LMFDB - Embedded newform 729.2.g.a.622.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [729,2,Mod(28,729)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("729.28"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(729, base_ring=CyclotomicField(54)) chi = DirichletCharacter(H, H._module([44])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 729 = 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	729.g (of order $27$, degree $18$, not minimal)

Newform invariants

comment:select newform

sage:traces = [144,-9,0,9,-9,0,9,18,0,-18,-9,0,9,-9,0,9,18,0,-18,-45] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(20)] == traces)

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

Self dual:	no
Analytic conductor:	$5.82109430735$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$8$ over $\Q(\zeta_{27})$
Twist minimal:	no (minimal twist has level 81)
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			622.6
Character	$\chi$	$=$	729.622
Dual form			729.2.g.a.109.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.464338 - 0.492169i) q^{2} +(0.0896686 + 1.53955i) q^{4} +(0.936797 + 0.109496i) q^{5} +(-1.30528 + 0.655538i) q^{7} +(1.83603 + 1.54061i) q^{8} +(0.488880 - 0.410219i) q^{10} +(-2.42430 + 5.62016i) q^{11} +(-5.10531 + 1.20998i) q^{13} +(-0.283457 + 0.946811i) q^{14} +(-1.45269 + 0.169795i) q^{16} +(0.00536485 + 0.0304256i) q^{17} +(0.634963 - 3.60105i) q^{19} +(-0.0845732 + 1.45207i) q^{20} +(1.64038 + 3.80282i) q^{22} +(-0.0934269 - 0.0469207i) q^{23} +(-3.99963 - 0.947929i) q^{25} +(-1.77507 + 3.07451i) q^{26} +(-1.12628 - 1.95077i) q^{28} +(0.147045 + 0.491165i) q^{29} +(6.82537 - 4.48912i) q^{31} +(-3.45346 + 4.63881i) q^{32} +(0.0174656 + 0.0114873i) q^{34} +(-1.29456 + 0.471183i) q^{35} +(5.42328 + 1.97391i) q^{37} +(-1.47749 - 1.98461i) q^{38} +(1.55129 + 1.64427i) q^{40} +(3.00983 + 3.19024i) q^{41} +(0.822094 + 1.10426i) q^{43} +(-8.86991 - 3.22838i) q^{44} +(-0.0664745 + 0.0241947i) q^{46} +(4.68685 + 3.08259i) q^{47} +(-2.90608 + 3.90354i) q^{49} +(-2.32372 + 1.52833i) q^{50} +(-2.32061 - 7.75138i) q^{52} +(4.89106 + 8.47157i) q^{53} +(-2.88646 + 4.99950i) q^{55} +(-3.40646 - 0.807346i) q^{56} +(0.310015 + 0.155695i) q^{58} +(2.23761 + 5.18737i) q^{59} +(-0.0998805 + 1.71488i) q^{61} +(0.959872 - 5.44370i) q^{62} +(0.171556 + 0.972942i) q^{64} +(-4.91512 + 0.574495i) q^{65} +(-0.785171 + 2.62265i) q^{67} +(-0.0463607 + 0.0109877i) q^{68} +(-0.369213 + 0.855932i) q^{70} +(-1.66448 + 1.39666i) q^{71} +(-6.38204 - 5.35517i) q^{73} +(3.48973 - 1.75261i) q^{74} +(5.60094 + 0.654656i) q^{76} +(-0.519830 - 8.92513i) q^{77} +(8.65544 - 9.17423i) q^{79} -1.37947 q^{80} +2.96771 q^{82} +(12.2319 - 12.9650i) q^{83} +(0.00169430 + 0.0290900i) q^{85} +(0.925214 + 0.108142i) q^{86} +(-13.1096 + 6.58387i) q^{88} +(10.6853 + 8.96604i) q^{89} +(5.87068 - 4.92609i) q^{91} +(0.0638594 - 0.148043i) q^{92} +(3.69344 - 0.875361i) q^{94} +(0.989131 - 3.30393i) q^{95} +(6.96396 - 0.813970i) q^{97} +(0.571800 + 3.24284i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8} - 18 q^{10} - 9 q^{11} + 9 q^{13} - 9 q^{14} + 9 q^{16} + 18 q^{17} - 18 q^{19} - 45 q^{20} + 9 q^{22} + 45 q^{23} + 9 q^{25} - 45 q^{26} - 9 q^{28}+ \cdots - 81 q^{98}+O(q^{100}) $ 144 * q - 9 * q^2 + 9 * q^4 - 9 * q^5 + 9 * q^7 + 18 * q^8 - 18 * q^10 - 9 * q^11 + 9 * q^13 - 9 * q^14 + 9 * q^16 + 18 * q^17 - 18 * q^19 - 45 * q^20 + 9 * q^22 + 45 * q^23 + 9 * q^25 - 45 * q^26 - 9 * q^28 - 36 * q^29 + 9 * q^31 + 99 * q^32 + 9 * q^34 - 9 * q^35 - 18 * q^37 - 18 * q^38 + 9 * q^40 - 27 * q^41 + 9 * q^43 - 54 * q^44 - 18 * q^46 + 99 * q^47 + 9 * q^49 - 126 * q^50 - 27 * q^52 - 45 * q^53 - 9 * q^55 + 225 * q^56 + 9 * q^58 - 72 * q^59 + 9 * q^61 - 81 * q^62 - 18 * q^64 + 81 * q^65 - 45 * q^67 - 117 * q^68 - 99 * q^70 + 90 * q^71 - 18 * q^73 - 81 * q^74 - 153 * q^76 - 81 * q^77 - 99 * q^79 + 288 * q^80 - 36 * q^82 - 45 * q^83 - 99 * q^85 - 81 * q^86 - 153 * q^88 + 81 * q^89 - 18 * q^91 - 207 * q^92 - 99 * q^94 + 171 * q^95 - 45 * q^97 - 81 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{20}{27}\right)$

Coefficient data

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

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

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

$2$	0.464338	−	0.492169i	0.328336	−	0.348016i	−0.542085	−	0.840324i	$-0.682365\pi$
$2$	0.464338	−	0.492169i	0.328336	−	0.348016i	0.870421	+	0.492308i	$0.163846\pi$
$3$		0			0
$3$		0			0
$4$	0.0896686	+	1.53955i	0.0448343	+	0.769776i
$5$	0.936797	+	0.109496i	0.418948	+	0.0489680i	0.322956	−	0.946414i	$-0.395323\pi$
$5$	0.936797	+	0.109496i	0.418948	+	0.0489680i	0.0959924	+	0.995382i	$0.469398\pi$
$6$		0			0
$7$	−1.30528	+	0.655538i	−0.493351	+	0.247770i	−0.678037	−	0.735027i	$-0.737169\pi$
$7$	−1.30528	+	0.655538i	−0.493351	+	0.247770i	0.184687	+	0.982797i	$0.440873\pi$
$8$	1.83603	+	1.54061i	0.649133	+	0.544688i
$9$		0			0
$10$	0.488880	−	0.410219i	0.154598	−	0.129723i
$11$	−2.42430	+	5.62016i	−0.730955	+	1.69454i	−0.0115680	+	0.999933i	$0.503682\pi$
$11$	−2.42430	+	5.62016i	−0.730955	+	1.69454i	−0.719387	+	0.694610i	$0.755577\pi$
$12$		0			0
$13$	−5.10531	+	1.20998i	−1.41596	+	0.335588i	−0.866184	−	0.499726i	$-0.833434\pi$
$13$	−5.10531	+	1.20998i	−1.41596	+	0.335588i	−0.549773	+	0.835314i	$0.685286\pi$
$14$	−0.283457	+	0.946811i	−0.0757570	+	0.253046i
$15$		0			0
$16$	−1.45269	+	0.169795i	−0.363172	+	0.0424488i
$17$	0.00536485	+	0.0304256i	0.00130117	+	0.00737929i	0.985451	−	0.169957i	$-0.0543630\pi$
$17$	0.00536485	+	0.0304256i	0.00130117	+	0.00737929i	−0.984150	+	0.177337i	$0.943252\pi$
$18$		0			0
$19$	0.634963	−	3.60105i	0.145670	−	0.826138i	−0.821156	−	0.570704i	$-0.806670\pi$
$19$	0.634963	−	3.60105i	0.145670	−	0.826138i	0.966826	−	0.255434i	$-0.0822184\pi$
$20$	−0.0845732	+	1.45207i	−0.0189111	+	0.324692i
$21$		0			0
$22$	1.64038	+	3.80282i	0.349729	+	0.810764i
$23$	−0.0934269	−	0.0469207i	−0.0194808	−	0.00978365i	0.439032	−	0.898471i	$-0.355321\pi$
$23$	−0.0934269	−	0.0469207i	−0.0194808	−	0.00978365i	−0.458513	+	0.888688i	$0.651618\pi$
$24$		0			0
$25$	−3.99963	−	0.947929i	−0.799925	−	0.189586i
$26$	−1.77507	+	3.07451i	−0.348120	+	0.602961i
$27$		0			0
$28$	−1.12628	−	1.95077i	−0.212846	−	0.368661i
$29$	0.147045	+	0.491165i	0.0273056	+	0.0912071i	0.970556	−	0.240875i	$-0.0774342\pi$
$29$	0.147045	+	0.491165i	0.0273056	+	0.0912071i	−0.943251	+	0.332082i	$0.892249\pi$
$30$		0			0
$31$	6.82537	−	4.48912i	1.22587	−	0.806269i	0.239517	−	0.970892i	$-0.423011\pi$
$31$	6.82537	−	4.48912i	1.22587	−	0.806269i	0.986357	+	0.164623i	$0.0526407\pi$
$32$	−3.45346	+	4.63881i	−0.610492	+	0.820033i
$33$		0			0
$34$	0.0174656	+	0.0114873i	0.00299533	+	0.00197006i
$35$	−1.29456	+	0.471183i	−0.218821	+	0.0796444i
$36$		0			0
$37$	5.42328	+	1.97391i	0.891581	+	0.324509i	0.746874	−	0.664965i	$-0.231554\pi$
$37$	5.42328	+	1.97391i	0.891581	+	0.324509i	0.144707	+	0.989475i	$0.453776\pi$
$38$	−1.47749	−	1.98461i	−0.239680	−	0.321947i
$39$		0			0
$40$	1.55129	+	1.64427i	0.245281	+	0.259983i
$41$	3.00983	+	3.19024i	0.470057	+	0.498231i	0.918413	−	0.395624i	$-0.129472\pi$
$41$	3.00983	+	3.19024i	0.470057	+	0.498231i	−0.448356	+	0.893855i	$0.647990\pi$
$42$		0			0
$43$	0.822094	+	1.10426i	0.125368	+	0.168399i	0.860376	−	0.509660i	$-0.170229\pi$
$43$	0.822094	+	1.10426i	0.125368	+	0.168399i	−0.735008	+	0.678059i	$0.762821\pi$
$44$	−8.86991	−	3.22838i	−1.33719	−	0.486697i
$45$		0			0
$46$	−0.0664745	+	0.0241947i	−0.00980113	+	0.00356732i
$47$	4.68685	+	3.08259i	0.683648	+	0.449642i	0.843237	−	0.537541i	$-0.180647\pi$
$47$	4.68685	+	3.08259i	0.683648	+	0.449642i	−0.159590	+	0.987183i	$0.551017\pi$
$48$		0			0
$49$	−2.90608	+	3.90354i	−0.415154	+	0.557648i
$50$	−2.32372	+	1.52833i	−0.328623	+	0.216139i
$51$		0			0
$52$	−2.32061	−	7.75138i	−0.321811	−	1.07492i
$53$	4.89106	+	8.47157i	0.671839	+	1.16366i	0.977382	+	0.211481i	$0.0678288\pi$
$53$	4.89106	+	8.47157i	0.671839	+	1.16366i	−0.305543	+	0.952178i	$0.598838\pi$
$54$		0			0
$55$	−2.88646	+	4.99950i	−0.389211	+	0.674132i
$56$	−3.40646	−	0.807346i	−0.455208	−	0.107886i
