LMFDB - Embedded newform 351.2.h.a.334.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [351,2,Mod(289,351)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(351, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("351.289"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 351 = 3^{3} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	351.h (of order $3$, degree $2$, 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:	$2.80274911095$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{3})$
Twist minimal:	no (minimal twist has level 117)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			334.9
Character	$\chi$	$=$	351.334
Dual form			351.2.h.a.289.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.20426 q^{2} -0.549753 q^{4} +(-1.89177 + 3.27665i) q^{5} +(-0.150228 + 0.260203i) q^{7} -3.07057 q^{8} +(-2.27819 + 3.94594i) q^{10} -1.28462 q^{11} +(0.423704 + 3.58057i) q^{13} +(-0.180914 + 0.313352i) q^{14} -2.59827 q^{16} +(2.63848 + 4.56998i) q^{17} +(-0.829906 - 1.43744i) q^{19} +(1.04001 - 1.80135i) q^{20} -1.54702 q^{22} +(-1.67399 - 2.89944i) q^{23} +(-4.65760 - 8.06721i) q^{25} +(0.510251 + 4.31194i) q^{26} +(0.0825883 - 0.143047i) q^{28} +9.63240 q^{29} +(-3.29700 + 5.71056i) q^{31} +3.01215 q^{32} +(3.17742 + 5.50346i) q^{34} +(-0.568394 - 0.984488i) q^{35} +(1.97702 - 3.42430i) q^{37} +(-0.999424 - 1.73105i) q^{38} +(5.80882 - 10.0612i) q^{40} +(1.43368 + 2.48321i) q^{41} +(0.0104220 - 0.0180514i) q^{43} +0.706223 q^{44} +(-2.01592 - 3.49168i) q^{46} +(-0.954216 - 1.65275i) q^{47} +(3.45486 + 5.98400i) q^{49} +(-5.60898 - 9.71503i) q^{50} +(-0.232933 - 1.96843i) q^{52} +7.15248 q^{53} +(2.43021 - 4.20924i) q^{55} +(0.461286 - 0.798970i) q^{56} +11.5999 q^{58} -8.73826 q^{59} +(-2.56839 + 4.44858i) q^{61} +(-3.97045 + 6.87702i) q^{62} +8.82395 q^{64} +(-12.5338 - 5.38529i) q^{65} +(-4.15570 - 7.19788i) q^{67} +(-1.45051 - 2.51236i) q^{68} +(-0.684496 - 1.18558i) q^{70} +(-4.64070 - 8.03792i) q^{71} -4.69504 q^{73} +(2.38085 - 4.12376i) q^{74} +(0.456243 + 0.790236i) q^{76} +(0.192986 - 0.334261i) q^{77} +(6.65302 + 11.5234i) q^{79} +(4.91533 - 8.51360i) q^{80} +(1.72653 + 2.99044i) q^{82} +(6.45522 + 11.1808i) q^{83} -19.9656 q^{85} +(0.0125508 - 0.0217386i) q^{86} +3.94451 q^{88} +(-3.19907 + 5.54096i) q^{89} +(-0.995325 - 0.427653i) q^{91} +(0.920281 + 1.59397i) q^{92} +(-1.14913 - 1.99035i) q^{94} +6.27997 q^{95} +(1.88195 - 3.25964i) q^{97} +(4.16056 + 7.20630i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 2 q^{2} + 18 q^{4} + 2 q^{5} + 3 q^{7} + 18 q^{8} - 6 q^{11} - 2 q^{14} + 6 q^{16} - 6 q^{17} - 3 q^{19} + 11 q^{20} - 18 q^{22} - 17 q^{23} - 6 q^{25} + 12 q^{26} + 24 q^{29} - 6 q^{31} + 38 q^{32}+ \cdots + 61 q^{98}+O(q^{100}) $ 24 * q + 2 * q^2 + 18 * q^4 + 2 * q^5 + 3 * q^7 + 18 * q^8 - 6 * q^11 - 2 * q^14 + 6 * q^16 - 6 * q^17 - 3 * q^19 + 11 * q^20 - 18 * q^22 - 17 * q^23 - 6 * q^25 + 12 * q^26 + 24 * q^29 - 6 * q^31 + 38 * q^32 - 18 * q^35 - 3 * q^37 - 8 * q^38 - 12 * q^40 - 5 * q^41 - 3 * q^43 - 44 * q^44 - 6 * q^46 - 21 * q^47 + 3 * q^49 + 20 * q^50 - 24 * q^52 + 20 * q^53 + 3 * q^55 - 40 * q^56 + 18 * q^58 - 38 * q^59 - 6 * q^61 - 19 * q^62 - 42 * q^64 + 2 * q^65 - 6 * q^67 + 27 * q^70 - 14 * q^71 + 6 * q^73 - 29 * q^74 - 15 * q^76 - 4 * q^77 + 3 * q^79 + 16 * q^80 - 9 * q^82 + 33 * q^83 - 72 * q^86 - 78 * q^88 + q^89 - 6 * q^91 + 10 * q^92 - 9 * q^94 + 100 * q^95 + 24 * q^97 + 61 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/351\mathbb{Z}\right)^\times$.

$n$	$28$	$326$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	1.20426			0.851542			0.425771	−	0.904831i	$-0.360003\pi$
$2$	1.20426			0.851542			0.425771	+	0.904831i	$0.360003\pi$
$3$		0			0
$3$		0			0
$4$	−0.549753			−0.274876
$5$	−1.89177	+	3.27665i	−0.846026	+	1.46536i	0.0387007	+	0.999251i	$0.487678\pi$
$5$	−1.89177	+	3.27665i	−0.846026	+	1.46536i	−0.884727	+	0.466110i	$0.845655\pi$
$6$		0			0
$7$	−0.150228	+	0.260203i	−0.0567809	+	0.0983473i	−0.893019	−	0.450020i	$-0.851417\pi$
$7$	−0.150228	+	0.260203i	−0.0567809	+	0.0983473i	0.836238	+	0.548367i	$0.184750\pi$
$8$	−3.07057			−1.08561
$9$		0			0
$10$	−2.27819	+	3.94594i	−0.720427	+	1.24782i
$11$	−1.28462			−0.387327			−0.193664	−	0.981068i	$-0.562037\pi$
$11$	−1.28462			−0.387327			−0.193664	+	0.981068i	$0.562037\pi$
$12$		0			0
$13$	0.423704	+	3.58057i	0.117514	+	0.993071i
$13$	0.423704	+	3.58057i	0.117514	+	0.993071i
$14$	−0.180914	+	0.313352i	−0.0483513	+	0.0837469i
$15$		0			0
$16$	−2.59827			−0.649567
$17$	2.63848	+	4.56998i	0.639926	+	1.10838i	0.985449	+	0.169974i	$0.0543683\pi$
$17$	2.63848	+	4.56998i	0.639926	+	1.10838i	−0.345523	+	0.938410i	$0.612298\pi$
$18$		0			0
$19$	−0.829906	−	1.43744i	−0.190393	−	0.329771i	0.754987	−	0.655739i	$-0.227643\pi$
$19$	−0.829906	−	1.43744i	−0.190393	−	0.329771i	−0.945381	+	0.325968i	$0.894310\pi$
$20$	1.04001	−	1.80135i	0.232553	−	0.402793i
$21$		0			0
$22$	−1.54702			−0.329825
$23$	−1.67399	−	2.89944i	−0.349051	−	0.604574i	0.637030	−	0.770839i	$-0.280163\pi$
$23$	−1.67399	−	2.89944i	−0.349051	−	0.604574i	−0.986081	+	0.166265i	$0.946829\pi$
$24$		0			0
$25$	−4.65760	−	8.06721i	−0.931521	−	1.61344i
$26$	0.510251	+	4.31194i	0.100068	+	0.845642i
$27$		0			0
$28$	0.0825883	−	0.143047i	0.0156077	−	0.0270334i
$29$	9.63240			1.78869			0.894346	−	0.447376i	$-0.147641\pi$
$29$	9.63240			1.78869			0.894346	+	0.447376i	$0.147641\pi$
$30$		0			0
$31$	−3.29700	+	5.71056i	−0.592158	+	1.02565i	0.401783	+	0.915735i	$0.368391\pi$
$31$	−3.29700	+	5.71056i	−0.592158	+	1.02565i	−0.993941	+	0.109913i	$0.964943\pi$
$32$	3.01215			0.532478
$33$		0			0
$34$	3.17742	+	5.50346i	0.544924	+	0.943836i
$35$	−0.568394	−	0.984488i	−0.0960762	−	0.166409i
$36$		0			0
$37$	1.97702	−	3.42430i	0.325020	−	0.562952i	−0.656496	−	0.754329i	$-0.727962\pi$
$37$	1.97702	−	3.42430i	0.325020	−	0.562952i	0.981517	+	0.191378i	$0.0612955\pi$
$38$	−0.999424	−	1.73105i	−0.162128	−	0.280814i
$39$		0			0
$40$	5.80882	−	10.0612i	0.918455	−	1.59081i
$41$	1.43368	+	2.48321i	0.223904	+	0.387813i	0.955990	−	0.293399i	$-0.0947866\pi$
$41$	1.43368	+	2.48321i	0.223904	+	0.387813i	−0.732086	+	0.681212i	$0.761453\pi$
$42$		0			0
$43$	0.0104220	−	0.0180514i	0.00158933	−	0.00275281i	−0.865230	−	0.501376i	$-0.832827\pi$
$43$	0.0104220	−	0.0180514i	0.00158933	−	0.00275281i	0.866819	+	0.498623i	$0.166161\pi$
$44$	0.706223			0.106467
$45$		0			0
$46$	−2.01592	−	3.49168i	−0.297232	−	0.514821i
$47$	−0.954216	−	1.65275i	−0.139187	−	0.241079i	0.788002	−	0.615672i	$-0.211116\pi$
$47$	−0.954216	−	1.65275i	−0.139187	−	0.241079i	−0.927189	+	0.374594i	$0.877782\pi$
$48$		0			0
$49$	3.45486	+	5.98400i	0.493552	+	0.854857i
$50$	−5.60898	−	9.71503i	−0.793229	−	1.37391i
$51$		0			0
$52$	−0.232933	−	1.96843i	−0.0323019	−	0.272972i
$53$	7.15248			0.982469			0.491235	−	0.871027i	$-0.336546\pi$
$53$	7.15248			0.982469			0.491235	+	0.871027i	$0.336546\pi$
$54$		0			0
$55$	2.43021	−	4.20924i	0.327689	−	0.567574i
$56$	0.461286	−	0.798970i	0.0616419	−	0.106767i
$57$		0			0
$58$	11.5999			1.52315
$59$	−8.73826			−1.13762			−0.568812	−	0.822468i	$-0.692597\pi$
$59$	−8.73826			−1.13762			−0.568812	+	0.822468i	$0.692597\pi$
$60$		0			0
$61$	−2.56839	+	4.44858i	−0.328849	+	0.569583i	−0.982284	−	0.187400i	$-0.939994\pi$
