LMFDB - Embedded newform 6025.2.a.h.1.1

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			1.1
Root			$2.70063$ 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)

$f(q)$	$=$	$q-2.70063 q^{2} +2.50808 q^{3} +5.29342 q^{4} -6.77340 q^{6} -0.354992 q^{7} -8.89432 q^{8} +3.29045 q^{9} +O(q^{10})$	\(q-2.70063 q^{2} +2.50808 q^{3} +5.29342 q^{4} -6.77340 q^{6} -0.354992 q^{7} -8.89432 q^{8} +3.29045 q^{9} +4.18781 q^{11} +13.2763 q^{12} +3.72447 q^{13} +0.958703 q^{14} +13.4334 q^{16} +6.46259 q^{17} -8.88631 q^{18} -1.31002 q^{19} -0.890347 q^{21} -11.3097 q^{22} +4.10799 q^{23} -22.3076 q^{24} -10.0584 q^{26} +0.728479 q^{27} -1.87912 q^{28} -8.85227 q^{29} +5.11371 q^{31} -18.4902 q^{32} +10.5034 q^{33} -17.4531 q^{34} +17.4177 q^{36} -5.41403 q^{37} +3.53789 q^{38} +9.34127 q^{39} +11.8244 q^{41} +2.40450 q^{42} -0.673253 q^{43} +22.1678 q^{44} -11.0942 q^{46} -5.22965 q^{47} +33.6921 q^{48} -6.87398 q^{49} +16.2087 q^{51} +19.7152 q^{52} +9.92404 q^{53} -1.96735 q^{54} +3.15741 q^{56} -3.28564 q^{57} +23.9067 q^{58} -1.23315 q^{59} +4.04837 q^{61} -13.8102 q^{62} -1.16808 q^{63} +23.0683 q^{64} -28.3657 q^{66} +14.0522 q^{67} +34.2092 q^{68} +10.3032 q^{69} +13.0525 q^{71} -29.2663 q^{72} -7.76916 q^{73} +14.6213 q^{74} -6.93450 q^{76} -1.48664 q^{77} -25.2273 q^{78} -1.17673 q^{79} -8.04428 q^{81} -31.9333 q^{82} -6.25297 q^{83} -4.71298 q^{84} +1.81821 q^{86} -22.2022 q^{87} -37.2477 q^{88} +3.80839 q^{89} -1.32216 q^{91} +21.7453 q^{92} +12.8256 q^{93} +14.1234 q^{94} -46.3748 q^{96} +9.91591 q^{97} +18.5641 q^{98} +13.7798 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.70063	−1.90964	−0.954818	−	0.297191i	$-0.903950\pi$
$2$	−2.70063	−1.90964	−0.954818	+	0.297191i	$0.903950\pi$
$3$	2.50808	1.44804	0.724020	−	0.689779i	$-0.242292\pi$
$3$	2.50808	1.44804	0.724020	+	0.689779i	$0.242292\pi$
$4$	5.29342	2.64671
$5$	0	0
$5$	0	0
$6$	−6.77340	−2.76523
$7$	−0.354992	−0.134174	−0.0670872	−	0.997747i	$-0.521371\pi$
$7$	−0.354992	−0.134174	−0.0670872	+	0.997747i	$0.521371\pi$
$8$	−8.89432	−3.14462
$9$	3.29045	1.09682
$10$	0	0
$11$	4.18781	1.26267	0.631336	−	0.775509i	$-0.282507\pi$
$11$	4.18781	1.26267	0.631336	+	0.775509i	$0.282507\pi$
$12$	13.2763	3.83254
$13$	3.72447	1.03298	0.516492	−	0.856292i	$-0.327238\pi$
$13$	3.72447	1.03298	0.516492	+	0.856292i	$0.327238\pi$
$14$	0.958703	0.256224
$15$	0	0
$16$	13.4334	3.35836
$17$	6.46259	1.56741	0.783704	−	0.621134i	$-0.213328\pi$
$17$	6.46259	1.56741	0.783704	+	0.621134i	$0.213328\pi$
$18$	−8.88631	−2.09452
$19$	−1.31002	−0.300540	−0.150270	−	0.988645i	$-0.548014\pi$
$19$	−1.31002	−0.300540	−0.150270	+	0.988645i	$0.548014\pi$
$20$	0	0
$21$	−0.890347	−0.194290
$22$	−11.3097	−2.41124
$23$	4.10799	0.856576	0.428288	−	0.903642i	$-0.359117\pi$
$23$	4.10799	0.856576	0.428288	+	0.903642i	$0.359117\pi$
$24$	−22.3076	−4.55353
$25$	0	0
$26$	−10.0584	−1.97262
$27$	0.728479	0.140196
$28$	−1.87912	−0.355121
$29$	−8.85227	−1.64382	−0.821912	−	0.569614i	$-0.807093\pi$
$29$	−8.85227	−1.64382	−0.821912	+	0.569614i	$0.807093\pi$
$30$	0	0
$31$	5.11371	0.918449	0.459225	−	0.888320i	$-0.348127\pi$
$31$	5.11371	0.918449	0.459225	+	0.888320i	$0.348127\pi$
$32$	−18.4902	−3.26863
$33$	10.5034	1.82840
$34$	−17.4531	−2.99318
$35$	0	0
$36$	17.4177	2.90296
$37$	−5.41403	−0.890061	−0.445030	−	0.895515i	$-0.646807\pi$
$37$	−5.41403	−0.890061	−0.445030	+	0.895515i	$0.646807\pi$
$38$	3.53789	0.573922
$39$	9.34127	1.49580
$40$	0	0
$41$	11.8244	1.84665	0.923327	−	0.384014i	$-0.125459\pi$
$41$	11.8244	1.84665	0.923327	+	0.384014i	$0.125459\pi$
$42$	2.40450	0.371023
$43$	−0.673253	−0.102670	−0.0513350	−	0.998681i	$-0.516348\pi$
$43$	−0.673253	−0.102670	−0.0513350	+	0.998681i	$0.516348\pi$
$44$	22.1678	3.34193
$45$	0	0
$46$	−11.0942	−1.63575
$47$	−5.22965	−0.762823	−0.381412	−	0.924405i	$-0.624562\pi$
$47$	−5.22965	−0.762823	−0.381412	+	0.924405i	$0.624562\pi$
$48$	33.6921	4.86304
$49$	−6.87398	−0.981997
$50$	0	0
$51$	16.2087	2.26967
$52$	19.7152	2.73401
$53$	9.92404	1.36317	0.681586	−	0.731738i	$-0.261291\pi$
$53$	9.92404	1.36317	0.681586	+	0.731738i	$0.261291\pi$
$54$	−1.96735	−0.267723
$55$	0	0
$56$	3.15741	0.421927
$57$	−3.28564	−0.435194
$58$	23.9067	3.13911
$59$	−1.23315	−0.160542	−0.0802710	−	0.996773i	$-0.525579\pi$
$59$	−1.23315	−0.160542	−0.0802710	+	0.996773i	$0.525579\pi$
$60$	0	0
$61$	4.04837	0.518341	0.259170	−	0.965832i	$-0.416551\pi$
$61$	4.04837	0.518341	0.259170	+	0.965832i	$0.416551\pi$
$62$	−13.8102	−1.75390
$63$	−1.16808	−0.147165
$64$	23.0683	2.88354
$65$	0	0
$66$	−28.3657	−3.49158
$67$	14.0522	1.71675	0.858375	−	0.513022i	$-0.171474\pi$
$67$	14.0522	1.71675	0.858375	+	0.513022i	$0.171474\pi$
$68$	34.2092	4.14847
$69$	10.3032	1.24036
$70$	0	0
$71$	13.0525	1.54905	0.774526	−	0.632542i	$-0.217989\pi$
$71$	13.0525	1.54905	0.774526	+	0.632542i	$0.217989\pi$
$72$	−29.2663	−3.44907
$73$	−7.76916	−0.909312	−0.454656	−	0.890667i	$-0.650238\pi$
$73$	−7.76916	−0.909312	−0.454656	+	0.890667i	$0.650238\pi$
$74$	14.6213	1.69969
$75$	0	0
$76$	−6.93450	−0.795442
$77$	−1.48664	−0.169418
$78$	−25.2273	−2.85643
