LMFDB - Embedded newform 75.22.a.n.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [75,22,Mod(1,75)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(75, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 22, names="a")

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

chi := DirichletCharacter("75.1");

S:= CuspForms(chi, 22);

N := Newforms(S);

Level:	$ N $	$=$	$ 75 = 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 22 $
Character orbit:	$[\chi]$	$=$	75.a (trivial)

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:	yes
Analytic conductor:	$209.608008215$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 5 x^{9} - 15486550 x^{8} - 930225020 x^{7} + 80619202368510 x^{6} + \cdots + 47\!\cdots\!18 $ x^10 - 5x^9 - 15486550x^8 - 930225020x^7 + 80619202368510x^6 + 14206919536731394x^5 - 159833300365521427920x^4 - 53427455410418539963580x^3 + 93639331506281672292832825x^2 + 44269185428005803484908321595*x + 4729332062567824907768533377518
Coefficient ring:	$\Z[a_1, \ldots, a_{23}]$
Coefficient ring index:	$ 2^{24}\cdot 3^{14}\cdot 5^{24}\cdot 7^{2} $
Twist minimal:	no (minimal twist has level 15)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$1793.04$ of defining polynomial
Character	$\chi$	$=$	75.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1728.04 q^{2} -59049.0 q^{3} +888953. q^{4} +1.02039e8 q^{6} +3.15759e8 q^{7} +2.08781e9 q^{8} +3.48678e9 q^{9} +O(q^{10})$	\(q-1728.04 q^{2} -59049.0 q^{3} +888953. q^{4} +1.02039e8 q^{6} +3.15759e8 q^{7} +2.08781e9 q^{8} +3.48678e9 q^{9} -4.66012e10 q^{11} -5.24918e10 q^{12} -7.73108e11 q^{13} -5.45642e11 q^{14} -5.47208e12 q^{16} -8.80023e12 q^{17} -6.02529e12 q^{18} -2.41329e13 q^{19} -1.86452e13 q^{21} +8.05285e13 q^{22} -1.52075e13 q^{23} -1.23283e14 q^{24} +1.33596e15 q^{26} -2.05891e14 q^{27} +2.80695e14 q^{28} -2.37036e15 q^{29} +5.25633e15 q^{31} +5.07749e15 q^{32} +2.75175e15 q^{33} +1.52071e16 q^{34} +3.09959e15 q^{36} -2.94975e16 q^{37} +4.17024e16 q^{38} +4.56513e16 q^{39} -1.01452e17 q^{41} +3.22196e16 q^{42} +1.67010e17 q^{43} -4.14263e16 q^{44} +2.62791e16 q^{46} -3.47616e17 q^{47} +3.23121e17 q^{48} -4.58842e17 q^{49} +5.19645e17 q^{51} -6.87257e17 q^{52} +7.88240e17 q^{53} +3.55787e17 q^{54} +6.59244e17 q^{56} +1.42502e18 q^{57} +4.09606e18 q^{58} -3.82213e18 q^{59} -5.59536e18 q^{61} -9.08312e18 q^{62} +1.10098e18 q^{63} +2.70170e18 q^{64} -4.75513e18 q^{66} +1.79663e19 q^{67} -7.82299e18 q^{68} +8.97987e17 q^{69} +8.97666e18 q^{71} +7.27974e18 q^{72} -2.61140e19 q^{73} +5.09728e19 q^{74} -2.14530e19 q^{76} -1.47147e19 q^{77} -7.88870e19 q^{78} -1.46427e20 q^{79} +1.21577e19 q^{81} +1.75313e20 q^{82} +1.51636e20 q^{83} -1.65747e19 q^{84} -2.88599e20 q^{86} +1.39967e20 q^{87} -9.72945e19 q^{88} -4.37859e20 q^{89} -2.44116e20 q^{91} -1.35187e19 q^{92} -3.10381e20 q^{93} +6.00693e20 q^{94} -2.99821e20 q^{96} -7.85145e20 q^{97} +7.92896e20 q^{98} -1.62488e20 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 645 q^{2} - 590490 q^{3} + 10043205 q^{4} - 38086605 q^{6} + 115357290 q^{7} + 314142735 q^{8} + 34867844010 q^{9}+O(q^{10}) $ 10 * q + 645 * q^2 - 590490 * q^3 + 10043205 * q^4 - 38086605 * q^6 + 115357290 * q^7 + 314142735 * q^8 + 34867844010 * q^9	$ 10 q + 645 q^{2} - 590490 q^{3} + 10043205 q^{4} - 38086605 q^{6} + 115357290 q^{7} + 314142735 q^{8} + 34867844010 q^{9} + 5976221790 q^{11} - 593041212045 q^{12} + 842570747430 q^{13} + 1605059874570 q^{14} + 6061861547825 q^{16} + 12910340404230 q^{17} + 2248975938645 q^{18} - 76155422176280 q^{19} - 6811732617210 q^{21} + 461780887241010 q^{22} + 82640920915920 q^{23} - 18549814359015 q^{24} + 286555331159670 q^{26} - 20\!\cdots\!90 q^{27}+ \cdots + 20\!\cdots\!90 q^{99}+O(q^{100}) $ 10 * q + 645 * q^2 - 590490 * q^3 + 10043205 * q^4 - 38086605 * q^6 + 115357290 * q^7 + 314142735 * q^8 + 34867844010 * q^9 + 5976221790 * q^11 - 593041212045 * q^12 + 842570747430 * q^13 + 1605059874570 * q^14 + 6061861547825 * q^16 + 12910340404230 * q^17 + 2248975938645 * q^18 - 76155422176280 * q^19 - 6811732617210 * q^21 + 461780887241010 * q^22 + 82640920915920 * q^23 - 18549814359015 * q^24 + 286555331159670 * q^26 - 2058911320946490 * q^27 + 1520428218531930 * q^28 - 2553653160731010 * q^29 - 5579671364724940 * q^31 + 29255856594217815 * q^32 - 352889920477710 * q^33 + 36285968426431010 * q^34 + 35018490530045205 * q^36 + 1797908431222890 * q^37 + 10684960744876320 * q^38 - 49752960064994070 * q^39 - 157319729506021440 * q^41 - 94777180533483930 * q^42 - 148924853700743400 * q^43 + 49118820773767290 * q^44 - 238453286038259540 * q^46 - 43171138083158100 * q^47 - 357946862537518425 * q^48 + 453692886452454950 * q^49 - 762342690529377270 * q^51 + 5077473324432504030 * q^52 + 1835165786666252970 * q^53 - 132799780201048605 * q^54 - 5146515624013530450 * q^56 + 4496901524087157720 * q^57 + 3684042125074285440 * q^58 + 4936135121536323630 * q^59 - 4443080871007408300 * q^61 + 39366851097921260280 * q^62 + 402225999313633290 * q^63 - 14877283608188093455 * q^64 - 27267699610694399490 * q^66 + 33664559574358232580 * q^67 + 44791395195934111290 * q^68 - 4879863739164160080 * q^69 - 74662724971386630180 * q^71 + 1095347988085476735 * q^72 + 16062862692682477620 * q^73 - 130249023546610518030 * q^74 - 258736483662380220720 * q^76 + 56216747719240740180 * q^77 - 16920805749647353830 * q^78 - 49130708010799643300 * q^79 + 121576654590569288010 * q^81 + 117185080045656261930 * q^82 + 118408383608453695560 * q^83 - 89779765876091934570 * q^84 - 1007271272794707382260 * q^86 + 150790665488005409490 * q^87 + 41803519849182967710 * q^88 - 572103976713991581780 * q^89 - 1669810835257196575140 * q^91 - 1206545757146297440260 * q^92 + 329474014415642982060 * q^93 - 1671319720124696594920 * q^94 - 1727529076031967757935 * q^96 - 1299275526640742173920 * q^97 - 2683959884079093505455 * q^98 + 20837796914288297790 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	−1728.04	−1.19327	−0.596633	−	0.802514i	$-0.703495\pi$
$2$	−1728.04	−1.19327	−0.596633	+	0.802514i	$0.703495\pi$
$3$	−59049.0	−0.577350
$3$	−59049.0	−0.577350
$4$	888953.	0.423886
$5$	0	0
$5$	0	0
$6$	1.02039e8	0.688933
$7$	3.15759e8	0.422499	0.211250	−	0.977432i	$-0.432247\pi$
$7$	3.15759e8	0.422499	0.211250	+	0.977432i	$0.432247\pi$
$8$	2.08781e9	0.687458
$9$	3.48678e9	0.333333
$10$	0	0
$11$	−4.66012e10	−0.541719	−0.270859	−	0.962619i	$-0.587308\pi$
