LMFDB - Embedded newform 702.2.bc.a.683.2

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			683.2
Character	$\chi$	$=$	702.683
Dual form			702.2.bc.a.665.2

$q$-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 $\left(\mathbb{Z}/702\mathbb{Z}\right)^\times$.

$n$	$379$	$677$
$\chi(n)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−0.965926	−	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	−0.0893855	−	0.995997i	$-0.528490\pi$
$5$	−1.48652	−	0.398313i	−0.664794	−	0.178131i	−0.575409	+	0.817866i	$0.695157\pi$
$6$		0			0
$7$	1.01155	−	1.01155i	0.382331	−	0.382331i	−0.489610	−	0.871941i	$-0.662861\pi$
$7$	1.01155	−	1.01155i	0.382331	−	0.382331i	0.871941	+	0.489610i	$0.162861\pi$
$8$	−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	−0.982582	−	0.185830i	$-0.940502\pi$
$11$	−0.128439	+	0.479340i	−0.0387258	+	0.144527i	0.943856	+	0.330357i	$0.107169\pi$
$12$		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	0.700327	−	0.713823i	$-0.253038\pi$
$17$	−1.10510	−	1.91408i	−0.268025	−	0.464233i	−0.968352	+	0.249589i	$0.919704\pi$
$18$		0			0
$19$	0.805124	−	3.00476i	0.184708	−	0.689340i	−0.809985	−	0.586451i	$-0.800525\pi$
$19$	0.805124	−	3.00476i	0.184708	−	0.689340i	0.994693	−	0.102889i	$-0.0328086\pi$
$20$	−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	−0.0708596	−	0.997486i	$-0.522574\pi$
$29$	4.07958	−	2.35535i	0.757559	−	0.437377i	0.828419	+	0.560109i	$0.189241\pi$
$30$		0			0
$31$	−0.0814346	+	0.303918i	−0.0146261	+	0.0545853i	−0.972853	−	0.231423i	$-0.925662\pi$
$31$	−0.0814346	+	0.303918i	−0.0146261	+	0.0545853i	0.958227	+	0.286008i	$0.0923285\pi$
$32$	−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	−0.577559	−	0.816349i	$-0.695995\pi$
$37$	−2.95350	−	11.0226i	−0.485553	−	1.81211i	0.0920063	−	0.995758i	$-0.470672\pi$
$38$	−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	−0.105041	−	0.994468i	$-0.533498\pi$
$41$	5.69511	−	5.69511i	0.889426	−	0.889426i	0.994468	+	0.105041i	$0.0334975\pi$
$42$		0			0
$43$		−	1.62219i		−	0.247381i	−0.992321	−	0.123691i	$-0.960527\pi$
$43$		−	1.62219i		−	0.247381i	0.992321	−	0.123691i	$-0.0394731\pi$
$44$	−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	0.747406	−	0.664368i	$-0.231299\pi$
$47$	11.8388	−	3.17219i	1.72686	−	0.462711i	0.979456	+	0.201656i	$0.0646324\pi$
$48$		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	$0.0444621\pi$
$53$			2.02719i			0.278456i	−0.990260	+	0.139228i	$0.955538\pi$
$54$		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	−0.0783431	−	0.996926i	$-0.524963\pi$
$59$	2.70586	−	0.725033i	0.352273	−	0.0943913i	0.430616	+	0.902535i	$0.358296\pi$
$60$		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	0.276604	−	0.960984i	$-0.410791\pi$
$67$	−5.60189	−	5.60189i	−0.684379	−	0.684379i	−0.960984	+	0.276604i	$0.910791\pi$
$68$		−	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	−0.451374	−	0.892335i	$-0.649066\pi$
$71$	−10.8566	−	2.90902i	−1.28844	−	0.345237i	−0.837069	+	0.547097i	$0.815733\pi$
$72$		0			0
$73$	4.45270	−	4.45270i	0.521149	−	0.521149i	−0.396769	−	0.917918i	$-0.629869\pi$
$73$	4.45270	−	4.45270i	0.521149	−	0.521149i	0.917918	+	0.396769i	$0.129869\pi$
$74$			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	−0.462051	−	0.886853i	$-0.652886\pi$
$79$	4.77307	−	8.26720i	0.537012	−	0.930133i	0.999063	−	0.0432790i	$-0.0137805\pi$
$80$	−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	−0.976231	−	0.216734i	$-0.930460\pi$
$83$	−2.17883	−	8.13149i	−0.239157	−	0.892547i	0.737073	−	0.675813i	$-0.236207\pi$
