LMFDB - Embedded newform 576.2.bd.a.109.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [576,2,Mod(37,576)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(576, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([0, 9, 0]))

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

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

chi := DirichletCharacter("576.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 576 = 2^{6} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	576.bd (of order $16$, degree $8$, 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:	$4.59938315643$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$7$ over $\Q(\zeta_{16})$
Twist minimal:	no (minimal twist has level 64)
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			109.2
Character	$\chi$	$=$	576.109
Dual form			576.2.bd.a.37.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.797087 + 1.16818i) q^{2} +(-0.729306 - 1.86229i) q^{4} +(-0.631428 - 3.17440i) q^{5} +(-0.127129 - 0.306917i) q^{7} +(2.75681 + 0.632441i) q^{8} +O(q^{10})$	\(q+(-0.797087 + 1.16818i) q^{2} +(-0.729306 - 1.86229i) q^{4} +(-0.631428 - 3.17440i) q^{5} +(-0.127129 - 0.306917i) q^{7} +(2.75681 + 0.632441i) q^{8} +(4.21159 + 1.79265i) q^{10} +(-3.52624 - 2.35616i) q^{11} +(-0.690738 + 3.47257i) q^{13} +(0.459869 + 0.0961292i) q^{14} +(-2.93623 + 2.71635i) q^{16} +(2.19074 + 2.19074i) q^{17} +(-6.74130 - 1.34093i) q^{19} +(-5.45115 + 3.49101i) q^{20} +(5.56314 - 2.24123i) q^{22} +(0.672631 + 0.278613i) q^{23} +(-5.05873 + 2.09540i) q^{25} +(-3.50602 - 3.57485i) q^{26} +(-0.478852 + 0.460588i) q^{28} +(-7.95458 + 5.31508i) q^{29} -0.880409i q^{31} +(-0.832774 - 5.59522i) q^{32} +(-4.30540 + 0.812978i) q^{34} +(-0.894006 + 0.597355i) q^{35} +(-5.44280 + 1.08264i) q^{37} +(6.93985 - 6.80624i) q^{38} +(0.266893 - 9.15058i) q^{40} +(-3.05507 - 1.26545i) q^{41} +(1.59134 - 2.38161i) q^{43} +(-1.81614 + 8.28523i) q^{44} +(-0.861616 + 0.563678i) q^{46} +(-3.23201 - 3.23201i) q^{47} +(4.87171 - 4.87171i) q^{49} +(1.58444 - 7.57974i) q^{50} +(6.97069 - 1.24622i) q^{52} +(7.45949 + 4.98427i) q^{53} +(-5.25283 + 12.6815i) q^{55} +(-0.156365 - 0.926515i) q^{56} +(0.131499 - 13.5290i) q^{58} +(-0.795535 - 3.99942i) q^{59} +(2.62163 + 3.92355i) q^{61} +(1.02848 + 0.701762i) q^{62} +(7.20004 + 3.48704i) q^{64} +11.4595 q^{65} +(-3.03636 - 4.54423i) q^{67} +(2.48207 - 5.67751i) q^{68} +(0.0147790 - 1.52051i) q^{70} +(-2.69641 - 6.50971i) q^{71} +(4.10841 - 9.91857i) q^{73} +(3.07366 - 7.22115i) q^{74} +(2.41928 + 13.5322i) q^{76} +(-0.274857 + 1.38180i) q^{77} +(-1.54370 + 1.54370i) q^{79} +(10.4768 + 7.60558i) q^{80} +(3.91344 - 2.56021i) q^{82} +(-14.5352 - 2.89122i) q^{83} +(5.57100 - 8.33759i) q^{85} +(1.51372 + 3.75733i) q^{86} +(-8.23105 - 8.72563i) q^{88} +(1.64085 - 0.679662i) q^{89} +(1.15360 - 0.229466i) q^{91} +(0.0283034 - 1.45583i) q^{92} +(6.35178 - 1.19939i) q^{94} +22.2463i q^{95} +2.43552i q^{97} +(1.80788 + 9.57423i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 8 q^{2} - 8 q^{4} + 8 q^{5} - 8 q^{7} + 8 q^{8}+O(q^{10}) $ 56 * q + 8 * q^2 - 8 * q^4 + 8 * q^5 - 8 * q^7 + 8 * q^8	$ 56 q + 8 q^{2} - 8 q^{4} + 8 q^{5} - 8 q^{7} + 8 q^{8} - 8 q^{10} + 8 q^{11} - 8 q^{13} + 8 q^{14} - 8 q^{16} + 8 q^{17} - 8 q^{19} + 8 q^{20} + 8 q^{23} - 8 q^{25} - 32 q^{26} + 32 q^{28} + 8 q^{29} - 32 q^{32} + 32 q^{34} + 8 q^{35} - 8 q^{37} - 32 q^{38} + 32 q^{40} + 8 q^{41} - 8 q^{43} - 8 q^{46} + 8 q^{47} - 8 q^{49} + 32 q^{50} - 56 q^{52} + 8 q^{53} + 56 q^{55} + 64 q^{56} - 80 q^{58} - 56 q^{59} - 8 q^{61} + 40 q^{62} - 104 q^{64} + 16 q^{65} + 72 q^{67} + 56 q^{68} - 104 q^{70} - 56 q^{71} - 8 q^{73} + 64 q^{74} - 72 q^{76} + 8 q^{77} + 24 q^{79} - 32 q^{80} + 72 q^{82} + 8 q^{83} - 8 q^{85} - 96 q^{86} + 72 q^{88} + 8 q^{89} - 8 q^{91} - 144 q^{92} + 88 q^{94} - 128 q^{98}+O(q^{100}) $ 56 * q + 8 * q^2 - 8 * q^4 + 8 * q^5 - 8 * q^7 + 8 * q^8 - 8 * q^10 + 8 * q^11 - 8 * q^13 + 8 * q^14 - 8 * q^16 + 8 * q^17 - 8 * q^19 + 8 * q^20 + 8 * q^23 - 8 * q^25 - 32 * q^26 + 32 * q^28 + 8 * q^29 - 32 * q^32 + 32 * q^34 + 8 * q^35 - 8 * q^37 - 32 * q^38 + 32 * q^40 + 8 * q^41 - 8 * q^43 - 8 * q^46 + 8 * q^47 - 8 * q^49 + 32 * q^50 - 56 * q^52 + 8 * q^53 + 56 * q^55 + 64 * q^56 - 80 * q^58 - 56 * q^59 - 8 * q^61 + 40 * q^62 - 104 * q^64 + 16 * q^65 + 72 * q^67 + 56 * q^68 - 104 * q^70 - 56 * q^71 - 8 * q^73 + 64 * q^74 - 72 * q^76 + 8 * q^77 + 24 * q^79 - 32 * q^80 + 72 * q^82 + 8 * q^83 - 8 * q^85 - 96 * q^86 + 72 * q^88 + 8 * q^89 - 8 * q^91 - 144 * q^92 + 88 * q^94 - 128 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/576\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$325$
$\chi(n)$	$1$	$1$	$e\left(\frac{7}{16}\right)$

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 $

$2$	−0.797087	+	1.16818i	−0.563625	+	0.826031i
$2$	−0.797087	+	1.16818i	−0.563625	+	0.826031i
$3$		0			0
$3$		0			0
$4$	−0.729306	−	1.86229i	−0.364653	−	0.931143i
$5$	−0.631428	−	3.17440i	−0.282383	−	1.41964i	−0.818021	−	0.575188i	$-0.804929\pi$
$5$	−0.631428	−	3.17440i	−0.282383	−	1.41964i	0.535638	−	0.844448i	$-0.320071\pi$
$6$		0			0
$7$	−0.127129	−	0.306917i	−0.0480503	−	0.116004i	0.898032	−	0.439930i	$-0.144997\pi$
$7$	−0.127129	−	0.306917i	−0.0480503	−	0.116004i	−0.946082	+	0.323927i	$0.894997\pi$
$8$	2.75681	+	0.632441i	0.974681	+	0.223602i
$9$		0			0
$10$	4.21159	+	1.79265i	1.33182	+	0.566886i
$11$	−3.52624	−	2.35616i	−1.06320	−	0.710409i	−0.104414	−	0.994534i	$-0.533297\pi$
$11$	−3.52624	−	2.35616i	−1.06320	−	0.710409i	−0.958787	+	0.284125i	$0.908297\pi$
$12$		0			0
$13$	−0.690738	+	3.47257i	−0.191576	+	0.963118i	0.758636	+	0.651515i	$0.225866\pi$
$13$	−0.690738	+	3.47257i	−0.191576	+	0.963118i	−0.950212	+	0.311604i	$0.899134\pi$
$14$	0.459869	+	0.0961292i	0.122905	+	0.0256916i
$15$		0			0
$16$	−2.93623	+	2.71635i	−0.734056	+	0.679088i
$17$	2.19074	+	2.19074i	0.531333	+	0.531333i	0.920969	−	0.389636i	$-0.127399\pi$
$17$	2.19074	+	2.19074i	0.531333	+	0.531333i	−0.389636	+	0.920969i	$0.627399\pi$
$18$		0			0
$19$	−6.74130	−	1.34093i	−1.54656	−	0.307630i	−0.653275	−	0.757121i	$-0.726605\pi$
$19$	−6.74130	−	1.34093i	−1.54656	−	0.307630i	−0.893285	+	0.449491i	$0.851605\pi$
$20$	−5.45115	+	3.49101i	−1.21891	+	0.780614i
$21$		0			0
$22$	5.56314	−	2.24123i	1.18607	−	0.477833i
$23$	0.672631	+	0.278613i	0.140253	+	0.0580948i	0.451706	−	0.892167i	$-0.350816\pi$
$23$	0.672631	+	0.278613i	0.140253	+	0.0580948i	−0.311453	+	0.950262i	$0.600816\pi$
$24$		0			0
$25$	−5.05873	+	2.09540i	−1.01175	+	0.419079i
$26$	−3.50602	−	3.57485i	−0.687588	−	0.701086i
$27$		0			0
$28$	−0.478852	+	0.460588i	−0.0904945	+	0.0870429i
$29$	−7.95458	+	5.31508i	−1.47713	+	0.986985i	−0.483371	+	0.875415i	$0.660588\pi$
$29$	−7.95458	+	5.31508i	−1.47713	+	0.986985i	−0.993757	+	0.111570i	$0.964412\pi$
$30$		0			0
$31$		−	0.880409i		−	0.158126i	−0.996870	−	0.0790630i	$-0.974807\pi$
$31$		−	0.880409i		−	0.158126i	0.996870	−	0.0790630i	$-0.0251928\pi$
$32$	−0.832774	−	5.59522i	−0.147215	−	0.989105i
$33$		0			0
$34$	−4.30540	+	0.812978i	−0.738370	+	0.139425i
$35$	−0.894006	+	0.597355i	−0.151115	+	0.100972i
$36$		0			0
$37$	−5.44280	+	1.08264i	−0.894791	+	0.177985i	−0.621006	−	0.783806i	$-0.713276\pi$
$37$	−5.44280	+	1.08264i	−0.894791	+	0.177985i	−0.273785	+	0.961791i	$0.588276\pi$
$38$	6.93985	−	6.80624i	1.12579	−	1.10412i
$39$		0			0
$40$	0.266893	−	9.15058i	0.0421995	−	1.44683i
$41$	−3.05507	−	1.26545i	−0.477122	−	0.197631i	0.131144	−	0.991363i	$-0.458135\pi$
$41$	−3.05507	−	1.26545i	−0.477122	−	0.197631i	−0.608267	+	0.793733i	$0.708135\pi$
$42$		0			0
$43$	1.59134	−	2.38161i	0.242677	−	0.363192i	−0.690058	−	0.723754i	$-0.742415\pi$
$43$	1.59134	−	2.38161i	0.242677	−	0.363192i	0.932735	+	0.360562i	$0.117415\pi$
$44$	−1.81614	+	8.28523i	−0.273793	+	1.24905i
$45$		0			0
$46$	−0.861616	+	0.563678i	−0.127038	+	0.0831098i
$47$	−3.23201	−	3.23201i	−0.471438	−	0.471438i	0.430942	−	0.902380i	$-0.358181\pi$
$47$	−3.23201	−	3.23201i	−0.471438	−	0.471438i	−0.902380	+	0.430942i	$0.858181\pi$
$48$		0			0
$49$	4.87171	−	4.87171i	0.695959	−	0.695959i
