971i	$-0.502432\pi$
$619$	−0.380216			−0.0152822			−0.00764109	+	0.999971i	$0.502432\pi$
$620$	−2.48582	+	0.402913i	−0.0998330	+	0.0161814i
$621$			6.61293i			0.265368i
$622$		−	44.9907i		−	1.80396i
$623$	21.7203			0.870205
$624$			18.6505i			0.746617i
$625$	20.0113	−	14.9850i	0.800451	−	0.599398i
$626$	−14.5977			−0.583441
$627$	−0.631308			−0.0252120
$628$			2.18215i			0.0870772i
$629$	6.86874	−	40.7157i	0.273875	−	1.62344i
$630$	5.28380	−	0.856424i	0.210512	−	0.0341207i
$631$			47.5960i			1.89477i	0.320103	+	0.947383i	$0.396283\pi$
$631$			47.5960i			1.89477i	−0.320103	+	0.947383i	$0.603717\pi$
$632$			41.3931i			1.64653i
$633$		−	2.19686i		−	0.0873172i
$634$		−	30.5579i		−	1.21361i
$635$	22.7248	−	3.68334i	0.901805	−	0.146169i
$636$	0.996560			0.0395162
$637$	−18.8350			−0.746269
$638$		−	0.633037i		−	0.0250622i
$639$	11.0257			0.436168
$640$	4.51095	+	27.8308i	0.178311	+	1.10011i
$641$	−4.84843			−0.191501			−0.0957507	−	0.995405i	$-0.530525\pi$
$641$	−4.84843			−0.191501			−0.0957507	+	0.995405i	$0.530525\pi$
$642$	−5.47385			−0.216036
$643$	1.05850			0.0417432			0.0208716	−	0.999782i	$-0.493356\pi$
$643$	1.05850			0.0417432			0.0208716	+	0.999782i	$0.493356\pi$
$644$		−	1.95184i		−	0.0769133i
$645$	−20.5841	+	3.33637i	−0.810499	+	0.131369i
$646$			36.2636i			1.42677i
$647$	26.1608			1.02849			0.514245	−	0.857644i	$-0.328072\pi$
$647$	26.1608			1.02849			0.514245	+	0.857644i	$0.328072\pi$
$648$	2.68536			0.105491
$649$			0.525436i			0.0206252i
$650$	−30.1772	+	10.0464i	−1.18365	+	0.394054i
$651$			10.0200i			0.392716i
$652$	−1.04011			−0.0407338
$653$	−19.8982			−0.778678			−0.389339	−	0.921095i	$-0.627297\pi$
$653$	−19.8982			−0.778678			−0.389339	+	0.921095i	$0.627297\pi$
$654$	13.3382			0.521564
$655$	33.4514	−	5.42196i	1.30705	−	0.211853i
$656$	−50.2188			−1.96072
$657$		−	7.16903i		−	0.279690i
$658$	−28.3861			−1.10661
$659$	−20.2165			−0.787522			−0.393761	−	0.919213i	$-0.628826\pi$
$659$	−20.2165			−0.787522			−0.393761	+	0.919213i	$0.628826\pi$
$660$	−0.0701808	+	0.0113752i	−0.00273179	+	0.000442781i
$661$		−	16.2597i		−	0.632428i	−0.948688	−	0.316214i	$-0.897588\pi$
$661$		−	16.2597i		−	0.632428i	0.948688	−	0.316214i	$-0.102412\pi$
$662$			17.9424i			0.697353i
$663$		−	29.2312i		−	1.13524i
$664$		−	29.2092i		−	1.13354i
$665$	−2.09663	−	12.9354i	−0.0813040	−	0.501614i
$666$	1.49473	−	8.86030i	0.0579198	−	0.343329i
$667$			16.2336i			0.628569i
$668$	2.06523			0.0799062
$669$	12.3815			0.478697
$670$	6.65376	−	1.07847i	0.257057	−	0.0416650i
$671$			2.00253i			0.0773067i
$672$	−1.66461			−0.0642136
$673$		−	25.6780i		−	0.989814i	−0.868946	−	0.494907i	$-0.835202\pi$
$673$		−	25.6780i		−	0.989814i	0.868946	−	0.494907i	$-0.164798\pi$
$674$			21.2304i			0.817764i
