LMFDB - Embedded newform 702.2.bb.a.71.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [702,2,Mod(71,702)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(702, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([10, 5]))

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

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

chi := DirichletCharacter("702.71");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 702 = 2 \cdot 3^{3} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	702.bb (of order $12$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.60549822189$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 234)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			71.5
Character	$\chi$	$=$	702.71
Dual form			702.2.bb.a.89.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{4} +(0.670386 - 0.179629i) q^{5} +(-4.43374 + 1.18802i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.601052 - 0.347017i) q^{10} +(1.59115 - 1.59115i) q^{11} +(3.60547 - 0.0239902i) q^{13} +(3.97518 + 2.29507i) q^{14} -1.00000 q^{16} +(-2.32181 - 4.02149i) q^{17} +(-2.81042 - 0.753050i) q^{19} +(0.179629 + 0.670386i) q^{20} -2.25023 q^{22} +(-2.37251 - 4.10931i) q^{23} +(-3.91298 + 2.25916i) q^{25} +(-2.56642 - 2.53249i) q^{26} +(-1.18802 - 4.43374i) q^{28} -4.88226i q^{29} +(-1.74651 - 6.51808i) q^{31} +(0.707107 + 0.707107i) q^{32} +(-1.20186 + 4.48539i) q^{34} +(-2.75891 + 1.59286i) q^{35} +(3.44953 - 0.924299i) q^{37} +(1.45478 + 2.51976i) q^{38} +(0.347017 - 0.601052i) q^{40} +(1.48606 - 5.54605i) q^{41} +(4.59562 + 2.65328i) q^{43} +(1.59115 + 1.59115i) q^{44} +(-1.22810 + 4.58334i) q^{46} +(-11.6601 - 3.12430i) q^{47} +(12.1845 - 7.03470i) q^{49} +(4.36436 + 1.16943i) q^{50} +(0.0239902 + 3.60547i) q^{52} +5.06576i q^{53} +(0.780869 - 1.35250i) q^{55} +(-2.29507 + 3.97518i) q^{56} +(-3.45228 + 3.45228i) q^{58} +(-3.79710 + 3.79710i) q^{59} +(-1.56055 + 2.70295i) q^{61} +(-3.37401 + 5.84395i) q^{62} -1.00000i q^{64} +(2.41275 - 0.663731i) q^{65} +(-12.6377 - 3.38625i) q^{67} +(4.02149 - 2.32181i) q^{68} +(3.07717 + 0.824524i) q^{70} +(4.16970 - 15.5615i) q^{71} +(-5.55110 - 5.55110i) q^{73} +(-3.09276 - 1.78561i) q^{74} +(0.753050 - 2.81042i) q^{76} +(-5.16444 + 8.94507i) q^{77} +(-1.55400 - 2.69161i) q^{79} +(-0.670386 + 0.179629i) q^{80} +(-4.97245 + 2.87085i) q^{82} +(-2.45977 + 9.17998i) q^{83} +(-2.27888 - 2.27888i) q^{85} +(-1.37344 - 5.12575i) q^{86} -2.25023i q^{88} +(0.648204 + 2.41913i) q^{89} +(-15.9572 + 4.38972i) q^{91} +(4.10931 - 2.37251i) q^{92} +(6.03569 + 10.4541i) q^{94} -2.01934 q^{95} +(-0.317765 - 1.18591i) q^{97} +(-13.5900 - 3.64143i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 4 q^{7} - 56 q^{16} - 8 q^{19} - 4 q^{28} + 8 q^{31} - 24 q^{35} - 4 q^{37} + 36 q^{38} + 48 q^{41} + 12 q^{43} - 60 q^{47} + 24 q^{50} - 4 q^{52} + 120 q^{65} - 56 q^{67} - 24 q^{71} + 28 q^{73}+ \cdots + 48 q^{98}+O(q^{100}) $ 56 * q + 4 * q^7 - 56 * q^16 - 8 * q^19 - 4 * q^28 + 8 * q^31 - 24 * q^35 - 4 * q^37 + 36 * q^38 + 48 * q^41 + 12 * q^43 - 60 * q^47 + 24 * q^50 - 4 * q^52 + 120 * q^65 - 56 * q^67 - 24 * q^71 + 28 * q^73 - 48 * q^74 + 4 * q^76 + 24 * q^77 - 24 * q^79 + 60 * q^83 - 48 * q^86 + 4 * q^91 + 24 * q^92 + 20 * q^97 + 48 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/702\mathbb{Z}\right)^\times$.

$n$	$379$	$677$
$\chi(n)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$3$		0			0
$3$		0			0
$4$			1.00000i			0.500000i
$5$	0.670386	−	0.179629i	0.299806	−	0.0803327i	−0.105780	−	0.994390i	$-0.533734\pi$
$5$	0.670386	−	0.179629i	0.299806	−	0.0803327i	0.405586	+	0.914057i	$0.367067\pi$
$6$		0			0
$7$	−4.43374	+	1.18802i	−1.67579	+	0.449028i	−0.966664	−	0.256049i	$-0.917579\pi$
$7$	−4.43374	+	1.18802i	−1.67579	+	0.449028i	−0.709131	+	0.705077i	$0.750912\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$		0			0
$10$	−0.601052	−	0.347017i	−0.190069	−	0.109736i
$11$	1.59115	−	1.59115i	0.479751	−	0.479751i	−0.425301	−	0.905052i	$-0.639832\pi$
$11$	1.59115	−	1.59115i	0.479751	−	0.479751i	0.905052	+	0.425301i	$0.139832\pi$
$12$		0			0
$13$	3.60547	−	0.0239902i	0.999978	−	0.00665368i
$13$	3.60547	−	0.0239902i	0.999978	−	0.00665368i
$14$	3.97518	+	2.29507i	1.06241	+	0.613383i
$15$		0			0
$16$	−1.00000			−0.250000
$17$	−2.32181	−	4.02149i	−0.563121	−	0.975354i	−0.997222	−	0.0744895i	$-0.976267\pi$
$17$	−2.32181	−	4.02149i	−0.563121	−	0.975354i	0.434101	−	0.900864i	$-0.357066\pi$
$18$		0			0
$19$	−2.81042	−	0.753050i	−0.644755	−	0.172762i	−0.0783988	−	0.996922i	$-0.524981\pi$
$19$	−2.81042	−	0.753050i	−0.644755	−	0.172762i	−0.566356	+	0.824160i	$0.691647\pi$
$20$	0.179629	+	0.670386i	0.0401663	+	0.149903i
$21$		0			0
$22$	−2.25023			−0.479751
$23$	−2.37251	−	4.10931i	−0.494703	−	0.856851i	0.505278	−	0.862957i	$-0.331390\pi$
$23$	−2.37251	−	4.10931i	−0.494703	−	0.856851i	−0.999981	+	0.00610531i	$0.998057\pi$
$24$		0			0
$25$	−3.91298	+	2.25916i	−0.782595	+	0.451832i
$26$	−2.56642	−	2.53249i	−0.503316	−	0.496662i
$27$		0			0
$28$	−1.18802	−	4.43374i	−0.224514	−	0.837897i
$29$		−	4.88226i		−	0.906613i	−0.891355	−	0.453307i	$-0.850244\pi$
$29$		−	4.88226i		−	0.906613i	0.891355	−	0.453307i	$-0.149756\pi$
$30$		0			0
$31$	−1.74651	−	6.51808i	−0.313683	−	1.17068i	−0.925209	−	0.379457i	$-0.876111\pi$
$31$	−1.74651	−	6.51808i	−0.313683	−	1.17068i	0.611526	−	0.791224i	$-0.290556\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$		0			0
$34$	−1.20186	+	4.48539i	−0.206116	+	0.769237i
$35$	−2.75891	+	1.59286i	−0.466341	+	0.269242i
$36$		0			0
$37$	3.44953	−	0.924299i	0.567099	−	0.151954i	0.0361333	−	0.999347i	$-0.488496\pi$
$37$	3.44953	−	0.924299i	0.567099	−	0.151954i	0.530966	+	0.847393i	$0.321829\pi$
$38$	1.45478	+	2.51976i	0.235997	+	0.408758i
$39$		0			0
$40$	0.347017	−	0.601052i	0.0548682	−	0.0950346i
$41$	1.48606	−	5.54605i	0.232083	−	0.866147i	−0.747358	−	0.664421i	$-0.768678\pi$
$41$	1.48606	−	5.54605i	0.232083	−	0.866147i	0.979442	−	0.201726i	$-0.0646551\pi$
$42$		0			0
$43$	4.59562	+	2.65328i	0.700826	+	0.404622i	0.807655	−	0.589655i	$-0.200736\pi$
$43$	4.59562	+	2.65328i	0.700826	+	0.404622i	−0.106829	+	0.994277i	$0.534070\pi$
$44$	1.59115	+	1.59115i	0.239875	+	0.239875i
$45$		0			0
$46$	−1.22810	+	4.58334i	−0.181074	+	0.675777i
$47$	−11.6601	−	3.12430i	−1.70080	−	0.455727i	−0.727656	−	0.685943i	$-0.759390\pi$
$47$	−11.6601	−	3.12430i	−1.70080	−	0.455727i	−0.973140	+	0.230216i	$0.926057\pi$
$48$		0			0
$49$	12.1845	−	7.03470i	1.74064	−	1.00496i
$50$	4.36436	+	1.16943i	0.617213	+	0.165382i
$51$		0			0
$52$	0.0239902	+	3.60547i	0.00332684	+	0.499989i
$53$			5.06576i			0.695835i	0.937525	+	0.347918i	$0.113111\pi$
$53$			5.06576i			0.695835i	−0.937525	+	0.347918i	$0.886889\pi$
$54$		0			0
$55$	0.780869	−	1.35250i	0.105292	−	0.182372i
$56$	−2.29507	+	3.97518i	−0.306692	+	0.531206i
$57$		0			0
$58$	−3.45228	+	3.45228i	−0.453307	+	0.453307i
$59$	−3.79710	+	3.79710i	−0.494341	+	0.494341i	−0.909671	−	0.415330i	$-0.863666\pi$
$59$	−3.79710	+	3.79710i	−0.494341	+	0.494341i	0.415330	+	0.909671i	$0.363666\pi$
$60$		0			0
$61$	−1.56055	+	2.70295i	−0.199808	+	0.346078i	−0.948466	−	0.316879i	$-0.897365\pi$
$61$	−1.56055	+	2.70295i	−0.199808	+	0.346078i	0.748658	+	0.662956i	$0.230699\pi$
$62$	−3.37401	+	5.84395i	−0.428499	+	0.742182i
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$	2.41275	−	0.663731i	0.299265	−	0.0823257i
$66$		0			0
$67$	−12.6377	−	3.38625i	−1.54393	−	0.413696i	−0.616400	−	0.787433i	$-0.711410\pi$
$67$	−12.6377	−	3.38625i	−1.54393	−	0.413696i	−0.927535	+	0.373737i	$0.878076\pi$
