LMFDB - Embedded newform 702.2.t.a.181.3

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			181.3
Character	$\chi$	$=$	702.181
Dual form			702.2.t.a.415.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-0.515076 + 0.297379i) q^{5} +(-1.45217 - 0.838409i) q^{7} -1.00000i q^{8} +0.594758 q^{10} +(0.416337 + 0.240372i) q^{11} +(-2.27160 + 2.79997i) q^{13} +(0.838409 + 1.45217i) q^{14} +(-0.500000 + 0.866025i) q^{16} +2.09349 q^{17} +0.480744i q^{19} +(-0.515076 - 0.297379i) q^{20} +(-0.240372 - 0.416337i) q^{22} +(1.83339 + 3.17553i) q^{23} +(-2.32313 + 4.02378i) q^{25} +(3.36725 - 1.28905i) q^{26} -1.67682i q^{28} +(-1.23339 + 2.13629i) q^{29} +(-0.993791 + 0.573765i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-1.81302 - 1.04675i) q^{34} +0.997301 q^{35} +3.65012i q^{37} +(0.240372 - 0.416337i) q^{38} +(0.297379 + 0.515076i) q^{40} +(-8.58235 + 4.95502i) q^{41} +(-3.45822 + 5.98981i) q^{43} +0.480744i q^{44} -3.66679i q^{46} +(5.40488 + 3.12051i) q^{47} +(-2.09414 - 3.62716i) q^{49} +(4.02378 - 2.32313i) q^{50} +(-3.56065 - 0.567277i) q^{52} +5.08592 q^{53} -0.285927 q^{55} +(-0.838409 + 1.45217i) q^{56} +(2.13629 - 1.23339i) q^{58} +(-8.13185 + 4.69493i) q^{59} +(-3.90635 + 6.76599i) q^{61} +1.14753 q^{62} -1.00000 q^{64} +(0.337393 - 2.11772i) q^{65} +(12.4551 - 7.19096i) q^{67} +(1.04675 + 1.81302i) q^{68} +(-0.863688 - 0.498651i) q^{70} +6.51028i q^{71} +5.91514i q^{73} +(1.82506 - 3.16110i) q^{74} +(-0.416337 + 0.240372i) q^{76} +(-0.403061 - 0.698121i) q^{77} +(1.02895 - 1.78219i) q^{79} -0.594758i q^{80} +9.91005 q^{82} +(9.57834 + 5.53006i) q^{83} +(-1.07831 + 0.622560i) q^{85} +(5.98981 - 3.45822i) q^{86} +(0.240372 - 0.416337i) q^{88} -9.48720i q^{89} +(5.64626 - 2.16150i) q^{91} +(-1.83339 + 3.17553i) q^{92} +(-3.12051 - 5.40488i) q^{94} +(-0.142963 - 0.247620i) q^{95} +(8.41374 + 4.85767i) q^{97} +4.18828i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	−0.610733	−	0.791837i	$-0.709125\pi$
$5$	−0.515076	+	0.297379i	−0.230349	+	0.132992i	0.380384	+	0.924829i	$0.375792\pi$
$6$		0			0
$7$	−1.45217	−	0.838409i	−0.548868	−	0.316889i	0.199798	−	0.979837i	$-0.435972\pi$
$7$	−1.45217	−	0.838409i	−0.548868	−	0.316889i	−0.748665	+	0.662948i	$0.769305\pi$
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	0.594758			0.188079
$11$	0.416337	+	0.240372i	0.125530	+	0.0724750i	0.561450	−	0.827510i	$-0.310244\pi$
$11$	0.416337	+	0.240372i	0.125530	+	0.0724750i	−0.435920	+	0.899985i	$0.643577\pi$
$12$		0			0
$13$	−2.27160	+	2.79997i	−0.630028	+	0.776572i
$13$	−2.27160	+	2.79997i	−0.630028	+	0.776572i
$14$	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	$0.0175622\pi$
$19$			0.480744i			0.110290i	−0.998478	+	0.0551452i	$0.982438\pi$
$20$	−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	−0.586583	−	0.809889i	$-0.699527\pi$
$31$	−0.993791	+	0.573765i	−0.178490	+	0.103051i	0.408093	+	0.912940i	$0.366194\pi$
$32$	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	$0.0969994\pi$
$37$			3.65012i			0.600076i	−0.953927	+	0.300038i	$0.903001\pi$
$38$	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	−0.986857	−	0.161597i	$-0.948336\pi$
$41$	−8.58235	+	4.95502i	−1.34034	+	0.773845i	−0.353481	+	0.935442i	$0.615002\pi$
$42$		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	0.839393	−	0.543525i	$-0.182911\pi$
