LMFDB - Embedded newform 252.2.be.a.107.3

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			107.3
Character	$\chi$	$=$	252.107
Dual form			252.2.be.a.179.3

$q$-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 $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

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

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	1.00000		0.000677187i	$-0.000215555\pi$
$5$	3.35279	+	1.93573i	1.49941	+	0.865687i	0.499413	+	0.866364i	$0.333549\pi$
$6$		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	−0.999640	−	0.0268369i	$-0.991457\pi$
$11$	−1.73480	−	3.00476i	−0.523061	−	0.905969i	0.476578	−	0.879132i	$-0.341877\pi$
$12$		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	−0.326274	−	0.945275i	$-0.605793\pi$
$17$	1.35741	−	0.783703i	0.329221	−	0.190076i	0.655495	+	0.755199i	$0.272460\pi$
$18$		0			0
$19$	6.12694	+	3.53739i	1.40562	+	0.811533i	0.994961	−	0.100258i	$-0.0319668\pi$
$19$	6.12694	+	3.53739i	1.40562	+	0.811533i	0.410655	+	0.911791i	$0.365300\pi$
$20$	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	0.430215	+	0.902726i	$0.358438\pi$
$23$	−2.71768	+	4.70717i	−0.566676	+	0.981512i	−0.996892	+	0.0787860i	$0.974896\pi$
$24$		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	$-0.780467\pi$
$29$		−	6.85309i		−	1.27259i	0.771447	−	0.636293i	$-0.219533\pi$
$30$		0			0
$31$	−2.43792	+	1.40753i	−0.437863	+	0.252800i	−0.702691	−	0.711495i	$-0.748018\pi$
$31$	−2.43792	+	1.40753i	−0.437863	+	0.252800i	0.264828	+	0.964296i	$0.414685\pi$
$32$	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	−0.950636	−	0.310309i	$-0.899567\pi$
$37$	−1.25659	+	2.17648i	−0.206582	+	0.357811i	0.744053	+	0.668120i	$0.232901\pi$
$38$	−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	$0.0895173\pi$
$41$			3.55418i			0.555069i	−0.960716	+	0.277535i	$0.910483\pi$
$42$		0			0
$43$		−	0.682082i		−	0.104017i	−0.998647	−	0.0520083i	$-0.983438\pi$
$43$		−	0.682082i		−	0.104017i	0.998647	−	0.0520083i	$-0.0165622\pi$
$44$	−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	−0.939398	−	0.342829i	$-0.888615\pi$
$47$	−1.18466	+	2.05189i	−0.172800	+	0.299298i	0.766598	+	0.642128i	$0.221948\pi$
$48$		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	−0.536636	−	0.843814i	$-0.680305\pi$
$53$	−0.540117	+	0.311837i	−0.0741907	+	0.0428340i	0.462446	+	0.886648i	$0.346972\pi$
$54$		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	−0.995884	−	0.0906393i	$-0.971109\pi$
$59$	−4.42770	−	7.66901i	−0.576438	−	0.998420i	0.419446	−	0.907780i	$-0.362224\pi$
$60$		0			0
$61$	−1.33268	+	2.30827i	−0.170632	+	0.295544i	−0.938641	−	0.344895i	$-0.887914\pi$
$61$	−1.33268	+	2.30827i	−0.170632	+	0.295544i	0.768009	+	0.640439i	$0.221248\pi$
$62$	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	−0.942251	−	0.334908i	$-0.891295\pi$
$67$	−9.19491	+	5.30868i	−1.12334	+	0.648559i	−0.181086	+	0.983467i	$0.557961\pi$
$68$	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	0.564340	−	0.825542i	$-0.309131\pi$
$73$	−3.69760	−	6.40442i	−0.432771	−	0.749581i	−0.997111	+	0.0759615i	$0.975797\pi$
$74$	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	0.769343	−	0.638836i	$-0.220584\pi$
