LMFDB - Embedded newform 507.4.a.l.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,4,Mod(1,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("507.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	507.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:	$29.9139683729$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.1362828.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 23x^{2} + 48 $ x^4 - 23*x^2 + 48
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 39)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$4.54739$ of defining polynomial
Character	$\chi$	$=$	507.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+4.54739 q^{2} +3.00000 q^{3} +12.6788 q^{4} +12.9118 q^{5} +13.6422 q^{6} +16.7289 q^{7} +21.2762 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+4.54739 q^{2} +3.00000 q^{3} +12.6788 q^{4} +12.9118 q^{5} +13.6422 q^{6} +16.7289 q^{7} +21.2762 q^{8} +9.00000 q^{9} +58.7151 q^{10} +24.9280 q^{11} +38.0363 q^{12} +76.0727 q^{14} +38.7355 q^{15} -4.67878 q^{16} -134.145 q^{17} +40.9265 q^{18} -14.9376 q^{19} +163.706 q^{20} +50.1866 q^{21} +113.358 q^{22} +72.0000 q^{23} +63.8287 q^{24} +41.7151 q^{25} +27.0000 q^{27} +212.101 q^{28} -206.145 q^{29} +176.145 q^{30} -249.142 q^{31} -191.486 q^{32} +74.7841 q^{33} -610.012 q^{34} +216.000 q^{35} +114.109 q^{36} +293.955 q^{37} -67.9273 q^{38} +274.715 q^{40} +250.506 q^{41} +228.218 q^{42} +432.145 q^{43} +316.057 q^{44} +116.206 q^{45} +327.412 q^{46} -159.889 q^{47} -14.0363 q^{48} -63.1454 q^{49} +189.695 q^{50} -402.436 q^{51} -194.581 q^{53} +122.780 q^{54} +321.866 q^{55} +355.927 q^{56} -44.8129 q^{57} -937.424 q^{58} +232.647 q^{59} +491.118 q^{60} -185.006 q^{61} -1132.94 q^{62} +150.560 q^{63} -833.333 q^{64} +340.073 q^{66} -39.4393 q^{67} -1700.80 q^{68} +216.000 q^{69} +982.237 q^{70} +920.460 q^{71} +191.486 q^{72} -549.078 q^{73} +1336.73 q^{74} +125.145 q^{75} -189.391 q^{76} +417.018 q^{77} +933.140 q^{79} -60.4116 q^{80} +81.0000 q^{81} +1139.15 q^{82} -1095.38 q^{83} +636.304 q^{84} -1732.06 q^{85} +1965.13 q^{86} -618.436 q^{87} +530.375 q^{88} -532.114 q^{89} +528.436 q^{90} +912.872 q^{92} -747.425 q^{93} -727.079 q^{94} -192.872 q^{95} -574.459 q^{96} -362.661 q^{97} -287.147 q^{98} +224.352 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 12 q^{3} + 14 q^{4} + 36 q^{9}+O(q^{10}) $ 4 * q + 12 * q^3 + 14 * q^4 + 36 * q^9	$ 4 q + 12 q^{3} + 14 q^{4} + 36 q^{9} + 88 q^{10} + 42 q^{12} + 84 q^{14} + 18 q^{16} - 96 q^{17} + 380 q^{22} + 288 q^{23} + 20 q^{25} + 108 q^{27} - 384 q^{29} + 264 q^{30} + 864 q^{35} + 126 q^{36} - 492 q^{38} + 952 q^{40} + 252 q^{42} + 1288 q^{43} + 54 q^{48} + 188 q^{49} - 288 q^{51} + 984 q^{53} - 328 q^{55} + 1644 q^{56} + 288 q^{61} - 1668 q^{62} - 1314 q^{64} + 1140 q^{66} - 4380 q^{68} + 864 q^{69} + 3144 q^{74} + 60 q^{75} - 1416 q^{77} + 4320 q^{79} + 324 q^{81} + 3088 q^{82} - 1152 q^{87} - 1036 q^{88} + 792 q^{90} + 1008 q^{92} - 1660 q^{94} + 1872 q^{95}+O(q^{100}) $ 4 * q + 12 * q^3 + 14 * q^4 + 36 * q^9 + 88 * q^10 + 42 * q^12 + 84 * q^14 + 18 * q^16 - 96 * q^17 + 380 * q^22 + 288 * q^23 + 20 * q^25 + 108 * q^27 - 384 * q^29 + 264 * q^30 + 864 * q^35 + 126 * q^36 - 492 * q^38 + 952 * q^40 + 252 * q^42 + 1288 * q^43 + 54 * q^48 + 188 * q^49 - 288 * q^51 + 984 * q^53 - 328 * q^55 + 1644 * q^56 + 288 * q^61 - 1668 * q^62 - 1314 * q^64 + 1140 * q^66 - 4380 * q^68 + 864 * q^69 + 3144 * q^74 + 60 * q^75 - 1416 * q^77 + 4320 * q^79 + 324 * q^81 + 3088 * q^82 - 1152 * q^87 - 1036 * q^88 + 792 * q^90 + 1008 * q^92 - 1660 * q^94 + 1872 * q^95

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 $

$2$	4.54739	1.60775	0.803873	−	0.594801i	$-0.202769\pi$
$2$	4.54739	1.60775	0.803873	+	0.594801i	$0.202769\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	12.6788	1.58485
$5$	12.9118	1.15487	0.577434	−	0.816437i	$-0.304054\pi$
$5$	12.9118	1.15487	0.577434	+	0.816437i	$0.304054\pi$
$6$	13.6422	0.928233
$7$	16.7289	0.903273	0.451637	−	0.892202i	$-0.350840\pi$
$7$	16.7289	0.903273	0.451637	+	0.892202i	$0.350840\pi$
$8$	21.2762	0.940286
$9$	9.00000	0.333333
$10$	58.7151	1.85674
$11$	24.9280	0.683280	0.341640	−	0.939831i	$-0.389018\pi$
$11$	24.9280	0.683280	0.341640	+	0.939831i	$0.389018\pi$
$12$	38.0363	0.915012
$13$	0	0
$13$	0	0
$14$	76.0727	1.45223
$15$	38.7355	0.666764
$16$	−4.67878	−0.0731059
$17$	−134.145	−1.91383	−0.956913	−	0.290376i	$-0.906220\pi$
$17$	−134.145	−1.91383	−0.956913	+	0.290376i	$0.906220\pi$
$18$	40.9265	0.535915
$19$	−14.9376	−0.180365	−0.0901824	−	0.995925i	$-0.528745\pi$
$19$	−14.9376	−0.180365	−0.0901824	+	0.995925i	$0.528745\pi$
$20$	163.706	1.83029
$21$	50.1866	0.521505
$22$	113.358	1.09854
$23$	72.0000	0.652741	0.326370	−	0.945242i	$-0.394174\pi$
$23$	72.0000	0.652741	0.326370	+	0.945242i	$0.394174\pi$
$24$	63.8287	0.542875
$25$	41.7151	0.333721
$26$	0	0
$27$	27.0000	0.192450
$28$	212.101	1.43155
$29$	−206.145	−1.32001	−0.660004	−	0.751262i	$-0.729445\pi$
$29$	−206.145	−1.32001	−0.660004	+	0.751262i	$0.729445\pi$
$30$	176.145	1.07199
$31$	−249.142	−1.44346	−0.721728	−	0.692176i	$-0.756652\pi$
$31$	−249.142	−1.44346	−0.721728	+	0.692176i	$0.756652\pi$
$32$	−191.486	−1.05782
$33$	74.7841	0.394492
$34$	−610.012	−3.07694
$35$	216.000	1.04316
$36$	114.109	0.528282
$37$	293.955	1.30610	0.653052	−	0.757313i	$-0.273488\pi$
$37$	293.955	1.30610	0.653052	+	0.757313i	$0.273488\pi$
$38$	−67.9273	−0.289981
$39$	0	0
$40$	274.715	1.08591
$41$	250.506	0.954208	0.477104	−	0.878847i	$-0.341686\pi$
$41$	250.506	0.954208	0.477104	+	0.878847i	$0.341686\pi$
$42$	228.218	0.838448
$43$	432.145	1.53259	0.766297	−	0.642486i	$-0.222097\pi$
$43$	432.145	1.53259	0.766297	+	0.642486i	$0.222097\pi$
$44$	316.057	1.08290
$45$	116.206	0.384956
$46$	327.412	1.04944
