LMFDB - Embedded newform 1295.2.a.h.1.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1295,2,Mod(1,1295)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1295.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1295, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1295 = 5 \cdot 7 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1295.a (trivial)

Newform invariants

comment:select newform

sage:traces = [12,5] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$10.3406270618$
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} - 5 x^{11} - 7 x^{10} + 63 x^{9} - 11 x^{8} - 279 x^{7} + 171 x^{6} + 503 x^{5} - 367 x^{4} + \cdots - 26 $ x^12 - 5x^11 - 7x^10 + 63x^9 - 11x^8 - 279x^7 + 171x^6 + 503x^5 - 367x^4 - 310x^3 + 216x^2 + 42*x - 26
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Root			$2.68572$ of defining polynomial
Character	$\chi$	$=$	1295.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.68572 q^{2} -2.63795 q^{3} +5.21310 q^{4} +1.00000 q^{5} -7.08481 q^{6} -1.00000 q^{7} +8.62948 q^{8} +3.95881 q^{9} +2.68572 q^{10} +1.13341 q^{11} -13.7519 q^{12} +2.39306 q^{13} -2.68572 q^{14} -2.63795 q^{15} +12.7502 q^{16} +2.66063 q^{17} +10.6322 q^{18} -6.13281 q^{19} +5.21310 q^{20} +2.63795 q^{21} +3.04402 q^{22} +6.65282 q^{23} -22.7642 q^{24} +1.00000 q^{25} +6.42709 q^{26} -2.52928 q^{27} -5.21310 q^{28} +1.97736 q^{29} -7.08481 q^{30} -1.15585 q^{31} +16.9845 q^{32} -2.98989 q^{33} +7.14571 q^{34} -1.00000 q^{35} +20.6376 q^{36} -1.00000 q^{37} -16.4710 q^{38} -6.31278 q^{39} +8.62948 q^{40} +10.4136 q^{41} +7.08481 q^{42} -10.5999 q^{43} +5.90858 q^{44} +3.95881 q^{45} +17.8676 q^{46} +7.80249 q^{47} -33.6344 q^{48} +1.00000 q^{49} +2.68572 q^{50} -7.01862 q^{51} +12.4752 q^{52} +11.7655 q^{53} -6.79295 q^{54} +1.13341 q^{55} -8.62948 q^{56} +16.1781 q^{57} +5.31065 q^{58} -6.92707 q^{59} -13.7519 q^{60} -2.57934 q^{61} -3.10429 q^{62} -3.95881 q^{63} +20.1152 q^{64} +2.39306 q^{65} -8.03000 q^{66} -6.24070 q^{67} +13.8701 q^{68} -17.5498 q^{69} -2.68572 q^{70} -5.10743 q^{71} +34.1624 q^{72} -11.9912 q^{73} -2.68572 q^{74} -2.63795 q^{75} -31.9709 q^{76} -1.13341 q^{77} -16.9544 q^{78} +7.60555 q^{79} +12.7502 q^{80} -5.20428 q^{81} +27.9680 q^{82} -7.36059 q^{83} +13.7519 q^{84} +2.66063 q^{85} -28.4684 q^{86} -5.21620 q^{87} +9.78074 q^{88} -5.13957 q^{89} +10.6322 q^{90} -2.39306 q^{91} +34.6818 q^{92} +3.04908 q^{93} +20.9553 q^{94} -6.13281 q^{95} -44.8042 q^{96} +3.81785 q^{97} +2.68572 q^{98} +4.48695 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 5 q^{2} + 4 q^{3} + 15 q^{4} + 12 q^{5} + 6 q^{6} - 12 q^{7} + 21 q^{8} + 18 q^{9} + 5 q^{10} - 4 q^{11} + 8 q^{12} + 6 q^{13} - 5 q^{14} + 4 q^{15} + 21 q^{16} + 20 q^{17} + 14 q^{18} - 4 q^{19}+ \cdots - 24 q^{99}+O(q^{100}) $ 12 * q + 5 * q^2 + 4 * q^3 + 15 * q^4 + 12 * q^5 + 6 * q^6 - 12 * q^7 + 21 * q^8 + 18 * q^9 + 5 * q^10 - 4 * q^11 + 8 * q^12 + 6 * q^13 - 5 * q^14 + 4 * q^15 + 21 * q^16 + 20 * q^17 + 14 * q^18 - 4 * q^19 + 15 * q^20 - 4 * q^21 + 2 * q^22 + 20 * q^23 + 4 * q^24 + 12 * q^25 + 6 * q^26 + 10 * q^27 - 15 * q^28 - 12 * q^29 + 6 * q^30 + 47 * q^32 + 20 * q^33 - 28 * q^34 - 12 * q^35 + 39 * q^36 - 12 * q^37 + 8 * q^38 + 21 * q^40 + 24 * q^41 - 6 * q^42 + 14 * q^43 - 16 * q^44 + 18 * q^45 + 20 * q^46 + 18 * q^47 - 19 * q^48 + 12 * q^49 + 5 * q^50 - 20 * q^51 + 22 * q^52 + 36 * q^53 - 46 * q^54 - 4 * q^55 - 21 * q^56 + 36 * q^57 + 28 * q^58 + 4 * q^59 + 8 * q^60 - 39 * q^62 - 18 * q^63 + 9 * q^64 + 6 * q^65 - 21 * q^66 + 6 * q^67 - 6 * q^68 - 6 * q^69 - 5 * q^70 - 12 * q^71 + 17 * q^72 + 32 * q^73 - 5 * q^74 + 4 * q^75 - 13 * q^76 + 4 * q^77 + 74 * q^78 + 14 * q^79 + 21 * q^80 - 16 * q^81 - 26 * q^82 - 18 * q^83 - 8 * q^84 + 20 * q^85 - 36 * q^86 - 18 * q^87 + 27 * q^88 + 14 * q^90 - 6 * q^91 + 39 * q^92 + 52 * q^93 + 38 * q^94 - 4 * q^95 - 53 * q^96 + 38 * q^97 + 5 * q^98 - 24 * q^99

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 $

$2$	2.68572	1.89909	0.949546	−	0.313629i	$-0.101545\pi$
$2$	2.68572	1.89909	0.949546	+	0.313629i	$0.101545\pi$
$3$	−2.63795	−1.52302	−0.761512	−	0.648151i	$-0.775543\pi$
$3$	−2.63795	−1.52302	−0.761512	+	0.648151i	$0.775543\pi$
$4$	5.21310	2.60655
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−7.08481	−2.89236
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	8.62948	3.05098
$9$	3.95881	1.31960
$10$	2.68572	0.849299
$11$	1.13341	0.341736	0.170868	−	0.985294i	$-0.445343\pi$
$11$	1.13341	0.341736	0.170868	+	0.985294i	$0.445343\pi$
$12$	−13.7519	−3.96983
$13$	2.39306	0.663715	0.331858	−	0.943329i	$-0.392325\pi$
$13$	2.39306	0.663715	0.331858	+	0.943329i	$0.392325\pi$
$14$	−2.68572	−0.717789
$15$	−2.63795	−0.681117
$16$	12.7502	3.18754
$17$	2.66063	0.645297	0.322649	−	0.946519i	$-0.395427\pi$
$17$	2.66063	0.645297	0.322649	+	0.946519i	$0.395427\pi$
$18$	10.6322	2.50604
$19$	−6.13281	−1.40696	−0.703482	−	0.710713i	$-0.748372\pi$
$19$	−6.13281	−1.40696	−0.703482	+	0.710713i	$0.748372\pi$
$20$	5.21310	1.16568
$21$	2.63795	0.575649
$22$	3.04402	0.648988
$23$	6.65282	1.38721	0.693604	−	0.720357i	$-0.256022\pi$
$23$	6.65282	1.38721	0.693604	+	0.720357i	$0.256022\pi$
$24$	−22.7642	−4.64672
$25$	1.00000	0.200000
$26$	6.42709	1.26046
$27$	−2.52928	−0.486761
$28$	−5.21310	−0.985183
$29$	1.97736	0.367187	0.183594	−	0.983002i	$-0.441227\pi$
$29$	1.97736	0.367187	0.183594	+	0.983002i	$0.441227\pi$
$30$	−7.08481	−1.29350
$31$	−1.15585	−0.207597	−0.103798	−	0.994598i	$-0.533100\pi$
$31$	−1.15585	−0.207597	−0.103798	+	0.994598i	$0.533100\pi$
$32$	16.9845	3.00246
$33$	−2.98989	−0.520472
$34$	7.14571	1.22548
$35$	−1.00000	−0.169031
$36$	20.6376	3.43961
$37$	−1.00000	−0.164399
$37$	−1.00000	−0.164399
$38$	−16.4710	−2.67195
$39$	−6.31278	−1.01085
$40$	8.62948	1.36444
$41$	10.4136	1.62633	0.813166	−	0.582032i	$-0.197742\pi$
$41$	10.4136	1.62633	0.813166	+	0.582032i	$0.197742\pi$
$42$	7.08481	1.09321
