LMFDB - Embedded newform 1710.2.n.g.647.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1710,2,Mod(647,1710)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage: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")

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:traces = [8,0,0,0,8,0,-8,0,0,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(10)] == traces)

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

Self dual:	no
Analytic conductor:	$13.6544187456$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.110166016.2
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 10x^{6} + 19x^{4} + 10x^{2} + 1 $ x^8 + 10x^6 + 19x^4 + 10*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			647.1
Root			$-1.22833i$ of defining polynomial
Character	$\chi$	$=$	1710.647
Dual form			1710.2.n.g.1673.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(1.70711 - 1.44423i) q^{5} +(0.414214 + 0.414214i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-0.185885 + 2.22833i) q^{10} +2.58579i q^{11} +(-2.88845 + 2.88845i) q^{13} -0.585786 q^{14} -1.00000 q^{16} +(-5.60799 + 5.60799i) q^{17} -1.00000i q^{19} +(-1.44423 - 1.70711i) q^{20} +(-1.82843 - 1.82843i) q^{22} +(-0.322905 - 0.322905i) q^{23} +(0.828427 - 4.93089i) q^{25} -4.08489i q^{26} +(0.414214 - 0.414214i) q^{28} -5.77690 q^{29} -5.13109 q^{31} +(0.707107 - 0.707107i) q^{32} -7.93089i q^{34} +(1.30532 + 0.108889i) q^{35} +(-1.41421 - 1.41421i) q^{37} +(0.707107 + 0.707107i) q^{38} +(2.22833 + 0.185885i) q^{40} +5.47424i q^{41} +(2.47424 - 2.47424i) q^{43} +2.58579 q^{44} +0.456656 q^{46} +(-9.45400 + 9.45400i) q^{47} -6.65685i q^{49} +(2.90088 + 4.07245i) q^{50} +(2.88845 + 2.88845i) q^{52} +(4.24264 + 4.24264i) q^{53} +(3.73446 + 4.41421i) q^{55} +0.585786i q^{56} +(4.08489 - 4.08489i) q^{58} -0.302664 q^{59} +1.25646 q^{61} +(3.62823 - 3.62823i) q^{62} +1.00000i q^{64} +(-0.759320 + 9.10247i) q^{65} +(4.30266 + 4.30266i) q^{67} +(5.60799 + 5.60799i) q^{68} +(-1.00000 + 0.846008i) q^{70} +7.25646i q^{71} +(-1.82843 + 1.82843i) q^{73} +2.00000 q^{74} -1.00000 q^{76} +(-1.07107 + 1.07107i) q^{77} -2.61065i q^{79} +(-1.70711 + 1.44423i) q^{80} +(-3.87087 - 3.87087i) q^{82} +(-5.45023 - 5.45023i) q^{83} +(-1.47424 + 17.6726i) q^{85} +3.49910i q^{86} +(-1.82843 + 1.82843i) q^{88} +7.43908 q^{89} -2.39287 q^{91} +(-0.322905 + 0.322905i) q^{92} -13.3700i q^{94} +(-1.44423 - 1.70711i) q^{95} +(-6.23356 - 6.23356i) q^{97} +(4.70711 + 4.70711i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{5} - 8 q^{7} - 4 q^{10} - 16 q^{14} - 8 q^{16} + 8 q^{22} - 8 q^{23} - 16 q^{25} - 8 q^{28} + 16 q^{31} + 4 q^{40} + 8 q^{43} + 32 q^{44} - 24 q^{46} - 24 q^{47} - 16 q^{50} + 32 q^{59} + 24 q^{62}+ \cdots + 32 q^{98}+O(q^{100}) $ 8 * q + 8 * q^5 - 8 * q^7 - 4 * q^10 - 16 * q^14 - 8 * q^16 + 8 * q^22 - 8 * q^23 - 16 * q^25 - 8 * q^28 + 16 * q^31 + 4 * q^40 + 8 * q^43 + 32 * q^44 - 24 * q^46 - 24 * q^47 - 16 * q^50 + 32 * q^59 + 24 * q^62 + 56 * q^65 - 8 * q^70 + 8 * q^73 + 16 * q^74 - 8 * q^76 + 48 * q^77 - 8 * q^80 + 8 * q^82 + 8 * q^88 + 16 * q^89 - 8 * q^92 + 24 * q^97 + 32 * q^98

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
$5$	1.70711	−	1.44423i	0.763441	−	0.645877i
$5$	1.70711	−	1.44423i	0.763441	−	0.645877i
$6$		0			0
$7$	0.414214	+	0.414214i	0.156558	+	0.156558i	0.781040	−	0.624482i	$-0.214690\pi$
$7$	0.414214	+	0.414214i	0.156558	+	0.156558i	−0.624482	+	0.781040i	$0.714690\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$		0			0
$10$	−0.185885	+	2.22833i	−0.0587821	+	0.704659i
$11$			2.58579i			0.779644i	0.920890	+	0.389822i	$0.127463\pi$
$11$			2.58579i			0.779644i	−0.920890	+	0.389822i	$0.872537\pi$
$12$		0			0
$13$	−2.88845	+	2.88845i	−0.801112	+	0.801112i	−0.983269	−	0.182157i	$-0.941692\pi$
$13$	−2.88845	+	2.88845i	−0.801112	+	0.801112i	0.182157	+	0.983269i	$0.441692\pi$
$14$	−0.585786			−0.156558
$15$		0			0
$16$	−1.00000			−0.250000
$17$	−5.60799	+	5.60799i	−1.36014	+	1.36014i	−0.486402	+	0.873735i	$0.661691\pi$
$17$	−5.60799	+	5.60799i	−1.36014	+	1.36014i	−0.873735	+	0.486402i	$0.838309\pi$
$18$		0			0
$19$		−	1.00000i		−	0.229416i
$19$		−	1.00000i		−	0.229416i
$20$	−1.44423	−	1.70711i	−0.322939	−	0.381721i
$21$		0			0
$22$	−1.82843	−	1.82843i	−0.389822	−	0.389822i
$23$	−0.322905	−	0.322905i	−0.0673303	−	0.0673303i	0.672640	−	0.739970i	$-0.265160\pi$
$23$	−0.322905	−	0.322905i	−0.0673303	−	0.0673303i	−0.739970	+	0.672640i	$0.765160\pi$
$24$		0			0
$25$	0.828427	−	4.93089i	0.165685	−	0.986179i
$26$		−	4.08489i		−	0.801112i
$27$		0			0
$28$	0.414214	−	0.414214i	0.0782790	−	0.0782790i
$29$	−5.77690			−1.07274			−0.536372	−	0.843982i	$-0.680205\pi$
$29$	−5.77690			−1.07274			−0.536372	+	0.843982i	$0.680205\pi$
$30$		0			0
$31$	−5.13109			−0.921571			−0.460786	−	0.887511i	$-0.652432\pi$
$31$	−5.13109			−0.921571			−0.460786	+	0.887511i	$0.652432\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$		0			0
$34$		−	7.93089i		−	1.36014i
$35$	1.30532	+	0.108889i	0.220640	+	0.0184056i
$36$		0			0
$37$	−1.41421	−	1.41421i	−0.232495	−	0.232495i	0.581238	−	0.813733i	$-0.302568\pi$
$37$	−1.41421	−	1.41421i	−0.232495	−	0.232495i	−0.813733	+	0.581238i	$0.802568\pi$
$38$	0.707107	+	0.707107i	0.114708	+	0.114708i
$39$		0			0
$40$	2.22833	+	0.185885i	0.352330	+	0.0293911i
$41$			5.47424i			0.854932i	0.904031	+	0.427466i	$0.140594\pi$
$41$			5.47424i			0.854932i	−0.904031	+	0.427466i	$0.859406\pi$
$42$		0			0
$43$	2.47424	−	2.47424i	0.377318	−	0.377318i	−0.492816	−	0.870134i	$-0.664032\pi$
$43$	2.47424	−	2.47424i	0.377318	−	0.377318i	0.870134	+	0.492816i	$0.164032\pi$
$44$	2.58579			0.389822
$45$		0			0
$46$	0.456656			0.0673303
$47$	−9.45400	+	9.45400i	−1.37901	+	1.37901i	−0.532708	+	0.846299i	$0.678826\pi$
$47$	−9.45400	+	9.45400i	−1.37901	+	1.37901i	−0.846299	+	0.532708i	$0.821174\pi$
$48$		0			0
$49$		−	6.65685i		−	0.950979i
$50$	2.90088	+	4.07245i	0.410247	+	0.575932i
$51$		0			0
$52$	2.88845	+	2.88845i	0.400556	+	0.400556i
$53$	4.24264	+	4.24264i	0.582772	+	0.582772i	0.935664	−	0.352892i	$-0.114802\pi$
$53$	4.24264	+	4.24264i	0.582772	+	0.582772i	−0.352892	+	0.935664i	$0.614802\pi$
$54$		0			0
$55$	3.73446	+	4.41421i	0.503554	+	0.595212i
$56$			0.585786i			0.0782790i
$57$		0			0
$58$	4.08489	−	4.08489i	0.536372	−	0.536372i
$59$	−0.302664			−0.0394035			−0.0197017	−	0.999806i	$-0.506272\pi$
$59$	−0.302664			−0.0394035			−0.0197017	+	0.999806i	$0.506272\pi$
$60$		0			0
$61$	1.25646			0.160873			0.0804365	−	0.996760i	$-0.474369\pi$
$61$	1.25646			0.160873			0.0804365	+	0.996760i	$0.474369\pi$
$62$	3.62823	−	3.62823i	0.460786	−	0.460786i
$63$		0			0
$64$			1.00000i			0.125000i
$65$	−0.759320	+	9.10247i	−0.0941821	+	1.12902i
$66$		0			0
$67$	4.30266	+	4.30266i	0.525654	+	0.525654i	0.919273	−	0.393619i	$-0.128777\pi$
$67$	4.30266	+	4.30266i	0.525654	+	0.525654i	−0.393619	+	0.919273i	$0.628777\pi$
$68$	5.60799	+	5.60799i	0.680068	+	0.680068i
$69$		0			0
$70$	−1.00000	+	0.846008i	−0.119523	+	0.101117i
