LMFDB - Embedded newform 702.2.t.a.181.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [702,2,Mod(181,702)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(702, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 3]))

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

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

chi := DirichletCharacter("702.181");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 702 = 2 \cdot 3^{3} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	702.t (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.60549822189$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 234)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			181.12
Character	$\chi$	$=$	702.181
Dual form			702.2.t.a.415.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(0.515076 - 0.297379i) q^{5} +(1.45217 + 0.838409i) q^{7} +1.00000i q^{8} +0.594758 q^{10} +(-0.416337 - 0.240372i) q^{11} +(3.56065 - 0.567277i) q^{13} +(0.838409 + 1.45217i) q^{14} +(-0.500000 + 0.866025i) q^{16} +2.09349 q^{17} -0.480744i q^{19} +(0.515076 + 0.297379i) q^{20} +(-0.240372 - 0.416337i) q^{22} +(1.83339 + 3.17553i) q^{23} +(-2.32313 + 4.02378i) q^{25} +(3.36725 + 1.28905i) q^{26} +1.67682i q^{28} +(-1.23339 + 2.13629i) q^{29} +(0.993791 - 0.573765i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(1.81302 + 1.04675i) q^{34} +0.997301 q^{35} -3.65012i q^{37} +(0.240372 - 0.416337i) q^{38} +(0.297379 + 0.515076i) q^{40} +(8.58235 - 4.95502i) q^{41} +(-3.45822 + 5.98981i) q^{43} -0.480744i q^{44} +3.66679i q^{46} +(-5.40488 - 3.12051i) q^{47} +(-2.09414 - 3.62716i) q^{49} +(-4.02378 + 2.32313i) q^{50} +(2.27160 + 2.79997i) q^{52} +5.08592 q^{53} -0.285927 q^{55} +(-0.838409 + 1.45217i) q^{56} +(-2.13629 + 1.23339i) q^{58} +(8.13185 - 4.69493i) q^{59} +(-3.90635 + 6.76599i) q^{61} +1.14753 q^{62} -1.00000 q^{64} +(1.66531 - 1.35105i) q^{65} +(-12.4551 + 7.19096i) q^{67} +(1.04675 + 1.81302i) q^{68} +(0.863688 + 0.498651i) q^{70} -6.51028i q^{71} -5.91514i q^{73} +(1.82506 - 3.16110i) q^{74} +(0.416337 - 0.240372i) q^{76} +(-0.403061 - 0.698121i) q^{77} +(1.02895 - 1.78219i) q^{79} +0.594758i q^{80} +9.91005 q^{82} +(-9.57834 - 5.53006i) q^{83} +(1.07831 - 0.622560i) q^{85} +(-5.98981 + 3.45822i) q^{86} +(0.240372 - 0.416337i) q^{88} +9.48720i q^{89} +(5.64626 + 2.16150i) q^{91} +(-1.83339 + 3.17553i) q^{92} +(-3.12051 - 5.40488i) q^{94} +(-0.142963 - 0.247620i) q^{95} +(-8.41374 - 4.85767i) q^{97} -4.18828i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 14 q^{4} + 2 q^{13} - 8 q^{14} - 14 q^{16} - 16 q^{17} + 8 q^{23} + 14 q^{25} - 8 q^{26} + 16 q^{29} + 68 q^{35} - 4 q^{43} + 10 q^{49} - 2 q^{52} + 120 q^{53} + 8 q^{56} + 28 q^{61} - 68 q^{62}+ \cdots - 8 q^{92}+O(q^{100}) $ 28 * q + 14 * q^4 + 2 * q^13 - 8 * q^14 - 14 * q^16 - 16 * q^17 + 8 * q^23 + 14 * q^25 - 8 * q^26 + 16 * q^29 + 68 * q^35 - 4 * q^43 + 10 * q^49 - 2 * q^52 + 120 * q^53 + 8 * q^56 + 28 * q^61 - 68 * q^62 - 28 * q^64 + 8 * q^65 - 8 * q^68 - 16 * q^74 + 24 * q^77 + 28 * q^79 - 48 * q^82 - 8 * q^92

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/702\mathbb{Z}\right)^\times$.

$n$	$379$	$677$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	0.515076	−	0.297379i	0.230349	−	0.132992i	−0.380384	−	0.924829i	$-0.624208\pi$
$5$	0.515076	−	0.297379i	0.230349	−	0.132992i	0.610733	+	0.791837i	$0.290875\pi$
$6$		0			0
$7$	1.45217	+	0.838409i	0.548868	+	0.316889i	0.748665	−	0.662948i	$-0.230695\pi$
$7$	1.45217	+	0.838409i	0.548868	+	0.316889i	−0.199798	+	0.979837i	$0.564028\pi$
$8$			1.00000i			0.353553i
$9$		0			0
$10$	0.594758			0.188079
$11$	−0.416337	−	0.240372i	−0.125530	−	0.0724750i	0.435920	−	0.899985i	$-0.356423\pi$
$11$	−0.416337	−	0.240372i	−0.125530	−	0.0724750i	−0.561450	+	0.827510i	$0.689756\pi$
$12$		0			0
$13$	3.56065	−	0.567277i	0.987545	−	0.157334i
$13$	3.56065	−	0.567277i	0.987545	−	0.157334i
$14$	0.838409	+	1.45217i	0.224074	+	0.388108i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	2.09349			0.507746			0.253873	−	0.967238i	$-0.418295\pi$
$17$	2.09349			0.507746			0.253873	+	0.967238i	$0.418295\pi$
$18$		0			0
$19$		−	0.480744i		−	0.110290i	−0.998478	−	0.0551452i	$-0.982438\pi$
$19$		−	0.480744i		−	0.110290i	0.998478	−	0.0551452i	$-0.0175622\pi$
$20$	0.515076	+	0.297379i	0.115174	+	0.0664960i
$21$		0			0
$22$	−0.240372	−	0.416337i	−0.0512475	−	0.0887633i
$23$	1.83339	+	3.17553i	0.382289	+	0.662144i	0.991389	−	0.130950i	$-0.0418026\pi$
$23$	1.83339	+	3.17553i	0.382289	+	0.662144i	−0.609100	+	0.793093i	$0.708469\pi$
$24$		0			0
$25$	−2.32313	+	4.02378i	−0.464626	+	0.804756i
$26$	3.36725	+	1.28905i	0.660372	+	0.252803i
$27$		0			0
$28$			1.67682i			0.316889i
$29$	−1.23339	+	2.13629i	−0.229035	+	0.396700i	−0.957522	−	0.288359i	$-0.906890\pi$
$29$	−1.23339	+	2.13629i	−0.229035	+	0.396700i	0.728488	+	0.685059i	$0.240224\pi$
$30$		0			0
$31$	0.993791	−	0.573765i	0.178490	−	0.103051i	−0.408093	−	0.912940i	$-0.633806\pi$
$31$	0.993791	−	0.573765i	0.178490	−	0.103051i	0.586583	+	0.809889i	$0.300473\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$		0			0
$34$	1.81302	+	1.04675i	0.310930	+	0.179515i
$35$	0.997301			0.168575
$36$		0			0
$37$		−	3.65012i		−	0.600076i	−0.953927	−	0.300038i	$-0.903001\pi$
$37$		−	3.65012i		−	0.600076i	0.953927	−	0.300038i	$-0.0969994\pi$
$38$	0.240372	−	0.416337i	0.0389935	−	0.0675388i
$39$		0			0
$40$	0.297379	+	0.515076i	0.0470198	+	0.0814406i
$41$	8.58235	−	4.95502i	1.34034	−	0.773845i	0.353481	−	0.935442i	$-0.384998\pi$
$41$	8.58235	−	4.95502i	1.34034	−	0.773845i	0.986857	+	0.161597i	$0.0516645\pi$
$42$		0			0
$43$	−3.45822	+	5.98981i	−0.527374	+	0.913438i	0.472117	+	0.881536i	$0.343490\pi$
$43$	−3.45822	+	5.98981i	−0.527374	+	0.913438i	−0.999491	+	0.0319023i	$0.989843\pi$
$44$		−	0.480744i		−	0.0724750i
$45$		0			0
$46$			3.66679i			0.540638i
$47$	−5.40488	−	3.12051i	−0.788383	−	0.455173i	0.0510099	−	0.998698i	$-0.483756\pi$
$47$	−5.40488	−	3.12051i	−0.788383	−	0.455173i	−0.839393	+	0.543525i	$0.817089\pi$
$48$		0			0
$49$	−2.09414	−	3.62716i	−0.299163	−	0.518165i
$50$	−4.02378	+	2.32313i	−0.569049	+	0.328540i
$51$		0			0
$52$	2.27160	+	2.79997i	0.315014	+	0.388286i
$53$	5.08592			0.698605			0.349302	−	0.937010i	$-0.386419\pi$
$53$	5.08592			0.698605			0.349302	+	0.937010i	$0.386419\pi$
$54$		0			0
$55$	−0.285927			−0.0385544
$56$	−0.838409	+	1.45217i	−0.112037	+	0.194054i
$57$		0			0
$58$	−2.13629	+	1.23339i	−0.280509	+	0.161952i
$59$	8.13185	−	4.69493i	1.05868	−	0.611227i	0.133611	−	0.991034i	$-0.457343\pi$
$59$	8.13185	−	4.69493i	1.05868	−	0.611227i	0.925066	+	0.379807i	$0.124009\pi$
$60$		0			0
$61$	−3.90635	+	6.76599i	−0.500157	+	0.866297i	0.499843	+	0.866116i	$0.333391\pi$
$61$	−3.90635	+	6.76599i	−0.500157	+	0.866297i	−1.00000		0.000180927i	$0.999942\pi$
$62$	1.14753			0.145737
$63$		0			0
$64$	−1.00000			−0.125000
$65$	1.66531	−	1.35105i	0.206556	−	0.167577i
$66$		0			0
$67$	−12.4551	+	7.19096i	−1.52163	+	0.878516i	−0.521960	+	0.852970i	$0.674799\pi$
$67$	−12.4551	+	7.19096i	−1.52163	+	0.878516i	−0.999674	+	0.0255454i	$0.991868\pi$
$68$	1.04675	+	1.81302i	0.126936	+	0.219860i
$69$		0			0
$70$	0.863688	+	0.498651i	0.103231	+	0.0596002i
$71$		−	6.51028i		−	0.772628i	−0.922367	−	0.386314i	$-0.873748\pi$
