LMFDB - Embedded newform 1710.2.n.g.647.4

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			647.4
Root			$-0.360409i$ of defining polynomial
Character	$\chi$	$=$	1710.647
Dual form			1710.2.n.g.1673.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(0.292893 + 2.21680i) q^{5} +(-2.41421 - 2.41421i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(1.77462 + 1.36041i) q^{10} +5.41421i q^{11} +(4.43361 - 4.43361i) q^{13} -3.41421 q^{14} -1.00000 q^{16} +(1.20309 - 1.20309i) q^{17} -1.00000i q^{19} +(2.21680 - 0.292893i) q^{20} +(3.82843 + 3.82843i) q^{22} +(-0.904518 - 0.904518i) q^{23} +(-4.82843 + 1.29857i) q^{25} -6.27006i q^{26} +(-2.41421 + 2.41421i) q^{28} +8.86721 q^{29} +10.6762 q^{31} +(-0.707107 + 0.707107i) q^{32} -1.70143i q^{34} +(4.64473 - 6.05894i) q^{35} +(1.41421 + 1.41421i) q^{37} +(-0.707107 - 0.707107i) q^{38} +(1.36041 - 1.77462i) q^{40} +0.980608i q^{41} +(-2.01939 + 2.01939i) q^{43} +5.41421 q^{44} -1.27918 q^{46} +(5.77173 - 5.77173i) q^{47} +4.65685i q^{49} +(-2.49598 + 4.33244i) q^{50} +(-4.43361 - 4.43361i) q^{52} +(-4.24264 - 4.24264i) q^{53} +(-12.0022 + 1.58579i) q^{55} +3.41421i q^{56} +(6.27006 - 6.27006i) q^{58} +9.84782 q^{59} +9.09849 q^{61} +(7.54925 - 7.54925i) q^{62} +1.00000i q^{64} +(11.1270 + 8.52985i) q^{65} +(-5.84782 - 5.84782i) q^{67} +(-1.20309 - 1.20309i) q^{68} +(-1.00000 - 7.56864i) q^{70} +15.0985i q^{71} +(3.82843 - 3.82843i) q^{73} +2.00000 q^{74} -1.00000 q^{76} +(13.0711 - 13.0711i) q^{77} -9.28946i q^{79} +(-0.292893 - 2.21680i) q^{80} +(0.693395 + 0.693395i) q^{82} +(-9.30961 - 9.30961i) q^{83} +(3.01939 + 2.31464i) q^{85} +2.85585i q^{86} +(3.82843 - 3.82843i) q^{88} +8.46103 q^{89} -21.4073 q^{91} +(-0.904518 + 0.904518i) q^{92} -8.16246i q^{94} +(2.21680 - 0.292893i) q^{95} +(10.1464 + 10.1464i) q^{97} +(3.29289 + 3.29289i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	0.292893	+	2.21680i	0.130986	+	0.991384i
$5$	0.292893	+	2.21680i	0.130986	+	0.991384i
$6$		0			0
$7$	−2.41421	−	2.41421i	−0.912487	−	0.912487i	0.0839804	−	0.996467i	$-0.473237\pi$
$7$	−2.41421	−	2.41421i	−0.912487	−	0.912487i	−0.996467	+	0.0839804i	$0.973237\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$		0			0
$10$	1.77462	+	1.36041i	0.561185	+	0.430199i
$11$			5.41421i			1.63245i	0.577736	+	0.816223i	$0.303936\pi$
$11$			5.41421i			1.63245i	−0.577736	+	0.816223i	$0.696064\pi$
$12$		0			0
$13$	4.43361	−	4.43361i	1.22966	−	1.22966i	0.265569	−	0.964092i	$-0.414440\pi$
$13$	4.43361	−	4.43361i	1.22966	−	1.22966i	0.964092	−	0.265569i	$-0.0855598\pi$
$14$	−3.41421			−0.912487
$15$		0			0
$16$	−1.00000			−0.250000
$17$	1.20309	−	1.20309i	0.291792	−	0.291792i	−0.545996	−	0.837788i	$-0.683848\pi$
$17$	1.20309	−	1.20309i	0.291792	−	0.291792i	0.837788	+	0.545996i	$0.183848\pi$
$18$		0			0
$19$		−	1.00000i		−	0.229416i
$19$		−	1.00000i		−	0.229416i
$20$	2.21680	−	0.292893i	0.495692	−	0.0654929i
$21$		0			0
$22$	3.82843	+	3.82843i	0.816223	+	0.816223i
$23$	−0.904518	−	0.904518i	−0.188605	−	0.188605i	0.606488	−	0.795093i	$-0.292578\pi$
$23$	−0.904518	−	0.904518i	−0.188605	−	0.188605i	−0.795093	+	0.606488i	$0.792578\pi$
$24$		0			0
$25$	−4.82843	+	1.29857i	−0.965685	+	0.259715i
$26$		−	6.27006i		−	1.22966i
$27$		0			0
$28$	−2.41421	+	2.41421i	−0.456243	+	0.456243i
$29$	8.86721			1.64660			0.823300	−	0.567607i	$-0.192131\pi$
$29$	8.86721			1.64660			0.823300	+	0.567607i	$0.192131\pi$
$30$		0			0
$31$	10.6762			1.91751			0.958755	−	0.284233i	$-0.0917390\pi$
$31$	10.6762			1.91751			0.958755	+	0.284233i	$0.0917390\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$		0			0
$34$		−	1.70143i		−	0.291792i
$35$	4.64473	−	6.05894i	0.785102	−	1.02415i
$36$		0			0
$37$	1.41421	+	1.41421i	0.232495	+	0.232495i	0.813733	−	0.581238i	$-0.197432\pi$
$37$	1.41421	+	1.41421i	0.232495	+	0.232495i	−0.581238	+	0.813733i	$0.697432\pi$
$38$	−0.707107	−	0.707107i	−0.114708	−	0.114708i
$39$		0			0
$40$	1.36041	−	1.77462i	0.215100	−	0.280593i
$41$			0.980608i			0.153145i	0.997064	+	0.0765727i	$0.0243977\pi$
$41$			0.980608i			0.153145i	−0.997064	+	0.0765727i	$0.975602\pi$
$42$		0			0
$43$	−2.01939	+	2.01939i	−0.307954	+	0.307954i	−0.844116	−	0.536161i	$-0.819874\pi$
$43$	−2.01939	+	2.01939i	−0.307954	+	0.307954i	0.536161	+	0.844116i	$0.319874\pi$
$44$	5.41421			0.816223
$45$		0			0
$46$	−1.27918			−0.188605
$47$	5.77173	−	5.77173i	0.841893	−	0.841893i	−0.147212	−	0.989105i	$-0.547030\pi$
$47$	5.77173	−	5.77173i	0.841893	−	0.841893i	0.989105	+	0.147212i	$0.0470299\pi$
$48$		0			0
$49$			4.65685i			0.665265i
$50$	−2.49598	+	4.33244i	−0.352985	+	0.612700i
$51$		0			0
$52$	−4.43361	−	4.43361i	−0.614830	−	0.614830i
$53$	−4.24264	−	4.24264i	−0.582772	−	0.582772i	0.352892	−	0.935664i	$-0.385198\pi$
$53$	−4.24264	−	4.24264i	−0.582772	−	0.582772i	−0.935664	+	0.352892i	$0.885198\pi$
$54$		0			0
$55$	−12.0022	+	1.58579i	−1.61838	+	0.213827i
$56$			3.41421i			0.456243i
$57$		0			0
$58$	6.27006	−	6.27006i	0.823300	−	0.823300i
$59$	9.84782			1.28208			0.641038	−	0.767509i	$-0.278504\pi$
$59$	9.84782			1.28208			0.641038	+	0.767509i	$0.278504\pi$
$60$		0			0
$61$	9.09849			1.16494			0.582471	−	0.812851i	$-0.302086\pi$
$61$	9.09849			1.16494			0.582471	+	0.812851i	$0.302086\pi$
$62$	7.54925	−	7.54925i	0.958755	−	0.958755i
$63$		0			0
$64$			1.00000i			0.125000i
$65$	11.1270	+	8.52985i	1.38013	+	1.05800i
$66$		0			0
$67$	−5.84782	−	5.84782i	−0.714425	−	0.714425i	0.253033	−	0.967458i	$-0.418572\pi$
$67$	−5.84782	−	5.84782i	−0.714425	−	0.714425i	−0.967458	+	0.253033i	$0.918572\pi$
$68$	−1.20309	−	1.20309i	−0.145896	−	0.145896i
$69$		0			0
$70$	−1.00000	−	7.56864i	−0.119523	−	0.904625i
$71$			15.0985i			1.79186i	0.444194	+	0.895931i	$0.353490\pi$
$71$			15.0985i			1.79186i	−0.444194	+	0.895931i	$0.646510\pi$
$72$		0			0
$73$	3.82843	−	3.82843i	0.448084	−	0.448084i	−0.446634	−	0.894717i	$-0.647377\pi$
$73$	3.82843	−	3.82843i	0.448084	−	0.448084i	0.894717	+	0.446634i	$0.147377\pi$
$74$	2.00000			0.232495
$75$		0			0
$76$	−1.00000			−0.114708
$77$	13.0711	−	13.0711i	1.48959	−	1.48959i
$78$		0			0
$79$		−	9.28946i		−	1.04515i	−0.852595	−	0.522573i	$-0.824972\pi$
$79$		−	9.28946i		−	1.04515i	0.852595	−	0.522573i	$-0.175028\pi$
$80$	−0.292893	−	2.21680i	−0.0327465	−	0.247846i
$81$		0			0
$82$	0.693395	+	0.693395i	0.0765727	+	0.0765727i
$83$	−9.30961	−	9.30961i	−1.02186	−	1.02186i	−0.999756	−	0.0221073i	$-0.992962\pi$
$83$	−9.30961	−	9.30961i	−1.02186	−	1.02186i	−0.0221073	−	0.999756i	$-0.507038\pi$
$84$		0			0
$85$	3.01939	+	2.31464i	0.327499	+	0.251058i
$86$			2.85585i			0.307954i
$87$		0			0
$88$	3.82843	−	3.82843i	0.408112	−	0.408112i
$89$	8.46103			0.896867			0.448434	−	0.893816i	$-0.351982\pi$
