LMFDB - Embedded newform 387.2.h.g.208.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [387,2,Mod(208,387)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(387, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("387.208");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 387 = 3^{2} \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	387.h (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.09021055822$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 11x^{10} + 89x^{8} + 314x^{6} + 815x^{4} + 608x^{2} + 361 $ x^12 + 11x^10 + 89x^8 + 314x^6 + 815x^4 + 608*x^2 + 361
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			208.5
Root			$-0.953356 + 1.65126i$ of defining polynomial
Character	$\chi$	$=$	387.208
Dual form			387.2.h.g.307.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.90671 q^{2} +1.63555 q^{4} +(-0.795331 - 1.37755i) q^{5} +(2.01647 - 3.49262i) q^{7} -0.694898 q^{8} +O(q^{10})$	\(q+1.90671 q^{2} +1.63555 q^{4} +(-0.795331 - 1.37755i) q^{5} +(2.01647 - 3.49262i) q^{7} -0.694898 q^{8} +(-1.51647 - 2.62660i) q^{10} +4.19227 q^{11} +(0.417122 - 0.722476i) q^{13} +(3.84482 - 6.65943i) q^{14} -4.59607 q^{16} +(-2.09614 + 3.63061i) q^{17} +(3.38092 + 5.85592i) q^{19} +(-1.30080 - 2.25306i) q^{20} +7.99346 q^{22} +(-0.158025 - 0.273708i) q^{23} +(1.23490 - 2.13891i) q^{25} +(0.795331 - 1.37755i) q^{26} +(3.29804 - 5.71237i) q^{28} +(-5.24606 + 9.08644i) q^{29} +(-2.61581 - 4.53072i) q^{31} -7.37360 q^{32} +(-3.99673 + 6.92254i) q^{34} -6.41503 q^{35} +(-0.298037 - 0.516215i) q^{37} +(6.44643 + 11.1655i) q^{38} +(0.552674 + 0.957259i) q^{40} -2.48643 q^{41} +(6.06914 + 2.48305i) q^{43} +6.85668 q^{44} +(-0.301309 - 0.521882i) q^{46} -3.11853 q^{47} +(-4.63228 - 8.02334i) q^{49} +(2.35459 - 4.07828i) q^{50} +(0.682224 - 1.18165i) q^{52} +(2.54402 + 4.40637i) q^{53} +(-3.33424 - 5.77508i) q^{55} +(-1.40124 + 2.42702i) q^{56} +(-10.0027 + 17.3252i) q^{58} -10.6073 q^{59} +(4.56914 - 7.91398i) q^{61} +(-4.98760 - 8.63878i) q^{62} -4.86718 q^{64} -1.32700 q^{65} +(5.68495 + 9.84663i) q^{67} +(-3.42834 + 5.93806i) q^{68} -12.2316 q^{70} +(4.50832 - 7.80864i) q^{71} +(-2.61581 + 4.53072i) q^{73} +(-0.568271 - 0.984273i) q^{74} +(5.52966 + 9.57766i) q^{76} +(8.45358 - 14.6420i) q^{77} +(-2.18823 + 3.79012i) q^{79} +(3.65540 + 6.33134i) q^{80} -4.74090 q^{82} +(1.69110 + 2.92906i) q^{83} +6.66849 q^{85} +(11.5721 + 4.73446i) q^{86} -2.91320 q^{88} +(5.20322 + 9.01224i) q^{89} +(-1.68222 - 2.91370i) q^{91} +(-0.258459 - 0.447663i) q^{92} -5.94613 q^{94} +(5.37789 - 9.31478i) q^{95} +0.563139 q^{97} +(-8.83243 - 15.2982i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 20 q^{4} + 2 q^{7}+O(q^{10}) $ 12 * q + 20 * q^4 + 2 * q^7	$ 12 q + 20 q^{4} + 2 q^{7} + 4 q^{10} - 6 q^{13} + 12 q^{16} + 18 q^{19} - 16 q^{22} + 4 q^{25} + 6 q^{28} + 2 q^{31} + 8 q^{34} + 30 q^{37} - 4 q^{40} + 40 q^{43} - 26 q^{46} + 8 q^{52} - 18 q^{55} - 54 q^{58} + 22 q^{61} + 8 q^{64} + 2 q^{67} - 80 q^{70} + 2 q^{73} - 34 q^{76} - 16 q^{79} - 36 q^{82} + 36 q^{85} - 148 q^{88} - 20 q^{91} - 140 q^{94} - 16 q^{97}+O(q^{100}) $ 12 * q + 20 * q^4 + 2 * q^7 + 4 * q^10 - 6 * q^13 + 12 * q^16 + 18 * q^19 - 16 * q^22 + 4 * q^25 + 6 * q^28 + 2 * q^31 + 8 * q^34 + 30 * q^37 - 4 * q^40 + 40 * q^43 - 26 * q^46 + 8 * q^52 - 18 * q^55 - 54 * q^58 + 22 * q^61 + 8 * q^64 + 2 * q^67 - 80 * q^70 + 2 * q^73 - 34 * q^76 - 16 * q^79 - 36 * q^82 + 36 * q^85 - 148 * q^88 - 20 * q^91 - 140 * q^94 - 16 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/387\mathbb{Z}\right)^\times$.

$n$	$46$	$173$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	1.90671			1.34825			0.674125	−	0.738618i	$-0.264521\pi$
$2$	1.90671			1.34825			0.674125	+	0.738618i	$0.264521\pi$
$3$		0			0
$3$		0			0
$4$	1.63555			0.817776
$5$	−0.795331	−	1.37755i	−0.355683	−	0.616061i	0.631552	−	0.775334i	$-0.282418\pi$
$5$	−0.795331	−	1.37755i	−0.355683	−	0.616061i	−0.987235	+	0.159273i	$0.949085\pi$
$6$		0			0
$7$	2.01647	−	3.49262i	0.762153	−	1.32009i	−0.179586	−	0.983742i	$-0.557476\pi$
$7$	2.01647	−	3.49262i	0.762153	−	1.32009i	0.941739	−	0.336345i	$-0.109191\pi$
$8$	−0.694898			−0.245683
$9$		0			0
$10$	−1.51647	−	2.62660i	−0.479549	−	0.830603i
$11$	4.19227			1.26402			0.632009	−	0.774961i	$-0.282231\pi$
$11$	4.19227			1.26402			0.632009	+	0.774961i	$0.282231\pi$
$12$		0			0
$13$	0.417122	−	0.722476i	0.115689	−	0.200379i	−0.802366	−	0.596832i	$-0.796426\pi$
$13$	0.417122	−	0.722476i	0.115689	−	0.200379i	0.918055	+	0.396453i	$0.129759\pi$
$14$	3.84482	−	6.65943i	1.02757	−	1.77981i
$15$		0			0
$16$	−4.59607			−1.14902
$17$	−2.09614	+	3.63061i	−0.508388	+	0.880553i	0.491565	+	0.870841i	$0.336425\pi$
$17$	−2.09614	+	3.63061i	−0.508388	+	0.880553i	−0.999953	+	0.00971242i	$0.996908\pi$
$18$		0			0
$19$	3.38092	+	5.85592i	0.775635	+	1.34344i	0.934437	+	0.356129i	$0.115904\pi$
$19$	3.38092	+	5.85592i	0.775635	+	1.34344i	−0.158802	+	0.987311i	$0.550763\pi$
$20$	−1.30080	−	2.25306i	−0.290869	−	0.503800i
$21$		0			0
$22$	7.99346			1.70421
$23$	−0.158025	−	0.273708i	−0.0329505	−	0.0570720i	0.849080	−	0.528265i	$-0.177157\pi$
$23$	−0.158025	−	0.273708i	−0.0329505	−	0.0570720i	−0.882030	+	0.471192i	$0.843824\pi$
$24$		0			0
$25$	1.23490	−	2.13891i	0.246980	−	0.427781i
$26$	0.795331	−	1.37755i	0.155977	−	0.270160i
$27$		0			0
$28$	3.29804	−	5.71237i	0.623270	−	1.07954i
$29$	−5.24606	+	9.08644i	−0.974169	+	1.68731i	−0.291519	+	0.956565i	$0.594161\pi$
$29$	−5.24606	+	9.08644i	−0.974169	+	1.68731i	−0.682650	+	0.730745i	$0.739173\pi$
$30$		0			0
$31$	−2.61581	−	4.53072i	−0.469814	−	0.813741i	0.529590	−	0.848253i	$-0.322346\pi$
$31$	−2.61581	−	4.53072i	−0.469814	−	0.813741i	−0.999404	+	0.0345120i	$0.989012\pi$
$32$	−7.37360			−1.30348
$33$		0			0
$34$	−3.99673	+	6.92254i	−0.685433	+	1.18721i
$35$	−6.41503			−1.08434
$36$		0			0
$37$	−0.298037	−	0.516215i	−0.0489970	−	0.0848652i	0.840487	−	0.541832i	$-0.182269\pi$
$37$	−0.298037	−	0.516215i	−0.0489970	−	0.0848652i	−0.889484	+	0.456967i	$0.848936\pi$
$38$	6.44643	+	11.1655i	1.04575	+	1.81129i
$39$		0			0
$40$	0.552674	+	0.957259i	0.0873854	+	0.151356i
$41$	−2.48643			−0.388314			−0.194157	−	0.980970i	$-0.562197\pi$
$41$	−2.48643			−0.388314			−0.194157	+	0.980970i	$0.562197\pi$
$42$		0			0
$43$	6.06914	+	2.48305i	0.925535	+	0.378661i
$43$	6.06914	+	2.48305i	0.925535	+	0.378661i
$44$	6.85668			1.03368
$45$		0			0
$46$	−0.301309	−	0.521882i	−0.0444256	−	0.0769473i
$47$	−3.11853			−0.454884			−0.227442	−	0.973792i	$-0.573036\pi$
$47$	−3.11853			−0.454884			−0.227442	+	0.973792i	$0.573036\pi$
$48$		0			0
$49$	−4.63228	−	8.02334i	−0.661754	−	1.14619i
$50$	2.35459	−	4.07828i	0.332990	−	0.576755i
$51$		0			0
$52$	0.682224	−	1.18165i	0.0946075	−	0.163865i
$53$	2.54402	+	4.40637i	0.349448	+	0.605261i	0.986151	−	0.165847i	$-0.0530359\pi$
$53$	2.54402	+	4.40637i	0.349448	+	0.605261i	−0.636704	+	0.771109i	$0.719703\pi$
$54$		0			0
$55$	−3.33424	−	5.77508i	−0.449589	−	0.778711i
$56$	−1.40124	+	2.42702i	−0.187248	+	0.324324i
$57$		0			0
$58$	−10.0027	+	17.3252i	−1.31342	+	2.27491i
$59$	−10.6073			−1.38095			−0.690477	−	0.723355i	$-0.742599\pi$
$59$	−10.6073			−1.38095			−0.690477	+	0.723355i	$0.742599\pi$
