LMFDB - Embedded newform 1805.2.b.k.1084.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1805,2,Mod(1084,1805)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1805, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1805.1084");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1805 = 5 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1805.b (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:	$14.4129975648$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1084.17
Character	$\chi$	$=$	1805.1084
Dual form			1805.2.b.k.1084.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.22159i q^{2} -0.804421i q^{3} +0.507728 q^{4} +(-2.23387 + 0.0991400i) q^{5} +0.982669 q^{6} -3.79180i q^{7} +3.06341i q^{8} +2.35291 q^{9} +O(q^{10})$	\(q+1.22159i q^{2} -0.804421i q^{3} +0.507728 q^{4} +(-2.23387 + 0.0991400i) q^{5} +0.982669 q^{6} -3.79180i q^{7} +3.06341i q^{8} +2.35291 q^{9} +(-0.121108 - 2.72886i) q^{10} -1.23733 q^{11} -0.408427i q^{12} +3.45598i q^{13} +4.63201 q^{14} +(0.0797502 + 1.79697i) q^{15} -2.72676 q^{16} -3.00695i q^{17} +2.87428i q^{18} +(-1.13420 + 0.0503361i) q^{20} -3.05020 q^{21} -1.51150i q^{22} +6.14780i q^{23} +2.46427 q^{24} +(4.98034 - 0.442931i) q^{25} -4.22178 q^{26} -4.30599i q^{27} -1.92520i q^{28} +4.28727 q^{29} +(-2.19515 + 0.0974218i) q^{30} +5.10134 q^{31} +2.79584i q^{32} +0.995330i q^{33} +3.67325 q^{34} +(0.375919 + 8.47038i) q^{35} +1.19464 q^{36} -9.13084i q^{37} +2.78006 q^{39} +(-0.303706 - 6.84325i) q^{40} +5.33021 q^{41} -3.72608i q^{42} -9.12495i q^{43} -0.628225 q^{44} +(-5.25609 + 0.233267i) q^{45} -7.51007 q^{46} -7.30333i q^{47} +2.19346i q^{48} -7.37774 q^{49} +(0.541079 + 6.08392i) q^{50} -2.41886 q^{51} +1.75470i q^{52} -3.33235i q^{53} +5.26014 q^{54} +(2.76402 - 0.122668i) q^{55} +11.6158 q^{56} +5.23727i q^{58} +0.817318 q^{59} +(0.0404914 + 0.912372i) q^{60} +6.40201 q^{61} +6.23172i q^{62} -8.92175i q^{63} -8.86888 q^{64} +(-0.342626 - 7.72022i) q^{65} -1.21588 q^{66} +1.01092i q^{67} -1.52671i q^{68} +4.94542 q^{69} +(-10.3473 + 0.459217i) q^{70} +13.6795 q^{71} +7.20791i q^{72} -11.0627i q^{73} +11.1541 q^{74} +(-0.356303 - 4.00629i) q^{75} +4.69169i q^{77} +3.39609i q^{78} +1.38420 q^{79} +(6.09122 - 0.270331i) q^{80} +3.59490 q^{81} +6.51132i q^{82} -2.52052i q^{83} -1.54867 q^{84} +(0.298109 + 6.71714i) q^{85} +11.1469 q^{86} -3.44877i q^{87} -3.79043i q^{88} -2.69842 q^{89} +(-0.284956 - 6.42076i) q^{90} +13.1044 q^{91} +3.12141i q^{92} -4.10362i q^{93} +8.92164 q^{94} +2.24903 q^{96} -3.06253i q^{97} -9.01254i q^{98} -2.91131 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 18 q^{4} - 3 q^{5} - 12 q^{6} - 12 q^{9}+O(q^{10}) $ 24 * q - 18 * q^4 - 3 * q^5 - 12 * q^6 - 12 * q^9	$ 24 q - 18 q^{4} - 3 q^{5} - 12 q^{6} - 12 q^{9} - 6 q^{10} + 12 q^{11} - 24 q^{14} - 9 q^{15} + 6 q^{16} + 21 q^{20} + 6 q^{21} + 42 q^{24} - 3 q^{25} - 12 q^{26} - 36 q^{29} - 18 q^{30} + 42 q^{31} - 6 q^{34} + 27 q^{35} - 6 q^{36} - 24 q^{39} + 12 q^{40} + 60 q^{41} + 30 q^{44} + 9 q^{45} + 6 q^{46} - 12 q^{49} + 18 q^{50} + 30 q^{51} + 24 q^{54} + 33 q^{55} + 18 q^{56} - 60 q^{59} - 42 q^{60} + 30 q^{61} + 18 q^{65} + 36 q^{66} - 66 q^{69} + 9 q^{70} + 96 q^{71} - 24 q^{74} + 36 q^{75} - 72 q^{79} - 42 q^{80} - 96 q^{81} + 54 q^{84} - 27 q^{85} + 108 q^{86} - 84 q^{89} - 93 q^{90} + 96 q^{91} - 36 q^{94} - 120 q^{96}+O(q^{100}) $ 24 * q - 18 * q^4 - 3 * q^5 - 12 * q^6 - 12 * q^9 - 6 * q^10 + 12 * q^11 - 24 * q^14 - 9 * q^15 + 6 * q^16 + 21 * q^20 + 6 * q^21 + 42 * q^24 - 3 * q^25 - 12 * q^26 - 36 * q^29 - 18 * q^30 + 42 * q^31 - 6 * q^34 + 27 * q^35 - 6 * q^36 - 24 * q^39 + 12 * q^40 + 60 * q^41 + 30 * q^44 + 9 * q^45 + 6 * q^46 - 12 * q^49 + 18 * q^50 + 30 * q^51 + 24 * q^54 + 33 * q^55 + 18 * q^56 - 60 * q^59 - 42 * q^60 + 30 * q^61 + 18 * q^65 + 36 * q^66 - 66 * q^69 + 9 * q^70 + 96 * q^71 - 24 * q^74 + 36 * q^75 - 72 * q^79 - 42 * q^80 - 96 * q^81 + 54 * q^84 - 27 * q^85 + 108 * q^86 - 84 * q^89 - 93 * q^90 + 96 * q^91 - 36 * q^94 - 120 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1805\mathbb{Z}\right)^\times$.

$n$	$362$	$1446$
$\chi(n)$	$-1$	$1$

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 $

$2$			1.22159i			0.863792i	0.901923	+	0.431896i	$0.142155\pi$
$2$			1.22159i			0.863792i	−0.901923	+	0.431896i	$0.857845\pi$
$3$		−	0.804421i		−	0.464432i	−0.972664	−	0.232216i	$-0.925402\pi$
$3$		−	0.804421i		−	0.464432i	0.972664	−	0.232216i	$-0.0745977\pi$
$4$	0.507728			0.253864
$5$	−2.23387	+	0.0991400i	−0.999017	+	0.0443367i
$5$	−2.23387	+	0.0991400i	−0.999017	+	0.0443367i
$6$	0.982669			0.401173
$7$		−	3.79180i		−	1.43317i	−0.697502	−	0.716583i	$-0.745705\pi$
$7$		−	3.79180i		−	1.43317i	0.697502	−	0.716583i	$-0.254295\pi$
$8$			3.06341i			1.08308i
$9$	2.35291			0.784303
$10$	−0.121108	−	2.72886i	−0.0382977	−	0.862942i
$11$	−1.23733			−0.373068			−0.186534	−	0.982449i	$-0.559725\pi$
$11$	−1.23733			−0.373068			−0.186534	+	0.982449i	$0.559725\pi$
$12$		−	0.408427i		−	0.117903i
$13$			3.45598i			0.958517i	0.877674	+	0.479259i	$0.159094\pi$
$13$			3.45598i			0.958517i	−0.877674	+	0.479259i	$0.840906\pi$
$14$	4.63201			1.23796
$15$	0.0797502	+	1.79697i	0.0205914	+	0.463976i
$16$	−2.72676			−0.681689
$17$		−	3.00695i		−	0.729293i	−0.931146	−	0.364647i	$-0.881190\pi$
$17$		−	3.00695i		−	0.729293i	0.931146	−	0.364647i	$-0.118810\pi$
$18$			2.87428i			0.677474i
$19$		0			0
$19$		0			0
$20$	−1.13420	+	0.0503361i	−0.253614	+	0.0112555i
$21$	−3.05020			−0.665608
$22$		−	1.51150i		−	0.322253i
$23$			6.14780i			1.28191i	0.767580	+	0.640953i	$0.221461\pi$
$23$			6.14780i			1.28191i	−0.767580	+	0.640953i	$0.778539\pi$
$24$	2.46427			0.503016
$25$	4.98034	−	0.442931i	0.996069	−	0.0885863i
$26$	−4.22178			−0.827959
$27$		−	4.30599i		−	0.828688i
$28$		−	1.92520i		−	0.363829i
$29$	4.28727			0.796126			0.398063	−	0.917358i	$-0.369683\pi$
$29$	4.28727			0.796126			0.398063	+	0.917358i	$0.369683\pi$
$30$	−2.19515	+	0.0974218i	−0.400778	+	0.0177867i
$31$	5.10134			0.916227			0.458114	−	0.888894i	$-0.348525\pi$
$31$	5.10134			0.916227			0.458114	+	0.888894i	$0.348525\pi$
$32$			2.79584i			0.494240i
$33$			0.995330i			0.173265i
$34$	3.67325			0.629958
$35$	0.375919	+	8.47038i	0.0635419	+	1.43176i
$36$	1.19464			0.199106
$37$		−	9.13084i		−	1.50110i	−0.660813	−	0.750550i	$-0.729789\pi$
$37$		−	9.13084i		−	1.50110i	0.660813	−	0.750550i	$-0.270211\pi$
$38$		0			0
$39$	2.78006			0.445167
$40$	−0.303706	−	6.84325i	−0.0480201	−	1.08201i
$41$	5.33021			0.832440			0.416220	−	0.909264i	$-0.363355\pi$
$41$	5.33021			0.832440			0.416220	+	0.909264i	$0.363355\pi$
$42$		−	3.72608i		−	0.574947i
$43$		−	9.12495i		−	1.39154i	−0.718264	−	0.695771i	$-0.755063\pi$
$43$		−	9.12495i		−	1.39154i	0.718264	−	0.695771i	$-0.244937\pi$
$44$	−0.628225			−0.0947084
$45$	−5.25609	+	0.233267i	−0.783531	+	0.0347734i
$46$	−7.51007			−1.10730
$47$		−	7.30333i		−	1.06530i	−0.846336	−	0.532650i	$-0.821196\pi$
$47$		−	7.30333i		−	1.06530i	0.846336	−	0.532650i	$-0.178804\pi$
$48$			2.19346i			0.316599i
$49$	−7.37774			−1.05396
$50$	0.541079	+	6.08392i	0.0765201	+	0.860396i
$51$	−2.41886			−0.338707
$52$			1.75470i			0.243333i
$53$		−	3.33235i		−	0.457734i	−0.973458	−	0.228867i	$-0.926498\pi$