$79$	5.33972	+	3.08289i	0.600766	+	0.346852i	−0.168577	+	0.985688i	$0.553917\pi$
$80$	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	−0.145862	−	0.989305i	$-0.546595\pi$
$89$	−10.1468	−	5.85824i	−1.07556	−	0.620972i	−0.929694	+	0.368333i	$0.879929\pi$
$90$		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	−0.338984	−	0.940792i	$-0.610083\pi$
$101$	3.07801	−	1.77709i	0.306273	−	0.176827i	0.645258	+	0.763965i	$0.276750\pi$
$102$		0			0
$103$	1.81687	+	1.04897i	0.179021	+	0.103358i	0.586833	−	0.809708i	$-0.300375\pi$
$103$	1.81687	+	1.04897i	0.179021	+	0.103358i	−0.407811	+	0.913066i	$0.633708\pi$
$104$	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	0.464781	+	0.885426i	$0.346133\pi$
$107$	−5.52799	+	9.57475i	−0.534411	+	0.925626i	−0.999192	+	0.0402007i	$0.987200\pi$
$108$		0			0
$109$	−6.65949	−	11.5346i	−0.637864	−	1.10481i	−0.985901	−	0.167332i	$-0.946485\pi$
$109$	−6.65949	−	11.5346i	−0.637864	−	1.10481i	0.348037	−	0.937481i	$-0.386848\pi$
$110$	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	$0.102857\pi$
$113$			6.75101i			0.635082i	−0.948245	+	0.317541i	$0.897143\pi$
$114$		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	$0.357421\pi$
$127$			20.3153i			1.80270i	−0.433097	+	0.901348i	$0.642579\pi$
$128$	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	−0.192587	−	0.981280i	$-0.561688\pi$
$131$	8.62443	−	14.9380i	0.753520	−	1.30514i	0.946107	−	0.323855i	$-0.104979\pi$
$132$		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	0.263381	−	0.964692i	$-0.415162\pi$
$137$	14.4029	−	8.31550i	1.23052	−	0.710441i	0.967138	+	0.254251i	$0.0818290\pi$
$138$		0			0
$139$		−	16.2475i		−	1.37809i	−0.724716	−	0.689047i	$-0.758029\pi$
$139$		−	16.2475i		−	1.37809i	0.724716	−	0.689047i	$-0.241971\pi$
$140$	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	0.687062	−	0.726599i	$-0.258900\pi$
$149$	4.89898	+	2.82843i	0.401340	+	0.231714i	−0.285722	+	0.958313i	$0.592233\pi$
$150$		0			0
$151$	3.46216	−	1.99888i	0.281746	−	0.162666i	−0.352467	−	0.935824i	$-0.614657\pi$
$151$	3.46216	−	1.99888i	0.281746	−	0.162666i	0.634214	+	0.773158i	$0.281324\pi$
$152$	−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	0.997453	−	0.0713229i	$-0.0227221\pi$
$157$	5.47508	+	9.48312i	0.436959	+	0.756836i	−0.560494	+	0.828158i	$0.689389\pi$
$158$	−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	−0.430473	−	0.902604i	$-0.641653\pi$
$163$	−18.2237	−	10.5214i	−1.42739	−	0.824102i	−0.996914	+	0.0785017i	$0.974986\pi$
$164$	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	−0.0840445	−	0.996462i	$-0.526784\pi$
$173$	−13.0086	−	7.51054i	−0.989028	−	0.571016i	−0.904984	+	0.425446i	$0.860117\pi$
$174$		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	0.910144	−	0.414292i	$-0.135971\pi$
$179$	1.28820	+	2.23123i	0.0962847	+	0.166770i	−0.813859	+	0.581062i	$0.802637\pi$
$180$		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	−0.976153	−	0.217082i	$-0.930346\pi$
$191$	−4.14717	+	7.18311i	−0.300079	+	0.519751i	0.676075	+	0.736833i	$0.263680\pi$
$192$		0			0
$193$	10.6765	+	18.4922i	0.768510	+	1.33110i	0.938371	+	0.345630i	$0.112335\pi$
$193$	10.6765	+	18.4922i	0.768510	+	1.33110i	−0.169861	+	0.985468i	$0.554332\pi$