$79$	−1.17673	−0.132393	−0.0661963	−	0.997807i	$-0.521086\pi$
$79$	−1.17673	−0.132393	−0.0661963	+	0.997807i	$0.521086\pi$
$80$	0	0
$81$	−8.04428	−0.893809
$82$	−31.9333	−3.52644
$83$	−6.25297	−0.686353	−0.343176	−	0.939271i	$-0.611503\pi$
$83$	−6.25297	−0.686353	−0.343176	+	0.939271i	$0.611503\pi$
$84$	−4.71298	−0.514228
$85$	0	0
$86$	1.81821	0.196062
$87$	−22.2022	−2.38032
$88$	−37.2477	−3.97062
$89$	3.80839	0.403688	0.201844	−	0.979418i	$-0.435307\pi$
$89$	3.80839	0.403688	0.201844	+	0.979418i	$0.435307\pi$
$90$	0	0
$91$	−1.32216	−0.138600
$92$	21.7453	2.26711
$93$	12.8256	1.32995
$94$	14.1234	1.45671
$95$	0	0
$96$	−46.3748	−4.73311
$97$	9.91591	1.00681	0.503404	−	0.864051i	$-0.332081\pi$
$97$	9.91591	1.00681	0.503404	+	0.864051i	$0.332081\pi$
$98$	18.5641	1.87526
$99$	13.7798	1.38492
$100$	0	0
$101$	7.46224	0.742521	0.371260	−	0.928529i	$-0.378926\pi$
$101$	7.46224	0.742521	0.371260	+	0.928529i	$0.378926\pi$
$102$	−43.7737	−4.33424
$103$	−7.83988	−0.772486	−0.386243	−	0.922397i	$-0.626227\pi$
$103$	−7.83988	−0.772486	−0.386243	+	0.922397i	$0.626227\pi$
$104$	−33.1267	−3.24834
$105$	0	0
$106$	−26.8012	−2.60316
$107$	0.890206	0.0860595	0.0430297	−	0.999074i	$-0.486299\pi$
$107$	0.890206	0.0860595	0.0430297	+	0.999074i	$0.486299\pi$
$108$	3.85614	0.371058
$109$	3.92555	0.375999	0.188000	−	0.982169i	$-0.439800\pi$
$109$	3.92555	0.375999	0.188000	+	0.982169i	$0.439800\pi$
$110$	0	0
$111$	−13.5788	−1.28884
$112$	−4.76877	−0.450606
$113$	−17.3995	−1.63681	−0.818404	−	0.574643i	$-0.805141\pi$
$113$	−17.3995	−1.63681	−0.818404	+	0.574643i	$0.805141\pi$
$114$	8.87331	0.831061
$115$	0	0
$116$	−46.8588	−4.35073
$117$	12.2552	1.13299
$118$	3.33028	0.306577
$119$	−2.29417	−0.210306
$120$	0	0
$121$	6.53776	0.594342
$122$	−10.9332	−0.989842
$123$	29.6564	2.67403
$124$	27.0690	2.43087
$125$	0	0
$126$	3.15457	0.281031
$127$	−18.7331	−1.66230	−0.831148	−	0.556052i	$-0.812316\pi$
$127$	−18.7331	−1.66230	−0.831148	+	0.556052i	$0.812316\pi$
$128$	−25.3187	−2.23787
$129$	−1.68857	−0.148670
$130$	0	0
$131$	−1.40627	−0.122867	−0.0614333	−	0.998111i	$-0.519567\pi$
$131$	−1.40627	−0.122867	−0.0614333	+	0.998111i	$0.519567\pi$
$132$	55.5987	4.83924
$133$	0.465048	0.0403247
$134$	−37.9499	−3.27837
$135$	0	0
$136$	−57.4803	−4.92890
$137$	−5.54974	−0.474146	−0.237073	−	0.971492i	$-0.576188\pi$
$137$	−5.54974	−0.474146	−0.237073	+	0.971492i	$0.576188\pi$
$138$	−27.8251	−2.36863
$139$	−11.1540	−0.946072	−0.473036	−	0.881043i	$-0.656842\pi$
$139$	−11.1540	−0.946072	−0.473036	+	0.881043i	$0.656842\pi$
$140$	0	0
$141$	−13.1164	−1.10460
$142$	−35.2501	−2.95812
$143$	15.5974	1.30432
$144$	44.2021	3.68351
$145$	0	0
$146$	20.9817	1.73645
$147$	−17.2405	−1.42197
$148$	−28.6587	−2.35573
$149$	8.27009	0.677512	0.338756	−	0.940874i	$-0.389994\pi$
$149$	8.27009	0.677512	0.338756	+	0.940874i	$0.389994\pi$
$150$	0	0
$151$	−11.8990	−0.968323	−0.484162	−	0.874979i	$-0.660875\pi$
$151$	−11.8990	−0.968323	−0.484162	+	0.874979i	$0.660875\pi$
$152$	11.6518	0.945083
$153$	21.2648	1.71916
$154$	4.01487	0.323527
$155$	0	0
$156$	49.4473	3.95895
$157$	5.88156	0.469399	0.234700	−	0.972068i	$-0.424589\pi$
$157$	5.88156	0.469399	0.234700	+	0.972068i	$0.424589\pi$
$158$	3.17792	0.252822
$159$	24.8903	1.97393
$160$	0	0
$161$	−1.45830	−0.114930
$162$	21.7246	1.70685
$163$	3.21033	0.251452	0.125726	−	0.992065i	$-0.459874\pi$
$163$	3.21033	0.251452	0.125726	+	0.992065i	$0.459874\pi$
$164$	62.5913	4.88756
$165$	0	0
$166$	16.8870	1.31068
$167$	9.62511	0.744813	0.372407	−	0.928070i	$-0.378533\pi$
$167$	9.62511	0.744813	0.372407	+	0.928070i	$0.378533\pi$
$168$	7.91903	0.610967
$169$	0.871711	0.0670547
$170$	0	0
$171$	−4.31057	−0.329637
$172$	−3.56381	−0.271738
$173$	11.7677	0.894682	0.447341	−	0.894364i	$-0.352371\pi$
$173$	11.7677	0.894682	0.447341	+	0.894364i	$0.352371\pi$
$174$	59.9599	4.54555
$175$	0	0
$176$	56.2567	4.24051
$177$	−3.09283	−0.232471
$178$	−10.2851	−0.770898
$179$	−4.74606	−0.354737	−0.177369	−	0.984144i	$-0.556759\pi$
$179$	−4.74606	−0.354737	−0.177369	+	0.984144i	$0.556759\pi$
$180$	0	0
$181$	−9.56167	−0.710713	−0.355357	−	0.934731i	$-0.615641\pi$
$181$	−9.56167	−0.710713	−0.355357	+	0.934731i	$0.615641\pi$
$182$	3.57066	0.264675
$183$	10.1536	0.750578
$184$	−36.5378	−2.69360
$185$	0	0
$186$	−34.6372	−2.53972
$187$	27.0641	1.97912
$188$	−27.6827	−2.01897
$189$	−0.258604	−0.0188107
$190$	0	0
$191$	23.1412	1.67444	0.837218	−	0.546870i	$-0.184181\pi$
$191$	23.1412	1.67444	0.837218	+	0.546870i	$0.184181\pi$
$192$	57.8571	4.17548
$193$	−9.15643	−0.659095	−0.329547	−	0.944139i	$-0.606896\pi$
$193$	−9.15643	−0.659095	−0.329547	+	0.944139i	$0.606896\pi$
$194$	−26.7792	−1.92264
$195$	0	0
$196$	−36.3869	−2.59906
$197$	6.75045	0.480950	0.240475	−	0.970655i	$-0.422697\pi$
$197$	6.75045	0.480950	0.240475	+	0.970655i	$0.422697\pi$
$198$	−37.2142	−2.64470
$199$	3.26300	0.231308	0.115654	−	0.993290i	$-0.463104\pi$
$199$	3.26300	0.231308	0.115654	+	0.993290i	$0.463104\pi$
$200$	0	0
$201$	35.2440	2.48592
$202$	−20.1528	−1.41794
$203$	3.14248	0.220559
$204$	85.7993	6.00715
$205$	0	0
$206$	21.1726	1.47517
$207$	13.5172	0.939507
