LMFDB - Embedded newform 252.2.be.a.179.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,2,Mod(107,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 2]))

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

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

chi := DirichletCharacter("252.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	252.be (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.01223013094$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			179.3
Character	$\chi$	$=$	252.179
Dual form			252.2.be.a.107.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.30138 - 0.553555i) q^{2} +(1.38715 + 1.44076i) q^{4} +(3.35279 - 1.93573i) q^{5} +(1.03277 + 2.43585i) q^{7} +(-1.00767 - 2.64284i) q^{8} +O(q^{10})$	\(q+(-1.30138 - 0.553555i) q^{2} +(1.38715 + 1.44076i) q^{4} +(3.35279 - 1.93573i) q^{5} +(1.03277 + 2.43585i) q^{7} +(-1.00767 - 2.64284i) q^{8} +(-5.43477 + 0.663164i) q^{10} +(-1.73480 + 3.00476i) q^{11} -0.296538 q^{13} +(0.00435270 - 3.74165i) q^{14} +(-0.151605 + 3.99713i) q^{16} +(1.35741 + 0.783703i) q^{17} +(6.12694 - 3.53739i) q^{19} +(7.43977 + 2.14542i) q^{20} +(3.92092 - 2.95001i) q^{22} +(-2.71768 - 4.70717i) q^{23} +(4.99413 - 8.65009i) q^{25} +(0.385907 + 0.164150i) q^{26} +(-2.07687 + 4.86689i) q^{28} +6.85309i q^{29} +(-2.43792 - 1.40753i) q^{31} +(2.40992 - 5.11784i) q^{32} +(-1.33268 - 1.77129i) q^{34} +(8.17783 + 6.16773i) q^{35} +(-1.25659 - 2.17648i) q^{37} +(-9.93158 + 1.21188i) q^{38} +(-8.49433 - 6.91032i) q^{40} -3.55418i q^{41} +0.682082i q^{43} +(-6.73558 + 1.66863i) q^{44} +(0.931053 + 7.63018i) q^{46} +(-1.18466 - 2.05189i) q^{47} +(-4.86676 + 5.03137i) q^{49} +(-11.2875 + 8.49249i) q^{50} +(-0.411344 - 0.427241i) q^{52} +(-0.540117 - 0.311837i) q^{53} +13.4324i q^{55} +(5.39688 - 5.18398i) q^{56} +(3.79356 - 8.91844i) q^{58} +(-4.42770 + 7.66901i) q^{59} +(-1.33268 - 2.30827i) q^{61} +(2.39350 + 3.18125i) q^{62} +(-5.96922 + 5.32621i) q^{64} +(-0.994229 + 0.574019i) q^{65} +(-9.19491 - 5.30868i) q^{67} +(0.753810 + 3.04283i) q^{68} +(-7.22826 - 12.5534i) q^{70} +0.539214 q^{71} +(-3.69760 + 6.40442i) q^{73} +(0.430496 + 3.52801i) q^{74} +(13.5956 + 3.92057i) q^{76} +(-9.11080 - 1.12248i) q^{77} +(5.33972 - 3.08289i) q^{79} +(7.22908 + 13.6950i) q^{80} +(-1.96743 + 4.62532i) q^{82} -6.15982 q^{83} +6.06816 q^{85} +(0.377570 - 0.887645i) q^{86} +(9.68920 + 1.55700i) q^{88} +(-10.1468 + 5.85824i) q^{89} +(-0.306256 - 0.722323i) q^{91} +(3.01207 - 10.4451i) q^{92} +(0.405852 + 3.32604i) q^{94} +(13.6949 - 23.7202i) q^{95} -6.84782 q^{97} +(9.11862 - 3.85368i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q + 16 q^{13} + 4 q^{16} - 32 q^{22} + 24 q^{25} - 44 q^{28} - 16 q^{34} + 8 q^{37} - 52 q^{40} - 24 q^{46} - 16 q^{49} - 52 q^{52} - 12 q^{58} - 16 q^{61} + 120 q^{64} + 60 q^{70} - 8 q^{73} + 72 q^{76} + 68 q^{82} - 32 q^{85} + 44 q^{88} + 60 q^{94} - 176 q^{97}+O(q^{100}) $ 32 * q + 16 * q^13 + 4 * q^16 - 32 * q^22 + 24 * q^25 - 44 * q^28 - 16 * q^34 + 8 * q^37 - 52 * q^40 - 24 * q^46 - 16 * q^49 - 52 * q^52 - 12 * q^58 - 16 * q^61 + 120 * q^64 + 60 * q^70 - 8 * q^73 + 72 * q^76 + 68 * q^82 - 32 * q^85 + 44 * q^88 + 60 * q^94 - 176 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.30138	−	0.553555i	−0.920211	−	0.391422i
$2$	−1.30138	−	0.553555i	−0.920211	−	0.391422i
$3$		0			0
$3$		0			0
$4$	1.38715	+	1.44076i	0.693577	+	0.720382i
$5$	3.35279	−	1.93573i	1.49941	−	0.865687i	0.499413	−	0.866364i	$-0.333549\pi$
$5$	3.35279	−	1.93573i	1.49941	−	0.865687i	1.00000		0.000677187i	$0.000215555\pi$
$6$		0			0
$7$	1.03277	+	2.43585i	0.390351	+	0.920666i
$7$	1.03277	+	2.43585i	0.390351	+	0.920666i
$8$	−1.00767	−	2.64284i	−0.356264	−	0.934385i
$9$		0			0
$10$	−5.43477	+	0.663164i	−1.71863	+	0.209711i
$11$	−1.73480	+	3.00476i	−0.523061	+	0.905969i	0.476578	+	0.879132i	$0.341877\pi$
$11$	−1.73480	+	3.00476i	−0.523061	+	0.905969i	−0.999640	+	0.0268369i	$0.991457\pi$
$12$		0			0
$13$	−0.296538			−0.0822448			−0.0411224	−	0.999154i	$-0.513093\pi$
$13$	−0.296538			−0.0822448			−0.0411224	+	0.999154i	$0.513093\pi$
$14$	0.00435270	−	3.74165i	0.00116331	−	0.999999i
$15$		0			0
$16$	−0.151605	+	3.99713i	−0.0379011	+	0.999281i
$17$	1.35741	+	0.783703i	0.329221	+	0.190076i	0.655495	−	0.755199i	$-0.272460\pi$
$17$	1.35741	+	0.783703i	0.329221	+	0.190076i	−0.326274	+	0.945275i	$0.605793\pi$
$18$		0			0
$19$	6.12694	−	3.53739i	1.40562	−	0.811533i	0.410655	−	0.911791i	$-0.365300\pi$
$19$	6.12694	−	3.53739i	1.40562	−	0.811533i	0.994961	+	0.100258i	$0.0319668\pi$
$20$	7.43977	+	2.14542i	1.66358	+	0.479730i
$21$		0			0
$22$	3.92092	−	2.95001i	0.835943	−	0.628945i
$23$	−2.71768	−	4.70717i	−0.566676	−	0.981512i	−0.996892	−	0.0787860i	$-0.974896\pi$
$23$	−2.71768	−	4.70717i	−0.566676	−	0.981512i	0.430215	−	0.902726i	$-0.358438\pi$
$24$		0			0
$25$	4.99413	−	8.65009i	0.998827	−	1.73002i
$26$	0.385907	+	0.164150i	0.0756826	+	0.0321924i
$27$		0			0
$28$	−2.07687	+	4.86689i	−0.392492	+	0.919755i
$29$			6.85309i			1.27259i	0.771447	+	0.636293i	$0.219533\pi$
$29$			6.85309i			1.27259i	−0.771447	+	0.636293i	$0.780467\pi$
$30$		0			0
$31$	−2.43792	−	1.40753i	−0.437863	−	0.252800i	0.264828	−	0.964296i	$-0.414685\pi$
$31$	−2.43792	−	1.40753i	−0.437863	−	0.252800i	−0.702691	+	0.711495i	$0.748018\pi$
$32$	2.40992	−	5.11784i	0.426018	−	0.904715i
$33$		0			0
$34$	−1.33268	−	1.77129i	−0.228553	−	0.303774i
$35$	8.17783	+	6.16773i	1.38231	+	1.04254i
$36$		0			0
$37$	−1.25659	−	2.17648i	−0.206582	−	0.357811i	0.744053	−	0.668120i	$-0.232901\pi$
$37$	−1.25659	−	2.17648i	−0.206582	−	0.357811i	−0.950636	+	0.310309i	$0.899567\pi$
$38$	−9.93158	+	1.21188i	−1.61112	+	0.196592i
$39$		0			0
$40$	−8.49433	−	6.91032i	−1.34307	−	1.09262i
$41$		−	3.55418i		−	0.555069i	−0.960716	−	0.277535i	$-0.910483\pi$
$41$		−	3.55418i		−	0.555069i	0.960716	−	0.277535i	$-0.0895173\pi$
$42$		0			0
$43$			0.682082i			0.104017i	0.998647	+	0.0520083i	$0.0165622\pi$
$43$			0.682082i			0.104017i	−0.998647	+	0.0520083i	$0.983438\pi$
$44$	−6.73558	+	1.66863i	−1.01543	+	0.251555i
$45$		0			0
$46$	0.931053	+	7.63018i	0.137276	+	1.12501i
$47$	−1.18466	−	2.05189i	−0.172800	−	0.299298i	0.766598	−	0.642128i	$-0.221948\pi$
$47$	−1.18466	−	2.05189i	−0.172800	−	0.299298i	−0.939398	+	0.342829i	$0.888615\pi$
$48$		0			0
$49$	−4.86676	+	5.03137i	−0.695251	+	0.718767i
$50$	−11.2875	+	8.49249i	−1.59630	+	1.20102i
$51$		0			0
$52$	−0.411344	−	0.427241i	−0.0570431	−	0.0592477i
$53$	−0.540117	−	0.311837i	−0.0741907	−	0.0428340i	0.462446	−	0.886648i	$-0.346972\pi$
$53$	−0.540117	−	0.311837i	−0.0741907	−	0.0428340i	−0.536636	+	0.843814i	$0.680305\pi$
$54$		0			0
$55$			13.4324i			1.81123i
$56$	5.39688	−	5.18398i	0.721189	−	0.692739i
$57$		0			0
$58$	3.79356	−	8.91844i	0.498119	−	1.17105i
$59$	−4.42770	+	7.66901i	−0.576438	+	0.998420i	0.419446	+	0.907780i	$0.362224\pi$
$59$	−4.42770	+	7.66901i	−0.576438	+	0.998420i	−0.995884	+	0.0906393i	$0.971109\pi$
$60$		0			0
$61$	−1.33268	−	2.30827i	−0.170632	−	0.295544i	0.768009	−	0.640439i	$-0.221248\pi$
$61$	−1.33268	−	2.30827i	−0.170632	−	0.295544i	−0.938641	+	0.344895i	$0.887914\pi$
$62$	2.39350	+	3.18125i	0.303975	+	0.404019i
$63$		0			0
$64$	−5.96922	+	5.32621i	−0.746152	+	0.665776i
$65$	−0.994229	+	0.574019i	−0.123319	+	0.0711982i
$66$		0			0
$67$	−9.19491	−	5.30868i	−1.12334	−	0.648559i	−0.181086	−	0.983467i	$-0.557961\pi$
$67$	−9.19491	−	5.30868i	−1.12334	−	0.648559i	−0.942251	+	0.334908i	$0.891295\pi$
$68$	0.753810	+	3.04283i	0.0914129	+	0.368997i
$69$		0			0
$70$	−7.22826	−	12.5534i	−0.863942	−	1.50042i
