LMFDB - Embedded newform 525.4.d.m.274.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,4,Mod(274,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("525.274");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	525.d (of order $2$, degree $1$, not minimal)

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:	no
Analytic conductor:	$30.9760027530$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{17})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 9x^{2} + 16 $ x^4 + 9*x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			274.2
Root			$-1.56155i$ of defining polynomial
Character	$\chi$	$=$	525.274
Dual form			525.4.d.m.274.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.561553i q^{2} +3.00000i q^{3} +7.68466 q^{4} +1.68466 q^{6} -7.00000i q^{7} -8.80776i q^{8} -9.00000 q^{9} +O(q^{10})$	\(q-0.561553i q^{2} +3.00000i q^{3} +7.68466 q^{4} +1.68466 q^{6} -7.00000i q^{7} -8.80776i q^{8} -9.00000 q^{9} -25.8078 q^{11} +23.0540i q^{12} +15.5464i q^{13} -3.93087 q^{14} +56.5312 q^{16} -95.1619i q^{17} +5.05398i q^{18} +143.447 q^{19} +21.0000 q^{21} +14.4924i q^{22} -77.5227i q^{23} +26.4233 q^{24} +8.73012 q^{26} -27.0000i q^{27} -53.7926i q^{28} +204.170 q^{29} -40.6998 q^{31} -102.207i q^{32} -77.4233i q^{33} -53.4384 q^{34} -69.1619 q^{36} +95.6695i q^{37} -80.5530i q^{38} -46.6392 q^{39} +24.7301 q^{41} -11.7926i q^{42} -282.430i q^{43} -198.324 q^{44} -43.5331 q^{46} +257.417i q^{47} +169.594i q^{48} -49.0000 q^{49} +285.486 q^{51} +119.469i q^{52} -257.978i q^{53} -15.1619 q^{54} -61.6543 q^{56} +430.341i q^{57} -114.652i q^{58} +651.365 q^{59} +451.304 q^{61} +22.8551i q^{62} +63.0000i q^{63} +394.855 q^{64} -43.4773 q^{66} +832.071i q^{67} -731.287i q^{68} +232.568 q^{69} -174.965 q^{71} +79.2699i q^{72} +47.4166i q^{73} +53.7235 q^{74} +1102.34 q^{76} +180.654i q^{77} +26.1904i q^{78} +1.16006 q^{79} +81.0000 q^{81} -13.8873i q^{82} -1494.03i q^{83} +161.378 q^{84} -158.599 q^{86} +612.511i q^{87} +227.309i q^{88} -1309.13 q^{89} +108.825 q^{91} -595.736i q^{92} -122.099i q^{93} +144.553 q^{94} +306.622 q^{96} -1365.33i q^{97} +27.5161i q^{98} +232.270 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 6 q^{4} - 18 q^{6} - 36 q^{9}+O(q^{10}) $ 4 * q + 6 * q^4 - 18 * q^6 - 36 * q^9	$ 4 q + 6 q^{4} - 18 q^{6} - 36 q^{9} - 62 q^{11} + 42 q^{14} - 46 q^{16} + 112 q^{19} + 84 q^{21} - 18 q^{24} + 406 q^{26} + 124 q^{29} - 270 q^{31} - 222 q^{34} - 54 q^{36} + 234 q^{39} + 470 q^{41} - 348 q^{44} + 1170 q^{46} - 196 q^{49} + 474 q^{51} + 162 q^{54} + 42 q^{56} + 882 q^{59} - 446 q^{61} + 862 q^{64} + 24 q^{66} + 1524 q^{69} + 1238 q^{71} - 16 q^{74} + 3024 q^{76} + 854 q^{79} + 324 q^{81} + 126 q^{84} + 3398 q^{86} - 932 q^{89} - 546 q^{91} + 1040 q^{94} + 1746 q^{96} + 558 q^{99}+O(q^{100}) $ 4 * q + 6 * q^4 - 18 * q^6 - 36 * q^9 - 62 * q^11 + 42 * q^14 - 46 * q^16 + 112 * q^19 + 84 * q^21 - 18 * q^24 + 406 * q^26 + 124 * q^29 - 270 * q^31 - 222 * q^34 - 54 * q^36 + 234 * q^39 + 470 * q^41 - 348 * q^44 + 1170 * q^46 - 196 * q^49 + 474 * q^51 + 162 * q^54 + 42 * q^56 + 882 * q^59 - 446 * q^61 + 862 * q^64 + 24 * q^66 + 1524 * q^69 + 1238 * q^71 - 16 * q^74 + 3024 * q^76 + 854 * q^79 + 324 * q^81 + 126 * q^84 + 3398 * q^86 - 932 * q^89 - 546 * q^91 + 1040 * q^94 + 1746 * q^96 + 558 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$-1$	$1$	$1$

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 $

$2$	− 0.561553i	− 0.198539i	−0.995061	−	0.0992695i	$-0.968349\pi$
$2$	− 0.561553i	− 0.198539i	0.995061	−	0.0992695i	$-0.0316506\pi$
$3$	3.00000i	0.577350i
$3$	3.00000i	0.577350i
$4$	7.68466	0.960582
$5$	0	0
$5$	0	0
$6$	1.68466	0.114626
$7$	− 7.00000i	− 0.377964i
$7$	− 7.00000i	− 0.377964i
$8$	− 8.80776i	− 0.389252i
$9$	−9.00000	−0.333333
$10$	0	0
$11$	−25.8078	−0.707394	−0.353697	−	0.935360i	$-0.615076\pi$
$11$	−25.8078	−0.707394	−0.353697	+	0.935360i	$0.615076\pi$
$12$	23.0540i	0.554592i
$13$	15.5464i	0.331677i	0.986153	+	0.165838i	$0.0530330\pi$
$13$	15.5464i	0.331677i	−0.986153	+	0.165838i	$0.946967\pi$
$14$	−3.93087	−0.0750407
$15$	0	0
$16$	56.5312	0.883301
$17$	− 95.1619i	− 1.35766i	−0.734297	−	0.678828i	$-0.762488\pi$
$17$	− 95.1619i	− 1.35766i	0.734297	−	0.678828i	$-0.237512\pi$
$18$	5.05398i	0.0661796i
$19$	143.447	1.73205	0.866026	−	0.499999i	$-0.166666\pi$
$19$	143.447	1.73205	0.866026	+	0.499999i	$0.166666\pi$
$20$	0	0
$21$	21.0000	0.218218
$22$	14.4924i	0.140445i
$23$	− 77.5227i	− 0.702809i	−0.936224	−	0.351405i	$-0.885704\pi$
$23$	− 77.5227i	− 0.702809i	0.936224	−	0.351405i	$-0.114296\pi$
$24$	26.4233	0.224735
$25$	0	0
$26$	8.73012	0.0658507
$27$	− 27.0000i	− 0.192450i
$28$	− 53.7926i	− 0.363066i
$29$	204.170	1.30736	0.653681	−	0.756770i	$-0.273224\pi$
$29$	204.170	1.30736	0.653681	+	0.756770i	$0.273224\pi$
$30$	0	0
$31$	−40.6998	−0.235803	−0.117902	−	0.993025i	$-0.537617\pi$
$31$	−40.6998	−0.235803	−0.117902	+	0.993025i	$0.537617\pi$
$32$	− 102.207i	− 0.564621i
$33$	− 77.4233i	− 0.408414i
$34$	−53.4384	−0.269548
$35$	0	0
$36$	−69.1619	−0.320194
$37$	95.6695i	0.425080i	0.977152	+	0.212540i	$0.0681736\pi$
$37$	95.6695i	0.425080i	−0.977152	+	0.212540i	$0.931826\pi$
$38$	− 80.5530i	− 0.343880i
$39$	−46.6392	−0.191494
$40$	0	0
$41$	24.7301	0.0941999	0.0471000	−	0.998890i	$-0.485002\pi$
$41$	24.7301	0.0941999	0.0471000	+	0.998890i	$0.485002\pi$
$42$	− 11.7926i	− 0.0433247i
$43$	− 282.430i	− 1.00163i	−0.865554	−	0.500816i	$-0.833033\pi$
$43$	− 282.430i	− 1.00163i	0.865554	−	0.500816i	$-0.166967\pi$
$44$	−198.324	−0.679510
$45$	0	0
$46$	−43.5331	−0.139535
$47$	257.417i	0.798895i	0.916756	+	0.399448i	$0.130798\pi$
$47$	257.417i	0.798895i	−0.916756	+	0.399448i	$0.869202\pi$
$48$	169.594i	0.509974i
$49$	−49.0000	−0.142857
