LMFDB - Embedded newform 4025.2.a.l.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4025,2,Mod(1,4025)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4025, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4025.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4025 = 5^{2} \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4025.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:	$32.1397868136$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	4.4.2777.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 4x^{2} + x + 2 $ x^4 - x^3 - 4*x^2 + x + 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 805)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$2.36234$ of defining polynomial
Character	$\chi$	$=$	4025.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.36234 q^{2} -2.51572 q^{3} -0.144030 q^{4} -3.42727 q^{6} +1.00000 q^{7} -2.92090 q^{8} +3.32886 q^{9} +O(q^{10})$	\(q+1.36234 q^{2} -2.51572 q^{3} -0.144030 q^{4} -3.42727 q^{6} +1.00000 q^{7} -2.92090 q^{8} +3.32886 q^{9} -0.362340 q^{11} +0.362340 q^{12} -1.06493 q^{13} +1.36234 q^{14} -3.69119 q^{16} -1.33090 q^{17} +4.53503 q^{18} +6.02209 q^{19} -2.51572 q^{21} -0.493630 q^{22} +1.00000 q^{23} +7.34817 q^{24} -1.45079 q^{26} -0.827308 q^{27} -0.144030 q^{28} +4.12986 q^{29} +2.39582 q^{31} +0.813134 q^{32} +0.911546 q^{33} -1.81313 q^{34} -0.479456 q^{36} -4.95716 q^{37} +8.20414 q^{38} +2.67906 q^{39} -1.25179 q^{41} -3.42727 q^{42} -5.32607 q^{43} +0.0521879 q^{44} +1.36234 q^{46} -4.61692 q^{47} +9.28602 q^{48} +1.00000 q^{49} +3.34817 q^{51} +0.153382 q^{52} +1.14403 q^{53} -1.12707 q^{54} -2.92090 q^{56} -15.1499 q^{57} +5.62627 q^{58} +0.321545 q^{59} -9.71051 q^{61} +3.26393 q^{62} +3.32886 q^{63} +8.49015 q^{64} +1.24184 q^{66} +9.69429 q^{67} +0.191689 q^{68} -2.51572 q^{69} -0.0407948 q^{71} -9.72325 q^{72} +9.48533 q^{73} -6.75334 q^{74} -0.867363 q^{76} -0.362340 q^{77} +3.64979 q^{78} -6.10119 q^{79} -7.90529 q^{81} -1.70537 q^{82} -15.9823 q^{83} +0.362340 q^{84} -7.25592 q^{86} -10.3896 q^{87} +1.05836 q^{88} +12.6849 q^{89} -1.06493 q^{91} -0.144030 q^{92} -6.02723 q^{93} -6.28981 q^{94} -2.04562 q^{96} -6.43180 q^{97} +1.36234 q^{98} -1.20618 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 3 q^{2} - 6 q^{3} + 3 q^{4} + 4 q^{6} + 4 q^{7} - 6 q^{8} + 6 q^{9}+O(q^{10}) $ 4 * q - 3 * q^2 - 6 * q^3 + 3 * q^4 + 4 * q^6 + 4 * q^7 - 6 * q^8 + 6 * q^9	$ 4 q - 3 q^{2} - 6 q^{3} + 3 q^{4} + 4 q^{6} + 4 q^{7} - 6 q^{8} + 6 q^{9} + 7 q^{11} - 7 q^{12} + 5 q^{13} - 3 q^{14} + q^{16} - 5 q^{17} - 2 q^{18} + 8 q^{19} - 6 q^{21} - 14 q^{22} + 4 q^{23} + 6 q^{24} - 11 q^{26} - 15 q^{27} + 3 q^{28} - 2 q^{29} - 10 q^{33} - 4 q^{34} + q^{36} - 13 q^{37} + 13 q^{38} - 13 q^{39} + q^{41} + 4 q^{42} - 14 q^{43} + 15 q^{44} - 3 q^{46} - 4 q^{47} + 23 q^{48} + 4 q^{49} - 10 q^{51} + 5 q^{52} + q^{53} + 14 q^{54} - 6 q^{56} - 19 q^{57} + 16 q^{58} - 7 q^{59} - 7 q^{61} + 15 q^{62} + 6 q^{63} + 23 q^{66} - 15 q^{67} + 11 q^{68} - 6 q^{69} + 17 q^{72} - 3 q^{73} - 2 q^{74} - 22 q^{76} + 7 q^{77} + 31 q^{78} - 14 q^{79} + 28 q^{81} - 6 q^{82} - 3 q^{83} - 7 q^{84} + 16 q^{86} + 14 q^{87} - 13 q^{88} - 11 q^{89} + 5 q^{91} + 3 q^{92} + 23 q^{93} - 19 q^{94} - 15 q^{96} - 9 q^{97} - 3 q^{98} + 8 q^{99}+O(q^{100}) $ 4 * q - 3 * q^2 - 6 * q^3 + 3 * q^4 + 4 * q^6 + 4 * q^7 - 6 * q^8 + 6 * q^9 + 7 * q^11 - 7 * q^12 + 5 * q^13 - 3 * q^14 + q^16 - 5 * q^17 - 2 * q^18 + 8 * q^19 - 6 * q^21 - 14 * q^22 + 4 * q^23 + 6 * q^24 - 11 * q^26 - 15 * q^27 + 3 * q^28 - 2 * q^29 - 10 * q^33 - 4 * q^34 + q^36 - 13 * q^37 + 13 * q^38 - 13 * q^39 + q^41 + 4 * q^42 - 14 * q^43 + 15 * q^44 - 3 * q^46 - 4 * q^47 + 23 * q^48 + 4 * q^49 - 10 * q^51 + 5 * q^52 + q^53 + 14 * q^54 - 6 * q^56 - 19 * q^57 + 16 * q^58 - 7 * q^59 - 7 * q^61 + 15 * q^62 + 6 * q^63 + 23 * q^66 - 15 * q^67 + 11 * q^68 - 6 * q^69 + 17 * q^72 - 3 * q^73 - 2 * q^74 - 22 * q^76 + 7 * q^77 + 31 * q^78 - 14 * q^79 + 28 * q^81 - 6 * q^82 - 3 * q^83 - 7 * q^84 + 16 * q^86 + 14 * q^87 - 13 * q^88 - 11 * q^89 + 5 * q^91 + 3 * q^92 + 23 * q^93 - 19 * q^94 - 15 * q^96 - 9 * q^97 - 3 * q^98 + 8 * 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 $

$2$	1.36234	0.963320	0.481660	−	0.876358i	$-0.340034\pi$
$2$	1.36234	0.963320	0.481660	+	0.876358i	$0.340034\pi$
$3$	−2.51572	−1.45245	−0.726226	−	0.687456i	$-0.758728\pi$
$3$	−2.51572	−1.45245	−0.726226	+	0.687456i	$0.758728\pi$
$4$	−0.144030	−0.0720151
$5$	0	0
$5$	0	0
$6$	−3.42727	−1.39918
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−2.92090	−1.03269
$9$	3.32886	1.10962
$10$	0	0
$11$	−0.362340	−0.109250	−0.0546248	−	0.998507i	$-0.517396\pi$
$11$	−0.362340	−0.109250	−0.0546248	+	0.998507i	$0.517396\pi$
$12$	0.362340	0.104599
$13$	−1.06493	−0.295358	−0.147679	−	0.989035i	$-0.547180\pi$
$13$	−1.06493	−0.295358	−0.147679	+	0.989035i	$0.547180\pi$
$14$	1.36234	0.364101
$15$	0	0
$16$	−3.69119	−0.922799
$17$	−1.33090	−0.322790	−0.161395	−	0.986890i	$-0.551599\pi$
$17$	−1.33090	−0.322790	−0.161395	+	0.986890i	$0.551599\pi$
$18$	4.53503	1.06892
$19$	6.02209	1.38156	0.690781	−	0.723064i	$-0.257267\pi$
$19$	6.02209	1.38156	0.690781	+	0.723064i	$0.257267\pi$
$20$	0	0
$21$	−2.51572	−0.548975
$22$	−0.493630	−0.105242
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	7.34817	1.49994
$25$	0	0
$26$	−1.45079	−0.284524
$27$	−0.827308	−0.159215
$28$	−0.144030	−0.0272191
$29$	4.12986	0.766895	0.383447	−	0.923563i	$-0.374737\pi$
$29$	4.12986	0.766895	0.383447	+	0.923563i	$0.374737\pi$
$30$	0	0
$31$	2.39582	0.430303	0.215151	−	0.976581i	$-0.430976\pi$
$31$	2.39582	0.430303	0.215151	+	0.976581i	$0.430976\pi$
$32$	0.813134	0.143743
$33$	0.911546	0.158680
$34$	−1.81313	−0.310950
$35$	0	0
