LMFDB - Embedded newform 9025.2.a.cf.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9025,2,Mod(1,9025)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9025, 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("9025.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 9025 = 5^{2} \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	9025.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:	$72.0649878242$
Analytic rank:	$0$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 3x^{8} - 6x^{7} + 16x^{6} + 12x^{5} - 27x^{4} - 8x^{3} + 15x^{2} - 1 $ x^9 - 3x^8 - 6x^7 + 16x^6 + 12x^5 - 27x^4 - 8x^3 + 15*x^2 - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 95)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$-1.13237$ of defining polynomial
Character	$\chi$	$=$	9025.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.13237 q^{2} +2.23040 q^{3} +2.54700 q^{4} +4.75604 q^{6} -1.48562 q^{7} +1.16642 q^{8} +1.97468 q^{9} +O(q^{10})$	\(q+2.13237 q^{2} +2.23040 q^{3} +2.54700 q^{4} +4.75604 q^{6} -1.48562 q^{7} +1.16642 q^{8} +1.97468 q^{9} +4.68135 q^{11} +5.68084 q^{12} -0.361027 q^{13} -3.16790 q^{14} -2.60678 q^{16} +5.47806 q^{17} +4.21075 q^{18} -3.31354 q^{21} +9.98238 q^{22} +6.16739 q^{23} +2.60157 q^{24} -0.769842 q^{26} -2.28687 q^{27} -3.78389 q^{28} +0.895958 q^{29} -4.80024 q^{31} -7.89145 q^{32} +10.4413 q^{33} +11.6812 q^{34} +5.02952 q^{36} +11.3982 q^{37} -0.805233 q^{39} +5.23604 q^{41} -7.06569 q^{42} -7.21827 q^{43} +11.9234 q^{44} +13.1512 q^{46} +10.8655 q^{47} -5.81416 q^{48} -4.79292 q^{49} +12.2183 q^{51} -0.919536 q^{52} -6.52279 q^{53} -4.87645 q^{54} -1.73286 q^{56} +1.91051 q^{58} +9.80717 q^{59} +2.34965 q^{61} -10.2359 q^{62} -2.93364 q^{63} -11.6139 q^{64} +22.2647 q^{66} +8.85223 q^{67} +13.9526 q^{68} +13.7557 q^{69} -6.41207 q^{71} +2.30330 q^{72} -2.86169 q^{73} +24.3051 q^{74} -6.95473 q^{77} -1.71706 q^{78} -2.06549 q^{79} -11.0247 q^{81} +11.1652 q^{82} -6.16397 q^{83} -8.43959 q^{84} -15.3920 q^{86} +1.99834 q^{87} +5.46040 q^{88} +3.32015 q^{89} +0.536350 q^{91} +15.7084 q^{92} -10.7064 q^{93} +23.1693 q^{94} -17.6011 q^{96} +4.71678 q^{97} -10.2203 q^{98} +9.24418 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q + 6 q^{2} + 9 q^{3} + 6 q^{4} + 12 q^{6} + 6 q^{8} + 6 q^{9}+O(q^{10}) $ 9 * q + 6 * q^2 + 9 * q^3 + 6 * q^4 + 12 * q^6 + 6 * q^8 + 6 * q^9	$ 9 q + 6 q^{2} + 9 q^{3} + 6 q^{4} + 12 q^{6} + 6 q^{8} + 6 q^{9} + 18 q^{12} + 9 q^{13} + 12 q^{16} + 9 q^{17} + 24 q^{18} - 12 q^{21} + 24 q^{22} + 12 q^{23} + 3 q^{24} - 3 q^{26} + 24 q^{27} + 15 q^{28} - 9 q^{29} - 18 q^{31} + 3 q^{32} - 9 q^{33} + 24 q^{34} + 18 q^{36} + 18 q^{37} + 18 q^{39} - 6 q^{41} + 12 q^{43} + 48 q^{44} + 9 q^{46} - 15 q^{47} - 21 q^{48} - 9 q^{49} + 6 q^{51} + 33 q^{52} + 15 q^{53} + 63 q^{54} - 6 q^{58} - 21 q^{59} - 12 q^{61} + 36 q^{62} - 21 q^{63} - 36 q^{64} + 3 q^{66} + 60 q^{67} + 51 q^{68} + 15 q^{69} + 18 q^{71} - 27 q^{73} + 27 q^{74} + 30 q^{77} - 6 q^{78} - 15 q^{79} + 33 q^{81} - 24 q^{82} + 48 q^{84} + 39 q^{86} - 15 q^{87} + 27 q^{88} + 39 q^{89} - 21 q^{91} + 6 q^{92} - 15 q^{93} - 15 q^{94} - 33 q^{96} + 15 q^{97} - 15 q^{98} - 36 q^{99}+O(q^{100}) $ 9 * q + 6 * q^2 + 9 * q^3 + 6 * q^4 + 12 * q^6 + 6 * q^8 + 6 * q^9 + 18 * q^12 + 9 * q^13 + 12 * q^16 + 9 * q^17 + 24 * q^18 - 12 * q^21 + 24 * q^22 + 12 * q^23 + 3 * q^24 - 3 * q^26 + 24 * q^27 + 15 * q^28 - 9 * q^29 - 18 * q^31 + 3 * q^32 - 9 * q^33 + 24 * q^34 + 18 * q^36 + 18 * q^37 + 18 * q^39 - 6 * q^41 + 12 * q^43 + 48 * q^44 + 9 * q^46 - 15 * q^47 - 21 * q^48 - 9 * q^49 + 6 * q^51 + 33 * q^52 + 15 * q^53 + 63 * q^54 - 6 * q^58 - 21 * q^59 - 12 * q^61 + 36 * q^62 - 21 * q^63 - 36 * q^64 + 3 * q^66 + 60 * q^67 + 51 * q^68 + 15 * q^69 + 18 * q^71 - 27 * q^73 + 27 * q^74 + 30 * q^77 - 6 * q^78 - 15 * q^79 + 33 * q^81 - 24 * q^82 + 48 * q^84 + 39 * q^86 - 15 * q^87 + 27 * q^88 + 39 * q^89 - 21 * q^91 + 6 * q^92 - 15 * q^93 - 15 * q^94 - 33 * q^96 + 15 * q^97 - 15 * 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 $

$2$	2.13237	1.50781	0.753907	−	0.656981i	$-0.228167\pi$
$2$	2.13237	1.50781	0.753907	+	0.656981i	$0.228167\pi$
$3$	2.23040	1.28772	0.643861	−	0.765143i	$-0.277332\pi$
$3$	2.23040	1.28772	0.643861	+	0.765143i	$0.277332\pi$
$4$	2.54700	1.27350
$5$	0	0
$5$	0	0
$6$	4.75604	1.94164
$7$	−1.48562	−0.561513	−0.280757	−	0.959779i	$-0.590585\pi$
$7$	−1.48562	−0.561513	−0.280757	+	0.959779i	$0.590585\pi$
$8$	1.16642	0.412390
$9$	1.97468	0.658227
$10$	0	0
$11$	4.68135	1.41148	0.705741	−	0.708470i	$-0.250614\pi$
$11$	4.68135	1.41148	0.705741	+	0.708470i	$0.250614\pi$
$12$	5.68084	1.63992
$13$	−0.361027	−0.100131	−0.0500654	−	0.998746i	$-0.515943\pi$
$13$	−0.361027	−0.100131	−0.0500654	+	0.998746i	$0.515943\pi$
$14$	−3.16790	−0.846658
$15$	0	0
$16$	−2.60678	−0.651695
$17$	5.47806	1.32862	0.664312	−	0.747455i	$-0.268725\pi$
$17$	5.47806	1.32862	0.664312	+	0.747455i	$0.268725\pi$
$18$	4.21075	0.992484
$19$	0	0
$19$	0	0
$20$	0	0
$21$	−3.31354	−0.723073
$22$	9.98238	2.12825
$23$	6.16739	1.28599	0.642995	−	0.765871i	$-0.277692\pi$
$23$	6.16739	1.28599	0.642995	+	0.765871i	$0.277692\pi$
$24$	2.60157	0.531044
$25$	0	0
$26$	−0.769842	−0.150978
$27$	−2.28687	−0.440108
$28$	−3.78389	−0.715089
$29$	0.895958	0.166375	0.0831876	−	0.996534i	$-0.473490\pi$
$29$	0.895958	0.166375	0.0831876	+	0.996534i	$0.473490\pi$
$30$	0	0
$31$	−4.80024	−0.862148	−0.431074	−	0.902317i	$-0.641865\pi$
$31$	−4.80024	−0.862148	−0.431074	+	0.902317i	$0.641865\pi$
$32$	−7.89145	−1.39502
$33$	10.4413	1.81759
$34$	11.6812	2.00332
$35$	0	0
$36$	5.02952	0.838254
$37$	11.3982	1.87385	0.936924	−	0.349534i	$-0.113660\pi$
