LMFDB - Embedded newform 1710.2.n.i.647.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1710,2,Mod(647,1710)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1710, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 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("1710.647");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1710.n (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$13.6544187456$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 4 x^{19} - 10 x^{18} + 56 x^{17} + 50 x^{16} - 336 x^{15} + 672 x^{14} - 776 x^{13} + 626 x^{12} + \cdots + 32 $ x^20 - 4x^19 - 10x^18 + 56x^17 + 50x^16 - 336x^15 + 672x^14 - 776x^13 + 626x^12 - 748x^11 + 514x^10 + 1340x^9 - 648x^8 - 2216x^7 + 3348x^6 - 2684x^5 + 1761x^4 - 728x^3 + 408x^2 - 96*x + 32
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{10} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			647.8
Root			$3.60603 + 1.49367i$ of defining polynomial
Character	$\chi$	$=$	1710.647
Dual form			1710.2.n.i.1673.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(0.975056 + 2.01228i) q^{5} +(-3.02518 - 3.02518i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.11236 + 0.733428i) q^{10} -6.04990i q^{11} +(-2.89899 + 2.89899i) q^{13} -4.27825 q^{14} -1.00000 q^{16} +(-2.45144 + 2.45144i) q^{17} +1.00000i q^{19} +(2.01228 - 0.975056i) q^{20} +(-4.27792 - 4.27792i) q^{22} +(1.29092 + 1.29092i) q^{23} +(-3.09853 + 3.92417i) q^{25} +4.09979i q^{26} +(-3.02518 + 3.02518i) q^{28} -4.48523 q^{29} +0.106387 q^{31} +(-0.707107 + 0.707107i) q^{32} +3.46686i q^{34} +(3.13779 - 9.03723i) q^{35} +(-2.89899 - 2.89899i) q^{37} +(0.707107 + 0.707107i) q^{38} +(0.733428 - 2.11236i) q^{40} +5.65335i q^{41} +(-4.17154 + 4.17154i) q^{43} -6.04990 q^{44} +1.82564 q^{46} +(-5.35509 + 5.35509i) q^{47} +11.3035i q^{49} +(0.583812 + 4.96580i) q^{50} +(2.89899 + 2.89899i) q^{52} +(-9.19614 - 9.19614i) q^{53} +(12.1741 - 5.89899i) q^{55} +4.27825i q^{56} +(-3.17154 + 3.17154i) q^{58} -4.35348 q^{59} +6.09068 q^{61} +(0.0752273 - 0.0752273i) q^{62} +1.00000i q^{64} +(-8.66024 - 3.00690i) q^{65} +(2.45144 + 2.45144i) q^{68} +(-4.17154 - 8.60904i) q^{70} -15.2852i q^{71} +(7.19707 - 7.19707i) q^{73} -4.09979 q^{74} +1.00000 q^{76} +(-18.3020 + 18.3020i) q^{77} -8.46020i q^{79} +(-0.975056 - 2.01228i) q^{80} +(3.99752 + 3.99752i) q^{82} +(-7.44455 - 7.44455i) q^{83} +(-7.32326 - 2.54269i) q^{85} +5.89944i q^{86} +(-4.27792 + 4.27792i) q^{88} -13.7025 q^{89} +17.5399 q^{91} +(1.29092 - 1.29092i) q^{92} +7.57324i q^{94} +(-2.01228 + 0.975056i) q^{95} +(2.34568 + 2.34568i) q^{97} +(7.99275 + 7.99275i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 4 q^{10} - 12 q^{13} - 20 q^{16} - 16 q^{22} + 16 q^{31} - 12 q^{37} - 8 q^{46} + 12 q^{52} + 20 q^{58} - 16 q^{61} + 20 q^{73} + 20 q^{76} - 28 q^{82} - 8 q^{85} - 16 q^{88} + 32 q^{91} - 20 q^{97}+O(q^{100}) $ 20 * q + 4 * q^10 - 12 * q^13 - 20 * q^16 - 16 * q^22 + 16 * q^31 - 12 * q^37 - 8 * q^46 + 12 * q^52 + 20 * q^58 - 16 * q^61 + 20 * q^73 + 20 * q^76 - 28 * q^82 - 8 * q^85 - 16 * q^88 + 32 * q^91 - 20 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1710\mathbb{Z}\right)^\times$.

$n$	$191$	$1027$	$1351$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$1$

Coefficient data

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

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

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

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$3$		0			0
$3$		0			0
$4$		−	1.00000i		−	0.500000i
$5$	0.975056	+	2.01228i	0.436058	+	0.899918i
$5$	0.975056	+	2.01228i	0.436058	+	0.899918i
$6$		0			0
$7$	−3.02518	−	3.02518i	−1.14341	−	1.14341i	−0.987822	−	0.155590i	$-0.950272\pi$
$7$	−3.02518	−	3.02518i	−1.14341	−	1.14341i	−0.155590	−	0.987822i	$-0.549728\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$		0			0
$10$	2.11236	+	0.733428i	0.667988	+	0.231930i
$11$		−	6.04990i		−	1.82411i	−0.410065	−	0.912056i	$-0.634494\pi$
$11$		−	6.04990i		−	1.82411i	0.410065	−	0.912056i	$-0.365506\pi$
$12$		0			0
$13$	−2.89899	+	2.89899i	−0.804034	+	0.804034i	−0.983723	−	0.179689i	$-0.942491\pi$
$13$	−2.89899	+	2.89899i	−0.804034	+	0.804034i	0.179689	+	0.983723i	$0.442491\pi$
$14$	−4.27825			−1.14341
$15$		0			0
$16$	−1.00000			−0.250000
$17$	−2.45144	+	2.45144i	−0.594561	+	0.594561i	−0.938860	−	0.344299i	$-0.888117\pi$
$17$	−2.45144	+	2.45144i	−0.594561	+	0.594561i	0.344299	+	0.938860i	$0.388117\pi$
$18$		0			0
$19$			1.00000i			0.229416i
$19$			1.00000i			0.229416i
$20$	2.01228	−	0.975056i	0.449959	−	0.218029i
$21$		0			0
$22$	−4.27792	−	4.27792i	−0.912056	−	0.912056i
$23$	1.29092	+	1.29092i	0.269175	+	0.269175i	0.828768	−	0.559593i	$-0.189042\pi$
$23$	1.29092	+	1.29092i	0.269175	+	0.269175i	−0.559593	+	0.828768i	$0.689042\pi$
$24$		0			0
$25$	−3.09853	+	3.92417i	−0.619707	+	0.784834i
$26$			4.09979i			0.804034i
$27$		0			0
$28$	−3.02518	+	3.02518i	−0.571706	+	0.571706i
$29$	−4.48523			−0.832886			−0.416443	−	0.909162i	$-0.636723\pi$
$29$	−4.48523			−0.832886			−0.416443	+	0.909162i	$0.636723\pi$
$30$		0			0
$31$	0.106387			0.0191078			0.00955388	−	0.999954i	$-0.496959\pi$
$31$	0.106387			0.0191078			0.00955388	+	0.999954i	$0.496959\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$		0			0
$34$			3.46686i			0.594561i
$35$	3.13779	−	9.03723i	0.530383	−	1.52757i
$36$		0			0
$37$	−2.89899	−	2.89899i	−0.476590	−	0.476590i	0.427449	−	0.904039i	$-0.359412\pi$
$37$	−2.89899	−	2.89899i	−0.476590	−	0.476590i	−0.904039	+	0.427449i	$0.859412\pi$
$38$	0.707107	+	0.707107i	0.114708	+	0.114708i
$39$		0			0
$40$	0.733428	−	2.11236i	0.115965	−	0.333994i
$41$			5.65335i			0.882904i	0.897285	+	0.441452i	$0.145536\pi$
$41$			5.65335i			0.882904i	−0.897285	+	0.441452i	$0.854464\pi$
$42$		0			0
$43$	−4.17154	+	4.17154i	−0.636153	+	0.636153i	−0.949604	−	0.313451i	$-0.898515\pi$
$43$	−4.17154	+	4.17154i	−0.636153	+	0.636153i	0.313451	+	0.949604i	$0.398515\pi$
$44$	−6.04990			−0.912056
$45$		0			0
$46$	1.82564			0.269175
$47$	−5.35509	+	5.35509i	−0.781120	+	0.781120i	−0.980020	−	0.198900i	$-0.936263\pi$
$47$	−5.35509	+	5.35509i	−0.781120	+	0.781120i	0.198900	+	0.980020i	$0.436263\pi$
$48$		0			0
$49$			11.3035i			1.61478i
$50$	0.583812	+	4.96580i	0.0825635	+	0.702270i
$51$		0			0
$52$	2.89899	+	2.89899i	0.402017	+	0.402017i
$53$	−9.19614	−	9.19614i	−1.26319	−	1.26319i	−0.949540	−	0.313647i	$-0.898449\pi$
$53$	−9.19614	−	9.19614i	−1.26319	−	1.26319i	−0.313647	−	0.949540i	$-0.601551\pi$
$54$		0			0
$55$	12.1741	−	5.89899i	1.64155	−	0.795419i
$56$			4.27825i			0.571706i
$57$		0			0
$58$	−3.17154	+	3.17154i	−0.416443	+	0.416443i
$59$	−4.35348			−0.566775			−0.283387	−	0.959005i	$-0.591458\pi$
$59$	−4.35348			−0.566775			−0.283387	+	0.959005i	$0.591458\pi$
$60$		0			0
$61$	6.09068			0.779831			0.389916	−	0.920851i	$-0.372504\pi$
$61$	6.09068			0.779831			0.389916	+	0.920851i	$0.372504\pi$
