LMFDB - Embedded newform 864.2.w.a.107.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [864,2,Mod(107,864)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(864, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 5, 4]))

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

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

chi := DirichletCharacter("864.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.w (of order $8$, degree $4$, 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:	$6.89907473464$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$32$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			107.15
Character	$\chi$	$=$	864.107
Dual form			864.2.w.a.323.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0811033 - 1.41189i) q^{2} +(-1.98684 + 0.229017i) q^{4} +(1.02313 + 0.423795i) q^{5} +(-0.549738 + 0.549738i) q^{7} +(0.484486 + 2.78662i) q^{8} +O(q^{10})$	\(q+(-0.0811033 - 1.41189i) q^{2} +(-1.98684 + 0.229017i) q^{4} +(1.02313 + 0.423795i) q^{5} +(-0.549738 + 0.549738i) q^{7} +(0.484486 + 2.78662i) q^{8} +(0.515371 - 1.47892i) q^{10} +(-2.44818 - 1.01407i) q^{11} +(-2.24462 - 5.41899i) q^{13} +(0.820752 + 0.731581i) q^{14} +(3.89510 - 0.910043i) q^{16} +0.515040 q^{17} +(2.66603 - 1.10431i) q^{19} +(-2.12986 - 0.607700i) q^{20} +(-1.23320 + 3.53880i) q^{22} +(-3.26913 + 3.26913i) q^{23} +(-2.66834 - 2.66834i) q^{25} +(-7.46894 + 3.60864i) q^{26} +(0.966344 - 1.21814i) q^{28} +(-2.83677 - 6.84857i) q^{29} -5.60227i q^{31} +(-1.60078 - 5.42563i) q^{32} +(-0.0417714 - 0.727177i) q^{34} +(-0.795430 + 0.329478i) q^{35} +(2.58718 - 6.24599i) q^{37} +(-1.77538 - 3.67457i) q^{38} +(-0.685265 + 3.05641i) q^{40} +(-8.45953 - 8.45953i) q^{41} +(1.31637 - 3.17800i) q^{43} +(5.09640 + 1.45412i) q^{44} +(4.88078 + 4.35051i) q^{46} +2.34853i q^{47} +6.39558i q^{49} +(-3.55098 + 3.98380i) q^{50} +(5.70075 + 10.2526i) q^{52} +(-3.08254 + 7.44190i) q^{53} +(-2.07506 - 2.07506i) q^{55} +(-1.79825 - 1.26557i) q^{56} +(-9.43932 + 4.56064i) q^{58} +(-2.96161 + 7.14996i) q^{59} +(5.36346 - 2.22162i) q^{61} +(-7.90977 + 0.454363i) q^{62} +(-7.53055 + 2.70016i) q^{64} -6.49559i q^{65} +(0.398752 + 0.962673i) q^{67} +(-1.02330 + 0.117953i) q^{68} +(0.529697 + 1.09634i) q^{70} +(5.43150 + 5.43150i) q^{71} +(2.98447 - 2.98447i) q^{73} +(-9.02846 - 3.14623i) q^{74} +(-5.04409 + 2.80466i) q^{76} +(1.90333 - 0.788386i) q^{77} -6.13141 q^{79} +(4.37088 + 0.719631i) q^{80} +(-11.2578 + 12.6300i) q^{82} +(1.05703 + 2.55189i) q^{83} +(0.526954 + 0.218271i) q^{85} +(-4.59374 - 1.60082i) q^{86} +(1.63972 - 7.31347i) q^{88} +(-0.656796 + 0.656796i) q^{89} +(4.21297 + 1.74507i) q^{91} +(5.74657 - 7.24395i) q^{92} +(3.31586 - 0.190474i) q^{94} +3.19570 q^{95} -10.9570 q^{97} +(9.02983 - 0.518703i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q+O(q^{10}) $ 128 * q	$ 128 q - 16 q^{10} + 32 q^{16} + 16 q^{22} - 32 q^{40} - 32 q^{46} + 16 q^{52} - 32 q^{55} - 32 q^{58} - 64 q^{61} - 48 q^{64} - 64 q^{67} + 96 q^{70} - 32 q^{76} + 64 q^{79} - 80 q^{82} - 80 q^{88} + 96 q^{91} - 144 q^{94}+O(q^{100}) $ 128 * q - 16 * q^10 + 32 * q^16 + 16 * q^22 - 32 * q^40 - 32 * q^46 + 16 * q^52 - 32 * q^55 - 32 * q^58 - 64 * q^61 - 48 * q^64 - 64 * q^67 + 96 * q^70 - 32 * q^76 + 64 * q^79 - 80 * q^82 - 80 * q^88 + 96 * q^91 - 144 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/864\mathbb{Z}\right)^\times$.

$n$	$325$	$353$	$703$
$\chi(n)$	$e\left(\frac{5}{8}\right)$	$-1$	$-1$

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 $

$2$	−0.0811033	−	1.41189i	−0.0573487	−	0.998354i
$2$	−0.0811033	−	1.41189i	−0.0573487	−	0.998354i
$3$		0			0
$3$		0			0
$4$	−1.98684	+	0.229017i	−0.993422	+	0.114509i
$5$	1.02313	+	0.423795i	0.457559	+	0.189527i	0.599544	−	0.800342i	$-0.295349\pi$
$5$	1.02313	+	0.423795i	0.457559	+	0.189527i	−0.141985	+	0.989869i	$0.545349\pi$
$6$		0			0
$7$	−0.549738	+	0.549738i	−0.207781	+	0.207781i	−0.803324	−	0.595543i	$-0.796937\pi$
$7$	−0.549738	+	0.549738i	−0.207781	+	0.207781i	0.595543	+	0.803324i	$0.296937\pi$
$8$	0.484486	+	2.78662i	0.171292	+	0.985220i
$9$		0			0
$10$	0.515371	−	1.47892i	0.162975	−	0.467675i
$11$	−2.44818	−	1.01407i	−0.738155	−	0.305754i	−0.0182567	−	0.999833i	$-0.505812\pi$
$11$	−2.44818	−	1.01407i	−0.738155	−	0.305754i	−0.719898	+	0.694080i	$0.755812\pi$
$12$		0			0
$13$	−2.24462	−	5.41899i	−0.622545	−	1.50296i	−0.848705	−	0.528866i	$-0.822617\pi$
$13$	−2.24462	−	5.41899i	−0.622545	−	1.50296i	0.226161	−	0.974090i	$-0.427383\pi$
$14$	0.820752	+	0.731581i	0.219355	+	0.195523i
$15$		0			0
$16$	3.89510	−	0.910043i	0.973776	−	0.227511i
$17$	0.515040			0.124915			0.0624577	−	0.998048i	$-0.480106\pi$
$17$	0.515040			0.124915			0.0624577	+	0.998048i	$0.480106\pi$
$18$		0			0
$19$	2.66603	−	1.10431i	0.611630	−	0.253346i	−0.0552952	−	0.998470i	$-0.517610\pi$
$19$	2.66603	−	1.10431i	0.611630	−	0.253346i	0.666925	+	0.745125i	$0.267610\pi$
$20$	−2.12986	−	0.607700i	−0.476251	−	0.135886i
$21$		0			0
$22$	−1.23320	+	3.53880i	−0.262918	+	0.754475i
$23$	−3.26913	+	3.26913i	−0.681661	+	0.681661i	−0.960374	−	0.278713i	$-0.910092\pi$
$23$	−3.26913	+	3.26913i	−0.681661	+	0.681661i	0.278713	+	0.960374i	$0.410092\pi$
$24$		0			0
$25$	−2.66834	−	2.66834i	−0.533667	−	0.533667i
$26$	−7.46894	+	3.60864i	−1.46478	+	0.707713i
$27$		0			0
$28$	0.966344	−	1.21814i	0.182622	−	0.230207i
$29$	−2.83677	−	6.84857i	−0.526775	−	1.27175i	−0.933625	−	0.358252i	$-0.883373\pi$
$29$	−2.83677	−	6.84857i	−0.526775	−	1.27175i	0.406850	−	0.913495i	$-0.366627\pi$
$30$		0			0
$31$		−	5.60227i		−	1.00620i	−0.864229	−	0.503099i	$-0.832193\pi$
$31$		−	5.60227i		−	1.00620i	0.864229	−	0.503099i	$-0.167807\pi$
$32$	−1.60078	−	5.42563i	−0.282981	−	0.959125i
$33$		0			0
$34$	−0.0417714	−	0.727177i	−0.00716374	−	0.124710i
$35$	−0.795430	+	0.329478i	−0.134452	+	0.0556919i
$36$		0			0
$37$	2.58718	−	6.24599i	0.425329	−	1.02684i	−0.555421	−	0.831569i	$-0.687443\pi$
$37$	2.58718	−	6.24599i	0.425329	−	1.02684i	0.980750	−	0.195266i	$-0.0625570\pi$
$38$	−1.77538	−	3.67457i	−0.288005	−	0.596095i
$39$		0			0
$40$	−0.685265	+	3.05641i	−0.108350	+	0.483260i
$41$	−8.45953	−	8.45953i	−1.32116	−	1.32116i	−0.912841	−	0.408316i	$-0.866116\pi$
$41$	−8.45953	−	8.45953i	−1.32116	−	1.32116i	−0.408316	−	0.912841i	$-0.633884\pi$
$42$		0			0
$43$	1.31637	−	3.17800i	0.200745	−	0.484640i	−0.791162	−	0.611606i	$-0.790524\pi$
$43$	1.31637	−	3.17800i	0.200745	−	0.484640i	0.991907	+	0.126966i	$0.0405238\pi$
$44$	5.09640	+	1.45412i	0.768311	+	0.219218i
$45$		0			0
$46$	4.88078	+	4.35051i	0.719632	+	0.641447i
$47$			2.34853i			0.342569i	0.985222	+	0.171284i	$0.0547917\pi$
$47$			2.34853i			0.342569i	−0.985222	+	0.171284i	$0.945208\pi$
$48$		0			0
$49$			6.39558i			0.913654i
$50$	−3.55098	+	3.98380i	−0.502184	+	0.563394i
$51$		0			0
$52$	5.70075	+	10.2526i	0.790551	+	1.42178i
$53$	−3.08254	+	7.44190i	−0.423419	+	1.02222i	0.557913	+	0.829900i	$0.311602\pi$
$53$	−3.08254	+	7.44190i	−0.423419	+	1.02222i	−0.981331	+	0.192324i	$0.938398\pi$
$54$		0			0
$55$	−2.07506	−	2.07506i	−0.279801	−	0.279801i
$56$	−1.79825	−	1.26557i	−0.240302	−	0.169119i
$57$		0			0
$58$	−9.43932	+	4.56064i	−1.23944	+	0.598841i
$59$	−2.96161	+	7.14996i	−0.385569	+	0.930846i	0.605298	+	0.795999i	$0.293054\pi$
$59$	−2.96161	+	7.14996i	−0.385569	+	0.930846i	−0.990867	+	0.134846i	$0.956946\pi$
$60$		0			0
$61$	5.36346	−	2.22162i	0.686721	−	0.284449i	−0.0119123	−	0.999929i	$-0.503792\pi$
$61$	5.36346	−	2.22162i	0.686721	−	0.284449i	0.698633	+	0.715480i	$0.253792\pi$
$62$	−7.90977	+	0.454363i	−1.00454	+	0.0577041i
$63$		0			0
