LMFDB - Embedded newform 882.2.bl.a.395.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [882,2,Mod(17,882)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(882, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([21, 25]))

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

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

chi := DirichletCharacter("882.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	882.bl (of order $42$, degree $12$, 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:	$7.04280545828$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$20$ over $\Q(\zeta_{42})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label			395.2
Character	$\chi$	$=$	882.395
Dual form			882.2.bl.a.719.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.930874 - 0.365341i) q^{2} +(0.733052 + 0.680173i) q^{4} +(-2.87414 - 1.95955i) q^{5} +(2.56704 + 0.640539i) q^{7} +(-0.433884 - 0.900969i) q^{8} +O(q^{10})$	\(q+(-0.930874 - 0.365341i) q^{2} +(0.733052 + 0.680173i) q^{4} +(-2.87414 - 1.95955i) q^{5} +(2.56704 + 0.640539i) q^{7} +(-0.433884 - 0.900969i) q^{8} +(1.95955 + 2.87414i) q^{10} +(0.594093 + 3.94155i) q^{11} +(1.87967 - 1.49899i) q^{13} +(-2.15558 - 1.53411i) q^{14} +(0.0747301 + 0.997204i) q^{16} +(-0.398865 - 0.123034i) q^{17} +(-2.31881 + 1.33876i) q^{19} +(-0.774056 - 3.39136i) q^{20} +(0.886984 - 3.88613i) q^{22} +(1.11907 + 3.62795i) q^{23} +(2.59411 + 6.60968i) q^{25} +(-2.29738 + 0.708647i) q^{26} +(1.44610 + 2.21558i) q^{28} +(8.14957 - 1.86009i) q^{29} +(-4.25632 - 2.45739i) q^{31} +(0.294755 - 0.955573i) q^{32} +(0.326344 + 0.260250i) q^{34} +(-6.12286 - 6.87125i) q^{35} +(5.45393 - 5.06051i) q^{37} +(2.64762 - 0.399065i) q^{38} +(-0.518455 + 3.43973i) q^{40} +(8.95505 - 4.31252i) q^{41} +(-1.85771 - 0.894625i) q^{43} +(-2.24543 + 3.29344i) q^{44} +(0.283722 - 3.78600i) q^{46} +(0.249013 - 0.634474i) q^{47} +(6.17942 + 3.28858i) q^{49} -7.10051i q^{50} +(2.39747 + 0.179665i) q^{52} +(7.14646 - 7.70205i) q^{53} +(6.01617 - 12.4927i) q^{55} +(-0.536692 - 2.59075i) q^{56} +(-8.26578 - 1.24587i) q^{58} +(-3.11393 + 2.12304i) q^{59} +(5.34933 + 5.76521i) q^{61} +(3.06431 + 3.84253i) q^{62} +(-0.623490 + 0.781831i) q^{64} +(-8.33977 + 0.624980i) q^{65} +(-0.00633555 + 0.0109735i) q^{67} +(-0.208705 - 0.361487i) q^{68} +(3.18926 + 8.63320i) q^{70} +(9.97398 + 2.27650i) q^{71} +(7.14472 - 2.80410i) q^{73} +(-6.92573 + 2.71815i) q^{74} +(-2.61040 - 0.595806i) q^{76} +(-0.999654 + 10.4987i) q^{77} +(6.41219 + 11.1062i) q^{79} +(1.73929 - 3.01254i) q^{80} +(-9.91156 + 0.742769i) q^{82} +(-4.36670 + 5.47567i) q^{83} +(0.905301 + 1.13521i) q^{85} +(1.40245 + 1.51148i) q^{86} +(3.29344 - 2.24543i) q^{88} +(-3.60909 - 0.543983i) q^{89} +(5.78535 - 2.64396i) q^{91} +(-1.64729 + 3.42064i) q^{92} +(-0.463599 + 0.499641i) q^{94} +(9.28795 + 0.696035i) q^{95} -15.0896i q^{97} +(-4.55081 - 5.31885i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 20 q^{4} - 4 q^{7}+O(q^{10}) $ 240 * q - 20 * q^4 - 4 * q^7	$ 240 q - 20 q^{4} - 4 q^{7} - 12 q^{10} + 20 q^{16} + 24 q^{19} - 20 q^{22} + 24 q^{25} + 4 q^{28} + 12 q^{31} - 32 q^{37} + 44 q^{40} - 48 q^{43} + 204 q^{49} + 140 q^{55} + 136 q^{58} + 88 q^{61} + 40 q^{64} - 32 q^{67} - 16 q^{70} - 24 q^{73} - 28 q^{79} - 48 q^{82} - 112 q^{85} + 4 q^{88} + 80 q^{91} + 80 q^{94}+O(q^{100}) $ 240 * q - 20 * q^4 - 4 * q^7 - 12 * q^10 + 20 * q^16 + 24 * q^19 - 20 * q^22 + 24 * q^25 + 4 * q^28 + 12 * q^31 - 32 * q^37 + 44 * q^40 - 48 * q^43 + 204 * q^49 + 140 * q^55 + 136 * q^58 + 88 * q^61 + 40 * q^64 - 32 * q^67 - 16 * q^70 - 24 * q^73 - 28 * q^79 - 48 * q^82 - 112 * q^85 + 4 * q^88 + 80 * q^91 + 80 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/882\mathbb{Z}\right)^\times$.

$n$	$199$	$785$
$\chi(n)$	$e\left(\frac{1}{42}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.930874	−	0.365341i	−0.658227	−	0.258335i
$2$	−0.930874	−	0.365341i	−0.658227	−	0.258335i
$3$		0			0
$3$		0			0
$4$	0.733052	+	0.680173i	0.366526	+	0.340086i
$5$	−2.87414	−	1.95955i	−1.28535	−	0.876339i	−0.288647	−	0.957436i	$-0.593205\pi$
$5$	−2.87414	−	1.95955i	−1.28535	−	0.876339i	−0.996706	+	0.0810970i	$0.974158\pi$
$6$		0			0
$7$	2.56704	+	0.640539i	0.970251	+	0.242101i
$7$	2.56704	+	0.640539i	0.970251	+	0.242101i
$8$	−0.433884	−	0.900969i	−0.153401	−	0.318541i
$9$		0			0
$10$	1.95955	+	2.87414i	0.619665	+	0.908882i
$11$	0.594093	+	3.94155i	0.179126	+	1.18842i	0.879943	+	0.475080i	$0.157581\pi$
$11$	0.594093	+	3.94155i	0.179126	+	1.18842i	−0.700817	+	0.713341i	$0.747181\pi$
$12$		0			0
$13$	1.87967	−	1.49899i	0.521327	−	0.415744i	−0.327154	−	0.944971i	$-0.606089\pi$
$13$	1.87967	−	1.49899i	0.521327	−	0.415744i	0.848480	+	0.529227i	$0.177518\pi$
$14$	−2.15558	−	1.53411i	−0.576102	−	0.410007i
$15$		0			0
$16$	0.0747301	+	0.997204i	0.0186825	+	0.249301i
$17$	−0.398865	−	0.123034i	−0.0967389	−	0.0298400i	0.246008	−	0.969268i	$-0.420881\pi$
$17$	−0.398865	−	0.123034i	−0.0967389	−	0.0298400i	−0.342747	+	0.939428i	$0.611357\pi$
$18$		0			0
$19$	−2.31881	+	1.33876i	−0.531971	+	0.307134i	−0.741819	−	0.670601i	$-0.766036\pi$
$19$	−2.31881	+	1.33876i	−0.531971	+	0.307134i	0.209848	+	0.977734i	$0.432703\pi$
$20$	−0.774056	−	3.39136i	−0.173084	−	0.758332i
$21$		0			0
$22$	0.886984	−	3.88613i	0.189106	−	0.828526i
$23$	1.11907	+	3.62795i	0.233343	+	0.756479i	0.994199	+	0.107558i	$0.0343032\pi$
$23$	1.11907	+	3.62795i	0.233343	+	0.756479i	−0.760856	+	0.648921i	$0.775221\pi$
$24$		0			0
$25$	2.59411	+	6.60968i	0.518821	+	1.32194i
$26$	−2.29738	+	0.708647i	−0.450553	+	0.138977i
$27$		0			0
$28$	1.44610	+	2.21558i	0.273287	+	0.418705i
$29$	8.14957	−	1.86009i	1.51334	−	0.345409i	0.616352	−	0.787471i	$-0.288610\pi$
$29$	8.14957	−	1.86009i	1.51334	−	0.345409i	0.896985	+	0.442062i	$0.145753\pi$
$30$		0			0
$31$	−4.25632	−	2.45739i	−0.764458	−	0.441360i	0.0664361	−	0.997791i	$-0.478837\pi$
$31$	−4.25632	−	2.45739i	−0.764458	−	0.441360i	−0.830894	+	0.556431i	$0.812170\pi$
$32$	0.294755	−	0.955573i	0.0521058	−	0.168923i
$33$		0			0
$34$	0.326344	+	0.260250i	0.0559675	+	0.0446326i
$35$	−6.12286	−	6.87125i	−1.03495	−	1.16145i
$36$		0			0
$37$	5.45393	−	5.06051i	0.896620	−	0.831942i	−0.0898377	−	0.995956i	$-0.528635\pi$
$37$	5.45393	−	5.06051i	0.896620	−	0.831942i	0.986458	+	0.164014i	$0.0524444\pi$
$38$	2.64762	−	0.399065i	0.429501	−	0.0647369i
$39$		0			0
$40$	−0.518455	+	3.43973i	−0.0819750	+	0.543868i
$41$	8.95505	−	4.31252i	1.39854	−	0.673503i	0.425678	−	0.904875i	$-0.360036\pi$
$41$	8.95505	−	4.31252i	1.39854	−	0.673503i	0.972865	+	0.231372i	$0.0743214\pi$
$42$		0			0
$43$	−1.85771	−	0.894625i	−0.283298	−	0.136429i	0.286839	−	0.957979i	$-0.407396\pi$
$43$	−1.85771	−	0.894625i	−0.283298	−	0.136429i	−0.570137	+	0.821550i	$0.693110\pi$
$44$	−2.24543	+	3.29344i	−0.338512	+	0.496505i
$45$		0			0
$46$	0.283722	−	3.78600i	0.0418325	−	0.558216i
$47$	0.249013	−	0.634474i	0.0363222	−	0.0925476i	−0.911562	−	0.411163i	$-0.865123\pi$
$47$	0.249013	−	0.634474i	0.0363222	−	0.0925476i	0.947884	+	0.318616i	$0.103218\pi$
$48$		0			0
$49$	6.17942	+	3.28858i	0.882774	+	0.469798i
$50$		−	7.10051i		−	1.00416i
$51$		0			0
$52$	2.39747	+	0.179665i	0.332469	+	0.0249151i
$53$	7.14646	−	7.70205i	0.981642	−	1.05796i	−0.0166693	−	0.999861i	$-0.505306\pi$
$53$	7.14646	−	7.70205i	0.981642	−	1.05796i	0.998311	−	0.0580970i	$-0.0185033\pi$
$54$		0			0
$55$	6.01617	−	12.4927i	0.811220	−	1.68452i
$56$	−0.536692	−	2.59075i	−0.0717185	−	0.346203i
$57$		0			0
$58$	−8.26578	−	1.24587i	−1.08535	−	0.163590i
$59$	−3.11393	+	2.12304i	−0.405399	+	0.276396i	−0.748805	−	0.662791i	$-0.769372\pi$
$59$	−3.11393	+	2.12304i	−0.405399	+	0.276396i	0.343405	+	0.939187i	$0.388419\pi$
$60$		0			0
$61$	5.34933	+	5.76521i	0.684912	+	0.738160i	0.975816	−	0.218593i	$-0.0701466\pi$
$61$	5.34933	+	5.76521i	0.684912	+	0.738160i	−0.290904	+	0.956752i	$0.593956\pi$
$62$	3.06431	+	3.84253i	0.389168	+	0.488001i
