LMFDB - Embedded newform 6025.2.a.h.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6025,2,Mod(1,6025)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6025, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("6025.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6025 = 5^{2} \cdot 241 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6025.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:	$48.1098672178$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} - 14 x^{10} + 44 x^{9} + 65 x^{8} - 219 x^{7} - 123 x^{6} + 444 x^{5} + 105 x^{4} + \cdots - 1 $ x^12 - 3x^11 - 14x^10 + 44x^9 + 65x^8 - 219x^7 - 123x^6 + 444x^5 + 105x^4 - 328x^3 - 45x^2 + 18*x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 241)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$2.49073$ of defining polynomial
Character	$\chi$	$=$	6025.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.49073 q^{2} -1.22208 q^{3} +4.20371 q^{4} +3.04385 q^{6} -0.136122 q^{7} -5.48885 q^{8} -1.50653 q^{9} +O(q^{10})$	\(q-2.49073 q^{2} -1.22208 q^{3} +4.20371 q^{4} +3.04385 q^{6} -0.136122 q^{7} -5.48885 q^{8} -1.50653 q^{9} -0.905365 q^{11} -5.13726 q^{12} +0.123706 q^{13} +0.339044 q^{14} +5.26378 q^{16} -1.26034 q^{17} +3.75236 q^{18} -2.13460 q^{19} +0.166352 q^{21} +2.25502 q^{22} -6.64978 q^{23} +6.70778 q^{24} -0.308118 q^{26} +5.50732 q^{27} -0.572220 q^{28} +5.36862 q^{29} -9.78467 q^{31} -2.13295 q^{32} +1.10642 q^{33} +3.13917 q^{34} -6.33303 q^{36} -5.76688 q^{37} +5.31669 q^{38} -0.151178 q^{39} +6.43642 q^{41} -0.414337 q^{42} +3.18712 q^{43} -3.80590 q^{44} +16.5628 q^{46} -12.9849 q^{47} -6.43274 q^{48} -6.98147 q^{49} +1.54023 q^{51} +0.520025 q^{52} -3.90862 q^{53} -13.7172 q^{54} +0.747155 q^{56} +2.60864 q^{57} -13.3718 q^{58} +8.15085 q^{59} -14.3712 q^{61} +24.3709 q^{62} +0.205073 q^{63} -5.21498 q^{64} -2.75580 q^{66} +4.89534 q^{67} -5.29812 q^{68} +8.12653 q^{69} +4.32869 q^{71} +8.26912 q^{72} -5.64935 q^{73} +14.3637 q^{74} -8.97323 q^{76} +0.123241 q^{77} +0.376543 q^{78} +1.43490 q^{79} -2.21077 q^{81} -16.0314 q^{82} +11.7625 q^{83} +0.699296 q^{84} -7.93825 q^{86} -6.56086 q^{87} +4.96941 q^{88} -13.7381 q^{89} -0.0168392 q^{91} -27.9538 q^{92} +11.9576 q^{93} +32.3419 q^{94} +2.60662 q^{96} -13.6204 q^{97} +17.3889 q^{98} +1.36396 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{2} - q^{3} + 13 q^{4} - q^{6} - 3 q^{7} - 9 q^{8} + 15 q^{9}+O(q^{10}) $ 12 * q - 3 * q^2 - q^3 + 13 * q^4 - q^6 - 3 * q^7 - 9 * q^8 + 15 * q^9	$ 12 q - 3 q^{2} - q^{3} + 13 q^{4} - q^{6} - 3 q^{7} - 9 q^{8} + 15 q^{9} + 22 q^{11} + 7 q^{12} + 5 q^{13} + 6 q^{14} + 15 q^{16} + 4 q^{17} + q^{18} - 6 q^{19} - 14 q^{21} + 12 q^{22} - 32 q^{23} - 15 q^{24} + 8 q^{26} + 5 q^{27} + 11 q^{28} + 6 q^{29} + 8 q^{31} - q^{32} + 24 q^{33} - 19 q^{34} - 8 q^{36} + 8 q^{37} + 10 q^{38} + 31 q^{39} - q^{41} + 49 q^{42} + 2 q^{43} + 42 q^{44} - 25 q^{46} - 34 q^{47} + 49 q^{48} - 9 q^{49} - 3 q^{51} + 41 q^{52} - 5 q^{53} - 40 q^{54} + q^{56} + 22 q^{57} + 33 q^{58} + 26 q^{59} - 26 q^{61} + 17 q^{62} + 4 q^{63} + 13 q^{64} - 2 q^{66} - 6 q^{67} + 35 q^{68} - 2 q^{69} + 94 q^{71} - 17 q^{72} + 22 q^{73} + 26 q^{74} - 20 q^{76} + 7 q^{77} - 54 q^{78} + 9 q^{79} + 4 q^{81} - 15 q^{82} + 8 q^{83} + 2 q^{84} + 9 q^{86} - 4 q^{87} - 6 q^{88} - 3 q^{89} - 20 q^{91} - 36 q^{92} - 12 q^{93} + 48 q^{94} - 23 q^{96} + 29 q^{97} - 28 q^{98} + 36 q^{99}+O(q^{100}) $ 12 * q - 3 * q^2 - q^3 + 13 * q^4 - q^6 - 3 * q^7 - 9 * q^8 + 15 * q^9 + 22 * q^11 + 7 * q^12 + 5 * q^13 + 6 * q^14 + 15 * q^16 + 4 * q^17 + q^18 - 6 * q^19 - 14 * q^21 + 12 * q^22 - 32 * q^23 - 15 * q^24 + 8 * q^26 + 5 * q^27 + 11 * q^28 + 6 * q^29 + 8 * q^31 - q^32 + 24 * q^33 - 19 * q^34 - 8 * q^36 + 8 * q^37 + 10 * q^38 + 31 * q^39 - q^41 + 49 * q^42 + 2 * q^43 + 42 * q^44 - 25 * q^46 - 34 * q^47 + 49 * q^48 - 9 * q^49 - 3 * q^51 + 41 * q^52 - 5 * q^53 - 40 * q^54 + q^56 + 22 * q^57 + 33 * q^58 + 26 * q^59 - 26 * q^61 + 17 * q^62 + 4 * q^63 + 13 * q^64 - 2 * q^66 - 6 * q^67 + 35 * q^68 - 2 * q^69 + 94 * q^71 - 17 * q^72 + 22 * q^73 + 26 * q^74 - 20 * q^76 + 7 * q^77 - 54 * q^78 + 9 * q^79 + 4 * q^81 - 15 * q^82 + 8 * q^83 + 2 * q^84 + 9 * q^86 - 4 * q^87 - 6 * q^88 - 3 * q^89 - 20 * q^91 - 36 * q^92 - 12 * q^93 + 48 * q^94 - 23 * q^96 + 29 * q^97 - 28 * q^98 + 36 * 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 $

$2$	−2.49073	−1.76121	−0.880604	−	0.473852i	$-0.842863\pi$
$2$	−2.49073	−1.76121	−0.880604	+	0.473852i	$0.842863\pi$
$3$	−1.22208	−0.705566	−0.352783	−	0.935705i	$-0.614765\pi$
$3$	−1.22208	−0.705566	−0.352783	+	0.935705i	$0.614765\pi$
$4$	4.20371	2.10186
$5$	0	0
$5$	0	0
$6$	3.04385	1.24265
$7$	−0.136122	−0.0514495	−0.0257247	−	0.999669i	$-0.508189\pi$
$7$	−0.136122	−0.0514495	−0.0257247	+	0.999669i	$0.508189\pi$
$8$	−5.48885	−1.94060
$9$	−1.50653	−0.502177
$10$	0	0
$11$	−0.905365	−0.272978	−0.136489	−	0.990642i	$-0.543582\pi$
$11$	−0.905365	−0.272978	−0.136489	+	0.990642i	$0.543582\pi$
$12$	−5.13726	−1.48300
$13$	0.123706	0.0343099	0.0171549	−	0.999853i	$-0.494539\pi$
$13$	0.123706	0.0343099	0.0171549	+	0.999853i	$0.494539\pi$
$14$	0.339044	0.0906133
$15$	0	0
$16$	5.26378	1.31595
$17$	−1.26034	−0.305678	−0.152839	−	0.988251i	$-0.548842\pi$
$17$	−1.26034	−0.305678	−0.152839	+	0.988251i	$0.548842\pi$
$18$	3.75236	0.884439
$19$	−2.13460	−0.489710	−0.244855	−	0.969560i	$-0.578740\pi$
$19$	−2.13460	−0.489710	−0.244855	+	0.969560i	$0.578740\pi$
$20$	0	0
$21$	0.166352	0.0363010
$22$	2.25502	0.480771
$23$	−6.64978	−1.38657	−0.693287	−	0.720661i	$-0.743838\pi$
$23$	−6.64978	−1.38657	−0.693287	+	0.720661i	$0.743838\pi$
$24$	6.70778	1.36922
$25$	0	0
$26$	−0.308118	−0.0604269
$27$	5.50732	1.05988
$28$	−0.572220	−0.108139
