LMFDB - Embedded newform 882.2.bl.a.395.4

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			395.4
Character	$\chi$	$=$	882.395
Dual form			882.2.bl.a.719.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.930874 - 0.365341i) q^{2} +(0.733052 + 0.680173i) q^{4} +(-0.668488 - 0.455768i) q^{5} +(1.56257 + 2.13503i) q^{7} +(-0.433884 - 0.900969i) q^{8} +O(q^{10})$	\(q+(-0.930874 - 0.365341i) q^{2} +(0.733052 + 0.680173i) q^{4} +(-0.668488 - 0.455768i) q^{5} +(1.56257 + 2.13503i) q^{7} +(-0.433884 - 0.900969i) q^{8} +(0.455768 + 0.668488i) q^{10} +(0.205813 + 1.36548i) q^{11} +(-4.63979 + 3.70011i) q^{13} +(-0.674542 - 2.55832i) q^{14} +(0.0747301 + 0.997204i) q^{16} +(-6.36675 - 1.96388i) q^{17} +(-0.313177 + 0.180813i) q^{19} +(-0.180036 - 0.788789i) q^{20} +(0.307280 - 1.34628i) q^{22} +(-0.919782 - 2.98186i) q^{23} +(-1.58755 - 4.04502i) q^{25} +(5.67087 - 1.74923i) q^{26} +(-0.306745 + 2.62791i) q^{28} +(2.15561 - 0.492003i) q^{29} +(4.11108 + 2.37353i) q^{31} +(0.294755 - 0.955573i) q^{32} +(5.20916 + 4.15416i) q^{34} +(-0.0714819 - 2.13942i) q^{35} +(-0.607955 + 0.564100i) q^{37} +(0.357587 - 0.0538975i) q^{38} +(-0.120586 + 0.800038i) q^{40} +(-10.1084 + 4.86797i) q^{41} +(-9.83641 - 4.73696i) q^{43} +(-0.777892 + 1.14096i) q^{44} +(-0.233195 + 3.11177i) q^{46} +(-2.32313 + 5.91923i) q^{47} +(-2.11674 + 6.67229i) q^{49} +4.34540i q^{50} +(-5.91793 - 0.443487i) q^{52} +(2.08863 - 2.25100i) q^{53} +(0.484759 - 1.00661i) q^{55} +(1.24562 - 2.33419i) q^{56} +(-2.18635 - 0.329539i) q^{58} +(3.04261 - 2.07442i) q^{59} +(4.15111 + 4.47383i) q^{61} +(-2.95975 - 3.71141i) q^{62} +(-0.623490 + 0.781831i) q^{64} +(4.78804 - 0.358814i) q^{65} +(-0.0121720 + 0.0210825i) q^{67} +(-3.33138 - 5.77012i) q^{68} +(-0.715076 + 2.01764i) q^{70} +(-14.0589 - 3.20886i) q^{71} +(-5.89791 + 2.31476i) q^{73} +(0.772018 - 0.302995i) q^{74} +(-0.352559 - 0.0804693i) q^{76} +(-2.59375 + 2.57308i) q^{77} +(4.89112 + 8.47167i) q^{79} +(0.404537 - 0.700679i) q^{80} +(11.1881 - 0.838436i) q^{82} +(-8.22704 + 10.3164i) q^{83} +(3.36103 + 4.21459i) q^{85} +(7.42585 + 8.00316i) q^{86} +(1.14096 - 0.777892i) q^{88} +(3.30899 + 0.498750i) q^{89} +(-15.1499 - 4.12442i) q^{91} +(1.35393 - 2.81147i) q^{92} +(4.32507 - 4.66132i) q^{94} +(0.291764 + 0.0218647i) q^{95} -6.58675i q^{97} +(4.40808 - 5.43773i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−0.668488	−	0.455768i	−0.298957	−	0.203826i	0.404546	−	0.914518i	$-0.367430\pi$
$5$	−0.668488	−	0.455768i	−0.298957	−	0.203826i	−0.703503	+	0.710692i	$0.748382\pi$
$6$		0			0
$7$	1.56257	+	2.13503i	0.590597	+	0.806967i
$7$	1.56257	+	2.13503i	0.590597	+	0.806967i
$8$	−0.433884	−	0.900969i	−0.153401	−	0.318541i
$9$		0			0
$10$	0.455768	+	0.668488i	0.144126	+	0.211395i
$11$	0.205813	+	1.36548i	0.0620550	+	0.411708i	0.998194	+	0.0600772i	$0.0191347\pi$
$11$	0.205813	+	1.36548i	0.0620550	+	0.411708i	−0.936139	+	0.351631i	$0.885627\pi$
$12$		0			0
$13$	−4.63979	+	3.70011i	−1.28685	+	1.02623i	−0.289228	+	0.957260i	$0.593399\pi$
$13$	−4.63979	+	3.70011i	−1.28685	+	1.02623i	−0.997619	+	0.0689664i	$0.978030\pi$
$14$	−0.674542	−	2.55832i	−0.180279	−	0.683739i
$15$		0			0
$16$	0.0747301	+	0.997204i	0.0186825	+	0.249301i
$17$	−6.36675	−	1.96388i	−1.54416	−	0.476312i	−0.598409	−	0.801191i	$-0.704200\pi$
$17$	−6.36675	−	1.96388i	−1.54416	−	0.476312i	−0.945756	+	0.324879i	$0.894676\pi$
$18$		0			0
$19$	−0.313177	+	0.180813i	−0.0718478	+	0.0414813i	−0.535494	−	0.844539i	$-0.679874\pi$
$19$	−0.313177	+	0.180813i	−0.0718478	+	0.0414813i	0.463646	+	0.886021i	$0.346541\pi$
$20$	−0.180036	−	0.788789i	−0.0402573	−	0.176379i
$21$		0			0
$22$	0.307280	−	1.34628i	0.0655124	−	0.287028i
$23$	−0.919782	−	2.98186i	−0.191788	−	0.621761i	−0.999483	−	0.0321602i	$-0.989761\pi$
$23$	−0.919782	−	2.98186i	−0.191788	−	0.621761i	0.807695	−	0.589601i	$-0.200715\pi$
$24$		0			0
$25$	−1.58755	−	4.04502i	−0.317511	−	0.809004i
$26$	5.67087	−	1.74923i	1.11215	−	0.343052i
$27$		0			0
$28$	−0.306745	+	2.62791i	−0.0579694	+	0.496628i
$29$	2.15561	−	0.492003i	0.400286	−	0.0913627i	−0.0176384	−	0.999844i	$-0.505615\pi$
$29$	2.15561	−	0.492003i	0.400286	−	0.0913627i	0.417925	+	0.908482i	$0.362758\pi$
$30$		0			0
$31$	4.11108	+	2.37353i	0.738372	+	0.426299i	0.821477	−	0.570242i	$-0.193150\pi$
$31$	4.11108	+	2.37353i	0.738372	+	0.426299i	−0.0831053	+	0.996541i	$0.526484\pi$
$32$	0.294755	−	0.955573i	0.0521058	−	0.168923i
$33$		0			0
$34$	5.20916	+	4.15416i	0.893363	+	0.712433i
$35$	−0.0714819	−	2.13942i	−0.0120827	−	0.361627i
$36$		0			0
$37$	−0.607955	+	0.564100i	−0.0999471	+	0.0927374i	−0.728564	−	0.684978i	$-0.759812\pi$
$37$	−0.607955	+	0.564100i	−0.0999471	+	0.0927374i	0.628617	+	0.777715i	$0.283621\pi$
$38$	0.357587	−	0.0538975i	0.0580082	−	0.00874334i
$39$		0			0
$40$	−0.120586	+	0.800038i	−0.0190664	+	0.126497i
$41$	−10.1084	+	4.86797i	−1.57867	+	0.760249i	−0.998527	−	0.0542640i	$-0.982719\pi$
$41$	−10.1084	+	4.86797i	−1.57867	+	0.760249i	−0.580146	+	0.814513i	$0.697004\pi$
$42$		0			0
$43$	−9.83641	−	4.73696i	−1.50004	−	0.722380i	−0.509610	−	0.860406i	$-0.670210\pi$
$43$	−9.83641	−	4.73696i	−1.50004	−	0.722380i	−0.990429	+	0.138025i	$0.955924\pi$
$44$	−0.777892	+	1.14096i	−0.117272	+	0.172006i
$45$		0			0
$46$	−0.233195	+	3.11177i	−0.0343827	+	0.458805i
$47$	−2.32313	+	5.91923i	−0.338863	+	0.863408i	0.655285	+	0.755381i	$0.272548\pi$
$47$	−2.32313	+	5.91923i	−0.338863	+	0.863408i	−0.994148	+	0.108026i	$0.965547\pi$
$48$		0			0
$49$	−2.11674	+	6.67229i	−0.302391	+	0.953184i
$50$			4.34540i			0.614532i
$51$		0			0
$52$	−5.91793	−	0.443487i	−0.820669	−	0.0615006i
$53$	2.08863	−	2.25100i	0.286895	−	0.309199i	−0.573117	−	0.819474i	$-0.694266\pi$
$53$	2.08863	−	2.25100i	0.286895	−	0.309199i	0.860011	+	0.510275i	$0.170456\pi$
$54$		0			0
$55$	0.484759	−	1.00661i	0.0653648	−	0.135731i
$56$	1.24562	−	2.33419i	0.166454	−	0.311919i
$57$		0			0
$58$	−2.18635	−	0.329539i	−0.287081	−	0.0432706i
$59$	3.04261	−	2.07442i	0.396114	−	0.270066i	−0.348839	−	0.937183i	$-0.613424\pi$
$59$	3.04261	−	2.07442i	0.396114	−	0.270066i	0.744953	+	0.667117i	$0.232472\pi$
$60$		0			0
$61$	4.15111	+	4.47383i	0.531495	+	0.572815i	0.940533	−	0.339702i	$-0.110326\pi$
$61$	4.15111	+	4.47383i	0.531495	+	0.572815i	−0.409038	+	0.912517i	$0.634136\pi$
$62$	−2.95975	−	3.71141i	−0.375888	−	0.471349i
$63$		0			0
$64$	−0.623490	+	0.781831i	−0.0779362	+	0.0977289i
$65$	4.78804	−	0.358814i	0.593883	−	0.0445054i
$66$		0			0
$67$	−0.0121720	+	0.0210825i	−0.00148704	+	0.00257563i	−0.866768	−	0.498712i	$-0.833807\pi$
$67$	−0.0121720	+	0.0210825i	−0.00148704	+	0.00257563i	0.865281	+	0.501287i	$0.167140\pi$
$68$	−3.33138	−	5.77012i	−0.403989	−	0.699730i
$69$		0			0
$70$	−0.715076	+	2.01764i	−0.0854679	+	0.241154i
$71$	−14.0589	−	3.20886i	−1.66849	−	0.380822i	−0.719096	−	0.694911i	$-0.755444\pi$
$71$	−14.0589	−	3.20886i	−1.66849	−	0.380822i	−0.949394	+	0.314089i	$0.898301\pi$
$72$		0			0
$73$	−5.89791	+	2.31476i	−0.690298	+	0.270922i	−0.684449	−	0.729061i	$-0.739957\pi$
$73$	−5.89791	+	2.31476i	−0.690298	+	0.270922i	−0.00584927	+	0.999983i	$0.501862\pi$
$74$	0.772018	−	0.302995i	0.0897452	−	0.0352224i
$75$		0			0
$76$	−0.352559	−	0.0804693i	−0.0404413	−	0.00923047i
$77$	−2.59375	+	2.57308i	−0.295585	+	0.293230i
$78$		0			0
$79$	4.89112	+	8.47167i	0.550294	+	0.953138i	0.998253	+	0.0590835i	$0.0188178\pi$
$79$	4.89112	+	8.47167i	0.550294	+	0.953138i	−0.447959	+	0.894054i	$0.647849\pi$
$80$	0.404537	−	0.700679i	0.0452286	−	0.0783383i
$81$		0			0
$82$	11.1881	−	0.838436i	1.23552	−	0.0925897i
$83$	−8.22704	+	10.3164i	−0.903035	+	1.13237i	0.0876437	+	0.996152i	$0.472066\pi$