$43$	−10.5999	−1.61647	−0.808235	−	0.588860i	$-0.799577\pi$
$43$	−10.5999	−1.61647	−0.808235	+	0.588860i	$0.799577\pi$
$44$	5.90858	0.890752
$45$	3.95881	0.590144
$46$	17.8676	2.63443
$47$	7.80249	1.13811	0.569055	−	0.822300i	$-0.307309\pi$
$47$	7.80249	1.13811	0.569055	+	0.822300i	$0.307309\pi$
$48$	−33.6344	−4.85471
$49$	1.00000	0.142857
$50$	2.68572	0.379818
$51$	−7.01862	−0.982803
$52$	12.4752	1.73001
$53$	11.7655	1.61612	0.808058	−	0.589103i	$-0.200519\pi$
$53$	11.7655	1.61612	0.808058	+	0.589103i	$0.200519\pi$
$54$	−6.79295	−0.924404
$55$	1.13341	0.152829
$56$	−8.62948	−1.15316
$57$	16.1781	2.14284
$58$	5.31065	0.697322
$59$	−6.92707	−0.901828	−0.450914	−	0.892567i	$-0.648902\pi$
$59$	−6.92707	−0.901828	−0.450914	+	0.892567i	$0.648902\pi$
$60$	−13.7519	−1.77536
$61$	−2.57934	−0.330251	−0.165125	−	0.986273i	$-0.552803\pi$
$61$	−2.57934	−0.330251	−0.165125	+	0.986273i	$0.552803\pi$
$62$	−3.10429	−0.394245
$63$	−3.95881	−0.498763
$64$	20.1152	2.51440
$65$	2.39306	0.296823
$66$	−8.03000	−0.988425
$67$	−6.24070	−0.762423	−0.381212	−	0.924488i	$-0.624493\pi$
$67$	−6.24070	−0.762423	−0.381212	+	0.924488i	$0.624493\pi$
$68$	13.8701	1.68200
$69$	−17.5498	−2.11275
$70$	−2.68572	−0.321005
$71$	−5.10743	−0.606141	−0.303071	−	0.952968i	$-0.598012\pi$
$71$	−5.10743	−0.606141	−0.303071	+	0.952968i	$0.598012\pi$
$72$	34.1624	4.02608
$73$	−11.9912	−1.40346	−0.701731	−	0.712442i	$-0.747589\pi$
$73$	−11.9912	−1.40346	−0.701731	+	0.712442i	$0.747589\pi$
$74$	−2.68572	−0.312209
$75$	−2.63795	−0.304605
$76$	−31.9709	−3.66732
$77$	−1.13341	−0.129164
$78$	−16.9544	−1.91970
$79$	7.60555	0.855691	0.427846	−	0.903852i	$-0.359273\pi$
$79$	7.60555	0.855691	0.427846	+	0.903852i	$0.359273\pi$
$80$	12.7502	1.42551
$81$	−5.20428	−0.578253
$82$	27.9680	3.08855
$83$	−7.36059	−0.807930	−0.403965	−	0.914774i	$-0.632368\pi$
$83$	−7.36059	−0.807930	−0.403965	+	0.914774i	$0.632368\pi$
$84$	13.7519	1.50046
$85$	2.66063	0.288586
$86$	−28.4684	−3.06982
$87$	−5.21620	−0.559235
$88$	9.78074	1.04263
$89$	−5.13957	−0.544793	−0.272396	−	0.962185i	$-0.587816\pi$
$89$	−5.13957	−0.544793	−0.272396	+	0.962185i	$0.587816\pi$
$90$	10.6322	1.12074
$91$	−2.39306	−0.250861
$92$	34.6818	3.61582
$93$	3.04908	0.316175
$94$	20.9553	2.16137
$95$	−6.13281	−0.629213
$96$	−44.8042	−4.57281
$97$	3.81785	0.387644	0.193822	−	0.981037i	$-0.437912\pi$
$97$	3.81785	0.387644	0.193822	+	0.981037i	$0.437912\pi$
$98$	2.68572	0.271299
$99$	4.48695	0.450956
$100$	5.21310	0.521310
$101$	−0.378222	−0.0376345	−0.0188173	−	0.999823i	$-0.505990\pi$
$101$	−0.378222	−0.0376345	−0.0188173	+	0.999823i	$0.505990\pi$
$102$	−18.8500	−1.86643
$103$	9.70427	0.956190	0.478095	−	0.878308i	$-0.341327\pi$
$103$	9.70427	0.956190	0.478095	+	0.878308i	$0.341327\pi$
$104$	20.6509	2.02498
$105$	2.63795	0.257438
$106$	31.5988	3.06915
$107$	17.9059	1.73103	0.865516	−	0.500881i	$-0.166991\pi$
$107$	17.9059	1.73103	0.865516	+	0.500881i	$0.166991\pi$
$108$	−13.1854	−1.26877
$109$	−11.0040	−1.05400	−0.526998	−	0.849866i	$-0.676683\pi$
$109$	−11.0040	−1.05400	−0.526998	+	0.849866i	$0.676683\pi$
$110$	3.04402	0.290236
$111$	2.63795	0.250384
$112$	−12.7502	−1.20478
$113$	−18.8356	−1.77190	−0.885951	−	0.463778i	$-0.846494\pi$
$113$	−18.8356	−1.77190	−0.885951	+	0.463778i	$0.846494\pi$
$114$	43.4498	4.06945
$115$	6.65282	0.620378
$116$	10.3082	0.957091
$117$	9.47366	0.875840
$118$	−18.6042	−1.71265
$119$	−2.66063	−0.243899
$120$	−22.7642	−2.07808
$121$	−9.71538	−0.883216
$122$	−6.92739	−0.627177
$123$	−27.4706	−2.47694
$124$	−6.02555	−0.541111
$125$	1.00000	0.0894427
$126$	−10.6322	−0.947196
$127$	−12.0340	−1.06785	−0.533925	−	0.845532i	$-0.679283\pi$
$127$	−12.0340	−1.06785	−0.533925	+	0.845532i	$0.679283\pi$
$128$	20.0548	1.77261
$129$	27.9621	2.46192
$130$	6.42709	0.563693
$131$	−0.676979	−0.0591479	−0.0295739	−	0.999563i	$-0.509415\pi$
$131$	−0.676979	−0.0591479	−0.0295739	+	0.999563i	$0.509415\pi$
$132$	−15.5866	−1.35664
$133$	6.13281	0.531782
$134$	−16.7608	−1.44791
$135$	−2.52928	−0.217686
$136$	22.9598	1.96879
$137$	−11.9047	−1.01709	−0.508544	−	0.861036i	$-0.669816\pi$
$137$	−11.9047	−1.01709	−0.508544	+	0.861036i	$0.669816\pi$
$138$	−47.1339	−4.01231
$139$	−18.5910	−1.57687	−0.788433	−	0.615121i	$-0.789107\pi$
$139$	−18.5910	−1.57687	−0.788433	+	0.615121i	$0.789107\pi$
$140$	−5.21310	−0.440587
$141$	−20.5826	−1.73337
$142$	−13.7171	−1.15112
$143$	2.71232	0.226816
$144$	50.4755	4.20629
$145$	1.97736	0.164211
$146$	−32.2050	−2.66530
$147$	−2.63795	−0.217575
$148$	−5.21310	−0.428514
$149$	−15.2717	−1.25110	−0.625552	−	0.780182i	$-0.715126\pi$
$149$	−15.2717	−1.25110	−0.625552	+	0.780182i	$0.715126\pi$
$150$	−7.08481	−0.578472
$151$	0.795527	0.0647391	0.0323695	−	0.999476i	$-0.489695\pi$
$151$	0.795527	0.0647391	0.0323695	+	0.999476i	$0.489695\pi$
$152$	−52.9230	−4.29262
$153$	10.5329	0.851535
$154$	−3.04402	−0.245294
$155$	−1.15585	−0.0928400
$156$	−32.9091	−2.63484
$157$	14.2562	1.13777	0.568886	−	0.822416i	$-0.307374\pi$
$157$	14.2562	1.13777	0.568886	+	0.822416i	$0.307374\pi$
$158$	20.4264	1.62504
$159$	−31.0369	−2.46138
$160$	16.9845	1.34274
$161$	−6.65282	−0.524315
$162$	−13.9772	−1.09816
$163$	6.39293	0.500733	0.250366	−	0.968151i	$-0.419449\pi$
$163$	6.39293	0.500733	0.250366	+	0.968151i	$0.419449\pi$
$164$	54.2871	4.23911
$165$	−2.98989	−0.232762
$166$	−19.7685	−1.53433
$167$	7.05817	0.546178	0.273089	−	0.961989i	$-0.411955\pi$
$167$	7.05817	0.546178	0.273089	+	0.961989i	$0.411955\pi$
$168$	22.7642	1.75629
$169$	−7.27327	−0.559482
$170$	7.14571	0.548051
$171$	−24.2786	−1.85663
$172$	−55.2583	−4.21341
$173$	8.20768	0.624018	0.312009	−	0.950079i	$-0.398998\pi$
$173$	8.20768	0.624018	0.312009	+	0.950079i	$0.398998\pi$
$174$	−14.0092	−1.06204
$175$	−1.00000	−0.0755929
$176$	14.4512	1.08930
$177$	18.2733	1.37351
$178$	−13.8034	−1.03461
$179$	−22.8550	−1.70826	−0.854130	−	0.520060i	$-0.825910\pi$
