LMFDB - Embedded newform 475.2.j.d.349.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [475,2,Mod(49,475)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(475, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4]))

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

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

chi := DirichletCharacter("475.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 475 = 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	475.j (of order $6$, degree $2$, not 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:	$3.79289409601$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			349.7
Character	$\chi$	$=$	475.349
Dual form			475.2.j.d.49.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.269427 - 0.155554i) q^{2} +(-0.891863 + 0.514917i) q^{3} +(-0.951606 + 1.64823i) q^{4} +(-0.160195 + 0.277466i) q^{6} -3.28038i q^{7} +1.21432i q^{8} +(-0.969720 + 1.67960i) q^{9} +O(q^{10})$	\(q+(0.269427 - 0.155554i) q^{2} +(-0.891863 + 0.514917i) q^{3} +(-0.951606 + 1.64823i) q^{4} +(-0.160195 + 0.277466i) q^{6} -3.28038i q^{7} +1.21432i q^{8} +(-0.969720 + 1.67960i) q^{9} -5.16792 q^{11} -1.95999i q^{12} +(3.06115 + 1.76735i) q^{13} +(-0.510276 - 0.883825i) q^{14} +(-1.71432 - 2.96929i) q^{16} +(-0.874064 + 0.504641i) q^{17} +0.603375i q^{18} +(-2.42346 - 3.62310i) q^{19} +(1.68913 + 2.92565i) q^{21} +(-1.39238 + 0.803890i) q^{22} +(-6.63680 - 3.83176i) q^{23} +(-0.625274 - 1.08301i) q^{24} +1.09968 q^{26} -5.08681i q^{27} +(5.40683 + 3.12163i) q^{28} +(-2.01303 + 3.48667i) q^{29} -4.60077 q^{31} +(-3.02703 - 1.74766i) q^{32} +(4.60908 - 2.66105i) q^{33} +(-0.156998 + 0.271928i) q^{34} +(-1.84558 - 3.19664i) q^{36} -6.48831i q^{37} +(-1.21653 - 0.599183i) q^{38} -3.64017 q^{39} +(3.40277 + 5.89377i) q^{41} +(0.910193 + 0.525500i) q^{42} +(-5.46481 + 3.15511i) q^{43} +(4.91782 - 8.51792i) q^{44} -2.38418 q^{46} +(3.32690 + 1.92079i) q^{47} +(3.05788 + 1.76547i) q^{48} -3.76091 q^{49} +(0.519697 - 0.900141i) q^{51} +(-5.82601 + 3.36365i) q^{52} +(-6.16516 - 3.55946i) q^{53} +(-0.791273 - 1.37052i) q^{54} +3.98343 q^{56} +(4.02699 + 1.98343i) q^{57} +1.25254i q^{58} +(6.73649 + 11.6679i) q^{59} +(-3.06850 + 5.31480i) q^{61} +(-1.23957 + 0.715668i) q^{62} +(5.50975 + 3.18105i) q^{63} +5.76986 q^{64} +(0.827874 - 1.43392i) q^{66} +(9.69770 + 5.59897i) q^{67} -1.92088i q^{68} +7.89215 q^{69} +(0.227702 + 0.394391i) q^{71} +(-2.03958 - 1.17755i) q^{72} +(-3.57999 + 2.06691i) q^{73} +(-1.00928 - 1.74813i) q^{74} +(8.27788 - 0.546653i) q^{76} +16.9528i q^{77} +(-0.980760 + 0.566242i) q^{78} +(1.44414 + 2.50132i) q^{79} +(-0.289876 - 0.502080i) q^{81} +(1.83360 + 1.05863i) q^{82} +5.50061i q^{83} -6.42953 q^{84} +(-0.981579 + 1.70014i) q^{86} -4.14617i q^{87} -6.27551i q^{88} +(-3.56433 + 6.17360i) q^{89} +(5.79760 - 10.0417i) q^{91} +(12.6312 - 7.29264i) q^{92} +(4.10326 - 2.36902i) q^{93} +1.19514 q^{94} +3.59960 q^{96} +(-9.37476 + 5.41252i) q^{97} +(-1.01329 + 0.585025i) q^{98} +(5.01144 - 8.68006i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 4 q^{4} + 2 q^{6} + 14 q^{9}+O(q^{10}) $ 24 * q + 4 * q^4 + 2 * q^6 + 14 * q^9	$ 24 q + 4 q^{4} + 2 q^{6} + 14 q^{9} - 4 q^{11} - 12 q^{14} + 12 q^{16} + 12 q^{19} - 6 q^{21} + 22 q^{24} + 76 q^{26} + 6 q^{29} - 12 q^{31} - 2 q^{34} - 26 q^{36} - 32 q^{39} - 22 q^{41} + 42 q^{44} - 48 q^{46} - 16 q^{49} + 34 q^{51} + 36 q^{54} + 16 q^{56} + 8 q^{59} - 50 q^{61} + 88 q^{64} - 68 q^{66} - 52 q^{69} - 36 q^{71} - 12 q^{74} + 48 q^{76} + 6 q^{79} - 4 q^{81} - 148 q^{84} - 18 q^{86} + 24 q^{89} + 22 q^{91} - 32 q^{94} - 52 q^{96} - 40 q^{99}+O(q^{100}) $ 24 * q + 4 * q^4 + 2 * q^6 + 14 * q^9 - 4 * q^11 - 12 * q^14 + 12 * q^16 + 12 * q^19 - 6 * q^21 + 22 * q^24 + 76 * q^26 + 6 * q^29 - 12 * q^31 - 2 * q^34 - 26 * q^36 - 32 * q^39 - 22 * q^41 + 42 * q^44 - 48 * q^46 - 16 * q^49 + 34 * q^51 + 36 * q^54 + 16 * q^56 + 8 * q^59 - 50 * q^61 + 88 * q^64 - 68 * q^66 - 52 * q^69 - 36 * q^71 - 12 * q^74 + 48 * q^76 + 6 * q^79 - 4 * q^81 - 148 * q^84 - 18 * q^86 + 24 * q^89 + 22 * q^91 - 32 * q^94 - 52 * q^96 - 40 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/475\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	0.269427	−	0.155554i	0.190514	−	0.109993i	−0.401709	−	0.915767i	$-0.631584\pi$
$2$	0.269427	−	0.155554i	0.190514	−	0.109993i	0.592223	+	0.805774i	$0.298250\pi$
$3$	−0.891863	+	0.514917i	−0.514917	+	0.297288i	−0.734853	−	0.678227i	$-0.762749\pi$
$3$	−0.891863	+	0.514917i	−0.514917	+	0.297288i	0.219935	+	0.975514i	$0.429415\pi$
$4$	−0.951606	+	1.64823i	−0.475803	+	0.824115i
$5$		0			0
$5$		0			0
$6$	−0.160195	+	0.277466i	−0.0653993	+	0.113275i
$7$		−	3.28038i		−	1.23987i	−0.784654	−	0.619934i	$-0.787159\pi$
$7$		−	3.28038i		−	1.23987i	0.784654	−	0.619934i	$-0.212841\pi$
$8$			1.21432i			0.429327i
$9$	−0.969720	+	1.67960i	−0.323240	+	0.559868i
$10$		0			0
$11$	−5.16792			−1.55819			−0.779093	−	0.626908i	$-0.784320\pi$
$11$	−5.16792			−1.55819			−0.779093	+	0.626908i	$0.784320\pi$
$12$		−	1.95999i		−	0.565801i
$13$	3.06115	+	1.76735i	0.849010	+	0.490176i	0.860317	−	0.509760i	$-0.170266\pi$
$13$	3.06115	+	1.76735i	0.849010	+	0.490176i	−0.0113069	+	0.999936i	$0.503599\pi$
$14$	−0.510276	−	0.883825i	−0.136377	−	0.236212i
$15$		0			0
$16$	−1.71432	−	2.96929i	−0.428580	−	0.742322i
$17$	−0.874064	+	0.504641i	−0.211992	+	0.122393i	−0.602237	−	0.798318i	$-0.705724\pi$
$17$	−0.874064	+	0.504641i	−0.211992	+	0.122393i	0.390245	+	0.920711i	$0.372390\pi$
$18$			0.603375i			0.142217i
$19$	−2.42346	−	3.62310i	−0.555979	−	0.831196i
$19$	−2.42346	−	3.62310i	−0.555979	−	0.831196i
$20$		0			0
$21$	1.68913	+	2.92565i	0.368598	+	0.638430i
$22$	−1.39238	+	0.803890i	−0.296856	+	0.171390i
$23$	−6.63680	−	3.83176i	−1.38387	−	0.798976i	−0.391253	−	0.920283i	$-0.627958\pi$
$23$	−6.63680	−	3.83176i	−1.38387	−	0.798976i	−0.992615	+	0.121307i	$0.961291\pi$
$24$	−0.625274	−	1.08301i	−0.127634	−	0.221068i
$25$		0			0
$26$	1.09968			0.215664
$27$		−	5.08681i		−	0.978956i
$28$	5.40683	+	3.12163i	1.02179	+	0.589933i
$29$	−2.01303	+	3.48667i	−0.373810	+	0.647458i	−0.990148	−	0.140024i	$-0.955282\pi$
$29$	−2.01303	+	3.48667i	−0.373810	+	0.647458i	0.616338	+	0.787482i	$0.288615\pi$
$30$		0			0
$31$	−4.60077			−0.826323			−0.413162	−	0.910658i	$-0.635576\pi$
$31$	−4.60077			−0.826323			−0.413162	+	0.910658i	$0.635576\pi$
$32$	−3.02703	−	1.74766i	−0.535109	−	0.308945i
$33$	4.60908	−	2.66105i	0.802337	−	0.463230i
$34$	−0.156998	+	0.271928i	−0.0269249	+	0.0466353i
$35$		0			0
$36$	−1.84558	−	3.19664i	−0.307597	−	0.532774i
$37$		−	6.48831i		−	1.06667i	−0.845904	−	0.533336i	$-0.820938\pi$
$37$		−	6.48831i		−	1.06667i	0.845904	−	0.533336i	$-0.179062\pi$
$38$	−1.21653	−	0.599183i	−0.197348	−	0.0972004i
$39$	−3.64017			−0.582893
$40$		0			0
$41$	3.40277	+	5.89377i	0.531423	+	0.920451i	0.999327	+	0.0366724i	$0.0116758\pi$
$41$	3.40277	+	5.89377i	0.531423	+	0.920451i	−0.467904	+	0.883779i	$0.654991\pi$
$42$	0.910193	+	0.525500i	0.140446	+	0.0810865i
$43$	−5.46481	+	3.15511i	−0.833376	+	0.481150i	−0.855007	−	0.518616i	$-0.826447\pi$
$43$	−5.46481	+	3.15511i	−0.833376	+	0.481150i	0.0216315	+	0.999766i	$0.493114\pi$
$44$	4.91782	−	8.51792i	0.741390	−	1.28412i
$45$		0			0
$46$	−2.38418			−0.351528
$47$	3.32690	+	1.92079i	0.485278	+	0.280175i	0.722613	−	0.691252i	$-0.242941\pi$
$47$	3.32690	+	1.92079i	0.485278	+	0.280175i	−0.237335	+	0.971428i	$0.576274\pi$
$48$	3.05788	+	1.76547i	0.441366	+	0.254823i
$49$	−3.76091			−0.537273
$50$		0			0
$51$	0.519697	−	0.900141i	0.0727721	−	0.126045i
$52$	−5.82601	+	3.36365i	−0.807923	+	0.466454i
$53$	−6.16516	−	3.55946i	−0.846850	−	0.488929i	0.0127367	−	0.999919i	$-0.495946\pi$
$53$	−6.16516	−	3.55946i	−0.846850	−	0.488929i	−0.859587	+	0.510990i	$0.829279\pi$
$54$	−0.791273	−	1.37052i	−0.107679	−	0.186505i
$55$		0			0
$56$	3.98343			0.532309
$57$	4.02699	+	1.98343i	0.533388	+	0.262711i
$58$			1.25254i			0.164466i
$59$	6.73649	+	11.6679i	0.877016	+	1.51904i	0.854599	+	0.519288i	$0.173803\pi$