$37$	11.3982	1.87385	0.936924	+	0.349534i	$0.113660\pi$
$38$	0	0
$39$	−0.805233	−0.128941
$40$	0	0
$41$	5.23604	0.817732	0.408866	−	0.912594i	$-0.365924\pi$
$41$	5.23604	0.817732	0.408866	+	0.912594i	$0.365924\pi$
$42$	−7.06569	−1.09026
$43$	−7.21827	−1.10078	−0.550388	−	0.834909i	$-0.685520\pi$
$43$	−7.21827	−1.10078	−0.550388	+	0.834909i	$0.685520\pi$
$44$	11.9234	1.79752
$45$	0	0
$46$	13.1512	1.93903
$47$	10.8655	1.58490	0.792450	−	0.609936i	$-0.208805\pi$
$47$	10.8655	1.58490	0.792450	+	0.609936i	$0.208805\pi$
$48$	−5.81416	−0.839201
$49$	−4.79292	−0.684703
$50$	0	0
$51$	12.2183	1.71090
$52$	−0.919536	−0.127517
$53$	−6.52279	−0.895974	−0.447987	−	0.894040i	$-0.647859\pi$
$53$	−6.52279	−0.895974	−0.447987	+	0.894040i	$0.647859\pi$
$54$	−4.87645	−0.663601
$55$	0	0
$56$	−1.73286	−0.231563
$57$	0	0
$58$	1.91051	0.250863
$59$	9.80717	1.27678	0.638392	−	0.769711i	$-0.279600\pi$
$59$	9.80717	1.27678	0.638392	+	0.769711i	$0.279600\pi$
$60$	0	0
$61$	2.34965	0.300841	0.150421	−	0.988622i	$-0.451937\pi$
$61$	2.34965	0.300841	0.150421	+	0.988622i	$0.451937\pi$
$62$	−10.2359	−1.29996
$63$	−2.93364	−0.369603
$64$	−11.6139	−1.45174
$65$	0	0
$66$	22.2647	2.74059
$67$	8.85223	1.08147	0.540736	−	0.841193i	$-0.318146\pi$
$67$	8.85223	1.08147	0.540736	+	0.841193i	$0.318146\pi$
$68$	13.9526	1.69201
$69$	13.7557	1.65600
$70$	0	0
$71$	−6.41207	−0.760973	−0.380486	−	0.924786i	$-0.624243\pi$
$71$	−6.41207	−0.760973	−0.380486	+	0.924786i	$0.624243\pi$
$72$	2.30330	0.271446
$73$	−2.86169	−0.334936	−0.167468	−	0.985878i	$-0.553559\pi$
$73$	−2.86169	−0.334936	−0.167468	+	0.985878i	$0.553559\pi$
$74$	24.3051	2.82541
$75$	0	0
$76$	0	0
$77$	−6.95473	−0.792566
$78$	−1.71706	−0.194418
$79$	−2.06549	−0.232386	−0.116193	−	0.993227i	$-0.537069\pi$
$79$	−2.06549	−0.232386	−0.116193	+	0.993227i	$0.537069\pi$
$80$	0	0
$81$	−11.0247	−1.22496
$82$	11.1652	1.23299
$83$	−6.16397	−0.676584	−0.338292	−	0.941041i	$-0.609849\pi$
$83$	−6.16397	−0.676584	−0.338292	+	0.941041i	$0.609849\pi$
$84$	−8.43959	−0.920835
$85$	0	0
$86$	−15.3920	−1.65976
$87$	1.99834	0.214245
$88$	5.46040	0.582081
$89$	3.32015	0.351935	0.175968	−	0.984396i	$-0.443695\pi$
$89$	3.32015	0.351935	0.175968	+	0.984396i	$0.443695\pi$
$90$	0	0
$91$	0.536350	0.0562248
$92$	15.7084	1.63771
$93$	−10.7064	−1.11021
$94$	23.1693	2.38974
$95$	0	0
$96$	−17.6011	−1.79640
$97$	4.71678	0.478916	0.239458	−	0.970907i	$-0.423030\pi$
$97$	4.71678	0.478916	0.239458	+	0.970907i	$0.423030\pi$
$98$	−10.2203	−1.03240
$99$	9.24418	0.929075
$100$	0	0
$101$	9.04245	0.899757	0.449878	−	0.893090i	$-0.351467\pi$
$101$	9.04245	0.899757	0.449878	+	0.893090i	$0.351467\pi$
$102$	26.0539	2.57972
$103$	7.79867	0.768426	0.384213	−	0.923244i	$-0.374473\pi$
$103$	7.79867	0.768426	0.384213	+	0.923244i	$0.374473\pi$
$104$	−0.421107	−0.0412929
$105$	0	0
$106$	−13.9090	−1.35096
$107$	0.518303	0.0501063	0.0250531	−	0.999686i	$-0.492025\pi$
$107$	0.518303	0.0501063	0.0250531	+	0.999686i	$0.492025\pi$
$108$	−5.82466	−0.560479
$109$	2.76442	0.264784	0.132392	−	0.991197i	$-0.457734\pi$
$109$	2.76442	0.264784	0.132392	+	0.991197i	$0.457734\pi$
$110$	0	0
$111$	25.4225	2.41299
$112$	3.87269	0.365935
$113$	12.4325	1.16955	0.584774	−	0.811197i	$-0.301183\pi$
$113$	12.4325	1.16955	0.584774	+	0.811197i	$0.301183\pi$
$114$	0	0
$115$	0	0
$116$	2.28201	0.211879
$117$	−0.712913	−0.0659088
$118$	20.9125	1.92515
$119$	−8.13834	−0.746040
$120$	0	0
$121$	10.9151	0.992279
$122$	5.01032	0.453613
$123$	11.6785	1.05301
$124$	−12.2262	−1.09795
$125$	0	0
$126$	−6.25560	−0.557293
$127$	−1.36099	−0.120769	−0.0603843	−	0.998175i	$-0.519233\pi$
$127$	−1.36099	−0.120769	−0.0603843	+	0.998175i	$0.519233\pi$
$128$	−8.98232	−0.793932
$129$	−16.0996	−1.41749
$130$	0	0
$131$	−19.5241	−1.70583	−0.852915	−	0.522050i	$-0.825168\pi$
$131$	−19.5241	−1.70583	−0.852915	+	0.522050i	$0.825168\pi$
$132$	26.5940	2.31471
$133$	0	0
$134$	18.8762	1.63066
$135$	0	0
$136$	6.38969	0.547912
$137$	−10.6804	−0.912488	−0.456244	−	0.889855i	$-0.650806\pi$
$137$	−10.6804	−0.912488	−0.456244	+	0.889855i	$0.650806\pi$
$138$	29.3323	2.49693
$139$	−7.19122	−0.609951	−0.304976	−	0.952360i	$-0.598648\pi$
$139$	−7.19122	−0.609951	−0.304976	+	0.952360i	$0.598648\pi$
$140$	0	0
$141$	24.2345	2.04091
$142$	−13.6729	−1.14741
$143$	−1.69009	−0.141333
$144$	−5.14756	−0.428963
$145$	0	0
$146$	−6.10219	−0.505021
$147$	−10.6901	−0.881706
$148$	29.0312	2.38635
$149$	4.24727	0.347950	0.173975	−	0.984750i	$-0.444339\pi$
$149$	4.24727	0.347950	0.173975	+	0.984750i	$0.444339\pi$
$150$	0	0
$151$	19.5373	1.58992	0.794961	−	0.606660i	$-0.207491\pi$
$151$	19.5373	1.58992	0.794961	+	0.606660i	$0.207491\pi$
$152$	0	0
$153$	10.8174	0.874537
$154$	−14.8301	−1.19504
$155$	0	0
$156$	−2.05093	−0.164206
$157$	−0.286422	−0.0228590	−0.0114295	−	0.999935i	$-0.503638\pi$
$157$	−0.286422	−0.0228590	−0.0114295	+	0.999935i	$0.503638\pi$
$158$	−4.40440	−0.350395
$159$	−14.5484	−1.15376
$160$	0	0
$161$	−9.16243	−0.722100
$162$	−23.5087	−1.84702
$163$	20.6255	1.61552	0.807759	−	0.589513i	$-0.200680\pi$
$163$	20.6255	1.61552	0.807759	+	0.589513i	$0.200680\pi$
$164$	13.3362	1.04138
$165$	0	0
$166$	−13.1439	−1.02016
$167$	10.8538	0.839895	0.419948	−	0.907548i	$-0.362048\pi$
$167$	10.8538	0.839895	0.419948	+	0.907548i	$0.362048\pi$
$168$	−3.86496	−0.298188
$169$	−12.8697	−0.989974
$170$	0	0
$171$	0	0
$172$	−18.3850	−1.40184
$173$	−17.5490	−1.33422	−0.667111	−	0.744958i	$-0.732469\pi$
$173$	−17.5490	−1.33422	−0.667111	+	0.744958i	$0.732469\pi$
$174$	4.26121	0.323041
$175$	0	0
$176$	−12.2032	−0.919854
$177$	21.8739	1.64414
$178$	7.07979	0.530653
$179$	−15.0644	−1.12597	−0.562983	−	0.826468i	$-0.690347\pi$
