LMFDB - Embedded newform 245.4.a.p.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [245,4,Mod(1,245)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(245, 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("245.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 245 = 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	245.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:	$14.4554679514$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.6.1163891200.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} - 23x^{4} + 12x^{3} + 154x^{2} + 152x + 28 $ x^6 - 2x^5 - 23x^4 + 12x^3 + 154x^2 + 152*x + 28
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2\cdot 7 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$4.29508$ of defining polynomial
Character	$\chi$	$=$	245.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.88087 q^{2} -2.89052 q^{3} +0.299392 q^{4} -5.00000 q^{5} +8.32721 q^{6} +22.1844 q^{8} -18.6449 q^{9} +O(q^{10})$	\(q-2.88087 q^{2} -2.89052 q^{3} +0.299392 q^{4} -5.00000 q^{5} +8.32721 q^{6} +22.1844 q^{8} -18.6449 q^{9} +14.4043 q^{10} -46.4881 q^{11} -0.865401 q^{12} -31.0537 q^{13} +14.4526 q^{15} -66.3055 q^{16} -61.8516 q^{17} +53.7134 q^{18} +24.6214 q^{19} -1.49696 q^{20} +133.926 q^{22} -154.942 q^{23} -64.1246 q^{24} +25.0000 q^{25} +89.4616 q^{26} +131.938 q^{27} +200.436 q^{29} -41.6361 q^{30} +129.255 q^{31} +13.5419 q^{32} +134.375 q^{33} +178.186 q^{34} -5.58213 q^{36} -77.9662 q^{37} -70.9309 q^{38} +89.7615 q^{39} -110.922 q^{40} +235.479 q^{41} -278.388 q^{43} -13.9182 q^{44} +93.2244 q^{45} +446.366 q^{46} +368.085 q^{47} +191.658 q^{48} -72.0217 q^{50} +178.784 q^{51} -9.29725 q^{52} -169.584 q^{53} -380.095 q^{54} +232.440 q^{55} -71.1686 q^{57} -577.429 q^{58} +691.490 q^{59} +4.32700 q^{60} +696.572 q^{61} -372.365 q^{62} +491.432 q^{64} +155.269 q^{65} -387.116 q^{66} +2.33311 q^{67} -18.5179 q^{68} +447.863 q^{69} -866.599 q^{71} -413.626 q^{72} +752.443 q^{73} +224.610 q^{74} -72.2631 q^{75} +7.37145 q^{76} -258.591 q^{78} +842.783 q^{79} +331.528 q^{80} +122.043 q^{81} -678.384 q^{82} -1443.44 q^{83} +309.258 q^{85} +801.998 q^{86} -579.364 q^{87} -1031.31 q^{88} -1438.06 q^{89} -268.567 q^{90} -46.3884 q^{92} -373.613 q^{93} -1060.40 q^{94} -123.107 q^{95} -39.1433 q^{96} +23.4509 q^{97} +866.764 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 2 q^{2} + 16 q^{3} + 14 q^{4} - 30 q^{5} + 24 q^{6} - 66 q^{8} + 70 q^{9}+O(q^{10}) $ 6 * q - 2 * q^2 + 16 * q^3 + 14 * q^4 - 30 * q^5 + 24 * q^6 - 66 * q^8 + 70 * q^9	\( 6 q - 2 q^{2} + 16 q^{3} + 14 q^{4} - 30 q^{5} + 24 q^{6} - 66 q^{8} + 70 q^{9} + 10 q^{10} - 16 q^{11} + 