$194$	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	$0.00649288\pi$
$197$			0.572559i			0.0407932i	−0.999792	+	0.0203966i	$0.993507\pi$
$198$		0			0
$199$	15.1557	−	8.75014i	1.07436	−	0.620281i	0.144989	−	0.989433i	$-0.453685\pi$
$199$	15.1557	−	8.75014i	1.07436	−	0.620281i	0.929369	+	0.369152i	$0.120352\pi$
$200$	−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	$0.0882167\pi$
$211$			7.94873i			0.547213i	−0.961842	+	0.273607i	$0.911783\pi$
$212$	−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	$0.0125640\pi$
$223$			1.17855i			0.0789216i	−0.999221	+	0.0394608i	$0.987436\pi$
$224$	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	0.780639	−	0.624983i	$-0.214894\pi$
$227$	−2.27401	−	3.93870i	−0.150931	−	0.261421i	−0.931570	+	0.363562i	$0.881561\pi$
$228$		0			0
$229$	−8.06436	+	13.9679i	−0.532908	+	0.923023i	0.466354	+	0.884598i	$0.345567\pi$
$229$	−8.06436	+	13.9679i	−0.532908	+	0.923023i	−0.999261	+	0.0384248i	$0.987766\pi$
$230$	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	0.246434	−	0.969160i	$-0.420741\pi$
$233$	−7.16914	−	4.13910i	−0.469666	−	0.271162i	−0.716100	+	0.697998i	$0.754074\pi$
$234$		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	0.988439	+	0.151620i	$0.0484490\pi$
$241$	9.71078	+	16.8196i	0.625526	+	1.08344i	−0.362913	+	0.931823i	$0.618218\pi$
$242$	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	0.693291	−	0.720658i	$-0.256160\pi$
$257$	6.66624	+	3.84875i	0.415829	+	0.240079i	−0.277462	+	0.960736i	$0.589493\pi$
$258$		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	0.668360	−	0.743838i	$-0.266997\pi$
$263$	−5.02740	−	8.70772i	−0.310003	−	0.536941i	−0.978363	+	0.206897i	$0.933663\pi$
$264$		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	0.484376	−	0.874860i	$-0.339047\pi$
$269$	24.3429	−	14.0544i	1.48421	−	0.856912i	0.999839	+	0.0179481i	$0.00571336\pi$
$270$		0			0
$271$	21.9127	+	12.6513i	1.33110	+	0.768511i	0.985468	−	0.169859i	$-0.0543313\pi$
$271$	21.9127	+	12.6513i	1.33110	+	0.768511i	0.345632	+	0.938370i	$0.387665\pi$
$272$	−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	0.825541	−	0.564343i	$-0.190870\pi$
$277$	−1.26430	−	2.18984i	−0.0759647	−	0.131575i	−0.901505	+	0.432768i	$0.857537\pi$
$278$	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	$0.0767841\pi$
$281$			8.00911i			0.477784i	−0.971046	+	0.238892i	$0.923216\pi$
$282$		0			0
$283$	6.12694	−	3.53739i	0.364209	−	0.210276i	−0.306717	−	0.951801i	$-0.599230\pi$
$283$	6.12694	−	3.53739i	0.364209	−	0.210276i	0.670925	+	0.741525i	$0.265897\pi$
$284$	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	$0.197982\pi$
$293$			19.9465i			1.16529i	−0.812728	+	0.582643i	$0.802018\pi$
$294$		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	$-0.903845\pi$
$307$		−	10.4255i		−	0.595014i	0.954720	−	0.297507i	$-0.0961552\pi$
$308$	−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	0.984584	+	0.174914i	$0.0559648\pi$
$311$	11.3530	+	19.6640i	0.643772	+	1.11505i	−0.340812	+	0.940132i	$0.610702\pi$
$312$		0			0
$313$	11.1917	−	19.3846i	0.632594	−	1.09568i	−0.354426	−	0.935084i	$-0.615324\pi$
$313$	11.1917	−	19.3846i	0.632594	−	1.09568i	0.987019	−	0.160601i	$-0.0513431\pi$