$71$	0.539214			0.0639929			0.0319964	−	0.999488i	$-0.489813\pi$
$71$	0.539214			0.0639929			0.0319964	+	0.999488i	$0.489813\pi$
$72$		0			0
$73$	−3.69760	+	6.40442i	−0.432771	+	0.749581i	−0.997111	−	0.0759615i	$-0.975797\pi$
$73$	−3.69760	+	6.40442i	−0.432771	+	0.749581i	0.564340	+	0.825542i	$0.309131\pi$
$74$	0.430496	+	3.52801i	0.0500442	+	0.410123i
$75$		0			0
$76$	13.5956	+	3.92057i	1.55952	+	0.449720i
$77$	−9.11080	−	1.12248i	−1.03827	−	0.127918i
$78$		0			0
$79$	5.33972	−	3.08289i	0.600766	−	0.346852i	−0.168577	−	0.985688i	$-0.553917\pi$
$79$	5.33972	−	3.08289i	0.600766	−	0.346852i	0.769343	+	0.638836i	$0.220584\pi$
$80$	7.22908	+	13.6950i	0.808235	+	1.53115i
$81$		0			0
$82$	−1.96743	+	4.62532i	−0.217266	+	0.510781i
$83$	−6.15982			−0.676128			−0.338064	−	0.941123i	$-0.609772\pi$
$83$	−6.15982			−0.676128			−0.338064	+	0.941123i	$0.609772\pi$
$84$		0			0
$85$	6.06816			0.658184
$86$	0.377570	−	0.887645i	0.0407144	−	0.0957172i
$87$		0			0
$88$	9.68920	+	1.55700i	1.03287	+	0.165977i
$89$	−10.1468	+	5.85824i	−1.07556	+	0.620972i	−0.929694	−	0.368333i	$-0.879929\pi$
$89$	−10.1468	+	5.85824i	−1.07556	+	0.620972i	−0.145862	+	0.989305i	$0.546595\pi$
$90$		0			0
$91$	−0.306256	−	0.722323i	−0.0321044	−	0.0757200i
$92$	3.01207	−	10.4451i	0.314030	−	1.08898i
$93$		0			0
$94$	0.405852	+	3.32604i	0.0418604	+	0.343055i
$95$	13.6949	−	23.7202i	1.40507	−	2.43365i
$96$		0			0
$97$	−6.84782			−0.695291			−0.347645	−	0.937626i	$-0.613019\pi$
$97$	−6.84782			−0.695291			−0.347645	+	0.937626i	$0.613019\pi$
$98$	9.11862	−	3.85368i	0.921119	−	0.389280i
$99$		0			0
$100$	19.3904	−	4.80365i	1.93904	−	0.480365i
$101$	3.07801	+	1.77709i	0.306273	+	0.176827i	0.645258	−	0.763965i	$-0.276750\pi$
$101$	3.07801	+	1.77709i	0.306273	+	0.176827i	−0.338984	+	0.940792i	$0.610083\pi$
$102$		0			0
$103$	1.81687	−	1.04897i	0.179021	−	0.103358i	−0.407811	−	0.913066i	$-0.633708\pi$
$103$	1.81687	−	1.04897i	0.179021	−	0.103358i	0.586833	+	0.809708i	$0.300375\pi$
$104$	0.298811	+	0.783703i	0.0293009	+	0.0768484i
$105$		0			0
$106$	0.530276	+	0.704801i	0.0515050	+	0.0684563i
$107$	−5.52799	−	9.57475i	−0.534411	−	0.925626i	−0.999192	−	0.0402007i	$-0.987200\pi$
$107$	−5.52799	−	9.57475i	−0.534411	−	0.925626i	0.464781	−	0.885426i	$-0.346133\pi$
$108$		0			0
$109$	−6.65949	+	11.5346i	−0.637864	+	1.10481i	0.348037	+	0.937481i	$0.386848\pi$
$109$	−6.65949	+	11.5346i	−0.637864	+	1.10481i	−0.985901	+	0.167332i	$0.946485\pi$
$110$	7.43559	−	17.4806i	0.708955	−	1.66671i
$111$		0			0
$112$	−9.89298	+	3.75884i	−0.934799	+	0.355177i
$113$		−	6.75101i		−	0.635082i	−0.948245	−	0.317541i	$-0.897143\pi$
$113$		−	6.75101i		−	0.635082i	0.948245	−	0.317541i	$-0.102857\pi$
$114$		0			0
$115$	−18.2237	−	10.5214i	−1.69936	−	0.981128i
$116$	−9.87368	+	9.50629i	−0.916749	+	0.882637i
$117$		0			0
$118$	10.0073	−	7.52928i	0.921248	−	0.693126i
$119$	−0.507085	+	4.11584i	−0.0464844	+	0.377299i
$120$		0			0
$121$	−0.519050	−	0.899021i	−0.0471864	−	0.0817292i
$122$	0.456564	+	3.74164i	0.0413353	+	0.338752i
$123$		0			0
$124$	−1.35385	−	5.46493i	−0.121579	−	0.490766i
$125$		−	19.3119i		−	1.72731i
$126$		0			0
$127$		−	20.3153i		−	1.80270i	−0.433097	−	0.901348i	$-0.642579\pi$
$127$		−	20.3153i		−	1.80270i	0.433097	−	0.901348i	$-0.357421\pi$
$128$	10.7165	−	3.62710i	0.947217	−	0.320594i
$129$		0			0
$130$	1.61162	−	0.196653i	0.141348	−	0.0172476i
$131$	8.62443	+	14.9380i	0.753520	+	1.30514i	0.946107	+	0.323855i	$0.104979\pi$
$131$	8.62443	+	14.9380i	0.753520	+	1.30514i	−0.192587	+	0.981280i	$0.561688\pi$
$132$		0			0
$133$	14.9443	+	11.2710i	1.29584	+	0.977320i
$134$	9.02738	+	11.9985i	0.779847	+	1.03651i
$135$		0			0
$136$	0.703382	−	4.37714i	0.0603145	−	0.375336i
$137$	14.4029	+	8.31550i	1.23052	+	0.710441i	0.967138	−	0.254251i	$-0.0818290\pi$
$137$	14.4029	+	8.31550i	1.23052	+	0.710441i	0.263381	+	0.964692i	$0.415162\pi$
$138$		0			0
$139$			16.2475i			1.37809i	0.724716	+	0.689047i	$0.241971\pi$
$139$			16.2475i			1.37809i	−0.724716	+	0.689047i	$0.758029\pi$
$140$	2.45767	+	20.3379i	0.207711	+	1.71887i
$141$		0			0
$142$	−0.701719	−	0.298484i	−0.0588870	−	0.0250482i
$143$	0.514433	−	0.891025i	0.0430191	−	0.0745112i
$144$		0			0
$145$	13.2658	+	22.9770i	1.10166	+	1.90813i
$146$	8.35716	−	6.28774i	0.691643	−	0.520377i
$147$		0			0
$148$	1.39271	−	4.82957i	0.114480	−	0.396988i
$149$	4.89898	−	2.82843i	0.401340	−	0.231714i	−0.285722	−	0.958313i	$-0.592233\pi$
$149$	4.89898	−	2.82843i	0.401340	−	0.231714i	0.687062	+	0.726599i	$0.258900\pi$
$150$		0			0
$151$	3.46216	+	1.99888i	0.281746	+	0.162666i	0.634214	−	0.773158i	$-0.281324\pi$
$151$	3.46216	+	1.99888i	0.281746	+	0.162666i	−0.352467	+	0.935824i	$0.614657\pi$
$152$	−15.5227	−	12.6280i	−1.25905	−	1.02427i
$153$		0			0
$154$	11.2352	+	6.50410i	0.905360	+	0.524115i
$155$	−10.8984			−0.875384
$156$		0			0
$157$	5.47508	−	9.48312i	0.436959	−	0.756836i	−0.560494	−	0.828158i	$-0.689389\pi$
$157$	5.47508	−	9.48312i	0.436959	−	0.756836i	0.997453	+	0.0713229i	$0.0227221\pi$
$158$	−8.65553	+	1.05617i	−0.688597	+	0.0840243i
$159$		0			0
$160$	−1.82681	−	21.8240i	−0.144422	−	1.72534i
$161$	8.65922	−	11.4813i	0.682442	−	0.904854i
$162$		0			0
$163$	−18.2237	+	10.5214i	−1.42739	+	0.824102i	−0.996914	−	0.0785017i	$-0.974986\pi$
$163$	−18.2237	+	10.5214i	−1.42739	+	0.824102i	−0.430473	+	0.902604i	$0.641653\pi$
$164$	5.12073	−	4.93019i	0.399862	−	0.384983i
$165$		0			0
$166$	8.01623	+	3.40980i	0.622180	+	0.264651i
$167$	8.39346			0.649505			0.324753	−	0.945799i	$-0.394719\pi$
$167$	8.39346			0.649505			0.324753	+	0.945799i	$0.394719\pi$
$168$		0			0
$169$	−12.9121			−0.993236
$170$	−7.89695	−	3.35906i	−0.605668	−	0.257628i
$171$		0			0
$172$	−0.982720	+	0.946154i	−0.0749317	+	0.0721435i
$173$	−13.0086	+	7.51054i	−0.989028	+	0.571016i	−0.904984	−	0.425446i	$-0.860117\pi$
$173$	−13.0086	+	7.51054i	−0.989028	+	0.571016i	−0.0840445	+	0.996462i	$0.526784\pi$
$174$		0			0
$175$	26.2282	+	3.23139i	1.98266	+	0.244270i
$176$	−11.7474	−	7.38974i	−0.885493	−	0.557023i
$177$		0			0
$178$	16.4476	−	2.00698i	1.23280	−	0.150429i
$179$	1.28820	−	2.23123i	0.0962847	−	0.166770i	−0.813859	−	0.581062i	$-0.802637\pi$
$179$	1.28820	−	2.23123i	0.0962847	−	0.166770i	0.910144	+	0.414292i	$0.135971\pi$
$180$		0			0
$181$	−22.3412			−1.66061			−0.830305	−	0.557309i	$-0.811834\pi$
$181$	−22.3412			−1.66061			−0.830305	+	0.557309i	$0.811834\pi$
$182$	−0.00129074	+	1.10954i	−9.56761e−5	+	0.0822448i
$183$		0			0
$184$	−9.70178	+	11.9257i	−0.715224	+	0.879172i
$185$	−8.42618	−	4.86485i	−0.619505	−	0.357671i
$186$		0			0
$187$	−4.70967	+	2.71913i	−0.344405	+	0.198843i
$188$	1.31298	−	4.55309i	0.0957590	−	0.332068i
$189$		0			0
$190$	−30.9526	+	23.2881i	−2.24554	+	1.68949i
$191$	−4.14717	−	7.18311i	−0.300079	−	0.519751i	0.676075	−	0.736833i	$-0.263680\pi$
$191$	−4.14717	−	7.18311i	−0.300079	−	0.519751i	−0.976153	+	0.217082i	$0.930346\pi$
$192$		0			0
$193$	10.6765	−	18.4922i	0.768510	−	1.33110i	−0.169861	−	0.985468i	$-0.554332\pi$
$193$	10.6765	−	18.4922i	0.768510	−	1.33110i	0.938371	−	0.345630i	$-0.112335\pi$
$194$	8.91158	+	3.79064i	0.639815	+	0.272152i
$195$		0			0
$196$	−14.0000	−	0.0325726i	−0.999997	−	0.00232662i
$197$		−	0.572559i		−	0.0407932i	−0.999792	−	0.0203966i	$-0.993507\pi$
$197$		−	0.572559i		−	0.0407932i	0.999792	−	0.0203966i	$-0.00649288\pi$
$198$		0			0
$199$	15.1557	+	8.75014i	1.07436	+	0.620281i	0.929369	−	0.369152i	$-0.120352\pi$
$199$	15.1557	+	8.75014i	1.07436	+	0.620281i	0.144989	+	0.989433i	$0.453685\pi$
$200$	−27.8932	−	4.48229i	−1.97235	−	0.316946i
$201$		0			0
$202$	−3.02193	−	4.01651i	−0.212622	−	0.282600i