$47$	5.40488	+	3.12051i	0.788383	+	0.455173i	−0.0510099	+	0.998698i	$0.516244\pi$
$48$		0			0
$49$	−2.09414	−	3.62716i	−0.299163	−	0.518165i
$50$	4.02378	−	2.32313i	0.569049	−	0.328540i
$51$		0			0
$52$	−3.56065	−	0.567277i	−0.493773	−	0.0786671i
$53$	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	−0.925066	−	0.379807i	$-0.875991\pi$
$59$	−8.13185	+	4.69493i	−1.05868	+	0.611227i	−0.133611	+	0.991034i	$0.542657\pi$
$60$		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
$65$	0.337393	−	2.11772i	0.0418484	−	0.262671i
$66$		0			0
$67$	12.4551	−	7.19096i	1.52163	−	0.878516i	0.521960	−	0.852970i	$-0.325201\pi$
$67$	12.4551	−	7.19096i	1.52163	−	0.878516i	0.999674	−	0.0255454i	$-0.00813225\pi$
$68$	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	$0.126252\pi$
$71$			6.51028i			0.772628i	−0.922367	+	0.386314i	$0.873748\pi$
$72$		0			0
$73$			5.91514i			0.692315i	0.938176	+	0.346157i	$0.112514\pi$
$73$			5.91514i			0.692315i	−0.938176	+	0.346157i	$0.887486\pi$
$74$	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	0.923030	−	0.384729i	$-0.125705\pi$
$83$	9.57834	+	5.53006i	1.05136	+	0.607003i	0.128330	+	0.991732i	$0.459038\pi$
$84$		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	$-0.832296\pi$
$89$		−	9.48720i		−	1.00564i	0.864391	−	0.502821i	$-0.167704\pi$
$90$		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	0.862095	−	0.506747i	$-0.169152\pi$
$97$	8.41374	+	4.85767i	0.854286	+	0.493222i	−0.00780887	+	0.999970i	$0.502486\pi$
$98$			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	$0.860245\pi$
$104$	2.79997	+	2.27160i	0.274560	+	0.222749i
$105$		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	$0.341575\pi$
$109$			18.3474i			1.75736i	−0.477413	+	0.878679i	$0.658425\pi$
$110$	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
$130$	−1.35105	+	1.66531i	−0.118495	+	0.146057i
$131$	−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	−0.0661784	−	0.997808i	$-0.521081\pi$
$137$	−11.2762	−	6.51034i	−0.963395	−	0.556216i	−0.897216	+	0.441592i	$0.854414\pi$
$138$		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	−0.674624	−	0.738162i	$-0.735694\pi$
$149$	−4.54901	+	2.62637i	−0.372669	+	0.215161i	0.301955	+	0.953322i	$0.402361\pi$
$150$		0			0
$151$	10.3258	+	5.96162i	0.840304	+	0.485150i	0.857367	−	0.514705i	$-0.172098\pi$
$151$	10.3258	+	5.96162i	0.840304	+	0.485150i	−0.0170637	+	0.999854i	$0.505432\pi$
$152$	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	$-0.684519\pi$
$163$		−	21.3629i		−	1.67327i	0.547760	−	0.836635i	$-0.315481\pi$
$164$	−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	0.0829768	−	0.996551i	$-0.473557\pi$
$167$	12.7614	−	7.36778i	0.987504	−	0.570136i	0.904527	+	0.426416i	$0.140224\pi$
$168$		0			0
$169$	−2.67968	−	12.7208i	−0.206129	−	0.978525i
$170$	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	$0.483171\pi$
$182$	−5.97056	−	0.951220i	−0.442567	−	0.0705091i
$183$		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	−0.870471	−	0.492219i	$-0.836186\pi$
$193$	−12.2175	+	7.05376i	−0.879433	+	0.507741i	−0.00896136	+	0.999960i	$0.502853\pi$
$194$	−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	$0.00501805\pi$
$197$			0.442517i			0.0315280i	−0.999876	+	0.0157640i	$0.994982\pi$
$198$		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
$221$	−4.75557	+	5.86171i	−0.319894	+	0.394301i