$179$	−15.0644	−1.12597	−0.562983	+	0.826468i	$0.690347\pi$
$180$	0	0
$181$	−14.9205	−1.10903	−0.554515	−	0.832174i	$-0.687096\pi$
$181$	−14.9205	−1.10903	−0.554515	+	0.832174i	$0.687096\pi$
$182$	1.14370	0.0847765
$183$	5.24065	0.387400
$184$	7.19374	0.530330
$185$	0	0
$186$	−22.8301	−1.67398
$187$	25.6447	1.87533
$188$	27.6746	2.01837
$189$	3.39743	0.247127
$190$	0	0
$191$	−0.00677854	−0.000490478 0	−0.000245239	−	1.00000i	$-0.500078\pi$
$191$	−0.00677854	−0.000490478 0	−0.000245239		1.00000i	$0.500078\pi$
$192$	−25.9037	−1.86944
$193$	13.7262	0.988036	0.494018	−	0.869452i	$-0.335528\pi$
$193$	13.7262	0.988036	0.494018	+	0.869452i	$0.335528\pi$
$194$	10.0579	0.722117
$195$	0	0
$196$	−12.2076	−0.871970
$197$	−0.479780	−0.0341829	−0.0170915	−	0.999854i	$-0.505441\pi$
$197$	−0.479780	−0.0341829	−0.0170915	+	0.999854i	$0.505441\pi$
$198$	19.7120	1.40087
$199$	−26.8207	−1.90127	−0.950636	−	0.310308i	$-0.899568\pi$
$199$	−26.8207	−1.90127	−0.950636	+	0.310308i	$0.899568\pi$
$200$	0	0
$201$	19.7440	1.39263
$202$	19.2818	1.35667
$203$	−1.33106	−0.0934219
$204$	31.1200	2.17883
$205$	0	0
$206$	16.6297	1.15864
$207$	12.1786	0.846473
$208$	0.941116	0.0652547
$209$	0	0
$210$	0	0
$211$	−8.24119	−0.567347	−0.283674	−	0.958921i	$-0.591553\pi$
$211$	−8.24119	−0.567347	−0.283674	+	0.958921i	$0.591553\pi$
$212$	−16.6136	−1.14102
$213$	−14.3015	−0.979921
$214$	1.10521	0.0755509
$215$	0	0
$216$	−2.66744	−0.181496
$217$	7.13135	0.484108
$218$	5.89477	0.399244
$219$	−6.38272	−0.431304
$220$	0	0
$221$	−1.97772	−0.133036
$222$	54.2101	3.63835
$223$	1.71804	0.115049	0.0575243	−	0.998344i	$-0.481679\pi$
$223$	1.71804	0.115049	0.0575243	+	0.998344i	$0.481679\pi$
$224$	11.7237	0.783325
$225$	0	0
$226$	26.5106	1.76346
$227$	4.22601	0.280490	0.140245	−	0.990117i	$-0.455211\pi$
$227$	4.22601	0.280490	0.140245	+	0.990117i	$0.455211\pi$
$228$	0	0
$229$	5.52322	0.364985	0.182492	−	0.983207i	$-0.441583\pi$
$229$	5.52322	0.364985	0.182492	+	0.983207i	$0.441583\pi$
$230$	0	0
$231$	−15.5118	−1.02060
$232$	1.04506	0.0686115
$233$	−28.1959	−1.84718	−0.923588	−	0.383387i	$-0.874757\pi$
$233$	−28.1959	−1.84718	−0.923588	+	0.383387i	$0.874757\pi$
$234$	−1.52019	−0.0993782
$235$	0	0
$236$	24.9789	1.62599
$237$	−4.60688	−0.299249
$238$	−17.3540	−1.12489
$239$	−11.3204	−0.732256	−0.366128	−	0.930565i	$-0.619317\pi$
$239$	−11.3204	−0.732256	−0.366128	+	0.930565i	$0.619317\pi$
$240$	0	0
$241$	−16.3640	−1.05410	−0.527050	−	0.849834i	$-0.676702\pi$
$241$	−16.3640	−1.05410	−0.527050	+	0.849834i	$0.676702\pi$
$242$	23.2750	1.49617
$243$	−17.7288	−1.13730
$244$	5.98456	0.383122
$245$	0	0
$246$	24.9028	1.58774
$247$	0	0
$248$	−5.59907	−0.355541
$249$	−13.7481	−0.871252
$250$	0	0
$251$	−7.34480	−0.463600	−0.231800	−	0.972763i	$-0.574461\pi$
$251$	−7.34480	−0.463600	−0.231800	+	0.972763i	$0.574461\pi$
$252$	−7.47198	−0.470691
$253$	28.8717	1.81515
$254$	−2.90214	−0.182096
$255$	0	0
$256$	4.07424	0.254640
$257$	−6.01306	−0.375084	−0.187542	−	0.982257i	$-0.560052\pi$
$257$	−6.01306	−0.375084	−0.187542	+	0.982257i	$0.560052\pi$
$258$	−34.3303	−2.13731
$259$	−16.9334	−1.05219
$260$	0	0
$261$	1.76923	0.109513
$262$	−41.6327	−2.57207
$263$	−7.37883	−0.454998	−0.227499	−	0.973778i	$-0.573055\pi$
$263$	−7.37883	−0.454998	−0.227499	+	0.973778i	$0.573055\pi$
$264$	12.1789	0.749558
$265$	0	0
$266$	0	0
$267$	7.40526	0.453194
$268$	22.5467	1.37726
$269$	10.8629	0.662324	0.331162	−	0.943574i	$-0.392559\pi$
$269$	10.8629	0.662324	0.331162	+	0.943574i	$0.392559\pi$
$270$	0	0
$271$	2.84873	0.173048	0.0865240	−	0.996250i	$-0.472424\pi$
$271$	2.84873	0.173048	0.0865240	+	0.996250i	$0.472424\pi$
$272$	−14.2801	−0.865857
$273$	1.19627	0.0724018
$274$	−22.7746	−1.37586
$275$	0	0
$276$	35.0359	2.10892
$277$	16.1443	0.970015	0.485008	−	0.874510i	$-0.338817\pi$
$277$	16.1443	0.970015	0.485008	+	0.874510i	$0.338817\pi$
$278$	−15.3343	−0.919693
$279$	−9.47894	−0.567489
$280$	0	0
$281$	−3.21606	−0.191854	−0.0959270	−	0.995388i	$-0.530582\pi$
$281$	−3.21606	−0.191854	−0.0959270	+	0.995388i	$0.530582\pi$
$282$	51.6769	3.07731
$283$	−12.8743	−0.765297	−0.382649	−	0.923894i	$-0.624988\pi$
$283$	−12.8743	−0.765297	−0.382649	+	0.923894i	$0.624988\pi$
$284$	−16.3316	−0.969101
$285$	0	0
$286$	−3.60390	−0.213103
$287$	−7.77879	−0.459167
$288$	−15.5831	−0.918243
$289$	13.0091	0.765242
$290$	0	0
$291$	10.5203	0.616711
$292$	−7.28875	−0.426542
$293$	−30.8110	−1.80000	−0.899999	−	0.435891i	$-0.856433\pi$
$293$	−30.8110	−1.80000	−0.899999	+	0.435891i	$0.856433\pi$
$294$	−22.7953	−1.32945
$295$	0	0
$296$	13.2950	0.772756
$297$	−10.7056	−0.621204
$298$	9.05675	0.524644
$299$	−2.22659	−0.128767
$300$	0	0
$301$	10.7236	0.618100
$302$	41.6608	2.39731
$303$	20.1683	1.15864
$304$	0	0
$305$	0	0
$306$	23.0667	1.31864
$307$	16.3812	0.934927	0.467463	−	0.884012i	$-0.345168\pi$
$307$	16.3812	0.934927	0.467463	+	0.884012i	$0.345168\pi$
$308$	−17.7137	−1.00933
$309$	17.3942	0.989519
$310$	0	0
$311$	24.7746	1.40484	0.702420	−	0.711763i	$-0.252103\pi$
$311$	24.7746	1.40484	0.702420	+	0.711763i	$0.252103\pi$
$312$	−0.939237	−0.0531738
$313$	−10.2734	−0.580684	−0.290342	−	0.956923i	$-0.593769\pi$
$313$	−10.2734	−0.580684	−0.290342	+	0.956923i	$0.593769\pi$
$314$	−0.610758	−0.0344671
$315$	0	0
$316$	−5.26082	−0.295944
$317$	6.07632	0.341280	0.170640	−	0.985333i	$-0.445416\pi$
$317$	6.07632	0.341280	0.170640	+	0.985333i	$0.445416\pi$
$318$	−31.0226	−1.73966
$319$	4.19429	0.234835
$320$	0	0
$321$	1.15602	0.0645229
$322$	−19.5377	−1.08879
$323$	0	0
$324$	−28.0799	−1.55999
$325$	0	0
$326$	43.9813	2.43590
$327$	6.16577	0.340968
$328$	6.10740	0.337225
$329$	−16.1421	−0.889943
$330$	0	0
