LMFDB - Embedded newform 702.2.bb.a.449.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [702,2,Mod(71,702)] 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("702.71"); 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([10, 5])) N = Newforms(chi, 2, names="a")

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

Newform invariants

comment:select newform

sage: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			449.2
Character	$\chi$	$=$	702.449
Dual form			702.2.bb.a.197.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(-0.398313 - 1.48652i) q^{5} +(0.370254 + 1.38181i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.33278 + 0.769482i) q^{10} +(0.350901 + 0.350901i) q^{11} +(0.183180 - 3.60090i) q^{13} +(-1.23890 - 0.715277i) q^{14} -1.00000 q^{16} +(1.10510 + 1.91408i) q^{17} +(0.805124 - 3.00476i) q^{19} +(-1.48652 + 0.398313i) q^{20} -0.496250 q^{22} +(0.887787 + 1.53769i) q^{23} +(2.27902 - 1.31580i) q^{25} +(2.41669 + 2.67575i) q^{26} +(1.38181 - 0.370254i) q^{28} -4.71069i q^{29} +(0.303918 - 0.0814346i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-2.13488 - 0.572040i) q^{34} +(1.90661 - 1.10078i) q^{35} +(-2.95350 - 11.0226i) q^{37} +(1.55538 + 2.69400i) q^{38} +(0.769482 - 1.33278i) q^{40} +(7.77966 + 2.08455i) q^{41} +(1.40486 + 0.811094i) q^{43} +(0.350901 - 0.350901i) q^{44} +(-1.71507 - 0.459552i) q^{46} +(3.17219 - 11.8388i) q^{47} +(4.28987 - 2.47676i) q^{49} +(-0.681106 + 2.54192i) q^{50} +(-3.60090 - 0.183180i) q^{52} -2.02719i q^{53} +(0.381855 - 0.661392i) q^{55} +(-0.715277 + 1.23890i) q^{56} +(3.33096 + 3.33096i) q^{58} +(1.98083 + 1.98083i) q^{59} +(-3.39659 + 5.88306i) q^{61} +(-0.157320 + 0.272485i) q^{62} +1.00000i q^{64} +(-5.42578 + 1.16198i) q^{65} +(-2.05043 + 7.65232i) q^{67} +(1.91408 - 1.10510i) q^{68} +(-0.569808 + 2.12655i) q^{70} +(10.8566 + 2.90902i) q^{71} +(4.45270 - 4.45270i) q^{73} +(9.88261 + 5.70573i) q^{74} +(-3.00476 - 0.805124i) q^{76} +(-0.354956 + 0.614801i) q^{77} +(4.77307 + 8.26720i) q^{79} +(0.398313 + 1.48652i) q^{80} +(-6.97505 + 4.02705i) q^{82} +(-8.13149 - 2.17883i) q^{83} +(2.40516 - 2.40516i) q^{85} +(-1.56691 + 0.419853i) q^{86} +0.496250i q^{88} +(3.41203 - 0.914251i) q^{89} +(5.04357 - 1.08013i) q^{91} +(1.53769 - 0.887787i) q^{92} +(6.12820 + 10.6144i) q^{94} -4.78735 q^{95} +(-7.11700 + 1.90700i) q^{97} +(-1.28206 + 4.78473i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 4 q^{7} - 56 q^{16} - 8 q^{19} - 4 q^{28} + 8 q^{31} - 24 q^{35} - 4 q^{37} + 36 q^{38} + 48 q^{41} + 12 q^{43} - 60 q^{47} + 24 q^{50} - 4 q^{52} + 120 q^{65} - 56 q^{67} - 24 q^{71} + 28 q^{73}+ \cdots + 48 q^{98}+O(q^{100}) $ 56 * q + 4 * q^7 - 56 * q^16 - 8 * q^19 - 4 * q^28 + 8 * q^31 - 24 * q^35 - 4 * q^37 + 36 * q^38 + 48 * q^41 + 12 * q^43 - 60 * q^47 + 24 * q^50 - 4 * q^52 + 120 * q^65 - 56 * q^67 - 24 * q^71 + 28 * q^73 - 48 * q^74 + 4 * q^76 + 24 * q^77 - 24 * q^79 + 60 * q^83 - 48 * q^86 + 4 * q^91 + 24 * q^92 + 20 * q^97 + 48 * q^98

Character values

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

$n$	$379$	$677$
$\chi(n)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$		0			0
$3$		0			0
$4$		−	1.00000i		−	0.500000i
$5$	−0.398313	−	1.48652i	−0.178131	−	0.664794i	−0.995997	−	0.0893855i	$-0.971510\pi$
$5$	−0.398313	−	1.48652i	−0.178131	−	0.664794i	0.817866	−	0.575409i	$-0.195157\pi$
$6$		0			0
$7$	0.370254	+	1.38181i	0.139943	+	0.522274i	0.999929	+	0.0119560i	$0.00380579\pi$
$7$	0.370254	+	1.38181i	0.139943	+	0.522274i	−0.859986	+	0.510318i	$0.829528\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$		0			0
$10$	1.33278	+	0.769482i	0.421463	+	0.243332i
$11$	0.350901	+	0.350901i	0.105801	+	0.105801i	0.758026	−	0.652225i	$-0.226164\pi$
$11$	0.350901	+	0.350901i	0.105801	+	0.105801i	−0.652225	+	0.758026i	$0.726164\pi$
$12$		0			0
$13$	0.183180	−	3.60090i	0.0508050	−	0.998709i
$13$	0.183180	−	3.60090i	0.0508050	−	0.998709i
$14$	−1.23890	−	0.715277i	−0.331109	−	0.191166i
$15$		0			0
$16$	−1.00000			−0.250000
$17$	1.10510	+	1.91408i	0.268025	+	0.464233i	0.968352	−	0.249589i	$-0.0802956\pi$
$17$	1.10510	+	1.91408i	0.268025	+	0.464233i	−0.700327	+	0.713823i	$0.746962\pi$
$18$		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	$-0.0328086\pi$
$20$	−1.48652	+	0.398313i	−0.332397	+	0.0890655i
$21$		0			0
$22$	−0.496250			−0.105801
$23$	0.887787	+	1.53769i	0.185116	+	0.320631i	0.943616	−	0.331043i	$-0.107400\pi$
$23$	0.887787	+	1.53769i	0.185116	+	0.320631i	−0.758499	+	0.651674i	$0.774067\pi$
$24$		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
$29$		−	4.71069i		−	0.874754i	−0.899278	−	0.437377i	$-0.855908\pi$
$29$		−	4.71069i		−	0.874754i	0.899278	−	0.437377i	$-0.144092\pi$
$30$		0			0
$31$	0.303918	−	0.0814346i	0.0545853	−	0.0146261i	−0.231423	−	0.972853i	$-0.574338\pi$
$31$	0.303918	−	0.0814346i	0.0545853	−	0.0146261i	0.286008	+	0.958227i	$0.407671\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$		0			0
$34$	−2.13488	−	0.572040i	−0.366129	−	0.0981040i
$35$	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
$41$	7.77966	+	2.08455i	1.21498	+	0.325553i	0.808714	−	0.588202i	$-0.200164\pi$
$41$	7.77966	+	2.08455i	1.21498	+	0.325553i	0.406265	+	0.913755i	$0.366831\pi$
$42$		0			0
$43$	1.40486	+	0.811094i	0.214239	+	0.123691i	0.603280	−	0.797530i	$-0.293860\pi$
$43$	1.40486	+	0.811094i	0.214239	+	0.123691i	−0.389041	+	0.921220i	$0.627194\pi$
$44$	0.350901	−	0.350901i	0.0529004	−	0.0529004i
$45$		0			0
$46$	−1.71507	−	0.459552i	−0.252874	−	0.0677573i
$47$	3.17219	−	11.8388i	0.462711	−	1.72686i	−0.201656	−	0.979456i	$-0.564632\pi$
$47$	3.17219	−	11.8388i	0.462711	−	1.72686i	0.664368	−	0.747406i	$-0.268701\pi$
$48$		0			0
$49$	4.28987	−	2.47676i	0.612839	−	0.353823i
$50$	−0.681106	+	2.54192i	−0.0963229	+	0.359482i
$51$		0			0
$52$	−3.60090	−	0.183180i	−0.499354	−	0.0254025i
$53$		−	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
$56$	−0.715277	+	1.23890i	−0.0955828	+	0.165554i
$57$		0			0
$58$	3.33096	+	3.33096i	0.437377	+	0.437377i
$59$	1.98083	+	1.98083i	0.257882	+	0.257882i	0.824192	−	0.566310i	$-0.191630\pi$
$59$	1.98083	+	1.98083i	0.257882	+	0.257882i	−0.566310	+	0.824192i	$0.691630\pi$
$60$		0			0
$61$	−3.39659	+	5.88306i	−0.434888	+	0.753249i	−0.997287	−	0.0736177i	$-0.976546\pi$
$61$	−3.39659	+	5.88306i	−0.434888	+	0.753249i	0.562398	+	0.826867i	$0.309879\pi$
$62$	−0.157320	+	0.272485i	−0.0199796	+	0.0346057i
$63$		0			0
$64$			1.00000i			0.125000i