$50$	0	0
$51$	285.486	0.783843
$52$	119.469i	0.318603i
$53$	− 257.978i	− 0.668604i	−0.942466	−	0.334302i	$-0.891499\pi$
$53$	− 257.978i	− 0.668604i	0.942466	−	0.334302i	$-0.108501\pi$
$54$	−15.1619	−0.0382088
$55$	0	0
$56$	−61.6543	−0.147123
$57$	430.341i	1.00000i
$58$	− 114.652i	− 0.259562i
$59$	651.365	1.43730	0.718648	−	0.695374i	$-0.244761\pi$
$59$	651.365	1.43730	0.718648	+	0.695374i	$0.244761\pi$
$60$	0	0
$61$	451.304	0.947271	0.473636	−	0.880721i	$-0.342941\pi$
$61$	451.304	0.947271	0.473636	+	0.880721i	$0.342941\pi$
$62$	22.8551i	0.0468161i
$63$	63.0000i	0.125988i
$64$	394.855	0.771201
$65$	0	0
$66$	−43.4773	−0.0810861
$67$	832.071i	1.51722i	0.651546	+	0.758609i	$0.274121\pi$
$67$	832.071i	1.51722i	−0.651546	+	0.758609i	$0.725879\pi$
$68$	− 731.287i	− 1.30414i
$69$	232.568	0.405767
$70$	0	0
$71$	−174.965	−0.292458	−0.146229	−	0.989251i	$-0.546714\pi$
$71$	−174.965	−0.292458	−0.146229	+	0.989251i	$0.546714\pi$
$72$	79.2699i	0.129751i
$73$	47.4166i	0.0760233i	0.999277	+	0.0380116i	$0.0121024\pi$
$73$	47.4166i	0.0760233i	−0.999277	+	0.0380116i	$0.987898\pi$
$74$	53.7235	0.0843950
$75$	0	0
$76$	1102.34	1.66378
$77$	180.654i	0.267370i
$78$	26.1904i	0.0380189i
$79$	1.16006	0.00165211	0.000826057	−	1.00000i	$-0.499737\pi$
$79$	1.16006	0.00165211	0.000826057		1.00000i	$0.499737\pi$
$80$	0	0
$81$	81.0000	0.111111
$82$	− 13.8873i	− 0.0187023i
$83$	− 1494.03i	− 1.97580i	−0.155107	−	0.987898i	$-0.549572\pi$
$83$	− 1494.03i	− 1.97580i	0.155107	−	0.987898i	$-0.450428\pi$
$84$	161.378	0.209616
$85$	0	0
$86$	−158.599	−0.198863
$87$	612.511i	0.754806i
$88$	227.309i	0.275354i
$89$	−1309.13	−1.55919	−0.779593	−	0.626286i	$-0.784574\pi$
$89$	−1309.13	−1.55919	−0.779593	+	0.626286i	$0.784574\pi$
$90$	0	0
$91$	108.825	0.125362
$92$	− 595.736i	− 0.675106i
$93$	− 122.099i	− 0.136141i
$94$	144.553	0.158612
$95$	0	0
$96$	306.622	0.325984
$97$	− 1365.33i	− 1.42916i	−0.699553	−	0.714580i	$-0.746618\pi$
$97$	− 1365.33i	− 1.42916i	0.699553	−	0.714580i	$-0.253382\pi$
$98$	27.5161i	0.0283627i
$99$	232.270	0.235798
$100$	0	0
$101$	1155.99	1.13887	0.569434	−	0.822037i	$-0.307162\pi$
$101$	1155.99	1.13887	0.569434	+	0.822037i	$0.307162\pi$
$102$	− 160.315i	− 0.155623i
$103$	78.2074i	0.0748156i	0.999300	+	0.0374078i	$0.0119100\pi$
$103$	78.2074i	0.0748156i	−0.999300	+	0.0374078i	$0.988090\pi$
$104$	136.929	0.129106
$105$	0	0
$106$	−144.868	−0.132744
$107$	− 94.0814i	− 0.0850018i	−0.999096	−	0.0425009i	$-0.986467\pi$
$107$	− 94.0814i	− 0.0850018i	0.999096	−	0.0425009i	$-0.0135325\pi$
$108$	− 207.486i	− 0.184864i
$109$	2128.25	1.87018	0.935088	−	0.354417i	$-0.115321\pi$
$109$	2128.25	1.87018	0.935088	+	0.354417i	$0.115321\pi$
$110$	0	0
$111$	−287.009	−0.245420
$112$	− 395.719i	− 0.333856i
$113$	596.493i	0.496578i	0.968686	+	0.248289i	$0.0798683\pi$
$113$	596.493i	0.496578i	−0.968686	+	0.248289i	$0.920132\pi$
$114$	241.659	0.198539
$115$	0	0
$116$	1568.98	1.25583
$117$	− 139.918i	− 0.110559i
$118$	− 365.776i	− 0.285359i
$119$	−666.133	−0.513146
$120$	0	0
$121$	−664.959	−0.499594
$122$	− 253.431i	− 0.188070i
$123$	74.1904i	0.0543863i
$124$	−312.764	−0.226508
$125$	0	0
$126$	35.3778	0.0250136
$127$	2088.21i	1.45904i	0.683957	+	0.729522i	$0.260257\pi$
$127$	2088.21i	1.45904i	−0.683957	+	0.729522i	$0.739743\pi$
$128$	− 1039.39i	− 0.717735i
$129$	847.290	0.578292
$130$	0	0
$131$	416.142	0.277546	0.138773	−	0.990324i	$-0.455684\pi$
$131$	416.142	0.277546	0.138773	+	0.990324i	$0.455684\pi$
$132$	− 594.972i	− 0.392315i
$133$	− 1004.13i	− 0.654654i
$134$	467.252	0.301227
$135$	0	0
$136$	−838.164	−0.528470
$137$	619.252i	0.386177i	0.981181	+	0.193089i	$0.0618505\pi$
$137$	619.252i	0.386177i	−0.981181	+	0.193089i	$0.938150\pi$
$138$	− 130.599i	− 0.0805605i
$139$	266.994	0.162922	0.0814610	−	0.996677i	$-0.474041\pi$
$139$	266.994	0.162922	0.0814610	+	0.996677i	$0.474041\pi$
$140$	0	0
$141$	−772.250	−0.461242
$142$	98.2520i	0.0580643i
$143$	− 401.218i	− 0.234626i
$144$	−508.781	−0.294434
$145$	0	0
$146$	26.6270	0.0150936
$147$	− 147.000i	− 0.0824786i
$148$	735.187i	0.408325i
$149$	−2551.80	−1.40303	−0.701515	−	0.712655i	$-0.747493\pi$
$149$	−2551.80	−1.40303	−0.701515	+	0.712655i	$0.747493\pi$
$150$	0	0
$151$	1117.38	0.602195	0.301097	−	0.953593i	$-0.402647\pi$
$151$	1117.38	0.602195	0.301097	+	0.953593i	$0.402647\pi$
$152$	− 1263.45i	− 0.674204i
$153$	856.457i	0.452552i
$154$	101.447	0.0530833
$155$	0	0
$156$	−358.406	−0.183945
$157$	− 456.104i	− 0.231854i	−0.993258	−	0.115927i	$-0.963016\pi$
$157$	− 456.104i	− 0.231854i	0.993258	−	0.115927i	$-0.0369839\pi$
$158$	− 0.651435i	0 0.000328009i
$159$	773.935	0.386019
$160$	0	0
$161$	−542.659	−0.265637
$162$	− 45.4858i	− 0.0220599i
$163$	105.490i	0.0506907i	0.999679	+	0.0253453i	$0.00806853\pi$
$163$	105.490i	0.0506907i	−0.999679	+	0.0253453i	$0.991931\pi$
$164$	190.043	0.0904868
$165$	0	0
$166$	−838.976	−0.392272
$167$	− 2482.54i	− 1.15033i	−0.818038	−	0.575164i	$-0.804938\pi$
$167$	− 2482.54i	− 1.15033i	0.818038	−	0.575164i	$-0.195062\pi$
$168$	− 184.963i	− 0.0849417i
$169$	1955.31	0.889991
$170$	0	0
$171$	−1291.02	−0.577351
$172$	− 2170.38i	− 0.962150i
$173$	− 516.708i	− 0.227079i	−0.993534	−	0.113539i	$-0.963781\pi$
$173$	− 516.708i	− 0.227079i	0.993534	−	0.113539i	$-0.0362188\pi$
$174$	343.957	0.149858
$175$	0	0
$176$	−1458.94	−0.624842
$177$	1954.09i	0.829823i
$178$	735.146i	0.309559i
$179$	−3847.77	−1.60668	−0.803341	−	0.595519i	$-0.796946\pi$
$179$	−3847.77	−1.60668	−0.803341	+	0.595519i	$0.796946\pi$
$180$	0	0
$181$	−3026.41	−1.24282	−0.621411	−	0.783484i	$-0.713440\pi$
$181$	−3026.41	−1.24282	−0.621411	+	0.783484i	$0.713440\pi$
$182$	− 61.1109i	− 0.0248892i
$183$	1353.91i	0.546907i
$184$	−682.802	−0.273570
$185$	0	0