$84$		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	−0.435080	−	0.900392i	$-0.643280\pi$
$89$	−3.41203	+	0.914251i	−0.361674	+	0.0969104i	0.0734055	+	0.997302i	$0.476613\pi$
$90$		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	0.920273	−	0.391277i	$-0.127967\pi$
$97$	5.21001	+	5.21001i	0.528996	+	0.528996i	−0.391277	+	0.920273i	$0.627967\pi$
$98$	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	0.695457	−	0.718568i	$-0.255202\pi$
$101$	−2.75939	−	4.77940i	−0.274569	−	0.475568i	−0.970026	+	0.243000i	$0.921869\pi$
$102$		0			0
$103$	−13.0560	+	7.53787i	−1.28644	+	0.742729i	−0.978018	−	0.208520i	$-0.933135\pi$
$103$	−13.0560	+	7.53787i	−1.28644	+	0.742729i	−0.308426	+	0.951248i	$0.599802\pi$
$104$	−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	0.922743	−	0.385416i	$-0.125942\pi$
$107$	10.8647	+	6.27276i	1.05033	+	0.606411i	0.127591	+	0.991827i	$0.459276\pi$
$108$		0			0
$109$	−6.92733	−	6.92733i	−0.663518	−	0.663518i	0.292690	−	0.956208i	$-0.405450\pi$
$109$	−6.92733	−	6.92733i	−0.663518	−	0.663518i	−0.956208	+	0.292690i	$0.905450\pi$
$110$	−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	0.952625	−	0.304149i	$-0.0983720\pi$
$113$	12.3898	+	7.15327i	1.16554	+	0.672923i	0.212912	+	0.977071i	$0.431705\pi$
$114$		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	0.607106	−	0.794621i	$-0.292330\pi$
$127$	2.50743	+	1.44766i	0.222498	+	0.128459i	−0.384608	+	0.923080i	$0.625663\pi$
$128$	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	−0.905031	−	0.425346i	$-0.860153\pi$
$131$	−11.3218	+	6.53662i	−0.989186	+	0.571107i	−0.0841553	+	0.996453i	$0.526819\pi$
$132$		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	0.482494	−	0.875899i	$-0.339731\pi$
$137$	−4.60469	−	4.60469i	−0.393405	−	0.393405i	−0.875899	+	0.482494i	$0.839731\pi$
$138$		0			0
$139$	−8.34095	+	14.4469i	−0.707470	+	1.22537i	0.258322	+	0.966059i	$0.416830\pi$
$139$	−8.34095	+	14.4469i	−0.707470	+	1.22537i	−0.965793	+	0.259316i	$0.916503\pi$
$140$	−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	0.983159	+	0.182752i	$0.0585005\pi$
$149$	2.72321	+	10.1632i	0.223094	+	0.832599i	−0.760065	+	0.649847i	$0.774833\pi$
$150$		0			0
$151$	4.44836	+	16.6015i	0.362002	+	1.35101i	0.871440	+	0.490503i	$0.163187\pi$
$151$	4.44836	+	16.6015i	0.362002	+	1.35101i	−0.509437	+	0.860508i	$0.670146\pi$
$152$	−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	−0.857775	−	0.514025i	$-0.828154\pi$
$157$	−10.9518	−	18.9690i	−0.874046	−	1.51389i	−0.0162709	−	0.999868i	$-0.505179\pi$
$158$	−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	0.454310	−	0.890844i	$-0.349886\pi$
$163$	5.13664	+	1.37636i	0.402333	+	0.107805i	−0.0519776	+	0.998648i	$0.516552\pi$
$164$	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	0.344968	−	0.938615i	$-0.387890\pi$
$167$	−7.67161	−	7.67161i	−0.593647	−	0.593647i	−0.938615	+	0.344968i	$0.887890\pi$
$168$		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	−0.990459	−	0.137805i	$-0.955995\pi$
$179$	−5.02903	+	8.71053i	−0.375887	+	0.651056i	0.614572	+	0.788861i	$0.289329\pi$
$180$		0			0
$181$			11.9484i			0.888116i	0.895998	+	0.444058i	$0.146462\pi$
$181$			11.9484i			0.888116i	−0.895998	+	0.444058i	$0.853538\pi$
$182$	−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	$0.290100\pi$
$191$			21.8456i			1.58069i	−0.612659	+	0.790347i	$0.709900\pi$
$192$		0			0
$193$	9.25729	−	9.25729i	0.666354	−	0.666354i	−0.290516	−	0.956870i	$-0.593827\pi$
$193$	9.25729	−	9.25729i	0.666354	−	0.666354i	0.956870	+	0.290516i	$0.0938269\pi$