$64$	−7.53055	+	2.70016i	−0.941318	+	0.337520i
$65$		−	6.49559i		−	0.805679i
$66$		0			0
$67$	0.398752	+	0.962673i	0.0487153	+	0.117609i	0.946364	−	0.323103i	$-0.104726\pi$
$67$	0.398752	+	0.962673i	0.0487153	+	0.117609i	−0.897649	+	0.440712i	$0.854726\pi$
$68$	−1.02330	+	0.117953i	−0.124094	+	0.0143039i
$69$		0			0
$70$	0.529697	+	1.09634i	0.0633110	+	0.131037i
$71$	5.43150	+	5.43150i	0.644601	+	0.644601i	0.951683	−	0.307082i	$-0.0993527\pi$
$71$	5.43150	+	5.43150i	0.644601	+	0.644601i	−0.307082	+	0.951683i	$0.599353\pi$
$72$		0			0
$73$	2.98447	−	2.98447i	0.349306	−	0.349306i	−0.510545	−	0.859851i	$-0.670556\pi$
$73$	2.98447	−	2.98447i	0.349306	−	0.349306i	0.859851	+	0.510545i	$0.170556\pi$
$74$	−9.02846	−	3.14623i	−1.04954	−	0.365741i
$75$		0			0
$76$	−5.04409	+	2.80466i	−0.578597	+	0.321716i
$77$	1.90333	−	0.788386i	0.216905	−	0.0898449i
$78$		0			0
$79$	−6.13141			−0.689838			−0.344919	−	0.938632i	$-0.612094\pi$
$79$	−6.13141			−0.689838			−0.344919	+	0.938632i	$0.612094\pi$
$80$	4.37088	+	0.719631i	0.488679	+	0.0804572i
$81$		0			0
$82$	−11.2578	+	12.6300i	−1.24322	+	1.39475i
$83$	1.05703	+	2.55189i	0.116024	+	0.280106i	0.971214	−	0.238208i	$-0.0765599\pi$
$83$	1.05703	+	2.55189i	0.116024	+	0.280106i	−0.855190	+	0.518314i	$0.826560\pi$
$84$		0			0
$85$	0.526954	+	0.218271i	0.0571561	+	0.0236749i
$86$	−4.59374	−	1.60082i	−0.495355	−	0.172621i
$87$		0			0
$88$	1.63972	−	7.31347i	0.174795	−	0.779618i
$89$	−0.656796	+	0.656796i	−0.0696202	+	0.0696202i	−0.741060	−	0.671439i	$-0.765676\pi$
$89$	−0.656796	+	0.656796i	−0.0696202	+	0.0696202i	0.671439	+	0.741060i	$0.265676\pi$
$90$		0			0
$91$	4.21297	+	1.74507i	0.441639	+	0.182933i
$92$	5.74657	−	7.24395i	0.599121	−	0.755234i
$93$		0			0
$94$	3.31586	−	0.190474i	0.342005	−	0.0196459i
$95$	3.19570			0.327872
$96$		0			0
$97$	−10.9570			−1.11251			−0.556256	−	0.831011i	$-0.687763\pi$
$97$	−10.9570			−1.11251			−0.556256	+	0.831011i	$0.687763\pi$
$98$	9.02983	−	0.518703i	0.912150	−	0.0523969i
$99$		0			0
$100$	5.91267	+	4.69048i	0.591267	+	0.469048i
$101$	−1.68484	−	0.697884i	−0.167648	−	0.0694420i	0.297281	−	0.954790i	$-0.403920\pi$
$101$	−1.68484	−	0.697884i	−0.167648	−	0.0694420i	−0.464929	+	0.885348i	$0.653920\pi$
$102$		0			0
$103$	2.98561	−	2.98561i	0.294181	−	0.294181i	−0.544548	−	0.838729i	$-0.683299\pi$
$103$	2.98561	−	2.98561i	0.294181	−	0.294181i	0.838729	+	0.544548i	$0.183299\pi$
$104$	14.0132	−	8.88033i	1.37411	−	0.870788i
$105$		0			0
$106$	10.7571	+	3.74863i	1.04482	+	0.364099i
$107$	5.79461	+	2.40021i	0.560186	+	0.232037i	0.644766	−	0.764380i	$-0.276955\pi$
$107$	5.79461	+	2.40021i	0.560186	+	0.232037i	−0.0845799	+	0.996417i	$0.526955\pi$
$108$		0			0
$109$	1.10348	+	2.66404i	0.105694	+	0.255169i	0.967875	−	0.251432i	$-0.0809016\pi$
$109$	1.10348	+	2.66404i	0.105694	+	0.255169i	−0.862180	+	0.506601i	$0.830902\pi$
$110$	−2.76145	+	3.09804i	−0.263294	+	0.295386i
$111$		0			0
$112$	−1.64100	+	2.64157i	−0.155060	+	0.249605i
$113$	17.4090			1.63770			0.818850	−	0.574008i	$-0.194612\pi$
$113$	17.4090			1.63770			0.818850	+	0.574008i	$0.194612\pi$
$114$		0			0
$115$	−4.73020	+	1.95931i	−0.441093	+	0.182707i
$116$	7.20466	+	12.9574i	0.668936	+	1.20306i
$117$		0			0
$118$	10.3351	+	3.60157i	0.951425	+	0.331551i
$119$	−0.283137	+	0.283137i	−0.0259551	+	0.0259551i
$120$		0			0
$121$	−2.81291	−	2.81291i	−0.255719	−	0.255719i
$122$	−3.57167	−	7.39242i	−0.323364	−	0.669278i
$123$		0			0
$124$	1.28302	+	11.1308i	0.115218	+	0.999579i
$125$	−3.71821	−	8.97655i	−0.332567	−	0.802887i
$126$		0			0
$127$		−	16.8370i		−	1.49404i	−0.664801	−	0.747020i	$-0.731484\pi$
$127$		−	16.8370i		−	1.49404i	0.664801	−	0.747020i	$-0.268516\pi$
$128$	4.42307	+	10.4133i	0.390948	+	0.920413i
$129$		0			0
$130$	−9.17104	+	0.526814i	−0.804353	+	0.0462047i
$131$	−7.92259	+	3.28164i	−0.692200	+	0.286718i	−0.700916	−	0.713244i	$-0.747225\pi$
$131$	−7.92259	+	3.28164i	−0.692200	+	0.286718i	0.00871665	+	0.999962i	$0.497225\pi$
$132$		0			0
$133$	−0.858540	+	2.07270i	−0.0744449	+	0.179726i
$134$	1.32684	−	0.641068i	0.114622	−	0.0553799i
$135$		0			0
$136$	0.249530	+	1.43522i	0.0213970	+	0.123069i
$137$	1.62791	+	1.62791i	0.139082	+	0.139082i	0.773220	−	0.634138i	$-0.218645\pi$
$137$	1.62791	+	1.62791i	0.139082	+	0.139082i	−0.634138	+	0.773220i	$0.718645\pi$
$138$		0			0
$139$	−0.595578	+	1.43785i	−0.0505163	+	0.121957i	−0.947123	−	0.320870i	$-0.896025\pi$
$139$	−0.595578	+	1.43785i	−0.0505163	+	0.121957i	0.896607	+	0.442828i	$0.146025\pi$
$140$	1.50494	−	0.836789i	0.127191	−	0.0707216i
$141$		0			0
$142$	7.22815	−	8.10918i	0.606573	−	0.680507i
$143$			15.5429i			1.29976i
$144$		0			0
$145$		−	8.20920i		−	0.681737i
$146$	−4.45579	−	3.97169i	−0.368764	−	0.328699i
$147$		0			0
$148$	−3.70988	+	13.0023i	−0.304950	+	1.06878i
$149$	7.63812	−	18.4401i	0.625739	−	1.51067i	−0.219130	−	0.975696i	$-0.570322\pi$
$149$	7.63812	−	18.4401i	0.625739	−	1.51067i	0.844869	−	0.534973i	$-0.179678\pi$
$150$		0			0
$151$	−6.02666	−	6.02666i	−0.490443	−	0.490443i	0.418003	−	0.908446i	$-0.362730\pi$
$151$	−6.02666	−	6.02666i	−0.490443	−	0.490443i	−0.908446	+	0.418003i	$0.862730\pi$
$152$	4.36895	+	6.89421i	0.354368	+	0.559195i
$153$		0			0
$154$	−1.26748	−	2.62335i	−0.102136	−	0.211395i
$155$	2.37421	−	5.73186i	0.190701	−	0.460394i
$156$		0			0
$157$	13.9023	−	5.75854i	1.10953	−	0.459582i	0.248753	−	0.968567i	$-0.419979\pi$
$157$	13.9023	−	5.75854i	1.10953	−	0.459582i	0.860775	+	0.508985i	$0.169979\pi$
$158$	0.497278	+	8.65686i	0.0395613	+	0.688703i
$159$		0			0
$160$	0.661544	−	6.22954i	0.0522997	−	0.492489i
$161$		−	3.59433i		−	0.283273i
$162$		0			0
$163$	5.81643	+	14.0421i	0.455578	+	1.09986i	0.970169	+	0.242428i	$0.0779437\pi$
$163$	5.81643	+	14.0421i	0.455578	+	1.09986i	−0.514591	+	0.857436i	$0.672056\pi$
$164$	18.7452	+	14.8704i	1.46375	+	1.16118i
$165$		0			0
$166$	3.51725	−	1.69937i	0.272992	−	0.131897i
$167$	−14.5368	−	14.5368i	−1.12489	−	1.12489i	−0.990995	−	0.133896i	$-0.957251\pi$
$167$	−14.5368	−	14.5368i	−1.12489	−	1.12489i	−0.133896	−	0.990995i	$-0.542749\pi$
$168$		0			0
$169$	−15.1347	+	15.1347i	−1.16421	+	1.16421i
$170$	0.265437	−	0.761701i	0.0203581	−	0.0584198i
$171$		0			0
$172$	−1.88761	+	6.61566i	−0.143929	+	0.504440i
$173$	4.13825	−	1.71412i	0.314626	−	0.130322i	−0.219782	−	0.975549i	$-0.570535\pi$
$173$	4.13825	−	1.71412i	0.314626	−	0.130322i	0.534408	+	0.845227i	$0.320535\pi$
$174$		0			0
$175$	2.93377			0.221772
$176$	−10.4588	−	1.72196i	−0.788360	−	0.129797i
$177$		0			0
$178$	0.980589	+	0.874053i	0.0734983	+	0.0655130i
$179$	9.61242	+	23.2064i	0.718466	+	1.73453i	0.677673	+	0.735363i	$0.262989\pi$
$179$	9.61242	+	23.2064i	0.718466	+	1.73453i	0.0407933	+	0.999168i	$0.487011\pi$
$180$		0			0
$181$	4.05011	+	1.67761i	0.301043	+	0.124696i	0.528092	−	0.849187i	$-0.322908\pi$
$181$	4.05011	+	1.67761i	0.301043	+	0.124696i	−0.227049	+	0.973883i	$0.572908\pi$
$182$	2.12215	−	6.08977i	0.157304	−	0.451403i
$183$		0			0
$184$	−10.6937	−	7.52599i	−0.788349	−	0.554824i
$185$	5.29404	−	5.29404i	0.389226	−	0.389226i
$186$		0			0
$187$	−1.26091	−	0.522287i	−0.0922070	−	0.0381934i
$188$	−0.537855	−	4.66617i	−0.0392271	−	0.340316i
$189$		0			0
$190$	−0.259182	−	4.51197i	−0.0188031	−	0.327333i
$191$	22.1321			1.60142			0.800710	−	0.599053i	$-0.204456\pi$
$191$	22.1321			1.60142			0.800710	+	0.599053i	$0.204456\pi$
$192$		0			0
$193$	10.1418			0.730026			0.365013	−	0.931002i	$-0.381065\pi$
$193$	10.1418			0.730026			0.365013	+	0.931002i	$0.381065\pi$
$194$	0.888647	+	15.4700i	0.0638011	+	1.11068i
$195$		0			0
$196$	−1.46470	−	12.7070i	−0.104621	−	0.907644i