$208$	50.0325	3.46913
$209$	−5.48613	−0.379483
$210$	0	0
$211$	−23.1474	−1.59354	−0.796768	−	0.604285i	$-0.793459\pi$
$211$	−23.1474	−1.59354	−0.796768	+	0.604285i	$0.793459\pi$
$212$	52.5321	3.60792
$213$	32.7368	2.24309
$214$	−2.40412	−0.164342
$215$	0	0
$216$	−6.47932	−0.440862
$217$	−1.81532	−0.123232
$218$	−10.6015	−0.718022
$219$	−19.4857	−1.31672
$220$	0	0
$221$	24.0698	1.61911
$222$	36.6714	2.46122
$223$	18.2948	1.22511	0.612557	−	0.790427i	$-0.290141\pi$
$223$	18.2948	1.22511	0.612557	+	0.790427i	$0.290141\pi$
$224$	6.56387	0.438567
$225$	0	0
$226$	46.9897	3.12571
$227$	−10.4809	−0.695642	−0.347821	−	0.937561i	$-0.613078\pi$
$227$	−10.4809	−0.695642	−0.347821	+	0.937561i	$0.613078\pi$
$228$	−17.3923	−1.15183
$229$	−5.51626	−0.364524	−0.182262	−	0.983250i	$-0.558342\pi$
$229$	−5.51626	−0.364524	−0.182262	+	0.983250i	$0.558342\pi$
$230$	0	0
$231$	−3.72861	−0.245324
$232$	78.7349	5.16920
$233$	−27.7343	−1.81693	−0.908466	−	0.417959i	$-0.862746\pi$
$233$	−27.7343	−1.81693	−0.908466	+	0.417959i	$0.862746\pi$
$234$	−33.0968	−2.16361
$235$	0	0
$236$	−6.52756	−0.424908
$237$	−2.95133	−0.191710
$238$	6.19570	0.401608
$239$	6.60568	0.427286	0.213643	−	0.976912i	$-0.431467\pi$
$239$	6.60568	0.427286	0.213643	+	0.976912i	$0.431467\pi$
$240$	0	0
$241$	1.00000	0.0644157
$241$	1.00000	0.0644157
$242$	−17.6561	−1.13498
$243$	−22.3611	−1.43447
$244$	21.4297	1.37190
$245$	0	0
$246$	−80.0911	−5.10642
$247$	−4.87915	−0.310453
$248$	−45.4829	−2.88817
$249$	−15.6829	−0.993865
$250$	0	0
$251$	21.2628	1.34210	0.671049	−	0.741413i	$-0.265844\pi$
$251$	21.2628	1.34210	0.671049	+	0.741413i	$0.265844\pi$
$252$	−6.18316	−0.389502
$253$	17.2035	1.08157
$254$	50.5913	3.17438
$255$	0	0
$256$	22.2398	1.38999
$257$	−7.33227	−0.457374	−0.228687	−	0.973500i	$-0.573443\pi$
$257$	−7.33227	−0.457374	−0.228687	+	0.973500i	$0.573443\pi$
$258$	4.56021	0.283906
$259$	1.92194	0.119423
$260$	0	0
$261$	−29.1280	−1.80298
$262$	3.79782	0.234630
$263$	−20.6204	−1.27151	−0.635753	−	0.771892i	$-0.719310\pi$
$263$	−20.6204	−1.27151	−0.635753	+	0.771892i	$0.719310\pi$
$264$	−93.4202	−5.74961
$265$	0	0
$266$	−1.25592	−0.0770056
$267$	9.55173	0.584557
$268$	74.3842	4.54374
$269$	−0.178772	−0.0108999	−0.00544997	−	0.999985i	$-0.501735\pi$
$269$	−0.178772	−0.0108999	−0.00544997	+	0.999985i	$0.501735\pi$
$270$	0	0
$271$	−17.9311	−1.08923	−0.544617	−	0.838685i	$-0.683325\pi$
$271$	−17.9311	−1.08923	−0.544617	+	0.838685i	$0.683325\pi$
$272$	86.8149	5.26392
$273$	−3.31608	−0.200698
$274$	14.9878	0.905446
$275$	0	0
$276$	54.5390	3.28286
$277$	−2.56354	−0.154028	−0.0770140	−	0.997030i	$-0.524539\pi$
$277$	−2.56354	−0.154028	−0.0770140	+	0.997030i	$0.524539\pi$
$278$	30.1229	1.80665
$279$	16.8264	1.00737
$280$	0	0
$281$	−22.4531	−1.33944	−0.669720	−	0.742614i	$-0.733586\pi$
$281$	−22.4531	−1.33944	−0.669720	+	0.742614i	$0.733586\pi$
$282$	35.4225	2.10938
$283$	−13.1240	−0.780141	−0.390070	−	0.920785i	$-0.627549\pi$
$283$	−13.1240	−0.780141	−0.390070	+	0.920785i	$0.627549\pi$
$284$	69.0926	4.09989
$285$	0	0
$286$	−42.1228	−2.49078
$287$	−4.19755	−0.247774
$288$	−60.8411	−3.58509
$289$	24.7651	1.45677
$290$	0	0
$291$	24.8699	1.45790
$292$	−41.1254	−2.40668
$293$	32.3935	1.89245	0.946225	−	0.323509i	$-0.104863\pi$
$293$	32.3935	1.89245	0.946225	+	0.323509i	$0.104863\pi$
$294$	46.5602	2.71545
$295$	0	0
$296$	48.1541	2.79890
$297$	3.05073	0.177021
$298$	−22.3345	−1.29380
$299$	15.3001	0.884829
$300$	0	0
$301$	0.238999	0.0137757
$302$	32.1347	1.84914
$303$	18.7159	1.07520
$304$	−17.5981	−1.00932
$305$	0	0
$306$	−57.4286	−3.28297
$307$	−12.6847	−0.723952	−0.361976	−	0.932187i	$-0.617898\pi$
$307$	−12.6847	−0.723952	−0.361976	+	0.932187i	$0.617898\pi$
$308$	−7.86940	−0.448401
$309$	−19.6630	−1.11859
$310$	0	0
$311$	22.1050	1.25346	0.626730	−	0.779236i	$-0.284393\pi$
$311$	22.1050	1.25346	0.626730	+	0.779236i	$0.284393\pi$
$312$	−83.0842	−4.70372
$313$	−10.8859	−0.615305	−0.307653	−	0.951499i	$-0.599543\pi$
$313$	−10.8859	−0.615305	−0.307653	+	0.951499i	$0.599543\pi$
$314$	−15.8839	−0.896382
$315$	0	0
$316$	−6.22893	−0.350405
$317$	7.76634	0.436201	0.218101	−	0.975926i	$-0.430014\pi$
$317$	7.76634	0.436201	0.218101	+	0.975926i	$0.430014\pi$
$318$	−67.2195	−3.76948
$319$	−37.0716	−2.07561
$320$	0	0
$321$	2.23271	0.124618
$322$	3.93835	0.219475
$323$	−8.46614	−0.471069
$324$	−42.5817	−2.36565
$325$	0	0
$326$	−8.66992	−0.480182
$327$	9.84558	0.544462
$328$	−105.170	−5.80702
$329$	1.85648	0.102351
$330$	0	0
$331$	0.317941	0.0174756	0.00873781	−	0.999962i	$-0.497219\pi$
$331$	0.317941	0.0174756	0.00873781	+	0.999962i	$0.497219\pi$
$332$	−33.0996	−1.81658
$333$	−17.8146	−0.976235
$334$	−25.9939	−1.42232
$335$	0	0
$336$	−11.9604	−0.652495
$337$	10.0901	0.549641	0.274821	−	0.961496i	$-0.411382\pi$
$337$	10.0901	0.549641	0.274821	+	0.961496i	$0.411382\pi$
$338$	−2.35417	−0.128050
$339$	−43.6393	−2.37016
$340$	0	0
$341$	21.4152	1.15970
$342$	11.6413	0.629488
$343$	4.92515	0.265933
$344$	5.98812	0.322858
$345$	0	0
$346$	−31.7802	−1.70852
$347$	12.2330	0.656700	0.328350	−	0.944556i	$-0.393508\pi$
