LMFDB - Embedded newform 882.2.bl.a.395.17

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [882,2,Mod(17,882)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("882.17"); S:= CuspForms(chi, 2); N := Newforms(S);

sage: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")

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:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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			395.17
Character	$\chi$	$=$	882.395
Dual form			882.2.bl.a.719.17

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

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

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	0.703503	−	0.710692i	$-0.251618\pi$
$5$	0.668488	+	0.455768i	0.298957	+	0.203826i	−0.404546	+	0.914518i	$0.632570\pi$
$6$		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	$-0.980865\pi$
$11$	−0.205813	−	1.36548i	−0.0620550	−	0.411708i	0.936139	−	0.351631i	$-0.114373\pi$
$12$		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	0.945756	−	0.324879i	$-0.105324\pi$
$17$	6.36675	+	1.96388i	1.54416	+	0.476312i	0.598409	+	0.801191i	$0.295800\pi$
$18$		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	$0.0102387\pi$
$23$	0.919782	+	2.98186i	0.191788	+	0.621761i	−0.807695	+	0.589601i	$0.799285\pi$
$24$		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	−0.417925	−	0.908482i	$-0.637242\pi$
$29$	−2.15561	+	0.492003i	−0.400286	+	0.0913627i	0.0176384	+	0.999844i	$0.494385\pi$
$30$		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	0.580146	−	0.814513i	$-0.302996\pi$
$41$	10.1084	−	4.86797i	1.57867	−	0.760249i	0.998527	+	0.0542640i	$0.0172813\pi$
$42$		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	$-0.727452\pi$
$47$	2.32313	−	5.91923i	0.338863	−	0.863408i	0.994148	−	0.108026i	$-0.0344531\pi$
$48$		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	−0.860011	−	0.510275i	$-0.829544\pi$
$53$	−2.08863	+	2.25100i	−0.286895	+	0.309199i	0.573117	+	0.819474i	$0.305734\pi$
$54$		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	−0.744953	−	0.667117i	$-0.767528\pi$
$59$	−3.04261	+	2.07442i	−0.396114	+	0.270066i	0.348839	+	0.937183i	$0.386576\pi$
$60$		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	0.949394	−	0.314089i	$-0.101699\pi$
$71$	14.0589	+	3.20886i	1.66849	+	0.380822i	0.719096	+	0.694911i	$0.244556\pi$
$72$		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	$-0.527934\pi$
$83$	8.22704	−	10.3164i	0.903035	−	1.13237i	0.990679	−	0.136218i	$-0.0434949\pi$
$84$		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	−0.0286966	−	0.999588i	$-0.509136\pi$
$89$	−3.30899	−	0.498750i	−0.350752	−	0.0528674i	−0.322056	+	0.946721i	$0.604374\pi$
$90$		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	$-0.914972\pi$
$101$	0.287104	−	3.83114i	0.0285679	−	0.381212i	0.993102	−	0.117254i	$-0.0374091\pi$
$102$		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	$-0.729620\pi$
$107$	1.98598	−	13.1761i	0.191992	−	1.27378i	0.852406	−	0.522880i	$-0.175142\pi$
$108$		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	$-0.983809\pi$
$113$	−13.5057	−	10.7704i	−1.27051	−	1.01320i	−0.271800	−	0.962354i	$-0.587619\pi$
$114$		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	$-0.976422\pi$
$131$	−0.253729	−	3.38577i	−0.0221684	−	0.295816i	0.975090	−	0.221812i	$-0.0711970\pi$
$132$		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	0.431495	−	0.902116i	$-0.357986\pi$
$137$	−6.62373	−	9.71523i	−0.565904	−	0.830028i	−0.997398	+	0.0720871i	$0.977034\pi$
$138$		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	−0.0996366	−	0.995024i	$-0.531768\pi$
$149$	−10.3690	−	4.06954i	−0.849463	−	0.333390i	−0.749827	+	0.661634i	$0.769863\pi$