$71$			7.25646i			0.861183i	0.902547	+	0.430592i	$0.141695\pi$
$71$			7.25646i			0.861183i	−0.902547	+	0.430592i	$0.858305\pi$
$72$		0			0
$73$	−1.82843	+	1.82843i	−0.214001	+	0.214001i	−0.805965	−	0.591964i	$-0.798353\pi$
$73$	−1.82843	+	1.82843i	−0.214001	+	0.214001i	0.591964	+	0.805965i	$0.298353\pi$
$74$	2.00000			0.232495
$75$		0			0
$76$	−1.00000			−0.114708
$77$	−1.07107	+	1.07107i	−0.122060	+	0.122060i
$78$		0			0
$79$		−	2.61065i		−	0.293721i	−0.989157	−	0.146860i	$-0.953083\pi$
$79$		−	2.61065i		−	0.293721i	0.989157	−	0.146860i	$-0.0469168\pi$
$80$	−1.70711	+	1.44423i	−0.190860	+	0.161469i
$81$		0			0
$82$	−3.87087	−	3.87087i	−0.427466	−	0.427466i
$83$	−5.45023	−	5.45023i	−0.598241	−	0.598241i	0.341603	−	0.939844i	$-0.389030\pi$
$83$	−5.45023	−	5.45023i	−0.598241	−	0.598241i	−0.939844	+	0.341603i	$0.889030\pi$
$84$		0			0
$85$	−1.47424	+	17.6726i	−0.159903	+	1.91687i
$86$			3.49910i			0.377318i
$87$		0			0
$88$	−1.82843	+	1.82843i	−0.194911	+	0.194911i
$89$	7.43908			0.788540			0.394270	−	0.918995i	$-0.370997\pi$
$89$	7.43908			0.788540			0.394270	+	0.918995i	$0.370997\pi$
$90$		0			0
$91$	−2.39287			−0.250841
$92$	−0.322905	+	0.322905i	−0.0336652	+	0.0336652i
$93$		0			0
$94$		−	13.3700i		−	1.37901i
$95$	−1.44423	−	1.70711i	−0.148174	−	0.175145i
$96$		0			0
$97$	−6.23356	−	6.23356i	−0.632922	−	0.632922i	0.315878	−	0.948800i	$-0.397701\pi$
$97$	−6.23356	−	6.23356i	−0.632922	−	0.632922i	−0.948800	+	0.315878i	$0.897701\pi$
$98$	4.70711	+	4.70711i	0.475490	+	0.475490i
$99$		0			0
$100$	−4.93089	−	0.828427i	−0.493089	−	0.0828427i
$101$		−	1.75736i		−	0.174864i	−0.996170	−	0.0874319i	$-0.972134\pi$
$101$		−	1.75736i		−	0.174864i	0.996170	−	0.0874319i	$-0.0278660\pi$
$102$		0			0
$103$	−1.56821	+	1.56821i	−0.154520	+	0.154520i	−0.780133	−	0.625613i	$-0.784849\pi$
$103$	−1.56821	+	1.56821i	−0.154520	+	0.154520i	0.625613	+	0.780133i	$0.284849\pi$
$104$	−4.08489			−0.400556
$105$		0			0
$106$	−6.00000			−0.582772
$107$	−8.82843	+	8.82843i	−0.853476	+	0.853476i	−0.990560	−	0.137083i	$-0.956227\pi$
$107$	−8.82843	+	8.82843i	−0.853476	+	0.853476i	0.137083	+	0.990560i	$0.456227\pi$
$108$		0			0
$109$			6.81558i			0.652814i	0.945229	+	0.326407i	$0.105838\pi$
$109$			6.81558i			0.652814i	−0.945229	+	0.326407i	$0.894162\pi$
$110$	−5.76198	−	0.480660i	−0.549383	−	0.0458291i
$111$		0			0
$112$	−0.414214	−	0.414214i	−0.0391395	−	0.0391395i
$113$	8.32753	+	8.32753i	0.783388	+	0.783388i	0.980401	−	0.197013i	$-0.0631241\pi$
$113$	8.32753	+	8.32753i	0.783388	+	0.783388i	−0.197013	+	0.980401i	$0.563124\pi$
$114$		0			0
$115$	−1.01758	−	0.0848857i	−0.0948899	−	0.00791564i
$116$			5.77690i			0.536372i
$117$		0			0
$118$	0.214016	−	0.214016i	0.0197017	−	0.0197017i
$119$	−4.64581			−0.425881
$120$		0			0
$121$	4.31371			0.392155
$122$	−0.888450	+	0.888450i	−0.0804365	+	0.0804365i
$123$		0			0
$124$			5.13109i			0.460786i
$125$	−5.70711	−	9.61400i	−0.510459	−	0.859902i
$126$		0			0
$127$	0.311747	+	0.311747i	0.0276631	+	0.0276631i	0.720803	−	0.693140i	$-0.243773\pi$
$127$	0.311747	+	0.311747i	0.0276631	+	0.0276631i	−0.693140	+	0.720803i	$0.743773\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$		0			0
$130$	−5.89949	−	6.97334i	−0.517420	−	0.611602i
$131$		−	8.46042i		−	0.739190i	−0.929193	−	0.369595i	$-0.879496\pi$
$131$		−	8.46042i		−	0.739190i	0.929193	−	0.369595i	$-0.120504\pi$
$132$		0			0
$133$	0.414214	−	0.414214i	0.0359169	−	0.0359169i
$134$	−6.08489			−0.525654
$135$		0			0
$136$	−7.93089			−0.680068
$137$	−7.52310	+	7.52310i	−0.642742	+	0.642742i	−0.951229	−	0.308487i	$-0.900177\pi$
$137$	−7.52310	+	7.52310i	−0.642742	+	0.642742i	0.308487	+	0.951229i	$0.400177\pi$
$138$		0			0
$139$		−	8.20493i		−	0.695933i	−0.937507	−	0.347967i	$-0.886872\pi$
$139$		−	8.20493i		−	0.695933i	0.937507	−	0.347967i	$-0.113128\pi$
$140$	0.108889	−	1.30532i	0.00920281	−	0.110320i
$141$		0			0
$142$	−5.13109	−	5.13109i	−0.430592	−	0.430592i
$143$	−7.46892	−	7.46892i	−0.624582	−	0.624582i
$144$		0			0
$145$	−9.86179	+	8.34315i	−0.818977	+	0.692861i
$146$		−	2.58579i		−	0.214001i
$147$		0			0
$148$	−1.41421	+	1.41421i	−0.116248	+	0.116248i
$149$	18.4920			1.51492			0.757461	−	0.652881i	$-0.226440\pi$
$149$	18.4920			1.51492			0.757461	+	0.652881i	$0.226440\pi$
$150$		0			0
$151$	−15.9595			−1.29877			−0.649384	−	0.760461i	$-0.724973\pi$
$151$	−15.9595			−1.29877			−0.649384	+	0.760461i	$0.724973\pi$
$152$	0.707107	−	0.707107i	0.0573539	−	0.0573539i
$153$		0			0
$154$		−	1.51472i		−	0.122060i
$155$	−8.75932	+	7.41045i	−0.703566	+	0.595222i
$156$		0			0
$157$	13.6302	+	13.6302i	1.08781	+	1.08781i	0.995754	+	0.0920536i	$0.0293431\pi$
$157$	13.6302	+	13.6302i	1.08781	+	1.08781i	0.0920536	+	0.995754i	$0.470657\pi$
$158$	1.84601	+	1.84601i	0.146860	+	0.146860i
$159$		0			0
$160$	0.185885	−	2.22833i	0.0146955	−	0.176165i
$161$		−	0.267503i		−	0.0210822i
$162$		0			0
$163$	7.14867	−	7.14867i	0.559927	−	0.559927i	−0.369359	−	0.929287i	$-0.620423\pi$
$163$	7.14867	−	7.14867i	0.559927	−	0.559927i	0.929287	+	0.369359i	$0.120423\pi$
$164$	5.47424			0.427466
$165$		0			0
$166$	7.70779			0.598241
$167$	15.9467	−	15.9467i	1.23399	−	1.23399i	0.271573	−	0.962418i	$-0.412456\pi$
$167$	15.9467	−	15.9467i	1.23399	−	1.23399i	0.962418	−	0.271573i	$-0.0875437\pi$
$168$		0			0
$169$		−	3.68629i		−	0.283561i
$170$	−11.4540	−	13.5389i	−0.878481	−	1.03838i
$171$		0			0
$172$	−2.47424	−	2.47424i	−0.188659	−	0.188659i
$173$	4.76840	+	4.76840i	0.362535	+	0.362535i	0.864745	−	0.502210i	$-0.167480\pi$
$173$	4.76840	+	4.76840i	0.362535	+	0.362535i	−0.502210	+	0.864745i	$0.667480\pi$
$174$		0			0
$175$	2.38559	−	1.69930i	0.180334	−	0.128455i
$176$		−	2.58579i		−	0.194911i
$177$		0			0
$178$	−5.26022	+	5.26022i	−0.394270	+	0.394270i
$179$	−19.7289			−1.47461			−0.737303	−	0.675562i	$-0.763901\pi$
$179$	−19.7289			−1.47461			−0.737303	+	0.675562i	$0.763901\pi$
$180$		0			0
$181$	3.87463			0.287999			0.144000	−	0.989578i	$-0.454004\pi$
$181$	3.87463			0.287999			0.144000	+	0.989578i	$0.454004\pi$
$182$	1.69202	−	1.69202i	0.125421	−	0.125421i
$183$		0			0
$184$		−	0.456656i		−	0.0336652i
$185$	−4.45666	−	0.371771i	−0.327660	−	0.0273331i
$186$		0			0
$187$	−14.5011	−	14.5011i	−1.06042	−	1.06042i
$188$	9.45400	+	9.45400i	0.689504	+	0.689504i
$189$		0			0
$190$	2.22833	+	0.185885i	0.161660	+	0.0134855i
$191$		−	25.5382i		−	1.84788i	−0.382540	−	0.923939i	$-0.624951\pi$
$191$		−	25.5382i		−	1.84788i	0.382540	−	0.923939i	$-0.375049\pi$
$192$		0			0
$193$	−10.5362	+	10.5362i	−0.758414	+	0.758414i	−0.976034	−	0.217620i	$-0.930171\pi$
$193$	−10.5362	+	10.5362i	−0.758414	+	0.758414i	0.217620	+	0.976034i	$0.430171\pi$
$194$	8.81558			0.632922
$195$		0			0
$196$	−6.65685			−0.475490
$197$	−13.1357	+	13.1357i	−0.935881	+	0.935881i	−0.998065	−	0.0621839i	$-0.980193\pi$
$197$	−13.1357	+	13.1357i	−0.935881	+	0.935881i	0.0621839	+	0.998065i	$0.480193\pi$
$198$		0			0
$199$			24.0039i			1.70159i	0.525495	+	0.850796i	$0.323880\pi$
