LMFDB - Embedded newform 925.2.o.d.174.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [925,2,Mod(174,925)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(925, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 2]))

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

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

chi := DirichletCharacter("925.174");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 925 = 5^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	925.o (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:	$7.38616218697$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			174.10
Character	$\chi$	$=$	925.174
Dual form			925.2.o.d.824.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.479496 + 0.276837i) q^{2} +(1.80447 + 1.04181i) q^{3} +(-0.846722 + 1.46657i) q^{4} -1.15365 q^{6} +(-3.61105 - 2.08484i) q^{7} -2.04497i q^{8} +(0.670751 + 1.16177i) q^{9} +O(q^{10})$	\(q+(-0.479496 + 0.276837i) q^{2} +(1.80447 + 1.04181i) q^{3} +(-0.846722 + 1.46657i) q^{4} -1.15365 q^{6} +(-3.61105 - 2.08484i) q^{7} -2.04497i q^{8} +(0.670751 + 1.16177i) q^{9} -3.31014 q^{11} +(-3.05578 + 1.76425i) q^{12} +(0.365690 + 0.211131i) q^{13} +2.30865 q^{14} +(-1.12732 - 1.95258i) q^{16} +(1.57487 - 0.909250i) q^{17} +(-0.643245 - 0.371378i) q^{18} +(1.28344 - 2.22298i) q^{19} +(-4.34403 - 7.52408i) q^{21} +(1.58720 - 0.916369i) q^{22} -0.981927i q^{23} +(2.13047 - 3.69009i) q^{24} -0.233796 q^{26} -3.45569i q^{27} +(6.11511 - 3.53056i) q^{28} -7.35038 q^{29} -6.58707 q^{31} +(4.62308 + 2.66914i) q^{32} +(-5.97305 - 3.44854i) q^{33} +(-0.503428 + 0.871964i) q^{34} -2.27176 q^{36} +(-2.66173 - 5.46948i) q^{37} +1.42121i q^{38} +(0.439919 + 0.761962i) q^{39} +(-3.14561 + 5.44835i) q^{41} +(4.16589 + 2.40518i) q^{42} +8.10974i q^{43} +(2.80277 - 4.85453i) q^{44} +(0.271834 + 0.470830i) q^{46} -10.6399i q^{47} -4.69784i q^{48} +(5.19312 + 8.99475i) q^{49} +3.78908 q^{51} +(-0.619276 + 0.357539i) q^{52} +(5.40388 - 3.11993i) q^{53} +(0.956664 + 1.65699i) q^{54} +(-4.26343 + 7.38447i) q^{56} +(4.63185 - 2.67420i) q^{57} +(3.52448 - 2.03486i) q^{58} +(-0.556448 - 0.963795i) q^{59} +(3.40650 - 5.90023i) q^{61} +(3.15847 - 1.82355i) q^{62} -5.59364i q^{63} +1.55362 q^{64} +3.81874 q^{66} +(6.05892 + 3.49812i) q^{67} +3.07953i q^{68} +(1.02298 - 1.77186i) q^{69} +(-6.43743 + 11.1500i) q^{71} +(2.37579 - 1.37166i) q^{72} -7.36078i q^{73} +(2.79044 + 1.88573i) q^{74} +(2.17343 + 3.76449i) q^{76} +(11.9531 + 6.90110i) q^{77} +(-0.421879 - 0.243572i) q^{78} +(-7.18467 + 12.4442i) q^{79} +(5.61244 - 9.72103i) q^{81} -3.48329i q^{82} +(-0.959744 + 0.554108i) q^{83} +14.7128 q^{84} +(-2.24508 - 3.88859i) q^{86} +(-13.2636 - 7.65772i) q^{87} +6.76911i q^{88} +(-3.18082 - 5.50934i) q^{89} +(-0.880351 - 1.52481i) q^{91} +(1.44006 + 0.831419i) q^{92} +(-11.8862 - 6.86250i) q^{93} +(2.94552 + 5.10179i) q^{94} +(5.56148 + 9.63277i) q^{96} +8.47676i q^{97} +(-4.98016 - 2.87530i) q^{98} +(-2.22028 - 3.84563i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 22 q^{4} + 20 q^{9}+O(q^{10}) $ 48 * q + 22 * q^4 + 20 * q^9	$ 48 q + 22 q^{4} + 20 q^{9} - 40 q^{14} - 26 q^{16} - 10 q^{19} - 12 q^{21} + 42 q^{24} - 40 q^{26} - 12 q^{29} + 76 q^{31} + 10 q^{34} - 4 q^{36} - 28 q^{39} - 26 q^{41} + 30 q^{44} - 26 q^{46} + 52 q^{49} - 92 q^{51} + 74 q^{54} + 14 q^{59} + 32 q^{61} - 40 q^{64} + 164 q^{66} - 42 q^{69} - 4 q^{71} - 96 q^{74} + 34 q^{76} + 42 q^{79} - 32 q^{81} - 152 q^{84} - 32 q^{86} - 58 q^{89} + 64 q^{91} + 26 q^{94} + 52 q^{96} + 30 q^{99}+O(q^{100}) $ 48 * q + 22 * q^4 + 20 * q^9 - 40 * q^14 - 26 * q^16 - 10 * q^19 - 12 * q^21 + 42 * q^24 - 40 * q^26 - 12 * q^29 + 76 * q^31 + 10 * q^34 - 4 * q^36 - 28 * q^39 - 26 * q^41 + 30 * q^44 - 26 * q^46 + 52 * q^49 - 92 * q^51 + 74 * q^54 + 14 * q^59 + 32 * q^61 - 40 * q^64 + 164 * q^66 - 42 * q^69 - 4 * q^71 - 96 * q^74 + 34 * q^76 + 42 * q^79 - 32 * q^81 - 152 * q^84 - 32 * q^86 - 58 * q^89 + 64 * q^91 + 26 * q^94 + 52 * q^96 + 30 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/925\mathbb{Z}\right)^\times$.

$n$	$76$	$852$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.479496	+	0.276837i	−0.339055	+	0.195753i	−0.659854	−	0.751394i	$-0.729382\pi$
$2$	−0.479496	+	0.276837i	−0.339055	+	0.195753i	0.320799	+	0.947147i	$0.396049\pi$
$3$	1.80447	+	1.04181i	1.04181	+	0.601491i	0.920346	−	0.391104i	$-0.127907\pi$
$3$	1.80447	+	1.04181i	1.04181	+	0.601491i	0.121467	+	0.992595i	$0.461240\pi$
$4$	−0.846722	+	1.46657i	−0.423361	+	0.733283i
$5$		0			0
$5$		0			0
$6$	−1.15365			−0.470976
$7$	−3.61105	−	2.08484i	−1.36485	−	0.787996i	−0.374584	−	0.927193i	$-0.622214\pi$
$7$	−3.61105	−	2.08484i	−1.36485	−	0.787996i	−0.990265	+	0.139197i	$0.955548\pi$
$8$		−	2.04497i		−	0.723005i
$9$	0.670751	+	1.16177i	0.223584	+	0.387258i
$10$		0			0
$11$	−3.31014			−0.998043			−0.499022	−	0.866590i	$-0.666307\pi$
$11$	−3.31014			−0.998043			−0.499022	+	0.866590i	$0.666307\pi$
$12$	−3.05578	+	1.76425i	−0.882127	+	0.509296i
$13$	0.365690	+	0.211131i	0.101424	+	0.0585573i	0.549854	−	0.835261i	$-0.314683\pi$
$13$	0.365690	+	0.211131i	0.101424	+	0.0585573i	−0.448430	+	0.893818i	$0.648017\pi$
$14$	2.30865			0.617012
$15$		0			0
$16$	−1.12732	−	1.95258i	−0.281830	−	0.488145i
$17$	1.57487	−	0.909250i	0.381961	−	0.220525i	−0.296710	−	0.954968i	$-0.595889\pi$
$17$	1.57487	−	0.909250i	0.381961	−	0.220525i	0.678671	+	0.734442i	$0.262556\pi$
$18$	−0.643245	−	0.371378i	−0.151614	−	0.0875346i
$19$	1.28344	−	2.22298i	0.294440	−	0.509986i	−0.680414	−	0.732828i	$-0.738200\pi$
$19$	1.28344	−	2.22298i	0.294440	−	0.509986i	0.974855	+	0.222842i	$0.0715334\pi$
$20$		0			0
$21$	−4.34403	−	7.52408i	−0.947945	−	1.64189i
$22$	1.58720	−	0.916369i	0.338392	−	0.195370i
$23$		−	0.981927i		−	0.204746i	−0.994746	−	0.102373i	$-0.967356\pi$
$23$		−	0.981927i		−	0.204746i	0.994746	−	0.102373i	$-0.0326435\pi$
$24$	2.13047	−	3.69009i	0.434881	−	0.753236i
$25$		0			0
$26$	−0.233796			−0.0458512
$27$		−	3.45569i		−	0.665048i
$28$	6.11511	−	3.53056i	1.15565	−	0.667214i
$29$	−7.35038			−1.36493			−0.682466	−	0.730918i	$-0.739092\pi$
$29$	−7.35038			−1.36493			−0.682466	+	0.730918i	$0.739092\pi$
$30$		0			0
$31$	−6.58707			−1.18307			−0.591536	−	0.806278i	$-0.701478\pi$
$31$	−6.58707			−1.18307			−0.591536	+	0.806278i	$0.701478\pi$
$32$	4.62308	+	2.66914i	0.817252	+	0.471841i
$33$	−5.97305	−	3.44854i	−1.03978	−	0.600314i
$34$	−0.503428	+	0.871964i	−0.0863373	+	0.149541i
$35$		0			0
$36$	−2.27176			−0.378626
$37$	−2.66173	−	5.46948i	−0.437586	−	0.899177i
$37$	−2.66173	−	5.46948i	−0.437586	−	0.899177i
$38$			1.42121i			0.230551i
$39$	0.439919	+	0.761962i	0.0704434	+	0.122012i
$40$		0			0
$41$	−3.14561	+	5.44835i	−0.491261	+	0.850890i	−0.999949	−	0.0100613i	$-0.996797\pi$
$41$	−3.14561	+	5.44835i	−0.491261	+	0.850890i	0.508688	+	0.860951i	$0.330131\pi$
$42$	4.16589	+	2.40518i	0.642811	+	0.371127i
$43$			8.10974i			1.23672i	0.785894	+	0.618362i	$0.212203\pi$
$43$			8.10974i			1.23672i	−0.785894	+	0.618362i	$0.787797\pi$
$44$	2.80277	−	4.85453i	0.422533	−	0.731848i
$45$		0			0
$46$	0.271834	+	0.470830i	0.0400797	+	0.0694201i
$47$		−	10.6399i		−	1.55199i	−0.630739	−	0.775995i	$-0.717248\pi$
$47$		−	10.6399i		−	1.55199i	0.630739	−	0.775995i	$-0.282752\pi$
$48$		−	4.69784i		−	0.678074i
$49$	5.19312	+	8.99475i	0.741875	+	1.28496i
$50$		0			0
$51$	3.78908			0.530577
$52$	−0.619276	+	0.357539i	−0.0858782	+	0.0495818i
$53$	5.40388	−	3.11993i	0.742279	−	0.428555i	−0.0806181	−	0.996745i	$-0.525689\pi$
$53$	5.40388	−	3.11993i	0.742279	−	0.428555i	0.822897	+	0.568190i	$0.192356\pi$
$54$	0.956664	+	1.65699i	0.130186	+	0.225488i
$55$		0			0
$56$	−4.26343	+	7.38447i	−0.569725	+	0.986792i
$57$	4.63185	−	2.67420i	0.613504	−	0.354207i
$58$	3.52448	−	2.03486i	0.462787	−	0.267190i
$59$	−0.556448	−	0.963795i	−0.0724433	−	0.125475i	0.827528	−	0.561424i	$-0.189746\pi$