$89$	8.46103			0.896867			0.448434	+	0.893816i	$0.351982\pi$
$90$		0			0
$91$	−21.4073			−2.24410
$92$	−0.904518	+	0.904518i	−0.0943025	+	0.0943025i
$93$		0			0
$94$		−	8.16246i		−	0.841893i
$95$	2.21680	−	0.292893i	0.227439	−	0.0300502i
$96$		0			0
$97$	10.1464	+	10.1464i	1.03021	+	1.03021i	0.999529	+	0.0306807i	$0.00976752\pi$
$97$	10.1464	+	10.1464i	1.03021	+	1.03021i	0.0306807	+	0.999529i	$0.490232\pi$
$98$	3.29289	+	3.29289i	0.332632	+	0.332632i
$99$		0			0
$100$	1.29857	+	4.82843i	0.129857	+	0.482843i
$101$		−	10.2426i		−	1.01918i	−0.860417	−	0.509590i	$-0.829797\pi$
$101$		−	10.2426i		−	1.01918i	0.860417	−	0.509590i	$-0.170203\pi$
$102$		0			0
$103$	−7.15442	+	7.15442i	−0.704946	+	0.704946i	−0.965468	−	0.260522i	$-0.916105\pi$
$103$	−7.15442	+	7.15442i	−0.704946	+	0.704946i	0.260522	+	0.965468i	$0.416105\pi$
$104$	−6.27006			−0.614830
$105$		0			0
$106$	−6.00000			−0.582772
$107$	−3.17157	+	3.17157i	−0.306608	+	0.306608i	−0.843592	−	0.536985i	$-0.819563\pi$
$107$	−3.17157	+	3.17157i	−0.306608	+	0.306608i	0.536985	+	0.843592i	$0.319563\pi$
$108$		0			0
$109$			12.3492i			1.18284i	0.806365	+	0.591418i	$0.201432\pi$
$109$			12.3492i			1.18284i	−0.806365	+	0.591418i	$0.798568\pi$
$110$	−7.36555	+	9.60819i	−0.702277	+	0.916105i
$111$		0			0
$112$	2.41421	+	2.41421i	0.228122	+	0.228122i
$113$	2.02742	+	2.02742i	0.190724	+	0.190724i	0.796009	−	0.605285i	$-0.206941\pi$
$113$	2.02742	+	2.02742i	0.190724	+	0.190724i	−0.605285	+	0.796009i	$0.706941\pi$
$114$		0			0
$115$	1.74021	−	2.27006i	0.162275	−	0.211685i
$116$		−	8.86721i		−	0.823300i
$117$		0			0
$118$	6.96346	−	6.96346i	0.641038	−	0.641038i
$119$	−5.80904			−0.532513
$120$		0			0
$121$	−18.3137			−1.66488
$122$	6.43361	−	6.43361i	0.582471	−	0.582471i
$123$		0			0
$124$		−	10.6762i		−	0.958755i
$125$	−4.29289	−	10.3233i	−0.383968	−	0.923346i
$126$		0			0
$127$	−1.94407	−	1.94407i	−0.172508	−	0.172508i	0.615572	−	0.788080i	$-0.288925\pi$
$127$	−1.94407	−	1.94407i	−0.172508	−	0.172508i	−0.788080	+	0.615572i	$0.788925\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$		0			0
$130$	13.8995	−	1.83646i	1.21907	−	0.161068i
$131$			12.3605i			1.07994i	0.841683	+	0.539972i	$0.181565\pi$
$131$			12.3605i			1.07994i	−0.841683	+	0.539972i	$0.818435\pi$
$132$		0			0
$133$	−2.41421	+	2.41421i	−0.209339	+	0.209339i
$134$	−8.27006			−0.714425
$135$		0			0
$136$	−1.70143			−0.145896
$137$	1.47316	−	1.47316i	0.125860	−	0.125860i	−0.641371	−	0.767231i	$-0.721634\pi$
$137$	1.47316	−	1.47316i	0.125860	−	0.125860i	0.767231	+	0.641371i	$0.221634\pi$
$138$		0			0
$139$		−	7.05971i		−	0.598797i	−0.954128	−	0.299398i	$-0.903214\pi$
$139$		−	7.05971i		−	0.598797i	0.954128	−	0.299398i	$-0.0967859\pi$
$140$	−6.05894	−	4.64473i	−0.512074	−	0.392551i
$141$		0			0
$142$	10.6762	+	10.6762i	0.895931	+	0.895931i
$143$	24.0045	+	24.0045i	2.00736	+	2.00736i
$144$		0			0
$145$	2.59715	+	19.6569i	0.215681	+	1.63241i
$146$		−	5.41421i		−	0.448084i
$147$		0			0
$148$	1.41421	−	1.41421i	0.116248	−	0.116248i
$149$	−10.4175			−0.853438			−0.426719	−	0.904384i	$-0.640331\pi$
$149$	−10.4175			−0.853438			−0.426719	+	0.904384i	$0.640331\pi$
$150$		0			0
$151$	5.50467			0.447964			0.223982	−	0.974593i	$-0.428094\pi$
$151$	5.50467			0.447964			0.223982	+	0.974593i	$0.428094\pi$
$152$	−0.707107	+	0.707107i	−0.0573539	+	0.0573539i
$153$		0			0
$154$		−	18.4853i		−	1.48959i
$155$	3.12700	+	23.6671i	0.251167	+	1.90099i
$156$		0			0
$157$	−2.82039	−	2.82039i	−0.225092	−	0.225092i	0.585547	−	0.810639i	$-0.300880\pi$
$157$	−2.82039	−	2.82039i	−0.225092	−	0.225092i	−0.810639	+	0.585547i	$0.800880\pi$
$158$	−6.56864	−	6.56864i	−0.522573	−	0.522573i
$159$		0			0
$160$	−1.77462	−	1.36041i	−0.140296	−	0.107550i
$161$			4.36740i			0.344199i
$162$		0			0
$163$	−11.4165	+	11.4165i	−0.894206	+	0.894206i	−0.994916	−	0.100710i	$-0.967889\pi$
$163$	−11.4165	+	11.4165i	−0.894206	+	0.894206i	0.100710	+	0.994916i	$0.467889\pi$
$164$	0.980608			0.0765727
$165$		0			0
$166$	−13.1658			−1.02186
$167$	5.67292	−	5.67292i	0.438984	−	0.438984i	−0.452686	−	0.891670i	$-0.649534\pi$
$167$	5.67292	−	5.67292i	0.438984	−	0.438984i	0.891670	+	0.452686i	$0.149534\pi$
$168$		0			0
$169$		−	26.3137i		−	2.02413i
$170$	3.77173	−	0.498336i	0.289278	−	0.0382207i
$171$		0			0
$172$	2.01939	+	2.01939i	0.153977	+	0.153977i
$173$	0.776751	+	0.776751i	0.0590553	+	0.0590553i	0.736018	−	0.676962i	$-0.236704\pi$
$173$	0.776751	+	0.776751i	0.0590553	+	0.0590553i	−0.676962	+	0.736018i	$0.736704\pi$
$174$		0			0
$175$	14.7919	+	8.52182i	1.11816	+	0.644189i
$176$		−	5.41421i		−	0.408112i
$177$		0			0
$178$	5.98285	−	5.98285i	0.448434	−	0.448434i
$179$	−21.7908			−1.62872			−0.814361	−	0.580359i	$-0.802912\pi$
$179$	−21.7908			−1.62872			−0.814361	+	0.580359i	$0.802912\pi$
$180$		0			0
$181$	−19.7747			−1.46984			−0.734922	−	0.678151i	$-0.762781\pi$
$181$	−19.7747			−1.46984			−0.734922	+	0.678151i	$0.762781\pi$
$182$	−15.1373	+	15.1373i	−1.12205	+	1.12205i
$183$		0			0
$184$			1.27918i			0.0943025i
$185$	−2.72082	+	3.54925i	−0.200039	+	0.260946i
$186$		0			0
$187$	6.51379	+	6.51379i	0.476335	+	0.476335i
$188$	−5.77173	−	5.77173i	−0.420947	−	0.420947i
$189$		0			0
$190$	1.36041	−	1.77462i	0.0986945	−	0.128745i
$191$			21.3639i			1.54583i	0.634507	+	0.772917i	$0.281203\pi$
$191$			21.3639i			1.54583i	−0.634507	+	0.772917i	$0.718797\pi$
$192$		0			0
$193$	15.9942	−	15.9942i	1.15129	−	1.15129i	0.164994	−	0.986295i	$-0.447240\pi$
$193$	15.9942	−	15.9942i	1.15129	−	1.15129i	0.986295	−	0.164994i	$-0.0527604\pi$
$194$	14.3492			1.03021
$195$		0			0
$196$	4.65685			0.332632
$197$	9.55334	−	9.55334i	0.680647	−	0.680647i	−0.279499	−	0.960146i	$-0.590168\pi$
$197$	9.55334	−	9.55334i	0.680647	−	0.680647i	0.960146	+	0.279499i	$0.0901683\pi$
$198$		0			0
$199$		−	16.7393i		−	1.18662i	−0.804975	−	0.593308i	$-0.797822\pi$
$199$		−	16.7393i		−	1.18662i	0.804975	−	0.593308i	$-0.202178\pi$
$200$	4.33244	+	2.49598i	0.306350	+	0.176493i
$201$		0			0
$202$	−7.24264	−	7.24264i	−0.509590	−	0.509590i
$203$	−21.4073	−	21.4073i	−1.50250	−	1.50250i
$204$		0			0
$205$	−2.17382	+	0.287214i	−0.151826	+	0.0200599i
$206$			10.1179i			0.704946i
$207$		0			0
$208$	−4.43361	+	4.43361i	−0.307415	+	0.307415i
$209$	5.41421			0.374509
$210$		0			0
$211$	−9.11456			−0.627472			−0.313736	−	0.949510i	$-0.601581\pi$
$211$	−9.11456			−0.627472			−0.313736	+	0.949510i	$0.601581\pi$
$212$	−4.24264	+	4.24264i	−0.291386	+	0.291386i
$213$		0			0
$214$			4.48528i			0.306608i
$215$	−5.06806	−	3.88513i	−0.345639	−	0.264963i
$216$		0			0
$217$	−25.7747	−	25.7747i	−1.74970	−	1.74970i
$218$	8.73218	+	8.73218i	0.591418	+	0.591418i
$219$		0			0
