LMFDB - Embedded newform 475.2.j.d.49.7

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			49.7
Character	$\chi$	$=$	475.49
Dual form			475.2.j.d.349.7

$q$-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} -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} - 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}+ \cdots - 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

Character values

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

$n$	$77$	$401$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$

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	0.592223	−	0.805774i	$-0.298250\pi$
$2$	0.269427	+	0.155554i	0.190514	+	0.109993i	−0.401709	+	0.915767i	$0.631584\pi$
$3$	−0.891863	−	0.514917i	−0.514917	−	0.297288i	0.219935	−	0.975514i	$-0.429415\pi$
$3$	−0.891863	−	0.514917i	−0.514917	−	0.297288i	−0.734853	+	0.678227i	$0.762749\pi$
$4$	−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	$0.212841\pi$
$7$			3.28038i			1.23987i	−0.784654	+	0.619934i	$0.787159\pi$
$8$		−	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	−0.0113069	−	0.999936i	$-0.503599\pi$
$13$	3.06115	−	1.76735i	0.849010	−	0.490176i	0.860317	+	0.509760i	$0.170266\pi$
$14$	−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	0.390245	−	0.920711i	$-0.372390\pi$
$17$	−0.874064	−	0.504641i	−0.211992	−	0.122393i	−0.602237	+	0.798318i	$0.705724\pi$
$18$		−	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	−0.992615	−	0.121307i	$-0.961291\pi$
$23$	−6.63680	+	3.83176i	−1.38387	+	0.798976i	−0.391253	+	0.920283i	$0.627958\pi$
$24$	−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	0.616338	−	0.787482i	$-0.288615\pi$
$29$	−2.01303	−	3.48667i	−0.373810	−	0.647458i	−0.990148	+	0.140024i	$0.955282\pi$
$30$		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	$0.179062\pi$
$37$			6.48831i			1.06667i	−0.845904	+	0.533336i	$0.820938\pi$
$38$	−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	−0.467904	−	0.883779i	$-0.654991\pi$
$41$	3.40277	−	5.89377i	0.531423	−	0.920451i	0.999327	−	0.0366724i	$-0.0116758\pi$
$42$	0.910193	−	0.525500i	0.140446	−	0.0810865i
$43$	−5.46481	−	3.15511i	−0.833376	−	0.481150i	0.0216315	−	0.999766i	$-0.493114\pi$
$43$	−5.46481	−	3.15511i	−0.833376	−	0.481150i	−0.855007	+	0.518616i	$0.826447\pi$
$44$	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	−0.237335	−	0.971428i	$-0.576274\pi$
$47$	3.32690	−	1.92079i	0.485278	−	0.280175i	0.722613	+	0.691252i	$0.242941\pi$
$48$	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	−0.859587	−	0.510990i	$-0.829279\pi$
$53$	−6.16516	+	3.55946i	−0.846850	+	0.488929i	0.0127367	+	0.999919i	$0.495946\pi$
$54$	−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	0.0224174	−	0.999749i	$-0.492864\pi$
$59$	6.73649	−	11.6679i	0.877016	−	1.51904i	0.854599	−	0.519288i	$-0.173803\pi$
$60$		0			0
$61$	−3.06850	−	5.31480i	−0.392881	−	0.680491i	0.599947	−	0.800040i	$-0.295188\pi$
$61$	−3.06850	−	5.31480i	−0.392881	−	0.680491i	−0.992828	+	0.119549i	$0.961855\pi$
$62$	−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	0.227652	−	0.973743i	$-0.426895\pi$
$67$	9.69770	−	5.59897i	1.18476	−	0.684023i	0.957112	+	0.289719i	$0.0935620\pi$
$68$			1.92088i			0.232941i
$69$	7.89215			0.950103
$70$		0			0
$71$	0.227702	−	0.394391i	0.0270233	−	0.0468056i	−0.852198	−	0.523220i	$-0.824731\pi$
$71$	0.227702	−	0.394391i	0.0270233	−	0.0468056i	0.879221	+	0.476415i	$0.158064\pi$
