LMFDB - Embedded newform 605.2.a.m.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [605,2,Mod(1,605)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(605, 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("605.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	605.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:	$4.83094932229$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.6.27433728.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 9x^{4} + 15x^{2} - 3 $ x^6 - 9x^4 + 15x^2 - 3
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-2.62383$ of defining polynomial
Character	$\chi$	$=$	605.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.62383 q^{2} +1.33988 q^{3} +4.88448 q^{4} +1.00000 q^{5} -3.51561 q^{6} +2.62383 q^{7} -7.56839 q^{8} -1.20473 q^{9} +O(q^{10})$	\(q-2.62383 q^{2} +1.33988 q^{3} +4.88448 q^{4} +1.00000 q^{5} -3.51561 q^{6} +2.62383 q^{7} -7.56839 q^{8} -1.20473 q^{9} -2.62383 q^{10} +6.54461 q^{12} +6.72812 q^{13} -6.88448 q^{14} +1.33988 q^{15} +10.0892 q^{16} -1.78356 q^{17} +3.16101 q^{18} +1.48046 q^{19} +4.88448 q^{20} +3.51561 q^{21} +5.20473 q^{23} -10.1407 q^{24} +1.00000 q^{25} -17.6535 q^{26} -5.63382 q^{27} +12.8161 q^{28} -1.17737 q^{29} -3.51561 q^{30} -4.56424 q^{31} -11.3356 q^{32} +4.67975 q^{34} +2.62383 q^{35} -5.88448 q^{36} -0.679754 q^{37} -3.88448 q^{38} +9.01486 q^{39} -7.56839 q^{40} -5.49925 q^{41} -9.22436 q^{42} -3.80120 q^{43} -1.20473 q^{45} -13.6563 q^{46} +6.66012 q^{47} +13.5183 q^{48} -0.115516 q^{49} -2.62383 q^{50} -2.38975 q^{51} +32.8634 q^{52} +14.2939 q^{53} +14.7822 q^{54} -19.8582 q^{56} +1.98364 q^{57} +3.08921 q^{58} -3.88448 q^{59} +6.54461 q^{60} -3.21251 q^{61} +11.9758 q^{62} -3.16101 q^{63} +9.56424 q^{64} +6.72812 q^{65} +4.66012 q^{67} -8.71176 q^{68} +6.97370 q^{69} -6.88448 q^{70} +3.88448 q^{71} +9.11787 q^{72} +3.56712 q^{73} +1.78356 q^{74} +1.33988 q^{75} +7.23130 q^{76} -23.6535 q^{78} +15.1368 q^{79} +10.0892 q^{80} -3.93444 q^{81} +14.4291 q^{82} -7.33431 q^{83} +17.1719 q^{84} -1.78356 q^{85} +9.97370 q^{86} -1.57753 q^{87} +3.44872 q^{89} +3.16101 q^{90} +17.6535 q^{91} +25.4224 q^{92} -6.11552 q^{93} -17.4750 q^{94} +1.48046 q^{95} -15.1883 q^{96} +1.47502 q^{97} +0.303095 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{3} + 6 q^{4} + 6 q^{5} + 12 q^{9}+O(q^{10}) $ 6 * q + 6 * q^3 + 6 * q^4 + 6 * q^5 + 12 * q^9	$ 6 q + 6 q^{3} + 6 q^{4} + 6 q^{5} + 12 q^{9} + 18 q^{12} - 18 q^{14} + 6 q^{15} + 18 q^{16} + 6 q^{20} + 12 q^{23} + 6 q^{25} - 36 q^{26} + 30 q^{27} + 24 q^{34} - 12 q^{36} - 30 q^{42} + 12 q^{45} + 42 q^{47} - 6 q^{48} - 24 q^{49} + 24 q^{53} - 30 q^{56} - 24 q^{58} + 18 q^{60} + 30 q^{64} + 30 q^{67} - 24 q^{69} - 18 q^{70} + 6 q^{75} - 72 q^{78} + 18 q^{80} + 30 q^{81} + 42 q^{82} - 6 q^{86} - 30 q^{89} + 36 q^{91} + 36 q^{92} - 60 q^{93} + 24 q^{97}+O(q^{100}) $ 6 * q + 6 * q^3 + 6 * q^4 + 6 * q^5 + 12 * q^9 + 18 * q^12 - 18 * q^14 + 6 * q^15 + 18 * q^16 + 6 * q^20 + 12 * q^23 + 6 * q^25 - 36 * q^26 + 30 * q^27 + 24 * q^34 - 12 * q^36 - 30 * q^42 + 12 * q^45 + 42 * q^47 - 6 * q^48 - 24 * q^49 + 24 * q^53 - 30 * q^56 - 24 * q^58 + 18 * q^60 + 30 * q^64 + 30 * q^67 - 24 * q^69 - 18 * q^70 + 6 * q^75 - 72 * q^78 + 18 * q^80 + 30 * q^81 + 42 * q^82 - 6 * q^86 - 30 * q^89 + 36 * q^91 + 36 * q^92 - 60 * q^93 + 24 * q^97

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 $

$2$	−2.62383	−1.85533	−0.927664	−	0.373416i	$-0.878186\pi$
$2$	−2.62383	−1.85533	−0.927664	+	0.373416i	$0.878186\pi$
$3$	1.33988	0.773578	0.386789	−	0.922168i	$-0.373584\pi$
$3$	1.33988	0.773578	0.386789	+	0.922168i	$0.373584\pi$
$4$	4.88448	2.44224
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−3.51561	−1.43524
$7$	2.62383	0.991715	0.495857	−	0.868404i	$-0.334854\pi$
$7$	2.62383	0.991715	0.495857	+	0.868404i	$0.334854\pi$
$8$	−7.56839	−2.67583
$9$	−1.20473	−0.401577
$10$	−2.62383	−0.829728
$11$	0	0
$11$	0	0
$12$	6.54461	1.88927
$13$	6.72812	1.86605	0.933023	−	0.359817i	$-0.117161\pi$
$13$	6.72812	1.86605	0.933023	+	0.359817i	$0.117161\pi$
$14$	−6.88448	−1.83996
$15$	1.33988	0.345955
$16$	10.0892	2.52230
$17$	−1.78356	−0.432576	−0.216288	−	0.976330i	$-0.569395\pi$
$17$	−1.78356	−0.432576	−0.216288	+	0.976330i	$0.569395\pi$
$18$	3.16101	0.745056
$19$	1.48046	0.339642	0.169821	−	0.985475i	$-0.445681\pi$
$19$	1.48046	0.339642	0.169821	+	0.985475i	$0.445681\pi$
$20$	4.88448	1.09220
$21$	3.51561	0.767169
$22$	0	0
$23$	5.20473	1.08526	0.542631	−	0.839971i	$-0.317428\pi$
$23$	5.20473	1.08526	0.542631	+	0.839971i	$0.317428\pi$
$24$	−10.1407	−2.06997
$25$	1.00000	0.200000
$26$	−17.6535	−3.46213
$27$	−5.63382	−1.08423
$28$	12.8161	2.42201
$29$	−1.17737	−0.218632	−0.109316	−	0.994007i	$-0.534866\pi$
$29$	−1.17737	−0.218632	−0.109316	+	0.994007i	$0.534866\pi$
$30$	−3.51561	−0.641859
$31$	−4.56424	−0.819761	−0.409881	−	0.912139i	$-0.634430\pi$
$31$	−4.56424	−0.819761	−0.409881	+	0.912139i	$0.634430\pi$
$32$	−11.3356	−2.00387
$33$	0	0
$34$	4.67975	0.802571
$35$	2.62383	0.443508
$36$	−5.88448	−0.980747
$37$	−0.679754	−0.111751	−0.0558754	−	0.998438i	$-0.517795\pi$
$37$	−0.679754	−0.111751	−0.0558754	+	0.998438i	$0.517795\pi$
$38$	−3.88448	−0.630146
$39$	9.01486	1.44353
$40$	−7.56839	−1.19667
$41$	−5.49925	−0.858838	−0.429419	−	0.903105i	$-0.641282\pi$
$41$	−5.49925	−0.858838	−0.429419	+	0.903105i	$0.641282\pi$
$42$	−9.22436	−1.42335
$43$	−3.80120	−0.579677	−0.289839	−	0.957076i	$-0.593602\pi$
$43$	−3.80120	−0.579677	−0.289839	+	0.957076i	$0.593602\pi$
$44$	0	0
$45$	−1.20473	−0.179591
$46$	−13.6563	−2.01352
$47$	6.66012	0.971479	0.485739	−	0.874104i	$-0.338550\pi$
$47$	6.66012	0.971479	0.485739	+	0.874104i	$0.338550\pi$
$48$	13.5183	1.95120
$49$	−0.115516	−0.0165023
$50$	−2.62383	−0.371066
$51$	−2.38975	−0.334632