$347$	12.2330	0.656700	0.328350	+	0.944556i	$0.393508\pi$
$348$	−117.525	−6.30002
$349$	0.0471917	0.00252612	0.00126306	−	0.999999i	$-0.499598\pi$
$349$	0.0471917	0.00252612	0.00126306	+	0.999999i	$0.499598\pi$
$350$	0	0
$351$	2.71320	0.144820
$352$	−77.4334	−4.12721
$353$	−9.38275	−0.499393	−0.249697	−	0.968324i	$-0.580331\pi$
$353$	−9.38275	−0.499393	−0.249697	+	0.968324i	$0.580331\pi$
$354$	8.35259	0.443935
$355$	0	0
$356$	20.1594	1.06845
$357$	−5.75395	−0.304531
$358$	12.8174	0.677419
$359$	4.83057	0.254948	0.127474	−	0.991842i	$-0.459313\pi$
$359$	4.83057	0.254948	0.127474	+	0.991842i	$0.459313\pi$
$360$	0	0
$361$	−17.2838	−0.909676
$362$	25.8226	1.35720
$363$	16.3972	0.860630
$364$	−6.99874	−0.366834
$365$	0	0
$366$	−27.4212	−1.43333
$367$	26.6792	1.39264	0.696322	−	0.717730i	$-0.254819\pi$
$367$	26.6792	1.39264	0.696322	+	0.717730i	$0.254819\pi$
$368$	55.1845	2.87669
$369$	38.9075	2.02544
$370$	0	0
$371$	−3.52295	−0.182903
$372$	67.8911	3.51999
$373$	1.30441	0.0675400	0.0337700	−	0.999430i	$-0.489249\pi$
$373$	1.30441	0.0675400	0.0337700	+	0.999430i	$0.489249\pi$
$374$	−73.0902	−3.77940
$375$	0	0
$376$	46.5142	2.39879
$377$	−32.9700	−1.69804
$378$	0.698395	0.0359216
$379$	−3.62474	−0.186191	−0.0930953	−	0.995657i	$-0.529676\pi$
$379$	−3.62474	−0.186191	−0.0930953	+	0.995657i	$0.529676\pi$
$380$	0	0
$381$	−46.9841	−2.40707
$382$	−62.4958	−3.19756
$383$	28.5501	1.45884	0.729420	−	0.684066i	$-0.239790\pi$
$383$	28.5501	1.45884	0.729420	+	0.684066i	$0.239790\pi$
$384$	−63.5011	−3.24053
$385$	0	0
$386$	24.7282	1.25863
$387$	−2.21531	−0.112610
$388$	52.4891	2.66473
$389$	29.3393	1.48756	0.743780	−	0.668424i	$-0.233031\pi$
$389$	29.3393	1.48756	0.743780	+	0.668424i	$0.233031\pi$
$390$	0	0
$391$	26.5483	1.34260
$392$	61.1394	3.08800
$393$	−3.52704	−0.177916
$394$	−18.2305	−0.918439
$395$	0	0
$396$	72.9422	3.66548
$397$	−3.94029	−0.197758	−0.0988788	−	0.995099i	$-0.531526\pi$
$397$	−3.94029	−0.197758	−0.0988788	+	0.995099i	$0.531526\pi$
$398$	−8.81218	−0.441715
$399$	1.16638	0.0583918
$400$	0	0
$401$	0.0336542	0.00168061	0.000840304	−	1.00000i	$-0.499733\pi$
$401$	0.0336542	0.00168061	0.000840304		1.00000i	$0.499733\pi$
$402$	−95.1812	−4.74721
$403$	19.0459	0.948743
$404$	39.5008	1.96524
$405$	0	0
$406$	−8.48669	−0.421188
$407$	−22.6729	−1.12386
$408$	−144.165	−7.13724
$409$	−8.89629	−0.439893	−0.219947	−	0.975512i	$-0.570588\pi$
$409$	−8.89629	−0.439893	−0.219947	+	0.975512i	$0.570588\pi$
$410$	0	0
$411$	−13.9192	−0.686582
$412$	−41.4998	−2.04455
$413$	0.437757	0.0215406
$414$	−36.5049	−1.79412
$415$	0	0
$416$	−68.8662	−3.37644
$417$	−27.9752	−1.36995
$418$	14.8160	0.724675
$419$	−29.8619	−1.45885	−0.729425	−	0.684061i	$-0.760212\pi$
$419$	−29.8619	−1.45885	−0.729425	+	0.684061i	$0.760212\pi$
$420$	0	0
$421$	15.9683	0.778247	0.389124	−	0.921186i	$-0.372778\pi$
$421$	15.9683	0.778247	0.389124	+	0.921186i	$0.372778\pi$
$422$	62.5128	3.04307
$423$	−17.2079	−0.836678
$424$	−88.2676	−4.28665
$425$	0	0
$426$	−88.4100	−4.28348
$427$	−1.43714	−0.0695480
$428$	4.71223	0.227774
$429$	39.1195	1.88871
$430$	0	0
$431$	24.8345	1.19624	0.598118	−	0.801408i	$-0.295915\pi$
$431$	24.8345	1.19624	0.598118	+	0.801408i	$0.295915\pi$
$432$	9.78598	0.470828
$433$	31.1730	1.49808	0.749040	−	0.662524i	$-0.230515\pi$
$433$	31.1730	1.49808	0.749040	+	0.662524i	$0.230515\pi$
$434$	4.90253	0.235329
$435$	0	0
$436$	20.7796	0.995161
$437$	−5.38157	−0.257435
$438$	52.6236	2.51445
$439$	−0.959384	−0.0457889	−0.0228944	−	0.999738i	$-0.507288\pi$
$439$	−0.959384	−0.0457889	−0.0228944	+	0.999738i	$0.507288\pi$
$440$	0	0
$441$	−22.6185	−1.07707
$442$	−65.0036	−3.09190
$443$	−6.52446	−0.309986	−0.154993	−	0.987916i	$-0.549536\pi$
$443$	−6.52446	−0.309986	−0.154993	+	0.987916i	$0.549536\pi$
$444$	−71.8783	−3.41119
$445$	0	0
$446$	−49.4077	−2.33952
$447$	20.7420	0.981065
$448$	−8.18906	−0.386897
$449$	−9.39811	−0.443524	−0.221762	−	0.975101i	$-0.571181\pi$
$449$	−9.39811	−0.443524	−0.221762	+	0.975101i	$0.571181\pi$
$450$	0	0
$451$	49.5182	2.33172
$452$	−92.1029	−4.33216
$453$	−29.8435	−1.40217
$454$	28.3051	1.32842
$455$	0	0
$456$	29.2235	1.36852
$457$	27.0904	1.26724	0.633618	−	0.773646i	$-0.281569\pi$
$457$	27.0904	1.26724	0.633618	+	0.773646i	$0.281569\pi$
$458$	14.8974	0.696109
$459$	4.70786	0.219744
$460$	0	0
$461$	−32.1068	−1.49536	−0.747682	−	0.664057i	$-0.768833\pi$
$461$	−32.1068	−1.49536	−0.747682	+	0.664057i	$0.768833\pi$
$462$	10.0696	0.468480
$463$	−17.5754	−0.816797	−0.408399	−	0.912804i	$-0.633913\pi$
$463$	−17.5754	−0.816797	−0.408399	+	0.912804i	$0.633913\pi$
$464$	−118.916	−5.52056
$465$	0	0
$466$	74.9001	3.46968
$467$	−12.9732	−0.600329	−0.300164	−	0.953887i	$-0.597042\pi$
$467$	−12.9732	−0.600329	−0.300164	+	0.953887i	$0.597042\pi$
$468$	64.8720	2.99871
$469$	−4.98842	−0.230344
$470$	0	0
$471$	14.7514	0.679708
$472$	10.9680	0.504843
$473$	−2.81945	−0.129639
$474$	7.97046	0.366096
$475$	0	0
$476$	−12.1440	−0.556619
$477$	32.6546	1.49515
$478$	−17.8395	−0.815960
$479$	−6.68222	−0.305319	−0.152659	−	0.988279i	$-0.548784\pi$
$479$	−6.68222	−0.305319	−0.152659	+	0.988279i	$0.548784\pi$
$480$	0	0
