LMFDB - Embedded newform 684.2.ce.a.575.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [684,2,Mod(35,684)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(684, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 9, 4]))

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

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

chi := DirichletCharacter("684.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	684.ce (of order $18$, degree $6$, 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:	$5.46176749826$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$40$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			575.3
Character	$\chi$	$=$	684.575
Dual form			684.2.ce.a.251.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.37865 + 0.315165i) q^{2} +(1.80134 - 0.869002i) q^{4} +(0.327179 - 0.389916i) q^{5} +(0.521928 - 0.301335i) q^{7} +(-2.20954 + 1.76577i) q^{8} +O(q^{10})$	\(q+(-1.37865 + 0.315165i) q^{2} +(1.80134 - 0.869002i) q^{4} +(0.327179 - 0.389916i) q^{5} +(0.521928 - 0.301335i) q^{7} +(-2.20954 + 1.76577i) q^{8} +(-0.328177 + 0.640673i) q^{10} +(-1.96865 + 3.40980i) q^{11} +(0.0259850 + 0.147368i) q^{13} +(-0.624585 + 0.579929i) q^{14} +(2.48967 - 3.13074i) q^{16} +(0.961951 + 2.64294i) q^{17} +(0.595713 + 4.31800i) q^{19} +(0.250523 - 0.986692i) q^{20} +(1.63943 - 5.32137i) q^{22} +(-2.36324 + 1.98299i) q^{23} +(0.823252 + 4.66889i) q^{25} +(-0.0822693 - 0.194979i) q^{26} +(0.678310 - 0.996365i) q^{28} +(1.82411 - 5.01169i) q^{29} +(5.59472 - 3.23011i) q^{31} +(-2.44568 + 5.10085i) q^{32} +(-2.15915 - 3.34051i) q^{34} +(0.0532682 - 0.302099i) q^{35} +1.10553 q^{37} +(-2.18216 - 5.76526i) q^{38} +(-0.0344121 + 1.43926i) q^{40} +(7.17421 + 1.26501i) q^{41} +(1.16671 - 1.39043i) q^{43} +(-0.583087 + 7.85298i) q^{44} +(2.63310 - 3.47866i) q^{46} +(-0.0981258 - 0.0357149i) q^{47} +(-3.31839 + 5.74763i) q^{49} +(-2.60645 - 6.17730i) q^{50} +(0.174871 + 0.242879i) q^{52} +(5.53984 + 6.60213i) q^{53} +(0.685438 + 1.88322i) q^{55} +(-0.621132 + 1.58742i) q^{56} +(-0.935293 + 7.48425i) q^{58} +(1.44720 - 0.526737i) q^{59} +(-7.83716 + 6.57616i) q^{61} +(-6.69513 + 6.21644i) q^{62} +(1.76412 - 7.80307i) q^{64} +(0.0659630 + 0.0380837i) q^{65} +(-1.27718 + 3.50903i) q^{67} +(4.02952 + 3.92490i) q^{68} +(0.0217728 + 0.433276i) q^{70} +(5.64305 + 4.73508i) q^{71} +(-1.91034 + 10.8341i) q^{73} +(-1.52414 + 0.348424i) q^{74} +(4.82544 + 7.26052i) q^{76} +2.37290i q^{77} +(-1.45523 - 0.256597i) q^{79} +(-0.406161 - 1.99508i) q^{80} +(-10.2894 + 0.517058i) q^{82} +(-4.22123 - 7.31138i) q^{83} +(1.34526 + 0.489633i) q^{85} +(-1.17026 + 2.28461i) q^{86} +(-1.67111 - 11.0103i) q^{88} +(12.7602 - 2.24996i) q^{89} +(0.0579695 + 0.0690853i) q^{91} +(-2.53377 + 5.62570i) q^{92} +(0.146537 + 0.0183125i) q^{94} +(1.87856 + 1.18048i) q^{95} +(-2.02671 + 0.737663i) q^{97} +(2.76345 - 8.96980i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 12 q^{4}+O(q^{10}) $ 240 * q + 12 * q^4	$ 240 q + 12 q^{4} + 12 q^{10} + 24 q^{13} - 12 q^{16} - 12 q^{34} + 120 q^{49} - 48 q^{52} - 144 q^{58} + 48 q^{61} - 12 q^{64} - 72 q^{70} + 72 q^{73} - 144 q^{76} - 72 q^{82} + 240 q^{85} - 48 q^{88} - 48 q^{94}+O(q^{100}) $ 240 * q + 12 * q^4 + 12 * q^10 + 24 * q^13 - 12 * q^16 - 12 * q^34 + 120 * q^49 - 48 * q^52 - 144 * q^58 + 48 * q^61 - 12 * q^64 - 72 * q^70 + 72 * q^73 - 144 * q^76 - 72 * q^82 + 240 * q^85 - 48 * q^88 - 48 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/684\mathbb{Z}\right)^\times$.

$n$	$325$	$343$	$533$
$\chi(n)$	$e\left(\frac{8}{9}\right)$	$-1$	$-1$

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 $

$2$	−1.37865	+	0.315165i	−0.974852	+	0.222855i
$2$	−1.37865	+	0.315165i	−0.974852	+	0.222855i
$3$		0			0
$3$		0			0
$4$	1.80134	−	0.869002i	0.900671	−	0.434501i
$5$	0.327179	−	0.389916i	0.146319	−	0.174376i	−0.687907	−	0.725799i	$-0.741470\pi$
$5$	0.327179	−	0.389916i	0.146319	−	0.174376i	0.834226	+	0.551423i	$0.185915\pi$
$6$		0			0
$7$	0.521928	−	0.301335i	0.197270	−	0.113894i	−0.398111	−	0.917337i	$-0.630334\pi$
$7$	0.521928	−	0.301335i	0.197270	−	0.113894i	0.595382	+	0.803443i	$0.297001\pi$
$8$	−2.20954	+	1.76577i	−0.781190	+	0.624293i
$9$		0			0
$10$	−0.328177	+	0.640673i	−0.103779	+	0.202599i
$11$	−1.96865	+	3.40980i	−0.593570	+	1.02809i	0.400176	+	0.916438i	$0.368949\pi$
$11$	−1.96865	+	3.40980i	−0.593570	+	1.02809i	−0.993747	+	0.111656i	$0.964384\pi$
$12$		0			0
$13$	0.0259850	+	0.147368i	0.00720693	+	0.0408725i	0.988199	−	0.153175i	$-0.0489497\pi$
$13$	0.0259850	+	0.147368i	0.00720693	+	0.0408725i	−0.980992	+	0.194047i	$0.937839\pi$
$14$	−0.624585	+	0.579929i	−0.166927	+	0.154992i
$15$		0			0
$16$	2.48967	−	3.13074i	0.622417	−	0.782686i
$17$	0.961951	+	2.64294i	0.233307	+	0.641007i	0.999999	−	0.00100808i	$-0.000320883\pi$
$17$	0.961951	+	2.64294i	0.233307	+	0.641007i	−0.766692	+	0.642015i	$0.778099\pi$
$18$		0			0
$19$	0.595713	+	4.31800i	0.136666	+	0.990617i
$19$	0.595713	+	4.31800i	0.136666	+	0.990617i
$20$	0.250523	−	0.986692i	0.0560186	−	0.220631i
$21$		0			0
$22$	1.63943	−	5.32137i	0.349527	−	1.13452i
$23$	−2.36324	+	1.98299i	−0.492769	+	0.413482i	−0.855017	−	0.518599i	$-0.826454\pi$
$23$	−2.36324	+	1.98299i	−0.492769	+	0.413482i	0.362248	+	0.932082i	$0.382009\pi$
$24$		0			0
$25$	0.823252	+	4.66889i	0.164650	+	0.933779i
$26$	−0.0822693	−	0.194979i	−0.0161343	−	0.0382386i
$27$		0			0
$28$	0.678310	−	0.996365i	0.128189	−	0.188295i
$29$	1.82411	−	5.01169i	0.338728	−	0.930647i	−0.647028	−	0.762466i	$-0.723988\pi$
$29$	1.82411	−	5.01169i	0.338728	−	0.930647i	0.985756	−	0.168181i	$-0.0537893\pi$
$30$		0			0
$31$	5.59472	−	3.23011i	1.00484	−	0.580145i	0.0951639	−	0.995462i	$-0.469662\pi$
$31$	5.59472	−	3.23011i	1.00484	−	0.580145i	0.909677	+	0.415316i	$0.136329\pi$
$32$	−2.44568	+	5.10085i	−0.432339	+	0.901711i
$33$		0			0
$34$	−2.15915	−	3.34051i	−0.370292	−	0.572893i
$35$	0.0532682	−	0.302099i	0.00900396	−	0.0510640i
$36$		0			0
$37$	1.10553			0.181748			0.0908741	−	0.995862i	$-0.471034\pi$
$37$	1.10553			0.181748			0.0908741	+	0.995862i	$0.471034\pi$
$38$	−2.18216	−	5.76526i	−0.353993	−	0.935248i
$39$		0			0
$40$	−0.0344121	+	1.43926i	−0.00544103	+	0.227567i
$41$	7.17421	+	1.26501i	1.12042	+	0.197561i	0.703027	−	0.711163i	$-0.251831\pi$
$41$	7.17421	+	1.26501i	1.12042	+	0.197561i	0.417397	+	0.908724i	$0.362942\pi$
$42$		0			0
$43$	1.16671	−	1.39043i	0.177921	−	0.212038i	−0.669712	−	0.742621i	$-0.733582\pi$
$43$	1.16671	−	1.39043i	0.177921	−	0.212038i	0.847633	+	0.530583i	$0.178027\pi$
$44$	−0.583087	+	7.85298i	−0.0879036	+	1.18388i
$45$		0			0
$46$	2.63310	−	3.47866i	0.388230	−	0.512900i
$47$	−0.0981258	−	0.0357149i	−0.0143131	−	0.00520955i	0.334854	−	0.942270i	$-0.391313\pi$
$47$	−0.0981258	−	0.0357149i	−0.0143131	−	0.00520955i	−0.349167	+	0.937061i	$0.613535\pi$
$48$		0			0
$49$	−3.31839	+	5.74763i	−0.474056	+	0.821090i
$50$	−2.60645	−	6.17730i	−0.368607	−	0.873603i
$51$		0			0
$52$	0.174871	+	0.242879i	0.0242502	+	0.0336813i
$53$	5.53984	+	6.60213i	0.760956	+	0.906872i	0.997908	−	0.0646491i	$-0.0205928\pi$
$53$	5.53984	+	6.60213i	0.760956	+	0.906872i	−0.236952	+	0.971521i	$0.576148\pi$
$54$		0			0
$55$	0.685438	+	1.88322i	0.0924244	+	0.253934i
$56$	−0.621132	+	1.58742i	−0.0830022	+	0.212127i
$57$		0			0
$58$	−0.935293	+	7.48425i	−0.122810	+	0.982730i
$59$	1.44720	−	0.526737i	0.188409	−	0.0685754i	−0.246092	−	0.969246i	$-0.579147\pi$
$59$	1.44720	−	0.526737i	0.188409	−	0.0685754i	0.434502	+	0.900671i	$0.356924\pi$
$60$		0			0
$61$	−7.83716	+	6.57616i	−1.00345	+	0.841991i	−0.987458	−	0.157881i	$-0.949534\pi$
$61$	−7.83716	+	6.57616i	−1.00345	+	0.841991i	−0.0159877	+	0.999872i	$0.505089\pi$
$62$	−6.69513	+	6.21644i	−0.850282	+	0.789489i
$63$		0			0
$64$	1.76412	−	7.80307i	0.220516	−	0.975383i
$65$	0.0659630	+	0.0380837i	0.00818170	+	0.00472370i
$66$		0			0
$67$	−1.27718	+	3.50903i	−0.156033	+	0.428696i	−0.992936	−	0.118655i	$-0.962142\pi$