$61$	−2.56839	+	4.44858i	−0.328849	+	0.569583i	0.653435	+	0.756983i	$0.273327\pi$
$62$	−3.97045	+	6.87702i	−0.504247	+	0.873382i
$63$		0			0
$64$	8.82395			1.10299
$65$	−12.5338	−	5.38529i	−1.55463	−	0.667963i
$66$		0			0
$67$	−4.15570	−	7.19788i	−0.507700	−	0.879361i	−0.999960	−	0.00891361i	$-0.997163\pi$
$67$	−4.15570	−	7.19788i	−0.507700	−	0.879361i	0.492261	−	0.870448i	$-0.336171\pi$
$68$	−1.45051	−	2.51236i	−0.175901	−	0.304669i
$69$		0			0
$70$	−0.684496	−	1.18558i	−0.0818129	−	0.141704i
$71$	−4.64070	−	8.03792i	−0.550749	−	0.953926i	−0.998221	−	0.0596277i	$-0.981009\pi$
$71$	−4.64070	−	8.03792i	−0.550749	−	0.953926i	0.447471	−	0.894298i	$-0.352325\pi$
$72$		0			0
$73$	−4.69504			−0.549512			−0.274756	−	0.961514i	$-0.588597\pi$
$73$	−4.69504			−0.549512			−0.274756	+	0.961514i	$0.588597\pi$
$74$	2.38085	−	4.12376i	0.276769	−	0.479377i
$75$		0			0
$76$	0.456243	+	0.790236i	0.0523346	+	0.0906463i
$77$	0.192986	−	0.334261i	0.0219928	−	0.0380926i
$78$		0			0
$79$	6.65302	+	11.5234i	0.748523	+	1.29648i	0.948530	+	0.316686i	$0.102570\pi$
$79$	6.65302	+	11.5234i	0.748523	+	1.29648i	−0.200007	+	0.979794i	$0.564097\pi$
$80$	4.91533	−	8.51360i	0.549550	−	0.951849i
$81$		0			0
$82$	1.72653	+	2.99044i	0.190663	+	0.330239i
$83$	6.45522	+	11.1808i	0.708552	+	1.22725i	0.965394	+	0.260795i	$0.0839848\pi$
$83$	6.45522	+	11.1808i	0.708552	+	1.22725i	−0.256842	+	0.966453i	$0.582682\pi$
$84$		0			0
$85$	−19.9656			−2.16558
$86$	0.0125508	−	0.0217386i	0.00135339	−	0.00234413i
$87$		0			0
$88$	3.94451			0.420486
$89$	−3.19907	+	5.54096i	−0.339101	+	0.587340i	−0.984264	−	0.176705i	$-0.943456\pi$
$89$	−3.19907	+	5.54096i	−0.339101	+	0.587340i	0.645163	+	0.764045i	$0.276790\pi$
$90$		0			0
$91$	−0.995325	−	0.427653i	−0.104338	−	0.0448302i
$92$	0.920281	+	1.59397i	0.0959459	+	0.166183i
$93$		0			0
$94$	−1.14913	−	1.99035i	−0.118523	−	0.205289i
$95$	6.27997			0.644311
$96$		0			0
$97$	1.88195	−	3.25964i	0.191083	−	0.330966i	−0.754526	−	0.656270i	$-0.772133\pi$
$97$	1.88195	−	3.25964i	0.191083	−	0.330966i	0.945610	+	0.325304i	$0.105467\pi$
$98$	4.16056	+	7.20630i	0.420280	+	0.727946i
$99$		0			0
$100$	2.56053	+	4.43497i	0.256053	+	0.443497i
$101$	4.99159			0.496681			0.248341	−	0.968673i	$-0.420115\pi$
$101$	4.99159			0.496681			0.248341	+	0.968673i	$0.420115\pi$
$102$		0			0
$103$	2.16757	−	3.75434i	0.213577	−	0.369926i	−0.739254	−	0.673426i	$-0.764822\pi$
$103$	2.16757	−	3.75434i	0.213577	−	0.369926i	0.952831	+	0.303500i	$0.0981553\pi$
$104$	−1.30101	−	10.9944i	−0.127575	−	1.07809i
$105$		0			0
$106$	8.61347			0.836614
$107$	−1.57507	+	2.72809i	−0.152267	+	0.263735i	−0.932061	−	0.362302i	$-0.881991\pi$
$107$	−1.57507	+	2.72809i	−0.152267	+	0.263735i	0.779793	+	0.626037i	$0.215324\pi$
$108$		0			0
$109$	14.2728			1.36708			0.683542	−	0.729911i	$-0.260439\pi$
$109$	14.2728			1.36708			0.683542	+	0.729911i	$0.260439\pi$
$110$	2.92661	−	5.06903i	0.279041	−	0.483313i
$111$		0			0
$112$	0.390332	−	0.676076i	0.0368829	−	0.0638831i
$113$	−5.27775			−0.496489			−0.248244	−	0.968697i	$-0.579854\pi$
$113$	−5.27775			−0.496489			−0.248244	+	0.968697i	$0.579854\pi$
$114$		0			0
$115$	12.6672			1.18123
$116$	−5.29544			−0.491669
$117$		0			0
$118$	−10.5232			−0.968735
$119$	−1.58550			−0.145342
$120$		0			0
$121$	−9.34975			−0.849978
$122$	−3.09301	+	5.35726i	−0.280028	+	0.485023i
$123$		0			0
$124$	1.81253	−	3.13940i	0.162770	−	0.281926i
$125$	16.3268			1.46031
$126$		0			0
$127$	−5.36180	+	9.28691i	−0.475783	+	0.824080i	−0.999615	−	0.0277416i	$-0.991168\pi$
$127$	−5.36180	+	9.28691i	−0.475783	+	0.824080i	0.523832	+	0.851821i	$0.324502\pi$
$128$	4.60205			0.406768
$129$		0			0
$130$	−15.0940	−	6.48530i	−1.32383	−	0.568799i
$131$	−1.67220	+	2.89633i	−0.146101	+	0.253054i	−0.929783	−	0.368108i	$-0.880006\pi$
$131$	−1.67220	+	2.89633i	−0.146101	+	0.253054i	0.783682	+	0.621162i	$0.213339\pi$
$132$		0			0
$133$	0.498700			0.0432428
$134$	−5.00455	−	8.66814i	−0.432327	−	0.748813i
$135$		0			0
$136$	−8.10165	−	14.0325i	−0.694710	−	1.20327i
$137$	−7.87786	+	13.6448i	−0.673051	+	1.16576i	0.303984	+	0.952677i	$0.401683\pi$
$137$	−7.87786	+	13.6448i	−0.673051	+	1.16576i	−0.977035	+	0.213081i	$0.931650\pi$
$138$		0			0
$139$	21.5508			1.82791			0.913956	−	0.405813i	$-0.133012\pi$
$139$	21.5508			1.82791			0.913956	+	0.405813i	$0.133012\pi$
$140$	0.312476	+	0.541225i	0.0264091	+	0.0457419i
$141$		0			0
$142$	−5.58862	−	9.67977i	−0.468986	−	0.812308i
$143$	−0.544298	−	4.59967i	−0.0455165	−	0.384643i
$144$		0			0
$145$	−18.2223	+	31.5620i	−1.51328	+	2.62108i
$146$	−5.65405			−0.467933
$147$		0			0
$148$	−1.08687	+	1.88252i	−0.0893405	+	0.154742i
$149$	12.8737			1.05466			0.527328	−	0.849662i	$-0.323194\pi$
$149$	12.8737			1.05466			0.527328	+	0.849662i	$0.323194\pi$
$150$		0			0
$151$	−6.21526	−	10.7652i	−0.505791	−	0.876056i	−0.999978	−	0.00669978i	$-0.997867\pi$
$151$	−6.21526	−	10.7652i	−0.505791	−	0.876056i	0.494187	−	0.869356i	$-0.335466\pi$
$152$	2.54828	+	4.41376i	0.206693	+	0.358003i
$153$		0			0
$154$	0.232405	−	0.402538i	0.0187278	−	0.0324374i
$155$	−12.4743	−	21.6062i	−1.00196	−	1.73545i
$156$		0			0
$157$	5.64417	−	9.77599i	0.450454	−	0.780209i	−0.547960	−	0.836504i	$-0.684596\pi$
$157$	5.64417	−	9.77599i	0.450454	−	0.780209i	0.998414	+	0.0562954i	$0.0179288\pi$
$158$	8.01198	+	13.8772i	0.637399	+	1.10401i
$159$		0			0
$160$	−5.69830	+	9.86974i	−0.450490	+	0.780271i
$161$	1.00592			0.0792777
$162$		0			0
$163$	−3.30893	−	5.73124i	−0.259176	−	0.448905i	0.706846	−	0.707368i	$-0.250118\pi$
$163$	−3.30893	−	5.73124i	−0.259176	−	0.448905i	−0.966021	+	0.258462i	$0.916784\pi$
$164$	−0.788171	−	1.36515i	−0.0615458	−	0.106601i
$165$		0			0
$166$	7.77378	+	13.4646i	0.603362	+	1.04505i
$167$	5.42722	+	9.40022i	0.419971	+	0.727411i	0.995936	−	0.0900632i	$-0.0287069\pi$
$167$	5.42722	+	9.40022i	0.419971	+	0.727411i	−0.575965	+	0.817474i	$0.695374\pi$
$168$		0			0
$169$	−12.6409	+	3.03420i	−0.972381	+	0.233400i
$170$	−24.0438			−1.84408
$171$		0			0
$172$	−0.00572950	+	0.00992379i	−0.000436871	+	0.000756682i
$173$	0.103551	−	0.179356i	0.00787286	−	0.0136362i	−0.862062	−	0.506803i	$-0.830827\pi$
$173$	0.103551	−	0.179356i	0.00787286	−	0.0136362i	0.869935	+	0.493166i	$0.164161\pi$
$174$		0			0
$175$	2.79881			0.211570
$176$	3.33778			0.251595
$177$		0			0
$178$	−3.85252	+	6.67276i	−0.288759	+	0.500145i
$179$	4.98833	−	8.64004i	0.372845	−	0.645787i	−0.617157	−	0.786840i	$-0.711715\pi$
$179$	4.98833	−	8.64004i	0.372845	−	0.645787i	0.990002	+	0.141053i	$0.0450488\pi$
$180$		0			0
$181$	13.9599			1.03763			0.518814	−	0.854887i	$-0.326374\pi$
$181$	13.9599			1.03763			0.518814	+	0.854887i	$0.326374\pi$
$182$	−1.19863	−	0.515006i	−0.0888486	−	0.0381748i
$183$		0			0
$184$	5.14011	+	8.90293i	0.378934	+	0.656333i
$185$	7.48015	+	12.9560i	0.549952	+	0.952544i
$186$		0			0
$187$	−3.38944	−	5.87069i	−0.247861	−	0.429307i
$188$	0.524583	+	0.908605i	0.0382592	+	0.0662668i
$189$		0			0
$190$	7.56273			0.548658
$191$	−6.93963	+	12.0198i	−0.502134	+	0.869721i	0.497863	+	0.867256i	$0.334118\pi$
$191$	−6.93963	+	12.0198i	−0.502134	+	0.869721i	−0.999997	+	0.00246553i	$0.999215\pi$
$192$		0			0
$193$	−4.02111	−	6.96477i	−0.289446	−	0.501335i	0.684232	−	0.729265i	$-0.260138\pi$
$193$	−4.02111	−	6.96477i	−0.289446	−	0.501335i	−0.973678	+	0.227930i	$0.926804\pi$
