LMFDB - Embedded newform 207.8.a.a.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [207,8,Mod(1,207)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(207, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("207.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 207 = 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	207.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	yes
Analytic conductor:	$64.6637002752$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 455x^{3} - 474x^{2} + 42284x + 127016 $ x^5 - 455x^3 - 474x^2 + 42284*x + 127016
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{5}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 69)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-3.24502$ of defining polynomial
Character	$\chi$	$=$	207.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3.24502 q^{2} -117.470 q^{4} -168.083 q^{5} +149.817 q^{7} -796.555 q^{8} +O(q^{10})$	\(q+3.24502 q^{2} -117.470 q^{4} -168.083 q^{5} +149.817 q^{7} -796.555 q^{8} -545.434 q^{10} +18.5452 q^{11} +10200.4 q^{13} +486.159 q^{14} +12451.3 q^{16} +25924.5 q^{17} -16166.5 q^{19} +19744.7 q^{20} +60.1797 q^{22} -12167.0 q^{23} -49873.0 q^{25} +33100.5 q^{26} -17599.0 q^{28} +92885.5 q^{29} -52229.9 q^{31} +142364. q^{32} +84125.5 q^{34} -25181.7 q^{35} -76601.8 q^{37} -52460.7 q^{38} +133888. q^{40} -108892. q^{41} -791546. q^{43} -2178.50 q^{44} -39482.2 q^{46} +992576. q^{47} -801098. q^{49} -161839. q^{50} -1.19824e6 q^{52} -1.60859e6 q^{53} -3117.14 q^{55} -119337. q^{56} +301416. q^{58} -733660. q^{59} +114090. q^{61} -169487. q^{62} -1.13179e6 q^{64} -1.71452e6 q^{65} +447189. q^{67} -3.04534e6 q^{68} -81715.2 q^{70} +671180. q^{71} -406192. q^{73} -248575. q^{74} +1.89908e6 q^{76} +2778.39 q^{77} +883156. q^{79} -2.09286e6 q^{80} -353358. q^{82} +4.07716e6 q^{83} -4.35747e6 q^{85} -2.56858e6 q^{86} -14772.3 q^{88} -5.07507e6 q^{89} +1.52819e6 q^{91} +1.42926e6 q^{92} +3.22093e6 q^{94} +2.71732e6 q^{95} -1.23228e6 q^{97} -2.59958e6 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 270 q^{4} + 266 q^{5} - 496 q^{7} - 1422 q^{8}+O(q^{10}) $ 5 * q + 270 * q^4 + 266 * q^5 - 496 * q^7 - 1422 * q^8	$ 5 q + 270 q^{4} + 266 q^{5} - 496 q^{7} - 1422 q^{8} + 1452 q^{10} + 1148 q^{11} - 642 q^{13} - 5756 q^{14} - 22606 q^{16} + 5798 q^{17} - 6036 q^{19} + 27376 q^{20} - 97896 q^{22} - 60835 q^{23} - 262477 q^{25} + 355992 q^{26} - 507124 q^{28} + 169162 q^{29} - 199640 q^{31} + 284794 q^{32} - 1027740 q^{34} + 137680 q^{35} - 202002 q^{37} + 554924 q^{38} - 340904 q^{40} - 541282 q^{41} - 909596 q^{43} + 1236032 q^{44} - 80208 q^{47} + 850589 q^{49} + 941416 q^{50} + 146940 q^{52} + 278138 q^{53} - 933560 q^{55} + 539932 q^{56} - 3522712 q^{58} + 3177380 q^{59} + 147782 q^{61} - 4606456 q^{62} - 4142622 q^{64} - 3877332 q^{65} - 464916 q^{67} - 7513072 q^{68} + 2093200 q^{70} - 1576792 q^{71} - 38190 q^{73} - 12164864 q^{74} + 6889436 q^{76} - 10332384 q^{77} - 3913336 q^{79} - 6334776 q^{80} + 6799360 q^{82} - 15774716 q^{83} - 8520740 q^{85} - 24874084 q^{86} + 53216 q^{88} - 1116482 q^{89} - 27369552 q^{91} - 3285090 q^{92} - 7153744 q^{94} + 6067832 q^{95} - 15738566 q^{97} - 11730488 q^{98}+O(q^{100}) $ 5 * q + 270 * q^4 + 266 * q^5 - 496 * q^7 - 1422 * q^8 + 1452 * q^10 + 1148 * q^11 - 642 * q^13 - 5756 * q^14 - 22606 * q^16 + 5798 * q^17 - 6036 * q^19 + 27376 * q^20 - 97896 * q^22 - 60835 * q^23 - 262477 * q^25 + 355992 * q^26 - 507124 * q^28 + 169162 * q^29 - 199640 * q^31 + 284794 * q^32 - 1027740 * q^34 + 137680 * q^35 - 202002 * q^37 + 554924 * q^38 - 340904 * q^40 - 541282 * q^41 - 909596 * q^43 + 1236032 * q^44 - 80208 * q^47 + 850589 * q^49 + 941416 * q^50 + 146940 * q^52 + 278138 * q^53 - 933560 * q^55 + 539932 * q^56 - 3522712 * q^58 + 3177380 * q^59 + 147782 * q^61 - 4606456 * q^62 - 4142622 * q^64 - 3877332 * q^65 - 464916 * q^67 - 7513072 * q^68 + 2093200 * q^70 - 1576792 * q^71 - 38190 * q^73 - 12164864 * q^74 + 6889436 * q^76 - 10332384 * q^77 - 3913336 * q^79 - 6334776 * q^80 + 6799360 * q^82 - 15774716 * q^83 - 8520740 * q^85 - 24874084 * q^86 + 53216 * q^88 - 1116482 * q^89 - 27369552 * q^91 - 3285090 * q^92 - 7153744 * q^94 + 6067832 * q^95 - 15738566 * q^97 - 11730488 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	3.24502	0.286822	0.143411	−	0.989663i	$-0.454193\pi$
$2$	3.24502	0.286822	0.143411	+	0.989663i	$0.454193\pi$
$3$	0	0
$3$	0	0
$4$	−117.470	−0.917733
$5$	−168.083	−0.601353	−0.300677	−	0.953726i	$-0.597212\pi$
$5$	−168.083	−0.601353	−0.300677	+	0.953726i	$0.597212\pi$
$6$	0	0
$7$	149.817	0.165089	0.0825444	−	0.996587i	$-0.473695\pi$
$7$	149.817	0.165089	0.0825444	+	0.996587i	$0.473695\pi$
$8$	−796.555	−0.550048
$9$	0	0
$10$	−545.434	−0.172481
$11$	18.5452	0.00420105	0.00210052	−	0.999998i	$-0.499331\pi$
$11$	18.5452	0.00420105	0.00210052	+	0.999998i	$0.499331\pi$
$12$	0	0
$13$	10200.4	1.28770	0.643851	−	0.765151i	$-0.277336\pi$
$13$	10200.4	1.28770	0.643851	+	0.765151i	$0.277336\pi$
$14$	486.159	0.0473511
$15$	0	0
$16$	12451.3	0.759967
$17$	25924.5	1.27979	0.639895	−	0.768462i	$-0.278978\pi$
$17$	25924.5	1.27979	0.639895	+	0.768462i	$0.278978\pi$
$18$	0	0
$19$	−16166.5	−0.540728	−0.270364	−	0.962758i	$-0.587144\pi$
$19$	−16166.5	−0.540728	−0.270364	+	0.962758i	$0.587144\pi$
$20$	19744.7	0.551882
$21$	0	0
$22$	60.1797	0.00120495
$23$	−12167.0	−0.208514
$23$	−12167.0	−0.208514
$24$	0	0
$25$	−49873.0	−0.638374
$26$	33100.5	0.369341
$27$	0	0
$28$	−17599.0	−0.151507
$29$	92885.5	0.707221	0.353610	−	0.935393i	$-0.384954\pi$
$29$	92885.5	0.707221	0.353610	+	0.935393i	$0.384954\pi$
$30$	0	0
$31$	−52229.9	−0.314886	−0.157443	−	0.987528i	$-0.550325\pi$