$59$	−0.556448	−	0.963795i	−0.0724433	−	0.125475i	−0.899972	+	0.435949i	$0.856413\pi$
$60$		0			0
$61$	3.40650	−	5.90023i	0.436157	−	0.755447i	−0.561232	−	0.827659i	$-0.689672\pi$
$61$	3.40650	−	5.90023i	0.436157	−	0.755447i	0.997389	+	0.0722117i	$0.0230057\pi$
$62$	3.15847	−	1.82355i	0.401127	−	0.231591i
$63$		−	5.59364i		−	0.704732i
$64$	1.55362			0.194203
$65$		0			0
$66$	3.81874			0.470055
$67$	6.05892	+	3.49812i	0.740215	+	0.427363i	0.822147	−	0.569275i	$-0.192776\pi$
$67$	6.05892	+	3.49812i	0.740215	+	0.427363i	−0.0819325	+	0.996638i	$0.526109\pi$
$68$			3.07953i			0.373448i
$69$	1.02298	−	1.77186i	0.123153	−	0.213307i
$70$		0			0
$71$	−6.43743	+	11.1500i	−0.763983	+	1.32326i	0.176800	+	0.984247i	$0.443425\pi$
$71$	−6.43743	+	11.1500i	−0.763983	+	1.32326i	−0.940783	+	0.339010i	$0.889908\pi$
$72$	2.37579	−	1.37166i	0.279989	−	0.161652i
$73$		−	7.36078i		−	0.861514i	−0.902468	−	0.430757i	$-0.858247\pi$
$73$		−	7.36078i		−	0.861514i	0.902468	−	0.430757i	$-0.141753\pi$
$74$	2.79044	+	1.88573i	0.324383	+	0.219211i
$75$		0			0
$76$	2.17343	+	3.76449i	0.249309	+	0.431816i
$77$	11.9531	+	6.90110i	1.36218	+	0.786454i
$78$	−0.421879	−	0.243572i	−0.0477684	−	0.0275791i
$79$	−7.18467	+	12.4442i	−0.808338	+	1.40008i	0.105676	+	0.994401i	$0.466299\pi$
$79$	−7.18467	+	12.4442i	−0.808338	+	1.40008i	−0.914014	+	0.405682i	$0.867034\pi$
$80$		0			0
$81$	5.61244	−	9.72103i	0.623604	−	1.08011i
$82$		−	3.48329i		−	0.384664i
$83$	−0.959744	+	0.554108i	−0.105346	+	0.0608213i	−0.551747	−	0.834011i	$-0.686039\pi$
$83$	−0.959744	+	0.554108i	−0.105346	+	0.0608213i	0.446402	+	0.894833i	$0.352705\pi$
$84$	14.7128			1.60529
$85$		0			0
$86$	−2.24508	−	3.88859i	−0.242093	−	0.419317i
$87$	−13.2636	−	7.65772i	−1.42200	−	0.820994i
$88$			6.76911i			0.721590i
$89$	−3.18082	−	5.50934i	−0.337166	−	0.583989i	0.646732	−	0.762717i	$-0.276135\pi$
$89$	−3.18082	−	5.50934i	−0.337166	−	0.583989i	−0.983899	+	0.178728i	$0.942802\pi$
$90$		0			0
$91$	−0.880351	−	1.52481i	−0.0922858	−	0.159844i
$92$	1.44006	+	0.831419i	0.150137	+	0.0866815i
$93$	−11.8862	−	6.86250i	−1.23254	−	0.711608i
$94$	2.94552	+	5.10179i	0.303807	+	0.526210i
$95$		0			0
$96$	5.56148	+	9.63277i	0.567616	+	0.983141i
$97$			8.47676i			0.860684i	0.902666	+	0.430342i	$0.141607\pi$
$97$			8.47676i			0.860684i	−0.902666	+	0.430342i	$0.858393\pi$
$98$	−4.98016	−	2.87530i	−0.503073	−	0.290449i
$99$	−2.22028	−	3.84563i	−0.223146	−	0.386500i
$100$		0			0
$101$	−11.5548			−1.14975			−0.574873	−	0.818242i	$-0.694949\pi$
$101$	−11.5548			−1.14975			−0.574873	+	0.818242i	$0.694949\pi$
$102$	−1.81685	+	1.04896i	−0.179895	+	0.103862i
$103$			5.40037i			0.532115i	0.963957	+	0.266057i	$0.0857210\pi$
$103$			5.40037i			0.532115i	−0.963957	+	0.266057i	$0.914279\pi$
$104$	0.431757	−	0.747824i	0.0423372	−	0.0733302i
$105$		0			0
$106$	−1.72743	+	2.99199i	−0.167782	+	0.290608i
$107$	−6.94328	−	4.00870i	−0.671232	−	0.387536i	0.125311	−	0.992117i	$-0.460007\pi$
$107$	−6.94328	−	4.00870i	−0.671232	−	0.387536i	−0.796543	+	0.604581i	$0.793340\pi$
$108$	5.06800	+	2.92601i	0.487669	+	0.281556i
$109$	−6.07788	−	10.5272i	−0.582156	−	1.00832i	−0.995223	−	0.0976229i	$-0.968876\pi$
$109$	−6.07788	−	10.5272i	−0.582156	−	1.00832i	0.413068	−	0.910700i	$-0.364457\pi$
$110$		0			0
$111$	0.895156	−	12.6426i	0.0849645	−	1.19998i
$112$			9.40115i			0.888325i
$113$	7.32611	−	4.22973i	0.689183	−	0.397900i	−0.114123	−	0.993467i	$-0.536406\pi$
$113$	7.32611	−	4.22973i	0.689183	−	0.397900i	0.803306	+	0.595567i	$0.203072\pi$
$114$	−1.48064	+	2.56454i	−0.138674	+	0.240191i
$115$		0			0
$116$	6.22373	−	10.7798i	0.577859	−	1.00088i
$117$			0.566466i			0.0523698i
$118$	0.533629	+	0.308091i	0.0491245	+	0.0283621i
$119$	−7.58256			−0.695093
$120$		0			0
$121$	−0.0430050			−0.00390955
$122$			3.77218i			0.341517i
$123$	−11.3523	+	6.55427i	−1.02361	+	0.590979i
$124$	5.57742	−	9.66037i	0.500867	−	0.867527i
$125$		0			0
$126$	1.54853	+	2.68213i	0.137954	+	0.238943i
$127$	−16.2371	+	9.37450i	−1.44081	+	0.831852i	−0.997904	−	0.0647153i	$-0.979386\pi$
$127$	−16.2371	+	9.37450i	−1.44081	+	0.831852i	−0.442907	+	0.896568i	$0.646053\pi$
$128$	−9.99111	+	5.76837i	−0.883098	+	0.509857i
$129$	−8.44883	+	14.6338i	−0.743878	+	1.28844i
$130$		0			0
$131$	5.42707	+	9.39997i	0.474166	+	0.821279i	0.999562	−	0.0295784i	$-0.00941646\pi$
$131$	5.42707	+	9.39997i	0.474166	+	0.821279i	−0.525397	+	0.850857i	$0.676083\pi$
$132$	10.1150	−	5.83992i	0.880401	−	0.508300i
$133$	−9.26910	+	5.35152i	−0.803733	+	0.464036i
$134$	−3.87364			−0.334631
$135$		0			0
$136$	−1.85939	−	3.22055i	−0.159441	−	0.276160i
$137$		−	2.59845i		−	0.222001i	−0.993820	−	0.111000i	$-0.964595\pi$
$137$		−	2.59845i		−	0.222001i	0.993820	−	0.111000i	$-0.0354054\pi$
$138$			1.13280i			0.0964304i
$139$	−2.51498	−	4.35606i	−0.213317	−	0.369477i	0.739433	−	0.673230i	$-0.235094\pi$
$139$	−2.51498	−	4.35606i	−0.213317	−	0.369477i	−0.952751	+	0.303753i	$0.901760\pi$
$140$		0			0
$141$	11.0848	−	19.1994i	0.933508	−	1.61688i
$142$		−	7.12849i		−	0.598209i
$143$	−1.21048	−	0.698874i	−0.101226	−	0.0584427i
$144$	1.51230	−	2.61939i	0.126025	−	0.218282i
$145$		0			0
$146$	2.03774	+	3.52946i	0.168644	+	0.292101i
$147$			21.6411i			1.78492i
$148$	10.2751	+	0.727528i	0.844608	+	0.0598025i
$149$	11.8318			0.969299			0.484650	−	0.874708i	$-0.338947\pi$
$149$	11.8318			0.969299			0.484650	+	0.874708i	$0.338947\pi$
$150$		0			0
$151$	5.23991	−	9.07580i	0.426418	−	0.738578i	−0.570134	−	0.821552i	$-0.693109\pi$
$151$	5.23991	−	9.07580i	0.426418	−	0.738578i	0.996552	+	0.0829741i	$0.0264419\pi$
$152$	−4.54591	−	2.62458i	−0.368722	−	0.212882i
$153$	2.11269	+	1.21976i	0.170801	+	0.0986118i
$154$	−7.64193			−0.615804
$155$		0			0
$156$	−1.48996			−0.119292
$157$	−7.16021	+	4.13395i	−0.571447	+	0.329925i	−0.757727	−	0.652572i	$-0.773690\pi$
$157$	−7.16021	+	4.13395i	−0.571447	+	0.329925i	0.186280	+	0.982497i	$0.440357\pi$
$158$		−	7.95593i		−	0.632940i
$159$	13.0015			1.03109
$160$		0			0
$161$	−2.04716	+	3.54579i	−0.161339	+	0.279447i
$162$			6.21493i			0.488291i
$163$	−9.06508	+	5.23373i	−0.710032	+	0.409937i	−0.811073	−	0.584945i	$-0.801116\pi$
$163$	−9.06508	+	5.23373i	−0.710032	+	0.409937i	0.101041	+	0.994882i	$0.467783\pi$
$164$	−5.32691	−	9.22648i	−0.415962	−	0.720467i
$165$		0			0
$166$	0.306796	−	0.531386i	0.0238120	−	0.0412435i
$167$	−13.4474	−	7.76387i	−1.04059	−	0.600786i	−0.120592	−	0.992702i	$-0.538479\pi$
$167$	−13.4474	−	7.76387i	−1.04059	−	0.600786i	−0.920001	+	0.391916i	$0.871812\pi$
$168$	−15.3865	+	8.88340i	−1.18709	+	0.685369i
$169$	−6.41085	−	11.1039i	−0.493142	−	0.854147i
$170$		0			0
$171$	3.44346			0.263328
$172$	−11.8935	−	6.86670i	−0.906868	−	0.523581i
$173$	17.6698	−	10.2016i	1.34341	−	0.775616i	0.356101	−	0.934448i	$-0.384106\pi$
$173$	17.6698	−	10.2016i	1.34341	−	0.775616i	0.987306	+	0.158832i	$0.0507727\pi$
$174$	8.47977			0.642850
$175$		0			0
$176$	3.73159	+	6.46330i	0.281279	+	0.487190i
$177$		−	2.31886i		−	0.174296i
$178$	3.05038	+	1.76114i	0.228636	+	0.132003i
$179$	5.25745			0.392960			0.196480	−	0.980508i	$-0.437049\pi$
$179$	5.25745			0.392960			0.196480	+	0.980508i	$0.437049\pi$
$180$		0			0
$181$	−8.10382	+	14.0362i	−0.602352	+	1.04330i	0.390112	+	0.920767i	$0.372436\pi$
$181$	−8.10382	+	14.0362i	−0.602352	+	1.04330i	−0.992464	+	0.122537i	$0.960897\pi$
$182$	0.844250	+	0.487428i	0.0625800	+	0.0361306i
$183$	12.2939	−	7.09787i	0.908790	−	0.524690i
$184$	−2.00801			−0.148032
$185$		0			0
$186$	7.59918			0.557199
$187$	−5.21302	+	3.00974i	−0.381214	+	0.220094i
$188$	15.6041	+	9.00904i	1.13805	+	0.657052i
$189$	−7.20457	+	12.4787i	−0.524055	+	0.907690i
$190$		0			0
$191$	26.7359			1.93454			0.967270	−	0.253750i	$-0.0816642\pi$
$191$	26.7359			1.93454			0.967270	+	0.253750i	$0.0816642\pi$
$192$	2.80347	+	1.61859i	0.202323	+	0.116811i
$193$		−	19.0038i		−	1.36792i	−0.729519	−	0.683961i	$-0.760256\pi$
$193$		−	19.0038i		−	1.36792i	0.729519	−	0.683961i	$-0.239744\pi$