$194$	2.26637	−	3.92546i	0.162716	−	0.281832i
$195$		0			0
$196$	−1.89932	−	3.28972i	−0.135666	−	0.234980i
$197$	−1.50401	+	2.60502i	−0.107156	+	0.185600i	−0.914617	−	0.404321i	$-0.867508\pi$
$197$	−1.50401	+	2.60502i	−0.107156	+	0.185600i	0.807461	+	0.589921i	$0.200841\pi$
$198$		0			0
$199$	−10.4398	−	18.0823i	−0.740057	−	1.28182i	−0.952469	−	0.304637i	$-0.901465\pi$
$199$	−10.4398	−	18.0823i	−0.740057	−	1.28182i	0.212411	−	0.977180i	$-0.431868\pi$
$200$	14.3015	+	24.7709i	1.01127	+	1.75157i
$201$		0			0
$202$	6.01118			0.422945
$203$	−1.44706	+	2.50638i	−0.101563	+	0.175913i
$204$		0			0
$205$	−10.8488			−0.757714
$206$	2.61032	−	4.52121i	0.181870	−	0.315008i
$207$		0			0
$208$	−1.10090	−	9.30327i	−0.0763334	−	0.645066i
$209$	1.06611	+	1.84656i	0.0737445	+	0.127729i
$210$		0			0
$211$	9.04250	+	15.6621i	0.622511	+	1.07822i	0.989017	+	0.147805i	$0.0472208\pi$
$211$	9.04250	+	15.6621i	0.622511	+	1.07822i	−0.366505	+	0.930416i	$0.619446\pi$
$212$	−3.93210			−0.270058
$213$		0			0
$214$	−1.89679	+	3.28534i	−0.129662	+	0.224581i
$215$	0.0394320	+	0.0682982i	0.00268924	+	0.00465790i
$216$		0			0
$217$	−0.990602	−	1.71577i	−0.0672465	−	0.116474i
$218$	17.1882			1.16413
$219$		0			0
$220$	−1.33601	+	2.31404i	−0.0900739	+	0.156013i
$221$	−15.2452	+	11.3836i	−1.02550	+	0.765743i
$222$		0			0
$223$	22.7398			1.52277			0.761385	−	0.648300i	$-0.224520\pi$
$223$	22.7398			1.52277			0.761385	+	0.648300i	$0.224520\pi$
$224$	−0.452509	+	0.783769i	−0.0302345	+	0.0523677i
$225$		0			0
$226$	−6.35579			−0.422781
$227$	2.45568	−	4.25336i	0.162989	−	0.282305i	−0.772950	−	0.634467i	$-0.781220\pi$
$227$	2.45568	−	4.25336i	0.162989	−	0.282305i	0.935939	+	0.352161i	$0.114553\pi$
$228$		0			0
$229$	1.97040	−	3.41283i	0.130208	−	0.225526i	−0.793549	−	0.608506i	$-0.791769\pi$
$229$	1.97040	−	3.41283i	0.130208	−	0.225526i	0.923757	+	0.382980i	$0.125102\pi$
$230$	15.2547			1.00586
$231$		0			0
$232$	−29.5770			−1.94182
$233$	−2.49782			−0.163637			−0.0818187	−	0.996647i	$-0.526073\pi$
$233$	−2.49782			−0.163637			−0.0818187	+	0.996647i	$0.526073\pi$
$234$		0			0
$235$	7.22064			0.471023
$236$	4.80388			0.312706
$237$		0			0
$238$	−1.90935			−0.123765
$239$	4.25640	−	7.37230i	0.275324	−	0.476874i	−0.694893	−	0.719113i	$-0.744548\pi$
$239$	4.25640	−	7.37230i	0.275324	−	0.476874i	0.970217	+	0.242239i	$0.0778817\pi$
$240$		0			0
$241$	−8.11525	+	14.0560i	−0.522749	+	0.905428i	0.476900	+	0.878957i	$0.341760\pi$
$241$	−8.11525	+	14.0560i	−0.522749	+	0.905428i	−0.999650	+	0.0264707i	$0.991573\pi$
$242$	−11.2596			−0.723792
$243$		0			0
$244$	1.41198	−	2.44562i	0.0903927	−	0.156565i
$245$	−26.1433			−1.67023
$246$		0			0
$247$	4.79521	−	3.58058i	0.305112	−	0.227827i
$248$	10.1237	−	17.5347i	0.642853	−	1.11345i
$249$		0			0
$250$	19.6617			1.24352
$251$	−11.7453	−	20.3434i	−0.741356	−	1.28407i	−0.951878	−	0.306477i	$-0.900850\pi$
$251$	−11.7453	−	20.3434i	−0.741356	−	1.28407i	0.210522	−	0.977589i	$-0.432484\pi$
$252$		0			0
$253$	2.15044	+	3.72467i	0.135197	+	0.234168i
$254$	−6.45701	+	11.1839i	−0.405149	+	0.701738i
$255$		0			0
$256$	−12.1058			−0.756614
$257$	−2.86567	−	4.96348i	−0.178756	−	0.309614i	0.762699	−	0.646754i	$-0.223874\pi$
$257$	−2.86567	−	4.96348i	−0.178756	−	0.309614i	−0.941455	+	0.337140i	$0.890540\pi$
$258$		0			0
$259$	0.594008	+	1.02885i	0.0369099	+	0.0639298i
$260$	6.89050	+	2.96058i	0.427330	+	0.183607i
$261$		0			0
$262$	−2.01376	+	3.48794i	−0.124411	+	0.215486i
$263$	0.533324			0.0328862			0.0164431	−	0.999865i	$-0.494766\pi$
$263$	0.533324			0.0328862			0.0164431	+	0.999865i	$0.494766\pi$
$264$		0			0
$265$	−13.5309	+	23.4362i	−0.831195	+	1.43967i
$266$	0.600566			0.0368231
$267$		0			0
$268$	2.28461	+	3.95706i	0.139555	+	0.241716i
$269$	−0.841875	−	1.45817i	−0.0513300	−	0.0889062i	0.839219	−	0.543794i	$-0.183013\pi$
$269$	−0.841875	−	1.45817i	−0.0513300	−	0.0889062i	−0.890549	+	0.454888i	$0.849679\pi$
$270$		0			0
$271$	−2.99018	+	5.17914i	−0.181640	+	0.314610i	−0.942439	−	0.334377i	$-0.891474\pi$
$271$	−2.99018	+	5.17914i	−0.181640	+	0.314610i	0.760799	+	0.648988i	$0.224807\pi$
$272$	−6.85548	−	11.8740i	−0.415674	−	0.719969i
$273$		0			0
$274$	−9.48700	+	16.4320i	−0.573131	+	0.992692i
$275$	5.98325	+	10.3633i	0.360803	+	0.624930i
$276$		0			0
$277$	0.241067	−	0.417541i	0.0144843	−	0.0250876i	−0.858692	−	0.512491i	$-0.828723\pi$
$277$	0.241067	−	0.417541i	0.0144843	−	0.0250876i	0.873177	+	0.487404i	$0.162056\pi$
$278$	25.9528			1.55654
$279$		0			0
$280$	1.74530	+	3.02294i	0.104301	+	0.180655i
$281$	−6.37082	−	11.0346i	−0.380051	−	0.658268i	0.611018	−	0.791617i	$-0.290760\pi$
$281$	−6.37082	−	11.0346i	−0.380051	−	0.658268i	−0.991069	+	0.133349i	$0.957427\pi$
$282$		0			0
$283$	−4.55670	−	7.89244i	−0.270868	−	0.469157i	0.698217	−	0.715887i	$-0.253977\pi$
$283$	−4.55670	−	7.89244i	−0.270868	−	0.469157i	−0.969084	+	0.246730i	$0.920644\pi$
$284$	2.55124	+	4.41887i	0.151388	+	0.262212i
$285$		0			0
$286$	−0.655478	−	5.53920i	−0.0387592	−	0.327540i
$287$	−0.861518			−0.0508538
$288$		0			0
$289$	−5.42317	+	9.39321i	−0.319010	+	0.552542i
$290$	−21.9444	+	38.0089i	−1.28862	+	2.23196i
$291$		0			0
$292$	2.58111			0.151048
$293$	−4.10386			−0.239750			−0.119875	−	0.992789i	$-0.538249\pi$
$293$	−4.10386			−0.239750			−0.119875	+	0.992789i	$0.538249\pi$
$294$		0			0
$295$	16.5308	−	28.6322i	0.962460	−	1.66703i
$296$	−6.07059	+	10.5146i	−0.352846	+	0.611147i
$297$		0			0
$298$	15.5033			0.898083
$299$	9.67236	−	7.22234i	0.559367	−	0.417679i
$300$		0			0
$301$	0.00313134	+	0.00542364i	0.000180488	+	0.000312614i
$302$	−7.48481	−	12.9641i	−0.430702	−	0.745998i
$303$		0			0
$304$	2.15632	+	3.73485i	0.123673	+	0.214208i
$305$	−9.71762	−	16.8314i	−0.556429	−	0.963764i
$306$		0			0
$307$	21.0459			1.20115			0.600575	−	0.799568i	$-0.294938\pi$
$307$	21.0459			1.20115			0.600575	+	0.799568i	$0.294938\pi$
$308$	−0.106094	+	0.183761i	−0.00604529	+	0.0104708i
$309$		0			0
$310$	−15.0224	−	26.0195i	−0.853213	−	1.47781i
$311$	13.8275	−	23.9500i	0.784087	−	1.35808i	−0.145456	−	0.989365i	$-0.546465\pi$
$311$	13.8275	−	23.9500i	0.784087	−	1.35808i	0.929543	−	0.368714i	$-0.120202\pi$
$312$		0			0
$313$	−1.14415	−	1.98173i	−0.0646712	−	0.112014i	0.831877	−	0.554960i	$-0.187267\pi$
$313$	−1.14415	−	1.98173i	−0.0646712	−	0.112014i	−0.896548	+	0.442946i	$0.853933\pi$
$314$	6.79706	−	11.7729i	0.383580	−	0.664381i
$315$		0			0
$316$	−3.65752	−	6.33500i	−0.205751	−	0.356372i
$317$	−10.1830	−	17.6374i	−0.571932	−	0.990615i	−0.996368	−	0.0851568i	$-0.972861\pi$
$317$	−10.1830	−	17.6374i	−0.571932	−	0.990615i	0.424436	−	0.905458i	$-0.360472\pi$
$318$		0			0
$319$	−12.3740			−0.692809
$320$	−16.6929	+	28.9130i	−0.933161	+	1.61628i
$321$		0			0
$322$	1.21139			0.0675083
$323$	4.37938	−	7.58531i	0.243675	−	0.422058i
$324$		0			0
$325$	26.9117	−	20.0950i	1.49280	−	1.11467i
$326$	−3.98482	−	6.90192i	−0.220699	−	0.382262i
$327$		0			0
$328$	−4.40223	−	7.62488i	−0.243072	−	0.421013i
$329$	0.573400			0.0316126
$330$		0			0
$331$	−8.72183	+	15.1067i	−0.479395	+	0.830337i	−0.999721	−	0.0236311i	$-0.992477\pi$
$331$	−8.72183	+	15.1067i	−0.479395	+	0.830337i	0.520325	+	0.853968i	$0.325811\pi$
$332$	−3.54877	−	6.14666i	−0.194764	−	0.337342i
$333$		0			0
$334$	6.53580	+	11.3203i	0.357623	+	0.619421i
$335$	31.4466			1.71811