$186$	−68.5653	−0.0270293
$187$	2455.92i	0.960398i
$188$	1978.16i	0.767405i
$189$	−189.000	−0.0727393
$190$	0	0
$191$	1271.09	0.481532	0.240766	−	0.970583i	$-0.422601\pi$
$191$	1271.09	0.481532	0.240766	+	0.970583i	$0.422601\pi$
$192$	1184.57i	0.445253i
$193$	1896.09i	0.707170i	0.935402	+	0.353585i	$0.115037\pi$
$193$	1896.09i	0.707170i	−0.935402	+	0.353585i	$0.884963\pi$
$194$	−766.707	−0.283744
$195$	0	0
$196$	−376.548	−0.137226
$197$	4067.89i	1.47119i	0.677419	+	0.735597i	$0.263098\pi$
$197$	4067.89i	1.47119i	−0.677419	+	0.735597i	$0.736902\pi$
$198$	− 130.432i	− 0.0468151i
$199$	−78.1366	−0.0278340	−0.0139170	−	0.999903i	$-0.504430\pi$
$199$	−78.1366	−0.0278340	−0.0139170	+	0.999903i	$0.504430\pi$
$200$	0	0
$201$	−2496.21	−0.875967
$202$	− 649.152i	− 0.226110i
$203$	− 1429.19i	− 0.494136i
$204$	2193.86	0.752946
$205$	0	0
$206$	43.9176	0.0148538
$207$	697.705i	0.234270i
$208$	878.857i	0.292970i
$209$	−3702.05	−1.22524
$210$	0	0
$211$	−1293.02	−0.421872	−0.210936	−	0.977500i	$-0.567651\pi$
$211$	−1293.02	−0.421872	−0.210936	+	0.977500i	$0.567651\pi$
$212$	− 1982.47i	− 0.642250i
$213$	− 524.895i	− 0.168851i
$214$	−52.8317	−0.0168762
$215$	0	0
$216$	−237.810	−0.0749116
$217$	284.899i	0.0891253i
$218$	− 1195.12i	− 0.371303i
$219$	−142.250	−0.0438921
$220$	0	0
$221$	1479.43	0.450303
$222$	161.170i	0.0487255i
$223$	1786.65i	0.536515i	0.963347	+	0.268257i	$0.0864478\pi$
$223$	1786.65i	0.536515i	−0.963347	+	0.268257i	$0.913552\pi$
$224$	−715.452	−0.213407
$225$	0	0
$226$	334.962	0.0985901
$227$	− 4242.02i	− 1.24032i	−0.784475	−	0.620161i	$-0.787067\pi$
$227$	− 4242.02i	− 1.24032i	0.784475	−	0.620161i	$-0.212933\pi$
$228$	3307.02i	0.960583i
$229$	−3403.36	−0.982096	−0.491048	−	0.871132i	$-0.663386\pi$
$229$	−3403.36	−0.982096	−0.491048	+	0.871132i	$0.663386\pi$
$230$	0	0
$231$	−541.963	−0.154366
$232$	− 1798.29i	− 0.508893i
$233$	3904.09i	1.09771i	0.835919	+	0.548853i	$0.184935\pi$
$233$	3904.09i	1.09771i	−0.835919	+	0.548853i	$0.815065\pi$
$234$	−78.5711	−0.0219502
$235$	0	0
$236$	5005.51	1.38064
$237$	3.48018i	0 0.000953848i
$238$	374.069i	0.101879i
$239$	−6667.83	−1.80463	−0.902314	−	0.431079i	$-0.858133\pi$
$239$	−6667.83	−1.80463	−0.902314	+	0.431079i	$0.858133\pi$
$240$	0	0
$241$	−6003.99	−1.60478	−0.802388	−	0.596803i	$-0.796437\pi$
$241$	−6003.99	−1.60478	−0.802388	+	0.596803i	$0.796437\pi$
$242$	373.410i	0.0991888i
$243$	243.000i	0.0641500i
$244$	3468.12	0.909932
$245$	0	0
$246$	41.6618	0.0107978
$247$	2230.08i	0.574481i
$248$	358.474i	0.0917869i
$249$	4482.09	1.14073
$250$	0	0
$251$	728.467	0.183189	0.0915945	−	0.995796i	$-0.470804\pi$
$251$	728.467	0.183189	0.0915945	+	0.995796i	$0.470804\pi$
$252$	484.133i	0.121022i
$253$	2000.69i	0.497163i
$254$	1172.64	0.289677
$255$	0	0
$256$	2575.17	0.628703
$257$	− 1479.86i	− 0.359187i	−0.983741	−	0.179593i	$-0.942522\pi$
$257$	− 1479.86i	− 0.359187i	0.983741	−	0.179593i	$-0.0574782\pi$
$258$	− 475.798i	− 0.114814i
$259$	669.687	0.160665
$260$	0	0
$261$	−1837.53	−0.435787
$262$	− 233.686i	− 0.0551036i
$263$	6367.31i	1.49287i	0.665458	+	0.746435i	$0.268236\pi$
$263$	6367.31i	1.49287i	−0.665458	+	0.746435i	$0.731764\pi$
$264$	−681.926	−0.158976
$265$	0	0
$266$	−563.871	−0.129974
$267$	− 3927.39i	− 0.900197i
$268$	6394.18i	1.45741i
$269$	−1787.18	−0.405079	−0.202539	−	0.979274i	$-0.564919\pi$
$269$	−1787.18	−0.405079	−0.202539	+	0.979274i	$0.564919\pi$
$270$	0	0
$271$	3907.65	0.875915	0.437957	−	0.898996i	$-0.355702\pi$
$271$	3907.65	0.875915	0.437957	+	0.898996i	$0.355702\pi$
$272$	− 5379.62i	− 1.19922i
$273$	326.474i	0.0723778i
$274$	347.743	0.0766712
$275$	0	0
$276$	1787.21	0.389773
$277$	3978.33i	0.862942i	0.902127	+	0.431471i	$0.142005\pi$
$277$	3978.33i	0.862942i	−0.902127	+	0.431471i	$0.857995\pi$
$278$	− 149.931i	− 0.0323464i
$279$	366.298	0.0786011
$280$	0	0
$281$	−6488.04	−1.37738	−0.688690	−	0.725055i	$-0.741814\pi$
$281$	−6488.04	−1.37738	−0.688690	+	0.725055i	$0.741814\pi$
$282$	433.659i	0.0915746i
$283$	164.336i	0.0345185i	0.999851	+	0.0172592i	$0.00549406\pi$
$283$	164.336i	0.0345185i	−0.999851	+	0.0172592i	$0.994506\pi$
$284$	−1344.55	−0.280930
$285$	0	0
$286$	−225.305	−0.0465824
$287$	− 173.111i	− 0.0356042i
$288$	919.867i	0.188207i
$289$	−4142.79	−0.843231
$290$	0	0
$291$	4096.00	0.825126
$292$	364.381i	0.0730266i
$293$	− 5004.57i	− 0.997851i	−0.866645	−	0.498925i	$-0.833728\pi$
$293$	− 5004.57i	− 0.997851i	0.866645	−	0.498925i	$-0.166272\pi$
$294$	−82.5483	−0.0163752
$295$	0	0
$296$	842.634	0.165463
$297$	696.810i	0.136138i
$298$	1432.97i	0.278556i
$299$	1205.20	0.233105
$300$	0	0
$301$	−1977.01	−0.378581
$302$	− 627.470i	− 0.119559i
$303$	3467.98i	0.657526i
$304$	8109.23	1.52992
$305$	0	0
$306$	480.946	0.0898492
$307$	− 190.167i	− 0.0353531i	−0.999844	−	0.0176765i	$-0.994373\pi$
$307$	− 190.167i	− 0.0353531i	0.999844	−	0.0176765i	$-0.00562691\pi$
$308$	1388.27i	0.256831i
$309$	−234.622	−0.0431948
$310$	0	0
$311$	−1182.57	−0.215619	−0.107810	−	0.994172i	$-0.534384\pi$
$311$	−1182.57	−0.215619	−0.107810	+	0.994172i	$0.534384\pi$
$312$	410.787i	0.0745392i
$313$	4659.05i	0.841358i	0.907209	+	0.420679i	$0.138208\pi$
$313$	4659.05i	0.841358i	−0.907209	+	0.420679i	$0.861792\pi$
$314$	−256.127	−0.0460320
$315$	0	0
$316$	8.91467	0.00158699
$317$	− 3694.55i	− 0.654595i	−0.944921	−	0.327297i	$-0.893862\pi$
$317$	− 3694.55i	− 0.654595i	0.944921	−	0.327297i	$-0.106138\pi$
$318$	− 434.605i	− 0.0766398i
$319$	−5269.18	−0.924820
$320$	0	0
$321$	282.244	0.0490758
$322$	304.732i	0.0527392i
$323$	− 13650.7i	− 2.35153i
$324$	622.457	0.106731
$325$	0	0
$326$	59.2379	0.0100641
$327$	6384.74i	1.07975i
$328$	− 217.817i	− 0.0366675i
$329$	1801.92	0.301954
$330$	0	0
$331$	−8632.79	−1.43354	−0.716769	−	0.697310i	$-0.754380\pi$
