LMFDB - Embedded newform 4802.2.a.c.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4802,2,Mod(1,4802)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4802, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4802.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4802 = 2 \cdot 7^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4802.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:	$38.3441630506$
Analytic rank:	$0$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - x^{8} - 21x^{7} + 27x^{6} + 142x^{5} - 221x^{4} - 293x^{3} + 567x^{2} - 61x - 113 $ x^9 - x^8 - 21x^7 + 27x^6 + 142x^5 - 221x^4 - 293x^3 + 567x^2 - 61*x - 113
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 98)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$-3.07434$ of defining polynomial
Character	$\chi$	$=$	4802.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +3.07434 q^{3} +1.00000 q^{4} +3.02538 q^{5} -3.07434 q^{6} -1.00000 q^{8} +6.45155 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +3.07434 q^{3} +1.00000 q^{4} +3.02538 q^{5} -3.07434 q^{6} -1.00000 q^{8} +6.45155 q^{9} -3.02538 q^{10} +3.02538 q^{11} +3.07434 q^{12} +2.39132 q^{13} +9.30104 q^{15} +1.00000 q^{16} +0.643016 q^{17} -6.45155 q^{18} -0.629295 q^{19} +3.02538 q^{20} -3.02538 q^{22} -9.39694 q^{23} -3.07434 q^{24} +4.15293 q^{25} -2.39132 q^{26} +10.6112 q^{27} +4.26461 q^{29} -9.30104 q^{30} +2.51075 q^{31} -1.00000 q^{32} +9.30104 q^{33} -0.643016 q^{34} +6.45155 q^{36} -6.42392 q^{37} +0.629295 q^{38} +7.35171 q^{39} -3.02538 q^{40} -2.07039 q^{41} +1.35656 q^{43} +3.02538 q^{44} +19.5184 q^{45} +9.39694 q^{46} -1.06025 q^{47} +3.07434 q^{48} -4.15293 q^{50} +1.97685 q^{51} +2.39132 q^{52} +4.68623 q^{53} -10.6112 q^{54} +9.15293 q^{55} -1.93466 q^{57} -4.26461 q^{58} -3.14452 q^{59} +9.30104 q^{60} +5.39679 q^{61} -2.51075 q^{62} +1.00000 q^{64} +7.23464 q^{65} -9.30104 q^{66} +6.32287 q^{67} +0.643016 q^{68} -28.8893 q^{69} +14.1609 q^{71} -6.45155 q^{72} -4.15896 q^{73} +6.42392 q^{74} +12.7675 q^{75} -0.629295 q^{76} -7.35171 q^{78} -11.2211 q^{79} +3.02538 q^{80} +13.2678 q^{81} +2.07039 q^{82} -7.62465 q^{83} +1.94537 q^{85} -1.35656 q^{86} +13.1108 q^{87} -3.02538 q^{88} -1.19130 q^{89} -19.5184 q^{90} -9.39694 q^{92} +7.71890 q^{93} +1.06025 q^{94} -1.90386 q^{95} -3.07434 q^{96} -16.3992 q^{97} +19.5184 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q - 9 q^{2} - q^{3} + 9 q^{4} + q^{6} - 9 q^{8} + 16 q^{9}+O(q^{10}) $ 9 * q - 9 * q^2 - q^3 + 9 * q^4 + q^6 - 9 * q^8 + 16 * q^9	$ 9 q - 9 q^{2} - q^{3} + 9 q^{4} + q^{6} - 9 q^{8} + 16 q^{9} - q^{12} + 5 q^{13} + 9 q^{16} + 17 q^{17} - 16 q^{18} + 22 q^{19} - 7 q^{23} + q^{24} + 25 q^{25} - 5 q^{26} + 23 q^{27} + 2 q^{29} + 12 q^{31} - 9 q^{32} - 17 q^{34} + 16 q^{36} - 3 q^{37} - 22 q^{38} - 5 q^{39} - 25 q^{41} - 5 q^{43} + 7 q^{45} + 7 q^{46} + 8 q^{47} - q^{48} - 25 q^{50} - 24 q^{51} + 5 q^{52} - 2 q^{53} - 23 q^{54} + 70 q^{55} - 43 q^{57} - 2 q^{58} + 25 q^{59} + 4 q^{61} - 12 q^{62} + 9 q^{64} + 21 q^{65} - 43 q^{67} + 17 q^{68} - 7 q^{69} + 14 q^{71} - 16 q^{72} + 29 q^{73} + 3 q^{74} - 2 q^{75} + 22 q^{76} + 5 q^{78} - 33 q^{79} - 15 q^{81} + 25 q^{82} + 18 q^{83} + 7 q^{85} + 5 q^{86} + 6 q^{87} - 24 q^{89} - 7 q^{90} - 7 q^{92} + 2 q^{93} - 8 q^{94} - 7 q^{95} + q^{96} + 16 q^{97} + 7 q^{99}+O(q^{100}) $ 9 * q - 9 * q^2 - q^3 + 9 * q^4 + q^6 - 9 * q^8 + 16 * q^9 - q^12 + 5 * q^13 + 9 * q^16 + 17 * q^17 - 16 * q^18 + 22 * q^19 - 7 * q^23 + q^24 + 25 * q^25 - 5 * q^26 + 23 * q^27 + 2 * q^29 + 12 * q^31 - 9 * q^32 - 17 * q^34 + 16 * q^36 - 3 * q^37 - 22 * q^38 - 5 * q^39 - 25 * q^41 - 5 * q^43 + 7 * q^45 + 7 * q^46 + 8 * q^47 - q^48 - 25 * q^50 - 24 * q^51 + 5 * q^52 - 2 * q^53 - 23 * q^54 + 70 * q^55 - 43 * q^57 - 2 * q^58 + 25 * q^59 + 4 * q^61 - 12 * q^62 + 9 * q^64 + 21 * q^65 - 43 * q^67 + 17 * q^68 - 7 * q^69 + 14 * q^71 - 16 * q^72 + 29 * q^73 + 3 * q^74 - 2 * q^75 + 22 * q^76 + 5 * q^78 - 33 * q^79 - 15 * q^81 + 25 * q^82 + 18 * q^83 + 7 * q^85 + 5 * q^86 + 6 * q^87 - 24 * q^89 - 7 * q^90 - 7 * q^92 + 2 * q^93 - 8 * q^94 - 7 * q^95 + q^96 + 16 * q^97 + 7 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	3.07434	1.77497	0.887485	−	0.460837i	$-0.152451\pi$
$3$	3.07434	1.77497	0.887485	+	0.460837i	$0.152451\pi$
$4$	1.00000	0.500000
$5$	3.02538	1.35299	0.676496	−	0.736447i	$-0.263498\pi$
$5$	3.02538	1.35299	0.676496	+	0.736447i	$0.263498\pi$
$6$	−3.07434	−1.25509
$7$	0	0
$7$	0	0
$8$	−1.00000	−0.353553
$9$	6.45155	2.15052
$10$	−3.02538	−0.956709
$11$	3.02538	0.912187	0.456093	−	0.889932i	$-0.349248\pi$
$11$	3.02538	0.912187	0.456093	+	0.889932i	$0.349248\pi$
$12$	3.07434	0.887485
$13$	2.39132	0.663232	0.331616	−	0.943414i	$-0.392406\pi$
$13$	2.39132	0.663232	0.331616	+	0.943414i	$0.392406\pi$
$14$	0	0
$15$	9.30104	2.40152
$16$	1.00000	0.250000
$17$	0.643016	0.155954	0.0779772	−	0.996955i	$-0.475154\pi$
$17$	0.643016	0.155954	0.0779772	+	0.996955i	$0.475154\pi$
$18$	−6.45155	−1.52064
$19$	−0.629295	−0.144370	−0.0721851	−	0.997391i	$-0.522997\pi$
$19$	−0.629295	−0.144370	−0.0721851	+	0.997391i	$0.522997\pi$
$20$	3.02538	0.676496
$21$	0	0
$22$	−3.02538	−0.645013
$23$	−9.39694	−1.95940	−0.979698	−	0.200478i	$-0.935751\pi$
$23$	−9.39694	−1.95940	−0.979698	+	0.200478i	$0.935751\pi$
$24$	−3.07434	−0.627546
$25$	4.15293	0.830585
$26$	−2.39132	−0.468976
$27$	10.6112	2.04213
$28$	0	0
$29$	4.26461	0.791918	0.395959	−	0.918268i	$-0.370412\pi$
$29$	4.26461	0.791918	0.395959	+	0.918268i	$0.370412\pi$
$30$	−9.30104	−1.69813
$31$	2.51075	0.450944	0.225472	−	0.974250i	$-0.427608\pi$
$31$	2.51075	0.450944	0.225472	+	0.974250i	$0.427608\pi$
$32$	−1.00000	−0.176777
$33$	9.30104	1.61910
$34$	−0.643016	−0.110276
$35$	0	0
$36$	6.45155	1.07526
$37$	−6.42392	−1.05609	−0.528043	−	0.849218i	$-0.677074\pi$
$37$	−6.42392	−1.05609	−0.528043	+	0.849218i	$0.677074\pi$
$38$	0.629295	0.102085