$29$	5.36862	0.996928	0.498464	−	0.866911i	$-0.333898\pi$
$29$	5.36862	0.996928	0.498464	+	0.866911i	$0.333898\pi$
$30$	0	0
$31$	−9.78467	−1.75738	−0.878689	−	0.477395i	$-0.841581\pi$
$31$	−9.78467	−1.75738	−0.878689	+	0.477395i	$0.841581\pi$
$32$	−2.13295	−0.377055
$33$	1.10642	0.192604
$34$	3.13917	0.538363
$35$	0	0
$36$	−6.33303	−1.05550
$37$	−5.76688	−0.948070	−0.474035	−	0.880506i	$-0.657203\pi$
$37$	−5.76688	−0.948070	−0.474035	+	0.880506i	$0.657203\pi$
$38$	5.31669	0.862481
$39$	−0.151178	−0.0242079
$40$	0	0
$41$	6.43642	1.00520	0.502600	−	0.864519i	$-0.332377\pi$
$41$	6.43642	1.00520	0.502600	+	0.864519i	$0.332377\pi$
$42$	−0.414337	−0.0639336
$43$	3.18712	0.486032	0.243016	−	0.970022i	$-0.421863\pi$
$43$	3.18712	0.486032	0.243016	+	0.970022i	$0.421863\pi$
$44$	−3.80590	−0.573761
$45$	0	0
$46$	16.5628	2.44205
$47$	−12.9849	−1.89404	−0.947022	−	0.321168i	$-0.895925\pi$
$47$	−12.9849	−1.89404	−0.947022	+	0.321168i	$0.895925\pi$
$48$	−6.43274	−0.928486
$49$	−6.98147	−0.997353
$50$	0	0
$51$	1.54023	0.215676
$52$	0.520025	0.0721145
$53$	−3.90862	−0.536890	−0.268445	−	0.963295i	$-0.586510\pi$
$53$	−3.90862	−0.536890	−0.268445	+	0.963295i	$0.586510\pi$
$54$	−13.7172	−1.86668
$55$	0	0
$56$	0.747155	0.0998429
$57$	2.60864	0.345522
$58$	−13.3718	−1.75580
$59$	8.15085	1.06115	0.530575	−	0.847638i	$-0.321976\pi$
$59$	8.15085	1.06115	0.530575	+	0.847638i	$0.321976\pi$
$60$	0	0
$61$	−14.3712	−1.84004	−0.920021	−	0.391870i	$-0.871828\pi$
$61$	−14.3712	−1.84004	−0.920021	+	0.391870i	$0.871828\pi$
$62$	24.3709	3.09511
$63$	0.205073	0.0258368
$64$	−5.21498	−0.651873
$65$	0	0
$66$	−2.75580	−0.339216
$67$	4.89534	0.598062	0.299031	−	0.954243i	$-0.403337\pi$
$67$	4.89534	0.598062	0.299031	+	0.954243i	$0.403337\pi$
$68$	−5.29812	−0.642491
$69$	8.12653	0.978319
$70$	0	0
$71$	4.32869	0.513720	0.256860	−	0.966449i	$-0.417312\pi$
$71$	4.32869	0.513720	0.256860	+	0.966449i	$0.417312\pi$
$72$	8.26912	0.974525
$73$	−5.64935	−0.661206	−0.330603	−	0.943770i	$-0.607252\pi$
$73$	−5.64935	−0.661206	−0.330603	+	0.943770i	$0.607252\pi$
$74$	14.3637	1.66975
$75$	0	0
$76$	−8.97323	−1.02930
$77$	0.123241	0.0140446
$78$	0.376543	0.0426351
$79$	1.43490	0.161439	0.0807195	−	0.996737i	$-0.474278\pi$
$79$	1.43490	0.161439	0.0807195	+	0.996737i	$0.474278\pi$
$80$	0	0
$81$	−2.21077	−0.245641
$82$	−16.0314	−1.77037
$83$	11.7625	1.29110	0.645549	−	0.763718i	$-0.276628\pi$
$83$	11.7625	1.29110	0.645549	+	0.763718i	$0.276628\pi$
$84$	0.699296	0.0762994
$85$	0	0
$86$	−7.93825	−0.856004
$87$	−6.56086	−0.703398
$88$	4.96941	0.529741
$89$	−13.7381	−1.45624	−0.728118	−	0.685452i	$-0.759605\pi$
$89$	−13.7381	−1.45624	−0.728118	+	0.685452i	$0.759605\pi$
$90$	0	0
$91$	−0.0168392	−0.00176523
$92$	−27.9538	−2.91438
$93$	11.9576	1.23995
$94$	32.3419	3.33581
$95$	0	0
$96$	2.60662	0.266037
$97$	−13.6204	−1.38294	−0.691472	−	0.722404i	$-0.743037\pi$
$97$	−13.6204	−1.38294	−0.691472	+	0.722404i	$0.743037\pi$
$98$	17.3889	1.75655
$99$	1.36396	0.137083
$100$	0	0
$101$	−0.0787660	−0.00783751	−0.00391876	−	0.999992i	$-0.501247\pi$
$101$	−0.0787660	−0.00783751	−0.00391876	+	0.999992i	$0.501247\pi$
$102$	−3.83630	−0.379850
$103$	6.36701	0.627360	0.313680	−	0.949529i	$-0.398438\pi$
$103$	6.36701	0.627360	0.313680	+	0.949529i	$0.398438\pi$
$104$	−0.679004	−0.0665818
$105$	0	0
$106$	9.73529	0.945575
$107$	1.99570	0.192932	0.0964660	−	0.995336i	$-0.469246\pi$
$107$	1.99570	0.192932	0.0964660	+	0.995336i	$0.469246\pi$
$108$	23.1512	2.22773
$109$	14.8223	1.41972	0.709861	−	0.704341i	$-0.248758\pi$
$109$	14.8223	1.41972	0.709861	+	0.704341i	$0.248758\pi$
$110$	0	0
$111$	7.04756	0.668925
$112$	−0.716519	−0.0677047
$113$	12.3669	1.16338	0.581690	−	0.813410i	$-0.302392\pi$
$113$	12.3669	1.16338	0.581690	+	0.813410i	$0.302392\pi$
$114$	−6.49740	−0.608537
$115$	0	0
$116$	22.5681	2.09540
$117$	−0.186367	−0.0172296
$118$	−20.3015	−1.86891
$119$	0.171561	0.0157270
$120$	0	0
$121$	−10.1803	−0.925483
$122$	35.7947	3.24070
$123$	−7.86579	−0.709234
$124$	−41.1319	−3.69376
$125$	0	0
$126$	−0.510780	−0.0455039
$127$	−15.9678	−1.41691	−0.708456	−	0.705754i	$-0.750608\pi$
$127$	−15.9678	−1.41691	−0.708456	+	0.705754i	$0.750608\pi$
$128$	17.2550	1.52514
$129$	−3.89491	−0.342927
$130$	0	0
$131$	−12.1390	−1.06059	−0.530293	−	0.847814i	$-0.677918\pi$
$131$	−12.1390	−1.06059	−0.530293	+	0.847814i	$0.677918\pi$
$132$	4.65109	0.404826
$133$	0.290566	0.0251953
$134$	−12.1930	−1.05331
$135$	0	0
$136$	6.91783	0.593199
$137$	−0.846052	−0.0722831	−0.0361416	−	0.999347i	$-0.511507\pi$
$137$	−0.846052	−0.0722831	−0.0361416	+	0.999347i	$0.511507\pi$
$138$	−20.2410	−1.72302
$139$	15.6472	1.32717	0.663587	−	0.748099i	$-0.269033\pi$
$139$	15.6472	1.32717	0.663587	+	0.748099i	$0.269033\pi$
$140$	0	0
$141$	15.8685	1.33637
$142$	−10.7816	−0.904769
$143$	−0.111999	−0.00936584
$144$	−7.93006	−0.660838
$145$	0	0
$146$	14.0710	1.16452
$147$	8.53188	0.703698
$148$	−24.2423	−1.99271
$149$	−0.542212	−0.0444198	−0.0222099	−	0.999753i	$-0.507070\pi$
$149$	−0.542212	−0.0444198	−0.0222099	+	0.999753i	$0.507070\pi$
$150$	0	0
$151$	8.53046	0.694199	0.347100	−	0.937828i	$-0.387167\pi$
$151$	8.53046	0.694199	0.347100	+	0.937828i	$0.387167\pi$
$152$	11.7165	0.950331
$153$	1.89875	0.153505
$154$	−0.306958	−0.0247354
$155$	0	0
$156$	−0.635510	−0.0508815
$157$	16.2204	1.29453	0.647263	−	0.762267i	$-0.275914\pi$
$157$	16.2204	1.29453	0.647263	+	0.762267i	$0.275914\pi$
$158$	−3.57394	−0.284328
$159$	4.77662	0.378811
$160$	0	0
$161$	0.905184	0.0713385
$162$	5.50641	0.432625
$163$	−1.36363	−0.106808	−0.0534039	−	0.998573i	$-0.517007\pi$
$163$	−1.36363	−0.106808	−0.0534039	+	0.998573i	$0.517007\pi$
$164$	27.0569	2.11279
$165$	0	0
$166$	−29.2971	−2.27389
$167$	−13.4045	−1.03727	−0.518636	−	0.854995i	$-0.673560\pi$