$72$	−2.03958	+	1.17755i	−0.240367	+	0.138776i
$73$	−3.57999	−	2.06691i	−0.419007	−	0.241914i	0.275646	−	0.961259i	$-0.411108\pi$
$73$	−3.57999	−	2.06691i	−0.419007	−	0.241914i	−0.694652	+	0.719346i	$0.744442\pi$
$74$	−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	−0.773278	−	0.634067i	$-0.781385\pi$
$79$	1.44414	−	2.50132i	0.162478	−	0.281421i	0.935757	+	0.352646i	$0.114718\pi$
$80$		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	$-0.902384\pi$
$83$		−	5.50061i		−	0.603770i	0.953344	−	0.301885i	$-0.0976159\pi$
$84$	−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	0.612926	−	0.790140i	$-0.289992\pi$
$89$	−3.56433	−	6.17360i	−0.377818	−	0.654400i	−0.990745	+	0.135740i	$0.956659\pi$
$90$		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	−0.0582034	−	0.998305i	$-0.518537\pi$
$97$	−9.37476	−	5.41252i	−0.951862	−	0.549558i	−0.893659	+	0.448747i	$0.851871\pi$
$98$	−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	0.977810	−	0.209494i	$-0.0671818\pi$
$101$	3.09011	+	5.35223i	0.307478	+	0.532567i	−0.670332	+	0.742061i	$0.733848\pi$
$102$			0.323363i			0.0320177i
$103$			18.3217i			1.80529i	0.430387	+	0.902644i	$0.358377\pi$
$103$			18.3217i			1.80529i	−0.430387	+	0.902644i	$0.641623\pi$
$104$	−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	$-0.861260\pi$
$107$		−	8.73445i		−	0.844391i	0.906505	−	0.422196i	$-0.138740\pi$
$108$	8.38423	−	4.84064i	0.806773	−	0.465790i
$109$	−3.04839	+	5.27997i	−0.291983	+	0.505730i	−0.974279	−	0.225347i	$-0.927648\pi$
$109$	−3.04839	+	5.27997i	−0.291983	+	0.505730i	0.682295	+	0.731077i	$0.260982\pi$
$110$		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	$0.161747\pi$
$113$			10.3443i			0.973111i	−0.873650	+	0.486556i	$0.838253\pi$
$114$	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	−0.623766	−	0.781611i	$-0.714398\pi$
$127$	−2.91602	+	1.68356i	−0.258755	+	0.149392i	0.365012	+	0.931003i	$0.381065\pi$
$128$	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	−0.914063	−	0.405572i	$-0.867072\pi$
$131$	−1.21089	+	2.09732i	−0.105796	+	0.183244i	0.808267	+	0.588816i	$0.200406\pi$
$132$		−	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	−0.00913057	−	0.999958i	$-0.502906\pi$
$137$	9.97584	−	5.75955i	0.852293	−	0.492072i	0.861424	+	0.507886i	$0.169573\pi$
$138$	2.12636	+	1.22765i	0.181008	+	0.104505i
$139$	3.53776	+	6.12759i	0.300069	+	0.519735i	0.976151	−	0.217091i	$-0.0696569\pi$
$139$	3.53776	+	6.12759i	0.300069	+	0.519735i	−0.676082	+	0.736826i	$0.736324\pi$
$140$		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	−0.477425	−	0.878673i	$-0.658430\pi$
$149$	6.37476	−	11.0414i	0.522240	−	0.904547i	0.999665	−	0.0258744i	$-0.00823700\pi$
$150$		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	0.602805	−	0.797888i	$-0.294050\pi$
$157$	2.67159	+	1.54244i	0.213216	+	0.123101i	−0.389589	+	0.920989i	$0.627383\pi$
$158$	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	$-0.657491\pi$
$163$		−	22.4721i		−	1.76015i	0.474831	−	0.880077i	$-0.342509\pi$
$164$	−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	−0.809698	−	0.586847i	$-0.800369\pi$
$167$	−9.12769	+	5.26987i	−0.706322	+	0.407795i	0.103376	+	0.994642i	$0.467036\pi$
$168$	−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	−0.999928	−	0.0120281i	$-0.996171\pi$
$173$	−19.8650	−	11.4691i	−1.51031	−	0.871977i	−0.510380	−	0.859949i	$-0.670495\pi$