$314$	−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	0.996073	−	0.0885318i	$-0.0282175\pi$
$317$	25.2368	+	14.5705i	1.41744	+	0.818359i	0.421366	+	0.906891i	$0.361551\pi$
$318$		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	0.900007	−	0.435876i	$-0.143561\pi$
$331$	17.6936	+	10.2154i	0.972531	+	0.561491i	0.0725241	+	0.997367i	$0.476895\pi$
$332$	−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	0.588584	−	0.808436i	$-0.299686\pi$
$347$	−7.55986	−	13.0941i	−0.405834	−	0.702926i	−0.994418	+	0.105510i	$0.966352\pi$
$348$		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	−0.724530	−	0.689243i	$-0.757943\pi$
$353$	−9.20426	+	5.31408i	−0.489893	+	0.282840i	0.234637	+	0.972083i	$0.424610\pi$
$354$		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	−0.826573	−	0.562829i	$-0.809713\pi$
$359$	1.40470	−	2.43302i	0.0741374	−	0.128410i	0.900711	+	0.434419i	$0.143046\pi$
$360$		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	−0.00830274	−	0.999966i	$-0.502643\pi$
$367$	16.3515	−	9.44054i	0.853541	−	0.492792i	0.861844	+	0.507173i	$0.169310\pi$
$368$	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	0.00713304	−	0.999975i	$-0.497729\pi$
$373$	16.7942	−	29.0884i	0.869570	−	1.50614i	0.862437	−	0.506165i	$-0.168937\pi$
$374$	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	$0.0623281\pi$
$379$			7.57538i			0.389121i	−0.980890	+	0.194561i	$0.937672\pi$
$380$	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	−0.145308	+	0.989387i	$0.546417\pi$
$383$	−18.1904	+	31.5068i	−0.929488	+	1.60992i	−0.784180	+	0.620533i	$0.786916\pi$
$384$		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	−0.423088	−	0.906088i	$-0.639054\pi$
$389$	2.95971	−	1.70879i	0.150063	−	0.0866391i	0.573152	+	0.819449i	$0.305721\pi$
$390$		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	−0.999990	−	0.00443461i	$-0.998588\pi$
$397$	−9.88581	+	17.1227i	−0.496155	+	0.859365i	0.503836	+	0.863800i	$0.331922\pi$
$398$	−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	0.580110	−	0.814538i	$-0.303010\pi$
$401$	3.29921	+	1.90480i	0.164755	+	0.0951211i	−0.415356	+	0.909659i	$0.636343\pi$
$402$		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	−0.957231	−	0.289324i	$-0.906569\pi$
$409$	−14.7467	−	25.5420i	−0.729178	−	1.26297i	0.228054	−	0.973649i	$-0.426764\pi$
$410$	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	0.511314	−	0.859394i	$-0.329159\pi$
$431$	−10.1436	−	17.5692i	−0.488600	−	0.846281i	−0.999914	+	0.0131135i	$0.995826\pi$
$432$		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	−0.0823105	−	0.996607i	$-0.526230\pi$
$439$	−20.6706	−	11.9342i	−0.986553	−	0.569586i	−0.904242	+	0.427020i	$0.859563\pi$
$440$	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	−0.928471	−	0.371406i	$-0.878876\pi$
$443$	−3.00114	+	5.19813i	−0.142589	+	0.246971i	0.785882	+	0.618376i	$0.212209\pi$
$444$		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	$0.0370600\pi$
$449$			4.92296i			0.232329i	−0.993230	+	0.116165i	$0.962940\pi$
$450$		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	−0.371272	−	0.928524i	$-0.621078\pi$
$457$	13.2218	−	22.9008i	0.618489	−	1.07125i	0.989762	−	0.142731i	$-0.0455882\pi$
$458$	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	$0.0666147\pi$