$65$	−5.42578	+	1.16198i	−0.672986	+	0.144126i
$66$		0			0
$67$	−2.05043	+	7.65232i	−0.250500	+	0.934880i	0.720038	+	0.693934i	$0.244124\pi$
$67$	−2.05043	+	7.65232i	−0.250500	+	0.934880i	−0.970539	+	0.240945i	$0.922542\pi$
$68$	1.91408	−	1.10510i	0.232117	−	0.134013i
$69$		0			0
$70$	−0.569808	+	2.12655i	−0.0681051	+	0.254172i
$71$	10.8566	+	2.90902i	1.28844	+	0.345237i	0.837069	−	0.547097i	$-0.184267\pi$
$71$	10.8566	+	2.90902i	1.28844	+	0.345237i	0.451374	+	0.892335i	$0.350934\pi$
$72$		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	$0.129869\pi$
$74$	9.88261	+	5.70573i	1.14883	+	0.663277i
$75$		0			0
$76$	−3.00476	−	0.805124i	−0.344670	−	0.0923540i
$77$	−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
$83$	−8.13149	−	2.17883i	−0.892547	−	0.239157i	−0.216734	−	0.976231i	$-0.569540\pi$
$83$	−8.13149	−	2.17883i	−0.892547	−	0.239157i	−0.675813	+	0.737073i	$0.736207\pi$
$84$		0			0
$85$	2.40516	−	2.40516i	0.260876	−	0.260876i
$86$	−1.56691	+	0.419853i	−0.168965	+	0.0452739i
$87$		0			0
$88$			0.496250i			0.0529004i
$89$	3.41203	−	0.914251i	0.361674	−	0.0969104i	−0.0734055	−	0.997302i	$-0.523387\pi$
$89$	3.41203	−	0.914251i	0.361674	−	0.0969104i	0.435080	+	0.900392i	$0.356720\pi$
$90$		0			0
$91$	5.04357	−	1.08013i	0.528710	−	0.113228i
$92$	1.53769	−	0.887787i	0.160315	−	0.0925582i
$93$		0			0
$94$	6.12820	+	10.6144i	0.632075	+	1.09479i
$95$	−4.78735			−0.491171
$96$		0			0
$97$	−7.11700	+	1.90700i	−0.722622	+	0.193626i	−0.601341	−	0.798992i	$-0.705367\pi$
$97$	−7.11700	+	1.90700i	−0.722622	+	0.193626i	−0.121281	+	0.992618i	$0.538700\pi$
$98$	−1.28206	+	4.78473i	−0.129508	+	0.483331i
$99$		0			0
$100$	−1.31580	−	2.27902i	−0.131580	−	0.227902i
$101$	−5.51878			−0.549139			−0.274569	−	0.961567i	$-0.588535\pi$
$101$	−5.51878			−0.549139			−0.274569	+	0.961567i	$0.588535\pi$
$102$		0			0
$103$	13.0560	+	7.53787i	1.28644	+	0.742729i	0.978018	−	0.208520i	$-0.0668646\pi$
$103$	13.0560	+	7.53787i	1.28644	+	0.742729i	0.308426	+	0.951248i	$0.400198\pi$
$104$	2.67575	−	2.41669i	0.262378	−	0.236976i
$105$		0			0
$106$	1.43344	+	1.43344i	0.139228	+	0.139228i
$107$	−10.8647	−	6.27276i	−1.05033	−	0.606411i	−0.127591	−	0.991827i	$-0.540724\pi$
$107$	−10.8647	−	6.27276i	−1.05033	−	0.606411i	−0.922743	+	0.385416i	$0.874058\pi$
$108$		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	$0.905450\pi$
$110$	0.197663	+	0.737687i	0.0188464	+	0.0703357i
$111$		0			0
$112$	−0.370254	−	1.38181i	−0.0349858	−	0.130569i
$113$			14.3065i			1.34585i	0.739713	+	0.672923i	$0.234961\pi$
$113$			14.3065i			1.34585i	−0.739713	+	0.672923i	$0.765039\pi$
$114$		0			0
$115$	1.93220	−	1.93220i	0.180179	−	0.180179i
$116$	−4.71069			−0.437377
$117$		0			0
$118$	−2.80131			−0.257882
$119$	−2.23573	+	2.23573i	−0.204949	+	0.204949i
$120$		0			0
$121$		−	10.7537i		−	0.977612i
$122$	−1.75820	−	6.56170i	−0.159180	−	0.594069i
$123$		0			0
$124$	−0.0814346	−	0.303918i	−0.00731304	−	0.0272926i
$125$	−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	$0.625663\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$		0			0
$130$	3.01496	−	4.65825i	0.264430	−	0.408556i
$131$	−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
$133$	4.45011			0.385873
$134$	−3.96113	−	6.86088i	−0.342190	−	0.592690i
$135$		0			0
$136$	−0.572040	+	2.13488i	−0.0490520	+	0.183065i
$137$	−6.29012	+	1.68543i	−0.537401	+	0.143996i	−0.517304	−	0.855802i	$-0.673064\pi$
$137$	−6.29012	+	1.68543i	−0.537401	+	0.143996i	−0.0200975	+	0.999798i	$0.506398\pi$
$138$		0			0
$139$	16.6819			1.41494			0.707470	−	0.706743i	$-0.249836\pi$
$139$	16.6819			1.41494			0.707470	+	0.706743i	$0.249836\pi$
$140$	−1.10078	−	1.90661i	−0.0930333	−	0.161138i
$141$		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
$146$			6.29707i			0.521149i
$147$		0			0
$148$	−11.0226	+	2.95350i	−0.906054	+	0.242776i
$149$	−7.43995	+	7.43995i	−0.609505	+	0.609505i	−0.942817	−	0.333312i	$-0.891834\pi$
$149$	−7.43995	+	7.43995i	−0.609505	+	0.609505i	0.333312	+	0.942817i	$0.391834\pi$
$150$		0			0
$151$	−16.6015	−	4.44836i	−1.35101	−	0.362002i	−0.490503	−	0.871440i	$-0.663187\pi$
$151$	−16.6015	−	4.44836i	−1.35101	−	0.362002i	−0.860508	+	0.509437i	$0.829854\pi$
$152$	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	$0.828154\pi$
$158$	−9.22086	−	2.47072i	−0.733572	−	0.196560i
$159$		0			0
$160$	−1.33278	−	0.769482i	−0.105366	−	0.0608329i
$161$	−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	$0.516552\pi$
$164$	2.08455	−	7.77966i	0.162776	−	0.607490i
$165$		0			0
$166$	7.29049	−	4.20917i	0.565852	−	0.326695i
$167$	2.80800	−	10.4796i	0.217290	−	0.810937i	−0.768058	−	0.640380i	$-0.778777\pi$
$167$	2.80800	−	10.4796i	0.217290	−	0.810937i	0.985348	−	0.170557i	$-0.0545566\pi$
$168$		0			0
$169$	−12.9329	−	1.31923i	−0.994838	−	0.101479i
$170$			3.40141i			0.260876i
$171$		0			0
$172$	0.811094	−	1.40486i	0.0618453	−	0.107119i
$173$	−0.802919	+	1.39070i	−0.0610448	+	0.105733i	−0.894933	−	0.446201i	$-0.852777\pi$
$173$	−0.802919	+	1.39070i	−0.0610448	+	0.105733i	0.833888	+	0.551934i	$0.186110\pi$
$174$		0			0
$175$	2.66200	+	2.66200i	0.201228	+	0.201228i
$176$	−0.350901	−	0.350901i	−0.0264502	−	0.0264502i
$177$		0			0
$178$	−1.76620	+	3.05914i	−0.132382	+	0.229292i
$179$	5.02903	−	8.71053i	0.375887	−	0.651056i	−0.614572	−	0.788861i	$-0.710671\pi$
$179$	5.02903	−	8.71053i	0.375887	−	0.651056i	0.990459	+	0.137805i	$0.0440047\pi$
$180$		0			0
$181$			11.9484i			0.888116i	0.895998	+	0.444058i	$0.146462\pi$
$181$			11.9484i			0.888116i	−0.895998	+	0.444058i	$0.853538\pi$
$182$	−2.80258	+	4.33011i	−0.207741	+	0.320969i
$183$		0			0
$184$	−0.459552	+	1.71507i	−0.0338786	+	0.126437i
$185$	−15.2090	+	8.78091i	−1.11819	+	0.645585i
$186$		0			0
$187$	−0.283875	+	1.05943i	−0.0207590	+	0.0774735i
$188$	−11.8388	−	3.17219i	−0.863431	−	0.231356i
$189$		0			0
$190$	3.38516	−	3.38516i	0.245586	−	0.245586i
$191$	18.9189	+	10.9228i	1.36892	+	0.790347i	0.990790	−	0.135405i	$-0.0432335\pi$
$191$	18.9189	+	10.9228i	1.36892	+	0.790347i	0.378131	+	0.925752i	$0.376567\pi$
$192$		0			0
$193$	−12.6457	−	3.38840i	−0.910257	−	0.243903i	−0.226841	−	0.973932i	$-0.572840\pi$
$193$	−12.6457	−	3.38840i	−0.910257	−	0.243903i	−0.683416	+	0.730029i	$0.739506\pi$
$194$	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	$-0.111327\pi$
$197$	−0.638138	−	2.38157i	−0.0454655	−	0.169680i	−0.984926	+	0.172979i	$0.944661\pi$
$198$		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	$0.599787\pi$
$200$	2.54192	+	0.681106i	0.179741	+	0.0481615i
