LMFDB - Embedded newform 252.2.be.a.179.8

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			179.8
Character	$\chi$	$=$	252.179
Dual form			252.2.be.a.107.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.171295 + 1.40380i) q^{2} +(-1.94132 - 0.480929i) q^{4} +(3.35279 - 1.93573i) q^{5} +(-1.03277 - 2.43585i) q^{7} +(1.00767 - 2.64284i) q^{8} +O(q^{10})$	\(q+(-0.171295 + 1.40380i) q^{2} +(-1.94132 - 0.480929i) q^{4} +(3.35279 - 1.93573i) q^{5} +(-1.03277 - 2.43585i) q^{7} +(1.00767 - 2.64284i) q^{8} +(2.14307 + 5.03823i) q^{10} +(1.73480 - 3.00476i) q^{11} -0.296538 q^{13} +(3.59636 - 1.03256i) q^{14} +(3.53741 + 1.86727i) q^{16} +(1.35741 + 0.783703i) q^{17} +(-6.12694 + 3.53739i) q^{19} +(-7.43977 + 2.14542i) q^{20} +(3.92092 + 2.95001i) q^{22} +(2.71768 + 4.70717i) q^{23} +(4.99413 - 8.65009i) q^{25} +(0.0507955 - 0.416280i) q^{26} +(0.833467 + 5.22545i) q^{28} +6.85309i q^{29} +(2.43792 + 1.40753i) q^{31} +(-3.22722 + 4.64597i) q^{32} +(-1.33268 + 1.77129i) q^{34} +(-8.17783 - 6.16773i) q^{35} +(-1.25659 - 2.17648i) q^{37} +(-3.91628 - 9.20694i) q^{38} +(-1.73734 - 10.8115i) q^{40} -3.55418i q^{41} -0.682082i q^{43} +(-4.81287 + 4.99887i) q^{44} +(-7.07345 + 3.00877i) q^{46} +(1.18466 + 2.05189i) q^{47} +(-4.86676 + 5.03137i) q^{49} +(11.2875 + 8.49249i) q^{50} +(0.575674 + 0.142614i) q^{52} +(-0.540117 - 0.311837i) q^{53} -13.4324i q^{55} +(-7.47826 + 0.274927i) q^{56} +(-9.62037 - 1.17390i) q^{58} +(4.42770 - 7.66901i) q^{59} +(-1.33268 - 2.30827i) q^{61} +(-2.39350 + 3.18125i) q^{62} +(-5.96922 - 5.32621i) q^{64} +(-0.994229 + 0.574019i) q^{65} +(9.19491 + 5.30868i) q^{67} +(-2.25826 - 2.17423i) q^{68} +(10.0591 - 10.4236i) q^{70} -0.539214 q^{71} +(-3.69760 + 6.40442i) q^{73} +(3.27059 - 1.39118i) q^{74} +(13.5956 - 3.92057i) q^{76} +(-9.11080 - 1.12248i) q^{77} +(-5.33972 + 3.08289i) q^{79} +(15.4747 - 0.586932i) q^{80} +(4.98936 + 0.608814i) q^{82} +6.15982 q^{83} +6.06816 q^{85} +(0.957508 + 0.116837i) q^{86} +(-6.19300 - 7.61259i) q^{88} +(-10.1468 + 5.85824i) q^{89} +(0.306256 + 0.722323i) q^{91} +(-3.01207 - 10.4451i) q^{92} +(-3.08337 + 1.31154i) q^{94} +(-13.6949 + 23.7202i) q^{95} -6.84782 q^{97} +(-6.22939 - 7.69381i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.171295	+	1.40380i	−0.121124	+	0.992637i
$2$	−0.171295	+	1.40380i	−0.121124	+	0.992637i
$3$		0			0
$3$		0			0
$4$	−1.94132	−	0.480929i	−0.970658	−	0.240464i
$5$	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
$10$	2.14307	+	5.03823i	0.677698	+	1.59323i
$11$	1.73480	−	3.00476i	0.523061	−	0.905969i	−0.476578	−	0.879132i	$-0.658123\pi$
$11$	1.73480	−	3.00476i	0.523061	−	0.905969i	0.999640	−	0.0268369i	$-0.00854348\pi$
$12$		0			0
$13$	−0.296538			−0.0822448			−0.0411224	−	0.999154i	$-0.513093\pi$
$13$	−0.296538			−0.0822448			−0.0411224	+	0.999154i	$0.513093\pi$
$14$	3.59636	−	1.03256i	0.961168	−	0.275963i
$15$		0			0
$16$	3.53741	+	1.86727i	0.884354	+	0.466817i
$17$	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	−0.994961	−	0.100258i	$-0.968033\pi$
$19$	−6.12694	+	3.53739i	−1.40562	+	0.811533i	−0.410655	+	0.911791i	$0.634700\pi$
$20$	−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	$0.0251044\pi$
$23$	2.71768	+	4.70717i	0.566676	+	0.981512i	−0.430215	+	0.902726i	$0.641562\pi$
$24$		0			0
$25$	4.99413	−	8.65009i	0.998827	−	1.73002i
$26$	0.0507955	−	0.416280i	0.00996182	−	0.0816393i
$27$		0			0
$28$	0.833467	+	5.22545i	0.157510	+	0.987517i
$29$			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	0.702691	−	0.711495i	$-0.251982\pi$
$31$	2.43792	+	1.40753i	0.437863	+	0.252800i	−0.264828	+	0.964296i	$0.585315\pi$
$32$	−3.22722	+	4.64597i	−0.570497	+	0.821300i
$33$		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	$0.899567\pi$
$38$	−3.91628	−	9.20694i	−0.635304	−	1.49356i
$39$		0			0
$40$	−1.73734	−	10.8115i	−0.274698	−	1.70944i
$41$		−	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	$-0.983438\pi$
$43$		−	0.682082i		−	0.104017i	0.998647	−	0.0520083i	$-0.0165622\pi$
$44$	−4.81287	+	4.99887i	−0.725567	+	0.753608i
$45$		0			0
$46$	−7.07345	+	3.00877i	−1.04292	+	0.443620i
$47$	1.18466	+	2.05189i	0.172800	+	0.299298i	0.939398	−	0.342829i	$-0.111385\pi$
$47$	1.18466	+	2.05189i	0.172800	+	0.299298i	−0.766598	+	0.642128i	$0.778052\pi$
$48$		0			0
$49$	−4.86676	+	5.03137i	−0.695251	+	0.718767i
$50$	11.2875	+	8.49249i	1.59630	+	1.20102i
$51$		0			0
$52$	0.575674	+	0.142614i	0.0798316	+	0.0197770i
$53$	−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
$56$	−7.47826	+	0.274927i	−0.999325	+	0.0367386i
$57$		0			0
$58$	−9.62037	−	1.17390i	−1.26322	−	0.154141i
$59$	4.42770	−	7.66901i	0.576438	−	0.998420i	−0.419446	−	0.907780i	$-0.637776\pi$
$59$	4.42770	−	7.66901i	0.576438	−	0.998420i	0.995884	−	0.0906393i	$-0.0288910\pi$