$331$	−8632.79	−1.43354	−0.716769	+	0.697310i	$0.754380\pi$
$332$	− 11481.1i	− 1.89791i
$333$	− 861.026i	− 0.141693i
$334$	−1394.08	−0.228385
$335$	0	0
$336$	1187.16	0.192752
$337$	− 8136.61i	− 1.31522i	−0.753358	−	0.657610i	$-0.771567\pi$
$337$	− 8136.61i	− 1.31522i	0.753358	−	0.657610i	$-0.228433\pi$
$338$	− 1098.01i	− 0.176698i
$339$	−1789.48	−0.286700
$340$	0	0
$341$	1050.37	0.166806
$342$	724.977i	0.114627i
$343$	343.000i	0.0539949i
$344$	−2487.58	−0.389887
$345$	0	0
$346$	−290.159	−0.0450839
$347$	8646.33i	1.33763i	0.743427	+	0.668817i	$0.233199\pi$
$347$	8646.33i	1.33763i	−0.743427	+	0.668817i	$0.766801\pi$
$348$	4706.94i	0.725053i
$349$	7455.43	1.14350	0.571748	−	0.820429i	$-0.306266\pi$
$349$	7455.43	1.14350	0.571748	+	0.820429i	$0.306266\pi$
$350$	0	0
$351$	419.753	0.0638312
$352$	2637.74i	0.399410i
$353$	− 5450.21i	− 0.821771i	−0.911687	−	0.410886i	$-0.865220\pi$
$353$	− 5450.21i	− 0.821771i	0.911687	−	0.410886i	$-0.134780\pi$
$354$	1097.33	0.164752
$355$	0	0
$356$	−10060.2	−1.49773
$357$	− 1998.40i	− 0.296265i
$358$	2160.73i	0.318989i
$359$	−4775.79	−0.702107	−0.351053	−	0.936355i	$-0.614176\pi$
$359$	−4775.79	−0.702107	−0.351053	+	0.936355i	$0.614176\pi$
$360$	0	0
$361$	13718.0	2.00000
$362$	1699.49i	0.246749i
$363$	− 1994.88i	− 0.288441i
$364$	836.281	0.120420
$365$	0	0
$366$	760.293	0.108582
$367$	9636.30i	1.37060i	0.728260	+	0.685301i	$0.240329\pi$
$367$	9636.30i	1.37060i	−0.728260	+	0.685301i	$0.759671\pi$
$368$	− 4382.46i	− 0.620792i
$369$	−222.571	−0.0314000
$370$	0	0
$371$	−1805.85	−0.252709
$372$	− 938.292i	− 0.130775i
$373$	− 12180.4i	− 1.69082i	−0.534115	−	0.845412i	$-0.679355\pi$
$373$	− 12180.4i	− 1.69082i	0.534115	−	0.845412i	$-0.320645\pi$
$374$	1379.13	0.190676
$375$	0	0
$376$	2267.27	0.310971
$377$	3174.11i	0.433621i
$378$	106.133i	0.0144416i
$379$	−1689.39	−0.228966	−0.114483	−	0.993425i	$-0.536521\pi$
$379$	−1689.39	−0.228966	−0.114483	+	0.993425i	$0.536521\pi$
$380$	0	0
$381$	−6264.63	−0.842380
$382$	− 713.783i	− 0.0956029i
$383$	− 1513.13i	− 0.201872i	−0.994893	−	0.100936i	$-0.967816\pi$
$383$	− 1513.13i	− 0.201872i	0.994893	−	0.100936i	$-0.0321838\pi$
$384$	3118.17	0.414384
$385$	0	0
$386$	1064.76	0.140401
$387$	2541.87i	0.333877i
$388$	− 10492.1i	− 1.37283i
$389$	−12165.5	−1.58564	−0.792822	−	0.609453i	$-0.791389\pi$
$389$	−12165.5	−1.58564	−0.792822	+	0.609453i	$0.791389\pi$
$390$	0	0
$391$	−7377.21	−0.954173
$392$	431.580i	0.0556074i
$393$	1248.43i	0.160241i
$394$	2284.34	0.292089
$395$	0	0
$396$	1784.91	0.226503
$397$	7353.40i	0.929613i	0.885412	+	0.464807i	$0.153876\pi$
$397$	7353.40i	0.929613i	−0.885412	+	0.464807i	$0.846124\pi$
$398$	43.8778i	0.00552612i
$399$	3012.39	0.377965
$400$	0	0
$401$	7481.62	0.931707	0.465853	−	0.884862i	$-0.345747\pi$
$401$	7481.62	0.931707	0.465853	+	0.884862i	$0.345747\pi$
$402$	1401.76i	0.173913i
$403$	− 632.735i	− 0.0782104i
$404$	8883.42	1.09398
$405$	0	0
$406$	−802.567	−0.0981053
$407$	− 2469.02i	− 0.300699i
$408$	− 2514.49i	− 0.305112i
$409$	−9248.94	−1.11817	−0.559084	−	0.829111i	$-0.688847\pi$
$409$	−9248.94	−1.11817	−0.559084	+	0.829111i	$0.688847\pi$
$410$	0	0
$411$	−1857.76	−0.222959
$412$	600.997i	0.0718665i
$413$	− 4559.55i	− 0.543247i
$414$	391.798	0.0465116
$415$	0	0
$416$	1588.96	0.187272
$417$	800.983i	0.0940631i
$418$	2078.89i	0.243258i
$419$	3363.39	0.392154	0.196077	−	0.980589i	$-0.437180\pi$
$419$	3363.39	0.392154	0.196077	+	0.980589i	$0.437180\pi$
$420$	0	0
$421$	−3638.86	−0.421252	−0.210626	−	0.977567i	$-0.567550\pi$
$421$	−3638.86	−0.421252	−0.210626	+	0.977567i	$0.567550\pi$
$422$	726.097i	0.0837579i
$423$	− 2316.75i	− 0.266298i
$424$	−2272.21	−0.260255
$425$	0	0
$426$	−294.756	−0.0335234
$427$	− 3159.13i	− 0.358035i
$428$	− 722.983i	− 0.0816512i
$429$	1203.65	0.135461
$430$	0	0
$431$	11243.2	1.25653	0.628264	−	0.778000i	$-0.283766\pi$
$431$	11243.2	1.25653	0.628264	+	0.778000i	$0.283766\pi$
$432$	− 1526.34i	− 0.169991i
$433$	− 187.332i	− 0.0207912i	−0.999946	−	0.0103956i	$-0.996691\pi$
$433$	− 187.332i	− 0.0207912i	0.999946	−	0.0103956i	$-0.00330909\pi$
$434$	159.986	0.0176948
$435$	0	0
$436$	16354.9	1.79646
$437$	− 11120.4i	− 1.21730i
$438$	79.8809i	0.00871428i
$439$	11479.4	1.24802	0.624011	−	0.781415i	$-0.285502\pi$
$439$	11479.4	1.24802	0.624011	+	0.781415i	$0.285502\pi$
$440$	0	0
$441$	441.000	0.0476190
$442$	− 830.775i	− 0.0894026i
$443$	9490.56i	1.01786i	0.860809	+	0.508928i	$0.169958\pi$
$443$	9490.56i	1.01786i	−0.860809	+	0.508928i	$0.830042\pi$
$444$	−2205.56	−0.235746
$445$	0	0
$446$	1003.30	0.106519
$447$	− 7655.39i	− 0.810039i
$448$	− 2763.99i	− 0.291487i
$449$	5546.58	0.582982	0.291491	−	0.956574i	$-0.405849\pi$
$449$	5546.58	0.582982	0.291491	+	0.956574i	$0.405849\pi$
$450$	0	0
$451$	−638.229	−0.0666364
$452$	4583.85i	0.477004i
$453$	3352.15i	0.347677i
$454$	−2382.12	−0.246252
$455$	0	0
$456$	3790.34	0.389252
$457$	1776.94i	0.181885i	0.995856	+	0.0909426i	$0.0289880\pi$
$457$	1776.94i	0.181885i	−0.995856	+	0.0909426i	$0.971012\pi$
$458$	1911.16i	0.194984i
$459$	−2569.37	−0.261281
$460$	0	0
$461$	−9059.81	−0.915309	−0.457655	−	0.889130i	$-0.651310\pi$
$461$	−9059.81	−0.915309	−0.457655	+	0.889130i	$0.651310\pi$
$462$	304.341i	0.0306477i
$463$	− 14878.5i	− 1.49344i	−0.665139	−	0.746719i	$-0.731628\pi$
$463$	− 14878.5i	− 1.49344i	0.665139	−	0.746719i	$-0.268372\pi$
$464$	11542.0	1.15479
$465$	0	0
$466$	2192.35	0.217937
$467$	14275.8i	1.41458i	0.706926	+	0.707288i	$0.250082\pi$
$467$	14275.8i	1.41458i	−0.706926	+	0.707288i	$0.749918\pi$
$468$	− 1075.22i	− 0.106201i
$469$	5824.50	0.573455
$470$	0	0
$471$	1368.31	0.133861
$472$	− 5737.07i	− 0.559470i
$473$	7288.89i	0.708548i
$474$	1.95431	0.000189376 0
$475$	0	0
$476$	−5119.01	−0.492919