$50$	1.58444	−	7.57974i	0.224074	−	1.07194i
$51$		0			0
$52$	6.97069	−	1.24622i	0.966660	−	0.172819i
$53$	7.45949	+	4.98427i	1.02464	+	0.684643i	0.949898	−	0.312560i	$-0.101187\pi$
$53$	7.45949	+	4.98427i	1.02464	+	0.684643i	0.0747420	+	0.997203i	$0.476187\pi$
$54$		0			0
$55$	−5.25283	+	12.6815i	−0.708291	+	1.70997i
$56$	−0.156365	−	0.926515i	−0.0208951	−	0.123811i
$57$		0			0
$58$	0.131499	−	13.5290i	0.0172667	−	1.77644i
$59$	−0.795535	−	3.99942i	−0.103570	−	0.520681i	−0.997387	−	0.0722484i	$-0.976983\pi$
$59$	−0.795535	−	3.99942i	−0.103570	−	0.520681i	0.893817	−	0.448432i	$-0.148017\pi$
$60$		0			0
$61$	2.62163	+	3.92355i	0.335666	+	0.502359i	0.960455	−	0.278434i	$-0.0898153\pi$
$61$	2.62163	+	3.92355i	0.335666	+	0.502359i	−0.624790	+	0.780793i	$0.714815\pi$
$62$	1.02848	+	0.701762i	0.130617	+	0.0891238i
$63$		0			0
$64$	7.20004	+	3.48704i	0.900005	+	0.435880i
$65$	11.4595			1.42138
$66$		0			0
$67$	−3.03636	−	4.54423i	−0.370950	−	0.555166i	0.598291	−	0.801279i	$-0.295847\pi$
$67$	−3.03636	−	4.54423i	−0.370950	−	0.555166i	−0.969241	+	0.246113i	$0.920847\pi$
$68$	2.48207	−	5.67751i	0.300995	−	0.688499i
$69$		0			0
$70$	0.0147790	−	1.52051i	0.00176643	−	0.181735i
$71$	−2.69641	−	6.50971i	−0.320005	−	0.772561i	−0.999253	−	0.0386517i	$-0.987694\pi$
$71$	−2.69641	−	6.50971i	−0.320005	−	0.772561i	0.679248	−	0.733909i	$-0.262306\pi$
$72$		0			0
$73$	4.10841	−	9.91857i	0.480853	−	1.16088i	−0.478352	−	0.878168i	$-0.658766\pi$
$73$	4.10841	−	9.91857i	0.480853	−	1.16088i	0.959205	−	0.282713i	$-0.0912344\pi$
$74$	3.07366	−	7.22115i	0.357306	−	0.839441i
$75$		0			0
$76$	2.41928	+	13.5322i	0.277510	+	1.55225i
$77$	−0.274857	+	1.38180i	−0.0313229	+	0.157471i
$78$		0			0
$79$	−1.54370	+	1.54370i	−0.173680	+	0.173680i	−0.788594	−	0.614914i	$-0.789191\pi$
$79$	−1.54370	+	1.54370i	−0.173680	+	0.173680i	0.614914	+	0.788594i	$0.289191\pi$
$80$	10.4768	+	7.60558i	1.17134	+	0.850330i
$81$		0			0
$82$	3.91344	−	2.56021i	0.432167	−	0.282728i
$83$	−14.5352	−	2.89122i	−1.59544	−	0.317353i	−0.684221	−	0.729275i	$-0.739858\pi$
$83$	−14.5352	−	2.89122i	−1.59544	−	0.317353i	−0.911219	+	0.411922i	$0.864858\pi$
$84$		0			0
$85$	5.57100	−	8.33759i	0.604260	−	0.904339i
$86$	1.51372	+	3.75733i	0.163229	+	0.405163i
$87$		0			0
$88$	−8.23105	−	8.72563i	−0.877433	−	0.930155i
$89$	1.64085	−	0.679662i	0.173930	−	0.0720441i	−0.294019	−	0.955799i	$-0.594993\pi$
$89$	1.64085	−	0.679662i	0.173930	−	0.0720441i	0.467949	+	0.883755i	$0.344993\pi$
$90$		0			0
$91$	1.15360	−	0.229466i	0.120931	−	0.0240546i
$92$	0.0283034	−	1.45583i	0.00295083	−	0.151780i
$93$		0			0
$94$	6.35178	−	1.19939i	0.655136	−	0.123708i
$95$			22.2463i			2.28242i
$96$		0			0
$97$			2.43552i			0.247289i	0.992327	+	0.123645i	$0.0394583\pi$
$97$			2.43552i			0.247289i	−0.992327	+	0.123645i	$0.960542\pi$
$98$	1.80788	+	9.57423i	0.182623	+	0.967143i
$99$		0			0
$100$	7.59159	+	7.89263i	0.759159	+	0.789263i
$101$	0.776702	−	0.154496i	0.0772847	−	0.0153729i	−0.156296	−	0.987710i	$-0.549956\pi$
$101$	0.776702	−	0.154496i	0.0772847	−	0.0153729i	0.233581	+	0.972337i	$0.424956\pi$
$102$		0			0
$103$	−5.94004	+	2.46045i	−0.585290	+	0.242435i	−0.655623	−	0.755089i	$-0.727594\pi$
$103$	−5.94004	+	2.46045i	−0.585290	+	0.242435i	0.0703329	+	0.997524i	$0.477594\pi$
$104$	−4.10043	+	9.13638i	−0.402080	+	0.895896i
$105$		0			0
$106$	−11.7684	+	4.74116i	−1.14305	+	0.460502i
$107$	−3.42296	+	5.12283i	−0.330910	+	0.495242i	−0.959197	−	0.282740i	$-0.908757\pi$
$107$	−3.42296	+	5.12283i	−0.330910	+	0.495242i	0.628286	+	0.777982i	$0.283757\pi$
$108$		0			0
$109$	−9.42451	−	1.87465i	−0.902704	−	0.179559i	−0.278148	−	0.960538i	$-0.589720\pi$
$109$	−9.42451	−	1.87465i	−0.902704	−	0.179559i	−0.624557	+	0.780979i	$0.714720\pi$
$110$	−10.6273	−	16.2445i	−1.01327	−	1.54885i
$111$		0			0
$112$	1.20698	+	0.555850i	0.114048	+	0.0525229i
$113$	4.53709	−	4.53709i	0.426814	−	0.426814i	−0.460728	−	0.887541i	$-0.652412\pi$
$113$	4.53709	−	4.53709i	0.426814	−	0.426814i	0.887541	+	0.460728i	$0.152412\pi$
$114$		0			0
$115$	0.459712	−	2.31113i	0.0428683	−	0.215514i
$116$	15.6995	+	10.9374i	1.45766	+	1.01551i
$117$		0			0
$118$	5.30617	+	2.25856i	0.488473	+	0.207917i
$119$	0.393869	−	0.950883i	0.0361059	−	0.0871673i
$120$		0			0
$121$	2.67337	+	6.45409i	0.243034	+	0.586735i
$122$	−6.67310	−	0.0648613i	−0.604154	−	0.00587226i
$123$		0			0
$124$	−1.63957	+	0.642087i	−0.147238	+	0.0576611i
$125$	0.855086	+	1.27973i	0.0764812	+	0.114462i
$126$		0			0
$127$	−13.1460			−1.16652			−0.583260	−	0.812285i	$-0.698223\pi$
$127$	−13.1460			−1.16652			−0.583260	+	0.812285i	$0.698223\pi$
$128$	−9.81256	+	5.63149i	−0.867316	+	0.497758i
$129$		0			0
$130$	−9.13421	+	13.3868i	−0.801123	+	1.17410i
$131$	8.01070	+	11.9889i	0.699898	+	1.04747i	0.995737	+	0.0922342i	$0.0294008\pi$
$131$	8.01070	+	11.9889i	0.699898	+	1.04747i	−0.295839	+	0.955238i	$0.595599\pi$
$132$		0			0
$133$	0.445462	+	2.23949i	0.0386265	+	0.194188i
$134$	7.72874	+	0.0751219i	0.667661	+	0.00648954i
$135$		0			0
$136$	4.65395	+	7.42498i	0.399073	+	0.636687i
$137$	2.01913	−	4.87460i	0.172506	−	0.416465i	−0.813854	−	0.581069i	$-0.802635\pi$
$137$	2.01913	−	4.87460i	0.172506	−	0.416465i	0.986360	+	0.164604i	$0.0526345\pi$
$138$		0			0
$139$	−4.06094	−	2.71344i	−0.344445	−	0.230151i	0.371299	−	0.928513i	$-0.378912\pi$
$139$	−4.06094	−	2.71344i	−0.344445	−	0.230151i	−0.715744	+	0.698363i	$0.753912\pi$
$140$	1.76445	+	1.22924i	0.149123	+	0.103890i
$141$		0			0
$142$	9.75382	+	2.03890i	0.818522	+	0.171101i
$143$	10.6176	−	10.6176i	0.887891	−	0.887891i
$144$		0			0
$145$	21.8949	+	21.8949i	1.81828	+	1.81828i
$146$	8.31196	+	12.7053i	0.687903	+	1.05150i
$147$		0			0
$148$	5.98565	+	9.34648i	0.492018	+	0.768276i
$149$	5.32373	−	7.96752i	0.436137	−	0.652725i	−0.546673	−	0.837346i	$-0.684106\pi$
$149$	5.32373	−	7.96752i	0.436137	−	0.652725i	0.982810	+	0.184622i	$0.0591059\pi$
$150$		0			0
$151$	15.2438	+	6.31419i	1.24052	+	0.513841i	0.903878	−	0.427791i	$-0.140708\pi$
$151$	15.2438	+	6.31419i	1.24052	+	0.513841i	0.336645	+	0.941632i	$0.390708\pi$
$152$	−17.7364	−	7.96016i	−1.43861	−	0.645654i
$153$		0			0
$154$	−1.39511	−	1.42250i	−0.112421	−	0.114628i
$155$	−2.79477	+	0.555915i	−0.224481	+	0.0446521i
$156$		0			0
$157$	0.183668	−	0.122723i	0.0146583	−	0.00979438i	−0.548219	−	0.836335i	$-0.684694\pi$
$157$	0.183668	−	0.122723i	0.0146583	−	0.00979438i	0.562878	+	0.826540i	$0.309694\pi$
$158$	−0.572863	−	3.03379i	−0.0455746	−	0.241356i
$159$		0			0
$160$	−17.2356	+	6.17654i	−1.36260	+	0.488298i
$161$		−	0.241862i		−	0.0190614i
$162$		0			0
$163$	14.8711	−	9.93653i	1.16479	−	0.778289i	0.185880	−	0.982572i	$-0.440486\pi$
$163$	14.8711	−	9.93653i	1.16479	−	0.778289i	0.978912	+	0.204283i	$0.0654864\pi$
$164$	−0.128553	+	6.61233i	−0.0100383	+	0.516336i
$165$		0			0
$166$	14.9633	−	14.6752i	1.16137	−	1.13901i
$167$	−16.9720	+	7.03005i	−1.31334	+	0.544001i	−0.925856	−	0.377877i	$-0.876654\pi$
$167$	−16.9720	+	7.03005i	−1.31334	+	0.544001i	−0.387480	+	0.921878i	$0.626654\pi$
$168$		0			0
$169$	0.428795	+	0.177613i	0.0329842	+	0.0136625i
$170$	5.29927	+	13.1537i	0.406435	+	1.00885i
$171$		0			0
$172$	−5.59582	−	1.22661i	−0.426677	−	0.0935283i
$173$	12.9081	+	2.56758i	0.981384	+	0.195210i	0.659611	−	0.751607i	$-0.270721\pi$
$173$	12.9081	+	2.56758i	0.981384	+	0.195210i	0.321773	+	0.946817i	$0.395721\pi$
$174$		0			0
$175$	1.28623	+	1.28623i	0.0972296	+	0.0972296i
$176$	16.7540	−	2.66030i	1.26288	−	0.200528i
$177$		0			0
$178$	−0.513929	+	2.45856i	−0.0385206	+	0.184277i
$179$	4.41588	−	22.2001i	0.330058	−	1.65932i	−0.358046	−	0.933704i	$-0.616557\pi$
$179$	4.41588	−	22.2001i	0.330058	−	1.65932i	0.688105	−	0.725612i	$-0.258443\pi$
$180$		0			0
$181$	−12.2894	−	8.21153i	−0.913466	−	0.610358i	0.00751269	−	0.999972i	$-0.497609\pi$
$181$	−12.2894	−	8.21153i	−0.913466	−	0.610358i	−0.920978	+	0.389613i	$0.872609\pi$
$182$	−0.651464	+	1.53053i	−0.0482897	+	0.113450i
$183$		0			0
$184$	1.67811	+	1.19348i	0.123712	+	0.0879848i
$185$	6.87347	+	16.5940i	0.505348	+	1.22002i
$186$		0			0
$187$	−2.56335	−	12.8868i	−0.187450	−	0.942377i