$31$	−52229.9	−0.314886	−0.157443	+	0.987528i	$0.550325\pi$
$32$	142364.	0.768024
$33$	0	0
$34$	84125.5	0.367072
$35$	−25181.7	−0.0992766
$36$	0	0
$37$	−76601.8	−0.248618	−0.124309	−	0.992244i	$-0.539671\pi$
$37$	−76601.8	−0.248618	−0.124309	+	0.992244i	$0.539671\pi$
$38$	−52460.7	−0.155093
$39$	0	0
$40$	133888.	0.330773
$41$	−108892.	−0.246748	−0.123374	−	0.992360i	$-0.539371\pi$
$41$	−108892.	−0.246748	−0.123374	+	0.992360i	$0.539371\pi$
$42$	0	0
$43$	−791546.	−1.51823	−0.759113	−	0.650958i	$-0.774367\pi$
$43$	−791546.	−1.51823	−0.759113	+	0.650958i	$0.774367\pi$
$44$	−2178.50	−0.00385544
$45$	0	0
$46$	−39482.2	−0.0598066
$47$	992576.	1.39451	0.697254	−	0.716824i	$-0.254405\pi$
$47$	992576.	1.39451	0.697254	+	0.716824i	$0.254405\pi$
$48$	0	0
$49$	−801098.	−0.972746
$50$	−161839.	−0.183100
$51$	0	0
$52$	−1.19824e6	−1.18177
$53$	−1.60859e6	−1.48416	−0.742078	−	0.670313i	$-0.766160\pi$
$53$	−1.60859e6	−1.48416	−0.742078	+	0.670313i	$0.766160\pi$
$54$	0	0
$55$	−3117.14	−0.00252631
$56$	−119337.	−0.0908068
$57$	0	0
$58$	301416.	0.202847
$59$	−733660.	−0.465064	−0.232532	−	0.972589i	$-0.574701\pi$
$59$	−733660.	−0.465064	−0.232532	+	0.972589i	$0.574701\pi$
$60$	0	0
$61$	114090.	0.0643569	0.0321784	−	0.999482i	$-0.489756\pi$
$61$	114090.	0.0643569	0.0321784	+	0.999482i	$0.489756\pi$
$62$	−169487.	−0.0903163
$63$	0	0
$64$	−1.13179e6	−0.539681
$65$	−1.71452e6	−0.774364
$66$	0	0
$67$	447189.	0.181647	0.0908237	−	0.995867i	$-0.471050\pi$
$67$	447189.	0.181647	0.0908237	+	0.995867i	$0.471050\pi$
$68$	−3.04534e6	−1.17451
$69$	0	0
$70$	−81715.2	−0.0284747
$71$	671180.	0.222554	0.111277	−	0.993789i	$-0.464506\pi$
$71$	671180.	0.222554	0.111277	+	0.993789i	$0.464506\pi$
$72$	0	0
$73$	−406192.	−0.122209	−0.0611043	−	0.998131i	$-0.519462\pi$
$73$	−406192.	−0.122209	−0.0611043	+	0.998131i	$0.519462\pi$
$74$	−248575.	−0.0713092
$75$	0	0
$76$	1.89908e6	0.496244
$77$	2778.39	0.000693546 0
$78$	0	0
$79$	883156.	0.201531	0.100766	−	0.994910i	$-0.467871\pi$
$79$	883156.	0.201531	0.100766	+	0.994910i	$0.467871\pi$
$80$	−2.09286e6	−0.457009
$81$	0	0
$82$	−353358.	−0.0707728
$83$	4.07716e6	0.782680	0.391340	−	0.920246i	$-0.372012\pi$
$83$	4.07716e6	0.782680	0.391340	+	0.920246i	$0.372012\pi$
$84$	0	0
$85$	−4.35747e6	−0.769606
$86$	−2.56858e6	−0.435461
$87$	0	0
$88$	−14772.3	−0.00231078
$89$	−5.07507e6	−0.763092	−0.381546	−	0.924350i	$-0.624608\pi$
$89$	−5.07507e6	−0.763092	−0.381546	+	0.924350i	$0.624608\pi$
$90$	0	0
$91$	1.52819e6	0.212585
$92$	1.42926e6	0.191361
$93$	0	0
$94$	3.22093e6	0.399976
$95$	2.71732e6	0.325169
$96$	0	0
$97$	−1.23228e6	−0.137091	−0.0685454	−	0.997648i	$-0.521836\pi$
$97$	−1.23228e6	−0.137091	−0.0685454	+	0.997648i	$0.521836\pi$
$98$	−2.59958e6	−0.279005
$99$	0	0
$100$	5.85857e6	0.585857
$101$	−4.65370e6	−0.449442	−0.224721	−	0.974423i	$-0.572147\pi$
$101$	−4.65370e6	−0.449442	−0.224721	+	0.974423i	$0.572147\pi$
$102$	0	0
$103$	−1.60768e7	−1.44967	−0.724834	−	0.688923i	$-0.758084\pi$
$103$	−1.60768e7	−1.44967	−0.724834	+	0.688923i	$0.758084\pi$
$104$	−8.12518e6	−0.708298
$105$	0	0
$106$	−5.21991e6	−0.425689
$107$	5.90678e6	0.466131	0.233065	−	0.972461i	$-0.425124\pi$
$107$	5.90678e6	0.466131	0.233065	+	0.972461i	$0.425124\pi$
$108$	0	0
$109$	−2.42125e7	−1.79080	−0.895399	−	0.445264i	$-0.853110\pi$
$109$	−2.42125e7	−1.79080	−0.895399	+	0.445264i	$0.853110\pi$
$110$	−10115.2	−0.000724603 0
$111$	0	0
$112$	1.86541e6	0.125462
$113$	1.27303e7	0.829972	0.414986	−	0.909828i	$-0.363786\pi$
$113$	1.27303e7	0.829972	0.414986	+	0.909828i	$0.363786\pi$
$114$	0	0
$115$	2.04507e6	0.125391
$116$	−1.09112e7	−0.649040
$117$	0	0
$118$	−2.38074e6	−0.133391
$119$	3.88392e6	0.211279
$120$	0	0
$121$	−1.94868e7	−0.999982
$122$	370226.	0.0184590
$123$	0	0
$124$	6.13544e6	0.288981
$125$	2.15143e7	0.985242
$126$	0	0
$127$	−4.28814e7	−1.85762	−0.928808	−	0.370562i	$-0.879165\pi$
$127$	−4.28814e7	−1.85762	−0.928808	+	0.370562i	$0.879165\pi$
$128$	−2.18953e7	−0.922816
$129$	0	0
$130$	−5.56364e6	−0.222105
$131$	1.56206e7	0.607084	0.303542	−	0.952818i	$-0.401831\pi$
$131$	1.56206e7	0.607084	0.303542	+	0.952818i	$0.401831\pi$
$132$	0	0
$133$	−2.42202e6	−0.0892682
$134$	1.45114e6	0.0521005
$135$	0	0
$136$	−2.06503e7	−0.703946
$137$	−2.94587e7	−0.978793	−0.489397	−	0.872061i	$-0.662783\pi$
$137$	−2.94587e7	−0.978793	−0.489397	+	0.872061i	$0.662783\pi$
$138$	0	0
$139$	2.71105e7	0.856219	0.428110	−	0.903727i	$-0.359180\pi$
$139$	2.71105e7	0.856219	0.428110	+	0.903727i	$0.359180\pi$
$140$	2.95809e6	0.0911095
$141$	0	0
$142$	2.17799e6	0.0638333
$143$	189169.	0.00540970
$144$	0	0
$145$	−1.56125e7	−0.425289
$146$	−1.31810e6	−0.0350521
$147$	0	0
$148$	8.99840e6	0.228165
$149$	−2.30596e7	−0.571085	−0.285542	−	0.958366i	$-0.592174\pi$
$149$	−2.30596e7	−0.571085	−0.285542	+	0.958366i	$0.592174\pi$
$150$	0	0
$151$	−5.65968e7	−1.33774	−0.668871	−	0.743378i	$-0.733222\pi$
$151$	−5.65968e7	−1.33774	−0.668871	+	0.743378i	$0.733222\pi$
$152$	1.28775e7	0.297427
$153$	0	0
$154$	9015.93	0.000198924 0
$155$	8.77898e6	0.189358
$156$	0	0
$157$	1.82778e7	0.376943	0.188472	−	0.982079i	$-0.439647\pi$
$157$	1.82778e7	0.376943	0.188472	+	0.982079i	$0.439647\pi$
$158$	2.86586e6	0.0578036
$159$	0	0
$160$	−2.39290e7	−0.461854
$161$	−1.82282e6	−0.0344234
$162$	0	0
$163$	4.46297e7	0.807174	0.403587	−	0.914941i	$-0.367763\pi$
$163$	4.46297e7	0.807174	0.403587	+	0.914941i	$0.367763\pi$
$164$	1.27916e7	0.226449
$165$	0	0
$166$	1.32305e7	0.224490
$167$	9.93656e7	1.65093	0.825465	−	0.564453i	$-0.190913\pi$
$167$	9.93656e7	1.65093	0.825465	+	0.564453i	$0.190913\pi$
$168$	0	0
$169$	4.12995e7	0.658175
$170$	−1.41401e7	−0.220740
$171$	0	0
$172$	9.29828e7	1.39333
$173$	−7.06790e7	−1.03784	−0.518919	−	0.854824i	$-0.673665\pi$
