LMFDB - Embedded newform 1470.2.d.c.1469.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1470,2,Mod(1469,1470)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1470, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 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("1470.1469");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1470.d (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:	$11.7380090971$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-11})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 2x^{2} - 3x + 9 $ x^4 - x^3 - 2x^2 - 3x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1469.3
Root			$-1.18614 + 1.26217i$ of defining polynomial
Character	$\chi$	$=$	1470.1469
Dual form			1470.2.d.c.1469.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(1.18614 - 1.26217i) q^{3} +1.00000 q^{4} +(0.686141 + 2.12819i) q^{5} +(1.18614 - 1.26217i) q^{6} +1.00000 q^{8} +(-0.186141 - 2.99422i) q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(1.18614 - 1.26217i) q^{3} +1.00000 q^{4} +(0.686141 + 2.12819i) q^{5} +(1.18614 - 1.26217i) q^{6} +1.00000 q^{8} +(-0.186141 - 2.99422i) q^{9} +(0.686141 + 2.12819i) q^{10} +4.25639i q^{11} +(1.18614 - 1.26217i) q^{12} +2.00000 q^{13} +(3.50000 + 1.65831i) q^{15} +1.00000 q^{16} +6.63325i q^{17} +(-0.186141 - 2.99422i) q^{18} +3.46410i q^{19} +(0.686141 + 2.12819i) q^{20} +4.25639i q^{22} +4.37228 q^{23} +(1.18614 - 1.26217i) q^{24} +(-4.05842 + 2.92048i) q^{25} +2.00000 q^{26} +(-4.00000 - 3.31662i) q^{27} -3.31662i q^{29} +(3.50000 + 1.65831i) q^{30} -2.37686i q^{31} +1.00000 q^{32} +(5.37228 + 5.04868i) q^{33} +6.63325i q^{34} +(-0.186141 - 2.99422i) q^{36} -11.6819i q^{37} +3.46410i q^{38} +(2.37228 - 2.52434i) q^{39} +(0.686141 + 2.12819i) q^{40} +1.62772 q^{41} -11.0371i q^{43} +4.25639i q^{44} +(6.24456 - 2.45060i) q^{45} +4.37228 q^{46} +1.87953i q^{47} +(1.18614 - 1.26217i) q^{48} +(-4.05842 + 2.92048i) q^{50} +(8.37228 + 7.86797i) q^{51} +2.00000 q^{52} +1.37228 q^{53} +(-4.00000 - 3.31662i) q^{54} +(-9.05842 + 2.92048i) q^{55} +(4.37228 + 4.10891i) q^{57} -3.31662i q^{58} -4.11684 q^{59} +(3.50000 + 1.65831i) q^{60} +2.81929i q^{61} -2.37686i q^{62} +1.00000 q^{64} +(1.37228 + 4.25639i) q^{65} +(5.37228 + 5.04868i) q^{66} -7.57301i q^{67} +6.63325i q^{68} +(5.18614 - 5.51856i) q^{69} +1.87953i q^{71} +(-0.186141 - 2.99422i) q^{72} +2.00000 q^{73} -11.6819i q^{74} +(-1.12772 + 8.58652i) q^{75} +3.46410i q^{76} +(2.37228 - 2.52434i) q^{78} -8.11684 q^{79} +(0.686141 + 2.12819i) q^{80} +(-8.93070 + 1.11469i) q^{81} +1.62772 q^{82} +1.43710i q^{83} +(-14.1168 + 4.55134i) q^{85} -11.0371i q^{86} +(-4.18614 - 3.93398i) q^{87} +4.25639i q^{88} -4.37228 q^{89} +(6.24456 - 2.45060i) q^{90} +4.37228 q^{92} +(-3.00000 - 2.81929i) q^{93} +1.87953i q^{94} +(-7.37228 + 2.37686i) q^{95} +(1.18614 - 1.26217i) q^{96} -2.11684 q^{97} +(12.7446 - 0.792287i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} - q^{3} + 4 q^{4} - 3 q^{5} - q^{6} + 4 q^{8} + 5 q^{9}+O(q^{10}) $ 4 * q + 4 * q^2 - q^3 + 4 * q^4 - 3 * q^5 - q^6 + 4 * q^8 + 5 * q^9	$ 4 q + 4 q^{2} - q^{3} + 4 q^{4} - 3 q^{5} - q^{6} + 4 q^{8} + 5 q^{9} - 3 q^{10} - q^{12} + 8 q^{13} + 14 q^{15} + 4 q^{16} + 5 q^{18} - 3 q^{20} + 6 q^{23} - q^{24} + q^{25} + 8 q^{26} - 16 q^{27} + 14 q^{30} + 4 q^{32} + 10 q^{33} + 5 q^{36} - 2 q^{39} - 3 q^{40} + 18 q^{41} + 2 q^{45} + 6 q^{46} - q^{48} + q^{50} + 22 q^{51} + 8 q^{52} - 6 q^{53} - 16 q^{54} - 19 q^{55} + 6 q^{57} + 18 q^{59} + 14 q^{60} + 4 q^{64} - 6 q^{65} + 10 q^{66} + 15 q^{69} + 5 q^{72} + 8 q^{73} - 16 q^{75} - 2 q^{78} + 2 q^{79} - 3 q^{80} - 7 q^{81} + 18 q^{82} - 22 q^{85} - 11 q^{87} - 6 q^{89} + 2 q^{90} + 6 q^{92} - 12 q^{93} - 18 q^{95} - q^{96} + 26 q^{97} + 28 q^{99}+O(q^{100}) $ 4 * q + 4 * q^2 - q^3 + 4 * q^4 - 3 * q^5 - q^6 + 4 * q^8 + 5 * q^9 - 3 * q^10 - q^12 + 8 * q^13 + 14 * q^15 + 4 * q^16 + 5 * q^18 - 3 * q^20 + 6 * q^23 - q^24 + q^25 + 8 * q^26 - 16 * q^27 + 14 * q^30 + 4 * q^32 + 10 * q^33 + 5 * q^36 - 2 * q^39 - 3 * q^40 + 18 * q^41 + 2 * q^45 + 6 * q^46 - q^48 + q^50 + 22 * q^51 + 8 * q^52 - 6 * q^53 - 16 * q^54 - 19 * q^55 + 6 * q^57 + 18 * q^59 + 14 * q^60 + 4 * q^64 - 6 * q^65 + 10 * q^66 + 15 * q^69 + 5 * q^72 + 8 * q^73 - 16 * q^75 - 2 * q^78 + 2 * q^79 - 3 * q^80 - 7 * q^81 + 18 * q^82 - 22 * q^85 - 11 * q^87 - 6 * q^89 + 2 * q^90 + 6 * q^92 - 12 * q^93 - 18 * q^95 - q^96 + 26 * q^97 + 28 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times$.

$n$	$491$	$1081$	$1177$
$\chi(n)$	$-1$	$-1$	$-1$

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 $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	1.18614	−	1.26217i	0.684819	−	0.728714i
$3$	1.18614	−	1.26217i	0.684819	−	0.728714i
$4$	1.00000			0.500000
$5$	0.686141	+	2.12819i	0.306851	+	0.951757i
$5$	0.686141	+	2.12819i	0.306851	+	0.951757i
$6$	1.18614	−	1.26217i	0.484240	−	0.515278i
$7$		0			0
$7$		0			0
$8$	1.00000			0.353553
$9$	−0.186141	−	2.99422i	−0.0620469	−	0.998073i
$10$	0.686141	+	2.12819i	0.216977	+	0.672994i
$11$			4.25639i			1.28335i	0.766977	+	0.641675i	$0.221760\pi$
$11$			4.25639i			1.28335i	−0.766977	+	0.641675i	$0.778240\pi$
$12$	1.18614	−	1.26217i	0.342409	−	0.364357i
$13$	2.00000			0.554700			0.277350	−	0.960769i	$-0.410544\pi$
$13$	2.00000			0.554700			0.277350	+	0.960769i	$0.410544\pi$
$14$		0			0
$15$	3.50000	+	1.65831i	0.903696	+	0.428174i
$16$	1.00000			0.250000
$17$			6.63325i			1.60880i	0.594089	+	0.804400i	$0.297513\pi$
$17$			6.63325i			1.60880i	−0.594089	+	0.804400i	$0.702487\pi$
$18$	−0.186141	−	2.99422i	−0.0438738	−	0.705744i
$19$			3.46410i			0.794719i	0.917663	+	0.397360i	$0.130073\pi$
$19$			3.46410i			0.794719i	−0.917663	+	0.397360i	$0.869927\pi$
$20$	0.686141	+	2.12819i	0.153426	+	0.475879i
$21$		0			0
$22$			4.25639i			0.907465i
$23$	4.37228			0.911684			0.455842	−	0.890061i	$-0.349338\pi$
$23$	4.37228			0.911684			0.455842	+	0.890061i	$0.349338\pi$
$24$	1.18614	−	1.26217i	0.242120	−	0.257639i
$25$	−4.05842	+	2.92048i	−0.811684	+	0.584096i
$26$	2.00000			0.392232
$27$	−4.00000	−	3.31662i	−0.769800	−	0.638285i
$28$		0			0
$29$		−	3.31662i		−	0.615882i	−0.951405	−	0.307941i	$-0.900360\pi$
$29$		−	3.31662i		−	0.615882i	0.951405	−	0.307941i	$-0.0996399\pi$
$30$	3.50000	+	1.65831i	0.639010	+	0.302765i
$31$		−	2.37686i		−	0.426897i	−0.976954	−	0.213448i	$-0.931530\pi$
$31$		−	2.37686i		−	0.426897i	0.976954	−	0.213448i	$-0.0684695\pi$
$32$	1.00000			0.176777
$33$	5.37228	+	5.04868i	0.935194	+	0.878862i
$34$			6.63325i			1.13759i
$35$		0			0
$36$	−0.186141	−	2.99422i	−0.0310234	−	0.499037i
$37$		−	11.6819i		−	1.92050i	−0.279147	−	0.960248i	$-0.590052\pi$
$37$		−	11.6819i		−	1.92050i	0.279147	−	0.960248i	$-0.409948\pi$
$38$			3.46410i			0.561951i
$39$	2.37228	−	2.52434i	0.379869	−	0.404218i
$40$	0.686141	+	2.12819i	0.108488	+	0.336497i
$41$	1.62772			0.254207			0.127103	−	0.991889i	$-0.459432\pi$
$41$	1.62772			0.254207			0.127103	+	0.991889i	$0.459432\pi$
$42$		0			0
$43$		−	11.0371i		−	1.68314i	−0.540145	−	0.841572i	$-0.681631\pi$
$43$		−	11.0371i		−	1.68314i	0.540145	−	0.841572i	$-0.318369\pi$
$44$			4.25639i			0.641675i
$45$	6.24456	−	2.45060i	0.930884	−	0.365314i
$46$	4.37228			0.644658
$47$			1.87953i			0.274157i	0.990560	+	0.137079i	$0.0437713\pi$
$47$			1.87953i			0.274157i	−0.990560	+	0.137079i	$0.956229\pi$
$48$	1.18614	−	1.26217i	0.171205	−	0.182178i
$49$		0			0
$50$	−4.05842	+	2.92048i	−0.573948	+	0.413018i
$51$	8.37228	+	7.86797i	1.17235	+	1.10174i
$52$	2.00000			0.277350
$53$	1.37228			0.188497			0.0942487	−	0.995549i	$-0.469955\pi$
$53$	1.37228			0.188497			0.0942487	+	0.995549i	$0.469955\pi$