$675$	1.57935	+	4.74401i	0.0607894	+	0.182597i
$676$	1.00961			0.0388312
$677$		−	24.8858i		−	0.956438i	−0.878241	−	0.478219i	$-0.841283\pi$
$677$		−	24.8858i		−	0.956438i	0.878241	−	0.478219i	$-0.158717\pi$
$678$		−	18.3214i		−	0.703628i
$679$		−	10.1080i		−	0.387910i
$680$	−6.52157	−	40.2356i	−0.250091	−	1.54296i
$681$			1.90018i			0.0728151i
$682$		−	1.59450i		−	0.0610566i
$683$	14.0761			0.538606			0.269303	−	0.963055i	$-0.413207\pi$
$683$	14.0761			0.538606			0.269303	+	0.963055i	$0.413207\pi$
$684$			0.658679i			0.0251852i
$685$	31.9020	−	5.17082i	1.21891	−	0.197567i
$686$		−	27.2273i		−	1.03954i
$687$		−	5.07678i		−	0.193691i
$688$	40.3903			1.53986
$689$			23.5612i			0.897609i
$690$	21.5620	−	3.49487i	0.820851	−	0.133047i
$691$	46.6637			1.77517			0.887586	−	0.460642i	$-0.152381\pi$
$691$	46.6637			1.77517			0.887586	+	0.460642i	$0.152381\pi$
$692$		−	0.263224i		−	0.0100063i
$693$			0.282890i			0.0107461i
$694$	−11.8247			−0.448860
$695$	0.568845	+	3.50955i	0.0215775	+	0.133125i
$696$	6.59210			0.249873
$697$	78.7087			2.98131
$698$	24.5694			0.929964
$699$	0.381223			0.0144192
$700$	−0.466155	−	1.40022i	−0.0176190	−	0.0529233i
$701$		−	36.6906i		−	1.38578i	−0.721041	−	0.692892i	$-0.756336\pi$
$701$		−	36.6906i		−	1.38578i	0.721041	−	0.692892i	$-0.243664\pi$
$702$		−	6.36111i		−	0.240085i
$703$	−21.6911	−	3.65930i	−0.818097	−	0.138013i
$704$	−1.24726			−0.0470078
$705$	−4.24237	−	26.1738i	−0.159777	−	0.985762i
$706$	1.32468			0.0498551
$707$			2.64939i			0.0996407i
$708$	0.548216			0.0206032
$709$		−	0.467718i		−	0.0175655i	−0.999961	−	0.00878275i	$-0.997204\pi$
$709$		−	0.467718i		−	0.0175655i	0.999961	−	0.00878275i	$-0.00279567\pi$
$710$	−5.82695	−	35.9501i	−0.218682	−	1.34918i
$711$		−	15.4144i		−	0.578084i
$712$		−	35.9928i		−	1.34889i
$713$			40.8895i			1.53132i
$714$	16.2498			0.608132
$715$	−0.268939	−	1.65925i	−0.0100577	−	0.0620524i
$716$		−	0.974162i		−	0.0364061i
$717$	2.59160			0.0967851
$718$	−45.4036			−1.69445
$719$	2.90651			0.108394			0.0541972	−	0.998530i	$-0.482740\pi$
$719$	2.90651			0.108394			0.0541972	+	0.998530i	$0.482740\pi$
$720$	−1.54951	−	9.55987i	−0.0577468	−	0.356275i
$721$		−	23.9888i		−	0.893390i
$722$	−8.74762			−0.325553
$723$	−1.08953			−0.0405199
$724$	3.71428			0.138040
$725$	3.87705	+	11.6457i	0.143990	+	0.432512i
$726$			16.2042i			0.601396i
$727$	−38.4833			−1.42727			−0.713633	−	0.700520i	$-0.752951\pi$
$727$	−38.4833			−1.42727			−0.713633	+	0.700520i	$0.752951\pi$
$728$		−	18.7390i		−	0.694512i
$729$	−1.00000			−0.0370370
$730$	−23.3752	+	3.78876i	−0.865154	+	0.140228i
$731$	−63.3043			−2.34139
$732$	2.08935			0.0772245
$733$		−	28.3333i		−	1.04651i	−0.852175	−	0.523256i	$-0.824717\pi$
$733$		−	28.3333i		−	1.04651i	0.852175	−	0.523256i	$-0.175283\pi$