$62$	0.0752273	−	0.0752273i	0.00955388	−	0.00955388i
$63$		0			0
$64$			1.00000i			0.125000i
$65$	−8.66024	−	3.00690i	−1.07417	−	0.372959i
$66$		0			0
$67$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$67$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$68$	2.45144	+	2.45144i	0.297280	+	0.297280i
$69$		0			0
$70$	−4.17154	−	8.60904i	−0.498594	−	1.02898i
$71$		−	15.2852i		−	1.81401i	−0.421115	−	0.907007i	$-0.638361\pi$
$71$		−	15.2852i		−	1.81401i	0.421115	−	0.907007i	$-0.361639\pi$
$72$		0			0
$73$	7.19707	−	7.19707i	0.842353	−	0.842353i	−0.146812	−	0.989164i	$-0.546901\pi$
$73$	7.19707	−	7.19707i	0.842353	−	0.842353i	0.989164	+	0.146812i	$0.0469011\pi$
$74$	−4.09979			−0.476590
$75$		0			0
$76$	1.00000			0.114708
$77$	−18.3020	+	18.3020i	−2.08571	+	2.08571i
$78$		0			0
$79$		−	8.46020i		−	0.951847i	−0.879487	−	0.475924i	$-0.842114\pi$
$79$		−	8.46020i		−	0.951847i	0.879487	−	0.475924i	$-0.157886\pi$
$80$	−0.975056	−	2.01228i	−0.109015	−	0.224980i
$81$		0			0
$82$	3.99752	+	3.99752i	0.441452	+	0.441452i
$83$	−7.44455	−	7.44455i	−0.817145	−	0.817145i	0.168548	−	0.985693i	$-0.446092\pi$
$83$	−7.44455	−	7.44455i	−0.817145	−	0.817145i	−0.985693	+	0.168548i	$0.946092\pi$
$84$		0			0
$85$	−7.32326	−	2.54269i	−0.794319	−	0.275793i
$86$			5.89944i			0.636153i
$87$		0			0
$88$	−4.27792	+	4.27792i	−0.456028	+	0.456028i
$89$	−13.7025			−1.45246			−0.726229	−	0.687453i	$-0.758729\pi$
$89$	−13.7025			−1.45246			−0.726229	+	0.687453i	$0.758729\pi$
$90$		0			0
$91$	17.5399			1.83868
$92$	1.29092	−	1.29092i	0.134588	−	0.134588i
$93$		0			0
$94$			7.57324i			0.781120i
$95$	−2.01228	+	0.975056i	−0.206455	+	0.100039i
$96$		0			0
$97$	2.34568	+	2.34568i	0.238168	+	0.238168i	0.816091	−	0.577923i	$-0.196137\pi$
$97$	2.34568	+	2.34568i	0.238168	+	0.238168i	−0.577923	+	0.816091i	$0.696137\pi$
$98$	7.99275	+	7.99275i	0.807390	+	0.807390i
$99$		0			0
$100$	3.92417	+	3.09853i	0.392417	+	0.309853i
$101$		−	13.8994i		−	1.38305i	−0.722354	−	0.691523i	$-0.756940\pi$
$101$		−	13.8994i		−	1.38305i	0.722354	−	0.691523i	$-0.243060\pi$
$102$		0			0
$103$	1.73940	−	1.73940i	0.171389	−	0.171389i	−0.616201	−	0.787589i	$-0.711329\pi$
$103$	1.73940	−	1.73940i	0.171389	−	0.171389i	0.787589	+	0.616201i	$0.211329\pi$
$104$	4.09979			0.402017
$105$		0			0
$106$	−13.0053			−1.26319
$107$	−3.13123	+	3.13123i	−0.302707	+	0.302707i	−0.842072	−	0.539365i	$-0.818664\pi$
$107$	−3.13123	+	3.13123i	−0.302707	+	0.302707i	0.539365	+	0.842072i	$0.318664\pi$
$108$		0			0
$109$		−	5.09046i		−	0.487578i	−0.969828	−	0.243789i	$-0.921610\pi$
$109$		−	5.09046i		−	0.487578i	0.969828	−	0.243789i	$-0.0783904\pi$
$110$	4.43716	−	12.7796i	0.423067	−	1.21849i
$111$		0			0
$112$	3.02518	+	3.02518i	0.285853	+	0.285853i
$113$	8.08873	+	8.08873i	0.760924	+	0.760924i	0.976489	−	0.215566i	$-0.0691595\pi$
$113$	8.08873	+	8.08873i	0.760924	+	0.760924i	−0.215566	+	0.976489i	$0.569160\pi$
$114$		0			0
$115$	−1.33897	+	3.85641i	−0.124860	+	0.359612i
$116$			4.48523i			0.416443i
$117$		0			0
$118$	−3.07838	+	3.07838i	−0.283387	+	0.283387i
$119$	14.8321			1.35966
$120$		0			0
$121$	−25.6012			−2.32739
$122$	4.30676	−	4.30676i	0.389916	−	0.389916i
$123$		0			0
$124$		−	0.106387i		−	0.00955388i
$125$	−10.9178	−	2.40883i	−0.976514	−	0.215452i
$126$		0			0
$127$	−2.05857	−	2.05857i	−0.182668	−	0.182668i	0.609849	−	0.792517i	$-0.291230\pi$
$127$	−2.05857	−	2.05857i	−0.182668	−	0.182668i	−0.792517	+	0.609849i	$0.791230\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$		0			0
$130$	−8.24991	+	3.99752i	−0.723565	+	0.350606i
$131$		−	17.6814i		−	1.54483i	−0.635116	−	0.772416i	$-0.719048\pi$
$131$		−	17.6814i		−	1.54483i	0.635116	−	0.772416i	$-0.280952\pi$
$132$		0			0
$133$	3.02518	−	3.02518i	0.262317	−	0.262317i
$134$		0			0
$135$		0			0
$136$	3.46686			0.297280
$137$	−1.39816	+	1.39816i	−0.119453	+	0.119453i	−0.764306	−	0.644853i	$-0.776918\pi$
$137$	−1.39816	+	1.39816i	−0.119453	+	0.119453i	0.644853	+	0.764306i	$0.276918\pi$
$138$		0			0
$139$			15.0210i			1.27407i	0.770837	+	0.637033i	$0.219838\pi$
$139$			15.0210i			1.27407i	−0.770837	+	0.637033i	$0.780162\pi$
$140$	−9.03723	−	3.13779i	−0.763785	−	0.265192i
$141$		0			0
$142$	−10.8082	−	10.8082i	−0.907007	−	0.907007i
$143$	17.5386	+	17.5386i	1.46665	+	1.46665i
$144$		0			0
$145$	−4.37335	−	9.02553i	−0.363187	−	0.749530i
$146$		−	10.1782i		−	0.842353i
$147$		0			0
$148$	−2.89899	+	2.89899i	−0.238295	+	0.238295i
$149$	14.3677			1.17705			0.588525	−	0.808479i	$-0.299709\pi$
$149$	14.3677			1.17705			0.588525	+	0.808479i	$0.299709\pi$
$150$		0			0
$151$	20.2474			1.64771			0.823856	−	0.566799i	$-0.191818\pi$
$151$	20.2474			1.64771			0.823856	+	0.566799i	$0.191818\pi$
$152$	0.707107	−	0.707107i	0.0573539	−	0.0573539i
$153$		0			0
$154$			25.8830i			2.08571i
$155$	0.103734	+	0.214081i	0.00833209	+	0.0171954i
$156$		0			0
$157$	13.7423	+	13.7423i	1.09675	+	1.09675i	0.994788	+	0.101967i	$0.0325136\pi$
$157$	13.7423	+	13.7423i	1.09675	+	1.09675i	0.101967	+	0.994788i	$0.467486\pi$
$158$	−5.98227	−	5.98227i	−0.475924	−	0.475924i
$159$		0			0
$160$	−2.11236	−	0.733428i	−0.166997	−	0.0579825i
$161$		−	7.81053i		−	0.615556i
$162$		0			0
$163$	−5.46255	+	5.46255i	−0.427860	+	0.427860i	−0.887899	−	0.460039i	$-0.847836\pi$
$163$	−5.46255	+	5.46255i	−0.427860	+	0.427860i	0.460039	+	0.887899i	$0.347836\pi$
$164$	5.65335			0.441452
$165$		0			0
$166$	−10.5282			−0.817145
$167$	2.45989	−	2.45989i	0.190352	−	0.190352i	−0.605496	−	0.795848i	$-0.707025\pi$
$167$	2.45989	−	2.45989i	0.190352	−	0.190352i	0.795848	+	0.605496i	$0.207025\pi$
$168$		0			0
$169$		−	3.80824i		−	0.292941i
$170$	−6.97628	+	3.38038i	−0.535056	+	0.259263i
$171$		0			0
$172$	4.17154	+	4.17154i	0.318077	+	0.318077i
$173$	10.1212	+	10.1212i	0.769499	+	0.769499i	0.978018	−	0.208520i	$-0.0668645\pi$
$173$	10.1212	+	10.1212i	0.769499	+	0.769499i	−0.208520	+	0.978018i	$0.566864\pi$
$174$		0			0
$175$	21.2449	−	2.49770i	1.60597	−	0.188808i
$176$			6.04990i			0.456028i
$177$		0			0
$178$	−9.68910	+	9.68910i	−0.726229	+	0.726229i
$179$	7.88157			0.589096			0.294548	−	0.955637i	$-0.404831\pi$
$179$	7.88157			0.589096			0.294548	+	0.955637i	$0.404831\pi$
$180$		0			0
$181$	10.7019			0.795462			0.397731	−	0.917502i	$-0.369798\pi$
$181$	10.7019			0.795462			0.397731	+	0.917502i	$0.369798\pi$
$182$	12.4026	−	12.4026i	0.919342	−	0.919342i
$183$		0			0
$184$		−	1.82564i		−	0.134588i
$185$	3.00690	−	8.66024i	0.221071	−	0.636714i
$186$		0			0
$187$	14.8309	+	14.8309i	1.08455	+	1.08455i
$188$	5.35509	+	5.35509i	0.390560	+	0.390560i
$189$		0			0
$190$	−0.733428	+	2.11236i	−0.0532084	+	0.153247i
$191$			16.6132i			1.20209i	0.799215	+	0.601045i	$0.205249\pi$
$191$			16.6132i			1.20209i	−0.799215	+	0.601045i	$0.794751\pi$
$192$		0			0
$193$	7.86143	−	7.86143i	0.565878	−	0.565878i	−0.365093	−	0.930971i	$-0.618963\pi$
$193$	7.86143	−	7.86143i	0.565878	−	0.565878i	0.930971	+	0.365093i	$0.118963\pi$