$199$			24.0039i			1.70159i	−0.525495	+	0.850796i	$0.676120\pi$
$200$	4.07245	−	2.90088i	0.287966	−	0.205123i
$201$		0			0
$202$	1.24264	+	1.24264i	0.0874319	+	0.0874319i
$203$	−2.39287	−	2.39287i	−0.167947	−	0.167947i
$204$		0			0
$205$	7.90603	+	9.34511i	0.552181	+	0.652691i
$206$		−	2.21778i		−	0.154520i
$207$		0			0
$208$	2.88845	−	2.88845i	0.200278	−	0.200278i
$209$	2.58579			0.178863
$210$		0			0
$211$	−22.8600			−1.57375			−0.786873	−	0.617115i	$-0.788301\pi$
$211$	−22.8600			−1.57375			−0.786873	+	0.617115i	$0.788301\pi$
$212$	4.24264	−	4.24264i	0.291386	−	0.291386i
$213$		0			0
$214$		−	12.4853i		−	0.853476i
$215$	0.650431	−	7.79714i	0.0443590	−	0.531761i
$216$		0			0
$217$	−2.12537	−	2.12537i	−0.144279	−	0.144279i
$218$	−4.81934	−	4.81934i	−0.326407	−	0.326407i
$219$		0			0
$220$	4.41421	−	3.73446i	0.297606	−	0.251777i
$221$		−	32.3968i		−	2.17924i
$222$		0			0
$223$	−2.33406	+	2.33406i	−0.156300	+	0.156300i	−0.780925	−	0.624625i	$-0.785252\pi$
$223$	−2.33406	+	2.33406i	−0.156300	+	0.156300i	0.624625	+	0.780925i	$0.285252\pi$
$224$	0.585786			0.0391395
$225$		0			0
$226$	−11.7769			−0.783388
$227$	−5.35419	+	5.35419i	−0.355370	+	0.355370i	−0.862103	−	0.506733i	$-0.830853\pi$
$227$	−5.35419	+	5.35419i	−0.355370	+	0.355370i	0.506733	+	0.862103i	$0.330853\pi$
$228$		0			0
$229$		−	6.96664i		−	0.460369i	−0.973147	−	0.230184i	$-0.926067\pi$
$229$		−	6.96664i		−	0.460369i	0.973147	−	0.230184i	$-0.0739329\pi$
$230$	0.779561	−	0.659515i	0.0514027	−	0.0434871i
$231$		0			0
$232$	−4.08489	−	4.08489i	−0.268186	−	0.268186i
$233$	12.3635	+	12.3635i	0.809963	+	0.809963i	0.984628	−	0.174665i	$-0.0558843\pi$
$233$	12.3635	+	12.3635i	0.809963	+	0.809963i	−0.174665	+	0.984628i	$0.555884\pi$
$234$		0			0
$235$	−2.48528	+	29.7927i	−0.162122	+	1.94346i
$236$			0.302664i			0.0197017i
$237$		0			0
$238$	3.28508	−	3.28508i	0.212940	−	0.212940i
$239$	−14.6302			−0.946348			−0.473174	−	0.880969i	$-0.656892\pi$
$239$	−14.6302			−0.946348			−0.473174	+	0.880969i	$0.656892\pi$
$240$		0			0
$241$	18.8951			1.21714			0.608572	−	0.793499i	$-0.291743\pi$
$241$	18.8951			1.21714			0.608572	+	0.793499i	$0.291743\pi$
$242$	−3.05025	+	3.05025i	−0.196078	+	0.196078i
$243$		0			0
$244$		−	1.25646i		−	0.0804365i
$245$	−9.61400	−	11.3640i	−0.614216	−	0.726017i
$246$		0			0
$247$	2.88845	+	2.88845i	0.183788	+	0.183788i
$248$	−3.62823	−	3.62823i	−0.230393	−	0.230393i
$249$		0			0
$250$	10.8337	+	2.76259i	0.685181	+	0.174721i
$251$		−	27.6987i		−	1.74833i	−0.485632	−	0.874164i	$-0.661410\pi$
$251$		−	27.6987i		−	1.74833i	0.485632	−	0.874164i	$-0.338590\pi$
$252$		0			0
$253$	0.834963	−	0.834963i	0.0524937	−	0.0524937i
$254$	−0.440877			−0.0276631
$255$		0			0
$256$	1.00000			0.0625000
$257$	−6.76840	+	6.76840i	−0.422201	+	0.422201i	−0.885961	−	0.463760i	$-0.846500\pi$
$257$	−6.76840	+	6.76840i	−0.422201	+	0.422201i	0.463760	+	0.885961i	$0.346500\pi$
$258$		0			0
$259$		−	1.17157i		−	0.0727980i
$260$	9.10247	+	0.759320i	0.564511	+	0.0470911i
$261$		0			0
$262$	5.98242	+	5.98242i	0.369595	+	0.369595i
$263$	17.9016	+	17.9016i	1.10386	+	1.10386i	0.993941	+	0.109917i	$0.0350586\pi$
$263$	17.9016	+	17.9016i	1.10386	+	1.10386i	0.109917	+	0.993941i	$0.464941\pi$
$264$		0			0
$265$	13.3700	+	1.11531i	0.821311	+	0.0685131i
$266$			0.585786i			0.0359169i
$267$		0			0
$268$	4.30266	−	4.30266i	0.262827	−	0.262827i
$269$	−12.8636			−0.784307			−0.392153	−	0.919900i	$-0.628270\pi$
$269$	−12.8636			−0.784307			−0.392153	+	0.919900i	$0.628270\pi$
$270$		0			0
$271$	2.62349			0.159366			0.0796830	−	0.996820i	$-0.474609\pi$
$271$	2.62349			0.159366			0.0796830	+	0.996820i	$0.474609\pi$
$272$	5.60799	−	5.60799i	0.340034	−	0.340034i
$273$		0			0
$274$		−	10.6393i		−	0.642742i
$275$	12.7502	+	2.14214i	0.768868	+	0.129176i
$276$		0			0
$277$	21.0916	+	21.0916i	1.26727	+	1.26727i	0.947493	+	0.319778i	$0.103608\pi$
$277$	21.0916	+	21.0916i	1.26727	+	1.26727i	0.319778	+	0.947493i	$0.396392\pi$
$278$	5.80176	+	5.80176i	0.347967	+	0.347967i
$279$		0			0
$280$	0.846008	+	1.00000i	0.0505586	+	0.0597614i
$281$			20.0262i			1.19467i	0.801994	+	0.597333i	$0.203773\pi$
$281$			20.0262i			1.19467i	−0.801994	+	0.597333i	$0.796227\pi$
$282$		0			0
$283$	2.01104	−	2.01104i	0.119544	−	0.119544i	−0.644804	−	0.764348i	$-0.723061\pi$
$283$	2.01104	−	2.01104i	0.119544	−	0.119544i	0.764348	+	0.644804i	$0.223061\pi$
$284$	7.25646			0.430592
$285$		0			0
$286$	10.5626			0.624582
$287$	−2.26750	+	2.26750i	−0.133846	+	0.133846i
$288$		0			0
$289$		−	45.8991i		−	2.69995i
$290$	1.07384	−	12.8728i	0.0630581	−	0.755919i
$291$		0			0
$292$	1.82843	+	1.82843i	0.107001	+	0.107001i
$293$	14.8480	+	14.8480i	0.867428	+	0.867428i	0.992187	−	0.124759i	$-0.0398159\pi$
$293$	14.8480	+	14.8480i	0.867428	+	0.867428i	−0.124759	+	0.992187i	$0.539816\pi$
$294$		0			0
$295$	−0.516680	+	0.437115i	−0.0300823	+	0.0254498i
$296$		−	2.00000i		−	0.116248i
$297$		0			0
$298$	−13.0758	+	13.0758i	−0.757461	+	0.757461i
$299$	1.86539			0.107878
$300$		0			0
$301$	2.04972			0.118144
$302$	11.2851	−	11.2851i	0.649384	−	0.649384i
$303$		0			0
$304$			1.00000i			0.0573539i
$305$	2.14491	−	1.81461i	0.122817	−	0.103904i
$306$		0			0
$307$	10.2675	+	10.2675i	0.585997	+	0.585997i	0.936545	−	0.350548i	$-0.114005\pi$
$307$	10.2675	+	10.2675i	0.585997	+	0.585997i	−0.350548	+	0.936545i	$0.614005\pi$
$308$	1.07107	+	1.07107i	0.0610298	+	0.0610298i
$309$		0			0
$310$	0.953795	−	11.4338i	0.0541719	−	0.649394i
$311$		−	14.8257i		−	0.840686i	−0.907365	−	0.420343i	$-0.861910\pi$
$311$		−	14.8257i		−	0.840686i	0.907365	−	0.420343i	$-0.138090\pi$
$312$		0			0
$313$	16.9881	−	16.9881i	0.960227	−	0.960227i	−0.0390121	−	0.999239i	$-0.512421\pi$
$313$	16.9881	−	16.9881i	0.960227	−	0.960227i	0.999239	+	0.0390121i	$0.0124211\pi$
$314$	−19.2760			−1.08781
$315$		0			0
$316$	−2.61065			−0.146860
$317$	−3.53426	+	3.53426i	−0.198504	+	0.198504i	−0.799358	−	0.600855i	$-0.794827\pi$
$317$	−3.53426	+	3.53426i	−0.198504	+	0.198504i	0.600855	+	0.799358i	$0.294827\pi$
$318$		0			0
$319$		−	14.9378i		−	0.836358i
$320$	1.44423	+	1.70711i	0.0807346	+	0.0954302i
$321$		0			0
$322$	0.189153	+	0.189153i	0.0105411	+	0.0105411i
$323$	5.60799	+	5.60799i	0.312037	+	0.312037i
$324$		0			0
$325$	11.8498	+	16.6355i	0.657307	+	0.922772i
$326$			10.1097i			0.559927i
$327$		0			0
$328$	−3.87087	+	3.87087i	−0.213733	+	0.213733i
$329$	−7.83195			−0.431789
$330$		0			0
$331$	−26.6274			−1.46358			−0.731788	−	0.681533i	$-0.761314\pi$
$331$	−26.6274			−1.46358			−0.731788	+	0.681533i	$0.761314\pi$
$332$	−5.45023	+	5.45023i	−0.299120	+	0.299120i
$333$		0			0
$334$			22.5520i			1.23399i
$335$	13.5591	+	1.13109i	0.740814	+	0.0617981i
$336$		0			0
$337$	14.9291	+	14.9291i	0.813239	+	0.813239i	0.985118	−	0.171879i	$-0.0549837\pi$
$337$	14.9291	+	14.9291i	0.813239	+	0.813239i	−0.171879	+	0.985118i	$0.554984\pi$
$338$	2.60660	+	2.60660i	0.141780	+	0.141780i
$339$		0			0
$340$	17.6726	+	1.47424i	0.958433	+	0.0799517i