$52$	32.8634	4.55733
$53$	14.2939	1.96342	0.981712	−	0.190372i	$-0.0609693\pi$
$53$	14.2939	1.96342	0.981712	+	0.190372i	$0.0609693\pi$
$54$	14.7822	2.01160
$55$	0	0
$56$	−19.8582	−2.65366
$57$	1.98364	0.262739
$58$	3.08921	0.405634
$59$	−3.88448	−0.505717	−0.252858	−	0.967503i	$-0.581371\pi$
$59$	−3.88448	−0.505717	−0.252858	+	0.967503i	$0.581371\pi$
$60$	6.54461	0.844905
$61$	−3.21251	−0.411320	−0.205660	−	0.978623i	$-0.565934\pi$
$61$	−3.21251	−0.411320	−0.205660	+	0.978623i	$0.565934\pi$
$62$	11.9758	1.52093
$63$	−3.16101	−0.398249
$64$	9.56424	1.19553
$65$	6.72812	0.834521
$66$	0	0
$67$	4.66012	0.569325	0.284662	−	0.958628i	$-0.408119\pi$
$67$	4.66012	0.569325	0.284662	+	0.958628i	$0.408119\pi$
$68$	−8.71176	−1.05646
$69$	6.97370	0.839535
$70$	−6.88448	−0.822853
$71$	3.88448	0.461003	0.230502	−	0.973072i	$-0.425963\pi$
$71$	3.88448	0.461003	0.230502	+	0.973072i	$0.425963\pi$
$72$	9.11787	1.07455
$73$	3.56712	0.417499	0.208750	−	0.977969i	$-0.433061\pi$
$73$	3.56712	0.417499	0.208750	+	0.977969i	$0.433061\pi$
$74$	1.78356	0.207334
$75$	1.33988	0.154716
$76$	7.23130	0.829487
$77$	0	0
$78$	−23.6535	−2.67823
$79$	15.1368	1.70302	0.851511	−	0.524337i	$-0.175687\pi$
$79$	15.1368	1.70302	0.851511	+	0.524337i	$0.175687\pi$
$80$	10.0892	1.12801
$81$	−3.93444	−0.437160
$82$	14.4291	1.59343
$83$	−7.33431	−0.805045	−0.402523	−	0.915410i	$-0.631867\pi$
$83$	−7.33431	−0.805045	−0.402523	+	0.915410i	$0.631867\pi$
$84$	17.1719	1.87361
$85$	−1.78356	−0.193454
$86$	9.97370	1.07549
$87$	−1.57753	−0.169129
$88$	0	0
$89$	3.44872	0.365564	0.182782	−	0.983153i	$-0.441490\pi$
$89$	3.44872	0.365564	0.182782	+	0.983153i	$0.441490\pi$
$90$	3.16101	0.333199
$91$	17.6535	1.85058
$92$	25.4224	2.65047
$93$	−6.11552	−0.634149
$94$	−17.4750	−1.80241
$95$	1.48046	0.151892
$96$	−15.1883	−1.55015
$97$	1.47502	0.149766	0.0748830	−	0.997192i	$-0.476142\pi$
$97$	1.47502	0.149766	0.0748830	+	0.997192i	$0.476142\pi$
$98$	0.303095	0.0306172
$99$	0	0
$100$	4.88448	0.488448
$101$	3.41259	0.339566	0.169783	−	0.985481i	$-0.445693\pi$
$101$	3.41259	0.339566	0.169783	+	0.985481i	$0.445693\pi$
$102$	6.27029	0.620852
$103$	−4.97370	−0.490073	−0.245036	−	0.969514i	$-0.578800\pi$
$103$	−4.97370	−0.490073	−0.245036	+	0.969514i	$0.578800\pi$
$104$	−50.9211	−4.99322
$105$	3.51561	0.343088
$106$	−37.5049	−3.64280
$107$	−7.06522	−0.683021	−0.341510	−	0.939878i	$-0.610938\pi$
$107$	−7.06522	−0.683021	−0.341510	+	0.939878i	$0.610938\pi$
$108$	−27.5183	−2.64795
$109$	10.6439	1.01950	0.509750	−	0.860323i	$-0.329738\pi$
$109$	10.6439	1.01950	0.509750	+	0.860323i	$0.329738\pi$
$110$	0	0
$111$	−0.910786	−0.0864480
$112$	26.4724	2.50140
$113$	−13.7690	−1.29528	−0.647638	−	0.761948i	$-0.724243\pi$
$113$	−13.7690	−1.29528	−0.647638	+	0.761948i	$0.724243\pi$
$114$	−5.20473	−0.487468
$115$	5.20473	0.485344
$116$	−5.75084	−0.533952
$117$	−8.10557	−0.749360
$118$	10.1922	0.938270
$119$	−4.67975	−0.428992
$120$	−10.1407	−0.925717
$121$	0	0
$122$	8.42909	0.763134
$123$	−7.36831	−0.664379
$124$	−22.2939	−2.00206
$125$	1.00000	0.0894427
$126$	8.29394	0.738883
$127$	12.3129	1.09259	0.546296	−	0.837592i	$-0.316037\pi$
$127$	12.3129	1.09259	0.546296	+	0.837592i	$0.316037\pi$
$128$	−2.42375	−0.214231
$129$	−5.09314	−0.448426
$130$	−17.6535	−1.54831
$131$	−19.5102	−1.70461	−0.852306	−	0.523043i	$-0.824797\pi$
$131$	−19.5102	−1.70461	−0.852306	+	0.523043i	$0.824797\pi$
$132$	0	0
$133$	3.88448	0.336827
$134$	−12.2274	−1.05628
$135$	−5.63382	−0.484882
$136$	13.4987	1.15750
$137$	−8.56424	−0.731692	−0.365846	−	0.930675i	$-0.619220\pi$
$137$	−8.56424	−0.731692	−0.365846	+	0.930675i	$0.619220\pi$
$138$	−18.2978	−1.55761
$139$	−1.98364	−0.168250	−0.0841250	−	0.996455i	$-0.526810\pi$
$139$	−1.98364	−0.168250	−0.0841250	+	0.996455i	$0.526810\pi$
$140$	12.8161	1.08315
$141$	8.92375	0.751515
$142$	−10.1922	−0.855313
$143$	0	0
$144$	−12.1548	−1.01290
$145$	−1.17737	−0.0977751
$146$	−9.35951	−0.774598
$147$	−0.154778	−0.0127658
$148$	−3.32025	−0.272923
$149$	18.3493	1.50323	0.751617	−	0.659600i	$-0.229274\pi$
$149$	18.3493	1.50323	0.751617	+	0.659600i	$0.229274\pi$
$150$	−3.51561	−0.287048
$151$	−17.2234	−1.40162	−0.700812	−	0.713346i	$-0.747179\pi$
$151$	−17.2234	−1.40162	−0.700812	+	0.713346i	$0.747179\pi$
$152$	−11.2047	−0.908824
$153$	2.14871	0.173713
$154$	0	0
$155$	−4.56424	−0.366608
$156$	44.0329	3.52546
$157$	−20.8974	−1.66780	−0.833899	−	0.551917i	$-0.813896\pi$
$157$	−20.8974	−1.66780	−0.833899	+	0.551917i	$0.813896\pi$
$158$	−39.7164	−3.15966
$159$	19.1521	1.51886
$160$	−11.3356	−0.896157
$161$	13.6563	1.07627
$162$	10.3233	0.811074
$163$	9.45539	0.740604	0.370302	−	0.928912i	$-0.379254\pi$
$163$	9.45539	0.740604	0.370302	+	0.928912i	$0.379254\pi$
$164$	−26.8610	−2.09749
$165$	0	0
$166$	19.2440	1.49362
$167$	9.44902	0.731187	0.365593	−	0.930775i	$-0.380866\pi$
$167$	9.44902	0.731187	0.365593	+	0.930775i	$0.380866\pi$
$168$	−26.6075	−2.05281
$169$	32.2676	2.48213
$170$	4.67975	0.358921
$171$	−1.78356	−0.136392
$172$	−18.5669	−1.41571
$173$	9.08286	0.690557	0.345279	−	0.938500i	$-0.387784\pi$
$173$	9.08286	0.690557	0.345279	+	0.938500i	$0.387784\pi$
$174$	4.13917	0.313789
$175$	2.62383	0.198343
$176$	0	0
$177$	−5.20473	−0.391211
$178$	−9.04886	−0.678241
$179$	−13.7690	−1.02914	−0.514570	−	0.857448i	$-0.672049\pi$
$179$	−13.7690	−1.02914	−0.514570	+	0.857448i	$0.672049\pi$
$180$	−5.88448	−0.438604
$181$	−23.8582	−1.77336	−0.886682	−	0.462379i	$-0.846996\pi$
$181$	−23.8582	−1.77336	−0.886682	+	0.462379i	$0.846996\pi$
$182$	−46.3197	−3.43344
$183$	−4.30437	−0.318188
$184$	−39.3915	−2.90398
$185$	−0.679754	−0.0499765
$186$	16.0461	1.17656
$187$	0	0
$188$	32.5313	2.37259
$189$	−14.7822	−1.07525
$190$	−3.88448	−0.281810
$191$	16.0629	1.16227	0.581136	−	0.813807i	$-0.302609\pi$