$203$	−16.6931	+	7.07768i	−1.17163	+	0.496756i
$204$		0			0
$205$	−6.87994	−	11.9164i	−0.480516	−	0.832278i
$206$	−2.94509	+	0.359367i	−0.205194	+	0.0250383i
$207$		0			0
$208$	0.0449565	−	1.18530i	0.00311717	−	0.0821857i
$209$			24.5466i			1.69793i
$210$		0			0
$211$		−	7.94873i		−	0.547213i	−0.961842	−	0.273607i	$-0.911783\pi$
$211$		−	7.94873i		−	0.547213i	0.961842	−	0.273607i	$-0.0882167\pi$
$212$	−0.299942	−	1.21075i	−0.0206001	−	0.0831544i
$213$		0			0
$214$	1.89384	+	15.5204i	0.129460	+	1.06095i
$215$	1.32033	+	2.28688i	0.0900458	+	0.155964i
$216$		0			0
$217$	0.910728	−	7.39208i	0.0618242	−	0.501807i
$218$	15.0515	−	11.3244i	1.01942	−	0.766987i
$219$		0			0
$220$	−19.3530	+	18.6329i	−1.30478	+	1.25623i
$221$	−0.402524	−	0.232397i	−0.0270767	−	0.0156327i
$222$		0			0
$223$		−	1.17855i		−	0.0789216i	−0.999221	−	0.0394608i	$-0.987436\pi$
$223$		−	1.17855i		−	0.0789216i	0.999221	−	0.0394608i	$-0.0125640\pi$
$224$	14.9552	+	0.584650i	0.999237	+	0.0390636i
$225$		0			0
$226$	−3.73705	+	8.78560i	−0.248585	+	0.584409i
$227$	−2.27401	+	3.93870i	−0.150931	+	0.261421i	−0.931570	−	0.363562i	$-0.881561\pi$
$227$	−2.27401	+	3.93870i	−0.150931	+	0.261421i	0.780639	+	0.624983i	$0.214894\pi$
$228$		0			0
$229$	−8.06436	−	13.9679i	−0.532908	−	0.923023i	−0.999261	−	0.0384248i	$-0.987766\pi$
$229$	−8.06436	−	13.9679i	−0.532908	−	0.923023i	0.466354	−	0.884598i	$-0.345567\pi$
$230$	17.8916	+	23.7801i	1.17974	+	1.56801i
$231$		0			0
$232$	18.1116	−	6.90563i	1.18909	−	0.453377i
$233$	−7.16914	+	4.13910i	−0.469666	+	0.271162i	−0.716100	−	0.697998i	$-0.754074\pi$
$233$	−7.16914	+	4.13910i	−0.469666	+	0.271162i	0.246434	+	0.969160i	$0.420741\pi$
$234$		0			0
$235$	−7.94381	−	4.58636i	−0.518197	−	0.299181i
$236$	−17.1911	+	4.25882i	−1.11905	+	0.277226i
$237$		0			0
$238$	2.93825	−	5.07556i	0.190459	−	0.329000i
$239$	18.1308			1.17279			0.586393	−	0.810027i	$-0.300547\pi$
$239$	18.1308			1.17279			0.586393	+	0.810027i	$0.300547\pi$
$240$		0			0
$241$	9.71078	−	16.8196i	0.625526	−	1.08344i	−0.362913	−	0.931823i	$-0.618218\pi$
$241$	9.71078	−	16.8196i	0.625526	−	1.08344i	0.988439	−	0.151620i	$-0.0484490\pi$
$242$	0.177822	+	1.45729i	0.0114308	+	0.0936779i
$243$		0			0
$244$	1.47704	−	5.12201i	0.0945578	−	0.327903i
$245$	−6.57784	+	26.2899i	−0.420243	+	1.67960i
$246$		0			0
$247$	−1.81687	+	1.04897i	−0.115605	+	0.0667444i
$248$	−1.26328	+	7.86136i	−0.0802182	+	0.499197i
$249$		0			0
$250$	−10.6902	+	25.1320i	−0.676108	+	1.58949i
$251$	−13.8654			−0.875175			−0.437587	−	0.899176i	$-0.644167\pi$
$251$	−13.8654			−0.875175			−0.437587	+	0.899176i	$0.644167\pi$
$252$		0			0
$253$	18.8585			1.18563
$254$	−11.2457	+	26.4379i	−0.705615	+	1.65886i
$255$		0			0
$256$	−15.9540	−	1.21196i	−0.997127	−	0.0757478i
$257$	6.66624	−	3.84875i	0.415829	−	0.240079i	−0.277462	−	0.960736i	$-0.589493\pi$
$257$	6.66624	−	3.84875i	0.415829	−	0.240079i	0.693291	+	0.720658i	$0.256160\pi$
$258$		0			0
$259$	4.00381	−	5.30868i	0.248785	−	0.329866i
$260$	−2.20618	−	0.636198i	−0.136821	−	0.0394553i
$261$		0			0
$262$	−2.95465	−	24.2140i	−0.182539	−	1.49594i
$263$	−5.02740	+	8.70772i	−0.310003	+	0.536941i	−0.978363	−	0.206897i	$-0.933663\pi$
$263$	−5.02740	+	8.70772i	−0.310003	+	0.536941i	0.668360	+	0.743838i	$0.266997\pi$
$264$		0			0
$265$	−2.41453			−0.148323
$266$	−13.2090	−	22.9403i	−0.809897	−	1.40656i
$267$		0			0
$268$	−5.10620	−	20.6117i	−0.311911	−	1.25906i
$269$	24.3429	+	14.0544i	1.48421	+	0.856912i	0.999839	−	0.0179481i	$-0.00571336\pi$
$269$	24.3429	+	14.0544i	1.48421	+	0.856912i	0.484376	+	0.874860i	$0.339047\pi$
$270$		0			0
$271$	21.9127	−	12.6513i	1.33110	−	0.768511i	0.345632	−	0.938370i	$-0.387665\pi$
$271$	21.9127	−	12.6513i	1.33110	−	0.768511i	0.985468	+	0.169859i	$0.0543313\pi$
$272$	−3.33835	+	5.30694i	−0.202417	+	0.321780i
$273$		0			0
$274$	−14.1404	−	18.7944i	−0.854255	−	1.13541i
$275$	17.3276	+	30.0123i	1.04490	+	1.80981i
$276$		0			0
$277$	−1.26430	+	2.18984i	−0.0759647	+	0.131575i	−0.901505	−	0.432768i	$-0.857537\pi$
$277$	−1.26430	+	2.18984i	−0.0759647	+	0.131575i	0.825541	+	0.564343i	$0.190870\pi$
$278$	8.99388	−	21.1441i	0.539417	−	1.26814i
$279$		0			0
$280$	8.05980	−	27.8277i	0.481665	−	1.66302i
$281$		−	8.00911i		−	0.477784i	−0.971046	−	0.238892i	$-0.923216\pi$
$281$		−	8.00911i		−	0.477784i	0.971046	−	0.238892i	$-0.0767841\pi$
$282$		0			0
$283$	6.12694	+	3.53739i	0.364209	+	0.210276i	0.670925	−	0.741525i	$-0.265897\pi$
$283$	6.12694	+	3.53739i	0.364209	+	0.210276i	−0.306717	+	0.951801i	$0.599230\pi$
$284$	0.747973	+	0.776880i	0.0443840	+	0.0460993i
$285$		0			0
$286$	−1.16270	+	0.874791i	−0.0687520	+	0.0517275i
$287$	8.65746	−	3.67066i	0.511033	−	0.216672i
$288$		0			0
$289$	−7.27162	−	12.5948i	−0.427742	−	0.740872i
$290$	−4.54472	−	37.2450i	−0.266875	−	2.18710i
$291$		0			0
$292$	−14.3564	+	3.55656i	−0.840145	+	0.208132i
$293$		−	19.9465i		−	1.16529i	−0.812728	−	0.582643i	$-0.802018\pi$
$293$		−	19.9465i		−	1.16529i	0.812728	−	0.582643i	$-0.197982\pi$
$294$		0			0
$295$			34.2834i			1.99606i
$296$	−4.48587	+	5.51414i	−0.260736	+	0.320503i
$297$		0			0
$298$	−7.94110	+	0.968992i	−0.460016	+	0.0561322i
$299$	0.805897	+	1.39585i	0.0466062	+	0.0807243i
$300$		0			0
$301$	−1.66145	+	0.704436i	−0.0957645	+	0.0406030i
$302$	−3.39908	−	4.51778i	−0.195595	−	0.259969i
$303$		0			0
$304$	13.2105	+	25.0264i	0.757675	+	1.43536i
$305$	−8.93640	−	5.15943i	−0.511697	−	0.295428i
$306$		0			0
$307$			10.4255i			0.595014i	0.954720	+	0.297507i	$0.0961552\pi$
$307$			10.4255i			0.595014i	−0.954720	+	0.297507i	$0.903845\pi$
$308$	−11.0209	−	14.6836i	−0.627972	−	0.836674i
$309$		0			0
$310$	14.1830	+	6.03288i	0.805538	+	0.342645i
$311$	11.3530	−	19.6640i	0.643772	−	1.11505i	−0.340812	−	0.940132i	$-0.610702\pi$
$311$	11.3530	−	19.6640i	0.643772	−	1.11505i	0.984584	−	0.174914i	$-0.0559648\pi$
$312$		0			0
$313$	11.1917	+	19.3846i	0.632594	+	1.09568i	0.987019	+	0.160601i	$0.0513431\pi$
$313$	11.1917	+	19.3846i	0.632594	+	1.09568i	−0.354426	+	0.935084i	$0.615324\pi$
$314$	−12.3746	+	9.31034i	−0.698337	+	0.525413i
$315$		0			0
$316$	11.8487	+	3.41684i	0.666544	+	0.192212i
$317$	25.2368	−	14.5705i	1.41744	−	0.818359i	0.421366	−	0.906891i	$-0.361551\pi$
$317$	25.2368	−	14.5705i	1.41744	−	0.818359i	0.996073	+	0.0885318i	$0.0282175\pi$
$318$		0			0
$319$	−20.5919	−	11.8887i	−1.15292	−	0.665641i
$320$	−9.70341	+	29.4125i	−0.542437	+	1.64421i
$321$		0			0
$322$	−17.6244	+	10.1481i	−0.982171	+	0.565534i
$323$	11.0890			0.617011
$324$		0			0
$325$	−1.48095	+	2.56508i	−0.0821483	+	0.142285i
$326$	29.5400	−	3.60454i	1.63607	−	0.199637i
$327$		0			0
$328$	−9.39313	+	3.58143i	−0.518649	+	0.197751i
$329$	3.77461	−	5.00478i	0.208101	−	0.275922i
$330$		0			0
$331$	17.6936	−	10.2154i	0.972531	−	0.561491i	0.0725241	−	0.997367i	$-0.476895\pi$
$331$	17.6936	−	10.2154i	0.972531	−	0.561491i	0.900007	+	0.435876i	$0.143561\pi$
$332$	−8.54462	−	8.87485i	−0.468947	−	0.487070i
$333$		0			0
$334$	−10.9230	−	4.64624i	−0.597682	−	0.254231i
$335$	−41.1048			−2.24579
$336$		0			0
$337$	−6.16681			−0.335928			−0.167964	−	0.985793i	$-0.553719\pi$
$337$	−6.16681			−0.335928			−0.167964	+	0.985793i	$0.553719\pi$
$338$	16.8034	+	7.14753i	0.913987	+	0.388775i
$339$		0			0
$340$	8.41747	+	8.74279i	0.456502	+	0.474144i
$341$	8.45860	−	4.88357i	0.458059	−	0.264460i
$342$		0			0
$343$	−17.2819	−	6.65845i	−0.933136	−	0.359523i
$344$	1.80264	−	0.687312i	0.0971916	−	0.0370574i
$345$		0			0
$346$	21.0866	−	2.57304i	1.13362	−	0.138327i
$347$	−7.55986	+	13.0941i	−0.405834	+	0.702926i	−0.994418	−	0.105510i	$-0.966352\pi$