$68$	4.02149	−	2.32181i	0.487677	−	0.281560i
$69$		0			0
$70$	3.07717	+	0.824524i	0.367792	+	0.0985495i
$71$	4.16970	−	15.5615i	0.494852	−	1.84681i	−0.0360054	−	0.999352i	$-0.511463\pi$
$71$	4.16970	−	15.5615i	0.494852	−	1.84681i	0.530857	−	0.847461i	$-0.321870\pi$
$72$		0			0
$73$	−5.55110	−	5.55110i	−0.649707	−	0.649707i	0.303215	−	0.952922i	$-0.401940\pi$
$73$	−5.55110	−	5.55110i	−0.649707	−	0.649707i	−0.952922	+	0.303215i	$0.901940\pi$
$74$	−3.09276	−	1.78561i	−0.359526	−	0.207573i
$75$		0			0
$76$	0.753050	−	2.81042i	0.0863808	−	0.322378i
$77$	−5.16444	+	8.94507i	−0.588542	+	1.01939i
$78$		0			0
$79$	−1.55400	−	2.69161i	−0.174839	−	0.302829i	0.765267	−	0.643713i	$-0.222607\pi$
$79$	−1.55400	−	2.69161i	−0.174839	−	0.302829i	−0.940105	+	0.340884i	$0.889274\pi$
$80$	−0.670386	+	0.179629i	−0.0749514	+	0.0200832i
$81$		0			0
$82$	−4.97245	+	2.87085i	−0.549115	+	0.317032i
$83$	−2.45977	+	9.17998i	−0.269995	+	1.00763i	0.689127	+	0.724640i	$0.257994\pi$
$83$	−2.45977	+	9.17998i	−0.269995	+	1.00763i	−0.959122	+	0.282993i	$0.908673\pi$
$84$		0			0
$85$	−2.27888	−	2.27888i	−0.247180	−	0.247180i
$86$	−1.37344	−	5.12575i	−0.148102	−	0.552724i
$87$		0			0
$88$		−	2.25023i		−	0.239875i
$89$	0.648204	+	2.41913i	0.0687095	+	0.256427i	0.991733	−	0.128315i	$-0.0409569\pi$
$89$	0.648204	+	2.41913i	0.0687095	+	0.256427i	−0.923024	+	0.384743i	$0.874290\pi$
$90$		0			0
$91$	−15.9572	+	4.38972i	−1.67277	+	0.460168i
$92$	4.10931	−	2.37251i	0.428426	−	0.247352i
$93$		0			0
$94$	6.03569	+	10.4541i	0.622534	+	1.07826i
$95$	−2.01934			−0.207180
$96$		0			0
$97$	−0.317765	−	1.18591i	−0.0322641	−	0.120411i	0.947916	−	0.318521i	$-0.103186\pi$
$97$	−0.317765	−	1.18591i	−0.0322641	−	0.120411i	−0.980180	+	0.198110i	$0.936520\pi$
$98$	−13.5900	−	3.64143i	−1.37280	−	0.367840i
$99$		0			0
$100$	−2.25916	−	3.91298i	−0.225916	−	0.391298i
$101$	3.76440			0.374572			0.187286	−	0.982305i	$-0.440031\pi$
$101$	3.76440			0.374572			0.187286	+	0.982305i	$0.440031\pi$
$102$		0			0
$103$	13.1567	+	7.59604i	1.29637	+	0.748460i	0.979775	−	0.200100i	$-0.0641268\pi$
$103$	13.1567	+	7.59604i	1.29637	+	0.748460i	0.316596	+	0.948561i	$0.397460\pi$
$104$	2.53249	−	2.56642i	0.248331	−	0.251658i
$105$		0			0
$106$	3.58203	−	3.58203i	0.347918	−	0.347918i
$107$	4.73458	+	2.73351i	0.457709	+	0.264259i	0.711081	−	0.703111i	$-0.248206\pi$
$107$	4.73458	+	2.73351i	0.457709	+	0.264259i	−0.253371	+	0.967369i	$0.581539\pi$
$108$		0			0
$109$	5.10130	−	5.10130i	0.488616	−	0.488616i	−0.419253	−	0.907869i	$-0.637708\pi$
$109$	5.10130	−	5.10130i	0.488616	−	0.488616i	0.907869	+	0.419253i	$0.137708\pi$
$110$	−1.50852	+	0.404207i	−0.143832	+	0.0385397i
$111$		0			0
$112$	4.43374	−	1.18802i	0.418949	−	0.112257i
$113$		−	0.472893i		−	0.0444861i	−0.999753	−	0.0222430i	$-0.992919\pi$
$113$		−	0.472893i		−	0.0444861i	0.999753	−	0.0222430i	$-0.00708076\pi$
$114$		0			0
$115$	−2.32865	−	2.32865i	−0.217148	−	0.217148i
$116$	4.88226			0.453307
$117$		0			0
$118$	5.36992			0.494341
$119$	15.0719	+	15.0719i	1.38164	+	1.38164i
$120$		0			0
$121$			5.93646i			0.539678i
$122$	3.01475	−	0.807800i	0.272943	−	0.0731348i
$123$		0			0
$124$	6.51808	−	1.74651i	0.585341	−	0.156842i
$125$	−4.67118	+	4.67118i	−0.417803	+	0.417803i
$126$		0			0
$127$	−0.377096	−	0.217716i	−0.0334618	−	0.0193192i	0.483176	−	0.875523i	$-0.339483\pi$
$127$	−0.377096	−	0.217716i	−0.0334618	−	0.0193192i	−0.516638	+	0.856204i	$0.672817\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$		0			0
$130$	−2.17540	−	1.23674i	−0.190795	−	0.108469i
$131$	9.02321	+	5.20955i	0.788361	+	0.455161i	0.839385	−	0.543537i	$-0.182915\pi$
$131$	9.02321	+	5.20955i	0.788361	+	0.455161i	−0.0510241	+	0.998697i	$0.516249\pi$
$132$		0			0
$133$	13.3553			1.15805
$134$	6.54173	+	11.3306i	0.565119	+	0.978815i
$135$		0			0
$136$	−4.48539	−	1.20186i	−0.384619	−	0.103058i
$137$	−1.97943	−	7.38734i	−0.169114	−	0.631143i	−0.997480	−	0.0709549i	$-0.977395\pi$
$137$	−1.97943	−	7.38734i	−0.169114	−	0.631143i	0.828365	−	0.560188i	$-0.189271\pi$
$138$		0			0
$139$	11.1732			0.947702			0.473851	−	0.880605i	$-0.342863\pi$
$139$	11.1732			0.947702			0.473851	+	0.880605i	$0.342863\pi$
$140$	−1.59286	−	2.75891i	−0.134621	−	0.233171i
$141$		0			0
$142$	−13.9521	+	8.05524i	−1.17083	+	0.675980i
$143$	5.69869	−	5.77503i	0.476548	−	0.482932i
$144$		0			0
$145$	−0.876997	−	3.27300i	−0.0728307	−	0.271808i
$146$			7.85044i			0.649707i
$147$		0			0
$148$	0.924299	+	3.44953i	0.0759769	+	0.283550i
$149$	5.23203	+	5.23203i	0.428625	+	0.428625i	0.888160	−	0.459535i	$-0.151984\pi$
$149$	5.23203	+	5.23203i	0.428625	+	0.428625i	−0.459535	+	0.888160i	$0.651984\pi$
$150$		0			0
$151$	−3.70881	+	13.8415i	−0.301818	+	1.12640i	0.633831	+	0.773471i	$0.281481\pi$
$151$	−3.70881	+	13.8415i	−0.301818	+	1.12640i	−0.935650	+	0.352930i	$0.885185\pi$
$152$	−2.51976	+	1.45478i	−0.204379	+	0.117998i
$153$		0			0
$154$	9.97693	−	2.67331i	0.803964	−	0.215421i
$155$	−2.34168	−	4.05590i	−0.188088	−	0.325778i
$156$		0			0
$157$	−2.86104	+	4.95546i	−0.228336	+	0.395489i	−0.957315	−	0.289047i	$-0.906662\pi$
$157$	−2.86104	+	4.95546i	−0.228336	+	0.395489i	0.728979	+	0.684536i	$0.239995\pi$
$158$	−0.804409	+	3.00210i	−0.0639954	+	0.238834i
$159$		0			0
$160$	0.601052	+	0.347017i	0.0475173	+	0.0274341i
$161$	15.4010	+	15.4010i	1.21377	+	1.21377i
$162$		0			0
$163$	−1.44621	+	5.39731i	−0.113276	+	0.422750i	−0.999152	−	0.0411708i	$-0.986891\pi$
$163$	−1.44621	+	5.39731i	−0.113276	+	0.422750i	0.885877	+	0.463921i	$0.153558\pi$
$164$	5.54605	+	1.48606i	0.433074	+	0.116042i
$165$		0			0
$166$	8.23054	−	4.75191i	0.638814	−	0.368819i
$167$	−23.6549	−	6.33832i	−1.83047	−	0.490474i	−0.832495	−	0.554033i	$-0.813088\pi$
$167$	−23.6549	−	6.33832i	−1.83047	−	0.490474i	−0.997978	+	0.0635593i	$0.979755\pi$
$168$		0			0
$169$	12.9988	−	0.172992i	0.999911	−	0.0133071i
$170$			3.22283i			0.247180i
$171$		0			0
$172$	−2.65328	+	4.59562i	−0.202311	+	0.350413i
$173$	5.29699	−	9.17465i	0.402722	−	0.697536i	−0.591331	−	0.806429i	$-0.701397\pi$
$173$	5.29699	−	9.17465i	0.402722	−	0.697536i	0.994053	+	0.108893i	$0.0347307\pi$
$174$		0			0
$175$	14.6652	−	14.6652i	1.10858	−	1.10858i
$176$	−1.59115	+	1.59115i	−0.119938	+	0.119938i
$177$		0			0
$178$	1.25223	−	2.16893i	0.0938590	−	0.162569i
$179$	6.22591	−	10.7836i	0.465346	−	0.806003i	−0.533871	−	0.845566i	$-0.679263\pi$
$179$	6.22591	−	10.7836i	0.465346	−	0.806003i	0.999217	+	0.0395630i	$0.0125966\pi$
$180$		0			0
$181$		−	18.4465i		−	1.37112i	−0.728018	−	0.685558i	$-0.759558\pi$
$181$		−	18.4465i		−	1.37112i	0.728018	−	0.685558i	$-0.240442\pi$
$182$	14.3875	+	8.17945i	1.06647	+	0.606301i
$183$		0			0
$184$	−4.58334	−	1.22810i	−0.337889	−	0.0905370i
$185$	2.14648	−	1.23927i	0.157813	−	0.0911132i
$186$		0			0
$187$	−10.0932	−	2.70445i	−0.738084	−	0.197769i
$188$	3.12430	−	11.6601i	0.227863	−	0.850398i
$189$		0			0
$190$	1.42789	+	1.42789i	0.103590	+	0.103590i
$191$	−7.37477	−	4.25783i	−0.533620	−	0.308085i	0.208870	−	0.977944i	$-0.433022\pi$
$191$	−7.37477	−	4.25783i	−0.533620	−	0.308085i	−0.742489	+	0.669858i	$0.766355\pi$
$192$		0			0
$193$	−4.89947	+	18.2851i	−0.352671	+	1.31619i	0.530718	+	0.847548i	$0.321922\pi$
$193$	−4.89947	+	18.2851i	−0.352671	+	1.31619i	−0.883390	+	0.468639i	$0.844744\pi$
$194$	−0.613875	+	1.06326i	−0.0440736	+	0.0763378i
$195$		0			0
$196$	7.03470	+	12.1845i	0.502478	+	0.870318i
$197$	16.8453	−	4.51369i	1.20018	−	0.321587i	0.397278	−	0.917698i	$-0.369955\pi$
$197$	16.8453	−	4.51369i	1.20018	−	0.321587i	0.802902	+	0.596111i	$0.203288\pi$
$198$		0			0