$83$	−8.22704	+	10.3164i	−0.903035	+	1.13237i	−0.990679	+	0.136218i	$0.956505\pi$
$84$		0			0
$85$	3.36103	+	4.21459i	0.364555	+	0.457137i
$86$	7.42585	+	8.00316i	0.800750	+	0.863003i
$87$		0			0
$88$	1.14096	−	0.777892i	0.121626	−	0.0829235i
$89$	3.30899	+	0.498750i	0.350752	+	0.0528674i	0.322056	−	0.946721i	$-0.395626\pi$
$89$	3.30899	+	0.498750i	0.350752	+	0.0528674i	0.0286966	+	0.999588i	$0.490864\pi$
$90$		0			0
$91$	−15.1499	−	4.12442i	−1.58814	−	0.432357i
$92$	1.35393	−	2.81147i	0.141157	−	0.293116i
$93$		0			0
$94$	4.32507	−	4.66132i	0.446097	−	0.480778i
$95$	0.291764	+	0.0218647i	0.0299344	+	0.00224327i
$96$		0			0
$97$		−	6.58675i		−	0.668783i	−0.942434	−	0.334392i	$-0.891469\pi$
$97$		−	6.58675i		−	0.668783i	0.942434	−	0.334392i	$-0.108531\pi$
$98$	4.40808	−	5.43773i	0.445283	−	0.549293i
$99$		0			0
$100$	1.58755	−	4.04502i	0.158755	−	0.404502i
$101$	−0.287104	+	3.83114i	−0.0285679	+	0.381212i	0.964534	+	0.263958i	$0.0850282\pi$
$101$	−0.287104	+	3.83114i	−0.0285679	+	0.381212i	−0.993102	+	0.117254i	$0.962591\pi$
$102$		0			0
$103$	8.38158	−	12.2935i	0.825862	−	1.21132i	−0.149073	−	0.988826i	$-0.547629\pi$
$103$	8.38158	−	12.2935i	0.825862	−	1.21132i	0.974935	−	0.222490i	$-0.0714186\pi$
$104$	5.34682	+	2.57489i	0.524299	+	0.252489i
$105$		0			0
$106$	−2.76663	+	1.33234i	−0.268719	+	0.129408i
$107$	−1.98598	+	13.1761i	−0.191992	+	1.27378i	0.660415	+	0.750901i	$0.270380\pi$
$107$	−1.98598	+	13.1761i	−0.191992	+	1.27378i	−0.852406	+	0.522880i	$0.824858\pi$
$108$		0			0
$109$	−17.3001	+	2.60757i	−1.65705	+	0.249759i	−0.909878	−	0.414876i	$-0.863825\pi$
$109$	−17.3001	+	2.60757i	−1.65705	+	0.249759i	−0.747168	+	0.664636i	$0.768587\pi$
$110$	−0.819006	+	0.759926i	−0.0780891	+	0.0724561i
$111$		0			0
$112$	−2.01229	+	1.71775i	−0.190144	+	0.162312i
$113$	13.5057	+	10.7704i	1.27051	+	1.01320i	0.998707	+	0.0508421i	$0.0161905\pi$
$113$	13.5057	+	10.7704i	1.27051	+	1.01320i	0.271800	+	0.962354i	$0.412381\pi$
$114$		0			0
$115$	−0.744172	+	2.41255i	−0.0693944	+	0.224971i
$116$	1.91482	+	1.10552i	0.177787	+	0.102645i
$117$		0			0
$118$	−3.59015	+	0.819429i	−0.330500	+	0.0754346i
$119$	−5.75555	−	16.6619i	−0.527611	−	1.52740i
$120$		0			0
$121$	8.68912	−	2.68024i	0.789920	−	0.243658i
$122$	−2.22968	−	5.68114i	−0.201866	−	0.514346i
$123$		0			0
$124$	1.39922	+	4.53617i	0.125654	+	0.407360i
$125$	−1.68251	+	7.37155i	−0.150488	+	0.659331i
$126$		0			0
$127$	−3.91639	−	17.1588i	−0.347524	−	1.52260i	−0.782782	−	0.622296i	$-0.786200\pi$
$127$	−3.91639	−	17.1588i	−0.347524	−	1.52260i	0.435258	−	0.900306i	$-0.356657\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$		0			0
$130$	−4.58815	−	1.41526i	−0.402407	−	0.124126i
$131$	0.253729	+	3.38577i	0.0221684	+	0.295816i	0.997258	+	0.0740047i	$0.0235780\pi$
$131$	0.253729	+	3.38577i	0.0221684	+	0.295816i	−0.975090	+	0.221812i	$0.928803\pi$
$132$		0			0
$133$	−0.875404	−	0.386111i	−0.0759071	−	0.0334800i
$134$	0.0190328	−	0.0151782i	0.00164419	−	0.00131120i
$135$		0			0
$136$	0.993033	+	6.58834i	0.0851519	+	0.564946i
$137$	6.62373	+	9.71523i	0.565904	+	0.830028i	0.997398	−	0.0720871i	$-0.0229660\pi$
$137$	6.62373	+	9.71523i	0.565904	+	0.830028i	−0.431495	+	0.902116i	$0.642014\pi$
$138$		0			0
$139$	5.30386	+	11.0136i	0.449867	+	0.934159i	0.995376	+	0.0960539i	$0.0306221\pi$
$139$	5.30386	+	11.0136i	0.449867	+	0.934159i	−0.545509	+	0.838105i	$0.683664\pi$
$140$	1.40277	−	1.61692i	0.118556	−	0.136655i
$141$		0			0
$142$	11.9148	+	8.12336i	0.999866	+	0.681697i
$143$	−6.00737	−	5.57402i	−0.502361	−	0.466123i
$144$		0			0
$145$	−1.66524	−	0.653558i	−0.138290	−	0.0542750i
$146$	6.33589			0.524362
$147$		0			0
$148$	−0.829347			−0.0681719
$149$	10.3690	+	4.06954i	0.849463	+	0.333390i	0.749827	−	0.661634i	$-0.230137\pi$
$149$	10.3690	+	4.06954i	0.849463	+	0.333390i	0.0996366	+	0.995024i	$0.468232\pi$
$150$		0			0
$151$	−9.98544	−	9.26514i	−0.812604	−	0.753986i	0.159835	−	0.987144i	$-0.448904\pi$
$151$	−9.98544	−	9.26514i	−0.812604	−	0.753986i	−0.972439	+	0.233157i	$0.925094\pi$
$152$	0.298789	+	0.203711i	0.0242350	+	0.0165232i
$153$		0			0
$154$	3.35451	−	1.44761i	0.270314	−	0.116652i
$155$	−1.66643	−	3.46038i	−0.133851	−	0.277944i
$156$		0			0
$157$	−2.59326	−	3.80361i	−0.206964	−	0.303561i	0.708696	−	0.705514i	$-0.249284\pi$
$157$	−2.59326	−	3.80361i	−0.206964	−	0.303561i	−0.915660	+	0.401953i	$0.868331\pi$
$158$	−1.45797	−	9.67299i	−0.115990	−	0.769541i
$159$		0			0
$160$	−0.632560	+	0.504450i	−0.0500082	+	0.0398802i
$161$	4.92915	−	6.62314i	0.388471	−	0.521976i
$162$		0			0
$163$	0.0554094	+	0.739387i	0.00434000	+	0.0579133i	0.998953	−	0.0457419i	$-0.0145652\pi$
$163$	0.0554094	+	0.739387i	0.00434000	+	0.0579133i	−0.994613	+	0.103655i	$0.966946\pi$
$164$	−10.7211	−	3.30701i	−0.837175	−	0.258234i
$165$		0			0
$166$	11.4273	−	6.59758i	0.886933	−	0.512071i
$167$	1.40519	+	6.15654i	0.108737	+	0.476407i	0.999748	+	0.0224268i	$0.00713929\pi$
$167$	1.40519	+	6.15654i	0.108737	+	0.476407i	−0.891012	+	0.453981i	$0.850004\pi$
$168$		0			0
$169$	4.94409	−	21.6615i	0.380314	−	1.66627i
$170$	−1.58893	−	5.15118i	−0.121865	−	0.395077i
$171$		0			0
$172$	−3.98864	−	10.1629i	−0.304131	−	0.774914i
$173$	8.86804	−	2.73543i	0.674224	−	0.207971i	0.0613085	−	0.998119i	$-0.480473\pi$
$173$	8.86804	−	2.73543i	0.674224	−	0.207971i	0.612916	+	0.790148i	$0.289996\pi$
$174$		0			0
$175$	6.15558	−	9.71011i	0.465318	−	0.734015i
$176$	−1.34628	+	0.307280i	−0.101480	+	0.0231621i
$177$		0			0
$178$	−2.89804	−	1.67318i	−0.217217	−	0.125410i
$179$	−3.79605	+	12.3065i	−0.283730	+	0.919829i	0.695750	+	0.718284i	$0.255072\pi$
$179$	−3.79605	+	12.3065i	−0.283730	+	0.919829i	−0.979479	+	0.201545i	$0.935404\pi$
$180$		0			0
$181$	14.7601	+	11.7708i	1.09711	+	0.874918i	0.992819	−	0.119629i	$-0.0381705\pi$
$181$	14.7601	+	11.7708i	1.09711	+	0.874918i	0.104293	+	0.994547i	$0.466742\pi$
$182$	12.5958	+	9.37419i	0.933663	+	0.694861i
$183$		0			0
$184$	−2.28748	+	2.12248i	−0.168636	+	0.156471i
$185$	0.663509	−	0.100008i	0.0487822	−	0.00735273i
$186$		0			0
$187$	1.37128	−	9.09788i	0.100278	−	0.665303i
$188$	−5.72907	+	2.75897i	−0.417835	+	0.201219i
$189$		0			0
$190$	−0.263607	−	0.126947i	−0.0191241	−	0.00920968i
$191$	1.67246	−	2.45304i	0.121015	−	0.177496i	−0.760951	−	0.648809i	$-0.775267\pi$
$191$	1.67246	−	2.45304i	0.121015	−	0.177496i	0.881966	+	0.471313i	$0.156220\pi$
$192$		0			0
$193$	−0.337090	+	4.49815i	−0.0242642	+	0.323784i	0.971843	+	0.235631i	$0.0757155\pi$
$193$	−0.337090	+	4.49815i	−0.0242642	+	0.323784i	−0.996107	+	0.0881532i	$0.971904\pi$
$194$	−2.40641	+	6.13144i	−0.172770	+	0.440211i
$195$		0			0
$196$	−6.08999	+	3.45139i	−0.434999	+	0.246528i
$197$		−	22.5995i		−	1.61015i	−0.593174	−	0.805075i	$-0.702125\pi$
$197$		−	22.5995i		−	1.61015i	0.593174	−	0.805075i	$-0.297875\pi$
$198$		0			0
$199$	7.37865	+	0.552953i	0.523059	+	0.0391978i	0.333644	−	0.942699i	$-0.391722\pi$
$199$	7.37865	+	0.552953i	0.523059	+	0.0391978i	0.189415	+	0.981897i	$0.439341\pi$
$200$	−2.95562	+	3.18540i	−0.208994	+	0.225242i
$201$		0			0
$202$	1.66693	−	3.46141i	0.117285	−	0.243544i
$203$	4.41874	+	3.83350i	0.310134	+	0.269059i
$204$		0			0
$205$	8.97603	+	1.35292i	0.626913	+	0.0944920i
$206$	−12.2935	+	8.38158i	−0.856530	+	0.583972i
$207$		0			0
$208$	−4.03650	−	4.35031i	−0.279881	−	0.301640i
$209$	−0.311353	−	0.390424i	−0.0215367	−	0.0270062i
$210$		0			0
$211$	17.5294	−	21.9812i	1.20677	−	1.51325i	0.406456	−	0.913670i	$-0.366764\pi$
$211$	17.5294	−	21.9812i	1.20677	−	1.51325i	0.800318	−	0.599576i	$-0.204664\pi$
$212$	3.06214	−	0.229476i	0.210309	−	0.0157605i
$213$		0			0
$214$	6.66246	−	11.5397i	0.455436	−	0.788839i