$167$	−13.4045	−1.03727	−0.518636	+	0.854995i	$0.673560\pi$
$168$	−0.913080	−0.0704457
$169$	−12.9847	−0.998823
$170$	0	0
$171$	3.21584	0.245921
$172$	13.3978	1.02157
$173$	13.6007	1.03404	0.517022	−	0.855972i	$-0.327041\pi$
$173$	13.6007	1.03404	0.517022	+	0.855972i	$0.327041\pi$
$174$	16.3413	1.23883
$175$	0	0
$176$	−4.76565	−0.359224
$177$	−9.96096	−0.748711
$178$	34.2179	2.56474
$179$	23.9070	1.78689	0.893445	−	0.449172i	$-0.148281\pi$
$179$	23.9070	1.78689	0.893445	+	0.449172i	$0.148281\pi$
$180$	0	0
$181$	−11.6044	−0.862545	−0.431273	−	0.902222i	$-0.641935\pi$
$181$	−11.6044	−0.862545	−0.431273	+	0.902222i	$0.641935\pi$
$182$	0.0419418	0.00310893
$183$	17.5627	1.29827
$184$	36.4996	2.69079
$185$	0	0
$186$	−29.7831	−2.18380
$187$	1.14107	0.0834433
$188$	−54.5849	−3.98101
$189$	−0.749670	−0.0545305
$190$	0	0
$191$	−4.85929	−0.351606	−0.175803	−	0.984425i	$-0.556252\pi$
$191$	−4.85929	−0.351606	−0.175803	+	0.984425i	$0.556252\pi$
$192$	6.37310	0.459939
$193$	−25.6451	−1.84597	−0.922987	−	0.384831i	$-0.874260\pi$
$193$	−25.6451	−1.84597	−0.922987	+	0.384831i	$0.874260\pi$
$194$	33.9247	2.43565
$195$	0	0
$196$	−29.3481	−2.09629
$197$	−1.46990	−0.104726	−0.0523629	−	0.998628i	$-0.516675\pi$
$197$	−1.46990	−0.104726	−0.0523629	+	0.998628i	$0.516675\pi$
$198$	−3.39725	−0.241432
$199$	7.46714	0.529332	0.264666	−	0.964340i	$-0.414738\pi$
$199$	7.46714	0.529332	0.264666	+	0.964340i	$0.414738\pi$
$200$	0	0
$201$	−5.98248	−0.421972
$202$	0.196185	0.0138035
$203$	−0.730790	−0.0512914
$204$	6.47470	0.453320
$205$	0	0
$206$	−15.8585	−1.10491
$207$	10.0181	0.696306
$208$	0.651162	0.0451500
$209$	1.93259	0.133680
$210$	0	0
$211$	−20.1549	−1.38752	−0.693759	−	0.720208i	$-0.744047\pi$
$211$	−20.1549	−1.38752	−0.693759	+	0.720208i	$0.744047\pi$
$212$	−16.4307	−1.12847
$213$	−5.28998	−0.362463
$214$	−4.97075	−0.339793
$215$	0	0
$216$	−30.2288	−2.05681
$217$	1.33191	0.0904162
$218$	−36.9184	−2.50043
$219$	6.90393	0.466524
$220$	0	0
$221$	−0.155912	−0.0104878
$222$	−17.5535	−1.17812
$223$	8.91317	0.596870	0.298435	−	0.954430i	$-0.403535\pi$
$223$	8.91317	0.596870	0.298435	+	0.954430i	$0.403535\pi$
$224$	0.290342	0.0193993
$225$	0	0
$226$	−30.8026	−2.04896
$227$	17.2725	1.14642	0.573209	−	0.819409i	$-0.305698\pi$
$227$	17.2725	1.14642	0.573209	+	0.819409i	$0.305698\pi$
$228$	10.9660	0.726239
$229$	−12.9392	−0.855044	−0.427522	−	0.904005i	$-0.640613\pi$
$229$	−12.9392	−0.855044	−0.427522	+	0.904005i	$0.640613\pi$
$230$	0	0
$231$	−0.150609	−0.00990936
$232$	−29.4675	−1.93464
$233$	24.8301	1.62668	0.813338	−	0.581791i	$-0.197648\pi$
$233$	24.8301	1.62668	0.813338	+	0.581791i	$0.197648\pi$
$234$	0.464189	0.0303450
$235$	0	0
$236$	34.2639	2.23039
$237$	−1.75356	−0.113906
$238$	−0.427311	−0.0276985
$239$	7.52122	0.486507	0.243254	−	0.969963i	$-0.421785\pi$
$239$	7.52122	0.486507	0.243254	+	0.969963i	$0.421785\pi$
$240$	0	0
$241$	1.00000	0.0644157
$241$	1.00000	0.0644157
$242$	25.3564	1.62997
$243$	−13.8202	−0.886569
$244$	−60.4123	−3.86750
$245$	0	0
$246$	19.5915	1.24911
$247$	−0.264062	−0.0168019
$248$	53.7065	3.41037
$249$	−14.3746	−0.910955
$250$	0	0
$251$	−30.0279	−1.89534	−0.947671	−	0.319250i	$-0.896569\pi$
$251$	−30.0279	−1.89534	−0.947671	+	0.319250i	$0.896569\pi$
$252$	0.862068	0.0543052
$253$	6.02048	0.378504
$254$	39.7714	2.49548
$255$	0	0
$256$	−32.5475	−2.03422
$257$	9.93458	0.619702	0.309851	−	0.950785i	$-0.399721\pi$
$257$	9.93458	0.619702	0.309851	+	0.950785i	$0.399721\pi$
$258$	9.70114	0.603967
$259$	0.785002	0.0487777
$260$	0	0
$261$	−8.08800	−0.500634
$262$	30.2348	1.86791
$263$	−18.4575	−1.13814	−0.569069	−	0.822290i	$-0.692696\pi$
$263$	−18.4575	−1.13814	−0.569069	+	0.822290i	$0.692696\pi$
$264$	−6.07300	−0.373767
$265$	0	0
$266$	−0.723721	−0.0443742
$267$	16.7890	1.02747
$268$	20.5786	1.25704
$269$	−1.14902	−0.0700569	−0.0350285	−	0.999386i	$-0.511152\pi$
$269$	−1.14902	−0.0700569	−0.0350285	+	0.999386i	$0.511152\pi$
$270$	0	0
$271$	12.2034	0.741303	0.370651	−	0.928772i	$-0.379134\pi$
$271$	12.2034	0.741303	0.370651	+	0.928772i	$0.379134\pi$
$272$	−6.63417	−0.402256
$273$	0.0205787	0.00124548
$274$	2.10728	0.127306
$275$	0	0
$276$	34.1616	2.05629
$277$	4.31327	0.259159	0.129580	−	0.991569i	$-0.458637\pi$
$277$	4.31327	0.259159	0.129580	+	0.991569i	$0.458637\pi$
$278$	−38.9728	−2.33743
$279$	14.7409	0.882515
$280$	0	0
$281$	−17.1399	−1.02248	−0.511240	−	0.859438i	$-0.670814\pi$
$281$	−17.1399	−1.02248	−0.511240	+	0.859438i	$0.670814\pi$
$282$	−39.5242	−2.35363
$283$	−13.8905	−0.825704	−0.412852	−	0.910798i	$-0.635467\pi$
$283$	−13.8905	−0.825704	−0.412852	+	0.910798i	$0.635467\pi$
$284$	18.1966	1.07977
$285$	0	0
$286$	0.278959	0.0164952
$287$	−0.876142	−0.0517170
$288$	3.21335	0.189349
$289$	−15.4115	−0.906561
$290$	0	0
$291$	16.6452	0.975757
$292$	−23.7482	−1.38976
$293$	0.325090	0.0189920	0.00949598	−	0.999955i	$-0.496977\pi$
$293$	0.325090	0.0189920	0.00949598	+	0.999955i	$0.496977\pi$
$294$	−21.2506	−1.23936
$295$	0	0
$296$	31.6535	1.83982
$297$	−4.98614	−0.289325
$298$	1.35050	0.0782325
$299$	−0.822618	−0.0475732
$300$	0	0
$301$	−0.433839	−0.0250061
$302$	−21.2470	−1.22263
$303$	0.0962580	0.00552988
$304$	−11.2360	−0.644432
$305$	0	0
$306$	−4.72926	−0.270354
$307$	14.3600	0.819566	0.409783	−	0.912183i	$-0.365604\pi$
$307$	14.3600	0.819566	0.409783	+	0.912183i	$0.365604\pi$
$308$	0.518068	0.0295197
$309$	−7.78096	−0.442644
$310$	0	0
$311$	−11.2072	−0.635502	−0.317751	−	0.948174i	$-0.602928\pi$
$311$	−11.2072	−0.635502	−0.317751	+	0.948174i	$0.602928\pi$
$312$	0.829794	0.0469778
$313$	−19.3860	−1.09576	−0.547879	−	0.836557i	$-0.684565\pi$
$313$	−19.3860	−1.09576	−0.547879	+	0.836557i	$0.684565\pi$
$314$	−40.4005	−2.27993
$315$	0	0
$316$	6.03191	0.339322