$734$			54.1191i			1.99757i
$735$	9.65445	−	1.56484i	0.356110	−	0.0577199i
$736$	−6.79288			−0.250389
$737$			0.356237i			0.0131221i
$738$	17.1281			0.630494
$739$	18.1409			0.667324			0.333662	−	0.942693i	$-0.391716\pi$
$739$	18.1409			0.667324			0.333662	+	0.942693i	$0.391716\pi$
$740$	−2.47728	−	0.0159523i	−0.0910667	−	0.000586418i
$741$	−15.5728			−0.572081
$742$	−13.0978			−0.480835
$743$			13.1998i			0.484255i	0.970244	+	0.242127i	$0.0778452\pi$
$743$			13.1998i			0.484255i	−0.970244	+	0.242127i	$0.922155\pi$
$744$	16.6043			0.608742
$745$	4.55146	+	28.0808i	0.166753	+	1.02880i
$746$		−	2.61348i		−	0.0956864i
$747$			10.8772i			0.397977i
$748$	−0.215834			−0.00789166
$749$	6.00488			0.219413
$750$	14.6336	−	7.65678i	0.534342	−	0.279586i
$751$	−36.4942			−1.33169			−0.665845	−	0.746090i	$-0.731929\pi$
$751$	−36.4942			−1.33169			−0.665845	+	0.746090i	$0.731929\pi$
$752$			51.3584i			1.87285i
$753$	−17.5464			−0.639428
$754$		−	15.6154i		−	0.568681i
$755$	−6.02603	−	37.1783i	−0.219310	−	1.35306i
$756$	0.295155			0.0107347
$757$	8.13828			0.295791			0.147895	−	0.989003i	$-0.452750\pi$
$757$	8.13828			0.295791			0.147895	+	0.989003i	$0.452750\pi$
$758$	−0.110425			−0.00401083
$759$			1.15441i			0.0419025i
$760$	−21.4354	+	3.47435i	−0.777543	+	0.126028i
$761$	36.3100			1.31624			0.658118	−	0.752915i	$-0.271353\pi$
$761$	36.3100			1.31624			0.658118	+	0.752915i	$0.271353\pi$
$762$	15.2085			0.550946
$763$	−14.6321			−0.529718
$764$		−	1.53310i		−	0.0554656i
$765$	2.42857	+	14.9833i	0.0878051	+	0.541723i
$766$	12.1066			0.437429
$767$			12.9612i			0.468002i
$768$			4.33614i			0.156467i
$769$		−	19.5648i		−	0.705526i	−0.935713	−	0.352763i	$-0.885242\pi$
$769$		−	19.5648i		−	0.705526i	0.935713	−	0.352763i	$-0.114758\pi$
$770$	0.922387	−	0.149505i	0.0332405	−	0.00538778i
$771$			0.704289i			0.0253643i
$772$	1.39033			0.0500391
$773$			37.4349i			1.34644i	0.739442	+	0.673221i	$0.235090\pi$
$773$			37.4349i			1.34644i	−0.739442	+	0.673221i	$0.764910\pi$
$774$	−13.7759			−0.495164
$775$	9.76556	+	29.3335i	0.350789	+	1.05369i
$776$	−16.7501			−0.601293
$777$	−1.63974	+	9.71984i	−0.0588253	+	0.348697i
$778$			46.3247i			1.66082i
$779$		−	41.9318i		−	1.50236i
$780$	−1.73119	+	0.280599i	−0.0619864	+	0.0100471i
$781$	1.92474			0.0688724
$782$	66.3116			2.37130
$783$	−2.45483			−0.0877285
$784$	−18.9440			−0.676571
$785$	26.4448	−	4.28629i	0.943855	−	0.152984i
$786$	22.3873			0.798528
$787$			45.8917i			1.63586i	0.575315	+	0.817932i	$0.304879\pi$
$787$			45.8917i			1.63586i	−0.575315	+	0.817932i	$0.695121\pi$
$788$		−	3.71755i		−	0.132432i
$789$	−2.40942			−0.0857778
$790$	−50.2598	+	8.14634i	−1.78816	+	0.289834i
$791$			20.0987i			0.714629i
$792$	0.468779			0.0166573