$461$			8.92124i			0.415504i	−0.978182	+	0.207752i	$0.933385\pi$
$462$		0			0
$463$		−	14.3310i		−	0.666020i	−0.942923	−	0.333010i	$-0.891936\pi$
$463$		−	14.3310i		−	0.666020i	0.942923	−	0.333010i	$-0.108064\pi$
$464$	−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	−0.505637	−	0.862746i	$-0.668742\pi$
$467$	10.6828	−	18.5032i	0.494342	−	0.856225i	0.999979	+	0.00652102i	$0.00207572\pi$
$468$		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	0.952560	+	0.304351i	$0.0984395\pi$
$479$	16.1925	+	28.0463i	0.739856	+	1.28147i	−0.212704	+	0.977117i	$0.568227\pi$
$480$		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	−0.442319	−	0.896858i	$-0.645844\pi$
$487$	2.49862	−	1.44258i	0.113223	−	0.0653695i	0.555542	+	0.831488i	$0.312511\pi$
$488$	−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	−0.0990552	−	0.995082i	$-0.531582\pi$
$499$	−22.5695	−	13.0305i	−1.01035	−	0.583325i	−0.911294	+	0.411757i	$0.864915\pi$
$500$	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	0.771474	−	0.636260i	$-0.219520\pi$
$509$	13.6764	+	7.89605i	0.606194	+	0.349986i	−0.165280	+	0.986247i	$0.552853\pi$
$510$		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	−0.433821	−	0.900999i	$-0.642835\pi$
$521$	2.95718	−	1.70733i	0.129557	−	0.0747995i	0.563378	+	0.826200i	$0.309502\pi$
$522$		0			0
$523$	−5.72733	−	3.30668i	−0.250439	−	0.144591i	0.369526	−	0.929220i	$-0.379520\pi$
$523$	−5.72733	−	3.30668i	−0.250439	−	0.144591i	−0.619965	+	0.784629i	$0.712853\pi$
$524$	−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	−0.949135	−	0.314871i	$-0.898039\pi$
$541$	−4.69564	+	8.13308i	−0.201881	+	0.349669i	0.747253	+	0.664539i	$0.231372\pi$
$542$	−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	$-0.897505\pi$
$547$		−	14.8029i		−	0.632924i	0.948605	−	0.316462i	$-0.102495\pi$
$548$	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	−0.564585	−	0.825375i	$-0.690964\pi$
$557$	−3.11722	+	1.79973i	−0.132081	+	0.0762569i	0.432504	+	0.901632i	$0.357630\pi$
$558$		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	0.590946	−	0.806711i	$-0.298754\pi$
$563$	−9.56600	−	16.5688i	−0.403159	−	0.698292i	−0.994105	+	0.108419i	$0.965421\pi$
$564$		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	−0.206766	−	0.978390i	$-0.566294\pi$
$569$	−27.6097	−	15.9405i	−1.15746	−	0.668260i	−0.950694	+	0.310131i	$0.899627\pi$
$570$		0			0
$571$	19.6409	−	11.3397i	0.821947	−	0.474551i	−0.0291406	−	0.999575i	$-0.509277\pi$
$571$	19.6409	−	11.3397i	0.821947	−	0.474551i	0.851087	+	0.525024i	$0.175944\pi$
$572$	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	0.880036	−	0.474907i	$-0.157518\pi$
$577$	0.690279	+	1.19560i	0.0287367	+	0.0497734i	−0.851299	+	0.524680i	$0.824185\pi$
$578$	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	0.0379417	−	0.999280i	$-0.487920\pi$
$593$	−19.6880	−	11.3669i	−0.808489	−	0.466781i	−0.846431	+	0.532498i	$0.821253\pi$
$594$		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	0.701717	−	0.712456i	$-0.252417\pi$
$599$	−6.51380	−	11.2822i	−0.266147	−	0.460979i	−0.967863	+	0.251477i	$0.919084\pi$
$600$		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	0.650632	−	0.759393i	$-0.274504\pi$