$67$	−1.27718	+	3.50903i	−0.156033	+	0.428696i	0.836903	+	0.547351i	$0.184364\pi$
$68$	4.02952	+	3.92490i	0.488652	+	0.475964i
$69$		0			0
$70$	0.0217728	+	0.433276i	0.00260235	+	0.0517864i
$71$	5.64305	+	4.73508i	0.669706	+	0.561950i	0.912978	−	0.408008i	$-0.133776\pi$
$71$	5.64305	+	4.73508i	0.669706	+	0.561950i	−0.243272	+	0.969958i	$0.578221\pi$
$72$		0			0
$73$	−1.91034	+	10.8341i	−0.223589	+	1.26804i	0.641776	+	0.766892i	$0.278198\pi$
$73$	−1.91034	+	10.8341i	−0.223589	+	1.26804i	−0.865365	+	0.501143i	$0.832913\pi$
$74$	−1.52414	+	0.348424i	−0.177177	+	0.0405035i
$75$		0			0
$76$	4.82544	+	7.26052i	0.553515	+	0.832839i
$77$			2.37290i			0.270416i
$78$		0			0
$79$	−1.45523	−	0.256597i	−0.163727	−	0.0288694i	0.0911839	−	0.995834i	$-0.470935\pi$
$79$	−1.45523	−	0.256597i	−0.163727	−	0.0288694i	−0.254910	+	0.966965i	$0.582046\pi$
$80$	−0.406161	−	1.99508i	−0.0454102	−	0.223056i
$81$		0			0
$82$	−10.2894	+	0.517058i	−1.13627	+	0.0570995i
$83$	−4.22123	−	7.31138i	−0.463340	−	0.802528i	0.535785	−	0.844354i	$-0.320016\pi$
$83$	−4.22123	−	7.31138i	−0.463340	−	0.802528i	−0.999125	+	0.0418262i	$0.986682\pi$
$84$		0			0
$85$	1.34526	+	0.489633i	0.145913	+	0.0531082i
$86$	−1.17026	+	2.28461i	−0.126193	+	0.246356i
$87$		0			0
$88$	−1.67111	−	11.0103i	−0.178141	−	1.17370i
$89$	12.7602	−	2.24996i	1.35258	−	0.238496i	0.550060	−	0.835125i	$-0.314605\pi$
$89$	12.7602	−	2.24996i	1.35258	−	0.238496i	0.802517	+	0.596630i	$0.203494\pi$
$90$		0			0
$91$	0.0579695	+	0.0690853i	0.00607685	+	0.00724211i
$92$	−2.53377	+	5.62570i	−0.264164	+	0.586520i
$93$		0			0
$94$	0.146537	+	0.0183125i	0.0151141	+	0.00188879i
$95$	1.87856	+	1.18048i	0.192737	+	0.121115i
$96$		0			0
$97$	−2.02671	+	0.737663i	−0.205781	+	0.0748983i	−0.442854	−	0.896594i	$-0.646034\pi$
$97$	−2.02671	+	0.737663i	−0.205781	+	0.0748983i	0.237073	+	0.971492i	$0.423812\pi$
$98$	2.76345	−	8.96980i	0.279151	−	0.906086i
$99$		0			0
$100$	5.54024	+	7.69487i	0.554024	+	0.769487i
$101$	−2.63663	+	0.464910i	−0.262355	+	0.0462602i	−0.303278	−	0.952902i	$-0.598081\pi$
$101$	−2.63663	+	0.464910i	−0.262355	+	0.0462602i	0.0409234	+	0.999162i	$0.486970\pi$
$102$		0			0
$103$	3.67374	+	2.12104i	0.361985	+	0.208992i	0.669951	−	0.742405i	$-0.266315\pi$
$103$	3.67374	+	2.12104i	0.361985	+	0.208992i	−0.307966	+	0.951397i	$0.599648\pi$
$104$	−0.317633	−	0.279732i	−0.0311464	−	0.0274300i
$105$		0			0
$106$	−9.71826	−	7.35605i	−0.943920	−	0.714483i
$107$	−5.80001	−	10.0459i	−0.560708	−	0.971175i	−0.997435	−	0.0715810i	$-0.977196\pi$
$107$	−5.80001	−	10.0459i	−0.560708	−	0.971175i	0.436726	−	0.899594i	$-0.356138\pi$
$108$		0			0
$109$	4.09771	+	3.43839i	0.392490	+	0.329338i	0.817582	−	0.575812i	$-0.195314\pi$
$109$	4.09771	+	3.43839i	0.392490	+	0.329338i	−0.425093	+	0.905150i	$0.639758\pi$
$110$	−1.53850	−	2.38028i	−0.146691	−	0.226951i
$111$		0			0
$112$	0.356025	−	2.38425i	0.0336412	−	0.225290i
$113$			8.24168i			0.775312i	0.921804	+	0.387656i	$0.126715\pi$
$113$			8.24168i			0.775312i	−0.921804	+	0.387656i	$0.873285\pi$
$114$		0			0
$115$			1.57026i			0.146427i
$116$	−1.06933	−	10.6129i	−0.0992849	−	0.985385i
$117$		0			0
$118$	−1.82917	+	1.18229i	−0.168389	+	0.108839i
$119$	1.29848	+	1.08955i	0.119031	+	0.0998793i
$120$		0			0
$121$	−2.25117	−	3.89914i	−0.204652	−	0.354467i
$122$	8.73212	−	11.5362i	0.790569	−	1.04444i
$123$		0			0
$124$	7.27103	−	10.6804i	0.652957	−	0.959125i
$125$	4.29386	+	2.47906i	0.384055	+	0.221734i
$126$		0			0
$127$	−8.93361	+	1.57524i	−0.792729	+	0.139780i	−0.555327	−	0.831632i	$-0.687407\pi$
$127$	−8.93361	+	1.57524i	−0.792729	+	0.139780i	−0.237402	+	0.971411i	$0.576296\pi$
$128$	0.0271437	+	11.3137i	0.00239918	+	0.999997i
$129$		0			0
$130$	−0.102942	−	0.0317149i	−0.00902864	−	0.00278158i
$131$	6.03152	−	2.19530i	0.526977	−	0.191804i	−0.0648112	−	0.997898i	$-0.520645\pi$
$131$	6.03152	−	2.19530i	0.526977	−	0.191804i	0.591788	+	0.806094i	$0.298422\pi$
$132$		0			0
$133$	1.61208	+	2.07418i	0.139785	+	0.179854i
$134$	0.654863	−	5.24024i	0.0565716	−	0.452688i
$135$		0			0
$136$	−6.79229	−	4.14109i	−0.582434	−	0.355096i
$137$	−12.5479	−	14.9540i	−1.07204	−	1.27760i	−0.958814	−	0.284035i	$-0.908327\pi$
$137$	−12.5479	−	14.9540i	−1.07204	−	1.27760i	−0.113224	−	0.993570i	$-0.536118\pi$
$138$		0			0
$139$	−0.240547	+	0.0424150i	−0.0204030	+	0.00359759i	−0.183840	−	0.982956i	$-0.558853\pi$
$139$	−0.240547	+	0.0424150i	−0.0204030	+	0.00359759i	0.163437	+	0.986554i	$0.447742\pi$
$140$	−0.166570	−	0.590473i	−0.0140778	−	0.0499041i
$141$		0			0
$142$	−9.27210	−	4.74952i	−0.778098	−	0.398571i
$143$	−0.553651	−	0.201513i	−0.0462986	−	0.0168513i
$144$		0			0
$145$	−1.35733	−	2.35097i	−0.112720	−	0.195237i
$146$	−0.780833	−	15.5385i	−0.0646222	−	1.28597i
$147$		0			0
$148$	1.99144	−	0.960709i	0.163695	−	0.0789698i
$149$	−13.1632	−	2.32103i	−1.07837	−	0.190146i	−0.393877	−	0.919163i	$-0.628867\pi$
$149$	−13.1632	−	2.32103i	−1.07837	−	0.190146i	−0.684496	+	0.729017i	$0.739978\pi$
$150$		0			0
$151$		−	18.4184i		−	1.49887i	−0.662079	−	0.749434i	$-0.730326\pi$
$151$		−	18.4184i		−	1.49887i	0.662079	−	0.749434i	$-0.269674\pi$
$152$	−8.94084	−	8.48890i	−0.725198	−	0.688541i
$153$		0			0
$154$	−0.747853	−	3.27139i	−0.0602637	−	0.263616i
$155$	0.570999	−	3.23830i	0.0458637	−	0.260106i
$156$		0			0
$157$	5.81100	+	4.87601i	0.463768	+	0.389148i	0.844515	−	0.535531i	$-0.179889\pi$
$157$	5.81100	+	4.87601i	0.463768	+	0.389148i	−0.380747	+	0.924679i	$0.624333\pi$
$158$	2.08713	−	0.104881i	0.166043	−	0.00834390i
$159$		0			0
$160$	1.18873	+	2.62250i	0.0939774	+	0.207327i
$161$	−0.635894	+	1.74711i	−0.0501155	+	0.137691i
$162$		0			0
$163$	−17.9887	−	10.3858i	−1.40899	−	0.813479i	−0.413696	−	0.910415i	$-0.635762\pi$
$163$	−17.9887	−	10.3858i	−1.40899	−	0.813479i	−0.995291	+	0.0969360i	$0.969096\pi$
$164$	14.0225	−	3.95570i	1.09497	−	0.308888i
$165$		0			0
$166$	8.12388	+	8.74944i	0.630535	+	0.679088i
$167$	12.6655	−	10.6276i	0.980089	−	0.822392i	−0.00401403	−	0.999992i	$-0.501278\pi$
$167$	12.6655	−	10.6276i	0.980089	−	0.822392i	0.984103	+	0.177600i	$0.0568333\pi$
$168$		0			0
$169$	12.1950	−	4.43860i	0.938074	−	0.341431i
$170$	−2.00895	−	0.251055i	−0.154079	−	0.0192550i
$171$		0			0
$172$	0.893353	−	3.51850i	0.0681176	−	0.268283i
$173$	−3.89481	−	10.7009i	−0.296117	−	0.813574i	−0.995140	−	0.0984748i	$-0.968604\pi$
$173$	−3.89481	−	10.7009i	−0.296117	−	0.813574i	0.699023	−	0.715099i	$-0.253619\pi$
$174$		0			0
$175$	1.83658	+	2.18875i	0.138832	+	0.165454i
$176$	5.77392	+	14.6526i	0.435226	+	1.10448i
$177$		0			0
$178$	−16.8827	+	7.12347i	−1.26541	+	0.533926i
$179$	0.781271	−	1.35320i	0.0583950	−	0.101143i	−0.835350	−	0.549718i	$-0.814735\pi$
$179$	0.781271	−	1.35320i	0.0583950	−	0.101143i	0.893745	+	0.448575i	$0.148068\pi$
$180$		0			0
$181$	−14.0040	−	5.09704i	−1.04091	−	0.378860i	−0.235685	−	0.971830i	$-0.575733\pi$
$181$	−14.0040	−	5.09704i	−1.04091	−	0.378860i	−0.805225	+	0.592969i	$0.797956\pi$
$182$	−0.101693	−	0.0769744i	−0.00753797	−	0.00570572i
$183$		0			0
$184$	1.72016	−	8.55443i	0.126812	−	0.630641i
$185$	0.361706	−	0.431065i	0.0265932	−	0.0316925i
$186$		0			0
$187$	−10.9056	−	1.92296i	−0.797500	−	0.140621i
$188$	−0.207794	+	0.0209368i	−0.0151550	+	0.00152698i
$189$		0			0
$190$	−2.96192	−	1.03541i	−0.214881	−	0.0751165i
$191$	14.7598			1.06798			0.533989	−	0.845491i	$-0.320692\pi$
$191$	14.7598			1.06798			0.533989	+	0.845491i	$0.320692\pi$
$192$		0			0
$193$	3.66179	−	20.7670i	0.263581	−	1.49484i	−0.509463	−	0.860493i	$-0.670156\pi$
$193$	3.66179	−	20.7670i	0.263581	−	1.49484i	0.773044	−	0.634352i	$-0.218733\pi$
$194$	2.56164	−	1.65573i	0.183915	−	0.118874i
$195$		0			0
$196$	−0.982862	+	13.2371i	−0.0702044	+	0.945510i
$197$	3.05305	−	1.76268i	0.217520	−	0.125586i	−0.387281	−	0.921962i	$-0.626586\pi$
$197$	3.05305	−	1.76268i	0.217520	−	0.125586i	0.604802	+	0.796376i	$0.293252\pi$