$215$	4.41657	+	7.64972i	0.301208	+	0.521707i
$216$		0			0
$217$	1.35629	+	12.4861i	0.0920706	+	0.847612i
$218$	17.0568	+	3.89311i	1.15523	+	0.263675i
$219$		0			0
$220$	1.04002	−	0.408179i	0.0701183	−	0.0275194i
$221$	36.8070	−	14.4457i	2.47591	−	0.971722i
$222$		0			0
$223$	−12.3711	−	2.82362i	−0.828428	−	0.189083i	−0.212776	−	0.977101i	$-0.568250\pi$
$223$	−12.3711	−	2.82362i	−0.828428	−	0.189083i	−0.615653	+	0.788018i	$0.711108\pi$
$224$	2.50076	−	0.863839i	0.167089	−	0.0577177i
$225$		0			0
$226$	−8.63720	−	14.9601i	−0.574538	−	0.995130i
$227$	0.0164312	−	0.0284598i	0.00109058	−	0.00188894i	−0.865480	−	0.500944i	$-0.832986\pi$
$227$	0.0164312	−	0.0284598i	0.00109058	−	0.00188894i	0.866570	+	0.499055i	$0.166320\pi$
$228$		0			0
$229$	9.98576	−	0.748329i	0.659877	−	0.0494510i	0.259418	−	0.965765i	$-0.416469\pi$
$229$	9.98576	−	0.748329i	0.659877	−	0.0494510i	0.400460	+	0.916314i	$0.368850\pi$
$230$	1.57413	−	1.97390i	0.103795	−	0.130155i
$231$		0			0
$232$	−1.37856	−	1.72866i	−0.0905071	−	0.113492i
$233$	−11.2044	−	12.0755i	−0.734025	−	0.791091i	0.250166	−	0.968203i	$-0.419515\pi$
$233$	−11.2044	−	12.0755i	−0.734025	−	0.791091i	−0.984191	+	0.177112i	$0.943324\pi$
$234$		0			0
$235$	4.25077	−	2.89813i	0.277290	−	0.189053i
$236$	3.64135	+	0.548845i	0.237032	+	0.0357268i
$237$		0			0
$238$	−0.729597	+	17.6129i	−0.0472928	+	1.14167i
$239$	−2.80524	+	5.82514i	−0.181456	+	0.376797i	−0.971779	−	0.235893i	$-0.924198\pi$
$239$	−2.80524	+	5.82514i	−0.181456	+	0.376797i	0.790323	+	0.612690i	$0.209913\pi$
$240$		0			0
$241$	−7.76305	+	8.36657i	−0.500062	+	0.538938i	−0.931758	−	0.363081i	$-0.881725\pi$
$241$	−7.76305	+	8.36657i	−0.500062	+	0.538938i	0.431696	+	0.902019i	$0.357915\pi$
$242$	−9.06768	−	0.679528i	−0.582892	−	0.0436817i
$243$		0			0
$244$			6.10302i			0.390706i
$245$	4.45603	−	3.49561i	0.284685	−	0.223326i
$246$		0			0
$247$	0.784050	−	1.99773i	0.0498879	−	0.127112i
$248$	0.354749	−	4.73379i	0.0225266	−	0.300596i
$249$		0			0
$250$	4.25933	−	6.24729i	0.269384	−	0.395113i
$251$	−8.92524	−	4.29817i	−0.563356	−	0.271298i	0.130456	−	0.991454i	$-0.458356\pi$
$251$	−8.92524	−	4.29817i	−0.563356	−	0.271298i	−0.693812	+	0.720156i	$0.744070\pi$
$252$		0			0
$253$	3.88237	−	1.86965i	0.244083	−	0.117544i
$254$	−2.62316	+	17.4035i	−0.164592	+	1.09200i
$255$		0			0
$256$	−0.988831	+	0.149042i	−0.0618019	+	0.00931514i
$257$	15.0091	−	13.9264i	0.936243	−	0.868707i	−0.0553017	−	0.998470i	$-0.517612\pi$
$257$	15.0091	−	13.9264i	0.936243	−	0.868707i	0.991545	+	0.129763i	$0.0414216\pi$
$258$		0			0
$259$	−2.15434	−	0.416558i	−0.133864	−	0.0258836i
$260$	3.75394	+	2.99367i	0.232809	+	0.185659i
$261$		0			0
$262$	1.00077	−	3.24443i	0.0618280	−	0.200441i
$263$	5.74828	+	3.31877i	0.354454	+	0.204644i	0.666645	−	0.745375i	$-0.267730\pi$
$263$	5.74828	+	3.31877i	0.354454	+	0.204644i	−0.312191	+	0.950019i	$0.601063\pi$
$264$		0			0
$265$	−2.42216	+	0.552841i	−0.148792	+	0.0339608i
$266$	0.673828	+	0.679241i	0.0413151	+	0.0416469i
$267$		0			0
$268$	−0.0232624	+	0.00717550i	−0.00142098	+	0.000438313i
$269$	−6.81828	−	17.3727i	−0.415718	−	1.05923i	−0.973387	−	0.229168i	$-0.926399\pi$
$269$	−6.81828	−	17.3727i	−0.415718	−	1.05923i	0.557669	−	0.830063i	$-0.311696\pi$
$270$		0			0
$271$	−6.13797	−	19.8988i	−0.372855	−	1.20877i	−0.926590	−	0.376074i	$-0.877274\pi$
$271$	−6.13797	−	19.8988i	−0.372855	−	1.20877i	0.553734	−	0.832693i	$-0.313202\pi$
$272$	1.48260	−	6.49571i	0.0898961	−	0.393860i
$273$		0			0
$274$	−2.61649	−	11.4636i	−0.158068	−	0.692540i
$275$	5.19666	−	3.00029i	0.313370	−	0.180924i
$276$		0			0
$277$	−7.55134	−	2.32928i	−0.453716	−	0.139953i	0.0594704	−	0.998230i	$-0.481059\pi$
$277$	−7.55134	−	2.32928i	−0.453716	−	0.139953i	−0.513186	+	0.858277i	$0.671535\pi$
$278$	−0.913511	−	12.1900i	−0.0547888	−	0.731105i
$279$		0			0
$280$	−1.89653	+	0.992661i	−0.113339	+	0.0593228i
$281$	4.04295	−	3.22415i	0.241182	−	0.192336i	−0.495437	−	0.868644i	$-0.664992\pi$
$281$	4.04295	−	3.22415i	0.241182	−	0.192336i	0.736620	+	0.676307i	$0.236421\pi$
$282$		0			0
$283$	4.37219	+	29.0076i	0.259900	+	1.72432i	0.614164	+	0.789178i	$0.289493\pi$
$283$	4.37219	+	29.0076i	0.259900	+	1.72432i	−0.354264	+	0.935145i	$0.615269\pi$
$284$	−8.12336	−	11.9148i	−0.482032	−	0.707012i
$285$		0			0
$286$	3.55568	+	7.38345i	0.210252	+	0.436592i
$287$	−26.1884	−	13.9753i	−1.54585	−	0.824936i
$288$		0			0
$289$	22.6326	+	15.4307i	1.33133	+	0.907687i
$290$	1.31135	+	1.21676i	0.0770054	+	0.0714506i
$291$		0			0
$292$	−5.89791	−	2.31476i	−0.345149	−	0.135461i
$293$	−10.3997			−0.607559			−0.303779	−	0.952742i	$-0.598249\pi$
$293$	−10.3997			−0.607559			−0.303779	+	0.952742i	$0.598249\pi$
$294$		0			0
$295$	−2.97940			−0.173467
$296$	0.772018	+	0.302995i	0.0448726	+	0.0176112i
$297$		0			0
$298$	−8.16548	−	7.57646i	−0.473014	−	0.438892i
$299$	15.3008	+	10.4319i	0.884869	+	0.603294i
$300$		0			0
$301$	−5.25652	−	28.4029i	−0.302981	−	1.63712i
$302$	5.91025	+	12.2728i	0.340097	+	0.706218i
$303$		0			0
$304$	−0.203711	−	0.298789i	−0.0116836	−	0.0171367i
$305$	−0.735940	−	4.88265i	−0.0421398	−	0.279579i
$306$		0			0
$307$	1.21288	−	0.967243i	0.0692230	−	0.0552035i	−0.588267	−	0.808667i	$-0.700190\pi$
$307$	1.21288	−	0.967243i	0.0692230	−	0.0552035i	0.657490	+	0.753463i	$0.271618\pi$
$308$	−3.65149	+	0.122003i	−0.208063	+	0.00695179i
$309$		0			0
$310$	0.287018	+	3.82999i	0.0163015	+	0.217529i
$311$	−11.3983	−	3.51591i	−0.646339	−	0.199369i	−0.0457821	−	0.998951i	$-0.514578\pi$
$311$	−11.3983	−	3.51591i	−0.646339	−	0.199369i	−0.600556	+	0.799582i	$0.705054\pi$
$312$		0			0
$313$	8.08192	−	4.66610i	0.456817	−	0.263743i	−0.253888	−	0.967234i	$-0.581709\pi$
$313$	8.08192	−	4.66610i	0.456817	−	0.263743i	0.710705	+	0.703490i	$0.248376\pi$
$314$	1.02438	+	4.48810i	0.0578091	+	0.253278i
$315$		0			0
$316$	−2.17675	+	9.53698i	−0.122452	+	0.536497i
$317$	10.0798	+	32.6780i	0.566139	+	1.83538i	0.549463	+	0.835518i	$0.314832\pi$
$317$	10.0798	+	32.6780i	0.566139	+	1.83538i	0.0166765	+	0.999861i	$0.494691\pi$
$318$		0			0
$319$	1.11547	+	2.84218i	0.0624546	+	0.159132i
$320$	0.773129	−	0.238479i	0.0432192	−	0.0133314i
$321$		0			0
$322$	−7.00812	+	4.36449i	−0.390547	+	0.243223i
$323$	2.34902	−	0.536148i	0.130703	−	0.0298321i
$324$		0			0
$325$	22.3329	+	12.8939i	1.23881	+	0.715226i
$326$	0.218549	−	0.708519i	0.0121043	−	0.0392413i
$327$		0			0
$328$	8.77177	+	6.99525i	0.484340	+	0.386248i
$329$	−16.2678	+	4.28927i	−0.896873	+	0.236475i
$330$		0			0
$331$	4.93318	−	4.57732i	0.271152	−	0.251592i	−0.532863	−	0.846202i	$-0.678884\pi$
$331$	4.93318	−	4.57732i	0.271152	−	0.251592i	0.804015	+	0.594609i	$0.202693\pi$
$332$	−13.0478	+	1.96664i	−0.716089	+	0.107933i
$333$		0			0
$334$	0.941182	−	6.24433i	0.0514992	−	0.341675i
$335$	0.0177455	−	0.00854579i	0.000969541	−	0.000466906i
$336$		0			0
$337$	−7.53356	−	3.62797i	−0.410379	−	0.197628i	0.217292	−	0.976107i	$-0.430278\pi$
$337$	−7.53356	−	3.62797i	−0.410379	−	0.197628i	−0.627671	+	0.778478i	$0.715992\pi$
$338$	−12.5161	+	18.3578i	−0.680788	+	0.998533i
$339$		0			0
$340$	−0.402845	+	5.37559i	−0.0218473	+	0.291533i
$341$	−2.39490	+	6.10211i	−0.129691	+	0.330448i
$342$		0			0
$343$	−17.5531	+	5.90662i	−0.947779	+	0.318928i
$344$			10.9176i			0.588637i
$345$		0			0
$346$	−9.25439	−	0.693520i	−0.497519	−	0.0372839i
$347$	6.92701	−	7.46554i	0.371861	−	0.400771i	−0.519201	−	0.854652i	$-0.673770\pi$
$347$	6.92701	−	7.46554i	0.371861	−	0.400771i	0.891062	+	0.453881i	$0.149961\pi$
$348$		0			0
$349$	−1.77345	+	3.68260i	−0.0949305	+	0.197125i	−0.943027	−	0.332717i	$-0.892035\pi$
$349$	−1.77345	+	3.68260i	−0.0949305	+	0.197125i	0.848096	+	0.529842i	$0.177749\pi$
