LMFDB - Embedded newform 702.2.bc.a.665.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [702,2,Mod(305,702)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("702.305"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(702, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([2, 5])) N = Newforms(chi, 2, names="a")

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

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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			665.2
Character	$\chi$	$=$	702.665
Dual form			702.2.bc.a.683.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.965926 + 0.258819i) q^{2} +(0.866025 - 0.500000i) q^{4} +(-1.48652 + 0.398313i) q^{5} +(1.01155 + 1.01155i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(1.33278 - 0.769482i) q^{10} +(-0.128439 - 0.479340i) q^{11} +(3.02688 - 1.95909i) q^{13} +(-1.23890 - 0.715277i) q^{14} +(0.500000 - 0.866025i) q^{16} +(-1.10510 + 1.91408i) q^{17} +(0.805124 + 3.00476i) q^{19} +(-1.08821 + 1.08821i) q^{20} +(0.248125 + 0.429765i) q^{22} +1.77557 q^{23} +(-2.27902 + 1.31580i) q^{25} +(-2.41669 + 2.67575i) q^{26} +(1.38181 + 0.370254i) q^{28} +(4.07958 + 2.35535i) q^{29} +(-0.0814346 - 0.303918i) q^{31} +(-0.258819 + 0.965926i) q^{32} +(0.572040 - 2.13488i) q^{34} +(-1.90661 - 1.10078i) q^{35} +(-2.95350 + 11.0226i) q^{37} +(-1.55538 - 2.69400i) q^{38} +(0.769482 - 1.33278i) q^{40} +(5.69511 + 5.69511i) q^{41} +1.62219i q^{43} +(-0.350901 - 0.350901i) q^{44} +(-1.71507 + 0.459552i) q^{46} +(11.8388 + 3.17219i) q^{47} -4.95352i q^{49} +(1.86082 - 1.86082i) q^{50} +(1.64181 - 3.21006i) q^{52} -2.02719i q^{53} +(0.381855 + 0.661392i) q^{55} -1.43055 q^{56} +(-4.55018 - 1.21922i) q^{58} +(2.70586 + 0.725033i) q^{59} +6.79318 q^{61} +(0.157320 + 0.272485i) q^{62} -1.00000i q^{64} +(-3.71920 + 4.11787i) q^{65} +(-5.60189 + 5.60189i) q^{67} +2.21019i q^{68} +(2.12655 + 0.569808i) q^{70} +(-10.8566 + 2.90902i) q^{71} +(4.45270 + 4.45270i) q^{73} -11.4115i q^{74} +(2.19964 + 2.19964i) q^{76} +(0.354956 - 0.614801i) q^{77} +(4.77307 + 8.26720i) q^{79} +(-0.398313 + 1.48652i) q^{80} +(-6.97505 - 4.02705i) q^{82} +(-2.17883 + 8.13149i) q^{83} +(0.880349 - 3.28551i) q^{85} +(-0.419853 - 1.56691i) q^{86} +(0.429765 + 0.248125i) q^{88} +(-3.41203 - 0.914251i) q^{89} +(5.04357 + 1.08013i) q^{91} +(1.53769 - 0.887787i) q^{92} -12.2564 q^{94} +(-2.39367 - 4.14596i) q^{95} +(5.21001 - 5.21001i) q^{97} +(1.28206 + 4.78473i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 8 q^{7} + 24 q^{11} + 28 q^{16} - 8 q^{19} - 4 q^{28} - 4 q^{31} + 24 q^{35} - 4 q^{37} - 36 q^{38} + 48 q^{41} + 36 q^{47} + 24 q^{50} + 8 q^{52} + 36 q^{65} + 28 q^{67} + 24 q^{71} + 28 q^{73}+ \cdots - 48 q^{98}+O(q^{100}) $ 56 * q - 8 * q^7 + 24 * q^11 + 28 * q^16 - 8 * q^19 - 4 * q^28 - 4 * q^31 + 24 * q^35 - 4 * q^37 - 36 * q^38 + 48 * q^41 + 36 * q^47 + 24 * q^50 + 8 * q^52 + 36 * q^65 + 28 * q^67 + 24 * q^71 + 28 * q^73 + 4 * q^76 - 24 * q^77 - 24 * q^79 + 96 * q^83 - 72 * q^85 + 4 * q^91 + 24 * q^92 - 52 * q^97 - 48 * q^98

Character values

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

$n$	$379$	$677$
$\chi(n)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.965926	+	0.258819i	−0.683013	+	0.183013i
$2$	−0.965926	+	0.258819i	−0.683013	+	0.183013i
$3$		0			0
$3$		0			0
$4$	0.866025	−	0.500000i	0.433013	−	0.250000i
$5$	−1.48652	+	0.398313i	−0.664794	+	0.178131i	−0.575409	−	0.817866i	$-0.695157\pi$
$5$	−1.48652	+	0.398313i	−0.664794	+	0.178131i	−0.0893855	+	0.995997i	$0.528490\pi$
$6$		0			0
$7$	1.01155	+	1.01155i	0.382331	+	0.382331i	0.871941	−	0.489610i	$-0.162861\pi$
$7$	1.01155	+	1.01155i	0.382331	+	0.382331i	−0.489610	+	0.871941i	$0.662861\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$		0			0
$10$	1.33278	−	0.769482i	0.421463	−	0.243332i
$11$	−0.128439	−	0.479340i	−0.0387258	−	0.144527i	0.943856	−	0.330357i	$-0.107169\pi$
$11$	−0.128439	−	0.479340i	−0.0387258	−	0.144527i	−0.982582	+	0.185830i	$0.940502\pi$
$12$		0			0
$13$	3.02688	−	1.95909i	0.839504	−	0.543353i
$13$	3.02688	−	1.95909i	0.839504	−	0.543353i
$14$	−1.23890	−	0.715277i	−0.331109	−	0.191166i
$15$		0			0
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−1.10510	+	1.91408i	−0.268025	+	0.464233i	−0.968352	−	0.249589i	$-0.919704\pi$
$17$	−1.10510	+	1.91408i	−0.268025	+	0.464233i	0.700327	+	0.713823i	$0.253038\pi$
$18$		0			0
$19$	0.805124	+	3.00476i	0.184708	+	0.689340i	0.994693	+	0.102889i	$0.0328086\pi$
$19$	0.805124	+	3.00476i	0.184708	+	0.689340i	−0.809985	+	0.586451i	$0.800525\pi$
$20$	−1.08821	+	1.08821i	−0.243332	+	0.243332i
$21$		0			0
$22$	0.248125	+	0.429765i	0.0529004	+	0.0916262i
$23$	1.77557			0.370233			0.185116	−	0.982717i	$-0.440734\pi$
$23$	1.77557			0.370233			0.185116	+	0.982717i	$0.440734\pi$
$24$		0			0
$25$	−2.27902	+	1.31580i	−0.455805	+	0.263159i
$26$	−2.41669	+	2.67575i	−0.473952	+	0.524757i
$27$		0			0
$28$	1.38181	+	0.370254i	0.261137	+	0.0699715i
$29$	4.07958	+	2.35535i	0.757559	+	0.437377i	0.828419	−	0.560109i	$-0.189241\pi$
$29$	4.07958	+	2.35535i	0.757559	+	0.437377i	−0.0708596	+	0.997486i	$0.522574\pi$
$30$		0			0
$31$	−0.0814346	−	0.303918i	−0.0146261	−	0.0545853i	0.958227	−	0.286008i	$-0.0923285\pi$
$31$	−0.0814346	−	0.303918i	−0.0146261	−	0.0545853i	−0.972853	+	0.231423i	$0.925662\pi$
$32$	−0.258819	+	0.965926i	−0.0457532	+	0.170753i
$33$		0			0
$34$	0.572040	−	2.13488i	0.0981040	−	0.366129i
$35$	−1.90661	−	1.10078i	−0.322277	−	0.186067i
$36$		0			0
$37$	−2.95350	+	11.0226i	−0.485553	+	1.81211i	0.0920063	+	0.995758i	$0.470672\pi$
$37$	−2.95350	+	11.0226i	−0.485553	+	1.81211i	−0.577559	+	0.816349i	$0.695995\pi$
$38$	−1.55538	−	2.69400i	−0.252316	−	0.437024i
$39$		0			0
$40$	0.769482	−	1.33278i	0.121666	−	0.210731i
$41$	5.69511	+	5.69511i	0.889426	+	0.889426i	0.994468	−	0.105041i	$-0.0334975\pi$
$41$	5.69511	+	5.69511i	0.889426	+	0.889426i	−0.105041	+	0.994468i	$0.533498\pi$
$42$		0			0
$43$			1.62219i			0.247381i	0.992321	+	0.123691i	$0.0394731\pi$
$43$			1.62219i			0.247381i	−0.992321	+	0.123691i	$0.960527\pi$
$44$	−0.350901	−	0.350901i	−0.0529004	−	0.0529004i
$45$		0			0
$46$	−1.71507	+	0.459552i	−0.252874	+	0.0677573i
$47$	11.8388	+	3.17219i	1.72686	+	0.462711i	0.979456	−	0.201656i	$-0.0646324\pi$
$47$	11.8388	+	3.17219i	1.72686	+	0.462711i	0.747406	+	0.664368i	$0.231299\pi$
$48$		0			0
$49$		−	4.95352i		−	0.707645i
$50$	1.86082	−	1.86082i	0.263159	−	0.263159i
$51$		0			0
$52$	1.64181	−	3.21006i	0.227678	−	0.445155i
$53$		−	2.02719i		−	0.278456i	−0.990260	−	0.139228i	$-0.955538\pi$
$53$		−	2.02719i		−	0.278456i	0.990260	−	0.139228i	$-0.0444621\pi$
$54$		0			0
$55$	0.381855	+	0.661392i	0.0514893	+	0.0891821i
$56$	−1.43055			−0.191166
$57$		0			0
$58$	−4.55018	−	1.21922i	−0.597468	−	0.160091i
$59$	2.70586	+	0.725033i	0.352273	+	0.0943913i	0.430616	−	0.902535i	$-0.358296\pi$
$59$	2.70586	+	0.725033i	0.352273	+	0.0943913i	−0.0783431	+	0.996926i	$0.524963\pi$
$60$		0			0
$61$	6.79318			0.869777			0.434888	−	0.900484i	$-0.356788\pi$
$61$	6.79318			0.869777			0.434888	+	0.900484i	$0.356788\pi$
$62$	0.157320	+	0.272485i	0.0199796	+	0.0346057i
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$	−3.71920	+	4.11787i	−0.461310	+	0.510760i
$66$		0			0
$67$	−5.60189	+	5.60189i	−0.684379	+	0.684379i	−0.960984	−	0.276604i	$-0.910791\pi$
$67$	−5.60189	+	5.60189i	−0.684379	+	0.684379i	0.276604	+	0.960984i	$0.410791\pi$
$68$			2.21019i			0.268025i
$69$		0			0
$70$	2.12655	+	0.569808i	0.254172	+	0.0681051i
$71$	−10.8566	+	2.90902i	−1.28844	+	0.345237i	−0.837069	−	0.547097i	$-0.815733\pi$