$59$	6.73649	+	11.6679i	0.877016	+	1.51904i	0.0224174	+	0.999749i	$0.492864\pi$
$60$		0			0
$61$	−3.06850	+	5.31480i	−0.392881	+	0.680491i	−0.992828	−	0.119549i	$-0.961855\pi$
$61$	−3.06850	+	5.31480i	−0.392881	+	0.680491i	0.599947	+	0.800040i	$0.295188\pi$
$62$	−1.23957	+	0.715668i	−0.157426	+	0.0908899i
$63$	5.50975	+	3.18105i	0.694163	+	0.400775i
$64$	5.76986			0.721232
$65$		0			0
$66$	0.827874	−	1.43392i	0.101904	−	0.176503i
$67$	9.69770	+	5.59897i	1.18476	+	0.684023i	0.957112	−	0.289719i	$-0.0935620\pi$
$67$	9.69770	+	5.59897i	1.18476	+	0.684023i	0.227652	+	0.973743i	$0.426895\pi$
$68$		−	1.92088i		−	0.232941i
$69$	7.89215			0.950103
$70$		0			0
$71$	0.227702	+	0.394391i	0.0270233	+	0.0468056i	0.879221	−	0.476415i	$-0.158064\pi$
$71$	0.227702	+	0.394391i	0.0270233	+	0.0468056i	−0.852198	+	0.523220i	$0.824731\pi$
$72$	−2.03958	−	1.17755i	−0.240367	−	0.138776i
$73$	−3.57999	+	2.06691i	−0.419007	+	0.241914i	−0.694652	−	0.719346i	$-0.744442\pi$
$73$	−3.57999	+	2.06691i	−0.419007	+	0.241914i	0.275646	+	0.961259i	$0.411108\pi$
$74$	−1.00928	−	1.74813i	−0.117327	−	0.203216i
$75$		0			0
$76$	8.27788	−	0.546653i	0.949538	−	0.0627054i
$77$			16.9528i			1.93195i
$78$	−0.980760	+	0.566242i	−0.111049	+	0.0641143i
$79$	1.44414	+	2.50132i	0.162478	+	0.281421i	0.935757	−	0.352646i	$-0.114718\pi$
$79$	1.44414	+	2.50132i	0.162478	+	0.281421i	−0.773278	+	0.634067i	$0.781385\pi$
$80$		0			0
$81$	−0.289876	−	0.502080i	−0.0322085	−	0.0557867i
$82$	1.83360	+	1.05863i	0.202487	+	0.116906i
$83$			5.50061i			0.603770i	0.953344	+	0.301885i	$0.0976159\pi$
$83$			5.50061i			0.603770i	−0.953344	+	0.301885i	$0.902384\pi$
$84$	−6.42953			−0.701519
$85$		0			0
$86$	−0.981579	+	1.70014i	−0.105846	+	0.183331i
$87$		−	4.14617i		−	0.444516i
$88$		−	6.27551i		−	0.668971i
$89$	−3.56433	+	6.17360i	−0.377818	+	0.654400i	−0.990745	−	0.135740i	$-0.956659\pi$
$89$	−3.56433	+	6.17360i	−0.377818	+	0.654400i	0.612926	+	0.790140i	$0.289992\pi$
$90$		0			0
$91$	5.79760	−	10.0417i	0.607754	−	1.05266i
$92$	12.6312	−	7.29264i	1.31690	−	0.760311i
$93$	4.10326	−	2.36902i	0.425488	−	0.245656i
$94$	1.19514			0.123270
$95$		0			0
$96$	3.59960			0.367382
$97$	−9.37476	+	5.41252i	−0.951862	+	0.549558i	−0.893659	−	0.448747i	$-0.851871\pi$
$97$	−9.37476	+	5.41252i	−0.951862	+	0.549558i	−0.0582034	+	0.998305i	$0.518537\pi$
$98$	−1.01329	+	0.585025i	−0.102358	+	0.0590964i
$99$	5.01144	−	8.68006i	0.503668	−	0.872379i
$100$		0			0
$101$	3.09011	−	5.35223i	0.307478	−	0.532567i	−0.670332	−	0.742061i	$-0.733848\pi$
$101$	3.09011	−	5.35223i	0.307478	−	0.532567i	0.977810	+	0.209494i	$0.0671818\pi$
$102$		−	0.323363i		−	0.0320177i
$103$		−	18.3217i		−	1.80529i	−0.430387	−	0.902644i	$-0.641623\pi$
$103$		−	18.3217i		−	1.80529i	0.430387	−	0.902644i	$-0.358377\pi$
$104$	−2.14613	+	3.71721i	−0.210446	+	0.364503i
$105$		0			0
$106$	−2.21475			−0.215116
$107$			8.73445i			0.844391i	0.906505	+	0.422196i	$0.138740\pi$
$107$			8.73445i			0.844391i	−0.906505	+	0.422196i	$0.861260\pi$
$108$	8.38423	+	4.84064i	0.806773	+	0.465790i
$109$	−3.04839	−	5.27997i	−0.291983	−	0.505730i	0.682295	−	0.731077i	$-0.260982\pi$
$109$	−3.04839	−	5.27997i	−0.291983	−	0.505730i	−0.974279	+	0.225347i	$0.927648\pi$
$110$		0			0
$111$	3.34094	+	5.78668i	0.317108	+	0.549248i
$112$	−9.74041	+	5.62363i	−0.920382	+	0.531383i
$113$		−	10.3443i		−	0.973111i	−0.873650	−	0.486556i	$-0.838253\pi$
$113$		−	10.3443i		−	0.973111i	0.873650	−	0.486556i	$-0.161747\pi$
$114$	1.39351	−	0.0920244i	0.130514	−	0.00861887i
$115$		0			0
$116$	−3.83122	−	6.63587i	−0.355720	−	0.616125i
$117$	−5.93692	+	3.42768i	−0.548868	+	0.316889i
$118$	3.62999	+	2.09578i	0.334168	+	0.192932i
$119$	1.65542	+	2.86726i	0.151752	+	0.262842i
$120$		0			0
$121$	15.7074			1.42794
$122$			1.90927i			0.172857i
$123$	−6.06960	−	3.50429i	−0.547278	−	0.315971i
$124$	4.37812	−	7.58313i	0.393167	−	0.680985i
$125$		0			0
$126$	1.97930			0.176330
$127$	−2.91602	−	1.68356i	−0.258755	−	0.149392i	0.365012	−	0.931003i	$-0.381065\pi$
$127$	−2.91602	−	1.68356i	−0.258755	−	0.149392i	−0.623766	+	0.781611i	$0.714398\pi$
$128$	7.60862	−	4.39284i	0.672514	−	0.388276i
$129$	3.24924	−	5.62785i	0.286080	−	0.495504i
$130$		0			0
$131$	−1.21089	−	2.09732i	−0.105796	−	0.183244i	0.808267	−	0.588816i	$-0.200406\pi$
$131$	−1.21089	−	2.09732i	−0.105796	−	0.183244i	−0.914063	+	0.405572i	$0.867072\pi$
$132$			10.1291i			0.881624i
$133$	−11.8852	+	7.94987i	−1.03057	+	0.689341i
$134$	3.48377			0.300952
$135$		0			0
$136$	−0.612795	−	1.06139i	−0.0525468	−	0.0910137i
$137$	9.97584	+	5.75955i	0.852293	+	0.492072i	0.861424	−	0.507886i	$-0.169573\pi$
$137$	9.97584	+	5.75955i	0.852293	+	0.492072i	−0.00913057	+	0.999958i	$0.502906\pi$
$138$	2.12636	−	1.22765i	0.181008	−	0.104505i
$139$	3.53776	−	6.12759i	0.300069	−	0.519735i	−0.676082	−	0.736826i	$-0.736324\pi$
$139$	3.53776	−	6.12759i	0.300069	−	0.519735i	0.976151	+	0.217091i	$0.0696569\pi$
$140$		0			0
$141$	−3.95618			−0.333171
$142$	0.122698	+	0.0708399i	0.0102966	+	0.00594475i
$143$	−15.8198	−	9.13355i	−1.32292	−	0.763785i
$144$	6.64964			0.554137
$145$		0			0
$146$	−0.643032	+	1.11376i	−0.0532177	+	0.0921758i
$147$	3.35422	−	1.93656i	0.276651	−	0.159725i
$148$	10.6942	+	6.17431i	0.879060	+	0.507525i
$149$	6.37476	+	11.0414i	0.522240	+	0.904547i	0.999665	+	0.0258744i	$0.00823700\pi$
$149$	6.37476	+	11.0414i	0.522240	+	0.904547i	−0.477425	+	0.878673i	$0.658430\pi$
$150$		0			0
$151$	−19.6361			−1.59797			−0.798983	−	0.601353i	$-0.794628\pi$
$151$	−19.6361			−1.59797			−0.798983	+	0.601353i	$0.794628\pi$
$152$	4.39960	−	2.94285i	0.356855	−	0.238697i
$153$		−	1.95744i		−	0.158250i
$154$	2.63707	+	4.56753i	0.212501	+	0.368062i
$155$		0			0
$156$	3.46400	−	5.99983i	0.277342	−	0.480371i
$157$	2.67159	−	1.54244i	0.213216	−	0.123101i	−0.389589	−	0.920989i	$-0.627383\pi$
$157$	2.67159	−	1.54244i	0.213216	−	0.123101i	0.602805	+	0.797888i	$0.294050\pi$
$158$	0.778182	+	0.449283i	0.0619088	+	0.0357431i
$159$	7.33131			0.581410
$160$		0			0
$161$	−12.5696	+	21.7712i	−0.990625	+	1.71581i
$162$	−0.156201	−	0.0901827i	−0.0122723	−	0.00708542i
$163$			22.4721i			1.76015i	0.474831	+	0.880077i	$0.342509\pi$
$163$			22.4721i			1.76015i	−0.474831	+	0.880077i	$0.657491\pi$
$164$	−12.9524			−1.01141
$165$		0			0
$166$	0.855642	+	1.48201i	0.0664107	+	0.115027i
$167$	−9.12769	−	5.26987i	−0.706322	−	0.407795i	0.103376	−	0.994642i	$-0.467036\pi$
$167$	−9.12769	−	5.26987i	−0.706322	−	0.407795i	−0.809698	+	0.586847i	$0.800369\pi$
$168$	−3.55268	+	2.05114i	−0.274095	+	0.158249i
$169$	−0.252915	−	0.438062i	−0.0194550	−	0.0336970i
$170$		0			0
$171$	8.43545	−	0.557059i	0.645075	−	0.0425994i
$172$		−	12.0097i		−	0.915730i
$173$	−19.8650	+	11.4691i	−1.51031	+	0.871977i	−0.510380	+	0.859949i	$0.670495\pi$
$173$	−19.8650	+	11.4691i	−1.51031	+	0.871977i	−0.999928	+	0.0120281i	$0.996171\pi$
$174$	−0.644953	−	1.11709i	−0.0488938	−	0.0846865i
$175$		0			0
$176$	8.85947	+	15.3450i	0.667807	+	1.15668i
$177$	−12.0161	−	6.93747i	−0.903182	−	0.521452i
$178$			2.21778i			0.166230i
$179$	−23.2705			−1.73932			−0.869661	−	0.493649i	$-0.835663\pi$
$179$	−23.2705			−1.73932			−0.869661	+	0.493649i	$0.835663\pi$
$180$		0			0
$181$	7.98346	−	13.8278i	0.593406	−	1.02781i	−0.400364	−	0.916356i	$-0.631116\pi$
$181$	7.98346	−	13.8278i	0.593406	−	1.02781i	0.993770	−	0.111453i	$-0.0355503\pi$
$182$		−	3.60736i		−	0.267395i
$183$		−	6.32010i		−	0.467195i
$184$	4.65298	−	8.05919i	0.343022	−	0.594132i
$185$		0			0
$186$	0.737020	−	1.27656i	0.0540409	−	0.0936016i
$187$	4.51709	−	2.60794i	0.330322	−	0.190712i
$188$	−6.33179	+	3.65566i	−0.461793	+	0.266617i
$189$	−16.6867			−1.21378
$190$		0			0
$191$	−2.44600			−0.176986			−0.0884930	−	0.996077i	$-0.528205\pi$
$191$	−2.44600			−0.176986			−0.0884930	+	0.996077i	$0.528205\pi$
$192$	−5.14592	+	2.97100i	−0.371375	+	0.214413i
$193$	16.4940	−	9.52280i	1.18726	−	0.685466i	0.229579	−	0.973290i	$-0.426265\pi$
$193$	16.4940	−	9.52280i	1.18726	−	0.685466i	0.957683	+	0.287824i	$0.0929317\pi$