$191$	16.0629	1.16227	0.581136	+	0.813807i	$0.302609\pi$
$192$	12.8149	0.924836
$193$	−21.4588	−1.54464	−0.772319	−	0.635235i	$-0.780903\pi$
$193$	−21.4588	−1.54464	−0.772319	+	0.635235i	$0.780903\pi$
$194$	−3.87021	−0.277865
$195$	9.01486	0.645567
$196$	−0.564237	−0.0403027
$197$	−9.21494	−0.656537	−0.328269	−	0.944584i	$-0.606465\pi$
$197$	−9.21494	−0.656537	−0.328269	+	0.944584i	$0.606465\pi$
$198$	0	0
$199$	−16.4880	−1.16880	−0.584401	−	0.811465i	$-0.698670\pi$
$199$	−16.4880	−1.16880	−0.584401	+	0.811465i	$0.698670\pi$
$200$	−7.56839	−0.535166
$201$	6.24399	0.440417
$202$	−8.95407	−0.630006
$203$	−3.08921	−0.216820
$204$	−11.6727	−0.817252
$205$	−5.49925	−0.384084
$206$	13.0501	0.909246
$207$	−6.27029	−0.435816
$208$	67.8815	4.70673
$209$	0	0
$210$	−9.22436	−0.636541
$211$	−14.8337	−1.02119	−0.510597	−	0.859820i	$-0.670576\pi$
$211$	−14.8337	−1.02119	−0.510597	+	0.859820i	$0.670576\pi$
$212$	69.8185	4.79516
$213$	5.20473	0.356622
$214$	18.5379	1.26723
$215$	−3.80120	−0.259240
$216$	42.6390	2.90121
$217$	−11.9758	−0.812969
$218$	−27.9278	−1.89151
$219$	4.77950	0.322968
$220$	0	0
$221$	−12.0000	−0.807207
$222$	2.38975	0.160389
$223$	23.4028	1.56717	0.783583	−	0.621287i	$-0.213390\pi$
$223$	23.4028	1.56717	0.783583	+	0.621287i	$0.213390\pi$
$224$	−29.7427	−1.98727
$225$	−1.20473	−0.0803153
$226$	36.1274	2.40316
$227$	2.62383	0.174150	0.0870749	−	0.996202i	$-0.472248\pi$
$227$	2.62383	0.174150	0.0870749	+	0.996202i	$0.472248\pi$
$228$	9.68905	0.641673
$229$	−22.0366	−1.45622	−0.728110	−	0.685460i	$-0.759601\pi$
$229$	−22.0366	−1.45622	−0.728110	+	0.685460i	$0.759601\pi$
$230$	−13.6563	−0.900471
$231$	0	0
$232$	8.91079	0.585022
$233$	−5.34473	−0.350145	−0.175072	−	0.984556i	$-0.556016\pi$
$233$	−5.34473	−0.350145	−0.175072	+	0.984556i	$0.556016\pi$
$234$	21.2676	1.39031
$235$	6.66012	0.434459
$236$	−18.9737	−1.23508
$237$	20.2814	1.31742
$238$	12.2789	0.795921
$239$	12.5820	0.813860	0.406930	−	0.913459i	$-0.366599\pi$
$239$	12.5820	0.813860	0.406930	+	0.913459i	$0.366599\pi$
$240$	13.5183	0.872603
$241$	4.28687	0.276141	0.138071	−	0.990422i	$-0.455910\pi$
$241$	4.28687	0.276141	0.138071	+	0.990422i	$0.455910\pi$
$242$	0	0
$243$	11.6298	0.746052
$244$	−15.6915	−1.00454
$245$	−0.115516	−0.00738007
$246$	19.3332	1.23264
$247$	9.96074	0.633787
$248$	34.5440	2.19354
$249$	−9.82708	−0.622766
$250$	−2.62383	−0.165946
$251$	10.0629	0.635165	0.317583	−	0.948231i	$-0.397129\pi$
$251$	10.0629	0.635165	0.317583	+	0.948231i	$0.397129\pi$
$252$	−15.4399	−0.972621
$253$	0	0
$254$	−32.3069	−2.02712
$255$	−2.38975	−0.149652
$256$	−12.7690	−0.798060
$257$	−3.16547	−0.197457	−0.0987283	−	0.995114i	$-0.531477\pi$
$257$	−3.16547	−0.197457	−0.0987283	+	0.995114i	$0.531477\pi$
$258$	13.3635	0.831977
$259$	−1.78356	−0.110825
$260$	32.8634	2.03810
$261$	1.41841	0.0877974
$262$	51.1914	3.16261
$263$	−22.3681	−1.37928	−0.689638	−	0.724155i	$-0.742230\pi$
$263$	−22.3681	−1.37928	−0.689638	+	0.724155i	$0.742230\pi$
$264$	0	0
$265$	14.2939	0.878070
$266$	−10.1922	−0.624925
$267$	4.62086	0.282792
$268$	22.7623	1.39043
$269$	15.9737	0.973934	0.486967	−	0.873421i	$-0.338103\pi$
$269$	15.9737	0.973934	0.486967	+	0.873421i	$0.338103\pi$
$270$	14.7822	0.899615
$271$	15.6400	0.950060	0.475030	−	0.879970i	$-0.342437\pi$
$271$	15.6400	0.950060	0.475030	+	0.879970i	$0.342437\pi$
$272$	−17.9947	−1.09109
$273$	23.6535	1.43157
$274$	22.4711	1.35753
$275$	0	0
$276$	34.0629	2.05035
$277$	−23.8836	−1.43502	−0.717512	−	0.696546i	$-0.754719\pi$
$277$	−23.8836	−1.43502	−0.717512	+	0.696546i	$0.754719\pi$
$278$	5.20473	0.312159
$279$	5.49867	0.329197
$280$	−19.8582	−1.18675
$281$	−12.2439	−0.730408	−0.365204	−	0.930928i	$-0.619001\pi$
$281$	−12.2439	−0.730408	−0.365204	+	0.930928i	$0.619001\pi$
$282$	−23.4144	−1.39431
$283$	20.8536	1.23962	0.619810	−	0.784752i	$-0.287210\pi$
$283$	20.8536	1.23962	0.619810	+	0.784752i	$0.287210\pi$
$284$	18.9737	1.12588
$285$	1.98364	0.117501
$286$	0	0
$287$	−14.4291	−0.851722
$288$	13.6563	0.804707
$289$	−13.8189	−0.812878
$290$	3.08921	0.181405
$291$	1.97635	0.115856
$292$	17.4235	1.01963
$293$	−14.3305	−0.837198	−0.418599	−	0.908171i	$-0.637479\pi$
$293$	−14.3305	−0.837198	−0.418599	+	0.908171i	$0.637479\pi$
$294$	0.406110	0.0236848
$295$	−3.88448	−0.226163
$296$	5.14464	0.299026
$297$	0	0
$298$	−48.1455	−2.78899
$299$	35.0181	2.02515
$300$	6.54461	0.377853
$301$	−9.97370	−0.574874
$302$	45.1914	2.60047
$303$	4.57246	0.262681
$304$	14.9367	0.856679
$305$	−3.21251	−0.183948
$306$	−5.63784	−0.322294
$307$	−10.2952	−0.587580	−0.293790	−	0.955870i	$-0.594917\pi$
$307$	−10.2952	−0.587580	−0.293790	+	0.955870i	$0.594917\pi$
$308$	0	0
$309$	−6.66414	−0.379110
$310$	11.9758	0.680179
$311$	−19.1521	−1.08602	−0.543009	−	0.839727i	$-0.682715\pi$
$311$	−19.1521	−1.08602	−0.543009	+	0.839727i	$0.682715\pi$
$312$	−68.2280	−3.86265
$313$	−14.9737	−0.846363	−0.423182	−	0.906045i	$-0.639087\pi$
$313$	−14.9737	−0.846363	−0.423182	+	0.906045i	$0.639087\pi$
$314$	54.8313	3.09431
$315$	−3.16101	−0.178103
$316$	73.9354	4.15919
$317$	12.1784	0.684009	0.342004	−	0.939698i	$-0.388894\pi$
$317$	12.1784	0.684009	0.342004	+	0.939698i	$0.388894\pi$
$318$	−50.2519	−2.81799
$319$	0	0
$320$	9.56424	0.534657
$321$	−9.46652	−0.528370
$322$	−35.8319	−1.99683
$323$	−2.64049	−0.146921
$324$	−19.2177	−1.06765
$325$	6.72812	0.373209
$326$	−24.8093	−1.37406
$327$	14.2615	0.788663
$328$	41.6205	2.29811
$329$	17.4750	0.963430
$330$	0	0
$331$	−15.8319	−0.870199	−0.435099	−	0.900382i	$-0.643287\pi$
$331$	−15.8319	−0.870199	−0.435099	+	0.900382i	$0.643287\pi$
$332$	−35.8243	−1.96612
$333$	0.818920	0.0448765
$334$	−24.7926	−1.35659
$335$	4.66012	0.254610
$336$	35.4697	1.93503
$337$	−6.72812	−0.366504	−0.183252	−	0.983066i	$-0.558662\pi$