$197$	0.114773	+	0.0475406i	0.00817726	+	0.00338713i	0.386768	−	0.922177i	$-0.373591\pi$
$197$	0.114773	+	0.0475406i	0.00817726	+	0.00338713i	−0.378591	+	0.925564i	$0.623591\pi$
$198$		0			0
$199$	−5.93135	+	5.93135i	−0.420462	+	0.420462i	−0.885363	−	0.464901i	$-0.846090\pi$
$199$	−5.93135	+	5.93135i	−0.420462	+	0.420462i	0.464901	+	0.885363i	$0.346090\pi$
$200$	6.14288	−	8.72842i	0.434367	−	0.617193i
$201$		0			0
$202$	−0.848686	+	2.43540i	−0.0597133	+	0.171354i
$203$	5.32439	+	2.20544i	0.373699	+	0.154791i
$204$		0			0
$205$	−5.07011	−	12.2403i	−0.354112	−	0.854901i
$206$	−4.45749	−	3.97320i	−0.310568	−	0.276826i
$207$		0			0
$208$	−13.6745	−	19.0648i	−0.948158	−	1.32191i
$209$	−7.64679			−0.528939
$210$		0			0
$211$	22.0729	−	9.14290i	1.51956	−	0.629423i	0.542058	−	0.840341i	$-0.317645\pi$
$211$	22.0729	−	9.14290i	1.51956	−	0.629423i	0.977504	+	0.210918i	$0.0676454\pi$
$212$	4.42020	−	15.4919i	0.303580	−	1.06398i
$213$		0			0
$214$	2.91886	−	8.37599i	0.199529	−	0.572571i
$215$	2.69364	−	2.69364i	0.183705	−	0.183705i
$216$		0			0
$217$	3.07978	+	3.07978i	0.209069	+	0.209069i
$218$	3.67183	−	1.77405i	0.248688	−	0.120154i
$219$		0			0
$220$	4.59804	+	3.64759i	0.310000	+	0.245920i
$221$	−1.15607	−	2.79099i	−0.0777655	−	0.187742i
$222$		0			0
$223$		−	1.52014i		−	0.101796i	−0.998704	−	0.0508979i	$-0.983792\pi$
$223$		−	1.52014i		−	0.101796i	0.998704	−	0.0508979i	$-0.0162083\pi$
$224$	3.86269	+	2.10266i	0.258087	+	0.140490i
$225$		0			0
$226$	−1.41193	−	24.5795i	−0.0939199	−	1.63500i
$227$	−17.6896	+	7.32726i	−1.17410	+	0.486328i	−0.882546	−	0.470227i	$-0.844172\pi$
$227$	−17.6896	+	7.32726i	−1.17410	+	0.486328i	−0.291553	+	0.956555i	$0.594172\pi$
$228$		0			0
$229$	9.31877	−	22.4975i	0.615801	−	1.48668i	−0.240736	−	0.970591i	$-0.577389\pi$
$229$	9.31877	−	22.4975i	0.615801	−	1.48668i	0.856537	−	0.516085i	$-0.172611\pi$
$230$	3.14996	+	6.51959i	0.207702	+	0.429889i
$231$		0			0
$232$	17.7100	−	11.2230i	1.16272	−	0.736829i
$233$	−6.47985	−	6.47985i	−0.424509	−	0.424509i	0.462244	−	0.886753i	$-0.347044\pi$
$233$	−6.47985	−	6.47985i	−0.424509	−	0.424509i	−0.886753	+	0.462244i	$0.847044\pi$
$234$		0			0
$235$	−0.995297	+	2.40286i	−0.0649260	+	0.156745i
$236$	4.24680	−	14.8841i	0.276443	−	0.968874i
$237$		0			0
$238$	0.422720	+	0.376793i	0.0274009	+	0.0244239i
$239$			28.5450i			1.84642i	0.384291	+	0.923212i	$0.374446\pi$
$239$			28.5450i			1.84642i	−0.384291	+	0.923212i	$0.625554\pi$
$240$		0			0
$241$			27.4173i			1.76610i	0.469278	+	0.883051i	$0.344514\pi$
$241$			27.4173i			1.76610i	−0.469278	+	0.883051i	$0.655486\pi$
$242$	−3.74338	+	4.19965i	−0.240633	+	0.269964i
$243$		0			0
$244$	−10.1476	+	5.64234i	−0.649632	+	0.361214i
$245$	−2.71041	+	6.54352i	−0.173162	+	0.418050i
$246$		0			0
$247$	−11.9685	−	11.9685i	−0.761534	−	0.761534i
$248$	15.6114	−	2.71422i	0.991326	−	0.172353i
$249$		0			0
$250$	−12.3723	+	5.97771i	−0.782493	+	0.378064i
$251$	7.40685	−	17.8817i	0.467516	−	1.12868i	−0.497728	−	0.867333i	$-0.665832\pi$
$251$	7.40685	−	17.8817i	0.467516	−	1.12868i	0.965244	−	0.261351i	$-0.0841679\pi$
$252$		0			0
$253$	11.3186	−	4.68830i	0.711592	−	0.294751i
$254$	−23.7719	+	1.36554i	−1.49158	+	0.0856813i
$255$		0			0
$256$	14.3436	−	7.08942i	0.896478	−	0.443089i
$257$		−	13.2444i		−	0.826160i	−0.910695	−	0.413080i	$-0.864453\pi$
$257$		−	13.2444i		−	0.826160i	0.910695	−	0.413080i	$-0.135547\pi$
$258$		0			0
$259$	2.01139	+	4.85593i	0.124982	+	0.301733i
$260$	1.48760	+	12.9057i	0.0922573	+	0.800380i
$261$		0			0
$262$	5.27585	+	10.9196i	0.325943	+	0.674618i
$263$	−6.63410	−	6.63410i	−0.409076	−	0.409076i	0.472340	−	0.881416i	$-0.343409\pi$
$263$	−6.63410	−	6.63410i	−0.409076	−	0.409076i	−0.881416	+	0.472340i	$0.843409\pi$
$264$		0			0
$265$	−6.30768	+	6.30768i	−0.387478	+	0.387478i
$266$	2.99604	+	1.04406i	0.183699	+	0.0640153i
$267$		0			0
$268$	−1.01273	−	1.82136i	−0.0618621	−	0.111257i
$269$	3.41644	−	1.41514i	0.208304	−	0.0862824i	−0.276092	−	0.961131i	$-0.589039\pi$
$269$	3.41644	−	1.41514i	0.208304	−	0.0862824i	0.484396	+	0.874849i	$0.339039\pi$
$270$		0			0
$271$	−29.3563			−1.78327			−0.891635	−	0.452754i	$-0.850441\pi$
$271$	−29.3563			−1.78327			−0.891635	+	0.452754i	$0.850441\pi$
$272$	2.00613	−	0.468709i	0.121640	−	0.0284196i
$273$		0			0
$274$	2.16640	−	2.43046i	0.130877	−	0.146829i
$275$	3.82670	+	9.23846i	0.230758	+	0.557100i
$276$		0			0
$277$	−15.8026	−	6.54564i	−0.949484	−	0.393289i	−0.146447	−	0.989218i	$-0.546784\pi$
$277$	−15.8026	−	6.54564i	−0.949484	−	0.393289i	−0.803037	+	0.595929i	$0.796784\pi$
$278$	2.07839	+	0.724274i	0.124653	+	0.0434391i
$279$		0			0
$280$	−1.30351	−	2.05694i	−0.0778994	−	0.122926i
$281$	−4.81127	+	4.81127i	−0.287016	+	0.287016i	−0.835899	−	0.548883i	$-0.815053\pi$
$281$	−4.81127	+	4.81127i	−0.287016	+	0.287016i	0.548883	+	0.835899i	$0.315053\pi$
$282$		0			0
$283$	15.2722	+	6.32597i	0.907841	+	0.376040i	0.787230	−	0.616660i	$-0.211515\pi$
$283$	15.2722	+	6.32597i	0.907841	+	0.376040i	0.120611	+	0.992700i	$0.461515\pi$
$284$	−12.0355	−	9.54764i	−0.714173	−	0.566548i
$285$		0			0
$286$	21.9448	−	1.26058i	1.29762	−	0.0745396i
$287$	9.30104			0.549023
$288$		0			0
$289$	−16.7347			−0.984396
$290$	−11.5904	+	0.665793i	−0.680615	+	0.0390967i
$291$		0			0
$292$	−5.24619	+	6.61318i	−0.307010	+	0.387007i
$293$	20.9184	+	8.66470i	1.22207	+	0.506197i	0.898067	−	0.439860i	$-0.144972\pi$
$293$	20.9184	+	8.66470i	1.22207	+	0.506197i	0.324001	+	0.946057i	$0.394972\pi$
$294$		0			0
$295$	−6.06024	+	6.06024i	−0.352841	+	0.352841i
$296$	18.6587	+	4.18339i	1.08451	+	0.243155i
$297$		0			0
$298$	−26.6547	−	9.28861i	−1.54407	−	0.538075i
$299$	25.0533	+	10.3774i	1.44887	+	0.600142i
$300$		0			0
$301$	1.02341	+	2.47072i	0.0589882	+	0.142410i
$302$	−8.02018	+	8.99774i	−0.461509	+	0.517762i
$303$		0			0
$304$	9.37951	−	6.72760i	0.537952	−	0.385854i
$305$	6.42904			0.368126
$306$		0			0
$307$	23.9065	−	9.90242i	1.36442	−	0.565161i	0.424149	−	0.905592i	$-0.360573\pi$
$307$	23.9065	−	9.90242i	1.36442	−	0.565161i	0.940269	+	0.340432i	$0.110573\pi$
$308$	−3.60107	+	2.00230i	−0.205190	+	0.114091i
$309$		0			0
$310$	−8.28529	−	2.88725i	−0.470573	−	0.163985i
$311$	−13.5439	+	13.5439i	−0.768007	+	0.768007i	−0.977755	−	0.209749i	$-0.932735\pi$
$311$	−13.5439	+	13.5439i	−0.768007	+	0.768007i	0.209749	+	0.977755i	$0.432735\pi$
$312$		0			0
$313$	4.30307	+	4.30307i	0.243224	+	0.243224i	0.818183	−	0.574959i	$-0.194982\pi$
$313$	4.30307	+	4.30307i	0.243224	+	0.243224i	−0.574959	+	0.818183i	$0.694982\pi$
$314$	−9.25793	−	19.1615i	−0.522455	−	1.08135i
$315$		0			0
$316$	12.1822	−	1.40420i	0.685300	−	0.0789924i
$317$	−12.0099	−	28.9944i	−0.674541	−	1.62849i	−0.773804	−	0.633425i	$-0.781649\pi$
$317$	−12.0099	−	28.9944i	−0.674541	−	1.62849i	0.0992630	−	0.995061i	$-0.468351\pi$
$318$		0			0
$319$			19.6432i			1.09981i
$320$	−8.84906	−	0.428788i	−0.494677	−	0.0239700i
$321$		0			0
$322$	−5.07479	+	0.291512i	−0.282807	+	0.0162453i
$323$	1.37311	−	0.568762i	0.0764021	−	0.0316468i
$324$		0			0
$325$	−8.47028	+	20.4491i	−0.469847	+	1.13431i
$326$	19.3541	−	9.35100i	1.07193	−	0.517904i
$327$		0			0
$328$	19.4750	−	27.6721i	1.07533	−	1.52793i
$329$	−1.29108	−	1.29108i	−0.0711794	−	0.0711794i
$330$		0			0
$331$	−12.6627	+	30.5704i	−0.696003	+	1.68030i	0.0363165	+	0.999340i	$0.488438\pi$
$331$	−12.6627	+	30.5704i	−0.696003	+	1.68030i	−0.732320	+	0.680961i	$0.761562\pi$
$332$	−2.68458	−	4.82813i	−0.147335	−	0.264978i
$333$		0			0
$334$	−19.3453	+	21.7033i	−1.05853	+	1.18755i
$335$			1.15393i			0.0630459i
$336$		0			0
$337$			17.6737i			0.962748i	0.876515	+	0.481374i	$0.159862\pi$