$60$		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	0.942251	−	0.334908i	$-0.108705\pi$
$67$	9.19491	+	5.30868i	1.12334	+	0.648559i	0.181086	+	0.983467i	$0.442039\pi$
$68$	−2.25826	−	2.17423i	−0.273854	−	0.263664i
$69$		0			0
$70$	10.0591	−	10.4236i	1.20229	−	1.24585i
$71$	−0.539214			−0.0639929			−0.0319964	−	0.999488i	$-0.510187\pi$
$71$	−0.539214			−0.0639929			−0.0319964	+	0.999488i	$0.510187\pi$
$72$		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	$0.309131\pi$
$74$	3.27059	−	1.39118i	0.380199	−	0.161722i
$75$		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	$-0.779416\pi$
$79$	−5.33972	+	3.08289i	−0.600766	+	0.346852i	0.168577	+	0.985688i	$0.446083\pi$
$80$	15.4747	−	0.586932i	1.73013	−	0.0656210i
$81$		0			0
$82$	4.98936	+	0.608814i	0.550983	+	0.0672322i
$83$	6.15982			0.676128			0.338064	−	0.941123i	$-0.390228\pi$
$83$	6.15982			0.676128			0.338064	+	0.941123i	$0.390228\pi$
$84$		0			0
$85$	6.06816			0.658184
$86$	0.957508	+	0.116837i	0.103251	+	0.0125989i
$87$		0			0
$88$	−6.19300	−	7.61259i	−0.660176	−	0.811505i
$89$	−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
$94$	−3.08337	+	1.31154i	−0.318025	+	0.135275i
$95$	−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	$0.613019\pi$
$98$	−6.22939	−	7.69381i	−0.629263	−	0.777192i
$99$		0			0
$100$	−13.8553	+	14.3907i	−1.38553	+	1.43907i
$101$	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	−0.586833	−	0.809708i	$-0.699625\pi$
$103$	−1.81687	+	1.04897i	−0.179021	+	0.103358i	0.407811	+	0.913066i	$0.366292\pi$
$104$	−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	$0.0127997\pi$
$107$	5.52799	+	9.57475i	0.534411	+	0.925626i	−0.464781	+	0.885426i	$0.653867\pi$
$108$		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	$0.946485\pi$
$110$	18.8565	+	2.30091i	1.79789	+	0.219383i
$111$		0			0
$112$	0.895048	−	10.5451i	0.0845741	−	0.996417i
$113$		−	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
$116$	3.29585	−	13.3040i	0.306012	−	1.23525i
$117$		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
$122$	3.46864	−	1.47542i	0.314035	−	0.133579i
$123$		0			0
$124$	−4.05585	−	3.90493i	−0.364226	−	0.350673i
$125$		−	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	$0.642579\pi$
$128$	8.49943	−	7.46724i	0.751251	−	0.660017i
$129$		0			0
$130$	−0.635501	−	1.49403i	−0.0557371	−	0.131035i
$131$	−8.62443	−	14.9380i	−0.753520	−	1.30514i	−0.946107	−	0.323855i	$-0.895021\pi$
$131$	−8.62443	−	14.9380i	−0.753520	−	1.30514i	0.192587	−	0.981280i	$-0.438312\pi$
$132$		0			0
$133$	14.9443	+	11.2710i	1.29584	+	0.977320i
$134$	−9.02738	+	11.9985i	−0.779847	+	1.03651i
$135$		0			0
$136$	3.43902	−	2.79771i	0.294894	−	0.239902i
$137$	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	$-0.758029\pi$
$139$		−	16.2475i		−	1.37809i	0.724716	−	0.689047i	$-0.241971\pi$
$140$	12.9095	+	15.9065i	1.09105	+	1.34434i
$141$		0			0
$142$	0.0923647	−	0.756949i	0.00775107	−	0.0635217i
$143$	−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	0.352467	−	0.935824i	$-0.385343\pi$
$151$	−3.46216	−	1.99888i	−0.281746	−	0.162666i	−0.634214	+	0.773158i	$0.718676\pi$
$152$	3.17485	+	19.7570i	0.257514	+	1.60251i
$153$		0			0
$154$	3.13638	−	12.5975i	0.252736	−	1.01513i
$155$	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	$0.0227221\pi$
$158$	−3.41310	−	8.02400i	−0.271531	−	0.638355i
$159$		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	$-0.358347\pi$
$163$	18.2237	−	10.5214i	1.42739	−	0.824102i	0.996914	+	0.0785017i	$0.0250136\pi$
$164$	−1.70931	+	6.89978i	−0.133474	+	0.538782i
$165$		0			0
$166$	−1.05515	+	8.64716i	−0.0818953	+	0.671150i
$167$	−8.39346			−0.649505			−0.324753	−	0.945799i	$-0.605281\pi$
$167$	−8.39346			−0.649505			−0.324753	+	0.945799i	$0.605281\pi$
$168$		0			0
$169$	−12.9121			−0.993236
$170$	−1.03945	+	8.51849i	−0.0797219	+	0.653338i
$171$		0			0
$172$	−0.328033	+	1.32414i	−0.0250123	+	0.100965i
$173$	−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
$178$	−6.48571	−	15.2475i	−0.486125	−	1.14285i
$179$	−1.28820	+	2.23123i	−0.0962847	+	0.166770i	−0.910144	−	0.414292i	$-0.864029\pi$
$179$	−1.28820	+	2.23123i	−0.0962847	+	0.166770i	0.813859	+	0.581062i	$0.197363\pi$
$180$		0			0
$181$	−22.3412			−1.66061			−0.830305	−	0.557309i	$-0.811834\pi$
$181$	−22.3412			−1.66061			−0.830305	+	0.557309i	$0.811834\pi$
$182$	−1.06646	+	0.306193i	−0.0790511	+	0.0226965i
$183$		0			0
$184$	15.1788	−	2.43915i	1.11900	−	0.179817i
$185$	−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	$-0.0696538\pi$
$191$	4.14717	+	7.18311i	0.300079	+	0.519751i	−0.676075	+	0.736833i	$0.736320\pi$
$192$		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	$-0.112335\pi$
$194$	1.17300	−	9.61298i	0.0842164	−	0.690172i
$195$		0			0
$196$	11.8676	−	7.42691i	0.847689	−	0.530493i