$60$		0			0
$61$	4.56914	−	7.91398i	0.585019	−	1.01328i	−0.409855	−	0.912151i	$-0.634421\pi$
$61$	4.56914	−	7.91398i	0.585019	−	1.01328i	0.994873	−	0.101131i	$-0.0322461\pi$
$62$	−4.98760	−	8.63878i	−0.633426	−	1.09713i
$63$		0			0
$64$	−4.86718			−0.608397
$65$	−1.32700			−0.164594
$66$		0			0
$67$	5.68495	+	9.84663i	0.694528	+	1.20296i	0.970340	+	0.241746i	$0.0777199\pi$
$67$	5.68495	+	9.84663i	0.694528	+	1.20296i	−0.275812	+	0.961212i	$0.588947\pi$
$68$	−3.42834	+	5.93806i	−0.415747	+	0.720095i
$69$		0			0
$70$	−12.2316			−1.46196
$71$	4.50832	−	7.80864i	0.535039	−	0.926715i	−0.464122	−	0.885771i	$-0.653630\pi$
$71$	4.50832	−	7.80864i	0.535039	−	0.926715i	0.999161	−	0.0409442i	$-0.0130366\pi$
$72$		0			0
$73$	−2.61581	+	4.53072i	−0.306158	+	0.530281i	−0.977518	−	0.210850i	$-0.932377\pi$
$73$	−2.61581	+	4.53072i	−0.306158	+	0.530281i	0.671361	+	0.741131i	$0.265710\pi$
$74$	−0.568271	−	0.984273i	−0.0660601	−	0.114419i
$75$		0			0
$76$	5.52966	+	9.57766i	0.634296	+	1.09863i
$77$	8.45358	−	14.6420i	0.963375	−	1.66861i
$78$		0			0
$79$	−2.18823	+	3.79012i	−0.246195	+	0.426422i	−0.962467	−	0.271399i	$-0.912514\pi$
$79$	−2.18823	+	3.79012i	−0.246195	+	0.426422i	0.716272	+	0.697821i	$0.245847\pi$
$80$	3.65540	+	6.33134i	0.408686	+	0.707865i
$81$		0			0
$82$	−4.74090			−0.523545
$83$	1.69110	+	2.92906i	0.185622	+	0.321506i	0.943786	−	0.330557i	$-0.107237\pi$
$83$	1.69110	+	2.92906i	0.185622	+	0.321506i	−0.758164	+	0.652064i	$0.773903\pi$
$84$		0			0
$85$	6.66849			0.723299
$86$	11.5721	+	4.73446i	1.24785	+	0.510530i
$87$		0			0
$88$	−2.91320			−0.310548
$89$	5.20322	+	9.01224i	0.551540	+	0.955296i	0.998164	+	0.0605737i	$0.0192930\pi$
$89$	5.20322	+	9.01224i	0.551540	+	0.955296i	−0.446624	+	0.894722i	$0.647374\pi$
$90$		0			0
$91$	−1.68222	−	2.91370i	−0.176345	−	0.305438i
$92$	−0.258459	−	0.447663i	−0.0269462	−	0.0466721i
$93$		0			0
$94$	−5.94613			−0.613297
$95$	5.37789	−	9.31478i	0.551760	−	0.955677i
$96$		0			0
$97$	0.563139			0.0571781			0.0285891	−	0.999591i	$-0.490899\pi$
$97$	0.563139			0.0571781			0.0285891	+	0.999591i	$0.490899\pi$
$98$	−8.83243	−	15.2982i	−0.892210	−	1.54535i
$99$		0			0
$100$	2.01974	−	3.49829i	0.201974	−	0.349829i
$101$	5.11943	−	8.86712i	0.509403	−	0.882311i	−0.490538	−	0.871420i	$-0.663200\pi$
$101$	5.11943	−	8.86712i	0.509403	−	0.882311i	0.999941	−	0.0108916i	$-0.00346697\pi$
$102$		0			0
$103$	−7.27830	+	12.6064i	−0.717152	+	1.24214i	0.244972	+	0.969530i	$0.421221\pi$
$103$	−7.27830	+	12.6064i	−0.717152	+	1.24214i	−0.962124	+	0.272613i	$0.912112\pi$
$104$	−0.289857	+	0.502047i	−0.0284228	+	0.0492297i
$105$		0			0
$106$	4.85071	+	8.40168i	0.471143	+	0.816043i
$107$	7.36319			0.711826			0.355913	−	0.934519i	$-0.384170\pi$
$107$	7.36319			0.711826			0.355913	+	0.934519i	$0.384170\pi$
$108$		0			0
$109$	−8.28103	−	14.3432i	−0.793179	−	1.37383i	−0.923989	−	0.382418i	$-0.875091\pi$
$109$	−8.28103	−	14.3432i	−0.793179	−	1.37383i	0.130811	−	0.991407i	$-0.458242\pi$
$110$	−6.35744	−	11.0114i	−0.606158	−	1.04990i
$111$		0			0
$112$	−9.26783	+	16.0524i	−0.875728	+	1.51681i
$113$	7.74203			0.728309			0.364155	−	0.931339i	$-0.381358\pi$
$113$	7.74203			0.728309			0.364155	+	0.931339i	$0.381358\pi$
$114$		0			0
$115$	−0.251365	+	0.435377i	−0.0234399	+	0.0405991i
$116$	−8.58021	+	14.8614i	−0.796652	+	1.37984i
$117$		0			0
$118$	−20.2251			−1.86187
$119$	8.45358	+	14.6420i	0.774938	+	1.34223i
$120$		0			0
$121$	6.57514			0.597740
$122$	8.71204	−	15.0897i	0.788751	−	1.36616i
$123$		0			0
$124$	−4.27830	−	7.41023i	−0.384202	−	0.665458i
$125$	−11.8819			−1.06275
$126$		0			0
$127$	0.927587			0.0823101			0.0411550	−	0.999153i	$-0.486896\pi$
$127$	0.927587			0.0823101			0.0411550	+	0.999153i	$0.486896\pi$
$128$	5.46688			0.483209
$129$		0			0
$130$	−2.53020			−0.221914
$131$	−12.2608			−1.07123			−0.535614	−	0.844463i	$-0.679920\pi$
$131$	−12.2608			−1.07123			−0.535614	+	0.844463i	$0.679920\pi$
$132$		0			0
$133$	27.2700			2.36461
$134$	10.8396	+	18.7747i	0.936396	+	1.62189i
$135$		0			0
$136$	1.45660	−	2.52290i	0.124902	−	0.216337i
$137$	11.4403			0.977409			0.488704	−	0.872449i	$-0.337470\pi$
$137$	11.4403			0.977409			0.488704	+	0.872449i	$0.337470\pi$
$138$		0			0
$139$	−1.08888	−	1.88600i	−0.0923576	−	0.159968i	0.816145	−	0.577847i	$-0.196107\pi$
$139$	−1.08888	−	1.88600i	−0.0923576	−	0.159968i	−0.908503	+	0.417879i	$0.862774\pi$
$140$	−10.4921			−0.886746
$141$		0			0
$142$	8.59607	−	14.8888i	0.721366	−	1.24944i
$143$	1.74869	−	3.02881i	0.146233	−	0.253282i
$144$		0			0
$145$	16.6894			1.38598
$146$	−4.98760	+	8.63878i	−0.412777	+	0.714951i
$147$		0			0
$148$	−0.487455	−	0.844296i	−0.0400685	−	0.0694007i
$149$	−4.37649	−	7.58030i	−0.358536	−	0.621003i	0.629180	−	0.777259i	$-0.283391\pi$
$149$	−4.37649	−	7.58030i	−0.358536	−	0.621003i	−0.987717	+	0.156257i	$0.950057\pi$
$150$		0			0
$151$	−20.4633			−1.66528			−0.832638	−	0.553818i	$-0.813170\pi$
$151$	−20.4633			−1.66528			−0.832638	+	0.553818i	$0.813170\pi$
$152$	−2.34939	−	4.06926i	−0.190561	−	0.330061i
$153$		0			0
$154$	16.1185	−	27.9181i	1.29887	−	2.24971i
$155$	−4.16087	+	7.20684i	−0.334209	+	0.578868i
$156$		0			0
$157$	−1.29804	+	2.24827i	−0.103595	+	0.179431i	−0.913163	−	0.407594i	$-0.866368\pi$
$157$	−1.29804	+	2.24827i	−0.103595	+	0.179431i	0.809569	+	0.587025i	$0.199701\pi$
$158$	−4.17232	+	7.22666i	−0.331932	+	0.574923i
$159$		0			0
$160$	5.86445	+	10.1575i	0.463625	+	0.803023i
$161$	−1.27461			−0.100453
$162$		0			0
$163$	9.84744	−	17.0563i	0.771311	−	1.33595i	−0.165534	−	0.986204i	$-0.552935\pi$
$163$	9.84744	−	17.0563i	0.771311	−	1.33595i	0.936845	−	0.349746i	$-0.113732\pi$
$164$	−4.06668			−0.317554
$165$		0			0
$166$	3.22443	+	5.58488i	0.250264	+	0.433471i
$167$	−7.97950	−	13.8209i	−0.617472	−	1.06949i	−0.989945	−	0.141451i	$-0.954823\pi$
$167$	−7.97950	−	13.8209i	−0.617472	−	1.06949i	0.372473	−	0.928043i	$-0.378510\pi$
$168$		0			0
$169$	6.15202	+	10.6556i	0.473232	+	0.819662i
$170$	12.7149			0.975187
$171$		0			0
$172$	9.92639	+	4.06116i	0.756881	+	0.309660i
$173$	−18.5502			−1.41035			−0.705173	−	0.709035i	$-0.749131\pi$
$173$	−18.5502			−1.41035			−0.705173	+	0.709035i	$0.749131\pi$
$174$		0			0
$175$	−4.98026	−	8.62606i	−0.376472	−	0.652069i
$176$	−19.2680			−1.45238
$177$		0			0
$178$	9.92104	+	17.1838i	0.743614	+	1.28798i
$179$	0.953356	−	1.65126i	0.0712572	−	0.123421i	−0.828195	−	0.560440i	$-0.810632\pi$
$179$	0.953356	−	1.65126i	0.0712572	−	0.123421i	0.899453	+	0.437018i	$0.143966\pi$
$180$		0			0
$181$	−1.37491	+	2.38142i	−0.102197	+	0.177010i	−0.912589	−	0.408877i	$-0.865920\pi$
$181$	−1.37491	+	2.38142i	−0.102197	+	0.177010i	0.810393	+	0.585887i	$0.199254\pi$
$182$	−3.20752	−	5.55558i	−0.237757	−	0.411807i
$183$		0			0
$184$	0.109811	+	0.190199i	0.00809540	+	0.0140216i
$185$	−0.474076	+	0.821123i	−0.0348547	+	0.0603702i
$186$		0			0
$187$	−8.78757	+	15.2205i	−0.642611	+	1.11303i
$188$	−5.10051			−0.371993
$189$		0			0
$190$	10.2541	−	17.7606i	0.743910	−	1.28849i
$191$	4.67155	+	8.09137i	0.338022	+	0.585471i	0.984061	−	0.177834i	$-0.0569090\pi$
$191$	4.67155	+	8.09137i	0.338022	+	0.585471i	−0.646039	+	0.763304i	$0.723576\pi$
$192$		0			0