$179$	−22.8550	−1.70826	−0.854130	+	0.520060i	$0.825910\pi$
$180$	20.6376	1.53824
$181$	−8.33307	−0.619392	−0.309696	−	0.950836i	$-0.600227\pi$
$181$	−8.33307	−0.619392	−0.309696	+	0.950836i	$0.600227\pi$
$182$	−6.42709	−0.476408
$183$	6.80419	0.502980
$184$	57.4103	4.23235
$185$	−1.00000	−0.0735215
$186$	8.18897	0.600444
$187$	3.01559	0.220521
$188$	40.6751	2.96654
$189$	2.52928	0.183978
$190$	−16.4710	−1.19493
$191$	1.48828	0.107688	0.0538439	−	0.998549i	$-0.482853\pi$
$191$	1.48828	0.107688	0.0538439	+	0.998549i	$0.482853\pi$
$192$	−53.0629	−3.82948
$193$	3.84787	0.276976	0.138488	−	0.990364i	$-0.455776\pi$
$193$	3.84787	0.276976	0.138488	+	0.990364i	$0.455776\pi$
$194$	10.2537	0.736172
$195$	−6.31278	−0.452068
$196$	5.21310	0.372364
$197$	22.2813	1.58748	0.793738	−	0.608260i	$-0.208132\pi$
$197$	22.2813	1.58748	0.793738	+	0.608260i	$0.208132\pi$
$198$	12.0507	0.856406
$199$	2.30318	0.163268	0.0816342	−	0.996662i	$-0.473986\pi$
$199$	2.30318	0.163268	0.0816342	+	0.996662i	$0.473986\pi$
$200$	8.62948	0.610196
$201$	16.4627	1.16119
$202$	−1.01580	−0.0714714
$203$	−1.97736	−0.138784
$204$	−36.5887	−2.56172
$205$	10.4136	0.727317
$206$	26.0630	1.81589
$207$	26.3372	1.83056
$208$	30.5119	2.11562
$209$	−6.95099	−0.480810
$210$	7.08481	0.488898
$211$	−17.4658	−1.20240	−0.601198	−	0.799100i	$-0.705310\pi$
$211$	−17.4658	−1.20240	−0.601198	+	0.799100i	$0.705310\pi$
$212$	61.3347	4.21248
$213$	13.4732	0.923167
$214$	48.0904	3.28739
$215$	−10.5999	−0.722907
$216$	−21.8264	−1.48510
$217$	1.15585	0.0784641
$218$	−29.5538	−2.00164
$219$	31.6322	2.13751
$220$	5.90858	0.398356
$221$	6.36704	0.428294
$222$	7.08481	0.475501
$223$	−22.5861	−1.51248	−0.756239	−	0.654295i	$-0.772965\pi$
$223$	−22.5861	−1.51248	−0.756239	+	0.654295i	$0.772965\pi$
$224$	−16.9845	−1.13482
$225$	3.95881	0.263920
$226$	−50.5871	−3.36501
$227$	−17.4492	−1.15814	−0.579071	−	0.815277i	$-0.696585\pi$
$227$	−17.4492	−1.15814	−0.579071	+	0.815277i	$0.696585\pi$
$228$	84.3379	5.58541
$229$	−0.677338	−0.0447598	−0.0223799	−	0.999750i	$-0.507124\pi$
$229$	−0.677338	−0.0447598	−0.0223799	+	0.999750i	$0.507124\pi$
$230$	17.8676	1.17815
$231$	2.98989	0.196720
$232$	17.0636	1.12028
$233$	11.3982	0.746719	0.373360	−	0.927687i	$-0.378206\pi$
$233$	11.3982	0.746719	0.373360	+	0.927687i	$0.378206\pi$
$234$	25.4436	1.66330
$235$	7.80249	0.508978
$236$	−36.1115	−2.35066
$237$	−20.0631	−1.30324
$238$	−7.14571	−0.463187
$239$	7.61118	0.492326	0.246163	−	0.969228i	$-0.420830\pi$
$239$	7.61118	0.492326	0.246163	+	0.969228i	$0.420830\pi$
$240$	−33.6344	−2.17109
$241$	17.2539	1.11142	0.555710	−	0.831376i	$-0.312446\pi$
$241$	17.2539	1.11142	0.555710	+	0.831376i	$0.312446\pi$
$242$	−26.0928	−1.67731
$243$	21.3165	1.36745
$244$	−13.4464	−0.860815
$245$	1.00000	0.0638877
$246$	−73.7784	−4.70394
$247$	−14.6762	−0.933823
$248$	−9.97438	−0.633373
$249$	19.4169	1.23050
$250$	2.68572	0.169860
$251$	−24.0020	−1.51499	−0.757497	−	0.652838i	$-0.773578\pi$
$251$	−24.0020	−1.51499	−0.757497	+	0.652838i	$0.773578\pi$
$252$	−20.6376	−1.30005
$253$	7.54037	0.474059
$254$	−32.3201	−2.02794
$255$	−7.01862	−0.439523
$256$	13.6312	0.851953
$257$	27.5951	1.72134	0.860668	−	0.509166i	$-0.170046\pi$
$257$	27.5951	1.72134	0.860668	+	0.509166i	$0.170046\pi$
$258$	75.0983	4.67542
$259$	1.00000	0.0621370
$260$	12.4752	0.773682
$261$	7.82800	0.484541
$262$	−1.81818	−0.112327
$263$	8.76498	0.540472	0.270236	−	0.962794i	$-0.412898\pi$
$263$	8.76498	0.540472	0.270236	+	0.962794i	$0.412898\pi$
$264$	−25.8012	−1.58795
$265$	11.7655	0.722749
$266$	16.4710	1.00990
$267$	13.5579	0.829733
$268$	−32.5334	−1.98729
$269$	−24.9951	−1.52398	−0.761989	−	0.647590i	$-0.775777\pi$
$269$	−24.9951	−1.52398	−0.761989	+	0.647590i	$0.775777\pi$
$270$	−6.79295	−0.413406
$271$	21.9919	1.33591	0.667956	−	0.744201i	$-0.267169\pi$
$271$	21.9919	1.33591	0.667956	+	0.744201i	$0.267169\pi$
$272$	33.9235	2.05691
$273$	6.31278	0.382067
$274$	−31.9727	−1.93154
$275$	1.13341	0.0683472
$276$	−91.4889	−5.50699
$277$	20.2087	1.21423	0.607113	−	0.794616i	$-0.292328\pi$
$277$	20.2087	1.21423	0.607113	+	0.794616i	$0.292328\pi$
$278$	−49.9302	−2.99461
$279$	−4.57578	−0.273945
$280$	−8.62948	−0.515710
$281$	−7.52218	−0.448736	−0.224368	−	0.974505i	$-0.572032\pi$
$281$	−7.52218	−0.448736	−0.224368	+	0.974505i	$0.572032\pi$
$282$	−55.2791	−3.29182
$283$	5.02530	0.298723	0.149361	−	0.988783i	$-0.452278\pi$
$283$	5.02530	0.298723	0.149361	+	0.988783i	$0.452278\pi$
$284$	−26.6255	−1.57994
$285$	16.1781	0.958307
$286$	7.28453	0.430743
$287$	−10.4136	−0.614695
$288$	67.2382	3.96205
$289$	−9.92105	−0.583591
$290$	5.31065	0.311852
$291$	−10.0713	−0.590391
$292$	−62.5112	−3.65819
$293$	9.61902	0.561949	0.280975	−	0.959715i	$-0.409342\pi$
$293$	9.61902	0.561949	0.280975	+	0.959715i	$0.409342\pi$
$294$	−7.08481	−0.413195
$295$	−6.92707	−0.403310
$296$	−8.62948	−0.501578
$297$	−2.86672	−0.166344
$298$	−41.0155	−2.37596
$299$	15.9206	0.920711
$300$	−13.7519	−0.793967
$301$	10.5999	0.610968
$302$	2.13656	0.122945
$303$	0.997733	0.0573183
$304$	−78.1944	−4.48476
$305$	−2.57934	−0.147693
$306$	28.2885	1.61714
$307$	−5.85093	−0.333930	−0.166965	−	0.985963i	$-0.553397\pi$
$307$	−5.85093	−0.333930	−0.166965	+	0.985963i	$0.553397\pi$
$308$	−5.90858	−0.336673
$309$	−25.5994	−1.45630
$310$	−3.10429	−0.176312
$311$	22.5592	1.27921	0.639607	−	0.768702i	$-0.279097\pi$
$311$	22.5592	1.27921	0.639607	+	0.768702i	$0.279097\pi$
$312$	−54.4760	−3.08410
$313$	−2.83215	−0.160083	−0.0800413	−	0.996792i	$-0.525505\pi$
$313$	−2.83215	−0.160083	−0.0800413	+	0.996792i	$0.525505\pi$
$314$	38.2883	2.16073
$315$	−3.95881	−0.223053
$316$	39.6485	2.23040
$317$	20.8339	1.17015	0.585073	−	0.810980i	$-0.301066\pi$
$317$	20.8339	1.17015	0.585073	+	0.810980i	$0.301066\pi$
$318$	−83.3563	−4.67439
$319$	2.24116	0.125481
$320$	20.1152	1.12447
$321$	−47.2351	−2.63640
$322$	−17.8676	−0.995723
$323$	−16.3171	−0.907910
$324$	−27.1304	−1.50724