$71$		−	6.51028i		−	0.772628i	0.922367	−	0.386314i	$-0.126252\pi$
$72$		0			0
$73$		−	5.91514i		−	0.692315i	−0.938176	−	0.346157i	$-0.887486\pi$
$73$		−	5.91514i		−	0.692315i	0.938176	−	0.346157i	$-0.112514\pi$
$74$	1.82506	−	3.16110i	0.212159	−	0.367470i
$75$		0			0
$76$	0.416337	−	0.240372i	0.0477571	−	0.0275726i
$77$	−0.403061	−	0.698121i	−0.0459330	−	0.0795583i
$78$		0			0
$79$	1.02895	−	1.78219i	0.115766	−	0.200512i	−0.802320	−	0.596894i	$-0.796401\pi$
$79$	1.02895	−	1.78219i	0.115766	−	0.200512i	0.918086	+	0.396382i	$0.129734\pi$
$80$			0.594758i			0.0664960i
$81$		0			0
$82$	9.91005			1.09438
$83$	−9.57834	−	5.53006i	−1.05136	−	0.607003i	−0.128330	−	0.991732i	$-0.540962\pi$
$83$	−9.57834	−	5.53006i	−1.05136	−	0.607003i	−0.923030	+	0.384729i	$0.874295\pi$
$84$		0			0
$85$	1.07831	−	0.622560i	0.116959	−	0.0675261i
$86$	−5.98981	+	3.45822i	−0.645898	+	0.372909i
$87$		0			0
$88$	0.240372	−	0.416337i	0.0256238	−	0.0443817i
$89$			9.48720i			1.00564i	0.864391	+	0.502821i	$0.167704\pi$
$89$			9.48720i			1.00564i	−0.864391	+	0.502821i	$0.832296\pi$
$90$		0			0
$91$	5.64626	+	2.16150i	0.591889	+	0.226586i
$92$	−1.83339	+	3.17553i	−0.191144	+	0.331072i
$93$		0			0
$94$	−3.12051	−	5.40488i	−0.321856	−	0.557471i
$95$	−0.142963	−	0.247620i	−0.0146677	−	0.0254053i
$96$		0			0
$97$	−8.41374	−	4.85767i	−0.854286	−	0.493222i	0.00780887	−	0.999970i	$-0.497514\pi$
$97$	−8.41374	−	4.85767i	−0.854286	−	0.493222i	−0.862095	+	0.506747i	$0.830848\pi$
$98$		−	4.18828i		−	0.423080i
$99$		0			0
$100$	−4.64626			−0.464626
$101$	−2.89748	+	5.01858i	−0.288310	+	0.499367i	−0.973406	−	0.229085i	$-0.926427\pi$
$101$	−2.89748	+	5.01858i	−0.288310	+	0.499367i	0.685097	+	0.728452i	$0.259760\pi$
$102$		0			0
$103$	−0.857037	−	1.48443i	−0.0844463	−	0.146265i	0.820709	−	0.571347i	$-0.193579\pi$
$103$	−0.857037	−	1.48443i	−0.0844463	−	0.146265i	−0.905155	+	0.425081i	$0.860245\pi$
$104$	0.567277	+	3.56065i	0.0556261	+	0.349150i
$105$		0			0
$106$	4.40453	+	2.54296i	0.427806	+	0.246994i
$107$	−14.1021			−1.36330			−0.681651	−	0.731678i	$-0.738738\pi$
$107$	−14.1021			−1.36330			−0.681651	+	0.731678i	$0.738738\pi$
$108$		0			0
$109$		−	18.3474i		−	1.75736i	−0.477413	−	0.878679i	$-0.658425\pi$
$109$		−	18.3474i		−	1.75736i	0.477413	−	0.878679i	$-0.341575\pi$
$110$	−0.247620	−	0.142963i	−0.0236096	−	0.0136310i
$111$		0			0
$112$	−1.45217	+	0.838409i	−0.137217	+	0.0792222i
$113$	−10.1390	−	17.5612i	−0.953793	−	1.65202i	−0.737107	−	0.675776i	$-0.763809\pi$
$113$	−10.1390	−	17.5612i	−0.953793	−	1.65202i	−0.216686	−	0.976241i	$-0.569525\pi$
$114$		0			0
$115$	1.88867	+	1.09043i	0.176120	+	0.101683i
$116$	−2.46678			−0.229035
$117$		0			0
$118$	9.38985			0.864406
$119$	3.04010	+	1.75520i	0.278685	+	0.160899i
$120$		0			0
$121$	−5.38444	−	9.32613i	−0.489495	−	0.847830i
$122$	−6.76599	+	3.90635i	−0.612564	+	0.353664i
$123$		0			0
$124$	0.993791	+	0.573765i	0.0892450	+	0.0515256i
$125$			5.73719i			0.513150i
$126$		0			0
$127$	18.5473			1.64581			0.822904	−	0.568180i	$-0.192352\pi$
$127$	18.5473			1.64581			0.822904	+	0.568180i	$0.192352\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$		0			0
$130$	2.11772	−	0.337393i	0.185737	−	0.0295913i
$131$	−2.32256	−	4.02280i	−0.202923	−	0.351474i	0.746546	−	0.665334i	$-0.231711\pi$
$131$	−2.32256	−	4.02280i	−0.202923	−	0.351474i	−0.949469	+	0.313861i	$0.898378\pi$
$132$		0			0
$133$	0.403061	−	0.698121i	0.0349498	−	0.0605348i
$134$	−14.3819			−1.24241
$135$		0			0
$136$			2.09349i			0.179515i
$137$	11.2762	+	6.51034i	0.963395	+	0.556216i	0.897216	−	0.441592i	$-0.145586\pi$
$137$	11.2762	+	6.51034i	0.963395	+	0.556216i	0.0661784	+	0.997808i	$0.478919\pi$
$138$		0			0
$139$	−5.09027	−	8.81661i	−0.431751	−	0.747815i	0.565273	−	0.824904i	$-0.308771\pi$
$139$	−5.09027	−	8.81661i	−0.431751	−	0.747815i	−0.997024	+	0.0770888i	$0.975437\pi$
$140$	0.498651	+	0.863688i	0.0421437	+	0.0729950i
$141$		0			0
$142$	3.25514	−	5.63807i	0.273165	−	0.473136i
$143$	−1.61879	−	0.619702i	−0.135370	−	0.0518221i
$144$		0			0
$145$			1.46714i			0.121839i
$146$	2.95757	−	5.12266i	0.244770	−	0.423955i
$147$		0			0
$148$	3.16110	−	1.82506i	0.259841	−	0.150019i
$149$	4.54901	−	2.62637i	0.372669	−	0.215161i	−0.301955	−	0.953322i	$-0.597639\pi$
$149$	4.54901	−	2.62637i	0.372669	−	0.215161i	0.674624	+	0.738162i	$0.264306\pi$
$150$		0			0
$151$	−10.3258	−	5.96162i	−0.840304	−	0.485150i	0.0170637	−	0.999854i	$-0.494568\pi$
$151$	−10.3258	−	5.96162i	−0.840304	−	0.485150i	−0.857367	+	0.514705i	$0.827902\pi$
$152$	0.480744			0.0389935
$153$		0			0
$154$		−	0.806121i		−	0.0649591i
$155$	0.341252	−	0.591065i	0.0274100	−	0.0474755i
$156$		0			0
$157$	−6.19540	−	10.7307i	−0.494446	−	0.856406i	0.505533	−	0.862807i	$-0.331296\pi$
$157$	−6.19540	−	10.7307i	−0.494446	−	0.856406i	−0.999980	+	0.00640095i	$0.997962\pi$
$158$	1.78219	−	1.02895i	0.141784	−	0.0818588i
$159$		0			0
$160$	−0.297379	+	0.515076i	−0.0235099	+	0.0407203i
$161$			6.14853i			0.484572i
$162$		0			0
$163$			21.3629i			1.67327i	0.547760	+	0.836635i	$0.315481\pi$
$163$			21.3629i			1.67327i	−0.547760	+	0.836635i	$0.684519\pi$
$164$	8.58235	+	4.95502i	0.670169	+	0.386922i
$165$		0			0
$166$	−5.53006	−	9.57834i	−0.429216	−	0.743423i
$167$	−12.7614	+	7.36778i	−0.987504	+	0.570136i	−0.904527	−	0.426416i	$-0.859776\pi$
$167$	−12.7614	+	7.36778i	−0.987504	+	0.570136i	−0.0829768	+	0.996551i	$0.526443\pi$
$168$		0			0
$169$	12.3564	−	4.03974i	0.950492	−	0.310749i
$170$	1.24512			0.0954964
$171$		0			0
$172$	−6.91644			−0.527374
$173$	5.82435	−	10.0881i	0.442817	−	0.766982i	−0.555080	−	0.831797i	$-0.687312\pi$
$173$	5.82435	−	10.0881i	0.442817	−	0.766982i	0.997897	+	0.0648152i	$0.0206458\pi$
$174$		0			0
$175$	−6.74715	+	3.89547i	−0.510037	+	0.294470i
$176$	0.416337	−	0.240372i	0.0313826	−	0.0181187i
$177$		0			0
$178$	−4.74360	+	8.21616i	−0.355548	+	0.615827i
$179$	0.896158			0.0669820			0.0334910	−	0.999439i	$-0.489337\pi$
$179$	0.896158			0.0669820			0.0334910	+	0.999439i	$0.489337\pi$
$180$		0			0
$181$	1.42191			0.105689			0.0528447	−	0.998603i	$-0.483171\pi$
$181$	1.42191			0.105689			0.0528447	+	0.998603i	$0.483171\pi$
$182$	3.80906	+	4.69504i	0.282346	+	0.348020i
$183$		0			0
$184$	−3.17553	+	1.83339i	−0.234103	+	0.135160i
$185$	−1.08547	−	1.88009i	−0.0798053	−	0.138227i
$186$		0			0
$187$	−0.871597	−	0.503217i	−0.0637375	−	0.0367989i
$188$		−	6.24102i		−	0.455173i
$189$		0			0
$190$		−	0.285927i		−	0.0207433i
$191$	−7.42036	+	12.8524i	−0.536918	+	0.929970i	0.462150	+	0.886802i	$0.347078\pi$
$191$	−7.42036	+	12.8524i	−0.536918	+	0.929970i	−0.999068	+	0.0431677i	$0.986255\pi$
$192$		0			0
$193$	12.2175	−	7.05376i	0.879433	−	0.507741i	0.00896136	−	0.999960i	$-0.497147\pi$
$193$	12.2175	−	7.05376i	0.879433	−	0.507741i	0.870471	+	0.492219i	$0.163814\pi$
$194$	−4.85767	−	8.41374i	−0.348761	−	0.604071i
$195$		0			0
$196$	2.09414	−	3.62716i	0.149581	−	0.259083i
$197$		−	0.442517i		−	0.0315280i	−0.999876	−	0.0157640i	$-0.994982\pi$
$197$		−	0.442517i		−	0.0315280i	0.999876	−	0.0157640i	$-0.00501805\pi$
$198$		0			0
$199$	−13.2925			−0.942282			−0.471141	−	0.882058i	$-0.656158\pi$
$199$	−13.2925			−0.942282			−0.471141	+	0.882058i	$0.656158\pi$
$200$	−4.02378	−	2.32313i	−0.284524	−	0.164270i