$173$	−7.06790e7	−1.03784	−0.518919	+	0.854824i	$0.673665\pi$
$174$	0	0
$175$	−7.47181e6	−0.105388
$176$	230912.	0.00319266
$177$	0	0
$178$	−1.64687e7	−0.218872
$179$	−5.86892e7	−0.764844	−0.382422	−	0.923988i	$-0.624910\pi$
$179$	−5.86892e7	−0.764844	−0.382422	+	0.923988i	$0.624910\pi$
$180$	0	0
$181$	−7.29280e7	−0.914154	−0.457077	−	0.889427i	$-0.651104\pi$
$181$	−7.29280e7	−0.914154	−0.457077	+	0.889427i	$0.651104\pi$
$182$	4.95901e6	0.0609741
$183$	0	0
$184$	9.69168e6	0.114693
$185$	1.28755e7	0.149507
$186$	0	0
$187$	480775.	0.00537646
$188$	−1.16598e8	−1.27979
$189$	0	0
$190$	8.81778e6	0.0932656
$191$	−1.28471e8	−1.33410	−0.667049	−	0.745014i	$-0.732443\pi$
$191$	−1.28471e8	−1.33410	−0.667049	+	0.745014i	$0.732443\pi$
$192$	0	0
$193$	1.81759e8	1.81989	0.909945	−	0.414730i	$-0.136124\pi$
$193$	1.81759e8	1.81989	0.909945	+	0.414730i	$0.136124\pi$
$194$	−3.99878e6	−0.0393207
$195$	0	0
$196$	9.41048e7	0.892721
$197$	−5.33642e7	−0.497300	−0.248650	−	0.968593i	$-0.579987\pi$
$197$	−5.33642e7	−0.497300	−0.248650	+	0.968593i	$0.579987\pi$
$198$	0	0
$199$	4.64692e7	0.418003	0.209002	−	0.977915i	$-0.432979\pi$
$199$	4.64692e7	0.418003	0.209002	+	0.977915i	$0.432979\pi$
$200$	3.97266e7	0.351137
$201$	0	0
$202$	−1.51014e7	−0.128910
$203$	1.39158e7	0.116754
$204$	0	0
$205$	1.83030e7	0.148383
$206$	−5.21695e7	−0.415797
$207$	0	0
$208$	1.27008e8	0.978611
$209$	−299812.	−0.00227163
$210$	0	0
$211$	−3.75261e7	−0.275008	−0.137504	−	0.990501i	$-0.543908\pi$
$211$	−3.75261e7	−0.275008	−0.137504	+	0.990501i	$0.543908\pi$
$212$	1.88961e8	1.36206
$213$	0	0
$214$	1.91676e7	0.133697
$215$	1.33046e8	0.912991
$216$	0	0
$217$	−7.82492e6	−0.0519841
$218$	−7.85701e7	−0.513641
$219$	0	0
$220$	366170.	0.00231848
$221$	2.64440e8	1.64799
$222$	0	0
$223$	−1.04665e8	−0.632028	−0.316014	−	0.948755i	$-0.602345\pi$
$223$	−1.04665e8	−0.632028	−0.316014	+	0.948755i	$0.602345\pi$
$224$	2.13285e7	0.126792
$225$	0	0
$226$	4.13100e7	0.238054
$227$	2.30736e7	0.130926	0.0654629	−	0.997855i	$-0.479148\pi$
$227$	2.30736e7	0.130926	0.0654629	+	0.997855i	$0.479148\pi$
$228$	0	0
$229$	2.26806e8	1.24804	0.624022	−	0.781407i	$-0.285497\pi$
$229$	2.26806e8	1.24804	0.624022	+	0.781407i	$0.285497\pi$
$230$	6.63630e6	0.0359649
$231$	0	0
$232$	−7.39884e7	−0.389006
$233$	2.91144e8	1.50787	0.753933	−	0.656952i	$-0.228154\pi$
$233$	2.91144e8	1.50787	0.753933	+	0.656952i	$0.228154\pi$
$234$	0	0
$235$	−1.66835e8	−0.838592
$236$	8.61829e7	0.426804
$237$	0	0
$238$	1.26034e7	0.0605995
$239$	−1.45226e8	−0.688098	−0.344049	−	0.938952i	$-0.611799\pi$
$239$	−1.45226e8	−0.688098	−0.344049	+	0.938952i	$0.611799\pi$
$240$	0	0
$241$	−2.91763e8	−1.34267	−0.671336	−	0.741153i	$-0.734279\pi$
$241$	−2.91763e8	−1.34267	−0.671336	+	0.741153i	$0.734279\pi$
$242$	−6.32352e7	−0.286817
$243$	0	0
$244$	−1.34022e7	−0.0590624
$245$	1.34651e8	0.584964
$246$	0	0
$247$	−1.64905e8	−0.696297
$248$	4.16040e7	0.173203
$249$	0	0
$250$	6.98145e7	0.282589
$251$	3.16146e7	0.126191	0.0630957	−	0.998007i	$-0.479903\pi$
$251$	3.16146e7	0.126191	0.0630957	+	0.998007i	$0.479903\pi$
$252$	0	0
$253$	−225640.	−0.000875979 0
$254$	−1.39151e8	−0.532805
$255$	0	0
$256$	7.38189e7	0.274997
$257$	−4.73473e6	−0.0173992	−0.00869960	−	0.999962i	$-0.502769\pi$
$257$	−4.73473e6	−0.0173992	−0.00869960	+	0.999962i	$0.502769\pi$
$258$	0	0
$259$	−1.14762e7	−0.0410441
$260$	2.01404e8	0.710659
$261$	0	0
$262$	5.06893e7	0.174125
$263$	−6.07617e7	−0.205961	−0.102980	−	0.994683i	$-0.532838\pi$
$263$	−6.07617e7	−0.205961	−0.102980	+	0.994683i	$0.532838\pi$
$264$	0	0
$265$	2.70377e8	0.892502
$266$	−7.85950e6	−0.0256041
$267$	0	0
$268$	−5.25312e7	−0.166704
$269$	8.38261e7	0.262571	0.131285	−	0.991345i	$-0.458090\pi$
$269$	8.38261e7	0.262571	0.131285	+	0.991345i	$0.458090\pi$
$270$	0	0
$271$	2.81295e8	0.858558	0.429279	−	0.903172i	$-0.358768\pi$
$271$	2.81295e8	0.858558	0.429279	+	0.903172i	$0.358768\pi$
$272$	3.22793e8	0.972598
$273$	0	0
$274$	−9.55940e7	−0.280740
$275$	−924906.	−0.00268184
$276$	0	0
$277$	3.90136e8	1.10290	0.551451	−	0.834207i	$-0.314074\pi$
$277$	3.90136e8	1.10290	0.551451	+	0.834207i	$0.314074\pi$
$278$	8.79740e7	0.245583
$279$	0	0
$280$	2.00586e7	0.0546069
$281$	−2.37822e8	−0.639410	−0.319705	−	0.947517i	$-0.603584\pi$
$281$	−2.37822e8	−0.639410	−0.319705	+	0.947517i	$0.603584\pi$
$282$	0	0
$283$	1.71342e8	0.449378	0.224689	−	0.974431i	$-0.427863\pi$
$283$	1.71342e8	0.449378	0.224689	+	0.974431i	$0.427863\pi$
$284$	−7.88434e7	−0.204245
$285$	0	0
$286$	613856.	0.00155162
$287$	−1.63139e7	−0.0407353
$288$	0	0
$289$	2.61739e8	0.637862
$290$	−5.06629e7	−0.121982
$291$	0	0
$292$	4.77153e7	0.112155
$293$	−1.93284e8	−0.448909	−0.224455	−	0.974485i	$-0.572060\pi$
$293$	−1.93284e8	−0.448909	−0.224455	+	0.974485i	$0.572060\pi$
$294$	0	0
$295$	1.23316e8	0.279668
$296$	6.10176e7	0.136752
$297$	0	0
$298$	−7.48291e7	−0.163800
$299$	−1.24108e8	−0.268504
$300$	0	0
$301$	−1.18587e8	−0.250642
$302$	−1.83658e8	−0.383694
$303$	0	0
$304$	−2.01294e8	−0.410936
$305$	−1.91767e7	−0.0387012
$306$	0	0
$307$	−4.20067e8	−0.828579	−0.414290	−	0.910145i	$-0.635970\pi$
$307$	−4.20067e8	−0.828579	−0.414290	+	0.910145i	$0.635970\pi$
$308$	−326377.	−0.000636490 0
$309$	0	0
$310$	2.84880e7	0.0543120
$311$	4.75218e8	0.895842	0.447921	−	0.894073i	$-0.352165\pi$
$311$	4.75218e8	0.895842	0.447921	+	0.894073i	$0.352165\pi$
$312$	0	0
$313$	8.20300e8	1.51205	0.756027	−	0.654540i	$-0.227138\pi$
$313$	8.20300e8	1.51205	0.756027	+	0.654540i	$0.227138\pi$
$314$	5.93120e7	0.108116
$315$	0	0
$316$	−1.03744e8	−0.184952
$317$	−9.09355e8	−1.60334	−0.801671	−	0.597765i	$-0.796055\pi$
$317$	−9.09355e8	−1.60334	−0.801671	+	0.597765i	$0.796055\pi$
$318$	0	0