$337$			17.6737i			0.962748i	−0.876515	+	0.481374i	$0.840138\pi$
$338$	22.5960	+	20.1410i	1.22906	+	1.09553i
$339$		0			0
$340$	−1.09696	−	0.312990i	−0.0594912	−	0.0169743i
$341$	−5.68110	+	13.7154i	−0.307649	+	0.742729i
$342$		0			0
$343$	−7.36405	−	7.36405i	−0.397621	−	0.397621i
$344$	9.49365	+	2.12853i	0.511864	+	0.114763i
$345$		0			0
$346$	−2.75577	−	5.70372i	−0.148151	−	0.306634i
$347$	7.92952	−	19.1436i	0.425679	−	1.02768i	−0.554964	−	0.831875i	$-0.687268\pi$
$347$	7.92952	−	19.1436i	0.425679	−	1.02768i	0.980643	−	0.195806i	$-0.0627322\pi$
$348$		0			0
$349$	−1.37363	+	0.568978i	−0.0735289	+	0.0304567i	−0.419145	−	0.907919i	$-0.637670\pi$
$349$	−1.37363	+	0.568978i	−0.0735289	+	0.0304567i	0.345616	+	0.938376i	$0.387670\pi$
$350$	−0.237939	−	4.14215i	−0.0127183	−	0.221407i
$351$		0			0
$352$	−1.58296	+	14.9063i	−0.0843723	+	0.794506i
$353$			2.64701i			0.140886i	0.997516	+	0.0704431i	$0.0224413\pi$
$353$			2.64701i			0.140886i	−0.997516	+	0.0704431i	$0.977559\pi$
$354$		0			0
$355$	3.25530	+	7.85899i	0.172773	+	0.417112i
$356$	1.15453	−	1.45537i	0.0611902	−	0.0771344i
$357$		0			0
$358$	31.9853	−	15.4538i	1.69047	−	0.816757i
$359$	−13.3235	−	13.3235i	−0.703189	−	0.703189i	0.261904	−	0.965094i	$-0.415649\pi$
$359$	−13.3235	−	13.3235i	−0.703189	−	0.703189i	−0.965094	+	0.261904i	$0.915649\pi$
$360$		0			0
$361$	−7.54679	+	7.54679i	−0.397199	+	0.397199i
$362$	2.04012	−	5.85436i	0.107226	−	0.307698i
$363$		0			0
$364$	−8.77017	−	2.50234i	−0.459682	−	0.131158i
$365$	4.31832	−	1.78871i	0.226031	−	0.0936251i
$366$		0			0
$367$	2.91350			0.152083			0.0760417	−	0.997105i	$-0.475772\pi$
$367$	2.91350			0.152083			0.0760417	+	0.997105i	$0.475772\pi$
$368$	−9.75855	+	15.7087i	−0.508700	+	0.818870i
$369$		0			0
$370$	−7.90395	−	7.04522i	−0.410907	−	0.366264i
$371$	−2.39651	−	5.78568i	−0.124420	−	0.300377i
$372$		0			0
$373$	26.3018	+	10.8946i	1.36186	+	0.564100i	0.939568	−	0.342362i	$-0.111227\pi$
$373$	26.3018	+	10.8946i	1.36186	+	0.564100i	0.422289	+	0.906461i	$0.361227\pi$
$374$	−0.635145	+	1.82262i	−0.0328426	+	0.0942456i
$375$		0			0
$376$	−6.54448	+	1.13783i	−0.337506	+	0.0586792i
$377$	−30.7448	+	30.7448i	−1.58344	+	1.58344i
$378$		0			0
$379$	29.2228	+	12.1045i	1.50108	+	0.621766i	0.973693	−	0.227862i	$-0.0731737\pi$
$379$	29.2228	+	12.1045i	1.50108	+	0.621766i	0.527382	+	0.849628i	$0.323174\pi$
$380$	−6.34937	+	0.731872i	−0.325716	+	0.0375442i
$381$		0			0
$382$	−1.79498	−	31.2479i	−0.0918393	−	1.59878i
$383$	−21.2542			−1.08604			−0.543018	−	0.839721i	$-0.682719\pi$
$383$	−21.2542			−1.08604			−0.543018	+	0.839721i	$0.682719\pi$
$384$		0			0
$385$	2.28147			0.116275
$386$	−0.822537	−	14.3191i	−0.0418660	−	0.728824i
$387$		0			0
$388$	21.7698	−	2.50934i	1.10519	−	0.127392i
$389$	0.560211	+	0.232047i	0.0284038	+	0.0117652i	0.396840	−	0.917888i	$-0.370107\pi$
$389$	0.560211	+	0.232047i	0.0284038	+	0.0117652i	−0.368436	+	0.929653i	$0.620107\pi$
$390$		0			0
$391$	−1.68373	+	1.68373i	−0.0851501	+	0.0851501i
$392$	−17.8221	+	3.09857i	−0.900150	+	0.156501i
$393$		0			0
$394$	0.0578135	−	0.165902i	0.00291260	−	0.00835804i
$395$	−6.27324	−	2.59846i	−0.315641	−	0.130743i
$396$		0			0
$397$	6.50947	+	15.7153i	0.326701	+	0.788726i	0.998833	+	0.0482949i	$0.0153787\pi$
$397$	6.50947	+	15.7153i	0.326701	+	0.788726i	−0.672132	+	0.740431i	$0.734621\pi$
$398$	8.85544	+	7.89334i	0.443883	+	0.395657i
$399$		0			0
$400$	−12.8217	−	7.96514i	−0.641087	−	0.398257i
$401$	31.5480			1.57543			0.787717	−	0.616038i	$-0.211263\pi$
$401$	31.5480			1.57543			0.787717	+	0.616038i	$0.211263\pi$
$402$		0			0
$403$	−30.3586	+	12.5749i	−1.51227	+	0.626403i
$404$	3.50734	+	1.00073i	0.174497	+	0.0497881i
$405$		0			0
$406$	2.68200	−	7.69630i	0.133105	−	0.381961i
$407$	−12.6678	+	12.6678i	−0.627918	+	0.627918i
$408$		0			0
$409$	7.70292	+	7.70292i	0.380885	+	0.380885i	0.871421	−	0.490536i	$-0.163199\pi$
$409$	7.70292	+	7.70292i	0.380885	+	0.380885i	−0.490536	+	0.871421i	$0.663199\pi$
$410$	−16.8707	+	8.15115i	−0.833186	+	0.402556i
$411$		0			0
$412$	−5.24819	+	6.61570i	−0.258560	+	0.325932i
$413$	−2.30249	−	5.55871i	−0.113298	−	0.273526i
$414$		0			0
$415$			3.05888i			0.150155i
$416$	−25.8083	+	20.8531i	−1.26535	+	1.02241i
$417$		0			0
$418$	0.620180	+	10.7964i	0.0303340	+	0.528069i
$419$	−37.3177	+	15.4575i	−1.82309	+	0.755149i	−0.849223	+	0.528034i	$0.822929\pi$
$419$	−37.3177	+	15.4575i	−1.82309	+	0.755149i	−0.973868	+	0.227116i	$0.927071\pi$
$420$		0			0
$421$	10.7666	−	25.9930i	0.524734	−	1.26682i	−0.410199	−	0.911996i	$-0.634541\pi$
$421$	10.7666	−	25.9930i	0.524734	−	1.26682i	0.934933	−	0.354824i	$-0.115459\pi$
$422$	−14.6989	−	30.4229i	−0.715532	−	1.48096i
$423$		0			0
$424$	−22.2312	−	4.98437i	−1.07964	−	0.242063i
$425$	−1.37430	−	1.37430i	−0.0666633	−	0.0666633i
$426$		0			0
$427$	−1.72719	+	4.16981i	−0.0835846	+	0.201791i
$428$	−12.0627	−	3.44177i	−0.583072	−	0.166364i
$429$		0			0
$430$	−4.02158	−	3.58465i	−0.193938	−	0.172867i
$431$		−	25.8873i		−	1.24695i	−0.781844	−	0.623474i	$-0.785721\pi$
$431$		−	25.8873i		−	1.24695i	0.781844	−	0.623474i	$-0.214279\pi$
$432$		0			0
$433$		−	14.8695i		−	0.714583i	−0.933993	−	0.357292i	$-0.883700\pi$
$433$		−	14.8695i		−	0.714583i	0.933993	−	0.357292i	$-0.116300\pi$
$434$	4.09852	−	4.59808i	0.196735	−	0.220715i
$435$		0			0
$436$	−2.80256	−	5.04032i	−0.134218	−	0.241388i
$437$	−5.10549	+	12.3257i	−0.244229	+	0.589620i
$438$		0			0
$439$	4.49359	+	4.49359i	0.214467	+	0.214467i	0.806162	−	0.591695i	$-0.201541\pi$
$439$	4.49359	+	4.49359i	0.214467	+	0.214467i	−0.591695	+	0.806162i	$0.701541\pi$
$440$	4.77707	−	6.78774i	0.227738	−	0.323593i
$441$		0			0
$442$	−3.84680	+	1.85859i	−0.182974	+	0.0884043i
$443$	1.53078	−	3.69564i	0.0727297	−	0.175585i	−0.883334	−	0.468744i	$-0.844707\pi$
$443$	1.53078	−	3.69564i	0.0727297	−	0.175585i	0.956064	+	0.293159i	$0.0947066\pi$
$444$		0			0
$445$	−0.950336	+	0.393642i	−0.0450502	+	0.0186604i
$446$	−2.14626	+	0.123288i	−0.101628	+	0.00583786i
$447$		0			0
$448$	2.65545	−	5.62420i	0.125458	−	0.265719i
$449$			7.05855i			0.333114i	0.986032	+	0.166557i	$0.0532649\pi$
$449$			7.05855i			0.333114i	−0.986032	+	0.166557i	$0.946735\pi$
$450$		0			0
$451$	12.1319	+	29.2890i	0.571270	+	1.37917i
$452$	−34.5889	+	3.98696i	−1.62693	+	0.187531i
$453$		0			0
$454$	11.7799	+	24.3814i	0.552860	+	1.14428i
$455$	3.57087	+	3.57087i	0.167405	+	0.167405i
$456$		0			0
$457$	−21.4531	+	21.4531i	−1.00353	+	1.00353i	−0.00353826	+	0.999994i	$0.501126\pi$
$457$	−21.4531	+	21.4531i	−1.00353	+	1.00353i	−0.999994	+	0.00353826i	$0.998874\pi$
$458$	−32.5197	−	11.3324i	−1.51954	−	0.529529i
$459$		0			0
$460$	8.94945	−	4.97614i	0.417270	−	0.232014i
$461$	14.0545	−	5.82154i	0.654581	−	0.271136i	−0.0305752	−	0.999532i	$-0.509734\pi$
$461$	14.0545	−	5.82154i	0.654581	−	0.271136i	0.685156	+	0.728396i	$0.259734\pi$
$462$		0			0
$463$	23.0001			1.06890			0.534452	−	0.845199i	$-0.320518\pi$
$463$	23.0001			1.06890			0.534452	+	0.845199i	$0.320518\pi$
$464$	−17.2820	−	24.0943i	−0.802297	−	1.11855i
$465$		0			0
$466$	−8.62327	+	9.67435i	−0.399465	+	0.448155i
$467$	−5.98019	−	14.4375i	−0.276730	−	0.668086i	0.723011	−	0.690837i	$-0.242758\pi$
$467$	−5.98019	−	14.4375i	−0.276730	−	0.668086i	−0.999741	+	0.0227507i	$0.992758\pi$
$468$		0			0
$469$	−0.748426	−	0.310008i	−0.0345591	−	0.0143149i
$470$	3.47329	+	1.21037i	0.160211	+	0.0558300i
$471$		0			0
$472$	−21.3591	−	4.78884i	−0.983133	−	0.220424i
$473$	−6.44543	+	6.44543i	−0.296361	+	0.296361i
$474$		0			0
$475$	−10.0605	−	4.16721i	−0.461609	−	0.191205i
$476$	0.497705	−	0.627392i	0.0228123	−	0.0287565i
