LMFDB - Embedded newform 6025.2.a.h.1.9

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			1.9
Root			$-1.28632$ 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)

$f(q)$	$=$	$q+1.28632 q^{2} +0.126224 q^{3} -0.345373 q^{4} +0.162365 q^{6} -1.03110 q^{7} -3.01691 q^{8} -2.98407 q^{9} +O(q^{10})$	\(q+1.28632 q^{2} +0.126224 q^{3} -0.345373 q^{4} +0.162365 q^{6} -1.03110 q^{7} -3.01691 q^{8} -2.98407 q^{9} +0.227935 q^{11} -0.0435945 q^{12} -3.38088 q^{13} -1.32633 q^{14} -3.18997 q^{16} -7.12130 q^{17} -3.83847 q^{18} +3.40112 q^{19} -0.130150 q^{21} +0.293198 q^{22} -6.91488 q^{23} -0.380807 q^{24} -4.34890 q^{26} -0.755335 q^{27} +0.356115 q^{28} +0.569431 q^{29} +4.93697 q^{31} +1.93048 q^{32} +0.0287710 q^{33} -9.16030 q^{34} +1.03062 q^{36} +5.37832 q^{37} +4.37494 q^{38} -0.426749 q^{39} +10.7559 q^{41} -0.167415 q^{42} +0.910247 q^{43} -0.0787228 q^{44} -8.89477 q^{46} +8.50333 q^{47} -0.402652 q^{48} -5.93683 q^{49} -0.898882 q^{51} +1.16766 q^{52} +7.76696 q^{53} -0.971605 q^{54} +3.11074 q^{56} +0.429304 q^{57} +0.732472 q^{58} +11.2505 q^{59} -3.65450 q^{61} +6.35054 q^{62} +3.07688 q^{63} +8.86317 q^{64} +0.0370088 q^{66} +12.0694 q^{67} +2.45951 q^{68} -0.872826 q^{69} -9.48630 q^{71} +9.00266 q^{72} +7.10488 q^{73} +6.91825 q^{74} -1.17466 q^{76} -0.235024 q^{77} -0.548937 q^{78} +0.366201 q^{79} +8.85686 q^{81} +13.8356 q^{82} -17.8030 q^{83} +0.0449504 q^{84} +1.17087 q^{86} +0.0718760 q^{87} -0.687660 q^{88} -7.54236 q^{89} +3.48603 q^{91} +2.38822 q^{92} +0.623166 q^{93} +10.9380 q^{94} +0.243674 q^{96} +7.85505 q^{97} -7.63668 q^{98} -0.680174 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.28632	0.909568	0.454784	−	0.890602i	$-0.349717\pi$
$2$	1.28632	0.909568	0.454784	+	0.890602i	$0.349717\pi$
$3$	0.126224	0.0728757	0.0364378	−	0.999336i	$-0.488399\pi$
$3$	0.126224	0.0728757	0.0364378	+	0.999336i	$0.488399\pi$
$4$	−0.345373	−0.172687
$5$	0	0
$5$	0	0
$6$	0.162365	0.0662853
$7$	−1.03110	−0.389720	−0.194860	−	0.980831i	$-0.562425\pi$
$7$	−1.03110	−0.389720	−0.194860	+	0.980831i	$0.562425\pi$
$8$	−3.01691	−1.06664
$9$	−2.98407	−0.994689
$10$	0	0
$11$	0.227935	0.0687251	0.0343625	−	0.999409i	$-0.489060\pi$
$11$	0.227935	0.0687251	0.0343625	+	0.999409i	$0.489060\pi$
$12$	−0.0435945	−0.0125847
$13$	−3.38088	−0.937686	−0.468843	−	0.883281i	$-0.655329\pi$
$13$	−3.38088	−0.937686	−0.468843	+	0.883281i	$0.655329\pi$
$14$	−1.32633	−0.354477
$15$	0	0
$16$	−3.18997	−0.797493
$17$	−7.12130	−1.72717	−0.863585	−	0.504203i	$-0.831786\pi$
$17$	−7.12130	−1.72717	−0.863585	+	0.504203i	$0.831786\pi$
$18$	−3.83847	−0.904737
$19$	3.40112	0.780270	0.390135	−	0.920758i	$-0.372428\pi$
$19$	3.40112	0.780270	0.390135	+	0.920758i	$0.372428\pi$
$20$	0	0
$21$	−0.130150	−0.0284011
$22$	0.293198	0.0625101
$23$	−6.91488	−1.44185	−0.720926	−	0.693012i	$-0.756283\pi$
$23$	−6.91488	−1.44185	−0.720926	+	0.693012i	$0.756283\pi$
$24$	−0.380807	−0.0777319
$25$	0	0
$26$	−4.34890	−0.852889
$27$	−0.755335	−0.145364
$28$	0.356115	0.0672995
$29$	0.569431	0.105741	0.0528703	−	0.998601i	$-0.483163\pi$
$29$	0.569431	0.105741	0.0528703	+	0.998601i	$0.483163\pi$
$30$	0	0
$31$	4.93697	0.886706	0.443353	−	0.896347i	$-0.353789\pi$
$31$	4.93697	0.886706	0.443353	+	0.896347i	$0.353789\pi$
$32$	1.93048	0.341264
$33$	0.0287710	0.00500838
$34$	−9.16030	−1.57098
$35$	0	0
$36$	1.03062	0.171770
$37$	5.37832	0.884190	0.442095	−	0.896968i	$-0.354235\pi$
$37$	5.37832	0.884190	0.442095	+	0.896968i	$0.354235\pi$
$38$	4.37494	0.709709
$39$	−0.426749	−0.0683345
$40$	0	0
$41$	10.7559	1.67979	0.839897	−	0.542747i	$-0.182616\pi$
$41$	10.7559	1.67979	0.839897	+	0.542747i	$0.182616\pi$
$42$	−0.167415	−0.0258327
$43$	0.910247	0.138811	0.0694057	−	0.997589i	$-0.477890\pi$
$43$	0.910247	0.138811	0.0694057	+	0.997589i	$0.477890\pi$
$44$	−0.0787228	−0.0118679
$45$	0	0
$46$	−8.89477	−1.31146
$47$	8.50333	1.24034	0.620169	−	0.784468i	$-0.287064\pi$
$47$	8.50333	1.24034	0.620169	+	0.784468i	$0.287064\pi$
$48$	−0.402652	−0.0581178
$49$	−5.93683	−0.848118
$50$	0	0
$51$	−0.898882	−0.125869
$52$	1.16766	0.161926
$53$	7.76696	1.06687	0.533437	−	0.845840i	$-0.320900\pi$
$53$	7.76696	1.06687	0.533437	+	0.845840i	$0.320900\pi$
$54$	−0.971605	−0.132219
$55$	0	0
$56$	3.11074	0.415690
$57$	0.429304	0.0568627
$58$	0.732472	0.0961783
$59$	11.2505	1.46468	0.732342	−	0.680937i	$-0.238427\pi$
$59$	11.2505	1.46468	0.732342	+	0.680937i	$0.238427\pi$
$60$	0	0
$61$	−3.65450	−0.467910	−0.233955	−	0.972247i	$-0.575167\pi$
$61$	−3.65450	−0.467910	−0.233955	+	0.972247i	$0.575167\pi$
$62$	6.35054	0.806519
$63$	3.07688	0.387650
$64$	8.86317	1.10790
$65$	0	0
$66$	0.0370088	0.00455546
$67$	12.0694	1.47451	0.737257	−	0.675613i	$-0.236121\pi$
$67$	12.0694	1.47451	0.737257	+	0.675613i	$0.236121\pi$
$68$	2.45951	0.298259
$69$	−0.872826	−0.105076
$70$	0	0
$71$	−9.48630	−1.12582	−0.562908	−	0.826519i	$-0.690318\pi$
$71$	−9.48630	−1.12582	−0.562908	+	0.826519i	$0.690318\pi$
$72$	9.00266	1.06097
$73$	7.10488	0.831563	0.415782	−	0.909464i	$-0.363508\pi$
$73$	7.10488	0.831563	0.415782	+	0.909464i	$0.363508\pi$
$74$	6.91825	0.804231
$75$	0	0
$76$	−1.17466	−0.134742
$77$	−0.235024	−0.0267835
$78$	−0.548937	−0.0621548