$350$	−9.27757	+	6.79000i	−0.495907	+	0.362941i
$351$		0			0
$352$	1.36548	+	0.205813i	0.0727804	+	0.0109699i
$353$	7.37182	−	5.02602i	0.392362	−	0.267508i	−0.351029	−	0.936364i	$-0.614168\pi$
$353$	7.37182	−	5.02602i	0.392362	−	0.267508i	0.743392	+	0.668856i	$0.233216\pi$
$354$		0			0
$355$	7.93575	+	8.55270i	0.421186	+	0.453930i
$356$	2.08642	+	2.61629i	0.110580	+	0.138663i
$357$		0			0
$358$	8.02970	−	10.0689i	0.424383	−	0.532159i
$359$	−1.43128	+	0.107260i	−0.0755402	+	0.00566096i	−0.112447	−	0.993658i	$-0.535869\pi$
$359$	−1.43128	+	0.107260i	−0.0755402	+	0.00566096i	0.0369064	+	0.999319i	$0.488250\pi$
$360$		0			0
$361$	−9.43461	+	16.3412i	−0.496559	+	0.860065i
$362$	−9.43946	−	16.3496i	−0.496127	−	0.859317i
$363$		0			0
$364$	−8.30032	−	13.3280i	−0.435055	−	0.698574i
$365$	4.99768	+	1.14069i	0.261590	+	0.0597063i
$366$		0			0
$367$	−19.8957	+	7.80850i	−1.03855	+	0.407601i	−0.822490	−	0.568780i	$-0.807416\pi$
$367$	−19.8957	+	7.80850i	−1.03855	+	0.407601i	−0.216059	+	0.976380i	$0.569320\pi$
$368$	2.90479	−	1.14004i	0.151422	−	0.0594290i
$369$		0			0
$370$	−0.654180	−	0.149312i	−0.0340092	−	0.00776238i
$371$	8.06960	+	0.941932i	0.418953	+	0.0489027i
$372$		0			0
$373$	10.4259	+	18.0581i	0.539830	+	0.935014i	0.998913	+	0.0466200i	$0.0148450\pi$
$373$	10.4259	+	18.0581i	0.539830	+	0.935014i	−0.459082	+	0.888394i	$0.651822\pi$
$374$	−4.60032	+	7.96799i	−0.237877	+	0.412015i
$375$		0			0
$376$	6.34100	−	0.475193i	0.327012	−	0.0245062i
$377$	−8.18111	+	10.2588i	−0.421348	+	0.528354i
$378$		0			0
$379$	3.47253	+	4.35442i	0.178372	+	0.223671i	0.862977	−	0.505242i	$-0.168597\pi$
$379$	3.47253	+	4.35442i	0.178372	+	0.223671i	−0.684605	+	0.728914i	$0.740025\pi$
$380$	0.199006	+	0.214478i	0.0102088	+	0.0110025i
$381$		0			0
$382$	−2.45304	+	1.67246i	−0.125509	+	0.0855704i
$383$	−24.0718	−	3.62823i	−1.23001	−	0.185394i	−0.498296	−	0.867007i	$-0.666041\pi$
$383$	−24.0718	−	3.62823i	−1.23001	−	0.185394i	−0.731713	+	0.681613i	$0.761279\pi$
$384$		0			0
$385$	2.90662	−	0.537927i	0.148135	−	0.0274153i
$386$	1.95715	−	4.06406i	0.0996161	−	0.206855i
$387$		0			0
$388$	4.48013	−	4.82843i	0.227444	−	0.245126i
$389$	16.8929	+	1.26595i	0.856506	+	0.0641863i	0.495741	−	0.868470i	$-0.334896\pi$
$389$	16.8929	+	1.26595i	0.856506	+	0.0641863i	0.360765	+	0.932657i	$0.382516\pi$
$390$		0			0
$391$			20.7911i			1.05145i
$392$	6.92994	−	0.987883i	0.350015	−	0.0498956i
$393$		0			0
$394$	−8.25653	+	21.0373i	−0.415958	+	1.05984i
$395$	0.591456	−	7.89243i	0.0297594	−	0.397111i
$396$		0			0
$397$	−16.6841	+	24.4711i	−0.837353	+	1.22817i	0.134107	+	0.990967i	$0.457184\pi$
$397$	−16.6841	+	24.4711i	−0.837353	+	1.22817i	−0.971460	+	0.237205i	$0.923769\pi$
$398$	−6.66657	−	3.21045i	−0.334165	−	0.160925i
$399$		0			0
$400$	3.91507	−	1.88540i	0.195753	−	0.0942699i
$401$	1.22129	−	8.10274i	0.0609884	−	0.404632i	−0.937418	−	0.348205i	$-0.886791\pi$
$401$	1.22129	−	8.10274i	0.0609884	−	0.404632i	0.998407	−	0.0564265i	$-0.0179707\pi$
$402$		0			0
$403$	−27.8569	+	4.19875i	−1.38765	+	0.209155i
$404$	−2.81630	+	2.61314i	−0.140116	+	0.130009i
$405$		0			0
$406$	−2.71275	−	5.18285i	−0.134631	−	0.257221i
$407$	−0.895393	−	0.714052i	−0.0443830	−	0.0353942i
$408$		0			0
$409$	−9.38081	+	30.4118i	−0.463851	+	1.50377i	0.357811	+	0.933794i	$0.383523\pi$
$409$	−9.38081	+	30.4118i	−0.463851	+	1.50377i	−0.821662	+	0.569974i	$0.806953\pi$
$410$	−7.86128	−	4.53871i	−0.388241	−	0.224151i
$411$		0			0
$412$	14.5058	−	3.31087i	0.714652	−	0.163115i
$413$	9.18324	+	3.25465i	0.451878	+	0.160151i
$414$		0			0
$415$	10.2016	−	3.14676i	0.500775	−	0.154469i
$416$	2.16812	+	5.52429i	0.106301	+	0.270851i
$417$		0			0
$418$	0.147192	+	0.477185i	0.00719941	+	0.0233399i
$419$	−0.196413	+	0.860540i	−0.00959539	+	0.0420402i	−0.979499	−	0.201449i	$-0.935435\pi$
$419$	−0.196413	+	0.860540i	−0.00959539	+	0.0420402i	0.969904	+	0.243489i	$0.0782921\pi$
$420$		0			0
$421$	8.14920	+	35.7040i	0.397168	+	1.74010i	0.638463	+	0.769653i	$0.279571\pi$
$421$	8.14920	+	35.7040i	0.397168	+	1.74010i	−0.241295	+	0.970452i	$0.577572\pi$
$422$	−24.3483	+	14.0575i	−1.18526	+	0.684308i
$423$		0			0
$424$	−2.93430	−	0.905113i	−0.142502	−	0.0439562i
$425$	2.16361	+	28.8714i	0.104951	+	1.40047i
$426$		0			0
$427$	−3.06537	+	15.8534i	−0.148344	+	0.767202i
$428$	−10.4178	+	8.30795i	−0.503565	+	0.401580i
$429$		0			0
$430$	−1.31651	−	8.73448i	−0.0634878	−	0.421214i
$431$	−21.3607	−	31.3304i	−1.02891	−	1.50913i	−0.851057	−	0.525073i	$-0.824038\pi$
$431$	−21.3607	−	31.3304i	−1.02891	−	1.50913i	−0.177851	−	0.984057i	$-0.556915\pi$
$432$		0			0
$433$	−10.0476	−	20.8641i	−0.482857	−	1.00266i	−0.990035	−	0.140822i	$-0.955026\pi$
$433$	−10.0476	−	20.8641i	−0.482857	−	1.00266i	0.507178	−	0.861841i	$-0.330689\pi$
$434$	3.29916	−	12.1185i	0.158365	−	0.581706i
$435$		0			0
$436$	−14.4554	−	9.85555i	−0.692290	−	0.471995i
$437$	0.827214	+	0.767542i	0.0395710	+	0.0367165i
$438$		0			0
$439$	−5.43591	−	2.13344i	−0.259442	−	0.101823i	0.232055	−	0.972703i	$-0.425455\pi$
$439$	−5.43591	−	2.13344i	−0.259442	−	0.101823i	−0.491497	+	0.870879i	$0.663550\pi$
$440$	−1.11725			−0.0532630
$441$		0			0
$442$	−39.5403			−1.88074
$443$	−4.37960	−	1.71887i	−0.208081	−	0.0816658i	0.259012	−	0.965874i	$-0.416603\pi$
$443$	−4.37960	−	1.71887i	−0.208081	−	0.0816658i	−0.467092	+	0.884208i	$0.654698\pi$
$444$		0			0
$445$	−1.98471	−	1.84154i	−0.0940841	−	0.0872973i
$446$	10.4843	+	7.14809i	0.496447	+	0.338472i
$447$		0			0
$448$	−2.64348	−	0.109504i	−0.124893	−	0.00517356i
$449$	4.53724	+	9.42168i	0.214126	+	0.444636i	0.980172	−	0.198149i	$-0.0634930\pi$
$449$	4.53724	+	9.42168i	0.214126	+	0.444636i	−0.766046	+	0.642785i	$0.777779\pi$
$450$		0			0
$451$	−8.72757	−	12.8010i	−0.410965	−	0.602775i
$452$	2.57462	+	17.0815i	0.121100	+	0.803445i
$453$		0			0
$454$	−0.0256929	+	0.0204894i	−0.00120583	+	0.000961617i
$455$	8.24774	+	9.66196i	0.386660	+	0.452959i
$456$		0			0
$457$	−1.17274	−	15.6491i	−0.0548585	−	0.732036i	−0.955032	−	0.296504i	$-0.904179\pi$
$457$	−1.17274	−	15.6491i	−0.0548585	−	0.732036i	0.900173	−	0.435532i	$-0.143440\pi$
$458$	−9.56887	−	2.95161i	−0.447124	−	0.137920i
$459$		0			0
$460$	−2.18646	+	1.26236i	−0.101944	+	0.0588577i
$461$	2.12162	+	9.29541i	0.0988136	+	0.432930i	1.00000		0.000501439i	$-0.000159613\pi$
$461$	2.12162	+	9.29541i	0.0988136	+	0.432930i	−0.901186	+	0.433432i	$0.857302\pi$
$462$		0			0
$463$	0.514181	−	2.25277i	0.0238960	−	0.104695i	−0.961574	−	0.274548i	$-0.911472\pi$
$463$	0.514181	−	2.25277i	0.0238960	−	0.104695i	0.985470	+	0.169852i	$0.0543291\pi$
$464$	0.651716	+	2.11281i	0.0302552	+	0.0980849i
$465$		0			0
$466$	6.01822	+	15.3342i	0.278789	+	0.710342i
$467$	−25.0886	+	7.73882i	−1.16096	+	0.358110i	−0.814619	−	0.579997i	$-0.803054\pi$
$467$	−25.0886	+	7.73882i	−1.16096	+	0.358110i	−0.346345	+	0.938107i	$0.612577\pi$
$468$		0			0
$469$	−0.0640313	+	0.00695531i	−0.00295669	+	0.000321166i
$470$	−5.01574	+	1.14481i	−0.231359	+	0.0528061i
$471$		0			0
$472$	−3.18912	−	1.84124i	−0.146791	−	0.0847499i
$473$	4.44377	−	14.4064i	0.204325	−	0.662405i
$474$		0			0
$475$	1.22858	+	0.979757i	0.0563710	+	0.0449544i
$476$	7.11388	−	16.1288i	0.326064	−	0.739264i
$477$		0			0
$478$	4.73949	−	4.39760i	0.216779	−	0.201142i
$479$	22.7560	−	3.42991i	1.03975	−	0.156717i	0.393092	−	0.919499i	$-0.371405\pi$
$479$	22.7560	−	3.42991i	1.03975	−	0.156717i	0.646655	+	0.762782i	$0.276167\pi$
$480$		0			0
$481$	0.733553	−	4.86681i	0.0334471	−	0.221907i
$482$	10.2831	−	4.95206i	0.468381	−	0.225560i
$483$		0			0
$484$	8.19260	+	3.94535i	0.372391	+	0.179334i
$485$	−3.00203	+	4.40317i	−0.136315	+	0.199938i