$199$	20.0170	−	11.5568i	1.41897	−	0.819243i	0.422761	−	0.906241i	$-0.361061\pi$
$199$	20.0170	−	11.5568i	1.41897	−	0.819243i	0.996208	+	0.0869986i	$0.0277276\pi$
$200$	−1.16943	+	4.36436i	−0.0826909	+	0.308607i
$201$		0			0
$202$	−2.66184	−	2.66184i	−0.187286	−	0.187286i
$203$	5.80020	+	21.6467i	0.407095	+	1.51930i
$204$		0			0
$205$		−	3.98493i		−	0.278320i
$206$	−3.93200	−	14.6744i	−0.273955	−	1.02242i
$207$		0			0
$208$	−3.60547	+	0.0239902i	−0.249994	+	0.00166342i
$209$	−5.67003	+	3.27359i	−0.392204	+	0.226439i
$210$		0			0
$211$	5.19424	+	8.99669i	0.357586	+	0.619358i	0.987557	−	0.157261i	$-0.0502665\pi$
$211$	5.19424	+	8.99669i	0.357586	+	0.619358i	−0.629971	+	0.776619i	$0.716933\pi$
$212$	−5.06576			−0.347918
$213$		0			0
$214$	−1.41497	−	5.28074i	−0.0967254	−	0.360984i
$215$	3.55745	+	0.953215i	0.242616	+	0.0650087i
$216$		0			0
$217$	15.4872	+	26.8246i	1.05134	+	1.82097i
$218$	−7.21433			−0.488616
$219$		0			0
$220$	1.35250	+	0.780869i	0.0911858	+	0.0526462i
$221$	−8.46768	−	14.4437i	−0.569598	−	0.971585i
$222$		0			0
$223$	11.2191	−	11.2191i	0.751283	−	0.751283i	−0.223435	−	0.974719i	$-0.571727\pi$
$223$	11.2191	−	11.2191i	0.751283	−	0.751283i	0.974719	+	0.223435i	$0.0717271\pi$
$224$	−3.97518	−	2.29507i	−0.265603	−	0.153346i
$225$		0			0
$226$	−0.334386	+	0.334386i	−0.0222430	+	0.0222430i
$227$	−6.15723	+	1.64982i	−0.408669	+	0.109503i	−0.457296	−	0.889314i	$-0.651182\pi$
$227$	−6.15723	+	1.64982i	−0.408669	+	0.109503i	0.0486270	+	0.998817i	$0.484515\pi$
$228$		0			0
$229$	12.3575	−	3.31118i	0.816606	−	0.218809i	0.173744	−	0.984791i	$-0.444414\pi$
$229$	12.3575	−	3.31118i	0.816606	−	0.218809i	0.642862	+	0.765982i	$0.277747\pi$
$230$			3.29321i			0.217148i
$231$		0			0
$232$	−3.45228	−	3.45228i	−0.226653	−	0.226653i
$233$	−18.2644			−1.19654			−0.598271	−	0.801294i	$-0.704145\pi$
$233$	−18.2644			−1.19654			−0.598271	+	0.801294i	$0.704145\pi$
$234$		0			0
$235$	−8.37796			−0.546518
$236$	−3.79710	−	3.79710i	−0.247170	−	0.247170i
$237$		0			0
$238$		−	21.3148i		−	1.38164i
$239$	−19.3192	+	5.17656i	−1.24965	+	0.334844i	−0.822203	−	0.569195i	$-0.807255\pi$
$239$	−19.3192	+	5.17656i	−1.24965	+	0.334844i	−0.427451	+	0.904039i	$0.640588\pi$
$240$		0			0
$241$	−14.5426	+	3.89667i	−0.936768	+	0.251006i	−0.694739	−	0.719262i	$-0.744480\pi$
$241$	−14.5426	+	3.89667i	−0.936768	+	0.251006i	−0.242030	+	0.970269i	$0.577813\pi$
$242$	4.19771	−	4.19771i	0.269839	−	0.269839i
$243$		0			0
$244$	−2.70295	−	1.56055i	−0.173039	−	0.0999040i
$245$	6.90465	−	6.90465i	0.441122	−	0.441122i
$246$		0			0
$247$	−10.1510	−	2.64768i	−0.645890	−	0.168468i
$248$	−5.84395	−	3.37401i	−0.371091	−	0.214250i
$249$		0			0
$250$	6.60604			0.417803
$251$	13.1431	+	22.7645i	0.829586	+	1.43689i	0.898363	+	0.439253i	$0.144757\pi$
$251$	13.1431	+	22.7645i	0.829586	+	1.43689i	−0.0687771	+	0.997632i	$0.521910\pi$
$252$		0			0
$253$	−10.3136	−	2.76352i	−0.648409	−	0.173741i
$254$	0.112698	+	0.420596i	0.00707132	+	0.0263905i
$255$		0			0
$256$	1.00000			0.0625000
$257$	−6.83291	−	11.8349i	−0.426225	−	0.738244i	0.570309	−	0.821430i	$-0.306824\pi$
$257$	−6.83291	−	11.8349i	−0.426225	−	0.738244i	−0.996534	+	0.0831866i	$0.973490\pi$
$258$		0			0
$259$	−14.1962	+	8.19619i	−0.882110	+	0.509286i
$260$	0.663731	+	2.41275i	0.0411629	+	0.149632i
$261$		0			0
$262$	−2.69666	−	10.0641i	−0.166600	−	0.621761i
$263$		−	4.79600i		−	0.295734i	−0.989007	−	0.147867i	$-0.952759\pi$
$263$		−	4.79600i		−	0.295734i	0.989007	−	0.147867i	$-0.0472408\pi$
$264$		0			0
$265$	0.909959	+	3.39601i	0.0558983	+	0.208615i
$266$	−9.44363	−	9.44363i	−0.579026	−	0.579026i
$267$		0			0
$268$	3.38625	−	12.6377i	0.206848	−	0.771967i
$269$	−21.5499	+	12.4418i	−1.31392	+	0.758591i	−0.982743	−	0.184978i	$-0.940779\pi$
$269$	−21.5499	+	12.4418i	−1.31392	+	0.758591i	−0.331176	+	0.943569i	$0.607445\pi$
$270$		0			0
$271$	−0.766787	+	0.205460i	−0.0465790	+	0.0124808i	−0.282033	−	0.959405i	$-0.591009\pi$
$271$	−0.766787	+	0.205460i	−0.0465790	+	0.0124808i	0.235454	+	0.971885i	$0.424342\pi$
$272$	2.32181	+	4.02149i	0.140780	+	0.243838i
$273$		0			0
$274$	−3.82397	+	6.62331i	−0.231015	+	0.400129i
$275$	−2.63148	+	9.82081i	−0.158684	+	0.592217i
$276$		0			0
$277$	28.5357	+	16.4751i	1.71455	+	0.989893i	0.928179	+	0.372133i	$0.121373\pi$
$277$	28.5357	+	16.4751i	1.71455	+	0.989893i	0.786366	+	0.617760i	$0.211960\pi$
$278$	−7.90068	−	7.90068i	−0.473851	−	0.473851i
$279$		0			0
$280$	−0.824524	+	3.07717i	−0.0492747	+	0.183896i
$281$	17.5706	+	4.70802i	1.04817	+	0.280857i	0.741496	−	0.670957i	$-0.234117\pi$
$281$	17.5706	+	4.70802i	1.04817	+	0.280857i	0.306676	+	0.951814i	$0.400783\pi$
$282$		0			0
$283$	−21.1331	+	12.2012i	−1.25624	+	0.725288i	−0.972341	−	0.233568i	$-0.924960\pi$
$283$	−21.1331	+	12.2012i	−1.25624	+	0.725288i	−0.283895	+	0.958856i	$0.591627\pi$
$284$	15.5615	+	4.16970i	0.923406	+	0.247426i
$285$		0			0
$286$	−8.11314	+	0.0539834i	−0.479740	+	0.00319211i
$287$			26.3552i			1.55570i
$288$		0			0
$289$	−2.28157	+	3.95179i	−0.134210	+	0.232458i
$290$	−1.69423	+	2.93449i	−0.0994886	+	0.172319i
$291$		0			0
$292$	5.55110	−	5.55110i	0.324853	−	0.324853i
$293$	−2.57215	+	2.57215i	−0.150266	+	0.150266i	−0.778237	−	0.627971i	$-0.783886\pi$
$293$	−2.57215	+	2.57215i	−0.150266	+	0.150266i	0.627971	+	0.778237i	$0.283886\pi$
$294$		0			0
$295$	−1.86345	+	3.22760i	−0.108494	+	0.187918i
$296$	1.78561	−	3.09276i	0.103786	−	0.179763i
$297$		0			0
$298$		−	7.39921i		−	0.428625i
$299$	−8.65261	−	14.7591i	−0.500394	−	0.853541i
$300$		0			0
$301$	−23.5279	−	6.30429i	−1.35613	−	0.363373i
$302$	12.4099	−	7.16486i	0.714110	−	0.412291i
$303$		0			0
$304$	2.81042	+	0.753050i	0.161189	+	0.0431904i
$305$	−0.560641	+	2.09234i	−0.0321022	+	0.119807i
$306$		0			0
$307$	10.8993	+	10.8993i	0.622055	+	0.622055i	0.946057	−	0.324001i	$-0.105028\pi$
$307$	10.8993	+	10.8993i	0.622055	+	0.622055i	−0.324001	+	0.946057i	$0.605028\pi$
$308$	−8.94507	−	5.16444i	−0.509693	−	0.294271i
$309$		0			0
$310$	−1.21214	+	4.52377i	−0.0688450	+	0.256933i
$311$	5.37895	−	9.31661i	0.305012	−	0.528296i	−0.672252	−	0.740322i	$-0.734673\pi$
$311$	5.37895	−	9.31661i	0.305012	−	0.528296i	0.977264	+	0.212026i	$0.0680062\pi$
$312$		0			0
$313$	6.34655	+	10.9926i	0.358728	+	0.621336i	0.987749	−	0.156053i	$-0.0498771\pi$
$313$	6.34655	+	10.9926i	0.358728	+	0.621336i	−0.629020	+	0.777389i	$0.716544\pi$
$314$	5.52710	−	1.48098i	0.311912	−	0.0835766i
$315$		0			0
$316$	2.69161	−	1.55400i	0.151415	−	0.0874193i
$317$	6.74033	−	25.1552i	0.378574	−	1.41286i	−0.469477	−	0.882945i	$-0.655557\pi$
$317$	6.74033	−	25.1552i	0.378574	−	1.41286i	0.848051	−	0.529914i	$-0.177776\pi$
$318$		0			0
$319$	−7.76843	−	7.76843i	−0.434948	−	0.434948i
$320$	−0.179629	−	0.670386i	−0.0100416	−	0.0374757i
$321$		0			0
$322$		−	21.7803i		−	1.21377i
$323$	3.49687	+	13.0505i	0.194571	+	0.726150i
$324$		0			0
$325$	−14.0539	+	8.23920i	−0.779572	+	0.457029i
$326$	4.83910	−	2.79386i	0.268013	−	0.154737i
$327$		0			0
$328$	−2.87085	−	4.97245i	−0.158516	−	0.274558i
$329$	55.4094			3.05482
$330$		0			0
$331$	−5.24463	−	19.5732i	−0.288271	−	1.07584i	−0.946416	−	0.322950i	$-0.895325\pi$
$331$	−5.24463	−	19.5732i	−0.288271	−	1.07584i	0.658145	−	0.752891i	$-0.271341\pi$
$332$	−9.17998	−	2.45977i	−0.503817	−	0.134997i
$333$		0			0
$334$	12.2447	+	21.2084i	0.670000	+	1.16047i
$335$	−9.08037			−0.496114
$336$		0			0
$337$	−6.82932	−	3.94291i	−0.372017	−	0.214784i	0.302322	−	0.953206i	$-0.402238\pi$
$337$	−6.82932	−	3.94291i	−0.372017	−	0.214784i	−0.674339	+	0.738422i	$0.735571\pi$
$338$	−9.31390	−	9.06925i	−0.506609	−	0.493302i