$201$		0			0
$202$	−5.01858	+	2.89748i	−0.353106	+	0.203866i
$203$	−3.58217	+	2.06817i	−0.251419	+	0.145157i
$204$		0			0
$205$	2.94704	−	5.10442i	0.205830	−	0.356508i
$206$		−	1.71407i		−	0.119425i
$207$		0			0
$208$	−1.28905	+	3.36725i	−0.0893793	+	0.233477i
$209$	−0.115558	+	0.200152i	−0.00799329	+	0.0138448i
$210$		0			0
$211$	4.82032	+	8.34904i	0.331845	+	0.574772i	0.982874	−	0.184281i	$-0.0589957\pi$
$211$	4.82032	+	8.34904i	0.331845	+	0.574772i	−0.651029	+	0.759053i	$0.725662\pi$
$212$	2.54296	+	4.40453i	0.174651	+	0.302505i
$213$		0			0
$214$	−12.2128	−	7.05105i	−0.834848	−	0.482000i
$215$			4.11361i			0.280546i
$216$		0			0
$217$	1.92420			0.130623
$218$	9.17368	−	15.8893i	0.621320	−	1.07616i
$219$		0			0
$220$	−0.142963	−	0.247620i	−0.00963859	−	0.0166945i
$221$	7.45418	−	1.18759i	0.501422	−	0.0798858i
$222$		0			0
$223$	20.0340	+	11.5666i	1.34158	+	0.774559i	0.987039	−	0.160482i	$-0.0513050\pi$
$223$	20.0340	+	11.5666i	1.34158	+	0.774559i	0.354537	+	0.935042i	$0.384638\pi$
$224$	−1.67682			−0.112037
$225$		0			0
$226$		−	20.2779i		−	1.34887i
$227$	−11.5239	−	6.65331i	−0.764866	−	0.441595i	0.0661743	−	0.997808i	$-0.478921\pi$
$227$	−11.5239	−	6.65331i	−0.764866	−	0.441595i	−0.831040	+	0.556213i	$0.812254\pi$
$228$		0			0
$229$	0.700965	−	0.404702i	0.0463211	−	0.0267435i	−0.476661	−	0.879087i	$-0.658153\pi$
$229$	0.700965	−	0.404702i	0.0463211	−	0.0267435i	0.522982	+	0.852344i	$0.324820\pi$
$230$	1.09043	+	1.88867i	0.0719005	+	0.124535i
$231$		0			0
$232$	−2.13629	−	1.23339i	−0.140254	−	0.0809760i
$233$	15.4712			1.01355			0.506776	−	0.862078i	$-0.330837\pi$
$233$	15.4712			1.01355			0.506776	+	0.862078i	$0.330837\pi$
$234$		0			0
$235$	−3.71190			−0.242138
$236$	8.13185	+	4.69493i	0.529338	+	0.305614i
$237$		0			0
$238$	1.75520	+	3.04010i	0.113773	+	0.197060i
$239$	−25.2511	+	14.5788i	−1.63336	+	0.943021i	−0.650313	+	0.759666i	$0.725362\pi$
$239$	−25.2511	+	14.5788i	−1.63336	+	0.943021i	−0.983047	+	0.183355i	$0.941304\pi$
$240$		0			0
$241$	13.5054	+	7.79735i	0.869959	+	0.502271i	0.867335	−	0.497725i	$-0.165831\pi$
$241$	13.5054	+	7.79735i	0.869959	+	0.502271i	0.00262472	+	0.999997i	$0.499165\pi$
$242$		−	10.7689i		−	0.692250i
$243$		0			0
$244$	−7.81270			−0.500157
$245$	−2.15728	−	1.24551i	−0.137824	−	0.0795725i
$246$		0			0
$247$	−0.272715	−	1.71176i	−0.0173524	−	0.108917i
$248$	0.573765	+	0.993791i	0.0364341	+	0.0631058i
$249$		0			0
$250$	−2.86860	+	4.96856i	−0.181426	+	0.314239i
$251$	2.79495			0.176416			0.0882079	−	0.996102i	$-0.471886\pi$
$251$	2.79495			0.176416			0.0882079	+	0.996102i	$0.471886\pi$
$252$		0			0
$253$		−	1.76279i		−	0.110825i
$254$	16.0624	+	9.27366i	1.00785	+	0.581881i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	10.4798	+	18.1515i	0.653712	+	1.13226i	0.982215	+	0.187759i	$0.0601225\pi$
$257$	10.4798	+	18.1515i	0.653712	+	1.13226i	−0.328503	+	0.944503i	$0.606544\pi$
$258$		0			0
$259$	3.06029	−	5.30059i	0.190157	−	0.329362i
$260$	2.00270	+	0.766671i	0.124202	+	0.0475469i
$261$		0			0
$262$		−	4.64513i		−	0.286977i
$263$	7.92418	−	13.7251i	0.488626	−	0.846325i	−0.511288	−	0.859409i	$-0.670832\pi$
$263$	7.92418	−	13.7251i	0.488626	−	0.846325i	0.999914	+	0.0130839i	$0.00416487\pi$
$264$		0			0
$265$	2.61963	−	1.51245i	0.160923	−	0.0929088i
$266$	0.698121	−	0.403061i	0.0428046	−	0.0247132i
$267$		0			0
$268$	−12.4551	−	7.19096i	−0.760817	−	0.439258i
$269$	−18.9028			−1.15252			−0.576261	−	0.817266i	$-0.695489\pi$
$269$	−18.9028			−1.15252			−0.576261	+	0.817266i	$0.695489\pi$
$270$		0			0
$271$			9.63804i			0.585469i	0.956194	+	0.292735i	$0.0945653\pi$
$271$			9.63804i			0.585469i	−0.956194	+	0.292735i	$0.905435\pi$
$272$	−1.04675	+	1.81302i	−0.0634682	+	0.109930i
$273$		0			0
$274$	6.51034	+	11.2762i	0.393304	+	0.681223i
$275$	1.93441	−	1.11683i	0.116649	−	0.0673475i
$276$		0			0
$277$	−1.35010	+	2.33844i	−0.0811197	+	0.140503i	−0.903731	−	0.428100i	$-0.859183\pi$
$277$	−1.35010	+	2.33844i	−0.0811197	+	0.140503i	0.822611	+	0.568604i	$0.192516\pi$
$278$		−	10.1805i		−	0.610588i
$279$		0			0
$280$			0.997301i			0.0596002i
$281$	−9.34820	−	5.39719i	−0.557667	−	0.321969i	0.194542	−	0.980894i	$-0.437678\pi$
$281$	−9.34820	−	5.39719i	−0.557667	−	0.321969i	−0.752208	+	0.658925i	$0.771011\pi$
$282$		0			0
$283$	14.6088	+	25.3032i	0.868403	+	1.50412i	0.863628	+	0.504129i	$0.168187\pi$
$283$	14.6088	+	25.3032i	0.868403	+	1.50412i	0.00477479	+	0.999989i	$0.498480\pi$
$284$	5.63807	−	3.25514i	0.334558	−	0.193157i
$285$		0			0
$286$	−1.09206	−	1.34607i	−0.0645748	−	0.0795948i
$287$	16.6173			0.980891
$288$		0			0
$289$	−12.6173			−0.742194
$290$	−0.733568	+	1.27058i	−0.0430766	+	0.0746109i
$291$		0			0
$292$	5.12266	−	2.95757i	0.299781	−	0.173079i
$293$	20.5199	−	11.8472i	1.19879	−	0.692120i	0.238502	−	0.971142i	$-0.423344\pi$
$293$	20.5199	−	11.8472i	1.19879	−	0.692120i	0.960285	+	0.279022i	$0.0900104\pi$
$294$		0			0
$295$	2.79235	−	4.83649i	0.162577	−	0.281591i
$296$	3.65012			0.212159
$297$		0			0
$298$	5.25274			0.304283
$299$	8.32947	+	10.2669i	0.481706	+	0.593750i
$300$		0			0
$301$	−10.0438	+	5.79881i	−0.578917	+	0.334238i
$302$	−5.96162	−	10.3258i	−0.343053	−	0.594184i
$303$		0			0
$304$	0.416337	+	0.240372i	0.0238786	+	0.0137863i
$305$			4.64667i			0.266067i
$306$		0			0
$307$			6.55237i			0.373963i	0.982363	+	0.186982i	$0.0598705\pi$
$307$			6.55237i			0.373963i	−0.982363	+	0.186982i	$0.940129\pi$
$308$	0.403061	−	0.698121i	0.0229665	−	0.0397792i
$309$		0			0
$310$	0.591065	−	0.341252i	0.0335702	−	0.0193818i
$311$	12.7115	+	22.0169i	0.720802	+	1.24847i	0.960679	+	0.277663i	$0.0895597\pi$
$311$	12.7115	+	22.0169i	0.720802	+	1.24847i	−0.239876	+	0.970803i	$0.577107\pi$
$312$		0			0
$313$	−0.590728	+	1.02317i	−0.0333899	+	0.0578331i	−0.882237	−	0.470805i	$-0.843964\pi$
$313$	−0.590728	+	1.02317i	−0.0333899	+	0.0578331i	0.848848	+	0.528638i	$0.177297\pi$
$314$		−	12.3908i		−	0.699253i
$315$		0			0
$316$	2.05790			0.115766
$317$	−24.2009	−	13.9724i	−1.35926	−	0.784769i	−0.369735	−	0.929137i	$-0.620552\pi$
$317$	−24.2009	−	13.9724i	−1.35926	−	0.784769i	−0.989524	+	0.144368i	$0.953885\pi$
$318$		0			0
$319$	1.02701	−	0.592945i	0.0575016	−	0.0331985i
$320$	−0.515076	+	0.297379i	−0.0287936	+	0.0166240i
$321$		0			0
$322$	−3.07427	+	5.32479i	−0.171322	+	0.296739i
$323$		−	1.00643i		−	0.0559995i
$324$		0			0
$325$	−5.98925	+	15.6451i	−0.332224	+	0.867835i
$326$	−10.6814	+	18.5008i	−0.591591	+	1.02466i
$327$		0			0
$328$	4.95502	+	8.58235i	0.273595	+	0.473881i
$329$	−5.23253	−	9.06301i	−0.288479	−	0.499660i
$330$		0			0
$331$	−21.3503	−	12.3266i	−1.17352	−	0.677530i	−0.219010	−	0.975723i	$-0.570283\pi$
$331$	−21.3503	−	12.3266i	−1.17352	−	0.677530i	−0.954506	+	0.298193i	$0.903616\pi$
$332$		−	11.0601i		−	0.607003i
$333$		0			0
$334$	−14.7356			−0.806294
$335$	−4.27688	+	7.40778i	−0.233671	+	0.404730i
$336$		0			0
$337$	7.63940	+	13.2318i	0.416145	+	0.720784i	0.995548	−	0.0942571i	$-0.0300476\pi$
$337$	7.63940	+	13.2318i	0.416145	+	0.720784i	−0.579403	+	0.815041i	$0.696714\pi$
$338$	12.7208	+	2.67968i	0.691922	+	0.145755i
$339$		0			0
$340$	1.07831	+	0.622560i	0.0584794	+	0.0337631i
$341$	−0.551669			−0.0298745
$342$		0			0
$343$		−	18.7607i		−	1.01298i
$344$	−5.98981	−	3.45822i	−0.322949	−	0.186455i