$331$	−11.8110	−0.649190	−0.324595	−	0.945853i	$-0.605228\pi$
$331$	−11.8110	−0.649190	−0.324595	+	0.945853i	$0.605228\pi$
$332$	−15.6997	−0.861631
$333$	22.5078	1.23342
$334$	23.1444	1.26641
$335$	0	0
$336$	8.63766	0.471223
$337$	15.2265	0.829439	0.414719	−	0.909949i	$-0.363880\pi$
$337$	15.2265	0.829439	0.414719	+	0.909949i	$0.363880\pi$
$338$	−27.4429	−1.49270
$339$	27.7293	1.50605
$340$	0	0
$341$	−22.4716	−1.21691
$342$	0	0
$343$	17.5199	0.945983
$344$	−8.41950	−0.453949
$345$	0	0
$346$	−37.4209	−2.01176
$347$	30.1804	1.62017	0.810085	−	0.586312i	$-0.199421\pi$
$347$	30.1804	1.62017	0.810085	+	0.586312i	$0.199421\pi$
$348$	5.08979	0.272841
$349$	−2.73771	−0.146546	−0.0732732	−	0.997312i	$-0.523344\pi$
$349$	−2.73771	−0.146546	−0.0732732	+	0.997312i	$0.523344\pi$
$350$	0	0
$351$	0.825620	0.0440684
$352$	−36.9427	−1.96905
$353$	4.60924	0.245325	0.122663	−	0.992448i	$-0.460857\pi$
$353$	4.60924	0.245325	0.122663	+	0.992448i	$0.460857\pi$
$354$	46.6433	2.47906
$355$	0	0
$356$	8.45643	0.448190
$357$	−18.1517	−0.960692
$358$	−32.1229	−1.69775
$359$	12.3399	0.651277	0.325639	−	0.945494i	$-0.394421\pi$
$359$	12.3399	0.651277	0.325639	+	0.945494i	$0.394421\pi$
$360$	0	0
$361$	0	0
$362$	−31.8160	−1.67221
$363$	24.3450	1.27778
$364$	1.36609	0.0716023
$365$	0	0
$366$	11.1750	0.584127
$367$	1.63612	0.0854049	0.0427024	−	0.999088i	$-0.486403\pi$
$367$	1.63612	0.0854049	0.0427024	+	0.999088i	$0.486403\pi$
$368$	−16.0770	−0.838072
$369$	10.3395	0.538253
$370$	0	0
$371$	9.69041	0.503101
$372$	−27.2694	−1.41385
$373$	−14.7587	−0.764178	−0.382089	−	0.924126i	$-0.624795\pi$
$373$	−14.7587	−0.764178	−0.382089	+	0.924126i	$0.624795\pi$
$374$	54.6840	2.82764
$375$	0	0
$376$	12.6737	0.653598
$377$	−0.323464	−0.0166593
$378$	7.24458	0.372621
$379$	1.75865	0.0903358	0.0451679	−	0.998979i	$-0.485618\pi$
$379$	1.75865	0.0903358	0.0451679	+	0.998979i	$0.485618\pi$
$380$	0	0
$381$	−3.03556	−0.155516
$382$	−0.0144544	−0.000739550 0
$383$	−8.49861	−0.434259	−0.217129	−	0.976143i	$-0.569669\pi$
$383$	−8.49861	−0.434259	−0.217129	+	0.976143i	$0.569669\pi$
$384$	−20.0342	−1.02236
$385$	0	0
$386$	29.2694	1.48977
$387$	−14.2538	−0.724560
$388$	12.0137	0.609901
$389$	−33.9416	−1.72091	−0.860454	−	0.509527i	$-0.829820\pi$
$389$	−33.9416	−1.72091	−0.860454	+	0.509527i	$0.829820\pi$
$390$	0	0
$391$	33.7853	1.70860
$392$	−5.59054	−0.282365
$393$	−43.5466	−2.19663
$394$	−1.02307	−0.0515414
$395$	0	0
$396$	23.5450	1.18318
$397$	−7.77709	−0.390321	−0.195160	−	0.980771i	$-0.562523\pi$
$397$	−7.77709	−0.390321	−0.195160	+	0.980771i	$0.562523\pi$
$398$	−57.1918	−2.86676
$399$	0	0
$400$	0	0
$401$	−31.1878	−1.55744	−0.778722	−	0.627370i	$-0.784132\pi$
$401$	−31.1878	−1.55744	−0.778722	+	0.627370i	$0.784132\pi$
$402$	42.1015	2.09983
$403$	1.73301	0.0863275
$404$	23.0311	1.14584
$405$	0	0
$406$	−2.83831	−0.140863
$407$	53.3589	2.64490
$408$	14.2516	0.705558
$409$	14.6754	0.725654	0.362827	−	0.931857i	$-0.381812\pi$
$409$	14.6754	0.725654	0.362827	+	0.931857i	$0.381812\pi$
$410$	0	0
$411$	−23.8215	−1.17503
$412$	19.8632	0.978592
$413$	−14.5698	−0.716932
$414$	25.9694	1.27632
$415$	0	0
$416$	2.84902	0.139685
$417$	−16.0393	−0.785447
$418$	0	0
$419$	−20.6063	−1.00668	−0.503341	−	0.864088i	$-0.667896\pi$
$419$	−20.6063	−1.00668	−0.503341	+	0.864088i	$0.667896\pi$
$420$	0	0
$421$	−27.6791	−1.34900	−0.674499	−	0.738276i	$-0.735640\pi$
$421$	−27.6791	−1.34900	−0.674499	+	0.738276i	$0.735640\pi$
$422$	−17.5733	−0.855454
$423$	21.4560	1.04323
$424$	−7.60828	−0.369491
$425$	0	0
$426$	−30.4961	−1.47754
$427$	−3.49069	−0.168926
$428$	1.32012	0.0638104
$429$	−3.76958	−0.181997
$430$	0	0
$431$	20.8960	1.00652	0.503262	−	0.864134i	$-0.332133\pi$
$431$	20.8960	1.00652	0.503262	+	0.864134i	$0.332133\pi$
$432$	5.96136	0.286816
$433$	1.92594	0.0925550	0.0462775	−	0.998929i	$-0.485264\pi$
$433$	1.92594	0.0925550	0.0462775	+	0.998929i	$0.485264\pi$
$434$	15.2067	0.729944
$435$	0	0
$436$	7.04100	0.337203
$437$	0	0
$438$	−13.6103	−0.650327
$439$	−34.6994	−1.65611	−0.828056	−	0.560645i	$-0.810553\pi$
$439$	−34.6994	−1.65611	−0.828056	+	0.560645i	$0.810553\pi$
$440$	0	0
$441$	−9.46449	−0.450690
$442$	−4.21724	−0.200594
$443$	−26.3209	−1.25054	−0.625271	−	0.780408i	$-0.715011\pi$
$443$	−26.3209	−1.25054	−0.625271	+	0.780408i	$0.715011\pi$
$444$	64.7511	3.07295
$445$	0	0
$446$	3.66350	0.173472
$447$	9.47311	0.448063
$448$	17.2540	0.815173
$449$	13.4316	0.633878	0.316939	−	0.948446i	$-0.397345\pi$
$449$	13.4316	0.633878	0.316939	+	0.948446i	$0.397345\pi$
$450$	0	0
$451$	24.5117	1.15421
$452$	31.6655	1.48942
$453$	43.5760	2.04738
$454$	9.01143	0.422927
$455$	0	0
$456$	0	0
$457$	−0.205882	−0.00963073	−0.00481537	−	0.999988i	$-0.501533\pi$
$457$	−0.205882	−0.00963073	−0.00481537	+	0.999988i	$0.501533\pi$
$458$	11.7776	0.550329
$459$	−12.5276	−0.584738
$460$	0	0
$461$	39.0276	1.81769	0.908847	−	0.417129i	$-0.136964\pi$
$461$	39.0276	1.81769	0.908847	+	0.417129i	$0.136964\pi$
$462$	−33.0770	−1.53888
$463$	7.42468	0.345054	0.172527	−	0.985005i	$-0.444807\pi$
$463$	7.42468	0.345054	0.172527	+	0.985005i	$0.444807\pi$
$464$	−2.33556	−0.108426
$465$	0	0
$466$	−60.1241	−2.78520
$467$	−21.9255	−1.01459	−0.507295	−	0.861773i	$-0.669354\pi$
$467$	−21.9255	−1.01459	−0.507295	+	0.861773i	$0.669354\pi$
$468$	−1.81579	−0.0839350
$469$	−13.1511	−0.607261
$470$	0	0
$471$	−0.638836	−0.0294360
$472$	11.4392	0.526534
$473$	−33.7912	−1.55372
$474$	−9.82357	−0.451211
$475$	0	0
$476$	−20.7284	−0.950084
$477$	−12.8804	−0.589754
$478$	−24.1393	−1.10411
$479$	−28.0795	−1.28299	−0.641493	−	0.767129i	$-0.721685\pi$
$479$	−28.0795	−1.28299	−0.641493	+	0.767129i	$0.721685\pi$