$325$	2.39306	0.132743
$326$	17.1696	0.950937
$327$	29.0282	1.60526
$328$	89.8640	4.96191
$329$	−7.80249	−0.430165
$330$	−8.03000	−0.442037
$331$	12.9477	0.711672	0.355836	−	0.934548i	$-0.384196\pi$
$331$	12.9477	0.711672	0.355836	+	0.934548i	$0.384196\pi$
$332$	−38.3715	−2.10591
$333$	−3.95881	−0.216941
$334$	18.9563	1.03724
$335$	−6.24070	−0.340966
$336$	33.6344	1.83491
$337$	9.54523	0.519962	0.259981	−	0.965614i	$-0.416284\pi$
$337$	9.54523	0.519962	0.259981	+	0.965614i	$0.416284\pi$
$338$	−19.5340	−1.06251
$339$	49.6874	2.69865
$340$	13.8701	0.752213
$341$	−1.31005	−0.0709433
$342$	−65.2056	−3.52591
$343$	−1.00000	−0.0539949
$344$	−91.4716	−4.93182
$345$	−17.5498	−0.944851
$346$	22.0435	1.18507
$347$	−17.8500	−0.958239	−0.479120	−	0.877750i	$-0.659044\pi$
$347$	−17.8500	−0.958239	−0.479120	+	0.877750i	$0.659044\pi$
$348$	−27.1925	−1.45767
$349$	−3.55069	−0.190064	−0.0950320	−	0.995474i	$-0.530295\pi$
$349$	−3.55069	−0.190064	−0.0950320	+	0.995474i	$0.530295\pi$
$350$	−2.68572	−0.143558
$351$	−6.05273	−0.323071
$352$	19.2504	1.02605
$353$	−26.3798	−1.40406	−0.702028	−	0.712150i	$-0.747722\pi$
$353$	−26.3798	−1.40406	−0.702028	+	0.712150i	$0.747722\pi$
$354$	49.0770	2.60841
$355$	−5.10743	−0.271074
$356$	−26.7931	−1.42003
$357$	7.01862	0.371465
$358$	−61.3820	−3.24414
$359$	−28.5075	−1.50457	−0.752285	−	0.658838i	$-0.771048\pi$
$359$	−28.5075	−1.50457	−0.752285	+	0.658838i	$0.771048\pi$
$360$	34.1624	1.80052
$361$	18.6114	0.979546
$362$	−22.3803	−1.17628
$363$	25.6287	1.34516
$364$	−12.4752	−0.653881
$365$	−11.9912	−0.627647
$366$	18.2741	0.955205
$367$	−12.3056	−0.642349	−0.321175	−	0.947020i	$-0.604078\pi$
$367$	−12.3056	−0.642349	−0.321175	+	0.947020i	$0.604078\pi$
$368$	84.8246	4.42179
$369$	41.2254	2.14611
$370$	−2.68572	−0.139624
$371$	−11.7655	−0.610834
$372$	15.8951	0.824124
$373$	−25.6944	−1.33041	−0.665204	−	0.746662i	$-0.731655\pi$
$373$	−25.6944	−1.33041	−0.665204	+	0.746662i	$0.731655\pi$
$374$	8.09902	0.418790
$375$	−2.63795	−0.136223
$376$	67.3314	3.47235
$377$	4.73195	0.243708
$378$	6.79295	0.349392
$379$	31.0662	1.59576	0.797881	−	0.602815i	$-0.205954\pi$
$379$	31.0662	1.59576	0.797881	+	0.602815i	$0.205954\pi$
$380$	−31.9709	−1.64007
$381$	31.7453	1.62636
$382$	3.99709	0.204509
$383$	16.3775	0.836850	0.418425	−	0.908251i	$-0.362582\pi$
$383$	16.3775	0.836850	0.418425	+	0.908251i	$0.362582\pi$
$384$	−52.9036	−2.69973
$385$	−1.13341	−0.0577640
$386$	10.3343	0.526003
$387$	−41.9630	−2.13310
$388$	19.9028	1.01041
$389$	8.68408	0.440300	0.220150	−	0.975466i	$-0.429345\pi$
$389$	8.68408	0.440300	0.220150	+	0.975466i	$0.429345\pi$
$390$	−16.9544	−0.858518
$391$	17.7007	0.895162
$392$	8.62948	0.435855
$393$	1.78584	0.0900836
$394$	59.8413	3.01476
$395$	7.60555	0.382677
$396$	23.3909	1.17544
$397$	21.4876	1.07843	0.539216	−	0.842167i	$-0.318721\pi$
$397$	21.4876	1.07843	0.539216	+	0.842167i	$0.318721\pi$
$398$	6.18571	0.310062
$399$	−16.1781	−0.809917
$400$	12.7502	0.637509
$401$	−11.7463	−0.586582	−0.293291	−	0.956023i	$-0.594751\pi$
$401$	−11.7463	−0.586582	−0.293291	+	0.956023i	$0.594751\pi$
$402$	44.2142	2.20520
$403$	−2.76602	−0.137785
$404$	−1.97171	−0.0980962
$405$	−5.20428	−0.258603
$406$	−5.31065	−0.263563
$407$	−1.13341	−0.0561811
$408$	−60.5670	−2.99851
$409$	21.7221	1.07409	0.537044	−	0.843554i	$-0.319541\pi$
$409$	21.7221	1.07409	0.537044	+	0.843554i	$0.319541\pi$
$410$	27.9680	1.38124
$411$	31.4041	1.54905
$412$	50.5893	2.49236
$413$	6.92707	0.340859
$414$	70.7344	3.47640
$415$	−7.36059	−0.361317
$416$	40.6448	1.99278
$417$	49.0422	2.40160
$418$	−18.6684	−0.913103
$419$	20.9252	1.02226	0.511132	−	0.859502i	$-0.329226\pi$
$419$	20.9252	1.02226	0.511132	+	0.859502i	$0.329226\pi$
$420$	13.7519	0.671025
$421$	28.5789	1.39285	0.696426	−	0.717628i	$-0.254772\pi$
$421$	28.5789	1.39285	0.696426	+	0.717628i	$0.254772\pi$
$422$	−46.9083	−2.28346
$423$	30.8885	1.50185
$424$	101.530	4.93074
$425$	2.66063	0.129059
$426$	36.1852	1.75318
$427$	2.57934	0.124823
$428$	93.3454	4.51202
$429$	−7.15498	−0.345445
$430$	−28.4684	−1.37287
$431$	−34.2084	−1.64776	−0.823879	−	0.566765i	$-0.808195\pi$
$431$	−34.2084	−1.64776	−0.823879	+	0.566765i	$0.808195\pi$
$432$	−32.2488	−1.55157
$433$	−21.2786	−1.02259	−0.511293	−	0.859407i	$-0.670833\pi$
$433$	−21.2786	−1.02259	−0.511293	+	0.859407i	$0.670833\pi$
$434$	3.10429	0.149011
$435$	−5.21620	−0.250097
$436$	−57.3652	−2.74729
$437$	−40.8005	−1.95175
$438$	84.9553	4.05932
$439$	0.167388	0.00798902	0.00399451	−	0.999992i	$-0.498729\pi$
$439$	0.167388	0.00798902	0.00399451	+	0.999992i	$0.498729\pi$
$440$	9.78074	0.466279
$441$	3.95881	0.188515
$442$	17.1001	0.813369
$443$	20.4222	0.970288	0.485144	−	0.874434i	$-0.338767\pi$
$443$	20.4222	0.970288	0.485144	+	0.874434i	$0.338767\pi$
$444$	13.7519	0.652637
$445$	−5.13957	−0.243639
$446$	−60.6600	−2.87233
$447$	40.2860	1.90546
$448$	−20.1152	−0.950352
$449$	4.85292	0.229023	0.114512	−	0.993422i	$-0.463470\pi$
$449$	4.85292	0.229023	0.114512	+	0.993422i	$0.463470\pi$
$450$	10.6322	0.501209
$451$	11.8029	0.555776
$452$	−98.1917	−4.61855
$453$	−2.09856	−0.0985991
$454$	−46.8636	−2.19942
$455$	−2.39306	−0.112188
$456$	139.608	6.53776
$457$	5.07145	0.237233	0.118616	−	0.992940i	$-0.462154\pi$
$457$	5.07145	0.237233	0.118616	+	0.992940i	$0.462154\pi$
$458$	−1.81914	−0.0850029
$459$	−6.72949	−0.314106
$460$	34.6818	1.61705
$461$	12.4230	0.578597	0.289298	−	0.957239i	$-0.406578\pi$
$461$	12.4230	0.578597	0.289298	+	0.957239i	$0.406578\pi$
$462$	8.03000	0.373589
$463$	−22.5378	−1.04742	−0.523711	−	0.851896i	$-0.675453\pi$
$463$	−22.5378	−1.04742	−0.523711	+	0.851896i	$0.675453\pi$
$464$	25.2117	1.17043
$465$	3.04908	0.141398
$466$	30.6123	1.41809
$467$	20.9780	0.970744	0.485372	−	0.874308i	$-0.338684\pi$
$467$	20.9780	0.970744	0.485372	+	0.874308i	$0.338684\pi$
$468$	49.3871	2.28292
$469$	6.24070	0.288169
$470$	20.9553	0.966596