$477$	2321.80i	0.222868i
$478$	3744.34i	0.358289i
$479$	15377.8	1.46687	0.733433	−	0.679761i	$-0.237917\pi$
$479$	15377.8	1.46687	0.733433	+	0.679761i	$0.237917\pi$
$480$	0	0
$481$	−1487.32	−0.140989
$482$	3371.56i	0.318610i
$483$	− 1627.98i	− 0.153365i
$484$	−5109.99	−0.479901
$485$	0	0
$486$	136.457	0.0127363
$487$	19683.3i	1.83149i	0.401756	+	0.915747i	$0.368400\pi$
$487$	19683.3i	1.83149i	−0.401756	+	0.915747i	$0.631600\pi$
$488$	− 3974.98i	− 0.368727i
$489$	−316.469	−0.0292663
$490$	0	0
$491$	19585.1	1.80013	0.900065	−	0.435755i	$-0.143519\pi$
$491$	19585.1	1.80013	0.900065	+	0.435755i	$0.143519\pi$
$492$	570.128i	0.0522426i
$493$	− 19429.3i	− 1.77495i
$494$	1252.31	0.114057
$495$	0	0
$496$	−2300.81	−0.208285
$497$	1224.75i	0.110539i
$498$	− 2516.93i	− 0.226478i
$499$	6888.47	0.617977	0.308988	−	0.951066i	$-0.400010\pi$
$499$	6888.47	0.617977	0.308988	+	0.951066i	$0.400010\pi$
$500$	0	0
$501$	7447.62	0.664142
$502$	− 409.073i	− 0.0363701i
$503$	− 14878.0i	− 1.31885i	−0.751772	−	0.659423i	$-0.770801\pi$
$503$	− 14878.0i	− 1.31885i	0.751772	−	0.659423i	$-0.229199\pi$
$504$	554.889	0.0490411
$505$	0	0
$506$	1123.49	0.0987062
$507$	5865.93i	0.513836i
$508$	16047.2i	1.40153i
$509$	−1935.28	−0.168526	−0.0842629	−	0.996444i	$-0.526854\pi$
$509$	−1935.28	−0.168526	−0.0842629	+	0.996444i	$0.526854\pi$
$510$	0	0
$511$	331.917	0.0287341
$512$	− 9761.22i	− 0.842557i
$513$	− 3873.07i	− 0.333334i
$514$	−831.019	−0.0713126
$515$	0	0
$516$	6511.13	0.555497
$517$	− 6643.35i	− 0.565134i
$518$	− 376.064i	− 0.0318983i
$519$	1550.12	0.131104
$520$	0	0
$521$	−6892.28	−0.579570	−0.289785	−	0.957092i	$-0.593584\pi$
$521$	−6892.28	−0.579570	−0.289785	+	0.957092i	$0.593584\pi$
$522$	1031.87i	0.0865207i
$523$	1074.60i	0.0898447i	0.998990	+	0.0449223i	$0.0143040\pi$
$523$	1074.60i	0.0898447i	−0.998990	+	0.0449223i	$0.985696\pi$
$524$	3197.91	0.266606
$525$	0	0
$526$	3575.58	0.296393
$527$	3873.07i	0.320140i
$528$	− 4376.83i	− 0.360752i
$529$	6157.23	0.506060
$530$	0	0
$531$	−5862.28	−0.479099
$532$	− 7716.39i	− 0.628849i
$533$	384.464i	0.0312439i
$534$	−2205.44	−0.178724
$535$	0	0
$536$	7328.69	0.590580
$537$	− 11543.3i	− 0.927619i
$538$	1003.60i	0.0804239i
$539$	1264.58	0.101056
$540$	0	0
$541$	8660.23	0.688230	0.344115	−	0.938928i	$-0.388179\pi$
$541$	8660.23	0.688230	0.344115	+	0.938928i	$0.388179\pi$
$542$	− 2194.35i	− 0.173903i
$543$	− 9079.22i	− 0.717544i
$544$	−9726.25	−0.766562
$545$	0	0
$546$	183.333	0.0143698
$547$	− 15346.1i	− 1.19954i	−0.800171	−	0.599771i	$-0.795258\pi$
$547$	− 15346.1i	− 1.19954i	0.800171	−	0.599771i	$-0.204742\pi$
$548$	4758.74i	0.370955i
$549$	−4061.74	−0.315757
$550$	0	0
$551$	29287.6	2.26442
$552$	− 2048.41i	− 0.157946i
$553$	− 8.12042i	0 0.000624440i
$554$	2234.04	0.171328
$555$	0	0
$556$	2051.76	0.156500
$557$	15544.9i	1.18251i	0.806483	+	0.591257i	$0.201368\pi$
$557$	15544.9i	1.18251i	−0.806483	+	0.591257i	$0.798632\pi$
$558$	− 205.696i	− 0.0156054i
$559$	4390.77	0.332218
$560$	0	0
$561$	−7367.75	−0.554486
$562$	3643.38i	0.273464i
$563$	18511.9i	1.38576i	0.721052	+	0.692881i	$0.243659\pi$
$563$	18511.9i	1.38576i	−0.721052	+	0.692881i	$0.756341\pi$
$564$	−5934.48	−0.443061
$565$	0	0
$566$	92.2831	0.00685326
$567$	− 567.000i	− 0.0419961i
$568$	1541.05i	0.113840i
$569$	−2157.36	−0.158948	−0.0794738	−	0.996837i	$-0.525324\pi$
$569$	−2157.36	−0.158948	−0.0794738	+	0.996837i	$0.525324\pi$
$570$	0	0
$571$	16010.3	1.17340	0.586700	−	0.809805i	$-0.300427\pi$
$571$	16010.3	1.17340	0.586700	+	0.809805i	$0.300427\pi$
$572$	− 3083.22i	− 0.225378i
$573$	3813.26i	0.278013i
$574$	−97.2109	−0.00706882
$575$	0	0
$576$	−3553.70	−0.257067
$577$	− 2164.01i	− 0.156134i	−0.996948	−	0.0780668i	$-0.975125\pi$
$577$	− 2164.01i	− 0.156134i	0.996948	−	0.0780668i	$-0.0248747\pi$
$578$	2326.40i	0.167414i
$579$	−5688.28	−0.408285
$580$	0	0
$581$	−10458.2	−0.746780
$582$	− 2300.12i	− 0.163820i
$583$	6657.84i	0.472967i
$584$	417.635	0.0295922
$585$	0	0
$586$	−2810.33	−0.198112
$587$	27616.6i	1.94184i	0.239412	+	0.970918i	$0.423045\pi$
$587$	27616.6i	1.94184i	−0.239412	+	0.970918i	$0.576955\pi$
$588$	− 1129.64i	− 0.0792275i
$589$	−5838.26	−0.408424
$590$	0	0
$591$	−12203.7	−0.849395
$592$	5408.32i	0.375474i
$593$	10205.4i	0.706718i	0.935488	+	0.353359i	$0.114961\pi$
$593$	10205.4i	0.706718i	−0.935488	+	0.353359i	$0.885039\pi$
$594$	391.295	0.0270287
$595$	0	0
$596$	−19609.7	−1.34773
$597$	− 234.410i	− 0.0160699i
$598$	− 676.783i	− 0.0462805i
$599$	−11090.5	−0.756501	−0.378251	−	0.925703i	$-0.623474\pi$
$599$	−11090.5	−0.756501	−0.378251	+	0.925703i	$0.623474\pi$
$600$	0	0
$601$	−26537.0	−1.80111	−0.900555	−	0.434742i	$-0.856839\pi$
$601$	−26537.0	−1.80111	−0.900555	+	0.434742i	$0.856839\pi$
$602$	1110.20i	0.0751631i
$603$	− 7488.64i	− 0.505740i
$604$	8586.71	0.578457
$605$	0	0
$606$	1947.46	0.130544
$607$	− 11234.5i	− 0.751226i	−0.926777	−	0.375613i	$-0.877432\pi$
$607$	− 11234.5i	− 0.751226i	0.926777	−	0.375613i	$-0.122568\pi$
$608$	− 14661.3i	− 0.977954i
$609$	4287.58	0.285290
$610$	0	0
$611$	−4001.90	−0.264975
$612$	6581.58i	0.434714i
$613$	10622.5i	0.699900i	0.936768	+	0.349950i	$0.113801\pi$
$613$	10622.5i	0.699900i	−0.936768	+	0.349950i	$0.886199\pi$
$614$	−106.789	−0.00701896
$615$	0	0
$616$	1591.16	0.104074
$617$	20433.3i	1.33325i	0.745395	+	0.666623i	$0.232261\pi$
$617$	20433.3i	1.33325i	−0.745395	+	0.666623i	$0.767739\pi$
$618$	131.753i	0.00857585i
$619$	7963.57	0.517097	0.258549	−	0.965998i	$-0.416756\pi$
$619$	7963.57	0.517097	0.258549	+	0.965998i	$0.416756\pi$
$620$	0	0
$621$	−2093.11	−0.135256
$622$	664.077i	0.0428088i
$623$	9163.91i	0.589317i
$624$	−2636.57	−0.169146
$625$	0	0
$626$	2616.30	0.167042
$627$	− 11106.1i	− 0.707394i
$628$	− 3505.01i	− 0.222715i