$194$	−2.34668	−	4.06457i	−0.168482	−	0.291819i
$195$		0			0
$196$	−17.5885			−1.25632
$197$	4.06860	−	2.34901i	0.289876	−	0.167360i	−0.348010	−	0.937491i	$-0.613142\pi$
$197$	4.06860	−	2.34901i	0.289876	−	0.167360i	0.637886	+	0.770131i	$0.279809\pi$
$198$	2.12923	+	1.22931i	0.151318	+	0.0873633i
$199$	−19.5322			−1.38460			−0.692302	−	0.721608i	$-0.743403\pi$
$199$	−19.5322			−1.38460			−0.692302	+	0.721608i	$0.743403\pi$
$200$		0			0
$201$	7.28878	+	12.6245i	0.514111	+	0.890466i
$202$	5.54049	−	3.19880i	0.389827	−	0.225067i
$203$	26.5426	+	15.3244i	1.86292	+	1.07556i
$204$	−3.20829	+	5.55693i	−0.224626	+	0.389063i
$205$		0			0
$206$	−1.49502	−	2.58946i	−0.104163	−	0.180416i
$207$	1.14078	−	0.658628i	0.0792895	−	0.0457778i
$208$		−	0.952052i		−	0.0660129i
$209$	−4.24835	+	7.35835i	−0.293864	+	0.508988i
$210$		0			0
$211$	22.6710			1.56074			0.780369	−	0.625319i	$-0.215031\pi$
$211$	22.6710			1.56074			0.780369	+	0.625319i	$0.215031\pi$
$212$			10.5669i			0.725734i
$213$	−23.2324	+	13.4132i	−1.59186	+	0.919058i
$214$	4.43903			0.303446
$215$		0			0
$216$	−7.06677			−0.480833
$217$	23.7862	+	13.7330i	1.61471	+	0.932256i
$218$	5.82864	+	3.36517i	0.394766	+	0.227918i
$219$	7.66856	−	13.2823i	0.518193	−	0.897537i
$220$		0			0
$221$	0.767885			0.0516535
$222$	3.07071	+	6.30987i	0.206092	+	0.423491i
$223$			17.5950i			1.17825i	0.808043	+	0.589124i	$0.200527\pi$
$223$			17.5950i			1.17825i	−0.808043	+	0.589124i	$0.799473\pi$
$224$	−11.1294	−	19.2768i	−0.743617	−	1.28798i
$225$		0			0
$226$	−2.34190	+	4.05628i	−0.155781	+	0.269820i
$227$	−18.6352	−	10.7590i	−1.23686	−	0.714103i	−0.268411	−	0.963304i	$-0.586499\pi$
$227$	−18.6352	−	10.7590i	−1.23686	−	0.714103i	−0.968452	+	0.249201i	$0.919832\pi$
$228$			9.05723i			0.599829i
$229$	−6.78627	+	11.7542i	−0.448449	+	0.776737i	−0.998285	−	0.0585357i	$-0.981357\pi$
$229$	−6.78627	+	11.7542i	−0.448449	+	0.776737i	0.549836	+	0.835273i	$0.314690\pi$
$230$		0			0
$231$	14.3793	+	24.9057i	0.946090	+	1.63868i
$232$			15.0313i			0.986852i
$233$			15.6285i			1.02386i	0.859029	+	0.511928i	$0.171068\pi$
$233$			15.6285i			1.02386i	−0.859029	+	0.511928i	$0.828932\pi$
$234$	−0.156819	−	0.271618i	−0.0102516	−	0.0177563i
$235$		0			0
$236$	1.88463			0.122679
$237$	−25.9291	+	14.9702i	−1.68428	+	0.972417i
$238$	3.63581	−	2.09914i	0.235675	−	0.136067i
$239$	−10.0045	−	17.3283i	−0.647138	−	1.12088i	−0.983803	−	0.179251i	$-0.942633\pi$
$239$	−10.0045	−	17.3283i	−0.647138	−	1.12088i	0.336666	−	0.941624i	$-0.390701\pi$
$240$		0			0
$241$	−7.48121	+	12.9578i	−0.481907	+	0.834688i	−0.999784	−	0.0207671i	$-0.993389\pi$
$241$	−7.48121	+	12.9578i	−0.481907	+	0.834688i	0.517877	+	0.855455i	$0.326722\pi$
$242$	0.0206208	−	0.0119054i	0.00132555	−	0.000765308i
$243$	11.2769	−	6.51069i	0.723410	−	0.417661i
$244$	5.76872	+	9.99171i	0.369304	+	0.639654i
$245$		0			0
$246$	3.62893	−	6.28550i	0.231372	−	0.400749i
$247$	0.938680	−	0.541947i	0.0597268	−	0.0344833i
$248$			13.4703i			0.855367i
$249$	−2.30911			−0.146334
$250$		0			0
$251$	1.77587			0.112092			0.0560459	−	0.998428i	$-0.482151\pi$
$251$	1.77587			0.112092			0.0560459	+	0.998428i	$0.482151\pi$
$252$	8.20344	+	4.73626i	0.516768	+	0.298356i
$253$			3.25031i			0.204345i
$254$	5.19042	−	8.99007i	0.325676	−	0.564087i
$255$		0			0
$256$	1.64018	−	2.84087i	0.102511	−	0.177554i
$257$	23.4582	−	13.5436i	1.46328	−	0.844826i	0.464121	−	0.885772i	$-0.346370\pi$
$257$	23.4582	−	13.5436i	1.46328	−	0.844826i	0.999161	+	0.0409457i	$0.0130371\pi$
$258$		−	9.35581i		−	0.582467i
$259$	−1.79136	+	25.2998i	−0.111309	+	1.57206i
$260$		0			0
$261$	−4.93027	−	8.53948i	−0.305176	−	0.528581i
$262$	−5.20452	−	3.00483i	−0.321536	−	0.185639i
$263$	−23.4529	−	13.5405i	−1.44617	−	0.834944i	−0.447916	−	0.894076i	$-0.647834\pi$
$263$	−23.4529	−	13.5405i	−1.44617	−	0.834944i	−0.998250	+	0.0591313i	$0.981167\pi$
$264$	−7.05215	+	12.2147i	−0.434030	+	0.751762i
$265$		0			0
$266$	2.96300	−	5.13207i	0.181673	−	0.314667i
$267$		−	13.2553i		−	0.811211i
$268$	−10.2604	+	5.92387i	−0.626756	+	0.361858i
$269$	25.7066			1.56736			0.783678	−	0.621167i	$-0.213341\pi$
$269$	25.7066			1.56736			0.783678	+	0.621167i	$0.213341\pi$
$270$		0			0
$271$	3.56720	+	6.17856i	0.216692	+	0.375321i	0.953795	−	0.300460i	$-0.0971400\pi$
$271$	3.56720	+	6.17856i	0.216692	+	0.375321i	−0.737103	+	0.675781i	$0.763807\pi$
$272$	−3.55076	−	2.05003i	−0.215297	−	0.124302i
$273$		−	3.66865i		−	0.222037i
$274$	0.719348	+	1.24595i	0.0434574	+	0.0752704i
$275$		0			0
$276$	1.73237	+	3.00055i	0.104276	+	0.180612i
$277$	16.1217	+	9.30784i	0.968656	+	0.559254i	0.898826	−	0.438305i	$-0.144421\pi$
$277$	16.1217	+	9.30784i	0.968656	+	0.559254i	0.0698300	+	0.997559i	$0.477754\pi$
$278$	2.41184	+	1.39248i	0.144653	+	0.0835153i
$279$	−4.41828	−	7.65269i	−0.264516	−	0.458155i
$280$		0			0
$281$	6.85706	+	11.8768i	0.409058	+	0.708509i	0.994784	−	0.102000i	$-0.0325241\pi$
$281$	6.85706	+	11.8768i	0.409058	+	0.708509i	−0.585727	+	0.810509i	$0.699191\pi$
$282$			12.2747i			0.730950i
$283$	−22.3546	−	12.9064i	−1.32884	−	0.767207i	−0.343720	−	0.939072i	$-0.611687\pi$
$283$	−22.3546	−	12.9064i	−1.32884	−	0.767207i	−0.985120	+	0.171865i	$0.945021\pi$
$284$	−10.9014	−	18.8818i	−0.646881	−	1.12043i
$285$		0			0
$286$	0.773897			0.0457615
$287$	22.7179	−	13.1162i	1.34099	−	0.774224i
$288$			7.16130i			0.421984i
$289$	−6.84653	+	11.8585i	−0.402737	+	0.697561i
$290$		0			0
$291$	−8.83120	+	15.2961i	−0.517694	+	0.896673i
$292$	10.7951	+	6.23253i	0.631733	+	0.364731i
$293$	6.65437	+	3.84190i	0.388753	+	0.224446i	0.681619	−	0.731707i	$-0.261276\pi$
$293$	6.65437	+	3.84190i	0.388753	+	0.224446i	−0.292867	+	0.956153i	$0.594609\pi$
$294$	−5.99105	−	10.3768i	−0.349405	−	0.605188i
$295$		0			0
$296$	−11.1849	+	5.44315i	−0.650109	+	0.316376i
$297$			11.4388i			0.663747i
$298$	−5.67330	+	3.27548i	−0.328646	+	0.189744i
$299$	0.207316	−	0.359081i	0.0119894	−	0.0207662i
$300$		0			0
$301$	16.9075	−	29.2847i	0.974533	−	1.68794i
$302$			5.80241i			0.333891i
$303$	−20.8504	−	12.0380i	−1.19782	−	0.691563i
$304$	−5.78738			−0.331929
$305$		0			0
$306$	−1.35070			−0.0772144
$307$		−	22.2658i		−	1.27077i	−0.772194	−	0.635387i	$-0.780841\pi$
$307$		−	22.2658i		−	1.27077i	0.772194	−	0.635387i	$-0.219159\pi$
$308$	−20.2419	+	11.6866i	−1.15339	+	0.665908i
$309$	−5.62618	+	9.74483i	−0.320062	+	0.554364i
$310$		0			0
$311$	−0.205634	−	0.356168i	−0.0116604	−	0.0201964i	0.860136	−	0.510064i	$-0.170378\pi$
$311$	−0.205634	−	0.356168i	−0.0116604	−	0.0201964i	−0.871797	+	0.489868i	$0.837045\pi$
$312$	1.55819	−	0.899620i	0.0882150	−	0.0509309i
$313$	−7.41781	+	4.28268i	−0.419280	+	0.242071i	−0.694769	−	0.719233i	$-0.744493\pi$
$313$	−7.41781	+	4.28268i	−0.419280	+	0.242071i	0.275489	+	0.961304i	$0.411160\pi$
$314$	2.28886	−	3.96442i	0.129168	−	0.223725i
$315$		0			0
$316$	−12.1668	−	21.0736i	−0.684438	−	1.18548i
$317$	6.56223	−	3.78870i	0.368571	−	0.212795i	−0.304263	−	0.952588i	$-0.598410\pi$
$317$	6.56223	−	3.78870i	0.368571	−	0.212795i	0.672834	+	0.739793i	$0.265077\pi$
$318$	−6.23419	+	3.59931i	−0.349596	+	0.201839i
$319$	24.3307			1.36226
$320$		0			0
$321$	−8.35265	−	14.4672i	−0.466199	−	0.807481i
$322$		−	2.26692i		−	0.126331i
$323$		−	4.66786i		−	0.259726i
$324$	9.50435	+	16.4620i	0.528020	+	0.914557i
$325$		0			0
$326$	2.89778	−	5.01911i	0.160493	−	0.277983i
$327$		−	25.3281i		−	1.40065i
$328$	11.1417	+	6.43266i	0.615197	+	0.355184i
$329$	−22.1825	+	38.4212i	−1.22296	+	2.11823i
$330$		0			0
$331$	−5.99113	−	10.3769i	−0.329302	−	0.570368i	0.653071	−	0.757296i	$-0.273480\pi$
$331$	−5.99113	−	10.3769i	−0.329302	−	0.570368i	−0.982374	+	0.186928i	$0.940147\pi$
$332$		−	1.87670i		−	0.102998i
$333$	4.56894	−	6.76099i	0.250377	−	0.370500i
$334$	8.59732			0.470424
$335$		0			0
$336$	−9.79424	+	16.9641i	−0.534320	+	0.925469i
$337$	−11.3161	−	6.53336i	−0.616428	−	0.355895i	0.159049	−	0.987271i	$-0.449157\pi$