$174$	−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	0.993770	+	0.111453i	$0.0355503\pi$
$181$	7.98346	+	13.8278i	0.593406	+	1.02781i	−0.400364	+	0.916356i	$0.631116\pi$
$182$			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	0.957683	−	0.287824i	$-0.0929317\pi$
$193$	16.4940	+	9.52280i	1.18726	+	0.685466i	0.229579	+	0.973290i	$0.426265\pi$
$194$	−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	$0.0707167\pi$
$197$			6.18524i			0.440680i	−0.975423	+	0.220340i	$0.929283\pi$
$198$			3.11819i			0.221600i
$199$	3.60525	+	6.24447i	0.255569	+	0.442659i	0.965050	−	0.262066i	$-0.0844038\pi$
$199$	3.60525	+	6.24447i	0.255569	+	0.442659i	−0.709481	+	0.704725i	$0.751070\pi$
$200$		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	−0.299831	−	0.953992i	$-0.596930\pi$
$211$	9.82333	−	17.0145i	0.676266	−	1.17133i	0.976097	−	0.217335i	$-0.0697362\pi$
$212$	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	0.791242	−	0.611504i	$-0.209435\pi$
$223$	9.81536	+	5.66690i	0.657285	+	0.379484i	−0.133957	+	0.990987i	$0.542768\pi$
$224$	−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	$0.120502\pi$
$227$			11.1369i			0.739180i	−0.929195	+	0.369590i	$0.879498\pi$
$228$	−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	0.314020	−	0.949417i	$-0.398324\pi$
$233$	−5.36068	−	3.09499i	−0.351190	−	0.202759i	−0.665209	+	0.746657i	$0.731658\pi$
$234$	−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	0.936416	−	0.350893i	$-0.114122\pi$
$241$	2.55102	+	4.41849i	0.164326	+	0.284620i	−0.772090	+	0.635513i	$0.780789\pi$
$242$	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	−0.918042	−	0.396483i	$-0.870231\pi$
$251$	−12.7122	−	22.0181i	−0.802385	−	1.38977i	0.115657	−	0.993289i	$-0.463103\pi$
$252$	−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	−0.907265	−	0.420559i	$-0.861834\pi$
$257$	−15.9781	+	9.22493i	−0.996684	+	0.575436i	−0.0894183	+	0.995994i	$0.528501\pi$
$258$			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	0.112624	−	0.993638i	$-0.464075\pi$
$263$	−11.2155	−	6.47530i	−0.691580	−	0.399284i	−0.804204	+	0.594354i	$0.797408\pi$
$264$	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	−0.863630	−	0.504126i	$-0.831815\pi$
$269$	0.0782471	−	0.135528i	0.00477081	−	0.00826329i	0.868401	+	0.495863i	$0.165148\pi$
$270$		0			0
$271$	−13.9095	+	24.0920i	−0.844944	+	1.46349i	0.0407264	+	0.999170i	$0.487033\pi$
$271$	−13.9095	+	24.0920i	−0.844944	+	1.46349i	−0.885670	+	0.464315i	$0.846301\pi$
$272$	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	$0.00501165\pi$
$277$			0.524062i			0.0314878i	−0.999876	+	0.0157439i	$0.994988\pi$
$278$			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	0.929673	−	0.368386i	$-0.120090\pi$
$281$	2.44413	+	4.23336i	0.145804	+	0.252541i	−0.783868	+	0.620927i	$0.786756\pi$
$282$	−1.06590	−	0.615400i	−0.0634736	−	0.0366465i
$283$	15.4833	+	8.93931i	0.920389	+	0.531387i	0.883759	−	0.467942i	$-0.155004\pi$
$283$	15.4833	+	8.93931i	0.920389	+	0.531387i	0.0366299	+	0.999329i	$0.488338\pi$
$284$	−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	$0.0679623\pi$
$293$			7.25399i			0.423783i	−0.977293	+	0.211891i	$0.932038\pi$
$294$	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	0.811346	−	0.584566i	$-0.198735\pi$
$307$	12.4537	+	7.19015i	0.710771	+	0.410364i	−0.100576	+	0.994929i	$0.532068\pi$
