LMFDB - Embedded newform 476.2.bl.a.465.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [476,2,Mod(5,476)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(476, base_ring=CyclotomicField(48))

chi = DirichletCharacter(H, H._module([0, 40, 15]))

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

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

chi := DirichletCharacter("476.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 476 = 2^{2} \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	476.bl (of order $48$, degree $16$, 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:	$3.80087913621$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$12$ over $\Q(\zeta_{48})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{48}]$

Embedding invariants

Embedding label			465.3
Character	$\chi$	$=$	476.465
Dual form			476.2.bl.a.173.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.30001 - 0.780747i) q^{3} +(0.0538253 - 0.821215i) q^{5} +(-0.638390 + 2.56758i) q^{7} +(2.30040 + 1.76516i) q^{9} +O(q^{10})$	\(q+(-2.30001 - 0.780747i) q^{3} +(0.0538253 - 0.821215i) q^{5} +(-0.638390 + 2.56758i) q^{7} +(2.30040 + 1.76516i) q^{9} +(-3.59684 - 3.15434i) q^{11} +(3.71099 + 3.71099i) q^{13} +(-0.764960 + 1.84678i) q^{15} +(-1.92217 + 3.64764i) q^{17} +(6.20071 - 0.816339i) q^{19} +(3.47293 - 5.40703i) q^{21} +(-0.231981 - 0.683394i) q^{23} +(4.28573 + 0.564227i) q^{25} +(0.135488 + 0.202773i) q^{27} +(3.61338 + 2.41438i) q^{29} +(-1.93947 + 5.71349i) q^{31} +(5.81001 + 10.0632i) q^{33} +(2.07417 + 0.662456i) q^{35} +(1.91391 + 2.18240i) q^{37} +(-5.63796 - 11.4327i) q^{39} +(5.45597 - 3.64556i) q^{41} +(9.88489 - 4.09446i) q^{43} +(1.57340 - 1.79412i) q^{45} +(-2.68453 + 10.0188i) q^{47} +(-6.18492 - 3.27823i) q^{49} +(7.26889 - 6.88886i) q^{51} +(-1.17707 + 0.903197i) q^{53} +(-2.78399 + 2.78399i) q^{55} +(-14.8990 - 2.96360i) q^{57} +(-1.16868 + 8.87703i) q^{59} +(-3.70220 + 7.50731i) q^{61} +(-6.00075 + 4.77961i) q^{63} +(3.24727 - 2.84778i) q^{65} +(-8.69425 - 5.01963i) q^{67} +1.75293i q^{69} +(-12.4883 + 2.48408i) q^{71} +(10.5408 - 5.19814i) q^{73} +(-9.41668 - 4.64379i) q^{75} +(10.3952 - 7.22147i) q^{77} +(-3.24424 + 1.10127i) q^{79} +(-2.40472 - 8.97454i) q^{81} +(-2.54251 - 1.05314i) q^{83} +(2.89203 + 1.77485i) q^{85} +(-6.42578 - 8.37424i) q^{87} +(-7.93622 - 2.12650i) q^{89} +(-11.8973 + 7.15920i) q^{91} +(8.92157 - 11.6268i) q^{93} +(-0.336635 - 5.13606i) q^{95} +(-4.85571 + 7.26708i) q^{97} +(-2.70626 - 13.6053i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q+O(q^{10}) $ 192 * q	$ 192 q + 8 q^{11} + 48 q^{15} - 24 q^{21} + 8 q^{25} - 32 q^{35} - 32 q^{37} - 16 q^{39} + 64 q^{49} + 32 q^{51} - 32 q^{53} - 48 q^{61} + 96 q^{63} + 16 q^{65} - 32 q^{71} + 120 q^{73} - 144 q^{75} + 16 q^{77} + 48 q^{81} - 160 q^{85} + 144 q^{87} - 64 q^{91} + 64 q^{93} + 32 q^{95} - 368 q^{99}+O(q^{100}) $ 192 * q + 8 * q^11 + 48 * q^15 - 24 * q^21 + 8 * q^25 - 32 * q^35 - 32 * q^37 - 16 * q^39 + 64 * q^49 + 32 * q^51 - 32 * q^53 - 48 * q^61 + 96 * q^63 + 16 * q^65 - 32 * q^71 + 120 * q^73 - 144 * q^75 + 16 * q^77 + 48 * q^81 - 160 * q^85 + 144 * q^87 - 64 * q^91 + 64 * q^93 + 32 * q^95 - 368 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/476\mathbb{Z}\right)^\times$.

$n$	$239$	$309$	$409$
$\chi(n)$	$1$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−2.30001	−	0.780747i	−1.32791	−	0.450764i	−0.434769	−	0.900542i	$-0.643170\pi$
$3$	−2.30001	−	0.780747i	−1.32791	−	0.450764i	−0.893141	+	0.449778i	$0.851503\pi$
$4$		0			0
$5$	0.0538253	−	0.821215i	0.0240714	−	0.367258i	−0.968782	−	0.247915i	$-0.920254\pi$
$5$	0.0538253	−	0.821215i	0.0240714	−	0.367258i	0.992853	−	0.119343i	$-0.0380788\pi$
$6$		0			0
$7$	−0.638390	+	2.56758i	−0.241289	+	0.970453i
$7$	−0.638390	+	2.56758i	−0.241289	+	0.970453i
$8$		0			0
$9$	2.30040	+	1.76516i	0.766801	+	0.588387i
$10$		0			0
$11$	−3.59684	−	3.15434i	−1.08449	−	0.951070i	−0.0855128	−	0.996337i	$-0.527253\pi$
$11$	−3.59684	−	3.15434i	−1.08449	−	0.951070i	−0.998975	+	0.0452669i	$0.985586\pi$
$12$		0			0
$13$	3.71099	+	3.71099i	1.02924	+	1.02924i	0.999559	+	0.0296846i	$0.00945029\pi$
$13$	3.71099	+	3.71099i	1.02924	+	1.02924i	0.0296846	+	0.999559i	$0.490550\pi$
$14$		0			0
$15$	−0.764960	+	1.84678i	−0.197512	+	0.476835i
$16$		0			0
$17$	−1.92217	+	3.64764i	−0.466195	+	0.884682i
$17$	−1.92217	+	3.64764i	−0.466195	+	0.884682i
$18$		0			0
$19$	6.20071	−	0.816339i	1.42254	−	0.187281i	0.620339	−	0.784334i	$-0.286995\pi$
$19$	6.20071	−	0.816339i	1.42254	−	0.187281i	0.802202	+	0.597053i	$0.203662\pi$
$20$		0			0
$21$	3.47293	−	5.40703i	0.757855	−	1.17991i
$22$		0			0
$23$	−0.231981	−	0.683394i	−0.0483714	−	0.142497i	0.920060	−	0.391777i	$-0.128140\pi$
$23$	−0.231981	−	0.683394i	−0.0483714	−	0.142497i	−0.968432	+	0.249280i	$0.919806\pi$
$24$		0			0
$25$	4.28573	+	0.564227i	0.857146	+	0.112845i
$26$		0			0
$27$	0.135488	+	0.202773i	0.0260748	+	0.0390236i
$28$		0			0
$29$	3.61338	+	2.41438i	0.670988	+	0.448340i	0.843831	−	0.536610i	$-0.180295\pi$
$29$	3.61338	+	2.41438i	0.670988	+	0.448340i	−0.172843	+	0.984949i	$0.555295\pi$
$30$		0			0
$31$	−1.93947	+	5.71349i	−0.348339	+	1.02617i	0.621707	+	0.783250i	$0.286439\pi$
$31$	−1.93947	+	5.71349i	−0.348339	+	1.02617i	−0.970046	+	0.242923i	$0.921894\pi$
$32$		0			0
$33$	5.81001	+	10.0632i	1.01139	+	1.75178i
$34$		0			0
$35$	2.07417	+	0.662456i	0.350599	+	0.111975i
$36$		0			0
$37$	1.91391	+	2.18240i	0.314646	+	0.358785i	0.887447	−	0.460910i	$-0.152477\pi$
$37$	1.91391	+	2.18240i	0.314646	+	0.358785i	−0.572802	+	0.819694i	$0.694143\pi$
$38$		0			0
$39$	−5.63796	−	11.4327i	−0.902796	−	1.83069i
$40$		0			0
$41$	5.45597	−	3.64556i	0.852079	−	0.569341i	−0.0510569	−	0.998696i	$-0.516259\pi$
$41$	5.45597	−	3.64556i	0.852079	−	0.569341i	0.903136	+	0.429355i	$0.141259\pi$
$42$		0			0
$43$	9.88489	−	4.09446i	1.50743	−	0.624399i	0.532406	−	0.846489i	$-0.321288\pi$
$43$	9.88489	−	4.09446i	1.50743	−	0.624399i	0.975026	+	0.222091i	$0.0712881\pi$
$44$		0			0
$45$	1.57340	−	1.79412i	0.234548	−	0.267451i
$46$		0			0
$47$	−2.68453	+	10.0188i	−0.391579	+	1.46139i	0.435951	+	0.899970i	$0.356412\pi$
$47$	−2.68453	+	10.0188i	−0.391579	+	1.46139i	−0.827530	+	0.561422i	$0.810255\pi$
$48$		0			0
$49$	−6.18492	−	3.27823i	−0.883560	−	0.468319i
$50$		0			0
$51$	7.26889	−	6.88886i	1.01785	−	0.964634i
$52$		0			0
$53$	−1.17707	+	0.903197i	−0.161683	+	0.124064i	−0.686434	−	0.727192i	$-0.740825\pi$
$53$	−1.17707	+	0.903197i	−0.161683	+	0.124064i	0.524751	+	0.851256i	$0.324158\pi$
$54$		0			0
$55$	−2.78399	+	2.78399i	−0.375394	+	0.375394i
$56$		0			0
$57$	−14.8990	−	2.96360i	−1.97343	−	0.392539i
$58$		0			0
$59$	−1.16868	+	8.87703i	−0.152150	+	1.15569i	0.729566	+	0.683910i	$0.239722\pi$
$59$	−1.16868	+	8.87703i	−0.152150	+	1.15569i	−0.881716	+	0.471781i	$0.843611\pi$
$60$		0			0
$61$	−3.70220	+	7.50731i	−0.474018	+	0.961213i	0.520222	+	0.854031i	$0.325849\pi$
$61$	−3.70220	+	7.50731i	−0.474018	+	0.961213i	−0.994239	+	0.107181i	$0.965817\pi$
$62$		0			0