$345$		0			0
$346$	10.0881	−	5.82435i	0.542338	−	0.313119i
$347$	−0.607688	−	1.05255i	−0.0326224	−	0.0565036i	0.849253	−	0.527986i	$-0.177053\pi$
$347$	−0.607688	−	1.05255i	−0.0326224	−	0.0565036i	−0.881876	+	0.471482i	$0.843719\pi$
$348$		0			0
$349$	3.30094	+	1.90580i	0.176695	+	0.102015i	0.585739	−	0.810500i	$-0.300804\pi$
$349$	3.30094	+	1.90580i	0.176695	+	0.102015i	−0.409044	+	0.912515i	$0.634138\pi$
$350$	−7.79094			−0.416443
$351$		0			0
$352$	0.480744			0.0256238
$353$	17.3353	+	10.0086i	0.922667	+	0.532702i	0.884485	−	0.466569i	$-0.154510\pi$
$353$	17.3353	+	10.0086i	0.922667	+	0.532702i	0.0381819	+	0.999271i	$0.487843\pi$
$354$		0			0
$355$	−1.93602	−	3.35329i	−0.102753	−	0.177974i
$356$	−8.21616	+	4.74360i	−0.435455	+	0.251410i
$357$		0			0
$358$	0.776096	+	0.448079i	0.0410179	+	0.0236817i
$359$		−	9.96717i		−	0.526047i	−0.964789	−	0.263024i	$-0.915280\pi$
$359$		−	9.96717i		−	0.526047i	0.964789	−	0.263024i	$-0.0847197\pi$
$360$		0			0
$361$	18.7689			0.987836
$362$	1.23141	+	0.710953i	0.0647213	+	0.0373669i
$363$		0			0
$364$	0.951220	+	5.97056i	0.0498575	+	0.312942i
$365$	−1.75904	−	3.04675i	−0.0920723	−	0.159474i
$366$		0			0
$367$	−7.16334	+	12.4073i	−0.373923	+	0.647654i	−0.990165	−	0.139903i	$-0.955321\pi$
$367$	−7.16334	+	12.4073i	−0.373923	+	0.647654i	0.616242	+	0.787557i	$0.288654\pi$
$368$	−3.66679			−0.191144
$369$		0			0
$370$		−	2.17094i		−	0.112862i
$371$	7.38560	+	4.26408i	0.383441	+	0.221380i
$372$		0			0
$373$	13.9877	+	24.2275i	0.724257	+	1.25445i	0.959279	+	0.282460i	$0.0911505\pi$
$373$	13.9877	+	24.2275i	0.724257	+	1.25445i	−0.235022	+	0.971990i	$0.575516\pi$
$374$	−0.503217	−	0.871597i	−0.0260207	−	0.0450692i
$375$		0			0
$376$	3.12051	−	5.40488i	0.160928	−	0.278736i
$377$	−3.17979	+	8.30625i	−0.163768	+	0.427794i
$378$		0			0
$379$			4.05068i			0.208069i	0.994574	+	0.104035i	$0.0331753\pi$
$379$			4.05068i			0.208069i	−0.994574	+	0.104035i	$0.966825\pi$
$380$	0.142963	−	0.247620i	0.00733387	−	0.0127026i
$381$		0			0
$382$	−12.8524	+	7.42036i	−0.657588	+	0.379659i
$383$	−27.1033	+	15.6481i	−1.38492	+	0.799581i	−0.992737	−	0.120308i	$-0.961612\pi$
$383$	−27.1033	+	15.6481i	−1.38492	+	0.799581i	−0.392179	+	0.919889i	$0.628279\pi$
$384$		0			0
$385$	−0.415213	−	0.239724i	−0.0211612	−	0.0122174i
$386$	14.1075			0.718054
$387$		0			0
$388$		−	9.71535i		−	0.493222i
$389$	−7.66964	+	13.2842i	−0.388866	+	0.673536i	−0.992297	−	0.123879i	$-0.960467\pi$
$389$	−7.66964	+	13.2842i	−0.388866	+	0.673536i	0.603431	+	0.797415i	$0.293800\pi$
$390$		0			0
$391$	3.83819	+	6.64794i	0.194106	+	0.336201i
$392$	3.62716	−	2.09414i	0.183199	−	0.105770i
$393$		0			0
$394$	0.221259	−	0.383231i	0.0111468	−	0.0193069i
$395$		−	1.22395i		−	0.0615837i
$396$		0			0
$397$			24.1832i			1.21372i	0.794808	+	0.606860i	$0.207571\pi$
$397$			24.1832i			1.21372i	−0.794808	+	0.606860i	$0.792429\pi$
$398$	−11.5117	−	6.64626i	−0.577028	−	0.333147i
$399$		0			0
$400$	−2.32313	−	4.02378i	−0.116157	−	0.201189i
$401$	24.8876	−	14.3689i	1.24283	−	0.717548i	0.273160	−	0.961969i	$-0.411931\pi$
$401$	24.8876	−	14.3689i	1.24283	−	0.717548i	0.969669	+	0.244421i	$0.0785978\pi$
$402$		0			0
$403$	3.21305	−	2.60673i	0.160054	−	0.129850i
$404$	−5.79495			−0.288310
$405$		0			0
$406$	−4.13634			−0.205283
$407$	−0.877388	+	1.51968i	−0.0434905	+	0.0753278i
$408$		0			0
$409$	25.9100	−	14.9591i	1.28117	−	0.739682i	0.304105	−	0.952638i	$-0.401643\pi$
$409$	25.9100	−	14.9591i	1.28117	−	0.739682i	0.977062	+	0.212956i	$0.0683092\pi$
$410$	5.10442	−	2.94704i	0.252090	−	0.145544i
$411$		0			0
$412$	0.857037	−	1.48443i	0.0422232	−	0.0731327i
$413$	15.7451			0.774764
$414$		0			0
$415$	−6.57809			−0.322906
$416$	−2.79997	+	2.27160i	−0.137280	+	0.111374i
$417$		0			0
$418$	−0.200152	+	0.115558i	−0.00978974	+	0.00565211i
$419$	12.2858	+	21.2796i	0.600200	+	1.03958i	0.992790	+	0.119863i	$0.0382457\pi$
$419$	12.2858	+	21.2796i	0.600200	+	1.03958i	−0.392590	+	0.919713i	$0.628421\pi$
$420$		0			0
$421$	−24.6735	−	14.2452i	−1.20251	−	0.694271i	−0.241399	−	0.970426i	$-0.577606\pi$
$421$	−24.6735	−	14.2452i	−1.20251	−	0.694271i	−0.961113	+	0.276155i	$0.910940\pi$
$422$			9.64064i			0.469299i
$423$		0			0
$424$			5.08592i			0.246994i
$425$	−4.86345	+	8.42375i	−0.235912	+	0.408612i
$426$		0			0
$427$	−11.3453	+	6.55024i	−0.549040	+	0.316988i
$428$	−7.05105	−	12.2128i	−0.340825	−	0.590327i
$429$		0			0
$430$	−2.05681	+	3.56249i	−0.0991880	+	0.171799i
$431$			7.13767i			0.343809i	0.985114	+	0.171905i	$0.0549921\pi$
$431$			7.13767i			0.343809i	−0.985114	+	0.171905i	$0.945008\pi$
$432$		0			0
$433$	−7.85282			−0.377382			−0.188691	−	0.982036i	$-0.560424\pi$
$433$	−7.85282			−0.377382			−0.188691	+	0.982036i	$0.560424\pi$
$434$	1.66641	+	0.962100i	0.0799901	+	0.0461823i
$435$		0			0
$436$	15.8893	−	9.17368i	0.760959	−	0.439340i
$437$	1.52662	−	0.881394i	0.0730281	−	0.0421628i
$438$		0			0
$439$	2.07427	−	3.59274i	0.0989994	−	0.171472i	−0.812271	−	0.583280i	$-0.801769\pi$
$439$	2.07427	−	3.59274i	0.0989994	−	0.171472i	0.911271	+	0.411808i	$0.135102\pi$
$440$		−	0.285927i		−	0.0136310i
$441$		0			0
$442$	7.04930	+	2.69861i	0.335301	+	0.128360i
$443$	8.92349	−	15.4559i	0.423968	−	0.734334i	−0.572356	−	0.820006i	$-0.693970\pi$
$443$	8.92349	−	15.4559i	0.423968	−	0.734334i	0.996323	+	0.0856716i	$0.0273036\pi$
$444$		0			0
$445$	2.82130	+	4.88663i	0.133742	+	0.231648i
$446$	11.5666	+	20.0340i	0.547696	+	0.948638i
$447$		0			0
$448$	−1.45217	−	0.838409i	−0.0686084	−	0.0396111i
$449$			19.7308i			0.931152i	0.885008	+	0.465576i	$0.154153\pi$
$449$			19.7308i			0.931152i	−0.885008	+	0.465576i	$0.845847\pi$
$450$		0			0
$451$	−4.76420			−0.224337
$452$	10.1390	−	17.5612i	0.476896	−	0.826009i
$453$		0			0
$454$	−6.65331	−	11.5239i	−0.312255	−	0.540842i
$455$	3.55104	−	0.565746i	0.166475	−	0.0265226i
$456$		0			0
$457$	31.4762	+	18.1728i	1.47240	+	0.850088i	0.999518	−	0.0310408i	$-0.00988217\pi$
$457$	31.4762	+	18.1728i	1.47240	+	0.850088i	0.472877	+	0.881128i	$0.343216\pi$
$458$	0.809405			0.0378210
$459$		0			0
$460$			2.18085i			0.101683i
$461$	−19.8630	−	11.4679i	−0.925112	−	0.534114i	−0.0398498	−	0.999206i	$-0.512688\pi$
$461$	−19.8630	−	11.4679i	−0.925112	−	0.534114i	−0.885262	+	0.465092i	$0.846021\pi$
$462$		0			0
$463$	25.6143	−	14.7884i	1.19040	−	0.687277i	0.232002	−	0.972715i	$-0.425472\pi$
$463$	25.6143	−	14.7884i	1.19040	−	0.687277i	0.958397	+	0.285438i	$0.0921391\pi$
$464$	−1.23339	−	2.13629i	−0.0572586	−	0.0991749i
$465$		0			0
$466$	13.3984	+	7.73559i	0.620671	+	0.358344i
$467$	12.5970			0.582920			0.291460	−	0.956583i	$-0.405859\pi$
$467$	12.5970			0.582920			0.291460	+	0.956583i	$0.405859\pi$
$468$		0			0
$469$	−24.1159			−1.11357
$470$	−3.21460	−	1.85595i	−0.148278	−	0.0856086i
$471$		0			0
$472$	4.69493	+	8.13185i	0.216101	+	0.374299i
$473$	2.87957	−	1.66252i	0.132403	−	0.0764428i
$474$		0			0
$475$	1.93441	+	1.11683i	0.0887568	+	0.0512438i
$476$			3.51040i			0.160899i
$477$		0			0
$478$	−29.1575			−1.33363
$479$	11.0404	+	6.37417i	0.504448	+	0.291243i	0.730549	−	0.682861i	$-0.239264\pi$
$479$	11.0404	+	6.37417i	0.504448	+	0.291243i	−0.226101	+	0.974104i	$0.572598\pi$
$480$		0			0
$481$	−2.07063	−	12.9968i	−0.0944126	−	0.592603i
$482$	7.79735	+	13.5054i	0.355159	+	0.615154i