$54$	−4.00000	−	3.31662i	−0.544331	−	0.451335i
$55$	−9.05842	+	2.92048i	−1.22144	+	0.393798i
$56$		0			0
$57$	4.37228	+	4.10891i	0.579123	+	0.544239i
$58$		−	3.31662i		−	0.435494i
$59$	−4.11684			−0.535967			−0.267984	−	0.963423i	$-0.586357\pi$
$59$	−4.11684			−0.535967			−0.267984	+	0.963423i	$0.586357\pi$
$60$	3.50000	+	1.65831i	0.451848	+	0.214087i
$61$			2.81929i			0.360973i	0.983577	+	0.180487i	$0.0577673\pi$
$61$			2.81929i			0.360973i	−0.983577	+	0.180487i	$0.942233\pi$
$62$		−	2.37686i		−	0.301862i
$63$		0			0
$64$	1.00000			0.125000
$65$	1.37228	+	4.25639i	0.170211	+	0.527940i
$66$	5.37228	+	5.04868i	0.661282	+	0.621449i
$67$		−	7.57301i		−	0.925191i	−0.886569	−	0.462595i	$-0.846918\pi$
$67$		−	7.57301i		−	0.925191i	0.886569	−	0.462595i	$-0.153082\pi$
$68$			6.63325i			0.804400i
$69$	5.18614	−	5.51856i	0.624338	−	0.664356i
$70$		0			0
$71$			1.87953i			0.223059i	0.993761	+	0.111529i	$0.0355749\pi$
$71$			1.87953i			0.223059i	−0.993761	+	0.111529i	$0.964425\pi$
$72$	−0.186141	−	2.99422i	−0.0219369	−	0.352872i
$73$	2.00000			0.234082			0.117041	−	0.993127i	$-0.462659\pi$
$73$	2.00000			0.234082			0.117041	+	0.993127i	$0.462659\pi$
$74$		−	11.6819i		−	1.35800i
$75$	−1.12772	+	8.58652i	−0.130218	+	0.991485i
$76$			3.46410i			0.397360i
$77$		0			0
$78$	2.37228	−	2.52434i	0.268608	−	0.285825i
$79$	−8.11684			−0.913216			−0.456608	−	0.889668i	$-0.650936\pi$
$79$	−8.11684			−0.913216			−0.456608	+	0.889668i	$0.650936\pi$
$80$	0.686141	+	2.12819i	0.0767129	+	0.237939i
$81$	−8.93070	+	1.11469i	−0.992300	+	0.123855i
$82$	1.62772			0.179751
$83$			1.43710i			0.157742i	0.996885	+	0.0788710i	$0.0251315\pi$
$83$			1.43710i			0.157742i	−0.996885	+	0.0788710i	$0.974868\pi$
$84$		0			0
$85$	−14.1168	+	4.55134i	−1.53119	+	0.493662i
$86$		−	11.0371i		−	1.19016i
$87$	−4.18614	−	3.93398i	−0.448801	−	0.421767i
$88$			4.25639i			0.453733i
$89$	−4.37228			−0.463461			−0.231730	−	0.972780i	$-0.574439\pi$
$89$	−4.37228			−0.463461			−0.231730	+	0.972780i	$0.574439\pi$
$90$	6.24456	−	2.45060i	0.658235	−	0.258316i
$91$		0			0
$92$	4.37228			0.455842
$93$	−3.00000	−	2.81929i	−0.311086	−	0.292347i
$94$			1.87953i			0.193858i
$95$	−7.37228	+	2.37686i	−0.756380	+	0.243861i
$96$	1.18614	−	1.26217i	0.121060	−	0.128820i
$97$	−2.11684			−0.214933			−0.107466	−	0.994209i	$-0.534274\pi$
$97$	−2.11684			−0.214933			−0.107466	+	0.994209i	$0.534274\pi$
$98$		0			0
$99$	12.7446	−	0.792287i	1.28088	−	0.0796278i
$100$	−4.05842	+	2.92048i	−0.405842	+	0.292048i
$101$	−16.3723			−1.62910			−0.814551	−	0.580091i	$-0.803017\pi$
$101$	−16.3723			−1.62910			−0.814551	+	0.580091i	$0.803017\pi$
$102$	8.37228	+	7.86797i	0.828979	+	0.779045i
$103$	15.1168			1.48951			0.744753	−	0.667340i	$-0.232567\pi$
$103$	15.1168			1.48951			0.744753	+	0.667340i	$0.232567\pi$
$104$	2.00000			0.196116
$105$		0			0
$106$	1.37228			0.133288
$107$	17.7446			1.71543			0.857716	−	0.514124i	$-0.171883\pi$
$107$	17.7446			1.71543			0.857716	+	0.514124i	$0.171883\pi$
$108$	−4.00000	−	3.31662i	−0.384900	−	0.319142i
$109$	9.11684			0.873235			0.436618	−	0.899647i	$-0.356176\pi$
$109$	9.11684			0.873235			0.436618	+	0.899647i	$0.356176\pi$
$110$	−9.05842	+	2.92048i	−0.863687	+	0.278457i
$111$	−14.7446	−	13.8564i	−1.39949	−	1.31519i
$112$		0			0
$113$	−3.25544			−0.306246			−0.153123	−	0.988207i	$-0.548933\pi$
$113$	−3.25544			−0.306246			−0.153123	+	0.988207i	$0.548933\pi$
$114$	4.37228	+	4.10891i	0.409502	+	0.384835i
$115$	3.00000	+	9.30506i	0.279751	+	0.867702i
$116$		−	3.31662i		−	0.307941i
$117$	−0.372281	−	5.98844i	−0.0344174	−	0.553631i
$118$	−4.11684			−0.378986
$119$		0			0
$120$	3.50000	+	1.65831i	0.319505	+	0.151383i
$121$	−7.11684			−0.646986
$122$			2.81929i			0.255247i
$123$	1.93070	−	2.05446i	0.174086	−	0.185244i
$124$		−	2.37686i		−	0.213448i
$125$	−9.00000	−	6.63325i	−0.804984	−	0.593296i
$126$		0			0
$127$		−	2.37686i		−	0.210912i	−0.994424	−	0.105456i	$-0.966370\pi$
$127$		−	2.37686i		−	0.210912i	0.994424	−	0.105456i	$-0.0336303\pi$
$128$	1.00000			0.0883883
$129$	−13.9307	−	13.0916i	−1.22653	−	1.15265i
$130$	1.37228	+	4.25639i	0.120357	+	0.373310i
$131$	−4.62772			−0.404326			−0.202163	−	0.979352i	$-0.564797\pi$
$131$	−4.62772			−0.404326			−0.202163	+	0.979352i	$0.564797\pi$
$132$	5.37228	+	5.04868i	0.467597	+	0.439431i
$133$		0			0
$134$		−	7.57301i		−	0.654209i
$135$	4.31386	−	10.7884i	0.371278	−	0.928522i
$136$			6.63325i			0.568796i
$137$	2.74456			0.234484			0.117242	−	0.993103i	$-0.462595\pi$
$137$	2.74456			0.234484			0.117242	+	0.993103i	$0.462595\pi$
$138$	5.18614	−	5.51856i	0.441474	−	0.469771i
$139$		−	11.6819i		−	0.990848i	−0.868651	−	0.495424i	$-0.835013\pi$
$139$		−	11.6819i		−	0.990848i	0.868651	−	0.495424i	$-0.164987\pi$
$140$		0			0
$141$	2.37228	+	2.22938i	0.199782	+	0.187748i
$142$			1.87953i			0.157726i
$143$			8.51278i			0.711874i
$144$	−0.186141	−	2.99422i	−0.0155117	−	0.249518i
$145$	7.05842	−	2.27567i	0.586170	−	0.188984i
$146$	2.00000			0.165521
$147$		0			0
$148$		−	11.6819i		−	0.960248i
$149$			14.2063i			1.16382i	0.813252	+	0.581911i	$0.197695\pi$
$149$			14.2063i			1.16382i	−0.813252	+	0.581911i	$0.802305\pi$
$150$	−1.12772	+	8.58652i	−0.0920778	+	0.701086i
$151$	−8.11684			−0.660539			−0.330270	−	0.943887i	$-0.607140\pi$
$151$	−8.11684			−0.660539			−0.330270	+	0.943887i	$0.607140\pi$
$152$			3.46410i			0.280976i
$153$	19.8614	−	1.23472i	1.60570	−	0.0998210i
$154$		0			0
$155$	5.05842	−	1.63086i	0.406302	−	0.130994i
$156$	2.37228	−	2.52434i	0.189935	−	0.202109i
$157$	8.00000			0.638470			0.319235	−	0.947676i	$-0.396574\pi$
$157$	8.00000			0.638470			0.319235	+	0.947676i	$0.396574\pi$
$158$	−8.11684			−0.645741
$159$	1.62772	−	1.73205i	0.129086	−	0.137361i
$160$	0.686141	+	2.12819i	0.0542442	+	0.168249i
$161$		0			0
$162$	−8.93070	+	1.11469i	−0.701662	+	0.0875785i
$163$			3.46410i			0.271329i	0.990755	+	0.135665i	$0.0433170\pi$
$163$			3.46410i			0.271329i	−0.990755	+	0.135665i	$0.956683\pi$
$164$	1.62772			0.127103
$165$	−7.05842	+	14.8974i	−0.549497	+	1.15976i
$166$			1.43710i			0.111540i
$167$		−	11.3321i		−	0.876902i	−0.898755	−	0.438451i	$-0.855527\pi$
$167$		−	11.3321i		−	0.876902i	0.898755	−	0.438451i	$-0.144473\pi$
$168$		0			0
$169$	−9.00000			−0.692308
$170$	−14.1168	+	4.55134i	−1.08271	+	0.349072i
$171$	10.3723	−	0.644810i	0.793188	−	0.0493099i
$172$		−	11.0371i		−	0.841572i
$173$		−	3.75906i		−	0.285796i	−0.989737	−	0.142898i	$-0.954358\pi$
$173$		−	3.75906i		−	0.285796i	0.989737	−	0.142898i	$-0.0456420\pi$
$174$	−4.18614	−	3.93398i	−0.317351	−	0.298235i
$175$		0			0
$176$			4.25639i			0.320837i
$177$	−4.88316	+	5.19615i	−0.367040	+	0.390567i
$178$	−4.37228			−0.327716
$179$		−	2.87419i		−	0.214827i	−0.994214	−	0.107414i	$-0.965743\pi$
$179$		−	2.87419i		−	0.214827i	0.994214	−	0.107414i	$-0.0342569\pi$
$180$	6.24456	−	2.45060i	0.465442	−	0.182657i
$181$			17.9653i			1.33535i	0.744452	+	0.667676i	$0.232711\pi$
$181$			17.9653i			1.33535i	−0.744452	+	0.667676i	$0.767289\pi$
$182$		0			0
$183$	3.55842	+	3.34408i	0.263046	+	0.247201i
$184$	4.37228			0.322329
$185$	24.8614	−	8.01544i	1.82785	−	0.589307i
$186$	−3.00000	−	2.81929i	−0.219971	−	0.206720i
$187$	−28.2337			−2.06465
$188$			1.87953i			0.137079i
$189$		0			0
$190$	−7.37228	+	2.37686i	−0.534842	+	0.172436i
$191$		−	3.75906i		−	0.271996i	−0.990709	−	0.135998i	$-0.956576\pi$
$191$		−	3.75906i		−	0.271996i	0.990709	−	0.135998i	$-0.0434240\pi$
$192$	1.18614	−	1.26217i	0.0856023	−	0.0910892i
$193$		−	8.01544i		−	0.576964i	−0.957485	−	0.288482i	$-0.906849\pi$
$193$		−	8.01544i		−	0.576964i	0.957485	−	0.288482i	$-0.0931506\pi$
$194$	−2.11684			−0.151981