$63$		0			0
$64$	−0.623490	+	0.781831i	−0.0779362	+	0.0977289i
$65$	−8.33977	+	0.624980i	−1.03442	+	0.0775192i
$66$		0			0
$67$	−0.00633555	+	0.0109735i	−0.000774011	+	0.00134063i	−0.866412	−	0.499330i	$-0.833580\pi$
$67$	−0.00633555	+	0.0109735i	−0.000774011	+	0.00134063i	0.865638	+	0.500670i	$0.166913\pi$
$68$	−0.208705	−	0.361487i	−0.0253091	−	0.0438367i
$69$		0			0
$70$	3.18926	+	8.63320i	0.381189	+	1.03186i
$71$	9.97398	+	2.27650i	1.18369	+	0.270170i	0.768673	−	0.639642i	$-0.220917\pi$
$71$	9.97398	+	2.27650i	1.18369	+	0.270170i	0.415020	+	0.909812i	$0.363775\pi$
$72$		0			0
$73$	7.14472	−	2.80410i	0.836226	−	0.328195i	0.0916991	−	0.995787i	$-0.470770\pi$
$73$	7.14472	−	2.80410i	0.836226	−	0.328195i	0.744527	+	0.667592i	$0.232675\pi$
$74$	−6.92573	+	2.71815i	−0.805100	+	0.315978i
$75$		0			0
$76$	−2.61040	−	0.595806i	−0.299433	−	0.0683436i
$77$	−0.999654	+	10.4987i	−0.113921	+	1.19643i
$78$		0			0
$79$	6.41219	+	11.1062i	0.721427	+	1.24955i	0.960428	+	0.278530i	$0.0898470\pi$
$79$	6.41219	+	11.1062i	0.721427	+	1.24955i	−0.239000	+	0.971020i	$0.576820\pi$
$80$	1.73929	−	3.01254i	0.194458	−	0.336812i
$81$		0			0
$82$	−9.91156	+	0.742769i	−1.09455	+	0.0820251i
$83$	−4.36670	+	5.47567i	−0.479308	+	0.601033i	−0.961423	−	0.275075i	$-0.911297\pi$
$83$	−4.36670	+	5.47567i	−0.479308	+	0.601033i	0.482115	+	0.876108i	$0.339869\pi$
$84$		0			0
$85$	0.905301	+	1.13521i	0.0981937	+	0.123131i
$86$	1.40245	+	1.51148i	0.151230	+	0.162987i
$87$		0			0
$88$	3.29344	−	2.24543i	0.351082	−	0.239364i
$89$	−3.60909	−	0.543983i	−0.382563	−	0.0576620i	−0.0450542	−	0.998985i	$-0.514346\pi$
$89$	−3.60909	−	0.543983i	−0.382563	−	0.0576620i	−0.337508	+	0.941323i	$0.609584\pi$
$90$		0			0
$91$	5.78535	−	2.64396i	0.606470	−	0.277163i
$92$	−1.64729	+	3.42064i	−0.171742	+	0.356626i
$93$		0			0
$94$	−0.463599	+	0.499641i	−0.0478166	+	0.0515340i
$95$	9.28795	+	0.696035i	0.952923	+	0.0714117i
$96$		0			0
$97$		−	15.0896i		−	1.53212i	−0.642768	−	0.766061i	$-0.722214\pi$
$97$		−	15.0896i		−	1.53212i	0.642768	−	0.766061i	$-0.277786\pi$
$98$	−4.55081	−	5.31885i	−0.459701	−	0.537285i
$99$		0			0
$100$	−2.59411	+	6.60968i	−0.259411	+	0.660968i
$101$	1.07319	−	14.3207i	0.106786	−	1.42496i	−0.644309	−	0.764766i	$-0.722855\pi$
$101$	1.07319	−	14.3207i	0.106786	−	1.42496i	0.751095	−	0.660195i	$-0.229526\pi$
$102$		0			0
$103$	1.65671	−	2.42995i	0.163241	−	0.239430i	−0.735899	−	0.677091i	$-0.763240\pi$
$103$	1.65671	−	2.42995i	0.163241	−	0.239430i	0.899140	+	0.437660i	$0.144193\pi$
$104$	−2.16610	−	1.04314i	−0.212404	−	0.102288i
$105$		0			0
$106$	−9.46633	+	4.55874i	−0.919451	+	0.442784i
$107$	1.81825	−	12.0633i	0.175777	−	1.16620i	−0.710722	−	0.703473i	$-0.751631\pi$
$107$	1.81825	−	12.0633i	0.175777	−	1.16620i	0.886499	−	0.462731i	$-0.153130\pi$
$108$		0			0
$109$	−13.6903	+	2.06348i	−1.31129	+	0.197645i	−0.767214	−	0.641391i	$-0.778358\pi$
$109$	−13.6903	+	2.06348i	−1.31129	+	0.197645i	−0.544076	+	0.839036i	$0.683120\pi$
$110$	−10.1644	+	9.43117i	−0.969136	+	0.899227i
$111$		0			0
$112$	−0.446913	+	2.60773i	−0.0422293	+	0.246408i
$113$	8.70565	+	6.94252i	0.818959	+	0.653098i	0.940615	−	0.339475i	$-0.110249\pi$
$113$	8.70565	+	6.94252i	0.818959	+	0.653098i	−0.121657	+	0.992572i	$0.538821\pi$
$114$		0			0
$115$	3.89278	−	12.6201i	0.363004	−	1.17683i
$116$	7.23923	+	4.17957i	0.672146	+	0.388064i
$117$		0			0
$118$	3.67431	−	0.838637i	0.338248	−	0.0772028i
$119$	−0.945095	−	0.571321i	−0.0866368	−	0.0523729i
$120$		0			0
$121$	−4.67155	+	1.44098i	−0.424686	+	0.130998i
$122$	−2.87329	−	7.32102i	−0.260135	−	0.662814i
$123$		0			0
$124$	−1.44866	−	4.69643i	−0.130093	−	0.421752i
$125$	1.62591	−	7.12358i	0.145426	−	0.637152i
$126$		0			0
$127$	2.68588	+	11.7676i	0.238333	+	1.04421i	0.942509	+	0.334181i	$0.108460\pi$
$127$	2.68588	+	11.7676i	0.238333	+	1.04421i	−0.704176	+	0.710026i	$0.748683\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$		0			0
$130$	7.99161	+	2.46508i	0.700910	+	0.216202i
$131$	1.46622	+	19.5653i	0.128104	+	1.70943i	0.577744	+	0.816218i	$0.303933\pi$
$131$	1.46622	+	19.5653i	0.128104	+	1.70943i	−0.449640	+	0.893210i	$0.648448\pi$
$132$		0			0
$133$	−6.81001	+	1.95138i	−0.590503	+	0.169206i
$134$	0.00990667	−	0.00790031i	0.000855806	−	0.000682483i
$135$		0			0
$136$	0.0622116	+	0.412747i	0.00533460	+	0.0353928i
$137$	5.32746	+	7.81395i	0.455156	+	0.667591i	0.983389	−	0.181508i	$-0.0580979\pi$
$137$	5.32746	+	7.81395i	0.455156	+	0.667591i	−0.528234	+	0.849099i	$0.677146\pi$
$138$		0			0
$139$	−8.69013	−	18.0452i	−0.737087	−	1.53058i	−0.844020	−	0.536311i	$-0.819817\pi$
$139$	−8.69013	−	18.0452i	−0.737087	−	1.53058i	0.106933	−	0.994266i	$-0.465897\pi$
$140$	0.185264	−	9.20159i	0.0156577	−	0.777676i
$141$		0			0
$142$	−8.45282	−	5.76303i	−0.709345	−	0.483623i
$143$	7.02503	+	6.51827i	0.587462	+	0.545085i
$144$		0			0
$145$	−27.0679	−	10.6234i	−2.24787	−	0.882223i
$146$	−7.67528			−0.635211
$147$		0			0
$148$	7.44003			0.611567
$149$	−13.3742	−	5.24899i	−1.09566	−	0.430014i	−0.252454	−	0.967609i	$-0.581238\pi$
$149$	−13.3742	−	5.24899i	−1.09566	−	0.430014i	−0.843203	+	0.537595i	$0.819333\pi$
$150$		0			0
$151$	−8.70608	−	8.07806i	−0.708491	−	0.657383i	0.241235	−	0.970467i	$-0.422448\pi$
$151$	−8.70608	−	8.07806i	−0.708491	−	0.657383i	−0.949726	+	0.313083i	$0.898638\pi$
$152$	2.21228	+	1.50831i	0.179439	+	0.122340i
$153$		0			0
$154$	4.76614	−	9.40771i	0.384067	−	0.758095i
$155$	7.41787	+	15.4034i	0.595817	+	1.23723i
$156$		0			0
$157$	6.30193	+	9.24323i	0.502949	+	0.737690i	0.990814	−	0.135228i	$-0.0431768\pi$
$157$	6.30193	+	9.24323i	0.502949	+	0.737690i	−0.487866	+	0.872919i	$0.662224\pi$
$158$	−1.91137	−	12.6811i	−0.152061	−	1.00886i
$159$		0			0
$160$	−2.71966	+	2.16886i	−0.215008	+	0.171463i
$161$	0.548868	+	10.0299i	0.0432568	+	0.790467i
$162$		0			0
$163$	−1.06799	−	14.2513i	−0.0836512	−	1.11625i	−0.868211	−	0.496195i	$-0.834730\pi$
$163$	−1.06799	−	14.2513i	−0.0836512	−	1.11625i	0.784560	−	0.620053i	$-0.212889\pi$
$164$	9.49777	+	2.92968i	0.741652	+	0.228769i
$165$		0			0
$166$	6.06534	−	3.50182i	0.470761	−	0.271794i
$167$	1.85690	+	8.13562i	0.143691	+	0.629553i	0.994559	+	0.104173i	$0.0332197\pi$
$167$	1.85690	+	8.13562i	0.143691	+	0.629553i	−0.850868	+	0.525380i	$0.823923\pi$
$168$		0			0
$169$	−1.60657	+	7.03886i	−0.123583	+	0.541451i
$170$	−0.427982	−	1.38748i	−0.0328247	−	0.106415i
$171$		0			0
$172$	−0.753296	−	1.91937i	−0.0574383	−	0.146350i
$173$	13.3643	−	4.12236i	1.01607	−	0.313417i	0.258390	−	0.966041i	$-0.416808\pi$
$173$	13.3643	−	4.12236i	1.01607	−	0.313417i	0.757682	+	0.652624i	$0.226332\pi$
$174$		0			0
$175$	2.42543	+	18.6289i	0.183345	+	1.40822i
$176$	−3.88613	+	0.886984i	−0.292928	+	0.0668589i
$177$		0			0
$178$	3.16087	+	1.82493i	0.236917	+	0.136784i
$179$	5.15275	−	16.7048i	0.385135	−	1.24858i	−0.530886	−	0.847443i	$-0.678141\pi$
$179$	5.15275	−	16.7048i	0.385135	−	1.24858i	0.916020	−	0.401132i	$-0.131383\pi$
$180$		0			0
$181$	2.11452	+	1.68628i	0.157171	+	0.125340i	0.698918	−	0.715202i	$-0.253665\pi$
$181$	2.11452	+	1.68628i	0.157171	+	0.125340i	−0.541747	+	0.840542i	$0.682237\pi$
$182$	−6.35138	+	0.347568i	−0.470796	+	0.0257634i
$183$		0			0
$184$	2.78312	−	2.58236i	0.205174	−	0.190374i
$185$	−25.5917	+	3.85732i	−1.88154	+	0.283596i
$186$		0			0
$187$	0.247980	−	1.64524i	0.0181341	−	0.120312i
$188$	0.614091	−	0.295731i	0.0447872	−	0.0215684i
$189$		0			0
$190$	−8.39162	−	4.04119i	−0.608792	−	0.293179i
$191$	−11.6093	+	17.0277i	−0.840021	+	1.23208i	0.130592	+	0.991436i	$0.458312\pi$
$191$	−11.6093	+	17.0277i	−0.840021	+	1.23208i	−0.970612	+	0.240648i	$0.922640\pi$
$192$		0			0
$193$	−1.82529	+	24.3569i	−0.131388	+	1.75324i	0.409647	+	0.912244i	$0.365652\pi$
$193$	−1.82529	+	24.3569i	−0.131388	+	1.75324i	−0.541034	+	0.841000i	$0.681967\pi$
$194$	−5.51287	+	14.0466i	−0.395801	+	1.00848i
$195$		0			0
$196$	2.29303	+	6.61377i	0.163788	+	0.472412i