$793$			49.3974i			1.75415i
$794$		−	17.0569i		−	0.605326i
$795$	−1.95750	−	12.0770i	−0.0694252	−	0.428327i
$796$		−	1.70800i		−	0.0605384i
$797$	25.6048			0.906968			0.453484	−	0.891264i	$-0.350181\pi$
$797$	25.6048			0.906968			0.453484	+	0.891264i	$0.350181\pi$
$798$		−	8.65701i		−	0.306455i
$799$		−	80.4947i		−	2.84770i
$800$	−4.87310	+	1.62233i	−0.172290	+	0.0573581i
$801$			13.4034i			0.473585i
$802$		−	16.8500i		−	0.594995i
$803$		−	1.25149i		−	0.0441640i
$804$	0.371681			0.0131082
$805$	−23.6537	+	3.83391i	−0.833685	+	0.135128i
$806$		−	39.3324i		−	1.38542i
$807$		−	31.2880i		−	1.10139i
$808$	4.39033			0.154451
$809$		−	8.26091i		−	0.290438i	−0.989400	−	0.145219i	$-0.953611\pi$
$809$		−	8.26091i		−	0.290438i	0.989400	−	0.145219i	$-0.0463887\pi$
$810$	0.528490	+	3.26058i	0.0185693	+	0.114565i
$811$	−24.8860			−0.873866			−0.436933	−	0.899494i	$-0.643935\pi$
$811$	−24.8860			−0.873866			−0.436933	+	0.899494i	$0.643935\pi$
$812$	0.724556			0.0254269
$813$		−	1.13176i		−	0.0396927i
$814$	0.260934	−	1.54673i	0.00914572	−	0.0542129i
$815$	2.04304	+	12.6048i	0.0715645	+	0.441526i
$816$		−	29.4004i		−	1.02922i
$817$			33.7251i			1.17989i
$818$		−	17.1721i		−	0.600408i
$819$			6.97820i			0.243838i
$820$	−0.755549	−	4.66145i	−0.0263849	−	0.162785i
$821$	12.4789			0.435517			0.217758	−	0.976003i	$-0.430126\pi$
$821$	12.4789			0.435517			0.217758	+	0.976003i	$0.430126\pi$
$822$	21.3503			0.744678
$823$			36.8738i			1.28534i	0.766143	+	0.642670i	$0.222173\pi$
$823$			36.8738i			1.28534i	−0.766143	+	0.642670i	$0.777827\pi$
$824$	−39.7520			−1.38483
$825$	0.275706	+	0.828156i	0.00959885	+	0.0288327i
$826$	−7.20521			−0.250701
$827$	−19.2791			−0.670401			−0.335200	−	0.942147i	$-0.608804\pi$
$827$	−19.2791			−0.670401			−0.335200	+	0.942147i	$0.608804\pi$
$828$	1.20446			0.0418579
$829$			5.96225i			0.207077i	0.994625	+	0.103539i	$0.0330166\pi$
$829$			5.96225i			0.207077i	−0.994625	+	0.103539i	$0.966983\pi$
$830$	35.4661	−	5.74850i	1.23104	−	0.199534i
$831$		−	1.15138i		−	0.0399410i
$832$	−30.7668			−1.06665
$833$	29.6912			1.02874
$834$			2.34876i			0.0813310i
$835$	−4.05664	−	25.0279i	−0.140386	−	0.866125i
$836$			0.114985i			0.00397683i
$837$	−6.18326			−0.213725
$838$	−34.4426			−1.18980
$839$	42.1147			1.45396			0.726980	−	0.686659i	$-0.240923\pi$
$839$	42.1147			1.45396			0.726980	+	0.686659i	$0.240923\pi$
$840$	1.55686	+	9.60523i	0.0537168	+	0.331412i
$841$	22.9738			0.792200
$842$		−	17.9928i		−	0.620074i
$843$	15.7460			0.542320
$844$	−0.400129			−0.0137730
$845$	−1.98313	−	12.2352i	−0.0682219	−	0.420903i
$846$		−	17.5168i		−	0.602239i
$847$		−	17.7762i		−	0.610798i
$848$			23.6975i			0.813777i
$849$			8.55489i			0.293603i
$850$	47.5709	−	15.8371i	1.63167	−	0.543207i
$851$	−6.69140	+	39.6644i	−0.229378	+	1.35968i