$36$	−0.479456	−0.0799093
$37$	−4.95716	−0.814953	−0.407476	−	0.913216i	$-0.633591\pi$
$37$	−4.95716	−0.814953	−0.407476	+	0.913216i	$0.633591\pi$
$38$	8.20414	1.33089
$39$	2.67906	0.428993
$40$	0	0
$41$	−1.25179	−0.195497	−0.0977487	−	0.995211i	$-0.531164\pi$
$41$	−1.25179	−0.195497	−0.0977487	+	0.995211i	$0.531164\pi$
$42$	−3.42727	−0.528839
$43$	−5.32607	−0.812219	−0.406109	−	0.913825i	$-0.633115\pi$
$43$	−5.32607	−0.812219	−0.406109	+	0.913825i	$0.633115\pi$
$44$	0.0521879	0.00786762
$45$	0	0
$46$	1.36234	0.200866
$47$	−4.61692	−0.673446	−0.336723	−	0.941604i	$-0.609319\pi$
$47$	−4.61692	−0.673446	−0.336723	+	0.941604i	$0.609319\pi$
$48$	9.28602	1.34032
$49$	1.00000	0.142857
$50$	0	0
$51$	3.34817	0.468837
$52$	0.153382	0.0212702
$53$	1.14403	0.157145	0.0785723	−	0.996908i	$-0.474964\pi$
$53$	1.14403	0.157145	0.0785723	+	0.996908i	$0.474964\pi$
$54$	−1.12707	−0.153375
$55$	0	0
$56$	−2.92090	−0.390321
$57$	−15.1499	−2.00665
$58$	5.62627	0.738765
$59$	0.321545	0.0418616	0.0209308	−	0.999781i	$-0.493337\pi$
$59$	0.321545	0.0418616	0.0209308	+	0.999781i	$0.493337\pi$
$60$	0	0
$61$	−9.71051	−1.24330	−0.621651	−	0.783294i	$-0.713538\pi$
$61$	−9.71051	−1.24330	−0.621651	+	0.783294i	$0.713538\pi$
$62$	3.26393	0.414519
$63$	3.32886	0.419396
$64$	8.49015	1.06127
$65$	0	0
$66$	1.24184	0.152859
$67$	9.69429	1.18435	0.592173	−	0.805811i	$-0.298270\pi$
$67$	9.69429	1.18435	0.592173	+	0.805811i	$0.298270\pi$
$68$	0.191689	0.0232457
$69$	−2.51572	−0.302857
$70$	0	0
$71$	−0.0407948	−0.00484145	−0.00242072	−	0.999997i	$-0.500771\pi$
$71$	−0.0407948	−0.00484145	−0.00242072	+	0.999997i	$0.500771\pi$
$72$	−9.72325	−1.14590
$73$	9.48533	1.11017	0.555087	−	0.831792i	$-0.312685\pi$
$73$	9.48533	1.11017	0.555087	+	0.831792i	$0.312685\pi$
$74$	−6.75334	−0.785060
$75$	0	0
$76$	−0.867363	−0.0994934
$77$	−0.362340	−0.0412925
$78$	3.64979	0.413258
$79$	−6.10119	−0.686438	−0.343219	−	0.939255i	$-0.611517\pi$
$79$	−6.10119	−0.686438	−0.343219	+	0.939255i	$0.611517\pi$
$80$	0	0
$81$	−7.90529	−0.878365
$82$	−1.70537	−0.188327
$83$	−15.9823	−1.75429	−0.877145	−	0.480225i	$-0.840555\pi$
$83$	−15.9823	−1.75429	−0.877145	+	0.480225i	$0.840555\pi$
$84$	0.362340	0.0395345
$85$	0	0
$86$	−7.25592	−0.782426
$87$	−10.3896	−1.11388
$88$	1.05836	0.112821
$89$	12.6849	1.34460	0.672300	−	0.740278i	$-0.265306\pi$
$89$	12.6849	1.34460	0.672300	+	0.740278i	$0.265306\pi$
$90$	0	0
$91$	−1.06493	−0.111635
$92$	−0.144030	−0.0150162
$93$	−6.02723	−0.624994
$94$	−6.28981	−0.648744
$95$	0	0
$96$	−2.04562	−0.208780
$97$	−6.43180	−0.653050	−0.326525	−	0.945189i	$-0.605878\pi$
$97$	−6.43180	−0.653050	−0.326525	+	0.945189i	$0.605878\pi$
$98$	1.36234	0.137617
$99$	−1.20618	−0.121225
$100$	0	0
$101$	7.70568	0.766744	0.383372	−	0.923594i	$-0.374763\pi$
$101$	7.70568	0.766744	0.383372	+	0.923594i	$0.374763\pi$
$102$	4.56134	0.451640
$103$	−1.42870	−0.140774	−0.0703871	−	0.997520i	$-0.522423\pi$
$103$	−1.42870	−0.140774	−0.0703871	+	0.997520i	$0.522423\pi$
$104$	3.11055	0.305014
$105$	0	0
$106$	1.55856	0.151381
$107$	−6.50433	−0.628797	−0.314399	−	0.949291i	$-0.601803\pi$
$107$	−6.50433	−0.628797	−0.314399	+	0.949291i	$0.601803\pi$
$108$	0.119157	0.0114659
$109$	−12.3053	−1.17864	−0.589318	−	0.807901i	$-0.700604\pi$
$109$	−12.3053	−1.17864	−0.589318	+	0.807901i	$0.700604\pi$
$110$	0	0
$111$	12.4708	1.18368
$112$	−3.69119	−0.348785
$113$	−9.14403	−0.860198	−0.430099	−	0.902782i	$-0.641521\pi$
$113$	−9.14403	−0.860198	−0.430099	+	0.902782i	$0.641521\pi$
$114$	−20.6393	−1.93305
$115$	0	0
$116$	−0.594824	−0.0552280
$117$	−3.54499	−0.327735
$118$	0.438054	0.0403261
$119$	−1.33090	−0.122003
$120$	0	0
$121$	−10.8687	−0.988065
$122$	−13.2290	−1.19770
$123$	3.14917	0.283951
$124$	−0.345071	−0.0309883
$125$	0	0
$126$	4.53503	0.404013
$127$	−5.44597	−0.483252	−0.241626	−	0.970369i	$-0.577681\pi$
$127$	−5.44597	−0.483252	−0.241626	+	0.970369i	$0.577681\pi$
$128$	9.94021	0.878599
$129$	13.3989	1.17971
$130$	0	0
$131$	−6.17404	−0.539428	−0.269714	−	0.962940i	$-0.586929\pi$
$131$	−6.17404	−0.539428	−0.269714	+	0.962940i	$0.586929\pi$
$132$	−0.131290	−0.0114273
$133$	6.02209	0.522182
$134$	13.2069	1.14090
$135$	0	0
$136$	3.88741	0.333343
$137$	2.32742	0.198845	0.0994225	−	0.995045i	$-0.468300\pi$
$137$	2.32742	0.198845	0.0994225	+	0.995045i	$0.468300\pi$
$138$	−3.42727	−0.291748
$139$	3.33677	0.283021	0.141511	−	0.989937i	$-0.454804\pi$
$139$	3.33677	0.283021	0.141511	+	0.989937i	$0.454804\pi$
$140$	0	0
$141$	11.6149	0.978149
$142$	−0.0555763	−0.00466386
$143$	0.385866	0.0322677
$144$	−12.2875	−1.02395
$145$	0	0
$146$	12.9222	1.06945
$147$	−2.51572	−0.207493
$148$	0.713981	0.0586889
$149$	−22.1571	−1.81518	−0.907589	−	0.419859i	$-0.862080\pi$
$149$	−22.1571	−1.81518	−0.907589	+	0.419859i	$0.862080\pi$
$150$	0	0
$151$	−18.6971	−1.52155	−0.760773	−	0.649018i	$-0.775180\pi$
$151$	−18.6971	−1.52155	−0.760773	+	0.649018i	$0.775180\pi$
$152$	−17.5899	−1.42673
$153$	−4.43036	−0.358174
$154$	−0.493630	−0.0397778
$155$	0	0
$156$	−0.385866	−0.0308940
$157$	6.90190	0.550832	0.275416	−	0.961325i	$-0.411184\pi$
$157$	6.90190	0.550832	0.275416	+	0.961325i	$0.411184\pi$
$158$	−8.31190	−0.661259
$159$	−2.87806	−0.228245
$160$	0	0
$161$	1.00000	0.0788110
$162$	−10.7697	−0.846147
$163$	−7.53503	−0.590189	−0.295095	−	0.955468i	$-0.595351\pi$
$163$	−7.53503	−0.590189	−0.295095	+	0.955468i	$0.595351\pi$
$164$	0.180296	0.0140788
$165$	0	0
$166$	−21.7734	−1.68994
$167$	−4.32742	−0.334866	−0.167433	−	0.985883i	$-0.553548\pi$
$167$	−4.32742	−0.334866	−0.167433	+	0.985883i	$0.553548\pi$
$168$	7.34817	0.566923
$169$	−11.8659	−0.912764
$170$	0	0
$171$	20.0467	1.53301
$172$	0.767115	0.0584920
$173$	14.8715	1.13066	0.565329	−	0.824865i	$-0.308749\pi$