$483$		0			0
$484$	5.38444	−	9.32613i	0.244747	−	0.423915i
$485$	−5.77828			−0.262378
$486$		0			0
$487$		−	20.8054i		−	0.942782i	−0.881924	−	0.471391i	$-0.843752\pi$
$487$		−	20.8054i		−	0.942782i	0.881924	−	0.471391i	$-0.156248\pi$
$488$	−6.76599	−	3.90635i	−0.306282	−	0.176832i
$489$		0			0
$490$	−1.24551	−	2.15728i	−0.0562663	−	0.0974561i
$491$	−7.37362	−	12.7715i	−0.332767	−	0.576369i	0.650286	−	0.759689i	$-0.274649\pi$
$491$	−7.37362	−	12.7715i	−0.332767	−	0.576369i	−0.983053	+	0.183320i	$0.941316\pi$
$492$		0			0
$493$	−2.58209	+	4.47231i	−0.116291	+	0.201423i
$494$	0.619702	−	1.61879i	0.0278817	−	0.0728326i
$495$		0			0
$496$			1.14753i			0.0515256i
$497$	5.45828	−	9.45402i	0.244837	−	0.424071i
$498$		0			0
$499$	−25.7627	+	14.8741i	−1.15330	+	0.665856i	−0.949688	−	0.313197i	$-0.898600\pi$
$499$	−25.7627	+	14.8741i	−1.15330	+	0.665856i	−0.203608	+	0.979053i	$0.565267\pi$
$500$	−4.96856	+	2.86860i	−0.222201	+	0.128288i
$501$		0			0
$502$	2.42050	+	1.39748i	0.108032	+	0.0623724i
$503$	26.1270			1.16495			0.582473	−	0.812850i	$-0.302085\pi$
$503$	26.1270			1.16495			0.582473	+	0.812850i	$0.302085\pi$
$504$		0			0
$505$			3.44660i			0.153372i
$506$	0.881394	−	1.52662i	0.0391827	−	0.0678665i
$507$		0			0
$508$	9.27366	+	16.0624i	0.411452	+	0.712656i
$509$	15.4810	−	8.93795i	0.686182	−	0.396168i	−0.115998	−	0.993249i	$-0.537007\pi$
$509$	15.4810	−	8.93795i	0.686182	−	0.396168i	0.802180	+	0.597082i	$0.203673\pi$
$510$		0			0
$511$	4.95931	−	8.58977i	0.219387	−	0.379989i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$			20.9596i			0.924488i
$515$	−0.882878	−	0.509730i	−0.0389042	−	0.0224614i
$516$		0			0
$517$	1.50017	+	2.59837i	0.0659773	+	0.114276i
$518$	5.30059	−	3.06029i	0.232894	−	0.134462i
$519$		0			0
$520$	1.35105	+	1.66531i	0.0592476	+	0.0730285i
$521$	13.7904			0.604168			0.302084	−	0.953281i	$-0.402318\pi$
$521$	13.7904			0.604168			0.302084	+	0.953281i	$0.402318\pi$
$522$		0			0
$523$	−0.523640			−0.0228972			−0.0114486	−	0.999934i	$-0.503644\pi$
$523$	−0.523640			−0.0228972			−0.0114486	+	0.999934i	$0.503644\pi$
$524$	2.32256	−	4.02280i	0.101462	−	0.175737i
$525$		0			0
$526$	13.7251	−	7.92418i	0.598442	−	0.345511i
$527$	2.08049	−	1.20117i	0.0906276	−	0.0523239i
$528$		0			0
$529$	4.77734	−	8.27459i	0.207710	−	0.359765i
$530$	3.02489			0.131393
$531$		0			0
$532$	0.806121			0.0349498
$533$	27.7478	−	22.5116i	1.20189	−	0.975088i
$534$		0			0
$535$	−7.26365	+	4.19367i	−0.314035	+	0.181308i
$536$	−7.19096	−	12.4551i	−0.310602	−	0.537979i
$537$		0			0
$538$	−16.3703	−	9.45139i	−0.705773	−	0.407478i
$539$			2.01349i			0.0867273i
$540$		0			0
$541$			11.3636i			0.488558i	0.969705	+	0.244279i	$0.0785513\pi$
$541$			11.3636i			0.488558i	−0.969705	+	0.244279i	$0.921449\pi$
$542$	−4.81902	+	8.34679i	−0.206995	+	0.358525i
$543$		0			0
$544$	−1.81302	+	1.04675i	−0.0777324	+	0.0448788i
$545$	−5.45612	−	9.45028i	−0.233715	−	0.404806i
$546$		0			0
$547$	4.14239	−	7.17484i	0.177116	−	0.306774i	−0.763776	−	0.645482i	$-0.776657\pi$
$547$	4.14239	−	7.17484i	0.177116	−	0.306774i	0.940892	+	0.338708i	$0.109990\pi$
$548$			13.0207i			0.556216i
$549$		0			0
$550$	2.23366			0.0952438
$551$	1.02701	+	0.592945i	0.0437521	+	0.0252603i
$552$		0			0
$553$	2.98841	−	1.72536i	0.127080	−	0.0733698i
$554$	−2.33844	+	1.35010i	−0.0993510	+	0.0573603i
$555$		0			0
$556$	5.09027	−	8.81661i	0.215876	−	0.373908i
$557$		−	26.7334i		−	1.13273i	−0.824154	−	0.566365i	$-0.808349\pi$
$557$		−	26.7334i		−	1.13273i	0.824154	−	0.566365i	$-0.191651\pi$
$558$		0			0
$559$	−8.91562	+	23.2894i	−0.377090	+	0.985035i
$560$	−0.498651	+	0.863688i	−0.0210718	+	0.0364975i
$561$		0			0
$562$	−5.39719	−	9.34820i	−0.227667	−	0.394330i
$563$	2.36071	+	4.08888i	0.0994922	+	0.172326i	0.911475	−	0.411356i	$-0.134945\pi$
$563$	2.36071	+	4.08888i	0.0994922	+	0.172326i	−0.811982	+	0.583682i	$0.801611\pi$
$564$		0			0
$565$	−10.4447	−	6.03023i	−0.439410	−	0.253694i
$566$			29.2176i			1.22811i
$567$		0			0
$568$	6.51028			0.273165
$569$	−21.0546	+	36.4676i	−0.882653	+	1.52880i	−0.0342730	+	0.999413i	$0.510912\pi$
$569$	−21.0546	+	36.4676i	−0.882653	+	1.52880i	−0.848380	+	0.529388i	$0.822422\pi$
$570$		0			0
$571$	5.89219	+	10.2056i	0.246581	+	0.427090i	0.962575	−	0.271016i	$-0.0873597\pi$
$571$	5.89219	+	10.2056i	0.246581	+	0.427090i	−0.715994	+	0.698106i	$0.754026\pi$
$572$	−0.272715	−	1.71176i	−0.0114028	−	0.0715723i
$573$		0			0
$574$	14.3910	+	8.30867i	0.600671	+	0.346797i
$575$	−17.0369			−0.710486
$576$		0			0
$577$		−	21.5466i		−	0.896997i	−0.893784	−	0.448498i	$-0.851959\pi$
$577$		−	21.5466i		−	0.896997i	0.893784	−	0.448498i	$-0.148041\pi$
$578$	−10.9269	−	6.30865i	−0.454499	−	0.262405i
$579$		0			0
$580$	−1.27058	+	0.733568i	−0.0527579	+	0.0304598i
$581$	−9.27290	−	16.0611i	−0.384705	−	0.666328i
$582$		0			0
$583$	−2.11746	−	1.22251i	−0.0876961	−	0.0506313i
$584$	5.91514			0.244770
$585$		0			0
$586$	23.6944			0.978805
$587$	7.62960	+	4.40495i	0.314907	+	0.181812i	0.649120	−	0.760686i	$-0.275137\pi$
$587$	7.62960	+	4.40495i	0.314907	+	0.181812i	−0.334213	+	0.942498i	$0.608470\pi$
$588$		0			0
$589$	−0.275834	−	0.477759i	−0.0113656	−	0.0196857i
$590$	4.83649	−	2.79235i	0.199115	−	0.114959i
$591$		0			0
$592$	3.16110	+	1.82506i	0.129920	+	0.0750095i
$593$			26.7483i			1.09842i	0.835685	+	0.549210i	$0.185071\pi$
$593$			26.7483i			1.09842i	−0.835685	+	0.549210i	$0.814929\pi$
$594$		0			0
$595$	2.08784			0.0855931
$596$	4.54901	+	2.62637i	0.186335	+	0.107580i
$597$		0			0
$598$	2.08008	+	13.0561i	0.0850609	+	0.533905i
$599$	−23.9224	−	41.4349i	−0.977445	−	1.69298i	−0.671620	−	0.740896i	$-0.734401\pi$
$599$	−23.9224	−	41.4349i	−0.977445	−	1.69298i	−0.305825	−	0.952088i	$-0.598932\pi$
$600$		0			0
$601$	10.5193	−	18.2199i	0.429091	−	0.743207i	−0.567702	−	0.823234i	$-0.692167\pi$
$601$	10.5193	−	18.2199i	0.429091	−	0.743207i	0.996793	+	0.0800273i	$0.0255008\pi$
$602$	−11.5976			−0.472683
$603$		0			0
$604$		−	11.9232i		−	0.485150i
$605$	−5.54679	−	3.20244i	−0.225509	−	0.130198i
$606$		0			0
$607$	−11.7683	−	20.3833i	−0.477662	−	0.827334i	0.522011	−	0.852939i	$-0.325182\pi$
$607$	−11.7683	−	20.3833i	−0.477662	−	0.827334i	−0.999672	+	0.0256049i	$0.991849\pi$
$608$	0.240372	+	0.416337i	0.00974838	+	0.0168847i
$609$		0			0
$610$	−2.32333	+	4.02413i	−0.0940690	+	0.162932i
$611$	−21.0151	−	8.04497i	−0.850179	−	0.325465i
$612$		0			0
$613$		−	40.7009i		−	1.64390i	−0.569563	−	0.821948i	$-0.692888\pi$
$613$		−	40.7009i		−	1.64390i	0.569563	−	0.821948i	$-0.307112\pi$
$614$	−3.27618	+	5.67452i	−0.132216	+	0.229005i
$615$		0			0
$616$	0.698121	−	0.403061i	0.0281281	−	0.0162398i
$617$	−34.0924	+	19.6832i	−1.37251	+	0.792417i	−0.991243	−	0.132049i	$-0.957844\pi$
$617$	−34.0924	+	19.6832i	−1.37251	+	0.792417i	−0.381264	+	0.924466i	$0.624511\pi$
$618$		0			0
$619$	−21.1669	−	12.2207i	−0.850770	−	0.491192i	0.0101406	−	0.999949i	$-0.496772\pi$
$619$	−21.1669	−	12.2207i	−0.850770	−	0.491192i	−0.860911	+	0.508756i	$0.830105\pi$
$620$	0.682503			0.0274100
$621$		0			0
$622$			25.4230i			1.01937i
$623$	−7.95416	+	13.7770i	−0.318677	+	0.551964i
$624$		0			0
$625$	−9.90953	−	17.1638i	−0.396381	−	0.686553i
$626$	−1.02317	+	0.590728i	−0.0408942	+	0.0236103i
$627$		0			0