$222$		0			0
$223$	−20.0340	−	11.5666i	−1.34158	−	0.774559i	−0.354537	−	0.935042i	$-0.615362\pi$
$223$	−20.0340	−	11.5666i	−1.34158	−	0.774559i	−0.987039	+	0.160482i	$0.948695\pi$
$224$	−1.67682			−0.112037
$225$		0			0
$226$			20.2779i			1.34887i
$227$	11.5239	+	6.65331i	0.764866	+	0.441595i	0.831040	−	0.556213i	$-0.187746\pi$
$227$	11.5239	+	6.65331i	0.764866	+	0.441595i	−0.0661743	+	0.997808i	$0.521079\pi$
$228$		0			0
$229$	−0.700965	+	0.404702i	−0.0463211	+	0.0267435i	−0.522982	−	0.852344i	$-0.675180\pi$
$229$	−0.700965	+	0.404702i	−0.0463211	+	0.0267435i	0.476661	+	0.879087i	$0.341847\pi$
$230$	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	$-0.274638\pi$
$239$	25.2511	−	14.5788i	1.63336	−	0.943021i	0.983047	−	0.183355i	$-0.0586958\pi$
$240$		0			0
$241$	−13.5054	−	7.79735i	−0.869959	−	0.502271i	−0.00262472	−	0.999997i	$-0.500835\pi$
$241$	−13.5054	−	7.79735i	−0.869959	−	0.502271i	−0.867335	+	0.497725i	$0.834169\pi$
$242$			10.7689i			0.692250i
$243$		0			0
$244$	−7.81270			−0.500157
$245$	2.15728	+	1.24551i	0.137824	+	0.0795725i
$246$		0			0
$247$	−1.34607	−	1.09206i	−0.0856484	−	0.0694860i
$248$	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	$-0.905435\pi$
$271$		−	9.63804i		−	0.585469i	0.956194	−	0.292735i	$-0.0945653\pi$
$272$	−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	0.752208	−	0.658925i	$-0.228989\pi$
$281$	9.34820	+	5.39719i	0.557667	+	0.321969i	−0.194542	+	0.980894i	$0.562322\pi$
$282$		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
$286$	1.71176	+	0.272715i	0.101219	+	0.0161260i
$287$	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	−0.960285	−	0.279022i	$-0.909990\pi$
$293$	−20.5199	+	11.8472i	−1.19879	+	0.692120i	−0.238502	+	0.971142i	$0.576656\pi$
$294$		0			0
$295$	2.79235	−	4.83649i	0.162577	−	0.281591i
$296$	3.65012			0.212159
$297$		0			0
$298$	5.25274			0.304283
$299$	−13.0561	−	2.08008i	−0.755055	−	0.120294i
$300$		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	$-0.940129\pi$
$307$		−	6.55237i		−	0.373963i	0.982363	−	0.186982i	$-0.0598705\pi$
$308$	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	0.989524	−	0.144368i	$-0.0461151\pi$
$317$	24.2009	+	13.9724i	1.35926	+	0.784769i	0.369735	+	0.929137i	$0.379448\pi$
$318$		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	0.954506	−	0.298193i	$-0.0963838\pi$
$331$	21.3503	+	12.3266i	1.17352	+	0.677530i	0.219010	+	0.975723i	$0.429717\pi$
$332$			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	$0.696714\pi$
$338$	−4.03974	+	12.3564i	−0.219733	+	0.672099i
$339$		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	0.409044	−	0.912515i	$-0.365862\pi$
$349$	−3.30094	−	1.90580i	−0.176695	−	0.102015i	−0.585739	+	0.810500i	$0.699196\pi$
$350$	−7.79094			−0.416443
$351$		0			0
$352$	0.480744			0.0256238
$353$	−17.3353	−	10.0086i	−0.922667	−	0.532702i	−0.0381819	−	0.999271i	$-0.512157\pi$
$353$	−17.3353	−	10.0086i	−0.922667	−	0.532702i	−0.884485	+	0.466569i	$0.845490\pi$
$354$		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	$0.0847197\pi$
$359$			9.96717i			0.526047i	−0.964789	+	0.263024i	$0.915280\pi$
$360$		0			0
$361$	18.7689			0.987836
$362$	−1.23141	−	0.710953i	−0.0647213	−	0.0373669i
$363$		0			0
$364$	4.69504	+	3.80906i	0.246087	+	0.199649i
$365$	−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	$-0.966825\pi$