$63$	−6.00075	+	4.77961i	−0.756023	+	0.602174i
$64$		0			0
$65$	3.24727	−	2.84778i	0.402774	−	0.353223i
$66$		0			0
$67$	−8.69425	−	5.01963i	−1.06217	−	0.613245i	−0.136140	−	0.990690i	$-0.543470\pi$
$67$	−8.69425	−	5.01963i	−1.06217	−	0.613245i	−0.926032	+	0.377444i	$0.876803\pi$
$68$		0			0
$69$			1.75293i			0.211028i
$70$		0			0
$71$	−12.4883	+	2.48408i	−1.48209	+	0.294807i	−0.868845	−	0.495084i	$-0.835137\pi$
$71$	−12.4883	+	2.48408i	−1.48209	+	0.294807i	−0.613248	+	0.789891i	$0.710137\pi$
$72$		0			0
$73$	10.5408	−	5.19814i	1.23370	−	0.608396i	0.295787	−	0.955254i	$-0.404418\pi$
$73$	10.5408	−	5.19814i	1.23370	−	0.608396i	0.937918	+	0.346858i	$0.112751\pi$
$74$		0			0
$75$	−9.41668	−	4.64379i	−1.08734	−	0.536219i
$76$		0			0
$77$	10.3952	−	7.22147i	1.18464	−	0.822962i
$78$		0			0
$79$	−3.24424	+	1.10127i	−0.365006	+	0.123903i	−0.497916	−	0.867225i	$-0.665901\pi$
$79$	−3.24424	+	1.10127i	−0.365006	+	0.123903i	0.132910	+	0.991128i	$0.457568\pi$
$80$		0			0
$81$	−2.40472	−	8.97454i	−0.267191	−	0.997172i
$82$		0			0
$83$	−2.54251	−	1.05314i	−0.279077	−	0.115597i	0.238755	−	0.971080i	$-0.423261\pi$
$83$	−2.54251	−	1.05314i	−0.279077	−	0.115597i	−0.517832	+	0.855482i	$0.673261\pi$
$84$		0			0
$85$	2.89203	+	1.77485i	0.313685	+	0.192510i
$86$		0			0
$87$	−6.42578	−	8.37424i	−0.688916	−	0.897812i
$88$		0			0
$89$	−7.93622	−	2.12650i	−0.841238	−	0.225409i	−0.187627	−	0.982240i	$-0.560080\pi$
$89$	−7.93622	−	2.12650i	−0.841238	−	0.225409i	−0.653610	+	0.756831i	$0.726746\pi$
$90$		0			0
$91$	−11.8973	+	7.15920i	−1.24718	+	0.750488i
$92$		0			0
$93$	8.92157	−	11.6268i	0.925124	−	1.20565i
$94$		0			0
$95$	−0.336635	−	5.13606i	−0.0345380	−	0.526948i
$96$		0			0
$97$	−4.85571	+	7.26708i	−0.493022	+	0.737860i	−0.991650	−	0.128956i	$-0.958837\pi$
$97$	−4.85571	+	7.26708i	−0.493022	+	0.737860i	0.498628	+	0.866816i	$0.333837\pi$
$98$		0			0
$99$	−2.70626	−	13.6053i	−0.271989	−	1.36738i
$100$		0			0
$101$	2.88274	−	4.99306i	0.286844	−	0.496828i	−0.686211	−	0.727403i	$-0.740727\pi$
$101$	2.88274	−	4.99306i	0.286844	−	0.496828i	0.973055	+	0.230575i	$0.0740606\pi$
$102$		0			0
$103$	3.02874	−	1.74864i	0.298431	−	0.172299i	−0.343307	−	0.939223i	$-0.611547\pi$
$103$	3.02874	−	1.74864i	0.298431	−	0.172299i	0.641738	+	0.766924i	$0.278214\pi$
$104$		0			0
$105$	−4.25340	−	3.14306i	−0.415089	−	0.306731i
$106$		0			0
$107$	19.5037	+	1.27834i	1.88549	+	0.123582i	0.964181	−	0.265245i	$-0.0854527\pi$
$107$	19.5037	+	1.27834i	1.88549	+	0.123582i	0.921311	+	0.388826i	$0.127119\pi$
$108$		0			0
$109$	−7.60669	+	0.498569i	−0.728589	+	0.0477543i	−0.425183	−	0.905107i	$-0.639790\pi$
$109$	−7.60669	+	0.498569i	−0.728589	+	0.0477543i	−0.303406	+	0.952861i	$0.598124\pi$
$110$		0			0
$111$	−2.69811	−	6.51382i	−0.256093	−	0.618264i
$112$		0			0
$113$	−0.0869925	+	0.437341i	−0.00818356	+	0.0411415i	−0.984661	−	0.174477i	$-0.944177\pi$
$113$	−0.0869925	+	0.437341i	−0.00818356	+	0.0411415i	0.976478	+	0.215618i	$0.0691767\pi$
$114$		0			0
$115$	−0.573700	+	0.153722i	−0.0534978	+	0.0143347i
$116$		0			0
$117$	1.98628	+	15.0873i	0.183631	+	1.39482i
$118$		0			0
$119$	−8.13850	−	7.26394i	−0.746055	−	0.665884i
$120$		0			0
$121$	1.55158	+	11.7854i	0.141053	+	1.07140i
$122$		0			0
$123$	−15.3950	+	4.12508i	−1.38812	+	0.371946i
$124$		0			0
$125$	1.49681	−	7.52495i	0.133878	−	0.673052i
$126$		0			0
$127$	2.57893	+	6.22608i	0.228843	+	0.552475i	0.996037	−	0.0889395i	$-0.0283478\pi$
$127$	2.57893	+	6.22608i	0.228843	+	0.552475i	−0.767194	+	0.641415i	$0.778348\pi$
$128$		0			0
$129$	−25.9320	+	1.69968i	−2.28319	+	0.149648i
$130$		0			0
$131$	15.8914	+	1.04158i	1.38844	+	0.0910029i	0.741199	−	0.671286i	$-0.234258\pi$
$131$	15.8914	+	1.04158i	1.38844	+	0.0910029i	0.647237	+	0.762288i	$0.275924\pi$
$132$		0			0
$133$	−1.86246	+	16.4420i	−0.161495	+	1.42570i
$134$		0			0
$135$	0.173813	−	0.100351i	0.0149594	−	0.00863683i
$136$		0			0
$137$	−3.47330	+	6.01593i	−0.296744	+	0.513976i	−0.975389	−	0.220491i	$-0.929234\pi$
$137$	−3.47330	+	6.01593i	−0.296744	+	0.513976i	0.678645	+	0.734466i	$0.262567\pi$
$138$		0			0
$139$	−1.10378	−	5.54907i	−0.0936213	−	0.470666i	−0.998944	−	0.0459420i	$-0.985371\pi$
$139$	−1.10378	−	5.54907i	−0.0936213	−	0.470666i	0.905323	−	0.424724i	$-0.139629\pi$
$140$		0			0
$141$	13.9966	−	20.9474i	1.17872	−	1.76409i
$142$		0			0
$143$	−1.64210	−	25.0536i	−0.137319	−	2.09509i
$144$		0			0
$145$	2.17722	−	2.83741i	0.180808	−	0.235634i
$146$		0			0
$147$	11.6659	+	12.3688i	0.962185	+	1.02016i
$148$		0			0
$149$	−4.88353	−	1.30854i	−0.400074	−	0.107200i	0.0531711	−	0.998585i	$-0.483067\pi$
$149$	−4.88353	−	1.30854i	−0.400074	−	0.107200i	−0.453245	+	0.891386i	$0.649734\pi$
$150$		0			0
$151$	12.3777	+	16.1309i	1.00728	+	1.31272i	0.949291	+	0.314399i	$0.101803\pi$
$151$	12.3777	+	16.1309i	1.00728	+	1.31272i	0.0579919	+	0.998317i	$0.481530\pi$
$152$		0			0
$153$	−10.8604	+	4.99810i	−0.878015	+	0.404072i
$154$		0			0
$155$	4.58761	+	1.90025i	0.368485	+	0.152632i
$156$		0			0
$157$	1.81121	+	6.75952i	0.144550	+	0.539468i	0.999775	+	0.0212112i	$0.00675225\pi$
$157$	1.81121	+	6.75952i	0.144550	+	0.539468i	−0.855225	+	0.518257i	$0.826581\pi$
$158$		0			0
$159$	3.41243	−	1.15837i	0.270624	−	0.0918643i
$160$		0			0
$161$	1.90276	−	0.159358i	0.149959	−	0.0125591i
$162$		0			0
$163$	7.06138	+	3.48229i	0.553090	+	0.272754i	0.697283	−	0.716796i	$-0.254392\pi$
$163$	7.06138	+	3.48229i	0.553090	+	0.272754i	−0.144193	+	0.989550i	$0.546059\pi$
$164$		0			0
$165$	8.57680	−	4.22961i	0.667703	−	0.329275i
$166$		0			0
$167$	6.65632	−	1.32402i	0.515082	−	0.102456i	0.0692964	−	0.997596i	$-0.477925\pi$
$167$	6.65632	−	1.32402i	0.515082	−	0.102456i	0.445785	+	0.895140i	$0.352925\pi$
$168$		0			0
$169$			14.5429i			1.11869i
$170$		0			0
$171$	15.7051	+	9.06735i	1.20100	+	0.693398i
$172$		0			0
$173$	−19.0776	+	16.7306i	−1.45045	+	1.27201i	−0.551338	+	0.834282i	$0.685882\pi$
$173$	−19.0776	+	16.7306i	−1.45045	+	1.27201i	−0.899109	+	0.437725i	$0.855784\pi$
$174$		0			0
$175$	−4.18466	+	10.6437i	−0.316331	+	0.804591i
$176$		0			0
$177$	9.61869	−	19.5048i	0.722985	−	1.46607i
$178$		0			0
$179$	1.33847	−	10.1667i	0.100042	−	0.759896i	−0.865731	−	0.500509i	$-0.833146\pi$
$179$	1.33847	−	10.1667i	0.100042	−	0.759896i	0.965774	−	0.259387i	$-0.0835204\pi$
$180$		0			0
$181$	1.48827	+	0.296036i	0.110622	+	0.0220042i	0.250091	−	0.968222i	$-0.419539\pi$
$181$	1.48827	+	0.296036i	0.110622	+	0.0220042i	−0.139469	+	0.990226i	$0.544539\pi$
$182$		0			0
$183$	14.3764	−	14.3764i	1.06273	−	1.06273i
$184$		0			0
$185$	1.89524	−	1.45427i	0.139341	−	0.106920i
$186$		0			0
$187$	18.4196	−	7.05678i	1.34698	−	0.516043i
$188$		0			0
$189$	−0.607130	+	0.218429i	−0.0441622	+	0.0158884i
$190$		0			0
$191$	−1.80723	+	6.74468i	−0.130767	+	0.488028i	−0.999979	−	0.00641012i	$-0.997960\pi$
$191$	−1.80723	+	6.74468i	−0.130767	+	0.488028i	0.869213	+	0.494438i	$0.164626\pi$
$192$		0			0
$193$	0.783983	−	0.893961i	0.0564323	−	0.0643487i	−0.722935	−	0.690916i	$-0.757207\pi$
$193$	0.783983	−	0.893961i	0.0564323	−	0.0643487i	0.779367	+	0.626567i	$0.215541\pi$