$194$	3.31730			0.238168
$195$		0			0
$196$	11.3035			0.807390
$197$	−9.53010	+	9.53010i	−0.678992	+	0.678992i	−0.959772	−	0.280780i	$-0.909407\pi$
$197$	−9.53010	+	9.53010i	−0.678992	+	0.678992i	0.280780	+	0.959772i	$0.409407\pi$
$198$		0			0
$199$			10.3991i			0.737172i	0.929594	+	0.368586i	$0.120158\pi$
$199$			10.3991i			0.737172i	−0.929594	+	0.368586i	$0.879842\pi$
$200$	4.96580	−	0.583812i	0.351135	−	0.0412818i
$201$		0			0
$202$	−9.82840	−	9.82840i	−0.691523	−	0.691523i
$203$	13.5686	+	13.5686i	0.952331	+	0.952331i
$204$		0			0
$205$	−11.3761	+	5.51233i	−0.794542	+	0.384998i
$206$		−	2.45989i		−	0.171389i
$207$		0			0
$208$	2.89899	−	2.89899i	0.201009	−	0.201009i
$209$	6.04990			0.418480
$210$		0			0
$211$	−22.0447			−1.51762			−0.758810	−	0.651312i	$-0.774219\pi$
$211$	−22.0447			−1.51762			−0.758810	+	0.651312i	$0.774219\pi$
$212$	−9.19614	+	9.19614i	−0.631593	+	0.631593i
$213$		0			0
$214$			4.42823i			0.302707i
$215$	−12.4618	−	4.32681i	−0.849886	−	0.295086i
$216$		0			0
$217$	−0.321841	−	0.321841i	−0.0218480	−	0.0218480i
$218$	−3.59950	−	3.59950i	−0.243789	−	0.243789i
$219$		0			0
$220$	−5.89899	−	12.1741i	−0.397710	−	0.820776i
$221$		−	14.2134i		−	0.956094i
$222$		0			0
$223$	5.49706	−	5.49706i	0.368111	−	0.368111i	−0.498677	−	0.866788i	$-0.666181\pi$
$223$	5.49706	−	5.49706i	0.368111	−	0.368111i	0.866788	+	0.498677i	$0.166181\pi$
$224$	4.27825			0.285853
$225$		0			0
$226$	11.4392			0.760924
$227$	15.1349	−	15.1349i	1.00454	−	1.00454i	0.00454820	−	0.999990i	$-0.498552\pi$
$227$	15.1349	−	15.1349i	1.00454	−	1.00454i	0.999990	−	0.00454820i	$-0.00144774\pi$
$228$		0			0
$229$		−	9.08041i		−	0.600051i	−0.953931	−	0.300025i	$-0.903005\pi$
$229$		−	9.08041i		−	0.600051i	0.953931	−	0.300025i	$-0.0969951\pi$
$230$	1.78010	+	3.67369i	0.117376	+	0.242236i
$231$		0			0
$232$	3.17154	+	3.17154i	0.208221	+	0.208221i
$233$	−8.57256	−	8.57256i	−0.561607	−	0.561607i	0.368157	−	0.929764i	$-0.379989\pi$
$233$	−8.57256	−	8.57256i	−0.561607	−	0.561607i	−0.929764	+	0.368157i	$0.879989\pi$
$234$		0			0
$235$	−15.9974	−	5.55443i	−1.04356	−	0.362331i
$236$			4.35348i			0.283387i
$237$		0			0
$238$	10.4879	−	10.4879i	0.679828	−	0.679828i
$239$	−21.9823			−1.42192			−0.710958	−	0.703235i	$-0.751738\pi$
$239$	−21.9823			−1.42192			−0.710958	+	0.703235i	$0.751738\pi$
$240$		0			0
$241$	−15.9894			−1.02997			−0.514983	−	0.857200i	$-0.672202\pi$
$241$	−15.9894			−1.02997			−0.514983	+	0.857200i	$0.672202\pi$
$242$	−18.1028	+	18.1028i	−1.16369	+	1.16369i
$243$		0			0
$244$		−	6.09068i		−	0.389916i
$245$	−22.7457	+	11.0215i	−1.45317	+	0.704138i
$246$		0			0
$247$	−2.89899	−	2.89899i	−0.184458	−	0.184458i
$248$	−0.0752273	−	0.0752273i	−0.00477694	−	0.00477694i
$249$		0			0
$250$	−9.42332	+	6.01672i	−0.595983	+	0.380531i
$251$		−	18.4375i		−	1.16376i	−0.813273	−	0.581882i	$-0.802317\pi$
$251$		−	18.4375i		−	1.16376i	0.813273	−	0.581882i	$-0.197683\pi$
$252$		0			0
$253$	7.80993	−	7.80993i	0.491006	−	0.491006i
$254$	−2.91125			−0.182668
$255$		0			0
$256$	1.00000			0.0625000
$257$	−10.5893	+	10.5893i	−0.660540	+	0.660540i	−0.955507	−	0.294968i	$-0.904691\pi$
$257$	−10.5893	+	10.5893i	−0.660540	+	0.660540i	0.294968	+	0.955507i	$0.404691\pi$
$258$		0			0
$259$			17.5399i			1.08988i
$260$	−3.00690	+	8.66024i	−0.186480	+	0.537085i
$261$		0			0
$262$	−12.5027	−	12.5027i	−0.772416	−	0.772416i
$263$	−9.08683	−	9.08683i	−0.560318	−	0.560318i	0.369080	−	0.929398i	$-0.379673\pi$
$263$	−9.08683	−	9.08683i	−0.560318	−	0.560318i	−0.929398	+	0.369080i	$0.879673\pi$
$264$		0			0
$265$	9.53845	−	27.4719i	0.585942	−	1.68759i
$266$		−	4.27825i		−	0.262317i
$267$		0			0
$268$		0			0
$269$	24.7846			1.51114			0.755572	−	0.655066i	$-0.227359\pi$
$269$	24.7846			1.51114			0.755572	+	0.655066i	$0.227359\pi$
$270$		0			0
$271$	20.7713			1.26177			0.630883	−	0.775878i	$-0.282693\pi$
$271$	20.7713			1.26177			0.630883	+	0.775878i	$0.282693\pi$
$272$	2.45144	−	2.45144i	0.148640	−	0.148640i
$273$		0			0
$274$			1.97730i			0.119453i
$275$	23.7408	+	18.7458i	1.43162	+	1.13041i
$276$		0			0
$277$	14.7122	+	14.7122i	0.883973	+	0.883973i	0.993936	−	0.109962i	$-0.0350730\pi$
$277$	14.7122	+	14.7122i	0.883973	+	0.883973i	−0.109962	+	0.993936i	$0.535073\pi$
$278$	10.6215	+	10.6215i	0.637033	+	0.637033i
$279$		0			0
$280$	−8.60904	+	4.17154i	−0.514489	+	0.249297i
$281$		−	11.4607i		−	0.683685i	−0.939757	−	0.341843i	$-0.888949\pi$
$281$		−	11.4607i		−	0.683685i	0.939757	−	0.341843i	$-0.111051\pi$
$282$		0			0
$283$	−13.6768	+	13.6768i	−0.813001	+	0.813001i	−0.985083	−	0.172081i	$-0.944951\pi$
$283$	−13.6768	+	13.6768i	−0.813001	+	0.813001i	0.172081	+	0.985083i	$0.444951\pi$
$284$	−15.2852			−0.907007
$285$		0			0
$286$	24.8033			1.46665
$287$	17.1024	−	17.1024i	1.00952	−	1.00952i
$288$		0			0
$289$			4.98092i			0.292995i
$290$	−9.47444	−	3.28959i	−0.556358	−	0.193171i
$291$		0			0
$292$	−7.19707	−	7.19707i	−0.421176	−	0.421176i
$293$	−12.4849	−	12.4849i	−0.729377	−	0.729377i	0.241118	−	0.970496i	$-0.422486\pi$
$293$	−12.4849	−	12.4849i	−0.729377	−	0.729377i	−0.970496	+	0.241118i	$0.922486\pi$
$294$		0			0
$295$	−4.24489	−	8.76042i	−0.247147	−	0.510051i
$296$			4.09979i			0.238295i
$297$		0			0
$298$	10.1595	−	10.1595i	0.588525	−	0.588525i
$299$	−7.48471			−0.432852
$300$		0			0
$301$	25.2393			1.45477
$302$	14.3171	−	14.3171i	0.823856	−	0.823856i
$303$		0			0
$304$		−	1.00000i		−	0.0573539i
$305$	5.93875	+	12.2561i	0.340052	+	0.701785i
$306$		0			0
$307$	5.51575	+	5.51575i	0.314800	+	0.314800i	0.846766	−	0.531966i	$-0.178546\pi$
$307$	5.51575	+	5.51575i	0.314800	+	0.314800i	−0.531966	+	0.846766i	$0.678546\pi$
$308$	18.3020	+	18.3020i	1.04286	+	1.04286i
$309$		0			0
$310$	0.224729	+	0.0780275i	0.0127638	+	0.00443166i
$311$		−	13.8509i		−	0.785413i	−0.919664	−	0.392706i	$-0.871539\pi$
$311$		−	13.8509i		−	0.785413i	0.919664	−	0.392706i	$-0.128461\pi$
$312$		0			0
$313$	−12.0521	+	12.0521i	−0.681222	+	0.681222i	−0.960276	−	0.279053i	$-0.909979\pi$
$313$	−12.0521	+	12.0521i	−0.681222	+	0.681222i	0.279053	+	0.960276i	$0.409979\pi$
$314$	19.4345			1.09675
$315$		0			0
$316$	−8.46020			−0.475924
$317$	16.2141	−	16.2141i	0.910674	−	0.910674i	−0.0856508	−	0.996325i	$-0.527297\pi$
$317$	16.2141	−	16.2141i	0.910674	−	0.910674i	0.996325	+	0.0856508i	$0.0272969\pi$
$318$		0			0
$319$			27.1352i			1.51928i
$320$	−2.01228	+	0.975056i	−0.112490	+	0.0545073i
$321$		0			0
$322$	−5.52288	−	5.52288i	−0.307778	−	0.307778i
$323$	−2.45144	−	2.45144i	−0.136402	−	0.136402i
$324$		0			0
$325$	−2.39350	−	20.3587i	−0.132768	−	1.12930i
$326$			7.72522i			0.427860i
$327$		0			0
$328$	3.99752	−	3.99752i	0.220726	−	0.220726i
$329$	32.4003			1.78628
$330$		0			0
$331$	−11.3278			−0.622634			−0.311317	−	0.950306i	$-0.600770\pi$
$331$	−11.3278			−0.622634			−0.311317	+	0.950306i	$0.600770\pi$
$332$	−7.44455	+	7.44455i	−0.408573	+	0.408573i
$333$		0			0