$341$		−	13.2679i		−	0.718497i
$342$		0			0
$343$	5.65685	−	5.65685i	0.305441	−	0.305441i
$344$	3.49910			0.188659
$345$		0			0
$346$	−6.74354			−0.362535
$347$	−0.844906	+	0.844906i	−0.0453569	+	0.0453569i	−0.729421	−	0.684065i	$-0.760211\pi$
$347$	−0.844906	+	0.844906i	−0.0453569	+	0.0453569i	0.684065	+	0.729421i	$0.260211\pi$
$348$		0			0
$349$			2.94095i			0.157425i	0.996897	+	0.0787127i	$0.0250810\pi$
$349$			2.94095i			0.157425i	−0.996897	+	0.0787127i	$0.974919\pi$
$350$	−0.485281	+	2.88845i	−0.0259394	+	0.154394i
$351$		0			0
$352$	1.82843	+	1.82843i	0.0974555	+	0.0974555i
$353$	−22.1404	−	22.1404i	−1.17842	−	1.17842i	−0.980148	−	0.198270i	$-0.936468\pi$
$353$	−22.1404	−	22.1404i	−1.17842	−	1.17842i	−0.198270	−	0.980148i	$-0.563532\pi$
$354$		0			0
$355$	10.4800	+	12.3875i	0.556219	+	0.657463i
$356$		−	7.43908i		−	0.394270i
$357$		0			0
$358$	13.9504	−	13.9504i	0.737303	−	0.737303i
$359$	33.7080			1.77904			0.889519	−	0.456898i	$-0.151040\pi$
$359$	33.7080			1.77904			0.889519	+	0.456898i	$0.151040\pi$
$360$		0			0
$361$	−1.00000			−0.0526316
$362$	−2.73978	+	2.73978i	−0.144000	+	0.144000i
$363$		0			0
$364$			2.39287i			0.125421i
$365$	−0.480660	+	5.76198i	−0.0251589	+	0.301596i
$366$		0			0
$367$	−11.6993	−	11.6993i	−0.610698	−	0.610698i	0.332430	−	0.943128i	$-0.392132\pi$
$367$	−11.6993	−	11.6993i	−0.610698	−	0.610698i	−0.943128	+	0.332430i	$0.892132\pi$
$368$	0.322905	+	0.322905i	0.0168326	+	0.0168326i
$369$		0			0
$370$	3.41421	−	2.88845i	0.177497	−	0.150163i
$371$			3.51472i			0.182475i
$372$		0			0
$373$	20.4476	−	20.4476i	1.05874	−	1.05874i	0.0605713	−	0.998164i	$-0.480708\pi$
$373$	20.4476	−	20.4476i	1.05874	−	1.05874i	0.998164	−	0.0605713i	$-0.0192923\pi$
$374$	20.5076			1.06042
$375$		0			0
$376$	−13.3700			−0.689504
$377$	16.6863	−	16.6863i	0.859388	−	0.859388i
$378$		0			0
$379$			22.0039i			1.13027i	0.825000	+	0.565133i	$0.191175\pi$
$379$			22.0039i			1.13027i	−0.825000	+	0.565133i	$0.808825\pi$
$380$	−1.70711	+	1.44423i	−0.0875727	+	0.0740872i
$381$		0			0
$382$	18.0582	+	18.0582i	0.923939	+	0.923939i
$383$	−16.3471	−	16.3471i	−0.835296	−	0.835296i	0.152939	−	0.988236i	$-0.451126\pi$
$383$	−16.3471	−	16.3471i	−0.835296	−	0.835296i	−0.988236	+	0.152939i	$0.951126\pi$
$384$		0			0
$385$	−0.281564	+	3.37529i	−0.0143498	+	0.172021i
$386$		−	14.9005i		−	0.758414i
$387$		0			0
$388$	−6.23356	+	6.23356i	−0.316461	+	0.316461i
$389$	16.6355			0.843454			0.421727	−	0.906723i	$-0.361424\pi$
$389$	16.6355			0.843454			0.421727	+	0.906723i	$0.361424\pi$
$390$		0			0
$391$	3.62169			0.183157
$392$	4.70711	−	4.70711i	0.237745	−	0.237745i
$393$		0			0
$394$		−	18.5767i		−	0.935881i
$395$	−3.77036	−	4.45666i	−0.189708	−	0.224239i
$396$		0			0
$397$	−4.83039	−	4.83039i	−0.242430	−	0.242430i	0.575425	−	0.817855i	$-0.304837\pi$
$397$	−4.83039	−	4.83039i	−0.242430	−	0.242430i	−0.817855	+	0.575425i	$0.804837\pi$
$398$	−16.9733	−	16.9733i	−0.850796	−	0.850796i
$399$		0			0
$400$	−0.828427	+	4.93089i	−0.0414214	+	0.246545i
$401$		−	0.0625708i		−	0.00312464i	−0.999999	−	0.00156232i	$-0.999503\pi$
$401$		−	0.0625708i		−	0.00312464i	0.999999	−	0.00156232i	$-0.000497302\pi$
$402$		0			0
$403$	14.8209	−	14.8209i	0.738282	−	0.738282i
$404$	−1.75736			−0.0874319
$405$		0			0
$406$	3.38403			0.167947
$407$	3.65685	−	3.65685i	0.181264	−	0.181264i
$408$		0			0
$409$		−	1.75991i		−	0.0870218i	−0.999053	−	0.0435109i	$-0.986146\pi$
$409$		−	1.75991i		−	0.0870218i	0.999053	−	0.0435109i	$-0.0138543\pi$
$410$	−12.1984	−	1.01758i	−0.602436	−	0.0502547i
$411$		0			0
$412$	1.56821	+	1.56821i	0.0772600	+	0.0772600i
$413$	−0.125368	−	0.125368i	−0.00616893	−	0.00616893i
$414$		0			0
$415$	−17.1755	−	1.43277i	−0.843112	−	0.0703317i
$416$			4.08489i			0.200278i
$417$		0			0
$418$	−1.82843	+	1.82843i	−0.0894313	+	0.0894313i
$419$	10.9147			0.533217			0.266609	−	0.963805i	$-0.414097\pi$
$419$	10.9147			0.533217			0.266609	+	0.963805i	$0.414097\pi$
$420$		0			0
$421$	17.1350			0.835109			0.417555	−	0.908652i	$-0.362887\pi$
$421$	17.1350			0.835109			0.417555	+	0.908652i	$0.362887\pi$
$422$	16.1645	−	16.1645i	0.786873	−	0.786873i
$423$		0			0
$424$			6.00000i			0.291386i
$425$	23.0066	+	32.2982i	1.11598	+	1.56669i
$426$		0			0
$427$	0.520442	+	0.520442i	0.0251860	+	0.0251860i
$428$	8.82843	+	8.82843i	0.426738	+	0.426738i
$429$		0			0
$430$	5.05349	+	5.97334i	0.243701	+	0.288060i
$431$			17.5814i			0.846868i	0.905927	+	0.423434i	$0.139175\pi$
$431$			17.5814i			0.846868i	−0.905927	+	0.423434i	$0.860825\pi$
$432$		0			0
$433$	−20.4829	+	20.4829i	−0.984345	+	0.984345i	−0.999879	−	0.0155343i	$-0.995055\pi$
$433$	−20.4829	+	20.4829i	−0.984345	+	0.984345i	0.0155343	+	0.999879i	$0.495055\pi$
$434$	3.00572			0.144279
$435$		0			0
$436$	6.81558			0.326407
$437$	−0.322905	+	0.322905i	−0.0154466	+	0.0154466i
$438$		0			0
$439$			37.2199i			1.77641i	0.459448	+	0.888204i	$0.348047\pi$
$439$			37.2199i			1.77641i	−0.459448	+	0.888204i	$0.651953\pi$
$440$	−0.480660	+	5.76198i	−0.0229146	+	0.274692i
$441$		0			0
$442$	22.9080	+	22.9080i	1.08962	+	1.08962i
$443$	11.8978	+	11.8978i	0.565282	+	0.565282i	0.930803	−	0.365521i	$-0.119109\pi$
$443$	11.8978	+	11.8978i	0.565282	+	0.565282i	−0.365521	+	0.930803i	$0.619109\pi$
$444$		0			0
$445$	12.6993	−	10.7437i	0.602004	−	0.509300i
$446$		−	3.30086i		−	0.156300i
$447$		0			0
$448$	−0.414214	+	0.414214i	−0.0195698	+	0.0195698i
$449$	29.9670			1.41423			0.707116	−	0.707097i	$-0.249996\pi$
$449$	29.9670			1.41423			0.707116	+	0.707097i	$0.249996\pi$
$450$		0			0
$451$	−14.1552			−0.666543
$452$	8.32753	−	8.32753i	0.391694	−	0.391694i
$453$		0			0
$454$		−	7.57197i		−	0.355370i
$455$	−4.08489	+	3.45584i	−0.191502	+	0.162012i
$456$		0			0
$457$	−13.0572	−	13.0572i	−0.610792	−	0.610792i	0.332360	−	0.943153i	$-0.392155\pi$
$457$	−13.0572	−	13.0572i	−0.610792	−	0.610792i	−0.943153	+	0.332360i	$0.892155\pi$
$458$	4.92616	+	4.92616i	0.230184	+	0.230184i
$459$		0			0
$460$	−0.0848857	+	1.01758i	−0.00395782	+	0.0474449i
$461$		−	18.5729i		−	0.865028i	−0.901627	−	0.432514i	$-0.857627\pi$
$461$		−	18.5729i		−	0.865028i	0.901627	−	0.432514i	$-0.142373\pi$
$462$		0			0
$463$	16.4780	−	16.4780i	0.765798	−	0.765798i	−0.211566	−	0.977364i	$-0.567856\pi$
$463$	16.4780	−	16.4780i	0.765798	−	0.765798i	0.977364	+	0.211566i	$0.0678564\pi$
$464$	5.77690			0.268186
$465$		0			0
$466$	−17.4847			−0.809963
$467$	−18.4364	+	18.4364i	−0.853136	+	0.853136i	−0.990518	−	0.137383i	$-0.956131\pi$
$467$	−18.4364	+	18.4364i	−0.853136	+	0.853136i	0.137383	+	0.990518i	$0.456131\pi$
$468$		0			0
$469$			3.56444i			0.164591i
$470$	−19.3092	−	22.8240i	−0.890669	−	1.05279i
$471$		0			0
$472$	−0.214016	−	0.214016i	−0.00985087	−	0.00985087i
$473$	6.39785	+	6.39785i	0.294173	+	0.294173i
$474$		0			0
$475$	−4.93089	−	0.828427i	−0.226245	−	0.0380108i
$476$			4.64581i			0.212940i
$477$		0			0
$478$	10.3451	−	10.3451i	0.473174	−	0.473174i
$479$	−4.15775			−0.189973			−0.0949863	−	0.995479i	$-0.530281\pi$