$195$	7.00000	+	3.31662i	0.501280	+	0.237508i
$196$		0			0
$197$	−20.2337			−1.44159			−0.720795	−	0.693148i	$-0.756223\pi$
$197$	−20.2337			−1.44159			−0.720795	+	0.693148i	$0.756223\pi$
$198$	12.7446	−	0.792287i	0.905717	−	0.0563054i
$199$		−	18.6101i		−	1.31924i	−0.751601	−	0.659619i	$-0.770718\pi$
$199$		−	18.6101i		−	1.31924i	0.751601	−	0.659619i	$-0.229282\pi$
$200$	−4.05842	+	2.92048i	−0.286974	+	0.206509i
$201$	−9.55842	−	8.98266i	−0.674199	−	0.633588i
$202$	−16.3723			−1.15195
$203$		0			0
$204$	8.37228	+	7.86797i	0.586177	+	0.550868i
$205$	1.11684	+	3.46410i	0.0780038	+	0.241943i
$206$	15.1168			1.05324
$207$	−0.813859	−	13.0916i	−0.0565671	−	0.909927i
$208$	2.00000			0.138675
$209$	−14.7446			−1.01990
$210$		0			0
$211$	−18.2337			−1.25526			−0.627629	−	0.778512i	$-0.715975\pi$
$211$	−18.2337			−1.25526			−0.627629	+	0.778512i	$0.715975\pi$
$212$	1.37228			0.0942487
$213$	2.37228	+	2.22938i	0.162546	+	0.152755i
$214$	17.7446			1.21299
$215$	23.4891	−	7.57301i	1.60195	−	0.516475i
$216$	−4.00000	−	3.31662i	−0.272166	−	0.225668i
$217$		0			0
$218$	9.11684			0.617471
$219$	2.37228	−	2.52434i	0.160304	−	0.170579i
$220$	−9.05842	+	2.92048i	−0.610719	+	0.196899i
$221$			13.2665i			0.892401i
$222$	−14.7446	−	13.8564i	−0.989590	−	0.929981i
$223$	18.1168			1.21319			0.606597	−	0.795010i	$-0.292534\pi$
$223$	18.1168			1.21319			0.606597	+	0.795010i	$0.292534\pi$
$224$		0			0
$225$	9.50000	+	11.6082i	0.633333	+	0.773879i
$226$	−3.25544			−0.216548
$227$		−	15.6434i		−	1.03829i	−0.854687	−	0.519143i	$-0.826251\pi$
$227$		−	15.6434i		−	1.03829i	0.854687	−	0.519143i	$-0.173749\pi$
$228$	4.37228	+	4.10891i	0.289561	+	0.272119i
$229$		−	13.8564i		−	0.915657i	−0.889041	−	0.457829i	$-0.848627\pi$
$229$		−	13.8564i		−	0.915657i	0.889041	−	0.457829i	$-0.151373\pi$
$230$	3.00000	+	9.30506i	0.197814	+	0.613558i
$231$		0			0
$232$		−	3.31662i		−	0.217747i
$233$	−23.4891			−1.53882			−0.769412	−	0.638753i	$-0.779451\pi$
$233$	−23.4891			−1.53882			−0.769412	+	0.638753i	$0.779451\pi$
$234$	−0.372281	−	5.98844i	−0.0243368	−	0.391477i
$235$	−4.00000	+	1.28962i	−0.260931	+	0.0841256i
$236$	−4.11684			−0.267984
$237$	−9.62772	+	10.2448i	−0.625388	+	0.665473i
$238$		0			0
$239$		−	2.87419i		−	0.185916i	−0.995670	−	0.0929581i	$-0.970368\pi$
$239$		−	2.87419i		−	0.185916i	0.995670	−	0.0929581i	$-0.0296323\pi$
$240$	3.50000	+	1.65831i	0.225924	+	0.107044i
$241$			10.5947i			0.682464i	0.939979	+	0.341232i	$0.110844\pi$
$241$			10.5947i			0.682464i	−0.939979	+	0.341232i	$0.889156\pi$
$242$	−7.11684			−0.457488
$243$	−9.18614	+	12.5942i	−0.589291	+	0.807921i
$244$			2.81929i			0.180487i
$245$		0			0
$246$	1.93070	−	2.05446i	0.123097	−	0.130987i
$247$			6.92820i			0.440831i
$248$		−	2.37686i		−	0.150931i
$249$	1.81386	+	1.70460i	0.114949	+	0.108025i
$250$	−9.00000	−	6.63325i	−0.569210	−	0.419524i
$251$	16.1168			1.01729			0.508643	−	0.860977i	$-0.330147\pi$
$251$	16.1168			1.01729			0.508643	+	0.860977i	$0.330147\pi$
$252$		0			0
$253$			18.6101i			1.17001i
$254$		−	2.37686i		−	0.149138i
$255$	−11.0000	+	23.2164i	−0.688847	+	1.45387i
$256$	1.00000			0.0625000
$257$		−	8.51278i		−	0.531012i	−0.964109	−	0.265506i	$-0.914461\pi$
$257$		−	8.51278i		−	0.531012i	0.964109	−	0.265506i	$-0.0855391\pi$
$258$	−13.9307	−	13.0916i	−0.867288	−	0.815046i
$259$		0			0
$260$	1.37228	+	4.25639i	0.0851053	+	0.263970i
$261$	−9.93070	+	0.617359i	−0.614695	+	0.0382135i
$262$	−4.62772			−0.285901
$263$	1.62772			0.100369			0.0501847	−	0.998740i	$-0.484019\pi$
$263$	1.62772			0.100369			0.0501847	+	0.998740i	$0.484019\pi$
$264$	5.37228	+	5.04868i	0.330641	+	0.310725i
$265$	0.941578	+	2.92048i	0.0578407	+	0.179404i
$266$		0			0
$267$	−5.18614	+	5.51856i	−0.317387	+	0.337730i
$268$		−	7.57301i		−	0.462595i
$269$	−19.9783			−1.21810			−0.609048	−	0.793134i	$-0.708448\pi$
$269$	−19.9783			−1.21810			−0.609048	+	0.793134i	$0.708448\pi$
$270$	4.31386	−	10.7884i	0.262533	−	0.656564i
$271$			20.9870i			1.27487i	0.770505	+	0.637434i	$0.220004\pi$
$271$			20.9870i			1.27487i	−0.770505	+	0.637434i	$0.779996\pi$
$272$			6.63325i			0.402200i
$273$		0			0
$274$	2.74456			0.165805
$275$	−12.4307	−	17.2742i	−0.749600	−	1.04167i
$276$	5.18614	−	5.51856i	0.312169	−	0.332178i
$277$			29.0024i			1.74259i	0.490762	+	0.871294i	$0.336718\pi$
$277$			29.0024i			1.74259i	−0.490762	+	0.871294i	$0.663282\pi$
$278$		−	11.6819i		−	0.700635i
$279$	−7.11684	+	0.442430i	−0.426074	+	0.0264876i
$280$		0			0
$281$			21.7793i			1.29924i	0.760258	+	0.649621i	$0.225073\pi$
$281$			21.7793i			1.29924i	−0.760258	+	0.649621i	$0.774927\pi$
$282$	2.37228	+	2.22938i	0.141267	+	0.132758i
$283$	−16.0000			−0.951101			−0.475551	−	0.879688i	$-0.657751\pi$
$283$	−16.0000			−0.951101			−0.475551	+	0.879688i	$0.657751\pi$
$284$			1.87953i			0.111529i
$285$	−5.74456	+	12.1244i	−0.340279	+	0.718185i
$286$			8.51278i			0.503371i
$287$		0			0
$288$	−0.186141	−	2.99422i	−0.0109684	−	0.176436i
$289$	−27.0000			−1.58824
$290$	7.05842	−	2.27567i	0.414485	−	0.133632i
$291$	−2.51087	+	2.67181i	−0.147190	+	0.156625i
$292$	2.00000			0.117041
$293$			25.0410i			1.46291i	0.681889	+	0.731455i	$0.261159\pi$
$293$			25.0410i			1.46291i	−0.681889	+	0.731455i	$0.738841\pi$
$294$		0			0
$295$	−2.82473	−	8.76144i	−0.164462	−	0.510111i
$296$		−	11.6819i		−	0.678998i
$297$	14.1168	−	17.0256i	0.819142	−	0.987923i
$298$			14.2063i			0.822947i
$299$	8.74456			0.505711
$300$	−1.12772	+	8.58652i	−0.0651089	+	0.495743i
$301$		0			0
$302$	−8.11684			−0.467072
$303$	−19.4198	+	20.6646i	−1.11564	+	1.18715i
$304$			3.46410i			0.198680i
$305$	−6.00000	+	1.93443i	−0.343559	+	0.110765i
$306$	19.8614	−	1.23472i	1.13540	−	0.0705841i
$307$	6.88316			0.392842			0.196421	−	0.980520i	$-0.437068\pi$
$307$	6.88316			0.392842			0.196421	+	0.980520i	$0.437068\pi$
$308$		0			0
$309$	17.9307	−	19.0800i	1.02004	−	1.08542i
$310$	5.05842	−	1.63086i	0.287299	−	0.0926267i
$311$	14.2337			0.807118			0.403559	−	0.914954i	$-0.367773\pi$
$311$	14.2337			0.807118			0.403559	+	0.914954i	$0.367773\pi$
$312$	2.37228	−	2.52434i	0.134304	−	0.142912i
$313$	−14.1168			−0.797931			−0.398966	−	0.916966i	$-0.630631\pi$
$313$	−14.1168			−0.797931			−0.398966	+	0.916966i	$0.630631\pi$
$314$	8.00000			0.451466
$315$		0			0
$316$	−8.11684			−0.456608
$317$	16.1168			0.905212			0.452606	−	0.891711i	$-0.350494\pi$
$317$	16.1168			0.905212			0.452606	+	0.891711i	$0.350494\pi$
$318$	1.62772	−	1.73205i	0.0912779	−	0.0971286i
$319$	14.1168			0.790392
$320$	0.686141	+	2.12819i	0.0383564	+	0.118970i
$321$	21.0475	−	22.3966i	1.17476	−	1.25006i
$322$		0			0
$323$	−22.9783			−1.27854
$324$	−8.93070	+	1.11469i	−0.496150	+	0.0619273i
$325$	−8.11684	+	5.84096i	−0.450241	+	0.323998i
$326$			3.46410i			0.191859i
$327$	10.8139	−	11.5070i	0.598008	−	0.636338i
$328$	1.62772			0.0898757
$329$		0			0
$330$	−7.05842	+	14.8974i	−0.388553	+	0.820073i
$331$	10.2337			0.562494			0.281247	−	0.959635i	$-0.409252\pi$
$331$	10.2337			0.562494			0.281247	+	0.959635i	$0.409252\pi$
$332$			1.43710i			0.0788710i
$333$	−34.9783	+	2.17448i	−1.91680	+	0.119161i
$334$		−	11.3321i		−	0.620063i
$335$	16.1168	−	5.19615i	0.880557	−	0.283896i
$336$		0			0
$337$		−	9.30506i		−	0.506879i	−0.967351	−	0.253440i	$-0.918438\pi$
$337$		−	9.30506i		−	0.506879i	0.967351	−	0.253440i	$-0.0815619\pi$
$338$	−9.00000			−0.489535
$339$	−3.86141	+	4.10891i	−0.209723	+	0.223165i
$340$	−14.1168	+	4.55134i	−0.765593	+	0.246831i
$341$	10.1168			0.547858
$342$	10.3723	−	0.644810i	0.560869	−	0.0348673i
$343$		0			0
$344$		−	11.0371i		−	0.595081i
$345$	15.3030	+	7.25061i	0.823885	+	0.390360i
$346$		−	3.75906i		−	0.202088i