$220$	1.58579	+	12.0022i	0.106914	+	0.809191i
$221$		−	10.6681i		−	0.717611i
$222$		0			0
$223$	−5.75310	+	5.75310i	−0.385256	+	0.385256i	−0.872992	−	0.487735i	$-0.837823\pi$
$223$	−5.75310	+	5.75310i	−0.385256	+	0.385256i	0.487735	+	0.872992i	$0.337823\pi$
$224$	3.41421			0.228122
$225$		0			0
$226$	2.86721			0.190724
$227$	−4.19096	+	4.19096i	−0.278164	+	0.278164i	−0.832376	−	0.554212i	$-0.813020\pi$
$227$	−4.19096	+	4.19096i	−0.278164	+	0.278164i	0.554212	+	0.832376i	$0.313020\pi$
$228$		0			0
$229$		−	13.7687i		−	0.909863i	−0.890527	−	0.454931i	$-0.849664\pi$
$229$		−	13.7687i		−	0.909863i	0.890527	−	0.454931i	$-0.150336\pi$
$230$	−0.374664	−	2.83569i	−0.0247046	−	0.186980i
$231$		0			0
$232$	−6.27006	−	6.27006i	−0.411650	−	0.411650i
$233$	12.7513	+	12.7513i	0.835362	+	0.835362i	0.988244	−	0.152882i	$-0.0488555\pi$
$233$	12.7513	+	12.7513i	0.835362	+	0.835362i	−0.152882	+	0.988244i	$0.548855\pi$
$234$		0			0
$235$	14.4853	+	11.1043i	0.944916	+	0.724363i
$236$		−	9.84782i		−	0.641038i
$237$		0			0
$238$	−4.10761	+	4.10761i	−0.266257	+	0.266257i
$239$	1.82039			0.117752			0.0588758	−	0.998265i	$-0.481248\pi$
$239$	1.82039			0.117752			0.0588758	+	0.998265i	$0.481248\pi$
$240$		0			0
$241$	−0.365864			−0.0235674			−0.0117837	−	0.999931i	$-0.503751\pi$
$241$	−0.365864			−0.0235674			−0.0117837	+	0.999931i	$0.503751\pi$
$242$	−12.9497	+	12.9497i	−0.832441	+	0.832441i
$243$		0			0
$244$		−	9.09849i		−	0.582471i
$245$	−10.3233	+	1.36396i	−0.659533	+	0.0871403i
$246$		0			0
$247$	−4.43361	−	4.43361i	−0.282104	−	0.282104i
$248$	−7.54925	−	7.54925i	−0.479378	−	0.479378i
$249$		0			0
$250$	−10.3352	−	4.26416i	−0.653657	−	0.269689i
$251$			1.06953i			0.0675084i	0.999430	+	0.0337542i	$0.0107463\pi$
$251$			1.06953i			0.0675084i	−0.999430	+	0.0337542i	$0.989254\pi$
$252$		0			0
$253$	4.89725	−	4.89725i	0.307888	−	0.307888i
$254$	−2.74933			−0.172508
$255$		0			0
$256$	1.00000			0.0625000
$257$	−2.77675	+	2.77675i	−0.173209	+	0.173209i	−0.788388	−	0.615179i	$-0.789084\pi$
$257$	−2.77675	+	2.77675i	−0.173209	+	0.173209i	0.615179	+	0.788388i	$0.289084\pi$
$258$		0			0
$259$		−	6.82843i		−	0.424298i
$260$	8.52985	−	11.1270i	0.528999	−	0.690067i
$261$		0			0
$262$	8.74021	+	8.74021i	0.539972	+	0.539972i
$263$	−6.95466	−	6.95466i	−0.428843	−	0.428843i	0.459391	−	0.888234i	$-0.348068\pi$
$263$	−6.95466	−	6.95466i	−0.428843	−	0.428843i	−0.888234	+	0.459391i	$0.848068\pi$
$264$		0			0
$265$	8.16246	−	10.6477i	0.501416	−	0.654085i
$266$			3.41421i			0.209339i
$267$		0			0
$268$	−5.84782	+	5.84782i	−0.357212	+	0.357212i
$269$	−1.69115			−0.103111			−0.0515557	−	0.998670i	$-0.516418\pi$
$269$	−1.69115			−0.103111			−0.0515557	+	0.998670i	$0.516418\pi$
$270$		0			0
$271$	−1.88814			−0.114696			−0.0573480	−	0.998354i	$-0.518264\pi$
$271$	−1.88814			−0.114696			−0.0573480	+	0.998354i	$0.518264\pi$
$272$	−1.20309	+	1.20309i	−0.0729481	+	0.0729481i
$273$		0			0
$274$		−	2.08336i		−	0.125860i
$275$	−7.03075	−	26.1421i	−0.423970	−	1.57643i
$276$		0			0
$277$	11.3378	+	11.3378i	0.681223	+	0.681223i	0.960276	−	0.279053i	$-0.0900205\pi$
$277$	11.3378	+	11.3378i	0.681223	+	0.681223i	−0.279053	+	0.960276i	$0.590021\pi$
$278$	−4.99197	−	4.99197i	−0.299398	−	0.299398i
$279$		0			0
$280$	−7.56864	+	1.00000i	−0.452313	+	0.0597614i
$281$		−	15.0421i		−	0.897337i	−0.893698	−	0.448669i	$-0.851898\pi$
$281$		−	15.0421i		−	0.897337i	0.893698	−	0.448669i	$-0.148102\pi$
$282$		0			0
$283$	−10.4659	+	10.4659i	−0.622133	+	0.622133i	−0.946076	−	0.323944i	$-0.894991\pi$
$283$	−10.4659	+	10.4659i	−0.622133	+	0.622133i	0.323944	+	0.946076i	$0.394991\pi$
$284$	15.0985			0.895931
$285$		0			0
$286$	33.9475			2.00736
$287$	2.36740	−	2.36740i	0.139743	−	0.139743i
$288$		0			0
$289$			14.1051i			0.829714i
$290$	15.7360	+	12.0630i	0.924047	+	0.708366i
$291$		0			0
$292$	−3.82843	−	3.82843i	−0.224042	−	0.224042i
$293$	−13.9383	−	13.9383i	−0.814283	−	0.814283i	0.170990	−	0.985273i	$-0.445303\pi$
$293$	−13.9383	−	13.9383i	−0.814283	−	0.814283i	−0.985273	+	0.170990i	$0.945303\pi$
$294$		0			0
$295$	2.88436	+	21.8307i	0.167934	+	1.27103i
$296$		−	2.00000i		−	0.116248i
$297$		0			0
$298$	−7.36631	+	7.36631i	−0.426719	+	0.426719i
$299$	−8.02055			−0.463840
$300$		0			0
$301$	9.75048			0.562009
$302$	3.89239	−	3.89239i	0.223982	−	0.223982i
$303$		0			0
$304$			1.00000i			0.0573539i
$305$	2.66489	+	20.1696i	0.152591	+	1.15491i
$306$		0			0
$307$	5.63260	+	5.63260i	0.321470	+	0.321470i	0.849331	−	0.527861i	$-0.177006\pi$
$307$	5.63260	+	5.63260i	0.321470	+	0.321470i	−0.527861	+	0.849331i	$0.677006\pi$
$308$	−13.0711	−	13.0711i	−0.744793	−	0.744793i
$309$		0			0
$310$	18.9463	+	14.5241i	1.07608	+	0.824911i
$311$			19.6354i			1.11342i	0.830706	+	0.556712i	$0.187937\pi$
$311$			19.6354i			1.11342i	−0.830706	+	0.556712i	$0.812063\pi$
$312$		0			0
$313$	−19.7108	+	19.7108i	−1.11412	+	1.11412i	−0.121531	+	0.992588i	$0.538780\pi$
$313$	−19.7108	+	19.7108i	−1.11412	+	1.11412i	−0.992588	+	0.121531i	$0.961220\pi$
$314$	−3.98864			−0.225092
$315$		0			0
$316$	−9.28946			−0.522573
$317$	2.62457	−	2.62457i	0.147411	−	0.147411i	−0.629550	−	0.776960i	$-0.716761\pi$
$317$	2.62457	−	2.62457i	0.147411	−	0.147411i	0.776960	+	0.629550i	$0.216761\pi$
$318$		0			0
$319$			48.0090i			2.68799i
$320$	−2.21680	+	0.292893i	−0.123923	+	0.0163732i
$321$		0			0
$322$	3.08822	+	3.08822i	0.172100	+	0.172100i
$323$	−1.20309	−	1.20309i	−0.0669418	−	0.0669418i
$324$		0			0
$325$	−15.6500	+	27.1647i	−0.868105	+	1.50683i
$326$			16.1453i			0.894206i
$327$		0			0
$328$	0.693395	−	0.693395i	0.0382863	−	0.0382863i
$329$	−27.8684			−1.53643
$330$		0			0
$331$	18.6274			1.02386			0.511928	−	0.859029i	$-0.328932\pi$
$331$	18.6274			1.02386			0.511928	+	0.859029i	$0.328932\pi$
$332$	−9.30961	+	9.30961i	−0.510931	+	0.510931i
$333$		0			0
$334$		−	8.02272i		−	0.438984i
$335$	11.2507	−	14.6762i	0.614690	−	0.801849i
$336$		0			0
$337$	7.41313	+	7.41313i	0.403819	+	0.403819i	0.879576	−	0.475758i	$-0.157826\pi$
$337$	7.41313	+	7.41313i	0.403819	+	0.403819i	−0.475758	+	0.879576i	$0.657826\pi$
$338$	−18.6066	−	18.6066i	−1.01207	−	1.01207i
$339$		0			0
$340$	2.31464	−	3.01939i	0.125529	−	0.163749i
$341$			57.8035i			3.13023i
$342$		0			0
$343$	−5.65685	+	5.65685i	−0.305441	+	0.305441i
$344$	2.85585			0.153977
$345$		0			0
$346$	1.09849			0.0590553
$347$	−25.0053	+	25.0053i	−1.34235	+	1.34235i	−0.448639	+	0.893713i	$0.648091\pi$
$347$	−25.0053	+	25.0053i	−1.34235	+	1.34235i	−0.893713	+	0.448639i	$0.851909\pi$
$348$		0			0
$349$			32.1239i			1.71955i	0.510670	+	0.859777i	$0.329397\pi$
$349$			32.1239i			1.71955i	−0.510670	+	0.859777i	$0.670603\pi$
$350$	16.4853	−	4.43361i	0.881175	−	0.236986i