$477$		0			0
$478$	40.3023	−	2.31510i	1.84339	−	0.105890i
$479$	21.2145			0.969314			0.484657	−	0.874704i	$-0.338944\pi$
$479$	21.2145			0.969314			0.484657	+	0.874704i	$0.338944\pi$
$480$		0			0
$481$	−39.6542			−1.80807
$482$	38.7101	−	2.22363i	1.76319	−	0.101284i
$483$		0			0
$484$	6.23303	+	4.94462i	0.283319	+	0.224755i
$485$	−11.2104	−	4.64351i	−0.509039	−	0.210851i
$486$		0			0
$487$	3.68805	−	3.68805i	0.167121	−	0.167121i	−0.618591	−	0.785713i	$-0.712296\pi$
$487$	3.68805	−	3.68805i	0.167121	−	0.167121i	0.785713	+	0.618591i	$0.212296\pi$
$488$	8.78934	+	13.8696i	0.397875	+	0.627848i
$489$		0			0
$490$	9.45853	+	3.29610i	0.427293	+	0.148902i
$491$	−36.8386	−	15.2590i	−1.66250	−	0.688631i	−0.664238	−	0.747521i	$-0.731244\pi$
$491$	−36.8386	−	15.2590i	−1.66250	−	0.688631i	−0.998264	+	0.0588902i	$0.981244\pi$
$492$		0			0
$493$	−1.46105	−	3.52728i	−0.0658023	−	0.158861i
$494$	−15.9274	+	17.8688i	−0.716608	+	0.803954i
$495$		0			0
$496$	−5.09831	−	21.8214i	−0.228921	−	0.979810i
$497$	−5.97180			−0.267872
$498$		0			0
$499$	−30.4487	+	12.6123i	−1.36307	+	0.564603i	−0.939901	−	0.341447i	$-0.889083\pi$
$499$	−30.4487	+	12.6123i	−1.36307	+	0.564603i	−0.423171	+	0.906050i	$0.639083\pi$
$500$	9.44329	+	16.9835i	0.422317	+	0.759524i
$501$		0			0
$502$	−25.8477	−	9.00736i	−1.15364	−	0.402018i
$503$	20.2577	−	20.2577i	0.903248	−	0.903248i	−0.0924678	−	0.995716i	$-0.529476\pi$
$503$	20.2577	−	20.2577i	0.903248	−	0.903248i	0.995716	+	0.0924678i	$0.0294755\pi$
$504$		0			0
$505$	−1.42805	−	1.42805i	−0.0635476	−	0.0635476i
$506$	−7.53732	−	15.6003i	−0.335075	−	0.693518i
$507$		0			0
$508$	3.85596	+	33.4525i	0.171081	+	1.48421i
$509$	−5.53680	−	13.3670i	−0.245414	−	0.592483i	0.752390	−	0.658718i	$-0.228901\pi$
$509$	−5.53680	−	13.3670i	−0.245414	−	0.592483i	−0.997804	+	0.0662355i	$0.978901\pi$
$510$		0			0
$511$			3.28136i			0.145159i
$512$	−11.1728	−	19.6766i	−0.493772	−	0.869592i
$513$		0			0
$514$	−18.6995	+	1.07416i	−0.824801	+	0.0473792i
$515$	4.31996	−	1.78939i	0.190360	−	0.0788498i
$516$		0			0
$517$	2.38158	−	5.74964i	0.104742	−	0.252869i
$518$	6.69288	−	3.23369i	0.294068	−	0.142080i
$519$		0			0
$520$	18.1008	−	3.14702i	0.793772	−	0.138006i
$521$	−31.1921	−	31.1921i	−1.36655	−	1.36655i	−0.865306	−	0.501244i	$-0.832876\pi$
$521$	−31.1921	−	31.1921i	−1.36655	−	1.36655i	−0.501244	−	0.865306i	$-0.667124\pi$
$522$		0			0
$523$	6.74337	−	16.2799i	0.294867	−	0.711872i	−0.705129	−	0.709079i	$-0.749111\pi$
$523$	6.74337	−	16.2799i	0.294867	−	0.711872i	0.999996	−	0.00279304i	$-0.000889052\pi$
$524$	14.9894	−	8.33452i	0.654815	−	0.364095i
$525$		0			0
$526$	−8.82855	+	9.90465i	−0.384943	+	0.431863i
$527$		−	2.88539i		−	0.125690i
$528$		0			0
$529$			1.62554i			0.0706757i
$530$	9.41730	+	8.39416i	0.409062	+	0.364619i
$531$		0			0
$532$	1.23110	−	4.31475i	0.0533750	−	0.187068i
$533$	−26.8537	+	64.8305i	−1.16316	+	2.80812i
$534$		0			0
$535$	4.91145	+	4.91145i	0.212341	+	0.212341i
$536$	−2.48942	+	1.57757i	−0.107526	+	0.0681408i
$537$		0			0
$538$	−2.27510	−	4.70885i	−0.0980863	−	0.203013i
$539$	6.48557	−	15.6575i	0.279353	−	0.674418i
$540$		0			0
$541$	−18.2188	+	7.54647i	−0.783287	+	0.324448i	−0.738241	−	0.674537i	$-0.764343\pi$
$541$	−18.2188	+	7.54647i	−0.783287	+	0.324448i	−0.0450459	+	0.998985i	$0.514343\pi$
$542$	2.38090	+	41.4478i	0.102268	+	1.78034i
$543$		0			0
$544$	−0.824467	−	2.79442i	−0.0353487	−	0.119810i
$545$			3.19332i			0.136787i
$546$		0			0
$547$	1.49915	+	3.61926i	0.0640988	+	0.154748i	0.952683	−	0.303965i	$-0.0983105\pi$
$547$	1.49915	+	3.61926i	0.0640988	+	0.154748i	−0.888584	+	0.458713i	$0.848311\pi$
$548$	−3.60723	−	2.86159i	−0.154093	−	0.122241i
$549$		0			0
$550$	12.7333	−	6.15213i	0.542950	−	0.262328i
$551$	−15.1258	−	15.1258i	−0.644383	−	0.644383i
$552$		0			0
$553$	3.37067	−	3.37067i	0.143335	−	0.143335i
$554$	−7.96005	+	22.8423i	−0.338190	+	0.970476i
$555$		0			0
$556$	0.854028	−	2.99319i	0.0362189	−	0.126939i
$557$	−22.8281	+	9.45572i	−0.967259	+	0.400652i	−0.809691	−	0.586856i	$-0.800365\pi$
$557$	−22.8281	+	9.45572i	−0.967259	+	0.400652i	−0.157568	+	0.987508i	$0.550365\pi$
$558$		0			0
$559$	−20.1763			−0.853366
$560$	−2.79844	+	2.00723i	−0.118256	+	0.0848208i
$561$		0			0
$562$	7.18317	+	6.40275i	0.303004	+	0.270084i
$563$	13.1864	+	31.8347i	0.555740	+	1.34167i	0.913111	+	0.407712i	$0.133673\pi$
$563$	13.1864	+	31.8347i	0.555740	+	1.34167i	−0.357371	+	0.933963i	$0.616327\pi$
$564$		0			0
$565$	17.8117	+	7.37784i	0.749343	+	0.310388i
$566$	7.69292	−	22.0757i	0.323358	−	0.927912i
$567$		0			0
$568$	−12.5041	+	17.7670i	−0.524659	+	0.745488i
$569$	−10.7413	+	10.7413i	−0.450298	+	0.450298i	−0.895454	−	0.445155i	$-0.853149\pi$
$569$	−10.7413	+	10.7413i	−0.450298	+	0.450298i	0.445155	+	0.895454i	$0.353149\pi$
$570$		0			0
$571$	−4.73710	−	1.96217i	−0.198241	−	0.0821143i	0.281354	−	0.959604i	$-0.409217\pi$
$571$	−4.73710	−	1.96217i	−0.198241	−	0.0821143i	−0.479595	+	0.877490i	$0.659217\pi$
$572$	−3.55959	−	30.8813i	−0.148834	−	1.29121i
$573$		0			0
$574$	−0.754346	−	13.1320i	−0.0314858	−	0.548120i
$575$	17.4463			0.727561
$576$		0			0
$577$	33.2804			1.38548			0.692740	−	0.721187i	$-0.256403\pi$
$577$	33.2804			1.38548			0.692740	+	0.721187i	$0.256403\pi$
$578$	1.35724	+	23.6275i	0.0564538	+	0.982776i
$579$		0			0
$580$	1.88005	+	16.3104i	0.0780647	+	0.677252i
$581$	−1.98396	−	0.821782i	−0.0823085	−	0.0340933i
$582$		0			0
$583$	15.0932	−	15.0932i	0.625098	−	0.625098i
$584$	9.76254	+	6.87067i	0.403977	+	0.284310i
$585$		0			0
$586$	10.5370	−	30.2372i	0.435280	−	1.24909i
$587$	20.7958	+	8.61391i	0.858335	+	0.355534i	0.768056	−	0.640382i	$-0.221224\pi$
$587$	20.7958	+	8.61391i	0.858335	+	0.355534i	0.0902789	+	0.995917i	$0.471224\pi$
$588$		0			0
$589$	−6.18663	−	14.9358i	−0.254916	−	0.615421i
$590$	9.04787	+	8.06486i	0.372495	+	0.332025i
$591$		0			0
$592$	4.39319	−	26.6832i	0.180559	−	1.09667i
$593$	31.7996			1.30585			0.652927	−	0.757420i	$-0.273541\pi$
$593$	31.7996			1.30585			0.652927	+	0.757420i	$0.273541\pi$
$594$		0			0
$595$	−0.409678	+	0.169694i	−0.0167952	+	0.00695679i
$596$	−10.9527	+	38.3868i	−0.448639	+	1.57238i
$597$		0			0
$598$	12.6198	−	36.2141i	0.516064	−	1.48090i
$599$	12.0277	−	12.0277i	0.491440	−	0.491440i	−0.417319	−	0.908760i	$-0.637030\pi$
$599$	12.0277	−	12.0277i	0.491440	−	0.491440i	0.908760	+	0.417319i	$0.137030\pi$
$600$		0			0
$601$	13.1841	+	13.1841i	0.537791	+	0.537791i	0.922880	−	0.385089i	$-0.125829\pi$
$601$	13.1841	+	13.1841i	0.537791	+	0.537791i	−0.385089	+	0.922880i	$0.625829\pi$
$602$	3.40538	−	1.64532i	0.138793	−	0.0670582i
$603$		0			0
$604$	13.3542	+	10.5938i	0.543377	+	0.431057i
$605$	−1.68588	−	4.07008i	−0.0685409	−	0.165472i
$606$		0			0
$607$		−	29.6602i		−	1.20387i	−0.798545	−	0.601935i	$-0.794397\pi$
$607$		−	29.6602i		−	1.20387i	0.798545	−	0.601935i	$-0.205603\pi$
$608$	−10.2593	−	12.6972i	−0.416070	−	0.514938i
$609$		0			0
$610$	−0.521417	−	9.07707i	−0.0211115	−	0.367520i
$611$	12.7267	−	5.27156i	0.514866	−	0.213264i
$612$		0			0
$613$	−3.95354	+	9.54469i	−0.159682	+	0.385507i	−0.983389	−	0.181509i	$-0.941902\pi$
$613$	−3.95354	+	9.54469i	−0.159682	+	0.385507i	0.823707	+	0.567015i	$0.191902\pi$
$614$	−15.9200	−	32.9502i	−0.642478	−	1.32976i
$615$		0			0
$616$	3.11907	+	4.92191i	0.125671	+	0.198309i
$617$	3.41501	+	3.41501i	0.137483	+	0.137483i	0.772499	−	0.635016i	$-0.219006\pi$
$617$	3.41501	+	3.41501i	0.137483	+	0.137483i	−0.635016	+	0.772499i	$0.719006\pi$
$618$		0			0
$619$	10.1724	−	24.5583i	0.408863	−	0.987082i	−0.576575	−	0.817044i	$-0.695611\pi$