$71$	−10.8566	+	2.90902i	−1.28844	+	0.345237i	−0.451374	+	0.892335i	$0.649066\pi$
$72$		0			0
$73$	4.45270	+	4.45270i	0.521149	+	0.521149i	0.917918	−	0.396769i	$-0.129869\pi$
$73$	4.45270	+	4.45270i	0.521149	+	0.521149i	−0.396769	+	0.917918i	$0.629869\pi$
$74$		−	11.4115i		−	1.32655i
$75$		0			0
$76$	2.19964	+	2.19964i	0.252316	+	0.252316i
$77$	0.354956	−	0.614801i	0.0404510	−	0.0700631i
$78$		0			0
$79$	4.77307	+	8.26720i	0.537012	+	0.930133i	0.999063	+	0.0432790i	$0.0137805\pi$
$79$	4.77307	+	8.26720i	0.537012	+	0.930133i	−0.462051	+	0.886853i	$0.652886\pi$
$80$	−0.398313	+	1.48652i	−0.0445328	+	0.166199i
$81$		0			0
$82$	−6.97505	−	4.02705i	−0.770266	−	0.444713i
$83$	−2.17883	+	8.13149i	−0.239157	+	0.892547i	0.737073	+	0.675813i	$0.236207\pi$
$83$	−2.17883	+	8.13149i	−0.239157	+	0.892547i	−0.976231	+	0.216734i	$0.930460\pi$
$84$		0			0
$85$	0.880349	−	3.28551i	0.0954872	−	0.356363i
$86$	−0.419853	−	1.56691i	−0.0452739	−	0.168965i
$87$		0			0
$88$	0.429765	+	0.248125i	0.0458131	+	0.0264502i
$89$	−3.41203	−	0.914251i	−0.361674	−	0.0969104i	0.0734055	−	0.997302i	$-0.476613\pi$
$89$	−3.41203	−	0.914251i	−0.361674	−	0.0969104i	−0.435080	+	0.900392i	$0.643280\pi$
$90$		0			0
$91$	5.04357	+	1.08013i	0.528710	+	0.113228i
$92$	1.53769	−	0.887787i	0.160315	−	0.0925582i
$93$		0			0
$94$	−12.2564			−1.26415
$95$	−2.39367	−	4.14596i	−0.245586	−	0.425367i
$96$		0			0
$97$	5.21001	−	5.21001i	0.528996	−	0.528996i	−0.391277	−	0.920273i	$-0.627967\pi$
$97$	5.21001	−	5.21001i	0.528996	−	0.528996i	0.920273	+	0.391277i	$0.127967\pi$
$98$	1.28206	+	4.78473i	0.129508	+	0.483331i
$99$		0			0
$100$	−1.31580	+	2.27902i	−0.131580	+	0.227902i
$101$	−2.75939	+	4.77940i	−0.274569	+	0.475568i	−0.970026	−	0.243000i	$-0.921869\pi$
$101$	−2.75939	+	4.77940i	−0.274569	+	0.475568i	0.695457	+	0.718568i	$0.255202\pi$
$102$		0			0
$103$	−13.0560	−	7.53787i	−1.28644	−	0.742729i	−0.308426	−	0.951248i	$-0.599802\pi$
$103$	−13.0560	−	7.53787i	−1.28644	−	0.742729i	−0.978018	+	0.208520i	$0.933135\pi$
$104$	−0.755042	+	3.52561i	−0.0740379	+	0.345714i
$105$		0			0
$106$	0.524676	+	1.95812i	0.0509610	+	0.190189i
$107$	10.8647	−	6.27276i	1.05033	−	0.606411i	0.127591	−	0.991827i	$-0.459276\pi$
$107$	10.8647	−	6.27276i	1.05033	−	0.606411i	0.922743	+	0.385416i	$0.125942\pi$
$108$		0			0
$109$	−6.92733	+	6.92733i	−0.663518	+	0.663518i	−0.956208	−	0.292690i	$-0.905450\pi$
$109$	−6.92733	+	6.92733i	−0.663518	+	0.663518i	0.292690	+	0.956208i	$0.405450\pi$
$110$	−0.540025	−	0.540025i	−0.0514893	−	0.0514893i
$111$		0			0
$112$	1.38181	−	0.370254i	0.130569	−	0.0349858i
$113$	12.3898	−	7.15327i	1.16554	−	0.672923i	0.212912	−	0.977071i	$-0.431705\pi$
$113$	12.3898	−	7.15327i	1.16554	−	0.672923i	0.952625	+	0.304149i	$0.0983720\pi$
$114$		0			0
$115$	−2.63943	+	0.707234i	−0.246128	+	0.0659499i
$116$	4.71069			0.437377
$117$		0			0
$118$	−2.80131			−0.257882
$119$	−3.05406	+	0.818333i	−0.279965	+	0.0750165i
$120$		0			0
$121$	9.31301	−	5.37687i	0.846637	−	0.488806i
$122$	−6.56170	+	1.75820i	−0.594069	+	0.159180i
$123$		0			0
$124$	−0.222483	−	0.222483i	−0.0199796	−	0.0199796i
$125$	8.30479	−	8.30479i	0.742803	−	0.742803i
$126$		0			0
$127$	2.50743	−	1.44766i	0.222498	−	0.128459i	−0.384608	−	0.923080i	$-0.625663\pi$
$127$	2.50743	−	1.44766i	0.222498	−	0.128459i	0.607106	+	0.794621i	$0.292330\pi$
$128$	0.258819	+	0.965926i	0.0228766	+	0.0853766i
$129$		0			0
$130$	2.52668	−	4.94016i	0.221605	−	0.433281i
$131$	−11.3218	−	6.53662i	−0.989186	−	0.571107i	−0.0841553	−	0.996453i	$-0.526819\pi$
$131$	−11.3218	−	6.53662i	−0.989186	−	0.571107i	−0.905031	+	0.425346i	$0.860153\pi$
$132$		0			0
$133$	−2.22505	+	3.85391i	−0.192937	+	0.334176i
$134$	3.96113	−	6.86088i	0.342190	−	0.592690i
$135$		0			0
$136$	−0.572040	−	2.13488i	−0.0490520	−	0.183065i
$137$	−4.60469	+	4.60469i	−0.393405	+	0.393405i	−0.875899	−	0.482494i	$-0.839731\pi$
$137$	−4.60469	+	4.60469i	−0.393405	+	0.393405i	0.482494	+	0.875899i	$0.339731\pi$
$138$		0			0
$139$	−8.34095	−	14.4469i	−0.707470	−	1.22537i	−0.965793	−	0.259316i	$-0.916503\pi$
$139$	−8.34095	−	14.4469i	−0.707470	−	1.22537i	0.258322	−	0.966059i	$-0.416830\pi$
$140$	−2.20157			−0.186067
$141$		0			0
$142$	9.73378	−	5.61980i	0.816840	−	0.471603i
$143$	−1.32784	−	1.19928i	−0.111039	−	0.100289i
$144$		0			0
$145$	−7.00256	−	1.87633i	−0.581531	−	0.155821i
$146$	−5.45342	−	3.14853i	−0.451328	−	0.260575i
$147$		0			0
$148$	2.95350	+	11.0226i	0.242776	+	0.906054i
$149$	2.72321	−	10.1632i	0.223094	−	0.832599i	−0.760065	−	0.649847i	$-0.774833\pi$
$149$	2.72321	−	10.1632i	0.223094	−	0.832599i	0.983159	−	0.182752i	$-0.0585005\pi$
$150$		0			0
$151$	4.44836	−	16.6015i	0.362002	−	1.35101i	−0.509437	−	0.860508i	$-0.670146\pi$
$151$	4.44836	−	16.6015i	0.362002	−	1.35101i	0.871440	−	0.490503i	$-0.163187\pi$
$152$	−2.69400	−	1.55538i	−0.218512	−	0.126158i
$153$		0			0
$154$	−0.183739	+	0.685722i	−0.0148061	+	0.0552570i
$155$	0.242109	+	0.419345i	0.0194467	+	0.0336826i
$156$		0			0
$157$	−10.9518	+	18.9690i	−0.874046	+	1.51389i	−0.0162709	+	0.999868i	$0.505179\pi$
$157$	−10.9518	+	18.9690i	−0.874046	+	1.51389i	−0.857775	+	0.514025i	$0.828154\pi$
$158$	−6.75014	−	6.75014i	−0.537012	−	0.537012i
$159$		0			0
$160$		−	1.53896i		−	0.121666i
$161$	1.79609	+	1.79609i	0.141552	+	0.141552i
$162$		0			0
$163$	5.13664	−	1.37636i	0.402333	−	0.107805i	−0.0519776	−	0.998648i	$-0.516552\pi$
$163$	5.13664	−	1.37636i	0.402333	−	0.107805i	0.454310	+	0.890844i	$0.349886\pi$
$164$	7.77966	+	2.08455i	0.607490	+	0.162776i
$165$		0			0
$166$		−	8.41834i		−	0.653390i
$167$	−7.67161	+	7.67161i	−0.593647	+	0.593647i	−0.938615	−	0.344968i	$-0.887890\pi$
$167$	−7.67161	+	7.67161i	−0.593647	+	0.593647i	0.344968	+	0.938615i	$0.387890\pi$
$168$		0			0
$169$	5.32396	−	11.8598i	0.409536	−	0.912294i
$170$			3.40141i			0.260876i
$171$		0			0
$172$	0.811094	+	1.40486i	0.0618453	+	0.107119i
$173$	−1.60584			−0.122090			−0.0610448	−	0.998135i	$-0.519443\pi$
$173$	−1.60584			−0.122090			−0.0610448	+	0.998135i	$0.519443\pi$
$174$		0			0
$175$	−3.63635	−	0.974358i	−0.274882	−	0.0736545i
$176$	−0.479340	−	0.128439i	−0.0361316	−	0.00968144i
$177$		0			0
$178$	3.53239			0.264764
$179$	−5.02903	−	8.71053i	−0.375887	−	0.651056i	0.614572	−	0.788861i	$-0.289329\pi$
$179$	−5.02903	−	8.71053i	−0.375887	−	0.651056i	−0.990459	+	0.137805i	$0.955995\pi$
$180$		0			0
$181$		−	11.9484i		−	0.888116i	−0.895998	−	0.444058i	$-0.853538\pi$
$181$		−	11.9484i		−	0.888116i	0.895998	−	0.444058i	$-0.146462\pi$
$182$	−5.15127	+	0.262049i	−0.381838	+	0.0194244i
$183$		0			0
$184$	−1.25552	+	1.25552i	−0.0925582	+	0.0925582i
$185$		−	17.5618i		−	1.29117i
$186$		0			0
$187$	1.05943	+	0.283875i	0.0774735	+	0.0207590i
$188$	11.8388	−	3.17219i	0.863431	−	0.231356i
$189$		0			0
$190$	3.38516	+	3.38516i	0.245586	+	0.245586i
$191$		−	21.8456i		−	1.58069i	−0.612659	−	0.790347i	$-0.709900\pi$
$191$		−	21.8456i		−	1.58069i	0.612659	−	0.790347i	$-0.290100\pi$
$192$		0			0
$193$	9.25729	+	9.25729i	0.666354	+	0.666354i	0.956870	−	0.290516i	$-0.0938269\pi$
$193$	9.25729	+	9.25729i	0.666354	+	0.666354i	−0.290516	+	0.956870i	$0.593827\pi$
$194$	−3.68403	+	6.38093i	−0.264498	+	0.458124i
$195$		0			0
$196$	−2.47676	−	4.28987i	−0.176911	−	0.306419i
$197$	0.638138	−	2.38157i	0.0454655	−	0.169680i	−0.939460	−	0.342659i	$-0.888673\pi$
$197$	0.638138	−	2.38157i	0.0454655	−	0.169680i	0.984926	+	0.172979i	$0.0553393\pi$
$198$		0			0
$199$	−18.1467	−	10.4770i	−1.28639	−	0.742697i	−0.308380	−	0.951263i	$-0.599787\pi$
$199$	−18.1467	−	10.4770i	−1.28639	−	0.742697i	−0.978008	+	0.208567i	$0.933120\pi$