$337$	−11.3161	−	6.53336i	−0.616428	−	0.355895i	−0.775477	+	0.631376i	$0.782491\pi$
$338$	6.14795	+	3.54952i	0.334405	+	0.193069i
$339$	17.6264			0.957333
$340$		0			0
$341$	21.8041			1.18076
$342$	−1.65113	+	0.953279i	−0.0892828	+	0.0515474i
$343$		−	14.1196i		−	0.762385i
$344$	16.5841			0.894157
$345$		0			0
$346$	−5.64839	+	9.78329i	−0.303659	+	0.525953i
$347$			19.0759i			1.02405i	0.858970	+	0.512025i	$0.171105\pi$
$347$			19.0759i			1.02405i	−0.858970	+	0.512025i	$0.828895\pi$
$348$	22.4611	−	12.9679i	1.20404	−	0.695154i
$349$	3.18681	+	5.51972i	0.170586	+	0.295464i	0.938625	−	0.344940i	$-0.112101\pi$
$349$	3.18681	+	5.51972i	0.170586	+	0.295464i	−0.768039	+	0.640403i	$0.778767\pi$
$350$		0			0
$351$	0.729605	−	1.26371i	0.0389434	−	0.0674520i
$352$	−15.3030	−	8.83520i	−0.815653	−	0.470918i
$353$	27.3421	−	15.7860i	1.45528	−	0.840204i	0.456503	−	0.889722i	$-0.349102\pi$
$353$	27.3421	−	15.7860i	1.45528	−	0.840204i	0.998773	+	0.0495182i	$0.0157686\pi$
$354$	0.641946	+	1.11188i	0.0341191	+	0.0590960i
$355$		0			0
$356$	10.7731			0.570973
$357$	−13.6825	−	7.89962i	−0.724157	−	0.418092i
$358$	−2.52093	+	1.45546i	−0.133235	+	0.0769233i
$359$	5.95281			0.314178			0.157089	−	0.987584i	$-0.449789\pi$
$359$	5.95281			0.314178			0.157089	+	0.987584i	$0.449789\pi$
$360$		0			0
$361$	6.20558	+	10.7484i	0.326610	+	0.565705i
$362$		−	8.97375i		−	0.471650i
$363$	−0.0776015	−	0.0448032i	−0.00407302	−	0.00235156i
$364$	2.98165			0.156281
$365$		0			0
$366$	−3.92991	+	6.80681i	−0.205420	+	0.355797i
$367$	2.16022	+	1.24720i	0.112762	+	0.0651034i	0.555320	−	0.831636i	$-0.312596\pi$
$367$	2.16022	+	1.24720i	0.112762	+	0.0651034i	−0.442558	+	0.896740i	$0.645929\pi$
$368$	−1.91729	+	1.10695i	−0.0999456	+	0.0577036i
$369$	−8.43968			−0.439352
$370$		0			0
$371$	−26.0182			−1.35080
$372$	20.1286	−	11.6213i	1.04362	−	0.602534i
$373$	−4.91257	−	2.83628i	−0.254363	−	0.146857i	0.367397	−	0.930064i	$-0.380249\pi$
$373$	−4.91257	−	2.83628i	−0.254363	−	0.146857i	−0.621761	+	0.783207i	$0.713582\pi$
$374$	1.66642	−	2.88632i	0.0861683	−	0.149248i
$375$		0			0
$376$	−21.7582			−1.12210
$377$	−2.68796	−	1.55190i	−0.138437	−	0.0799267i
$378$		−	7.97797i		−	0.410342i
$379$	9.31248	+	16.1297i	0.478350	+	0.828527i	0.999692	−	0.0248212i	$-0.00790164\pi$
$379$	9.31248	+	16.1297i	0.478350	+	0.828527i	−0.521342	+	0.853348i	$0.674568\pi$
$380$		0			0
$381$	−39.0659			−2.00141
$382$	−12.8197	+	7.40148i	−0.655915	+	0.378693i
$383$	7.52514	+	4.34464i	0.384517	+	0.222001i	0.679782	−	0.733415i	$-0.262075\pi$
$383$	7.52514	+	4.34464i	0.384517	+	0.222001i	−0.295265	+	0.955415i	$0.595408\pi$
$384$	−24.0383			−1.22670
$385$		0			0
$386$	5.26095	+	9.11223i	0.267775	+	0.463800i
$387$	−9.42169	+	5.43961i	−0.478931	+	0.276511i
$388$	−12.4317	−	7.17746i	−0.631125	−	0.364380i
$389$	18.4517	−	31.9593i	0.935538	−	1.62040i	0.161866	−	0.986813i	$-0.448249\pi$
$389$	18.4517	−	31.9593i	0.935538	−	1.62040i	0.773672	−	0.633587i	$-0.218418\pi$
$390$		0			0
$391$	−0.892817	−	1.54640i	−0.0451517	−	0.0782050i
$392$	18.3940	−	10.6198i	0.929035	−	0.536379i
$393$			22.6160i			1.14083i
$394$	−1.30059	+	2.25268i	−0.0655226	+	0.113488i
$395$		0			0
$396$	7.51983			0.377886
$397$			9.74587i			0.489131i	0.969633	+	0.244566i	$0.0786453\pi$
$397$			9.74587i			0.489131i	−0.969633	+	0.244566i	$0.921355\pi$
$398$	9.36564	−	5.40725i	0.469457	−	0.271041i
$399$	−22.3011			−1.11645
$400$		0			0
$401$	18.5290			0.925295			0.462648	−	0.886542i	$-0.346900\pi$
$401$	18.5290			0.925295			0.462648	+	0.886542i	$0.346900\pi$
$402$	−6.98988	−	4.03561i	−0.348624	−	0.201278i
$403$	−2.40883	−	1.39074i	−0.119992	−	0.0692776i
$404$	9.78372	−	16.9459i	0.486758	−	0.843090i
$405$		0			0
$406$	−16.9694			−0.842178
$407$	8.81068	+	18.1047i	0.436729	+	0.897417i
$408$		−	7.74853i		−	0.383609i
$409$	13.5142	+	23.4073i	0.668234	+	1.15741i	0.978398	+	0.206732i	$0.0662827\pi$
$409$	13.5142	+	23.4073i	0.668234	+	1.15741i	−0.310164	+	0.950683i	$0.600384\pi$
$410$		0			0
$411$	2.70710	−	4.68883i	0.133531	−	0.231283i
$412$	−7.92000	−	4.57262i	−0.390191	−	0.225277i
$413$			4.64042i			0.228340i
$414$	−0.364666	+	0.631620i	−0.0179223	+	0.0310424i
$415$		0			0
$416$	1.12708	+	1.95215i	0.0552595	+	0.0957122i
$417$		−	10.4805i		−	0.513234i
$418$		−	4.70440i		−	0.230100i
$419$	7.13420	+	12.3568i	0.348528	+	0.603669i	0.985988	−	0.166815i	$-0.0533482\pi$
$419$	7.13420	+	12.3568i	0.348528	+	0.603669i	−0.637460	+	0.770483i	$0.720015\pi$
$420$		0			0
$421$	−10.2023			−0.497228			−0.248614	−	0.968603i	$-0.579975\pi$
$421$	−10.2023			−0.497228			−0.248614	+	0.968603i	$0.579975\pi$
$422$	−10.8707	+	6.27619i	−0.529176	+	0.305520i
$423$	12.3612	−	7.13672i	0.601021	−	0.346999i
$424$	−6.38015	−	11.0507i	−0.309847	−	0.536671i
$425$		0			0
$426$	7.42655	−	12.8632i	0.359818	−	0.623223i
$427$	−24.6021	+	14.2040i	−1.19058	+	0.687380i
$428$	11.7581	−	6.78852i	0.568347	−	0.328135i
$429$	−1.45619	−	2.52220i	−0.0703056	−	0.121773i
$430$		0			0
$431$	10.7429	−	18.6073i	0.517469	−	0.896283i	−0.482325	−	0.875993i	$-0.660207\pi$
$431$	10.7429	−	18.6073i	0.517469	−	0.896283i	0.999794	−	0.0202909i	$-0.00645923\pi$
$432$	−6.74751	+	3.89568i	−0.324640	+	0.187431i
$433$			3.74389i			0.179920i	0.995945	+	0.0899600i	$0.0286739\pi$
$433$			3.74389i			0.179920i	−0.995945	+	0.0899600i	$0.971326\pi$
$434$	−15.2072			−0.729970
$435$		0			0
$436$	20.5851			0.985848
$437$	−2.18280	−	1.26024i	−0.104418	−	0.0602855i
$438$			8.49177i			0.405752i
$439$	14.3980	−	24.9380i	0.687178	−	1.19023i	−0.285569	−	0.958358i	$-0.592182\pi$
$439$	14.3980	−	24.9380i	0.687178	−	1.19023i	0.972747	−	0.231870i	$-0.0744842\pi$
$440$		0			0
$441$	−6.96658	+	12.0665i	−0.331742	+	0.574594i
$442$	−0.368198	+	0.212579i	−0.0175134	+	0.0101114i
$443$		−	17.7114i		−	0.841493i	−0.907178	−	0.420747i	$-0.861768\pi$
$443$		−	17.7114i		−	0.841493i	0.907178	−	0.420747i	$-0.138232\pi$
$444$	17.7832	+	12.0175i	0.843953	+	0.570327i
$445$		0			0
$446$	−4.87095	−	8.43673i	−0.230646	−	0.399491i
$447$	21.3502	+	12.3265i	1.00983	+	0.583025i
$448$	−5.61021	−	3.23906i	−0.265058	−	0.153031i
$449$	4.14130	−	7.17293i	0.195440	−	0.338512i	−0.751605	−	0.659614i	$-0.770720\pi$
$449$	4.14130	−	7.17293i	0.195440	−	0.338512i	0.947045	+	0.321102i	$0.104053\pi$
$450$		0			0
$451$	10.4124	−	18.0348i	0.490300	−	0.849225i
$452$			14.3256i			0.673821i
$453$	18.9106	−	10.9180i	0.888496	−	0.512974i
$454$	11.9140			0.559153
$455$		0			0
$456$	−5.46865	−	9.47198i	−0.256093	−	0.443566i
$457$	−15.4665	−	8.92960i	−0.723493	−	0.417709i	0.0925438	−	0.995709i	$-0.470500\pi$
$457$	−15.4665	−	8.92960i	−0.723493	−	0.417709i	−0.816037	+	0.578000i	$0.803834\pi$
$458$		−	7.51477i		−	0.351142i
$459$	−3.14209	−	5.44225i	−0.146660	−	0.254023i
$460$		0			0
$461$	−17.1084	−	29.6325i	−0.796816	−	1.38013i	−0.921680	−	0.387951i	$-0.873183\pi$
$461$	−17.1084	−	29.6325i	−0.796816	−	1.38013i	0.124864	−	0.992174i	$-0.460150\pi$
$462$	−13.7897	−	7.96147i	−0.641553	−	0.370401i
$463$	4.42662	+	2.55571i	0.205722	+	0.118774i	0.599322	−	0.800508i	$-0.295437\pi$
$463$	4.42662	+	2.55571i	0.205722	+	0.118774i	−0.393599	+	0.919282i	$0.628770\pi$
$464$	8.28624	+	14.3522i	0.384679	+	0.666284i
$465$		0			0
$466$	−4.32654	−	7.49379i	−0.200423	−	0.347143i
$467$			19.2722i			0.891811i	0.895080	+	0.445906i	$0.147118\pi$
$467$			19.2722i			0.891811i	−0.895080	+	0.445906i	$0.852882\pi$
$468$	−0.830760	−	0.479640i	−0.0384019	−	0.0221714i
$469$	−14.5860	−	25.2638i	−0.673521	−	1.16657i
$470$		0			0
$471$	−17.2272			−0.793788
$472$	−1.97093	+	1.13792i	−0.0907194	+	0.0523768i
$473$		−	26.8443i		−	1.23430i
$474$	8.28860	−	14.3563i	0.380708	−	0.659406i
$475$		0			0
$476$	6.42033	−	11.1203i	0.294275	−	0.509700i
$477$	7.24931	+	4.18539i	0.331923	+	0.191636i
$478$	9.59425	+	5.53924i	0.438831	+	0.253359i
$479$	−17.3117	−	29.9848i	−0.790993	−	1.37004i	−0.925353	−	0.379107i	$-0.876231\pi$
$479$	−17.3117	−	29.9848i	−0.790993	−	1.37004i	0.134360	−	0.990933i	$-0.457102\pi$