$334$		−	3.47881i		−	0.190352i
$335$		0			0
$336$		0			0
$337$	−23.7048	−	23.7048i	−1.29128	−	1.29128i	−0.933994	−	0.357289i	$-0.883701\pi$
$337$	−23.7048	−	23.7048i	−1.29128	−	1.29128i	−0.357289	−	0.933994i	$-0.616299\pi$
$338$	−2.69283	−	2.69283i	−0.146471	−	0.146471i
$339$		0			0
$340$	−2.54269	+	7.32326i	−0.137897	+	0.397160i
$341$		−	0.643633i		−	0.0348547i
$342$		0			0
$343$	13.0187	−	13.0187i	0.702945	−	0.702945i
$344$	5.89944			0.318077
$345$		0			0
$346$	14.3135			0.769499
$347$	3.14728	−	3.14728i	0.168955	−	0.168955i	−0.617565	−	0.786520i	$-0.711881\pi$
$347$	3.14728	−	3.14728i	0.168955	−	0.168955i	0.786520	+	0.617565i	$0.211881\pi$
$348$		0			0
$349$		−	26.4388i		−	1.41524i	−0.706594	−	0.707619i	$-0.749769\pi$
$349$		−	26.4388i		−	1.41524i	0.706594	−	0.707619i	$-0.250231\pi$
$350$	13.2563	−	16.7886i	0.708580	−	0.897388i
$351$		0			0
$352$	4.27792	+	4.27792i	0.228014	+	0.228014i
$353$	−0.920487	−	0.920487i	−0.0489926	−	0.0489926i	0.682186	−	0.731179i	$-0.261029\pi$
$353$	−0.920487	−	0.920487i	−0.0489926	−	0.0489926i	−0.731179	+	0.682186i	$0.761029\pi$
$354$		0			0
$355$	30.7580	−	14.9039i	1.63247	−	0.791016i
$356$			13.7025i			0.726229i
$357$		0			0
$358$	5.57311	−	5.57311i	0.294548	−	0.294548i
$359$	−20.7621			−1.09578			−0.547891	−	0.836550i	$-0.684569\pi$
$359$	−20.7621			−1.09578			−0.547891	+	0.836550i	$0.684569\pi$
$360$		0			0
$361$	−1.00000			−0.0526316
$362$	7.56735	−	7.56735i	0.397731	−	0.397731i
$363$		0			0
$364$		−	17.5399i		−	0.919342i
$365$	21.5000	+	7.46496i	1.12536	+	0.390734i
$366$		0			0
$367$	−22.9415	−	22.9415i	−1.19754	−	1.19754i	−0.974902	−	0.222634i	$-0.928534\pi$
$367$	−22.9415	−	22.9415i	−1.19754	−	1.19754i	−0.222634	−	0.974902i	$-0.571466\pi$
$368$	−1.29092	−	1.29092i	−0.0672938	−	0.0672938i
$369$		0			0
$370$	−3.99752	−	8.24991i	−0.207821	−	0.428892i
$371$			55.6400i			2.88868i
$372$		0			0
$373$	23.1273	−	23.1273i	1.19749	−	1.19749i	0.222571	−	0.974916i	$-0.428555\pi$
$373$	23.1273	−	23.1273i	1.19749	−	1.19749i	0.974916	−	0.222571i	$-0.0714451\pi$
$374$	20.9741			1.08455
$375$		0			0
$376$	7.57324			0.390560
$377$	13.0026	−	13.0026i	0.669669	−	0.669669i
$378$		0			0
$379$			18.2545i			0.937673i	0.883285	+	0.468836i	$0.155327\pi$
$379$			18.2545i			0.937673i	−0.883285	+	0.468836i	$0.844673\pi$
$380$	0.975056	+	2.01228i	0.0500193	+	0.103228i
$381$		0			0
$382$	11.7473	+	11.7473i	0.601045	+	0.601045i
$383$	7.58085	+	7.58085i	0.387363	+	0.387363i	0.873746	−	0.486383i	$-0.161684\pi$
$383$	7.58085	+	7.58085i	0.387363	+	0.387363i	−0.486383	+	0.873746i	$0.661684\pi$
$384$		0			0
$385$	−54.6743	−	18.9833i	−2.78646	−	0.967479i
$386$		−	11.1177i		−	0.565878i
$387$		0			0
$388$	2.34568	−	2.34568i	0.119084	−	0.119084i
$389$	10.1767			0.515978			0.257989	−	0.966148i	$-0.416940\pi$
$389$	10.1767			0.515978			0.257989	+	0.966148i	$0.416940\pi$
$390$		0			0
$391$	−6.32921			−0.320082
$392$	7.99275	−	7.99275i	0.403695	−	0.403695i
$393$		0			0
$394$			13.4776i			0.678992i
$395$	17.0243	−	8.24917i	0.856585	−	0.415061i
$396$		0			0
$397$	−4.40091	−	4.40091i	−0.220876	−	0.220876i	0.587992	−	0.808867i	$-0.299919\pi$
$397$	−4.40091	−	4.40091i	−0.220876	−	0.220876i	−0.808867	+	0.587992i	$0.799919\pi$
$398$	7.35327	+	7.35327i	0.368586	+	0.368586i
$399$		0			0
$400$	3.09853	−	3.92417i	0.154927	−	0.196208i
$401$		−	21.2664i		−	1.06199i	−0.847374	−	0.530997i	$-0.821818\pi$
$401$		−	21.2664i		−	1.06199i	0.847374	−	0.530997i	$-0.178182\pi$
$402$		0			0
$403$	−0.308416	+	0.308416i	−0.0153633	+	0.0153633i
$404$	−13.8994			−0.691523
$405$		0			0
$406$	19.1889			0.952331
$407$	−17.5386	+	17.5386i	−0.869354	+	0.869354i
$408$		0			0
$409$		−	6.78915i		−	0.335702i	−0.985812	−	0.167851i	$-0.946317\pi$
$409$		−	6.78915i		−	0.335702i	0.985812	−	0.167851i	$-0.0536828\pi$
$410$	−4.14632	+	11.9419i	−0.204772	+	0.589770i
$411$		0			0
$412$	−1.73940	−	1.73940i	−0.0856943	−	0.0856943i
$413$	13.1701	+	13.1701i	0.648057	+	0.648057i
$414$		0			0
$415$	7.72166	−	22.2394i	0.379041	−	1.09169i
$416$		−	4.09979i		−	0.201009i
$417$		0			0
$418$	4.27792	−	4.27792i	0.209240	−	0.209240i
$419$	−13.4924			−0.659148			−0.329574	−	0.944130i	$-0.606905\pi$
$419$	−13.4924			−0.659148			−0.329574	+	0.944130i	$0.606905\pi$
$420$		0			0
$421$	26.4411			1.28866			0.644331	−	0.764747i	$-0.277136\pi$
$421$	26.4411			1.28866			0.644331	+	0.764747i	$0.277136\pi$
$422$	−15.5880	+	15.5880i	−0.758810	+	0.758810i
$423$		0			0
$424$			13.0053i			0.631593i
$425$	−2.02399	−	17.2157i	−0.0981780	−	0.835084i
$426$		0			0
$427$	−18.4254	−	18.4254i	−0.891668	−	0.891668i
$428$	3.13123	+	3.13123i	0.151354	+	0.151354i
$429$		0			0
$430$	−11.8713	+	5.75228i	−0.572486	+	0.277400i
$431$		−	20.9690i		−	1.01004i	−0.863107	−	0.505021i	$-0.831485\pi$
$431$		−	20.9690i		−	1.01004i	0.863107	−	0.505021i	$-0.168515\pi$
$432$		0			0
$433$	−24.6838	+	24.6838i	−1.18623	+	1.18623i	−0.208125	+	0.978102i	$0.566736\pi$
$433$	−24.6838	+	24.6838i	−1.18623	+	1.18623i	−0.978102	+	0.208125i	$0.933264\pi$
$434$	−0.455153			−0.0218480
$435$		0			0
$436$	−5.09046			−0.243789
$437$	−1.29092	+	1.29092i	−0.0617530	+	0.0617530i
$438$		0			0
$439$		−	23.3746i		−	1.11561i	−0.829973	−	0.557804i	$-0.811644\pi$
$439$		−	23.3746i		−	1.11561i	0.829973	−	0.557804i	$-0.188356\pi$
$440$	−12.7796	−	4.43716i	−0.609243	−	0.211533i
$441$		0			0
$442$	−10.0504	−	10.0504i	−0.478047	−	0.478047i
$443$	6.76580	+	6.76580i	0.321453	+	0.321453i	0.849324	−	0.527872i	$-0.177010\pi$
$443$	6.76580	+	6.76580i	0.321453	+	0.321453i	−0.527872	+	0.849324i	$0.677010\pi$
$444$		0			0
$445$	−13.3607	−	27.5732i	−0.633356	−	1.30709i
$446$		−	7.77402i		−	0.368111i
$447$		0			0
$448$	3.02518	−	3.02518i	0.142926	−	0.142926i
$449$	−20.7890			−0.981095			−0.490548	−	0.871414i	$-0.663203\pi$
$449$	−20.7890			−0.981095			−0.490548	+	0.871414i	$0.663203\pi$
$450$		0			0
$451$	34.2022			1.61052
$452$	8.08873	−	8.08873i	0.380462	−	0.380462i
$453$		0			0
$454$		−	21.4040i		−	1.00454i
$455$	17.1024	+	35.2952i	0.801773	+	1.65467i
$456$		0			0
$457$	−4.74195	−	4.74195i	−0.221819	−	0.221819i	0.587445	−	0.809264i	$-0.300134\pi$
$457$	−4.74195	−	4.74195i	−0.221819	−	0.221819i	−0.809264	+	0.587445i	$0.800134\pi$
$458$	−6.42082	−	6.42082i	−0.300025	−	0.300025i
$459$		0			0
$460$	3.85641	+	1.33897i	0.179806	+	0.0624299i
$461$			27.5735i			1.28423i	0.766610	+	0.642113i	$0.221942\pi$
$461$			27.5735i			1.28423i	−0.766610	+	0.642113i	$0.778058\pi$
$462$		0			0
$463$	−16.9975	+	16.9975i	−0.789942	+	0.789942i	−0.981484	−	0.191543i	$-0.938651\pi$
$463$	−16.9975	+	16.9975i	−0.789942	+	0.789942i	0.191543	+	0.981484i	$0.438651\pi$
$464$	4.48523			0.208221
$465$		0			0
$466$	−12.1234			−0.561607
$467$	−13.7802	+	13.7802i	−0.637670	+	0.637670i	−0.949980	−	0.312310i	$-0.898897\pi$
$467$	−13.7802	+	13.7802i	−0.637670	+	0.637670i	0.312310	+	0.949980i	$0.398897\pi$
$468$		0			0
$469$		0			0
$470$	−15.2395	+	7.38433i	−0.702945	+	0.340614i