$480$	0	0
$481$	−4.11504	−0.187630
$482$	−34.8942	−1.58939
$483$	−20.4359	−0.929864
$484$	27.8007	1.26367
$485$	0	0
$486$	−37.8044	−1.71484
$487$	−14.1348	−0.640508	−0.320254	−	0.947332i	$-0.603768\pi$
$487$	−14.1348	−0.640508	−0.320254	+	0.947332i	$0.603768\pi$
$488$	2.74066	0.124064
$489$	46.0032	2.08034
$490$	0	0
$491$	−23.1941	−1.04674	−0.523368	−	0.852106i	$-0.675325\pi$
$491$	−23.1941	−1.04674	−0.523368	+	0.852106i	$0.675325\pi$
$492$	29.7451	1.34101
$493$	4.90811	0.221050
$494$	0	0
$495$	0	0
$496$	12.5131	0.561857
$497$	9.52593	0.427297
$498$	−29.3161	−1.31368
$499$	−42.4334	−1.89958	−0.949790	−	0.312887i	$-0.898704\pi$
$499$	−42.4334	−1.89958	−0.949790	+	0.312887i	$0.898704\pi$
$500$	0	0
$501$	24.2084	1.08155
$502$	−15.6618	−0.699022
$503$	−5.84757	−0.260730	−0.130365	−	0.991466i	$-0.541615\pi$
$503$	−5.84757	−0.260730	−0.130365	+	0.991466i	$0.541615\pi$
$504$	−3.42184	−0.152421
$505$	0	0
$506$	61.5652	2.73691
$507$	−28.7045	−1.27481
$508$	−3.46645	−0.153799
$509$	−8.34459	−0.369868	−0.184934	−	0.982751i	$-0.559207\pi$
$509$	−8.34459	−0.369868	−0.184934	+	0.982751i	$0.559207\pi$
$510$	0	0
$511$	4.25141	0.188071
$512$	26.6524	1.17788
$513$	0	0
$514$	−12.8221	−0.565557
$515$	0	0
$516$	−41.0058	−1.80518
$517$	50.8654	2.23706
$518$	−36.1083	−1.58651
$519$	−39.1412	−1.71811
$520$	0	0
$521$	−30.8838	−1.35304	−0.676521	−	0.736423i	$-0.736513\pi$
$521$	−30.8838	−1.35304	−0.676521	+	0.736423i	$0.736513\pi$
$522$	3.77266	0.165125
$523$	22.9057	1.00160	0.500798	−	0.865564i	$-0.333040\pi$
$523$	22.9057	1.00160	0.500798	+	0.865564i	$0.333040\pi$
$524$	−49.7280	−2.17238
$525$	0	0
$526$	−15.7344	−0.686052
$527$	−26.2960	−1.14547
$528$	−27.2181	−1.18452
$529$	15.0367	0.653769
$530$	0	0
$531$	19.3660	0.840415
$532$	0	0
$533$	−1.89035	−0.0818801
$534$	15.7908	0.683333
$535$	0	0
$536$	10.3254	0.445988
$537$	−33.5997	−1.44993
$538$	23.1638	0.998662
$539$	−22.4373	−0.966445
$540$	0	0
$541$	−4.00347	−0.172123	−0.0860613	−	0.996290i	$-0.527428\pi$
$541$	−4.00347	−0.172123	−0.0860613	+	0.996290i	$0.527428\pi$
$542$	6.07455	0.260924
$543$	−33.2786	−1.42812
$544$	−43.2298	−1.85346
$545$	0	0
$546$	2.55090	0.109168
$547$	41.6721	1.78177	0.890886	−	0.454227i	$-0.150085\pi$
$547$	41.6721	1.78177	0.890886	+	0.454227i	$0.150085\pi$
$548$	−27.2030	−1.16205
$549$	4.63980	0.198022
$550$	0	0
$551$	0	0
$552$	16.0449	0.682917
$553$	3.06855	0.130488
$554$	34.4256	1.46260
$555$	0	0
$556$	−18.3161	−0.776774
$557$	3.17499	0.134529	0.0672644	−	0.997735i	$-0.478573\pi$
$557$	3.17499	0.134529	0.0672644	+	0.997735i	$0.478573\pi$
$558$	−20.2126	−0.855668
$559$	2.60599	0.110221
$560$	0	0
$561$	57.1980	2.41490
$562$	−6.85783	−0.289280
$563$	14.4059	0.607137	0.303568	−	0.952810i	$-0.401822\pi$
$563$	14.4059	0.607137	0.303568	+	0.952810i	$0.401822\pi$
$564$	61.7253	2.59910
$565$	0	0
$566$	−27.4528	−1.15393
$567$	16.3785	0.687834
$568$	−7.47914	−0.313818
$569$	−24.9795	−1.04719	−0.523597	−	0.851966i	$-0.675410\pi$
$569$	−24.9795	−1.04719	−0.523597	+	0.851966i	$0.675410\pi$
$570$	0	0
$571$	13.1086	0.548579	0.274289	−	0.961647i	$-0.411557\pi$
$571$	13.1086	0.548579	0.274289	+	0.961647i	$0.411557\pi$
$572$	−4.30467	−0.179987
$573$	−0.0151189	−0.000631600 0
$574$	−16.5873	−0.692339
$575$	0	0
$576$	−22.9338	−0.955576
$577$	−8.25496	−0.343659	−0.171829	−	0.985127i	$-0.554968\pi$
$577$	−8.25496	−0.343659	−0.171829	+	0.985127i	$0.554968\pi$
$578$	27.7402	1.15384
$579$	30.6150	1.27232
$580$	0	0
$581$	9.15735	0.379911
$582$	22.4332	0.929885
$583$	−30.5355	−1.26465
$584$	−3.33793	−0.138124
$585$	0	0
$586$	−65.7005	−2.71406
$587$	7.90606	0.326318	0.163159	−	0.986600i	$-0.447832\pi$
$587$	7.90606	0.326318	0.163159	+	0.986600i	$0.447832\pi$
$588$	−27.2278	−1.12286
$589$	0	0
$590$	0	0
$591$	−1.07010	−0.0440181
$592$	−29.7125	−1.22118
$593$	3.55568	0.146014	0.0730071	−	0.997331i	$-0.476740\pi$
$593$	3.55568	0.146014	0.0730071	+	0.997331i	$0.476740\pi$
$594$	−22.8284	−0.936660
$595$	0	0
$596$	10.8178	0.443115
$597$	−59.8210	−2.44831
$598$	−4.74792	−0.194157
$599$	−11.0561	−0.451739	−0.225870	−	0.974158i	$-0.572522\pi$
$599$	−11.0561	−0.451739	−0.225870	+	0.974158i	$0.572522\pi$
$600$	0	0
$601$	45.5444	1.85780	0.928898	−	0.370336i	$-0.120758\pi$
$601$	45.5444	1.85780	0.928898	+	0.370336i	$0.120758\pi$
$602$	22.8668	0.931980
$603$	17.4803	0.711854
$604$	49.7616	2.02477
$605$	0	0
$606$	43.0062	1.74701
$607$	36.4498	1.47945	0.739727	−	0.672907i	$-0.234955\pi$
$607$	36.4498	1.47945	0.739727	+	0.672907i	$0.234955\pi$
$608$	0	0
$609$	−2.96879	−0.120301
$610$	0	0
$611$	−3.92275	−0.158697
$612$	27.5520	1.11372
$613$	−6.74383	−0.272381	−0.136190	−	0.990683i	$-0.543486\pi$
$613$	−6.74383	−0.272381	−0.136190	+	0.990683i	$0.543486\pi$
$614$	34.9309	1.40970
$615$	0	0
$616$	−8.11211	−0.326846
$617$	−25.2478	−1.01644	−0.508219	−	0.861228i	$-0.669696\pi$
$617$	−25.2478	−1.01644	−0.508219	+	0.861228i	$0.669696\pi$
$618$	37.0908	1.49201
$619$	22.3223	0.897209	0.448604	−	0.893730i	$-0.351921\pi$
$619$	22.3223	0.897209	0.448604	+	0.893730i	$0.351921\pi$
$620$	0	0
$621$	−14.1040	−0.565974
$622$	52.8287	2.11824
$623$	−4.93250	−0.197616
$624$	2.09906	0.0840298
$625$	0	0
$626$	−21.9066	−0.875564
$627$	0	0
$628$	−0.729519	−0.0291110
$629$	62.4398	2.48964
$630$	0	0
$631$	3.53935	0.140899	0.0704496	−	0.997515i	$-0.477557\pi$
$631$	3.53935	0.140899	0.0704496	+	0.997515i	$0.477557\pi$
$632$	−2.40922	−0.0958338
$633$	−18.3812	−0.730585
$634$	12.9570	0.514587
$635$	0	0
$636$	−37.0549	−1.46932
$637$	1.73037	0.0685598
$638$	8.94379	0.354088
$639$	−12.6618	−0.500893
$640$	0	0
$641$	−26.3668	−1.04143	−0.520714	−	0.853731i	$-0.674334\pi$
$641$	−26.3668	−1.04143	−0.520714	+	0.853731i	$0.674334\pi$