$319$	1.72258e6	0.00297107
$320$	1.90236e8	0.324539
$321$	0	0
$322$	−5.91510e6	−0.00987339
$323$	−4.19109e8	−0.692019
$324$	0	0
$325$	−5.08724e8	−0.822036
$326$	1.44824e8	0.231515
$327$	0	0
$328$	8.67387e7	0.135723
$329$	1.48705e8	0.230218
$330$	0	0
$331$	−2.32731e8	−0.352741	−0.176370	−	0.984324i	$-0.556436\pi$
$331$	−2.32731e8	−0.352741	−0.176370	+	0.984324i	$0.556436\pi$
$332$	−4.78943e8	−0.718291
$333$	0	0
$334$	3.22444e8	0.473523
$335$	−7.51650e7	−0.109234
$336$	0	0
$337$	2.05391e8	0.292332	0.146166	−	0.989260i	$-0.453307\pi$
$337$	2.05391e8	0.292332	0.146166	+	0.989260i	$0.453307\pi$
$338$	1.34018e8	0.188779
$339$	0	0
$340$	5.11871e8	0.706293
$341$	−968616.	−0.00132285
$342$	0	0
$343$	−2.43399e8	−0.325678
$344$	6.30510e8	0.835098
$345$	0	0
$346$	−2.29355e8	−0.297675
$347$	−4.46363e8	−0.573502	−0.286751	−	0.958005i	$-0.592575\pi$
$347$	−4.46363e8	−0.573502	−0.286751	+	0.958005i	$0.592575\pi$
$348$	0	0
$349$	−7.98585e8	−1.00562	−0.502808	−	0.864398i	$-0.667700\pi$
$349$	−7.98585e8	−1.00562	−0.502808	+	0.864398i	$0.667700\pi$
$350$	−2.42462e7	−0.0302277
$351$	0	0
$352$	2.64017e6	0.00322651
$353$	−1.49174e9	−1.80502	−0.902510	−	0.430670i	$-0.858277\pi$
$353$	−1.49174e9	−1.80502	−0.902510	+	0.430670i	$0.858277\pi$
$354$	0	0
$355$	−1.12814e8	−0.133833
$356$	5.96167e8	0.700314
$357$	0	0
$358$	−1.90448e8	−0.219374
$359$	−9.03992e8	−1.03118	−0.515590	−	0.856836i	$-0.672427\pi$
$359$	−9.03992e8	−1.03118	−0.515590	+	0.856836i	$0.672427\pi$
$360$	0	0
$361$	−6.32515e8	−0.707613
$362$	−2.36653e8	−0.262199
$363$	0	0
$364$	−1.79516e8	−0.195096
$365$	6.82741e7	0.0734905
$366$	0	0
$367$	−5.78376e8	−0.610772	−0.305386	−	0.952229i	$-0.598786\pi$
$367$	−5.78376e8	−0.610772	−0.305386	+	0.952229i	$0.598786\pi$
$368$	−1.51495e8	−0.158464
$369$	0	0
$370$	4.17813e7	0.0428820
$371$	−2.40994e8	−0.245018
$372$	0	0
$373$	−9.27782e8	−0.925689	−0.462844	−	0.886440i	$-0.653171\pi$
$373$	−9.27782e8	−0.925689	−0.462844	+	0.886440i	$0.653171\pi$
$374$	1.56013e6	0.00154209
$375$	0	0
$376$	−7.90641e8	−0.767047
$377$	9.47469e8	0.910689
$378$	0	0
$379$	−1.54337e9	−1.45624	−0.728119	−	0.685451i	$-0.759605\pi$
$379$	−1.54337e9	−1.45624	−0.728119	+	0.685451i	$0.759605\pi$
$380$	−3.19204e8	−0.298418
$381$	0	0
$382$	−4.16890e8	−0.382649
$383$	−1.01378e8	−0.0922040	−0.0461020	−	0.998937i	$-0.514680\pi$
$383$	−1.01378e8	−0.0922040	−0.0461020	+	0.998937i	$0.514680\pi$
$384$	0	0
$385$	−467001.	−0.000417066 0
$386$	5.89811e8	0.521985
$387$	0	0
$388$	1.44756e8	0.125813
$389$	6.88033e8	0.592633	0.296316	−	0.955090i	$-0.404242\pi$
$389$	6.88033e8	0.592633	0.296316	+	0.955090i	$0.404242\pi$
$390$	0	0
$391$	−3.15423e8	−0.266855
$392$	6.38119e8	0.535057
$393$	0	0
$394$	−1.73168e8	−0.142637
$395$	−1.48444e8	−0.121191
$396$	0	0
$397$	5.50236e7	0.0441349	0.0220674	−	0.999756i	$-0.492975\pi$
$397$	5.50236e7	0.0441349	0.0220674	+	0.999756i	$0.492975\pi$
$398$	1.50794e8	0.119893
$399$	0	0
$400$	−6.20984e8	−0.485143
$401$	−1.90663e9	−1.47660	−0.738299	−	0.674474i	$-0.764370\pi$
$401$	−1.90663e9	−1.47660	−0.738299	+	0.674474i	$0.764370\pi$
$402$	0	0
$403$	−5.32766e8	−0.405479
$404$	5.46669e8	0.412468
$405$	0	0
$406$	4.51571e7	0.0334877
$407$	−1.42060e6	−0.00104446
$408$	0	0
$409$	−1.37032e9	−0.990351	−0.495175	−	0.868793i	$-0.664896\pi$
$409$	−1.37032e9	−0.990351	−0.495175	+	0.868793i	$0.664896\pi$
$410$	5.93936e7	0.0425595
$411$	0	0
$412$	1.88854e9	1.33041
$413$	−1.09915e8	−0.0767768
$414$	0	0
$415$	−6.85302e8	−0.470667
$416$	1.45217e9	0.988985
$417$	0	0
$418$	−972897.	−0.000651553 0
$419$	2.11477e9	1.40447	0.702237	−	0.711943i	$-0.252185\pi$
$419$	2.11477e9	1.40447	0.702237	+	0.711943i	$0.252185\pi$
$420$	0	0
$421$	−1.59467e9	−1.04156	−0.520780	−	0.853691i	$-0.674359\pi$
$421$	−1.59467e9	−1.04156	−0.520780	+	0.853691i	$0.674359\pi$
$422$	−1.21773e8	−0.0788783
$423$	0	0
$424$	1.28133e9	0.816358
$425$	−1.29293e9	−0.816985
$426$	0	0
$427$	1.70927e7	0.0106246
$428$	−6.93869e8	−0.427784
$429$	0	0
$430$	4.31736e8	0.261866
$431$	7.74220e6	0.00465794	0.00232897	−	0.999997i	$-0.499259\pi$
$431$	7.74220e6	0.00465794	0.00232897	+	0.999997i	$0.499259\pi$
$432$	0	0
$433$	−7.28017e8	−0.430957	−0.215478	−	0.976509i	$-0.569131\pi$
$433$	−7.28017e8	−0.430957	−0.215478	+	0.976509i	$0.569131\pi$
$434$	−2.53920e7	−0.0149102
$435$	0	0
$436$	2.84424e9	1.64347
$437$	1.96698e8	0.112750
$438$	0	0
$439$	−5.29464e8	−0.298683	−0.149341	−	0.988786i	$-0.547715\pi$
$439$	−5.29464e8	−0.298683	−0.149341	+	0.988786i	$0.547715\pi$
$440$	2.48298e6	0.00138960
$441$	0	0
$442$	8.58113e8	0.472679
$443$	−2.17075e9	−1.18631	−0.593154	−	0.805089i	$-0.702118\pi$
$443$	−2.17075e9	−1.18631	−0.593154	+	0.805089i	$0.702118\pi$
$444$	0	0
$445$	8.53034e8	0.458888
$446$	−3.39642e8	−0.181280
$447$	0	0
$448$	−1.69562e8	−0.0890952
$449$	−2.08538e9	−1.08723	−0.543616	−	0.839334i	$-0.682945\pi$
$449$	−2.08538e9	−1.08723	−0.543616	+	0.839334i	$0.682945\pi$
$450$	0	0
$451$	−2.01943e6	−0.00103660
$452$	−1.49542e9	−0.761693
$453$	0	0
$454$	7.48744e7	0.0375524
$455$	−2.56863e8	−0.127839
$456$	0	0
$457$	2.95584e9	1.44868	0.724342	−	0.689440i	$-0.242143\pi$
$457$	2.95584e9	1.44868	0.724342	+	0.689440i	$0.242143\pi$
$458$	7.35990e8	0.357967
$459$	0	0
$460$	−2.40234e8	−0.115075
$461$	2.49440e9	1.18581	0.592903	−	0.805274i	$-0.297982\pi$
$461$	2.49440e9	1.18581	0.592903	+	0.805274i	$0.297982\pi$
$462$	0	0
$463$	−3.46592e9	−1.62288	−0.811438	−	0.584439i	$-0.801315\pi$
$463$	−3.46592e9	−1.62288	−0.811438	+	0.584439i	$0.801315\pi$
$464$	1.15655e9	0.537464
$465$	0	0
$466$	9.44770e8	0.432489
$467$	3.83153e9	1.74086	0.870428	−	0.492296i	$-0.163842\pi$
$467$	3.83153e9	1.74086	0.870428	+	0.492296i	$0.163842\pi$
$468$	0	0
$469$	6.69964e7	0.0299879