$79$	0.366201	0.0412008	0.0206004	−	0.999788i	$-0.493442\pi$
$79$	0.366201	0.0412008	0.0206004	+	0.999788i	$0.493442\pi$
$80$	0	0
$81$	8.85686	0.984096
$82$	13.8356	1.52789
$83$	−17.8030	−1.95413	−0.977067	−	0.212932i	$-0.931699\pi$
$83$	−17.8030	−1.95413	−0.977067	+	0.212932i	$0.931699\pi$
$84$	0.0449504	0.00490449
$85$	0	0
$86$	1.17087	0.126258
$87$	0.0718760	0.00770592
$88$	−0.687660	−0.0733048
$89$	−7.54236	−0.799489	−0.399744	−	0.916627i	$-0.630901\pi$
$89$	−7.54236	−0.799489	−0.399744	+	0.916627i	$0.630901\pi$
$90$	0	0
$91$	3.48603	0.365435
$92$	2.38822	0.248989
$93$	0.623166	0.0646193
$94$	10.9380	1.12817
$95$	0	0
$96$	0.243674	0.0248699
$97$	7.85505	0.797560	0.398780	−	0.917047i	$-0.369434\pi$
$97$	7.85505	0.797560	0.398780	+	0.917047i	$0.369434\pi$
$98$	−7.63668	−0.771421
$99$	−0.680174	−0.0683601
$100$	0	0
$101$	17.4801	1.73933	0.869666	−	0.493640i	$-0.164334\pi$
$101$	17.4801	1.73933	0.869666	+	0.493640i	$0.164334\pi$
$102$	−1.15625	−0.114486
$103$	−6.10361	−0.601407	−0.300703	−	0.953718i	$-0.597221\pi$
$103$	−6.10361	−0.601407	−0.300703	+	0.953718i	$0.597221\pi$
$104$	10.1998	1.00017
$105$	0	0
$106$	9.99081	0.970394
$107$	−7.86203	−0.760051	−0.380026	−	0.924976i	$-0.624085\pi$
$107$	−7.86203	−0.760051	−0.380026	+	0.924976i	$0.624085\pi$
$108$	0.260873	0.0251025
$109$	−4.17241	−0.399644	−0.199822	−	0.979832i	$-0.564036\pi$
$109$	−4.17241	−0.399644	−0.199822	+	0.979832i	$0.564036\pi$
$110$	0	0
$111$	0.678875	0.0644359
$112$	3.28919	0.310799
$113$	−3.62203	−0.340732	−0.170366	−	0.985381i	$-0.554495\pi$
$113$	−3.62203	−0.340732	−0.170366	+	0.985381i	$0.554495\pi$
$114$	0.552224	0.0517205
$115$	0	0
$116$	−0.196666	−0.0182600
$117$	10.0888	0.932706
$118$	14.4717	1.33223
$119$	7.34279	0.673113
$120$	0	0
$121$	−10.9480	−0.995277
$122$	−4.70086	−0.425596
$123$	1.35766	0.122416
$124$	−1.70510	−0.153122
$125$	0	0
$126$	3.95786	0.352594
$127$	−13.5446	−1.20189	−0.600943	−	0.799292i	$-0.705208\pi$
$127$	−13.5446	−1.20189	−0.600943	+	0.799292i	$0.705208\pi$
$128$	7.53993	0.666442
$129$	0.114895	0.0101160
$130$	0	0
$131$	1.03003	0.0899942	0.0449971	−	0.998987i	$-0.485672\pi$
$131$	1.03003	0.0899942	0.0449971	+	0.998987i	$0.485672\pi$
$132$	−0.00993673	−0.000864881 0
$133$	−3.50690	−0.304087
$134$	15.5252	1.34117
$135$	0	0
$136$	21.4843	1.84226
$137$	11.5780	0.989180	0.494590	−	0.869127i	$-0.335318\pi$
$137$	11.5780	0.989180	0.494590	+	0.869127i	$0.335318\pi$
$138$	−1.12274	−0.0955736
$139$	0.110960	0.00941151	0.00470575	−	0.999989i	$-0.498502\pi$
$139$	0.110960	0.00941151	0.00470575	+	0.999989i	$0.498502\pi$
$140$	0	0
$141$	1.07333	0.0903904
$142$	−12.2024	−1.02401
$143$	−0.770621	−0.0644425
$144$	9.51909	0.793257
$145$	0	0
$146$	9.13917	0.756363
$147$	−0.749372	−0.0618072
$148$	−1.85753	−0.152688
$149$	−19.5413	−1.60089	−0.800443	−	0.599409i	$-0.795402\pi$
$149$	−19.5413	−1.60089	−0.800443	+	0.599409i	$0.795402\pi$
$150$	0	0
$151$	17.7745	1.44647	0.723233	−	0.690604i	$-0.242655\pi$
$151$	17.7745	1.44647	0.723233	+	0.690604i	$0.242655\pi$
$152$	−10.2609	−0.832266
$153$	21.2505	1.71800
$154$	−0.302317	−0.0243614
$155$	0	0
$156$	0.147388	0.0118005
$157$	−6.98884	−0.557770	−0.278885	−	0.960325i	$-0.589965\pi$
$157$	−6.98884	−0.557770	−0.278885	+	0.960325i	$0.589965\pi$
$158$	0.471053	0.0374749
$159$	0.980379	0.0777491
$160$	0	0
$161$	7.12995	0.561918
$162$	11.3928	0.895102
$163$	8.87693	0.695295	0.347647	−	0.937625i	$-0.386981\pi$
$163$	8.87693	0.695295	0.347647	+	0.937625i	$0.386981\pi$
$164$	−3.71481	−0.290078
$165$	0	0
$166$	−22.9004	−1.77742
$167$	−4.85435	−0.375641	−0.187820	−	0.982203i	$-0.560142\pi$
$167$	−4.85435	−0.375641	−0.187820	+	0.982203i	$0.560142\pi$
$168$	0.392651	0.0302937
$169$	−1.56968	−0.120745
$170$	0	0
$171$	−10.1492	−0.776126
$172$	−0.314375	−0.0239709
$173$	13.5277	1.02849	0.514247	−	0.857642i	$-0.328072\pi$
$173$	13.5277	1.02849	0.514247	+	0.857642i	$0.328072\pi$
$174$	0.0924558	0.00700905
$175$	0	0
$176$	−0.727107	−0.0548077
$177$	1.42008	0.106740
$178$	−9.70191	−0.727189
$179$	−10.4800	−0.783310	−0.391655	−	0.920112i	$-0.628097\pi$
$179$	−10.4800	−0.783310	−0.391655	+	0.920112i	$0.628097\pi$
$180$	0	0
$181$	−8.82686	−0.656095	−0.328048	−	0.944661i	$-0.606391\pi$
$181$	−8.82686	−0.656095	−0.328048	+	0.944661i	$0.606391\pi$
$182$	4.48416	0.332388
$183$	−0.461286	−0.0340993
$184$	20.8616	1.53793
$185$	0	0
$186$	0.801593	0.0587756
$187$	−1.62320	−0.118700
$188$	−2.93682	−0.214190
$189$	0.778827	0.0566514
$190$	0	0
$191$	−3.25920	−0.235827	−0.117914	−	0.993024i	$-0.537621\pi$
$191$	−3.25920	−0.235827	−0.117914	+	0.993024i	$0.537621\pi$
$192$	1.11875	0.0807386
$193$	−16.9658	−1.22123	−0.610613	−	0.791929i	$-0.709077\pi$
$193$	−16.9658	−1.22123	−0.610613	+	0.791929i	$0.709077\pi$
$194$	10.1041	0.725434
$195$	0	0
$196$	2.05042	0.146459
$197$	18.5572	1.32214	0.661072	−	0.750322i	$-0.270102\pi$
$197$	18.5572	1.32214	0.661072	+	0.750322i	$0.270102\pi$
$198$	−0.874924	−0.0621781
$199$	−19.6484	−1.39284	−0.696420	−	0.717634i	$-0.745225\pi$
$199$	−19.6484	−1.39284	−0.696420	+	0.717634i	$0.745225\pi$
$200$	0	0
$201$	1.52345	0.107456
$202$	22.4850	1.58204
$203$	−0.587141	−0.0412092
$204$	0.310450	0.0217358
$205$	0	0