$481$	−20.1644	−0.919418
$482$	−2.70063	−0.123010
$483$	−3.65754	−0.166424
$484$	34.6071	1.57305
$485$	0	0
$486$	60.3892	2.73931
$487$	−19.6021	−0.888256	−0.444128	−	0.895963i	$-0.646486\pi$
$487$	−19.6021	−0.888256	−0.444128	+	0.895963i	$0.646486\pi$
$488$	−36.0075	−1.62998
$489$	8.05175	0.364113
$490$	0	0
$491$	−6.61946	−0.298732	−0.149366	−	0.988782i	$-0.547723\pi$
$491$	−6.61946	−0.298732	−0.149366	+	0.988782i	$0.547723\pi$
$492$	156.984	7.07738
$493$	−57.2086	−2.57654
$494$	13.1768	0.592852
$495$	0	0
$496$	68.6947	3.08448
$497$	−4.63355	−0.207843
$498$	42.3538	1.89792
$499$	39.6828	1.77645	0.888223	−	0.459413i	$-0.151940\pi$
$499$	39.6828	1.77645	0.888223	+	0.459413i	$0.151940\pi$
$500$	0	0
$501$	24.1405	1.07852
$502$	−57.4231	−2.56292
$503$	13.9042	0.619960	0.309980	−	0.950743i	$-0.399678\pi$
$503$	13.9042	0.619960	0.309980	+	0.950743i	$0.399678\pi$
$504$	10.3893	0.462777
$505$	0	0
$506$	−46.4603	−2.06541
$507$	2.18632	0.0970979
$508$	−99.1622	−4.39961
$509$	33.7260	1.49488	0.747439	−	0.664331i	$-0.231283\pi$
$509$	33.7260	1.49488	0.747439	+	0.664331i	$0.231283\pi$
$510$	0	0
$511$	2.75799	0.122006
$512$	−9.42420	−0.416495
$513$	−0.954324	−0.0421344
$514$	19.8018	0.873418
$515$	0	0
$516$	−8.93831	−0.393487
$517$	−21.9008	−0.963196
$518$	−5.19045	−0.228055
$519$	29.5143	1.29553
$520$	0	0
$521$	−37.2520	−1.63204	−0.816020	−	0.578023i	$-0.803824\pi$
$521$	−37.2520	−1.63204	−0.816020	+	0.578023i	$0.803824\pi$
$522$	78.6639	3.44303
$523$	14.7673	0.645730	0.322865	−	0.946445i	$-0.395354\pi$
$523$	14.7673	0.645730	0.322865	+	0.946445i	$0.395354\pi$
$524$	−7.44399	−0.325192
$525$	0	0
$526$	55.6880	2.42811
$527$	33.0478	1.43958
$528$	141.096	6.14043
$529$	−6.12439	−0.266278
$530$	0	0
$531$	−4.05761	−0.176085
$532$	2.46169	0.106728
$533$	44.0395	1.90756
$534$	−25.7957	−1.11629
$535$	0	0
$536$	−124.985	−5.39852
$537$	−11.9035	−0.513674
$538$	0.482799	0.0208149
$539$	−28.7869	−1.23994
$540$	0	0
$541$	0.345044	0.0148346	0.00741730	−	0.999972i	$-0.497639\pi$
$541$	0.345044	0.0148346	0.00741730	+	0.999972i	$0.497639\pi$
$542$	48.4252	2.08004
$543$	−23.9814	−1.02914
$544$	−119.494	−5.12328
$545$	0	0
$546$	8.95550	0.383260
$547$	6.16271	0.263498	0.131749	−	0.991283i	$-0.457941\pi$
$547$	6.16271	0.263498	0.131749	+	0.991283i	$0.457941\pi$
$548$	−29.3771	−1.25493
$549$	13.3210	0.568525
$550$	0	0
$551$	11.5967	0.494035
$552$	−91.6396	−3.90044
$553$	0.417730	0.0177637
$554$	6.92318	0.294138
$555$	0	0
$556$	−59.0429	−2.50398
$557$	−7.45145	−0.315728	−0.157864	−	0.987461i	$-0.550461\pi$
$557$	−7.45145	−0.315728	−0.157864	+	0.987461i	$0.550461\pi$
$558$	−45.4420	−1.92371
$559$	−2.50751	−0.106056
$560$	0	0
$561$	67.8789	2.86585
$562$	60.6376	2.55784
$563$	14.5393	0.612760	0.306380	−	0.951909i	$-0.400882\pi$
$563$	14.5393	0.612760	0.306380	+	0.951909i	$0.400882\pi$
$564$	−69.4305	−2.92355
$565$	0	0
$566$	35.4431	1.48978
$567$	2.85565	0.119926
$568$	−116.093	−4.87117
$569$	12.1696	0.510175	0.255088	−	0.966918i	$-0.417896\pi$
$569$	12.1696	0.510175	0.255088	+	0.966918i	$0.417896\pi$
$570$	0	0
$571$	−16.0026	−0.669687	−0.334843	−	0.942274i	$-0.608683\pi$
$571$	−16.0026	−0.669687	−0.334843	+	0.942274i	$0.608683\pi$
$572$	82.5635	3.45216
$573$	58.0398	2.42465
$574$	11.3360	0.473157
$575$	0	0
$576$	75.9052	3.16271
$577$	−0.0727829	−0.00302999	−0.00151500	−	0.999999i	$-0.500482\pi$
$577$	−0.0727829	−0.00302999	−0.00151500	+	0.999999i	$0.500482\pi$
$578$	−66.8814	−2.78190
$579$	−22.9650	−0.954395
$580$	0	0
$581$	2.21975	0.0920909
$582$	−67.1644	−2.78405
$583$	41.5600	1.72124
$584$	69.1014	2.85944
$585$	0	0
$586$	−87.4830	−3.61389
$587$	−0.902377	−0.0372451	−0.0186225	−	0.999827i	$-0.505928\pi$
$587$	−0.902377	−0.0372451	−0.0186225	+	0.999827i	$0.505928\pi$
$588$	−91.2611	−3.76354
$589$	−6.69907	−0.276031
$590$	0	0
$591$	16.9307	0.696434
$592$	−72.7291	−2.98915
$593$	23.7787	0.976476	0.488238	−	0.872711i	$-0.337640\pi$
$593$	23.7787	0.976476	0.488238	+	0.872711i	$0.337640\pi$
$594$	−8.23891	−0.338046
$595$	0	0
$596$	43.7771	1.79318
$597$	8.18387	0.334943
$598$	−41.3200	−1.68970
$599$	48.7217	1.99072	0.995358	−	0.0962439i	$-0.0306829\pi$
$599$	48.7217	1.99072	0.995358	+	0.0962439i	$0.0306829\pi$
$600$	0	0
$601$	−3.90565	−0.159315	−0.0796573	−	0.996822i	$-0.525383\pi$
$601$	−3.90565	−0.159315	−0.0796573	+	0.996822i	$0.525383\pi$
$602$	−0.645449	−0.0263066
$603$	46.2381	1.88296
$604$	−62.9862	−2.56287
$605$	0	0
$606$	−50.5447	−2.05324
$607$	15.1915	0.616605	0.308302	−	0.951288i	$-0.400239\pi$
$607$	15.1915	0.616605	0.308302	+	0.951288i	$0.400239\pi$
$608$	24.2226	0.982355
$609$	7.88159	0.319378
$610$	0	0
$611$	−19.4777	−0.787984
$612$	112.564	4.55012
$613$	29.1406	1.17698	0.588490	−	0.808505i	$-0.299723\pi$
$613$	29.1406	1.17698	0.588490	+	0.808505i	$0.299723\pi$
$614$	34.2566	1.38248
$615$	0	0
$616$	13.2226	0.532755
$617$	31.1143	1.25261	0.626307	−	0.779576i	$-0.284565\pi$
$617$	31.1143	1.25261	0.626307	+	0.779576i	$0.284565\pi$
$618$	53.1026	2.13610
$619$	40.3950	1.62361	0.811806	−	0.583927i	$-0.198484\pi$
$619$	40.3950	1.62361	0.811806	+	0.583927i	$0.198484\pi$
$620$	0	0