$308$	−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	−0.921436	−	0.388530i	$-0.872983\pi$
$313$	−18.4999	+	10.6809i	−1.04568	+	0.603722i	−0.124241	+	0.992252i	$0.539650\pi$
$314$	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	−0.990474	−	0.137702i	$-0.956028\pi$
$317$	−24.3291	+	14.0464i	−1.36646	+	0.788924i	−0.375983	+	0.926626i	$0.622695\pi$
$318$	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	0.0267383	−	0.999642i	$-0.491488\pi$
$337$	−15.1562	−	8.75041i	−0.825608	−	0.476665i	−0.852347	+	0.522977i	$0.824821\pi$
$338$	−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	0.846081	−	0.533054i	$-0.178956\pi$
$347$	15.0417	+	8.68435i	0.807483	+	0.466201i	−0.0385980	+	0.999255i	$0.512289\pi$
$348$	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	$0.379791\pi$
$353$			34.9287i			1.85907i	−0.368736	+	0.929534i	$0.620209\pi$
$354$	−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	−0.878623	−	0.477516i	$-0.841537\pi$
$359$	−0.488273	+	0.845713i	−0.0257701	+	0.0446350i	0.852853	+	0.522151i	$0.174870\pi$
$360$		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	−0.706148	−	0.708064i	$-0.749569\pi$
$367$	−8.54451	+	4.93318i	−0.446020	+	0.257510i	0.260128	+	0.965574i	$0.416235\pi$
$368$		−	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	$-0.891157\pi$
$373$		−	12.9521i		−	0.670634i	0.942105	−	0.335317i	$-0.108843\pi$
$374$	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	−0.483993	−	0.875072i	$-0.660814\pi$
$383$	−29.0390	−	16.7657i	−1.48382	−	0.856686i	−0.999831	+	0.0183857i	$0.994147\pi$
$384$	−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	0.967318	+	0.253565i	$0.0816031\pi$
$389$	13.8703	+	24.0241i	0.703253	+	1.21807i	−0.264066	+	0.964505i	$0.585064\pi$
$390$		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	0.375701	−	0.926741i	$-0.377402\pi$
$397$	−4.76264	−	2.74971i	−0.239030	−	0.138004i	−0.614731	+	0.788737i	$0.710735\pi$
$398$			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	−0.739954	−	0.672658i	$-0.765153\pi$
$401$	4.25655	−	7.37256i	0.212562	−	0.368168i	0.952516	+	0.304490i	$0.0984860\pi$
$402$	−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	−0.999353	−	0.0359683i	$-0.988548\pi$
$409$	−10.7353	−	18.5941i	−0.530826	−	0.919418i	0.468527	−	0.883449i	$-0.344785\pi$
$410$		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	−0.926695	−	0.375815i	$-0.877363\pi$
$421$	−2.82911	+	4.90017i	−0.137883	+	0.238820i	0.788812	+	0.614634i	$0.210696\pi$
$422$	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	0.793109	+	0.609079i	$0.208461\pi$
$431$	19.1834	+	33.2267i	0.924033	+	1.60047i	0.130923	+	0.991392i	$0.458206\pi$
$432$	−15.1042	−	8.72041i	−0.726701	−	0.419561i
$433$	6.02970	−	3.48125i	0.289769	−	0.167298i	−0.348069	−	0.937469i	$-0.613162\pi$
$433$	6.02970	−	3.48125i	0.289769	−	0.167298i	0.637838	+	0.770171i	$0.279829\pi$
$434$	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	−0.729674	−	0.683796i	$-0.760328\pi$
$439$	4.76346	−	8.25055i	0.227347	−	0.393777i	0.957021	+	0.290018i	$0.0936613\pi$
$440$		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	0.430971	−	0.902366i	$-0.358171\pi$
$443$	30.0544	−	17.3519i	1.42793	−	0.824414i	0.996957	+	0.0779516i	$0.0248380\pi$
$444$	−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	$-0.995049\pi$
$457$		−	0.664998i		−	0.0311073i	0.999879	−	0.0155536i	$-0.00495108\pi$