$480$		0			0
$481$	0.181410	−	2.56211i	0.00827159	−	0.116822i
$482$		−	8.28431i		−	0.377340i
$483$	−7.38810	+	4.26552i	−0.336170	+	0.194088i
$484$	0.0364133	−	0.0630697i	0.00165515	−	0.00286681i
$485$		0			0
$486$	−3.60480	+	6.24370i	−0.163517	+	0.283220i
$487$		−	15.7551i		−	0.713932i	−0.934117	−	0.356966i	$-0.883811\pi$
$487$		−	15.7551i		−	0.713932i	0.934117	−	0.356966i	$-0.116189\pi$
$488$	−12.0658	−	6.96617i	−0.546192	−	0.315344i
$489$	−21.8103			−0.986295
$490$		0			0
$491$	−22.4017			−1.01098			−0.505488	−	0.862834i	$-0.668688\pi$
$491$	−22.4017			−1.01098			−0.505488	+	0.862834i	$0.668688\pi$
$492$		−	22.1986i		−	1.00079i
$493$	−11.5759	+	6.68333i	−0.521351	+	0.301002i
$494$	−0.300062	+	0.519723i	−0.0135004	+	0.0233835i
$495$		0			0
$496$	7.42575	+	12.8618i	0.333426	+	0.577511i
$497$	46.4918	−	26.8421i	2.08544	−	1.20403i
$498$	1.10721	−	0.639248i	0.0496153	−	0.0286454i
$499$	3.05728	−	5.29537i	0.136863	−	0.237053i	−0.789445	−	0.613822i	$-0.789631\pi$
$499$	3.05728	−	5.29537i	0.136863	−	0.237053i	0.926308	+	0.376768i	$0.122965\pi$
$500$		0			0
$501$	−16.1770	−	28.0194i	−0.722736	−	1.25182i
$502$	−0.851522	+	0.491627i	−0.0380053	+	0.0219424i
$503$	11.2819	−	6.51360i	0.503035	−	0.290427i	−0.226931	−	0.973911i	$-0.572869\pi$
$503$	11.2819	−	6.51360i	0.503035	−	0.290427i	0.729966	+	0.683484i	$0.239536\pi$
$504$	−11.4388			−0.509524
$505$		0			0
$506$	−0.899807	−	1.55851i	−0.0400013	−	0.0692843i
$507$		−	26.7156i		−	1.18648i
$508$		−	31.7504i		−	1.40870i
$509$	−19.1425	−	33.1558i	−0.848476	−	1.46960i	−0.882568	−	0.470185i	$-0.844187\pi$
$509$	−19.1425	−	33.1558i	−0.848476	−	1.46960i	0.0340913	−	0.999419i	$-0.489146\pi$
$510$		0			0
$511$	−15.3460	+	26.5801i	−0.678869	+	1.17584i
$512$		−	21.2572i		−	0.939446i
$513$	−7.68192	−	4.43516i	−0.339165	−	0.195817i
$514$	−7.49874	+	12.9882i	−0.330755	+	0.572885i
$515$		0			0
$516$	−14.3076	−	24.7815i	−0.629858	−	1.09095i
$517$			35.2195i			1.54895i
$518$	−6.14499	−	12.6271i	−0.269995	−	0.554803i
$519$	42.5128			1.86611
$520$		0			0
$521$	−15.3868	+	26.6507i	−0.674108	+	1.16759i	0.302621	+	0.953111i	$0.402138\pi$
$521$	−15.3868	+	26.6507i	−0.674108	+	1.16759i	−0.976729	+	0.214478i	$0.931195\pi$
$522$	4.72809	+	2.72977i	0.206943	+	0.119479i
$523$	−27.9344	−	16.1279i	−1.22149	−	0.705225i	−0.256252	−	0.966610i	$-0.582488\pi$
$523$	−27.9344	−	16.1279i	−1.22149	−	0.705225i	−0.965235	+	0.261385i	$0.915821\pi$
$524$	−18.3809			−0.802973
$525$		0			0
$526$	14.9941			0.653773
$527$	−10.3738	+	5.98929i	−0.451888	+	0.260898i
$528$			15.5505i			0.676748i
$529$	22.0358			0.958079
$530$		0			0
$531$	0.746475	−	1.29293i	0.0323943	−	0.0561085i
$532$		−	18.1250i		−	0.785819i
$533$	−2.30064	+	1.32827i	−0.0996516	+	0.0575339i
$534$	3.66956	+	6.35586i	0.158797	+	0.275045i
$535$		0			0
$536$	7.15353	−	12.3903i	0.308986	−	0.535179i
$537$	9.48693	+	5.47728i	0.409391	+	0.236362i
$538$	−12.3262	+	7.11653i	−0.531420	+	0.306816i
$539$	−17.1899	−	29.7738i	−0.740423	−	1.28245i
$540$		0			0
$541$	−31.2603			−1.34399			−0.671993	−	0.740557i	$-0.734562\pi$
$541$	−31.2603			−1.34399			−0.671993	+	0.740557i	$0.734562\pi$
$542$	−3.42091	−	1.97506i	−0.146941	−	0.0848363i
$543$	−29.2462	+	16.8853i	−1.25508	+	0.724619i
$544$	9.70764			0.416212
$545$		0			0
$546$	1.01562	+	1.75910i	0.0434644	+	0.0752826i
$547$		−	22.2524i		−	0.951445i	−0.879596	−	0.475722i	$-0.842187\pi$
$547$		−	22.2524i		−	0.951445i	0.879596	−	0.475722i	$-0.157813\pi$
$548$	3.81080	+	2.20017i	0.162789	+	0.0939864i
$549$	9.13965			0.390071
$550$		0			0
$551$	−9.43374	+	16.3397i	−0.401891	+	0.696095i
$552$	−3.62340	−	2.09197i	−0.154222	−	0.0890401i
$553$	51.8884	−	29.9578i	2.20652	−	1.27393i
$554$	−10.3070			−0.437904
$555$		0			0
$556$	8.51794			0.361241
$557$	24.0139	−	13.8644i	1.01750	−	0.587455i	0.104123	−	0.994564i	$-0.466796\pi$
$557$	24.0139	−	13.8644i	1.01750	−	0.587455i	0.913380	+	0.407109i	$0.133463\pi$
$558$	4.23710	+	2.44629i	0.179371	+	0.103560i
$559$	−1.71222	+	2.96565i	−0.0724192	+	0.125434i
$560$		0			0
$561$	−12.5424			−0.529538
$562$	−6.57587	−	3.79658i	−0.277386	−	0.160149i
$563$			2.34779i			0.0989477i	0.998775	+	0.0494739i	$0.0157545\pi$
$563$			2.34779i			0.0989477i	−0.998775	+	0.0494739i	$0.984246\pi$
$564$	18.7715	+	32.5132i	0.790422	+	1.36905i
$565$		0			0
$566$	14.2919			0.600733
$567$	−40.5336	+	23.4021i	−1.70225	+	0.982795i
$568$	22.8013	+	13.1643i	0.956721	+	0.552363i
$569$	37.8548			1.58695			0.793477	−	0.608600i	$-0.208268\pi$
$569$	37.8548			1.58695			0.793477	+	0.608600i	$0.208268\pi$
$570$		0			0
$571$	−6.98035	−	12.0903i	−0.292119	−	0.505965i	0.682192	−	0.731173i	$-0.261027\pi$
$571$	−6.98035	−	12.0903i	−0.292119	−	0.505965i	−0.974311	+	0.225209i	$0.927694\pi$
$572$	2.04989	−	1.18350i	0.0857101	−	0.0494848i
$573$	48.2442	+	27.8538i	2.01543	+	1.16361i
$574$	−7.26209	+	12.5783i	−0.303114	+	0.525009i
$575$		0			0
$576$	1.04209	+	1.80496i	0.0434206	+	0.0752067i
$577$	32.3664	−	18.6868i	1.34743	−	0.777940i	0.359547	−	0.933127i	$-0.382931\pi$
$577$	32.3664	−	18.6868i	1.34743	−	0.777940i	0.987885	+	0.155186i	$0.0495978\pi$
$578$		−	7.58150i		−	0.315349i
$579$	19.7984	−	34.2918i	0.822793	−	1.42512i
$580$		0			0
$581$	4.62091			0.191708
$582$		−	9.77922i		−	0.405362i
$583$	−17.8876	+	10.3274i	−0.740827	+	0.427717i
$584$	−15.0525			−0.622878
$585$		0			0
$586$	−4.25433			−0.175745
$587$	31.1660	+	17.9937i	1.28636	+	0.742680i	0.978003	−	0.208591i	$-0.0668878\pi$
$587$	31.1660	+	17.9937i	1.28636	+	0.742680i	0.308356	+	0.951271i	$0.400221\pi$
$588$	−31.7380	−	18.3240i	−1.30885	−	0.755668i
$589$	−8.45408	+	14.6429i	−0.348344	+	0.603350i
$590$		0			0
$591$	9.78892			0.402662
$592$	−7.67896	+	11.3631i	−0.315603	+	0.467020i
$593$			17.1423i			0.703948i	0.936010	+	0.351974i	$0.114489\pi$
$593$			17.1423i			0.703948i	−0.936010	+	0.351974i	$0.885511\pi$
$594$	−3.16669	−	5.48486i	−0.129931	−	0.225047i
$595$		0			0
$596$	−10.0183	+	17.3521i	−0.410364	+	0.710771i
$597$	−35.2454	−	20.3490i	−1.44250	−	0.832828i
$598$			0.229571i			0.00938785i
$599$	−17.1858	+	29.7667i	−0.702193	+	1.21623i	0.265502	+	0.964110i	$0.414462\pi$
$599$	−17.1858	+	29.7667i	−0.702193	+	1.21623i	−0.967695	+	0.252123i	$0.918871\pi$
$600$		0			0
$601$	−10.8607	−	18.8114i	−0.443019	−	0.767332i	0.554893	−	0.831922i	$-0.312759\pi$
$601$	−10.8607	−	18.8114i	−0.443019	−	0.767332i	−0.997912	+	0.0645903i	$0.979426\pi$
$602$			18.7225i			0.763073i
$603$			9.38547i			0.382206i
$604$	8.87350	+	15.3694i	0.361058	+	0.625370i
$605$		0			0
$606$	13.3302			0.541503
$607$	19.9809	−	11.5360i	0.811001	−	0.468232i	−0.0363022	−	0.999341i	$-0.511558\pi$
$607$	19.9809	−	11.5360i	0.811001	−	0.468232i	0.847303	+	0.531109i	$0.178225\pi$
$608$	11.8668	−	6.85133i	0.481264	−	0.277858i
$609$	31.9303	+	55.3049i	1.29388	+	2.24107i
$610$		0			0
$611$	2.24642	−	3.89091i	0.0908803	−	0.157409i
$612$	−3.57772	+	2.06560i	−0.144621	+	0.0834968i
$613$	−20.0694	+	11.5871i	−0.810595	+	0.467997i	−0.847163	−	0.531334i	$-0.821691\pi$
$613$	−20.0694	+	11.5871i	−0.810595	+	0.467997i	0.0365672	+	0.999331i	$0.488358\pi$
$614$	6.16399	+	10.6763i	0.248758	+	0.430862i
$615$		0			0
$616$	14.1125	−	24.4436i	0.568610	−	0.984861i
$617$	6.23115	−	3.59756i	0.250857	−	0.144832i	−0.369300	−	0.929310i	$-0.620402\pi$
$617$	6.23115	−	3.59756i	0.250857	−	0.144832i	0.620156	+	0.784478i	$0.287069\pi$
$618$		−	6.23015i		−	0.250613i
$619$	−15.6038			−0.627169			−0.313584	−	0.949560i	$-0.601530\pi$
$619$	−15.6038			−0.627169			−0.313584	+	0.949560i	$0.601530\pi$
$620$		0			0
$621$	−3.39324			−0.136166
$622$	0.197201	+	0.113854i	0.00790704	+	0.00456513i
$623$			26.5260i			1.06274i
$624$	0.991861	−	1.71795i	0.0397062	−	0.0687732i
$625$		0			0
$626$	2.37121	−	4.10705i	0.0947726	−	0.164151i
$627$	−15.3321	+	8.85197i	−0.612304	+	0.353514i
$628$		−	14.0012i		−	0.558710i
$629$	−9.16499	−	6.19352i	−0.365432	−	0.246952i
$630$		0			0