$197$		−	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	−0.144989	−	0.989433i	$-0.546315\pi$
$199$	−15.1557	−	8.75014i	−1.07436	−	0.620281i	−0.929369	+	0.369152i	$0.879648\pi$
$200$	−17.8284	−	21.9151i	−1.26066	−	1.54963i
$201$		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
$206$	−1.16132	−	2.73021i	−0.0809133	−	0.190223i
$207$		0			0
$208$	−1.04898	−	0.553716i	−0.0727335	−	0.0383933i
$209$			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	$0.911783\pi$
$212$	0.898566	+	0.865131i	0.0617138	+	0.0594174i
$213$		0			0
$214$	−14.3880	+	6.12008i	−0.983541	+	0.418360i
$215$	−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
$220$	−6.46004	+	26.0766i	−0.435536	+	1.75808i
$221$	−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	$0.987436\pi$
$224$	14.6499	+	3.06279i	0.978837	+	0.204641i
$225$		0			0
$226$	9.47708	+	1.15642i	0.630406	+	0.0769236i
$227$	2.27401	−	3.93870i	0.150931	−	0.261421i	−0.780639	−	0.624983i	$-0.785106\pi$
$227$	2.27401	−	3.93870i	0.150931	−	0.261421i	0.931570	+	0.363562i	$0.118439\pi$
$228$		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
$236$	−12.2838	+	12.7586i	−0.799608	+	0.830511i
$237$		0			0
$238$	5.69097	+	1.41687i	0.368891	+	0.0918421i
$239$	−18.1308			−1.17279			−0.586393	−	0.810027i	$-0.699453\pi$
$239$	−18.1308			−1.17279			−0.586393	+	0.810027i	$0.699453\pi$
$240$		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	$-0.0484490\pi$
$242$	1.35096	−	0.574645i	0.0868429	−	0.0369396i
$243$		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
$248$	6.17650	−	5.02471i	0.392208	−	0.319069i
$249$		0			0
$250$	27.1101	+	3.30804i	1.71459	+	0.209219i
$251$	13.8654			0.875175			0.437587	−	0.899176i	$-0.355833\pi$
$251$	13.8654			0.875175			0.437587	+	0.899176i	$0.355833\pi$
$252$		0			0
$253$	18.8585			1.18563
$254$	−28.5187	−	3.47992i	−1.78942	−	0.218350i
$255$		0			0
$256$	9.02661	+	13.2106i	0.564163	+	0.825663i
$257$	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
$262$	22.4472	−	9.54819i	1.38680	−	0.589889i
$263$	5.02740	−	8.70772i	0.310003	−	0.536941i	−0.668360	−	0.743838i	$-0.733003\pi$
$263$	5.02740	−	8.70772i	0.310003	−	0.536941i	0.978363	+	0.206897i	$0.0663366\pi$
$264$		0			0
$265$	−2.41453			−0.148323
$266$	−18.3821	+	19.0482i	−1.12708	+	1.16792i
$267$		0			0
$268$	−15.2971	−	14.7279i	−0.934421	−	0.899651i
$269$	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	−0.985468	−	0.169859i	$-0.945669\pi$
$271$	−21.9127	+	12.6513i	−1.33110	+	0.768511i	−0.345632	+	0.938370i	$0.612335\pi$
$272$	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	$0.190870\pi$
$278$	22.8083	+	2.78312i	1.36795	+	0.166920i
$279$		0			0
$280$	−24.5409	+	15.3977i	−1.46660	+	0.920189i
$281$		−	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	0.306717	−	0.951801i	$-0.400770\pi$
$283$	−6.12694	−	3.53739i	−0.364209	−	0.210276i	−0.670925	+	0.741525i	$0.734103\pi$
$284$	1.04678	+	0.259323i	0.0621152	+	0.0153880i
$285$		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
$290$	−34.5274	+	14.6866i	−2.02752	+	0.862429i
$291$		0			0
$292$	10.2583	−	10.6547i	0.600320	−	0.623521i
$293$		−	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
$296$	−7.01832	+	1.12780i	−0.407931	+	0.0655523i
$297$		0			0
$298$	3.13138	+	7.36169i	0.181396	+	0.426451i
$299$	−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
$304$	−28.2788	+	1.07257i	−1.62190	+	0.0615160i
$305$	−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	$-0.0961552\pi$
$308$	17.1471	+	6.56074i	0.977048	+	0.373833i
$309$		0			0
$310$	−1.86685	+	15.2992i	−0.106030	+	0.868939i
$311$	−11.3530	+	19.6640i	−0.643772	+	1.11505i	0.340812	+	0.940132i	$0.389298\pi$
$311$	−11.3530	+	19.6640i	−0.643772	+	1.11505i	−0.984584	+	0.174914i	$0.944035\pi$
$312$		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
$320$	−30.3236	−	6.30283i	−1.69514	−	0.352339i
$321$		0			0
$322$	14.6342	+	14.1225i	0.815532	+	0.787017i
$323$	−11.0890			−0.617011
$324$		0			0
$325$	−1.48095	+	2.56508i	−0.0821483	+	0.142285i
$326$	11.6484	+	27.3847i	0.645144	+	1.51670i
$327$		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	$-0.856439\pi$
$331$	−17.6936	+	10.2154i	−0.972531	+	0.561491i	−0.0725241	+	0.997367i	$0.523105\pi$
$332$	−11.9582	−	2.96243i	−0.656289	−	0.162585i
$333$		0			0
$334$	1.43776	−	11.7827i	0.0786707	−	0.644723i
$335$	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	$0.553719\pi$
$338$	2.21177	−	18.1260i	0.120305	−	0.985923i
$339$		0			0
$340$	−11.7802	−	2.91835i	−0.638872	−	0.158270i
$341$	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
$346$	−8.31499	−	19.5481i	−0.447016	−	1.05091i
$347$	7.55986	−	13.0941i	0.405834	−	0.702926i	−0.588584	−	0.808436i	$-0.700314\pi$
$347$	7.55986	−	13.0941i	0.405834	−	0.702926i	0.994418	+	0.105510i	$0.0336477\pi$