$194$	−1.68388	+	2.91656i	−0.120895	+	0.209397i
$195$		0			0
$196$	3.57891	−	6.19885i	0.255636	−	0.442775i
$197$		−	6.18524i		−	0.440680i	−0.975423	−	0.220340i	$-0.929283\pi$
$197$		−	6.18524i		−	0.440680i	0.975423	−	0.220340i	$-0.0707167\pi$
$198$		−	3.11819i		−	0.221600i
$199$	3.60525	−	6.24447i	0.255569	−	0.442659i	−0.709481	−	0.704725i	$-0.751070\pi$
$199$	3.60525	−	6.24447i	0.255569	−	0.442659i	0.965050	+	0.262066i	$0.0844038\pi$
$200$		0			0
$201$	−11.5320			−0.813407
$202$		−	1.92272i		−	0.135282i
$203$	11.4376	+	6.60350i	0.802763	+	0.463475i
$204$	0.989093	+	1.71316i	0.0692504	+	0.119945i
$205$		0			0
$206$	−2.85001	−	4.93636i	−0.198570	−	0.343933i
$207$	12.8717	−	7.43146i	0.894643	−	0.516522i
$208$		−	12.1192i		−	0.840318i
$209$	12.5242	+	18.7239i	0.866320	+	1.29516i
$210$		0			0
$211$	9.82333	+	17.0145i	0.676266	+	1.17133i	0.976097	+	0.217335i	$0.0697362\pi$
$211$	9.82333	+	17.0145i	0.676266	+	1.17133i	−0.299831	+	0.953992i	$0.596930\pi$
$212$	11.7336	−	6.77440i	0.805868	−	0.465268i
$213$	−0.406158	−	0.234495i	−0.0278295	−	0.0160674i
$214$	1.35868	+	2.35330i	0.0928773	+	0.160868i
$215$		0			0
$216$	6.17701			0.420292
$217$			15.0923i			1.02453i
$218$	−1.64264	−	0.948379i	−0.111254	−	0.0642323i
$219$	2.12858	−	3.68680i	0.143836	−	0.249131i
$220$		0			0
$221$	−3.56752			−0.239977
$222$	1.80028	+	1.03939i	0.120827	+	0.0697595i
$223$	9.81536	−	5.66690i	0.657285	−	0.379484i	−0.133957	−	0.990987i	$-0.542768\pi$
$223$	9.81536	−	5.66690i	0.657285	−	0.379484i	0.791242	+	0.611504i	$0.209435\pi$
$224$	−5.73299	+	9.92983i	−0.383051	+	0.663464i
$225$		0			0
$226$	−1.60910	−	2.78704i	−0.107036	−	0.185391i
$227$		−	11.1369i		−	0.739180i	−0.929195	−	0.369590i	$-0.879498\pi$
$227$		−	11.1369i		−	0.739180i	0.929195	−	0.369590i	$-0.120502\pi$
$228$	−7.10125	+	4.74996i	−0.470292	+	0.314574i
$229$	−3.51221			−0.232093			−0.116047	−	0.993244i	$-0.537022\pi$
$229$	−3.51221			−0.232093			−0.116047	+	0.993244i	$0.537022\pi$
$230$		0			0
$231$	−8.72927	−	15.1195i	−0.574344	−	0.994792i
$232$	−4.23393	−	2.44446i	−0.277971	−	0.160487i
$233$	−5.36068	+	3.09499i	−0.351190	+	0.202759i	−0.665209	−	0.746657i	$-0.731658\pi$
$233$	−5.36068	+	3.09499i	−0.351190	+	0.202759i	0.314020	+	0.949417i	$0.398324\pi$
$234$	−1.06638	+	1.84702i	−0.0697113	+	0.120744i
$235$		0			0
$236$	−25.6419			−1.66915
$237$	−2.57595	−	1.48723i	−0.167326	−	0.0966057i
$238$	0.892028	+	0.515013i	0.0578216	+	0.0333833i
$239$	−12.1221			−0.784116			−0.392058	−	0.919940i	$-0.628237\pi$
$239$	−12.1221			−0.784116			−0.392058	+	0.919940i	$0.628237\pi$
$240$		0			0
$241$	2.55102	−	4.41849i	0.164326	−	0.284620i	−0.772090	−	0.635513i	$-0.780789\pi$
$241$	2.55102	−	4.41849i	0.164326	−	0.284620i	0.936416	+	0.350893i	$0.114122\pi$
$242$	4.23200	−	2.44335i	0.272043	−	0.157064i
$243$	13.7330	+	7.92873i	0.880971	+	0.508629i
$244$	−5.84001	−	10.1152i	−0.373868	−	0.647559i
$245$		0			0
$246$	−2.18042			−0.139019
$247$	−1.01526	−	15.3740i	−0.0645996	−	0.978221i
$248$		−	5.58681i		−	0.354763i
$249$	−2.83236	−	4.90579i	−0.179494	−	0.310892i
$250$		0			0
$251$	−12.7122	+	22.0181i	−0.802385	+	1.38977i	0.115657	+	0.993289i	$0.463103\pi$
$251$	−12.7122	+	22.0181i	−0.802385	+	1.38977i	−0.918042	+	0.396483i	$0.870231\pi$
$252$	−10.4862	+	6.05422i	−0.660570	+	0.381380i
$253$	34.2984	+	19.8022i	2.15632	+	1.24495i
$254$	−1.04754			−0.0657285
$255$		0			0
$256$	−4.40321	+	7.62659i	−0.275201	+	0.476662i
$257$	−15.9781	−	9.22493i	−0.996684	−	0.575436i	−0.0894183	−	0.995994i	$-0.528501\pi$
$257$	−15.9781	−	9.22493i	−0.996684	−	0.575436i	−0.907265	+	0.420559i	$0.861834\pi$
$258$		−	2.02173i		−	0.125867i
$259$	−21.2841			−1.32253
$260$		0			0
$261$	−3.90415	−	6.76218i	−0.241661	−	0.418569i
$262$	−0.652493	−	0.376717i	−0.0403111	−	0.0232737i
$263$	−11.2155	+	6.47530i	−0.691580	+	0.399284i	−0.804204	−	0.594354i	$-0.797408\pi$
$263$	−11.2155	+	6.47530i	−0.691580	+	0.399284i	0.112624	+	0.993638i	$0.464075\pi$
$264$	3.23137	+	5.59689i	0.198877	+	0.344465i
$265$		0			0
$266$	−1.96555	+	3.99069i	−0.120516	+	0.244685i
$267$		−	7.34134i		−	0.449283i
$268$	−18.4568	+	10.6560i	−1.12743	+	0.650921i
$269$	0.0782471	+	0.135528i	0.00477081	+	0.00826329i	0.868401	−	0.495863i	$-0.165148\pi$
$269$	0.0782471	+	0.135528i	0.00477081	+	0.00826329i	−0.863630	+	0.504126i	$0.831815\pi$
$270$		0			0
$271$	−13.9095	−	24.0920i	−0.844944	−	1.46349i	−0.885670	−	0.464315i	$-0.846301\pi$
$271$	−13.9095	−	24.0920i	−0.844944	−	1.46349i	0.0407264	−	0.999170i	$-0.487033\pi$
$272$	2.99685	+	1.73023i	0.181711	+	0.104911i
$273$			11.9411i			0.722711i
$274$	3.58368			0.216498
$275$		0			0
$276$	−7.51022	+	13.0081i	−0.452062	+	0.782994i
$277$		−	0.524062i		−	0.0314878i	−0.999876	−	0.0157439i	$-0.994988\pi$
$277$		−	0.524062i		−	0.0314878i	0.999876	−	0.0157439i	$-0.00501165\pi$
$278$		−	2.20125i		−	0.132022i
$279$	4.46146	−	7.72748i	0.267101	−	0.462632i
$280$		0			0
$281$	2.44413	−	4.23336i	0.145804	−	0.252541i	−0.783868	−	0.620927i	$-0.786756\pi$
$281$	2.44413	−	4.23336i	0.145804	−	0.252541i	0.929673	+	0.368386i	$0.120090\pi$
$282$	−1.06590	+	0.615400i	−0.0634736	+	0.0366465i
$283$	15.4833	−	8.93931i	0.920389	−	0.531387i	0.0366299	−	0.999329i	$-0.488338\pi$
$283$	15.4833	−	8.93931i	0.920389	−	0.531387i	0.883759	+	0.467942i	$0.155004\pi$
$284$	−0.866730			−0.0514310
$285$		0			0
$286$	−5.68304			−0.336045
$287$	19.3338	−	11.1624i	1.14124	−	0.658894i
$288$	5.87075	−	3.38948i	0.345937	−	0.199727i
$289$	−7.99068	+	13.8403i	−0.470040	+	0.814133i
$290$		0			0
$291$	5.57400	−	9.65445i	0.326754	−	0.565954i
$292$		−	7.86754i		−	0.460413i
$293$		−	7.25399i		−	0.423783i	−0.977293	−	0.211891i	$-0.932038\pi$
$293$		−	7.25399i		−	0.423783i	0.977293	−	0.211891i	$-0.0679623\pi$
$294$	0.602479	−	1.04352i	0.0351373	−	0.0608595i
$295$		0			0
$296$	7.87888			0.457951
$297$			26.2882i			1.52540i
$298$	3.43507	+	1.98324i	0.198988	+	0.114886i
$299$	−13.5441	−	23.4591i	−0.783278	−	1.35668i
$300$		0			0
$301$	10.3500	+	17.9267i	0.596562	+	1.03328i
$302$	−5.29051	+	3.05448i	−0.304435	+	0.175766i
$303$			6.36461i			0.365637i
$304$	−6.60345	+	13.4071i	−0.378734	+	0.768950i
$305$		0			0
$306$	−0.304488	−	0.527388i	−0.0174064	−	0.0301488i
$307$	12.4537	−	7.19015i	0.710771	−	0.410364i	−0.100576	−	0.994929i	$-0.532068\pi$
$307$	12.4537	−	7.19015i	0.710771	−	0.410364i	0.811346	+	0.584566i	$0.198735\pi$
$308$	−27.9420	−	16.1323i	−1.59215	−	0.919226i
$309$	9.43415	+	16.3404i	0.536690	+	0.929574i
$310$		0			0
$311$	8.52590			0.483459			0.241730	−	0.970344i	$-0.422285\pi$
$311$	8.52590			0.483459			0.241730	+	0.970344i	$0.422285\pi$
$312$		−	4.42033i		−	0.250252i
$313$	−18.4999	−	10.6809i	−1.04568	−	0.603722i	−0.124241	−	0.992252i	$-0.539650\pi$
$313$	−18.4999	−	10.6809i	−1.04568	−	0.603722i	−0.921436	+	0.388530i	$0.872983\pi$
$314$	0.479867	−	0.831153i	0.0270804	−	0.0469047i
$315$		0			0
$316$	−5.49701			−0.309231
$317$	−24.3291	−	14.0464i	−1.36646	−	0.788924i	−0.375983	−	0.926626i	$-0.622695\pi$
$317$	−24.3291	−	14.0464i	−1.36646	−	0.788924i	−0.990474	+	0.137702i	$0.956028\pi$
$318$	1.97525	−	1.14041i	0.110767	−	0.0639512i
$319$	10.4032	−	18.0188i	0.582466	−	1.00886i
$320$		0			0
$321$	−4.49752	−	7.78993i	−0.251027	−	0.434792i
$322$			7.82102i			0.435848i
$323$	3.94662	+	1.94384i	0.219596	+	0.108158i
$324$	1.10339			0.0612995
$325$		0			0
$326$	3.49563	+	6.05461i	0.193605	+	0.335334i
$327$	5.43750	+	3.13934i	0.300694	+	0.173606i
$328$	−7.15692	+	4.13205i	−0.395175	+	0.228154i
$329$	6.30091	−	10.9135i	0.347381	−	0.601681i
$330$		0			0
$331$	15.1725			0.833957			0.416979	−	0.908916i	$-0.363089\pi$
$331$	15.1725			0.833957			0.416979	+	0.908916i	$0.363089\pi$
$332$	−9.06627	−	5.23441i	−0.497576	−	0.287276i
$333$	10.8978	+	6.29184i	0.597195	+	0.344791i
$334$	−3.27900			−0.179419
$335$		0			0
$336$	5.79140	−	10.0310i	0.315947	−	0.547236i
$337$	−15.1562	+	8.75041i	−0.825608	+	0.476665i	−0.852347	−	0.522977i	$-0.824821\pi$
$337$	−15.1562	+	8.75041i	−0.825608	+	0.476665i	0.0267383	+	0.999642i	$0.491488\pi$