$53$		−	3.33235i		−	0.457734i	0.973458	−	0.228867i	$-0.0735021\pi$
$54$	5.26014			0.715814
$55$	2.76402	−	0.122668i	0.372701	−	0.0165406i
$56$	11.6158			1.55223
$57$		0			0
$58$			5.23727i			0.687687i
$59$	0.817318			0.106406			0.0532029	−	0.998584i	$-0.483057\pi$
$59$	0.817318			0.106406			0.0532029	+	0.998584i	$0.483057\pi$
$60$	0.0404914	+	0.912372i	0.00522742	+	0.117787i
$61$	6.40201			0.819693			0.409847	−	0.912154i	$-0.365582\pi$
$61$	6.40201			0.819693			0.409847	+	0.912154i	$0.365582\pi$
$62$			6.23172i			0.791430i
$63$		−	8.92175i		−	1.12404i
$64$	−8.86888			−1.10861
$65$	−0.342626	−	7.72022i	−0.0424975	−	0.957575i
$66$	−1.21588			−0.149665
$67$			1.01092i			0.123504i	0.998092	+	0.0617520i	$0.0196688\pi$
$67$			1.01092i			0.123504i	−0.998092	+	0.0617520i	$0.980331\pi$
$68$		−	1.52671i		−	0.185141i
$69$	4.94542			0.595359
$70$	−10.3473	+	0.459217i	−1.23674	+	0.0548869i
$71$	13.6795			1.62346			0.811731	−	0.584032i	$-0.198526\pi$
$71$	13.6795			1.62346			0.811731	+	0.584032i	$0.198526\pi$
$72$			7.20791i			0.849460i
$73$		−	11.0627i		−	1.29479i	−0.762155	−	0.647395i	$-0.775858\pi$
$73$		−	11.0627i		−	1.29479i	0.762155	−	0.647395i	$-0.224142\pi$
$74$	11.1541			1.29664
$75$	−0.356303	−	4.00629i	−0.0411423	−	0.462607i
$76$		0			0
$77$			4.69169i			0.534668i
$78$			3.39609i			0.384531i
$79$	1.38420			0.155735			0.0778673	−	0.996964i	$-0.475189\pi$
$79$	1.38420			0.155735			0.0778673	+	0.996964i	$0.475189\pi$
$80$	6.09122	−	0.270331i	0.681019	−	0.0302239i
$81$	3.59490			0.399433
$82$			6.51132i			0.719054i
$83$		−	2.52052i		−	0.276663i	−0.990386	−	0.138332i	$-0.955826\pi$
$83$		−	2.52052i		−	0.276663i	0.990386	−	0.138332i	$-0.0441740\pi$
$84$	−1.54867			−0.168974
$85$	0.298109	+	6.71714i	0.0323345	+	0.728576i
$86$	11.1469			1.20200
$87$		−	3.44877i		−	0.369747i
$88$		−	3.79043i		−	0.404061i
$89$	−2.69842			−0.286032			−0.143016	−	0.989720i	$-0.545680\pi$
$89$	−2.69842			−0.286032			−0.143016	+	0.989720i	$0.545680\pi$
$90$	−0.284956	−	6.42076i	−0.0300370	−	0.676808i
$91$	13.1044			1.37371
$92$			3.12141i			0.325430i
$93$		−	4.10362i		−	0.425526i
$94$	8.92164			0.920197
$95$		0			0
$96$	2.24903			0.229541
$97$		−	3.06253i		−	0.310953i	−0.987840	−	0.155476i	$-0.950309\pi$
$97$		−	3.06253i		−	0.310953i	0.987840	−	0.155476i	$-0.0496912\pi$
$98$		−	9.01254i		−	0.910404i
$99$	−2.91131			−0.292598
$100$	2.52866	−	0.224889i	0.252866	−	0.0224889i
$101$	3.72705			0.370856			0.185428	−	0.982658i	$-0.440633\pi$
$101$	3.72705			0.370856			0.185428	+	0.982658i	$0.440633\pi$
$102$		−	2.95484i		−	0.292573i
$103$			13.2086i			1.30149i	0.759298	+	0.650743i	$0.225543\pi$
$103$			13.2086i			1.30149i	−0.759298	+	0.650743i	$0.774457\pi$
$104$	−10.5871			−1.03815
$105$	6.81375	−	0.302397i	0.664954	−	0.0295109i
$106$	4.07076			0.395387
$107$		−	5.13305i		−	0.496230i	−0.968731	−	0.248115i	$-0.920189\pi$
$107$		−	5.13305i		−	0.496230i	0.968731	−	0.248115i	$-0.0798112\pi$
$108$		−	2.18627i		−	0.210374i
$109$	1.58777			0.152081			0.0760404	−	0.997105i	$-0.475772\pi$
$109$	1.58777			0.152081			0.0760404	+	0.997105i	$0.475772\pi$
$110$	0.149850	+	3.37649i	0.0142876	+	0.321936i
$111$	−7.34503			−0.697160
$112$			10.3393i			0.976973i
$113$			20.0832i			1.88927i	0.328126	+	0.944634i	$0.393583\pi$
$113$			20.0832i			1.88927i	−0.328126	+	0.944634i	$0.606417\pi$
$114$		0			0
$115$	−0.609493	−	13.7334i	−0.0568355	−	1.28065i
$116$	2.17676			0.202108
$117$			8.13161i			0.751768i
$118$			0.998424i			0.0919124i
$119$	−11.4018			−1.04520
$120$	−5.50485	+	0.244307i	−0.502522	+	0.0223021i
$121$	−9.46903			−0.860821
$122$			7.82061i			0.708044i
$123$		−	4.28773i		−	0.386612i
$124$	2.59009			0.232597
$125$	−11.0815	+	1.48320i	−0.991161	+	0.132662i
$126$	10.8987			0.970932
$127$		−	3.45304i		−	0.306408i	−0.988195	−	0.153204i	$-0.951041\pi$
$127$		−	3.45304i		−	0.306408i	0.988195	−	0.153204i	$-0.0489592\pi$
$128$		−	5.24241i		−	0.463368i
$129$	−7.34030			−0.646277
$130$	9.43091	−	0.418547i	0.827145	−	0.0367090i
$131$	−7.58746			−0.662920			−0.331460	−	0.943469i	$-0.607541\pi$
$131$	−7.58746			−0.662920			−0.331460	+	0.943469i	$0.607541\pi$
$132$			0.505357i			0.0439857i
$133$		0			0
$134$	−1.23493			−0.106682
$135$	0.426896	+	9.61902i	0.0367413	+	0.827873i
$136$	9.21152			0.789881
$137$			3.68633i			0.314944i	0.987523	+	0.157472i	$0.0503344\pi$
$137$			3.68633i			0.314944i	−0.987523	+	0.157472i	$0.949666\pi$
$138$			6.04126i			0.514266i
$139$	18.6273			1.57994			0.789972	−	0.613143i	$-0.210095\pi$
$139$	18.6273			1.57994			0.789972	+	0.613143i	$0.210095\pi$
$140$	0.190864	+	4.30065i	0.0161310	+	0.363471i
$141$	−5.87494			−0.494760
$142$			16.7107i			1.40233i
$143$		−	4.27618i		−	0.357592i
$144$	−6.41581			−0.534651
$145$	−9.57719	+	0.425040i	−0.795343	+	0.0352976i
$146$	13.5140			1.11843
$147$			5.93480i			0.489494i
$148$		−	4.63598i		−	0.381075i
$149$	−1.68785			−0.138274			−0.0691369	−	0.997607i	$-0.522025\pi$
$149$	−1.68785			−0.138274			−0.0691369	+	0.997607i	$0.522025\pi$
$150$	4.89403	−	0.435255i	0.399596	−	0.0355384i
$151$	1.33890			0.108958			0.0544791	−	0.998515i	$-0.482650\pi$
$151$	1.33890			0.108958			0.0544791	+	0.998515i	$0.482650\pi$
$152$		0			0
$153$		−	7.07508i		−	0.571987i
$154$	−5.73130			−0.461841
$155$	−11.3957	+	0.505746i	−0.915326	+	0.0406225i
$156$	1.41152			0.113012
$157$		−	6.04267i		−	0.482258i	−0.970493	−	0.241129i	$-0.922482\pi$
$157$		−	6.04267i		−	0.482258i	0.970493	−	0.241129i	$-0.0775176\pi$
$158$			1.69092i			0.134522i
$159$	−2.68061			−0.212587
$160$	−0.277180	−	6.24555i	−0.0219130	−	0.493754i
$161$	23.3112			1.83718
$162$			4.39147i			0.345027i
$163$		−	9.79728i		−	0.767382i	−0.923462	−	0.383691i	$-0.874653\pi$
$163$		−	9.79728i		−	0.767382i	0.923462	−	0.383691i	$-0.125347\pi$
$164$	2.70630			0.211326
$165$	−0.0986770	−	2.22344i	−0.00768199	−	0.173094i
$166$	3.07903			0.238979
$167$		−	3.87632i		−	0.299959i	−0.988689	−	0.149979i	$-0.952079\pi$
$167$		−	3.87632i		−	0.299959i	0.988689	−	0.149979i	$-0.0479207\pi$
$168$		−	9.34400i		−	0.720905i
$169$	1.05618			0.0812444
$170$	−8.20556	+	0.364166i	−0.629338	+	0.0279303i
$171$		0			0
$172$		−	4.63299i		−	0.353262i
$173$		−	4.73220i		−	0.359782i	−0.983687	−	0.179891i	$-0.942425\pi$
$173$		−	4.73220i		−	0.359782i	0.983687	−	0.179891i	$-0.0575745\pi$
$174$	4.21296			0.319384
$175$	−1.67951	−	18.8845i	−0.126959	−	1.42753i
$176$	3.37389			0.254316
$177$		−	0.657468i		−	0.0494183i
$178$		−	3.29635i		−	0.247072i
$179$	9.37815			0.700956			0.350478	−	0.936571i	$-0.386019\pi$
$179$	9.37815			0.700956			0.350478	+	0.936571i	$0.386019\pi$
$180$	−2.66866	+	0.118436i	−0.198910	+	0.00882772i
$181$	−19.5008			−1.44948			−0.724741	−	0.689022i	$-0.758040\pi$
$181$	−19.5008			−1.44948			−0.724741	+	0.689022i	$0.758040\pi$
$182$			16.0081i			1.18660i
$183$		−	5.14991i		−	0.380692i
$184$	−18.8332			−1.38840
$185$	0.905231	+	20.3971i	0.0665539	+	1.49962i
$186$	5.01293			0.367566
$187$			3.72058i			0.272076i
$188$		−	3.70810i		−	0.270441i
$189$	−16.3274			−1.18765
$190$		0			0
$191$	15.5024			1.12171			0.560857	−	0.827913i	$-0.310472\pi$
$191$	15.5024			1.12171			0.560857	+	0.827913i	$0.310472\pi$
$192$			7.13431i			0.514874i
$193$			19.8432i			1.42834i	0.699970	+	0.714172i	$0.253196\pi$