$197$			1.10682i			0.0788575i	0.999222	+	0.0394288i	$0.0125538\pi$
$197$			1.10682i			0.0788575i	−0.999222	+	0.0394288i	$0.987446\pi$
$198$		0			0
$199$	−0.118856	−	0.00890703i	−0.00842549	−	0.000631403i	0.0705167	−	0.997511i	$-0.477535\pi$
$199$	−0.118856	−	0.00890703i	−0.00842549	−	0.000631403i	−0.0789422	+	0.996879i	$0.525154\pi$
$200$	4.82957	−	5.20504i	0.341502	−	0.368052i
$201$		0			0
$202$	−6.23093	+	12.9387i	−0.438407	+	0.910361i
$203$	22.1117	+	0.445196i	1.55194	+	0.0312467i
$204$		0			0
$205$	−34.1886	−	5.15311i	−2.38784	−	0.359909i
$206$	−2.42995	+	1.65671i	−0.169303	+	0.115429i
$207$		0			0
$208$	1.63526	+	1.76240i	0.113385	+	0.122200i
$209$	−6.65439	−	8.34434i	−0.460294	−	0.577190i
$210$		0			0
$211$	−6.39610	+	8.02046i	−0.440326	+	0.552151i	−0.951629	−	0.307249i	$-0.900591\pi$
$211$	−6.39610	+	8.02046i	−0.440326	+	0.552151i	0.511303	+	0.859400i	$0.329163\pi$
$212$	10.4775	−	0.785176i	0.719594	−	0.0539261i
$213$		0			0
$214$	−6.09978	+	10.5651i	−0.416973	+	0.722218i
$215$	3.58624	+	6.21155i	0.244579	+	0.423624i
$216$		0			0
$217$	−9.35211	−	9.03456i	−0.634862	−	0.613306i
$218$	13.4978	+	3.08078i	0.914186	+	0.208657i
$219$		0			0
$220$	12.9074	−	5.06576i	0.870214	−	0.341534i
$221$	−0.934160	+	0.366631i	−0.0628384	+	0.0246623i
$222$		0			0
$223$	6.13083	+	1.39932i	0.410551	+	0.0937055i	0.422808	−	0.906219i	$-0.361045\pi$
$223$	6.13083	+	1.39932i	0.410551	+	0.0937055i	−0.0122571	+	0.999925i	$0.503902\pi$
$224$	1.36873	−	2.26419i	0.0914522	−	0.151283i
$225$		0			0
$226$	−5.56747	−	9.64314i	−0.370343	−	0.641452i
$227$	−13.2070	+	22.8752i	−0.876581	+	1.51828i	−0.0215130	+	0.999769i	$0.506848\pi$
$227$	−13.2070	+	22.8752i	−0.876581	+	1.51828i	−0.855068	+	0.518515i	$0.826485\pi$
$228$		0			0
$229$	0.516712	−	0.0387222i	0.0341453	−	0.00255883i	−0.0576465	−	0.998337i	$-0.518360\pi$
$229$	0.516712	−	0.0387222i	0.0341453	−	0.00255883i	0.0917918	+	0.995778i	$0.470741\pi$
$230$	−8.23433	+	10.3255i	−0.542956	+	0.680845i
$231$		0			0
$232$	−5.21184	−	6.53544i	−0.342174	−	0.429073i
$233$	0.297149	+	0.320251i	0.0194669	+	0.0209803i	0.742710	−	0.669613i	$-0.233540\pi$
$233$	0.297149	+	0.320251i	0.0194669	+	0.0209803i	−0.723243	+	0.690593i	$0.757350\pi$
$234$		0			0
$235$	−1.95898	+	1.33561i	−0.127790	+	0.0871257i
$236$	−3.72671	−	0.561711i	−0.242588	−	0.0365643i
$237$		0			0
$238$	0.671038	+	0.877110i	0.0434969	+	0.0568546i
$239$	−7.93304	+	16.4731i	−0.513146	+	1.06556i	0.469988	+	0.882673i	$0.344258\pi$
$239$	−7.93304	+	16.4731i	−0.513146	+	1.06556i	−0.983134	+	0.182886i	$0.941456\pi$
$240$		0			0
$241$	17.5469	−	18.9111i	1.13030	−	1.21817i	0.157251	−	0.987559i	$-0.449737\pi$
$241$	17.5469	−	18.9111i	1.13030	−	1.21817i	0.973046	−	0.230612i	$-0.0740728\pi$
$242$	4.87507	+	0.365336i	0.313381	+	0.0234847i
$243$		0			0
$244$			7.86467i			0.503484i
$245$	−11.3163	−	21.5607i	−0.722975	−	1.37746i
$246$		0			0
$247$	−2.35180	+	5.99230i	−0.149642	+	0.381281i
$248$	−0.367282	+	4.90103i	−0.0233224	+	0.311216i
$249$		0			0
$250$	−4.11605	+	6.03714i	−0.260322	+	0.381822i
$251$	−23.8256	−	11.4738i	−1.50386	−	0.724219i	−0.512905	−	0.858445i	$-0.671431\pi$
$251$	−23.8256	−	11.4738i	−1.50386	−	0.724219i	−0.990951	+	0.134227i	$0.957145\pi$
$252$		0			0
$253$	−13.6349	+	6.56622i	−0.857218	+	0.412814i
$254$	1.79898	−	11.9354i	0.112878	−	0.748895i
$255$		0			0
$256$	−0.988831	+	0.149042i	−0.0618019	+	0.00931514i
$257$	−9.44870	+	8.76712i	−0.589394	+	0.546878i	−0.917486	−	0.397768i	$-0.869785\pi$
$257$	−9.44870	+	8.76712i	−0.589394	+	0.546878i	0.328092	+	0.944646i	$0.393594\pi$
$258$		0			0
$259$	17.2419	−	9.49708i	1.07136	−	0.590120i
$260$	−6.53858	−	5.21434i	−0.405506	−	0.323380i
$261$		0			0
$262$	5.78314	−	18.7485i	0.357284	−	1.15829i
$263$	−24.3480	−	14.0573i	−1.50136	−	0.866812i	−0.999999	−	0.00157534i	$-0.999499\pi$
$263$	−24.3480	−	14.0573i	−1.50136	−	0.866812i	−0.501364	−	0.865237i	$-0.667168\pi$
$264$		0			0
$265$	−35.6325	+	8.13288i	−2.18889	+	0.499599i
$266$	7.05218	+	0.671489i	0.432397	+	0.0411716i
$267$		0			0
$268$	−0.0121082	+	0.00373487i	−0.000739624	+	0.000228144i
$269$	−6.20856	−	15.8191i	−0.378543	−	0.964511i	−0.985485	−	0.169765i	$-0.945699\pi$
$269$	−6.20856	−	15.8191i	−0.378543	−	0.964511i	0.606942	−	0.794746i	$-0.292396\pi$
$270$		0			0
$271$	8.81948	+	28.5921i	0.535746	+	1.73684i	0.666574	+	0.745439i	$0.267760\pi$
$271$	8.81948	+	28.5921i	0.535746	+	1.73684i	−0.130828	+	0.991405i	$0.541764\pi$
$272$	0.0928823	−	0.406944i	0.00563181	−	0.0246746i
$273$		0			0
$274$	−2.10444	−	9.22014i	−0.127134	−	0.557009i
$275$	−24.5112	+	14.1516i	−1.47808	+	0.853371i
$276$		0			0
$277$	0.539610	+	0.166448i	0.0324220	+	0.0100009i	0.310924	−	0.950435i	$-0.399362\pi$
$277$	0.539610	+	0.166448i	0.0324220	+	0.0100009i	−0.278502	+	0.960436i	$0.589838\pi$
$278$	1.49675	+	19.9727i	0.0897689	+	1.19788i
$279$		0			0
$280$	−3.53418	+	8.49783i	−0.211207	+	0.507843i
$281$	−11.2078	+	8.93793i	−0.668602	+	0.533192i	−0.897920	−	0.440159i	$-0.854922\pi$
$281$	−11.2078	+	8.93793i	−0.668602	+	0.533192i	0.229318	+	0.973352i	$0.426351\pi$
$282$		0			0
$283$	3.31423	+	21.9885i	0.197011	+	1.30708i	0.840578	+	0.541690i	$0.182215\pi$
$283$	3.31423	+	21.9885i	0.197011	+	1.30708i	−0.643568	+	0.765389i	$0.722547\pi$
$284$	5.76303	+	8.45282i	0.341973	+	0.501582i
$285$		0			0
$286$	−4.15802	−	8.63422i	−0.245869	−	0.510552i
$287$	25.7503	−	5.33437i	1.51999	−	0.314878i
$288$		0			0
$289$	−13.9021	−	9.47829i	−0.817771	−	0.557547i
$290$	21.3156	+	19.7780i	1.25170	+	1.16141i
$291$		0			0
$292$	7.14472	+	2.80410i	0.418113	+	0.164097i
$293$	−3.05273			−0.178342			−0.0891711	−	0.996016i	$-0.528422\pi$
$293$	−3.05273			−0.178342			−0.0891711	+	0.996016i	$0.528422\pi$
$294$		0			0
$295$	13.1101			0.763298
$296$	−6.92573	−	2.71815i	−0.402550	−	0.157989i
$297$		0			0
$298$	10.5320	+	9.77229i	0.610104	+	0.566093i
$299$	7.54173	+	5.14187i	0.436150	+	0.297362i
$300$		0			0
$301$	−4.19577	−	3.48647i	−0.241840	−	0.200957i
$302$	5.15301	+	10.7003i	0.296523	+	0.615736i
$303$		0			0
$304$	−1.50831	−	2.21228i	−0.0865072	−	0.126883i
$305$	−4.07748	−	27.0523i	−0.233476	−	1.54901i
$306$		0			0
$307$	26.0973	−	20.8119i	1.48945	−	1.18780i	0.554927	−	0.831899i	$-0.312746\pi$
$307$	26.0973	−	20.8119i	1.48945	−	1.18780i	0.934525	−	0.355899i	$-0.115825\pi$
$308$	−7.87370	+	7.01613i	−0.448646	+	0.399781i
$309$		0			0
$310$	−1.27762	−	17.0486i	−0.0725638	−	0.968297i
$311$	10.8636	+	3.35099i	0.616020	+	0.190017i	0.587033	−	0.809563i	$-0.300296\pi$
$311$	10.8636	+	3.35099i	0.616020	+	0.190017i	0.0289869	+	0.999580i	$0.490772\pi$
$312$		0			0
$313$	−9.29322	+	5.36544i	−0.525284	+	0.303273i	−0.739094	−	0.673603i	$-0.764746\pi$
$313$	−9.29322	+	5.36544i	−0.525284	+	0.303273i	0.213810	+	0.976875i	$0.431413\pi$
$314$	−2.48937	−	10.9066i	−0.140483	−	0.615497i
$315$		0			0
$316$	−2.85369	+	12.5028i	−0.160533	+	0.703340i
$317$	4.73512	+	15.3509i	0.265951	+	0.862192i	0.985780	+	0.168041i	$0.0537440\pi$
$317$	4.73512	+	15.3509i	0.265951	+	0.862192i	−0.719829	+	0.694151i	$0.755780\pi$
$318$		0			0
$319$	12.1732	+	31.0168i	0.681569	+	1.73661i
$320$	3.32403	−	1.02533i	0.185819	−	0.0573176i
$321$		0			0
$322$	3.15341	−	9.53710i	0.175733	−	0.531482i
$323$	1.08960	−	0.248695i	0.0606272	−	0.0138378i
$324$		0			0
$325$	14.7839	+	8.53548i	0.820062	+	0.473463i
$326$	−4.21242	+	13.6563i	−0.233305	+	0.756355i
$327$		0			0
$328$	−7.77090	−	6.19708i	−0.429076	−	0.342177i
$329$	1.04563	−	1.46922i	0.0576476	−	0.0810007i
$330$		0			0
$331$	8.29753	−	7.69899i	0.456074	−	0.423175i	−0.418389	−	0.908268i	$-0.637405\pi$
$331$	8.29753	−	7.69899i	0.456074	−	0.423175i	0.874462	+	0.485094i	$0.161214\pi$
$332$	−6.92542	+	1.04384i	−0.380082	+	0.0572881i
$333$		0			0
$334$	1.24373	−	8.25164i	0.0680541	−	0.451510i
$335$	0.0397124	−	0.0191245i	0.00216972	−	0.00104488i
$336$		0			0
$337$	30.5368	+	14.7057i	1.66345	+	0.801073i	0.998533	+	0.0541521i	$0.0172456\pi$