$39$	7.35171	1.17722
$40$	−3.02538	−0.478355
$41$	−2.07039	−0.323341	−0.161670	−	0.986845i	$-0.551688\pi$
$41$	−2.07039	−0.323341	−0.161670	+	0.986845i	$0.551688\pi$
$42$	0	0
$43$	1.35656	0.206873	0.103436	−	0.994636i	$-0.467016\pi$
$43$	1.35656	0.206873	0.103436	+	0.994636i	$0.467016\pi$
$44$	3.02538	0.456093
$45$	19.5184	2.90963
$46$	9.39694	1.38550
$47$	−1.06025	−0.154654	−0.0773268	−	0.997006i	$-0.524638\pi$
$47$	−1.06025	−0.154654	−0.0773268	+	0.997006i	$0.524638\pi$
$48$	3.07434	0.443742
$49$	0	0
$50$	−4.15293	−0.587313
$51$	1.97685	0.276814
$52$	2.39132	0.331616
$53$	4.68623	0.643704	0.321852	−	0.946790i	$-0.395695\pi$
$53$	4.68623	0.643704	0.321852	+	0.946790i	$0.395695\pi$
$54$	−10.6112	−1.44400
$55$	9.15293	1.23418
$56$	0	0
$57$	−1.93466	−0.256253
$58$	−4.26461	−0.559971
$59$	−3.14452	−0.409381	−0.204691	−	0.978827i	$-0.565619\pi$
$59$	−3.14452	−0.409381	−0.204691	+	0.978827i	$0.565619\pi$
$60$	9.30104	1.20076
$61$	5.39679	0.690988	0.345494	−	0.938421i	$-0.387711\pi$
$61$	5.39679	0.690988	0.345494	+	0.938421i	$0.387711\pi$
$62$	−2.51075	−0.318866
$63$	0	0
$64$	1.00000	0.125000
$65$	7.23464	0.897347
$66$	−9.30104	−1.14488
$67$	6.32287	0.772462	0.386231	−	0.922402i	$-0.373777\pi$
$67$	6.32287	0.772462	0.386231	+	0.922402i	$0.373777\pi$
$68$	0.643016	0.0779772
$69$	−28.8893	−3.47787
$70$	0	0
$71$	14.1609	1.68059	0.840296	−	0.542127i	$-0.182381\pi$
$71$	14.1609	1.68059	0.840296	+	0.542127i	$0.182381\pi$
$72$	−6.45155	−0.760322
$73$	−4.15896	−0.486769	−0.243385	−	0.969930i	$-0.578258\pi$
$73$	−4.15896	−0.486769	−0.243385	+	0.969930i	$0.578258\pi$
$74$	6.42392	0.746766
$75$	12.7675	1.47426
$76$	−0.629295	−0.0721851
$77$	0	0
$78$	−7.35171	−0.832418
$79$	−11.2211	−1.26247	−0.631236	−	0.775590i	$-0.717452\pi$
$79$	−11.2211	−1.26247	−0.631236	+	0.775590i	$0.717452\pi$
$80$	3.02538	0.338248
$81$	13.2678	1.47420
$82$	2.07039	0.228636
$83$	−7.62465	−0.836914	−0.418457	−	0.908237i	$-0.637429\pi$
$83$	−7.62465	−0.836914	−0.418457	+	0.908237i	$0.637429\pi$
$84$	0	0
$85$	1.94537	0.211005
$86$	−1.35656	−0.146281
$87$	13.1108	1.40563
$88$	−3.02538	−0.322507
$89$	−1.19130	−0.126278	−0.0631388	−	0.998005i	$-0.520111\pi$
$89$	−1.19130	−0.126278	−0.0631388	+	0.998005i	$0.520111\pi$
$90$	−19.5184	−2.05742
$91$	0	0
$92$	−9.39694	−0.979698
$93$	7.71890	0.800412
$94$	1.06025	0.109357
$95$	−1.90386	−0.195332
$96$	−3.07434	−0.313773
$97$	−16.3992	−1.66509	−0.832543	−	0.553961i	$-0.813116\pi$
$97$	−16.3992	−1.66509	−0.832543	+	0.553961i	$0.813116\pi$
$98$	0	0
$99$	19.5184	1.96167
$100$	4.15293	0.415293
$101$	−14.3697	−1.42984	−0.714921	−	0.699205i	$-0.753537\pi$
$101$	−14.3697	−1.42984	−0.714921	+	0.699205i	$0.753537\pi$
$102$	−1.97685	−0.195737
$103$	16.3323	1.60927	0.804633	−	0.593773i	$-0.202362\pi$
$103$	16.3323	1.60927	0.804633	+	0.593773i	$0.202362\pi$
$104$	−2.39132	−0.234488
$105$	0	0
$106$	−4.68623	−0.455167
$107$	16.6838	1.61288	0.806441	−	0.591315i	$-0.201391\pi$
$107$	16.6838	1.61288	0.806441	+	0.591315i	$0.201391\pi$
$108$	10.6112	1.02106
$109$	1.66514	0.159492	0.0797458	−	0.996815i	$-0.474589\pi$
$109$	1.66514	0.159492	0.0797458	+	0.996815i	$0.474589\pi$
$110$	−9.15293	−0.872697
$111$	−19.7493	−1.87452
$112$	0	0
$113$	−9.25578	−0.870711	−0.435355	−	0.900259i	$-0.643377\pi$
$113$	−9.25578	−0.870711	−0.435355	+	0.900259i	$0.643377\pi$
$114$	1.93466	0.181198
$115$	−28.4293	−2.65105
$116$	4.26461	0.395959
$117$	15.4277	1.42629
$118$	3.14452	0.289476
$119$	0	0
$120$	−9.30104	−0.849065
$121$	−1.84707	−0.167916
$122$	−5.39679	−0.488602
$123$	−6.36508	−0.573920
$124$	2.51075	0.225472
$125$	−2.56272	−0.229217
$126$	0	0
$127$	−13.3955	−1.18866	−0.594328	−	0.804223i	$-0.702582\pi$
$127$	−13.3955	−1.18866	−0.594328	+	0.804223i	$0.702582\pi$
$128$	−1.00000	−0.0883883
$129$	4.17051	0.367193
$130$	−7.23464	−0.634520
$131$	−19.4378	−1.69829	−0.849146	−	0.528158i	$-0.822883\pi$
$131$	−19.4378	−1.69829	−0.849146	+	0.528158i	$0.822883\pi$
$132$	9.30104	0.809551
$133$	0	0
$134$	−6.32287	−0.546213
$135$	32.1030	2.76298
$136$	−0.643016	−0.0551382
$137$	7.88612	0.673757	0.336879	−	0.941548i	$-0.390629\pi$
$137$	7.88612	0.673757	0.336879	+	0.941548i	$0.390629\pi$
$138$	28.8893	2.45922
$139$	0.293193	0.0248683	0.0124342	−	0.999923i	$-0.496042\pi$
$139$	0.293193	0.0248683	0.0124342	+	0.999923i	$0.496042\pi$
$140$	0	0
$141$	−3.25957	−0.274505
$142$	−14.1609	−1.18836
$143$	7.23464	0.604991
$144$	6.45155	0.537629
$145$	12.9021	1.07146
$146$	4.15896	0.344198
$147$	0	0
$148$	−6.42392	−0.528043
$149$	−7.09335	−0.581110	−0.290555	−	0.956858i	$-0.593840\pi$
$149$	−7.09335	−0.581110	−0.290555	+	0.956858i	$0.593840\pi$
$150$	−12.7675	−1.04246
$151$	11.7970	0.960025	0.480013	−	0.877262i	$-0.340632\pi$
$151$	11.7970	0.960025	0.480013	+	0.877262i	$0.340632\pi$
$152$	0.629295	0.0510426
$153$	4.14845	0.335382
$154$	0	0
$155$	7.59598	0.610124
$156$	7.35171	0.588608
$157$	13.1571	1.05005	0.525024	−	0.851087i	$-0.324056\pi$
$157$	13.1571	1.05005	0.525024	+	0.851087i	$0.324056\pi$
$158$	11.2211	0.892703
$159$	14.4071	1.14255
$160$	−3.02538	−0.239177
$161$	0	0
$162$	−13.2678	−1.04242
$163$	13.4107	1.05041	0.525204	−	0.850977i	$-0.323989\pi$
$163$	13.4107	1.05041	0.525204	+	0.850977i	$0.323989\pi$
$164$	−2.07039	−0.161670
$165$	28.1392	2.19063
$166$	7.62465	0.591787
$167$	9.48237	0.733768	0.366884	−	0.930267i	$-0.380425\pi$
$167$	9.48237	0.733768	0.366884	+	0.930267i	$0.380425\pi$
$168$	0	0
$169$	−7.28160	−0.560123
$170$	−1.94537	−0.149203
$171$	−4.05993	−0.310470
$172$	1.35656	0.103436
$173$	1.05249	0.0800192	0.0400096	−	0.999199i	$-0.487261\pi$
$173$	1.05249	0.0800192	0.0400096	+	0.999199i	$0.487261\pi$
$174$	−13.1108	−0.993930
$175$	0	0
$176$	3.02538	0.228047
$177$	−9.66730	−0.726639
$178$	1.19130	0.0892917
$179$	−10.1920	−0.761787	−0.380894	−	0.924619i	$-0.624384\pi$
$179$	−10.1920	−0.761787	−0.380894	+	0.924619i	$0.624384\pi$
$180$	19.5184	1.45481