$173$	14.8715	1.13066	0.565329	+	0.824865i	$0.308749\pi$
$174$	−14.1541	−1.07302
$175$	0	0
$176$	1.33747	0.100815
$177$	−0.808918	−0.0608020
$178$	17.2812	1.29528
$179$	−4.56473	−0.341184	−0.170592	−	0.985342i	$-0.554568\pi$
$179$	−4.56473	−0.341184	−0.170592	+	0.985342i	$0.554568\pi$
$180$	0	0
$181$	0.959651	0.0713303	0.0356651	−	0.999364i	$-0.488645\pi$
$181$	0.959651	0.0713303	0.0356651	+	0.999364i	$0.488645\pi$
$182$	−1.45079	−0.107540
$183$	24.4289	1.80584
$184$	−2.92090	−0.215331
$185$	0	0
$186$	−8.21113	−0.602069
$187$	0.482237	0.0352647
$188$	0.664975	0.0484983
$189$	−0.827308	−0.0601778
$190$	0	0
$191$	−13.8054	−0.998927	−0.499463	−	0.866335i	$-0.666469\pi$
$191$	−13.8054	−0.998927	−0.499463	+	0.866335i	$0.666469\pi$
$192$	−21.3589	−1.54144
$193$	0.748519	0.0538796	0.0269398	−	0.999637i	$-0.491424\pi$
$193$	0.748519	0.0538796	0.0269398	+	0.999637i	$0.491424\pi$
$194$	−8.76229	−0.629096
$195$	0	0
$196$	−0.144030	−0.0102879
$197$	4.31921	0.307731	0.153865	−	0.988092i	$-0.450828\pi$
$197$	4.31921	0.307731	0.153865	+	0.988092i	$0.450828\pi$
$198$	−1.64322	−0.116779
$199$	1.73260	0.122821	0.0614103	−	0.998113i	$-0.480440\pi$
$199$	1.73260	0.122821	0.0614103	+	0.998113i	$0.480440\pi$
$200$	0	0
$201$	−24.3881	−1.72021
$202$	10.4978	0.738620
$203$	4.12986	0.289859
$204$	−0.482237	−0.0337633
$205$	0	0
$206$	−1.94638	−0.135611
$207$	3.32886	0.231371
$208$	3.93086	0.272556
$209$	−2.18204	−0.150935
$210$	0	0
$211$	−24.6304	−1.69563	−0.847814	−	0.530294i	$-0.822082\pi$
$211$	−24.6304	−1.69563	−0.847814	+	0.530294i	$0.822082\pi$
$212$	−0.164775	−0.0113168
$213$	0.102628	0.00703197
$214$	−8.86111	−0.605733
$215$	0	0
$216$	2.41648	0.164421
$217$	2.39582	0.162639
$218$	−16.7640	−1.13540
$219$	−23.8625	−1.61248
$220$	0	0
$221$	1.41731	0.0953385
$222$	16.9895	1.14026
$223$	6.85628	0.459131	0.229565	−	0.973293i	$-0.426270\pi$
$223$	6.85628	0.459131	0.229565	+	0.973293i	$0.426270\pi$
$224$	0.813134	0.0543298
$225$	0	0
$226$	−12.4573	−0.828646
$227$	24.4028	1.61967	0.809834	−	0.586659i	$-0.199557\pi$
$227$	24.4028	1.61967	0.809834	+	0.586659i	$0.199557\pi$
$228$	2.18204	0.144509
$229$	−15.2363	−1.00684	−0.503422	−	0.864041i	$-0.667926\pi$
$229$	−15.2363	−1.00684	−0.503422	+	0.864041i	$0.667926\pi$
$230$	0	0
$231$	0.911546	0.0599753
$232$	−12.0629	−0.791967
$233$	−13.0510	−0.855003	−0.427501	−	0.904015i	$-0.640606\pi$
$233$	−13.0510	−0.855003	−0.427501	+	0.904015i	$0.640606\pi$
$234$	−4.82948	−0.315713
$235$	0	0
$236$	−0.0463122	−0.00301467
$237$	15.3489	0.997019
$238$	−1.81313	−0.117528
$239$	−24.4591	−1.58213	−0.791063	−	0.611735i	$-0.790472\pi$
$239$	−24.4591	−1.58213	−0.791063	+	0.611735i	$0.790472\pi$
$240$	0	0
$241$	−13.7522	−0.885857	−0.442929	−	0.896557i	$-0.646060\pi$
$241$	−13.7522	−0.885857	−0.442929	+	0.896557i	$0.646060\pi$
$242$	−14.8069	−0.951822
$243$	22.3694	1.43500
$244$	1.39861	0.0895366
$245$	0	0
$246$	4.29023	0.273535
$247$	−6.41309	−0.408055
$248$	−6.99796	−0.444371
$249$	40.2071	2.54802
$250$	0	0
$251$	23.7834	1.50119	0.750596	−	0.660762i	$-0.229767\pi$
$251$	23.7834	1.50119	0.750596	+	0.660762i	$0.229767\pi$
$252$	−0.479456	−0.0302029
$253$	−0.362340	−0.0227801
$254$	−7.41926	−0.465526
$255$	0	0
$256$	−3.43837	−0.214898
$257$	12.4808	0.778531	0.389266	−	0.921126i	$-0.372729\pi$
$257$	12.4808	0.778531	0.389266	+	0.921126i	$0.372729\pi$
$258$	18.2539	1.13644
$259$	−4.95716	−0.308023
$260$	0	0
$261$	13.7477	0.850961
$262$	−8.41114	−0.519642
$263$	−31.0204	−1.91280	−0.956399	−	0.292064i	$-0.905658\pi$
$263$	−31.0204	−1.91280	−0.956399	+	0.292064i	$0.905658\pi$
$264$	−2.66253	−0.163868
$265$	0	0
$266$	8.20414	0.503028
$267$	−31.9118	−1.95297
$268$	−1.39627	−0.0852908
$269$	5.56443	0.339270	0.169635	−	0.985507i	$-0.445741\pi$
$269$	5.56443	0.339270	0.169635	+	0.985507i	$0.445741\pi$
$270$	0	0
$271$	−29.4030	−1.78611	−0.893054	−	0.449950i	$-0.851442\pi$
$271$	−29.4030	−1.78611	−0.893054	+	0.449950i	$0.851442\pi$
$272$	4.91260	0.297870
$273$	2.67906	0.162144
$274$	3.17074	0.191551
$275$	0	0
$276$	0.362340	0.0218103
$277$	9.21439	0.553639	0.276819	−	0.960922i	$-0.410720\pi$
$277$	9.21439	0.553639	0.276819	+	0.960922i	$0.410720\pi$
$278$	4.54582	0.272640
$279$	7.97535	0.477472
$280$	0	0
$281$	21.4711	1.28086	0.640428	−	0.768018i	$-0.278757\pi$
$281$	21.4711	1.28086	0.640428	+	0.768018i	$0.278757\pi$
$282$	15.8234	0.942270
$283$	−11.4273	−0.679281	−0.339640	−	0.940555i	$-0.610305\pi$
$283$	−11.4273	−0.679281	−0.339640	+	0.940555i	$0.610305\pi$
$284$	0.00587568	0.000348657 0
$285$	0	0
$286$	0.525680	0.0310841
$287$	−1.25179	−0.0738911
$288$	2.70680	0.159500
$289$	−15.2287	−0.895807
$290$	0	0
$291$	16.1806	0.948524
$292$	−1.36617	−0.0799493
$293$	3.21905	0.188059	0.0940294	−	0.995569i	$-0.470025\pi$
$293$	3.21905	0.188059	0.0940294	+	0.995569i	$0.470025\pi$
$294$	−3.42727	−0.199882
$295$	0	0
$296$	14.4794	0.841596
$297$	0.299767	0.0173942
$298$	−30.1855	−1.74860
$299$	−1.06493	−0.0615864
$300$	0	0
$301$	−5.32607	−0.306990
$302$	−25.4718	−1.46574
$303$	−19.3854	−1.11366
$304$	−22.2287	−1.27490
$305$	0	0
$306$	−6.03566	−0.345036
$307$	−0.183478	−0.0104716	−0.00523582	−	0.999986i	$-0.501667\pi$
$307$	−0.183478	−0.0104716	−0.00523582	+	0.999986i	$0.501667\pi$
$308$	0.0521879	0.00297368
$309$	3.59422	0.204468
$310$	0	0
$311$	−9.56051	−0.542127	−0.271063	−	0.962561i	$-0.587375\pi$
$311$	−9.56051	−0.542127	−0.271063	+	0.962561i	$0.587375\pi$
$312$	−7.82527	−0.443018
$313$	−33.1105	−1.87151	−0.935757	−	0.352644i	$-0.885283\pi$
$313$	−33.1105	−1.87151	−0.935757	+	0.352644i	$0.885283\pi$
$314$	9.40273	0.530627
$315$	0	0
$316$	0.878756	0.0494339
$317$	−6.79865	−0.381850	−0.190925	−	0.981605i	$-0.561149\pi$
$317$	−6.79865	−0.381850	−0.190925	+	0.981605i	$0.561149\pi$