$337$	−6.72812	−0.366504	−0.183252	+	0.983066i	$0.558662\pi$
$338$	−84.6648	−4.60516
$339$	−18.4487	−1.00200
$340$	−8.71176	−0.472462
$341$	0	0
$342$	4.67975	0.253052
$343$	−18.6699	−1.00808
$344$	28.7690	1.55112
$345$	6.97370	0.375451
$346$	−23.8319	−1.28121
$347$	−33.5036	−1.79857	−0.899284	−	0.437366i	$-0.855912\pi$
$347$	−33.5036	−1.79857	−0.899284	+	0.437366i	$0.855912\pi$
$348$	−7.70541	−0.413053
$349$	−22.7742	−1.21907	−0.609537	−	0.792757i	$-0.708645\pi$
$349$	−22.7742	−1.21907	−0.609537	+	0.792757i	$0.708645\pi$
$350$	−6.88448	−0.367991
$351$	−37.9050	−2.02322
$352$	0	0
$353$	−15.4617	−0.822942	−0.411471	−	0.911423i	$-0.634985\pi$
$353$	−15.4617	−0.822942	−0.411471	+	0.911423i	$0.634985\pi$
$354$	13.6563	0.725826
$355$	3.88448	0.206167
$356$	16.8452	0.892795
$357$	−6.27029	−0.331859
$358$	36.1274	1.90939
$359$	−9.58603	−0.505932	−0.252966	−	0.967475i	$-0.581406\pi$
$359$	−9.58603	−0.505932	−0.252966	+	0.967475i	$0.581406\pi$
$360$	9.11787	0.480554
$361$	−16.8082	−0.884644
$362$	62.5998	3.29017
$363$	0	0
$364$	86.2280	4.51957
$365$	3.56712	0.186711
$366$	11.2939	0.590344
$367$	−10.8386	−0.565768	−0.282884	−	0.959154i	$-0.591291\pi$
$367$	−10.8386	−0.565768	−0.282884	+	0.959154i	$0.591291\pi$
$368$	52.5116	2.73736
$369$	6.62511	0.344889
$370$	1.78356	0.0927228
$371$	37.5049	1.94716
$372$	−29.8711	−1.54875
$373$	10.0212	0.518878	0.259439	−	0.965759i	$-0.416462\pi$
$373$	10.0212	0.518878	0.259439	+	0.965759i	$0.416462\pi$
$374$	0	0
$375$	1.33988	0.0691909
$376$	−50.4064	−2.59951
$377$	−7.92148	−0.407977
$378$	38.7859	1.99493
$379$	4.19177	0.215317	0.107658	−	0.994188i	$-0.465665\pi$
$379$	4.19177	0.215317	0.107658	+	0.994188i	$0.465665\pi$
$380$	7.23130	0.370958
$381$	16.4977	0.845205
$382$	−42.1463	−2.15639
$383$	19.2440	0.983322	0.491661	−	0.870787i	$-0.336390\pi$
$383$	19.2440	0.983322	0.491661	+	0.870787i	$0.336390\pi$
$384$	−3.24753	−0.165725
$385$	0	0
$386$	56.3042	2.86581
$387$	4.57942	0.232785
$388$	7.20473	0.365765
$389$	−28.4224	−1.44107	−0.720537	−	0.693417i	$-0.756105\pi$
$389$	−28.4224	−1.44107	−0.720537	+	0.693417i	$0.756105\pi$
$390$	−23.6535	−1.19774
$391$	−9.28294	−0.469458
$392$	0.874273	0.0441575
$393$	−26.1412	−1.31865
$394$	24.1784	1.21809
$395$	15.1368	0.761615
$396$	0	0
$397$	−22.1784	−1.11310	−0.556552	−	0.830813i	$-0.687876\pi$
$397$	−22.1784	−1.11310	−0.556552	+	0.830813i	$0.687876\pi$
$398$	43.2617	2.16851
$399$	5.20473	0.260562
$400$	10.0892	0.504461
$401$	22.0759	1.10242	0.551208	−	0.834368i	$-0.314167\pi$
$401$	22.0759	1.10242	0.551208	+	0.834368i	$0.314167\pi$
$402$	−16.3832	−0.817118
$403$	−30.7088	−1.52971
$404$	16.6688	0.829302
$405$	−3.93444	−0.195504
$406$	8.10557	0.402273
$407$	0	0
$408$	18.0866	0.895418
$409$	−24.6713	−1.21992	−0.609959	−	0.792433i	$-0.708814\pi$
$409$	−24.6713	−1.21992	−0.609959	+	0.792433i	$0.708814\pi$
$410$	14.4291	0.712602
$411$	−11.4750	−0.566021
$412$	−24.2939	−1.19688
$413$	−10.1922	−0.501527
$414$	16.4522	0.808581
$415$	−7.33431	−0.360027
$416$	−76.2673	−3.73931
$417$	−2.65783	−0.130155
$418$	0	0
$419$	17.6535	0.862428	0.431214	−	0.902250i	$-0.358085\pi$
$419$	17.6535	0.862428	0.431214	+	0.902250i	$0.358085\pi$
$420$	17.1719	0.837905
$421$	1.52498	0.0743228	0.0371614	−	0.999309i	$-0.488168\pi$
$421$	1.52498	0.0743228	0.0371614	+	0.999309i	$0.488168\pi$
$422$	38.9211	1.89465
$423$	−8.02365	−0.390123
$424$	−108.182	−5.25379
$425$	−1.78356	−0.0865153
$426$	−13.6563	−0.661651
$427$	−8.42909	−0.407912
$428$	−34.5099	−1.66810
$429$	0	0
$430$	9.97370	0.480974
$431$	16.7493	0.806787	0.403393	−	0.915027i	$-0.367831\pi$
$431$	16.7493	0.806787	0.403393	+	0.915027i	$0.367831\pi$
$432$	−56.8408	−2.73476
$433$	7.47502	0.359227	0.179613	−	0.983737i	$-0.442515\pi$
$433$	7.47502	0.359227	0.179613	+	0.983737i	$0.442515\pi$
$434$	31.4224	1.50832
$435$	−1.57753	−0.0756367
$436$	51.9899	2.48987
$437$	7.70541	0.368600
$438$	−12.5406	−0.599212
$439$	−17.4585	−0.833250	−0.416625	−	0.909078i	$-0.636787\pi$
$439$	−17.4585	−0.833250	−0.416625	+	0.909078i	$0.636787\pi$
$440$	0	0
$441$	0.139166	0.00662695
$442$	31.4860	1.49763
$443$	−14.6838	−0.697647	−0.348824	−	0.937188i	$-0.613419\pi$
$443$	−14.6838	−0.697647	−0.348824	+	0.937188i	$0.613419\pi$
$444$	−4.44872	−0.211127
$445$	3.44872	0.163485
$446$	−61.4049	−2.90761
$447$	24.5858	1.16287
$448$	25.0949	1.18562
$449$	−1.30729	−0.0616947	−0.0308474	−	0.999524i	$-0.509821\pi$
$449$	−1.30729	−0.0616947	−0.0308474	+	0.999524i	$0.509821\pi$
$450$	3.16101	0.149011
$451$	0	0
$452$	−67.2543	−3.16338
$453$	−23.0773	−1.08427
$454$	−6.88448	−0.323105
$455$	17.6535	0.827607
$456$	−15.0130	−0.703046
$457$	−10.1922	−0.476772	−0.238386	−	0.971170i	$-0.576618\pi$
$457$	−10.1922	−0.476772	−0.238386	+	0.971170i	$0.576618\pi$
$458$	57.8203	2.70177
$459$	10.0482	0.469012
$460$	25.4224	1.18533
$461$	4.12180	0.191971	0.0959857	−	0.995383i	$-0.469400\pi$
$461$	4.12180	0.191971	0.0959857	+	0.995383i	$0.469400\pi$
$462$	0	0
$463$	32.7623	1.52259	0.761296	−	0.648404i	$-0.224563\pi$
$463$	32.7623	1.52259	0.761296	+	0.648404i	$0.224563\pi$
$464$	−11.8787	−0.551456
$465$	−6.11552	−0.283600
$466$	14.0236	0.649633
$467$	37.9144	1.75447	0.877235	−	0.480061i	$-0.159386\pi$
$467$	37.9144	1.75447	0.877235	+	0.480061i	$0.159386\pi$
$468$	−39.5915	−1.83012
$469$	12.2274	0.564608
$470$	−17.4750	−0.806063
$471$	−28.0000	−1.29017
$472$	29.3993	1.35321
$473$	0	0
$474$	−53.2150	−2.44425
$475$	1.48046	0.0679283
$476$	−22.8582	−1.04770
$477$	−17.2203	−0.788465
$478$	−33.0130	−1.50998
$479$	6.46004	0.295167	0.147583	−	0.989050i	$-0.452851\pi$
$479$	6.46004	0.295167	0.147583	+	0.989050i	$0.452851\pi$
$480$	−15.1883	−0.693248
$481$	−4.57347	−0.208532
$482$	−11.2480	−0.512333
$483$	18.2978	0.832579
$484$	0	0
$485$	1.47502	0.0669774
$486$	−30.5146	−1.38417