$458$	−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	0.122524	−	0.992466i	$-0.460901\pi$
$461$	19.7696	−	34.2420i	0.920762	−	1.59481i	0.798238	−	0.602342i	$-0.205766\pi$
$462$	−4.70381	+	2.71574i	−0.218841	+	0.126348i
$463$		−	15.5782i		−	0.723981i	−0.932182	−	0.361991i	$-0.882097\pi$
$463$		−	15.5782i		−	0.723981i	0.932182	−	0.361991i	$-0.117903\pi$
$464$	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	$-0.601636\pi$
$467$		−	41.0358i		−	1.89891i	0.313901	−	0.949456i	$-0.398364\pi$
$468$			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	−0.999000	−	0.0447012i	$-0.985766\pi$
$479$	−11.7794	−	20.4024i	−0.538213	−	0.932211i	0.460788	−	0.887510i	$-0.347567\pi$
$480$		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	$0.182288\pi$
$487$			23.9166i			1.08377i	−0.840454	+	0.541883i	$0.817712\pi$
$488$	−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	−0.989390	−	0.145284i	$-0.953590\pi$
$491$	−8.17373	+	14.1573i	−0.368875	+	0.638911i	0.620515	+	0.784195i	$0.286924\pi$
$492$	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	0.244009	+	0.969773i	$0.421537\pi$
$499$	−16.0354	+	27.7742i	−0.717844	+	1.24334i	−0.961852	+	0.273569i	$0.911796\pi$
$500$		0			0
$501$	10.8542			0.484930
$502$		−	7.90972i		−	0.353028i
$503$	12.7525	−	7.36269i	0.568608	−	0.328286i	−0.187985	−	0.982172i	$-0.560196\pi$
$503$	12.7525	−	7.36269i	0.568608	−	0.328286i	0.756593	+	0.653886i	$0.226862\pi$
$504$	−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	0.510884	−	0.859650i	$-0.329318\pi$
$509$	−11.0332	−	19.1100i	−0.489037	−	0.847036i	−0.999920	+	0.0126136i	$0.995985\pi$
$510$		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	−0.720962	−	0.692975i	$-0.756300\pi$
$523$	−11.0072	+	6.35498i	−0.481309	+	0.277884i	0.239653	+	0.970859i	$0.422966\pi$
$524$	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	0.983137	+	0.182873i	$0.0585396\pi$
$541$	15.1172	+	26.1838i	0.649941	+	1.12573i	−0.333196	+	0.942858i	$0.608127\pi$
$542$	−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	−0.348437	−	0.937332i	$-0.613287\pi$
$547$	6.76144	−	3.90372i	0.289098	−	0.166911i	0.637535	+	0.770421i	$0.279954\pi$
$548$	−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	−0.543653	−	0.839310i	$-0.682959\pi$
$557$	−2.09141	+	1.20747i	−0.0886157	+	0.0511623i	0.455037	+	0.890472i	$0.349626\pi$
$558$			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	$0.179297\pi$
$563$			25.3392i			1.06792i	−0.845510	+	0.533960i	$0.820703\pi$
$564$	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	$0.0588493\pi$
$577$			8.83145i			0.367658i	−0.982958	+	0.183829i	$0.941151\pi$
$578$		−	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	−0.0671982	−	0.997740i	$-0.521406\pi$
$587$	−23.3768	−	13.4966i	−0.964865	−	0.557065i	−0.897667	+	0.440674i	$0.854739\pi$
$588$		−	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	−0.827552	−	0.561389i	$-0.810267\pi$
$593$	−18.3891	+	10.6170i	−0.755151	+	0.435987i	0.0724009	+	0.997376i	$0.476934\pi$
$594$	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	−0.989556	−	0.144146i	$-0.953957\pi$
$599$	−15.1647	−	26.2660i	−0.619612	−	1.07320i	0.369945	−	0.929054i	$-0.379377\pi$
$600$		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	$-0.942748\pi$
$607$		−	8.81498i		−	0.357789i	0.983868	−	0.178894i	$-0.0572521\pi$
$608$	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	0.0145856	−	0.999894i	$-0.495357\pi$