$631$	23.8415	+	41.2947i	0.949115	+	1.64392i	0.747295	+	0.664493i	$0.231352\pi$
$631$	23.8415	+	41.2947i	0.949115	+	1.64392i	0.201820	+	0.979423i	$0.435314\pi$
$632$	25.4480	+	14.6924i	1.01227	+	0.584432i
$633$	40.9093	+	23.6190i	1.62600	+	0.938771i
$634$	−2.09771	+	3.63334i	−0.0833107	+	0.144298i
$635$		0			0
$636$	−11.0087	+	19.0676i	−0.436523	+	0.756080i
$637$			4.38573i			0.173769i
$638$	−11.6665	+	6.73566i	−0.461881	+	0.266667i
$639$	−17.2717			−0.683256
$640$		0			0
$641$	0.152125	+	0.263489i	0.00600859	+	0.0104072i	0.869014	−	0.494787i	$-0.164754\pi$
$641$	0.152125	+	0.263489i	0.00600859	+	0.0104072i	−0.863005	+	0.505195i	$0.831421\pi$
$642$	8.01012	+	4.62465i	0.316134	+	0.182520i
$643$		−	8.63335i		−	0.340466i	−0.985404	−	0.170233i	$-0.945548\pi$
$643$		−	8.63335i		−	0.340466i	0.985404	−	0.170233i	$-0.0544521\pi$
$644$	−3.46675	−	6.00459i	−0.136609	−	0.236614i
$645$		0			0
$646$	1.29224	+	2.23822i	0.0508424	+	0.0880615i
$647$	3.97510	+	2.29503i	0.156277	+	0.0902268i	0.576099	−	0.817380i	$-0.304574\pi$
$647$	3.97510	+	2.29503i	0.156277	+	0.0902268i	−0.419822	+	0.907607i	$0.637907\pi$
$648$	−19.8792	−	11.4772i	−0.780928	−	0.450869i
$649$	1.84192	+	3.19029i	0.0723016	+	0.125230i
$650$		0			0
$651$	28.6144	+	49.5616i	1.12149	+	1.94247i
$652$		−	17.7261i		−	0.694206i
$653$	−16.2993	−	9.41039i	−0.637840	−	0.368257i	0.145942	−	0.989293i	$-0.453379\pi$
$653$	−16.2993	−	9.41039i	−0.637840	−	0.368257i	−0.783782	+	0.621036i	$0.786712\pi$
$654$	7.01176	+	12.1447i	0.274181	+	0.474896i
$655$		0			0
$656$	14.1844			0.553810
$657$	8.55156	−	4.93725i	0.333628	−	0.192620i
$658$		−	24.5638i		−	0.957596i
$659$	−7.01863	+	12.1566i	−0.273407	+	0.473555i	−0.969732	−	0.244172i	$-0.921484\pi$
$659$	−7.01863	+	12.1566i	−0.273407	+	0.473555i	0.696325	+	0.717727i	$0.254817\pi$
$660$		0			0
$661$	−11.0696	+	19.1731i	−0.430556	+	0.745746i	−0.996921	−	0.0784091i	$-0.975016\pi$
$661$	−11.0696	+	19.1731i	−0.430556	+	0.745746i	0.566365	+	0.824155i	$0.308349\pi$
$662$	5.74545	+	3.31714i	0.223303	+	0.128924i
$663$	1.38563	+	0.799993i	0.0538133	+	0.0310691i
$664$	1.13313	+	1.96264i	0.0439741	+	0.0761653i
$665$		0			0
$666$	−0.319098	+	4.50672i	−0.0123648	+	0.174632i
$667$			7.21754i			0.279464i
$668$	22.7725	−	13.1477i	0.881093	−	0.508699i
$669$	−18.3307	+	31.7497i	−0.708705	+	1.22751i
$670$		0			0
$671$	−11.2760	+	19.5306i	−0.435304	+	0.753969i
$672$		−	46.3792i		−	1.78912i
$673$	34.3744	+	19.8461i	1.32504	+	0.765009i	0.984527	−	0.175232i	$-0.0560676\pi$
$673$	34.3744	+	19.8461i	1.32504	+	0.765009i	0.340508	+	0.940242i	$0.389401\pi$
$674$	7.23471			0.278671
$675$		0			0
$676$	21.7128			0.835109
$677$			18.7951i			0.722356i	0.932497	+	0.361178i	$0.117625\pi$
$677$			18.7951i			0.722356i	−0.932497	+	0.361178i	$0.882375\pi$
$678$	−8.45178	+	4.87964i	−0.324589	+	0.187401i
$679$	17.6727	−	30.6100i	0.678216	−	1.17470i
$680$		0			0
$681$	−22.4178	−	38.8288i	−0.859054	−	1.48792i
$682$	−10.4550	+	6.03618i	−0.400342	+	0.231137i
$683$	−4.28743	+	2.47535i	−0.164054	+	0.0947167i	−0.579779	−	0.814774i	$-0.696861\pi$
$683$	−4.28743	+	2.47535i	−0.164054	+	0.0947167i	0.415725	+	0.909490i	$0.363528\pi$
$684$	−2.91566	+	5.05007i	−0.111483	+	0.193094i
$685$		0			0
$686$	3.90882	+	6.77027i	0.149239	+	0.258490i
$687$	−24.4913	+	14.1401i	−0.934401	+	0.539477i
$688$	15.8349	−	9.14228i	0.603700	−	0.348546i
$689$	2.63486			0.100380
$690$		0			0
$691$	2.46194	+	4.26420i	0.0936566	+	0.162218i	0.909047	−	0.416693i	$-0.136811\pi$
$691$	2.46194	+	4.26420i	0.0936566	+	0.162218i	−0.815391	+	0.578911i	$0.803478\pi$
$692$			34.5518i			1.31346i
$693$			18.5157i			0.703353i
$694$	−5.28093	−	9.14684i	−0.200461	−	0.347209i
$695$		0			0
$696$	−15.6598	+	27.1235i	−0.593583	+	1.02812i
$697$			11.4406i			0.433343i
$698$	−3.05613	−	1.76445i	−0.115676	−	0.0667856i
$699$	−16.2820	+	28.2012i	−0.615840	+	1.06667i
$700$		0			0
$701$	−14.3244	−	24.8106i	−0.541025	−	0.937083i	−0.998845	−	0.0480383i	$-0.984703\pi$
$701$	−14.3244	−	24.8106i	−0.541025	−	0.937083i	0.457820	−	0.889045i	$-0.348630\pi$
$702$			0.807928i			0.0304933i
$703$	−15.5747	−	1.10277i	−0.587410	−	0.0415916i
$704$	−5.14270			−0.193823
$705$		0			0
$706$	−8.74030	+	15.1387i	−0.328946	+	0.569751i
$707$	41.7250	+	24.0899i	1.56923	+	0.905996i
$708$	3.40076	+	1.96343i	0.127808	+	0.0737902i
$709$	15.6018			0.585936			0.292968	−	0.956122i	$-0.405357\pi$
$709$	15.6018			0.585936			0.292968	+	0.956122i	$0.405357\pi$
$710$		0			0
$711$	−19.2765			−0.722925
$712$	−11.2664	+	6.50467i	−0.422227	+	0.243773i
$713$			6.46802i			0.242229i
$714$	8.74763			0.327372
$715$		0			0
$716$	−4.45160	+	7.71039i	−0.166364	+	0.288151i
$717$		−	41.6913i		−	1.55699i
$718$	−2.85435	+	1.64796i	−0.106523	+	0.0615014i
$719$	−7.84836	−	13.5938i	−0.292694	−	0.506961i	0.681752	−	0.731584i	$-0.261218\pi$
$719$	−7.84836	−	13.5938i	−0.292694	−	0.506961i	−0.974446	+	0.224622i	$0.927885\pi$
$720$		0			0
$721$	11.2589	−	19.5010i	0.419304	−	0.726256i
$722$	−5.95111	−	3.43587i	−0.221477	−	0.127870i
$723$	−26.9993	+	15.5881i	−1.00412	+	0.579726i
$724$	−13.7234	−	23.7696i	−0.510025	−	0.883389i
$725$		0			0
$726$	0.0496128			0.00184130
$727$	−45.7798	−	26.4310i	−1.69788	−	0.980270i	−0.947771	−	0.318953i	$-0.896669\pi$
$727$	−45.7798	−	26.4310i	−1.69788	−	0.980270i	−0.750107	−	0.661317i	$-0.769998\pi$
$728$	−3.11819	+	1.80029i	−0.115568	+	0.0667231i
$729$	−6.54292			−0.242331
$730$		0			0
$731$	7.37378	+	12.7718i	0.272729	+	0.472380i
$732$			24.0397i			0.888533i
$733$	−27.2860	−	15.7536i	−1.00783	−	0.581873i	−0.0972764	−	0.995257i	$-0.531013\pi$
$733$	−27.2860	−	15.7536i	−1.00783	−	0.581873i	−0.910556	+	0.413385i	$0.864346\pi$
$734$	−1.38109			−0.0509768
$735$		0			0
$736$	2.62090	−	4.53953i	0.0966075	−	0.167329i
$737$	−20.0558	−	11.5792i	−0.738767	−	0.426527i
$738$	4.04679	−	2.33642i	0.148964	−	0.0860047i
$739$	27.2457			1.00225			0.501125	−	0.865375i	$-0.332920\pi$
$739$	27.2457			1.00225			0.501125	+	0.865375i	$0.332920\pi$
$740$		0			0
$741$	2.25843			0.0829656
$742$	12.4756	−	7.20281i	0.457995	−	0.264424i
$743$	−35.7055	−	20.6146i	−1.30991	−	0.756276i	−0.327829	−	0.944737i	$-0.606317\pi$
$743$	−35.7055	−	20.6146i	−1.30991	−	0.756276i	−0.982081	+	0.188461i	$0.939650\pi$
$744$	−14.0336	+	24.3069i	−0.514496	+	0.891133i
$745$		0			0
$746$	3.14075			0.114991
$747$	−1.28750	−	0.743337i	−0.0471071	−	0.0271973i
$748$		−	10.1937i		−	0.372717i
$749$	16.7150	+	28.9513i	0.610754	+	1.05786i
$750$		0			0
$751$	43.6030			1.59110			0.795548	−	0.605891i	$-0.207183\pi$
$751$	43.6030			1.59110			0.795548	+	0.605891i	$0.207183\pi$
$752$	−20.7752	+	11.9946i	−0.757595	+	0.437398i
$753$	3.20451	+	1.85012i	0.116779	+	0.0674223i
$754$	1.71849			0.0625837
$755$		0			0
$756$	−12.2005	−	21.1319i	−0.443729	−	0.768561i
$757$	35.7546	−	20.6429i	1.29952	−	0.750280i	0.319201	−	0.947687i	$-0.396585\pi$
$757$	35.7546	−	20.6429i	1.29952	−	0.750280i	0.980322	+	0.197407i	$0.0632521\pi$
$758$	−8.93060	−	5.15608i	−0.324374	−	0.187277i
$759$	−3.38622	+	5.86510i	−0.122912	+	0.212890i
$760$		0			0
$761$	14.5704	+	25.2367i	0.528176	+	0.914828i	0.999460	+	0.0328468i	$0.0104573\pi$
$761$	14.5704	+	25.2367i	0.528176	+	0.914828i	−0.471284	+	0.881982i	$0.656209\pi$
$762$	18.7320	−	10.8149i	0.678587	−	0.391783i
$763$			50.6857i			1.83494i
$764$	−22.6379	+	39.2099i	−0.819009	+	1.41856i
$765$		0			0
$766$	−4.81103			−0.173830
$767$		−	0.469934i		−	0.0169683i
$768$	5.91931	−	3.41752i	0.213595	−	0.123319i
$769$	−4.06948			−0.146749			−0.0733746	−	0.997304i	$-0.523377\pi$
$769$	−4.06948			−0.146749			−0.0733746	+	0.997304i	$0.523377\pi$
$770$		0			0
$771$	56.4396			2.03262
$772$	27.8703	+	16.0909i	1.00307	+	0.579125i
$773$	−1.45509	−	0.840097i	−0.0523360	−	0.0302162i	0.473604	−	0.880738i	$-0.342953\pi$
$773$	−1.45509	−	0.840097i	−0.0523360	−	0.0302162i	−0.525940	+	0.850522i	$0.676286\pi$
$774$	3.01178	−	5.21655i	0.108256	−	0.187505i
$775$		0			0
$776$	17.3347			0.622279
$777$	−29.5902	+	43.7867i	−1.06154	+	1.57084i