$193$	9.46325			0.681180			0.340590	−	0.940212i	$-0.389373\pi$
$193$	9.46325			0.681180			0.340590	+	0.940212i	$0.389373\pi$
$194$	1.07374			0.0770904
$195$		0			0
$196$	−7.57633	−	13.1226i	−0.541167	−	0.937328i
$197$	10.2285	−	17.7162i	0.728748	−	1.26223i	−0.228665	−	0.973505i	$-0.573436\pi$
$197$	10.2285	−	17.7162i	0.728748	−	1.26223i	0.957413	−	0.288723i	$-0.0932306\pi$
$198$		0			0
$199$	−11.9330			−0.845911			−0.422956	−	0.906150i	$-0.639007\pi$
$199$	−11.9330			−0.845911			−0.422956	+	0.906150i	$0.639007\pi$
$200$	−0.858127	+	1.48632i	−0.0606788	+	0.105099i
$201$		0			0
$202$	9.76129	−	16.9070i	0.686802	−	1.18958i
$203$	21.1570	+	36.6450i	1.48493	+	2.57198i
$204$		0			0
$205$	1.97753	+	3.42518i	0.138117	+	0.239225i
$206$	−13.8776	+	24.0367i	−0.966900	+	1.67472i
$207$		0			0
$208$	−1.91712	+	3.32055i	−0.132928	+	0.230239i
$209$	14.1737	+	24.5496i	0.980416	+	1.69813i
$210$		0			0
$211$	−16.1712			−1.11327			−0.556636	−	0.830756i	$-0.687908\pi$
$211$	−16.1712			−1.11327			−0.556636	+	0.830756i	$0.687908\pi$
$212$	4.16087	+	7.20684i	0.285770	+	0.494968i
$213$		0			0
$214$	14.0395			0.959719
$215$	−1.40644	−	10.3354i	−0.0959186	−	0.704869i
$216$		0			0
$217$	−21.0988			−1.43228
$218$	−15.7895	−	27.3483i	−1.06940	−	1.85226i
$219$		0			0
$220$	−5.45333	−	9.44544i	−0.367663	−	0.636812i
$221$	1.74869	+	3.02881i	0.117629	+	0.203740i
$222$		0			0
$223$	−20.1658			−1.35040			−0.675199	−	0.737635i	$-0.735942\pi$
$223$	−20.1658			−1.35040			−0.675199	+	0.737635i	$0.735942\pi$
$224$	−14.8686	+	25.7532i	−0.993451	+	1.72071i
$225$		0			0
$226$	14.7618			0.981942
$227$	−12.3988	−	21.4754i	−0.822940	−	1.42537i	−0.903484	−	0.428622i	$-0.858999\pi$
$227$	−12.3988	−	21.4754i	−0.822940	−	1.42537i	0.0805443	−	0.996751i	$-0.474334\pi$
$228$		0			0
$229$	11.5027	−	19.9233i	0.760122	−	1.31657i	−0.182666	−	0.983175i	$-0.558473\pi$
$229$	11.5027	−	19.9233i	0.760122	−	1.31657i	0.942787	−	0.333394i	$-0.108194\pi$
$230$	−0.479280	+	0.830138i	−0.0316028	+	0.0547377i
$231$		0			0
$232$	3.64548	−	6.31415i	0.239337	−	0.414544i
$233$	12.9933	−	22.5051i	0.851219	−	1.47436i	−0.0288892	−	0.999583i	$-0.509197\pi$
$233$	12.9933	−	22.5051i	0.851219	−	1.47436i	0.880109	−	0.474772i	$-0.157470\pi$
$234$		0			0
$235$	2.48026	+	4.29594i	0.161794	+	0.280236i
$236$	−17.3488			−1.12931
$237$		0			0
$238$	16.1185	+	27.9181i	1.04481	+	1.80966i
$239$	−1.77488	−	3.07418i	−0.114807	−	0.198852i	0.802895	−	0.596120i	$-0.203292\pi$
$239$	−1.77488	−	3.07418i	−0.114807	−	0.198852i	−0.917703	+	0.397268i	$0.869958\pi$
$240$		0			0
$241$	3.48026	−	6.02799i	0.224183	−	0.388297i	−0.731891	−	0.681422i	$-0.761362\pi$
$241$	3.48026	−	6.02799i	0.224183	−	0.388297i	0.956074	+	0.293125i	$0.0946952\pi$
$242$	12.5369			0.805903
$243$		0			0
$244$	7.47307	−	12.9437i	0.478414	−	0.828638i
$245$	−7.36839	+	12.7624i	−0.470749	+	0.815362i
$246$		0			0
$247$	5.64101			0.358929
$248$	1.81772	+	3.14839i	0.115425	+	0.199923i
$249$		0			0
$250$	−22.6554			−1.43285
$251$	15.6064	−	27.0310i	0.985064	−	1.70618i	0.343413	−	0.939184i	$-0.388417\pi$
$251$	15.6064	−	27.0310i	0.985064	−	1.70618i	0.641651	−	0.766997i	$-0.278250\pi$
$252$		0			0
$253$	−0.662485	−	1.14746i	−0.0416501	−	0.0721400i
$254$	1.76864			0.110974
$255$		0			0
$256$	20.1581			1.25988
$257$	−27.8409			−1.73667			−0.868335	−	0.495979i	$-0.834809\pi$
$257$	−27.8409			−1.73667			−0.868335	+	0.495979i	$0.834809\pi$
$258$		0			0
$259$	−2.40393			−0.149373
$260$	−2.17038			−0.134601
$261$		0			0
$262$	−23.3778			−1.44428
$263$	11.4979	+	19.9149i	0.708989	+	1.22800i	0.965233	+	0.261392i	$0.0841817\pi$
$263$	11.4979	+	19.9149i	0.708989	+	1.22800i	−0.256244	+	0.966612i	$0.582485\pi$
$264$		0			0
$265$	4.04667	−	7.00904i	0.248585	−	0.430562i
$266$	51.9961			3.18808
$267$		0			0
$268$	9.29804	+	16.1047i	0.567968	+	0.983749i
$269$	18.3826			1.12081			0.560405	−	0.828219i	$-0.310646\pi$
$269$	18.3826			1.12081			0.560405	+	0.828219i	$0.310646\pi$
$270$		0			0
$271$	−1.82051	+	3.15321i	−0.110588	+	0.191544i	−0.916007	−	0.401161i	$-0.868607\pi$
$271$	−1.82051	+	3.15321i	−0.110588	+	0.191544i	0.805420	+	0.592705i	$0.201940\pi$
$272$	9.63399	−	16.6866i	0.584147	−	1.01177i
$273$		0			0
$274$	21.8133			1.31779
$275$	5.17703	−	8.96687i	0.312186	−	0.540723i
$276$		0			0
$277$	6.96379	+	12.0616i	0.418414	+	0.724714i	0.995780	−	0.0917713i	$-0.0292529\pi$
$277$	6.96379	+	12.0616i	0.418414	+	0.724714i	−0.577366	+	0.816485i	$0.695920\pi$
$278$	−2.07618	−	3.59605i	−0.124521	−	0.215677i
$279$		0			0
$280$	4.45779			0.266404
$281$	−13.4360	−	23.2718i	−0.801523	−	1.38828i	−0.918613	−	0.395158i	$-0.870690\pi$
$281$	−13.4360	−	23.2718i	−0.801523	−	1.38828i	0.117090	−	0.993121i	$-0.462643\pi$
$282$		0			0
$283$	−1.43959	+	2.49344i	−0.0855748	+	0.148220i	−0.905636	−	0.424056i	$-0.860606\pi$
$283$	−1.43959	+	2.49344i	−0.0855748	+	0.148220i	0.820061	+	0.572276i	$0.193939\pi$
$284$	7.37360	−	12.7714i	0.437542	−	0.757846i
$285$		0			0
$286$	3.33424	−	5.77508i	0.197158	−	0.341488i
$287$	−5.01380	+	8.68415i	−0.295955	+	0.512609i
$288$		0			0
$289$	−0.287571	−	0.498088i	−0.0169159	−	0.0292993i
$290$	31.8219			1.86865
$291$		0			0
$292$	−4.27830	+	7.41023i	−0.250368	+	0.433651i
$293$	19.5820			1.14399			0.571996	−	0.820257i	$-0.306169\pi$
$293$	19.5820			1.14399			0.571996	+	0.820257i	$0.306169\pi$
$294$		0			0
$295$	8.43632	+	14.6121i	0.491181	+	0.850751i
$296$	0.207105	+	0.358717i	0.0120377	+	0.0208500i
$297$		0			0
$298$	−8.34471	−	14.4535i	−0.483396	−	0.837266i
$299$	−0.263663			−0.0152480
$300$		0			0
$301$	20.9106	−	16.1902i	1.20527	−	0.933190i
$302$	−39.0175			−2.24521
$303$		0			0
$304$	−15.5389	−	26.9142i	−0.891219	−	1.54364i
$305$	−14.5359			−0.832324
$306$		0			0
$307$	4.24809	+	7.35791i	0.242451	+	0.419938i	0.961412	−	0.275113i	$-0.0887151\pi$
$307$	4.24809	+	7.35791i	0.242451	+	0.419938i	−0.718961	+	0.695051i	$0.755382\pi$
$308$	13.8263	−	23.9478i	0.787825	−	1.36455i
$309$		0			0
$310$	−7.93359	+	13.7414i	−0.450598	+	0.780458i
$311$	5.72014	+	9.90757i	0.324359	+	0.561807i	0.981382	−	0.192064i	$-0.0615180\pi$
$311$	5.72014	+	9.90757i	0.324359	+	0.561807i	−0.657023	+	0.753870i	$0.728185\pi$
$312$		0			0
$313$	−4.11308	−	7.12407i	−0.232485	−	0.402676i	0.726054	−	0.687638i	$-0.241352\pi$
$313$	−4.11308	−	7.12407i	−0.232485	−	0.402676i	−0.958539	+	0.284962i	$0.908019\pi$
$314$	−2.47498	+	4.28680i	−0.139671	+	0.241918i
$315$		0			0
$316$	−3.57896	+	6.19893i	−0.201332	+	0.348717i
$317$	−15.4945			−0.870256			−0.435128	−	0.900368i	$-0.643297\pi$
$317$	−15.4945			−0.870256			−0.435128	+	0.900368i	$0.643297\pi$
$318$		0			0
$319$	−21.9929	+	38.0928i	−1.23137	+	2.13279i
$320$	3.87102	+	6.70480i	0.216396	+	0.374810i
$321$		0			0
$322$	−2.43032			−0.135436
$323$	−28.3474			−1.57729
$324$		0			0
$325$	−1.03020	−	1.78437i	−0.0571455	−	0.0989789i
$326$	18.7762	−	32.5214i	1.03992	−	1.80119i
$327$		0			0
$328$	1.72781			0.0954024
$329$	−6.28841	+	10.8918i	−0.346691	+	0.600487i
$330$		0			0
$331$	−15.8002	+	27.3668i	−0.868459	+	1.50421i	−0.00488760	+	0.999988i	$0.501556\pi$
$331$	−15.8002	+	27.3668i	−0.868459	+	1.50421i	−0.863571	+	0.504227i	$0.831778\pi$
$332$	2.76587	+	4.79063i	0.151797	+	0.262920i
$333$		0			0