$336$		0			0
$337$	12.4840	−	21.6229i	0.680048	−	1.17788i	−0.294918	−	0.955523i	$-0.595292\pi$
$337$	12.4840	−	21.6229i	0.680048	−	1.17788i	0.974966	−	0.222355i	$-0.0713743\pi$
$338$	−15.2230	+	3.65398i	−0.828023	+	0.198750i
$339$		0			0
$340$	10.9762			0.595266
$341$	4.23538	−	7.33590i	0.229359	−	0.397261i
$342$		0			0
$343$	−4.17926			−0.225659
$344$	−0.0320014	+	0.0554280i	−0.00172540	+	0.00298848i
$345$		0			0
$346$	0.124703	−	0.215992i	0.00670407	−	0.0116118i
$347$	10.1284			0.543722			0.271861	−	0.962336i	$-0.412361\pi$
$347$	10.1284			0.543722			0.271861	+	0.962336i	$0.412361\pi$
$348$		0			0
$349$	22.5689			1.20809			0.604044	−	0.796951i	$-0.293555\pi$
$349$	22.5689			1.20809			0.604044	+	0.796951i	$0.293555\pi$
$350$	3.37050			0.180161
$351$		0			0
$352$	−3.86946			−0.206243
$353$	−24.9017			−1.32539			−0.662693	−	0.748891i	$-0.730587\pi$
$353$	−24.9017			−1.32539			−0.662693	+	0.748891i	$0.730587\pi$
$354$		0			0
$355$	35.1166			1.86379
$356$	1.75870	−	3.04616i	0.0932109	−	0.161446i
$357$		0			0
$358$	6.00726	−	10.4049i	0.317494	−	0.549915i
$359$	35.7532			1.88698			0.943492	−	0.331395i	$-0.107519\pi$
$359$	35.7532			1.88698			0.943492	+	0.331395i	$0.107519\pi$
$360$		0			0
$361$	8.12251	−	14.0686i	0.427501	−	0.740453i
$362$	16.8113			0.883584
$363$		0			0
$364$	0.547183	+	0.235103i	0.0286802	+	0.0123228i
$365$	8.88194	−	15.3840i	0.464902	−	0.805234i
$366$		0			0
$367$	−13.3838			−0.698627			−0.349313	−	0.937006i	$-0.613585\pi$
$367$	−13.3838			−0.698627			−0.349313	+	0.937006i	$0.613585\pi$
$368$	4.34947	+	7.53351i	0.226732	+	0.392711i
$369$		0			0
$370$	9.00806	+	15.6024i	0.468307	+	0.811131i
$371$	−1.07450	+	1.86109i	−0.0557854	+	0.0966232i
$372$		0			0
$373$	7.14941			0.370182			0.185091	−	0.982721i	$-0.440742\pi$
$373$	7.14941			0.370182			0.185091	+	0.982721i	$0.440742\pi$
$374$	−4.08178	−	7.06985i	−0.211064	−	0.365573i
$375$		0			0
$376$	2.92999	+	5.07489i	0.151103	+	0.261717i
$377$	4.08129	+	34.4895i	0.210197	+	1.77630i
$378$		0			0
$379$	13.7475	−	23.8114i	0.706162	−	1.22311i	−0.260109	−	0.965579i	$-0.583758\pi$
$379$	13.7475	−	23.8114i	0.706162	−	1.22311i	0.966271	−	0.257529i	$-0.0829082\pi$
$380$	−3.45243			−0.177106
$381$		0			0
$382$	−8.35713	+	14.4750i	−0.427588	+	0.740604i
$383$	11.3250			0.578680			0.289340	−	0.957226i	$-0.406564\pi$
$383$	11.3250			0.578680			0.289340	+	0.957226i	$0.406564\pi$
$384$		0			0
$385$	0.730170	+	1.26469i	0.0372129	+	0.0644547i
$386$	−4.84247	−	8.38741i	−0.246475	−	0.426908i
$387$		0			0
$388$	−1.03461	+	1.79200i	−0.0525243	+	0.0909748i
$389$	7.75413	+	13.4306i	0.393150	+	0.680956i	0.992863	−	0.119259i	$-0.0380519\pi$
$389$	7.75413	+	13.4306i	0.393150	+	0.680956i	−0.599713	+	0.800215i	$0.704719\pi$
$390$		0			0
$391$	8.83359	−	15.3002i	0.446734	−	0.773766i
$392$	−10.6084	−	18.3743i	−0.535805	−	0.928042i
$393$		0			0
$394$	−1.81122	+	3.13713i	−0.0912481	+	0.158046i
$395$	−50.3440			−2.53308
$396$		0			0
$397$	−5.84662	−	10.1266i	−0.293434	−	0.508242i	0.681186	−	0.732111i	$-0.261465\pi$
$397$	−5.84662	−	10.1266i	−0.293434	−	0.508242i	−0.974619	+	0.223869i	$0.928131\pi$
$398$	−12.5722	−	21.7758i	−0.630190	−	1.09152i
$399$		0			0
$400$	12.1017	+	20.9608i	0.605085	+	1.04804i
$401$	0.357848	+	0.619811i	0.0178701	+	0.0309519i	0.874822	−	0.484444i	$-0.160978\pi$
$401$	0.357848	+	0.619811i	0.0178701	+	0.0309519i	−0.856952	+	0.515396i	$0.827645\pi$
$402$		0			0
$403$	−21.8440	−	9.38553i	−1.08813	−	0.467527i
$404$	−2.74414			−0.136526
$405$		0			0
$406$	−1.74264	+	3.01833i	−0.0864855	+	0.149797i
$407$	−2.53972	+	4.39892i	−0.125889	+	0.218047i
$408$		0			0
$409$	−3.49404			−0.172769			−0.0863846	−	0.996262i	$-0.527531\pi$
$409$	−3.49404			−0.172769			−0.0863846	+	0.996262i	$0.527531\pi$
$410$	−13.0648			−0.645225
$411$		0			0
$412$	−1.19163	+	2.06396i	−0.0587073	+	0.101684i
$413$	1.31273	−	2.27372i	0.0645953	−	0.111882i
$414$		0			0
$415$	−48.8472			−2.39782
$416$	1.27626	+	10.7852i	0.0625738	+	0.528788i
$417$		0			0
$418$	1.28388	+	2.22374i	0.0627965	+	0.108767i
$419$	−9.13962	−	15.8303i	−0.446500	−	0.773360i	0.551656	−	0.834072i	$-0.313996\pi$
$419$	−9.13962	−	15.8303i	−0.446500	−	0.773360i	−0.998155	+	0.0607117i	$0.980663\pi$
$420$		0			0
$421$	−1.70275	−	2.94926i	−0.0829871	−	0.143738i	0.821545	−	0.570144i	$-0.193113\pi$
$421$	−1.70275	−	2.94926i	−0.0829871	−	0.143738i	−0.904532	+	0.426406i	$0.859779\pi$
$422$	10.8895	+	18.8612i	0.530094	+	0.918150i
$423$		0			0
$424$	−21.9622			−1.06658
$425$	24.5780	−	42.5704i	1.19221	−	2.06497i
$426$		0			0
$427$	−0.771688	−	1.33660i	−0.0373446	−	0.0646828i
$428$	0.865896	−	1.49978i	0.0418547	−	0.0724944i
$429$		0			0
$430$	0.0474864	+	0.0822489i	0.00229000	+	0.00396639i
$431$	7.51196	−	13.0111i	0.361839	−	0.626723i	−0.626425	−	0.779482i	$-0.715482\pi$
$431$	7.51196	−	13.0111i	0.361839	−	0.626723i	0.988263	+	0.152759i	$0.0488158\pi$
$432$		0			0
$433$	1.01128	+	1.75159i	0.0485991	+	0.0841762i	0.889302	−	0.457321i	$-0.151191\pi$
$433$	1.01128	+	1.75159i	0.0485991	+	0.0841762i	−0.840703	+	0.541497i	$0.817858\pi$
$434$	−1.19294	−	2.06624i	−0.0572632	−	0.0991827i
$435$		0			0
$436$	−7.84649			−0.375779
$437$	−2.77851	+	4.81252i	−0.132914	+	0.230214i
$438$		0			0
$439$	13.1733			0.628725			0.314363	−	0.949303i	$-0.398209\pi$
$439$	13.1733			0.628725			0.314363	+	0.949303i	$0.398209\pi$
$440$	−7.46212	+	12.9248i	−0.355743	+	0.616164i
$441$		0			0
$442$	−18.3592	+	13.7088i	−0.873259	+	0.652062i
$443$	5.48308	+	9.49698i	0.260509	+	0.451215i	0.966377	−	0.257128i	$-0.0827762\pi$
$443$	5.48308	+	9.49698i	0.260509	+	0.451215i	−0.705868	+	0.708343i	$0.749443\pi$
$444$		0			0
$445$	−12.1038	−	20.9645i	−0.573777	−	0.993811i
$446$	27.3847			1.29670
$447$		0			0
$448$	−1.32560	+	2.29601i	−0.0626289	+	0.108476i
$449$	18.1471	+	31.4318i	0.856416	+	1.48336i	0.875325	+	0.483535i	$0.160647\pi$
$449$	18.1471	+	31.4318i	0.856416	+	1.48336i	−0.0189089	+	0.999821i	$0.506019\pi$
$450$		0			0
$451$	−1.84174	−	3.18998i	−0.0867240	−	0.150210i
$452$	2.90146			0.136473
$453$		0			0
$454$	2.95728	−	5.12216i	0.138792	−	0.240395i
$455$	3.28420	−	2.45231i	0.153965	−	0.114966i
$456$		0			0
$457$	−33.9786			−1.58945			−0.794726	−	0.606968i	$-0.792386\pi$
$457$	−33.9786			−1.58945			−0.794726	+	0.606968i	$0.792386\pi$
$458$	2.37288	−	4.10994i	0.110877	−	0.192045i
$459$		0			0
$460$	−6.96385			−0.324691
$461$	−5.76497	+	9.98523i	−0.268502	+	0.465058i	−0.968475	−	0.249110i	$-0.919862\pi$
$461$	−5.76497	+	9.98523i	−0.268502	+	0.465058i	0.699973	+	0.714169i	$0.253195\pi$
$462$		0			0
$463$	−15.1765	+	26.2864i	−0.705310	+	1.22163i	0.261270	+	0.965266i	$0.415859\pi$
$463$	−15.1765	+	26.2864i	−0.705310	+	1.22163i	−0.966580	+	0.256366i	$0.917475\pi$
$464$	−25.0275			−1.16187
$465$		0			0
$466$	−3.00803			−0.139344
$467$	1.64762			0.0762426			0.0381213	−	0.999273i	$-0.487863\pi$
$467$	1.64762			0.0762426			0.0381213	+	0.999273i	$0.487863\pi$
$468$		0			0
$469$	2.49721			0.115310
$470$	8.69554			0.401096
$471$		0			0
$472$	26.8314			1.23502
$473$	−0.0133883	+	0.0231891i	−0.000615592	+	0.00106624i
$474$		0			0
$475$	−7.73074	+	13.3900i	−0.354711	+	0.614377i
$476$	0.871631			0.0399511
$477$		0			0
$478$	5.12582	−	8.87818i	0.234450	−	0.406079i
$479$	10.5874			0.483753			0.241876	−	0.970307i	$-0.422237\pi$