$348$		0			0
$349$	18.8933			1.01134			0.505668	−	0.862728i	$-0.331246\pi$
$349$	18.8933			1.01134			0.505668	+	0.862728i	$0.331246\pi$
$350$	9.02899	−	36.2656i	0.482620	−	1.93848i
$351$		0			0
$352$	8.36146	+	17.7568i	0.445667	+	0.946443i
$353$	−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	0.826573	−	0.562829i	$-0.190287\pi$
$359$	−1.40470	−	2.43302i	−0.0741374	−	0.128410i	−0.900711	+	0.434419i	$0.856954\pi$
$360$		0			0
$361$	15.5263	−	26.8923i	0.817171	−	1.41538i
$362$	3.82695	−	31.3626i	0.201140	−	1.64838i
$363$		0			0
$364$	−0.247154	−	1.54954i	−0.0129544	−	0.0812182i
$365$			28.6302i			1.49858i
$366$		0			0
$367$	−16.3515	−	9.44054i	−0.853541	−	0.492792i	0.00830274	−	0.999966i	$-0.497357\pi$
$367$	−16.3515	−	9.44054i	−0.853541	−	0.492792i	−0.861844	+	0.507173i	$0.830690\pi$
$368$	0.824027	+	21.7259i	0.0429554	+	1.13254i
$369$		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	$0.497729\pi$
$374$	3.01038	+	7.07722i	0.155663	+	0.365954i
$375$		0			0
$376$	6.61655	−	1.06324i	0.341222	−	0.0548325i
$377$		−	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	$0.937672\pi$
$380$	37.9939	−	39.4622i	1.94904	−	2.02437i
$381$		0			0
$382$	−10.7940	+	4.59137i	−0.552271	+	0.234915i
$383$	18.1904	+	31.5068i	0.929488	+	1.60992i	0.784180	+	0.620533i	$0.213084\pi$
$383$	18.1904	+	31.5068i	0.929488	+	1.60992i	0.145308	+	0.989387i	$0.453583\pi$
$384$		0			0
$385$	−32.7194	+	13.8727i	−1.66754	+	0.707016i
$386$	24.1306	+	18.1553i	1.22821	+	0.924080i
$387$		0			0
$388$	13.2938	+	3.29331i	0.674890	+	0.167193i
$389$	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
$392$	8.39303	+	17.9320i	0.423912	+	0.905703i
$393$		0			0
$394$	0.803760	+	0.0980767i	0.0404928	+	0.00494103i
$395$	−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
$404$	−5.12073	−	4.93019i	−0.254766	−	0.245286i
$405$		0			0
$406$	7.07621	+	24.6462i	0.351186	+	1.22317i
$407$	−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	$0.906569\pi$
$410$	17.9068	−	7.61685i	0.884353	−	0.376169i
$411$		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
$416$	0.956992	−	1.37771i	0.0469204	−	0.0675476i
$417$		0			0
$418$	−34.4586	−	4.20472i	−1.68542	−	0.205660i
$419$	4.99528			0.244035			0.122018	−	0.992528i	$-0.461064\pi$
$419$	4.99528			0.244035			0.122018	+	0.992528i	$0.461064\pi$
$420$		0			0
$421$	−4.51318			−0.219959			−0.109980	−	0.993934i	$-0.535079\pi$
$421$	−4.51318			−0.219959			−0.109980	+	0.993934i	$0.535079\pi$
$422$	−11.1584	−	1.36158i	−0.543184	−	0.0662807i
$423$		0			0
$424$	−1.36839	+	1.11322i	−0.0664550	+	0.0540625i
$425$	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
$430$	3.43649	−	1.46175i	0.165722	−	0.0704918i
$431$	10.1436	−	17.5692i	0.488600	−	0.846281i	−0.511314	−	0.859394i	$-0.670841\pi$
$431$	10.1436	−	17.5692i	0.488600	−	0.846281i	0.999914	+	0.0131135i	$0.00417428\pi$
$432$		0			0
$433$	8.34123			0.400854			0.200427	−	0.979709i	$-0.435767\pi$
$433$	8.34123			0.400854			0.200427	+	0.979709i	$0.435767\pi$
$434$	10.2210	+	2.54471i	0.490624	+	0.122150i
$435$		0			0
$436$	18.4755	−	19.1895i	0.884816	−	0.919012i
$437$	−33.3022	−	19.2270i	−1.59306	−	0.919753i
$438$		0			0
$439$	20.6706	−	11.9342i	0.986553	−	0.569586i	0.0823105	−	0.996607i	$-0.473770\pi$
$439$	20.6706	−	11.9342i	0.986553	−	0.569586i	0.904242	+	0.427020i	$0.140437\pi$
$440$	−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	$-0.121124\pi$
$443$	3.00114	+	5.19813i	0.142589	+	0.246971i	−0.785882	+	0.618376i	$0.787791\pi$
$444$		0			0
$445$	−22.6800	+	39.2829i	−1.07513	+	1.86219i
$446$	−1.65445	−	0.201880i	−0.0783405	−	0.00955930i
$447$		0			0
$448$	−6.80901	+	20.0409i	−0.321695	+	0.946843i
$449$		−	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
$452$	−3.24676	+	13.1058i	−0.152715	+	0.616447i
$453$		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	$0.621078\pi$
$458$	20.9895	−	8.92812i	0.980775	−	0.417184i
$459$		0			0
$460$	−30.3178	−	29.1897i	−1.41357	−	1.36098i
$461$		−	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	$-0.891936\pi$
$463$		−	14.3310i		−	0.666020i	0.942923	−	0.333010i	$-0.108064\pi$
$464$	−12.7966	+	24.2422i	−0.594065	+	1.12542i
$465$		0			0
$466$	−4.58244	−	10.7731i	−0.212277	−	0.499052i
$467$	−10.6828	−	18.5032i	−0.494342	−	0.856225i	0.505637	−	0.862746i	$-0.331258\pi$
$467$	−10.6828	−	18.5032i	−0.494342	−	0.856225i	−0.999979	+	0.00652102i	$0.997924\pi$
$468$		0			0
$469$	3.43492	−	27.8801i	0.158610	−	1.28738i
$470$	−7.79907	+	10.3659i	−0.359744	+	0.478144i
$471$		0			0
$472$	−15.8063	−	19.4295i	−0.727545	−	0.894316i
$473$	−2.04949	−	1.18328i	−0.0942358	−	0.0544071i
$474$		0			0
$475$			70.6648i			3.24232i
$476$	−2.96384	+	7.74628i	−0.135847	+	0.355050i
$477$		0			0
$478$	3.10573	−	25.4521i	0.142053	−	1.16415i