$351$		0			0
$352$	−3.82843	−	3.82843i	−0.204056	−	0.204056i
$353$	−7.88404	−	7.88404i	−0.419625	−	0.419625i	0.465449	−	0.885075i	$-0.345893\pi$
$353$	−7.88404	−	7.88404i	−0.419625	−	0.419625i	−0.885075	+	0.465449i	$0.845893\pi$
$354$		0			0
$355$	−33.4704	+	4.42225i	−1.77642	+	0.234708i
$356$		−	8.46103i		−	0.448434i
$357$		0			0
$358$	−15.4084	+	15.4084i	−0.814361	+	0.814361i
$359$	−8.82372			−0.465698			−0.232849	−	0.972513i	$-0.574805\pi$
$359$	−8.82372			−0.465698			−0.232849	+	0.972513i	$0.574805\pi$
$360$		0			0
$361$	−1.00000			−0.0526316
$362$	−13.9829	+	13.9829i	−0.734922	+	0.734922i
$363$		0			0
$364$			21.4073i			1.12205i
$365$	9.60819	+	7.36555i	0.502916	+	0.385530i
$366$		0			0
$367$	−1.47818	−	1.47818i	−0.0771603	−	0.0771603i	0.667473	−	0.744634i	$-0.267376\pi$
$367$	−1.47818	−	1.47818i	−0.0771603	−	0.0771603i	−0.744634	+	0.667473i	$0.767376\pi$
$368$	0.904518	+	0.904518i	0.0471512	+	0.0471512i
$369$		0			0
$370$	0.585786	+	4.43361i	0.0304536	+	0.230492i
$371$			20.4853i			1.06354i
$372$		0			0
$373$	10.8171	−	10.8171i	0.560087	−	0.560087i	−0.369245	−	0.929332i	$-0.620384\pi$
$373$	10.8171	−	10.8171i	0.560087	−	0.560087i	0.929332	+	0.369245i	$0.120384\pi$
$374$	9.21189			0.476335
$375$		0			0
$376$	−8.16246			−0.420947
$377$	39.3137	−	39.3137i	2.02476	−	2.02476i
$378$		0			0
$379$		−	18.7393i		−	0.962572i	−0.876564	−	0.481286i	$-0.840170\pi$
$379$		−	18.7393i		−	0.962572i	0.876564	−	0.481286i	$-0.159830\pi$
$380$	−0.292893	−	2.21680i	−0.0150251	−	0.113720i
$381$		0			0
$382$	15.1065	+	15.1065i	0.772917	+	0.772917i
$383$	13.0824	+	13.0824i	0.668481	+	0.668481i	0.957364	−	0.288883i	$-0.0932840\pi$
$383$	13.0824	+	13.0824i	0.668481	+	0.668481i	−0.288883	+	0.957364i	$0.593284\pi$
$384$		0			0
$385$	32.8044	+	25.1475i	1.67187	+	1.28164i
$386$		−	22.6192i		−	1.15129i
$387$		0			0
$388$	10.1464	−	10.1464i	0.515105	−	0.515105i
$389$	27.1647			1.37730			0.688652	−	0.725092i	$-0.258203\pi$
$389$	27.1647			1.37730			0.688652	+	0.725092i	$0.258203\pi$
$390$		0			0
$391$	−2.17643			−0.110067
$392$	3.29289	−	3.29289i	0.166316	−	0.166316i
$393$		0			0
$394$		−	13.5105i		−	0.680647i
$395$	20.5929	−	2.72082i	1.03614	−	0.136899i
$396$		0			0
$397$	21.1981	+	21.1981i	1.06390	+	1.06390i	0.997814	+	0.0660866i	$0.0210514\pi$
$397$	21.1981	+	21.1981i	1.06390	+	1.06390i	0.0660866	+	0.997814i	$0.478949\pi$
$398$	−11.8365	−	11.8365i	−0.593308	−	0.593308i
$399$		0			0
$400$	4.82843	−	1.29857i	0.241421	−	0.0649286i
$401$			3.42711i			0.171142i	0.996332	+	0.0855708i	$0.0272714\pi$
$401$			3.42711i			0.171142i	−0.996332	+	0.0855708i	$0.972729\pi$
$402$		0			0
$403$	47.3343	−	47.3343i	2.35789	−	2.35789i
$404$	−10.2426			−0.509590
$405$		0			0
$406$	−30.2745			−1.50250
$407$	−7.65685	+	7.65685i	−0.379536	+	0.379536i
$408$		0			0
$409$		−	8.42071i		−	0.416377i	−0.978089	−	0.208189i	$-0.933243\pi$
$409$		−	8.42071i		−	0.416377i	0.978089	−	0.208189i	$-0.0667568\pi$
$410$	−1.33403	+	1.74021i	−0.0658830	+	0.0859429i
$411$		0			0
$412$	7.15442	+	7.15442i	0.352473	+	0.352473i
$413$	−23.7747	−	23.7747i	−1.16988	−	1.16988i
$414$		0			0
$415$	17.9109	−	23.3643i	0.879209	−	1.14691i
$416$			6.27006i			0.307415i
$417$		0			0
$418$	3.82843	−	3.82843i	0.187254	−	0.187254i
$419$	−31.4757			−1.53769			−0.768845	−	0.639436i	$-0.779168\pi$
$419$	−31.4757			−1.53769			−0.768845	+	0.639436i	$0.779168\pi$
$420$		0			0
$421$	−39.4155			−1.92100			−0.960498	−	0.278288i	$-0.910233\pi$
$421$	−39.4155			−1.92100			−0.960498	+	0.278288i	$0.910233\pi$
$422$	−6.44496	+	6.44496i	−0.313736	+	0.313736i
$423$		0			0
$424$			6.00000i			0.291386i
$425$	−4.24673	+	7.37134i	−0.205997	+	0.357562i
$426$		0			0
$427$	−21.9657	−	21.9657i	−1.06299	−	1.06299i
$428$	3.17157	+	3.17157i	0.153304	+	0.153304i
$429$		0			0
$430$	−6.33086	+	0.836459i	−0.305301	+	0.0403377i
$431$			20.9478i			1.00902i	0.863405	+	0.504511i	$0.168327\pi$
$431$			20.9478i			1.00902i	−0.863405	+	0.504511i	$0.831673\pi$
$432$		0			0
$433$	16.3213	−	16.3213i	0.784351	−	0.784351i	−0.196211	−	0.980562i	$-0.562864\pi$
$433$	16.3213	−	16.3213i	0.784351	−	0.784351i	0.980562	+	0.196211i	$0.0628636\pi$
$434$	−36.4510			−1.74970
$435$		0			0
$436$	12.3492			0.591418
$437$	−0.904518	+	0.904518i	−0.0432690	+	0.0432690i
$438$		0			0
$439$		−	17.1455i		−	0.818308i	−0.912465	−	0.409154i	$-0.865824\pi$
$439$		−	17.1455i		−	0.818308i	0.912465	−	0.409154i	$-0.134176\pi$
$440$	9.60819	+	7.36555i	0.458052	+	0.351139i
$441$		0			0
$442$	−7.54346	−	7.54346i	−0.358806	−	0.358806i
$443$	6.12668	+	6.12668i	0.291087	+	0.291087i	0.837510	−	0.546422i	$-0.184011\pi$
$443$	6.12668	+	6.12668i	0.291087	+	0.291087i	−0.546422	+	0.837510i	$0.684011\pi$
$444$		0			0
$445$	2.47818	+	18.7564i	0.117477	+	0.889140i
$446$			8.13612i			0.385256i
$447$		0			0
$448$	2.41421	−	2.41421i	0.114061	−	0.114061i
$449$	−29.6674			−1.40009			−0.700045	−	0.714099i	$-0.746837\pi$
$449$	−29.6674			−1.40009			−0.700045	+	0.714099i	$0.746837\pi$
$450$		0			0
$451$	−5.30922			−0.250002
$452$	2.02742	−	2.02742i	0.0953620	−	0.0953620i
$453$		0			0
$454$			5.92692i			0.278164i
$455$	−6.27006	−	47.4558i	−0.293945	−	2.22476i
$456$		0			0
$457$	17.4122	+	17.4122i	0.814508	+	0.814508i	0.985306	−	0.170798i	$-0.0546345\pi$
$457$	17.4122	+	17.4122i	0.814508	+	0.814508i	−0.170798	+	0.985306i	$0.554634\pi$
$458$	−9.73595	−	9.73595i	−0.454931	−	0.454931i
$459$		0			0
$460$	−2.27006	−	1.74021i	−0.105842	−	0.0811377i
$461$		−	32.5918i		−	1.51795i	−0.651119	−	0.758976i	$-0.725700\pi$
$461$		−	32.5918i		−	1.51795i	0.651119	−	0.758976i	$-0.274300\pi$
$462$		0			0
$463$	−7.10073	+	7.10073i	−0.329999	+	0.329999i	−0.852586	−	0.522587i	$-0.824967\pi$
$463$	−7.10073	+	7.10073i	−0.329999	+	0.329999i	0.522587	+	0.852586i	$0.324967\pi$
$464$	−8.86721			−0.411650
$465$		0			0
$466$	18.0330			0.835362
$467$	−5.96848	+	5.96848i	−0.276188	+	0.276188i	−0.831585	−	0.555397i	$-0.812566\pi$
$467$	−5.96848	+	5.96848i	−0.276188	+	0.276188i	0.555397	+	0.831585i	$0.312566\pi$
$468$		0			0
$469$			28.2358i			1.30381i
$470$	18.0946	−	2.39073i	0.834640	−	0.110276i
$471$		0			0
$472$	−6.96346	−	6.96346i	−0.320519	−	0.320519i
$473$	−10.9334	−	10.9334i	−0.502719	−	0.502719i
$474$		0			0
$475$	1.29857	+	4.82843i	0.0595826	+	0.221543i
$476$			5.80904i			0.266257i
$477$		0			0
$478$	1.28721	−	1.28721i	0.0588758	−	0.0588758i
$479$	6.51271			0.297573			0.148787	−	0.988869i	$-0.452463\pi$
$479$	6.51271			0.297573			0.148787	+	0.988869i	$0.452463\pi$
$480$		0			0
$481$	12.5401			0.571781
$482$	−0.258705	+	0.258705i	−0.0117837	+	0.0117837i
$483$		0			0
$484$			18.3137i			0.832441i
$485$	−19.5207	+	25.4644i	−0.886391	+	1.15628i
$486$		0			0