$471$	−37.6073	−1.73285
$472$	−59.7770	−2.75146
$473$	−12.0140	−0.552406
$474$	−53.8839	−2.47497
$475$	−6.13281	−0.281393
$476$	−13.8701	−0.635736
$477$	46.5773	2.13263
$478$	20.4415	0.934972
$479$	35.9008	1.64035	0.820175	−	0.572113i	$-0.193876\pi$
$479$	35.9008	1.64035	0.820175	+	0.572113i	$0.193876\pi$
$480$	−44.8042	−2.04502
$481$	−2.39306	−0.109114
$482$	46.3391	2.11069
$483$	17.5498	0.798545
$484$	−50.6472	−2.30215
$485$	3.81785	0.173360
$486$	57.2502	2.59692
$487$	40.3182	1.82699	0.913496	−	0.406848i	$-0.133372\pi$
$487$	40.3182	1.82699	0.913496	+	0.406848i	$0.133372\pi$
$488$	−22.2584	−1.00759
$489$	−16.8643	−0.762628
$490$	2.68572	0.121328
$491$	13.1017	0.591271	0.295635	−	0.955301i	$-0.404469\pi$
$491$	13.1017	0.591271	0.295635	+	0.955301i	$0.404469\pi$
$492$	−143.207	−6.45627
$493$	5.26103	0.236945
$494$	−39.4161	−1.77342
$495$	4.48695	0.201673
$496$	−14.7373	−0.661724
$497$	5.10743	0.229100
$498$	52.1484	2.33683
$499$	−29.1071	−1.30301	−0.651506	−	0.758644i	$-0.725862\pi$
$499$	−29.1071	−1.30301	−0.651506	+	0.758644i	$0.725862\pi$
$500$	5.21310	0.233137
$501$	−18.6191	−0.831842
$502$	−64.4627	−2.87711
$503$	−8.57030	−0.382131	−0.191065	−	0.981577i	$-0.561194\pi$
$503$	−8.57030	−0.382131	−0.191065	+	0.981577i	$0.561194\pi$
$504$	−34.1624	−1.52172
$505$	−0.378222	−0.0168307
$506$	20.2513	0.900282
$507$	19.1865	0.852104
$508$	−62.7346	−2.78340
$509$	−6.39654	−0.283522	−0.141761	−	0.989901i	$-0.545276\pi$
$509$	−6.39654	−0.283522	−0.141761	+	0.989901i	$0.545276\pi$
$510$	−18.8500	−0.834694
$511$	11.9912	0.530459
$512$	−3.49986	−0.154674
$513$	15.5116	0.684855
$514$	74.1128	3.26898
$515$	9.70427	0.427621
$516$	145.769	6.41712
$517$	8.84342	0.388933
$518$	2.68572	0.118004
$519$	−21.6515	−0.950395
$520$	20.6509	0.905600
$521$	23.9935	1.05117	0.525587	−	0.850740i	$-0.323846\pi$
$521$	23.9935	1.05117	0.525587	+	0.850740i	$0.323846\pi$
$522$	21.0238	0.920187
$523$	−42.9519	−1.87816	−0.939078	−	0.343705i	$-0.888318\pi$
$523$	−42.9519	−1.87816	−0.939078	+	0.343705i	$0.888318\pi$
$524$	−3.52915	−0.154172
$525$	2.63795	0.115130
$526$	23.5403	1.02641
$527$	−3.07529	−0.133962
$528$	−38.1216	−1.65903
$529$	21.2600	0.924346
$530$	31.5988	1.37257
$531$	−27.4229	−1.19005
$532$	31.9709	1.38612
$533$	24.9204	1.07942
$534$	36.4129	1.57574
$535$	17.9059	0.774141
$536$	−53.8540	−2.32614
$537$	60.2903	2.60172
$538$	−67.1298	−2.89417
$539$	1.13341	0.0488195
$540$	−13.1854	−0.567410
$541$	18.4901	0.794950	0.397475	−	0.917613i	$-0.369886\pi$
$541$	18.4901	0.794950	0.397475	+	0.917613i	$0.369886\pi$
$542$	59.0641	2.53702
$543$	21.9823	0.943349
$544$	45.1894	1.93748
$545$	−11.0040	−0.471362
$546$	16.9544	0.725580
$547$	−31.0430	−1.32730	−0.663651	−	0.748042i	$-0.730994\pi$
$547$	−31.0430	−1.32730	−0.663651	+	0.748042i	$0.730994\pi$
$548$	−62.0604	−2.65109
$549$	−10.2111	−0.435800
$550$	3.04402	0.129798
$551$	−12.1268	−0.516619
$552$	−151.446	−6.44596
$553$	−7.60555	−0.323421
$554$	54.2750	2.30593
$555$	2.63795	0.111975
$556$	−96.9165	−4.11018
$557$	−31.1647	−1.32049	−0.660246	−	0.751049i	$-0.729548\pi$
$557$	−31.1647	−1.32049	−0.660246	+	0.751049i	$0.729548\pi$
$558$	−12.2893	−0.520246
$559$	−25.3662	−1.07288
$560$	−12.7502	−0.538793
$561$	−7.95498	−0.335859
$562$	−20.2025	−0.852190
$563$	28.8568	1.21617	0.608084	−	0.793872i	$-0.291938\pi$
$563$	28.8568	1.21617	0.608084	+	0.793872i	$0.291938\pi$
$564$	−107.299	−4.51811
$565$	−18.8356	−0.792419
$566$	13.4965	0.567302
$567$	5.20428	0.218559
$568$	−44.0745	−1.84933
$569$	29.8956	1.25329	0.626644	−	0.779306i	$-0.284428\pi$
$569$	29.8956	1.25329	0.626644	+	0.779306i	$0.284428\pi$
$570$	43.4498	1.81991
$571$	−27.2726	−1.14132	−0.570662	−	0.821185i	$-0.693313\pi$
$571$	−27.2726	−1.14132	−0.570662	+	0.821185i	$0.693313\pi$
$572$	14.1396	0.591206
$573$	−3.92600	−0.164011
$574$	−27.9680	−1.16736
$575$	6.65282	0.277442
$576$	79.6320	3.31800
$577$	−7.90107	−0.328926	−0.164463	−	0.986383i	$-0.552589\pi$
$577$	−7.90107	−0.328926	−0.164463	+	0.986383i	$0.552589\pi$
$578$	−26.6452	−1.10829
$579$	−10.1505	−0.421841
$580$	10.3082	0.428024
$581$	7.36059	0.305369
$582$	−27.0488	−1.12121
$583$	13.3351	0.552285
$584$	−103.478	−4.28194
$585$	9.47366	0.391687
$586$	25.8340	1.06719
$587$	31.7082	1.30874	0.654368	−	0.756176i	$-0.272935\pi$
$587$	31.7082	1.30874	0.654368	+	0.756176i	$0.272935\pi$
$588$	−13.7519	−0.567119
$589$	7.08860	0.292081
$590$	−18.6042	−0.765922
$591$	−58.7770	−2.41776
$592$	−12.7502	−0.524029
$593$	−16.1150	−0.661762	−0.330881	−	0.943672i	$-0.607346\pi$
$593$	−16.1150	−0.661762	−0.330881	+	0.943672i	$0.607346\pi$
$594$	−7.69921	−0.315902
$595$	−2.66063	−0.109075
$596$	−79.6127	−3.26106
$597$	−6.07570	−0.248662
$598$	42.7582	1.74851
$599$	−4.66076	−0.190433	−0.0952167	−	0.995457i	$-0.530354\pi$
$599$	−4.66076	−0.190433	−0.0952167	+	0.995457i	$0.530354\pi$
$600$	−22.7642	−0.929344
$601$	37.1173	1.51405	0.757024	−	0.653388i	$-0.226653\pi$
$601$	37.1173	1.51405	0.757024	+	0.653388i	$0.226653\pi$
$602$	28.4684	1.16028
$603$	−24.7057	−1.00610
$604$	4.14716	0.168745
$605$	−9.71538	−0.394986
$606$	2.67963	0.108853
$607$	−0.0411726	−0.00167114	−0.000835572	−	1.00000i	$-0.500266\pi$
$607$	−0.0411726	−0.00167114	−0.000835572		1.00000i	$0.500266\pi$
$608$	−104.163	−4.22435
$609$	5.21620	0.211371
$610$	−6.92739	−0.280482
$611$	18.6718	0.755381
$612$	54.9091	2.21957
$613$	20.1686	0.814604	0.407302	−	0.913294i	$-0.366470\pi$
$613$	20.1686	0.814604	0.407302	+	0.913294i	$0.366470\pi$
$614$	−15.7140	−0.634164
$615$	−27.4706	−1.10772
$616$	−9.78074	−0.394077
$617$	−15.0055	−0.604098	−0.302049	−	0.953292i	$-0.597671\pi$
$617$	−15.0055	−0.604098	−0.302049	+	0.953292i	$0.597671\pi$
$618$	−68.7529	−2.76565
$619$	−6.29562	−0.253042	−0.126521	−	0.991964i	$-0.540381\pi$
$619$	−6.29562	−0.253042	−0.126521	+	0.991964i	$0.540381\pi$
$620$	−6.02555	−0.241992
$621$	−16.8269	−0.675239
$622$	60.5877	2.42935
$623$	5.13957	0.205912