$11$	−4.66012e10	−0.541719	−0.270859	+	0.962619i	$0.587308\pi$
$12$	−5.24918e10	−0.244731
$13$	−7.73108e11	−1.55537	−0.777687	−	0.628651i	$-0.783607\pi$
$13$	−7.73108e11	−1.55537	−0.777687	+	0.628651i	$0.783607\pi$
$14$	−5.45642e11	−0.504154
$15$	0	0
$16$	−5.47208e12	−1.24421
$17$	−8.80023e12	−1.05872	−0.529359	−	0.848398i	$-0.677567\pi$
$17$	−8.80023e12	−1.05872	−0.529359	+	0.848398i	$0.677567\pi$
$18$	−6.02529e12	−0.397756
$19$	−2.41329e13	−0.903017	−0.451508	−	0.892267i	$-0.649114\pi$
$19$	−2.41329e13	−0.903017	−0.451508	+	0.892267i	$0.649114\pi$
$20$	0	0
$21$	−1.86452e13	−0.243930
$22$	8.05285e13	0.646415
$23$	−1.52075e13	−0.0765447	−0.0382723	−	0.999267i	$-0.512185\pi$
$23$	−1.52075e13	−0.0765447	−0.0382723	+	0.999267i	$0.512185\pi$
$24$	−1.23283e14	−0.396904
$25$	0	0
$26$	1.33596e15	1.85598
$27$	−2.05891e14	−0.192450
$28$	2.80695e14	0.179091
$29$	−2.37036e15	−1.04625	−0.523124	−	0.852256i	$-0.675234\pi$
$29$	−2.37036e15	−1.04625	−0.523124	+	0.852256i	$0.675234\pi$
$30$	0	0
$31$	5.25633e15	1.15182	0.575910	−	0.817513i	$-0.304648\pi$
$31$	5.25633e15	1.15182	0.575910	+	0.817513i	$0.304648\pi$
$32$	5.07749e15	0.797213
$33$	2.75175e15	0.312761
$34$	1.52071e16	1.26333
$35$	0	0
$36$	3.09959e15	0.141295
$37$	−2.94975e16	−1.00848	−0.504241	−	0.863563i	$-0.668228\pi$
$37$	−2.94975e16	−1.00848	−0.504241	+	0.863563i	$0.668228\pi$
$38$	4.17024e16	1.07754
$39$	4.56513e16	0.897996
$40$	0	0
$41$	−1.01452e17	−1.18041	−0.590204	−	0.807254i	$-0.700953\pi$
$41$	−1.01452e17	−1.18041	−0.590204	+	0.807254i	$0.700953\pi$
$42$	3.22196e16	0.291074
$43$	1.67010e17	1.17848	0.589242	−	0.807957i	$-0.299427\pi$
$43$	1.67010e17	1.17848	0.589242	+	0.807957i	$0.299427\pi$
$44$	−4.14263e16	−0.229627
$45$	0	0
$46$	2.62791e16	0.0913382
$47$	−3.47616e17	−0.963990	−0.481995	−	0.876174i	$-0.660088\pi$
$47$	−3.47616e17	−0.963990	−0.481995	+	0.876174i	$0.660088\pi$
$48$	3.23121e17	0.718343
$49$	−4.58842e17	−0.821495
$50$	0	0
$51$	5.19645e17	0.611251
$52$	−6.87257e17	−0.659301
$53$	7.88240e17	0.619102	0.309551	−	0.950883i	$-0.399821\pi$
$53$	7.88240e17	0.619102	0.309551	+	0.950883i	$0.399821\pi$
$54$	3.55787e17	0.229644
$55$	0	0
$56$	6.59244e17	0.290450
$57$	1.42502e18	0.521357
$58$	4.09606e18	1.24845
$59$	−3.82213e18	−0.973552	−0.486776	−	0.873527i	$-0.661827\pi$
$59$	−3.82213e18	−0.973552	−0.486776	+	0.873527i	$0.661827\pi$
$60$	0	0
$61$	−5.59536e18	−1.00430	−0.502152	−	0.864780i	$-0.667458\pi$
$61$	−5.59536e18	−1.00430	−0.502152	+	0.864780i	$0.667458\pi$
$62$	−9.08312e18	−1.37443
$63$	1.10098e18	0.140833
$64$	2.70170e18	0.292919
$65$	0	0
$66$	−4.75513e18	−0.373208
$67$	1.79663e19	1.20413	0.602063	−	0.798448i	$-0.294345\pi$
$67$	1.79663e19	1.20413	0.602063	+	0.798448i	$0.294345\pi$
$68$	−7.82299e18	−0.448775
$69$	8.97987e17	0.0441931
$70$	0	0
$71$	8.97666e18	0.327267	0.163634	−	0.986521i	$-0.447679\pi$
$71$	8.97666e18	0.327267	0.163634	+	0.986521i	$0.447679\pi$
$72$	7.27974e18	0.229153
$73$	−2.61140e19	−0.711186	−0.355593	−	0.934641i	$-0.615721\pi$
$73$	−2.61140e19	−0.711186	−0.355593	+	0.934641i	$0.615721\pi$
$74$	5.09728e19	1.20339
$75$	0	0
$76$	−2.14530e19	−0.382776
$77$	−1.47147e19	−0.228876
$78$	−7.88870e19	−1.07155
$79$	−1.46427e20	−1.73996	−0.869978	−	0.493091i	$-0.835867\pi$
$79$	−1.46427e20	−1.73996	−0.869978	+	0.493091i	$0.835867\pi$
$80$	0	0
$81$	1.21577e19	0.111111
$82$	1.75313e20	1.40854
$83$	1.51636e20	1.07271	0.536354	−	0.843993i	$-0.319801\pi$
$83$	1.51636e20	1.07271	0.536354	+	0.843993i	$0.319801\pi$
$84$	−1.65747e19	−0.103398
$85$	0	0
$86$	−2.88599e20	−1.40624
$87$	1.39967e20	0.604052
$88$	−9.72945e19	−0.372409
$89$	−4.37859e20	−1.48847	−0.744233	−	0.667920i	$-0.767185\pi$
$89$	−4.37859e20	−1.48847	−0.744233	+	0.667920i	$0.767185\pi$
$90$	0	0
$91$	−2.44116e20	−0.657144
$92$	−1.35187e19	−0.0324462
$93$	−3.10381e20	−0.665004
$94$	6.00693e20	1.15030
$95$	0	0
$96$	−2.99821e20	−0.460271
$97$	−7.85145e20	−1.08105	−0.540526	−	0.841327i	$-0.681775\pi$
$97$	−7.85145e20	−1.08105	−0.540526	+	0.841327i	$0.681775\pi$
$98$	7.92896e20	0.980262
$99$	−1.62488e20	−0.180573
$100$	0	0
$101$	4.63094e20	0.417152	0.208576	−	0.978006i	$-0.433117\pi$
$101$	4.63094e20	0.417152	0.208576	+	0.978006i	$0.433117\pi$
$102$	−8.97964e20	−0.729385
$103$	8.05040e20	0.590237	0.295119	−	0.955461i	$-0.404641\pi$
$103$	8.05040e20	0.590237	0.295119	+	0.955461i	$0.404641\pi$
$104$	−1.61410e21	−1.06925
$105$	0	0
$106$	−1.36211e21	−0.738754
$107$	−6.63108e20	−0.325878	−0.162939	−	0.986636i	$-0.552097\pi$
$107$	−6.63108e20	−0.325878	−0.162939	+	0.986636i	$0.552097\pi$
$108$	−1.83028e20	−0.0815769
$109$	−3.78211e21	−1.53023	−0.765113	−	0.643895i	$-0.777317\pi$
$109$	−3.78211e21	−1.53023	−0.765113	+	0.643895i	$0.777317\pi$
$110$	0	0
$111$	1.74180e21	0.582247
$112$	−1.72786e21	−0.525676
$113$	−4.54389e21	−1.25923	−0.629613	−	0.776909i	$-0.716787\pi$
$113$	−4.54389e21	−1.25923	−0.629613	+	0.776909i	$0.716787\pi$
$114$	−2.46249e21	−0.622118
$115$	0	0
$116$	−2.10714e21	−0.443490
$117$	−2.69566e21	−0.518458
$118$	6.60477e21	1.16171
$119$	−2.77875e21	−0.447307
$120$	0	0
$121$	−5.22858e21	−0.706541
$122$	9.66898e21	1.19840
$123$	5.99067e21	0.681509
$124$	4.67263e21	0.488241
$125$	0	0
$126$	−1.90254e21	−0.168051
$127$	8.25773e21	0.671307	0.335654	−	0.941985i	$-0.391043\pi$
$127$	8.25773e21	0.671307	0.335654	+	0.941985i	$0.391043\pi$
$128$	−1.53169e22	−1.14674
$129$	−9.86177e21	−0.680397
$130$	0	0
$131$	6.83765e21	0.401383	0.200691	−	0.979655i	$-0.435681\pi$
$131$	6.83765e21	0.401383	0.200691	+	0.979655i	$0.435681\pi$
$132$	2.44618e21	0.132575
$133$	−7.62016e21	−0.381524
$134$	−3.10463e22	−1.43684
$135$	0	0
$136$	−1.83732e22	−0.727824
$137$	2.64975e22	0.971938	0.485969	−	0.873976i	$-0.338467\pi$
$137$	2.64975e22	0.971938	0.485969	+	0.873976i	$0.338467\pi$
$138$	−1.55175e21	−0.0527342
$139$	−1.89755e22	−0.597777	−0.298888	−	0.954288i	$-0.596616\pi$
$139$	−1.89755e22	−0.597777	−0.298888	+	0.954288i	$0.596616\pi$
$140$	0	0
$141$	2.05264e22	0.556560
$142$	−1.55120e22	−0.390517
$143$	3.60278e22	0.842576
$144$	−1.90800e22	−0.414736
$145$	0	0
$146$	4.51259e22	0.848634
$147$	2.70942e22	0.474290
$148$	−2.62219e22	−0.427481
$149$	−6.80798e22	−1.03410	−0.517050	−	0.855955i	$-0.672970\pi$
$149$	−6.80798e22	−1.03410	−0.517050	+	0.855955i	$0.672970\pi$
$150$	0	0
$151$	−9.70507e22	−1.28157	−0.640783	−	0.767722i	$-0.721390\pi$
$151$	−9.70507e22	−1.28157	−0.640783	+	0.767722i	$0.721390\pi$
$152$	−5.03848e22	−0.620786
$153$	−3.06845e22	−0.352906