$347$	−7.55986	+	13.0941i	−0.405834	+	0.702926i	0.588584	+	0.808436i	$0.299686\pi$
$348$		0			0
$349$	18.8933			1.01134			0.505668	−	0.862728i	$-0.331246\pi$
$349$	18.8933			1.01134			0.505668	+	0.862728i	$0.331246\pi$
$350$	−32.3439	−	18.7240i	−1.72886	−	1.00084i
$351$		0			0
$352$	11.1971	+	16.1197i	0.596810	+	0.859180i
$353$	−9.20426	−	5.31408i	−0.489893	−	0.282840i	0.234637	−	0.972083i	$-0.424610\pi$
$353$	−9.20426	−	5.31408i	−0.489893	−	0.282840i	−0.724530	+	0.689243i	$0.757943\pi$
$354$		0			0
$355$	1.80787	−	1.04377i	0.0959518	−	0.0553978i
$356$	−22.5155	−	6.49282i	−1.19332	−	0.344119i
$357$		0			0
$358$	−2.91154	+	2.19058i	−0.153880	+	0.115776i
$359$	1.40470	+	2.43302i	0.0741374	+	0.128410i	0.900711	−	0.434419i	$-0.143046\pi$
$359$	1.40470	+	2.43302i	0.0741374	+	0.128410i	−0.826573	+	0.562829i	$0.809713\pi$
$360$		0			0
$361$	15.5263	−	26.8923i	0.817171	−	1.41538i
$362$	29.0743	+	12.3671i	1.52811	+	0.650000i
$363$		0			0
$364$	0.615872	−	1.44322i	0.0322805	−	0.0756451i
$365$			28.6302i			1.49858i
$366$		0			0
$367$	16.3515	+	9.44054i	0.853541	+	0.492792i	0.861844	−	0.507173i	$-0.169310\pi$
$367$	16.3515	+	9.44054i	0.853541	+	0.492792i	−0.00830274	+	0.999966i	$0.502643\pi$
$368$	19.2272	−	10.1493i	1.00228	−	0.529069i
$369$		0			0
$370$	8.27265	+	10.9953i	0.430075	+	0.571621i
$371$	0.201770	−	1.63770i	0.0104754	−	0.0850252i
$372$		0			0
$373$	16.7942	+	29.0884i	0.869570	+	1.50614i	0.862437	+	0.506165i	$0.168937\pi$
$373$	16.7942	+	29.0884i	0.869570	+	1.50614i	0.00713304	+	0.999975i	$0.497729\pi$
$374$	7.63424	−	0.931548i	0.394757	−	0.0481692i
$375$		0			0
$376$	−4.22907	+	5.19848i	−0.218098	+	0.268091i
$377$		−	2.03220i		−	0.104664i
$378$		0			0
$379$		−	7.57538i		−	0.389121i	−0.980890	−	0.194561i	$-0.937672\pi$
$379$		−	7.57538i		−	0.389121i	0.980890	−	0.194561i	$-0.0623281\pi$
$380$	53.1722	−	13.1725i	2.72768	−	0.675737i
$381$		0			0
$382$	1.42078	+	11.6436i	0.0726934	+	0.595738i
$383$	−18.1904	−	31.5068i	−0.929488	−	1.60992i	−0.784180	−	0.620533i	$-0.786916\pi$
$383$	−18.1904	−	31.5068i	−0.929488	−	1.60992i	−0.145308	−	0.989387i	$-0.546417\pi$
$384$		0			0
$385$	−32.7194	+	13.8727i	−1.66754	+	0.707016i
$386$	−24.1306	+	18.1553i	−1.22821	+	0.924080i
$387$		0			0
$388$	−9.49899	−	9.86610i	−0.482238	−	0.500875i
$389$	2.95971	+	1.70879i	0.150063	+	0.0866391i	0.573152	−	0.819449i	$-0.305721\pi$
$389$	2.95971	+	1.70879i	0.150063	+	0.0866391i	−0.423088	+	0.906088i	$0.639054\pi$
$390$		0			0
$391$		−	8.51943i		−	0.430846i
$392$	18.2012	+	7.79213i	0.919298	+	0.393562i
$393$		0			0
$394$	−0.316943	+	0.745115i	−0.0159674	+	0.0375383i
$395$	11.9353	−	20.6726i	0.600531	−	1.04015i
$396$		0			0
$397$	−9.88581	−	17.1227i	−0.496155	−	0.859365i	0.503836	−	0.863800i	$-0.331922\pi$
$397$	−9.88581	−	17.1227i	−0.496155	−	0.859365i	−0.999990	+	0.00443461i	$0.998588\pi$
$398$	−14.8795	−	19.7767i	−0.745844	−	0.991317i
$399$		0			0
$400$	33.8184	+	21.2736i	1.69092	+	1.06368i
$401$	3.29921	−	1.90480i	0.164755	−	0.0951211i	−0.415356	−	0.909659i	$-0.636343\pi$
$401$	3.29921	−	1.90480i	0.164755	−	0.0951211i	0.580110	+	0.814538i	$0.303010\pi$
$402$		0			0
$403$	0.722936	+	0.417387i	0.0360120	+	0.0207915i
$404$	1.70931	+	6.89978i	0.0850412	+	0.343277i
$405$		0			0
$406$	25.6419	+	0.0298294i	1.27259	+	0.00148041i
$407$	8.71973			0.432221
$408$		0			0
$409$	−14.7467	+	25.5420i	−0.729178	+	1.26297i	0.228054	+	0.973649i	$0.426764\pi$
$409$	−14.7467	+	25.5420i	−0.729178	+	1.26297i	−0.957231	+	0.289324i	$0.906569\pi$
$410$	2.35700	+	19.3161i	0.116404	+	0.953956i
$411$		0			0
$412$	4.03160	+	1.16260i	0.198623	+	0.0572771i
$413$	−23.2534	−	2.86489i	−1.14422	−	0.140972i
$414$		0			0
$415$	−20.6526	+	11.9238i	−1.01379	+	0.585315i
$416$	−0.714633	+	1.51763i	−0.0350378	+	0.0744081i
$417$		0			0
$418$	13.5879	−	31.9444i	0.664606	−	1.56245i
$419$	−4.99528			−0.244035			−0.122018	−	0.992528i	$-0.538936\pi$
$419$	−4.99528			−0.244035			−0.122018	+	0.992528i	$0.538936\pi$
$420$		0			0
$421$	−4.51318			−0.219959			−0.109980	−	0.993934i	$-0.535079\pi$
$421$	−4.51318			−0.219959			−0.109980	+	0.993934i	$0.535079\pi$
$422$	−4.40006	+	10.3443i	−0.214191	+	0.503552i
$423$		0			0
$424$	−0.279877	+	1.74167i	−0.0135920	+	0.0845830i
$425$	13.5582	−	7.82783i	0.657669	−	0.379705i
$426$		0			0
$427$	4.24625	−	5.63013i	0.205491	−	0.272461i
$428$	6.12679	−	21.2462i	0.296150	−	1.02697i
$429$		0			0
$430$	−0.452332	−	3.70696i	−0.0218134	−	0.178766i
$431$	−10.1436	+	17.5692i	−0.488600	+	0.846281i	−0.999914	−	0.0131135i	$-0.995826\pi$
$431$	−10.1436	+	17.5692i	−0.488600	+	0.846281i	0.511314	+	0.859394i	$0.329159\pi$
$432$		0			0
$433$	8.34123			0.400854			0.200427	−	0.979709i	$-0.435767\pi$
$433$	8.34123			0.400854			0.200427	+	0.979709i	$0.435767\pi$
$434$	−5.27712	+	9.11573i	−0.253310	+	0.437569i
$435$		0			0
$436$	−25.8564	+	6.40549i	−1.23830	+	0.306767i
$437$	−33.3022	−	19.2270i	−1.59306	−	0.919753i
$438$		0			0
$439$	−20.6706	+	11.9342i	−0.986553	+	0.569586i	−0.904242	−	0.427020i	$-0.859563\pi$
$439$	−20.6706	+	11.9342i	−0.986553	+	0.569586i	−0.0823105	+	0.996607i	$0.526230\pi$
$440$	35.4998	−	13.5354i	1.69239	−	0.645276i
$441$		0			0
$442$	0.395190	+	0.525256i	0.0187973	+	0.0249839i
$443$	−3.00114	−	5.19813i	−0.142589	−	0.246971i	0.785882	−	0.618376i	$-0.212209\pi$
$443$	−3.00114	−	5.19813i	−0.142589	−	0.246971i	−0.928471	+	0.371406i	$0.878876\pi$
$444$		0			0
$445$	−22.6800	+	39.2829i	−1.07513	+	1.86219i
$446$	−0.652392	+	1.53374i	−0.0308917	+	0.0726245i
$447$		0			0
$448$	−19.1387	−	9.03937i	−0.904218	−	0.427070i
$449$		−	4.92296i		−	0.232329i	−0.993230	−	0.116165i	$-0.962940\pi$
$449$		−	4.92296i		−	0.232329i	0.993230	−	0.116165i	$-0.0370600\pi$
$450$		0			0
$451$	10.6794	+	6.16578i	0.502876	+	0.290335i
$452$	9.72661	−	9.36469i	0.457501	−	0.440478i
$453$		0			0
$454$	5.13963	−	3.86694i	0.241215	−	0.181485i
$455$	−2.42504	−	1.82897i	−0.113688	−	0.0857432i
$456$		0			0
$457$	13.2218	+	22.9008i	0.618489	+	1.07125i	0.989762	+	0.142731i	$0.0455882\pi$
$457$	13.2218	+	22.9008i	0.618489	+	1.07125i	−0.371272	+	0.928524i	$0.621078\pi$
$458$	2.76277	+	22.6415i	0.129096	+	1.05797i
$459$		0			0
$460$	−10.1201	−	40.8508i	−0.471853	−	1.90468i
$461$		−	8.92124i		−	0.415504i	−0.978182	−	0.207752i	$-0.933385\pi$
$461$		−	8.92124i		−	0.415504i	0.978182	−	0.207752i	$-0.0666147\pi$
$462$		0			0
$463$			14.3310i			0.666020i	0.942923	+	0.333010i	$0.108064\pi$
$463$			14.3310i			0.666020i	−0.942923	+	0.333010i	$0.891936\pi$
$464$	−27.3927	−	1.03896i	−1.27167	−	0.0482325i
$465$		0			0
$466$	11.6210	−	1.41802i	0.538331	−	0.0656884i
$467$	10.6828	+	18.5032i	0.494342	+	0.856225i	0.999979	−	0.00652102i	$-0.00207572\pi$
$467$	10.6828	+	18.5032i	0.494342	+	0.856225i	−0.505637	+	0.862746i	$0.668742\pi$
$468$		0			0
$469$	3.43492	−	27.8801i	0.158610	−	1.28738i
$470$	7.79907	+	10.3659i	0.359744	+	0.478144i
$471$		0			0
$472$	24.7296	+	3.97391i	1.13827	+	0.182914i
$473$	−2.04949	−	1.18328i	−0.0942358	−	0.0544071i
$474$		0			0
$475$		−	70.6648i		−	3.24232i
$476$	−6.63337	+	4.97872i	−0.304040	+	0.228199i
$477$		0			0
$478$	−23.5950	−	10.0364i	−1.07921	−	0.459055i
$479$	16.1925	−	28.0463i	0.739856	−	1.28147i	−0.212704	−	0.977117i	$-0.568227\pi$
$479$	16.1925	−	28.0463i	0.739856	−	1.28147i	0.952560	−	0.304351i	$-0.0984395\pi$
$480$		0			0
$481$	0.372627	+	0.645409i	0.0169903	+	0.0294281i
$482$	−21.9479	+	16.5131i	−0.999700	+	0.752152i
$483$		0			0
$484$	0.575275	−	1.99491i	0.0261489	−	0.0906778i
$485$	−22.9593	+	13.2556i	−1.04253	+	0.601904i
$486$		0			0
$487$	2.49862	+	1.44258i	0.113223	+	0.0653695i	0.555542	−	0.831488i	$-0.312511\pi$