160 q^{12} + 168 q^{13} - 80 q^{15} + 298 q^{16} - 4 q^{17} + 354 q^{18} + 308 q^{19} - 70 q^{20} - 236 q^{22} - 336 q^{23} - 92 q^{24} + 150 q^{25} + 56 q^{26} + 964 q^{27} + 176 q^{29} - 120 q^{30} + 392 q^{31} - 770 q^{32} + 188 q^{33} + 812 q^{34} + 230 q^{36} - 140 q^{37} + 20 q^{38} + 140 q^{39} + 330 q^{40} + 656 q^{41} - 388 q^{43} - 160 q^{44} - 350 q^{45} - 388 q^{46} + 628 q^{47} + 1396 q^{48} - 50 q^{50} + 744 q^{51} + 1520 q^{52} - 676 q^{53} + 2284 q^{54} + 80 q^{55} + 1468 q^{57} - 2012 q^{58} + 996 q^{59} - 800 q^{60} + 740 q^{61} - 364 q^{62} + 1426 q^{64} - 840 q^{65} - 3620 q^{66} + 1768 q^{67} - 2940 q^{68} - 1048 q^{69} - 224 q^{71} + 2858 q^{72} + 2640 q^{73} + 928 q^{74} + 400 q^{75} - 1340 q^{76} + 8 q^{78} + 1636 q^{79} - 1490 q^{80} + 4442 q^{81} - 1756 q^{82} + 140 q^{83} + 20 q^{85} + 1180 q^{86} + 1940 q^{87} - 5652 q^{88} - 1904 q^{89} - 1770 q^{90} - 1952 q^{92} - 1592 q^{93} - 3332 q^{94} - 1540 q^{95} - 6460 q^{96} + 516 q^{97} - 2804 q^{99}+O(q^{100}) \) 6 * q - 2 * q^2 + 16 * q^3 + 14 * q^4 - 30 * q^5 + 24 * q^6 - 66 * q^8 + 70 * q^9 + 10 * q^10 - 16 * q^11 + 160 * q^12 + 168 * q^13 - 80 * q^15 + 298 * q^16 - 4 * q^17 + 354 * q^18 + 308 * q^19 - 70 * q^20 - 236 * q^22 - 336 * q^23 - 92 * q^24 + 150 * q^25 + 56 * q^26 + 964 * q^27 + 176 * q^29 - 120 * q^30 + 392 * q^31 - 770 * q^32 + 188 * q^33 + 812 * q^34 + 230 * q^36 - 140 * q^37 + 20 * q^38 + 140 * q^39 + 330 * q^40 + 656 * q^41 - 388 * q^43 - 160 * q^44 - 350 * q^45 - 388 * q^46 + 628 * q^47 + 1396 * q^48 - 50 * q^50 + 744 * q^51 + 1520 * q^52 - 676 * q^53 + 2284 * q^54 + 80 * q^55 + 1468 * q^57 - 2012 * q^58 + 996 * q^59 - 800 * q^60 + 740 * q^61 - 364 * q^62 + 1426 * q^64 - 840 * q^65 - 3620 * q^66 + 1768 * q^67 - 2940 * q^68 - 1048 * q^69 - 224 * q^71 + 2858 * q^72 + 2640 * q^73 + 928 * q^74 + 400 * q^75 - 1340 * q^76 + 8 * q^78 + 1636 * q^79 - 1490 * q^80 + 4442 * q^81 - 1756 * q^82 + 140 * q^83 + 20 * q^85 + 1180 * q^86 + 1940 * q^87 - 5652 * q^88 - 1904 * q^89 - 1770 * q^90 - 1952 * q^92 - 1592 * q^93 - 3332 * q^94 - 1540 * q^95 - 6460 * q^96 + 516 * q^97 - 2804 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.88087	−1.01854	−0.509270	−	0.860607i	$-0.670085\pi$
$2$	−2.88087	−1.01854	−0.509270	+	0.860607i	$0.670085\pi$
$3$	−2.89052	−0.556281	−0.278141	−	0.960540i	$-0.589718\pi$
$3$	−2.89052	−0.556281	−0.278141	+	0.960540i	$0.589718\pi$
$4$	0.299392	0.0374241
$5$	−5.00000	−0.447214
$5$	−5.00000	−0.447214
$6$	8.32721	0.566595
$7$	0	0
$7$	0	0
$8$	22.1844	0.980422
$9$	−18.6449	−0.690551
$10$	14.4043	0.455505
$11$	−46.4881	−1.27424	−0.637122	−	0.770763i	$-0.719875\pi$