$150$		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	$-0.992861\pi$
$167$	−1.40519	−	6.15654i	−0.108737	−	0.476407i	0.891012	−	0.453981i	$-0.149996\pi$
$168$		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	−0.612916	−	0.790148i	$-0.710004\pi$
$173$	−8.86804	+	2.73543i	−0.674224	+	0.207971i	−0.0613085	+	0.998119i	$0.519527\pi$
$174$		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	$-0.744928\pi$
$179$	3.79605	−	12.3065i	0.283730	−	0.919829i	0.979479	−	0.201545i	$-0.0645962\pi$
$180$		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	−0.881966	−	0.471313i	$-0.843780\pi$
$191$	−1.67246	+	2.45304i	−0.121015	+	0.177496i	0.760951	+	0.648809i	$0.224733\pi$
$192$		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	$0.297875\pi$
$197$			22.5995i			1.61015i	−0.593174	+	0.805075i	$0.702125\pi$
$198$		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	−0.866570	−	0.499055i	$-0.833680\pi$
$227$	−0.0164312	+	0.0284598i	−0.00109058	+	0.00188894i	0.865480	+	0.500944i	$0.167014\pi$
$228$		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	0.984191	−	0.177112i	$-0.0566756\pi$
$233$	11.2044	+	12.0755i	0.734025	+	0.791091i	−0.250166	+	0.968203i	$0.580485\pi$
$234$		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	−0.790323	−	0.612690i	$-0.790087\pi$
$239$	2.80524	−	5.82514i	0.181456	−	0.376797i	0.971779	+	0.235893i	$0.0758016\pi$
$240$		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	0.693812	−	0.720156i	$-0.255930\pi$
$251$	8.92524	+	4.29817i	0.563356	+	0.271298i	−0.130456	+	0.991454i	$0.541644\pi$
$252$		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	−0.991545	−	0.129763i	$-0.958578\pi$
$257$	−15.0091	+	13.9264i	−0.936243	+	0.868707i	0.0553017	+	0.998470i	$0.482388\pi$
$258$		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	0.312191	−	0.950019i	$-0.398937\pi$
$263$	−5.74828	−	3.31877i	−0.354454	−	0.204644i	−0.666645	+	0.745375i	$0.732270\pi$
$264$		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	$0.0736006\pi$
$269$	6.81828	+	17.3727i	0.415718	+	1.05923i	−0.557669	+	0.830063i	$0.688304\pi$
$270$		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	−0.736620	−	0.676307i	$-0.763579\pi$
$281$	−4.04295	+	3.22415i	−0.241182	+	0.192336i	0.495437	+	0.868644i	$0.335008\pi$
$282$		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	$-0.401751\pi$
$293$	10.3997			0.607559			0.303779	+	0.952742i	$0.401751\pi$
$294$		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	0.600556	−	0.799582i	$-0.294946\pi$
$311$	11.3983	+	3.51591i	0.646339	+	0.199369i	0.0457821	+	0.998951i	$0.485422\pi$
$312$		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	$-0.685168\pi$
$317$	−10.0798	−	32.6780i	−0.566139	−	1.83538i	−0.0166765	−	0.999861i	$-0.505309\pi$
$318$		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	−0.891062	−	0.453881i	$-0.850039\pi$
$347$	−6.92701	+	7.46554i	−0.371861	+	0.400771i	0.519201	+	0.854652i	$0.326230\pi$
$348$		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	−0.743392	−	0.668856i	$-0.766784\pi$
$353$	−7.37182	+	5.02602i	−0.392362	+	0.267508i	0.351029	+	0.936364i	$0.385832\pi$
$354$		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	−0.0369064	−	0.999319i	$-0.511750\pi$
$359$	1.43128	−	0.107260i	0.0755402	−	0.00566096i	0.112447	+	0.993658i	$0.464131\pi$
$360$		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	0.731713	−	0.681613i	$-0.238721\pi$
$383$	24.0718	+	3.62823i	1.23001	+	0.185394i	0.498296	+	0.867007i	$0.333959\pi$
$384$		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	−0.360765	−	0.932657i	$-0.617484\pi$
$389$	−16.8929	−	1.26595i	−0.856506	−	0.0641863i	−0.495741	+	0.868470i	$0.665104\pi$