$154$	2.54276e22	0.273110
$155$	0	0
$156$	4.05818e22	0.380648
$157$	−5.18580e22	−0.454851	−0.227426	−	0.973795i	$-0.573031\pi$
$157$	−5.18580e22	−0.454851	−0.227426	+	0.973795i	$0.573031\pi$
$158$	2.53032e23	2.07623
$159$	−4.65448e22	−0.357439
$160$	0	0
$161$	−4.80189e21	−0.0323401
$162$	−2.10089e22	−0.132585
$163$	−9.90367e22	−0.585904	−0.292952	−	0.956127i	$-0.594638\pi$
$163$	−9.90367e22	−0.585904	−0.292952	+	0.956127i	$0.594638\pi$
$164$	−9.01865e22	−0.500358
$165$	0	0
$166$	−2.62032e23	−1.28003
$167$	−3.58670e23	−1.64503	−0.822513	−	0.568747i	$-0.807428\pi$
$167$	−3.58670e23	−1.64503	−0.822513	+	0.568747i	$0.807428\pi$
$168$	−3.89277e22	−0.167692
$169$	3.50632e23	1.41919
$170$	0	0
$171$	−8.41461e22	−0.301006
$172$	1.48464e23	0.499542
$173$	−2.63657e23	−0.834749	−0.417375	−	0.908735i	$-0.637050\pi$
$173$	−2.63657e23	−0.834749	−0.417375	+	0.908735i	$0.637050\pi$
$174$	−2.41868e23	−0.720795
$175$	0	0
$176$	2.55005e23	0.674010
$177$	2.25693e23	0.562081
$178$	7.56635e23	1.77614
$179$	−2.41136e22	−0.0533710	−0.0266855	−	0.999644i	$-0.508495\pi$
$179$	−2.41136e22	−0.0533710	−0.0266855	+	0.999644i	$0.508495\pi$
$180$	0	0
$181$	−2.71368e23	−0.534483	−0.267242	−	0.963630i	$-0.586112\pi$
$181$	−2.71368e23	−0.534483	−0.267242	+	0.963630i	$0.586112\pi$
$182$	4.21840e23	0.784149
$183$	3.30401e23	0.579835
$184$	−3.17503e22	−0.0526213
$185$	0	0
$186$	5.36349e23	0.793527
$187$	4.10101e23	0.573527
$188$	−3.09015e23	−0.408622
$189$	−6.50119e22	−0.0813100
$190$	0	0
$191$	9.56126e23	1.07069	0.535346	−	0.844633i	$-0.320181\pi$
$191$	9.56126e23	1.07069	0.535346	+	0.844633i	$0.320181\pi$
$192$	−1.59533e23	−0.169117
$193$	−4.42930e23	−0.444615	−0.222307	−	0.974977i	$-0.571359\pi$
$193$	−4.42930e23	−0.444615	−0.222307	+	0.974977i	$0.571359\pi$
$194$	1.35676e24	1.28998
$195$	0	0
$196$	−4.07889e23	−0.348220
$197$	1.83068e24	1.48155	0.740775	−	0.671753i	$-0.234458\pi$
$197$	1.83068e24	1.48155	0.740775	+	0.671753i	$0.234458\pi$
$198$	2.80786e23	0.215472
$199$	2.14431e24	1.56074	0.780369	−	0.625319i	$-0.215031\pi$
$199$	2.14431e24	1.56074	0.780369	+	0.625319i	$0.215031\pi$
$200$	0	0
$201$	−1.06089e24	−0.695203
$202$	−8.00243e23	−0.497774
$203$	−7.48461e23	−0.442039
$204$	4.61940e23	0.259101
$205$	0	0
$206$	−1.39114e24	−0.704311
$207$	−5.30252e22	−0.0255149
$208$	4.23051e24	1.93521
$209$	1.12462e24	0.489181
$210$	0	0
$211$	2.25993e24	0.889464	0.444732	−	0.895664i	$-0.353299\pi$
$211$	2.25993e24	0.889464	0.444732	+	0.895664i	$0.353299\pi$
$212$	7.00709e23	0.262428
$213$	−5.30063e23	−0.188948
$214$	1.14587e24	0.388859
$215$	0	0
$216$	−4.29862e23	−0.132301
$217$	1.65973e24	0.486643
$218$	6.53562e24	1.82597
$219$	1.54200e24	0.410603
$220$	0	0
$221$	6.80353e24	1.64670
$222$	−3.00989e24	−0.694776
$223$	−9.63379e23	−0.212127	−0.106064	−	0.994359i	$-0.533825\pi$
$223$	−9.63379e23	−0.212127	−0.106064	+	0.994359i	$0.533825\pi$
$224$	1.60326e24	0.336822
$225$	0	0
$226$	7.85199e24	1.50259
$227$	−4.39920e24	−0.803716	−0.401858	−	0.915702i	$-0.631635\pi$
$227$	−4.39920e24	−0.803716	−0.401858	+	0.915702i	$0.631635\pi$
$228$	1.26678e24	0.220996
$229$	−1.14991e25	−1.91599	−0.957995	−	0.286786i	$-0.907413\pi$
$229$	−1.14991e25	−1.91599	−0.957995	+	0.286786i	$0.907413\pi$
$230$	0	0
$231$	8.68890e23	0.132141
$232$	−4.94886e24	−0.719252
$233$	1.26381e25	1.75568	0.877841	−	0.478952i	$-0.158983\pi$
$233$	1.26381e25	1.75568	0.877841	+	0.478952i	$0.158983\pi$
$234$	4.65820e24	0.618659
$235$	0	0
$236$	−3.39769e24	−0.412675
$237$	8.64640e24	1.00456
$238$	4.80177e24	0.533757
$239$	1.01322e25	1.07777	0.538886	−	0.842379i	$-0.318845\pi$
$239$	1.01322e25	1.07777	0.538886	+	0.842379i	$0.318845\pi$
$240$	0	0
$241$	−1.25666e25	−1.22472	−0.612362	−	0.790577i	$-0.709781\pi$
$241$	−1.25666e25	−1.22472	−0.612362	+	0.790577i	$0.709781\pi$
$242$	9.03517e24	0.843092
$243$	−7.17898e23	−0.0641500
$244$	−4.97401e24	−0.425710
$245$	0	0
$246$	−1.03521e25	−0.813222
$247$	1.86573e25	1.40453
$248$	1.09742e25	0.791828
$249$	−8.95394e24	−0.619329
$250$	0	0
$251$	−2.33238e25	−1.48329	−0.741643	−	0.670795i	$-0.765953\pi$
$251$	−2.33238e25	−1.48329	−0.741643	+	0.670795i	$0.765953\pi$
$252$	9.78721e23	0.0596971
$253$	7.08687e23	0.0414657
$254$	−1.42696e25	−0.801049
$255$	0	0
$256$	2.08023e25	1.07545
$257$	1.43233e24	0.0710798	0.0355399	−	0.999368i	$-0.488685\pi$
$257$	1.43233e24	0.0710798	0.0355399	+	0.999368i	$0.488685\pi$
$258$	1.70415e25	0.811896
$259$	−9.31410e24	−0.426082
$260$	0	0
$261$	−8.26492e24	−0.348749
$262$	−1.18157e25	−0.478957
$263$	−4.01426e24	−0.156340	−0.0781701	−	0.996940i	$-0.524908\pi$
$263$	−4.01426e24	−0.156340	−0.0781701	+	0.996940i	$0.524908\pi$
$264$	5.74514e24	0.215010
$265$	0	0
$266$	1.31679e25	0.455260
$267$	2.58551e25	0.859366
$268$	1.59712e25	0.510412
$269$	−5.12361e25	−1.57462	−0.787312	−	0.616555i	$-0.788528\pi$
$269$	−5.12361e25	−1.57462	−0.787312	+	0.616555i	$0.788528\pi$
$270$	0	0
$271$	4.23208e24	0.120331	0.0601653	−	0.998188i	$-0.480837\pi$
$271$	4.23208e24	0.120331	0.0601653	+	0.998188i	$0.480837\pi$
$272$	4.81555e25	1.31726
$273$	1.44148e25	0.379403
$274$	−4.57885e25	−1.15978
$275$	0	0
$276$	7.98268e23	0.0187328
$277$	2.34217e24	0.0529152	0.0264576	−	0.999650i	$-0.491577\pi$
$277$	2.34217e24	0.0529152	0.0264576	+	0.999650i	$0.491577\pi$
$278$	3.27904e25	0.713307
$279$	1.83277e25	0.383940
$280$	0	0
$281$	−5.55207e25	−1.07904	−0.539521	−	0.841972i	$-0.681395\pi$
$281$	−5.55207e25	−1.07904	−0.539521	+	0.841972i	$0.681395\pi$
$282$	−3.54703e25	−0.664125
$283$	8.63657e25	1.55806	0.779029	−	0.626988i	$-0.215712\pi$
$283$	8.63657e25	1.55806	0.779029	+	0.626988i	$0.215712\pi$
$284$	7.97983e24	0.138724
$285$	0	0
$286$	−6.22572e25	−1.00542
$287$	−3.20345e25	−0.498721
$288$	1.77041e25	0.265738
$289$	8.35204e24	0.120883
$290$	0	0
$291$	4.63620e25	0.624146
$292$	−2.32141e25	−0.301462
$293$	1.17682e26	1.47435	0.737175	−	0.675702i	$-0.236159\pi$
$293$	1.17682e26	1.47435	0.737175	+	0.675702i	$0.236159\pi$
$294$	−4.68197e25	−0.565955
$295$	0	0
$296$	−6.15853e25	−0.693288
$297$	9.59477e24	0.104254
$298$	1.17644e26	1.23396
$299$	1.17570e25	0.119056
$300$	0	0
$301$	5.27348e25	0.497908
$302$	1.67707e26	1.52925
$303$	−2.73452e25	−0.240843
$304$	1.32057e26	1.12354
$305$	0	0
$306$	5.30239e25	0.421111
$307$	−1.03472e26	−0.794091	−0.397046	−	0.917799i	$-0.629965\pi$
$307$	−1.03472e26	−0.794091	−0.397046	+	0.917799i	$0.629965\pi$
$308$	−1.30807e25	−0.0970172
$309$	−4.75368e25	−0.340774
$310$	0	0