$198$		0			0
$199$	8.17086	−	22.4493i	0.579217	−	1.59139i	−0.210286	−	0.977640i	$-0.567440\pi$
$199$	8.17086	−	22.4493i	0.579217	−	1.59139i	0.789503	−	0.613746i	$-0.210338\pi$
$200$	−10.0632	−	8.86243i	−0.711575	−	0.626669i
$201$		0			0
$202$	3.48847	−	1.47192i	0.245448	−	0.103564i
$203$	−0.558147	−	3.16541i	−0.0391742	−	0.222168i
$204$		0			0
$205$	2.84050	−	2.38346i	0.198389	−	0.166468i
$206$	−5.73328	−	1.76633i	−0.399456	−	0.123066i
$207$		0			0
$208$	0.526065	+	0.285546i	0.0364761	+	0.0197990i
$209$	−15.8963	−	6.46937i	−1.09957	−	0.447496i
$210$		0			0
$211$	9.16245	+	25.1736i	0.630769	+	1.73302i	0.678949	+	0.734185i	$0.262436\pi$
$211$	9.16245	+	25.1736i	0.630769	+	1.73302i	−0.0481803	+	0.998839i	$0.515342\pi$
$212$	15.7164	+	7.07856i	1.07941	+	0.486157i
$213$		0			0
$214$	11.1623	+	12.0218i	0.763039	+	0.821795i
$215$	−0.160429	−	0.909836i	−0.0109411	−	0.0620503i
$216$		0			0
$217$	1.94669	−	3.37177i	0.132150	−	0.228891i
$218$	−6.73296	−	3.44887i	−0.456014	−	0.233587i
$219$		0			0
$220$	2.87123	+	2.79668i	0.193579	+	0.188552i
$221$	−0.364489	+	0.210438i	−0.0245182	+	0.0141556i
$222$		0			0
$223$	−9.60375	+	11.4453i	−0.643115	+	0.766435i	−0.984859	−	0.173359i	$-0.944538\pi$
$223$	−9.60375	+	11.4453i	−0.643115	+	0.766435i	0.341744	+	0.939793i	$0.388982\pi$
$224$	0.260597	+	3.39924i	0.0174119	+	0.227122i
$225$		0			0
$226$	−2.59749	−	11.3624i	−0.172782	−	0.755814i
$227$	−22.6090			−1.50061			−0.750307	−	0.661090i	$-0.770094\pi$
$227$	−22.6090			−1.50061			−0.750307	+	0.661090i	$0.770094\pi$
$228$		0			0
$229$	6.58793			0.435343			0.217671	−	0.976022i	$-0.430154\pi$
$229$	6.58793			0.435343			0.217671	+	0.976022i	$0.430154\pi$
$230$	−0.494890	−	2.16483i	−0.0326321	−	0.142745i
$231$		0			0
$232$	4.81905	+	14.2945i	0.316386	+	0.938478i
$233$	−10.6309	+	12.6694i	−0.696454	+	0.830001i	−0.992120	−	0.125290i	$-0.960014\pi$
$233$	−10.6309	+	12.6694i	−0.696454	+	0.830001i	0.295666	+	0.955291i	$0.404458\pi$
$234$		0			0
$235$	−0.0460305	+	0.0265757i	−0.00300270	+	0.00173361i
$236$	2.14917	−	2.20645i	0.139899	−	0.143628i
$237$		0			0
$238$	−2.13354	−	1.09288i	−0.138297	−	0.0708407i
$239$	−7.90785	+	13.6968i	−0.511516	+	0.885972i	0.488395	+	0.872623i	$0.337583\pi$
$239$	−7.90785	+	13.6968i	−0.511516	+	0.885972i	−0.999911	+	0.0133493i	$0.995751\pi$
$240$		0			0
$241$	−2.36770	−	13.4279i	−0.152517	−	0.864966i	−0.961021	−	0.276475i	$-0.910834\pi$
$241$	−2.36770	−	13.4279i	−0.152517	−	0.864966i	0.808504	−	0.588490i	$-0.200278\pi$
$242$	4.33244	+	4.66606i	0.278500	+	0.299945i
$243$		0			0
$244$	−8.40271	+	18.6564i	−0.537929	+	1.19436i
$245$	1.15539	+	3.17440i	0.0738149	+	0.202805i
$246$		0			0
$247$	−0.620856	+	0.199992i	−0.0395041	+	0.0127252i
$248$	−6.65812	+	17.0160i	−0.422791	+	1.08052i
$249$		0			0
$250$	−6.70104	−	2.06448i	−0.423811	−	0.130569i
$251$	2.64742	−	2.22145i	0.167104	−	0.140217i	−0.555401	−	0.831583i	$-0.687435\pi$
$251$	2.64742	−	2.22145i	0.167104	−	0.140217i	0.722505	+	0.691366i	$0.242991\pi$
$252$		0			0
$253$	−2.10922	−	11.9620i	−0.132606	−	0.752044i
$254$	11.8198	−	4.98725i	0.741643	−	0.312928i
$255$		0			0
$256$	−3.60309	−	15.5890i	−0.225193	−	0.974314i
$257$	−1.14835	+	3.15506i	−0.0716320	+	0.196807i	−0.970342	−	0.241736i	$-0.922283\pi$
$257$	−1.14835	+	3.15506i	−0.0716320	+	0.196807i	0.898710	+	0.438543i	$0.144505\pi$
$258$		0			0
$259$	0.577007	−	0.333135i	0.0358535	−	0.0207000i
$260$	0.151917	+	0.0112799i	0.00942147	+	0.000699548i
$261$		0			0
$262$	−7.62347	+	4.92746i	−0.470980	+	0.304420i
$263$	−4.37746	+	24.8258i	−0.269926	+	1.53082i	0.484707	+	0.874677i	$0.338926\pi$
$263$	−4.37746	+	24.8258i	−0.269926	+	1.53082i	−0.754633	+	0.656148i	$0.772185\pi$
$264$		0			0
$265$	4.38680			0.269479
$266$	−2.87620	−	2.35149i	−0.176351	−	0.144179i
$267$		0			0
$268$	0.748713	+	7.43084i	0.0457349	+	0.453911i
$269$	28.0326	+	4.94290i	1.70918	+	0.301374i	0.940886	−	0.338725i	$-0.109996\pi$
$269$	28.0326	+	4.94290i	1.70918	+	0.301374i	0.768293	+	0.640099i	$0.221107\pi$
$270$		0			0
$271$	13.2034	−	15.7352i	0.802051	−	0.955847i	−0.197650	−	0.980273i	$-0.563331\pi$
$271$	13.2034	−	15.7352i	0.802051	−	0.955847i	0.999702	+	0.0244251i	$0.00777552\pi$
$272$	10.6693	+	3.56842i	0.646921	+	0.216367i
$273$		0			0
$274$	22.0121	+	16.6616i	1.32980	+	1.00657i
$275$	−17.5407	−	6.38429i	−1.05774	−	0.384987i
$276$		0			0
$277$	2.31312	−	4.00644i	0.138982	−	0.240723i	−0.788130	−	0.615509i	$-0.788950\pi$
$277$	2.31312	−	4.00644i	0.138982	−	0.240723i	0.927111	+	0.374786i	$0.122284\pi$
$278$	0.318262	−	0.134287i	0.0190881	−	0.00805402i
$279$		0			0
$280$	0.415738	+	0.761558i	0.0248451	+	0.0455118i
$281$	−8.36941	−	9.97428i	−0.499277	−	0.595016i	0.456274	−	0.889839i	$-0.349184\pi$
$281$	−8.36941	−	9.97428i	−0.499277	−	0.595016i	−0.955552	+	0.294824i	$0.904739\pi$
$282$		0			0
$283$	10.6465	+	29.2511i	0.632870	+	1.73879i	0.673044	+	0.739602i	$0.264986\pi$
$283$	10.6465	+	29.2511i	0.632870	+	1.73879i	−0.0401748	+	0.999193i	$0.512791\pi$
$284$	14.2799	+	3.62568i	0.847353	+	0.215144i
$285$		0			0
$286$	0.826800	+	0.103324i	0.0488897	+	0.00610966i
$287$	4.12561	−	1.50160i	0.243527	−	0.0886367i
$288$		0			0
$289$	6.96298	−	5.84263i	0.409587	−	0.343684i
$290$	2.61222	+	2.81337i	0.153395	+	0.165207i
$291$		0			0
$292$	5.97367	+	21.1760i	0.349583	+	1.23923i
$293$	−18.7971	−	10.8525i	−1.09814	−	0.634011i	−0.162407	−	0.986724i	$-0.551926\pi$
$293$	−18.7971	−	10.8525i	−1.09814	−	0.634011i	−0.935731	+	0.352713i	$0.885259\pi$
$294$		0			0
$295$	0.268109	−	0.736624i	0.0156099	−	0.0428879i
$296$	−2.44271	+	1.95211i	−0.141980	+	0.113464i
$297$		0			0
$298$	18.8790	−	0.948697i	1.09363	−	0.0549565i
$299$	−0.353638	−	0.296738i	−0.0204514	−	0.0171608i
$300$		0			0
$301$	0.189952	−	1.07727i	0.0109487	−	0.0620929i
$302$	5.80483	+	25.3925i	0.334030	+	1.46117i
$303$		0			0
$304$	15.0017	+	8.88537i	0.860405	+	0.509611i
$305$			5.20742i			0.298176i
$306$		0			0
$307$	−17.5761	−	3.09914i	−1.00312	−	0.176877i	−0.352121	−	0.935954i	$-0.614539\pi$
$307$	−17.5761	−	3.09914i	−1.00312	−	0.176877i	−0.651001	+	0.759077i	$0.725651\pi$
$308$	2.06205	+	4.27440i	0.117496	+	0.243556i
$309$		0			0
$310$	0.233390	+	4.64443i	0.0132556	+	0.263786i
$311$	8.14008	+	14.0990i	0.461582	+	0.799483i	0.999040	−	0.0438072i	$-0.0139487\pi$
$311$	8.14008	+	14.0990i	0.461582	+	0.799483i	−0.537458	+	0.843290i	$0.680615\pi$
$312$		0			0
$313$	−18.1134	−	6.59274i	−1.02383	−	0.372644i	−0.225102	−	0.974335i	$-0.572271\pi$
$313$	−18.1134	−	6.59274i	−1.02383	−	0.372644i	−0.798729	+	0.601691i	$0.794494\pi$
$314$	−9.54807	−	4.89088i	−0.538829	−	0.276008i
$315$		0			0
$316$	−2.84436	+	0.802382i	−0.160008	+	0.0451375i
$317$	−11.2643	+	1.98620i	−0.632665	+	0.111556i	−0.480779	−	0.876842i	$-0.659646\pi$
$317$	−11.2643	+	1.98620i	−0.632665	+	0.111556i	−0.151886	+	0.988398i	$0.548535\pi$
$318$		0			0
$319$	13.4978	+	16.0861i	0.755734	+	0.900649i
$320$	−2.46536	−	3.24086i	−0.137818	−	0.181170i
$321$		0			0
$322$	0.326049	−	2.60905i	0.0181700	−	0.145397i
$323$	−10.8392	+	5.72814i	−0.603107	+	0.318722i
$324$		0			0
$325$	−0.666654	+	0.242642i	−0.0369793	+	0.0134594i
$326$	28.0734	+	8.64896i	1.55484	+	0.479021i
$327$		0			0
$328$	−18.0854	+	9.87291i	−0.998600	+	0.545140i
$329$	−0.0619767	+	0.0109282i	−0.00341689	+	0.000602489i
$330$		0			0
$331$	−1.47337	−	0.850650i	−0.0809837	−	0.0467560i	0.458961	−	0.888456i	$-0.348222\pi$
$331$	−1.47337	−	0.850650i	−0.0809837	−	0.0467560i	−0.539945	+	0.841700i	$0.681555\pi$
$332$	−13.9575	−	9.50204i	−0.766017	−	0.521492i
$333$		0			0
$334$	−14.1119	+	18.6435i	−0.772167	+	1.02013i
$335$	0.950361	+	1.64607i	0.0519238	+	0.0899346i
$336$		0			0
$337$	0.656697	+	0.551035i	0.0357726	+	0.0300168i	0.660499	−	0.750827i	$-0.270345\pi$
$337$	0.656697	+	0.551035i	0.0357726	+	0.0300168i	−0.624726	+	0.780844i	$0.714789\pi$
$338$	−15.4137	+	9.96269i	−0.838393	+	0.541899i
$339$		0			0
$340$	2.84876	−	0.287034i	0.154496	−	0.0155666i