$57$		0			0
$58$	0.310015	+	0.155695i	0.0407070	+	0.0204438i
$59$	2.23761	+	5.18737i	0.291313	+	0.675339i	0.999530	−	0.0306559i	$-0.00975961\pi$
$59$	2.23761	+	5.18737i	0.291313	+	0.675339i	−0.708217	+	0.705994i	$0.750500\pi$
$60$		0			0
$61$	−0.0998805	+	1.71488i	−0.0127884	+	0.219568i	0.985859	+	0.167576i	$0.0535940\pi$
$61$	−0.0998805	+	1.71488i	−0.0127884	+	0.219568i	−0.998648	+	0.0519919i	$0.983443\pi$
$62$	0.959872	−	5.44370i	0.121904	−	0.691351i
$63$		0			0
$64$	0.171556	+	0.972942i	0.0214445	+	0.121618i
$65$	−4.91512	+	0.574495i	−0.609646	+	0.0712574i
$66$		0			0
$67$	−0.785171	+	2.62265i	−0.0959239	+	0.320408i	−0.992461	−	0.122560i	$-0.960889\pi$
$67$	−0.785171	+	2.62265i	−0.0959239	+	0.320408i	0.896537	+	0.442969i	$0.146075\pi$
$68$	−0.0463607	+	0.0109877i	−0.00562206	+	0.00133245i
$69$		0			0
$70$	−0.369213	+	0.855932i	−0.0441294	+	0.102303i
$71$	−1.66448	+	1.39666i	−0.197537	+	0.165753i	−0.736191	−	0.676774i	$-0.763377\pi$
$71$	−1.66448	+	1.39666i	−0.197537	+	0.165753i	0.538654	+	0.842527i	$0.318933\pi$
$72$		0			0
$73$	−6.38204	−	5.35517i	−0.746961	−	0.626775i	0.187736	−	0.982219i	$-0.439885\pi$
$73$	−6.38204	−	5.35517i	−0.746961	−	0.626775i	−0.934697	+	0.355445i	$0.884329\pi$
$74$	3.48973	−	1.75261i	0.405673	−	0.203737i
$75$		0			0
$76$	5.60094	+	0.654656i	0.642472	+	0.0750942i
$77$	−0.519830	−	8.92513i	−0.0592401	−	1.01711i
$78$		0			0
$79$	8.65544	−	9.17423i	0.973813	−	1.03218i	−0.0256586	−	0.999671i	$-0.508168\pi$
$79$	8.65544	−	9.17423i	0.973813	−	1.03218i	0.999471	−	0.0325105i	$-0.0103502\pi$
$80$	−1.37947			−0.154229
$81$		0			0
$82$	2.96771			0.327729
$83$	12.2319	−	12.9650i	1.34262	−	1.42310i	0.520406	−	0.853919i	$-0.325781\pi$
$83$	12.2319	−	12.9650i	1.34262	−	1.42310i	0.822216	−	0.569176i	$-0.192738\pi$
$84$		0			0
$85$	0.00169430	+	0.0290900i	0.000183773	+	0.00315526i
$86$	0.925214	+	0.108142i	0.0997683	+	0.0116612i
$87$		0			0
$88$	−13.1096	+	6.58387i	−1.39748	+	0.701843i
$89$	10.6853	+	8.96604i	1.13264	+	0.950399i	0.999173	−	0.0406545i	$-0.0129443\pi$
$89$	10.6853	+	8.96604i	1.13264	+	0.950399i	0.133468	+	0.991053i	$0.457389\pi$
$90$		0			0
$91$	5.87068	−	4.92609i	0.615415	−	0.516394i
$92$	0.0638594	−	0.148043i	0.00665780	−	0.0154345i
$93$		0			0
$94$	3.69344	−	0.875361i	0.380949	−	0.0902865i
$95$	0.989131	−	3.30393i	0.101483	−	0.338976i
$96$		0			0
$97$	6.96396	−	0.813970i	0.707083	−	0.0826461i	0.245052	−	0.969510i	$-0.421195\pi$
$97$	6.96396	−	0.813970i	0.707083	−	0.0826461i	0.462031	+	0.886864i	$0.347121\pi$
$98$	0.571800	+	3.24284i	0.0577605	+	0.327576i
$99$		0			0
$100$	1.10074	−	6.24263i	0.110074	−	0.624263i
$101$	−0.505324	+	8.67608i	−0.0502816	+	0.863302i	0.875024	+	0.484080i	$0.160846\pi$
$101$	−0.505324	+	8.67608i	−0.0502816	+	0.863302i	−0.925306	+	0.379222i	$0.876192\pi$
$102$		0			0
$103$	−2.03098	−	4.70833i	−0.200118	−	0.463926i	0.788374	−	0.615196i	$-0.210923\pi$
$103$	−2.03098	−	4.70833i	−0.200118	−	0.463926i	−0.988492	+	0.151270i	$0.951664\pi$
$104$	−11.2376	−	5.64373i	−1.10194	−	0.553413i
$105$		0			0
$106$	6.44055	+	1.52644i	0.625561	+	0.148261i
$107$	4.97642	−	8.61941i	0.481089	−	0.833270i	−0.518676	−	0.854971i	$-0.673575\pi$
$107$	4.97642	−	8.61941i	0.481089	−	0.833270i	0.999765	+	0.0217011i	$0.00690820\pi$
$108$		0			0
$109$	6.36856	+	11.0307i	0.609997	+	1.05655i	0.991240	+	0.132071i	$0.0421627\pi$
$109$	6.36856	+	11.0307i	0.609997	+	1.05655i	−0.381243	+	0.924475i	$0.624504\pi$
$110$	1.12031	+	3.74208i	0.106817	+	0.356794i
$111$		0			0
$112$	1.78486	−	1.17392i	0.168654	−	0.110925i
$113$	−3.43180	+	4.60971i	−0.322837	+	0.433645i	−0.933681	−	0.358106i	$-0.883423\pi$
$113$	−3.43180	+	4.60971i	−0.322837	+	0.433645i	0.610844	+	0.791751i	$0.290830\pi$
$114$		0			0
$115$	−0.0823844	−	0.0541850i	−0.00768238	−	0.00505278i
$116$	−0.742989	+	0.270426i	−0.0689848	+	0.0251084i
$117$		0			0
$118$	3.59207	+	1.30741i	0.330677	+	0.120357i
$119$	−0.0269478	−	0.0361972i	−0.00247030	−	0.00331819i
$120$		0			0
$121$	−18.1603	−	19.2488i	−1.65094	−	1.74989i
$122$	0.797633	+	0.845442i	0.0722143	+	0.0765427i
$123$		0			0
$124$	7.52325	+	10.1055i	0.675608	+	0.907499i
$125$	−8.07451	−	2.93888i	−0.722206	−	0.262862i
$126$		0			0
$127$	−9.96192	+	3.62584i	−0.883977	+	0.321741i	−0.743814	−	0.668387i	$-0.766985\pi$
$127$	−9.96192	+	3.62584i	−0.883977	+	0.321741i	−0.140163	+	0.990128i	$0.544763\pi$
$128$	−9.10501	−	5.98846i	−0.804777	−	0.529310i
$129$		0			0
$130$	−1.99953	+	2.68583i	−0.175370	+	0.235563i
$131$	11.9172	−	7.83807i	1.04121	−	0.684815i	0.0908184	−	0.995867i	$-0.471052\pi$
$131$	11.9172	−	7.83807i	1.04121	−	0.684815i	0.950393	+	0.311052i	$0.100681\pi$
$132$		0			0
$133$	1.53182	+	5.11664i	0.132826	+	0.443669i
$134$	0.926205	+	1.60423i	0.0800119	+	0.138585i
$135$		0			0
$136$	−0.0370239	+	0.0641273i	−0.00317478	+	0.00549887i
$137$	−5.19234	−	1.23061i	−0.443612	−	0.105138i	0.00273858	−	0.999996i	$-0.499128\pi$
$137$	−5.19234	−	1.23061i	−0.443612	−	0.105138i	−0.446350	+	0.894858i	$0.647276\pi$
$138$		0			0
$139$	−3.65867	−	1.83745i	−0.310324	−	0.155851i	0.286820	−	0.957984i	$-0.407402\pi$
$139$	−3.65867	−	1.83745i	−0.310324	−	0.155851i	−0.597144	+	0.802134i	$0.703698\pi$
$140$	−0.841492	−	1.95080i	−0.0711190	−	0.164872i
$141$		0			0
$142$	−0.0854853	+	1.46773i	−0.00717376	+	0.123169i
$143$	5.57652	−	31.6260i	0.466332	−	2.64470i
$144$		0			0
$145$	0.0839709	+	0.476223i	0.00697341	+	0.0395482i
$146$	−5.59907	+	0.654437i	−0.463382	+	0.0541616i
$147$		0			0
$148$	−2.55264	+	8.52641i	−0.209826	+	0.700867i
$149$	18.3677	−	4.35323i	1.50474	−	0.356630i	0.606127	−	0.795368i	$-0.292722\pi$
$149$	18.3677	−	4.35323i	1.50474	−	0.356630i	0.898615	+	0.438738i	$0.144574\pi$
$150$		0			0
$151$	−1.22010	+	2.82850i	−0.0992901	+	0.230180i	−0.960620	−	0.277866i	$-0.910373\pi$
$151$	−1.22010	+	2.82850i	−0.0992901	+	0.230180i	0.861330	+	0.508046i	$0.169632\pi$
$152$	6.71362	−	5.63340i	0.544547	−	0.456929i
$153$		0			0
$154$	−4.63405	−	3.88843i	−0.373422	−	0.313338i
$155$	6.88553	−	3.45804i	0.553059	−	0.277757i
$156$		0			0
$157$	3.40543	+	0.398037i	0.271783	+	0.0317668i	0.250893	−	0.968015i	$-0.419276\pi$
$157$	3.40543	+	0.398037i	0.271783	+	0.0317668i	0.0208901	+	0.999782i	$0.493350\pi$
$158$	−0.496226	−	8.51988i	−0.0394776	−	0.677805i
$159$		0			0
$160$	−3.74312	+	3.96748i	−0.295920	+	0.313657i
$161$	0.152707			0.0120350
$162$		0			0
$163$	−19.7151			−1.54420			−0.772101	−	0.635500i	$-0.780794\pi$
$163$	−19.7151			−1.54420			−0.772101	+	0.635500i	$0.780794\pi$
$164$	−4.64165	+	4.91986i	−0.362452	+	0.384176i
$165$		0			0
$166$	−0.701267	−	12.0403i	−0.0544289	−	0.934507i
$167$	−19.2117	−	2.24553i	−1.48665	−	0.173764i	−0.666324	−	0.745663i	$-0.732133\pi$
$167$	−19.2117	−	2.24553i	−1.48665	−	0.173764i	−0.820324	+	0.571898i	$0.806207\pi$
$168$		0			0
$169$	12.9829	−	6.52024i	0.998682	−	0.501557i
$170$	0.0151039	+	0.0126737i	0.00115842	+	0.000972029i
$171$		0			0
$172$	−1.62635	+	1.36467i	−0.124008	+	0.104055i
$173$	2.44275	−	5.66294i	0.185719	−	0.430545i	−0.799765	−	0.600313i	$-0.795043\pi$
$173$	2.44275	−	5.66294i	0.185719	−	0.430545i	0.985484	+	0.169768i	$0.0543018\pi$
$174$		0			0
$175$	5.84205	−	1.38459i	0.441617	−	0.104665i
$176$	2.56748	−	8.57599i	0.193531	−	0.646439i
$177$		0			0
$178$	9.37440	−	1.09571i	0.702641	−	0.0821270i
$179$	0.601129	+	3.40917i	0.0449305	+	0.254814i	0.998997	−	0.0447821i	$-0.0142593\pi$
$179$	0.601129	+	3.40917i	0.0449305	+	0.254814i	−0.954066	+	0.299596i	$0.903148\pi$
$180$		0			0
$181$	−3.31327	+	18.7905i	−0.246273	+	1.39668i	0.571244	+	0.820780i	$0.306461\pi$
$181$	−3.31327	+	18.7905i	−0.246273	+	1.39668i	−0.817517	+	0.575904i	$0.804650\pi$
$182$	0.301511	−	5.17674i	0.0223494	−	0.383725i
$183$		0			0
$184$	−0.0992477	−	0.230082i	−0.00731664	−	0.0169619i
$185$	4.86437	+	2.44298i	0.357636	+	0.179612i
$186$		0			0
$187$	−0.184003	−	0.0436095i	−0.0134556	−	0.00318904i
$188$	−4.32554	+	7.49206i	−0.315473	+	0.546415i
$189$		0			0
$190$	−1.16680	−	2.02096i	−0.0846486	−	0.146616i
$191$	−5.71535	−	19.0906i	−0.413548	−	1.38135i	−0.870637	−	0.491926i	$-0.836293\pi$
$191$	−5.71535	−	19.0906i	−0.413548	−	1.38135i	0.457089	−	0.889421i	$-0.348892\pi$