$47$	−159.889	−0.496217	−0.248109	−	0.968732i	$-0.579809\pi$
$47$	−159.889	−0.496217	−0.248109	+	0.968732i	$0.579809\pi$
$48$	−14.0363	−0.0422077
$49$	−63.1454	−0.184097
$50$	189.695	0.536539
$51$	−402.436	−1.10495
$52$	0	0
$53$	−194.581	−0.504298	−0.252149	−	0.967688i	$-0.581137\pi$
$53$	−194.581	−0.504298	−0.252149	+	0.967688i	$0.581137\pi$
$54$	122.780	0.309411
$55$	321.866	0.789099
$56$	355.927	0.849336
$57$	−44.8129	−0.104134
$58$	−937.424	−2.12224
$59$	232.647	0.513358	0.256679	−	0.966497i	$-0.417372\pi$
$59$	232.647	0.513358	0.256679	+	0.966497i	$0.417372\pi$
$60$	491.118	1.05672
$61$	−185.006	−0.388321	−0.194160	−	0.980970i	$-0.562198\pi$
$61$	−185.006	−0.388321	−0.194160	+	0.980970i	$0.562198\pi$
$62$	−1132.94	−2.32071
$63$	150.560	0.301091
$64$	−833.333	−1.62760
$65$	0	0
$66$	340.073	0.634243
$67$	−39.4393	−0.0719145	−0.0359573	−	0.999353i	$-0.511448\pi$
$67$	−39.4393	−0.0719145	−0.0359573	+	0.999353i	$0.511448\pi$
$68$	−1700.80	−3.03312
$69$	216.000	0.376860
$70$	982.237	1.67714
$71$	920.460	1.53857	0.769286	−	0.638905i	$-0.220612\pi$
$71$	920.460	1.53857	0.769286	+	0.638905i	$0.220612\pi$
$72$	191.486	0.313429
$73$	−549.078	−0.880338	−0.440169	−	0.897915i	$-0.645082\pi$
$73$	−549.078	−0.880338	−0.440169	+	0.897915i	$0.645082\pi$
$74$	1336.73	2.09988
$75$	125.145	0.192674
$76$	−189.391	−0.285851
$77$	417.018	0.617189
$78$	0	0
$79$	933.140	1.32894	0.664471	−	0.747314i	$-0.268657\pi$
$79$	933.140	1.32894	0.664471	+	0.747314i	$0.268657\pi$
$80$	−60.4116	−0.0844277
$81$	81.0000	0.111111
$82$	1139.15	1.53412
$83$	−1095.38	−1.44860	−0.724301	−	0.689484i	$-0.757837\pi$
$83$	−1095.38	−1.44860	−0.724301	+	0.689484i	$0.757837\pi$
$84$	636.304	0.826506
$85$	−1732.06	−2.21022
$86$	1965.13	2.46402
$87$	−618.436	−0.762107
$88$	530.375	0.642479
$89$	−532.114	−0.633753	−0.316876	−	0.948467i	$-0.602634\pi$
$89$	−532.114	−0.633753	−0.316876	+	0.948467i	$0.602634\pi$
$90$	528.436	0.618912
$91$	0	0
$92$	912.872	1.03449
$93$	−747.425	−0.833380
$94$	−727.079	−0.797792
$95$	−192.872	−0.208298
$96$	−574.459	−0.610734
$97$	−362.661	−0.379615	−0.189808	−	0.981821i	$-0.560786\pi$
$97$	−362.661	−0.379615	−0.189808	+	0.981821i	$0.560786\pi$
$98$	−287.147	−0.295982
$99$	224.352	0.227760
$100$	528.897	0.528897
$101$	1490.58	1.46850	0.734249	−	0.678880i	$-0.237534\pi$
$101$	1490.58	1.46850	0.734249	+	0.678880i	$0.237534\pi$
$102$	−1830.03	−1.77648
$103$	628.436	0.601181	0.300591	−	0.953753i	$-0.402816\pi$
$103$	628.436	0.601181	0.300591	+	0.953753i	$0.402816\pi$
$104$	0	0
$105$	648.000	0.602270
$106$	−884.838	−0.810784
$107$	477.454	0.431376	0.215688	−	0.976462i	$-0.430801\pi$
$107$	477.454	0.431376	0.215688	+	0.976462i	$0.430801\pi$
$108$	342.327	0.305004
$109$	−378.207	−0.332345	−0.166173	−	0.986097i	$-0.553141\pi$
$109$	−378.207	−0.332345	−0.166173	+	0.986097i	$0.553141\pi$
$110$	1463.65	1.26867
$111$	881.864	0.754079
$112$	−78.2706	−0.0660346
$113$	13.2732	0.0110499	0.00552495	−	0.999985i	$-0.498241\pi$
$113$	13.2732	0.0110499	0.00552495	+	0.999985i	$0.498241\pi$
$114$	−203.782	−0.167420
$115$	929.651	0.753830
$116$	−2613.67	−2.09201
$117$	0	0
$118$	1057.94	0.825349
$119$	−2244.10	−1.72871
$120$	824.145	0.626949
$121$	−709.593	−0.533128
$122$	−841.294	−0.624321
$123$	751.519	0.550912
$124$	−3158.81	−2.28766
$125$	−1075.36	−0.769465
$126$	684.654	0.484078
$127$	145.988	0.102003	0.0510015	−	0.998699i	$-0.483759\pi$
$127$	145.988	0.102003	0.0510015	+	0.998699i	$0.483759\pi$
$128$	−2257.60	−1.55895
$129$	1296.44	0.884844
$130$	0	0
$131$	317.163	0.211532	0.105766	−	0.994391i	$-0.466271\pi$
$131$	317.163	0.211532	0.105766	+	0.994391i	$0.466271\pi$
$132$	948.171	0.625210
$133$	−249.890	−0.162919
$134$	−179.346	−0.115620
$135$	348.619	0.222255
$136$	−2854.11	−1.79954
$137$	443.149	0.276356	0.138178	−	0.990407i	$-0.455875\pi$
$137$	443.149	0.276356	0.138178	+	0.990407i	$0.455875\pi$
$138$	982.237	0.605895
$139$	785.018	0.479024	0.239512	−	0.970893i	$-0.423013\pi$
$139$	785.018	0.479024	0.239512	+	0.970893i	$0.423013\pi$
$140$	2738.62	1.65325
$141$	−479.667	−0.286491
$142$	4185.69	2.47363
$143$	0	0
$144$	−42.1090	−0.0243686
$145$	−2661.71	−1.52444
$146$	−2496.87	−1.41536
$147$	−189.436	−0.106289
$148$	3726.99	2.06997
$149$	135.420	0.0744566	0.0372283	−	0.999307i	$-0.488147\pi$
$149$	135.420	0.0744566	0.0372283	+	0.999307i	$0.488147\pi$
$150$	569.085	0.309771
$151$	−2373.74	−1.27929	−0.639643	−	0.768672i	$-0.720918\pi$
$151$	−2373.74	−1.27929	−0.639643	+	0.768672i	$0.720918\pi$
$152$	−317.817	−0.169594
$153$	−1207.31	−0.637942
$154$	1896.34	0.992283
$155$	−3216.87	−1.66700
$156$	0	0
$157$	−1166.73	−0.593089	−0.296544	−	0.955019i	$-0.595834\pi$
$157$	−1166.73	−0.593089	−0.296544	+	0.955019i	$0.595834\pi$
$158$	4243.35	2.13660
$159$	−583.744	−0.291157
$160$	−2472.44	−1.22165
$161$	1204.48	0.589603
$162$	368.339	0.178638
$163$	−2309.19	−1.10963	−0.554815	−	0.831974i	$-0.687211\pi$
$163$	−2309.19	−1.10963	−0.554815	+	0.831974i	$0.687211\pi$
$164$	3176.12	1.51227
$165$	965.599	0.455587
$166$	−4981.14	−2.32898
$167$	−600.788	−0.278386	−0.139193	−	0.990265i	$-0.544451\pi$
$167$	−600.788	−0.278386	−0.139193	+	0.990265i	$0.544451\pi$
$168$	1067.78	0.490364
$169$	0	0
$170$	−7876.36	−3.55347
$171$	−134.439	−0.0601216
$172$	5479.08	2.42893
$173$	3430.36	1.50755	0.753773	−	0.657135i	$-0.228232\pi$
$173$	3430.36	1.50755	0.753773	+	0.657135i	$0.228232\pi$
$174$	−2812.27	−1.22527
$175$	697.846	0.301441
$176$	−116.633	−0.0499519
$177$	697.942	0.296387
$178$	−2419.73	−1.01891
$179$	978.837	0.408725	0.204362	−	0.978895i	$-0.434488\pi$
$179$	978.837	0.408725	0.204362	+	0.978895i	$0.434488\pi$
$180$	1473.36	0.610097
$181$	−3839.09	−1.57656	−0.788279	−	0.615318i	$-0.789028\pi$
$181$	−3839.09	−1.57656	−0.788279	+	0.615318i	$0.789028\pi$
$182$	0	0
$183$	−555.018	−0.224197
$184$	1531.89	0.613763