$479$	−16.1925	+	28.0463i	−0.739856	+	1.28147i	0.212704	+	0.977117i	$0.431773\pi$
$479$	−16.1925	+	28.0463i	−0.739856	+	1.28147i	−0.952560	+	0.304351i	$0.901560\pi$
$480$		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	$-0.354156\pi$
$487$	−2.49862	−	1.44258i	−0.113223	−	0.0653695i	−0.555542	+	0.831488i	$0.687489\pi$
$488$	−7.44329	+	1.19610i	−0.336942	+	0.0541447i
$489$		0			0
$490$	−35.7790	−	13.7373i	−1.61633	−	0.620588i
$491$	−16.6547			−0.751617			−0.375808	−	0.926697i	$-0.622635\pi$
$491$	−16.6547			−0.751617			−0.375808	+	0.926697i	$0.622635\pi$
$492$		0			0
$493$	−5.37078	+	9.30247i	−0.241888	+	0.418962i
$494$	1.16132	+	2.73021i	0.0522505	+	0.122838i
$495$		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	$-0.468418\pi$
$499$	22.5695	−	13.0305i	1.01035	−	0.583325i	0.911294	+	0.411757i	$0.135085\pi$
$500$	−9.28766	+	37.4905i	−0.415357	+	1.67663i
$501$		0			0
$502$	−2.37507	+	19.4642i	−0.106005	+	0.868731i
$503$	−28.7302			−1.28102			−0.640509	−	0.767951i	$-0.721277\pi$
$503$	−28.7302			−1.28102			−0.640509	+	0.767951i	$0.721277\pi$
$504$		0			0
$505$	13.7599			0.612307
$506$	−3.23038	+	26.4736i	−0.143608	+	1.17690i
$507$		0			0
$508$	9.77023	−	39.4385i	0.433484	−	1.74980i
$509$	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
$514$	4.26099	+	10.0173i	0.187944	+	0.441846i
$515$	−4.06105	+	7.03395i	−0.178951	+	0.309953i
$516$		0			0
$517$	8.22056			0.361540
$518$	−6.76650	−	6.52991i	−0.297303	−	0.286908i
$519$		0			0
$520$	0.515188	+	3.20601i	0.0225925	+	0.140593i
$521$	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	−0.369526	−	0.929220i	$-0.620480\pi$
$523$	5.72733	−	3.30668i	0.250439	−	0.144591i	0.619965	+	0.784629i	$0.287147\pi$
$524$	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
$530$	0.413598	−	3.38952i	0.0179655	−	0.147231i
$531$		0			0
$532$	−23.5911	−	29.0677i	−1.02280	−	1.26025i
$533$			1.05395i			0.0456516i
$534$		0			0
$535$	37.0684	+	21.4014i	1.60260	+	0.925264i
$536$	23.2954	−	18.9513i	1.00621	−	0.818571i
$537$		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	$0.898039\pi$
$542$	−14.0064	−	32.9281i	−0.601625	−	1.41438i
$543$		0			0
$544$	−8.02173	+	3.77732i	−0.343929	+	0.161951i
$545$			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	$-0.102495\pi$
$548$	−23.9613	−	23.0698i	−1.02358	−	0.985491i
$549$		0			0
$550$	45.0995	−	19.1836i	1.92305	−	0.817990i
$551$	−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
$556$	−7.81389	+	31.5415i	−0.331383	+	1.33766i
$557$	−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
$560$	−17.4116	−	37.0880i	−0.735774	−	1.56726i
$561$		0			0
$562$	11.2432	+	1.37192i	0.474266	+	0.0578711i
$563$	9.56600	−	16.5688i	0.403159	−	0.698292i	−0.590946	−	0.806711i	$-0.701246\pi$
$563$	9.56600	−	16.5688i	0.403159	−	0.698292i	0.994105	+	0.108419i	$0.0345789\pi$
$564$		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	0.0291406	−	0.999575i	$-0.490723\pi$
$571$	−19.6409	−	11.3397i	−0.821947	−	0.474551i	−0.851087	+	0.525024i	$0.824056\pi$
$572$	1.42720	−	1.48235i	0.0596741	−	0.0619804i
$573$		0			0
$574$	−3.66989	−	12.7821i	−0.153178	−	0.533515i
$575$	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	$0.157518\pi$
$578$	18.9262	−	8.05048i	0.787227	−	0.334856i
$579$		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
$584$	13.1999	+	16.2257i	0.546217	+	0.671423i
$585$		0			0
$586$	28.0009	+	3.41674i	1.15671	+	0.141144i
$587$	−39.5737			−1.63338			−0.816692	−	0.577074i	$-0.804194\pi$
$587$	−39.5737			−1.63338			−0.816692	+	0.577074i	$0.804194\pi$
$588$		0			0
$589$	−19.9160			−0.820624
$590$	48.1271	+	5.87259i	1.98136	+	0.241771i
$591$		0			0
$592$	−0.381010	−	10.0455i	−0.0156594	−	0.412868i
$593$	−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
$598$	2.09755	−	0.892216i	0.0857751	−	0.0364854i
$599$	6.51380	−	11.2822i	0.266147	−	0.460979i	−0.701717	−	0.712456i	$-0.747583\pi$
$599$	6.51380	−	11.2822i	0.266147	−	0.460979i	0.967863	+	0.251477i	$0.0809162\pi$
$600$		0			0
$601$	−43.6907			−1.78218			−0.891091	−	0.453825i	$-0.850059\pi$
$601$	−43.6907			−1.78218			−0.891091	+	0.453825i	$0.850059\pi$
$602$	−0.704290	−	2.45302i	−0.0287047	−	0.0999774i
$603$		0			0
$604$	5.75982	+	5.54550i	0.234364	+	0.225643i
$605$	−3.48053	−	2.00949i	−0.141504	−	0.0816972i
$606$		0			0
$607$	−7.84192	+	4.52754i	−0.318294	+	0.183767i	−0.650632	−	0.759393i	$-0.725496\pi$
$607$	−7.84192	+	4.52754i	−0.318294	+	0.183767i	0.332338	+	0.943160i	$0.392163\pi$
$608$	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	$0.242115\pi$
$614$	14.6353	+	1.78584i	0.590634	+	0.0720705i
$615$		0			0
$616$	−12.1472	+	22.9473i	−0.489424	+	0.924574i
$617$		−	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	0.0503285	−	0.998733i	$-0.483973\pi$