$341$			25.4358i			1.37743i
$342$		0			0
$343$			8.21849i			0.443757i
$344$	−0.122712	+	5.13233i	−0.00661619	+	0.276717i
$345$		0			0
$346$	8.74212	+	13.5253i	0.469979	+	0.727123i
$347$	3.19586	+	2.68165i	0.171563	+	0.143958i	0.724526	−	0.689247i	$-0.242059\pi$
$347$	3.19586	+	2.68165i	0.171563	+	0.143958i	−0.552963	+	0.833206i	$0.686503\pi$
$348$		0			0
$349$	0.527648	+	0.913914i	0.0282444	+	0.0489207i	0.879802	−	0.475340i	$-0.157675\pi$
$349$	0.527648	+	0.913914i	0.0282444	+	0.0489207i	−0.851558	+	0.524261i	$0.824342\pi$
$350$	−3.22182	−	2.43869i	−0.172213	−	0.130354i
$351$		0			0
$352$	−12.5782	−	18.3811i	−0.670420	−	0.979714i
$353$	−2.38079	−	1.37455i	−0.126717	−	0.0731599i	0.435302	−	0.900285i	$-0.356642\pi$
$353$	−2.38079	−	1.37455i	−0.126717	−	0.0731599i	−0.562018	+	0.827125i	$0.689975\pi$
$354$		0			0
$355$	3.69257	−	0.651100i	0.195981	−	0.0345568i
$356$	21.0302	−	15.1416i	1.11460	−	0.802502i
$357$		0			0
$358$	−0.650617	+	2.11182i	−0.0343862	+	0.111613i
$359$	28.2348	−	10.2766i	1.49018	−	0.542380i	0.536681	−	0.843785i	$-0.319678\pi$
$359$	28.2348	−	10.2766i	1.49018	−	0.542380i	0.953496	+	0.301405i	$0.0974555\pi$
$360$		0			0
$361$	−18.2903	+	5.14457i	−0.962645	+	0.270767i
$362$	20.9130	+	2.61346i	1.09916	+	0.137360i
$363$		0			0
$364$	0.164458	+	0.0740707i	0.00861995	+	0.00388236i
$365$	3.59937	+	4.28956i	0.188400	+	0.224526i
$366$		0			0
$367$	26.2344	−	4.62584i	1.36943	−	0.241467i	0.559905	−	0.828557i	$-0.310838\pi$
$367$	26.2344	−	4.62584i	1.36943	−	0.241467i	0.809522	+	0.587090i	$0.199726\pi$
$368$	0.324555	+	12.3357i	0.0169186	+	0.643042i
$369$		0			0
$370$	−0.362809	+	0.708283i	−0.0188616	+	0.0368219i
$371$	4.88085	+	1.77649i	0.253401	+	0.0922305i
$372$		0			0
$373$	−15.8984	−	27.5368i	−0.823186	−	1.42580i	−0.903298	−	0.429014i	$-0.858861\pi$
$373$	−15.8984	−	27.5368i	−0.823186	−	1.42580i	0.0801123	−	0.996786i	$-0.474472\pi$
$374$	15.6411	−	0.785989i	0.808782	−	0.0406425i
$375$		0			0
$376$	0.279877	−	0.0943540i	0.0144335	−	0.00486594i
$377$	0.785962	+	0.138586i	0.0404791	+	0.00713756i
$378$		0			0
$379$		−	26.5376i		−	1.36314i	−0.731751	−	0.681572i	$-0.761297\pi$
$379$		−	26.5376i		−	1.36314i	0.731751	−	0.681572i	$-0.238703\pi$
$380$	4.40978	+	0.493972i	0.226217	+	0.0253402i
$381$		0			0
$382$	−20.3485	+	4.65175i	−1.04112	+	0.238004i
$383$	−1.26872	+	7.19524i	−0.0648283	+	0.367660i	0.935084	+	0.354426i	$0.115324\pi$
$383$	−1.26872	+	7.19524i	−0.0648283	+	0.367660i	−0.999912	+	0.0132338i	$0.995787\pi$
$384$		0			0
$385$	0.925231	+	0.776361i	0.0471541	+	0.0395670i
$386$	1.49672	+	29.7845i	0.0761809	+	1.51599i
$387$		0			0
$388$	−3.00977	+	3.09000i	−0.152798	+	0.156871i
$389$	7.13812	−	19.6118i	0.361917	−	0.994359i	−0.616434	−	0.787407i	$-0.711423\pi$
$389$	7.13812	−	19.6118i	0.361917	−	0.994359i	0.978351	−	0.206953i	$-0.0663546\pi$
$390$		0			0
$391$	−7.51424	−	4.33835i	−0.380012	−	0.219400i
$392$	−2.81686	−	18.5591i	−0.142273	−	0.937377i
$393$		0			0
$394$	−3.65354	+	3.39232i	−0.184063	+	0.170903i
$395$	−0.576173	+	0.483466i	−0.0289904	+	0.0243258i
$396$		0			0
$397$	22.4275	−	8.16295i	1.12560	−	0.409687i	0.288910	−	0.957356i	$-0.406707\pi$
$397$	22.4275	−	8.16295i	1.12560	−	0.409687i	0.836695	+	0.547670i	$0.184485\pi$
$398$	−4.18953	+	33.5248i	−0.210002	+	1.68045i
$399$		0			0
$400$	16.6667	+	9.04661i	0.833336	+	0.452331i
$401$	−3.28137	−	9.01548i	−0.163864	−	0.450212i	0.830400	−	0.557167i	$-0.188112\pi$
$401$	−3.28137	−	9.01548i	−0.163864	−	0.450212i	−0.994264	+	0.106956i	$0.965890\pi$
$402$		0			0
$403$	0.621394	+	0.740548i	0.0309538	+	0.0368893i
$404$	−4.34547	+	3.12870i	−0.216195	+	0.155659i
$405$		0			0
$406$	1.76711	+	4.18807i	0.0877003	+	0.207851i
$407$	−2.17640	+	3.76964i	−0.107880	+	0.186854i
$408$		0			0
$409$	20.2993	+	7.38836i	1.00374	+	0.365331i	0.791025	−	0.611784i	$-0.209548\pi$
$409$	20.2993	+	7.38836i	1.00374	+	0.365331i	0.212713	+	0.977115i	$0.431770\pi$
$410$	−3.16486	+	4.18118i	−0.156301	+	0.206494i
$411$		0			0
$412$	8.46086	+	0.628222i	0.416837	+	0.0309503i
$413$	0.596609	−	0.711011i	0.0293572	−	0.0349866i
$414$		0			0
$415$	−4.23192	−	0.746202i	−0.207737	−	0.0366296i
$416$	−0.815253	−	0.227870i	−0.0399711	−	0.0111722i
$417$		0			0
$418$	23.9543	+	3.90904i	1.17164	+	0.191197i
$419$	−29.4210			−1.43731			−0.718655	−	0.695366i	$-0.755242\pi$
$419$	−29.4210			−1.43731			−0.718655	+	0.695366i	$0.755242\pi$
$420$		0			0
$421$	−0.215245	+	1.22072i	−0.0104904	+	0.0594941i	−0.989604	−	0.143822i	$-0.954061\pi$
$421$	−0.215245	+	1.22072i	−0.0104904	+	0.0594941i	0.979113	+	0.203316i	$0.0651719\pi$
$422$	−20.5656	−	31.8179i	−1.00112	−	1.54887i
$423$		0			0
$424$	−23.8983	−	4.80558i	−1.16061	−	0.233380i
$425$	−11.5477	+	6.66705i	−0.560145	+	0.323400i
$426$		0			0
$427$	−2.10881	+	5.79389i	−0.102052	+	0.280386i
$428$	−19.1777	−	13.0559i	−0.926991	−	0.631081i
$429$		0			0
$430$	0.507923	+	1.20378i	0.0244942	+	0.0580515i
$431$	3.66653	+	20.7939i	0.176610	+	1.00161i	0.936269	+	0.351285i	$0.114255\pi$
$431$	3.66653	+	20.7939i	0.176610	+	1.00161i	−0.759658	+	0.650322i	$0.774634\pi$
$432$		0			0
$433$	−2.90615	+	2.43855i	−0.139660	+	0.117189i	−0.709942	−	0.704261i	$-0.751279\pi$
$433$	−2.90615	+	2.43855i	−0.139660	+	0.117189i	0.570281	+	0.821450i	$0.306834\pi$
$434$	−1.62114	+	5.26201i	−0.0778173	+	0.252585i
$435$		0			0
$436$	10.3693	+	2.63279i	0.496602	+	0.126088i
$437$	−9.97037	−	9.02316i	−0.476947	−	0.431636i
$438$		0			0
$439$	−0.307783	−	0.845626i	−0.0146897	−	0.0403595i	0.932131	−	0.362121i	$-0.117947\pi$
$439$	−0.307783	−	0.845626i	−0.0146897	−	0.0403595i	−0.946821	+	0.321761i	$0.895725\pi$
$440$	−4.83984	−	2.95073i	−0.230730	−	0.140671i
$441$		0			0
$442$	0.436179	−	0.404993i	0.0207469	−	0.0192636i
$443$	−2.97651	−	16.8806i	−0.141418	−	0.802022i	−0.970174	−	0.242411i	$-0.922062\pi$
$443$	−2.97651	−	16.8806i	−0.141418	−	0.802022i	0.828755	−	0.559611i	$-0.189049\pi$
$444$		0			0
$445$	3.29756	−	5.71154i	0.156319	−	0.270753i
$446$	9.63304	−	18.8058i	0.456138	−	0.890481i
$447$		0			0
$448$	−1.43059	−	4.60423i	−0.0675892	−	0.217530i
$449$	27.9430	−	16.1329i	1.31871	−	0.761357i	0.335189	−	0.942151i	$-0.391200\pi$
$449$	27.9430	−	16.1329i	1.31871	−	0.761357i	0.983521	+	0.180794i	$0.0578666\pi$
$450$		0			0
$451$	−18.4369	+	21.9723i	−0.868162	+	1.03463i
$452$	7.16204	+	14.8461i	0.336874	+	0.698301i
$453$		0			0
$454$	31.1699	−	7.12556i	1.46288	−	0.334419i
$455$	0.0459039			0.00215201
$456$		0			0
$457$	13.0552			0.610697			0.305348	−	0.952241i	$-0.401227\pi$
$457$	13.0552			0.610697			0.305348	+	0.952241i	$0.401227\pi$
$458$	−9.08244	+	2.07628i	−0.424395	+	0.0970183i
$459$		0			0
$460$	1.36456	+	2.82857i	0.0636228	+	0.131883i
$461$	−24.9412	+	29.7238i	−1.16163	+	1.38438i	−0.252637	+	0.967561i	$0.581298\pi$
$461$	−24.9412	+	29.7238i	−1.16163	+	1.38438i	−0.908992	+	0.416814i	$0.863147\pi$
$462$		0			0
$463$	8.59565	−	4.96270i	0.399474	−	0.230636i	−0.286783	−	0.957996i	$-0.592586\pi$
$463$	8.59565	−	4.96270i	0.399474	−	0.230636i	0.686257	+	0.727359i	$0.259253\pi$
$464$	−11.1489	−	18.1882i	−0.517574	−	0.844368i
$465$		0			0
$466$	10.6633	−	20.8172i	0.493969	−	0.964336i
$467$	−9.28927	+	16.0895i	−0.429856	+	0.744533i	−0.996860	−	0.0791823i	$-0.974769\pi$
$467$	−9.28927	+	16.0895i	−0.429856	+	0.744533i	0.567004	+	0.823715i	$0.308102\pi$
$468$		0			0
$469$	0.390797	+	2.21632i	0.0180453	+	0.102340i
$470$	0.0550841	−	0.0511457i	0.00254084	−	0.00235918i
$471$		0			0
$472$	−2.26755	+	3.71927i	−0.104372	+	0.171193i
$473$	2.44424	+	6.71550i	0.112386	+	0.308779i
$474$		0			0
$475$	−19.6699	+	6.33612i	−0.902515	+	0.290721i
$476$	3.28583	+	0.834278i	0.150606	+	0.0382391i
$477$		0			0
$478$	6.58540	−	21.3753i	0.301209	−	0.977685i
$479$	−13.0104	+	10.9171i	−0.594462	+	0.498813i	−0.889660	−	0.456623i	$-0.849059\pi$
$479$	−13.0104	+	10.9171i	−0.594462	+	0.498813i	0.295198	+	0.955436i	$0.404614\pi$
$480$		0			0