$470$	−5.41385e8	−0.240527
$471$	0	0
$472$	5.84400e8	0.255808
$473$	−1.46794e7	−0.00637815
$474$	0	0
$475$	8.06273e8	0.345187
$476$	−4.56244e8	−0.193898
$477$	0	0
$478$	−4.71260e8	−0.197362
$479$	2.73741e9	1.13806	0.569030	−	0.822317i	$-0.307319\pi$
$479$	2.73741e9	1.13806	0.569030	+	0.822317i	$0.307319\pi$
$480$	0	0
$481$	−7.81369e8	−0.320146
$482$	−9.46777e8	−0.385108
$483$	0	0
$484$	2.28911e9	0.917717
$485$	2.07126e8	0.0824400
$486$	0	0
$487$	−9.56818e8	−0.375386	−0.187693	−	0.982228i	$-0.560101\pi$
$487$	−9.56818e8	−0.375386	−0.187693	+	0.982228i	$0.560101\pi$
$488$	−9.08793e7	−0.0353994
$489$	0	0
$490$	4.36946e8	0.167781
$491$	−2.40556e9	−0.917132	−0.458566	−	0.888660i	$-0.651637\pi$
$491$	−2.40556e9	−0.917132	−0.458566	+	0.888660i	$0.651637\pi$
$492$	0	0
$493$	2.40801e9	0.905094
$494$	−5.35120e8	−0.199713
$495$	0	0
$496$	−6.50330e8	−0.239303
$497$	1.00554e8	0.0367411
$498$	0	0
$499$	1.17148e9	0.422068	0.211034	−	0.977479i	$-0.432317\pi$
$499$	1.17148e9	0.422068	0.211034	+	0.977479i	$0.432317\pi$
$500$	−2.52728e9	−0.904189
$501$	0	0
$502$	1.02590e8	0.0361945
$503$	1.89152e9	0.662710	0.331355	−	0.943506i	$-0.392494\pi$
$503$	1.89152e9	0.662710	0.331355	+	0.943506i	$0.392494\pi$
$504$	0	0
$505$	7.82209e8	0.270273
$506$	−732206.	−0.000251250 0
$507$	0	0
$508$	5.03727e9	1.70480
$509$	−2.84363e9	−0.955786	−0.477893	−	0.878418i	$-0.658599\pi$
$509$	−2.84363e9	−0.955786	−0.477893	+	0.878418i	$0.658599\pi$
$510$	0	0
$511$	−6.08544e7	−0.0201752
$512$	3.04214e9	1.00169
$513$	0	0
$514$	−1.53643e7	−0.00499047
$515$	2.70224e9	0.871763
$516$	0	0
$517$	1.84075e7	0.00585840
$518$	−3.72407e7	−0.0117724
$519$	0	0
$520$	1.36571e9	0.425937
$521$	−1.32906e9	−0.411731	−0.205865	−	0.978580i	$-0.566001\pi$
$521$	−1.32906e9	−0.411731	−0.205865	+	0.978580i	$0.566001\pi$
$522$	0	0
$523$	2.97968e9	0.910779	0.455390	−	0.890292i	$-0.349500\pi$
$523$	2.97968e9	0.910779	0.455390	+	0.890292i	$0.349500\pi$
$524$	−1.83495e9	−0.557141
$525$	0	0
$526$	−1.97173e8	−0.0590741
$527$	−1.35403e9	−0.402988
$528$	0	0
$529$	1.48036e8	0.0434783
$530$	8.77380e8	0.255989
$531$	0	0
$532$	2.84514e8	0.0819244
$533$	−1.11074e9	−0.317738
$534$	0	0
$535$	−9.92832e8	−0.280309
$536$	−3.56210e8	−0.0999148
$537$	0	0
$538$	2.72017e8	0.0753111
$539$	−1.48565e7	−0.00408655
$540$	0	0
$541$	−2.27719e9	−0.618313	−0.309156	−	0.951011i	$-0.600047\pi$
$541$	−2.27719e9	−0.618313	−0.309156	+	0.951011i	$0.600047\pi$
$542$	9.12809e8	0.246253
$543$	0	0
$544$	3.69071e9	0.982909
$545$	4.06972e9	1.07690
$546$	0	0
$547$	2.31024e9	0.603534	0.301767	−	0.953382i	$-0.402424\pi$
$547$	2.31024e9	0.603534	0.301767	+	0.953382i	$0.402424\pi$
$548$	3.46050e9	0.898271
$549$	0	0
$550$	−3.00134e6	−0.000769212 0
$551$	−1.50164e9	−0.382414
$552$	0	0
$553$	1.32312e8	0.0332705
$554$	1.26600e9	0.316337
$555$	0	0
$556$	−3.18466e9	−0.785781
$557$	2.07806e9	0.509523	0.254762	−	0.967004i	$-0.418003\pi$
$557$	2.07806e9	0.509523	0.254762	+	0.967004i	$0.418003\pi$
$558$	0	0
$559$	−8.07408e9	−1.95502
$560$	−3.13545e8	−0.0754470
$561$	0	0
$562$	−7.71737e8	−0.183397
$563$	−8.30273e9	−1.96084	−0.980418	−	0.196925i	$-0.936904\pi$
$563$	−8.30273e9	−1.96084	−0.980418	+	0.196925i	$0.936904\pi$
$564$	0	0
$565$	−2.13975e9	−0.499106
$566$	5.56009e8	0.128892
$567$	0	0
$568$	−5.34632e8	−0.122415
$569$	2.36999e9	0.539329	0.269664	−	0.962954i	$-0.413087\pi$
$569$	2.36999e9	0.539329	0.269664	+	0.962954i	$0.413087\pi$
$570$	0	0
$571$	−2.85722e9	−0.642270	−0.321135	−	0.947033i	$-0.604064\pi$
$571$	−2.85722e9	−0.642270	−0.321135	+	0.947033i	$0.604064\pi$
$572$	−2.22216e7	−0.00496466
$573$	0	0
$574$	−5.29390e7	−0.0116838
$575$	6.06805e8	0.133110
$576$	0	0
$577$	5.93632e9	1.28648	0.643238	−	0.765666i	$-0.277590\pi$
$577$	5.93632e9	1.28648	0.643238	+	0.765666i	$0.277590\pi$
$578$	8.49350e8	0.182953
$579$	0	0
$580$	1.83400e9	0.390302
$581$	6.10827e8	0.129212
$582$	0	0
$583$	−2.98317e7	−0.00623501
$584$	3.23554e8	0.0672206
$585$	0	0
$586$	−6.27210e8	−0.128757
$587$	−3.99412e8	−0.0815057	−0.0407529	−	0.999169i	$-0.512976\pi$
$587$	−3.99412e8	−0.0815057	−0.0407529	+	0.999169i	$0.512976\pi$
$588$	0	0
$589$	8.44376e8	0.170268
$590$	4.00163e8	0.0802149
$591$	0	0
$592$	−9.53792e8	−0.188942
$593$	−4.93660e9	−0.972157	−0.486078	−	0.873915i	$-0.661573\pi$
$593$	−4.93660e9	−0.972157	−0.486078	+	0.873915i	$0.661573\pi$
$594$	0	0
$595$	−6.52823e8	−0.127053
$596$	2.70881e9	0.524103
$597$	0	0
$598$	−4.02734e8	−0.0770130
$599$	6.69136e9	1.27210	0.636049	−	0.771649i	$-0.280568\pi$
$599$	6.69136e9	1.27210	0.636049	+	0.771649i	$0.280568\pi$
$600$	0	0
$601$	−2.24773e9	−0.422361	−0.211181	−	0.977447i	$-0.567731\pi$
$601$	−2.24773e9	−0.422361	−0.211181	+	0.977447i	$0.567731\pi$
$602$	−3.84817e8	−0.0718897
$603$	0	0
$604$	6.64841e9	1.22769
$605$	3.27541e9	0.601343
$606$	0	0
$607$	8.07058e9	1.46468	0.732342	−	0.680937i	$-0.238427\pi$
$607$	8.07058e9	1.46468	0.732342	+	0.680937i	$0.238427\pi$
$608$	−2.30153e9	−0.415292
$609$	0	0
$610$	−6.22288e7	−0.0111004
$611$	1.01247e10	1.79571
$612$	0	0
$613$	3.17148e9	0.556097	0.278048	−	0.960567i	$-0.410312\pi$
$613$	3.17148e9	0.556097	0.278048	+	0.960567i	$0.410312\pi$
$614$	−1.36313e9	−0.237655
$615$	0	0
$616$	−2.21314e6	−0.000381484 0
$617$	3.21472e9	0.550993	0.275496	−	0.961302i	$-0.411158\pi$
$617$	3.21472e9	0.550993	0.275496	+	0.961302i	$0.411158\pi$
$618$	0	0
$619$	−3.88507e9	−0.658388	−0.329194	−	0.944262i	$-0.606777\pi$
$619$	−3.88507e9	−0.658388	−0.329194	+	0.944262i	$0.606777\pi$
$620$	−1.03127e9	−0.173780
$621$	0	0
$622$	1.54209e9	0.256947
$623$	−7.60330e8	−0.125978
$624$	0	0
$625$	2.80127e8	0.0458960
$626$	2.66189e9	0.433691
$627$	0	0
$628$	−2.14709e9	−0.345933
$629$	−1.98586e9	−0.318179
$630$	0	0