$201$		0			0
$202$	3.90236	−	3.90236i	0.274569	−	0.274569i
$203$	6.50928	−	1.74416i	0.456862	−	0.122416i
$204$		0			0
$205$		−	12.3950i		−	0.865702i
$206$	−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
$211$	7.06391	+	12.2350i	0.486299	+	0.842295i	0.999876	−	0.0157485i	$-0.00501311\pi$
$211$	7.06391	+	12.2350i	0.486299	+	0.842295i	−0.513577	+	0.858044i	$0.671680\pi$
$212$	−2.02719			−0.139228
$213$		0			0
$214$	12.1180	−	3.24702i	0.828372	−	0.221962i
$215$	0.646139	−	2.41142i	0.0440663	−	0.164458i
$216$		0			0
$217$	0.225054	+	0.389805i	0.0152777	+	0.0264617i
$218$	9.79673			0.663518
$219$		0			0
$220$	−0.661392	−	0.381855i	−0.0445911	−	0.0257447i
$221$	7.09484	−	3.62871i	0.477251	−	0.244094i
$222$		0			0
$223$	−6.48118	−	6.48118i	−0.434012	−	0.434012i	0.455979	−	0.889991i	$-0.349289\pi$
$223$	−6.48118	−	6.48118i	−0.434012	−	0.434012i	−0.889991	+	0.455979i	$0.849289\pi$
$224$	1.23890	+	0.715277i	0.0827772	+	0.0477914i
$225$		0			0
$226$	−10.1162	−	10.1162i	−0.672923	−	0.672923i
$227$	6.83510	+	25.5089i	0.453661	+	1.69309i	0.691994	+	0.721903i	$0.256733\pi$
$227$	6.83510	+	25.5089i	0.453661	+	1.69309i	−0.238333	+	0.971184i	$0.576601\pi$
$228$		0			0
$229$	−3.68017	−	13.7346i	−0.243193	−	0.907607i	−0.974283	−	0.225327i	$-0.927655\pi$
$229$	−3.68017	−	13.7346i	−0.243193	−	0.907607i	0.731091	−	0.682280i	$-0.239012\pi$
$230$			2.73254i			0.180179i
$231$		0			0
$232$	3.33096	−	3.33096i	0.218688	−	0.218688i
$233$	−21.4490			−1.40517			−0.702586	−	0.711599i	$-0.747971\pi$
$233$	−21.4490			−1.40517			−0.702586	+	0.711599i	$0.747971\pi$
$234$		0			0
$235$	−18.8622			−1.23043
$236$	1.98083	−	1.98083i	0.128941	−	0.128941i
$237$		0			0
$238$		−	3.16180i		−	0.204949i
$239$	−2.03511	−	7.59513i	−0.131640	−	0.491288i	0.868349	−	0.495954i	$-0.165181\pi$
$239$	−2.03511	−	7.59513i	−0.131640	−	0.491288i	−0.999989	+	0.00466587i	$0.998515\pi$
$240$		0			0
$241$	4.79042	+	17.8781i	0.308578	+	1.15163i	0.929821	+	0.368011i	$0.119961\pi$
$241$	4.79042	+	17.8781i	0.308578	+	1.15163i	−0.621243	+	0.783618i	$0.713372\pi$
$242$	7.60404	+	7.60404i	0.488806	+	0.488806i
$243$		0			0
$244$	5.88306	+	3.39659i	0.376624	+	0.217444i
$245$	−5.39048	−	5.39048i	−0.344385	−	0.344385i
$246$		0			0
$247$	−10.6724	−	3.44958i	−0.679066	−	0.219491i
$248$	0.272485	+	0.157320i	0.0173028	+	0.00998980i
$249$		0			0
$250$	11.7447			0.742803
$251$	11.0446	+	19.1298i	0.697127	+	1.20746i	0.969458	+	0.245256i	$0.0788722\pi$
$251$	11.0446	+	19.1298i	0.697127	+	1.20746i	−0.272331	+	0.962204i	$0.587795\pi$
$252$		0			0
$253$	−0.228053	+	0.851104i	−0.0143375	+	0.0535084i
$254$	−2.79667	+	0.749366i	−0.175479	+	0.0470194i
$255$		0			0
$256$	1.00000			0.0625000
$257$	15.1040	+	26.1609i	0.942162	+	1.63187i	0.761336	+	0.648357i	$0.224544\pi$
$257$	15.1040	+	26.1609i	0.942162	+	1.63187i	0.180825	+	0.983515i	$0.442123\pi$
$258$		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
$263$		−	5.51204i		−	0.339887i	−0.985454	−	0.169943i	$-0.945641\pi$
$263$		−	5.51204i		−	0.339887i	0.985454	−	0.169943i	$-0.0543585\pi$
$264$		0			0
$265$	−3.01347	+	0.807457i	−0.185116	+	0.0496017i
$266$	−3.14670	+	3.14670i	−0.192937	+	0.192937i
$267$		0			0
$268$	7.65232	+	2.05043i	0.467440	+	0.125250i
$269$	16.8180	−	9.70985i	1.02541	−	0.592020i	0.109743	−	0.993960i	$-0.464997\pi$
$269$	16.8180	−	9.70985i	1.02541	−	0.592020i	0.915666	+	0.401940i	$0.131664\pi$
$270$		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
$275$	1.26143	+	0.337999i	0.0760669	+	0.0203821i
$276$		0			0
$277$	−7.64138	−	4.41176i	−0.459126	−	0.265077i	0.252551	−	0.967584i	$-0.418731\pi$
$277$	−7.64138	−	4.41176i	−0.459126	−	0.265077i	−0.711677	+	0.702507i	$0.752064\pi$
$278$	−11.7959	+	11.7959i	−0.707470	+	0.707470i
$279$		0			0
$280$	2.12655	+	0.569808i	0.127086	+	0.0340525i
$281$	4.63444	−	17.2960i	0.276467	−	1.03179i	−0.678384	−	0.734707i	$-0.737320\pi$
$281$	4.63444	−	17.2960i	0.276467	−	1.03179i	0.954852	−	0.297083i	$-0.0960138\pi$
$282$		0			0
$283$	−6.33288	+	3.65629i	−0.376451	+	0.217344i	−0.676273	−	0.736651i	$-0.736406\pi$
$283$	−6.33288	+	3.65629i	−0.376451	+	0.217344i	0.299822	+	0.953995i	$0.403073\pi$
$284$	2.90902	−	10.8566i	0.172619	−	0.644222i
$285$		0			0
$286$	−0.0909031	+	1.78694i	−0.00537521	+	0.105664i
$287$			11.5218i			0.680111i
$288$		0			0
$289$	6.05752	−	10.4919i	0.356325	−	0.617173i
$290$	3.62479	−	6.27833i	0.212855	−	0.368676i
$291$		0			0
$292$	−4.45270	−	4.45270i	−0.260575	−	0.260575i
$293$	−10.0863	−	10.0863i	−0.589246	−	0.589246i	0.348181	−	0.937427i	$-0.386799\pi$
$293$	−10.0863	−	10.0863i	−0.589246	−	0.589246i	−0.937427	+	0.348181i	$0.886799\pi$
$294$		0			0
$295$	2.15556	−	3.73354i	0.125502	−	0.217375i
$296$	5.70573	−	9.88261i	0.331639	−	0.574415i
$297$		0			0
$298$		−	10.5217i		−	0.609505i
$299$	5.69969	−	2.91515i	0.329622	−	0.168588i
$300$		0			0
$301$	−0.600622	+	2.24155i	−0.0346193	+	0.129201i
$302$	14.8845	−	8.59357i	0.856506	−	0.494504i
$303$		0			0
$304$	−0.805124	+	3.00476i	−0.0461770	+	0.172335i
$305$	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	$0.0334273\pi$
$308$	0.614801	+	0.354956i	0.0350316	+	0.0202255i
$309$		0			0
$310$	0.467719	+	0.125325i	0.0265646	+	0.00711798i
$311$	12.3786	−	21.4403i	0.701923	−	1.21577i	−0.265867	−	0.964010i	$-0.585658\pi$
$311$	12.3786	−	21.4403i	0.701923	−	1.21577i	0.967790	−	0.251757i	$-0.0810084\pi$
$312$		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
$317$	−28.9067	−	7.74554i	−1.62356	−	0.435033i	−0.671518	−	0.740988i	$-0.734357\pi$
$317$	−28.9067	−	7.74554i	−1.62356	−	0.435033i	−0.952046	+	0.305956i	$0.901024\pi$
$318$		0			0
$319$	1.65299	−	1.65299i	0.0925496	−	0.0925496i
$320$	1.48652	−	0.398313i	0.0830993	−	0.0222664i
$321$		0			0
$322$		−	2.54005i		−	0.141552i
$323$	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
$328$	4.02705	+	6.97505i	0.222357	+	0.385133i
$329$	17.5334			0.966649
$330$		0			0
$331$	−6.40799	+	1.71702i	−0.352215	+	0.0943758i	−0.430589	−	0.902548i	$-0.641694\pi$
$331$	−6.40799	+	1.71702i	−0.352215	+	0.0943758i	0.0783735	+	0.996924i	$0.475027\pi$
$332$	−2.17883	+	8.13149i	−0.119579	+	0.446273i
$333$		0			0
$334$	5.42465	+	9.39577i	0.296824	+	0.514113i
$335$	12.1921			0.666124
$336$		0			0
$337$	−20.1675	−	11.6437i	−1.09859	−	0.634274i	−0.162743	−	0.986669i	$-0.552034\pi$
$337$	−20.1675	−	11.6437i	−1.09859	−	0.634274i	−0.935851	+	0.352395i	$0.885367\pi$
$338$	10.0778	−	8.21210i	0.548158	−	0.446679i
$339$		0			0
$340$	−2.40516	−	2.40516i	−0.130438	−	0.130438i