$471$		0			0
$472$	3.07838	+	3.07838i	0.141694	+	0.141694i
$473$	25.2374	+	25.2374i	1.16041	+	1.16041i
$474$		0			0
$475$	−3.92417	−	3.09853i	−0.180053	−	0.142170i
$476$		−	14.8321i		−	0.679828i
$477$		0			0
$478$	−15.5438	+	15.5438i	−0.710958	+	0.710958i
$479$	11.5548			0.527951			0.263976	−	0.964529i	$-0.414966\pi$
$479$	11.5548			0.527951			0.263976	+	0.964529i	$0.414966\pi$
$480$		0			0
$481$	16.8082			0.766390
$482$	−11.3062	+	11.3062i	−0.514983	+	0.514983i
$483$		0			0
$484$			25.6012i			1.16369i
$485$	−2.43300	+	7.00734i	−0.110477	+	0.318187i
$486$		0			0
$487$	19.9875	+	19.9875i	0.905721	+	0.905721i	0.995923	−	0.0902020i	$-0.0287513\pi$
$487$	19.9875	+	19.9875i	0.905721	+	0.905721i	−0.0902020	+	0.995923i	$0.528751\pi$
$488$	−4.30676	−	4.30676i	−0.194958	−	0.194958i
$489$		0			0
$490$	−8.29026	+	23.8770i	−0.374516	+	1.07865i
$491$		−	9.03147i		−	0.407585i	−0.979014	−	0.203792i	$-0.934673\pi$
$491$		−	9.03147i		−	0.407585i	0.979014	−	0.203792i	$-0.0653267\pi$
$492$		0			0
$493$	10.9953	−	10.9953i	0.495201	−	0.495201i
$494$	−4.09979			−0.184458
$495$		0			0
$496$	−0.106387			−0.00477694
$497$	−46.2404	+	46.2404i	−2.07416	+	2.07416i
$498$		0			0
$499$			6.15516i			0.275543i	0.990464	+	0.137772i	$0.0439940\pi$
$499$			6.15516i			0.275543i	−0.990464	+	0.137772i	$0.956006\pi$
$500$	−2.40883	+	10.9178i	−0.107726	+	0.488257i
$501$		0			0
$502$	−13.0373	−	13.0373i	−0.581882	−	0.581882i
$503$	−4.49738	−	4.49738i	−0.200528	−	0.200528i	0.599698	−	0.800226i	$-0.295287\pi$
$503$	−4.49738	−	4.49738i	−0.200528	−	0.200528i	−0.800226	+	0.599698i	$0.795287\pi$
$504$		0			0
$505$	27.9696	−	13.5527i	1.24463	−	0.603089i
$506$		−	11.0449i		−	0.491006i
$507$		0			0
$508$	−2.05857	+	2.05857i	−0.0913341	+	0.0913341i
$509$	−17.0624			−0.756277			−0.378139	−	0.925749i	$-0.623436\pi$
$509$	−17.0624			−0.756277			−0.378139	+	0.925749i	$0.623436\pi$
$510$		0			0
$511$	−43.5449			−1.92631
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$		0			0
$514$			14.9755i			0.660540i
$515$	5.19618	+	1.80415i	0.228971	+	0.0795004i
$516$		0			0
$517$	32.3977	+	32.3977i	1.42485	+	1.42485i
$518$	12.4026	+	12.4026i	0.544939	+	0.544939i
$519$		0			0
$520$	3.99752	+	8.24991i	0.175303	+	0.361783i
$521$		−	4.92329i		−	0.215693i	−0.994168	−	0.107847i	$-0.965604\pi$
$521$		−	4.92329i		−	0.215693i	0.994168	−	0.107847i	$-0.0343955\pi$
$522$		0			0
$523$	−26.1723	+	26.1723i	−1.14444	+	1.14444i	−0.156806	+	0.987629i	$0.550120\pi$
$523$	−26.1723	+	26.1723i	−1.14444	+	1.14444i	−0.987629	+	0.156806i	$0.949880\pi$
$524$	−17.6814			−0.772416
$525$		0			0
$526$	−12.8507			−0.560318
$527$	−0.260802	+	0.260802i	−0.0113607	+	0.0113607i
$528$		0			0
$529$		−	19.6671i		−	0.855089i
$530$	−12.6809	−	26.1703i	−0.550823	−	1.13677i
$531$		0			0
$532$	−3.02518	−	3.02518i	−0.131158	−	0.131158i
$533$	−16.3890	−	16.3890i	−0.709885	−	0.709885i
$534$		0			0
$535$	−9.35403	−	3.24779i	−0.404410	−	0.140414i
$536$		0			0
$537$		0			0
$538$	17.5254	−	17.5254i	0.755572	−	0.755572i
$539$	68.3847			2.94554
$540$		0			0
$541$	−5.51982			−0.237316			−0.118658	−	0.992935i	$-0.537859\pi$
$541$	−5.51982			−0.237316			−0.118658	+	0.992935i	$0.537859\pi$
$542$	14.6875	−	14.6875i	0.630883	−	0.630883i
$543$		0			0
$544$		−	3.46686i		−	0.148640i
$545$	10.2434	−	4.96348i	0.438780	−	0.212612i
$546$		0			0
$547$	−29.0550	−	29.0550i	−1.24230	−	1.24230i	−0.959044	−	0.283257i	$-0.908585\pi$
$547$	−29.0550	−	29.0550i	−1.24230	−	1.24230i	−0.283257	−	0.959044i	$-0.591415\pi$
$548$	1.39816	+	1.39816i	0.0597265	+	0.0597265i
$549$		0			0
$550$	30.0426	−	3.53200i	1.28102	−	0.150605i
$551$		−	4.48523i		−	0.191077i
$552$		0			0
$553$	−25.5937	+	25.5937i	−1.08835	+	1.08835i
$554$	20.8063			0.883973
$555$		0			0
$556$	15.0210			0.637033
$557$	−24.9185	+	24.9185i	−1.05583	+	1.05583i	−0.0574844	+	0.998346i	$0.518308\pi$
$557$	−24.9185	+	24.9185i	−1.05583	+	1.05583i	−0.998346	+	0.0574844i	$0.981692\pi$
$558$		0			0
$559$		−	24.1864i		−	1.02298i
$560$	−3.13779	+	9.03723i	−0.132596	+	0.381893i
$561$		0			0
$562$	−8.10391	−	8.10391i	−0.341843	−	0.341843i
$563$	−28.3656	−	28.3656i	−1.19547	−	1.19547i	−0.975510	−	0.219957i	$-0.929408\pi$
$563$	−28.3656	−	28.3656i	−1.19547	−	1.19547i	−0.219957	−	0.975510i	$-0.570592\pi$
$564$		0			0
$565$	−8.38982	+	24.1637i	−0.352962	+	1.01658i
$566$			19.3419i			0.813001i
$567$		0			0
$568$	−10.8082	+	10.8082i	−0.453504	+	0.453504i
$569$	−40.9892			−1.71836			−0.859178	−	0.511676i	$-0.829025\pi$
$569$	−40.9892			−1.71836			−0.859178	+	0.511676i	$0.829025\pi$
$570$		0			0
$571$	42.7416			1.78868			0.894340	−	0.447388i	$-0.147646\pi$
$571$	42.7416			1.78868			0.894340	+	0.447388i	$0.147646\pi$
$572$	17.5386	−	17.5386i	0.733324	−	0.733324i
$573$		0			0
$574$		−	24.1864i		−	1.00952i
$575$	−9.06574	+	1.06583i	−0.378067	+	0.0444481i
$576$		0			0
$577$	29.7487	+	29.7487i	1.23846	+	1.23846i	0.960632	+	0.277823i	$0.0896130\pi$
$577$	29.7487	+	29.7487i	1.23846	+	1.23846i	0.277823	+	0.960632i	$0.410387\pi$
$578$	3.52204	+	3.52204i	0.146498	+	0.146498i
$579$		0			0
$580$	−9.02553	+	4.37335i	−0.374765	+	0.181593i
$581$			45.0422i			1.86867i
$582$		0			0
$583$	−55.6357	+	55.6357i	−2.30419	+	2.30419i
$584$	−10.1782			−0.421176
$585$		0			0
$586$	−17.6564			−0.729377
$587$	27.5003	−	27.5003i	1.13506	−	1.13506i	0.145737	−	0.989323i	$-0.453445\pi$
$587$	27.5003	−	27.5003i	1.13506	−	1.13506i	0.989323	−	0.145737i	$-0.0465554\pi$
$588$		0			0
$589$			0.106387i			0.00438362i
$590$	−9.19614	−	3.19296i	−0.378599	−	0.131452i
$591$		0			0
$592$	2.89899	+	2.89899i	0.119148	+	0.119148i
$593$	11.7043	+	11.7043i	0.480637	+	0.480637i	0.905335	−	0.424698i	$-0.139620\pi$
$593$	11.7043	+	11.7043i	0.480637	+	0.480637i	−0.424698	+	0.905335i	$0.639620\pi$
$594$		0			0
$595$	14.4621	+	29.8463i	0.592889	+	1.22358i
$596$		−	14.3677i		−	0.588525i
$597$		0			0
$598$	−5.29249	+	5.29249i	−0.216426	+	0.216426i
$599$	20.2471			0.827275			0.413638	−	0.910442i	$-0.364258\pi$
$599$	20.2471			0.827275			0.413638	+	0.910442i	$0.364258\pi$
$600$		0			0
$601$	22.6559			0.924153			0.462076	−	0.886840i	$-0.347105\pi$
$601$	22.6559			0.924153			0.462076	+	0.886840i	$0.347105\pi$
$602$	17.8469	−	17.8469i	0.727385	−	0.727385i
$603$		0			0
$604$		−	20.2474i		−	0.823856i
$605$	−24.9626	−	51.5169i	−1.01488	−	2.09446i
$606$		0			0
$607$	12.7604	+	12.7604i	0.517929	+	0.517929i	0.916944	−	0.399015i	$-0.130648\pi$
$607$	12.7604	+	12.7604i	0.517929	+	0.517929i	−0.399015	+	0.916944i	$0.630648\pi$
$608$	−0.707107	−	0.707107i	−0.0286770	−	0.0286770i
$609$		0			0
$610$	12.8657	+	4.46707i	0.520918	+	0.180866i
$611$		−	31.0487i		−	1.25609i
$612$		0			0
$613$	−14.3081	+	14.3081i	−0.577897	+	0.577897i	−0.934324	−	0.356426i	$-0.883995\pi$
$613$	−14.3081	+	14.3081i	−0.577897	+	0.577897i	0.356426	+	0.934324i	$0.383995\pi$
$614$	7.80045			0.314800
$615$		0			0
$616$	25.8830			1.04286
$617$	8.75912	−	8.75912i	0.352629	−	0.352629i	−0.508458	−	0.861087i	$-0.669784\pi$