$334$	−15.2146	−	26.3525i	−0.832507	−	1.44194i
$335$	9.04284	−	15.6627i	0.494063	−	0.855742i
$336$		0			0
$337$	−3.41385	+	5.91296i	−0.185964	+	0.322100i	−0.943901	−	0.330228i	$-0.892874\pi$
$337$	−3.41385	+	5.91296i	−0.185964	+	0.322100i	0.757937	+	0.652328i	$0.226208\pi$
$338$	11.7301	+	20.3172i	0.638035	+	1.10511i
$339$		0			0
$340$	10.9067			0.591496
$341$	−10.9662	−	18.9940i	−0.593853	−	1.02858i
$342$		0			0
$343$	−9.13282			−0.493126
$344$	−4.21743	−	1.72546i	−0.227389	−	0.0930308i
$345$		0			0
$346$	−35.3699			−1.90150
$347$	9.41214	+	16.3023i	0.505270	+	0.875153i	0.999981	+	0.00609612i	$0.00194047\pi$
$347$	9.41214	+	16.3023i	0.505270	+	0.875153i	−0.494711	+	0.869057i	$0.664726\pi$
$348$		0			0
$349$	−5.14275	−	8.90750i	−0.275285	−	0.476807i	0.694922	−	0.719085i	$-0.255439\pi$
$349$	−5.14275	−	8.90750i	−0.275285	−	0.476807i	−0.970207	+	0.242278i	$0.922106\pi$
$350$	−9.49592	−	16.4474i	−0.507579	−	0.879152i
$351$		0			0
$352$	−30.9121			−1.64762
$353$	−4.94145	+	8.55885i	−0.263007	+	0.455542i	−0.967040	−	0.254626i	$-0.918048\pi$
$353$	−4.94145	+	8.55885i	−0.263007	+	0.455542i	0.704033	+	0.710168i	$0.251381\pi$
$354$		0			0
$355$	−14.3424			−0.761217
$356$	8.51014	+	14.7400i	0.451036	+	0.781218i
$357$		0			0
$358$	1.81778	−	3.14848i	0.0960724	−	0.166402i
$359$	−7.84247	+	13.5836i	−0.413910	+	0.716912i	−0.995313	−	0.0967028i	$-0.969170\pi$
$359$	−7.84247	+	13.5836i	−0.413910	+	0.716912i	0.581404	+	0.813615i	$0.302504\pi$
$360$		0			0
$361$	−13.3612	+	23.1422i	−0.703220	+	1.21801i
$362$	−2.62157	+	4.54068i	−0.137786	+	0.238653i
$363$		0			0
$364$	−2.75136	−	4.76550i	−0.144211	−	0.249780i
$365$	8.32175			0.435580
$366$		0			0
$367$	11.1619	+	19.3331i	0.582649	+	1.00918i	0.995164	+	0.0982265i	$0.0313170\pi$
$367$	11.1619	+	19.3331i	0.582649	+	1.00918i	−0.412515	+	0.910951i	$0.635350\pi$
$368$	0.726296	+	1.25798i	0.0378608	+	0.0655768i
$369$		0			0
$370$	−0.903926	+	1.56565i	−0.0469929	+	0.0813941i
$371$	20.5197			1.06533
$372$		0			0
$373$	3.82224	−	6.62031i	0.197908	−	0.342787i	−0.749942	−	0.661504i	$-0.769919\pi$
$373$	3.82224	−	6.62031i	0.197908	−	0.342787i	0.947850	+	0.318717i	$0.103252\pi$
$374$	−16.7554	+	29.0212i	−0.866400	+	1.50065i
$375$		0			0
$376$	2.16706			0.111757
$377$	4.37649	+	7.58030i	0.225401	+	0.390406i
$378$		0			0
$379$	17.4896			0.898383			0.449191	−	0.893436i	$-0.351712\pi$
$379$	17.4896			0.898383			0.449191	+	0.893436i	$0.351712\pi$
$380$	8.79582	−	15.2348i	0.451216	−	0.781529i
$381$		0			0
$382$	8.90731	+	15.4279i	0.455737	+	0.789360i
$383$	−37.1108			−1.89627			−0.948137	−	0.317861i	$-0.897035\pi$
$383$	−37.1108			−1.89627			−0.948137	+	0.317861i	$0.897035\pi$
$384$		0			0
$385$	−26.8936			−1.37062
$386$	18.0437			0.918400
$387$		0			0
$388$	0.921044			0.0467589
$389$	13.9666			0.708135			0.354068	−	0.935220i	$-0.384798\pi$
$389$	13.9666			0.708135			0.354068	+	0.935220i	$0.384798\pi$
$390$		0			0
$391$	1.32497			0.0670066
$392$	3.21896	+	5.57540i	0.162582	+	0.281600i
$393$		0			0
$394$	19.5027	−	33.7797i	0.982533	−	1.70180i
$395$	6.96145			0.350269
$396$		0			0
$397$	1.38419	+	2.39748i	0.0694704	+	0.120326i	0.898668	−	0.438629i	$-0.144536\pi$
$397$	1.38419	+	2.39748i	0.0694704	+	0.120326i	−0.829198	+	0.558955i	$0.811202\pi$
$398$	−22.7529			−1.14050
$399$		0			0
$400$	−5.67568	+	9.83057i	−0.283784	+	0.491528i
$401$	−11.2760	+	19.5306i	−0.563097	+	0.975313i	0.434127	+	0.900852i	$0.357057\pi$
$401$	−11.2760	+	19.5306i	−0.563097	+	0.975313i	−0.997224	+	0.0744610i	$0.976276\pi$
$402$		0			0
$403$	−4.36445			−0.217409
$404$	8.37310	−	14.5026i	0.416577	−	0.721533i
$405$		0			0
$406$	40.3404	+	69.8715i	2.00206	+	3.46767i
$407$	−1.24945	−	2.16411i	−0.0619330	−	0.107271i
$408$		0			0
$409$	−18.8517			−0.932157			−0.466078	−	0.884743i	$-0.654334\pi$
$409$	−18.8517			−0.932157			−0.466078	+	0.884743i	$0.654334\pi$
$410$	3.77058	+	6.53084i	0.186216	+	0.322535i
$411$		0			0
$412$	−11.9040	+	20.6184i	−0.586470	+	1.01580i
$413$	−21.3893	+	37.0473i	−1.05250	+	1.82298i
$414$		0			0
$415$	2.68996	−	4.65915i	0.132045	−	0.228709i
$416$	−3.07569	+	5.32724i	−0.150798	+	0.261190i
$417$		0			0
$418$	27.0252	+	46.8090i	1.32185	+	2.28950i
$419$	−19.1823			−0.937117			−0.468559	−	0.883432i	$-0.655226\pi$
$419$	−19.1823			−0.937117			−0.468559	+	0.883432i	$0.655226\pi$
$420$		0			0
$421$	−7.80850	+	13.5247i	−0.380563	+	0.659155i	−0.991143	−	0.132800i	$-0.957603\pi$
$421$	−7.80850	+	13.5247i	−0.380563	+	0.659155i	0.610580	+	0.791955i	$0.290936\pi$
$422$	−30.8339			−1.50097
$423$		0			0
$424$	−1.76783	−	3.06197i	−0.0858535	−	0.148703i
$425$	5.17703	+	8.96687i	0.251123	+	0.434957i
$426$		0			0
$427$	−18.4270	−	31.9166i	−0.891747	−	1.54455i
$428$	12.0429			0.582114
$429$		0			0
$430$	−2.68168	−	19.7067i	−0.129322	−	0.950339i
$431$	−12.9453			−0.623551			−0.311775	−	0.950156i	$-0.600924\pi$
$431$	−12.9453			−0.623551			−0.311775	+	0.950156i	$0.600924\pi$
$432$		0			0
$433$	10.1679	+	17.6114i	0.488640	+	0.846350i	0.999915	−	0.0130679i	$-0.00415975\pi$
$433$	10.1679	+	17.6114i	0.488640	+	0.846350i	−0.511274	+	0.859418i	$0.670826\pi$
$434$	−40.2293			−1.93107
$435$		0			0
$436$	−13.5441	−	23.4590i	−0.648642	−	1.12348i
$437$	1.06854	−	1.85077i	0.0511152	−	0.0885341i
$438$		0			0
$439$	9.32497	−	16.1513i	0.445057	−	0.770861i	−0.553000	−	0.833181i	$-0.686517\pi$
$439$	9.32497	−	16.1513i	0.445057	−	0.770861i	0.998056	+	0.0623210i	$0.0198502\pi$
$440$	2.31696	+	4.01309i	0.110457	+	0.191316i
$441$		0			0
$442$	3.33424	+	5.77508i	0.158594	+	0.274692i
$443$	−5.18326	+	8.97768i	−0.246264	+	0.426542i	−0.962486	−	0.271330i	$-0.912536\pi$
$443$	−5.18326	+	8.97768i	−0.246264	+	0.426542i	0.716222	+	0.697873i	$0.245870\pi$
$444$		0			0
$445$	8.27656	−	14.3354i	0.392347	−	0.679564i
$446$	−38.4503			−1.82067
$447$		0			0
$448$	−9.81450	+	16.9992i	−0.463692	+	0.803138i
$449$	−8.58021	−	14.8614i	−0.404925	−	0.701351i	0.589388	−	0.807850i	$-0.299369\pi$
$449$	−8.58021	−	14.8614i	−0.404925	−	0.701351i	−0.994313	+	0.106500i	$0.966036\pi$
$450$		0			0
$451$	−10.4238			−0.490836
$452$	12.6625			0.595594
$453$		0			0
$454$	−23.6410	−	40.9474i	−1.10953	−	1.92176i
$455$	−2.67585	+	4.63471i	−0.125446	+	0.217278i
$456$		0			0
$457$	−24.3788			−1.14039			−0.570197	−	0.821508i	$-0.693133\pi$
$457$	−24.3788			−1.14039			−0.570197	+	0.821508i	$0.693133\pi$
$458$	21.9324	−	37.9880i	1.02483	−	1.77506i
$459$		0			0
$460$	−0.411120	+	0.712081i	−0.0191686	+	0.0332009i
$461$	7.52642	+	13.0361i	0.350540	+	0.607153i	0.986344	−	0.164697i	$-0.0526647\pi$
$461$	7.52642	+	13.0361i	0.350540	+	0.607153i	−0.635804	+	0.771851i	$0.719331\pi$
$462$		0			0
$463$	−1.38692	−	2.40221i	−0.0644555	−	0.111640i	0.831997	−	0.554780i	$-0.187198\pi$
$463$	−1.38692	−	2.40221i	−0.0644555	−	0.111640i	−0.896452	+	0.443140i	$0.853864\pi$
$464$	24.1113	−	41.7620i	1.11934	−	1.93875i
$465$		0			0
$466$	24.7745	−	42.9107i	1.14766	−	1.98780i
$467$	0.126627	+	0.219324i	0.00585960	+	0.0101491i	0.868940	−	0.494917i	$-0.164801\pi$
$467$	0.126627	+	0.219324i	0.00585960	+	0.0101491i	−0.863081	+	0.505066i	$0.831468\pi$
$468$		0			0
$469$	45.8541			2.11735
$470$	4.72914	+	8.19112i	0.218139	+	0.377828i
$471$		0			0
$472$	7.37099			0.339277