$621$	2.99259	0.120088
$622$	−59.6976	−2.39365
$623$	−1.35195	−0.0541646
$624$	125.485	5.02344
$625$	0	0
$626$	29.3987	1.17501
$627$	−13.7596	−0.549507
$628$	31.1335	1.24236
$629$	−34.9886	−1.39509
$630$	0	0
$631$	7.99234	0.318170	0.159085	−	0.987265i	$-0.449146\pi$
$631$	7.99234	0.318170	0.159085	+	0.987265i	$0.449146\pi$
$632$	10.4662	0.416324
$633$	−58.0556	−2.30750
$634$	−20.9740	−0.832986
$635$	0	0
$636$	131.755	5.22441
$637$	−25.6020	−1.01439
$638$	100.117	3.96366
$639$	42.9488	1.69903
$640$	0	0
$641$	−25.0212	−0.988277	−0.494139	−	0.869383i	$-0.664516\pi$
$641$	−25.0212	−0.988277	−0.494139	+	0.869383i	$0.664516\pi$
$642$	−6.02972	−0.237974
$643$	9.88861	0.389969	0.194984	−	0.980806i	$-0.437534\pi$
$643$	9.88861	0.389969	0.194984	+	0.980806i	$0.437534\pi$
$644$	−7.71942	−0.304188
$645$	0	0
$646$	22.8639	0.899570
$647$	−43.3237	−1.70323	−0.851615	−	0.524168i	$-0.824376\pi$
$647$	−43.3237	−1.70323	−0.851615	+	0.524168i	$0.824376\pi$
$648$	71.5484	2.81068
$649$	−5.16419	−0.202712
$650$	0	0
$651$	−4.55298	−0.178445
$652$	16.9936	0.665521
$653$	13.6441	0.533936	0.266968	−	0.963705i	$-0.413978\pi$
$653$	13.6441	0.533936	0.266968	+	0.963705i	$0.413978\pi$
$654$	−26.5893	−1.03972
$655$	0	0
$656$	158.842	6.20173
$657$	−25.5641	−0.997349
$658$	−5.01368	−0.195454
$659$	−18.6052	−0.724756	−0.362378	−	0.932031i	$-0.618035\pi$
$659$	−18.6052	−0.724756	−0.362378	+	0.932031i	$0.618035\pi$
$660$	0	0
$661$	−39.9082	−1.55225	−0.776124	−	0.630580i	$-0.782817\pi$
$661$	−39.9082	−1.55225	−0.776124	+	0.630580i	$0.782817\pi$
$662$	−0.858643	−0.0333721
$663$	60.3688	2.34453
$664$	55.6159	2.15832
$665$	0	0
$666$	48.1107	1.86425
$667$	−36.3650	−1.40806
$668$	50.9497	1.97130
$669$	45.8849	1.77401
$670$	0	0
$671$	16.9538	0.654494
$672$	16.4627	0.635062
$673$	0.931169	0.0358939	0.0179470	−	0.999839i	$-0.494287\pi$
$673$	0.931169	0.0358939	0.0179470	+	0.999839i	$0.494287\pi$
$674$	−27.2496	−1.04961
$675$	0	0
$676$	4.61433	0.177474
$677$	−35.1023	−1.34909	−0.674546	−	0.738233i	$-0.735661\pi$
$677$	−35.1023	−1.34909	−0.674546	+	0.738233i	$0.735661\pi$
$678$	117.854	4.52615
$679$	−3.52007	−0.135088
$680$	0	0
$681$	−26.2869	−1.00732
$682$	−57.8347	−2.21461
$683$	17.5204	0.670399	0.335199	−	0.942147i	$-0.391196\pi$
$683$	17.5204	0.670399	0.335199	+	0.942147i	$0.391196\pi$
$684$	−22.8177	−0.872455
$685$	0	0
$686$	−13.3010	−0.507836
$687$	−13.8352	−0.527846
$688$	−9.04410	−0.344803
$689$	36.9618	1.40813
$690$	0	0
$691$	33.6421	1.27981	0.639903	−	0.768455i	$-0.278974\pi$
$691$	33.6421	1.27981	0.639903	+	0.768455i	$0.278974\pi$
$692$	62.2914	2.36796
$693$	−4.89172	−0.185821
$694$	−33.0367	−1.25406
$695$	0	0
$696$	197.473	7.48520
$697$	76.4160	2.89446
$698$	−0.127448	−0.00482396
$699$	−69.5597	−2.63099
$700$	0	0
$701$	−20.5783	−0.777232	−0.388616	−	0.921400i	$-0.627047\pi$
$701$	−20.5783	−0.777232	−0.388616	+	0.921400i	$0.627047\pi$
$702$	−7.32736	−0.276553
$703$	7.09250	0.267499
$704$	96.6057	3.64096
$705$	0	0
$706$	25.3394	0.953660
$707$	−2.64904	−0.0996272
$708$	−16.3716	−0.615284
$709$	−16.3548	−0.614216	−0.307108	−	0.951675i	$-0.599361\pi$
$709$	−16.3548	−0.614216	−0.307108	+	0.951675i	$0.599361\pi$
$710$	0	0
$711$	−3.87198	−0.145210
$712$	−33.8730	−1.26944
$713$	21.0071	0.786721
$714$	15.5393	0.581544
$715$	0	0
$716$	−25.1229	−0.938887
$717$	16.5675	0.618726
$718$	−13.0456	−0.486858
$719$	21.1731	0.789624	0.394812	−	0.918762i	$-0.370810\pi$
$719$	21.1731	0.789624	0.394812	+	0.918762i	$0.370810\pi$
$720$	0	0
$721$	2.78309	0.103648
$722$	46.6773	1.73715
$723$	2.50808	0.0932764
$724$	−50.6139	−1.88105
$725$	0	0
$726$	−44.2828	−1.64349
$727$	15.8288	0.587059	0.293530	−	0.955950i	$-0.405170\pi$
$727$	15.8288	0.587059	0.293530	+	0.955950i	$0.405170\pi$
$728$	11.7597	0.435843
$729$	−31.9506	−1.18335
$730$	0	0
$731$	−4.35096	−0.160926
$732$	53.7474	1.98656
$733$	8.66500	0.320049	0.160025	−	0.987113i	$-0.448843\pi$
$733$	8.66500	0.320049	0.160025	+	0.987113i	$0.448843\pi$
$734$	−72.0507	−2.65944
$735$	0	0
$736$	−75.9575	−2.79983
$737$	58.8480	2.16769
$738$	−105.075	−3.86786
$739$	−51.3157	−1.88768	−0.943840	−	0.330403i	$-0.892815\pi$
$739$	−51.3157	−1.88768	−0.943840	+	0.330403i	$0.892815\pi$
$740$	0	0
$741$	−12.2373	−0.449548
$742$	9.51421	0.349278
$743$	−19.9955	−0.733563	−0.366781	−	0.930307i	$-0.619540\pi$
$743$	−19.9955	−0.733563	−0.366781	+	0.930307i	$0.619540\pi$
$744$	−114.075	−4.18218
$745$	0	0
$746$	−3.52274	−0.128977
$747$	−20.5751	−0.752804
$748$	143.262	5.23816
$749$	−0.316016	−0.0115470
$750$	0	0
$751$	−30.4912	−1.11264	−0.556320	−	0.830968i	$-0.687787\pi$
$751$	−30.4912	−1.11264	−0.556320	+	0.830968i	$0.687787\pi$
$752$	−70.2523	−2.56184
$753$	53.3288	1.94341
$754$	89.0400	3.24264
$755$	0	0
$756$	−1.36890	−0.0497864
$757$	−10.7919	−0.392238	−0.196119	−	0.980580i	$-0.562834\pi$
$757$	−10.7919	−0.392238	−0.196119	+	0.980580i	$0.562834\pi$
$758$	9.78910	0.355556
$759$	43.1477	1.56616
$760$	0	0
$761$	14.3354	0.519657	0.259828	−	0.965655i	$-0.416334\pi$
$761$	14.3354	0.519657	0.259828	+	0.965655i	$0.416334\pi$
$762$	126.887	4.59662
$763$	−1.39354	−0.0504495
$764$	122.496	4.43174