$347$	19.1168			1.02625			0.513123	−	0.858315i	$-0.328488\pi$
$347$	19.1168			1.02625			0.513123	+	0.858315i	$0.328488\pi$
$348$	−4.18614	−	3.93398i	−0.224401	−	0.210884i
$349$			24.0087i			1.28515i	0.766221	+	0.642577i	$0.222135\pi$
$349$			24.0087i			1.28515i	−0.766221	+	0.642577i	$0.777865\pi$
$350$		0			0
$351$	−8.00000	−	6.63325i	−0.427008	−	0.354057i
$352$			4.25639i			0.226866i
$353$		−	18.9051i		−	1.00622i	−0.864224	−	0.503108i	$-0.832190\pi$
$353$		−	18.9051i		−	1.00622i	0.864224	−	0.503108i	$-0.167810\pi$
$354$	−4.88316	+	5.19615i	−0.259537	+	0.276172i
$355$	−4.00000	+	1.28962i	−0.212298	+	0.0684459i
$356$	−4.37228			−0.231730
$357$		0			0
$358$		−	2.87419i		−	0.151906i
$359$		−	14.1514i		−	0.746880i	−0.927654	−	0.373440i	$-0.878178\pi$
$359$		−	14.1514i		−	0.746880i	0.927654	−	0.373440i	$-0.121822\pi$
$360$	6.24456	−	2.45060i	0.329117	−	0.129158i
$361$	7.00000			0.368421
$362$			17.9653i			0.944236i
$363$	−8.44158	+	8.98266i	−0.443068	+	0.471467i
$364$		0			0
$365$	1.37228	+	4.25639i	0.0718285	+	0.222790i
$366$	3.55842	+	3.34408i	0.186002	+	0.174798i
$367$	−21.2337			−1.10839			−0.554195	−	0.832387i	$-0.686974\pi$
$367$	−21.2337			−1.10839			−0.554195	+	0.832387i	$0.686974\pi$
$368$	4.37228			0.227921
$369$	−0.302985	−	4.87375i	−0.0157727	−	0.253717i
$370$	24.8614	−	8.01544i	1.29248	−	0.416703i
$371$		0			0
$372$	−3.00000	−	2.81929i	−0.155543	−	0.146173i
$373$			16.4356i			0.851006i	0.904957	+	0.425503i	$0.139903\pi$
$373$			16.4356i			0.851006i	−0.904957	+	0.425503i	$0.860097\pi$
$374$	−28.2337			−1.45993
$375$	−19.0475	+	3.49155i	−0.983611	+	0.180303i
$376$			1.87953i			0.0969292i
$377$		−	6.63325i		−	0.341630i
$378$		0			0
$379$	22.2337			1.14207			0.571034	−	0.820926i	$-0.306542\pi$
$379$	22.2337			1.14207			0.571034	+	0.820926i	$0.306542\pi$
$380$	−7.37228	+	2.37686i	−0.378190	+	0.121930i
$381$	−3.00000	−	2.81929i	−0.153695	−	0.144437i
$382$		−	3.75906i		−	0.192330i
$383$		−	20.8395i		−	1.06485i	−0.846477	−	0.532425i	$-0.821281\pi$
$383$		−	20.8395i		−	1.06485i	0.846477	−	0.532425i	$-0.178719\pi$
$384$	1.18614	−	1.26217i	0.0605300	−	0.0644098i
$385$		0			0
$386$		−	8.01544i		−	0.407975i
$387$	−33.0475	+	2.05446i	−1.67990	+	0.104434i
$388$	−2.11684			−0.107466
$389$		−	34.0511i		−	1.72646i	−0.504811	−	0.863230i	$-0.668438\pi$
$389$		−	34.0511i		−	1.72646i	0.504811	−	0.863230i	$-0.331562\pi$
$390$	7.00000	+	3.31662i	0.354459	+	0.167944i
$391$			29.0024i			1.46672i
$392$		0			0
$393$	−5.48913	+	5.84096i	−0.276890	+	0.294638i
$394$	−20.2337			−1.01936
$395$	−5.56930	−	17.2742i	−0.280222	−	0.869160i
$396$	12.7446	−	0.792287i	0.640438	−	0.0398139i
$397$	8.00000			0.401508			0.200754	−	0.979642i	$-0.435661\pi$
$397$	8.00000			0.401508			0.200754	+	0.979642i	$0.435661\pi$
$398$		−	18.6101i		−	0.932841i
$399$		0			0
$400$	−4.05842	+	2.92048i	−0.202921	+	0.146024i
$401$			19.8448i			0.991004i	0.868607	+	0.495502i	$0.165016\pi$
$401$			19.8448i			0.991004i	−0.868607	+	0.495502i	$0.834984\pi$
$402$	−9.55842	−	8.98266i	−0.476731	−	0.448014i
$403$		−	4.75372i		−	0.236800i
$404$	−16.3723			−0.814551
$405$	−8.50000	−	18.2414i	−0.422368	−	0.906424i
$406$		0			0
$407$	49.7228			2.46467
$408$	8.37228	+	7.86797i	0.414490	+	0.389522i
$409$		−	35.4882i		−	1.75478i	−0.479779	−	0.877389i	$-0.659283\pi$
$409$		−	35.4882i		−	1.75478i	0.479779	−	0.877389i	$-0.340717\pi$
$410$	1.11684	+	3.46410i	0.0551570	+	0.171080i
$411$	3.25544	−	3.46410i	0.160579	−	0.170872i
$412$	15.1168			0.744753
$413$		0			0
$414$	−0.813859	−	13.0916i	−0.0399990	−	0.643416i
$415$	−3.05842	+	0.986051i	−0.150132	+	0.0484033i
$416$	2.00000			0.0980581
$417$	−14.7446	−	13.8564i	−0.722044	−	0.678551i
$418$	−14.7446			−0.721180
$419$	−29.4891			−1.44064			−0.720319	−	0.693643i	$-0.756005\pi$
$419$	−29.4891			−1.44064			−0.720319	+	0.693643i	$0.756005\pi$
$420$		0			0
$421$	15.1168			0.736750			0.368375	−	0.929677i	$-0.379914\pi$
$421$	15.1168			0.736750			0.368375	+	0.929677i	$0.379914\pi$
$422$	−18.2337			−0.887602
$423$	5.62772	−	0.349857i	0.273629	−	0.0170106i
$424$	1.37228			0.0666439
$425$	−19.3723	−	26.9205i	−0.939694	−	1.30584i
$426$	2.37228	+	2.22938i	0.114937	+	0.108014i
$427$		0			0
$428$	17.7446			0.857716
$429$	10.7446	+	10.0974i	0.518752	+	0.487505i
$430$	23.4891	−	7.57301i	1.13275	−	0.365203i
$431$		−	3.75906i		−	0.181067i	−0.995893	−	0.0905337i	$-0.971143\pi$
$431$		−	3.75906i		−	0.181067i	0.995893	−	0.0905337i	$-0.0288573\pi$
$432$	−4.00000	−	3.31662i	−0.192450	−	0.159571i
$433$	−34.0000			−1.63394			−0.816968	−	0.576683i	$-0.804347\pi$
$433$	−34.0000			−1.63394			−0.816968	+	0.576683i	$0.804347\pi$
$434$		0			0
$435$	5.50000	−	11.6082i	0.263705	−	0.556570i
$436$	9.11684			0.436618
$437$			15.1460i			0.724533i
$438$	2.37228	−	2.52434i	0.113352	−	0.120618i
$439$			12.7692i			0.609439i	0.952442	+	0.304720i	$0.0985627\pi$
$439$			12.7692i			0.609439i	−0.952442	+	0.304720i	$0.901437\pi$
$440$	−9.05842	+	2.92048i	−0.431843	+	0.139228i
$441$		0			0
$442$			13.2665i			0.631023i
$443$	9.00000			0.427603			0.213801	−	0.976877i	$-0.431415\pi$
$443$	9.00000			0.427603			0.213801	+	0.976877i	$0.431415\pi$
$444$	−14.7446	−	13.8564i	−0.699746	−	0.657596i
$445$	−3.00000	−	9.30506i	−0.142214	−	0.441102i
$446$	18.1168			0.857857
$447$	17.9307	+	16.8506i	0.848093	+	0.797007i
$448$		0			0
$449$		−	35.9855i		−	1.69826i	−0.528182	−	0.849131i	$-0.677126\pi$
$449$		−	35.9855i		−	1.69826i	0.528182	−	0.849131i	$-0.322874\pi$
$450$	9.50000	+	11.6082i	0.447834	+	0.547215i
$451$			6.92820i			0.326236i
$452$	−3.25544			−0.153123
$453$	−9.62772	+	10.2448i	−0.452350	+	0.481344i
$454$		−	15.6434i		−	0.734179i
$455$		0			0
$456$	4.37228	+	4.10891i	0.204751	+	0.192417i
$457$		−	12.7692i		−	0.597316i	−0.954360	−	0.298658i	$-0.903461\pi$
$457$		−	12.7692i		−	0.597316i	0.954360	−	0.298658i	$-0.0965390\pi$
$458$		−	13.8564i		−	0.647467i
$459$	22.0000	−	26.5330i	1.02687	−	1.23845i
$460$	3.00000	+	9.30506i	0.139876	+	0.433851i
$461$	−0.510875			−0.0237938			−0.0118969	−	0.999929i	$-0.503787\pi$
$461$	−0.510875			−0.0237938			−0.0118969	+	0.999929i	$0.503787\pi$
$462$		0			0
$463$			36.5754i			1.69981i	0.526940	+	0.849903i	$0.323339\pi$
$463$			36.5754i			1.69981i	−0.526940	+	0.849903i	$0.676661\pi$
$464$		−	3.31662i		−	0.153970i
$465$	3.94158	−	8.31901i	0.182786	−	0.385785i
$466$	−23.4891			−1.08811
$467$		−	0.0549029i		−	0.00254060i	−0.999999	−	0.00127030i	$-0.999596\pi$
$467$		−	0.0549029i		−	0.00254060i	0.999999	−	0.00127030i	$-0.000404349\pi$
$468$	−0.372281	−	5.98844i	−0.0172087	−	0.276816i
$469$		0			0
$470$	−4.00000	+	1.28962i	−0.184506	+	0.0594858i
$471$	9.48913	−	10.0974i	0.437236	−	0.465261i
$472$	−4.11684			−0.189493
$473$	46.9783			2.16006
$474$	−9.62772	+	10.2448i	−0.442216	+	0.470561i
$475$	−10.1168	−	14.0588i	−0.464193	−	0.645061i
$476$		0			0
$477$	−0.255437	−	4.10891i	−0.0116957	−	0.188134i
$478$		−	2.87419i		−	0.131463i
$479$	8.74456			0.399549			0.199775	−	0.979842i	$-0.435979\pi$
$479$	8.74456			0.399549			0.199775	+	0.979842i	$0.435979\pi$
$480$	3.50000	+	1.65831i	0.159752	+	0.0756913i
$481$		−	23.3639i		−	1.06530i
$482$			10.5947i			0.482575i
$483$		0			0
$484$	−7.11684			−0.323493
$485$	−1.45245	−	4.50506i	−0.0659525	−	0.204564i
$486$	−9.18614	+	12.5942i	−0.416692	+	0.571286i
$487$			4.55134i			0.206241i	0.994669	+	0.103121i	$0.0328827\pi$
$487$			4.55134i			0.206241i	−0.994669	+	0.103121i	$0.967117\pi$
$488$			2.81929i			0.127623i
$489$	4.37228	+	4.10891i	0.197721	+	0.185811i
$490$		0			0
$491$		−	26.9205i		−	1.21491i	−0.794355	−	0.607453i	$-0.792191\pi$
$491$		−	26.9205i		−	1.21491i	0.794355	−	0.607453i	$-0.207809\pi$