$624$	−80.4891	−3.22214
$625$	1.00000	0.0400000
$626$	−7.60637	−0.304012
$627$	18.3364	0.732286
$628$	74.3192	2.96566
$629$	−2.66063	−0.106086
$630$	−10.6322	−0.423599
$631$	21.3939	0.851677	0.425839	−	0.904799i	$-0.359979\pi$
$631$	21.3939	0.851677	0.425839	+	0.904799i	$0.359979\pi$
$632$	65.6319	2.61070
$633$	46.0740	1.83128
$634$	55.9539	2.22222
$635$	−12.0340	−0.477557
$636$	−161.798	−6.41571
$637$	2.39306	0.0948165
$638$	6.01914	0.238300
$639$	−20.2193	−0.799865
$640$	20.0548	0.792735
$641$	−20.1107	−0.794326	−0.397163	−	0.917748i	$-0.630005\pi$
$641$	−20.1107	−0.794326	−0.397163	+	0.917748i	$0.630005\pi$
$642$	−126.860	−5.00677
$643$	−48.4990	−1.91261	−0.956307	−	0.292363i	$-0.905558\pi$
$643$	−48.4990	−1.91261	−0.956307	+	0.292363i	$0.905558\pi$
$644$	−34.6818	−1.36665
$645$	27.9621	1.10101
$646$	−43.8233	−1.72420
$647$	35.9296	1.41254	0.706270	−	0.707943i	$-0.250377\pi$
$647$	35.9296	1.41254	0.706270	+	0.707943i	$0.250377\pi$
$648$	−44.9102	−1.76424
$649$	−7.85122	−0.308187
$650$	6.42709	0.252091
$651$	−3.04908	−0.119503
$652$	33.3270	1.30518
$653$	21.9900	0.860534	0.430267	−	0.902702i	$-0.358419\pi$
$653$	21.9900	0.860534	0.430267	+	0.902702i	$0.358419\pi$
$654$	77.9616	3.04854
$655$	−0.676979	−0.0264517
$656$	132.775	5.18400
$657$	−47.4708	−1.85201
$658$	−20.9553	−0.816923
$659$	19.4302	0.756892	0.378446	−	0.925623i	$-0.376459\pi$
$659$	19.4302	0.756892	0.378446	+	0.925623i	$0.376459\pi$
$660$	−15.5866	−0.606706
$661$	−42.2905	−1.64491	−0.822455	−	0.568830i	$-0.807396\pi$
$661$	−42.2905	−1.64491	−0.822455	+	0.568830i	$0.807396\pi$
$662$	34.7740	1.35153
$663$	−16.7960	−0.652301
$664$	−63.5181	−2.46498
$665$	6.13281	0.237820
$666$	−10.6322	−0.411991
$667$	13.1550	0.509365
$668$	36.7949	1.42364
$669$	59.5811	2.30354
$670$	−16.7608	−0.647526
$671$	−2.92345	−0.112859
$672$	44.8042	1.72836
$673$	11.2088	0.432069	0.216035	−	0.976386i	$-0.430688\pi$
$673$	11.2088	0.432069	0.216035	+	0.976386i	$0.430688\pi$
$674$	25.6358	0.987455
$675$	−2.52928	−0.0973522
$676$	−37.9162	−1.45832
$677$	−49.1491	−1.88895	−0.944477	−	0.328577i	$-0.893431\pi$
$677$	−49.1491	−1.88895	−0.944477	+	0.328577i	$0.893431\pi$
$678$	133.447	5.12498
$679$	−3.81785	−0.146516
$680$	22.9598	0.880470
$681$	46.0301	1.76388
$682$	−3.51843	−0.134728
$683$	26.5764	1.01692	0.508458	−	0.861087i	$-0.330216\pi$
$683$	26.5764	1.01692	0.508458	+	0.861087i	$0.330216\pi$
$684$	−126.567	−4.83940
$685$	−11.9047	−0.454855
$686$	−2.68572	−0.102541
$687$	1.78679	0.0681702
$688$	−135.151	−5.15257
$689$	28.1555	1.07264
$690$	−47.1339	−1.79436
$691$	48.2316	1.83482	0.917408	−	0.397947i	$-0.130277\pi$
$691$	48.2316	1.83482	0.917408	+	0.397947i	$0.130277\pi$
$692$	42.7874	1.62653
$693$	−4.48695	−0.170445
$694$	−47.9402	−1.81978
$695$	−18.5910	−0.705196
$696$	−45.0130	−1.70622
$697$	27.7067	1.04947
$698$	−9.53616	−0.360949
$699$	−30.0679	−1.13727
$700$	−5.21310	−0.197037
$701$	29.7452	1.12346	0.561730	−	0.827321i	$-0.310136\pi$
$701$	29.7452	1.12346	0.561730	+	0.827321i	$0.310136\pi$
$702$	−16.2559	−0.613541
$703$	6.13281	0.231303
$704$	22.7987	0.859260
$705$	−20.5826	−0.775186
$706$	−70.8488	−2.66643
$707$	0.378222	0.0142245
$708$	95.2605	3.58011
$709$	−11.3743	−0.427170	−0.213585	−	0.976925i	$-0.568514\pi$
$709$	−11.3743	−0.427170	−0.213585	+	0.976925i	$0.568514\pi$
$710$	−13.7171	−0.514795
$711$	30.1089	1.12917
$712$	−44.3518	−1.66215
$713$	−7.68965	−0.287980
$714$	18.8500	0.705445
$715$	2.71232	0.101435
$716$	−119.145	−4.45266
$717$	−20.0779	−0.749824
$718$	−76.5633	−2.85732
$719$	10.9236	0.407383	0.203692	−	0.979035i	$-0.434706\pi$
$719$	10.9236	0.407383	0.203692	+	0.979035i	$0.434706\pi$
$720$	50.4755	1.88111
$721$	−9.70427	−0.361406
$722$	49.9850	1.86025
$723$	−45.5150	−1.69272
$724$	−43.4411	−1.61448
$725$	1.97736	0.0734374
$726$	68.8316	2.55458
$727$	−24.7288	−0.917140	−0.458570	−	0.888658i	$-0.651638\pi$
$727$	−24.7288	−0.917140	−0.458570	+	0.888658i	$0.651638\pi$
$728$	−20.6509	−0.765372
$729$	−40.6191	−1.50441
$730$	−32.2050	−1.19196
$731$	−28.2024	−1.04310
$732$	35.4709	1.31104
$733$	19.1479	0.707242	0.353621	−	0.935389i	$-0.384950\pi$
$733$	19.1479	0.707242	0.353621	+	0.935389i	$0.384950\pi$
$734$	−33.0495	−1.21988
$735$	−2.63795	−0.0973024
$736$	112.994	4.16503
$737$	−7.07328	−0.260548
$738$	110.720	4.07566
$739$	−44.6732	−1.64333	−0.821664	−	0.569972i	$-0.806954\pi$
$739$	−44.6732	−1.64333	−0.821664	+	0.569972i	$0.806954\pi$
$740$	−5.21310	−0.191637
$741$	38.7151	1.42223
$742$	−31.5988	−1.16003
$743$	−9.81654	−0.360134	−0.180067	−	0.983654i	$-0.557631\pi$
$743$	−9.81654	−0.360134	−0.180067	+	0.983654i	$0.557631\pi$
$744$	26.3120	0.964643
$745$	−15.2717	−0.559511
$746$	−69.0081	−2.52657
$747$	−29.1392	−1.06615
$748$	15.7205	0.574800
$749$	−17.9059	−0.654269
$750$	−7.08481	−0.258701
$751$	−9.94489	−0.362894	−0.181447	−	0.983401i	$-0.558078\pi$
$751$	−9.94489	−0.362894	−0.181447	+	0.983401i	$0.558078\pi$
$752$	99.4831	3.62778
$753$	63.3163	2.30737
$754$	12.7087	0.462823
$755$	0.795527	0.0289522
$756$	13.1854	0.479549
$757$	−9.25447	−0.336360	−0.168180	−	0.985756i	$-0.553789\pi$
$757$	−9.25447	−0.336360	−0.168180	+	0.985756i	$0.553789\pi$
$758$	83.4351	3.03050
$759$	−19.8912	−0.722003
$760$	−52.9230	−1.91972
$761$	17.0295	0.617318	0.308659	−	0.951173i	$-0.400120\pi$
$761$	17.0295	0.617318	0.308659	+	0.951173i	$0.400120\pi$
$762$	85.2589	3.08861
$763$	11.0040	0.398373
$764$	7.75852	0.280693
$765$	10.5329	0.380818
$766$	43.9853	1.58925
$767$	−16.5769	−0.598557
$768$	−35.9586	−1.29754
$769$	−35.9995	−1.29818	−0.649088	−	0.760713i	$-0.724849\pi$
$769$	−35.9995	−1.29818	−0.649088	+	0.760713i	$0.724849\pi$
$770$	−3.04402	−0.109699
$771$	−72.7947	−2.62164
$772$	20.0593	0.721951
$773$	−27.1991	−0.978284	−0.489142	−	0.872204i	$-0.662690\pi$
$773$	−27.1991	−0.978284	−0.489142	+	0.872204i	$0.662690\pi$
$774$	−112.701	−4.05095
$775$	−1.15585	−0.0415193
$776$	32.9461	1.18270
$777$	−2.63795	−0.0946361