$194$	−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	0.984926	−	0.172979i	$-0.0553393\pi$
$197$	0.638138	+	2.38157i	0.0454655	+	0.169680i	−0.939460	+	0.342659i	$0.888673\pi$
$198$		0			0
$199$	−18.1467	+	10.4770i	−1.28639	+	0.742697i	−0.978008	−	0.208567i	$-0.933120\pi$
$199$	−18.1467	+	10.4770i	−1.28639	+	0.742697i	−0.308380	+	0.951263i	$0.599787\pi$
$200$	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	0.839884	+	0.542765i	$0.182623\pi$
$223$	−2.37228	+	8.85346i	−0.158859	+	0.592872i	−0.998744	+	0.0501063i	$0.984044\pi$
$224$	−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	−0.279190	+	0.960236i	$0.590066\pi$
$227$	−18.6738	+	18.6738i	−1.23943	+	1.23943i	−0.960236	+	0.279190i	$0.909934\pi$
$228$		0			0
$229$	13.7346	+	3.68017i	0.907607	+	0.243193i	0.682280	−	0.731091i	$-0.260988\pi$
$229$	13.7346	+	3.68017i	0.907607	+	0.243193i	0.225327	+	0.974283i	$0.427655\pi$
$230$	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	0.00466587	−	0.999989i	$-0.498515\pi$
$239$	−7.59513	−	2.03511i	−0.491288	−	0.131640i	−0.495954	+	0.868349i	$0.665181\pi$
$240$		0			0
$241$	13.0877	−	13.0877i	0.843051	−	0.843051i	−0.146203	−	0.989255i	$-0.546705\pi$
$241$	13.0877	−	13.0877i	0.843051	−	0.843051i	0.989255	+	0.146203i	$0.0467054\pi$
$242$	−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	−0.969458	−	0.245256i	$-0.921128\pi$
$251$	−11.0446	−	19.1298i	−0.697127	−	1.20746i	0.272331	−	0.962204i	$-0.412205\pi$
$252$		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	−0.345552	−	0.938400i	$-0.612308\pi$
$263$	4.77357	−	2.75602i	0.294351	−	0.169943i	0.639902	+	0.768456i	$0.278975\pi$
$264$		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	−0.915666	−	0.401940i	$-0.868336\pi$
$269$	−16.8180	+	9.70985i	−1.02541	+	0.592020i	−0.109743	+	0.993960i	$0.535003\pi$
$270$		0			0
$271$	5.79813	+	21.6389i	0.352212	+	1.31447i	0.883957	+	0.467567i	$0.154869\pi$
$271$	5.79813	+	21.6389i	0.352212	+	1.31447i	−0.531746	+	0.846904i	$0.678464\pi$
$272$	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	$0.0853973\pi$
$277$			8.82351i			0.530153i	−0.964227	+	0.265077i	$0.914603\pi$
$278$	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	0.297083	−	0.954852i	$-0.403986\pi$
$281$	17.2960	−	4.63444i	1.03179	−	0.276467i	0.734707	+	0.678384i	$0.237320\pi$
$282$		0			0
$283$		−	7.31258i		−	0.434688i	−0.976095	−	0.217344i	$-0.930261\pi$
$283$		−	7.31258i		−	0.434688i	0.976095	−	0.217344i	$-0.0697393\pi$
$284$	−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	−0.637745	−	0.770247i	$-0.720133\pi$
$293$	−13.7781	+	3.69183i	−0.804925	+	0.215679i	−0.167180	+	0.985926i	$0.553466\pi$
$294$		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	−0.104822	−	0.994491i	$-0.533427\pi$
$307$	15.5883	−	15.5883i	0.889669	−	0.889669i	0.994491	+	0.104822i	$0.0334273\pi$
$308$			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	−0.967790	−	0.251757i	$-0.918992\pi$
$311$	−12.3786	−	21.4403i	−0.701923	−	1.21577i	0.265867	−	0.964010i	$-0.414342\pi$
$312$		0			0
$313$	16.0705	−	27.8349i	0.908359	−	1.57332i	0.0920148	−	0.995758i	$-0.470669\pi$
$313$	16.0705	−	27.8349i	0.908359	−	1.57332i	0.816344	−	0.577566i	$-0.195997\pi$
$314$	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	−0.740988	−	0.671518i	$-0.765643\pi$
$317$	−7.74554	−	28.9067i	−0.435033	−	1.62356i	0.305956	−	0.952046i	$-0.401024\pi$
$318$		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	0.824175	−	0.566335i	$-0.191639\pi$
$331$	4.69098	+	4.69098i	0.257839	+	0.257839i	−0.566335	+	0.824175i	$0.691639\pi$