$192$		0			0
$193$	8.95424	−	5.88930i	0.644540	−	0.423921i	−0.184714	−	0.982792i	$-0.559136\pi$
$193$	8.95424	−	5.88930i	0.644540	−	0.423921i	0.829254	+	0.558871i	$0.188765\pi$
$194$	2.83302	−	3.80540i	0.203399	−	0.273212i
$195$		0			0
$196$	−6.27028	−	4.12403i	−0.447877	−	0.294573i
$197$	−22.2725	+	8.10651i	−1.58685	+	0.577565i	−0.976679	−	0.214707i	$-0.931120\pi$
$197$	−22.2725	+	8.10651i	−1.58685	+	0.577565i	−0.610169	+	0.792272i	$0.708898\pi$
$198$		0			0
$199$	−8.20833	−	2.98759i	−0.581873	−	0.211785i	0.0342781	−	0.999412i	$-0.489087\pi$
$199$	−8.20833	−	2.98759i	−0.581873	−	0.211785i	−0.616151	+	0.787628i	$0.711309\pi$
$200$	−5.88303	−	7.90228i	−0.415993	−	0.558776i
$201$		0			0
$202$	4.03546	+	4.27733i	0.283934	+	0.300952i
$203$	−0.513913	−	0.544716i	−0.0360696	−	0.0382316i
$204$		0			0
$205$	2.47028	+	3.31817i	0.172532	+	0.231751i
$206$	−3.26035	−	1.18667i	−0.227160	−	0.0826793i
$207$		0			0
$208$	7.21098	−	2.62458i	0.499991	−	0.181982i
$209$	18.6992	+	12.2986i	1.29345	+	0.850714i
$210$		0			0
$211$	−4.34616	+	5.83790i	−0.299202	+	0.401898i	−0.926145	−	0.377167i	$-0.876898\pi$
$211$	−4.34616	+	5.83790i	−0.299202	+	0.401898i	0.626943	+	0.779065i	$0.284306\pi$
$212$	−12.6038	+	8.28968i	−0.865635	+	0.569337i
$213$		0			0
$214$	−1.93147	−	6.45155i	−0.132032	−	0.441019i
$215$	0.649223	+	1.12449i	0.0442766	+	0.0766894i
$216$		0			0
$217$	−5.96626	+	10.3339i	−0.405016	+	0.701508i
$218$	8.38611	+	1.98754i	0.567979	+	0.134614i
$219$		0			0
$220$	−7.95581	−	3.99556i	−0.536381	−	0.269381i
$221$	−0.0642036	−	0.148841i	−0.00431880	−	0.0100121i
$222$		0			0
$223$	−0.0435199	+	0.747208i	−0.00291431	+	0.0500367i	−0.999452	−	0.0331082i	$-0.989459\pi$
$223$	−0.0435199	+	0.747208i	−0.00291431	+	0.0500367i	0.996537	+	0.0831449i	$0.0264964\pi$
$224$	1.46684	−	8.31884i	0.0980071	−	0.555826i
$225$		0			0
$226$	0.675242	+	3.82949i	0.0449164	+	0.254734i
$227$	7.55453	−	0.882998i	0.501412	−	0.0586067i	0.138372	−	0.990380i	$-0.455813\pi$
$227$	7.55453	−	0.882998i	0.501412	−	0.0586067i	0.363040	+	0.931774i	$0.381739\pi$
$228$		0			0
$229$	4.47466	−	14.9464i	0.295694	−	0.987686i	−0.673045	−	0.739602i	$-0.735014\pi$
$229$	4.47466	−	14.9464i	0.295694	−	0.987686i	0.968739	−	0.248084i	$-0.0798009\pi$
$230$	−0.0649224	+	0.0153869i	−0.00428085	+	0.00101458i
$231$		0			0
$232$	−0.486715	+	1.12833i	−0.0319544	+	0.0740786i
$233$	12.6227	−	10.5917i	0.826940	−	0.693885i	−0.127647	−	0.991820i	$-0.540742\pi$
$233$	12.6227	−	10.5917i	0.826940	−	0.693885i	0.954586	+	0.297935i	$0.0962979\pi$
$234$		0			0
$235$	4.05310	+	3.40095i	0.264395	+	0.221854i
$236$	−7.78558	+	3.91007i	−0.506798	+	0.254524i
$237$		0			0
$238$	−0.0303280	−	0.00354483i	−0.00196587	−	0.000229777i
$239$	1.12492	+	19.3142i	0.0727653	+	1.24933i	0.815107	+	0.579310i	$0.196678\pi$
$239$	1.12492	+	19.3142i	0.0727653	+	1.24933i	−0.742342	+	0.670021i	$0.766285\pi$
$240$		0			0
$241$	−3.95611	+	4.19324i	−0.254836	+	0.270110i	−0.842143	−	0.539254i	$-0.818706\pi$
$241$	−3.95611	+	4.19324i	−0.254836	+	0.270110i	0.587308	+	0.809364i	$0.300188\pi$
$242$	−17.9062			−1.15105
$243$		0			0
$244$	−2.64910			−0.169591
$245$	−3.14982	+	3.33862i	−0.201235	+	0.213296i
$246$		0			0
$247$	1.11552	+	19.1528i	0.0709789	+	1.21866i
$248$	19.4475	+	2.27309i	1.23492	+	0.144341i
$249$		0			0
$250$	−5.19572	+	2.60939i	−0.328607	+	0.165032i
$251$	14.4752	+	12.1462i	0.913668	+	0.766659i	0.972813	−	0.231591i	$-0.0743930\pi$
$251$	14.4752	+	12.1462i	0.913668	+	0.766659i	−0.0591449	+	0.998249i	$0.518837\pi$
$252$		0			0
$253$	0.490197	−	0.411324i	0.0308184	−	0.0258597i
$254$	−2.84116	+	6.58656i	−0.178271	+	0.413278i
$255$		0			0
$256$	−9.09777	+	2.15621i	−0.568611	+	0.134763i
$257$	−5.19708	+	17.3594i	−0.324185	+	1.08285i	0.628225	+	0.778032i	$0.283782\pi$
$257$	−5.19708	+	17.3594i	−0.324185	+	1.08285i	−0.952410	+	0.304821i	$0.901403\pi$
$258$		0			0
$259$	−8.37289	+	0.978650i	−0.520266	+	0.0608104i
$260$	−1.32520	−	7.51557i	−0.0821853	−	0.466096i
$261$		0			0
$262$	1.67595	−	9.50479i	0.103541	−	0.587208i
$263$	0.504066	−	8.65448i	0.0310821	−	0.533658i	−0.946447	−	0.322859i	$-0.895356\pi$
$263$	0.504066	−	8.65448i	0.0310821	−	0.533658i	0.977529	−	0.210800i	$-0.0676068\pi$
$264$		0			0
$265$	3.65433	+	8.47169i	0.224484	+	0.520412i
$266$	3.22953	+	1.62193i	0.198015	+	0.0994470i
$267$		0			0
$268$	−4.10812	−	0.973641i	−0.250943	−	0.0594746i
$269$	5.59305	−	9.68745i	0.341014	−	0.590654i	−0.643607	−	0.765356i	$-0.722563\pi$
$269$	5.59305	−	9.68745i	0.341014	−	0.590654i	0.984621	+	0.174702i	$0.0558962\pi$
$270$		0			0
$271$	5.08705	+	8.81103i	0.309016	+	0.535232i	0.978147	−	0.207912i	$-0.0666669\pi$
$271$	5.08705	+	8.81103i	0.309016	+	0.535232i	−0.669131	+	0.743144i	$0.733334\pi$
$272$	−0.0129596	−	0.0432880i	−0.000785790	−	0.00262472i
$273$		0			0
$274$	−3.01667	+	1.98409i	−0.182243	+	0.119863i
$275$	15.0238	−	20.1805i	0.905970	−	1.21693i
$276$		0			0
$277$	1.08784	+	0.715482i	0.0653618	+	0.0429892i	0.581769	−	0.813354i	$-0.302361\pi$
$277$	1.08784	+	0.715482i	0.0653618	+	0.0429892i	−0.516408	+	0.856343i	$0.672731\pi$
$278$	−2.60319	+	0.947485i	−0.156129	+	0.0568264i
$279$		0			0
$280$	−3.10276	−	1.12931i	−0.185425	−	0.0674894i
$281$	3.82768	+	5.14146i	0.228340	+	0.306714i	0.901497	−	0.432786i	$-0.142469\pi$
$281$	3.82768	+	5.14146i	0.228340	+	0.306714i	−0.673157	+	0.739500i	$0.735062\pi$
$282$		0			0
$283$	13.1190	+	13.9053i	0.779842	+	0.826584i	0.988471	−	0.151411i	$-0.0483816\pi$
$283$	13.1190	+	13.9053i	0.779842	+	0.826584i	−0.208629	+	0.977995i	$0.566900\pi$
$284$	−2.29948	−	2.43731i	−0.136449	−	0.144628i
$285$		0			0
$286$	−12.9760	−	17.4297i	−0.767284	−	1.03064i
$287$	−6.02001	−	2.19110i	−0.355350	−	0.129337i
$288$		0			0
$289$	15.9739	−	5.81402i	0.939640	−	0.342001i
$290$	0.273373	+	0.179800i	0.0160530	+	0.0105582i
$291$		0			0
$292$	7.67228	−	10.3057i	0.448986	−	0.603093i
$293$	−1.52565	+	1.00344i	−0.0891296	+	0.0586214i	−0.593291	−	0.804988i	$-0.702172\pi$
$293$	−1.52565	+	1.00344i	−0.0891296	+	0.0586214i	0.504162	+	0.863609i	$0.331801\pi$
$294$		0			0
$295$	1.52819	+	5.10452i	0.0889749	+	0.297197i
$296$	6.91625	+	11.9793i	0.401999	+	0.696283i
$297$		0			0
$298$	6.38629	−	11.0614i	0.369948	−	0.640769i
$299$	0.533746	+	0.126500i	0.0308673	+	0.00731569i
$300$		0			0
$301$	−1.79695	−	0.902464i	−0.103575	−	0.0520171i
$302$	0.825565	+	1.91387i	0.0475059	+	0.110131i
$303$		0			0
$304$	−0.310963	+	5.33903i	−0.0178349	+	0.306214i
$305$	−0.281340	+	1.59556i	−0.0161095	+	0.0913614i
$306$		0			0
$307$	−2.60207	−	14.7571i	−0.148508	−	0.842232i	−0.964483	−	0.264145i	$-0.914910\pi$
$307$	−2.60207	−	14.7571i	−0.148508	−	0.842232i	0.815975	−	0.578087i	$-0.196201\pi$
$308$	13.6941	−	1.60061i	0.780293	−	0.0912031i
$309$		0			0
$310$	1.49527	−	4.99454i	0.0849255	−	0.283671i
$311$	−20.1029	+	4.76447i	−1.13993	+	0.270168i	−0.756876	−	0.653558i	$-0.773275\pi$
$311$	−20.1029	+	4.76447i	−1.13993	+	0.270168i	−0.383053	+	0.923726i	$0.625127\pi$
$312$		0			0
$313$	8.84187	−	20.4977i	0.499772	−	1.15860i	−0.462527	−	0.886605i	$-0.653057\pi$
$313$	8.84187	−	20.4977i	0.499772	−	1.15860i	0.962298	−	0.271996i	$-0.0876837\pi$
$314$	1.77717	−	1.49122i	0.100291	−	0.0841545i
$315$		0			0
$316$	14.9003	+	12.5028i	0.838208	+	0.703340i
$317$	−10.1518	+	5.09842i	−0.570181	+	0.286356i	−0.710438	−	0.703759i	$-0.751503\pi$
$317$	−10.1518	+	5.09842i	−0.570181	+	0.286356i	0.140257	+	0.990115i	$0.455207\pi$
$318$		0			0
$319$	−3.11691	−	0.364315i	−0.174514	−	0.0203977i
$320$	0.0541799	+	0.930234i	0.00302875	+	0.0520016i
$321$		0			0
$322$	0.0709075	−	0.0751576i	0.00395152	−	0.00418837i
$323$	0.112971			0.00628586
$324$		0			0
$325$	21.5663			1.19628
$326$	−9.15444	+	9.70314i	−0.507017	+	0.537407i
$327$		0			0
$328$	0.611225	+	10.4943i	0.0337493	+	0.579453i
$329$	−8.13843	−	0.951245i	−0.448686	−	0.0524439i
$330$		0			0
$331$	12.8748	−	6.46596i	0.707662	−	0.355401i	−0.0582896	−	0.998300i	$-0.518565\pi$
$331$	12.8748	−	6.46596i	0.707662	−	0.355401i	0.765951	+	0.642899i	$0.222268\pi$
$332$	21.0571	+	17.6690i	1.15566	+	0.969714i
$333$		0			0
$334$	−10.0259	+	8.41273i	−0.548593	+	0.460324i
$335$	−1.02272	+	2.37092i	−0.0558769	+	0.129537i