$341$	0.135221	+	0.0780698i	0.00732262	+	0.00422772i
$342$		0			0
$343$	12.0916	+	12.0916i	0.652886	+	0.652886i
$344$	0.419853	+	1.56691i	0.0226370	+	0.0844823i
$345$		0			0
$346$	−0.415621	−	1.55112i	−0.0223439	−	0.0833887i
$347$			20.1798i			1.08331i	0.840601	+	0.541655i	$0.182202\pi$
$347$			20.1798i			1.08331i	−0.840601	+	0.541655i	$0.817798\pi$
$348$		0			0
$349$	17.7481	−	17.7481i	0.950033	−	0.950033i	−0.0487771	−	0.998810i	$-0.515532\pi$
$349$	17.7481	−	17.7481i	0.950033	−	0.950033i	0.998810	+	0.0487771i	$0.0155324\pi$
$350$	−3.76463			−0.201228
$351$		0			0
$352$	0.496250			0.0264502
$353$	−18.4478	+	18.4478i	−0.981880	+	0.981880i	−0.999839	−	0.0179591i	$-0.994283\pi$
$353$	−18.4478	+	18.4478i	−0.981880	+	0.981880i	0.0179591	+	0.999839i	$0.494283\pi$
$354$		0			0
$355$		−	17.2973i		−	0.918047i
$356$	−0.914251	−	3.41203i	−0.0484552	−	0.180837i
$357$		0			0
$358$	2.60322	+	9.71534i	0.137584	+	0.513471i
$359$	23.1726	+	23.1726i	1.22300	+	1.22300i	0.966559	+	0.256444i	$0.0825509\pi$
$359$	23.1726	+	23.1726i	1.22300	+	1.22300i	0.256444	+	0.966559i	$0.417449\pi$
$360$		0			0
$361$	8.07411	+	4.66159i	0.424953	+	0.245347i
$362$	−8.44878	−	8.44878i	−0.444058	−	0.444058i
$363$		0			0
$364$	−1.08013	−	5.04357i	−0.0566141	−	0.264355i
$365$	−8.39262	−	4.84548i	−0.439290	−	0.253624i
$366$		0			0
$367$	0.585320			0.0305535			0.0152767	−	0.999883i	$-0.495137\pi$
$367$	0.585320			0.0305535			0.0152767	+	0.999883i	$0.495137\pi$
$368$	−0.887787	−	1.53769i	−0.0462791	−	0.0801577i
$369$		0			0
$370$	4.54533	−	16.9634i	0.236301	−	0.881886i
$371$	2.80119	−	0.750577i	0.145431	−	0.0389680i
$372$		0			0
$373$	27.3780			1.41758			0.708790	−	0.705420i	$-0.249242\pi$
$373$	27.3780			1.41758			0.708790	+	0.705420i	$0.249242\pi$
$374$	−0.548404	−	0.949863i	−0.0283573	−	0.0491162i
$375$		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	$0.390237\pi$
$380$			4.78735i			0.245586i
$381$		0			0
$382$	−21.1013	+	5.65407i	−1.07963	+	0.289287i
$383$	9.97127	−	9.97127i	0.509508	−	0.509508i	−0.404867	−	0.914375i	$-0.632682\pi$
$383$	9.97127	−	9.97127i	0.509508	−	0.509508i	0.914375	+	0.404867i	$0.132682\pi$
$384$		0			0
$385$	1.05530	+	0.282767i	0.0537831	+	0.0144111i
$386$	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	$0.00211132\pi$
$389$	9.97462	+	17.2765i	0.505733	+	0.875956i	−0.494245	+	0.869323i	$0.664555\pi$
$390$		0			0
$391$	−1.96218	+	3.39859i	−0.0992317	+	0.171874i
$392$	4.78473	+	1.28206i	0.241665	+	0.0647540i
$393$		0			0
$394$	2.13525	+	1.23279i	0.107572	+	0.0621070i
$395$	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	$0.429351\pi$
$398$	5.42331	−	20.2401i	0.271846	−	1.01454i
$399$		0			0
$400$	−2.27902	+	1.31580i	−0.113951	+	0.0657898i
$401$	−4.08357	+	15.2401i	−0.203924	+	0.761055i	0.785851	+	0.618416i	$0.212225\pi$
$401$	−4.08357	+	15.2401i	−0.203924	+	0.761055i	−0.989775	+	0.142639i	$0.954441\pi$
$402$		0			0
$403$	−0.237566	−	1.10929i	−0.0118340	−	0.0552579i
$404$			5.51878i			0.274569i
$405$		0			0
$406$	−3.36945	+	5.83606i	−0.167223	+	0.289639i
$407$	2.83147	−	4.90424i	0.140351	−	0.243094i
$408$		0			0
$409$	7.86755	+	7.86755i	0.389025	+	0.389025i	0.874340	−	0.485314i	$-0.161295\pi$
$409$	7.86755	+	7.86755i	0.389025	+	0.389025i	−0.485314	+	0.874340i	$0.661295\pi$
$410$	8.76456	+	8.76456i	0.432851	+	0.432851i
$411$		0			0
$412$	7.53787	−	13.0560i	0.371364	−	0.643222i
$413$	−2.00371	+	3.47053i	−0.0985963	+	0.170774i
$414$		0			0
$415$			12.9555i			0.635961i
$416$	−2.41669	−	2.67575i	−0.118488	−	0.131189i
$417$		0			0
$418$	−0.399542	+	1.49111i	−0.0195423	+	0.0729327i
$419$	−0.396684	+	0.229025i	−0.0193793	+	0.0111886i	−0.509658	−	0.860377i	$-0.670228\pi$
$419$	−0.396684	+	0.229025i	−0.0193793	+	0.0111886i	0.490279	+	0.871566i	$0.336895\pi$
$420$		0			0
$421$	−1.17205	+	4.37413i	−0.0571220	+	0.213182i	−0.988588	−	0.150647i	$-0.951864\pi$
$421$	−1.17205	+	4.37413i	−0.0571220	+	0.213182i	0.931466	+	0.363829i	$0.118531\pi$
$422$	−13.6464	−	3.65655i	−0.664297	−	0.177998i
$423$		0			0
$424$	1.43344	−	1.43344i	0.0696140	−	0.0696140i
$425$	5.03708	+	2.90816i	0.244334	+	0.141067i
$426$		0			0
$427$	−9.38686	−	2.51520i	−0.454262	−	0.121719i
$428$	−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	$0.0337648\pi$
$431$	3.86478	+	14.4235i	0.186160	+	0.694758i	−0.808220	+	0.588881i	$0.799569\pi$
$432$		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	$0.367989\pi$
$434$	−0.434771	−	0.116497i	−0.0208697	−	0.00559201i
$435$		0			0
$436$	−6.92733	+	6.92733i	−0.331759	+	0.331759i
$437$	5.33518	−	1.42956i	0.255216	−	0.0683850i
$438$		0			0
$439$		−	13.3562i		−	0.637455i	−0.947846	−	0.318728i	$-0.896744\pi$
$439$		−	13.3562i		−	0.637455i	0.947846	−	0.318728i	$-0.103256\pi$
$440$	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
$445$	−2.71811	−	4.70791i	−0.128851	−	0.223176i
$446$	9.16578			0.434012
$447$		0			0
$448$	−1.38181	+	0.370254i	−0.0652843	+	0.0174929i
$449$	10.3894	−	38.7738i	0.490306	−	1.82985i	−0.0645682	−	0.997913i	$-0.520567\pi$
$449$	10.3894	−	38.7738i	0.490306	−	1.82985i	0.554874	−	0.831934i	$-0.312766\pi$
$450$		0			0
$451$	1.99842	+	3.46137i	0.0941020	+	0.162989i
$452$	14.3065			0.672923
$453$		0			0
$454$	−22.8707	−	13.2044i	−1.07337	−	0.619713i
$455$	−3.61456	−	7.06716i	−0.169453	−	0.331314i
$456$		0			0
$457$	−11.6746	−	11.6746i	−0.546115	−	0.546115i	0.379199	−	0.925315i	$-0.376199\pi$
$457$	−11.6746	−	11.6746i	−0.546115	−	0.546115i	−0.925315	+	0.379199i	$0.876199\pi$
$458$	12.3141	+	7.10955i	0.575400	+	0.332207i
$459$		0			0
$460$	−1.93220	−	1.93220i	−0.0900893	−	0.0900893i
$461$	−3.57300	−	13.3346i	−0.166411	−	0.621055i	−0.997856	−	0.0654474i	$-0.979153\pi$
$461$	−3.57300	−	13.3346i	−0.166411	−	0.621055i	0.831445	−	0.555607i	$-0.187514\pi$
$462$		0			0
$463$	−9.96318	−	37.1831i	−0.463028	−	1.72805i	−0.663345	−	0.748314i	$-0.730864\pi$
$463$	−9.96318	−	37.1831i	−0.463028	−	1.72805i	0.200316	−	0.979731i	$-0.435803\pi$
$464$			4.71069i			0.218688i
$465$		0			0
$466$	15.1667	−	15.1667i	0.702586	−	0.702586i
$467$	8.54433			0.395385			0.197692	−	0.980264i	$-0.436655\pi$
$467$	8.54433			0.395385			0.197692	+	0.980264i	$0.436655\pi$
$468$		0			0
$469$	−11.3332			−0.523319
$470$	13.3376	−	13.3376i	0.615216	−	0.615216i
$471$		0			0
$472$			2.80131i			0.128941i
$473$	0.208352	+	0.777580i	0.00958003	+	0.0357532i
$474$		0			0
$475$	−2.11876	−	7.90731i	−0.0972152	−	0.362812i
$476$	2.23573	+	2.23573i	0.102474	+	0.102474i
$477$		0			0
$478$	6.80960	+	3.93153i	0.311464	+	0.179824i