$193$			19.8432i			1.42834i	−0.699970	+	0.714172i	$0.746804\pi$
$194$	3.74114			0.268598
$195$	−6.21030	+	0.275615i	−0.444729	+	0.0197372i
$196$	−3.74588			−0.267563
$197$			25.9708i			1.85034i	0.379553	+	0.925170i	$0.376078\pi$
$197$			25.9708i			1.85034i	−0.379553	+	0.925170i	$0.623922\pi$
$198$		−	3.55642i		−	0.252744i
$199$	5.41593			0.383925			0.191963	−	0.981402i	$-0.438515\pi$
$199$	5.41593			0.383925			0.191963	+	0.981402i	$0.438515\pi$
$200$	1.35688	+	15.2568i	0.0959458	+	1.07882i
$201$	0.813208			0.0573593
$202$			4.55291i			0.320342i
$203$		−	16.2565i		−	1.14098i
$204$	−1.22812			−0.0859856
$205$	−11.9070	+	0.528437i	−0.831621	+	0.0369077i
$206$	−16.1355			−1.12421
$207$			14.4652i			1.00540i
$208$		−	9.42363i		−	0.653411i
$209$		0			0
$210$	0.369404	+	8.32358i	0.0254913	+	0.574382i
$211$	−20.1197			−1.38510			−0.692550	−	0.721370i	$-0.743513\pi$
$211$	−20.1197			−1.38510			−0.692550	+	0.721370i	$0.743513\pi$
$212$		−	1.69193i		−	0.116202i
$213$		−	11.0041i		−	0.753988i
$214$	6.27046			0.428640
$215$	0.904647	+	20.3839i	0.0616964	+	1.39017i
$216$	13.1910			0.897533
$217$		−	19.3432i		−	1.31311i
$218$			1.93960i			0.131366i
$219$	−8.89905			−0.601342
$220$	1.40337	−	0.0622822i	0.0946153	−	0.00419906i
$221$	10.3920			0.699040
$222$		−	8.97259i		−	0.602201i
$223$		−	10.8496i		−	0.726546i	−0.931683	−	0.363273i	$-0.881659\pi$
$223$		−	10.8496i		−	0.726546i	0.931683	−	0.363273i	$-0.118341\pi$
$224$	10.6013			0.708327
$225$	11.7183	−	1.04218i	0.781219	−	0.0694784i
$226$	−24.5333			−1.63193
$227$		−	8.78226i		−	0.582899i	−0.956586	−	0.291449i	$-0.905862\pi$
$227$		−	8.78226i		−	0.582899i	0.956586	−	0.291449i	$-0.0941375\pi$
$228$		0			0
$229$	−18.0824			−1.19492			−0.597459	−	0.801899i	$-0.703823\pi$
$229$	−18.0824			−1.19492			−0.597459	+	0.801899i	$0.703823\pi$
$230$	16.7765	−	0.744548i	1.10621	−	0.0490941i
$231$	3.77409			0.248317
$232$			13.1336i			0.862265i
$233$			26.3658i			1.72728i	0.504109	+	0.863640i	$0.331821\pi$
$233$			26.3658i			1.72728i	−0.504109	+	0.863640i	$0.668179\pi$
$234$	−9.93346			−0.649371
$235$	0.724051	+	16.3147i	0.0472319	+	1.06425i
$236$	0.414975			0.0270126
$237$		−	1.11348i		−	0.0723282i
$238$		−	13.9282i		−	0.902833i
$239$	9.16897			0.593091			0.296546	−	0.955019i	$-0.404165\pi$
$239$	9.16897			0.593091			0.296546	+	0.955019i	$0.404165\pi$
$240$	−0.217459	−	4.89990i	−0.0140369	−	0.316287i
$241$	26.5167			1.70809			0.854045	−	0.520199i	$-0.174142\pi$
$241$	26.5167			1.70809			0.854045	+	0.520199i	$0.174142\pi$
$242$		−	11.5672i		−	0.743570i
$243$		−	15.8098i		−	1.01420i
$244$	3.25048			0.208091
$245$	16.4809	−	0.731429i	1.05293	−	0.0467293i
$246$	5.23784			0.333952
$247$		0			0
$248$			15.6275i			0.992345i
$249$	−2.02756			−0.128491
$250$	−1.81186	−	13.5370i	−0.114592	−	0.856157i
$251$	−14.9471			−0.943451			−0.471726	−	0.881745i	$-0.656369\pi$
$251$	−14.9471			−0.943451			−0.471726	+	0.881745i	$0.656369\pi$
$252$		−	4.52982i		−	0.285352i
$253$		−	7.60684i		−	0.478238i
$254$	4.21819			0.264673
$255$	5.40341	−	0.239805i	0.338374	−	0.0150172i
$256$	−11.3337			−0.708356
$257$			10.7988i			0.673610i	0.941574	+	0.336805i	$0.109346\pi$
$257$			10.7988i			0.673610i	−0.941574	+	0.336805i	$0.890654\pi$
$258$		−	8.96680i		−	0.558249i
$259$	−34.6223			−2.15132
$260$	−0.173961	−	3.91977i	−0.0107886	−	0.243094i
$261$	10.0875			0.624403
$262$		−	9.26874i		−	0.572624i
$263$		−	0.549168i		−	0.0338632i	−0.999857	−	0.0169316i	$-0.994610\pi$
$263$		−	0.549168i		−	0.0338632i	0.999857	−	0.0169316i	$-0.00538975\pi$
$264$	−3.04910			−0.187659
$265$	0.330370	+	7.44404i	0.0202944	+	0.457284i
$266$		0			0
$267$			2.17066i			0.132842i
$268$			0.513275i			0.0313532i
$269$	−21.9270			−1.33691			−0.668455	−	0.743752i	$-0.733044\pi$
$269$	−21.9270			−1.33691			−0.668455	+	0.743752i	$0.733044\pi$
$270$	−11.7505	+	0.521490i	−0.715110	+	0.0317369i
$271$	−5.28538			−0.321064			−0.160532	−	0.987031i	$-0.551321\pi$
$271$	−5.28538			−0.321064			−0.160532	+	0.987031i	$0.551321\pi$
$272$			8.19923i			0.497151i
$273$		−	10.5414i		−	0.637997i
$274$	−4.50316			−0.272046
$275$	−6.16230	+	0.548050i	−0.371601	+	0.0330487i
$276$	2.51093			0.151140
$277$			17.4391i			1.04781i	0.851776	+	0.523906i	$0.175526\pi$
$277$			17.4391i			1.04781i	−0.851776	+	0.523906i	$0.824474\pi$
$278$			22.7548i			1.36474i
$279$	12.0030			0.718599
$280$	−25.9482	+	1.15159i	−1.55070	+	0.0688208i
$281$	−23.1841			−1.38305			−0.691524	−	0.722354i	$-0.743060\pi$
$281$	−23.1841			−1.38305			−0.691524	+	0.722354i	$0.743060\pi$
$282$		−	7.17675i		−	0.427369i
$283$		−	4.59388i		−	0.273078i	−0.990635	−	0.136539i	$-0.956402\pi$
$283$		−	4.59388i		−	0.273078i	0.990635	−	0.136539i	$-0.0435979\pi$
$284$	6.94548			0.412138
$285$		0			0
$286$	5.22372			0.308885
$287$		−	20.2111i		−	1.19302i
$288$			6.57836i			0.387633i
$289$	7.95823			0.468131
$290$	−0.519222	−	11.6994i	−0.0304898	−	0.687010i
$291$	−2.46356			−0.144416
$292$		−	5.61684i		−	0.328700i
$293$			18.1326i			1.05932i	0.848211	+	0.529659i	$0.177680\pi$
$293$			18.1326i			1.05932i	−0.848211	+	0.529659i	$0.822320\pi$
$294$	−7.24987			−0.422821
$295$	−1.82578	+	0.0810289i	−0.106301	+	0.00471769i
$296$	27.9715			1.62581
$297$			5.32791i			0.309157i
$298$		−	2.06185i		−	0.119440i
$299$	−21.2467			−1.22873
$300$	−0.180905	−	2.03410i	−0.0104446	−	0.117439i
$301$	−34.6000			−1.99431
$302$			1.63558i			0.0941171i
$303$		−	2.99812i		−	0.172237i
$304$		0			0
$305$	−14.3013	+	0.634695i	−0.818887	+	0.0363425i
$306$	8.64282			0.494077
$307$			4.41407i			0.251924i	0.992035	+	0.125962i	$0.0402018\pi$
$307$			4.41407i			0.251924i	−0.992035	+	0.125962i	$0.959798\pi$
$308$			2.38210i			0.135733i
$309$	10.6253			0.604452
$310$	−0.617813	−	13.9209i	−0.0350894	−	0.790651i
$311$	15.0338			0.852487			0.426243	−	0.904609i	$-0.359837\pi$
$311$	15.0338			0.852487			0.426243	+	0.904609i	$0.359837\pi$
$312$			8.51646i			0.482150i
$313$		−	7.80549i		−	0.441193i	−0.975365	−	0.220596i	$-0.929200\pi$
$313$		−	7.80549i		−	0.441193i	0.975365	−	0.220596i	$-0.0708003\pi$
$314$	7.38164			0.416570
$315$	0.884502	+	19.9300i	0.0498361	+	1.12293i
$316$	0.702796			0.0395354
$317$			27.2310i			1.52944i	0.644361	+	0.764722i	$0.277123\pi$
$317$			27.2310i			1.52944i	−0.644361	+	0.764722i	$0.722877\pi$
$318$		−	3.27460i		−	0.183631i
$319$	−5.30474			−0.297009
$320$	19.8119	−	0.879260i	1.10752	−	0.0491521i
$321$	−4.12913			−0.230466
$322$			28.4767i			1.58694i
$323$		0			0
$324$	1.82523			0.101402
$325$	1.53076	+	17.2120i	0.0849115	+	0.954749i
$326$	11.9682			0.662858
$327$		−	1.27724i		−	0.0706313i
$328$			16.3286i			0.901596i
$329$	−27.6927			−1.52675
$330$	2.71612	−	0.120542i	0.149517	−	0.00663564i
$331$	−11.9800			−0.658480			−0.329240	−	0.944246i	$-0.606792\pi$
$331$	−11.9800			−0.658480			−0.329240	+	0.944246i	$0.606792\pi$
$332$		−	1.27974i		−	0.0702348i
$333$		−	21.4840i		−	1.17732i
$334$	4.73526			0.259102
$335$	−0.100223	−	2.25827i	−0.00547577	−	0.123383i
$336$	8.31716			0.453738
$337$			4.14343i			0.225707i	0.993612	+	0.112853i	$0.0359991\pi$
$337$			4.14343i			0.225707i	−0.993612	+	0.112853i	$0.964001\pi$
$338$			1.29021i			0.0701782i
$339$	16.1553			0.877437
$340$	0.151358	+	3.41048i	0.00820856	+	0.184959i
$341$	−6.31201			−0.341815