$619$	10.1724	−	24.5583i	0.408863	−	0.987082i	0.985438	−	0.170038i	$-0.0543890\pi$
$620$	−3.40450	+	11.9321i	−0.136728	+	0.479203i
$621$		0			0
$622$	20.2210	+	18.0240i	0.810787	+	0.722698i
$623$		−	0.722131i		−	0.0289316i
$624$		0			0
$625$			8.10804i			0.324322i
$626$	5.72645	−	6.42444i	0.228875	−	0.256772i
$627$		0			0
$628$	−26.3030	+	14.6252i	−1.04960	+	0.583609i
$629$	1.33250	−	3.21694i	0.0531302	−	0.128268i
$630$		0			0
$631$	−22.4300	−	22.4300i	−0.892924	−	0.892924i	0.101874	−	0.994797i	$-0.467516\pi$
$631$	−22.4300	−	22.4300i	−0.892924	−	0.892924i	−0.994797	+	0.101874i	$0.967516\pi$
$632$	−2.97058	−	17.0859i	−0.118163	−	0.679642i
$633$		0			0
$634$	−39.9627	+	19.3081i	−1.58712	+	0.766823i
$635$	7.13543	−	17.2265i	0.283161	−	0.683611i
$636$		0			0
$637$	34.6575	−	14.3556i	1.37318	−	0.568790i
$638$	27.7340	−	1.59313i	1.09800	−	0.0630727i
$639$		0			0
$640$	0.112288	+	12.5286i	0.00443855	+	0.495238i
$641$			21.6739i			0.856067i	0.903763	+	0.428034i	$0.140794\pi$
$641$			21.6739i			0.856067i	−0.903763	+	0.428034i	$0.859206\pi$
$642$		0			0
$643$	−9.95208	−	24.0264i	−0.392472	−	0.947511i	−0.989400	−	0.145216i	$-0.953612\pi$
$643$	−9.95208	−	24.0264i	−0.392472	−	0.947511i	0.596928	−	0.802295i	$-0.296388\pi$
$644$	0.823164	+	7.14138i	0.0324372	+	0.281410i
$645$		0			0
$646$	−0.914392	−	1.89255i	−0.0359763	−	0.0744614i
$647$	−17.5596	−	17.5596i	−0.690340	−	0.690340i	0.271967	−	0.962307i	$-0.412326\pi$
$647$	−17.5596	−	17.5596i	−0.690340	−	0.690340i	−0.962307	+	0.271967i	$0.912326\pi$
$648$		0			0
$649$	14.5011	−	14.5011i	0.569219	−	0.569219i
$650$	29.5587	+	10.3006i	1.15939	+	0.404022i
$651$		0			0
$652$	−14.7722	−	26.5674i	−0.578525	−	1.04046i
$653$	27.2736	−	11.2971i	1.06730	−	0.442089i	0.221261	−	0.975215i	$-0.428983\pi$
$653$	27.2736	−	11.2971i	1.06730	−	0.442089i	0.846036	+	0.533125i	$0.178983\pi$
$654$		0			0
$655$	−9.49660			−0.371063
$656$	−40.6493	−	25.2522i	−1.58709	−	0.985933i
$657$		0			0
$658$	−1.71814	+	1.92756i	−0.0669802	+	0.0751443i
$659$	−9.50276	−	22.9417i	−0.370175	−	0.893681i	−0.993720	−	0.111894i	$-0.964308\pi$
$659$	−9.50276	−	22.9417i	−0.370175	−	0.893681i	0.623545	−	0.781787i	$-0.285692\pi$
$660$		0			0
$661$	−12.4726	−	5.16632i	−0.485128	−	0.200947i	0.126694	−	0.991942i	$-0.459563\pi$
$661$	−12.4726	−	5.16632i	−0.485128	−	0.200947i	−0.611822	+	0.790995i	$0.709563\pi$
$662$	44.1889	+	15.3989i	1.71745	+	0.598495i
$663$		0			0
$664$	−6.59904	+	4.18189i	−0.256093	+	0.162289i
$665$	−1.75680	+	1.75680i	−0.0681258	+	0.0681258i
$666$		0			0
$667$	31.6626	+	13.1151i	1.22598	+	0.507819i
$668$	32.2115	+	25.5532i	1.24630	+	0.988682i
$669$		0			0
$670$	1.62922	−	0.0935876i	0.0629422	−	0.00361560i
$671$	−15.3836			−0.593878
$672$		0			0
$673$	−24.4439			−0.942245			−0.471122	−	0.882068i	$-0.656151\pi$
$673$	−24.4439			−0.942245			−0.471122	+	0.882068i	$0.656151\pi$
$674$	24.9532	−	1.43340i	0.961163	−	0.0552123i
$675$		0			0
$676$	26.6042	−	33.5364i	1.02324	−	1.28986i
$677$	29.4250	+	12.1882i	1.13089	+	0.468431i	0.868084	−	0.496417i	$-0.165351\pi$
$677$	29.4250	+	12.1882i	1.13089	+	0.468431i	0.262808	+	0.964848i	$0.415351\pi$
$678$		0			0
$679$	6.02346	−	6.02346i	0.231159	−	0.231159i
$680$	−0.352939	+	1.57417i	−0.0135346	+	0.0603667i
$681$		0			0
$682$	19.8253	+	6.90870i	0.759150	+	0.264548i
$683$	5.00090	+	2.07144i	0.191354	+	0.0792614i	0.476303	−	0.879281i	$-0.341977\pi$
$683$	5.00090	+	2.07144i	0.191354	+	0.0792614i	−0.284949	+	0.958543i	$0.591977\pi$
$684$		0			0
$685$	0.975668	+	2.35547i	0.0372784	+	0.0899979i
$686$	−9.79995	+	10.9945i	−0.374164	+	0.419770i
$687$		0			0
$688$	2.23528	−	13.5766i	0.0852193	−	0.517603i
$689$	47.2467			1.79995
$690$		0			0
$691$	29.6641	−	12.2873i	1.12848	−	0.467431i	0.261214	−	0.965281i	$-0.415877\pi$
$691$	29.6641	−	12.2873i	1.12848	−	0.467431i	0.867263	+	0.497850i	$0.165877\pi$
$692$	−7.82950	+	4.35342i	−0.297633	+	0.165492i
$693$		0			0
$694$	−27.6716	−	9.64298i	−1.05040	−	0.366042i
$695$	−1.21871	+	1.21871i	−0.0462283	+	0.0462283i
$696$		0			0
$697$	−4.35699	−	4.35699i	−0.165033	−	0.165033i
$698$	0.914738	+	1.89327i	0.0346233	+	0.0716613i
$699$		0			0
$700$	−5.82895	+	0.671884i	−0.220313	+	0.0253948i
$701$	−3.53387	−	8.53152i	−0.133472	−	0.322231i	0.842986	−	0.537935i	$-0.180795\pi$
$701$	−3.53387	−	8.53152i	−0.133472	−	0.322231i	−0.976459	+	0.215704i	$0.930795\pi$
$702$		0			0
$703$		−	19.5091i		−	0.735799i
$704$	21.1743	+	1.02602i	0.798037	+	0.0386695i
$705$		0			0
$706$	3.73728	−	0.214681i	0.140654	−	0.00807964i
$707$	1.30987	−	0.542567i	0.0492628	−	0.0204053i
$708$		0			0
$709$	7.15181	−	17.2660i	0.268592	−	0.648438i	−0.730826	−	0.682564i	$-0.760865\pi$
$709$	7.15181	−	17.2660i	0.268592	−	0.648438i	0.999418	+	0.0341261i	$0.0108648\pi$
$710$	10.8320	−	5.23350i	0.406517	−	0.196410i
$711$		0			0
$712$	−2.14845	−	1.51203i	−0.0805166	−	0.0566659i
$713$	18.3146	+	18.3146i	0.685886	+	0.685886i
$714$		0			0
$715$	−6.58699	+	15.9024i	−0.246340	+	0.594716i
$716$	−24.4131	−	43.9062i	−0.912359	−	1.64085i
$717$		0			0
$718$	−17.7307	+	19.8919i	−0.661705	+	0.742359i
$719$			14.3048i			0.533478i	0.963769	+	0.266739i	$0.0859462\pi$
$719$			14.3048i			0.533478i	−0.963769	+	0.266739i	$0.914054\pi$
$720$		0			0
$721$			3.28261i			0.122251i
$722$	11.2673	+	10.0431i	0.419324	+	0.373767i
$723$		0			0
$724$	−8.43115	−	2.40561i	−0.313341	−	0.0894037i
$725$	−10.7048	+	25.8437i	−0.397567	+	0.959812i
$726$		0			0
$727$	22.6384	+	22.6384i	0.839610	+	0.839610i	0.988807	−	0.149197i	$-0.0476690\pi$
$727$	22.6384	+	22.6384i	0.839610	+	0.839610i	−0.149197	+	0.988807i	$0.547669\pi$
$728$	−2.82173	+	12.5854i	−0.104580	+	0.466447i
$729$		0			0
$730$	−2.87568	−	5.95190i	−0.106434	−	0.220290i
$731$	0.677983	−	1.63680i	0.0250761	−	0.0605391i
$732$		0			0
$733$	−18.9242	+	7.83864i	−0.698980	+	0.289527i	−0.703736	−	0.710462i	$-0.748486\pi$
$733$	−18.9242	+	7.83864i	−0.698980	+	0.289527i	0.00475595	+	0.999989i	$0.498486\pi$
$734$	−0.236294	−	4.11353i	−0.00872178	−	0.151833i
$735$		0			0
$736$	22.9703	+	12.5039i	0.846696	+	0.460901i
$737$		−	2.76116i		−	0.101709i
$738$		0			0
$739$	−13.0834	−	31.5861i	−0.481281	−	1.16191i	−0.959001	−	0.283403i	$-0.908537\pi$
$739$	−13.0834	−	31.5861i	−0.481281	−	1.16191i	0.477720	−	0.878512i	$-0.341463\pi$
$740$	−9.30602	+	11.7309i	−0.342096	+	0.431235i
$741$		0			0
$742$	−7.97435	+	3.85283i	−0.292748	+	0.141442i
$743$	−6.99193	−	6.99193i	−0.256509	−	0.256509i	0.567124	−	0.823633i	$-0.308056\pi$
$743$	−6.99193	−	6.99193i	−0.256509	−	0.256509i	−0.823633	+	0.567124i	$0.808056\pi$
$744$		0			0
$745$	15.6296	−	15.6296i	0.572625	−	0.572625i
$746$	13.2487	−	38.0188i	0.485071	−	1.39197i
$747$		0			0
$748$	2.62485	+	0.748932i	0.0959740	+	0.0273837i
$749$	−4.50500	+	1.86603i	−0.164609	+	0.0681833i
$750$		0			0
$751$	−36.9772			−1.34932			−0.674658	−	0.738130i	$-0.735709\pi$
$751$	−36.9772			−1.34932			−0.674658	+	0.738130i	$0.735709\pi$
$752$	2.13727	+	9.14778i	0.0779381	+	0.333585i
$753$		0			0
$754$	45.9017	+	40.9147i	1.67164	+	1.49002i
$755$	−3.61200	−	8.72014i	−0.131454	−	0.317358i
$756$		0			0
$757$	−0.561827	−	0.232716i	−0.0204199	−	0.00845822i	0.372450	−	0.928052i	$-0.378518\pi$
$757$	−0.561827	−	0.232716i	−0.0204199	−	0.00845822i	−0.392870	+	0.919594i	$0.628518\pi$
$758$	14.7201	−	42.2410i	0.534658	−	1.53426i
$759$		0			0
$760$	1.54827	+	8.90523i	0.0561618	+	0.323027i
$761$	−25.2794	+	25.2794i	−0.916379	+	0.916379i	−0.996764	−	0.0803851i	$-0.974385\pi$
$761$	−25.2794	+	25.2794i	−0.916379	+	0.916379i	0.0803851	+	0.996764i	$0.474385\pi$
$762$		0			0
$763$	−2.07115	−	0.857899i	−0.0749807	−	0.0310580i
$764$	−43.9729	+	5.06862i	−1.59089	+	0.183376i