$486$		0			0
$487$	0.441527	−	5.89176i	0.0200075	−	0.266981i	−0.978225	−	0.207548i	$-0.933452\pi$
$487$	0.441527	−	5.89176i	0.0200075	−	0.266981i	0.998232	−	0.0594332i	$-0.0189293\pi$
$488$	2.22968	−	5.68114i	0.100933	−	0.257173i
$489$		0			0
$490$	−5.42509	+	1.62600i	−0.245080	+	0.0734551i
$491$		−	11.1264i		−	0.502126i	−0.967971	−	0.251063i	$-0.919220\pi$
$491$		−	11.1264i		−	0.502126i	0.967971	−	0.251063i	$-0.0807801\pi$
$492$		0			0
$493$	−14.6905	−	1.10090i	−0.661625	−	0.0495819i
$494$	−1.45970	+	1.57319i	−0.0656751	+	0.0707809i
$495$		0			0
$496$	−2.05967	+	4.27696i	−0.0924821	+	0.192041i
$497$	−15.1171	−	35.0304i	−0.678094	−	1.57133i
$498$		0			0
$499$	40.0868	+	6.04211i	1.79453	+	0.270482i	0.959903	−	0.280334i	$-0.0904452\pi$
$499$	40.0868	+	6.04211i	1.79453	+	0.270482i	0.834627	+	0.550816i	$0.185683\pi$
$500$	−6.24729	+	4.25933i	−0.279387	+	0.190483i
$501$		0			0
$502$	6.73797	+	7.26181i	0.300730	+	0.324110i
$503$	−7.54921	−	9.46642i	−0.336603	−	0.422087i	0.584507	−	0.811388i	$-0.301288\pi$
$503$	−7.54921	−	9.46642i	−0.336603	−	0.422087i	−0.921110	+	0.389302i	$0.872716\pi$
$504$		0			0
$505$	1.93803	−	2.43022i	0.0862414	−	0.108143i
$506$	−4.29706	+	0.322020i	−0.191028	+	0.0143155i
$507$		0			0
$508$	8.80006	−	15.2421i	0.390439	−	0.676261i
$509$	21.1952	+	36.7111i	0.939459	+	1.62719i	0.766483	+	0.642265i	$0.222005\pi$
$509$	21.1952	+	36.7111i	0.939459	+	1.62719i	0.172976	+	0.984926i	$0.444662\pi$
$510$		0			0
$511$	−14.1580	−	8.97526i	−0.626313	−	0.397042i
$512$	0.974928	+	0.222521i	0.0430861	+	0.00983413i
$513$		0			0
$514$	−19.0595	+	7.48030i	−0.840678	+	0.329942i
$515$	−11.2060	+	4.39802i	−0.493794	+	0.193800i
$516$		0			0
$517$	−8.56072	−	1.95393i	−0.376500	−	0.0859337i
$518$	1.85324	+	1.17483i	0.0814266	+	0.0516192i
$519$		0			0
$520$	−2.40073	−	4.15819i	−0.105279	−	0.182349i
$521$	−1.44499	+	2.50280i	−0.0633063	+	0.109650i	−0.895941	−	0.444172i	$-0.853498\pi$
$521$	−1.44499	+	2.50280i	−0.0633063	+	0.109650i	0.832635	+	0.553822i	$0.186831\pi$
$522$		0			0
$523$	3.56518	−	0.267174i	0.155895	−	0.0116827i	0.00344585	−	0.999994i	$-0.498903\pi$
$523$	3.56518	−	0.267174i	0.155895	−	0.0116827i	0.152449	+	0.988311i	$0.451284\pi$
$524$	−2.11692	+	2.65453i	−0.0924779	+	0.115964i
$525$		0			0
$526$	−4.13844	−	5.18944i	−0.180445	−	0.226270i
$527$	−21.5129	−	23.1854i	−0.937116	−	1.00997i
$528$		0			0
$529$	10.9580	−	7.47104i	0.476435	−	0.324828i
$530$	2.45670	+	0.370288i	0.106712	+	0.0160843i
$531$		0			0
$532$	−0.379094	−	0.878465i	−0.0164358	−	0.0380863i
$533$	28.8890	−	59.9887i	1.25132	−	2.59840i
$534$		0			0
$535$	7.33284	−	7.90292i	0.317026	−	0.341673i
$536$	0.0242759	+	0.00181922i	0.00104856	+	7.85785e-5i
$537$		0			0
$538$			18.6628i			0.804609i
$539$	−9.54654	−	1.51712i	−0.411198	−	0.0653470i
$540$		0			0
$541$	1.97269	−	5.02632i	0.0848124	−	0.216098i	−0.882175	−	0.470921i	$-0.843922\pi$
$541$	1.97269	−	5.02632i	0.0848124	−	0.216098i	0.966988	+	0.254822i	$0.0820170\pi$
$542$	−1.55618	+	20.7657i	−0.0668435	+	0.891965i
$543$		0			0
$544$	−3.75327	+	5.50503i	−0.160920	+	0.236026i
$545$	12.7533	+	6.14168i	0.546293	+	0.263081i
$546$		0			0
$547$	18.5500	−	8.93322i	0.793142	−	0.381957i	0.00697834	−	0.999976i	$-0.497779\pi$
$547$	18.5500	−	8.93322i	0.793142	−	0.381957i	0.786163	+	0.618019i	$0.212064\pi$
$548$	−1.75250	+	11.6271i	−0.0748629	+	0.496683i
$549$		0			0
$550$	−5.93356	+	0.894341i	−0.253008	+	0.0381348i
$551$	−0.586127	+	0.543846i	−0.0249698	+	0.0231686i
$552$		0			0
$553$	−10.4446	+	23.6803i	−0.444149	+	1.00699i
$554$	6.17836	+	4.92708i	0.262493	+	0.209331i
$555$		0			0
$556$	−3.60313	+	11.6811i	−0.152807	+	0.495387i
$557$	−26.4713	−	15.2832i	−1.12162	−	0.647569i	−0.179808	−	0.983702i	$-0.557548\pi$
$557$	−26.4713	−	15.2832i	−1.12162	−	0.647569i	−0.941815	+	0.336132i	$0.890881\pi$
$558$		0			0
$559$	63.1662	−	14.4173i	2.67165	−	0.609786i
$560$	2.12809	−	0.231161i	0.0899283	−	0.00976833i
$561$		0			0
$562$	−4.94139	+	1.52422i	−0.208440	+	0.0642952i
$563$	−0.608740	−	1.55104i	−0.0256553	−	0.0653687i	0.917472	−	0.397800i	$-0.130226\pi$
$563$	−0.608740	−	1.55104i	−0.0256553	−	0.0653687i	−0.943127	+	0.332431i	$0.892131\pi$
$564$		0			0
$565$	−4.11958	−	13.3554i	−0.173312	−	0.561864i
$566$	6.52771	−	28.5998i	0.274380	−	1.20214i
$567$		0			0
$568$	3.20886	+	14.0589i	0.134641	+	0.589900i
$569$	30.3266	−	17.5091i	1.27136	−	0.734018i	0.296114	−	0.955153i	$-0.404309\pi$
$569$	30.3266	−	17.5091i	1.27136	−	0.734018i	0.975243	+	0.221134i	$0.0709759\pi$
$570$		0			0
$571$	−33.2568	−	10.2584i	−1.39175	−	0.429299i	−0.493871	−	0.869535i	$-0.664418\pi$
$571$	−33.2568	−	10.2584i	−1.39175	−	0.429299i	−0.897882	+	0.440236i	$0.854895\pi$
$572$	−0.612414	−	8.17209i	−0.0256063	−	0.341692i
$573$		0			0
$574$	19.2724	+	22.5770i	0.804413	+	0.942344i
$575$	−10.6015	+	8.45440i	−0.442112	+	0.352573i
$576$		0			0
$577$	3.13270	+	20.7841i	0.130416	+	0.865253i	0.954377	+	0.298606i	$0.0965216\pi$
$577$	3.13270	+	20.7841i	0.130416	+	0.865253i	−0.823961	+	0.566647i	$0.808240\pi$
$578$	−15.4307	−	22.6326i	−0.641832	−	0.941394i
$579$		0			0
$580$	−0.776174	−	1.61174i	−0.0322289	−	0.0669239i
$581$	−34.8812	−	1.44492i	−1.44711	−	0.0599453i
$582$		0			0
$583$	3.50357	+	2.38869i	0.145103	+	0.0989296i
$584$	4.64453	+	4.30950i	0.192192	+	0.178328i
$585$		0			0
$586$	9.68084	+	3.79945i	0.399912	+	0.156954i
$587$	−18.5502			−0.765648			−0.382824	−	0.923821i	$-0.625048\pi$
$587$	−18.5502			−0.765648			−0.382824	+	0.923821i	$0.625048\pi$
$588$		0			0
$589$	−1.71666			−0.0707338
$590$	2.77345	+	1.08850i	0.114181	+	0.0448127i
$591$		0			0
$592$	−0.607955	−	0.564100i	−0.0249868	−	0.0231843i
$593$	35.2233	+	24.0148i	1.44645	+	0.986172i	0.995613	+	0.0935641i	$0.0298260\pi$
$593$	35.2233	+	24.0148i	1.44645	+	0.986172i	0.450835	+	0.892607i	$0.351126\pi$
$594$		0			0
$595$	−3.74645	+	13.7615i	−0.153590	+	0.564167i
$596$	4.83304	+	10.0359i	0.197969	+	0.411087i
$597$		0			0
$598$	−10.4319	−	15.3008i	−0.426593	−	0.625697i
$599$	4.84128	+	32.1198i	0.197809	+	1.31238i	0.838636	+	0.544693i	$0.183354\pi$
$599$	4.84128	+	32.1198i	0.197809	+	1.31238i	−0.640826	+	0.767686i	$0.721408\pi$
$600$		0			0
$601$	−32.4457	+	25.8746i	−1.32349	+	1.05545i	−0.329708	+	0.944083i	$0.606950\pi$
$601$	−32.4457	+	25.8746i	−1.32349	+	1.05545i	−0.993780	+	0.111363i	$0.964478\pi$
$602$	−5.48359	+	28.3599i	−0.223495	+	1.15587i
$603$		0			0
$604$	−1.01795	−	13.5837i	−0.0414200	−	0.552711i
$605$	−7.03014	−	2.16851i	−0.285816	−	0.0881625i
$606$		0			0
$607$	−24.0498	+	13.8852i	−0.976152	+	0.563582i	−0.901106	−	0.433599i	$-0.857244\pi$
$607$	−24.0498	+	13.8852i	−0.976152	+	0.563582i	−0.0750457	+	0.997180i	$0.523910\pi$
$608$	0.0804693	+	0.352559i	0.00326346	+	0.0142982i
$609$		0			0
$610$	−1.09876	+	4.81400i	−0.0444876	+	0.194913i
$611$	−11.1230	−	36.0598i	−0.449988	−	1.45882i
$612$		0			0
$613$	11.1602	+	28.4358i	0.450757	+	1.14851i	0.958015	+	0.286717i	$0.0925638\pi$
$613$	11.1602	+	28.4358i	0.450757	+	1.14851i	−0.507258	+	0.861794i	$0.669341\pi$
$614$	−1.48242	+	0.457265i	−0.0598255	+	0.0184537i
$615$		0			0
$616$	3.44365	+	1.22047i	0.138749	+	0.0491742i
$617$	−19.3209	+	4.40987i	−0.777831	+	0.177535i	−0.592964	−	0.805229i	$-0.702042\pi$
$617$	−19.3209	+	4.40987i	−0.777831	+	0.177535i	−0.184867	+	0.982764i	$0.559185\pi$
$618$		0			0
$619$	27.2689	+	15.7437i	1.09603	+	0.632793i	0.935176	−	0.354185i	$-0.115242\pi$
$619$	27.2689	+	15.7437i	1.09603	+	0.632793i	0.160855	+	0.986978i	$0.448575\pi$
$620$	1.13207	−	3.67010i	0.0454652	−	0.147395i
$621$		0			0
$622$	9.32588	+	7.43714i	0.373934	+	0.298202i
$623$	4.10569	+	7.84414i	0.164491	+	0.314269i