$642$	2.46507	0.0972886
$643$	14.7489	0.581641	0.290821	−	0.956778i	$-0.406072\pi$
$643$	14.7489	0.581641	0.290821	+	0.956778i	$0.406072\pi$
$644$	−23.3367	−0.919596
$645$	0	0
$646$	0	0
$647$	−5.04555	−0.198361	−0.0991804	−	0.995069i	$-0.531622\pi$
$647$	−5.04555	−0.198361	−0.0991804	+	0.995069i	$0.531622\pi$
$648$	−12.8594	−0.505163
$649$	45.9108	1.80216
$650$	0	0
$651$	15.9058	0.623396
$652$	52.5333	2.05736
$653$	44.6725	1.74817	0.874084	−	0.485775i	$-0.161462\pi$
$653$	44.6725	1.74817	0.874084	+	0.485775i	$0.161462\pi$
$654$	13.1477	0.514116
$655$	0	0
$656$	−13.6492	−0.532911
$657$	−5.65094	−0.220464
$658$	−34.4210	−1.34187
$659$	−29.3909	−1.14491	−0.572453	−	0.819938i	$-0.694008\pi$
$659$	−29.3909	−1.14491	−0.572453	+	0.819938i	$0.694008\pi$
$660$	0	0
$661$	20.2246	0.786645	0.393322	−	0.919401i	$-0.371326\pi$
$661$	20.2246	0.786645	0.393322	+	0.919401i	$0.371326\pi$
$662$	−25.1854	−0.978858
$663$	−4.41111	−0.171313
$664$	−7.18975	−0.279016
$665$	0	0
$666$	47.9949	1.85976
$667$	5.52572	0.213957
$668$	27.6448	1.06961
$669$	3.83192	0.148151
$670$	0	0
$671$	10.9995	0.424632
$672$	26.1486	1.00870
$673$	−27.6662	−1.06645	−0.533227	−	0.845972i	$-0.679021\pi$
$673$	−27.6662	−1.06645	−0.533227	+	0.845972i	$0.679021\pi$
$674$	32.4685	1.25064
$675$	0	0
$676$	−32.7791	−1.26073
$677$	31.6740	1.21733	0.608665	−	0.793428i	$-0.291705\pi$
$677$	31.6740	1.21733	0.608665	+	0.793428i	$0.291705\pi$
$678$	59.1292	2.27084
$679$	−7.00737	−0.268918
$680$	0	0
$681$	9.42570	0.361194
$682$	−47.9178	−1.83487
$683$	−4.75181	−0.181823	−0.0909114	−	0.995859i	$-0.528978\pi$
$683$	−4.75181	−0.181823	−0.0909114	+	0.995859i	$0.528978\pi$
$684$	0	0
$685$	0	0
$686$	37.3588	1.42637
$687$	12.3190	0.469999
$688$	18.8164	0.717369
$689$	2.35490	0.0897145
$690$	0	0
$691$	−0.423541	−0.0161123	−0.00805613	−	0.999968i	$-0.502564\pi$
$691$	−0.423541	−0.0161123	−0.00805613	+	0.999968i	$0.502564\pi$
$692$	−44.6973	−1.69914
$693$	−13.7334	−0.521688
$694$	64.3559	2.44292
$695$	0	0
$696$	2.33090	0.0883525
$697$	28.6833	1.08646
$698$	−5.83782	−0.220965
$699$	−62.8881	−2.37865
$700$	0	0
$701$	7.94597	0.300115	0.150058	−	0.988677i	$-0.452054\pi$
$701$	7.94597	0.300115	0.150058	+	0.988677i	$0.452054\pi$
$702$	1.76053	0.0664469
$703$	0	0
$704$	−54.3689	−2.04911
$705$	0	0
$706$	9.82861	0.369905
$707$	−13.4337	−0.505226
$708$	55.7129	2.09382
$709$	11.7378	0.440824	0.220412	−	0.975407i	$-0.429260\pi$
$709$	11.7378	0.440824	0.220412	+	0.975407i	$0.429260\pi$
$710$	0	0
$711$	−4.07869	−0.152963
$712$	3.87267	0.145135
$713$	−29.6049	−1.10871
$714$	−38.7062	−1.44854
$715$	0	0
$716$	−38.3691	−1.43392
$717$	−25.2490	−0.942942
$718$	26.3133	0.982005
$719$	−50.4477	−1.88138	−0.940691	−	0.339264i	$-0.889822\pi$
$719$	−50.4477	−1.88138	−0.940691	+	0.339264i	$0.889822\pi$
$720$	0	0
$721$	−11.5859	−0.431481
$722$	0	0
$723$	−36.4983	−1.35739
$724$	−38.0025	−1.41235
$725$	0	0
$726$	51.9125	1.92665
$727$	−26.0654	−0.966714	−0.483357	−	0.875423i	$-0.660583\pi$
$727$	−26.0654	−0.966714	−0.483357	+	0.875423i	$0.660583\pi$
$728$	0.625607	0.0231865
$729$	−6.46834	−0.239568
$730$	0	0
$731$	−39.5421	−1.46252
$732$	13.3480	0.493355
$733$	−17.0861	−0.631090	−0.315545	−	0.948911i	$-0.602187\pi$
$733$	−17.0861	−0.631090	−0.315545	+	0.948911i	$0.602187\pi$
$734$	3.48882	0.128775
$735$	0	0
$736$	−48.6696	−1.79399
$737$	41.4404	1.52648
$738$	22.0477	0.811586
$739$	−24.6148	−0.905471	−0.452736	−	0.891645i	$-0.649552\pi$
$739$	−24.6148	−0.905471	−0.452736	+	0.891645i	$0.649552\pi$
$740$	0	0
$741$	0	0
$742$	20.6636	0.758583
$743$	−7.66985	−0.281379	−0.140690	−	0.990054i	$-0.544932\pi$
$743$	−7.66985	−0.281379	−0.140690	+	0.990054i	$0.544932\pi$
$744$	−12.4882	−0.457838
$745$	0	0
$746$	−31.4711	−1.15224
$747$	−12.1719	−0.445346
$748$	65.3172	2.38823
$749$	−0.770004	−0.0281353
$750$	0	0
$751$	−21.0630	−0.768600	−0.384300	−	0.923208i	$-0.625557\pi$
$751$	−21.0630	−0.768600	−0.384300	+	0.923208i	$0.625557\pi$
$752$	−28.3240	−1.03287
$753$	−16.3818	−0.596987
$754$	−0.689746	−0.0251191
$755$	0	0
$756$	8.65327	0.314716
$757$	−4.30729	−0.156551	−0.0782755	−	0.996932i	$-0.524941\pi$
$757$	−4.30729	−0.156551	−0.0782755	+	0.996932i	$0.524941\pi$
$758$	3.75010	0.136210
$759$	64.3955	2.33741
$760$	0	0
$761$	−1.11318	−0.0403529	−0.0201764	−	0.999796i	$-0.506423\pi$
$761$	−1.11318	−0.0403529	−0.0201764	+	0.999796i	$0.506423\pi$
$762$	−6.47293	−0.234490
$763$	−4.10690	−0.148680
$764$	−0.0172650	−0.000624625 0
$765$	0	0
$766$	−18.1222	−0.654781
$767$	−3.54065	−0.127845
$768$	9.08718	0.327906
$769$	9.87109	0.355961	0.177980	−	0.984034i	$-0.443044\pi$
$769$	9.87109	0.355961	0.177980	+	0.984034i	$0.443044\pi$
$770$	0	0
$771$	−13.4115	−0.483004
$772$	34.9608	1.25827
$773$	−17.0731	−0.614077	−0.307039	−	0.951697i	$-0.599338\pi$
$773$	−17.0731	−0.614077	−0.307039	+	0.951697i	$0.599338\pi$
$774$	−30.3943	−1.09250
$775$	0	0
$776$	5.50173	0.197500
$777$	−37.7683	−1.35493
$778$	−72.3761	−2.59481
$779$	0	0
$780$	0	0
$781$	−30.0172	−1.07410
$782$	72.0428	2.57625
$783$	−2.04894	−0.0732231
$784$	12.4941	0.446217
$785$	0	0
$786$	−92.8575	−3.31212
$787$	−11.6565	−0.415510	−0.207755	−	0.978181i	$-0.566616\pi$
$787$	−11.6565	−0.415510	−0.207755	+	0.978181i	$0.566616\pi$
$788$	−1.22200	−0.0435320
$789$	−16.4577	−0.585911
$790$	0	0
$791$	−18.4700	−0.656717
$792$	10.7826	0.383142
$793$	−0.848285	−0.0301235
$794$	−16.5836	−0.588531
$795$	0	0
$796$	−68.3126	−2.42127
$797$	−29.8609	−1.05773	−0.528864	−	0.848707i	$-0.677382\pi$
$797$	−29.8609	−1.05773	−0.528864	+	0.848707i	$0.677382\pi$
$798$	0	0
$799$	59.5220	2.10574
$800$	0	0
$801$	6.55624	0.231653
$802$	−66.5039	−2.34833