$200$	0.681106	−	2.54192i	0.0481615	−	0.179741i
$201$		0			0
$202$	1.42836	−	5.33073i	0.100499	−	0.375069i
$203$	1.74416	+	6.50928i	0.122416	+	0.456862i
$204$		0			0
$205$	−10.7344	−	6.19748i	−0.749720	−	0.432851i
$206$	14.5621	+	3.90189i	1.01459	+	0.271858i
$207$		0			0
$208$	−0.183180	−	3.60090i	−0.0127013	−	0.249677i
$209$	1.33689	−	0.771857i	0.0924750	−	0.0533904i
$210$		0			0
$211$	−14.1278			−0.972599			−0.486299	−	0.873792i	$-0.661654\pi$
$211$	−14.1278			−0.972599			−0.486299	+	0.873792i	$0.661654\pi$
$212$	−1.01360	−	1.75560i	−0.0696140	−	0.120575i
$213$		0			0
$214$	−8.87102	+	8.87102i	−0.606411	+	0.606411i
$215$	−0.646139	−	2.41142i	−0.0440663	−	0.164458i
$216$		0			0
$217$	0.225054	−	0.389805i	0.0152777	−	0.0264617i
$218$	4.89836	−	8.48421i	0.331759	−	0.574623i
$219$		0			0
$220$	0.661392	+	0.381855i	0.0445911	+	0.0257447i
$221$	0.404863	+	7.95867i	0.0272341	+	0.535358i
$222$		0			0
$223$	−2.37228	−	8.85346i	−0.158859	−	0.592872i	−0.998744	−	0.0501063i	$-0.984044\pi$
$223$	−2.37228	−	8.85346i	−0.158859	−	0.592872i	0.839884	−	0.542765i	$-0.182623\pi$
$224$	−1.23890	+	0.715277i	−0.0827772	+	0.0477914i
$225$		0			0
$226$	−10.1162	+	10.1162i	−0.672923	+	0.672923i
$227$	−18.6738	−	18.6738i	−1.23943	−	1.23943i	−0.960236	−	0.279190i	$-0.909934\pi$
$227$	−18.6738	−	18.6738i	−1.23943	−	1.23943i	−0.279190	−	0.960236i	$-0.590066\pi$
$228$		0			0
$229$	13.7346	−	3.68017i	0.907607	−	0.243193i	0.225327	−	0.974283i	$-0.427655\pi$
$229$	13.7346	−	3.68017i	0.907607	−	0.243193i	0.682280	+	0.731091i	$0.260988\pi$
$230$	2.36645	−	1.36627i	0.156039	−	0.0900893i
$231$		0			0
$232$	−4.55018	+	1.21922i	−0.298734	+	0.0800455i
$233$	21.4490			1.40517			0.702586	−	0.711599i	$-0.252029\pi$
$233$	21.4490			1.40517			0.702586	+	0.711599i	$0.252029\pi$
$234$		0			0
$235$	−18.8622			−1.23043
$236$	2.70586	−	0.725033i	0.176137	−	0.0471956i
$237$		0			0
$238$	2.73820	−	1.58090i	0.177491	−	0.102474i
$239$	−7.59513	+	2.03511i	−0.491288	+	0.131640i	−0.495954	−	0.868349i	$-0.665181\pi$
$239$	−7.59513	+	2.03511i	−0.491288	+	0.131640i	0.00466587	+	0.999989i	$0.498515\pi$
$240$		0			0
$241$	13.0877	+	13.0877i	0.843051	+	0.843051i	0.989255	−	0.146203i	$-0.0467054\pi$
$241$	13.0877	+	13.0877i	0.843051	+	0.843051i	−0.146203	+	0.989255i	$0.546705\pi$
$242$	−7.60404	+	7.60404i	−0.488806	+	0.488806i
$243$		0			0
$244$	5.88306	−	3.39659i	0.376624	−	0.217444i
$245$	1.97305	+	7.36353i	0.126054	+	0.470438i
$246$		0			0
$247$	8.32360	+	7.51774i	0.529618	+	0.478342i
$248$	0.272485	+	0.157320i	0.0173028	+	0.00998980i
$249$		0			0
$250$	−5.87237	+	10.1712i	−0.371401	+	0.643286i
$251$	−11.0446	+	19.1298i	−0.697127	+	1.20746i	0.272331	+	0.962204i	$0.412205\pi$
$251$	−11.0446	+	19.1298i	−0.697127	+	1.20746i	−0.969458	+	0.245256i	$0.921128\pi$
$252$		0			0
$253$	−0.228053	−	0.851104i	−0.0143375	−	0.0535084i
$254$	−2.04731	+	2.04731i	−0.128459	+	0.128459i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	30.2080			1.88432			0.942162	−	0.335158i	$-0.108790\pi$
$257$	30.2080			1.88432			0.942162	+	0.335158i	$0.108790\pi$
$258$		0			0
$259$	−14.1376	+	8.16235i	−0.878468	+	0.507183i
$260$	−1.16198	+	5.42578i	−0.0720631	+	0.336493i
$261$		0			0
$262$	12.6278	+	3.38360i	0.780147	+	0.209040i
$263$	4.77357	+	2.75602i	0.294351	+	0.169943i	0.639902	−	0.768456i	$-0.278975\pi$
$263$	4.77357	+	2.75602i	0.294351	+	0.169943i	−0.345552	+	0.938400i	$0.612308\pi$
$264$		0			0
$265$	0.807457	+	3.01347i	0.0496017	+	0.185116i
$266$	1.15177	−	4.29847i	0.0706197	−	0.263556i
$267$		0			0
$268$	−2.05043	+	7.65232i	−0.125250	+	0.467440i
$269$	−16.8180	−	9.70985i	−1.02541	−	0.592020i	−0.109743	−	0.993960i	$-0.535003\pi$
$269$	−16.8180	−	9.70985i	−1.02541	−	0.592020i	−0.915666	+	0.401940i	$0.868336\pi$
$270$		0			0
$271$	5.79813	−	21.6389i	0.352212	−	1.31447i	−0.531746	−	0.846904i	$-0.678464\pi$
$271$	5.79813	−	21.6389i	0.352212	−	1.31447i	0.883957	−	0.467567i	$-0.154869\pi$
$272$	1.10510	+	1.91408i	0.0670063	+	0.116058i
$273$		0			0
$274$	3.25601	−	5.63957i	0.196703	−	0.340699i
$275$	0.923429	+	0.923429i	0.0556849	+	0.0556849i
$276$		0			0
$277$		−	8.82351i		−	0.530153i	−0.964227	−	0.265077i	$-0.914603\pi$
$277$		−	8.82351i		−	0.530153i	0.964227	−	0.265077i	$-0.0853973\pi$
$278$	11.7959	+	11.7959i	0.707470	+	0.707470i
$279$		0			0
$280$	2.12655	−	0.569808i	0.127086	−	0.0340525i
$281$	17.2960	+	4.63444i	1.03179	+	0.276467i	0.734707	−	0.678384i	$-0.237320\pi$
$281$	17.2960	+	4.63444i	1.03179	+	0.276467i	0.297083	+	0.954852i	$0.403986\pi$
$282$		0			0
$283$			7.31258i			0.434688i	0.976095	+	0.217344i	$0.0697393\pi$
$283$			7.31258i			0.434688i	−0.976095	+	0.217344i	$0.930261\pi$
$284$	−7.94760	+	7.94760i	−0.471603	+	0.471603i
$285$		0			0
$286$	1.59299	+	0.814747i	0.0941954	+	0.0481770i
$287$			11.5218i			0.680111i
$288$		0			0
$289$	6.05752	+	10.4919i	0.356325	+	0.617173i
$290$	7.24959			0.425710
$291$		0			0
$292$	6.08250	+	1.62980i	0.355952	+	0.0953769i
$293$	−13.7781	−	3.69183i	−0.804925	−	0.215679i	−0.167180	−	0.985926i	$-0.553466\pi$
$293$	−13.7781	−	3.69183i	−0.804925	−	0.215679i	−0.637745	+	0.770247i	$0.720133\pi$
$294$		0			0
$295$	−4.31112			−0.251003
$296$	−5.70573	−	9.88261i	−0.331639	−	0.574415i
$297$		0			0
$298$			10.5217i			0.609505i
$299$	5.37444	−	3.47850i	0.310812	−	0.201167i
$300$		0			0
$301$	−1.64093	+	1.64093i	−0.0945817	+	0.0945817i
$302$			17.1871i			0.989008i
$303$		0			0
$304$	3.00476	+	0.805124i	0.172335	+	0.0461770i
$305$	−10.0982	+	2.70581i	−0.578223	+	0.154934i
$306$		0			0
$307$	15.5883	+	15.5883i	0.889669	+	0.889669i	0.994491	−	0.104822i	$-0.0334273\pi$
$307$	15.5883	+	15.5883i	0.889669	+	0.889669i	−0.104822	+	0.994491i	$0.533427\pi$
$308$		−	0.709911i		−	0.0404510i
$309$		0			0
$310$	−0.342394	−	0.342394i	−0.0194467	−	0.0194467i
$311$	−12.3786	+	21.4403i	−0.701923	+	1.21577i	0.265867	+	0.964010i	$0.414342\pi$
$311$	−12.3786	+	21.4403i	−0.701923	+	1.21577i	−0.967790	+	0.251757i	$0.918992\pi$
$312$		0			0
$313$	16.0705	+	27.8349i	0.908359	+	1.57332i	0.816344	+	0.577566i	$0.195997\pi$
$313$	16.0705	+	27.8349i	0.908359	+	1.57332i	0.0920148	+	0.995758i	$0.470669\pi$
$314$	5.66905	−	21.1572i	0.319923	−	1.19397i
$315$		0			0
$316$	8.26720	+	4.77307i	0.465066	+	0.268506i
$317$	−7.74554	+	28.9067i	−0.435033	+	1.62356i	0.305956	+	0.952046i	$0.401024\pi$
$317$	−7.74554	+	28.9067i	−0.435033	+	1.62356i	−0.740988	+	0.671518i	$0.765643\pi$
$318$		0			0
$319$	0.605036	−	2.25803i	0.0338755	−	0.126425i
$320$	0.398313	+	1.48652i	0.0222664	+	0.0830993i
$321$		0			0
$322$	−2.19975	−	1.27003i	−0.122587	−	0.0707758i
$323$	−6.64110	−	1.77948i	−0.369521	−	0.0990128i
$324$		0			0
$325$	−4.32057	+	8.44756i	−0.239662	+	0.468586i
$326$	−4.60538	+	2.65892i	−0.255069	+	0.147264i
$327$		0			0
$328$	−8.05410			−0.444713
$329$	8.76671	+	15.1844i	0.483325	+	0.837143i
$330$		0			0
$331$	4.69098	−	4.69098i	0.257839	−	0.257839i	−0.566335	−	0.824175i	$-0.691639\pi$
$331$	4.69098	−	4.69098i	0.257839	−	0.257839i	0.824175	+	0.566335i	$0.191639\pi$
$332$	2.17883	+	8.13149i	0.119579	+	0.446273i
$333$		0			0
$334$	5.42465	−	9.39577i	0.296824	−	0.514113i
$335$	6.09604	−	10.5586i	0.333062	−	0.576881i
$336$		0			0
$337$	20.1675	+	11.6437i	1.09859	+	0.634274i	0.935851	−	0.352395i	$-0.114633\pi$
$337$	20.1675	+	11.6437i	1.09859	+	0.634274i	0.162743	+	0.986669i	$0.447966\pi$
$338$	−2.07300	+	12.8337i	−0.112757	+	0.698059i
$339$		0			0
$340$	−0.880349	−	3.28551i	−0.0477436	−	0.178182i
$341$	−0.135221	+	0.0780698i	−0.00732262	+	0.00422772i
$342$		0			0
$343$	12.0916	−	12.0916i	0.652886	−	0.652886i