$332$	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	0.162743	−	0.986669i	$-0.447966\pi$
$337$	20.1675	−	11.6437i	1.09859	−	0.634274i	0.935851	+	0.352395i	$0.114633\pi$
$338$	−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	0.889388	−	0.457154i	$-0.151131\pi$
$347$	17.4763	+	10.0899i	0.938175	+	0.541655i	0.0487871	+	0.998809i	$0.484464\pi$
$348$		0			0
$349$	−24.2443	−	6.49625i	−1.29777	−	0.347736i	−0.457163	−	0.889383i	$-0.651134\pi$
$349$	−24.2443	−	6.49625i	−1.29777	−	0.347736i	−0.840606	+	0.541647i	$0.817801\pi$
$350$	3.76463			0.201228
$351$		0			0
$352$	0.496250			0.0264502
$353$	−25.2002	−	6.75238i	−1.34127	−	0.359393i	−0.484366	−	0.874865i	$-0.660950\pi$
$353$	−25.2002	−	6.75238i	−1.34127	−	0.359393i	−0.856906	+	0.515472i	$0.827616\pi$
$354$		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	−0.966559	−	0.256444i	$-0.917449\pi$
$359$	−23.1726	−	23.1726i	−1.22300	−	1.22300i	−0.256444	−	0.966559i	$-0.582551\pi$
$360$		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	0.858286	−	0.513172i	$-0.171530\pi$
$367$	−0.292660	−	0.506902i	−0.0152767	−	0.0264601i	−0.873563	+	0.486712i	$0.838196\pi$
$368$	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	0.256517	+	0.966540i	$0.417425\pi$
$373$	−13.6890	+	23.7100i	−0.708790	+	1.22766i	−0.965306	+	0.261120i	$0.915908\pi$
$374$	−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	−0.177818	−	0.984063i	$-0.556904\pi$
$379$	3.11912	−	0.835766i	0.160219	−	0.0429304i	0.338037	+	0.941133i	$0.390237\pi$
$380$	−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	−0.994306	−	0.106562i	$-0.966016\pi$
$383$	−3.64974	−	13.6210i	−0.186493	−	0.696001i	0.807813	−	0.589439i	$-0.200651\pi$
$384$		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	0.494245	+	0.869323i	$0.335445\pi$
$389$	−9.97462	+	17.2765i	−0.505733	+	0.875956i	−0.999978	+	0.00663286i	$0.997889\pi$
$390$		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	0.678376	−	0.734715i	$-0.262684\pi$
$397$	17.9027	+	4.79700i	0.898509	+	0.240755i	0.220133	+	0.975470i	$0.429351\pi$
$398$	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	0.928489	−	0.371359i	$-0.121108\pi$
$401$	11.1565	+	11.1565i	0.557131	+	0.557131i	−0.371359	+	0.928489i	$0.621108\pi$
$402$		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	−0.514543	−	0.857464i	$-0.672038\pi$
$409$	−10.7473	+	2.87972i	−0.531418	+	0.142393i	−0.0168752	+	0.999858i	$0.505372\pi$
$410$	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	$0.00356152\pi$
$419$			0.458051i			0.0223772i	−0.999937	+	0.0111886i	$0.996438\pi$
$420$		0			0
$421$	4.37413	−	1.17205i	0.213182	−	0.0571220i	−0.150647	−	0.988588i	$-0.548136\pi$
$421$	4.37413	−	1.17205i	0.213182	−	0.0571220i	0.363829	+	0.931466i	$0.381469\pi$
$422$	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	−0.994379	−	0.105876i	$-0.966235\pi$
$431$	−3.86478	−	14.4235i	−0.186160	−	0.694758i	0.808220	−	0.588881i	$-0.200431\pi$
$432$		0			0
$433$	−3.91621	+	2.26103i	−0.188201	+	0.108658i	−0.591140	−	0.806569i	$-0.701322\pi$
$433$	−3.91621	+	2.26103i	−0.188201	+	0.108658i	0.402939	+	0.915227i	$0.367989\pi$
$434$	−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	−0.749949	−	0.661495i	$-0.769922\pi$
$439$	−11.5668	+	6.67809i	−0.552053	+	0.318728i	0.197897	+	0.980223i	$0.436589\pi$
$440$	−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	−0.293903	−	0.955835i	$-0.594954\pi$
$443$	−26.7016	−	15.4162i	−1.26863	−	0.732445i	−0.974729	+	0.223390i	$0.928288\pi$
$444$		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	0.0645682	+	0.997913i	$0.479433\pi$