$339$		0			0
$340$	2.27888	−	2.27888i	0.123590	−	0.123590i
$341$	−13.1502	−	7.59229i	−0.712125	−	0.411146i
$342$		0			0
$343$	−22.9453	+	22.9453i	−1.23893	+	1.23893i
$344$	5.12575	−	1.37344i	0.276362	−	0.0740510i
$345$		0			0
$346$	−10.2330	+	2.74192i	−0.550129	+	0.147407i
$347$			16.9956i			0.912370i	0.889885	+	0.456185i	$0.150784\pi$
$347$			16.9956i			0.912370i	−0.889885	+	0.456185i	$0.849216\pi$
$348$		0			0
$349$	−10.2799	−	10.2799i	−0.550269	−	0.550269i	0.376250	−	0.926518i	$-0.377214\pi$
$349$	−10.2799	−	10.2799i	−0.550269	−	0.550269i	−0.926518	+	0.376250i	$0.877214\pi$
$350$	−20.7397			−1.10858
$351$		0			0
$352$	2.25023			0.119938
$353$	6.02030	+	6.02030i	0.320428	+	0.320428i	0.848931	−	0.528503i	$-0.177246\pi$
$353$	6.02030	+	6.02030i	0.320428	+	0.320428i	−0.528503	+	0.848931i	$0.677246\pi$
$354$		0			0
$355$		−	11.1812i		−	0.593438i
$356$	−2.41913	+	0.648204i	−0.128214	+	0.0343548i
$357$		0			0
$358$	−12.0275	+	3.22277i	−0.635674	+	0.170328i
$359$	−2.80645	+	2.80645i	−0.148119	+	0.148119i	−0.777277	−	0.629158i	$-0.783400\pi$
$359$	−2.80645	+	2.80645i	−0.148119	+	0.148119i	0.629158	+	0.777277i	$0.283400\pi$
$360$		0			0
$361$	−9.12309	−	5.26722i	−0.480163	−	0.277222i
$362$	−13.0436	+	13.0436i	−0.685558	+	0.685558i
$363$		0			0
$364$	−4.38972	−	15.9572i	−0.230084	−	0.836385i
$365$	−4.71852	−	2.72424i	−0.246979	−	0.142593i
$366$		0			0
$367$	−24.3581			−1.27148			−0.635742	−	0.771901i	$-0.719306\pi$
$367$	−24.3581			−1.27148			−0.635742	+	0.771901i	$0.719306\pi$
$368$	2.37251	+	4.10931i	0.123676	+	0.214213i
$369$		0			0
$370$	−2.39409	−	0.641495i	−0.124463	−	0.0333497i
$371$	−6.01820	−	22.4602i	−0.312449	−	1.16608i
$372$		0			0
$373$	−9.25807			−0.479365			−0.239682	−	0.970851i	$-0.577043\pi$
$373$	−9.25807			−0.479365			−0.239682	+	0.970851i	$0.577043\pi$
$374$	5.22460	+	9.04927i	0.270158	+	0.467927i
$375$		0			0
$376$	−10.4541	+	6.03569i	−0.539130	+	0.311267i
$377$	−0.117126	−	17.6029i	−0.00603231	−	0.906593i
$378$		0			0
$379$	−3.58050	−	13.3626i	−0.183918	−	0.686391i	−0.994860	−	0.101264i	$-0.967711\pi$
$379$	−3.58050	−	13.3626i	−0.183918	−	0.686391i	0.810942	−	0.585127i	$-0.198955\pi$
$380$		−	2.01934i		−	0.103590i
$381$		0			0
$382$	2.20401	+	8.22549i	0.112767	+	0.420853i
$383$	−12.5916	−	12.5916i	−0.643398	−	0.643398i	0.307991	−	0.951389i	$-0.400343\pi$
$383$	−12.5916	−	12.5916i	−0.643398	−	0.643398i	−0.951389	+	0.307991i	$0.900343\pi$
$384$		0			0
$385$	−1.85537	+	6.92433i	−0.0945584	+	0.352897i
$386$	16.3939	−	9.46505i	0.834430	−	0.481758i
$387$		0			0
$388$	1.18591	−	0.317765i	0.0602057	−	0.0161321i
$389$	−7.46970	−	12.9379i	−0.378729	−	0.655978i	0.612149	−	0.790743i	$-0.290305\pi$
$389$	−7.46970	−	12.9379i	−0.378729	−	0.655978i	−0.990878	+	0.134765i	$0.956972\pi$
$390$		0			0
$391$	−11.0170	+	19.0821i	−0.557155	+	0.965021i
$392$	3.64143	−	13.5900i	0.183920	−	0.686398i
$393$		0			0
$394$	−15.1031	−	8.71978i	−0.760884	−	0.439296i
$395$	−1.52527	−	1.52527i	−0.0767447	−	0.0767447i
$396$		0			0
$397$	0.691339	−	2.58011i	0.0346973	−	0.129492i	−0.946405	−	0.322983i	$-0.895314\pi$
$397$	0.691339	−	2.58011i	0.0346973	−	0.129492i	0.981102	+	0.193491i	$0.0619810\pi$
$398$	−22.3261	−	5.98226i	−1.11911	−	0.299864i
$399$		0			0
$400$	3.91298	−	2.25916i	0.195649	−	0.112958i
$401$	0.0650204	+	0.0174222i	0.00324697	+	0.000870022i	0.260442	−	0.965489i	$-0.416132\pi$
$401$	0.0650204	+	0.0174222i	0.00324697	+	0.000870022i	−0.257195	+	0.966359i	$0.582798\pi$
$402$		0			0
$403$	−6.45338	−	23.4588i	−0.321466	−	1.16857i
$404$			3.76440i			0.187286i
$405$		0			0
$406$	11.2051	−	19.4079i	0.556101	−	0.963196i
$407$	4.01803	−	6.95943i	0.199166	−	0.344966i
$408$		0			0
$409$	−14.4433	+	14.4433i	−0.714173	+	0.714173i	−0.967405	−	0.253233i	$-0.918506\pi$
$409$	−14.4433	+	14.4433i	−0.714173	+	0.714173i	0.253233	+	0.967405i	$0.418506\pi$
$410$	−2.81777	+	2.81777i	−0.139160	+	0.139160i
$411$		0			0
$412$	−7.59604	+	13.1567i	−0.374230	+	0.648186i
$413$	12.3243	−	21.3464i	0.606441	−	1.05039i
$414$		0			0
$415$			6.59597i			0.323784i
$416$	2.56642	+	2.53249i	0.125829	+	0.124166i
$417$		0			0
$418$	6.32410	+	1.69454i	0.309322	+	0.0828825i
$419$	19.8836	−	11.4798i	0.971378	−	0.560826i	0.0717221	−	0.997425i	$-0.477151\pi$
$419$	19.8836	−	11.4798i	0.971378	−	0.560826i	0.899656	+	0.436599i	$0.143817\pi$
$420$		0			0
$421$	10.9066	+	2.92242i	0.531556	+	0.142430i	0.514607	−	0.857426i	$-0.327938\pi$
$421$	10.9066	+	2.92242i	0.531556	+	0.142430i	0.0169495	+	0.999856i	$0.494605\pi$
$422$	2.68874	−	10.0345i	0.130886	−	0.488472i
$423$		0			0
$424$	3.58203	+	3.58203i	0.173959	+	0.173959i
$425$	18.1703	+	10.4907i	0.881391	+	0.508871i
$426$		0			0
$427$	3.70792	−	13.8381i	0.179439	−	0.669674i
$428$	−2.73351	+	4.73458i	−0.132129	+	0.228855i
$429$		0			0
$430$	−1.84147	−	3.18952i	−0.0888036	−	0.153812i
$431$	−8.79469	+	2.35653i	−0.423625	+	0.113510i	−0.464332	−	0.885661i	$-0.653706\pi$
$431$	−8.79469	+	2.35653i	−0.423625	+	0.113510i	0.0407069	+	0.999171i	$0.487039\pi$
$432$		0			0
$433$	19.6096	−	11.3216i	0.942379	−	0.544083i	0.0516737	−	0.998664i	$-0.483544\pi$
$433$	19.6096	−	11.3216i	0.942379	−	0.544083i	0.890705	+	0.454581i	$0.150211\pi$
$434$	8.01675	−	29.9189i	0.384816	−	1.43615i
$435$		0			0
$436$	5.10130	+	5.10130i	0.244308	+	0.244308i
$437$	3.57325	+	13.3355i	0.170931	+	0.637925i
$438$		0			0
$439$		−	21.3894i		−	1.02086i	−0.859920	−	0.510430i	$-0.829486\pi$
$439$		−	21.3894i		−	1.02086i	0.859920	−	0.510430i	$-0.170514\pi$
$440$	−0.404207	−	1.50852i	−0.0192698	−	0.0719160i
$441$		0			0
$442$	−4.22565	+	16.2008i	−0.200994	+	0.770592i
$443$	−27.1059	+	15.6496i	−1.28784	+	0.743535i	−0.978269	−	0.207341i	$-0.933519\pi$
$443$	−27.1059	+	15.6496i	−1.28784	+	0.743535i	−0.309571	+	0.950876i	$0.600186\pi$
$444$		0			0
$445$	0.869094	+	1.50532i	0.0411990	+	0.0713588i
$446$	−15.8661			−0.751283
$447$		0			0
$448$	1.18802	+	4.43374i	0.0561285	+	0.209474i
$449$	−12.7731	−	3.42254i	−0.602800	−	0.161520i	−0.0555034	−	0.998458i	$-0.517676\pi$
$449$	−12.7731	−	3.42254i	−0.602800	−	0.161520i	−0.547297	+	0.836939i	$0.684343\pi$
$450$		0			0
$451$	−6.46007	−	11.1892i	−0.304193	−	0.526877i
$452$	0.472893			0.0222430
$453$		0			0
$454$	5.52042	+	3.18721i	0.259086	+	0.149583i
$455$	−9.90896	+	5.80919i	−0.464539	+	0.272339i
$456$		0			0
$457$	8.28185	−	8.28185i	0.387409	−	0.387409i	−0.486354	−	0.873762i	$-0.661673\pi$
$457$	8.28185	−	8.28185i	0.387409	−	0.387409i	0.873762	+	0.486354i	$0.161673\pi$
$458$	−11.0794	−	6.39671i	−0.517707	−	0.298898i
$459$		0			0
$460$	2.32865	−	2.32865i	0.108574	−	0.108574i
$461$	−7.07647	+	1.89613i	−0.329584	+	0.0883118i	−0.419817	−	0.907609i	$-0.637906\pi$
$461$	−7.07647	+	1.89613i	−0.329584	+	0.0883118i	0.0902326	+	0.995921i	$0.471239\pi$
$462$		0			0
$463$	−14.1615	+	3.79457i	−0.658142	+	0.176349i	−0.572407	−	0.819969i	$-0.693990\pi$
$463$	−14.1615	+	3.79457i	−0.658142	+	0.176349i	−0.0857346	+	0.996318i	$0.527324\pi$
$464$			4.88226i			0.226653i
$465$		0			0
$466$	12.9149	+	12.9149i	0.598271	+	0.598271i
$467$	18.0118			0.833488			0.416744	−	0.909024i	$-0.363171\pi$
$467$	18.0118			0.833488			0.416744	+	0.909024i	$0.363171\pi$
$468$		0			0
$469$	60.0549			2.77308
$470$	5.92411	+	5.92411i	0.273259	+	0.273259i
$471$		0			0
$472$			5.36992i			0.247170i
$473$	11.5341	−	3.09056i	0.530339	−	0.142104i
$474$		0			0
$475$	12.6984	−	3.40252i	0.582641	−	0.156118i
$476$	−15.0719	+	15.0719i	−0.690818	+	0.690818i
$477$		0			0
$478$	17.3211	+	10.0003i	0.792249	+	0.457405i
$479$	5.08536	−	5.08536i	0.232356	−	0.232356i	−0.581319	−	0.813675i	$-0.697463\pi$