$338$	−0.136284	−	0.0786838i	−0.00741289	−	0.00427984i
$339$	5.32647	+	9.22571i	0.289294	+	0.501072i
$340$		0			0
$341$	23.7764			1.28757
$342$	2.18609	−	1.46225i	0.118210	−	0.0790697i
$343$		−	10.6254i		−	0.573720i
$344$	−3.83131	−	6.63603i	−0.206570	−	0.357791i
$345$		0			0
$346$	−3.56812	+	6.18016i	−0.191823	+	0.332247i
$347$	15.0417	−	8.68435i	0.807483	−	0.466201i	−0.0385980	−	0.999255i	$-0.512289\pi$
$347$	15.0417	−	8.68435i	0.807483	−	0.466201i	0.846081	+	0.533054i	$0.178956\pi$
$348$	6.83385	+	3.94552i	0.366333	+	0.211502i
$349$	34.2563			1.83370			0.916850	−	0.399232i	$-0.130723\pi$
$349$	34.2563			1.83370			0.916850	+	0.399232i	$0.130723\pi$
$350$		0			0
$351$	8.99019	−	15.5715i	0.479861	−	0.831144i
$352$	15.6435	+	9.03176i	0.833799	+	0.481394i
$353$		−	34.9287i		−	1.85907i	−0.368736	−	0.929534i	$-0.620209\pi$
$353$		−	34.9287i		−	1.85907i	0.368736	−	0.929534i	$-0.379791\pi$
$354$	−4.31660			−0.229425
$355$		0			0
$356$	−6.78367	−	11.7497i	−0.359534	−	0.622731i
$357$	−2.95281	−	1.70480i	−0.156279	−	0.0902278i
$358$	−6.26972	+	3.61982i	−0.331365	+	0.191314i
$359$	−0.488273	−	0.845713i	−0.0257701	−	0.0446350i	0.852853	−	0.522151i	$-0.174870\pi$
$359$	−0.488273	−	0.845713i	−0.0257701	−	0.0446350i	−0.878623	+	0.477516i	$0.841537\pi$
$360$		0			0
$361$	−7.25370	+	17.5609i	−0.381774	+	0.924256i
$362$		−	4.96743i		−	0.261082i
$363$	−14.0088	+	8.08801i	−0.735273	+	0.424510i
$364$	11.0341	+	19.1116i	0.578342	+	1.00172i
$365$		0			0
$366$	−0.983116	−	1.70281i	−0.0513883	−	0.0890071i
$367$	−8.54451	−	4.93318i	−0.446020	−	0.257510i	0.260128	−	0.965574i	$-0.416235\pi$
$367$	−8.54451	−	4.93318i	−0.446020	−	0.257510i	−0.706148	+	0.708064i	$0.749569\pi$
$368$			26.2754i			1.36970i
$369$	−13.1989			−0.687109
$370$		0			0
$371$	−11.6764	+	20.2241i	−0.606208	+	1.04998i
$372$			9.01748i			0.467535i
$373$			12.9521i			0.670634i	0.942105	+	0.335317i	$0.108843\pi$
$373$			12.9521i			0.670634i	−0.942105	+	0.335317i	$0.891157\pi$
$374$	0.811352	−	1.40530i	0.0419540	−	0.0726664i
$375$		0			0
$376$	−2.33245	+	4.03992i	−0.120287	+	0.208343i
$377$	−12.3244	+	7.11547i	−0.634737	+	0.366465i
$378$	−4.49585	+	2.59568i	−0.231241	+	0.133507i
$379$	−5.21597			−0.267926			−0.133963	−	0.990986i	$-0.542770\pi$
$379$	−5.21597			−0.267926			−0.133963	+	0.990986i	$0.542770\pi$
$380$		0			0
$381$	3.46758			0.177650
$382$	−0.659018	+	0.380484i	−0.0337183	+	0.0194673i
$383$	−29.0390	+	16.7657i	−1.48382	+	0.856686i	−0.999831	−	0.0183857i	$-0.994147\pi$
$383$	−29.0390	+	16.7657i	−1.48382	+	0.856686i	−0.483993	+	0.875072i	$0.660814\pi$
$384$	−4.52390	+	7.83562i	−0.230859	+	0.399860i
$385$		0			0
$386$	2.96262	−	5.13141i	0.150793	−	0.261182i
$387$		−	12.2383i		−	0.622107i
$388$		−	20.6023i		−	1.04593i
$389$	13.8703	−	24.0241i	0.703253	−	1.21807i	−0.264066	−	0.964505i	$-0.585064\pi$
$389$	13.8703	−	24.0241i	0.703253	−	1.21807i	0.967318	−	0.253565i	$-0.0816031\pi$
$390$		0			0
$391$	7.73464			0.391158
$392$		−	4.56695i		−	0.230666i
$393$	2.15989	+	1.24702i	0.108952	+	0.0629036i
$394$	−0.962139	−	1.66647i	−0.0484718	−	0.0839557i
$395$		0			0
$396$	9.53783	+	16.5200i	0.479294	+	0.830161i
$397$	−4.76264	+	2.74971i	−0.239030	+	0.138004i	−0.614731	−	0.788737i	$-0.710735\pi$
$397$	−4.76264	+	2.74971i	−0.239030	+	0.138004i	0.375701	+	0.926741i	$0.377402\pi$
$398$		−	2.24324i		−	0.112444i
$399$	6.50640	−	13.2101i	0.325728	−	0.661331i
$400$		0			0
$401$	4.25655	+	7.37256i	0.212562	+	0.368168i	0.952516	−	0.304490i	$-0.0984860\pi$
$401$	4.25655	+	7.37256i	0.212562	+	0.368168i	−0.739954	+	0.672658i	$0.765153\pi$
$402$	−3.10704	+	1.79385i	−0.154965	+	0.0894692i
$403$	−14.0836	−	8.13120i	−0.701556	−	0.405044i
$404$	5.88114	+	10.1864i	0.292597	+	0.506794i
$405$		0			0
$406$	4.10880			0.203917
$407$			33.5311i			1.66207i
$408$	1.09306	+	0.631078i	0.0541145	+	0.0312430i
$409$	−10.7353	+	18.5941i	−0.530826	+	0.919418i	0.468527	+	0.883449i	$0.344785\pi$
$409$	−10.7353	+	18.5941i	−0.530826	+	0.919418i	−0.999353	+	0.0359683i	$0.988548\pi$
$410$		0			0
$411$	−11.8628			−0.585148
$412$	30.1983	+	17.4350i	1.48777	+	0.858962i
$413$	38.2753	−	22.0983i	1.88341	−	1.08738i
$414$	2.31199	−	4.00448i	0.113628	−	0.196809i
$415$		0			0
$416$	−6.17746	−	10.6997i	−0.302875	−	0.524595i
$417$			7.28662i			0.356827i
$418$	6.28694	+	3.09653i	0.307504	+	0.151456i
$419$	5.09378			0.248848			0.124424	−	0.992229i	$-0.460292\pi$
$419$	5.09378			0.248848			0.124424	+	0.992229i	$0.460292\pi$
$420$		0			0
$421$	−2.82911	−	4.90017i	−0.137883	−	0.238820i	0.788812	−	0.614634i	$-0.210696\pi$
$421$	−2.82911	−	4.90017i	−0.137883	−	0.238820i	−0.926695	+	0.375815i	$0.877363\pi$
$422$	5.29335	+	3.05611i	0.257676	+	0.148769i
$423$	−6.45232	+	3.72525i	−0.313723	+	0.181128i
$424$	4.32232	−	7.48648i	0.209910	−	0.363576i
$425$		0			0
$426$	−0.145907			−0.00706920
$427$	17.4346	+	10.0659i	0.843719	+	0.487121i
$428$	−14.3964	−	8.31176i	−0.695876	−	0.401764i
$429$	18.8121			0.908256
$430$		0			0
$431$	19.1834	−	33.2267i	0.924033	−	1.60047i	0.130923	−	0.991392i	$-0.458206\pi$
$431$	19.1834	−	33.2267i	0.924033	−	1.60047i	0.793109	−	0.609079i	$-0.208461\pi$
$432$	−15.1042	+	8.72041i	−0.726701	+	0.419561i
$433$	6.02970	+	3.48125i	0.289769	+	0.167298i	0.637838	−	0.770171i	$-0.279829\pi$
$433$	6.02970	+	3.48125i	0.289769	+	0.167298i	−0.348069	+	0.937469i	$0.613162\pi$
$434$	2.34767	+	4.06628i	0.112692	+	0.195188i
$435$		0			0
$436$	11.6035			0.555706
$437$	2.20116	+	33.3319i	0.105296	+	1.59448i
$438$		−	1.32443i		−	0.0632839i
$439$	4.76346	+	8.25055i	0.227347	+	0.393777i	0.957021	−	0.290018i	$-0.0936613\pi$
$439$	4.76346	+	8.25055i	0.227347	+	0.393777i	−0.729674	+	0.683796i	$0.760328\pi$
$440$		0			0
$441$	3.64703	−	6.31685i	0.173668	−	0.300802i
$442$	−0.961187	+	0.554941i	−0.0457190	+	0.0263959i
$443$	30.0544	+	17.3519i	1.42793	+	0.824414i	0.996957	−	0.0779516i	$-0.0248380\pi$
$443$	30.0544	+	17.3519i	1.42793	+	0.824414i	0.430971	+	0.902366i	$0.358171\pi$
$444$	−12.7170			−0.603524
$445$		0			0
$446$	1.76302	−	3.05363i	0.0834813	−	0.144594i
$447$	−11.3708	−	6.56495i	−0.537821	−	0.310511i
$448$		−	18.9273i		−	0.894233i
$449$	8.84228			0.417293			0.208646	−	0.977991i	$-0.433094\pi$
$449$	8.84228			0.417293			0.208646	+	0.977991i	$0.433094\pi$
$450$		0			0
$451$	−17.5852	−	30.4585i	−0.828056	−	1.43423i
$452$	17.0498	+	9.84371i	0.801956	+	0.463009i
$453$	17.5127	−	10.1110i	0.822821	−	0.475056i
$454$	−1.73238	−	3.00058i	−0.0813048	−	0.140824i
$455$		0			0
$456$	−2.40852	+	4.89005i	−0.112789	+	0.228998i
$457$			0.664998i			0.0311073i	0.999879	+	0.0155536i	$0.00495108\pi$
$457$			0.664998i			0.0311073i	−0.999879	+	0.0155536i	$0.995049\pi$
$458$	−0.946285	+	0.546338i	−0.0442170	+	0.0255287i
$459$	2.56701	+	4.44619i	0.119818	+	0.207531i
$460$		0			0
$461$	19.7696	+	34.2420i	0.920762	+	1.59481i	0.798238	+	0.602342i	$0.205766\pi$
$461$	19.7696	+	34.2420i	0.920762	+	1.59481i	0.122524	+	0.992466i	$0.460901\pi$
$462$	−4.70381	−	2.71574i	−0.218841	−	0.126348i
$463$			15.5782i			0.723981i	0.932182	+	0.361991i	$0.117903\pi$
$463$			15.5782i			0.723981i	−0.932182	+	0.361991i	$0.882097\pi$
$464$	13.8039			0.640830
$465$		0			0
$466$	−0.962875	+	1.66775i	−0.0446043	+	0.0772569i
$467$			41.0358i			1.89891i	0.313901	+	0.949456i	$0.398364\pi$
$467$			41.0358i			1.89891i	−0.313901	+	0.949456i	$0.601636\pi$
$468$		−	13.0472i		−	0.603107i
$469$	18.3668	−	31.8122i	0.848099	−	1.46895i
$470$		0			0
$471$	−1.58846	+	2.75130i	−0.0731925	+	0.126773i
$472$	−14.1686	+	8.18025i	−0.652163	+	0.376527i
$473$	28.2417	−	16.3053i	1.29855	−	0.749721i
$474$	−0.925375			−0.0425039
$475$		0			0
$476$	−6.30121			−0.288816
$477$	11.9570	−	6.90336i	0.547472	−	0.316083i
$478$	−3.26604	+	1.88565i	−0.149385	+	0.0862475i
$479$	−11.7794	+	20.4024i	−0.538213	+	0.932211i	0.460788	+	0.887510i	$0.347567\pi$
$479$	−11.7794	+	20.4024i	−0.538213	+	0.932211i	−0.999000	+	0.0447012i	$0.985766\pi$
$480$		0			0
$481$	11.4671	−	19.8617i	0.522857	−	0.905614i
$482$		−	1.58728i		−	0.0722988i