$473$	25.4435	+	10.4096i	1.16989	+	0.478635i
$474$		0			0
$475$	16.7003			0.766264
$476$	13.8263	+	23.9478i	0.633726	+	1.09765i
$477$		0			0
$478$	−3.38419	−	5.86158i	−0.154789	−	0.268103i
$479$	4.14612	+	7.18130i	0.189441	+	0.328122i	0.945064	−	0.326885i	$-0.105999\pi$
$479$	4.14612	+	7.18130i	0.189441	+	0.328122i	−0.755623	+	0.655007i	$0.772666\pi$
$480$		0			0
$481$	−0.497270			−0.0226736
$482$	6.63586	−	11.4936i	0.302255	−	0.523521i
$483$		0			0
$484$	10.7540			0.488818
$485$	−0.447882	−	0.775755i	−0.0203373	−	0.0352252i
$486$		0			0
$487$	7.65921	−	13.2661i	0.347072	−	0.601146i	−0.638656	−	0.769492i	$-0.720509\pi$
$487$	7.65921	−	13.2661i	0.347072	−	0.601146i	0.985728	+	0.168346i	$0.0538426\pi$
$488$	−3.17508	+	5.49941i	−0.143729	+	0.248947i
$489$		0			0
$490$	−14.0494	+	24.3343i	−0.634687	+	1.09931i
$491$	−3.30171	+	5.71873i	−0.149004	+	0.258083i	−0.930860	−	0.365377i	$-0.880940\pi$
$491$	−3.30171	+	5.71873i	−0.149004	+	0.258083i	0.781855	+	0.623460i	$0.214273\pi$
$492$		0			0
$493$	−21.9929	−	38.0928i	−0.990511	−	1.71562i
$494$	10.7558			0.483926
$495$		0			0
$496$	12.0225	+	20.8235i	0.539825	+	0.935004i
$497$	−18.1818	−	31.4917i	−0.815564	−	1.41260i
$498$		0			0
$499$	0.271104	−	0.469566i	0.0121363	−	0.0210206i	−0.859893	−	0.510474i	$-0.829470\pi$
$499$	0.271104	−	0.469566i	0.0121363	−	0.0210206i	0.872030	+	0.489453i	$0.162803\pi$
$500$	−19.4335			−0.869092
$501$		0			0
$502$	29.7568	−	51.5403i	1.32811	−	2.30036i
$503$	−11.8819	+	20.5801i	−0.529789	+	0.917621i	0.469608	+	0.882875i	$0.344395\pi$
$503$	−11.8819	+	20.5801i	−0.529789	+	0.917621i	−0.999396	+	0.0347454i	$0.988938\pi$
$504$		0			0
$505$	−16.2866			−0.724743
$506$	−1.26317	−	2.18787i	−0.0561547	−	0.0972628i
$507$		0			0
$508$	1.51712			0.0673112
$509$	19.2451	−	33.3335i	0.853024	−	1.47748i	−0.0254417	−	0.999676i	$-0.508099\pi$
$509$	19.2451	−	33.3335i	0.853024	−	1.47748i	0.878466	−	0.477805i	$-0.158567\pi$
$510$		0			0
$511$	10.5494	+	18.2721i	0.466678	+	0.808310i
$512$	27.5020			1.21543
$513$		0			0
$514$	−53.0846			−2.34146
$515$	23.1546			1.02031
$516$		0			0
$517$	−13.0737			−0.574981
$518$	−4.58360			−0.201392
$519$		0			0
$520$	0.922128			0.0404380
$521$	0.859161	+	1.48811i	0.0376405	+	0.0651953i	0.884232	−	0.467048i	$-0.154682\pi$
$521$	0.859161	+	1.48811i	0.0376405	+	0.0651953i	−0.846591	+	0.532243i	$0.821349\pi$
$522$		0			0
$523$	−16.3502	+	28.3193i	−0.714943	+	1.23832i	0.248039	+	0.968750i	$0.420214\pi$
$523$	−16.3502	+	28.3193i	−0.714943	+	1.23832i	−0.962982	+	0.269567i	$0.913119\pi$
$524$	−20.0531			−0.876024
$525$		0			0
$526$	21.9231	+	37.9720i	0.955894	+	1.65566i
$527$	21.9324			0.955390
$528$		0			0
$529$	11.4501	−	19.8321i	0.497829	−	0.862264i
$530$	7.71584	−	13.3642i	0.335155	−	0.580505i
$531$		0			0
$532$	44.6015			1.93372
$533$	−1.03714	+	1.79638i	−0.0449236	+	0.0778100i
$534$		0			0
$535$	−5.85617	−	10.1432i	−0.253184	−	0.438528i
$536$	−3.95046	−	6.84240i	−0.170634	−	0.295547i
$537$		0			0
$538$	35.0504			1.51113
$539$	−19.4198	−	33.6360i	−0.836469	−	1.44881i
$540$		0			0
$541$	−11.0132	+	19.0754i	−0.473494	+	0.820116i	−0.999540	−	0.0303404i	$-0.990341\pi$
$541$	−11.0132	+	19.0754i	−0.473494	+	0.820116i	0.526045	+	0.850457i	$0.323674\pi$
$542$	−3.47118	+	6.01226i	−0.149100	+	0.258249i
$543$		0			0
$544$	15.4561	−	26.7707i	0.662673	−	1.14778i
$545$	−13.1723	+	22.8151i	−0.564240	+	0.977292i
$546$		0			0
$547$	14.5566	+	25.2128i	0.622395	+	1.07802i	0.989038	+	0.147658i	$0.0471736\pi$
$547$	14.5566	+	25.2128i	0.622395	+	1.07802i	−0.366643	+	0.930362i	$0.619493\pi$
$548$	18.7112			0.799301
$549$		0			0
$550$	9.87110	−	17.0972i	0.420905	−	0.729029i
$551$	−70.9460			−3.02240
$552$		0			0
$553$	8.82497	+	15.2853i	0.375276	+	0.649997i
$554$	13.2780	+	22.9981i	0.564126	+	0.977095i
$555$		0			0
$556$	−1.78092	−	3.08464i	−0.0755278	−	0.130818i
$557$	11.4403			0.484740			0.242370	−	0.970184i	$-0.422075\pi$
$557$	11.4403			0.484740			0.242370	+	0.970184i	$0.422075\pi$
$558$		0			0
$559$	4.32551	−	3.34907i	0.182950	−	0.141651i
$560$	29.4840			1.24593
$561$		0			0
$562$	−25.6185	−	44.3726i	−1.08065	−	1.87175i
$563$	40.0094			1.68619			0.843097	−	0.537761i	$-0.180730\pi$
$563$	40.0094			1.68619			0.843097	+	0.537761i	$0.180730\pi$
$564$		0			0
$565$	−6.15748	−	10.6651i	−0.259047	−	0.448683i
$566$	−2.74488	+	4.75428i	−0.115376	+	0.199837i
$567$		0			0
$568$	−3.13282	+	5.42621i	−0.131450	+	0.227679i
$569$	3.82818	+	6.63059i	0.160485	+	0.277969i	0.935043	−	0.354535i	$-0.115361\pi$
$569$	3.82818	+	6.63059i	0.160485	+	0.277969i	−0.774557	+	0.632504i	$0.782027\pi$
$570$		0			0
$571$	−2.63228	−	4.55924i	−0.110157	−	0.190798i	0.805676	−	0.592356i	$-0.201802\pi$
$571$	−2.63228	−	4.55924i	−0.110157	−	0.190798i	−0.915834	+	0.401558i	$0.868469\pi$
$572$	2.86007	−	4.95378i	0.119585	−	0.207128i
$573$		0			0
$574$	−9.55987	+	16.5582i	−0.399021	+	0.691125i
$575$	−0.780580			−0.0325524
$576$		0			0
$577$	0.454520	−	0.787252i	0.0189219	−	0.0327737i	−0.856409	−	0.516297i	$-0.827310\pi$
$577$	0.454520	−	0.787252i	0.0189219	−	0.0327737i	0.875331	+	0.483524i	$0.160643\pi$
$578$	−0.548315	−	0.949710i	−0.0228069	−	0.0395027i
$579$		0			0
$580$	27.2964			1.13342
$581$	13.6402			0.565889
$582$		0			0
$583$	10.6652	+	18.4727i	0.441708	+	0.765061i
$584$	1.81772	−	3.14839i	0.0752179	−	0.130281i
$585$		0			0
$586$	37.3372			1.54239
$587$	4.19748	−	7.27024i	0.173248	−	0.300075i	−0.766305	−	0.642477i	$-0.777907\pi$
$587$	4.19748	−	7.27024i	0.173248	−	0.300075i	0.939554	+	0.342402i	$0.111240\pi$
$588$		0			0
$589$	17.6877	−	30.6360i	0.728808	−	1.26233i
$590$	16.0856	+	27.8611i	0.662235	+	1.14702i
$591$		0			0
$592$	1.36980	+	2.37256i	0.0562984	+	0.0975117i
$593$	13.6682	−	23.6741i	0.561287	−	0.972178i	−0.436097	−	0.899900i	$-0.643640\pi$
$593$	13.6682	−	23.6741i	0.561287	−	0.972178i	0.997384	−	0.0722787i	$-0.0230271\pi$
$594$		0			0
$595$	13.4468	−	23.2905i	0.551264	−	0.954818i
$596$	−7.15798	−	12.3980i	−0.293202	−	0.507841i
$597$		0			0
$598$	−0.502730			−0.0205581
$599$	−0.553520	−	0.958724i	−0.0226162	−	0.0391724i	0.854496	−	0.519458i	$-0.173866\pi$
$599$	−0.553520	−	0.958724i	−0.0226162	−	0.0391724i	−0.877112	+	0.480286i	$0.840533\pi$
$600$		0			0
$601$	14.7433			0.601391			0.300696	−	0.953720i	$-0.402781\pi$
$601$	14.7433			0.601391			0.300696	+	0.953720i	$0.402781\pi$
$602$	39.8705	−	30.8701i	1.62500	−	1.25817i
$603$		0			0
$604$	−33.4687			−1.36182
$605$	−5.22941	−	9.05761i	−0.212606	−	0.368244i
$606$		0			0
$607$	−7.10862	−	12.3125i	−0.288530	−	0.499749i	0.684929	−	0.728610i	$-0.259833\pi$
$607$	−7.10862	−	12.3125i	−0.288530	−	0.499749i	−0.973459	+	0.228861i	$0.926500\pi$
$608$	−24.9295	−	43.1792i	−1.01102	−	1.75115i
$609$		0			0
$610$	−27.7158			−1.12218
$611$	−1.30080	+	2.25306i	−0.0526249	+	0.0911491i
$612$		0			0
$613$	45.1756			1.82462			0.912312	−	0.409495i	$-0.134295\pi$
$613$	45.1756			1.82462			0.912312	+	0.409495i	$0.134295\pi$
$614$	8.09989	+	14.0294i	0.326885	+	0.566181i
$615$		0			0
$616$	−5.87437	+	10.1747i	−0.236685	+	0.409951i
$617$	1.51642	−	2.62652i	0.0610489	−	0.105740i	−0.833886	−	0.551937i	$-0.813889\pi$
$617$	1.51642	−	2.62652i	0.0610489	−	0.105740i	0.894935	+	0.446198i	$0.147222\pi$
$618$		0			0