$449$	−10.3894	+	38.7738i	−0.490306	+	1.82985i	−0.554874	+	0.831934i	$0.687234\pi$
$450$		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	0.791054	+	0.611747i	$0.209533\pi$
$457$	−4.27321	+	15.9478i	−0.199892	+	0.746008i	−0.990946	+	0.134261i	$0.957134\pi$
$458$	−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	−0.442249	−	0.896892i	$-0.645819\pi$
$461$	9.76161	−	9.76161i	0.454643	−	0.454643i	0.896892	+	0.442249i	$0.145819\pi$
$462$		0			0
$463$	37.1831	+	9.96318i	1.72805	+	0.463028i	0.979731	−	0.200316i	$-0.0641970\pi$
$463$	37.1831	+	9.96318i	1.72805	+	0.463028i	0.748314	+	0.663345i	$0.230864\pi$
$464$	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	−0.998324	−	0.0578691i	$-0.981569\pi$
$479$	−2.29400	+	8.56132i	−0.104816	+	0.391177i	0.893509	+	0.449046i	$0.148236\pi$
$480$		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	−0.999915	−	0.0130276i	$-0.995853\pi$
$487$	−2.81256	+	10.4966i	−0.127449	+	0.475648i	0.872466	+	0.488675i	$0.162520\pi$
$488$	−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	0.863157	+	0.504936i	$0.168484\pi$
$499$	−3.05648	+	11.4069i	−0.136827	+	0.510644i	−0.999984	+	0.00570844i	$0.998183\pi$
$500$	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	0.0209877	−	0.999780i	$-0.493319\pi$
$503$	20.1247	−	11.6190i	0.897316	−	0.518066i	0.876329	+	0.481714i	$0.159986\pi$
$504$		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	−0.648780	−	0.760976i	$-0.724721\pi$
$509$	2.53125	−	2.53125i	0.112195	−	0.112195i	0.760976	+	0.648780i	$0.224721\pi$
$510$		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	$-0.965787\pi$
$521$		−	4.89726i		−	0.214553i	0.994229	−	0.107277i	$-0.0342130\pi$
$522$		0			0
$523$	0.745466	−	1.29119i	0.0325970	−	0.0564596i	−0.849267	−	0.527964i	$-0.822956\pi$
$523$	0.745466	−	1.29119i	0.0325970	−	0.0564596i	0.881864	+	0.471504i	$0.156289\pi$
$524$	−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	−0.742761	−	0.669557i	$-0.766484\pi$
$541$	−1.70268	+	1.70268i	−0.0732039	+	0.0732039i	0.669557	+	0.742761i	$0.266484\pi$
$542$		−	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	−0.696753	−	0.717311i	$-0.745373\pi$
$547$	6.38104	−	11.0523i	0.272833	−	0.472561i	0.969586	+	0.244750i	$0.0787059\pi$
$548$	−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	−0.0132513	−	0.999912i	$-0.504218\pi$
$557$	11.2158	−	3.00527i	0.475229	−	0.127337i	0.488480	+	0.872575i	$0.337551\pi$
$558$		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	0.00973001	+	0.999953i	$0.496903\pi$
$563$	−20.4323	+	35.3898i	−0.861119	+	1.49150i	−0.870849	+	0.491550i	$0.836431\pi$
$564$		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	0.925382	−	0.379035i	$-0.123744\pi$
$569$	3.20683	+	5.55440i	0.134437	+	0.232852i	−0.790945	+	0.611887i	$0.790411\pi$
$570$		0			0
$571$	11.8701	−	6.85319i	0.496747	−	0.286797i	−0.230622	−	0.973043i	$-0.574076\pi$
$571$	11.8701	−	6.85319i	0.496747	−	0.286797i	0.727369	+	0.686246i	$0.240743\pi$
$572$	−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	0.443875	−	0.896089i	$-0.353604\pi$
$577$	−10.8626	−	10.8626i	−0.452214	−	0.452214i	−0.896089	+	0.443875i	$0.853604\pi$
$578$	−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	0.207481	−	0.978239i	$-0.433473\pi$
$587$	−2.47016	−	0.661876i	−0.101954	−	0.0273186i	−0.309435	+	0.950920i	$0.600140\pi$
$588$		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	0.954480	−	0.298276i	$-0.0964115\pi$
$593$	15.9796	+	15.9796i	0.656204	+	0.656204i	−0.298276	+	0.954480i	$0.596412\pi$
$594$		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	−0.859041	−	0.511907i	$-0.828939\pi$