$479$	6.26732	+	6.26732i	0.286361	+	0.286361i	0.835640	−	0.549278i	$-0.185097\pi$
$479$	6.26732	+	6.26732i	0.286361	+	0.286361i	−0.549278	+	0.835640i	$0.685097\pi$
$480$		0			0
$481$	−40.2323	+	8.61612i	−1.83444	+	0.392861i
$482$	−16.0291	−	9.25438i	−0.730104	−	0.421526i
$483$		0			0
$484$	−10.7537			−0.488806
$485$	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	$0.162520\pi$
$488$	−6.56170	+	1.75820i	−0.297034	+	0.0795901i
$489$		0			0
$490$	7.62328			0.344385
$491$	8.67309	+	15.0222i	0.391411	+	0.677944i	0.992636	−	0.121136i	$-0.0386537\pi$
$491$	8.67309	+	15.0222i	0.391411	+	0.677944i	−0.601225	+	0.799080i	$0.705320\pi$
$492$		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
$497$			16.0788i			0.721235i
$498$		0			0
$499$	11.4069	−	3.05648i	0.510644	−	0.136827i	0.00570844	−	0.999984i	$-0.498183\pi$
$499$	11.4069	−	3.05648i	0.510644	−	0.136827i	0.504936	+	0.863157i	$0.331516\pi$
$500$	−8.30479	+	8.30479i	−0.371401	+	0.371401i
$501$		0			0
$502$	−21.3365	−	5.71709i	−0.952294	−	0.255166i
$503$	−20.1247	+	11.6190i	−0.897316	+	0.518066i	−0.876329	−	0.481714i	$-0.840014\pi$
$503$	−20.1247	+	11.6190i	−0.897316	+	0.518066i	−0.0209877	+	0.999780i	$0.506681\pi$
$504$		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
$509$	3.45775	+	0.926500i	0.153262	+	0.0410664i	0.334634	−	0.942348i	$-0.391387\pi$
$509$	3.45775	+	0.926500i	0.153262	+	0.0410664i	−0.181372	+	0.983415i	$0.558054\pi$
$510$		0			0
$511$	7.80141	+	4.50415i	0.345114	+	0.199252i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$		0			0
$514$	−29.1787	−	7.81841i	−1.28702	−	0.344855i
$515$	6.00487	−	22.4105i	0.264606	−	0.987523i
$516$		0			0
$517$	5.26737	−	3.04112i	0.231659	−	0.133748i
$518$	−4.22514	+	15.7684i	−0.185642	+	0.692826i
$519$		0			0
$520$	−4.65825	−	3.01496i	−0.204278	−	0.132215i
$521$			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	−0.849267	−	0.527964i	$-0.822956\pi$
$523$	0.745466	−	1.29119i	0.0325970	−	0.0564596i	0.881864	+	0.471504i	$0.156289\pi$
$524$	−6.53662	+	11.3218i	−0.285553	+	0.494593i
$525$		0			0
$526$	3.89760	+	3.89760i	0.169943	+	0.169943i
$527$	0.491731	+	0.491731i	0.0214202	+	0.0214202i
$528$		0			0
$529$	9.92367	−	17.1883i	0.431464	−	0.747317i
$530$	1.55989	−	2.70180i	0.0677572	−	0.117359i
$531$		0			0
$532$		−	4.45011i		−	0.192937i
$533$	8.93134	−	27.6319i	0.386859	−	1.19687i
$534$		0			0
$535$	−4.99704	+	18.6492i	−0.216041	+	0.806276i
$536$	−6.86088	+	3.96113i	−0.296345	+	0.171095i
$537$		0			0
$538$	−5.02619	+	18.7580i	−0.216694	+	0.808714i
$539$	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	$0.266484\pi$
$542$	−19.4009	−	11.2011i	−0.833341	−	0.481130i
$543$		0			0
$544$	2.13488	+	0.572040i	0.0915323	+	0.0245260i
$545$	−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
$551$	−14.1545	−	3.79269i	−0.603003	−	0.161574i
$552$		0			0
$553$	−9.65643	+	9.65643i	−0.410633	+	0.410633i
$554$	8.52286	−	2.28369i	0.362102	−	0.0970248i
$555$		0			0
$556$		−	16.6819i		−	0.707470i
$557$	−11.2158	+	3.00527i	−0.475229	+	0.127337i	−0.488480	−	0.872575i	$-0.662449\pi$
$557$	−11.2158	+	3.00527i	−0.475229	+	0.127337i	0.0132513	+	0.999912i	$0.495782\pi$
$558$		0			0
$559$	3.17801	−	4.91016i	0.134415	−	0.207678i
$560$	−1.90661	+	1.10078i	−0.0805692	+	0.0465166i
$561$		0			0
$562$	8.95305	+	15.5071i	0.377661	+	0.654129i
$563$	−40.8646			−1.72224			−0.861119	−	0.508403i	$-0.830236\pi$
$563$	−40.8646			−1.72224			−0.861119	+	0.508403i	$0.830236\pi$
$564$		0			0
$565$	21.2670	−	5.69848i	0.894710	−	0.239737i
$566$	1.89264	−	7.06341i	0.0795534	−	0.296897i
$567$		0			0
$568$	5.61980	+	9.73378i	0.235802	+	0.408420i
$569$	6.41366			0.268875			0.134437	−	0.990922i	$-0.457077\pi$
$569$	6.41366			0.268875			0.134437	+	0.990922i	$0.457077\pi$
$570$		0			0
$571$	−11.8701	−	6.85319i	−0.496747	−	0.286797i	0.230622	−	0.973043i	$-0.425924\pi$
$571$	−11.8701	−	6.85319i	−0.496747	−	0.286797i	−0.727369	+	0.686246i	$0.759257\pi$
$572$	−1.19928	−	1.32784i	−0.0501445	−	0.0555197i
$573$		0			0
$574$	−8.14715	−	8.14715i	−0.340056	−	0.340056i
$575$	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	$0.853604\pi$
$578$	3.13561	+	11.7022i	0.130424	+	0.486749i
$579$		0			0
$580$	1.87633	+	7.00256i	0.0779104	+	0.290766i
$581$		−	12.0429i		−	0.499623i
$582$		0			0
$583$	0.711344	−	0.711344i	0.0294609	−	0.0294609i
$584$	6.29707			0.260575
$585$		0			0
$586$	14.2641			0.589246
$587$	−1.80828	+	1.80828i	−0.0746357	+	0.0746357i	−0.743439	−	0.668804i	$-0.766807\pi$
$587$	−1.80828	+	1.80828i	−0.0746357	+	0.0746357i	0.668804	+	0.743439i	$0.266807\pi$
$588$		0			0
$589$		−	0.978767i		−	0.0403294i
$590$	1.11580	+	4.16422i	0.0459368	+	0.171438i
$591$		0			0
$592$	2.95350	+	11.0226i	0.121388	+	0.453027i
$593$	−15.9796	−	15.9796i	−0.656204	−	0.656204i	0.298276	−	0.954480i	$-0.403588\pi$
$593$	−15.9796	−	15.9796i	−0.656204	−	0.656204i	−0.954480	+	0.298276i	$0.903588\pi$
$594$		0			0
$595$	4.21399	+	2.43295i	0.172757	+	0.0997411i
$596$	7.43995	+	7.43995i	0.304752	+	0.304752i
$597$		0			0
$598$	−1.96897	+	6.09161i	−0.0805170	+	0.249105i
$599$	−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
$601$	−25.4119			−1.03657			−0.518287	−	0.855207i	$-0.673430\pi$
$601$	−25.4119			−1.03657			−0.518287	+	0.855207i	$0.673430\pi$
$602$	−1.16031	−	2.00972i	−0.0472908	−	0.0819101i
$603$		0			0
$604$	−4.44836	+	16.6015i	−0.181001	+	0.675505i
$605$	−15.9857	+	4.28335i	−0.649911	+	0.174143i
$606$		0			0
$607$	20.6007			0.836156			0.418078	−	0.908411i	$-0.362704\pi$
$607$	20.6007			0.836156			0.418078	+	0.908411i	$0.362704\pi$
$608$	−1.55538	−	2.69400i	−0.0630790	−	0.109256i
$609$		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	$0.458873\pi$
$614$			22.0451i			0.889669i
$615$		0			0
$616$	−0.685722	+	0.183739i	−0.0276285	+	0.00740304i
$617$	−11.2968	+	11.2968i	−0.454794	+	0.454794i	−0.896942	−	0.442148i	$-0.854216\pi$
$617$	−11.2968	+	11.2968i	−0.454794	+	0.454794i	0.442148	+	0.896942i	$0.354216\pi$
$618$		0			0
$619$	−21.8012	−	5.84160i	−0.876263	−	0.234794i	−0.207469	−	0.978242i	$-0.566523\pi$
$619$	−21.8012	−	5.84160i	−0.876263	−	0.234794i	−0.668794	+	0.743448i	$0.733189\pi$
$620$	−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
$626$	−31.0458	−	8.31871i	−1.24084	−	0.332482i
$627$		0			0
$628$	18.9690	+	10.9518i	0.756946	+	0.437023i
$629$	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	$0.696375\pi$
$632$	−2.47072	+	9.22086i	−0.0982801	+	0.366786i
$633$		0			0
$634$	25.9171	−	14.9632i	1.02930	−	0.594266i