$379$		−	4.05068i		−	0.208069i	0.994574	−	0.104035i	$-0.0331753\pi$
$380$	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	0.392179	−	0.919889i	$-0.371721\pi$
$383$	27.1033	−	15.6481i	1.38492	−	0.799581i	0.992737	+	0.120308i	$0.0383882\pi$
$384$		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	$-0.792429\pi$
$397$		−	24.1832i		−	1.21372i	0.794808	−	0.606860i	$-0.207571\pi$
$398$	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	−0.969669	−	0.244421i	$-0.921402\pi$
$401$	−24.8876	+	14.3689i	−1.24283	+	0.717548i	−0.273160	+	0.961969i	$0.588069\pi$
$402$		0			0
$403$	0.650967	−	4.08595i	0.0324270	−	0.203536i
$404$	−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	−0.977062	−	0.212956i	$-0.931691\pi$
$409$	−25.9100	+	14.9591i	−1.28117	+	0.739682i	−0.304105	+	0.952638i	$0.598357\pi$
$410$	−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
$416$	−0.567277	+	3.56065i	−0.0278130	+	0.174575i
$417$		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	0.961113	−	0.276155i	$-0.0890603\pi$
$421$	24.6735	+	14.2452i	1.20251	+	0.694271i	0.241399	+	0.970426i	$0.422394\pi$
$422$		−	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	$-0.945008\pi$
$431$		−	7.13767i		−	0.343809i	0.985114	−	0.171905i	$-0.0549921\pi$
$432$		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	$-0.845847\pi$
$449$		−	19.7308i		−	0.931152i	0.885008	−	0.465576i	$-0.154153\pi$
$450$		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
$455$	−2.26547	+	2.79242i	−0.106207	+	0.130910i
$456$		0			0
$457$	−31.4762	−	18.1728i	−1.47240	−	0.850088i	−0.472877	−	0.881128i	$-0.656784\pi$
$457$	−31.4762	−	18.1728i	−1.47240	−	0.850088i	−0.999518	+	0.0310408i	$0.990118\pi$
$458$	0.809405			0.0378210
$459$		0			0
$460$		−	2.18085i		−	0.101683i
$461$	19.8630	+	11.4679i	0.925112	+	0.534114i	0.885262	−	0.465092i	$-0.153979\pi$
$461$	19.8630	+	11.4679i	0.925112	+	0.534114i	0.0398498	+	0.999206i	$0.487312\pi$
$462$		0			0
$463$	−25.6143	+	14.7884i	−1.19040	+	0.687277i	−0.958397	−	0.285438i	$-0.907861\pi$
$463$	−25.6143	+	14.7884i	−1.19040	+	0.687277i	−0.232002	+	0.972715i	$0.574528\pi$
$464$	−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	0.226101	−	0.974104i	$-0.427402\pi$
$479$	−11.0404	−	6.37417i	−0.504448	−	0.291243i	−0.730549	+	0.682861i	$0.760736\pi$
$480$		0			0
$481$	−10.2202	−	8.29161i	−0.466003	−	0.378065i
$482$	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	$0.156248\pi$
$487$			20.8054i			0.942782i	−0.881924	+	0.471391i	$0.843752\pi$
$488$	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	0.203608	−	0.979053i	$-0.434733\pi$
$499$	25.7627	−	14.8741i	1.15330	−	0.665856i	0.949688	+	0.313197i	$0.101400\pi$
$500$	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	−0.802180	−	0.597082i	$-0.796327\pi$
$509$	−15.4810	+	8.93795i	−0.686182	+	0.396168i	0.115998	+	0.993249i	$0.462993\pi$
$510$		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
$520$	−2.11772	−	0.337393i	−0.0928683	−	0.0147956i
$521$	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
$533$	5.62174	−	35.2862i	0.243505	−	1.52841i
$534$		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	$-0.921449\pi$
$541$		−	11.3636i		−	0.488558i	0.969705	−	0.244279i	$-0.0785513\pi$
$542$	−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	$0.191651\pi$