$481$	0.0287272	+	0.162920i	0.00130985	+	0.00742851i
$482$	7.49621	+	17.7661i	0.341443	+	0.809224i
$483$		0			0
$484$	−7.44349	−	5.06742i	−0.338341	−	0.230337i
$485$	−0.375470	+	1.03160i	−0.0170492	+	0.0468424i
$486$		0			0
$487$	27.6925	−	15.9883i	1.25487	−	0.724499i	0.282796	−	0.959180i	$-0.408738\pi$
$487$	27.6925	−	15.9883i	1.25487	−	0.724499i	0.972072	+	0.234681i	$0.0754046\pi$
$488$	5.70454	−	28.3689i	0.258232	−	1.28420i
$489$		0			0
$490$	−2.59333	−	4.01224i	−0.117155	−	0.181255i
$491$	1.63995	−	9.30060i	0.0740097	−	0.419730i	−0.925182	−	0.379524i	$-0.876088\pi$
$491$	1.63995	−	9.30060i	0.0740097	−	0.419730i	0.999191	−	0.0402056i	$-0.0128013\pi$
$492$		0			0
$493$	15.0003			0.675579
$494$	0.792911	−	0.471391i	0.0356748	−	0.0212089i
$495$		0			0
$496$	3.81635	−	25.5575i	0.171359	−	1.14757i
$497$	4.37211	+	0.770921i	0.196116	+	0.0345805i
$498$		0			0
$499$	9.55357	−	11.3855i	0.427677	−	0.509685i	−0.508574	−	0.861018i	$-0.669827\pi$
$499$	9.55357	−	11.3855i	0.427677	−	0.509685i	0.936251	+	0.351333i	$0.114272\pi$
$500$	9.88903	+	0.734264i	0.442251	+	0.0328373i
$501$		0			0
$502$	−2.94974	+	3.89697i	−0.131653	+	0.173930i
$503$	−12.6203	−	4.59340i	−0.562710	−	0.204810i	0.0449748	−	0.998988i	$-0.485679\pi$
$503$	−12.6203	−	4.59340i	−0.562710	−	0.204810i	−0.607685	+	0.794179i	$0.707901\pi$
$504$		0			0
$505$	−0.681375	+	1.18018i	−0.0303208	+	0.0525171i
$506$	6.67787	+	15.8266i	0.296868	+	0.703579i
$507$		0			0
$508$	−14.7236	+	10.6009i	−0.653254	+	0.470337i
$509$	−24.5376	−	29.2427i	−1.08761	−	1.29616i	−0.952235	−	0.305366i	$-0.901221\pi$
$509$	−24.5376	−	29.2427i	−1.08761	−	1.29616i	−0.135373	−	0.990795i	$-0.543223\pi$
$510$		0			0
$511$	2.26763	+	6.23027i	0.100314	+	0.275611i
$512$	9.88051	+	20.3562i	0.436661	+	0.899626i
$513$		0			0
$514$	0.588805	−	4.71164i	0.0259711	−	0.207821i
$515$	2.02900	−	0.738495i	0.0894083	−	0.0325420i
$516$		0			0
$517$	0.314956	−	0.264279i	0.0138517	−	0.0116230i
$518$	−0.690498	+	0.641129i	−0.0303387	+	0.0281696i
$519$		0			0
$520$	−0.212995	+	0.0323278i	−0.00934044	+	0.00141767i
$521$	13.9301	+	8.04252i	0.610287	+	0.352349i	0.773078	−	0.634311i	$-0.218716\pi$
$521$	13.9301	+	8.04252i	0.610287	+	0.352349i	−0.162791	+	0.986661i	$0.552050\pi$
$522$		0			0
$523$	−8.18978	+	22.5012i	−0.358114	+	0.983910i	0.621569	+	0.783359i	$0.286495\pi$
$523$	−8.18978	+	22.5012i	−0.358114	+	0.983910i	−0.979683	+	0.200551i	$0.935727\pi$
$524$	8.95712	−	9.19589i	0.391294	−	0.401724i
$525$		0			0
$526$	−1.78924	−	35.6057i	−0.0780145	−	1.55248i
$527$	13.9188	+	11.6793i	0.606314	+	0.508758i
$528$		0			0
$529$	−2.34127	+	13.2780i	−0.101795	+	0.577305i
$530$	−6.04785	+	1.38256i	−0.262702	+	0.0600547i
$531$		0			0
$532$	4.70638	+	2.33540i	0.204047	+	0.101252i
$533$			1.09012i			0.0472184i
$534$		0			0
$535$	−5.81471	−	1.02529i	−0.251392	−	0.0443272i
$536$	−3.37415	−	10.0085i	−0.145741	−	0.432303i
$537$		0			0
$538$	−40.2049	+	2.02036i	−1.73336	+	0.0871039i
$539$	−13.0655	−	22.6301i	−0.562772	−	0.974749i
$540$		0			0
$541$	−36.9610	−	13.4527i	−1.58908	−	0.578377i	−0.611925	−	0.790916i	$-0.709605\pi$
$541$	−36.9610	−	13.4527i	−1.58908	−	0.578377i	−0.977153	+	0.212538i	$0.931827\pi$
$542$	−13.2437	+	25.8546i	−0.568866	+	1.11055i
$543$		0			0
$544$	−15.8339	−	1.55701i	−0.678871	−	0.0667565i
$545$	2.68137	−	0.472797i	0.114857	−	0.0202524i
$546$		0			0
$547$	13.9110	+	16.5785i	0.594791	+	0.708844i	0.976519	−	0.215431i	$-0.0691155\pi$
$547$	13.9110	+	16.5785i	0.594791	+	0.708844i	−0.381729	+	0.924274i	$0.624671\pi$
$548$	−35.5981	−	16.0331i	−1.52067	−	0.684900i
$549$		0			0
$550$	26.1946	+	3.27349i	1.11694	+	0.139582i
$551$	22.7271	+	4.89096i	0.968207	+	0.208362i
$552$		0			0
$553$	−0.836849	+	0.304588i	−0.0355864	+	0.0129524i
$554$	−1.92629	+	6.25248i	−0.0818401	+	0.265642i
$555$		0			0
$556$	−0.396449	+	0.285440i	−0.0168132	+	0.0121054i
$557$	33.3571	−	5.88176i	1.41339	−	0.249218i	0.585754	−	0.810489i	$-0.300799\pi$
$557$	33.3571	−	5.88176i	1.41339	−	0.249218i	0.827632	+	0.561271i	$0.189687\pi$
$558$		0			0
$559$	0.235221	+	0.135805i	0.00994880	+	0.00574394i
$560$	−0.813173	−	0.918895i	−0.0343628	−	0.0388304i
$561$		0			0
$562$	14.6820	+	11.1133i	0.619323	+	0.468785i
$563$	−21.8196	−	37.7927i	−0.919589	−	1.59277i	−0.800041	−	0.599946i	$-0.795189\pi$
$563$	−21.8196	−	37.7927i	−0.919589	−	1.59277i	−0.119548	−	0.992828i	$-0.538144\pi$
$564$		0			0
$565$	3.21357	+	2.69650i	0.135196	+	0.113443i
$566$	−23.8967	−	36.9715i	−1.00445	−	1.55403i
$567$		0			0
$568$	−20.8296	−	0.498027i	−0.873990	−	0.0208968i
$569$			16.7773i			0.703339i	0.936124	+	0.351670i	$0.114386\pi$
$569$			16.7773i			0.703339i	−0.936124	+	0.351670i	$0.885614\pi$
$570$		0			0
$571$		−	23.4062i		−	0.979520i	−0.871857	−	0.489760i	$-0.837084\pi$
$571$		−	23.4062i		−	0.979520i	0.871857	−	0.489760i	$-0.162916\pi$
$572$	−1.17243	+	0.118131i	−0.0490218	+	0.00493931i
$573$		0			0
$574$	−5.21452	+	3.37043i	−0.217650	+	0.140679i
$575$	−11.2039	−	9.40120i	−0.467236	−	0.392057i
$576$		0			0
$577$	12.2432	+	21.2059i	0.509692	+	0.882812i	0.999937	+	0.0112277i	$0.00357397\pi$
$577$	12.2432	+	21.2059i	0.509692	+	0.882812i	−0.490245	+	0.871585i	$0.663093\pi$
$578$	−7.75811	+	10.2494i	−0.322695	+	0.426320i
$579$		0			0
$580$	−4.48801	−	3.05537i	−0.186355	−	0.126867i
$581$	−4.40635	−	2.54401i	−0.182806	−	0.105543i
$582$		0			0
$583$	−33.4180	+	5.89249i	−1.38403	+	0.244042i
$584$	−14.9095	−	27.3116i	−0.616961	−	1.13016i
$585$		0			0
$586$	29.3349	+	9.03762i	1.21181	+	0.373340i
$587$	33.5930	−	12.2269i	1.38653	−	0.504656i	0.462380	−	0.886682i	$-0.346995\pi$
$587$	33.5930	−	12.2269i	1.38653	−	0.504656i	0.924152	+	0.382025i	$0.124773\pi$
$588$		0			0
$589$	17.2805	+	22.2338i	0.712029	+	0.916127i
$590$	−0.137470	+	1.10004i	−0.00565957	+	0.0452881i
$591$		0			0
$592$	2.75241	−	3.46113i	0.113123	−	0.142252i
$593$	11.2461	+	13.4025i	0.461820	+	0.550376i	0.945820	−	0.324693i	$-0.105261\pi$
$593$	11.2461	+	13.4025i	0.461820	+	0.550376i	−0.484000	+	0.875068i	$0.660816\pi$
$594$		0			0
$595$	0.849670	−	0.149820i	0.0348331	−	0.00614201i
$596$	−25.7285	+	7.25790i	−1.05388	+	0.297295i
$597$		0			0
$598$	0.581064	+	0.297643i	0.0237615	+	0.0121715i
$599$	38.3055	+	13.9420i	1.56512	+	0.569656i	0.971902	−	0.235387i	$-0.0756356\pi$
$599$	38.3055	+	13.9420i	1.56512	+	0.569656i	0.593216	+	0.805043i	$0.297858\pi$
$600$		0			0
$601$	−10.7755	−	18.6637i	−0.439542	−	0.761309i	0.558112	−	0.829765i	$-0.311526\pi$
$601$	−10.7755	−	18.6637i	−0.439542	−	0.761309i	−0.997654	+	0.0684567i	$0.978193\pi$
$602$	0.0776409	+	1.54505i	0.00316441	+	0.0629713i
$603$		0			0
$604$	−16.0056	−	33.1778i	−0.651260	−	1.34999i
$605$	−2.25687	−	0.397948i	−0.0917550	−	0.0161789i
$606$		0			0
$607$		−	28.5236i		−	1.15774i	−0.815421	−	0.578868i	$-0.803495\pi$
$607$		−	28.5236i		−	1.15774i	0.815421	−	0.578868i	$-0.196505\pi$
$608$	−23.4824	−	7.52180i	−0.952337	−	0.305049i
$609$		0			0
$610$	−1.64119	−	7.17920i	−0.0664500	−	0.290677i
$611$	0.00271343	−	0.0153886i	0.000109774	−	0.000622558i
$612$		0			0
$613$	29.2311	+	24.5278i	1.18063	+	0.990670i	0.999975	+	0.00712462i	$0.00226786\pi$
$613$	29.2311	+	24.5278i	1.18063	+	0.990670i	0.180660	+	0.983546i	$0.442177\pi$
$614$	25.2080	−	1.26674i	1.01731	−	0.0511215i
$615$		0			0
$616$	−4.18998	−	5.24300i	−0.168819	−	0.211247i
$617$	14.2763	−	39.2237i	0.574741	−	1.57909i	−0.222180	−	0.975006i	$-0.571317\pi$
$617$	14.2763	−	39.2237i	0.574741	−	1.57909i	0.796921	−	0.604083i	$-0.206460\pi$
$618$		0			0
$619$	−19.8416	−	11.4556i	−0.797502	−	0.460438i	0.0450950	−	0.998983i	$-0.485641\pi$
$619$	−19.8416	−	11.4556i	−0.797502	−	0.460438i	−0.842597	+	0.538545i	$0.818974\pi$
$620$	−1.78552	−	6.32948i	−0.0717083	−	0.254198i
$621$		0			0
$622$	−15.6658	−	16.8722i	−0.628143	−	0.676512i
$623$	5.98190	−	5.01941i	0.239660	−	0.201098i
$624$		0			0
$625$	−19.9035	+	7.24430i	−0.796142	+	0.289772i
$626$	27.0498	+	3.38037i	1.08113	+	0.135107i