$185$	3795.49	1.50838
$186$	−3398.83	−1.33986
$187$	−3343.98	−1.30768
$188$	−2027.20	−0.786429
$189$	451.679	0.173835
$190$	−877.065	−0.334890
$191$	−487.709	−0.184761	−0.0923806	−	0.995724i	$-0.529448\pi$
$191$	−487.709	−0.184761	−0.0923806	+	0.995724i	$0.529448\pi$
$192$	−2500.00	−0.939697
$193$	4245.61	1.58345	0.791725	−	0.610878i	$-0.209183\pi$
$193$	4245.61	1.58345	0.791725	+	0.610878i	$0.209183\pi$
$194$	−1649.16	−0.610325
$195$	0	0
$196$	−800.606	−0.291766
$197$	−2712.71	−0.981079	−0.490539	−	0.871419i	$-0.663200\pi$
$197$	−2712.71	−0.981079	−0.490539	+	0.871419i	$0.663200\pi$
$198$	1020.22	0.366180
$199$	3116.90	1.11031	0.555153	−	0.831748i	$-0.312660\pi$
$199$	3116.90	1.11031	0.555153	+	0.831748i	$0.312660\pi$
$200$	887.541	0.313793
$201$	−118.318	−0.0415199
$202$	6778.26	2.36097
$203$	−3448.58	−1.19233
$204$	−5102.40	−1.75117
$205$	3234.49	1.10198
$206$	2857.75	0.966546
$207$	648.000	0.217580
$208$	0	0
$209$	−372.366	−0.123240
$210$	2946.71	0.968297
$211$	−1051.22	−0.342981	−0.171491	−	0.985186i	$-0.554858\pi$
$211$	−1051.22	−0.342981	−0.171491	+	0.985186i	$0.554858\pi$
$212$	−2467.06	−0.799236
$213$	2761.38	0.888294
$214$	2171.17	0.693542
$215$	5579.78	1.76994
$216$	574.459	0.180958
$217$	−4167.85	−1.30384
$218$	−1719.85	−0.534327
$219$	−1647.23	−0.508264
$220$	4080.87	1.25060
$221$	0	0
$222$	4010.18	1.21237
$223$	5496.12	1.65044	0.825218	−	0.564814i	$-0.191052\pi$
$223$	5496.12	1.65044	0.825218	+	0.564814i	$0.191052\pi$
$224$	−3203.35	−0.955502
$225$	375.436	0.111240
$226$	60.3585	0.0177654
$227$	−921.570	−0.269457	−0.134729	−	0.990883i	$-0.543016\pi$
$227$	−921.570	−0.269457	−0.134729	+	0.990883i	$0.543016\pi$
$228$	−568.173	−0.165036
$229$	192.941	0.0556764	0.0278382	−	0.999612i	$-0.491138\pi$
$229$	192.941	0.0556764	0.0278382	+	0.999612i	$0.491138\pi$
$230$	4227.49	1.21197
$231$	1251.05	0.356334
$232$	−4386.00	−1.24119
$233$	913.779	0.256926	0.128463	−	0.991714i	$-0.458996\pi$
$233$	913.779	0.256926	0.128463	+	0.991714i	$0.458996\pi$
$234$	0	0
$235$	−2064.46	−0.573066
$236$	2949.68	0.813594
$237$	2799.42	0.767265
$238$	−10204.8	−2.77932
$239$	−1976.86	−0.535032	−0.267516	−	0.963553i	$-0.586203\pi$
$239$	−1976.86	−0.535032	−0.267516	+	0.963553i	$0.586203\pi$
$240$	−181.235	−0.0487444
$241$	3904.45	1.04360	0.521800	−	0.853068i	$-0.325261\pi$
$241$	3904.45	1.04360	0.521800	+	0.853068i	$0.325261\pi$
$242$	−3226.80	−0.857134
$243$	243.000	0.0641500
$244$	−2345.65	−0.615429
$245$	−815.322	−0.212608
$246$	3417.45	0.885727
$247$	0	0
$248$	−5300.80	−1.35726
$249$	−3286.15	−0.836350
$250$	−4890.08	−1.23710
$251$	−942.035	−0.236895	−0.118448	−	0.992960i	$-0.537792\pi$
$251$	−942.035	−0.236895	−0.118448	+	0.992960i	$0.537792\pi$
$252$	1908.91	0.477183
$253$	1794.82	0.446005
$254$	663.866	0.163995
$255$	−5196.18	−1.27607
$256$	−3599.54	−0.878794
$257$	−812.616	−0.197236	−0.0986179	−	0.995125i	$-0.531442\pi$
$257$	−812.616	−0.197236	−0.0986179	+	0.995125i	$0.531442\pi$
$258$	5895.40	1.42260
$259$	4917.52	1.17977
$260$	0	0
$261$	−1855.31	−0.440003
$262$	1442.26	0.340089
$263$	−2608.29	−0.611536	−0.305768	−	0.952106i	$-0.598913\pi$
$263$	−2608.29	−0.611536	−0.305768	+	0.952106i	$0.598913\pi$
$264$	1591.13	0.370936
$265$	−2512.40	−0.582398
$266$	−1136.35	−0.261932
$267$	−1596.34	−0.365897
$268$	−500.042	−0.113974
$269$	−4791.02	−1.08592	−0.542962	−	0.839757i	$-0.682697\pi$
$269$	−4791.02	−1.08592	−0.542962	+	0.839757i	$0.682697\pi$
$270$	1585.31	0.357329
$271$	−3663.62	−0.821214	−0.410607	−	0.911812i	$-0.634683\pi$
$271$	−3663.62	−0.821214	−0.410607	+	0.911812i	$0.634683\pi$
$272$	627.637	0.139912
$273$	0	0
$274$	2015.17	0.444311
$275$	1039.88	0.228025
$276$	2738.62	0.597266
$277$	−624.326	−0.135423	−0.0677114	−	0.997705i	$-0.521570\pi$
$277$	−624.326	−0.135423	−0.0677114	+	0.997705i	$0.521570\pi$
$278$	3569.78	0.770149
$279$	−2242.27	−0.481152
$280$	4595.67	0.980871
$281$	5535.12	1.17508	0.587540	−	0.809195i	$-0.300096\pi$
$281$	5535.12	1.17508	0.587540	+	0.809195i	$0.300096\pi$
$282$	−2181.24	−0.460605
$283$	175.151	0.0367903	0.0183952	−	0.999831i	$-0.494144\pi$
$283$	175.151	0.0367903	0.0183952	+	0.999831i	$0.494144\pi$
$284$	11670.3	2.43840
$285$	−578.616	−0.120261
$286$	0	0
$287$	4190.69	0.861911
$288$	−1723.38	−0.352607
$289$	13082.0	2.66273
$290$	−12103.8	−2.45091
$291$	−1087.98	−0.219171
$292$	−6961.64	−1.39520
$293$	−7774.33	−1.55011	−0.775054	−	0.631895i	$-0.782277\pi$
$293$	−7774.33	−1.55011	−0.775054	+	0.631895i	$0.782277\pi$
$294$	−861.440	−0.170885
$295$	3003.90	0.592861
$296$	6254.25	1.22811
$297$	673.057	0.131497
$298$	615.808	0.119707
$299$	0	0
$300$	1586.69	0.305359
$301$	7229.30	1.38435
$302$	−10794.3	−2.05677
$303$	4471.74	0.847838
$304$	69.8899	0.0131857
$305$	−2388.76	−0.448459
$306$	−5490.10	−1.02565
$307$	8022.85	1.49149	0.745746	−	0.666230i	$-0.232093\pi$
$307$	8022.85	1.49149	0.745746	+	0.666230i	$0.232093\pi$
$308$	5287.27	0.978150
$309$	1885.31	0.347092
$310$	−14628.4	−2.68012
$311$	−9264.87	−1.68927	−0.844635	−	0.535343i	$-0.820182\pi$
$311$	−9264.87	−1.68927	−0.844635	+	0.535343i	$0.820182\pi$
$312$	0	0
$313$	7423.57	1.34059	0.670296	−	0.742094i	$-0.266167\pi$
$313$	7423.57	1.34059	0.670296	+	0.742094i	$0.266167\pi$
$314$	−5305.56	−0.953536
$315$	1944.00	0.347721
$316$	11831.1	2.10617
$317$	2641.04	0.467935	0.233968	−	0.972244i	$-0.424829\pi$
$317$	2641.04	0.467935	0.233968	+	0.972244i	$0.424829\pi$
$318$	−2654.51	−0.468106
$319$	−5138.80	−0.901936
$320$	−10759.8	−1.87967
$321$	1432.36	0.249055
$322$	5477.23	0.947932
$323$	2003.82	0.345187
$324$	1026.98	0.176094
$325$	0	0
$326$	−10500.8	−1.78400
$327$	−1134.62	−0.191880
$328$	5329.84	0.897229
$329$	−2674.76	−0.448220
$330$	4390.96	0.732467
$331$	10779.5	1.79001	0.895007	−	0.446052i	$-0.147170\pi$
$331$	10779.5	1.79001	0.895007	+	0.446052i	$0.147170\pi$