$479$	5.08536	−	5.08536i	0.232356	−	0.232356i	0.813675	+	0.581319i	$0.197463\pi$
$480$		0			0
$481$	12.4150	−	3.41529i	0.566075	−	0.155724i
$482$	13.0385	+	7.52778i	0.593887	+	0.342881i
$483$		0			0
$484$	−5.93646			−0.269839
$485$	−0.426050	−	0.737940i	−0.0193459	−	0.0335082i
$486$		0			0
$487$	0.324094	+	0.0868407i	0.0146861	+	0.00393513i	0.266155	−	0.963930i	$-0.414247\pi$
$487$	0.324094	+	0.0868407i	0.0146861	+	0.00393513i	−0.251469	+	0.967865i	$0.580913\pi$
$488$	0.807800	+	3.01475i	0.0365674	+	0.136471i
$489$		0			0
$490$	−9.76464			−0.441122
$491$	1.96382	+	3.40144i	0.0886260	+	0.153505i	0.906931	−	0.421280i	$-0.138419\pi$
$491$	1.96382	+	3.40144i	0.0886260	+	0.153505i	−0.818305	+	0.574785i	$0.805086\pi$
$492$		0			0
$493$	−19.6339	+	11.3357i	−0.884269	+	0.510533i
$494$	5.30562	+	9.05001i	0.238711	+	0.407179i
$495$		0			0
$496$	1.74651	+	6.51808i	0.0784208	+	0.292670i
$497$			73.9493i			3.31708i
$498$		0			0
$499$	−5.25372	−	19.6072i	−0.235189	−	0.877737i	−0.978064	−	0.208307i	$-0.933205\pi$
$499$	−5.25372	−	19.6072i	−0.235189	−	0.877737i	0.742875	−	0.669431i	$-0.233462\pi$
$500$	−4.67118	−	4.67118i	−0.208901	−	0.208901i
$501$		0			0
$502$	6.80338	−	25.3906i	0.303650	−	1.13324i
$503$	−24.7833	+	14.3086i	−1.10503	+	0.637991i	−0.937538	−	0.347882i	$-0.886901\pi$
$503$	−24.7833	+	14.3086i	−1.10503	+	0.637991i	−0.167494	+	0.985873i	$0.553568\pi$
$504$		0			0
$505$	2.52360	−	0.676198i	0.112299	−	0.0300904i
$506$	5.33870	+	9.24691i	0.237334	+	0.411075i
$507$		0			0
$508$	0.217716	−	0.377096i	0.00965960	−	0.0167309i
$509$	4.15448	−	15.5047i	0.184144	−	0.687235i	−0.810668	−	0.585506i	$-0.800896\pi$
$509$	4.15448	−	15.5047i	0.184144	−	0.687235i	0.994812	−	0.101729i	$-0.0324375\pi$
$510$		0			0
$511$	31.2069	+	18.0173i	1.38051	+	0.797039i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$		0			0
$514$	−3.53697	+	13.2002i	−0.156009	+	0.582235i
$515$	10.1846	+	2.72894i	0.448785	+	0.120252i
$516$		0			0
$517$	−23.5242	+	13.5817i	−1.03459	+	0.597323i
$518$	15.8338	+	4.24266i	0.695698	+	0.186412i
$519$		0			0
$520$	1.23674	−	2.17540i	0.0542347	−	0.0953976i
$521$		−	19.3205i		−	0.846448i	−0.906025	−	0.423224i	$-0.860898\pi$
$521$		−	19.3205i		−	0.846448i	0.906025	−	0.423224i	$-0.139102\pi$
$522$		0			0
$523$	4.17667	−	7.23421i	0.182633	−	0.316330i	−0.760143	−	0.649755i	$-0.774871\pi$
$523$	4.17667	−	7.23421i	0.182633	−	0.316330i	0.942776	+	0.333426i	$0.108205\pi$
$524$	−5.20955	+	9.02321i	−0.227580	+	0.394181i
$525$		0			0
$526$	−3.39129	+	3.39129i	−0.147867	+	0.147867i
$527$	−22.1573	+	22.1573i	−0.965187	+	0.965187i
$528$		0			0
$529$	0.242357	−	0.419774i	0.0105372	−	0.0182510i
$530$	1.75791	−	3.04478i	0.0763585	−	0.132257i
$531$		0			0
$532$			13.3553i			0.579026i
$533$	5.22489	−	20.0318i	0.226315	−	0.867672i
$534$		0			0
$535$	3.66502	+	0.982038i	0.158452	+	0.0424572i
$536$	−11.3306	+	6.54173i	−0.489408	+	0.282560i
$537$		0			0
$538$	24.0358	+	6.44036i	1.03625	+	0.277664i
$539$	8.19405	−	30.5806i	0.352943	−	1.31720i
$540$		0			0
$541$	18.5480	+	18.5480i	0.797443	+	0.797443i	0.982692	−	0.185249i	$-0.0593092\pi$
$541$	18.5480	+	18.5480i	0.797443	+	0.797443i	−0.185249	+	0.982692i	$0.559309\pi$
$542$	0.687482	+	0.396918i	0.0295299	+	0.0170491i
$543$		0			0
$544$	1.20186	−	4.48539i	0.0515291	−	0.192309i
$545$	2.50350	−	4.33618i	0.107238	−	0.185742i
$546$		0			0
$547$	−11.1826	−	19.3688i	−0.478133	−	0.828151i	0.521552	−	0.853219i	$-0.325353\pi$
$547$	−11.1826	−	19.3688i	−0.478133	−	0.828151i	−0.999686	+	0.0250681i	$0.992020\pi$
$548$	7.38734	−	1.97943i	0.315572	−	0.0845572i
$549$		0			0
$550$	8.80510	−	5.08363i	0.375451	−	0.216767i
$551$	−3.67659	+	13.7212i	−0.156628	+	0.584544i
$552$		0			0
$553$	10.0877	+	10.0877i	0.428972	+	0.428972i
$554$	−8.52814	−	31.8275i	−0.362326	−	1.35222i
$555$		0			0
$556$			11.1732i			0.473851i
$557$	3.13004	+	11.6815i	0.132624	+	0.494959i	0.999996	−	0.00270033i	$-0.000859542\pi$
$557$	3.13004	+	11.6815i	0.132624	+	0.494959i	−0.867372	+	0.497660i	$0.834193\pi$
$558$		0			0
$559$	16.6330	+	9.45609i	0.703503	+	0.399950i
$560$	2.75891	−	1.59286i	0.116585	−	0.0673105i
$561$		0			0
$562$	−9.09520	−	15.7533i	−0.383658	−	0.664515i
$563$	−35.1807			−1.48269			−0.741345	−	0.671124i	$-0.765812\pi$
$563$	−35.1807			−1.48269			−0.741345	+	0.671124i	$0.765812\pi$
$564$		0			0
$565$	−0.0849455	−	0.317021i	−0.00357368	−	0.0133372i
$566$	23.5710	+	6.31582i	0.990761	+	0.265474i
$567$		0			0
$568$	−8.05524	−	13.9521i	−0.337990	−	0.585416i
$569$	11.2623			0.472141			0.236071	−	0.971736i	$-0.424140\pi$
$569$	11.2623			0.472141			0.236071	+	0.971736i	$0.424140\pi$
$570$		0			0
$571$	27.0909	+	15.6409i	1.13372	+	0.654553i	0.944868	−	0.327452i	$-0.106190\pi$
$571$	27.0909	+	15.6409i	1.13372	+	0.654553i	0.188852	+	0.982006i	$0.439523\pi$
$572$	5.77503	+	5.69869i	0.241466	+	0.238274i
$573$		0			0
$574$	18.6359	−	18.6359i	0.777848	−	0.777848i
$575$	18.5672	+	10.7198i	0.774305	+	0.447045i
$576$		0			0
$577$	−26.9790	+	26.9790i	−1.12315	+	1.12315i	−0.131887	+	0.991265i	$0.542103\pi$
$577$	−26.9790	+	26.9790i	−1.12315	+	1.12315i	−0.991265	+	0.131887i	$0.957897\pi$
$578$	4.40765	−	1.18103i	0.183334	−	0.0491242i
$579$		0			0
$580$	3.27300	−	0.876997i	0.135904	−	0.0364153i
$581$		−	43.6238i		−	1.80982i
$582$		0			0
$583$	8.06040	+	8.06040i	0.333828	+	0.333828i
$584$	−7.85044			−0.324853
$585$		0			0
$586$	3.63756			0.150266
$587$	−1.61436	−	1.61436i	−0.0666316	−	0.0666316i	0.673006	−	0.739637i	$-0.265003\pi$
$587$	−1.61436	−	1.61436i	−0.0666316	−	0.0666316i	−0.739637	+	0.673006i	$0.765003\pi$
$588$		0			0
$589$			19.6338i			0.808995i
$590$	3.59992	−	0.964595i	0.148206	−	0.0397117i
$591$		0			0
$592$	−3.44953	+	0.924299i	−0.141775	+	0.0379884i
$593$	21.4122	−	21.4122i	0.879295	−	0.879295i	−0.114166	−	0.993462i	$-0.536420\pi$
$593$	21.4122	−	21.4122i	0.879295	−	0.879295i	0.993462	+	0.114166i	$0.0364197\pi$
$594$		0			0
$595$	12.8113	+	7.39662i	0.525213	+	0.303232i
$596$	−5.23203	+	5.23203i	−0.214312	+	0.214312i
$597$		0			0
$598$	−4.31794	+	16.5546i	−0.176574	+	0.676967i
$599$	27.0669	+	15.6271i	1.10593	+	0.638506i	0.937771	−	0.347255i	$-0.112886\pi$
$599$	27.0669	+	15.6271i	1.10593	+	0.638506i	0.168154	+	0.985761i	$0.446219\pi$
$600$		0			0
$601$	−27.8755			−1.13707			−0.568533	−	0.822661i	$-0.692489\pi$
$601$	−27.8755			−1.13707			−0.568533	+	0.822661i	$0.692489\pi$
$602$	12.1789	+	21.0946i	0.496377	+	0.859750i
$603$		0			0
$604$	−13.8415	−	3.70881i	−0.563201	−	0.150909i
$605$	1.06636	+	3.97972i	0.0433538	+	0.161799i
$606$		0			0
$607$	−2.84557			−0.115498			−0.0577490	−	0.998331i	$-0.518392\pi$
$607$	−2.84557			−0.115498			−0.0577490	+	0.998331i	$0.518392\pi$
$608$	−1.45478	−	2.51976i	−0.0589992	−	0.102190i
$609$		0			0
$610$	1.87594	−	1.08308i	0.0759547	−	0.0438525i
$611$	−42.1150	−	10.9849i	−1.70379	−	0.444400i
$612$		0			0
$613$	0.202550	+	0.755928i	0.00818093	+	0.0305316i	0.969896	−	0.243521i	$-0.0783024\pi$
$613$	0.202550	+	0.755928i	0.00818093	+	0.0305316i	−0.961715	+	0.274053i	$0.911636\pi$
$614$		−	15.4139i		−	0.622055i
$615$		0			0
$616$	2.67331	+	9.97693i	0.107711	+	0.401982i
$617$	19.5997	+	19.5997i	0.789055	+	0.789055i	0.981339	−	0.192284i	$-0.0615896\pi$
$617$	19.5997	+	19.5997i	0.789055	+	0.789055i	−0.192284	+	0.981339i	$0.561590\pi$
$618$		0			0
$619$	1.73266	−	6.46639i	0.0696417	−	0.259906i	−0.922323	−	0.386419i	$-0.873712\pi$
$619$	1.73266	−	6.46639i	0.0696417	−	0.259906i	0.991965	+	0.126513i	$0.0403785\pi$
$620$	4.05590	−	2.34168i	0.162889	−	0.0940440i
$621$		0			0
$622$	−10.3913	+	2.78435i	−0.416654	+	0.111642i