$803$	−13.3966	−0.472756
$804$	50.2881	1.77352
$805$	0	0
$806$	3.69542	0.130166
$807$	24.2287	0.852889
$808$	10.5473	0.371051
$809$	−38.3513	−1.34836	−0.674180	−	0.738567i	$-0.735503\pi$
$809$	−38.3513	−1.34836	−0.674180	+	0.738567i	$0.735503\pi$
$810$	0	0
$811$	−11.1629	−0.391982	−0.195991	−	0.980606i	$-0.562792\pi$
$811$	−11.1629	−0.391982	−0.195991	+	0.980606i	$0.562792\pi$
$812$	−3.39021	−0.118973
$813$	6.35381	0.222838
$814$	113.781	3.98802
$815$	0	0
$816$	−31.8503	−1.11498
$817$	0	0
$818$	31.2935	1.09415
$819$	1.05912	0.0370087
$820$	0	0
$821$	7.65073	0.267012	0.133506	−	0.991048i	$-0.457376\pi$
$821$	7.65073	0.267012	0.133506	+	0.991048i	$0.457376\pi$
$822$	−50.7964	−1.77173
$823$	−33.2218	−1.15804	−0.579020	−	0.815313i	$-0.696565\pi$
$823$	−33.2218	−1.15804	−0.579020	+	0.815313i	$0.696565\pi$
$824$	9.09649	0.316891
$825$	0	0
$826$	−31.0682	−1.08100
$827$	−3.40736	−0.118485	−0.0592427	−	0.998244i	$-0.518869\pi$
$827$	−3.40736	−0.118485	−0.0592427	+	0.998244i	$0.518869\pi$
$828$	31.0190	1.07799
$829$	−4.42435	−0.153664	−0.0768320	−	0.997044i	$-0.524481\pi$
$829$	−4.42435	−0.153664	−0.0768320	+	0.997044i	$0.524481\pi$
$830$	0	0
$831$	36.0082	1.24911
$832$	4.19294	0.145364
$833$	−26.2559	−0.909712
$834$	−34.2017	−1.18431
$835$	0	0
$836$	0	0
$837$	10.9775	0.379438
$838$	−43.9402	−1.51789
$839$	23.8114	0.822062	0.411031	−	0.911621i	$-0.365169\pi$
$839$	23.8114	0.822062	0.411031	+	0.911621i	$0.365169\pi$
$840$	0	0
$841$	−28.1973	−0.972319
$842$	−59.0221	−2.03404
$843$	−7.17310	−0.247055
$844$	−20.9904	−0.722518
$845$	0	0
$846$	45.7521	1.57299
$847$	−16.2157	−0.557178
$848$	17.0035	0.583901
$849$	−28.7148	−0.985490
$850$	0	0
$851$	70.2970	2.40975
$852$	−36.4259	−1.24793
$853$	4.43369	0.151807	0.0759034	−	0.997115i	$-0.475816\pi$
$853$	4.43369	0.151807	0.0759034	+	0.997115i	$0.475816\pi$
$854$	−7.44345	−0.254710
$855$	0	0
$856$	0.604557	0.0206633
$857$	26.9976	0.922219	0.461109	−	0.887343i	$-0.347452\pi$
$857$	26.9976	0.922219	0.461109	+	0.887343i	$0.347452\pi$
$858$	−8.03814	−0.274418
$859$	−13.7120	−0.467846	−0.233923	−	0.972255i	$-0.575156\pi$
$859$	−13.7120	−0.467846	−0.233923	+	0.972255i	$0.575156\pi$
$860$	0	0
$861$	−17.3498	−0.591280
$862$	44.5580	1.51765
$863$	52.4480	1.78535	0.892676	−	0.450699i	$-0.148825\pi$
$863$	52.4480	1.78535	0.892676	+	0.450699i	$0.148825\pi$
$864$	18.0467	0.613961
$865$	0	0
$866$	4.10683	0.139556
$867$	29.0155	0.985419
$868$	18.1636	0.616512
$869$	−9.66930	−0.328009
$870$	0	0
$871$	−3.19589	−0.108289
$872$	3.22447	0.109194
$873$	9.31414	0.315236
$874$	0	0
$875$	0	0
$876$	−16.2568	−0.549267
$877$	−40.8256	−1.37858	−0.689291	−	0.724484i	$-0.742078\pi$
$877$	−40.8256	−1.37858	−0.689291	+	0.724484i	$0.742078\pi$
$878$	−73.9920	−2.49711
$879$	−68.7209	−2.31790
$880$	0	0
$881$	−47.7615	−1.60913	−0.804563	−	0.593867i	$-0.797600\pi$
$881$	−47.7615	−1.60913	−0.804563	+	0.593867i	$0.797600\pi$
$882$	−20.1818	−0.679557
$883$	−32.1045	−1.08040	−0.540201	−	0.841536i	$-0.681652\pi$
$883$	−32.1045	−1.08040	−0.540201	+	0.841536i	$0.681652\pi$
$884$	−5.03727	−0.169422
$885$	0	0
$886$	−56.1258	−1.88558
$887$	−8.81815	−0.296085	−0.148042	−	0.988981i	$-0.547297\pi$
$887$	−8.81815	−0.296085	−0.148042	+	0.988981i	$0.547297\pi$
$888$	29.6532	0.995095
$889$	2.02192	0.0678131
$890$	0	0
$891$	−51.6104	−1.72901
$892$	4.37586	0.146515
$893$	0	0
$894$	20.2002	0.675595
$895$	0	0
$896$	13.3444	0.445804
$897$	−4.96619	−0.165816
$898$	28.6412	0.955770
$899$	−4.30081	−0.143440
$900$	0	0
$901$	−35.7322	−1.19041
$902$	52.2681	1.74034
$903$	23.9180	0.795941
$904$	14.5014	0.482310
$905$	0	0
$906$	92.9201	3.08706
$907$	10.3405	0.343352	0.171676	−	0.985153i	$-0.445082\pi$
$907$	10.3405	0.343352	0.171676	+	0.985153i	$0.445082\pi$
$908$	10.7637	0.357205
$909$	17.8560	0.592245
$910$	0	0
$911$	−5.25941	−0.174252	−0.0871260	−	0.996197i	$-0.527768\pi$
$911$	−5.25941	−0.174252	−0.0871260	+	0.996197i	$0.527768\pi$
$912$	0	0
$913$	−28.8557	−0.954985
$914$	−0.439016	−0.0145214
$915$	0	0
$916$	14.0677	0.464809
$917$	29.0055	0.957847
$918$	−26.7135	−0.881676
$919$	0.202368	0.00667549	0.00333774	−	0.999994i	$-0.498938\pi$
$919$	0.202368	0.00667549	0.00333774	+	0.999994i	$0.498938\pi$
$920$	0	0
$921$	36.5367	1.20393
$922$	83.2212	2.74074
$923$	2.31493	0.0761968
$924$	−39.5087	−1.29974
$925$	0	0
$926$	15.8322	0.520278
$927$	15.3999	0.505799
$928$	−7.07040	−0.232097
$929$	18.6410	0.611593	0.305796	−	0.952097i	$-0.401077\pi$
$929$	18.6410	0.611593	0.305796	+	0.952097i	$0.401077\pi$
$930$	0	0
$931$	0	0
$932$	−71.8151	−2.35238
$933$	55.2573	1.80904
$934$	−46.7532	−1.52981
$935$	0	0
$936$	−0.831552	−0.0271801
$937$	50.5108	1.65011	0.825057	−	0.565049i	$-0.191143\pi$
$937$	50.5108	1.65011	0.825057	+	0.565049i	$0.191143\pi$
$938$	−28.0430	−0.915636
$939$	−22.9137	−0.747760
$940$	0	0
$941$	16.5797	0.540482	0.270241	−	0.962793i	$-0.412897\pi$
$941$	16.5797	0.540482	0.270241	+	0.962793i	$0.412897\pi$
$942$	−1.36224	−0.0443840
$943$	32.2927	1.05159
$944$	−25.5651	−0.832074
$945$	0	0
$946$	−72.0555	−2.34273
$947$	−37.4346	−1.21646	−0.608230	−	0.793761i	$-0.708120\pi$
$947$	−37.4346	−1.21646	−0.608230	+	0.793761i	$0.708120\pi$
$948$	−11.7337	−0.381094
$949$	1.03315	0.0335374
$950$	0	0
$951$	13.5526	0.439474
$952$	−9.49269	−0.307660
$953$	42.4683	1.37568	0.687842	−	0.725860i	$-0.258558\pi$
$953$	42.4683	1.37568	0.687842	+	0.725860i	$0.258558\pi$
$954$	−27.4658	−0.889240
$955$	0	0
$956$	−28.8331	−0.932529
$957$	9.35495	0.302403
$958$	−59.8759	−1.93450
$959$	15.8671	0.512374
$960$	0	0
$961$	−7.95774	−0.256701
$962$	−8.77479	−0.282911
$963$	1.02348	0.0329813
$964$	−41.6793	−1.34240
$965$	0	0
$966$	−43.5769	−1.40206