$332$	−13888.1	−2.29581
$333$	2645.59	0.435368
$334$	−2732.02	−0.447573
$335$	−509.233	−0.0830518
$336$	−234.812	−0.0381251
$337$	−313.465	−0.0506693	−0.0253346	−	0.999679i	$-0.508065\pi$
$337$	−313.465	−0.0506693	−0.0253346	+	0.999679i	$0.508065\pi$
$338$	0	0
$339$	39.8196	0.00637966
$340$	−21960.4	−3.50286
$341$	−6210.61	−0.986286
$342$	−611.346	−0.0966602
$343$	−6794.35	−1.06956
$344$	9194.43	1.44108
$345$	2788.95	0.435224
$346$	15599.2	2.42375
$347$	−2849.23	−0.440792	−0.220396	−	0.975410i	$-0.570735\pi$
$347$	−2849.23	−0.440792	−0.220396	+	0.975410i	$0.570735\pi$
$348$	−7841.01	−1.20782
$349$	6466.94	0.991883	0.495941	−	0.868356i	$-0.334823\pi$
$349$	6466.94	0.991883	0.495941	+	0.868356i	$0.334823\pi$
$350$	3173.38	0.484641
$351$	0	0
$352$	−4773.38	−0.722789
$353$	−2773.10	−0.418122	−0.209061	−	0.977903i	$-0.567041\pi$
$353$	−2773.10	−0.418122	−0.209061	+	0.977903i	$0.567041\pi$
$354$	3173.82	0.476515
$355$	11884.8	1.77685
$356$	−6746.56	−1.00440
$357$	−6732.30	−0.998070
$358$	4451.16	0.657126
$359$	−1467.11	−0.215685	−0.107843	−	0.994168i	$-0.534394\pi$
$359$	−1467.11	−0.215685	−0.107843	+	0.994168i	$0.534394\pi$
$360$	2472.44	0.361969
$361$	−6635.87	−0.967469
$362$	−17457.8	−2.53471
$363$	−2128.78	−0.307801
$364$	0	0
$365$	−7089.59	−1.01667
$366$	−2523.88	−0.360452
$367$	4648.22	0.661130	0.330565	−	0.943783i	$-0.392761\pi$
$367$	4648.22	0.661130	0.330565	+	0.943783i	$0.392761\pi$
$368$	−336.872	−0.0477192
$369$	2254.56	0.318069
$370$	17259.6	2.42509
$371$	−3255.12	−0.455519
$372$	−9476.44	−1.32078
$373$	1763.72	0.244831	0.122416	−	0.992479i	$-0.460936\pi$
$373$	1763.72	0.244831	0.122416	+	0.992479i	$0.460936\pi$
$374$	−15206.4	−2.10242
$375$	−3226.08	−0.444251
$376$	−3401.84	−0.466586
$377$	0	0
$378$	2053.96	0.279483
$379$	1930.47	0.261640	0.130820	−	0.991406i	$-0.458239\pi$
$379$	1930.47	0.261640	0.130820	+	0.991406i	$0.458239\pi$
$380$	−2445.38	−0.330120
$381$	437.965	0.0588914
$382$	−2217.81	−0.297049
$383$	−8845.93	−1.18017	−0.590086	−	0.807340i	$-0.700906\pi$
$383$	−8845.93	−1.18017	−0.590086	+	0.807340i	$0.700906\pi$
$384$	−6772.81	−0.900061
$385$	5384.46	0.712772
$386$	19306.5	2.54579
$387$	3889.31	0.510865
$388$	−4598.10	−0.601632
$389$	−1598.08	−0.208292	−0.104146	−	0.994562i	$-0.533211\pi$
$389$	−1598.08	−0.208292	−0.104146	+	0.994562i	$0.533211\pi$
$390$	0	0
$391$	−9658.47	−1.24923
$392$	−1343.50	−0.173104
$393$	951.489	0.122128
$394$	−12335.8	−1.57733
$395$	12048.5	1.53475
$396$	2844.51	0.360965
$397$	3578.82	0.452433	0.226217	−	0.974077i	$-0.427364\pi$
$397$	3578.82	0.452433	0.226217	+	0.974077i	$0.427364\pi$
$398$	14173.7	1.78509
$399$	−749.669	−0.0940611
$400$	−195.176	−0.0243970
$401$	−3485.99	−0.434120	−0.217060	−	0.976158i	$-0.569647\pi$
$401$	−3485.99	−0.434120	−0.217060	+	0.976158i	$0.569647\pi$
$402$	−538.038	−0.0667534
$403$	0	0
$404$	18898.8	2.32735
$405$	1045.86	0.128319
$406$	−15682.0	−1.91696
$407$	7327.71	0.892435
$408$	−8562.33	−1.03897
$409$	14709.1	1.77828	0.889139	−	0.457637i	$-0.151304\pi$
$409$	14709.1	1.77828	0.889139	+	0.457637i	$0.151304\pi$
$410$	14708.5	1.77171
$411$	1329.45	0.159554
$412$	7967.80	0.952780
$413$	3891.92	0.463702
$414$	2946.71	0.349814
$415$	−14143.4	−1.67294
$416$	0	0
$417$	2355.05	0.276565
$418$	−1693.29	−0.198138
$419$	3709.01	0.432451	0.216226	−	0.976343i	$-0.430625\pi$
$419$	3709.01	0.432451	0.216226	+	0.976343i	$0.430625\pi$
$420$	8215.85	0.954506
$421$	794.029	0.0919207	0.0459603	−	0.998943i	$-0.485365\pi$
$421$	794.029	0.0919207	0.0459603	+	0.998943i	$0.485365\pi$
$422$	−4780.32	−0.551427
$423$	−1439.00	−0.165406
$424$	−4139.96	−0.474185
$425$	−5595.89	−0.638684
$426$	12557.1	1.42815
$427$	−3094.94	−0.350760
$428$	6053.53	0.683664
$429$	0	0
$430$	25373.5	2.84562
$431$	2891.52	0.323155	0.161577	−	0.986860i	$-0.448342\pi$
$431$	2891.52	0.323155	0.161577	+	0.986860i	$0.448342\pi$
$432$	−126.327	−0.0140692
$433$	5560.94	0.617186	0.308593	−	0.951194i	$-0.400142\pi$
$433$	5560.94	0.617186	0.308593	+	0.951194i	$0.400142\pi$
$434$	−18952.9	−2.09624
$435$	−7985.14	−0.880133
$436$	−4795.20	−0.526717
$437$	−1075.51	−0.117731
$438$	−7490.62	−0.817159
$439$	15127.2	1.64460	0.822302	−	0.569051i	$-0.192689\pi$
$439$	15127.2	1.64460	0.822302	+	0.569051i	$0.192689\pi$
$440$	6848.11	0.741979
$441$	−568.308	−0.0613658
$442$	0	0
$443$	2357.89	0.252883	0.126441	−	0.991974i	$-0.459644\pi$
$443$	2357.89	0.252883	0.126441	+	0.991974i	$0.459644\pi$
$444$	11181.0	1.19510
$445$	−6870.56	−0.731901
$446$	24993.0	2.65348
$447$	406.260	0.0429876
$448$	−13940.7	−1.47017
$449$	−7165.06	−0.753096	−0.376548	−	0.926397i	$-0.622889\pi$
$449$	−7165.06	−0.753096	−0.376548	+	0.926397i	$0.622889\pi$
$450$	1707.26	0.178846
$451$	6244.63	0.651992
$452$	168.288	0.0175124
$453$	−7121.22	−0.738596
$454$	−4190.74	−0.433219
$455$	0	0
$456$	−953.451	−0.0979154
$457$	8020.96	0.821017	0.410508	−	0.911857i	$-0.365351\pi$
$457$	8020.96	0.821017	0.410508	+	0.911857i	$0.365351\pi$
$458$	877.378	0.0895135
$459$	−3621.92	−0.368316
$460$	11786.8	1.19471
$461$	−4146.59	−0.418928	−0.209464	−	0.977816i	$-0.567172\pi$
$461$	−4146.59	−0.418928	−0.209464	+	0.977816i	$0.567172\pi$
$462$	5689.03	0.572895
$463$	7118.21	0.714495	0.357248	−	0.934010i	$-0.383715\pi$
$463$	7118.21	0.714495	0.357248	+	0.934010i	$0.383715\pi$
$464$	964.509	0.0965004
$465$	−9650.62	−0.962444
$466$	4155.31	0.413071
$467$	−2128.22	−0.210883	−0.105441	−	0.994426i	$-0.533626\pi$
$467$	−2128.22	−0.210883	−0.105441	+	0.994426i	$0.533626\pi$
$468$	0	0
$469$	−659.774	−0.0649585
$470$	−9387.91	−0.921344
$471$	−3500.18	−0.342420
$472$	4949.86	0.482703
$473$	10772.5	1.04719
$474$	12730.1	1.23357
$475$	−623.125	−0.0601915
$476$	−28452.4	−2.73974
$477$	−1751.23	−0.168099
$478$	−8989.57	−0.860196
$479$	−3715.30	−0.354397	−0.177199	−	0.984175i	$-0.556704\pi$