$624$		0			0
$625$	−11.4426	+	10.6171i	−0.457703	+	0.424686i
$626$	−9.22796	+	1.39089i	−0.368824	+	0.0555912i
$627$		0			0
$628$	0.686119	−	4.55210i	0.0273791	−	0.181649i
$629$	4.97852	−	2.39753i	0.198507	−	0.0955958i
$630$		0			0
$631$	2.67693	+	1.28914i	0.106567	+	0.0513199i	0.486408	−	0.873732i	$-0.338307\pi$
$631$	2.67693	+	1.28914i	0.106567	+	0.0513199i	−0.379841	+	0.925052i	$0.624021\pi$
$632$	5.51054	−	8.08247i	0.219197	−	0.321503i
$633$		0			0
$634$	2.55557	−	34.1017i	0.101494	−	1.35435i
$635$	−5.20238	+	13.2555i	−0.206450	+	0.526027i
$636$		0			0
$637$	−14.8670	−	38.7902i	−0.589052	−	1.53692i
$638$		−	3.05324i		−	0.120879i
$639$		0			0
$640$	−0.806812	−	0.0604622i	−0.0318920	−	0.00238998i
$641$	−11.5502	+	12.4482i	−0.456206	+	0.491673i	−0.918704	−	0.394947i	$-0.870763\pi$
$641$	−11.5502	+	12.4482i	−0.456206	+	0.491673i	0.462498	+	0.886620i	$0.346953\pi$
$642$		0			0
$643$	−5.15989	+	10.7146i	−0.203486	+	0.422544i	−0.977591	−	0.210514i	$-0.932486\pi$
$643$	−5.15989	+	10.7146i	−0.203486	+	0.422544i	0.774104	+	0.633058i	$0.218200\pi$
$644$	8.11820	−	1.50243i	0.319902	−	0.0592041i
$645$		0			0
$646$	−2.38252	−	0.359106i	−0.0937388	−	0.0141289i
$647$	21.7468	−	14.8267i	0.854956	−	0.582899i	−0.0545868	−	0.998509i	$-0.517384\pi$
$647$	21.7468	−	14.8267i	0.854956	−	0.582899i	0.909543	+	0.415610i	$0.136432\pi$
$648$		0			0
$649$	3.45878	+	3.72768i	0.135769	+	0.146324i
$650$	−16.0785	−	20.1618i	−0.630649	−	0.790809i
$651$		0			0
$652$	−0.462293	+	0.579697i	−0.0181048	+	0.0227027i
$653$	−27.6330	+	2.07080i	−1.08136	+	0.0810369i	−0.603473	−	0.797383i	$-0.706217\pi$
$653$	−27.6330	+	2.07080i	−1.08136	+	0.0810369i	−0.477889	+	0.878420i	$0.658598\pi$
$654$		0			0
$655$	1.37351	−	2.37899i	0.0536676	−	0.0929549i
$656$	−5.60976	−	9.71639i	−0.219024	−	0.379361i
$657$		0			0
$658$	16.7103	+	1.95053i	0.651436	+	0.0760395i
$659$	34.7609	+	7.93394i	1.35409	+	0.309062i	0.837157	−	0.546963i	$-0.184216\pi$
$659$	34.7609	+	7.93394i	1.35409	+	0.309062i	0.516934	+	0.856025i	$0.327073\pi$
$660$		0			0
$661$	9.58966	−	3.76366i	0.372994	−	0.146390i	−0.171437	−	0.985195i	$-0.554841\pi$
$661$	9.58966	−	3.76366i	0.372994	−	0.146390i	0.544431	+	0.838806i	$0.316746\pi$
$662$	−6.26445	+	2.45862i	−0.243475	+	0.0955568i
$663$		0			0
$664$	12.8643	+	2.93620i	0.499232	+	0.113947i
$665$	0.409221	+	0.657091i	0.0158689	+	0.0254809i
$666$		0			0
$667$	−3.44977	−	5.97518i	−0.133576	−	0.231360i
$668$	−3.15743	+	5.46883i	−0.122165	+	0.211596i
$669$		0			0
$670$	−0.0196410	+	0.00147189i	−0.000758797	+	5.68639e-5i
$671$	−5.25458	+	6.58904i	−0.202851	+	0.254367i
$672$		0			0
$673$	−2.04694	−	2.56679i	−0.0789039	−	0.0989423i	0.740813	−	0.671712i	$-0.234441\pi$
$673$	−2.04694	−	2.56679i	−0.0789039	−	0.0989423i	−0.819717	+	0.572769i	$0.805869\pi$
$674$	5.68735	+	6.12950i	0.219068	+	0.236100i
$675$		0			0
$676$	18.3578	−	12.5161i	0.706069	−	0.481390i
$677$	−26.3138	−	3.96617i	−1.01132	−	0.152432i	−0.377581	−	0.925977i	$-0.623244\pi$
$677$	−26.3138	−	3.96617i	−1.01132	−	0.152432i	−0.633742	+	0.773544i	$0.718482\pi$
$678$		0			0
$679$	14.0629	−	10.2923i	0.539686	−	0.394981i
$680$	2.33892	−	4.85682i	0.0896936	−	0.186251i
$681$		0			0
$682$	4.45870	−	4.80534i	0.170732	−	0.184006i
$683$	48.4611	+	3.63166i	1.85431	+	0.138961i	0.954670	−	0.297667i	$-0.0962084\pi$
$683$	48.4611	+	3.63166i	1.85431	+	0.138961i	0.899642	+	0.436628i	$0.143827\pi$
$684$		0			0
$685$		−	9.51341i		−	0.363489i
$686$	18.4977	+	0.914551i	0.706244	+	0.0349177i
$687$		0			0
$688$	3.98864	−	10.1629i	0.152066	−	0.387457i
$689$	−1.36183	+	18.1723i	−0.0518815	+	0.692311i
$690$		0			0
$691$	2.49429	−	3.65845i	0.0948872	−	0.139174i	−0.775860	−	0.630906i	$-0.782684\pi$
$691$	2.49429	−	3.65845i	0.0948872	−	0.139174i	0.870747	+	0.491732i	$0.163636\pi$
$692$	8.36129	+	4.02659i	0.317849	+	0.153068i
$693$		0			0
$694$	−9.17563	+	4.41875i	−0.348302	+	0.167734i
$695$	1.47406	−	9.77977i	0.0559144	−	0.370968i
$696$		0			0
$697$	73.9180	−	11.1414i	2.79985	−	0.422009i
$698$	2.99626	−	2.78012i	0.113410	−	0.105229i
$699$		0			0
$700$	11.1169	−	2.93115i	0.420180	−	0.110787i
$701$	0.967874	+	0.771854i	0.0365561	+	0.0291525i	0.641597	−	0.767042i	$-0.278272\pi$
$701$	0.967874	+	0.771854i	0.0365561	+	0.0291525i	−0.605041	+	0.796194i	$0.706843\pi$
$702$		0			0
$703$	0.0884011	−	0.286589i	0.00333411	−	0.0108089i
$704$	−1.19590	−	0.690453i	−0.0450721	−	0.0260224i
$705$		0			0
$706$	−8.69844	+	1.98536i	−0.327370	+	0.0747201i
$707$	−8.62822	+	5.37345i	−0.324498	+	0.202089i
$708$		0			0
$709$	−22.3383	+	6.89045i	−0.838933	+	0.258776i	−0.684305	−	0.729196i	$-0.739894\pi$
$709$	−22.3383	+	6.89045i	−0.838933	+	0.258776i	−0.154628	+	0.987973i	$0.549418\pi$
$710$	−4.26253	−	10.8607i	−0.159970	−	0.407596i
$711$		0			0
$712$	−0.986358	−	3.19770i	−0.0369653	−	0.119839i
$713$	3.29625	−	14.4418i	0.123445	−	0.540850i
$714$		0			0
$715$	1.47540	+	6.46413i	0.0551767	+	0.241745i
$716$	−11.1532	+	6.43932i	−0.416816	+	0.240649i
$717$		0			0
$718$	1.37153	+	0.423061i	0.0511850	+	0.0157885i
$719$	−3.41198	−	45.5297i	−0.127245	−	1.69797i	−0.586728	−	0.809784i	$-0.699584\pi$
$719$	−3.41198	−	45.5297i	−0.127245	−	1.69797i	0.459483	−	0.888187i	$-0.348035\pi$
$720$		0			0
$721$	39.3439	−	1.31455i	1.46524	−	0.0489566i
$722$	14.7526	−	11.7648i	0.549033	−	0.437839i
$723$		0			0
$724$	2.81376	+	18.6681i	0.104572	+	0.693793i
$725$	−5.41230	−	7.93839i	−0.201008	−	0.294824i
$726$		0			0
$727$	−2.73141	−	5.67184i	−0.101302	−	0.210357i	0.844157	−	0.536095i	$-0.180101\pi$
$727$	−2.73141	−	5.67184i	−0.101302	−	0.210357i	−0.945460	+	0.325739i	$0.894387\pi$
$728$	2.85731	+	15.4391i	0.105899	+	0.572211i
$729$		0			0
$730$	−4.23547	−	2.88769i	−0.156762	−	0.106878i
$731$	53.3231	+	49.4766i	1.97223	+	1.82996i
$732$		0			0
$733$	−21.1906	−	8.31668i	−0.782691	−	0.307184i	−0.0598585	−	0.998207i	$-0.519065\pi$
$733$	−21.1906	−	8.31668i	−0.782691	−	0.307184i	−0.722833	+	0.691023i	$0.757160\pi$
$734$	21.3732			0.788899
$735$		0			0
$736$	−3.12050			−0.115023
$737$	−0.0312929	−	0.0122815i	−0.00115269	−	0.000452396i
$738$		0			0
$739$	18.4673	+	17.1352i	0.679331	+	0.630327i	0.942415	−	0.334446i	$-0.108549\pi$
$739$	18.4673	+	17.1352i	0.679331	+	0.630327i	−0.263084	+	0.964773i	$0.584740\pi$
$740$	0.554409	+	0.377990i	0.0203805	+	0.0138952i
$741$		0			0
$742$	−7.16765	−	3.82497i	−0.263133	−	0.140419i
$743$	−3.80760	−	7.90657i	−0.139687	−	0.290064i	0.819375	−	0.573257i	$-0.194320\pi$
$743$	−3.80760	−	7.90657i	−0.139687	−	0.290064i	−0.959063	+	0.283193i	$0.908606\pi$
$744$		0			0
$745$	−5.07681	−	7.44631i	−0.186000	−	0.272812i
$746$	−3.10779	−	20.6188i	−0.113784	−	0.754909i
$747$		0			0
$748$	7.19335	−	5.73651i	0.263015	−	0.209747i
$749$	−31.2346	+	16.3485i	−1.14129	+	0.597360i
$750$		0			0
$751$	−2.32296	−	30.9978i	−0.0847661	−	1.13112i	−0.863696	−	0.504013i	$-0.831856\pi$
$751$	−2.32296	−	30.9978i	−0.0847661	−	1.13112i	0.778930	−	0.627111i	$-0.215763\pi$
$752$	−6.07628	−	1.87428i	−0.221579	−	0.0683481i
$753$		0			0
$754$	11.3635	−	6.56074i	0.413835	−	0.238928i
$755$	2.45240	+	10.7447i	0.0892521	+	0.391039i
$756$		0			0
$757$	6.28875	−	27.5528i	0.228568	−	1.00142i	−0.722240	−	0.691643i	$-0.756887\pi$
$757$	6.28875	−	27.5528i	0.228568	−	1.00142i	0.950808	−	0.309781i	$-0.100256\pi$
$758$	−1.64164	−	5.32207i	−0.0596271	−	0.193306i
$759$		0			0
$760$	−0.106892	−	0.272357i	−0.00387739	−	0.00987943i
$761$	25.9375	−	8.00066i	0.940234	−	0.290024i	0.213500	−	0.976943i	$-0.431514\pi$
$761$	25.9375	−	8.00066i	0.940234	−	0.290024i	0.726734	+	0.686919i	$0.241037\pi$
$762$		0			0
$763$	−32.5998	−	32.8617i	−1.18019	−	1.18967i
$764$	2.89449	−	0.660649i	0.104719	−	0.0239014i