$336$		0			0
$337$	−9.64054	+	2.28485i	−0.525154	+	0.124464i	−0.484637	−	0.874715i	$-0.661048\pi$
$337$	−9.64054	+	2.28485i	−0.525154	+	0.124464i	−0.0405164	+	0.999179i	$0.512900\pi$
$338$	2.81937	−	9.41736i	0.153354	−	0.512237i
$339$		0			0
$340$	−0.0446337	+	0.00521693i	−0.00242060	+	0.000282928i
$341$	8.68281	+	49.2427i	0.470201	+	2.66664i
$342$		0			0
$343$	3.00981	−	17.0695i	0.162514	−	0.921665i
$344$	−0.191853	+	3.29398i	−0.0103440	+	0.177600i
$345$		0			0
$346$	−1.65286	−	3.83176i	−0.0888583	−	0.205997i
$347$	3.01890	+	1.51615i	0.162063	+	0.0813912i	0.527982	−	0.849256i	$-0.322949\pi$
$347$	3.01890	+	1.51615i	0.162063	+	0.0813912i	−0.365919	+	0.930647i	$0.619245\pi$
$348$		0			0
$349$	−1.29409	−	0.306704i	−0.0692708	−	0.0164175i	0.195834	−	0.980637i	$-0.437259\pi$
$349$	−1.29409	−	0.306704i	−0.0692708	−	0.0164175i	−0.265105	+	0.964220i	$0.585407\pi$
$350$	2.03123	−	3.51819i	0.108574	−	0.188055i
$351$		0			0
$352$	−17.6986	−	30.6549i	−0.943340	−	1.63391i
$353$	3.38243	+	11.2981i	0.180029	+	0.601338i	0.999598	+	0.0283577i	$0.00902775\pi$
$353$	3.38243	+	11.2981i	0.180029	+	0.601338i	−0.819569	+	0.572981i	$0.805787\pi$
$354$		0			0
$355$	−1.71220	+	1.12613i	−0.0908744	+	0.0597690i
$356$	−12.8455	+	17.2546i	−0.680812	+	0.914490i
$357$		0			0
$358$	1.95702	+	1.28715i	0.103432	+	0.0680280i
$359$	−27.9195	+	10.1619i	−1.47353	+	0.536323i	−0.949058	−	0.315102i	$-0.897961\pi$
$359$	−27.9195	+	10.1619i	−1.47353	+	0.536323i	−0.524477	+	0.851425i	$0.675739\pi$
$360$		0			0
$361$	5.28976	+	1.92531i	0.278408	+	0.101332i
$362$	7.70961	+	10.3558i	0.405208	+	0.544289i
$363$		0			0
$364$	8.11038	+	8.59650i	0.425100	+	0.450579i
$365$	−5.39230	−	5.71551i	−0.282246	−	0.299163i
$366$		0			0
$367$	−4.79340	−	6.43865i	−0.250213	−	0.336095i	0.659216	−	0.751954i	$-0.270888\pi$
$367$	−4.79340	−	6.43865i	−0.250213	−	0.336095i	−0.909429	+	0.415859i	$0.863481\pi$
$368$	0.143687	+	0.0522978i	0.00749021	+	0.00272621i
$369$		0			0
$370$	3.46107	−	1.25973i	0.179933	−	0.0654901i
$371$	−11.9377	−	7.85152i	−0.619772	−	0.407631i
$372$		0			0
$373$	−1.78779	+	2.40142i	−0.0925681	+	0.124341i	−0.845994	−	0.533192i	$-0.820992\pi$
$373$	−1.78779	+	2.40142i	−0.0925681	+	0.124341i	0.753426	+	0.657533i	$0.228400\pi$
$374$	−0.106903	+	0.0703110i	−0.00552781	+	0.00363570i
$375$		0			0
$376$	3.85612	+	12.8803i	0.198864	+	0.664252i
$377$	−1.34501	−	2.32963i	−0.0692716	−	0.119982i
$378$		0			0
$379$	11.0537	−	19.1456i	0.567792	−	0.983444i	−0.428992	−	0.903308i	$-0.641131\pi$
$379$	11.0537	−	19.1456i	0.567792	−	0.983444i	0.996784	−	0.0801362i	$-0.0255355\pi$
$380$	5.17526	+	1.22656i	0.265485	+	0.0629212i
$381$		0			0
$382$	−12.0497	−	6.05156i	−0.616514	−	0.309625i
$383$	−5.68677	−	13.1834i	−0.290580	−	0.673641i	0.708919	−	0.705290i	$-0.249183\pi$
$383$	−5.68677	−	13.1834i	−0.290580	−	0.673641i	−0.999499	+	0.0316494i	$0.989924\pi$
$384$		0			0
$385$	0.490290	−	8.41795i	0.0249875	−	0.429018i
$386$	1.25926	−	7.14162i	0.0640947	−	0.363499i
$387$		0			0
$388$	1.87760	+	10.6484i	0.0953206	+	0.540590i
$389$	−18.1068	+	2.11638i	−0.918049	+	0.107305i	−0.561976	−	0.827154i	$-0.689959\pi$
$389$	−18.1068	+	2.11638i	−0.918049	+	0.107305i	−0.356073	+	0.934458i	$0.615885\pi$
$390$		0			0
$391$	0.000926370	−	0.00309429i	4.68485e−5	−	0.000156485i
$392$	−11.3495	+	2.68987i	−0.573234	+	0.135859i
$393$		0			0
$394$	−6.35216	+	14.7260i	−0.320017	+	0.741884i
$395$	9.11293	−	7.64665i	0.458521	−	0.384745i
$396$		0			0
$397$	1.06250	+	0.891545i	0.0533255	+	0.0447454i	0.669061	−	0.743208i	$-0.266697\pi$
$397$	1.06250	+	0.891545i	0.0533255	+	0.0447454i	−0.615735	+	0.787953i	$0.711141\pi$
$398$	−5.28184	+	2.65264i	−0.264754	+	0.132965i
$399$		0			0
$400$	5.97117	+	0.697930i	0.298558	+	0.0348965i
$401$	1.28420	+	22.0489i	0.0641301	+	1.10107i	0.864849	+	0.502031i	$0.167414\pi$
$401$	1.28420	+	22.0489i	0.0641301	+	1.10107i	−0.800719	+	0.599040i	$0.795549\pi$
$402$		0			0
$403$	−29.4139	+	31.1769i	−1.46521	+	1.55303i
$404$	−13.4026			−0.666803
$405$		0			0
$406$	−0.506722			−0.0251482
$407$	−24.2414	+	25.6944i	−1.20160	+	1.27362i
$408$		0			0
$409$	−0.0335717	−	0.576405i	−0.00166002	−	0.0285014i	0.997376	−	0.0723896i	$-0.0230625\pi$
$409$	−0.0335717	−	0.576405i	−0.00166002	−	0.0285014i	−0.999036	+	0.0438882i	$0.986025\pi$
$410$	2.78015	+	0.324952i	0.137302	+	0.0160483i
$411$		0			0
$412$	7.06660	−	3.54898i	0.348147	−	0.174846i
$413$	−6.32124	−	5.30415i	−0.311048	−	0.261000i
$414$		0			0
$415$	12.8784	−	10.8062i	0.632175	−	0.530458i
$416$	12.0181	−	27.8612i	0.589237	−	1.36601i
$417$		0			0
$418$	14.7357	−	3.49243i	0.720748	−	0.170820i
$419$	−3.62277	+	12.1009i	−0.176984	+	0.591167i	0.822757	+	0.568393i	$0.192435\pi$
$419$	−3.62277	+	12.1009i	−0.176984	+	0.591167i	−0.999741	+	0.0227734i	$0.992750\pi$
$420$		0			0
$421$	−21.2812	+	2.48741i	−1.03718	+	0.121229i	−0.617602	−	0.786490i	$-0.711896\pi$
$421$	−21.2812	+	2.48741i	−1.03718	+	0.121229i	−0.419578	+	0.907719i	$0.637822\pi$
$422$	0.855151	+	4.84980i	0.0416281	+	0.236085i
$423$		0			0
$424$	−4.07126	+	23.0892i	−0.197718	+	1.12131i
$425$	0.00738389	−	0.126777i	0.000358171	−	0.00614956i
$426$		0			0
$427$	−0.993798	−	2.30388i	−0.0480932	−	0.111493i
$428$	13.7163	+	6.88856i	0.663000	+	0.332971i
$429$		0			0
$430$	0.854896	+	0.202614i	0.0412267	+	0.00977092i
$431$	2.23566	−	3.87227i	0.107688	−	0.186521i	−0.807145	−	0.590353i	$-0.798989\pi$
$431$	2.23566	−	3.87227i	0.107688	−	0.186521i	0.914833	+	0.403832i	$0.132322\pi$
$432$		0			0
$433$	−4.56671	−	7.90977i	−0.219462	−	0.380119i	0.735182	−	0.677870i	$-0.237097\pi$
$433$	−4.56671	−	7.90977i	−0.219462	−	0.380119i	−0.954644	+	0.297751i	$0.903763\pi$
$434$	2.31565	+	7.73481i	0.111155	+	0.371283i
$435$		0			0
$436$	−16.4112	+	10.7938i	−0.785955	+	0.516930i
$437$	−0.228287	+	0.306642i	−0.0109204	+	0.0146687i
$438$		0			0
$439$	−2.38000	−	1.56535i	−0.113591	−	0.0747101i	0.491442	−	0.870910i	$-0.336470\pi$
$439$	−2.38000	−	1.56535i	−0.113591	−	0.0747101i	−0.605033	+	0.796200i	$0.706840\pi$
$440$	−13.0019	+	4.73230i	−0.619841	+	0.225604i
$441$		0			0
$442$	−0.103067	−	0.0375133i	−0.00490239	−	0.00178432i
$443$	7.38778	+	9.92352i	0.351004	+	0.471480i	0.942202	−	0.335046i	$-0.108752\pi$
$443$	7.38778	+	9.92352i	0.351004	+	0.471480i	−0.591197	+	0.806527i	$0.701345\pi$
$444$		0			0
$445$	9.02822	+	9.56936i	0.427979	+	0.453631i
$446$	0.347544	+	0.368376i	0.0164567	+	0.0174431i
$447$		0			0
$448$	−0.861730	−	1.15750i	−0.0407129	−	0.0546869i
$449$	16.1389	+	5.87407i	0.761640	+	0.277214i	0.693495	−	0.720461i	$-0.256070\pi$
$449$	16.1389	+	5.87407i	0.761640	+	0.277214i	0.0681449	+	0.997675i	$0.478292\pi$
$450$		0			0
$451$	−25.2264	+	9.18166i	−1.18786	+	0.432347i
$452$	−7.40461	−	4.87009i	−0.348284	−	0.229070i
$453$		0			0
$454$	3.07327	−	4.12812i	0.144236	−	0.193742i
$455$	6.03902	−	3.97193i	0.283114	−	0.186207i
$456$		0			0
$457$	−0.253753	−	0.847594i	−0.0118701	−	0.0396488i	0.951849	−	0.306566i	$-0.0991801\pi$
$457$	−0.253753	−	0.847594i	−0.0118701	−	0.0396488i	−0.963719	+	0.266917i	$0.913995\pi$
$458$	−5.27840	−	9.14246i	−0.246644	−	0.427199i
$459$		0			0
$460$	0.0760334	−	0.131694i	0.00354507	−	0.00614025i
$461$	14.8212	+	3.51270i	0.690294	+	0.163603i	0.560768	−	0.827973i	$-0.310506\pi$
$461$	14.8212	+	3.51270i	0.690294	+	0.163603i	0.129526	+	0.991576i	$0.458654\pi$
$462$		0			0
$463$	30.0591	+	15.0962i	1.39696	+	0.701582i	0.978422	−	0.206615i	$-0.0662449\pi$
$463$	30.0591	+	15.0962i	1.39696	+	0.701582i	0.418542	+	0.908197i	$0.362541\pi$
$464$	−0.297009	−	0.688543i	−0.0137883	−	0.0319648i
$465$		0			0
$466$	0.648284	−	11.1306i	0.0300312	−	0.515616i
$467$	−1.91520	+	10.8616i	−0.0886249	+	0.502617i	0.907890	+	0.419207i	$0.137692\pi$
$467$	−1.91520	+	10.8616i	−0.0886249	+	0.502617i	−0.996515	+	0.0834093i	$0.973419\pi$
$468$		0			0
$469$	−0.694378	−	3.93802i	−0.0320634	−	0.181841i
$470$	3.55585	−	0.415619i	0.164019	−	0.0191711i
$471$		0			0
$472$	−3.88340	+	12.9714i	−0.178748	+	0.597059i
$473$	−8.19915	+	1.94323i	−0.376997	+	0.0893500i
$474$		0			0
$475$	−5.95315	+	13.8010i	−0.273149	+	0.633232i
$476$	0.0533110	−	0.0447333i	0.00244351	−	0.00205035i