$479$	−3715.30	−0.354397	−0.177199	+	0.984175i	$0.556704\pi$
$480$	−7417.31	−0.705317
$481$	0	0
$482$	17755.0	1.67784
$483$	3613.43	0.340408
$484$	−8996.77	−0.844926
$485$	−4682.62	−0.438405
$486$	1105.02	0.103137
$487$	−8139.28	−0.757343	−0.378671	−	0.925531i	$-0.623619\pi$
$487$	−8139.28	−0.757343	−0.378671	+	0.925531i	$0.623619\pi$
$488$	−3936.23	−0.365133
$489$	−6927.57	−0.640645
$490$	−3707.59	−0.341820
$491$	18081.7	1.66194	0.830972	−	0.556315i	$-0.187785\pi$
$491$	18081.7	1.66194	0.830972	+	0.556315i	$0.187785\pi$
$492$	9528.35	0.873112
$493$	27653.4	2.52626
$494$	0	0
$495$	2896.80	0.263033
$496$	1165.68	0.105525
$497$	15398.3	1.38975
$498$	−14943.4	−1.34464
$499$	11031.5	0.989659	0.494829	−	0.868990i	$-0.335231\pi$
$499$	11031.5	0.989659	0.494829	+	0.868990i	$0.335231\pi$
$500$	−13634.2	−1.21948
$501$	−1802.37	−0.160726
$502$	−4283.80	−0.380868
$503$	8016.14	0.710581	0.355290	−	0.934756i	$-0.384382\pi$
$503$	8016.14	0.710581	0.355290	+	0.934756i	$0.384382\pi$
$504$	3203.35	0.283112
$505$	19246.1	1.69592
$506$	8161.74	0.717063
$507$	0	0
$508$	1850.95	0.161659
$509$	20173.9	1.75676	0.878382	−	0.477959i	$-0.158623\pi$
$509$	20173.9	1.75676	0.878382	+	0.477959i	$0.158623\pi$
$510$	−23629.1	−2.05159
$511$	−9185.44	−0.795186
$512$	1692.30	0.146074
$513$	−403.316	−0.0347112
$514$	−3695.29	−0.317105
$515$	8114.25	0.694285
$516$	16437.2	1.40234
$517$	−3985.72	−0.339056
$518$	22361.9	1.89677
$519$	10291.1	0.870382
$520$	0	0
$521$	9746.95	0.819619	0.409810	−	0.912171i	$-0.365595\pi$
$521$	9746.95	0.819619	0.409810	+	0.912171i	$0.365595\pi$
$522$	−8436.81	−0.707413
$523$	−18929.3	−1.58264	−0.791320	−	0.611402i	$-0.790606\pi$
$523$	−18929.3	−1.58264	−0.791320	+	0.611402i	$0.790606\pi$
$524$	4021.24	0.335245
$525$	2093.54	0.174037
$526$	−11860.9	−0.983195
$527$	33421.2	2.76252
$528$	−349.898	−0.0288397
$529$	−6983.00	−0.573929
$530$	−11424.9	−0.936349
$531$	2093.83	0.171119
$532$	−3168.30	−0.258201
$533$	0	0
$534$	−7259.20	−0.588270
$535$	6164.80	0.498182
$536$	−839.120	−0.0676203
$537$	2936.51	0.235977
$538$	−21786.6	−1.74589
$539$	−1574.09	−0.125790
$540$	4420.07	0.352240
$541$	−11366.8	−0.903321	−0.451661	−	0.892190i	$-0.649168\pi$
$541$	−11366.8	−0.903321	−0.451661	+	0.892190i	$0.649168\pi$
$542$	−16659.9	−1.32030
$543$	−11517.3	−0.910227
$544$	25687.0	2.02449
$545$	−4883.34	−0.383815
$546$	0	0
$547$	17495.4	1.36755	0.683775	−	0.729693i	$-0.260337\pi$
$547$	17495.4	1.36755	0.683775	+	0.729693i	$0.260337\pi$
$548$	5618.59	0.437983
$549$	−1665.05	−0.129440
$550$	4728.72	0.366606
$551$	3079.33	0.238083
$552$	4595.67	0.354356
$553$	15610.4	1.20040
$554$	−2839.05	−0.217725
$555$	11386.5	0.870862
$556$	9953.06	0.759180
$557$	−11873.1	−0.903192	−0.451596	−	0.892223i	$-0.649145\pi$
$557$	−11873.1	−0.903192	−0.451596	+	0.892223i	$0.649145\pi$
$558$	−10196.5	−0.773571
$559$	0	0
$560$	−1010.62	−0.0762613
$561$	−10031.9	−0.754989
$562$	25170.4	1.88923
$563$	−2829.31	−0.211796	−0.105898	−	0.994377i	$-0.533772\pi$
$563$	−2829.31	−0.211796	−0.105898	+	0.994377i	$0.533772\pi$
$564$	−6081.60	−0.454045
$565$	171.381	0.0127612
$566$	796.481	0.0591495
$567$	1355.04	0.100364
$568$	19583.9	1.44670
$569$	16136.8	1.18891	0.594453	−	0.804130i	$-0.297368\pi$
$569$	16136.8	1.18891	0.594453	+	0.804130i	$0.297368\pi$
$570$	−2631.20	−0.193349
$571$	−17840.5	−1.30754	−0.653769	−	0.756695i	$-0.726813\pi$
$571$	−17840.5	−1.30754	−0.653769	+	0.756695i	$0.726813\pi$
$572$	0	0
$573$	−1463.13	−0.106672
$574$	19056.7	1.38573
$575$	3003.49	0.217833
$576$	−7500.00	−0.542534
$577$	8516.17	0.614442	0.307221	−	0.951638i	$-0.400601\pi$
$577$	8516.17	0.614442	0.307221	+	0.951638i	$0.400601\pi$
$578$	59488.9	4.28099
$579$	12736.8	0.914205
$580$	−33747.3	−2.41600
$581$	−18324.5	−1.30848
$582$	−4947.49	−0.352371
$583$	−4850.53	−0.344577
$584$	−11682.3	−0.827770
$585$	0	0
$586$	−35352.9	−2.49218
$587$	−20688.3	−1.45468	−0.727340	−	0.686277i	$-0.759244\pi$
$587$	−20688.3	−1.45468	−0.727340	+	0.686277i	$0.759244\pi$
$588$	−2401.82	−0.168451
$589$	3721.59	0.260349
$590$	13659.9	0.953169
$591$	−8138.13	−0.566426
$592$	−1375.35	−0.0954839
$593$	11435.9	0.791933	0.395966	−	0.918265i	$-0.370410\pi$
$593$	11435.9	0.791933	0.395966	+	0.918265i	$0.370410\pi$
$594$	3060.65	0.211414
$595$	−28975.4	−1.99643
$596$	1716.96	0.118002
$597$	9350.69	0.641035
$598$	0	0
$599$	1260.80	0.0860016	0.0430008	−	0.999075i	$-0.486308\pi$
$599$	1260.80	0.0860016	0.0430008	+	0.999075i	$0.486308\pi$
$600$	2662.62	0.181169
$601$	6261.10	0.424951	0.212476	−	0.977166i	$-0.431847\pi$
$601$	6261.10	0.424951	0.212476	+	0.977166i	$0.431847\pi$
$602$	32874.5	2.22569
$603$	−354.954	−0.0239715
$604$	−30096.1	−2.02747
$605$	−9162.14	−0.615692
$606$	20334.8	1.36311
$607$	3230.33	0.216005	0.108003	−	0.994151i	$-0.465555\pi$
$607$	3230.33	0.216005	0.108003	+	0.994151i	$0.465555\pi$
$608$	2860.35	0.190794
$609$	−10345.7	−0.688391
$610$	−10862.6	−0.721009
$611$	0	0
$612$	−15307.2	−1.01104
$613$	14868.5	0.979660	0.489830	−	0.871818i	$-0.337059\pi$
$613$	14868.5	0.979660	0.489830	+	0.871818i	$0.337059\pi$
$614$	36483.0	2.39794
$615$	9703.48	0.636231
$616$	8872.57	0.580334
$617$	−19952.8	−1.30190	−0.650949	−	0.759121i	$-0.725629\pi$
$617$	−19952.8	−1.30190	−0.650949	+	0.759121i	$0.725629\pi$
$618$	8573.24	0.558036
$619$	8316.48	0.540012	0.270006	−	0.962859i	$-0.412974\pi$
$619$	8316.48	0.540012	0.270006	+	0.962859i	$0.412974\pi$
$620$	−40786.0	−2.64194
$621$	1944.00	0.125620
$622$	−42131.0	−2.71592
$623$	−8901.66	−0.572452
$624$	0	0
$625$	−19099.2	−1.22235
$626$	33757.9	2.15533
$627$	−1117.10	−0.0711525
$628$	−14792.7	−0.939955
$629$	−39432.6	−2.49965
$630$	8840.13	0.559046
$631$	−12605.9	−0.795299	−0.397649	−	0.917537i	$-0.630174\pi$
$631$	−12605.9	−0.795299	−0.397649	+	0.917537i	$0.630174\pi$
$632$	19853.7	1.24959
$633$	−3153.66	−0.198020