$479$	10.5874			0.483753			0.241876	+	0.970307i	$0.422237\pi$
$480$		0			0
$481$	13.0986	+	5.62797i	0.597246	+	0.256614i
$482$	−9.77289	+	16.9271i	−0.445143	+	0.771010i
$483$		0			0
$484$	5.14005			0.233639
$485$	7.12045	+	12.3330i	0.323323	+	0.560012i
$486$		0			0
$487$	13.3185	+	23.0683i	0.603517	+	1.04532i	0.992284	+	0.123986i	$0.0395679\pi$
$487$	13.3185	+	23.0683i	0.603517	+	1.04532i	−0.388767	+	0.921336i	$0.627099\pi$
$488$	7.88642	−	13.6597i	0.357002	−	0.618345i
$489$		0			0
$490$	−31.4833			−1.42227
$491$	11.6757	+	20.2228i	0.526915	+	0.912644i	0.999508	+	0.0313629i	$0.00998477\pi$
$491$	11.6757	+	20.2228i	0.526915	+	0.912644i	−0.472593	+	0.881281i	$0.656682\pi$
$492$		0			0
$493$	25.4149	+	44.0199i	1.14463	+	1.98256i
$494$	5.77469	−	4.31196i	0.259816	−	0.194004i
$495$		0			0
$496$	8.56647	−	14.8376i	0.384646	−	0.666226i
$497$	2.78865			0.125088
$498$		0			0
$499$	−0.396185	+	0.686212i	−0.0177357	+	0.0307191i	−0.874757	−	0.484562i	$-0.838979\pi$
$499$	−0.396185	+	0.686212i	−0.0177357	+	0.0307191i	0.857021	+	0.515281i	$0.172312\pi$
$500$	−8.97570			−0.401405
$501$		0			0
$502$	−14.1444	−	24.4988i	−0.631296	−	1.09344i
$503$	−11.9019	−	20.6147i	−0.530681	−	0.919166i	−0.999359	−	0.0357971i	$-0.988603\pi$
$503$	−11.9019	−	20.6147i	−0.530681	−	0.919166i	0.468678	−	0.883369i	$-0.344730\pi$
$504$		0			0
$505$	−9.44294	+	16.3557i	−0.420206	+	0.727817i
$506$	2.58969	+	4.48548i	0.115126	+	0.199404i
$507$		0			0
$508$	2.94766	−	5.10550i	0.130781	−	0.226520i
$509$	12.1015	+	20.9604i	0.536388	+	0.929052i	0.999095	+	0.0425404i	$0.0135451\pi$
$509$	12.1015	+	20.9604i	0.536388	+	0.929052i	−0.462706	+	0.886512i	$0.653122\pi$
$510$		0			0
$511$	0.705326	−	1.22166i	0.0312018	−	0.0540431i
$512$	−23.7827			−1.05106
$513$		0			0
$514$	−3.45102	−	5.97734i	−0.152218	−	0.263649i
$515$	8.20109	+	14.2047i	0.361383	+	0.625934i
$516$		0			0
$517$	1.22580	+	2.12316i	0.0539108	+	0.0933763i
$518$	0.715342	+	1.23901i	0.0314303	+	0.0544389i
$519$		0			0
$520$	38.4859	+	16.5359i	1.68772	+	0.725148i
$521$	10.2515			0.449125			0.224563	−	0.974460i	$-0.427905\pi$
$521$	10.2515			0.449125			0.224563	+	0.974460i	$0.427905\pi$
$522$		0			0
$523$	−13.3127	+	23.0583i	−0.582124	+	1.00827i	0.413103	+	0.910684i	$0.364445\pi$
$523$	−13.3127	+	23.0583i	−0.582124	+	1.00827i	−0.995227	+	0.0975847i	$0.968888\pi$
$524$	0.919295	−	1.59227i	0.0401596	−	0.0695584i
$525$		0			0
$526$	0.642262			0.0280040
$527$	−34.7963			−1.51575
$528$		0			0
$529$	5.89551	−	10.2113i	0.256326	−	0.443970i
$530$	−16.2947	+	28.2233i	−0.707797	+	1.22594i
$531$		0			0
$532$	−0.274162			−0.0118864
$533$	−8.28385	+	6.18555i	−0.358814	+	0.267926i
$534$		0			0
$535$	−5.95933	−	10.3219i	−0.257644	−	0.446253i
$536$	12.7604	+	22.1016i	0.551164	+	0.954644i
$537$		0			0
$538$	−1.01384	−	1.75602i	−0.0437096	−	0.0757073i
$539$	−4.43818	−	7.68716i	−0.191166	−	0.331109i
$540$		0			0
$541$	−11.7447			−0.504943			−0.252471	−	0.967604i	$-0.581243\pi$
$541$	−11.7447			−0.504943			−0.252471	+	0.967604i	$0.581243\pi$
$542$	−3.60096	+	6.23704i	−0.154674	+	0.267904i
$543$		0			0
$544$	7.94750	+	13.7655i	0.340746	+	0.590190i
$545$	−27.0008	+	46.7668i	−1.15659	+	2.00327i
$546$		0			0
$547$	0.492671	+	0.853331i	0.0210651	+	0.0364858i	0.876366	−	0.481646i	$-0.159961\pi$
$547$	0.492671	+	0.853331i	0.0210651	+	0.0364858i	−0.855301	+	0.518132i	$0.826628\pi$
$548$	4.33087	−	7.50129i	0.185006	−	0.320439i
$549$		0			0
$550$	7.20540	+	12.4801i	0.307239	+	0.532154i
$551$	−7.99398	−	13.8460i	−0.340555	−	0.589859i
$552$		0			0
$553$	−3.99788			−0.170007
$554$	0.290308	−	0.502828i	0.0123340	−	0.0213631i
$555$		0			0
$556$	−11.8476			−0.502450
$557$	−12.1835	+	21.1025i	−0.516233	+	0.894141i	0.483590	+	0.875295i	$0.339333\pi$
$557$	−12.1835	+	21.1025i	−0.516233	+	0.894141i	−0.999822	+	0.0188462i	$0.994001\pi$
$558$		0			0
$559$	0.0690500	+	0.0296681i	0.00292050	+	0.00125483i
$560$	1.47684	+	2.55796i	0.0624079	+	0.108094i
$561$		0			0
$562$	−7.67213	−	13.2885i	−0.323629	−	0.560543i
$563$	−33.9591			−1.43121			−0.715603	−	0.698507i	$-0.753848\pi$
$563$	−33.9591			−1.43121			−0.715603	+	0.698507i	$0.753848\pi$
$564$		0			0
$565$	9.98430	−	17.2933i	0.420043	−	0.727535i
$566$	−5.48746	−	9.50456i	−0.230655	−	0.399507i
$567$		0			0
$568$	14.2496	+	24.6810i	0.597899	+	1.03559i
$569$	24.0616			1.00871			0.504356	−	0.863496i	$-0.331730\pi$
$569$	24.0616			1.00871			0.504356	+	0.863496i	$0.331730\pi$
$570$		0			0
$571$	−2.33817	+	4.04984i	−0.0978495	+	0.169480i	−0.910794	−	0.412860i	$-0.864530\pi$
$571$	−2.33817	+	4.04984i	−0.0978495	+	0.169480i	0.812945	+	0.582341i	$0.197863\pi$
$572$	0.299229	+	2.52868i	0.0125114	+	0.105729i
$573$		0			0
$574$	−1.03749			−0.0433041
$575$	−15.5936	+	27.0089i	−0.650297	+	1.12635i
$576$		0			0
$577$	−24.2913			−1.01126			−0.505630	−	0.862750i	$-0.668740\pi$
$577$	−24.2913			−1.01126			−0.505630	+	0.862750i	$0.668740\pi$
$578$	−6.53092	+	11.3119i	−0.271651	+	0.470513i
$579$		0			0
$580$	10.0178	−	17.3513i	0.415965	−	0.720473i
$581$	−3.87902			−0.160929
$582$		0			0
$583$	−9.18822			−0.380537
$584$	14.4164			0.596557
$585$		0			0
$586$	−4.94212			−0.204157
$587$	17.0334			0.703045			0.351522	−	0.936179i	$-0.385664\pi$
$587$	17.0334			0.703045			0.351522	+	0.936179i	$0.385664\pi$
$588$		0			0
$589$	10.9448			0.450972
$590$	19.9074	−	34.4806i	0.819575	−	1.41955i
$591$		0			0
$592$	−5.13683	+	8.89725i	−0.211122	+	0.365675i
$593$	−16.1029			−0.661266			−0.330633	−	0.943759i	$-0.607262\pi$
$593$	−16.1029			−0.661266			−0.330633	+	0.943759i	$0.607262\pi$
$594$		0			0
$595$	2.99940	−	5.19511i	0.122963	−	0.212979i
$596$	−7.07736			−0.289900
$597$		0			0
$598$	11.6481	−	8.69760i	0.476324	−	0.355671i
$599$	10.4601	−	18.1175i	0.427390	−	0.740261i	−0.569250	−	0.822164i	$-0.692766\pi$
$599$	10.4601	−	18.1175i	0.427390	−	0.740261i	0.996640	+	0.0819032i	$0.0260998\pi$
$600$		0			0
$601$	2.39968			0.0978850			0.0489425	−	0.998802i	$-0.484415\pi$
$601$	2.39968			0.0978850			0.0489425	+	0.998802i	$0.484415\pi$
$602$	0.00377096	+	0.00653149i	0.000153693	+	0.000266204i
$603$		0			0
$604$	3.41686	+	5.91817i	0.139030	+	0.240807i
$605$	17.6876	−	30.6358i	0.719103	−	1.24552i
$606$		0			0
$607$	−41.9024			−1.70076			−0.850382	−	0.526165i	$-0.823629\pi$
$607$	−41.9024			−1.70076			−0.850382	+	0.526165i	$0.823629\pi$
$608$	−2.49980	−	4.32978i	−0.101380	−	0.175596i
$609$		0			0
$610$	−11.7026	−	20.2694i	−0.473823	−	0.820685i
$611$	5.51349	−	4.11692i	0.223052	−	0.166553i
$612$		0			0
$613$	−6.47866	+	11.2214i	−0.261671	+	0.453227i	−0.966686	−	0.255965i	$-0.917607\pi$
$613$	−6.47866	+	11.2214i	−0.261671	+	0.453227i	0.705015	+	0.709192i	$0.250940\pi$
$614$	25.3447			1.02283
$615$		0			0
$616$	−0.592576	+	1.02637i	−0.0238756	+	0.0413537i
$617$	14.5666			0.586431			0.293216	−	0.956046i	$-0.405275\pi$
$617$	14.5666			0.586431			0.293216	+	0.956046i	$0.405275\pi$
$618$		0			0
$619$	4.73531	+	8.20179i	0.190328	+	0.329658i	0.945359	−	0.326031i	$-0.105711\pi$
$619$	4.73531	+	8.20179i	0.190328	+	0.329658i	−0.755031	+	0.655689i	$0.772378\pi$
$620$	6.85780	+	11.8781i	0.275416	+	0.477034i
$621$		0			0
$622$	16.6520	−	28.8420i	0.667683	−	1.15646i
$623$	−0.961181	−	1.66481i	−0.0385089	−	0.0666994i
$624$		0			0
$625$	−7.59854	+	13.1611i	−0.303941	+	0.526442i
$626$	−1.37786	−	2.38652i	−0.0550703	−	0.0953845i