$635$	1.15325	−	4.30397i	0.0457652	−	0.170798i
$636$		0			0
$637$	−8.13273	−	15.9011i	−0.322230	−	0.630023i
$638$			2.33768i			0.0925496i
$639$		0			0
$640$	−0.769482	+	1.33278i	−0.0304164	+	0.0526828i
$641$	18.2842	−	31.6691i	0.722182	−	1.25086i	−0.237941	−	0.971280i	$-0.576473\pi$
$641$	18.2842	−	31.6691i	0.722182	−	1.25086i	0.960123	−	0.279577i	$-0.0901941\pi$
$642$		0			0
$643$	24.7378	+	24.7378i	0.975563	+	0.975563i	0.999708	−	0.0241455i	$-0.00768651\pi$
$643$	24.7378	+	24.7378i	0.975563	+	0.975563i	−0.0241455	+	0.999708i	$0.507687\pi$
$644$	1.79609	+	1.79609i	0.0707758	+	0.0707758i
$645$		0			0
$646$	−3.43769	+	5.95425i	−0.135254	+	0.234267i
$647$	−9.58684	+	16.6049i	−0.376897	+	0.652806i	−0.990609	−	0.136725i	$-0.956342\pi$
$647$	−9.58684	+	16.6049i	−0.376897	+	0.652806i	0.613712	+	0.789530i	$0.289676\pi$
$648$		0			0
$649$			1.39015i			0.0545682i
$650$	9.02843	+	2.91822i	0.354124	+	0.114462i
$651$		0			0
$652$	1.37636	−	5.13664i	0.0539023	−	0.201166i
$653$	−5.74222	+	3.31527i	−0.224710	+	0.129737i	−0.608129	−	0.793838i	$-0.708080\pi$
$653$	−5.74222	+	3.31527i	−0.224710	+	0.129737i	0.383419	+	0.923574i	$0.374747\pi$
$654$		0			0
$655$	−5.20724	+	19.4337i	−0.203464	+	0.759337i
$656$	−7.77966	−	2.08455i	−0.303745	−	0.0813882i
$657$		0			0
$658$	−12.3980	+	12.3980i	−0.483325	+	0.483325i
$659$	18.7561	+	10.8289i	0.730636	+	0.421833i	0.818655	−	0.574286i	$-0.194720\pi$
$659$	18.7561	+	10.8289i	0.730636	+	0.421833i	−0.0880190	+	0.996119i	$0.528054\pi$
$660$		0			0
$661$	−9.98561	−	2.67564i	−0.388395	−	0.104070i	0.0593368	−	0.998238i	$-0.481101\pi$
$661$	−9.98561	−	2.67564i	−0.388395	−	0.104070i	−0.447732	+	0.894168i	$0.647768\pi$
$662$	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
$668$	−10.4796	−	2.80800i	−0.405469	−	0.108645i
$669$		0			0
$670$	−8.62110	+	8.62110i	−0.333062	+	0.333062i
$671$	−3.25624	+	0.872508i	−0.125706	+	0.0336828i
$672$		0			0
$673$			26.3007i			1.01382i	0.862000	+	0.506908i	$0.169212\pi$
$673$			26.3007i			1.01382i	−0.862000	+	0.506908i	$0.830788\pi$
$674$	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
$679$	−5.27020	−	9.12826i	−0.202252	−	0.350310i
$680$	3.40141			0.130438
$681$		0			0
$682$	−0.150819	+	0.0404119i	−0.00577517	+	0.00154745i
$683$	0.894421	−	3.33802i	0.0342241	−	0.127726i	−0.946700	−	0.322116i	$-0.895606\pi$
$683$	0.894421	−	3.33802i	0.0342241	−	0.127726i	0.980924	+	0.194390i	$0.0622727\pi$
$684$		0			0
$685$	5.01088	+	8.67909i	0.191456	+	0.331611i
$686$	−17.1001			−0.652886
$687$		0			0
$688$	−1.40486	−	0.811094i	−0.0535596	−	0.0309227i
$689$	−7.29970	−	0.371341i	−0.278097	−	0.0141470i
$690$		0			0
$691$	23.6513	+	23.6513i	0.899738	+	0.899738i	0.995413	−	0.0956749i	$-0.0305009\pi$
$691$	23.6513	+	23.6513i	0.899738	+	0.899738i	−0.0956749	+	0.995413i	$0.530501\pi$
$692$	1.39070	+	0.802919i	0.0528663	+	0.0305224i
$693$		0			0
$694$	−14.2693	−	14.2693i	−0.541655	−	0.541655i
$695$	−6.64462	−	24.7981i	−0.252045	−	0.940644i
$696$		0			0
$697$	4.60727	+	17.1946i	0.174513	+	0.651290i
$698$			25.0996i			0.950033i
$699$		0			0
$700$	2.66200	−	2.66200i	0.100614	−	0.100614i
$701$	14.8908			0.562418			0.281209	−	0.959647i	$-0.409265\pi$
$701$	14.8908			0.562418			0.281209	+	0.959647i	$0.409265\pi$
$702$		0			0
$703$	−35.4983			−1.33884
$704$	−0.350901	+	0.350901i	−0.0132251	+	0.0132251i
$705$		0			0
$706$		−	26.0892i		−	0.981880i
$707$	−2.04335	−	7.62589i	−0.0768481	−	0.286801i
$708$		0			0
$709$	−6.37553	−	23.7938i	−0.239438	−	0.893595i	−0.976098	−	0.217332i	$-0.930265\pi$
$709$	−6.37553	−	23.7938i	−0.239438	−	0.893595i	0.736660	−	0.676264i	$-0.236402\pi$
$710$	12.2311	+	12.2311i	0.459024	+	0.459024i
$711$		0			0
$712$	3.05914	+	1.76620i	0.114646	+	0.0661910i
$713$	0.395036	+	0.395036i	0.0147942	+	0.0147942i
$714$		0			0
$715$	−2.31166	−	1.49617i	−0.0864510	−	0.0559537i
$716$	−8.71053	−	5.02903i	−0.325528	−	0.187944i
$717$		0			0
$718$	−32.7710			−1.22300
$719$	−17.8371	−	30.8948i	−0.665213	−	1.15218i	−0.979227	−	0.202765i	$-0.935007\pi$
$719$	−17.8371	−	30.8948i	−0.665213	−	1.15218i	0.314014	−	0.949418i	$-0.398326\pi$
$720$		0			0
$721$	−5.58186	+	20.8318i	−0.207879	+	0.775816i
$722$	−9.00550	+	2.41302i	−0.335150	+	0.0898031i
$723$		0			0
$724$	11.9484			0.444058
$725$	−6.19831	−	10.7358i	−0.230199	−	0.398717i
$726$		0			0
$727$	8.14708	−	4.70372i	0.302159	−	0.174451i	−0.341254	−	0.939971i	$-0.610851\pi$
$727$	8.14708	−	4.70372i	0.302159	−	0.174451i	0.643412	+	0.765520i	$0.277518\pi$
$728$	4.33011	+	2.80258i	0.160484	+	0.103870i
$729$		0			0
$730$	9.36075	−	2.50821i	0.346457	−	0.0928328i
$731$			3.58535i			0.132609i
$732$		0			0
$733$	31.2706	−	8.37893i	1.15501	−	0.309483i	0.370037	−	0.929017i	$-0.379345\pi$
$733$	31.2706	−	8.37893i	1.15501	−	0.309483i	0.784970	+	0.619534i	$0.212678\pi$
$734$	−0.413884	+	0.413884i	−0.0152767	+	0.0152767i
$735$		0			0
$736$	1.71507	+	0.459552i	0.0632184	+	0.0169393i
$737$	−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
$743$	23.8066	+	6.37897i	0.873381	+	0.234022i	0.667549	−	0.744566i	$-0.267343\pi$
$743$	23.8066	+	6.37897i	0.873381	+	0.234022i	0.205832	+	0.978587i	$0.434010\pi$
$744$		0			0
$745$	14.0231	+	8.09624i	0.513767	+	0.296623i
$746$	−19.3592	+	19.3592i	−0.708790	+	0.708790i
$747$		0			0
$748$	1.05943	+	0.283875i	0.0387368	+	0.0103795i
$749$	4.64503	−	17.3355i	0.169726	−	0.633425i
$750$		0			0
$751$	−19.1669	+	11.0660i	−0.699411	+	0.403805i	−0.807128	−	0.590376i	$-0.798979\pi$
$751$	−19.1669	+	11.0660i	−0.699411	+	0.403805i	0.107717	+	0.994182i	$0.465646\pi$
$752$	−3.17219	+	11.8388i	−0.115678	+	0.431716i
$753$		0			0
$754$	12.6046	−	11.3843i	0.459033	−	0.414591i
$755$			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	$-0.200258\pi$
$758$	−1.61458	+	2.79653i	−0.0586440	+	0.101574i
$759$		0			0
$760$	−3.38516	−	3.38516i	−0.122793	−	0.122793i
$761$	−5.92790	−	5.92790i	−0.214886	−	0.214886i	0.591453	−	0.806339i	$-0.298554\pi$
$761$	−5.92790	−	5.92790i	−0.214886	−	0.214886i	−0.806339	+	0.591453i	$0.798554\pi$
$762$		0			0
$763$	7.00737	−	12.1371i	0.253684	−	0.439393i
$764$	10.9228	−	18.9189i	0.395174	−	0.684461i
$765$		0			0
$766$			14.1015i			0.509508i
$767$	7.49560	−	6.76990i	0.270650	−	0.244447i
$768$		0			0
$769$	−4.01166	+	14.9717i	−0.144664	+	0.539894i	0.855106	+	0.518453i	$0.173492\pi$
$769$	−4.01166	+	14.9717i	−0.144664	+	0.539894i	−0.999770	+	0.0214405i	$0.993175\pi$
$770$	−0.946157	+	0.546264i	−0.0340971	+	0.0196860i
$771$		0			0
$772$	−3.38840	+	12.6457i	−0.121951	+	0.455128i