$487$	43.4617	1.96944	0.984718	−	0.174154i	$-0.0557192\pi$
$487$	43.4617	1.96944	0.984718	+	0.174154i	$0.0557192\pi$
$488$	24.3136	1.10062
$489$	12.6691	0.572915
$490$	0.303095	0.0136924
$491$	5.45369	0.246122	0.123061	−	0.992399i	$-0.460729\pi$
$491$	5.45369	0.246122	0.123061	+	0.992399i	$0.460729\pi$
$492$	−35.9904	−1.62257
$493$	2.09990	0.0945749
$494$	−26.1353	−1.17588
$495$	0	0
$496$	−46.0496	−2.06769
$497$	10.1922	0.457184
$498$	25.7846	1.15543
$499$	12.4880	0.559039	0.279519	−	0.960140i	$-0.409825\pi$
$499$	12.4880	0.559039	0.279519	+	0.960140i	$0.409825\pi$
$500$	4.88448	0.218441
$501$	12.6605	0.565630
$502$	−26.4034	−1.17844
$503$	20.8536	0.929817	0.464909	−	0.885359i	$-0.346087\pi$
$503$	20.8536	0.929817	0.464909	+	0.885359i	$0.346087\pi$
$504$	23.9237	1.06565
$505$	3.41259	0.151858
$506$	0	0
$507$	43.2347	1.92012
$508$	60.1421	2.66837
$509$	−26.5772	−1.17801	−0.589007	−	0.808128i	$-0.700481\pi$
$509$	−26.5772	−1.17801	−0.589007	+	0.808128i	$0.700481\pi$
$510$	6.27029	0.277653
$511$	9.35951	0.414040
$512$	38.3511	1.69490
$513$	−8.34066	−0.368249
$514$	8.30565	0.366347
$515$	−4.97370	−0.219167
$516$	−24.8773	−1.09516
$517$	0	0
$518$	4.67975	0.205617
$519$	12.1699	0.534200
$520$	−50.9211	−2.23304
$521$	−23.0393	−1.00937	−0.504684	−	0.863304i	$-0.668391\pi$
$521$	−23.0393	−1.00937	−0.504684	+	0.863304i	$0.668391\pi$
$522$	−3.72167	−0.162893
$523$	1.18332	0.0517429	0.0258714	−	0.999665i	$-0.491764\pi$
$523$	1.18332	0.0517429	0.0258714	+	0.999665i	$0.491764\pi$
$524$	−95.2971	−4.16307
$525$	3.51561	0.153434
$526$	58.6901	2.55901
$527$	8.14058	0.354609
$528$	0	0
$529$	4.08921	0.177792
$530$	−37.5049	−1.62911
$531$	4.67975	0.203084
$532$	18.9737	0.822614
$533$	−36.9996	−1.60263
$534$	−12.1244	−0.524672
$535$	−7.06522	−0.305456
$536$	−35.2697	−1.52342
$537$	−18.4487	−0.796121
$538$	−41.9123	−1.80697
$539$	0	0
$540$	−27.5183	−1.18420
$541$	31.6055	1.35883	0.679413	−	0.733756i	$-0.262235\pi$
$541$	31.6055	1.35883	0.679413	+	0.733756i	$0.262235\pi$
$542$	−41.0366	−1.76267
$543$	−31.9670	−1.37184
$544$	20.2177	0.866826
$545$	10.6439	0.455934
$546$	−62.0626	−2.65604
$547$	4.97958	0.212911	0.106456	−	0.994317i	$-0.466050\pi$
$547$	4.97958	0.212911	0.106456	+	0.994317i	$0.466050\pi$
$548$	−41.8319	−1.78697
$549$	3.87021	0.165177
$550$	0	0
$551$	−1.74305	−0.0742564
$552$	−52.7797	−2.24645
$553$	39.7164	1.68891
$554$	62.6664	2.66244
$555$	−0.910786	−0.0386607
$556$	−9.68905	−0.410907
$557$	25.1289	1.06475	0.532374	−	0.846510i	$-0.321300\pi$
$557$	25.1289	1.06475	0.532374	+	0.846510i	$0.321300\pi$
$558$	−14.4276	−0.610768
$559$	−25.5749	−1.08170
$560$	26.4724	1.11866
$561$	0	0
$562$	32.1258	1.35515
$563$	11.3356	0.477738	0.238869	−	0.971052i	$-0.423223\pi$
$563$	11.3356	0.477738	0.238869	+	0.971052i	$0.423223\pi$
$564$	43.5879	1.83538
$565$	−13.7690	−0.579265
$566$	−54.7164	−2.29990
$567$	−10.3233	−0.433537
$568$	−29.3993	−1.23357
$569$	11.9593	0.501359	0.250680	−	0.968070i	$-0.419346\pi$
$569$	11.9593	0.501359	0.250680	+	0.968070i	$0.419346\pi$
$570$	−5.20473	−0.218002
$571$	29.8054	1.24732	0.623659	−	0.781697i	$-0.285645\pi$
$571$	29.8054	1.24732	0.623659	+	0.781697i	$0.285645\pi$
$572$	0	0
$573$	21.5223	0.899108
$574$	37.8595	1.58022
$575$	5.20473	0.217052
$576$	−11.5223	−0.480097
$577$	−18.4857	−0.769570	−0.384785	−	0.923006i	$-0.625724\pi$
$577$	−18.4857	−0.769570	−0.384785	+	0.923006i	$0.625724\pi$
$578$	36.2585	1.50815
$579$	−28.7522	−1.19490
$580$	−5.75084	−0.238790
$581$	−19.2440	−0.798375
$582$	−5.18561	−0.214950
$583$	0	0
$584$	−26.9973	−1.11716
$585$	−8.10557	−0.335124
$586$	37.6008	1.55328
$587$	−2.68377	−0.110771	−0.0553856	−	0.998465i	$-0.517639\pi$
$587$	−2.68377	−0.110771	−0.0553856	+	0.998465i	$0.517639\pi$
$588$	−0.756009	−0.0311773
$589$	−6.75719	−0.278425
$590$	10.1922	0.419607
$591$	−12.3469	−0.507883
$592$	−6.85818	−0.281870
$593$	28.7251	1.17960	0.589800	−	0.807550i	$-0.299207\pi$
$593$	28.7251	1.17960	0.589800	+	0.807550i	$0.299207\pi$
$594$	0	0
$595$	−4.67975	−0.191851
$596$	89.6269	3.67126
$597$	−22.0919	−0.904160
$598$	−91.8814	−3.75731
$599$	−34.1807	−1.39659	−0.698293	−	0.715812i	$-0.746057\pi$
$599$	−34.1807	−1.39659	−0.698293	+	0.715812i	$0.746057\pi$
$600$	−10.1407	−0.413993
$601$	32.4573	1.32396	0.661980	−	0.749521i	$-0.269716\pi$
$601$	32.4573	1.32396	0.661980	+	0.749521i	$0.269716\pi$
$602$	26.1693	1.06658
$603$	−5.61419	−0.228627
$604$	−84.1276	−3.42310
$605$	0	0
$606$	−11.9973	−0.487359
$607$	−5.34473	−0.216936	−0.108468	−	0.994100i	$-0.534594\pi$
$607$	−5.34473	−0.216936	−0.108468	+	0.994100i	$0.534594\pi$
$608$	−16.7819	−0.680597
$609$	−4.13917	−0.167727
$610$	8.42909	0.341284
$611$	44.8101	1.81282
$612$	10.4953	0.424248
$613$	30.2056	1.21999	0.609996	−	0.792405i	$-0.291171\pi$
$613$	30.2056	1.21999	0.609996	+	0.792405i	$0.291171\pi$
$614$	27.0130	1.09015
$615$	−7.36831	−0.297119
$616$	0	0
$617$	0.973697	0.0391996	0.0195998	−	0.999808i	$-0.493761\pi$
$617$	0.973697	0.0391996	0.0195998	+	0.999808i	$0.493761\pi$
$618$	17.4856	0.703373
$619$	1.82157	0.0732152	0.0366076	−	0.999330i	$-0.488345\pi$
$619$	1.82157	0.0732152	0.0366076	+	0.999330i	$0.488345\pi$
$620$	−22.2939	−0.895346
$621$	−29.3225	−1.17667
$622$	50.2519	2.01492
$623$	9.04886	0.362535
$624$	90.9528	3.64103
$625$	1.00000	0.0400000
$626$	39.2884	1.57028
$627$	0	0
$628$	−102.073	−4.07316
$629$	1.21238	0.0483408
$630$	8.29394	0.330439
$631$	−32.3569	−1.28811	−0.644053	−	0.764981i	$-0.722748\pi$
$631$	−32.3569	−1.28811	−0.644053	+	0.764981i	$0.722748\pi$
$632$	−114.561	−4.55700
$633$	−19.8753	−0.789973
$634$	−31.9541	−1.26906
$635$	12.3129	0.488622
$636$	93.5482	3.70943
$637$	−0.777208	−0.0307941
$638$	0	0
$639$	−4.67975	−0.185128
$640$	−2.42375	−0.0958071
$641$	−13.7690	−0.543842	−0.271921	−	0.962320i	$-0.587659\pi$