$613$	−20.8978	−	12.0654i	−0.844055	−	0.487315i	−0.858640	+	0.512578i	$0.828690\pi$
$614$	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	−0.205564	−	0.978644i	$-0.565903\pi$
$617$	13.3930	−	7.73248i	0.539183	−	0.311298i	0.744748	+	0.667346i	$0.232570\pi$
$618$	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	0.791177	−	0.611587i	$-0.209469\pi$
$631$	−3.36758	−	5.83282i	−0.134061	−	0.232201i	−0.925238	+	0.379386i	$0.876135\pi$
$632$	−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	0.453980	+	0.891012i	$0.350004\pi$
$641$	−13.7894	+	23.8840i	−0.544649	+	0.943360i	−0.998629	+	0.0523477i	$0.983330\pi$
$642$	−2.42351	+	1.39921i	−0.0956483	+	0.0552226i
$643$	−10.3128	−	5.95407i	−0.406695	−	0.234806i	0.282673	−	0.959216i	$-0.408779\pi$
$643$	−10.3128	−	5.95407i	−0.406695	−	0.234806i	−0.689369	+	0.724410i	$0.742112\pi$
$644$	−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	$0.0736421\pi$
$647$			11.6648i			0.458590i	−0.973357	+	0.229295i	$0.926358\pi$
$648$	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	$-0.706215\pi$
$653$		−	40.7527i		−	1.59477i	0.603468	−	0.797387i	$-0.293785\pi$
$654$	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	0.547643	−	0.836712i	$-0.315525\pi$
$659$	−11.5723	−	20.0438i	−0.450793	−	0.780796i	−0.998435	+	0.0559165i	$0.982192\pi$
$660$		0			0
$661$	−2.44485	−	4.23460i	−0.0950936	−	0.164707i	0.814554	−	0.580088i	$-0.196982\pi$
$661$	−2.44485	−	4.23460i	−0.0950936	−	0.164707i	−0.909648	+	0.415381i	$0.863648\pi$
$662$	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	$0.192614\pi$
$673$			29.5149i			1.13771i	−0.822436	+	0.568857i	$0.807386\pi$
$674$	−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	$0.191295\pi$
$677$			29.4248i			1.13089i	−0.824788	+	0.565443i	$0.808705\pi$
$678$	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	$0.194172\pi$
$683$			29.9433i			1.14575i	−0.819643	+	0.572875i	$0.805828\pi$
$684$	−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	−0.690999	−	0.722856i	$-0.742829\pi$
$701$	7.42695	−	12.8639i	0.280512	−	0.485861i	0.971511	+	0.236995i	$0.0761624\pi$
$702$			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	−0.997530	−	0.0702441i	$-0.977622\pi$
$709$	−14.9004	−	25.8083i	−0.559598	−	0.969252i	0.437932	−	0.899008i	$-0.355711\pi$
$710$		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	−0.999805	−	0.0197322i	$-0.993719\pi$
$719$	−12.9463	+	22.4236i	−0.482814	+	0.836258i	0.516991	+	0.855991i	$0.327052\pi$
$720$		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	0.642567	−	0.766229i	$-0.277869\pi$
$727$	8.09634	+	4.67442i	0.300277	+	0.173365i	−0.342291	+	0.939594i	$0.611203\pi$
$728$	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	$0.0424768\pi$
$733$			7.20434i			0.266098i	−0.991109	+	0.133049i	$0.957523\pi$
$734$	−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	−0.721692	−	0.692214i	$-0.756635\pi$
$739$	6.48702	−	11.2359i	0.238629	−	0.413318i	0.960321	+	0.278897i	$0.0899687\pi$
$740$		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	0.346139	−	0.938183i	$-0.387492\pi$
$743$	−7.99428	−	4.61550i	−0.293282	−	0.169326i	−0.639421	+	0.768857i	$0.720826\pi$
$744$	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	0.697175	−	0.716901i	$-0.254440\pi$
$751$	−7.46131	−	12.9234i	−0.272267	−	0.471580i	−0.969442	+	0.245321i	$0.921107\pi$