$181$	−13.8789	−1.03161	−0.515806	−	0.856706i	$-0.672507\pi$
$181$	−13.8789	−1.03161	−0.515806	+	0.856706i	$0.672507\pi$
$182$	0	0
$183$	16.5915	1.22648
$184$	9.39694	0.692751
$185$	−19.4348	−1.42888
$186$	−7.71890	−0.565977
$187$	1.94537	0.142259
$188$	−1.06025	−0.0773268
$189$	0	0
$190$	1.90386	0.138120
$191$	6.72199	0.486386	0.243193	−	0.969978i	$-0.421805\pi$
$191$	6.72199	0.486386	0.243193	+	0.969978i	$0.421805\pi$
$192$	3.07434	0.221871
$193$	−2.32059	−0.167039	−0.0835197	−	0.996506i	$-0.526616\pi$
$193$	−2.32059	−0.167039	−0.0835197	+	0.996506i	$0.526616\pi$
$194$	16.3992	1.17739
$195$	22.2417	1.59276
$196$	0	0
$197$	8.72306	0.621492	0.310746	−	0.950493i	$-0.399421\pi$
$197$	8.72306	0.621492	0.310746	+	0.950493i	$0.399421\pi$
$198$	−19.5184	−1.38711
$199$	10.6790	0.757017	0.378509	−	0.925598i	$-0.376437\pi$
$199$	10.6790	0.757017	0.378509	+	0.925598i	$0.376437\pi$
$200$	−4.15293	−0.293656
$201$	19.4386	1.37110
$202$	14.3697	1.01105
$203$	0	0
$204$	1.97685	0.138407
$205$	−6.26372	−0.437477
$206$	−16.3323	−1.13792
$207$	−60.6248	−4.21371
$208$	2.39132	0.165808
$209$	−1.90386	−0.131693
$210$	0	0
$211$	−14.2225	−0.979115	−0.489557	−	0.871971i	$-0.662842\pi$
$211$	−14.2225	−0.979115	−0.489557	+	0.871971i	$0.662842\pi$
$212$	4.68623	0.321852
$213$	43.5355	2.98300
$214$	−16.6838	−1.14048
$215$	4.10410	0.279897
$216$	−10.6112	−0.722002
$217$	0	0
$218$	−1.66514	−0.112778
$219$	−12.7860	−0.864000
$220$	9.15293	0.617090
$221$	1.53766	0.103434
$222$	19.7493	1.32549
$223$	9.69578	0.649278	0.324639	−	0.945838i	$-0.394757\pi$
$223$	9.69578	0.649278	0.324639	+	0.945838i	$0.394757\pi$
$224$	0	0
$225$	26.7928	1.78619
$226$	9.25578	0.615686
$227$	6.19599	0.411242	0.205621	−	0.978632i	$-0.434079\pi$
$227$	6.19599	0.411242	0.205621	+	0.978632i	$0.434079\pi$
$228$	−1.93466	−0.128126
$229$	−0.547320	−0.0361679	−0.0180840	−	0.999836i	$-0.505757\pi$
$229$	−0.547320	−0.0361679	−0.0180840	+	0.999836i	$0.505757\pi$
$230$	28.4293	1.87457
$231$	0	0
$232$	−4.26461	−0.279985
$233$	6.77776	0.444026	0.222013	−	0.975044i	$-0.428737\pi$
$233$	6.77776	0.444026	0.222013	+	0.975044i	$0.428737\pi$
$234$	−15.4277	−1.00854
$235$	−3.20767	−0.209245
$236$	−3.14452	−0.204691
$237$	−34.4975	−2.24085
$238$	0	0
$239$	−6.80155	−0.439956	−0.219978	−	0.975505i	$-0.570599\pi$
$239$	−6.80155	−0.439956	−0.219978	+	0.975505i	$0.570599\pi$
$240$	9.30104	0.600379
$241$	−26.0644	−1.67895	−0.839477	−	0.543395i	$-0.817139\pi$
$241$	−26.0644	−1.67895	−0.839477	+	0.543395i	$0.817139\pi$
$242$	1.84707	0.118734
$243$	8.95609	0.574533
$244$	5.39679	0.345494
$245$	0	0
$246$	6.36508	0.405822
$247$	−1.50484	−0.0957509
$248$	−2.51075	−0.159433
$249$	−23.4407	−1.48550
$250$	2.56272	0.162081
$251$	26.1920	1.65322	0.826611	−	0.562774i	$-0.190266\pi$
$251$	26.1920	1.65322	0.826611	+	0.562774i	$0.190266\pi$
$252$	0	0
$253$	−28.4293	−1.78734
$254$	13.3955	0.840507
$255$	5.98072	0.374527
$256$	1.00000	0.0625000
$257$	−13.4073	−0.836326	−0.418163	−	0.908372i	$-0.637326\pi$
$257$	−13.4073	−0.836326	−0.418163	+	0.908372i	$0.637326\pi$
$258$	−4.17051	−0.259644
$259$	0	0
$260$	7.23464	0.448674
$261$	27.5133	1.70303
$262$	19.4378	1.20087
$263$	−10.5626	−0.651320	−0.325660	−	0.945487i	$-0.605586\pi$
$263$	−10.5626	−0.651320	−0.325660	+	0.945487i	$0.605586\pi$
$264$	−9.30104	−0.572439
$265$	14.1776	0.870925
$266$	0	0
$267$	−3.66246	−0.224139
$268$	6.32287	0.386231
$269$	11.9198	0.726761	0.363380	−	0.931641i	$-0.381623\pi$
$269$	11.9198	0.726761	0.363380	+	0.931641i	$0.381623\pi$
$270$	−32.1030	−1.95372
$271$	−24.8700	−1.51075	−0.755373	−	0.655295i	$-0.772545\pi$
$271$	−24.8700	−1.51075	−0.755373	+	0.655295i	$0.772545\pi$
$272$	0.643016	0.0389886
$273$	0	0
$274$	−7.88612	−0.476418
$275$	12.5642	0.757649
$276$	−28.8893	−1.73893
$277$	27.7796	1.66911	0.834557	−	0.550921i	$-0.185723\pi$
$277$	27.7796	1.66911	0.834557	+	0.550921i	$0.185723\pi$
$278$	−0.293193	−0.0175846
$279$	16.1982	0.969763
$280$	0	0
$281$	−31.1896	−1.86061	−0.930306	−	0.366783i	$-0.880459\pi$
$281$	−31.1896	−1.86061	−0.930306	+	0.366783i	$0.880459\pi$
$282$	3.25957	0.194105
$283$	18.9829	1.12841	0.564207	−	0.825634i	$-0.309182\pi$
$283$	18.9829	1.12841	0.564207	+	0.825634i	$0.309182\pi$
$284$	14.1609	0.840296
$285$	−5.85310	−0.346708
$286$	−7.23464	−0.427793
$287$	0	0
$288$	−6.45155	−0.380161
$289$	−16.5865	−0.975678
$290$	−12.9021	−0.757635
$291$	−50.4166	−2.95548
$292$	−4.15896	−0.243385
$293$	−19.6220	−1.14633	−0.573163	−	0.819441i	$-0.694284\pi$
$293$	−19.6220	−1.14633	−0.573163	+	0.819441i	$0.694284\pi$
$294$	0	0
$295$	−9.51336	−0.553889
$296$	6.42392	0.373383
$297$	32.1030	1.86280
$298$	7.09335	0.410907
$299$	−22.4711	−1.29953
$300$	12.7675	0.737132
$301$	0	0
$302$	−11.7970	−0.678840
$303$	−44.1774	−2.53793
$304$	−0.629295	−0.0360925
$305$	16.3273	0.934901
$306$	−4.14845	−0.237151
$307$	−21.0550	−1.20167	−0.600836	−	0.799372i	$-0.705165\pi$
$307$	−21.0550	−1.20167	−0.600836	+	0.799372i	$0.705165\pi$
$308$	0	0
$309$	50.2109	2.85640
$310$	−7.59598	−0.431423
$311$	11.7755	0.667728	0.333864	−	0.942621i	$-0.391647\pi$
$311$	11.7755	0.667728	0.333864	+	0.942621i	$0.391647\pi$
$312$	−7.35171	−0.416209
$313$	−21.4522	−1.21255	−0.606275	−	0.795255i	$-0.707337\pi$
$313$	−21.4522	−1.21255	−0.606275	+	0.795255i	$0.707337\pi$
$314$	−13.1571	−0.742497
$315$	0	0
$316$	−11.2211	−0.631236
$317$	29.6833	1.66718	0.833591	−	0.552382i	$-0.186281\pi$
$317$	29.6833	1.66718	0.833591	+	0.552382i	$0.186281\pi$
$318$	−14.4071	−0.807908
$319$	12.9021	0.722377
$320$	3.02538	0.169124
$321$	51.2915	2.86281
$322$	0	0
$323$	−0.404647	−0.0225152
$324$	13.2678	0.737101
$325$	9.93096	0.550871
$326$	−13.4107	−0.742750
$327$	5.11920	0.283093
$328$	2.07039	0.114318
$329$	0	0
$330$	−28.1392	−1.54901
$331$	−0.820937	−0.0451228	−0.0225614	−	0.999745i	$-0.507182\pi$
$331$	−0.820937	−0.0451228	−0.0225614	+	0.999745i	$0.507182\pi$
$332$	−7.62465	−0.418457
$333$	−41.4442	−2.27113