$479$	−4.15775			−0.189973			−0.0949863	+	0.995479i	$0.530281\pi$
$480$		0			0
$481$	8.16977			0.372510
$482$	−13.3609	+	13.3609i	−0.608572	+	0.608572i
$483$		0			0
$484$		−	4.31371i		−	0.196078i
$485$	−19.6440	−	1.63869i	−0.891988	−	0.0744090i
$486$		0			0
$487$	1.35795	+	1.35795i	0.0615347	+	0.0615347i	0.737204	−	0.675670i	$-0.236145\pi$
$487$	1.35795	+	1.35795i	0.0615347	+	0.0615347i	−0.675670	+	0.737204i	$0.736145\pi$
$488$	0.888450	+	0.888450i	0.0402183	+	0.0402183i
$489$		0			0
$490$	14.8337	+	1.23741i	0.670116	+	0.0559006i
$491$		−	11.1794i		−	0.504521i	−0.967659	−	0.252261i	$-0.918826\pi$
$491$		−	11.1794i		−	0.504521i	0.967659	−	0.252261i	$-0.0811740\pi$
$492$		0			0
$493$	32.3968	−	32.3968i	1.45908	−	1.45908i
$494$	−4.08489			−0.183788
$495$		0			0
$496$	5.13109			0.230393
$497$	−3.00572	+	3.00572i	−0.134825	+	0.134825i
$498$		0			0
$499$			7.15341i			0.320230i	0.987098	+	0.160115i	$0.0511866\pi$
$499$			7.15341i			0.320230i	−0.987098	+	0.160115i	$0.948813\pi$
$500$	−9.61400	+	5.70711i	−0.429951	+	0.255230i
$501$		0			0
$502$	19.5859	+	19.5859i	0.874164	+	0.874164i
$503$	−5.91974	−	5.91974i	−0.263948	−	0.263948i	0.562708	−	0.826656i	$-0.309760\pi$
$503$	−5.91974	−	5.91974i	−0.263948	−	0.263948i	−0.826656	+	0.562708i	$0.809760\pi$
$504$		0			0
$505$	−2.53802	−	3.00000i	−0.112941	−	0.133498i
$506$			1.18082i			0.0524937i
$507$		0			0
$508$	0.311747	−	0.311747i	0.0138316	−	0.0138316i
$509$	2.87815			0.127572			0.0637859	−	0.997964i	$-0.479683\pi$
$509$	2.87815			0.127572			0.0637859	+	0.997964i	$0.479683\pi$
$510$		0			0
$511$	−1.51472			−0.0670072
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$		0			0
$514$		−	9.57197i		−	0.422201i
$515$	−0.412252	+	4.94194i	−0.0181660	+	0.217768i
$516$		0			0
$517$	−24.4460	−	24.4460i	−1.07513	−	1.07513i
$518$	0.828427	+	0.828427i	0.0363990	+	0.0363990i
$519$		0			0
$520$	−6.97334	+	5.89949i	−0.305801	+	0.258710i
$521$		−	26.1865i		−	1.14725i	−0.819117	−	0.573627i	$-0.805536\pi$
$521$		−	26.1865i		−	1.14725i	0.819117	−	0.573627i	$-0.194464\pi$
$522$		0			0
$523$	−8.12929	+	8.12929i	−0.355469	+	0.355469i	−0.862140	−	0.506671i	$-0.830876\pi$
$523$	−8.12929	+	8.12929i	−0.355469	+	0.355469i	0.506671	+	0.862140i	$0.330876\pi$
$524$	−8.46042			−0.369595
$525$		0			0
$526$	−25.3166			−1.10386
$527$	28.7751	−	28.7751i	1.25346	−	1.25346i
$528$		0			0
$529$		−	22.7915i		−	0.990933i
$530$	−10.2426	+	8.66535i	−0.444912	+	0.376399i
$531$		0			0
$532$	−0.414214	−	0.414214i	−0.0179584	−	0.0179584i
$533$	−15.8121	−	15.8121i	−0.684896	−	0.684896i
$534$		0			0
$535$	−2.32083	+	27.8213i	−0.100338	+	1.20282i
$536$			6.08489i			0.262827i
$537$		0			0
$538$	9.09593	−	9.09593i	0.392153	−	0.392153i
$539$	17.2132			0.741425
$540$		0			0
$541$	−4.59780			−0.197675			−0.0988375	−	0.995104i	$-0.531512\pi$
$541$	−4.59780			−0.197675			−0.0988375	+	0.995104i	$0.531512\pi$
$542$	−1.85509	+	1.85509i	−0.0796830	+	0.0796830i
$543$		0			0
$544$			7.93089i			0.340034i
$545$	9.84323	+	11.6349i	0.421638	+	0.498385i
$546$		0			0
$547$	20.6679	+	20.6679i	0.883696	+	0.883696i	0.993908	−	0.110213i	$-0.0351531\pi$
$547$	20.6679	+	20.6679i	0.883696	+	0.883696i	−0.110213	+	0.993908i	$0.535153\pi$
$548$	7.52310	+	7.52310i	0.321371	+	0.321371i
$549$		0			0
$550$	−10.5305	+	7.50106i	−0.449022	+	0.319846i
$551$			5.77690i			0.246104i
$552$		0			0
$553$	1.08137	−	1.08137i	0.0459844	−	0.0459844i
$554$	−29.8280			−1.26727
$555$		0			0
$556$	−8.20493			−0.347967
$557$	−0.618873	+	0.618873i	−0.0262225	+	0.0262225i	−0.720096	−	0.693874i	$-0.755902\pi$
$557$	−0.618873	+	0.618873i	−0.0262225	+	0.0262225i	0.693874	+	0.720096i	$0.255902\pi$
$558$		0			0
$559$			14.2934i			0.604547i
$560$	−1.30532	−	0.108889i	−0.0551600	−	0.00460140i
$561$		0			0
$562$	−14.1607	−	14.1607i	−0.597333	−	0.597333i
$563$	−13.0462	−	13.0462i	−0.549832	−	0.549832i	0.376560	−	0.926392i	$-0.377107\pi$
$563$	−13.0462	−	13.0462i	−0.549832	−	0.549832i	−0.926392	+	0.376560i	$0.877107\pi$
$564$		0			0
$565$	26.2428	+	2.18915i	1.10404	+	0.0920984i
$566$			2.84405i			0.119544i
$567$		0			0
$568$	−5.13109	+	5.13109i	−0.215296	+	0.215296i
$569$	−6.82311			−0.286039			−0.143020	−	0.989720i	$-0.545681\pi$
$569$	−6.82311			−0.286039			−0.143020	+	0.989720i	$0.545681\pi$
$570$		0			0
$571$	17.9637			0.751756			0.375878	−	0.926669i	$-0.377341\pi$
$571$	17.9637			0.751756			0.375878	+	0.926669i	$0.377341\pi$
$572$	−7.46892	+	7.46892i	−0.312291	+	0.312291i
$573$		0			0
$574$		−	3.20673i		−	0.133846i
$575$	−1.85971	+	1.32471i	−0.0775554	+	0.0552441i
$576$		0			0
$577$	−14.4456	−	14.4456i	−0.601379	−	0.601379i	0.339300	−	0.940678i	$-0.389810\pi$
$577$	−14.4456	−	14.4456i	−0.601379	−	0.601379i	−0.940678	+	0.339300i	$0.889810\pi$
$578$	32.4555	+	32.4555i	1.34997	+	1.34997i
$579$		0			0
$580$	8.34315	+	9.86179i	0.346430	+	0.409488i
$581$		−	4.51512i		−	0.187319i
$582$		0			0
$583$	−10.9706	+	10.9706i	−0.454354	+	0.454354i
$584$	−2.58579			−0.107001
$585$		0			0
$586$	−20.9982			−0.867428
$587$	29.4164	−	29.4164i	1.21415	−	1.21415i	0.244497	−	0.969650i	$-0.421377\pi$
$587$	29.4164	−	29.4164i	1.21415	−	1.21415i	0.969650	−	0.244497i	$-0.0786227\pi$
$588$		0			0
$589$			5.13109i			0.211423i
$590$	0.0562608	−	0.674435i	0.00231622	−	0.0277660i
$591$		0			0
$592$	1.41421	+	1.41421i	0.0581238	+	0.0581238i
$593$	−11.7724	−	11.7724i	−0.483436	−	0.483436i	0.422791	−	0.906227i	$-0.361050\pi$
$593$	−11.7724	−	11.7724i	−0.483436	−	0.483436i	−0.906227	+	0.422791i	$0.861050\pi$
$594$		0			0
$595$	−7.93089	+	6.70960i	−0.325135	+	0.275067i
$596$		−	18.4920i		−	0.757461i
$597$		0			0
$598$	−1.31903	+	1.31903i	−0.0539391	+	0.0539391i
$599$	−23.1258			−0.944893			−0.472447	−	0.881359i	$-0.656629\pi$
$599$	−23.1258			−0.944893			−0.472447	+	0.881359i	$0.656629\pi$
$600$		0			0
$601$	9.92458			0.404832			0.202416	−	0.979300i	$-0.435121\pi$
$601$	9.92458			0.404832			0.202416	+	0.979300i	$0.435121\pi$
$602$	−1.44937	+	1.44937i	−0.0590721	+	0.0590721i
$603$		0			0
$604$			15.9595i			0.649384i
$605$	7.36396	−	6.22997i	0.299388	−	0.253284i
$606$		0			0
$607$	−30.4486	−	30.4486i	−1.23587	−	1.23587i	−0.961674	−	0.274195i	$-0.911589\pi$
$607$	−30.4486	−	30.4486i	−1.23587	−	1.23587i	−0.274195	−	0.961674i	$-0.588411\pi$
$608$	−0.707107	−	0.707107i	−0.0286770	−	0.0286770i
$609$		0			0
$610$	−0.233557	+	2.79980i	−0.00945646	+	0.113361i
$611$		−	54.6148i		−	2.20948i
$612$		0			0
$613$	0.667153	−	0.667153i	0.0269460	−	0.0269460i	−0.693505	−	0.720451i	$-0.743935\pi$
$613$	0.667153	−	0.667153i	0.0269460	−	0.0269460i	0.720451	+	0.693505i	$0.243935\pi$
$614$	−14.5204			−0.585997
$615$		0			0
$616$	−1.51472			−0.0610298
$617$	−7.47510	+	7.47510i	−0.300936	+	0.300936i	−0.841380	−	0.540444i	$-0.818256\pi$
$617$	−7.47510	+	7.47510i	−0.300936	+	0.300936i	0.540444	+	0.841380i	$0.318256\pi$
$618$		0			0
$619$		−	23.7694i		−	0.955372i	−0.878531	−	0.477686i	$-0.841476\pi$
$619$		−	23.7694i		−	0.955372i	0.878531	−	0.477686i	$-0.158524\pi$