$11$	−46.4881	−1.27424	−0.637122	+	0.770763i	$0.719875\pi$
$12$	−0.865401	−0.0208183
$13$	−31.0537	−0.662519	−0.331260	−	0.943540i	$-0.607474\pi$
$13$	−31.0537	−0.662519	−0.331260	+	0.943540i	$0.607474\pi$
$14$	0	0
$15$	14.4526	0.248777
$16$	−66.3055	−1.03602
$17$	−61.8516	−0.882425	−0.441212	−	0.897403i	$-0.645451\pi$
$17$	−61.8516	−0.882425	−0.441212	+	0.897403i	$0.645451\pi$
$18$	53.7134	0.703354
$19$	24.6214	0.297291	0.148645	−	0.988891i	$-0.452509\pi$
$19$	24.6214	0.297291	0.148645	+	0.988891i	$0.452509\pi$
$20$	−1.49696	−0.0167365
$21$	0	0
$22$	133.926	1.29787
$23$	−154.942	−1.40468	−0.702339	−	0.711843i	$-0.747861\pi$
$23$	−154.942	−1.40468	−0.702339	+	0.711843i	$0.747861\pi$
$24$	−64.1246	−0.545391
$25$	25.0000	0.200000
$26$	89.4616	0.674803
$27$	131.938	0.940422
$28$	0	0
$29$	200.436	1.28345	0.641724	−	0.766936i	$-0.278219\pi$
$29$	200.436	1.28345	0.641724	+	0.766936i	$0.278219\pi$
$30$	−41.6361	−0.253389
$31$	129.255	0.748865	0.374432	−	0.927254i	$-0.377838\pi$
$31$	129.255	0.748865	0.374432	+	0.927254i	$0.377838\pi$
$32$	13.5419	0.0748093
$33$	134.375	0.708838
$34$	178.186	0.898785
$35$	0	0
$36$	−5.58213	−0.0258432
$37$	−77.9662	−0.346421	−0.173210	−	0.984885i	$-0.555414\pi$
$37$	−77.9662	−0.346421	−0.173210	+	0.984885i	$0.555414\pi$
$38$	−70.9309	−0.302803
$39$	89.7615	0.368547
$40$	−110.922	−0.438458
$41$	235.479	0.896967	0.448483	−	0.893791i	$-0.351964\pi$
$41$	235.479	0.896967	0.448483	+	0.893791i	$0.351964\pi$
$42$	0	0
$43$	−278.388	−0.987296	−0.493648	−	0.869662i	$-0.664337\pi$
$43$	−278.388	−0.987296	−0.493648	+	0.869662i	$0.664337\pi$
$44$	−13.9182	−0.0476874
$45$	93.2244	0.308824
$46$	446.366	1.43072
$47$	368.085	1.14235	0.571177	−	0.820827i	$-0.306487\pi$
$47$	368.085	1.14235	0.571177	+	0.820827i	$0.306487\pi$
$48$	191.658	0.576321
$49$	0	0
$50$	−72.0217	−0.203708
$51$	178.784	0.490877
$52$	−9.29725	−0.0247942
$53$	−169.584	−0.439512	−0.219756	−	0.975555i	$-0.570526\pi$
$53$	−169.584	−0.439512	−0.219756	+	0.975555i	$0.570526\pi$
$54$	−380.095	−0.957858
$55$	232.440	0.569859
$56$	0	0
$57$	−71.1686	−0.165377
$58$	−577.429	−1.30724
$59$	691.490	1.52584	0.762918	−	0.646496i	$-0.223766\pi$
$59$	691.490	1.52584	0.762918	+	0.646496i	$0.223766\pi$
$60$	4.32700	0.00931023
$61$	696.572	1.46208	0.731041	−	0.682334i	$-0.239035\pi$
$61$	696.572	1.46208	0.731041	+	0.682334i	$0.239035\pi$
$62$	−372.365	−0.762749
$63$	0	0
$64$	491.432	0.959827
$65$	155.269	0.296288
$66$	−387.116	−0.721980
$67$	2.33311	0.00425426	0.00212713	−	0.999998i	$-0.499323\pi$
$67$	2.33311	0.00425426	0.00212713	+	0.999998i	$0.499323\pi$
$68$	−18.5179	−0.0330239
$69$	447.863	0.781396
$70$	0	0
$71$	−866.599	−1.44854	−0.724270	−	0.689516i	$-0.757823\pi$
