LMFDB - Embedded newform 475.2.j.d.49.6

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			49.6
Character	$\chi$	$=$	475.49
Dual form			475.2.j.d.349.6

$q$-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	0.401709	−	0.915767i	$-0.368416\pi$
$2$	−0.269427	−	0.155554i	−0.190514	−	0.109993i	−0.592223	+	0.805774i	$0.701750\pi$
$3$	0.891863	+	0.514917i	0.514917	+	0.297288i	0.734853	−	0.678227i	$-0.237251\pi$
$3$	0.891863	+	0.514917i	0.514917	+	0.297288i	−0.219935	+	0.975514i	$0.570585\pi$
$4$	−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	$-0.829734\pi$
$13$	−3.06115	+	1.76735i	−0.849010	+	0.490176i	0.0113069	+	0.999936i	$0.496401\pi$
$14$	−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	$-0.294276\pi$
$17$	0.874064	+	0.504641i	0.211992	+	0.122393i	−0.390245	+	0.920711i	$0.627610\pi$
$18$			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	$-0.372042\pi$
$23$	6.63680	−	3.83176i	1.38387	−	0.798976i	0.992615	+	0.121307i	$0.0387085\pi$
$24$	−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	$-0.820938\pi$
$37$		−	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	−0.467904	−	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	0.855007	−	0.518616i	$-0.173553\pi$
$43$	5.46481	+	3.15511i	0.833376	+	0.481150i	−0.0216315	+	0.999766i	$0.506886\pi$
$44$	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	$-0.757059\pi$
$47$	−3.32690	+	1.92079i	−0.485278	+	0.280175i	0.237335	+	0.971428i	$0.423726\pi$
$48$	−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	$-0.504054\pi$
$53$	6.16516	−	3.55946i	0.846850	−	0.488929i	0.859587	+	0.510990i	$0.170721\pi$
$54$	−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	−0.957112	−	0.289719i	$-0.906438\pi$
$67$	−9.69770	+	5.59897i	−1.18476	+	0.684023i	−0.227652	+	0.973743i	$0.573105\pi$
$68$		−	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	0.694652	−	0.719346i	$-0.255558\pi$
$73$	3.57999	+	2.06691i	0.419007	+	0.241914i	−0.275646	+	0.961259i	$0.588892\pi$
$74$	−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	$0.0976159\pi$
$83$			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	0.612926	−	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	0.893659	−	0.448747i	$-0.148129\pi$
$97$	9.37476	+	5.41252i	0.951862	+	0.549558i	0.0582034	+	0.998305i	$0.481463\pi$
$98$	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	$-0.641623\pi$
$103$		−	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	−0.974279	−	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	$-0.838253\pi$
$113$		−	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	$-0.618935\pi$
$127$	2.91602	−	1.68356i	0.258755	−	0.149392i	0.623766	+	0.781611i	$0.285602\pi$
$128$	−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	−0.861424	−	0.507886i	$-0.830427\pi$
$137$	−9.97584	+	5.75955i	−0.852293	+	0.492072i	0.00913057	+	0.999958i	$0.497094\pi$
$138$	−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	0.389589	−	0.920989i	$-0.372617\pi$
$157$	−2.67159	−	1.54244i	−0.213216	−	0.123101i	−0.602805	+	0.797888i	$0.705950\pi$
$158$	−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	$-0.532964\pi$
$167$	9.12769	−	5.26987i	0.706322	−	0.407795i	0.809698	+	0.586847i	$0.199631\pi$
$168$	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	$0.00382875\pi$
$173$	19.8650	+	11.4691i	1.51031	+	0.871977i	0.510380	+	0.859949i	$0.329505\pi$
$174$	−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	−0.229579	−	0.973290i	$-0.573735\pi$
$193$	−16.4940	−	9.52280i	−1.18726	−	0.685466i	−0.957683	+	0.287824i	$0.907068\pi$
$194$	−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	0.965050	−	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	0.133957	−	0.990987i	$-0.457232\pi$
$223$	−9.81536	−	5.66690i	−0.657285	−	0.379484i	−0.791242	+	0.611504i	$0.790565\pi$
$224$	−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	$-0.268342\pi$
$233$	5.36068	+	3.09499i	0.351190	+	0.202759i	−0.314020	+	0.949417i	$0.601676\pi$
$234$	−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	0.0894183	−	0.995994i	$-0.471499\pi$
$257$	15.9781	−	9.22493i	0.996684	−	0.575436i	0.907265	+	0.420559i	$0.138166\pi$
$258$		−	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	$-0.202592\pi$
$263$	11.2155	+	6.47530i	0.691580	+	0.399284i	−0.112624	+	0.993638i	$0.535925\pi$