$477$		0			0
$478$	10.0282	+	8.41465i	0.458679	+	0.384877i
$479$	10.6546	−	5.35095i	0.486822	−	0.244491i	−0.188418	−	0.982089i	$-0.560336\pi$
$479$	10.6546	−	5.35095i	0.486822	−	0.244491i	0.675241	+	0.737598i	$0.264040\pi$
$480$		0			0
$481$	−30.0759	−	3.51537i	−1.37134	−	0.160287i
$482$	0.226809	+	3.89415i	0.0103308	+	0.177374i
$483$		0			0
$484$	28.0062	−	29.6848i	1.27301	−	1.34931i
$485$	6.61294			0.300278
$486$		0			0
$487$	38.2435			1.73298			0.866489	−	0.499196i	$-0.166371\pi$
$487$	38.2435			1.73298			0.866489	+	0.499196i	$0.166371\pi$
$488$	−2.82534	+	2.99469i	−0.127897	+	0.135563i
$489$		0			0
$490$	0.180583	+	3.10049i	0.00815791	+	0.140066i
$491$	4.21090	+	0.492183i	0.190035	+	0.0222119i	0.210578	−	0.977577i	$-0.432465\pi$
$491$	4.21090	+	0.492183i	0.190035	+	0.0222119i	−0.0205429	+	0.999789i	$0.506539\pi$
$492$		0			0
$493$	−0.0141551	+	0.00710897i	−0.000637515	+	0.000320172i
$494$	9.94438	+	8.34432i	0.447419	+	0.375429i
$495$		0			0
$496$	−9.15292	+	7.68021i	−0.410978	+	0.344852i
$497$	1.25705	−	2.91417i	0.0563863	−	0.130718i
$498$		0			0
$499$	36.3957	−	8.62595i	1.62930	−	0.386151i	0.688531	−	0.725207i	$-0.258256\pi$
$499$	36.3957	−	8.62595i	1.62930	−	0.386151i	0.940766	+	0.339056i	$0.110108\pi$
$500$	3.80053	−	12.6946i	0.169965	−	0.567722i
$501$		0			0
$502$	12.6994	−	1.48434i	0.566800	−	0.0662494i
$503$	−0.0594062	−	0.336909i	−0.00264879	−	0.0150220i	0.983455	−	0.181154i	$-0.0579833\pi$
$503$	−0.0594062	−	0.336909i	−0.00264879	−	0.0150220i	−0.986104	+	0.166132i	$0.946872\pi$
$504$		0			0
$505$	−1.42338	+	8.07239i	−0.0633396	+	0.359217i
$506$	0.0251759	−	0.432253i	0.00111920	−	0.0192160i
$507$		0			0
$508$	−6.47544	−	15.0118i	−0.287301	−	0.666039i
$509$	5.58869	+	2.80675i	0.247714	+	0.124407i	0.568325	−	0.822804i	$-0.307592\pi$
$509$	5.58869	+	2.80675i	0.247714	+	0.124407i	−0.320610	+	0.947211i	$0.603888\pi$
$510$		0			0
$511$	11.8409	+	2.80634i	0.523810	+	0.124145i
$512$	7.73462	−	13.3968i	0.341825	−	0.592059i
$513$		0			0
$514$	6.13058	+	10.6185i	0.270408	+	0.468361i
$515$	−1.38707	−	4.63313i	−0.0611216	−	0.204160i
$516$		0			0
$517$	−28.6870	+	18.8677i	−1.26165	+	0.829802i
$518$	−3.40619	+	4.57530i	−0.149659	+	0.201027i
$519$		0			0
$520$	−9.90937	−	6.51749i	−0.434554	−	0.285811i
$521$	−29.5418	+	10.7523i	−1.29425	+	0.471068i	−0.895119	−	0.445827i	$-0.852910\pi$
$521$	−29.5418	+	10.7523i	−1.29425	+	0.471068i	−0.399129	+	0.916895i	$0.630687\pi$
$522$		0			0
$523$	−20.1279	−	7.32597i	−0.880134	−	0.320342i	−0.137870	−	0.990450i	$-0.544026\pi$
$523$	−20.1279	−	7.32597i	−0.880134	−	0.320342i	−0.742264	+	0.670108i	$0.766248\pi$
$524$	13.1357	+	17.6443i	0.573836	+	0.770796i
$525$		0			0
$526$	−4.02541	−	4.26669i	−0.175516	−	0.186036i
$527$	0.173201	+	0.183583i	0.00754477	+	0.00799698i
$528$		0			0
$529$	−13.7281	−	18.4401i	−0.596875	−	0.801742i
$530$	5.86635	+	2.13518i	0.254818	+	0.0927461i
$531$		0			0
$532$	−7.73997	+	2.81712i	−0.335570	+	0.122138i
$533$	−19.2262	−	12.6453i	−0.832781	−	0.547729i
$534$		0			0
$535$	5.60568	−	7.52974i	0.242355	−	0.325539i
$536$	−5.48208	+	3.60562i	−0.236790	+	0.155739i
$537$		0			0
$538$	−2.17080	−	7.25097i	−0.0935898	−	0.312612i
$539$	−14.8933	−	25.7960i	−0.641500	−	1.11111i
$540$		0			0
$541$	0.188033	−	0.325682i	0.00808416	−	0.0140022i	−0.861955	−	0.506985i	$-0.830760\pi$
$541$	0.188033	−	0.325682i	0.00808416	−	0.0140022i	0.870039	+	0.492983i	$0.164093\pi$
$542$	6.69862	+	1.58760i	0.287731	+	0.0681934i
$543$		0			0
$544$	−0.159666	−	0.0801872i	−0.00684562	−	0.00343800i
$545$	4.75823	+	11.0308i	0.203820	+	0.472508i
$546$		0			0
$547$	0.388245	−	6.66590i	0.0166001	−	0.285013i	−0.979784	−	0.200056i	$-0.935888\pi$
$547$	0.388245	−	6.66590i	0.0166001	−	0.285013i	0.996385	−	0.0849573i	$-0.0270754\pi$
$548$	1.42899	−	8.10422i	0.0610436	−	0.346195i
$549$		0			0
$550$	−2.95609	−	16.7648i	−0.126048	−	0.714854i
$551$	1.86208	−	0.217646i	0.0793273	−	0.00927203i
$552$		0			0
$553$	−5.28374	+	17.6489i	−0.224688	+	0.750509i
$554$	0.857262	−	0.203175i	0.0364216	−	0.00863207i
$555$		0			0
$556$	2.50078	−	5.79747i	0.106057	−	0.245867i
$557$	−2.30382	+	1.93313i	−0.0976160	+	0.0819095i	−0.690290	−	0.723533i	$-0.742517\pi$
$557$	−2.30382	+	1.93313i	−0.0976160	+	0.0819095i	0.592674	+	0.805443i	$0.298072\pi$
$558$		0			0
$559$	−5.53318	−	4.64289i	−0.234028	−	0.196373i
$560$	1.80060	−	0.904293i	0.0760890	−	0.0382134i
$561$		0			0
$562$	4.30780	+	0.503510i	0.181714	+	0.0212393i
$563$	−1.90779	−	32.7554i	−0.0804036	−	1.38048i	−0.761444	−	0.648231i	$-0.775509\pi$
$563$	−1.90779	−	32.7554i	−0.0804036	−	1.38048i	0.681040	−	0.732246i	$-0.261528\pi$
$564$		0			0
$565$	−3.71965	+	3.94260i	−0.156487	+	0.165866i
$566$	12.9354			0.543715
$567$		0			0
$568$	−5.20773			−0.218511
$569$	17.9432	−	19.0186i	0.752217	−	0.797303i	−0.232291	−	0.972646i	$-0.574622\pi$
$569$	17.9432	−	19.0186i	0.752217	−	0.797303i	0.984507	+	0.175343i	$0.0561035\pi$
$570$		0			0
$571$	0.0465596	+	0.799398i	0.00194846	+	0.0334538i	0.999142	−	0.0414098i	$-0.0131849\pi$
$571$	0.0465596	+	0.799398i	0.00194846	+	0.0334538i	−0.997194	+	0.0748636i	$0.976148\pi$
$572$	49.1899	+	5.74947i	2.05673	+	0.240398i
$573$		0			0
$574$	−3.87371	+	1.94545i	−0.161685	+	0.0812015i
$575$	0.329195	+	0.276227i	0.0137284	+	0.0115195i
$576$		0			0
$577$	−32.3968	+	27.1841i	−1.34869	+	1.13169i	−0.369395	+	0.929273i	$0.620435\pi$
$577$	−32.3968	+	27.1841i	−1.34869	+	1.13169i	−0.979300	+	0.202416i	$0.935121\pi$
$578$	4.55579	−	10.5615i	0.189496	−	0.439301i
$579$		0			0
$580$	−0.725640	+	0.171980i	−0.0301306	+	0.00714107i
$581$	−7.46699	+	24.9415i	−0.309783	+	1.03475i
$582$		0			0
$583$	−59.4690	+	6.95093i	−2.46296	+	0.287878i
$584$	−3.46737	−	19.6644i	−0.143481	−	0.813721i
$585$		0			0
$586$	−0.214557	+	1.21681i	−0.00886326	+	0.0502661i
$587$	0.775932	−	13.3222i	0.0320261	−	0.549868i	−0.943690	−	0.330830i	$-0.892671\pi$
$587$	0.775932	−	13.3222i	0.0320261	−	0.549868i	0.975716	−	0.219037i	$-0.0702917\pi$
$588$		0			0
$589$	−11.8317	−	27.4289i	−0.487516	−	1.13019i
$590$	3.22189	+	1.61809i	0.132643	+	0.0666158i
$591$		0			0
$592$	−8.21350	−	1.94664i	−0.337573	−	0.0800062i
$593$	17.2045	−	29.7990i	0.706503	−	1.22370i	−0.259644	−	0.965704i	$-0.583605\pi$
$593$	17.2045	−	29.7990i	0.706503	−	1.22370i	0.966147	−	0.257994i	$-0.0830615\pi$
$594$		0			0
$595$	−0.0212812	−	0.0368601i	−0.000872443	−	0.00151112i
$596$	8.34903	+	27.8877i	0.341989	+	1.14232i
$597$		0			0
$598$	0.310098	−	0.203954i	0.0126808	−	0.00834032i
$599$	23.9225	−	32.1334i	0.977445	−	1.31294i	0.0277982	−	0.999614i	$-0.491150\pi$
$599$	23.9225	−	32.1334i	0.977445	−	1.31294i	0.949647	−	0.313323i	$-0.101442\pi$
$600$		0			0
$601$	36.0814	+	23.7311i	1.47179	+	0.968013i	0.996084	+	0.0884094i	$0.0281784\pi$
$601$	36.0814	+	23.7311i	1.47179	+	0.968013i	0.475708	+	0.879603i	$0.342192\pi$
$602$	−1.27856	+	0.465357i	−0.0521101	+	0.0189665i
$603$		0			0
$604$	−4.46403	−	1.62477i	−0.181639	−	0.0661111i
$605$	−14.9049	−	20.0207i	−0.605970	−	0.813958i
$606$		0			0
$607$	−12.0916	−	12.8163i	−0.490782	−	0.520199i	0.433889	−	0.900967i	$-0.357141\pi$
$607$	−12.0916	−	12.8163i	−0.490782	−	0.520199i	−0.924671	+	0.380768i	$0.875660\pi$
$608$	14.5118	+	15.3816i	0.588530	+	0.623805i
$609$		0			0
$610$	0.654648	+	0.879345i	0.0265059	+	0.0356036i
$611$	−27.6577	−	10.0666i	−1.11891	−	0.407250i
$612$		0			0
$613$	25.9691	−	9.45198i	1.04888	−	0.381762i	0.240641	−	0.970614i	$-0.422642\pi$
$613$	25.9691	−	9.45198i	1.04888	−	0.381762i	0.808241	+	0.588852i	$0.200420\pi$
$614$	−8.47123	−	5.57161i	−0.341871	−	0.224852i
$615$		0			0
$616$	12.7957	−	17.1876i	0.515554	−	0.692509i
$617$	3.68414	−	2.42310i	0.148318	−	0.0975503i	−0.473181	−	0.880965i	$-0.656894\pi$
$617$	3.68414	−	2.42310i	0.148318	−	0.0975503i	0.621499	+	0.783415i	$0.286524\pi$
$618$		0			0
$619$	7.17467	+	23.9651i	0.288374	+	0.963237i	0.972310	+	0.233695i	$0.0750816\pi$
$619$	7.17467	+	23.9651i	0.288374	+	0.963237i	−0.683936	+	0.729542i	$0.739733\pi$
$620$	5.94125	+	10.2905i	0.238606	+	0.413278i
$621$		0			0
$622$	−6.98959	+	12.1063i	−0.280257	+	0.485420i
$623$	−19.8249	−	4.69860i	−0.794270	−	0.188245i
$624$		0			0