$334$	−9.48237	−0.518852
$335$	19.1291	1.04513
$336$	0	0
$337$	3.60599	0.196431	0.0982154	−	0.995165i	$-0.468687\pi$
$337$	3.60599	0.196431	0.0982154	+	0.995165i	$0.468687\pi$
$338$	7.28160	0.396067
$339$	−28.4554	−1.54549
$340$	1.94537	0.105502
$341$	7.59598	0.411345
$342$	4.05993	0.219536
$343$	0	0
$344$	−1.35656	−0.0731406
$345$	−87.4013	−4.70553
$346$	−1.05249	−0.0565821
$347$	−16.5428	−0.888066	−0.444033	−	0.896010i	$-0.646453\pi$
$347$	−16.5428	−0.888066	−0.444033	+	0.896010i	$0.646453\pi$
$348$	13.1108	0.702815
$349$	−2.36067	−0.126364	−0.0631819	−	0.998002i	$-0.520125\pi$
$349$	−2.36067	−0.126364	−0.0631819	+	0.998002i	$0.520125\pi$
$350$	0	0
$351$	25.3748	1.35441
$352$	−3.02538	−0.161253
$353$	3.79697	0.202092	0.101046	−	0.994882i	$-0.467781\pi$
$353$	3.79697	0.202092	0.101046	+	0.994882i	$0.467781\pi$
$354$	9.66730	0.513811
$355$	42.8422	2.27383
$356$	−1.19130	−0.0631388
$357$	0	0
$358$	10.1920	0.538665
$359$	−27.9367	−1.47444	−0.737221	−	0.675652i	$-0.763862\pi$
$359$	−27.9367	−1.47444	−0.737221	+	0.675652i	$0.763862\pi$
$360$	−19.5184	−1.02871
$361$	−18.6040	−0.979157
$362$	13.8789	0.729459
$363$	−5.67853	−0.298045
$364$	0	0
$365$	−12.5824	−0.658594
$366$	−16.5915	−0.867254
$367$	31.1857	1.62788	0.813941	−	0.580948i	$-0.197318\pi$
$367$	31.1857	1.62788	0.813941	+	0.580948i	$0.197318\pi$
$368$	−9.39694	−0.489849
$369$	−13.3572	−0.695349
$370$	19.4348	1.01037
$371$	0	0
$372$	7.71890	0.400206
$373$	−16.2454	−0.841155	−0.420578	−	0.907257i	$-0.638173\pi$
$373$	−16.2454	−0.841155	−0.420578	+	0.907257i	$0.638173\pi$
$374$	−1.94537	−0.100593
$375$	−7.87866	−0.406852
$376$	1.06025	0.0546783
$377$	10.1980	0.525225
$378$	0	0
$379$	29.4790	1.51423	0.757117	−	0.653279i	$-0.226607\pi$
$379$	29.4790	1.51423	0.757117	+	0.653279i	$0.226607\pi$
$380$	−1.90386	−0.0976658
$381$	−41.1822	−2.10983
$382$	−6.72199	−0.343927
$383$	16.7973	0.858304	0.429152	−	0.903232i	$-0.358813\pi$
$383$	16.7973	0.858304	0.429152	+	0.903232i	$0.358813\pi$
$384$	−3.07434	−0.156887
$385$	0	0
$386$	2.32059	0.118115
$387$	8.75188	0.444883
$388$	−16.3992	−0.832543
$389$	−11.5943	−0.587853	−0.293927	−	0.955828i	$-0.594962\pi$
$389$	−11.5943	−0.587853	−0.293927	+	0.955828i	$0.594962\pi$
$390$	−22.2417	−1.12625
$391$	−6.04238	−0.305576
$392$	0	0
$393$	−59.7585	−3.01442
$394$	−8.72306	−0.439461
$395$	−33.9481	−1.70811
$396$	19.5184	0.980836
$397$	−13.6535	−0.685252	−0.342626	−	0.939472i	$-0.611316\pi$
$397$	−13.6535	−0.685252	−0.342626	+	0.939472i	$0.611316\pi$
$398$	−10.6790	−0.535292
$399$	0	0
$400$	4.15293	0.207646
$401$	12.0822	0.603355	0.301677	−	0.953410i	$-0.402453\pi$
$401$	12.0822	0.603355	0.301677	+	0.953410i	$0.402453\pi$
$402$	−19.4386	−0.969512
$403$	6.00400	0.299081
$404$	−14.3697	−0.714921
$405$	40.1402	1.99458
$406$	0	0
$407$	−19.4348	−0.963348
$408$	−1.97685	−0.0978686
$409$	25.1668	1.24442	0.622209	−	0.782851i	$-0.286235\pi$
$409$	25.1668	1.24442	0.622209	+	0.782851i	$0.286235\pi$
$410$	6.26372	0.309343
$411$	24.2446	1.19590
$412$	16.3323	0.804633
$413$	0	0
$414$	60.6248	2.97955
$415$	−23.0675	−1.13234
$416$	−2.39132	−0.117244
$417$	0.901375	0.0441405
$418$	1.90386	0.0931207
$419$	−21.5314	−1.05188	−0.525940	−	0.850522i	$-0.676286\pi$
$419$	−21.5314	−1.05188	−0.525940	+	0.850522i	$0.676286\pi$
$420$	0	0
$421$	−27.9955	−1.36442	−0.682208	−	0.731158i	$-0.738980\pi$
$421$	−27.9955	−1.36442	−0.682208	+	0.731158i	$0.738980\pi$
$422$	14.2225	0.692339
$423$	−6.84026	−0.332585
$424$	−4.68623	−0.227584
$425$	2.67040	0.129533
$426$	−43.5355	−2.10930
$427$	0	0
$428$	16.6838	0.806441
$429$	22.2417	1.07384
$430$	−4.10410	−0.197917
$431$	−17.6794	−0.851587	−0.425794	−	0.904820i	$-0.640005\pi$
$431$	−17.6794	−0.851587	−0.425794	+	0.904820i	$0.640005\pi$
$432$	10.6112	0.510532
$433$	1.18020	0.0567168	0.0283584	−	0.999598i	$-0.490972\pi$
$433$	1.18020	0.0567168	0.0283584	+	0.999598i	$0.490972\pi$
$434$	0	0
$435$	39.6653	1.90181
$436$	1.66514	0.0797458
$437$	5.91344	0.282878
$438$	12.7860	0.610941
$439$	21.3498	1.01897	0.509486	−	0.860479i	$-0.329836\pi$
$439$	21.3498	1.01897	0.509486	+	0.860479i	$0.329836\pi$
$440$	−9.15293	−0.436349
$441$	0	0
$442$	−1.53766	−0.0731388
$443$	8.62280	0.409682	0.204841	−	0.978795i	$-0.434332\pi$
$443$	8.62280	0.409682	0.204841	+	0.978795i	$0.434332\pi$
$444$	−19.7493	−0.937260
$445$	−3.60414	−0.170852
$446$	−9.69578	−0.459109
$447$	−21.8074	−1.03145
$448$	0	0
$449$	16.7479	0.790381	0.395190	−	0.918599i	$-0.370679\pi$
$449$	16.7479	0.790381	0.395190	+	0.918599i	$0.370679\pi$
$450$	−26.7928	−1.26302
$451$	−6.26372	−0.294947
$452$	−9.25578	−0.435355
$453$	36.2679	1.70402
$454$	−6.19599	−0.290792
$455$	0	0
$456$	1.93466	0.0905990
$457$	8.01576	0.374962	0.187481	−	0.982268i	$-0.439968\pi$
$457$	8.01576	0.374962	0.187481	+	0.982268i	$0.439968\pi$
$458$	0.547320	0.0255746
$459$	6.82319	0.318479
$460$	−28.4293	−1.32552
$461$	−18.1143	−0.843668	−0.421834	−	0.906673i	$-0.638613\pi$
$461$	−18.1143	−0.843668	−0.421834	+	0.906673i	$0.638613\pi$
$462$	0	0
$463$	5.32065	0.247272	0.123636	−	0.992328i	$-0.460545\pi$
$463$	5.32065	0.247272	0.123636	+	0.992328i	$0.460545\pi$
$464$	4.26461	0.197979
$465$	23.3526	1.08295
$466$	−6.77776	−0.313974
$467$	33.5558	1.55278	0.776388	−	0.630256i	$-0.217050\pi$
$467$	33.5558	1.55278	0.776388	+	0.630256i	$0.217050\pi$
$468$	15.4277	0.713145
$469$	0	0
$470$	3.20767	0.147959
$471$	40.4493	1.86380
$472$	3.14452	0.144738
$473$	4.10410	0.188707
$474$	34.4975	1.58452
$475$	−2.61342	−0.119912
$476$	0	0
$477$	30.2335	1.38429
$478$	6.80155	0.311096
$479$	16.7425	0.764983	0.382492	−	0.923959i	$-0.375066\pi$
$479$	16.7425	0.764983	0.382492	+	0.923959i	$0.375066\pi$
$480$	−9.30104	−0.424532
$481$	−15.3616	−0.700430
$482$	26.0644	1.18720
$483$	0	0
$484$	−1.84707	−0.0839579
$485$	−49.6138	−2.25285
$486$	−8.95609	−0.406256
$487$	26.6484	1.20756	0.603778	−	0.797152i	$-0.293661\pi$
$487$	26.6484	1.20756	0.603778	+	0.797152i	$0.293661\pi$