$628$	6.19540	−	10.7307i	0.247223	−	0.428203i
$629$		−	7.64149i		−	0.304686i
$630$		0			0
$631$			5.70930i			0.227284i	0.993522	+	0.113642i	$0.0362516\pi$
$631$			5.70930i			0.227284i	−0.993522	+	0.113642i	$0.963748\pi$
$632$	1.78219	+	1.02895i	0.0708918	+	0.0409294i
$633$		0			0
$634$	−13.9724	−	24.2009i	−0.554915	−	0.961141i
$635$	9.55327	−	5.51558i	0.379110	−	0.218879i
$636$		0			0
$637$	−9.51409	−	11.7271i	−0.376962	−	0.464643i
$638$	1.18589			0.0469498
$639$		0			0
$640$	−0.594758			−0.0235099
$641$	19.7411	−	34.1925i	0.779725	−	1.35052i	−0.152375	−	0.988323i	$-0.548692\pi$
$641$	19.7411	−	34.1925i	0.779725	−	1.35052i	0.932100	−	0.362201i	$-0.117974\pi$
$642$		0			0
$643$	25.5467	−	14.7494i	1.00747	−	0.581660i	0.0970167	−	0.995283i	$-0.469070\pi$
$643$	25.5467	−	14.7494i	1.00747	−	0.581660i	0.910449	+	0.413622i	$0.135737\pi$
$644$	−5.32479	+	3.07427i	−0.209826	+	0.121143i
$645$		0			0
$646$	0.503217	−	0.871597i	0.0197988	−	0.0342925i
$647$	−47.5940			−1.87111			−0.935556	−	0.353178i	$-0.885101\pi$
$647$	−47.5940			−1.87111			−0.935556	+	0.353178i	$0.885101\pi$
$648$		0			0
$649$	−4.51412			−0.177195
$650$	−13.0094	+	10.5544i	−0.510271	+	0.413979i
$651$		0			0
$652$	−18.5008	+	10.6814i	−0.724548	+	0.418318i
$653$	6.23738	+	10.8035i	0.244088	+	0.422772i	0.961875	−	0.273490i	$-0.0881782\pi$
$653$	6.23738	+	10.8035i	0.244088	+	0.422772i	−0.717787	+	0.696263i	$0.754845\pi$
$654$		0			0
$655$	−2.39259	−	1.38136i	−0.0934863	−	0.0539744i
$656$			9.91005i			0.386922i
$657$		0			0
$658$		−	10.4651i		−	0.407970i
$659$	1.87306	−	3.24423i	0.0729639	−	0.126377i	−0.827235	−	0.561856i	$-0.810088\pi$
$659$	1.87306	−	3.24423i	0.0729639	−	0.126377i	0.900199	+	0.435479i	$0.143421\pi$
$660$		0			0
$661$	−28.6397	+	16.5352i	−1.11396	+	0.643143i	−0.939851	−	0.341584i	$-0.889037\pi$
$661$	−28.6397	+	16.5352i	−1.11396	+	0.643143i	−0.174105	+	0.984727i	$0.555703\pi$
$662$	−12.3266	−	21.3503i	−0.479086	−	0.829801i
$663$		0			0
$664$	5.53006	−	9.57834i	0.214608	−	0.371712i
$665$		−	0.479447i		−	0.0185922i
$666$		0			0
$667$	−9.04515			−0.350230
$668$	−12.7614	−	7.36778i	−0.493752	−	0.285068i
$669$		0			0
$670$	−7.40778	+	4.27688i	−0.286187	+	0.165230i
$671$	3.25271	−	1.87796i	0.125570	−	0.0724977i
$672$		0			0
$673$	7.07178	−	12.2487i	0.272597	−	0.472152i	−0.696929	−	0.717140i	$-0.745451\pi$
$673$	7.07178	−	12.2487i	0.272597	−	0.472152i	0.969526	+	0.244988i	$0.0787840\pi$
$674$			15.2788i			0.588518i
$675$		0			0
$676$	9.67672	+	8.68108i	0.372181	+	0.333888i
$677$	−17.1064	+	29.6291i	−0.657451	+	1.13874i	0.323823	+	0.946118i	$0.395032\pi$
$677$	−17.1064	+	29.6291i	−0.657451	+	1.13874i	−0.981273	+	0.192620i	$0.938301\pi$
$678$		0			0
$679$	−8.14544	−	14.1083i	−0.312593	−	0.541427i
$680$	0.622560	+	1.07831i	0.0238741	+	0.0413512i
$681$		0			0
$682$	−0.477759	−	0.275834i	−0.0182944	−	0.0105622i
$683$		−	16.3144i		−	0.624255i	−0.950040	−	0.312127i	$-0.898958\pi$
$683$		−	16.3144i		−	0.624255i	0.950040	−	0.312127i	$-0.101042\pi$
$684$		0			0
$685$	7.74416			0.295889
$686$	9.38036	−	16.2473i	0.358144	−	0.620323i
$687$		0			0
$688$	−3.45822	−	5.98981i	−0.131843	−	0.228359i
$689$	18.1092	−	2.88512i	0.689904	−	0.109914i
$690$		0			0
$691$	21.9516	+	12.6738i	0.835078	+	0.482132i	0.855588	−	0.517657i	$-0.173196\pi$
$691$	21.9516	+	12.6738i	0.835078	+	0.482132i	−0.0205104	+	0.999790i	$0.506529\pi$
$692$	11.6487			0.442817
$693$		0			0
$694$		−	1.21538i		−	0.0461350i
$695$	−5.24375	−	3.02748i	−0.198907	−	0.114839i
$696$		0			0
$697$	17.9671	−	10.3733i	0.680551	−	0.392916i
$698$	1.90580	+	3.30094i	0.0721355	+	0.124942i
$699$		0			0
$700$	−6.74715	−	3.89547i	−0.255018	−	0.147235i
$701$	−35.4651			−1.33950			−0.669750	−	0.742587i	$-0.733599\pi$
$701$	−35.4651			−1.33950			−0.669750	+	0.742587i	$0.733599\pi$
$702$		0			0
$703$	−1.75478			−0.0661826
$704$	0.416337	+	0.240372i	0.0156913	+	0.00905937i
$705$		0			0
$706$	10.0086	+	17.3353i	0.376677	+	0.652424i
$707$	−8.41524	+	4.85854i	−0.316488	+	0.182724i
$708$		0			0
$709$	−18.7687	−	10.8361i	−0.704874	−	0.406959i	0.104286	−	0.994547i	$-0.466744\pi$
$709$	−18.7687	−	10.8361i	−0.704874	−	0.406959i	−0.809160	+	0.587588i	$0.800077\pi$
$710$		−	3.87204i		−	0.145315i
$711$		0			0
$712$	−9.48720			−0.355548
$713$	3.64402	+	2.10387i	0.136470	+	0.0787907i
$714$		0			0
$715$	−1.01808	+	0.162200i	−0.0380742	+	0.00606592i
$716$	0.448079	+	0.776096i	0.0167455	+	0.0290041i
$717$		0			0
$718$	4.98359	−	8.63182i	0.185986	−	0.322137i
$719$	−15.4819			−0.577378			−0.288689	−	0.957423i	$-0.593219\pi$
$719$	−15.4819			−0.577378			−0.288689	+	0.957423i	$0.593219\pi$
$720$		0			0
$721$		−	2.87419i		−	0.107040i
$722$	16.2543	+	9.38444i	0.604924	+	0.349253i
$723$		0			0
$724$	0.710953	+	1.23141i	0.0264224	+	0.0457649i
$725$	−5.73065	−	9.92578i	−0.212831	−	0.368634i
$726$		0			0
$727$	2.73280	−	4.73335i	0.101354	−	0.175550i	−0.810889	−	0.585200i	$-0.801016\pi$
$727$	2.73280	−	4.73335i	0.101354	−	0.175550i	0.912243	+	0.409650i	$0.134349\pi$
$728$	−2.16150	+	5.64626i	−0.0801104	+	0.209264i
$729$		0			0
$730$		−	3.51808i		−	0.130210i
$731$	−7.23975	+	12.5396i	−0.267772	+	0.463794i
$732$		0			0
$733$	−16.5705	+	9.56700i	−0.612046	+	0.353365i	−0.773766	−	0.633472i	$-0.781629\pi$
$733$	−16.5705	+	9.56700i	−0.612046	+	0.353365i	0.161720	+	0.986837i	$0.448296\pi$
$734$	−12.4073	+	7.16334i	−0.457960	+	0.264404i
$735$		0			0
$736$	−3.17553	−	1.83339i	−0.117052	−	0.0675798i
$737$	6.91403			0.254681
$738$		0			0
$739$		−	3.40317i		−	0.125188i	−0.998039	−	0.0625938i	$-0.980063\pi$
$739$		−	3.40317i		−	0.125188i	0.998039	−	0.0625938i	$-0.0199373\pi$
$740$	1.08547	−	1.88009i	0.0399027	−	0.0691134i
$741$		0			0
$742$	4.26408	+	7.38560i	0.156539	+	0.271134i
$743$	−19.8454	+	11.4578i	−0.728058	+	0.420345i	−0.817711	−	0.575628i	$-0.804757\pi$
$743$	−19.8454	+	11.4578i	−0.728058	+	0.420345i	0.0896532	+	0.995973i	$0.471424\pi$
$744$		0			0
$745$	1.56206	−	2.70556i	0.0572293	−	0.0991240i
$746$			27.9755i			1.02425i
$747$		0			0
$748$		−	1.00643i		−	0.0367989i
$749$	−20.4786	−	11.8233i	−0.748272	−	0.432015i
$750$		0			0
$751$	7.68694	+	13.3142i	0.280500	+	0.485841i	0.971508	−	0.237006i	$-0.0761663\pi$
$751$	7.68694	+	13.3142i	0.280500	+	0.485841i	−0.691008	+	0.722847i	$0.742833\pi$
$752$	5.40488	−	3.12051i	0.197096	−	0.113793i
$753$		0			0
$754$	−6.90691	+	5.60353i	−0.251535	+	0.204069i
$755$	−7.09144			−0.258084
$756$		0			0
$757$	41.9292			1.52394			0.761971	−	0.647611i	$-0.224232\pi$
$757$	41.9292			1.52394			0.761971	+	0.647611i	$0.224232\pi$
$758$	−2.02534	+	3.50799i	−0.0735637	+	0.127416i
$759$		0			0
$760$	0.247620	−	0.142963i	0.00898211	−	0.00518583i
$761$	−2.20005	+	1.27020i	−0.0797518	+	0.0460447i	−0.539346	−	0.842085i	$-0.681328\pi$
$761$	−2.20005	+	1.27020i	−0.0797518	+	0.0460447i	0.459594	+	0.888129i	$0.347995\pi$
$762$		0			0
$763$	15.3826	−	26.6434i	0.556887	−	0.964557i
$764$	−14.8407			−0.536918
$765$		0			0
$766$	−31.2962			−1.13078
$767$	26.2913	−	21.3300i	0.949324	−	0.770181i
$768$		0			0
$769$	−8.65130	+	4.99483i	−0.311974	+	0.180118i	−0.647809	−	0.761802i	$-0.724315\pi$
$769$	−8.65130	+	4.99483i	−0.311974	+	0.180118i	0.335836	+	0.941921i	$0.390981\pi$
$770$	−0.239724	−	0.415213i	−0.00863904	−	0.0149633i
$771$		0			0
$772$	12.2175	+	7.05376i	0.439716	+	0.253870i