$765$		0			0
$766$	21.0822	+	12.1718i	0.761732	+	0.439786i
$767$	−6.44151	+	20.8829i	−0.232589	+	0.754036i
$768$		0			0
$769$	−16.4789	−	13.1415i	−0.594245	−	0.473895i	0.279588	−	0.960120i	$-0.409802\pi$
$769$	−16.4789	−	13.1415i	−0.594245	−	0.473895i	−0.873834	+	0.486225i	$0.838374\pi$
$770$	−2.90222	−	0.561165i	−0.104589	−	0.0202230i
$771$		0			0
$772$	−3.30662	+	3.06810i	−0.119008	+	0.110423i
$773$	14.2654	−	2.15016i	0.513090	−	0.0773358i	0.112606	−	0.993640i	$-0.464080\pi$
$773$	14.2654	−	2.15016i	0.513090	−	0.0773358i	0.400484	+	0.916304i	$0.368842\pi$
$774$		0			0
$775$	3.07443	−	20.3975i	0.110437	−	0.732700i
$776$	−5.93446	+	2.85789i	−0.213035	+	0.102592i
$777$		0			0
$778$	−15.2627	−	7.35013i	−0.547194	−	0.263515i
$779$	2.28554	−	3.35227i	0.0818880	−	0.120108i
$780$		0			0
$781$	1.48813	−	19.8577i	0.0532493	−	0.710563i
$782$	7.59585	−	19.3539i	0.271627	−	0.692094i
$783$		0			0
$784$	−6.81181	−	1.61220i	−0.243279	−	0.0575785i
$785$			3.72459i			0.132936i
$786$		0			0
$787$	−51.0630	−	3.82664i	−1.82020	−	0.136405i	−0.879554	−	0.475799i	$-0.842159\pi$
$787$	−51.0630	−	3.82664i	−1.82020	−	0.136405i	−0.940644	+	0.339394i	$0.889778\pi$
$788$	15.3716	−	16.5666i	0.547590	−	0.590161i
$789$		0			0
$790$	−3.43400	+	7.13077i	−0.122176	+	0.253702i
$791$	−1.89161	+	45.6646i	−0.0672580	+	1.62365i
$792$		0			0
$793$	−35.8140	−	5.39809i	−1.27179	−	0.191692i
$794$	24.4711	−	16.6841i	0.868448	−	0.592098i
$795$		0			0
$796$	5.03283	+	5.42410i	0.178384	+	0.192252i
$797$	16.6044	+	20.8212i	0.588157	+	0.737526i	0.983480	−	0.181017i	$-0.0579388\pi$
$797$	16.6044	+	20.8212i	0.588157	+	0.737526i	−0.395323	+	0.918542i	$0.629367\pi$
$798$		0			0
$799$	26.4154	−	33.1239i	0.934511	−	1.17184i
$800$	−4.33325	+	0.324732i	−0.153203	+	0.0114810i
$801$		0			0
$802$	−4.09713	+	7.09644i	−0.144675	+	0.250584i
$803$	−4.37463	−	7.57708i	−0.154377	−	0.267389i
$804$		0			0
$805$	−6.31369	+	2.18095i	−0.222528	+	0.0768682i
$806$	27.4652	+	6.26876i	0.967422	+	0.220808i
$807$		0			0
$808$	3.57630	−	1.40360i	0.125814	−	0.0493783i
$809$	13.5064	−	5.30089i	0.474861	−	0.186369i	−0.115827	−	0.993269i	$-0.536952\pi$
$809$	13.5064	−	5.30089i	0.474861	−	0.186369i	0.590688	+	0.806900i	$0.298857\pi$
$810$		0			0
$811$	−21.7049	−	4.95400i	−0.762162	−	0.173958i	−0.176263	−	0.984343i	$-0.556401\pi$
$811$	−21.7049	−	4.95400i	−0.762162	−	0.173958i	−0.585898	+	0.810385i	$0.699258\pi$
$812$	0.631718	+	5.81566i	0.0221689	+	0.204090i
$813$		0			0
$814$	0.572625	+	0.991816i	0.0200705	+	0.0347631i
$815$	0.299948	−	0.519526i	0.0105067	−	0.0181982i
$816$		0			0
$817$	3.93704	−	0.295041i	0.137740	−	0.0103222i
$818$	19.8430	−	24.8824i	0.693795	−	0.869992i
$819$		0			0
$820$	5.65968	+	7.09701i	0.197645	+	0.247838i
$821$	16.8051	+	18.1116i	0.586502	+	0.632099i	0.954672	−	0.297660i	$-0.0962060\pi$
$821$	16.8051	+	18.1116i	0.586502	+	0.632099i	−0.368170	+	0.929759i	$0.620016\pi$
$822$		0			0
$823$	−18.0787	+	12.3258i	−0.630182	+	0.429651i	−0.835840	−	0.548973i	$-0.815019\pi$
$823$	−18.0787	+	12.3258i	−0.630182	+	0.429651i	0.205658	+	0.978624i	$0.434067\pi$
$824$	−14.7127	−	2.21758i	−0.512542	−	0.0772532i
$825$		0			0
$826$	−7.35938	−	6.38468i	−0.256066	−	0.222151i
$827$	−20.9286	+	43.4586i	−0.727758	+	1.51120i	0.126846	+	0.991922i	$0.459515\pi$
$827$	−20.9286	+	43.4586i	−0.727758	+	1.51120i	−0.854603	+	0.519282i	$0.826200\pi$
$828$		0			0
$829$	22.6838	−	24.4473i	0.787840	−	0.849090i	−0.203681	−	0.979037i	$-0.565290\pi$
$829$	22.6838	−	24.4473i	0.787840	−	0.849090i	0.991521	+	0.129948i	$0.0414809\pi$
$830$	−10.6460	−	0.797808i	−0.369528	−	0.0276923i
$831$		0			0
$832$		−	5.93452i		−	0.205742i
$833$	26.5803	−	38.3238i	0.920954	−	1.32784i
$834$		0			0
$835$	1.86660	−	4.75602i	0.0645963	−	0.164589i
$836$	0.0373180	−	0.497975i	0.00129067	−	0.0172228i
$837$		0			0
$838$	0.497226	−	0.729297i	0.0171764	−	0.0251931i
$839$	−39.4419	−	18.9942i	−1.36169	−	0.655754i	−0.396675	−	0.917959i	$-0.629836\pi$
$839$	−39.4419	−	18.9942i	−1.36169	−	0.655754i	−0.965012	+	0.262205i	$0.915550\pi$
$840$		0			0
$841$	−21.7235	+	10.4615i	−0.749087	+	0.360741i
$842$	5.45825	−	36.2131i	0.188104	−	1.24799i
$843$		0			0
$844$	27.8010	−	4.19032i	0.956948	−	0.144237i
$845$	−13.1777	+	12.2271i	−0.453325	+	0.420624i
$846$		0			0
$847$	19.2998	+	14.3635i	0.663148	+	0.493536i
$848$	2.40079	+	1.91457i	0.0824435	+	0.0657465i
$849$		0			0
$850$	8.53386	−	27.6661i	0.292709	−	0.948939i
$851$	2.24125	+	1.29399i	0.0768291	+	0.0443573i
$852$		0			0
$853$	36.1336	−	8.24725i	1.23719	−	0.282381i	0.446604	−	0.894732i	$-0.352633\pi$
$853$	36.1336	−	8.24725i	1.23719	−	0.282381i	0.790586	+	0.612351i	$0.209776\pi$
$854$	8.64539	−	13.6376i	0.295839	−	0.466671i
$855$		0			0
$856$	12.7329	−	3.92759i	0.435203	−	0.134242i
$857$	−4.67474	−	11.9110i	−0.159686	−	0.406873i	0.828529	−	0.559946i	$-0.189178\pi$
$857$	−4.67474	−	11.9110i	−0.159686	−	0.406873i	−0.988215	+	0.153073i	$0.951083\pi$
$858$		0			0
$859$	1.52058	+	4.92959i	0.0518815	+	0.168196i	0.977806	−	0.209514i	$-0.0671881\pi$
$859$	1.52058	+	4.92959i	0.0518815	+	0.168196i	−0.925924	+	0.377709i	$0.876712\pi$
$860$	−1.96556	+	8.61168i	−0.0670250	+	0.293656i
$861$		0			0
$862$	8.43783	+	36.9686i	0.287394	+	1.25915i
$863$	4.54255	−	2.62264i	0.154630	−	0.0892757i	−0.420688	−	0.907205i	$-0.638211\pi$
$863$	4.54255	−	2.62264i	0.154630	−	0.0892757i	0.575319	+	0.817929i	$0.304878\pi$
$864$		0			0
$865$	−7.17490	−	2.21316i	−0.243954	−	0.0752498i
$866$	1.73055	+	23.0926i	0.0588066	+	0.784719i
$867$		0			0
$868$	−7.49848	+	10.0755i	−0.254515	+	0.341984i
$869$	−10.5613	+	8.42232i	−0.358266	+	0.285708i
$870$		0			0
$871$	−0.0215321	−	0.142856i	−0.000729586	−	0.00484049i
$872$	9.85555	+	14.4554i	0.333751	+	0.489523i
$873$		0			0
$874$	−0.489617	−	1.01670i	−0.0165615	−	0.0343904i
$875$	−18.3675	+	7.92636i	−0.620936	+	0.267960i
$876$		0			0
$877$	−1.79308	−	1.22250i	−0.0605479	−	0.0412809i	0.532668	−	0.846324i	$-0.321190\pi$
$877$	−1.79308	−	1.22250i	−0.0605479	−	0.0412809i	−0.593216	+	0.805044i	$0.702142\pi$
$878$	4.28071	+	3.97192i	0.144467	+	0.134046i
$879$		0			0
$880$	1.04002	+	0.408179i	0.0350592	+	0.0137597i
$881$	−39.2851			−1.32355			−0.661775	−	0.749703i	$-0.730196\pi$
$881$	−39.2851			−1.32355			−0.661775	+	0.749703i	$0.730196\pi$
$882$		0			0
$883$	−58.3420			−1.96336			−0.981682	−	0.190526i	$-0.938981\pi$
$883$	−58.3420			−1.96336			−0.981682	+	0.190526i	$0.938981\pi$
$884$	36.8070	+	14.4457i	1.23795	+	0.485861i
$885$		0			0
$886$	3.44888	+	3.20009i	0.115867	+	0.107509i
$887$	18.3650	+	12.5210i	0.616635	+	0.420415i	0.830948	−	0.556351i	$-0.187799\pi$
$887$	18.3650	+	12.5210i	0.616635	+	0.420415i	−0.214313	+	0.976765i	$0.568751\pi$
$888$		0			0
$889$	30.5151	−	35.1736i	1.02344	−	1.17968i
$890$	1.17472	+	2.43934i	0.0393768	+	0.0817667i
$891$		0			0
$892$	−7.14809	−	10.4843i	−0.239336	−	0.351041i
$893$	−0.342723	−	2.27382i	−0.0114688	−	0.0760904i
$894$		0			0
$895$	8.14651	−	6.49662i	0.272308	−	0.217158i
$896$	2.42074	+	1.06771i	0.0808714	+	0.0356696i
$897$		0			0
$898$	−0.781473	−	10.4280i	−0.0260781	−	0.347988i
$899$	10.0297	+	3.09374i	0.334508	+	0.103182i
$900$		0			0
$901$	−17.7185	+	10.2298i	−0.590288	+	0.340803i
$902$	3.44754	+	15.1046i	0.114790	+	0.502930i
$903$		0			0
$904$	3.84392	−	16.8413i	0.127847	−	0.560133i
$905$	−4.50222	−	14.5958i	−0.149659	−	0.485182i
$906$		0			0
$907$	2.69058	+	6.85548i	0.0893392	+	0.227632i	0.968559	−	0.248784i	$-0.0800308\pi$
$907$	2.69058	+	6.85548i	0.0893392	+	0.227632i	−0.879220	+	0.476416i	$0.841936\pi$
$908$	0.0314025	−	0.00968639i	0.00104213	−	0.000321454i
$909$		0			0
$910$	−4.14769	−	12.0073i	−0.137495	−	0.398038i