$619$	−19.6409	−	11.3397i	−0.789435	−	0.455781i	−0.839764	+	0.542952i	$0.817306\pi$
$620$	−21.1573	−	5.24138i	−0.849698	−	0.210499i
$621$		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
$626$	−29.1293	+	12.3905i	−1.16424	+	0.495223i
$627$		0			0
$628$	−15.1896	+	15.7766i	−0.606130	+	0.629555i
$629$		−	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	$0.815005\pi$
$632$	2.76693	+	17.2186i	0.110063	+	0.684918i
$633$		0			0
$634$	16.1311	+	37.9233i	0.640648	+	1.50613i
$635$	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
$640$	14.0422	−	41.4887i	0.555067	−	1.63999i
$641$	−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	$-0.728783\pi$
$643$		−	38.1698i		−	1.50527i	0.658438	−	0.752635i	$-0.271217\pi$
$644$	−22.3320	+	18.1244i	−0.880003	+	0.714201i
$645$		0			0
$646$	1.89950	−	15.5668i	0.0747348	−	0.612468i
$647$	22.8942	−	39.6540i	0.900066	−	1.55896i	0.0726586	−	0.997357i	$-0.476852\pi$
$647$	22.8942	−	39.6540i	0.900066	−	1.55896i	0.827407	−	0.561603i	$-0.189815\pi$
$648$		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
$656$	6.63661	−	12.5726i	0.259116	−	0.490878i
$657$		0			0
$658$	6.37915	+	6.15610i	0.248685	+	0.239990i
$659$	8.45187			0.329238			0.164619	−	0.986357i	$-0.447361\pi$
$659$	8.45187			0.329238			0.164619	+	0.986357i	$0.447361\pi$
$660$		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	$0.0440391\pi$
$662$	−11.3096	−	26.5882i	−0.439560	−	1.03338i
$663$		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
$668$	16.2944	+	4.03666i	0.630447	+	0.156183i
$669$		0			0
$670$	−7.04105	+	57.7030i	−0.272020	+	2.22926i
$671$	−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	$0.299795\pi$
$674$	1.05635	−	8.65698i	0.0406889	−	0.333454i
$675$		0			0
$676$	25.0664	+	6.20978i	0.964092	+	0.238838i
$677$	−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
$682$	5.40665	+	12.7107i	0.207031	+	0.486719i
$683$	−13.6866	+	23.7060i	−0.523705	+	0.907084i	0.475914	+	0.879492i	$0.342117\pi$
$683$	−13.6866	+	23.7060i	−0.523705	+	0.907084i	−0.999619	+	0.0275921i	$0.991216\pi$
$684$		0			0
$685$	64.3864			2.46008
$686$	−12.3075	+	23.1198i	−0.469901	+	0.882719i
$687$		0			0
$688$	1.27363	−	2.41281i	0.0485567	−	0.0919874i
$689$	0.160165	+	0.0924714i	0.00610180	+	0.00352288i
$690$		0			0
$691$	41.8799	−	24.1794i	1.59319	−	0.919827i	0.600431	−	0.799676i	$-0.294996\pi$
$691$	41.8799	−	24.1794i	1.59319	−	0.919827i	0.992756	−	0.120151i	$-0.0383377\pi$
$692$	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
$698$	−3.23633	+	26.5224i	−0.122497	+	1.00389i
$699$		0			0
$700$	49.3631	+	18.8870i	1.86575	+	0.713863i
$701$		−	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
$704$	−26.3593	+	8.69616i	−0.993455	+	0.327749i
$705$		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	$0.667952\pi$
$710$	−1.15557	−	2.71668i	−0.0433678	−	0.101955i
$711$		0			0
$712$	5.25784	+	32.7195i	0.197046	+	1.22621i
$713$			15.3009i			0.573024i
$714$		0			0
$715$			3.98323i			0.148964i
$716$	3.57387	−	3.71199i	0.133562	−	0.138724i
$717$		0			0
$718$	3.65609	−	1.55516i	0.136444	−	0.0580380i
$719$	−17.3772	−	30.0982i	−0.648060	−	1.12247i	−0.983586	−	0.180441i	$-0.942247\pi$
$719$	−17.3772	−	30.0982i	−0.648060	−	1.12247i	0.335526	−	0.942031i	$-0.391086\pi$
$720$		0			0
$721$	4.43155	+	3.34228i	0.165040	+	0.124473i
$722$	35.0918	+	26.4023i	1.30598	+	0.982592i
$723$		0			0
$724$	43.3714	+	10.7445i	1.61188	+	0.399318i
$725$	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	$0.859883\pi$
$728$	2.21759	−	0.0815262i	0.0821893	−	0.00302156i
$729$		0			0
$730$	−40.1912	−	4.90422i	−1.48754	−	0.181513i
$731$	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	0.385986	−	0.922504i	$-0.373861\pi$
$739$	−5.97877	−	3.45185i	−0.219933	−	0.126978i	−0.605919	+	0.795526i	$0.707194\pi$
$740$	14.0182	+	13.4966i	0.515320	+	0.496145i
$741$		0			0
$742$	−2.26445	−	0.563776i	−0.0831304	−	0.0206969i
$743$	−12.7592			−0.468091			−0.234046	−	0.972226i	$-0.575197\pi$
$743$	−12.7592			−0.468091			−0.234046	+	0.972226i	$0.575197\pi$
$744$		0			0
$745$	10.9502	−	18.9662i	0.401183	−	0.694869i
$746$	−43.7111	+	18.5930i	−1.60038	+	0.680738i
$747$		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	$0.726441\pi$
$751$	−44.8145	+	25.8737i	−1.63530	+	0.944143i	−0.982420	+	0.186686i	$0.940225\pi$
$752$	0.359199	+	9.47044i	0.0130986	+	0.345352i
$753$		0			0
$754$	2.85280	+	0.348106i	0.103893	+	0.0126773i
$755$	−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	$0.645339\pi$
$758$	−10.6343	−	1.29763i	−0.386256	−	0.0471319i
$759$		0			0
$760$	48.8890	+	60.0955i	1.77339	+	2.17989i
$761$	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
$766$	−47.3452	+	20.1388i	−1.71065	+	0.727644i
$767$	−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	$0.302853\pi$
$770$	−13.8698	−	48.3079i	−0.499832	−	1.74090i