$627$		0			0
$628$	14.7049	+	3.73359i	0.586788	+	0.148986i
$629$	1.06347	+	2.92185i	0.0424032	+	0.116502i
$630$		0			0
$631$	−23.7291	−	28.2793i	−0.944641	−	1.12578i	−0.991916	−	0.126898i	$-0.959498\pi$
$631$	−23.7291	−	28.2793i	−0.944641	−	1.12578i	0.0472745	−	0.998882i	$-0.484946\pi$
$632$	3.66849	−	2.00264i	0.145925	−	0.0796609i
$633$		0			0
$634$	14.9035	−	6.28837i	0.591894	−	0.249743i
$635$	−2.30868	+	3.99874i	−0.0916170	+	0.158685i
$636$		0			0
$637$	−0.933245	−	0.339673i	−0.0369765	−	0.0134583i
$638$	−23.6785	−	17.9230i	−0.937443	−	0.709580i
$639$		0			0
$640$	4.42027	+	3.69101i	0.174726	+	0.145900i
$641$	9.75301	−	11.6232i	0.385221	−	0.459088i	−0.538234	−	0.842795i	$-0.680908\pi$
$641$	9.75301	−	11.6232i	0.385221	−	0.459088i	0.923455	+	0.383707i	$0.125353\pi$
$642$		0			0
$643$	−11.8149	−	2.08328i	−0.465933	−	0.0821565i	−0.0642468	−	0.997934i	$-0.520464\pi$
$643$	−11.8149	−	2.08328i	−0.465933	−	0.0821565i	−0.401686	+	0.915778i	$0.631576\pi$
$644$	0.372775	+	3.69973i	0.0146894	+	0.145790i
$645$		0			0
$646$	13.1381	−	11.3132i	0.516911	−	0.445112i
$647$	41.2818			1.62295			0.811477	−	0.584385i	$-0.198664\pi$
$647$	41.2818			1.62295			0.811477	+	0.584385i	$0.198664\pi$
$648$		0			0
$649$	−1.05296	+	5.97163i	−0.0413322	+	0.234407i
$650$	0.842609	−	0.544624i	0.0330498	−	0.0213619i
$651$		0			0
$652$	−41.4292	−	3.07613i	−1.62249	−	0.120471i
$653$	−8.56072	+	4.94253i	−0.335007	+	0.193416i	−0.658062	−	0.752964i	$-0.728623\pi$
$653$	−8.56072	+	4.94253i	−0.335007	+	0.193416i	0.323055	+	0.946380i	$0.395290\pi$
$654$		0			0
$655$	1.11740	−	3.07004i	0.0436606	−	0.119957i
$656$	21.8218	−	19.3112i	0.851999	−	0.753974i
$657$		0			0
$658$	0.0819999	−	0.0345990i	0.00319669	−	0.00134881i
$659$	−2.95321	−	16.7485i	−0.115041	−	0.652428i	−0.986730	−	0.162369i	$-0.948086\pi$
$659$	−2.95321	−	16.7485i	−0.115041	−	0.652428i	0.871689	−	0.490059i	$-0.163025\pi$
$660$		0			0
$661$	−29.7400	+	24.9548i	−1.15675	+	0.970631i	−0.999856	−	0.0169843i	$-0.994593\pi$
$661$	−29.7400	+	24.9548i	−1.15675	+	0.970631i	−0.156897	+	0.987615i	$0.550149\pi$
$662$	2.29935	+	0.708394i	0.0893669	+	0.0275325i
$663$		0			0
$664$	22.2372	+	8.70107i	0.862970	+	0.337667i
$665$	1.33619	+	0.0500479i	0.0518154	+	0.00194077i
$666$		0			0
$667$	5.62734	+	15.4610i	0.217891	+	0.598652i
$668$	13.5795	−	30.1504i	0.525407	−	1.16655i
$669$		0			0
$670$	−1.82900	−	1.96984i	−0.0706604	−	0.0761014i
$671$	−6.99477	−	39.6693i	−0.270030	−	1.53142i
$672$		0			0
$673$	−20.9678	+	36.3172i	−0.808248	+	1.39993i	0.105828	+	0.994384i	$0.466251\pi$
$673$	−20.9678	+	36.3172i	−0.808248	+	1.39993i	−0.914076	+	0.405542i	$0.867083\pi$
$674$	−1.07902	−	0.552715i	−0.0415624	−	0.0212898i
$675$		0			0
$676$	18.1101	−	18.5929i	0.696544	−	0.715111i
$677$	16.8113	−	9.70600i	0.646110	−	0.373032i	−0.140854	−	0.990030i	$-0.544985\pi$
$677$	16.8113	−	9.70600i	0.646110	−	0.373032i	0.786964	+	0.616998i	$0.211651\pi$
$678$		0			0
$679$	−0.835514	+	0.995727i	−0.0320641	+	0.0382125i
$680$	−3.83697	+	1.29355i	−0.147141	+	0.0496052i
$681$		0			0
$682$	−8.01648	−	35.0671i	−0.306967	−	1.34279i
$683$	−9.83602			−0.376365			−0.188182	−	0.982134i	$-0.560260\pi$
$683$	−9.83602			−0.376365			−0.188182	+	0.982134i	$0.560260\pi$
$684$		0			0
$685$	−9.93620			−0.379643
$686$	−2.59018	−	11.3304i	−0.0988934	−	0.432597i
$687$		0			0
$688$	−1.44835	−	7.11436i	−0.0552180	−	0.271232i
$689$	−0.828990	+	0.987952i	−0.0315820	+	0.0376380i
$690$		0			0
$691$	20.4657	−	11.8159i	0.778553	−	0.449498i	−0.0573644	−	0.998353i	$-0.518270\pi$
$691$	20.4657	−	11.8159i	0.778553	−	0.449498i	0.835917	+	0.548856i	$0.184936\pi$
$692$	−16.3150	−	15.8914i	−0.620203	−	0.604100i
$693$		0			0
$694$	−5.25113	−	2.68982i	−0.199330	−	0.102104i
$695$	−0.0621637	+	0.107671i	−0.00235800	+	0.00408418i
$696$		0			0
$697$	3.55791	+	20.1779i	0.134765	+	0.764292i
$698$	−1.01547	−	1.09367i	−0.0384363	−	0.0413960i
$699$		0			0
$700$	5.21034	+	2.34670i	0.196932	+	0.0886968i
$701$	9.75052	+	26.7893i	0.368272	+	1.01182i	0.976018	+	0.217688i	$0.0698515\pi$
$701$	9.75052	+	26.7893i	0.368272	+	1.01182i	−0.607746	+	0.794131i	$0.707926\pi$
$702$		0			0
$703$	0.658579	+	4.77368i	0.0248388	+	0.180043i
$704$	23.1340	+	21.3768i	0.871895	+	0.805670i
$705$		0			0
$706$	3.71548	+	1.14468i	0.139834	+	0.0430806i
$707$	−1.23604	+	1.03716i	−0.0464860	+	0.0390064i
$708$		0			0
$709$	−0.552270	−	3.13208i	−0.0207409	−	0.117628i	0.972680	−	0.232152i	$-0.0745767\pi$
$709$	−0.552270	−	3.13208i	−0.0207409	−	0.117628i	−0.993420	+	0.114524i	$0.963466\pi$
$710$	−4.88555	+	2.06140i	−0.183351	+	0.0773631i
$711$		0			0
$712$	−24.2212	+	27.5029i	−0.907728	+	1.03071i
$713$	−6.81636	+	18.7278i	−0.255275	+	0.701361i
$714$		0			0
$715$	−0.259716	+	0.149947i	−0.00971283	+	0.00560770i
$716$	0.231402	−	3.11651i	0.00864789	−	0.116469i
$717$		0			0
$718$	−35.6871	+	23.0665i	−1.33183	+	0.860834i
$719$	1.45202	−	8.23479i	0.0541511	−	0.307106i	−0.945687	−	0.325077i	$-0.894610\pi$
$719$	1.45202	−	8.23479i	0.0541511	−	0.307106i	0.999839	+	0.0179714i	$0.00572078\pi$
$720$		0			0
$721$	2.55657			0.0952117
$722$	23.5944	−	12.8570i	0.878094	−	0.478488i
$723$		0			0
$724$	−29.6554	+	2.98800i	−1.10213	+	0.111048i
$725$	24.9007	+	4.39067i	0.924790	+	0.163065i
$726$		0			0
$727$	17.9937	−	21.4440i	0.667348	−	0.795314i	−0.321073	−	0.947055i	$-0.604043\pi$
$727$	17.9937	−	21.4440i	0.667348	−	0.795314i	0.988420	+	0.151740i	$0.0484878\pi$
$728$	−0.250074	−	0.0502861i	−0.00926838	−	0.00186373i
$729$		0			0
$730$	−6.31418	−	4.77940i	−0.233698	−	0.176894i
$731$	4.79713	+	1.74601i	0.177428	+	0.0645786i
$732$		0			0
$733$	−18.3956	+	31.8622i	−0.679459	+	1.17686i	0.295686	+	0.955285i	$0.404452\pi$
$733$	−18.3956	+	31.8622i	−0.679459	+	1.17686i	−0.975144	+	0.221571i	$0.928881\pi$
$734$	−34.7102	+	14.6456i	−1.28118	+	0.540578i
$735$		0			0
$736$	−4.33522	−	16.9043i	−0.159798	−	0.623100i
$737$	−9.45077	−	11.2630i	−0.348124	−	0.414878i
$738$		0			0
$739$	14.7695	+	40.5790i	0.543306	+	1.49272i	0.842589	+	0.538557i	$0.181030\pi$
$739$	14.7695	+	40.5790i	0.543306	+	1.49272i	−0.299283	+	0.954165i	$0.596747\pi$
$740$	0.276960	−	1.09082i	0.0101813	−	0.0400993i
$741$		0			0
$742$	−7.28887	−	0.910876i	−0.267583	−	0.0334393i
$743$	11.4943	−	4.18357i	0.421684	−	0.153480i	−0.122458	−	0.992474i	$-0.539078\pi$
$743$	11.4943	−	4.18357i	0.421684	−	0.153480i	0.544142	+	0.838993i	$0.316855\pi$
$744$		0			0
$745$	−5.21174	+	4.37317i	−0.190943	+	0.160220i
$746$	30.5969	+	32.9529i	1.12023	+	1.20649i
$747$		0			0
$748$	−21.3159	+	6.01313i	−0.779385	+	0.219862i
$749$	−6.05438	−	3.49550i	−0.221222	−	0.127723i
$750$		0			0
$751$	−11.3740	+	31.2499i	−0.415045	+	1.14033i	0.539429	+	0.842031i	$0.318640\pi$
$751$	−11.3740	+	31.2499i	−0.415045	+	1.14033i	−0.954474	+	0.298295i	$0.903582\pi$
$752$	−0.356115	+	0.218288i	−0.0129862	+	0.00796015i
$753$		0			0
$754$	−1.12724	+	0.0566457i	−0.0410518	+	0.00206291i
$755$	−7.18164	−	6.02611i	−0.261366	−	0.219313i
$756$		0			0
$757$	−2.51918	+	14.2870i	−0.0915613	+	0.519270i	0.904186	+	0.427140i	$0.140479\pi$
$757$	−2.51918	+	14.2870i	−0.0915613	+	0.519270i	−0.995747	+	0.0921302i	$0.970632\pi$
$758$	8.36371	+	36.5860i	0.303784	+	1.32886i
$759$		0			0
$760$	−6.23521	+	0.708792i	−0.226175	+	0.0257106i
$761$			34.6326i			1.25543i	0.778443	+	0.627715i	$0.216010\pi$
$761$			34.6326i			1.25543i	−0.778443	+	0.627715i	$0.783990\pi$
$762$		0			0
$763$	3.17482	+	0.559806i	0.114936	+	0.0202663i
$764$	26.5874	−	12.8263i	0.961897	−	0.464038i
$765$		0			0
$766$	−0.518574	−	10.3196i	−0.0187368	−	0.372861i
$767$	0.115230	+	0.199584i	0.00416070	+	0.00720655i
$768$		0			0
$769$	3.74370	+	1.36260i	0.135001	+	0.0491365i	0.408637	−	0.912697i	$-0.366004\pi$
$769$	3.74370	+	1.36260i	0.135001	+	0.0491365i	−0.273636	+	0.961833i	$0.588226\pi$
$770$	−1.52025	−	0.778728i	−0.0547860	−	0.0280634i
$771$		0			0
$772$	−11.4505	−	40.5907i	−0.412112	−	1.46089i