$71$	−866.599	−1.44854	−0.724270	+	0.689516i	$0.757823\pi$
$72$	−413.626	−0.677032
$73$	752.443	1.20639	0.603197	−	0.797592i	$-0.293893\pi$
$73$	752.443	1.20639	0.603197	+	0.797592i	$0.293893\pi$
$74$	224.610	0.352843
$75$	−72.2631	−0.111256
$76$	7.37145	0.0111258
$77$	0	0
$78$	−258.591	−0.375380
$79$	842.783	1.20026	0.600130	−	0.799903i	$-0.295116\pi$
$79$	842.783	1.20026	0.600130	+	0.799903i	$0.295116\pi$
$80$	331.528	0.463324
$81$	122.043	0.167412
$82$	−678.384	−0.913597
$83$	−1443.44	−1.90890	−0.954450	−	0.298372i	$-0.903556\pi$
$83$	−1443.44	−1.90890	−0.954450	+	0.298372i	$0.903556\pi$
$84$	0	0
$85$	309.258	0.394632
$86$	801.998	1.00560
$87$	−579.364	−0.713958
$88$	−1031.31	−1.24930
$89$	−1438.06	−1.71274	−0.856372	−	0.516360i	$-0.827287\pi$
$89$	−1438.06	−1.71274	−0.856372	+	0.516360i	$0.827287\pi$
$90$	−268.567	−0.314549
$91$	0	0
$92$	−46.3884	−0.0525687
$93$	−373.613	−0.416579
$94$	−1060.40	−1.16353
$95$	−123.107	−0.132953
$96$	−39.1433	−0.0416150
$97$	23.4509	0.0245472	0.0122736	−	0.999925i	$-0.496093\pi$
$97$	23.4509	0.0245472	0.0122736	+	0.999925i	$0.496093\pi$
$98$	0	0
$99$	866.764	0.879930
$100$	7.48481	0.00748481
$101$	−1476.41	−1.45454	−0.727271	−	0.686350i	$-0.759212\pi$
$101$	−1476.41	−1.45454	−0.727271	+	0.686350i	$0.759212\pi$
$102$	−515.052	−0.499978
$103$	1009.44	0.965663	0.482831	−	0.875713i	$-0.339608\pi$
$103$	1009.44	0.965663	0.482831	+	0.875713i	$0.339608\pi$
$104$	−688.909	−0.649549
$105$	0	0
$106$	488.549	0.447661
$107$	1418.51	1.28161	0.640805	−	0.767704i	$-0.278601\pi$
$107$	1418.51	1.28161	0.640805	+	0.767704i	$0.278601\pi$
$108$	39.5011	0.0351944
$109$	−877.860	−0.771410	−0.385705	−	0.922622i	$-0.626042\pi$
$109$	−877.860	−0.771410	−0.385705	+	0.922622i	$0.626042\pi$
$110$	−669.629	−0.580424
$111$	225.363	0.192707
$112$	0	0
$113$	−1500.11	−1.24884	−0.624419	−	0.781090i	$-0.714664\pi$
$113$	−1500.11	−1.24884	−0.624419	+	0.781090i	$0.714664\pi$
$114$	205.027	0.168444
$115$	774.708	0.628191
$116$	60.0090	0.0480318
$117$	578.993	0.457503
$118$	−1992.09	−1.55412
$119$	0	0
$120$	320.623	0.243906
$121$	830.140	0.623696
$122$	−2006.73	−1.48919
$123$	−680.658	−0.498966
$124$	38.6978	0.0280255
$125$	−125.000	−0.0894427
$126$	0	0
$127$	416.639	0.291108	0.145554	−	0.989350i	$-0.453503\pi$
$127$	416.639	0.291108	0.145554	+	0.989350i	$0.453503\pi$
$128$	−1524.08	−1.05243
$129$	804.686	0.549214
$130$	−447.308	−0.301781
$131$	−410.496	−0.273780	−0.136890	−	0.990586i	$-0.543711\pi$
$131$	−410.496	−0.273780	−0.136890	+	0.990586i	$0.543711\pi$
$132$	40.2308	0.0265276
$133$	0	0
$134$	−6.72139	−0.00433313
$135$	−659.688	−0.420570
$136$	−1372.14	−0.865149