$317$	−5.19578	−0.291824	−0.145912	−	0.989298i	$-0.546612\pi$
$317$	−5.19578	−0.291824	−0.145912	+	0.989298i	$0.546612\pi$
$318$	−11.8973	−0.667165
$319$	−4.86056	−0.272139
$320$	0	0
$321$	−2.43890	−0.136126
$322$	−2.25457	−0.125642
$323$	2.69032	0.149693
$324$	−9.29343	−0.516302
$325$	0	0
$326$	3.39643	0.188111
$327$	−18.1140	−1.00171
$328$	−35.3285	−1.95069
$329$	1.76754	0.0974476
$330$	0	0
$331$	0.0173250	0.000952268 0	0.000476134	−	1.00000i	$-0.499848\pi$
$331$	0.0173250	0.000952268 0	0.000476134		1.00000i	$0.499848\pi$
$332$	49.4461	2.71371
$333$	8.68799	0.476099
$334$	33.3869	1.82685
$335$	0	0
$336$	0.875641	0.0477701
$337$	−0.347899	−0.0189513	−0.00947563	−	0.999955i	$-0.503016\pi$
$337$	−0.347899	−0.0189513	−0.00947563	+	0.999955i	$0.503016\pi$
$338$	32.3413	1.75914
$339$	−15.1133	−0.820841
$340$	0	0
$341$	8.85870	0.479725
$342$	−8.00976	−0.433118
$343$	1.90319	0.102763
$344$	−17.4936	−0.943194
$345$	0	0
$346$	−33.8756	−1.82117
$347$	−6.37601	−0.342282	−0.171141	−	0.985247i	$-0.554745\pi$
$347$	−6.37601	−0.342282	−0.171141	+	0.985247i	$0.554745\pi$
$348$	−27.5800	−1.47844
$349$	−0.970720	−0.0519614	−0.0259807	−	0.999662i	$-0.508271\pi$
$349$	−0.970720	−0.0519614	−0.0259807	+	0.999662i	$0.508271\pi$
$350$	0	0
$351$	0.681289	0.0363645
$352$	1.93110	0.102928
$353$	−30.5488	−1.62595	−0.812975	−	0.582299i	$-0.802153\pi$
$353$	−30.5488	−1.62595	−0.812975	+	0.582299i	$0.802153\pi$
$354$	24.8100	1.31864
$355$	0	0
$356$	−57.7511	−3.06080
$357$	−0.209660	−0.0110964
$358$	−59.5457	−3.14709
$359$	8.22124	0.433901	0.216950	−	0.976183i	$-0.430389\pi$
$359$	8.22124	0.433901	0.216950	+	0.976183i	$0.430389\pi$
$360$	0	0
$361$	−14.4435	−0.760184
$362$	28.9033	1.51912
$363$	12.4411	0.652989
$364$	−0.0707871	−0.00371025
$365$	0	0
$366$	−43.7438	−2.28652
$367$	−25.1108	−1.31077	−0.655387	−	0.755294i	$-0.727494\pi$
$367$	−25.1108	−1.31077	−0.655387	+	0.755294i	$0.727494\pi$
$368$	−35.0030	−1.82466
$369$	−9.69667	−0.504789
$370$	0	0
$371$	0.532051	0.0276227
$372$	50.2663	2.60619
$373$	27.0231	1.39920	0.699601	−	0.714534i	$-0.253361\pi$
$373$	27.0231	1.39920	0.699601	+	0.714534i	$0.253361\pi$
$374$	−2.84209	−0.146961
$375$	0	0
$376$	71.2722	3.67558
$377$	0.664131	0.0342045
$378$	1.86722	0.0960396
$379$	22.9961	1.18123	0.590616	−	0.806953i	$-0.298885\pi$
$379$	22.9961	1.18123	0.590616	+	0.806953i	$0.298885\pi$
$380$	0	0
$381$	19.5139	0.999725
$382$	12.1032	0.619252
$383$	−3.72670	−0.190425	−0.0952126	−	0.995457i	$-0.530353\pi$
$383$	−3.72670	−0.190425	−0.0952126	+	0.995457i	$0.530353\pi$
$384$	−21.0869	−1.07609
$385$	0	0
$386$	63.8749	3.25115
$387$	−4.80151	−0.244074
$388$	−57.2563	−2.90675
$389$	4.72525	0.239580	0.119790	−	0.992799i	$-0.461778\pi$
$389$	4.72525	0.239580	0.119790	+	0.992799i	$0.461778\pi$
$390$	0	0
$391$	8.38100	0.423845
$392$	38.3202	1.93546
$393$	14.8347	0.748313
$394$	3.66111	0.184444
$395$	0	0
$396$	5.73370	0.288129
$397$	−32.2227	−1.61721	−0.808606	−	0.588350i	$-0.799778\pi$
$397$	−32.2227	−1.61721	−0.808606	+	0.588350i	$0.799778\pi$
$398$	−18.5986	−0.932264
$399$	−0.355094	−0.0177769
$400$	0	0
$401$	−6.02370	−0.300809	−0.150405	−	0.988625i	$-0.548058\pi$
$401$	−6.02370	−0.300809	−0.150405	+	0.988625i	$0.548058\pi$
$402$	14.9007	0.743180
$403$	−1.21042	−0.0602955
$404$	−0.331110	−0.0164733
$405$	0	0
$406$	1.82020	0.0903349
$407$	5.22113	0.258802
$408$	−8.45411	−0.418541
$409$	18.5405	0.916767	0.458384	−	0.888754i	$-0.348429\pi$
$409$	18.5405	0.916767	0.458384	+	0.888754i	$0.348429\pi$
$410$	0	0
$411$	1.03394	0.0510005
$412$	26.7651	1.31862
$413$	−1.10951	−0.0545956
$414$	−24.9523	−1.22634
$415$	0	0
$416$	−0.263858	−0.0129367
$417$	−19.1220	−0.936409
$418$	−4.81355	−0.235438
$419$	29.7394	1.45286	0.726432	−	0.687238i	$-0.241177\pi$
$419$	29.7394	1.45286	0.726432	+	0.687238i	$0.241177\pi$
$420$	0	0
$421$	2.65516	0.129405	0.0647023	−	0.997905i	$-0.479390\pi$
$421$	2.65516	0.129405	0.0647023	+	0.997905i	$0.479390\pi$
$422$	50.2002	2.44371
$423$	19.5622	0.951146
$424$	21.4538	1.04189
$425$	0	0
$426$	13.1759	0.638374
$427$	1.95624	0.0946691
$428$	8.38937	0.405515
$429$	0.136871	0.00660822
$430$	0	0
$431$	27.9512	1.34636	0.673181	−	0.739478i	$-0.264927\pi$
$431$	27.9512	1.34636	0.673181	+	0.739478i	$0.264927\pi$
$432$	28.9893	1.39475
$433$	−13.5815	−0.652687	−0.326344	−	0.945251i	$-0.605817\pi$
$433$	−13.5815	−0.652687	−0.326344	+	0.945251i	$0.605817\pi$
$434$	−3.31743	−0.159242
$435$	0	0
$436$	62.3089	2.98405
$437$	14.1946	0.679019
$438$	−17.1958	−0.821647
$439$	27.3113	1.30350	0.651748	−	0.758435i	$-0.274036\pi$
$439$	27.3113	1.30350	0.651748	+	0.758435i	$0.274036\pi$
$440$	0	0
$441$	10.5178	0.500848
$442$	0.388334	0.0184712
$443$	−4.06001	−0.192897	−0.0964484	−	0.995338i	$-0.530748\pi$
$443$	−4.06001	−0.192897	−0.0964484	+	0.995338i	$0.530748\pi$
$444$	29.6259	1.40599
$445$	0	0
$446$	−22.2003	−1.05121
$447$	0.662624	0.0313410
$448$	0.709876	0.0335385
$449$	−1.53571	−0.0724746	−0.0362373	−	0.999343i	$-0.511537\pi$
$449$	−1.53571	−0.0724746	−0.0362373	+	0.999343i	$0.511537\pi$
$450$	0	0
$451$	−5.82731	−0.274397
$452$	51.9869	2.44526
$453$	−10.4249	−0.489803
$454$	−43.0211	−2.01908
$455$	0	0
$456$	−14.3184	−0.670521
$457$	4.50705	0.210831	0.105415	−	0.994428i	$-0.466383\pi$
$457$	4.50705	0.210831	0.105415	+	0.994428i	$0.466383\pi$
$458$	32.2279	1.50591
$459$	−6.94111	−0.323983
$460$	0	0
$461$	17.5820	0.818875	0.409438	−	0.912338i	$-0.365725\pi$
$461$	17.5820	0.818875	0.409438	+	0.912338i	$0.365725\pi$
$462$	0.375126	0.0174525
$463$	42.1082	1.95693	0.978466	−	0.206407i	$-0.0661772\pi$
$463$	42.1082	1.95693	0.978466	+	0.206407i	$0.0661772\pi$
$464$	28.2592	1.31190
$465$	0	0
$466$	−61.8451	−2.86492
$467$	−10.6368	−0.492210	−0.246105	−	0.969243i	$-0.579151\pi$