$771$		0			0
$772$	−29.6199	+	30.7646i	−1.06604	+	1.10724i
$773$	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
$782$	−11.9596	−	1.45934i	−0.427674	−	0.0521858i
$783$		0			0
$784$	−26.6107	+	8.71048i	−0.950381	+	0.311088i
$785$		−	42.3932i		−	1.51308i
$786$		0			0
$787$	−30.4775	−	17.5962i	−1.08641	−	0.627237i	−0.153789	−	0.988104i	$-0.549148\pi$
$787$	−30.4775	−	17.5962i	−1.08641	−	0.627237i	−0.932617	+	0.360867i	$0.882481\pi$
$788$	−0.275360	+	1.11152i	−0.00980931	+	0.0395962i
$789$		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
$794$	25.7303	−	10.9447i	0.913134	−	0.388412i
$795$		0			0
$796$	25.2138	+	24.2756i	0.893679	+	0.860425i
$797$			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
$800$	24.0709	+	51.1183i	0.851036	+	1.80731i
$801$		0			0
$802$	2.10882	+	4.95771i	0.0744650	+	0.175063i
$803$	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
$808$	7.79817	−	6.34397i	0.274339	−	0.223180i
$809$	−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	$-0.989287\pi$
$811$		−	1.91646i		−	0.0672961i	0.999434	−	0.0336480i	$-0.0107125\pi$
$812$	−35.8105	+	5.71182i	−1.25670	+	0.200446i
$813$		0			0
$814$	1.49365	−	12.2408i	0.0523523	−	0.429039i
$815$	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	0.577391	−	0.816468i	$-0.304071\pi$
$823$	4.56151	+	2.63359i	0.159004	+	0.0918011i	−0.418387	+	0.908269i	$0.637404\pi$
$824$	0.941462	+	5.85871i	0.0327974	+	0.204098i
$825$		0			0
$826$	8.00493	−	32.1524i	0.278527	−	1.11872i
$827$	43.4115			1.50957			0.754784	−	0.655974i	$-0.227742\pi$
$827$	43.4115			1.50957			0.754784	+	0.655974i	$0.227742\pi$
$828$		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	$0.216429\pi$
$830$	13.2009	+	31.0346i	0.458210	+	1.07723i
$831$		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
$836$	11.8052	−	47.6528i	0.408291	−	1.64811i
$837$		0			0
$838$	−0.855667	+	7.01238i	−0.0295585	+	0.242238i
$839$	−36.4358			−1.25790			−0.628952	−	0.777444i	$-0.716516\pi$
$839$	−36.4358			−1.25790			−0.628952	+	0.777444i	$0.716516\pi$
$840$		0			0
$841$	−17.9648			−0.619476
$842$	0.773087	−	6.33561i	0.0266423	−	0.218340i
$843$		0			0
$844$	3.82278	−	15.4310i	0.131585	−	0.531157i
$845$	−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
$850$	8.66626	+	20.3739i	0.297250	+	0.698818i
$851$	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	$0.477728\pi$
$854$	−7.17623	−	6.92531i	−0.245565	−	0.236979i
$855$		0			0
$856$	30.8749	−	4.96143i	1.05528	−	0.169578i
$857$	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	−0.904125	−	0.427269i	$-0.859476\pi$
$859$	−28.9031	+	16.6872i	−0.986161	+	0.569360i	−0.0820365	+	0.996629i	$0.526142\pi$
$860$	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	$-0.0275832\pi$
$863$	12.4315	+	21.5319i	0.423172	+	0.732956i	−0.573076	+	0.819503i	$0.694250\pi$
$864$		0			0
$865$	−29.0768	+	50.3625i	−0.988641	+	1.71238i
$866$	−1.42881	+	11.7094i	−0.0485530	+	0.397903i
$867$		0			0
$868$	−5.32307	+	13.9124i	−0.180677	+	0.472216i
$869$			21.3928i			0.725700i
$870$		0			0
$871$	−2.72664	−	1.57423i	−0.0923886	−	0.0533406i
$872$	23.7735	+	29.2230i	0.805073	+	0.989616i
$873$		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	$-0.450551\pi$
$878$	13.2124	+	31.0616i	0.445898	+	1.04828i
$879$		0			0
$880$	25.0820	−	47.5161i	0.845513	−	1.60177i
$881$			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	$-0.742830\pi$
$883$		−	42.9597i		−	1.44571i	0.691001	−	0.722854i	$-0.257170\pi$
$884$	0.669660	+	0.644742i	0.0225231	+	0.0216850i
$885$		0			0
$886$	−7.81123	+	3.32259i	−0.262423	+	0.111625i
$887$	9.76216	+	16.9086i	0.327781	+	0.567734i	0.982071	−	0.188510i	$-0.0603657\pi$
$887$	9.76216	+	16.9086i	0.327781	+	0.567734i	−0.654290	+	0.756244i	$0.727032\pi$
$888$		0			0
$889$	49.4852	−	20.9811i	1.65968	−	0.703685i
$890$	−51.2604	−	38.5672i	−1.71825	−	1.29277i
$891$		0			0
$892$	0.566799	−	2.28794i	0.0189778	−	0.0766059i
$893$	−14.5166	−	8.38118i	−0.485781	−	0.280466i
$894$		0			0
$895$			9.97446i			0.333410i
$896$	−26.9671	−	12.9914i	−0.900907	−	0.434012i
$897$		0			0
$898$	6.91086	+	0.843280i	0.230619	+	0.0281406i
$899$	−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	$-0.501097\pi$
$907$	−26.2372	−	15.1480i	−0.871191	−	0.502982i	−0.867744	+	0.497012i	$0.834431\pi$
$908$	−6.30881	+	6.55263i	−0.209365	+	0.217457i
$909$		0			0
$910$	−2.98290	+	3.09098i	−0.0988822	+	0.102465i
$911$	25.1485			0.833207			0.416604	−	0.909088i	$-0.363220\pi$
$911$	25.1485			0.833207			0.416604	+	0.909088i	$0.363220\pi$
$912$		0			0
$913$	10.6860	−	18.5088i	0.353656	−	0.612551i
$914$	−34.4130	+	14.6380i	−1.13828	+	0.484181i
$915$		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	$-0.644838\pi$
$919$	3.59797	−	2.07729i	0.118686	−	0.0685235i	0.558168	+	0.829728i	$0.311505\pi$