$619$	−7.99727	+	13.8517i	−0.321437	+	0.556746i	−0.980785	−	0.195092i	$-0.937499\pi$
$619$	−7.99727	+	13.8517i	−0.321437	+	0.556746i	0.659347	+	0.751838i	$0.270833\pi$
$620$	−6.80532	+	11.7872i	−0.273308	+	0.473384i
$621$		0			0
$622$	10.9067	+	18.8909i	0.437317	+	0.757455i
$623$	41.9685			1.68143
$624$		0			0
$625$	3.27557	+	5.67345i	0.131023	+	0.226938i
$626$	−7.84247	−	13.5836i	−0.313448	−	0.542908i
$627$		0			0
$628$	−2.12301	+	3.67716i	−0.0847172	+	0.146734i
$629$	2.49890			0.0996378
$630$		0			0
$631$	18.3172	−	31.7264i	0.729198	−	1.26301i	−0.228025	−	0.973655i	$-0.573227\pi$
$631$	18.3172	−	31.7264i	0.729198	−	1.26301i	0.957223	−	0.289352i	$-0.0934398\pi$
$632$	1.52059	−	2.63374i	0.0604859	−	0.104765i
$633$		0			0
$634$	−29.5435			−1.17332
$635$	−0.737739	−	1.27780i	−0.0292763	−	0.0507080i
$636$		0			0
$637$	−7.72890			−0.306230
$638$	−41.9342	+	72.6321i	−1.66019	+	2.87553i
$639$		0			0
$640$	−4.34798	−	7.53092i	−0.171869	−	0.297686i
$641$	33.4459			1.32103			0.660516	−	0.750812i	$-0.270337\pi$
$641$	33.4459			1.32103			0.660516	+	0.750812i	$0.270337\pi$
$642$		0			0
$643$	19.3106			0.761535			0.380768	−	0.924671i	$-0.375660\pi$
$643$	19.3106			0.761535			0.380768	+	0.924671i	$0.375660\pi$
$644$	−2.08469			−0.0821484
$645$		0			0
$646$	−54.0504			−2.12658
$647$	39.9990			1.57252			0.786261	−	0.617894i	$-0.212014\pi$
$647$	39.9990			1.57252			0.786261	+	0.617894i	$0.212014\pi$
$648$		0			0
$649$	−44.4687			−1.74555
$650$	−1.96430	−	3.40227i	−0.0770464	−	0.133448i
$651$		0			0
$652$	16.1060	−	27.8964i	0.630760	−	1.09251i
$653$	−23.5963			−0.923393			−0.461697	−	0.887038i	$-0.652759\pi$
$653$	−23.5963			−0.923393			−0.461697	+	0.887038i	$0.652759\pi$
$654$		0			0
$655$	9.75136	+	16.8899i	0.381017	+	0.659941i
$656$	11.4278			0.446181
$657$		0			0
$658$	−11.9902	+	20.7676i	−0.467426	+	0.809606i
$659$	14.4669	−	25.0574i	0.563550	−	0.976097i	−0.433633	−	0.901089i	$-0.642769\pi$
$659$	14.4669	−	25.0574i	0.563550	−	0.976097i	0.997183	−	0.0750072i	$-0.0238980\pi$
$660$		0			0
$661$	27.1867			1.05744			0.528720	−	0.848796i	$-0.322672\pi$
$661$	27.1867			1.05744			0.528720	+	0.848796i	$0.322672\pi$
$662$	−30.1265	+	52.1806i	−1.17090	+	2.02806i
$663$		0			0
$664$	−1.17514	−	2.03540i	−0.0456042	−	0.0789888i
$665$	−21.6887	−	37.5659i	−0.841051	−	1.45674i
$666$		0			0
$667$	3.31604			0.128398
$668$	−13.0509	−	22.6048i	−0.504954	−	0.874606i
$669$		0			0
$670$	17.2421	−	29.8642i	0.666120	−	1.15375i
$671$	19.1551	−	33.1776i	0.739474	−	1.28081i
$672$		0			0
$673$	−3.50273	+	6.06691i	−0.135020	+	0.233862i	−0.925605	−	0.378490i	$-0.876443\pi$
$673$	−3.50273	+	6.06691i	−0.135020	+	0.233862i	0.790585	+	0.612352i	$0.209777\pi$
$674$	−6.50923	+	11.2743i	−0.250726	+	0.434270i
$675$		0			0
$676$	10.0619	+	17.4278i	0.386998	+	0.670300i
$677$	−14.3475			−0.551420			−0.275710	−	0.961241i	$-0.588913\pi$
$677$	−14.3475			−0.551420			−0.275710	+	0.961241i	$0.588913\pi$
$678$		0			0
$679$	1.13555	−	1.96683i	0.0435785	−	0.0754801i
$680$	−4.63392			−0.177703
$681$		0			0
$682$	−20.9094	−	36.2161i	−0.800662	−	1.38679i
$683$	3.25556	+	5.63880i	0.124571	+	0.215763i	0.921565	−	0.388224i	$-0.126911\pi$
$683$	3.25556	+	5.63880i	0.124571	+	0.215763i	−0.796994	+	0.603987i	$0.793578\pi$
$684$		0			0
$685$	−9.09880	−	15.7596i	−0.347647	−	0.602143i
$686$	−17.4137			−0.664857
$687$		0			0
$688$	−27.8942	−	11.4123i	−1.06346	−	0.435089i
$689$	4.24466			0.161709
$690$		0			0
$691$	−7.12301	−	12.3374i	−0.270972	−	0.469337i	0.698139	−	0.715962i	$-0.254012\pi$
$691$	−7.12301	−	12.3374i	−0.270972	−	0.469337i	−0.969111	+	0.246625i	$0.920678\pi$
$692$	−30.3398			−1.15335
$693$		0			0
$694$	17.9462	+	31.0838i	0.681230	+	1.17993i
$695$	−1.73204	+	2.99998i	−0.0657000	+	0.113796i
$696$		0			0
$697$	5.21189	−	9.02725i	0.197414	−	0.341932i
$698$	−9.80574	−	16.9840i	−0.371153	−	0.642855i
$699$		0			0
$700$	−8.14548	−	14.1084i	−0.307870	−	0.533247i
$701$	−20.7667	+	35.9690i	−0.784349	+	1.35853i	0.145039	+	0.989426i	$0.453669\pi$
$701$	−20.7667	+	35.9690i	−0.784349	+	1.35853i	−0.929387	+	0.369106i	$0.879664\pi$
$702$		0			0
$703$	2.01527	−	3.49056i	0.0760075	−	0.131649i
$704$	−20.4045			−0.769025
$705$		0			0
$706$	−9.42193	+	16.3193i	−0.354599	+	0.614184i
$707$	−20.6463	−	35.7605i	−0.776486	−	1.34491i
$708$		0			0
$709$	43.2131			1.62290			0.811451	−	0.584421i	$-0.198678\pi$
$709$	43.2131			1.62290			0.811451	+	0.584421i	$0.198678\pi$
$710$	−27.3469			−1.02631
$711$		0			0
$712$	−3.61571	−	6.26258i	−0.135504	−	0.234700i
$713$	−0.826729	+	1.43194i	−0.0309612	+	0.0536265i
$714$		0			0
$715$	−5.56314			−0.208050
$716$	1.55926	−	2.70072i	0.0582724	−	0.100931i
$717$		0			0
$718$	−14.9533	+	25.8999i	−0.558053	+	0.966577i
$719$	2.99190	+	5.18212i	0.111579	+	0.193261i	0.916407	−	0.400247i	$-0.131076\pi$
$719$	2.99190	+	5.18212i	0.111579	+	0.193261i	−0.804828	+	0.593508i	$0.797743\pi$
$720$		0			0
$721$	29.3529	+	50.8407i	1.09316	+	1.89341i
$722$	−25.4759	+	44.1256i	−0.948116	+	1.64218i
$723$		0			0
$724$	−2.24874	+	3.89494i	−0.0835739	+	0.144754i
$725$	12.9567	+	22.4417i	0.481200	+	0.833462i
$726$		0			0
$727$	46.0164			1.70665			0.853326	−	0.521377i	$-0.174581\pi$
$727$	46.0164			1.70665			0.853326	+	0.521377i	$0.174581\pi$
$728$	1.16897	+	2.02472i	0.0433250	+	0.0750412i
$729$		0			0
$730$	15.8672			0.587271
$731$	−21.7367	+	16.8299i	−0.803962	+	0.622476i
$732$		0			0
$733$	3.75945			0.138858			0.0694291	−	0.997587i	$-0.477882\pi$
$733$	3.75945			0.138858			0.0694291	+	0.997587i	$0.477882\pi$
$734$	21.2826	+	36.8626i	0.785556	+	1.36062i
$735$		0			0
$736$	1.16521	+	2.01821i	0.0429504	+	0.0743922i
$737$	23.8329	+	41.2797i	0.877895	+	1.52056i
$738$		0			0
$739$	−22.2944			−0.820114			−0.410057	−	0.912060i	$-0.634491\pi$
$739$	−22.2944			−0.820114			−0.410057	+	0.912060i	$0.634491\pi$
$740$	−0.775376	+	1.34299i	−0.0285034	+	0.0493693i
$741$		0			0
$742$	39.1252			1.43633
$743$	−13.7092	−	23.7450i	−0.502941	−	0.871120i	−0.999994	−	0.00339960i	$-0.998918\pi$
$743$	−13.7092	−	23.7450i	−0.502941	−	0.871120i	0.497053	−	0.867720i	$-0.334415\pi$
$744$		0			0
$745$	−6.96152	+	12.0577i	−0.255050	+	0.441760i
$746$	7.28791	−	12.6230i	0.266829	−	0.462162i
$747$		0			0
$748$	−14.3725	+	24.8940i	−0.525512	+	0.910213i
$749$	14.8476	−	25.7168i	0.542520	−	0.939673i
$750$		0			0
$751$	−9.93632	−	17.2102i	−0.362581	−	0.628009i	0.625803	−	0.779981i	$-0.284771\pi$
$751$	−9.93632	−	17.2102i	−0.362581	−	0.628009i	−0.988385	+	0.151971i	$0.951438\pi$
$752$	14.3330			0.522670
$753$		0			0
$754$	8.34471	+	14.4535i	0.303896	+	0.526364i
$755$	16.2751	+	28.1892i	0.592310	+	1.02591i
$756$		0			0
$757$	4.27383	−	7.40250i	0.155335	−	0.269048i	−0.777846	−	0.628455i	$-0.783688\pi$
$757$	4.27383	−	7.40250i	0.155335	−	0.269048i	0.933181	+	0.359407i	$0.117021\pi$
$758$	33.3477			1.21124
$759$		0			0
$760$	−3.73708	+	6.47282i	−0.135558	+	0.234794i
$761$	2.37558	−	4.11463i	0.0861148	−	0.149155i	−0.819751	−	0.572720i	$-0.805888\pi$
$761$	2.37558	−	4.11463i	0.0861148	−	0.149155i	0.905866	+	0.423565i	$0.139221\pi$
$762$		0			0
$763$	−66.7937			−2.41809
$764$	7.64057	+	13.2338i	0.276426	+	0.478784i
$765$		0			0
$766$	−70.7597			−2.55665
$767$	−4.42454	+	7.66352i	−0.159761	+	0.276714i