$390$		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	$0.113209\pi$
$401$	−1.22129	+	8.10274i	−0.0609884	+	0.404632i	−0.998407	+	0.0564265i	$0.982029\pi$
$402$		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	−0.969904	−	0.243489i	$-0.921708\pi$
$419$	0.196413	−	0.860540i	0.00959539	−	0.0420402i	0.979499	+	0.201449i	$0.0645651\pi$
$420$		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	$0.175962\pi$
$431$	21.3607	+	31.3304i	1.02891	+	1.50913i	0.177851	+	0.984057i	$0.443085\pi$
$432$		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	0.467092	−	0.884208i	$-0.345302\pi$
$443$	4.37960	+	1.71887i	0.208081	+	0.0816658i	−0.259012	+	0.965874i	$0.583397\pi$
$444$		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	0.766046	−	0.642785i	$-0.222221\pi$
$449$	−4.53724	−	9.42168i	−0.214126	−	0.444636i	−0.980172	+	0.198149i	$0.936507\pi$
$450$		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	0.901186	−	0.433432i	$-0.142698\pi$
$461$	−2.12162	−	9.29541i	−0.0988136	−	0.432930i	−1.00000		0.000501439i	$0.999840\pi$
$462$		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	0.346345	−	0.938107i	$-0.387423\pi$
$467$	25.0886	−	7.73882i	1.16096	−	0.358110i	0.814619	+	0.579997i	$0.196946\pi$
$468$		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	−0.646655	−	0.762782i	$-0.723833\pi$
$479$	−22.7560	+	3.42991i	−1.03975	+	0.156717i	−0.393092	+	0.919499i	$0.628595\pi$
$480$		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	$0.0807801\pi$
$491$			11.1264i			0.502126i	−0.967971	+	0.251063i	$0.919220\pi$
$492$		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	0.921110	−	0.389302i	$-0.127284\pi$
$503$	7.54921	+	9.46642i	0.336603	+	0.422087i	−0.584507	+	0.811388i	$0.698712\pi$
$504$		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	$-0.777995\pi$
$509$	−21.1952	−	36.7111i	−0.939459	−	1.62719i	−0.172976	−	0.984926i	$-0.555338\pi$
$510$		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	−0.832635	−	0.553822i	$-0.813169\pi$
$521$	1.44499	−	2.50280i	0.0633063	−	0.109650i	0.895941	+	0.444172i	$0.146502\pi$
$522$		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	0.941815	−	0.336132i	$-0.109119\pi$
$557$	26.4713	+	15.2832i	1.12162	+	0.647569i	0.179808	+	0.983702i	$0.442452\pi$
$558$		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	0.943127	−	0.332431i	$-0.107869\pi$
$563$	0.608740	+	1.55104i	0.0256553	+	0.0653687i	−0.917472	+	0.397800i	$0.869774\pi$
$564$		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	−0.975243	−	0.221134i	$-0.929024\pi$
$569$	−30.3266	+	17.5091i	−1.27136	+	0.734018i	−0.296114	+	0.955153i	$0.595691\pi$
$570$		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	$-0.374952\pi$
$587$	18.5502			0.765648			0.382824	+	0.923821i	$0.374952\pi$
$588$		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	$-0.970174\pi$
$593$	−35.2233	−	24.0148i	−1.44645	−	0.986172i	−0.450835	−	0.892607i	$-0.648874\pi$
$594$		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	$-0.816646\pi$
$599$	−4.84128	−	32.1198i	−0.197809	−	1.31238i	0.640826	−	0.767686i	$-0.278592\pi$
$600$		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	0.184867	−	0.982764i	$-0.440815\pi$
$617$	19.3209	−	4.40987i	0.777831	−	0.177535i	0.592964	+	0.805229i	$0.297958\pi$
$618$		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	−0.462498	−	0.886620i	$-0.653047\pi$
$641$	11.5502	−	12.4482i	0.456206	−	0.491673i	0.918704	+	0.394947i	$0.129237\pi$
$642$		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	−0.909543	−	0.415610i	$-0.863568\pi$
$647$	−21.7468	+	14.8267i	−0.854956	+	0.582899i	0.0545868	+	0.998509i	$0.482616\pi$
$648$		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	0.477889	−	0.878420i	$-0.341402\pi$