$488$	−5.39679	−0.244301
$489$	41.2290	1.86444
$490$	0	0
$491$	7.56655	0.341474	0.170737	−	0.985317i	$-0.445385\pi$
$491$	7.56655	0.341474	0.170737	+	0.985317i	$0.445385\pi$
$492$	−6.36508	−0.286960
$493$	2.74221	0.123503
$494$	1.50484	0.0677061
$495$	59.0505	2.65412
$496$	2.51075	0.112736
$497$	0	0
$498$	23.4407	1.05040
$499$	−10.4872	−0.469473	−0.234736	−	0.972059i	$-0.575423\pi$
$499$	−10.4872	−0.469473	−0.234736	+	0.972059i	$0.575423\pi$
$500$	−2.56272	−0.114608
$501$	29.1520	1.30242
$502$	−26.1920	−1.16900
$503$	0.490508	0.0218707	0.0109353	−	0.999940i	$-0.496519\pi$
$503$	0.490508	0.0218707	0.0109353	+	0.999940i	$0.496519\pi$
$504$	0	0
$505$	−43.4739	−1.93456
$506$	28.4293	1.26384
$507$	−22.3861	−0.994202
$508$	−13.3955	−0.594328
$509$	15.9439	0.706703	0.353351	−	0.935491i	$-0.385042\pi$
$509$	15.9439	0.706703	0.353351	+	0.935491i	$0.385042\pi$
$510$	−5.98072	−0.264831
$511$	0	0
$512$	−1.00000	−0.0441942
$513$	−6.67759	−0.294823
$514$	13.4073	0.591372
$515$	49.4113	2.17732
$516$	4.17051	0.183596
$517$	−3.20767	−0.141073
$518$	0	0
$519$	3.23570	0.142032
$520$	−7.23464	−0.317260
$521$	−31.8495	−1.39535	−0.697677	−	0.716413i	$-0.745783\pi$
$521$	−31.8495	−1.39535	−0.697677	+	0.716413i	$0.745783\pi$
$522$	−27.5133	−1.20423
$523$	42.4318	1.85541	0.927706	−	0.373311i	$-0.121778\pi$
$523$	42.4318	1.85541	0.927706	+	0.373311i	$0.121778\pi$
$524$	−19.4378	−0.849146
$525$	0	0
$526$	10.5626	0.460553
$527$	1.61445	0.0703267
$528$	9.30104	0.404776
$529$	65.3024	2.83923
$530$	−14.1776	−0.615837
$531$	−20.2870	−0.880381
$532$	0	0
$533$	−4.95096	−0.214450
$534$	3.66246	0.158490
$535$	50.4748	2.18221
$536$	−6.32287	−0.273107
$537$	−31.3337	−1.35215
$538$	−11.9198	−0.513898
$539$	0	0
$540$	32.1030	1.38149
$541$	6.54151	0.281241	0.140621	−	0.990064i	$-0.455090\pi$
$541$	6.54151	0.281241	0.140621	+	0.990064i	$0.455090\pi$
$542$	24.8700	1.06826
$543$	−42.6684	−1.83108
$544$	−0.643016	−0.0275691
$545$	5.03768	0.215791
$546$	0	0
$547$	18.2734	0.781314	0.390657	−	0.920536i	$-0.372248\pi$
$547$	18.2734	0.781314	0.390657	+	0.920536i	$0.372248\pi$
$548$	7.88612	0.336879
$549$	34.8176	1.48598
$550$	−12.5642	−0.535739
$551$	−2.68370	−0.114329
$552$	28.8893	1.22961
$553$	0	0
$554$	−27.7796	−1.18024
$555$	−59.7492	−2.53621
$556$	0.293193	0.0124342
$557$	−36.4469	−1.54431	−0.772153	−	0.635436i	$-0.780820\pi$
$557$	−36.4469	−1.54431	−0.772153	+	0.635436i	$0.780820\pi$
$558$	−16.1982	−0.685726
$559$	3.24395	0.137205
$560$	0	0
$561$	5.98072	0.252506
$562$	31.1896	1.31565
$563$	−6.15519	−0.259410	−0.129705	−	0.991553i	$-0.541403\pi$
$563$	−6.15519	−0.259410	−0.129705	+	0.991553i	$0.541403\pi$
$564$	−3.25957	−0.137253
$565$	−28.0023	−1.17806
$566$	−18.9829	−0.797909
$567$	0	0
$568$	−14.1609	−0.594179
$569$	8.41931	0.352956	0.176478	−	0.984305i	$-0.443530\pi$
$569$	8.41931	0.352956	0.176478	+	0.984305i	$0.443530\pi$
$570$	5.85310	0.245159
$571$	−35.0354	−1.46619	−0.733094	−	0.680128i	$-0.761924\pi$
$571$	−35.0354	−1.46619	−0.733094	+	0.680128i	$0.761924\pi$
$572$	7.23464	0.302496
$573$	20.6657	0.863320
$574$	0	0
$575$	−39.0248	−1.62745
$576$	6.45155	0.268814
$577$	34.8056	1.44898	0.724488	−	0.689287i	$-0.242076\pi$
$577$	34.8056	1.44898	0.724488	+	0.689287i	$0.242076\pi$
$578$	16.5865	0.689909
$579$	−7.13426	−0.296490
$580$	12.9021	0.535729
$581$	0	0
$582$	50.4166	2.08984
$583$	14.1776	0.587178
$584$	4.15896	0.172099
$585$	46.6746	1.92976
$586$	19.6220	0.810575
$587$	−19.8051	−0.817443	−0.408722	−	0.912659i	$-0.634025\pi$
$587$	−19.8051	−0.817443	−0.408722	+	0.912659i	$0.634025\pi$
$588$	0	0
$589$	−1.58000	−0.0651029
$590$	9.51336	0.391659
$591$	26.8176	1.10313
$592$	−6.42392	−0.264022
$593$	−10.5375	−0.432724	−0.216362	−	0.976313i	$-0.569419\pi$
$593$	−10.5375	−0.432724	−0.216362	+	0.976313i	$0.569419\pi$
$594$	−32.1030	−1.31720
$595$	0	0
$596$	−7.09335	−0.290555
$597$	32.8310	1.34368
$598$	22.4711	0.918910
$599$	−3.72145	−0.152054	−0.0760271	−	0.997106i	$-0.524224\pi$
$599$	−3.72145	−0.152054	−0.0760271	+	0.997106i	$0.524224\pi$
$600$	−12.7675	−0.521231
$601$	−0.194282	−0.00792491	−0.00396246	−	0.999992i	$-0.501261\pi$
$601$	−0.194282	−0.00792491	−0.00396246	+	0.999992i	$0.501261\pi$
$602$	0	0
$603$	40.7923	1.66119
$604$	11.7970	0.480013
$605$	−5.58810	−0.227189
$606$	44.1774	1.79458
$607$	20.2928	0.823658	0.411829	−	0.911261i	$-0.364890\pi$
$607$	20.2928	0.823658	0.411829	+	0.911261i	$0.364890\pi$
$608$	0.629295	0.0255213
$609$	0	0
$610$	−16.3273	−0.661075
$611$	−2.53540	−0.102571
$612$	4.14845	0.167691
$613$	14.6071	0.589977	0.294988	−	0.955501i	$-0.404684\pi$
$613$	14.6071	0.589977	0.294988	+	0.955501i	$0.404684\pi$
$614$	21.0550	0.849710
$615$	−19.2568	−0.776508
$616$	0	0
$617$	11.6953	0.470837	0.235418	−	0.971894i	$-0.424354\pi$
$617$	11.6953	0.470837	0.235418	+	0.971894i	$0.424354\pi$
$618$	−50.2109	−2.01978
$619$	37.4631	1.50577	0.752885	−	0.658152i	$-0.228662\pi$
$619$	37.4631	1.50577	0.752885	+	0.658152i	$0.228662\pi$
$620$	7.59598	0.305062
$621$	−99.7129	−4.00134
$622$	−11.7755	−0.472155
$623$	0	0
$624$	7.35171	0.294304
$625$	−28.5178	−1.14071
$626$	21.4522	0.857402
$627$	−5.85310	−0.233750
$628$	13.1571	0.525024
$629$	−4.13069	−0.164701
$630$	0	0
$631$	−13.1060	−0.521740	−0.260870	−	0.965374i	$-0.584009\pi$
$631$	−13.1060	−0.521740	−0.260870	+	0.965374i	$0.584009\pi$
$632$	11.2211	0.446352
$633$	−43.7246	−1.73790
$634$	−29.6833	−1.17888
$635$	−40.5264	−1.60824
$636$	14.4071	0.571277
$637$	0	0
$638$	−12.9021	−0.510798
$639$	91.3599	3.61414
$640$	−3.02538	−0.119589
$641$	−11.5281	−0.455331	−0.227666	−	0.973739i	$-0.573109\pi$
$641$	−11.5281	−0.455331	−0.227666	+	0.973739i	$0.573109\pi$
$642$	−51.2915	−2.02432
$643$	22.9575	0.905357	0.452678	−	0.891674i	$-0.350469\pi$
$643$	22.9575	0.905357	0.452678	+	0.891674i	$0.350469\pi$
$644$	0	0
$645$	12.6174	0.496809
$646$	0.404647	0.0159206
$647$	−2.60155	−0.102277	−0.0511387	−	0.998692i	$-0.516285\pi$