$342$		0			0
$343$			1.43230i			0.0773370i
$344$	27.9534			1.50715
$345$	−11.0474	+	0.490289i	−0.594773	+	0.0263963i
$346$	5.78078			0.310777
$347$		−	9.16935i		−	0.492237i	−0.969240	−	0.246118i	$-0.920845\pi$
$347$		−	9.16935i		−	0.492237i	0.969240	−	0.246118i	$-0.0791552\pi$
$348$		−	1.75103i		−	0.0938653i
$349$	32.6883			1.74976			0.874881	−	0.484337i	$-0.160939\pi$
$349$	32.6883			1.74976			0.874881	+	0.484337i	$0.160939\pi$
$350$	23.0690	−	2.05166i	1.23309	−	0.109666i
$351$	14.8814			0.794312
$352$		−	3.45937i		−	0.184385i
$353$		−	26.4701i		−	1.40886i	−0.709773	−	0.704431i	$-0.751202\pi$
$353$		−	26.4701i		−	1.40886i	0.709773	−	0.704431i	$-0.248798\pi$
$354$	0.803153			0.0426871
$355$	−30.5583	+	1.35619i	−1.62187	+	0.0719790i
$356$	−1.37006			−0.0726131
$357$			9.17181i			0.485424i
$358$			11.4562i			0.605480i
$359$	−12.4121			−0.655083			−0.327542	−	0.944837i	$-0.606220\pi$
$359$	−12.4121			−0.655083			−0.327542	+	0.944837i	$0.606220\pi$
$360$	−0.714592	−	16.1015i	−0.0376623	−	0.848625i
$361$		0			0
$362$		−	23.8219i		−	1.25205i
$363$			7.61708i			0.399793i
$364$	6.65347			0.348736
$365$	1.09675	+	24.7126i	0.0574068	+	1.29352i
$366$	6.29106			0.328839
$367$		−	5.32121i		−	0.277765i	−0.990309	−	0.138882i	$-0.955649\pi$
$367$		−	5.32121i		−	0.277765i	0.990309	−	0.138882i	$-0.0443510\pi$
$368$		−	16.7636i		−	0.873861i
$369$	12.5415			0.652885
$370$	−24.9168	+	1.10582i	−1.29536	+	0.0574887i
$371$	−12.6356			−0.656009
$372$		−	2.08352i		−	0.108026i
$373$		−	19.3050i		−	0.999575i	−0.866148	−	0.499788i	$-0.833411\pi$
$373$		−	19.3050i		−	0.999575i	0.866148	−	0.499788i	$-0.166589\pi$
$374$	−4.54501			−0.235017
$375$	1.19312	+	8.91420i	0.0616124	+	0.460327i
$376$	22.3730			1.15380
$377$			14.8167i			0.763100i
$378$		−	19.9454i		−	1.02588i
$379$	−20.5109			−1.05357			−0.526787	−	0.849997i	$-0.676603\pi$
$379$	−20.5109			−1.05357			−0.526787	+	0.849997i	$0.676603\pi$
$380$		0			0
$381$	−2.77770			−0.142306
$382$			18.9375i			0.968927i
$383$		−	22.7253i		−	1.16121i	−0.814186	−	0.580605i	$-0.802816\pi$
$383$		−	22.7253i		−	1.16121i	0.814186	−	0.580605i	$-0.197184\pi$
$384$	−4.21710			−0.215203
$385$	−0.465134	−	10.4806i	−0.0237054	−	0.534142i
$386$	−24.2402			−1.23379
$387$		−	21.4702i		−	1.09139i
$388$		−	1.55493i		−	0.0789396i
$389$	−5.04493			−0.255788			−0.127894	−	0.991788i	$-0.540822\pi$
$389$	−5.04493			−0.255788			−0.127894	+	0.991788i	$0.540822\pi$
$390$	−0.336688	−	7.58641i	−0.0170489	−	0.384153i
$391$	18.4862			0.934885
$392$		−	22.6010i		−	1.14152i
$393$			6.10351i			0.307881i
$394$	−31.7255			−1.59831
$395$	−3.09212	+	0.137229i	−0.155581	+	0.00690476i
$396$	−1.47815			−0.0742800
$397$		−	22.9429i		−	1.15147i	−0.817636	−	0.575735i	$-0.804716\pi$
$397$		−	22.9429i		−	1.15147i	0.817636	−	0.575735i	$-0.195284\pi$
$398$			6.61603i			0.331632i
$399$		0			0
$400$	−13.5802	+	1.20777i	−0.679009	+	0.0603883i
$401$	−22.7649			−1.13683			−0.568413	−	0.822744i	$-0.692442\pi$
$401$	−22.7649			−1.13683			−0.568413	+	0.822744i	$0.692442\pi$
$402$			0.993404i			0.0495465i
$403$			17.6301i			0.878220i
$404$	1.89233			0.0941468
$405$	−8.03053	+	0.356398i	−0.399040	+	0.0177096i
$406$	19.8587			0.985568
$407$			11.2978i			0.560012i
$408$		−	7.40993i		−	0.366846i
$409$	−23.8028			−1.17697			−0.588486	−	0.808507i	$-0.700276\pi$
$409$	−23.8028			−1.17697			−0.588486	+	0.808507i	$0.700276\pi$
$410$	−0.645532	−	14.5454i	−0.0318805	−	0.718347i
$411$	2.96536			0.146270
$412$			6.70640i			0.330400i
$413$		−	3.09911i		−	0.152497i
$414$	−17.6705			−0.868458
$415$	0.249884	+	5.63051i	0.0122663	+	0.276391i
$416$	−9.66239			−0.473737
$417$		−	14.9842i		−	0.733777i
$418$		0			0
$419$	15.9374			0.778593			0.389296	−	0.921113i	$-0.372718\pi$
$419$	15.9374			0.778593			0.389296	+	0.921113i	$0.372718\pi$
$420$	3.45953	−	0.153535i	0.168808	−	0.00749175i
$421$	−2.65354			−0.129326			−0.0646629	−	0.997907i	$-0.520597\pi$
$421$	−2.65354			−0.129326			−0.0646629	+	0.997907i	$0.520597\pi$
$422$		−	24.5780i		−	1.19644i
$423$		−	17.1840i		−	0.835517i
$424$	10.2084			0.495761
$425$	−1.33187	−	14.9757i	−0.0646054	−	0.726426i
$426$	13.4424			0.651289
$427$		−	24.2751i		−	1.17476i
$428$		−	2.60619i		−	0.125975i
$429$	−3.43984			−0.166077
$430$	−24.9007	+	1.10510i	−1.20082	+	0.0532929i
$431$	33.3222			1.60507			0.802536	−	0.596604i	$-0.203484\pi$
$431$	33.3222			1.60507			0.802536	+	0.596604i	$0.203484\pi$
$432$			11.7414i			0.564908i
$433$			22.3800i			1.07552i	0.843099	+	0.537758i	$0.180728\pi$
$433$			22.3800i			1.07552i	−0.843099	+	0.537758i	$0.819272\pi$
$434$	23.6294			1.13425
$435$	0.341911	+	7.70409i	0.0163934	+	0.369383i
$436$	0.806155			0.0386078
$437$		0			0
$438$		−	10.8710i		−	0.519435i
$439$	17.4561			0.833132			0.416566	−	0.909105i	$-0.363233\pi$
$439$	17.4561			0.833132			0.416566	+	0.909105i	$0.363233\pi$
$440$	0.375783	+	8.46732i	0.0179148	+	0.403664i
$441$	−17.3591			−0.826625
$442$			12.6947i			0.603825i
$443$			1.49859i			0.0712001i	0.999366	+	0.0356001i	$0.0113342\pi$
$443$			1.49859i			0.0712001i	−0.999366	+	0.0356001i	$0.988666\pi$
$444$	−3.72928			−0.176984
$445$	6.02791	−	0.267521i	0.285750	−	0.0126817i
$446$	13.2538			0.627584
$447$			1.35774i			0.0642189i
$448$			33.6290i			1.58882i
$449$	−11.9911			−0.565896			−0.282948	−	0.959135i	$-0.591312\pi$
$449$	−11.9911			−0.565896			−0.282948	+	0.959135i	$0.591312\pi$
$450$	1.27311	+	14.3149i	0.0600149	+	0.674811i
$451$	−6.59521			−0.310556
$452$			10.1968i			0.479617i
$453$		−	1.07704i		−	0.0506037i
$454$	10.7283			0.503503
$455$	−29.2735	+	1.29917i	−1.37236	+	0.0609060i
$456$		0			0
$457$			12.9472i			0.605646i	0.953047	+	0.302823i	$0.0979291\pi$
$457$			12.9472i			0.605646i	−0.953047	+	0.302823i	$0.902071\pi$
$458$		−	22.0892i		−	1.03216i
$459$	−12.9479			−0.604357
$460$	−0.309457	−	6.97283i	−0.0144285	−	0.325110i
$461$	13.8680			0.645899			0.322949	−	0.946416i	$-0.395326\pi$
$461$	13.8680			0.645899			0.322949	+	0.946416i	$0.395326\pi$
$462$			4.61038i			0.214494i
$463$		−	4.18473i		−	0.194481i	−0.995261	−	0.0972405i	$-0.968998\pi$
$463$		−	4.18473i		−	0.194481i	0.995261	−	0.0972405i	$-0.0310016\pi$
$464$	−11.6903			−0.542710
$465$	0.406833	+	9.16695i	0.0188664	+	0.425107i
$466$	−32.2081			−1.49201
$467$		−	23.3019i		−	1.07828i	−0.842216	−	0.539141i	$-0.818749\pi$
$467$		−	23.3019i		−	1.07828i	0.842216	−	0.539141i	$-0.181251\pi$
$468$			4.12864i			0.190847i
$469$	3.83322			0.177002
$470$	−19.9298	+	0.884491i	−0.919292	+	0.0407985i
$471$	−4.86085			−0.223976
$472$			2.50378i			0.115246i
$473$			11.2905i			0.519139i
$474$	1.36021			0.0624765
$475$		0			0
$476$	−5.78899			−0.265338
$477$		−	7.84072i		−	0.359002i
$478$			11.2007i			0.512307i
$479$	−35.1170			−1.60454			−0.802268	−	0.596963i	$-0.796374\pi$
$479$	−35.1170			−1.60454			−0.802268	+	0.596963i	$0.796374\pi$
$480$	−5.02405	+	0.222969i	−0.229315	+	0.0101771i
$481$	31.5560			1.43883
$482$			32.3924i			1.47543i
$483$		−	18.7520i		−	0.853247i
$484$	−4.80769			−0.218531
$485$	0.303619	+	6.84128i	0.0137866	+	0.310647i
$486$	19.3130			0.876055
$487$			33.4209i			1.51445i	0.653156	+	0.757223i	$0.273444\pi$
$487$			33.4209i			1.51445i	−0.653156	+	0.757223i	$0.726556\pi$
$488$			19.6120i			0.887791i
$489$	−7.88113			−0.356397