$620$	7.41045	+	8.75932i	0.297611	+	0.351783i
$621$		0			0
$622$	10.4833	+	10.4833i	0.420343	+	0.420343i
$623$	3.08137	+	3.08137i	0.123452	+	0.123452i
$624$		0			0
$625$	−23.6274	−	8.16977i	−0.945097	−	0.326791i
$626$			24.0249i			0.960227i
$627$		0			0
$628$	13.6302	−	13.6302i	0.543904	−	0.543904i
$629$	15.8618			0.632451
$630$		0			0
$631$	−17.4168			−0.693350			−0.346675	−	0.937985i	$-0.612689\pi$
$631$	−17.4168			−0.693350			−0.346675	+	0.937985i	$0.612689\pi$
$632$	1.84601	−	1.84601i	0.0734302	−	0.0734302i
$633$		0			0
$634$		−	4.99820i		−	0.198504i
$635$	0.982420	+	0.0819527i	0.0389861	+	0.00325219i
$636$		0			0
$637$	19.2280	+	19.2280i	0.761841	+	0.761841i
$638$	10.5626	+	10.5626i	0.418179	+	0.418179i
$639$		0			0
$640$	−2.22833	−	0.185885i	−0.0880824	−	0.00734776i
$641$			0.0444040i			0.00175385i	1.00000		0.000876925i	$0.000279134\pi$
$641$			0.0444040i			0.00175385i	−1.00000		0.000876925i	$0.999721\pi$
$642$		0			0
$643$	6.15873	−	6.15873i	0.242876	−	0.242876i	−0.575163	−	0.818039i	$-0.695061\pi$
$643$	6.15873	−	6.15873i	0.242876	−	0.242876i	0.818039	+	0.575163i	$0.195061\pi$
$644$	−0.267503			−0.0105411
$645$		0			0
$646$	−7.93089			−0.312037
$647$	−25.3237	+	25.3237i	−0.995575	+	0.995575i	−0.999990	−	0.00441480i	$-0.998595\pi$
$647$	−25.3237	+	25.3237i	−0.995575	+	0.995575i	0.00441480	+	0.999990i	$0.498595\pi$
$648$		0			0
$649$		−	0.782624i		−	0.0307207i
$650$	−20.1421	−	3.38403i	−0.790040	−	0.132733i
$651$		0			0
$652$	−7.14867	−	7.14867i	−0.279964	−	0.279964i
$653$	21.4945	+	21.4945i	0.841144	+	0.841144i	0.989008	−	0.147864i	$-0.0472397\pi$
$653$	21.4945	+	21.4945i	0.841144	+	0.841144i	−0.147864	+	0.989008i	$0.547240\pi$
$654$		0			0
$655$	−12.2188	−	14.4428i	−0.477426	−	0.564328i
$656$		−	5.47424i		−	0.213733i
$657$		0			0
$658$	5.53802	−	5.53802i	0.215895	−	0.215895i
$659$	49.7013			1.93609			0.968043	−	0.250784i	$-0.0806884\pi$
$659$	49.7013			1.93609			0.968043	+	0.250784i	$0.0806884\pi$
$660$		0			0
$661$	−13.6334			−0.530276			−0.265138	−	0.964210i	$-0.585418\pi$
$661$	−13.6334			−0.530276			−0.265138	+	0.964210i	$0.585418\pi$
$662$	18.8284	−	18.8284i	0.731788	−	0.731788i
$663$		0			0
$664$		−	7.70779i		−	0.299120i
$665$	0.108889	−	1.30532i	0.00422254	−	0.0506183i
$666$		0			0
$667$	1.86539	+	1.86539i	0.0722282	+	0.0722282i
$668$	−15.9467	−	15.9467i	−0.616995	−	0.616995i
$669$		0			0
$670$	−10.3875	+	8.78795i	−0.401306	+	0.339508i
$671$			3.24893i			0.125424i
$672$		0			0
$673$	18.0878	−	18.0878i	0.697234	−	0.697234i	−0.266579	−	0.963813i	$-0.585893\pi$
$673$	18.0878	−	18.0878i	0.697234	−	0.697234i	0.963813	+	0.266579i	$0.0858933\pi$
$674$	−21.1129			−0.813239
$675$		0			0
$676$	−3.68629			−0.141780
$677$	−26.8000	+	26.8000i	−1.03001	+	1.03001i	−0.0304705	+	0.999536i	$0.509701\pi$
$677$	−26.8000	+	26.8000i	−1.03001	+	1.03001i	−0.999536	+	0.0304705i	$0.990299\pi$
$678$		0			0
$679$		−	5.16405i		−	0.198178i
$680$	−13.5389	+	11.4540i	−0.519192	+	0.439241i
$681$		0			0
$682$	9.38183	+	9.38183i	0.359249	+	0.359249i
$683$	−33.1755	−	33.1755i	−1.26943	−	1.26943i	−0.946385	−	0.323040i	$-0.895295\pi$
$683$	−33.1755	−	33.1755i	−1.26943	−	1.26943i	−0.323040	−	0.946385i	$-0.604705\pi$
$684$		0			0
$685$	−1.97769	+	23.7078i	−0.0755635	+	0.905828i
$686$			8.00000i			0.305441i
$687$		0			0
$688$	−2.47424	+	2.47424i	−0.0943294	+	0.0943294i
$689$	−24.5093			−0.933731
$690$		0			0
$691$	−0.173374			−0.00659547			−0.00329773	−	0.999995i	$-0.501050\pi$
$691$	−0.173374			−0.00659547			−0.00329773	+	0.999995i	$0.501050\pi$
$692$	4.76840	−	4.76840i	0.181268	−	0.181268i
$693$		0			0
$694$		−	1.19488i		−	0.0453569i
$695$	−11.8498	−	14.0067i	−0.449487	−	0.531304i
$696$		0			0
$697$	−30.6995	−	30.6995i	−1.16282	−	1.16282i
$698$	−2.07956	−	2.07956i	−0.0787127	−	0.0787127i
$699$		0			0
$700$	−1.69930	−	2.38559i	−0.0642274	−	0.0901668i
$701$			29.3502i			1.10854i	0.832336	+	0.554272i	$0.187003\pi$
$701$			29.3502i			1.10854i	−0.832336	+	0.554272i	$0.812997\pi$
$702$		0			0
$703$	−1.41421	+	1.41421i	−0.0533381	+	0.0533381i
$704$	−2.58579			−0.0974555
$705$		0			0
$706$	31.3113			1.17842
$707$	0.727922	−	0.727922i	0.0273763	−	0.0273763i
$708$		0			0
$709$		−	8.10697i		−	0.304464i	−0.988345	−	0.152232i	$-0.951354\pi$
$709$		−	8.10697i		−	0.304464i	0.988345	−	0.152232i	$-0.0486461\pi$
$710$	−16.1698	−	1.34887i	−0.606841	−	0.0506222i
$711$		0			0
$712$	5.26022	+	5.26022i	0.197135	+	0.197135i
$713$	1.65685	+	1.65685i	0.0620497	+	0.0620497i
$714$		0			0
$715$	−23.5370	−	1.96344i	−0.880235	−	0.0734285i
$716$			19.7289i			0.737303i
$717$		0			0
$718$	−23.8351	+	23.8351i	−0.889519	+	0.889519i
$719$	7.30169			0.272307			0.136154	−	0.990688i	$-0.456526\pi$
$719$	7.30169			0.272307			0.136154	+	0.990688i	$0.456526\pi$
$720$		0			0
$721$	−1.29914			−0.0483827
$722$	0.707107	−	0.707107i	0.0263158	−	0.0263158i
$723$		0			0
$724$		−	3.87463i		−	0.144000i
$725$	−4.78574	+	28.4853i	−0.177738	+	1.05792i
$726$		0			0
$727$	5.44464	+	5.44464i	0.201931	+	0.201931i	0.800827	−	0.598896i	$-0.204394\pi$
$727$	5.44464	+	5.44464i	0.201931	+	0.201931i	−0.598896	+	0.800827i	$0.704394\pi$
$728$	−1.69202	−	1.69202i	−0.0627103	−	0.0627103i
$729$		0			0
$730$	−3.73446	−	4.41421i	−0.138218	−	0.163377i
$731$			27.7510i			1.02641i
$732$		0			0
$733$	32.7419	−	32.7419i	1.20935	−	1.20935i	0.238112	−	0.971238i	$-0.423471\pi$
$733$	32.7419	−	32.7419i	1.20935	−	1.20935i	0.971238	−	0.238112i	$-0.0765285\pi$
$734$	16.5453			0.610698
$735$		0			0
$736$	−0.456656			−0.0168326
$737$	−11.1258	+	11.1258i	−0.409823	+	0.409823i
$738$		0			0
$739$		−	5.63116i		−	0.207146i	−0.994622	−	0.103573i	$-0.966973\pi$
$739$		−	5.63116i		−	0.207146i	0.994622	−	0.103573i	$-0.0330275\pi$
$740$	−0.371771	+	4.45666i	−0.0136666	+	0.163830i
$741$		0			0
$742$	−2.48528	−	2.48528i	−0.0912375	−	0.0912375i
$743$	16.0316	+	16.0316i	0.588141	+	0.588141i	0.937128	−	0.348987i	$-0.113474\pi$
$743$	16.0316	+	16.0316i	0.588141	+	0.588141i	−0.348987	+	0.937128i	$0.613474\pi$
$744$		0			0
$745$	31.5678	−	26.7066i	1.15655	−	0.978453i
$746$			28.9172i			1.05874i
$747$		0			0
$748$	−14.5011	+	14.5011i	−0.530211	+	0.530211i
$749$	−7.31371			−0.267237
$750$		0			0
$751$	−1.26930			−0.0463176			−0.0231588	−	0.999732i	$-0.507372\pi$
$751$	−1.26930			−0.0463176			−0.0231588	+	0.999732i	$0.507372\pi$
$752$	9.45400	−	9.45400i	0.344752	−	0.344752i
$753$		0			0
$754$			23.5980i			0.859388i
$755$	−27.2446	+	23.0491i	−0.991533	+	0.838844i
$756$		0			0
$757$	9.23732	+	9.23732i	0.335736	+	0.335736i	0.854760	−	0.519024i	$-0.173704\pi$
$757$	9.23732	+	9.23732i	0.335736	+	0.335736i	−0.519024	+	0.854760i	$0.673704\pi$
$758$	−15.5591	−	15.5591i	−0.565133	−	0.565133i
$759$		0			0
$760$	0.185885	−	2.22833i	0.00674277	−	0.0808300i
$761$		−	44.0533i		−	1.59693i	−0.602041	−	0.798466i	$-0.705645\pi$
$761$		−	44.0533i		−	1.59693i	0.602041	−	0.798466i	$-0.294355\pi$
$762$		0			0
$763$	−2.82311	+	2.82311i	−0.102203	+	0.102203i
$764$	−25.5382			−0.923939
$765$		0			0
$766$	23.1182			0.835296