$625$	11.1237	+	5.58651i	0.444946	+	0.223460i
$626$	−5.98275	−	13.8696i	−0.239119	−	0.554339i
$627$		0			0
$628$	−0.307439	+	5.27852i	−0.0122681	+	0.210636i
$629$	−0.0309624	+	0.175596i	−0.00123455	+	0.00700148i
$630$		0			0
$631$	2.45133	+	13.9022i	0.0975857	+	0.553436i	0.993924	+	0.110066i	$0.0351062\pi$
$631$	2.45133	+	13.9022i	0.0975857	+	0.553436i	−0.896339	+	0.443370i	$0.853783\pi$
$632$	30.0255	−	3.50948i	1.19435	−	0.139600i
$633$		0			0
$634$	−2.20457	+	7.36378i	−0.0875547	+	0.292453i
$635$	−9.72931	+	2.30589i	−0.386096	+	0.0915064i
$636$		0			0
$637$	10.1132	−	23.4450i	0.400700	−	0.928926i
$638$	−1.62660	+	1.36488i	−0.0643978	+	0.0540362i
$639$		0			0
$640$	−7.87383	−	6.60693i	−0.311241	−	0.261162i
$641$	−30.5703	+	15.3530i	−1.20746	+	0.606407i	−0.934618	−	0.355653i	$-0.884258\pi$
$641$	−30.5703	+	15.3530i	−1.20746	+	0.606407i	−0.272838	+	0.962060i	$0.587962\pi$
$642$		0			0
$643$	13.3953	+	1.56569i	0.528260	+	0.0617447i	0.376043	−	0.926602i	$-0.377285\pi$
$643$	13.3953	+	1.56569i	0.528260	+	0.0617447i	0.152217	+	0.988347i	$0.451359\pi$
$644$	0.0136930	+	0.235100i	0.000539581	+	0.00926424i
$645$		0			0
$646$	0.0524565	−	0.0556007i	0.00206387	−	0.00218758i
$647$	−3.19249			−0.125510			−0.0627548	−	0.998029i	$-0.519989\pi$
$647$	−3.19249			−0.125510			−0.0627548	+	0.998029i	$0.519989\pi$
$648$		0			0
$649$	−34.5785			−1.35733
$650$	10.0140	−	10.6143i	0.392783	−	0.416325i
$651$		0			0
$652$	−1.76782	−	30.3523i	−0.0692333	−	1.18869i
$653$	−31.9500	−	3.73442i	−1.25030	−	0.146139i	−0.534936	−	0.844892i	$-0.679664\pi$
$653$	−31.9500	−	3.73442i	−1.25030	−	0.146139i	−0.715363	+	0.698753i	$0.753739\pi$
$654$		0			0
$655$	12.0222	−	6.03779i	0.469748	−	0.235916i
$656$	−4.91404	−	4.12337i	−0.191861	−	0.160991i
$657$		0			0
$658$	−4.24715	+	3.56378i	−0.165571	+	0.138931i
$659$	−5.78047	+	13.4006i	−0.225175	+	0.522015i	−0.992926	−	0.118734i	$-0.962117\pi$
$659$	−5.78047	+	13.4006i	−0.225175	+	0.522015i	0.767751	+	0.640748i	$0.221376\pi$
$660$		0			0
$661$	−7.58170	+	1.79690i	−0.294894	+	0.0698912i	−0.375400	−	0.926863i	$-0.622495\pi$
$661$	−7.58170	+	1.79690i	−0.294894	+	0.0698912i	0.0805058	+	0.996754i	$0.474346\pi$
$662$	2.79590	−	9.33895i	0.108666	−	0.362969i
$663$		0			0
$664$	42.4320	−	4.95959i	1.64668	−	0.192470i
$665$	0.874754	+	4.96098i	0.0339215	+	0.192378i
$666$		0			0
$667$	0.00930786	−	0.0527875i	0.000360402	−	0.00204394i
$668$	1.73442	−	29.7788i	0.0671066	−	1.15218i
$669$		0			0
$670$	0.692009	+	1.60426i	0.0267346	+	0.0619778i
$671$	−9.39577	−	4.71873i	−0.362720	−	0.182165i
$672$		0			0
$673$	7.80154	+	1.84900i	0.300727	+	0.0712737i	0.378209	−	0.925720i	$-0.376540\pi$
$673$	7.80154	+	1.84900i	0.300727	+	0.0712737i	−0.0774821	+	0.996994i	$0.524688\pi$
$674$	−3.35193	+	5.80572i	−0.129112	+	0.223628i
$675$		0			0
$676$	11.2024	+	19.4031i	0.430862	+	0.746274i
$677$	2.44329	+	8.16115i	0.0939031	+	0.313658i	0.992017	−	0.126105i	$-0.0402476\pi$
$677$	2.44329	+	8.16115i	0.0939031	+	0.313658i	−0.898114	+	0.439763i	$0.855062\pi$
$678$		0			0
$679$	−8.55635	+	5.62760i	−0.328363	+	0.215968i
$680$	−0.0417056	+	0.0560203i	−0.00159934	+	0.00214828i
$681$		0			0
$682$	28.2675	+	18.5918i	1.08242	+	0.711917i
$683$	13.5460	−	4.93034i	0.518323	−	0.188654i	−0.0695940	−	0.997575i	$-0.522170\pi$
$683$	13.5460	−	4.93034i	0.518323	−	0.188654i	0.587917	+	0.808921i	$0.299948\pi$
$684$		0			0
$685$	−4.72942	−	1.72137i	−0.180702	−	0.0657701i
$686$	−7.00350	−	9.40733i	−0.267395	−	0.359174i
$687$		0			0
$688$	−1.38175	−	1.46457i	−0.0526786	−	0.0558360i
$689$	−35.2208	−	37.3319i	−1.34181	−	1.42223i
$690$		0			0
$691$	21.7780	+	29.2530i	0.828475	+	1.11283i	0.991993	+	0.126294i	$0.0403084\pi$
$691$	21.7780	+	29.2530i	0.828475	+	1.11283i	−0.163518	+	0.986540i	$0.552284\pi$
$692$	8.93742	+	3.25296i	0.339750	+	0.123659i
$693$		0			0
$694$	2.14799	−	0.781805i	0.0815366	−	0.0296769i
$695$	−3.22623	−	2.12193i	−0.122378	−	0.0804893i
$696$		0			0
$697$	−0.0809176	+	0.108691i	−0.00306497	+	0.00411697i
$698$	−0.751843	+	0.494495i	−0.0284577	+	0.0187169i
$699$		0			0
$700$	2.65550	+	8.86998i	0.100368	+	0.335254i
$701$	4.76010	+	8.24474i	0.179787	+	0.311399i	0.941807	−	0.336153i	$-0.109126\pi$
$701$	4.76010	+	8.24474i	0.179787	+	0.311399i	−0.762021	+	0.647553i	$0.775793\pi$
$702$		0			0
$703$	10.5517	−	18.2761i	0.397966	−	0.689298i
$704$	−5.88400	−	1.39453i	−0.221761	−	0.0525584i
$705$		0			0
$706$	7.13118	+	3.58141i	0.268385	+	0.134788i
$707$	−5.02791	−	11.6560i	−0.189094	−	0.438369i
$708$		0			0
$709$	−0.695397	+	11.9395i	−0.0261162	+	0.448398i	0.959749	+	0.280858i	$0.0906191\pi$
$709$	−0.695397	+	11.9395i	−0.0261162	+	0.448398i	−0.985865	+	0.167539i	$0.946418\pi$
$710$	−0.240792	+	1.36560i	−0.00903677	+	0.0512501i
$711$		0			0
$712$	5.80535	+	32.9238i	0.217565	+	1.23387i
$713$	−0.848306	+	0.0991527i	−0.0317693	+	0.00371330i
$714$		0			0
$715$	8.68698	−	29.0165i	0.324875	−	1.08516i
$716$	−5.19470	+	1.23117i	−0.194135	+	0.0460108i
$717$		0			0
$718$	−7.96272	+	18.4596i	−0.297166	+	0.688908i
$719$	16.3766	−	13.7416i	0.610743	−	0.512474i	−0.284135	−	0.958784i	$-0.591706\pi$
$719$	16.3766	−	13.7416i	0.610743	−	0.512474i	0.894879	+	0.446310i	$0.147262\pi$
$720$		0			0
$721$	5.73749	+	4.81433i	0.213675	+	0.179295i
$722$	3.40381	−	1.70946i	0.126677	−	0.0636195i
$723$		0			0
$724$	−29.2260	−	3.41603i	−1.08617	−	0.126956i
$725$	−0.122536	−	2.10387i	−0.00455088	−	0.0781356i
$726$		0			0
$727$	5.40837	−	5.73254i	0.200585	−	0.212608i	−0.619271	−	0.785177i	$-0.712572\pi$
$727$	5.40837	−	5.73254i	0.200585	−	0.212608i	0.819856	+	0.572569i	$0.194053\pi$
$728$	18.3679			0.680760
$729$		0			0
$730$	−5.31685			−0.196785
$731$	−0.0291875	+	0.0309369i	−0.00107954	+	0.00114424i
$732$		0			0
$733$	−2.02479	−	34.7644i	−0.0747875	−	1.28405i	−0.801869	−	0.597500i	$-0.796161\pi$
$733$	−2.02479	−	34.7644i	−0.0747875	−	1.28405i	0.727081	−	0.686551i	$-0.240876\pi$
$734$	−5.39466	−	0.630545i	−0.199120	−	0.0232738i
$735$		0			0
$736$	0.540303	−	0.271350i	0.0199158	−	0.0100021i
$737$	−12.8363	−	10.7709i	−0.472829	−	0.396751i
$738$		0			0
$739$	33.5899	−	28.1853i	1.23563	−	1.03681i	0.237772	−	0.971321i	$-0.423583\pi$
$739$	33.5899	−	28.1853i	1.23563	−	1.03681i	0.997853	−	0.0654916i	$-0.0208615\pi$
$740$	−3.32491	+	7.70801i	−0.122226	+	0.283352i
$741$		0			0
$742$	−9.40738	+	2.22959i	−0.345356	+	0.0818508i
$743$	6.12394	−	20.4554i	0.224666	−	0.750435i	−0.769118	−	0.639107i	$-0.779304\pi$
$743$	6.12394	−	20.4554i	0.224666	−	0.750435i	0.993784	−	0.111329i	$-0.0355106\pi$
$744$		0			0
$745$	17.6835	−	2.06690i	0.647872	−	0.0757254i
$746$	0.351765	+	1.99496i	0.0128790	+	0.0730407i
$747$		0			0
$748$	0.0506397	−	0.287192i	0.00185157	−	0.0105008i
$749$	−0.845286	+	14.5130i	−0.0308861	+	0.530294i
$750$		0			0
$751$	1.79352	+	4.15784i	0.0654464	+	0.151722i	0.947800	−	0.318865i	$-0.103302\pi$
$751$	1.79352	+	4.15784i	0.0654464	+	0.151722i	−0.882354	+	0.470587i	$0.844042\pi$
$752$	−7.33195	−	3.68224i	−0.267369	−	0.134278i
$753$		0			0
$754$	−1.77111	−	0.419761i	−0.0645000	−	0.0152868i
$755$	−1.45269	+	2.51614i	−0.0528689	+	0.0915716i
$756$		0			0
$757$	−15.3969	−	26.6682i	−0.559610	−	0.969273i	−0.997529	−	0.0702583i	$-0.977618\pi$
$757$	−15.3969	−	26.6682i	−0.559610	−	0.969273i	0.437919	−	0.899014i	$-0.355716\pi$
$758$	−4.29022	−	14.3303i	−0.155828	−	0.520501i
$759$		0			0
$760$	6.90613	−	4.54224i	0.250512	−	0.164764i
$761$	2.13712	−	2.87064i	0.0774704	−	0.104061i	−0.761699	−	0.647931i	$-0.775634\pi$
$761$	2.13712	−	2.87064i	0.0774704	−	0.104061i	0.839169	+	0.543871i	$0.183042\pi$
$762$		0			0
$763$	−15.5438	−	10.2233i	−0.562723	−	0.370109i
$764$	28.8785	−	10.5109i	1.04479	−	0.380271i
$765$		0			0
$766$	−9.12904	−	3.32270i	−0.329846	−	0.120054i
$767$	−17.7003	−	23.7757i	−0.639122	−	0.858489i
$768$		0			0
$769$	10.0226	+	10.6233i	0.361423	+	0.383085i	0.882412	−	0.470478i	$-0.155918\pi$
$769$	10.0226	+	10.6233i	0.361423	+	0.383085i	−0.520989	+	0.853563i	$0.674437\pi$
$770$	−3.91539	−	4.15008i	−0.141101	−	0.149558i
$771$		0			0
$772$	9.86979	+	13.2574i	0.355221	+	0.477145i
$773$	18.7983	+	6.84203i	0.676129	+	0.246091i	0.657184	−	0.753730i	$-0.271747\pi$