$467$	−10.6368	−0.492210	−0.246105	+	0.969243i	$0.579151\pi$
$468$	−0.783434	−0.0362143
$469$	−0.666367	−0.0307699
$470$	0	0
$471$	−19.8225	−0.913373
$472$	−44.7388	−2.05927
$473$	−2.88551	−0.132676
$474$	4.36763	0.200612
$475$	0	0
$476$	0.721193	0.0330558
$477$	5.88845	0.269614
$478$	−18.7333	−0.856841
$479$	24.3303	1.11168	0.555839	−	0.831290i	$-0.312397\pi$
$479$	24.3303	1.11168	0.555839	+	0.831290i	$0.312397\pi$
$480$	0	0
$481$	−0.713398	−0.0325282
$482$	−2.49073	−0.113449
$483$	−1.10620	−0.0503340
$484$	−42.7951	−1.94523
$485$	0	0
$486$	34.4224	1.56143
$487$	−15.1777	−0.687768	−0.343884	−	0.939012i	$-0.611743\pi$
$487$	−15.1777	−0.687768	−0.343884	+	0.939012i	$0.611743\pi$
$488$	78.8812	3.57079
$489$	1.66646	0.0753598
$490$	0	0
$491$	10.0194	0.452169	0.226084	−	0.974108i	$-0.427408\pi$
$491$	10.0194	0.452169	0.226084	+	0.974108i	$0.427408\pi$
$492$	−33.0655	−1.49071
$493$	−6.76630	−0.304739
$494$	0.657707	0.0295916
$495$	0	0
$496$	−51.5044	−2.31261
$497$	−0.589231	−0.0264306
$498$	35.8032	1.60438
$499$	−7.82989	−0.350514	−0.175257	−	0.984523i	$-0.556076\pi$
$499$	−7.82989	−0.350514	−0.175257	+	0.984523i	$0.556076\pi$
$500$	0	0
$501$	16.3813	0.731863
$502$	74.7911	3.33809
$503$	7.39455	0.329707	0.164853	−	0.986318i	$-0.447285\pi$
$503$	7.39455	0.329707	0.164853	+	0.986318i	$0.447285\pi$
$504$	−1.12561	−0.0501388
$505$	0	0
$506$	−14.9954	−0.666625
$507$	15.8683	0.704735
$508$	−67.1241	−2.97815
$509$	13.7526	0.609572	0.304786	−	0.952421i	$-0.401415\pi$
$509$	13.7526	0.609572	0.304786	+	0.952421i	$0.401415\pi$
$510$	0	0
$511$	0.769003	0.0340187
$512$	46.5568	2.05754
$513$	−11.7559	−0.519036
$514$	−24.7443	−1.09143
$515$	0	0
$516$	−16.3731	−0.720784
$517$	11.7561	0.517032
$518$	−1.95523	−0.0859077
$519$	−16.6211	−0.729585
$520$	0	0
$521$	−14.2825	−0.625730	−0.312865	−	0.949798i	$-0.601289\pi$
$521$	−14.2825	−0.625730	−0.312865	+	0.949798i	$0.601289\pi$
$522$	20.1450	0.881722
$523$	29.4674	1.28852	0.644260	−	0.764806i	$-0.277165\pi$
$523$	29.4674	1.28852	0.644260	+	0.764806i	$0.277165\pi$
$524$	−51.0287	−2.22920
$525$	0	0
$526$	45.9726	2.00450
$527$	12.3320	0.537192
$528$	5.82398	0.253456
$529$	21.2195	0.922589
$530$	0	0
$531$	−12.2795	−0.532886
$532$	1.22146	0.0529569
$533$	0.796224	0.0344883
$534$	−41.8168	−1.80959
$535$	0	0
$536$	−26.8698	−1.16060
$537$	−29.2161	−1.26077
$538$	2.86189	0.123385
$539$	6.32078	0.272255
$540$	0	0
$541$	31.6583	1.36110	0.680549	−	0.732703i	$-0.261741\pi$
$541$	31.6583	1.36110	0.680549	+	0.732703i	$0.261741\pi$
$542$	−30.3953	−1.30559
$543$	14.1814	0.608582
$544$	2.68824	0.115257
$545$	0	0
$546$	−0.0512560	−0.00219355
$547$	31.5186	1.34764	0.673820	−	0.738896i	$-0.264652\pi$
$547$	31.5186	1.34764	0.673820	+	0.738896i	$0.264652\pi$
$548$	−3.55656	−0.151929
$549$	21.6506	0.924027
$550$	0	0
$551$	−11.4598	−0.488205
$552$	−44.6053	−1.89853
$553$	−0.195322	−0.00830595
$554$	−10.7432	−0.456434
$555$	0	0
$556$	65.7762	2.78953
$557$	32.3589	1.37109	0.685545	−	0.728030i	$-0.259564\pi$
$557$	32.3589	1.37109	0.685545	+	0.728030i	$0.259564\pi$
$558$	−36.7156	−1.55429
$559$	0.394267	0.0166757
$560$	0	0
$561$	−1.39447	−0.0588747
$562$	42.6907	1.80080
$563$	−20.8428	−0.878419	−0.439209	−	0.898385i	$-0.644741\pi$
$563$	−20.8428	−0.878419	−0.439209	+	0.898385i	$0.644741\pi$
$564$	66.7068	2.80886
$565$	0	0
$566$	34.5974	1.45424
$567$	0.300935	0.0126381
$568$	−23.7595	−0.996926
$569$	26.6787	1.11843	0.559215	−	0.829022i	$-0.311103\pi$
$569$	26.6787	1.11843	0.559215	+	0.829022i	$0.311103\pi$
$570$	0	0
$571$	0.500659	0.0209519	0.0104760	−	0.999945i	$-0.496665\pi$
$571$	0.500659	0.0209519	0.0104760	+	0.999945i	$0.496665\pi$
$572$	−0.470813	−0.0196857
$573$	5.93842	0.248081
$574$	2.18223	0.0910844
$575$	0	0
$576$	7.85654	0.327356
$577$	9.59281	0.399354	0.199677	−	0.979862i	$-0.436011\pi$
$577$	9.59281	0.399354	0.199677	+	0.979862i	$0.436011\pi$
$578$	38.3859	1.59664
$579$	31.3402	1.30246
$580$	0	0
$581$	−1.60114	−0.0664263
$582$	−41.4586	−1.71851
$583$	3.53873	0.146559
$584$	31.0084	1.28314
$585$	0	0
$586$	−0.809710	−0.0334488
$587$	−19.6676	−0.811770	−0.405885	−	0.913924i	$-0.633037\pi$
$587$	−19.6676	−0.811770	−0.405885	+	0.913924i	$0.633037\pi$
$588$	35.8656	1.47907
$589$	20.8863	0.860605
$590$	0	0
$591$	1.79632	0.0738909
$592$	−30.3556	−1.24761
$593$	−35.9622	−1.47679	−0.738394	−	0.674369i	$-0.764416\pi$
$593$	−35.9622	−1.47679	−0.738394	+	0.674369i	$0.764416\pi$
$594$	12.4191	0.509562
$595$	0	0
$596$	−2.27931	−0.0933640
$597$	−9.12541	−0.373478
$598$	2.04892	0.0837864
$599$	−8.60123	−0.351437	−0.175718	−	0.984440i	$-0.556225\pi$
$599$	−8.60123	−0.351437	−0.175718	+	0.984440i	$0.556225\pi$
$600$	0	0
$601$	36.8567	1.50342	0.751708	−	0.659496i	$-0.229230\pi$
$601$	36.8567	1.50342	0.751708	+	0.659496i	$0.229230\pi$
$602$	1.08057	0.0440409
$603$	−7.37499	−0.300333
$604$	35.8596	1.45911
$605$	0	0
$606$	−0.239752	−0.00973927
$607$	38.6665	1.56942	0.784712	−	0.619861i	$-0.212811\pi$
$607$	38.6665	1.56942	0.784712	+	0.619861i	$0.212811\pi$
$608$	4.55298	0.184648
$609$	0.893080	0.0361894
$610$	0	0
$611$	−1.60631	−0.0649845
$612$	7.98179	0.322645
$613$	38.3341	1.54830	0.774150	−	0.633002i	$-0.218178\pi$
$613$	38.3341	1.54830	0.774150	+	0.633002i	$0.218178\pi$
$614$	−35.7667	−1.44343
$615$	0	0
$616$	−0.676449	−0.0272549
$617$	44.3829	1.78679	0.893395	−	0.449272i	$-0.148317\pi$
$617$	44.3829	1.78679	0.893395	+	0.449272i	$0.148317\pi$
$618$	19.3802	0.779588
$619$	−15.6150	−0.627619	−0.313810	−	0.949486i	$-0.601605\pi$
$619$	−15.6150	−0.627619	−0.313810	+	0.949486i	$0.601605\pi$
$620$	0	0
$621$	−36.6225	−1.46961
$622$	27.9141	1.11925
$623$	1.87007	0.0749226
$624$	−0.795769	−0.0318563
$625$	0	0
$626$	48.2851	1.92986
$627$	−2.36177	−0.0943200
$628$	68.1858	2.72091
$629$	7.26825	0.289804