$188$	−3.66181	+	8.37606i	−0.267065	+	0.610887i
$189$		0			0
$190$	−25.9877	−	17.7322i	−1.88535	−	1.28643i
$191$	−6.69554			−0.484472			−0.242236	−	0.970217i	$-0.577881\pi$
$191$	−6.69554			−0.484472			−0.242236	+	0.970217i	$0.577881\pi$
$192$		0			0
$193$	3.13547			0.225696			0.112848	−	0.993612i	$-0.464003\pi$
$193$	3.13547			0.225696			0.112848	+	0.993612i	$0.464003\pi$
$194$	−2.84513	−	1.94132i	−0.204268	−	0.139378i
$195$		0			0
$196$	−12.6255	−	5.51956i	−0.901821	−	0.394254i
$197$	−3.05543	−	15.3607i	−0.217690	−	1.09440i	−0.922793	−	0.385297i	$-0.874099\pi$
$197$	−3.05543	−	15.3607i	−0.217690	−	1.09440i	0.705102	−	0.709106i	$-0.250901\pi$
$198$		0			0
$199$	−1.63780	−	3.95399i	−0.116100	−	0.280291i	0.855138	−	0.518400i	$-0.173472\pi$
$199$	−1.63780	−	3.95399i	−0.116100	−	0.280291i	−0.971238	+	0.238109i	$0.923472\pi$
$200$	−15.2712	+	2.57727i	−1.07984	+	0.182240i
$201$		0			0
$202$	−0.438619	+	1.03048i	−0.0308612	+	0.0725041i
$203$	2.64255	+	1.76569i	0.185471	+	0.123927i
$204$		0			0
$205$	−2.08800	+	10.4971i	−0.145832	+	0.733148i
$206$	1.86048	−	8.90025i	0.129625	−	0.620110i
$207$		0			0
$208$	−7.40457	−	12.0725i	−0.513415	−	0.837080i
$209$	20.6120	+	20.6120i	1.42576	+	1.42576i
$210$		0			0
$211$	20.2759	+	4.03313i	1.39585	+	0.277652i	0.834993	−	0.550261i	$-0.185472\pi$
$211$	20.2759	+	4.03313i	1.39585	+	0.277652i	0.560857	+	0.827912i	$0.310472\pi$
$212$	3.84190	−	17.5268i	0.263862	−	1.20374i
$213$		0			0
$214$	−3.25600	−	8.08199i	−0.222576	−	0.552473i
$215$	−8.56501	−	3.54775i	−0.584129	−	0.241954i
$216$		0			0
$217$	−0.270212	+	0.111926i	−0.0183432	+	0.00759801i
$218$	9.70209	−	9.51530i	0.657108	−	0.644457i
$219$		0			0
$220$	27.4474	+	0.533618i	1.85050	+	0.0359765i
$221$	−9.12074	+	6.09428i	−0.613527	+	0.409946i
$222$		0			0
$223$			18.1462i			1.21516i	0.794258	+	0.607581i	$0.207860\pi$
$223$			18.1462i			1.21516i	−0.794258	+	0.607581i	$0.792140\pi$
$224$	−1.61140	+	0.966909i	−0.107666	+	0.0646043i
$225$		0			0
$226$	1.68370	+	8.91661i	0.111998	+	0.593124i
$227$	13.4874	−	9.01200i	0.895191	−	0.598148i	−0.0206063	−	0.999788i	$-0.506560\pi$
$227$	13.4874	−	9.01200i	0.895191	−	0.598148i	0.915798	+	0.401640i	$0.131560\pi$
$228$		0			0
$229$	1.15657	−	0.230055i	0.0764281	−	0.0152025i	−0.156728	−	0.987642i	$-0.550095\pi$
$229$	1.15657	−	0.230055i	0.0764281	−	0.0152025i	0.233156	+	0.972439i	$0.425095\pi$
$230$	2.33339	+	2.37920i	0.153859	+	0.156879i
$231$		0			0
$232$	−25.2908	+	9.62188i	−1.66042	+	0.631707i
$233$	3.25867	+	1.34979i	0.213483	+	0.0884274i	0.486862	−	0.873479i	$-0.338141\pi$
$233$	3.25867	+	1.34979i	0.213483	+	0.0884274i	−0.273379	+	0.961906i	$0.588141\pi$
$234$		0			0
$235$	−8.21893	+	12.3005i	−0.536144	+	0.802396i
$236$	−6.86789	+	4.39832i	−0.447061	+	0.286306i
$237$		0			0
$238$	0.796859	+	1.21805i	0.0516527	+	0.0789543i
$239$	5.54582	+	5.54582i	0.358729	+	0.358729i	0.863344	−	0.504615i	$-0.168366\pi$
$239$	5.54582	+	5.54582i	0.358729	+	0.358729i	−0.504615	+	0.863344i	$0.668366\pi$
$240$		0			0
$241$	−5.98668	+	5.98668i	−0.385636	+	0.385636i	−0.873128	−	0.487492i	$-0.837912\pi$
$241$	−5.98668	+	5.98668i	−0.385636	+	0.385636i	0.487492	+	0.873128i	$0.337912\pi$
$242$	−9.67047	−	2.02148i	−0.621641	−	0.129946i
$243$		0			0
$244$	5.39481	−	7.74371i	0.345367	−	0.495740i
$245$	−18.5409	−	12.3886i	−1.18454	−	0.791481i
$246$		0			0
$247$	9.31293	−	22.4834i	0.592568	−	1.43058i
$248$	0.556806	−	2.42712i	0.0353572	−	0.154122i
$249$		0			0
$250$	−2.17653	−	0.0211555i	−0.137656	−	0.00133799i
$251$	−0.437354	−	2.19873i	−0.0276055	−	0.138782i	0.964525	−	0.263993i	$-0.0850395\pi$
$251$	−0.437354	−	2.19873i	−0.0276055	−	0.138782i	−0.992130	+	0.125210i	$0.960039\pi$
$252$		0			0
$253$	−1.71540	−	2.56728i	−0.107846	−	0.161404i
$254$	10.4785	−	15.3570i	0.657480	−	0.963581i
$255$		0			0
$256$	1.24284	−	15.9517i	0.0776777	−	0.996979i
$257$	−19.0558			−1.18867			−0.594334	−	0.804218i	$-0.702584\pi$
$257$	−19.0558			−1.18867			−0.594334	+	0.804218i	$0.702584\pi$
$258$		0			0
$259$	1.02422	+	1.53285i	0.0636419	+	0.0952469i
$260$	−8.35748	−	21.3409i	−0.518309	−	1.32350i
$261$		0			0
$262$	−20.3904	−	0.198191i	−1.25972	−	0.0122443i
$263$	−2.42000	−	5.84240i	−0.149224	−	0.360258i	0.831538	−	0.555468i	$-0.187461\pi$
$263$	−2.42000	−	5.84240i	−0.149224	−	0.360258i	−0.980761	+	0.195211i	$0.937461\pi$
$264$		0			0
$265$	11.1120	−	26.8266i	0.682602	−	1.64795i
$266$	−2.97121	−	1.26469i	−0.182176	−	0.0775429i
$267$		0			0
$268$	−6.24823	+	8.96871i	−0.381671	+	0.547851i
$269$	2.01219	−	10.1159i	0.122685	−	0.616780i	−0.869697	−	0.493585i	$-0.835686\pi$
$269$	2.01219	−	10.1159i	0.122685	−	0.616780i	0.992383	−	0.123195i	$-0.0393139\pi$
$270$		0			0
$271$	4.18042	−	4.18042i	0.253942	−	0.253942i	−0.568642	−	0.822585i	$-0.692531\pi$
$271$	4.18042	−	4.18042i	0.253942	−	0.253942i	0.822585	+	0.568642i	$0.192531\pi$
$272$	−12.3833	−	0.481682i	−0.750850	−	0.0292063i
$273$		0			0
$274$	4.08501	+	6.24419i	0.246785	+	0.377225i
$275$	22.7754	+	4.53031i	1.37341	+	0.273188i
$276$		0			0
$277$	−1.05525	+	1.57930i	−0.0634040	+	0.0948909i	−0.861817	−	0.507220i	$-0.830673\pi$
$277$	−1.05525	+	1.57930i	−0.0634040	+	0.0948909i	0.798413	+	0.602110i	$0.205673\pi$
$278$	6.40672	−	2.58108i	0.384249	−	0.154803i
$279$		0			0
$280$	−2.84240	+	1.08139i	−0.169866	+	0.0646255i
$281$	−20.6297	+	8.54511i	−1.23067	+	0.509759i	−0.900786	−	0.434264i	$-0.857009\pi$
$281$	−20.6297	+	8.54511i	−1.23067	+	0.509759i	−0.329881	+	0.944023i	$0.607009\pi$
$282$		0			0
$283$	0.153600	−	0.0305529i	0.00913055	−	0.00181618i	−0.190523	−	0.981683i	$-0.561018\pi$
$283$	0.153600	−	0.0305529i	0.00913055	−	0.00181618i	0.199653	+	0.979867i	$0.436018\pi$
$284$	−10.1564	+	9.76907i	−0.602674	+	0.579687i
$285$		0			0
$286$	3.94017	+	20.8665i	0.232987	+	1.23386i
$287$			1.09853i			0.0648442i
$288$		0			0
$289$		−	7.40130i		−	0.435371i
$290$	−43.0295	+	8.12515i	−2.52678	+	0.477125i
$291$		0			0
$292$	−21.4675	−	0.417360i	−1.25629	−	0.0244241i
$293$	8.18241	−	1.62758i	0.478022	−	0.0950844i	0.0498021	−	0.998759i	$-0.484141\pi$
$293$	8.18241	−	1.62758i	0.478022	−	0.0950844i	0.428220	+	0.903675i	$0.359141\pi$
$294$		0			0
$295$	−12.1935	+	5.05070i	−0.709931	+	0.294063i
$296$	−15.6895	−	0.457612i	−0.911933	−	0.0265981i
$297$		0			0
$298$	5.06405	+	12.5699i	0.293353	+	0.728154i
$299$	−1.43212	+	2.14331i	−0.0828214	+	0.123951i
$300$		0			0
$301$	−0.933264	−	0.185638i	−0.0537924	−	0.0107000i
$302$	−19.5268	+	12.7746i	−1.12364	+	0.735095i
$303$		0			0
$304$	23.4364	−	14.3745i	1.34417	−	0.824433i
$305$	10.7996	−	10.7996i	0.618381	−	0.618381i
$306$		0			0
$307$	6.67898	−	33.5775i	0.381190	−	1.91637i	−0.0187412	−	0.999824i	$-0.505966\pi$
$307$	6.67898	−	33.5775i	0.381190	−	1.91637i	0.399931	−	0.916545i	$-0.369034\pi$
$308$	2.77376	−	0.495892i	0.158050	−	0.0282561i
$309$		0			0
$310$	1.57826	−	3.70792i	0.0896394	−	0.210596i
$311$	5.03970	−	12.1669i	0.285775	−	0.689923i	−0.714174	−	0.699968i	$-0.753198\pi$
$311$	5.03970	−	12.1669i	0.285775	−	0.689923i	0.999950	+	0.0100453i	$0.00319757\pi$
$312$		0			0
$313$	−0.161015	−	0.388724i	−0.00910110	−	0.0219720i	0.919264	−	0.393642i	$-0.128785\pi$
$313$	−0.161015	−	0.388724i	−0.00910110	−	0.0219720i	−0.928365	+	0.371670i	$0.878785\pi$
$314$	−0.00303627	+	0.312379i	−0.000171347	+	0.0176286i
$315$		0			0
$316$	4.00065	+	1.74899i	0.225054	+	0.0983881i
$317$	9.33099	+	13.9648i	0.524081	+	0.784342i	0.995214	−	0.0977198i	$-0.0311549\pi$
$317$	9.33099	+	13.9648i	0.524081	+	0.784342i	−0.471133	+	0.882062i	$0.656155\pi$
$318$		0			0
$319$	40.5729			2.27165
$320$	6.52297	−	25.0576i	0.364645	−	1.40076i
$321$		0			0
$322$	0.282539	+	0.192785i	0.0157453	+	0.0107435i
$323$	−11.8308	−	17.7061i	−0.658284	−	0.985192i
$324$		0			0
$325$	−3.78216	−	19.0142i	−0.209796	−	1.05472i
$326$	−0.245837	+	25.2924i	−0.0136157	+	1.40082i
$327$		0			0
$328$	−7.62195	−	5.42077i	−0.420852	−	0.299312i
$329$	−0.581077	+	1.40284i	−0.0320358	+	0.0773413i
$330$		0			0
$331$	−27.3548	−	18.2779i	−1.50355	−	1.00464i	−0.989120	−	0.147112i	$-0.953002\pi$
$331$	−27.3548	−	18.2779i	−1.50355	−	1.00464i	−0.514433	−	0.857530i	$-0.671998\pi$