$778$			20.4325i			0.732539i
$779$	8.07437	+	13.9852i	0.289294	+	0.501073i
$780$		0			0
$781$	21.3088	−	36.9079i	0.762488	−	1.32067i
$782$	0.856205	+	0.494330i	0.0306178	+	0.0176772i
$783$			25.4006i			0.907745i
$784$	11.7086	−	20.2800i	0.418166	−	0.724284i
$785$		0			0
$786$	−6.26095	−	10.8443i	−0.223321	−	0.386803i
$787$		−	1.39842i		−	0.0498484i	−0.999689	−	0.0249242i	$-0.992066\pi$
$787$		−	1.39842i		−	0.0498484i	0.999689	−	0.0249242i	$-0.00793444\pi$
$788$			7.95583i			0.283415i
$789$	−28.2134	−	48.8670i	−1.00442	−	1.73971i
$790$		0			0
$791$	−35.2733			−1.25417
$792$	−7.86419	+	4.54039i	−0.279442	+	0.161336i
$793$	2.49145	−	1.43844i	0.0884739	−	0.0510804i
$794$	−2.69802	−	4.67311i	−0.0957491	−	0.165842i
$795$		0			0
$796$	16.5384	−	28.6453i	0.586188	−	1.01531i
$797$	5.29087	−	3.05469i	0.187412	−	0.108203i	−0.403358	−	0.915042i	$-0.632157\pi$
$797$	5.29087	−	3.05469i	0.187412	−	0.108203i	0.590771	+	0.806840i	$0.298824\pi$
$798$	10.6933	−	6.17379i	0.378539	−	0.218550i
$799$	−9.67433	−	16.7564i	−0.342253	−	0.592800i
$800$		0			0
$801$	4.26708	−	7.39080i	0.150770	−	0.261141i
$802$	−8.88459	+	5.12952i	−0.313726	+	0.181130i
$803$			24.3652i			0.859828i
$804$	−24.6863			−0.870618
$805$		0			0
$806$	1.54003			0.0542453
$807$	46.3868	+	26.7814i	1.63289	+	0.942751i
$808$			23.6292i			0.831272i
$809$	−8.50506	+	14.7312i	−0.299022	+	0.517921i	−0.975912	−	0.218163i	$-0.929994\pi$
$809$	−8.50506	+	14.7312i	−0.299022	+	0.517921i	0.676891	+	0.736084i	$0.263327\pi$
$810$		0			0
$811$	−23.1744	+	40.1392i	−0.813762	+	1.40948i	0.0964519	+	0.995338i	$0.469251\pi$
$811$	−23.1744	+	40.1392i	−0.813762	+	1.40948i	−0.910214	+	0.414139i	$0.864083\pi$
$812$	−44.9484	+	25.9510i	−1.57738	+	0.910701i
$813$			14.8654i			0.521353i
$814$	−9.23675	−	6.24202i	−0.323748	−	0.218783i
$815$		0			0
$816$	−4.27151	−	7.39847i	−0.149533	−	0.258998i
$817$	18.0278	+	10.4083i	0.630711	+	0.364141i
$818$	−12.9600	−	7.48246i	−0.453136	−	0.261618i
$819$	1.18099	−	2.04554i	0.0412672	−	0.0714769i
$820$		0			0
$821$	15.3620	−	26.6078i	0.536137	−	0.928617i	−0.462970	−	0.886374i	$-0.653216\pi$
$821$	15.3620	−	26.6078i	0.536137	−	0.928617i	0.999107	−	0.0422430i	$-0.0134504\pi$
$822$			2.99770i			0.104557i
$823$	11.7785	−	6.80032i	0.410573	−	0.237044i	−0.280463	−	0.959865i	$-0.590488\pi$
$823$	11.7785	−	6.80032i	0.410573	−	0.237044i	0.691036	+	0.722821i	$0.257155\pi$
$824$	11.0436			0.384721
$825$		0			0
$826$	−1.28464	−	2.22506i	−0.0446984	−	0.0774198i
$827$	−20.4646	−	11.8152i	−0.711624	−	0.410856i	0.100038	−	0.994984i	$-0.468104\pi$
$827$	−20.4646	−	11.8152i	−0.711624	−	0.410856i	−0.811662	+	0.584127i	$0.801437\pi$
$828$			2.23070i			0.0775222i
$829$	−10.1184	−	17.5256i	−0.351427	−	0.608690i	0.635072	−	0.772453i	$-0.280970\pi$
$829$	−10.1184	−	17.5256i	−0.351427	−	0.608690i	−0.986500	+	0.163763i	$0.947637\pi$
$830$		0			0
$831$	19.3941	+	33.5915i	0.672773	+	1.16528i
$832$	0.568145	+	0.328019i	0.0196969	+	0.0113720i
$833$	16.3570	+	9.44369i	0.566735	+	0.327204i
$834$	2.90140	+	5.02538i	0.100467	+	0.174015i
$835$		0			0
$836$	−7.19434	−	12.4610i	−0.248821	−	0.430971i
$837$			22.7629i			0.786800i
$838$	−6.84164	−	3.95002i	−0.236340	−	0.136451i
$839$	−26.0544	−	45.1275i	−0.899496	−	1.55797i	−0.828139	−	0.560522i	$-0.810600\pi$
$839$	−26.0544	−	45.1275i	−0.899496	−	1.55797i	−0.0713567	−	0.997451i	$-0.522733\pi$
$840$		0			0
$841$	25.0281			0.863037
$842$	4.89195	−	2.82437i	0.168588	−	0.0973342i
$843$			28.5751i			0.984179i
$844$	−19.1961	+	33.2486i	−0.660756	+	1.14446i
$845$		0			0
$846$	−3.95142	+	6.84406i	−0.135853	+	0.235304i
$847$	0.155293	+	0.0896587i	0.00533594	+	0.00308071i
$848$	−12.1838	−	7.03433i	−0.418394	−	0.241560i
$849$	−26.8922	−	46.5786i	−0.922936	−	1.59857i
$850$		0			0
$851$	−5.37063	+	2.61362i	−0.184103	+	0.0895939i
$852$		−	45.4291i		−	1.55637i
$853$	−1.38563	+	0.799996i	−0.0474432	+	0.0273913i	−0.523534	−	0.852005i	$-0.675387\pi$
$853$	−1.38563	+	0.799996i	−0.0474432	+	0.0273913i	0.476091	+	0.879396i	$0.342053\pi$
$854$	7.86440	−	13.6215i	0.269114	−	0.466120i
$855$		0			0
$856$	−8.19766	+	14.1988i	−0.280190	+	0.485304i
$857$		−	20.1657i		−	0.688847i	−0.938814	−	0.344424i	$-0.888074\pi$
$857$		−	20.1657i		−	0.688847i	0.938814	−	0.344424i	$-0.111926\pi$
$858$	1.39648	+	0.806256i	0.0476749	+	0.0275251i
$859$	−14.7102			−0.501906			−0.250953	−	0.967999i	$-0.580744\pi$
$859$	−14.7102			−0.501906			−0.250953	+	0.967999i	$0.580744\pi$
$860$		0			0
$861$	54.6585			1.86276
$862$			11.8962i			0.405186i
$863$	29.7769	−	17.1917i	1.01362	−	0.585212i	0.101368	−	0.994849i	$-0.467678\pi$
$863$	29.7769	−	17.1917i	1.01362	−	0.585212i	0.912249	+	0.409637i	$0.134345\pi$
$864$	9.22371	−	15.9759i	0.313797	−	0.543512i
$865$		0			0
$866$	−1.03645	−	1.79518i	−0.0352200	−	0.0610028i
$867$	−24.7088	+	14.2656i	−0.839154	+	0.484486i
$868$	−40.2807	+	23.2561i	−1.36722	+	0.789362i
$869$	23.7822	−	41.1920i	0.806756	−	1.39734i
$870$		0			0
$871$	1.47713	+	2.55846i	0.0500505	+	0.0866900i
$872$	−21.5278	+	12.4291i	−0.729022	+	0.420901i
$873$	−9.84808	+	5.68579i	−0.333307	+	0.192435i
$874$	1.39553			0.0472044
$875$		0			0
$876$	12.9863	+	22.4929i	0.438766	+	0.759964i
$877$		−	9.66405i		−	0.326332i	−0.986599	−	0.163166i	$-0.947829\pi$
$877$		−	9.66405i		−	0.326332i	0.986599	−	0.163166i	$-0.0521706\pi$
$878$			15.9436i			0.538070i
$879$	8.00509	+	13.8652i	0.270005	+	0.467663i
$880$		0			0
$881$	0.00906752	−	0.0157054i	0.000305492	−	0.000529128i	−0.865873	−	0.500265i	$-0.833236\pi$
$881$	0.00906752	−	0.0157054i	0.000305492	−	0.000529128i	0.866178	+	0.499735i	$0.166569\pi$
$882$		−	7.71444i		−	0.259759i
$883$	21.2846	+	12.2887i	0.716285	+	0.413547i	0.813384	−	0.581727i	$-0.197623\pi$
$883$	21.2846	+	12.2887i	0.716285	+	0.413547i	−0.0970988	+	0.995275i	$0.530956\pi$
$884$	−0.650185	+	1.12615i	−0.0218681	+	0.0378767i
$885$		0			0
$886$	4.90317	+	8.49254i	0.164725	+	0.285313i
$887$			34.7479i			1.16672i	0.812214	+	0.583360i	$0.198262\pi$
$887$			34.7479i			1.16672i	−0.812214	+	0.583360i	$0.801738\pi$
$888$	−25.8536	−	1.83056i	−0.867590	−	0.0614297i
$889$	78.1774			2.62198
$890$		0			0
$891$	−18.5779	+	32.1779i	−0.622384	+	1.07800i
$892$	−25.8042	−	14.8981i	−0.863989	−	0.498824i
$893$	−23.6523	−	13.6556i	−0.791492	−	0.456968i
$894$	−13.6498			−0.456517
$895$		0			0
$896$	48.1045			1.60706
$897$	0.748191	−	0.431969i	0.0249814	−	0.0144230i
$898$			4.58586i			0.153032i
$899$	48.4175			1.61481
$900$		0			0
$901$	5.67359	−	9.82695i	0.189015	−	0.327383i
$902$			11.5301i			0.383912i
$903$	61.0183	−	35.2289i	2.03056	−	1.17235i
$904$	−8.64966	−	14.9817i	−0.287683	−	0.498282i
$905$		0			0
$906$	−6.04503	+	10.4703i	−0.200833	+	0.347853i
$907$	17.3959	+	10.0436i	0.577623	+	0.333491i	0.760188	−	0.649703i	$-0.225107\pi$
$907$	17.3959	+	10.0436i	0.577623	+	0.333491i	−0.182565	+	0.983194i	$0.558440\pi$
$908$	31.5577	−	18.2199i	1.04728	−	0.604647i
$909$	−7.75040	−	13.4241i	−0.257065	−	0.445249i
$910$		0			0
$911$	−55.2571			−1.83075			−0.915374	−	0.402605i	$-0.868105\pi$
$911$	−55.2571			−1.83075			−0.915374	+	0.402605i	$0.868105\pi$
$912$	−10.4432	−	6.02937i	−0.345808	−	0.199652i
$913$	3.17688	−	1.83417i	0.105139	−	0.0607023i
$914$	9.88818			0.327072
$915$		0			0
$916$	−11.4922	−	19.9050i	−0.379712	−	0.657680i
$917$		−	45.2583i		−	1.49456i
$918$	3.01324	+	1.73969i	0.0994517	+	0.0574184i
$919$	−26.9446			−0.888819			−0.444410	−	0.895824i	$-0.646586\pi$
$919$	−26.9446			−0.888819			−0.444410	+	0.895824i	$0.646586\pi$
$920$		0			0
$921$	23.1968	−	40.1780i	0.764360	−	1.32391i
$922$	16.4068	+	9.47246i	0.540329	+	0.311959i
$923$	−4.70822	+	2.71829i	−0.154973	+	0.0894736i
$924$	−48.7012			−1.60215
$925$		0			0
$926$	−2.83006			−0.0930016
$927$	−6.27402	+	3.62230i	−0.206066	+	0.118972i
$928$	−33.9814	−	19.6192i	−1.11549	−	0.644030i
$929$	20.9188	−	36.2324i	0.686323	−	1.18875i	−0.286697	−	0.958021i	$-0.592557\pi$