$629$	9104.09	0.577113
$630$	0	0
$631$	−14703.1	−0.927608	−0.463804	−	0.885938i	$-0.653516\pi$
$631$	−14703.1	−0.927608	−0.463804	+	0.885938i	$0.653516\pi$
$632$	− 10.2175i	0 0.000643088i
$633$	− 3879.05i	− 0.243568i
$634$	−2074.68	−0.129963
$635$	0	0
$636$	5947.42	0.370803
$637$	− 761.773i	− 0.0473824i
$638$	2958.92i	0.183613i
$639$	1574.68	0.0974860
$640$	0	0
$641$	3353.41	0.206633	0.103317	−	0.994649i	$-0.467055\pi$
$641$	3353.41	0.206633	0.103317	+	0.994649i	$0.467055\pi$
$642$	− 158.495i	− 0.00974345i
$643$	− 31862.0i	− 1.95415i	−0.212906	−	0.977073i	$-0.568293\pi$
$643$	− 31862.0i	− 1.95415i	0.212906	−	0.977073i	$-0.431707\pi$
$644$	−4170.15	−0.255166
$645$	0	0
$646$	−7665.58	−0.466870
$647$	− 8518.46i	− 0.517612i	−0.965929	−	0.258806i	$-0.916671\pi$
$647$	− 8518.46i	− 0.517612i	0.965929	−	0.258806i	$-0.0833291\pi$
$648$	− 713.429i	− 0.0432502i
$649$	−16810.3	−1.01673
$650$	0	0
$651$	−854.696	−0.0514565
$652$	810.651i	0.0486925i
$653$	28509.3i	1.70851i	0.519856	+	0.854254i	$0.325986\pi$
$653$	28509.3i	1.70851i	−0.519856	+	0.854254i	$0.674014\pi$
$654$	3585.37	0.214372
$655$	0	0
$656$	1398.02	0.0832068
$657$	− 426.750i	− 0.0253411i
$658$	− 1011.87i	− 0.0599496i
$659$	27632.4	1.63339	0.816697	−	0.577066i	$-0.195803\pi$
$659$	27632.4	1.63339	0.816697	+	0.577066i	$0.195803\pi$
$660$	0	0
$661$	−27052.8	−1.59188	−0.795941	−	0.605374i	$-0.793023\pi$
$661$	−27052.8	−1.59188	−0.795941	+	0.605374i	$0.793023\pi$
$662$	4847.77i	0.284613i
$663$	4438.28i	0.259982i
$664$	−13159.1	−0.769082
$665$	0	0
$666$	−483.511	−0.0281317
$667$	− 15827.9i	− 0.918826i
$668$	− 19077.5i	− 1.10498i
$669$	−5359.94	−0.309757
$670$	0	0
$671$	−11647.1	−0.670094
$672$	− 2146.36i	− 0.123210i
$673$	1569.99i	0.0899235i	0.998989	+	0.0449618i	$0.0143166\pi$
$673$	1569.99i	0.0899235i	−0.998989	+	0.0449618i	$0.985683\pi$
$674$	−4569.13	−0.261122
$675$	0	0
$676$	15025.9	0.854909
$677$	13853.9i	0.786482i	0.919435	+	0.393241i	$0.128646\pi$
$677$	13853.9i	0.786482i	−0.919435	+	0.393241i	$0.871354\pi$
$678$	1004.89i	0.0569210i
$679$	−9557.33	−0.540172
$680$	0	0
$681$	12726.1	0.716100
$682$	− 589.839i	− 0.0331174i
$683$	28337.1i	1.58754i	0.608219	+	0.793769i	$0.291884\pi$
$683$	28337.1i	1.58754i	−0.608219	+	0.793769i	$0.708116\pi$
$684$	−9921.07	−0.554593
$685$	0	0
$686$	192.613	0.0107201
$687$	− 10210.1i	− 0.567014i
$688$	− 15966.1i	− 0.884742i
$689$	4010.63	0.221760
$690$	0	0
$691$	16936.5	0.932410	0.466205	−	0.884677i	$-0.345621\pi$
$691$	16936.5	0.932410	0.466205	+	0.884677i	$0.345621\pi$
$692$	− 3970.73i	− 0.218128i
$693$	− 1625.89i	− 0.0891233i
$694$	4855.37	0.265572
$695$	0	0
$696$	5394.86	0.293810
$697$	− 2353.37i	− 0.127891i
$698$	− 4186.62i	− 0.227028i
$699$	−11712.3	−0.633760
$700$	0	0
$701$	−29744.0	−1.60259	−0.801294	−	0.598271i	$-0.795855\pi$
$701$	−29744.0	−1.60259	−0.801294	+	0.598271i	$0.795855\pi$
$702$	− 235.713i	− 0.0126730i
$703$	13723.5i	0.736261i
$704$	−10190.3	−0.545543
$705$	0	0
$706$	−3060.58	−0.163154
$707$	− 8091.96i	− 0.430452i
$708$	15016.5i	0.797113i
$709$	−34264.7	−1.81500	−0.907502	−	0.420047i	$-0.862014\pi$
$709$	−34264.7	−1.81500	−0.907502	+	0.420047i	$0.862014\pi$
$710$	0	0
$711$	−10.4405	−0.000550705 0
$712$	11530.5i	0.606916i
$713$	3155.16i	0.165725i
$714$	−1122.21	−0.0588201
$715$	0	0
$716$	−29568.8	−1.54335
$717$	− 20003.5i	− 1.04190i
$718$	2681.86i	0.139396i
$719$	25469.2	1.32106	0.660529	−	0.750801i	$-0.270332\pi$
$719$	25469.2	1.32106	0.660529	+	0.750801i	$0.270332\pi$
$720$	0	0
$721$	547.452	0.0282776
$722$	− 7703.40i	− 0.397079i
$723$	− 18012.0i	− 0.926518i
$724$	−23256.9	−1.19383
$725$	0	0
$726$	−1120.23	−0.0572667
$727$	− 24294.6i	− 1.23939i	−0.784843	−	0.619695i	$-0.787256\pi$
$727$	− 24294.6i	− 1.23939i	0.784843	−	0.619695i	$-0.212744\pi$
$728$	− 958.503i	− 0.0487974i
$729$	−729.000	−0.0370370
$730$	0	0
$731$	−26876.6	−1.35987
$732$	10404.3i	0.525349i
$733$	34870.8i	1.75714i	0.477615	+	0.878569i	$0.341501\pi$
$733$	34870.8i	1.75714i	−0.477615	+	0.878569i	$0.658499\pi$
$734$	5411.29	0.272118
$735$	0	0
$736$	−7923.40	−0.396821
$737$	− 21473.9i	− 1.07327i
$738$	124.985i	0.00623412i
$739$	−7028.81	−0.349877	−0.174938	−	0.984579i	$-0.555973\pi$
$739$	−7028.81	−0.349877	−0.174938	+	0.984579i	$0.555973\pi$
$740$	0	0
$741$	−6690.25	−0.331677
$742$	1014.08i	0.0501725i
$743$	1368.74i	0.0675831i	0.999429	+	0.0337915i	$0.0107582\pi$
$743$	1368.74i	0.0675831i	−0.999429	+	0.0337915i	$0.989242\pi$
$744$	−1075.42	−0.0529932
$745$	0	0
$746$	−6839.94	−0.335694
$747$	13446.3i	0.658598i
$748$	18872.9i	0.922541i
$749$	−658.570	−0.0321276
$750$	0	0
$751$	37144.0	1.80480	0.902400	−	0.430900i	$-0.141804\pi$
$751$	37144.0	1.80480	0.902400	+	0.430900i	$0.141804\pi$
$752$	14552.1i	0.705665i
$753$	2185.40i	0.105764i
$754$	1782.43	0.0860907
$755$	0	0
$756$	−1452.40	−0.0698721
$757$	− 12042.4i	− 0.578189i	−0.957301	−	0.289095i	$-0.906646\pi$
$757$	− 12042.4i	− 0.578189i	0.957301	−	0.289095i	$-0.0933542\pi$
$758$	948.683i	0.0454588i
$759$	−6002.07	−0.287037
$760$	0	0
$761$	6112.92	0.291187	0.145593	−	0.989345i	$-0.453491\pi$
$761$	6112.92	0.291187	0.145593	+	0.989345i	$0.453491\pi$
$762$	3517.92i	0.167245i
$763$	− 14897.7i	− 0.706860i
$764$	9767.88	0.462552
$765$	0	0
$766$	−849.700	−0.0400795
$767$	10126.4i	0.476717i
$768$	7725.50i	0.362982i
$769$	957.146	0.0448837	0.0224418	−	0.999748i	$-0.492856\pi$
$769$	957.146	0.0448837	0.0224418	+	0.999748i	$0.492856\pi$
$770$	0	0
$771$	4439.58	0.207377
$772$	14570.8i	0.679295i
$773$	32867.9i	1.52934i	0.644424	+	0.764668i	$0.277097\pi$
$773$	32867.9i	1.52934i	−0.644424	+	0.764668i	$0.722903\pi$
$774$	1427.39	0.0662876
$775$	0	0
$776$	−12025.5	−0.556303
$777$	2009.06i	0.0927601i
$778$	6831.58i	0.314812i
$779$	3547.46	0.163159