$137$	1761.97	1.09880	0.549400	−	0.835560i	$-0.314856\pi$
$137$	1761.97	1.09880	0.549400	+	0.835560i	$0.314856\pi$
$138$	−1290.23	−0.795883
$139$	865.719	0.528268	0.264134	−	0.964486i	$-0.414914\pi$
$139$	865.719	0.528268	0.264134	+	0.964486i	$0.414914\pi$
$140$	0	0
$141$	−1063.96	−0.635470
$142$	2496.56	1.47540
$143$	1443.63	0.844211
$144$	1236.26	0.715427
$145$	−1002.18	−0.573975
$146$	−2167.69	−1.22876
$147$	0	0
$148$	−23.3425	−0.0129645
$149$	3019.23	1.66004	0.830018	−	0.557737i	$-0.188330\pi$
$149$	3019.23	1.66004	0.830018	+	0.557737i	$0.188330\pi$
$150$	208.180	0.113319
$151$	541.896	0.292045	0.146023	−	0.989281i	$-0.453353\pi$
$151$	541.896	0.292045	0.146023	+	0.989281i	$0.453353\pi$
$152$	546.211	0.291471
$153$	1153.22	0.609359
$154$	0	0
$155$	−646.273	−0.334902
$156$	26.8739	0.0137925
$157$	2586.09	1.31460	0.657300	−	0.753629i	$-0.271698\pi$
$157$	2586.09	1.31460	0.657300	+	0.753629i	$0.271698\pi$
$158$	−2427.94	−1.22251
$159$	490.186	0.244493
$160$	−67.7096	−0.0334557
$161$	0	0
$162$	−351.590	−0.170515
$163$	−2466.14	−1.18505	−0.592525	−	0.805552i	$-0.701869\pi$
$163$	−2466.14	−1.18505	−0.592525	+	0.805552i	$0.701869\pi$
$164$	70.5006	0.0335681
$165$	−671.874	−0.317002
$166$	4158.37	1.94429
$167$	459.020	0.212695	0.106347	−	0.994329i	$-0.466084\pi$
$167$	459.020	0.212695	0.106347	+	0.994329i	$0.466084\pi$
$168$	0	0
$169$	−1232.67	−0.561068
$170$	−890.931	−0.401949
$171$	−459.062	−0.205295
$172$	−83.3471	−0.0369486
$173$	−4501.46	−1.97826	−0.989132	−	0.147032i	$-0.953028\pi$
$173$	−4501.46	−1.97826	−0.989132	+	0.147032i	$0.953028\pi$
$174$	1669.07	0.727195
$175$	0	0
$176$	3082.41	1.32015
$177$	−1998.77	−0.848794
$178$	4142.86	1.74450
$179$	1960.11	0.818467	0.409233	−	0.912430i	$-0.365796\pi$
$179$	1960.11	0.818467	0.409233	+	0.912430i	$0.365796\pi$
$180$	27.9107	0.0115574
$181$	3645.47	1.49705	0.748524	−	0.663108i	$-0.230763\pi$
$181$	3645.47	1.49705	0.748524	+	0.663108i	$0.230763\pi$
$182$	0	0
$183$	−2013.46	−0.813329
$184$	−3437.29	−1.37718
$185$	389.831	0.154924
$186$	1076.33	0.424303
$187$	2875.36	1.12442
$188$	110.202	0.0427515
$189$	0	0
$190$	354.654	0.135417
$191$	2514.45	0.952560	0.476280	−	0.879294i	$-0.341985\pi$
$191$	2514.45	0.952560	0.476280	+	0.879294i	$0.341985\pi$
$192$	−1420.49	−0.533934
$193$	2189.36	0.816549	0.408274	−	0.912859i	$-0.366131\pi$
$193$	2189.36	0.816549	0.408274	+	0.912859i	$0.366131\pi$
$194$	−67.5590	−0.0250023
$195$	−448.808	−0.164819
$196$	0	0
$197$	−3886.50	−1.40559	−0.702795	−	0.711392i	$-0.748065\pi$
$197$	−3886.50	−1.40559	−0.702795	+	0.711392i	$0.748065\pi$
$198$	−2497.03	−0.896244
$199$	969.361	0.345307	0.172654	−	0.984983i	$-0.444766\pi$