$483$		−	25.8893i		−	1.17800i
$484$	−14.9472	+	25.8894i	−0.679420	+	1.17679i
$485$		0			0
$486$	4.93338			0.223783
$487$		−	23.9166i		−	1.08377i	−0.840454	−	0.541883i	$-0.817712\pi$
$487$		−	23.9166i		−	1.08377i	0.840454	−	0.541883i	$-0.182288\pi$
$488$	−6.45387	−	3.72614i	−0.292153	−	0.168675i
$489$	−11.5713	−	20.0421i	−0.523272	−	0.906334i
$490$		0			0
$491$	−8.17373	−	14.1573i	−0.368875	−	0.638911i	0.620515	−	0.784195i	$-0.286924\pi$
$491$	−8.17373	−	14.1573i	−0.368875	−	0.638911i	−0.989390	+	0.145284i	$0.953590\pi$
$492$	11.5517	−	6.66940i	0.520793	−	0.300680i
$493$		−	4.06343i		−	0.183007i
$494$	−2.66502	−	3.98423i	−0.119905	−	0.179259i
$495$		0			0
$496$	7.88720	+	13.6610i	0.354146	+	0.613398i
$497$	1.29375	−	0.746950i	0.0580328	−	0.0335053i
$498$	−1.52623	−	0.881169i	−0.0683920	−	0.0394861i
$499$	−16.0354	−	27.7742i	−0.717844	−	1.24334i	−0.961852	−	0.273569i	$-0.911796\pi$
$499$	−16.0354	−	27.7742i	−0.717844	−	1.24334i	0.244009	−	0.969773i	$-0.421537\pi$
$500$		0			0
$501$	10.8542			0.484930
$502$			7.90972i			0.353028i
$503$	12.7525	+	7.36269i	0.568608	+	0.328286i	0.756593	−	0.653886i	$-0.226862\pi$
$503$	12.7525	+	7.36269i	0.568608	+	0.328286i	−0.187985	+	0.982172i	$0.560196\pi$
$504$	−3.86282	+	6.69060i	−0.172064	+	0.298023i
$505$		0			0
$506$	12.3212			0.547746
$507$	0.451131	+	0.260461i	0.0200354	+	0.0115675i
$508$	5.54980	−	3.20418i	0.246232	−	0.142162i
$509$	−11.0332	+	19.1100i	−0.489037	+	0.847036i	−0.999920	−	0.0126136i	$-0.995985\pi$
$509$	−11.0332	+	19.1100i	−0.489037	+	0.847036i	0.510884	+	0.859650i	$0.329318\pi$
$510$		0			0
$511$	6.78026	+	11.7438i	0.299941	+	0.519513i
$512$			20.3111i			0.897633i
$513$	−18.4300	+	12.3277i	−0.813705	+	0.544280i
$514$	−5.73990			−0.253176
$515$		0			0
$516$	6.18399	+	10.7110i	0.272235	+	0.471525i
$517$	−17.1931	−	9.92647i	−0.756154	−	0.436565i
$518$	−5.73453	+	3.31083i	−0.251961	+	0.145470i
$519$	11.8112	−	20.4577i	0.518456	−	0.897992i
$520$		0			0
$521$	−14.7781			−0.647442			−0.323721	−	0.946153i	$-0.604934\pi$
$521$	−14.7781			−0.647442			−0.323721	+	0.946153i	$0.604934\pi$
$522$	−2.10377	−	1.21461i	−0.0920794	−	0.0531621i
$523$	−11.0072	−	6.35498i	−0.481309	−	0.277884i	0.239653	−	0.970859i	$-0.422966\pi$
$523$	−11.0072	−	6.35498i	−0.481309	−	0.277884i	−0.720962	+	0.692975i	$0.756300\pi$
$524$	4.60916			0.201352
$525$		0			0
$526$	−2.01452	+	3.48924i	−0.0878371	+	0.152138i
$527$	4.02137	−	2.32174i	0.175174	−	0.101136i
$528$	−15.8029	−	9.12378i	−0.687731	−	0.397062i
$529$	17.8647	+	30.9426i	0.776726	+	1.34533i
$530$		0			0
$531$	−26.1301			−1.13395
$532$	−1.79323	−	27.1546i	−0.0777464	−	1.17730i
$533$			24.0556i			1.04196i
$534$	−1.14197	−	1.97796i	−0.0494180	−	0.0855946i
$535$		0			0
$536$	−6.79894	+	11.7761i	−0.293670	+	0.508651i
$537$	20.7541	−	11.9824i	0.895607	−	0.517079i
$538$	0.0421638	+	0.0243433i	0.00181781	+	0.00104951i
$539$	19.4361			0.837172
$540$		0			0
$541$	15.1172	−	26.1838i	0.649941	−	1.12573i	−0.333196	−	0.942858i	$-0.608127\pi$
$541$	15.1172	−	26.1838i	0.649941	−	1.12573i	0.983137	−	0.182873i	$-0.0585396\pi$
$542$	−7.49521	−	4.32736i	−0.321947	−	0.185876i
$543$			16.4433i			0.705649i
$544$	3.52776			0.151251
$545$		0			0
$546$	1.85749	+	3.21727i	0.0794933	+	0.137686i
$547$	6.76144	+	3.90372i	0.289098	+	0.166911i	0.637535	−	0.770421i	$-0.279954\pi$
$547$	6.76144	+	3.90372i	0.289098	+	0.166911i	−0.348437	+	0.937332i	$0.613287\pi$
$548$	−18.9861	+	10.9617i	−0.811048	+	0.468259i
$549$	−5.95118	−	10.3077i	−0.253990	−	0.439924i
$550$		0			0
$551$	17.5110	−	1.15639i	0.745995	−	0.0492639i
$552$			9.58359i			0.407905i
$553$	8.20530	−	4.73733i	0.348925	−	0.201452i
$554$	−0.0815198	−	0.141196i	−0.00346345	−	0.00599886i
$555$		0			0
$556$	6.73311	+	11.6621i	0.285548	+	0.494583i
$557$	−2.09141	−	1.20747i	−0.0886157	−	0.0511623i	0.455037	−	0.890472i	$-0.349626\pi$
$557$	−2.09141	−	1.20747i	−0.0886157	−	0.0511623i	−0.543653	+	0.839310i	$0.682959\pi$
$558$		−	2.77599i		−	0.117517i
$559$	−22.3048			−0.943392
$560$		0			0
$561$	−2.68575	+	4.65186i	−0.113392	+	0.196402i
$562$		−	1.52078i		−	0.0641500i
$563$		−	25.3392i		−	1.06792i	−0.845510	−	0.533960i	$-0.820703\pi$
$563$		−	25.3392i		−	1.06792i	0.845510	−	0.533960i	$-0.179297\pi$
$564$	3.76473	−	6.52070i	0.158524	−	0.274571i
$565$		0			0
$566$	2.78109	−	4.81699i	0.116898	−	0.202473i
$567$	−1.64702	+	0.950905i	−0.0691681	+	0.0399342i
$568$	−0.478917	+	0.276503i	−0.0200949	+	0.0116018i
$569$	45.1046			1.89088			0.945441	−	0.325793i	$-0.105631\pi$
$569$	45.1046			1.89088			0.945441	+	0.325793i	$0.105631\pi$
$570$		0			0
$571$	−9.73299			−0.407313			−0.203656	−	0.979042i	$-0.565283\pi$
$571$	−9.73299			−0.407313			−0.203656	+	0.979042i	$0.565283\pi$
$572$	30.1084	−	17.3831i	1.25889	−	0.726823i
$573$	2.18149	−	1.25949i	0.0911332	−	0.0526158i
$574$	3.47270	−	6.01490i	0.144948	−	0.251057i
$575$		0			0
$576$	−5.59515	+	9.69108i	−0.233131	+	0.403795i
$577$		−	8.83145i		−	0.367658i	−0.982958	−	0.183829i	$-0.941151\pi$
$577$		−	8.83145i		−	0.367658i	0.982958	−	0.183829i	$-0.0588493\pi$
$578$			4.97192i			0.206805i
$579$	−9.80691	+	16.9861i	−0.407561	+	0.705917i
$580$		0			0
$581$	18.0441			0.748596
$582$		−	3.46823i		−	0.143763i
$583$	31.8611	+	18.3950i	1.31955	+	0.761843i
$584$	−2.50989	−	4.34726i	−0.103860	−	0.179891i
$585$		0			0
$586$	−1.12839	−	1.95442i	−0.0466132	−	0.0807365i
$587$	−23.3768	+	13.4966i	−0.964865	+	0.557065i	−0.897667	−	0.440674i	$-0.854739\pi$
$587$	−23.3768	+	13.4966i	−0.964865	+	0.557065i	−0.0671982	+	0.997740i	$0.521406\pi$
$588$			7.37137i			0.303990i
$589$	11.1498	+	16.6691i	0.459419	+	0.686837i
$590$		0			0
$591$	3.18489	+	5.51639i	0.131009	+	0.226914i
$592$	−19.2657	+	11.1230i	−0.791814	+	0.457154i
$593$	−18.3891	−	10.6170i	−0.755151	−	0.435987i	0.0724009	−	0.997376i	$-0.476934\pi$
$593$	−18.3891	−	10.6170i	−0.755151	−	0.435987i	−0.827552	+	0.561389i	$0.810267\pi$
$594$	4.08923	+	7.08276i	0.167783	+	0.290609i
$595$		0			0
$596$	−24.2650			−0.993934
$597$			7.42562i			0.303910i
$598$	−7.29832	−	4.21369i	−0.298451	−	0.172311i
$599$	−15.1647	+	26.2660i	−0.619612	+	1.07320i	0.369945	+	0.929054i	$0.379377\pi$
$599$	−15.1647	+	26.2660i	−0.619612	+	1.07320i	−0.989556	+	0.144146i	$0.953957\pi$
$600$		0			0
$601$	−10.7285			−0.437624			−0.218812	−	0.975767i	$-0.570218\pi$
$601$	−10.7285			−0.437624			−0.218812	+	0.975767i	$0.570218\pi$
$602$	5.57713	+	3.21996i	0.227307	+	0.131236i
$603$	−18.8081	+	10.8589i	−0.765926	+	0.442208i
$604$	18.6859	−	32.3649i	0.760317	−	1.31691i
$605$		0			0
$606$	0.990039	+	1.71480i	0.0402176	+	0.0696589i
$607$			8.81498i			0.357789i	0.983868	+	0.178894i	$0.0572521\pi$
$607$			8.81498i			0.357789i	−0.983868	+	0.178894i	$0.942748\pi$
$608$	1.00395	+	15.2026i	0.0407154	+	0.616548i
$609$	−13.6010			−0.551142
$610$		0			0
$611$	6.78942	+	11.7596i	0.274671	+	0.475743i
$612$	3.22631	+	1.86271i	0.130416	+	0.0752957i
$613$	−20.8978	+	12.0654i	−0.844055	+	0.487315i	−0.858640	−	0.512578i	$-0.828690\pi$
$613$	−20.8978	+	12.0654i	−0.844055	+	0.487315i	0.0145856	+	0.999894i	$0.495357\pi$
$614$	2.23691	−	3.87445i	0.0902744	−	0.156360i
$615$		0			0
$616$	−20.5861			−0.829436
$617$	13.3930	+	7.73248i	0.539183	+	0.311298i	0.744748	−	0.667346i	$-0.232570\pi$
$617$	13.3930	+	7.73248i	0.539183	+	0.311298i	−0.205564	+	0.978644i	$0.565903\pi$
$618$	5.08363	+	2.93504i	0.204494	+	0.118065i
$619$	−0.0390990			−0.00157152			−0.000785761	−	1.00000i	$-0.500250\pi$
$619$	−0.0390990			−0.00157152			−0.000785761		1.00000i	$0.500250\pi$
$620$		0			0
$621$	−19.4914	+	33.7601i	−0.782163	+	1.35475i
$622$	2.29711	−	1.32624i	0.0921057	−	0.0531772i
$623$	20.2518	+	11.6924i	0.811370	+	0.468445i
$624$	6.24041	+	10.8087i	0.249816	+	0.432694i
$625$		0			0
$626$	−6.64584			−0.265621
$627$	−20.8112	−	10.2502i	−0.831117	−	0.409353i
$628$			5.87120i			0.234286i
$629$	3.27427	+	5.67119i	0.130554	+	0.226125i
$630$		0			0
$631$	−3.36758	+	5.83282i	−0.134061	+	0.232201i	−0.925238	−	0.379386i	$-0.876135\pi$