$773$	36.7176	−	6.47430i	1.32064	−	0.232864i	0.531489	−	0.847065i	$-0.321633\pi$
$773$	36.7176	−	6.47430i	1.32064	−	0.232864i	0.789150	+	0.614201i	$0.210521\pi$
$774$		0			0
$775$	19.6869	+	23.4619i	0.707175	+	0.842778i
$776$	3.17556	−	5.20860i	0.113996	−	0.186978i
$777$		0			0
$778$	−3.66001	+	29.2875i	−0.131218	+	1.05001i
$779$	−1.18853	+	31.7318i	−0.0425836	+	1.13691i
$780$		0			0
$781$	−27.2549	+	9.91996i	−0.975256	+	0.354964i
$782$	11.7268	+	3.61284i	0.419349	+	0.129195i
$783$		0			0
$784$	9.73263	+	24.6987i	0.347594	+	0.882097i
$785$	3.80247	−	0.670479i	0.135716	−	0.0239304i
$786$		0			0
$787$	−25.0320	−	14.4522i	−0.892295	−	0.515167i	−0.0176027	−	0.999845i	$-0.505603\pi$
$787$	−25.0320	−	14.4522i	−0.892295	−	0.515167i	−0.874693	+	0.484678i	$0.838937\pi$
$788$	3.96781	−	5.82829i	0.141347	−	0.207624i
$789$		0			0
$790$	0.641968	−	0.848119i	0.0228402	−	0.0301747i
$791$	2.48351	+	4.30156i	0.0883034	+	0.152946i
$792$		0			0
$793$	−1.17276	−	0.984066i	−0.0416461	−	0.0349452i
$794$	−28.3470	+	18.3222i	−1.00600	+	0.650230i
$795$		0			0
$796$	−4.78994	−	47.5393i	−0.169775	−	1.68499i
$797$			14.3302i			0.507601i	0.967257	+	0.253801i	$0.0816807\pi$
$797$			14.3302i			0.507601i	−0.967257	+	0.253801i	$0.918319\pi$
$798$		0			0
$799$		−	0.293696i		−	0.0103902i
$800$	−25.8287	−	7.21933i	−0.913184	−	0.255242i
$801$		0			0
$802$	7.36521	+	11.3950i	0.260075	+	0.402372i
$803$	−33.1813	−	27.8425i	−1.17094	−	0.982539i
$804$		0			0
$805$	0.473174	+	0.819561i	0.0166772	+	0.0288857i
$806$	−1.09008	−	0.825114i	−0.0383964	−	0.0290634i
$807$		0			0
$808$	5.00482	−	5.68292i	0.176069	−	0.199924i
$809$	20.6115	+	11.9000i	0.724661	+	0.418383i	0.816466	−	0.577394i	$-0.195930\pi$
$809$	20.6115	+	11.9000i	0.724661	+	0.418383i	−0.0918048	+	0.995777i	$0.529264\pi$
$810$		0			0
$811$	−17.4260	+	3.07268i	−0.611911	+	0.107896i	−0.471011	−	0.882127i	$-0.656111\pi$
$811$	−17.4260	+	3.07268i	−0.611911	+	0.107896i	−0.140900	+	0.990024i	$0.545000\pi$
$812$	−3.75616	−	5.21695i	−0.131815	−	0.183079i
$813$		0			0
$814$	1.81244	−	5.88294i	0.0635259	−	0.206197i
$815$	−9.93513	+	3.61609i	−0.348012	+	0.126666i
$816$		0			0
$817$	6.69888	+	4.20954i	0.234364	+	0.147273i
$818$	−30.3142	−	3.78831i	−1.05991	−	0.132455i
$819$		0			0
$820$	3.04547	−	6.76183i	0.106353	−	0.236133i
$821$	10.0124	+	11.9324i	0.349437	+	0.416443i	0.911921	−	0.410365i	$-0.134599\pi$
$821$	10.0124	+	11.9324i	0.349437	+	0.416443i	−0.562484	+	0.826808i	$0.690154\pi$
$822$		0			0
$823$	47.0431	−	8.29496i	1.63982	−	0.289144i	0.723719	−	0.690095i	$-0.242431\pi$
$823$	47.0431	−	8.29496i	1.63982	−	0.289144i	0.916099	+	0.400951i	$0.131320\pi$
$824$	−11.8625	+	1.80047i	−0.413251	+	0.0627222i
$825$		0			0
$826$	−0.598429	+	1.16826i	−0.0208220	+	0.0406491i
$827$	−0.387752	−	0.141130i	−0.0134835	−	0.00490758i	0.335270	−	0.942122i	$-0.391173\pi$
$827$	−0.387752	−	0.141130i	−0.0134835	−	0.00490758i	−0.348753	+	0.937215i	$0.613395\pi$
$828$		0			0
$829$	17.3210	+	30.0008i	0.601583	+	1.04197i	0.992582	+	0.121580i	$0.0387962\pi$
$829$	17.3210	+	30.0008i	0.601583	+	1.04197i	−0.390999	+	0.920391i	$0.627870\pi$
$830$	6.06951	−	0.305002i	0.210676	−	0.0105868i
$831$		0			0
$832$	1.19576	+	0.0572132i	0.0414556	+	0.00198351i
$833$	−18.3828	−	3.24138i	−0.636925	−	0.112307i
$834$		0			0
$835$		−	8.41564i		−	0.291235i
$836$	−34.2565	+	2.16035i	−1.18479	+	0.0747174i
$837$		0			0
$838$	40.5612	−	9.27246i	1.40116	−	0.320312i
$839$	1.72021	−	9.75582i	0.0593884	−	0.336808i	−0.940608	−	0.339495i	$-0.889744\pi$
$839$	1.72021	−	9.75582i	0.0593884	−	0.336808i	0.999996	+	0.00268623i	$0.000855056\pi$
$840$		0			0
$841$	0.425635	+	0.357150i	0.0146771	+	0.0123155i
$842$	−0.0879792	−	1.75078i	−0.00303196	−	0.0603358i
$843$		0			0
$844$	38.3807	+	37.3841i	1.32112	+	1.28681i
$845$	2.25925	−	6.20723i	0.0777205	−	0.213535i
$846$		0			0
$847$	−2.34990	−	1.35671i	−0.0807434	−	0.0466172i
$848$	34.4619	−	0.906704i	1.18343	−	0.0311364i
$849$		0			0
$850$	13.8190	−	12.8309i	0.473987	−	0.440098i
$851$	−2.61263	+	2.19226i	−0.0895598	+	0.0751496i
$852$		0			0
$853$	24.9712	−	9.08876i	0.854996	−	0.311193i	0.122920	−	0.992417i	$-0.460774\pi$
$853$	24.9712	−	9.08876i	0.854996	−	0.311193i	0.732076	+	0.681223i	$0.238552\pi$
$854$	1.08127	−	8.65236i	0.0370003	−	0.296078i
$855$		0			0
$856$	30.5541	+	11.9554i	1.04432	+	0.408626i
$857$	−5.57985	−	15.3305i	−0.190604	−	0.523680i	0.807173	−	0.590314i	$-0.200996\pi$
$857$	−5.57985	−	15.3305i	−0.190604	−	0.523680i	−0.997777	+	0.0666341i	$0.978774\pi$
$858$		0			0
$859$	−4.90498	−	5.84552i	−0.167356	−	0.199447i	0.675848	−	0.737041i	$-0.263778\pi$
$859$	−4.90498	−	5.84552i	−0.167356	−	0.199447i	−0.843204	+	0.537594i	$0.819333\pi$
$860$	−1.07964	−	1.49951i	−0.0368153	−	0.0511330i
$861$		0			0
$862$	−11.6084	−	27.5119i	−0.395382	−	0.937060i
$863$	−14.0956	+	24.4143i	−0.479819	+	0.831072i	−0.999732	−	0.0231479i	$-0.992631\pi$
$863$	−14.0956	+	24.4143i	−0.479819	+	0.831072i	0.519913	+	0.854219i	$0.325964\pi$
$864$		0			0
$865$	−5.44675	−	1.98246i	−0.185195	−	0.0674055i
$866$	3.23801	−	4.27781i	0.110032	−	0.145366i
$867$		0			0
$868$	0.576583	−	7.76539i	0.0195705	−	0.263575i
$869$	3.73979	−	4.45691i	0.126864	−	0.151190i
$870$		0			0
$871$	−0.550306	−	0.0970339i	−0.0186464	−	0.00328787i
$872$	−15.1254	−	0.361644i	−0.512212	−	0.0122468i
$873$		0			0
$874$	16.5894	+	9.29746i	0.561145	+	0.314491i
$875$	2.98812			0.101017
$876$		0			0
$877$	7.50534	−	42.5649i	0.253437	−	1.43731i	−0.546615	−	0.837384i	$-0.684084\pi$
$877$	7.50534	−	42.5649i	0.253437	−	1.43731i	0.800052	−	0.599930i	$-0.204805\pi$
$878$	0.690836	+	1.06882i	0.0233146	+	0.0360709i
$879$		0			0
$880$	7.60240	+	2.54268i	0.256277	+	0.0857136i
$881$	−1.39863	+	0.807498i	−0.0471210	+	0.0272053i	−0.523375	−	0.852102i	$-0.675327\pi$
$881$	−1.39863	+	0.807498i	−0.0471210	+	0.0272053i	0.476254	+	0.879308i	$0.341994\pi$
$882$		0			0
$883$	−12.9922	+	35.6958i	−0.437223	+	1.20126i	0.504069	+	0.863664i	$0.331836\pi$
$883$	−12.9922	+	35.6958i	−0.437223	+	1.20126i	−0.941291	+	0.337596i	$0.890386\pi$
$884$	−0.473698	+	0.695812i	−0.0159322	+	0.0234027i
$885$		0			0
$886$	9.42373	+	22.3343i	0.316597	+	0.750337i
$887$	10.0039	+	56.7347i	0.335897	+	1.90497i	0.418194	+	0.908358i	$0.362663\pi$
$887$	10.0039	+	56.7347i	0.335897	+	1.90497i	−0.0822972	+	0.996608i	$0.526226\pi$
$888$		0			0
$889$	−4.18802	+	3.51417i	−0.140462	+	0.117861i
$890$	−2.74610	+	8.91348i	−0.0920495	+	0.298781i
$891$		0			0
$892$	−7.35365	+	28.9626i	−0.246218	+	0.969740i
$893$	0.0957620	−	0.444983i	0.00320455	−	0.0148908i
$894$		0			0
$895$	−0.272020	−	0.747369i	−0.00909263	−	0.0249818i
$896$	3.42338	+	5.89674i	0.114367	+	0.196996i
$897$		0			0
$898$	−33.4390	+	31.0482i	−1.11587	+	1.03609i
$899$	−5.98296	−	33.9310i	−0.199543	−	1.13166i
$900$		0			0
$901$	−12.1200	+	20.9924i	−0.403775	+	0.699358i
$902$	18.4932	−	36.1027i	0.615755	−	1.20209i
$903$		0			0
$904$	−14.5529	−	18.2103i	−0.484022	−	0.605666i
$905$	−6.56924	+	3.79275i	−0.218369	+	0.126075i
$906$		0			0
$907$	29.3382	−	34.9640i	0.974160	−	1.16096i	−0.0127874	−	0.999918i	$-0.504070\pi$
$907$	29.3382	−	34.9640i	0.974160	−	1.16096i	0.986948	−	0.161041i	$-0.0514851\pi$
$908$	−40.7266	+	19.6473i	−1.35156	+	0.652018i
$909$		0			0
$910$	−0.0632853	+	0.0144673i	−0.00209789	+	0.000479586i
$911$	−3.64895			−0.120895			−0.0604476	−	0.998171i	$-0.519253\pi$
$911$	−3.64895			−0.120895			−0.0604476	+	0.998171i	$0.519253\pi$
$912$		0			0
$913$	33.2405			1.10010
$914$	−17.9985	+	4.11454i	−0.595339	+	0.136097i
$915$		0			0
$916$	11.8671	−	5.72493i	0.392101	−	0.189157i
$917$	2.48650	−	2.96330i	0.0821115	−	0.0978567i
$918$		0			0
$919$	31.6853	−	18.2935i	1.04520	−	0.603448i	0.123900	−	0.992295i	$-0.460460\pi$
$919$	31.6853	−	18.2935i	1.04520	−	0.603448i	0.921303	+	0.388846i	$0.127126\pi$
$920$	−2.77271	−	3.46954i	−0.0914136	−	0.114388i
$921$		0			0
$922$	25.0173	−	48.8393i	0.823901	−	1.60844i