$318$	−3.92090	−0.219873
$319$	−1.49641	−0.0837829
$320$	0	0
$321$	16.3631	0.913298
$322$	1.36234	0.0759202
$323$	−8.01478	−0.445954
$324$	1.13860	0.0632556
$325$	0	0
$326$	−10.2653	−0.568541
$327$	30.9568	1.71191
$328$	3.65636	0.201889
$329$	−4.61692	−0.254539
$330$	0	0
$331$	17.6428	0.969738	0.484869	−	0.874587i	$-0.338867\pi$
$331$	17.6428	0.969738	0.484869	+	0.874587i	$0.338867\pi$
$332$	2.30194	0.126335
$333$	−16.5017	−0.904286
$334$	−5.89542	−0.322583
$335$	0	0
$336$	9.28602	0.506594
$337$	9.25592	0.504202	0.252101	−	0.967701i	$-0.418878\pi$
$337$	9.25592	0.504202	0.252101	+	0.967701i	$0.418878\pi$
$338$	−16.1654	−0.879283
$339$	23.0038	1.24940
$340$	0	0
$341$	−0.868103	−0.0470104
$342$	27.3104	1.47678
$343$	1.00000	0.0539949
$344$	15.5569	0.838773
$345$	0	0
$346$	20.2600	1.08919
$347$	14.2355	0.764201	0.382101	−	0.924121i	$-0.375201\pi$
$347$	14.2355	0.764201	0.382101	+	0.924121i	$0.375201\pi$
$348$	1.49641	0.0802161
$349$	10.2100	0.546529	0.273265	−	0.961939i	$-0.411897\pi$
$349$	10.2100	0.546529	0.273265	+	0.961939i	$0.411897\pi$
$350$	0	0
$351$	0.881023	0.0470255
$352$	−0.294631	−0.0157039
$353$	19.1189	1.01760	0.508798	−	0.860886i	$-0.330090\pi$
$353$	19.1189	1.01760	0.508798	+	0.860886i	$0.330090\pi$
$354$	−1.10202	−0.0585718
$355$	0	0
$356$	−1.82701	−0.0968315
$357$	3.34817	0.177204
$358$	−6.21871	−0.328669
$359$	−15.3220	−0.808664	−0.404332	−	0.914612i	$-0.632496\pi$
$359$	−15.3220	−0.808664	−0.404332	+	0.914612i	$0.632496\pi$
$360$	0	0
$361$	17.2656	0.908715
$362$	1.30737	0.0687139
$363$	27.3426	1.43512
$364$	0.153382	0.00803939
$365$	0	0
$366$	33.2805	1.73960
$367$	9.72194	0.507481	0.253741	−	0.967272i	$-0.418339\pi$
$367$	9.72194	0.507481	0.253741	+	0.967272i	$0.418339\pi$
$368$	−3.69119	−0.192417
$369$	−4.16704	−0.216928
$370$	0	0
$371$	1.14403	0.0593951
$372$	0.868103	0.0450090
$373$	30.1482	1.56101	0.780507	−	0.625147i	$-0.214961\pi$
$373$	30.1482	1.56101	0.780507	+	0.625147i	$0.214961\pi$
$374$	0.656970	0.0339711
$375$	0	0
$376$	13.4855	0.695464
$377$	−4.39800	−0.226508
$378$	−1.12707	−0.0579705
$379$	−12.5862	−0.646511	−0.323256	−	0.946312i	$-0.604777\pi$
$379$	−12.5862	−0.646511	−0.323256	+	0.946312i	$0.604777\pi$
$380$	0	0
$381$	13.7005	0.701900
$382$	−18.8077	−0.962286
$383$	−18.2816	−0.934148	−0.467074	−	0.884218i	$-0.654692\pi$
$383$	−18.2816	−0.934148	−0.467074	+	0.884218i	$0.654692\pi$
$384$	−25.0068	−1.27612
$385$	0	0
$386$	1.01974	0.0519032
$387$	−17.7297	−0.901253
$388$	0.926373	0.0470295
$389$	28.0843	1.42393	0.711965	−	0.702215i	$-0.247806\pi$
$389$	28.0843	1.42393	0.711965	+	0.702215i	$0.247806\pi$
$390$	0	0
$391$	−1.33090	−0.0673063
$392$	−2.92090	−0.147528
$393$	15.5322	0.783494
$394$	5.88423	0.296443
$395$	0	0
$396$	0.173726	0.00873005
$397$	6.14268	0.308292	0.154146	−	0.988048i	$-0.450737\pi$
$397$	6.14268	0.308292	0.154146	+	0.988048i	$0.450737\pi$
$398$	2.36039	0.118315
$399$	−15.1499	−0.758444
$400$	0	0
$401$	18.6924	0.933454	0.466727	−	0.884401i	$-0.345433\pi$
$401$	18.6924	0.933454	0.466727	+	0.884401i	$0.345433\pi$
$402$	−33.2249	−1.65711
$403$	−2.55138	−0.127093
$404$	−1.10985	−0.0552171
$405$	0	0
$406$	5.62627	0.279227
$407$	1.79618	0.0890332
$408$	−9.77965	−0.484165
$409$	13.8484	0.684760	0.342380	−	0.939562i	$-0.388767\pi$
$409$	13.8484	0.684760	0.342380	+	0.939562i	$0.388767\pi$
$410$	0	0
$411$	−5.85514	−0.288813
$412$	0.205776	0.0101379
$413$	0.321545	0.0158222
$414$	4.53503	0.222885
$415$	0	0
$416$	−0.865929	−0.0424556
$417$	−8.39439	−0.411075
$418$	−2.97269	−0.145399
$419$	−28.0372	−1.36971	−0.684853	−	0.728681i	$-0.740134\pi$
$419$	−28.0372	−1.36971	−0.684853	+	0.728681i	$0.740134\pi$
$420$	0	0
$421$	−0.979950	−0.0477598	−0.0238799	−	0.999715i	$-0.507602\pi$
$421$	−0.979950	−0.0477598	−0.0238799	+	0.999715i	$0.507602\pi$
$422$	−33.5550	−1.63343
$423$	−15.3690	−0.747268
$424$	−3.34160	−0.162282
$425$	0	0
$426$	0.139815	0.00677404
$427$	−9.71051	−0.469924
$428$	0.936820	0.0452829
$429$	−0.970731	−0.0468673
$430$	0	0
$431$	19.2787	0.928623	0.464311	−	0.885672i	$-0.346302\pi$
$431$	19.2787	0.928623	0.464311	+	0.885672i	$0.346302\pi$
$432$	3.05375	0.146924
$433$	−17.1395	−0.823673	−0.411836	−	0.911258i	$-0.635112\pi$
$433$	−17.1395	−0.823673	−0.411836	+	0.911258i	$0.635112\pi$
$434$	3.26393	0.156674
$435$	0	0
$436$	1.77234	0.0848796
$437$	6.02209	0.288076
$438$	−32.5088	−1.55333
$439$	37.0875	1.77009	0.885046	−	0.465504i	$-0.154127\pi$
$439$	37.0875	1.77009	0.885046	+	0.465504i	$0.154127\pi$
$440$	0	0
$441$	3.32886	0.158517
$442$	1.93086	0.0918415
$443$	−25.9758	−1.23415	−0.617073	−	0.786906i	$-0.711682\pi$
$443$	−25.9758	−1.23415	−0.617073	+	0.786906i	$0.711682\pi$
$444$	−1.79618	−0.0852428
$445$	0	0
$446$	9.34059	0.442290
$447$	55.7411	2.63646
$448$	8.49015	0.401122
$449$	27.4405	1.29500	0.647498	−	0.762068i	$-0.275816\pi$
$449$	27.4405	1.29500	0.647498	+	0.762068i	$0.275816\pi$
$450$	0	0
$451$	0.453575	0.0213580
$452$	1.31702	0.0619472
$453$	47.0366	2.20997
$454$	33.2448	1.56026
$455$	0	0
$456$	44.2513	2.07226
$457$	3.05248	0.142789	0.0713945	−	0.997448i	$-0.477255\pi$
$457$	3.05248	0.142789	0.0713945	+	0.997448i	$0.477255\pi$
$458$	−20.7570	−0.969913
$459$	1.10106	0.0513931
$460$	0	0
$461$	−21.2366	−0.989089	−0.494544	−	0.869152i	$-0.664665\pi$
$461$	−21.2366	−0.989089	−0.494544	+	0.869152i	$0.664665\pi$
$462$	1.24184	0.0577754
$463$	−11.0623	−0.514108	−0.257054	−	0.966397i	$-0.582752\pi$
$463$	−11.0623	−0.514108	−0.257054	+	0.966397i	$0.582752\pi$
$464$	−15.2441	−0.707690
$465$	0	0
$466$	−17.7800	−0.823641
$467$	−20.4458	−0.946121	−0.473060	−	0.881030i	$-0.656851\pi$
$467$	−20.4458	−0.946121	−0.473060	+	0.881030i	$0.656851\pi$
$468$	0.510586	0.0236018
$469$	9.69429	0.447641