$311$	2.86125e26	1.91678	0.958390	−	0.285462i	$-0.0921471\pi$
$311$	2.86125e26	1.91678	0.958390	+	0.285462i	$0.0921471\pi$
$312$	9.53112e25	0.617335
$313$	−6.52715e25	−0.408797	−0.204399	−	0.978888i	$-0.565524\pi$
$313$	−6.52715e25	−0.408797	−0.204399	+	0.978888i	$0.565524\pi$
$314$	8.96125e25	0.542759
$315$	0	0
$316$	−1.30167e26	−0.737543
$317$	−5.80357e25	−0.318107	−0.159053	−	0.987270i	$-0.550844\pi$
$317$	−5.80357e25	−0.318107	−0.159053	+	0.987270i	$0.550844\pi$
$318$	8.04310e25	0.426520
$319$	1.10461e26	0.566772
$320$	0	0
$321$	3.91559e25	0.188146
$322$	8.29784e24	0.0385903
$323$	2.12375e26	0.956040
$324$	1.08076e25	0.0470984
$325$	0	0
$326$	1.71139e26	0.699139
$327$	2.23330e26	0.883477
$328$	−2.11813e26	−0.811481
$329$	−1.09763e26	−0.407285
$330$	0	0
$331$	−9.26374e25	−0.322547	−0.161273	−	0.986910i	$-0.551560\pi$
$331$	−9.26374e25	−0.322547	−0.161273	+	0.986910i	$0.551560\pi$
$332$	1.34797e26	0.454706
$333$	−1.02852e26	−0.336160
$334$	6.19795e26	1.96295
$335$	0	0
$336$	1.02028e26	0.303499
$337$	−3.16971e26	−0.913916	−0.456958	−	0.889488i	$-0.651061\pi$
$337$	−3.16971e26	−0.913916	−0.456958	+	0.889488i	$0.651061\pi$
$338$	−6.05904e26	−1.69347
$339$	2.68312e26	0.727015
$340$	0	0
$341$	−2.44951e26	−0.623963
$342$	1.45407e26	0.359180
$343$	−3.21249e26	−0.769580
$344$	3.48685e26	0.810157
$345$	0	0
$346$	4.55609e26	0.996079
$347$	−1.75663e26	−0.372581	−0.186290	−	0.982495i	$-0.559647\pi$
$347$	−1.75663e26	−0.372581	−0.186290	+	0.982495i	$0.559647\pi$
$348$	1.24424e26	0.256049
$349$	−1.16246e25	−0.0232120	−0.0116060	−	0.999933i	$-0.503694\pi$
$349$	−1.16246e25	−0.0232120	−0.0116060	+	0.999933i	$0.503694\pi$
$350$	0	0
$351$	1.59176e26	0.299332
$352$	−2.36617e26	−0.431865
$353$	1.00660e27	1.78329	0.891647	−	0.452732i	$-0.149550\pi$
$353$	1.00660e27	1.78329	0.891647	+	0.452732i	$0.149550\pi$
$354$	−3.90005e26	−0.670712
$355$	0	0
$356$	−3.89236e26	−0.630940
$357$	1.64082e26	0.258253
$358$	4.16692e25	0.0636859
$359$	−2.25042e26	−0.334020	−0.167010	−	0.985955i	$-0.553411\pi$
$359$	−2.25042e26	−0.334020	−0.167010	+	0.985955i	$0.553411\pi$
$360$	0	0
$361$	−1.31815e26	−0.184560
$362$	4.68934e26	0.637781
$363$	3.08742e26	0.407921
$364$	−2.17007e26	−0.278554
$365$	0	0
$366$	−5.70944e26	−0.691898
$367$	−1.59004e27	−1.87247	−0.936233	−	0.351381i	$-0.885712\pi$
$367$	−1.59004e27	−1.87247	−0.936233	+	0.351381i	$0.885712\pi$
$368$	8.32165e25	0.0952374
$369$	−3.53743e26	−0.393469
$370$	0	0
$371$	2.48894e26	0.261570
$372$	−2.75914e26	−0.281886
$373$	−1.18905e27	−1.18102	−0.590510	−	0.807030i	$-0.701074\pi$
$373$	−1.18905e27	−1.18102	−0.590510	+	0.807030i	$0.701074\pi$
$374$	−7.08669e26	−0.684371
$375$	0	0
$376$	−7.25757e26	−0.662703
$377$	1.83254e27	1.62731
$378$	1.12343e26	0.0970245
$379$	−1.20908e27	−1.01565	−0.507824	−	0.861461i	$-0.669550\pi$
$379$	−1.20908e27	−1.01565	−0.507824	+	0.861461i	$0.669550\pi$
$380$	0	0
$381$	−4.87611e26	−0.387580
$382$	−1.65222e27	−1.27762
$383$	−1.01567e27	−0.764125	−0.382063	−	0.924136i	$-0.624786\pi$
$383$	−1.01567e27	−0.764125	−0.382063	+	0.924136i	$0.624786\pi$
$384$	9.04448e26	0.662073
$385$	0	0
$386$	7.65399e26	0.530544
$387$	5.82327e26	0.392828
$388$	−6.97957e26	−0.458243
$389$	2.05615e27	1.31397	0.656983	−	0.753905i	$-0.271832\pi$
$389$	2.05615e27	1.31397	0.656983	+	0.753905i	$0.271832\pi$
$390$	0	0
$391$	1.33829e26	0.0810392
$392$	−9.57976e26	−0.564743
$393$	−4.03757e26	−0.231738
$394$	−3.16348e27	−1.76789
$395$	0	0
$396$	−1.44445e26	−0.0765423
$397$	−2.64704e27	−1.36603	−0.683015	−	0.730404i	$-0.739332\pi$
$397$	−2.64704e27	−1.36603	−0.683015	+	0.730404i	$0.739332\pi$
$398$	−3.70544e27	−1.86238
$399$	4.49963e26	0.220273
$400$	0	0
$401$	−1.01816e27	−0.472935	−0.236468	−	0.971639i	$-0.575990\pi$
$401$	−1.01816e27	−0.472935	−0.236468	+	0.971639i	$0.575990\pi$
$402$	1.83325e27	0.829563
$403$	−4.06371e27	−1.79151
$404$	4.11669e26	0.176825
$405$	0	0
$406$	1.29337e27	0.527470
$407$	1.37462e27	0.546313
$408$	1.08492e27	0.420209
$409$	−2.69010e27	−1.01549	−0.507743	−	0.861508i	$-0.669520\pi$
$409$	−2.69010e27	−1.01549	−0.507743	+	0.861508i	$0.669520\pi$
$410$	0	0
$411$	−1.56465e27	−0.561148
$412$	7.15643e26	0.250193
$413$	−1.20687e27	−0.411325
$414$	9.16294e25	0.0304461
$415$	0	0
$416$	−3.92545e27	−1.23996
$417$	1.12049e27	0.345126
$418$	−1.94338e27	−0.583724
$419$	−3.94276e27	−1.15492	−0.577462	−	0.816418i	$-0.695957\pi$
$419$	−3.94276e27	−1.15492	−0.577462	+	0.816418i	$0.695957\pi$
$420$	0	0
$421$	3.39019e27	0.944631	0.472316	−	0.881429i	$-0.343418\pi$
$421$	3.39019e27	0.944631	0.472316	+	0.881429i	$0.343418\pi$
$422$	−3.90523e27	−1.06137
$423$	−1.21206e27	−0.321330
$424$	1.64570e27	0.425606
$425$	0	0
$426$	9.15967e26	0.225465
$427$	−1.76678e27	−0.424317
$428$	−5.89472e26	−0.138135
$429$	−2.12740e27	−0.486461
$430$	0	0
$431$	5.81358e27	1.26600	0.632998	−	0.774153i	$-0.281824\pi$
$431$	5.81358e27	1.26600	0.632998	+	0.774153i	$0.281824\pi$
$432$	1.12665e27	0.239448
$433$	−8.74072e26	−0.181311	−0.0906555	−	0.995882i	$-0.528896\pi$
$433$	−8.74072e26	−0.181311	−0.0906555	+	0.995882i	$0.528896\pi$
$434$	−2.86807e27	−0.580695
$435$	0	0
$436$	−3.36212e27	−0.648642
$437$	3.67000e26	0.0691211
$438$	−2.66464e27	−0.489959
$439$	2.01090e27	0.361005	0.180503	−	0.983574i	$-0.442228\pi$
$439$	2.01090e27	0.361005	0.180503	+	0.983574i	$0.442228\pi$
$440$	0	0
$441$	−1.59988e27	−0.273832
$442$	−1.17567e28	−1.96496
$443$	4.02234e26	0.0656507	0.0328254	−	0.999461i	$-0.489549\pi$
$443$	4.02234e26	0.0656507	0.0328254	+	0.999461i	$0.489549\pi$
$444$	1.54838e27	0.246806
$445$	0	0
$446$	1.66475e27	0.253124
$447$	4.02004e27	0.597038
$448$	8.53086e26	0.123758
$449$	6.97848e27	0.988950	0.494475	−	0.869192i	$-0.335360\pi$
$449$	6.97848e27	0.988950	0.494475	+	0.869192i	$0.335360\pi$
$450$	0	0
$451$	4.72781e27	0.639449
$452$	−4.03930e27	−0.533768
$453$	5.73075e27	0.739912
$454$	7.60198e27	0.959047
$455$	0	0
$456$	2.97517e27	0.358411
$457$	3.95256e27	0.465327	0.232664	−	0.972557i	$-0.425256\pi$
$457$	3.95256e27	0.465327	0.232664	+	0.972557i	$0.425256\pi$
$458$	1.98709e28	2.28629
$459$	1.81189e27	0.203750
$460$	0	0
$461$	4.02350e27	0.432260	0.216130	−	0.976365i	$-0.430657\pi$
$461$	4.02350e27	0.432260	0.216130	+	0.976365i	$0.430657\pi$
$462$	−1.50147e27	−0.157680
$463$	−3.76014e27	−0.386015	−0.193007	−	0.981197i	$-0.561824\pi$
$463$	−3.76014e27	−0.386015	−0.193007	+	0.981197i	$0.561824\pi$
$464$	1.29708e28	1.30175
$465$	0	0
$466$	−2.18392e28	−2.09500