$929$	20.9188	−	36.2324i	0.686323	−	1.18875i	0.973019	−	0.230724i	$-0.0741095\pi$
$930$		0			0
$931$	26.6602			0.873751
$932$	−22.9202	−	13.2330i	−0.750776	−	0.433461i
$933$		−	0.856928i		−	0.0280545i
$934$	−5.33527	−	9.24095i	−0.174575	−	0.302373i
$935$		0			0
$936$	1.15840			0.0378636
$937$	−1.67687	+	0.968142i	−0.0547810	+	0.0316278i	−0.527140	−	0.849778i	$-0.676736\pi$
$937$	−1.67687	+	0.968142i	−0.0547810	+	0.0316278i	0.472359	+	0.881406i	$0.343402\pi$
$938$	13.9879	+	8.07592i	0.456721	+	0.263688i
$939$	−17.8470			−0.582415
$940$		0			0
$941$	−5.50157	−	9.52899i	−0.179346	−	0.310636i	0.762311	−	0.647211i	$-0.224065\pi$
$941$	−5.50157	−	9.52899i	−0.179346	−	0.310636i	−0.941657	+	0.336575i	$0.890731\pi$
$942$	8.26038	−	4.76913i	0.269138	−	0.155387i
$943$	5.34988	+	3.08876i	0.174216	+	0.100584i
$944$	−1.25459	+	2.17302i	−0.0408335	+	0.0707256i
$945$		0			0
$946$	7.43151	+	12.8718i	0.241619	+	0.418497i
$947$	−16.6237	+	9.59773i	−0.540199	+	0.311884i	−0.745160	−	0.666886i	$-0.767627\pi$
$947$	−16.6237	+	9.59773i	−0.540199	+	0.311884i	0.204960	+	0.978770i	$0.434293\pi$
$948$		−	50.7023i		−	1.64673i
$949$	1.55409	−	2.69176i	0.0504479	−	0.0873784i
$950$		0			0
$951$	15.7885			0.511977
$952$			15.5061i			0.502555i
$953$	12.0355	−	6.94870i	0.389868	−	0.225091i	−0.292235	−	0.956347i	$-0.594399\pi$
$953$	12.0355	−	6.94870i	0.389868	−	0.225091i	0.682103	+	0.731256i	$0.261066\pi$
$954$	−4.63469			−0.150054
$955$		0			0
$956$	33.8842			1.09589
$957$	43.9042	+	25.3481i	1.41922	+	0.819388i
$958$	16.6018	+	9.58506i	0.536380	+	0.309679i
$959$	−5.41735	+	9.38313i	−0.174935	+	0.302997i
$960$		0			0
$961$	12.3895			0.399661
$962$	0.622302	+	1.27874i	0.0200638	+	0.0412283i
$963$		−	10.7554i		−	0.346587i
$964$	−12.6690	−	21.9434i	−0.408042	−	0.706749i
$965$		0			0
$966$	2.36171	−	4.09060i	0.0759868	−	0.131613i
$967$	44.0957	+	25.4586i	1.41802	+	0.818695i	0.996125	−	0.0879497i	$-0.0280315\pi$
$967$	44.0957	+	25.4586i	1.41802	+	0.818695i	0.421896	+	0.906644i	$0.361365\pi$
$968$			0.0879438i			0.00282662i
$969$	4.86304	−	8.42302i	0.156223	−	0.270587i
$970$		0			0
$971$	−3.96947	−	6.87533i	−0.127386	−	0.220640i	0.795277	−	0.606246i	$-0.207326\pi$
$971$	−3.96947	−	6.87533i	−0.127386	−	0.220640i	−0.922663	+	0.385607i	$0.873992\pi$
$972$			22.0510i			0.707286i
$973$			20.9733i			0.672373i
$974$	4.36160	+	7.55451i	0.139755	+	0.242062i
$975$		0			0
$976$	−15.3609			−0.491690
$977$	−35.9598	+	20.7614i	−1.15046	+	0.664217i	−0.948999	−	0.315280i	$-0.897901\pi$
$977$	−35.9598	+	20.7614i	−1.15046	+	0.664217i	−0.201459	+	0.979497i	$0.564568\pi$
$978$	10.4579	−	6.03790i	0.334408	−	0.193071i
$979$	10.5289	+	18.2367i	0.336507	+	0.582847i
$980$		0			0
$981$	8.15349	−	14.1223i	0.260321	−	0.450889i
$982$	10.7415	−	6.20163i	0.342777	−	0.197902i
$983$	−2.78694	+	1.60904i	−0.0888896	+	0.0513204i	−0.543786	−	0.839224i	$-0.683010\pi$
$983$	−2.78694	+	1.60904i	−0.0888896	+	0.0513204i	0.454896	+	0.890544i	$0.349676\pi$
$984$	13.4033	+	23.2151i	0.427280	+	0.740071i
$985$		0			0
$986$	3.70039	−	6.40926i	0.117844	−	0.204113i
$987$	−80.0555	+	46.2201i	−2.54819	+	1.47120i
$988$			1.83552i			0.0583955i
$989$	7.96317			0.253214
$990$		0			0
$991$	−9.32198			−0.296122			−0.148061	−	0.988978i	$-0.547303\pi$
$991$	−9.32198			−0.296122			−0.148061	+	0.988978i	$0.547303\pi$
$992$	−30.4525	−	17.5818i	−0.966869	−	0.558222i
$993$		−	24.9666i		−	0.792290i
$994$	−14.8618	+	25.7413i	−0.471386	+	0.816465i
$995$		0			0
$996$	1.95518	−	3.38646i	0.0619521	−	0.107304i
$997$	−30.4543	+	17.5828i	−0.964498	+	0.556853i	−0.897554	−	0.440904i	$-0.854658\pi$
$997$	−30.4543	+	17.5828i	−0.964498	+	0.556853i	−0.0669433	+	0.997757i	$0.521325\pi$
$998$			3.38548i			0.107165i
$999$	−18.9008	+	9.19812i	−0.597996	+	0.291015i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	925.2.o.d.174.10		48
5.2	odd	4		925.2.e.d.26.5	✓	24
5.3	odd	4		925.2.e.e.26.8	yes	24
5.4	even	2	inner	925.2.o.d.174.15		48
37.10	even	3	inner	925.2.o.d.824.15		48
185.47	odd	12		925.2.e.d.676.5	yes	24
185.84	even	6	inner	925.2.o.d.824.10		48
185.158	odd	12		925.2.e.e.676.8	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
925.2.e.d.26.5	✓	24	5.2	odd	4
925.2.e.d.676.5	yes	24	185.47	odd	12
925.2.e.e.26.8	yes	24	5.3	odd	4
925.2.e.e.676.8	yes	24	185.158	odd	12
925.2.o.d.174.10		48	1.1	even	1	trivial
925.2.o.d.174.15		48	5.4	even	2	inner
925.2.o.d.824.10		48	185.84	even	6	inner
925.2.o.d.824.15		48	37.10	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 925 = 5^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	925.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.479496 + 0.276837i) q^{2} +(1.80447 + 1.04181i) q^{3} +(-0.846722 + 1.46657i) q^{4} -1.15365 q^{6} +(-3.61105 - 2.08484i) q^{7} -2.04497i q^{8} +(0.670751 + 1.16177i) q^{9} +O(q^{10})\)	\(q+(-0.479496 + 0.276837i) q^{2} +(1.80447 + 1.04181i) q^{3} +(-0.846722 + 1.46657i) q^{4} -1.15365 q^{6} +(-3.61105 - 2.08484i) q^{7} -2.04497i q^{8} +(0.670751 + 1.16177i) q^{9} -3.31014 q^{11} +(-3.05578 + 1.76425i) q^{12} +(0.365690 + 0.211131i) q^{13} +2.30865 q^{14} +(-1.12732 - 1.95258i) q^{16} +(1.57487 - 0.909250i) q^{17} +(-0.643245 - 0.371378i) q^{18} +(1.28344 - 2.22298i) q^{19} +(-4.34403 - 7.52408i) q^{21} +(1.58720 - 0.916369i) q^{22} -0.981927i q^{23} +(2.13047 - 3.69009i) q^{24} -0.233796 q^{26} -3.45569i q^{27} +(6.11511 - 3.53056i) q^{28} -7.35038 q^{29} -6.58707 q^{31} +(4.62308 + 2.66914i) q^{32} +(-5.97305 - 3.44854i) q^{33} +(-0.503428 + 0.871964i) q^{34} -2.27176 q^{36} +(-2.66173 - 5.46948i) q^{37} +1.42121i q^{38} +(0.439919 + 0.761962i) q^{39} +(-3.14561 + 5.44835i) q^{41} +(4.16589 + 2.40518i) q^{42} +8.10974i q^{43} +(2.80277 - 4.85453i) q^{44} +(0.271834 + 0.470830i) q^{46} -10.6399i q^{47} -4.69784i q^{48} +(5.19312 + 8.99475i) q^{49} +3.78908 q^{51} +(-0.619276 + 0.357539i) q^{52} +(5.40388 - 3.11993i) q^{53} +(0.956664 + 1.65699i) q^{54} +(-4.26343 + 7.38447i) q^{56} +(4.63185 - 2.67420i) q^{57} +(3.52448 - 2.03486i) q^{58} +(-0.556448 - 0.963795i) q^{59} +(3.40650 - 5.90023i) q^{61} +(3.15847 - 1.82355i) q^{62} -5.59364i q^{63} +1.55362 q^{64} +3.81874 q^{66} +(6.05892 + 3.49812i) q^{67} +3.07953i q^{68} +(1.02298 - 1.77186i) q^{69} +(-6.43743 + 11.1500i) q^{71} +(2.37579 - 1.37166i) q^{72} -7.36078i q^{73} +(2.79044 + 1.88573i) q^{74} +(2.17343 + 3.76449i) q^{76} +(11.9531 + 6.90110i) q^{77} +(-0.421879 - 0.243572i) q^{78} +(-7.18467 + 12.4442i) q^{79} +(5.61244 - 9.72103i) q^{81} -3.48329i q^{82} +(-0.959744 + 0.554108i) q^{83} +14.7128 q^{84} +(-2.24508 - 3.88859i) q^{86} +(-13.2636 - 7.65772i) q^{87} +6.76911i q^{88} +(-3.18082 - 5.50934i) q^{89} +(-0.880351 - 1.52481i) q^{91} +(1.44006 + 0.831419i) q^{92} +(-11.8862 - 6.86250i) q^{93} +(2.94552 + 5.10179i) q^{94} +(5.56148 + 9.63277i) q^{96} +8.47676i q^{97} +(-4.98016 - 2.87530i) q^{98} +(-2.22028 - 3.84563i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 22 q^{4} + 20 q^{9}+O(q^{10}) \) 48 * q + 22 * q^4 + 20 * q^9	\( 48 q + 22 q^{4} + 20 q^{9} - 40 q^{14} - 26 q^{16} - 10 q^{19} - 12 q^{21} + 42 q^{24} - 40 q^{26} - 12 q^{29} + 76 q^{31} + 10 q^{34} - 4 q^{36} - 28 q^{39} - 26 q^{41} + 30 q^{44} - 26 q^{46} + 52 q^{49} - 92 q^{51} + 74 q^{54} + 14 q^{59} + 32 q^{61} - 40 q^{64} + 164 q^{66} - 42 q^{69} - 4 q^{71} - 96 q^{74} + 34 q^{76} + 42 q^{79} - 32 q^{81} - 152 q^{84} - 32 q^{86} - 58 q^{89} + 64 q^{91} + 26 q^{94} + 52 q^{96} + 30 q^{99}+O(q^{100}) \) 48 * q + 22 * q^4 + 20 * q^9 - 40 * q^14 - 26 * q^16 - 10 * q^19 - 12 * q^21 + 42 * q^24 - 40 * q^26 - 12 * q^29 + 76 * q^31 + 10 * q^34 - 4 * q^36 - 28 * q^39 - 26 * q^41 + 30 * q^44 - 26 * q^46 + 52 * q^49 - 92 * q^51 + 74 * q^54 + 14 * q^59 + 32 * q^61 - 40 * q^64 + 164 * q^66 - 42 * q^69 - 4 * q^71 - 96 * q^74 + 34 * q^76 + 42 * q^79 - 32 * q^81 - 152 * q^84 - 32 * q^86 - 58 * q^89 + 64 * q^91 + 26 * q^94 + 52 * q^96 + 30 * q^99

Introduction

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