$647$	−2.60155	−0.102277	−0.0511387	+	0.998692i	$0.516285\pi$
$648$	−13.2678	−0.521209
$649$	−9.51336	−0.373432
$650$	−9.93096	−0.389524
$651$	0	0
$652$	13.4107	0.525204
$653$	35.4045	1.38548	0.692742	−	0.721186i	$-0.256403\pi$
$653$	35.4045	1.38548	0.692742	+	0.721186i	$0.256403\pi$
$654$	−5.11920	−0.200177
$655$	−58.8069	−2.29777
$656$	−2.07039	−0.0808351
$657$	−26.8317	−1.04680
$658$	0	0
$659$	−27.3486	−1.06535	−0.532675	−	0.846320i	$-0.678813\pi$
$659$	−27.3486	−1.06535	−0.532675	+	0.846320i	$0.678813\pi$
$660$	28.1392	1.09532
$661$	−3.45634	−0.134436	−0.0672181	−	0.997738i	$-0.521412\pi$
$661$	−3.45634	−0.134436	−0.0672181	+	0.997738i	$0.521412\pi$
$662$	0.820937	0.0319066
$663$	4.72727	0.183592
$664$	7.62465	0.295894
$665$	0	0
$666$	41.4442	1.60593
$667$	−40.0743	−1.55168
$668$	9.48237	0.366884
$669$	29.8081	1.15245
$670$	−19.1291	−0.739022
$671$	16.3273	0.630310
$672$	0	0
$673$	−21.4177	−0.825592	−0.412796	−	0.910823i	$-0.635448\pi$
$673$	−21.4177	−0.825592	−0.412796	+	0.910823i	$0.635448\pi$
$674$	−3.60599	−0.138898
$675$	44.0676	1.69616
$676$	−7.28160	−0.280062
$677$	18.6228	0.715734	0.357867	−	0.933773i	$-0.383504\pi$
$677$	18.6228	0.715734	0.357867	+	0.933773i	$0.383504\pi$
$678$	28.4554	1.09282
$679$	0	0
$680$	−1.94537	−0.0746015
$681$	19.0486	0.729942
$682$	−7.59598	−0.290865
$683$	−6.22994	−0.238382	−0.119191	−	0.992871i	$-0.538030\pi$
$683$	−6.22994	−0.238382	−0.119191	+	0.992871i	$0.538030\pi$
$684$	−4.05993	−0.155235
$685$	23.8585	0.911587
$686$	0	0
$687$	−1.68264	−0.0641969
$688$	1.35656	0.0517182
$689$	11.2063	0.426925
$690$	87.4013	3.32731
$691$	22.4779	0.855100	0.427550	−	0.903992i	$-0.359377\pi$
$691$	22.4779	0.855100	0.427550	+	0.903992i	$0.359377\pi$
$692$	1.05249	0.0400096
$693$	0	0
$694$	16.5428	0.627958
$695$	0.887021	0.0336466
$696$	−13.1108	−0.496965
$697$	−1.33129	−0.0504264
$698$	2.36067	0.0893526
$699$	20.8371	0.788132
$700$	0	0
$701$	−24.5946	−0.928924	−0.464462	−	0.885593i	$-0.653752\pi$
$701$	−24.5946	−0.928924	−0.464462	+	0.885593i	$0.653752\pi$
$702$	−25.3748	−0.957710
$703$	4.04254	0.152467
$704$	3.02538	0.114023
$705$	−9.86144	−0.371403
$706$	−3.79697	−0.142901
$707$	0	0
$708$	−9.66730	−0.363319
$709$	4.20095	0.157770	0.0788850	−	0.996884i	$-0.474864\pi$
$709$	4.20095	0.157770	0.0788850	+	0.996884i	$0.474864\pi$
$710$	−42.8422	−1.60784
$711$	−72.3935	−2.71497
$712$	1.19130	0.0446459
$713$	−23.5934	−0.883579
$714$	0	0
$715$	21.8875	0.818548
$716$	−10.1920	−0.380894
$717$	−20.9103	−0.780908
$718$	27.9367	1.04259
$719$	−46.2368	−1.72434	−0.862172	−	0.506616i	$-0.830896\pi$
$719$	−46.2368	−1.72434	−0.862172	+	0.506616i	$0.830896\pi$
$720$	19.5184	0.727407
$721$	0	0
$722$	18.6040	0.692369
$723$	−80.1307	−2.98009
$724$	−13.8789	−0.515806
$725$	17.7106	0.657755
$726$	5.67853	0.210750
$727$	−0.541534	−0.0200844	−0.0100422	−	0.999950i	$-0.503197\pi$
$727$	−0.541534	−0.0200844	−0.0100422	+	0.999950i	$0.503197\pi$
$728$	0	0
$729$	−12.2694	−0.454423
$730$	12.5824	0.465697
$731$	0.872287	0.0322627
$732$	16.5915	0.613241
$733$	−16.8334	−0.621756	−0.310878	−	0.950450i	$-0.600623\pi$
$733$	−16.8334	−0.621756	−0.310878	+	0.950450i	$0.600623\pi$
$734$	−31.1857	−1.15109
$735$	0	0
$736$	9.39694	0.346376
$737$	19.1291	0.704630
$738$	13.3572	0.491686
$739$	−13.3478	−0.491007	−0.245504	−	0.969396i	$-0.578953\pi$
$739$	−13.3478	−0.491007	−0.245504	+	0.969396i	$0.578953\pi$
$740$	−19.4348	−0.714438
$741$	−4.62640	−0.169955
$742$	0	0
$743$	−40.5560	−1.48786	−0.743928	−	0.668260i	$-0.767039\pi$
$743$	−40.5560	−1.48786	−0.743928	+	0.668260i	$0.767039\pi$
$744$	−7.71890	−0.282988
$745$	−21.4601	−0.786237
$746$	16.2454	0.594787
$747$	−49.1908	−1.79980
$748$	1.94537	0.0711297
$749$	0	0
$750$	7.87866	0.287688
$751$	−22.1713	−0.809044	−0.404522	−	0.914528i	$-0.632562\pi$
$751$	−22.1713	−0.809044	−0.404522	+	0.914528i	$0.632562\pi$
$752$	−1.06025	−0.0386634
$753$	80.5229	2.93442
$754$	−10.1980	−0.371390
$755$	35.6904	1.29891
$756$	0	0
$757$	18.3097	0.665479	0.332739	−	0.943019i	$-0.392027\pi$
$757$	18.3097	0.665479	0.332739	+	0.943019i	$0.392027\pi$
$758$	−29.4790	−1.07073
$759$	−87.4013	−3.17246
$760$	1.90386	0.0690601
$761$	−26.4821	−0.959975	−0.479988	−	0.877275i	$-0.659359\pi$
$761$	−26.4821	−0.959975	−0.479988	+	0.877275i	$0.659359\pi$
$762$	41.1822	1.49187
$763$	0	0
$764$	6.72199	0.243193
$765$	12.5506	0.453769
$766$	−16.7973	−0.606912
$767$	−7.51953	−0.271515
$768$	3.07434	0.110936
$769$	50.0568	1.80509	0.902547	−	0.430591i	$-0.141695\pi$
$769$	50.0568	1.80509	0.902547	+	0.430591i	$0.141695\pi$
$770$	0	0
$771$	−41.2187	−1.48445
$772$	−2.32059	−0.0835197
$773$	9.47987	0.340967	0.170484	−	0.985361i	$-0.445467\pi$
$773$	9.47987	0.340967	0.170484	+	0.985361i	$0.445467\pi$
$774$	−8.75188	−0.314580
$775$	10.4270	0.374548
$776$	16.3992	0.588697
$777$	0	0
$778$	11.5943	0.415675
$779$	1.30289	0.0466807
$780$	22.2417	0.796382
$781$	42.8422	1.53301
$782$	6.04238	0.216075
$783$	45.2527	1.61720
$784$	0	0
$785$	39.8052	1.42071
$786$	59.7585	2.13151
$787$	43.6250	1.55506	0.777531	−	0.628845i	$-0.216472\pi$
$787$	43.6250	1.55506	0.777531	+	0.628845i	$0.216472\pi$
$788$	8.72306	0.310746
$789$	−32.4731	−1.15607
$790$	33.9481	1.20782
$791$	0	0
$792$	−19.5184	−0.693556
$793$	12.9054	0.458285
$794$	13.6535	0.484546
$795$	43.5868	1.54587
$796$	10.6790	0.378509
$797$	6.57856	0.233024	0.116512	−	0.993189i	$-0.462829\pi$
$797$	6.57856	0.233024	0.116512	+	0.993189i	$0.462829\pi$
$798$	0	0
$799$	−0.681759	−0.0241189
$800$	−4.15293	−0.146828
$801$	−7.68573	−0.271562
$802$	−12.0822	−0.426636
$803$	−12.5824	−0.444024
$804$	19.4386	0.685548
$805$	0	0
$806$	−6.00400	−0.211482
$807$	36.6454	1.28998
$808$	14.3697	0.505526
$809$	35.8429	1.26017	0.630084	−	0.776527i	$-0.283020\pi$
$809$	35.8429	1.26017	0.630084	+	0.776527i	$0.283020\pi$
$810$	−40.1402	−1.41038
$811$	−26.2868	−0.923053	−0.461526	−	0.887126i	$-0.652698\pi$