$467$	1.74547e28	1.63713	0.818567	−	0.574411i	$-0.194769\pi$
$467$	1.74547e28	1.63713	0.818567	+	0.574411i	$0.194769\pi$
$468$	−2.39632e27	−0.219767
$469$	5.67300e27	0.508742
$470$	0	0
$471$	3.06216e27	0.262609
$472$	−7.97988e27	−0.669276
$473$	−7.78286e27	−0.638406
$474$	−1.49413e28	−1.19871
$475$	0	0
$476$	−2.47018e27	−0.189607
$477$	2.74842e27	0.206367
$478$	−1.75088e28	−1.28607
$479$	5.89693e27	0.423744	0.211872	−	0.977297i	$-0.432044\pi$
$479$	5.89693e27	0.423744	0.211872	+	0.977297i	$0.432044\pi$
$480$	0	0
$481$	2.28048e28	1.56857
$482$	2.17155e28	1.46142
$483$	2.83547e26	0.0186715
$484$	−4.64796e27	−0.299493
$485$	0	0
$486$	1.24055e27	0.0765481
$487$	−2.99361e28	−1.80776	−0.903881	−	0.427784i	$-0.859294\pi$
$487$	−2.99361e28	−1.80776	−0.903881	+	0.427784i	$0.859294\pi$
$488$	−1.16821e28	−0.690416
$489$	5.84802e27	0.338272
$490$	0	0
$491$	6.37441e26	0.0353252	0.0176626	−	0.999844i	$-0.494378\pi$
$491$	6.37441e26	0.0353252	0.0176626	+	0.999844i	$0.494378\pi$
$492$	5.32542e27	0.288882
$493$	2.08597e28	1.10768
$494$	−3.22405e28	−1.67598
$495$	0	0
$496$	−2.87631e28	−1.43310
$497$	2.83446e27	0.138270
$498$	1.54727e28	0.739025
$499$	3.56806e28	1.66869	0.834347	−	0.551239i	$-0.185845\pi$
$499$	3.56806e28	1.66869	0.834347	+	0.551239i	$0.185845\pi$
$500$	0	0
$501$	2.11791e28	0.949756
$502$	4.03043e28	1.76996
$503$	−9.70968e27	−0.417581	−0.208791	−	0.977960i	$-0.566953\pi$
$503$	−9.70968e27	−0.417581	−0.208791	+	0.977960i	$0.566953\pi$
$504$	2.29864e27	0.0968168
$505$	0	0
$506$	−1.22464e27	−0.0494796
$507$	−2.07045e28	−0.819370
$508$	7.34073e27	0.284558
$509$	1.79566e28	0.681848	0.340924	−	0.940091i	$-0.389260\pi$
$509$	1.79566e28	0.681848	0.340924	+	0.940091i	$0.389260\pi$
$510$	0	0
$511$	−8.24571e27	−0.300475
$512$	−3.82517e27	−0.136558
$513$	4.96874e27	0.173786
$514$	−2.47512e27	−0.0848171
$515$	0	0
$516$	−8.76665e27	−0.288411
$517$	1.61993e28	0.522212
$518$	1.60951e28	0.508430
$519$	1.55687e28	0.481943
$520$	0	0
$521$	−2.27247e28	−0.675620	−0.337810	−	0.941214i	$-0.609686\pi$
$521$	−2.27247e28	−0.675620	−0.337810	+	0.941214i	$0.609686\pi$
$522$	1.42821e28	0.416151
$523$	5.14644e28	1.46973	0.734867	−	0.678211i	$-0.237244\pi$
$523$	5.14644e28	1.46973	0.734867	+	0.678211i	$0.237244\pi$
$524$	6.07835e27	0.170140
$525$	0	0
$526$	6.93679e27	0.186556
$527$	−4.62569e28	−1.21945
$528$	−1.50578e28	−0.389140
$529$	−3.92403e28	−0.994141
$530$	0	0
$531$	−1.33269e28	−0.324517
$532$	−6.77396e27	−0.161723
$533$	7.84337e28	1.83598
$534$	−4.46786e28	−1.02545
$535$	0	0
$536$	3.75101e28	0.827786
$537$	1.42388e27	0.0308138
$538$	8.85377e28	1.87895
$539$	2.13826e28	0.445019
$540$	0	0
$541$	6.98724e28	1.39873	0.699366	−	0.714764i	$-0.253466\pi$
$541$	6.98724e28	1.39873	0.699366	+	0.714764i	$0.253466\pi$
$542$	−7.31318e27	−0.143587
$543$	1.60240e28	0.308584
$544$	−4.46830e28	−0.844023
$545$	0	0
$546$	−2.49092e28	−0.452728
$547$	7.97605e28	1.42207	0.711035	−	0.703156i	$-0.248227\pi$
$547$	7.97605e28	1.42207	0.711035	+	0.703156i	$0.248227\pi$
$548$	2.35550e28	0.411991
$549$	−1.95098e28	−0.334768
$550$	0	0
$551$	5.72035e28	0.944780
$552$	1.87483e27	0.0303809
$553$	−4.62357e28	−0.735130
$554$	−4.04735e27	−0.0631420
$555$	0	0
$556$	−1.68684e28	−0.253389
$557$	−5.78595e28	−0.852894	−0.426447	−	0.904513i	$-0.640235\pi$
$557$	−5.78595e28	−0.852894	−0.426447	+	0.904513i	$0.640235\pi$
$558$	−3.16709e28	−0.458143
$559$	−1.29117e29	−1.83298
$560$	0	0
$561$	−2.42161e28	−0.331126
$562$	9.59417e28	1.28759
$563$	4.79091e28	0.631074	0.315537	−	0.948913i	$-0.397815\pi$
$563$	4.79091e28	0.631074	0.315537	+	0.948913i	$0.397815\pi$
$564$	1.82470e28	0.235918
$565$	0	0
$566$	−1.49243e29	−1.85918
$567$	3.83889e27	0.0469443
$568$	1.87416e28	0.224982
$569$	1.91482e28	0.225657	0.112829	−	0.993614i	$-0.464009\pi$
$569$	1.91482e28	0.225657	0.112829	+	0.993614i	$0.464009\pi$
$570$	0	0
$571$	4.76629e28	0.541379	0.270690	−	0.962667i	$-0.412748\pi$
$571$	4.76629e28	0.541379	0.270690	+	0.962667i	$0.412748\pi$
$572$	3.20270e28	0.357156
$573$	−5.64583e28	−0.618164
$574$	5.53567e28	0.595107
$575$	0	0
$576$	9.42026e27	0.0976397
$577$	−5.04428e28	−0.513397	−0.256698	−	0.966492i	$-0.582635\pi$
$577$	−5.04428e28	−0.513397	−0.256698	+	0.966492i	$0.582635\pi$
$578$	−1.44326e28	−0.144246
$579$	2.61546e28	0.256698
$580$	0	0
$581$	4.78803e28	0.453218
$582$	−8.01152e28	−0.744773
$583$	−3.67329e28	−0.335379
$584$	−5.45210e28	−0.488910
$585$	0	0
$586$	−2.03359e29	−1.75929
$587$	1.26001e29	1.07071	0.535356	−	0.844626i	$-0.320177\pi$
$587$	1.26001e29	1.07071	0.535356	+	0.844626i	$0.320177\pi$
$588$	2.40855e28	0.201045
$589$	−1.26850e29	−1.04011
$590$	0	0
$591$	−1.08100e29	−0.855374
$592$	1.61413e29	1.25476
$593$	−1.37996e29	−1.05388	−0.526941	−	0.849902i	$-0.676661\pi$
$593$	−1.37996e29	−1.05388	−0.526941	+	0.849902i	$0.676661\pi$
$594$	−1.65801e28	−0.124403
$595$	0	0
$596$	−6.05198e28	−0.438340
$597$	−1.26619e29	−0.901093
$598$	−2.03166e28	−0.142065
$599$	2.38779e29	1.64064	0.820321	−	0.571904i	$-0.193795\pi$
$599$	2.38779e29	1.64064	0.820321	+	0.571904i	$0.193795\pi$
$600$	0	0
$601$	1.84907e29	1.22679	0.613396	−	0.789776i	$-0.289803\pi$
$601$	1.84907e29	1.22679	0.613396	+	0.789776i	$0.289803\pi$
$602$	−9.11276e28	−0.594137
$603$	6.26445e28	0.401376
$604$	−8.62735e28	−0.543237
$605$	0	0
$606$	4.72535e28	0.287390
$607$	2.81548e29	1.68295	0.841474	−	0.540297i	$-0.181688\pi$
$607$	2.81548e29	1.68295	0.841474	+	0.540297i	$0.181688\pi$
$608$	−1.22534e29	−0.719896
$609$	4.41958e28	0.255211
$610$	0	0
$611$	2.68745e29	1.49937
$612$	−2.72771e28	−0.149592
$613$	2.85577e29	1.53953	0.769764	−	0.638328i	$-0.220374\pi$
$613$	2.85577e29	1.53953	0.769764	+	0.638328i	$0.220374\pi$
$614$	1.78803e29	0.947563
$615$	0	0
$616$	−3.07216e28	−0.157342
$617$	−7.64366e28	−0.384864	−0.192432	−	0.981310i	$-0.561637\pi$
$617$	−7.64366e28	−0.384864	−0.192432	+	0.981310i	$0.561637\pi$
$618$	8.21453e28	0.406634
$619$	1.06835e29	0.519950	0.259975	−	0.965615i	$-0.416286\pi$
$619$	1.06835e29	0.519950	0.259975	+	0.965615i	$0.416286\pi$
$620$	0	0
$621$	3.13109e27	0.0147310
$622$	−4.94435e29	−2.28723
$623$	−1.38258e29	−0.628876
$624$	−2.49807e29	−1.11729
$625$	0	0
$626$	1.12791e29	0.487804
$627$	−6.64077e28	−0.282429
$628$	−4.60993e28	−0.192805
$629$	2.59585e29	1.06770
$630$	0	0
$631$	6.97813e28	0.277607	0.138804	−	0.990320i	$-0.455674\pi$
$631$	6.97813e28	0.277607	0.138804	+	0.990320i	$0.455674\pi$
$632$	−3.05713e29	−1.19615
$633$	−1.33446e29	−0.513533
$634$	1.00288e29	0.379586