$487$	−18.8904	−	18.8904i	−0.856005	−	0.856005i	0.134860	−	0.990865i	$-0.456942\pi$
$487$	−18.8904	−	18.8904i	−0.856005	−	0.856005i	−0.990865	+	0.134860i	$0.956942\pi$
$488$	−6.43361	−	6.43361i	−0.291236	−	0.291236i
$489$		0			0
$490$	−6.33523	+	8.26416i	−0.286196	+	0.373337i
$491$		−	41.9916i		−	1.89505i	−0.319676	−	0.947527i	$-0.603574\pi$
$491$		−	41.9916i		−	1.89505i	0.319676	−	0.947527i	$-0.396426\pi$
$492$		0			0
$493$	10.6681	−	10.6681i	0.480465	−	0.480465i
$494$	−6.27006			−0.282104
$495$		0			0
$496$	−10.6762			−0.479378
$497$	36.4510	−	36.4510i	1.63505	−	1.63505i
$498$		0			0
$499$		−	2.97907i		−	0.133362i	−0.997774	−	0.0666808i	$-0.978759\pi$
$499$		−	2.97907i		−	0.133362i	0.997774	−	0.0666808i	$-0.0212409\pi$
$500$	−10.3233	+	4.29289i	−0.461673	+	0.191984i
$501$		0			0
$502$	0.756275	+	0.756275i	0.0337542	+	0.0337542i
$503$	3.14716	+	3.14716i	0.140325	+	0.140325i	0.773780	−	0.633455i	$-0.218364\pi$
$503$	3.14716	+	3.14716i	0.140325	+	0.140325i	−0.633455	+	0.773780i	$0.718364\pi$
$504$		0			0
$505$	22.7059	−	3.00000i	1.01040	−	0.133498i
$506$		−	6.92576i		−	0.307888i
$507$		0			0
$508$	−1.94407	+	1.94407i	−0.0862541	+	0.0862541i
$509$	4.92206			0.218166			0.109083	−	0.994033i	$-0.465209\pi$
$509$	4.92206			0.218166			0.109083	+	0.994033i	$0.465209\pi$
$510$		0			0
$511$	−18.4853			−0.817741
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$		0			0
$514$			3.92692i			0.173209i
$515$	−17.9554	−	13.7645i	−0.791211	−	0.606535i
$516$		0			0
$517$	31.2494	+	31.2494i	1.37435	+	1.37435i
$518$	−4.82843	−	4.82843i	−0.212149	−	0.212149i
$519$		0			0
$520$	−1.83646	−	13.8995i	−0.0805341	−	0.609533i
$521$			21.3767i			0.936532i	0.883588	+	0.468266i	$0.155121\pi$
$521$			21.3767i			0.936532i	−0.883588	+	0.468266i	$0.844879\pi$
$522$		0			0
$523$	8.96454	−	8.96454i	0.391992	−	0.391992i	−0.483405	−	0.875397i	$-0.660600\pi$
$523$	8.96454	−	8.96454i	0.391992	−	0.391992i	0.875397	+	0.483405i	$0.160600\pi$
$524$	12.3605			0.539972
$525$		0			0
$526$	−9.83537			−0.428843
$527$	12.8445	−	12.8445i	0.559515	−	0.559515i
$528$		0			0
$529$		−	21.3637i		−	0.928856i
$530$	−1.75736	−	13.3008i	−0.0763348	−	0.577750i
$531$		0			0
$532$	2.41421	+	2.41421i	0.104669	+	0.104669i
$533$	4.34763	+	4.34763i	0.188317	+	0.188317i
$534$		0			0
$535$	−7.95968	−	6.10182i	−0.344127	−	0.263805i
$536$			8.27006i			0.357212i
$537$		0			0
$538$	−1.19583	+	1.19583i	−0.0515557	+	0.0515557i
$539$	−25.2132			−1.08601
$540$		0			0
$541$	−22.4670			−0.965934			−0.482967	−	0.875639i	$-0.660441\pi$
$541$	−22.4670			−0.965934			−0.482967	+	0.875639i	$0.660441\pi$
$542$	−1.33511	+	1.33511i	−0.0573480	+	0.0573480i
$543$		0			0
$544$			1.70143i			0.0729481i
$545$	−27.3757	+	3.61699i	−1.17264	+	0.154935i
$546$		0			0
$547$	−3.12274	−	3.12274i	−0.133519	−	0.133519i	0.637189	−	0.770708i	$-0.280097\pi$
$547$	−3.12274	−	3.12274i	−0.133519	−	0.133519i	−0.770708	+	0.637189i	$0.780097\pi$
$548$	−1.47316	−	1.47316i	−0.0629301	−	0.0629301i
$549$		0			0
$550$	−23.4568	−	13.5138i	−1.00020	−	0.576230i
$551$		−	8.86721i		−	0.377756i
$552$		0			0
$553$	−22.4267	+	22.4267i	−0.953682	+	0.953682i
$554$	16.0341			0.681223
$555$		0			0
$556$	−7.05971			−0.299398
$557$	−2.98896	+	2.98896i	−0.126646	+	0.126646i	−0.767589	−	0.640943i	$-0.778544\pi$
$557$	−2.98896	+	2.98896i	−0.126646	+	0.126646i	0.640943	+	0.767589i	$0.278544\pi$
$558$		0			0
$559$			17.9064i			0.757359i
$560$	−4.64473	+	6.05894i	−0.196276	+	0.256037i
$561$		0			0
$562$	−10.6364	−	10.6364i	−0.448669	−	0.448669i
$563$	4.94631	+	4.94631i	0.208462	+	0.208462i	0.803614	−	0.595151i	$-0.202908\pi$
$563$	4.94631	+	4.94631i	0.208462	+	0.208462i	−0.595151	+	0.803614i	$0.702908\pi$
$564$		0			0
$565$	−3.90058	+	5.08822i	−0.164099	+	0.214063i
$566$			14.8010i			0.622133i
$567$		0			0
$568$	10.6762	−	10.6762i	0.447965	−	0.447965i
$569$	25.8135			1.08216			0.541080	−	0.840971i	$-0.318016\pi$
$569$	25.8135			1.08216			0.541080	+	0.840971i	$0.318016\pi$
$570$		0			0
$571$	−13.6150			−0.569770			−0.284885	−	0.958562i	$-0.591955\pi$
$571$	−13.6150			−0.569770			−0.284885	+	0.958562i	$0.591955\pi$
$572$	24.0045	−	24.0045i	1.00368	−	1.00368i
$573$		0			0
$574$		−	3.34801i		−	0.139743i
$575$	5.54198	+	3.19282i	0.231117	+	0.133150i
$576$		0			0
$577$	−25.1867	−	25.1867i	−1.04854	−	1.04854i	−0.998760	−	0.0497760i	$-0.984149\pi$
$577$	−25.1867	−	25.1867i	−1.04854	−	1.04854i	−0.0497760	−	0.998760i	$-0.515851\pi$
$578$	9.97384	+	9.97384i	0.414857	+	0.414857i
$579$		0			0
$580$	19.6569	−	2.59715i	0.816206	−	0.107841i
$581$			44.9508i			1.86487i
$582$		0			0
$583$	22.9706	−	22.9706i	0.951344	−	0.951344i
$584$	−5.41421			−0.224042
$585$		0			0
$586$	−19.7117			−0.814283
$587$	−0.127318	+	0.127318i	−0.00525496	+	0.00525496i	−0.709729	−	0.704474i	$-0.751183\pi$
$587$	−0.127318	+	0.127318i	−0.00525496	+	0.00525496i	0.704474	+	0.709729i	$0.251183\pi$
$588$		0			0
$589$		−	10.6762i		−	0.439907i
$590$	17.4762	+	13.3971i	0.719482	+	0.551548i
$591$		0			0
$592$	−1.41421	−	1.41421i	−0.0581238	−	0.0581238i
$593$	17.6481	+	17.6481i	0.724719	+	0.724719i	0.969563	−	0.244844i	$-0.0787367\pi$
$593$	17.6481	+	17.6481i	0.724719	+	0.724719i	−0.244844	+	0.969563i	$0.578737\pi$
$594$		0			0
$595$	−1.70143	−	12.8775i	−0.0697517	−	0.527925i
$596$			10.4175i			0.426719i
$597$		0			0
$598$	−5.67138	+	5.67138i	−0.231920	+	0.231920i
$599$	19.6613			0.803341			0.401670	−	0.915784i	$-0.368430\pi$
$599$	19.6613			0.803341			0.401670	+	0.915784i	$0.368430\pi$
$600$		0			0
$601$	24.6047			1.00365			0.501823	−	0.864970i	$-0.332663\pi$
$601$	24.6047			1.00365			0.501823	+	0.864970i	$0.332663\pi$
$602$	6.89463	−	6.89463i	0.281004	−	0.281004i
$603$		0			0
$604$		−	5.50467i		−	0.223982i
$605$	−5.36396	−	40.5979i	−0.218076	−	1.65054i
$606$		0			0
$607$	27.0713	+	27.0713i	1.09879	+	1.09879i	0.994552	+	0.104238i	$0.0332402\pi$
$607$	27.0713	+	27.0713i	1.09879	+	1.09879i	0.104238	+	0.994552i	$0.466760\pi$
$608$	0.707107	+	0.707107i	0.0286770	+	0.0286770i
$609$		0			0
$610$	16.1464	+	12.3777i	0.653748	+	0.501157i
$611$		−	51.1791i		−	2.07049i
$612$		0			0
$613$	−20.0125	+	20.0125i	−0.808298	+	0.808298i	−0.984376	−	0.176078i	$-0.943659\pi$
$613$	−20.0125	+	20.0125i	−0.808298	+	0.808298i	0.176078	+	0.984376i	$0.443659\pi$
$614$	7.96570			0.321470
$615$		0			0
$616$	−18.4853			−0.744793
$617$	−15.1849	+	15.1849i	−0.611319	+	0.611319i	−0.943290	−	0.331970i	$-0.892287\pi$
$617$	−15.1849	+	15.1849i	−0.611319	+	0.611319i	0.331970	+	0.943290i	$0.392287\pi$
$618$		0			0
$619$		−	47.2955i		−	1.90097i	−0.310777	−	0.950483i	$-0.600589\pi$
$619$		−	47.2955i		−	1.90097i	0.310777	−	0.950483i	$-0.399411\pi$
$620$	23.6671	−	3.12700i	0.950495	−	0.125583i