$811$	−26.2868	−0.923053	−0.461526	+	0.887126i	$0.652698\pi$
$812$	0	0
$813$	−76.4589	−2.68153
$814$	19.4348	0.681190
$815$	40.5725	1.42119
$816$	1.97685	0.0692035
$817$	−0.853673	−0.0298663
$818$	−25.1668	−0.879936
$819$	0	0
$820$	−6.26372	−0.218738
$821$	35.0033	1.22162	0.610812	−	0.791775i	$-0.290843\pi$
$821$	35.0033	1.22162	0.610812	+	0.791775i	$0.290843\pi$
$822$	−24.2446	−0.845628
$823$	27.0562	0.943120	0.471560	−	0.881834i	$-0.343691\pi$
$823$	27.0562	0.943120	0.471560	+	0.881834i	$0.343691\pi$
$824$	−16.3323	−0.568961
$825$	38.6265	1.34480
$826$	0	0
$827$	−31.4179	−1.09251	−0.546254	−	0.837620i	$-0.683947\pi$
$827$	−31.4179	−1.09251	−0.546254	+	0.837620i	$0.683947\pi$
$828$	−60.6248	−2.10686
$829$	19.1143	0.663867	0.331934	−	0.943303i	$-0.392299\pi$
$829$	19.1143	0.663867	0.331934	+	0.943303i	$0.392299\pi$
$830$	23.0675	0.800683
$831$	85.4039	2.96263
$832$	2.39132	0.0829040
$833$	0	0
$834$	−0.901375	−0.0312121
$835$	28.6878	0.992782
$836$	−1.90386	−0.0658463
$837$	26.6421	0.920887
$838$	21.5314	0.743791
$839$	−10.9451	−0.377868	−0.188934	−	0.981990i	$-0.560503\pi$
$839$	−10.9451	−0.377868	−0.188934	+	0.981990i	$0.560503\pi$
$840$	0	0
$841$	−10.8131	−0.372866
$842$	27.9955	0.964788
$843$	−95.8872	−3.30253
$844$	−14.2225	−0.489557
$845$	−22.0296	−0.757842
$846$	6.84026	0.235173
$847$	0	0
$848$	4.68623	0.160926
$849$	58.3597	2.00290
$850$	−2.67040	−0.0915939
$851$	60.3652	2.06929
$852$	43.5355	1.49150
$853$	49.0131	1.67818	0.839088	−	0.543995i	$-0.183089\pi$
$853$	49.0131	1.67818	0.839088	+	0.543995i	$0.183089\pi$
$854$	0	0
$855$	−12.2828	−0.420064
$856$	−16.6838	−0.570240
$857$	11.0683	0.378084	0.189042	−	0.981969i	$-0.439462\pi$
$857$	11.0683	0.378084	0.189042	+	0.981969i	$0.439462\pi$
$858$	−22.2417	−0.759320
$859$	14.7784	0.504233	0.252116	−	0.967697i	$-0.418873\pi$
$859$	14.7784	0.504233	0.252116	+	0.967697i	$0.418873\pi$
$860$	4.10410	0.139948
$861$	0	0
$862$	17.6794	0.602163
$863$	−7.06992	−0.240663	−0.120331	−	0.992734i	$-0.538396\pi$
$863$	−7.06992	−0.240663	−0.120331	+	0.992734i	$0.538396\pi$
$864$	−10.6112	−0.361001
$865$	3.18418	0.108265
$866$	−1.18020	−0.0401049
$867$	−50.9926	−1.73180
$868$	0	0
$869$	−33.9481	−1.15161
$870$	−39.6653	−1.34478
$871$	15.1200	0.512322
$872$	−1.66514	−0.0563888
$873$	−105.800	−3.58079
$874$	−5.91344	−0.200025
$875$	0	0
$876$	−12.7860	−0.432000
$877$	48.1941	1.62740	0.813699	−	0.581286i	$-0.197450\pi$
$877$	48.1941	1.62740	0.813699	+	0.581286i	$0.197450\pi$
$878$	−21.3498	−0.720522
$879$	−60.3245	−2.03469
$880$	9.15293	0.308545
$881$	−5.91801	−0.199383	−0.0996915	−	0.995018i	$-0.531786\pi$
$881$	−5.91801	−0.199383	−0.0996915	+	0.995018i	$0.531786\pi$
$882$	0	0
$883$	−29.4616	−0.991461	−0.495730	−	0.868477i	$-0.665100\pi$
$883$	−29.4616	−0.991461	−0.495730	+	0.868477i	$0.665100\pi$
$884$	1.53766	0.0517170
$885$	−29.2473	−0.983136
$886$	−8.62280	−0.289689
$887$	−23.2506	−0.780679	−0.390340	−	0.920671i	$-0.627642\pi$
$887$	−23.2506	−0.780679	−0.390340	+	0.920671i	$0.627642\pi$
$888$	19.7493	0.662743
$889$	0	0
$890$	3.60414	0.120811
$891$	40.1402	1.34475
$892$	9.69578	0.324639
$893$	0.667211	0.0223274
$894$	21.8074	0.729347
$895$	−30.8347	−1.03069
$896$	0	0
$897$	−69.0836	−2.30663
$898$	−16.7479	−0.558884
$899$	10.7074	0.357111
$900$	26.7928	0.893093
$901$	3.01332	0.100388
$902$	6.26372	0.208559
$903$	0	0
$904$	9.25578	0.307843
$905$	−41.9890	−1.39576
$906$	−36.2679	−1.20492
$907$	16.8991	0.561126	0.280563	−	0.959836i	$-0.409479\pi$
$907$	16.8991	0.561126	0.280563	+	0.959836i	$0.409479\pi$
$908$	6.19599	0.205621
$909$	−92.7070	−3.07490
$910$	0	0
$911$	48.2207	1.59762	0.798812	−	0.601581i	$-0.205462\pi$
$911$	48.2207	1.59762	0.798812	+	0.601581i	$0.205462\pi$
$912$	−1.93466	−0.0640632
$913$	−23.0675	−0.763421
$914$	−8.01576	−0.265138
$915$	50.1958	1.65942
$916$	−0.547320	−0.0180840
$917$	0	0
$918$	−6.82319	−0.225199
$919$	−10.5044	−0.346507	−0.173253	−	0.984877i	$-0.555428\pi$
$919$	−10.5044	−0.346507	−0.173253	+	0.984877i	$0.555428\pi$
$920$	28.4293	0.937286
$921$	−64.7301	−2.13293
$922$	18.1143	0.596563
$923$	33.8633	1.11462
$924$	0	0
$925$	−26.6781	−0.877170
$926$	−5.32065	−0.174848
$927$	105.368	3.46075
$928$	−4.26461	−0.139993
$929$	−35.1667	−1.15378	−0.576891	−	0.816821i	$-0.695734\pi$
$929$	−35.1667	−1.15378	−0.576891	+	0.816821i	$0.695734\pi$
$930$	−23.3526	−0.765762
$931$	0	0
$932$	6.77776	0.222013
$933$	36.2019	1.18520
$934$	−33.5558	−1.09798
$935$	5.88548	0.192476
$936$	−15.4277	−0.504270
$937$	−25.7519	−0.841276	−0.420638	−	0.907228i	$-0.638194\pi$
$937$	−25.7519	−0.841276	−0.420638	+	0.907228i	$0.638194\pi$
$938$	0	0
$939$	−65.9513	−2.15224
$940$	−3.20767	−0.104622
$941$	1.03902	0.0338711	0.0169355	−	0.999857i	$-0.494609\pi$
$941$	1.03902	0.0338711	0.0169355	+	0.999857i	$0.494609\pi$
$942$	−40.4493	−1.31791
$943$	19.4553	0.633552
$944$	−3.14452	−0.102345
$945$	0	0
$946$	−4.10410	−0.133436
$947$	−34.2003	−1.11136	−0.555680	−	0.831396i	$-0.687542\pi$
$947$	−34.2003	−1.11136	−0.555680	+	0.831396i	$0.687542\pi$
$948$	−34.4975	−1.12043
$949$	−9.94539	−0.322841
$950$	2.61342	0.0847904
$951$	91.2566	2.95920
$952$	0	0
$953$	−21.6131	−0.700116	−0.350058	−	0.936728i	$-0.613838\pi$
$953$	−21.6131	−0.700116	−0.350058	+	0.936728i	$0.613838\pi$
$954$	−30.2335	−0.978844
$955$	20.3366	0.658076
$956$	−6.80155	−0.219978
$957$	39.6653	1.28220
$958$	−16.7425	−0.540925
$959$	0	0
$960$	9.30104	0.300190
$961$	−24.6961	−0.796649
$962$	15.3616	0.495279
$963$	107.636	3.46853
$964$	−26.0644	−0.839477
$965$	−7.02065	−0.226003
$966$	0	0
$967$	−31.2390	−1.00458	−0.502289	−	0.864700i	$-0.667509\pi$
$967$	−31.2390	−1.00458	−0.502289	+	0.864700i	$0.667509\pi$
$968$	1.84707	0.0593672
$969$	−1.24402	−0.0399637
$970$	49.6138	1.59300
$971$	−8.49816	−0.272719	−0.136359	−	0.990659i	$-0.543540\pi$
$971$	−8.49816	−0.272719	−0.136359	+	0.990659i	$0.543540\pi$
$972$	8.95609	0.287267
$973$	0	0