$641$	−13.7690	−0.543842	−0.271921	+	0.962320i	$0.587659\pi$
$642$	24.8386	0.980299
$643$	32.1611	1.26831	0.634154	−	0.773207i	$-0.281348\pi$
$643$	32.1611	1.26831	0.634154	+	0.773207i	$0.281348\pi$
$644$	66.7041	2.62851
$645$	−5.09314	−0.200542
$646$	6.92820	0.272587
$647$	19.4813	0.765889	0.382945	−	0.923771i	$-0.374910\pi$
$647$	19.4813	0.765889	0.382945	+	0.923771i	$0.374910\pi$
$648$	29.7774	1.16977
$649$	0	0
$650$	−17.6535	−0.692425
$651$	−16.0461	−0.628895
$652$	46.1847	1.80873
$653$	0.779658	0.0305104	0.0152552	−	0.999884i	$-0.495144\pi$
$653$	0.779658	0.0305104	0.0152552	+	0.999884i	$0.495144\pi$
$654$	−37.4198	−1.46323
$655$	−19.5102	−0.762326
$656$	−55.4831	−2.16625
$657$	−4.29741	−0.167658
$658$	−45.8515	−1.78748
$659$	28.1929	1.09824	0.549119	−	0.835744i	$-0.314963\pi$
$659$	28.1929	1.09824	0.549119	+	0.835744i	$0.314963\pi$
$660$	0	0
$661$	1.70340	0.0662547	0.0331274	−	0.999451i	$-0.489453\pi$
$661$	1.70340	0.0662547	0.0331274	+	0.999451i	$0.489453\pi$
$662$	41.5402	1.61450
$663$	−16.0785	−0.624438
$664$	55.5090	2.15417
$665$	3.88448	0.150634
$666$	−2.14871	−0.0832607
$667$	−6.12788	−0.237273
$668$	46.1536	1.78574
$669$	31.3569	1.21233
$670$	−12.2274	−0.472385
$671$	0	0
$672$	−39.8515	−1.53731
$673$	−11.0044	−0.424190	−0.212095	−	0.977249i	$-0.568029\pi$
$673$	−11.0044	−0.424190	−0.212095	+	0.977249i	$0.568029\pi$
$674$	17.6535	0.679986
$675$	−5.63382	−0.216846
$676$	157.611	6.06195
$677$	21.3908	0.822115	0.411058	−	0.911609i	$-0.365160\pi$
$677$	21.3908	0.822115	0.411058	+	0.911609i	$0.365160\pi$
$678$	48.4063	1.85903
$679$	3.87021	0.148525
$680$	13.4987	0.517650
$681$	3.51561	0.134718
$682$	0	0
$683$	34.0959	1.30464	0.652321	−	0.757942i	$-0.273795\pi$
$683$	34.0959	1.30464	0.652321	+	0.757942i	$0.273795\pi$
$684$	−8.71176	−0.333103
$685$	−8.56424	−0.327223
$686$	48.9867	1.87032
$687$	−29.5263	−1.12650
$688$	−38.3511	−1.46212
$689$	96.1714	3.66384
$690$	−18.2978	−0.696585
$691$	46.3199	1.76209	0.881045	−	0.473032i	$-0.156840\pi$
$691$	46.3199	1.76209	0.881045	+	0.473032i	$0.156840\pi$
$692$	44.3651	1.68651
$693$	0	0
$694$	87.9077	3.33693
$695$	−1.98364	−0.0752437
$696$	11.9394	0.452560
$697$	9.80823	0.371513
$698$	59.7556	2.26178
$699$	−7.16127	−0.270864
$700$	12.8161	0.484401
$701$	−43.3647	−1.63786	−0.818931	−	0.573893i	$-0.805433\pi$
$701$	−43.3647	−1.63786	−0.818931	+	0.573893i	$0.805433\pi$
$702$	99.4564	3.75374
$703$	−1.00635	−0.0379552
$704$	0	0
$705$	8.92375	0.336088
$706$	40.5688	1.52683
$707$	8.95407	0.336752
$708$	−25.4224	−0.955433
$709$	19.1784	0.720261	0.360130	−	0.932902i	$-0.382732\pi$
$709$	19.1784	0.720261	0.360130	+	0.932902i	$0.382732\pi$
$710$	−10.1922	−0.382507
$711$	−18.2357	−0.683894
$712$	−26.1013	−0.978187
$713$	−23.7556	−0.889655
$714$	16.4522	0.615708
$715$	0	0
$716$	−67.2543	−2.51341
$717$	16.8583	0.629585
$718$	25.1521	0.938669
$719$	−32.2939	−1.20436	−0.602180	−	0.798360i	$-0.705701\pi$
$719$	−32.2939	−1.20436	−0.602180	+	0.798360i	$0.705701\pi$
$720$	−12.1548	−0.452982
$721$	−13.0501	−0.486012
$722$	44.1019	1.64130
$723$	5.74387	0.213617
$724$	−116.535	−4.33099
$725$	−1.17737	−0.0437264
$726$	0	0
$727$	−40.8622	−1.51550	−0.757748	−	0.652548i	$-0.773700\pi$
$727$	−40.8622	−1.51550	−0.757748	+	0.652548i	$0.773700\pi$
$728$	−133.608	−4.95185
$729$	27.3858	1.01429
$730$	−9.35951	−0.346411
$731$	6.77966	0.250755
$732$	−21.0246	−0.777093
$733$	9.92414	0.366557	0.183278	−	0.983061i	$-0.441329\pi$
$733$	9.92414	0.366557	0.183278	+	0.983061i	$0.441329\pi$
$734$	28.4385	1.04968
$735$	−0.154778	−0.00570906
$736$	−58.9987	−2.17472
$737$	0	0
$738$	−17.3832	−0.639883
$739$	−33.3725	−1.22763	−0.613814	−	0.789450i	$-0.710366\pi$
$739$	−33.3725	−1.22763	−0.613814	+	0.789450i	$0.710366\pi$
$740$	−3.32025	−0.122055
$741$	13.3462	0.490284
$742$	−98.4064	−3.61261
$743$	−3.80715	−0.139671	−0.0698354	−	0.997559i	$-0.522247\pi$
$743$	−3.80715	−0.139671	−0.0698354	+	0.997559i	$0.522247\pi$
$744$	46.2846	1.69688
$745$	18.3493	0.672266
$746$	−26.2939	−0.962690
$747$	8.83587	0.323287
$748$	0	0
$749$	−18.5379	−0.677361
$750$	−3.51561	−0.128372
$751$	22.5094	0.821378	0.410689	−	0.911775i	$-0.365288\pi$
$751$	22.5094	0.821378	0.410689	+	0.911775i	$0.365288\pi$
$752$	67.1954	2.45036
$753$	13.4831	0.491350
$754$	20.7846	0.756931
$755$	−17.2234	−0.626825
$756$	−72.2034	−2.62601
$757$	−33.6927	−1.22458	−0.612291	−	0.790632i	$-0.709752\pi$
$757$	−33.6927	−1.22458	−0.612291	+	0.790632i	$0.709752\pi$
$758$	−10.9985	−0.399483
$759$	0	0
$760$	−11.2047	−0.406438
$761$	−18.7719	−0.680481	−0.340241	−	0.940338i	$-0.610509\pi$
$761$	−18.7719	−0.680481	−0.340241	+	0.940338i	$0.610509\pi$
$762$	−43.2873	−1.56813
$763$	27.9278	1.01105
$764$	78.4590	2.83855
$765$	2.14871	0.0776866
$766$	−50.4930	−1.82438
$767$	−26.1353	−0.943690
$768$	−17.1088	−0.617362
$769$	21.5618	0.777539	0.388770	−	0.921335i	$-0.372900\pi$
$769$	21.5618	0.777539	0.388770	+	0.921335i	$0.372900\pi$
$770$	0	0
$771$	−4.24134	−0.152748
$772$	−104.815	−3.77238
$773$	−23.3832	−0.841034	−0.420517	−	0.907285i	$-0.638151\pi$
$773$	−23.3832	−0.841034	−0.420517	+	0.907285i	$0.638151\pi$
$774$	−12.0156	−0.431892
$775$	−4.56424	−0.163952
$776$	−11.1636	−0.400749
$777$	−2.38975	−0.0857318
$778$	74.5756	2.67366
$779$	−8.14143	−0.291697
$780$	44.0329	1.57663
$781$	0	0
$782$	24.3569	0.870999
$783$	6.63308	0.237047
$784$	−1.16547	−0.0416239
$785$	−20.8974	−0.745862
$786$	68.5902	2.44653
$787$	−25.0949	−0.894538	−0.447269	−	0.894400i	$-0.647603\pi$
$787$	−25.0949	−0.894538	−0.447269	+	0.894400i	$0.647603\pi$
$788$	−45.0102	−1.60342
$789$	−29.9705	−1.06698
$790$	−39.7164	−1.41304
$791$	−36.1274	−1.28454
$792$	0	0
$793$	−21.6142	−0.767542
$794$	58.1924	2.06517
$795$	19.1521	0.679256
$796$	−80.5353	−2.85450
$797$	−12.0763	−0.427763	−0.213881	−	0.976860i	$-0.568611\pi$