$621$		0			0
$622$	13.8844	+	13.8844i	0.556712	+	0.556712i
$623$	−20.4267	−	20.4267i	−0.818380	−	0.818380i
$624$		0			0
$625$	21.6274	−	12.5401i	0.865097	−	0.501605i
$626$			27.8752i			1.11412i
$627$		0			0
$628$	−2.82039	+	2.82039i	−0.112546	+	0.112546i
$629$	3.40285			0.135681
$630$		0			0
$631$	−12.7639			−0.508121			−0.254061	−	0.967188i	$-0.581766\pi$
$631$	−12.7639			−0.508121			−0.254061	+	0.967188i	$0.581766\pi$
$632$	−6.56864	+	6.56864i	−0.261286	+	0.261286i
$633$		0			0
$634$		−	3.71170i		−	0.147411i
$635$	3.74021	−	4.87902i	0.148426	−	0.193618i
$636$		0			0
$637$	20.6467	+	20.6467i	0.818050	+	0.818050i
$638$	33.9475	+	33.9475i	1.34399	+	1.34399i
$639$		0			0
$640$	−1.36041	+	1.77462i	−0.0537749	+	0.0701481i
$641$		−	19.2346i		−	0.759721i	−0.925044	−	0.379861i	$-0.875972\pi$
$641$		−	19.2346i		−	0.759721i	0.925044	−	0.379861i	$-0.124028\pi$
$642$		0			0
$643$	23.0060	−	23.0060i	0.907269	−	0.907269i	−0.0887822	−	0.996051i	$-0.528298\pi$
$643$	23.0060	−	23.0060i	0.907269	−	0.907269i	0.996051	+	0.0887822i	$0.0282975\pi$
$644$	4.36740			0.172100
$645$		0			0
$646$	−1.70143			−0.0669418
$647$	−22.7943	+	22.7943i	−0.896136	+	0.896136i	−0.995092	−	0.0989558i	$-0.968450\pi$
$647$	−22.7943	+	22.7943i	−0.896136	+	0.896136i	0.0989558	+	0.995092i	$0.468450\pi$
$648$		0			0
$649$			53.3182i			2.09292i
$650$	8.14214	+	30.2745i	0.319361	+	1.18747i
$651$		0			0
$652$	11.4165	+	11.4165i	0.447103	+	0.447103i
$653$	27.7329	+	27.7329i	1.08527	+	1.08527i	0.996008	+	0.0892662i	$0.0284522\pi$
$653$	27.7329	+	27.7329i	1.08527	+	1.08527i	0.0892662	+	0.996008i	$0.471548\pi$
$654$		0			0
$655$	−27.4008	+	3.62031i	−1.07064	+	0.141457i
$656$		−	0.980608i		−	0.0382863i
$657$		0			0
$658$	−19.7059	+	19.7059i	−0.768216	+	0.768216i
$659$	19.1085			0.744363			0.372181	−	0.928160i	$-0.378610\pi$
$659$	19.1085			0.744363			0.372181	+	0.928160i	$0.378610\pi$
$660$		0			0
$661$	40.4494			1.57330			0.786651	−	0.617398i	$-0.211813\pi$
$661$	40.4494			1.57330			0.786651	+	0.617398i	$0.211813\pi$
$662$	13.1716	−	13.1716i	0.511928	−	0.511928i
$663$		0			0
$664$			13.1658i			0.510931i
$665$	−6.05894	−	4.64473i	−0.234956	−	0.180115i
$666$		0			0
$667$	−8.02055	−	8.02055i	−0.310557	−	0.310557i
$668$	−5.67292	−	5.67292i	−0.219492	−	0.219492i
$669$		0			0
$670$	−2.42225	−	18.3331i	−0.0935795	−	0.708269i
$671$			49.2612i			1.90171i
$672$		0			0
$673$	27.4191	−	27.4191i	1.05693	−	1.05693i	0.0586520	−	0.998278i	$-0.481320\pi$
$673$	27.4191	−	27.4191i	1.05693	−	1.05693i	0.998278	−	0.0586520i	$-0.0186802\pi$
$674$	10.4837			0.403819
$675$		0			0
$676$	−26.3137			−1.01207
$677$	−14.7197	+	14.7197i	−0.565725	+	0.565725i	−0.930928	−	0.365203i	$-0.881000\pi$
$677$	−14.7197	+	14.7197i	−0.565725	+	0.565725i	0.365203	+	0.930928i	$0.381000\pi$
$678$		0			0
$679$		−	48.9911i		−	1.88011i
$680$	−0.498336	−	3.77173i	−0.0191103	−	0.144639i
$681$		0			0
$682$	40.8732	+	40.8732i	1.56512	+	1.56512i
$683$	1.91085	+	1.91085i	0.0731168	+	0.0731168i	0.742719	−	0.669603i	$-0.233536\pi$
$683$	1.91085	+	1.91085i	0.0731168	+	0.0731168i	−0.669603	+	0.742719i	$0.733536\pi$
$684$		0			0
$685$	3.69717	+	2.83422i	0.141262	+	0.108290i
$686$			8.00000i			0.305441i
$687$		0			0
$688$	2.01939	−	2.01939i	0.0769886	−	0.0769886i
$689$	−37.6204			−1.43322
$690$		0			0
$691$	−7.11673			−0.270733			−0.135366	−	0.990796i	$-0.543221\pi$
$691$	−7.11673			−0.270733			−0.135366	+	0.990796i	$0.543221\pi$
$692$	0.776751	−	0.776751i	0.0295276	−	0.0295276i
$693$		0			0
$694$			35.3628i			1.34235i
$695$	15.6500	−	2.06774i	0.593638	−	0.0784339i
$696$		0			0
$697$	1.17976	+	1.17976i	0.0446866	+	0.0446866i
$698$	22.7150	+	22.7150i	0.859777	+	0.859777i
$699$		0			0
$700$	8.52182	−	14.7919i	0.322095	−	0.559081i
$701$		−	37.7115i		−	1.42434i	−0.702006	−	0.712172i	$-0.747712\pi$
$701$		−	37.7115i		−	1.42434i	0.702006	−	0.712172i	$-0.252288\pi$
$702$		0			0
$703$	1.41421	−	1.41421i	0.0533381	−	0.0533381i
$704$	−5.41421			−0.204056
$705$		0			0
$706$	−11.1497			−0.419625
$707$	−24.7279	+	24.7279i	−0.929989	+	0.929989i
$708$		0			0
$709$			14.6617i			0.550632i	0.961354	+	0.275316i	$0.0887825\pi$
$709$			14.6617i			0.550632i	−0.961354	+	0.275316i	$0.911217\pi$
$710$	−20.5401	+	26.7941i	−0.770857	+	1.00557i
$711$		0			0
$712$	−5.98285	−	5.98285i	−0.224217	−	0.224217i
$713$	−9.65685	−	9.65685i	−0.361652	−	0.361652i
$714$		0			0
$715$	−46.1825	+	60.2440i	−1.72713	+	2.25300i
$716$			21.7908i			0.814361i
$717$		0			0
$718$	−6.23931	+	6.23931i	−0.232849	+	0.232849i
$719$	−30.3665			−1.13248			−0.566240	−	0.824240i	$-0.691603\pi$
$719$	−30.3665			−1.13248			−0.566240	+	0.824240i	$0.691603\pi$
$720$		0			0
$721$	34.5446			1.28651
$722$	−0.707107	+	0.707107i	−0.0263158	+	0.0263158i
$723$		0			0
$724$			19.7747i			0.734922i
$725$	−42.8147	+	11.5147i	−1.59010	+	0.427646i
$726$		0			0
$727$	−11.3320	−	11.3320i	−0.420281	−	0.420281i	0.465019	−	0.885301i	$-0.346047\pi$
$727$	−11.3320	−	11.3320i	−0.420281	−	0.420281i	−0.885301	+	0.465019i	$0.846047\pi$
$728$	15.1373	+	15.1373i	0.561025	+	0.561025i
$729$		0			0
$730$	12.0022	−	1.58579i	0.444223	−	0.0586926i
$731$			4.85902i			0.179717i
$732$		0			0
$733$	1.95527	−	1.95527i	0.0722196	−	0.0722196i	−0.670074	−	0.742294i	$-0.733738\pi$
$733$	1.95527	−	1.95527i	0.0722196	−	0.0722196i	0.742294	+	0.670074i	$0.233738\pi$
$734$	−2.09046			−0.0771603
$735$		0			0
$736$	1.27918			0.0471512
$737$	31.6613	−	31.6613i	1.16626	−	1.16626i
$738$		0			0
$739$		−	16.6983i		−	0.614258i	−0.951668	−	0.307129i	$-0.900632\pi$
$739$		−	16.6983i		−	0.614258i	0.951668	−	0.307129i	$-0.0993683\pi$
$740$	3.54925	+	2.72082i	0.130473	+	0.100019i
$741$		0			0
$742$	14.4853	+	14.4853i	0.531771	+	0.531771i
$743$	7.94298	+	7.94298i	0.291400	+	0.291400i	0.837633	−	0.546233i	$-0.183939\pi$
$743$	7.94298	+	7.94298i	0.291400	+	0.291400i	−0.546233	+	0.837633i	$0.683939\pi$
$744$		0			0
$745$	−3.05123	−	23.0936i	−0.111788	−	0.846085i
$746$		−	15.2976i		−	0.560087i
$747$		0			0
$748$	6.51379	−	6.51379i	0.238168	−	0.238168i
$749$	15.3137			0.559551
$750$		0			0
$751$	2.07910			0.0758674			0.0379337	−	0.999280i	$-0.487922\pi$
$751$	2.07910			0.0758674			0.0379337	+	0.999280i	$0.487922\pi$
$752$	−5.77173	+	5.77173i	−0.210473	+	0.210473i
$753$		0			0
$754$		−	55.5980i		−	2.02476i
$755$	1.61228	+	12.2028i	0.0586769	+	0.444104i
$756$		0			0
$757$	−26.2277	−	26.2277i	−0.953263	−	0.953263i	0.0456924	−	0.998956i	$-0.485451\pi$
$757$	−26.2277	−	26.2277i	−0.953263	−	0.953263i	−0.998956	+	0.0456924i	$0.985451\pi$
$758$	−13.2507	−	13.2507i	−0.481286	−	0.481286i
$759$		0			0
$760$	−1.77462	−	1.36041i	−0.0643723	−	0.0493472i
$761$			52.3146i			1.89640i	0.317667	+	0.948202i	$0.397100\pi$