$765$		0			0
$766$	1.72378	+	30.0084i	0.0622828	+	1.08425i
$767$	45.3932			1.63905
$768$		0			0
$769$	21.2233			0.765331			0.382666	−	0.923887i	$-0.375006\pi$
$769$	21.2233			0.765331			0.382666	+	0.923887i	$0.375006\pi$
$770$	−0.185035	−	3.22118i	−0.00666820	−	0.116083i
$771$		0			0
$772$	−20.1503	+	2.32266i	−0.725224	+	0.0835943i
$773$	37.9146	+	15.7047i	1.36369	+	0.564860i	0.940071	−	0.340978i	$-0.110758\pi$
$773$	37.9146	+	15.7047i	1.36369	+	0.564860i	0.423623	+	0.905839i	$0.360758\pi$
$774$		0			0
$775$	−14.9487	+	14.9487i	−0.536975	+	0.536975i
$776$	−5.30850	−	30.5330i	−0.190564	−	1.09607i
$777$		0			0
$778$	0.282189	−	0.809773i	0.0101170	−	0.0290318i
$779$	−31.8953	−	13.2115i	−1.14277	−	0.473350i
$780$		0			0
$781$	−7.78939	−	18.8052i	−0.278726	−	0.672904i
$782$	2.51380	+	2.24068i	0.0898932	+	0.0801267i
$783$		0			0
$784$	5.82025	+	24.9114i	0.207866	+	0.889694i
$785$	16.6644			0.594777
$786$		0			0
$787$	5.68394	−	2.35436i	0.202610	−	0.0839240i	−0.279071	−	0.960271i	$-0.590026\pi$
$787$	5.68394	−	2.35436i	0.202610	−	0.0839240i	0.481681	+	0.876347i	$0.340026\pi$
$788$	−0.238924	−	0.0681708i	−0.00851132	−	0.00242848i
$789$		0			0
$790$	−3.15995	+	9.06785i	−0.112426	+	0.322620i
$791$	−9.57037	+	9.57037i	−0.340283	+	0.340283i
$792$		0			0
$793$	−24.0778	−	24.0778i	−0.855029	−	0.855029i
$794$	21.6602	−	10.4652i	0.768692	−	0.371396i
$795$		0			0
$796$	10.4263	−	13.1431i	0.369550	−	0.465843i
$797$	5.85957	+	14.1463i	0.207557	+	0.501086i	0.993037	−	0.117800i	$-0.0375842\pi$
$797$	5.85957	+	14.1463i	0.207557	+	0.501086i	−0.785481	+	0.618886i	$0.787584\pi$
$798$		0			0
$799$			1.20959i			0.0427922i
$800$	−10.2060	+	18.7488i	−0.360836	+	0.662872i
$801$		0			0
$802$	−2.55865	−	44.5422i	−0.0903491	−	1.57284i
$803$	−10.3330	+	4.28007i	−0.364644	+	0.151040i
$804$		0			0
$805$	1.52326	−	3.67747i	0.0536879	−	0.129614i
$806$	20.2166	+	41.8430i	0.712099	+	1.47386i
$807$		0			0
$808$	1.12846	−	5.03313i	0.0396990	−	0.177065i
$809$	−2.43655	−	2.43655i	−0.0856644	−	0.0856644i	0.662976	−	0.748641i	$-0.269293\pi$
$809$	−2.43655	−	2.43655i	−0.0856644	−	0.0856644i	−0.748641	+	0.662976i	$0.769293\pi$
$810$		0			0
$811$	−0.650076	+	1.56942i	−0.0228272	+	0.0551099i	−0.934882	−	0.354958i	$-0.884495\pi$
$811$	−0.650076	+	1.56942i	−0.0228272	+	0.0551099i	0.912055	+	0.410068i	$0.134495\pi$
$812$	−11.0838	−	3.16248i	−0.388966	−	0.110981i
$813$		0			0
$814$	18.9128	+	16.8580i	0.662894	+	0.590874i
$815$			16.8319i			0.589596i
$816$		0			0
$817$		−	9.92634i		−	0.347279i
$818$	10.2509	−	11.5004i	0.358415	−	0.402101i
$819$		0			0
$820$	12.8768	+	23.1585i	0.449676	+	0.808729i
$821$	−10.6124	+	25.6206i	−0.370376	+	0.894166i	0.623311	+	0.781974i	$0.285787\pi$
$821$	−10.6124	+	25.6206i	−0.370376	+	0.894166i	−0.993687	+	0.112192i	$0.964213\pi$
$822$		0			0
$823$	6.68156	+	6.68156i	0.232905	+	0.232905i	0.813904	−	0.580999i	$-0.197338\pi$
$823$	6.68156	+	6.68156i	0.232905	+	0.232905i	−0.580999	+	0.813904i	$0.697338\pi$
$824$	9.76626	+	6.87329i	0.340224	+	0.239442i
$825$		0			0
$826$	−7.66153	+	3.70169i	−0.266579	+	0.128798i
$827$	16.6369	−	40.1651i	0.578523	−	1.39668i	−0.315616	−	0.948887i	$-0.602211\pi$
$827$	16.6369	−	40.1651i	0.578523	−	1.39668i	0.894139	−	0.447790i	$-0.147789\pi$
$828$		0			0
$829$	−13.1960	+	5.46597i	−0.458316	+	0.189841i	−0.599883	−	0.800088i	$-0.704786\pi$
$829$	−13.1960	+	5.46597i	−0.458316	+	0.189841i	0.141566	+	0.989929i	$0.454786\pi$
$830$	4.31880	−	0.248086i	0.149908	−	0.00861118i
$831$		0			0
$832$	31.5353	+	34.7471i	1.09329	+	1.20464i
$833$			3.29398i			0.114130i
$834$		0			0
$835$	−8.71244	−	21.0337i	−0.301506	−	0.727901i
$836$	15.1930	−	1.75125i	0.525460	−	0.0605681i
$837$		0			0
$838$	24.8508	+	51.4348i	0.858458	+	1.77678i
$839$	−21.9623	−	21.9623i	−0.758223	−	0.758223i	0.217776	−	0.975999i	$-0.430120\pi$
$839$	−21.9623	−	21.9623i	−0.758223	−	0.758223i	−0.975999	+	0.217776i	$0.930120\pi$
$840$		0			0
$841$	−18.3495	+	18.3495i	−0.632742	+	0.632742i
$842$	−37.5723	−	13.0931i	−1.29483	−	0.451220i
$843$		0			0
$844$	−41.7615	+	23.2206i	−1.43749	+	0.799286i
$845$	−21.8988	+	9.07079i	−0.753342	+	0.312045i
$846$		0			0
$847$	3.09273			0.106267
$848$	−5.23434	+	31.7922i	−0.179748	+	1.09175i
$849$		0			0
$850$	−1.82889	+	2.05181i	−0.0627306	+	0.0703767i
$851$	11.9612	+	28.8768i	0.410023	+	0.989884i
$852$		0			0
$853$	13.8064	+	5.71880i	0.472722	+	0.195808i	0.606309	−	0.795229i	$-0.292649\pi$
$853$	13.8064	+	5.71880i	0.472722	+	0.195808i	−0.133587	+	0.991037i	$0.542649\pi$
$854$	6.02737	+	2.10041i	0.206252	+	0.0718746i
$855$		0			0
$856$	−3.88106	+	17.3103i	−0.132652	+	0.591653i
$857$	1.67134	−	1.67134i	0.0570919	−	0.0570919i	−0.677984	−	0.735076i	$-0.737146\pi$
$857$	1.67134	−	1.67134i	0.0570919	−	0.0570919i	0.735076	+	0.677984i	$0.237146\pi$
$858$		0			0
$859$	−40.2493	−	16.6718i	−1.37329	−	0.568835i	−0.430610	−	0.902538i	$-0.641702\pi$
$859$	−40.2493	−	16.6718i	−1.37329	−	0.568835i	−0.942678	+	0.333703i	$0.891702\pi$
$860$	−4.73496	+	5.96874i	−0.161461	+	0.203532i
$861$		0			0
$862$	−36.5500	+	2.09955i	−1.24490	+	0.0715109i
$863$	37.8609			1.28880			0.644400	−	0.764689i	$-0.277107\pi$
$863$	37.8609			1.28880			0.644400	+	0.764689i	$0.277107\pi$
$864$		0			0
$865$	4.96042			0.168659
$866$	−20.9941	+	1.20597i	−0.713407	+	0.0409804i
$867$		0			0
$868$	−6.82436	−	5.41372i	−0.231634	−	0.183754i
$869$	15.0108	+	6.21769i	0.509207	+	0.210921i
$870$		0			0
$871$	4.32166	−	4.32166i	0.146434	−	0.146434i
$872$	−6.88907	+	4.36568i	−0.233293	+	0.147841i
$873$		0			0
$874$	17.8166	+	6.20871i	0.602656	+	0.210013i
$875$	6.97879	+	2.89071i	0.235926	+	0.0977238i
$876$		0			0
$877$	−2.12312	−	5.12567i	−0.0716928	−	0.173082i	0.883971	−	0.467542i	$-0.154860\pi$
$877$	−2.12312	−	5.12567i	−0.0716928	−	0.173082i	−0.955664	+	0.294460i	$0.904860\pi$
$878$	5.97999	−	6.70888i	0.201815	−	0.226414i
$879$		0			0
$880$	−9.97095	−	6.19416i	−0.336121	−	0.208805i
$881$	1.75770			0.0592186			0.0296093	−	0.999562i	$-0.490574\pi$
$881$	1.75770			0.0592186			0.0296093	+	0.999562i	$0.490574\pi$
$882$		0			0
$883$	−1.38750	+	0.574723i	−0.0466932	+	0.0193410i	−0.405908	−	0.913914i	$-0.633045\pi$
$883$	−1.38750	+	0.574723i	−0.0466932	+	0.0193410i	0.359215	+	0.933255i	$0.383045\pi$
$884$	2.93611	+	5.28051i	0.0987521	+	0.177603i
$885$		0			0
$886$	−5.34197	−	1.86156i	−0.179467	−	0.0625404i
$887$	37.6403	−	37.6403i	1.26384	−	1.26384i	0.314622	−	0.949217i	$-0.398122\pi$
$887$	37.6403	−	37.6403i	1.26384	−	1.26384i	0.949217	−	0.314622i	$-0.101878\pi$
$888$		0			0
$889$	9.25592	+	9.25592i	0.310434	+	0.310434i
$890$	0.632853	+	1.30984i	0.0212133	+	0.0439059i
$891$		0			0
$892$	0.348137	+	3.02027i	0.0116565	+	0.101126i
$893$	2.59350	+	6.26127i	0.0867883	+	0.209525i
$894$		0			0
$895$			27.8170i			0.929818i
$896$	−8.15610	−	3.29304i	−0.272476	−	0.110013i
$897$		0			0
$898$	9.96587	−	0.572472i	0.332565	−	0.0191036i
$899$	−38.3675	+	15.8923i	−1.27963	+	0.530039i
$900$		0			0
$901$	−1.58763	+	3.83287i	−0.0528916	+	0.127692i
$902$	40.3689	−	19.5043i	1.34414	−	0.649423i
$903$		0			0
$904$	8.43441	+	48.5123i	0.280524	+	1.61349i
$905$	3.43284	+	3.43284i	0.114111	+	0.114111i
$906$		0			0
$907$	17.6501	−	42.6112i	0.586063	−	1.41488i	−0.301175	−	0.953569i	$-0.597379\pi$
$907$	17.6501	−	42.6112i	0.586063	−	1.41488i	0.887238	−	0.461312i	$-0.152621\pi$
$908$	33.4684	−	18.6094i	1.11069	−	0.617573i
$909$		0			0
$910$	4.75206	−	5.33128i	0.157529	−	0.176730i
$911$		−	26.0899i		−	0.864398i	−0.901778	−	0.432199i	$-0.857738\pi$
$911$		−	26.0899i		−	0.864398i	0.901778	−	0.432199i	$-0.142262\pi$
$912$		0			0
$913$		−	7.31940i		−	0.242237i