$911$	−35.3111	+	8.05953i	−1.16991	+	0.267024i	−0.762971	−	0.646432i	$-0.776260\pi$
$911$	−35.3111	+	8.05953i	−1.16991	+	0.267024i	−0.406937	+	0.913456i	$0.633403\pi$
$912$		0			0
$913$	−15.7801	−	9.11063i	−0.522244	−	0.301518i
$914$	−4.62560	+	14.9958i	−0.153001	+	0.496018i
$915$		0			0
$916$	7.82907	+	6.24348i	0.258680	+	0.206290i
$917$	−6.83227	+	5.83224i	−0.225622	+	0.192597i
$918$		0			0
$919$	34.7798	−	32.2709i	1.14728	−	1.06452i	0.150160	−	0.988662i	$-0.452021\pi$
$919$	34.7798	−	32.2709i	1.14728	−	1.06452i	0.997119	−	0.0758571i	$-0.0241693\pi$
$920$	2.49651	−	0.376289i	0.0823076	−	0.0124059i
$921$		0			0
$922$	1.42104	−	9.42797i	0.0467994	−	0.310494i
$923$	77.1038	−	37.1312i	2.53790	−	1.22219i
$924$		0			0
$925$	3.24695	+	1.56365i	0.106759	+	0.0514125i
$926$	−1.30167	+	1.90920i	−0.0427755	+	0.0627401i
$927$		0			0
$928$	0.165231	−	2.20486i	0.00542399	−	0.0723781i
$929$	−21.4029	+	54.5338i	−0.702207	+	1.78920i	−0.0937696	+	0.995594i	$0.529892\pi$
$929$	−21.4029	+	54.5338i	−0.702207	+	1.78920i	−0.608438	+	0.793602i	$0.708204\pi$
$930$		0			0
$931$	−0.543522	−	2.47234i	−0.0178132	−	0.0810277i
$932$		−	16.4729i		−	0.539587i
$933$		0			0
$934$	26.1817	+	1.96204i	0.856690	+	0.0642001i
$935$	−5.06321	+	5.45684i	−0.165585	+	0.178458i
$936$		0			0
$937$	9.72811	−	20.2006i	0.317804	−	0.659926i	−0.679471	−	0.733702i	$-0.737791\pi$
$937$	9.72811	−	20.2006i	0.317804	−	0.659926i	0.997275	+	0.0737762i	$0.0235051\pi$
$938$	0.0621461	+	0.0169188i	0.00202914	+	0.000552417i
$939$		0			0
$940$	5.08727	+	0.766782i	0.165928	+	0.0250097i
$941$	13.4484	−	9.16899i	0.438406	−	0.298900i	−0.323930	−	0.946081i	$-0.605004\pi$
$941$	13.4484	−	9.16899i	0.438406	−	0.298900i	0.762337	+	0.647180i	$0.224052\pi$
$942$		0			0
$943$	23.8132	+	25.6645i	0.775463	+	0.835750i
$944$	2.29599	+	2.87908i	0.0747281	+	0.0937060i
$945$		0			0
$946$	−9.39983	+	11.7870i	−0.305615	+	0.383229i
$947$	27.6413	−	2.07143i	0.898220	−	0.0673123i	0.382388	−	0.924002i	$-0.375102\pi$
$947$	27.6413	−	2.07143i	0.898220	−	0.0673123i	0.515832	+	0.856690i	$0.327483\pi$
$948$		0			0
$949$	18.8002	−	32.5629i	0.610281	−	1.05704i
$950$	−0.785704	−	1.36088i	−0.0254916	−	0.0441528i
$951$		0			0
$952$	−12.5146	+	12.4149i	−0.405602	+	0.402370i
$953$	−11.5695	−	2.64067i	−0.374774	−	0.0855396i	0.0309852	−	0.999520i	$-0.490136\pi$
$953$	−11.5695	−	2.64067i	−0.374774	−	0.0855396i	−0.405759	+	0.913980i	$0.632993\pi$
$954$		0			0
$955$	−2.23604	+	0.877580i	−0.0723565	+	0.0283978i
$956$	−6.01849	+	2.36208i	−0.194652	+	0.0763952i
$957$		0			0
$958$	−22.4360	−	5.12088i	−0.724875	−	0.165448i
$959$	−10.3923	+	29.3226i	−0.335585	+	0.946878i
$960$		0			0
$961$	−4.23268	−	7.33122i	−0.136538	−	0.236491i
$962$	−2.46089	+	4.26239i	−0.0793423	+	0.137425i
$963$		0			0
$964$	−11.3814	+	0.852920i	−0.366571	+	0.0274707i
$965$	2.27545	−	2.85333i	0.0732494	−	0.0918518i
$966$		0			0
$967$	31.3712	+	39.3382i	1.00883	+	1.26503i	0.963962	+	0.266040i	$0.0857153\pi$
$967$	31.3712	+	39.3382i	1.00883	+	1.26503i	0.0448679	+	0.998993i	$0.485713\pi$
$968$	−6.18488	−	6.66571i	−0.198790	−	0.214244i
$969$		0			0
$970$	4.40317	−	3.00203i	0.141377	−	0.0963894i
$971$	25.1856	+	3.79612i	0.808245	+	0.121823i	0.540150	−	0.841569i	$-0.318368\pi$
$971$	25.1856	+	3.79612i	0.808245	+	0.121823i	0.268095	+	0.963392i	$0.413606\pi$
$972$		0			0
$973$	−15.2267	+	28.5334i	−0.488145	+	0.914739i
$974$	−2.56351	+	5.32318i	−0.0821401	+	0.170566i
$975$		0			0
$976$	−4.15111	+	4.47383i	−0.132874	+	0.143204i
$977$	−3.72121	−	0.278866i	−0.119052	−	0.00892171i	0.0150708	−	0.999886i	$-0.495203\pi$
$977$	−3.72121	−	0.278866i	−0.119052	−	0.00892171i	−0.134123	+	0.990965i	$0.542822\pi$
$978$		0			0
$979$			4.62101i			0.147688i
$980$	5.64412	+	0.468408i	0.180295	+	0.0149627i
$981$		0			0
$982$	−4.06492	+	10.3572i	−0.129717	+	0.330513i
$983$	−2.45882	+	32.8106i	−0.0784241	+	1.04650i	0.809685	+	0.586865i	$0.199638\pi$
$983$	−2.45882	+	32.8106i	−0.0784241	+	1.04650i	−0.888109	+	0.459633i	$0.847981\pi$
$984$		0			0
$985$	−10.3001	+	15.1075i	−0.328189	+	0.481366i
$986$	13.2728	+	6.39182i	0.422691	+	0.203557i
$987$		0			0
$988$	1.93355	−	0.931147i	0.0615143	−	0.0296237i
$989$	−5.07761	+	33.6878i	−0.161459	+	1.07121i
$990$		0			0
$991$	−5.27811	+	0.795548i	−0.167665	+	0.0252714i	−0.232338	−	0.972635i	$-0.574638\pi$
$991$	−5.27811	+	0.795548i	−0.167665	+	0.0252714i	0.0646733	+	0.997906i	$0.479399\pi$
$992$	3.47985	−	3.22882i	0.110485	−	0.102515i
$993$		0			0
$994$	1.27406	+	38.1318i	0.0404106	+	1.20947i
$995$	−4.68052	−	3.73259i	−0.148383	−	0.118331i
$996$		0			0
$997$	14.8014	−	47.9848i	0.468764	−	1.51970i	−0.345058	−	0.938581i	$-0.612141\pi$
$997$	14.8014	−	47.9848i	0.468764	−	1.51970i	0.813822	−	0.581114i	$-0.197383\pi$
$998$	−35.1083	−	20.2698i	−1.11133	−	0.641628i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.2.bl.a.395.4	✓	240
3.2	odd	2	inner	882.2.bl.a.395.17	yes	240
49.33	odd	42	inner	882.2.bl.a.719.17	yes	240
147.131	even	42	inner	882.2.bl.a.719.4	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
882.2.bl.a.395.4	✓	240	1.1	even	1	trivial
882.2.bl.a.395.17	yes	240	3.2	odd	2	inner
882.2.bl.a.719.4	yes	240	147.131	even	42	inner
882.2.bl.a.719.17	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)

\(f(q)\)	\(=\)	\(q+(-0.930874 - 0.365341i) q^{2} +(0.733052 + 0.680173i) q^{4} +(-0.668488 - 0.455768i) q^{5} +(1.56257 + 2.13503i) q^{7} +(-0.433884 - 0.900969i) q^{8} +O(q^{10})\)	\(q+(-0.930874 - 0.365341i) q^{2} +(0.733052 + 0.680173i) q^{4} +(-0.668488 - 0.455768i) q^{5} +(1.56257 + 2.13503i) q^{7} +(-0.433884 - 0.900969i) q^{8} +(0.455768 + 0.668488i) q^{10} +(0.205813 + 1.36548i) q^{11} +(-4.63979 + 3.70011i) q^{13} +(-0.674542 - 2.55832i) q^{14} +(0.0747301 + 0.997204i) q^{16} +(-6.36675 - 1.96388i) q^{17} +(-0.313177 + 0.180813i) q^{19} +(-0.180036 - 0.788789i) q^{20} +(0.307280 - 1.34628i) q^{22} +(-0.919782 - 2.98186i) q^{23} +(-1.58755 - 4.04502i) q^{25} +(5.67087 - 1.74923i) q^{26} +(-0.306745 + 2.62791i) q^{28} +(2.15561 - 0.492003i) q^{29} +(4.11108 + 2.37353i) q^{31} +(0.294755 - 0.955573i) q^{32} +(5.20916 + 4.15416i) q^{34} +(-0.0714819 - 2.13942i) q^{35} +(-0.607955 + 0.564100i) q^{37} +(0.357587 - 0.0538975i) q^{38} +(-0.120586 + 0.800038i) q^{40} +(-10.1084 + 4.86797i) q^{41} +(-9.83641 - 4.73696i) q^{43} +(-0.777892 + 1.14096i) q^{44} +(-0.233195 + 3.11177i) q^{46} +(-2.32313 + 5.91923i) q^{47} +(-2.11674 + 6.67229i) q^{49} +4.34540i q^{50} +(-5.91793 - 0.443487i) q^{52} +(2.08863 - 2.25100i) q^{53} +(0.484759 - 1.00661i) q^{55} +(1.24562 - 2.33419i) q^{56} +(-2.18635 - 0.329539i) q^{58} +(3.04261 - 2.07442i) q^{59} +(4.15111 + 4.47383i) q^{61} +(-2.95975 - 3.71141i) q^{62} +(-0.623490 + 0.781831i) q^{64} +(4.78804 - 0.358814i) q^{65} +(-0.0121720 + 0.0210825i) q^{67} +(-3.33138 - 5.77012i) q^{68} +(-0.715076 + 2.01764i) q^{70} +(-14.0589 - 3.20886i) q^{71} +(-5.89791 + 2.31476i) q^{73} +(0.772018 - 0.302995i) q^{74} +(-0.352559 - 0.0804693i) q^{76} +(-2.59375 + 2.57308i) q^{77} +(4.89112 + 8.47167i) q^{79} +(0.404537 - 0.700679i) q^{80} +(11.1881 - 0.838436i) q^{82} +(-8.22704 + 10.3164i) q^{83} +(3.36103 + 4.21459i) q^{85} +(7.42585 + 8.00316i) q^{86} +(1.14096 - 0.777892i) q^{88} +(3.30899 + 0.498750i) q^{89} +(-15.1499 - 4.12442i) q^{91} +(1.35393 - 2.81147i) q^{92} +(4.32507 - 4.66132i) q^{94} +(0.291764 + 0.0218647i) q^{95} -6.58675i q^{97} +(4.40808 - 5.43773i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 20 q^{4} - 4 q^{7}+O(q^{10}) \) 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

Fields

Representations

Groups

Database

Properties

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