$631$	−3.36758	+	5.83282i	−0.134061	+	0.232201i	0.791177	+	0.611587i	$0.209469\pi$
$632$	−3.03741	+	1.75365i	−0.120822	+	0.0697564i
$633$	−17.5221	−	10.1164i	−0.696442	−	0.402091i
$634$	−8.73989			−0.347105
$635$		0			0
$636$	−6.97651	+	12.0837i	−0.276637	+	0.479149i
$637$	−11.5127	−	6.64687i	−0.456150	−	0.263358i
$638$		−	6.47301i		−	0.256269i
$639$	−0.883229			−0.0349400
$640$		0			0
$641$	−13.7894	−	23.8840i	−0.544649	−	0.943360i	−0.998629	−	0.0523477i	$-0.983330\pi$
$641$	−13.7894	−	23.8840i	−0.544649	−	0.943360i	0.453980	−	0.891012i	$-0.350004\pi$
$642$	−2.42351	−	1.39921i	−0.0956483	−	0.0552226i
$643$	−10.3128	+	5.95407i	−0.406695	+	0.234806i	−0.689369	−	0.724410i	$-0.742112\pi$
$643$	−10.3128	+	5.95407i	−0.406695	+	0.234806i	0.282673	+	0.959216i	$0.408779\pi$
$644$	−23.9227	−	41.4353i	−0.942685	−	1.63278i
$645$		0			0
$646$	1.36570	−	0.0901878i	0.0537327	−	0.00354839i
$647$		−	11.6648i		−	0.458590i	−0.973357	−	0.229295i	$-0.926358\pi$
$647$		−	11.6648i		−	0.458590i	0.973357	−	0.229295i	$-0.0736421\pi$
$648$	0.609686	−	0.352002i	0.0239507	−	0.0138280i
$649$	−34.8136	−	60.2990i	−1.36656	−	2.36694i
$650$		0			0
$651$	−7.77128	−	13.4603i	−0.304581	−	0.527549i
$652$	−37.0393	−	21.3846i	−1.45057	−	0.837487i
$653$			40.7527i			1.59477i	0.603468	+	0.797387i	$0.293785\pi$
$653$			40.7527i			1.59477i	−0.603468	+	0.797387i	$0.706215\pi$
$654$	1.95335			0.0763819
$655$		0			0
$656$	11.6669	−	20.2076i	0.455514	−	0.788974i
$657$		−	8.01730i		−	0.312785i
$658$		−	3.92053i		−	0.152838i
$659$	−11.5723	+	20.0438i	−0.450793	+	0.780796i	−0.998435	−	0.0559165i	$-0.982192\pi$
$659$	−11.5723	+	20.0438i	−0.450793	+	0.780796i	0.547643	+	0.836712i	$0.315525\pi$
$660$		0			0
$661$	−2.44485	+	4.23460i	−0.0950936	+	0.164707i	−0.909648	−	0.415381i	$-0.863648\pi$
$661$	−2.44485	+	4.23460i	−0.0950936	+	0.164707i	0.814554	+	0.580088i	$0.196982\pi$
$662$	4.08789	−	2.36015i	0.158880	−	0.0917297i
$663$	3.18174	−	1.83698i	0.123568	−	0.0713423i
$664$	−6.67950			−0.259215
$665$		0			0
$666$	3.91488			0.151699
$667$	26.7201	−	15.4269i	1.03461	−	0.597331i
$668$	17.3719	−	10.0297i	0.672140	−	0.388060i
$669$	−5.83597	+	10.1082i	−0.225632	+	0.390805i
$670$		0			0
$671$	15.8578	−	27.4665i	0.612182	−	1.06033i
$672$		−	11.8081i		−	0.455506i
$673$		−	29.5149i		−	1.13771i	−0.822436	−	0.568857i	$-0.807386\pi$
$673$		−	29.5149i		−	1.13771i	0.822436	−	0.568857i	$-0.192614\pi$
$674$	−2.72232	+	4.71520i	−0.104860	+	0.181623i
$675$		0			0
$676$	0.962701			0.0370270
$677$		−	29.4248i		−	1.13089i	−0.824788	−	0.565443i	$-0.808705\pi$
$677$		−	29.4248i		−	1.13089i	0.824788	−	0.565443i	$-0.191295\pi$
$678$	2.87019	+	1.65711i	0.110229	+	0.0636408i
$679$	17.7551	+	30.7528i	0.681380	+	1.18018i
$680$		0			0
$681$	5.73457	+	9.93256i	0.219749	+	0.380616i
$682$	6.40602	−	3.69852i	0.245299	−	0.141623i
$683$		−	29.9433i		−	1.14575i	−0.819643	−	0.572875i	$-0.805828\pi$
$683$		−	29.9433i		−	1.14575i	0.819643	−	0.572875i	$-0.194172\pi$
$684$	−7.10907	+	14.4337i	−0.271822	+	0.551885i
$685$		0			0
$686$	−1.65283	−	2.86278i	−0.0631053	−	0.109302i
$687$	3.13241	−	1.80850i	0.119509	−	0.0689985i
$688$	18.7369	+	10.8177i	0.714336	+	0.412422i
$689$	−12.5816	−	21.7921i	−0.479323	−	0.830211i
$690$		0			0
$691$	−24.2225			−0.921467			−0.460733	−	0.887539i	$-0.652414\pi$
$691$	−24.2225			−0.921467			−0.460733	+	0.887539i	$0.652414\pi$
$692$		−	43.6561i		−	1.65956i
$693$	−28.4739	−	16.4394i	−1.08164	−	0.624482i
$694$	2.70177	−	4.67960i	0.102558	−	0.177635i
$695$		0			0
$696$	5.03478			0.190843
$697$	−5.94847	−	3.43435i	−0.225314	−	0.130085i
$698$	9.22959	−	5.32871i	0.349345	−	0.201695i
$699$	3.18733	−	5.52061i	0.120556	−	0.208809i
$700$		0			0
$701$	7.42695	+	12.8639i	0.280512	+	0.485861i	0.971511	−	0.236995i	$-0.0761624\pi$
$701$	7.42695	+	12.8639i	0.280512	+	0.485861i	−0.690999	+	0.722856i	$0.742829\pi$
$702$		−	5.59384i		−	0.211126i
$703$	−23.5078	+	15.7241i	−0.886613	+	0.593047i
$704$	−29.8182			−1.12381
$705$		0			0
$706$	−5.43330	−	9.41075i	−0.204485	−	0.354178i
$707$	−17.5574	−	10.1367i	−0.660313	−	0.381232i
$708$	22.8691	−	13.2035i	0.859473	−	0.496217i
$709$	−14.9004	+	25.8083i	−0.559598	+	0.969252i	0.437932	+	0.899008i	$0.355711\pi$
$709$	−14.9004	+	25.8083i	−0.559598	+	0.969252i	−0.997530	+	0.0702441i	$0.977622\pi$
$710$		0			0
$711$	−5.60165			−0.210078
$712$	−7.49672	−	4.32823i	−0.280952	−	0.162207i
$713$	30.5344	+	17.6290i	1.14352	+	0.660213i
$714$	−1.06076			−0.0396978
$715$		0			0
$716$	22.1444	−	38.3552i	0.827575	−	1.43340i
$717$	10.8113	−	6.24190i	0.403755	−	0.233108i
$718$	−0.263108	−	0.151905i	−0.00981910	−	0.00566906i
$719$	−12.9463	−	22.4236i	−0.482814	−	0.836258i	0.516991	−	0.855991i	$-0.327052\pi$
$719$	−12.9463	−	22.4236i	−0.482814	−	0.836258i	−0.999805	+	0.0197322i	$0.993719\pi$
$720$		0			0
$721$	−60.1021			−2.23832
$722$	0.777316	+	5.85972i	0.0289287	+	0.218076i
$723$			5.25426i			0.195408i
$724$	15.1942	+	26.3171i	0.564688	+	0.978069i
$725$		0			0
$726$	−2.51624	+	4.35826i	−0.0933865	+	0.161750i
$727$	8.09634	−	4.67442i	0.300277	−	0.173365i	−0.342291	−	0.939594i	$-0.611203\pi$
$727$	8.09634	−	4.67442i	0.300277	−	0.173365i	0.642567	+	0.766229i	$0.277869\pi$
$728$	12.1939	+	7.04014i	0.451935	+	0.260925i
$729$	−14.5913			−0.540419
$730$		0			0
$731$	3.18439	−	5.51553i	0.117779	−	0.203999i
$732$	10.4170	+	6.01424i	0.385022	+	0.222293i
$733$		−	7.20434i		−	0.266098i	−0.991109	−	0.133049i	$-0.957523\pi$
$733$		−	7.20434i		−	0.266098i	0.991109	−	0.133049i	$-0.0424768\pi$
$734$	−3.06950			−0.113297
$735$		0			0
$736$	13.3932	+	23.1977i	0.493680	+	0.855079i
$737$	−50.1170	−	28.9350i	−1.84608	−	1.06584i
$738$	−3.55615	+	2.05314i	−0.130904	+	0.0755773i
$739$	6.48702	+	11.2359i	0.238629	+	0.413318i	0.960321	−	0.278897i	$-0.0899687\pi$
$739$	6.48702	+	11.2359i	0.238629	+	0.413318i	−0.721692	+	0.692214i	$0.756635\pi$
$740$		0			0
$741$	8.82179	+	13.1887i	0.324077	+	0.484498i
$742$			7.26523i			0.266715i
$743$	−7.99428	+	4.61550i	−0.293282	+	0.169326i	−0.639421	−	0.768857i	$-0.720826\pi$
$743$	−7.99428	+	4.61550i	−0.293282	+	0.169326i	0.346139	+	0.938183i	$0.387492\pi$
$744$	2.87674	+	4.98267i	0.105467	+	0.182673i
$745$		0			0
$746$	2.01475	+	3.48965i	0.0737652	+	0.127765i
$747$	−9.23885	−	5.33405i	−0.338032	−	0.195163i
$748$			9.92694i			0.362965i
$749$	28.6523			1.04693
$750$		0			0
$751$	−7.46131	+	12.9234i	−0.272267	+	0.471580i	−0.969442	−	0.245321i	$-0.921107\pi$
$751$	−7.46131	+	12.9234i	−0.272267	+	0.471580i	0.697175	+	0.716901i	$0.254440\pi$
$752$		−	13.1714i		−	0.480310i
$753$		−	26.1829i		−	0.954157i
$754$	−2.21368	+	3.83420i	−0.0806174	+	0.139633i
$755$		0			0
$756$	15.8791	−	27.5035i	0.577519	−	1.00029i
$757$	21.2156	−	12.2488i	0.771093	−	0.445191i	−0.0621711	−	0.998066i	$-0.519802\pi$
$757$	21.2156	−	12.2488i	0.771093	−	0.445191i	0.833265	+	0.552874i	$0.186469\pi$
$758$	−1.40532	+	0.811365i	−0.0510437	+	0.0294701i
$759$	−40.7860			−1.48044
$760$		0			0
$761$	−15.8968			−0.576260			−0.288130	−	0.957591i	$-0.593034\pi$
$761$	−15.8968			−0.576260			−0.288130	+	0.957591i	$0.593034\pi$
$762$	0.934262	−	0.539396i	0.0338447	−	0.0195403i
$763$	−17.3203	+	9.99990i	−0.627038	+	0.362021i
$764$	2.32762	−	4.03156i	0.0842105	−	0.145857i
$765$		0			0
$766$	−5.21593	+	9.03426i	−0.188459	+	0.326421i
$767$			47.6231i			1.71957i
$768$		−	9.06916i		−	0.327255i
$769$	−14.7925	+	25.6214i	−0.533432	+	0.923931i	0.465806	+	0.884887i	$0.345765\pi$
$769$	−14.7925	+	25.6214i	−0.533432	+	0.923931i	−0.999238	+	0.0390437i	$0.987569\pi$
$770$		0			0
$771$	19.0003			0.684280
$772$			36.2478i			1.30459i
$773$	12.2378	+	7.06551i	0.440164	+	0.254129i	0.703667	−	0.710530i	$-0.251545\pi$
$773$	12.2378	+	7.06551i	0.440164	+	0.254129i	−0.263503	+	0.964658i	$0.584878\pi$
$774$	−1.90371	−	3.29733i	−0.0684276	−	0.118520i
$775$		0			0
$776$	−6.57253	−	11.3840i	−0.235940	−	0.408660i
$777$	18.9825	−	10.9596i	0.680995	−	0.393172i
$778$		−	8.63032i		−	0.309412i
$779$	13.1072	−	26.6119i	0.469615	−	0.953469i
$780$		0			0
$781$	−1.17675	−	2.03818i	−0.0421073	−	0.0729319i