$557$			26.7334i			1.13273i	−0.824154	+	0.566365i	$0.808349\pi$
$558$		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	$0.754026\pi$
$572$	−1.34607	−	1.09206i	−0.0562820	−	0.0456613i
$573$		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	$0.148041\pi$
$577$			21.5466i			0.896997i	−0.893784	+	0.448498i	$0.851959\pi$
$578$	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	0.334213	−	0.942498i	$-0.391530\pi$
$587$	−7.62960	−	4.40495i	−0.314907	−	0.181812i	−0.649120	+	0.760686i	$0.724863\pi$
$588$		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	$-0.814929\pi$
$593$		−	26.7483i		−	1.09842i	0.835685	−	0.549210i	$-0.185071\pi$
$594$		0			0
$595$	2.08784			0.0855931
$596$	−4.54901	−	2.62637i	−0.186335	−	0.107580i
$597$		0			0
$598$	10.2669	+	8.32947i	0.419845	+	0.340617i
$599$	−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	$0.307112\pi$
$613$			40.7009i			1.64390i	−0.569563	+	0.821948i	$0.692888\pi$
$614$	−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	0.381264	−	0.924466i	$-0.375489\pi$
$617$	34.0924	−	19.6832i	1.37251	−	0.792417i	0.991243	+	0.132049i	$0.0421557\pi$
$618$		0			0
$619$	21.1669	+	12.2207i	0.850770	+	0.491192i	0.860911	−	0.508756i	$-0.169895\pi$
$619$	21.1669	+	12.2207i	0.850770	+	0.491192i	−0.0101406	+	0.999949i	$0.503228\pi$
$620$	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	$-0.963748\pi$
$631$		−	5.70930i		−	0.227284i	0.993522	−	0.113642i	$-0.0362516\pi$
$632$	−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
$637$	14.9130	+	2.37591i	0.590874	+	0.0941372i
$638$	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	−0.910449	−	0.413622i	$-0.864263\pi$
$643$	−25.5467	+	14.7494i	−1.00747	+	0.581660i	−0.0970167	+	0.995283i	$0.530930\pi$
$644$	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
$650$	−2.63572	+	16.5437i	−0.103381	+	0.648897i
$651$		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	0.174105	−	0.984727i	$-0.444297\pi$
$661$	28.6397	−	16.5352i	1.11396	−	0.643143i	0.939851	+	0.341584i	$0.110963\pi$
$662$	−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	$0.101042\pi$
$683$			16.3144i			0.624255i	−0.950040	+	0.312127i	$0.898958\pi$
$684$		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
$689$	−11.5532	+	14.2404i	−0.440141	+	0.542517i
$690$		0			0
$691$	−21.9516	−	12.6738i	−0.835078	−	0.482132i	0.0205104	−	0.999790i	$-0.493471\pi$
$691$	−21.9516	−	12.6738i	−0.835078	−	0.482132i	−0.855588	+	0.517657i	$0.826804\pi$
$692$	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	0.809160	−	0.587588i	$-0.199923\pi$
$709$	18.7687	+	10.8361i	0.704874	+	0.406959i	−0.104286	+	0.994547i	$0.533256\pi$
$710$			3.87204i			0.145315i
$711$		0			0
$712$	−9.48720			−0.355548
$713$	−3.64402	−	2.10387i	−0.136470	−	0.0787907i
$714$		0			0
$715$	0.649511	−	0.800587i	0.0242903	−	0.0299402i
$716$	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	−0.161720	−	0.986837i	$-0.551704\pi$
$733$	16.5705	−	9.56700i	0.612046	−	0.353365i	0.773766	+	0.633472i	$0.218371\pi$
$734$	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	$0.0199373\pi$
$739$			3.40317i			0.125188i	−0.998039	+	0.0625938i	$0.980063\pi$
$740$	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	−0.0896532	−	0.995973i	$-0.528576\pi$
$743$	19.8454	−	11.4578i	0.728058	−	0.420345i	0.817711	+	0.575628i	$0.195243\pi$