$470$	0	0
$471$	−17.3633	−0.800057
$472$	−0.939200	−0.0432302
$473$	1.92985	0.0887345
$474$	20.9104	0.960448
$475$	0	0
$476$	0.191689	0.00878606
$477$	3.80831	0.174371
$478$	−33.3216	−1.52409
$479$	4.03656	0.184435	0.0922176	−	0.995739i	$-0.470604\pi$
$479$	4.03656	0.184435	0.0922176	+	0.995739i	$0.470604\pi$
$480$	0	0
$481$	5.27902	0.240703
$482$	−18.7352	−0.853364
$483$	−2.51572	−0.114469
$484$	1.56542	0.0711556
$485$	0	0
$486$	30.4748	1.38236
$487$	5.39892	0.244648	0.122324	−	0.992490i	$-0.460965\pi$
$487$	5.39892	0.244648	0.122324	+	0.992490i	$0.460965\pi$
$488$	28.3634	1.28395
$489$	18.9560	0.857222
$490$	0	0
$491$	40.4037	1.82339	0.911696	−	0.410866i	$-0.134774\pi$
$491$	40.4037	1.82339	0.911696	+	0.410866i	$0.134774\pi$
$492$	−0.453575	−0.0204487
$493$	−5.49641	−0.247546
$494$	−8.73681	−0.393088
$495$	0	0
$496$	−8.84346	−0.397083
$497$	−0.0407948	−0.00182989
$498$	54.7758	2.45456
$499$	12.4697	0.558221	0.279111	−	0.960259i	$-0.409960\pi$
$499$	12.4697	0.558221	0.279111	+	0.960259i	$0.409960\pi$
$500$	0	0
$501$	10.8866	0.486377
$502$	32.4010	1.44613
$503$	18.3201	0.816853	0.408427	−	0.912791i	$-0.366078\pi$
$503$	18.3201	0.816853	0.408427	+	0.912791i	$0.366078\pi$
$504$	−9.72325	−0.433108
$505$	0	0
$506$	−0.493630	−0.0219445
$507$	29.8514	1.32575
$508$	0.784384	0.0348014
$509$	−6.97723	−0.309260	−0.154630	−	0.987972i	$-0.549419\pi$
$509$	−6.97723	−0.309260	−0.154630	+	0.987972i	$0.549419\pi$
$510$	0	0
$511$	9.48533	0.419606
$512$	−24.5646	−1.08561
$513$	−4.98212	−0.219966
$514$	17.0031	0.749974
$515$	0	0
$516$	−1.92985	−0.0849569
$517$	1.67289	0.0735737
$518$	−6.75334	−0.296725
$519$	−37.4125	−1.64223
$520$	0	0
$521$	16.1976	0.709628	0.354814	−	0.934937i	$-0.384544\pi$
$521$	16.1976	0.709628	0.354814	+	0.934937i	$0.384544\pi$
$522$	18.7290	0.819747
$523$	−8.61956	−0.376907	−0.188454	−	0.982082i	$-0.560348\pi$
$523$	−8.61956	−0.376907	−0.188454	+	0.982082i	$0.560348\pi$
$524$	0.889248	0.0388470
$525$	0	0
$526$	−42.2603	−1.84264
$527$	−3.18859	−0.138897
$528$	−3.36469	−0.146430
$529$	1.00000	0.0434783
$530$	0	0
$531$	1.07038	0.0464504
$532$	−0.867363	−0.0376050
$533$	1.33307	0.0577417
$534$	−43.4747	−1.88133
$535$	0	0
$536$	−28.3160	−1.22307
$537$	11.4836	0.495553
$538$	7.58065	0.326825
$539$	−0.362340	−0.0156071
$540$	0	0
$541$	−34.7028	−1.49199	−0.745995	−	0.665952i	$-0.768026\pi$
$541$	−34.7028	−1.49199	−0.745995	+	0.665952i	$0.768026\pi$
$542$	−40.0569	−1.72059
$543$	−2.41421	−0.103604
$544$	−1.08220	−0.0463988
$545$	0	0
$546$	3.64979	0.156197
$547$	13.5053	0.577446	0.288723	−	0.957413i	$-0.406769\pi$
$547$	13.5053	0.577446	0.288723	+	0.957413i	$0.406769\pi$
$548$	−0.335219	−0.0143198
$549$	−32.3249	−1.37959
$550$	0	0
$551$	24.8704	1.05951
$552$	7.34817	0.312759
$553$	−6.10119	−0.259449
$554$	12.5531	0.533331
$555$	0	0
$556$	−0.480596	−0.0203818
$557$	23.1940	0.982763	0.491382	−	0.870944i	$-0.336492\pi$
$557$	23.1940	0.982763	0.491382	+	0.870944i	$0.336492\pi$
$558$	10.8651	0.459958
$559$	5.67188	0.239895
$560$	0	0
$561$	−1.21317	−0.0512202
$562$	29.2509	1.23387
$563$	3.44792	0.145313	0.0726564	−	0.997357i	$-0.476852\pi$
$563$	3.44792	0.145313	0.0726564	+	0.997357i	$0.476852\pi$
$564$	−1.67289	−0.0704415
$565$	0	0
$566$	−15.5678	−0.654364
$567$	−7.90529	−0.331991
$568$	0.119157	0.00499973
$569$	10.1165	0.424106	0.212053	−	0.977258i	$-0.431985\pi$
$569$	10.1165	0.424106	0.212053	+	0.977258i	$0.431985\pi$
$570$	0	0
$571$	31.0036	1.29746	0.648730	−	0.761018i	$-0.275300\pi$
$571$	31.0036	1.29746	0.648730	+	0.761018i	$0.275300\pi$
$572$	−0.0555763	−0.00232376
$573$	34.7306	1.45089
$574$	−1.70537	−0.0711807
$575$	0	0
$576$	28.2625	1.17760
$577$	28.6449	1.19250	0.596251	−	0.802798i	$-0.296656\pi$
$577$	28.6449	1.19250	0.596251	+	0.802798i	$0.296656\pi$
$578$	−20.7467	−0.862948
$579$	−1.88306	−0.0782575
$580$	0	0
$581$	−15.9823	−0.663060
$582$	22.0435	0.913732
$583$	−0.414528	−0.0171680
$584$	−27.7057	−1.14647
$585$	0	0
$586$	4.38544	0.181161
$587$	−18.9813	−0.783443	−0.391721	−	0.920084i	$-0.628120\pi$
$587$	−18.9813	−0.783443	−0.391721	+	0.920084i	$0.628120\pi$
$588$	0.362340	0.0149426
$589$	14.4279	0.594490
$590$	0	0
$591$	−10.8659	−0.446965
$592$	18.2979	0.752037
$593$	32.0593	1.31652	0.658258	−	0.752792i	$-0.271293\pi$
$593$	32.0593	1.31652	0.658258	+	0.752792i	$0.271293\pi$
$594$	0.408384	0.0167562
$595$	0	0
$596$	3.19129	0.130720
$597$	−4.35873	−0.178391
$598$	−1.45079	−0.0593274
$599$	−27.3549	−1.11769	−0.558846	−	0.829271i	$-0.688756\pi$
$599$	−27.3549	−1.11769	−0.558846	+	0.829271i	$0.688756\pi$
$600$	0	0
$601$	−30.8825	−1.25972	−0.629862	−	0.776707i	$-0.716888\pi$
$601$	−30.8825	−1.25972	−0.629862	+	0.776707i	$0.716888\pi$
$602$	−7.25592	−0.295729
$603$	32.2709	1.31417
$604$	2.69294	0.109574
$605$	0	0
$606$	−26.4094	−1.07281
$607$	−35.9184	−1.45788	−0.728941	−	0.684576i	$-0.759987\pi$
$607$	−35.9184	−1.45788	−0.728941	+	0.684576i	$0.759987\pi$
$608$	4.89676	0.198590
$609$	−10.3896	−0.421007
$610$	0	0
$611$	4.91668	0.198908
$612$	0.638106	0.0257939
$613$	−30.2918	−1.22347	−0.611736	−	0.791062i	$-0.709529\pi$
$613$	−30.2918	−1.22347	−0.611736	+	0.791062i	$0.709529\pi$
$614$	−0.249959	−0.0100875
$615$	0	0
$616$	1.05836	0.0426424
$617$	−6.00662	−0.241817	−0.120909	−	0.992664i	$-0.538581\pi$
$617$	−6.00662	−0.241817	−0.120909	+	0.992664i	$0.538581\pi$
$618$	4.89654	0.196968
$619$	−9.20533	−0.369993	−0.184997	−	0.982739i	$-0.559227\pi$
$619$	−9.20533	−0.369993	−0.184997	+	0.982739i	$0.559227\pi$
$620$	0	0
$621$	−0.827308	−0.0331987
$622$	−13.0247	−0.522242
$623$	12.6849	0.508211
$624$	−9.88894	−0.395874
$625$	0	0
$626$	−45.1077	−1.80287
$627$	5.48941	0.219226
$628$	−0.994082	−0.0396682
$629$	6.59747	0.263058
$630$	0	0