$923$	−0.551165	+	0.954645i	−0.0181418	+	0.0314225i
$924$		0			0
$925$	0.910130	+	5.16161i	0.0299249	+	0.169713i
$926$	−10.2863	+	9.55086i	−0.338029	+	0.313861i
$927$		0			0
$928$	21.1027	+	21.5615i	0.692729	+	0.707790i
$929$	4.33264	+	11.9038i	0.142149	+	0.390552i	0.990253	−	0.139278i	$-0.0444781\pi$
$929$	4.33264	+	11.9038i	0.142149	+	0.390552i	−0.848104	+	0.529830i	$0.822256\pi$
$930$		0			0
$931$	−26.7951	−	10.9049i	−0.878173	−	0.357393i
$932$	−8.14014	+	32.0602i	−0.266639	+	1.05017i
$933$		0			0
$934$	7.73580	−	25.1094i	0.253123	−	0.821605i
$935$	−4.31789	+	3.62314i	−0.141210	+	0.118489i
$936$		0			0
$937$	−6.34510	−	35.9848i	−0.207285	−	1.17557i	−0.893803	−	0.448460i	$-0.851973\pi$
$937$	−6.34510	−	35.9848i	−0.207285	−	1.17557i	0.686517	−	0.727113i	$-0.259139\pi$
$938$	−1.23728	−	2.93236i	−0.0403985	−	0.0957450i
$939$		0			0
$940$	−0.0598223	+	0.0878725i	−0.00195119	+	0.00286609i
$941$	11.5639	−	31.7717i	0.376974	−	1.03573i	−0.595630	−	0.803259i	$-0.703098\pi$
$941$	11.5639	−	31.7717i	0.376974	−	1.03573i	0.972604	−	0.232468i	$-0.0746801\pi$
$942$		0			0
$943$	−19.4629	+	11.2369i	−0.633798	+	0.365923i
$944$	1.95397	−	5.84221i	0.0635963	−	0.190148i
$945$		0			0
$946$	−5.48624	−	8.48798i	−0.178373	−	0.275968i
$947$	−8.87358	+	50.3246i	−0.288352	+	1.63533i	0.404706	+	0.914447i	$0.367374\pi$
$947$	−8.87358	+	50.3246i	−0.288352	+	1.63533i	−0.693058	+	0.720881i	$0.743737\pi$
$948$		0			0
$949$	−1.64624			−0.0534392
$950$	25.1209	−	14.9345i	0.815030	−	0.484540i
$951$		0			0
$952$	−4.79294	−	0.114597i	−0.155340	−	0.00371412i
$953$	−3.57695	−	0.630712i	−0.115869	−	0.0204308i	0.115413	−	0.993318i	$-0.463181\pi$
$953$	−3.57695	−	0.630712i	−0.115869	−	0.0204308i	−0.231282	+	0.972887i	$0.574292\pi$
$954$		0			0
$955$	4.82908	−	5.75507i	0.156265	−	0.186230i
$956$	−2.34219	+	31.5446i	−0.0757520	+	1.02022i
$957$		0			0
$958$	14.4962	−	19.1512i	0.468349	−	0.618748i
$959$	−11.0552	−	4.02378i	−0.356993	−	0.129935i
$960$		0			0
$961$	5.36724	−	9.29633i	0.173137	−	0.299882i
$962$	−0.0909513	−	0.215555i	−0.00293239	−	0.00694979i
$963$		0			0
$964$	−15.9339	−	22.1307i	−0.513196	−	0.712781i
$965$	−6.89935	−	8.22233i	−0.222098	−	0.264686i
$966$		0			0
$967$	1.51615	+	4.16559i	0.0487561	+	0.133956i	0.961681	−	0.274172i	$-0.0884038\pi$
$967$	1.51615	+	4.16559i	0.0487561	+	0.133956i	−0.912925	+	0.408128i	$0.866182\pi$
$968$	11.8590	+	4.64026i	0.381164	+	0.149144i
$969$		0			0
$970$	0.192519	−	1.54054i	0.00618141	−	0.0494639i
$971$	48.7113	−	17.7295i	1.56322	−	0.568966i	0.591750	−	0.806122i	$-0.298437\pi$
$971$	48.7113	−	17.7295i	1.56322	−	0.568966i	0.971472	+	0.237156i	$0.0762151\pi$
$972$		0			0
$973$	−0.112767	+	0.0946229i	−0.00361515	+	0.00303347i
$974$	−33.1393	+	30.7699i	−1.06185	+	0.985933i
$975$		0			0
$976$	1.07632	+	40.9086i	0.0344521	+	1.30945i
$977$	−10.1720	−	5.87280i	−0.325431	−	0.187888i	0.328380	−	0.944546i	$-0.393497\pi$
$977$	−10.1720	−	5.87280i	−0.325431	−	0.187888i	−0.653811	+	0.756658i	$0.726831\pi$
$978$		0			0
$979$	−17.4484	+	47.9391i	−0.557653	+	1.53214i
$980$	4.83981	+	4.71414i	0.154602	+	0.150588i
$981$		0			0
$982$	0.670310	+	13.3391i	0.0213905	+	0.425668i
$983$	−12.7167	−	10.6706i	−0.405601	−	0.340340i	0.417053	−	0.908882i	$-0.363063\pi$
$983$	−12.7167	−	10.6706i	−0.405601	−	0.340340i	−0.822654	+	0.568543i	$0.807507\pi$
$984$		0			0
$985$	0.311595	−	1.76714i	0.00992824	−	0.0563059i
$986$	−20.6801	+	4.72756i	−0.658589	+	0.150556i
$987$		0			0
$988$	−0.944580	+	0.899779i	−0.0300511	+	0.0286258i
$989$			5.59947i			0.178053i
$990$		0			0
$991$	33.2091	+	5.85567i	1.05492	+	0.186011i	0.674103	−	0.738638i	$-0.264530\pi$
$991$	33.2091	+	5.85567i	1.05492	+	0.186011i	0.380820	+	0.924649i	$0.375642\pi$
$992$	2.79342	+	36.4376i	0.0886913	+	1.15690i
$993$		0			0
$994$	−6.27057	+	0.315106i	−0.198890	+	0.00999454i
$995$	−6.08000	−	10.5309i	−0.192749	−	0.333851i
$996$		0			0
$997$	18.3130	+	6.66540i	0.579980	+	0.211095i	0.615317	−	0.788280i	$-0.289028\pi$
$997$	18.3130	+	6.66540i	0.579980	+	0.211095i	−0.0353368	+	0.999375i	$0.511250\pi$
$998$	−9.58271	+	18.7076i	−0.303335	+	0.592177i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.2.ce.a.575.3	yes	240
3.2	odd	2	inner	684.2.ce.a.575.38	yes	240
4.3	odd	2	inner	684.2.ce.a.575.34	yes	240
12.11	even	2	inner	684.2.ce.a.575.7	yes	240
19.4	even	9	inner	684.2.ce.a.251.7	yes	240
57.23	odd	18	inner	684.2.ce.a.251.34	yes	240
76.23	odd	18	inner	684.2.ce.a.251.38	yes	240
228.23	even	18	inner	684.2.ce.a.251.3	✓	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
684.2.ce.a.251.3	✓	240	228.23	even	18	inner
684.2.ce.a.251.7	yes	240	19.4	even	9	inner
684.2.ce.a.251.34	yes	240	57.23	odd	18	inner
684.2.ce.a.251.38	yes	240	76.23	odd	18	inner
684.2.ce.a.575.3	yes	240	1.1	even	1	trivial
684.2.ce.a.575.7	yes	240	12.11	even	2	inner
684.2.ce.a.575.34	yes	240	4.3	odd	2	inner
684.2.ce.a.575.38	yes	240	3.2	odd	2	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:	\( N \)	\(=\)	\( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	684.ce (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.37865 + 0.315165i) q^{2} +(1.80134 - 0.869002i) q^{4} +(0.327179 - 0.389916i) q^{5} +(0.521928 - 0.301335i) q^{7} +(-2.20954 + 1.76577i) q^{8} +O(q^{10})\)	\(q+(-1.37865 + 0.315165i) q^{2} +(1.80134 - 0.869002i) q^{4} +(0.327179 - 0.389916i) q^{5} +(0.521928 - 0.301335i) q^{7} +(-2.20954 + 1.76577i) q^{8} +(-0.328177 + 0.640673i) q^{10} +(-1.96865 + 3.40980i) q^{11} +(0.0259850 + 0.147368i) q^{13} +(-0.624585 + 0.579929i) q^{14} +(2.48967 - 3.13074i) q^{16} +(0.961951 + 2.64294i) q^{17} +(0.595713 + 4.31800i) q^{19} +(0.250523 - 0.986692i) q^{20} +(1.63943 - 5.32137i) q^{22} +(-2.36324 + 1.98299i) q^{23} +(0.823252 + 4.66889i) q^{25} +(-0.0822693 - 0.194979i) q^{26} +(0.678310 - 0.996365i) q^{28} +(1.82411 - 5.01169i) q^{29} +(5.59472 - 3.23011i) q^{31} +(-2.44568 + 5.10085i) q^{32} +(-2.15915 - 3.34051i) q^{34} +(0.0532682 - 0.302099i) q^{35} +1.10553 q^{37} +(-2.18216 - 5.76526i) q^{38} +(-0.0344121 + 1.43926i) q^{40} +(7.17421 + 1.26501i) q^{41} +(1.16671 - 1.39043i) q^{43} +(-0.583087 + 7.85298i) q^{44} +(2.63310 - 3.47866i) q^{46} +(-0.0981258 - 0.0357149i) q^{47} +(-3.31839 + 5.74763i) q^{49} +(-2.60645 - 6.17730i) q^{50} +(0.174871 + 0.242879i) q^{52} +(5.53984 + 6.60213i) q^{53} +(0.685438 + 1.88322i) q^{55} +(-0.621132 + 1.58742i) q^{56} +(-0.935293 + 7.48425i) q^{58} +(1.44720 - 0.526737i) q^{59} +(-7.83716 + 6.57616i) q^{61} +(-6.69513 + 6.21644i) q^{62} +(1.76412 - 7.80307i) q^{64} +(0.0659630 + 0.0380837i) q^{65} +(-1.27718 + 3.50903i) q^{67} +(4.02952 + 3.92490i) q^{68} +(0.0217728 + 0.433276i) q^{70} +(5.64305 + 4.73508i) q^{71} +(-1.91034 + 10.8341i) q^{73} +(-1.52414 + 0.348424i) q^{74} +(4.82544 + 7.26052i) q^{76} +2.37290i q^{77} +(-1.45523 - 0.256597i) q^{79} +(-0.406161 - 1.99508i) q^{80} +(-10.2894 + 0.517058i) q^{82} +(-4.22123 - 7.31138i) q^{83} +(1.34526 + 0.489633i) q^{85} +(-1.17026 + 2.28461i) q^{86} +(-1.67111 - 11.0103i) q^{88} +(12.7602 - 2.24996i) q^{89} +(0.0579695 + 0.0690853i) q^{91} +(-2.53377 + 5.62570i) q^{92} +(0.146537 + 0.0183125i) q^{94} +(1.87856 + 1.18048i) q^{95} +(-2.02671 + 0.737663i) q^{97} +(2.76345 - 8.96980i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 12 q^{4}+O(q^{10}) \) 240 * q + 12 * q^4	\( 240 q + 12 q^{4} + 12 q^{10} + 24 q^{13} - 12 q^{16} - 12 q^{34} + 120 q^{49} - 48 q^{52} - 144 q^{58} + 48 q^{61} - 12 q^{64} - 72 q^{70} + 72 q^{73} - 144 q^{76} - 72 q^{82} + 240 q^{85} - 48 q^{88} - 48 q^{94}+O(q^{100}) \) 240 * q + 12 * q^4 + 12 * q^10 + 24 * q^13 - 12 * q^16 - 12 * q^34 + 120 * q^49 - 48 * q^52 - 144 * q^58 + 48 * q^61 - 12 * q^64 - 72 * q^70 + 72 * q^73 - 144 * q^76 - 72 * q^82 + 240 * q^85 - 48 * q^88 - 48 * q^94

Introduction

L-functions

Modular forms

Varieties

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Database

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