$635$	0	0
$636$	−4.13761e28	−0.151513
$637$	3.54735e29	1.27773
$638$	−1.90881e29	−0.676311
$639$	3.12997e28	0.109089
$640$	0	0
$641$	−1.95481e29	−0.659320	−0.329660	−	0.944100i	$-0.606934\pi$
$641$	−1.95481e29	−0.659320	−0.329660	+	0.944100i	$0.606934\pi$
$642$	−6.76627e28	−0.224508
$643$	−4.44774e29	−1.45186	−0.725929	−	0.687770i	$-0.758590\pi$
$643$	−4.44774e29	−1.45186	−0.725929	+	0.687770i	$0.758590\pi$
$644$	−4.26866e27	−0.0137085
$645$	0	0
$646$	−3.66991e29	−1.14081
$647$	−1.34661e29	−0.411856	−0.205928	−	0.978567i	$-0.566021\pi$
$647$	−1.34661e29	−0.411856	−0.205928	+	0.978567i	$0.566021\pi$
$648$	2.53829e28	0.0763842
$649$	1.78116e29	0.527391
$650$	0	0
$651$	−9.80055e28	−0.280964
$652$	−8.80390e28	−0.248356
$653$	4.08078e29	1.13280	0.566402	−	0.824129i	$-0.308335\pi$
$653$	4.08078e29	1.13280	0.566402	+	0.824129i	$0.308335\pi$
$654$	−3.85922e29	−1.05422
$655$	0	0
$656$	5.55156e29	1.46867
$657$	−9.10538e28	−0.237062
$658$	1.89674e29	0.486000
$659$	3.86877e29	0.975609	0.487805	−	0.872953i	$-0.337798\pi$
$659$	3.86877e29	0.975609	0.487805	+	0.872953i	$0.337798\pi$
$660$	0	0
$661$	−4.85497e29	−1.18596	−0.592982	−	0.805216i	$-0.702049\pi$
$661$	−4.85497e29	−1.18596	−0.592982	+	0.805216i	$0.702049\pi$
$662$	1.60081e29	0.384884
$663$	−4.01741e29	−0.950724
$664$	3.16587e29	0.737442
$665$	0	0
$666$	1.77731e29	0.401129
$667$	3.60472e28	0.0800848
$668$	−3.18841e29	−0.697303
$669$	5.68866e28	0.122472
$670$	0	0
$671$	2.60751e29	0.544050
$672$	−9.46709e28	−0.194464
$673$	−4.30463e29	−0.870517	−0.435259	−	0.900305i	$-0.643343\pi$
$673$	−4.30463e29	−0.870517	−0.435259	+	0.900305i	$0.643343\pi$
$674$	5.47738e29	1.09055
$675$	0	0
$676$	3.11695e29	0.601575
$677$	−3.60296e29	−0.684665	−0.342333	−	0.939579i	$-0.611217\pi$
$677$	−3.60296e29	−0.684665	−0.342333	+	0.939579i	$0.611217\pi$
$678$	−4.63652e29	−0.867522
$679$	−2.47916e29	−0.456744
$680$	0	0
$681$	2.59769e29	0.464026
$682$	4.23284e29	0.744554
$683$	−5.96910e29	−1.03393	−0.516965	−	0.856006i	$-0.672938\pi$
$683$	−5.96910e29	−1.03393	−0.516965	+	0.856006i	$0.672938\pi$
$684$	−7.48019e28	−0.127592
$685$	0	0
$686$	5.55130e29	0.918314
$687$	6.79013e29	1.10620
$688$	−9.13891e29	−1.46628
$689$	−6.09395e29	−0.962935
$690$	0	0
$691$	8.04018e29	1.23238	0.616192	−	0.787596i	$-0.288675\pi$
$691$	8.04018e29	1.23238	0.616192	+	0.787596i	$0.288675\pi$
$692$	−2.34379e29	−0.353838
$693$	−5.13071e28	−0.0762919
$694$	3.03551e29	0.444588
$695$	0	0
$696$	2.92225e29	0.415260
$697$	8.92805e29	1.24972
$698$	2.00878e28	0.0276981
$699$	−7.46270e29	−1.01364
$700$	0	0
$701$	−8.01191e29	−1.05608	−0.528040	−	0.849219i	$-0.677073\pi$
$701$	−8.01191e29	−1.05608	−0.528040	+	0.849219i	$0.677073\pi$
$702$	−2.75062e29	−0.357183
$703$	7.11860e29	0.910676
$704$	−1.25903e29	−0.158680
$705$	0	0
$706$	−1.73944e30	−2.12795
$707$	1.46226e29	0.176246
$708$	2.00630e29	0.238258
$709$	−1.41838e30	−1.65961	−0.829805	−	0.558054i	$-0.811548\pi$
$709$	−1.41838e30	−1.65961	−0.829805	+	0.558054i	$0.811548\pi$
$710$	0	0
$711$	−5.10561e29	−0.579985
$712$	−9.14166e29	−1.02326
$713$	−7.99356e28	−0.0881658
$714$	−2.83540e29	−0.308165
$715$	0	0
$716$	−2.14359e28	−0.0226232
$717$	−5.98298e29	−0.622252
$718$	3.88881e29	0.398575
$719$	3.78302e29	0.382107	0.191053	−	0.981580i	$-0.438810\pi$
$719$	3.78302e29	0.382107	0.191053	+	0.981580i	$0.438810\pi$
$720$	0	0
$721$	2.54198e29	0.249375
$722$	2.27781e29	0.220230
$723$	7.42044e29	0.707095
$724$	−2.41234e29	−0.226560
$725$	0	0
$726$	−5.33518e29	−0.486759
$727$	−1.41424e30	−1.27178	−0.635888	−	0.771782i	$-0.719366\pi$
$727$	−1.41424e30	−1.27178	−0.635888	+	0.771782i	$0.719366\pi$
$728$	−5.09667e29	−0.451759
$729$	4.23912e28	0.0370370
$730$	0	0
$731$	−1.46972e30	−1.24768
$732$	2.93711e29	0.245784
$733$	4.61684e29	0.380849	0.190425	−	0.981702i	$-0.439014\pi$
$733$	4.61684e29	0.380849	0.190425	+	0.981702i	$0.439014\pi$
$734$	2.74764e30	2.23435
$735$	0	0
$736$	−7.72158e28	−0.0610224
$737$	−8.37249e29	−0.652298
$738$	6.11280e29	0.469514
$739$	−2.60669e30	−1.97389	−0.986946	−	0.161050i	$-0.948512\pi$
$739$	−2.60669e30	−1.97389	−0.986946	+	0.161050i	$0.948512\pi$
$740$	0	0
$741$	−1.10170e30	−0.810906
$742$	−4.30097e29	−0.312123
$743$	−1.14154e30	−0.816784	−0.408392	−	0.912807i	$-0.633910\pi$
$743$	−1.14154e30	−0.816784	−0.408392	+	0.912807i	$0.633910\pi$
$744$	−6.48017e29	−0.457162
$745$	0	0
$746$	2.05472e30	1.40927
$747$	5.28721e29	0.357570
$748$	3.64561e29	0.243110
$749$	−2.09382e29	−0.137683
$750$	0	0
$751$	1.93322e29	0.123612	0.0618061	−	0.998088i	$-0.480314\pi$
$751$	1.93322e29	0.123612	0.0618061	+	0.998088i	$0.480314\pi$
$752$	1.90218e30	1.19940
$753$	1.37725e30	0.856375
$754$	−3.16670e30	−1.94181
$755$	0	0
$756$	−5.77925e28	−0.0344661
$757$	−3.23671e30	−1.90369	−0.951846	−	0.306576i	$-0.900817\pi$
$757$	−3.23671e30	−1.90369	−0.951846	+	0.306576i	$0.900817\pi$
$758$	2.08933e30	1.21194
$759$	−4.18473e28	−0.0239402
$760$	0	0
$761$	2.66876e29	0.148515	0.0742576	−	0.997239i	$-0.476341\pi$
$761$	2.66876e29	0.148515	0.0742576	+	0.997239i	$0.476341\pi$
$762$	8.42608e29	0.462486
$763$	−1.19423e30	−0.646519
$764$	8.49951e29	0.453851
$765$	0	0
$766$	1.75511e30	0.911805
$767$	2.95492e30	1.51424
$768$	−1.22835e30	−0.620912
$769$	−6.67567e29	−0.332865	−0.166433	−	0.986053i	$-0.553225\pi$
$769$	−6.67567e29	−0.332865	−0.166433	+	0.986053i	$0.553225\pi$
$770$	0	0
$771$	−8.45778e28	−0.0410379
$772$	−3.93744e29	−0.188466
$773$	3.24392e30	1.53174	0.765870	−	0.642995i	$-0.222308\pi$
$773$	3.24392e30	1.53174	0.765870	+	0.642995i	$0.222308\pi$
$774$	−1.00628e30	−0.468748
$775$	0	0
$776$	−1.63923e30	−0.743178
$777$	5.49988e29	0.245999
$778$	−3.55310e30	−1.56791
$779$	2.44834e30	1.06593
$780$	0	0
$781$	−4.18323e29	−0.177287
$782$	−2.31262e29	−0.0967014
$783$	4.88035e29	0.201351
$784$	2.51082e30	1.02211
$785$	0	0
$786$	6.97706e29	0.276526
$787$	3.51972e30	1.37649	0.688246	−	0.725478i	$-0.258381\pi$
$787$	3.51972e30	1.37649	0.688246	+	0.725478i	$0.258381\pi$
$788$	1.62739e30	0.628008
$789$	2.37038e29	0.0902630
$790$	0	0
$791$	−1.43477e30	−0.532022
$792$	−3.39245e29	−0.124136
$793$	4.32582e30	1.56207
$794$	4.57418e30	1.63004
$795$	0	0
$796$	1.90619e30	0.661575
$797$	1.43521e30	0.491591	0.245795	−	0.969322i	$-0.420951\pi$
$797$	1.43521e30	0.491591	0.245795	+	0.969322i	$0.420951\pi$
$798$	−7.77551e29	−0.262844
$799$	3.05910e30	1.02059
$800$	0	0
$801$	−1.52672e30	−0.496155
$802$	1.75942e30	0.564338
$803$	1.21694e30	0.385263