$487$	2.49862	+	1.44258i	0.113223	+	0.0653695i	−0.442319	+	0.896858i	$0.645844\pi$
$488$	−4.75749	+	5.84803i	−0.215362	+	0.264728i
$489$		0			0
$490$	23.1131	−	30.5718i	1.04414	−	1.38109i
$491$	16.6547			0.751617			0.375808	−	0.926697i	$-0.377365\pi$
$491$	16.6547			0.751617			0.375808	+	0.926697i	$0.377365\pi$
$492$		0			0
$493$	−5.37078	+	9.30247i	−0.241888	+	0.418962i
$494$	2.94509	−	0.359367i	0.132506	−	0.0161687i
$495$		0			0
$496$	5.99569	−	9.53128i	0.269214	−	0.427967i
$497$	0.556885	+	1.31345i	0.0249797	+	0.0589161i
$498$		0			0
$499$	−22.5695	+	13.0305i	−1.01035	+	0.583325i	−0.911294	−	0.411757i	$-0.864915\pi$
$499$	−22.5695	+	13.0305i	−1.01035	+	0.583325i	−0.0990552	+	0.995082i	$0.531582\pi$
$500$	27.8239	−	26.7886i	1.24432	−	1.19802i
$501$		0			0
$502$	18.0441	+	7.67524i	0.805346	+	0.342563i
$503$	28.7302			1.28102			0.640509	−	0.767951i	$-0.278723\pi$
$503$	28.7302			1.28102			0.640509	+	0.767951i	$0.278723\pi$
$504$		0			0
$505$	13.7599			0.612307
$506$	−24.5420	−	10.4392i	−1.09103	−	0.464080i
$507$		0			0
$508$	29.2696	−	28.1805i	1.29863	−	1.25031i
$509$	13.6764	−	7.89605i	0.606194	−	0.349986i	−0.165280	−	0.986247i	$-0.552853\pi$
$509$	13.6764	−	7.89605i	0.606194	−	0.349986i	0.771474	+	0.636260i	$0.219520\pi$
$510$		0			0
$511$	−19.4190	−	2.39248i	−0.859046	−	0.105837i
$512$	20.0913	+	10.4086i	0.887918	+	0.460002i
$513$		0			0
$514$	−10.8058	+	1.31855i	−0.476622	+	0.0581586i
$515$	4.06105	−	7.03395i	0.178951	−	0.309953i
$516$		0			0
$517$	8.22056			0.361540
$518$	−8.14911	+	4.69226i	−0.358051	+	0.206166i
$519$		0			0
$520$	2.51889	+	2.04917i	0.110461	+	0.0898621i
$521$	2.95718	+	1.70733i	0.129557	+	0.0747995i	0.563378	−	0.826200i	$-0.309502\pi$
$521$	2.95718	+	1.70733i	0.129557	+	0.0747995i	−0.433821	+	0.900999i	$0.642835\pi$
$522$		0			0
$523$	−5.72733	+	3.30668i	−0.250439	+	0.144591i	−0.619965	−	0.784629i	$-0.712853\pi$
$523$	−5.72733	+	3.30668i	−0.250439	+	0.144591i	0.369526	+	0.929220i	$0.379520\pi$
$524$	−9.55865	+	33.1470i	−0.417572	+	1.44803i
$525$		0			0
$526$	11.3627	−	8.54907i	0.495439	−	0.372757i
$527$	−2.20618	−	3.82121i	−0.0961025	−	0.166454i
$528$		0			0
$529$	−3.27162	+	5.66661i	−0.142244	+	0.246374i
$530$	3.14221	+	1.33657i	0.136489	+	0.0580571i
$531$		0			0
$532$	4.49119	+	37.1658i	0.194718	+	1.61134i
$533$			1.05395i			0.0456516i
$534$		0			0
$535$	−37.0684	−	21.4014i	−1.60260	−	0.925264i
$536$	−4.76460	+	29.6501i	−0.205799	+	1.28069i
$537$		0			0
$538$	−23.8994	−	31.7652i	−1.03038	−	1.36949i
$539$	−6.67519	−	23.3518i	−0.287521	−	1.00584i
$540$		0			0
$541$	−4.69564	−	8.13308i	−0.201881	−	0.349669i	0.747253	−	0.664539i	$-0.231372\pi$
$541$	−4.69564	−	8.13308i	−0.201881	−	0.349669i	−0.949135	+	0.314871i	$0.898039\pi$
$542$	−35.5198	+	4.33421i	−1.52571	+	0.186170i
$543$		0			0
$544$	7.28212	−	5.05836i	0.312218	−	0.216875i
$545$			51.5640i			2.20876i
$546$		0			0
$547$			14.8029i			0.632924i	0.948605	+	0.316462i	$0.102495\pi$
$547$			14.8029i			0.632924i	−0.948605	+	0.316462i	$0.897505\pi$
$548$	7.99832	+	32.2860i	0.341671	+	1.37919i
$549$		0			0
$550$	−5.93628	−	48.6491i	−0.253124	−	2.07440i
$551$	24.2420	+	41.9884i	1.03275	+	1.78877i
$552$		0			0
$553$	13.0242	+	9.82286i	0.553845	+	0.417710i
$554$	2.85753	−	2.14994i	0.121405	−	0.0913422i
$555$		0			0
$556$	−23.4088	+	22.5378i	−0.992755	+	0.955815i
$557$	−3.11722	−	1.79973i	−0.132081	−	0.0762569i	0.432504	−	0.901632i	$-0.357630\pi$
$557$	−3.11722	−	1.79973i	−0.132081	−	0.0762569i	−0.564585	+	0.825375i	$0.690964\pi$
$558$		0			0
$559$		−	0.202263i		−	0.00855482i
$560$	−25.8930	+	31.7528i	−1.09418	+	1.34180i
$561$		0			0
$562$	−4.43348	+	10.4229i	−0.187015	+	0.439662i
$563$	−9.56600	+	16.5688i	−0.403159	+	0.698292i	−0.994105	−	0.108419i	$-0.965421\pi$
$563$	−9.56600	+	16.5688i	−0.403159	+	0.698292i	0.590946	+	0.806711i	$0.298754\pi$
$564$		0			0
$565$	−13.0682	−	22.6347i	−0.549782	−	0.952250i
$566$	−6.01531	−	7.99507i	−0.252842	−	0.336058i
$567$		0			0
$568$	−0.543348	−	1.42506i	−0.0227984	−	0.0597940i
$569$	−27.6097	+	15.9405i	−1.15746	+	0.668260i	−0.950694	−	0.310131i	$-0.899627\pi$
$569$	−27.6097	+	15.9405i	−1.15746	+	0.668260i	−0.206766	+	0.978390i	$0.566294\pi$
$570$		0			0
$571$	19.6409	+	11.3397i	0.821947	+	0.474551i	0.851087	−	0.525024i	$-0.175944\pi$
$571$	19.6409	+	11.3397i	0.821947	+	0.474551i	−0.0291406	+	0.999575i	$0.509277\pi$
$572$	1.99736	−	0.494812i	0.0835136	−	0.0206891i
$573$		0			0
$574$	−13.2985	−	0.0154703i	−0.555069	−	0.000645717i
$575$	−54.2899			−2.26405
$576$		0			0
$577$	0.690279	−	1.19560i	0.0287367	−	0.0497734i	−0.851299	−	0.524680i	$-0.824185\pi$
$577$	0.690279	−	1.19560i	0.0287367	−	0.0497734i	0.880036	+	0.474907i	$0.157518\pi$
$578$	2.49119	+	20.4158i	0.103620	+	0.849186i
$579$		0			0
$580$	−14.7027	+	50.9854i	−0.610498	+	2.11705i
$581$	−6.36169	−	15.0044i	−0.263927	−	0.622488i
$582$		0			0
$583$	1.87399	−	1.08195i	0.0776126	−	0.0448097i
$584$	20.6518	+	3.31863i	0.854578	+	0.137326i
$585$		0			0
$586$	−11.0415	+	25.9579i	−0.456119	+	1.07231i
$587$	39.5737			1.63338			0.816692	−	0.577074i	$-0.195806\pi$
$587$	39.5737			1.63338			0.816692	+	0.577074i	$0.195806\pi$
$588$		0			0
$589$	−19.9160			−0.820624
$590$	18.9777	−	44.6156i	0.781301	−	1.83679i
$591$		0			0
$592$	8.89017	−	4.69279i	0.365384	−	0.192873i
$593$	−19.6880	+	11.3669i	−0.808489	+	0.466781i	−0.846431	−	0.532498i	$-0.821253\pi$
$593$	−19.6880	+	11.3669i	−0.808489	+	0.466781i	0.0379417	+	0.999280i	$0.487920\pi$
$594$		0			0
$595$	6.26703	+	14.7811i	0.256923	+	0.605968i
$596$	10.8707	+	3.13481i	0.445283	+	0.128407i
$597$		0			0
$598$	−0.276092	−	2.26264i	−0.0112903	−	0.0925261i
$599$	−6.51380	+	11.2822i	−0.266147	+	0.460979i	−0.967863	−	0.251477i	$-0.919084\pi$
$599$	−6.51380	+	11.2822i	−0.266147	+	0.460979i	0.701717	+	0.712456i	$0.252417\pi$
$600$		0			0
$601$	−43.6907			−1.78218			−0.891091	−	0.453825i	$-0.850059\pi$
$601$	−43.6907			−1.78218			−0.891091	+	0.453825i	$0.850059\pi$
$602$	2.55212	+	0.00296890i	0.104017	+	0.000121003i
$603$		0			0
$604$	1.92263	+	7.76090i	0.0782309	+	0.315787i
$605$	−3.48053	−	2.00949i	−0.141504	−	0.0816972i
$606$		0			0
$607$	7.84192	−	4.52754i	0.318294	−	0.183767i	−0.332338	−	0.943160i	$-0.607837\pi$
$607$	7.84192	−	4.52754i	0.318294	−	0.183767i	0.650632	+	0.759393i	$0.274504\pi$
$608$	−3.33835	−	39.8815i	−0.135388	−	1.61741i
$609$		0			0
$610$	8.77358	+	11.6611i	0.355232	+	0.472146i
$611$	0.351296	+	0.608462i	0.0142119	+	0.0246157i
$612$		0			0
$613$	−5.81374	+	10.0697i	−0.234815	+	0.406711i	−0.959219	−	0.282664i	$-0.908782\pi$
$613$	−5.81374	+	10.0697i	−0.234815	+	0.406711i	0.724404	+	0.689376i	$0.242115\pi$
$614$	5.77108	−	13.5675i	0.232902	−	0.547539i
$615$		0			0
$616$	6.21412	+	25.2095i	0.250374	+	1.01572i
$617$		−	18.3734i		−	0.739685i	−0.929094	−	0.369843i	$-0.879412\pi$
$617$		−	18.3734i		−	0.739685i	0.929094	−	0.369843i	$-0.120588\pi$
$618$		0			0
$619$	19.6409	+	11.3397i	0.789435	+	0.455781i	0.839764	−	0.542952i	$-0.182694\pi$
$619$	19.6409	+	11.3397i	0.789435	+	0.455781i	−0.0503285	+	0.998733i	$0.516027\pi$
$620$	−15.1178	−	15.7021i	−0.607146	−	0.630611i
$621$		0			0
$622$	−25.6597	+	19.3058i	−1.02886	+	0.774091i
$623$	−24.7491	−	18.6658i	−0.991553	−	0.747830i
$624$		0			0
$625$	−12.4121	−	21.4983i	−0.496483	−	0.859933i
$626$	−3.83418	−	31.4219i	−0.153245	−	1.25587i
$627$		0			0
$628$	21.2577	−	5.26625i	0.848276	−	0.210146i
$629$		−	3.93918i		−	0.157065i
$630$		0			0
$631$		−	27.5820i		−	1.09802i	−0.835815	−	0.549011i	$-0.815005\pi$
$631$		−	27.5820i		−	1.09802i	0.835815	−	0.549011i	$-0.184995\pi$
$632$	−13.5283	−	11.0055i	−0.538125	−	0.437776i
$633$		0			0