$599$	−20.6867	+	11.9435i	−0.845237	+	0.487998i	0.0138036	+	0.999905i	$0.495606\pi$
$600$		0			0
$601$	12.7060	+	22.0074i	0.518287	+	0.897700i	0.999774	+	0.0212465i	$0.00676348\pi$
$601$	12.7060	+	22.0074i	0.518287	+	0.897700i	−0.481487	+	0.876453i	$0.659903\pi$
$602$	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	−0.995746	−	0.0921396i	$-0.970629\pi$
$607$	−10.3003	+	17.8407i	−0.418078	+	0.724132i	0.577668	+	0.816272i	$0.303963\pi$
$608$	−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	−0.384249	−	0.923230i	$-0.625539\pi$
$613$	−6.32348	+	1.69437i	−0.255403	+	0.0684350i	0.128846	+	0.991665i	$0.458873\pi$
$614$	−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	0.997849	+	0.0655593i	$0.0208831\pi$
$617$	4.13493	+	15.4318i	0.166466	+	0.621260i	−0.831383	+	0.555700i	$0.812450\pi$
$618$		0			0
$619$	5.84160	+	21.8012i	0.234794	+	0.876263i	0.978242	+	0.207469i	$0.0665225\pi$
$619$	5.84160	+	21.8012i	0.234794	+	0.876263i	−0.743448	+	0.668794i	$0.766811\pi$
$620$	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	−0.0931960	−	0.995648i	$-0.529708\pi$
$631$	−16.8737	−	4.52128i	−0.671730	−	0.179989i	−0.578534	+	0.815658i	$0.696375\pi$
$632$	−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	−0.853700	−	0.520765i	$-0.825647\pi$
$643$	−33.7924	+	9.05466i	−1.33264	+	0.357081i	−0.478944	+	0.877846i	$0.658980\pi$
$644$	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	−0.613712	−	0.789530i	$-0.710324\pi$
$647$	9.58684	−	16.6049i	0.376897	−	0.652806i	0.990609	+	0.136725i	$0.0436576\pi$
$648$		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	$0.0414132\pi$
$653$			6.63054i			0.259473i	−0.991548	+	0.129737i	$0.958587\pi$
$654$		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	$0.138613\pi$
$659$			21.6577i			0.843665i	−0.906674	+	0.421833i	$0.861387\pi$
$660$		0			0
$661$	7.30997	−	7.30997i	0.284325	−	0.284325i	−0.550506	−	0.834831i	$-0.685565\pi$
$661$	7.30997	−	7.30997i	0.284325	−	0.284325i	0.834831	+	0.550506i	$0.185565\pi$
$662$	−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	0.00799497	−	0.999968i	$-0.497455\pi$
$673$	22.7770	−	13.1503i	0.877990	−	0.506908i	0.869995	+	0.493060i	$0.164122\pi$
$674$	−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	0.504994	−	0.863123i	$-0.331495\pi$
$677$	0.260338	+	0.150306i	0.0100056	+	0.00577673i	−0.494989	+	0.868899i	$0.664828\pi$
$678$		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	−0.980924	−	0.194390i	$-0.937727\pi$
$683$	−0.894421	+	3.33802i	−0.0342241	+	0.127726i	0.946700	+	0.322116i	$0.104394\pi$
$684$		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	−0.580563	−	0.814215i	$-0.697168\pi$
$691$	8.65698	−	32.3083i	0.329327	−	1.22906i	0.909890	−	0.414849i	$-0.136166\pi$
$692$	−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	−0.953991	−	0.299834i	$-0.903069\pi$
$709$	−17.4183	+	17.4183i	−0.654157	+	0.654157i	0.299834	+	0.953991i	$0.403069\pi$
$710$	−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	0.979227	+	0.202765i	$0.0649928\pi$
$719$	17.8371	+	30.8948i	0.665213	+	1.15218i	−0.314014	+	0.949418i	$0.601674\pi$
$720$		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	0.341254	−	0.939971i	$-0.389149\pi$
$727$	−8.14708	−	4.70372i	−0.302159	−	0.174451i	−0.643412	+	0.765520i	$0.722482\pi$
$728$	−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	0.619534	+	0.784970i	$0.287322\pi$
$733$	−8.37893	+	31.2706i	−0.309483	+	1.15501i	−0.929017	+	0.370037i	$0.879345\pi$
$734$	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	0.950436	+	0.310922i	$0.100638\pi$