$780$	0	0
$781$	4515.45	0.206883
$782$	4142.69i	0.189440i
$783$	− 5512.60i	− 0.251602i
$784$	−2770.03	−0.126186
$785$	0	0
$786$	701.057	0.0318141
$787$	− 15320.0i	− 0.693900i	−0.937884	−	0.346950i	$-0.887217\pi$
$787$	− 15320.0i	− 0.693900i	0.937884	−	0.346950i	$-0.112783\pi$
$788$	31260.4i	1.41320i
$789$	−19101.9	−0.861909
$790$	0	0
$791$	4175.45	0.187689
$792$	− 2045.78i	− 0.0917848i
$793$	7016.15i	0.314188i
$794$	4129.32	0.184564
$795$	0	0
$796$	−600.453	−0.0267368
$797$	− 43629.0i	− 1.93904i	−0.245004	−	0.969522i	$-0.578789\pi$
$797$	− 43629.0i	− 1.93904i	0.245004	−	0.969522i	$-0.421211\pi$
$798$	− 1691.61i	− 0.0750407i
$799$	24496.3	1.08463
$800$	0	0
$801$	11782.2	0.519729
$802$	− 4201.33i	− 0.184980i
$803$	− 1223.72i	− 0.0537784i
$804$	−19182.5	−0.841438
$805$	0	0
$806$	−355.314	−0.0155278
$807$	− 5361.54i	− 0.233872i
$808$	− 10181.7i	− 0.443307i
$809$	−127.735	−0.00555119	−0.00277560	−	0.999996i	$-0.500884\pi$
$809$	−127.735	−0.00555119	−0.00277560	+	0.999996i	$0.500884\pi$
$810$	0	0
$811$	16227.5	0.702618	0.351309	−	0.936260i	$-0.385737\pi$
$811$	16227.5	0.702618	0.351309	+	0.936260i	$0.385737\pi$
$812$	− 10982.9i	− 0.474659i
$813$	11723.0i	0.505710i
$814$	−1386.48	−0.0597005
$815$	0	0
$816$	16138.9	0.692369
$817$	− 40513.7i	− 1.73488i
$818$	5193.77i	0.222000i
$819$	−979.423	−0.0417873
$820$	0	0
$821$	34249.2	1.45591	0.727957	−	0.685623i	$-0.240470\pi$
$821$	34249.2	1.45591	0.727957	+	0.685623i	$0.240470\pi$
$822$	1043.23i	0.0442661i
$823$	− 6624.51i	− 0.280578i	−0.990111	−	0.140289i	$-0.955197\pi$
$823$	− 6624.51i	− 0.280578i	0.990111	−	0.140289i	$-0.0448032\pi$
$824$	688.832	0.0291221
$825$	0	0
$826$	−2560.43	−0.107856
$827$	33786.8i	1.42065i	0.703872	+	0.710327i	$0.251453\pi$
$827$	33786.8i	1.42065i	−0.703872	+	0.710327i	$0.748547\pi$
$828$	5361.62i	0.225035i
$829$	30283.8	1.26876	0.634378	−	0.773023i	$-0.281256\pi$
$829$	30283.8	1.26876	0.634378	+	0.773023i	$0.281256\pi$
$830$	0	0
$831$	−11935.0	−0.498220
$832$	6138.57i	0.255789i
$833$	4662.93i	0.193951i
$834$	449.794	0.0186752
$835$	0	0
$836$	−28449.0	−1.17695
$837$	1098.89i	0.0453804i
$838$	− 1888.72i	− 0.0778578i
$839$	−16810.9	−0.691750	−0.345875	−	0.938281i	$-0.612418\pi$
$839$	−16810.9	−0.691750	−0.345875	+	0.938281i	$0.612418\pi$
$840$	0	0
$841$	17296.6	0.709195
$842$	2043.41i	0.0836350i
$843$	− 19464.1i	− 0.795231i
$844$	−9936.39	−0.405242
$845$	0	0
$846$	−1300.98	−0.0528706
$847$	4654.72i	0.188829i
$848$	− 14583.8i	− 0.590579i
$849$	−493.007	−0.0199293
$850$	0	0
$851$	7416.56	0.298750
$852$	− 4033.64i	− 0.162195i
$853$	14875.8i	0.597112i	0.954392	+	0.298556i	$0.0965050\pi$
$853$	14875.8i	0.597112i	−0.954392	+	0.298556i	$0.903495\pi$
$854$	−1774.02	−0.0710839
$855$	0	0
$856$	−828.647	−0.0330871
$857$	3987.55i	0.158941i	0.996837	+	0.0794703i	$0.0253229\pi$
$857$	3987.55i	0.158941i	−0.996837	+	0.0794703i	$0.974677\pi$
$858$	− 675.915i	− 0.0268944i
$859$	−39344.7	−1.56278	−0.781388	−	0.624046i	$-0.785488\pi$
$859$	−39344.7	−1.56278	−0.781388	+	0.624046i	$0.785488\pi$
$860$	0	0
$861$	519.333	0.0205561
$862$	− 6313.63i	− 0.249470i
$863$	− 15627.0i	− 0.616397i	−0.951322	−	0.308198i	$-0.900274\pi$
$863$	− 15627.0i	− 0.616397i	0.951322	−	0.308198i	$-0.0997261\pi$
$864$	−2759.60	−0.108661
$865$	0	0
$866$	−105.197	−0.00412787
$867$	− 12428.4i	− 0.486839i
$868$	2189.35i	0.0856122i
$869$	−29.9386	−0.00116870
$870$	0	0
$871$	−12935.7	−0.503226
$872$	− 18745.1i	− 0.727969i
$873$	12288.0i	0.476387i
$874$	−6244.69	−0.241682
$875$	0	0
$876$	−1093.14	−0.0421619
$877$	14519.0i	0.559034i	0.960141	+	0.279517i	$0.0901743\pi$
$877$	14519.0i	0.559034i	−0.960141	+	0.279517i	$0.909826\pi$
$878$	− 6446.29i	− 0.247781i
$879$	15013.7	0.576109
$880$	0	0
$881$	24177.7	0.924592	0.462296	−	0.886726i	$-0.347026\pi$
$881$	24177.7	0.924592	0.462296	+	0.886726i	$0.347026\pi$
$882$	− 247.645i	− 0.00945423i
$883$	10340.3i	0.394089i	0.980395	+	0.197044i	$0.0631343\pi$
$883$	10340.3i	0.394089i	−0.980395	+	0.197044i	$0.936866\pi$
$884$	11368.9	0.432553
$885$	0	0
$886$	5329.45	0.202084
$887$	3222.62i	0.121990i	0.998138	+	0.0609949i	$0.0194274\pi$
$887$	3222.62i	0.121990i	−0.998138	+	0.0609949i	$0.980573\pi$
$888$	2527.90i	0.0955303i
$889$	14617.5	0.551467
$890$	0	0
$891$	−2090.43	−0.0785993
$892$	13729.8i	0.515367i
$893$	36925.6i	1.38373i
$894$	−4298.91	−0.160824
$895$	0	0
$896$	−7275.74	−0.271278
$897$	3615.60i	0.134583i
$898$	− 3114.70i	− 0.115745i
$899$	−8309.70	−0.308280
$900$	0	0
$901$	−24549.7	−0.907735
$902$	358.399i	0.0132299i
$903$	− 5931.03i	− 0.218574i
$904$	5253.77	0.193294
$905$	0	0
$906$	1882.41	0.0690274
$907$	31692.8i	1.16025i	0.814529	+	0.580123i	$0.196995\pi$
$907$	31692.8i	1.16025i	−0.814529	+	0.580123i	$0.803005\pi$
$908$	− 32598.5i	− 1.19143i
$909$	−10403.9	−0.379623
$910$	0	0
$911$	2403.15	0.0873985	0.0436993	−	0.999045i	$-0.486086\pi$
$911$	2403.15	0.0873985	0.0436993	+	0.999045i	$0.486086\pi$
$912$	24327.7i	0.883301i
$913$	38557.6i	1.39767i
$914$	997.843	0.0361113
$915$	0	0
$916$	−26153.6	−0.943385
$917$	− 2912.99i	− 0.104902i
$918$	1442.84i	0.0518745i
$919$	−19622.5	−0.704339	−0.352170	−	0.935936i	$-0.614556\pi$
$919$	−19622.5	−0.704339	−0.352170	+	0.935936i	$0.614556\pi$
$920$	0	0
$921$	570.501	0.0204111
$922$	5087.56i	0.181724i
$923$	− 2720.07i	− 0.0970014i
$924$	−4164.80	−0.148281
$925$	0	0
$926$	−8355.06	−0.296506
$927$	− 703.867i	− 0.0249385i
$928$	− 20867.7i	− 0.738165i
$929$	12930.5	0.456660	0.228330	−	0.973584i	$-0.426673\pi$
$929$	12930.5	0.456660	0.228330	+	0.973584i	$0.426673\pi$
$930$	0	0
$931$	−7028.90	−0.247436
$932$	30001.6i	1.05444i
$933$	− 3547.72i	− 0.124488i
$934$	8016.64	0.280848
$935$	0	0
$936$	−1232.36	−0.0430352
$937$	18717.1i	0.652573i	0.945271	+	0.326287i	$0.105797\pi$