$852$		−	2.00818i		−	0.0687992i
$853$	7.86345			0.269239			0.134620	−	0.990897i	$-0.457019\pi$
$853$	7.86345			0.269239			0.134620	+	0.990897i	$0.457019\pi$
$854$	−27.4603			−0.939672
$855$	7.98232	−	1.29381i	0.272990	−	0.0442474i
$856$		−	9.95072i		−	0.340109i
$857$	−55.2541			−1.88744			−0.943721	−	0.330742i	$-0.892701\pi$
$857$	−55.2541			−1.88744			−0.943721	+	0.330742i	$0.892701\pi$
$858$		−	1.11045i		−	0.0379101i
$859$			26.5002i			0.904176i	0.891973	+	0.452088i	$0.149321\pi$
$859$			26.5002i			0.904176i	−0.891973	+	0.452088i	$0.850679\pi$
$860$	0.607677	+	3.74913i	0.0207216	+	0.127844i
$861$	−18.7897			−0.640352
$862$			20.2479i			0.689647i
$863$		−	1.45128i		−	0.0494020i	−0.999695	−	0.0247010i	$-0.992137\pi$
$863$		−	1.45128i		−	0.0494020i	0.999695	−	0.0247010i	$-0.00786338\pi$
$864$		−	1.02721i		−	0.0349464i
$865$	−3.18993	+	0.517039i	−0.108461	+	0.0175799i
$866$		−	0.423171i		−	0.0143799i
$867$			29.0796i			0.987596i
$868$	1.82502			0.0619452
$869$		−	2.69087i		−	0.0912814i
$870$	1.29735	+	8.00417i	0.0439844	+	0.271367i
$871$			8.78747i			0.297752i
$872$			24.2470i			0.821106i
$873$	6.23756			0.211109
$874$		−	35.3273i		−	1.19496i
$875$	−16.0532	+	8.39956i	−0.542696	+	0.283957i
$876$	−1.30575			−0.0441170
$877$			1.34140i			0.0452959i	0.999744	+	0.0226480i	$0.00720969\pi$
$877$			1.34140i			0.0452959i	−0.999744	+	0.0226480i	$0.992790\pi$
$878$		−	30.9624i		−	1.04493i
$879$	−8.87914			−0.299486
$880$	−0.270496	−	1.66885i	−0.00911841	−	0.0562571i
$881$	−17.8018			−0.599759			−0.299879	−	0.953977i	$-0.596946\pi$
$881$	−17.8018			−0.599759			−0.299879	+	0.953977i	$0.596946\pi$
$882$	6.46122			0.217561
$883$	18.1336			0.610244			0.305122	−	0.952313i	$-0.401303\pi$
$883$	18.1336			0.610244			0.305122	+	0.952313i	$0.401303\pi$
$884$	−5.32408			−0.179068
$885$	−1.07684	−	6.64366i	−0.0361974	−	0.223324i
$886$			39.0996i			1.31358i
$887$		−	29.6277i		−	0.994800i	−0.867521	−	0.497400i	$-0.834288\pi$
$887$		−	29.6277i		−	0.994800i	0.867521	−	0.497400i	$-0.165712\pi$
$888$	16.1068	+	2.71722i	0.540509	+	0.0911840i
$889$	−16.6839			−0.559560
$890$	43.7028	−	7.08355i	1.46492	−	0.237441i
$891$	−0.174569			−0.00584827
$892$		−	2.25513i		−	0.0755074i
$893$	−42.8833			−1.43503
$894$			18.7930i			0.628532i
$895$	−11.8056	+	1.91350i	−0.394616	+	0.0639613i
$896$		−	20.4326i		−	0.682606i
$897$			28.4764i			0.950801i
$898$		−	43.1089i		−	1.43856i
$899$	−15.1789			−0.506243
$900$	0.864060	−	0.287659i	0.0288020	−	0.00958864i
$901$		−	37.1415i		−	1.23736i
$902$	2.99003			0.0995571
$903$	15.1123			0.502906
$904$	33.3057			1.10773
$905$	−7.29579	−	45.0122i	−0.242520	−	1.49626i
$906$		−	24.8815i		−	0.826633i
$907$	30.5959			1.01592			0.507960	−	0.861381i	$-0.330400\pi$