$634$	12009.8	0.752321
$635$	1884.98	0.117800
$636$	−7401.17	−0.461439
$637$	0	0
$638$	−23368.1	−1.45008
$639$	8284.14	0.512857
$640$	−29149.8	−1.80038
$641$	−9224.04	−0.568374	−0.284187	−	0.958769i	$-0.591724\pi$
$641$	−9224.04	−0.568374	−0.284187	+	0.958769i	$0.591724\pi$
$642$	6513.51	0.400417
$643$	4439.16	0.272260	0.136130	−	0.990691i	$-0.456533\pi$
$643$	4439.16	0.272260	0.136130	+	0.990691i	$0.456533\pi$
$644$	15271.3	0.934431
$645$	16739.4	1.02188
$646$	9112.13	0.554972
$647$	−9601.15	−0.583401	−0.291700	−	0.956510i	$-0.594221\pi$
$647$	−9601.15	−0.583401	−0.291700	+	0.956510i	$0.594221\pi$
$648$	1723.38	0.104476
$649$	5799.44	0.350767
$650$	0	0
$651$	−12503.6	−0.752770
$652$	−29277.7	−1.75859
$653$	27112.8	1.62482	0.812410	−	0.583087i	$-0.198155\pi$
$653$	27112.8	1.62482	0.812410	+	0.583087i	$0.198155\pi$
$654$	−5159.56	−0.308494
$655$	4095.15	0.244291
$656$	−1172.06	−0.0697583
$657$	−4941.70	−0.293446
$658$	−12163.2	−0.720624
$659$	5587.26	0.330271	0.165136	−	0.986271i	$-0.447194\pi$
$659$	5587.26	0.330271	0.165136	+	0.986271i	$0.447194\pi$
$660$	12242.6	0.722035
$661$	−3060.13	−0.180069	−0.0900343	−	0.995939i	$-0.528698\pi$
$661$	−3060.13	−0.180069	−0.0900343	+	0.995939i	$0.528698\pi$
$662$	49018.6	2.87789
$663$	0	0
$664$	−23305.6	−1.36210
$665$	−3226.53	−0.188150
$666$	12030.5	0.699961
$667$	−14842.5	−0.861623
$668$	−7617.26	−0.441199
$669$	16488.4	0.952880
$670$	−2315.68	−0.133526
$671$	−4611.83	−0.265332
$672$	−9610.04	−0.551660
$673$	4121.55	0.236069	0.118034	−	0.993010i	$-0.462341\pi$
$673$	4121.55	0.236069	0.118034	+	0.993010i	$0.462341\pi$
$674$	−1425.45	−0.0814633
$675$	1126.31	0.0642246
$676$	0	0
$677$	22889.5	1.29943	0.649715	−	0.760178i	$-0.274888\pi$
$677$	22889.5	1.29943	0.649715	+	0.760178i	$0.274888\pi$
$678$	181.075	0.0102569
$679$	−6066.91	−0.342896
$680$	−36851.8	−2.07824
$681$	−2764.71	−0.155571
$682$	−28242.1	−1.58570
$683$	−19297.9	−1.08113	−0.540566	−	0.841301i	$-0.681790\pi$
$683$	−19297.9	−1.08113	−0.540566	+	0.841301i	$0.681790\pi$
$684$	−1704.52	−0.0952835
$685$	5721.87	0.319155
$686$	−30896.6	−1.71959
$687$	578.823	0.0321448
$688$	−2021.91	−0.112042
$689$	0	0
$690$	12682.5	0.699729
$691$	−30317.8	−1.66910	−0.834548	−	0.550935i	$-0.814271\pi$
$691$	−30317.8	−1.66910	−0.834548	+	0.550935i	$0.814271\pi$
$692$	43492.8	2.38923
$693$	3753.16	0.205730
$694$	−12956.6	−0.708682
$695$	10136.0	0.553210
$696$	−13158.0	−0.716599
$697$	−33604.3	−1.82619
$698$	29407.7	1.59470
$699$	2741.34	0.148336
$700$	8847.84	0.477738
$701$	9606.16	0.517574	0.258787	−	0.965934i	$-0.416677\pi$
$701$	9606.16	0.517574	0.258787	+	0.965934i	$0.416677\pi$
$702$	0	0
$703$	−4390.99	−0.235575
$704$	−20773.4	−1.11211
$705$	−6193.38	−0.330860
$706$	−12610.4	−0.672235
$707$	24935.7	1.32646
$708$	8849.05	0.469729
$709$	−23398.8	−1.23944	−0.619718	−	0.784825i	$-0.712753\pi$
$709$	−23398.8	−1.23944	−0.619718	+	0.784825i	$0.712753\pi$
$710$	54044.9	2.85672
$711$	8398.26	0.442981
$712$	−11321.4	−0.595909
$713$	−17938.2	−0.942203
$714$	−30614.4	−1.60464
$715$	0	0
$716$	12410.5	0.647766
$717$	−5930.59	−0.308901
$718$	−6671.51	−0.346767
$719$	−23588.7	−1.22352	−0.611758	−	0.791045i	$-0.709537\pi$
$719$	−23588.7	−1.22352	−0.611758	+	0.791045i	$0.709537\pi$
$720$	−543.704	−0.0281426
$721$	10513.0	0.543031
$722$	−30175.9	−1.55544
$723$	11713.3	0.602522
$724$	−48674.9	−2.49861
$725$	−8599.38	−0.440514
$726$	−9680.40	−0.494867
$727$	15733.5	0.802644	0.401322	−	0.915937i	$-0.368551\pi$
$727$	15733.5	0.802644	0.401322	+	0.915937i	$0.368551\pi$
$728$	0	0
$729$	729.000	0.0370370
$730$	−32239.2	−1.63455
$731$	−57970.3	−2.93312
$732$	−7036.94	−0.355318
$733$	−17297.1	−0.871598	−0.435799	−	0.900044i	$-0.643534\pi$
$733$	−17297.1	−0.871598	−0.435799	+	0.900044i	$0.643534\pi$
$734$	21137.3	1.06293
$735$	−2445.96	−0.122749
$736$	−13787.0	−0.690484
$737$	−983.144	−0.0491378
$738$	10252.4	0.511375
$739$	38749.2	1.92884	0.964419	−	0.264377i	$-0.0851663\pi$
$739$	38749.2	1.92884	0.964419	+	0.264377i	$0.0851663\pi$
$740$	48122.2	2.39055
$741$	0	0
$742$	−14802.3	−0.732359
$743$	−3139.76	−0.155029	−0.0775144	−	0.996991i	$-0.524698\pi$
$743$	−3139.76	−0.155029	−0.0775144	+	0.996991i	$0.524698\pi$
$744$	−15902.4	−0.783616
$745$	1748.52	0.0859876
$746$	8020.33	0.393626
$747$	−9858.45	−0.482867
$748$	−42397.6	−2.07247
$749$	7987.25	0.389650
$750$	−14670.2	−0.714242
$751$	40628.6	1.97411	0.987055	−	0.160380i	$-0.0512721\pi$
$751$	40628.6	1.97411	0.987055	+	0.160380i	$0.0512721\pi$
$752$	748.086	0.0362764
$753$	−2826.11	−0.136772
$754$	0	0
$755$	−30649.3	−1.47741
$756$	5726.74	0.275502
$757$	24004.9	1.15254	0.576271	−	0.817259i	$-0.304507\pi$
$757$	24004.9	1.15254	0.576271	+	0.817259i	$0.304507\pi$
$758$	8778.62	0.420651
$759$	5384.46	0.257501
$760$	−4103.60	−0.195859
$761$	29540.1	1.40713	0.703566	−	0.710630i	$-0.251590\pi$
$761$	29540.1	1.40713	0.703566	+	0.710630i	$0.251590\pi$
$762$	1991.60	0.0946824
$763$	−6326.97	−0.300199
$764$	−6183.56	−0.292818
$765$	−15588.5	−0.736739
$766$	−40225.9	−1.89742
$767$	0	0
$768$	−10798.6	−0.507372
$769$	7585.63	0.355715	0.177857	−	0.984056i	$-0.443083\pi$
$769$	7585.63	0.355715	0.177857	+	0.984056i	$0.443083\pi$
$770$	24485.2	1.14596
$771$	−2437.85	−0.113874
$772$	53829.2	2.50953
$773$	3284.29	0.152817	0.0764086	−	0.997077i	$-0.475655\pi$
$773$	3284.29	0.152817	0.0764086	+	0.997077i	$0.475655\pi$
$774$	17686.2	0.821341
$775$	−10393.0	−0.481712
$776$	−7716.07	−0.356947
$777$	14752.6	0.681140
$778$	−7267.08	−0.334881
$779$	−3741.98	−0.172106
$780$	0	0
$781$	22945.3	1.05128
$782$	−43920.8	−2.00845
$783$	−5565.92	−0.254036
$784$	295.443	0.0134586
$785$	−15064.6	−0.684939
$786$	4326.79	0.196351
$787$	−41624.1	−1.88531	−0.942654	−	0.333772i	$-0.891679\pi$
$787$	−41624.1	−1.88531	−0.942654	+	0.333772i	$0.891679\pi$