$778$	23.3230	0.836171
$779$	−63.8647	−2.28819
$780$	−32.9091	−1.17834
$781$	−5.78882	−0.207140
$782$	47.5391	1.69999
$783$	−5.00132	−0.178732
$784$	12.7502	0.455364
$785$	14.2562	0.508827
$786$	4.79626	0.171077
$787$	−45.8780	−1.63537	−0.817687	−	0.575663i	$-0.804744\pi$
$787$	−45.8780	−1.63537	−0.817687	+	0.575663i	$0.804744\pi$
$788$	116.155	4.13783
$789$	−23.1216	−0.823152
$790$	20.4264	0.726738
$791$	18.8356	0.669716
$792$	38.7201	1.37586
$793$	−6.17252	−0.219193
$794$	57.7097	2.04804
$795$	−31.0369	−1.10076
$796$	12.0067	0.425567
$797$	−41.4841	−1.46944	−0.734721	−	0.678369i	$-0.762687\pi$
$797$	−41.4841	−1.46944	−0.734721	+	0.678369i	$0.762687\pi$
$798$	−43.4498	−1.53811
$799$	20.7595	0.734419
$800$	16.9845	0.600491
$801$	−20.3465	−0.718910
$802$	−31.5473	−1.11397
$803$	−13.5909	−0.479614
$804$	85.8216	3.02669
$805$	−6.65282	−0.234481
$806$	−7.42875	−0.261666
$807$	65.9359	2.32105
$808$	−3.26386	−0.114822
$809$	−15.1944	−0.534205	−0.267102	−	0.963668i	$-0.586066\pi$
$809$	−15.1944	−0.534205	−0.267102	+	0.963668i	$0.586066\pi$
$810$	−13.9772	−0.491110
$811$	15.5885	0.547386	0.273693	−	0.961817i	$-0.411755\pi$
$811$	15.5885	0.547386	0.273693	+	0.961817i	$0.411755\pi$
$812$	−10.3082	−0.361746
$813$	−58.0136	−2.03463
$814$	−3.04402	−0.106693
$815$	6.39293	0.223935
$816$	−89.4886	−3.13273
$817$	65.0072	2.27431
$818$	58.3394	2.03979
$819$	−9.47366	−0.331036
$820$	54.2871	1.89579
$821$	−16.4855	−0.575346	−0.287673	−	0.957729i	$-0.592882\pi$
$821$	−16.4855	−0.575346	−0.287673	+	0.957729i	$0.592882\pi$
$822$	84.3426	2.94178
$823$	37.9133	1.32158	0.660788	−	0.750573i	$-0.270222\pi$
$823$	37.9133	1.32158	0.660788	+	0.750573i	$0.270222\pi$
$824$	83.7428	2.91732
$825$	−2.98989	−0.104094
$826$	18.6042	0.647322
$827$	31.8294	1.10682	0.553408	−	0.832911i	$-0.313327\pi$
$827$	31.8294	1.10682	0.553408	+	0.832911i	$0.313327\pi$
$828$	137.298	4.77145
$829$	−3.75950	−0.130573	−0.0652865	−	0.997867i	$-0.520796\pi$
$829$	−3.75950	−0.130573	−0.0652865	+	0.997867i	$0.520796\pi$
$830$	−19.7685	−0.686175
$831$	−53.3097	−1.84929
$832$	48.1368	1.66884
$833$	2.66063	0.0921853
$834$	131.714	4.56087
$835$	7.05817	0.244258
$836$	−36.2362	−1.25326
$837$	2.92347	0.101050
$838$	56.1994	1.94137
$839$	47.4957	1.63973	0.819866	−	0.572555i	$-0.194048\pi$
$839$	47.4957	1.63973	0.819866	+	0.572555i	$0.194048\pi$
$840$	22.7642	0.785439
$841$	−25.0900	−0.865174
$842$	76.7551	2.64515
$843$	19.8432	0.683435
$844$	−91.0510	−3.13410
$845$	−7.27327	−0.250208
$846$	82.9580	2.85215
$847$	9.71538	0.333824
$848$	150.012	5.15144
$849$	−13.2565	−0.454962
$850$	7.14571	0.245096
$851$	−6.65282	−0.228056
$852$	70.2370	2.40628
$853$	11.4008	0.390355	0.195177	−	0.980768i	$-0.437472\pi$
$853$	11.4008	0.390355	0.195177	+	0.980768i	$0.437472\pi$
$854$	6.92739	0.237050
$855$	−24.2786	−0.830311
$856$	154.519	5.28135
$857$	−48.8854	−1.66989	−0.834946	−	0.550331i	$-0.814501\pi$
$857$	−48.8854	−1.66989	−0.834946	+	0.550331i	$0.814501\pi$
$858$	−19.2163	−0.656032
$859$	26.4508	0.902490	0.451245	−	0.892400i	$-0.350980\pi$
$859$	26.4508	0.902490	0.451245	+	0.892400i	$0.350980\pi$
$860$	−55.2583	−1.88429
$861$	27.4706	0.936196
$862$	−91.8741	−3.12924
$863$	−32.5774	−1.10895	−0.554474	−	0.832201i	$-0.687080\pi$
$863$	−32.5774	−1.10895	−0.554474	+	0.832201i	$0.687080\pi$
$864$	−42.9585	−1.46148
$865$	8.20768	0.279069
$866$	−57.1485	−1.94198
$867$	26.1713	0.888824
$868$	6.02555	0.204521
$869$	8.62021	0.292421
$870$	−14.0092	−0.474958
$871$	−14.9344	−0.506032
$872$	−94.9592	−3.21572
$873$	15.1141	0.511536
$874$	−109.579	−3.70655
$875$	−1.00000	−0.0338062
$876$	164.902	5.57151
$877$	24.7310	0.835106	0.417553	−	0.908652i	$-0.362888\pi$
$877$	24.7310	0.835106	0.417553	+	0.908652i	$0.362888\pi$
$878$	0.449559	0.0151719
$879$	−25.3745	−0.855862
$880$	14.4512	0.487149
$881$	−41.9206	−1.41234	−0.706171	−	0.708042i	$-0.749579\pi$
$881$	−41.9206	−1.41234	−0.706171	+	0.708042i	$0.749579\pi$
$882$	10.6322	0.358006
$883$	−38.3378	−1.29017	−0.645084	−	0.764112i	$-0.723178\pi$
$883$	−38.3378	−1.29017	−0.645084	+	0.764112i	$0.723178\pi$
$884$	33.1920	1.11637
$885$	18.2733	0.614250
$886$	54.8483	1.84267
$887$	−53.2824	−1.78905	−0.894525	−	0.447018i	$-0.852486\pi$
$887$	−53.2824	−1.78905	−0.894525	+	0.447018i	$0.852486\pi$
$888$	22.7642	0.763916
$889$	12.0340	0.403609
$890$	−13.8034	−0.462692
$891$	−5.89858	−0.197610
$892$	−117.744	−3.94235
$893$	−47.8512	−1.60128
$894$	108.197	3.61865
$895$	−22.8550	−0.763957
$896$	−20.0548	−0.669984
$897$	−41.9978	−1.40227
$898$	13.0336	0.434936
$899$	−2.28553	−0.0762268
$900$	20.6376	0.687921
$901$	31.3036	1.04287
$902$	31.6993	1.05547
$903$	−27.9621	−0.930519
$904$	−162.541	−5.40604
$905$	−8.33307	−0.277001
$906$	−5.63616	−0.187249
$907$	16.3153	0.541742	0.270871	−	0.962616i	$-0.412688\pi$
$907$	16.3153	0.541742	0.270871	+	0.962616i	$0.412688\pi$
$908$	−90.9642	−3.01875
$909$	−1.49731	−0.0496626
$910$	−6.42709	−0.213056
$911$	54.2742	1.79818	0.899091	−	0.437761i	$-0.144228\pi$
$911$	54.2742	1.79818	0.899091	+	0.437761i	$0.144228\pi$
$912$	206.273	6.83039
$913$	−8.34258	−0.276099
$914$	13.6205	0.450526
$915$	6.80419	0.224939
$916$	−3.53103	−0.116668
$917$	0.676979	0.0223558
$918$	−18.0735	−0.596515
$919$	11.1583	0.368078	0.184039	−	0.982919i	$-0.441083\pi$
$919$	11.1583	0.368078	0.184039	+	0.982919i	$0.441083\pi$
$920$	57.4103	1.89276
$921$	15.4345	0.508584
$922$	33.3647	1.09881
$923$	−12.2224	−0.402305
$924$	15.5866	0.512760
$925$	−1.00000	−0.0328798
$926$	−60.5304	−1.98915
$927$	38.4173	1.26179
$928$	33.5845	1.10246
$929$	44.6809	1.46593	0.732966	−	0.680265i	$-0.238135\pi$
$929$	44.6809	1.46593	0.732966	+	0.680265i	$0.238135\pi$
$930$	8.18897	0.268527
$931$	−6.13281	−0.200995
$932$	59.4198	1.94636
$933$	−59.5101	−1.94827
$934$	56.3409	1.84353
$935$	3.01559	0.0986202
$936$	81.7527	2.67217
$937$	39.3445	1.28533	0.642664	−	0.766148i	$-0.277829\pi$