$653$	27.6330	−	2.07080i	1.08136	−	0.0810369i	0.603473	+	0.797383i	$0.293783\pi$
$654$		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	−0.516934	−	0.856025i	$-0.672927\pi$
$659$	−34.7609	−	7.93394i	−1.35409	−	0.309062i	−0.837157	+	0.546963i	$0.815784\pi$
$660$		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	0.633742	−	0.773544i	$-0.281518\pi$
$677$	26.3138	+	3.96617i	1.01132	+	0.152432i	0.377581	+	0.925977i	$0.376756\pi$
$678$		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	−0.899642	−	0.436628i	$-0.856173\pi$
$683$	−48.4611	−	3.63166i	−1.85431	−	0.138961i	−0.954670	+	0.297667i	$0.903792\pi$
$684$		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	0.605041	−	0.796194i	$-0.293157\pi$
$701$	−0.967874	−	0.771854i	−0.0365561	−	0.0291525i	−0.641597	+	0.767042i	$0.721728\pi$
$702$		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	$0.300416\pi$
$719$	3.41198	+	45.5297i	0.127245	+	1.69797i	−0.459483	+	0.888187i	$0.651965\pi$
$720$		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	0.959063	−	0.283193i	$-0.0913938\pi$
$743$	3.80760	+	7.90657i	0.139687	+	0.290064i	−0.819375	+	0.573257i	$0.805680\pi$
$744$		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	−0.726734	−	0.686919i	$-0.758963\pi$
$761$	−25.9375	+	8.00066i	−0.940234	+	0.290024i	−0.213500	+	0.976943i	$0.568486\pi$
$762$		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	−0.400484	−	0.916304i	$-0.631158\pi$
$773$	−14.2654	+	2.15016i	−0.513090	+	0.0773358i	−0.112606	+	0.993640i	$0.535920\pi$
$774$		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	0.395323	−	0.918542i	$-0.370633\pi$
$797$	−16.6044	−	20.8212i	−0.588157	−	0.737526i	−0.983480	+	0.181017i	$0.942061\pi$
$798$		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	−0.590688	−	0.806900i	$-0.701143\pi$
$809$	−13.5064	+	5.30089i	−0.474861	+	0.186369i	0.115827	+	0.993269i	$0.463048\pi$
$810$		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	0.368170	−	0.929759i	$-0.379984\pi$
$821$	−16.8051	−	18.1116i	−0.586502	−	0.632099i	−0.954672	+	0.297660i	$0.903794\pi$
$822$		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	$-0.540485\pi$
$827$	20.9286	−	43.4586i	0.727758	−	1.51120i	0.854603	−	0.519282i	$-0.173800\pi$
$828$		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	0.965012	−	0.262205i	$-0.0844497\pi$
$839$	39.4419	+	18.9942i	1.36169	+	0.655754i	0.396675	+	0.917959i	$0.370164\pi$
$840$		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	0.988215	−	0.153073i	$-0.0489170\pi$
$857$	4.67474	+	11.9110i	0.159686	+	0.406873i	−0.828529	+	0.559946i	$0.810822\pi$
$858$		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	−0.575319	−	0.817929i	$-0.695122\pi$
$863$	−4.54255	+	2.62264i	−0.154630	+	0.0892757i	0.420688	+	0.907205i	$0.361789\pi$
$864$		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	$-0.269804\pi$
$881$	39.2851			1.32355			0.661775	+	0.749703i	$0.269804\pi$
$882$		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	0.214313	−	0.976765i	$-0.431249\pi$
$887$	−18.3650	−	12.5210i	−0.616635	−	0.420415i	−0.830948	+	0.556351i	$0.812201\pi$
$888$		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	0.406937	−	0.913456i	$-0.366597\pi$
$911$	35.3111	−	8.05953i	1.16991	−	0.267024i	0.762971	+	0.646432i	$0.223740\pi$
$912$		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	$-0.470108\pi$
$929$	21.4029	−	54.5338i	0.702207	−	1.78920i	0.608438	−	0.793602i	$-0.291796\pi$
$930$		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	−0.762337	−	0.647180i	$-0.775948\pi$
$941$	−13.4484	+	9.16899i	−0.438406	+	0.298900i	0.323930	+	0.946081i	$0.394996\pi$
$942$		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	−0.515832	−	0.856690i	$-0.672517\pi$