$630$	0	0
$631$	−7.52472	−0.299555	−0.149777	−	0.988720i	$-0.547856\pi$
$631$	−7.52472	−0.299555	−0.149777	+	0.988720i	$0.547856\pi$
$632$	−7.87595	−0.313288
$633$	24.6307	0.978984
$634$	12.9413	0.513963
$635$	0	0
$636$	20.0796	0.796206
$637$	−0.863650	−0.0342191
$638$	12.1063	0.479294
$639$	−6.52130	−0.257979
$640$	0	0
$641$	2.42509	0.0957851	0.0478926	−	0.998852i	$-0.484749\pi$
$641$	2.42509	0.0957851	0.0478926	+	0.998852i	$0.484749\pi$
$642$	6.07463	0.239747
$643$	−12.1224	−0.478061	−0.239030	−	0.971012i	$-0.576830\pi$
$643$	−12.1224	−0.478061	−0.239030	+	0.971012i	$0.576830\pi$
$644$	3.80514	0.149943
$645$	0	0
$646$	−6.70085	−0.263642
$647$	−12.4628	−0.489964	−0.244982	−	0.969528i	$-0.578782\pi$
$647$	−12.4628	−0.489964	−0.244982	+	0.969528i	$0.578782\pi$
$648$	12.1346	0.476691
$649$	−7.37950	−0.289671
$650$	0	0
$651$	−1.62770	−0.0637945
$652$	−5.73231	−0.224495
$653$	49.4695	1.93589	0.967945	−	0.251163i	$-0.0808131\pi$
$653$	49.4695	1.93589	0.967945	+	0.251163i	$0.0808131\pi$
$654$	45.1171	1.76422
$655$	0	0
$656$	33.8799	1.32279
$657$	8.51092	0.332043
$658$	−4.40245	−0.171626
$659$	19.5067	0.759874	0.379937	−	0.925012i	$-0.375946\pi$
$659$	19.5067	0.759874	0.379937	+	0.925012i	$0.375946\pi$
$660$	0	0
$661$	33.2398	1.29288	0.646439	−	0.762966i	$-0.276258\pi$
$661$	33.2398	1.29288	0.646439	+	0.762966i	$0.276258\pi$
$662$	−0.0431518	−0.00167714
$663$	0.190536	0.00739982
$664$	−64.5624	−2.50551
$665$	0	0
$666$	−21.6394	−0.838510
$667$	−35.7001	−1.38231
$668$	−56.3487	−2.18020
$669$	−10.8926	−0.421131
$670$	0	0
$671$	13.0112	0.502291
$672$	−0.354820	−0.0136875
$673$	−28.8764	−1.11310	−0.556552	−	0.830813i	$-0.687876\pi$
$673$	−28.8764	−1.11310	−0.556552	+	0.830813i	$0.687876\pi$
$674$	0.866521	0.0333771
$675$	0	0
$676$	−54.5840	−2.09938
$677$	−29.4480	−1.13178	−0.565889	−	0.824482i	$-0.691467\pi$
$677$	−29.4480	−1.13178	−0.565889	+	0.824482i	$0.691467\pi$
$678$	37.6431	1.44567
$679$	1.85404	0.0711517
$680$	0	0
$681$	−21.1083	−0.808873
$682$	−22.0646	−0.844897
$683$	−19.6959	−0.753643	−0.376821	−	0.926286i	$-0.622983\pi$
$683$	−19.6959	−0.753643	−0.376821	+	0.926286i	$0.622983\pi$
$684$	13.5185	0.516891
$685$	0	0
$686$	−4.74033	−0.180987
$687$	15.8126	0.603289
$688$	16.7763	0.639592
$689$	−0.483520	−0.0184206
$690$	0	0
$691$	15.6587	0.595683	0.297842	−	0.954615i	$-0.403733\pi$
$691$	15.6587	0.595683	0.297842	+	0.954615i	$0.403733\pi$
$692$	57.1735	2.17341
$693$	−0.185666	−0.00705286
$694$	15.8809	0.602830
$695$	0	0
$696$	36.0115	1.36501
$697$	−8.11209	−0.307267
$698$	2.41780	0.0915149
$699$	−30.3443	−1.14773
$700$	0	0
$701$	32.6726	1.23403	0.617014	−	0.786952i	$-0.288342\pi$
$701$	32.6726	1.23403	0.617014	+	0.786952i	$0.288342\pi$
$702$	−1.69690	−0.0640455
$703$	12.3100	0.464279
$704$	4.72146	0.177947
$705$	0	0
$706$	76.0887	2.86364
$707$	0.0107218	0.000403236 0
$708$	−41.8730	−1.57368
$709$	−5.63690	−0.211698	−0.105849	−	0.994382i	$-0.533756\pi$
$709$	−5.63690	−0.211698	−0.105849	+	0.994382i	$0.533756\pi$
$710$	0	0
$711$	−2.16172	−0.0810710
$712$	75.4064	2.82597
$713$	65.0659	2.43674
$714$	0.522207	0.0195431
$715$	0	0
$716$	100.498	3.75579
$717$	−9.19150	−0.343263
$718$	−20.4769	−0.764190
$719$	13.2196	0.493006	0.246503	−	0.969142i	$-0.420718\pi$
$719$	13.2196	0.493006	0.246503	+	0.969142i	$0.420718\pi$
$720$	0	0
$721$	−0.866693	−0.0322773
$722$	35.9748	1.33884
$723$	−1.22208	−0.0454495
$724$	−48.7814	−1.81295
$725$	0	0
$726$	−30.9874	−1.15005
$727$	−21.6517	−0.803018	−0.401509	−	0.915855i	$-0.631514\pi$
$727$	−21.6517	−0.803018	−0.401509	+	0.915855i	$0.631514\pi$
$728$	0.0924277	0.00342560
$729$	23.5217	0.871173
$730$	0	0
$731$	−4.01687	−0.148569
$732$	73.8284	2.72878
$733$	37.5385	1.38651	0.693257	−	0.720690i	$-0.256175\pi$
$733$	37.5385	1.38651	0.693257	+	0.720690i	$0.256175\pi$
$734$	62.5441	2.30855
$735$	0	0
$736$	14.1836	0.522815
$737$	−4.43208	−0.163258
$738$	24.1517	0.889038
$739$	−28.8751	−1.06219	−0.531093	−	0.847313i	$-0.678219\pi$
$739$	−28.8751	−1.06219	−0.531093	+	0.847313i	$0.678219\pi$
$740$	0	0
$741$	0.322704	0.0118548
$742$	−1.32519	−0.0486493
$743$	24.5272	0.899817	0.449909	−	0.893075i	$-0.351457\pi$
$743$	24.5272	0.899817	0.449909	+	0.893075i	$0.351457\pi$
$744$	−65.6334	−2.40624
$745$	0	0
$746$	−67.3070	−2.46429
$747$	−17.7205	−0.648361
$748$	4.79673	0.175386
$749$	−0.271660	−0.00992624
$750$	0	0
$751$	38.3355	1.39888	0.699442	−	0.714689i	$-0.253432\pi$
$751$	38.3355	1.39888	0.699442	+	0.714689i	$0.253432\pi$
$752$	−68.3498	−2.49246
$753$	36.6963	1.33729
$754$	−1.65417	−0.0602412
$755$	0	0
$756$	−3.15140	−0.114615
$757$	−31.6239	−1.14939	−0.574694	−	0.818368i	$-0.694879\pi$
$757$	−31.6239	−1.14939	−0.574694	+	0.818368i	$0.694879\pi$
$758$	−57.2771	−2.08040
$759$	−7.35748	−0.267060
$760$	0	0
$761$	−28.4924	−1.03285	−0.516424	−	0.856333i	$-0.672737\pi$
$761$	−28.4924	−1.03285	−0.516424	+	0.856333i	$0.672737\pi$
$762$	−48.6037	−1.76072
$763$	−2.01765	−0.0730440
$764$	−20.4271	−0.739026
$765$	0	0
$766$	9.28218	0.335379
$767$	1.00831	0.0364080
$768$	39.7755	1.43527
$769$	−8.72245	−0.314539	−0.157270	−	0.987556i	$-0.550269\pi$
$769$	−8.72245	−0.314539	−0.157270	+	0.987556i	$0.550269\pi$
$770$	0	0
$771$	−12.1408	−0.437241
$772$	−107.805	−3.87997
$773$	42.2655	1.52019	0.760093	−	0.649814i	$-0.225153\pi$
$773$	42.2655	1.52019	0.760093	+	0.649814i	$0.225153\pi$
$774$	11.9592	0.429866
$775$	0	0
$776$	74.7604	2.68374
$777$	−0.959332	−0.0344158
$778$	−11.7693	−0.421950
$779$	−13.7392	−0.492256
$780$	0	0
$781$	−3.91904	−0.140234
$782$	−20.8748	−0.746480
$783$	29.5667	1.05663
$784$	−36.7490	−1.31246
$785$	0	0
$786$	−36.9492	−1.31794
$787$	−17.5127	−0.624261	−0.312130	−	0.950039i	$-0.601043\pi$
$787$	−17.5127	−0.624261	−0.312130	+	0.950039i	$0.601043\pi$