$634$	−40.9081	+	4.99170i	−1.62467	+	0.198246i
$635$	−39.3251	−	68.1131i	−1.56057	−	2.70298i
$636$		0			0
$637$	1.44318	−	1.49199i	0.0571808	−	0.0591148i
$638$	20.2167	+	26.8704i	0.800387	+	1.06381i
$639$		0			0
$640$	28.9092	−	32.9053i	1.14274	−	1.30070i
$641$	−24.9390	−	14.3986i	−0.985032	−	0.568709i	−0.0812468	−	0.996694i	$-0.525890\pi$
$641$	−24.9390	−	14.3986i	−0.985032	−	0.568709i	−0.903786	+	0.427985i	$0.859224\pi$
$642$		0			0
$643$			38.1698i			1.50527i	0.658438	+	0.752635i	$0.271217\pi$
$643$			38.1698i			1.50527i	−0.658438	+	0.752635i	$0.728783\pi$
$644$	28.5535	−	3.45047i	1.12517	−	0.135967i
$645$		0			0
$646$	−14.4310	−	6.13839i	−0.567780	−	0.241512i
$647$	−22.8942	+	39.6540i	−0.900066	+	1.55896i	−0.0726586	+	0.997357i	$0.523148\pi$
$647$	−22.8942	+	39.6540i	−0.900066	+	1.55896i	−0.827407	+	0.561603i	$0.810185\pi$
$648$		0			0
$649$	−15.3623	−	26.6084i	−0.603025	−	1.04447i
$650$	3.34718	−	2.51835i	0.131287	−	0.0987776i
$651$		0			0
$652$	−40.4379	−	11.6611i	−1.58367	−	0.456685i
$653$	5.21310	−	3.00979i	0.204004	−	0.117782i	−0.394518	−	0.918888i	$-0.629088\pi$
$653$	5.21310	−	3.00979i	0.204004	−	0.117782i	0.598522	+	0.801106i	$0.295755\pi$
$654$		0			0
$655$	57.8318	+	33.3892i	2.25968	+	1.30462i
$656$	14.2065	+	0.538829i	0.554671	+	0.0210378i
$657$		0			0
$658$	−7.68260	+	4.42364i	−0.299499	+	0.172452i
$659$	−8.45187			−0.329238			−0.164619	−	0.986357i	$-0.552639\pi$
$659$	−8.45187			−0.329238			−0.164619	+	0.986357i	$0.552639\pi$
$660$		0			0
$661$	9.66145	−	16.7341i	0.375787	−	0.650882i	−0.614658	−	0.788794i	$-0.710706\pi$
$661$	9.66145	−	16.7341i	0.375787	−	0.650882i	0.990444	+	0.137912i	$0.0440391\pi$
$662$	−28.6809	+	3.49971i	−1.11471	+	0.136020i
$663$		0			0
$664$	6.20704	+	16.2794i	0.240880	+	0.631764i
$665$	71.9228	+	8.86111i	2.78904	+	0.343619i
$666$		0			0
$667$	32.2586	−	18.6245i	1.24906	−	0.721145i
$668$	11.6430	+	12.0930i	0.450482	+	0.467892i
$669$		0			0
$670$	53.4928	+	22.7537i	2.06661	+	0.879054i
$671$	9.24773			0.357005
$672$		0			0
$673$	30.5239			1.17661			0.588305	−	0.808639i	$-0.299795\pi$
$673$	30.5239			1.17661			0.588305	+	0.808639i	$0.299795\pi$
$674$	8.02533	+	3.41367i	0.309124	+	0.131490i
$675$		0			0
$676$	−17.9110	−	18.6032i	−0.688886	−	0.715509i
$677$	−17.2742	+	9.97325i	−0.663900	+	0.383303i	−0.793761	−	0.608229i	$-0.791880\pi$
$677$	−17.2742	+	9.97325i	−0.663900	+	0.383303i	0.129861	+	0.991532i	$0.458547\pi$
$678$		0			0
$679$	−7.07224	−	16.6803i	−0.271408	−	0.640131i
$680$	−6.11468	−	16.0372i	−0.234487	−	0.614998i
$681$		0			0
$682$	−13.7111	+	1.67307i	−0.525026	+	0.0640650i
$683$	13.6866	−	23.7060i	0.523705	−	0.907084i	−0.475914	−	0.879492i	$-0.657883\pi$
$683$	13.6866	−	23.7060i	0.523705	−	0.907084i	0.999619	−	0.0275921i	$-0.00878394\pi$
$684$		0			0
$685$	64.3864			2.46008
$686$	18.8045	+	18.2316i	0.717957	+	0.696087i
$687$		0			0
$688$	−2.72637	−	0.103407i	−0.103942	−	0.00394235i
$689$	0.160165	+	0.0924714i	0.00610180	+	0.00352288i
$690$		0			0
$691$	−41.8799	+	24.1794i	−1.59319	+	0.919827i	−0.600431	+	0.799676i	$0.705004\pi$
$691$	−41.8799	+	24.1794i	−1.59319	+	0.919827i	−0.992756	+	0.120151i	$0.961662\pi$
$692$	−28.8659	−	8.32410i	−1.09732	−	0.316435i
$693$		0			0
$694$	17.0865	−	12.8555i	0.648594	−	0.487987i
$695$	31.4508	+	54.4745i	1.19300	+	2.06633i
$696$		0			0
$697$	2.78542	−	4.82449i	0.105505	−	0.182740i
$698$	−24.5873	−	10.4585i	−0.930642	−	0.395859i
$699$		0			0
$700$	31.7268	+	42.2710i	1.19916	+	1.59770i
$701$		−	17.0447i		−	0.643768i	−0.946779	−	0.321884i	$-0.895684\pi$
$701$		−	17.0447i		−	0.643768i	0.946779	−	0.321884i	$-0.104316\pi$
$702$		0			0
$703$	−15.3981	−	8.89011i	−0.580751	−	0.335297i
$704$	−5.64858	−	27.1759i	−0.212889	−	1.02423i
$705$		0			0
$706$	9.03656	+	12.0107i	0.340095	+	0.452028i
$707$	−1.14984	+	9.33291i	−0.0432443	+	0.351000i
$708$		0			0
$709$	13.2203	+	22.8983i	0.496500	+	0.859964i	0.999992	−	0.00403654i	$-0.00128488\pi$
$709$	13.2203	+	22.8983i	0.496500	+	0.859964i	−0.503492	+	0.864000i	$0.667952\pi$
$710$	−2.93050	+	0.357587i	−0.109980	+	0.0134200i
$711$		0			0
$712$	25.7070	+	20.9131i	0.963409	+	0.783753i
$713$			15.3009i			0.573024i
$714$		0			0
$715$		−	3.98323i		−	0.148964i
$716$	5.00161	−	1.23907i	0.186919	−	0.0463061i
$717$		0			0
$718$	−0.481238	−	3.94385i	−0.0179596	−	0.147183i
$719$	17.3772	+	30.0982i	0.648060	+	1.12247i	0.983586	+	0.180441i	$0.0577526\pi$
$719$	17.3772	+	30.0982i	0.648060	+	1.12247i	−0.335526	+	0.942031i	$0.608914\pi$
$720$		0			0
$721$	4.43155	+	3.34228i	0.165040	+	0.124473i
$722$	−35.0918	+	26.4023i	−1.30598	+	0.982592i
$723$		0			0
$724$	−30.9907	−	32.1884i	−1.15176	−	1.19627i
$725$	59.2798	+	34.2252i	2.20160	+	1.27109i
$726$		0			0
$727$		−	22.9785i		−	0.852226i	−0.904670	−	0.426113i	$-0.859883\pi$
$727$		−	22.9785i		−	0.852226i	0.904670	−	0.426113i	$-0.140117\pi$
$728$	−1.60038	+	1.53725i	−0.0593140	+	0.0569742i
$729$		0			0
$730$	15.8484	−	37.2587i	0.586576	−	1.37901i
$731$	−0.534550	+	0.925867i	−0.0197710	+	0.0342444i
$732$		0			0
$733$	10.4388	+	18.0806i	0.385567	+	0.667821i	0.991848	−	0.127429i	$-0.0406726\pi$
$733$	10.4388	+	18.0806i	0.385567	+	0.667821i	−0.606281	+	0.795251i	$0.707339\pi$
$734$	−16.0536	−	21.3371i	−0.592548	−	0.787568i
$735$		0			0
$736$	−30.6399	+	2.56477i	−1.12940	+	0.0945385i
$737$	31.9026	−	18.4190i	1.17515	−	0.678472i
$738$		0			0
$739$	5.97877	+	3.45185i	0.219933	+	0.126978i	0.605919	−	0.795526i	$-0.292806\pi$
$739$	5.97877	+	3.45185i	0.219933	+	0.126978i	−0.385986	+	0.922504i	$0.626139\pi$
$740$	−4.67930	−	18.8884i	−0.172014	−	0.694353i
$741$		0			0
$742$	−1.16914	+	2.01957i	−0.0429203	+	0.0741409i
$743$	12.7592			0.468091			0.234046	−	0.972226i	$-0.424803\pi$
$743$	12.7592			0.468091			0.234046	+	0.972226i	$0.424803\pi$
$744$		0			0
$745$	10.9502	−	18.9662i	0.401183	−	0.694869i
$746$	−5.75353	−	47.1514i	−0.210652	−	1.72634i
$747$		0			0
$748$	−10.4507	−	3.01368i	−0.382114	−	0.110191i
$749$	17.6135	−	23.3539i	0.643585	−	0.853333i
$750$		0			0
$751$	44.8145	−	25.8737i	1.63530	−	0.944143i	0.652884	−	0.757458i	$-0.273559\pi$
$751$	44.8145	−	25.8737i	1.63530	−	0.944143i	0.982420	−	0.186686i	$-0.0597745\pi$
$752$	8.38124	−	4.42415i	0.305632	−	0.161332i
$753$		0			0
$754$	−1.12493	+	2.64465i	−0.0409677	+	0.0963126i
$755$	15.4772			0.563272
$756$		0			0
$757$	−24.2613			−0.881793			−0.440897	−	0.897558i	$-0.645339\pi$
$757$	−24.2613			−0.881793			−0.440897	+	0.897558i	$0.645339\pi$
$758$	−4.19339	+	9.85842i	−0.152311	+	0.358074i
$759$		0			0
$760$	−76.4887	−	12.2913i	−2.77454	−	0.445853i
$761$	41.6890	−	24.0692i	1.51123	−	0.872506i	0.511311	−	0.859395i	$-0.329160\pi$
$761$	41.6890	−	24.0692i	1.51123	−	0.872506i	0.999914	−	0.0131110i	$-0.00417347\pi$
$762$		0			0
$763$	−34.9743	−	4.30895i	−1.26615	−	0.155994i
$764$	4.59640	−	15.9392i	0.166292	−	0.576659i
$765$		0			0
$766$	6.23187	+	51.0715i	0.225167	+	1.84529i
$767$	1.31298	−	2.27415i	0.0474090	−	0.0821148i
$768$		0			0
$769$	32.1961			1.16102			0.580510	−	0.814253i	$-0.302853\pi$
$769$	32.1961			1.16102			0.580510	+	0.814253i	$0.302853\pi$
$770$	50.2595	+	0.0584674i	1.81123	+	0.00210702i
$771$		0			0
$772$	41.4528	−	10.2693i	1.49192	−	0.369599i
$773$	34.7804	+	20.0805i	1.25096	+	0.722245i	0.971301	−	0.237853i	$-0.0764438\pi$
$773$	34.7804	+	20.0805i	1.25096	+	0.722245i	0.279663	+	0.960098i	$0.409777\pi$
$774$		0			0
$775$	−24.3506	+	14.0588i	−0.874699	+	0.505008i
$776$	6.90032	+	18.0977i	0.247707	+	0.649670i
$777$		0			0
$778$	−2.90579	−	3.86214i	−0.104177	−	0.138464i
$779$	−12.5725	−	21.7762i	−0.450457	−	0.780214i
$780$		0			0
$781$	−0.935427	+	1.62021i	−0.0334722	+	0.0579756i