$490$	0.893503	+	20.1328i	0.0403643	+	0.909509i
$491$	−17.5387			−0.791511			−0.395755	−	0.918356i	$-0.629517\pi$
$491$	−17.5387			−0.791511			−0.395755	+	0.918356i	$0.629517\pi$
$492$		−	2.17700i		−	0.0981468i
$493$		−	12.8916i		−	0.580609i
$494$		0			0
$495$	6.50349	−	0.288627i	0.292310	−	0.0129728i
$496$	−13.9101			−0.624582
$497$		−	51.8700i		−	2.32669i
$498$		−	2.47684i		−	0.110990i
$499$	−32.6830			−1.46309			−0.731545	−	0.681793i	$-0.761201\pi$
$499$	−32.6830			−1.46309			−0.731545	+	0.681793i	$0.761201\pi$
$500$	−5.62640	+	0.753063i	−0.251620	+	0.0336780i
$501$	−3.11819			−0.139310
$502$		−	18.2591i		−	0.814946i
$503$			17.5243i			0.781370i	0.920524	+	0.390685i	$0.127762\pi$
$503$			17.5243i			0.781370i	−0.920524	+	0.390685i	$0.872238\pi$
$504$	27.3309			1.21742
$505$	−8.32575	+	0.369500i	−0.370491	+	0.0164425i
$506$	9.29240			0.413098
$507$		−	0.849611i		−	0.0377325i
$508$		−	1.75321i		−	0.0777860i
$509$	−29.9995			−1.32970			−0.664852	−	0.746975i	$-0.731505\pi$
$509$	−29.9995			−1.32970			−0.664852	+	0.746975i	$0.731505\pi$
$510$	0.292943	+	6.60072i	0.0129717	+	0.292285i
$511$	−41.9475			−1.85565
$512$		−	24.3299i		−	1.07524i
$513$		0			0
$514$	−13.1916			−0.581858
$515$	−1.30950	−	29.5064i	−0.0577037	−	1.30021i
$516$	−3.72687			−0.164066
$517$			9.03659i			0.397429i
$518$		−	42.2941i		−	1.85830i
$519$	−3.80668			−0.167094
$520$	23.6501	−	1.04960i	1.03713	−	0.0460281i
$521$	−10.4875			−0.459464			−0.229732	−	0.973254i	$-0.573785\pi$
$521$	−10.4875			−0.459464			−0.229732	+	0.973254i	$0.573785\pi$
$522$			12.3228i			0.539354i
$523$			32.7586i			1.43244i	0.697877	+	0.716218i	$0.254128\pi$
$523$			32.7586i			1.43244i	−0.697877	+	0.716218i	$0.745872\pi$
$524$	−3.85237			−0.168291
$525$	−15.1910	+	1.35103i	−0.662992	+	0.0589638i
$526$	0.670856			0.0292507
$527$		−	15.3395i		−	0.668198i
$528$		−	2.71402i		−	0.118113i
$529$	−14.7955			−0.643283
$530$	−9.09354	+	0.403575i	−0.394998	+	0.0175302i
$531$	1.92307			0.0834543
$532$		0			0
$533$			18.4211i			0.797908i
$534$	−2.65165			−0.114748
$535$	0.508890	+	11.4666i	0.0220012	+	0.495743i
$536$	−3.09687			−0.133764
$537$		−	7.54398i		−	0.325547i
$538$		−	26.7857i		−	1.15481i
$539$	9.12866			0.393199
$540$	0.216747	+	4.88384i	0.00932730	+	0.210167i
$541$	14.7958			0.636122			0.318061	−	0.948070i	$-0.396968\pi$
$541$	14.7958			0.636122			0.318061	+	0.948070i	$0.396968\pi$
$542$		−	6.45655i		−	0.277333i
$543$			15.6868i			0.673186i
$544$	8.40697			0.360446
$545$	−3.54687	+	0.157411i	−0.151931	+	0.00674277i
$546$	12.8773			0.551097
$547$			1.61001i			0.0688390i	0.999407	+	0.0344195i	$0.0109582\pi$
$547$			1.61001i			0.0688390i	−0.999407	+	0.0344195i	$0.989042\pi$
$548$			1.87165i			0.0799529i
$549$	15.0633			0.642888
$550$	−0.669491	−	7.52778i	−0.0285472	−	0.320986i
$551$		0			0
$552$			15.1498i			0.644819i
$553$		−	5.24860i		−	0.223193i
$554$	−21.3033			−0.905092
$555$	16.4078	−	0.728186i	0.696474	−	0.0309098i
$556$	9.45758			0.401091
$557$		−	22.3165i		−	0.945581i	−0.881175	−	0.472790i	$-0.843247\pi$
$557$		−	22.3165i		−	0.945581i	0.881175	−	0.472790i	$-0.156753\pi$
$558$			14.6627i			0.620720i
$559$	31.5357			1.33382
$560$	−1.02504	−	23.0967i	−0.0433158	−	0.976012i
$561$	2.99291			0.126361
$562$		−	28.3214i		−	1.19467i
$563$			2.42120i			0.102042i	0.998698	+	0.0510208i	$0.0162475\pi$
$563$			2.42120i			0.102042i	−0.998698	+	0.0510208i	$0.983753\pi$
$564$	−2.98287			−0.125602
$565$	−1.99105	−	44.8632i	−0.0837640	−	1.88741i
$566$	5.61182			0.235882
$567$		−	13.6311i		−	0.572453i
$568$			41.9059i			1.75833i
$569$	−25.3556			−1.06296			−0.531481	−	0.847070i	$-0.678364\pi$
$569$	−25.3556			−1.06296			−0.531481	+	0.847070i	$0.678364\pi$
$570$		0			0
$571$	3.79252			0.158712			0.0793561	−	0.996846i	$-0.474714\pi$
$571$	3.79252			0.158712			0.0793561	+	0.996846i	$0.474714\pi$
$572$		−	2.17113i		−	0.0907797i
$573$		−	12.4704i		−	0.520960i
$574$	24.6896			1.03052
$575$	2.72306	+	30.6182i	0.113559	+	1.27687i
$576$	−20.8676			−0.869485
$577$		−	36.8138i		−	1.53258i	−0.642496	−	0.766289i	$-0.722101\pi$
$577$		−	36.8138i		−	1.53258i	0.642496	−	0.766289i	$-0.277899\pi$
$578$			9.72166i			0.404368i
$579$	15.9623			0.663369
$580$	−4.86261	+	0.215804i	−0.201909	+	0.00896079i
$581$	−9.55731			−0.396504
$582$		−	3.00945i		−	0.124746i
$583$			4.12321i			0.170766i
$584$	33.8895			1.40236
$585$	−0.806168	−	18.1650i	−0.0333309	−	0.751028i
$586$	−22.1505			−0.915030
$587$		−	27.5764i		−	1.13820i	−0.822268	−	0.569100i	$-0.807292\pi$
$587$		−	27.5764i		−	1.13820i	0.822268	−	0.569100i	$-0.192708\pi$
$588$			3.01326i			0.124265i
$589$		0			0
$590$	−0.0989838	−	2.23035i	−0.00407510	−	0.0918220i
$591$	20.8914			0.859358
$592$			24.8976i			1.02328i
$593$		−	7.43391i		−	0.305274i	−0.988282	−	0.152637i	$-0.951223\pi$
$593$		−	7.43391i		−	0.305274i	0.988282	−	0.152637i	$-0.0487766\pi$
$594$	−6.50850			−0.267047
$595$	25.4700	−	1.13037i	1.04417	−	0.0463407i
$596$	−0.856967			−0.0351027
$597$		−	4.35669i		−	0.178307i
$598$		−	25.9547i		−	1.06137i
$599$	−7.48833			−0.305965			−0.152982	−	0.988229i	$-0.548888\pi$
$599$	−7.48833			−0.305965			−0.152982	+	0.988229i	$0.548888\pi$
$600$	12.2729	−	1.09150i	0.501039	−	0.0445603i
$601$	−24.9173			−1.01640			−0.508199	−	0.861240i	$-0.669688\pi$
$601$	−24.9173			−1.01640			−0.508199	+	0.861240i	$0.669688\pi$
$602$		−	42.2668i		−	1.72267i
$603$			2.37861i			0.0968646i
$604$	0.679797			0.0276605
$605$	21.1526	−	0.938759i	0.859974	−	0.0381660i
$606$	3.66246			0.148777
$607$			13.5201i			0.548764i	0.961621	+	0.274382i	$0.0884733\pi$
$607$			13.5201i			0.548764i	−0.961621	+	0.274382i	$0.911527\pi$
$608$		0			0
$609$	−13.0770			−0.529908
$610$	−0.775335	−	17.4702i	−0.0313924	−	0.707348i
$611$	25.2402			1.02111
$612$		−	3.59222i		−	0.145207i
$613$		−	5.65406i		−	0.228365i	−0.993460	−	0.114183i	$-0.963575\pi$
$613$		−	5.65406i		−	0.228365i	0.993460	−	0.114183i	$-0.0364249\pi$
$614$	−5.39217			−0.217610
$615$	0.425086	+	9.57824i	0.0171411	+	0.386232i
$616$	−14.3725			−0.579086
$617$			18.4368i			0.742239i	0.928585	+	0.371120i	$0.121026\pi$
$617$			18.4368i			0.742239i	−0.928585	+	0.371120i	$0.878974\pi$
$618$			12.9797i			0.522121i
$619$	6.99902			0.281314			0.140657	−	0.990058i	$-0.455078\pi$
$619$	6.99902			0.281314			0.140657	+	0.990058i	$0.455078\pi$
$620$	−5.78592	+	0.256782i	−0.232368	+	0.0103126i
$621$	26.4724			1.06230
$622$			18.3650i			0.736371i
$623$			10.2319i			0.409931i
$624$	−7.58056			−0.303465
$625$	24.6076	−	4.41190i	0.984305	−	0.176476i
$626$	9.53508			0.381099
$627$		0			0
$628$		−	3.06803i		−	0.122428i
$629$	−27.4560			−1.09474
$630$	−24.3462	+	1.08050i	−0.969977	+	0.0430480i
$631$	28.0613			1.11710			0.558551	−	0.829470i	$-0.311358\pi$
$631$	28.0613			1.11710			0.558551	+	0.829470i	$0.311358\pi$
$632$			4.24036i			0.168672i
$633$			16.1847i			0.643285i
$634$	−33.2650			−1.32112
$635$	0.342335	+	7.71365i	0.0135851	+	0.306107i
$636$	−1.36102			−0.0539681
$637$		−	25.4973i		−	1.01024i
$638$		−	6.48020i		−	0.256554i
$639$	32.1867			1.27328
$640$	0.519732	+	11.7109i	0.0205442	+	0.462912i
$641$	26.8330			1.05984			0.529921	−	0.848047i	$-0.322222\pi$
$641$	26.8330			1.05984			0.529921	+	0.848047i	$0.322222\pi$
$642$		−	5.04409i		−	0.199074i