$607$	7.84192	+	4.52754i	0.318294	+	0.183767i	−0.332338	+	0.943160i	$0.607837\pi$
$608$	−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	0.724404	−	0.689376i	$-0.242115\pi$
$613$	−5.81374	−	10.0697i	−0.234815	−	0.406711i	−0.959219	+	0.282664i	$0.908782\pi$
$614$	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	$0.120588\pi$
$617$			18.3734i			0.739685i	−0.929094	+	0.369843i	$0.879412\pi$
$618$		0			0
$619$	19.6409	−	11.3397i	0.789435	−	0.455781i	−0.0503285	−	0.998733i	$-0.516027\pi$
$619$	19.6409	−	11.3397i	0.789435	−	0.455781i	0.839764	+	0.542952i	$0.182694\pi$
$620$	−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	$0.184995\pi$
$631$			27.5820i			1.09802i	−0.835815	+	0.549011i	$0.815005\pi$
$632$	−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	−0.903786	−	0.427985i	$-0.859224\pi$
$641$	−24.9390	+	14.3986i	−0.985032	+	0.568709i	−0.0812468	+	0.996694i	$0.525890\pi$
$642$		0			0
$643$		−	38.1698i		−	1.50527i	−0.658438	−	0.752635i	$-0.728783\pi$
$643$		−	38.1698i		−	1.50527i	0.658438	−	0.752635i	$-0.271217\pi$
$644$	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	−0.827407	−	0.561603i	$-0.810185\pi$
$647$	−22.8942	−	39.6540i	−0.900066	−	1.55896i	−0.0726586	−	0.997357i	$-0.523148\pi$
$648$		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	0.598522	−	0.801106i	$-0.295755\pi$
$653$	5.21310	+	3.00979i	0.204004	+	0.117782i	−0.394518	+	0.918888i	$0.629088\pi$
$654$		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	0.990444	−	0.137912i	$-0.0440391\pi$
$661$	9.66145	+	16.7341i	0.375787	+	0.650882i	−0.614658	+	0.788794i	$0.710706\pi$
$662$	−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	0.129861	−	0.991532i	$-0.458547\pi$
$677$	−17.2742	−	9.97325i	−0.663900	−	0.383303i	−0.793761	+	0.608229i	$0.791880\pi$
$678$		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	0.999619	+	0.0275921i	$0.00878394\pi$
$683$	13.6866	+	23.7060i	0.523705	+	0.907084i	−0.475914	+	0.879492i	$0.657883\pi$
$684$		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	−0.992756	−	0.120151i	$-0.961662\pi$
$691$	−41.8799	−	24.1794i	−1.59319	−	0.919827i	−0.600431	−	0.799676i	$-0.705004\pi$
$692$	−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	$0.104316\pi$
$701$			17.0447i			0.643768i	−0.946779	+	0.321884i	$0.895684\pi$
$702$		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	−0.503492	−	0.864000i	$-0.667952\pi$
$709$	13.2203	−	22.8983i	0.496500	−	0.859964i	0.999992	+	0.00403654i	$0.00128488\pi$
$710$	−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	−0.335526	−	0.942031i	$-0.608914\pi$
$719$	17.3772	−	30.0982i	0.648060	−	1.12247i	0.983586	−	0.180441i	$-0.0577526\pi$
$720$		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	$0.140117\pi$
$727$			22.9785i			0.852226i	−0.904670	+	0.426113i	$0.859883\pi$
$728$	−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	−0.606281	−	0.795251i	$-0.707339\pi$
$733$	10.4388	−	18.0806i	0.385567	−	0.667821i	0.991848	+	0.127429i	$0.0406726\pi$
$734$	−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	−0.385986	−	0.922504i	$-0.626139\pi$
$739$	5.97877	−	3.45185i	0.219933	−	0.126978i	0.605919	+	0.795526i	$0.292806\pi$