$974$	−26.6484	−0.853871
$975$	30.5311	0.977779
$976$	5.39679	0.172747
$977$	2.17623	0.0696238	0.0348119	−	0.999394i	$-0.488917\pi$
$977$	2.17623	0.0696238	0.0348119	+	0.999394i	$0.488917\pi$
$978$	−41.2290	−1.31836
$979$	−3.60414	−0.115189
$980$	0	0
$981$	10.7427	0.342989
$982$	−7.56655	−0.241458
$983$	27.4934	0.876904	0.438452	−	0.898755i	$-0.355527\pi$
$983$	27.4934	0.876904	0.438452	+	0.898755i	$0.355527\pi$
$984$	6.36508	0.202911
$985$	26.3906	0.840873
$986$	−2.74221	−0.0873298
$987$	0	0
$988$	−1.50484	−0.0478755
$989$	−12.7475	−0.405346
$990$	−59.0505	−1.87675
$991$	−0.631072	−0.0200467	−0.0100233	−	0.999950i	$-0.503191\pi$
$991$	−0.631072	−0.0200467	−0.0100233	+	0.999950i	$0.503191\pi$
$992$	−2.51075	−0.0797164
$993$	−2.52384	−0.0800916
$994$	0	0
$995$	32.3082	1.02424
$996$	−23.4407	−0.742748
$997$	−20.4945	−0.649067	−0.324534	−	0.945874i	$-0.605207\pi$
$997$	−20.4945	−0.649067	−0.324534	+	0.945874i	$0.605207\pi$
$998$	10.4872	0.331967
$999$	−68.1657	−2.15667

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4802.2.a.c.1.9		9
7.6	odd	2		4802.2.a.d.1.1		9
49.3	odd	42		686.2.g.h.177.3		36
49.5	odd	42		686.2.g.h.67.1		36
49.6	odd	14		98.2.e.b.85.1	yes	18
49.8	even	7		686.2.e.b.99.3		18
49.10	odd	42		686.2.g.h.471.1		36
49.16	even	21		686.2.g.g.655.1		36
49.33	odd	42		686.2.g.h.655.3		36
49.39	even	21		686.2.g.g.471.3		36
49.41	odd	14		98.2.e.b.15.1	✓	18
49.43	even	7		686.2.e.b.589.3		18
49.44	even	21		686.2.g.g.67.3		36
49.46	even	21		686.2.g.g.177.1		36
147.41	even	14		882.2.u.g.505.3		18
147.104	even	14		882.2.u.g.379.3		18
196.55	even	14		784.2.u.d.673.3		18
196.139	even	14		784.2.u.d.113.3		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
98.2.e.b.15.1	✓	18	49.41	odd	14
98.2.e.b.85.1	yes	18	49.6	odd	14
686.2.e.b.99.3		18	49.8	even	7
686.2.e.b.589.3		18	49.43	even	7
686.2.g.g.67.3		36	49.44	even	21
686.2.g.g.177.1		36	49.46	even	21
686.2.g.g.471.3		36	49.39	even	21
686.2.g.g.655.1		36	49.16	even	21
686.2.g.h.67.1		36	49.5	odd	42
686.2.g.h.177.3		36	49.3	odd	42
686.2.g.h.471.1		36	49.10	odd	42
686.2.g.h.655.3		36	49.33	odd	42
784.2.u.d.113.3		18	196.139	even	14
784.2.u.d.673.3		18	196.55	even	14
882.2.u.g.379.3		18	147.104	even	14
882.2.u.g.505.3		18	147.41	even	14
4802.2.a.c.1.9		9	1.1	even	1	trivial
4802.2.a.d.1.1		9	7.6	odd	2

Overview	Random
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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:	\( N \)	\(=\)	\( 4802 = 2 \cdot 7^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4802.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +3.07434 q^{3} +1.00000 q^{4} +3.02538 q^{5} -3.07434 q^{6} -1.00000 q^{8} +6.45155 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +3.07434 q^{3} +1.00000 q^{4} +3.02538 q^{5} -3.07434 q^{6} -1.00000 q^{8} +6.45155 q^{9} -3.02538 q^{10} +3.02538 q^{11} +3.07434 q^{12} +2.39132 q^{13} +9.30104 q^{15} +1.00000 q^{16} +0.643016 q^{17} -6.45155 q^{18} -0.629295 q^{19} +3.02538 q^{20} -3.02538 q^{22} -9.39694 q^{23} -3.07434 q^{24} +4.15293 q^{25} -2.39132 q^{26} +10.6112 q^{27} +4.26461 q^{29} -9.30104 q^{30} +2.51075 q^{31} -1.00000 q^{32} +9.30104 q^{33} -0.643016 q^{34} +6.45155 q^{36} -6.42392 q^{37} +0.629295 q^{38} +7.35171 q^{39} -3.02538 q^{40} -2.07039 q^{41} +1.35656 q^{43} +3.02538 q^{44} +19.5184 q^{45} +9.39694 q^{46} -1.06025 q^{47} +3.07434 q^{48} -4.15293 q^{50} +1.97685 q^{51} +2.39132 q^{52} +4.68623 q^{53} -10.6112 q^{54} +9.15293 q^{55} -1.93466 q^{57} -4.26461 q^{58} -3.14452 q^{59} +9.30104 q^{60} +5.39679 q^{61} -2.51075 q^{62} +1.00000 q^{64} +7.23464 q^{65} -9.30104 q^{66} +6.32287 q^{67} +0.643016 q^{68} -28.8893 q^{69} +14.1609 q^{71} -6.45155 q^{72} -4.15896 q^{73} +6.42392 q^{74} +12.7675 q^{75} -0.629295 q^{76} -7.35171 q^{78} -11.2211 q^{79} +3.02538 q^{80} +13.2678 q^{81} +2.07039 q^{82} -7.62465 q^{83} +1.94537 q^{85} -1.35656 q^{86} +13.1108 q^{87} -3.02538 q^{88} -1.19130 q^{89} -19.5184 q^{90} -9.39694 q^{92} +7.71890 q^{93} +1.06025 q^{94} -1.90386 q^{95} -3.07434 q^{96} -16.3992 q^{97} +19.5184 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q - 9 q^{2} - q^{3} + 9 q^{4} + q^{6} - 9 q^{8} + 16 q^{9}+O(q^{10}) \) 9 * q - 9 * q^2 - q^3 + 9 * q^4 + q^6 - 9 * q^8 + 16 * q^9	\( 9 q - 9 q^{2} - q^{3} + 9 q^{4} + q^{6} - 9 q^{8} + 16 q^{9} - q^{12} + 5 q^{13} + 9 q^{16} + 17 q^{17} - 16 q^{18} + 22 q^{19} - 7 q^{23} + q^{24} + 25 q^{25} - 5 q^{26} + 23 q^{27} + 2 q^{29} + 12 q^{31} - 9 q^{32} - 17 q^{34} + 16 q^{36} - 3 q^{37} - 22 q^{38} - 5 q^{39} - 25 q^{41} - 5 q^{43} + 7 q^{45} + 7 q^{46} + 8 q^{47} - q^{48} - 25 q^{50} - 24 q^{51} + 5 q^{52} - 2 q^{53} - 23 q^{54} + 70 q^{55} - 43 q^{57} - 2 q^{58} + 25 q^{59} + 4 q^{61} - 12 q^{62} + 9 q^{64} + 21 q^{65} - 43 q^{67} + 17 q^{68} - 7 q^{69} + 14 q^{71} - 16 q^{72} + 29 q^{73} + 3 q^{74} - 2 q^{75} + 22 q^{76} + 5 q^{78} - 33 q^{79} - 15 q^{81} + 25 q^{82} + 18 q^{83} + 7 q^{85} + 5 q^{86} + 6 q^{87} - 24 q^{89} - 7 q^{90} - 7 q^{92} + 2 q^{93} - 8 q^{94} - 7 q^{95} + q^{96} + 16 q^{97} + 7 q^{99}+O(q^{100}) \) 9 * q - 9 * q^2 - q^3 + 9 * q^4 + q^6 - 9 * q^8 + 16 * q^9 - q^12 + 5 * q^13 + 9 * q^16 + 17 * q^17 - 16 * q^18 + 22 * q^19 - 7 * q^23 + q^24 + 25 * q^25 - 5 * q^26 + 23 * q^27 + 2 * q^29 + 12 * q^31 - 9 * q^32 - 17 * q^34 + 16 * q^36 - 3 * q^37 - 22 * q^38 - 5 * q^39 - 25 * q^41 - 5 * q^43 + 7 * q^45 + 7 * q^46 + 8 * q^47 - q^48 - 25 * q^50 - 24 * q^51 + 5 * q^52 - 2 * q^53 - 23 * q^54 + 70 * q^55 - 43 * q^57 - 2 * q^58 + 25 * q^59 + 4 * q^61 - 12 * q^62 + 9 * q^64 + 21 * q^65 - 43 * q^67 + 17 * q^68 - 7 * q^69 + 14 * q^71 - 16 * q^72 + 29 * q^73 + 3 * q^74 - 2 * q^75 + 22 * q^76 + 5 * q^78 - 33 * q^79 - 15 * q^81 + 25 * q^82 + 18 * q^83 + 7 * q^85 + 5 * q^86 + 6 * q^87 - 24 * q^89 - 7 * q^90 - 7 * q^92 + 2 * q^93 - 8 * q^94 - 7 * q^95 + q^96 + 16 * q^97 + 7 * q^99

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