$643$		−	26.8783i		−	1.05998i	−0.848005	−	0.529988i	$-0.822196\pi$
$643$		−	26.8783i		−	1.05998i	0.848005	−	0.529988i	$-0.177804\pi$
$644$	11.8358			0.466394
$645$	16.3973	−	0.727717i	0.645642	−	0.0286538i
$646$		0			0
$647$			8.88424i			0.349275i	0.984633	+	0.174638i	$0.0558754\pi$
$647$			8.88424i			0.349275i	−0.984633	+	0.174638i	$0.944125\pi$
$648$			11.0126i			0.432617i
$649$	−1.01129			−0.0396965
$650$	−21.0259	+	1.86996i	−0.824704	+	0.0733458i
$651$	−15.5601			−0.609849
$652$		−	4.97435i		−	0.194811i
$653$			39.4102i			1.54224i	0.636689	+	0.771121i	$0.280303\pi$
$653$			39.4102i			1.54224i	−0.636689	+	0.771121i	$0.719697\pi$
$654$	1.56025			0.0610107
$655$	16.9494	−	0.752221i	0.662268	−	0.0293917i
$656$	−14.5342			−0.567465
$657$		−	26.0295i		−	1.01551i
$658$		−	33.8291i		−	1.31879i
$659$	−17.3119			−0.674377			−0.337189	−	0.941437i	$-0.609476\pi$
$659$	−17.3119			−0.674377			−0.337189	+	0.941437i	$0.609476\pi$
$660$	−0.0501011	−	1.12890i	−0.00195018	−	0.0439424i
$661$	14.2421			0.553952			0.276976	−	0.960877i	$-0.410668\pi$
$661$	14.2421			0.553952			0.276976	+	0.960877i	$0.410668\pi$
$662$		−	14.6346i		−	0.568789i
$663$		−	8.35952i		−	0.324657i
$664$	7.72138			0.299647
$665$		0			0
$666$	26.2446			1.01696
$667$			26.3573i			1.02056i
$668$		−	1.96811i		−	0.0761486i
$669$	−8.72768			−0.337431
$670$	2.75867	−	0.122431i	0.106577	−	0.00472992i
$671$	−7.92137			−0.305801
$672$		−	8.52788i		−	0.328970i
$673$			3.86700i			0.149062i	0.997219	+	0.0745310i	$0.0237460\pi$
$673$			3.86700i			0.149062i	−0.997219	+	0.0745310i	$0.976254\pi$
$674$	−5.06155			−0.194964
$675$	−1.90726	−	21.4453i	−0.0734104	−	0.825430i
$676$	0.536250			0.0206250
$677$		−	15.7102i		−	0.603790i	−0.953341	−	0.301895i	$-0.902381\pi$
$677$		−	15.7102i		−	0.603790i	0.953341	−	0.301895i	$-0.0976193\pi$
$678$			19.7351i			0.757923i
$679$	−11.6125			−0.445646
$680$	−20.5773	+	0.913229i	−0.789104	+	0.0350208i
$681$	−7.06463			−0.270717
$682$		−	7.71067i		−	0.295257i
$683$			11.3613i			0.434727i	0.976091	+	0.217364i	$0.0697458\pi$
$683$			11.3613i			0.434727i	−0.976091	+	0.217364i	$0.930254\pi$
$684$		0			0
$685$	−0.365462	−	8.23477i	−0.0139636	−	0.314634i
$686$	−1.74968			−0.0668031
$687$			14.5458i			0.554959i
$688$			24.8815i			0.948599i
$689$	11.5166			0.438746
$690$	−0.598930	−	13.4954i	−0.0228009	−	0.513760i
$691$	−2.01088			−0.0764974			−0.0382487	−	0.999268i	$-0.512178\pi$
$691$	−2.01088			−0.0764974			−0.0382487	+	0.999268i	$0.512178\pi$
$692$		−	2.40267i		−	0.0913357i
$693$			11.0391i			0.419341i
$694$	11.2012			0.425190
$695$	−41.6109	+	1.84671i	−1.57839	+	0.0700496i
$696$	10.5650			0.400464
$697$		−	16.0277i		−	0.607093i
$698$			39.9315i			1.51143i
$699$	21.2092			0.802205
$700$	−0.852732	−	9.58816i	−0.0322303	−	0.362399i
$701$	12.4628			0.470713			0.235357	−	0.971909i	$-0.424374\pi$
$701$	12.4628			0.470713			0.235357	+	0.971909i	$0.424374\pi$
$702$			18.1789i			0.686120i
$703$		0			0
$704$	10.9737			0.413586
$705$	13.1239	−	0.582442i	0.494273	−	0.0219360i
$706$	32.3355			1.21696
$707$		−	14.1322i		−	0.531497i
$708$		−	0.333815i		−	0.0125455i
$709$	3.52250			0.132290			0.0661452	−	0.997810i	$-0.478930\pi$
$709$	3.52250			0.132290			0.0661452	+	0.997810i	$0.478930\pi$
$710$	−1.65670	−	37.3296i	−0.0621749	−	1.40095i
$711$	3.25689			0.122143
$712$		−	8.26634i		−	0.309794i
$713$			31.3620i			1.17452i
$714$	−11.2042			−0.419305
$715$	0.423940	+	9.55242i	0.0158545	+	0.357240i
$716$	4.76155			0.177947
$717$		−	7.37571i		−	0.275451i
$718$		−	15.1624i		−	0.565855i
$719$	23.9065			0.891563			0.445781	−	0.895142i	$-0.352926\pi$
$719$	23.9065			0.891563			0.445781	+	0.895142i	$0.352926\pi$
$720$	14.3321	−	0.636063i	0.534125	−	0.0237047i
$721$	50.0845			1.86524
$722$		0			0
$723$		−	21.3306i		−	0.793293i
$724$	−9.90109			−0.367971
$725$	21.3521	−	1.89897i	0.792996	−	0.0705258i
$726$	−9.30492			−0.345338
$727$			5.47926i			0.203214i	0.994825	+	0.101607i	$0.0323985\pi$
$727$			5.47926i			0.203214i	−0.994825	+	0.101607i	$0.967602\pi$
$728$			40.1441i			1.48784i
$729$	−1.93302			−0.0715933
$730$	−30.1886	+	1.33978i	−1.11733	+	0.0495875i
$731$	−27.4383			−1.01484
$732$		−	2.61475i		−	0.0966440i
$733$			18.8893i			0.697691i	0.937180	+	0.348846i	$0.113426\pi$
$733$			18.8893i			0.697691i	−0.937180	+	0.348846i	$0.886574\pi$
$734$	6.50031			0.239931
$735$	−0.588376	−	13.2576i	−0.0217026	−	0.489013i
$736$	−17.1883			−0.633569
$737$		−	1.25084i		−	0.0460754i
$738$			15.3205i			0.563956i
$739$	−34.9585			−1.28597			−0.642985	−	0.765879i	$-0.722304\pi$
$739$	−34.9585			−1.28597			−0.642985	+	0.765879i	$0.722304\pi$
$740$	0.459611	+	10.3562i	0.0168956	+	0.380700i
$741$		0			0
$742$		−	15.4355i		−	0.566655i
$743$			27.6384i			1.01395i	0.861960	+	0.506976i	$0.169237\pi$
$743$			27.6384i			1.01395i	−0.861960	+	0.506976i	$0.830763\pi$
$744$	12.5711			0.460877
$745$	3.77043	−	0.167333i	0.138138	−	0.00613061i
$746$	23.5827			0.863425
$747$		−	5.93055i		−	0.216988i
$748$			1.88904i			0.0690702i
$749$	−19.4635			−0.711180
$750$	−10.8895	+	1.45750i	−0.397627	+	0.0532202i
$751$	53.7087			1.95986			0.979929	−	0.199348i	$-0.0638824\pi$
$751$	53.7087			1.95986			0.979929	+	0.199348i	$0.0638824\pi$
$752$			19.9144i			0.726203i
$753$			12.0237i			0.438169i
$754$	−18.0999			−0.659160
$755$	−2.99093	+	0.132738i	−0.108851	+	0.00483085i
$756$	−8.28990			−0.301501
$757$			24.5798i			0.893368i	0.894692	+	0.446684i	$0.147395\pi$
$757$			24.5798i			0.893368i	−0.894692	+	0.446684i	$0.852605\pi$
$758$		−	25.0558i		−	0.910068i
$759$	−6.11909			−0.222109
$760$		0			0
$761$	−0.906887			−0.0328746			−0.0164373	−	0.999865i	$-0.505232\pi$
$761$	−0.906887			−0.0328746			−0.0164373	+	0.999865i	$0.505232\pi$
$762$		−	3.39320i		−	0.122923i
$763$		−	6.02051i		−	0.217957i
$764$	7.87099			0.284763
$765$	0.701424	+	15.8048i	0.0253600	+	0.571424i
$766$	27.7609			1.00304
$767$			2.82464i			0.101992i
$768$			9.11706i			0.328984i
$769$	−21.3193			−0.768792			−0.384396	−	0.923168i	$-0.625590\pi$
$769$	−21.3193			−0.768792			−0.384396	+	0.923168i	$0.625590\pi$
$770$	12.8030	−	0.568201i	0.461387	−	0.0204765i
$771$	8.68676			0.312846
$772$			10.0749i			0.362605i
$773$		−	16.6037i		−	0.597192i	−0.954380	−	0.298596i	$-0.903482\pi$
$773$		−	16.6037i		−	0.597192i	0.954380	−	0.298596i	$-0.0965184\pi$
$774$	26.2277			0.942733
$775$	25.4064	−	2.25954i	0.912625	−	0.0811652i
$776$	9.38176			0.336786
$777$			27.8509i			0.999145i
$778$		−	6.16282i		−	0.220948i
$779$		0			0
$780$	−3.15314	+	0.139938i	−0.112901	+	0.00501057i
$781$	−16.9260			−0.605661
$782$			22.5824i			0.807546i
$783$		−	18.4609i		−	0.659740i
$784$	20.1173			0.718475
$785$	0.599070	+	13.4985i	0.0213817	+	0.481783i
$786$	−7.45596			−0.265945
$787$			41.3474i			1.47388i	0.675960	+	0.736938i	$0.263729\pi$
$787$			41.3474i			1.47388i	−0.675960	+	0.736938i	$0.736271\pi$
$788$			13.1861i			0.469735i
$789$	−0.441762			−0.0157271
$790$	−0.167637	−	3.77729i	−0.00596427	−	0.134390i
$791$	76.1514			2.70763
$792$		−	8.91853i		−	0.316906i
$793$			22.1252i			0.785690i
$794$	28.0267			0.994631
$795$	5.98814	−	0.265756i	0.212378	−	0.00942540i
$796$	2.74982			0.0974648
$797$			22.7002i			0.804083i	0.915621	+	0.402042i	$0.131699\pi$
$797$			22.7002i			0.804083i	−0.915621	+	0.402042i	$0.868301\pi$