$194$		0			0
$195$	−9.69213	+	4.01461i	−0.694068	+	0.287492i
$196$		0			0
$197$	3.29954	−	2.20468i	0.235083	−	0.157077i	−0.432450	−	0.901658i	$-0.642351\pi$
$197$	3.29954	−	2.20468i	0.235083	−	0.157077i	0.667532	+	0.744581i	$0.267351\pi$
$198$		0			0
$199$	1.03107	+	2.09081i	0.0730908	+	0.148213i	0.930351	−	0.366670i	$-0.119502\pi$
$199$	1.03107	+	2.09081i	0.0730908	+	0.148213i	−0.857260	+	0.514883i	$0.827835\pi$
$200$		0			0
$201$	16.0778	+	18.3332i	1.13404	+	1.29312i
$202$		0			0
$203$	−8.50587	+	7.73632i	−0.596995	+	0.542983i
$204$		0			0
$205$	−2.70012	−	4.67675i	−0.188585	−	0.326638i
$206$		0			0
$207$	0.672651	−	1.98157i	0.0467525	−	0.137728i
$208$		0			0
$209$	−24.8780	−	16.6229i	−1.72085	−	1.14983i
$210$		0			0
$211$	−15.5927	−	23.3362i	−1.07345	−	1.60653i	−0.751452	−	0.659787i	$-0.770646\pi$
$211$	−15.5927	−	23.3362i	−1.07345	−	1.60653i	−0.321996	−	0.946741i	$-0.604354\pi$
$212$		0			0
$213$	30.6627	+	4.03682i	2.10097	+	0.276598i
$214$		0			0
$215$	−2.83037	−	8.33800i	−0.193030	−	0.568647i
$216$		0			0
$217$	−13.4317	−	8.62716i	−0.911802	−	0.585650i
$218$		0			0
$219$	−28.3023	+	3.72607i	−1.91249	+	0.251784i
$220$		0			0
$221$	−20.6695	+	6.40319i	−1.39038	+	0.430726i
$222$		0			0
$223$	0.338301	−	0.816730i	0.0226543	−	0.0546923i	−0.912148	−	0.409862i	$-0.865577\pi$
$223$	0.338301	−	0.816730i	0.0226543	−	0.0546923i	0.934802	+	0.355170i	$0.115577\pi$
$224$		0			0
$225$	8.86295	+	8.86295i	0.590864	+	0.590864i
$226$		0			0
$227$	−1.43849	−	1.26153i	−0.0954762	−	0.0837304i	0.610277	−	0.792188i	$-0.291058\pi$
$227$	−1.43849	−	1.26153i	−0.0954762	−	0.0837304i	−0.705753	+	0.708458i	$0.749391\pi$
$228$		0			0
$229$	−11.7311	−	9.00156i	−0.775211	−	0.594840i	0.143556	−	0.989642i	$-0.454146\pi$
$229$	−11.7311	−	9.00156i	−0.775211	−	0.594840i	−0.918766	+	0.394802i	$0.870813\pi$
$230$		0			0
$231$	−29.5472	+	8.49339i	−1.94406	+	0.558824i
$232$		0			0
$233$	0.515510	−	7.86517i	0.0337722	−	0.515264i	−0.947141	−	0.320818i	$-0.896042\pi$
$233$	0.515510	−	7.86517i	0.0337722	−	0.515264i	0.980913	−	0.194447i	$-0.0622911\pi$
$234$		0			0
$235$	8.08309	+	2.74384i	0.527283	+	0.178988i
$236$		0			0
$237$	8.32160			0.540546
$238$		0			0
$239$	6.44683			0.417011			0.208505	−	0.978021i	$-0.433140\pi$
$239$	6.44683			0.417011			0.208505	+	0.978021i	$0.433140\pi$
$240$		0			0
$241$	23.2139	+	7.88007i	1.49534	+	0.507600i	0.944924	−	0.327290i	$-0.106135\pi$
$241$	23.2139	+	7.88007i	1.49534	+	0.507600i	0.550417	+	0.834890i	$0.314469\pi$
$242$		0			0
$243$	−1.42812	+	21.7889i	−0.0916141	+	1.39776i
$244$		0			0
$245$	−3.02504	+	4.90269i	−0.193263	+	0.313222i
$246$		0			0
$247$	26.0402	+	19.9814i	1.65690	+	1.27138i
$248$		0			0
$249$	5.02556	+	4.40729i	0.318482	+	0.279301i
$250$		0			0
$251$	12.5899	+	12.5899i	0.794668	+	0.794668i	0.982249	−	0.187581i	$-0.0600647\pi$
$251$	12.5899	+	12.5899i	0.794668	+	0.794668i	−0.187581	+	0.982249i	$0.560065\pi$
$252$		0			0
$253$	−1.32126	+	3.18980i	−0.0830669	+	0.200541i
$254$		0			0
$255$	−5.26599	−	6.34011i	−0.329769	−	0.397033i
$256$		0			0
$257$	7.85902	−	1.03466i	0.490232	−	0.0645403i	0.118642	−	0.992937i	$-0.462146\pi$
$257$	7.85902	−	1.03466i	0.490232	−	0.0645403i	0.371590	+	0.928397i	$0.378813\pi$
$258$		0			0
$259$	−6.82531	+	3.52090i	−0.424104	+	0.218778i
$260$		0			0
$261$	4.05046	+	11.9323i	0.250717	+	0.738588i
$262$		0			0
$263$	13.2502	+	1.74443i	0.817045	+	0.107566i	0.527453	−	0.849584i	$-0.323147\pi$
$263$	13.2502	+	1.74443i	0.817045	+	0.107566i	0.289592	+	0.957150i	$0.406480\pi$
$264$		0			0
$265$	0.678362	+	1.01524i	0.0416715	+	0.0623658i
$266$		0			0
$267$	16.5931	+	11.0872i	1.01548	+	0.678523i
$268$		0			0
$269$	9.52121	−	28.0486i	0.580518	−	1.71015i	−0.116585	−	0.993181i	$-0.537195\pi$
$269$	9.52121	−	28.0486i	0.580518	−	1.71015i	0.697103	−	0.716971i	$-0.254472\pi$
$270$		0			0
$271$	−9.35220	−	16.1985i	−0.568106	−	0.983988i	−0.996753	−	0.0805164i	$-0.974343\pi$
$271$	−9.35220	−	16.1985i	−0.568106	−	0.983988i	0.428647	−	0.903472i	$-0.358990\pi$
$272$		0			0
$273$	32.9534	−	7.17741i	1.99443	−	0.434397i
$274$		0			0
$275$	−13.6353	−	15.5481i	−0.822240	−	0.937585i
$276$		0			0
$277$	4.36075	+	8.84273i	0.262012	+	0.531308i	0.987632	−	0.156787i	$-0.0501137\pi$
$277$	4.36075	+	8.84273i	0.262012	+	0.531308i	−0.725620	+	0.688095i	$0.758447\pi$
$278$		0			0
$279$	−14.5468	+	9.71985i	−0.870893	+	0.581912i
$280$		0			0
$281$	−22.3210	+	9.24567i	−1.33156	+	0.551550i	−0.931100	−	0.364764i	$-0.881150\pi$
$281$	−22.3210	+	9.24567i	−1.33156	+	0.551550i	−0.400460	+	0.916314i	$0.631150\pi$
$282$		0			0
$283$	−9.87237	+	11.2573i	−0.586851	+	0.669176i	−0.966712	−	0.255868i	$-0.917639\pi$
$283$	−9.87237	+	11.2573i	−0.586851	+	0.669176i	0.379860	+	0.925044i	$0.375972\pi$
$284$		0			0
$285$	−3.23570	+	12.0758i	−0.191666	+	0.715308i
$286$		0			0
$287$	5.87723	+	16.3359i	0.346922	+	0.964279i
$288$		0			0
$289$	−9.61052	−	14.0228i	−0.565325	−	0.824868i
$290$		0			0
$291$	16.8419	−	12.9232i	0.987290	−	0.757574i
$292$		0			0
$293$	21.5456	−	21.5456i	1.25871	−	1.25871i	0.307000	−	0.951710i	$-0.400675\pi$
$293$	21.5456	−	21.5456i	1.25871	−	1.25871i	0.951710	−	0.307000i	$-0.0993251\pi$
$294$		0			0
$295$	7.22704	+	1.43755i	0.420775	+	0.0836973i
$296$		0			0
$297$	0.152285	−	1.15672i	0.00883646	−	0.0671196i
$298$		0			0
$299$	1.67519	−	3.39695i	0.0968787	−	0.196451i
$300$		0			0
$301$	4.20242	+	27.9941i	0.242224	+	1.61355i
$302$		0			0
$303$	−10.5286	+	9.23338i	−0.604855	+	0.530444i
$304$		0			0
$305$	5.96584	+	3.44438i	0.341603	+	0.197225i
$306$		0			0
$307$			11.0382i			0.629981i	0.949095	+	0.314991i	$0.102001\pi$
$307$			11.0382i			0.629981i	−0.949095	+	0.314991i	$0.897999\pi$
$308$		0			0
$309$	−8.33137	+	1.65721i	−0.473955	+	0.0942756i
$310$		0			0
$311$	7.46702	−	3.68233i	0.423416	−	0.208806i	−0.218082	−	0.975930i	$-0.569980\pi$
$311$	7.46702	−	3.68233i	0.423416	−	0.208806i	0.641498	+	0.767125i	$0.278313\pi$
$312$		0			0
$313$	−18.0922	−	8.92209i	−1.02263	−	0.504307i	−0.147946	−	0.988995i	$-0.547266\pi$
$313$	−18.0922	−	8.92209i	−1.02263	−	0.504307i	−0.874687	+	0.484689i	$0.838933\pi$
$314$		0			0
$315$	3.60209	+	5.18517i	0.202955	+	0.292151i
$316$		0			0
$317$	0.0349596	−	0.0118672i	0.00196353	−	0.000666528i	−0.320458	−	0.947263i	$-0.603837\pi$
$317$	0.0349596	−	0.0118672i	0.00196353	−	0.000666528i	0.322421	+	0.946596i	$0.395503\pi$
$318$		0			0
$319$	−5.38095	−	20.0820i	−0.301276	−	1.12438i
$320$		0			0
$321$	−43.8605	−	18.1676i	−2.44806	−	1.01402i
$322$		0			0
$323$	−8.94112	+	24.1871i	−0.497497	+	1.34581i
$324$		0			0
$325$	13.8105	+	17.9981i	0.766066	+	0.998357i
$326$		0			0
$327$	17.8847	+	4.79219i	0.989026	+	0.265009i
$328$		0			0
$329$	−24.0103	−	13.2886i	−1.32373	−	0.732626i
$330$		0			0
$331$	11.6968	−	15.2436i	0.642914	−	0.837862i	−0.352269	−	0.935899i	$-0.614590\pi$
$331$	11.6968	−	15.2436i	0.642914	−	0.837862i	0.995183	+	0.0980369i	$0.0312563\pi$
$332$		0			0
$333$	0.550485	+	8.39877i	0.0301664	+	0.460250i
$334$		0			0
$335$	−4.59016	+	6.86967i	−0.250787	+	0.375330i
$336$		0			0