$617$	8.75912	−	8.75912i	0.352629	−	0.352629i	0.861087	+	0.508458i	$0.169784\pi$
$618$		0			0
$619$			9.66513i			0.388474i	0.980955	+	0.194237i	$0.0622231\pi$
$619$			9.66513i			0.388474i	−0.980955	+	0.194237i	$0.937777\pi$
$620$	0.214081	−	0.103734i	0.00859771	−	0.00416605i
$621$		0			0
$622$	−9.79407	−	9.79407i	−0.392706	−	0.392706i
$623$	41.4524	+	41.4524i	1.66076	+	1.66076i
$624$		0			0
$625$	−5.79819	−	24.3183i	−0.231928	−	0.972733i
$626$			17.0442i			0.681222i
$627$		0			0
$628$	13.7423	−	13.7423i	0.548377	−	0.548377i
$629$	14.2134			0.566724
$630$		0			0
$631$	17.0994			0.680715			0.340357	−	0.940296i	$-0.389452\pi$
$631$	17.0994			0.680715			0.340357	+	0.940296i	$0.389452\pi$
$632$	−5.98227	+	5.98227i	−0.237962	+	0.237962i
$633$		0			0
$634$		−	22.9302i		−	0.910674i
$635$	2.13519	−	6.14963i	0.0847326	−	0.244041i
$636$		0			0
$637$	−32.7686	−	32.7686i	−1.29834	−	1.29834i
$638$	19.1875	+	19.1875i	0.759639	+	0.759639i
$639$		0			0
$640$	−0.733428	+	2.11236i	−0.0289913	+	0.0834985i
$641$		−	6.80437i		−	0.268756i	−0.990930	−	0.134378i	$-0.957096\pi$
$641$		−	6.80437i		−	0.268756i	0.990930	−	0.134378i	$-0.0429037\pi$
$642$		0			0
$643$	−17.1258	+	17.1258i	−0.675375	+	0.675375i	−0.958950	−	0.283575i	$-0.908479\pi$
$643$	−17.1258	+	17.1258i	−0.675375	+	0.675375i	0.283575	+	0.958950i	$0.408479\pi$
$644$	−7.81053			−0.307778
$645$		0			0
$646$	−3.46686			−0.136402
$647$	−5.30837	+	5.30837i	−0.208694	+	0.208694i	−0.803712	−	0.595018i	$-0.797145\pi$
$647$	−5.30837	+	5.30837i	−0.208694	+	0.208694i	0.595018	+	0.803712i	$0.297145\pi$
$648$		0			0
$649$			26.3381i			1.03386i
$650$	−16.0882	−	12.7033i	−0.631033	−	0.498265i
$651$		0			0
$652$	5.46255	+	5.46255i	0.213930	+	0.213930i
$653$	16.1665	+	16.1665i	0.632645	+	0.632645i	0.948731	−	0.316086i	$-0.102369\pi$
$653$	16.1665	+	16.1665i	0.632645	+	0.632645i	−0.316086	+	0.948731i	$0.602369\pi$
$654$		0			0
$655$	35.5799	−	17.2404i	1.39022	−	0.673637i
$656$		−	5.65335i		−	0.220726i
$657$		0			0
$658$	22.9104	−	22.9104i	0.893142	−	0.893142i
$659$	−41.3861			−1.61217			−0.806087	−	0.591798i	$-0.798419\pi$
$659$	−41.3861			−1.61217			−0.806087	+	0.591798i	$0.798419\pi$
$660$		0			0
$661$	−23.9495			−0.931527			−0.465764	−	0.884909i	$-0.654220\pi$
$661$	−23.9495			−0.931527			−0.465764	+	0.884909i	$0.654220\pi$
$662$	−8.00999	+	8.00999i	−0.311317	+	0.311317i
$663$		0			0
$664$			10.5282i			0.408573i
$665$	9.03723	+	3.13779i	0.350449	+	0.121678i
$666$		0			0
$667$	−5.79007	−	5.79007i	−0.224192	−	0.224192i
$668$	−2.45989	−	2.45989i	−0.0951760	−	0.0951760i
$669$		0			0
$670$		0			0
$671$		−	36.8480i		−	1.42250i
$672$		0			0
$673$	−9.67849	+	9.67849i	−0.373078	+	0.373078i	−0.868597	−	0.495519i	$-0.834978\pi$
$673$	−9.67849	+	9.67849i	−0.373078	+	0.373078i	0.495519	+	0.868597i	$0.334978\pi$
$674$	−33.5237			−1.29128
$675$		0			0
$676$	−3.80824			−0.146471
$677$	−0.874008	+	0.874008i	−0.0335909	+	0.0335909i	−0.723703	−	0.690112i	$-0.757561\pi$
$677$	−0.874008	+	0.874008i	−0.0335909	+	0.0335909i	0.690112	+	0.723703i	$0.257561\pi$
$678$		0			0
$679$		−	14.1922i		−	0.544648i
$680$	3.38038	+	6.97628i	0.129632	+	0.267528i
$681$		0			0
$682$	−0.455117	−	0.455117i	−0.0174273	−	0.0174273i
$683$	6.34870	+	6.34870i	0.242926	+	0.242926i	0.818060	−	0.575133i	$-0.195050\pi$
$683$	6.34870	+	6.34870i	0.242926	+	0.242926i	−0.575133	+	0.818060i	$0.695050\pi$
$684$		0			0
$685$	−4.17678	−	1.45021i	−0.159586	−	0.0554095i
$686$		−	18.4113i		−	0.702945i
$687$		0			0
$688$	4.17154	−	4.17154i	0.159038	−	0.159038i
$689$	53.3190			2.03129
$690$		0			0
$691$	36.9338			1.40503			0.702515	−	0.711669i	$-0.252061\pi$
$691$	36.9338			1.40503			0.702515	+	0.711669i	$0.252061\pi$
$692$	10.1212	−	10.1212i	0.384749	−	0.384749i
$693$		0			0
$694$		−	4.45093i		−	0.168955i
$695$	−30.2265	+	14.6463i	−1.14656	+	0.555567i
$696$		0			0
$697$	−13.8588	−	13.8588i	−0.524940	−	0.524940i
$698$	−18.6951	−	18.6951i	−0.707619	−	0.707619i
$699$		0			0
$700$	−2.49770	−	21.2449i	−0.0944041	−	0.802984i
$701$			4.10587i			0.155076i	0.996989	+	0.0775382i	$0.0247060\pi$
$701$			4.10587i			0.155076i	−0.996989	+	0.0775382i	$0.975294\pi$
$702$		0			0
$703$	2.89899	−	2.89899i	0.109337	−	0.109337i
$704$	6.04990			0.228014
$705$		0			0
$706$	−1.30177			−0.0489926
$707$	−42.0484	+	42.0484i	−1.58139	+	1.58139i
$708$		0			0
$709$		−	40.8587i		−	1.53448i	−0.641359	−	0.767241i	$-0.721629\pi$
$709$		−	40.8587i		−	1.53448i	0.641359	−	0.767241i	$-0.278371\pi$
$710$	11.2106	−	32.2878i	0.420725	−	1.21174i
$711$		0			0
$712$	9.68910	+	9.68910i	0.363114	+	0.363114i
$713$	0.137338	+	0.137338i	0.00514333	+	0.00514333i
$714$		0			0
$715$	−18.1914	+	52.3936i	−0.680320	+	1.95941i
$716$		−	7.88157i		−	0.294548i
$717$		0			0
$718$	−14.6810	+	14.6810i	−0.547891	+	0.547891i
$719$	30.8224			1.14948			0.574741	−	0.818335i	$-0.305103\pi$
$719$	30.8224			1.14948			0.574741	+	0.818335i	$0.305103\pi$
$720$		0			0
$721$	−10.5240			−0.391935
$722$	−0.707107	+	0.707107i	−0.0263158	+	0.0263158i
$723$		0			0
$724$		−	10.7019i		−	0.397731i
$725$	13.8976	−	17.6008i	0.516145	−	0.653677i
$726$		0			0
$727$	11.4818	+	11.4818i	0.425835	+	0.425835i	0.887207	−	0.461372i	$-0.152643\pi$
$727$	11.4818	+	11.4818i	0.425835	+	0.425835i	−0.461372	+	0.887207i	$0.652643\pi$
$728$	−12.4026	−	12.4026i	−0.459671	−	0.459671i
$729$		0			0
$730$	20.4814	−	9.92430i	0.758049	−	0.367315i
$731$		−	20.4525i		−	0.756463i
$732$		0			0
$733$	6.69362	−	6.69362i	0.247235	−	0.247235i	−0.572600	−	0.819835i	$-0.694065\pi$
$733$	6.69362	−	6.69362i	0.247235	−	0.247235i	0.819835	+	0.572600i	$0.194065\pi$
$734$	−32.4442			−1.19754
$735$		0			0
$736$	−1.82564			−0.0672938
$737$		0			0
$738$		0			0
$739$			2.33543i			0.0859101i	0.999077	+	0.0429551i	$0.0136772\pi$
$739$			2.33543i			0.0859101i	−0.999077	+	0.0429551i	$0.986323\pi$
$740$	−8.66024	−	3.00690i	−0.318357	−	0.110536i
$741$		0			0
$742$	39.3434	+	39.3434i	1.44434	+	1.44434i
$743$	−18.5919	−	18.5919i	−0.682072	−	0.682072i	0.278395	−	0.960467i	$-0.410198\pi$
$743$	−18.5919	−	18.5919i	−0.682072	−	0.682072i	−0.960467	+	0.278395i	$0.910198\pi$
$744$		0			0
$745$	14.0093	+	28.9119i	0.513262	+	1.05925i
$746$		−	32.7070i		−	1.19749i
$747$		0			0
$748$	14.8309	−	14.8309i	0.542273	−	0.542273i
$749$	18.9451			0.692238
$750$		0			0
$751$	−25.6079			−0.934445			−0.467222	−	0.884140i	$-0.654745\pi$
$751$	−25.6079			−0.934445			−0.467222	+	0.884140i	$0.654745\pi$
$752$	5.35509	−	5.35509i	0.195280	−	0.195280i
$753$		0			0
$754$		−	18.3885i		−	0.669669i
$755$	19.7424	+	40.7435i	0.718498	+	1.48281i
$756$		0			0
$757$	7.16667	+	7.16667i	0.260477	+	0.260477i	0.825248	−	0.564771i	$-0.191035\pi$
$757$	7.16667	+	7.16667i	0.260477	+	0.260477i	−0.564771	+	0.825248i	$0.691035\pi$
$758$	12.9079	+	12.9079i	0.468836	+	0.468836i
$759$		0			0
$760$	2.11236	+	0.733428i	0.0766235	+	0.0266042i
$761$		−	0.433779i		−	0.0157245i	−0.999969	−	0.00786223i	$-0.997497\pi$