$206$	−7.85121	−0.547020
$207$	20.6345	1.43419
$208$	10.7849	0.747798
$209$	0.775235	0.0536241
$210$	0	0
$211$	−8.18657	−0.563587	−0.281794	−	0.959475i	$-0.590929\pi$
$211$	−8.18657	−0.563587	−0.281794	+	0.959475i	$0.590929\pi$
$212$	−2.68250	−0.184235
$213$	−1.19740	−0.0820446
$214$	−10.1131	−0.691318
$215$	0	0
$216$	2.27878	0.155051
$217$	−5.09052	−0.345567
$218$	−5.36706	−0.363503
$219$	0.896809	0.0606007
$220$	0	0
$221$	24.0762	1.61954
$222$	0.873252	0.0586088
$223$	−15.5070	−1.03843	−0.519213	−	0.854645i	$-0.673775\pi$
$223$	−15.5070	−1.03843	−0.519213	+	0.854645i	$0.673775\pi$
$224$	−1.99053	−0.132998
$225$	0	0
$226$	−4.65910	−0.309919
$227$	27.1128	1.79954	0.899769	−	0.436366i	$-0.143735\pi$
$227$	27.1128	1.79954	0.899769	+	0.436366i	$0.143735\pi$
$228$	−0.148270	−0.00981944
$229$	8.10947	0.535889	0.267944	−	0.963434i	$-0.413656\pi$
$229$	8.10947	0.535889	0.267944	+	0.963434i	$0.413656\pi$
$230$	0	0
$231$	−0.0296658	−0.00195187
$232$	−1.71792	−0.112787
$233$	4.34697	0.284780	0.142390	−	0.989811i	$-0.454521\pi$
$233$	4.34697	0.284780	0.142390	+	0.989811i	$0.454521\pi$
$234$	12.9774	0.848359
$235$	0	0
$236$	−3.88561	−0.252932
$237$	0.0462235	0.00300254
$238$	9.44520	0.612241
$239$	18.3619	1.18773	0.593867	−	0.804563i	$-0.297601\pi$
$239$	18.3619	1.18773	0.593867	+	0.804563i	$0.297601\pi$
$240$	0	0
$241$	1.00000	0.0644157
$241$	1.00000	0.0644157
$242$	−14.0827	−0.905272
$243$	3.38396	0.217081
$244$	1.26217	0.0808019
$245$	0	0
$246$	1.74639	0.111346
$247$	−11.4988	−0.731649
$248$	−14.8944	−0.945795
$249$	−2.24717	−0.142409
$250$	0	0
$251$	12.3629	0.780337	0.390169	−	0.920743i	$-0.372417\pi$
$251$	12.3629	0.780337	0.390169	+	0.920743i	$0.372417\pi$
$252$	−1.06267	−0.0669420
$253$	−1.57614	−0.0990914
$254$	−17.4227	−1.09320
$255$	0	0
$256$	−8.02755	−0.501722
$257$	12.1589	0.758452	0.379226	−	0.925304i	$-0.376190\pi$
$257$	12.1589	0.758452	0.379226	+	0.925304i	$0.376190\pi$
$258$	0.147793	0.00920116
$259$	−5.54560	−0.344587
$260$	0	0
$261$	−1.69922	−0.105179
$262$	1.32495	0.0818558
$263$	5.76048	0.355207	0.177603	−	0.984102i	$-0.443166\pi$
$263$	5.76048	0.355207	0.177603	+	0.984102i	$0.443166\pi$
$264$	−0.0867994	−0.00534213
$265$	0	0
$266$	−4.51101	−0.276588
$267$	−0.952030	−0.0582633
$268$	−4.16846	−0.254629
$269$	14.4585	0.881551	0.440776	−	0.897617i	$-0.354703\pi$
$269$	14.4585	0.881551	0.440776	+	0.897617i	$0.354703\pi$
$270$	0	0
$271$	6.81638	0.414065	0.207033	−	0.978334i	$-0.433619\pi$
$271$	6.81638	0.414065	0.207033	+	0.978334i	$0.433619\pi$
$272$	22.7167	1.37741
$273$	0.440022	0.0266313
$274$	14.8931	0.899726
$275$	0	0
$276$	0.301451	0.0181452
$277$	25.1323	1.51005	0.755027	−	0.655693i	$-0.227624\pi$
$277$	25.1323	1.51005	0.755027	+	0.655693i	$0.227624\pi$
$278$	0.142730	0.00856040
$279$	−14.7323	−0.881997
$280$	0	0
$281$	−6.03331	−0.359917	−0.179959	−	0.983674i	$-0.557596\pi$
$281$	−6.03331	−0.359917	−0.179959	+	0.983674i	$0.557596\pi$
$282$	1.38064	0.0822162
$283$	3.47423	0.206521	0.103261	−	0.994654i	$-0.467072\pi$
$283$	3.47423	0.206521	0.103261	+	0.994654i	$0.467072\pi$
$284$	3.27631	0.194414
$285$	0	0
$286$	−0.991267	−0.0586148
$287$	−11.0905	−0.654649
$288$	−5.76069	−0.339452
$289$	33.7130	1.98312
$290$	0	0
$291$	0.991499	0.0581227
$292$	−2.45384	−0.143600
$293$	19.7300	1.15264	0.576321	−	0.817224i	$-0.304488\pi$
$293$	19.7300	1.15264	0.576321	+	0.817224i	$0.304488\pi$
$294$	−0.963935	−0.0562178
$295$	0	0
$296$	−16.2259	−0.943111
$297$	−0.172167	−0.00999017
$298$	−25.1364	−1.45611
$299$	23.3783	1.35200
$300$	0	0
$301$	−0.938558	−0.0540976
$302$	22.8637	1.31566
$303$	2.20641	0.126755
$304$	−10.8495	−0.622260
$305$	0	0
$306$	27.3349	1.56263
$307$	0.0265060	0.00151278	0.000756388	−	1.00000i	$-0.499759\pi$
$307$	0.0265060	0.00151278	0.000756388		1.00000i	$0.499759\pi$
$308$	0.0811712	0.00462516
$309$	−0.770424	−0.0438279
$310$	0	0
$311$	21.2822	1.20680	0.603400	−	0.797439i	$-0.293812\pi$
$311$	21.2822	1.20680	0.603400	+	0.797439i	$0.293812\pi$
$312$	1.28746	0.0728882
$313$	−10.6916	−0.604323	−0.302161	−	0.953257i	$-0.597708\pi$
$313$	−10.6916	−0.604323	−0.302161	+	0.953257i	$0.597708\pi$
$314$	−8.98990	−0.507329
$315$	0	0
$316$	−0.126476	−0.00711484
$317$	2.07826	0.116727	0.0583633	−	0.998295i	$-0.481412\pi$
$317$	2.07826	0.116727	0.0583633	+	0.998295i	$0.481412\pi$
$318$	1.26108	0.0707181
$319$	0.129793	0.00726703
$320$	0	0
$321$	−0.992380	−0.0553892
$322$	9.17141	0.511103
$323$	−24.2204	−1.34766
$324$	−3.05892	−0.169940
$325$	0	0
$326$	11.4186	0.632418
$327$	−0.526659	−0.0291243
$328$	−32.4496	−1.79173
$329$	−8.76780	−0.483384
$330$	0	0
$331$	−28.1272	−1.54601	−0.773006	−	0.634399i	$-0.781248\pi$
$331$	−28.1272	−1.54601	−0.773006	+	0.634399i	$0.781248\pi$
$332$	6.14869	0.337453
$333$	−16.0493	−0.879494
$334$	−6.24426	−0.341671
$335$	0	0
$336$	0.415175	0.0226497
$337$	−23.5835	−1.28468	−0.642338	−	0.766422i	$-0.722035\pi$
$337$	−23.5835	−1.28468	−0.642338	+	0.766422i	$0.722035\pi$
$338$	−2.01911	−0.109825
$339$	−0.457188	−0.0248311
$340$	0	0
$341$	1.12531	0.0609389
$342$	−13.0551	−0.705940
$343$	13.3392	0.720249
$344$	−2.74613	−0.148061
$345$	0	0
$346$	17.4010	0.935484
$347$	21.8697	1.17403	0.587013	−	0.809578i	$-0.300304\pi$