$337$	−1.08361	−	5.44767i	−0.0590280	−	0.296754i	0.939983	−	0.341222i	$-0.110841\pi$
$337$	−1.08361	−	5.44767i	−0.0590280	−	0.296754i	−0.999011	+	0.0444681i	$0.985841\pi$
$338$		0			0
$339$	0.541536	−	0.937967i	0.0294122	−	0.0509434i
$340$		0			0
$341$	24.9982	−	14.4327i	1.35373	−	0.781577i
$342$		0			0
$343$	12.3655	−	13.7875i	0.667675	−	0.744453i
$344$		0			0
$345$	1.43953	+	0.0943518i	0.0775017	+	0.00507973i
$346$		0			0
$347$	9.55105	−	0.626009i	0.512727	−	0.0336059i	0.193156	−	0.981168i	$-0.438128\pi$
$347$	9.55105	−	0.626009i	0.512727	−	0.0336059i	0.319571	+	0.947562i	$0.396461\pi$
$348$		0			0
$349$	−0.812838	−	1.96236i	−0.0435102	−	0.105043i	0.900630	−	0.434586i	$-0.143105\pi$
$349$	−0.812838	−	1.96236i	−0.0435102	−	0.105043i	−0.944141	+	0.329543i	$0.893105\pi$
$350$		0			0
$351$	−0.249692	+	1.25528i	−0.0133276	+	0.0670021i
$352$		0			0
$353$	6.95595	−	1.86384i	0.370228	−	0.0992022i	−0.0689079	−	0.997623i	$-0.521951\pi$
$353$	6.95595	−	1.86384i	0.370228	−	0.0992022i	0.439136	+	0.898421i	$0.355285\pi$
$354$		0			0
$355$	1.36778	+	10.3893i	0.0725942	+	0.551408i
$356$		0			0
$357$	13.0473	+	23.0612i	0.690537	+	1.22053i
$358$		0			0
$359$	1.42113	+	10.7945i	0.0750043	+	0.569714i	0.987144	+	0.159834i	$0.0510960\pi$
$359$	1.42113	+	10.7945i	0.0750043	+	0.569714i	−0.912140	+	0.409880i	$0.865571\pi$
$360$		0			0
$361$	19.4298	−	5.20621i	1.02262	−	0.274011i
$362$		0			0
$363$	5.63279	−	28.3180i	0.295645	−	1.48631i
$364$		0			0
$365$	−3.70143	−	8.93603i	−0.193742	−	0.467733i
$366$		0			0
$367$	−22.2314	+	1.45712i	−1.16047	+	0.0760612i	−0.633444	−	0.773788i	$-0.718359\pi$
$367$	−22.2314	+	1.45712i	−1.16047	+	0.0760612i	−0.527025	+	0.849850i	$0.676693\pi$
$368$		0			0
$369$	18.9859	+	1.24440i	0.988368	+	0.0647811i
$370$		0			0
$371$	−1.56760	−	3.59881i	−0.0813857	−	0.186841i
$372$		0			0
$373$	24.2770	−	14.0163i	1.25702	−	0.725738i	0.284523	−	0.958669i	$-0.408165\pi$
$373$	24.2770	−	14.0163i	1.25702	−	0.725738i	0.972493	+	0.232931i	$0.0748316\pi$
$374$		0			0
$375$	−9.31775	+	16.1388i	−0.481166	+	0.833405i
$376$		0			0
$377$	4.44947	+	22.3690i	0.229159	+	1.15206i
$378$		0			0
$379$	4.36826	−	6.53757i	0.224383	−	0.335812i	−0.702148	−	0.712031i	$-0.747776\pi$
$379$	4.36826	−	6.53757i	0.224383	−	0.335812i	0.926531	+	0.376218i	$0.122776\pi$
$380$		0			0
$381$	−1.07056	−	16.3335i	−0.0548462	−	0.836791i
$382$		0			0
$383$	−0.240236	+	0.313081i	−0.0122755	+	0.0159977i	−0.799451	−	0.600732i	$-0.794876\pi$
$383$	−0.240236	+	0.313081i	−0.0122755	+	0.0159977i	0.787175	+	0.616729i	$0.211543\pi$
$384$		0			0
$385$	−5.37085	−	8.92540i	−0.273724	−	0.454880i
$386$		0			0
$387$	29.9666	+	8.02953i	1.52329	+	0.408164i
$388$		0			0
$389$	−4.50999	−	5.87754i	−0.228666	−	0.298003i	0.664903	−	0.746930i	$-0.268473\pi$
$389$	−4.50999	−	5.87754i	−0.228666	−	0.298003i	−0.893568	+	0.448927i	$0.851806\pi$
$390$		0			0
$391$	2.93868	+	0.467417i	0.148615	+	0.0236383i
$392$		0			0
$393$	−35.7371	−	14.8028i	−1.80270	−	0.746701i
$394$		0			0
$395$	0.729759	+	2.72350i	0.0367182	+	0.137034i
$396$		0			0
$397$	−9.99471	+	3.39275i	−0.501620	+	0.170277i	−0.560769	−	0.827972i	$-0.689495\pi$
$397$	−9.99471	+	3.39275i	−0.501620	+	0.170277i	0.0591492	+	0.998249i	$0.481161\pi$
$398$		0			0
$399$	17.1207	−	36.3625i	0.857106	−	1.82040i
$400$		0			0
$401$	3.21146	+	1.58372i	0.160373	+	0.0790871i	0.520704	−	0.853737i	$-0.325670\pi$
$401$	3.21146	+	1.58372i	0.160373	+	0.0790871i	−0.360331	+	0.932825i	$0.617336\pi$
$402$		0			0
$403$	−28.4000	+	14.0054i	−1.41471	+	0.697656i
$404$		0			0
$405$	−7.49946	+	1.49174i	−0.372651	+	0.0741250i
$406$		0			0
$407$		−	13.8869i		−	0.688347i
$408$		0			0
$409$	−1.85738	−	1.07236i	−0.0918414	−	0.0530246i	0.453376	−	0.891319i	$-0.350220\pi$
$409$	−1.85738	−	1.07236i	−0.0918414	−	0.0530246i	−0.545217	+	0.838295i	$0.683553\pi$
$410$		0			0
$411$	12.6855	−	11.1249i	0.625731	−	0.548751i
$412$		0			0
$413$	−22.0464	−	8.66769i	−1.08483	−	0.426509i
$414$		0			0
$415$	−1.00171	+	2.03126i	−0.0491719	+	0.0997108i
$416$		0			0
$417$	−1.79372	+	13.6247i	−0.0878390	+	0.667203i
$418$		0			0
$419$	16.0640	+	3.19533i	0.784779	+	0.156102i	0.571186	−	0.820821i	$-0.306483\pi$
$419$	16.0640	+	3.19533i	0.784779	+	0.156102i	0.213593	+	0.976923i	$0.431483\pi$
$420$		0			0
$421$	4.23343	−	4.23343i	0.206325	−	0.206325i	−0.596379	−	0.802703i	$-0.703394\pi$
$421$	4.23343	−	4.23343i	0.206325	−	0.206325i	0.802703	+	0.596379i	$0.203394\pi$
$422$		0			0
$423$	−23.8603	+	18.3087i	−1.16013	+	0.890197i
$424$		0			0
$425$	−10.2960	+	14.5482i	−0.499429	+	0.705693i
$426$		0			0
$427$	−16.9122	−	14.2983i	−0.818437	−	0.691942i
$428$		0			0
$429$	−15.7837	+	58.9055i	−0.762043	+	2.84398i
$430$		0			0
$431$	−6.83935	+	7.79879i	−0.329440	+	0.375654i	−0.892720	−	0.450612i	$-0.851206\pi$
$431$	−6.83935	+	7.79879i	−0.329440	+	0.375654i	0.563280	+	0.826266i	$0.309539\pi$
$432$		0			0
$433$	−9.38134	+	3.88588i	−0.450839	+	0.186743i	−0.596537	−	0.802586i	$-0.703457\pi$
$433$	−9.38134	+	3.88588i	−0.450839	+	0.186743i	0.145698	+	0.989329i	$0.453457\pi$
$434$		0			0
$435$	−7.22292	+	4.82620i	−0.346312	+	0.231398i
$436$		0			0
$437$	−1.99633	−	4.04815i	−0.0954973	−	0.193649i
$438$		0			0
$439$	−22.7294	−	25.9180i	−1.08482	−	1.23700i	−0.969870	−	0.243625i	$-0.921663\pi$
$439$	−22.7294	−	25.9180i	−1.08482	−	1.23700i	−0.114947	−	0.993372i	$-0.536670\pi$
$440$		0			0
$441$	−8.44120	−	18.4586i	−0.401962	−	0.878983i
$442$		0			0
$443$	−15.8085	−	27.3811i	−0.751083	−	1.30091i	−0.947298	−	0.320353i	$-0.896198\pi$
$443$	−15.8085	−	27.3811i	−0.751083	−	1.30091i	0.196215	−	0.980561i	$-0.437135\pi$
$444$		0			0
$445$	−2.17349	+	6.40288i	−0.103033	+	0.303526i
$446$		0			0
$447$	10.2105	+	6.82244i	0.482940	+	0.322690i
$448$		0			0
$449$	2.77341	+	4.15071i	0.130885	+	0.195884i	0.891124	−	0.453760i	$-0.149918\pi$
$449$	2.77341	+	4.15071i	0.130885	+	0.195884i	−0.760238	+	0.649644i	$0.774918\pi$
$450$		0			0
$451$	−31.1236	−	4.09750i	−1.46555	−	0.192944i
$452$		0			0
$453$	−15.8746	−	46.7651i	−0.745854	−	2.19722i
$454$		0			0
$455$	5.23887	+	10.1556i	0.245602	+	0.476102i
$456$		0			0
$457$	−36.0175	+	4.74179i	−1.68483	+	0.221812i	−0.911239	−	0.411878i	$-0.864873\pi$
$457$	−36.0175	+	4.74179i	−1.68483	+	0.221812i	−0.773588	+	0.633689i	$0.781540\pi$
$458$		0			0
$459$	−1.00007	+	0.104449i	−0.0466794	+	0.00487526i
$460$		0			0
$461$	−8.13119	+	19.6304i	−0.378707	+	0.914281i	0.613501	+	0.789694i	$0.289761\pi$
$461$	−8.13119	+	19.6304i	−0.378707	+	0.914281i	−0.992209	+	0.124587i	$0.960239\pi$
$462$		0			0
$463$	10.2610	+	10.2610i	0.476870	+	0.476870i	0.904129	−	0.427259i	$-0.140521\pi$
$463$	10.2610	+	10.2610i	0.476870	+	0.476870i	−0.427259	+	0.904129i	$0.640521\pi$
$464$		0			0
$465$	−9.06791	−	7.95235i	−0.420514	−	0.368781i
$466$		0			0
$467$	−29.3983	−	22.5581i	−1.36039	−	1.04386i	−0.993528	−	0.113588i	$-0.963766\pi$
$467$	−29.3983	−	22.5581i	−1.36039	−	1.04386i	−0.366861	−	0.930276i	$-0.619568\pi$
$468$		0			0
$469$	18.4386	−	19.1187i	0.851416	−	0.882819i
$470$		0			0
$471$	1.11168	−	16.9610i	0.0512237	−	0.781523i
$472$		0			0