$804$	−9.43081e29	−0.294687
$805$	0	0
$806$	7.02224e30	2.13775
$807$	3.02544e30	0.909110
$808$	9.66852e29	0.286775
$809$	5.27568e30	1.54461	0.772306	−	0.635251i	$-0.219103\pi$
$809$	5.27568e30	1.54461	0.772306	+	0.635251i	$0.219103\pi$
$810$	0	0
$811$	−4.74349e30	−1.35325	−0.676627	−	0.736326i	$-0.736559\pi$
$811$	−4.74349e30	−1.35325	−0.676627	+	0.736326i	$0.736559\pi$
$812$	−6.65346e29	−0.187374
$813$	−2.49900e29	−0.0694729
$814$	−2.37539e30	−0.651897
$815$	0	0
$816$	−2.84354e30	−0.760522
$817$	−4.03042e30	−1.06419
$818$	4.64859e30	1.21175
$819$	−8.51178e29	−0.219048
$820$	0	0
$821$	6.24260e30	1.56589	0.782947	−	0.622089i	$-0.213716\pi$
$821$	6.24260e30	1.56589	0.782947	+	0.622089i	$0.213716\pi$
$822$	2.70377e30	0.669600
$823$	−3.56237e30	−0.871046	−0.435523	−	0.900178i	$-0.643436\pi$
$823$	−3.56237e30	−0.871046	−0.435523	+	0.900178i	$0.643436\pi$
$824$	1.68077e30	0.405763
$825$	0	0
$826$	2.08551e30	0.490820
$827$	4.65157e30	1.08092	0.540458	−	0.841371i	$-0.318251\pi$
$827$	4.65157e30	1.08092	0.540458	+	0.841371i	$0.318251\pi$
$828$	−4.71369e28	−0.0108154
$829$	−2.98199e30	−0.675590	−0.337795	−	0.941220i	$-0.609681\pi$
$829$	−2.98199e30	−0.675590	−0.337795	+	0.941220i	$0.609681\pi$
$830$	0	0
$831$	−1.38303e29	−0.0305506
$832$	−2.08871e30	−0.455599
$833$	4.03792e30	0.869731
$834$	−1.93624e30	−0.411828
$835$	0	0
$836$	9.99734e29	0.207357
$837$	−1.08223e30	−0.221668
$838$	6.81323e30	1.37813
$839$	2.79104e30	0.557526	0.278763	−	0.960360i	$-0.410076\pi$
$839$	2.79104e30	0.557526	0.278763	+	0.960360i	$0.410076\pi$
$840$	0	0
$841$	4.85750e29	0.0946356
$842$	−5.85837e30	−1.12720
$843$	3.27844e30	0.622986
$844$	2.00897e30	0.377031
$845$	0	0
$846$	2.09449e30	0.383433
$847$	−1.65097e30	−0.298513
$848$	−4.31331e30	−0.770290
$849$	−5.09981e30	−0.899545
$850$	0	0
$851$	4.48583e29	0.0771939
$852$	−4.71201e29	−0.0800923
$853$	4.20283e30	0.705630	0.352815	−	0.935693i	$-0.385225\pi$
$853$	4.20283e30	0.705630	0.352815	+	0.935693i	$0.385225\pi$
$854$	3.05306e30	0.506324
$855$	0	0
$856$	−1.38444e30	−0.224027
$857$	3.95972e30	0.632945	0.316472	−	0.948602i	$-0.397502\pi$
$857$	3.95972e30	0.632945	0.316472	+	0.948602i	$0.397502\pi$
$858$	3.67623e30	0.580478
$859$	−1.21131e30	−0.188941	−0.0944705	−	0.995528i	$-0.530116\pi$
$859$	−1.21131e30	−0.188941	−0.0944705	+	0.995528i	$0.530116\pi$
$860$	0	0
$861$	1.89160e30	0.287937
$862$	−1.00461e31	−1.51067
$863$	−1.13213e31	−1.68183	−0.840917	−	0.541163i	$-0.817984\pi$
$863$	−1.13213e31	−1.68183	−0.840917	+	0.541163i	$0.817984\pi$
$864$	−1.04541e30	−0.153424
$865$	0	0
$866$	1.51043e30	0.216353
$867$	−4.93180e29	−0.0697918
$868$	1.47542e30	0.206281
$869$	6.82370e30	0.942567
$870$	0	0
$871$	−1.38899e31	−1.87287
$872$	−7.89633e30	−1.05197
$873$	−2.73763e30	−0.360351
$874$	−6.34189e29	−0.0824800
$875$	0	0
$876$	1.37077e30	0.174049
$877$	2.97190e30	0.372853	0.186427	−	0.982469i	$-0.440309\pi$
$877$	2.97190e30	0.372853	0.186427	+	0.982469i	$0.440309\pi$
$878$	−3.47491e30	−0.430776
$879$	−6.94901e30	−0.851216
$880$	0	0
$881$	4.00583e30	0.479122	0.239561	−	0.970881i	$-0.422997\pi$
$881$	4.00583e30	0.479122	0.239561	+	0.970881i	$0.422997\pi$
$882$	2.76466e30	0.326754
$883$	−6.21741e29	−0.0726143	−0.0363072	−	0.999341i	$-0.511559\pi$
$883$	−6.21741e29	−0.0726143	−0.0363072	+	0.999341i	$0.511559\pi$
$884$	6.04802e30	0.698014
$885$	0	0
$886$	−6.95074e29	−0.0783388
$887$	1.56467e31	1.74271	0.871353	−	0.490657i	$-0.163243\pi$
$887$	1.56467e31	1.74271	0.871353	+	0.490657i	$0.163243\pi$
$888$	3.63655e30	0.400270
$889$	2.60745e30	0.283627
$890$	0	0
$891$	−5.66562e29	−0.0601910
$892$	−8.56399e29	−0.0899177
$893$	8.38897e30	0.870500
$894$	−6.94678e30	−0.712426
$895$	0	0
$896$	−4.83644e30	−0.484498
$897$	−6.94241e29	−0.0687368
$898$	−1.20591e31	−1.18008
$899$	−1.24594e31	−1.20509
$900$	0	0
$901$	−6.93669e30	−0.655454
$902$	−8.16981e30	−0.763033
$903$	−3.11394e30	−0.287467
$904$	−9.48677e30	−0.865665
$905$	0	0
$906$	−9.90293e30	−0.882912
$907$	1.44979e31	1.27770	0.638848	−	0.769333i	$-0.279411\pi$
$907$	1.44979e31	1.27770	0.638848	+	0.769333i	$0.279411\pi$
$908$	−3.91068e30	−0.340684
$909$	1.61471e30	0.139051
$910$	0	0
$911$	−4.12115e30	−0.346797	−0.173398	−	0.984852i	$-0.555475\pi$
$911$	−4.12115e30	−0.346797	−0.173398	+	0.984852i	$0.555475\pi$
$912$	−7.79783e30	−0.648676
$913$	−7.06641e30	−0.581107
$914$	−6.83016e30	−0.555260
$915$	0	0
$916$	−1.02222e31	−0.812161
$917$	2.15905e30	0.169584
$918$	−3.13101e30	−0.243128
$919$	−9.06489e30	−0.695905	−0.347952	−	0.937512i	$-0.613123\pi$
$919$	−9.06489e30	−0.695905	−0.347952	+	0.937512i	$0.613123\pi$
$920$	0	0
$921$	6.10993e30	0.458469
$922$	−6.95275e30	−0.515801
$923$	−6.93993e30	−0.509023
$924$	7.72402e29	0.0560129
$925$	0	0
$926$	6.49766e30	0.460618
$927$	2.80700e30	0.196746
$928$	−1.20355e31	−0.834082
$929$	−7.61346e30	−0.521695	−0.260848	−	0.965380i	$-0.584002\pi$
$929$	−7.61346e30	−0.521695	−0.260848	+	0.965380i	$0.584002\pi$
$930$	0	0
$931$	1.10732e31	0.741823
$932$	1.12347e31	0.744209
$933$	−1.68954e31	−1.10665
$934$	−3.01623e31	−1.95354
$935$	0	0
$936$	−5.62803e30	−0.356418
$937$	2.01049e31	1.25903	0.629514	−	0.776989i	$-0.283254\pi$
$937$	2.01049e31	1.25903	0.629514	+	0.776989i	$0.283254\pi$
$938$	−9.80314e30	−0.607065
$939$	3.85422e30	0.236019
$940$	0	0
$941$	−1.25620e31	−0.752262	−0.376131	−	0.926566i	$-0.622746\pi$
$941$	−1.25620e31	−0.752262	−0.376131	+	0.926566i	$0.622746\pi$
$942$	−5.29153e30	−0.313362
$943$	1.54284e30	0.0903540
$944$	2.09150e31	1.21130
$945$	0	0
$946$	1.34491e31	0.761789
$947$	−1.94251e31	−1.08815	−0.544074	−	0.839038i	$-0.683119\pi$
$947$	−1.94251e31	−1.08815	−0.544074	+	0.839038i	$0.683119\pi$
$948$	7.68624e30	0.425820
$949$	2.01889e31	1.10616
$950$	0	0
$951$	3.42695e30	0.183659
$952$	−5.80150e30	−0.307505
$953$	2.91402e31	1.52763	0.763813	−	0.645437i	$-0.223325\pi$
$953$	2.91402e31	1.52763	0.763813	+	0.645437i	$0.223325\pi$
$954$	−4.74937e30	−0.246251
$955$	0	0
$956$	9.00707e30	0.456852
$957$	−6.52264e30	−0.327226
$958$	−1.01901e31	−0.505639
$959$	8.36680e30	0.410643
$960$	0	0
$961$	6.80351e30	0.326691
$962$	−3.94075e31	−1.87172
$963$	−2.31211e30	−0.108626
$964$	−1.11711e31	−0.519143
$965$	0	0
$966$	−4.89979e29	−0.0222801
$967$	3.07363e30	0.138253	0.0691264	−	0.997608i	$-0.477979\pi$
$967$	3.07363e30	0.138253	0.0691264	+	0.997608i	$0.477979\pi$
$968$	−1.09163e31	−0.485717
$969$	−1.25405e31	−0.551970
$970$	0	0
$971$	1.00411e31	0.432492	0.216246	−	0.976339i	$-0.430619\pi$