$797$	−12.0763	−0.427763	−0.213881	+	0.976860i	$0.568611\pi$
$798$	−13.6563	−0.483429
$799$	−11.8787	−0.420239
$800$	−11.3356	−0.400774
$801$	−4.15478	−0.146802
$802$	−57.9233	−2.04534
$803$	0	0
$804$	30.4987	1.07561
$805$	13.6563	0.481322
$806$	80.5745	2.83812
$807$	21.4028	0.753414
$808$	−25.8279	−0.908621
$809$	−9.11192	−0.320358	−0.160179	−	0.987088i	$-0.551207\pi$
$809$	−9.11192	−0.320358	−0.160179	+	0.987088i	$0.551207\pi$
$810$	10.3233	0.362723
$811$	−2.98999	−0.104993	−0.0524964	−	0.998621i	$-0.516718\pi$
$811$	−2.98999	−0.104993	−0.0524964	+	0.998621i	$0.516718\pi$
$812$	−15.0892	−0.529528
$813$	20.9556	0.734946
$814$	0	0
$815$	9.45539	0.331208
$816$	−24.1107	−0.844043
$817$	−5.62753	−0.196882
$818$	64.7333	2.26335
$819$	−21.2676	−0.743152
$820$	−26.8610	−0.938026
$821$	−35.2697	−1.23092	−0.615460	−	0.788168i	$-0.711030\pi$
$821$	−35.2697	−1.23092	−0.615460	+	0.788168i	$0.711030\pi$
$822$	30.1085	1.05015
$823$	15.5576	0.542303	0.271151	−	0.962537i	$-0.412596\pi$
$823$	15.5576	0.542303	0.271151	+	0.962537i	$0.412596\pi$
$824$	37.6429	1.31135
$825$	0	0
$826$	26.7427	0.930496
$827$	10.5293	0.366140	0.183070	−	0.983100i	$-0.441396\pi$
$827$	10.5293	0.366140	0.183070	+	0.983100i	$0.441396\pi$
$828$	−30.6271	−1.06437
$829$	25.6249	0.889989	0.444994	−	0.895533i	$-0.353206\pi$
$829$	25.6249	0.889989	0.444994	+	0.895533i	$0.353206\pi$
$830$	19.2440	0.667969
$831$	−32.0010	−1.11010
$832$	64.3494	2.23091
$833$	0.206030	0.00713852
$834$	6.97370	0.241479
$835$	9.44902	0.326997
$836$	0	0
$837$	25.7141	0.888809
$838$	−46.3197	−1.60009
$839$	26.1258	0.901964	0.450982	−	0.892533i	$-0.351074\pi$
$839$	26.1258	0.901964	0.450982	+	0.892533i	$0.351074\pi$
$840$	−26.6075	−0.918047
$841$	−27.6138	−0.952200
$842$	−4.00128	−0.137893
$843$	−16.4053	−0.565028
$844$	−72.4549	−2.49400
$845$	32.2676	1.11004
$846$	21.0527	0.723806
$847$	0	0
$848$	144.215	4.95235
$849$	27.9413	0.958943
$850$	4.67975	0.160514
$851$	−3.53793	−0.121279
$852$	25.4224	0.870958
$853$	−2.75490	−0.0943259	−0.0471629	−	0.998887i	$-0.515018\pi$
$853$	−2.75490	−0.0943259	−0.0471629	+	0.998887i	$0.515018\pi$
$854$	22.1165	0.756811
$855$	−1.78356	−0.0609964
$856$	53.4724	1.82765
$857$	−20.3164	−0.693997	−0.346998	−	0.937866i	$-0.612799\pi$
$857$	−20.3164	−0.693997	−0.346998	+	0.937866i	$0.612799\pi$
$858$	0	0
$859$	22.6249	0.771951	0.385975	−	0.922509i	$-0.373865\pi$
$859$	22.6249	0.771951	0.385975	+	0.922509i	$0.373865\pi$
$860$	−18.5669	−0.633126
$861$	−19.3332	−0.658874
$862$	−43.9474	−1.49685
$863$	43.1088	1.46744	0.733721	−	0.679451i	$-0.237782\pi$
$863$	43.1088	1.46744	0.733721	+	0.679451i	$0.237782\pi$
$864$	63.8627	2.17265
$865$	9.08286	0.308826
$866$	−19.6132	−0.666483
$867$	−18.5157	−0.628824
$868$	−58.4955	−1.98547
$869$	0	0
$870$	4.13917	0.140331
$871$	31.3539	1.06239
$872$	−80.5572	−2.72801
$873$	−1.77701	−0.0601425
$874$	−20.2177	−0.683874
$875$	2.62383	0.0887016
$876$	23.3454	0.788767
$877$	16.6853	0.563421	0.281711	−	0.959499i	$-0.409098\pi$
$877$	16.6853	0.563421	0.281711	+	0.959499i	$0.409098\pi$
$878$	45.8082	1.54595
$879$	−19.2011	−0.647638
$880$	0	0
$881$	−43.5116	−1.46594	−0.732972	−	0.680259i	$-0.761867\pi$
$881$	−43.5116	−1.46594	−0.732972	+	0.680259i	$0.761867\pi$
$882$	−0.365148	−0.0122952
$883$	−26.9996	−0.908609	−0.454305	−	0.890846i	$-0.650112\pi$
$883$	−26.9996	−0.908609	−0.454305	+	0.890846i	$0.650112\pi$
$884$	−58.6138	−1.97140
$885$	−5.20473	−0.174955
$886$	38.5277	1.29436
$887$	22.9403	0.770259	0.385130	−	0.922863i	$-0.374157\pi$
$887$	22.9403	0.770259	0.385130	+	0.922863i	$0.374157\pi$
$888$	6.89319	0.231320
$889$	32.3069	1.08354
$890$	−9.04886	−0.303318
$891$	0	0
$892$	114.311	3.82740
$893$	9.86007	0.329955
$894$	−64.5090	−2.15750
$895$	−13.7690	−0.460246
$896$	−6.35951	−0.212456
$897$	46.9199	1.56661
$898$	3.43010	0.114464
$899$	5.37379	0.179226
$900$	−5.88448	−0.196149
$901$	−25.4941	−0.849331
$902$	0	0
$903$	−13.3635	−0.444710
$904$	104.209	3.46594
$905$	−23.8582	−0.793073
$906$	60.5509	2.01167
$907$	41.7337	1.38575	0.692873	−	0.721060i	$-0.256345\pi$
$907$	41.7337	1.38575	0.692873	+	0.721060i	$0.256345\pi$
$908$	12.8161	0.425316
$909$	−4.11125	−0.136362
$910$	−46.3197	−1.53548
$911$	−38.7271	−1.28308	−0.641542	−	0.767088i	$-0.721705\pi$
$911$	−38.7271	−1.28308	−0.641542	+	0.767088i	$0.721705\pi$
$912$	20.0134	0.662708
$913$	0	0
$914$	26.7427	0.884569
$915$	−4.30437	−0.142298
$916$	−107.637	−3.55644
$917$	−51.1914	−1.69049
$918$	−26.3649	−0.870171
$919$	2.85196	0.0940775	0.0470388	−	0.998893i	$-0.485022\pi$
$919$	2.85196	0.0940775	0.0470388	+	0.998893i	$0.485022\pi$
$920$	−39.3915	−1.29870
$921$	−13.7944	−0.454539
$922$	−10.8149	−0.356170
$923$	26.1353	0.860253
$924$	0	0
$925$	−0.679754	−0.0223502
$926$	−85.9627	−2.82491
$927$	5.99196	0.196802
$928$	13.3462	0.438109
$929$	−13.2284	−0.434009	−0.217005	−	0.976171i	$-0.569629\pi$
$929$	−13.2284	−0.434009	−0.217005	+	0.976171i	$0.569629\pi$
$930$	16.0461	0.526172
$931$	−0.171018	−0.00560488
$932$	−26.1062	−0.855138
$933$	−25.6615	−0.840119
$934$	−99.4810	−3.25512
$935$	0	0
$936$	61.3462	2.00516
$937$	−1.68054	−0.0549010	−0.0274505	−	0.999623i	$-0.508739\pi$
$937$	−1.68054	−0.0549010	−0.0274505	+	0.999623i	$0.508739\pi$
$938$	−32.0825	−1.04753
$939$	−20.0629	−0.654728
$940$	32.5313	1.06105
$941$	14.6851	0.478721	0.239361	−	0.970931i	$-0.423062\pi$
$941$	14.6851	0.478721	0.239361	+	0.970931i	$0.423062\pi$
$942$	73.4672	2.39369
$943$	−28.6221	−0.932064
$944$	−39.1914	−1.27557
$945$	−14.7822	−0.480865
$946$	0	0
$947$	17.6535	0.573660	0.286830	−	0.957981i	$-0.407399\pi$
$947$	17.6535	0.573660	0.286830	+	0.957981i	$0.407399\pi$
$948$	99.0643	3.21746
$949$	24.0000	0.779073
$950$	−3.88448	−0.126029
$951$	16.3176	0.529134
$952$	35.4182	1.14791