$788$	−34393.8	−1.55486
$789$	−7824.87	−0.353071
$790$	54789.4	2.46749
$791$	222.046	0.00998108
$792$	4773.38	0.214160
$793$	0	0
$794$	16274.3	0.727398
$795$	−7537.20	−0.336248
$796$	39518.4	1.75967
$797$	−30333.3	−1.34813	−0.674066	−	0.738671i	$-0.735454\pi$
$797$	−30333.3	−1.34813	−0.674066	+	0.738671i	$0.735454\pi$
$798$	−3409.04	−0.151226
$799$	21448.4	0.949674
$800$	−7987.87	−0.353017
$801$	−4789.03	−0.211251
$802$	−15852.2	−0.697954
$803$	−13687.4	−0.601518
$804$	−1500.13	−0.0658027
$805$	15552.0	0.680914
$806$	0	0
$807$	−14373.1	−0.626958
$808$	31714.0	1.38081
$809$	−24853.9	−1.08012	−0.540060	−	0.841627i	$-0.681598\pi$
$809$	−24853.9	−1.08012	−0.540060	+	0.841627i	$0.681598\pi$
$810$	4755.92	0.206304
$811$	−17383.5	−0.752674	−0.376337	−	0.926483i	$-0.622816\pi$
$811$	−17383.5	−0.752674	−0.376337	+	0.926483i	$0.622816\pi$
$812$	−43723.7	−1.88966
$813$	−10990.9	−0.474128
$814$	33322.0	1.43481
$815$	−29815.8	−1.28148
$816$	1882.91	0.0807782
$817$	−6455.23	−0.276426
$818$	66887.8	2.85902
$819$	0	0
$820$	41009.4	1.74648
$821$	−31169.4	−1.32499	−0.662496	−	0.749065i	$-0.730503\pi$
$821$	−31169.4	−1.32499	−0.662496	+	0.749065i	$0.730503\pi$
$822$	6045.52	0.256523
$823$	5512.79	0.233492	0.116746	−	0.993162i	$-0.462754\pi$
$823$	5512.79	0.233492	0.116746	+	0.993162i	$0.462754\pi$
$824$	13370.8	0.565282
$825$	3119.63	0.131650
$826$	17698.1	0.745516
$827$	−13335.8	−0.560738	−0.280369	−	0.959892i	$-0.590457\pi$
$827$	−13335.8	−0.560738	−0.280369	+	0.959892i	$0.590457\pi$
$828$	8215.85	0.344832
$829$	−28338.5	−1.18726	−0.593628	−	0.804739i	$-0.702305\pi$
$829$	−28338.5	−1.18726	−0.593628	+	0.804739i	$0.702305\pi$
$830$	−64315.5	−2.68967
$831$	−1872.98	−0.0781864
$832$	0	0
$833$	8470.66	0.352330
$834$	10709.3	0.444646
$835$	−7757.27	−0.321499
$836$	−4721.15	−0.195316
$837$	−6726.82	−0.277793
$838$	16866.3	0.695272
$839$	−27149.5	−1.11717	−0.558585	−	0.829447i	$-0.688656\pi$
$839$	−27149.5	−1.11717	−0.558585	+	0.829447i	$0.688656\pi$
$840$	13787.0	0.566306
$841$	18106.9	0.742421
$842$	3610.76	0.147785
$843$	16605.4	0.678433
$844$	−13328.2	−0.543573
$845$	0	0
$846$	−6543.71	−0.265931
$847$	−11870.7	−0.481560
$848$	910.404	0.0368672
$849$	525.454	0.0212409
$850$	−25446.7	−1.02684
$851$	21164.7	0.852547
$852$	35010.9	1.40781
$853$	7978.22	0.320245	0.160123	−	0.987097i	$-0.448811\pi$
$853$	7978.22	0.320245	0.160123	+	0.987097i	$0.448811\pi$
$854$	−14073.9	−0.563933
$855$	−1735.85	−0.0694325
$856$	10158.4	0.405616
$857$	−13614.4	−0.542657	−0.271329	−	0.962487i	$-0.587463\pi$
$857$	−13614.4	−0.542657	−0.271329	+	0.962487i	$0.587463\pi$
$858$	0	0
$859$	−35007.7	−1.39051	−0.695255	−	0.718763i	$-0.744709\pi$
$859$	−35007.7	−1.39051	−0.695255	+	0.718763i	$0.744709\pi$
$860$	70744.8	2.80509
$861$	12572.1	0.497624
$862$	13148.9	0.519551
$863$	−24461.5	−0.964867	−0.482434	−	0.875933i	$-0.660247\pi$
$863$	−24461.5	−0.964867	−0.482434	+	0.875933i	$0.660247\pi$
$864$	−5170.13	−0.203578
$865$	44292.2	1.74102
$866$	25287.8	0.992278
$867$	39245.9	1.53733
$868$	−52843.3	−2.06638
$869$	23261.3	0.908040
$870$	−36311.5	−1.41503
$871$	0	0
$872$	−8046.82	−0.312500
$873$	−3263.95	−0.126538
$874$	−4890.77	−0.189282
$875$	−17989.5	−0.695037
$876$	−20884.9	−0.805520
$877$	−43121.6	−1.66034	−0.830168	−	0.557514i	$-0.811755\pi$
$877$	−43121.6	−1.66034	−0.830168	+	0.557514i	$0.811755\pi$
$878$	68789.3	2.64411
$879$	−23323.0	−0.894955
$880$	−1505.94	−0.0576878
$881$	−40824.5	−1.56120	−0.780598	−	0.625034i	$-0.785085\pi$
$881$	−40824.5	−1.56120	−0.780598	+	0.625034i	$0.785085\pi$
$882$	−2584.32	−0.0986605
$883$	8262.14	0.314885	0.157442	−	0.987528i	$-0.449675\pi$
$883$	8262.14	0.314885	0.157442	+	0.987528i	$0.449675\pi$
$884$	0	0
$885$	9011.70	0.342288
$886$	10722.3	0.406571
$887$	−40858.6	−1.54667	−0.773336	−	0.633997i	$-0.781413\pi$
$887$	−40858.6	−1.54667	−0.773336	+	0.633997i	$0.781413\pi$
$888$	18762.8	0.709050
$889$	2442.22	0.0921365
$890$	−31243.2	−1.17671
$891$	2019.17	0.0759201
$892$	69684.1	2.61569
$893$	2388.37	0.0895001
$894$	1847.42	0.0691131
$895$	12638.6	0.472023
$896$	−37767.1	−1.40816
$897$	0	0
$898$	−32582.3	−1.21079
$899$	51359.4	1.90537
$900$	4760.07	0.176299
$901$	26102.2	0.965139
$902$	28396.8	1.04824
$903$	21687.9	0.799256
$904$	282.404	0.0103901
$905$	−49569.6	−1.82072
$906$	−32383.0	−1.18747
$907$	−32729.3	−1.19819	−0.599095	−	0.800678i	$-0.704473\pi$
$907$	−32729.3	−1.19819	−0.599095	+	0.800678i	$0.704473\pi$
$908$	−11684.4	−0.427048
$909$	13415.2	0.489500
$910$	0	0
$911$	11065.9	0.402447	0.201223	−	0.979545i	$-0.435508\pi$
$911$	11065.9	0.402447	0.201223	+	0.979545i	$0.435508\pi$
$912$	209.670	0.00761279
$913$	−27305.7	−0.989801
$914$	36474.5	1.31999
$915$	−7166.29	−0.258918
$916$	2446.26	0.0882386
$917$	5305.77	0.191071
$918$	−16470.3	−0.592158
$919$	50682.2	1.81921	0.909604	−	0.415477i	$-0.136385\pi$
$919$	50682.2	1.81921	0.909604	+	0.415477i	$0.136385\pi$
$920$	19779.5	0.708816
$921$	24068.5	0.861114
$922$	−18856.2	−0.673531
$923$	0	0
$924$	15861.8	0.564735
$925$	12262.3	0.435874
$926$	32369.3	1.14873
$927$	5655.92	0.200394
$928$	39474.0	1.39633
$929$	41045.5	1.44958	0.724790	−	0.688970i	$-0.241937\pi$
$929$	41045.5	1.44958	0.724790	+	0.688970i	$0.241937\pi$
$930$	−43885.1	−1.54737
$931$	943.243	0.0332047
$932$	11585.6	0.407188
$933$	−27794.6	−0.975300
$934$	−9677.86	−0.339046
$935$	−43176.9	−1.51020
$936$	0	0
$937$	−788.985	−0.0275080	−0.0137540	−	0.999905i	$-0.504378\pi$
$937$	−788.985	−0.0275080	−0.0137540	+	0.999905i	$0.504378\pi$
$938$	−3000.25	−0.104437
$939$	22270.7	0.773991
$940$	−26174.8	−0.908222
$941$	−25676.2	−0.889499	−0.444750	−	0.895655i	$-0.646707\pi$
$941$	−25676.2	−0.889499	−0.444750	+	0.895655i	$0.646707\pi$
$942$	−15916.7	−0.550524
$943$	18036.5	0.622851
$944$	−1088.51	−0.0375295
$945$	5832.00	0.200757
$946$	48986.9	1.68362