$473$	−48.4697	−	16.4532i	−2.22864	−	0.756521i
$474$		0			0
$475$	27.0352			1.24046
$476$		0			0
$477$	−4.30202			−0.196976
$478$		0			0
$479$	11.3180	+	3.84196i	0.517135	+	0.175544i	0.567791	−	0.823172i	$-0.307798\pi$
$479$	11.3180	+	3.84196i	0.517135	+	0.175544i	−0.0506565	+	0.998716i	$0.516131\pi$
$480$		0			0
$481$	−0.996352	+	15.2014i	−0.0454297	+	0.693124i
$482$		0			0
$483$	−4.50078	−	1.11905i	−0.204793	−	0.0509186i
$484$		0			0
$485$	5.70647	+	4.37873i	0.259118	+	0.198828i
$486$		0			0
$487$	6.47505	+	5.67846i	0.293412	+	0.257316i	0.793378	−	0.608730i	$-0.208321\pi$
$487$	6.47505	+	5.67846i	0.293412	+	0.257316i	−0.499965	+	0.866045i	$0.666654\pi$
$488$		0			0
$489$	−13.5224	−	13.5224i	−0.611505	−	0.611505i
$490$		0			0
$491$	−7.95914	+	19.2151i	−0.359191	+	0.867164i	0.636223	+	0.771505i	$0.280496\pi$
$491$	−7.95914	+	19.2151i	−0.359191	+	0.867164i	−0.995414	+	0.0956588i	$0.969504\pi$
$492$		0			0
$493$	−15.7523	+	8.53945i	−0.709449	+	0.384597i
$494$		0			0
$495$	−11.3185	+	1.49011i	−0.508729	+	0.0669755i
$496$		0			0
$497$	1.59435	−	33.6506i	0.0715162	−	1.50944i
$498$		0			0
$499$	−3.98884	−	11.7507i	−0.178565	−	0.526035i	0.820387	−	0.571809i	$-0.193758\pi$
$499$	−3.98884	−	11.7507i	−0.178565	−	0.526035i	−0.998952	+	0.0457734i	$0.985425\pi$
$500$		0			0
$501$	−16.3433	−	2.15164i	−0.730165	−	0.0961281i
$502$		0			0
$503$	12.2131	+	18.2782i	0.544556	+	0.814986i	0.997048	−	0.0767828i	$-0.0244648\pi$
$503$	12.2131	+	18.2782i	0.544556	+	0.814986i	−0.452492	+	0.891769i	$0.649465\pi$
$504$		0			0
$505$	−3.94521	−	2.63611i	−0.175560	−	0.117305i
$506$		0			0
$507$	11.3543	−	33.4488i	0.504264	−	1.48551i
$508$		0			0
$509$	−11.7296	−	20.3163i	−0.519907	−	0.900506i	−0.999732	−	0.0231416i	$-0.992633\pi$
$509$	−11.7296	−	20.3163i	−0.519907	−	0.900506i	0.479825	−	0.877364i	$-0.340700\pi$
$510$		0			0
$511$	6.61750	+	30.3827i	0.292741	+	1.34405i
$512$		0			0
$513$	1.00566	+	1.14673i	0.0444008	+	0.0506294i
$514$		0			0
$515$	−1.27299	−	2.58137i	−0.0560946	−	0.113749i
$516$		0			0
$517$	41.2585	−	27.5681i	1.81455	−	1.21244i
$518$		0			0
$519$	56.9411	−	23.5858i	2.49944	−	1.03530i
$520$		0			0
$521$	−2.60603	+	2.97161i	−0.114172	+	0.130189i	−0.806103	−	0.591776i	$-0.798427\pi$
$521$	−2.60603	+	2.97161i	−0.114172	+	0.130189i	0.691930	+	0.721964i	$0.256760\pi$
$522$		0			0
$523$	−10.6987	+	39.9283i	−0.467824	+	1.74594i	0.179531	+	0.983752i	$0.442542\pi$
$523$	−10.6987	+	39.9283i	−0.467824	+	1.74594i	−0.647354	+	0.762189i	$0.724125\pi$
$524$		0			0
$525$	17.9348	−	21.2135i	0.782740	−	0.925834i
$526$		0			0
$527$	−17.1127	−	18.0568i	−0.745443	−	0.786565i
$528$		0			0
$529$	17.8339	−	13.6844i	0.775388	−	0.594976i
$530$		0			0
$531$	−18.3578	+	18.3578i	−0.796662	+	0.796662i
$532$		0			0
$533$	33.7757	+	6.71840i	1.46299	+	0.291006i
$534$		0			0
$535$	2.09958	−	15.9479i	0.0907728	−	0.689488i
$536$		0			0
$537$	−11.0161	+	22.3385i	−0.475381	+	0.963977i
$538$		0			0
$539$	11.9055	+	31.3006i	0.512805	+	1.34821i
$540$		0			0
$541$	12.5716	−	11.0250i	0.540497	−	0.474003i	−0.345030	−	0.938592i	$-0.612131\pi$
$541$	12.5716	−	11.0250i	0.540497	−	0.474003i	0.885527	+	0.464589i	$0.153798\pi$
$542$		0			0
$543$	−3.19191	−	1.84285i	−0.136978	−	0.0790842i
$544$		0			0
$545$			6.27357i			0.268730i
$546$		0			0
$547$	−3.15401	+	0.627371i	−0.134856	+	0.0268245i	−0.262057	−	0.965053i	$-0.584401\pi$
$547$	−3.15401	+	0.627371i	−0.134856	+	0.0268245i	0.127201	+	0.991877i	$0.459401\pi$
$548$		0			0
$549$	−21.7682	+	10.7349i	−0.929043	+	0.458153i
$550$		0			0
$551$	24.3765	+	12.0212i	1.03847	+	0.512119i
$552$		0			0
$553$	−0.756511	−	9.03289i	−0.0321701	−	0.384118i
$554$		0			0
$555$	−5.49447	+	1.86512i	−0.233227	+	0.0791700i
$556$		0			0
$557$	−3.16807	−	11.8234i	−0.134235	−	0.500973i	−1.00000		0.000521528i	$-0.999834\pi$
$557$	−3.16807	−	11.8234i	−0.134235	−	0.500973i	0.865765	−	0.500452i	$-0.166833\pi$
$558$		0			0
$559$	51.8772	+	21.4883i	2.19417	+	0.908856i
$560$		0			0
$561$	−47.8748	+	1.84956i	−2.02128	+	0.0780886i
$562$		0			0
$563$	0.964608	+	1.25710i	0.0406534	+	0.0529805i	0.813238	−	0.581932i	$-0.197703\pi$
$563$	0.964608	+	1.25710i	0.0406534	+	0.0529805i	−0.772584	+	0.634912i	$0.781036\pi$
$564$		0			0
$565$	0.354468	+	0.0949795i	0.0149126	+	0.00399582i
$566$		0			0
$567$	24.5780	−	0.445054i	1.03218	−	0.0186905i
$568$		0			0
$569$	−23.7407	+	30.9395i	−0.995264	+	1.29705i	−0.0406607	+	0.999173i	$0.512946\pi$
$569$	−23.7407	+	30.9395i	−0.995264	+	1.29705i	−0.954603	+	0.297880i	$0.903720\pi$
$570$		0			0
$571$	−2.59529	−	39.5965i	−0.108610	−	1.65706i	−0.610416	−	0.792081i	$-0.708998\pi$
$571$	−2.59529	−	39.5965i	−0.108610	−	1.65706i	0.501806	−	0.864980i	$-0.332669\pi$
$572$		0			0
$573$	9.42254	−	14.1018i	0.393632	−	0.589112i
$574$		0			0
$575$	−0.608618	−	3.05973i	−0.0253811	−	0.127600i
$576$		0			0
$577$	−15.4100	+	26.6909i	−0.641527	+	1.11116i	0.343565	+	0.939129i	$0.388366\pi$
$577$	−15.4100	+	26.6909i	−0.641527	+	1.11116i	−0.985092	+	0.172029i	$0.944968\pi$
$578$		0			0
$579$	−2.50112	+	1.44402i	−0.103943	+	0.0600116i
$580$		0			0
$581$	4.32714	−	5.85578i	0.179520	−	0.242939i
$582$		0			0
$583$	7.08272	+	0.464226i	0.293336	+	0.0192263i
$584$		0			0
$585$	12.4968	−	0.819084i	0.516680	−	0.0338650i
$586$		0			0
$587$	6.12017	+	14.7754i	0.252606	+	0.609846i	0.998413	−	0.0563168i	$-0.0179357\pi$
$587$	6.12017	+	14.7754i	0.252606	+	0.609846i	−0.745807	+	0.666163i	$0.767936\pi$
$588$		0			0
$589$	−7.36194	+	37.0109i	−0.303343	+	1.52501i
$590$		0			0
$591$	−9.31027	+	2.49468i	−0.382973	+	0.102617i
$592$		0			0
$593$	−1.75372	−	13.3209i	−0.0720168	−	0.547022i	−0.988980	−	0.148050i	$-0.952700\pi$
$593$	−1.75372	−	13.3209i	−0.0720168	−	0.547022i	0.916963	−	0.398972i	$-0.130633\pi$
$594$		0			0
$595$	−6.40331	+	6.29248i	−0.262510	+	0.257966i
$596$		0			0
$597$	−0.739081	−	5.61388i	−0.0302486	−	0.229761i
$598$		0			0
$599$	34.4541	−	9.23195i	1.40776	−	0.377207i	0.526632	−	0.850093i	$-0.323454\pi$
$599$	34.4541	−	9.23195i	1.40776	−	0.377207i	0.881124	+	0.472886i	$0.156788\pi$
$600$		0			0
$601$	0.605199	−	3.04254i	0.0246866	−	0.124108i	−0.966477	−	0.256753i	$-0.917347\pi$
$601$	0.605199	−	3.04254i	0.0246866	−	0.124108i	0.991164	+	0.132646i	$0.0423472\pi$
$602$		0			0
$603$	−11.1398	−	26.8939i	−0.453649	−	1.09521i
$604$		0			0
$605$	9.76189	−	0.639828i	0.396877	−	0.0260127i
$606$		0			0
$607$	−2.04473	−	0.134018i	−0.0829928	−	0.00543964i	0.0238501	−	0.999716i	$-0.492408\pi$
$607$	−2.04473	−	0.134018i	−0.0829928	−	0.00543964i	−0.106843	+	0.994276i	$0.534074\pi$
$608$		0			0
$609$	25.6037	−	11.1527i	1.03751	−	0.451929i
$610$		0			0
$611$	−47.1419	+	27.2174i	−1.90716	+	1.10110i
$612$		0			0
$613$	−1.10630	+	1.91618i	−0.0446832	+	0.0773936i	−0.887502	−	0.460804i	$-0.847561\pi$
$613$	−1.10630	+	1.91618i	−0.0446832	+	0.0773936i	0.842819	+	0.538197i	$0.180895\pi$
$614$		0			0
$615$	2.55894	+	12.8647i	0.103186	+	0.518753i
$616$		0			0
$617$	−6.65850	+	9.96515i	−0.268061	+	0.401182i	−0.940941	−	0.338570i	$-0.890057\pi$
$617$	−6.65850	+	9.96515i	−0.268061	+	0.401182i	0.672880	+	0.739751i	$0.265057\pi$