$332$	5.21629	+	29.1772i	0.286281	+	1.60131i
$333$		0			0
$334$	5.31580	−	25.4300i	0.290867	−	1.39147i
$335$	−12.5080	+	12.5080i	−0.683384	+	0.683384i
$336$		0			0
$337$	−1.93221	−	1.93221i	−0.105254	−	0.105254i	0.652519	−	0.757773i	$-0.273712\pi$
$337$	−1.93221	−	1.93221i	−0.105254	−	0.105254i	−0.757773	+	0.652519i	$0.773712\pi$
$338$	−0.549271	+	0.359338i	−0.0298764	+	0.0195454i
$339$		0			0
$340$	−19.5900	−	4.29415i	−1.06241	−	0.232883i
$341$	−2.07438	+	3.10453i	−0.112334	+	0.168120i
$342$		0			0
$343$	−4.26297	−	1.76578i	−0.230179	−	0.0953431i
$344$	5.89326	−	5.55923i	0.317743	−	0.299734i
$345$		0			0
$346$	−13.2883	+	13.0324i	−0.714382	+	0.700629i
$347$	−5.95710	+	1.18494i	−0.319794	+	0.0636110i	−0.352377	−	0.935858i	$-0.614627\pi$
$347$	−5.95710	+	1.18494i	−0.319794	+	0.0636110i	0.0325833	+	0.999469i	$0.489627\pi$
$348$		0			0
$349$	−2.40994	+	1.61027i	−0.129001	+	0.0861956i	−0.618397	−	0.785866i	$-0.712217\pi$
$349$	−2.40994	+	1.61027i	−0.129001	+	0.0861956i	0.489396	+	0.872062i	$0.337217\pi$
$350$	−2.52778	+	0.477315i	−0.135116	+	0.0255135i
$351$		0			0
$352$	−10.2467	+	21.6922i	−0.546149	+	1.15620i
$353$		−	34.9802i		−	1.86181i	−0.365261	−	0.930905i	$-0.619020\pi$
$353$		−	34.9802i		−	1.86181i	0.365261	−	0.930905i	$-0.380980\pi$
$354$		0			0
$355$	−18.9619	+	12.6699i	−1.00639	+	0.672449i
$356$	−2.46241	−	2.56005i	−0.130507	−	0.135682i
$357$		0			0
$358$	22.4140	+	22.8540i	1.18462	+	1.20787i
$359$	−11.4132	+	4.72748i	−0.602363	+	0.249507i	−0.662959	−	0.748655i	$-0.730700\pi$
$359$	−11.4132	+	4.72748i	−0.602363	+	0.249507i	0.0605961	+	0.998162i	$0.480700\pi$
$360$		0			0
$361$	26.0933	+	10.8082i	1.37333	+	0.568852i
$362$	19.3883	−	7.81100i	1.01903	−	0.410537i
$363$		0			0
$364$	−1.26866	−	1.98099i	−0.0664960	−	0.103832i
$365$	−34.0797	−	6.77888i	−1.78381	−	0.354823i
$366$		0			0
$367$	−7.30233	−	7.30233i	−0.381178	−	0.381178i	0.490348	−	0.871527i	$-0.336870\pi$
$367$	−7.30233	−	7.30233i	−0.381178	−	0.381178i	−0.871527	+	0.490348i	$0.836870\pi$
$368$	−2.73181	+	1.00903i	−0.142405	+	0.0525995i
$369$		0			0
$370$	−24.8636	−	5.19740i	−1.29260	−	0.270200i
$371$	0.581439	−	2.92309i	0.0301868	−	0.151759i
$372$		0			0
$373$	18.9156	+	12.6390i	0.979413	+	0.654423i	0.938695	−	0.344748i	$-0.112036\pi$
$373$	18.9156	+	12.6390i	0.979413	+	0.654423i	0.0407173	+	0.999171i	$0.487036\pi$
$374$	17.0974	+	7.27745i	0.884084	+	0.376308i
$375$		0			0
$376$	−6.86600	−	10.9541i	−0.354087	−	0.564915i
$377$	−12.9625	−	31.2942i	−0.667601	−	1.61173i
$378$		0			0
$379$	4.20965	+	21.1633i	0.216235	+	1.08709i	0.924512	+	0.381152i	$0.124473\pi$
$379$	4.20965	+	21.1633i	0.216235	+	1.08709i	−0.708277	+	0.705934i	$0.750527\pi$
$380$	41.4290	−	16.2243i	2.12526	−	0.832292i
$381$		0			0
$382$	5.33692	−	7.82162i	0.273061	−	0.400189i
$383$	18.3977			0.940079			0.470039	−	0.882646i	$-0.344240\pi$
$383$	18.3977			0.940079			0.470039	+	0.882646i	$0.344240\pi$
$384$		0			0
$385$	4.55994			0.232396
$386$	−2.49924	+	3.66280i	−0.127208	+	0.186432i
$387$		0			0
$388$	4.53563	−	1.77624i	0.230262	−	0.0901747i
$389$	3.48084	+	17.4994i	0.176486	+	0.887253i	0.962963	+	0.269634i	$0.0869026\pi$
$389$	3.48084	+	17.4994i	0.176486	+	0.887253i	−0.786477	+	0.617619i	$0.788097\pi$
$390$		0			0
$391$	0.863192	+	2.08393i	0.0436535	+	0.105389i
$392$	16.5115	−	10.3493i	0.833955	−	0.522720i
$393$		0			0
$394$	20.3795	+	8.67449i	1.02671	+	0.437014i
$395$	5.87507	+	3.92560i	0.295607	+	0.197518i
$396$		0			0
$397$	2.30374	−	11.5817i	0.115621	−	0.581268i	−0.878924	−	0.476962i	$-0.841738\pi$
$397$	2.30374	−	11.5817i	0.115621	−	0.581268i	0.994545	−	0.104306i	$-0.0332621\pi$
$398$	5.92445	+	1.23843i	0.296966	+	0.0620767i
$399$		0			0
$400$	9.16175	−	19.8939i	0.458087	−	0.994694i
$401$	14.2513	+	14.2513i	0.711677	+	0.711677i	0.966886	−	0.255209i	$-0.0821443\pi$
$401$	14.2513	+	14.2513i	0.711677	+	0.711677i	−0.255209	+	0.966886i	$0.582144\pi$
$402$		0			0
$403$	3.05728	+	0.608131i	0.152294	+	0.0302932i
$404$	−0.854169	−	1.33377i	−0.0424965	−	0.0663574i
$405$		0			0
$406$	−4.16899	+	1.67957i	−0.206904	+	0.0833557i
$407$	21.7435	+	9.00645i	1.07778	+	0.446433i
$408$		0			0
$409$	−21.7113	+	8.99313i	−1.07356	+	0.444682i	−0.848244	−	0.529605i	$-0.822340\pi$
$409$	−21.7113	+	8.99313i	−1.07356	+	0.444682i	−0.225312	+	0.974287i	$0.572340\pi$
$410$	−10.5982	−	10.8062i	−0.523408	−	0.533683i
$411$		0			0
$412$	8.91417	+	9.26765i	0.439169	+	0.456584i
$413$	−1.12636	+	0.752607i	−0.0554243	+	0.0370334i
$414$		0			0
$415$			47.9660i			2.35456i
$416$	20.0050	+	0.972961i	0.980827	+	0.0477033i
$417$		0			0
$418$	−40.5081	+	7.64905i	−1.98132	+	0.374127i
$419$	2.46480	−	1.64693i	0.120413	−	0.0804577i	−0.493905	−	0.869516i	$-0.664431\pi$
$419$	2.46480	−	1.64693i	0.120413	−	0.0804577i	0.614319	+	0.789058i	$0.289431\pi$
$420$		0			0
$421$	−33.4984	+	6.66325i	−1.63261	+	0.324747i	−0.924450	−	0.381303i	$-0.875475\pi$
$421$	−33.4984	+	6.66325i	−1.63261	+	0.324747i	−0.708162	+	0.706050i	$0.750475\pi$
$422$	−20.8731	+	20.4712i	−1.01609	+	0.996523i
$423$		0			0
$424$	17.4122	+	18.4584i	0.845610	+	0.896419i
$425$	−15.6729	−	6.49191i	−0.760245	−	0.314904i
$426$		0			0
$427$	0.870919	−	1.30342i	0.0421467	−	0.0630770i
$428$	12.0366	+	2.63843i	0.581809	+	0.127533i
$429$		0			0
$430$	10.9715	−	7.17765i	0.529092	−	0.346137i
$431$	27.7891	+	27.7891i	1.33855	+	1.33855i	0.897461	+	0.441094i	$0.145409\pi$
$431$	27.7891	+	27.7891i	1.33855	+	1.33855i	0.441094	+	0.897461i	$0.354591\pi$
$432$		0			0
$433$	19.5120	−	19.5120i	0.937689	−	0.937689i	−0.0604807	−	0.998169i	$-0.519263\pi$
$433$	19.5120	−	19.5120i	0.937689	−	0.937689i	0.998169	+	0.0604807i	$0.0192634\pi$
$434$	0.0846330	−	0.404872i	0.00406251	−	0.0194345i
$435$		0			0
$436$	3.38221	+	18.9183i	0.161979	+	0.906024i
$437$	−4.16081	−	2.78016i	−0.199038	−	0.132993i
$438$		0			0
$439$	10.7454	−	25.9416i	0.512849	−	1.23813i	−0.429370	−	0.903129i	$-0.641264\pi$
$439$	10.7454	−	25.9416i	0.512849	−	1.23813i	0.942219	−	0.334998i	$-0.108736\pi$
$440$	−22.5013	+	31.6383i	−1.07271	+	1.50830i
$441$		0			0
$442$	0.150777	−	15.5124i	0.00717174	−	0.737848i
$443$	−1.40022	−	7.03938i	−0.0665264	−	0.334451i	0.933161	−	0.359459i	$-0.117039\pi$
$443$	−1.40022	−	7.03938i	−0.0665264	−	0.334451i	−0.999687	+	0.0250082i	$0.992039\pi$
$444$		0			0
$445$	−3.19360	−	4.77956i	−0.151391	−	0.226573i
$446$	−21.1981	−	14.4641i	−1.00376	−	0.684896i
$447$		0			0
$448$	0.154898	−	2.65312i	0.00731823	−	0.125348i
$449$	−9.76361			−0.460773			−0.230387	−	0.973099i	$-0.573999\pi$
$449$	−9.76361			−0.460773			−0.230387	+	0.973099i	$0.573999\pi$
$450$		0			0
$451$	7.79132	+	11.6605i	0.366879	+	0.549073i
$452$	−11.7583	−	5.14044i	−0.553063	−	0.241786i
$453$		0			0
$454$	−0.222964	+	22.9391i	−0.0104642	+	1.07659i
$455$	−1.45684	−	3.51712i	−0.0682976	−	0.164885i
$456$		0			0
$457$	−12.2635	+	29.6067i	−0.573662	+	1.38494i	0.324755	+	0.945798i	$0.394718\pi$
$457$	−12.2635	+	29.6067i	−0.573662	+	1.38494i	−0.898417	+	0.439144i	$0.855282\pi$
$458$	−0.653137	+	1.53446i	−0.0305191	+	0.0717004i
$459$		0			0
$460$	−4.63925	+	0.829403i	−0.216306	+	0.0386711i
$461$	−6.86998	+	34.5377i	−0.319967	+	1.60858i	0.401314	+	0.915940i	$0.368553\pi$
$461$	−6.86998	+	34.5377i	−0.319967	+	1.60858i	−0.721281	+	0.692642i	$0.756447\pi$
$462$		0			0
$463$	−20.0285	+	20.0285i	−0.930804	+	0.930804i	−0.997756	−	0.0669525i	$-0.978672\pi$
$463$	−20.0285	+	20.0285i	−0.930804	+	0.930804i	0.0669525	+	0.997756i	$0.478672\pi$
$464$	8.91880	−	37.2137i	0.414045	−	1.72760i
$465$		0			0
$466$	−4.17424	+	2.73083i	−0.193368	+	0.126503i
$467$	15.7542	+	3.13370i	0.729015	+	0.145010i	0.545624	−	0.838030i	$-0.316293\pi$
$467$	15.7542	+	3.13370i	0.729015	+	0.145010i	0.183391	+	0.983040i	$0.441293\pi$
$468$		0			0
$469$	−1.00869	+	1.50962i	−0.0465771	+	0.0697076i
$470$	−7.81804	−	19.4058i	−0.360619	−	0.895122i
$471$		0			0
$472$	0.336258	−	11.5288i	0.0154775	−	0.530656i
$473$	−11.2229	+	4.64868i	−0.516030	+	0.213747i
$474$		0			0
$475$	36.9122	−	7.34229i	1.69365	−	0.336888i
$476$	−2.05807	−	0.0400118i	−0.0943314	−	0.00183394i
$477$		0			0