$752$			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	0.833265	−	0.552874i	$-0.186469\pi$
$757$	21.2156	+	12.2488i	0.771093	+	0.445191i	−0.0621711	+	0.998066i	$0.519802\pi$
$758$	−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	−0.999238	−	0.0390437i	$-0.987569\pi$
$769$	−14.7925	−	25.6214i	−0.533432	−	0.923931i	0.465806	−	0.884887i	$-0.345765\pi$
$770$		0			0
$771$	19.0003			0.684280
$772$		−	36.2478i		−	1.30459i
$773$	12.2378	−	7.06551i	0.440164	−	0.254129i	−0.263503	−	0.964658i	$-0.584878\pi$
$773$	12.2378	−	7.06551i	0.440164	−	0.254129i	0.703667	+	0.710530i	$0.251545\pi$
$774$	−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	$-0.857756\pi$
$787$		−	24.2465i		−	0.864293i	0.901803	−	0.432146i	$-0.142244\pi$
$788$	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	$0.164682\pi$
$797$			27.9258i			0.989184i	−0.869125	+	0.494592i	$0.835318\pi$
$798$	−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	0.962844	−	0.270057i	$-0.0870425\pi$
$811$	7.04963	+	12.2103i	0.247546	+	0.428762i	−0.715298	+	0.698819i	$0.753709\pi$
$812$	−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	0.999267	+	0.0382943i	$0.0121924\pi$
$821$	15.2663	+	26.4420i	0.532797	+	0.922832i	−0.466469	+	0.884537i	$0.654474\pi$
$822$	−3.19616	−	1.84530i	−0.111479	−	0.0643623i
$823$	−12.4346	+	7.17914i	−0.433444	+	0.250249i	−0.700813	−	0.713345i	$-0.747179\pi$
$823$	−12.4346	+	7.17914i	−0.433444	+	0.250249i	0.267369	+	0.963594i	$0.413846\pi$
$824$	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	−0.370221	−	0.928944i	$-0.620718\pi$
$827$	7.16518	−	4.13682i	0.249158	−	0.143851i	0.619379	+	0.785092i	$0.287385\pi$
$828$		−	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	−0.929472	−	0.368893i	$-0.879737\pi$
$839$	−4.20767	+	7.28790i	−0.145265	+	0.251606i	0.784207	+	0.620500i	$0.213070\pi$
$840$		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	−0.998648	−	0.0519802i	$-0.983447\pi$
$853$	−45.0648	−	26.0182i	−1.54299	−	0.890845i	−0.544340	−	0.838865i	$-0.683220\pi$
$854$	6.26314			0.214320
$855$		0			0
$856$	−10.6064			−0.362520
$857$	−18.5845	−	10.7298i	−0.634834	−	0.366522i	0.147788	−	0.989019i	$-0.452785\pi$
$857$	−18.5845	−	10.7298i	−0.634834	−	0.366522i	−0.782622	+	0.622497i	$0.786118\pi$
$858$	5.06849	+	2.92629i	0.173035	+	0.0999020i
$859$	9.07396	+	15.7166i	0.309599	+	0.536242i	0.978275	−	0.207313i	$-0.0664717\pi$
$859$	9.07396	+	15.7166i	0.309599	+	0.536242i	−0.668675	+	0.743554i	$0.733138\pi$
$860$		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	$-0.924605\pi$
$863$		−	13.7867i		−	0.469303i	0.972080	−	0.234652i	$-0.0753949\pi$
$864$	−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	0.157003	−	0.987598i	$-0.449817\pi$
$877$	−18.3543	−	10.5968i	−0.619780	−	0.357830i	−0.776783	+	0.629768i	$0.783150\pi$
$878$	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	−0.475119	−	0.879922i	$-0.657595\pi$
$883$	1.46665	−	0.846773i	0.0493568	−	0.0284962i	0.524475	+	0.851426i	$0.324261\pi$
$884$	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	−0.995236	−	0.0974969i	$-0.968916\pi$
$887$	−41.9463	+	24.2177i	−1.40842	+	0.813151i	−0.413183	+	0.910648i	$0.635583\pi$
$888$	−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	0.844660	−	0.535303i	$-0.179803\pi$
$907$	24.1957	+	13.9694i	0.803404	+	0.463846i	−0.0412557	+	0.999149i	$0.513136\pi$
$908$	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	−0.175304	−	0.984514i	$-0.556091\pi$