$767$	0.874230	−	0.874230i	0.0315666	−	0.0315666i
$768$		0			0
$769$			29.1403i			1.05083i	0.850847	+	0.525414i	$0.176089\pi$
$769$			29.1403i			1.05083i	−0.850847	+	0.525414i	$0.823911\pi$
$770$	−2.18759	−	2.58579i	−0.0788354	−	0.0931853i
$771$		0			0
$772$	10.5362	+	10.5362i	0.379207	+	0.379207i
$773$	22.7098	+	22.7098i	0.816813	+	0.816813i	0.985645	−	0.168832i	$-0.0539995\pi$
$773$	22.7098	+	22.7098i	0.816813	+	0.816813i	−0.168832	+	0.985645i	$0.553999\pi$
$774$		0			0
$775$	−4.25074	+	25.3009i	−0.152691	+	0.908834i
$776$		−	8.81558i		−	0.316461i
$777$		0			0
$778$	−11.7631	+	11.7631i	−0.421727	+	0.421727i
$779$	5.47424			0.196135
$780$		0			0
$781$	−18.7637			−0.671416
$782$	−2.56092	+	2.56092i	−0.0915785	+	0.0915785i
$783$		0			0
$784$			6.65685i			0.237745i
$785$	42.9533	+	3.58313i	1.53307	+	0.127887i
$786$		0			0
$787$	−19.3062	−	19.3062i	−0.688191	−	0.688191i	0.273641	−	0.961832i	$-0.411772\pi$
$787$	−19.3062	−	19.3062i	−0.688191	−	0.688191i	−0.961832	+	0.273641i	$0.911772\pi$
$788$	13.1357	+	13.1357i	0.467940	+	0.467940i
$789$		0			0
$790$	5.81738	+	0.485281i	0.206973	+	0.0172655i
$791$			6.89875i			0.245291i
$792$		0			0
$793$	−3.62922	+	3.62922i	−0.128877	+	0.128877i
$794$	6.83120			0.242430
$795$		0			0
$796$	24.0039			0.850796
$797$	−24.6302	+	24.6302i	−0.872446	+	0.872446i	−0.992739	−	0.120292i	$-0.961617\pi$
$797$	−24.6302	+	24.6302i	−0.872446	+	0.872446i	0.120292	+	0.992739i	$0.461617\pi$
$798$		0			0
$799$		−	106.036i		−	3.75128i
$800$	−2.90088	−	4.07245i	−0.102562	−	0.143983i
$801$		0			0
$802$	0.0442443	+	0.0442443i	0.00156232	+	0.00156232i
$803$	−4.72792	−	4.72792i	−0.166845	−	0.166845i
$804$		0			0
$805$	−0.386335	−	0.456656i	−0.0136165	−	0.0160950i
$806$			20.9599i			0.738282i
$807$		0			0
$808$	1.24264	−	1.24264i	0.0437159	−	0.0437159i
$809$	−1.48625			−0.0522539			−0.0261269	−	0.999659i	$-0.508317\pi$
$809$	−1.48625			−0.0522539			−0.0261269	+	0.999659i	$0.508317\pi$
$810$		0			0
$811$	−9.68089			−0.339942			−0.169971	−	0.985449i	$-0.554367\pi$
$811$	−9.68089			−0.339942			−0.169971	+	0.985449i	$0.554367\pi$
$812$	−2.39287	+	2.39287i	−0.0839733	+	0.0839733i
$813$		0			0
$814$			5.17157i			0.181264i
$815$	1.87925	−	22.5278i	0.0658274	−	0.789116i
$816$		0			0
$817$	−2.47424	−	2.47424i	−0.0865626	−	0.0865626i
$818$	1.24444	+	1.24444i	0.0435109	+	0.0435109i
$819$		0			0
$820$	9.34511	−	7.90603i	0.326345	−	0.276091i
$821$			38.3719i			1.33919i	0.742727	+	0.669595i	$0.233532\pi$
$821$			38.3719i			1.33919i	−0.742727	+	0.669595i	$0.766468\pi$
$822$		0			0
$823$	−6.50662	+	6.50662i	−0.226807	+	0.226807i	−0.811357	−	0.584551i	$-0.801271\pi$
$823$	−6.50662	+	6.50662i	−0.226807	+	0.226807i	0.584551	+	0.811357i	$0.301271\pi$
$824$	−2.21778			−0.0772600
$825$		0			0
$826$	0.177296			0.00616893
$827$	−32.9172	+	32.9172i	−1.14464	+	1.14464i	−0.157054	+	0.987590i	$0.550200\pi$
$827$	−32.9172	+	32.9172i	−1.14464	+	1.14464i	−0.987590	+	0.157054i	$0.949800\pi$
$828$		0			0
$829$			12.2217i			0.424477i	0.977218	+	0.212239i	$0.0680754\pi$
$829$			12.2217i			0.424477i	−0.977218	+	0.212239i	$0.931925\pi$
$830$	13.1580	−	11.1318i	0.456722	−	0.386390i
$831$		0			0
$832$	−2.88845	−	2.88845i	−0.100139	−	0.100139i
$833$	37.3316	+	37.3316i	1.29346	+	1.29346i
$834$		0			0
$835$	4.19209	−	50.2533i	0.145073	−	1.73909i
$836$		−	2.58579i		−	0.0894313i
$837$		0			0
$838$	−7.71785	+	7.71785i	−0.266609	+	0.266609i
$839$	53.6390			1.85182			0.925912	−	0.377739i	$-0.123298\pi$
$839$	53.6390			1.85182			0.925912	+	0.377739i	$0.123298\pi$
$840$		0			0
$841$	4.37258			0.150779
$842$	−12.1163	+	12.1163i	−0.417555	+	0.417555i
$843$		0			0
$844$			22.8600i			0.786873i
$845$	−5.32384	−	6.29289i	−0.183145	−	0.216482i
$846$		0			0
$847$	1.78680	+	1.78680i	0.0613951	+	0.0613951i
$848$	−4.24264	−	4.24264i	−0.145693	−	0.145693i
$849$		0			0
$850$	−39.1064	−	6.57017i	−1.34134	−	0.225355i
$851$			0.913313i			0.0313080i
$852$		0			0
$853$	−37.1202	+	37.1202i	−1.27097	+	1.27097i	−0.325393	+	0.945579i	$0.605496\pi$
$853$	−37.1202	+	37.1202i	−1.27097	+	1.27097i	−0.945579	+	0.325393i	$0.894504\pi$
$854$	−0.736016			−0.0251860
$855$		0			0
$856$	−12.4853			−0.426738
$857$	4.81281	−	4.81281i	0.164402	−	0.164402i	−0.620111	−	0.784514i	$-0.712913\pi$
$857$	4.81281	−	4.81281i	0.164402	−	0.164402i	0.784514	+	0.620111i	$0.212913\pi$
$858$		0			0
$859$			13.8969i			0.474158i	0.971490	+	0.237079i	$0.0761900\pi$
$859$			13.8969i			0.474158i	−0.971490	+	0.237079i	$0.923810\pi$
$860$	−7.79714	−	0.650431i	−0.265880	−	0.0221795i
$861$		0			0
$862$	−12.4320	−	12.4320i	−0.423434	−	0.423434i
$863$	−37.9338	−	37.9338i	−1.29128	−	1.29128i	−0.933994	−	0.357288i	$-0.883701\pi$
$863$	−37.9338	−	37.9338i	−1.29128	−	1.29128i	−0.357288	−	0.933994i	$-0.616299\pi$
$864$		0			0
$865$	15.0268	+	1.25353i	0.510927	+	0.0426211i
$866$		−	28.9672i		−	0.984345i
$867$		0			0
$868$	−2.12537	+	2.12537i	−0.0721397	+	0.0721397i
$869$	6.75058			0.228998
$870$		0			0
$871$	−24.8561			−0.842216
$872$	−4.81934	+	4.81934i	−0.163204	+	0.163204i
$873$		0			0
$874$		−	0.456656i		−	0.0154466i
$875$	1.61829	−	6.34621i	0.0547081	−	0.214541i
$876$		0			0
$877$	−33.2632	−	33.2632i	−1.12322	−	1.12322i	−0.991255	−	0.131962i	$-0.957872\pi$
$877$	−33.2632	−	33.2632i	−1.12322	−	1.12322i	−0.131962	−	0.991255i	$-0.542128\pi$
$878$	−26.3184	−	26.3184i	−0.888204	−	0.888204i
$879$		0			0
$880$	−3.73446	−	4.41421i	−0.125889	−	0.148803i
$881$			24.6436i			0.830263i	0.909761	+	0.415132i	$0.136264\pi$
$881$			24.6436i			0.830263i	−0.909761	+	0.415132i	$0.863736\pi$
$882$		0			0
$883$	−30.9401	+	30.9401i	−1.04122	+	1.04122i	−0.0421053	+	0.999113i	$0.513407\pi$
$883$	−30.9401	+	30.9401i	−1.04122	+	1.04122i	−0.999113	+	0.0421053i	$0.986593\pi$
$884$	−32.3968			−1.08962
$885$		0			0
$886$	−16.8260			−0.565282
$887$	−6.63689	+	6.63689i	−0.222845	+	0.222845i	−0.809695	−	0.586850i	$-0.800368\pi$
$887$	−6.63689	+	6.63689i	−0.222845	+	0.222845i	0.586850	+	0.809695i	$0.300368\pi$
$888$		0			0
$889$			0.258260i			0.00866176i
$890$	−1.38282	+	16.5767i	−0.0463521	+	0.555652i
$891$		0			0
$892$	2.33406	+	2.33406i	0.0781502	+	0.0781502i
$893$	9.45400	+	9.45400i	0.316366	+	0.316366i
$894$		0			0
$895$	−33.6793	+	28.4930i	−1.12578	+	0.952415i
$896$		−	0.585786i		−	0.0195698i
$897$		0			0
$898$	−21.1899	+	21.1899i	−0.707116	+	0.707116i
$899$	29.6418			0.988610
$900$		0			0
$901$	−47.5854			−1.58530
$902$	10.0092	−	10.0092i	0.333271	−	0.333271i
$903$		0			0
$904$			11.7769i			0.391694i
$905$	6.61441	−	5.59584i	0.219870	−	0.186012i
$906$		0			0
$907$	−16.5168	−	16.5168i	−0.548433	−	0.548433i	0.377555	−	0.925987i	$-0.376765\pi$
$907$	−16.5168	−	16.5168i	−0.548433	−	0.548433i	−0.925987	+	0.377555i	$0.876765\pi$
$908$	5.35419	+	5.35419i	0.177685	+	0.177685i
$909$		0			0
$910$	0.444800	−	5.33210i	0.0147450	−	0.176757i
$911$		−	13.8582i		−	0.459142i	−0.973292	−	0.229571i	$-0.926268\pi$
$911$		−	13.8582i		−	0.459142i	0.973292	−	0.229571i	$-0.0737323\pi$
$912$		0			0