$631$	10.6849	0.425361	0.212680	−	0.977122i	$-0.431781\pi$
$631$	10.6849	0.425361	0.212680	+	0.977122i	$0.431781\pi$
$632$	17.8210	0.708880
$633$	61.9633	2.46282
$634$	−9.26207	−0.367844
$635$	0	0
$636$	0.414528	0.0164371
$637$	−1.06493	−0.0421940
$638$	−2.03862	−0.0807098
$639$	−0.135800	−0.00537216
$640$	0	0
$641$	−32.0087	−1.26427	−0.632133	−	0.774860i	$-0.717821\pi$
$641$	−32.0087	−1.26427	−0.632133	+	0.774860i	$0.717821\pi$
$642$	22.2921	0.879798
$643$	−15.9336	−0.628358	−0.314179	−	0.949364i	$-0.601729\pi$
$643$	−15.9336	−0.628358	−0.314179	+	0.949364i	$0.601729\pi$
$644$	−0.144030	−0.00567558
$645$	0	0
$646$	−10.9189	−0.429597
$647$	−33.3993	−1.31306	−0.656531	−	0.754299i	$-0.727977\pi$
$647$	−33.3993	−1.31306	−0.656531	+	0.754299i	$0.727977\pi$
$648$	23.0905	0.907082
$649$	−0.116509	−0.00457336
$650$	0	0
$651$	−6.02723	−0.236226
$652$	1.08527	0.0425025
$653$	−9.26032	−0.362384	−0.181192	−	0.983448i	$-0.557996\pi$
$653$	−9.26032	−0.362384	−0.181192	+	0.983448i	$0.557996\pi$
$654$	42.1737	1.64912
$655$	0	0
$656$	4.62062	0.180405
$657$	31.5753	1.23187
$658$	−6.28981	−0.245202
$659$	−18.3799	−0.715980	−0.357990	−	0.933725i	$-0.616538\pi$
$659$	−18.3799	−0.715980	−0.357990	+	0.933725i	$0.616538\pi$
$660$	0	0
$661$	−37.8968	−1.47402	−0.737008	−	0.675884i	$-0.763762\pi$
$661$	−37.8968	−1.47402	−0.737008	+	0.675884i	$0.763762\pi$
$662$	24.0355	0.934168
$663$	−3.56555	−0.138475
$664$	46.6828	1.81164
$665$	0	0
$666$	−22.4809	−0.871117
$667$	4.12986	0.159909
$668$	0.623279	0.0241154
$669$	−17.2485	−0.666866
$670$	0	0
$671$	3.51850	0.135830
$672$	−2.04562	−0.0789114
$673$	19.5137	0.752197	0.376099	−	0.926580i	$-0.377265\pi$
$673$	19.5137	0.752197	0.376099	+	0.926580i	$0.377265\pi$
$674$	12.6097	0.485708
$675$	0	0
$676$	1.70905	0.0657328
$677$	46.9388	1.80401	0.902003	−	0.431730i	$-0.142097\pi$
$677$	46.9388	1.80401	0.902003	+	0.431730i	$0.142097\pi$
$678$	31.3390	1.20357
$679$	−6.43180	−0.246830
$680$	0	0
$681$	−61.3905	−2.35249
$682$	−1.18265	−0.0452860
$683$	−51.0747	−1.95432	−0.977159	−	0.212511i	$-0.931836\pi$
$683$	−51.0747	−1.95432	−0.977159	+	0.212511i	$0.931836\pi$
$684$	−2.88733	−0.110400
$685$	0	0
$686$	1.36234	0.0520144
$687$	38.3303	1.46239
$688$	19.6596	0.749514
$689$	−1.21831	−0.0464139
$690$	0	0
$691$	−34.6866	−1.31954	−0.659770	−	0.751468i	$-0.729346\pi$
$691$	−34.6866	−1.31954	−0.659770	+	0.751468i	$0.729346\pi$
$692$	−2.14194	−0.0814245
$693$	−1.20618	−0.0458189
$694$	19.3936	0.736170
$695$	0	0
$696$	30.3469	1.15029
$697$	1.66601	0.0631046
$698$	13.9095	0.526483
$699$	32.8328	1.24185
$700$	0	0
$701$	10.2957	0.388864	0.194432	−	0.980916i	$-0.437714\pi$
$701$	10.2957	0.388864	0.194432	+	0.980916i	$0.437714\pi$
$702$	1.20025	0.0453006
$703$	−29.8525	−1.12591
$704$	−3.07632	−0.115943
$705$	0	0
$706$	26.0465	0.980271
$707$	7.70568	0.289802
$708$	0.116509	0.00437866
$709$	28.3988	1.06654	0.533270	−	0.845945i	$-0.320963\pi$
$709$	28.3988	1.06654	0.533270	+	0.845945i	$0.320963\pi$
$710$	0	0
$711$	−20.3100	−0.761684
$712$	−37.0514	−1.38856
$713$	2.39582	0.0897243
$714$	4.56134	0.170704
$715$	0	0
$716$	0.657459	0.0245704
$717$	61.5322	2.29796
$718$	−20.8738	−0.779002
$719$	21.4397	0.799566	0.399783	−	0.916610i	$-0.369085\pi$
$719$	21.4397	0.799566	0.399783	+	0.916610i	$0.369085\pi$
$720$	0	0
$721$	−1.42870	−0.0532076
$722$	23.5216	0.875383
$723$	34.5967	1.28667
$724$	−0.138219	−0.00513686
$725$	0	0
$726$	37.2500	1.38248
$727$	−36.0470	−1.33691	−0.668455	−	0.743752i	$-0.733044\pi$
$727$	−36.0470	−1.33691	−0.668455	+	0.743752i	$0.733044\pi$
$728$	3.11055	0.115284
$729$	−32.5594	−1.20590
$730$	0	0
$731$	7.08845	0.262176
$732$	−3.51850	−0.130048
$733$	18.3814	0.678931	0.339465	−	0.940619i	$-0.389754\pi$
$733$	18.3814	0.678931	0.339465	+	0.940619i	$0.389754\pi$
$734$	13.2446	0.488867
$735$	0	0
$736$	0.813134	0.0299725
$737$	−3.51263	−0.129389
$738$	−5.67693	−0.208971
$739$	26.3563	0.969532	0.484766	−	0.874644i	$-0.338905\pi$
$739$	26.3563	0.969532	0.484766	+	0.874644i	$0.338905\pi$
$740$	0	0
$741$	16.1336	0.592681
$742$	1.55856	0.0572165
$743$	−22.9594	−0.842300	−0.421150	−	0.906991i	$-0.638373\pi$
$743$	−22.9594	−0.842300	−0.421150	+	0.906991i	$0.638373\pi$
$744$	17.6049	0.645428
$745$	0	0
$746$	41.0721	1.50376
$747$	−53.2029	−1.94659
$748$	−0.0694567	−0.00253959
$749$	−6.50433	−0.237663
$750$	0	0
$751$	42.4462	1.54889	0.774443	−	0.632644i	$-0.218030\pi$
$751$	42.4462	1.54889	0.774443	+	0.632644i	$0.218030\pi$
$752$	17.0419	0.621455
$753$	−59.8323	−2.18041
$754$	−5.99157	−0.218200
$755$	0	0
$756$	0.119157	0.00433371
$757$	−27.9077	−1.01432	−0.507161	−	0.861851i	$-0.669305\pi$
$757$	−27.9077	−1.01432	−0.507161	+	0.861851i	$0.669305\pi$
$758$	−17.1467	−0.622797
$759$	0.911546	0.0330870
$760$	0	0
$761$	−11.3993	−0.413224	−0.206612	−	0.978423i	$-0.566244\pi$
$761$	−11.3993	−0.413224	−0.206612	+	0.978423i	$0.566244\pi$
$762$	18.6648	0.676154
$763$	−12.3053	−0.445483
$764$	1.98840	0.0719378
$765$	0	0
$766$	−24.9058	−0.899883
$767$	−0.342422	−0.0123642
$768$	8.64997	0.312129
$769$	48.9532	1.76530	0.882648	−	0.470034i	$-0.155758\pi$
$769$	48.9532	1.76530	0.882648	+	0.470034i	$0.155758\pi$
$770$	0	0
$771$	−31.3982	−1.13078
$772$	−0.107809	−0.00388014
$773$	43.8053	1.57557	0.787783	−	0.615953i	$-0.211229\pi$
$773$	43.8053	1.57557	0.787783	+	0.615953i	$0.211229\pi$
$774$	−24.1539	−0.868195
$775$	0	0
$776$	18.7866	0.674400
$777$	12.4708	0.447389
$778$	38.2603	1.37170
$779$	−7.53842	−0.270092
$780$	0	0
$781$	0.0147816	0.000528926 0
$782$	−1.81313	−0.0648375
$783$	−3.41666	−0.122102
$784$	−3.69119	−0.131828
$785$	0	0
$786$	21.1601	0.754755
$787$	21.1522	0.753996	0.376998	−	0.926214i	$-0.376956\pi$
$787$	21.1522	0.753996	0.376998	+	0.926214i	$0.376956\pi$