$788$	−6.17903	−0.220119
$789$	22.5565	0.803031
$790$	0	0
$791$	−1.68341	−0.0598553
$792$	−7.48658	−0.266024
$793$	−1.77780	−0.0631316
$794$	80.2580	2.84825
$795$	0	0
$796$	31.3897	1.11258
$797$	44.6851	1.58283	0.791413	−	0.611281i	$-0.209346\pi$
$797$	44.6851	1.58283	0.791413	+	0.611281i	$0.209346\pi$
$798$	0.884442	0.0313089
$799$	16.3654	0.578968
$800$	0	0
$801$	20.6969	0.731289
$802$	15.0034	0.529788
$803$	5.11472	0.180495
$804$	−25.1486	−0.886924
$805$	0	0
$806$	3.01483	0.106193
$807$	1.40419	0.0494297
$808$	0.432335	0.0152095
$809$	37.7898	1.32862	0.664309	−	0.747458i	$-0.268726\pi$
$809$	37.7898	1.32862	0.664309	+	0.747458i	$0.268726\pi$
$810$	0	0
$811$	17.5453	0.616097	0.308049	−	0.951371i	$-0.400324\pi$
$811$	17.5453	0.616097	0.308049	+	0.951371i	$0.400324\pi$
$812$	−3.07203	−0.107807
$813$	−14.9135	−0.523038
$814$	−13.0044	−0.455804
$815$	0	0
$816$	8.10746	0.283818
$817$	−6.80322	−0.238015
$818$	−46.1792	−1.61462
$819$	0.0253688	0.000886456 0
$820$	0	0
$821$	−21.1741	−0.738980	−0.369490	−	0.929235i	$-0.620468\pi$
$821$	−21.1741	−0.738980	−0.369490	+	0.929235i	$0.620468\pi$
$822$	−2.57526	−0.0898225
$823$	47.1268	1.64274	0.821369	−	0.570397i	$-0.193211\pi$
$823$	47.1268	1.64274	0.821369	+	0.570397i	$0.193211\pi$
$824$	−34.9475	−1.21746
$825$	0	0
$826$	2.76350	0.0961543
$827$	13.3177	0.463103	0.231552	−	0.972823i	$-0.425620\pi$
$827$	13.3177	0.463103	0.231552	+	0.972823i	$0.425620\pi$
$828$	42.1132	1.46354
$829$	−41.6063	−1.44505	−0.722523	−	0.691347i	$-0.757017\pi$
$829$	−41.6063	−1.44505	−0.722523	+	0.691347i	$0.757017\pi$
$830$	0	0
$831$	−5.27114	−0.182854
$832$	−0.645125	−0.0223657
$833$	8.79904	0.304869
$834$	47.6277	1.64921
$835$	0	0
$836$	8.12405	0.280976
$837$	−53.8873	−1.86262
$838$	−74.0726	−2.55880
$839$	20.2863	0.700359	0.350180	−	0.936683i	$-0.386121\pi$
$839$	20.2863	0.700359	0.350180	+	0.936683i	$0.386121\pi$
$840$	0	0
$841$	−0.177928	−0.00613546
$842$	−6.61327	−0.227908
$843$	20.9462	0.721426
$844$	−84.7252	−2.91636
$845$	0	0
$846$	−48.7240	−1.67517
$847$	1.38577	0.0476156
$848$	−20.5741	−0.706518
$849$	16.9752	0.582588
$850$	0	0
$851$	38.3485	1.31457
$852$	−22.2376	−0.761846
$853$	26.7153	0.914715	0.457358	−	0.889283i	$-0.348796\pi$
$853$	26.7153	0.914715	0.457358	+	0.889283i	$0.348796\pi$
$854$	−4.87246	−0.166732
$855$	0	0
$856$	−10.9541	−0.374404
$857$	1.26642	0.0432602	0.0216301	−	0.999766i	$-0.493114\pi$
$857$	1.26642	0.0432602	0.0216301	+	0.999766i	$0.493114\pi$
$858$	−0.340909	−0.0116385
$859$	−45.0089	−1.53569	−0.767843	−	0.640638i	$-0.778670\pi$
$859$	−45.0089	−1.53569	−0.767843	+	0.640638i	$0.778670\pi$
$860$	0	0
$861$	1.07071	0.0364897
$862$	−69.6188	−2.37122
$863$	−26.1118	−0.888855	−0.444428	−	0.895815i	$-0.646593\pi$
$863$	−26.1118	−0.888855	−0.444428	+	0.895815i	$0.646593\pi$
$864$	−11.7468	−0.399635
$865$	0	0
$866$	33.8279	1.14952
$867$	18.8341	0.639638
$868$	5.59898	0.190042
$869$	−1.29911	−0.0440693
$870$	0	0
$871$	0.605584	0.0205194
$872$	−81.3576	−2.75511
$873$	20.5196	0.694483
$874$	−35.3548	−1.19589
$875$	0	0
$876$	29.0222	0.980568
$877$	−18.2107	−0.614931	−0.307466	−	0.951559i	$-0.599481\pi$
$877$	−18.2107	−0.614931	−0.307466	+	0.951559i	$0.599481\pi$
$878$	−68.0249	−2.29573
$879$	−0.397285	−0.0134001
$880$	0	0
$881$	7.40050	0.249329	0.124665	−	0.992199i	$-0.460214\pi$
$881$	7.40050	0.249329	0.124665	+	0.992199i	$0.460214\pi$
$882$	−26.1970	−0.882098
$883$	1.57266	0.0529243	0.0264621	−	0.999650i	$-0.491576\pi$
$883$	1.57266	0.0529243	0.0264621	+	0.999650i	$0.491576\pi$
$884$	−0.655410	−0.0220438
$885$	0	0
$886$	10.1124	0.339732
$887$	1.08367	0.0363861	0.0181930	−	0.999834i	$-0.494209\pi$
$887$	1.08367	0.0363861	0.0181930	+	0.999834i	$0.494209\pi$
$888$	−38.6830	−1.29812
$889$	2.17358	0.0728994
$890$	0	0
$891$	2.00155	0.0670545
$892$	37.4684	1.25453
$893$	27.7175	0.927532
$894$	−1.65042	−0.0551981
$895$	0	0
$896$	−2.34879	−0.0784676
$897$	1.00530	0.0335660
$898$	3.82503	0.127643
$899$	−52.5301	−1.75198
$900$	0	0
$901$	4.92620	0.164115
$902$	14.5142	0.483271
$903$	0.530184	0.0176434
$904$	−67.8801	−2.25766
$905$	0	0
$906$	25.9655	0.862646
$907$	−39.1868	−1.30118	−0.650588	−	0.759431i	$-0.725478\pi$
$907$	−39.1868	−1.30118	−0.650588	+	0.759431i	$0.725478\pi$
$908$	72.6088	2.40961
$909$	0.118664	0.00393582
$910$	0	0
$911$	11.8818	0.393662	0.196831	−	0.980437i	$-0.436935\pi$
$911$	11.8818	0.393662	0.196831	+	0.980437i	$0.436935\pi$
$912$	13.7313	0.454689
$913$	−10.6493	−0.352441
$914$	−11.2258	−0.371317
$915$	0	0
$916$	−54.3925	−1.79718
$917$	1.65239	0.0545666
$918$	17.2884	0.570602
$919$	−28.1347	−0.928077	−0.464039	−	0.885815i	$-0.653600\pi$
$919$	−28.1347	−0.928077	−0.464039	+	0.885815i	$0.653600\pi$
$920$	0	0
$921$	−17.5490	−0.578258
$922$	−43.7919	−1.44221
$923$	0.535485	0.0176257
$924$	−0.633118	−0.0208281
$925$	0	0
$926$	−104.880	−3.44657
$927$	−9.59210	−0.315046
$928$	−11.4510	−0.375897
$929$	59.5689	1.95439	0.977197	−	0.212335i	$-0.0681068\pi$
$929$	59.5689	1.95439	0.977197	+	0.212335i	$0.0681068\pi$
$930$	0	0
$931$	14.9026	0.488413
$932$	104.379	3.41904
$933$	13.6961	0.448389
$934$	26.4932	0.866885
$935$	0	0
$936$	1.02294	0.0334359
$937$	−25.8722	−0.845209	−0.422605	−	0.906314i	$-0.638884\pi$
$937$	−25.8722	−0.845209	−0.422605	+	0.906314i	$0.638884\pi$
$938$	1.65974	0.0541923
$939$	23.6911	0.773130
$940$	0	0
$941$	−43.2143	−1.40875	−0.704373	−	0.709830i	$-0.748772\pi$
$941$	−43.2143	−1.40875	−0.704373	+	0.709830i	$0.748772\pi$
$942$	49.3724	1.60864
$943$	−42.8008	−1.39378
$944$	42.9043	1.39642
$945$	0	0
$946$	7.18702	0.233670
$947$	53.0980	1.72545	0.862726	−	0.505672i	$-0.168755\pi$
$947$	53.0980	1.72545	0.862726	+	0.505672i	$0.168755\pi$
$948$	−7.37145	−0.239414
$949$	−0.698859	−0.0226859
$950$	0	0
$951$	6.34963	0.205901