$623$	−5.74793	−	9.95571i	−0.230286	−	0.398867i
$624$		0			0
$625$	9.00338	−	15.5943i	0.360135	−	0.623772i
$626$	3.28522	−	12.2606i	0.131304	−	0.490032i
$627$		0			0
$628$	−4.95546	−	2.86104i	−0.197744	−	0.114168i
$629$	−11.7262	−	11.7262i	−0.467554	−	0.467554i
$630$		0			0
$631$	−1.16111	+	4.33331i	−0.0462230	+	0.172506i	−0.985179	−	0.171532i	$-0.945128\pi$
$631$	−1.16111	+	4.33331i	−0.0462230	+	0.172506i	0.938956	+	0.344038i	$0.111795\pi$
$632$	−3.00210	−	0.804409i	−0.119417	−	0.0319977i
$633$		0			0
$634$	−22.5536	+	13.0213i	−0.895717	+	0.517142i
$635$	−0.291908	−	0.0782165i	−0.0115840	−	0.00310393i
$636$		0			0
$637$	43.7619	−	25.6557i	1.73391	−	1.01652i
$638$			10.9862i			0.434948i
$639$		0			0
$640$	−0.347017	+	0.601052i	−0.0137171	+	0.0237586i
$641$	−21.4910	+	37.2236i	−0.848845	+	1.47024i	0.0333945	+	0.999442i	$0.489368\pi$
$641$	−21.4910	+	37.2236i	−0.848845	+	1.47024i	−0.882240	+	0.470801i	$0.843965\pi$
$642$		0			0
$643$	16.1469	−	16.1469i	0.636771	−	0.636771i	−0.312987	−	0.949758i	$-0.601329\pi$
$643$	16.1469	−	16.1469i	0.636771	−	0.636771i	0.949758	+	0.312987i	$0.101329\pi$
$644$	−15.4010	+	15.4010i	−0.606886	+	0.606886i
$645$		0			0
$646$	6.75544	−	11.7008i	0.265789	−	0.460361i
$647$	18.2315	−	31.5780i	0.716756	−	1.24146i	−0.245523	−	0.969391i	$-0.578960\pi$
$647$	18.2315	−	31.5780i	0.716756	−	1.24146i	0.962278	−	0.272067i	$-0.0877071\pi$
$648$		0			0
$649$			12.0836i			0.474321i
$650$	15.7636	+	4.11163i	0.618300	+	0.161271i
$651$		0			0
$652$	−5.39731	−	1.44621i	−0.211375	−	0.0566378i
$653$	2.93974	−	1.69726i	0.115041	−	0.0664190i	−0.441375	−	0.897323i	$-0.645509\pi$
$653$	2.93974	−	1.69726i	0.115041	−	0.0664190i	0.556416	+	0.830904i	$0.312176\pi$
$654$		0			0
$655$	6.98482	+	1.87158i	0.272919	+	0.0731285i
$656$	−1.48606	+	5.54605i	−0.0580209	+	0.216537i
$657$		0			0
$658$	−39.1803	−	39.1803i	−1.52741	−	1.52741i
$659$	23.7208	+	13.6952i	0.924032	+	0.533490i	0.884919	−	0.465745i	$-0.154214\pi$
$659$	23.7208	+	13.6952i	0.924032	+	0.533490i	0.0391126	+	0.999235i	$0.487547\pi$
$660$		0			0
$661$	11.8777	−	44.3282i	0.461990	−	1.72417i	−0.204692	−	0.978826i	$-0.565619\pi$
$661$	11.8777	−	44.3282i	0.461990	−	1.72417i	0.666682	−	0.745342i	$-0.267714\pi$
$662$	−10.1318	+	17.5489i	−0.393785	+	0.682056i
$663$		0			0
$664$	4.75191	+	8.23054i	0.184410	+	0.319407i
$665$	8.95321	−	2.39900i	0.347191	−	0.0930294i
$666$		0			0
$667$	−20.0627	+	11.5832i	−0.776833	+	0.448505i
$668$	6.33832	−	23.6549i	0.245237	−	0.915236i
$669$		0			0
$670$	6.42079	+	6.42079i	0.248057	+	0.248057i
$671$	1.81774	+	6.78389i	0.0701730	+	0.261889i
$672$		0			0
$673$		−	20.6898i		−	0.797535i	−0.917052	−	0.398767i	$-0.869438\pi$
$673$		−	20.6898i		−	0.797535i	0.917052	−	0.398767i	$-0.130562\pi$
$674$	2.04100	+	7.61712i	0.0786164	+	0.293401i
$675$		0			0
$676$	0.172992	+	12.9988i	0.00665353	+	0.499956i
$677$	−6.49755	+	3.75136i	−0.249721	+	0.144176i	−0.619636	−	0.784889i	$-0.712720\pi$
$677$	−6.49755	+	3.75136i	−0.249721	+	0.144176i	0.369916	+	0.929065i	$0.379387\pi$
$678$		0			0
$679$	2.81777	+	4.88052i	0.108136	+	0.187297i
$680$	−3.22283			−0.123590
$681$		0			0
$682$	3.93006	+	14.6672i	0.150490	+	0.561635i
$683$	39.9739	+	10.7110i	1.52956	+	0.409844i	0.922875	−	0.385100i	$-0.125833\pi$
$683$	39.9739	+	10.7110i	1.52956	+	0.409844i	0.606683	+	0.794944i	$0.292500\pi$
$684$		0			0
$685$	−2.65397	−	4.59681i	−0.101403	−	0.175635i
$686$	32.4495			1.23893
$687$		0			0
$688$	−4.59562	−	2.65328i	−0.175206	−	0.101155i
$689$	0.121528	+	18.2644i	0.00462986	+	0.695820i
$690$		0			0
$691$	3.99681	−	3.99681i	0.152046	−	0.152046i	−0.626985	−	0.779031i	$-0.715711\pi$
$691$	3.99681	−	3.99681i	0.152046	−	0.152046i	0.779031	+	0.626985i	$0.215711\pi$
$692$	9.17465	+	5.29699i	0.348768	+	0.201361i
$693$		0			0
$694$	12.0177	−	12.0177i	0.456185	−	0.456185i
$695$	7.49039	−	2.00704i	0.284127	−	0.0761315i
$696$		0			0
$697$	−25.7537	+	6.90068i	−0.975491	+	0.261382i
$698$			14.5379i			0.550269i
$699$		0			0
$700$	14.6652	+	14.6652i	0.554292	+	0.554292i
$701$	−40.7022			−1.53730			−0.768651	−	0.639669i	$-0.779072\pi$
$701$	−40.7022			−1.53730			−0.768651	+	0.639669i	$0.779072\pi$
$702$		0			0
$703$	−10.3907			−0.391892
$704$	−1.59115	−	1.59115i	−0.0599688	−	0.0599688i
$705$		0			0
$706$		−	8.51399i		−	0.320428i
$707$	−16.6904	+	4.47217i	−0.627706	+	0.168193i
$708$		0			0
$709$	1.65798	−	0.444255i	0.0622668	−	0.0166843i	−0.227551	−	0.973766i	$-0.573072\pi$
$709$	1.65798	−	0.444255i	0.0622668	−	0.0166843i	0.289818	+	0.957082i	$0.406405\pi$
$710$	−7.90632	+	7.90632i	−0.296719	+	0.296719i
$711$		0			0
$712$	2.16893	+	1.25223i	0.0812843	+	0.0469295i
$713$	−22.6412	+	22.6412i	−0.847920	+	0.847920i
$714$		0			0
$715$	2.78295	−	4.89515i	0.104077	−	0.183068i
$716$	10.7836	+	6.22591i	0.403001	+	0.232673i
$717$		0			0
$718$	3.96892			0.148119
$719$	10.3528	+	17.9315i	0.386093	+	0.668732i	0.991920	−	0.126864i	$-0.0404911\pi$
$719$	10.3528	+	17.9315i	0.386093	+	0.668732i	−0.605827	+	0.795596i	$0.707158\pi$
$720$		0			0
$721$	−67.3577	−	18.0484i	−2.50853	−	0.672159i
$722$	2.72651	+	10.1755i	0.101470	+	0.378692i
$723$		0			0
$724$	18.4465			0.685558
$725$	11.0298	+	19.1042i	0.409637	+	0.709511i
$726$		0			0
$727$	38.1761	−	22.0410i	1.41587	−	0.817455i	0.419940	−	0.907552i	$-0.362051\pi$
$727$	38.1761	−	22.0410i	1.41587	−	0.817455i	0.995933	+	0.0900971i	$0.0287178\pi$
$728$	−8.17945	+	14.3875i	−0.303150	+	0.533234i
$729$		0			0
$730$	1.41017	+	5.26282i	0.0521927	+	0.194786i
$731$		−	24.6416i		−	0.911404i
$732$		0			0
$733$	−5.25644	−	19.6173i	−0.194151	−	0.724582i	−0.992485	−	0.122367i	$-0.960952\pi$
$733$	−5.25644	−	19.6173i	−0.194151	−	0.724582i	0.798334	−	0.602215i	$-0.205715\pi$
$734$	17.2238	+	17.2238i	0.635742	+	0.635742i
$735$		0			0
$736$	1.22810	−	4.58334i	0.0452685	−	0.168944i
$737$	−25.4965	+	14.7204i	−0.939175	+	0.542233i
$738$		0			0
$739$	37.8060	−	10.1301i	1.39072	−	0.372642i	0.515715	−	0.856760i	$-0.327526\pi$
$739$	37.8060	−	10.1301i	1.39072	−	0.372642i	0.875002	+	0.484118i	$0.160860\pi$
$740$	1.23927	+	2.14648i	0.0455566	+	0.0789063i
$741$		0			0
$742$	−11.6263	+	20.1373i	−0.426814	+	0.739263i
$743$	13.6576	−	50.9709i	0.501049	−	1.86994i	0.00794786	−	0.999968i	$-0.497470\pi$
$743$	13.6576	−	50.9709i	0.501049	−	1.86994i	0.493101	−	0.869972i	$-0.335863\pi$
$744$		0			0
$745$	4.44731	+	2.56765i	0.162937	+	0.0940716i
$746$	6.54644	+	6.54644i	0.239682	+	0.239682i
$747$		0			0
$748$	2.70445	−	10.0932i	0.0988845	−	0.369042i
$749$	−24.2393	−	6.49491i	−0.885686	−	0.237319i
$750$		0			0
$751$	−24.5558	+	14.1773i	−0.896053	+	0.517336i	−0.875917	−	0.482461i	$-0.839743\pi$
$751$	−24.5558	+	14.1773i	−0.896053	+	0.517336i	−0.0201351	+	0.999797i	$0.506410\pi$
$752$	11.6601	+	3.12430i	0.425199	+	0.113932i
$753$		0			0
$754$	−12.3643	+	12.5299i	−0.450280	+	0.456313i
$755$			9.94532i			0.361947i
$756$		0			0
$757$	24.6271	−	42.6555i	0.895089	−	1.55034i	0.0613944	−	0.998114i	$-0.480445\pi$
$757$	24.6271	−	42.6555i	0.895089	−	1.55034i	0.833694	−	0.552226i	$-0.186221\pi$
$758$	−6.91700	+	11.9806i	−0.251237	+	0.435155i
$759$		0			0
$760$	−1.42789	+	1.42789i	−0.0517949	+	0.0517949i
$761$	18.9582	−	18.9582i	0.687235	−	0.687235i	−0.274385	−	0.961620i	$-0.588474\pi$
$761$	18.9582	−	18.9582i	0.687235	−	0.687235i	0.961620	+	0.274385i	$0.0884744\pi$
$762$		0			0
$763$	−16.5574	+	28.6783i	−0.599418	+	1.03822i
$764$	4.25783	−	7.37477i	0.154043	−	0.266810i
$765$		0			0
$766$			17.8071i			0.643398i
$767$	−13.5993	+	13.7814i	−0.491041	+	0.497619i
$768$		0			0
$769$	41.4115	+	11.0962i	1.49334	+	0.400138i	0.910862	−	0.412711i	$-0.135418\pi$