$627$		0			0
$628$	−3.10290	+	5.37438i	−0.123819	+	0.214461i
$629$	20.8654			0.831956
$630$		0			0
$631$	24.2342	+	41.9749i	0.964749	+	1.67099i	0.710288	+	0.703911i	$0.248565\pi$
$631$	24.2342	+	41.9749i	0.964749	+	1.67099i	0.254461	+	0.967083i	$0.418102\pi$
$632$	−20.4286	−	35.3833i	−0.812605	−	1.40747i
$633$		0			0
$634$	−12.2629	−	21.2400i	−0.487024	−	0.843550i
$635$	−20.2866	−	35.1374i	−0.805049	−	1.39439i
$636$		0			0
$637$	−19.9623	+	14.9058i	−0.790934	+	0.590590i
$638$	−14.9015			−0.589956
$639$		0			0
$640$	−8.70603	+	15.0793i	−0.344136	+	0.596061i
$641$	−0.384354	+	0.665720i	−0.0151811	+	0.0262944i	−0.873516	−	0.486795i	$-0.838166\pi$
$641$	−0.384354	+	0.665720i	−0.0151811	+	0.0262944i	0.858335	+	0.513090i	$0.171499\pi$
$642$		0			0
$643$	−0.284528			−0.0112207			−0.00561034	−	0.999984i	$-0.501786\pi$
$643$	−0.284528			−0.0112207			−0.00561034	+	0.999984i	$0.501786\pi$
$644$	−0.553008			−0.0217916
$645$		0			0
$646$	5.27392	−	9.13470i	0.207500	−	0.359400i
$647$	−14.6716	+	25.4119i	−0.576798	+	0.999044i	0.419045	+	0.907965i	$0.362365\pi$
$647$	−14.6716	+	25.4119i	−0.576798	+	0.999044i	−0.995844	+	0.0910787i	$0.970969\pi$
$648$		0			0
$649$	11.2253			0.440633
$650$	32.4088	−	24.1996i	1.27118	−	0.949187i
$651$		0			0
$652$	1.81910	+	3.15077i	0.0712413	+	0.123394i
$653$	−24.8170	−	42.9843i	−0.971164	−	1.68211i	−0.692053	−	0.721846i	$-0.743294\pi$
$653$	−24.8170	−	42.9843i	−0.971164	−	1.68211i	−0.279111	−	0.960259i	$-0.590040\pi$
$654$		0			0
$655$	−6.32683	−	10.9584i	−0.247210	−	0.428180i
$656$	−3.72509	−	6.45205i	−0.145440	−	0.251910i
$657$		0			0
$658$	0.690524			0.0269194
$659$	−21.4051	+	37.0746i	−0.833823	+	1.44422i	0.0611628	+	0.998128i	$0.480519\pi$
$659$	−21.4051	+	37.0746i	−0.833823	+	1.44422i	−0.894985	+	0.446095i	$0.852814\pi$
$660$		0			0
$661$	17.6585	+	30.5855i	0.686837	+	1.18964i	0.972856	+	0.231413i	$0.0743348\pi$
$661$	17.6585	+	30.5855i	0.686837	+	1.18964i	−0.286019	+	0.958224i	$0.592332\pi$
$662$	−10.5034	+	18.1924i	−0.408225	+	0.707067i
$663$		0			0
$664$	−19.8212	−	34.3313i	−0.769212	−	1.33231i
$665$	−0.943427	+	1.63406i	−0.0365845	+	0.0633663i
$666$		0			0
$667$	−16.1246	−	27.9285i	−0.624345	−	1.08140i
$668$	−2.98363	−	5.16780i	−0.115440	−	0.199948i
$669$		0			0
$670$	37.8699			1.46304
$671$	3.29940	−	5.71473i	0.127372	−	0.220615i
$672$		0			0
$673$	34.7386			1.33907			0.669537	−	0.742779i	$-0.266493\pi$
$673$	34.7386			1.33907			0.669537	+	0.742779i	$0.266493\pi$
$674$	15.0340	−	26.0397i	0.579089	−	1.00301i
$675$		0			0
$676$	6.94940	−	1.66806i	0.267285	−	0.0641562i
$677$	−9.05262	−	15.6796i	−0.347920	−	0.602616i	0.637959	−	0.770070i	$-0.279779\pi$
$677$	−9.05262	−	15.6796i	−0.347920	−	0.602616i	−0.985880	+	0.167454i	$0.946445\pi$
$678$		0			0
$679$	0.565444	+	0.979378i	0.0216998	+	0.0375851i
$680$	61.3059			2.35097
$681$		0			0
$682$	5.10051	−	8.83434i	0.195309	−	0.338284i
$683$	11.6147	+	20.1173i	0.444426	+	0.769768i	0.998012	−	0.0630237i	$-0.0200744\pi$
$683$	11.6147	+	20.1173i	0.444426	+	0.769768i	−0.553586	+	0.832792i	$0.686741\pi$
$684$		0			0
$685$	−29.8062	−	51.6259i	−1.13884	−	1.97252i
$686$	−5.03293			−0.192158
$687$		0			0
$688$	−0.0270790	+	0.0469023i	−0.00103238	+	0.00178813i
$689$	3.03054	+	25.6100i	0.115454	+	0.975662i
$690$		0			0
$691$	−4.50951			−0.171550			−0.0857748	−	0.996315i	$-0.527337\pi$
$691$	−4.50951			−0.171550			−0.0857748	+	0.996315i	$0.527337\pi$
$692$	−0.0569276	+	0.0986015i	−0.00216406	+	0.00374827i
$693$		0			0
$694$	12.1973			0.463002
$695$	−40.7691	+	70.6142i	−1.54646	+	2.67855i
$696$		0			0
$697$	−7.56549	+	13.1038i	−0.286564	+	0.496343i
$698$	27.1789			1.02874
$699$		0			0
$700$	−1.53865			−0.0581557
$701$	12.6104			0.476288			0.238144	−	0.971230i	$-0.423461\pi$
$701$	12.6104			0.476288			0.238144	+	0.971230i	$0.423461\pi$
$702$		0			0
$703$	−6.56297			−0.247527
$704$	−11.3354			−0.427219
$705$		0			0
$706$	−29.9882			−1.12862
$707$	−0.749876	+	1.29882i	−0.0282020	+	0.0488473i
$708$		0			0
$709$	25.1270	−	43.5212i	0.943662	−	1.63447i	0.185255	−	0.982690i	$-0.440689\pi$
$709$	25.1270	−	43.5212i	0.943662	−	1.63447i	0.758407	−	0.651781i	$-0.225978\pi$
$710$	42.2896			1.58710
$711$		0			0
$712$	9.82298	−	17.0139i	0.368132	−	0.637623i
$713$	22.0766			0.826774
$714$		0			0
$715$	16.1012	+	6.91805i	0.602149	+	0.258720i
$716$	−2.74235	+	4.74989i	−0.102486	+	0.177512i
$717$		0			0
$718$	43.0563			1.60685
$719$	−21.5058	−	37.2492i	−0.802031	−	1.38916i	−0.918277	−	0.395939i	$-0.870419\pi$
$719$	−21.5058	−	37.2492i	−0.802031	−	1.38916i	0.116246	−	0.993221i	$-0.462914\pi$
$720$		0			0
$721$	0.651259	+	1.12801i	0.0242542	+	0.0420094i
$722$	9.78164	−	16.9423i	0.364035	−	0.630527i
$723$		0			0
$724$	−7.67448			−0.285220
$725$	−44.8639	−	77.7066i	−1.66620	−	2.88595i
$726$		0			0
$727$	6.80760	+	11.7911i	0.252480	+	0.437308i	0.964208	−	0.265147i	$-0.0854205\pi$
$727$	6.80760	+	11.7911i	0.252480	+	0.437308i	−0.711728	+	0.702455i	$0.752087\pi$
$728$	3.05622	+	1.31314i	0.113271	+	0.0486681i
$729$		0			0
$730$	10.6962	−	18.5263i	0.395884	−	0.685690i
$731$	0.109993			0.00406823
$732$		0			0
$733$	23.0761	−	39.9690i	0.852336	−	1.47629i	−0.0267594	−	0.999642i	$-0.508519\pi$
$733$	23.0761	−	39.9690i	0.852336	−	1.47629i	0.879095	−	0.476647i	$-0.158148\pi$
$734$	−16.1176			−0.594910
$735$		0			0
$736$	−5.04231	−	8.73353i	−0.185862	−	0.321922i
$737$	5.33849	+	9.24654i	0.196646	+	0.340601i
$738$		0			0
$739$	−0.339921	+	0.588761i	−0.0125042	+	0.0216579i	−0.872210	−	0.489132i	$-0.837314\pi$
$739$	−0.339921	+	0.588761i	−0.0125042	+	0.0216579i	0.859706	+	0.510790i	$0.170647\pi$
$740$	−4.11223	−	7.12260i	−0.151169	−	0.261832i
$741$		0			0
$742$	−1.29398	+	2.24125i	−0.0475036	+	0.0822787i
$743$	13.2649	+	22.9755i	0.486642	+	0.842889i	0.999882	−	0.0153563i	$-0.00488826\pi$
$743$	13.2649	+	22.9755i	0.486642	+	0.842889i	−0.513240	+	0.858245i	$0.671555\pi$
$744$		0			0
$745$	−24.3541	+	42.1826i	−0.892266	+	1.54545i
$746$	8.60976			0.315226
$747$		0			0
$748$	1.86336	+	3.22743i	0.0681310	+	0.118006i
$749$	−0.473238	−	0.819672i	−0.0172917	−	0.0299502i
$750$		0			0
$751$	−16.0066	−	27.7242i	−0.584088	−	1.01167i	−0.994988	−	0.0999903i	$-0.968119\pi$
$751$	−16.0066	−	27.7242i	−0.584088	−	1.01167i	0.410900	−	0.911680i	$-0.365215\pi$
$752$	2.47931	+	4.29429i	0.0904111	+	0.156597i
$753$		0			0
$754$	4.91494	+	41.5344i	0.178992	+	1.51259i
$755$	47.0315			1.71165
$756$		0			0
$757$	10.5610	−	18.2922i	0.383846	−	0.664840i	−0.607763	−	0.794119i	$-0.707933\pi$
$757$	10.5610	−	18.2922i	0.383846	−	0.664840i	0.991608	+	0.129278i	$0.0412661\pi$
$758$	16.5556	−	28.6751i	0.601326	−	1.04153i
$759$		0			0
$760$	−19.2831			−0.699471
$761$	24.4460			0.886166			0.443083	−	0.896481i	$-0.353885\pi$
$761$	24.4460			0.886166			0.443083	+	0.896481i	$0.353885\pi$
$762$		0			0
$763$	−2.14417	+	3.71381i	−0.0776242	+	0.134449i
$764$	3.81508	−	6.60791i	0.138025	−	0.239066i
$765$		0			0
$766$	13.6383			0.492770
$767$	−3.70244	−	31.2879i	−0.133687	−	1.12974i
$768$		0			0
$769$	4.36070	+	7.55296i	0.157251	+	0.272367i	0.933876	−	0.357596i	$-0.116404\pi$
$769$	4.36070	+	7.55296i	0.157251	+	0.272367i	−0.776625	+	0.629963i	$0.783070\pi$
$770$	0.879316	+	1.52302i	0.0316884	+	0.0548858i
$771$		0			0
$772$	2.21062	+	3.82890i	0.0795619	+	0.137805i