$907$	30.5959			1.01592			0.507960	+	0.861381i	$0.330400\pi$
$908$	0.346093			0.0114855
$909$	−1.63491			−0.0542267
$910$	22.7530	−	3.68791i	0.754254	−	0.122253i
$911$		−	9.21700i		−	0.305373i	−0.988275	−	0.152686i	$-0.951208\pi$
$911$		−	9.21700i		−	0.305373i	0.988275	−	0.152686i	$-0.0487924\pi$
$912$	−15.6629			−0.518652
$913$			1.89882i			0.0628418i
$914$	−25.7444			−0.851551
$915$	−4.10401	−	25.3201i	−0.135674	−	0.837058i
$916$	−0.924669			−0.0305519
$917$	−24.5591			−0.811012
$918$			10.0276i			0.330959i
$919$		−	30.0268i		−	0.990494i	−0.868752	−	0.495247i	$-0.835077\pi$
$919$		−	30.0268i		−	0.990494i	0.868752	−	0.495247i	$-0.164923\pi$
$920$	6.35319	+	39.1968i	0.209459	+	1.29228i
$921$	9.27241			0.305536
$922$			16.8498i			0.554919i
$923$	47.4784			1.56277
$924$	0.0515248			0.00169504
$925$	4.67269	+	30.0527i	0.153637	+	0.988127i
$926$	19.2572			0.632832
$927$	14.8032			0.486203
$928$		−	2.52163i		−	0.0827765i
$929$	13.5774			0.445458			0.222729	−	0.974880i	$-0.428503\pi$
$929$	13.5774			0.445458			0.222729	+	0.974880i	$0.428503\pi$
$930$	3.26779	+	20.1610i	0.107155	+	0.661106i
$931$		−	15.8179i		−	0.518410i
$932$		−	0.0694348i		−	0.00227441i
$933$	−30.4567			−0.997106
$934$	20.9948			0.686972
$935$	0.423952	+	2.61562i	0.0138647	+	0.0855399i
$936$	11.5636			0.377969
$937$			14.6712i			0.479288i	0.970861	+	0.239644i	$0.0770307\pi$
$937$			14.6712i			0.479288i	−0.970861	+	0.239644i	$0.922969\pi$
$938$	−4.88501			−0.159501
$939$			9.88196i			0.322486i
$940$	−4.76722	+	0.772693i	−0.155490	+	0.0252025i
$941$	−9.36196			−0.305191			−0.152596	−	0.988289i	$-0.548763\pi$
$941$	−9.36196			−0.305191			−0.152596	+	0.988289i	$0.548763\pi$
$942$	17.6981			0.576636
$943$	−76.6765			−2.49693
$944$			13.0362i			0.424293i
$945$	−0.579759	−	3.57689i	−0.0188596	−	0.116356i
$946$	−2.40484			−0.0781880
$947$	34.2769			1.11385			0.556925	−	0.830563i	$-0.311981\pi$
$947$	34.2769			1.11385			0.556925	+	0.830563i	$0.311981\pi$
$948$	−2.80753			−0.0911843
$949$		−	30.8711i		−	1.00212i
$950$	−8.43715	−	25.3432i	−0.273737	−	0.822243i
$951$	−20.6863			−0.670799
$952$			29.5399i			0.957392i
$953$			50.1895i			1.62580i	0.582405	+	0.812899i	$0.302112\pi$
$953$			50.1895i			1.62580i	−0.582405	+	0.812899i	$0.697888\pi$
$954$		−	8.08250i		−	0.261681i
$955$	−18.5792	+	3.01140i	−0.601207	+	0.0974465i
$956$		−	0.472026i		−	0.0152664i
$957$	−0.428537			−0.0138526
$958$		−	36.6700i		−	1.18475i
$959$	−23.4215			−0.756321
$960$	15.7704	−	2.55615i	0.508989	−	0.0824993i
$961$	−7.23271			−0.233313
$962$	6.43658	−	38.1540i	0.207524	−	1.23013i
$963$			3.70555i			0.119410i
$964$			0.198443i			0.00639143i
$965$	−2.73096	−	16.8490i	−0.0879127	−	0.542388i
$966$	−15.8302			−0.509329
$967$	−38.1299			−1.22618			−0.613088	−	0.790015i	$-0.710073\pi$