$347$	21.8697	1.17403	0.587013	+	0.809578i	$0.300304\pi$
$348$	−0.0248241	−0.00133071
$349$	18.8525	1.00915	0.504575	−	0.863368i	$-0.331649\pi$
$349$	18.8525	1.00915	0.504575	+	0.863368i	$0.331649\pi$
$350$	0	0
$351$	2.55369	0.136306
$352$	0.440025	0.0234534
$353$	11.3768	0.605526	0.302763	−	0.953066i	$-0.402091\pi$
$353$	11.3768	0.605526	0.302763	+	0.953066i	$0.402091\pi$
$354$	1.82668	0.0970871
$355$	0	0
$356$	2.60493	0.138061
$357$	0.926839	0.0490535
$358$	−13.4806	−0.712473
$359$	−0.146567	−0.00773548	−0.00386774	−	0.999993i	$-0.501231\pi$
$359$	−0.146567	−0.00773548	−0.00386774	+	0.999993i	$0.501231\pi$
$360$	0	0
$361$	−7.43238	−0.391178
$362$	−11.3542	−0.596763
$363$	−1.38191	−0.0725315
$364$	−1.20398	−0.0631058
$365$	0	0
$366$	−0.593363	−0.0310156
$367$	−32.6647	−1.70508	−0.852541	−	0.522660i	$-0.824940\pi$
$367$	−32.6647	−1.70508	−0.852541	+	0.522660i	$0.824940\pi$
$368$	22.0583	1.14987
$369$	−32.0964	−1.67087
$370$	0	0
$371$	−8.00852	−0.415782
$372$	−0.215225	−0.0111589
$373$	17.7530	0.919218	0.459609	−	0.888121i	$-0.347990\pi$
$373$	17.7530	0.919218	0.459609	+	0.888121i	$0.347990\pi$
$374$	−2.08795	−0.107966
$375$	0	0
$376$	−25.6538	−1.32299
$377$	−1.92517	−0.0991515
$378$	1.00182	0.0515282
$379$	−4.82435	−0.247810	−0.123905	−	0.992294i	$-0.539542\pi$
$379$	−4.82435	−0.247810	−0.123905	+	0.992294i	$0.539542\pi$
$380$	0	0
$381$	−1.70965	−0.0875882
$382$	−4.19238	−0.214501
$383$	−14.7127	−0.751783	−0.375892	−	0.926664i	$-0.622664\pi$
$383$	−14.7127	−0.751783	−0.375892	+	0.926664i	$0.622664\pi$
$384$	0.951722	0.0485674
$385$	0	0
$386$	−21.8235	−1.11079
$387$	−2.71624	−0.138074
$388$	−2.71293	−0.137728
$389$	4.90322	0.248603	0.124301	−	0.992244i	$-0.460331\pi$
$389$	4.90322	0.248603	0.124301	+	0.992244i	$0.460331\pi$
$390$	0	0
$391$	49.2430	2.49032
$392$	17.9109	0.904635
$393$	0.130015	0.00655839
$394$	23.8705	1.20258
$395$	0	0
$396$	0.234914	0.0118049
$397$	14.8959	0.747606	0.373803	−	0.927508i	$-0.378054\pi$
$397$	14.8959	0.747606	0.373803	+	0.927508i	$0.378054\pi$
$398$	−25.2742	−1.26688
$399$	−0.442656	−0.0221605
$400$	0	0
$401$	6.72128	0.335645	0.167822	−	0.985817i	$-0.446327\pi$
$401$	6.72128	0.335645	0.167822	+	0.985817i	$0.446327\pi$
$402$	1.95965	0.0977386
$403$	−16.6913	−0.831452
$404$	−6.03715	−0.300360
$405$	0	0
$406$	−0.755253	−0.0374826
$407$	1.22591	0.0607660
$408$	2.71184	0.134256
$409$	−2.59935	−0.128529	−0.0642647	−	0.997933i	$-0.520470\pi$
$409$	−2.59935	−0.128529	−0.0642647	+	0.997933i	$0.520470\pi$
$410$	0	0
$411$	1.46143	0.0720871
$412$	2.10803	0.103855
$413$	−11.6004	−0.570817
$414$	26.5426	1.30450
$415$	0	0
$416$	−6.52672	−0.319999
$417$	0.0140059	0.000685870 0
$418$	0.997203	0.0487748
$419$	−13.1622	−0.643018	−0.321509	−	0.946907i	$-0.604190\pi$
$419$	−13.1622	−0.643018	−0.321509	+	0.946907i	$0.604190\pi$
$420$	0	0
$421$	−6.53715	−0.318601	−0.159301	−	0.987230i	$-0.550924\pi$
$421$	−6.53715	−0.318601	−0.159301	+	0.987230i	$0.550924\pi$
$422$	−10.5306	−0.512620
$423$	−25.3745	−1.23375
$424$	−23.4322	−1.13797
$425$	0	0
$426$	−1.54025	−0.0746251
$427$	3.76816	0.182354
$428$	2.71534	0.131251
$429$	−0.0972711	−0.00469629
$430$	0	0
$431$	10.8319	0.521755	0.260878	−	0.965372i	$-0.415988\pi$
$431$	10.8319	0.521755	0.260878	+	0.965372i	$0.415988\pi$
$432$	2.40950	0.115927
$433$	25.6037	1.23044	0.615218	−	0.788357i	$-0.289068\pi$
$433$	25.6037	1.23044	0.615218	+	0.788357i	$0.289068\pi$
$434$	−6.54805	−0.314317
$435$	0	0
$436$	1.44104	0.0690132
$437$	−23.5183	−1.12503
$438$	1.15359	0.0551205
$439$	14.6842	0.700839	0.350419	−	0.936593i	$-0.386039\pi$
$439$	14.6842	0.700839	0.350419	+	0.936593i	$0.386039\pi$
$440$	0	0
$441$	17.7159	0.843614
$442$	30.9698	1.47308
$443$	15.2687	0.725436	0.362718	−	0.931899i	$-0.381849\pi$
$443$	15.2687	0.725436	0.362718	+	0.931899i	$0.381849\pi$
$444$	−0.234465	−0.0111272
$445$	0	0
$446$	−19.9470	−0.944518
$447$	−2.46659	−0.116666
$448$	−9.13883	−0.431769
$449$	31.2160	1.47317	0.736587	−	0.676343i	$-0.236436\pi$
$449$	31.2160	1.47317	0.736587	+	0.676343i	$0.236436\pi$
$450$	0	0
$451$	2.45165	0.115444
$452$	1.25095	0.0588399
$453$	2.24357	0.105412
$454$	34.8758	1.63680
$455$	0	0
$456$	−1.29517	−0.0606519
$457$	−9.43632	−0.441412	−0.220706	−	0.975340i	$-0.570836\pi$
$457$	−9.43632	−0.441412	−0.220706	+	0.975340i	$0.570836\pi$
$458$	10.4314	0.487427
$459$	5.37897	0.251069
$460$	0	0
$461$	8.65525	0.403115	0.201557	−	0.979477i	$-0.435400\pi$
$461$	8.65525	0.403115	0.201557	+	0.979477i	$0.435400\pi$
$462$	−0.0381598	−0.00177536
$463$	12.5415	0.582853	0.291426	−	0.956593i	$-0.405870\pi$
$463$	12.5415	0.582853	0.291426	+	0.956593i	$0.405870\pi$
$464$	−1.81647	−0.0843274
$465$	0	0
$466$	5.59161	0.259026
$467$	5.28477	0.244550	0.122275	−	0.992496i	$-0.460981\pi$
$467$	5.28477	0.244550	0.122275	+	0.992496i	$0.460981\pi$
$468$	−3.48439	−0.161066
$469$	−12.4448	−0.574647
$470$	0	0
$471$	−0.882161	−0.0406479
$472$	−33.9416	−1.56229
$473$	0.207477	0.00953982
$474$	0.0594583	0.00273101
$475$	0	0
$476$	−2.53601	−0.116238
$477$	−23.1771	−1.06121
$478$	23.6194	1.08032
$479$	−29.0596	−1.32777	−0.663884	−	0.747835i	$-0.731093\pi$
$479$	−29.0596	−1.32777	−0.663884	+	0.747835i	$0.731093\pi$