$337$	30.5368	+	14.7057i	1.66345	+	0.801073i	0.664913	+	0.746921i	$0.268469\pi$
$338$	4.06710	−	5.96534i	0.221221	−	0.324472i
$339$		0			0
$340$	−0.108507	+	1.44793i	−0.00588464	+	0.0785250i
$341$	7.15726	−	18.2364i	0.387588	−	0.987557i
$342$		0			0
$343$	13.7564	+	12.4001i	0.742774	+	0.669542i
$344$			2.06190i			0.111170i
$345$		0			0
$346$	−13.9466	−	1.04515i	−0.749773	−	0.0561877i
$347$	10.6354	−	11.4622i	0.570938	−	0.615325i	−0.379894	−	0.925030i	$-0.624040\pi$
$347$	10.6354	−	11.4622i	0.570938	−	0.615325i	0.950833	+	0.309705i	$0.100230\pi$
$348$		0			0
$349$	5.99989	−	12.4589i	0.321167	−	0.666909i	−0.676407	−	0.736528i	$-0.736464\pi$
$349$	5.99989	−	12.4589i	0.321167	−	0.666909i	0.997574	+	0.0696188i	$0.0221783\pi$
$350$	4.54815	−	18.2273i	0.243109	−	0.974290i
$351$		0			0
$352$	3.94155	+	0.594093i	0.210085	+	0.0316652i
$353$	−2.52713	+	1.72297i	−0.134506	+	0.0917044i	−0.628704	−	0.777645i	$-0.716414\pi$
$353$	−2.52713	+	1.72297i	−0.134506	+	0.0917044i	0.494198	+	0.869349i	$0.335462\pi$
$354$		0			0
$355$	−24.2057	−	26.0875i	−1.28470	−	1.38458i
$356$	−2.27565	−	2.85357i	−0.120609	−	0.151239i
$357$		0			0
$358$	−10.8995	+	13.6676i	−0.576057	+	0.722353i
$359$	11.5006	−	0.861851i	0.606979	−	0.0454868i	0.232304	−	0.972643i	$-0.425374\pi$
$359$	11.5006	−	0.861851i	0.606979	−	0.0454868i	0.374674	+	0.927156i	$0.377754\pi$
$360$		0			0
$361$	−5.91542	+	10.2458i	−0.311338	+	0.539253i
$362$	−1.35229	−	2.34223i	−0.0710747	−	0.123105i
$363$		0			0
$364$	6.03932	+	1.99688i	0.316546	+	0.104665i
$365$	−26.0297	−	5.94110i	−1.36246	−	0.310972i
$366$		0			0
$367$	2.29532	−	0.900848i	0.119815	−	0.0470239i	−0.304676	−	0.952456i	$-0.598548\pi$
$367$	2.29532	−	0.900848i	0.119815	−	0.0470239i	0.424491	+	0.905432i	$0.360453\pi$
$368$	−3.53417	+	1.38706i	−0.184232	+	0.0723055i
$369$		0			0
$370$	25.2318	+	5.75900i	1.31174	+	0.299396i
$371$	23.2787	−	15.1939i	1.20857	−	0.788829i
$372$		0			0
$373$	−12.6723	−	21.9491i	−0.656149	−	1.13648i	−0.981604	−	0.190926i	$-0.938851\pi$
$373$	−12.6723	−	21.9491i	−0.656149	−	1.13648i	0.325455	−	0.945557i	$-0.394482\pi$
$374$	−0.831911	+	1.44091i	−0.0430171	+	0.0745078i
$375$		0			0
$376$	−0.679684	+	0.0509353i	−0.0350520	+	0.00262679i
$377$	12.5303	−	15.7124i	0.645341	−	0.809232i
$378$		0			0
$379$	−18.5775	−	23.2955i	−0.954262	−	1.19661i	−0.980414	−	0.196949i	$-0.936897\pi$
$379$	−18.5775	−	23.2955i	−0.954262	−	1.19661i	0.0261513	−	0.999658i	$-0.491675\pi$
$380$	6.33512	+	6.82764i	0.324985	+	0.350250i
$381$		0			0
$382$	17.0277	−	11.6093i	0.871215	−	0.593984i
$383$	18.9421	+	2.85506i	0.967897	+	0.145887i	0.613921	−	0.789368i	$-0.289591\pi$
$383$	18.9421	+	2.85506i	0.967897	+	0.145887i	0.353976	+	0.935255i	$0.384829\pi$
$384$		0			0
$385$	23.4458	−	28.2157i	1.19491	−	1.43801i
$386$	10.5977	−	22.0063i	0.539407	−	1.12009i
$387$		0			0
$388$	10.2636	−	11.0615i	0.521054	−	0.561562i
$389$	9.00966	+	0.675180i	0.456808	+	0.0342330i	0.301147	−	0.953578i	$-0.402630\pi$
$389$	9.00966	+	0.675180i	0.456808	+	0.0342330i	0.155660	+	0.987811i	$0.450249\pi$
$390$		0			0
$391$		−	1.58474i		−	0.0801439i
$392$	0.281761	−	6.99433i	0.0142311	−	0.353267i
$393$		0			0
$394$	0.404366	−	1.03031i	0.0203717	−	0.0519062i
$395$	3.33375	−	44.4859i	0.167739	−	2.23833i
$396$		0			0
$397$	−8.44623	+	12.3883i	−0.423904	+	0.621753i	−0.977476	−	0.211049i	$-0.932312\pi$
$397$	−8.44623	+	12.3883i	−0.423904	+	0.621753i	0.553572	+	0.832802i	$0.313265\pi$
$398$	0.107386	+	0.0517143i	0.00538277	+	0.00259221i
$399$		0			0
$400$	−6.39734	+	3.08079i	−0.319867	+	0.154040i
$401$	5.70578	−	37.8554i	0.284933	−	1.89041i	−0.148010	−	0.988986i	$-0.547287\pi$
$401$	5.70578	−	37.8554i	0.284933	−	1.89041i	0.432943	−	0.901421i	$-0.357475\pi$
$402$		0			0
$403$	−11.6841	+	1.76109i	−0.582025	+	0.0877262i
$404$	10.5272	−	9.76784i	0.523749	−	0.485968i
$405$		0			0
$406$	−20.4206	−	8.49275i	−1.01346	−	0.421488i
$407$	23.1864	+	18.4905i	1.14931	+	0.916540i
$408$		0			0
$409$	8.48582	−	27.5103i	0.419597	−	1.36030i	−0.461406	−	0.887189i	$-0.652655\pi$
$409$	8.48582	−	27.5103i	0.419597	−	1.36030i	0.881003	−	0.473110i	$-0.156869\pi$
$410$	29.9427	+	17.2874i	1.47876	+	0.853764i
$411$		0			0
$412$	2.86724	−	0.654430i	0.141259	−	0.0322414i
$413$	−9.35348	+	3.45535i	−0.460255	+	0.170026i
$414$		0			0
$415$	23.2804	−	7.18104i	1.14279	−	0.352504i
$416$	−0.878349	−	2.23800i	−0.0430646	−	0.109727i
$417$		0			0
$418$	3.14587	+	10.1986i	0.153869	+	0.498832i
$419$	2.02519	−	8.87296i	0.0989372	−	0.433472i	−0.901063	−	0.433689i	$-0.857212\pi$
$419$	2.02519	−	8.87296i	0.0989372	−	0.433472i	1.00000		0.000216437i	$6.88941e-5\pi$
$420$		0			0
$421$	−2.16974	−	9.50624i	−0.105747	−	0.463306i	−0.999880	−	0.0155049i	$-0.995064\pi$
$421$	−2.16974	−	9.50624i	−0.105747	−	0.463306i	0.894133	−	0.447801i	$-0.147793\pi$
$422$	8.88416	−	5.12927i	0.432474	−	0.249689i
$423$		0			0
$424$	−10.0400	−	3.09694i	−0.487587	−	0.150401i
$425$	−0.221486	−	2.95553i	−0.0107437	−	0.143364i
$426$		0			0
$427$	10.0391	+	18.2260i	0.485827	+	0.882018i
$428$	9.53801	−	7.60631i	0.461037	−	0.367665i
$429$		0			0
$430$	−1.06900	−	7.09237i	−0.0515519	−	0.342024i
$431$	3.40480	+	4.99392i	0.164003	+	0.240549i	0.899440	−	0.437045i	$-0.143975\pi$
$431$	3.40480	+	4.99392i	0.164003	+	0.240549i	−0.735436	+	0.677594i	$0.763023\pi$
$432$		0			0
$433$	17.3351	+	35.9966i	0.833070	+	1.72989i	0.668760	+	0.743478i	$0.266825\pi$
$433$	17.3351	+	35.9966i	0.833070	+	1.72989i	0.164309	+	0.986409i	$0.447460\pi$
$434$	5.40494	+	11.8267i	0.259445	+	0.567702i
$435$		0			0
$436$	−11.4392	−	7.79912i	−0.547838	−	0.373510i
$437$	−7.45188	−	6.91433i	−0.356472	−	0.330757i
$438$		0			0
$439$	−6.72020	−	2.63748i	−0.320738	−	0.125880i	0.199510	−	0.979896i	$-0.436065\pi$
$439$	−6.72020	−	2.63748i	−0.320738	−	0.125880i	−0.520247	+	0.854016i	$0.674160\pi$
$440$	−13.8658			−0.661028
$441$		0			0
$442$	1.00353			0.0477331
$443$	−9.16446	−	3.59679i	−0.435417	−	0.170888i	0.137501	−	0.990502i	$-0.456093\pi$
$443$	−9.16446	−	3.59679i	−0.435417	−	0.170888i	−0.572917	+	0.819613i	$0.694188\pi$
$444$		0			0
$445$	9.30705	+	8.63568i	0.441196	+	0.409370i
$446$	−5.19580	−	3.54244i	−0.246028	−	0.167739i
$447$		0			0
$448$	−2.10132	+	1.60763i	−0.0992780	+	0.0759532i
$449$	−4.99845	−	10.3794i	−0.235891	−	0.489834i	0.749096	−	0.662462i	$-0.230488\pi$
$449$	−4.99845	−	10.3794i	−0.235891	−	0.489834i	−0.984987	+	0.172628i	$0.944774\pi$
$450$		0			0
$451$	22.3181	+	32.7347i	1.05092	+	1.54142i
$452$	1.65958	+	11.0106i	0.0780599	+	0.517894i
$453$		0			0
$454$	20.6513	−	16.4689i	0.969216	−	0.772924i
$455$	−21.8089	−	3.73760i	−1.02242	−	0.175221i
$456$		0			0
$457$	1.51510	+	20.2176i	0.0708733	+	0.945738i	0.913395	+	0.407075i	$0.133451\pi$
$457$	1.51510	+	20.2176i	0.0708733	+	0.945738i	−0.842521	+	0.538663i	$0.818930\pi$
$458$	−0.495140	−	0.152731i	−0.0231364	−	0.00713663i
$459$		0			0
$460$	11.4375	−	6.60342i	0.533274	−	0.307886i
$461$	5.43880	+	23.8289i	0.253310	+	1.10982i	0.928252	+	0.371953i	$0.121312\pi$
$461$	5.43880	+	23.8289i	0.253310	+	1.10982i	−0.674941	+	0.737871i	$0.735831\pi$
$462$		0			0
$463$	0.198483	−	0.869613i	0.00922431	−	0.0404143i	−0.970106	−	0.242680i	$-0.921973\pi$
$463$	0.198483	−	0.869613i	0.00922431	−	0.0404143i	0.979331	+	0.202266i	$0.0648305\pi$
$464$	2.46390	+	7.98777i	0.114384	+	0.370823i
$465$		0			0
$466$	−0.159608	−	0.406674i	−0.00739369	−	0.0188388i
$467$	4.78252	−	1.47521i	0.221309	−	0.0682647i	−0.182118	−	0.983277i	$-0.558295\pi$
$467$	4.78252	−	1.47521i	0.221309	−	0.0682647i	0.403427	+	0.915012i	$0.367819\pi$
$468$		0			0
$469$	−0.0232926	+	0.0241113i	−0.00107555	+	0.00111336i
$470$	2.31152	−	0.527589i	0.106622	−	0.0243359i
$471$		0			0
$472$	3.26388	+	1.88440i	0.150232	+	0.0867366i
$473$	2.42256	−	7.85373i	0.111389	−	0.361115i
$474$		0			0
$475$	−14.8640	−	11.8537i	−0.682008	−	0.543884i
$476$	−0.304207	−	1.06164i	−0.0139433	−	0.0486600i
$477$		0			0