$344$	−1.14706	−	1.14706i	−0.0618453	−	0.0618453i
$345$		0			0
$346$	1.55112	−	0.415621i	0.0833887	−	0.0223439i
$347$	17.4763	−	10.0899i	0.938175	−	0.541655i	0.0487871	−	0.998809i	$-0.484464\pi$
$347$	17.4763	−	10.0899i	0.938175	−	0.541655i	0.889388	+	0.457154i	$0.151131\pi$
$348$		0			0
$349$	−24.2443	+	6.49625i	−1.29777	+	0.347736i	−0.840606	−	0.541647i	$-0.817801\pi$
$349$	−24.2443	+	6.49625i	−1.29777	+	0.347736i	−0.457163	+	0.889383i	$0.651134\pi$
$350$	3.76463			0.201228
$351$		0			0
$352$	0.496250			0.0264502
$353$	−25.2002	+	6.75238i	−1.34127	+	0.359393i	−0.856906	−	0.515472i	$-0.827616\pi$
$353$	−25.2002	+	6.75238i	−1.34127	+	0.359393i	−0.484366	+	0.874865i	$0.660950\pi$
$354$		0			0
$355$	14.9799	−	8.64867i	0.795052	−	0.459024i
$356$	−3.41203	+	0.914251i	−0.180837	+	0.0484552i
$357$		0			0
$358$	7.11212	+	7.11212i	0.375887	+	0.375887i
$359$	−23.1726	+	23.1726i	−1.22300	+	1.22300i	−0.256444	+	0.966559i	$0.582551\pi$
$359$	−23.1726	+	23.1726i	−1.22300	+	1.22300i	−0.966559	+	0.256444i	$0.917449\pi$
$360$		0			0
$361$	8.07411	−	4.66159i	0.424953	−	0.245347i
$362$	3.09247	+	11.5412i	0.162537	+	0.606594i
$363$		0			0
$364$	4.90792	−	1.58637i	0.257245	−	0.0831482i
$365$	−8.39262	−	4.84548i	−0.439290	−	0.253624i
$366$		0			0
$367$	−0.292660	+	0.506902i	−0.0152767	+	0.0264601i	−0.873563	−	0.486712i	$-0.838196\pi$
$367$	−0.292660	+	0.506902i	−0.0152767	+	0.0264601i	0.858286	+	0.513172i	$0.171530\pi$
$368$	0.887787	−	1.53769i	0.0462791	−	0.0801577i
$369$		0			0
$370$	4.54533	+	16.9634i	0.236301	+	0.881886i
$371$	2.05061	−	2.05061i	0.106463	−	0.106463i
$372$		0			0
$373$	−13.6890	−	23.7100i	−0.708790	−	1.22766i	−0.965306	−	0.261120i	$-0.915908\pi$
$373$	−13.6890	−	23.7100i	−0.708790	−	1.22766i	0.256517	−	0.966540i	$-0.417425\pi$
$374$	−1.09681			−0.0567145
$375$		0			0
$376$	−10.6144	+	6.12820i	−0.547393	+	0.316038i
$377$	16.9627	−	0.862906i	0.873624	−	0.0444419i
$378$		0			0
$379$	3.11912	+	0.835766i	0.160219	+	0.0429304i	0.338037	−	0.941133i	$-0.390237\pi$
$379$	3.11912	+	0.835766i	0.160219	+	0.0429304i	−0.177818	+	0.984063i	$0.556904\pi$
$380$	−4.14596	−	2.39367i	−0.212683	−	0.122793i
$381$		0			0
$382$	5.65407	+	21.1013i	0.289287	+	1.07963i
$383$	−3.64974	+	13.6210i	−0.186493	+	0.696001i	0.807813	+	0.589439i	$0.200651\pi$
$383$	−3.64974	+	13.6210i	−0.186493	+	0.696001i	−0.994306	+	0.106562i	$0.966016\pi$
$384$		0			0
$385$	−0.282767	+	1.05530i	−0.0144111	+	0.0537831i
$386$	−11.3378	−	6.54589i	−0.577080	−	0.333177i
$387$		0			0
$388$	1.90700	−	7.11700i	0.0968130	−	0.361311i
$389$	−9.97462	−	17.2765i	−0.505733	−	0.875956i	−0.999978	−	0.00663286i	$-0.997889\pi$
$389$	−9.97462	−	17.2765i	−0.505733	−	0.875956i	0.494245	−	0.869323i	$-0.335445\pi$
$390$		0			0
$391$	−1.96218	+	3.39859i	−0.0992317	+	0.171874i
$392$	3.50267	+	3.50267i	0.176911	+	0.176911i
$393$		0			0
$394$			2.46558i			0.124214i
$395$	−10.3882	−	10.3882i	−0.522688	−	0.522688i
$396$		0			0
$397$	17.9027	−	4.79700i	0.898509	−	0.240755i	0.220133	−	0.975470i	$-0.429351\pi$
$397$	17.9027	−	4.79700i	0.898509	−	0.240755i	0.678376	+	0.734715i	$0.262684\pi$
$398$	20.2401	+	5.42331i	1.01454	+	0.271846i
$399$		0			0
$400$			2.63159i			0.131580i
$401$	11.1565	−	11.1565i	0.557131	−	0.557131i	−0.371359	−	0.928489i	$-0.621108\pi$
$401$	11.1565	−	11.1565i	0.557131	−	0.557131i	0.928489	+	0.371359i	$0.121108\pi$
$402$		0			0
$403$	−0.841894	−	0.760385i	−0.0419377	−	0.0378775i
$404$			5.51878i			0.274569i
$405$		0			0
$406$	−3.36945	−	5.83606i	−0.167223	−	0.289639i
$407$	5.66293			0.280701
$408$		0			0
$409$	−10.7473	−	2.87972i	−0.531418	−	0.142393i	−0.0168752	−	0.999858i	$-0.505372\pi$
$409$	−10.7473	−	2.87972i	−0.531418	−	0.142393i	−0.514543	+	0.857464i	$0.672038\pi$
$410$	11.9726	+	3.20805i	0.591285	+	0.158434i
$411$		0			0
$412$	−15.0757			−0.742729
$413$	2.00371	+	3.47053i	0.0985963	+	0.170774i
$414$		0			0
$415$		−	12.9555i		−	0.635961i
$416$	1.10892	+	3.43079i	0.0543692	+	0.168208i
$417$		0			0
$418$	−1.09157	+	1.09157i	−0.0533904	+	0.0533904i
$419$		−	0.458051i		−	0.0223772i	−0.999937	−	0.0111886i	$-0.996438\pi$
$419$		−	0.458051i		−	0.0223772i	0.999937	−	0.0111886i	$-0.00356152\pi$
$420$		0			0
$421$	4.37413	+	1.17205i	0.213182	+	0.0571220i	0.363829	−	0.931466i	$-0.381469\pi$
$421$	4.37413	+	1.17205i	0.213182	+	0.0571220i	−0.150647	+	0.988588i	$0.548136\pi$
$422$	13.6464	−	3.65655i	0.664297	−	0.177998i
$423$		0			0
$424$	1.43344	+	1.43344i	0.0696140	+	0.0696140i
$425$		−	5.81632i		−	0.282133i
$426$		0			0
$427$	6.87166	+	6.87166i	0.332543	+	0.332543i
$428$	6.27276	−	10.8647i	0.303205	−	0.525167i
$429$		0			0
$430$	1.24824	+	2.16202i	0.0601957	+	0.104262i
$431$	−3.86478	+	14.4235i	−0.186160	+	0.694758i	0.808220	+	0.588881i	$0.200431\pi$
$431$	−3.86478	+	14.4235i	−0.186160	+	0.694758i	−0.994379	+	0.105876i	$0.966235\pi$
$432$		0			0
$433$	−3.91621	−	2.26103i	−0.188201	−	0.108658i	0.402939	−	0.915227i	$-0.367989\pi$
$433$	−3.91621	−	2.26103i	−0.188201	−	0.108658i	−0.591140	+	0.806569i	$0.701322\pi$
$434$	−0.116497	+	0.434771i	−0.00559201	+	0.0208697i
$435$		0			0
$436$	−2.53558	+	9.46291i	−0.121432	+	0.453191i
$437$	1.42956	+	5.33518i	0.0683850	+	0.255216i
$438$		0			0
$439$	−11.5668	−	6.67809i	−0.552053	−	0.318728i	0.197897	−	0.980223i	$-0.436589\pi$
$439$	−11.5668	−	6.67809i	−0.552053	−	0.318728i	−0.749949	+	0.661495i	$0.769922\pi$
$440$	−0.737687	−	0.197663i	−0.0351679	−	0.00942320i
$441$		0			0
$442$	−2.45092	−	7.58270i	−0.116579	−	0.360672i
$443$	−26.7016	+	15.4162i	−1.26863	+	0.732445i	−0.974729	−	0.223390i	$-0.928288\pi$
$443$	−26.7016	+	15.4162i	−1.26863	+	0.732445i	−0.293903	+	0.955835i	$0.594954\pi$
$444$		0			0
$445$	5.43623			0.257702
$446$	4.58289	+	7.93780i	0.217006	+	0.375865i
$447$		0			0
$448$	1.01155	−	1.01155i	0.0477914	−	0.0477914i
$449$	−10.3894	−	38.7738i	−0.490306	−	1.82985i	−0.554874	−	0.831934i	$-0.687234\pi$
$449$	−10.3894	−	38.7738i	−0.490306	−	1.82985i	0.0645682	−	0.997913i	$-0.479433\pi$
$450$		0			0
$451$	1.99842	−	3.46137i	0.0941020	−	0.162989i
$452$	7.15327	−	12.3898i	0.336461	−	0.582768i
$453$		0			0
$454$	22.8707	+	13.2044i	1.07337	+	0.619713i
$455$	−7.92762	+	0.403284i	−0.371653	+	0.0189062i
$456$		0			0
$457$	−4.27321	−	15.9478i	−0.199892	−	0.746008i	−0.990946	−	0.134261i	$-0.957134\pi$
$457$	−4.27321	−	15.9478i	−0.199892	−	0.746008i	0.791054	−	0.611747i	$-0.209533\pi$
$458$	−12.3141	+	7.10955i	−0.575400	+	0.332207i
$459$		0			0
$460$	−1.93220	+	1.93220i	−0.0900893	+	0.0900893i
$461$	9.76161	+	9.76161i	0.454643	+	0.454643i	0.896892	−	0.442249i	$-0.145819\pi$
$461$	9.76161	+	9.76161i	0.454643	+	0.454643i	−0.442249	+	0.896892i	$0.645819\pi$
$462$		0			0
$463$	37.1831	−	9.96318i	1.72805	−	0.463028i	0.748314	−	0.663345i	$-0.230864\pi$
$463$	37.1831	−	9.96318i	1.72805	−	0.463028i	0.979731	+	0.200316i	$0.0641970\pi$
$464$	4.07958	−	2.35535i	0.189390	−	0.109344i
$465$		0			0
$466$	−20.7182	+	5.55141i	−0.959750	+	0.257164i
$467$	−8.54433			−0.395385			−0.197692	−	0.980264i	$-0.563345\pi$
$467$	−8.54433			−0.395385			−0.197692	+	0.980264i	$0.563345\pi$
$468$		0			0
$469$	−11.3332			−0.523319
$470$	18.2194	−	4.88188i	0.840400	−	0.225185i
$471$		0			0
$472$	−2.42601	+	1.40066i	−0.111666	+	0.0644704i
$473$	0.777580	−	0.208352i	0.0357532	−	0.00958003i
$474$		0			0
$475$	−5.78855	−	5.78855i	−0.265597	−	0.265597i
$476$	−2.23573	+	2.23573i	−0.102474	+	0.102474i
$477$		0			0
$478$	6.80960	−	3.93153i	0.311464	−	0.179824i
$479$	−2.29400	−	8.56132i	−0.104816	−	0.391177i	0.893509	−	0.449046i	$-0.148236\pi$
$479$	−2.29400	−	8.56132i	−0.104816	−	0.391177i	−0.998324	+	0.0578691i	$0.981569\pi$