$773$	0.571592	+	0.990027i	0.0205587	+	0.0356088i	0.876122	−	0.482090i	$-0.160122\pi$
$773$	0.571592	+	0.990027i	0.0205587	+	0.0356088i	−0.855563	+	0.517699i	$0.826789\pi$
$774$		0			0
$775$	61.4244			2.20643
$776$	−5.77867	+	10.0090i	−0.207442	+	0.359300i
$777$		0			0
$778$	9.33801	+	16.1739i	0.334784	+	0.579863i
$779$	2.37964	−	4.12166i	0.0852596	−	0.147674i
$780$		0			0
$781$	5.96153	+	10.3257i	0.213320	+	0.369481i
$782$	10.6380	−	18.4255i	0.380413	−	0.658894i
$783$		0			0
$784$	−8.97665	−	15.5480i	−0.320595	−	0.555286i
$785$	21.3550	+	36.9879i	0.762192	+	1.32015i
$786$		0			0
$787$	14.5911			0.520115			0.260058	−	0.965593i	$-0.416258\pi$
$787$	14.5911			0.520115			0.260058	+	0.965593i	$0.416258\pi$
$788$	0.826834	−	1.43212i	0.0294547	−	0.0510171i
$789$		0			0
$790$	−60.6274			−2.15702
$791$	0.792866	−	1.37328i	0.0281911	−	0.0488283i
$792$		0			0
$793$	−17.0167	−	7.31142i	−0.604281	−	0.259636i
$794$	−7.04087	−	12.1951i	−0.249871	−	0.432789i
$795$		0			0
$796$	5.73931	+	9.94077i	0.203424	+	0.352341i
$797$	19.7945			0.701158			0.350579	−	0.936533i	$-0.385985\pi$
$797$	19.7945			0.701158			0.350579	+	0.936533i	$0.385985\pi$
$798$		0			0
$799$	5.03537	−	8.72151i	0.178138	−	0.308545i
$800$	−14.0294	−	24.2996i	−0.496014	−	0.859121i
$801$		0			0
$802$	0.430943	+	0.746415i	0.0152171	+	0.0263568i
$803$	6.03133			0.212841
$804$		0			0
$805$	−1.90297	+	3.29605i	−0.0670710	+	0.116170i
$806$	−26.3059	−	11.3026i	−0.926587	−	0.398119i
$807$		0			0
$808$	−15.3270			−0.539203
$809$	−13.6595	+	23.6589i	−0.480241	+	0.831802i	−0.999743	−	0.0226673i	$-0.992784\pi$
$809$	−13.6595	+	23.6589i	−0.480241	+	0.831802i	0.519502	+	0.854469i	$0.326117\pi$
$810$		0			0
$811$	38.3231			1.34571			0.672854	−	0.739776i	$-0.265068\pi$
$811$	38.3231			1.34571			0.672854	+	0.739776i	$0.265068\pi$
$812$	0.795523	−	1.37789i	0.0279174	−	0.0483543i
$813$		0			0
$814$	−3.05849	+	5.29746i	−0.107200	+	0.185676i
$815$	25.0390			0.877078
$816$		0			0
$817$	−0.0345970			−0.00121040
$818$	−4.20774			−0.147120
$819$		0			0
$820$	5.96416			0.208278
$821$	−54.5956			−1.90540			−0.952700	−	0.303911i	$-0.901708\pi$
$821$	−54.5956			−1.90540			−0.952700	+	0.303911i	$0.901708\pi$
$822$		0			0
$823$	−52.8320			−1.84161			−0.920804	−	0.390026i	$-0.872466\pi$
$823$	−52.8320			−1.84161			−0.920804	+	0.390026i	$0.872466\pi$
$824$	−6.65567	+	11.5280i	−0.231861	+	0.401596i
$825$		0			0
$826$	1.58087	−	2.73815i	0.0550056	−	0.0952725i
$827$	−20.8919			−0.726482			−0.363241	−	0.931695i	$-0.618330\pi$
$827$	−20.8919			−0.726482			−0.363241	+	0.931695i	$0.618330\pi$
$828$		0			0
$829$	−7.33261	+	12.7005i	−0.254672	+	0.441105i	−0.964806	−	0.262961i	$-0.915301\pi$
$829$	−7.33261	+	12.7005i	−0.254672	+	0.441105i	0.710134	+	0.704066i	$0.248634\pi$
$830$	−58.8249			−2.04184
$831$		0			0
$832$	3.73874	+	31.5948i	0.129618	+	1.09535i
$833$	−18.2312	+	31.5773i	−0.631673	+	1.09409i
$834$		0			0
$835$	−41.0683			−1.42123
$836$	−0.586098	−	1.01515i	−0.0202706	−	0.0351098i
$837$		0			0
$838$	−11.0065	−	19.0638i	−0.380213	−	0.658549i
$839$	2.25553	−	3.90669i	0.0778696	−	0.134874i	−0.824461	−	0.565919i	$-0.808522\pi$
$839$	2.25553	−	3.90669i	0.0778696	−	0.134874i	0.902331	+	0.431045i	$0.141855\pi$
$840$		0			0
$841$	63.7831			2.19942
$842$	−2.05056	−	3.55168i	−0.0706670	−	0.122399i
$843$		0			0
$844$	−4.97114	−	8.61026i	−0.171114	−	0.296377i
$845$	13.9718	−	47.1599i	0.480644	−	1.62235i
$846$		0			0
$847$	1.40460	−	2.43283i	0.0482625	−	0.0835930i
$848$	−18.5841			−0.638179
$849$		0			0
$850$	29.5984	−	51.2659i	1.01522	−	1.75841i
$851$	−13.2381			−0.453795
$852$		0			0
$853$	11.4853	+	19.8932i	0.393250	+	0.681129i	0.992876	−	0.119151i	$-0.0380174\pi$
$853$	11.4853	+	19.8932i	0.393250	+	0.681129i	−0.599626	+	0.800280i	$0.704684\pi$
$854$	−0.929315	−	1.60962i	−0.0318005	−	0.0550801i
$855$		0			0
$856$	4.83635	−	8.37680i	0.165303	−	0.286313i
$857$	20.3594	+	35.2635i	0.695463	+	1.20458i	0.970024	+	0.243008i	$0.0781340\pi$
$857$	20.3594	+	35.2635i	0.695463	+	1.20458i	−0.274561	+	0.961570i	$0.588533\pi$
$858$		0			0
$859$	−26.7637	+	46.3561i	−0.913167	+	1.58165i	−0.103603	+	0.994619i	$0.533037\pi$
$859$	−26.7637	+	46.3561i	−0.913167	+	1.58165i	−0.809563	+	0.587033i	$0.800296\pi$
$860$	−0.0216778	−	0.0375471i	−0.000739208	−	0.00128035i
$861$		0			0
$862$	9.04637	−	15.6688i	0.308121	−	0.533681i
$863$	−26.8211			−0.913000			−0.456500	−	0.889724i	$-0.650897\pi$
$863$	−26.8211			−0.913000			−0.456500	+	0.889724i	$0.650897\pi$
$864$		0			0
$865$	0.391791	+	0.678601i	0.0133213	+	0.0230731i
$866$	1.21785	+	2.10938i	0.0413842	+	0.0716796i
$867$		0			0
$868$	0.544586	+	0.943251i	0.0184845	+	0.0320160i
$869$	−8.54659	−	14.8031i	−0.289923	−	0.502162i
$870$		0			0
$871$	24.0117	−	17.9295i	0.813606	−	0.607519i
$872$	−43.8255			−1.48412
$873$		0			0
$874$	−3.34605	+	5.79553i	−0.113182	+	0.196037i
$875$	−2.45274	+	4.24827i	−0.0829178	+	0.143618i
$876$		0			0
$877$	−24.6341			−0.831834			−0.415917	−	0.909403i	$-0.636539\pi$
$877$	−24.6341			−0.831834			−0.415917	+	0.909403i	$0.636539\pi$
$878$	15.8641			0.535386
$879$		0			0
$880$	−6.31432	+	10.9367i	−0.212856	+	0.368677i
$881$	14.7520	−	25.5512i	0.497008	−	0.860843i	−0.502986	−	0.864294i	$-0.667765\pi$
$881$	14.7520	−	25.5512i	0.497008	−	0.860843i	0.999994	+	0.00345150i	$0.00109865\pi$
$882$		0			0
$883$	−29.2625			−0.984761			−0.492380	−	0.870380i	$-0.663873\pi$
$883$	−29.2625			−0.984761			−0.492380	+	0.870380i	$0.663873\pi$
$884$	8.38110	−	6.25816i	0.281887	−	0.210485i
$885$		0			0
$886$	6.60307	+	11.4369i	0.221834	+	0.384229i
$887$	4.13251	+	7.15771i	0.138756	+	0.240332i	0.927026	−	0.374997i	$-0.122356\pi$
$887$	4.13251	+	7.15771i	0.138756	+	0.240332i	−0.788270	+	0.615330i	$0.789023\pi$
$888$		0			0
$889$	−1.61098	−	2.79031i	−0.0540307	−	0.0935839i
$890$	−14.5762	−	25.2467i	−0.488595	−	0.846271i
$891$		0			0
$892$	−12.5013			−0.418574
$893$	−1.58382	+	2.74326i	−0.0530005	+	0.0917995i
$894$		0			0
$895$	18.8736	+	32.6900i	0.630874	+	1.09271i
$896$	−0.691357	+	1.19747i	−0.0230966	+	0.0400045i
$897$		0			0
$898$	21.8539	+	37.8521i	0.729274	+	1.26314i
$899$	−31.7580	+	55.0064i	−1.05919	+	1.83457i
$900$		0			0
$901$	18.8717	+	32.6867i	0.628708	+	1.08895i
$902$	−2.21793	−	3.84157i	−0.0738491	−	0.127910i
$903$		0			0
$904$	16.2057			0.538994
$905$	−26.4089	+	45.7415i	−0.877861	+	1.52050i
$906$		0			0
$907$	18.4346			0.612111			0.306056	−	0.952014i	$-0.400991\pi$
$907$	18.4346			0.612111			0.306056	+	0.952014i	$0.400991\pi$
$908$	−1.35002	+	2.33830i	−0.0448019	+	0.0775991i
$909$		0			0
$910$	3.95503	−	2.95322i	0.131108	−	0.0978983i
$911$	23.0212	+	39.8739i	0.762726	+	1.32108i	0.941441	+	0.337179i	$0.109473\pi$
$911$	23.0212	+	39.8739i	0.762726	+	1.32108i	−0.178715	+	0.983901i	$0.557194\pi$
$912$		0			0
$913$	−8.29250	−	14.3630i	−0.274442	−	0.475347i
$914$	−40.9192			−1.35349
$915$		0			0
$916$	−1.08323	+	1.87621i	−0.0357910	+	0.0619918i
$917$	−0.502422	−	0.870220i	−0.0165914	−	0.0287372i
$918$		0			0
$919$	16.5071	+	28.5912i	0.544520	+	0.943136i	0.998637	+	0.0521939i	$0.0166214\pi$
$919$	16.5071	+	28.5912i	0.544520	+	0.943136i	−0.454117	+	0.890942i	$0.650045\pi$
$920$	−38.8957			−1.28235
$921$		0			0
$922$	−6.94254	+	12.0248i	−0.228640	+	0.396017i
$923$	26.8141	−	20.0220i	0.882595	−	0.659033i
$924$		0			0
$925$	−36.8328			−1.21105