$478$	13.4030	−	12.4361i	0.613038	−	0.568816i
$479$	−42.1941	+	6.35974i	−1.92790	+	0.290584i	−0.997173	−	0.0751351i	$-0.976061\pi$
$479$	−42.1941	+	6.35974i	−1.92790	+	0.290584i	−0.930725	+	0.365719i	$0.880823\pi$
$480$		0			0
$481$	2.66595	−	17.6875i	0.121557	−	0.806478i
$482$	−23.2430	+	11.1932i	−1.05869	+	0.509837i
$483$		0			0
$484$	−4.40460	−	2.12114i	−0.200209	−	0.0964157i
$485$	−29.5690	+	43.3697i	−1.34266	+	1.96932i
$486$		0			0
$487$	1.71379	−	22.8690i	0.0776594	−	1.03629i	−0.813191	−	0.581996i	$-0.802272\pi$
$487$	1.71379	−	22.8690i	0.0776594	−	1.03629i	0.890851	−	0.454296i	$-0.150109\pi$
$488$	2.87329	−	7.32102i	0.130068	−	0.331407i
$489$		0			0
$490$	2.65706	+	24.2046i	0.120034	+	1.09345i
$491$			9.57604i			0.432161i	0.976376	+	0.216080i	$0.0693273\pi$
$491$			9.57604i			0.432161i	−0.976376	+	0.216080i	$0.930673\pi$
$492$		0			0
$493$	−3.47943	−	0.260747i	−0.156706	−	0.0117435i
$494$	4.37846	−	4.71886i	0.196996	−	0.212312i
$495$		0			0
$496$	2.13244	−	4.42806i	0.0957495	−	0.198826i
$497$	24.1454	+	12.2326i	1.08307	+	0.548706i
$498$		0			0
$499$	−9.99056	−	1.50583i	−0.447239	−	0.0674104i	−0.0784383	−	0.996919i	$-0.524993\pi$
$499$	−9.99056	−	1.50583i	−0.447239	−	0.0674104i	−0.368801	+	0.929509i	$0.620231\pi$
$500$	6.03714	−	4.11605i	0.269989	−	0.184076i
$501$		0			0
$502$	17.9867	+	19.3851i	0.802788	+	0.865199i
$503$	−1.02237	−	1.28201i	−0.0455853	−	0.0571622i	0.758516	−	0.651654i	$-0.225925\pi$
$503$	−1.02237	−	1.28201i	−0.0455853	−	0.0571622i	−0.804102	+	0.594492i	$0.797353\pi$
$504$		0			0
$505$	−31.1466	+	39.0566i	−1.38601	+	1.73800i
$506$	15.0913	−	1.13093i	0.670889	−	0.0502762i
$507$		0			0
$508$	−6.03512	+	10.4531i	−0.267765	+	0.463783i
$509$	−8.67953	−	15.0334i	−0.384714	−	0.666343i	0.607016	−	0.794690i	$-0.292366\pi$
$509$	−8.67953	−	15.0334i	−0.384714	−	0.666343i	−0.991729	+	0.128346i	$0.959033\pi$
$510$		0			0
$511$	20.1369	−	2.62176i	0.890806	−	0.115980i
$512$	0.974928	+	0.222521i	0.0430861	+	0.00983413i
$513$		0			0
$514$	11.9985	−	4.70908i	0.529233	−	0.207709i
$515$	−9.52324	+	3.73760i	−0.419644	+	0.164698i
$516$		0			0
$517$	2.64875	+	0.604559i	0.116492	+	0.0265885i
$518$	−19.5197	+	2.54140i	−0.857647	+	0.111663i
$519$		0			0
$520$	4.18158	+	7.24271i	0.183374	+	0.317614i
$521$	16.0436	−	27.7883i	0.702881	−	1.21743i	−0.264570	−	0.964367i	$-0.585230\pi$
$521$	16.0436	−	27.7883i	0.702881	−	1.21743i	0.967451	−	0.253059i	$-0.0814368\pi$
$522$		0			0
$523$	−20.0145	+	1.49988i	−0.875172	+	0.0655851i	−0.504737	−	0.863273i	$-0.668411\pi$
$523$	−20.0145	+	1.49988i	−0.875172	+	0.0655851i	−0.370435	+	0.928858i	$0.620791\pi$
$524$	−12.2330	+	15.3397i	−0.534400	+	0.670116i
$525$		0			0
$526$	17.5292	+	21.9809i	0.764310	+	0.958414i
$527$	1.39536	+	1.50384i	0.0607827	+	0.0655081i
$528$		0			0
$529$	7.09382	−	4.83649i	0.308427	−	0.210282i
$530$	36.1406	+	5.44732i	1.56985	+	0.236616i
$531$		0			0
$532$	−6.31936	−	3.20152i	−0.273979	−	0.138804i
$533$	10.3681	−	21.5296i	0.449093	−	0.932551i
$534$		0			0
$535$	−28.8646	+	31.1086i	−1.24793	+	1.34494i
$536$	0.0126357		0.000946913i	0.000545778		4.09004e-5i
$537$		0			0
$538$			16.9939i			0.732658i
$539$	−9.29096	+	26.3102i	−0.400190	+	1.13326i
$540$		0			0
$541$	−11.1707	+	28.4625i	−0.480267	+	1.22370i	0.461412	+	0.887186i	$0.347343\pi$
$541$	−11.1707	+	28.4625i	−0.480267	+	1.22370i	−0.941679	+	0.336514i	$0.890752\pi$
$542$	2.23603	−	29.8377i	0.0960456	−	1.28164i
$543$		0			0
$544$	−0.235135	+	0.344880i	−0.0100813	+	0.0147866i
$545$	43.3912	+	20.8961i	1.85868	+	0.895091i
$546$		0			0
$547$	2.07267	−	0.998143i	0.0886208	−	0.0426775i	−0.389048	−	0.921217i	$-0.627196\pi$
$547$	2.07267	−	0.998143i	0.0886208	−	0.0426775i	0.477669	+	0.878540i	$0.341482\pi$
$548$	−1.40953	+	9.35162i	−0.0602121	+	0.399481i
$549$		0			0
$550$	27.9870	−	4.21836i	1.19337	−	0.179871i
$551$	−16.4071	+	15.2235i	−0.698964	+	0.648544i
$552$		0			0
$553$	9.34638	+	32.6174i	0.397449	+	1.38703i
$554$	−0.441498	−	0.352083i	−0.0187575	−	0.0149586i
$555$		0			0
$556$	5.90356	−	19.1389i	0.250367	−	0.811670i
$557$	−9.59159	−	5.53770i	−0.406409	−	0.234640i	0.282837	−	0.959168i	$-0.408724\pi$
$557$	−9.59159	−	5.53770i	−0.406409	−	0.234640i	−0.689245	+	0.724528i	$0.742058\pi$
$558$		0			0
$559$	−4.83291	+	1.10308i	−0.204410	+	0.0466553i
$560$	6.39448	−	6.61923i	0.270216	−	0.279714i
$561$		0			0
$562$	13.6985	−	4.22541i	0.577834	−	0.178238i
$563$	−14.1217	−	35.9815i	−0.595158	−	1.51644i	−0.837606	−	0.546275i	$-0.816046\pi$
$563$	−14.1217	−	35.9815i	−0.595158	−	1.51644i	0.242448	−	0.970164i	$-0.422050\pi$
$564$		0			0
$565$	−11.4170	−	37.0129i	−0.480316	−	1.55715i
$566$	4.94816	−	21.6793i	0.207987	−	0.911250i
$567$		0			0
$568$	−2.27650	−	9.97398i	−0.0955196	−	0.418499i
$569$	−17.6297	+	10.1785i	−0.739077	+	0.426706i	−0.821734	−	0.569872i	$-0.806993\pi$
$569$	−17.6297	+	10.1785i	−0.739077	+	0.426706i	0.0826566	+	0.996578i	$0.473660\pi$
$570$		0			0
$571$	28.0934	+	8.66565i	1.17567	+	0.362646i	0.820220	−	0.572049i	$-0.193851\pi$
$571$	28.0934	+	8.66565i	1.17567	+	0.362646i	0.355451	+	0.934695i	$0.384327\pi$
$572$	0.716158	+	9.55646i	0.0299441	+	0.399576i
$573$		0			0
$574$	−25.9192	−	4.44202i	−1.08185	−	0.185406i
$575$	−21.0766	+	16.8080i	−0.878953	+	0.700942i
$576$		0			0
$577$	−3.29103	−	21.8346i	−0.137008	−	0.908986i	−0.946697	−	0.322127i	$-0.895602\pi$
$577$	−3.29103	−	21.8346i	−0.137008	−	0.908986i	0.809689	−	0.586859i	$-0.199636\pi$
$578$	9.47829	+	13.9021i	0.394245	+	0.578251i
$579$		0			0
$580$	−12.6164	−	26.1983i	−0.523869	−	1.08783i
$581$	−14.7169	+	11.2592i	−0.610560	+	0.467112i
$582$		0			0
$583$	34.6037	+	23.5924i	1.43314	+	0.977096i
$584$	−5.62638	−	5.22052i	−0.232821	−	0.216027i
$585$		0			0
$586$	2.84170	+	1.11529i	0.117390	+	0.0460721i
$587$	9.62378			0.397216			0.198608	−	0.980079i	$-0.436358\pi$
$587$	9.62378			0.397216			0.198608	+	0.980079i	$0.436358\pi$
$588$		0			0
$589$	13.1595			0.542226
$590$	−12.2038	−	4.78965i	−0.502423	−	0.197187i
$591$		0			0
$592$	5.45393	+	5.06051i	0.224155	+	0.207985i
$593$	−25.7785	−	17.5755i	−1.05859	−	0.721737i	−0.0967428	−	0.995309i	$-0.530842\pi$
$593$	−25.7785	−	17.5755i	−1.05859	−	0.721737i	−0.961852	+	0.273572i	$0.911795\pi$
$594$		0			0
$595$	1.59680	+	3.49402i	0.0654624	+	0.143241i
$596$	−6.23376	−	12.9445i	−0.255345	−	0.530229i
$597$		0			0
$598$	−5.14187	−	7.54173i	−0.210267	−	0.308404i
$599$	−3.51393	−	23.3134i	−0.143575	−	0.952560i	−0.938358	−	0.345666i	$-0.887653\pi$
$599$	−3.51393	−	23.3134i	−0.143575	−	0.952560i	0.794782	−	0.606895i	$-0.207585\pi$
$600$		0			0
$601$	−5.60986	+	4.47372i	−0.228831	+	0.182487i	−0.731193	−	0.682171i	$-0.761036\pi$
$601$	−5.60986	+	4.47372i	−0.228831	+	0.182487i	0.502362	+	0.864658i	$0.332465\pi$
$602$	2.63198	+	4.77835i	0.107272	+	0.194751i
$603$		0			0
$604$	−0.887531	−	11.8433i	−0.0361131	−	0.481896i
$605$	16.2503	+	5.01257i	0.660670	+	0.203790i
$606$		0			0
$607$	−1.05823	+	0.610968i	−0.0429521	+	0.0247984i	−0.521322	−	0.853360i	$-0.674561\pi$
$607$	−1.05823	+	0.610968i	−0.0429521	+	0.0247984i	0.478370	+	0.878158i	$0.341228\pi$
$608$	0.595806	+	2.61040i	0.0241631	+	0.105866i
$609$		0			0
$610$	−6.08770	+	26.6720i	−0.246484	+	1.07992i
$611$	−0.483007	−	1.56587i	−0.0195404	−	0.0633483i
$612$		0			0
$613$	9.78314	+	24.9270i	0.395137	+	1.00679i	0.980587	+	0.196085i	$0.0628228\pi$
$613$	9.78314	+	24.9270i	0.395137	+	1.00679i	−0.585450	+	0.810709i	$0.699082\pi$
$614$	−31.8967	+	9.83884i	−1.28725	+	0.397063i
$615$		0			0
$616$	9.89270	−	3.65454i	0.398588	−	0.147246i
$617$	−11.2473	+	2.56712i	−0.452799	+	0.103348i	−0.442838	−	0.896602i	$-0.646028\pi$
$617$	−11.2473	+	2.56712i	−0.452799	+	0.103348i	−0.00996184	+	0.999950i	$0.503171\pi$
$618$		0			0
$619$	−36.4462	−	21.0422i	−1.46490	−	0.845758i	−0.465664	−	0.884962i	$-0.654184\pi$
$619$	−36.4462	−	21.0422i	−1.46490	−	0.845758i	−0.999231	+	0.0392040i	$0.987518\pi$
$620$	−5.03926	+	16.3369i	−0.202382	+	0.656105i