$769$	41.4115	+	11.0962i	1.49334	+	0.400138i	0.582474	+	0.812849i	$0.302085\pi$
$770$	6.20819	−	3.58430i	0.223728	−	0.129169i
$771$		0			0
$772$	−18.2851	−	4.89947i	−0.658094	−	0.176336i
$773$	−1.46006	+	5.44904i	−0.0525149	+	0.195988i	−0.987200	−	0.159490i	$-0.949015\pi$
$773$	−1.46006	+	5.44904i	−0.0525149	+	0.195988i	0.934685	+	0.355478i	$0.115682\pi$
$774$		0			0
$775$	21.5594	+	21.5594i	0.774438	+	0.774438i
$776$	−1.06326	−	0.613875i	−0.0381689	−	0.0220368i
$777$		0			0
$778$	−3.86660	+	14.4304i	−0.138624	+	0.517353i
$779$	−8.35291	+	14.4677i	−0.299274	+	0.518358i
$780$		0			0
$781$	−18.1261	−	31.3954i	−0.648604	−	1.12342i
$782$	21.2833	−	5.70284i	0.761088	−	0.203933i
$783$		0			0
$784$	−12.1845	+	7.03470i	−0.435159	+	0.251239i
$785$	−1.02785	+	3.83600i	−0.0366856	+	0.136913i
$786$		0			0
$787$	31.3617	+	31.3617i	1.11792	+	1.11792i	0.992046	+	0.125878i	$0.0401748\pi$
$787$	31.3617	+	31.3617i	1.11792	+	1.11792i	0.125878	+	0.992046i	$0.459825\pi$
$788$	4.51369	+	16.8453i	0.160794	+	0.600090i
$789$		0			0
$790$			2.15706i			0.0767447i
$791$	0.561805	+	2.09668i	0.0199755	+	0.0745495i
$792$		0			0
$793$	−5.56168	+	9.78286i	−0.197501	+	0.347399i
$794$	−2.31327	+	1.33556i	−0.0820947	+	0.0473974i
$795$		0			0
$796$	11.5568	+	20.0170i	0.409621	+	0.709485i
$797$	−0.0479352			−0.00169795			−0.000848975	−	1.00000i	$-0.500270\pi$
$797$	−0.0479352			−0.00169795			−0.000848975		1.00000i	$0.500270\pi$
$798$		0			0
$799$	14.5081	+	54.1448i	0.513258	+	1.91551i
$800$	−4.36436	−	1.16943i	−0.154303	−	0.0413455i
$801$		0			0
$802$	−0.0336571	−	0.0582957i	−0.00118847	−	0.00205849i
$803$	−17.6653			−0.623395
$804$		0			0
$805$	13.0911	+	7.55816i	0.461401	+	0.266390i
$806$	−12.0247	+	21.1511i	−0.423551	+	0.745017i
$807$		0			0
$808$	2.66184	−	2.66184i	0.0936431	−	0.0936431i
$809$	−11.0405	−	6.37425i	−0.388164	−	0.224107i	0.293200	−	0.956051i	$-0.405280\pi$
$809$	−11.0405	−	6.37425i	−0.388164	−	0.224107i	−0.681364	+	0.731944i	$0.738613\pi$
$810$		0			0
$811$	8.60363	−	8.60363i	0.302114	−	0.302114i	−0.539726	−	0.841841i	$-0.681472\pi$
$811$	8.60363	−	8.60363i	0.302114	−	0.302114i	0.841841	+	0.539726i	$0.181472\pi$
$812$	−21.6467	+	5.80020i	−0.759649	+	0.203547i
$813$		0			0
$814$	−7.76224	+	2.07988i	−0.272066	+	0.0728999i
$815$			3.87806i			0.135843i
$816$		0			0
$817$	−10.9176	−	10.9176i	−0.381958	−	0.381958i
$818$	20.4258			0.714173
$819$		0			0
$820$	3.98493			0.139160
$821$	13.8494	+	13.8494i	0.483349	+	0.483349i	0.906199	−	0.422850i	$-0.138970\pi$
$821$	13.8494	+	13.8494i	0.483349	+	0.483349i	−0.422850	+	0.906199i	$0.638970\pi$
$822$		0			0
$823$		−	3.20159i		−	0.111601i	−0.998442	−	0.0558003i	$-0.982229\pi$
$823$		−	3.20159i		−	0.111601i	0.998442	−	0.0558003i	$-0.0177710\pi$
$824$	14.6744	−	3.93200i	0.511208	−	0.136978i
$825$		0			0
$826$	−23.8088	+	6.37955i	−0.828414	+	0.221973i
$827$	35.9697	−	35.9697i	1.25079	−	1.25079i	0.295423	−	0.955367i	$-0.404539\pi$
$827$	35.9697	−	35.9697i	1.25079	−	1.25079i	0.955367	−	0.295423i	$-0.0954605\pi$
$828$		0			0
$829$	−19.7591	−	11.4079i	−0.686263	−	0.396214i	0.115947	−	0.993255i	$-0.463010\pi$
$829$	−19.7591	−	11.4079i	−0.686263	−	0.396214i	−0.802211	+	0.597041i	$0.796343\pi$
$830$	4.66406	−	4.66406i	0.161892	−	0.161892i
$831$		0			0
$832$	−0.0239902	−	3.60547i	−0.000831710	−	0.124997i
$833$	−56.5799	−	32.6664i	−1.96038	−	1.13182i
$834$		0			0
$835$	−16.9965			−0.588187
$836$	−3.27359	−	5.67003i	−0.113220	−	0.196102i
$837$		0			0
$838$	−22.1773	−	5.94239i	−0.766102	−	0.205276i
$839$	2.31329	+	8.63333i	0.0798638	+	0.298056i	0.994292	−	0.106692i	$-0.0340259\pi$
$839$	2.31329	+	8.63333i	0.0798638	+	0.298056i	−0.914428	+	0.404748i	$0.867359\pi$
$840$		0			0
$841$	5.16352			0.178052
$842$	−5.64568	−	9.77861i	−0.194563	−	0.336993i
$843$		0			0
$844$	−8.99669	+	5.19424i	−0.309679	+	0.178793i
$845$	8.68317	−	2.45095i	0.298710	−	0.0843151i
$846$		0			0
$847$	−7.05261	−	26.3207i	−0.242331	−	0.904390i
$848$		−	5.06576i		−	0.173959i
$849$		0			0
$850$	−5.43036	−	20.2664i	−0.186260	−	0.695131i
$851$	−11.9823	−	11.9823i	−0.410748	−	0.410748i
$852$		0			0
$853$	0.373895	−	1.39540i	0.0128019	−	0.0477774i	−0.959229	−	0.282629i	$-0.908794\pi$
$853$	0.373895	−	1.39540i	0.0128019	−	0.0477774i	0.972031	+	0.234851i	$0.0754603\pi$
$854$	−12.4069	+	7.16315i	−0.424557	+	0.245118i
$855$		0			0
$856$	5.28074	−	1.41497i	0.180492	−	0.0483627i
$857$	−14.4133	−	24.9645i	−0.492347	−	0.852770i	0.507614	−	0.861585i	$-0.330528\pi$
$857$	−14.4133	−	24.9645i	−0.492347	−	0.852770i	−0.999961	+	0.00881420i	$0.997194\pi$
$858$		0			0
$859$	7.53374	−	13.0488i	0.257048	−	0.445220i	−0.708402	−	0.705809i	$-0.750584\pi$
$859$	7.53374	−	13.0488i	0.257048	−	0.445220i	0.965450	+	0.260589i	$0.0839169\pi$
$860$	−0.953215	+	3.55745i	−0.0325044	+	0.121308i
$861$		0			0
$862$	7.88511	+	4.55247i	0.268568	+	0.155058i
$863$	−6.35047	−	6.35047i	−0.216173	−	0.216173i	0.590711	−	0.806883i	$-0.298847\pi$
$863$	−6.35047	−	6.35047i	−0.216173	−	0.216173i	−0.806883	+	0.590711i	$0.798847\pi$
$864$		0			0
$865$	1.90299	−	7.10205i	0.0647036	−	0.241477i
$866$	−21.8717	−	5.86051i	−0.743231	−	0.199148i
$867$		0			0
$868$	−26.8246	+	15.4872i	−0.910485	+	0.525669i
$869$	−6.75541	−	1.81011i	−0.229162	−	0.0614037i
$870$		0			0
$871$	−45.6459	−	11.9058i	−1.54665	−	0.403414i
$872$		−	7.21433i		−	0.244308i
$873$		0			0
$874$	6.90298	−	11.9563i	0.233497	−	0.404428i
$875$	15.1613	−	26.2602i	0.512546	−	0.887756i
$876$		0			0
$877$	22.4256	−	22.4256i	0.757260	−	0.757260i	−0.218563	−	0.975823i	$-0.570137\pi$
$877$	22.4256	−	22.4256i	0.757260	−	0.757260i	0.975823	+	0.218563i	$0.0701368\pi$
$878$	−15.1246	+	15.1246i	−0.510430	+	0.510430i
$879$		0			0
$880$	−0.780869	+	1.35250i	−0.0263231	+	0.0455929i
$881$	−25.4661	+	44.1086i	−0.857975	+	1.48606i	0.0158827	+	0.999874i	$0.494944\pi$
$881$	−25.4661	+	44.1086i	−0.857975	+	1.48606i	−0.873858	+	0.486182i	$0.838389\pi$
$882$		0			0
$883$			3.78144i			0.127256i	0.997974	+	0.0636278i	$0.0202671\pi$
$883$			3.78144i			0.127256i	−0.997974	+	0.0636278i	$0.979733\pi$
$884$	14.4437	−	8.46768i	0.485793	−	0.284799i
$885$		0			0
$886$	30.2327	+	8.10083i	1.01569	+	0.272153i
$887$	−14.0773	+	8.12754i	−0.472670	+	0.272896i	−0.717357	−	0.696706i	$-0.754648\pi$
$887$	−14.0773	+	8.12754i	−0.472670	+	0.272896i	0.244687	+	0.969602i	$0.421315\pi$
$888$		0			0
$889$	1.93059	+	0.517301i	0.0647500	+	0.0173497i
$890$	0.449876	−	1.67896i	0.0150799	−	0.0562789i
$891$		0			0
$892$	11.2191	+	11.2191i	0.375642	+	0.375642i
$893$	30.4169	+	17.5612i	1.01786	+	0.587664i
$894$		0			0
$895$	2.23671	−	8.34752i	0.0747650	−	0.279027i
$896$	2.29507	−	3.97518i	0.0766729	−	0.132801i
$897$		0			0
$898$	6.61184	+	11.4520i	0.220640	+	0.382160i
$899$	−31.8230	+	8.52694i	−1.06136	+	0.284389i
$900$		0			0
$901$	20.3719	−	11.7617i	0.678685	−	0.391839i
$902$	−3.34398	+	12.4799i	−0.111342	+	0.415535i
$903$		0			0
$904$	−0.334386	−	0.334386i	−0.0111215	−	0.0111215i
$905$	−3.31353	−	12.3663i	−0.110145	−	0.411068i
$906$		0			0
$907$			10.7409i			0.356645i	0.983972	+	0.178323i	$0.0570670\pi$
$907$			10.7409i			0.356645i	−0.983972	+	0.178323i	$0.942933\pi$
$908$	−1.64982	−	6.15723i	−0.0547513	−	0.204335i
$909$		0			0
$910$	11.1144	+	2.89898i	0.368439	+	0.0961001i
$911$	51.7103	−	29.8550i	1.71324	−	0.989139i	0.783130	−	0.621858i	$-0.213622\pi$
$911$	51.7103	−	29.8550i	1.71324	−	0.989139i	0.930110	−	0.367281i	$-0.119711\pi$
$912$		0			0
$913$	10.6929	+	18.5206i	0.353883	+	0.612943i
$914$	−11.7123			−0.387409
$915$		0			0
$916$	3.31118	+	12.3575i	0.109404	+	0.408303i
$917$	−46.1955	−	12.3781i	−1.52551	−	0.408759i