$631$	−3.88896e9	−0.616213	−0.308107	−	0.951352i	$-0.599695\pi$
$631$	−3.88896e9	−0.616213	−0.308107	+	0.951352i	$0.599695\pi$
$632$	−7.03482e8	−0.110852
$633$	0	0
$634$	−2.95088e9	−0.459874
$635$	7.20765e9	1.11708
$636$	0	0
$637$	−8.17151e9	−1.25261
$638$	5.58982e6	0.000852168 0
$639$	0	0
$640$	3.68023e9	0.554938
$641$	−1.29473e10	−1.94168	−0.970839	−	0.239731i	$-0.922941\pi$
$641$	−1.29473e10	−1.94168	−0.970839	+	0.239731i	$0.922941\pi$
$642$	0	0
$643$	1.18526e10	1.75822	0.879112	−	0.476615i	$-0.158136\pi$
$643$	1.18526e10	1.75822	0.879112	+	0.476615i	$0.158136\pi$
$644$	2.14127e8	0.0315915
$645$	0	0
$646$	−1.36002e9	−0.198486
$647$	8.17682e9	1.18691	0.593457	−	0.804866i	$-0.297763\pi$
$647$	8.17682e9	1.18691	0.593457	+	0.804866i	$0.297763\pi$
$648$	0	0
$649$	−1.36059e7	−0.00195376
$650$	−1.65082e9	−0.235778
$651$	0	0
$652$	−5.24264e9	−0.740770
$653$	−1.45664e9	−0.204718	−0.102359	−	0.994748i	$-0.532639\pi$
$653$	−1.45664e9	−0.204718	−0.102359	+	0.994748i	$0.532639\pi$
$654$	0	0
$655$	−2.62557e9	−0.365072
$656$	−1.35585e9	−0.187520
$657$	0	0
$658$	4.82550e8	0.0660315
$659$	7.97853e8	0.108598	0.0542992	−	0.998525i	$-0.482708\pi$
$659$	7.97853e8	0.108598	0.0542992	+	0.998525i	$0.482708\pi$
$660$	0	0
$661$	1.56979e8	0.0211416	0.0105708	−	0.999944i	$-0.496635\pi$
$661$	1.56979e8	0.0211416	0.0105708	+	0.999944i	$0.496635\pi$
$662$	−7.55216e8	−0.101174
$663$	0	0
$664$	−3.24768e9	−0.430512
$665$	4.07101e8	0.0536817
$666$	0	0
$667$	−1.13014e9	−0.147466
$668$	−1.16725e10	−1.51511
$669$	0	0
$670$	−2.43912e8	−0.0313308
$671$	2.11583e6	0.000270366 0
$672$	0	0
$673$	1.16317e10	1.47093	0.735463	−	0.677565i	$-0.236965\pi$
$673$	1.16317e10	1.47093	0.735463	+	0.677565i	$0.236965\pi$
$674$	6.66498e8	0.0838473
$675$	0	0
$676$	−4.85145e9	−0.604029
$677$	−1.12531e10	−1.39383	−0.696917	−	0.717152i	$-0.745445\pi$
$677$	−1.12531e10	−1.39383	−0.696917	+	0.717152i	$0.745445\pi$
$678$	0	0
$679$	−1.84616e8	−0.0226322
$680$	3.47097e9	0.423320
$681$	0	0
$682$	−3.14318e6	−0.000379423 0
$683$	2.86773e9	0.344403	0.172201	−	0.985062i	$-0.444912\pi$
$683$	2.86773e9	0.344403	0.172201	+	0.985062i	$0.444912\pi$
$684$	0	0
$685$	4.95151e9	0.588600
$686$	−7.89834e8	−0.0934117
$687$	0	0
$688$	−9.85578e9	−1.15380
$689$	−1.64082e10	−1.91115
$690$	0	0
$691$	−6.87429e9	−0.792602	−0.396301	−	0.918121i	$-0.629706\pi$
$691$	−6.87429e9	−0.792602	−0.396301	+	0.918121i	$0.629706\pi$
$692$	8.30265e9	0.952458
$693$	0	0
$694$	−1.44846e9	−0.164493
$695$	−4.55682e9	−0.514890
$696$	0	0
$697$	−2.82298e9	−0.315786
$698$	−2.59142e9	−0.288433
$699$	0	0
$700$	8.77713e8	0.0967184
$701$	−1.65668e10	−1.81646	−0.908231	−	0.418468i	$-0.862567\pi$
$701$	−1.65668e10	−1.81646	−0.908231	+	0.418468i	$0.862567\pi$
$702$	0	0
$703$	1.23839e9	0.134435
$704$	−2.09894e7	−0.00226723
$705$	0	0
$706$	−4.84073e9	−0.517719
$707$	−6.97203e8	−0.0741978
$708$	0	0
$709$	8.01915e9	0.845019	0.422510	−	0.906358i	$-0.361149\pi$
$709$	8.01915e9	0.845019	0.422510	+	0.906358i	$0.361149\pi$
$710$	−3.66085e8	−0.0383864
$711$	0	0
$712$	4.04257e9	0.419737
$713$	6.35481e8	0.0656583
$714$	0	0
$715$	−3.17961e7	−0.00325314
$716$	6.89421e9	0.701922
$717$	0	0
$718$	−2.93348e9	−0.295765
$719$	−1.97264e8	−0.0197923	−0.00989617	−	0.999951i	$-0.503150\pi$
$719$	−1.97264e8	−0.0197923	−0.00989617	+	0.999951i	$0.503150\pi$
$720$	0	0
$721$	−2.40857e9	−0.239324
$722$	−2.05253e9	−0.202959
$723$	0	0
$724$	8.56684e9	0.838949
$725$	−4.63248e9	−0.451471
$726$	0	0
$727$	−4.86101e9	−0.469198	−0.234599	−	0.972092i	$-0.575378\pi$
$727$	−4.86101e9	−0.469198	−0.234599	+	0.972092i	$0.575378\pi$
$728$	−1.21729e9	−0.116932
$729$	0	0
$730$	2.21551e8	0.0210787
$731$	−2.05204e10	−1.94301
$732$	0	0
$733$	7.01036e9	0.657471	0.328735	−	0.944422i	$-0.393378\pi$
$733$	7.01036e9	0.657471	0.328735	+	0.944422i	$0.393378\pi$
$734$	−1.87684e9	−0.175183
$735$	0	0
$736$	−1.73214e9	−0.160144
$737$	8.29322e6	0.000763109 0
$738$	0	0
$739$	−2.09461e10	−1.90918	−0.954590	−	0.297923i	$-0.903706\pi$
$739$	−2.09461e10	−1.90918	−0.954590	+	0.297923i	$0.903706\pi$
$740$	−1.51248e9	−0.137208
$741$	0	0
$742$	−7.82030e8	−0.0702764
$743$	1.60185e10	1.43271	0.716357	−	0.697734i	$-0.245808\pi$
$743$	1.60185e10	1.43271	0.716357	+	0.697734i	$0.245808\pi$
$744$	0	0
$745$	3.87594e9	0.343424
$746$	−3.01067e9	−0.265508
$747$	0	0
$748$	−5.64766e7	−0.00493416
$749$	8.84935e8	0.0769529
$750$	0	0
$751$	−9.22632e9	−0.794856	−0.397428	−	0.917633i	$-0.630097\pi$
$751$	−9.22632e9	−0.794856	−0.397428	+	0.917633i	$0.630097\pi$
$752$	1.23589e10	1.05978
$753$	0	0
$754$	3.07456e9	0.261206
$755$	9.51298e9	0.804456
$756$	0	0
$757$	−1.99486e10	−1.67139	−0.835694	−	0.549195i	$-0.814934\pi$
$757$	−1.99486e10	−1.67139	−0.835694	+	0.549195i	$0.814934\pi$
$758$	−5.00826e9	−0.417681
$759$	0	0
$760$	−2.16450e9	−0.178859
$761$	7.42197e9	0.610482	0.305241	−	0.952275i	$-0.401263\pi$
$761$	7.42197e9	0.610482	0.305241	+	0.952275i	$0.401263\pi$
$762$	0	0
$763$	−3.62744e9	−0.295641
$764$	1.50914e10	1.22435
$765$	0	0
$766$	−3.28975e8	−0.0264461
$767$	−7.48362e9	−0.598863
$768$	0	0
$769$	7.97515e9	0.632407	0.316204	−	0.948691i	$-0.397592\pi$
$769$	7.97515e9	0.632407	0.316204	+	0.948691i	$0.397592\pi$
$770$	−1.51543e6	−0.000119624 0
$771$	0	0
$772$	−2.13512e10	−1.67017
$773$	6.46602e9	0.503511	0.251756	−	0.967791i	$-0.418992\pi$
$773$	6.46602e9	0.503511	0.251756	+	0.967791i	$0.418992\pi$
$774$	0	0
$775$	2.60486e9	0.201015
$776$	9.81579e8	0.0754066
$777$	0	0
$778$	2.23268e9	0.169980
$779$	1.76041e9	0.133424
$780$	0	0
$781$	1.24472e7	0.000934959 0
$782$	−1.02355e9	−0.0765398
$783$	0	0
$784$	−9.97471e9	−0.739255
$785$	−3.07220e9	−0.226676
$786$	0	0
$787$	−3.77628e9	−0.276155	−0.138077	−	0.990421i	$-0.544092\pi$