$618$		0			0
$619$	0.882161	+	13.4592i	0.0354570	+	0.540970i	0.978229	+	0.207530i	$0.0665426\pi$
$619$	0.882161	+	13.4592i	0.0354570	+	0.540970i	−0.942772	+	0.333439i	$0.891791\pi$
$620$		0			0
$621$	0.107143	−	0.139631i	0.00429950	−	0.00560321i
$622$		0			0
$623$	10.5264	−	19.0193i	0.421730	−	0.761993i
$624$		0			0
$625$	14.7780	+	3.95977i	0.591122	+	0.158391i
$626$		0			0
$627$	44.2412	+	57.6563i	1.76682	+	2.30257i
$628$		0			0
$629$	−11.6395	+	2.78632i	−0.464096	+	0.111098i
$630$		0			0
$631$	0.139458	+	0.0577653i	0.00555173	+	0.00229960i	0.385458	−	0.922726i	$-0.374044\pi$
$631$	0.139458	+	0.0577653i	0.00555173	+	0.00229960i	−0.379906	+	0.925025i	$0.624044\pi$
$632$		0			0
$633$	17.6437	+	65.8473i	0.701276	+	2.61720i
$634$		0			0
$635$	5.25176	−	1.78273i	0.208410	−	0.0707456i
$636$		0			0
$637$	−10.7867	−	35.1177i	−0.427384	−	1.39141i
$638$		0			0
$639$	−33.1130	−	16.3295i	−1.30993	−	0.645987i
$640$		0			0
$641$	4.89689	−	2.41488i	0.193415	−	0.0953820i	−0.343002	−	0.939335i	$-0.611444\pi$
$641$	4.89689	−	2.41488i	0.193415	−	0.0953820i	0.536418	+	0.843953i	$0.319777\pi$
$642$		0			0
$643$	−20.4331	+	4.06440i	−0.805804	+	0.160284i	−0.580771	−	0.814067i	$-0.697249\pi$
$643$	−20.4331	+	4.06440i	−0.805804	+	0.160284i	−0.225033	+	0.974351i	$0.572249\pi$
$644$		0			0
$645$			21.3873i			0.842123i
$646$		0			0
$647$	3.76777	+	2.17532i	0.148126	+	0.0855208i	0.572231	−	0.820092i	$-0.306078\pi$
$647$	3.76777	+	2.17532i	0.148126	+	0.0855208i	−0.424105	+	0.905613i	$0.639411\pi$
$648$		0			0
$649$	32.2048	−	28.2428i	1.26415	−	1.10863i
$650$		0			0
$651$	24.1573	+	30.3293i	0.946800	+	1.18870i
$652$		0			0
$653$	6.42609	−	13.0308i	0.251472	−	0.509936i	−0.734131	−	0.679008i	$-0.762410\pi$
$653$	6.42609	−	13.0308i	0.251472	−	0.509936i	0.985604	+	0.169072i	$0.0540770\pi$
$654$		0			0
$655$	1.71072	−	12.9942i	0.0668432	−	0.507724i
$656$		0			0
$657$	33.4236	+	6.64837i	1.30398	+	0.259378i
$658$		0			0
$659$	14.3676	−	14.3676i	0.559684	−	0.559684i	−0.369534	−	0.929217i	$-0.620483\pi$
$659$	14.3676	−	14.3676i	0.559684	−	0.559684i	0.929217	+	0.369534i	$0.120483\pi$
$660$		0			0
$661$	−21.2668	+	16.3186i	−0.827181	+	0.634718i	−0.933084	−	0.359658i	$-0.882893\pi$
$661$	−21.2668	+	16.3186i	−0.827181	+	0.634718i	0.105903	+	0.994376i	$0.466227\pi$
$662$		0			0
$663$	52.5393	+	1.41027i	2.04046	+	0.0547703i
$664$		0			0
$665$	13.4021	+	2.41447i	0.519712	+	0.0936291i
$666$		0			0
$667$	0.811740	−	3.02945i	0.0314307	−	0.117301i
$668$		0			0
$669$	−1.41575	+	1.61436i	−0.0547362	+	0.0624147i
$670$		0			0
$671$	36.9968	−	15.3246i	1.42825	−	0.591599i
$672$		0			0
$673$	−15.0579	+	10.0614i	−0.580439	+	0.387837i	−0.810848	−	0.585257i	$-0.800994\pi$
$673$	−15.0579	+	10.0614i	−0.580439	+	0.387837i	0.230409	+	0.973094i	$0.425994\pi$
$674$		0			0
$675$	0.466257	+	0.945475i	0.0179462	+	0.0363914i
$676$		0			0
$677$	9.72992	+	11.0948i	0.373951	+	0.426410i	0.907952	−	0.419074i	$-0.137645\pi$
$677$	9.72992	+	11.0948i	0.373951	+	0.426410i	−0.534001	+	0.845484i	$0.679312\pi$
$678$		0			0
$679$	−15.5590	−	17.1066i	−0.597098	−	0.656492i
$680$		0			0
$681$	2.32361	+	4.02462i	0.0890411	+	0.154224i
$682$		0			0
$683$	14.6940	−	43.2873i	0.562252	−	1.65634i	−0.178015	−	0.984028i	$-0.556967\pi$
$683$	14.6940	−	43.2873i	0.562252	−	1.65634i	0.740267	−	0.672313i	$-0.234699\pi$
$684$		0			0
$685$	4.75342	+	3.17613i	0.181619	+	0.121354i
$686$		0			0
$687$	19.9536	+	29.8626i	0.761277	+	1.13933i
$688$		0			0
$689$	−7.71985	−	1.01634i	−0.294103	−	0.0387194i
$690$		0			0
$691$	−13.7178	−	40.4114i	−0.521851	−	1.53732i	−0.813950	−	0.580935i	$-0.802687\pi$
$691$	−13.7178	−	40.4114i	−0.521851	−	1.53732i	0.292099	−	0.956388i	$-0.405646\pi$
$692$		0			0
$693$	36.6602	+	1.73694i	1.39261	+	0.0659809i
$694$		0			0
$695$	−4.61639	+	0.607760i	−0.175110	+	0.0230536i
$696$		0			0
$697$	2.81039	+	26.9088i	0.106451	+	1.01924i
$698$		0			0
$699$	−7.32639	+	17.6875i	−0.277109	+	0.669001i
$700$		0			0
$701$	21.7002	+	21.7002i	0.819604	+	0.819604i	0.986050	−	0.166447i	$-0.0532293\pi$
$701$	21.7002	+	21.7002i	0.819604	+	0.819604i	−0.166447	+	0.986050i	$0.553229\pi$
$702$		0			0
$703$	13.6492	+	11.9700i	0.514790	+	0.451459i
$704$		0			0
$705$	−16.4489	−	12.6217i	−0.619502	−	0.475361i
$706$		0			0
$707$	10.9798	+	10.5892i	0.412936	+	0.398248i
$708$		0			0
$709$	0.397035	−	6.05758i	0.0149110	−	0.227497i	−0.983899	−	0.178725i	$-0.942803\pi$
$709$	0.397035	−	6.05758i	0.0149110	−	0.227497i	0.998810	−	0.0487719i	$-0.0155307\pi$
$710$		0			0
$711$	−9.40700	−	3.19324i	−0.352790	−	0.119756i
$712$		0			0
$713$	4.35448			0.163077
$714$		0			0
$715$	−20.6628			−0.772743
$716$		0			0
$717$	−14.8278	−	5.03335i	−0.553753	−	0.187974i
$718$		0			0
$719$	−2.67305	+	40.7829i	−0.0996881	+	1.52095i	0.596223	+	0.802819i	$0.296667\pi$
$719$	−2.67305	+	40.7829i	−0.0996881	+	1.52095i	−0.695911	+	0.718128i	$0.744999\pi$
$720$		0			0
$721$	2.55626	+	8.89285i	0.0952002	+	0.331187i
$722$		0			0
$723$	−47.2399	−	36.2484i	−1.75687	−	1.34809i
$724$		0			0
$725$	14.1237	+	12.3862i	0.524541	+	0.460010i
$726$		0			0
$727$	−34.5699	−	34.5699i	−1.28213	−	1.28213i	−0.939456	−	0.342670i	$-0.888669\pi$
$727$	−34.5699	−	34.5699i	−1.28213	−	1.28213i	−0.342670	−	0.939456i	$-0.611331\pi$
$728$		0			0
$729$	9.62965	−	23.2480i	0.356654	−	0.861038i
$730$		0			0
$731$	−4.06535	+	43.9267i	−0.150363	+	1.62469i
$732$		0			0
$733$	−10.4047	+	1.36980i	−0.384306	+	0.0505948i	−0.320204	−	0.947349i	$-0.603752\pi$
$733$	−10.4047	+	1.36980i	−0.384306	+	0.0505948i	−0.0641016	+	0.997943i	$0.520418\pi$
$734$		0			0
$735$	10.7854	−	8.91444i	0.397824	−	0.328814i
$736$		0			0
$737$	15.4382	+	45.4794i	0.568673	+	1.67526i
$738$		0			0
$739$	15.2647	+	2.00964i	0.561522	+	0.0739258i	0.405944	−	0.913898i	$-0.366943\pi$
$739$	15.2647	+	2.00964i	0.561522	+	0.0739258i	0.155578	+	0.987824i	$0.450276\pi$
$740$		0			0
$741$	−44.2923	−	66.2881i	−1.62712	−	2.43515i
$742$		0			0
$743$	33.4883	+	22.3762i	1.22857	+	0.820902i	0.988701	−	0.149904i	$-0.0478963\pi$
$743$	33.4883	+	22.3762i	1.22857	+	0.820902i	0.239866	+	0.970806i	$0.422896\pi$
$744$		0			0
$745$	−1.33745	+	3.93999i	−0.0490003	+	0.144350i
$746$		0			0
$747$	−3.98984	−	6.91060i	−0.145980	−	0.252846i
$748$		0			0
$749$	−15.7332	+	49.2612i	−0.574878	+	1.79996i
$750$		0			0
$751$	24.3658	+	27.7838i	0.889120	+	1.01385i	0.999800	+	0.0199907i	$0.00636365\pi$
$751$	24.3658	+	27.7838i	0.889120	+	1.01385i	−0.110680	+	0.993856i	$0.535303\pi$
$752$		0			0
$753$	−19.1273	−	38.7864i	−0.697039	−	1.41346i
$754$		0			0
$755$	13.9132	−	9.29650i	0.506353	−	0.338334i
$756$		0			0
$757$	−22.4984	+	9.31913i	−0.817717	+	0.338710i	−0.752029	−	0.659131i	$-0.770924\pi$
$757$	−22.4984	+	9.31913i	−0.817717	+	0.338710i	−0.0656888	+	0.997840i	$0.520924\pi$
$758$		0			0
$759$	5.52934	−	6.30500i	0.200702	−	0.228857i
$760$		0			0
$761$	9.03818	−	33.7310i	0.327634	−	1.22275i	−0.584004	−	0.811751i	$-0.698515\pi$
$761$	9.03818	−	33.7310i	0.327634	−	1.22275i	0.911637	−	0.410995i	$-0.134819\pi$
$762$		0			0
$763$	3.57592	−	19.8491i	0.129457	−	0.718584i