$480$		0			0
$481$	12.6544	+	39.1503i	0.576990	+	1.78510i
$482$	−16.0291	−	9.25438i	−0.730104	−	0.421526i
$483$		0			0
$484$	5.37687	−	9.31301i	0.244403	−	0.423319i
$485$	−5.66959	+	9.82002i	−0.257443	+	0.445904i
$486$		0			0
$487$	−2.81256	−	10.4966i	−0.127449	−	0.475648i	0.872466	−	0.488675i	$-0.162520\pi$
$487$	−2.81256	−	10.4966i	−0.127449	−	0.475648i	−0.999915	+	0.0130276i	$0.995853\pi$
$488$	−4.80350	+	4.80350i	−0.217444	+	0.217444i
$489$		0			0
$490$	−3.81164	−	6.60196i	−0.172192	−	0.298246i
$491$	17.3462			0.782822			0.391411	−	0.920216i	$-0.371987\pi$
$491$	17.3462			0.782822			0.391411	+	0.920216i	$0.371987\pi$
$492$		0			0
$493$	−9.01666	+	5.20577i	−0.406090	+	0.234456i
$494$	−9.98571	−	5.10727i	−0.449279	−	0.229787i
$495$		0			0
$496$	−0.303918	−	0.0814346i	−0.0136463	−	0.00365652i
$497$	−13.9247	−	8.03942i	−0.624607	−	0.360617i
$498$		0			0
$499$	−3.05648	−	11.4069i	−0.136827	−	0.510644i	−0.999984	−	0.00570844i	$-0.998183\pi$
$499$	−3.05648	−	11.4069i	−0.136827	−	0.510644i	0.863157	−	0.504936i	$-0.168484\pi$
$500$	3.03976	−	11.3445i	0.135942	−	0.507344i
$501$		0			0
$502$	5.71709	−	21.3365i	0.255166	−	0.952294i
$503$	20.1247	+	11.6190i	0.897316	+	0.518066i	0.876329	−	0.481714i	$-0.159986\pi$
$503$	20.1247	+	11.6190i	0.897316	+	0.518066i	0.0209877	+	0.999780i	$0.493319\pi$
$504$		0			0
$505$	2.19820	−	8.20380i	0.0978186	−	0.365064i
$506$	0.440564	+	0.763079i	0.0195855	+	0.0339230i
$507$		0			0
$508$	1.44766	−	2.50743i	0.0642297	−	0.111249i
$509$	2.53125	+	2.53125i	0.112195	+	0.112195i	0.760976	−	0.648780i	$-0.224721\pi$
$509$	2.53125	+	2.53125i	0.112195	+	0.112195i	−0.648780	+	0.760976i	$0.724721\pi$
$510$		0			0
$511$			9.00829i			0.398503i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$		0			0
$514$	−29.1787	+	7.81841i	−1.28702	+	0.344855i
$515$	22.4105	+	6.00487i	0.987523	+	0.264606i
$516$		0			0
$517$		−	6.08223i		−	0.267496i
$518$	11.5433	−	11.5433i	0.507183	−	0.507183i
$519$		0			0
$520$	−0.281908	−	5.54165i	−0.0123625	−	0.243017i
$521$			4.89726i			0.214553i	0.994229	+	0.107277i	$0.0342130\pi$
$521$			4.89726i			0.214553i	−0.994229	+	0.107277i	$0.965787\pi$
$522$		0			0
$523$	0.745466	+	1.29119i	0.0325970	+	0.0564596i	0.881864	−	0.471504i	$-0.156289\pi$
$523$	0.745466	+	1.29119i	0.0325970	+	0.0564596i	−0.849267	+	0.527964i	$0.822956\pi$
$524$	−13.0732			−0.571107
$525$		0			0
$526$	−5.32422	−	1.42662i	−0.232147	−	0.0622036i
$527$	0.671717	+	0.179986i	0.0292605	+	0.00784032i
$528$		0			0
$529$	−19.8473			−0.862928
$530$	−1.55989	−	2.70180i	−0.0677572	−	0.117359i
$531$		0			0
$532$			4.45011i			0.192937i
$533$	28.3956	+	6.08118i	1.22995	+	0.263405i
$534$		0			0
$535$	−13.6522	+	13.6522i	−0.590235	+	0.590235i
$536$		−	7.92226i		−	0.342190i
$537$		0			0
$538$	18.7580	+	5.02619i	0.808714	+	0.216694i
$539$	−2.37442	+	0.636224i	−0.102274	+	0.0274041i
$540$		0			0
$541$	−1.70268	−	1.70268i	−0.0732039	−	0.0732039i	0.669557	−	0.742761i	$-0.266484\pi$
$541$	−1.70268	−	1.70268i	−0.0732039	−	0.0732039i	−0.742761	+	0.669557i	$0.766484\pi$
$542$			22.4023i			0.962260i
$543$		0			0
$544$	−1.56284	−	1.56284i	−0.0670063	−	0.0670063i
$545$	7.53840	−	13.0569i	0.322910	−	0.559296i
$546$		0			0
$547$	6.38104	+	11.0523i	0.272833	+	0.472561i	0.969586	−	0.244750i	$-0.0787059\pi$
$547$	6.38104	+	11.0523i	0.272833	+	0.472561i	−0.696753	+	0.717311i	$0.745373\pi$
$548$	−1.68543	+	6.29012i	−0.0719981	+	0.268701i
$549$		0			0
$550$	−1.13097	−	0.652963i	−0.0482245	−	0.0278424i
$551$	−3.79269	+	14.1545i	−0.161574	+	0.603003i
$552$		0			0
$553$	−3.53450	+	13.1909i	−0.150302	+	0.560936i
$554$	2.28369	+	8.52286i	0.0970248	+	0.362102i
$555$		0			0
$556$	−14.4469	−	8.34095i	−0.612687	−	0.353735i
$557$	11.2158	+	3.00527i	0.475229	+	0.127337i	0.488480	−	0.872575i	$-0.337551\pi$
$557$	11.2158	+	3.00527i	0.475229	+	0.127337i	−0.0132513	+	0.999912i	$0.504218\pi$
$558$		0			0
$559$	3.17801	+	4.91016i	0.134415	+	0.207678i
$560$	−1.90661	+	1.10078i	−0.0805692	+	0.0465166i
$561$		0			0
$562$	−17.9061			−0.755323
$563$	−20.4323	−	35.3898i	−0.861119	−	1.49150i	−0.870849	−	0.491550i	$-0.836431\pi$
$563$	−20.4323	−	35.3898i	−0.861119	−	1.49150i	0.00973001	−	0.999953i	$-0.496903\pi$
$564$		0			0
$565$	−15.5685	+	15.5685i	−0.654973	+	0.654973i
$566$	−1.89264	−	7.06341i	−0.0795534	−	0.296897i
$567$		0			0
$568$	5.61980	−	9.73378i	0.235802	−	0.408420i
$569$	3.20683	−	5.55440i	0.134437	−	0.232852i	−0.790945	−	0.611887i	$-0.790411\pi$
$569$	3.20683	−	5.55440i	0.134437	−	0.232852i	0.925382	+	0.379035i	$0.123744\pi$
$570$		0			0
$571$	11.8701	+	6.85319i	0.496747	+	0.286797i	0.727369	−	0.686246i	$-0.240743\pi$
$571$	11.8701	+	6.85319i	0.496747	+	0.286797i	−0.230622	+	0.973043i	$0.574076\pi$
$572$	−1.74958	−	0.374689i	−0.0731537	−	0.0156665i
$573$		0			0
$574$	−2.98207	−	11.1292i	−0.124469	−	0.464525i
$575$	−4.04658	+	2.33629i	−0.168754	+	0.0974301i
$576$		0			0
$577$	−10.8626	+	10.8626i	−0.452214	+	0.452214i	−0.896089	−	0.443875i	$-0.853604\pi$
$577$	−10.8626	+	10.8626i	−0.452214	+	0.452214i	0.443875	+	0.896089i	$0.353604\pi$
$578$	−8.56663	−	8.56663i	−0.356325	−	0.356325i
$579$		0			0
$580$	−7.00256	+	1.87633i	−0.290766	+	0.0779104i
$581$	−10.4294	+	6.02144i	−0.432686	+	0.249811i
$582$		0			0
$583$	−0.971715	+	0.260370i	−0.0402443	+	0.0107834i
$584$	−6.29707			−0.260575
$585$		0			0
$586$	14.2641			0.589246
$587$	−2.47016	+	0.661876i	−0.101954	+	0.0273186i	−0.309435	−	0.950920i	$-0.600140\pi$
$587$	−2.47016	+	0.661876i	−0.101954	+	0.0273186i	0.207481	+	0.978239i	$0.433473\pi$
$588$		0			0
$589$	0.847637	−	0.489383i	0.0349263	−	0.0201647i
$590$	4.16422	−	1.11580i	0.171438	−	0.0459368i
$591$		0			0
$592$	8.06912	+	8.06912i	0.331639	+	0.331639i
$593$	15.9796	−	15.9796i	0.656204	−	0.656204i	−0.298276	−	0.954480i	$-0.596412\pi$
$593$	15.9796	−	15.9796i	0.656204	−	0.656204i	0.954480	+	0.298276i	$0.0964115\pi$
$594$		0			0
$595$	4.21399	−	2.43295i	0.172757	−	0.0997411i
$596$	−2.72321	−	10.1632i	−0.111547	−	0.416299i
$597$		0			0
$598$	−4.29101	+	4.75098i	−0.175472	+	0.194282i
$599$	−20.6867	−	11.9435i	−0.845237	−	0.487998i	0.0138036	−	0.999905i	$-0.495606\pi$
$599$	−20.6867	−	11.9435i	−0.845237	−	0.487998i	−0.859041	+	0.511907i	$0.828939\pi$
$600$		0			0
$601$	12.7060	−	22.0074i	0.518287	−	0.897700i	−0.481487	−	0.876453i	$-0.659903\pi$
$601$	12.7060	−	22.0074i	0.518287	−	0.897700i	0.999774	−	0.0212465i	$-0.00676348\pi$
$602$	1.16031	−	2.00972i	0.0472908	−	0.0819101i
$603$		0			0
$604$	−4.44836	−	16.6015i	−0.181001	−	0.675505i
$605$	−11.7023	+	11.7023i	−0.475768	+	0.475768i
$606$		0			0
$607$	−10.3003	−	17.8407i	−0.418078	−	0.724132i	0.577668	−	0.816272i	$-0.303963\pi$
$607$	−10.3003	−	17.8407i	−0.418078	−	0.724132i	−0.995746	+	0.0921396i	$0.970629\pi$
$608$	−3.11076			−0.126158
$609$		0			0
$610$	9.05382	−	5.22722i	0.366578	−	0.211644i
$611$	42.0491	−	13.5913i	1.70112	−	0.549847i
$612$		0			0
$613$	−6.32348	−	1.69437i	−0.255403	−	0.0684350i	0.128846	−	0.991665i	$-0.458873\pi$
$613$	−6.32348	−	1.69437i	−0.255403	−	0.0684350i	−0.384249	+	0.923230i	$0.625539\pi$
$614$	−19.0916	−	11.0226i	−0.770476	−	0.444835i
$615$		0			0
$616$	0.183739	+	0.685722i	0.00740304	+	0.0276285i
$617$	4.13493	−	15.4318i	0.166466	−	0.621260i	−0.831383	−	0.555700i	$-0.812450\pi$
$617$	4.13493	−	15.4318i	0.166466	−	0.621260i	0.997849	−	0.0655593i	$-0.0208831\pi$
$618$		0			0
$619$	5.84160	−	21.8012i	0.234794	−	0.876263i	−0.743448	−	0.668794i	$-0.766811\pi$
$619$	5.84160	−	21.8012i	0.234794	−	0.876263i	0.978242	−	0.207469i	$-0.0665225\pi$
$620$	0.419345	+	0.242109i	0.0168413	+	0.00972334i