$953$	−21.7678	−0.705130	−0.352565	−	0.935787i	$-0.614690\pi$
$953$	−21.7678	−0.705130	−0.352565	+	0.935787i	$0.614690\pi$
$954$	45.1832	1.46286
$955$	16.0629	0.519784
$956$	61.4564	1.98764
$957$	0	0
$958$	−16.9500	−0.547631
$959$	−22.4711	−0.725630
$960$	12.8149	0.413599
$961$	−10.1677	−0.327991
$962$	12.0000	0.386896
$963$	8.51168	0.274285
$964$	20.9391	0.674404
$965$	−21.4588	−0.690783
$966$	−48.0103	−1.54471
$967$	14.0684	0.452409	0.226204	−	0.974080i	$-0.427368\pi$
$967$	14.0684	0.452409	0.226204	+	0.974080i	$0.427368\pi$
$968$	0	0
$969$	−3.53793	−0.113655
$970$	−3.87021	−0.124265
$971$	−14.7324	−0.472784	−0.236392	−	0.971658i	$-0.575965\pi$
$971$	−14.7324	−0.472784	−0.236392	+	0.971658i	$0.575965\pi$
$972$	56.8056	1.82204
$973$	−5.20473	−0.166856
$974$	−114.036	−3.65395
$975$	9.01486	0.288706
$976$	−32.4117	−1.03747
$977$	13.1418	0.420444	0.210222	−	0.977654i	$-0.432581\pi$
$977$	13.1418	0.420444	0.210222	+	0.977654i	$0.432581\pi$
$978$	−33.2415	−1.06294
$979$	0	0
$980$	−0.564237	−0.0180239
$981$	−12.8230	−0.409407
$982$	−14.3096	−0.456636
$983$	18.4157	0.587371	0.293686	−	0.955902i	$-0.405118\pi$
$983$	18.4157	0.587371	0.293686	+	0.955902i	$0.405118\pi$
$984$	55.7663	1.77777
$985$	−9.21494	−0.293612
$986$	−5.50979	−0.175468
$987$	23.4144	0.745288
$988$	48.6531	1.54786
$989$	−19.7842	−0.629101
$990$	0	0
$991$	44.3591	1.40911	0.704557	−	0.709647i	$-0.251146\pi$
$991$	44.3591	1.40911	0.704557	+	0.709647i	$0.251146\pi$
$992$	51.7383	1.64269
$993$	−21.2128	−0.673167
$994$	−26.7427	−0.848226
$995$	−16.4880	−0.522704
$996$	−48.0002	−1.52094
$997$	−50.4930	−1.59913	−0.799564	−	0.600581i	$-0.794936\pi$
$997$	−50.4930	−1.59913	−0.799564	+	0.600581i	$0.794936\pi$
$998$	−32.7663	−1.03720
$999$	3.82961	0.121164

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.a.m.1.1	✓	6
3.2	odd	2		5445.2.a.bx.1.6		6
4.3	odd	2		9680.2.a.cw.1.3		6
5.4	even	2		3025.2.a.bg.1.6		6
11.2	odd	10		605.2.g.q.81.1		24
11.3	even	5		605.2.g.q.251.1		24
11.4	even	5		605.2.g.q.511.1		24
11.5	even	5		605.2.g.q.366.6		24
11.6	odd	10		605.2.g.q.366.1		24
11.7	odd	10		605.2.g.q.511.6		24
11.8	odd	10		605.2.g.q.251.6		24
11.9	even	5		605.2.g.q.81.6		24
11.10	odd	2	inner	605.2.a.m.1.6	yes	6
33.32	even	2		5445.2.a.bx.1.1		6
44.43	even	2		9680.2.a.cw.1.4		6
55.54	odd	2		3025.2.a.bg.1.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
605.2.a.m.1.1	✓	6	1.1	even	1	trivial
605.2.a.m.1.6	yes	6	11.10	odd	2	inner
605.2.g.q.81.1		24	11.2	odd	10
605.2.g.q.81.6		24	11.9	even	5
605.2.g.q.251.1		24	11.3	even	5
605.2.g.q.251.6		24	11.8	odd	10
605.2.g.q.366.1		24	11.6	odd	10
605.2.g.q.366.6		24	11.5	even	5
605.2.g.q.511.1		24	11.4	even	5
605.2.g.q.511.6		24	11.7	odd	10
3025.2.a.bg.1.1		6	55.54	odd	2
3025.2.a.bg.1.6		6	5.4	even	2
5445.2.a.bx.1.1		6	33.32	even	2
5445.2.a.bx.1.6		6	3.2	odd	2
9680.2.a.cw.1.3		6	4.3	odd	2
9680.2.a.cw.1.4		6	44.43	even	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:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.a (trivial)

\(f(q)\)	\(=\)	\(q-2.62383 q^{2} +1.33988 q^{3} +4.88448 q^{4} +1.00000 q^{5} -3.51561 q^{6} +2.62383 q^{7} -7.56839 q^{8} -1.20473 q^{9} +O(q^{10})\)	\(q-2.62383 q^{2} +1.33988 q^{3} +4.88448 q^{4} +1.00000 q^{5} -3.51561 q^{6} +2.62383 q^{7} -7.56839 q^{8} -1.20473 q^{9} -2.62383 q^{10} +6.54461 q^{12} +6.72812 q^{13} -6.88448 q^{14} +1.33988 q^{15} +10.0892 q^{16} -1.78356 q^{17} +3.16101 q^{18} +1.48046 q^{19} +4.88448 q^{20} +3.51561 q^{21} +5.20473 q^{23} -10.1407 q^{24} +1.00000 q^{25} -17.6535 q^{26} -5.63382 q^{27} +12.8161 q^{28} -1.17737 q^{29} -3.51561 q^{30} -4.56424 q^{31} -11.3356 q^{32} +4.67975 q^{34} +2.62383 q^{35} -5.88448 q^{36} -0.679754 q^{37} -3.88448 q^{38} +9.01486 q^{39} -7.56839 q^{40} -5.49925 q^{41} -9.22436 q^{42} -3.80120 q^{43} -1.20473 q^{45} -13.6563 q^{46} +6.66012 q^{47} +13.5183 q^{48} -0.115516 q^{49} -2.62383 q^{50} -2.38975 q^{51} +32.8634 q^{52} +14.2939 q^{53} +14.7822 q^{54} -19.8582 q^{56} +1.98364 q^{57} +3.08921 q^{58} -3.88448 q^{59} +6.54461 q^{60} -3.21251 q^{61} +11.9758 q^{62} -3.16101 q^{63} +9.56424 q^{64} +6.72812 q^{65} +4.66012 q^{67} -8.71176 q^{68} +6.97370 q^{69} -6.88448 q^{70} +3.88448 q^{71} +9.11787 q^{72} +3.56712 q^{73} +1.78356 q^{74} +1.33988 q^{75} +7.23130 q^{76} -23.6535 q^{78} +15.1368 q^{79} +10.0892 q^{80} -3.93444 q^{81} +14.4291 q^{82} -7.33431 q^{83} +17.1719 q^{84} -1.78356 q^{85} +9.97370 q^{86} -1.57753 q^{87} +3.44872 q^{89} +3.16101 q^{90} +17.6535 q^{91} +25.4224 q^{92} -6.11552 q^{93} -17.4750 q^{94} +1.48046 q^{95} -15.1883 q^{96} +1.47502 q^{97} +0.303095 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{3} + 6 q^{4} + 6 q^{5} + 12 q^{9}+O(q^{10}) \) 6 * q + 6 * q^3 + 6 * q^4 + 6 * q^5 + 12 * q^9	\( 6 q + 6 q^{3} + 6 q^{4} + 6 q^{5} + 12 q^{9} + 18 q^{12} - 18 q^{14} + 6 q^{15} + 18 q^{16} + 6 q^{20} + 12 q^{23} + 6 q^{25} - 36 q^{26} + 30 q^{27} + 24 q^{34} - 12 q^{36} - 30 q^{42} + 12 q^{45} + 42 q^{47} - 6 q^{48} - 24 q^{49} + 24 q^{53} - 30 q^{56} - 24 q^{58} + 18 q^{60} + 30 q^{64} + 30 q^{67} - 24 q^{69} - 18 q^{70} + 6 q^{75} - 72 q^{78} + 18 q^{80} + 30 q^{81} + 42 q^{82} - 6 q^{86} - 30 q^{89} + 36 q^{91} + 36 q^{92} - 60 q^{93} + 24 q^{97}+O(q^{100}) \) 6 * q + 6 * q^3 + 6 * q^4 + 6 * q^5 + 12 * q^9 + 18 * q^12 - 18 * q^14 + 6 * q^15 + 18 * q^16 + 6 * q^20 + 12 * q^23 + 6 * q^25 - 36 * q^26 + 30 * q^27 + 24 * q^34 - 12 * q^36 - 30 * q^42 + 12 * q^45 + 42 * q^47 - 6 * q^48 - 24 * q^49 + 24 * q^53 - 30 * q^56 - 24 * q^58 + 18 * q^60 + 30 * q^64 + 30 * q^67 - 24 * q^69 - 18 * q^70 + 6 * q^75 - 72 * q^78 + 18 * q^80 + 30 * q^81 + 42 * q^82 - 6 * q^86 - 30 * q^89 + 36 * q^91 + 36 * q^92 - 60 * q^93 + 24 * q^97

Introduction

L-functions

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