$621$		0			0
$622$	−8.88842	−	7.08828i	−0.356393	−	0.284214i
$623$	−8.91624	−	3.70819i	−0.357222	−	0.148565i
$624$		0			0
$625$	7.39308	−	6.85977i	0.295723	−	0.274391i
$626$	10.6110	−	1.59935i	0.424102	−	0.0639231i
$627$		0			0
$628$	−1.66735	+	11.0622i	−0.0665347	+	0.441429i
$629$	−2.79799	+	1.34744i	−0.111563	+	0.0537260i
$630$		0			0
$631$	−2.10413	−	1.01329i	−0.0837639	−	0.0403386i	0.391533	−	0.920164i	$-0.371945\pi$
$631$	−2.10413	−	1.01329i	−0.0837639	−	0.0403386i	−0.475297	+	0.879826i	$0.657659\pi$
$632$	7.22423	−	10.5960i	0.287364	−	0.421486i
$633$		0			0
$634$	1.20051	−	16.0197i	0.0476783	−	0.636223i
$635$	15.3397	−	39.0848i	0.608736	−	1.55103i
$636$		0			0
$637$	16.5448	−	3.08142i	0.655529	−	0.122090i
$638$		−	33.3201i		−	1.31916i
$639$		0			0
$640$	−3.46885	−	0.259954i	−0.137118	−	0.0102756i
$641$	−17.6126	+	18.9819i	−0.695657	+	0.749739i	−0.977779	−	0.209639i	$-0.932771\pi$
$641$	−17.6126	+	18.9819i	−0.695657	+	0.749739i	0.282122	+	0.959378i	$0.408962\pi$
$642$		0			0
$643$	2.72619	−	5.66100i	0.107511	−	0.223248i	−0.840272	−	0.542165i	$-0.817605\pi$
$643$	2.72619	−	5.66100i	0.107511	−	0.223248i	0.947783	+	0.318917i	$0.103319\pi$
$644$	−6.41972	+	7.72577i	−0.252972	+	0.304438i
$645$		0			0
$646$	−1.10514	−	0.166573i	−0.0434812	−	0.00655374i
$647$	13.7001	−	9.34055i	0.538605	−	0.367215i	−0.263255	−	0.964726i	$-0.584796\pi$
$647$	13.7001	−	9.34055i	0.538605	−	0.367215i	0.801860	+	0.597511i	$0.203844\pi$
$648$		0			0
$649$	−10.2180	−	11.0124i	−0.401093	−	0.432275i
$650$	−10.6436	−	13.3466i	−0.417475	−	0.523497i
$651$		0			0
$652$	8.91046	−	11.1734i	0.348960	−	0.437583i
$653$	36.4945	−	2.73489i	1.42814	−	0.107024i	0.661907	−	0.749586i	$-0.269747\pi$
$653$	36.4945	−	2.73489i	1.42814	−	0.107024i	0.766234	+	0.642561i	$0.222128\pi$
$654$		0			0
$655$	34.1251	−	59.1065i	1.33338	−	2.30948i
$656$	4.96968	+	8.60773i	0.194033	+	0.336075i
$657$		0			0
$658$	−1.51012	+	0.985646i	−0.0588705	+	0.0384245i
$659$	18.2810	+	4.17253i	0.712129	+	0.162539i	0.563214	−	0.826311i	$-0.309565\pi$
$659$	18.2810	+	4.17253i	0.712129	+	0.162539i	0.148915	+	0.988850i	$0.452422\pi$
$660$		0			0
$661$	−16.6366	+	6.52940i	−0.647090	+	0.253964i	−0.666108	−	0.745855i	$-0.732041\pi$
$661$	−16.6366	+	6.52940i	−0.647090	+	0.253964i	0.0190183	+	0.999819i	$0.493946\pi$
$662$	−10.5367	+	4.13535i	−0.409521	+	0.160725i
$663$		0			0
$664$	6.82805	+	1.55846i	0.264980	+	0.0604799i
$665$	23.3967	+	7.73605i	0.907286	+	0.299991i
$666$		0			0
$667$	15.8682	+	27.4846i	0.614421	+	1.06421i
$668$	−4.17242	+	7.22685i	−0.161436	+	0.279615i
$669$		0			0
$670$	−0.0439542	+	0.00329391i	−0.00169810	+	0.000127255i
$671$	−19.5459	+	24.5097i	−0.754559	+	0.946187i
$672$		0			0
$673$	4.36126	+	5.46884i	0.168114	+	0.210808i	0.858751	−	0.512393i	$-0.171241\pi$
$673$	4.36126	+	5.46884i	0.168114	+	0.210808i	−0.690637	+	0.723202i	$0.742670\pi$
$674$	−23.0533	−	24.8455i	−0.887980	−	0.957014i
$675$		0			0
$676$	−5.96534	+	4.06710i	−0.229436	+	0.156427i
$677$	−28.4719	−	4.29145i	−1.09426	−	0.164934i	−0.422984	−	0.906137i	$-0.639017\pi$
$677$	−28.4719	−	4.29145i	−1.09426	−	0.164934i	−0.671280	+	0.741204i	$0.734255\pi$
$678$		0			0
$679$	9.66551	−	38.7358i	0.370928	−	1.48654i
$680$	0.629995	−	1.30820i	0.0241592	−	0.0501671i
$681$		0			0
$682$	−13.3250	+	14.3610i	−0.510241	+	0.549909i
$683$	14.8332	+	1.11160i	0.567577	+	0.0425340i	0.355429	−	0.934703i	$-0.384335\pi$
$683$	14.8332	+	1.11160i	0.567577	+	0.0425340i	0.212149	+	0.977237i	$0.431954\pi$
$684$		0			0
$685$		−	32.8978i		−	1.25696i
$686$	−8.27518	−	16.5687i	−0.315948	−	0.632595i
$687$		0			0
$688$	0.753296	−	1.91937i	0.0287192	−	0.0731752i
$689$	1.88771	−	25.1898i	0.0719161	−	0.959654i
$690$		0			0
$691$	−23.4309	+	34.3668i	−0.891353	+	1.30737i	0.0596589	+	0.998219i	$0.480999\pi$
$691$	−23.4309	+	34.3668i	−0.891353	+	1.30737i	−0.951012	+	0.309155i	$0.899954\pi$
$692$	12.6007	+	6.06817i	0.479006	+	0.230677i
$693$		0			0
$694$	−14.0878	+	6.78435i	−0.534767	+	0.257530i
$695$	−10.3840	+	68.8932i	−0.393887	+	2.61327i
$696$		0			0
$697$	−4.10244	+	0.618343i	−0.155391	+	0.0234214i
$698$	−10.1369	+	9.40565i	−0.383687	+	0.356009i
$699$		0			0
$700$	−10.8929	+	15.3057i	−0.411714	+	0.578501i
$701$	21.0751	+	16.8068i	0.795996	+	0.634785i	0.934655	−	0.355555i	$-0.115708\pi$
$701$	21.0751	+	16.8068i	0.795996	+	0.634785i	−0.138660	+	0.990340i	$0.544279\pi$
$702$		0			0
$703$	−5.87179	+	19.0359i	−0.221459	+	0.717951i
$704$	−3.45204	−	1.99303i	−0.130104	−	0.0751153i
$705$		0			0
$706$	2.98191	−	0.680602i	0.112226	−	0.0256148i
$707$	11.9279	−	36.0744i	0.448593	−	1.35672i
$708$		0			0
$709$	−6.36700	+	1.96396i	−0.239118	+	0.0737581i	−0.411998	−	0.911185i	$-0.635169\pi$
$709$	−6.36700	+	1.96396i	−0.239118	+	0.0737581i	0.172880	+	0.984943i	$0.444693\pi$
$710$	13.0016	+	33.1275i	0.487941	+	1.24325i
$711$		0			0
$712$	1.07581	+	3.48770i	0.0403178	+	0.130707i
$713$	4.15214	−	18.1917i	0.155499	−	0.681285i
$714$		0			0
$715$	−7.41798	−	32.5003i	−0.277417	−	1.21544i
$716$	15.1394	−	8.74073i	0.565785	−	0.326656i
$717$		0			0
$718$	−11.0205	−	3.39937i	−0.411281	−	0.126863i
$719$	−0.665549	−	8.88114i	−0.0248208	−	0.331210i	−0.995767	−	0.0919128i	$-0.970702\pi$
$719$	−0.665549	−	8.88114i	−0.0248208	−	0.331210i	0.970946	−	0.239298i	$-0.0769172\pi$
$720$		0			0
$721$	5.80933	−	5.17660i	0.216351	−	0.192787i
$722$	9.24973	−	7.37641i	0.344239	−	0.274522i
$723$		0			0
$724$	0.403096	+	2.67437i	0.0149809	+	0.0993921i
$725$	33.4354	+	49.0407i	1.24176	+	1.82133i
$726$		0			0
$727$	14.0077	+	29.0873i	0.519518	+	1.07879i	0.981422	+	0.191860i	$0.0614519\pi$
$727$	14.0077	+	29.0873i	0.519518	+	1.07879i	−0.461905	+	0.886930i	$0.652834\pi$
$728$	−4.89230	−	4.06525i	−0.181321	−	0.150668i
$729$		0			0
$730$	22.0598	+	15.0401i	0.816470	+	0.556660i
$731$	0.630905	+	0.585395i	0.0233349	+	0.0216516i
$732$		0			0
$733$	−13.0388	−	5.11734i	−0.481598	−	0.189013i	0.112107	−	0.993696i	$-0.464240\pi$
$733$	−13.0388	−	5.11734i	−0.481598	−	0.189013i	−0.593705	+	0.804683i	$0.702335\pi$
$734$	−2.46577			−0.0910133
$735$		0			0
$736$	3.79662			0.139945
$737$	−0.0470165	−	0.0184526i	−0.00173187	−	0.000679711i
$738$		0			0
$739$	−29.2337	−	27.1249i	−1.07538	−	0.997807i	−1.00000		0.000651848i	$-0.999793\pi$
$739$	−29.2337	−	27.1249i	−1.07538	−	0.997807i	−0.0753801	−	0.997155i	$-0.524017\pi$
$740$	−21.3837	−	14.5791i	−0.786079	−	0.535940i
$741$		0			0
$742$	−27.2205	+	5.63894i	−0.999297	+	0.207012i
$743$	−6.78817	−	14.0958i	−0.249034	−	0.517124i	0.738554	−	0.674195i	$-0.235509\pi$
$743$	−6.78817	−	14.0958i	−0.249034	−	0.517124i	−0.987587	+	0.157071i	$0.949795\pi$
$744$		0			0
$745$	28.1536	+	41.2938i	1.03147	+	1.51289i
$746$	3.77743	+	25.0616i	0.138302	+	0.917571i
$747$		0			0
$748$	1.30083	−	1.03738i	0.0475630	−	0.0379302i
$749$	12.3946	−	29.8024i	0.452887	−	1.08896i
$750$		0			0
$751$	−1.04091	−	13.8900i	−0.0379833	−	0.506852i	−0.983456	−	0.181150i	$-0.942018\pi$
$751$	−1.04091	−	13.8900i	−0.0379833	−	0.506852i	0.945472	−	0.325703i	$-0.105601\pi$
$752$	0.651309	+	0.200902i	0.0237508	+	0.00732615i
$753$		0			0
$754$	−17.4045	+	10.0485i	−0.633834	+	0.365944i
$755$	9.19307	+	40.2775i	0.334570	+	1.46585i
$756$		0			0
$757$	3.45788	−	15.1500i	0.125679	−	0.550635i	−0.872406	−	0.488781i	$-0.837442\pi$
$757$	3.45788	−	15.1500i	0.125679	−	0.550635i	0.998085	−	0.0618539i	$-0.0197013\pi$
$758$	8.78253	+	28.4723i	0.318996	+	1.03416i
$759$		0			0
$760$	−3.40278	−	8.67015i	−0.123432	−	0.314499i
$761$	3.79944	−	1.17197i	0.137730	−	0.0424840i	−0.225124	−	0.974330i	$-0.572279\pi$
$761$	3.79944	−	1.17197i	0.137730	−	0.0424840i	0.362854	+	0.931846i	$0.381803\pi$
$762$		0			0
$763$	−36.4653	−	3.47212i	−1.32013	−	0.125699i
$764$	−20.0920	+	4.58588i	−0.726904	+	0.165911i
$765$		0			0
$766$	−16.5896	−	9.57804i	−0.599408	−	0.346068i
$767$	−2.67075	+	8.65836i	−0.0964352	+	0.312635i
$768$		0			0
$769$	−21.9405	−	17.4969i	−0.791194	−	0.630956i	0.142189	−	0.989840i	$-0.454586\pi$