$918$		0			0
$919$	−9.50921	−	16.4704i	−0.313680	−	0.543310i	0.665476	−	0.746419i	$-0.268229\pi$
$919$	−9.50921	−	16.4704i	−0.313680	−	0.543310i	−0.979156	+	0.203110i	$0.934895\pi$
$920$	−3.29321			−0.108574
$921$		0			0
$922$	6.34459	+	3.66305i	0.208948	+	0.120636i
$923$	14.6604	−	56.2067i	0.482553	−	1.85006i
$924$		0			0
$925$	−11.4098	+	11.4098i	−0.375152	+	0.375152i
$926$	12.6969	+	7.33055i	0.417245	+	0.240897i
$927$		0			0
$928$	3.45228	−	3.45228i	0.113327	−	0.113327i
$929$	−2.50922	+	0.672344i	−0.0823249	+	0.0220589i	−0.299746	−	0.954019i	$-0.596902\pi$
$929$	−2.50922	+	0.672344i	−0.0823249	+	0.0220589i	0.217422	+	0.976078i	$0.430235\pi$
$930$		0			0
$931$	−39.5409	+	10.5950i	−1.29590	+	0.347236i
$932$		−	18.2644i		−	0.598271i
$933$		0			0
$934$	−12.7363	−	12.7363i	−0.416744	−	0.416744i
$935$	−7.25210			−0.237169
$936$		0			0
$937$	−11.7808			−0.384863			−0.192431	−	0.981310i	$-0.561637\pi$
$937$	−11.7808			−0.384863			−0.192431	+	0.981310i	$0.561637\pi$
$938$	−42.4652	−	42.4652i	−1.38654	−	1.38654i
$939$		0			0
$940$		−	8.37796i		−	0.273259i
$941$	−44.3981	+	11.8964i	−1.44734	+	0.387813i	−0.895097	−	0.445871i	$-0.852894\pi$
$941$	−44.3981	+	11.8964i	−1.44734	+	0.387813i	−0.552241	+	0.833684i	$0.686227\pi$
$942$		0			0
$943$	−26.3162	+	7.05139i	−0.856972	+	0.229625i
$944$	3.79710	−	3.79710i	0.123585	−	0.123585i
$945$		0			0
$946$	−10.3412	−	5.97050i	−0.336222	−	0.194118i
$947$	3.12665	−	3.12665i	0.101603	−	0.101603i	−0.654478	−	0.756081i	$-0.727112\pi$
$947$	3.12665	−	3.12665i	0.101603	−	0.101603i	0.756081	+	0.654478i	$0.227112\pi$
$948$		0			0
$949$	−20.1475	−	19.8812i	−0.654015	−	0.645370i
$950$	−11.3851	−	6.57316i	−0.369380	−	0.213262i
$951$		0			0
$952$	21.3148			0.690818
$953$	15.6177	+	27.0507i	0.505908	+	0.876258i	0.999977	+	0.00683493i	$0.00217564\pi$
$953$	15.6177	+	27.0507i	0.505908	+	0.876258i	−0.494069	+	0.869423i	$0.664491\pi$
$954$		0			0
$955$	−5.70877	−	1.52966i	−0.184732	−	0.0494987i
$956$	−5.17656	−	19.3192i	−0.167422	−	0.624827i
$957$		0			0
$958$	−7.19178			−0.232356
$959$	17.5526	+	30.4019i	0.566802	+	0.981730i
$960$		0			0
$961$	−12.5883	+	7.26783i	−0.406073	+	0.234446i
$962$	−11.1937	−	6.36376i	−0.360900	−	0.205176i
$963$		0			0
$964$	−3.89667	−	14.5426i	−0.125503	−	0.468384i
$965$			13.1381i			0.422932i
$966$		0			0
$967$	−1.30625	−	4.87497i	−0.0420060	−	0.156769i	0.941737	−	0.336350i	$-0.109192\pi$
$967$	−1.30625	−	4.87497i	−0.0420060	−	0.156769i	−0.983743	+	0.179581i	$0.942526\pi$
$968$	4.19771	+	4.19771i	0.134920	+	0.134920i
$969$		0			0
$970$	−0.220540	+	0.823066i	−0.00708111	+	0.0264270i
$971$	44.8178	−	25.8756i	1.43827	−	0.830387i	0.440543	−	0.897732i	$-0.354786\pi$
$971$	44.8178	−	25.8756i	1.43827	−	0.830387i	0.997730	+	0.0673446i	$0.0214527\pi$
$972$		0			0
$973$	−49.5392	+	13.2740i	−1.58815	+	0.425545i
$974$	−0.167763	−	0.290575i	−0.00537549	−	0.00931061i
$975$		0			0
$976$	1.56055	−	2.70295i	0.0499520	−	0.0865194i
$977$	5.54212	−	20.6835i	0.177308	−	0.661723i	−0.818839	−	0.574023i	$-0.805382\pi$
$977$	5.54212	−	20.6835i	0.177308	−	0.661723i	0.996147	−	0.0876992i	$-0.0279514\pi$
$978$		0			0
$979$	4.88060	+	2.81782i	0.155985	+	0.0900578i
$980$	6.90465	+	6.90465i	0.220561	+	0.220561i
$981$		0			0
$982$	1.01655	−	3.79381i	0.0324394	−	0.121065i
$983$	46.7595	+	12.5292i	1.49140	+	0.399618i	0.910208	−	0.414151i	$-0.135922\pi$
$983$	46.7595	+	12.5292i	1.49140	+	0.399618i	0.581188	+	0.813769i	$0.302588\pi$
$984$		0			0
$985$	10.4821	−	6.05183i	0.333987	−	0.192827i
$986$	21.8988	+	5.86777i	0.697401	+	0.186868i
$987$		0			0
$988$	2.64768	−	10.1510i	0.0842339	−	0.322945i
$989$		−	25.1798i		−	0.800671i
$990$		0			0
$991$	18.5761	−	32.1748i	0.590090	−	1.02207i	−0.404130	−	0.914701i	$-0.632426\pi$
$991$	18.5761	−	32.1748i	0.590090	−	1.02207i	0.994220	−	0.107364i	$-0.0342409\pi$
$992$	3.37401	−	5.84395i	0.107125	−	0.185546i
$993$		0			0
$994$	52.2901	−	52.2901i	1.65854	−	1.65854i
$995$	11.3432	−	11.3432i	0.359603	−	0.359603i
$996$		0			0
$997$	−26.5059	+	45.9096i	−0.839451	+	1.45397i	0.0509038	+	0.998704i	$0.483790\pi$
$997$	−26.5059	+	45.9096i	−0.839451	+	1.45397i	−0.890355	+	0.455268i	$0.849544\pi$
$998$	−10.1494	+	17.5793i	−0.321274	+	0.556463i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	702.2.bb.a.71.5		56
3.2	odd	2		234.2.y.a.149.9	yes	56
9.2	odd	6		702.2.bc.a.305.12		56
9.7	even	3		234.2.z.a.227.4	yes	56
13.11	odd	12		702.2.bc.a.557.12		56
39.11	even	12		234.2.z.a.167.4	yes	56
117.11	even	12	inner	702.2.bb.a.89.5		56
117.115	odd	12		234.2.y.a.11.9	✓	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
234.2.y.a.11.9	✓	56	117.115	odd	12
234.2.y.a.149.9	yes	56	3.2	odd	2
234.2.z.a.167.4	yes	56	39.11	even	12
234.2.z.a.227.4	yes	56	9.7	even	3
702.2.bb.a.71.5		56	1.1	even	1	trivial
702.2.bb.a.89.5		56	117.11	even	12	inner
702.2.bc.a.305.12		56	9.2	odd	6
702.2.bc.a.557.12		56	13.11	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 702 = 2 \cdot 3^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	702.bb (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{4} +(0.670386 - 0.179629i) q^{5} +(-4.43374 + 1.18802i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.601052 - 0.347017i) q^{10} +(1.59115 - 1.59115i) q^{11} +(3.60547 - 0.0239902i) q^{13} +(3.97518 + 2.29507i) q^{14} -1.00000 q^{16} +(-2.32181 - 4.02149i) q^{17} +(-2.81042 - 0.753050i) q^{19} +(0.179629 + 0.670386i) q^{20} -2.25023 q^{22} +(-2.37251 - 4.10931i) q^{23} +(-3.91298 + 2.25916i) q^{25} +(-2.56642 - 2.53249i) q^{26} +(-1.18802 - 4.43374i) q^{28} -4.88226i q^{29} +(-1.74651 - 6.51808i) q^{31} +(0.707107 + 0.707107i) q^{32} +(-1.20186 + 4.48539i) q^{34} +(-2.75891 + 1.59286i) q^{35} +(3.44953 - 0.924299i) q^{37} +(1.45478 + 2.51976i) q^{38} +(0.347017 - 0.601052i) q^{40} +(1.48606 - 5.54605i) q^{41} +(4.59562 + 2.65328i) q^{43} +(1.59115 + 1.59115i) q^{44} +(-1.22810 + 4.58334i) q^{46} +(-11.6601 - 3.12430i) q^{47} +(12.1845 - 7.03470i) q^{49} +(4.36436 + 1.16943i) q^{50} +(0.0239902 + 3.60547i) q^{52} +5.06576i q^{53} +(0.780869 - 1.35250i) q^{55} +(-2.29507 + 3.97518i) q^{56} +(-3.45228 + 3.45228i) q^{58} +(-3.79710 + 3.79710i) q^{59} +(-1.56055 + 2.70295i) q^{61} +(-3.37401 + 5.84395i) q^{62} -1.00000i q^{64} +(2.41275 - 0.663731i) q^{65} +(-12.6377 - 3.38625i) q^{67} +(4.02149 - 2.32181i) q^{68} +(3.07717 + 0.824524i) q^{70} +(4.16970 - 15.5615i) q^{71} +(-5.55110 - 5.55110i) q^{73} +(-3.09276 - 1.78561i) q^{74} +(0.753050 - 2.81042i) q^{76} +(-5.16444 + 8.94507i) q^{77} +(-1.55400 - 2.69161i) q^{79} +(-0.670386 + 0.179629i) q^{80} +(-4.97245 + 2.87085i) q^{82} +(-2.45977 + 9.17998i) q^{83} +(-2.27888 - 2.27888i) q^{85} +(-1.37344 - 5.12575i) q^{86} -2.25023i q^{88} +(0.648204 + 2.41913i) q^{89} +(-15.9572 + 4.38972i) q^{91} +(4.10931 - 2.37251i) q^{92} +(6.03569 + 10.4541i) q^{94} -2.01934 q^{95} +(-0.317765 - 1.18591i) q^{97} +(-13.5900 - 3.64143i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 4 q^{7} - 56 q^{16} - 8 q^{19} - 4 q^{28} + 8 q^{31} - 24 q^{35} - 4 q^{37} + 36 q^{38} + 48 q^{41} + 12 q^{43} - 60 q^{47} + 24 q^{50} - 4 q^{52} + 120 q^{65} - 56 q^{67} - 24 q^{71} + 28 q^{73}+ \cdots + 48 q^{98}+O(q^{100}) \) 56 * q + 4 * q^7 - 56 * q^16 - 8 * q^19 - 4 * q^28 + 8 * q^31 - 24 * q^35 - 4 * q^37 + 36 * q^38 + 48 * q^41 + 12 * q^43 - 60 * q^47 + 24 * q^50 - 4 * q^52 + 120 * q^65 - 56 * q^67 - 24 * q^71 + 28 * q^73 - 48 * q^74 + 4 * q^76 + 24 * q^77 - 24 * q^79 + 60 * q^83 - 48 * q^86 + 4 * q^91 + 24 * q^92 + 20 * q^97 + 48 * q^98

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