$768$		0			0
$769$	−17.6981	−	30.6541i	−0.638212	−	1.10541i	−0.985825	−	0.167777i	$-0.946341\pi$
$769$	−17.6981	−	30.6541i	−0.638212	−	1.10541i	0.347613	−	0.937638i	$-0.386992\pi$
$770$	−51.2783			−1.84794
$771$		0			0
$772$	15.4776			0.557052
$773$	−23.9352			−0.860889			−0.430445	−	0.902617i	$-0.641643\pi$
$773$	−23.9352			−0.860889			−0.430445	+	0.902617i	$0.641643\pi$
$774$		0			0
$775$	−12.9210			−0.464138
$776$	−0.391324			−0.0140477
$777$		0			0
$778$	26.6303			0.954743
$779$	−8.40640	−	14.5603i	−0.301190	−	0.521677i
$780$		0			0
$781$	18.9001	−	32.7360i	0.676299	−	1.17138i
$782$	2.52634			0.0903416
$783$		0			0
$784$	21.2903	+	36.8759i	0.760368	+	1.31700i
$785$	4.12948			0.147387
$786$		0			0
$787$	23.3020	−	40.3602i	0.830625	−	1.43868i	−0.0669181	−	0.997758i	$-0.521317\pi$
$787$	23.3020	−	40.3602i	0.830625	−	1.43868i	0.897543	−	0.440926i	$-0.145350\pi$
$788$	16.7292	−	28.9758i	0.595952	−	1.03222i
$789$		0			0
$790$	13.2735			0.472250
$791$	15.6116	−	27.0400i	0.555083	−	0.961432i
$792$		0			0
$793$	−3.81177	−	6.60219i	−0.135360	−	0.234451i
$794$	2.63925	+	4.57131i	0.0936634	+	0.162230i
$795$		0			0
$796$	−19.5171			−0.691766
$797$	8.05808	+	13.9570i	0.285432	+	0.494383i	0.972714	−	0.232008i	$-0.0745296\pi$
$797$	8.05808	+	13.9570i	0.285432	+	0.494383i	−0.687282	+	0.726391i	$0.741196\pi$
$798$		0			0
$799$	6.53686	−	11.3222i	0.231257	−	0.400549i
$800$	−9.10563	+	15.7714i	−0.321933	+	0.557604i
$801$		0			0
$802$	−21.5001	+	37.2393i	−0.759195	+	1.31496i
$803$	−10.9662	+	18.9940i	−0.386989	+	0.670284i
$804$		0			0
$805$	1.01374	+	1.75585i	0.0357296	+	0.0618854i
$806$	−8.32175			−0.293121
$807$		0			0
$808$	−3.55748	+	6.16174i	−0.125152	+	0.216769i
$809$	−13.6002			−0.478159			−0.239079	−	0.971000i	$-0.576846\pi$
$809$	−13.6002			−0.478159			−0.239079	+	0.971000i	$0.576846\pi$
$810$		0			0
$811$	−9.84024	−	17.0438i	−0.345538	−	0.598489i	0.639914	−	0.768447i	$-0.278970\pi$
$811$	−9.84024	−	17.0438i	−0.345538	−	0.598489i	−0.985451	+	0.169958i	$0.945637\pi$
$812$	34.6034	+	59.9349i	1.21434	+	2.10330i
$813$		0			0
$814$	−2.38234	−	4.12634i	−0.0835011	−	0.144628i
$815$	−31.3279			−1.09737
$816$		0			0
$817$	5.97872	+	43.9354i	0.209169	+	1.53710i
$818$	−35.9448			−1.25678
$819$		0			0
$820$	3.23436	+	5.60207i	0.112949	+	0.195633i
$821$	−13.5458			−0.472751			−0.236376	−	0.971662i	$-0.575960\pi$
$821$	−13.5458			−0.472751			−0.236376	+	0.971662i	$0.575960\pi$
$822$		0			0
$823$	22.1323	+	38.3342i	0.771483	+	1.33625i	0.936750	+	0.349999i	$0.113818\pi$
$823$	22.1323	+	38.3342i	0.771483	+	1.33625i	−0.165267	+	0.986249i	$0.552849\pi$
$824$	5.05767	−	8.76014i	0.176192	−	0.305174i
$825$		0			0
$826$	−40.7832	+	70.6386i	−1.41903	+	2.45783i
$827$	−13.9090	−	24.0911i	−0.483664	−	0.837731i	0.516160	−	0.856492i	$-0.327361\pi$
$827$	−13.9090	−	24.0911i	−0.483664	−	0.837731i	−0.999824	+	0.0187616i	$0.994028\pi$
$828$		0			0
$829$	15.0955	+	26.1462i	0.524289	+	0.908096i	0.999600	+	0.0282780i	$0.00900235\pi$
$829$	15.0955	+	26.1462i	0.524289	+	0.908096i	−0.475311	+	0.879818i	$0.657664\pi$
$830$	5.12898	−	8.88365i	0.178030	−	0.308356i
$831$		0			0
$832$	−2.03020	+	3.51642i	−0.0703847	+	0.121910i
$833$	38.8396			1.34571
$834$		0			0
$835$	−12.6927	+	21.9844i	−0.439249	+	0.760801i
$836$	23.1818	+	40.1521i	0.801761	+	1.38869i
$837$		0			0
$838$	−36.5751			−1.26347
$839$	−28.5882			−0.986975			−0.493487	−	0.869753i	$-0.664278\pi$
$839$	−28.5882			−0.986975			−0.493487	+	0.869753i	$0.664278\pi$
$840$		0			0
$841$	−40.5423	−	70.2214i	−1.39801	−	2.42143i
$842$	−14.8886	+	25.7878i	−0.513094	+	0.888705i
$843$		0			0
$844$	−26.4489			−0.910407
$845$	9.78578	−	16.9495i	0.336641	−	0.583080i
$846$		0			0
$847$	13.2586	−	22.9645i	0.455569	−	0.789069i
$848$	−11.6925	−	20.2520i	−0.401522	−	0.695456i
$849$		0			0
$850$	9.87110	+	17.0972i	0.338576	+	0.586431i
$851$	−0.0941947	+	0.163150i	−0.00322895	+	0.00559271i
$852$		0			0
$853$	−15.4770	+	26.8069i	−0.529922	+	0.917852i	0.469469	+	0.882949i	$0.344445\pi$
$853$	−15.4770	+	26.8069i	−0.529922	+	0.917852i	−0.999391	+	0.0349027i	$0.988888\pi$
$854$	−35.1351	−	60.8557i	−1.20230	−	2.08244i
$855$		0			0
$856$	−5.11666			−0.174884
$857$	14.9429	+	25.8818i	0.510438	+	0.884105i	0.999927	+	0.0120951i	$0.00385010\pi$
$857$	14.9429	+	25.8818i	0.510438	+	0.884105i	−0.489489	+	0.872010i	$0.662817\pi$
$858$		0			0
$859$	−44.5280			−1.51928			−0.759638	−	0.650346i	$-0.774624\pi$
$859$	−44.5280			−1.51928			−0.759638	+	0.650346i	$0.774624\pi$
$860$	−2.30031	−	16.9041i	−0.0784399	−	0.576425i
$861$		0			0
$862$	−24.6829			−0.840702
$863$	−10.4345	−	18.0731i	−0.355196	−	0.615217i	0.631956	−	0.775004i	$-0.282252\pi$
$863$	−10.4345	−	18.0731i	−0.355196	−	0.615217i	−0.987151	+	0.159788i	$0.948919\pi$
$864$		0			0
$865$	14.7536	+	25.5539i	0.501636	+	0.868859i
$866$	19.3873	+	33.5799i	0.658809	+	1.14109i
$867$		0			0
$868$	−34.5082			−1.17128
$869$	−9.17364	+	15.8892i	−0.311194	+	0.539004i
$870$		0			0
$871$	9.48527			0.321396
$872$	5.75447	+	9.96703i	0.194871	+	0.337526i
$873$		0			0
$874$	2.03740	−	3.52888i	0.0689160	−	0.119366i
$875$	−23.9595	+	41.4991i	−0.809979	+	1.40292i
$876$		0			0
$877$	−4.02301	+	6.96806i	−0.135847	+	0.235295i	−0.925921	−	0.377718i	$-0.876709\pi$
$877$	−4.02301	+	6.96806i	−0.135847	+	0.235295i	0.790073	+	0.613012i	$0.210042\pi$
$878$	17.7800	−	30.7959i	0.600047	−	1.03931i
$879$		0			0
$880$	15.3244	+	26.5427i	0.516586	+	0.894754i
$881$	35.2794			1.18859			0.594296	−	0.804246i	$-0.297431\pi$
$881$	35.2794			1.18859			0.594296	+	0.804246i	$0.297431\pi$
$882$		0			0
$883$	−3.82324	−	6.62204i	−0.128662	−	0.222849i	0.794496	−	0.607269i	$-0.207735\pi$
$883$	−3.82324	−	6.62204i	−0.128662	−	0.222849i	−0.923158	+	0.384420i	$0.874402\pi$
$884$	2.86007	+	4.95378i	0.0961945	+	0.166614i
$885$		0			0
$886$	−9.88299	+	17.1178i	−0.332026	+	0.575085i
$887$	13.0080			0.436768			0.218384	−	0.975863i	$-0.429922\pi$
$887$	13.0080			0.436768			0.218384	+	0.975863i	$0.429922\pi$
$888$		0			0
$889$	1.87045	−	3.23971i	0.0627329	−	0.108657i
$890$	15.7810	−	27.3335i	0.528981	−	0.916222i
$891$		0			0
$892$	−32.9821			−1.10432
$893$	−10.5435	−	18.2618i	−0.352824	−	0.611109i
$894$		0			0
$895$	−3.03293			−0.101380
$896$	11.0238	−	19.0938i	0.368279	−	0.637878i
$897$		0			0
$898$	−16.3600	−	28.3363i	−0.545940	−	0.945595i
$899$	54.8909			1.83071
$900$		0			0
$901$	−21.3304			−0.710620
$902$	−19.8751			−0.661770
$903$		0			0
$904$	−5.37992			−0.178933
$905$	4.37405			0.145398
$906$		0			0
$907$	6.64101			0.220511			0.110256	−	0.993903i	$-0.464833\pi$
$907$	6.64101			0.220511			0.110256	+	0.993903i	$0.464833\pi$
$908$	−20.2789	−	35.1242i	−0.672980	−	1.16564i
$909$		0			0
$910$	−5.10208	+	8.83705i	−0.169132	+	0.292945i
$911$	42.3997			1.40477			0.702383	−	0.711799i	$-0.252120\pi$
$911$	42.3997			1.40477			0.702383	+	0.711799i	$0.252120\pi$
$912$		0			0
$913$	7.08953	+	12.2794i	0.234629	+	0.406390i
$914$	−46.4834			−1.53754
$915$		0			0
$916$	18.8133	−	32.5856i	0.621609	−	1.07666i
$917$	−24.7234	+	42.8222i	−0.816440	+	1.41411i
$918$		0			0
$919$	−28.1636			−0.929031			−0.464516	−	0.885565i	$-0.653772\pi$
$919$	−28.1636			−0.929031			−0.464516	+	0.885565i	$0.653772\pi$