$478$	−10.8990	+	2.05804i	−0.498511	+	0.0941325i
$479$			30.8222i			1.40830i	0.710050	+	0.704151i	$0.248672\pi$
$479$			30.8222i			1.40830i	−0.710050	+	0.704151i	$0.751328\pi$
$480$		0			0
$481$		−	19.6483i		−	0.895887i
$482$	−2.22164	−	11.7654i	−0.101193	−	0.535901i
$483$		0			0
$484$	10.0697	−	9.68559i	0.457712	−	0.440254i
$485$	7.73131	−	1.53785i	0.351061	−	0.0698303i
$486$		0			0
$487$	−33.8967	+	14.0405i	−1.53601	+	0.636235i	−0.980719	−	0.195423i	$-0.937392\pi$
$487$	−33.8967	+	14.0405i	−1.53601	+	0.636235i	−0.555288	+	0.831658i	$0.687392\pi$
$488$	4.74594	+	12.4745i	0.214839	+	0.564695i
$489$		0			0
$490$	29.2509	−	11.7844i	1.32142	−	0.532363i
$491$	−6.13196	+	9.17712i	−0.276731	+	0.414158i	−0.943636	−	0.330985i	$-0.892619\pi$
$491$	−6.13196	+	9.17712i	−0.276731	+	0.414158i	0.666904	+	0.745143i	$0.267619\pi$
$492$		0			0
$493$	−29.0704	−	5.78246i	−1.30926	−	0.260429i
$494$	18.8415	+	28.8004i	0.847721	+	1.29579i
$495$		0			0
$496$	2.39150	+	2.58508i	0.107382	+	0.116073i
$497$	−1.65515	+	1.65515i	−0.0742436	+	0.0742436i
$498$		0			0
$499$	−2.51984	+	12.6681i	−0.112804	+	0.567102i	0.882501	+	0.470310i	$0.155858\pi$
$499$	−2.51984	+	12.6681i	−0.112804	+	0.567102i	−0.995305	+	0.0967914i	$0.969142\pi$
$500$	1.75960	−	2.52573i	0.0786916	−	0.112954i
$501$		0			0
$502$	2.91713	+	1.24167i	0.130198	+	0.0554183i
$503$	5.73399	−	13.8431i	0.255666	−	0.617232i	−0.742977	−	0.669317i	$-0.766587\pi$
$503$	5.73399	−	13.8431i	0.255666	−	0.617232i	0.998643	+	0.0520853i	$0.0165868\pi$
$504$		0			0
$505$	−0.980863	−	2.36801i	−0.0436478	−	0.105375i
$506$	4.36638	+	0.0424404i	0.194109	+	0.00188671i
$507$		0			0
$508$	9.58747	+	24.4817i	0.425375	+	1.08620i
$509$	13.9117	+	20.8204i	0.616627	+	0.922848i	1.00000		0.000745744i	$-0.000237378\pi$
$509$	13.9117	+	20.8204i	0.616627	+	0.922848i	−0.383372	+	0.923594i	$0.625237\pi$
$510$		0			0
$511$	−3.56648			−0.157772
$512$	17.6438	+	14.1667i	0.779754	+	0.626087i
$513$		0			0
$514$	15.1891	−	22.2607i	0.669964	−	0.981876i
$515$	11.5612	+	17.3025i	0.509446	+	0.762439i
$516$		0			0
$517$	3.78172	+	19.0120i	0.166320	+	0.836146i
$518$	−2.60705	−	0.0253400i	−0.114547	−	0.00111338i
$519$		0			0
$520$	31.5917	+	7.24745i	1.38539	+	0.317822i
$521$	7.37291	−	17.7998i	0.323013	−	0.779822i	−0.676063	−	0.736844i	$-0.736315\pi$
$521$	7.37291	−	17.7998i	0.323013	−	0.779822i	0.999076	−	0.0429783i	$-0.0136846\pi$
$522$		0			0
$523$	−2.21124	−	1.47750i	−0.0966907	−	0.0646067i	0.506285	−	0.862366i	$-0.331018\pi$
$523$	−2.21124	−	1.47750i	−0.0966907	−	0.0646067i	−0.602976	+	0.797760i	$0.706018\pi$
$524$	16.4845	−	23.6618i	0.720127	−	1.03367i
$525$		0			0
$526$	8.75394	+	1.82989i	0.381690	+	0.0797871i
$527$	1.92875	−	1.92875i	0.0840176	−	0.0840176i
$528$		0			0
$529$	−15.8886	−	15.8886i	−0.690811	−	0.690811i
$530$	22.4812	+	34.3640i	0.976523	+	1.49268i
$531$		0			0
$532$	3.84570	−	2.46285i	0.166732	−	0.106778i
$533$	6.50463	−	9.73487i	0.281747	−	0.421664i
$534$		0			0
$535$	18.4233	+	7.63117i	0.796507	+	0.329924i
$536$	−5.49672	−	14.4479i	−0.237422	−	0.624055i
$537$		0			0
$538$	10.2134	+	10.4139i	0.440331	+	0.448974i
$539$	−28.6573	+	5.70030i	−1.23436	+	0.245529i
$540$		0			0
$541$	17.3178	−	11.5714i	0.744550	−	0.497492i	−0.124498	−	0.992220i	$-0.539732\pi$
$541$	17.3178	−	11.5714i	0.744550	−	0.497492i	0.869048	+	0.494728i	$0.164732\pi$
$542$	1.55134	+	8.21566i	0.0666358	+	0.352893i
$543$		0			0
$544$	10.4333	−	14.0821i	0.447324	−	0.603764i
$545$			31.1009i			1.33222i
$546$		0			0
$547$	3.42930	−	2.29138i	0.146626	−	0.0979725i	−0.480093	−	0.877217i	$-0.659397\pi$
$547$	3.42930	−	2.29138i	0.146626	−	0.0979725i	0.626719	+	0.779245i	$0.284397\pi$
$548$	−10.5505	−	0.205117i	−0.450694	−	0.00876214i
$549$		0			0
$550$	−23.4462	+	22.9948i	−0.999749	+	0.980502i
$551$	60.7513	−	25.1640i	2.58809	−	1.07202i
$552$		0			0
$553$	0.670038	+	0.277539i	0.0284929	+	0.0118022i
$554$	−1.00378	−	2.49157i	−0.0426466	−	0.105857i
$555$		0			0
$556$	−2.09153	+	9.54157i	−0.0887005	+	0.404653i
$557$	−29.9106	−	5.94959i	−1.26735	−	0.252092i	−0.484772	−	0.874640i	$-0.661098\pi$
$557$	−29.9106	−	5.94959i	−1.26735	−	0.252092i	−0.782582	+	0.622548i	$0.786098\pi$
$558$		0			0
$559$	7.17112	+	7.17112i	0.303306	+	0.303306i
$560$	1.00237	−	4.18241i	0.0423580	−	0.176739i
$561$		0			0
$562$	6.46142	−	30.9105i	0.272559	−	1.30388i
$563$	−2.46552	+	12.3950i	−0.103909	+	0.522387i	0.893412	+	0.449239i	$0.148305\pi$
$563$	−2.46552	+	12.3950i	−0.103909	+	0.522387i	−0.997321	+	0.0731484i	$0.976695\pi$
$564$		0			0
$565$	−17.2674	−	11.5377i	−0.726445	−	0.485395i
$566$	−0.0867409	+	0.203786i	−0.00364599	+	0.00856576i
$567$		0			0
$568$	−3.31650	−	19.6514i	−0.139157	−	0.824554i
$569$	−1.98587	−	4.79431i	−0.0832520	−	0.200988i	0.876772	−	0.480907i	$-0.159692\pi$
$569$	−1.98587	−	4.79431i	−0.0832520	−	0.200988i	−0.960024	+	0.279919i	$0.909692\pi$
$570$		0			0
$571$	5.46069	+	27.4528i	0.228523	+	1.14886i	0.909226	+	0.416303i	$0.136674\pi$
$571$	5.46069	+	27.4528i	0.228523	+	1.14886i	−0.680703	+	0.732559i	$0.738326\pi$
$572$	−27.5166	−	12.0296i	−1.15053	−	0.502982i
$573$		0			0
$574$	−1.28329	−	0.875624i	−0.0535633	−	0.0365478i
$575$	−3.98647			−0.166247
$576$		0			0
$577$	−5.80892			−0.241829			−0.120914	−	0.992663i	$-0.538583\pi$
$577$	−5.80892			−0.241829			−0.120914	+	0.992663i	$0.538583\pi$
$578$	8.64608	+	5.89948i	0.359630	+	0.245386i
$579$		0			0
$580$	24.8066	−	56.7428i	1.03004	−	2.35612i
$581$	0.960477	+	4.82865i	0.0398473	+	0.200326i
$582$		0			0
$583$	−14.5602	−	35.1515i	−0.603023	−	1.45583i
$584$	17.5990	−	24.7453i	0.728253	−	1.02397i
$585$		0			0
$586$	−4.62078	+	10.8559i	−0.190883	+	0.448453i
$587$	−38.7045	−	25.8615i	−1.59751	−	1.06742i	−0.953065	−	0.302766i	$-0.902090\pi$
$587$	−38.7045	−	25.8615i	−1.59751	−	1.06742i	−0.644441	−	0.764654i	$-0.722910\pi$
$588$		0			0
$589$	−1.18056	+	5.93509i	−0.0486443	+	0.244551i
$590$	3.81910	−	18.2700i	0.157230	−	0.752166i
$591$		0			0
$592$	13.0405	−	17.9634i	0.535959	−	0.738293i
$593$	−10.6123	−	10.6123i	−0.435796	−	0.435796i	0.454799	−	0.890594i	$-0.349711\pi$
$593$	−10.6123	−	10.6123i	−0.435796	−	0.435796i	−0.890594	+	0.454799i	$0.849711\pi$
$594$		0			0
$595$	−3.26719	−	0.649884i	−0.133942	−	0.0266426i
$596$	−18.7204	−	4.10355i	−0.766819	−	0.168088i
$597$		0			0
$598$	−1.36226	−	3.38138i	−0.0557070	−	0.138275i
$599$	−37.1396	−	15.3837i	−1.51748	−	0.628561i	−0.540396	−	0.841411i	$-0.681726\pi$
$599$	−37.1396	−	15.3837i	−1.51748	−	0.628561i	−0.977085	+	0.212850i	$0.931726\pi$
$600$		0			0
$601$	−10.9322	+	4.52827i	−0.445934	+	0.184712i	−0.594339	−	0.804215i	$-0.702586\pi$
$601$	−10.9322	+	4.52827i	−0.445934	+	0.184712i	0.148405	+	0.988927i	$0.452586\pi$
$602$	0.960751	−	0.942254i	0.0391573	−	0.0384034i
$603$		0			0
$604$	0.641438	−	32.9933i	0.0260997	−	1.34248i
$605$	18.7998	−	12.5616i	0.764322	−	0.510704i
$606$		0			0
$607$		−	20.3426i		−	0.825679i	−0.910804	−	0.412840i	$-0.864537\pi$
$607$		−	20.3426i		−	0.825679i	0.910804	−	0.412840i	$-0.135463\pi$
$608$	−1.88881	+	38.8357i	−0.0766012	+	1.57500i
$609$		0			0
$610$	4.00769	+	21.2241i	0.162266	+	0.859337i
$611$	13.4559	−	8.99093i	0.544366	−	0.363734i
$612$		0			0
$613$	26.9544	−	5.36156i	1.08868	−	0.216552i	0.382053	−	0.924140i	$-0.375217\pi$
$613$	26.9544	−	5.36156i	1.08868	−	0.216552i	0.706625	+	0.707589i	$0.250217\pi$
$614$	33.9010	+	34.5665i	1.36813	+	1.39499i
$615$		0			0
$616$	−1.63164	+	3.63553i	−0.0657405	+	0.146480i
$617$	−12.8642	−	5.32854i	−0.517895	−	0.214519i	0.108397	−	0.994108i	$-0.465428\pi$
$617$	−12.8642	−	5.32854i	−0.517895	−	0.214519i	−0.626292	+	0.779589i	$0.715428\pi$
$618$		0			0
$619$	−19.3117	+	28.9020i	−0.776204	+	1.16167i	0.206854	+	0.978372i	$0.433678\pi$
$619$	−19.3117	+	28.9020i	−0.776204	+	1.16167i	−0.983057	+	0.183299i	$0.941322\pi$
$620$	3.07352	+	4.79923i	0.123435	+	0.192742i
$621$		0			0
$622$	10.1961	+	15.5854i	0.408827	+	0.624917i
$623$	−0.417200	−	0.417200i	−0.0167148	−	0.0167148i
$624$		0			0
$625$	−15.8365	+	15.8365i	−0.633460	+	0.633460i
$626$	0.582444	+	0.121752i	0.0232792	+	0.00486619i
$627$		0			0
$628$	−0.362496	−	0.252540i	−0.0144652	−	0.0100775i