$761$			52.3146i			1.89640i	−0.317667	+	0.948202i	$0.602900\pi$
$762$		0			0
$763$	29.8135	−	29.8135i	1.07932	−	1.07932i
$764$	21.3639			0.772917
$765$		0			0
$766$	18.5013			0.668481
$767$	43.6613	−	43.6613i	1.57652	−	1.57652i
$768$		0			0
$769$		−	0.430434i		−	0.0155218i	−0.999970	−	0.00776092i	$-0.997530\pi$
$769$		−	0.430434i		−	0.0155218i	0.999970	−	0.00776092i	$-0.00247040\pi$
$770$	40.9782	−	5.41421i	1.47675	−	0.195115i
$771$		0			0
$772$	−15.9942	−	15.9942i	−0.575644	−	0.575644i
$773$	−18.5354	−	18.5354i	−0.666673	−	0.666673i	0.290271	−	0.956944i	$-0.406254\pi$
$773$	−18.5354	−	18.5354i	−0.666673	−	0.666673i	−0.956944	+	0.290271i	$0.906254\pi$
$774$		0			0
$775$	−51.5495	+	13.8639i	−1.85171	+	0.498005i
$776$		−	14.3492i		−	0.515105i
$777$		0			0
$778$	19.2083	−	19.2083i	0.688652	−	0.688652i
$779$	0.980608			0.0351339
$780$		0			0
$781$	−81.7465			−2.92512
$782$	−1.53897	+	1.53897i	−0.0550335	+	0.0550335i
$783$		0			0
$784$		−	4.65685i		−	0.166316i
$785$	5.42618	−	7.07833i	0.193669	−	0.252637i
$786$		0			0
$787$	−34.8490	−	34.8490i	−1.24223	−	1.24223i	−0.959073	−	0.283159i	$-0.908618\pi$
$787$	−34.8490	−	34.8490i	−1.24223	−	1.24223i	−0.283159	−	0.959073i	$-0.591382\pi$
$788$	−9.55334	−	9.55334i	−0.340324	−	0.340324i
$789$		0			0
$790$	12.6375	−	16.4853i	0.449621	−	0.586520i
$791$		−	9.78927i		−	0.348066i
$792$		0			0
$793$	40.3391	−	40.3391i	1.43248	−	1.43248i
$794$	29.9786			1.06390
$795$		0			0
$796$	−16.7393			−0.593308
$797$	−8.17961	+	8.17961i	−0.289736	+	0.289736i	−0.836976	−	0.547240i	$-0.815679\pi$
$797$	−8.17961	+	8.17961i	−0.289736	+	0.289736i	0.547240	+	0.836976i	$0.315679\pi$
$798$		0			0
$799$		−	13.8878i		−	0.491316i
$800$	2.49598	−	4.33244i	0.0882464	−	0.153175i
$801$		0			0
$802$	2.42333	+	2.42333i	0.0855708	+	0.0855708i
$803$	20.7279	+	20.7279i	0.731472	+	0.731472i
$804$		0			0
$805$	−9.68166	+	1.27918i	−0.341234	+	0.0450852i
$806$		−	66.9407i		−	2.35789i
$807$		0			0
$808$	−7.24264	+	7.24264i	−0.254795	+	0.254795i
$809$	−12.0334			−0.423073			−0.211537	−	0.977370i	$-0.567847\pi$
$809$	−12.0334			−0.423073			−0.211537	+	0.977370i	$0.567847\pi$
$810$		0			0
$811$	−28.4488			−0.998973			−0.499486	−	0.866322i	$-0.666478\pi$
$811$	−28.4488			−0.998973			−0.499486	+	0.866322i	$0.666478\pi$
$812$	−21.4073	+	21.4073i	−0.751250	+	0.751250i
$813$		0			0
$814$			10.8284i			0.379536i
$815$	−28.6518	−	21.9642i	−1.00363	−	0.769373i
$816$		0			0
$817$	2.01939	+	2.01939i	0.0706496	+	0.0706496i
$818$	−5.95434	−	5.95434i	−0.208189	−	0.208189i
$819$		0			0
$820$	0.287214	+	2.17382i	0.0100299	+	0.0759129i
$821$			12.7928i			0.446472i	0.974764	+	0.223236i	$0.0716621\pi$
$821$			12.7928i			0.446472i	−0.974764	+	0.223236i	$0.928338\pi$
$822$		0			0
$823$	32.3068	−	32.3068i	1.12615	−	1.12615i	0.135347	−	0.990798i	$-0.456785\pi$
$823$	32.3068	−	32.3068i	1.12615	−	1.12615i	0.990798	−	0.135347i	$-0.0432150\pi$
$824$	10.1179			0.352473
$825$		0			0
$826$	−33.6226			−1.16988
$827$	11.2976	−	11.2976i	0.392858	−	0.392858i	−0.482847	−	0.875705i	$-0.660397\pi$
$827$	11.2976	−	11.2976i	0.392858	−	0.392858i	0.875705	+	0.482847i	$0.160397\pi$
$828$		0			0
$829$		−	40.8572i		−	1.41903i	−0.704691	−	0.709514i	$-0.748915\pi$
$829$		−	40.8572i		−	1.41903i	0.704691	−	0.709514i	$-0.251085\pi$
$830$	−3.85617	−	29.1859i	−0.133850	−	1.01306i
$831$		0			0
$832$	4.43361	+	4.43361i	0.153708	+	0.153708i
$833$	5.60262	+	5.60262i	0.194119	+	0.194119i
$834$		0			0
$835$	14.2373	+	10.9142i	0.492702	+	0.377701i
$836$		−	5.41421i		−	0.187254i
$837$		0			0
$838$	−22.2567	+	22.2567i	−0.768845	+	0.768845i
$839$	−16.7802			−0.579318			−0.289659	−	0.957130i	$-0.593542\pi$
$839$	−16.7802			−0.579318			−0.289659	+	0.957130i	$0.593542\pi$
$840$		0			0
$841$	49.6274			1.71129
$842$	−27.8710	+	27.8710i	−0.960498	+	0.960498i
$843$		0			0
$844$			9.11456i			0.313736i
$845$	58.3323	−	7.70711i	2.00669	−	0.265133i
$846$		0			0
$847$	44.2132	+	44.2132i	1.51918	+	1.51918i
$848$	4.24264	+	4.24264i	0.145693	+	0.145693i
$849$		0			0
$850$	2.20943	+	8.21522i	0.0757827	+	0.281780i
$851$		−	2.55836i		−	0.0876995i
$852$		0			0
$853$	−12.1317	+	12.1317i	−0.415382	+	0.415382i	−0.883608	−	0.468227i	$-0.844893\pi$
$853$	−12.1317	+	12.1317i	−0.415382	+	0.415382i	0.468227	+	0.883608i	$0.344893\pi$
$854$	−31.0642			−1.06299
$855$		0			0
$856$	4.48528			0.153304
$857$	−18.4579	+	18.4579i	−0.630508	+	0.630508i	−0.948196	−	0.317687i	$-0.897094\pi$
$857$	−18.4579	+	18.4579i	−0.630508	+	0.630508i	0.317687	+	0.948196i	$0.397094\pi$
$858$		0			0
$859$		−	4.07757i		−	0.139125i	−0.997578	−	0.0695624i	$-0.977840\pi$
$859$		−	4.07757i		−	0.139125i	0.997578	−	0.0695624i	$-0.0221603\pi$
$860$	−3.88513	+	5.06806i	−0.132482	+	0.172819i
$861$		0			0
$862$	14.8124	+	14.8124i	0.504511	+	0.504511i
$863$	−38.8505	−	38.8505i	−1.32249	−	1.32249i	−0.911757	−	0.410730i	$-0.865274\pi$
$863$	−38.8505	−	38.8505i	−1.32249	−	1.32249i	−0.410730	−	0.911757i	$-0.634726\pi$
$864$		0			0
$865$	−1.49440	+	1.94941i	−0.0508111	+	0.0662819i
$866$		−	23.0818i		−	0.784351i
$867$		0			0
$868$	−25.7747	+	25.7747i	−0.874852	+	0.874852i
$869$	50.2951			1.70614
$870$		0			0
$871$	−51.8538			−1.75700
$872$	8.73218	−	8.73218i	0.295709	−	0.295709i
$873$		0			0
$874$			1.27918i			0.0432690i
$875$	−14.5588	+	35.2867i	−0.492176	+	1.19291i
$876$		0			0
$877$	−29.1662	−	29.1662i	−0.984874	−	0.984874i	0.0150136	−	0.999887i	$-0.495221\pi$
$877$	−29.1662	−	29.1662i	−0.984874	−	0.984874i	−0.999887	+	0.0150136i	$0.995221\pi$
$878$	−12.1237	−	12.1237i	−0.409154	−	0.409154i
$879$		0			0
$880$	12.0022	−	1.58579i	0.404596	−	0.0534568i
$881$		−	15.6849i		−	0.528438i	−0.964463	−	0.264219i	$-0.914886\pi$
$881$		−	15.6849i		−	0.528438i	0.964463	−	0.264219i	$-0.0851142\pi$
$882$		0			0
$883$	−10.9472	+	10.9472i	−0.368404	+	0.368404i	−0.866895	−	0.498491i	$-0.833888\pi$
$883$	−10.9472	+	10.9472i	−0.368404	+	0.368404i	0.498491	+	0.866895i	$0.333888\pi$
$884$	−10.6681			−0.358806
$885$		0			0
$886$	8.66444			0.291087
$887$	21.7527	−	21.7527i	0.730383	−	0.730383i	−0.240313	−	0.970695i	$-0.577250\pi$
$887$	21.7527	−	21.7527i	0.730383	−	0.730383i	0.970695	+	0.240313i	$0.0772500\pi$
$888$		0			0
$889$			9.38679i			0.314823i
$890$	15.0151	+	11.5105i	0.503308	+	0.385832i
$891$		0			0
$892$	5.75310	+	5.75310i	0.192628	+	0.192628i
$893$	−5.77173	−	5.77173i	−0.193144	−	0.193144i
$894$		0			0
$895$	−6.38238	−	48.3059i	−0.213339	−	1.61469i
$896$		−	3.41421i		−	0.114061i
$897$		0			0
$898$	−20.9780	+	20.9780i	−0.700045	+	0.700045i
$899$	94.6685			3.15737
$900$		0			0
$901$	−10.2086			−0.340097
$902$	−3.75419	+	3.75419i	−0.125001	+	0.125001i
$903$		0			0
$904$		−	2.86721i		−	0.0953620i