$264$	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	$-0.994988\pi$
$277$		−	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	0.929673	−	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	−0.0366299	−	0.999329i	$-0.511662\pi$
$283$	−15.4833	−	8.93931i	−0.920389	−	0.531387i	−0.883759	+	0.467942i	$0.844996\pi$
$284$	−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	$-0.467932\pi$
$307$	−12.4537	−	7.19015i	−0.710771	−	0.410364i	−0.811346	+	0.584566i	$0.801265\pi$
$308$	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	$-0.460350\pi$
$313$	18.4999	−	10.6809i	1.04568	−	0.603722i	0.921436	+	0.388530i	$0.127017\pi$
$314$	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	$-0.377305\pi$
$317$	24.3291	−	14.0464i	1.36646	−	0.788924i	0.990474	+	0.137702i	$0.0439717\pi$
$318$	−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	$-0.175179\pi$
$337$	15.1562	+	8.75041i	0.825608	+	0.476665i	−0.0267383	+	0.999642i	$0.508512\pi$
$338$	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	$-0.487711\pi$
$347$	−15.0417	−	8.68435i	−0.807483	−	0.466201i	−0.846081	+	0.533054i	$0.821044\pi$
$348$	−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	−0.878623	−	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	−0.260128	−	0.965574i	$-0.583765\pi$
$367$	8.54451	−	4.93318i	0.446020	−	0.257510i	0.706148	+	0.708064i	$0.250431\pi$
$368$			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	$-0.00585269\pi$
$383$	29.0390	+	16.7657i	1.48382	+	0.856686i	0.483993	+	0.875072i	$0.339186\pi$
$384$	−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	0.614731	−	0.788737i	$-0.289265\pi$
$397$	4.76264	+	2.74971i	0.239030	+	0.138004i	−0.375701	+	0.926741i	$0.622598\pi$
$398$		−	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	−0.637838	−	0.770171i	$-0.720171\pi$
$433$	−6.02970	+	3.48125i	−0.289769	+	0.167298i	0.348069	+	0.937469i	$0.386838\pi$
$434$	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	−0.996957	−	0.0779516i	$-0.975162\pi$
$443$	−30.0544	+	17.3519i	−1.42793	+	0.824414i	−0.430971	+	0.902366i	$0.641829\pi$
$444$	−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	0.122524	−	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	$0.117903\pi$
$463$			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	−0.999000	−	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	$-0.817712\pi$
$487$		−	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	−0.989390	−	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	−0.756593	−	0.653886i	$-0.773138\pi$
$503$	−12.7525	+	7.36269i	−0.568608	+	0.328286i	0.187985	+	0.982172i	$0.439804\pi$
$504$	−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	−0.239653	−	0.970859i	$-0.577034\pi$
$523$	11.0072	−	6.35498i	0.481309	−	0.277884i	0.720962	+	0.692975i	$0.243700\pi$
$524$	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	−0.637535	−	0.770421i	$-0.720046\pi$
$547$	−6.76144	+	3.90372i	−0.289098	+	0.166911i	0.348437	+	0.937332i	$0.386713\pi$
$548$	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	$-0.650374\pi$
$557$	2.09141	−	1.20747i	0.0886157	−	0.0511623i	0.543653	+	0.839310i	$0.317041\pi$
$558$		−	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	$-0.145261\pi$
$587$	23.3768	+	13.4966i	0.964865	+	0.557065i	0.0671982	+	0.997740i	$0.478594\pi$
$588$			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	$-0.523066\pi$
$593$	18.3891	−	10.6170i	0.755151	−	0.435987i	0.827552	+	0.561389i	$0.189733\pi$
$594$	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	$0.0572521\pi$
$607$			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	$-0.171310\pi$
$613$	20.8978	+	12.0654i	0.844055	+	0.487315i	−0.0145856	+	0.999894i	$0.504643\pi$
$614$	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	$-0.767430\pi$
$617$	−13.3930	+	7.73248i	−0.539183	+	0.311298i	0.205564	+	0.978644i	$0.434097\pi$
$618$	−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	0.689369	−	0.724410i	$-0.257888\pi$
$643$	10.3128	+	5.95407i	0.406695	+	0.234806i	−0.282673	+	0.959216i	$0.591221\pi$
$644$	−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	0.547643	−	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	$-0.807386\pi$
$673$		−	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	−0.690999	−	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	0.342291	−	0.939594i	$-0.388797\pi$