$629$	−14.2956	−	9.55198i	−0.570001	−	0.380862i
$630$		0			0
$631$	−10.3488	+	24.9842i	−0.411980	+	0.994607i	0.572626	+	0.819817i	$0.305925\pi$
$631$	−10.3488	+	24.9842i	−0.411980	+	0.994607i	−0.984606	+	0.174790i	$0.944075\pi$
$632$	−5.23200	+	3.27940i	−0.208118	+	0.130447i
$633$		0			0
$634$	−23.7511	−	0.230856i	−0.943276	−	0.00916846i
$635$	8.30076	+	41.7307i	0.329406	+	1.65603i
$636$		0			0
$637$	13.5523	+	20.2824i	0.536961	+	0.803620i
$638$	−32.3401	+	47.3966i	−1.28036	+	1.87645i
$639$		0			0
$640$	24.0725	+	27.5931i	0.951551	+	1.09071i
$641$	26.5599			1.04905			0.524527	−	0.851394i	$-0.324242\pi$
$641$	26.5599			1.04905			0.524527	+	0.851394i	$0.324242\pi$
$642$		0			0
$643$	−7.23987	−	10.8352i	−0.285513	−	0.427300i	0.660795	−	0.750566i	$-0.270219\pi$
$643$	−7.23987	−	10.8352i	−0.285513	−	0.427300i	−0.946308	+	0.323266i	$0.895219\pi$
$644$	−0.450416	+	0.176391i	−0.0177489	+	0.00695079i
$645$		0			0
$646$	30.1141	+	0.292703i	1.18482	+	0.0115163i
$647$	−4.72206	−	11.4001i	−0.185643	−	0.448183i	0.803469	−	0.595347i	$-0.202985\pi$
$647$	−4.72206	−	11.4001i	−0.185643	−	0.448183i	−0.989112	+	0.147164i	$0.952985\pi$
$648$		0			0
$649$	−6.61803	+	15.9773i	−0.259780	+	0.627165i
$650$	25.2268	+	10.7377i	0.989475	+	0.421167i
$651$		0			0
$652$	−29.3502	−	20.4474i	−1.14944	−	0.800783i
$653$	−1.67322	+	8.41182i	−0.0654780	+	0.329180i	−0.999615	−	0.0277336i	$-0.991171\pi$
$653$	−1.67322	+	8.41182i	−0.0654780	+	0.329180i	0.934137	+	0.356914i	$0.116171\pi$
$654$		0			0
$655$	32.9993	−	32.9993i	1.28939	−	1.28939i
$656$	12.4078	−	4.58301i	0.484443	−	0.178936i
$657$		0			0
$658$	−1.17561	−	1.79699i	−0.0458301	−	0.0700541i
$659$	30.9667	+	6.15965i	1.20629	+	0.239946i	0.756985	−	0.653432i	$-0.226672\pi$
$659$	30.9667	+	6.15965i	1.20629	+	0.239946i	0.449305	+	0.893378i	$0.351672\pi$
$660$		0			0
$661$	12.7193	−	19.0357i	0.494722	−	0.740403i	−0.497147	−	0.867666i	$-0.665619\pi$
$661$	12.7193	−	19.0357i	0.494722	−	0.740403i	0.991869	+	0.127263i	$0.0406192\pi$
$662$	43.1560	−	17.3863i	1.67731	−	0.675739i
$663$		0			0
$664$	−38.2422	−	17.1632i	−1.48408	−	0.666061i
$665$	6.82777	−	2.82815i	0.264769	−	0.109671i
$666$		0			0
$667$	−6.83135	+	1.35884i	−0.264511	+	0.0526145i
$668$	25.4698	+	26.4797i	0.985455	+	1.02453i
$669$		0			0
$670$	−4.64167	−	24.5816i	−0.179324	−	0.949669i
$671$		−	20.0124i		−	0.772569i
$672$		0			0
$673$			24.9965i			0.963543i	0.876297	+	0.481772i	$0.160007\pi$
$673$			24.9965i			0.963543i	−0.876297	+	0.481772i	$0.839993\pi$
$674$	3.79731	−	0.717037i	0.146267	−	0.0276192i
$675$		0			0
$676$	0.0180431	−	0.928073i	0.000693965	−	0.0356951i
$677$	−33.5580	+	6.67509i	−1.28974	+	0.256545i	−0.791860	−	0.610703i	$-0.790887\pi$
$677$	−33.5580	+	6.67509i	−1.28974	+	0.256545i	−0.497877	+	0.867247i	$0.665887\pi$
$678$		0			0
$679$	0.747501	−	0.309625i	0.0286865	−	0.0118823i
$680$	20.6312	−	19.4619i	0.791172	−	0.746328i
$681$		0			0
$682$	−1.97320	−	4.89784i	−0.0755578	−	0.187548i
$683$	−0.339438	+	0.508005i	−0.0129882	+	0.0194383i	−0.837907	−	0.545813i	$-0.816221\pi$
$683$	−0.339438	+	0.508005i	−0.0129882	+	0.0194383i	0.824919	+	0.565251i	$0.191221\pi$
$684$		0			0
$685$	−16.7489	−	3.33156i	−0.639942	−	0.127292i
$686$	5.46071	−	3.57245i	0.208491	−	0.136397i
$687$		0			0
$688$	1.79676	+	11.3156i	0.0685009	+	0.431403i
$689$	−22.4608	+	22.4608i	−0.855688	+	0.855688i
$690$		0			0
$691$	8.80950	−	44.2884i	0.335129	−	1.68481i	−0.334725	−	0.942316i	$-0.608643\pi$
$691$	8.80950	−	44.2884i	0.335129	−	1.68481i	0.669854	−	0.742492i	$-0.266357\pi$
$692$	−4.63238	−	25.9111i	−0.176097	−	0.984994i
$693$		0			0
$694$	3.36410	−	7.90349i	0.127699	−	0.300012i
$695$	−6.04935	+	14.6044i	−0.229465	+	0.553977i
$696$		0			0
$697$	−3.92060	−	9.46516i	−0.148503	−	0.358518i
$698$	0.0398393	−	4.09877i	0.00150794	−	0.155141i
$699$		0			0
$700$	1.45727	−	3.33337i	0.0550796	−	0.125990i
$701$	−18.1076	−	27.1000i	−0.683915	−	1.02355i	−0.997265	−	0.0739139i	$-0.976451\pi$
$701$	−18.1076	−	27.1000i	−0.683915	−	1.02355i	0.313349	−	0.949638i	$-0.398549\pi$
$702$		0			0
$703$	38.1433			1.43860
$704$	−17.1730	−	29.2606i	−0.647233	−	1.10280i
$705$		0			0
$706$	40.8633	+	27.8823i	1.53791	+	1.04936i
$707$	−0.146159	−	0.218742i	−0.00549687	−	0.00822665i
$708$		0			0
$709$	8.67202	+	43.5972i	0.325684	+	1.63733i	0.702963	+	0.711226i	$0.251860\pi$
$709$	8.67202	+	43.5972i	0.325684	+	1.63733i	−0.377279	+	0.926100i	$0.623140\pi$
$710$	0.313463	−	32.2500i	0.0117641	−	1.21032i
$711$		0			0
$712$	4.95336	−	0.835961i	0.185635	−	0.0313290i
$713$	0.245293	−	0.592190i	0.00918630	−	0.0221777i
$714$		0			0
$715$	−40.4089	−	27.0004i	−1.51121	−	1.00976i
$716$	−44.5635	+	7.96705i	−1.66542	+	0.297743i
$717$		0			0
$718$	3.57470	−	17.1009i	0.133407	−	0.638199i
$719$	10.7756	−	10.7756i	0.401864	−	0.401864i	−0.477026	−	0.878889i	$-0.658285\pi$
$719$	10.7756	−	10.7756i	0.401864	−	0.401864i	0.878889	+	0.477026i	$0.158285\pi$
$720$		0			0
$721$	1.51031	+	1.51031i	0.0562467	+	0.0562467i
$722$	−33.4245	+	21.8667i	−1.24393	+	0.813793i
$723$		0			0
$724$	−6.32948	+	28.8752i	−0.235233	+	1.07314i
$725$	29.1029	−	43.5556i	1.08085	−	1.61761i
$726$		0			0
$727$	8.49854	+	3.52021i	0.315193	+	0.130557i	0.534671	−	0.845060i	$-0.320435\pi$
$727$	8.49854	+	3.52021i	0.315193	+	0.130557i	−0.219478	+	0.975617i	$0.570435\pi$
$728$	3.32540	+	0.0969911i	0.123247	+	0.00359473i
$729$		0			0
$730$	35.0835	−	34.4080i	1.29850	−	1.27350i
$731$	8.70372	−	1.73128i	0.321919	−	0.0640336i
$732$		0			0
$733$	−5.58778	+	3.73364i	−0.206389	+	0.137905i	−0.654469	−	0.756088i	$-0.727108\pi$
$733$	−5.58778	+	3.73364i	−0.206389	+	0.137905i	0.448080	+	0.893993i	$0.352108\pi$
$734$	14.3510	−	2.70987i	0.529707	−	0.100023i
$735$		0			0
$736$	0.998751	−	3.99554i	0.0368145	−	0.147278i
$737$			23.1782i			0.853780i
$738$		0			0
$739$	−28.0412	+	18.7365i	−1.03151	+	0.689235i	−0.951528	−	0.307561i	$-0.900487\pi$
$739$	−28.0412	+	18.7365i	−1.03151	+	0.689235i	−0.0799848	+	0.996796i	$0.525487\pi$
$740$	25.8900	−	24.9025i	0.951735	−	0.915434i
$741$		0			0
$742$	2.95125	+	3.00919i	0.108344	+	0.110471i
$743$	−31.3039	+	12.9665i	−1.14843	+	0.475694i	−0.874006	−	0.485915i	$-0.838486\pi$
$743$	−31.3039	+	12.9665i	−1.14843	+	0.475694i	−0.274421	+	0.961610i	$0.588486\pi$
$744$		0			0
$745$	−28.6537	−	11.8687i	−1.04979	−	0.434837i
$746$	−29.8420	+	12.0225i	−1.09259	+	0.440176i
$747$		0			0
$748$	−22.1295	+	14.1721i	−0.809134	+	0.518184i
$749$	2.00744	+	0.399305i	0.0733503	+	0.0145903i
$750$		0			0
$751$	−22.7813	−	22.7813i	−0.831303	−	0.831303i	0.156392	−	0.987695i	$-0.450014\pi$
$751$	−22.7813	−	22.7813i	−0.831303	−	0.831303i	−0.987695	+	0.156392i	$0.950014\pi$
$752$	18.2692	+	0.710629i	0.666210	+	0.0259140i
$753$		0			0
$754$	46.8895	+	9.80162i	1.70762	+	0.356954i
$755$	10.4184	−	52.3769i	0.379165	−	1.90619i
$756$		0			0
$757$	−35.0984	−	23.4520i	−1.27567	−	0.852378i	−0.281437	−	0.959580i	$-0.590811\pi$
$757$	−35.0984	−	23.4520i	−1.27567	−	0.852378i	−0.994237	+	0.107202i	$0.965811\pi$
$758$	−28.0781	−	11.9514i	−1.01984	−	0.434093i
$759$		0			0
$760$	−14.0695	+	61.3289i	−0.510353	+	2.22463i
$761$	0.451808	+	1.09076i	0.0163780	+	0.0395401i	0.931857	−	0.362826i	$-0.118188\pi$
$761$	0.451808	+	1.09076i	0.0163780	+	0.0395401i	−0.915479	+	0.402366i	$0.868188\pi$
$762$		0			0
$763$	0.622768	+	3.13087i	0.0225457	+	0.113345i
$764$	4.88310	+	12.4690i	0.176664	+	0.451113i
$765$		0			0
$766$	−14.6646	+	21.4919i	−0.529852	+	0.776534i
$767$	14.4378			0.521318
$768$		0			0
$769$	−46.3441			−1.67121			−0.835605	−	0.549331i	$-0.814883\pi$
$769$	−46.3441			−1.67121			−0.835605	+	0.549331i	$0.814883\pi$
$770$	−3.63467	+	5.32685i	−0.130984	+	0.191966i
$771$		0			0
$772$	−2.28671	−	5.83914i	−0.0823007	−	0.210155i
$773$	3.29586	+	16.5694i	0.118544	+	0.595960i	0.993696	+	0.112111i	$0.0357614\pi$
$773$	3.29586	+	16.5694i	0.118544	+	0.595960i	−0.875152	+	0.483848i	$0.839239\pi$
$774$		0			0
$775$	1.84481	+	4.45375i	0.0662674	+	0.159984i
$776$	−1.54032	+	6.71426i	−0.0552942	+	0.241028i
$777$		0			0
$778$	−23.2170	−	9.88224i	−0.832369	−	0.354296i