$740$	−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	0.982420	+	0.186686i	$0.0597745\pi$
$751$	44.8145	+	25.8737i	1.63530	+	0.944143i	0.652884	+	0.757458i	$0.273559\pi$
$752$	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	0.999914	+	0.0131110i	$0.00417347\pi$
$761$	41.6890	+	24.0692i	1.51123	+	0.872506i	0.511311	+	0.859395i	$0.329160\pi$
$762$		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	0.279663	−	0.960098i	$-0.409777\pi$
$773$	34.7804	−	20.0805i	1.25096	−	0.722245i	0.971301	+	0.237853i	$0.0764438\pi$
$774$		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	0.153789	−	0.988104i	$-0.450852\pi$
$787$	30.4775	−	17.5962i	1.08641	−	0.627237i	0.932617	+	0.360867i	$0.117519\pi$
$788$	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	$-0.891936\pi$
$797$		−	18.8026i		−	0.666021i	0.942923	−	0.333010i	$-0.108064\pi$
$798$		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	−0.681658	+	0.731671i	$0.738741\pi$
$809$	−47.1053	+	27.1962i	−1.65613	+	0.956169i	−0.974475	+	0.224498i	$0.927926\pi$
$810$		0			0
$811$		−	1.91646i		−	0.0672961i	−0.999434	−	0.0336480i	$-0.989287\pi$
$811$		−	1.91646i		−	0.0672961i	0.999434	−	0.0336480i	$-0.0107125\pi$
$812$	−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	0.831555	−	0.555443i	$-0.187451\pi$
$821$	21.9570	+	12.6769i	0.766305	+	0.442426i	−0.0652500	+	0.997869i	$0.520785\pi$
$822$		0			0
$823$	−4.56151	+	2.63359i	−0.159004	+	0.0918011i	−0.577391	−	0.816468i	$-0.695929\pi$
$823$	−4.56151	+	2.63359i	−0.159004	+	0.0918011i	0.418387	+	0.908269i	$0.362596\pi$
$824$	−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	0.777615	−	0.628741i	$-0.216429\pi$
$829$	−4.48291	−	7.76462i	−0.155698	−	0.269677i	−0.933313	+	0.359064i	$0.883096\pi$
$830$	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	−0.315595	−	0.948894i	$-0.602204\pi$
$857$	10.1985	−	5.88810i	0.348374	−	0.201134i	0.663969	+	0.747760i	$0.268871\pi$
$858$		0			0
$859$	28.9031	+	16.6872i	0.986161	+	0.569360i	0.904125	−	0.427269i	$-0.140524\pi$
$859$	28.9031	+	16.6872i	0.986161	+	0.569360i	0.0820365	+	0.996629i	$0.473858\pi$
$860$	−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	−0.996248	−	0.0865468i	$-0.972417\pi$
$863$	−12.4315	+	21.5319i	−0.423172	+	0.732956i	0.573076	+	0.819503i	$0.305750\pi$
$864$		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	0.154725	+	0.987958i	$0.450551\pi$
$877$	−23.0468	+	39.9181i	−0.778234	+	1.34794i	−0.932959	+	0.359983i	$0.882783\pi$
$878$	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	$-0.913159\pi$
$881$		−	15.9952i		−	0.538893i	0.963015	−	0.269446i	$-0.0868407\pi$
$882$		0			0
$883$		−	42.9597i		−	1.44571i	−0.691001	−	0.722854i	$-0.742830\pi$
$883$		−	42.9597i		−	1.44571i	0.691001	−	0.722854i	$-0.257170\pi$
$884$	−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	−0.982071	−	0.188510i	$-0.939634\pi$
$887$	−9.76216	+	16.9086i	−0.327781	+	0.567734i	0.654290	+	0.756244i	$0.272968\pi$
$888$		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	0.00344687	−	0.999994i	$-0.498903\pi$
$907$	26.2372	−	15.1480i	0.871191	−	0.502982i	0.867744	+	0.497012i	$0.165569\pi$
$908$	−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	0.439482	−	0.898252i	$-0.355162\pi$