$914$	32.0292	+	28.5494i	1.05943	+	0.944329i
$915$		0			0
$916$	−13.3626	+	46.8332i	−0.441514	+	1.54741i
$917$	2.55130	−	6.15939i	0.0842514	−	0.203401i
$918$		0			0
$919$	−26.2752	−	26.2752i	−0.866738	−	0.866738i	0.125371	−	0.992110i	$-0.459988\pi$
$919$	−26.2752	−	26.2752i	−0.866738	−	0.866738i	−0.992110	+	0.125371i	$0.959988\pi$
$920$	−7.75158	−	12.2320i	−0.255562	−	0.403278i
$921$		0			0
$922$	−9.35922	−	19.3711i	−0.308230	−	0.637954i
$923$	17.2416	−	41.6249i	0.567514	−	1.37010i
$924$		0			0
$925$	−23.5699	+	9.76296i	−0.774973	+	0.321004i
$926$	−1.86538	−	32.4735i	−0.0613003	−	1.06715i
$927$		0			0
$928$	−32.6168	+	26.3543i	−1.07070	+	0.865124i
$929$		−	36.7712i		−	1.20642i	−0.797581	−	0.603212i	$-0.793887\pi$
$929$		−	36.7712i		−	1.20642i	0.797581	−	0.603212i	$-0.206113\pi$
$930$		0			0
$931$	7.06268	+	17.0508i	0.231470	+	0.558818i
$932$	14.3584	+	11.3905i	0.470327	+	0.373107i
$933$		0			0
$934$	−19.8990	+	9.61427i	−0.651116	+	0.314589i
$935$	−1.06874	−	1.06874i	−0.0349514	−	0.0349514i
$936$		0			0
$937$	32.0409	−	32.0409i	1.04673	−	1.04673i	0.0478763	−	0.998853i	$-0.484755\pi$
$937$	32.0409	−	32.0409i	1.04673	−	1.04673i	0.998853	−	0.0478763i	$-0.0152453\pi$
$938$	−0.376997	+	1.08184i	−0.0123094	+	0.0353232i
$939$		0			0
$940$	1.42720	−	5.00205i	0.0465503	−	0.163149i
$941$	6.96757	−	2.88606i	0.227136	−	0.0940829i	−0.266213	−	0.963914i	$-0.585772\pi$
$941$	6.96757	−	2.88606i	0.227136	−	0.0940829i	0.493349	+	0.869831i	$0.335772\pi$
$942$		0			0
$943$	55.3107			1.80116
$944$	−5.02900	+	30.5450i	−0.163680	+	0.994156i
$945$		0			0
$946$	9.62296	+	8.57747i	0.312870	+	0.278878i
$947$	−14.3279	−	34.5907i	−0.465595	−	1.12405i	−0.966067	−	0.258293i	$-0.916840\pi$
$947$	−14.3279	−	34.5907i	−0.465595	−	1.12405i	0.500471	−	0.865753i	$-0.333160\pi$
$948$		0			0
$949$	−22.8718	−	9.47382i	−0.742451	−	0.307533i
$950$	−5.06769	+	14.5423i	−0.164417	+	0.471815i
$951$		0			0
$952$	−0.926171	−	0.651820i	−0.0300174	−	0.0211256i
$953$	−14.6343	+	14.6343i	−0.474052	+	0.474052i	−0.903223	−	0.429171i	$-0.858806\pi$
$953$	−14.6343	+	14.6343i	−0.474052	+	0.474052i	0.429171	+	0.903223i	$0.358806\pi$
$954$		0			0
$955$	22.6440	+	9.37946i	0.732743	+	0.303512i
$956$	−6.53730	−	56.7145i	−0.211432	−	1.83428i
$957$		0			0
$958$	−1.72056	−	29.9524i	−0.0555889	−	0.967718i
$959$	−1.78985			−0.0577973
$960$		0			0
$961$	−0.385416			−0.0124328
$962$	3.21608	+	55.9872i	0.103691	+	1.80510i
$963$		0			0
$964$	−6.27903	−	54.4738i	−0.202234	−	1.75448i
$965$	10.3764	+	4.29806i	0.334030	+	0.138360i
$966$		0			0
$967$	−0.565755	+	0.565755i	−0.0181934	+	0.0181934i	−0.716145	−	0.697952i	$-0.754095\pi$
$967$	−0.565755	+	0.565755i	−0.0181934	+	0.0181934i	0.697952	+	0.716145i	$0.254095\pi$
$968$	6.47571	−	9.20135i	0.208137	−	0.295743i
$969$		0			0
$970$	−5.64691	+	16.2045i	−0.181311	+	0.520294i
$971$	22.8814	+	9.47779i	0.734299	+	0.304157i	0.718317	−	0.695716i	$-0.244913\pi$
$971$	22.8814	+	9.47779i	0.734299	+	0.304157i	0.0159818	+	0.999872i	$0.494913\pi$
$972$		0			0
$973$	−0.463030	−	1.11785i	−0.0148441	−	0.0358367i
$974$	−5.50622	−	4.90799i	−0.176431	−	0.157262i
$975$		0			0
$976$	18.8695	−	13.5344i	0.603997	−	0.433226i
$977$	−19.6124			−0.627458			−0.313729	−	0.949513i	$-0.601578\pi$
$977$	−19.6124			−0.627458			−0.313729	+	0.949513i	$0.601578\pi$
$978$		0			0
$979$	2.27399	−	0.941919i	0.0726772	−	0.0301039i
$980$	3.88659	−	13.6217i	0.124153	−	0.435129i
$981$		0			0
$982$	−18.5563	+	53.2495i	−0.592155	+	1.69926i
$983$	−32.1802	+	32.1802i	−1.02639	+	1.02639i	−0.0267454	+	0.999642i	$0.508514\pi$
$983$	−32.1802	+	32.1802i	−1.02639	+	1.02639i	−0.999642	+	0.0267454i	$0.991486\pi$
$984$		0			0
$985$	0.0972807	+	0.0972807i	0.00309962	+	0.00309962i
$986$	−4.86163	+	2.34891i	−0.154826	+	0.0748045i
$987$		0			0
$988$	26.5204	+	21.0385i	0.843727	+	0.669323i
$989$	6.08591	+	14.6927i	0.193521	+	0.467201i
$990$		0			0
$991$			37.1684i			1.18069i	0.807149	+	0.590347i	$0.201009\pi$
$991$			37.1684i			1.18069i	−0.807149	+	0.590347i	$0.798991\pi$
$992$	−30.3959	+	8.96802i	−0.965069	+	0.284735i
$993$		0			0
$994$	0.484333	+	8.43150i	0.0153621	+	0.267431i
$995$	−8.58223	+	3.55488i	−0.272075	+	0.112697i
$996$		0			0
$997$	4.81373	−	11.6214i	0.152452	−	0.368053i	−0.829140	−	0.559041i	$-0.811169\pi$
$997$	4.81373	−	11.6214i	0.152452	−	0.368053i	0.981592	+	0.190989i	$0.0611693\pi$
$998$	20.2766	+	41.9672i	0.641844	+	1.32845i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.w.a.107.15	✓	128
3.2	odd	2	inner	864.2.w.a.107.18	yes	128
32.3	odd	8	inner	864.2.w.a.323.18	yes	128
96.35	even	8	inner	864.2.w.a.323.15	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
864.2.w.a.107.15	✓	128	1.1	even	1	trivial
864.2.w.a.107.18	yes	128	3.2	odd	2	inner
864.2.w.a.323.15	yes	128	96.35	even	8	inner
864.2.w.a.323.18	yes	128	32.3	odd	8	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:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.w (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0811033 - 1.41189i) q^{2} +(-1.98684 + 0.229017i) q^{4} +(1.02313 + 0.423795i) q^{5} +(-0.549738 + 0.549738i) q^{7} +(0.484486 + 2.78662i) q^{8} +O(q^{10})\)	\(q+(-0.0811033 - 1.41189i) q^{2} +(-1.98684 + 0.229017i) q^{4} +(1.02313 + 0.423795i) q^{5} +(-0.549738 + 0.549738i) q^{7} +(0.484486 + 2.78662i) q^{8} +(0.515371 - 1.47892i) q^{10} +(-2.44818 - 1.01407i) q^{11} +(-2.24462 - 5.41899i) q^{13} +(0.820752 + 0.731581i) q^{14} +(3.89510 - 0.910043i) q^{16} +0.515040 q^{17} +(2.66603 - 1.10431i) q^{19} +(-2.12986 - 0.607700i) q^{20} +(-1.23320 + 3.53880i) q^{22} +(-3.26913 + 3.26913i) q^{23} +(-2.66834 - 2.66834i) q^{25} +(-7.46894 + 3.60864i) q^{26} +(0.966344 - 1.21814i) q^{28} +(-2.83677 - 6.84857i) q^{29} -5.60227i q^{31} +(-1.60078 - 5.42563i) q^{32} +(-0.0417714 - 0.727177i) q^{34} +(-0.795430 + 0.329478i) q^{35} +(2.58718 - 6.24599i) q^{37} +(-1.77538 - 3.67457i) q^{38} +(-0.685265 + 3.05641i) q^{40} +(-8.45953 - 8.45953i) q^{41} +(1.31637 - 3.17800i) q^{43} +(5.09640 + 1.45412i) q^{44} +(4.88078 + 4.35051i) q^{46} +2.34853i q^{47} +6.39558i q^{49} +(-3.55098 + 3.98380i) q^{50} +(5.70075 + 10.2526i) q^{52} +(-3.08254 + 7.44190i) q^{53} +(-2.07506 - 2.07506i) q^{55} +(-1.79825 - 1.26557i) q^{56} +(-9.43932 + 4.56064i) q^{58} +(-2.96161 + 7.14996i) q^{59} +(5.36346 - 2.22162i) q^{61} +(-7.90977 + 0.454363i) q^{62} +(-7.53055 + 2.70016i) q^{64} -6.49559i q^{65} +(0.398752 + 0.962673i) q^{67} +(-1.02330 + 0.117953i) q^{68} +(0.529697 + 1.09634i) q^{70} +(5.43150 + 5.43150i) q^{71} +(2.98447 - 2.98447i) q^{73} +(-9.02846 - 3.14623i) q^{74} +(-5.04409 + 2.80466i) q^{76} +(1.90333 - 0.788386i) q^{77} -6.13141 q^{79} +(4.37088 + 0.719631i) q^{80} +(-11.2578 + 12.6300i) q^{82} +(1.05703 + 2.55189i) q^{83} +(0.526954 + 0.218271i) q^{85} +(-4.59374 - 1.60082i) q^{86} +(1.63972 - 7.31347i) q^{88} +(-0.656796 + 0.656796i) q^{89} +(4.21297 + 1.74507i) q^{91} +(5.74657 - 7.24395i) q^{92} +(3.31586 - 0.190474i) q^{94} +3.19570 q^{95} -10.9570 q^{97} +(9.02983 - 0.518703i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q+O(q^{10}) \) 128 * q	\( 128 q - 16 q^{10} + 32 q^{16} + 16 q^{22} - 32 q^{40} - 32 q^{46} + 16 q^{52} - 32 q^{55} - 32 q^{58} - 64 q^{61} - 48 q^{64} - 64 q^{67} + 96 q^{70} - 32 q^{76} + 64 q^{79} - 80 q^{82} - 80 q^{88} + 96 q^{91} - 144 q^{94}+O(q^{100}) \) 128 * q - 16 * q^10 + 32 * q^16 + 16 * q^22 - 32 * q^40 - 32 * q^46 + 16 * q^52 - 32 * q^55 - 32 * q^58 - 64 * q^61 - 48 * q^64 - 64 * q^67 + 96 * q^70 - 32 * q^76 + 64 * q^79 - 80 * q^82 - 80 * q^88 + 96 * q^91 - 144 * q^94

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