$913$	14.0931	−	14.0931i	0.466415	−	0.466415i
$914$	18.4657			0.610792
$915$		0			0
$916$	−6.96664			−0.230184
$917$	3.50442	−	3.50442i	0.115726	−	0.115726i
$918$		0			0
$919$			15.3137i			0.505153i	0.967577	+	0.252576i	$0.0812779\pi$
$919$			15.3137i			0.505153i	−0.967577	+	0.252576i	$0.918722\pi$
$920$	−0.659515	−	0.779561i	−0.0217436	−	0.0257014i
$921$		0			0
$922$	13.1331	+	13.1331i	0.432514	+	0.432514i
$923$	−20.9599	−	20.9599i	−0.689904	−	0.689904i
$924$		0			0
$925$	−8.14491	+	5.80176i	−0.267803	+	0.190761i
$926$			23.3034i			0.765798i
$927$		0			0
$928$	−4.08489	+	4.08489i	−0.134093	+	0.134093i
$929$	−16.1192			−0.528854			−0.264427	−	0.964406i	$-0.585183\pi$
$929$	−16.1192			−0.528854			−0.264427	+	0.964406i	$0.585183\pi$
$930$		0			0
$931$	−6.65685			−0.218170
$932$	12.3635	−	12.3635i	0.404981	−	0.404981i
$933$		0			0
$934$		−	26.0730i		−	0.853136i
$935$	−45.6977	−	3.81206i	−1.49447	−	0.124668i
$936$		0			0
$937$	−7.44620	−	7.44620i	−0.243257	−	0.243257i	0.574939	−	0.818196i	$-0.305026\pi$
$937$	−7.44620	−	7.44620i	−0.243257	−	0.243257i	−0.818196	+	0.574939i	$0.805026\pi$
$938$	−2.52044	−	2.52044i	−0.0822954	−	0.0822954i
$939$		0			0
$940$	29.7927	+	2.48528i	0.971730	+	0.0810609i
$941$		−	39.9324i		−	1.30176i	−0.759181	−	0.650880i	$-0.774400\pi$
$941$		−	39.9324i		−	1.30176i	0.759181	−	0.650880i	$-0.225600\pi$
$942$		0			0
$943$	1.76766	−	1.76766i	0.0575629	−	0.0575629i
$944$	0.302664			0.00985087
$945$		0			0
$946$	−9.04792			−0.294173
$947$	−3.65517	+	3.65517i	−0.118777	+	0.118777i	−0.763997	−	0.645220i	$-0.776766\pi$
$947$	−3.65517	+	3.65517i	−0.118777	+	0.118777i	0.645220	+	0.763997i	$0.276766\pi$
$948$		0			0
$949$		−	10.5626i		−	0.342878i
$950$	4.07245	−	2.90088i	0.132128	−	0.0941170i
$951$		0			0
$952$	−3.28508	−	3.28508i	−0.106470	−	0.106470i
$953$	−9.64123	−	9.64123i	−0.312310	−	0.312310i	0.533494	−	0.845804i	$-0.320879\pi$
$953$	−9.64123	−	9.64123i	−0.312310	−	0.312310i	−0.845804	+	0.533494i	$0.820879\pi$
$954$		0			0
$955$	−36.8829	−	43.5964i	−1.19350	−	1.41075i
$956$			14.6302i			0.473174i
$957$		0			0
$958$	2.93998	−	2.93998i	0.0949863	−	0.0949863i
$959$	−6.23234			−0.201253
$960$		0			0
$961$	−4.67190			−0.150707
$962$	−5.77690	+	5.77690i	−0.186255	+	0.186255i
$963$		0			0
$964$		−	18.8951i		−	0.608572i
$965$	−2.76978	+	33.2031i	−0.0891623	+	1.06885i
$966$		0			0
$967$	7.76308	+	7.76308i	0.249644	+	0.249644i	0.820824	−	0.571181i	$-0.193514\pi$
$967$	7.76308	+	7.76308i	0.249644	+	0.249644i	−0.571181	+	0.820824i	$0.693514\pi$
$968$	3.05025	+	3.05025i	0.0980388	+	0.0980388i
$969$		0			0
$970$	15.0491	−	12.7317i	0.483199	−	0.408790i
$971$		−	19.7680i		−	0.634385i	−0.948361	−	0.317192i	$-0.897260\pi$
$971$		−	19.7680i		−	0.634385i	0.948361	−	0.317192i	$-0.102740\pi$
$972$		0			0
$973$	3.39859	−	3.39859i	0.108954	−	0.108954i
$974$	−1.92044			−0.0615347
$975$		0			0
$976$	−1.25646			−0.0402183
$977$	31.6856	−	31.6856i	1.01371	−	1.01371i	0.0138087	−	0.999905i	$-0.495604\pi$
$977$	31.6856	−	31.6856i	1.01371	−	1.01371i	0.999905	−	0.0138087i	$-0.00439560\pi$
$978$		0			0
$979$			19.2359i			0.614781i
$980$	−11.3640	+	9.61400i	−0.363008	+	0.307108i
$981$		0			0
$982$	7.90506	+	7.90506i	0.252261	+	0.252261i
$983$	4.93563	+	4.93563i	0.157422	+	0.157422i	0.781423	−	0.624001i	$-0.214494\pi$
$983$	4.93563	+	4.93563i	0.157422	+	0.157422i	−0.624001	+	0.781423i	$0.714494\pi$
$984$		0			0
$985$	−3.45314	+	41.3950i	−0.110026	+	1.31895i
$986$			45.8160i			1.45908i
$987$		0			0
$988$	2.88845	−	2.88845i	0.0918938	−	0.0918938i
$989$	−1.59789			−0.0508098
$990$		0			0
$991$	−12.9226			−0.410499			−0.205249	−	0.978710i	$-0.565801\pi$
$991$	−12.9226			−0.410499			−0.205249	+	0.978710i	$0.565801\pi$
$992$	−3.62823	+	3.62823i	−0.115196	+	0.115196i
$993$		0			0
$994$		−	4.25074i		−	0.134825i
$995$	34.6671	+	40.9773i	1.09902	+	1.29907i
$996$		0			0
$997$	30.0231	+	30.0231i	0.950840	+	0.950840i	0.998847	−	0.0480071i	$-0.0152870\pi$
$997$	30.0231	+	30.0231i	0.950840	+	0.950840i	−0.0480071	+	0.998847i	$0.515287\pi$
$998$	−5.05822	−	5.05822i	−0.160115	−	0.160115i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1710.2.n.g.647.1	yes	8
3.2	odd	2		1710.2.n.f.647.4	✓	8
5.3	odd	4		1710.2.n.f.1673.3	yes	8
15.8	even	4	inner	1710.2.n.g.1673.2	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1710.2.n.f.647.4	✓	8	3.2	odd	2
1710.2.n.f.1673.3	yes	8	5.3	odd	4
1710.2.n.g.647.1	yes	8	1.1	even	1	trivial
1710.2.n.g.1673.2	yes	8	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 $\F_{q}$
Belyi maps

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)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(1.70711 - 1.44423i) q^{5} +(0.414214 + 0.414214i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-0.185885 + 2.22833i) q^{10} +2.58579i q^{11} +(-2.88845 + 2.88845i) q^{13} -0.585786 q^{14} -1.00000 q^{16} +(-5.60799 + 5.60799i) q^{17} -1.00000i q^{19} +(-1.44423 - 1.70711i) q^{20} +(-1.82843 - 1.82843i) q^{22} +(-0.322905 - 0.322905i) q^{23} +(0.828427 - 4.93089i) q^{25} -4.08489i q^{26} +(0.414214 - 0.414214i) q^{28} -5.77690 q^{29} -5.13109 q^{31} +(0.707107 - 0.707107i) q^{32} -7.93089i q^{34} +(1.30532 + 0.108889i) q^{35} +(-1.41421 - 1.41421i) q^{37} +(0.707107 + 0.707107i) q^{38} +(2.22833 + 0.185885i) q^{40} +5.47424i q^{41} +(2.47424 - 2.47424i) q^{43} +2.58579 q^{44} +0.456656 q^{46} +(-9.45400 + 9.45400i) q^{47} -6.65685i q^{49} +(2.90088 + 4.07245i) q^{50} +(2.88845 + 2.88845i) q^{52} +(4.24264 + 4.24264i) q^{53} +(3.73446 + 4.41421i) q^{55} +0.585786i q^{56} +(4.08489 - 4.08489i) q^{58} -0.302664 q^{59} +1.25646 q^{61} +(3.62823 - 3.62823i) q^{62} +1.00000i q^{64} +(-0.759320 + 9.10247i) q^{65} +(4.30266 + 4.30266i) q^{67} +(5.60799 + 5.60799i) q^{68} +(-1.00000 + 0.846008i) q^{70} +7.25646i q^{71} +(-1.82843 + 1.82843i) q^{73} +2.00000 q^{74} -1.00000 q^{76} +(-1.07107 + 1.07107i) q^{77} -2.61065i q^{79} +(-1.70711 + 1.44423i) q^{80} +(-3.87087 - 3.87087i) q^{82} +(-5.45023 - 5.45023i) q^{83} +(-1.47424 + 17.6726i) q^{85} +3.49910i q^{86} +(-1.82843 + 1.82843i) q^{88} +7.43908 q^{89} -2.39287 q^{91} +(-0.322905 + 0.322905i) q^{92} -13.3700i q^{94} +(-1.44423 - 1.70711i) q^{95} +(-6.23356 - 6.23356i) q^{97} +(4.70711 + 4.70711i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{5} - 8 q^{7} - 4 q^{10} - 16 q^{14} - 8 q^{16} + 8 q^{22} - 8 q^{23} - 16 q^{25} - 8 q^{28} + 16 q^{31} + 4 q^{40} + 8 q^{43} + 32 q^{44} - 24 q^{46} - 24 q^{47} - 16 q^{50} + 32 q^{59} + 24 q^{62}+ \cdots + 32 q^{98}+O(q^{100}) \) 8 * q + 8 * q^5 - 8 * q^7 - 4 * q^10 - 16 * q^14 - 8 * q^16 + 8 * q^22 - 8 * q^23 - 16 * q^25 - 8 * q^28 + 16 * q^31 + 4 * q^40 + 8 * q^43 + 32 * q^44 - 24 * q^46 - 24 * q^47 - 16 * q^50 + 32 * q^59 + 24 * q^62 + 56 * q^65 - 8 * q^70 + 8 * q^73 + 16 * q^74 - 8 * q^76 + 48 * q^77 - 8 * q^80 + 8 * q^82 + 8 * q^88 + 16 * q^89 - 8 * q^92 + 24 * q^97 + 32 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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