$788$	−0.622097	−0.0221613
$789$	78.0386	2.77825
$790$	0	0
$791$	−9.14403	−0.325124
$792$	3.52312	0.125189
$793$	10.3410	0.367219
$794$	8.36842	0.296984
$795$	0	0
$796$	−0.249546	−0.00884493
$797$	5.36333	0.189979	0.0949894	−	0.995478i	$-0.469718\pi$
$797$	5.36333	0.189979	0.0949894	+	0.995478i	$0.469718\pi$
$798$	−20.6393	−0.730624
$799$	6.14464	0.217382
$800$	0	0
$801$	42.2263	1.49199
$802$	25.4654	0.899215
$803$	−3.43691	−0.121286
$804$	3.51263	0.123881
$805$	0	0
$806$	−3.47585	−0.122431
$807$	−13.9986	−0.492773
$808$	−22.5075	−0.791811
$809$	53.7732	1.89056	0.945282	−	0.326255i	$-0.105787\pi$
$809$	53.7732	1.89056	0.945282	+	0.326255i	$0.105787\pi$
$810$	0	0
$811$	−54.9942	−1.93111	−0.965554	−	0.260204i	$-0.916210\pi$
$811$	−54.9942	−1.93111	−0.965554	+	0.260204i	$0.916210\pi$
$812$	−0.594824	−0.0208742
$813$	73.9699	2.59424
$814$	2.44700	0.0857675
$815$	0	0
$816$	−12.3587	−0.432642
$817$	−32.0741	−1.12213
$818$	18.8662	0.659643
$819$	−3.54499	−0.123872
$820$	0	0
$821$	−29.7883	−1.03962	−0.519810	−	0.854282i	$-0.673997\pi$
$821$	−29.7883	−1.03962	−0.519810	+	0.854282i	$0.673997\pi$
$822$	−7.97669	−0.278219
$823$	−24.6064	−0.857726	−0.428863	−	0.903370i	$-0.641086\pi$
$823$	−24.6064	−0.857726	−0.428863	+	0.903370i	$0.641086\pi$
$824$	4.17309	0.145377
$825$	0	0
$826$	0.438054	0.0152418
$827$	−6.34025	−0.220472	−0.110236	−	0.993905i	$-0.535161\pi$
$827$	−6.34025	−0.220472	−0.110236	+	0.993905i	$0.535161\pi$
$828$	−0.479456	−0.0166622
$829$	−42.4940	−1.47588	−0.737939	−	0.674868i	$-0.764201\pi$
$829$	−42.4940	−1.47588	−0.737939	+	0.674868i	$0.764201\pi$
$830$	0	0
$831$	−23.1808	−0.804134
$832$	−9.04140	−0.313454
$833$	−1.33090	−0.0461128
$834$	−11.4360	−0.395997
$835$	0	0
$836$	0.314280	0.0108696
$837$	−1.98208	−0.0685109
$838$	−38.1962	−1.31946
$839$	35.0125	1.20877	0.604383	−	0.796694i	$-0.293420\pi$
$839$	35.0125	1.20877	0.604383	+	0.796694i	$0.293420\pi$
$840$	0	0
$841$	−11.9443	−0.411872
$842$	−1.33502	−0.0460080
$843$	−54.0152	−1.86038
$844$	3.54752	0.122111
$845$	0	0
$846$	−20.9379	−0.719858
$847$	−10.8687	−0.373453
$848$	−4.22284	−0.145013
$849$	28.7478	0.986623
$850$	0	0
$851$	−4.95716	−0.169929
$852$	−0.0147816	−0.000506408 0
$853$	−16.1072	−0.551501	−0.275751	−	0.961229i	$-0.588926\pi$
$853$	−16.1072	−0.551501	−0.275751	+	0.961229i	$0.588926\pi$
$854$	−13.2290	−0.452687
$855$	0	0
$856$	18.9985	0.649355
$857$	−17.3243	−0.591785	−0.295893	−	0.955221i	$-0.595617\pi$
$857$	−17.3243	−0.591785	−0.295893	+	0.955221i	$0.595617\pi$
$858$	−1.32247	−0.0451482
$859$	25.7948	0.880107	0.440053	−	0.897972i	$-0.354960\pi$
$859$	25.7948	0.880107	0.440053	+	0.897972i	$0.354960\pi$
$860$	0	0
$861$	3.14917	0.107323
$862$	26.2642	0.894561
$863$	−4.66571	−0.158823	−0.0794114	−	0.996842i	$-0.525304\pi$
$863$	−4.66571	−0.158823	−0.0794114	+	0.996842i	$0.525304\pi$
$864$	−0.672712	−0.0228861
$865$	0	0
$866$	−23.3499	−0.793460
$867$	38.3112	1.30112
$868$	−0.345071	−0.0117125
$869$	2.21071	0.0749931
$870$	0	0
$871$	−10.3237	−0.349806
$872$	35.9426	1.21717
$873$	−21.4105	−0.724636
$874$	8.20414	0.277509
$875$	0	0
$876$	3.43691	0.116123
$877$	−1.95544	−0.0660304	−0.0330152	−	0.999455i	$-0.510511\pi$
$877$	−1.95544	−0.0660304	−0.0330152	+	0.999455i	$0.510511\pi$
$878$	50.5258	1.70516
$879$	−8.09823	−0.273147
$880$	0	0
$881$	2.24154	0.0755195	0.0377597	−	0.999287i	$-0.487978\pi$
$881$	2.24154	0.0755195	0.0377597	+	0.999287i	$0.487978\pi$
$882$	4.53503	0.152702
$883$	50.0221	1.68338	0.841688	−	0.539964i	$-0.181562\pi$
$883$	50.0221	1.68338	0.841688	+	0.539964i	$0.181562\pi$
$884$	−0.204135	−0.00686581
$885$	0	0
$886$	−35.3878	−1.18888
$887$	−24.7297	−0.830341	−0.415170	−	0.909744i	$-0.636278\pi$
$887$	−24.7297	−0.830341	−0.415170	+	0.909744i	$0.636278\pi$
$888$	−36.4261	−1.22238
$889$	−5.44597	−0.182652
$890$	0	0
$891$	2.86440	0.0959610
$892$	−0.987512	−0.0330643
$893$	−27.8035	−0.930408
$894$	75.9383	2.53976
$895$	0	0
$896$	9.94021	0.332079
$897$	2.67906	0.0894513
$898$	37.3832	1.24749
$899$	9.89441	0.329997
$900$	0	0
$901$	−1.52259	−0.0507247
$902$	0.617923	0.0205746
$903$	13.3989	0.445888
$904$	26.7088	0.888321
$905$	0	0
$906$	64.0799	2.12891
$907$	−27.0249	−0.897346	−0.448673	−	0.893696i	$-0.648103\pi$
$907$	−27.0249	−0.897346	−0.448673	+	0.893696i	$0.648103\pi$
$908$	−3.51473	−0.116641
$909$	25.6511	0.850793
$910$	0	0
$911$	6.58215	0.218076	0.109038	−	0.994038i	$-0.465223\pi$
$911$	6.58215	0.218076	0.109038	+	0.994038i	$0.465223\pi$
$912$	55.9213	1.85174
$913$	5.79104	0.191656
$914$	4.15852	0.137552
$915$	0	0
$916$	2.19449	0.0725080
$917$	−6.17404	−0.203885
$918$	1.50002	0.0495080
$919$	−29.1085	−0.960202	−0.480101	−	0.877213i	$-0.659400\pi$
$919$	−29.1085	−0.960202	−0.480101	+	0.877213i	$0.659400\pi$
$920$	0	0
$921$	0.461580	0.0152096
$922$	−28.9315	−0.952808
$923$	0.0434435	0.00142996
$924$	−0.131290	−0.00431913
$925$	0	0
$926$	−15.0706	−0.495250
$927$	−4.75594	−0.156206
$928$	3.35812	0.110236
$929$	−32.7443	−1.07430	−0.537152	−	0.843485i	$-0.680500\pi$
$929$	−32.7443	−1.07430	−0.537152	+	0.843485i	$0.680500\pi$
$930$	0	0
$931$	6.02209	0.197366
$932$	1.87974	0.0615731
$933$	24.0516	0.787414
$934$	−27.8542	−0.911417
$935$	0	0
$936$	10.3546	0.338449
$937$	−14.3647	−0.469275	−0.234637	−	0.972083i	$-0.575390\pi$
$937$	−14.3647	−0.469275	−0.234637	+	0.972083i	$0.575390\pi$
$938$	13.2069	0.431221
$939$	83.2967	2.71829
$940$	0	0
$941$	−36.0898	−1.17649	−0.588247	−	0.808681i	$-0.700182\pi$
$941$	−36.0898	−1.17649	−0.588247	+	0.808681i	$0.700182\pi$
$942$	−23.6547	−0.770710
$943$	−1.25179	−0.0407640
$944$	−1.18689	−0.0386298
$945$	0	0
$946$	2.62911	0.0854797
$947$	−59.6092	−1.93704	−0.968520	−	0.248936i	$-0.919919\pi$
$947$	−59.6092	−1.93704	−0.968520	+	0.248936i	$0.919919\pi$