$739$	7.68766	+	28.6907i	0.282795	+	1.05541i	−0.667640	+	0.744484i	$0.732696\pi$
$740$	−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	−0.311038	−	0.950397i	$-0.600677\pi$
$743$	17.4277	−	17.4277i	0.639359	−	0.639359i	0.950397	+	0.311038i	$0.100677\pi$
$744$		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	$-0.867687\pi$
$751$		−	22.1321i		−	0.807610i	0.914845	−	0.403805i	$-0.132313\pi$
$752$	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	0.105336	−	0.994437i	$-0.466408\pi$
$757$	25.1440	−	43.5507i	0.913875	−	1.58288i	0.808540	−	0.588442i	$-0.200258\pi$
$758$	−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	−0.402584	−	0.915383i	$-0.631888\pi$
$761$	−8.09766	+	2.16976i	−0.293540	+	0.0786538i	0.109044	+	0.994037i	$0.465221\pi$
$762$		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	0.481317	−	0.876547i	$-0.340159\pi$
$769$	−10.9600	−	10.9600i	−0.395229	−	0.395229i	−0.876547	+	0.481317i	$0.840159\pi$
$770$			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	0.370018	−	0.929024i	$-0.379351\pi$
$773$	6.28210	+	1.68328i	0.225951	+	0.0605435i	−0.144067	+	0.989568i	$0.546018\pi$
$774$		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	−0.534164	−	0.845381i	$-0.679373\pi$
$787$	−13.8656	−	51.7471i	−0.494255	−	1.84458i	0.0399086	−	0.999203i	$-0.487293\pi$
$788$	−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	−0.0740951	−	0.997251i	$-0.523607\pi$
$797$	23.3358	−	40.4188i	0.826597	−	1.43171i	0.900692	−	0.434457i	$-0.143060\pi$
$798$		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	0.443939	−	0.896057i	$-0.353581\pi$
$809$	−3.13155	−	1.80800i	−0.110099	−	0.0635659i	−0.554039	+	0.832491i	$0.686914\pi$
$810$		0			0
$811$	0.430194	+	0.430194i	0.0151062	+	0.0151062i	0.714620	−	0.699513i	$-0.246600\pi$
$811$	0.430194	+	0.430194i	0.0151062	+	0.0151062i	−0.699513	+	0.714620i	$0.746600\pi$
$812$	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	−0.759580	−	0.650414i	$-0.774595\pi$
$821$	−49.9310	−	13.3790i	−1.74260	−	0.466929i	−0.983022	+	0.183485i	$0.941262\pi$
$822$		0			0
$823$	16.1344	+	9.31518i	0.562408	+	0.324707i	0.754112	−	0.656746i	$-0.228068\pi$
$823$	16.1344	+	9.31518i	0.562408	+	0.324707i	−0.191703	+	0.981453i	$0.561401\pi$
$824$	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	0.988094	−	0.153851i	$-0.0491675\pi$
$827$	23.9908	+	23.9908i	0.834244	+	0.834244i	−0.153851	+	0.988094i	$0.549167\pi$
$828$		0			0
$829$	−11.0843	−	6.39953i	−0.384974	−	0.222265i	0.295006	−	0.955495i	$-0.404678\pi$
$829$	−11.0843	−	6.39953i	−0.384974	−	0.222265i	−0.679980	+	0.733230i	$0.738012\pi$
$830$	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	0.916102	−	0.400946i	$-0.131319\pi$
$839$	14.9217	+	14.9217i	0.515155	+	0.515155i	−0.400946	+	0.916102i	$0.631319\pi$
$840$		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	0.911530	−	0.411233i	$-0.134902\pi$
$853$	−2.43856	−	9.10083i	−0.0834947	−	0.311606i	−0.995025	+	0.0996268i	$0.968235\pi$
$854$	−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	−0.964787	−	0.263031i	$-0.915278\pi$
$857$	−7.45337	+	12.9096i	−0.254602	+	0.440984i	0.710185	+	0.704015i	$0.248611\pi$
$858$		0			0
$859$	17.7711	+	30.7804i	0.606341	+	1.05021i	0.991838	+	0.127504i	$0.0406967\pi$
$859$	17.7711	+	30.7804i	0.606341	+	1.05021i	−0.385497	+	0.922709i	$0.625970\pi$
$860$	−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	−0.705091	−	0.709117i	$-0.749094\pi$
$863$	0.118264	−	0.118264i	0.00402577	−	0.00402577i	0.709117	+	0.705091i	$0.249094\pi$