$480$	0	0
$481$	−18.1834	−0.829093
$482$	1.28632	0.0585904
$483$	0.899973	0.0409502
$484$	3.78116	0.171871
$485$	0	0
$486$	4.35286	0.197450
$487$	36.2854	1.64425	0.822124	−	0.569309i	$-0.192789\pi$
$487$	36.2854	1.64425	0.822124	+	0.569309i	$0.192789\pi$
$488$	11.0253	0.499091
$489$	1.12048	0.0506701
$490$	0	0
$491$	−3.99282	−0.180193	−0.0900967	−	0.995933i	$-0.528718\pi$
$491$	−3.99282	−0.180193	−0.0900967	+	0.995933i	$0.528718\pi$
$492$	−0.468899	−0.0211396
$493$	−4.05509	−0.182632
$494$	−14.7911	−0.665484
$495$	0	0
$496$	−15.7488	−0.707142
$497$	9.78134	0.438753
$498$	−2.89059	−0.129530
$499$	9.25262	0.414204	0.207102	−	0.978319i	$-0.433597\pi$
$499$	9.25262	0.414204	0.207102	+	0.978319i	$0.433597\pi$
$500$	0	0
$501$	−0.612737	−0.0273751
$502$	15.9026	0.709769
$503$	−30.0225	−1.33864	−0.669319	−	0.742975i	$-0.733414\pi$
$503$	−30.0225	−1.33864	−0.669319	+	0.742975i	$0.733414\pi$
$504$	−9.28266	−0.413482
$505$	0	0
$506$	−2.02743	−0.0901303
$507$	−0.198132	−0.00879934
$508$	4.67793	0.207550
$509$	8.01192	0.355122	0.177561	−	0.984110i	$-0.443179\pi$
$509$	8.01192	0.355122	0.177561	+	0.984110i	$0.443179\pi$
$510$	0	0
$511$	−7.32586	−0.324077
$512$	−25.4059	−1.12279
$513$	−2.56898	−0.113423
$514$	15.6403	0.689864
$515$	0	0
$516$	−0.0396818	−0.00174689
$517$	1.93821	0.0852423
$518$	−7.13343	−0.313425
$519$	1.70753	0.0749521
$520$	0	0
$521$	−10.1940	−0.446608	−0.223304	−	0.974749i	$-0.571684\pi$
$521$	−10.1940	−0.446608	−0.223304	+	0.974749i	$0.571684\pi$
$522$	−2.18575	−0.0956675
$523$	41.0217	1.79375	0.896877	−	0.442281i	$-0.145830\pi$
$523$	41.0217	1.79375	0.896877	+	0.442281i	$0.145830\pi$
$524$	−0.355745	−0.0155408
$525$	0	0
$526$	7.40984	0.323084
$527$	−35.1577	−1.53149
$528$	−0.0917786	−0.00399415
$529$	24.8156	1.07894
$530$	0	0
$531$	−33.5721	−1.45691
$532$	1.21119	0.0525118
$533$	−36.3644	−1.57512
$534$	−1.22462	−0.0529944
$535$	0	0
$536$	−36.4123	−1.57277
$537$	−1.32283	−0.0570842
$538$	18.5983	0.801831
$539$	−1.35321	−0.0582870
$540$	0	0
$541$	−25.9044	−1.11372	−0.556858	−	0.830608i	$-0.687993\pi$
$541$	−25.9044	−1.11372	−0.556858	+	0.830608i	$0.687993\pi$
$542$	8.76806	0.376620
$543$	−1.11416	−0.0478134
$544$	−13.7476	−0.589422
$545$	0	0
$546$	0.566010	0.0242230
$547$	43.6488	1.86629	0.933145	−	0.359501i	$-0.117053\pi$
$547$	43.6488	1.86629	0.933145	+	0.359501i	$0.117053\pi$
$548$	−3.99875	−0.170818
$549$	10.9053	0.465425
$550$	0	0
$551$	1.93670	0.0825063
$552$	2.63324	0.112078
$553$	−0.377591	−0.0160568
$554$	32.3283	1.37350
$555$	0	0
$556$	−0.0383227	−0.00162524
$557$	−22.1122	−0.936925	−0.468463	−	0.883483i	$-0.655192\pi$
$557$	−22.1122	−0.936925	−0.468463	+	0.883483i	$0.655192\pi$
$558$	−18.9504	−0.802236
$559$	−3.07743	−0.130162
$560$	0	0
$561$	−0.204887	−0.00865033
$562$	−7.76078	−0.327369
$563$	−19.0461	−0.802697	−0.401348	−	0.915925i	$-0.631458\pi$
$563$	−19.0461	−0.802697	−0.401348	+	0.915925i	$0.631458\pi$
$564$	−0.370699	−0.0156092
$565$	0	0
$566$	4.46898	0.187845
$567$	−9.13233	−0.383522
$568$	28.6193	1.20084
$569$	−24.1421	−1.01209	−0.506045	−	0.862507i	$-0.668893\pi$
$569$	−24.1421	−1.01209	−0.506045	+	0.862507i	$0.668893\pi$
$570$	0	0
$571$	−37.2649	−1.55949	−0.779745	−	0.626098i	$-0.784651\pi$
$571$	−37.2649	−1.55949	−0.779745	+	0.626098i	$0.784651\pi$
$572$	0.266152	0.0111284
$573$	−0.411390	−0.0171861
$574$	−14.2659	−0.595447
$575$	0	0
$576$	−26.4483	−1.10201
$577$	6.94471	0.289112	0.144556	−	0.989497i	$-0.453825\pi$
$577$	6.94471	0.289112	0.144556	+	0.989497i	$0.453825\pi$
$578$	43.3658	1.80378
$579$	−2.14150	−0.0889977
$580$	0	0
$581$	18.3567	0.761565
$582$	1.27539	0.0528665
$583$	1.77036	0.0733209
$584$	−21.4348	−0.886977
$585$	0	0
$586$	25.3792	1.04841
$587$	33.6812	1.39017	0.695085	−	0.718927i	$-0.255367\pi$
$587$	33.6812	1.39017	0.695085	+	0.718927i	$0.255367\pi$
$588$	0.258813	0.0106733
$589$	16.7912	0.691871
$590$	0	0
$591$	2.34237	0.0963522
$592$	−17.1567	−0.705135
$593$	25.1034	1.03087	0.515437	−	0.856927i	$-0.327630\pi$
$593$	25.1034	1.03087	0.515437	+	0.856927i	$0.327630\pi$
$594$	−0.221463	−0.00908673
$595$	0	0
$596$	6.74905	0.276452
$597$	−2.48011	−0.101504
$598$	30.0721	1.22974
$599$	−5.93752	−0.242601	−0.121300	−	0.992616i	$-0.538706\pi$
$599$	−5.93752	−0.242601	−0.121300	+	0.992616i	$0.538706\pi$
$600$	0	0
$601$	−29.7235	−1.21245	−0.606223	−	0.795294i	$-0.707316\pi$
$601$	−29.7235	−1.21245	−0.606223	+	0.795294i	$0.707316\pi$
$602$	−1.20729	−0.0492054
$603$	−36.0159	−1.46668
$604$	−6.13883	−0.249785
$605$	0	0
$606$	2.83816	0.115292
$607$	−16.5792	−0.672929	−0.336464	−	0.941696i	$-0.609231\pi$
$607$	−16.5792	−0.672929	−0.336464	+	0.941696i	$0.609231\pi$
$608$	6.56580	0.266279
$609$	−0.0741115	−0.00300315
$610$	0	0
$611$	−28.7487	−1.16305
$612$	−7.33934	−0.296675
$613$	−39.4836	−1.59473	−0.797364	−	0.603499i	$-0.793773\pi$
$613$	−39.4836	−1.59473	−0.797364	+	0.603499i	$0.793773\pi$
$614$	0.0340952	0.00137597
$615$	0	0
$616$	0.709047	0.0285683
$617$	−38.4323	−1.54723	−0.773613	−	0.633658i	$-0.781553\pi$
$617$	−38.4323	−1.54723	−0.773613	+	0.633658i	$0.781553\pi$
$618$	−0.991014	−0.0398644
$619$	14.9244	0.599861	0.299931	−	0.953961i	$-0.403036\pi$
$619$	14.9244	0.599861	0.299931	+	0.953961i	$0.403036\pi$