$769$	−21.9405	−	17.4969i	−0.791194	−	0.630956i	−0.933382	+	0.358884i	$0.883158\pi$
$770$	−32.1335	+	17.6995i	−1.15801	+	0.637847i
$771$		0			0
$772$	−17.9049	+	16.6133i	−0.644412	+	0.597927i
$773$	−4.27590	+	0.644489i	−0.153794	+	0.0231807i	−0.225488	−	0.974246i	$-0.572398\pi$
$773$	−4.27590	+	0.644489i	−0.153794	+	0.0231807i	0.0716941	+	0.997427i	$0.477159\pi$
$774$		0			0
$775$	5.20119	−	34.5076i	0.186832	−	1.23955i
$776$	−13.5953	+	6.54715i	−0.488043	+	0.235029i
$777$		0			0
$778$	−8.14018	−	3.92011i	−0.291840	−	0.140543i
$779$	−14.9916	+	21.9886i	−0.537129	+	0.787824i
$780$		0			0
$781$	−3.04745	+	40.6653i	−0.109046	+	1.45512i
$782$	−0.578972	+	1.47520i	−0.0207040	+	0.0527529i
$783$		0			0
$784$	−2.81760	+	6.40790i	−0.100629	+	0.228853i
$785$		−	38.9153i		−	1.38895i
$786$		0			0
$787$	−42.6034	−	3.19268i	−1.51865	−	0.113807i	−0.710882	−	0.703311i	$-0.751704\pi$
$787$	−42.6034	−	3.19268i	−1.51865	−	0.113807i	−0.807765	+	0.589504i	$0.799323\pi$
$788$	−0.752828	+	0.811355i	−0.0268184	+	0.0289033i
$789$		0			0
$790$	−19.3558	+	40.1928i	−0.688649	+	1.42999i
$791$	17.9008	+	23.3981i	0.636480	+	0.831939i
$792$		0			0
$793$	18.6970	+	2.81811i	0.663949	+	0.100074i
$794$	12.3883	−	8.44623i	0.439646	−	0.299745i
$795$		0			0
$796$	−0.0810694	−	0.0873720i	−0.00287343	−	0.00309682i
$797$	−9.47522	−	11.8816i	−0.335630	−	0.420866i	0.585165	−	0.810914i	$-0.301030\pi$
$797$	−9.47522	−	11.8816i	−0.335630	−	0.420866i	−0.920794	+	0.390048i	$0.872458\pi$
$798$		0			0
$799$	−0.177384	+	0.222433i	−0.00627540	+	0.00786910i
$800$	7.08065	−	0.530622i	0.250339	−	0.0187603i
$801$		0			0
$802$	−19.1415	+	33.1540i	−0.675909	+	1.17071i
$803$	15.2971	+	26.4954i	0.539823	+	0.935001i
$804$		0			0
$805$	18.0766	−	29.9028i	0.637117	−	1.05394i
$806$	11.5198	+	2.62932i	0.405768	+	0.0926138i
$807$		0			0
$808$	−13.3681	+	5.24660i	−0.470289	+	0.184575i
$809$	−44.8960	+	17.6204i	−1.57846	+	0.619499i	−0.982954	−	0.183852i	$-0.941143\pi$
$809$	−44.8960	+	17.6204i	−1.57846	+	0.619499i	−0.595505	+	0.803352i	$0.703048\pi$
$810$		0			0
$811$	−5.98010	−	1.36492i	−0.209990	−	0.0479288i	0.116232	−	0.993222i	$-0.462918\pi$
$811$	−5.98010	−	1.36492i	−0.209990	−	0.0479288i	−0.326222	+	0.945293i	$0.605776\pi$
$812$	15.9062	+	15.3662i	0.558200	+	0.539246i
$813$		0			0
$814$	−14.8282	−	25.6833i	−0.519729	−	0.900198i
$815$	−24.8566	+	43.0530i	−0.870690	+	1.50808i
$816$		0			0
$817$	5.50536	−	0.412569i	0.192608	−	0.0144340i
$818$	−17.9499	+	22.5084i	−0.627603	+	0.786989i
$819$		0			0
$820$	−21.5570	−	27.0317i	−0.752805	−	0.943987i
$821$	15.9777	+	17.2198i	0.557624	+	0.600976i	0.947447	−	0.319914i	$-0.103654\pi$
$821$	15.9777	+	17.2198i	0.557624	+	0.600976i	−0.389822	+	0.920890i	$0.627464\pi$
$822$		0			0
$823$	6.77806	−	4.62121i	0.236268	−	0.161085i	−0.439398	−	0.898292i	$-0.644808\pi$
$823$	6.77806	−	4.62121i	0.236268	−	0.161085i	0.675667	+	0.737207i	$0.263856\pi$
$824$	−2.90813	−	0.438330i	−0.101310	−	0.0152700i
$825$		0			0
$826$	9.96929	+	0.200721i	0.346876	+	0.00698398i
$827$	4.90201	−	10.1791i	0.170460	−	0.353963i	−0.798185	−	0.602412i	$-0.794206\pi$
$827$	4.90201	−	10.1791i	0.170460	−	0.353963i	0.968645	+	0.248449i	$0.0799207\pi$
$828$		0			0
$829$	−33.9942	+	36.6371i	−1.18067	+	1.27246i	−0.226222	+	0.974076i	$0.572637\pi$
$829$	−33.9942	+	36.6371i	−1.18067	+	1.27246i	−0.954447	+	0.298382i	$0.903553\pi$
$830$	−24.2946	−	1.82063i	−0.843278	−	0.0631950i
$831$		0			0
$832$			2.40419i			0.0833503i
$833$	−2.06015	−	2.07198i	−0.0713799	−	0.0717897i
$834$		0			0
$835$	10.6052	−	27.0216i	0.367008	−	0.935120i
$836$	0.797580	−	10.6430i	0.0275849	−	0.368095i
$837$		0			0
$838$	−5.12686	+	7.51972i	−0.177104	+	0.259764i
$839$	−19.3103	−	9.29936i	−0.666666	−	0.321050i	0.0697634	−	0.997564i	$-0.477776\pi$
$839$	−19.3103	−	9.29936i	−0.666666	−	0.321050i	−0.736430	+	0.676514i	$0.763490\pi$
$840$		0			0
$841$	36.8274	−	17.7351i	1.26991	−	0.611557i
$842$	−1.45327	+	9.64180i	−0.0500829	+	0.332279i
$843$		0			0
$844$	−10.1440	+	1.52896i	−0.349170	+	0.0526289i
$845$	18.4105	−	17.0825i	0.633341	−	0.587655i
$846$		0			0
$847$	−12.9151	+	0.706753i	−0.443767	+	0.0242843i
$848$	8.21457	+	6.55090i	0.282089	+	0.224959i
$849$		0			0
$850$	−0.873600	+	2.83214i	−0.0299642	+	0.0971417i
$851$	24.4626	+	14.1235i	0.838567	+	0.484147i
$852$		0			0
$853$	38.9893	−	8.89905i	1.33497	−	0.304698i	0.505294	−	0.862947i	$-0.331384\pi$
$853$	38.9893	−	8.89905i	1.33497	−	0.304698i	0.829673	+	0.558250i	$0.188527\pi$
$854$	−2.68645	−	20.6338i	−0.0919286	−	0.706075i
$855$		0			0
$856$	−11.6576	+	3.59589i	−0.398448	+	0.122905i
$857$	12.0977	+	30.8246i	0.413251	+	1.05295i	0.974318	+	0.225176i	$0.0722958\pi$
$857$	12.0977	+	30.8246i	0.413251	+	1.05295i	−0.561067	+	0.827771i	$0.689609\pi$
$858$		0			0
$859$	−3.17865	−	10.3049i	−0.108454	−	0.351600i	0.885035	−	0.465524i	$-0.154134\pi$
$859$	−3.17865	−	10.3049i	−0.108454	−	0.351600i	−0.993489	+	0.113924i	$0.963658\pi$
$860$	−1.59603	+	6.99265i	−0.0544241	+	0.238447i
$861$		0			0
$862$	−1.34495	−	5.89263i	−0.0458093	−	0.200704i
$863$	29.3432	−	16.9413i	0.998855	−	0.576689i	0.0909459	−	0.995856i	$-0.471011\pi$
$863$	29.3432	−	16.9413i	0.998855	−	0.576689i	0.907909	+	0.419166i	$0.137678\pi$
$864$		0			0
$865$	−46.4889	−	14.3399i	−1.58067	−	0.487573i
$866$	−2.98571	−	39.8415i	−0.101459	−	1.35387i
$867$		0			0
$868$	−0.710517	−	12.9839i	−0.0241165	−	0.440701i
$869$	−39.9663	+	31.8721i	−1.35576	+	1.08119i
$870$		0			0
$871$	0.00454038	+	0.0301235i	0.000153845	+	0.00102070i
$872$	7.79912	+	11.4392i	0.264111	+	0.387380i
$873$		0			0
$874$	4.41067	+	9.15885i	0.149193	+	0.309803i
$875$	8.73671	−	17.2451i	0.295355	−	0.582990i
$876$		0			0
$877$	−2.65953	−	1.81324i	−0.0898059	−	0.0612286i	0.517585	−	0.855632i	$-0.326831\pi$
$877$	−2.65953	−	1.81324i	−0.0898059	−	0.0612286i	−0.607390	+	0.794403i	$0.707784\pi$
$878$	5.29208	+	4.91033i	0.178599	+	0.165716i
$879$		0			0
$880$	12.9074	+	5.06576i	0.435107	+	0.170767i
$881$	7.57631			0.255252			0.127626	−	0.991822i	$-0.459264\pi$
$881$	7.57631			0.255252			0.127626	+	0.991822i	$0.459264\pi$
$882$		0			0
$883$	−16.6964			−0.561877			−0.280939	−	0.959726i	$-0.590646\pi$
$883$	−16.6964			−0.561877			−0.280939	+	0.959726i	$0.590646\pi$
$884$	−0.934160	−	0.366631i	−0.0314192	−	0.0123311i
$885$		0			0
$886$	7.21690	+	6.69631i	0.242457	+	0.224967i
$887$	18.7746	+	12.8003i	0.630389	+	0.429792i	0.835914	−	0.548860i	$-0.184938\pi$
$887$	18.7746	+	12.8003i	0.630389	+	0.429792i	−0.205525	+	0.978652i	$0.565890\pi$
$888$		0			0
$889$	−0.642844	+	31.9284i	−0.0215603	+	1.07084i
$890$	−5.50872	−	11.4390i	−0.184653	−	0.383435i
$891$		0			0
$892$	3.54244	+	5.19580i	0.118610	+	0.173968i
$893$	0.271999	+	1.80459i	0.00910209	+	0.0603884i
$894$		0			0
$895$	−47.5437	+	37.9148i	−1.58921	+	1.26735i
$896$	2.54339	−	0.728798i	0.0849688	−	0.0243474i
$897$		0			0
$898$	0.860909	+	11.4880i	0.0287289	+	0.383361i
$899$	−39.2581	−	12.1095i	−1.30933	−	0.403875i
$900$		0			0
$901$	−3.79808	+	2.19282i	−0.126532	+	0.0730535i
$902$	−8.81604	−	38.6256i	−0.293542	−	1.28609i
$903$		0			0
$904$	2.47776	−	10.8558i	0.0824090	−	0.361057i
$905$	−2.77308	−	8.99010i	−0.0921803	−	0.298841i
$906$		0			0
$907$	10.1208	+	25.7874i	0.336056	+	0.856257i	0.994607	+	0.103720i	$0.0330746\pi$
$907$	10.1208	+	25.7874i	0.336056	+	0.856257i	−0.658551	+	0.752537i	$0.728830\pi$
$908$	−25.2406	+	7.78568i	−0.837637	+	0.258377i
$909$		0			0
$910$	18.9358	+	11.4469i	0.627716	+	0.379462i
$911$	−33.0890	+	7.55235i	−1.09629	+	0.250221i	−0.732163	−	0.681130i	$-0.761489\pi$
$911$	−33.0890	+	7.55235i	−1.09629	+	0.250221i	−0.364125	+	0.931350i	$0.618632\pi$
$912$		0			0
$913$	−24.1768	−	13.9585i	−0.800137	−	0.461959i
$914$	5.97594	−	19.3735i	0.197667	−	0.640819i
$915$		0			0
$916$	0.405114	+	0.323068i	0.0133854	+	0.0106745i
$917$	−8.76850	+	51.1641i	−0.289561	+	1.68959i
$918$		0			0