$773$		−	5.76343i		−	0.207296i	−0.994614	−	0.103648i	$-0.966948\pi$
$773$		−	5.76343i		−	0.207296i	0.994614	−	0.103648i	$-0.0330516\pi$
$774$		0			0
$775$			5.33173i			0.191521i
$776$	4.85767	−	8.41374i	0.174380	−	0.302036i
$777$		0			0
$778$	−13.2842	+	7.66964i	−0.476262	+	0.274970i
$779$	−2.38210	−	4.12592i	−0.0853476	−	0.147826i
$780$		0			0
$781$	−1.56489	+	2.71047i	−0.0559962	+	0.0969883i
$782$			7.67638i			0.274507i
$783$		0			0
$784$	4.18828			0.149581
$785$	−6.38220	−	3.68476i	−0.227790	−	0.131515i
$786$		0			0
$787$	8.20657	−	4.73806i	0.292533	−	0.168894i	−0.346551	−	0.938031i	$-0.612647\pi$
$787$	8.20657	−	4.73806i	0.292533	−	0.168894i	0.639083	+	0.769137i	$0.279314\pi$
$788$	0.383231	−	0.221259i	0.0136520	−	0.00788201i
$789$		0			0
$790$	0.611976	−	1.05997i	0.0217731	−	0.0377122i
$791$		−	34.0024i		−	1.20899i
$792$		0			0
$793$	−10.0709	+	26.3073i	−0.357629	+	0.934199i
$794$	−12.0916	+	20.9433i	−0.429115	+	0.743249i
$795$		0			0
$796$	−6.64626	−	11.5117i	−0.235571	−	0.408020i
$797$	−1.54871	−	2.68245i	−0.0548582	−	0.0950171i	0.837292	−	0.546756i	$-0.184137\pi$
$797$	−1.54871	−	2.68245i	−0.0548582	−	0.0950171i	−0.892150	+	0.451739i	$0.850804\pi$
$798$		0			0
$799$	−11.3151	−	6.53276i	−0.400298	−	0.231112i
$800$		−	4.64626i		−	0.164270i
$801$		0			0
$802$	28.7378			1.01477
$803$	−1.42184	+	2.46269i	−0.0501755	+	0.0869065i
$804$		0			0
$805$	1.82845	+	3.16696i	0.0644442	+	0.111621i
$806$	4.08595	−	0.650967i	0.143921	−	0.0229294i
$807$		0			0
$808$	−5.01858	−	2.89748i	−0.176553	−	0.101933i
$809$	−18.7613			−0.659612			−0.329806	−	0.944049i	$-0.606983\pi$
$809$	−18.7613			−0.659612			−0.329806	+	0.944049i	$0.606983\pi$
$810$		0			0
$811$		−	35.6282i		−	1.25108i	−0.780193	−	0.625538i	$-0.784879\pi$
$811$		−	35.6282i		−	1.25108i	0.780193	−	0.625538i	$-0.215121\pi$
$812$	−3.58217	−	2.06817i	−0.125710	−	0.0725785i
$813$		0			0
$814$	−1.51968	+	0.877388i	−0.0532648	+	0.0307524i
$815$	6.35288	+	11.0035i	0.222532	+	0.385436i
$816$		0			0
$817$	2.87957	+	1.66252i	0.100743	+	0.0581642i
$818$	29.9183			1.04607
$819$		0			0
$820$	5.89408			0.205830
$821$	−13.3975	−	7.73506i	−0.467577	−	0.269956i	0.247648	−	0.968850i	$-0.420342\pi$
$821$	−13.3975	−	7.73506i	−0.467577	−	0.269956i	−0.715225	+	0.698894i	$0.753676\pi$
$822$		0			0
$823$	4.04000	+	6.99748i	0.140825	+	0.243917i	0.927808	−	0.373059i	$-0.121691\pi$
$823$	4.04000	+	6.99748i	0.140825	+	0.243917i	−0.786982	+	0.616976i	$0.788358\pi$
$824$	1.48443	−	0.857037i	0.0517126	−	0.0298563i
$825$		0			0
$826$	13.6356	+	7.87254i	0.474444	+	0.273921i
$827$		−	27.7387i		−	0.964569i	−0.876015	−	0.482284i	$-0.839807\pi$
$827$		−	27.7387i		−	0.964569i	0.876015	−	0.482284i	$-0.160193\pi$
$828$		0			0
$829$	−38.2112			−1.32713			−0.663566	−	0.748118i	$-0.730958\pi$
$829$	−38.2112			−1.32713			−0.663566	+	0.748118i	$0.730958\pi$
$830$	−5.69680	−	3.28905i	−0.197739	−	0.114164i
$831$		0			0
$832$	−3.56065	+	0.567277i	−0.123443	+	0.0196668i
$833$	−4.38406	−	7.59342i	−0.151899	−	0.263096i
$834$		0			0
$835$	−4.38205	+	7.58993i	−0.151647	+	0.262660i
$836$	−0.231115			−0.00799329
$837$		0			0
$838$			24.5716i			0.848811i
$839$	32.5035	+	18.7659i	1.12215	+	0.647872i	0.941948	−	0.335758i	$-0.108993\pi$
$839$	32.5035	+	18.7659i	1.12215	+	0.647872i	0.180199	+	0.983630i	$0.442326\pi$
$840$		0			0
$841$	11.4575	+	19.8450i	0.395086	+	0.684310i
$842$	−14.2452	−	24.6735i	−0.490924	−	0.850305i
$843$		0			0
$844$	−4.82032	+	8.34904i	−0.165922	+	0.287386i
$845$	5.16314	−	5.75531i	0.177618	−	0.197989i
$846$		0			0
$847$		−	18.0575i		−	0.620462i
$848$	−2.54296	+	4.40453i	−0.0873256	+	0.151252i
$849$		0			0
$850$	−8.42375	+	4.86345i	−0.288932	+	0.166815i
$851$	11.5911	−	6.69211i	0.397337	−	0.229402i
$852$		0			0
$853$	−43.2259	−	24.9565i	−1.48003	−	0.854493i	−0.480281	−	0.877114i	$-0.659465\pi$
$853$	−43.2259	−	24.9565i	−1.48003	−	0.854493i	−0.999744	+	0.0226214i	$0.992799\pi$
$854$	−13.1005			−0.448289
$855$		0			0
$856$		−	14.1021i		−	0.482000i
$857$	4.36496	−	7.56033i	0.149104	−	0.258256i	−0.781792	−	0.623539i	$-0.785694\pi$
$857$	4.36496	−	7.56033i	0.149104	−	0.258256i	0.930897	+	0.365283i	$0.119028\pi$
$858$		0			0
$859$	−15.7588	−	27.2950i	−0.537683	−	0.931294i	−0.999028	−	0.0440737i	$-0.985966\pi$
$859$	−15.7588	−	27.2950i	−0.537683	−	0.931294i	0.461345	−	0.887221i	$-0.347367\pi$
$860$	−3.56249	+	2.05681i	−0.121480	+	0.0701365i
$861$		0			0
$862$	−3.56883	+	6.18140i	−0.121555	+	0.210539i
$863$		−	34.0790i		−	1.16006i	−0.814594	−	0.580031i	$-0.803040\pi$
$863$		−	34.0790i		−	1.16006i	0.814594	−	0.580031i	$-0.196960\pi$
$864$		0			0
$865$		−	6.92816i		−	0.235564i
$866$	−6.80074	−	3.92641i	−0.231098	−	0.133425i
$867$		0			0
$868$	0.962100	+	1.66641i	0.0326558	+	0.0565615i
$869$	−0.856779	+	0.494662i	−0.0290642	+	0.0167803i
$870$		0			0
$871$	−40.2690	+	32.6700i	−1.36446	+	1.10698i
$872$	18.3474			0.621320
$873$		0			0
$874$	1.76279			0.0596272
$875$	−4.81012	+	8.33137i	−0.162612	+	0.281652i
$876$		0			0
$877$	−7.79128	+	4.49830i	−0.263093	+	0.151897i	−0.625745	−	0.780028i	$-0.715205\pi$
$877$	−7.79128	+	4.49830i	−0.263093	+	0.151897i	0.362652	+	0.931925i	$0.381871\pi$
$878$	3.59274	−	2.07427i	0.121249	−	0.0700031i
$879$		0			0
$880$	0.142963	−	0.247620i	0.00481929	−	0.00834726i
$881$	40.3722			1.36017			0.680086	−	0.733132i	$-0.261942\pi$
$881$	40.3722			1.36017			0.680086	+	0.733132i	$0.261942\pi$
$882$		0			0
$883$	32.2736			1.08609			0.543046	−	0.839703i	$-0.317271\pi$
$883$	32.2736			1.08609			0.543046	+	0.839703i	$0.317271\pi$
$884$	4.75557	+	5.86171i	0.159947	+	0.197151i
$885$		0			0
$886$	15.4559	−	8.92349i	0.519253	−	0.299791i
$887$	26.8247	+	46.4617i	0.900685	+	1.56003i	0.826607	+	0.562780i	$0.190268\pi$
$887$	26.8247	+	46.4617i	0.900685	+	1.56003i	0.0740786	+	0.997252i	$0.476398\pi$
$888$		0			0
$889$	26.9338	+	15.5502i	0.903331	+	0.521538i
$890$			5.64259i			0.189140i
$891$		0			0
$892$			23.1333i			0.774559i
$893$	−1.50017	+	2.59837i	−0.0502012	+	0.0869510i
$894$		0			0
$895$	0.461589	−	0.266499i	0.0154292	−	0.00890807i
$896$	−0.838409	−	1.45217i	−0.0280093	−	0.0485135i
$897$		0			0
$898$	−9.86538	+	17.0873i	−0.329212	+	0.570212i
$899$			2.83070i			0.0944092i
$900$		0			0
$901$	10.6473			0.354714
$902$	−4.12592	−	2.38210i	−0.137378	−	0.0793152i
$903$		0			0
$904$	17.5612	−	10.1390i	0.584076	−	0.337217i
$905$	0.732390	−	0.422845i	0.0243455	−	0.0140559i
$906$		0			0
$907$	−22.1018	+	38.2814i	−0.733878	+	1.27111i	0.221336	+	0.975198i	$0.428958\pi$
$907$	−22.1018	+	38.2814i	−0.733878	+	1.27111i	−0.955214	+	0.295916i	$0.904375\pi$
$908$		−	13.3066i		−	0.441595i
$909$		0			0
$910$	3.35816	+	1.28557i	0.111322	+	0.0426162i
$911$	27.4816	−	47.5996i	0.910508	−	1.57705i	0.0971588	−	0.995269i	$-0.469025\pi$
$911$	27.4816	−	47.5996i	0.910508	−	1.57705i	0.813349	−	0.581776i	$-0.197642\pi$
$912$		0			0
$913$	2.65854	+	4.60473i	0.0879850	+	0.152394i
$914$	18.1728	+	31.4762i	0.601103	+	1.04114i
$915$		0			0
$916$	0.700965	+	0.404702i	0.0231605	+	0.0133717i
$917$		−	7.78903i		−	0.257217i
$918$		0			0
$919$	−21.0595			−0.694690			−0.347345	−	0.937737i	$-0.612917\pi$
$919$	−21.0595			−0.694690			−0.347345	+	0.937737i	$0.612917\pi$
$920$	−1.09043	+	1.88867i	−0.0359503	+	0.0622677i
$921$		0			0