$948$	−2.21071	−0.0718004
$949$	−10.1012	−0.327899
$950$	0	0
$951$	17.1035	0.554619
$952$	3.88741	0.125992
$953$	−44.8608	−1.45318	−0.726591	−	0.687070i	$-0.758897\pi$
$953$	−44.8608	−1.45318	−0.726591	+	0.687070i	$0.758897\pi$
$954$	5.18821	0.167975
$955$	0	0
$956$	3.52284	0.113937
$957$	3.76455	0.121691
$958$	5.49917	0.177670
$959$	2.32742	0.0751563
$960$	0	0
$961$	−25.2600	−0.814840
$962$	7.19182	0.231874
$963$	−21.6520	−0.697725
$964$	1.98073	0.0637951
$965$	0	0
$966$	−3.42727	−0.110271
$967$	19.9939	0.642961	0.321480	−	0.946916i	$-0.395820\pi$
$967$	19.9939	0.642961	0.321480	+	0.946916i	$0.395820\pi$
$968$	31.7464	1.02037
$969$	20.1630	0.647728
$970$	0	0
$971$	20.5934	0.660873	0.330437	−	0.943828i	$-0.392804\pi$
$971$	20.5934	0.660873	0.330437	+	0.943828i	$0.392804\pi$
$972$	−3.22187	−0.103342
$973$	3.33677	0.106972
$974$	7.35516	0.235675
$975$	0	0
$976$	35.8434	1.14732
$977$	42.8918	1.37223	0.686115	−	0.727493i	$-0.259315\pi$
$977$	42.8918	1.37223	0.686115	+	0.727493i	$0.259315\pi$
$978$	25.8246	0.825779
$979$	−4.59626	−0.146897
$980$	0	0
$981$	−40.9627	−1.30784
$982$	55.0435	1.75651
$983$	−27.9954	−0.892914	−0.446457	−	0.894805i	$-0.647314\pi$
$983$	−27.9954	−0.892914	−0.446457	+	0.894805i	$0.647314\pi$
$984$	−9.19839	−0.293234
$985$	0	0
$986$	−7.48798	−0.238466
$987$	11.6149	0.369706
$988$	0.923679	0.0293861
$989$	−5.32607	−0.169359
$990$	0	0
$991$	7.26603	0.230813	0.115407	−	0.993318i	$-0.463183\pi$
$991$	7.26603	0.230813	0.115407	+	0.993318i	$0.463183\pi$
$992$	1.94813	0.0618530
$993$	−44.3845	−1.40850
$994$	−0.0555763	−0.00176277
$995$	0	0
$996$	−5.79104	−0.183496
$997$	50.7417	1.60701	0.803503	−	0.595300i	$-0.202967\pi$
$997$	50.7417	1.60701	0.803503	+	0.595300i	$0.202967\pi$
$998$	16.9880	0.537746
$999$	4.10110	0.129753

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4025.2.a.l.1.4		4
5.4	even	2		805.2.a.j.1.1	✓	4
15.14	odd	2		7245.2.a.bc.1.4		4
35.34	odd	2		5635.2.a.w.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
805.2.a.j.1.1	✓	4	5.4	even	2
4025.2.a.l.1.4		4	1.1	even	1	trivial
5635.2.a.w.1.1		4	35.34	odd	2
7245.2.a.bc.1.4		4	15.14	odd	2

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:	\( N \)	\(=\)	\( 4025 = 5^{2} \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4025.a (trivial)

\(f(q)\)	\(=\)	\(q+1.36234 q^{2} -2.51572 q^{3} -0.144030 q^{4} -3.42727 q^{6} +1.00000 q^{7} -2.92090 q^{8} +3.32886 q^{9} +O(q^{10})\)	\(q+1.36234 q^{2} -2.51572 q^{3} -0.144030 q^{4} -3.42727 q^{6} +1.00000 q^{7} -2.92090 q^{8} +3.32886 q^{9} -0.362340 q^{11} +0.362340 q^{12} -1.06493 q^{13} +1.36234 q^{14} -3.69119 q^{16} -1.33090 q^{17} +4.53503 q^{18} +6.02209 q^{19} -2.51572 q^{21} -0.493630 q^{22} +1.00000 q^{23} +7.34817 q^{24} -1.45079 q^{26} -0.827308 q^{27} -0.144030 q^{28} +4.12986 q^{29} +2.39582 q^{31} +0.813134 q^{32} +0.911546 q^{33} -1.81313 q^{34} -0.479456 q^{36} -4.95716 q^{37} +8.20414 q^{38} +2.67906 q^{39} -1.25179 q^{41} -3.42727 q^{42} -5.32607 q^{43} +0.0521879 q^{44} +1.36234 q^{46} -4.61692 q^{47} +9.28602 q^{48} +1.00000 q^{49} +3.34817 q^{51} +0.153382 q^{52} +1.14403 q^{53} -1.12707 q^{54} -2.92090 q^{56} -15.1499 q^{57} +5.62627 q^{58} +0.321545 q^{59} -9.71051 q^{61} +3.26393 q^{62} +3.32886 q^{63} +8.49015 q^{64} +1.24184 q^{66} +9.69429 q^{67} +0.191689 q^{68} -2.51572 q^{69} -0.0407948 q^{71} -9.72325 q^{72} +9.48533 q^{73} -6.75334 q^{74} -0.867363 q^{76} -0.362340 q^{77} +3.64979 q^{78} -6.10119 q^{79} -7.90529 q^{81} -1.70537 q^{82} -15.9823 q^{83} +0.362340 q^{84} -7.25592 q^{86} -10.3896 q^{87} +1.05836 q^{88} +12.6849 q^{89} -1.06493 q^{91} -0.144030 q^{92} -6.02723 q^{93} -6.28981 q^{94} -2.04562 q^{96} -6.43180 q^{97} +1.36234 q^{98} -1.20618 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 3 q^{2} - 6 q^{3} + 3 q^{4} + 4 q^{6} + 4 q^{7} - 6 q^{8} + 6 q^{9}+O(q^{10}) \) 4 * q - 3 * q^2 - 6 * q^3 + 3 * q^4 + 4 * q^6 + 4 * q^7 - 6 * q^8 + 6 * q^9	\( 4 q - 3 q^{2} - 6 q^{3} + 3 q^{4} + 4 q^{6} + 4 q^{7} - 6 q^{8} + 6 q^{9} + 7 q^{11} - 7 q^{12} + 5 q^{13} - 3 q^{14} + q^{16} - 5 q^{17} - 2 q^{18} + 8 q^{19} - 6 q^{21} - 14 q^{22} + 4 q^{23} + 6 q^{24} - 11 q^{26} - 15 q^{27} + 3 q^{28} - 2 q^{29} - 10 q^{33} - 4 q^{34} + q^{36} - 13 q^{37} + 13 q^{38} - 13 q^{39} + q^{41} + 4 q^{42} - 14 q^{43} + 15 q^{44} - 3 q^{46} - 4 q^{47} + 23 q^{48} + 4 q^{49} - 10 q^{51} + 5 q^{52} + q^{53} + 14 q^{54} - 6 q^{56} - 19 q^{57} + 16 q^{58} - 7 q^{59} - 7 q^{61} + 15 q^{62} + 6 q^{63} + 23 q^{66} - 15 q^{67} + 11 q^{68} - 6 q^{69} + 17 q^{72} - 3 q^{73} - 2 q^{74} - 22 q^{76} + 7 q^{77} + 31 q^{78} - 14 q^{79} + 28 q^{81} - 6 q^{82} - 3 q^{83} - 7 q^{84} + 16 q^{86} + 14 q^{87} - 13 q^{88} - 11 q^{89} + 5 q^{91} + 3 q^{92} + 23 q^{93} - 19 q^{94} - 15 q^{96} - 9 q^{97} - 3 q^{98} + 8 q^{99}+O(q^{100}) \) 4 * q - 3 * q^2 - 6 * q^3 + 3 * q^4 + 4 * q^6 + 4 * q^7 - 6 * q^8 + 6 * q^9 + 7 * q^11 - 7 * q^12 + 5 * q^13 - 3 * q^14 + q^16 - 5 * q^17 - 2 * q^18 + 8 * q^19 - 6 * q^21 - 14 * q^22 + 4 * q^23 + 6 * q^24 - 11 * q^26 - 15 * q^27 + 3 * q^28 - 2 * q^29 - 10 * q^33 - 4 * q^34 + q^36 - 13 * q^37 + 13 * q^38 - 13 * q^39 + q^41 + 4 * q^42 - 14 * q^43 + 15 * q^44 - 3 * q^46 - 4 * q^47 + 23 * q^48 + 4 * q^49 - 10 * q^51 + 5 * q^52 + q^53 + 14 * q^54 - 6 * q^56 - 19 * q^57 + 16 * q^58 - 7 * q^59 - 7 * q^61 + 15 * q^62 + 6 * q^63 + 23 * q^66 - 15 * q^67 + 11 * q^68 - 6 * q^69 + 17 * q^72 - 3 * q^73 - 2 * q^74 - 22 * q^76 + 7 * q^77 + 31 * q^78 - 14 * q^79 + 28 * q^81 - 6 * q^82 - 3 * q^83 - 7 * q^84 + 16 * q^86 + 14 * q^87 - 13 * q^88 - 11 * q^89 + 5 * q^91 + 3 * q^92 + 23 * q^93 - 19 * q^94 - 15 * q^96 - 9 * q^97 - 3 * q^98 + 8 * q^99

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