$782$	2.08392	−	1.20315i	0.0745210	−	0.0430247i
$783$	17.7360	+	10.2399i	0.633833	+	0.365944i
$784$	6.44741	+	11.1672i	0.230265	+	0.398830i
$785$		0			0
$786$	0.775912			0.0276759
$787$			24.2465i			0.864293i	0.901803	+	0.432146i	$0.142244\pi$
$787$			24.2465i			0.864293i	−0.901803	+	0.432146i	$0.857756\pi$
$788$	10.1947	+	5.88591i	0.363171	+	0.209677i
$789$	6.66849	−	11.5502i	0.237404	−	0.411196i
$790$		0			0
$791$	−33.9333			−1.20653
$792$	10.5404	+	6.08549i	0.374536	+	0.216238i
$793$	−18.7863	+	10.8463i	−0.667120	+	0.385162i
$794$	−0.855456	+	1.48169i	−0.0303590	+	0.0525833i
$795$		0			0
$796$	6.86155	+	11.8846i	0.243201	+	0.421237i
$797$		−	27.9258i		−	0.989184i	−0.869125	−	0.494592i	$-0.835318\pi$
$797$		−	27.9258i		−	0.989184i	0.869125	−	0.494592i	$-0.164682\pi$
$798$	−0.301875	−	4.57125i	−0.0106863	−	0.161820i
$799$	−3.87723			−0.137166
$800$		0			0
$801$	−6.91280	−	11.9733i	−0.244252	−	0.423057i
$802$	2.29366	+	1.32425i	0.0809919	+	0.0467607i
$803$	18.5011	−	10.6816i	0.652890	−	0.376946i
$804$	10.9739	−	19.0074i	0.387021	−	0.670341i
$805$		0			0
$806$	−5.05936			−0.178208
$807$	−0.139571	−	0.0805816i	−0.00491315	−	0.00283661i
$808$	6.49932	+	3.75238i	0.228645	+	0.132008i
$809$	−8.78914			−0.309010			−0.154505	−	0.987992i	$-0.549378\pi$
$809$	−8.78914			−0.309010			−0.154505	+	0.987992i	$0.549378\pi$
$810$		0			0
$811$	7.04963	−	12.2103i	0.247546	−	0.428762i	−0.715298	−	0.698819i	$-0.753709\pi$
$811$	7.04963	−	12.2103i	0.247546	−	0.428762i	0.962844	+	0.270057i	$0.0870425\pi$
$812$	−21.7682	+	12.5679i	−0.763914	+	0.441046i
$813$	24.8108	+	14.3245i	0.870152	+	0.502383i
$814$	5.21589	+	9.03418i	0.182817	+	0.316648i
$815$		0			0
$816$	−3.56370			−0.124755
$817$	24.6750	+	12.1533i	0.863269	+	0.425189i
$818$			6.67967i			0.233549i
$819$	11.2441	+	19.4754i	0.392901	+	0.680524i
$820$		0			0
$821$	15.2663	−	26.4420i	0.532797	−	0.922832i	−0.466469	−	0.884537i	$-0.654474\pi$
$821$	15.2663	−	26.4420i	0.532797	−	0.922832i	0.999267	−	0.0382943i	$-0.0121924\pi$
$822$	−3.19616	+	1.84530i	−0.111479	+	0.0643623i
$823$	−12.4346	−	7.17914i	−0.433444	−	0.250249i	0.267369	−	0.963594i	$-0.413846\pi$
$823$	−12.4346	−	7.17914i	−0.433444	−	0.250249i	−0.700813	+	0.713345i	$0.747179\pi$
$824$	22.2484			0.775059
$825$		0			0
$826$	6.87495	−	11.9078i	0.239210	−	0.414324i
$827$	7.16518	+	4.13682i	0.249158	+	0.143851i	0.619379	−	0.785092i	$-0.287385\pi$
$827$	7.16518	+	4.13682i	0.249158	+	0.143851i	−0.370221	+	0.928944i	$0.620718\pi$
$828$			28.2873i			0.983052i
$829$	−13.1498			−0.456710			−0.228355	−	0.973578i	$-0.573335\pi$
$829$	−13.1498			−0.456710			−0.228355	+	0.973578i	$0.573335\pi$
$830$		0			0
$831$	0.269848	+	0.467391i	0.00936094	+	0.0162136i
$832$	17.6624	+	10.1974i	0.612333	+	0.353531i
$833$	3.28728	−	1.89791i	0.113897	−	0.0657587i
$834$	1.13346	+	1.96322i	0.0392486	+	0.0679806i
$835$		0			0
$836$	−42.7794	+	2.82506i	−1.47956	+	0.0977067i
$837$			23.4032i			0.808934i
$838$	1.37240	−	0.792358i	0.0474089	−	0.0273715i
$839$	−4.20767	−	7.28790i	−0.145265	−	0.251606i	0.784207	−	0.620500i	$-0.213070\pi$
$839$	−4.20767	−	7.28790i	−0.145265	−	0.251606i	−0.929472	+	0.368893i	$0.879737\pi$
$840$		0			0
$841$	6.39543	+	11.0772i	0.220532	+	0.381973i
$842$	−1.52448	−	0.880159i	−0.0525371	−	0.0303323i
$843$			5.03410i			0.173384i
$844$	−37.3918			−1.28708
$845$		0			0
$846$	−1.15895	+	2.00737i	−0.0398457	+	0.0690147i
$847$		−	51.5262i		−	1.77046i
$848$			24.4082i			0.838181i
$849$	−9.20601	+	15.9453i	−0.315950	+	0.547241i
$850$		0			0
$851$	−24.8616	+	43.0616i	−0.852245	+	1.47613i
$852$	0.773005	−	0.446294i	0.0264827	−	0.0152898i
$853$	−45.0648	+	26.0182i	−1.54299	+	0.890845i	−0.544340	+	0.838865i	$0.683220\pi$
$853$	−45.0648	+	26.0182i	−1.54299	+	0.890845i	−0.998648	+	0.0519802i	$0.983447\pi$
$854$	6.26314			0.214320
$855$		0			0
$856$	−10.6064			−0.362520
$857$	−18.5845	+	10.7298i	−0.634834	+	0.366522i	−0.782622	−	0.622497i	$-0.786118\pi$
$857$	−18.5845	+	10.7298i	−0.634834	+	0.366522i	0.147788	+	0.989019i	$0.452785\pi$
$858$	5.06849	−	2.92629i	0.173035	−	0.0999020i
$859$	9.07396	−	15.7166i	0.309599	−	0.536242i	−0.668675	−	0.743554i	$-0.733138\pi$
$859$	9.07396	−	15.7166i	0.309599	−	0.536242i	0.978275	+	0.207313i	$0.0664717\pi$
$860$		0			0
$861$	−11.4954	+	19.9106i	−0.391762	+	0.678552i
$862$		−	11.9362i		−	0.406549i
$863$			13.7867i			0.469303i	0.972080	+	0.234652i	$0.0753949\pi$
$863$			13.7867i			0.469303i	−0.972080	+	0.234652i	$0.924605\pi$
$864$	−8.89000	+	15.3979i	−0.302444	+	0.523848i
$865$		0			0
$866$	2.16609			0.0736066
$867$		−	16.4581i		−	0.558948i
$868$	−24.8756	−	14.3619i	−0.844332	−	0.487475i
$869$	−7.46320	−	12.9266i	−0.253172	−	0.438506i
$870$		0			0
$871$	19.7907	+	34.2786i	0.670584	+	1.16148i
$872$	6.41158	−	3.70173i	0.217123	−	0.125356i
$873$		−	20.9945i		−	0.710557i
$874$	5.77796	+	8.63812i	0.195442	+	0.292189i
$875$		0			0
$876$	4.05113	+	7.01676i	0.136875	+	0.237075i
$877$	−18.3543	+	10.5968i	−0.619780	+	0.357830i	−0.776783	−	0.629768i	$-0.783150\pi$
$877$	−18.3543	+	10.5968i	−0.619780	+	0.357830i	0.157003	+	0.987598i	$0.449817\pi$
$878$	2.56681	+	1.48195i	0.0866257	+	0.0500134i
$879$	3.73521	+	6.46957i	0.125985	+	0.218213i
$880$		0			0
$881$	44.5944			1.50242			0.751212	−	0.660061i	$-0.229469\pi$
$881$	44.5944			1.50242			0.751212	+	0.660061i	$0.229469\pi$
$882$		−	2.26924i		−	0.0764093i
$883$	1.46665	+	0.846773i	0.0493568	+	0.0284962i	0.524475	−	0.851426i	$-0.324261\pi$
$883$	1.46665	+	0.846773i	0.0493568	+	0.0284962i	−0.475119	+	0.879922i	$0.657595\pi$
$884$	3.39487	−	5.88009i	0.114182	−	0.197769i
$885$		0			0
$886$	10.7966			0.362720
$887$	−41.9463	−	24.2177i	−1.40842	−	0.813151i	−0.413183	−	0.910648i	$-0.635583\pi$
$887$	−41.9463	−	24.2177i	−1.40842	−	0.813151i	−0.995236	+	0.0974969i	$0.968916\pi$
$888$	−7.02688	+	4.05697i	−0.235807	+	0.136143i
$889$	−5.52273	+	9.56565i	−0.185227	+	0.320822i
$890$		0			0
$891$	1.49806	+	2.59471i	0.0501868	+	0.0869260i
$892$			21.5706i			0.722238i
$893$	−1.10340	−	16.7086i	−0.0369239	−	0.559133i
$894$	−4.08481			−0.136617
$895$		0			0
$896$	−14.4102	−	24.9592i	−0.481411	−	0.833828i
$897$	24.1590	+	13.9482i	0.806647	+	0.465718i
$898$	2.38235	−	1.37545i	0.0795001	−	0.0458994i
$899$	9.26149	−	16.0414i	0.308888	−	0.535009i
$900$		0			0
$901$	7.18499			0.239367
$902$	−9.47588	−	5.47090i	−0.315512	−	0.182161i
$903$	−18.4615	−	10.6588i	−0.614360	−	0.354701i
$904$	12.5613			0.417783
$905$		0			0
$906$	3.14561	−	5.44835i	0.104506	−	0.181009i
$907$	24.1957	−	13.9694i	0.803404	−	0.463846i	−0.0412557	−	0.999149i	$-0.513136\pi$
$907$	24.1957	−	13.9694i	0.803404	−	0.463846i	0.844660	+	0.535303i	$0.179803\pi$
$908$	18.3561	+	10.5979i	0.609169	+	0.351704i
$909$	5.99309	+	10.3803i	0.198778	+	0.344294i
$910$		0			0
$911$	45.0862			1.49377			0.746887	−	0.664951i	$-0.231548\pi$
$911$	45.0862			1.49377			0.746887	+	0.664951i	$0.231548\pi$
$912$	−1.01418	−	15.3575i	−0.0335828	−	0.508538i
$913$		−	28.4267i		−	0.940787i
$914$	0.103443	+	0.179169i	0.00342159	+	0.00592637i
$915$		0			0
$916$	3.34224	−	5.78893i	0.110431	−	0.191272i
$917$	−6.88002	+	3.97218i	−0.227198	+	0.131173i
$918$	1.38325	+	0.798617i	0.0456539	+	0.0263583i
$919$	5.86849			0.193584			0.0967918	−	0.995305i	$-0.469142\pi$
$919$	5.86849			0.193584			0.0967918	+	0.995305i	$0.469142\pi$
$920$		0			0
$921$	−7.40467	+	12.8253i	−0.243992	+	0.422607i
$922$	10.6529	+	6.15048i	0.350836	+	0.202555i
$923$			1.60972i			0.0529846i
$924$	33.2273			1.09310
$925$		0			0
$926$	2.42325	+	4.19720i	0.0796330	+	0.137928i
$927$	30.7732	+	17.7669i	1.01072	+	0.583542i
$928$	12.1870	−	7.03617i	0.400058	−	0.230974i
$929$	23.3157	+	40.3839i	0.764963	+	1.32495i	0.940266	+	0.340440i	$0.110576\pi$
$929$	23.3157	+	40.3839i	0.764963	+	1.32495i	−0.175304	+	0.984514i	$0.556091\pi$
$930$		0			0
$931$	9.11442	+	13.6262i	0.298713	+	0.446579i
$932$		−	11.7808i		−	0.385894i
$933$	−7.60393	+	4.39013i	−0.248942	+	0.143726i
$934$	6.38328	+	11.0562i	0.208867	+	0.361769i
$935$		0			0