$620$	0	0
$621$	5.22305	0.209594
$622$	27.3757	1.09767
$623$	7.77695	0.311577
$624$	1.36132	0.0544963
$625$	0	0
$626$	−13.7528	−0.549672
$627$	0.0978535	0.00390789
$628$	2.41376	0.0963195
$629$	−38.3006	−1.52715
$630$	0	0
$631$	30.8867	1.22958	0.614791	−	0.788690i	$-0.289241\pi$
$631$	30.8867	1.22958	0.614791	+	0.788690i	$0.289241\pi$
$632$	−1.10479	−0.0439464
$633$	−1.03334	−0.0410718
$634$	2.67331	0.106171
$635$	0	0
$636$	−0.338597	−0.0134262
$637$	20.0717	0.795269
$638$	0.166956	0.00660986
$639$	28.3077	1.11984
$640$	0	0
$641$	31.6649	1.25069	0.625344	−	0.780349i	$-0.284959\pi$
$641$	31.6649	1.25069	0.625344	+	0.780349i	$0.284959\pi$
$642$	−1.27652	−0.0503803
$643$	17.2630	0.680786	0.340393	−	0.940283i	$-0.389440\pi$
$643$	17.2630	0.680786	0.340393	+	0.940283i	$0.389440\pi$
$644$	−2.46249	−0.0970359
$645$	0	0
$646$	−31.1553	−1.22579
$647$	−35.2693	−1.38658	−0.693289	−	0.720659i	$-0.743839\pi$
$647$	−35.2693	−1.38658	−0.693289	+	0.720659i	$0.743839\pi$
$648$	−26.7203	−1.04967
$649$	2.56437	0.100661
$650$	0	0
$651$	−0.642548	−0.0251834
$652$	−3.06586	−0.120068
$653$	38.0371	1.48851	0.744253	−	0.667898i	$-0.232806\pi$
$653$	38.0371	1.48851	0.744253	+	0.667898i	$0.232806\pi$
$654$	−0.677454	−0.0264905
$655$	0	0
$656$	−34.3111	−1.33962
$657$	−21.2014	−0.827147
$658$	−11.2782	−0.439671
$659$	−7.14619	−0.278376	−0.139188	−	0.990266i	$-0.544449\pi$
$659$	−7.14619	−0.278376	−0.139188	+	0.990266i	$0.544449\pi$
$660$	0	0
$661$	33.6588	1.30917	0.654587	−	0.755986i	$-0.272842\pi$
$661$	33.6588	1.30917	0.654587	+	0.755986i	$0.272842\pi$
$662$	−36.1807	−1.40620
$663$	3.03901	0.118025
$664$	53.7100	2.08435
$665$	0	0
$666$	−20.6445	−0.799960
$667$	−3.93754	−0.152462
$668$	1.67656	0.0648682
$669$	−1.95736	−0.0756759
$670$	0	0
$671$	−0.832989	−0.0321572
$672$	−0.251253	−0.00969229
$673$	4.10894	0.158388	0.0791939	−	0.996859i	$-0.474765\pi$
$673$	4.10894	0.158388	0.0791939	+	0.996859i	$0.474765\pi$
$674$	−30.3360	−1.16850
$675$	0	0
$676$	0.542126	0.0208510
$677$	26.3822	1.01395	0.506976	−	0.861960i	$-0.330763\pi$
$677$	26.3822	1.01395	0.506976	+	0.861960i	$0.330763\pi$
$678$	−0.588092	−0.0225855
$679$	−8.09936	−0.310825
$680$	0	0
$681$	3.42229	0.131143
$682$	1.44751	0.0554281
$683$	18.1548	0.694676	0.347338	−	0.937740i	$-0.387086\pi$
$683$	18.1548	0.694676	0.347338	+	0.937740i	$0.387086\pi$
$684$	3.50525	0.134027
$685$	0	0
$686$	17.1585	0.655115
$687$	1.02361	0.0390532
$688$	−2.90366	−0.110701
$689$	−26.2591	−1.00039
$690$	0	0
$691$	28.1899	1.07239	0.536196	−	0.844093i	$-0.319861\pi$
$691$	28.1899	1.07239	0.536196	+	0.844093i	$0.319861\pi$
$692$	−4.67212	−0.177607
$693$	0.701329	0.0266413
$694$	28.1315	1.06786
$695$	0	0
$696$	−0.216843	−0.00821942
$697$	−76.5962	−2.90129
$698$	24.2504	0.917890
$699$	0.548694	0.0207535
$700$	0	0
$701$	39.3669	1.48687	0.743434	−	0.668809i	$-0.233196\pi$
$701$	39.3669	1.48687	0.743434	+	0.668809i	$0.233196\pi$
$702$	3.28487	0.123980
$703$	18.2923	0.689907
$704$	2.02023	0.0761402
$705$	0	0
$706$	14.6342	0.550766
$707$	−18.0237	−0.677853
$708$	−0.490458	−0.0184326
$709$	48.4112	1.81812	0.909060	−	0.416664i	$-0.136801\pi$
$709$	48.4112	1.81812	0.909060	+	0.416664i	$0.136801\pi$
$710$	0	0
$711$	−1.09277	−0.0409820
$712$	22.7546	0.852765
$713$	−34.1386	−1.27850
$714$	1.19221	0.0446175
$715$	0	0
$716$	3.61950	0.135267
$717$	2.31772	0.0865569
$718$	−0.188532	−0.00703595
$719$	−10.8564	−0.404877	−0.202438	−	0.979295i	$-0.564887\pi$
$719$	−10.8564	−0.404877	−0.202438	+	0.979295i	$0.564887\pi$
$720$	0	0
$721$	6.29345	0.234380
$722$	−9.56045	−0.355803
$723$	0.126224	0.00469433
$724$	3.04856	0.113299
$725$	0	0
$726$	−1.77758	−0.0659723
$727$	37.5110	1.39121	0.695604	−	0.718426i	$-0.255137\pi$
$727$	37.5110	1.39121	0.695604	+	0.718426i	$0.255137\pi$
$728$	−10.5170	−0.389787
$729$	−26.1434	−0.968276
$730$	0	0
$731$	−6.48215	−0.239751
$732$	0.159316	0.00588849
$733$	1.31177	0.0484512	0.0242256	−	0.999707i	$-0.492288\pi$
$733$	1.31177	0.0484512	0.0242256	+	0.999707i	$0.492288\pi$
$734$	−42.0173	−1.55089
$735$	0	0
$736$	−13.3491	−0.492053
$737$	2.75105	0.101336
$738$	−41.2863	−1.51977
$739$	52.6696	1.93748	0.968742	−	0.248072i	$-0.0797969\pi$
$739$	52.6696	1.93748	0.968742	+	0.248072i	$0.0797969\pi$
$740$	0	0
$741$	−1.45142	−0.0533194
$742$	−10.3015	−0.378182
$743$	−44.6512	−1.63809	−0.819046	−	0.573728i	$-0.805497\pi$
$743$	−44.6512	−1.63809	−0.819046	+	0.573728i	$0.805497\pi$
$744$	−1.88003	−0.0689254
$745$	0	0
$746$	22.8362	0.836091
$747$	53.1254	1.94376
$748$	0.560609	0.0204979
$749$	8.10656	0.296207
$750$	0	0
$751$	−30.0001	−1.09472	−0.547360	−	0.836897i	$-0.684367\pi$
$751$	−30.0001	−1.09472	−0.547360	+	0.836897i	$0.684367\pi$
$752$	−27.1254	−0.989160
$753$	1.56049	0.0568676
$754$	−2.47640	−0.0901850
$755$	0	0
$756$	−0.268986	−0.00978294
$757$	−10.8998	−0.396160	−0.198080	−	0.980186i	$-0.563471\pi$
$757$	−10.8998	−0.396160	−0.198080	+	0.980186i	$0.563471\pi$
$758$	−6.20568	−0.225400
$759$	−0.198948	−0.00722135
$760$	0	0
$761$	54.3944	1.97180	0.985898	−	0.167348i	$-0.0535203\pi$
$761$	54.3944	1.97180	0.985898	+	0.167348i	$0.0535203\pi$
$762$	−2.19917	−0.0796674
$763$	4.30218	0.155749
$764$	1.12564	0.0407242