$922$	−11.4679	−	19.8630i	−0.377676	−	0.654153i
$923$	−3.69313	−	23.1808i	−0.121561	−	0.763006i
$924$		0			0
$925$	14.6873	+	8.47971i	0.482915	+	0.278811i
$926$	29.5769			0.971957
$927$		0			0
$928$		−	2.46678i		−	0.0809760i
$929$	17.8307	+	10.2945i	0.585006	+	0.337753i	0.763120	−	0.646257i	$-0.223666\pi$
$929$	17.8307	+	10.2945i	0.585006	+	0.337753i	−0.178115	+	0.984010i	$0.557000\pi$
$930$		0			0
$931$	−1.74374	+	1.00675i	−0.0571486	+	0.0329948i
$932$	7.73559	+	13.3984i	0.253388	+	0.438881i
$933$		0			0
$934$	10.9093	+	6.29851i	0.356964	+	0.206093i
$935$	−0.598585			−0.0195758
$936$		0			0
$937$	−23.8463			−0.779023			−0.389512	−	0.921022i	$-0.627356\pi$
$937$	−23.8463			−0.779023			−0.389512	+	0.921022i	$0.627356\pi$
$938$	−20.8849	−	12.0579i	−0.681918	−	0.393705i
$939$		0			0
$940$	−1.85595	−	3.21460i	−0.0605344	−	0.104849i
$941$	−3.16693	+	1.82843i	−0.103239	+	0.0596051i	−0.550731	−	0.834683i	$-0.685651\pi$
$941$	−3.16693	+	1.82843i	−0.103239	+	0.0596051i	0.447492	+	0.894288i	$0.352317\pi$
$942$		0			0
$943$	31.4696	+	18.1690i	1.02479	+	0.591664i
$944$			9.38985i			0.305614i
$945$		0			0
$946$	3.32504			0.108106
$947$	17.6910	+	10.2139i	0.574879	+	0.331907i	0.759096	−	0.650979i	$-0.225641\pi$
$947$	17.6910	+	10.2139i	0.574879	+	0.331907i	−0.184217	+	0.982886i	$0.558975\pi$
$948$		0			0
$949$	−3.35552	−	21.0617i	−0.108925	−	0.683692i
$950$	1.11683	+	1.93441i	0.0362348	+	0.0627606i
$951$		0			0
$952$	−1.75520	+	3.04010i	−0.0568864	+	0.0985301i
$953$	40.9906			1.32782			0.663908	−	0.747814i	$-0.268896\pi$
$953$	40.9906			1.32782			0.663908	+	0.747814i	$0.268896\pi$
$954$		0			0
$955$			8.82664i			0.285623i
$956$	−25.2511	−	14.5788i	−0.816680	−	0.471510i
$957$		0			0
$958$	6.37417	+	11.0404i	0.205940	+	0.356699i
$959$	10.9167	+	18.9082i	0.352517	+	0.610578i
$960$		0			0
$961$	−14.8416	+	25.7064i	−0.478761	+	0.829238i
$962$	4.70518	−	12.2909i	0.151701	−	0.396273i
$963$		0			0
$964$			15.5947i			0.502271i
$965$	4.19528	−	7.26644i	0.135051	−	0.233915i
$966$		0			0
$967$	−3.24755	+	1.87497i	−0.104434	+	0.0602951i	−0.551307	−	0.834302i	$-0.685871\pi$
$967$	−3.24755	+	1.87497i	−0.104434	+	0.0602951i	0.446873	+	0.894597i	$0.352538\pi$
$968$	9.32613	−	5.38444i	0.299753	−	0.173063i
$969$		0			0
$970$	−5.00414	−	2.88914i	−0.160673	−	0.0927648i
$971$	48.6853			1.56239			0.781193	−	0.624289i	$-0.214611\pi$
$971$	48.6853			1.56239			0.781193	+	0.624289i	$0.214611\pi$
$972$		0			0
$973$		−	17.0709i		−	0.547269i
$974$	10.4027	−	18.0180i	0.333324	−	0.577334i
$975$		0			0
$976$	−3.90635	−	6.76599i	−0.125039	−	0.216574i
$977$	−19.1946	+	11.0820i	−0.614091	+	0.354546i	−0.774565	−	0.632495i	$-0.782031\pi$
$977$	−19.1946	+	11.0820i	−0.614091	+	0.354546i	0.160474	+	0.987040i	$0.448698\pi$
$978$		0			0
$979$	2.28046	−	3.94987i	0.0728838	−	0.126238i
$980$		−	2.49101i		−	0.0795725i
$981$		0			0
$982$		−	14.7472i		−	0.470604i
$983$	48.6127	+	28.0665i	1.55050	+	0.895183i	0.998101	+	0.0616059i	$0.0196222\pi$
$983$	48.6127	+	28.0665i	1.55050	+	0.895183i	0.552403	+	0.833577i	$0.313711\pi$
$984$		0			0
$985$	−0.131595	−	0.227930i	−0.00419298	−	0.00726245i
$986$	−4.47231	+	2.58209i	−0.142427	+	0.0822304i
$987$		0			0
$988$	1.34607	−	1.09206i	0.0428242	−	0.0347430i
$989$	−25.3611			−0.806436
$990$		0			0
$991$	36.3755			1.15551			0.577753	−	0.816212i	$-0.303930\pi$
$991$	36.3755			1.15551			0.577753	+	0.816212i	$0.303930\pi$
$992$	−0.573765	+	0.993791i	−0.0182171	+	0.0315529i
$993$		0			0
$994$	9.45402	−	5.45828i	0.299863	−	0.173126i
$995$	−6.84666	+	3.95292i	−0.217054	+	0.125316i
$996$		0			0
$997$	−28.6738	+	49.6644i	−0.908107	+	1.57289i	−0.0914167	+	0.995813i	$0.529140\pi$
$997$	−28.6738	+	49.6644i	−0.908107	+	1.57289i	−0.816691	+	0.577076i	$0.804194\pi$
$998$	−29.7482			−0.941662
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	702.2.t.a.181.12		28
3.2	odd	2		234.2.t.a.25.7	✓	28
9.2	odd	6		2106.2.b.c.649.10		14
9.4	even	3	inner	702.2.t.a.415.3		28
9.5	odd	6		234.2.t.a.103.14	yes	28
9.7	even	3		2106.2.b.d.649.5		14
13.12	even	2	inner	702.2.t.a.181.3		28
39.38	odd	2		234.2.t.a.25.14	yes	28
117.25	even	6		2106.2.b.d.649.10		14
117.38	odd	6		2106.2.b.c.649.5		14
117.77	odd	6		234.2.t.a.103.7	yes	28
117.103	even	6	inner	702.2.t.a.415.12		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
234.2.t.a.25.7	✓	28	3.2	odd	2
234.2.t.a.25.14	yes	28	39.38	odd	2
234.2.t.a.103.7	yes	28	117.77	odd	6
234.2.t.a.103.14	yes	28	9.5	odd	6
702.2.t.a.181.3		28	13.12	even	2	inner
702.2.t.a.181.12		28	1.1	even	1	trivial
702.2.t.a.415.3		28	9.4	even	3	inner
702.2.t.a.415.12		28	117.103	even	6	inner
2106.2.b.c.649.5		14	117.38	odd	6
2106.2.b.c.649.10		14	9.2	odd	6
2106.2.b.d.649.5		14	9.7	even	3
2106.2.b.d.649.10		14	117.25	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 702 = 2 \cdot 3^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	702.t (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(0.515076 - 0.297379i) q^{5} +(1.45217 + 0.838409i) q^{7} +1.00000i q^{8} +0.594758 q^{10} +(-0.416337 - 0.240372i) q^{11} +(3.56065 - 0.567277i) q^{13} +(0.838409 + 1.45217i) q^{14} +(-0.500000 + 0.866025i) q^{16} +2.09349 q^{17} -0.480744i q^{19} +(0.515076 + 0.297379i) q^{20} +(-0.240372 - 0.416337i) q^{22} +(1.83339 + 3.17553i) q^{23} +(-2.32313 + 4.02378i) q^{25} +(3.36725 + 1.28905i) q^{26} +1.67682i q^{28} +(-1.23339 + 2.13629i) q^{29} +(0.993791 - 0.573765i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(1.81302 + 1.04675i) q^{34} +0.997301 q^{35} -3.65012i q^{37} +(0.240372 - 0.416337i) q^{38} +(0.297379 + 0.515076i) q^{40} +(8.58235 - 4.95502i) q^{41} +(-3.45822 + 5.98981i) q^{43} -0.480744i q^{44} +3.66679i q^{46} +(-5.40488 - 3.12051i) q^{47} +(-2.09414 - 3.62716i) q^{49} +(-4.02378 + 2.32313i) q^{50} +(2.27160 + 2.79997i) q^{52} +5.08592 q^{53} -0.285927 q^{55} +(-0.838409 + 1.45217i) q^{56} +(-2.13629 + 1.23339i) q^{58} +(8.13185 - 4.69493i) q^{59} +(-3.90635 + 6.76599i) q^{61} +1.14753 q^{62} -1.00000 q^{64} +(1.66531 - 1.35105i) q^{65} +(-12.4551 + 7.19096i) q^{67} +(1.04675 + 1.81302i) q^{68} +(0.863688 + 0.498651i) q^{70} -6.51028i q^{71} -5.91514i q^{73} +(1.82506 - 3.16110i) q^{74} +(0.416337 - 0.240372i) q^{76} +(-0.403061 - 0.698121i) q^{77} +(1.02895 - 1.78219i) q^{79} +0.594758i q^{80} +9.91005 q^{82} +(-9.57834 - 5.53006i) q^{83} +(1.07831 - 0.622560i) q^{85} +(-5.98981 + 3.45822i) q^{86} +(0.240372 - 0.416337i) q^{88} +9.48720i q^{89} +(5.64626 + 2.16150i) q^{91} +(-1.83339 + 3.17553i) q^{92} +(-3.12051 - 5.40488i) q^{94} +(-0.142963 - 0.247620i) q^{95} +(-8.41374 - 4.85767i) q^{97} -4.18828i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 14 q^{4} + 2 q^{13} - 8 q^{14} - 14 q^{16} - 16 q^{17} + 8 q^{23} + 14 q^{25} - 8 q^{26} + 16 q^{29} + 68 q^{35} - 4 q^{43} + 10 q^{49} - 2 q^{52} + 120 q^{53} + 8 q^{56} + 28 q^{61} - 68 q^{62}+ \cdots - 8 q^{92}+O(q^{100}) \) 28 * q + 14 * q^4 + 2 * q^13 - 8 * q^14 - 14 * q^16 - 16 * q^17 + 8 * q^23 + 14 * q^25 - 8 * q^26 + 16 * q^29 + 68 * q^35 - 4 * q^43 + 10 * q^49 - 2 * q^52 + 120 * q^53 + 8 * q^56 + 28 * q^61 - 68 * q^62 - 28 * q^64 + 8 * q^65 - 8 * q^68 - 16 * q^74 + 24 * q^77 + 28 * q^79 - 48 * q^82 - 8 * q^92

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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