$787$	−3.77628e9	−0.276155	−0.138077	+	0.990421i	$0.544092\pi$
$788$	6.26868e9	0.456388
$789$	0	0
$790$	−4.81703e8	−0.0347604
$791$	1.90721e9	0.137019
$792$	0	0
$793$	1.16377e9	0.0828724
$794$	1.78553e8	0.0126589
$795$	0	0
$796$	−5.45873e9	−0.383615
$797$	−1.79598e9	−0.125660	−0.0628300	−	0.998024i	$-0.520013\pi$
$797$	−1.79598e9	−0.125660	−0.0628300	+	0.998024i	$0.520013\pi$
$798$	0	0
$799$	2.57320e10	1.78468
$800$	−7.10011e9	−0.490287
$801$	0	0
$802$	−6.18707e9	−0.423521
$803$	−7.53292e6	−0.000513404 0
$804$	0	0
$805$	3.06386e8	0.0207006
$806$	−1.72884e9	−0.116300
$807$	0	0
$808$	3.70693e9	0.247215
$809$	1.21567e10	0.807226	0.403613	−	0.914930i	$-0.367754\pi$
$809$	1.21567e10	0.807226	0.403613	+	0.914930i	$0.367754\pi$
$810$	0	0
$811$	−1.56560e9	−0.103064	−0.0515320	−	0.998671i	$-0.516410\pi$
$811$	−1.56560e9	−0.103064	−0.0515320	+	0.998671i	$0.516410\pi$
$812$	−1.63469e9	−0.107149
$813$	0	0
$814$	−4.60987e6	−0.000299574 0
$815$	−7.50151e9	−0.485397
$816$	0	0
$817$	1.27966e10	0.820948
$818$	−4.44670e9	−0.284055
$819$	0	0
$820$	−2.15005e9	−0.136176
$821$	2.53876e10	1.60110	0.800552	−	0.599263i	$-0.204540\pi$
$821$	2.53876e10	1.60110	0.800552	+	0.599263i	$0.204540\pi$
$822$	0	0
$823$	2.74439e10	1.71611	0.858056	−	0.513556i	$-0.171672\pi$
$823$	2.74439e10	1.71611	0.858056	+	0.513556i	$0.171672\pi$
$824$	1.28060e10	0.797388
$825$	0	0
$826$	−3.56675e8	−0.0220213
$827$	3.05050e10	1.87543	0.937716	−	0.347402i	$-0.112936\pi$
$827$	3.05050e10	1.87543	0.937716	+	0.347402i	$0.112936\pi$
$828$	0	0
$829$	1.27483e10	0.777162	0.388581	−	0.921414i	$-0.372965\pi$
$829$	1.27483e10	0.777162	0.388581	+	0.921414i	$0.372965\pi$
$830$	−2.22382e9	−0.134998
$831$	0	0
$832$	−1.15447e10	−0.694948
$833$	−2.07680e10	−1.24491
$834$	0	0
$835$	−1.67017e10	−0.992792
$836$	3.52189e7	0.00208475
$837$	0	0
$838$	6.86247e9	0.402834
$839$	−1.26629e10	−0.740230	−0.370115	−	0.928986i	$-0.620682\pi$
$839$	−1.26629e10	−0.740230	−0.370115	+	0.928986i	$0.620682\pi$
$840$	0	0
$841$	−8.62216e9	−0.499839
$842$	−5.17474e9	−0.298742
$843$	0	0
$844$	4.40819e9	0.252384
$845$	−6.94176e9	−0.395796
$846$	0	0
$847$	−2.91945e9	−0.165086
$848$	−2.00290e10	−1.12791
$849$	0	0
$850$	−4.19559e9	−0.234329
$851$	9.32014e8	0.0518405
$852$	0	0
$853$	5.68247e9	0.313484	0.156742	−	0.987640i	$-0.449901\pi$
$853$	5.68247e9	0.313484	0.156742	+	0.987640i	$0.449901\pi$
$854$	5.54661e7	0.00304737
$855$	0	0
$856$	−4.70508e9	−0.256394
$857$	−1.26235e10	−0.685088	−0.342544	−	0.939502i	$-0.611289\pi$
$857$	−1.26235e10	−0.685088	−0.342544	+	0.939502i	$0.611289\pi$
$858$	0	0
$859$	−1.84247e10	−0.991803	−0.495902	−	0.868379i	$-0.665162\pi$
$859$	−1.84247e10	−0.991803	−0.495902	+	0.868379i	$0.665162\pi$
$860$	−1.56289e10	−0.837882
$861$	0	0
$862$	2.51236e7	0.00133600
$863$	1.37297e10	0.727151	0.363576	−	0.931565i	$-0.381556\pi$
$863$	1.37297e10	0.727151	0.363576	+	0.931565i	$0.381556\pi$
$864$	0	0
$865$	1.18800e10	0.624107
$866$	−2.36243e9	−0.123608
$867$	0	0
$868$	9.19192e8	0.0477076
$869$	1.63783e7	0.000846643 0
$870$	0	0
$871$	4.56150e9	0.233908
$872$	1.92866e10	0.985026
$873$	0	0
$874$	6.38290e8	0.0323391
$875$	3.22321e9	0.162652
$876$	0	0
$877$	−2.79796e10	−1.40069	−0.700346	−	0.713803i	$-0.746971\pi$
$877$	−2.79796e10	−1.40069	−0.700346	+	0.713803i	$0.746971\pi$
$878$	−1.71812e9	−0.0856689
$879$	0	0
$880$	−3.88125e7	−0.00191992
$881$	2.85364e10	1.40600	0.702998	−	0.711192i	$-0.251844\pi$
$881$	2.85364e10	1.40600	0.702998	+	0.711192i	$0.251844\pi$
$882$	0	0
$883$	2.80960e10	1.37335	0.686676	−	0.726964i	$-0.259069\pi$
$883$	2.80960e10	1.37335	0.686676	+	0.726964i	$0.259069\pi$
$884$	−3.10637e10	−1.51241
$885$	0	0
$886$	−7.04414e9	−0.340259
$887$	3.35283e10	1.61317	0.806583	−	0.591121i	$-0.201314\pi$
$887$	3.35283e10	1.61317	0.806583	+	0.591121i	$0.201314\pi$
$888$	0	0
$889$	−6.42435e9	−0.306671
$890$	2.76811e9	0.131619
$891$	0	0
$892$	1.22950e10	0.580033
$893$	−1.60465e10	−0.754050
$894$	0	0
$895$	9.86468e9	0.459941
$896$	−3.28028e9	−0.152347
$897$	0	0
$898$	−6.76710e9	−0.311842
$899$	−4.85140e9	−0.222694
$900$	0	0
$901$	−4.17018e10	−1.89941
$902$	−6.55311e6	−0.000297320 0
$903$	0	0
$904$	−1.01404e10	−0.456525
$905$	1.22580e10	0.549729
$906$	0	0
$907$	3.90397e10	1.73733	0.868663	−	0.495404i	$-0.164980\pi$
$907$	3.90397e10	1.73733	0.868663	+	0.495404i	$0.164980\pi$
$908$	−2.71045e9	−0.120155
$909$	0	0
$910$	−8.33527e8	−0.0366670
$911$	−3.74924e10	−1.64297	−0.821483	−	0.570233i	$-0.806853\pi$
$911$	−3.74924e10	−1.64297	−0.821483	+	0.570233i	$0.806853\pi$
$912$	0	0
$913$	7.56118e7	0.00328808
$914$	9.59176e9	0.415515
$915$	0	0
$916$	−2.66428e10	−1.14537
$917$	2.34023e9	0.100223
$918$	0	0
$919$	2.71337e10	1.15320	0.576600	−	0.817026i	$-0.304379\pi$
$919$	2.71337e10	1.15320	0.576600	+	0.817026i	$0.304379\pi$
$920$	−1.62901e9	−0.0689710
$921$	0	0
$922$	8.09440e9	0.340115
$923$	6.84630e9	0.286583
$924$	0	0
$925$	3.82036e9	0.158712
$926$	−1.12470e10	−0.465477
$927$	0	0
$928$	1.32235e10	0.543162
$929$	−1.17269e10	−0.479875	−0.239938	−	0.970788i	$-0.577127\pi$
$929$	−1.17269e10	−0.479875	−0.239938	+	0.970788i	$0.577127\pi$
$930$	0	0
$931$	1.29510e10	0.525991
$932$	−3.42007e10	−1.38382
$933$	0	0
$934$	1.24334e10	0.499316
$935$	−8.08103e7	−0.00323315
$936$	0	0
$937$	2.65223e10	1.05323	0.526615	−	0.850104i	$-0.323461\pi$
$937$	2.65223e10	1.05323	0.526615	+	0.850104i	$0.323461\pi$
$938$	2.17405e8	0.00860120
$939$	0	0
$940$	1.95981e10	0.769604
$941$	4.09678e10	1.60280	0.801399	−	0.598130i	$-0.204089\pi$
$941$	4.09678e10	1.60280	0.801399	+	0.598130i	$0.204089\pi$
$942$	0	0
$943$	1.32489e9	0.0514505
$944$	−9.13502e9	−0.353433
$945$	0	0
$946$	−4.76350e7	−0.00182939
$947$	−9.37947e8	−0.0358883	−0.0179442	−	0.999839i	$-0.505712\pi$