$926$	−18.2764	+	31.6557i	−0.600601	+	1.04027i
$927$		0			0
$928$	29.0142			0.952438
$929$	17.2035	−	29.7974i	0.564429	−	0.977620i	−0.432673	−	0.901551i	$-0.642430\pi$
$929$	17.2035	−	29.7974i	0.564429	−	0.977620i	0.997103	−	0.0760691i	$-0.0242370\pi$
$930$		0			0
$931$	5.73442	−	9.93231i	0.187938	−	0.325518i
$932$	1.37318			0.0449801
$933$		0			0
$934$	1.98416			0.0649238
$935$	25.6482			0.838786
$936$		0			0
$937$	−3.49544			−0.114191			−0.0570956	−	0.998369i	$-0.518184\pi$
$937$	−3.49544			−0.114191			−0.0570956	+	0.998369i	$0.518184\pi$
$938$	3.00730			0.0981917
$939$		0			0
$940$	−3.96957			−0.129473
$941$	11.7060	−	20.2754i	0.381605	−	0.660959i	−0.609687	−	0.792642i	$-0.708705\pi$
$941$	11.7060	−	20.2754i	0.381605	−	0.660959i	0.991292	+	0.131684i	$0.0420383\pi$
$942$		0			0
$943$	4.79995	−	8.31375i	0.156308	−	0.270733i
$944$	22.7043			0.738963
$945$		0			0
$946$	−0.0161230	+	0.0279258i	−0.000524203	+	0.000907946i
$947$	40.6066			1.31954			0.659769	−	0.751468i	$-0.270654\pi$
$947$	40.6066			1.31954			0.659769	+	0.751468i	$0.270654\pi$
$948$		0			0
$949$	−1.98931	−	16.8109i	−0.0645756	−	0.545705i
$950$	−9.30984	+	16.1251i	−0.302051	+	0.523168i
$951$		0			0
$952$	4.86838			0.157785
$953$	−24.9334	−	43.1859i	−0.807672	−	1.39893i	−0.914473	−	0.404648i	$-0.867394\pi$
$953$	−24.9334	−	43.1859i	−0.807672	−	1.39893i	0.106801	−	0.994280i	$-0.465939\pi$
$954$		0			0
$955$	−26.2564	−	45.4774i	−0.849637	−	1.47161i
$956$	−2.33997	+	4.05294i	−0.0756799	+	0.131082i
$957$		0			0
$958$	12.7501			0.411936
$959$	−2.36695	−	4.09968i	−0.0764328	−	0.132385i
$960$		0			0
$961$	−6.24036	−	10.8086i	−0.201302	−	0.348665i
$962$	15.7742	+	6.77756i	0.508580	+	0.218517i
$963$		0			0
$964$	4.46138	−	7.72734i	0.143691	−	0.248881i
$965$	30.4281			0.979515
$966$		0			0
$967$	5.80396	−	10.0528i	0.186643	−	0.323275i	−0.757486	−	0.652851i	$-0.773573\pi$
$967$	5.80396	−	10.0528i	0.186643	−	0.323275i	0.944129	+	0.329576i	$0.106906\pi$
$968$	28.7091			0.922745
$969$		0			0
$970$	8.57489	+	14.8522i	0.275323	+	0.476874i
$971$	−7.04458	−	12.2016i	−0.226071	−	0.391567i	0.730569	−	0.682839i	$-0.239255\pi$
$971$	−7.04458	−	12.2016i	−0.226071	−	0.391567i	−0.956640	+	0.291272i	$0.905922\pi$
$972$		0			0
$973$	−3.23753	+	5.60756i	−0.103790	+	0.179770i
$974$	16.0389	+	27.7802i	0.513920	+	0.890136i
$975$		0			0
$976$	6.67336	−	11.5586i	0.213609	−	0.369982i
$977$	−6.67495	−	11.5613i	−0.213550	−	0.369880i	0.739273	−	0.673406i	$-0.235169\pi$
$977$	−6.67495	−	11.5613i	−0.213550	−	0.369880i	−0.952823	+	0.303526i	$0.901836\pi$
$978$		0			0
$979$	4.10959	−	7.11802i	0.131343	−	0.227493i
$980$	14.3723			0.459107
$981$		0			0
$982$	14.0606	+	24.3536i	0.448690	+	0.777154i
$983$	8.77579	+	15.2001i	0.279904	+	0.484808i	0.971361	−	0.237610i	$-0.0763639\pi$
$983$	8.77579	+	15.2001i	0.279904	+	0.484808i	−0.691456	+	0.722418i	$0.743031\pi$
$984$		0			0
$985$	−5.69049	−	9.85622i	−0.181314	−	0.314045i
$986$	30.6062	+	53.0115i	0.974701	+	1.68823i
$987$		0			0
$988$	−2.63618	+	1.96844i	−0.0838681	+	0.0626243i
$989$	−0.0697851			−0.00221904
$990$		0			0
$991$	12.8289	−	22.2202i	0.407522	−	0.705849i	−0.587089	−	0.809522i	$-0.699726\pi$
$991$	12.8289	−	22.2202i	0.407522	−	0.705849i	0.994611	+	0.103673i	$0.0330596\pi$
$992$	−9.93104	+	17.2011i	−0.315311	+	0.546134i
$993$		0			0
$994$	3.35827			0.106518
$995$	78.9988			2.50443
$996$		0			0
$997$	−9.11468	+	15.7871i	−0.288665	+	0.499982i	−0.973491	−	0.228724i	$-0.926545\pi$
$997$	−9.11468	+	15.7871i	−0.288665	+	0.499982i	0.684826	+	0.728706i	$0.259878\pi$
$998$	−0.477110	+	0.826379i	−0.0151027	+	0.0261586i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	351.2.h.a.334.9		24
3.2	odd	2		117.2.h.a.22.4	yes	24
9.2	odd	6		117.2.f.a.61.9	✓	24
9.7	even	3		351.2.f.a.100.4		24
13.3	even	3		351.2.f.a.172.4		24
39.29	odd	6		117.2.f.a.94.9	yes	24
117.16	even	3	inner	351.2.h.a.289.9		24
117.29	odd	6		117.2.h.a.16.4	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.2.f.a.61.9	✓	24	9.2	odd	6
117.2.f.a.94.9	yes	24	39.29	odd	6
117.2.h.a.16.4	yes	24	117.29	odd	6
117.2.h.a.22.4	yes	24	3.2	odd	2
351.2.f.a.100.4		24	9.7	even	3
351.2.f.a.172.4		24	13.3	even	3
351.2.h.a.289.9		24	117.16	even	3	inner
351.2.h.a.334.9		24	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:	\( N \)	\(=\)	\( 351 = 3^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	351.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.20426 q^{2} -0.549753 q^{4} +(-1.89177 + 3.27665i) q^{5} +(-0.150228 + 0.260203i) q^{7} -3.07057 q^{8} +(-2.27819 + 3.94594i) q^{10} -1.28462 q^{11} +(0.423704 + 3.58057i) q^{13} +(-0.180914 + 0.313352i) q^{14} -2.59827 q^{16} +(2.63848 + 4.56998i) q^{17} +(-0.829906 - 1.43744i) q^{19} +(1.04001 - 1.80135i) q^{20} -1.54702 q^{22} +(-1.67399 - 2.89944i) q^{23} +(-4.65760 - 8.06721i) q^{25} +(0.510251 + 4.31194i) q^{26} +(0.0825883 - 0.143047i) q^{28} +9.63240 q^{29} +(-3.29700 + 5.71056i) q^{31} +3.01215 q^{32} +(3.17742 + 5.50346i) q^{34} +(-0.568394 - 0.984488i) q^{35} +(1.97702 - 3.42430i) q^{37} +(-0.999424 - 1.73105i) q^{38} +(5.80882 - 10.0612i) q^{40} +(1.43368 + 2.48321i) q^{41} +(0.0104220 - 0.0180514i) q^{43} +0.706223 q^{44} +(-2.01592 - 3.49168i) q^{46} +(-0.954216 - 1.65275i) q^{47} +(3.45486 + 5.98400i) q^{49} +(-5.60898 - 9.71503i) q^{50} +(-0.232933 - 1.96843i) q^{52} +7.15248 q^{53} +(2.43021 - 4.20924i) q^{55} +(0.461286 - 0.798970i) q^{56} +11.5999 q^{58} -8.73826 q^{59} +(-2.56839 + 4.44858i) q^{61} +(-3.97045 + 6.87702i) q^{62} +8.82395 q^{64} +(-12.5338 - 5.38529i) q^{65} +(-4.15570 - 7.19788i) q^{67} +(-1.45051 - 2.51236i) q^{68} +(-0.684496 - 1.18558i) q^{70} +(-4.64070 - 8.03792i) q^{71} -4.69504 q^{73} +(2.38085 - 4.12376i) q^{74} +(0.456243 + 0.790236i) q^{76} +(0.192986 - 0.334261i) q^{77} +(6.65302 + 11.5234i) q^{79} +(4.91533 - 8.51360i) q^{80} +(1.72653 + 2.99044i) q^{82} +(6.45522 + 11.1808i) q^{83} -19.9656 q^{85} +(0.0125508 - 0.0217386i) q^{86} +3.94451 q^{88} +(-3.19907 + 5.54096i) q^{89} +(-0.995325 - 0.427653i) q^{91} +(0.920281 + 1.59397i) q^{92} +(-1.14913 - 1.99035i) q^{94} +6.27997 q^{95} +(1.88195 - 3.25964i) q^{97} +(4.16056 + 7.20630i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 2 q^{2} + 18 q^{4} + 2 q^{5} + 3 q^{7} + 18 q^{8} - 6 q^{11} - 2 q^{14} + 6 q^{16} - 6 q^{17} - 3 q^{19} + 11 q^{20} - 18 q^{22} - 17 q^{23} - 6 q^{25} + 12 q^{26} + 24 q^{29} - 6 q^{31} + 38 q^{32}+ \cdots + 61 q^{98}+O(q^{100}) \) 24 * q + 2 * q^2 + 18 * q^4 + 2 * q^5 + 3 * q^7 + 18 * q^8 - 6 * q^11 - 2 * q^14 + 6 * q^16 - 6 * q^17 - 3 * q^19 + 11 * q^20 - 18 * q^22 - 17 * q^23 - 6 * q^25 + 12 * q^26 + 24 * q^29 - 6 * q^31 + 38 * q^32 - 18 * q^35 - 3 * q^37 - 8 * q^38 - 12 * q^40 - 5 * q^41 - 3 * q^43 - 44 * q^44 - 6 * q^46 - 21 * q^47 + 3 * q^49 + 20 * q^50 - 24 * q^52 + 20 * q^53 + 3 * q^55 - 40 * q^56 + 18 * q^58 - 38 * q^59 - 6 * q^61 - 19 * q^62 - 42 * q^64 + 2 * q^65 - 6 * q^67 + 27 * q^70 - 14 * q^71 + 6 * q^73 - 29 * q^74 - 15 * q^76 - 4 * q^77 + 3 * q^79 + 16 * q^80 - 9 * q^82 + 33 * q^83 - 72 * q^86 - 78 * q^88 + q^89 - 6 * q^91 + 10 * q^92 - 9 * q^94 + 100 * q^95 + 24 * q^97 + 61 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

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Groups

Database

Properties

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