$936$	−4.16230	−	7.20931i	−0.136049	−	0.235644i
$937$	44.4219	+	25.6470i	1.45120	+	0.837850i	0.998550	−	0.0538383i	$-0.0171456\pi$
$937$	44.4219	+	25.6470i	1.45120	+	0.837850i	0.452649	+	0.891689i	$0.350479\pi$
$938$		−	11.4281i		−	0.373140i
$939$	21.9992			0.717916
$940$		0			0
$941$	5.67430	−	9.82817i	0.184977	−	0.320389i	−0.758592	−	0.651566i	$-0.774112\pi$
$941$	5.67430	−	9.82817i	0.184977	−	0.320389i	0.943569	+	0.331177i	$0.107446\pi$
$942$			0.988367i			0.0322027i
$943$		−	52.1543i		−	1.69838i
$944$	23.0970	−	40.0052i	0.751743	−	1.30206i
$945$		0			0
$946$	5.07272	−	8.78621i	0.164928	−	0.285664i
$947$	−6.24348	+	3.60467i	−0.202886	+	0.117136i	−0.598001	−	0.801495i	$-0.704038\pi$
$947$	−6.24348	+	3.60467i	−0.202886	+	0.117136i	0.395115	+	0.918632i	$0.370705\pi$
$948$	4.90258	−	2.83051i	0.159228	−	0.0919305i
$949$	−14.6119			−0.474321
$950$		0			0
$951$	28.9309			0.938150
$952$	−3.48177	+	2.01020i	−0.112845	+	0.0651511i
$953$	−17.7877	+	10.2697i	−0.576199	+	0.332669i	−0.759622	−	0.650365i	$-0.774616\pi$
$953$	−17.7877	+	10.2697i	−0.576199	+	0.332669i	0.183422	+	0.983034i	$0.441282\pi$
$954$	2.14769	−	3.71991i	0.0695340	−	0.120436i
$955$		0			0
$956$	11.5355	−	19.9801i	0.373085	−	0.646202i
$957$			21.4271i			0.692639i
$958$			7.32930i			0.236799i
$959$	18.8935	−	32.7246i	0.610104	−	1.05673i
$960$		0			0
$961$	−9.83289			−0.317190
$962$		−	7.13504i		−	0.230043i
$963$	−14.6704	−	8.46998i	−0.472748	−	0.272941i
$964$	4.85513	+	8.40933i	0.156373	+	0.270846i
$965$		0			0
$966$	−4.02718	−	6.97528i	−0.129572	−	0.224426i
$967$	−14.7804	+	8.53345i	−0.475305	+	0.274417i	−0.718458	−	0.695571i	$-0.755152\pi$
$967$	−14.7804	+	8.53345i	−0.475305	+	0.274417i	0.243153	+	0.969988i	$0.421818\pi$
$968$			19.0738i			0.613055i
$969$	−4.52076	+	0.298541i	−0.145228	+	0.00959053i
$970$		0			0
$971$	1.74085	+	3.01525i	0.0558667	+	0.0967639i	0.892606	−	0.450837i	$-0.148874\pi$
$971$	1.74085	+	3.01525i	0.0558667	+	0.0967639i	−0.836740	+	0.547601i	$0.815541\pi$
$972$	−26.1368	+	15.0901i	−0.838337	+	0.484014i
$973$	−20.1008	−	11.6052i	−0.644403	−	0.372046i
$974$	−3.72032	−	6.44379i	−0.119207	−	0.206472i
$975$		0			0
$976$	21.0416			0.673524
$977$			21.9600i			0.702562i	0.936270	+	0.351281i	$0.114254\pi$
$977$			21.9600i			0.702562i	−0.936270	+	0.351281i	$0.885746\pi$
$978$	−6.23524	−	3.59992i	−0.199381	−	0.115113i
$979$	18.4202	−	31.9047i	0.588711	−	1.01968i
$980$		0			0
$981$	11.8244			0.377523
$982$	−4.40445	−	2.54291i	−0.140552	−	0.0811476i
$983$	4.76057	−	2.74852i	0.151839	−	0.0876641i	−0.422156	−	0.906523i	$-0.638726\pi$
$983$	4.76057	−	2.74852i	0.151839	−	0.0876641i	0.573994	+	0.818859i	$0.305393\pi$
$984$	4.25533	−	7.37044i	0.135655	−	0.234961i
$985$		0			0
$986$	−0.632082	−	1.09480i	−0.0201296	−	0.0348655i
$987$			12.9778i			0.413088i
$988$	26.3059	+	12.9566i	0.836903	+	0.412203i
$989$	48.3584			1.53771
$990$		0			0
$991$	14.7485	+	25.5452i	0.468502	+	0.811469i	0.999352	−	0.0359970i	$-0.0114607\pi$
$991$	14.7485	+	25.5452i	0.468502	+	0.811469i	−0.530850	+	0.847466i	$0.678127\pi$
$992$	13.9267	+	8.04058i	0.442173	+	0.255289i
$993$	−13.5318	+	7.81259i	−0.429419	+	0.247925i
$994$	0.232382	−	0.402497i	0.00737071	−	0.0127664i
$995$		0			0
$996$	10.7812			0.341614
$997$	6.29123	+	3.63224i	0.199245	+	0.115034i	0.596303	−	0.802759i	$-0.296636\pi$
$997$	6.29123	+	3.63224i	0.199245	+	0.115034i	−0.397058	+	0.917793i	$0.629969\pi$
$998$	−8.64076	−	4.98874i	−0.273518	−	0.157916i
$999$	−33.0048			−1.04422

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	475.2.j.d.349.7		24
5.2	odd	4		475.2.e.h.26.4	yes	12
5.3	odd	4		475.2.e.f.26.3	✓	12
5.4	even	2	inner	475.2.j.d.349.6		24
19.11	even	3	inner	475.2.j.d.49.6		24
95.7	odd	12		9025.2.a.br.1.3		6
95.12	even	12		9025.2.a.by.1.4		6
95.49	even	6	inner	475.2.j.d.49.7		24
95.68	odd	12		475.2.e.f.201.3	yes	12
95.83	odd	12		9025.2.a.bz.1.4		6
95.87	odd	12		475.2.e.h.201.4	yes	12
95.88	even	12		9025.2.a.bs.1.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
475.2.e.f.26.3	✓	12	5.3	odd	4
475.2.e.f.201.3	yes	12	95.68	odd	12
475.2.e.h.26.4	yes	12	5.2	odd	4
475.2.e.h.201.4	yes	12	95.87	odd	12
475.2.j.d.49.6		24	19.11	even	3	inner
475.2.j.d.49.7		24	95.49	even	6	inner
475.2.j.d.349.6		24	5.4	even	2	inner
475.2.j.d.349.7		24	1.1	even	1	trivial
9025.2.a.br.1.3		6	95.7	odd	12
9025.2.a.bs.1.3		6	95.88	even	12
9025.2.a.by.1.4		6	95.12	even	12
9025.2.a.bz.1.4		6	95.83	odd	12

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:	\( N \)	\(=\)	\( 475 = 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	475.j (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.269427 - 0.155554i) q^{2} +(-0.891863 + 0.514917i) q^{3} +(-0.951606 + 1.64823i) q^{4} +(-0.160195 + 0.277466i) q^{6} -3.28038i q^{7} +1.21432i q^{8} +(-0.969720 + 1.67960i) q^{9} +O(q^{10})\)	\(q+(0.269427 - 0.155554i) q^{2} +(-0.891863 + 0.514917i) q^{3} +(-0.951606 + 1.64823i) q^{4} +(-0.160195 + 0.277466i) q^{6} -3.28038i q^{7} +1.21432i q^{8} +(-0.969720 + 1.67960i) q^{9} -5.16792 q^{11} -1.95999i q^{12} +(3.06115 + 1.76735i) q^{13} +(-0.510276 - 0.883825i) q^{14} +(-1.71432 - 2.96929i) q^{16} +(-0.874064 + 0.504641i) q^{17} +0.603375i q^{18} +(-2.42346 - 3.62310i) q^{19} +(1.68913 + 2.92565i) q^{21} +(-1.39238 + 0.803890i) q^{22} +(-6.63680 - 3.83176i) q^{23} +(-0.625274 - 1.08301i) q^{24} +1.09968 q^{26} -5.08681i q^{27} +(5.40683 + 3.12163i) q^{28} +(-2.01303 + 3.48667i) q^{29} -4.60077 q^{31} +(-3.02703 - 1.74766i) q^{32} +(4.60908 - 2.66105i) q^{33} +(-0.156998 + 0.271928i) q^{34} +(-1.84558 - 3.19664i) q^{36} -6.48831i q^{37} +(-1.21653 - 0.599183i) q^{38} -3.64017 q^{39} +(3.40277 + 5.89377i) q^{41} +(0.910193 + 0.525500i) q^{42} +(-5.46481 + 3.15511i) q^{43} +(4.91782 - 8.51792i) q^{44} -2.38418 q^{46} +(3.32690 + 1.92079i) q^{47} +(3.05788 + 1.76547i) q^{48} -3.76091 q^{49} +(0.519697 - 0.900141i) q^{51} +(-5.82601 + 3.36365i) q^{52} +(-6.16516 - 3.55946i) q^{53} +(-0.791273 - 1.37052i) q^{54} +3.98343 q^{56} +(4.02699 + 1.98343i) q^{57} +1.25254i q^{58} +(6.73649 + 11.6679i) q^{59} +(-3.06850 + 5.31480i) q^{61} +(-1.23957 + 0.715668i) q^{62} +(5.50975 + 3.18105i) q^{63} +5.76986 q^{64} +(0.827874 - 1.43392i) q^{66} +(9.69770 + 5.59897i) q^{67} -1.92088i q^{68} +7.89215 q^{69} +(0.227702 + 0.394391i) q^{71} +(-2.03958 - 1.17755i) q^{72} +(-3.57999 + 2.06691i) q^{73} +(-1.00928 - 1.74813i) q^{74} +(8.27788 - 0.546653i) q^{76} +16.9528i q^{77} +(-0.980760 + 0.566242i) q^{78} +(1.44414 + 2.50132i) q^{79} +(-0.289876 - 0.502080i) q^{81} +(1.83360 + 1.05863i) q^{82} +5.50061i q^{83} -6.42953 q^{84} +(-0.981579 + 1.70014i) q^{86} -4.14617i q^{87} -6.27551i q^{88} +(-3.56433 + 6.17360i) q^{89} +(5.79760 - 10.0417i) q^{91} +(12.6312 - 7.29264i) q^{92} +(4.10326 - 2.36902i) q^{93} +1.19514 q^{94} +3.59960 q^{96} +(-9.37476 + 5.41252i) q^{97} +(-1.01329 + 0.585025i) q^{98} +(5.01144 - 8.68006i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{4} + 2 q^{6} + 14 q^{9}+O(q^{10}) \) 24 * q + 4 * q^4 + 2 * q^6 + 14 * q^9	\( 24 q + 4 q^{4} + 2 q^{6} + 14 q^{9} - 4 q^{11} - 12 q^{14} + 12 q^{16} + 12 q^{19} - 6 q^{21} + 22 q^{24} + 76 q^{26} + 6 q^{29} - 12 q^{31} - 2 q^{34} - 26 q^{36} - 32 q^{39} - 22 q^{41} + 42 q^{44} - 48 q^{46} - 16 q^{49} + 34 q^{51} + 36 q^{54} + 16 q^{56} + 8 q^{59} - 50 q^{61} + 88 q^{64} - 68 q^{66} - 52 q^{69} - 36 q^{71} - 12 q^{74} + 48 q^{76} + 6 q^{79} - 4 q^{81} - 148 q^{84} - 18 q^{86} + 24 q^{89} + 22 q^{91} - 32 q^{94} - 52 q^{96} - 40 q^{99}+O(q^{100}) \) 24 * q + 4 * q^4 + 2 * q^6 + 14 * q^9 - 4 * q^11 - 12 * q^14 + 12 * q^16 + 12 * q^19 - 6 * q^21 + 22 * q^24 + 76 * q^26 + 6 * q^29 - 12 * q^31 - 2 * q^34 - 26 * q^36 - 32 * q^39 - 22 * q^41 + 42 * q^44 - 48 * q^46 - 16 * q^49 + 34 * q^51 + 36 * q^54 + 16 * q^56 + 8 * q^59 - 50 * q^61 + 88 * q^64 - 68 * q^66 - 52 * q^69 - 36 * q^71 - 12 * q^74 + 48 * q^76 + 6 * q^79 - 4 * q^81 - 148 * q^84 - 18 * q^86 + 24 * q^89 + 22 * q^91 - 32 * q^94 - 52 * q^96 - 40 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more