$765$	0	0
$766$	−18.9253	−0.683798
$767$	−38.0364	−1.37341
$768$	−1.01327	−0.0365633
$769$	−16.9359	−0.610723	−0.305361	−	0.952237i	$-0.598777\pi$
$769$	−16.9359	−0.610723	−0.305361	+	0.952237i	$0.598777\pi$
$770$	0	0
$771$	1.53475	0.0552727
$772$	5.85954	0.210890
$773$	29.5026	1.06113	0.530567	−	0.847643i	$-0.321979\pi$
$773$	29.5026	1.06113	0.530567	+	0.847643i	$0.321979\pi$
$774$	−3.49396	−0.125588
$775$	0	0
$776$	−23.6980	−0.850707
$777$	−0.699989	−0.0251120
$778$	6.30712	0.226121
$779$	36.5822	1.31069
$780$	0	0
$781$	−2.16226	−0.0773718
$782$	63.3423	2.26512
$783$	−0.430111	−0.0153709
$784$	18.9383	0.676368
$785$	0	0
$786$	0.167241	0.00596530
$787$	5.96992	0.212805	0.106402	−	0.994323i	$-0.466067\pi$
$787$	5.96992	0.212805	0.106402	+	0.994323i	$0.466067\pi$
$788$	−6.40916	−0.228317
$789$	0.727113	0.0258859
$790$	0	0
$791$	3.73468	0.132790
$792$	2.05202	0.0729154
$793$	12.3554	0.438753
$794$	19.1610	0.679998
$795$	0	0
$796$	6.78605	0.240525
$797$	−19.1226	−0.677357	−0.338679	−	0.940902i	$-0.609980\pi$
$797$	−19.1226	−0.677357	−0.338679	+	0.940902i	$0.609980\pi$
$798$	−0.569399	−0.0201565
$799$	−60.5548	−2.14227
$800$	0	0
$801$	22.5069	0.795243
$802$	8.64573	0.305291
$803$	1.61945	0.0571492
$804$	−0.526161	−0.0185563
$805$	0	0
$806$	−21.4704	−0.756262
$807$	1.82502	0.0642436
$808$	−52.7358	−1.85524
$809$	34.3768	1.20862	0.604312	−	0.796748i	$-0.293448\pi$
$809$	34.3768	1.20862	0.604312	+	0.796748i	$0.293448\pi$
$810$	0	0
$811$	18.2250	0.639967	0.319984	−	0.947423i	$-0.396323\pi$
$811$	18.2250	0.639967	0.319984	+	0.947423i	$0.396323\pi$
$812$	0.202783	0.00711629
$813$	0.860393	0.0301753
$814$	1.57691	0.0552708
$815$	0	0
$816$	2.86741	0.100379
$817$	3.09586	0.108310
$818$	−3.34360	−0.116906
$819$	−10.4025	−0.363494
$820$	0	0
$821$	36.2130	1.26384	0.631920	−	0.775033i	$-0.282267\pi$
$821$	36.2130	1.26384	0.631920	+	0.775033i	$0.282267\pi$
$822$	1.87987	0.0655681
$823$	42.2212	1.47174	0.735869	−	0.677124i	$-0.236774\pi$
$823$	42.2212	1.47174	0.735869	+	0.677124i	$0.236774\pi$
$824$	18.4140	0.641483
$825$	0	0
$826$	−14.9218	−0.519196
$827$	−15.1566	−0.527048	−0.263524	−	0.964653i	$-0.584885\pi$
$827$	−15.1566	−0.527048	−0.263524	+	0.964653i	$0.584885\pi$
$828$	−7.12660	−0.247666
$829$	−3.49294	−0.121315	−0.0606575	−	0.998159i	$-0.519320\pi$
$829$	−3.49294	−0.121315	−0.0606575	+	0.998159i	$0.519320\pi$
$830$	0	0
$831$	3.17231	0.110046
$832$	−29.9653	−1.03886
$833$	42.2780	1.46484
$834$	0.0180161	0.000623845 0
$835$	0	0
$836$	−0.267746	−0.00926017
$837$	−3.72907	−0.128895
$838$	−16.9309	−0.584868
$839$	−28.5020	−0.983999	−0.491999	−	0.870596i	$-0.663734\pi$
$839$	−28.5020	−0.983999	−0.491999	+	0.870596i	$0.663734\pi$
$840$	0	0
$841$	−28.6757	−0.988819
$842$	−8.40889	−0.289789
$843$	−0.761550	−0.0262292
$844$	2.82743	0.0973240
$845$	0	0
$846$	−32.6398	−1.12218
$847$	11.2886	0.387879
$848$	−24.7764	−0.850824
$849$	0.438532	0.0150504
$850$	0	0
$851$	−37.1904	−1.27487
$852$	0.413551	0.0141680
$853$	−5.52236	−0.189082	−0.0945410	−	0.995521i	$-0.530138\pi$
$853$	−5.52236	−0.189082	−0.0945410	+	0.995521i	$0.530138\pi$
$854$	4.84707	0.165863
$855$	0	0
$856$	23.7190	0.810700
$857$	17.0172	0.581298	0.290649	−	0.956830i	$-0.406129\pi$
$857$	17.0172	0.581298	0.290649	+	0.956830i	$0.406129\pi$
$858$	−0.125122	−0.00427160
$859$	−1.16642	−0.0397979	−0.0198989	−	0.999802i	$-0.506334\pi$
$859$	−1.16642	−0.0397979	−0.0198989	+	0.999802i	$0.506334\pi$
$860$	0	0
$861$	−1.39989	−0.0477080
$862$	13.9333	0.474572
$863$	8.50057	0.289363	0.144681	−	0.989478i	$-0.453784\pi$
$863$	8.50057	0.289363	0.144681	+	0.989478i	$0.453784\pi$
$864$	−1.45816	−0.0496077
$865$	0	0
$866$	32.9346	1.11916
$867$	4.25540	0.144521
$868$	1.75813	0.0596749
$869$	0.0834701	0.00283153
$870$	0	0
$871$	−40.8052	−1.38263
$872$	12.5878	0.426275
$873$	−23.4400	−0.793324
$874$	−30.2522	−1.02329
$875$	0	0
$876$	−0.309734	−0.0104649
$877$	−7.37310	−0.248972	−0.124486	−	0.992221i	$-0.539728\pi$
$877$	−7.37310	−0.248972	−0.124486	+	0.992221i	$0.539728\pi$
$878$	18.8886	0.637460
$879$	2.49041	0.0839995
$880$	0	0
$881$	−48.8726	−1.64656	−0.823279	−	0.567637i	$-0.807858\pi$
$881$	−48.8726	−1.64656	−0.823279	+	0.567637i	$0.807858\pi$
$882$	22.7884	0.767324
$883$	26.8006	0.901911	0.450956	−	0.892546i	$-0.351083\pi$
$883$	26.8006	0.901911	0.450956	+	0.892546i	$0.351083\pi$
$884$	−8.31529	−0.279674
$885$	0	0
$886$	19.6404	0.659833
$887$	3.15346	0.105883	0.0529414	−	0.998598i	$-0.483140\pi$
$887$	3.15346	0.105883	0.0529414	+	0.998598i	$0.483140\pi$
$888$	−2.04810	−0.0687298
$889$	13.9658	0.468399
$890$	0	0
$891$	2.01879	0.0676320
$892$	5.35571	0.179322
$893$	28.9208	0.967799
$894$	−3.17283	−0.106115
$895$	0	0
$896$	−7.77443	−0.259726
$897$	2.95092	0.0985282
$898$	40.1538	1.33995
$899$	2.81126	0.0937609
$900$	0	0
$901$	−55.3109	−1.84267
$902$	3.15362	0.105004
$903$	−0.118469	−0.00394240
$904$	10.9273	0.363438
$905$	0	0
$906$	2.88596	0.0958795
$907$	25.7319	0.854414	0.427207	−	0.904154i	$-0.359498\pi$
$907$	25.7319	0.854414	0.427207	+	0.904154i	$0.359498\pi$
$908$	−9.36404	−0.310756
$909$	−52.1617	−1.73010
$910$	0	0
$911$	10.3710	0.343606	0.171803	−	0.985131i	$-0.445041\pi$