$744$		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
$754$	−1.39935	+	8.78332i	−0.0509612	+	0.319870i
$755$	−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	−0.459594	−	0.888129i	$-0.652005\pi$
$761$	2.20005	−	1.27020i	0.0797518	−	0.0460447i	0.539346	+	0.842085i	$0.318672\pi$
$762$		0			0
$763$	15.3826	−	26.6434i	0.556887	−	0.964557i
$764$	−14.8407			−0.536918
$765$		0			0
$766$	−31.2962			−1.13078
$767$	5.32664	−	33.4339i	0.192334	−	1.20723i
$768$		0			0
$769$	8.65130	−	4.99483i	0.311974	−	0.180118i	−0.335836	−	0.941921i	$-0.609019\pi$
$769$	8.65130	−	4.99483i	0.311974	−	0.180118i	0.647809	+	0.761802i	$0.275685\pi$
$770$	−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	$0.0330516\pi$
$773$			5.76343i			0.207296i	−0.994614	+	0.103648i	$0.966948\pi$
$774$		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	−0.639083	−	0.769137i	$-0.720686\pi$
$787$	−8.20657	+	4.73806i	−0.292533	+	0.168894i	0.346551	+	0.938031i	$0.387353\pi$
$788$	−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
$806$	−2.60673	+	3.21305i	−0.0918181	+	0.113175i
$807$		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	$0.215121\pi$
$811$			35.6282i			1.25108i	−0.780193	+	0.625538i	$0.784879\pi$
$812$	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	0.715225	−	0.698894i	$-0.246324\pi$
$821$	13.3975	+	7.73506i	0.467577	+	0.269956i	−0.247648	+	0.968850i	$0.579658\pi$
$822$		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	$0.160193\pi$
$827$			27.7387i			0.964569i	−0.876015	+	0.482284i	$0.839807\pi$
$828$		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
$832$	2.27160	−	2.79997i	0.0787535	−	0.0970715i
$833$	−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	−0.180199	−	0.983630i	$-0.557674\pi$
$839$	−32.5035	−	18.7659i	−1.12215	−	0.647872i	−0.941948	+	0.335758i	$0.891007\pi$
$840$		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	0.999744	−	0.0226214i	$-0.00720122\pi$
$853$	43.2259	+	24.9565i	1.48003	+	0.854493i	0.480281	+	0.877114i	$0.340535\pi$
$854$	−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	$0.196960\pi$
$863$			34.0790i			1.16006i	−0.814594	+	0.580031i	$0.803040\pi$
$864$		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
$871$	−8.15853	+	51.2089i	−0.276441	+	1.73515i
$872$	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	−0.362652	−	0.931925i	$-0.618129\pi$
$877$	7.79128	−	4.49830i	0.263093	−	0.151897i	0.625745	+	0.780028i	$0.284795\pi$
$878$	−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	$0.317271\pi$
$884$	−7.45418	−	1.18759i	−0.250711	−	0.0399429i
$885$		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
$923$	−18.2286	−	14.7888i	−0.600002	−	0.486778i
$924$		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	0.178115	−	0.984010i	$-0.443000\pi$
$929$	−17.8307	−	10.2945i	−0.585006	−	0.337753i	−0.763120	+	0.646257i	$0.776334\pi$
$930$		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	−0.447492	−	0.894288i	$-0.647683\pi$
$941$	3.16693	−	1.82843i	0.103239	−	0.0596051i	0.550731	+	0.834683i	$0.314349\pi$
$942$		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	0.184217	−	0.982886i	$-0.441025\pi$
$947$	−17.6910	−	10.2139i	−0.574879	−	0.331907i	−0.759096	+	0.650979i	$0.774359\pi$
$948$		0			0
$949$	−16.5622	−	13.4368i	−0.537633	−	0.436178i
$950$	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	−0.446873	−	0.894597i	$-0.647462\pi$