$773$	18.7983	+	6.84203i	0.676129	+	0.246091i	0.0189442	+	0.999821i	$0.493970\pi$
$774$		0			0
$775$	−31.5543	+	11.4848i	−1.13346	+	0.412547i
$776$	14.0400	+	9.23427i	0.504007	+	0.331491i
$777$		0			0
$778$	−7.36603	+	9.89429i	−0.264085	+	0.354728i
$779$	13.3993	−	8.81289i	0.480081	−	0.315754i
$780$		0			0
$781$	−3.81427	−	12.7406i	−0.136485	−	0.455893i
$782$	−0.00109277	−	0.00189273i	−3.90772e−5	−	6.76838e-5i
$783$		0			0
$784$	3.55882	−	6.16407i	0.127101	−	0.220145i
$785$	3.14661	+	0.745760i	0.112307	+	0.0266173i
$786$		0			0
$787$	−12.1043	−	6.07901i	−0.431472	−	0.216693i	0.219789	−	0.975548i	$-0.429463\pi$
$787$	−12.1043	−	6.07901i	−0.431472	−	0.216693i	−0.651261	+	0.758854i	$0.725760\pi$
$788$	−14.4775	−	33.5627i	−0.515741	−	1.19562i
$789$		0			0
$790$	0.468028	−	8.03573i	0.0166517	−	0.285898i
$791$	1.45763	−	8.26666i	0.0518275	−	0.293929i
$792$		0			0
$793$	−1.56505	−	8.87585i	−0.0555766	−	0.315191i
$794$	0.932151	−	0.108953i	0.0330808	−	0.00386659i
$795$		0			0
$796$	3.86352	−	12.9050i	0.136939	−	0.457407i
$797$	29.1913	−	6.91847i	1.03401	−	0.245065i	0.321635	−	0.946864i	$-0.395768\pi$
$797$	29.1913	−	6.91847i	1.03401	−	0.245065i	0.712375	+	0.701799i	$0.247620\pi$
$798$		0			0
$799$	−0.0686454	+	0.159138i	−0.00242850	+	0.00562990i
$800$	18.2098	−	15.2799i	0.643814	−	0.540225i
$801$		0			0
$802$	11.4481	+	9.60610i	0.404247	+	0.339203i
$803$	45.5689	−	22.8856i	1.60809	−	0.807614i
$804$		0			0
$805$	0.143055	+	0.0167208i	0.00504204	+	0.000589330i
$806$	1.68633	+	28.9532i	0.0593985	+	1.01983i
$807$		0			0
$808$	−14.2942	+	15.1510i	−0.502869	+	0.533010i
$809$	−48.8577			−1.71774			−0.858872	−	0.512190i	$-0.828834\pi$
$809$	−48.8577			−1.71774			−0.858872	+	0.512190i	$0.828834\pi$
$810$		0			0
$811$	−14.0558			−0.493566			−0.246783	−	0.969071i	$-0.579373\pi$
$811$	−14.0558			−0.493566			−0.246783	+	0.969071i	$0.579373\pi$
$812$	0.792537	−	0.840040i	0.0278126	−	0.0294796i
$813$		0			0
$814$	1.38979	+	23.8617i	0.0487120	+	0.836352i
$815$	−18.4690	−	2.15872i	−0.646941	−	0.0756165i
$816$		0			0
$817$	4.49851	−	2.25924i	0.157383	−	0.0790407i
$818$	−0.299277	−	0.251123i	−0.0104640	−	0.00878032i
$819$		0			0
$820$	−4.88698	+	4.10067i	−0.170661	+	0.143201i
$821$	−12.7718	+	29.6084i	−0.445740	+	1.03334i	0.536190	+	0.844097i	$0.319863\pi$
$821$	−12.7718	+	29.6084i	−0.445740	+	1.03334i	−0.981930	+	0.189244i	$0.939396\pi$
$822$		0			0
$823$	−32.1897	+	7.62910i	−1.12206	+	0.265934i	−0.749455	−	0.662055i	$-0.769684\pi$
$823$	−32.1897	+	7.62910i	−1.12206	+	0.265934i	−0.372608	+	0.927989i	$0.621536\pi$
$824$	3.52477	−	11.7736i	0.122791	−	0.410151i
$825$		0			0
$826$	−5.54573	+	0.648203i	−0.192961	+	0.0225539i
$827$	−6.93056	−	39.3051i	−0.240999	−	1.36677i	−0.829604	−	0.558352i	$-0.811434\pi$
$827$	−6.93056	−	39.3051i	−0.240999	−	1.36677i	0.588605	−	0.808421i	$-0.299677\pi$
$828$		0			0
$829$	−3.03189	+	17.1947i	−0.105302	+	0.597198i	0.885797	+	0.464073i	$0.153612\pi$
$829$	−3.03189	+	17.1947i	−0.105302	+	0.597198i	−0.991099	+	0.133125i	$0.957499\pi$
$830$	0.661417	−	11.3561i	0.0229581	−	0.394176i
$831$		0			0
$832$	−2.05309	−	4.75959i	−0.0711779	−	0.165009i
$833$	−0.134358	−	0.0674772i	−0.00465523	−	0.00233795i
$834$		0			0
$835$	−17.7516	−	4.20721i	−0.614320	−	0.145596i
$836$	−17.2576	+	29.8911i	−0.596868	+	1.03381i
$837$		0			0
$838$	4.27349	+	7.40191i	0.147625	+	0.255695i
$839$	−11.3246	−	37.8267i	−0.390967	−	1.30592i	−0.896473	−	0.443099i	$-0.853879\pi$
$839$	−11.3246	−	37.8267i	−0.390967	−	1.30592i	0.505506	−	0.862823i	$-0.331306\pi$
$840$		0			0
$841$	24.0095	−	15.7913i	0.827915	−	0.544528i
$842$	−8.65741	+	11.6289i	−0.298354	+	0.400759i
$843$		0			0
$844$	−9.37747	−	6.16766i	−0.322786	−	0.212300i
$845$	12.8763	−	4.68657i	0.442957	−	0.161223i
$846$		0			0
$847$	36.3227	+	13.2204i	1.24806	+	0.454258i
$848$	−8.54363	−	11.4761i	−0.293389	−	0.394090i
$849$		0			0
$850$	−0.0589669	−	0.0625012i	−0.00202255	−	0.00214377i
$851$	−0.414062	−	0.438881i	−0.0141939	−	0.0150446i
$852$		0			0
$853$	−18.7024	−	25.1217i	−0.640359	−	0.860151i	0.356900	−	0.934143i	$-0.383834\pi$
$853$	−18.7024	−	25.1217i	−0.640359	−	0.860151i	−0.997259	+	0.0739915i	$0.976426\pi$
$854$	−1.59536	−	0.580662i	−0.0545920	−	0.0198699i
$855$		0			0
$856$	22.4160	−	8.15875i	0.766162	−	0.278860i
$857$	29.5322	+	19.4236i	1.00880	+	0.663498i	0.942467	−	0.334300i	$-0.108500\pi$
$857$	29.5322	+	19.4236i	1.00880	+	0.663498i	0.0663325	+	0.997798i	$0.478870\pi$
$858$		0			0
$859$	16.8713	−	22.6621i	0.575642	−	0.773221i	−0.414984	−	0.909829i	$-0.636213\pi$
$859$	16.8713	−	22.6621i	0.575642	−	0.773221i	0.990625	+	0.136608i	$0.0436201\pi$
$860$	−1.67299	+	1.10034i	−0.0570485	+	0.0375214i
$861$		0			0
$862$	−0.867712	−	2.89836i	−0.0295544	−	0.0987186i
$863$	1.91089	+	3.30976i	0.0650475	+	0.112666i	0.896715	−	0.442608i	$-0.145947\pi$
$863$	1.91089	+	3.30976i	0.0650475	+	0.112666i	−0.831668	+	0.555274i	$0.812613\pi$
$864$		0			0
$865$	2.90843	−	5.03755i	0.0988896	−	0.171282i
$866$	−6.01343	−	1.42521i	−0.204345	−	0.0484306i
$867$		0			0
$868$	−16.4445	−	8.25874i	−0.558163	−	0.280320i
$869$	30.5773	+	70.8861i	1.03726	+	2.40465i
$870$		0			0
$871$	0.835180	−	14.3395i	0.0282990	−	0.485875i
$872$	−5.30110	+	30.0640i	−0.179518	+	1.01810i
$873$		0			0
$874$	0.0449177	+	0.254741i	0.00151936	+	0.00861674i
$875$	12.4661	−	1.45708i	0.421430	−	0.0492581i
$876$		0			0
$877$	9.83442	−	32.8493i	0.332085	−	1.10924i	−0.615072	−	0.788471i	$-0.710873\pi$
$877$	9.83442	−	32.8493i	0.332085	−	1.10924i	0.947157	−	0.320770i	$-0.103942\pi$
$878$	−1.87554	+	0.444511i	−0.0632964	+	0.0150015i
$879$		0			0
$880$	3.34424	−	7.75283i	0.112734	−	0.261348i
$881$	−39.1151	+	32.8215i	−1.31782	+	1.10578i	−0.331059	+	0.943610i	$0.607406\pi$
$881$	−39.1151	+	32.8215i	−1.31782	+	1.10578i	−0.986762	+	0.162173i	$0.948150\pi$
$882$		0			0
$883$	−30.6669	−	25.7326i	−1.03202	−	0.865972i	−0.0409344	−	0.999162i	$-0.513033\pi$
$883$	−30.6669	−	25.7326i	−1.03202	−	0.865972i	−0.991091	+	0.133190i	$0.957478\pi$
$884$	0.223391	−	0.112191i	0.00751344	−	0.00377339i
$885$		0			0
$886$	8.31447	+	0.971822i	0.279330	+	0.0326490i
$887$	1.33144	+	22.8599i	0.0447053	+	0.767560i	0.943945	+	0.330103i	$0.107084\pi$
$887$	1.33144	+	22.8599i	0.0447053	+	0.767560i	−0.899240	+	0.437457i	$0.855879\pi$
$888$		0			0
$889$	10.6262	−	11.2632i	0.356393	−	0.377754i
$890$	8.90188			0.298392
$891$		0			0
$892$	−1.15427			−0.0386477
$893$	14.0765	−	14.9203i	0.471054	−	0.499288i
$894$		0			0
$895$	0.189846	+	3.25952i	0.00634584	+	0.108954i
$896$	15.8103	+	1.84796i	0.528184	+	0.0617359i
$897$		0			0
$898$	10.3849	−	5.21550i	0.346549	−	0.174044i
$899$	3.20854	+	2.69228i	0.107011	+	0.0897927i
$900$		0			0
$901$	−0.231513	+	0.194262i	−0.00771281	+	0.00647182i
$902$	−7.19463	+	16.6790i	−0.239555	+	0.555351i
$903$		0			0
$904$	−13.4026	+	3.17649i	−0.445765	+	0.105648i
$905$	−5.16133	+	17.2401i	−0.171569	+	0.573079i
$906$		0			0
$907$	23.7812	−	2.77963i	0.789643	−	0.0922960i	0.288295	−	0.957542i	$-0.406912\pi$
$907$	23.7812	−	2.77963i	0.789643	−	0.0922960i	0.501348	+	0.865246i	$0.332838\pi$
$908$	2.03683	+	11.5514i	0.0675944	+	0.383347i
$909$		0			0
$910$	0.849285	−	4.81654i	0.0281535	−	0.159667i
$911$	−1.78989	+	30.7312i	−0.0593016	+	1.01817i	0.829099	+	0.559101i	$0.188854\pi$
$911$	−1.78989	+	30.7312i	−0.0593016	+	1.01817i	−0.888401	+	0.459068i	$0.848183\pi$
$912$		0			0
$913$	43.2118	+	100.176i	1.43010	+	3.31535i
$914$	−0.534987	−	0.268680i	−0.0176958	−	0.00888716i
$915$		0			0
$916$	23.4120	+	5.54874i	0.773554	+	0.183336i
$917$	−10.4172	+	18.0431i	−0.344006	+	0.595835i
$918$		0			0
$919$	21.9894	+	38.0868i	0.725365	+	1.25637i	0.958824	+	0.284002i	$0.0916623\pi$
$919$	21.9894	+	38.0868i	0.725365	+	1.25637i	−0.233459	+	0.972367i	$0.575004\pi$
$920$	−0.0677819	−	0.226407i	−0.00223470	−	0.00746443i
$921$		0			0
$922$	8.61090	−	5.66348i	0.283585	−	0.186517i
$923$	6.80773	−	9.14436i	0.224079	−	0.300990i
$924$		0			0
$925$	−19.8200	−	13.0358i	−0.651676	−	0.428614i
$926$	21.3875	−	7.78440i	0.702836	−	0.255811i
$927$		0			0
$928$	−2.78624	−	1.01411i	−0.0914627	−	0.0332897i
$929$	16.9211	+	22.7289i	0.555162	+	0.745712i	0.987778	−	0.155866i	$-0.0498169\pi$