$947$	−9.37947e8	−0.0358883	−0.0179442	+	0.999839i	$0.505712\pi$
$948$	0	0
$949$	−4.14332e9	−0.157368
$950$	2.61637e9	0.0990073
$951$	0	0
$952$	−3.09376e9	−0.116214
$953$	−3.41919e10	−1.27967	−0.639836	−	0.768512i	$-0.720998\pi$
$953$	−3.41919e10	−1.27967	−0.639836	+	0.768512i	$0.720998\pi$
$954$	0	0
$955$	2.15938e10	0.802264
$956$	1.70596e10	0.631490
$957$	0	0
$958$	8.88294e9	0.326421
$959$	−4.41340e9	−0.161588
$960$	0	0
$961$	−2.47847e10	−0.900847
$962$	−2.53556e9	−0.0918250
$963$	0	0
$964$	3.42733e10	1.23222
$965$	−3.05506e10	−1.09440
$966$	0	0
$967$	3.92498e10	1.39587	0.697934	−	0.716162i	$-0.254103\pi$
$967$	3.92498e10	1.39587	0.697934	+	0.716162i	$0.254103\pi$
$968$	1.55223e10	0.550039
$969$	0	0
$970$	6.72128e8	0.0236456
$971$	4.68207e10	1.64123	0.820617	−	0.571478i	$-0.193630\pi$
$971$	4.68207e10	1.64123	0.820617	+	0.571478i	$0.193630\pi$
$972$	0	0
$973$	4.06160e9	0.141352
$974$	−3.10490e9	−0.107669
$975$	0	0
$976$	1.42057e9	0.0489091
$977$	4.91556e10	1.68633	0.843164	−	0.537657i	$-0.180690\pi$
$977$	4.91556e10	1.68633	0.843164	+	0.537657i	$0.180690\pi$
$978$	0	0
$979$	−9.41183e7	−0.00320579
$980$	−1.58175e10	−0.536841
$981$	0	0
$982$	−7.80611e9	−0.263054
$983$	−5.36541e10	−1.80163	−0.900814	−	0.434205i	$-0.857029\pi$
$983$	−5.36541e10	−1.80163	−0.900814	+	0.434205i	$0.857029\pi$
$984$	0	0
$985$	8.96963e9	0.299053
$986$	7.81404e9	0.259601
$987$	0	0
$988$	1.93714e10	0.639015
$989$	9.63074e9	0.316572
$990$	0	0
$991$	3.66380e9	0.119584	0.0597921	−	0.998211i	$-0.480956\pi$
$991$	3.66380e9	0.119584	0.0597921	+	0.998211i	$0.480956\pi$
$992$	−7.43565e9	−0.241840
$993$	0	0
$994$	3.26300e8	0.0105382
$995$	−7.81070e9	−0.251368
$996$	0	0
$997$	5.69179e10	1.81893	0.909464	−	0.415783i	$-0.136492\pi$
$997$	5.69179e10	1.81893	0.909464	+	0.415783i	$0.136492\pi$
$998$	3.80147e9	0.121058
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	207.8.a.a.1.3		5
3.2	odd	2		69.8.a.a.1.3	✓	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.8.a.a.1.3	✓	5	3.2	odd	2
207.8.a.a.1.3		5	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 207 = 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	207.a (trivial)

\(f(q)\)	\(=\)	\(q+3.24502 q^{2} -117.470 q^{4} -168.083 q^{5} +149.817 q^{7} -796.555 q^{8} +O(q^{10})\)	\(q+3.24502 q^{2} -117.470 q^{4} -168.083 q^{5} +149.817 q^{7} -796.555 q^{8} -545.434 q^{10} +18.5452 q^{11} +10200.4 q^{13} +486.159 q^{14} +12451.3 q^{16} +25924.5 q^{17} -16166.5 q^{19} +19744.7 q^{20} +60.1797 q^{22} -12167.0 q^{23} -49873.0 q^{25} +33100.5 q^{26} -17599.0 q^{28} +92885.5 q^{29} -52229.9 q^{31} +142364. q^{32} +84125.5 q^{34} -25181.7 q^{35} -76601.8 q^{37} -52460.7 q^{38} +133888. q^{40} -108892. q^{41} -791546. q^{43} -2178.50 q^{44} -39482.2 q^{46} +992576. q^{47} -801098. q^{49} -161839. q^{50} -1.19824e6 q^{52} -1.60859e6 q^{53} -3117.14 q^{55} -119337. q^{56} +301416. q^{58} -733660. q^{59} +114090. q^{61} -169487. q^{62} -1.13179e6 q^{64} -1.71452e6 q^{65} +447189. q^{67} -3.04534e6 q^{68} -81715.2 q^{70} +671180. q^{71} -406192. q^{73} -248575. q^{74} +1.89908e6 q^{76} +2778.39 q^{77} +883156. q^{79} -2.09286e6 q^{80} -353358. q^{82} +4.07716e6 q^{83} -4.35747e6 q^{85} -2.56858e6 q^{86} -14772.3 q^{88} -5.07507e6 q^{89} +1.52819e6 q^{91} +1.42926e6 q^{92} +3.22093e6 q^{94} +2.71732e6 q^{95} -1.23228e6 q^{97} -2.59958e6 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 270 q^{4} + 266 q^{5} - 496 q^{7} - 1422 q^{8}+O(q^{10}) \) 5 * q + 270 * q^4 + 266 * q^5 - 496 * q^7 - 1422 * q^8	\( 5 q + 270 q^{4} + 266 q^{5} - 496 q^{7} - 1422 q^{8} + 1452 q^{10} + 1148 q^{11} - 642 q^{13} - 5756 q^{14} - 22606 q^{16} + 5798 q^{17} - 6036 q^{19} + 27376 q^{20} - 97896 q^{22} - 60835 q^{23} - 262477 q^{25} + 355992 q^{26} - 507124 q^{28} + 169162 q^{29} - 199640 q^{31} + 284794 q^{32} - 1027740 q^{34} + 137680 q^{35} - 202002 q^{37} + 554924 q^{38} - 340904 q^{40} - 541282 q^{41} - 909596 q^{43} + 1236032 q^{44} - 80208 q^{47} + 850589 q^{49} + 941416 q^{50} + 146940 q^{52} + 278138 q^{53} - 933560 q^{55} + 539932 q^{56} - 3522712 q^{58} + 3177380 q^{59} + 147782 q^{61} - 4606456 q^{62} - 4142622 q^{64} - 3877332 q^{65} - 464916 q^{67} - 7513072 q^{68} + 2093200 q^{70} - 1576792 q^{71} - 38190 q^{73} - 12164864 q^{74} + 6889436 q^{76} - 10332384 q^{77} - 3913336 q^{79} - 6334776 q^{80} + 6799360 q^{82} - 15774716 q^{83} - 8520740 q^{85} - 24874084 q^{86} + 53216 q^{88} - 1116482 q^{89} - 27369552 q^{91} - 3285090 q^{92} - 7153744 q^{94} + 6067832 q^{95} - 15738566 q^{97} - 11730488 q^{98}+O(q^{100}) \) 5 * q + 270 * q^4 + 266 * q^5 - 496 * q^7 - 1422 * q^8 + 1452 * q^10 + 1148 * q^11 - 642 * q^13 - 5756 * q^14 - 22606 * q^16 + 5798 * q^17 - 6036 * q^19 + 27376 * q^20 - 97896 * q^22 - 60835 * q^23 - 262477 * q^25 + 355992 * q^26 - 507124 * q^28 + 169162 * q^29 - 199640 * q^31 + 284794 * q^32 - 1027740 * q^34 + 137680 * q^35 - 202002 * q^37 + 554924 * q^38 - 340904 * q^40 - 541282 * q^41 - 909596 * q^43 + 1236032 * q^44 - 80208 * q^47 + 850589 * q^49 + 941416 * q^50 + 146940 * q^52 + 278138 * q^53 - 933560 * q^55 + 539932 * q^56 - 3522712 * q^58 + 3177380 * q^59 + 147782 * q^61 - 4606456 * q^62 - 4142622 * q^64 - 3877332 * q^65 - 464916 * q^67 - 7513072 * q^68 + 2093200 * q^70 - 1576792 * q^71 - 38190 * q^73 - 12164864 * q^74 + 6889436 * q^76 - 10332384 * q^77 - 3913336 * q^79 - 6334776 * q^80 + 6799360 * q^82 - 15774716 * q^83 - 8520740 * q^85 - 24874084 * q^86 + 53216 * q^88 - 1116482 * q^89 - 27369552 * q^91 - 3285090 * q^92 - 7153744 * q^94 + 6067832 * q^95 - 15738566 * q^97 - 11730488 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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