$773$	−6.28210	−	1.68328i	−0.225951	−	0.0605435i	0.144067	−	0.989568i	$-0.453982\pi$
$773$	−6.28210	−	1.68328i	−0.225951	−	0.0605435i	−0.370018	+	0.929024i	$0.620649\pi$
$774$		0			0
$775$	0.585485	−	0.585485i	0.0210313	−	0.0210313i
$776$	−6.38093	−	3.68403i	−0.229062	−	0.132249i
$777$		0			0
$778$	−19.2695	−	5.16324i	−0.690844	−	0.185111i
$779$	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
$785$	32.5601	+	8.72447i	1.16212	+	0.311390i
$786$		0			0
$787$	−37.8815	+	37.8815i	−1.35033	+	1.35033i	−0.465040	+	0.885290i	$0.653960\pi$
$787$	−37.8815	+	37.8815i	−1.35033	+	1.35033i	−0.885290	+	0.465040i	$0.846040\pi$
$788$	−2.38157	+	0.638138i	−0.0848398	+	0.0227327i
$789$		0			0
$790$			14.6912i			0.522688i
$791$	−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
$796$	10.4770	+	18.1467i	0.371348	+	0.643194i
$797$	46.6716			1.65319			0.826597	−	0.562794i	$-0.190274\pi$
$797$	46.6716			1.65319			0.826597	+	0.562794i	$0.190274\pi$
$798$		0			0
$799$	26.1660	−	7.01115i	0.925685	−	0.248037i
$800$	0.681106	−	2.54192i	0.0240807	−	0.0898705i
$801$		0			0
$802$	−7.88886	−	13.6639i	−0.278565	−	0.482489i
$803$	3.12492			0.110276
$804$		0			0
$805$	3.38533	+	1.95452i	0.119317	+	0.0688879i
$806$	0.952374	+	0.616405i	0.0335459	+	0.0217119i
$807$		0			0
$808$	−3.90236	−	3.90236i	−0.137285	−	0.137285i
$809$	3.13155	+	1.80800i	0.110099	+	0.0635659i	0.554039	−	0.832491i	$-0.313086\pi$
$809$	3.13155	+	1.80800i	0.110099	+	0.0635659i	−0.443939	+	0.896057i	$0.646419\pi$
$810$		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	$0.746600\pi$
$812$	−1.74416	−	6.50928i	−0.0612078	−	0.228431i
$813$		0			0
$814$	1.46567	+	5.46997i	0.0513719	+	0.191722i
$815$		−	8.18396i		−	0.286672i
$816$		0			0
$817$	3.56823	−	3.56823i	0.124837	−	0.124837i
$818$	−11.1264			−0.389025
$819$		0			0
$820$	−12.3950			−0.432851
$821$	−36.5520	+	36.5520i	−1.27567	+	1.27567i	−0.332608	+	0.943065i	$0.607929\pi$
$821$	−36.5520	+	36.5520i	−1.27567	+	1.27567i	−0.943065	+	0.332608i	$0.892071\pi$
$822$		0			0
$823$		−	18.6304i		−	0.649413i	−0.945815	−	0.324707i	$-0.894734\pi$
$823$		−	18.6304i		−	0.649413i	0.945815	−	0.324707i	$-0.105266\pi$
$824$	3.90189	+	14.5621i	0.135929	+	0.507293i
$825$		0			0
$826$	−1.03720	−	3.87088i	−0.0360888	−	0.134685i
$827$	−23.9908	−	23.9908i	−0.834244	−	0.834244i	0.153851	−	0.988094i	$-0.450833\pi$
$827$	−23.9908	−	23.9908i	−0.834244	−	0.834244i	−0.988094	+	0.153851i	$0.950833\pi$
$828$		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	$0.738012\pi$
$830$	−9.16093	−	9.16093i	−0.317981	−	0.317981i
$831$		0			0
$832$	3.60090	+	0.183180i	0.124839	+	0.00635063i
$833$	9.48144	+	5.47411i	0.328513	+	0.189667i
$834$		0			0
$835$	−16.6967			−0.577812
$836$	−0.771857	−	1.33689i	−0.0266952	−	0.0462375i
$837$		0			0
$838$	0.118552	−	0.442443i	0.00409532	−	0.0152839i
$839$	20.3835	−	5.46173i	0.703715	−	0.188560i	0.110821	−	0.993840i	$-0.464652\pi$
$839$	20.3835	−	5.46173i	0.703715	−	0.188560i	0.592894	+	0.805280i	$0.297985\pi$
$840$		0			0
$841$	6.80936			0.234806
$842$	−2.26422	−	3.92174i	−0.0780301	−	0.135152i
$843$		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
$848$			2.02719i			0.0696140i
$849$		0			0
$850$	−5.61814	+	1.50537i	−0.192700	+	0.0516339i
$851$	14.3273	−	14.3273i	0.491134	−	0.491134i
$852$		0			0
$853$	9.10083	+	2.43856i	0.311606	+	0.0834947i	0.411233	−	0.911530i	$-0.365098\pi$
$853$	9.10083	+	2.43856i	0.311606	+	0.0834947i	−0.0996268	+	0.995025i	$0.531765\pi$
$854$	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	$-0.0847221\pi$
$857$	7.45337	+	12.9096i	0.254602	+	0.440984i	−0.710185	+	0.704015i	$0.751389\pi$
$858$		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	$-0.0406967\pi$
$860$	−2.41142	−	0.646139i	−0.0822288	−	0.0220331i
$861$		0			0
$862$	−12.9318	−	7.46617i	−0.440459	−	0.254299i
$863$	−0.118264	+	0.118264i	−0.00402577	+	0.00402577i	−0.709117	−	0.705091i	$-0.750906\pi$
$863$	−0.118264	+	0.118264i	−0.00402577	+	0.00402577i	0.705091	+	0.709117i	$0.250906\pi$
$864$		0			0
$865$	2.38712	+	0.639626i	0.0811644	+	0.0217479i
$866$	1.17039	−	4.36797i	0.0397716	−	0.148430i
$867$		0			0
$868$	0.389805	−	0.225054i	0.0132308	−	0.00763883i
$869$	−1.22610	+	4.57585i	−0.0415924	+	0.155225i
$870$		0			0
$871$	27.1796	+	8.78515i	0.920946	+	0.297673i
$872$		−	9.79673i		−	0.331759i
$873$		0			0
$874$	−2.76169	+	4.78339i	−0.0934156	+	0.161801i
$875$	8.40074	−	14.5505i	0.283997	−	0.491897i
$876$		0			0
$877$	30.2480	+	30.2480i	1.02140	+	1.02140i	0.999766	+	0.0216349i	$0.00688713\pi$
$877$	30.2480	+	30.2480i	1.02140	+	1.02140i	0.0216349	+	0.999766i	$0.493113\pi$
$878$	9.44424	+	9.44424i	0.318728	+	0.318728i
$879$		0			0
$880$	−0.381855	+	0.661392i	−0.0128723	+	0.0222955i
$881$	−13.3432	+	23.1111i	−0.449544	+	0.778633i	−0.998356	−	0.0573124i	$-0.981747\pi$
$881$	−13.3432	+	23.1111i	−0.449544	+	0.778633i	0.548812	+	0.835946i	$0.315080\pi$
$882$		0			0
$883$		−	11.8585i		−	0.399071i	−0.979891	−	0.199536i	$-0.936057\pi$
$883$		−	11.8585i		−	0.399071i	0.979891	−	0.199536i	$-0.0639433\pi$
$884$	−3.62871	−	7.09484i	−0.122047	−	0.238625i
$885$		0			0
$886$	7.98000	−	29.7818i	0.268093	−	1.00054i
$887$	−45.7185	+	26.3956i	−1.53508	+	0.886277i	−0.535960	+	0.844243i	$0.680050\pi$
$887$	−45.7185	+	26.3956i	−1.53508	+	0.886277i	−0.999116	+	0.0420331i	$0.986617\pi$
$888$		0			0
$889$	−1.07201	+	4.00079i	−0.0359540	+	0.134182i
$890$	5.25099	+	1.40700i	0.176014	+	0.0471627i
$891$		0			0
$892$	−6.48118	+	6.48118i	−0.217006	+	0.217006i
$893$	−33.0187	−	19.0634i	−1.10493	−	0.637931i
$894$		0			0
$895$	−14.9515	−	4.00626i	−0.499775	−	0.133914i
$896$	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
$902$	−3.86065	−	1.03446i	−0.128546	−	0.0344437i
$903$		0			0
$904$	−10.1162	+	10.1162i	−0.336461	+	0.336461i
$905$	17.7616	−	4.75920i	0.590414	−	0.158201i
$906$		0			0
$907$		−	18.4318i		−	0.612019i	−0.952028	−	0.306009i	$-0.901006\pi$
$907$		−	18.4318i		−	0.612019i	0.952028	−	0.306009i	$-0.0989939\pi$
$908$	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
$913$	−2.08880	−	3.61790i	−0.0691291	−	0.119735i
$914$	16.5104			0.546115
$915$		0			0
$916$	−13.7346	+	3.68017i	−0.453804	+	0.121596i
$917$	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	$-0.482445\pi$
$920$	2.73254			0.0900893
$921$		0			0
$922$	11.9555	+	6.90250i	0.393733	+	0.227322i
$923$	12.4638	−	38.5607i	0.410251	−	1.26924i
$924$		0			0
$925$	−21.2346	−	21.2346i	−0.698190	−	0.698190i
$926$	33.3375	+	19.2474i	1.09554	+	0.632508i
$927$		0			0