$937$	39.3445	1.28533	0.642664	+	0.766148i	$0.277829\pi$
$938$	16.7608	0.547259
$939$	7.47109	0.243810
$940$	40.6751	1.32668
$941$	−54.9858	−1.79249	−0.896243	−	0.443562i	$-0.853714\pi$
$941$	−54.9858	−1.79249	−0.896243	+	0.443562i	$0.853714\pi$
$942$	−101.003	−3.29085
$943$	69.2798	2.25606
$944$	−88.3214	−2.87462
$945$	2.52928	0.0822776
$946$	−32.2664	−1.04907
$947$	24.2351	0.787534	0.393767	−	0.919210i	$-0.371172\pi$
$947$	24.2351	0.787534	0.393767	+	0.919210i	$0.371172\pi$
$948$	−104.591	−3.39695
$949$	−28.6956	−0.931499
$950$	−16.4710	−0.534390
$951$	−54.9588	−1.78216
$952$	−22.9598	−0.744133
$953$	19.7233	0.638901	0.319451	−	0.947603i	$-0.396502\pi$
$953$	19.7233	0.638901	0.319451	+	0.947603i	$0.396502\pi$
$954$	125.094	4.05006
$955$	1.48828	0.0481595
$956$	39.6778	1.28327
$957$	−5.91209	−0.191111
$958$	96.4195	3.11517
$959$	11.9047	0.384423
$960$	−53.0629	−1.71260
$961$	−29.6640	−0.956904
$962$	−6.42709	−0.207218
$963$	70.8861	2.28427
$964$	89.9461	2.89697
$965$	3.84787	0.123867
$966$	47.1339	1.51651
$967$	45.6772	1.46888	0.734440	−	0.678674i	$-0.237445\pi$
$967$	45.6772	1.46888	0.734440	+	0.678674i	$0.237445\pi$
$968$	−83.8387	−2.69468
$969$	43.0439	1.38277
$970$	10.2537	0.329226
$971$	−29.0814	−0.933268	−0.466634	−	0.884451i	$-0.654533\pi$
$971$	−29.0814	−0.933268	−0.466634	+	0.884451i	$0.654533\pi$
$972$	111.125	3.56434
$973$	18.5910	0.595999
$974$	108.283	3.46962
$975$	−6.31278	−0.202171
$976$	−32.8871	−1.05269
$977$	−0.284694	−0.00910818	−0.00455409	−	0.999990i	$-0.501450\pi$
$977$	−0.284694	−0.00910818	−0.00455409	+	0.999990i	$0.501450\pi$
$978$	−45.2927	−1.44830
$979$	−5.82524	−0.186175
$980$	5.21310	0.166526
$981$	−43.5629	−1.39086
$982$	35.1875	1.12288
$983$	−14.1092	−0.450014	−0.225007	−	0.974357i	$-0.572240\pi$
$983$	−14.1092	−0.450014	−0.225007	+	0.974357i	$0.572240\pi$
$984$	−237.057	−7.55710
$985$	22.2813	0.709941
$986$	14.1297	0.449980
$987$	20.5826	0.655152
$988$	−76.5084	−2.43405
$989$	−70.5192	−2.24238
$990$	12.0507	0.382996
$991$	−37.1730	−1.18084	−0.590420	−	0.807096i	$-0.701038\pi$
$991$	−37.1730	−1.18084	−0.590420	+	0.807096i	$0.701038\pi$
$992$	−19.6315	−0.623300
$993$	−34.1555	−1.08389
$994$	13.7171	0.435081
$995$	2.30318	0.0730159
$996$	101.222	3.20735
$997$	−38.2049	−1.20996	−0.604981	−	0.796240i	$-0.706819\pi$
$997$	−38.2049	−1.20996	−0.604981	+	0.796240i	$0.706819\pi$
$998$	−78.1735	−2.47454
$999$	2.52928	0.0800230

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1295.2.a.h.1.11	✓	12
5.4	even	2		6475.2.a.r.1.2		12
7.6	odd	2		9065.2.a.m.1.11		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1295.2.a.h.1.11	✓	12	1.1	even	1	trivial
6475.2.a.r.1.2		12	5.4	even	2
9065.2.a.m.1.11		12	7.6	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1295 = 5 \cdot 7 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1295.a (trivial)

\(f(q)\)	\(=\)	\(q+2.68572 q^{2} -2.63795 q^{3} +5.21310 q^{4} +1.00000 q^{5} -7.08481 q^{6} -1.00000 q^{7} +8.62948 q^{8} +3.95881 q^{9} +2.68572 q^{10} +1.13341 q^{11} -13.7519 q^{12} +2.39306 q^{13} -2.68572 q^{14} -2.63795 q^{15} +12.7502 q^{16} +2.66063 q^{17} +10.6322 q^{18} -6.13281 q^{19} +5.21310 q^{20} +2.63795 q^{21} +3.04402 q^{22} +6.65282 q^{23} -22.7642 q^{24} +1.00000 q^{25} +6.42709 q^{26} -2.52928 q^{27} -5.21310 q^{28} +1.97736 q^{29} -7.08481 q^{30} -1.15585 q^{31} +16.9845 q^{32} -2.98989 q^{33} +7.14571 q^{34} -1.00000 q^{35} +20.6376 q^{36} -1.00000 q^{37} -16.4710 q^{38} -6.31278 q^{39} +8.62948 q^{40} +10.4136 q^{41} +7.08481 q^{42} -10.5999 q^{43} +5.90858 q^{44} +3.95881 q^{45} +17.8676 q^{46} +7.80249 q^{47} -33.6344 q^{48} +1.00000 q^{49} +2.68572 q^{50} -7.01862 q^{51} +12.4752 q^{52} +11.7655 q^{53} -6.79295 q^{54} +1.13341 q^{55} -8.62948 q^{56} +16.1781 q^{57} +5.31065 q^{58} -6.92707 q^{59} -13.7519 q^{60} -2.57934 q^{61} -3.10429 q^{62} -3.95881 q^{63} +20.1152 q^{64} +2.39306 q^{65} -8.03000 q^{66} -6.24070 q^{67} +13.8701 q^{68} -17.5498 q^{69} -2.68572 q^{70} -5.10743 q^{71} +34.1624 q^{72} -11.9912 q^{73} -2.68572 q^{74} -2.63795 q^{75} -31.9709 q^{76} -1.13341 q^{77} -16.9544 q^{78} +7.60555 q^{79} +12.7502 q^{80} -5.20428 q^{81} +27.9680 q^{82} -7.36059 q^{83} +13.7519 q^{84} +2.66063 q^{85} -28.4684 q^{86} -5.21620 q^{87} +9.78074 q^{88} -5.13957 q^{89} +10.6322 q^{90} -2.39306 q^{91} +34.6818 q^{92} +3.04908 q^{93} +20.9553 q^{94} -6.13281 q^{95} -44.8042 q^{96} +3.81785 q^{97} +2.68572 q^{98} +4.48695 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 5 q^{2} + 4 q^{3} + 15 q^{4} + 12 q^{5} + 6 q^{6} - 12 q^{7} + 21 q^{8} + 18 q^{9} + 5 q^{10} - 4 q^{11} + 8 q^{12} + 6 q^{13} - 5 q^{14} + 4 q^{15} + 21 q^{16} + 20 q^{17} + 14 q^{18} - 4 q^{19}+ \cdots - 24 q^{99}+O(q^{100}) \) 12 * q + 5 * q^2 + 4 * q^3 + 15 * q^4 + 12 * q^5 + 6 * q^6 - 12 * q^7 + 21 * q^8 + 18 * q^9 + 5 * q^10 - 4 * q^11 + 8 * q^12 + 6 * q^13 - 5 * q^14 + 4 * q^15 + 21 * q^16 + 20 * q^17 + 14 * q^18 - 4 * q^19 + 15 * q^20 - 4 * q^21 + 2 * q^22 + 20 * q^23 + 4 * q^24 + 12 * q^25 + 6 * q^26 + 10 * q^27 - 15 * q^28 - 12 * q^29 + 6 * q^30 + 47 * q^32 + 20 * q^33 - 28 * q^34 - 12 * q^35 + 39 * q^36 - 12 * q^37 + 8 * q^38 + 21 * q^40 + 24 * q^41 - 6 * q^42 + 14 * q^43 - 16 * q^44 + 18 * q^45 + 20 * q^46 + 18 * q^47 - 19 * q^48 + 12 * q^49 + 5 * q^50 - 20 * q^51 + 22 * q^52 + 36 * q^53 - 46 * q^54 - 4 * q^55 - 21 * q^56 + 36 * q^57 + 28 * q^58 + 4 * q^59 + 8 * q^60 - 39 * q^62 - 18 * q^63 + 9 * q^64 + 6 * q^65 - 21 * q^66 + 6 * q^67 - 6 * q^68 - 6 * q^69 - 5 * q^70 - 12 * q^71 + 17 * q^72 + 32 * q^73 - 5 * q^74 + 4 * q^75 - 13 * q^76 + 4 * q^77 + 74 * q^78 + 14 * q^79 + 21 * q^80 - 16 * q^81 - 26 * q^82 - 18 * q^83 - 8 * q^84 + 20 * q^85 - 36 * q^86 - 18 * q^87 + 27 * q^88 + 14 * q^90 - 6 * q^91 + 39 * q^92 + 52 * q^93 + 38 * q^94 - 4 * q^95 - 53 * q^96 + 38 * q^97 + 5 * q^98 - 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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