$952$	−0.941672	−0.0305198
$953$	28.8397	0.934210	0.467105	−	0.884202i	$-0.345297\pi$
$953$	28.8397	0.934210	0.467105	+	0.884202i	$0.345297\pi$
$954$	−14.6665	−0.474846
$955$	0	0
$956$	31.6171	1.02257
$957$	5.93997	0.192012
$958$	−60.6000	−1.95790
$959$	0.115167	0.00371893
$960$	0	0
$961$	64.7397	2.08838
$962$	1.77688	0.0572889
$963$	−3.00659	−0.0968860
$964$	4.20371	0.135393
$965$	0	0
$966$	2.75525	0.0886487
$967$	−6.08196	−0.195583	−0.0977914	−	0.995207i	$-0.531178\pi$
$967$	−6.08196	−0.195583	−0.0977914	+	0.995207i	$0.531178\pi$
$968$	55.8782	1.79599
$969$	−3.28778	−0.105619
$970$	0	0
$971$	2.57155	0.0825251	0.0412626	−	0.999148i	$-0.486862\pi$
$971$	2.57155	0.0825251	0.0412626	+	0.999148i	$0.486862\pi$
$972$	−58.0963	−1.86344
$973$	−2.12993	−0.0682824
$974$	37.8035	1.21130
$975$	0	0
$976$	−75.6468	−2.42139
$977$	−52.2605	−1.67196	−0.835980	−	0.548760i	$-0.815100\pi$
$977$	−52.2605	−1.67196	−0.835980	+	0.548760i	$0.815100\pi$
$978$	−4.15069	−0.132724
$979$	12.4380	0.397520
$980$	0	0
$981$	−22.3303	−0.712953
$982$	−24.9555	−0.796363
$983$	−5.96528	−0.190263	−0.0951314	−	0.995465i	$-0.530327\pi$
$983$	−5.96528	−0.190263	−0.0951314	+	0.995465i	$0.530327\pi$
$984$	43.1741	1.37634
$985$	0	0
$986$	16.8530	0.536709
$987$	−2.16007	−0.0687557
$988$	−1.11004	−0.0353152
$989$	−21.1937	−0.673920
$990$	0	0
$991$	1.36771	0.0434466	0.0217233	−	0.999764i	$-0.493085\pi$
$991$	1.36771	0.0434466	0.0217233	+	0.999764i	$0.493085\pi$
$992$	20.8702	0.662629
$993$	−0.0211725	−0.000671888 0
$994$	1.46761	0.0465499
$995$	0	0
$996$	−60.4268	−1.91470
$997$	17.2016	0.544780	0.272390	−	0.962187i	$-0.412186\pi$
$997$	17.2016	0.544780	0.272390	+	0.962187i	$0.412186\pi$
$998$	19.5021	0.617329
$999$	−31.7601	−1.00484

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6025.2.a.h.1.2		12
5.4	even	2		241.2.a.b.1.11	✓	12
15.14	odd	2		2169.2.a.h.1.2		12
20.19	odd	2		3856.2.a.n.1.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
241.2.a.b.1.11	✓	12	5.4	even	2
2169.2.a.h.1.2		12	15.14	odd	2
3856.2.a.n.1.5		12	20.19	odd	2
6025.2.a.h.1.2		12	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 6025 = 5^{2} \cdot 241 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6025.a (trivial)

\(f(q)\)	\(=\)	\(q-2.49073 q^{2} -1.22208 q^{3} +4.20371 q^{4} +3.04385 q^{6} -0.136122 q^{7} -5.48885 q^{8} -1.50653 q^{9} +O(q^{10})\)	\(q-2.49073 q^{2} -1.22208 q^{3} +4.20371 q^{4} +3.04385 q^{6} -0.136122 q^{7} -5.48885 q^{8} -1.50653 q^{9} -0.905365 q^{11} -5.13726 q^{12} +0.123706 q^{13} +0.339044 q^{14} +5.26378 q^{16} -1.26034 q^{17} +3.75236 q^{18} -2.13460 q^{19} +0.166352 q^{21} +2.25502 q^{22} -6.64978 q^{23} +6.70778 q^{24} -0.308118 q^{26} +5.50732 q^{27} -0.572220 q^{28} +5.36862 q^{29} -9.78467 q^{31} -2.13295 q^{32} +1.10642 q^{33} +3.13917 q^{34} -6.33303 q^{36} -5.76688 q^{37} +5.31669 q^{38} -0.151178 q^{39} +6.43642 q^{41} -0.414337 q^{42} +3.18712 q^{43} -3.80590 q^{44} +16.5628 q^{46} -12.9849 q^{47} -6.43274 q^{48} -6.98147 q^{49} +1.54023 q^{51} +0.520025 q^{52} -3.90862 q^{53} -13.7172 q^{54} +0.747155 q^{56} +2.60864 q^{57} -13.3718 q^{58} +8.15085 q^{59} -14.3712 q^{61} +24.3709 q^{62} +0.205073 q^{63} -5.21498 q^{64} -2.75580 q^{66} +4.89534 q^{67} -5.29812 q^{68} +8.12653 q^{69} +4.32869 q^{71} +8.26912 q^{72} -5.64935 q^{73} +14.3637 q^{74} -8.97323 q^{76} +0.123241 q^{77} +0.376543 q^{78} +1.43490 q^{79} -2.21077 q^{81} -16.0314 q^{82} +11.7625 q^{83} +0.699296 q^{84} -7.93825 q^{86} -6.56086 q^{87} +4.96941 q^{88} -13.7381 q^{89} -0.0168392 q^{91} -27.9538 q^{92} +11.9576 q^{93} +32.3419 q^{94} +2.60662 q^{96} -13.6204 q^{97} +17.3889 q^{98} +1.36396 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{2} - q^{3} + 13 q^{4} - q^{6} - 3 q^{7} - 9 q^{8} + 15 q^{9}+O(q^{10}) \) 12 * q - 3 * q^2 - q^3 + 13 * q^4 - q^6 - 3 * q^7 - 9 * q^8 + 15 * q^9	\( 12 q - 3 q^{2} - q^{3} + 13 q^{4} - q^{6} - 3 q^{7} - 9 q^{8} + 15 q^{9} + 22 q^{11} + 7 q^{12} + 5 q^{13} + 6 q^{14} + 15 q^{16} + 4 q^{17} + q^{18} - 6 q^{19} - 14 q^{21} + 12 q^{22} - 32 q^{23} - 15 q^{24} + 8 q^{26} + 5 q^{27} + 11 q^{28} + 6 q^{29} + 8 q^{31} - q^{32} + 24 q^{33} - 19 q^{34} - 8 q^{36} + 8 q^{37} + 10 q^{38} + 31 q^{39} - q^{41} + 49 q^{42} + 2 q^{43} + 42 q^{44} - 25 q^{46} - 34 q^{47} + 49 q^{48} - 9 q^{49} - 3 q^{51} + 41 q^{52} - 5 q^{53} - 40 q^{54} + q^{56} + 22 q^{57} + 33 q^{58} + 26 q^{59} - 26 q^{61} + 17 q^{62} + 4 q^{63} + 13 q^{64} - 2 q^{66} - 6 q^{67} + 35 q^{68} - 2 q^{69} + 94 q^{71} - 17 q^{72} + 22 q^{73} + 26 q^{74} - 20 q^{76} + 7 q^{77} - 54 q^{78} + 9 q^{79} + 4 q^{81} - 15 q^{82} + 8 q^{83} + 2 q^{84} + 9 q^{86} - 4 q^{87} - 6 q^{88} - 3 q^{89} - 20 q^{91} - 36 q^{92} - 12 q^{93} + 48 q^{94} - 23 q^{96} + 29 q^{97} - 28 q^{98} + 36 q^{99}+O(q^{100}) \) 12 * q - 3 * q^2 - q^3 + 13 * q^4 - q^6 - 3 * q^7 - 9 * q^8 + 15 * q^9 + 22 * q^11 + 7 * q^12 + 5 * q^13 + 6 * q^14 + 15 * q^16 + 4 * q^17 + q^18 - 6 * q^19 - 14 * q^21 + 12 * q^22 - 32 * q^23 - 15 * q^24 + 8 * q^26 + 5 * q^27 + 11 * q^28 + 6 * q^29 + 8 * q^31 - q^32 + 24 * q^33 - 19 * q^34 - 8 * q^36 + 8 * q^37 + 10 * q^38 + 31 * q^39 - q^41 + 49 * q^42 + 2 * q^43 + 42 * q^44 - 25 * q^46 - 34 * q^47 + 49 * q^48 - 9 * q^49 - 3 * q^51 + 41 * q^52 - 5 * q^53 - 40 * q^54 + q^56 + 22 * q^57 + 33 * q^58 + 26 * q^59 - 26 * q^61 + 17 * q^62 + 4 * q^63 + 13 * q^64 - 2 * q^66 - 6 * q^67 + 35 * q^68 - 2 * q^69 + 94 * q^71 - 17 * q^72 + 22 * q^73 + 26 * q^74 - 20 * q^76 + 7 * q^77 - 54 * q^78 + 9 * q^79 + 4 * q^81 - 15 * q^82 + 8 * q^83 + 2 * q^84 + 9 * q^86 - 4 * q^87 - 6 * q^88 - 3 * q^89 - 20 * q^91 - 36 * q^92 - 12 * q^93 + 48 * q^94 - 23 * q^96 + 29 * q^97 - 28 * q^98 + 36 * q^99

Introduction

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