$928$	−3.33096	−	3.33096i	−0.109344	−	0.109344i
$929$	12.0290	+	44.8930i	0.394660	+	1.47289i	0.822358	+	0.568970i	$0.192658\pi$
$929$	12.0290	+	44.8930i	0.394660	+	1.47289i	−0.427698	+	0.903922i	$0.640675\pi$
$930$		0			0
$931$	−3.98820	−	14.8841i	−0.130708	−	0.487808i
$932$			21.4490i			0.702586i
$933$		0			0
$934$	−6.04176	+	6.04176i	−0.197692	+	0.197692i
$935$	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	$0.573355\pi$
$938$	8.01380	−	8.01380i	0.261660	−	0.261660i
$939$		0			0
$940$			18.8622i			0.615216i
$941$	−6.63944	−	24.7787i	−0.216440	−	0.807764i	−0.985655	−	0.168774i	$-0.946019\pi$
$941$	−6.63944	−	24.7787i	−0.216440	−	0.807764i	0.769215	−	0.638990i	$-0.220647\pi$
$942$		0			0
$943$	3.70128	+	13.8134i	0.120530	+	0.449825i
$944$	−1.98083	−	1.98083i	−0.0644704	−	0.0644704i
$945$		0			0
$946$	−0.697159	−	0.402505i	−0.0226666	−	0.0130866i
$947$	1.95156	+	1.95156i	0.0634171	+	0.0634171i	0.738104	−	0.674687i	$-0.235721\pi$
$947$	1.95156	+	1.95156i	0.0634171	+	0.0634171i	−0.674687	+	0.738104i	$0.735721\pi$
$948$		0			0
$949$	−15.2181	−	16.8494i	−0.493999	−	0.546953i
$950$	7.08950	+	4.09312i	0.230014	+	0.132798i
$951$		0			0
$952$	−3.16180			−0.102474
$953$	14.2452	+	24.6735i	0.461448	+	0.799252i	0.999033	−	0.0439575i	$-0.0139966\pi$
$953$	14.2452	+	24.6735i	0.461448	+	0.799252i	−0.537585	+	0.843210i	$0.680663\pi$
$954$		0			0
$955$	8.70140	−	32.4741i	0.281571	−	1.05084i
$956$	−7.59513	+	2.03511i	−0.245644	+	0.0658201i
$957$		0			0
$958$	−8.86333			−0.286361
$959$	−4.65789	−	8.06770i	−0.150411	−	0.260520i
$960$		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
$965$			20.1478i			0.648580i
$966$		0			0
$967$	10.1930	−	2.73120i	0.327783	−	0.0878293i	−0.0911745	−	0.995835i	$-0.529062\pi$
$967$	10.1930	−	2.73120i	0.327783	−	0.0878293i	0.418958	+	0.908006i	$0.362395\pi$
$968$	7.60404	−	7.60404i	0.244403	−	0.244403i
$969$		0			0
$970$	−10.9528	−	2.93480i	−0.351674	−	0.0942306i
$971$	−36.5800	+	21.1195i	−1.17391	+	0.677756i	−0.954597	−	0.297899i	$-0.903714\pi$
$971$	−36.5800	+	21.1195i	−1.17391	+	0.677756i	−0.219310	+	0.975655i	$0.570381\pi$
$972$		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
$977$	50.9962	+	13.6644i	1.63151	+	0.437162i	0.954355	−	0.298676i	$-0.0965450\pi$
$977$	50.9962	+	13.6644i	1.63151	+	0.437162i	0.677157	+	0.735838i	$0.263212\pi$
$978$		0			0
$979$	1.51810	+	0.876475i	0.0485186	+	0.0280122i
$980$	−5.39048	+	5.39048i	−0.172192	+	0.172192i
$981$		0			0
$982$	−16.7551	−	4.48952i	−0.534678	−	0.143266i
$983$	−8.76515	+	32.7120i	−0.279565	+	1.04335i	0.673155	+	0.739501i	$0.264939\pi$
$983$	−8.76515	+	32.7120i	−0.279565	+	1.04335i	−0.952720	+	0.303849i	$0.901728\pi$
$984$		0			0
$985$	−3.28608	+	1.89722i	−0.104703	+	0.0604504i
$986$	−2.69470	+	10.0568i	−0.0858169	+	0.320273i
$987$		0			0
$988$	−3.44958	+	10.6724i	−0.109746	+	0.339533i
$989$			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	$-0.0566205\pi$
$992$	0.157320	−	0.272485i	0.00499490	−	0.00865142i
$993$		0			0
$994$	−11.3695	−	11.3695i	−0.360617	−	0.360617i
$995$	22.8024	+	22.8024i	0.722886	+	0.722886i
$996$		0			0
$997$	−7.67103	+	13.2866i	−0.242944	+	0.420791i	−0.961552	−	0.274624i	$-0.911446\pi$
$997$	−7.67103	+	13.2866i	−0.242944	+	0.420791i	0.718608	+	0.695416i	$0.244780\pi$
$998$	−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.bb.a.449.2		56
3.2	odd	2		234.2.y.a.59.12	✓	56
9.2	odd	6		702.2.bc.a.683.2		56
9.7	even	3		234.2.z.a.137.8	yes	56
13.2	odd	12		702.2.bc.a.665.2		56
39.2	even	12		234.2.z.a.41.8	yes	56
117.2	even	12	inner	702.2.bb.a.197.2		56
117.106	odd	12		234.2.y.a.119.12	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
234.2.y.a.59.12	✓	56	3.2	odd	2
234.2.y.a.119.12	yes	56	117.106	odd	12
234.2.z.a.41.8	yes	56	39.2	even	12
234.2.z.a.137.8	yes	56	9.7	even	3
702.2.bb.a.197.2		56	117.2	even	12	inner
702.2.bb.a.449.2		56	1.1	even	1	trivial
702.2.bc.a.665.2		56	13.2	odd	12
702.2.bc.a.683.2		56	9.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(-0.398313 - 1.48652i) q^{5} +(0.370254 + 1.38181i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.33278 + 0.769482i) q^{10} +(0.350901 + 0.350901i) q^{11} +(0.183180 - 3.60090i) q^{13} +(-1.23890 - 0.715277i) q^{14} -1.00000 q^{16} +(1.10510 + 1.91408i) q^{17} +(0.805124 - 3.00476i) q^{19} +(-1.48652 + 0.398313i) q^{20} -0.496250 q^{22} +(0.887787 + 1.53769i) q^{23} +(2.27902 - 1.31580i) q^{25} +(2.41669 + 2.67575i) q^{26} +(1.38181 - 0.370254i) q^{28} -4.71069i q^{29} +(0.303918 - 0.0814346i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-2.13488 - 0.572040i) q^{34} +(1.90661 - 1.10078i) q^{35} +(-2.95350 - 11.0226i) q^{37} +(1.55538 + 2.69400i) q^{38} +(0.769482 - 1.33278i) q^{40} +(7.77966 + 2.08455i) q^{41} +(1.40486 + 0.811094i) q^{43} +(0.350901 - 0.350901i) q^{44} +(-1.71507 - 0.459552i) q^{46} +(3.17219 - 11.8388i) q^{47} +(4.28987 - 2.47676i) q^{49} +(-0.681106 + 2.54192i) q^{50} +(-3.60090 - 0.183180i) q^{52} -2.02719i q^{53} +(0.381855 - 0.661392i) q^{55} +(-0.715277 + 1.23890i) q^{56} +(3.33096 + 3.33096i) q^{58} +(1.98083 + 1.98083i) q^{59} +(-3.39659 + 5.88306i) q^{61} +(-0.157320 + 0.272485i) q^{62} +1.00000i q^{64} +(-5.42578 + 1.16198i) q^{65} +(-2.05043 + 7.65232i) q^{67} +(1.91408 - 1.10510i) q^{68} +(-0.569808 + 2.12655i) q^{70} +(10.8566 + 2.90902i) q^{71} +(4.45270 - 4.45270i) q^{73} +(9.88261 + 5.70573i) q^{74} +(-3.00476 - 0.805124i) q^{76} +(-0.354956 + 0.614801i) q^{77} +(4.77307 + 8.26720i) q^{79} +(0.398313 + 1.48652i) q^{80} +(-6.97505 + 4.02705i) q^{82} +(-8.13149 - 2.17883i) q^{83} +(2.40516 - 2.40516i) q^{85} +(-1.56691 + 0.419853i) q^{86} +0.496250i q^{88} +(3.41203 - 0.914251i) q^{89} +(5.04357 - 1.08013i) q^{91} +(1.53769 - 0.887787i) q^{92} +(6.12820 + 10.6144i) q^{94} -4.78735 q^{95} +(-7.11700 + 1.90700i) q^{97} +(-1.28206 + 4.78473i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 4 q^{7} - 56 q^{16} - 8 q^{19} - 4 q^{28} + 8 q^{31} - 24 q^{35} - 4 q^{37} + 36 q^{38} + 48 q^{41} + 12 q^{43} - 60 q^{47} + 24 q^{50} - 4 q^{52} + 120 q^{65} - 56 q^{67} - 24 q^{71} + 28 q^{73}+ \cdots + 48 q^{98}+O(q^{100}) \) 56 * q + 4 * q^7 - 56 * q^16 - 8 * q^19 - 4 * q^28 + 8 * q^31 - 24 * q^35 - 4 * q^37 + 36 * q^38 + 48 * q^41 + 12 * q^43 - 60 * q^47 + 24 * q^50 - 4 * q^52 + 120 * q^65 - 56 * q^67 - 24 * q^71 + 28 * q^73 - 48 * q^74 + 4 * q^76 + 24 * q^77 - 24 * q^79 + 60 * q^83 - 48 * q^86 + 4 * q^91 + 24 * q^92 + 20 * q^97 + 48 * q^98

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