$967$	−38.1299			−1.22618			−0.613088	+	0.790015i	$0.710073\pi$
$968$	−29.4571			−0.946787
$969$	24.5488			0.788620
$970$	−3.29649	−	20.3381i	−0.105844	−	0.653016i
$971$	−2.96435			−0.0951305			−0.0475652	−	0.998868i	$-0.515146\pi$
$971$	−2.96435			−0.0951305			−0.0475652	+	0.998868i	$0.515146\pi$
$972$			0.182137i			0.00584205i
$973$		−	2.57662i		−	0.0826026i
$974$	16.5111			0.529050
$975$	6.80098	+	20.4285i	0.217806	+	0.654237i
$976$			49.6833i			1.59032i
$977$	−2.09963			−0.0671731			−0.0335866	−	0.999436i	$-0.510693\pi$
$977$	−2.09963			−0.0671731			−0.0335866	+	0.999436i	$0.510693\pi$
$978$			8.43571i			0.269744i
$979$			2.33981i			0.0747806i
$980$	−0.285015	−	1.75843i	−0.00910447	−	0.0561711i
$981$		−	9.02932i		−	0.288284i
$982$	−4.48988			−0.143278
$983$		−	3.19301i		−	0.101841i	−0.998703	−	0.0509207i	$-0.983784\pi$
$983$		−	3.19301i		−	0.101841i	0.998703	−	0.0509207i	$-0.0162156\pi$
$984$			31.1366i			0.992597i
$985$	−45.0518	+	7.30220i	−1.43547	+	0.232668i
$986$			24.6160i			0.783932i
$987$			19.2161i			0.611654i
$988$			2.83639i			0.0902374i
$989$	61.6698			1.96099
$990$	0.0922578	+	0.569195i	0.00293215	+	0.0180902i
$991$		−	41.6277i		−	1.32235i	−0.750233	−	0.661173i	$-0.770059\pi$
$991$		−	41.6277i		−	1.32235i	0.750233	−	0.661173i	$-0.229941\pi$
$992$		−	6.35151i		−	0.201661i
$993$	12.1462			0.385448
$994$			26.3935i			0.837152i
$995$	−20.6987	+	3.35494i	−0.656193	+	0.106359i
$996$	1.98115			0.0627750
$997$	35.9553			1.13872			0.569358	−	0.822090i	$-0.307192\pi$
$997$	35.9553			1.13872			0.569358	+	0.822090i	$0.307192\pi$
$998$		−	29.7732i		−	0.942454i
$999$	−5.99801	−	1.01187i	−0.189769	−	0.0320140i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	555.2.g.a.184.12	yes	40
3.2	odd	2		1665.2.g.e.739.30		40
5.4	even	2	inner	555.2.g.a.184.29	yes	40
15.14	odd	2		1665.2.g.e.739.11		40
37.36	even	2	inner	555.2.g.a.184.30	yes	40
111.110	odd	2		1665.2.g.e.739.12		40
185.184	even	2	inner	555.2.g.a.184.11	✓	40
555.554	odd	2		1665.2.g.e.739.29		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
555.2.g.a.184.11	✓	40	185.184	even	2	inner
555.2.g.a.184.12	yes	40	1.1	even	1	trivial
555.2.g.a.184.29	yes	40	5.4	even	2	inner
555.2.g.a.184.30	yes	40	37.36	even	2	inner
1665.2.g.e.739.11		40	15.14	odd	2
1665.2.g.e.739.12		40	111.110	odd	2
1665.2.g.e.739.29		40	555.554	odd	2
1665.2.g.e.739.30		40	3.2	odd	2