$779$	18.8983	+	12.6274i	0.677101	+	0.452425i
$780$		0			0
$781$	−5.82972	+	29.3080i	−0.208604	+	1.04872i
$782$	−3.12245	−	0.652706i	−0.111659	−	0.0233407i
$783$		0			0
$784$	−1.07115	+	27.5377i	−0.0382554	+	0.983491i
$785$	−0.505546	−	0.505546i	−0.0180437	−	0.0180437i
$786$		0			0
$787$	29.7168	+	5.91104i	1.05929	+	0.210706i	0.693843	−	0.720126i	$-0.255916\pi$
$787$	29.7168	+	5.91104i	1.05929	+	0.210706i	0.365447	+	0.930832i	$0.380916\pi$
$788$	−26.3776	+	16.8927i	−0.939665	+	0.601778i
$789$		0			0
$790$	−9.26876	+	3.73412i	−0.329768	+	0.132854i
$791$	−1.96931	−	0.815714i	−0.0700205	−	0.0290034i
$792$		0			0
$793$	−15.4357	+	6.39367i	−0.548137	+	0.227046i
$794$	11.6933	+	11.9228i	0.414978	+	0.423124i
$795$		0			0
$796$	−6.16901	+	5.93372i	−0.218655	+	0.210315i
$797$	25.2213	−	16.8523i	0.893385	−	0.596940i	−0.0218948	−	0.999760i	$-0.506970\pi$
$797$	25.2213	−	16.8523i	0.893385	−	0.596940i	0.915279	+	0.402820i	$0.131970\pi$
$798$		0			0
$799$		−	14.1610i		−	0.500981i
$800$	15.9370	+	26.5597i	0.563458	+	0.939029i
$801$		0			0
$802$	−28.0077	+	5.28862i	−0.988986	+	0.186748i
$803$	−37.8570	+	25.2952i	−1.33594	+	0.892649i
$804$		0			0
$805$	−0.767767	+	0.152718i	−0.0270602	+	0.00538261i
$806$	−3.14733	+	3.08673i	−0.110860	+	0.108726i
$807$		0			0
$808$	2.23893	+	0.0653024i	0.0787653	+	0.00229733i
$809$	2.77252	+	1.14841i	0.0974765	+	0.0403761i	0.430889	−	0.902405i	$-0.358200\pi$
$809$	2.77252	+	1.14841i	0.0974765	+	0.0403761i	−0.333412	+	0.942781i	$0.608200\pi$
$810$		0			0
$811$	23.3343	−	34.9223i	0.819378	−	1.22629i	−0.151913	−	0.988394i	$-0.548543\pi$
$811$	23.3343	−	34.9223i	0.819378	−	1.22629i	0.971291	−	0.237893i	$-0.0764566\pi$
$812$	1.36100	−	6.20891i	0.0477619	−	0.217890i
$813$		0			0
$814$	−27.8526	+	18.2215i	−0.976234	+	0.638662i
$815$	−40.9326	−	40.9326i	−1.43381	−	1.43381i
$816$		0			0
$817$	−13.9213	+	13.9213i	−0.487044	+	0.487044i
$818$	6.80019	−	32.5311i	0.237763	−	1.13742i
$819$		0			0
$820$	21.0714	−	3.76713i	0.735844	−	0.131554i
$821$	−32.4829	−	21.7044i	−1.13366	−	0.757487i	−0.160368	−	0.987057i	$-0.551268\pi$
$821$	−32.4829	−	21.7044i	−1.13366	−	0.757487i	−0.973292	+	0.229570i	$0.926268\pi$
$822$		0			0
$823$	13.3449	−	32.2174i	0.465173	−	1.12303i	−0.501073	−	0.865405i	$-0.667061\pi$
$823$	13.3449	−	32.2174i	0.465173	−	1.12303i	0.966246	−	0.257622i	$-0.0829388\pi$
$824$	−17.9317	+	3.02627i	−0.624680	+	0.105425i
$825$		0			0
$826$	0.0186201	−	1.91568i	0.000647875	−	0.0666551i
$827$	7.94105	+	39.9224i	0.276137	+	1.38824i	0.830990	+	0.556288i	$0.187775\pi$
$827$	7.94105	+	39.9224i	0.276137	+	1.38824i	−0.554852	+	0.831949i	$0.687225\pi$
$828$		0			0
$829$	31.8213	+	47.6240i	1.10520	+	1.65405i	0.638460	+	0.769655i	$0.279572\pi$
$829$	31.8213	+	47.6240i	1.10520	+	1.65405i	0.466740	+	0.884395i	$0.345428\pi$
$830$	−56.0331	−	38.2331i	−1.94494	−	1.32709i
$831$		0			0
$832$	−17.0823	+	22.5940i	−0.592224	+	0.783307i
$833$	21.3453			0.739571
$834$		0			0
$835$	33.0328	+	49.4371i	1.14315	+	1.71084i
$836$	23.3530	−	53.4179i	0.807680	−	1.84750i
$837$		0			0
$838$	−0.0407462	+	4.19208i	−0.00140756	+	0.144813i
$839$	14.5831	+	35.2068i	0.503465	+	1.21547i	0.947585	+	0.319505i	$0.103517\pi$
$839$	14.5831	+	35.2068i	0.503465	+	1.21547i	−0.444119	+	0.895968i	$0.646483\pi$
$840$		0			0
$841$	23.9274	−	57.7659i	0.825083	−	1.99193i
$842$	18.9172	−	44.4435i	0.651931	−	1.53162i
$843$		0			0
$844$	−7.27649	−	40.7009i	−0.250467	−	1.40098i
$845$	0.293061	−	1.47332i	0.0100816	−	0.0506836i
$846$		0			0
$847$	1.64101	−	1.64101i	0.0563856	−	0.0563856i
$848$	−35.4418	+	5.62767i	−1.21708	+	0.193255i
$849$		0			0
$850$	20.0764	−	13.1342i	0.688613	−	0.450498i
$851$	−3.96263	−	0.788217i	−0.135837	−	0.0270197i
$852$		0			0
$853$	30.9971	−	46.3904i	1.06132	−	1.58838i	0.284474	−	0.958684i	$-0.408181\pi$
$853$	30.9971	−	46.3904i	1.06132	−	1.58838i	0.776845	−	0.629692i	$-0.216819\pi$
$854$	0.828439	+	2.05633i	0.0283486	+	0.0703663i
$855$		0			0
$856$	−12.6764	+	11.9579i	−0.433269	+	0.408711i
$857$	−15.6625	+	6.48761i	−0.535020	+	0.221612i	−0.633800	−	0.773497i	$-0.718506\pi$
$857$	−15.6625	+	6.48761i	−0.535020	+	0.221612i	0.0987804	+	0.995109i	$0.468506\pi$
$858$		0			0
$859$	−5.32236	+	1.05868i	−0.181597	+	0.0361218i	−0.285051	−	0.958512i	$-0.592010\pi$
$859$	−5.32236	+	1.05868i	−0.181597	+	0.0361218i	0.103454	+	0.994634i	$0.467010\pi$
$860$	−0.360404	+	18.5379i	−0.0122897	+	0.632137i
$861$		0			0
$862$	−54.6131	+	10.3125i	−1.86013	+	0.351244i
$863$			12.0786i			0.411160i	0.978640	+	0.205580i	$0.0659081\pi$
$863$			12.0786i			0.411160i	−0.978640	+	0.205580i	$0.934092\pi$
$864$		0			0
$865$		−	42.5967i		−	1.44833i
$866$	7.24086	+	38.3464i	0.246054	+	1.30306i
$867$		0			0
$868$	0.405505	+	0.421585i	0.0137637	+	0.0143095i
$869$	9.08067	−	1.80626i	0.308041	−	0.0612731i
$870$		0			0
$871$	17.8775	−	7.40510i	0.605756	−	0.250912i
$872$	−24.7960	−	11.1285i	−0.839699	−	0.376859i
$873$		0			0
$874$	6.56426	−	2.64456i	0.222039	−	0.0894534i
$875$	0.284063	−	0.425131i	0.00960310	−	0.0143721i
$876$		0			0
$877$	19.9561	+	3.96951i	0.673868	+	0.134041i	0.520151	−	0.854074i	$-0.325876\pi$
$877$	19.9561	+	3.96951i	0.673868	+	0.134041i	0.153717	+	0.988115i	$0.450876\pi$
$878$	21.7396	+	33.2303i	0.733676	+	1.12147i
$879$		0			0
$880$	−19.0238	−	51.5041i	−0.641293	−	1.73620i
$881$	−20.2066	+	20.2066i	−0.680777	+	0.680777i	−0.960175	−	0.279398i	$-0.909865\pi$
$881$	−20.2066	+	20.2066i	−0.680777	+	0.680777i	0.279398	+	0.960175i	$0.409865\pi$
$882$		0			0
$883$	−2.71690	+	13.6588i	−0.0914310	+	0.459655i	0.907762	+	0.419486i	$0.137790\pi$
$883$	−2.71690	+	13.6588i	−0.0914310	+	0.459655i	−0.999193	+	0.0401690i	$0.987210\pi$
$884$	18.0011	+	12.5408i	0.605443	+	0.421794i
$885$		0			0
$886$	9.33938	+	3.97528i	0.313763	+	0.133552i
$887$	2.29326	−	5.53641i	0.0770000	−	0.185894i	−0.880692	−	0.473689i	$-0.842922\pi$
$887$	2.29326	−	5.53641i	0.0770000	−	0.185894i	0.957692	+	0.287795i	$0.0929221\pi$
$888$		0			0
$889$	1.67124	+	4.03474i	0.0560517	+	0.135321i
$890$	8.12898	+	0.0790121i	0.272484	+	0.00264849i
$891$		0			0
$892$	33.7935	−	13.2341i	1.13149	−	0.443112i
$893$	17.4541	+	26.1219i	0.584078	+	0.874134i
$894$		0			0
$895$	−73.2605			−2.44883
$896$	2.97586	+	2.29572i	0.0994166	+	0.0766945i
$897$		0			0
$898$	7.78244	−	11.4057i	0.259703	−	0.380613i
$899$	4.67944	+	7.00328i	0.156068	+	0.233572i
$900$		0			0
$901$	5.42256	+	27.2611i	0.180652	+	0.908198i
$902$	−19.8320	−	0.192763i	−0.660333	−	0.00641831i
$903$		0			0
$904$	15.3773	−	9.63847i	0.511443	−	0.320571i
$905$	−18.3068	+	44.1966i	−0.608539	+	1.46914i
$906$		0			0
$907$	41.9267	+	28.0145i	1.39215	+	0.930207i	0.999947	+	0.0103304i	$0.00328832\pi$
$907$	41.9267	+	28.0145i	1.39215	+	0.930207i	0.392207	+	0.919877i	$0.371712\pi$
$908$	−26.6194	−	18.5449i	−0.883396	−	0.615435i
$909$		0			0
$910$	5.26986	+	1.10159i	0.174694	+	0.0365174i
$911$	−10.6573	+	10.6573i	−0.353092	+	0.353092i	−0.861259	−	0.508167i	$-0.830323\pi$
$911$	−10.6573	+	10.6573i	−0.353092	+	0.353092i	0.508167	+	0.861259i	$0.330323\pi$
$912$		0			0
$913$	44.4423	+	44.4423i	1.47082	+	1.47082i
$914$	−24.8110	−	37.9251i	−0.820674	−	1.25445i
$915$		0			0
$916$	−1.27192	−	1.98608i	−0.0420254	−	0.0656219i
$917$	2.66119	−	3.98276i	0.0878804	−	0.131522i
$918$		0			0
$919$	−48.0863	−	19.9180i	−1.58622	−	0.657034i	−0.596837	−	0.802362i	$-0.703576\pi$
$919$	−48.0863	−	19.9180i	−1.58622	−	0.657034i	−0.989383	+	0.145328i	$0.953576\pi$
$920$	2.72899	−	6.08060i	0.0899721	−	0.200472i
$921$		0			0
$922$	−34.8704	−	35.5550i	−1.14840	−	1.17094i
$923$	24.4680	−	4.86698i	0.805373	−	0.160199i
$924$		0			0
$925$	25.2651	−	16.8816i	0.830712	−	0.555064i
$926$	−7.43252	−	39.3614i	−0.244248	−	1.29350i
$927$		0			0
$928$	36.3634	+	40.0814i	1.19369	+	1.31573i
$929$		−	47.7676i		−	1.56721i	−0.621262	−	0.783603i	$-0.713380\pi$
$929$		−	47.7676i		−	1.56721i	0.621262	−	0.783603i	$-0.286620\pi$
$930$		0			0
$931$	−39.3743	+	26.3090i	−1.29044	+	0.862244i
$932$	0.137120	−	7.05299i	0.00449153	−	0.231028i
$933$		0			0
$934$	−16.2182	+	15.9059i	−0.530674	+	0.520458i
$935$	−39.2894	+	16.2742i	−1.28490	+	0.532223i
$936$		0			0