$911$	10.3710	0.343606	0.171803	+	0.985131i	$0.445041\pi$
$912$	−1.36947	−0.0453476
$913$	−4.05793	−0.134298
$914$	−12.1381	−0.401494
$915$	0	0
$916$	−2.80079	−0.0925409
$917$	−1.06207	−0.0350725
$918$	6.91909	0.228364
$919$	−33.5553	−1.10689	−0.553444	−	0.832887i	$-0.686687\pi$
$919$	−33.5553	−1.10689	−0.553444	+	0.832887i	$0.686687\pi$
$920$	0	0
$921$	0.00334570	0.000110244 0
$922$	11.1334	0.366660
$923$	32.0720	1.05566
$924$	0.0102458	0.000337062 0
$925$	0	0
$926$	16.1324	0.530144
$927$	18.2136	0.598213
$928$	1.09928	0.0360855
$929$	11.6222	0.381314	0.190657	−	0.981657i	$-0.438938\pi$
$929$	11.6222	0.381314	0.190657	+	0.981657i	$0.438938\pi$
$930$	0	0
$931$	−20.1919	−0.661762
$932$	−1.50133	−0.0491777
$933$	2.68633	0.0879464
$934$	6.79792	0.222435
$935$	0	0
$936$	−30.4369	−0.994860
$937$	−46.3339	−1.51366	−0.756831	−	0.653611i	$-0.773253\pi$
$937$	−46.3339	−1.51366	−0.756831	+	0.653611i	$0.773253\pi$
$938$	−16.0080	−0.522681
$939$	−1.34954	−0.0440404
$940$	0	0
$941$	−7.22995	−0.235690	−0.117845	−	0.993032i	$-0.537599\pi$
$941$	−7.22995	−0.235690	−0.117845	+	0.993032i	$0.537599\pi$
$942$	−1.13474	−0.0369720
$943$	−74.3759	−2.42201
$944$	−35.8886	−1.16807
$945$	0	0
$946$	0.266883	0.00867711
$947$	−30.3453	−0.986091	−0.493045	−	0.870004i	$-0.664116\pi$
$947$	−30.3453	−0.986091	−0.493045	+	0.870004i	$0.664116\pi$
$948$	−0.0159644	−0.000518498 0
$949$	−24.0207	−0.779745
$950$	0	0
$951$	0.262327	0.00850653
$952$	−22.1525	−0.717967
$953$	−4.89634	−0.158608	−0.0793040	−	0.996850i	$-0.525270\pi$
$953$	−4.89634	−0.158608	−0.0793040	+	0.996850i	$0.525270\pi$
$954$	−29.8133	−0.965240
$955$	0	0
$956$	−6.34172	−0.205106
$957$	0.0163831	0.000529590 0
$958$	−37.3801	−1.20770
$959$	−11.9382	−0.385503
$960$	0	0
$961$	−6.62631	−0.213752
$962$	−23.3898	−0.754116
$963$	23.4608	0.756015
$964$	−0.345373	−0.0111237
$965$	0	0
$966$	1.15766	0.0372470
$967$	−25.6038	−0.823363	−0.411681	−	0.911328i	$-0.635058\pi$
$967$	−25.6038	−0.823363	−0.411681	+	0.911328i	$0.635058\pi$
$968$	33.0292	1.06160
$969$	−3.05720	−0.0982116
$970$	0	0
$971$	19.2440	0.617570	0.308785	−	0.951132i	$-0.400078\pi$
$971$	19.2440	0.617570	0.308785	+	0.951132i	$0.400078\pi$
$972$	−1.16873	−0.0374870
$973$	−0.114411	−0.00366785
$974$	46.6747	1.49555
$975$	0	0
$976$	11.6577	0.373155
$977$	−14.0956	−0.450957	−0.225479	−	0.974248i	$-0.572395\pi$
$977$	−14.0956	−0.450957	−0.225479	+	0.974248i	$0.572395\pi$
$978$	1.44131	0.0460879
$979$	−1.71917	−0.0549449
$980$	0	0
$981$	12.4507	0.397521
$982$	−5.13606	−0.163898
$983$	50.6189	1.61449	0.807246	−	0.590216i	$-0.200957\pi$
$983$	50.6189	1.61449	0.807246	+	0.590216i	$0.200957\pi$
$984$	−4.09593	−0.130574
$985$	0	0
$986$	−5.21615	−0.166116
$987$	−1.10671	−0.0352270
$988$	3.97137	0.126346
$989$	−6.29425	−0.200145
$990$	0	0
$991$	15.7226	0.499444	0.249722	−	0.968318i	$-0.419661\pi$
$991$	15.7226	0.499444	0.249722	+	0.968318i	$0.419661\pi$
$992$	9.53074	0.302601
$993$	−3.55034	−0.112667
$994$	12.5820	0.399076
$995$	0	0
$996$	0.776114	0.0245921
$997$	9.08507	0.287727	0.143864	−	0.989598i	$-0.454047\pi$
$997$	9.08507	0.287727	0.143864	+	0.989598i	$0.454047\pi$
$998$	11.9019	0.376747
$999$	−4.06243	−0.128530

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6025.2.a.h.1.9		12
5.4	even	2		241.2.a.b.1.4	✓	12
15.14	odd	2		2169.2.a.h.1.9		12
20.19	odd	2		3856.2.a.n.1.7		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
241.2.a.b.1.4	✓	12	5.4	even	2
2169.2.a.h.1.9		12	15.14	odd	2
3856.2.a.n.1.7		12	20.19	odd	2
6025.2.a.h.1.9		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)

\(f(q)\)	\(=\)	\(q+1.28632 q^{2} +0.126224 q^{3} -0.345373 q^{4} +0.162365 q^{6} -1.03110 q^{7} -3.01691 q^{8} -2.98407 q^{9} +O(q^{10})\)	\(q+1.28632 q^{2} +0.126224 q^{3} -0.345373 q^{4} +0.162365 q^{6} -1.03110 q^{7} -3.01691 q^{8} -2.98407 q^{9} +0.227935 q^{11} -0.0435945 q^{12} -3.38088 q^{13} -1.32633 q^{14} -3.18997 q^{16} -7.12130 q^{17} -3.83847 q^{18} +3.40112 q^{19} -0.130150 q^{21} +0.293198 q^{22} -6.91488 q^{23} -0.380807 q^{24} -4.34890 q^{26} -0.755335 q^{27} +0.356115 q^{28} +0.569431 q^{29} +4.93697 q^{31} +1.93048 q^{32} +0.0287710 q^{33} -9.16030 q^{34} +1.03062 q^{36} +5.37832 q^{37} +4.37494 q^{38} -0.426749 q^{39} +10.7559 q^{41} -0.167415 q^{42} +0.910247 q^{43} -0.0787228 q^{44} -8.89477 q^{46} +8.50333 q^{47} -0.402652 q^{48} -5.93683 q^{49} -0.898882 q^{51} +1.16766 q^{52} +7.76696 q^{53} -0.971605 q^{54} +3.11074 q^{56} +0.429304 q^{57} +0.732472 q^{58} +11.2505 q^{59} -3.65450 q^{61} +6.35054 q^{62} +3.07688 q^{63} +8.86317 q^{64} +0.0370088 q^{66} +12.0694 q^{67} +2.45951 q^{68} -0.872826 q^{69} -9.48630 q^{71} +9.00266 q^{72} +7.10488 q^{73} +6.91825 q^{74} -1.17466 q^{76} -0.235024 q^{77} -0.548937 q^{78} +0.366201 q^{79} +8.85686 q^{81} +13.8356 q^{82} -17.8030 q^{83} +0.0449504 q^{84} +1.17087 q^{86} +0.0718760 q^{87} -0.687660 q^{88} -7.54236 q^{89} +3.48603 q^{91} +2.38822 q^{92} +0.623166 q^{93} +10.9380 q^{94} +0.243674 q^{96} +7.85505 q^{97} -7.63668 q^{98} -0.680174 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{2} - q^{3} + 13 q^{4} - q^{6} - 3 q^{7} - 9 q^{8} + 15 q^{9}+O(q^{10}) \) 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