$782$	−4.71597	+	11.0870i	−0.168643	+	0.396469i
$783$		0			0
$784$	−19.3732	−	20.2158i	−0.691899	−	0.721994i
$785$		−	42.3932i		−	1.51308i
$786$		0			0
$787$	30.4775	+	17.5962i	1.08641	+	0.627237i	0.932617	−	0.360867i	$-0.117519\pi$
$787$	30.4775	+	17.5962i	1.08641	+	0.627237i	0.153789	+	0.988104i	$0.450852\pi$
$788$	0.824923	−	0.794228i	0.0293867	−	0.0282932i
$789$		0			0
$790$	−26.9757	+	20.2959i	−0.959753	+	0.722096i
$791$	16.4445	−	6.97226i	0.584698	−	0.247905i
$792$		0			0
$793$	0.395190	+	0.684490i	0.0140336	+	0.0243069i
$794$	3.38678	+	27.7554i	0.120192	+	0.985003i
$795$		0			0
$796$	8.41639	+	33.9736i	0.298311	+	1.20416i
$797$			18.8026i			0.666021i	0.942923	+	0.333010i	$0.108064\pi$
$797$			18.8026i			0.666021i	−0.942923	+	0.333010i	$0.891936\pi$
$798$		0			0
$799$		−	3.71367i		−	0.131380i
$800$	−32.2343	−	46.4052i	−1.13965	−	1.64067i
$801$		0			0
$802$	−5.34792	+	0.652566i	−0.188842	+	0.0230429i
$803$	−12.8292	−	22.2208i	−0.452731	−	0.784154i
$804$		0			0
$805$	6.80776	−	55.2564i	0.239942	−	1.94753i
$806$	−0.709764	−	0.943361i	−0.0250004	−	0.0332285i
$807$		0			0
$808$	1.59496	−	9.92540i	0.0561104	−	0.349174i
$809$	−47.1053	−	27.1962i	−1.65613	−	0.956169i	−0.974475	−	0.224498i	$-0.927926\pi$
$809$	−47.1053	−	27.1962i	−1.65613	−	0.956169i	−0.681658	−	0.731671i	$-0.738741\pi$
$810$		0			0
$811$			1.91646i			0.0672961i	0.999434	+	0.0336480i	$0.0107125\pi$
$811$			1.91646i			0.0672961i	−0.999434	+	0.0336480i	$0.989287\pi$
$812$	−33.3532	−	14.2330i	−1.17047	−	0.499481i
$813$		0			0
$814$	−11.3476	−	4.82685i	−0.397735	−	0.169181i
$815$	−40.7334	+	70.5523i	−1.42683	+	2.47134i
$816$		0			0
$817$	2.41279	+	4.17908i	0.0844129	+	0.146207i
$818$	33.3299	−	25.0767i	1.16535	−	0.876785i
$819$		0			0
$820$	7.62520	−	26.4423i	0.266283	−	0.923405i
$821$	21.9570	−	12.6769i	0.766305	−	0.442426i	−0.0652500	−	0.997869i	$-0.520785\pi$
$821$	21.9570	−	12.6769i	0.766305	−	0.442426i	0.831555	+	0.555443i	$0.187451\pi$
$822$		0			0
$823$	−4.56151	−	2.63359i	−0.159004	−	0.0918011i	0.418387	−	0.908269i	$-0.362596\pi$
$823$	−4.56151	−	2.63359i	−0.159004	−	0.0918011i	−0.577391	+	0.816468i	$0.695929\pi$
$824$	−4.60306	−	3.74469i	−0.160355	−	0.130452i
$825$		0			0
$826$	28.6755	+	16.6003i	0.997748	+	0.577599i
$827$	−43.4115			−1.50957			−0.754784	−	0.655974i	$-0.772258\pi$
$827$	−43.4115			−1.50957			−0.754784	+	0.655974i	$0.772258\pi$
$828$		0			0
$829$	−4.48291	+	7.76462i	−0.155698	+	0.269677i	−0.933313	−	0.359064i	$-0.883096\pi$
$829$	−4.48291	+	7.76462i	−0.155698	+	0.269677i	0.777615	+	0.628741i	$0.216429\pi$
$830$	33.4772	−	4.08497i	1.16201	−	0.141791i
$831$		0			0
$832$	1.77010	−	1.57942i	0.0613671	−	0.0547566i
$833$	−10.5493	+	3.01555i	−0.365511	+	0.104483i
$834$		0			0
$835$	28.1415	−	16.2475i	0.973877	−	0.562268i
$836$	−35.3659	+	34.0500i	−1.22316	+	1.17764i
$837$		0			0
$838$	6.50073	+	2.76516i	0.224564	+	0.0955208i
$839$	36.4358			1.25790			0.628952	−	0.777444i	$-0.283484\pi$
$839$	36.4358			1.25790			0.628952	+	0.777444i	$0.283484\pi$
$840$		0			0
$841$	−17.9648			−0.619476
$842$	5.87334	+	2.49829i	0.202409	+	0.0860969i
$843$		0			0
$844$	11.4523	−	11.0261i	0.394203	−	0.379535i
$845$	−43.2914	+	24.9943i	−1.48927	+	0.859831i
$846$		0			0
$847$	1.65382	−	2.19282i	0.0568260	−	0.0753460i
$848$	1.32833	−	2.11164i	0.0456152	−	0.0725140i
$849$		0			0
$850$	−21.9774	+	2.68174i	−0.753820	+	0.0919829i
$851$	−6.83004	+	11.8300i	−0.234131	+	0.405526i
$852$		0			0
$853$	4.08381			0.139827			0.0699135	−	0.997553i	$-0.477728\pi$
$853$	4.08381			0.139827			0.0699135	+	0.997553i	$0.477728\pi$
$854$	−8.64255	+	4.97638i	−0.295742	+	0.170288i
$855$		0			0
$856$	−19.7342	+	24.2577i	−0.674500	+	0.829113i
$857$	10.1985	+	5.88810i	0.348374	+	0.201134i	0.663969	−	0.747760i	$-0.268871\pi$
$857$	10.1985	+	5.88810i	0.348374	+	0.201134i	−0.315595	+	0.948894i	$0.602204\pi$
$858$		0			0
$859$	28.9031	−	16.6872i	0.986161	−	0.569360i	0.0820365	−	0.996629i	$-0.473858\pi$
$859$	28.9031	−	16.6872i	0.986161	−	0.569360i	0.904125	+	0.427269i	$0.140524\pi$
$860$	−1.46335	+	5.07454i	−0.0498999	+	0.173040i
$861$		0			0
$862$	22.9262	−	17.2491i	0.780869	−	0.587508i
$863$	−12.4315	−	21.5319i	−0.423172	−	0.732956i	0.573076	−	0.819503i	$-0.305750\pi$
$863$	−12.4315	−	21.5319i	−0.423172	−	0.732956i	−0.996248	+	0.0865468i	$0.972417\pi$
$864$		0			0
$865$	−29.0768	+	50.3625i	−0.988641	+	1.71238i
$866$	−10.8551	−	4.61733i	−0.368870	−	0.156903i
$867$		0			0
$868$	11.9136	−	8.94181i	0.404373	−	0.303505i
$869$			21.3928i			0.725700i
$870$		0			0
$871$	2.72664	+	1.57423i	0.0923886	+	0.0533406i
$872$	37.1946	+	5.97697i	1.25957	+	0.202406i
$873$		0			0
$874$	32.6954	+	43.4561i	1.10594	+	1.46993i
$875$	47.0410	−	19.9448i	1.59028	−	0.674258i
$876$		0			0
$877$	−23.0468	−	39.9181i	−0.778234	−	1.34794i	−0.932959	−	0.359983i	$-0.882783\pi$
$877$	−23.0468	−	39.9181i	−0.778234	−	1.34794i	0.154725	−	0.987958i	$-0.450551\pi$
$878$	33.5064	−	4.08853i	1.13079	−	0.137981i
$879$		0			0
$880$	−53.6911	−	2.03642i	−1.80993	−	0.0686476i
$881$			15.9952i			0.538893i	0.963015	+	0.269446i	$0.0868407\pi$
$881$			15.9952i			0.538893i	−0.963015	+	0.269446i	$0.913159\pi$
$882$		0			0
$883$			42.9597i			1.44571i	0.691001	+	0.722854i	$0.257170\pi$
$883$			42.9597i			1.44571i	−0.691001	+	0.722854i	$0.742830\pi$
$884$	−0.223533	−	0.902314i	−0.00751824	−	0.0303481i
$885$		0			0
$886$	1.02816	+	8.42602i	0.0345418	+	0.283078i
$887$	−9.76216	−	16.9086i	−0.327781	−	0.567734i	0.654290	−	0.756244i	$-0.272968\pi$
$887$	−9.76216	−	16.9086i	−0.327781	−	0.567734i	−0.982071	+	0.188510i	$0.939634\pi$
$888$		0			0
$889$	49.4852	−	20.9811i	1.65968	−	0.703685i
$890$	51.2604	−	38.5672i	1.71825	−	1.29277i
$891$		0			0
$892$	1.69801	−	1.63483i	0.0568537	−	0.0547382i
$893$	−14.5166	−	8.38118i	−0.485781	−	0.280466i
$894$		0			0
$895$		−	9.97446i		−	0.333410i
$896$	19.9028	+	22.3579i	0.664907	+	0.746926i
$897$		0			0
$898$	−2.72513	+	6.40662i	−0.0909388	+	0.213792i
$899$	9.64595	−	16.7073i	0.321710	−	0.557219i
$900$		0			0
$901$	−0.488774	−	0.846582i	−0.0162834	−	0.0282037i
$902$	−10.4849	−	13.9357i	−0.349108	−	0.464006i
$903$		0			0
$904$	−17.8418	+	6.80277i	−0.593411	+	0.226257i
$905$	−74.9054	+	43.2467i	−2.48994	+	1.43757i
$906$		0			0
$907$	26.2372	+	15.1480i	0.871191	+	0.502982i	0.867744	−	0.497012i	$-0.165569\pi$
$907$	26.2372	+	15.1480i	0.871191	+	0.502982i	0.00344687	+	0.999994i	$0.498903\pi$
$908$	−8.82915	+	2.18728i	−0.293006	+	0.0725873i
$909$		0			0
$910$	2.14345	+	3.72256i	0.0710547	+	0.123402i
$911$	−25.1485			−0.833207			−0.416604	−	0.909088i	$-0.636780\pi$
$911$	−25.1485			−0.833207			−0.416604	+	0.909088i	$0.636780\pi$
$912$		0			0
$913$	10.6860	−	18.5088i	0.353656	−	0.612551i
$914$	−4.52966	−	37.1215i	−0.149828	−	1.22787i
$915$		0			0
$916$	8.93791	−	30.9944i	0.295317	−	1.02408i
$917$	−27.4796	+	36.4354i	−0.907456	+	1.20320i
$918$		0			0
$919$	−3.59797	+	2.07729i	−0.118686	+	0.0685235i	−0.558168	−	0.829728i	$-0.688495\pi$
$919$	−3.59797	+	2.07729i	−0.118686	+	0.0685235i	0.439482	+	0.898252i	$0.355162\pi$
$920$	−9.44310	+	58.7643i	−0.311330	+	1.93740i
$921$		0			0
$922$	−4.93840	+	11.6099i	−0.162637	+	0.382351i
$923$	−0.159897			−0.00526308
$924$		0			0
$925$	−25.1023			−0.825360
$926$	7.93301	−	18.6501i	0.260695	−	0.612879i
$927$		0			0
$928$	35.0730	+	16.5154i	1.15133	+	0.542145i
$929$	37.5310	−	21.6686i	1.23135	−	0.710922i	0.264041	−	0.964511i	$-0.414945\pi$
$929$	37.5310	−	21.6686i	1.23135	−	0.710922i	0.967312	+	0.253589i	$0.0816112\pi$
$930$		0			0
$931$	−12.0204	+	48.0425i	−0.393954	+	1.57453i
$932$	−15.9082	−	4.58746i	−0.521090	−	0.150267i