$920$	0.174673	−	0.302542i	0.00575879	−	0.00997452i
$921$		0			0
$922$	14.3507	+	24.8562i	0.472615	+	0.818594i
$923$	−3.76104	−	6.51431i	−0.123796	−	0.214421i
$924$		0			0
$925$	−1.47218			−0.0484050
$926$	−2.64445	−	4.58032i	−0.0869021	−	0.150519i
$927$		0			0
$928$	38.6823	−	66.9998i	1.26981	−	2.19938i
$929$	−3.60301	+	6.24060i	−0.118211	+	0.204747i	−0.919059	−	0.394121i	$-0.871049\pi$
$929$	−3.60301	+	6.24060i	−0.118211	+	0.204747i	0.800848	+	0.598868i	$0.204383\pi$
$930$		0			0
$931$	31.3227	−	54.2525i	1.02656	−	1.77805i
$932$	21.2512	−	36.8082i	0.696107	−	1.20569i
$933$		0			0
$934$	0.241441	+	0.418189i	0.00790020	+	0.0136836i
$935$	27.9561			0.914262
$936$		0			0
$937$	−25.4330	+	44.0513i	−0.830861	+	1.43909i	0.0664946	+	0.997787i	$0.478818\pi$
$937$	−25.4330	+	44.0513i	−0.830861	+	1.43909i	−0.897356	+	0.441307i	$0.854515\pi$
$938$	87.4306			2.85471
$939$		0			0
$940$	4.05660	+	7.02623i	0.132312	+	0.229170i
$941$	−26.8310	−	46.4727i	−0.874666	−	1.51497i	−0.857118	−	0.515120i	$-0.827747\pi$
$941$	−26.8310	−	46.4727i	−0.874666	−	1.51497i	−0.0175477	−	0.999846i	$-0.505586\pi$
$942$		0			0
$943$	0.392918	+	0.680554i	0.0127952	+	0.0221619i
$944$	48.7520			1.58674
$945$		0			0
$946$	48.5134	+	19.8481i	1.57731	+	0.645319i
$947$	−9.79722			−0.318367			−0.159184	−	0.987249i	$-0.550886\pi$
$947$	−9.79722			−0.318367			−0.159184	+	0.987249i	$0.550886\pi$
$948$		0			0
$949$	2.18222	+	3.77972i	0.0708380	+	0.122695i
$950$	31.8427			1.03311
$951$		0			0
$952$	−5.87437	−	10.1747i	−0.190389	−	0.329764i
$953$	8.63676	−	14.9593i	0.279772	−	0.484580i	−0.691556	−	0.722323i	$-0.743074\pi$
$953$	8.63676	−	14.9593i	0.279772	−	0.484580i	0.971328	+	0.237743i	$0.0764077\pi$
$954$		0			0
$955$	7.43086	−	12.8706i	0.240457	−	0.416484i
$956$	−2.90291	−	5.02799i	−0.0938868	−	0.162617i
$957$		0			0
$958$	7.90546	+	13.6927i	0.255414	+	0.442390i
$959$	23.0689	−	39.9566i	0.744935	−	1.29026i
$960$		0			0
$961$	1.81505	−	3.14375i	0.0585499	−	0.101411i
$962$	−0.948152			−0.0305696
$963$		0			0
$964$	5.69215	−	9.85909i	0.183332	−	0.317540i
$965$	−7.52642	−	13.0361i	−0.242284	−	0.419648i
$966$		0			0
$967$	5.94067			0.191039			0.0955196	−	0.995428i	$-0.469549\pi$
$967$	5.94067			0.191039			0.0955196	+	0.995428i	$0.469549\pi$
$968$	−4.56905			−0.146855
$969$		0			0
$970$	−0.853982	−	1.47914i	−0.0274197	−	0.0474923i
$971$	−2.83198	+	4.90513i	−0.0908825	+	0.157413i	−0.907883	−	0.419224i	$-0.862302\pi$
$971$	−2.83198	+	4.90513i	−0.0908825	+	0.157413i	0.817000	+	0.576637i	$0.195635\pi$
$972$		0			0
$973$	−8.78276			−0.281562
$974$	14.6039	−	25.2947i	0.467940	−	0.810495i
$975$		0			0
$976$	−21.0001	+	36.3733i	−0.672197	+	1.16428i
$977$	−27.5773	−	47.7652i	−0.882275	−	1.52814i	−0.848806	−	0.528705i	$-0.822678\pi$
$977$	−27.5773	−	47.7652i	−0.882275	−	1.52814i	−0.0334690	−	0.999440i	$-0.510655\pi$
$978$		0			0
$979$	21.8133	+	37.7818i	0.697156	+	1.20751i
$980$	−12.0514	+	20.8736i	−0.384967	+	0.666783i
$981$		0			0
$982$	−6.29542	+	10.9040i	−0.200895	+	0.347960i
$983$	26.1498	+	45.2928i	0.834050	+	1.44462i	0.894802	+	0.446464i	$0.147317\pi$
$983$	26.1498	+	45.2928i	0.834050	+	1.44462i	−0.0607516	+	0.998153i	$0.519350\pi$
$984$		0			0
$985$	−32.5400			−1.03681
$986$	−41.9342	−	72.6321i	−1.33546	−	2.31308i
$987$		0			0
$988$	9.22617			0.293523
$989$	−0.279448	−	2.05356i	−0.00888592	−	0.0652993i
$990$		0			0
$991$	15.1557			0.481438			0.240719	−	0.970595i	$-0.422617\pi$
$991$	15.1557			0.481438			0.240719	+	0.970595i	$0.422617\pi$
$992$	19.2879	+	33.4077i	0.612393	+	1.06070i
$993$		0			0
$994$	−34.6674	−	60.0457i	−1.09958	−	1.90453i
$995$	9.49072	+	16.4384i	0.300876	+	0.521133i
$996$		0			0
$997$	42.9704			1.36088			0.680442	−	0.732802i	$-0.261788\pi$
$997$	42.9704			1.36088			0.680442	+	0.732802i	$0.261788\pi$
$998$	0.516917	−	0.895327i	0.0163627	−	0.0283411i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	387.2.h.g.208.5	yes	12
3.2	odd	2	inner	387.2.h.g.208.2	✓	12
43.6	even	3	inner	387.2.h.g.307.5	yes	12
129.92	odd	6	inner	387.2.h.g.307.2	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
387.2.h.g.208.2	✓	12	3.2	odd	2	inner
387.2.h.g.208.5	yes	12	1.1	even	1	trivial
387.2.h.g.307.2	yes	12	129.92	odd	6	inner
387.2.h.g.307.5	yes	12	43.6	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 387 = 3^{2} \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	387.h (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.90671 q^{2} +1.63555 q^{4} +(-0.795331 - 1.37755i) q^{5} +(2.01647 - 3.49262i) q^{7} -0.694898 q^{8} +O(q^{10})\)	\(q+1.90671 q^{2} +1.63555 q^{4} +(-0.795331 - 1.37755i) q^{5} +(2.01647 - 3.49262i) q^{7} -0.694898 q^{8} +(-1.51647 - 2.62660i) q^{10} +4.19227 q^{11} +(0.417122 - 0.722476i) q^{13} +(3.84482 - 6.65943i) q^{14} -4.59607 q^{16} +(-2.09614 + 3.63061i) q^{17} +(3.38092 + 5.85592i) q^{19} +(-1.30080 - 2.25306i) q^{20} +7.99346 q^{22} +(-0.158025 - 0.273708i) q^{23} +(1.23490 - 2.13891i) q^{25} +(0.795331 - 1.37755i) q^{26} +(3.29804 - 5.71237i) q^{28} +(-5.24606 + 9.08644i) q^{29} +(-2.61581 - 4.53072i) q^{31} -7.37360 q^{32} +(-3.99673 + 6.92254i) q^{34} -6.41503 q^{35} +(-0.298037 - 0.516215i) q^{37} +(6.44643 + 11.1655i) q^{38} +(0.552674 + 0.957259i) q^{40} -2.48643 q^{41} +(6.06914 + 2.48305i) q^{43} +6.85668 q^{44} +(-0.301309 - 0.521882i) q^{46} -3.11853 q^{47} +(-4.63228 - 8.02334i) q^{49} +(2.35459 - 4.07828i) q^{50} +(0.682224 - 1.18165i) q^{52} +(2.54402 + 4.40637i) q^{53} +(-3.33424 - 5.77508i) q^{55} +(-1.40124 + 2.42702i) q^{56} +(-10.0027 + 17.3252i) q^{58} -10.6073 q^{59} +(4.56914 - 7.91398i) q^{61} +(-4.98760 - 8.63878i) q^{62} -4.86718 q^{64} -1.32700 q^{65} +(5.68495 + 9.84663i) q^{67} +(-3.42834 + 5.93806i) q^{68} -12.2316 q^{70} +(4.50832 - 7.80864i) q^{71} +(-2.61581 + 4.53072i) q^{73} +(-0.568271 - 0.984273i) q^{74} +(5.52966 + 9.57766i) q^{76} +(8.45358 - 14.6420i) q^{77} +(-2.18823 + 3.79012i) q^{79} +(3.65540 + 6.33134i) q^{80} -4.74090 q^{82} +(1.69110 + 2.92906i) q^{83} +6.66849 q^{85} +(11.5721 + 4.73446i) q^{86} -2.91320 q^{88} +(5.20322 + 9.01224i) q^{89} +(-1.68222 - 2.91370i) q^{91} +(-0.258459 - 0.447663i) q^{92} -5.94613 q^{94} +(5.37789 - 9.31478i) q^{95} +0.563139 q^{97} +(-8.83243 - 15.2982i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 20 q^{4} + 2 q^{7}+O(q^{10}) \) 12 * q + 20 * q^4 + 2 * q^7	\( 12 q + 20 q^{4} + 2 q^{7} + 4 q^{10} - 6 q^{13} + 12 q^{16} + 18 q^{19} - 16 q^{22} + 4 q^{25} + 6 q^{28} + 2 q^{31} + 8 q^{34} + 30 q^{37} - 4 q^{40} + 40 q^{43} - 26 q^{46} + 8 q^{52} - 18 q^{55} - 54 q^{58} + 22 q^{61} + 8 q^{64} + 2 q^{67} - 80 q^{70} + 2 q^{73} - 34 q^{76} - 16 q^{79} - 36 q^{82} + 36 q^{85} - 148 q^{88} - 20 q^{91} - 140 q^{94} - 16 q^{97}+O(q^{100}) \) 12 * q + 20 * q^4 + 2 * q^7 + 4 * q^10 - 6 * q^13 + 12 * q^16 + 18 * q^19 - 16 * q^22 + 4 * q^25 + 6 * q^28 + 2 * q^31 + 8 * q^34 + 30 * q^37 - 4 * q^40 + 40 * q^43 - 26 * q^46 + 8 * q^52 - 18 * q^55 - 54 * q^58 + 22 * q^61 + 8 * q^64 + 2 * q^67 - 80 * q^70 + 2 * q^73 - 34 * q^76 - 16 * q^79 - 36 * q^82 + 36 * q^85 - 148 * q^88 - 20 * q^91 - 140 * q^94 - 16 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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