$764$		0			0
$765$	3.51995	+	9.18778i	0.127264	+	0.332185i
$766$		0			0
$767$	−37.2796	+	28.6056i	−1.34609	+	1.03289i
$768$		0			0
$769$	2.19828	−	2.19828i	0.0792719	−	0.0792719i	−0.666359	−	0.745631i	$-0.732148\pi$
$769$	2.19828	−	2.19828i	0.0792719	−	0.0792719i	0.745631	+	0.666359i	$0.232148\pi$
$770$		0			0
$771$	−18.8836	−	3.75618i	−0.680077	−	0.135276i
$772$		0			0
$773$	3.61176	−	27.4341i	0.129906	−	0.986735i	−0.795019	−	0.606585i	$-0.792539\pi$
$773$	3.61176	−	27.4341i	0.129906	−	0.986735i	0.924925	−	0.380150i	$-0.124128\pi$
$774$		0			0
$775$	−11.5357	+	23.3921i	−0.414376	+	0.840271i
$776$		0			0
$777$	18.4472	−	2.76926i	0.661789	−	0.0993466i
$778$		0			0
$779$	30.8549	−	27.0590i	1.10549	−	0.969489i
$780$		0			0
$781$	52.7542	+	30.4576i	1.88769	+	1.08986i
$782$		0			0
$783$			1.05982i			0.0378748i
$784$		0			0
$785$	5.64850	−	1.12356i	0.201604	−	0.0401015i
$786$		0			0
$787$	4.08811	−	2.01603i	0.145725	−	0.0718638i	−0.367964	−	0.929840i	$-0.619945\pi$
$787$	4.08811	−	2.01603i	0.145725	−	0.0718638i	0.513689	+	0.857976i	$0.328278\pi$
$788$		0			0
$789$	−29.1137	−	14.3573i	−1.03647	−	0.511133i
$790$		0			0
$791$	−1.06737	−	0.502554i	−0.0379514	−	0.0178688i
$792$		0			0
$793$	−41.5984	+	14.1207i	−1.47720	+	0.501443i
$794$		0			0
$795$	−0.767592	−	2.86469i	−0.0272237	−	0.101600i
$796$		0			0
$797$	−42.3920	−	17.5593i	−1.50160	−	0.621984i	−0.527797	−	0.849371i	$-0.676982\pi$
$797$	−42.3920	−	17.5593i	−1.50160	−	0.621984i	−0.973805	+	0.227387i	$0.926982\pi$
$798$		0			0
$799$	−31.3848	−	29.0500i	−1.11032	−	1.02772i
$800$		0			0
$801$	−14.5029	−	18.9005i	−0.512434	−	0.667817i
$802$		0			0
$803$	−54.3102	−	14.5524i	−1.91656	−	0.513542i
$804$		0			0
$805$	−0.0284502	−	1.57115i	−0.00100274	−	0.0553759i
$806$		0			0
$807$	−43.7977	+	57.0783i	−1.54175	+	2.00925i
$808$		0			0
$809$	1.82809	+	27.8912i	0.0642721	+	0.980602i	0.901232	+	0.433338i	$0.142664\pi$
$809$	1.82809	+	27.8912i	0.0642721	+	0.980602i	−0.836960	+	0.547265i	$0.815669\pi$
$810$		0			0
$811$	12.0850	−	18.0865i	0.424362	−	0.635102i	−0.556261	−	0.831008i	$-0.687765\pi$
$811$	12.0850	−	18.0865i	0.424362	−	0.635102i	0.980623	+	0.195905i	$0.0627645\pi$
$812$		0			0
$813$	8.86321	+	44.5583i	0.310846	+	1.56273i
$814$		0			0
$815$	3.23979	−	5.61147i	0.113485	−	0.196561i
$816$		0			0
$817$	57.9509	−	33.4580i	2.02745	−	1.17055i
$818$		0			0
$819$	−40.0058	−	4.53164i	−1.39792	−	0.158348i
$820$		0			0
$821$	44.2131	+	2.89788i	1.54305	+	0.101137i	0.813001	−	0.582262i	$-0.197832\pi$
$821$	44.2131	+	2.89788i	1.54305	+	0.101137i	0.730046	+	0.683398i	$0.239499\pi$
$822$		0			0
$823$	−10.8957	+	0.714143i	−0.379801	+	0.0248935i	−0.254108	−	0.967176i	$-0.581782\pi$
$823$	−10.8957	+	0.714143i	−0.379801	+	0.0248935i	−0.125693	+	0.992069i	$0.540115\pi$
$824$		0			0
$825$	19.2222	+	46.4064i	0.669230	+	1.61566i
$826$		0			0
$827$	−10.2398	+	51.4791i	−0.356074	+	1.79010i	0.222988	+	0.974821i	$0.428419\pi$
$827$	−10.2398	+	51.4791i	−0.356074	+	1.79010i	−0.579062	+	0.815283i	$0.696581\pi$
$828$		0			0
$829$	−15.5854	+	4.17610i	−0.541304	+	0.145042i	−0.519103	−	0.854711i	$-0.673734\pi$
$829$	−15.5854	+	4.17610i	−0.541304	+	0.145042i	−0.0222011	+	0.999754i	$0.507067\pi$
$830$		0			0
$831$	−3.12582	−	23.7430i	−0.108434	−	0.823635i
$832$		0			0
$833$	23.8463	−	16.2590i	0.826224	−	0.563342i
$834$		0			0
$835$	−0.729030	−	5.53754i	−0.0252291	−	0.191634i
$836$		0			0
$837$	−1.42131	+	0.380840i	−0.0491278	+	0.0131638i
$838$		0			0
$839$	−8.24270	+	41.4389i	−0.284570	+	1.43063i	0.528733	+	0.848788i	$0.322667\pi$
$839$	−8.24270	+	41.4389i	−0.284570	+	1.43063i	−0.813303	+	0.581841i	$0.802333\pi$
$840$		0			0
$841$	−3.87055	−	9.34433i	−0.133467	−	0.322218i
$842$		0			0
$843$	58.5570	−	3.83803i	2.01681	−	0.132189i
$844$		0			0
$845$	11.9429	+	0.782776i	0.410847	+	0.0269283i
$846$		0			0
$847$	−31.2505	−	3.53989i	−1.07378	−	0.121632i
$848$		0			0
$849$	31.4956	−	18.1840i	1.08093	−	0.624073i
$850$		0			0
$851$	1.04745	−	1.81423i	0.0359060	−	0.0621911i
$852$		0			0
$853$	2.68754	+	13.5112i	0.0920196	+	0.462614i	0.999129	+	0.0417196i	$0.0132836\pi$
$853$	2.68754	+	13.5112i	0.0920196	+	0.462614i	−0.907110	+	0.420894i	$0.861716\pi$
$854$		0			0
$855$	8.29158	−	12.4092i	0.283566	−	0.424386i
$856$		0			0
$857$	−1.78772	−	27.2753i	−0.0610673	−	0.931707i	−0.912975	−	0.408015i	$-0.866221\pi$
$857$	−1.78772	−	27.2753i	−0.0610673	−	0.931707i	0.851908	−	0.523692i	$-0.175446\pi$
$858$		0			0
$859$	11.9643	−	15.5922i	0.408218	−	0.532000i	−0.543322	−	0.839524i	$-0.682834\pi$
$859$	11.9643	−	15.5922i	0.408218	−	0.532000i	0.951540	+	0.307524i	$0.0995006\pi$
$860$		0			0
$861$	−0.763450	−	42.1613i	−0.0260183	−	1.43685i
$862$		0			0
$863$	−11.1053	−	2.97565i	−0.378029	−	0.101292i	0.0648011	−	0.997898i	$-0.479359\pi$
$863$	−11.1053	−	2.97565i	−0.378029	−	0.101292i	−0.442830	+	0.896606i	$0.646025\pi$
$864$		0			0
$865$	12.7126	+	16.5674i	0.432241	+	0.563308i
$866$		0			0
$867$	11.1560	+	39.7558i	0.378879	+	1.35018i
$868$		0			0
$869$	15.1428	+	6.27236i	0.513685	+	0.212775i
$870$		0			0
$871$	−13.6365	−	50.8921i	−0.462055	−	1.72441i
$872$		0			0
$873$	−23.9977	+	8.14611i	−0.812198	+	0.275704i
$874$		0			0
$875$	18.3654	+	8.64702i	0.620862	+	0.292323i
$876$		0			0
$877$	23.8283	+	11.7508i	0.804625	+	0.396797i	0.797606	−	0.603178i	$-0.206099\pi$
$877$	23.8283	+	11.7508i	0.804625	+	0.396797i	0.00701836	+	0.999975i	$0.497766\pi$
$878$		0			0
$879$	−66.3768	+	32.7334i	−2.23883	+	1.10407i
$880$		0			0
$881$	36.6381	−	7.28777i	1.23437	−	0.245531i	0.465563	−	0.885015i	$-0.345852\pi$
$881$	36.6381	−	7.28777i	1.23437	−	0.245531i	0.768805	+	0.639484i	$0.220852\pi$
$882$		0			0
$883$		−	34.3548i		−	1.15613i	−0.815990	−	0.578066i	$-0.803808\pi$
$883$		−	34.3548i		−	1.15613i	0.815990	−	0.578066i	$-0.196192\pi$
$884$		0			0
$885$	−15.4999	−	8.94886i	−0.521023	−	0.300813i
$886$		0			0
$887$	39.5554	−	34.6892i	1.32814	−	1.16475i	0.354914	−	0.934899i	$-0.384510\pi$
$887$	39.5554	−	34.6892i	1.32814	−	1.16475i	0.973226	−	0.229849i	$-0.0738232\pi$
$888$		0			0
$889$	−17.6323	+	2.64693i	−0.591369	+	0.0887752i
$890$		0			0
$891$	−19.6594	+	39.8653i	−0.658614	+	1.33554i
$892$		0			0
$893$	−8.46725	+	64.3152i	−0.283346	+	2.15223i
$894$		0			0
$895$	−8.27701	−	1.64640i	−0.276670	−	0.0550331i
$896$		0			0
$897$	−6.50510	+	6.50510i	−0.217199	+	0.217199i
$898$		0			0
$899$	−20.8026	+	15.9624i	−0.693805	+	0.532375i
$900$		0			0
$901$	−1.03201	−	6.02962i	−0.0343811	−	0.200876i
$902$		0			0
$903$	12.1907	−	67.6676i	0.405681	−	2.25184i
$904$		0			0
$905$	0.323216	−	1.20626i	0.0107441	−	0.0400974i
$906$		0			0
$907$	24.7510	−	28.2232i	0.821845	−	0.937135i	−0.177047	−	0.984202i	$-0.556654\pi$
$907$	24.7510	−	28.2232i	0.821845	−	0.937135i	0.998892	+	0.0470679i	$0.0149877\pi$
$908$		0			0
$909$	15.4450	−	6.39754i	0.512280	−	0.212193i
$910$		0			0
$911$	−1.20077	+	0.802330i	−0.0397833	+	0.0265824i	−0.575303	−	0.817940i	$-0.695116\pi$
$911$	−1.20077	+	0.802330i	−0.0397833	+	0.0265824i	0.535520	+	0.844523i	$0.320116\pi$
$912$		0			0
$913$	5.82303	+	11.8079i	0.192714	+	0.390786i