$727$	−8.09634	−	4.67442i	−0.300277	−	0.173365i	−0.642567	+	0.766229i	$0.722131\pi$
$728$	−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	−0.721692	−	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	0.639421	−	0.768857i	$-0.279174\pi$
$743$	7.99428	+	4.61550i	0.293282	+	0.169326i	−0.346139	+	0.938183i	$0.612508\pi$
$744$	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	0.0621711	−	0.998066i	$-0.480198\pi$
$757$	−21.2156	−	12.2488i	−0.771093	−	0.445191i	−0.833265	+	0.552874i	$0.813531\pi$
$758$	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	−0.703667	−	0.710530i	$-0.748455\pi$
$773$	−12.2378	+	7.06551i	−0.440164	+	0.254129i	0.263503	+	0.964658i	$0.415122\pi$
$774$	−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	0.962844	−	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	−0.267369	−	0.963594i	$-0.586154\pi$
$823$	12.4346	−	7.17914i	0.433444	−	0.250249i	0.700813	+	0.713345i	$0.252821\pi$
$824$	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	$-0.712615\pi$
$827$	−7.16518	+	4.13682i	−0.249158	+	0.143851i	0.370221	+	0.928944i	$0.379282\pi$
$828$			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	$0.0165533\pi$
$853$	45.0648	+	26.0182i	1.54299	+	0.890845i	0.544340	+	0.838865i	$0.316780\pi$
$854$	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	$-0.213882\pi$
$857$	18.5845	+	10.7298i	0.634834	+	0.366522i	−0.147788	+	0.989019i	$0.547215\pi$
$858$	−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	$0.0753949\pi$
$863$			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	$-0.216850\pi$
$877$	18.3543	+	10.5968i	0.619780	+	0.357830i	−0.157003	+	0.987598i	$0.550183\pi$
$878$	−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	$-0.675739\pi$
$883$	−1.46665	+	0.846773i	−0.0493568	+	0.0284962i	0.475119	+	0.879922i	$0.342405\pi$
$884$	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	$-0.364417\pi$
$887$	41.9463	−	24.2177i	1.40842	−	0.813151i	0.995236	+	0.0974969i	$0.0310836\pi$
$888$	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	$-0.486864\pi$
$907$	−24.1957	−	13.9694i	−0.803404	−	0.463846i	−0.844660	+	0.535303i	$0.820197\pi$
$908$	−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	−0.998550	−	0.0538383i	$-0.982854\pi$
$937$	−44.4219	+	25.6470i	−1.45120	+	0.837850i	−0.452649	+	0.891689i	$0.649521\pi$
$938$		−	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	0.598001	−	0.801495i	$-0.295962\pi$
$947$	6.24348	+	3.60467i	0.202886	+	0.117136i	−0.395115	+	0.918632i	$0.629295\pi$
$948$	−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	$-0.225384\pi$
$953$	17.7877	+	10.2697i	0.576199	+	0.332669i	−0.183422	+	0.983034i	$0.558718\pi$
$954$	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	$-0.244848\pi$
$967$	14.7804	+	8.53345i	0.475305	+	0.274417i	−0.243153	+	0.969988i	$0.578182\pi$
$968$			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	$0.114254\pi$
$977$			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	$-0.361274\pi$
$983$	−4.76057	−	2.74852i	−0.151839	−	0.0876641i	−0.573994	+	0.818859i	$0.694607\pi$
$984$	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	−0.596303	−	0.802759i	$-0.703364\pi$
$997$	−6.29123	+	3.63224i	−0.199245	+	0.115034i	0.397058	+	0.917793i	$0.370031\pi$
$998$	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.49.6		24
5.2	odd	4		475.2.e.h.201.4	yes	12
5.3	odd	4		475.2.e.f.201.3	yes	12
5.4	even	2	inner	475.2.j.d.49.7		24
19.7	even	3	inner	475.2.j.d.349.7		24
95.7	odd	12		475.2.e.h.26.4	yes	12
95.8	even	12		9025.2.a.bs.1.3		6
95.27	even	12		9025.2.a.by.1.4		6
95.64	even	6	inner	475.2.j.d.349.6		24
95.68	odd	12		9025.2.a.bz.1.4		6
95.83	odd	12		475.2.e.f.26.3	✓	12
95.87	odd	12		9025.2.a.br.1.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
475.2.e.f.26.3	✓	12	95.83	odd	12
475.2.e.f.201.3	yes	12	5.3	odd	4
475.2.e.h.26.4	yes	12	95.7	odd	12
475.2.e.h.201.4	yes	12	5.2	odd	4
475.2.j.d.49.6		24	1.1	even	1	trivial
475.2.j.d.49.7		24	5.4	even	2	inner
475.2.j.d.349.6		24	95.64	even	6	inner
475.2.j.d.349.7		24	19.7	even	3	inner
9025.2.a.br.1.3		6	95.87	odd	12
9025.2.a.bs.1.3		6	95.8	even	12
9025.2.a.by.1.4		6	95.27	even	12
9025.2.a.bz.1.4		6	95.68	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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