$929$	16.9211	+	22.7289i	0.555162	+	0.745712i	−0.432616	+	0.901578i	$0.642410\pi$
$930$		0			0
$931$	12.2116	+	12.9435i	0.400219	+	0.424207i
$932$	17.4383	+	18.4835i	0.571211	+	0.605448i
$933$		0			0
$934$	4.45646	+	5.98607i	0.145820	+	0.195870i
$935$	−0.167598	−	0.0610008i	−0.00548105	−	0.00199494i
$936$		0			0
$937$	12.4825	−	4.54327i	0.407787	−	0.148422i	−0.129979	−	0.991517i	$-0.541491\pi$
$937$	12.4825	−	4.54327i	0.407787	−	0.148422i	0.537765	+	0.843095i	$0.319269\pi$
$938$	−2.26060	−	1.48682i	−0.0738111	−	0.0485463i
$939$		0			0
$940$	−4.87250	+	6.54491i	−0.158924	+	0.213471i
$941$	−11.7823	+	7.74934i	−0.384092	+	0.252621i	−0.726841	−	0.686806i	$-0.759012\pi$
$941$	−11.7823	+	7.74934i	−0.384092	+	0.252621i	0.342749	+	0.939427i	$0.388642\pi$
$942$		0			0
$943$	−0.131511	−	0.439277i	−0.00428259	−	0.0143048i
$944$	−4.13135	−	7.15571i	−0.134464	−	0.232898i
$945$		0			0
$946$	−2.85077	+	4.93768i	−0.0926866	+	0.160538i
$947$	−23.5484	−	5.58108i	−0.765221	−	0.181361i	−0.170571	−	0.985345i	$-0.554561\pi$
$947$	−23.5484	−	5.58108i	−0.765221	−	0.181361i	−0.594650	+	0.803985i	$0.702709\pi$
$948$		0			0
$949$	39.0619	+	19.6176i	1.26800	+	0.636815i
$950$	4.02813	+	9.33826i	0.130690	+	0.302973i
$951$		0			0
$952$	0.00628883	−	0.107975i	0.000203822	−	0.00349949i
$953$	0.315523	−	1.78942i	0.0102208	−	0.0579650i	−0.979271	−	0.202555i	$-0.935075\pi$
$953$	0.315523	−	1.78942i	0.0102208	−	0.0579650i	0.989492	+	0.144590i	$0.0461865\pi$
$954$		0			0
$955$	−3.26378	−	18.5098i	−0.105613	−	0.598964i
$956$	−29.6343	+	3.46375i	−0.958442	+	0.112026i
$957$		0			0
$958$	2.31377	−	7.72852i	0.0747544	−	0.249697i
$959$	7.58419	−	1.79749i	0.244906	−	0.0580438i
$960$		0			0
$961$	14.1551	−	32.8151i	0.456615	−	1.05855i
$962$	−15.6955	+	13.1701i	−0.506044	+	0.424621i
$963$		0			0
$964$	−6.81044	−	5.71464i	−0.219350	−	0.184056i
$965$	9.03316	−	4.53662i	0.290788	−	0.146039i
$966$		0			0
$967$	1.88393	+	0.220200i	0.0605830	+	0.00708114i	0.146330	−	0.989236i	$-0.453254\pi$
$967$	1.88393	+	0.220200i	0.0605830	+	0.00708114i	−0.0857474	+	0.996317i	$0.527328\pi$
$968$	−3.68793	−	63.3193i	−0.118535	−	2.03516i
$969$		0			0
$970$	3.07064	−	3.25468i	0.0985922	−	0.104502i
$971$	27.1629			0.871698			0.435849	−	0.900020i	$-0.356448\pi$
$971$	27.1629			0.871698			0.435849	+	0.900020i	$0.356448\pi$
$972$		0			0
$973$	5.98012			0.191714
$974$	17.7579	−	18.8223i	0.569000	−	0.603104i
$975$		0			0
$976$	−0.146083	−	2.50815i	−0.00467601	−	0.0802839i
$977$	−25.4358	−	2.97302i	−0.813764	−	0.0951154i	−0.300977	−	0.953631i	$-0.597313\pi$
$977$	−25.4358	−	2.97302i	−0.813764	−	0.0951154i	−0.512787	+	0.858516i	$0.671387\pi$
$978$		0			0
$979$	−76.2951	+	38.3168i	−2.43840	+	1.22461i
$980$	−5.42241	−	4.54994i	−0.173213	−	0.145343i
$981$		0			0
$982$	2.19751	−	1.84393i	0.0701255	−	0.0588423i
$983$	11.5033	−	26.6677i	0.366898	−	0.850566i	−0.630341	−	0.776318i	$-0.717085\pi$
$983$	11.5033	−	26.6677i	0.366898	−	0.850566i	0.997240	−	0.0742480i	$-0.0236556\pi$
$984$		0			0
$985$	−21.7524	+	5.15541i	−0.693089	+	0.164265i
$986$	−0.00307394	+	0.0102677i	−9.78942e−5	+	0.000326989i
$987$		0			0
$988$	−29.3866	+	3.43481i	−0.934913	+	0.109276i
$989$	−0.0249928	−	0.141741i	−0.000794725	−	0.00450711i
$990$		0			0
$991$	6.28903	−	35.6669i	0.199778	−	1.13300i	−0.705671	−	0.708539i	$-0.749354\pi$
$991$	6.28903	−	35.6669i	0.199778	−	1.13300i	0.905449	−	0.424456i	$-0.139534\pi$
$992$	−2.74703	+	47.1646i	−0.0872181	+	1.49748i
$993$		0			0
$994$	−0.850567	−	1.97184i	−0.0269784	−	0.0625429i
$995$	−7.36241	−	3.69754i	−0.233404	−	0.117220i
$996$		0			0
$997$	−14.7650	−	3.49936i	−0.467611	−	0.110826i	−0.00994618	−	0.999951i	$-0.503166\pi$
$997$	−14.7650	−	3.49936i	−0.467611	−	0.110826i	−0.457665	+	0.889125i	$0.651314\pi$
$998$	12.6545	−	21.9182i	0.400571	−	0.693809i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.g.a.622.6		144
3.2	odd	2		729.2.g.d.622.3		144
9.2	odd	6		81.2.g.a.16.6	✓	144
9.4	even	3		729.2.g.b.379.6		144
9.5	odd	6		729.2.g.c.379.3		144
9.7	even	3		243.2.g.a.208.3		144
81.5	odd	54		729.2.g.c.352.3		144
81.22	even	27	inner	729.2.g.a.109.6		144
81.32	odd	54		81.2.g.a.76.6	yes	144
81.34	even	27		6561.2.a.d.1.27		72
81.47	odd	54		6561.2.a.c.1.46		72
81.49	even	27		243.2.g.a.118.3		144
81.59	odd	54		729.2.g.d.109.3		144
81.76	even	27		729.2.g.b.352.6		144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.2.g.a.16.6	✓	144	9.2	odd	6
81.2.g.a.76.6	yes	144	81.32	odd	54
243.2.g.a.118.3		144	81.49	even	27
243.2.g.a.208.3		144	9.7	even	3
729.2.g.a.109.6		144	81.22	even	27	inner
729.2.g.a.622.6		144	1.1	even	1	trivial
729.2.g.b.352.6		144	81.76	even	27
729.2.g.b.379.6		144	9.4	even	3
729.2.g.c.352.3		144	81.5	odd	54
729.2.g.c.379.3		144	9.5	odd	6
729.2.g.d.109.3		144	81.59	odd	54
729.2.g.d.622.3		144	3.2	odd	2
6561.2.a.c.1.46		72	81.47	odd	54
6561.2.a.d.1.27		72	81.34	even	27

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 729 = 3^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	729.g (of order \(27\), degree \(18\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.464338 - 0.492169i) q^{2} +(0.0896686 + 1.53955i) q^{4} +(0.936797 + 0.109496i) q^{5} +(-1.30528 + 0.655538i) q^{7} +(1.83603 + 1.54061i) q^{8} +(0.488880 - 0.410219i) q^{10} +(-2.42430 + 5.62016i) q^{11} +(-5.10531 + 1.20998i) q^{13} +(-0.283457 + 0.946811i) q^{14} +(-1.45269 + 0.169795i) q^{16} +(0.00536485 + 0.0304256i) q^{17} +(0.634963 - 3.60105i) q^{19} +(-0.0845732 + 1.45207i) q^{20} +(1.64038 + 3.80282i) q^{22} +(-0.0934269 - 0.0469207i) q^{23} +(-3.99963 - 0.947929i) q^{25} +(-1.77507 + 3.07451i) q^{26} +(-1.12628 - 1.95077i) q^{28} +(0.147045 + 0.491165i) q^{29} +(6.82537 - 4.48912i) q^{31} +(-3.45346 + 4.63881i) q^{32} +(0.0174656 + 0.0114873i) q^{34} +(-1.29456 + 0.471183i) q^{35} +(5.42328 + 1.97391i) q^{37} +(-1.47749 - 1.98461i) q^{38} +(1.55129 + 1.64427i) q^{40} +(3.00983 + 3.19024i) q^{41} +(0.822094 + 1.10426i) q^{43} +(-8.86991 - 3.22838i) q^{44} +(-0.0664745 + 0.0241947i) q^{46} +(4.68685 + 3.08259i) q^{47} +(-2.90608 + 3.90354i) q^{49} +(-2.32372 + 1.52833i) q^{50} +(-2.32061 - 7.75138i) q^{52} +(4.89106 + 8.47157i) q^{53} +(-2.88646 + 4.99950i) q^{55} +(-3.40646 - 0.807346i) q^{56} +(0.310015 + 0.155695i) q^{58} +(2.23761 + 5.18737i) q^{59} +(-0.0998805 + 1.71488i) q^{61} +(0.959872 - 5.44370i) q^{62} +(0.171556 + 0.972942i) q^{64} +(-4.91512 + 0.574495i) q^{65} +(-0.785171 + 2.62265i) q^{67} +(-0.0463607 + 0.0109877i) q^{68} +(-0.369213 + 0.855932i) q^{70} +(-1.66448 + 1.39666i) q^{71} +(-6.38204 - 5.35517i) q^{73} +(3.48973 - 1.75261i) q^{74} +(5.60094 + 0.654656i) q^{76} +(-0.519830 - 8.92513i) q^{77} +(8.65544 - 9.17423i) q^{79} -1.37947 q^{80} +2.96771 q^{82} +(12.2319 - 12.9650i) q^{83} +(0.00169430 + 0.0290900i) q^{85} +(0.925214 + 0.108142i) q^{86} +(-13.1096 + 6.58387i) q^{88} +(10.6853 + 8.96604i) q^{89} +(5.87068 - 4.92609i) q^{91} +(0.0638594 - 0.148043i) q^{92} +(3.69344 - 0.875361i) q^{94} +(0.989131 - 3.30393i) q^{95} +(6.96396 - 0.813970i) q^{97} +(0.571800 + 3.24284i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8} - 18 q^{10} - 9 q^{11} + 9 q^{13} - 9 q^{14} + 9 q^{16} + 18 q^{17} - 18 q^{19} - 45 q^{20} + 9 q^{22} + 45 q^{23} + 9 q^{25} - 45 q^{26} - 9 q^{28}+ \cdots - 81 q^{98}+O(q^{100}) \) 144 * q - 9 * q^2 + 9 * q^4 - 9 * q^5 + 9 * q^7 + 18 * q^8 - 18 * q^10 - 9 * q^11 + 9 * q^13 - 9 * q^14 + 9 * q^16 + 18 * q^17 - 18 * q^19 - 45 * q^20 + 9 * q^22 + 45 * q^23 + 9 * q^25 - 45 * q^26 - 9 * q^28 - 36 * q^29 + 9 * q^31 + 99 * q^32 + 9 * q^34 - 9 * q^35 - 18 * q^37 - 18 * q^38 + 9 * q^40 - 27 * q^41 + 9 * q^43 - 54 * q^44 - 18 * q^46 + 99 * q^47 + 9 * q^49 - 126 * q^50 - 27 * q^52 - 45 * q^53 - 9 * q^55 + 225 * q^56 + 9 * q^58 - 72 * q^59 + 9 * q^61 - 81 * q^62 - 18 * q^64 + 81 * q^65 - 45 * q^67 - 117 * q^68 - 99 * q^70 + 90 * q^71 - 18 * q^73 - 81 * q^74 - 153 * q^76 - 81 * q^77 - 99 * q^79 + 288 * q^80 - 36 * q^82 - 45 * q^83 - 99 * q^85 - 81 * q^86 - 153 * q^88 + 81 * q^89 - 18 * q^91 - 207 * q^92 - 99 * q^94 + 171 * q^95 - 45 * q^97 - 81 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more