$761$		−	0.433779i		−	0.0157245i	0.999969	−	0.00786223i	$-0.00250265\pi$
$762$		0			0
$763$	−15.3996	+	15.3996i	−0.557502	+	0.557502i
$764$	16.6132			0.601045
$765$		0			0
$766$	10.7209			0.387363
$767$	12.6207	−	12.6207i	0.455706	−	0.455706i
$768$		0			0
$769$			27.9476i			1.00782i	0.863757	+	0.503908i	$0.168105\pi$
$769$			27.9476i			1.00782i	−0.863757	+	0.503908i	$0.831895\pi$
$770$	−52.0838	+	25.2374i	−1.87697	+	0.909491i
$771$		0			0
$772$	−7.86143	−	7.86143i	−0.282939	−	0.282939i
$773$	−37.2574	−	37.2574i	−1.34006	−	1.34006i	−0.895999	−	0.444056i	$-0.853539\pi$
$773$	−37.2574	−	37.2574i	−1.34006	−	1.34006i	−0.444056	−	0.895999i	$-0.646461\pi$
$774$		0			0
$775$	−0.329645	+	0.417482i	−0.0118412	+	0.0149964i
$776$		−	3.31730i		−	0.119084i
$777$		0			0
$778$	7.19599	−	7.19599i	0.257989	−	0.257989i
$779$	−5.65335			−0.202552
$780$		0			0
$781$	−92.4736			−3.30897
$782$	−4.47543	+	4.47543i	−0.160041	+	0.160041i
$783$		0			0
$784$		−	11.3035i		−	0.403695i
$785$	−14.2538	+	41.0528i	−0.508741	+	1.46524i
$786$		0			0
$787$	−27.3238	−	27.3238i	−0.973987	−	0.973987i	0.0256829	−	0.999670i	$-0.491824\pi$
$787$	−27.3238	−	27.3238i	−0.973987	−	0.973987i	−0.999670	+	0.0256829i	$0.991824\pi$
$788$	9.53010	+	9.53010i	0.339496	+	0.339496i
$789$		0			0
$790$	6.20495	−	17.8710i	0.220762	−	0.635823i
$791$		−	48.9398i		−	1.74010i
$792$		0			0
$793$	−17.6568	+	17.6568i	−0.627011	+	0.627011i
$794$	−6.22383			−0.220876
$795$		0			0
$796$	10.3991			0.368586
$797$	9.55946	−	9.55946i	0.338614	−	0.338614i	−0.517232	−	0.855845i	$-0.673037\pi$
$797$	9.55946	−	9.55946i	0.338614	−	0.338614i	0.855845	+	0.517232i	$0.173037\pi$
$798$		0			0
$799$		−	26.2553i		−	0.928847i
$800$	−0.583812	−	4.96580i	−0.0206409	−	0.175568i
$801$		0			0
$802$	−15.0376	−	15.0376i	−0.530997	−	0.530997i
$803$	−43.5415	−	43.5415i	−1.53655	−	1.53655i
$804$		0			0
$805$	15.7170	−	7.61570i	0.553950	−	0.268418i
$806$			0.436166i			0.0153633i
$807$		0			0
$808$	−9.82840	+	9.82840i	−0.345762	+	0.345762i
$809$	49.2790			1.73256			0.866279	−	0.499560i	$-0.166505\pi$
$809$	49.2790			1.73256			0.866279	+	0.499560i	$0.166505\pi$
$810$		0			0
$811$	27.7776			0.975402			0.487701	−	0.873011i	$-0.337836\pi$
$811$	27.7776			0.975402			0.487701	+	0.873011i	$0.337836\pi$
$812$	13.5686	−	13.5686i	0.476166	−	0.476166i
$813$		0			0
$814$			24.8033i			0.869354i
$815$	−16.3185	−	5.66589i	−0.571611	−	0.198467i
$816$		0			0
$817$	−4.17154	−	4.17154i	−0.145944	−	0.145944i
$818$	−4.80066	−	4.80066i	−0.167851	−	0.167851i
$819$		0			0
$820$	5.51233	+	11.3761i	0.192499	+	0.397271i
$821$			31.8134i			1.11030i	0.831752	+	0.555148i	$0.187338\pi$
$821$			31.8134i			1.11030i	−0.831752	+	0.555148i	$0.812662\pi$
$822$		0			0
$823$	−0.429455	+	0.429455i	−0.0149699	+	0.0149699i	−0.714552	−	0.699582i	$-0.753369\pi$
$823$	−0.429455	+	0.429455i	−0.0149699	+	0.0149699i	0.699582	+	0.714552i	$0.253369\pi$
$824$	−2.45989			−0.0856943
$825$		0			0
$826$	18.6253			0.648057
$827$	−3.66864	+	3.66864i	−0.127571	+	0.127571i	−0.768010	−	0.640438i	$-0.778753\pi$
$827$	−3.66864	+	3.66864i	−0.127571	+	0.127571i	0.640438	+	0.768010i	$0.278753\pi$
$828$		0			0
$829$			12.3930i			0.430427i	0.976567	+	0.215213i	$0.0690447\pi$
$829$			12.3930i			0.430427i	−0.976567	+	0.215213i	$0.930955\pi$
$830$	−10.2656	−	21.1856i	−0.356323	−	0.735364i
$831$		0			0
$832$	−2.89899	−	2.89899i	−0.100504	−	0.100504i
$833$	−27.7097	−	27.7097i	−0.960084	−	0.960084i
$834$		0			0
$835$	7.34851	+	2.55145i	0.254306	+	0.0882967i
$836$		−	6.04990i		−	0.209240i
$837$		0			0
$838$	−9.54058	+	9.54058i	−0.329574	+	0.329574i
$839$	−9.37261			−0.323579			−0.161789	−	0.986825i	$-0.551726\pi$
$839$	−9.37261			−0.323579			−0.161789	+	0.986825i	$0.551726\pi$
$840$		0			0
$841$	−8.88273			−0.306301
$842$	18.6967	−	18.6967i	0.644331	−	0.644331i
$843$		0			0
$844$			22.0447i			0.758810i
$845$	7.66324	−	3.71324i	0.263623	−	0.127739i
$846$		0			0
$847$	77.4484	+	77.4484i	2.66116	+	2.66116i
$848$	9.19614	+	9.19614i	0.315797	+	0.315797i
$849$		0			0
$850$	−13.6045	−	10.7422i	−0.466631	−	0.368453i
$851$		−	7.48471i		−	0.256573i
$852$		0			0
$853$	17.6452	−	17.6452i	0.604160	−	0.604160i	−0.337254	−	0.941414i	$-0.609498\pi$
$853$	17.6452	−	17.6452i	0.604160	−	0.604160i	0.941414	+	0.337254i	$0.109498\pi$
$854$	−26.0575			−0.891668
$855$		0			0
$856$	4.42823			0.151354
$857$	−18.1205	+	18.1205i	−0.618983	+	0.618983i	−0.945271	−	0.326287i	$-0.894202\pi$
$857$	−18.1205	+	18.1205i	−0.618983	+	0.618983i	0.326287	+	0.945271i	$0.394202\pi$
$858$		0			0
$859$			34.6323i			1.18164i	0.806804	+	0.590819i	$0.201195\pi$
$859$			34.6323i			1.18164i	−0.806804	+	0.590819i	$0.798805\pi$
$860$	−4.32681	+	12.4618i	−0.147543	+	0.424943i
$861$		0			0
$862$	−14.8273	−	14.8273i	−0.505021	−	0.505021i
$863$	−34.6765	−	34.6765i	−1.18040	−	1.18040i	−0.979640	−	0.200761i	$-0.935658\pi$
$863$	−34.6765	−	34.6765i	−1.18040	−	1.18040i	−0.200761	−	0.979640i	$-0.564342\pi$
$864$		0			0
$865$	−10.4979	+	30.2353i	−0.356940	+	1.02803i
$866$			34.9082i			1.18623i
$867$		0			0
$868$	−0.321841	+	0.321841i	−0.0109240	+	0.0109240i
$869$	−51.1834			−1.73628
$870$		0			0
$871$		0			0
$872$	−3.59950	+	3.59950i	−0.121894	+	0.121894i
$873$		0			0
$874$			1.82564i			0.0617530i
$875$	25.7411	+	40.3154i	0.870207	+	1.36291i
$876$		0			0
$877$	−30.8133	−	30.8133i	−1.04049	−	1.04049i	−0.999145	−	0.0413448i	$-0.986836\pi$
$877$	−30.8133	−	30.8133i	−1.04049	−	1.04049i	−0.0413448	−	0.999145i	$-0.513164\pi$
$878$	−16.5283	−	16.5283i	−0.557804	−	0.557804i
$879$		0			0
$880$	−12.1741	+	5.89899i	−0.410388	+	0.198855i
$881$			33.0964i			1.11505i	0.830161	+	0.557524i	$0.188248\pi$
$881$			33.0964i			1.11505i	−0.830161	+	0.557524i	$0.811752\pi$
$882$		0			0
$883$	35.2607	−	35.2607i	1.18662	−	1.18662i	0.208618	−	0.977997i	$-0.433103\pi$
$883$	35.2607	−	35.2607i	1.18662	−	1.18662i	0.977997	−	0.208618i	$-0.0668966\pi$
$884$	−14.2134			−0.478047
$885$		0			0
$886$	9.56828			0.321453
$887$	30.8053	−	30.8053i	1.03434	−	1.03434i	0.0349518	−	0.999389i	$-0.488872\pi$
$887$	30.8053	−	30.8053i	1.03434	−	1.03434i	0.999389	−	0.0349518i	$-0.0111278\pi$
$888$		0			0
$889$			12.4551i			0.417730i
$890$	−28.9446	−	10.0498i	−0.970225	−	0.336869i
$891$		0			0
$892$	−5.49706	−	5.49706i	−0.184055	−	0.184055i
$893$	−5.35509	−	5.35509i	−0.179201	−	0.179201i
$894$		0			0
$895$	7.68497	+	15.8599i	0.256880	+	0.530138i
$896$		−	4.27825i		−	0.142926i
$897$		0			0
$898$	−14.7001	+	14.7001i	−0.490548	+	0.490548i
$899$	−0.477172			−0.0159146
$900$		0			0
$901$	45.0875			1.50208
$902$	24.1846	−	24.1846i	0.805258	−	0.805258i
$903$		0			0
$904$		−	11.4392i		−	0.380462i
$905$	10.4349	+	21.5351i	0.346868	+	0.715851i
$906$		0			0
$907$	23.5242	+	23.5242i	0.781109	+	0.781109i	0.980018	−	0.198909i	$-0.0637399\pi$
$907$	23.5242	+	23.5242i	0.781109	+	0.781109i	−0.198909	+	0.980018i	$0.563740\pi$