$919$	−6.82188	+	6.32978i	−0.225033	+	0.208800i	−0.784629	−	0.619965i	$-0.787147\pi$
$919$	−6.82188	+	6.32978i	−0.225033	+	0.208800i	0.559596	+	0.828765i	$0.310956\pi$
$920$	−13.0593	+	1.96838i	−0.430553	+	0.0648955i
$921$		0			0
$922$	3.64285	−	24.1688i	0.119971	−	0.795955i
$923$	22.1602	−	10.6718i	0.729413	−	0.351267i
$924$		0			0
$925$	47.5964	+	22.9212i	1.56496	+	0.753644i
$926$	−0.502468	+	0.736986i	−0.0165121	+	0.0242188i
$927$		0			0
$928$	0.624680	−	8.33577i	0.0205061	−	0.273635i
$929$	3.71490	−	9.46541i	0.121882	−	0.310550i	−0.856891	−	0.515498i	$-0.827607\pi$
$929$	3.71490	−	9.46541i	0.121882	−	0.310550i	0.978773	+	0.204948i	$0.0657024\pi$
$930$		0			0
$931$	−18.7315	+	0.647195i	−0.613901	+	0.0212110i
$932$			0.436873i			0.0143103i
$933$		0			0
$934$	−4.99088	−	0.374015i	−0.163306	−	0.0122381i
$935$	−3.93666	+	4.24271i	−0.128742	+	0.138751i
$936$		0			0
$937$	−0.555030	+	1.15253i	−0.0181321	+	0.0376516i	−0.909838	−	0.414963i	$-0.863794\pi$
$937$	−0.555030	+	1.15253i	−0.0181321	+	0.0376516i	0.891706	+	0.452615i	$0.149509\pi$
$938$	0.0304913	−	0.0139348i	0.000995576	−	0.000454988i
$939$		0			0
$940$	−2.34448	−	0.353374i	−0.0764686	−	0.0115258i
$941$	10.3380	−	7.04833i	0.337009	−	0.229769i	−0.382976	−	0.923758i	$-0.625101\pi$
$941$	10.3380	−	7.04833i	0.337009	−	0.229769i	0.719985	+	0.693989i	$0.244148\pi$
$942$		0			0
$943$	25.6670	+	27.6624i	0.835831	+	0.900812i
$944$	−2.34981	−	2.94657i	−0.0764798	−	0.0959026i
$945$		0			0
$946$	−5.12438	+	6.42577i	−0.166608	+	0.208920i
$947$	15.9180	−	1.19289i	0.517266	−	0.0387638i	0.186460	−	0.982462i	$-0.440298\pi$
$947$	15.9180	−	1.19289i	0.517266	−	0.0387638i	0.330806	+	0.943699i	$0.392679\pi$
$948$		0			0
$949$	9.22642	−	15.9806i	0.299502	−	0.518753i
$950$	9.50590	+	16.4647i	0.308412	+	0.534186i
$951$		0			0
$952$	−0.104681	+	1.09939i	−0.00339272	+	0.0356314i
$953$	21.7320	+	4.96018i	0.703968	+	0.160676i	0.559496	−	0.828833i	$-0.310995\pi$
$953$	21.7320	+	4.96018i	0.703968	+	0.160676i	0.144472	+	0.989509i	$0.453852\pi$
$954$		0			0
$955$	66.7335	−	26.1910i	2.15945	−	0.847520i
$956$	−17.0199	+	6.67982i	−0.550463	+	0.216041i
$957$		0			0
$958$	41.6009	+	9.49513i	1.34406	+	0.306774i
$959$	8.67068	+	23.4712i	0.279991	+	0.757924i
$960$		0			0
$961$	−3.42248	−	5.92791i	−0.110403	−	0.191223i
$962$	−8.94362	+	15.4908i	−0.288354	+	0.499443i
$963$		0			0
$964$	25.7256	−	1.92787i	0.828566	−	0.0620925i
$965$	52.9747	−	66.4282i	1.70532	−	2.13840i
$966$		0			0
$967$	−21.4158	−	26.8546i	−0.688687	−	0.863586i	0.307435	−	0.951569i	$-0.400529\pi$
$967$	−21.4158	−	26.8546i	−0.688687	−	0.863586i	−0.996122	+	0.0879832i	$0.971958\pi$
$968$	3.32519	+	3.58370i	0.106876	+	0.115184i
$969$		0			0
$970$	43.3697	−	29.5690i	1.39252	−	0.949402i
$971$	33.5870	+	5.06243i	1.07786	+	0.162461i	0.663890	−	0.747830i	$-0.268904\pi$
$971$	33.5870	+	5.06243i	1.07786	+	0.162461i	0.413969	+	0.910291i	$0.364142\pi$
$972$		0			0
$973$	−10.7493	−	51.8893i	−0.344605	−	1.66349i
$974$	−9.95030	+	20.6620i	−0.318828	+	0.662054i
$975$		0			0
$976$	−5.34933	+	5.76521i	−0.171228	+	0.184540i
$977$	−51.3503	−	3.84817i	−1.64284	−	0.123114i	−0.779049	−	0.626963i	$-0.784298\pi$
$977$	−51.3503	−	3.84817i	−1.64284	−	0.123114i	−0.863792	+	0.503849i	$0.831917\pi$
$978$		0			0
$979$		−	14.5486i		−	0.464974i
$980$	6.36956	−	23.5022i	0.203468	−	0.750750i
$981$		0			0
$982$	3.49852	−	8.91408i	0.111642	−	0.284460i
$983$	−2.63524	+	35.1648i	−0.0840510	+	1.12158i	0.782552	+	0.622585i	$0.213917\pi$
$983$	−2.63524	+	35.1648i	−0.0840510	+	1.12158i	−0.866603	+	0.498998i	$0.833702\pi$
$984$		0			0
$985$	2.16887	−	3.18115i	0.0691059	−	0.101360i
$986$	3.14365	+	1.51390i	0.100114	+	0.0482124i
$987$		0			0
$988$	−5.79979	+	2.79303i	−0.184516	+	0.0888582i
$989$	1.16674	−	7.74081i	0.0371002	−	0.246144i
$990$		0			0
$991$	−33.0515	+	4.98171i	−1.04992	+	0.158249i	−0.651263	−	0.758852i	$-0.725760\pi$
$991$	−33.0515	+	4.98171i	−1.04992	+	0.158249i	−0.398653	+	0.917102i	$0.630522\pi$
$992$	−3.60279	+	3.34290i	−0.114389	+	0.106137i
$993$		0			0
$994$	−18.0073	−	20.2083i	−0.571157	−	0.640969i
$995$	0.324155	+	0.258505i	0.0102764	+	0.00819516i
$996$		0			0
$997$	6.39015	−	20.7164i	0.202378	−	0.656094i	−0.796310	−	0.604889i	$-0.793218\pi$
$997$	6.39015	−	20.7164i	0.202378	−	0.656094i	0.998688	−	0.0512051i	$-0.0163062\pi$
$998$	8.74980	+	5.05170i	0.276970	+	0.159909i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.2.bl.a.395.2	✓	240
3.2	odd	2	inner	882.2.bl.a.395.19	yes	240
49.33	odd	42	inner	882.2.bl.a.719.19	yes	240
147.131	even	42	inner	882.2.bl.a.719.2	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
882.2.bl.a.395.2	✓	240	1.1	even	1	trivial
882.2.bl.a.395.19	yes	240	3.2	odd	2	inner
882.2.bl.a.719.2	yes	240	147.131	even	42	inner
882.2.bl.a.719.19	yes	240	49.33	odd	42	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	882.bl (of order \(42\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.930874 - 0.365341i) q^{2} +(0.733052 + 0.680173i) q^{4} +(-2.87414 - 1.95955i) q^{5} +(2.56704 + 0.640539i) q^{7} +(-0.433884 - 0.900969i) q^{8} +O(q^{10})\)	\(q+(-0.930874 - 0.365341i) q^{2} +(0.733052 + 0.680173i) q^{4} +(-2.87414 - 1.95955i) q^{5} +(2.56704 + 0.640539i) q^{7} +(-0.433884 - 0.900969i) q^{8} +(1.95955 + 2.87414i) q^{10} +(0.594093 + 3.94155i) q^{11} +(1.87967 - 1.49899i) q^{13} +(-2.15558 - 1.53411i) q^{14} +(0.0747301 + 0.997204i) q^{16} +(-0.398865 - 0.123034i) q^{17} +(-2.31881 + 1.33876i) q^{19} +(-0.774056 - 3.39136i) q^{20} +(0.886984 - 3.88613i) q^{22} +(1.11907 + 3.62795i) q^{23} +(2.59411 + 6.60968i) q^{25} +(-2.29738 + 0.708647i) q^{26} +(1.44610 + 2.21558i) q^{28} +(8.14957 - 1.86009i) q^{29} +(-4.25632 - 2.45739i) q^{31} +(0.294755 - 0.955573i) q^{32} +(0.326344 + 0.260250i) q^{34} +(-6.12286 - 6.87125i) q^{35} +(5.45393 - 5.06051i) q^{37} +(2.64762 - 0.399065i) q^{38} +(-0.518455 + 3.43973i) q^{40} +(8.95505 - 4.31252i) q^{41} +(-1.85771 - 0.894625i) q^{43} +(-2.24543 + 3.29344i) q^{44} +(0.283722 - 3.78600i) q^{46} +(0.249013 - 0.634474i) q^{47} +(6.17942 + 3.28858i) q^{49} -7.10051i q^{50} +(2.39747 + 0.179665i) q^{52} +(7.14646 - 7.70205i) q^{53} +(6.01617 - 12.4927i) q^{55} +(-0.536692 - 2.59075i) q^{56} +(-8.26578 - 1.24587i) q^{58} +(-3.11393 + 2.12304i) q^{59} +(5.34933 + 5.76521i) q^{61} +(3.06431 + 3.84253i) q^{62} +(-0.623490 + 0.781831i) q^{64} +(-8.33977 + 0.624980i) q^{65} +(-0.00633555 + 0.0109735i) q^{67} +(-0.208705 - 0.361487i) q^{68} +(3.18926 + 8.63320i) q^{70} +(9.97398 + 2.27650i) q^{71} +(7.14472 - 2.80410i) q^{73} +(-6.92573 + 2.71815i) q^{74} +(-2.61040 - 0.595806i) q^{76} +(-0.999654 + 10.4987i) q^{77} +(6.41219 + 11.1062i) q^{79} +(1.73929 - 3.01254i) q^{80} +(-9.91156 + 0.742769i) q^{82} +(-4.36670 + 5.47567i) q^{83} +(0.905301 + 1.13521i) q^{85} +(1.40245 + 1.51148i) q^{86} +(3.29344 - 2.24543i) q^{88} +(-3.60909 - 0.543983i) q^{89} +(5.78535 - 2.64396i) q^{91} +(-1.64729 + 3.42064i) q^{92} +(-0.463599 + 0.499641i) q^{94} +(9.28795 + 0.696035i) q^{95} -15.0896i q^{97} +(-4.55081 - 5.31885i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 20 q^{4} - 4 q^{7}+O(q^{10}) \) 240 * q - 20 * q^4 - 4 * q^7	\( 240 q - 20 q^{4} - 4 q^{7} - 12 q^{10} + 20 q^{16} + 24 q^{19} - 20 q^{22} + 24 q^{25} + 4 q^{28} + 12 q^{31} - 32 q^{37} + 44 q^{40} - 48 q^{43} + 204 q^{49} + 140 q^{55} + 136 q^{58} + 88 q^{61} + 40 q^{64} - 32 q^{67} - 16 q^{70} - 24 q^{73} - 28 q^{79} - 48 q^{82} - 112 q^{85} + 4 q^{88} + 80 q^{91} + 80 q^{94}+O(q^{100}) \) 240 * q - 20 * q^4 - 4 * q^7 - 12 * q^10 + 20 * q^16 + 24 * q^19 - 20 * q^22 + 24 * q^25 + 4 * q^28 + 12 * q^31 - 32 * q^37 + 44 * q^40 - 48 * q^43 + 204 * q^49 + 140 * q^55 + 136 * q^58 + 88 * q^61 + 40 * q^64 - 32 * q^67 - 16 * q^70 - 24 * q^73 - 28 * q^79 - 48 * q^82 - 112 * q^85 + 4 * q^88 + 80 * q^91 + 80 * q^94

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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