$914$		0			0
$915$	−11.0323	−	12.5799i	−0.364716	−	0.415879i
$916$		0			0
$917$	−12.8192	+	40.1374i	−0.423328	+	1.32545i
$918$		0			0
$919$	−27.1469	−	47.0199i	−0.895495	−	1.55104i	−0.833191	−	0.552986i	$-0.813488\pi$
$919$	−27.1469	−	47.0199i	−0.895495	−	1.55104i	−0.0623045	−	0.998057i	$-0.519845\pi$
$920$		0			0
$921$	8.61802	−	25.3879i	0.283973	−	0.836558i
$922$		0			0
$923$	−55.5625	−	37.1257i	−1.82886	−	1.22201i
$924$		0			0
$925$	6.97115	+	10.4331i	0.229210	+	0.343037i
$926$		0			0
$927$	10.0540	+	1.32363i	0.330216	+	0.0434737i
$928$		0			0
$929$	−2.03420	−	5.99255i	−0.0667398	−	0.196609i	0.908444	−	0.418007i	$-0.137271\pi$
$929$	−2.03420	−	5.99255i	−0.0667398	−	0.196609i	−0.975184	+	0.221398i	$0.928938\pi$
$930$		0			0
$931$	−41.0270	−	15.2784i	−1.34461	−	0.500729i
$932$		0			0
$933$	−20.0492	+	2.63952i	−0.656380	+	0.0864141i
$934$		0			0
$935$	−4.80369	−	15.5063i	−0.157098	−	0.507111i
$936$		0			0
$937$	10.2284	−	24.6935i	0.334147	−	0.806703i	−0.664107	−	0.747638i	$-0.731188\pi$
$937$	10.2284	−	24.6935i	0.334147	−	0.806703i	0.998254	−	0.0590652i	$-0.0188120\pi$
$938$		0			0
$939$	34.6463	+	34.6463i	1.13064	+	1.13064i
$940$		0			0
$941$	−11.5549	−	10.1333i	−0.376677	−	0.330337i	0.449984	−	0.893036i	$-0.351430\pi$
$941$	−11.5549	−	10.1333i	−0.376677	−	0.330337i	−0.826662	+	0.562699i	$0.809763\pi$
$942$		0			0
$943$	−3.75703	−	2.88287i	−0.122346	−	0.0938793i
$944$		0			0
$945$	0.146698	+	0.510341i	0.00477210	+	0.0166014i
$946$		0			0
$947$	−0.860656	+	13.1311i	−0.0279676	+	0.426702i	0.960800	+	0.277242i	$0.0894204\pi$
$947$	−0.860656	+	13.1311i	−0.0279676	+	0.426702i	−0.988768	+	0.149461i	$0.952246\pi$
$948$		0			0
$949$	58.4070	+	19.8265i	1.89597	+	0.643595i
$950$		0			0
$951$	−0.0896727			−0.00290784
$952$		0			0
$953$	−4.90889			−0.159015			−0.0795073	−	0.996834i	$-0.525335\pi$
$953$	−4.90889			−0.159015			−0.0795073	+	0.996834i	$0.525335\pi$
$954$		0			0
$955$	5.44156	+	1.84716i	0.176085	+	0.0597727i
$956$		0			0
$957$	−3.30273	+	50.3899i	−0.106762	+	1.62887i
$958$		0			0
$959$	−13.2291	−	12.7585i	−0.427188	−	0.411993i
$960$		0			0
$961$	−4.28843	−	3.29063i	−0.138337	−	0.106149i
$962$		0			0
$963$	42.6099	+	37.3679i	1.37308	+	1.20416i
$964$		0			0
$965$	−0.691936	−	0.691936i	−0.0222742	−	0.0222742i
$966$		0			0
$967$	21.7828	−	52.5883i	0.700488	−	1.69113i	−0.0220143	−	0.999758i	$-0.507008\pi$
$967$	21.7828	−	52.5883i	0.700488	−	1.69113i	0.722502	−	0.691369i	$-0.242992\pi$
$968$		0			0
$969$	39.4486	−	48.6497i	1.26727	−	1.56285i
$970$		0			0
$971$	−21.4222	+	2.82029i	−0.687473	+	0.0905075i	−0.466167	−	0.884697i	$-0.654365\pi$
$971$	−21.4222	+	2.82029i	−0.687473	+	0.0905075i	−0.221306	+	0.975204i	$0.571032\pi$
$972$		0			0
$973$	14.9523	+	0.708432i	0.479349	+	0.0227113i
$974$		0			0
$975$	−17.7122	−	52.1783i	−0.567243	−	1.67104i
$976$		0			0
$977$	32.6956	+	4.30446i	1.04603	+	0.137712i	0.633900	−	0.773415i	$-0.281453\pi$
$977$	32.6956	+	4.30446i	1.04603	+	0.137712i	0.412126	+	0.911127i	$0.364786\pi$
$978$		0			0
$979$	21.8376	+	32.6822i	0.697932	+	1.04453i
$980$		0			0
$981$	−18.3785	−	12.2801i	−0.586781	−	0.392075i
$982$		0			0
$983$	−15.1268	+	44.5621i	−0.482470	+	1.42131i	0.384582	+	0.923091i	$0.374346\pi$
$983$	−15.1268	+	44.5621i	−0.482470	+	1.42131i	−0.867051	+	0.498219i	$0.833988\pi$
$984$		0			0
$985$	−1.63292	−	2.82830i	−0.0520292	−	0.0901171i
$986$		0			0
$987$	44.8487	+	49.3099i	1.42755	+	1.56955i
$988$		0			0
$989$	−5.09123	−	5.80544i	−0.161892	−	0.184602i
$990$		0			0
$991$	7.46993	+	15.1475i	0.237290	+	0.481177i	0.982646	−	0.185490i	$-0.0593872\pi$
$991$	7.46993	+	15.1475i	0.237290	+	0.481177i	−0.745356	+	0.666667i	$0.767721\pi$
$992$		0			0
$993$	−38.8041	+	25.9281i	−1.23141	+	0.822802i
$994$		0			0
$995$	1.77250	−	0.734193i	0.0561920	−	0.0232755i
$996$		0			0
$997$	13.7522	−	15.6814i	0.435536	−	0.496634i	−0.491881	−	0.870663i	$-0.663690\pi$
$997$	13.7522	−	15.6814i	0.435536	−	0.496634i	0.927417	+	0.374029i	$0.122024\pi$
$998$		0			0
$999$	−0.183218	+	0.683780i	−0.00579677	+	0.0216338i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	476.2.bl.a.465.3	yes	192
7.5	odd	6	inner	476.2.bl.a.397.3	yes	192
17.3	odd	16	inner	476.2.bl.a.241.3	yes	192
119.54	even	48	inner	476.2.bl.a.173.3	✓	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
476.2.bl.a.173.3	✓	192	119.54	even	48	inner
476.2.bl.a.241.3	yes	192	17.3	odd	16	inner
476.2.bl.a.397.3	yes	192	7.5	odd	6	inner
476.2.bl.a.465.3	yes	192	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 476 = 2^{2} \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	476.bl (of order \(48\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.30001 - 0.780747i) q^{3} +(0.0538253 - 0.821215i) q^{5} +(-0.638390 + 2.56758i) q^{7} +(2.30040 + 1.76516i) q^{9} +O(q^{10})\)	\(q+(-2.30001 - 0.780747i) q^{3} +(0.0538253 - 0.821215i) q^{5} +(-0.638390 + 2.56758i) q^{7} +(2.30040 + 1.76516i) q^{9} +(-3.59684 - 3.15434i) q^{11} +(3.71099 + 3.71099i) q^{13} +(-0.764960 + 1.84678i) q^{15} +(-1.92217 + 3.64764i) q^{17} +(6.20071 - 0.816339i) q^{19} +(3.47293 - 5.40703i) q^{21} +(-0.231981 - 0.683394i) q^{23} +(4.28573 + 0.564227i) q^{25} +(0.135488 + 0.202773i) q^{27} +(3.61338 + 2.41438i) q^{29} +(-1.93947 + 5.71349i) q^{31} +(5.81001 + 10.0632i) q^{33} +(2.07417 + 0.662456i) q^{35} +(1.91391 + 2.18240i) q^{37} +(-5.63796 - 11.4327i) q^{39} +(5.45597 - 3.64556i) q^{41} +(9.88489 - 4.09446i) q^{43} +(1.57340 - 1.79412i) q^{45} +(-2.68453 + 10.0188i) q^{47} +(-6.18492 - 3.27823i) q^{49} +(7.26889 - 6.88886i) q^{51} +(-1.17707 + 0.903197i) q^{53} +(-2.78399 + 2.78399i) q^{55} +(-14.8990 - 2.96360i) q^{57} +(-1.16868 + 8.87703i) q^{59} +(-3.70220 + 7.50731i) q^{61} +(-6.00075 + 4.77961i) q^{63} +(3.24727 - 2.84778i) q^{65} +(-8.69425 - 5.01963i) q^{67} +1.75293i q^{69} +(-12.4883 + 2.48408i) q^{71} +(10.5408 - 5.19814i) q^{73} +(-9.41668 - 4.64379i) q^{75} +(10.3952 - 7.22147i) q^{77} +(-3.24424 + 1.10127i) q^{79} +(-2.40472 - 8.97454i) q^{81} +(-2.54251 - 1.05314i) q^{83} +(2.89203 + 1.77485i) q^{85} +(-6.42578 - 8.37424i) q^{87} +(-7.93622 - 2.12650i) q^{89} +(-11.8973 + 7.15920i) q^{91} +(8.92157 - 11.6268i) q^{93} +(-0.336635 - 5.13606i) q^{95} +(-4.85571 + 7.26708i) q^{97} +(-2.70626 - 13.6053i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q+O(q^{10}) \) 192 * q	\( 192 q + 8 q^{11} + 48 q^{15} - 24 q^{21} + 8 q^{25} - 32 q^{35} - 32 q^{37} - 16 q^{39} + 64 q^{49} + 32 q^{51} - 32 q^{53} - 48 q^{61} + 96 q^{63} + 16 q^{65} - 32 q^{71} + 120 q^{73} - 144 q^{75} + 16 q^{77} + 48 q^{81} - 160 q^{85} + 144 q^{87} - 64 q^{91} + 64 q^{93} + 32 q^{95} - 368 q^{99}+O(q^{100}) \) 192 * q + 8 * q^11 + 48 * q^15 - 24 * q^21 + 8 * q^25 - 32 * q^35 - 32 * q^37 - 16 * q^39 + 64 * q^49 + 32 * q^51 - 32 * q^53 - 48 * q^61 + 96 * q^63 + 16 * q^65 - 32 * q^71 + 120 * q^73 - 144 * q^75 + 16 * q^77 + 48 * q^81 - 160 * q^85 + 144 * q^87 - 64 * q^91 + 64 * q^93 + 32 * q^95 - 368 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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