$621$		0			0
$622$	6.40761	−	23.9135i	0.256922	−	0.958845i
$623$	−2.52664	−	4.37627i	−0.101228	−	0.175331i
$624$		0			0
$625$	−2.45839	+	4.25805i	−0.0983355	+	0.170322i
$626$	−22.7271	−	22.7271i	−0.908359	−	0.908359i
$627$		0			0
$628$			21.9035i			0.874046i
$629$	−17.8343	−	17.8343i	−0.711100	−	0.711100i
$630$		0			0
$631$	−16.8737	+	4.52128i	−0.671730	+	0.179989i	−0.578534	−	0.815658i	$-0.696375\pi$
$631$	−16.8737	+	4.52128i	−0.671730	+	0.179989i	−0.0931960	+	0.995648i	$0.529708\pi$
$632$	−9.22086	−	2.47072i	−0.366786	−	0.0982801i
$633$		0			0
$634$		−	29.9265i		−	1.18853i
$635$	−3.15073	+	3.15073i	−0.125033	+	0.125033i
$636$		0			0
$637$	−9.70437	−	14.9937i	−0.384501	−	0.594072i
$638$			2.33768i			0.0925496i
$639$		0			0
$640$	−0.769482	−	1.33278i	−0.0304164	−	0.0526828i
$641$	36.5684			1.44436			0.722182	−	0.691703i	$-0.243139\pi$
$641$	36.5684			1.44436			0.722182	+	0.691703i	$0.243139\pi$
$642$		0			0
$643$	−33.7924	−	9.05466i	−1.33264	−	0.357081i	−0.478944	−	0.877846i	$-0.658980\pi$
$643$	−33.7924	−	9.05466i	−1.33264	−	0.357081i	−0.853700	+	0.520765i	$0.825647\pi$
$644$	2.45350	+	0.657414i	0.0966815	+	0.0259057i
$645$		0			0
$646$	6.87538			0.270508
$647$	9.58684	+	16.6049i	0.376897	+	0.652806i	0.990609	−	0.136725i	$-0.0436576\pi$
$647$	9.58684	+	16.6049i	0.376897	+	0.652806i	−0.613712	+	0.789530i	$0.710324\pi$
$648$		0			0
$649$		−	1.39015i		−	0.0545682i
$650$	1.98696	−	9.27796i	0.0779350	−	0.363911i
$651$		0			0
$652$	3.76028	−	3.76028i	0.147264	−	0.147264i
$653$		−	6.63054i		−	0.259473i	−0.991548	−	0.129737i	$-0.958587\pi$
$653$		−	6.63054i		−	0.259473i	0.991548	−	0.129737i	$-0.0414132\pi$
$654$		0			0
$655$	19.4337	+	5.20724i	0.759337	+	0.203464i
$656$	7.77966	−	2.08455i	0.303745	−	0.0813882i
$657$		0			0
$658$	−12.3980	−	12.3980i	−0.483325	−	0.483325i
$659$		−	21.6577i		−	0.843665i	−0.906674	−	0.421833i	$-0.861387\pi$
$659$		−	21.6577i		−	0.843665i	0.906674	−	0.421833i	$-0.138613\pi$
$660$		0			0
$661$	7.30997	+	7.30997i	0.284325	+	0.284325i	0.834831	−	0.550506i	$-0.185565\pi$
$661$	7.30997	+	7.30997i	0.284325	+	0.284325i	−0.550506	+	0.834831i	$0.685565\pi$
$662$	−3.31702	+	5.74525i	−0.128920	+	0.223295i
$663$		0			0
$664$	−4.20917	−	7.29049i	−0.163347	−	0.282926i
$665$	1.77254	−	6.61519i	0.0687360	−	0.256526i
$666$		0			0
$667$	7.24360	+	4.18209i	0.280473	+	0.161931i
$668$	−2.80800	+	10.4796i	−0.108645	+	0.405469i
$669$		0			0
$670$	−3.15554	+	11.7766i	−0.121909	+	0.454971i
$671$	−0.872508	−	3.25624i	−0.0336828	−	0.125706i
$672$		0			0
$673$	22.7770	+	13.1503i	0.877990	+	0.506908i	0.869995	−	0.493060i	$-0.164122\pi$
$673$	22.7770	+	13.1503i	0.877990	+	0.506908i	0.00799497	+	0.999968i	$0.497455\pi$
$674$	−22.4939	−	6.02723i	−0.866434	−	0.232160i
$675$		0			0
$676$	−1.31923	−	12.9329i	−0.0507394	−	0.497419i
$677$	0.260338	−	0.150306i	0.0100056	−	0.00577673i	−0.494989	−	0.868899i	$-0.664828\pi$
$677$	0.260338	−	0.150306i	0.0100056	−	0.00577673i	0.504994	+	0.863123i	$0.331495\pi$
$678$		0			0
$679$	10.5404			0.404504
$680$	1.70070	+	2.94570i	0.0652190	+	0.112963i
$681$		0			0
$682$	0.110407	−	0.110407i	0.00422772	−	0.00422772i
$683$	−0.894421	−	3.33802i	−0.0342241	−	0.127726i	0.946700	−	0.322116i	$-0.104394\pi$
$683$	−0.894421	−	3.33802i	−0.0342241	−	0.127726i	−0.980924	+	0.194390i	$0.937727\pi$
$684$		0			0
$685$	5.01088	−	8.67909i	0.191456	−	0.331611i
$686$	−8.55007	+	14.8092i	−0.326443	+	0.565416i
$687$		0			0
$688$	1.40486	+	0.811094i	0.0535596	+	0.0309227i
$689$	−3.97144	−	6.13606i	−0.151300	−	0.233765i
$690$		0			0
$691$	8.65698	+	32.3083i	0.329327	+	1.22906i	0.909890	+	0.414849i	$0.136166\pi$
$691$	8.65698	+	32.3083i	0.329327	+	1.22906i	−0.580563	+	0.814215i	$0.697168\pi$
$692$	−1.39070	+	0.802919i	−0.0528663	+	0.0305224i
$693$		0			0
$694$	−14.2693	+	14.2693i	−0.541655	+	0.541655i
$695$	18.1534	+	18.1534i	0.688599	+	0.688599i
$696$		0			0
$697$	−17.1946	+	4.60727i	−0.651290	+	0.174513i
$698$	21.7369	−	12.5498i	0.822752	−	0.475016i
$699$		0			0
$700$	−3.63635	+	0.974358i	−0.137441	+	0.0368273i
$701$	−14.8908			−0.562418			−0.281209	−	0.959647i	$-0.590735\pi$
$701$	−14.8908			−0.562418			−0.281209	+	0.959647i	$0.590735\pi$
$702$		0			0
$703$	−35.4983			−1.33884
$704$	−0.479340	+	0.128439i	−0.0180658	+	0.00484072i
$705$		0			0
$706$	22.5939	−	13.0446i	0.850333	−	0.490940i
$707$	−7.62589	+	2.04335i	−0.286801	+	0.0768481i
$708$		0			0
$709$	−17.4183	−	17.4183i	−0.654157	−	0.654157i	0.299834	−	0.953991i	$-0.403069\pi$
$709$	−17.4183	−	17.4183i	−0.654157	−	0.654157i	−0.953991	+	0.299834i	$0.903069\pi$
$710$	−12.2311	+	12.2311i	−0.459024	+	0.459024i
$711$		0			0
$712$	3.05914	−	1.76620i	0.114646	−	0.0661910i
$713$	−0.144593	−	0.539629i	−0.00541505	−	0.0202093i
$714$		0			0
$715$	2.45155	+	1.25387i	0.0916829	+	0.0468919i
$716$	−8.71053	−	5.02903i	−0.325528	−	0.187944i
$717$		0			0
$718$	16.3855	−	28.3805i	0.611502	−	1.05915i
$719$	17.8371	−	30.8948i	0.665213	−	1.15218i	−0.314014	−	0.949418i	$-0.601674\pi$
$719$	17.8371	−	30.8948i	0.665213	−	1.15218i	0.979227	−	0.202765i	$-0.0649928\pi$
$720$		0			0
$721$	−5.58186	−	20.8318i	−0.207879	−	0.775816i
$722$	−6.59248	+	6.59248i	−0.245347	+	0.245347i
$723$		0			0
$724$	−5.97419	−	10.3476i	−0.222029	−	0.384565i
$725$	−12.3966			−0.460399
$726$		0			0
$727$	−8.14708	+	4.70372i	−0.302159	+	0.174451i	−0.643412	−	0.765520i	$-0.722482\pi$
$727$	−8.14708	+	4.70372i	−0.302159	+	0.174451i	0.341254	+	0.939971i	$0.389149\pi$
$728$	−4.33011	+	2.80258i	−0.160484	+	0.103870i
$729$		0			0
$730$	9.36075	+	2.50821i	0.346457	+	0.0928328i
$731$	−3.10500	−	1.79267i	−0.114843	−	0.0663044i
$732$		0			0
$733$	−8.37893	−	31.2706i	−0.309483	−	1.15501i	−0.929017	−	0.370037i	$-0.879345\pi$
$733$	−8.37893	−	31.2706i	−0.309483	−	1.15501i	0.619534	−	0.784970i	$-0.287322\pi$
$734$	0.151492	−	0.565376i	0.00559167	−	0.0208684i
$735$		0			0
$736$	−0.459552	+	1.71507i	−0.0169393	+	0.0632184i
$737$	3.40471	+	1.96571i	0.125414	+	0.0724079i
$738$		0			0
$739$	7.68766	−	28.6907i	0.282795	−	1.05541i	−0.667640	−	0.744484i	$-0.732696\pi$
$739$	7.68766	−	28.6907i	0.282795	−	1.05541i	0.950436	−	0.310922i	$-0.100638\pi$
$740$	−8.78091	−	15.2090i	−0.322793	−	0.559093i
$741$		0			0
$742$	−1.45000	+	2.51148i	−0.0532313	+	0.0921993i
$743$	17.4277	+	17.4277i	0.639359	+	0.639359i	0.950397	−	0.311038i	$-0.100677\pi$
$743$	17.4277	+	17.4277i	0.639359	+	0.639359i	−0.311038	+	0.950397i	$0.600677\pi$
$744$		0			0
$745$			16.1925i			0.593247i
$746$	19.3592	+	19.3592i	0.708790	+	0.708790i
$747$		0			0
$748$	1.05943	−	0.283875i	0.0387368	−	0.0103795i
$749$	17.3355	+	4.64503i	0.633425	+	0.169726i
$750$		0			0
$751$			22.1321i			0.807610i	0.914845	+	0.403805i	$0.132313\pi$
$751$			22.1321i			0.807610i	−0.914845	+	0.403805i	$0.867687\pi$
$752$	8.66658	−	8.66658i	0.316038	−	0.316038i
$753$		0			0
$754$	−16.1614	+	5.22378i	−0.588563	+	0.190239i
$755$			26.4504i			0.962628i
$756$		0			0
$757$	25.1440	+	43.5507i	0.913875	+	1.58288i	0.808540	+	0.588442i	$0.200258\pi$
$757$	25.1440	+	43.5507i	0.913875	+	1.58288i	0.105336	+	0.994437i	$0.466408\pi$
$758$	−3.22915			−0.117288
$759$		0			0
$760$	4.62422	+	1.23906i	0.167738	+	0.0449453i
$761$	−8.09766	−	2.16976i	−0.293540	−	0.0786538i	0.109044	−	0.994037i	$-0.465221\pi$
$761$	−8.09766	−	2.16976i	−0.293540	−	0.0786538i	−0.402584	+	0.915383i	$0.631888\pi$
$762$		0			0
$763$	−14.0147			−0.507368
$764$	−10.9228	−	18.9189i	−0.395174	−	0.684461i
$765$		0			0
$766$		−	14.1015i		−	0.509508i
$767$	9.61071	−	3.10643i	0.347023	−	0.112167i
$768$		0			0
$769$	−10.9600	+	10.9600i	−0.395229	+	0.395229i	−0.876547	−	0.481317i	$-0.840159\pi$