$798$		0			0
$799$	−21.9608			−0.776916
$800$	1.23837	+	13.9243i	0.0437829	+	0.492297i
$801$	−6.34913			−0.224335
$802$		−	27.8093i		−	0.981980i
$803$			13.6881i			0.483044i
$804$	0.412889			0.0145615
$805$	−52.0743	+	2.31108i	−1.83538	+	0.0814547i
$806$	−21.5367			−0.758599
$807$			17.6385i			0.620905i
$808$			11.4175i			0.401665i
$809$	27.1508			0.954571			0.477285	−	0.878748i	$-0.341621\pi$
$809$	27.1508			0.954571			0.477285	+	0.878748i	$0.341621\pi$
$810$	−0.435371	−	9.80998i	−0.0152974	−	0.344688i
$811$	−45.2598			−1.58929			−0.794644	−	0.607076i	$-0.792342\pi$
$811$	−45.2598			−1.58929			−0.794644	+	0.607076i	$0.792342\pi$
$812$		−	8.25385i		−	0.289653i
$813$			4.25167i			0.149113i
$814$	−13.8013			−0.483734
$815$	0.971302	+	21.8858i	0.0340232	+	0.766627i
$816$	6.59563			0.230893
$817$		0			0
$818$		−	29.0771i		−	1.01666i
$819$	30.8334			1.07741
$820$	−6.04552	+	0.268302i	−0.211119	+	0.00936952i
$821$	14.7796			0.515813			0.257907	−	0.966170i	$-0.416967\pi$
$821$	14.7796			0.515813			0.257907	+	0.966170i	$0.416967\pi$
$822$			3.62244i			0.126347i
$823$			38.1769i			1.33076i	0.746504	+	0.665381i	$0.231731\pi$
$823$			38.1769i			1.33076i	−0.746504	+	0.665381i	$0.768269\pi$
$824$	−40.4634			−1.40961
$825$	0.440863	+	4.95708i	0.0153489	+	0.172584i
$826$	3.78582			0.131726
$827$		−	45.3277i		−	1.57620i	−0.615548	−	0.788099i	$-0.711065\pi$
$827$		−	45.3277i		−	1.57620i	0.615548	−	0.788099i	$-0.288935\pi$
$828$			7.34439i			0.255235i
$829$	−37.9276			−1.31728			−0.658640	−	0.752458i	$-0.728868\pi$
$829$	−37.9276			−1.31728			−0.658640	+	0.752458i	$0.728868\pi$
$830$	−6.87816	+	0.305255i	−0.238744	+	0.0105956i
$831$	14.0284			0.486638
$832$		−	30.6507i		−	1.06262i
$833$			22.1845i			0.768648i
$834$	18.3044			0.633831
$835$	0.384298	+	8.65919i	0.0132992	+	0.299664i
$836$		0			0
$837$		−	21.9663i		−	0.759267i
$838$			19.4689i			0.672542i
$839$	7.14266			0.246592			0.123296	−	0.992370i	$-0.460654\pi$
$839$	7.14266			0.246592			0.123296	+	0.992370i	$0.460654\pi$
$840$	0.926364	+	20.8733i	0.0319626	+	0.720196i
$841$	−10.6193			−0.366184
$842$		−	3.24153i		−	0.111710i
$843$			18.6498i			0.642332i
$844$	−10.2153			−0.351627
$845$	−2.35936	+	0.104709i	−0.0811645	+	0.00360211i
$846$	20.9918			0.721713
$847$			35.9046i			1.23370i
$848$			9.08652i			0.312032i
$849$	−3.69541			−0.126826
$850$	18.2941	−	1.62700i	0.627481	−	0.0558056i
$851$	56.1346			1.92427
$852$		−	5.58709i		−	0.191410i
$853$			51.0391i			1.74755i	0.486335	+	0.873773i	$0.338334\pi$
$853$			51.0391i			1.74755i	−0.486335	+	0.873773i	$0.661666\pi$
$854$	29.6542			1.01474
$855$		0			0
$856$	15.7246			0.537456
$857$			13.6042i			0.464710i	0.972631	+	0.232355i	$0.0746431\pi$
$857$			13.6042i			0.464710i	−0.972631	+	0.232355i	$0.925357\pi$
$858$		−	4.20207i		−	0.143456i
$859$	38.4375			1.31147			0.655735	−	0.754991i	$-0.272359\pi$
$859$	38.4375			1.31147			0.655735	+	0.754991i	$0.272359\pi$
$860$	0.459315	+	10.3495i	0.0156625	+	0.352915i
$861$	−16.2582			−0.554079
$862$			40.7059i			1.38645i
$863$		−	54.3455i		−	1.84994i	−0.380039	−	0.924970i	$-0.624090\pi$
$863$		−	54.3455i		−	1.84994i	0.380039	−	0.924970i	$-0.375910\pi$
$864$	12.0389			0.409571
$865$	0.469150	+	10.5711i	0.0159516	+	0.359428i
$866$	−27.3391			−0.929021
$867$		−	6.40176i		−	0.217415i
$868$		−	9.82110i		−	0.333350i
$869$	−1.71270			−0.0580995
$870$	−9.41121	+	0.417673i	−0.319070	+	0.0141604i
$871$	−3.49374			−0.118381
$872$			4.86398i			0.164715i
$873$		−	7.20584i		−	0.243881i
$874$		0			0
$875$	5.62400	+	42.0189i	0.190126	+	1.42050i
$876$	−4.51830			−0.152659
$877$		−	13.5325i		−	0.456961i	−0.973548	−	0.228481i	$-0.926624\pi$
$877$		−	13.5325i		−	0.456961i	0.973548	−	0.228481i	$-0.0733758\pi$
$878$			21.3241i			0.719653i
$879$	14.5862			0.491982
$880$	−7.53682	+	0.334487i	−0.254066	+	0.0112756i
$881$	−27.9577			−0.941920			−0.470960	−	0.882155i	$-0.656092\pi$
$881$	−27.9577			−0.941920			−0.470960	+	0.882155i	$0.656092\pi$
$882$		−	21.2057i		−	0.714032i
$883$			54.5487i			1.83571i	0.396915	+	0.917855i	$0.370081\pi$
$883$			54.5487i			1.83571i	−0.396915	+	0.917855i	$0.629919\pi$
$884$	5.27630			0.177461
$885$	0.0651813	+	1.46870i	0.00219105	+	0.0493697i
$886$	−1.83066			−0.0615021
$887$			35.9778i			1.20802i	0.796979	+	0.604008i	$0.206430\pi$
$887$			35.9778i			1.20802i	−0.796979	+	0.604008i	$0.793570\pi$
$888$		−	22.5008i		−	0.755078i
$889$	−13.0932			−0.439133
$890$	0.326800	+	7.36361i	0.0109544	+	0.246829i
$891$	−4.44806			−0.149016
$892$		−	5.50867i		−	0.184444i
$893$		0			0
$894$	−1.65860			−0.0554717
$895$	−20.9496	+	0.929749i	−0.700266	+	0.0310781i
$896$	−19.8782			−0.664083
$897$			17.0913i			0.570662i
$898$		−	14.6482i		−	0.488817i
$899$	21.8708			0.729432
$900$	5.94970	−	0.529142i	0.198323	−	0.0176381i
$901$	−10.0202			−0.333822
$902$		−	8.05662i		−	0.268256i
$903$			27.8329i			0.926222i
$904$	−61.5230			−2.04622
$905$	43.5622	−	1.93331i	1.44806	−	0.0642653i
$906$	1.31570			0.0437110
$907$			4.40371i			0.146223i	0.997324	+	0.0731114i	$0.0232929\pi$
$907$			4.40371i			0.146223i	−0.997324	+	0.0731114i	$0.976707\pi$
$908$		−	4.45900i		−	0.147977i
$909$	8.76941			0.290863
$910$	−1.58705	−	35.7601i	−0.0526101	−	1.18544i
$911$	−14.2563			−0.472333			−0.236166	−	0.971713i	$-0.575891\pi$
$911$	−14.2563			−0.472333			−0.236166	+	0.971713i	$0.575891\pi$
$912$		0			0
$913$			3.11870i			0.103214i
$914$	−15.8162			−0.523152
$915$	0.510562	+	11.5042i	0.0168787	+	0.380318i
$916$	−9.18093			−0.303347
$917$			28.7701i			0.950073i
$918$		−	15.8170i		−	0.522038i
$919$	28.7276			0.947637			0.473819	−	0.880622i	$-0.342875\pi$
$919$	28.7276			0.947637			0.473819	+	0.880622i	$0.342875\pi$
$920$	42.0709	−	1.86712i	1.38704	−	0.0615573i
$921$	3.55077			0.117002
$922$			16.9410i			0.557922i
$923$			47.2762i			1.55612i
$924$	1.91621			0.0630387
$925$	−4.04433	−	45.4747i	−0.132977	−	1.49520i
$926$	5.11201			0.167991
$927$			31.0787i			1.02076i
$928$			11.9865i			0.393477i
$929$	30.6928			1.00700			0.503499	−	0.863996i	$-0.332046\pi$
$929$	30.6928			1.00700			0.503499	+	0.863996i	$0.332046\pi$
$930$	−11.1982	+	0.496981i	−0.367204	+	0.0162967i
$931$		0			0
$932$			13.3866i			0.438494i
$933$		−	12.0935i		−	0.395923i
$934$	28.4652			0.931411
$935$	−0.368858	−	8.31129i	−0.0120630	−	0.271808i
$936$	−24.9104			−0.814222
$937$			50.4315i			1.64752i	0.566936	+	0.823762i	$0.308129\pi$
$937$			50.4315i			1.64752i	−0.566936	+	0.823762i	$0.691871\pi$
$938$			4.68261i			0.152893i
$939$	−6.27890			−0.204904
$940$	0.367621	+	8.28341i	0.0119905	+	0.270175i
$941$	8.54594			0.278590			0.139295	−	0.990251i	$-0.455516\pi$
$941$	8.54594			0.278590			0.139295	+	0.990251i	$0.455516\pi$
$942$		−	5.93795i		−	0.193469i
$943$			32.7691i			1.06711i
$944$	−2.22863			−0.0725357
$945$	36.4734	−	1.61870i	1.18648	−	0.0526564i
$946$	−13.7924			−0.448428
$947$		−	20.5825i		−	0.668841i	−0.942424	−	0.334421i	$-0.891459\pi$
$947$		−	20.5825i		−	0.668841i	0.942424	−	0.334421i	$-0.108541\pi$
$948$		−	0.565344i		−	0.0183615i
$949$	38.2325			1.24108
$950$		0			0
$951$	21.9051			0.710323
$952$		−	34.9282i		−	1.13203i
$953$			59.1921i			1.91742i	0.284384	+	0.958711i	$0.408211\pi$
$953$			59.1921i			1.91742i	−0.284384	+	0.958711i	$0.591789\pi$