$908$	−15.1349	−	15.1349i	−0.502269	−	0.502269i
$909$		0			0
$910$	37.0507	+	12.8643i	1.22822	+	0.426446i
$911$			48.9596i			1.62210i	0.584975	+	0.811051i	$0.301104\pi$
$911$			48.9596i			1.62210i	−0.584975	+	0.811051i	$0.698896\pi$
$912$		0			0
$913$	−45.0388	+	45.0388i	−1.49057	+	1.49057i
$914$	−6.70613			−0.221819
$915$		0			0
$916$	−9.08041			−0.300025
$917$	−53.4895	+	53.4895i	−1.76638	+	1.76638i
$918$		0			0
$919$			52.3323i			1.72628i	0.504962	+	0.863142i	$0.331507\pi$
$919$			52.3323i			1.72628i	−0.504962	+	0.863142i	$0.668493\pi$
$920$	3.67369	−	1.78010i	0.121118	−	0.0586880i
$921$		0			0
$922$	19.4974	+	19.4974i	0.642113	+	0.642113i
$923$	44.3115	+	44.3115i	1.45853	+	1.45853i
$924$		0			0
$925$	20.3587	−	2.39350i	0.669390	−	0.0786979i
$926$			24.0381i			0.789942i
$927$		0			0
$928$	3.17154	−	3.17154i	0.104111	−	0.104111i
$929$	−46.3140			−1.51951			−0.759756	−	0.650208i	$-0.774682\pi$
$929$	−46.3140			−1.51951			−0.759756	+	0.650208i	$0.774682\pi$
$930$		0			0
$931$	−11.3035			−0.370456
$932$	−8.57256	+	8.57256i	−0.280804	+	0.280804i
$933$		0			0
$934$			19.4881i			0.637670i
$935$	−15.3830	+	44.3050i	−0.503078	+	1.44893i
$936$		0			0
$937$	−25.9197	−	25.9197i	−0.846760	−	0.846760i	0.142967	−	0.989727i	$-0.454336\pi$
$937$	−25.9197	−	25.9197i	−0.846760	−	0.846760i	−0.989727	+	0.142967i	$0.954336\pi$
$938$		0			0
$939$		0			0
$940$	−5.55443	+	15.9974i	−0.181165	+	0.521779i
$941$		−	3.72116i		−	0.121306i	−0.998159	−	0.0606532i	$-0.980682\pi$
$941$		−	3.72116i		−	0.121306i	0.998159	−	0.0606532i	$-0.0193184\pi$
$942$		0			0
$943$	−7.29801	+	7.29801i	−0.237656	+	0.237656i
$944$	4.35348			0.141694
$945$		0			0
$946$	35.6910			1.16041
$947$	15.0544	−	15.0544i	0.489203	−	0.489203i	−0.418851	−	0.908055i	$-0.637567\pi$
$947$	15.0544	−	15.0544i	0.489203	−	0.489203i	0.908055	+	0.418851i	$0.137567\pi$
$948$		0			0
$949$			41.7284i			1.35456i
$950$	−4.96580	+	0.583812i	−0.161112	+	0.0189414i
$951$		0			0
$952$	−10.4879	−	10.4879i	−0.339914	−	0.339914i
$953$	−6.93373	−	6.93373i	−0.224606	−	0.224606i	0.585829	−	0.810435i	$-0.300769\pi$
$953$	−6.93373	−	6.93373i	−0.224606	−	0.224606i	−0.810435	+	0.585829i	$0.800769\pi$
$954$		0			0
$955$	−33.4304	+	16.1988i	−1.08178	+	0.524181i
$956$			21.9823i			0.710958i
$957$		0			0
$958$	8.17046	−	8.17046i	0.263976	−	0.263976i
$959$	8.45939			0.273168
$960$		0			0
$961$	−30.9887			−0.999635
$962$	11.8852	−	11.8852i	0.383195	−	0.383195i
$963$		0			0
$964$			15.9894i			0.514983i
$965$	23.4847	+	8.15406i	0.756000	+	0.262488i
$966$		0			0
$967$	30.1816	+	30.1816i	0.970574	+	0.970574i	0.999579	−	0.0290051i	$-0.00923392\pi$
$967$	30.1816	+	30.1816i	0.970574	+	0.970574i	−0.0290051	+	0.999579i	$0.509234\pi$
$968$	18.1028	+	18.1028i	0.581847	+	0.581847i
$969$		0			0
$970$	3.23455	+	6.67533i	0.103855	+	0.214332i
$971$			24.8445i			0.797298i	0.917104	+	0.398649i	$0.130521\pi$
$971$			24.8445i			0.797298i	−0.917104	+	0.398649i	$0.869479\pi$
$972$		0			0
$973$	45.4413	−	45.4413i	1.45678	−	1.45678i
$974$	28.2666			0.905721
$975$		0			0
$976$	−6.09068			−0.194958
$977$	−17.9692	+	17.9692i	−0.574886	+	0.574886i	−0.933490	−	0.358604i	$-0.883253\pi$
$977$	−17.9692	+	17.9692i	−0.574886	+	0.574886i	0.358604	+	0.933490i	$0.383253\pi$
$978$		0			0
$979$			82.8985i			2.64945i
$980$	11.0215	+	22.7457i	0.352069	+	0.726585i
$981$		0			0
$982$	−6.38621	−	6.38621i	−0.203792	−	0.203792i
$983$	−0.571422	−	0.571422i	−0.0182255	−	0.0182255i	0.697935	−	0.716161i	$-0.254102\pi$
$983$	−0.571422	−	0.571422i	−0.0182255	−	0.0182255i	−0.716161	+	0.697935i	$0.754102\pi$
$984$		0			0
$985$	−28.4696	−	9.88485i	−0.907117	−	0.314957i
$986$		−	15.5496i		−	0.495201i
$987$		0			0
$988$	−2.89899	+	2.89899i	−0.0922290	+	0.0922290i
$989$	−10.7702			−0.342473
$990$		0			0
$991$	−17.2167			−0.546906			−0.273453	−	0.961885i	$-0.588166\pi$
$991$	−17.2167			−0.546906			−0.273453	+	0.961885i	$0.588166\pi$
$992$	−0.0752273	+	0.0752273i	−0.00238847	+	0.00238847i
$993$		0			0
$994$			65.3938i			2.07416i
$995$	−20.9259	+	10.1397i	−0.663395	+	0.321450i
$996$		0			0
$997$	5.04553	+	5.04553i	0.159794	+	0.159794i	0.782475	−	0.622682i	$-0.213957\pi$
$997$	5.04553	+	5.04553i	0.159794	+	0.159794i	−0.622682	+	0.782475i	$0.713957\pi$
$998$	4.35236	+	4.35236i	0.137772	+	0.137772i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1710.2.n.i.647.8	yes	20
3.2	odd	2	inner	1710.2.n.i.647.3	✓	20
5.3	odd	4	inner	1710.2.n.i.1673.3	yes	20
15.8	even	4	inner	1710.2.n.i.1673.8	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1710.2.n.i.647.3	✓	20	3.2	odd	2	inner
1710.2.n.i.647.8	yes	20	1.1	even	1	trivial
1710.2.n.i.1673.3	yes	20	5.3	odd	4	inner
1710.2.n.i.1673.8	yes	20	15.8	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1710.n (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(0.975056 + 2.01228i) q^{5} +(-3.02518 - 3.02518i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.11236 + 0.733428i) q^{10} -6.04990i q^{11} +(-2.89899 + 2.89899i) q^{13} -4.27825 q^{14} -1.00000 q^{16} +(-2.45144 + 2.45144i) q^{17} +1.00000i q^{19} +(2.01228 - 0.975056i) q^{20} +(-4.27792 - 4.27792i) q^{22} +(1.29092 + 1.29092i) q^{23} +(-3.09853 + 3.92417i) q^{25} +4.09979i q^{26} +(-3.02518 + 3.02518i) q^{28} -4.48523 q^{29} +0.106387 q^{31} +(-0.707107 + 0.707107i) q^{32} +3.46686i q^{34} +(3.13779 - 9.03723i) q^{35} +(-2.89899 - 2.89899i) q^{37} +(0.707107 + 0.707107i) q^{38} +(0.733428 - 2.11236i) q^{40} +5.65335i q^{41} +(-4.17154 + 4.17154i) q^{43} -6.04990 q^{44} +1.82564 q^{46} +(-5.35509 + 5.35509i) q^{47} +11.3035i q^{49} +(0.583812 + 4.96580i) q^{50} +(2.89899 + 2.89899i) q^{52} +(-9.19614 - 9.19614i) q^{53} +(12.1741 - 5.89899i) q^{55} +4.27825i q^{56} +(-3.17154 + 3.17154i) q^{58} -4.35348 q^{59} +6.09068 q^{61} +(0.0752273 - 0.0752273i) q^{62} +1.00000i q^{64} +(-8.66024 - 3.00690i) q^{65} +(2.45144 + 2.45144i) q^{68} +(-4.17154 - 8.60904i) q^{70} -15.2852i q^{71} +(7.19707 - 7.19707i) q^{73} -4.09979 q^{74} +1.00000 q^{76} +(-18.3020 + 18.3020i) q^{77} -8.46020i q^{79} +(-0.975056 - 2.01228i) q^{80} +(3.99752 + 3.99752i) q^{82} +(-7.44455 - 7.44455i) q^{83} +(-7.32326 - 2.54269i) q^{85} +5.89944i q^{86} +(-4.27792 + 4.27792i) q^{88} -13.7025 q^{89} +17.5399 q^{91} +(1.29092 - 1.29092i) q^{92} +7.57324i q^{94} +(-2.01228 + 0.975056i) q^{95} +(2.34568 + 2.34568i) q^{97} +(7.99275 + 7.99275i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 4 q^{10} - 12 q^{13} - 20 q^{16} - 16 q^{22} + 16 q^{31} - 12 q^{37} - 8 q^{46} + 12 q^{52} + 20 q^{58} - 16 q^{61} + 20 q^{73} + 20 q^{76} - 28 q^{82} - 8 q^{85} - 16 q^{88} + 32 q^{91} - 20 q^{97}+O(q^{100}) \) 20 * q + 4 * q^10 - 12 * q^13 - 20 * q^16 - 16 * q^22 + 16 * q^31 - 12 * q^37 - 8 * q^46 + 12 * q^52 + 20 * q^58 - 16 * q^61 + 20 * q^73 + 20 * q^76 - 28 * q^82 - 8 * q^85 - 16 * q^88 + 32 * q^91 - 20 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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