$967$	3.24755	−	1.87497i	0.104434	−	0.0602951i	0.551307	+	0.834302i	$0.314129\pi$
$968$	−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	−0.160474	−	0.987040i	$-0.551302\pi$
$977$	19.1946	−	11.0820i	0.614091	−	0.354546i	0.774565	+	0.632495i	$0.217969\pi$
$978$		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	$-0.980378\pi$
$983$	−48.6127	−	28.0665i	−1.55050	−	0.895183i	−0.552403	−	0.833577i	$-0.686289\pi$
$984$		0			0
$985$	−0.131595	−	0.227930i	−0.00419298	−	0.00726245i
$986$	4.47231	−	2.58209i	0.142427	−	0.0822304i
$987$		0			0
$988$	0.272715	−	1.71176i	0.00867622	−	0.0544584i
$989$	−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.181.3		28
3.2	odd	2		234.2.t.a.25.14	yes	28
9.2	odd	6		2106.2.b.c.649.5		14
9.4	even	3	inner	702.2.t.a.415.12		28
9.5	odd	6		234.2.t.a.103.7	yes	28
9.7	even	3		2106.2.b.d.649.10		14
13.12	even	2	inner	702.2.t.a.181.12		28
39.38	odd	2		234.2.t.a.25.7	✓	28
117.25	even	6		2106.2.b.d.649.5		14
117.38	odd	6		2106.2.b.c.649.10		14
117.77	odd	6		234.2.t.a.103.14	yes	28
117.103	even	6	inner	702.2.t.a.415.3		28

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

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)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-0.515076 + 0.297379i) q^{5} +(-1.45217 - 0.838409i) q^{7} -1.00000i q^{8} +0.594758 q^{10} +(0.416337 + 0.240372i) q^{11} +(-2.27160 + 2.79997i) q^{13} +(0.838409 + 1.45217i) q^{14} +(-0.500000 + 0.866025i) q^{16} +2.09349 q^{17} +0.480744i q^{19} +(-0.515076 - 0.297379i) q^{20} +(-0.240372 - 0.416337i) q^{22} +(1.83339 + 3.17553i) q^{23} +(-2.32313 + 4.02378i) q^{25} +(3.36725 - 1.28905i) q^{26} -1.67682i q^{28} +(-1.23339 + 2.13629i) q^{29} +(-0.993791 + 0.573765i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-1.81302 - 1.04675i) q^{34} +0.997301 q^{35} +3.65012i q^{37} +(0.240372 - 0.416337i) q^{38} +(0.297379 + 0.515076i) q^{40} +(-8.58235 + 4.95502i) q^{41} +(-3.45822 + 5.98981i) q^{43} +0.480744i q^{44} -3.66679i q^{46} +(5.40488 + 3.12051i) q^{47} +(-2.09414 - 3.62716i) q^{49} +(4.02378 - 2.32313i) q^{50} +(-3.56065 - 0.567277i) q^{52} +5.08592 q^{53} -0.285927 q^{55} +(-0.838409 + 1.45217i) q^{56} +(2.13629 - 1.23339i) q^{58} +(-8.13185 + 4.69493i) q^{59} +(-3.90635 + 6.76599i) q^{61} +1.14753 q^{62} -1.00000 q^{64} +(0.337393 - 2.11772i) q^{65} +(12.4551 - 7.19096i) q^{67} +(1.04675 + 1.81302i) q^{68} +(-0.863688 - 0.498651i) q^{70} +6.51028i q^{71} +5.91514i q^{73} +(1.82506 - 3.16110i) q^{74} +(-0.416337 + 0.240372i) q^{76} +(-0.403061 - 0.698121i) q^{77} +(1.02895 - 1.78219i) q^{79} -0.594758i q^{80} +9.91005 q^{82} +(9.57834 + 5.53006i) q^{83} +(-1.07831 + 0.622560i) q^{85} +(5.98981 - 3.45822i) q^{86} +(0.240372 - 0.416337i) q^{88} -9.48720i q^{89} +(5.64626 - 2.16150i) q^{91} +(-1.83339 + 3.17553i) q^{92} +(-3.12051 - 5.40488i) q^{94} +(-0.142963 - 0.247620i) q^{95} +(8.41374 + 4.85767i) q^{97} +4.18828i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 14 q^{4} + 2 q^{13} - 8 q^{14} - 14 q^{16} - 16 q^{17} + 8 q^{23} + 14 q^{25} - 8 q^{26} + 16 q^{29} + 68 q^{35} - 4 q^{43} + 10 q^{49} - 2 q^{52} + 120 q^{53} + 8 q^{56} + 28 q^{61} - 68 q^{62}+ \cdots - 8 q^{92}+O(q^{100}) \) 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

Related objects

Downloads

Learn more