$492$	1.93070	−	2.05446i	0.0870428	−	0.0926220i
$493$	22.0000			0.990830
$494$			6.92820i			0.311715i
$495$	10.4307	+	26.5793i	0.468825	+	1.19465i
$496$		−	2.37686i		−	0.106724i
$497$		0			0
$498$	1.81386	+	1.70460i	0.0812810	+	0.0763849i
$499$	28.2337			1.26391			0.631957	−	0.775004i	$-0.282252\pi$
$499$	28.2337			1.26391			0.631957	+	0.775004i	$0.282252\pi$
$500$	−9.00000	−	6.63325i	−0.402492	−	0.296648i
$501$	−14.3030	−	13.4414i	−0.639010	−	0.600519i
$502$	16.1168			0.719330
$503$			9.45254i			0.421468i	0.977543	+	0.210734i	$0.0675854\pi$
$503$			9.45254i			0.421468i	−0.977543	+	0.210734i	$0.932415\pi$
$504$		0			0
$505$	−11.2337	−	34.8434i	−0.499893	−	1.55051i
$506$			18.6101i			0.827321i
$507$	−10.6753	+	11.3595i	−0.474105	+	0.504494i
$508$		−	2.37686i		−	0.105456i
$509$	0.255437			0.0113221			0.00566103	−	0.999984i	$-0.498198\pi$
$509$	0.255437			0.0113221			0.00566103	+	0.999984i	$0.498198\pi$
$510$	−11.0000	+	23.2164i	−0.487088	+	1.02804i
$511$		0			0
$512$	1.00000			0.0441942
$513$	11.4891	−	13.8564i	0.507257	−	0.611775i
$514$		−	8.51278i		−	0.375483i
$515$	10.3723	+	32.1716i	0.457057	+	1.41765i
$516$	−13.9307	−	13.0916i	−0.613265	−	0.576324i
$517$	−8.00000			−0.351840
$518$		0			0
$519$	−4.74456	−	4.45877i	−0.208263	−	0.195718i
$520$	1.37228	+	4.25639i	0.0601785	+	0.186655i
$521$	3.25544			0.142623			0.0713116	−	0.997454i	$-0.477282\pi$
$521$	3.25544			0.142623			0.0713116	+	0.997454i	$0.477282\pi$
$522$	−9.93070	+	0.617359i	−0.434655	+	0.0270211i
$523$	−24.2337			−1.05967			−0.529833	−	0.848102i	$-0.677745\pi$
$523$	−24.2337			−1.05967			−0.529833	+	0.848102i	$0.677745\pi$
$524$	−4.62772			−0.202163
$525$		0			0
$526$	1.62772			0.0709719
$527$	15.7663			0.686791
$528$	5.37228	+	5.04868i	0.233799	+	0.219715i
$529$	−3.88316			−0.168833
$530$	0.941578	+	2.92048i	0.0408995	+	0.126858i
$531$	0.766312	+	12.3267i	0.0332551	+	0.534935i
$532$		0			0
$533$	3.25544			0.141009
$534$	−5.18614	+	5.51856i	−0.224426	+	0.238811i
$535$	12.1753	+	37.7639i	0.526383	+	1.63267i
$536$		−	7.57301i		−	0.327104i
$537$	−3.62772	−	3.40920i	−0.156548	−	0.147118i
$538$	−19.9783			−0.861324
$539$		0			0
$540$	4.31386	−	10.7884i	0.185639	−	0.464261i
$541$	−13.3505			−0.573984			−0.286992	−	0.957933i	$-0.592655\pi$
$541$	−13.3505			−0.573984			−0.286992	+	0.957933i	$0.592655\pi$
$542$			20.9870i			0.901468i
$543$	22.6753	+	21.3094i	0.973089	+	0.914474i
$544$			6.63325i			0.284398i
$545$	6.25544	+	19.4024i	0.267953	+	0.831108i
$546$		0			0
$547$		−	0.644810i		−	0.0275701i	−0.999905	−	0.0137850i	$-0.995612\pi$
$547$		−	0.644810i		−	0.0275701i	0.999905	−	0.0137850i	$-0.00438806\pi$
$548$	2.74456			0.117242
$549$	8.44158	−	0.524785i	0.360278	−	0.0223973i
$550$	−12.4307	−	17.2742i	−0.530047	−	0.736575i
$551$	11.4891			0.489453
$552$	5.18614	−	5.51856i	0.220737	−	0.234885i
$553$		0			0
$554$			29.0024i			1.23220i
$555$	19.3723	−	40.8867i	0.822308	−	1.73555i
$556$		−	11.6819i		−	0.495424i
$557$	−0.861407			−0.0364990			−0.0182495	−	0.999833i	$-0.505809\pi$
$557$	−0.861407			−0.0364990			−0.0182495	+	0.999833i	$0.505809\pi$
$558$	−7.11684	+	0.442430i	−0.301280	+	0.0187296i
$559$		−	22.0742i		−	0.933640i
$560$		0			0
$561$	−33.4891	+	35.6357i	−1.41391	+	1.50454i
$562$			21.7793i			0.918703i
$563$			11.8294i			0.498550i	0.968433	+	0.249275i	$0.0801923\pi$
$563$			11.8294i			0.498550i	−0.968433	+	0.249275i	$0.919808\pi$
$564$	2.37228	+	2.22938i	0.0998911	+	0.0938740i
$565$	−2.23369	−	6.92820i	−0.0939720	−	0.291472i
$566$	−16.0000			−0.672530
$567$		0			0
$568$			1.87953i			0.0788632i
$569$			21.7793i			0.913035i	0.889714	+	0.456517i	$0.150903\pi$
$569$			21.7793i			0.913035i	−0.889714	+	0.456517i	$0.849097\pi$
$570$	−5.74456	+	12.1244i	−0.240613	+	0.507833i
$571$	34.2337			1.43264			0.716318	−	0.697774i	$-0.245826\pi$
$571$	34.2337			1.43264			0.716318	+	0.697774i	$0.245826\pi$
$572$			8.51278i			0.355937i
$573$	−4.74456	−	4.45877i	−0.198207	−	0.186268i
$574$		0			0
$575$	−17.7446	+	12.7692i	−0.739999	+	0.532511i
$576$	−0.186141	−	2.99422i	−0.00775586	−	0.124759i
$577$	−17.8832			−0.744486			−0.372243	−	0.928135i	$-0.621411\pi$
$577$	−17.8832			−0.744486			−0.372243	+	0.928135i	$0.621411\pi$
$578$	−27.0000			−1.12305
$579$	−10.1168	−	9.50744i	−0.420442	−	0.395116i
$580$	7.05842	−	2.27567i	0.293085	−	0.0944921i
$581$		0			0
$582$	−2.51087	+	2.67181i	−0.104079	+	0.110750i
$583$			5.84096i			0.241908i
$584$	2.00000			0.0827606
$585$	12.4891	−	4.90120i	0.516362	−	0.202640i
$586$			25.0410i			1.03443i
$587$		−	36.4280i		−	1.50354i	−0.659424	−	0.751772i	$-0.729200\pi$
$587$		−	36.4280i		−	1.50354i	0.659424	−	0.751772i	$-0.270800\pi$
$588$		0			0
$589$	8.23369			0.339263
$590$	−2.82473	−	8.76144i	−0.116292	−	0.360703i
$591$	−24.0000	+	25.5383i	−0.987228	+	1.05051i
$592$		−	11.6819i		−	0.480124i
$593$		−	14.1514i		−	0.581127i	−0.956856	−	0.290563i	$-0.906157\pi$
$593$		−	14.1514i		−	0.581127i	0.956856	−	0.290563i	$-0.0938427\pi$
$594$	14.1168	−	17.0256i	0.579221	−	0.698567i
$595$		0			0
$596$			14.2063i			0.581911i
$597$	−23.4891	−	22.0742i	−0.961346	−	0.903438i
$598$	8.74456			0.357592
$599$		−	8.51278i		−	0.347823i	−0.984761	−	0.173911i	$-0.944359\pi$
$599$		−	8.51278i		−	0.347823i	0.984761	−	0.173911i	$-0.0556406\pi$
$600$	−1.12772	+	8.58652i	−0.0460389	+	0.350543i
$601$		−	10.5947i		−	0.432166i	−0.976375	−	0.216083i	$-0.930672\pi$
$601$		−	10.5947i		−	0.432166i	0.976375	−	0.216083i	$-0.0693282\pi$
$602$		0			0
$603$	−22.6753	+	1.40965i	−0.923408	+	0.0574052i
$604$	−8.11684			−0.330270
$605$	−4.88316	−	15.1460i	−0.198529	−	0.615774i
$606$	−19.4198	+	20.6646i	−0.788877	+	0.839441i
$607$	27.4674			1.11487			0.557433	−	0.830222i	$-0.311786\pi$
$607$	27.4674			1.11487			0.557433	+	0.830222i	$0.311786\pi$
$608$			3.46410i			0.140488i
$609$		0			0
$610$	−6.00000	+	1.93443i	−0.242933	+	0.0783228i
$611$			3.75906i			0.152075i
$612$	19.8614	−	1.23472i	0.802850	−	0.0499105i
$613$		−	12.9715i		−	0.523916i	−0.965079	−	0.261958i	$-0.915632\pi$
$613$		−	12.9715i		−	0.523916i	0.965079	−	0.261958i	$-0.0843682\pi$
$614$	6.88316			0.277782
$615$	5.69702	+	2.69927i	0.229726	+	0.108845i
$616$		0			0
$617$	−1.02175			−0.0411341			−0.0205670	−	0.999788i	$-0.506547\pi$
$617$	−1.02175			−0.0411341			−0.0205670	+	0.999788i	$0.506547\pi$
$618$	17.9307	−	19.0800i	0.721279	−	0.767511i
$619$			23.3639i			0.939072i	0.882913	+	0.469536i	$0.155579\pi$
$619$			23.3639i			0.939072i	−0.882913	+	0.469536i	$0.844421\pi$
$620$	5.05842	−	1.63086i	0.203151	−	0.0654970i
$621$	−17.4891	−	14.5012i	−0.701814	−	0.581914i
$622$	14.2337			0.570719
$623$		0			0
$624$	2.37228	−	2.52434i	0.0949673	−	0.101054i
$625$	7.94158	−	23.7051i	0.317663	−	0.948204i
$626$	−14.1168			−0.564223
$627$	−17.4891	+	18.6101i	−0.698448	+	0.743217i
$628$	8.00000			0.319235
$629$	77.4891			3.08969
$630$		0			0
$631$	30.1168			1.19893			0.599466	−	0.800400i	$-0.295380\pi$
$631$	30.1168			1.19893			0.599466	+	0.800400i	$0.295380\pi$
$632$	−8.11684			−0.322871
$633$	−21.6277	+	23.0140i	−0.859625	+	0.914724i
$634$	16.1168			0.640082
$635$	5.05842	−	1.63086i	0.200737	−	0.0647187i
$636$	1.62772	−	1.73205i	0.0645432	−	0.0686803i
$637$		0			0
$638$	14.1168			0.558891
$639$	5.62772	−	0.349857i	0.222629	−	0.0138401i
$640$	0.686141	+	2.12819i	0.0271221	+	0.0841243i
$641$			14.2063i			0.561114i	0.959837	+	0.280557i	$0.0905191\pi$
$641$			14.2063i			0.561114i	−0.959837	+	0.280557i	$0.909481\pi$
$642$	21.0475	−	22.3966i	0.830680	−	0.883925i
$643$	16.2337			0.640194			0.320097	−	0.947385i	$-0.396284\pi$
$643$	16.2337			0.640194			0.320097	+	0.947385i	$0.396284\pi$
$644$		0			0
$645$	18.3030	−	38.6299i	0.720679	−	1.52105i
$646$	−22.9783			−0.904067