$769$	−10.9600	+	10.9600i	−0.395229	+	0.395229i	0.481317	+	0.876547i	$0.340159\pi$
$770$		−	1.09253i		−	0.0393720i
$771$		0			0
$772$	12.6457	+	3.38840i	0.455128	+	0.121951i
$773$	6.28210	−	1.68328i	0.225951	−	0.0605435i	−0.144067	−	0.989568i	$-0.546018\pi$
$773$	6.28210	−	1.68328i	0.225951	−	0.0605435i	0.370018	+	0.929024i	$0.379351\pi$
$774$		0			0
$775$	0.585485	+	0.585485i	0.0210313	+	0.0210313i
$776$			7.36806i			0.264498i
$777$		0			0
$778$	14.1062	+	14.1062i	0.505733	+	0.505733i
$779$	−12.5272	+	21.6977i	−0.448833	+	0.777401i
$780$		0			0
$781$	2.78882	+	4.83038i	0.0997919	+	0.172845i
$782$	1.01570	−	3.79064i	0.0363213	−	0.135553i
$783$		0			0
$784$	−4.28987	−	2.47676i	−0.153210	−	0.0884557i
$785$	8.72447	−	32.5601i	0.311390	−	1.16212i
$786$		0			0
$787$	−13.8656	+	51.7471i	−0.494255	+	1.84458i	0.0399086	+	0.999203i	$0.487293\pi$
$787$	−13.8656	+	51.7471i	−0.494255	+	1.84458i	−0.534164	+	0.845381i	$0.679373\pi$
$788$	−0.638138	−	2.38157i	−0.0227327	−	0.0848398i
$789$		0			0
$790$	12.7229	+	7.34558i	0.452661	+	0.261344i
$791$	19.7689	+	5.29706i	0.702901	+	0.188342i
$792$		0			0
$793$	20.5621	−	13.3084i	0.730182	−	0.472596i
$794$	−16.0511	+	9.26710i	−0.569632	+	0.328877i
$795$		0			0
$796$	−20.9541			−0.742697
$797$	23.3358	+	40.4188i	0.826597	+	1.43171i	0.900692	+	0.434457i	$0.143060\pi$
$797$	23.3358	+	40.4188i	0.826597	+	1.43171i	−0.0740951	+	0.997251i	$0.523607\pi$
$798$		0			0
$799$	−19.1548	+	19.1548i	−0.677649	+	0.677649i
$800$	−0.681106	−	2.54192i	−0.0240807	−	0.0898705i
$801$		0			0
$802$	−7.88886	+	13.6639i	−0.278565	+	0.482489i
$803$	1.56246	−	2.70626i	0.0551380	−	0.0955018i
$804$		0			0
$805$	−3.38533	−	1.95452i	−0.119317	−	0.0688879i
$806$	1.01001	+	0.516577i	0.0355761	+	0.0181957i
$807$		0			0
$808$	−1.42836	−	5.33073i	−0.0502497	−	0.187534i
$809$	−3.13155	+	1.80800i	−0.110099	+	0.0635659i	−0.554039	−	0.832491i	$-0.686914\pi$
$809$	−3.13155	+	1.80800i	−0.110099	+	0.0635659i	0.443939	+	0.896057i	$0.353581\pi$
$810$		0			0
$811$	0.430194	−	0.430194i	0.0151062	−	0.0151062i	−0.699513	−	0.714620i	$-0.746600\pi$
$811$	0.430194	−	0.430194i	0.0151062	−	0.0151062i	0.714620	+	0.699513i	$0.246600\pi$
$812$	4.76512	+	4.76512i	0.167223	+	0.167223i
$813$		0			0
$814$	−5.46997	+	1.46567i	−0.191722	+	0.0513719i
$815$	−7.08752	+	4.09198i	−0.248265	+	0.143336i
$816$		0			0
$817$	−4.87429	+	1.30606i	−0.170530	+	0.0456933i
$818$	11.1264			0.389025
$819$		0			0
$820$	−12.3950			−0.432851
$821$	−49.9310	+	13.3790i	−1.74260	+	0.466929i	−0.983022	−	0.183485i	$-0.941262\pi$
$821$	−49.9310	+	13.3790i	−1.74260	+	0.466929i	−0.759580	+	0.650414i	$0.774595\pi$
$822$		0			0
$823$	16.1344	−	9.31518i	0.562408	−	0.324707i	−0.191703	−	0.981453i	$-0.561401\pi$
$823$	16.1344	−	9.31518i	0.562408	−	0.324707i	0.754112	+	0.656746i	$0.228068\pi$
$824$	14.5621	−	3.90189i	0.507293	−	0.135929i
$825$		0			0
$826$	−2.83368	−	2.83368i	−0.0985963	−	0.0985963i
$827$	23.9908	−	23.9908i	0.834244	−	0.834244i	−0.153851	−	0.988094i	$-0.549167\pi$
$827$	23.9908	−	23.9908i	0.834244	−	0.834244i	0.988094	+	0.153851i	$0.0491675\pi$
$828$		0			0
$829$	−11.0843	+	6.39953i	−0.384974	+	0.222265i	−0.679980	−	0.733230i	$-0.738012\pi$
$829$	−11.0843	+	6.39953i	−0.384974	+	0.222265i	0.295006	+	0.955495i	$0.404678\pi$
$830$	3.35313	+	12.5141i	0.116389	+	0.434370i
$831$		0			0
$832$	−1.95909	−	3.02688i	−0.0679191	−	0.104938i
$833$	9.48144	+	5.47411i	0.328513	+	0.189667i
$834$		0			0
$835$	8.34834	−	14.4597i	0.288906	−	0.500400i
$836$	0.771857	−	1.33689i	0.0266952	−	0.0462375i
$837$		0			0
$838$	0.118552	+	0.442443i	0.00409532	+	0.0152839i
$839$	14.9217	−	14.9217i	0.515155	−	0.515155i	−0.400946	−	0.916102i	$-0.631319\pi$
$839$	14.9217	−	14.9217i	0.515155	−	0.515155i	0.916102	+	0.400946i	$0.131319\pi$
$840$		0			0
$841$	−3.40468	−	5.89708i	−0.117403	−	0.203348i
$842$	−4.52844			−0.156060
$843$		0			0
$844$	−12.2350	+	7.06391i	−0.421148	+	0.243150i
$845$	−3.19028	+	19.7505i	−0.109749	+	0.679439i
$846$		0			0
$847$	14.8596	+	3.98162i	0.510582	+	0.136810i
$848$	−1.75560	−	1.01360i	−0.0602875	−	0.0348070i
$849$		0			0
$850$	1.50537	+	5.61814i	0.0516339	+	0.192700i
$851$	−5.24416	+	19.5715i	−0.179767	+	0.670901i
$852$		0			0
$853$	−2.43856	+	9.10083i	−0.0834947	+	0.311606i	−0.995025	−	0.0996268i	$-0.968235\pi$
$853$	−2.43856	+	9.10083i	−0.0834947	+	0.311606i	0.911530	+	0.411233i	$0.134902\pi$
$854$	−8.41603	−	4.85900i	−0.287991	−	0.166272i
$855$		0			0
$856$	−3.24702	+	12.1180i	−0.110981	+	0.414186i
$857$	−7.45337	−	12.9096i	−0.254602	−	0.440984i	0.710185	−	0.704015i	$-0.248611\pi$
$857$	−7.45337	−	12.9096i	−0.254602	−	0.440984i	−0.964787	+	0.263031i	$0.915278\pi$
$858$		0			0
$859$	17.7711	−	30.7804i	0.606341	−	1.05021i	−0.385497	−	0.922709i	$-0.625970\pi$
$859$	17.7711	−	30.7804i	0.606341	−	1.05021i	0.991838	−	0.127504i	$-0.0406967\pi$
$860$	−1.76528	−	1.76528i	−0.0601957	−	0.0601957i
$861$		0			0
$862$		−	14.9323i		−	0.508598i
$863$	0.118264	+	0.118264i	0.00402577	+	0.00402577i	0.709117	−	0.705091i	$-0.249094\pi$
$863$	0.118264	+	0.118264i	0.00402577	+	0.00402577i	−0.705091	+	0.709117i	$0.749094\pi$
$864$		0			0
$865$	2.38712	−	0.639626i	0.0811644	−	0.0217479i
$866$	4.36797	+	1.17039i	0.148430	+	0.0397716i
$867$		0			0
$868$		−	0.450108i		−	0.0152777i
$869$	3.34975	−	3.34975i	0.113633	−	0.113633i
$870$		0			0
$871$	−5.98164	+	27.9308i	−0.202680	+	0.946399i
$872$		−	9.79673i		−	0.331759i
$873$		0			0
$874$	−2.76169	−	4.78339i	−0.0934156	−	0.161801i
$875$	16.8015			0.567994
$876$		0			0
$877$	−41.3195	−	11.0715i	−1.39526	−	0.373859i	−0.518619	−	0.855005i	$-0.673554\pi$
$877$	−41.3195	−	11.0715i	−1.39526	−	0.373859i	−0.876640	+	0.481147i	$0.840220\pi$
$878$	12.9011	+	3.45683i	0.435390	+	0.116662i
$879$		0			0
$880$	0.763710			0.0257447
$881$	13.3432	+	23.1111i	0.449544	+	0.778633i	0.998356	−	0.0573124i	$-0.0182531\pi$
$881$	13.3432	+	23.1111i	0.449544	+	0.778633i	−0.548812	+	0.835946i	$0.684920\pi$
$882$		0			0
$883$			11.8585i			0.399071i	0.979891	+	0.199536i	$0.0639433\pi$
$883$			11.8585i			0.399071i	−0.979891	+	0.199536i	$0.936057\pi$
$884$	4.32996	+	6.68998i	0.145632	+	0.225008i
$885$		0			0
$886$	21.8018	−	21.8018i	0.732445	−	0.732445i
$887$		−	52.7911i		−	1.77255i	−0.463156	−	0.886277i	$-0.653283\pi$
$887$		−	52.7911i		−	1.77255i	0.463156	−	0.886277i	$-0.346717\pi$
$888$		0			0
$889$	4.00079	+	1.07201i	0.134182	+	0.0359540i
$890$	−5.25099	+	1.40700i	−0.176014	+	0.0471627i
$891$		0			0
$892$	−6.48118	−	6.48118i	−0.217006	−	0.217006i
$893$			38.1267i			1.27586i
$894$		0			0
$895$	10.9453	+	10.9453i	0.365861	+	0.365861i
$896$	−0.715277	+	1.23890i	−0.0238957	+	0.0413886i
$897$		0			0
$898$	20.0708	+	34.7636i	0.669771	+	1.16008i
$899$	0.383613	−	1.43167i	0.0127942	−	0.0477487i
$900$		0			0
$901$	3.88021	+	2.24024i	0.129269	+	0.0746333i
$902$	−1.03446	+	3.86065i	−0.0344437	+	0.128546i
$903$		0			0
$904$	−3.70280	+	13.8190i	−0.123153	+	0.459615i
$905$	4.75920	+	17.7616i	0.158201	+	0.590414i
$906$		0			0
$907$	−15.9624	−	9.21592i	−0.530024	−	0.306009i	0.211002	−	0.977486i	$-0.432327\pi$
$907$	−15.9624	−	9.21592i	−0.530024	−	0.306009i	−0.741026	+	0.671476i	$0.765661\pi$
$908$	−25.5089	−	6.83510i	−0.846544	−	0.226831i
$909$		0			0
$910$	7.55312	−	2.44136i	0.250383	−	0.0809303i
$911$	37.3282	−	21.5514i	1.23674	−	0.714030i	0.268311	−	0.963332i	$-0.413534\pi$
$911$	37.3282	−	21.5514i	1.23674	−	0.714030i	0.968426	+	0.249302i	$0.0802011\pi$
$912$		0			0
$913$	4.17760			0.138258
$914$	8.25520	+	14.2984i	0.273058	+	0.472950i
$915$		0			0