$929$	23.3157	−	40.3839i	0.764963	−	1.32495i	0.940266	−	0.340440i	$-0.110576\pi$
$930$		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	0.452649	−	0.891689i	$-0.350479\pi$
$937$	44.4219	−	25.6470i	1.45120	−	0.837850i	0.998550	+	0.0538383i	$0.0171456\pi$
$938$			11.4281i			0.373140i
$939$	21.9992			0.717916
$940$		0			0
$941$	5.67430	+	9.82817i	0.184977	+	0.320389i	0.943569	−	0.331177i	$-0.107446\pi$
$941$	5.67430	+	9.82817i	0.184977	+	0.320389i	−0.758592	+	0.651566i	$0.774112\pi$
$942$		−	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	0.395115	−	0.918632i	$-0.370705\pi$
$947$	−6.24348	−	3.60467i	−0.202886	−	0.117136i	−0.598001	+	0.801495i	$0.704038\pi$
$948$	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	0.183422	−	0.983034i	$-0.441282\pi$
$953$	−17.7877	−	10.2697i	−0.576199	−	0.332669i	−0.759622	+	0.650365i	$0.774616\pi$
$954$	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	0.243153	−	0.969988i	$-0.421818\pi$
$967$	−14.7804	−	8.53345i	−0.475305	−	0.274417i	−0.718458	+	0.695571i	$0.755152\pi$
$968$		−	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	−0.836740	−	0.547601i	$-0.815541\pi$
$971$	1.74085	−	3.01525i	0.0558667	−	0.0967639i	0.892606	+	0.450837i	$0.148874\pi$
$972$	−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	$-0.885746\pi$
$977$		−	21.9600i		−	0.702562i	0.936270	−	0.351281i	$-0.114254\pi$
$978$	−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	0.573994	−	0.818859i	$-0.305393\pi$
$983$	4.76057	+	2.74852i	0.151839	+	0.0876641i	−0.422156	+	0.906523i	$0.638726\pi$
$984$	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	−0.530850	−	0.847466i	$-0.678127\pi$
$991$	14.7485	−	25.5452i	0.468502	−	0.811469i	0.999352	+	0.0359970i	$0.0114607\pi$
$992$	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	−0.397058	−	0.917793i	$-0.629969\pi$
$997$	6.29123	−	3.63224i	0.199245	−	0.115034i	0.596303	+	0.802759i	$0.296636\pi$
$998$	−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.49.7		24
5.2	odd	4		475.2.e.f.201.3	yes	12
5.3	odd	4		475.2.e.h.201.4	yes	12
5.4	even	2	inner	475.2.j.d.49.6		24
19.7	even	3	inner	475.2.j.d.349.6		24
95.7	odd	12		475.2.e.f.26.3	✓	12
95.8	even	12		9025.2.a.by.1.4		6
95.27	even	12		9025.2.a.bs.1.3		6
95.64	even	6	inner	475.2.j.d.349.7		24
95.68	odd	12		9025.2.a.br.1.3		6
95.83	odd	12		475.2.e.h.26.4	yes	12
95.87	odd	12		9025.2.a.bz.1.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
475.2.e.f.26.3	✓	12	95.7	odd	12
475.2.e.f.201.3	yes	12	5.2	odd	4
475.2.e.h.26.4	yes	12	95.83	odd	12
475.2.e.h.201.4	yes	12	5.3	odd	4
475.2.j.d.49.6		24	5.4	even	2	inner
475.2.j.d.49.7		24	1.1	even	1	trivial
475.2.j.d.349.6		24	19.7	even	3	inner
475.2.j.d.349.7		24	95.64	even	6	inner
9025.2.a.br.1.3		6	95.68	odd	12
9025.2.a.bs.1.3		6	95.27	even	12
9025.2.a.by.1.4		6	95.8	even	12
9025.2.a.bz.1.4		6	95.87	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} -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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{4} + 2 q^{6} + 14 q^{9} - 4 q^{11} - 12 q^{14} + 12 q^{16} + 12 q^{19} - 6 q^{21} + 22 q^{24} + 76 q^{26} + 6 q^{29} - 12 q^{31} - 2 q^{34} - 26 q^{36} - 32 q^{39} - 22 q^{41} + 42 q^{44} - 48 q^{46}+ \cdots - 40 q^{99}+O(q^{100}) \) 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

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