$947$	−27.6413	+	2.07143i	−0.898220	+	0.0673123i	−0.382388	+	0.924002i	$0.624898\pi$
$948$		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	0.405759	−	0.913980i	$-0.367007\pi$
$953$	11.5695	+	2.64067i	0.374774	+	0.0855396i	−0.0309852	+	0.999520i	$0.509864\pi$
$954$		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	−0.268095	−	0.963392i	$-0.586394\pi$
$971$	−25.1856	−	3.79612i	−0.808245	−	0.121823i	−0.540150	+	0.841569i	$0.681632\pi$
$972$		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	0.134123	−	0.990965i	$-0.457178\pi$
$977$	3.72121	+	0.278866i	0.119052	+	0.00892171i	−0.0150708	+	0.999886i	$0.504797\pi$
$978$		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	$-0.800362\pi$
$983$	2.45882	−	32.8106i	0.0784241	−	1.04650i	0.888109	−	0.459633i	$-0.152019\pi$
$984$		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.395.17	yes	240
3.2	odd	2	inner	882.2.bl.a.395.4	✓	240
49.33	odd	42	inner	882.2.bl.a.719.4	yes	240
147.131	even	42	inner	882.2.bl.a.719.17	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
882.2.bl.a.395.4	✓	240	3.2	odd	2	inner
882.2.bl.a.395.17	yes	240	1.1	even	1	trivial
882.2.bl.a.719.4	yes	240	49.33	odd	42	inner
882.2.bl.a.719.17	yes	240	147.131	even	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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(0.930874 + 0.365341i) q^{2} +(0.733052 + 0.680173i) q^{4} +(0.668488 + 0.455768i) q^{5} +(1.56257 + 2.13503i) q^{7} +(0.433884 + 0.900969i) q^{8} +(0.455768 + 0.668488i) q^{10} +(-0.205813 - 1.36548i) q^{11} +(-4.63979 + 3.70011i) q^{13} +(0.674542 + 2.55832i) q^{14} +(0.0747301 + 0.997204i) q^{16} +(6.36675 + 1.96388i) q^{17} +(-0.313177 + 0.180813i) q^{19} +(0.180036 + 0.788789i) q^{20} +(0.307280 - 1.34628i) q^{22} +(0.919782 + 2.98186i) q^{23} +(-1.58755 - 4.04502i) q^{25} +(-5.67087 + 1.74923i) q^{26} +(-0.306745 + 2.62791i) q^{28} +(-2.15561 + 0.492003i) q^{29} +(4.11108 + 2.37353i) q^{31} +(-0.294755 + 0.955573i) q^{32} +(5.20916 + 4.15416i) q^{34} +(0.0714819 + 2.13942i) q^{35} +(-0.607955 + 0.564100i) q^{37} +(-0.357587 + 0.0538975i) q^{38} +(-0.120586 + 0.800038i) q^{40} +(10.1084 - 4.86797i) q^{41} +(-9.83641 - 4.73696i) q^{43} +(0.777892 - 1.14096i) q^{44} +(-0.233195 + 3.11177i) q^{46} +(2.32313 - 5.91923i) q^{47} +(-2.11674 + 6.67229i) q^{49} -4.34540i q^{50} +(-5.91793 - 0.443487i) q^{52} +(-2.08863 + 2.25100i) q^{53} +(0.484759 - 1.00661i) q^{55} +(-1.24562 + 2.33419i) q^{56} +(-2.18635 - 0.329539i) q^{58} +(-3.04261 + 2.07442i) q^{59} +(4.15111 + 4.47383i) q^{61} +(2.95975 + 3.71141i) q^{62} +(-0.623490 + 0.781831i) q^{64} +(-4.78804 + 0.358814i) q^{65} +(-0.0121720 + 0.0210825i) q^{67} +(3.33138 + 5.77012i) q^{68} +(-0.715076 + 2.01764i) q^{70} +(14.0589 + 3.20886i) q^{71} +(-5.89791 + 2.31476i) q^{73} +(-0.772018 + 0.302995i) q^{74} +(-0.352559 - 0.0804693i) q^{76} +(2.59375 - 2.57308i) q^{77} +(4.89112 + 8.47167i) q^{79} +(-0.404537 + 0.700679i) q^{80} +(11.1881 - 0.838436i) q^{82} +(8.22704 - 10.3164i) q^{83} +(3.36103 + 4.21459i) q^{85} +(-7.42585 - 8.00316i) q^{86} +(1.14096 - 0.777892i) q^{88} +(-3.30899 - 0.498750i) q^{89} +(-15.1499 - 4.12442i) q^{91} +(-1.35393 + 2.81147i) q^{92} +(4.32507 - 4.66132i) q^{94} +(-0.291764 - 0.0218647i) q^{95} -6.58675i q^{97} +(-4.40808 + 5.43773i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 20 q^{4} - 4 q^{7} - 12 q^{10} + 20 q^{16} + 24 q^{19} - 20 q^{22} + 24 q^{25} + 4 q^{28} + 12 q^{31} - 32 q^{37} + 44 q^{40} - 48 q^{43} + 204 q^{49} + 140 q^{55} + 136 q^{58} + 88 q^{61} + 40 q^{64}+ \cdots + 80 q^{94}+O(q^{100}) \) 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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