$864$		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	−0.876640	−	0.481147i	$-0.840220\pi$
$877$	−41.3195	+	11.0715i	−1.39526	+	0.373859i	−0.518619	+	0.855005i	$0.673554\pi$
$878$	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	−0.548812	−	0.835946i	$-0.684920\pi$
$881$	13.3432	−	23.1111i	0.449544	−	0.778633i	0.998356	+	0.0573124i	$0.0182531\pi$
$882$		0			0
$883$		−	11.8585i		−	0.399071i	−0.979891	−	0.199536i	$-0.936057\pi$
$883$		−	11.8585i		−	0.399071i	0.979891	−	0.199536i	$-0.0639433\pi$
$884$	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	$0.346717\pi$
$887$			52.7911i			1.77255i	−0.463156	+	0.886277i	$0.653283\pi$
$888$		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	−0.741026	−	0.671476i	$-0.765661\pi$
$907$	−15.9624	+	9.21592i	−0.530024	+	0.306009i	0.211002	+	0.977486i	$0.432327\pi$
$908$	−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	0.968426	−	0.249302i	$-0.0802011\pi$
$911$	37.3282	+	21.5514i	1.23674	+	0.714030i	0.268311	+	0.963332i	$0.413534\pi$
$912$		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	−0.892270	−	0.451502i	$-0.850888\pi$
$919$	−25.3781	−	43.9562i	−0.837147	−	1.44998i	0.0551224	−	0.998480i	$-0.482445\pi$
$920$	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	−0.0815633	+	0.996668i	$0.525991\pi$
$929$	−32.8640	+	32.8640i	−1.07823	+	1.07823i	−0.996668	+	0.0815633i	$0.974009\pi$
$930$		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	−0.168774	−	0.985655i	$-0.553981\pi$
$941$	−24.7787	−	6.63944i	−0.807764	−	0.216440i	−0.638990	+	0.769215i	$0.720647\pi$
$942$		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	−0.976560	−	0.215244i	$-0.930945\pi$
$947$	−0.714319	+	2.66588i	−0.0232123	+	0.0866293i	0.953348	+	0.301873i	$0.0976120\pi$
$948$		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	0.537585	−	0.843210i	$-0.319337\pi$
$953$	−14.2452	−	24.6735i	−0.461448	−	0.799252i	−0.999033	+	0.0439575i	$0.986003\pi$
$954$		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	−0.995835	−	0.0911745i	$-0.970938\pi$
$967$	−2.73120	+	10.1930i	−0.0878293	+	0.327783i	0.908006	+	0.418958i	$0.137605\pi$
$968$	−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	0.219310	−	0.975655i	$-0.429619\pi$
$971$	36.5800	−	21.1195i	1.17391	−	0.677756i	0.954597	+	0.297899i	$0.0962859\pi$
$972$		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	0.218516	−	0.975833i	$-0.429878\pi$
$977$	37.3318	−	37.3318i	1.19435	−	1.19435i	0.975833	−	0.218516i	$-0.0701217\pi$
$978$		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	−0.739501	−	0.673155i	$-0.764939\pi$
$983$	−32.7120	+	8.76515i	−1.04335	+	0.279565i	−0.303849	+	0.952720i	$0.598272\pi$
$984$		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	−0.338874	−	0.940832i	$-0.610046\pi$
$991$	20.3156	−	35.1877i	0.645347	−	1.11777i	0.984221	−	0.176942i	$-0.0566205\pi$
$992$	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.683.2		56
3.2	odd	2		234.2.z.a.137.8	yes	56
9.4	even	3		234.2.y.a.59.12	✓	56
9.5	odd	6		702.2.bb.a.449.2		56
13.2	odd	12		702.2.bb.a.197.2		56
39.2	even	12		234.2.y.a.119.12	yes	56
117.41	even	12	inner	702.2.bc.a.665.2		56
117.67	odd	12		234.2.z.a.41.8	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
234.2.y.a.59.12	✓	56	9.4	even	3
234.2.y.a.119.12	yes	56	39.2	even	12
234.2.z.a.41.8	yes	56	117.67	odd	12
234.2.z.a.137.8	yes	56	3.2	odd	2
702.2.bb.a.197.2		56	13.2	odd	12
702.2.bb.a.449.2		56	9.5	odd	6
702.2.bc.a.665.2		56	117.41	even	12	inner
702.2.bc.a.683.2		56	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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