$933$		0			0
$934$	−3.65983	−	29.9931i	−0.119753	−	0.981405i
$935$	−10.5270	+	18.2334i	−0.344271	+	0.596294i
$936$		0			0
$937$	−28.6116			−0.934701			−0.467350	−	0.884072i	$-0.654791\pi$
$937$	−28.6116			−0.934701			−0.467350	+	0.884072i	$0.654791\pi$
$938$	−19.9033	+	34.3811i	−0.649865	+	1.12258i
$939$		0			0
$940$	−4.41143	−	17.8071i	−0.143885	−	0.580805i
$941$	20.1360	+	11.6255i	0.656416	+	0.378982i	0.790910	−	0.611932i	$-0.209608\pi$
$941$	20.1360	+	11.6255i	0.656416	+	0.378982i	−0.134494	+	0.990914i	$0.542941\pi$
$942$		0			0
$943$	−16.7301	+	9.65914i	−0.544807	+	0.314545i
$944$	−29.9827	−	18.8607i	−0.975855	−	0.613865i
$945$		0			0
$946$	2.01215	+	2.67439i	0.0654207	+	0.0869520i
$947$	−24.8279	−	43.0032i	−0.806798	−	1.39742i	−0.915070	−	0.403294i	$-0.867865\pi$
$947$	−24.8279	−	43.0032i	−0.806798	−	1.39742i	0.108272	−	0.994121i	$-0.465468\pi$
$948$		0			0
$949$	1.09648	−	1.89915i	0.0355932	−	0.0616492i
$950$	−39.1168	+	91.9614i	−1.26912	+	2.98362i
$951$		0			0
$952$	11.3885	−	2.80725i	0.369103	−	0.0909836i
$953$			44.7824i			1.45065i	0.688409	+	0.725323i	$0.258310\pi$
$953$			44.7824i			1.45065i	−0.688409	+	0.725323i	$0.741690\pi$
$954$		0			0
$955$	−27.8092	−	16.0556i	−0.899883	−	0.519548i
$956$	25.1503	+	26.1223i	0.813418	+	0.844855i
$957$		0			0
$958$	−36.5977	+	27.5353i	−1.18242	+	0.889625i
$959$	−5.38044	+	43.6713i	−0.173743	+	1.41022i
$960$		0			0
$961$	−11.5377	−	19.9839i	−0.372184	−	0.644641i
$962$	−0.127658	−	1.04619i	−0.00411587	−	0.0337305i
$963$		0			0
$964$	37.7034	−	9.34039i	1.21434	−	0.300834i
$965$		−	82.6673i		−	2.66116i
$966$		0			0
$967$		−	13.2510i		−	0.426122i	−0.977039	−	0.213061i	$-0.931657\pi$
$967$		−	13.2510i		−	0.426122i	0.977039	−	0.213061i	$-0.0683433\pi$
$968$	−1.85294	+	2.27768i	−0.0595558	+	0.0732074i
$969$		0			0
$970$	37.2163	−	4.54123i	1.19494	−	0.145810i
$971$	2.19406	+	3.80023i	0.0704108	+	0.121955i	0.899081	−	0.437781i	$-0.144236\pi$
$971$	2.19406	+	3.80023i	0.0704108	+	0.121955i	−0.828671	+	0.559737i	$0.810902\pi$
$972$		0			0
$973$	−39.5765	+	16.7800i	−1.26877	+	0.537941i
$974$	−2.45309	−	3.26046i	−0.0786022	−	0.104472i
$975$		0			0
$976$	9.42849	−	4.97695i	0.301799	−	0.159308i
$977$	−30.7669	−	17.7633i	−0.984322	−	0.568298i	−0.0807496	−	0.996734i	$-0.525731\pi$
$977$	−30.7669	−	17.7633i	−0.984322	−	0.568298i	−0.903572	+	0.428436i	$0.859065\pi$
$978$		0			0
$979$		−	40.6515i		−	1.29923i
$980$	−47.0020	+	26.9910i	−1.50142	+	0.862196i
$981$		0			0
$982$	−21.6740	−	9.21930i	−0.691646	−	0.294200i
$983$	−6.14215	+	10.6385i	−0.195904	+	0.339316i	−0.947197	−	0.320654i	$-0.896097\pi$
$983$	−6.14215	+	10.6385i	−0.195904	+	0.339316i	0.751292	+	0.659969i	$0.229431\pi$
$984$		0			0
$985$	−1.10832	−	1.91967i	−0.0353141	−	0.0611658i
$986$	12.1388	−	9.13298i	0.386579	−	0.290853i
$987$		0			0
$988$	−4.03160	−	1.16260i	−0.128262	−	0.0369872i
$989$	3.21068	−	1.85368i	0.102094	−	0.0589437i
$990$		0			0
$991$	−26.3597	−	15.2188i	−0.837344	−	0.483441i	0.0190166	−	0.999819i	$-0.493946\pi$
$991$	−26.3597	−	15.2188i	−0.837344	−	0.483441i	−0.856360	+	0.516378i	$0.827280\pi$
$992$	−13.0787	+	9.08483i	−0.415250	+	0.288444i
$993$		0			0
$994$	0.00234704	−	2.01755i	7.44435e−5	−	0.0639928i
$995$	67.7518			2.14788
$996$		0			0
$997$	−25.7423	+	44.5869i	−0.815266	+	1.41208i	0.0938701	+	0.995584i	$0.470076\pi$
$997$	−25.7423	+	44.5869i	−0.815266	+	1.41208i	−0.909136	+	0.416498i	$0.863257\pi$
$998$	36.5845	−	4.46412i	1.15806	−	0.141309i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.2.be.a.179.3	yes	32
3.2	odd	2	inner	252.2.be.a.179.14	yes	32
4.3	odd	2	inner	252.2.be.a.179.8	yes	32
7.2	even	3	inner	252.2.be.a.107.9	yes	32
7.3	odd	6		1764.2.e.h.1079.13		16
7.4	even	3		1764.2.e.i.1079.13		16
12.11	even	2	inner	252.2.be.a.179.9	yes	32
21.2	odd	6	inner	252.2.be.a.107.8	yes	32
21.11	odd	6		1764.2.e.i.1079.4		16
21.17	even	6		1764.2.e.h.1079.4		16
28.3	even	6		1764.2.e.h.1079.3		16
28.11	odd	6		1764.2.e.i.1079.3		16
28.23	odd	6	inner	252.2.be.a.107.14	yes	32
84.11	even	6		1764.2.e.i.1079.14		16
84.23	even	6	inner	252.2.be.a.107.3	✓	32
84.59	odd	6		1764.2.e.h.1079.14		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.be.a.107.3	✓	32	84.23	even	6	inner
252.2.be.a.107.8	yes	32	21.2	odd	6	inner
252.2.be.a.107.9	yes	32	7.2	even	3	inner
252.2.be.a.107.14	yes	32	28.23	odd	6	inner
252.2.be.a.179.3	yes	32	1.1	even	1	trivial
252.2.be.a.179.8	yes	32	4.3	odd	2	inner
252.2.be.a.179.9	yes	32	12.11	even	2	inner
252.2.be.a.179.14	yes	32	3.2	odd	2	inner
1764.2.e.h.1079.3		16	28.3	even	6
1764.2.e.h.1079.4		16	21.17	even	6
1764.2.e.h.1079.13		16	7.3	odd	6
1764.2.e.h.1079.14		16	84.59	odd	6
1764.2.e.i.1079.3		16	28.11	odd	6
1764.2.e.i.1079.4		16	21.11	odd	6
1764.2.e.i.1079.13		16	7.4	even	3
1764.2.e.i.1079.14		16	84.11	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:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	252.be (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.30138 - 0.553555i) q^{2} +(1.38715 + 1.44076i) q^{4} +(3.35279 - 1.93573i) q^{5} +(1.03277 + 2.43585i) q^{7} +(-1.00767 - 2.64284i) q^{8} +O(q^{10})\)	\(q+(-1.30138 - 0.553555i) q^{2} +(1.38715 + 1.44076i) q^{4} +(3.35279 - 1.93573i) q^{5} +(1.03277 + 2.43585i) q^{7} +(-1.00767 - 2.64284i) q^{8} +(-5.43477 + 0.663164i) q^{10} +(-1.73480 + 3.00476i) q^{11} -0.296538 q^{13} +(0.00435270 - 3.74165i) q^{14} +(-0.151605 + 3.99713i) q^{16} +(1.35741 + 0.783703i) q^{17} +(6.12694 - 3.53739i) q^{19} +(7.43977 + 2.14542i) q^{20} +(3.92092 - 2.95001i) q^{22} +(-2.71768 - 4.70717i) q^{23} +(4.99413 - 8.65009i) q^{25} +(0.385907 + 0.164150i) q^{26} +(-2.07687 + 4.86689i) q^{28} +6.85309i q^{29} +(-2.43792 - 1.40753i) q^{31} +(2.40992 - 5.11784i) q^{32} +(-1.33268 - 1.77129i) q^{34} +(8.17783 + 6.16773i) q^{35} +(-1.25659 - 2.17648i) q^{37} +(-9.93158 + 1.21188i) q^{38} +(-8.49433 - 6.91032i) q^{40} -3.55418i q^{41} +0.682082i q^{43} +(-6.73558 + 1.66863i) q^{44} +(0.931053 + 7.63018i) q^{46} +(-1.18466 - 2.05189i) q^{47} +(-4.86676 + 5.03137i) q^{49} +(-11.2875 + 8.49249i) q^{50} +(-0.411344 - 0.427241i) q^{52} +(-0.540117 - 0.311837i) q^{53} +13.4324i q^{55} +(5.39688 - 5.18398i) q^{56} +(3.79356 - 8.91844i) q^{58} +(-4.42770 + 7.66901i) q^{59} +(-1.33268 - 2.30827i) q^{61} +(2.39350 + 3.18125i) q^{62} +(-5.96922 + 5.32621i) q^{64} +(-0.994229 + 0.574019i) q^{65} +(-9.19491 - 5.30868i) q^{67} +(0.753810 + 3.04283i) q^{68} +(-7.22826 - 12.5534i) q^{70} +0.539214 q^{71} +(-3.69760 + 6.40442i) q^{73} +(0.430496 + 3.52801i) q^{74} +(13.5956 + 3.92057i) q^{76} +(-9.11080 - 1.12248i) q^{77} +(5.33972 - 3.08289i) q^{79} +(7.22908 + 13.6950i) q^{80} +(-1.96743 + 4.62532i) q^{82} -6.15982 q^{83} +6.06816 q^{85} +(0.377570 - 0.887645i) q^{86} +(9.68920 + 1.55700i) q^{88} +(-10.1468 + 5.85824i) q^{89} +(-0.306256 - 0.722323i) q^{91} +(3.01207 - 10.4451i) q^{92} +(0.405852 + 3.32604i) q^{94} +(13.6949 - 23.7202i) q^{95} -6.84782 q^{97} +(9.11862 - 3.85368i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q + 16 q^{13} + 4 q^{16} - 32 q^{22} + 24 q^{25} - 44 q^{28} - 16 q^{34} + 8 q^{37} - 52 q^{40} - 24 q^{46} - 16 q^{49} - 52 q^{52} - 12 q^{58} - 16 q^{61} + 120 q^{64} + 60 q^{70} - 8 q^{73} + 72 q^{76} + 68 q^{82} - 32 q^{85} + 44 q^{88} + 60 q^{94} - 176 q^{97}+O(q^{100}) \) 32 * q + 16 * q^13 + 4 * q^16 - 32 * q^22 + 24 * q^25 - 44 * q^28 - 16 * q^34 + 8 * q^37 - 52 * q^40 - 24 * q^46 - 16 * q^49 - 52 * q^52 - 12 * q^58 - 16 * q^61 + 120 * q^64 + 60 * q^70 - 8 * q^73 + 72 * q^76 + 68 * q^82 - 32 * q^85 + 44 * q^88 + 60 * q^94 - 176 * q^97

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