$765$	0	0
$766$	−77.1032	−2.78585
$767$	−4.59282	−0.165837
$768$	55.7791	2.01276
$769$	20.7301	0.747547	0.373773	−	0.927520i	$-0.378064\pi$
$769$	20.7301	0.747547	0.373773	+	0.927520i	$0.378064\pi$
$770$	0	0
$771$	−18.3899	−0.662296
$772$	−48.4688	−1.74443
$773$	−40.3752	−1.45220	−0.726098	−	0.687591i	$-0.758668\pi$
$773$	−40.3752	−1.45220	−0.726098	+	0.687591i	$0.758668\pi$
$774$	5.98273	0.215045
$775$	0	0
$776$	−88.1952	−3.16602
$777$	4.82037	0.172930
$778$	−79.2346	−2.84070
$779$	−15.4902	−0.554993
$780$	0	0
$781$	54.6616	1.95594
$782$	−71.6971	−2.56388
$783$	−6.44869	−0.230457
$784$	−92.3413	−3.29790
$785$	0	0
$786$	9.52524	0.339754
$787$	18.3264	0.653266	0.326633	−	0.945151i	$-0.394086\pi$
$787$	18.3264	0.653266	0.326633	+	0.945151i	$0.394086\pi$
$788$	35.7330	1.27293
$789$	−51.7175	−1.84119
$790$	0	0
$791$	6.17668	0.219618
$792$	−122.562	−4.35505
$793$	15.0780	0.535437
$794$	10.6413	0.377645
$795$	0	0
$796$	17.2725	0.612206
$797$	36.1893	1.28189	0.640945	−	0.767587i	$-0.278543\pi$
$797$	36.1893	1.28189	0.640945	+	0.767587i	$0.278543\pi$
$798$	−3.14995	−0.111507
$799$	−33.7971	−1.19566
$800$	0	0
$801$	12.5313	0.442773
$802$	−0.0908875	−0.00320935
$803$	−32.5358	−1.14816
$804$	186.561	6.57952
$805$	0	0
$806$	−51.4359	−1.81175
$807$	−0.448375	−0.0157835
$808$	−66.3715	−2.33494
$809$	−0.129006	−0.00453561	−0.00226781	−	0.999997i	$-0.500722\pi$
$809$	−0.129006	−0.00453561	−0.00226781	+	0.999997i	$0.500722\pi$
$810$	0	0
$811$	−22.3392	−0.784434	−0.392217	−	0.919873i	$-0.628292\pi$
$811$	−22.3392	−0.784434	−0.392217	+	0.919873i	$0.628292\pi$
$812$	16.6345	0.583756
$813$	−44.9725	−1.57725
$814$	61.2313	2.14615
$815$	0	0
$816$	217.738	7.62237
$817$	0.881977	0.0308565
$818$	24.0256	0.840036
$819$	−4.35050	−0.152019
$820$	0	0
$821$	27.9841	0.976653	0.488327	−	0.872661i	$-0.337607\pi$
$821$	27.9841	0.976653	0.488327	+	0.872661i	$0.337607\pi$
$822$	37.5906	1.31112
$823$	−4.52041	−0.157572	−0.0787859	−	0.996892i	$-0.525104\pi$
$823$	−4.52041	−0.157572	−0.0787859	+	0.996892i	$0.525104\pi$
$824$	69.7303	2.42917
$825$	0	0
$826$	−1.18222	−0.0411347
$827$	10.2432	0.356189	0.178095	−	0.984013i	$-0.443007\pi$
$827$	10.2432	0.356189	0.178095	+	0.984013i	$0.443007\pi$
$828$	71.5520	2.48660
$829$	15.8251	0.549630	0.274815	−	0.961497i	$-0.411383\pi$
$829$	15.8251	0.549630	0.274815	+	0.961497i	$0.411383\pi$
$830$	0	0
$831$	−6.42955	−0.223039
$832$	85.9173	2.97865
$833$	−44.4237	−1.53919
$834$	75.5506	2.61610
$835$	0	0
$836$	−29.0404	−1.00438
$837$	3.72523	0.128763
$838$	80.6461	2.78587
$839$	33.9655	1.17262	0.586309	−	0.810087i	$-0.300580\pi$
$839$	33.9655	1.17262	0.586309	+	0.810087i	$0.300580\pi$
$840$	0	0
$841$	49.3626	1.70216
$842$	−43.1245	−1.48617
$843$	−56.3141	−1.93956
$844$	−122.529	−4.21763
$845$	0	0
$846$	46.4723	1.59775
$847$	−2.32085	−0.0797454
$848$	133.314	4.57802
$849$	−32.9160	−1.12967
$850$	0	0
$851$	−22.2408	−0.762405
$852$	173.290	5.93680
$853$	−51.3501	−1.75819	−0.879097	−	0.476643i	$-0.841853\pi$
$853$	−51.3501	−1.75819	−0.879097	+	0.476643i	$0.841853\pi$
$854$	3.88118	0.132811
$855$	0	0
$856$	−7.91778	−0.270624
$857$	27.2848	0.932030	0.466015	−	0.884777i	$-0.345689\pi$
$857$	27.2848	0.932030	0.466015	+	0.884777i	$0.345689\pi$
$858$	−105.647	−3.60674
$859$	−6.65604	−0.227101	−0.113551	−	0.993532i	$-0.536222\pi$
$859$	−6.65604	−0.227101	−0.113551	+	0.993532i	$0.536222\pi$
$860$	0	0
$861$	−10.5278	−0.358786
$862$	−67.0689	−2.28438
$863$	−43.1149	−1.46765	−0.733824	−	0.679340i	$-0.762266\pi$
$863$	−43.1149	−1.46765	−0.733824	+	0.679340i	$0.762266\pi$
$864$	−13.4697	−0.458249
$865$	0	0
$866$	−84.1870	−2.86079
$867$	62.1127	2.10946
$868$	−9.60928	−0.326160
$869$	−4.92793	−0.167168
$870$	0	0
$871$	52.3371	1.77338
$872$	−34.9151	−1.18237
$873$	32.6278	1.10429
$874$	14.5336	0.491607
$875$	0	0
$876$	−103.146	−3.48497
$877$	−30.7736	−1.03915	−0.519575	−	0.854425i	$-0.673910\pi$
$877$	−30.7736	−1.03915	−0.519575	+	0.854425i	$0.673910\pi$
$878$	2.59094	0.0874401
$879$	81.2455	2.74034
$880$	0	0
$881$	−35.5730	−1.19849	−0.599243	−	0.800567i	$-0.704532\pi$
$881$	−35.5730	−1.19849	−0.599243	+	0.800567i	$0.704532\pi$
$882$	61.0843	2.05682
$883$	39.0447	1.31396	0.656979	−	0.753909i	$-0.271834\pi$
$883$	39.0447	1.31396	0.656979	+	0.753909i	$0.271834\pi$
$884$	127.411	4.28531
$885$	0	0
$886$	17.6202	0.591961
$887$	35.4372	1.18987	0.594933	−	0.803775i	$-0.297179\pi$
$887$	35.4372	1.18987	0.594933	+	0.803775i	$0.297179\pi$
$888$	120.774	4.05292
$889$	6.65010	0.223037
$890$	0	0
$891$	−33.6879	−1.12859
$892$	96.8423	3.24252
$893$	6.85097	0.229259
$894$	−56.0166	−1.87348
$895$	0	0
$896$	8.98792	0.300265
$897$	38.3739	1.28127
$898$	25.3808	0.846970
$899$	−45.2679	−1.50977
$900$	0	0
$901$	64.1350	2.13665
$902$	−133.730	−4.45274
$903$	0.599429	0.0199477
$904$	154.757	5.14713
$905$	0	0
$906$	80.5964	2.67763
$907$	6.19074	0.205560	0.102780	−	0.994704i	$-0.467226\pi$
$907$	6.19074	0.205560	0.102780	+	0.994704i	$0.467226\pi$
$908$	−55.4798	−1.84116
$909$	24.5542	0.814410
$910$	0	0
$911$	0.700721	0.0232159	0.0116080	−	0.999933i	$-0.496305\pi$
$911$	0.700721	0.0232159	0.0116080	+	0.999933i	$0.496305\pi$