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.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.47721 q^{2} +1.00000i q^{3} +0.182137 q^{4} +(-0.357763 - 2.20726i) q^{5} -1.47721i q^{6} +1.62051i q^{7} +2.68536 q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-1.47721 q^{2} +1.00000i q^{3} +0.182137 q^{4} +(-0.357763 - 2.20726i) q^{5} -1.47721i q^{6} +1.62051i q^{7} +2.68536 q^{8} -1.00000 q^{9} +(0.528490 + 3.26058i) q^{10} -0.174569 q^{11} +0.182137i q^{12} -4.30618 q^{13} -2.39383i q^{14} +(2.20726 - 0.357763i) q^{15} -4.33110 q^{16} +6.78820 q^{17} +1.47721 q^{18} -3.61639i q^{19} +(-0.0651620 - 0.402024i) q^{20} -1.62051 q^{21} +0.257874 q^{22} -6.61293 q^{23} +2.68536i q^{24} +(-4.74401 + 1.57935i) q^{25} +6.36111 q^{26} -1.00000i q^{27} +0.295155i q^{28} -2.45483i q^{29} +(-3.26058 + 0.528490i) q^{30} -6.18326i q^{31} +1.02721 q^{32} -0.174569i q^{33} -10.0276 q^{34} +(3.57689 - 0.579759i) q^{35} -0.182137 q^{36} +(1.01187 - 5.99801i) q^{37} +5.34215i q^{38} -4.30618i q^{39} +(-0.960723 - 5.92729i) q^{40} +11.5949 q^{41} +2.39383 q^{42} -9.32564 q^{43} -0.0317954 q^{44} +(0.357763 + 2.20726i) q^{45} +9.76866 q^{46} -11.8580i q^{47} -4.33110i q^{48} +4.37395 q^{49} +(7.00788 - 2.33303i) q^{50} +6.78820i q^{51} -0.784314 q^{52} -5.47148i q^{53} +1.47721i q^{54} +(0.0624543 + 0.385319i) q^{55} +4.35165i q^{56} +3.61639 q^{57} +3.62629i q^{58} -3.00991i q^{59} +(0.402024 - 0.0651620i) q^{60} -11.4713i q^{61} +9.13395i q^{62} -1.62051i q^{63} +7.14480 q^{64} +(1.54059 + 9.50486i) q^{65} +0.257874i q^{66} -2.04067i q^{67} +1.23638 q^{68} -6.61293i q^{69} +(-5.28380 + 0.856424i) q^{70} -11.0257 q^{71} -2.68536 q^{72} +7.16903i q^{73} +(-1.49473 + 8.86030i) q^{74} +(-1.57935 - 4.74401i) q^{75} -0.658679i q^{76} -0.282890i q^{77} +6.36111i q^{78} +15.4144i q^{79} +(1.54951 + 9.55987i) q^{80} +1.00000 q^{81} -17.1281 q^{82} -10.8772i q^{83} -0.295155 q^{84} +(-2.42857 - 14.9833i) q^{85} +13.7759 q^{86} +2.45483 q^{87} -0.468779 q^{88} -13.4034i q^{89} +(-0.528490 - 3.26058i) q^{90} -6.97820i q^{91} -1.20446 q^{92} +6.18326 q^{93} +17.5168i q^{94} +(-7.98232 + 1.29381i) q^{95} +1.02721i q^{96} -6.23756 q^{97} -6.46122 q^{98} +0.174569 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 44 q^{4} - 40 q^{9}+O(q^{10}) \) 40 * q + 44 * q^4 - 40 * q^9	\( 40 q + 44 q^{4} - 40 q^{9} + 4 q^{10} + 8 q^{11} + 52 q^{16} - 16 q^{21} + 8 q^{25} - 16 q^{26} + 16 q^{30} - 32 q^{34} - 44 q^{36} - 28 q^{40} + 8 q^{41} + 16 q^{44} - 8 q^{46} - 24 q^{49} + 92 q^{64} - 48 q^{65} - 56 q^{70} + 24 q^{71} - 68 q^{74} + 8 q^{75} + 40 q^{81} - 16 q^{84} - 64 q^{85} + 80 q^{86} - 4 q^{90} + 32 q^{95} - 8 q^{99}+O(q^{100}) \) 40 * q + 44 * q^4 - 40 * q^9 + 4 * q^10 + 8 * q^11 + 52 * q^16 - 16 * q^21 + 8 * q^25 - 16 * q^26 + 16 * q^30 - 32 * q^34 - 44 * q^36 - 28 * q^40 + 8 * q^41 + 16 * q^44 - 8 * q^46 - 24 * q^49 + 92 * q^64 - 48 * q^65 - 56 * q^70 + 24 * q^71 - 68 * q^74 + 8 * q^75 + 40 * q^81 - 16 * q^84 - 64 * q^85 + 80 * q^86 - 4 * q^90 + 32 * q^95 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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