$937$	−40.2328	−	16.6650i	−1.31435	−	0.544421i	−0.388198	−	0.921576i	$-0.626902\pi$
$937$	−40.2328	−	16.6650i	−1.31435	−	0.544421i	−0.926150	+	0.377155i	$0.876902\pi$
$938$	−0.959492	−	2.38163i	−0.0313285	−	0.0777631i
$939$		0			0
$940$	28.9012	+	6.33518i	0.942652	+	0.206631i
$941$	38.6865	+	7.69522i	1.26114	+	0.250857i	0.779997	−	0.625783i	$-0.215220\pi$
$941$	38.6865	+	7.69522i	1.26114	+	0.250857i	0.481147	+	0.876640i	$0.340220\pi$
$942$		0			0
$943$	−1.70237	−	1.70237i	−0.0554367	−	0.0554367i
$944$	13.1997	+	9.58226i	0.429614	+	0.311876i
$945$		0			0
$946$	3.51512	−	16.8158i	0.114286	−	0.546730i
$947$	−3.32492	+	16.7155i	−0.108045	+	0.543180i	0.888410	+	0.459052i	$0.151811\pi$
$947$	−3.32492	+	16.7155i	−0.108045	+	0.543180i	−0.996455	+	0.0841288i	$0.973189\pi$
$948$		0			0
$949$	31.6051	+	21.1179i	1.02595	+	0.685515i
$950$	−20.8451	+	48.9727i	−0.676304	+	1.58888i
$951$		0			0
$952$	1.68720	−	2.37231i	0.0546825	−	0.0768870i
$953$	0.606561	+	1.46437i	0.0196484	+	0.0474355i	0.933399	−	0.358840i	$-0.116827\pi$
$953$	0.606561	+	1.46437i	0.0196484	+	0.0474355i	−0.913751	+	0.406275i	$0.866827\pi$
$954$		0			0
$955$	4.22775	+	21.2543i	0.136807	+	0.687774i
$956$	6.28331	−	14.3725i	0.203217	−	0.464840i
$957$		0			0
$958$	−36.0060	−	24.5680i	−1.16330	−	0.793755i
$959$	−1.75279			−0.0566005
$960$		0			0
$961$	30.2249			0.974996
$962$	22.9529	+	15.6614i	0.740030	+	0.504945i
$963$		0			0
$964$	15.5150	+	6.78279i	0.499705	+	0.218459i
$965$	−1.97982	−	9.95324i	−0.0637327	−	0.320406i
$966$		0			0
$967$	20.5832	+	49.6922i	0.661910	+	1.59799i	0.794806	+	0.606863i	$0.207572\pi$
$967$	20.5832	+	49.6922i	0.661910	+	1.59799i	−0.132896	+	0.991130i	$0.542428\pi$
$968$	3.28815	+	19.4835i	0.105685	+	0.626222i
$969$		0			0
$970$	−4.36603	+	10.2574i	−0.140185	+	0.329345i
$971$	−44.7859	−	29.9250i	−1.43725	−	0.960338i	−0.998080	−	0.0619328i	$-0.980274\pi$
$971$	−44.7859	−	29.9250i	−1.43725	−	0.960338i	−0.439167	−	0.898405i	$-0.644726\pi$
$972$		0			0
$973$	−0.316535	+	1.59133i	−0.0101477	+	0.0510157i
$974$	10.6168	−	50.7891i	0.340183	−	1.62739i
$975$		0			0
$976$	−18.3555	−	4.39915i	−0.587544	−	0.140813i
$977$	−10.3049	−	10.3049i	−0.329682	−	0.329682i	0.522783	−	0.852466i	$-0.324894\pi$
$977$	−10.3049	−	10.3049i	−0.329682	−	0.329682i	−0.852466	+	0.522783i	$0.824894\pi$
$978$		0			0
$979$	−7.38742	−	1.46945i	−0.236103	−	0.0469638i
$980$	−9.54921	+	43.5636i	−0.305038	+	1.39159i
$981$		0			0
$982$	−5.83286	−	14.4782i	−0.186134	−	0.462018i
$983$	3.68355	+	1.52578i	0.117487	+	0.0486647i	0.440653	−	0.897678i	$-0.354747\pi$
$983$	3.68355	+	1.52578i	0.117487	+	0.0486647i	−0.323166	+	0.946342i	$0.604747\pi$
$984$		0			0
$985$	−46.8317	+	19.3983i	−1.49218	+	0.618082i
$986$	29.9266	−	29.3504i	0.953057	−	0.934708i
$987$		0			0
$988$	−48.6625	−	0.946070i	−1.54816	−	0.0300985i
$989$	1.73393	−	1.15858i	0.0551359	−	0.0368406i
$990$		0			0
$991$			22.4878i			0.714348i	0.934038	+	0.357174i	$0.116260\pi$
$991$			22.4878i			0.714348i	−0.934038	+	0.357174i	$0.883740\pi$
$992$	−4.92608	+	0.733181i	−0.156403	+	0.0232785i
$993$		0			0
$994$	−0.614221	−	3.25282i	−0.0194819	−	0.103173i
$995$	−11.5174	+	7.69569i	−0.365127	+	0.243970i
$996$		0			0
$997$	36.8027	−	7.32050i	1.16555	−	0.231843i	0.425860	−	0.904789i	$-0.359972\pi$
$997$	36.8027	−	7.32050i	1.16555	−	0.231843i	0.739691	+	0.672946i	$0.234972\pi$
$998$	−12.7901	−	13.0412i	−0.404864	−	0.412812i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	576.2.bd.a.109.2		56
3.2	odd	2		64.2.i.a.45.6	yes	56
12.11	even	2		256.2.i.a.17.6		56
24.5	odd	2		512.2.i.b.289.6		56
24.11	even	2		512.2.i.a.289.2		56
64.37	even	16	inner	576.2.bd.a.37.2		56
192.5	odd	16		512.2.i.b.225.6		56
192.59	even	16		512.2.i.a.225.2		56
192.101	odd	16		64.2.i.a.37.6	✓	56
192.155	even	16		256.2.i.a.241.6		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
64.2.i.a.37.6	✓	56	192.101	odd	16
64.2.i.a.45.6	yes	56	3.2	odd	2
256.2.i.a.17.6		56	12.11	even	2
256.2.i.a.241.6		56	192.155	even	16
512.2.i.a.225.2		56	192.59	even	16
512.2.i.a.289.2		56	24.11	even	2
512.2.i.b.225.6		56	192.5	odd	16
512.2.i.b.289.6		56	24.5	odd	2
576.2.bd.a.37.2		56	64.37	even	16	inner
576.2.bd.a.109.2		56	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 576 = 2^{6} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	576.bd (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.797087 + 1.16818i) q^{2} +(-0.729306 - 1.86229i) q^{4} +(-0.631428 - 3.17440i) q^{5} +(-0.127129 - 0.306917i) q^{7} +(2.75681 + 0.632441i) q^{8} +O(q^{10})\)	\(q+(-0.797087 + 1.16818i) q^{2} +(-0.729306 - 1.86229i) q^{4} +(-0.631428 - 3.17440i) q^{5} +(-0.127129 - 0.306917i) q^{7} +(2.75681 + 0.632441i) q^{8} +(4.21159 + 1.79265i) q^{10} +(-3.52624 - 2.35616i) q^{11} +(-0.690738 + 3.47257i) q^{13} +(0.459869 + 0.0961292i) q^{14} +(-2.93623 + 2.71635i) q^{16} +(2.19074 + 2.19074i) q^{17} +(-6.74130 - 1.34093i) q^{19} +(-5.45115 + 3.49101i) q^{20} +(5.56314 - 2.24123i) q^{22} +(0.672631 + 0.278613i) q^{23} +(-5.05873 + 2.09540i) q^{25} +(-3.50602 - 3.57485i) q^{26} +(-0.478852 + 0.460588i) q^{28} +(-7.95458 + 5.31508i) q^{29} -0.880409i q^{31} +(-0.832774 - 5.59522i) q^{32} +(-4.30540 + 0.812978i) q^{34} +(-0.894006 + 0.597355i) q^{35} +(-5.44280 + 1.08264i) q^{37} +(6.93985 - 6.80624i) q^{38} +(0.266893 - 9.15058i) q^{40} +(-3.05507 - 1.26545i) q^{41} +(1.59134 - 2.38161i) q^{43} +(-1.81614 + 8.28523i) q^{44} +(-0.861616 + 0.563678i) q^{46} +(-3.23201 - 3.23201i) q^{47} +(4.87171 - 4.87171i) q^{49} +(1.58444 - 7.57974i) q^{50} +(6.97069 - 1.24622i) q^{52} +(7.45949 + 4.98427i) q^{53} +(-5.25283 + 12.6815i) q^{55} +(-0.156365 - 0.926515i) q^{56} +(0.131499 - 13.5290i) q^{58} +(-0.795535 - 3.99942i) q^{59} +(2.62163 + 3.92355i) q^{61} +(1.02848 + 0.701762i) q^{62} +(7.20004 + 3.48704i) q^{64} +11.4595 q^{65} +(-3.03636 - 4.54423i) q^{67} +(2.48207 - 5.67751i) q^{68} +(0.0147790 - 1.52051i) q^{70} +(-2.69641 - 6.50971i) q^{71} +(4.10841 - 9.91857i) q^{73} +(3.07366 - 7.22115i) q^{74} +(2.41928 + 13.5322i) q^{76} +(-0.274857 + 1.38180i) q^{77} +(-1.54370 + 1.54370i) q^{79} +(10.4768 + 7.60558i) q^{80} +(3.91344 - 2.56021i) q^{82} +(-14.5352 - 2.89122i) q^{83} +(5.57100 - 8.33759i) q^{85} +(1.51372 + 3.75733i) q^{86} +(-8.23105 - 8.72563i) q^{88} +(1.64085 - 0.679662i) q^{89} +(1.15360 - 0.229466i) q^{91} +(0.0283034 - 1.45583i) q^{92} +(6.35178 - 1.19939i) q^{94} +22.2463i q^{95} +2.43552i q^{97} +(1.80788 + 9.57423i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 8 q^{2} - 8 q^{4} + 8 q^{5} - 8 q^{7} + 8 q^{8}+O(q^{10}) \) 56 * q + 8 * q^2 - 8 * q^4 + 8 * q^5 - 8 * q^7 + 8 * q^8	\( 56 q + 8 q^{2} - 8 q^{4} + 8 q^{5} - 8 q^{7} + 8 q^{8} - 8 q^{10} + 8 q^{11} - 8 q^{13} + 8 q^{14} - 8 q^{16} + 8 q^{17} - 8 q^{19} + 8 q^{20} + 8 q^{23} - 8 q^{25} - 32 q^{26} + 32 q^{28} + 8 q^{29} - 32 q^{32} + 32 q^{34} + 8 q^{35} - 8 q^{37} - 32 q^{38} + 32 q^{40} + 8 q^{41} - 8 q^{43} - 8 q^{46} + 8 q^{47} - 8 q^{49} + 32 q^{50} - 56 q^{52} + 8 q^{53} + 56 q^{55} + 64 q^{56} - 80 q^{58} - 56 q^{59} - 8 q^{61} + 40 q^{62} - 104 q^{64} + 16 q^{65} + 72 q^{67} + 56 q^{68} - 104 q^{70} - 56 q^{71} - 8 q^{73} + 64 q^{74} - 72 q^{76} + 8 q^{77} + 24 q^{79} - 32 q^{80} + 72 q^{82} + 8 q^{83} - 8 q^{85} - 96 q^{86} + 72 q^{88} + 8 q^{89} - 8 q^{91} - 144 q^{92} + 88 q^{94} - 128 q^{98}+O(q^{100}) \) 56 * q + 8 * q^2 - 8 * q^4 + 8 * q^5 - 8 * q^7 + 8 * q^8 - 8 * q^10 + 8 * q^11 - 8 * q^13 + 8 * q^14 - 8 * q^16 + 8 * q^17 - 8 * q^19 + 8 * q^20 + 8 * q^23 - 8 * q^25 - 32 * q^26 + 32 * q^28 + 8 * q^29 - 32 * q^32 + 32 * q^34 + 8 * q^35 - 8 * q^37 - 32 * q^38 + 32 * q^40 + 8 * q^41 - 8 * q^43 - 8 * q^46 + 8 * q^47 - 8 * q^49 + 32 * q^50 - 56 * q^52 + 8 * q^53 + 56 * q^55 + 64 * q^56 - 80 * q^58 - 56 * q^59 - 8 * q^61 + 40 * q^62 - 104 * q^64 + 16 * q^65 + 72 * q^67 + 56 * q^68 - 104 * q^70 - 56 * q^71 - 8 * q^73 + 64 * q^74 - 72 * q^76 + 8 * q^77 + 24 * q^79 - 32 * q^80 + 72 * q^82 + 8 * q^83 - 8 * q^85 - 96 * q^86 + 72 * q^88 + 8 * q^89 - 8 * q^91 - 144 * q^92 + 88 * q^94 - 128 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more