$947$	−679.352	−0.0233115	−0.0116557	−	0.999932i	$-0.503710\pi$
$947$	−679.352	−0.0233115	−0.0116557	+	0.999932i	$0.503710\pi$
$948$	35493.2	1.21600
$949$	0	0
$950$	−2833.60	−0.0967726
$951$	7923.12	0.270163
$952$	−47746.0	−1.62548
$953$	−20238.4	−0.687917	−0.343958	−	0.938985i	$-0.611768\pi$
$953$	−20238.4	−0.687917	−0.343958	+	0.938985i	$0.611768\pi$
$954$	−7963.54	−0.270261
$955$	−6297.21	−0.213375
$956$	−25064.2	−0.847944
$957$	−15416.4	−0.520733
$958$	−16894.9	−0.569781
$959$	7413.38	0.249625
$960$	−32279.5	−1.08523
$961$	32280.6	1.08357
$962$	0	0
$963$	4297.08	0.143792
$964$	49503.6	1.65395
$965$	54818.6	1.82868
$966$	16431.7	0.547289
$967$	−6161.63	−0.204906	−0.102453	−	0.994738i	$-0.532669\pi$
$967$	−6161.63	−0.204906	−0.102453	+	0.994738i	$0.532669\pi$
$968$	−15097.5	−0.501293
$969$	6011.45	0.199294
$970$	−21293.7	−0.704845
$971$	−48569.5	−1.60522	−0.802610	−	0.596504i	$-0.796556\pi$
$971$	−48569.5	−1.60522	−0.802610	+	0.596504i	$0.796556\pi$
$972$	3080.94	0.101668
$973$	13132.4	0.432689
$974$	−37012.5	−1.21761
$975$	0	0
$976$	865.602	0.0283886
$977$	−44595.8	−1.46033	−0.730167	−	0.683269i	$-0.760558\pi$
$977$	−44595.8	−1.46033	−0.730167	+	0.683269i	$0.760558\pi$
$978$	−31502.4	−1.03000
$979$	−13264.6	−0.433031
$980$	−10337.3	−0.336951
$981$	−3403.86	−0.110782
$982$	82224.4	2.67198
$983$	−29599.0	−0.960389	−0.480195	−	0.877162i	$-0.659434\pi$
$983$	−29599.0	−0.960389	−0.480195	+	0.877162i	$0.659434\pi$
$984$	15989.5	0.518015
$985$	−35026.0	−1.13302
$986$	125751.	4.06159
$987$	−8024.29	−0.258780
$988$	0	0
$989$	31114.5	1.00039
$990$	13172.9	0.422890
$991$	5718.45	0.183302	0.0916511	−	0.995791i	$-0.470786\pi$
$991$	5718.45	0.183302	0.0916511	+	0.995791i	$0.470786\pi$
$992$	47707.2	1.52692
$993$	32338.5	1.03347
$994$	70021.9	2.23437
$995$	40244.8	1.28226
$996$	−41664.4	−1.32549
$997$	−1491.44	−0.0473766	−0.0236883	−	0.999719i	$-0.507541\pi$
$997$	−1491.44	−0.0473766	−0.0236883	+	0.999719i	$0.507541\pi$
$998$	50164.8	1.59112
$999$	7936.77	0.251360

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.4.a.l.1.4		4
3.2	odd	2		1521.4.a.w.1.1		4
13.5	odd	4		39.4.b.b.25.1	✓	4
13.8	odd	4		39.4.b.b.25.4	yes	4
13.12	even	2	inner	507.4.a.l.1.1		4
39.5	even	4		117.4.b.e.64.4		4
39.8	even	4		117.4.b.e.64.1		4
39.38	odd	2		1521.4.a.w.1.4		4
52.31	even	4		624.4.c.c.337.1		4
52.47	even	4		624.4.c.c.337.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.4.b.b.25.1	✓	4	13.5	odd	4
39.4.b.b.25.4	yes	4	13.8	odd	4
117.4.b.e.64.1		4	39.8	even	4
117.4.b.e.64.4		4	39.5	even	4
507.4.a.l.1.1		4	13.12	even	2	inner
507.4.a.l.1.4		4	1.1	even	1	trivial
624.4.c.c.337.1		4	52.31	even	4
624.4.c.c.337.4		4	52.47	even	4
1521.4.a.w.1.1		4	3.2	odd	2
1521.4.a.w.1.4		4	39.38	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	507.a (trivial)

\(f(q)\)	\(=\)	\(q+4.54739 q^{2} +3.00000 q^{3} +12.6788 q^{4} +12.9118 q^{5} +13.6422 q^{6} +16.7289 q^{7} +21.2762 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+4.54739 q^{2} +3.00000 q^{3} +12.6788 q^{4} +12.9118 q^{5} +13.6422 q^{6} +16.7289 q^{7} +21.2762 q^{8} +9.00000 q^{9} +58.7151 q^{10} +24.9280 q^{11} +38.0363 q^{12} +76.0727 q^{14} +38.7355 q^{15} -4.67878 q^{16} -134.145 q^{17} +40.9265 q^{18} -14.9376 q^{19} +163.706 q^{20} +50.1866 q^{21} +113.358 q^{22} +72.0000 q^{23} +63.8287 q^{24} +41.7151 q^{25} +27.0000 q^{27} +212.101 q^{28} -206.145 q^{29} +176.145 q^{30} -249.142 q^{31} -191.486 q^{32} +74.7841 q^{33} -610.012 q^{34} +216.000 q^{35} +114.109 q^{36} +293.955 q^{37} -67.9273 q^{38} +274.715 q^{40} +250.506 q^{41} +228.218 q^{42} +432.145 q^{43} +316.057 q^{44} +116.206 q^{45} +327.412 q^{46} -159.889 q^{47} -14.0363 q^{48} -63.1454 q^{49} +189.695 q^{50} -402.436 q^{51} -194.581 q^{53} +122.780 q^{54} +321.866 q^{55} +355.927 q^{56} -44.8129 q^{57} -937.424 q^{58} +232.647 q^{59} +491.118 q^{60} -185.006 q^{61} -1132.94 q^{62} +150.560 q^{63} -833.333 q^{64} +340.073 q^{66} -39.4393 q^{67} -1700.80 q^{68} +216.000 q^{69} +982.237 q^{70} +920.460 q^{71} +191.486 q^{72} -549.078 q^{73} +1336.73 q^{74} +125.145 q^{75} -189.391 q^{76} +417.018 q^{77} +933.140 q^{79} -60.4116 q^{80} +81.0000 q^{81} +1139.15 q^{82} -1095.38 q^{83} +636.304 q^{84} -1732.06 q^{85} +1965.13 q^{86} -618.436 q^{87} +530.375 q^{88} -532.114 q^{89} +528.436 q^{90} +912.872 q^{92} -747.425 q^{93} -727.079 q^{94} -192.872 q^{95} -574.459 q^{96} -362.661 q^{97} -287.147 q^{98} +224.352 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 12 q^{3} + 14 q^{4} + 36 q^{9}+O(q^{10}) \) 4 * q + 12 * q^3 + 14 * q^4 + 36 * q^9	\( 4 q + 12 q^{3} + 14 q^{4} + 36 q^{9} + 88 q^{10} + 42 q^{12} + 84 q^{14} + 18 q^{16} - 96 q^{17} + 380 q^{22} + 288 q^{23} + 20 q^{25} + 108 q^{27} - 384 q^{29} + 264 q^{30} + 864 q^{35} + 126 q^{36} - 492 q^{38} + 952 q^{40} + 252 q^{42} + 1288 q^{43} + 54 q^{48} + 188 q^{49} - 288 q^{51} + 984 q^{53} - 328 q^{55} + 1644 q^{56} + 288 q^{61} - 1668 q^{62} - 1314 q^{64} + 1140 q^{66} - 4380 q^{68} + 864 q^{69} + 3144 q^{74} + 60 q^{75} - 1416 q^{77} + 4320 q^{79} + 324 q^{81} + 3088 q^{82} - 1152 q^{87} - 1036 q^{88} + 792 q^{90} + 1008 q^{92} - 1660 q^{94} + 1872 q^{95}+O(q^{100}) \) 4 * q + 12 * q^3 + 14 * q^4 + 36 * q^9 + 88 * q^10 + 42 * q^12 + 84 * q^14 + 18 * q^16 - 96 * q^17 + 380 * q^22 + 288 * q^23 + 20 * q^25 + 108 * q^27 - 384 * q^29 + 264 * q^30 + 864 * q^35 + 126 * q^36 - 492 * q^38 + 952 * q^40 + 252 * q^42 + 1288 * q^43 + 54 * q^48 + 188 * q^49 - 288 * q^51 + 984 * q^53 - 328 * q^55 + 1644 * q^56 + 288 * q^61 - 1668 * q^62 - 1314 * q^64 + 1140 * q^66 - 4380 * q^68 + 864 * q^69 + 3144 * q^74 + 60 * q^75 - 1416 * q^77 + 4320 * q^79 + 324 * q^81 + 3088 * q^82 - 1152 * q^87 - 1036 * q^88 + 792 * q^90 + 1008 * q^92 - 1660 * q^94 + 1872 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more