$954$	9.57812			0.310103
$955$	−34.6303	+	1.53691i	−1.12061	+	0.0497331i
$956$	4.65534			0.150564
$957$			4.26725i			0.137940i
$958$		−	42.8984i		−	1.38599i
$959$	13.9778			0.451367
$960$	−0.707295	−	15.9371i	−0.0228278	−	0.514368i
$961$	−4.97635			−0.160528
$962$			38.5484i			1.24285i
$963$		−	12.0776i		−	0.389195i
$964$	13.4633			0.433623
$965$	−1.96725	−	44.3271i	−0.0633281	−	1.42694i
$966$	22.9072			0.737028
$967$		−	10.9970i		−	0.353639i	−0.984243	−	0.176819i	$-0.943419\pi$
$967$		−	10.9970i		−	0.353639i	0.984243	−	0.176819i	$-0.0565808\pi$
$968$		−	29.0075i		−	0.932335i
$969$		0			0
$970$	−8.35722	+	0.370897i	−0.268334	+	0.0119088i
$971$	32.3692			1.03878			0.519389	−	0.854538i	$-0.326160\pi$
$971$	32.3692			1.03878			0.519389	+	0.854538i	$0.326160\pi$
$972$		−	8.02706i		−	0.257468i
$973$		−	70.6309i		−	2.26432i
$974$	−40.8265			−1.30817
$975$	13.8457	−	1.23138i	0.443416	−	0.0394357i
$976$	−17.4567			−0.558776
$977$			11.1038i			0.355241i	0.984099	+	0.177621i	$0.0568400\pi$
$977$			11.1038i			0.355241i	−0.984099	+	0.177621i	$0.943160\pi$
$978$		−	9.62748i		−	0.307853i
$979$	3.33882			0.106709
$980$	8.36781	−	0.371367i	0.267300	−	0.0118629i
$981$	3.73588			0.119277
$982$		−	21.4250i		−	0.683701i
$983$			12.5322i			0.399716i	0.979825	+	0.199858i	$0.0640481\pi$
$983$			12.5322i			0.399716i	−0.979825	+	0.199858i	$0.935952\pi$
$984$	13.1351			0.418731
$985$	−2.57474	−	58.0153i	−0.0820380	−	1.84852i
$986$	15.7482			0.501525
$987$			22.2766i			0.709072i
$988$		0			0
$989$	56.0984			1.78383
$990$	0.352583	+	7.94457i	0.0112058	+	0.252495i
$991$	36.7597			1.16771			0.583856	−	0.811857i	$-0.301543\pi$
$991$	36.7597			1.16771			0.583856	+	0.811857i	$0.301543\pi$
$992$			14.2625i			0.452836i
$993$			9.63695i			0.305819i
$994$	63.3637			2.00977
$995$	−12.0985	+	0.536936i	−0.383548	+	0.0170220i
$996$	−1.02945			−0.0326193
$997$		−	24.4801i		−	0.775291i	−0.921808	−	0.387646i	$-0.873288\pi$
$997$		−	24.4801i		−	0.775291i	0.921808	−	0.387646i	$-0.126712\pi$
$998$		−	39.9251i		−	1.26381i
$999$	−39.3173			−1.24394

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1805.2.b.k.1084.17		24
5.2	odd	4		9025.2.a.cu.1.8		24
5.3	odd	4		9025.2.a.cu.1.17		24
5.4	even	2	inner	1805.2.b.k.1084.8		24
19.6	even	9		95.2.p.a.74.6	yes	48
19.16	even	9		95.2.p.a.9.3	✓	48
19.18	odd	2		1805.2.b.l.1084.8		24
57.35	odd	18		855.2.da.b.199.6		48
57.44	odd	18		855.2.da.b.739.3		48
95.18	even	4		9025.2.a.ct.1.8		24
95.37	even	4		9025.2.a.ct.1.17		24
95.44	even	18		95.2.p.a.74.3	yes	48
95.54	even	18		95.2.p.a.9.6	yes	48
95.63	odd	36		475.2.l.f.226.6		48
95.73	odd	36		475.2.l.f.351.6		48
95.82	odd	36		475.2.l.f.226.3		48
95.92	odd	36		475.2.l.f.351.3		48
95.94	odd	2		1805.2.b.l.1084.17		24
285.44	odd	18		855.2.da.b.739.6		48
285.149	odd	18		855.2.da.b.199.3		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.p.a.9.3	✓	48	19.16	even	9
95.2.p.a.9.6	yes	48	95.54	even	18
95.2.p.a.74.3	yes	48	95.44	even	18
95.2.p.a.74.6	yes	48	19.6	even	9
475.2.l.f.226.3		48	95.82	odd	36
475.2.l.f.226.6		48	95.63	odd	36
475.2.l.f.351.3		48	95.92	odd	36
475.2.l.f.351.6		48	95.73	odd	36
855.2.da.b.199.3		48	285.149	odd	18
855.2.da.b.199.6		48	57.35	odd	18
855.2.da.b.739.3		48	57.44	odd	18
855.2.da.b.739.6		48	285.44	odd	18
1805.2.b.k.1084.8		24	5.4	even	2	inner
1805.2.b.k.1084.17		24	1.1	even	1	trivial
1805.2.b.l.1084.8		24	19.18	odd	2
1805.2.b.l.1084.17		24	95.94	odd	2
9025.2.a.ct.1.8		24	95.18	even	4
9025.2.a.ct.1.17		24	95.37	even	4
9025.2.a.cu.1.8		24	5.2	odd	4
9025.2.a.cu.1.17		24	5.3	odd	4

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:	\( N \)	\(=\)	\( 1805 = 5 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1805.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.22159i q^{2} -0.804421i q^{3} +0.507728 q^{4} +(-2.23387 + 0.0991400i) q^{5} +0.982669 q^{6} -3.79180i q^{7} +3.06341i q^{8} +2.35291 q^{9} +O(q^{10})\)	\(q+1.22159i q^{2} -0.804421i q^{3} +0.507728 q^{4} +(-2.23387 + 0.0991400i) q^{5} +0.982669 q^{6} -3.79180i q^{7} +3.06341i q^{8} +2.35291 q^{9} +(-0.121108 - 2.72886i) q^{10} -1.23733 q^{11} -0.408427i q^{12} +3.45598i q^{13} +4.63201 q^{14} +(0.0797502 + 1.79697i) q^{15} -2.72676 q^{16} -3.00695i q^{17} +2.87428i q^{18} +(-1.13420 + 0.0503361i) q^{20} -3.05020 q^{21} -1.51150i q^{22} +6.14780i q^{23} +2.46427 q^{24} +(4.98034 - 0.442931i) q^{25} -4.22178 q^{26} -4.30599i q^{27} -1.92520i q^{28} +4.28727 q^{29} +(-2.19515 + 0.0974218i) q^{30} +5.10134 q^{31} +2.79584i q^{32} +0.995330i q^{33} +3.67325 q^{34} +(0.375919 + 8.47038i) q^{35} +1.19464 q^{36} -9.13084i q^{37} +2.78006 q^{39} +(-0.303706 - 6.84325i) q^{40} +5.33021 q^{41} -3.72608i q^{42} -9.12495i q^{43} -0.628225 q^{44} +(-5.25609 + 0.233267i) q^{45} -7.51007 q^{46} -7.30333i q^{47} +2.19346i q^{48} -7.37774 q^{49} +(0.541079 + 6.08392i) q^{50} -2.41886 q^{51} +1.75470i q^{52} -3.33235i q^{53} +5.26014 q^{54} +(2.76402 - 0.122668i) q^{55} +11.6158 q^{56} +5.23727i q^{58} +0.817318 q^{59} +(0.0404914 + 0.912372i) q^{60} +6.40201 q^{61} +6.23172i q^{62} -8.92175i q^{63} -8.86888 q^{64} +(-0.342626 - 7.72022i) q^{65} -1.21588 q^{66} +1.01092i q^{67} -1.52671i q^{68} +4.94542 q^{69} +(-10.3473 + 0.459217i) q^{70} +13.6795 q^{71} +7.20791i q^{72} -11.0627i q^{73} +11.1541 q^{74} +(-0.356303 - 4.00629i) q^{75} +4.69169i q^{77} +3.39609i q^{78} +1.38420 q^{79} +(6.09122 - 0.270331i) q^{80} +3.59490 q^{81} +6.51132i q^{82} -2.52052i q^{83} -1.54867 q^{84} +(0.298109 + 6.71714i) q^{85} +11.1469 q^{86} -3.44877i q^{87} -3.79043i q^{88} -2.69842 q^{89} +(-0.284956 - 6.42076i) q^{90} +13.1044 q^{91} +3.12141i q^{92} -4.10362i q^{93} +8.92164 q^{94} +2.24903 q^{96} -3.06253i q^{97} -9.01254i q^{98} -2.91131 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 18 q^{4} - 3 q^{5} - 12 q^{6} - 12 q^{9}+O(q^{10}) \) 24 * q - 18 * q^4 - 3 * q^5 - 12 * q^6 - 12 * q^9	\( 24 q - 18 q^{4} - 3 q^{5} - 12 q^{6} - 12 q^{9} - 6 q^{10} + 12 q^{11} - 24 q^{14} - 9 q^{15} + 6 q^{16} + 21 q^{20} + 6 q^{21} + 42 q^{24} - 3 q^{25} - 12 q^{26} - 36 q^{29} - 18 q^{30} + 42 q^{31} - 6 q^{34} + 27 q^{35} - 6 q^{36} - 24 q^{39} + 12 q^{40} + 60 q^{41} + 30 q^{44} + 9 q^{45} + 6 q^{46} - 12 q^{49} + 18 q^{50} + 30 q^{51} + 24 q^{54} + 33 q^{55} + 18 q^{56} - 60 q^{59} - 42 q^{60} + 30 q^{61} + 18 q^{65} + 36 q^{66} - 66 q^{69} + 9 q^{70} + 96 q^{71} - 24 q^{74} + 36 q^{75} - 72 q^{79} - 42 q^{80} - 96 q^{81} + 54 q^{84} - 27 q^{85} + 108 q^{86} - 84 q^{89} - 93 q^{90} + 96 q^{91} - 36 q^{94} - 120 q^{96}+O(q^{100}) \) 24 * q - 18 * q^4 - 3 * q^5 - 12 * q^6 - 12 * q^9 - 6 * q^10 + 12 * q^11 - 24 * q^14 - 9 * q^15 + 6 * q^16 + 21 * q^20 + 6 * q^21 + 42 * q^24 - 3 * q^25 - 12 * q^26 - 36 * q^29 - 18 * q^30 + 42 * q^31 - 6 * q^34 + 27 * q^35 - 6 * q^36 - 24 * q^39 + 12 * q^40 + 60 * q^41 + 30 * q^44 + 9 * q^45 + 6 * q^46 - 12 * q^49 + 18 * q^50 + 30 * q^51 + 24 * q^54 + 33 * q^55 + 18 * q^56 - 60 * q^59 - 42 * q^60 + 30 * q^61 + 18 * q^65 + 36 * q^66 - 66 * q^69 + 9 * q^70 + 96 * q^71 - 24 * q^74 + 36 * q^75 - 72 * q^79 - 42 * q^80 - 96 * q^81 + 54 * q^84 - 27 * q^85 + 108 * q^86 - 84 * q^89 - 93 * q^90 + 96 * q^91 - 36 * q^94 - 120 * q^96

Introduction

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