$647$			25.4834i			1.00186i	0.865489	+	0.500928i	$0.167008\pi$
$647$			25.4834i			1.00186i	−0.865489	+	0.500928i	$0.832992\pi$
$648$	−8.93070	+	1.11469i	−0.350831	+	0.0437892i
$649$		−	17.5229i		−	0.687834i
$650$	−8.11684	+	5.84096i	−0.318369	+	0.229101i
$651$		0			0
$652$			3.46410i			0.135665i
$653$	−10.6277			−0.415895			−0.207947	−	0.978140i	$-0.566678\pi$
$653$	−10.6277			−0.415895			−0.207947	+	0.978140i	$0.566678\pi$
$654$	10.8139	−	11.5070i	0.422855	−	0.449959i
$655$	−3.17527	−	9.84868i	−0.124068	−	0.384820i
$656$	1.62772			0.0635517
$657$	−0.372281	−	5.98844i	−0.0145241	−	0.233631i
$658$		0			0
$659$			36.9253i			1.43841i	0.694800	+	0.719203i	$0.255493\pi$
$659$			36.9253i			1.43841i	−0.694800	+	0.719203i	$0.744507\pi$
$660$	−7.05842	+	14.8974i	−0.274749	+	0.579879i
$661$			2.81929i			0.109658i	0.998496	+	0.0548289i	$0.0174613\pi$
$661$			2.81929i			0.109658i	−0.998496	+	0.0548289i	$0.982539\pi$
$662$	10.2337			0.397744
$663$	16.7446	+	15.7359i	0.650305	+	0.611133i
$664$			1.43710i			0.0557702i
$665$		0			0
$666$	−34.9783	+	2.17448i	−1.35538	+	0.0842594i
$667$		−	14.5012i		−	0.561489i
$668$		−	11.3321i		−	0.438451i
$669$	21.4891	−	22.8665i	0.830818	−	0.884071i
$670$	16.1168	−	5.19615i	0.622648	−	0.200745i
$671$	−12.0000			−0.463255
$672$		0			0
$673$		−	17.1181i		−	0.659855i	−0.944006	−	0.329928i	$-0.892976\pi$
$673$		−	17.1181i		−	0.659855i	0.944006	−	0.329928i	$-0.107024\pi$
$674$		−	9.30506i		−	0.358418i
$675$	25.9198	+	1.77834i	0.997655	+	0.0684483i
$676$	−9.00000			−0.346154
$677$			44.9407i			1.72721i	0.504166	+	0.863607i	$0.331800\pi$
$677$			44.9407i			1.72721i	−0.504166	+	0.863607i	$0.668200\pi$
$678$	−3.86141	+	4.10891i	−0.148296	+	0.157802i
$679$		0			0
$680$	−14.1168	+	4.55134i	−0.541356	+	0.174536i
$681$	−19.7446	−	18.5552i	−0.756613	−	0.711038i
$682$	10.1168			0.387394
$683$	−13.9783			−0.534863			−0.267431	−	0.963577i	$-0.586175\pi$
$683$	−13.9783			−0.534863			−0.267431	+	0.963577i	$0.586175\pi$
$684$	10.3723	−	0.644810i	0.396594	−	0.0246549i
$685$	1.88316	+	5.84096i	0.0719517	+	0.223172i
$686$		0			0
$687$	−17.4891	−	16.4356i	−0.667252	−	0.627059i
$688$		−	11.0371i		−	0.420786i
$689$	2.74456			0.104560
$690$	15.3030	+	7.25061i	0.582575	+	0.276026i
$691$			30.2921i			1.15236i	0.817321	+	0.576182i	$0.195458\pi$
$691$			30.2921i			1.15236i	−0.817321	+	0.576182i	$0.804542\pi$
$692$		−	3.75906i		−	0.142898i
$693$		0			0
$694$	19.1168			0.725665
$695$	24.8614	−	8.01544i	0.943047	−	0.304043i
$696$	−4.18614	−	3.93398i	−0.158675	−	0.149117i
$697$			10.7971i			0.408968i
$698$			24.0087i			0.908741i
$699$	−27.8614	+	29.6472i	−1.05382	+	1.12136i
$700$		0			0
$701$			12.7143i			0.480211i	0.970747	+	0.240106i	$0.0771821\pi$
$701$			12.7143i			0.480211i	−0.970747	+	0.240106i	$0.922818\pi$
$702$	−8.00000	−	6.63325i	−0.301941	−	0.250356i
$703$	40.4674			1.52626
$704$			4.25639i			0.160419i
$705$	−3.11684	+	6.57835i	−0.117387	+	0.247755i
$706$		−	18.9051i		−	0.711502i
$707$		0			0
$708$	−4.88316	+	5.19615i	−0.183520	+	0.195283i
$709$	−5.11684			−0.192167			−0.0960836	−	0.995373i	$-0.530632\pi$
$709$	−5.11684			−0.192167			−0.0960836	+	0.995373i	$0.530632\pi$
$710$	−4.00000	+	1.28962i	−0.150117	+	0.0483986i
$711$	1.51087	+	24.3036i	0.0566622	+	0.911457i
$712$	−4.37228			−0.163858
$713$		−	10.3923i		−	0.389195i
$714$		0			0
$715$	−18.1168	+	5.84096i	−0.677532	+	0.218440i
$716$		−	2.87419i		−	0.107414i
$717$	−3.62772	−	3.40920i	−0.135480	−	0.127319i
$718$		−	14.1514i		−	0.528124i
$719$	−33.2554			−1.24022			−0.620109	−	0.784515i	$-0.712912\pi$
$719$	−33.2554			−1.24022			−0.620109	+	0.784515i	$0.712912\pi$
$720$	6.24456	−	2.45060i	0.232721	−	0.0913284i
$721$		0			0
$722$	7.00000			0.260513
$723$	13.3723	+	12.5668i	0.497320	+	0.467364i
$724$			17.9653i			0.667676i
$725$	9.68614	+	13.4603i	0.359734	+	0.499902i
$726$	−8.44158	+	8.98266i	−0.313296	+	0.333378i
$727$	−19.0000			−0.704671			−0.352335	−	0.935874i	$-0.614612\pi$
$727$	−19.0000			−0.704671			−0.352335	+	0.935874i	$0.614612\pi$
$728$		0			0
$729$	5.00000	+	26.5330i	0.185185	+	0.982704i
$730$	1.37228	+	4.25639i	0.0507904	+	0.157536i
$731$	73.2119			2.70784
$732$	3.55842	+	3.34408i	0.131523	+	0.123601i
$733$	36.4674			1.34695			0.673477	−	0.739209i	$-0.264800\pi$
$733$	36.4674			1.34695			0.673477	+	0.739209i	$0.264800\pi$
$734$	−21.2337			−0.783750
$735$		0			0
$736$	4.37228			0.161164
$737$	32.2337			1.18734
$738$	−0.302985	−	4.87375i	−0.0111530	−	0.179405i
$739$	−36.2337			−1.33288			−0.666439	−	0.745560i	$-0.732182\pi$
$739$	−36.2337			−1.33288			−0.666439	+	0.745560i	$0.732182\pi$
$740$	24.8614	−	8.01544i	0.913923	−	0.294654i
$741$	8.74456	+	8.21782i	0.321240	+	0.301889i
$742$		0			0
$743$	−18.6060			−0.682587			−0.341293	−	0.939957i	$-0.610865\pi$
$743$	−18.6060			−0.682587			−0.341293	+	0.939957i	$0.610865\pi$
$744$	−3.00000	−	2.81929i	−0.109985	−	0.103360i
$745$	−30.2337	+	9.74749i	−1.10768	+	0.357121i
$746$			16.4356i			0.601752i
$747$	4.30298	−	0.267502i	0.157438	−	0.00978739i
$748$	−28.2337			−1.03233
$749$		0			0
$750$	−19.0475	+	3.49155i	−0.695518	+	0.127493i
$751$	42.1168			1.53687			0.768433	−	0.639931i	$-0.221037\pi$
$751$	42.1168			1.53687			0.768433	+	0.639931i	$0.221037\pi$
$752$			1.87953i			0.0685393i
$753$	19.1168	−	20.3422i	0.696657	−	0.741310i
$754$		−	6.63325i		−	0.241569i
$755$	−5.56930	−	17.2742i	−0.202687	−	0.628673i
$756$		0			0
$757$		−	5.63858i		−	0.204938i	−0.994736	−	0.102469i	$-0.967326\pi$
$757$		−	5.63858i		−	0.204938i	0.994736	−	0.102469i	$-0.0326742\pi$
$758$	22.2337			0.807564
$759$	23.4891	+	22.0742i	0.852601	+	0.801244i
$760$	−7.37228	+	2.37686i	−0.267421	+	0.0862178i
$761$	−52.9783			−1.92046			−0.960230	−	0.279210i	$-0.909927\pi$
$761$	−52.9783			−1.92046			−0.960230	+	0.279210i	$0.909927\pi$
$762$	−3.00000	−	2.81929i	−0.108679	−	0.102132i
$763$		0			0
$764$		−	3.75906i		−	0.135998i
$765$	16.2554	+	41.4217i	0.587717	+	1.49761i
$766$		−	20.8395i		−	0.752962i
$767$	−8.23369			−0.297301
$768$	1.18614	−	1.26217i	0.0428012	−	0.0455446i
$769$		−	40.4820i		−	1.45982i	−0.683545	−	0.729909i	$-0.739563\pi$
$769$		−	40.4820i		−	1.45982i	0.683545	−	0.729909i	$-0.260437\pi$
$770$		0			0
$771$	−10.7446	−	10.0974i	−0.386956	−	0.363647i
$772$		−	8.01544i		−	0.288482i
$773$			1.87953i			0.0676019i	0.999429	+	0.0338010i	$0.0107612\pi$
$773$			1.87953i			0.0676019i	−0.999429	+	0.0338010i	$0.989239\pi$
$774$	−33.0475	+	2.05446i	−1.18787	+	0.0738459i
$775$	6.94158	+	9.64630i	0.249349	+	0.346505i
$776$	−2.11684			−0.0759903
$777$		0			0
$778$		−	34.0511i		−	1.22079i
$779$			5.63858i			0.202023i
$780$	7.00000	+	3.31662i	0.250640	+	0.118754i
$781$	−8.00000			−0.286263
$782$			29.0024i			1.03712i
$783$	−11.0000	+	13.2665i	−0.393108	+	0.474106i
$784$		0			0
$785$	5.48913	+	17.0256i	0.195915	+	0.607668i
$786$	−5.48913	+	5.84096i	−0.195791	+	0.208340i
$787$	27.1168			0.966611			0.483306	−	0.875452i	$-0.339436\pi$
$787$	27.1168			0.966611			0.483306	+	0.875452i	$0.339436\pi$
$788$	−20.2337			−0.720795
$789$	1.93070	−	2.05446i	0.0687349	−	0.0731406i
$790$	−5.56930	−	17.2742i	−0.198147	−	0.614589i
$791$		0			0
$792$	12.7446	−	0.792287i	0.452858	−	0.0281527i
$793$			5.63858i			0.200232i
$794$	8.00000			0.283909
$795$	4.80298	+	2.27567i	0.170344	+	0.0807097i
$796$		−	18.6101i		−	0.659619i
$797$			4.25639i			0.150769i	0.997155	+	0.0753845i	$0.0240184\pi$
$797$			4.25639i			0.150769i	−0.997155	+	0.0753845i	$0.975982\pi$
$798$		0			0
$799$	−12.4674			−0.441064
$800$	−4.05842	+	2.92048i	−0.143487	+	0.103255i
$801$	0.813859	+	13.0916i	0.0287563	+	0.462568i
$802$			19.8448i			0.700746i
$803$			8.51278i			0.300409i