$916$	10.0544	−	10.0544i	0.332207	−	0.332207i
$917$	−4.84042	−	18.0647i	−0.159845	−	0.596549i
$918$		0			0
$919$	−25.3781	+	43.9562i	−0.837147	+	1.44998i	0.0551224	+	0.998480i	$0.482445\pi$
$919$	−25.3781	+	43.9562i	−0.837147	+	1.44998i	−0.892270	+	0.451502i	$0.850888\pi$
$920$	1.36627	−	2.36645i	0.0450446	−	0.0780196i
$921$		0			0
$922$	−11.9555	−	6.90250i	−0.393733	−	0.227322i
$923$	−27.1626	+	30.0743i	−0.894068	+	0.989908i
$924$		0			0
$925$	−7.77241	−	29.0070i	−0.255555	−	0.953745i
$926$	−33.3375	+	19.2474i	−1.09554	+	0.632508i
$927$		0			0
$928$	−3.33096	+	3.33096i	−0.109344	+	0.109344i
$929$	−32.8640	−	32.8640i	−1.07823	−	1.07823i	−0.996668	−	0.0815633i	$-0.974009\pi$
$929$	−32.8640	−	32.8640i	−1.07823	−	1.07823i	−0.0815633	−	0.996668i	$-0.525991\pi$
$930$		0			0
$931$	14.8841	−	3.98820i	0.487808	−	0.130708i
$932$	18.5754	−	10.7245i	0.608457	−	0.351293i
$933$		0			0
$934$	8.25319	−	2.21144i	0.270053	−	0.0723604i
$935$	−1.68795			−0.0552018
$936$		0			0
$937$	−13.9838			−0.456832			−0.228416	−	0.973564i	$-0.573355\pi$
$937$	−13.9838			−0.456832			−0.228416	+	0.973564i	$0.573355\pi$
$938$	10.9471	−	2.93325i	0.357434	−	0.0957741i
$939$		0			0
$940$	−16.3351	+	9.43108i	−0.532792	+	0.307608i
$941$	−24.7787	+	6.63944i	−0.807764	+	0.216440i	−0.638990	−	0.769215i	$-0.720647\pi$
$941$	−24.7787	+	6.63944i	−0.807764	+	0.216440i	−0.168774	+	0.985655i	$0.553981\pi$
$942$		0			0
$943$	10.1121	+	10.1121i	0.329295	+	0.329295i
$944$	1.98083	−	1.98083i	0.0644704	−	0.0644704i
$945$		0			0
$946$	−0.697159	+	0.402505i	−0.0226666	+	0.0130866i
$947$	−0.714319	−	2.66588i	−0.0232123	−	0.0866293i	0.953348	−	0.301873i	$-0.0976120\pi$
$947$	−0.714319	−	2.66588i	−0.0232123	−	0.0866293i	−0.976560	+	0.215244i	$0.930945\pi$
$948$		0			0
$949$	22.2010	+	4.75455i	0.720675	+	0.154339i
$950$	7.08950	+	4.09312i	0.230014	+	0.132798i
$951$		0			0
$952$	1.58090	−	2.73820i	0.0512372	−	0.0887455i
$953$	−14.2452	+	24.6735i	−0.461448	+	0.799252i	−0.999033	−	0.0439575i	$-0.986003\pi$
$953$	−14.2452	+	24.6735i	−0.461448	+	0.799252i	0.537585	+	0.843210i	$0.319337\pi$
$954$		0			0
$955$	8.70140	+	32.4741i	0.281571	+	1.05084i
$956$	−5.56002	+	5.56002i	−0.179824	+	0.179824i
$957$		0			0
$958$	4.43167	+	7.67587i	0.143181	+	0.247996i
$959$	−9.31578			−0.300822
$960$		0			0
$961$	26.7611	−	15.4505i	0.863260	−	0.498403i
$962$	−22.3560	−	34.5411i	−0.720787	−	1.11365i
$963$		0			0
$964$	17.8781	+	4.79042i	0.575815	+	0.154289i
$965$	−17.4485	−	10.0739i	−0.561687	−	0.324290i
$966$		0			0
$967$	−2.73120	−	10.1930i	−0.0878293	−	0.327783i	0.908006	−	0.418958i	$-0.137605\pi$
$967$	−2.73120	−	10.1930i	−0.0878293	−	0.327783i	−0.995835	+	0.0911745i	$0.970938\pi$
$968$	−2.78327	+	10.3873i	−0.0894577	+	0.333861i
$969$		0			0
$970$	2.93480	−	10.9528i	0.0942306	−	0.351674i
$971$	36.5800	+	21.1195i	1.17391	+	0.677756i	0.954597	−	0.297899i	$-0.0962859\pi$
$971$	36.5800	+	21.1195i	1.17391	+	0.677756i	0.219310	+	0.975655i	$0.429619\pi$
$972$		0			0
$973$	6.17655	−	23.0512i	0.198011	−	0.738987i
$974$	5.43346	+	9.41102i	0.174099	+	0.301549i
$975$		0			0
$976$	3.39659	−	5.88306i	0.108722	−	0.188312i
$977$	37.3318	+	37.3318i	1.19435	+	1.19435i	0.975833	+	0.218516i	$0.0701217\pi$
$977$	37.3318	+	37.3318i	1.19435	+	1.19435i	0.218516	+	0.975833i	$0.429878\pi$
$978$		0			0
$979$			1.75295i			0.0560245i
$980$	5.39048	+	5.39048i	0.172192	+	0.172192i
$981$		0			0
$982$	−16.7551	+	4.48952i	−0.534678	+	0.143266i
$983$	−32.7120	−	8.76515i	−1.04335	−	0.279565i	−0.303849	−	0.952720i	$-0.598272\pi$
$983$	−32.7120	−	8.76515i	−1.04335	−	0.279565i	−0.739501	+	0.673155i	$0.764939\pi$
$984$		0			0
$985$			3.79443i			0.120901i
$986$	7.36207	−	7.36207i	0.234456	−	0.234456i
$987$		0			0
$988$	10.9673	+	2.34875i	0.348917	+	0.0747238i
$989$			2.88031i			0.0915887i
$990$		0			0
$991$	20.3156	+	35.1877i	0.645347	+	1.11777i	0.984221	+	0.176942i	$0.0566205\pi$
$991$	20.3156	+	35.1877i	0.645347	+	1.11777i	−0.338874	+	0.940832i	$0.610046\pi$
$992$	0.314639			0.00998980
$993$		0			0
$994$	15.5310	+	4.16151i	0.492612	+	0.131995i
$995$	31.1487	+	8.34627i	0.987481	+	0.264595i
$996$		0			0
$997$	15.3421			0.485888			0.242944	−	0.970040i	$-0.421887\pi$
$997$	15.3421			0.485888			0.242944	+	0.970040i	$0.421887\pi$
$998$	5.90466	+	10.2272i	0.186909	+	0.323735i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	702.2.bc.a.665.2		56
3.2	odd	2		234.2.z.a.41.8	yes	56
9.2	odd	6		702.2.bb.a.197.2		56
9.7	even	3		234.2.y.a.119.12	yes	56
13.7	odd	12		702.2.bb.a.449.2		56
39.20	even	12		234.2.y.a.59.12	✓	56
117.7	odd	12		234.2.z.a.137.8	yes	56
117.20	even	12	inner	702.2.bc.a.683.2		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
234.2.y.a.59.12	✓	56	39.20	even	12
234.2.y.a.119.12	yes	56	9.7	even	3
234.2.z.a.41.8	yes	56	3.2	odd	2
234.2.z.a.137.8	yes	56	117.7	odd	12
702.2.bb.a.197.2		56	9.2	odd	6
702.2.bb.a.449.2		56	13.7	odd	12
702.2.bc.a.665.2		56	1.1	even	1	trivial
702.2.bc.a.683.2		56	117.20	even	12	inner

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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(-0.965926 + 0.258819i) q^{2} +(0.866025 - 0.500000i) q^{4} +(-1.48652 + 0.398313i) q^{5} +(1.01155 + 1.01155i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(1.33278 - 0.769482i) q^{10} +(-0.128439 - 0.479340i) q^{11} +(3.02688 - 1.95909i) q^{13} +(-1.23890 - 0.715277i) q^{14} +(0.500000 - 0.866025i) q^{16} +(-1.10510 + 1.91408i) q^{17} +(0.805124 + 3.00476i) q^{19} +(-1.08821 + 1.08821i) q^{20} +(0.248125 + 0.429765i) q^{22} +1.77557 q^{23} +(-2.27902 + 1.31580i) q^{25} +(-2.41669 + 2.67575i) q^{26} +(1.38181 + 0.370254i) q^{28} +(4.07958 + 2.35535i) q^{29} +(-0.0814346 - 0.303918i) q^{31} +(-0.258819 + 0.965926i) q^{32} +(0.572040 - 2.13488i) q^{34} +(-1.90661 - 1.10078i) q^{35} +(-2.95350 + 11.0226i) q^{37} +(-1.55538 - 2.69400i) q^{38} +(0.769482 - 1.33278i) q^{40} +(5.69511 + 5.69511i) q^{41} +1.62219i q^{43} +(-0.350901 - 0.350901i) q^{44} +(-1.71507 + 0.459552i) q^{46} +(11.8388 + 3.17219i) q^{47} -4.95352i q^{49} +(1.86082 - 1.86082i) q^{50} +(1.64181 - 3.21006i) q^{52} -2.02719i q^{53} +(0.381855 + 0.661392i) q^{55} -1.43055 q^{56} +(-4.55018 - 1.21922i) q^{58} +(2.70586 + 0.725033i) q^{59} +6.79318 q^{61} +(0.157320 + 0.272485i) q^{62} -1.00000i q^{64} +(-3.71920 + 4.11787i) q^{65} +(-5.60189 + 5.60189i) q^{67} +2.21019i q^{68} +(2.12655 + 0.569808i) q^{70} +(-10.8566 + 2.90902i) q^{71} +(4.45270 + 4.45270i) q^{73} -11.4115i q^{74} +(2.19964 + 2.19964i) q^{76} +(0.354956 - 0.614801i) q^{77} +(4.77307 + 8.26720i) q^{79} +(-0.398313 + 1.48652i) q^{80} +(-6.97505 - 4.02705i) q^{82} +(-2.17883 + 8.13149i) q^{83} +(0.880349 - 3.28551i) q^{85} +(-0.419853 - 1.56691i) q^{86} +(0.429765 + 0.248125i) q^{88} +(-3.41203 - 0.914251i) q^{89} +(5.04357 + 1.08013i) q^{91} +(1.53769 - 0.887787i) q^{92} -12.2564 q^{94} +(-2.39367 - 4.14596i) q^{95} +(5.21001 - 5.21001i) q^{97} +(1.28206 + 4.78473i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 8 q^{7} + 24 q^{11} + 28 q^{16} - 8 q^{19} - 4 q^{28} - 4 q^{31} + 24 q^{35} - 4 q^{37} - 36 q^{38} + 48 q^{41} + 36 q^{47} + 24 q^{50} + 8 q^{52} + 36 q^{65} + 28 q^{67} + 24 q^{71} + 28 q^{73}+ \cdots - 48 q^{98}+O(q^{100}) \) 56 * q - 8 * q^7 + 24 * q^11 + 28 * q^16 - 8 * q^19 - 4 * q^28 - 4 * q^31 + 24 * q^35 - 4 * q^37 - 36 * q^38 + 48 * q^41 + 36 * q^47 + 24 * q^50 + 8 * q^52 + 36 * q^65 + 28 * q^67 + 24 * q^71 + 28 * q^73 + 4 * q^76 - 24 * q^77 - 24 * q^79 + 96 * q^83 - 72 * q^85 + 4 * q^91 + 24 * q^92 - 52 * q^97 - 48 * q^98

Introduction

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