$912$	−44.1375	−1.46154
$913$	−26.1863	−0.866638
$914$	−73.1612	−2.41996
$915$	0	0
$916$	−29.1999	−0.964790
$917$	0.499215	0.0164855
$918$	−12.7142	−0.419631
$919$	−29.3520	−0.968233	−0.484117	−	0.875004i	$-0.660859\pi$
$919$	−29.3520	−0.968233	−0.484117	+	0.875004i	$0.660859\pi$
$920$	0	0
$921$	−31.8141	−1.04831
$922$	86.7088	2.85560
$923$	48.6139	1.60014
$924$	−19.7371	−0.649302
$925$	0	0
$926$	47.4646	1.55978
$927$	−25.7967	−0.847276
$928$	163.680	5.37306
$929$	52.4498	1.72082	0.860411	−	0.509601i	$-0.170207\pi$
$929$	52.4498	1.72082	0.860411	+	0.509601i	$0.170207\pi$
$930$	0	0
$931$	9.00507	0.295129
$932$	−146.809	−4.80889
$933$	55.4411	1.81506
$934$	35.0359	1.14641
$935$	0	0
$936$	−109.002	−3.56283
$937$	25.6384	0.837569	0.418784	−	0.908086i	$-0.362456\pi$
$937$	25.6384	0.837569	0.418784	+	0.908086i	$0.362456\pi$
$938$	13.4719	0.439873
$939$	−27.3026	−0.890986
$940$	0	0
$941$	−12.3906	−0.403921	−0.201960	−	0.979394i	$-0.564731\pi$
$941$	−12.3906	−0.403921	−0.201960	+	0.979394i	$0.564731\pi$
$942$	−39.8381	−1.29800
$943$	48.5744	1.58180
$944$	−16.5654	−0.539158
$945$	0	0
$946$	7.61431	0.247563
$947$	7.84757	0.255012	0.127506	−	0.991838i	$-0.459303\pi$
$947$	7.84757	0.255012	0.127506	+	0.991838i	$0.459303\pi$
$948$	−15.6226	−0.507400
$949$	−28.9361	−0.939304
$950$	0	0
$951$	19.4786	0.631637
$952$	20.4051	0.661331
$953$	31.9352	1.03448	0.517242	−	0.855839i	$-0.326959\pi$
$953$	31.9352	1.03448	0.517242	+	0.855839i	$0.326959\pi$
$954$	−88.1881	−2.85519
$955$	0	0
$956$	34.9666	1.13090
$957$	−92.9785	−3.00557
$958$	18.0462	0.583047
$959$	1.97011	0.0636182
$960$	0	0
$961$	−4.84999	−0.156451
$962$	54.4567	1.75575
$963$	2.92918	0.0943916
$964$	5.29342	0.170490
$965$	0	0
$966$	9.87767	0.317809
$967$	−8.42368	−0.270887	−0.135444	−	0.990785i	$-0.543246\pi$
$967$	−8.42368	−0.270887	−0.135444	+	0.990785i	$0.543246\pi$
$968$	−58.1489	−1.86898
$969$	−21.2337	−0.682126
$970$	0	0
$971$	−44.1565	−1.41705	−0.708525	−	0.705686i	$-0.750639\pi$
$971$	−44.1565	−1.41705	−0.708525	+	0.705686i	$0.750639\pi$
$972$	−118.367	−3.79661
$973$	3.95959	0.126939
$974$	52.9381	1.69625
$975$	0	0
$976$	54.3836	1.74078
$977$	5.28247	0.169001	0.0845006	−	0.996423i	$-0.473071\pi$
$977$	5.28247	0.169001	0.0845006	+	0.996423i	$0.473071\pi$
$978$	−21.7448	−0.695323
$979$	15.9488	0.509726
$980$	0	0
$981$	12.9168	0.412403
$982$	17.8767	0.570469
$983$	3.33673	0.106425	0.0532125	−	0.998583i	$-0.483054\pi$
$983$	3.33673	0.106425	0.0532125	+	0.998583i	$0.483054\pi$
$984$	−263.773	−8.40879
$985$	0	0
$986$	154.499	4.92026
$987$	4.65621	0.148209
$988$	−25.8274	−0.821678
$989$	−2.76572	−0.0879447
$990$	0	0
$991$	−21.6985	−0.689274	−0.344637	−	0.938736i	$-0.611998\pi$
$991$	−21.6985	−0.689274	−0.344637	+	0.938736i	$0.611998\pi$
$992$	−94.5534	−3.00207
$993$	0.797421	0.0253054
$994$	12.5135	0.396904
$995$	0	0
$996$	−83.0163	−2.63047
$997$	10.6834	0.338347	0.169174	−	0.985586i	$-0.445890\pi$
$997$	10.6834	0.338347	0.169174	+	0.985586i	$0.445890\pi$
$998$	−107.169	−3.39236
$999$	−3.94401	−0.124783

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6025.2.a.h.1.1		12
5.4	even	2		241.2.a.b.1.12	✓	12
15.14	odd	2		2169.2.a.h.1.1		12
20.19	odd	2		3856.2.a.n.1.11		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
241.2.a.b.1.12	✓	12	5.4	even	2
2169.2.a.h.1.1		12	15.14	odd	2
3856.2.a.n.1.11		12	20.19	odd	2
6025.2.a.h.1.1		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)

\(f(q)\)	\(=\)	\(q-2.70063 q^{2} +2.50808 q^{3} +5.29342 q^{4} -6.77340 q^{6} -0.354992 q^{7} -8.89432 q^{8} +3.29045 q^{9} +O(q^{10})\)	\(q-2.70063 q^{2} +2.50808 q^{3} +5.29342 q^{4} -6.77340 q^{6} -0.354992 q^{7} -8.89432 q^{8} +3.29045 q^{9} +4.18781 q^{11} +13.2763 q^{12} +3.72447 q^{13} +0.958703 q^{14} +13.4334 q^{16} +6.46259 q^{17} -8.88631 q^{18} -1.31002 q^{19} -0.890347 q^{21} -11.3097 q^{22} +4.10799 q^{23} -22.3076 q^{24} -10.0584 q^{26} +0.728479 q^{27} -1.87912 q^{28} -8.85227 q^{29} +5.11371 q^{31} -18.4902 q^{32} +10.5034 q^{33} -17.4531 q^{34} +17.4177 q^{36} -5.41403 q^{37} +3.53789 q^{38} +9.34127 q^{39} +11.8244 q^{41} +2.40450 q^{42} -0.673253 q^{43} +22.1678 q^{44} -11.0942 q^{46} -5.22965 q^{47} +33.6921 q^{48} -6.87398 q^{49} +16.2087 q^{51} +19.7152 q^{52} +9.92404 q^{53} -1.96735 q^{54} +3.15741 q^{56} -3.28564 q^{57} +23.9067 q^{58} -1.23315 q^{59} +4.04837 q^{61} -13.8102 q^{62} -1.16808 q^{63} +23.0683 q^{64} -28.3657 q^{66} +14.0522 q^{67} +34.2092 q^{68} +10.3032 q^{69} +13.0525 q^{71} -29.2663 q^{72} -7.76916 q^{73} +14.6213 q^{74} -6.93450 q^{76} -1.48664 q^{77} -25.2273 q^{78} -1.17673 q^{79} -8.04428 q^{81} -31.9333 q^{82} -6.25297 q^{83} -4.71298 q^{84} +1.81821 q^{86} -22.2022 q^{87} -37.2477 q^{88} +3.80839 q^{89} -1.32216 q^{91} +21.7453 q^{92} +12.8256 q^{93} +14.1234 q^{94} -46.3748 q^{96} +9.91591 q^{97} +18.5641 q^{98} +13.7798 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{2} - q^{3} + 13 q^{4} - q^{6} - 3 q^{7} - 9 q^{8} + 15 q^{9}+O(q^{10}) \) 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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more