$804$	−9.55842	−	8.98266i	−0.337100	−	0.316794i
$805$		0			0
$806$		−	4.75372i		−	0.167443i
$807$	−23.6970	+	25.2159i	−0.834174	+	0.887643i
$808$	−16.3723			−0.575975
$809$			25.4834i			0.895950i	0.894046	+	0.447975i	$0.147855\pi$
$809$			25.4834i			0.895950i	−0.894046	+	0.447975i	$0.852145\pi$
$810$	−8.50000	−	18.2414i	−0.298660	−	0.640939i
$811$		−	10.3923i		−	0.364923i	−0.983213	−	0.182462i	$-0.941593\pi$
$811$		−	10.3923i		−	0.364923i	0.983213	−	0.182462i	$-0.0584065\pi$
$812$		0			0
$813$	26.4891	+	24.8935i	0.929014	+	0.873054i
$814$	49.7228			1.74278
$815$	−7.37228	+	2.37686i	−0.258240	+	0.0832578i
$816$	8.37228	+	7.86797i	0.293088	+	0.275434i
$817$	38.2337			1.33763
$818$		−	35.4882i		−	1.24082i
$819$		0			0
$820$	1.11684	+	3.46410i	0.0390019	+	0.120972i
$821$		−	21.2819i		−	0.742745i	−0.928484	−	0.371372i	$-0.878887\pi$
$821$		−	21.2819i		−	0.742745i	0.928484	−	0.371372i	$-0.121113\pi$
$822$	3.25544	−	3.46410i	0.113546	−	0.120824i
$823$			43.5036i			1.51644i	0.651998	+	0.758221i	$0.273931\pi$
$823$			43.5036i			1.51644i	−0.651998	+	0.758221i	$0.726069\pi$
$824$	15.1168			0.526620
$825$	−36.5475	−	4.80001i	−1.27242	−	0.167115i
$826$		0			0
$827$	33.0000			1.14752			0.573761	−	0.819023i	$-0.305484\pi$
$827$	33.0000			1.14752			0.573761	+	0.819023i	$0.305484\pi$
$828$	−0.813859	−	13.0916i	−0.0282836	−	0.454964i
$829$		−	18.6101i		−	0.646356i	−0.946338	−	0.323178i	$-0.895249\pi$
$829$		−	18.6101i		−	0.646356i	0.946338	−	0.323178i	$-0.104751\pi$
$830$	−3.05842	+	0.986051i	−0.106159	+	0.0342263i
$831$	36.6060	+	34.4010i	1.26985	+	1.19336i
$832$	2.00000			0.0693375
$833$		0			0
$834$	−14.7446	−	13.8564i	−0.510562	−	0.479808i
$835$	24.1168	−	7.77539i	0.834598	−	0.269079i
$836$	−14.7446			−0.509951
$837$	−7.88316	+	9.50744i	−0.272482	+	0.328625i
$838$	−29.4891			−1.01868
$839$	1.72281			0.0594781			0.0297391	−	0.999558i	$-0.490532\pi$
$839$	1.72281			0.0594781			0.0297391	+	0.999558i	$0.490532\pi$
$840$		0			0
$841$	18.0000			0.620690
$842$	15.1168			0.520961
$843$	27.4891	+	25.8333i	0.946776	+	0.889746i
$844$	−18.2337			−0.627629
$845$	−6.17527	−	19.1537i	−0.212436	−	0.658909i
$846$	5.62772	−	0.349857i	0.193485	−	0.0120283i
$847$		0			0
$848$	1.37228			0.0471243
$849$	−18.9783	+	20.1947i	−0.651332	+	0.693080i
$850$	−19.3723	−	26.9205i	−0.664464	−	0.923366i
$851$		−	51.0767i		−	1.75089i
$852$	2.37228	+	2.22938i	0.0812730	+	0.0763774i
$853$	30.4674			1.04318			0.521592	−	0.853195i	$-0.325339\pi$
$853$	30.4674			1.04318			0.521592	+	0.853195i	$0.325339\pi$
$854$		0			0
$855$	8.48913	+	21.6318i	0.290322	+	0.739792i
$856$	17.7446			0.606497
$857$			37.8102i			1.29157i	0.763519	+	0.645785i	$0.223470\pi$
$857$			37.8102i			1.29157i	−0.763519	+	0.645785i	$0.776530\pi$
$858$	10.7446	+	10.0974i	0.366813	+	0.344718i
$859$		−	32.8713i		−	1.12155i	−0.827967	−	0.560777i	$-0.810502\pi$
$859$		−	32.8713i		−	1.12155i	0.827967	−	0.560777i	$-0.189498\pi$
$860$	23.4891	−	7.57301i	0.800973	−	0.258238i
$861$		0			0
$862$		−	3.75906i		−	0.128034i
$863$	7.62772			0.259651			0.129825	−	0.991537i	$-0.458558\pi$
$863$	7.62772			0.259651			0.129825	+	0.991537i	$0.458558\pi$
$864$	−4.00000	−	3.31662i	−0.136083	−	0.112834i
$865$	8.00000	−	2.57924i	0.272008	−	0.0876968i
$866$	−34.0000			−1.15537
$867$	−32.0258	+	34.0786i	−1.08765	+	1.15737i
$868$		0			0
$869$		−	34.5484i		−	1.17198i
$870$	5.50000	−	11.6082i	0.186467	−	0.393554i
$871$		−	15.1460i		−	0.513204i
$872$	9.11684			0.308735
$873$	0.394031	+	6.33830i	0.0133359	+	0.214519i
$874$			15.1460i			0.512322i
$875$		0			0
$876$	2.37228	−	2.52434i	0.0801520	−	0.0852895i
$877$			31.5817i			1.06644i	0.845977	+	0.533219i	$0.179018\pi$
$877$			31.5817i			1.06644i	−0.845977	+	0.533219i	$0.820982\pi$
$878$			12.7692i			0.430938i
$879$	31.6060	+	29.7021i	1.06604	+	1.00183i
$880$	−9.05842	+	2.92048i	−0.305359	+	0.0984494i
$881$	−51.3505			−1.73004			−0.865022	−	0.501734i	$-0.832695\pi$
$881$	−51.3505			−1.73004			−0.865022	+	0.501734i	$0.832695\pi$
$882$		0			0
$883$			54.9455i			1.84906i	0.381104	+	0.924532i	$0.375544\pi$
$883$			54.9455i			1.84906i	−0.381104	+	0.924532i	$0.624456\pi$
$884$			13.2665i			0.446201i
$885$	−14.4090	−	6.82701i	−0.484352	−	0.229488i
$886$	9.00000			0.302361
$887$			54.8906i			1.84305i	0.388323	+	0.921523i	$0.373055\pi$
$887$			54.8906i			1.84305i	−0.388323	+	0.921523i	$0.626945\pi$
$888$	−14.7446	−	13.8564i	−0.494795	−	0.464991i
$889$		0			0
$890$	−3.00000	−	9.30506i	−0.100560	−	0.311906i
$891$	−4.74456	−	38.0125i	−0.158949	−	1.27347i
$892$	18.1168			0.606597
$893$	−6.51087			−0.217878
$894$	17.9307	+	16.8506i	0.599692	+	0.563569i
$895$	6.11684	−	1.97210i	0.204464	−	0.0659201i
$896$		0			0
$897$	10.3723	−	11.0371i	0.346320	−	0.368519i
$898$		−	35.9855i		−	1.20085i
$899$	−7.88316			−0.262918
$900$	9.50000	+	11.6082i	0.316667	+	0.386940i
$901$			9.10268i			0.303254i
$902$			6.92820i			0.230684i
$903$		0			0
$904$	−3.25544			−0.108274
$905$	−38.2337	+	12.3267i	−1.27093	+	0.409755i
$906$	−9.62772	+	10.2448i	−0.319860	+	0.340362i
$907$		−	44.7933i		−	1.48734i	−0.668549	−	0.743668i	$-0.733084\pi$
$907$		−	44.7933i		−	1.48734i	0.668549	−	0.743668i	$-0.266916\pi$
$908$		−	15.6434i		−	0.519143i
$909$	3.04755	+	49.0222i	0.101081	+	1.62596i
$910$		0			0
$911$		−	24.5437i		−	0.813168i	−0.913613	−	0.406584i	$-0.866720\pi$
$911$		−	24.5437i		−	0.813168i	0.913613	−	0.406584i	$-0.133280\pi$
$912$	4.37228	+	4.10891i	0.144781	+	0.136060i
$913$	−6.11684			−0.202438
$914$		−	12.7692i		−	0.422366i
$915$	−4.67527	+	9.86752i	−0.154560	+	0.326210i
$916$		−	13.8564i		−	0.457829i
$917$		0			0
$918$	22.0000	−	26.5330i	0.726108	−	0.875719i
$919$	−18.2337			−0.601474			−0.300737	−	0.953707i	$-0.597233\pi$
$919$	−18.2337			−0.601474			−0.300737	+	0.953707i	$0.597233\pi$
$920$	3.00000	+	9.30506i	0.0989071	+	0.306779i
$921$	8.16439	−	8.68771i	0.269026	−	0.286270i
$922$	−0.510875			−0.0168248
$923$			3.75906i			0.123731i
$924$		0			0
$925$	34.1168	+	47.4102i	1.12175	+	1.55884i
$926$			36.5754i			1.20194i
$927$	−2.81386	−	45.2632i	−0.0924193	−	1.48664i
$928$		−	3.31662i		−	0.108874i
$929$	16.8832			0.553918			0.276959	−	0.960882i	$-0.410673\pi$
$929$	16.8832			0.553918			0.276959	+	0.960882i	$0.410673\pi$
$930$	3.94158	−	8.31901i	0.129249	−	0.272791i
$931$		0			0
$932$	−23.4891			−0.769412
$933$	16.8832	−	17.9653i	0.552730	−	0.588158i
$934$		−	0.0549029i		−	0.00179648i
$935$	−19.3723	−	60.0868i	−0.633541	−	1.96505i
$936$	−0.372281	−	5.98844i	−0.0121684	−	0.195738i
$937$	50.3505			1.64488			0.822440	−	0.568852i	$-0.192612\pi$
$937$	50.3505			1.64488			0.822440	+	0.568852i	$0.192612\pi$
$938$		0			0
$939$	−16.7446	+	17.8178i	−0.546438	+	0.581463i
$940$	−4.00000	+	1.28962i	−0.130466	+	0.0420628i
$941$	−24.3505			−0.793805			−0.396902	−	0.917861i	$-0.629915\pi$
$941$	−24.3505			−0.793805			−0.396902	+	0.917861i	$0.629915\pi$
$942$	9.48913	−	10.0974i	0.309172	−	0.328989i
$943$	7.11684			0.231756
$944$	−4.11684			−0.133992
$945$		0			0
$946$	46.9783			1.52739
$947$	43.1168			1.40111			0.700555	−	0.713599i	$-0.252936\pi$
$947$	43.1168			1.40111			0.700555	+	0.713599i	$0.252936\pi$
$948$	−9.62772	+	10.2448i	−0.312694	+	0.332737i
$949$	4.00000			0.129845
$950$	−10.1168	−	14.0588i	−0.328234	−	0.456127i
$951$	19.1168	−	20.3422i	0.619906	−	0.659640i
$952$		0			0
$953$	−48.0000			−1.55487			−0.777436	−	0.628962i	$-0.783480\pi$
$953$	−48.0000			−1.55487			−0.777436	+	0.628962i	$0.783480\pi$
$954$	−0.255437	−	4.10891i	−0.00827009	−	0.133031i
$955$	8.00000	−	2.57924i	0.258874	−	0.0834623i
$956$		−	2.87419i		−	0.0929581i
$957$	16.7446	−	17.8178i	0.541275	−	0.575969i
$958$	8.74456			0.282524
$959$		0			0