$905$	−5.79189	−	43.8367i	−0.192529	−	1.45718i
$906$		0			0
$907$	8.54230	+	8.54230i	0.283642	+	0.283642i	0.834560	−	0.550917i	$-0.185722\pi$
$907$	8.54230	+	8.54230i	0.283642	+	0.283642i	−0.550917	+	0.834560i	$0.685722\pi$
$908$	4.19096	+	4.19096i	0.139082	+	0.139082i
$909$		0			0
$910$	−37.9900	−	29.1227i	−1.25935	−	0.965410i
$911$			1.17374i			0.0388878i	0.999811	+	0.0194439i	$0.00618958\pi$
$911$			1.17374i			0.0388878i	−0.999811	+	0.0194439i	$0.993810\pi$
$912$		0			0
$913$	50.4042	−	50.4042i	1.66814	−	1.66814i
$914$	24.6246			0.814508
$915$		0			0
$916$	−13.7687			−0.454931
$917$	29.8409	−	29.8409i	0.985435	−	0.985435i
$918$		0			0
$919$		−	7.31371i		−	0.241257i	−0.992698	−	0.120628i	$-0.961509\pi$
$919$		−	7.31371i		−	0.241257i	0.992698	−	0.120628i	$-0.0384910\pi$
$920$	−2.83569	+	0.374664i	−0.0934900	+	0.0123523i
$921$		0			0
$922$	−23.0459	−	23.0459i	−0.758976	−	0.758976i
$923$	66.9407	+	66.9407i	2.20338	+	2.20338i
$924$		0			0
$925$	−8.66489	−	4.99197i	−0.284900	−	0.164135i
$926$			10.0420i			0.329999i
$927$		0			0
$928$	−6.27006	+	6.27006i	−0.205825	+	0.205825i
$929$	−39.0201			−1.28021			−0.640103	−	0.768289i	$-0.721109\pi$
$929$	−39.0201			−1.28021			−0.640103	+	0.768289i	$0.721109\pi$
$930$		0			0
$931$	4.65685			0.152622
$932$	12.7513	−	12.7513i	0.417681	−	0.417681i
$933$		0			0
$934$			8.44071i			0.276188i
$935$	−12.5319	+	16.3476i	−0.409838	+	0.534625i
$936$		0			0
$937$	−36.7344	−	36.7344i	−1.20006	−	1.20006i	−0.974147	−	0.225914i	$-0.927463\pi$
$937$	−36.7344	−	36.7344i	−1.20006	−	1.20006i	−0.225914	−	0.974147i	$-0.572537\pi$
$938$	19.9657	+	19.9657i	0.651903	+	0.651903i
$939$		0			0
$940$	11.1043	−	14.4853i	0.362182	−	0.472458i
$941$			26.8739i			0.876063i	0.898960	+	0.438031i	$0.144324\pi$
$941$			26.8739i			0.876063i	−0.898960	+	0.438031i	$0.855676\pi$
$942$		0			0
$943$	0.886978	−	0.886978i	0.0288840	−	0.0288840i
$944$	−9.84782			−0.320519
$945$		0			0
$946$	−15.4622			−0.502719
$947$	−6.36932	+	6.36932i	−0.206975	+	0.206975i	−0.802980	−	0.596005i	$-0.796754\pi$
$947$	−6.36932	+	6.36932i	−0.206975	+	0.206975i	0.596005	+	0.802980i	$0.296754\pi$
$948$		0			0
$949$		−	33.9475i		−	1.10198i
$950$	4.33244	+	2.49598i	0.140563	+	0.0809804i
$951$		0			0
$952$	4.10761	+	4.10761i	0.133128	+	0.133128i
$953$	19.2863	+	19.2863i	0.624744	+	0.624744i	0.946741	−	0.321997i	$-0.104354\pi$
$953$	19.2863	+	19.2863i	0.624744	+	0.624744i	−0.321997	+	0.946741i	$0.604354\pi$
$954$		0			0
$955$	−47.3594	+	6.25733i	−1.53252	+	0.202482i
$956$		−	1.82039i		−	0.0588758i
$957$		0			0
$958$	4.60518	−	4.60518i	0.148787	−	0.148787i
$959$	−7.11302			−0.229691
$960$		0			0
$961$	82.9822			2.67685
$962$	8.86721	−	8.86721i	0.285890	−	0.285890i
$963$		0			0
$964$			0.365864i			0.0117837i
$965$	40.1406	+	30.7714i	1.29217	+	0.990567i
$966$		0			0
$967$	−23.2083	−	23.2083i	−0.746330	−	0.746330i	0.227458	−	0.973788i	$-0.426959\pi$
$967$	−23.2083	−	23.2083i	−0.746330	−	0.746330i	−0.973788	+	0.227458i	$0.926959\pi$
$968$	12.9497	+	12.9497i	0.416221	+	0.416221i
$969$		0			0
$970$	4.20277	+	31.8093i	0.134943	+	1.02133i
$971$			24.4289i			0.783961i	0.919974	+	0.391980i	$0.128210\pi$
$971$			24.4289i			0.783961i	−0.919974	+	0.391980i	$0.871790\pi$
$972$		0			0
$973$	−17.0436	+	17.0436i	−0.546394	+	0.546394i
$974$	−26.7150			−0.856005
$975$		0			0
$976$	−9.09849			−0.291236
$977$	−16.5209	+	16.5209i	−0.528550	+	0.528550i	−0.920140	−	0.391590i	$-0.871925\pi$
$977$	−16.5209	+	16.5209i	−0.528550	+	0.528550i	0.391590	+	0.920140i	$0.371925\pi$
$978$		0			0
$979$			45.8098i			1.46409i
$980$	1.36396	+	10.3233i	0.0435701	+	0.329767i
$981$		0			0
$982$	−29.6925	−	29.6925i	−0.947527	−	0.947527i
$983$	7.13881	+	7.13881i	0.227693	+	0.227693i	0.811728	−	0.584035i	$-0.198527\pi$
$983$	7.13881	+	7.13881i	0.227693	+	0.227693i	−0.584035	+	0.811728i	$0.698527\pi$
$984$		0			0
$985$	23.9760	+	18.3798i	0.763938	+	0.585628i
$986$		−	15.0869i		−	0.480465i
$987$		0			0
$988$	−4.43361	+	4.43361i	−0.141052	+	0.141052i
$989$	3.65315			0.116163
$990$		0			0
$991$	4.31255			0.136993			0.0684963	−	0.997651i	$-0.478180\pi$
$991$	4.31255			0.136993			0.0684963	+	0.997651i	$0.478180\pi$
$992$	−7.54925	+	7.54925i	−0.239689	+	0.239689i
$993$		0			0
$994$		−	51.5495i		−	1.63505i
$995$	37.1077	−	4.90282i	1.17639	−	0.155430i
$996$		0			0
$997$	32.5869	+	32.5869i	1.03204	+	1.03204i	0.999469	+	0.0325694i	$0.0103690\pi$
$997$	32.5869	+	32.5869i	1.03204	+	1.03204i	0.0325694	+	0.999469i	$0.489631\pi$
$998$	−2.10652	−	2.10652i	−0.0666808	−	0.0666808i
$999$		0			0

Twists

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

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

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(0.292893 + 2.21680i) q^{5} +(-2.41421 - 2.41421i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(1.77462 + 1.36041i) q^{10} +5.41421i q^{11} +(4.43361 - 4.43361i) q^{13} -3.41421 q^{14} -1.00000 q^{16} +(1.20309 - 1.20309i) q^{17} -1.00000i q^{19} +(2.21680 - 0.292893i) q^{20} +(3.82843 + 3.82843i) q^{22} +(-0.904518 - 0.904518i) q^{23} +(-4.82843 + 1.29857i) q^{25} -6.27006i q^{26} +(-2.41421 + 2.41421i) q^{28} +8.86721 q^{29} +10.6762 q^{31} +(-0.707107 + 0.707107i) q^{32} -1.70143i q^{34} +(4.64473 - 6.05894i) q^{35} +(1.41421 + 1.41421i) q^{37} +(-0.707107 - 0.707107i) q^{38} +(1.36041 - 1.77462i) q^{40} +0.980608i q^{41} +(-2.01939 + 2.01939i) q^{43} +5.41421 q^{44} -1.27918 q^{46} +(5.77173 - 5.77173i) q^{47} +4.65685i q^{49} +(-2.49598 + 4.33244i) q^{50} +(-4.43361 - 4.43361i) q^{52} +(-4.24264 - 4.24264i) q^{53} +(-12.0022 + 1.58579i) q^{55} +3.41421i q^{56} +(6.27006 - 6.27006i) q^{58} +9.84782 q^{59} +9.09849 q^{61} +(7.54925 - 7.54925i) q^{62} +1.00000i q^{64} +(11.1270 + 8.52985i) q^{65} +(-5.84782 - 5.84782i) q^{67} +(-1.20309 - 1.20309i) q^{68} +(-1.00000 - 7.56864i) q^{70} +15.0985i q^{71} +(3.82843 - 3.82843i) q^{73} +2.00000 q^{74} -1.00000 q^{76} +(13.0711 - 13.0711i) q^{77} -9.28946i q^{79} +(-0.292893 - 2.21680i) q^{80} +(0.693395 + 0.693395i) q^{82} +(-9.30961 - 9.30961i) q^{83} +(3.01939 + 2.31464i) q^{85} +2.85585i q^{86} +(3.82843 - 3.82843i) q^{88} +8.46103 q^{89} -21.4073 q^{91} +(-0.904518 + 0.904518i) q^{92} -8.16246i q^{94} +(2.21680 - 0.292893i) q^{95} +(10.1464 + 10.1464i) q^{97} +(3.29289 + 3.29289i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{5} - 8 q^{7} - 4 q^{10} - 16 q^{14} - 8 q^{16} + 8 q^{22} - 8 q^{23} - 16 q^{25} - 8 q^{28} + 16 q^{31} + 4 q^{40} + 8 q^{43} + 32 q^{44} - 24 q^{46} - 24 q^{47} - 16 q^{50} + 32 q^{59} + 24 q^{62}+ \cdots + 32 q^{98}+O(q^{100}) \) 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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