$919$	−3.59797	−	2.07729i	−0.118686	−	0.0685235i	−0.558168	+	0.829728i	$0.688495\pi$
$920$	−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	0.967312	−	0.253589i	$-0.0816112\pi$
$929$	37.5310	+	21.6686i	1.23135	+	0.710922i	0.264041	+	0.964511i	$0.414945\pi$
$930$		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	−0.134494	−	0.990914i	$-0.542941\pi$
$941$	20.1360	−	11.6255i	0.656416	−	0.378982i	0.790910	+	0.611932i	$0.209608\pi$
$942$		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	0.108272	+	0.994121i	$0.465468\pi$
$947$	−24.8279	+	43.0032i	−0.806798	+	1.39742i	−0.915070	+	0.403294i	$0.867865\pi$
$948$		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	$-0.741690\pi$
$953$		−	44.7824i		−	1.45065i	0.688409	−	0.725323i	$-0.258310\pi$
$954$		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	$0.0683433\pi$
$967$			13.2510i			0.426122i	−0.977039	+	0.213061i	$0.931657\pi$
$968$	−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	−0.828671	−	0.559737i	$-0.810902\pi$
$971$	2.19406	−	3.80023i	0.0704108	−	0.121955i	0.899081	+	0.437781i	$0.144236\pi$
$972$		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	−0.903572	−	0.428436i	$-0.859065\pi$
$977$	−30.7669	+	17.7633i	−0.984322	+	0.568298i	−0.0807496	+	0.996734i	$0.525731\pi$
$978$		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	0.751292	−	0.659969i	$-0.229431\pi$
$983$	−6.14215	−	10.6385i	−0.195904	−	0.339316i	−0.947197	+	0.320654i	$0.896097\pi$
$984$		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	−0.856360	−	0.516378i	$-0.827280\pi$
$991$	−26.3597	+	15.2188i	−0.837344	+	0.483441i	0.0190166	+	0.999819i	$0.493946\pi$
$992$	−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	−0.909136	−	0.416498i	$-0.863257\pi$
$997$	−25.7423	−	44.5869i	−0.815266	−	1.41208i	0.0938701	−	0.995584i	$-0.470076\pi$
$998$	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.107.3	✓	32
3.2	odd	2	inner	252.2.be.a.107.14	yes	32
4.3	odd	2	inner	252.2.be.a.107.8	yes	32
7.2	even	3		1764.2.e.i.1079.14		16
7.4	even	3	inner	252.2.be.a.179.9	yes	32
7.5	odd	6		1764.2.e.h.1079.14		16
12.11	even	2	inner	252.2.be.a.107.9	yes	32
21.2	odd	6		1764.2.e.i.1079.3		16
21.5	even	6		1764.2.e.h.1079.3		16
21.11	odd	6	inner	252.2.be.a.179.8	yes	32
28.11	odd	6	inner	252.2.be.a.179.14	yes	32
28.19	even	6		1764.2.e.h.1079.4		16
28.23	odd	6		1764.2.e.i.1079.4		16
84.11	even	6	inner	252.2.be.a.179.3	yes	32
84.23	even	6		1764.2.e.i.1079.13		16
84.47	odd	6		1764.2.e.h.1079.13		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.be.a.107.3	✓	32	1.1	even	1	trivial
252.2.be.a.107.8	yes	32	4.3	odd	2	inner
252.2.be.a.107.9	yes	32	12.11	even	2	inner
252.2.be.a.107.14	yes	32	3.2	odd	2	inner
252.2.be.a.179.3	yes	32	84.11	even	6	inner
252.2.be.a.179.8	yes	32	21.11	odd	6	inner
252.2.be.a.179.9	yes	32	7.4	even	3	inner
252.2.be.a.179.14	yes	32	28.11	odd	6	inner
1764.2.e.h.1079.3		16	21.5	even	6
1764.2.e.h.1079.4		16	28.19	even	6
1764.2.e.h.1079.13		16	84.47	odd	6
1764.2.e.h.1079.14		16	7.5	odd	6
1764.2.e.i.1079.3		16	21.2	odd	6
1764.2.e.i.1079.4		16	28.23	odd	6
1764.2.e.i.1079.13		16	84.23	even	6
1764.2.e.i.1079.14		16	7.2	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:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more