$920$	46.1698	−	37.5601i	1.52217	−	1.23832i
$921$		0			0
$922$	12.5237	+	1.52817i	0.412445	+	0.0503275i
$923$	0.159897			0.00526308
$924$		0			0
$925$	−25.1023			−0.825360
$926$	20.1179	+	2.45484i	0.661116	+	0.0806710i
$927$		0			0
$928$	−31.8393	−	22.1164i	−1.04517	−	0.726006i
$929$	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
$934$	27.8047	−	11.8270i	0.909798	−	0.386993i
$935$	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	$0.654791\pi$
$938$	38.5497	+	9.59767i	1.25869	+	0.313375i
$939$		0			0
$940$	−13.2157	−	12.7240i	−0.431050	−	0.415010i
$941$	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	$0.132135\pi$
$947$	24.8279	+	43.0032i	0.806798	+	1.39742i	−0.108272	+	0.994121i	$0.534532\pi$
$948$		0			0
$949$	1.09648	−	1.89915i	0.0355932	−	0.0616492i
$950$	−99.1993	−	12.1045i	−3.21845	−	0.392723i
$951$		0			0
$952$	−10.3665	−	5.48754i	−0.335982	−	0.177852i
$953$			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
$956$	35.1977	+	8.71964i	1.13837	+	0.282013i
$957$		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
$962$	−0.969855	+	0.412539i	−0.0312694	+	0.0133008i
$963$		0			0
$964$	−26.9407	+	27.9819i	−0.867702	+	0.901236i
$965$		−	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	$0.931657\pi$
$968$	−2.89900	+	0.465853i	−0.0931774	+	0.0149731i
$969$		0			0
$970$	−14.6754	−	34.5009i	−0.471197	−	1.10776i
$971$	−2.19406	−	3.80023i	−0.0704108	−	0.121955i	0.828671	−	0.559737i	$-0.189098\pi$
$971$	−2.19406	−	3.80023i	−0.0704108	−	0.121955i	−0.899081	+	0.437781i	$0.855764\pi$
$972$		0			0
$973$	−39.5765	+	16.7800i	−1.26877	+	0.537941i
$974$	2.45309	−	3.26046i	0.0786022	−	0.104472i
$975$		0			0
$976$	−0.404081	−	10.6538i	−0.0129343	−	0.341019i
$977$	−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
$980$	25.4132	−	47.8735i	0.811795	−	1.52926i
$981$		0			0
$982$	2.85287	−	23.3799i	0.0910389	−	0.746083i
$983$	6.14215	−	10.6385i	0.195904	−	0.339316i	−0.751292	−	0.659969i	$-0.770569\pi$
$983$	6.14215	−	10.6385i	0.195904	−	0.339316i	0.947197	+	0.320654i	$0.103903\pi$
$984$		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	$-0.172720\pi$
$991$	26.3597	+	15.2188i	0.837344	+	0.483441i	−0.0190166	+	0.999819i	$0.506054\pi$
$992$	−14.4071	+	6.78409i	−0.457425	+	0.215395i
$993$		0			0
$994$	−1.93921	+	0.556769i	−0.0615079	+	0.0176597i
$995$	−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	$0.863257\pi$
$998$	14.4262	+	33.9151i	0.456653	+	1.07356i
$999$		0			0

Twists

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

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

\(f(q)\)	\(=\)	\(q+(-0.171295 + 1.40380i) q^{2} +(-1.94132 - 0.480929i) q^{4} +(3.35279 - 1.93573i) q^{5} +(-1.03277 - 2.43585i) q^{7} +(1.00767 - 2.64284i) q^{8} +O(q^{10})\)	\(q+(-0.171295 + 1.40380i) q^{2} +(-1.94132 - 0.480929i) q^{4} +(3.35279 - 1.93573i) q^{5} +(-1.03277 - 2.43585i) q^{7} +(1.00767 - 2.64284i) q^{8} +(2.14307 + 5.03823i) q^{10} +(1.73480 - 3.00476i) q^{11} -0.296538 q^{13} +(3.59636 - 1.03256i) q^{14} +(3.53741 + 1.86727i) q^{16} +(1.35741 + 0.783703i) q^{17} +(-6.12694 + 3.53739i) q^{19} +(-7.43977 + 2.14542i) q^{20} +(3.92092 + 2.95001i) q^{22} +(2.71768 + 4.70717i) q^{23} +(4.99413 - 8.65009i) q^{25} +(0.0507955 - 0.416280i) q^{26} +(0.833467 + 5.22545i) q^{28} +6.85309i q^{29} +(2.43792 + 1.40753i) q^{31} +(-3.22722 + 4.64597i) q^{32} +(-1.33268 + 1.77129i) q^{34} +(-8.17783 - 6.16773i) q^{35} +(-1.25659 - 2.17648i) q^{37} +(-3.91628 - 9.20694i) q^{38} +(-1.73734 - 10.8115i) q^{40} -3.55418i q^{41} -0.682082i q^{43} +(-4.81287 + 4.99887i) q^{44} +(-7.07345 + 3.00877i) q^{46} +(1.18466 + 2.05189i) q^{47} +(-4.86676 + 5.03137i) q^{49} +(11.2875 + 8.49249i) q^{50} +(0.575674 + 0.142614i) q^{52} +(-0.540117 - 0.311837i) q^{53} -13.4324i q^{55} +(-7.47826 + 0.274927i) q^{56} +(-9.62037 - 1.17390i) q^{58} +(4.42770 - 7.66901i) q^{59} +(-1.33268 - 2.30827i) q^{61} +(-2.39350 + 3.18125i) q^{62} +(-5.96922 - 5.32621i) q^{64} +(-0.994229 + 0.574019i) q^{65} +(9.19491 + 5.30868i) q^{67} +(-2.25826 - 2.17423i) q^{68} +(10.0591 - 10.4236i) q^{70} -0.539214 q^{71} +(-3.69760 + 6.40442i) q^{73} +(3.27059 - 1.39118i) q^{74} +(13.5956 - 3.92057i) q^{76} +(-9.11080 - 1.12248i) q^{77} +(-5.33972 + 3.08289i) q^{79} +(15.4747 - 0.586932i) q^{80} +(4.98936 + 0.608814i) q^{82} +6.15982 q^{83} +6.06816 q^{85} +(0.957508 + 0.116837i) q^{86} +(-6.19300 - 7.61259i) q^{88} +(-10.1468 + 5.85824i) q^{89} +(0.306256 + 0.722323i) q^{91} +(-3.01207 - 10.4451i) q^{92} +(-3.08337 + 1.31154i) q^{94} +(-13.6949 + 23.7202i) q^{95} -6.84782 q^{97} +(-6.22939 - 7.69381i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 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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