$967$	−16.2280	−0.521858	−0.260929	−	0.965358i	$-0.584029\pi$
$967$	−16.2280	−0.521858	−0.260929	+	0.965358i	$0.584029\pi$
$968$	12.7315	0.409206
$969$	0	0
$970$	0	0
$971$	17.6122	0.565203	0.282602	−	0.959237i	$-0.408803\pi$
$971$	17.6122	0.565203	0.282602	+	0.959237i	$0.408803\pi$
$972$	−45.1554	−1.44836
$973$	10.6835	0.342496
$974$	−30.1406	−0.965767
$975$	0	0
$976$	−6.12501	−0.196057
$977$	0.120875	0.00386713	0.00193357	−	0.999998i	$-0.499385\pi$
$977$	0.120875	0.00386713	0.00193357	+	0.999998i	$0.499385\pi$
$978$	98.0959	3.13676
$979$	15.5428	0.496750
$980$	0	0
$981$	5.45886	0.174288
$982$	−49.4585	−1.57828
$983$	22.6784	0.723330	0.361665	−	0.932308i	$-0.382208\pi$
$983$	22.6784	0.723330	0.361665	+	0.932308i	$0.382208\pi$
$984$	13.6219	0.434252
$985$	0	0
$986$	10.4659	0.333302
$987$	−36.0033	−1.14600
$988$	0	0
$989$	−44.5179	−1.41559
$990$	0	0
$991$	53.7663	1.70794	0.853972	−	0.520320i	$-0.174187\pi$
$991$	53.7663	1.70794	0.853972	+	0.520320i	$0.174187\pi$
$992$	37.8808	1.20272
$993$	−26.3432	−0.835976
$994$	20.3128	0.644284
$995$	0	0
$996$	−35.0165	−1.10954
$997$	−36.7435	−1.16368	−0.581840	−	0.813303i	$-0.697667\pi$
$997$	−36.7435	−1.16368	−0.581840	+	0.813303i	$0.697667\pi$
$998$	−90.4838	−2.86421
$999$	−26.0661	−0.824696

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9025.2.a.cf.1.7		9
5.4	even	2		1805.2.a.s.1.3		9
19.3	odd	18		475.2.l.c.351.1		18
19.13	odd	18		475.2.l.c.226.1		18
19.18	odd	2		9025.2.a.cc.1.3		9
95.3	even	36		475.2.u.b.199.2		36
95.13	even	36		475.2.u.b.74.5		36
95.22	even	36		475.2.u.b.199.5		36
95.32	even	36		475.2.u.b.74.2		36
95.79	odd	18		95.2.k.a.66.3	yes	18
95.89	odd	18		95.2.k.a.36.3	✓	18
95.94	odd	2		1805.2.a.v.1.7		9
285.89	even	18		855.2.bs.c.226.1		18
285.269	even	18		855.2.bs.c.541.1		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.k.a.36.3	✓	18	95.89	odd	18
95.2.k.a.66.3	yes	18	95.79	odd	18
475.2.l.c.226.1		18	19.13	odd	18
475.2.l.c.351.1		18	19.3	odd	18
475.2.u.b.74.2		36	95.32	even	36
475.2.u.b.74.5		36	95.13	even	36
475.2.u.b.199.2		36	95.3	even	36
475.2.u.b.199.5		36	95.22	even	36
855.2.bs.c.226.1		18	285.89	even	18
855.2.bs.c.541.1		18	285.269	even	18
1805.2.a.s.1.3		9	5.4	even	2
1805.2.a.v.1.7		9	95.94	odd	2
9025.2.a.cc.1.3		9	19.18	odd	2
9025.2.a.cf.1.7		9	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:	\( N \)	\(=\)	\( 9025 = 5^{2} \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9025.a (trivial)

\(f(q)\)	\(=\)	\(q+2.13237 q^{2} +2.23040 q^{3} +2.54700 q^{4} +4.75604 q^{6} -1.48562 q^{7} +1.16642 q^{8} +1.97468 q^{9} +O(q^{10})\)	\(q+2.13237 q^{2} +2.23040 q^{3} +2.54700 q^{4} +4.75604 q^{6} -1.48562 q^{7} +1.16642 q^{8} +1.97468 q^{9} +4.68135 q^{11} +5.68084 q^{12} -0.361027 q^{13} -3.16790 q^{14} -2.60678 q^{16} +5.47806 q^{17} +4.21075 q^{18} -3.31354 q^{21} +9.98238 q^{22} +6.16739 q^{23} +2.60157 q^{24} -0.769842 q^{26} -2.28687 q^{27} -3.78389 q^{28} +0.895958 q^{29} -4.80024 q^{31} -7.89145 q^{32} +10.4413 q^{33} +11.6812 q^{34} +5.02952 q^{36} +11.3982 q^{37} -0.805233 q^{39} +5.23604 q^{41} -7.06569 q^{42} -7.21827 q^{43} +11.9234 q^{44} +13.1512 q^{46} +10.8655 q^{47} -5.81416 q^{48} -4.79292 q^{49} +12.2183 q^{51} -0.919536 q^{52} -6.52279 q^{53} -4.87645 q^{54} -1.73286 q^{56} +1.91051 q^{58} +9.80717 q^{59} +2.34965 q^{61} -10.2359 q^{62} -2.93364 q^{63} -11.6139 q^{64} +22.2647 q^{66} +8.85223 q^{67} +13.9526 q^{68} +13.7557 q^{69} -6.41207 q^{71} +2.30330 q^{72} -2.86169 q^{73} +24.3051 q^{74} -6.95473 q^{77} -1.71706 q^{78} -2.06549 q^{79} -11.0247 q^{81} +11.1652 q^{82} -6.16397 q^{83} -8.43959 q^{84} -15.3920 q^{86} +1.99834 q^{87} +5.46040 q^{88} +3.32015 q^{89} +0.536350 q^{91} +15.7084 q^{92} -10.7064 q^{93} +23.1693 q^{94} -17.6011 q^{96} +4.71678 q^{97} -10.2203 q^{98} +9.24418 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 6 q^{2} + 9 q^{3} + 6 q^{4} + 12 q^{6} + 6 q^{8} + 6 q^{9}+O(q^{10}) \) 9 * q + 6 * q^2 + 9 * q^3 + 6 * q^4 + 12 * q^6 + 6 * q^8 + 6 * q^9	\( 9 q + 6 q^{2} + 9 q^{3} + 6 q^{4} + 12 q^{6} + 6 q^{8} + 6 q^{9} + 18 q^{12} + 9 q^{13} + 12 q^{16} + 9 q^{17} + 24 q^{18} - 12 q^{21} + 24 q^{22} + 12 q^{23} + 3 q^{24} - 3 q^{26} + 24 q^{27} + 15 q^{28} - 9 q^{29} - 18 q^{31} + 3 q^{32} - 9 q^{33} + 24 q^{34} + 18 q^{36} + 18 q^{37} + 18 q^{39} - 6 q^{41} + 12 q^{43} + 48 q^{44} + 9 q^{46} - 15 q^{47} - 21 q^{48} - 9 q^{49} + 6 q^{51} + 33 q^{52} + 15 q^{53} + 63 q^{54} - 6 q^{58} - 21 q^{59} - 12 q^{61} + 36 q^{62} - 21 q^{63} - 36 q^{64} + 3 q^{66} + 60 q^{67} + 51 q^{68} + 15 q^{69} + 18 q^{71} - 27 q^{73} + 27 q^{74} + 30 q^{77} - 6 q^{78} - 15 q^{79} + 33 q^{81} - 24 q^{82} + 48 q^{84} + 39 q^{86} - 15 q^{87} + 27 q^{88} + 39 q^{89} - 21 q^{91} + 6 q^{92} - 15 q^{93} - 15 q^{94} - 33 q^{96} + 15 q^{97} - 15 q^{98} - 36 q^{99}+O(q^{100}) \) 9 * q + 6 * q^2 + 9 * q^3 + 6 * q^4 + 12 * q^6 + 6 * q^8 + 6 * q^9 + 18 * q^12 + 9 * q^13 + 12 * q^16 + 9 * q^17 + 24 * q^18 - 12 * q^21 + 24 * q^22 + 12 * q^23 + 3 * q^24 - 3 * q^26 + 24 * q^27 + 15 * q^28 - 9 * q^29 - 18 * q^31 + 3 * q^32 - 9 * q^33 + 24 * q^34 + 18 * q^36 + 18 * q^37 + 18 * q^39 - 6 * q^41 + 12 * q^43 + 48 * q^44 + 9 * q^46 - 15 * q^47 - 21 * q^48 - 9 * q^49 + 6 * q^51 + 33 * q^52 + 15 * q^53 + 63 * q^54 - 6 * q^58 - 21 * q^59 - 12 * q^61 + 36 * q^62 - 21 * q^63 - 36 * q^64 + 3 * q^66 + 60 * q^67 + 51 * q^68 + 15 * q^69 + 18 * q^71 - 27 * q^73 + 27 * q^74 + 30 * q^77 - 6 * q^78 - 15 * q^79 + 33 * q^81 - 24 * q^82 + 48 * q^84 + 39 * q^86 - 15 * q^87 + 27 * q^88 + 39 * q^89 - 21 * q^91 + 6 * q^92 - 15 * q^93 - 15 * q^94 - 33 * q^96 + 15 * q^97 - 15 * q^98 - 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more