$937$	18717.1i	0.652573i	−0.945271	+	0.326287i	$0.894203\pi$
$938$	− 3270.76i	− 0.113853i
$939$	−13977.2	−0.485758
$940$	0	0
$941$	−10152.9	−0.351727	−0.175863	−	0.984415i	$-0.556272\pi$
$941$	−10152.9	−0.351727	−0.175863	+	0.984415i	$0.556272\pi$
$942$	− 768.380i	− 0.0265766i
$943$	− 1917.15i	− 0.0662045i
$944$	36822.4	1.26956
$945$	0	0
$946$	4093.09	0.140674
$947$	15836.2i	0.543408i	0.962381	+	0.271704i	$0.0875871\pi$
$947$	15836.2i	0.543408i	−0.962381	+	0.271704i	$0.912413\pi$
$948$	26.7440i	0 0.000916250i
$949$	−737.158	−0.0252151
$950$	0	0
$951$	11083.6	0.377930
$952$	5867.15i	0.199743i
$953$	− 4847.86i	− 0.164782i	−0.996600	−	0.0823911i	$-0.973744\pi$
$953$	− 4847.86i	− 0.164782i	0.996600	−	0.0823911i	$-0.0262557\pi$
$954$	1303.82	0.0442480
$955$	0	0
$956$	−51240.0	−1.73349
$957$	− 15807.5i	− 0.533945i
$958$	− 8635.44i	− 0.291230i
$959$	4334.76	0.145961
$960$	0	0
$961$	−28134.5	−0.944397
$962$	835.207i	0.0279918i
$963$	846.732i	0.0283339i
$964$	−46138.6	−1.54152
$965$	0	0
$966$	−914.195	−0.0304490
$967$	17153.8i	0.570454i	0.958460	+	0.285227i	$0.0920690\pi$
$967$	17153.8i	0.570454i	−0.958460	+	0.285227i	$0.907931\pi$
$968$	5856.80i	0.194468i
$969$	40952.1	1.35766
$970$	0	0
$971$	50352.2	1.66414	0.832070	−	0.554670i	$-0.187156\pi$
$971$	50352.2	1.66414	0.832070	+	0.554670i	$0.187156\pi$
$972$	1867.37i	0.0616214i
$973$	− 1868.96i	− 0.0615788i
$974$	11053.2	0.363623
$975$	0	0
$976$	25512.8	0.836725
$977$	1510.03i	0.0494474i	0.999694	+	0.0247237i	$0.00787061\pi$
$977$	1510.03i	0.0494474i	−0.999694	+	0.0247237i	$0.992129\pi$
$978$	177.714i	0.00581049i
$979$	33785.7	1.10296
$980$	0	0
$981$	−19154.2	−0.623392
$982$	− 10998.1i	− 0.357396i
$983$	5310.89i	0.172321i	0.996281	+	0.0861603i	$0.0274597\pi$
$983$	5310.89i	0.172321i	−0.996281	+	0.0861603i	$0.972540\pi$
$984$	653.451	0.0211700
$985$	0	0
$986$	−10910.6	−0.352396
$987$	5405.75i	0.174333i
$988$	17137.4i	0.551836i
$989$	−21894.7	−0.703956
$990$	0	0
$991$	35845.4	1.14901	0.574505	−	0.818501i	$-0.305195\pi$
$991$	35845.4	1.14901	0.574505	+	0.818501i	$0.305195\pi$
$992$	4159.82i	0.133140i
$993$	− 25898.4i	− 0.827654i
$994$	687.764	0.0219462
$995$	0	0
$996$	34443.3	1.09576
$997$	− 17857.5i	− 0.567253i	−0.958935	−	0.283627i	$-0.908462\pi$
$997$	− 17857.5i	− 0.567253i	0.958935	−	0.283627i	$-0.0915376\pi$
$998$	− 3868.24i	− 0.122692i
$999$	2583.08	0.0818067

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.4.d.m.274.2		4
5.2	odd	4		525.4.a.j.1.2	✓	2
5.3	odd	4		525.4.a.m.1.1	yes	2
5.4	even	2	inner	525.4.d.m.274.3		4
15.2	even	4		1575.4.a.x.1.1		2
15.8	even	4		1575.4.a.o.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.4.a.j.1.2	✓	2	5.2	odd	4
525.4.a.m.1.1	yes	2	5.3	odd	4
525.4.d.m.274.2		4	1.1	even	1	trivial
525.4.d.m.274.3		4	5.4	even	2	inner
1575.4.a.o.1.2		2	15.8	even	4
1575.4.a.x.1.1		2	15.2	even	4

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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	525.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-0.561553i q^{2} +3.00000i q^{3} +7.68466 q^{4} +1.68466 q^{6} -7.00000i q^{7} -8.80776i q^{8} -9.00000 q^{9} +O(q^{10})\)	\(q-0.561553i q^{2} +3.00000i q^{3} +7.68466 q^{4} +1.68466 q^{6} -7.00000i q^{7} -8.80776i q^{8} -9.00000 q^{9} -25.8078 q^{11} +23.0540i q^{12} +15.5464i q^{13} -3.93087 q^{14} +56.5312 q^{16} -95.1619i q^{17} +5.05398i q^{18} +143.447 q^{19} +21.0000 q^{21} +14.4924i q^{22} -77.5227i q^{23} +26.4233 q^{24} +8.73012 q^{26} -27.0000i q^{27} -53.7926i q^{28} +204.170 q^{29} -40.6998 q^{31} -102.207i q^{32} -77.4233i q^{33} -53.4384 q^{34} -69.1619 q^{36} +95.6695i q^{37} -80.5530i q^{38} -46.6392 q^{39} +24.7301 q^{41} -11.7926i q^{42} -282.430i q^{43} -198.324 q^{44} -43.5331 q^{46} +257.417i q^{47} +169.594i q^{48} -49.0000 q^{49} +285.486 q^{51} +119.469i q^{52} -257.978i q^{53} -15.1619 q^{54} -61.6543 q^{56} +430.341i q^{57} -114.652i q^{58} +651.365 q^{59} +451.304 q^{61} +22.8551i q^{62} +63.0000i q^{63} +394.855 q^{64} -43.4773 q^{66} +832.071i q^{67} -731.287i q^{68} +232.568 q^{69} -174.965 q^{71} +79.2699i q^{72} +47.4166i q^{73} +53.7235 q^{74} +1102.34 q^{76} +180.654i q^{77} +26.1904i q^{78} +1.16006 q^{79} +81.0000 q^{81} -13.8873i q^{82} -1494.03i q^{83} +161.378 q^{84} -158.599 q^{86} +612.511i q^{87} +227.309i q^{88} -1309.13 q^{89} +108.825 q^{91} -595.736i q^{92} -122.099i q^{93} +144.553 q^{94} +306.622 q^{96} -1365.33i q^{97} +27.5161i q^{98} +232.270 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 6 q^{4} - 18 q^{6} - 36 q^{9}+O(q^{10}) \) 4 * q + 6 * q^4 - 18 * q^6 - 36 * q^9	\( 4 q + 6 q^{4} - 18 q^{6} - 36 q^{9} - 62 q^{11} + 42 q^{14} - 46 q^{16} + 112 q^{19} + 84 q^{21} - 18 q^{24} + 406 q^{26} + 124 q^{29} - 270 q^{31} - 222 q^{34} - 54 q^{36} + 234 q^{39} + 470 q^{41} - 348 q^{44} + 1170 q^{46} - 196 q^{49} + 474 q^{51} + 162 q^{54} + 42 q^{56} + 882 q^{59} - 446 q^{61} + 862 q^{64} + 24 q^{66} + 1524 q^{69} + 1238 q^{71} - 16 q^{74} + 3024 q^{76} + 854 q^{79} + 324 q^{81} + 126 q^{84} + 3398 q^{86} - 932 q^{89} - 546 q^{91} + 1040 q^{94} + 1746 q^{96} + 558 q^{99}+O(q^{100}) \) 4 * q + 6 * q^4 - 18 * q^6 - 36 * q^9 - 62 * q^11 + 42 * q^14 - 46 * q^16 + 112 * q^19 + 84 * q^21 - 18 * q^24 + 406 * q^26 + 124 * q^29 - 270 * q^31 - 222 * q^34 - 54 * q^36 + 234 * q^39 + 470 * q^41 - 348 * q^44 + 1170 * q^46 - 196 * q^49 + 474 * q^51 + 162 * q^54 + 42 * q^56 + 882 * q^59 - 446 * q^61 + 862 * q^64 + 24 * q^66 + 1524 * q^69 + 1238 * q^71 - 16 * q^74 + 3024 * q^76 + 854 * q^79 + 324 * q^81 + 126 * q^84 + 3398 * q^86 - 932 * q^89 - 546 * q^91 + 1040 * q^94 + 1746 * q^96 + 558 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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