$960$	3.50000	+	1.65831i	0.112962	+	0.0535218i
$961$	25.3505			0.817759
$962$		−	23.3639i		−	0.753281i
$963$	−3.30298	−	53.1311i	−0.106437	−	1.71213i
$964$			10.5947i			0.341232i
$965$	17.0584	−	5.49972i	0.549130	−	0.177042i
$966$		0			0
$967$		−	51.9239i		−	1.66976i	−0.550433	−	0.834879i	$-0.685537\pi$
$967$		−	51.9239i		−	1.66976i	0.550433	−	0.834879i	$-0.314463\pi$
$968$	−7.11684			−0.228744
$969$	−27.2554	+	29.0024i	−0.875571	+	0.931692i
$970$	−1.45245	−	4.50506i	−0.0466354	−	0.144649i
$971$	28.6277			0.918707			0.459354	−	0.888253i	$-0.348081\pi$
$971$	28.6277			0.918707			0.459354	+	0.888253i	$0.348081\pi$
$972$	−9.18614	+	12.5942i	−0.294646	+	0.403960i
$973$		0			0
$974$			4.55134i			0.145834i
$975$	−2.25544	+	17.1730i	−0.0722318	+	0.549977i
$976$			2.81929i			0.0902433i
$977$	−40.4674			−1.29467			−0.647333	−	0.762207i	$-0.724116\pi$
$977$	−40.4674			−1.29467			−0.647333	+	0.762207i	$0.724116\pi$
$978$	4.37228	+	4.10891i	0.139810	+	0.131389i
$979$		−	18.6101i		−	0.594782i
$980$		0			0
$981$	−1.69702	−	27.2978i	−0.0541815	−	0.871553i
$982$		−	26.9205i		−	0.859069i
$983$		−	21.7244i		−	0.692900i	−0.938068	−	0.346450i	$-0.887387\pi$
$983$		−	21.7244i		−	0.692900i	0.938068	−	0.346450i	$-0.112613\pi$
$984$	1.93070	−	2.05446i	0.0615486	−	0.0654937i
$985$	−13.8832	−	43.0612i	−0.442354	−	1.37204i
$986$	22.0000			0.700623
$987$		0			0
$988$			6.92820i			0.220416i
$989$		−	48.2574i		−	1.53450i
$990$	10.4307	+	26.5793i	0.331510	+	0.844745i
$991$	−28.3505			−0.900584			−0.450292	−	0.892881i	$-0.648680\pi$
$991$	−28.3505			−0.900584			−0.450292	+	0.892881i	$0.648680\pi$
$992$		−	2.37686i		−	0.0754654i
$993$	12.1386	−	12.9166i	0.385207	−	0.409897i
$994$		0			0
$995$	39.6060	−	12.7692i	1.25559	−	0.404810i
$996$	1.81386	+	1.70460i	0.0574743	+	0.0540123i
$997$	30.4674			0.964911			0.482456	−	0.875920i	$-0.339745\pi$
$997$	30.4674			0.964911			0.482456	+	0.875920i	$0.339745\pi$
$998$	28.2337			0.893722
$999$	−38.7446	+	46.7277i	−1.22582	+	1.47840i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1470.2.d.c.1469.3		4
3.2	odd	2		1470.2.d.a.1469.4		4
5.4	even	2		1470.2.d.b.1469.2		4
7.4	even	3		210.2.t.b.89.1	yes	4
7.5	odd	6		210.2.t.a.59.1	✓	4
7.6	odd	2		1470.2.d.d.1469.2		4
15.14	odd	2		1470.2.d.d.1469.1		4
21.5	even	6		210.2.t.c.59.2	yes	4
21.11	odd	6		210.2.t.d.89.1	yes	4
21.20	even	2		1470.2.d.b.1469.1		4
35.4	even	6		210.2.t.c.89.2	yes	4
35.12	even	12		1050.2.s.e.101.3		8
35.18	odd	12		1050.2.s.d.551.4		8
35.19	odd	6		210.2.t.d.59.2	yes	4
35.32	odd	12		1050.2.s.d.551.1		8
35.33	even	12		1050.2.s.e.101.2		8
35.34	odd	2		1470.2.d.a.1469.3		4
105.32	even	12		1050.2.s.e.551.3		8
105.47	odd	12		1050.2.s.d.101.1		8
105.53	even	12		1050.2.s.e.551.2		8
105.68	odd	12		1050.2.s.d.101.4		8
105.74	odd	6		210.2.t.a.89.2	yes	4
105.89	even	6		210.2.t.b.59.1	yes	4
105.104	even	2	inner	1470.2.d.c.1469.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.t.a.59.1	✓	4	7.5	odd	6
210.2.t.a.89.2	yes	4	105.74	odd	6
210.2.t.b.59.1	yes	4	105.89	even	6
210.2.t.b.89.1	yes	4	7.4	even	3
210.2.t.c.59.2	yes	4	21.5	even	6
210.2.t.c.89.2	yes	4	35.4	even	6
210.2.t.d.59.2	yes	4	35.19	odd	6
210.2.t.d.89.1	yes	4	21.11	odd	6
1050.2.s.d.101.1		8	105.47	odd	12
1050.2.s.d.101.4		8	105.68	odd	12
1050.2.s.d.551.1		8	35.32	odd	12
1050.2.s.d.551.4		8	35.18	odd	12
1050.2.s.e.101.2		8	35.33	even	12
1050.2.s.e.101.3		8	35.12	even	12
1050.2.s.e.551.2		8	105.53	even	12
1050.2.s.e.551.3		8	105.32	even	12
1470.2.d.a.1469.3		4	35.34	odd	2
1470.2.d.a.1469.4		4	3.2	odd	2
1470.2.d.b.1469.1		4	21.20	even	2
1470.2.d.b.1469.2		4	5.4	even	2
1470.2.d.c.1469.3		4	1.1	even	1	trivial
1470.2.d.c.1469.4		4	105.104	even	2	inner
1470.2.d.d.1469.1		4	15.14	odd	2
1470.2.d.d.1469.2		4	7.6	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:	\( N \)	\(=\)	\( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1470.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(1.18614 - 1.26217i) q^{3} +1.00000 q^{4} +(0.686141 + 2.12819i) q^{5} +(1.18614 - 1.26217i) q^{6} +1.00000 q^{8} +(-0.186141 - 2.99422i) q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(1.18614 - 1.26217i) q^{3} +1.00000 q^{4} +(0.686141 + 2.12819i) q^{5} +(1.18614 - 1.26217i) q^{6} +1.00000 q^{8} +(-0.186141 - 2.99422i) q^{9} +(0.686141 + 2.12819i) q^{10} +4.25639i q^{11} +(1.18614 - 1.26217i) q^{12} +2.00000 q^{13} +(3.50000 + 1.65831i) q^{15} +1.00000 q^{16} +6.63325i q^{17} +(-0.186141 - 2.99422i) q^{18} +3.46410i q^{19} +(0.686141 + 2.12819i) q^{20} +4.25639i q^{22} +4.37228 q^{23} +(1.18614 - 1.26217i) q^{24} +(-4.05842 + 2.92048i) q^{25} +2.00000 q^{26} +(-4.00000 - 3.31662i) q^{27} -3.31662i q^{29} +(3.50000 + 1.65831i) q^{30} -2.37686i q^{31} +1.00000 q^{32} +(5.37228 + 5.04868i) q^{33} +6.63325i q^{34} +(-0.186141 - 2.99422i) q^{36} -11.6819i q^{37} +3.46410i q^{38} +(2.37228 - 2.52434i) q^{39} +(0.686141 + 2.12819i) q^{40} +1.62772 q^{41} -11.0371i q^{43} +4.25639i q^{44} +(6.24456 - 2.45060i) q^{45} +4.37228 q^{46} +1.87953i q^{47} +(1.18614 - 1.26217i) q^{48} +(-4.05842 + 2.92048i) q^{50} +(8.37228 + 7.86797i) q^{51} +2.00000 q^{52} +1.37228 q^{53} +(-4.00000 - 3.31662i) q^{54} +(-9.05842 + 2.92048i) q^{55} +(4.37228 + 4.10891i) q^{57} -3.31662i q^{58} -4.11684 q^{59} +(3.50000 + 1.65831i) q^{60} +2.81929i q^{61} -2.37686i q^{62} +1.00000 q^{64} +(1.37228 + 4.25639i) q^{65} +(5.37228 + 5.04868i) q^{66} -7.57301i q^{67} +6.63325i q^{68} +(5.18614 - 5.51856i) q^{69} +1.87953i q^{71} +(-0.186141 - 2.99422i) q^{72} +2.00000 q^{73} -11.6819i q^{74} +(-1.12772 + 8.58652i) q^{75} +3.46410i q^{76} +(2.37228 - 2.52434i) q^{78} -8.11684 q^{79} +(0.686141 + 2.12819i) q^{80} +(-8.93070 + 1.11469i) q^{81} +1.62772 q^{82} +1.43710i q^{83} +(-14.1168 + 4.55134i) q^{85} -11.0371i q^{86} +(-4.18614 - 3.93398i) q^{87} +4.25639i q^{88} -4.37228 q^{89} +(6.24456 - 2.45060i) q^{90} +4.37228 q^{92} +(-3.00000 - 2.81929i) q^{93} +1.87953i q^{94} +(-7.37228 + 2.37686i) q^{95} +(1.18614 - 1.26217i) q^{96} -2.11684 q^{97} +(12.7446 - 0.792287i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} - q^{3} + 4 q^{4} - 3 q^{5} - q^{6} + 4 q^{8} + 5 q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 - q^3 + 4 * q^4 - 3 * q^5 - q^6 + 4 * q^8 + 5 * q^9	\( 4 q + 4 q^{2} - q^{3} + 4 q^{4} - 3 q^{5} - q^{6} + 4 q^{8} + 5 q^{9} - 3 q^{10} - q^{12} + 8 q^{13} + 14 q^{15} + 4 q^{16} + 5 q^{18} - 3 q^{20} + 6 q^{23} - q^{24} + q^{25} + 8 q^{26} - 16 q^{27} + 14 q^{30} + 4 q^{32} + 10 q^{33} + 5 q^{36} - 2 q^{39} - 3 q^{40} + 18 q^{41} + 2 q^{45} + 6 q^{46} - q^{48} + q^{50} + 22 q^{51} + 8 q^{52} - 6 q^{53} - 16 q^{54} - 19 q^{55} + 6 q^{57} + 18 q^{59} + 14 q^{60} + 4 q^{64} - 6 q^{65} + 10 q^{66} + 15 q^{69} + 5 q^{72} + 8 q^{73} - 16 q^{75} - 2 q^{78} + 2 q^{79} - 3 q^{80} - 7 q^{81} + 18 q^{82} - 22 q^{85} - 11 q^{87} - 6 q^{89} + 2 q^{90} + 6 q^{92} - 12 q^{93} - 18 q^{95} - q^{96} + 26 q^{97} + 28 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 - q^3 + 4 * q^4 - 3 * q^5 - q^6 + 4 * q^8 + 5 * q^9 - 3 * q^10 - q^12 + 8 * q^13 + 14 * q^15 + 4 * q^16 + 5 * q^18 - 3 * q^20 + 6 * q^23 - q^24 + q^25 + 8 * q^26 - 16 * q^27 + 14 * q^30 + 4 * q^32 + 10 * q^33 + 5 * q^36 - 2 * q^39 - 3 * q^40 + 18 * q^41 + 2 * q^45 + 6 * q^46 - q^48 + q^50 + 22 * q^51 + 8 * q^52 - 6 * q^53 - 16 * q^54 - 19 * q^55 + 6 * q^57 + 18 * q^59 + 14 * q^60 + 4 * q^64 - 6 * q^65 + 10 * q^66 + 15 * q^69 + 5 * q^72 + 8 * q^73 - 16 * q^75 - 2 * q^78 + 2 * q^79 - 3 * q^80 - 7 * q^81 + 18 * q^82 - 22 * q^85 - 11 * q^87 - 6 * q^89 + 2 * q^90 + 6 * q^92 - 12 * q^93 - 18 * q^95 - q^96 + 26 * q^97 + 28 * q^99

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