$971$	1.00411e31	0.432492	0.216246	+	0.976339i	$0.430619\pi$
$972$	−6.38178e29	−0.0271923
$973$	−5.99169e30	−0.252560
$974$	5.17306e31	2.15714
$975$	0	0
$976$	3.06183e31	1.24956
$977$	−3.46386e31	−1.39852	−0.699258	−	0.714870i	$-0.746486\pi$
$977$	−3.46386e31	−1.39852	−0.699258	+	0.714870i	$0.746486\pi$
$978$	−1.01056e31	−0.403648
$979$	2.04047e31	0.806330
$980$	0	0
$981$	−1.31874e31	−0.510076
$982$	−1.10152e30	−0.0421524
$983$	−2.93055e31	−1.10953	−0.554763	−	0.832008i	$-0.687191\pi$
$983$	−2.93055e31	−1.10953	−0.554763	+	0.832008i	$0.687191\pi$
$984$	1.25074e31	0.468509
$985$	0	0
$986$	−3.60463e31	−1.32176
$987$	6.48139e30	0.235146
$988$	1.65855e31	0.595360
$989$	−2.53980e30	−0.0902066
$990$	0	0
$991$	2.17867e30	0.0757560	0.0378780	−	0.999282i	$-0.487940\pi$
$991$	2.17867e30	0.0757560	0.0378780	+	0.999282i	$0.487940\pi$
$992$	2.66890e31	0.918246
$993$	5.47015e30	0.186222
$994$	−4.89804e30	−0.164993
$995$	0	0
$996$	−7.95964e30	−0.262525
$997$	3.87778e30	0.126556	0.0632781	−	0.997996i	$-0.479844\pi$
$997$	3.87778e30	0.126556	0.0632781	+	0.997996i	$0.479844\pi$
$998$	−6.16574e31	−1.99120
$999$	6.07328e30	0.194082

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.22.a.n.1.3		10
5.2	odd	4		15.22.b.a.4.5	✓	20
5.3	odd	4		15.22.b.a.4.16	yes	20
5.4	even	2		75.22.a.m.1.8		10
15.2	even	4		45.22.b.d.19.16		20
15.8	even	4		45.22.b.d.19.5		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.22.b.a.4.5	✓	20	5.2	odd	4
15.22.b.a.4.16	yes	20	5.3	odd	4
45.22.b.d.19.5		20	15.8	even	4
45.22.b.d.19.16		20	15.2	even	4
75.22.a.m.1.8		10	5.4	even	2
75.22.a.n.1.3		10	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 75 = 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 22 \)
Character orbit:	\([\chi]\)	\(=\)	75.a (trivial)

\(f(q)\)	\(=\)	\(q-1728.04 q^{2} -59049.0 q^{3} +888953. q^{4} +1.02039e8 q^{6} +3.15759e8 q^{7} +2.08781e9 q^{8} +3.48678e9 q^{9} +O(q^{10})\)	\(q-1728.04 q^{2} -59049.0 q^{3} +888953. q^{4} +1.02039e8 q^{6} +3.15759e8 q^{7} +2.08781e9 q^{8} +3.48678e9 q^{9} -4.66012e10 q^{11} -5.24918e10 q^{12} -7.73108e11 q^{13} -5.45642e11 q^{14} -5.47208e12 q^{16} -8.80023e12 q^{17} -6.02529e12 q^{18} -2.41329e13 q^{19} -1.86452e13 q^{21} +8.05285e13 q^{22} -1.52075e13 q^{23} -1.23283e14 q^{24} +1.33596e15 q^{26} -2.05891e14 q^{27} +2.80695e14 q^{28} -2.37036e15 q^{29} +5.25633e15 q^{31} +5.07749e15 q^{32} +2.75175e15 q^{33} +1.52071e16 q^{34} +3.09959e15 q^{36} -2.94975e16 q^{37} +4.17024e16 q^{38} +4.56513e16 q^{39} -1.01452e17 q^{41} +3.22196e16 q^{42} +1.67010e17 q^{43} -4.14263e16 q^{44} +2.62791e16 q^{46} -3.47616e17 q^{47} +3.23121e17 q^{48} -4.58842e17 q^{49} +5.19645e17 q^{51} -6.87257e17 q^{52} +7.88240e17 q^{53} +3.55787e17 q^{54} +6.59244e17 q^{56} +1.42502e18 q^{57} +4.09606e18 q^{58} -3.82213e18 q^{59} -5.59536e18 q^{61} -9.08312e18 q^{62} +1.10098e18 q^{63} +2.70170e18 q^{64} -4.75513e18 q^{66} +1.79663e19 q^{67} -7.82299e18 q^{68} +8.97987e17 q^{69} +8.97666e18 q^{71} +7.27974e18 q^{72} -2.61140e19 q^{73} +5.09728e19 q^{74} -2.14530e19 q^{76} -1.47147e19 q^{77} -7.88870e19 q^{78} -1.46427e20 q^{79} +1.21577e19 q^{81} +1.75313e20 q^{82} +1.51636e20 q^{83} -1.65747e19 q^{84} -2.88599e20 q^{86} +1.39967e20 q^{87} -9.72945e19 q^{88} -4.37859e20 q^{89} -2.44116e20 q^{91} -1.35187e19 q^{92} -3.10381e20 q^{93} +6.00693e20 q^{94} -2.99821e20 q^{96} -7.85145e20 q^{97} +7.92896e20 q^{98} -1.62488e20 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 645 q^{2} - 590490 q^{3} + 10043205 q^{4} - 38086605 q^{6} + 115357290 q^{7} + 314142735 q^{8} + 34867844010 q^{9}+O(q^{10}) \) 10 * q + 645 * q^2 - 590490 * q^3 + 10043205 * q^4 - 38086605 * q^6 + 115357290 * q^7 + 314142735 * q^8 + 34867844010 * q^9	\( 10 q + 645 q^{2} - 590490 q^{3} + 10043205 q^{4} - 38086605 q^{6} + 115357290 q^{7} + 314142735 q^{8} + 34867844010 q^{9} + 5976221790 q^{11} - 593041212045 q^{12} + 842570747430 q^{13} + 1605059874570 q^{14} + 6061861547825 q^{16} + 12910340404230 q^{17} + 2248975938645 q^{18} - 76155422176280 q^{19} - 6811732617210 q^{21} + 461780887241010 q^{22} + 82640920915920 q^{23} - 18549814359015 q^{24} + 286555331159670 q^{26} - 20\!\cdots\!90 q^{27}+ \cdots + 20\!\cdots\!90 q^{99}+O(q^{100}) \) 10 * q + 645 * q^2 - 590490 * q^3 + 10043205 * q^4 - 38086605 * q^6 + 115357290 * q^7 + 314142735 * q^8 + 34867844010 * q^9 + 5976221790 * q^11 - 593041212045 * q^12 + 842570747430 * q^13 + 1605059874570 * q^14 + 6061861547825 * q^16 + 12910340404230 * q^17 + 2248975938645 * q^18 - 76155422176280 * q^19 - 6811732617210 * q^21 + 461780887241010 * q^22 + 82640920915920 * q^23 - 18549814359015 * q^24 + 286555331159670 * q^26 - 2058911320946490 * q^27 + 1520428218531930 * q^28 - 2553653160731010 * q^29 - 5579671364724940 * q^31 + 29255856594217815 * q^32 - 352889920477710 * q^33 + 36285968426431010 * q^34 + 35018490530045205 * q^36 + 1797908431222890 * q^37 + 10684960744876320 * q^38 - 49752960064994070 * q^39 - 157319729506021440 * q^41 - 94777180533483930 * q^42 - 148924853700743400 * q^43 + 49118820773767290 * q^44 - 238453286038259540 * q^46 - 43171138083158100 * q^47 - 357946862537518425 * q^48 + 453692886452454950 * q^49 - 762342690529377270 * q^51 + 5077473324432504030 * q^52 + 1835165786666252970 * q^53 - 132799780201048605 * q^54 - 5146515624013530450 * q^56 + 4496901524087157720 * q^57 + 3684042125074285440 * q^58 + 4936135121536323630 * q^59 - 4443080871007408300 * q^61 + 39366851097921260280 * q^62 + 402225999313633290 * q^63 - 14877283608188093455 * q^64 - 27267699610694399490 * q^66 + 33664559574358232580 * q^67 + 44791395195934111290 * q^68 - 4879863739164160080 * q^69 - 74662724971386630180 * q^71 + 1095347988085476735 * q^72 + 16062862692682477620 * q^73 - 130249023546610518030 * q^74 - 258736483662380220720 * q^76 + 56216747719240740180 * q^77 - 16920805749647353830 * q^78 - 49130708010799643300 * q^79 + 121576654590569288010 * q^81 + 117185080045656261930 * q^82 + 118408383608453695560 * q^83 - 89779765876091934570 * q^84 - 1007271272794707382260 * q^86 + 150790665488005409490 * q^87 + 41803519849182967710 * q^88 - 572103976713991581780 * q^89 - 1669810835257196575140 * q^91 - 1206545757146297440260 * q^92 + 329474014415642982060 * q^93 - 1671319720124696594920 * q^94 - 1727529076031967757935 * q^96 - 1299275526640742173920 * q^97 - 2683959884079093505455 * q^98 + 20837796914288297790 * q^99

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