$199$	969.361	0.345307	0.172654	+	0.984983i	$0.444766\pi$
$200$	554.611	0.196084
$201$	−6.74392	−0.00236656
$202$	4253.35	1.48151
$203$	0	0
$204$	53.5264	0.0183706
$205$	−1177.39	−0.401136
$206$	−2908.07	−0.983566
$207$	2888.87	0.970001
$208$	2059.03	0.686386
$209$	−1144.60	−0.378821
$210$	0	0
$211$	3079.69	1.00481	0.502404	−	0.864633i	$-0.332449\pi$
$211$	3079.69	1.00481	0.502404	+	0.864633i	$0.332449\pi$
$212$	−50.7722	−0.0164483
$213$	2504.93	0.805796
$214$	−4086.53	−1.30537
$215$	1391.94	0.441532
$216$	2926.96	0.922011
$217$	0	0
$218$	2529.00	0.785712
$219$	−2174.95	−0.671095
$220$	69.5909	0.0213264
$221$	1920.72	0.584624
$222$	−649.241	−0.196280
$223$	−162.003	−0.0486480	−0.0243240	−	0.999704i	$-0.507743\pi$
$223$	−162.003	−0.0486480	−0.0243240	+	0.999704i	$0.507743\pi$
$224$	0	0
$225$	−466.122	−0.138110
$226$	4321.62	1.27199
$227$	−379.952	−0.111094	−0.0555470	−	0.998456i	$-0.517690\pi$
$227$	−379.952	−0.111094	−0.0555470	+	0.998456i	$0.517690\pi$
$228$	−21.3073	−0.00618909
$229$	4781.50	1.37978	0.689892	−	0.723912i	$-0.257658\pi$
$229$	4781.50	1.37978	0.689892	+	0.723912i	$0.257658\pi$
$230$	−2231.83	−0.639838
$231$	0	0
$232$	4446.55	1.25832
$233$	−2524.54	−0.709819	−0.354910	−	0.934901i	$-0.615488\pi$
$233$	−2524.54	−0.709819	−0.354910	+	0.934901i	$0.615488\pi$
$234$	−1668.00	−0.465986
$235$	−1840.42	−0.510876
$236$	207.027	0.0571029
$237$	−2436.08	−0.667682
$238$	0	0
$239$	113.452	0.0307053	0.0153527	−	0.999882i	$-0.495113\pi$
$239$	113.452	0.0307053	0.0153527	+	0.999882i	$0.495113\pi$
$240$	−958.288	−0.257738
$241$	−6725.34	−1.79758	−0.898791	−	0.438377i	$-0.855553\pi$
$241$	−6725.34	−1.79758	−0.898791	+	0.438377i	$0.855553\pi$
$242$	−2391.52	−0.635260
$243$	−3915.08	−1.03355
$244$	208.549	0.0547170
$245$	0	0
$246$	1960.88	0.508217
$247$	−764.585	−0.196961
$248$	2867.44	0.734203
$249$	4172.31	1.06189
$250$	360.108	0.0911010
$251$	3815.00	0.959366	0.479683	−	0.877442i	$-0.340752\pi$
$251$	3815.00	0.959366	0.479683	+	0.877442i	$0.340752\pi$
$252$	0	0
$253$	7202.94	1.78990
$254$	−1200.28	−0.296506
$255$	−893.918	−0.219527
$256$	459.231	0.112117
$257$	−2201.90	−0.534439	−0.267220	−	0.963636i	$-0.586105\pi$
$257$	−2201.90	−0.534439	−0.267220	+	0.963636i	$0.586105\pi$
$258$	−2318.19	−0.559397
$259$	0	0
$260$	46.4862	0.0110883
$261$	−3737.10	−0.886286
$262$	1182.58	0.278856
$263$	−1204.18	−0.282330	−0.141165	−	0.989986i	$-0.545085\pi$
$263$	−1204.18	−0.282330	−0.141165	+	0.989986i	$0.545085\pi$
$264$	2981.03	0.694961
$265$	847.920	0.196556
$266$	0	0
$267$	4156.75	0.952767
$268$	0.698517	0.000159212 0
$269$	−5128.98	−1.16253	−0.581263	−	0.813716i	$-0.697441\pi$
$269$	−5128.98	−1.16253	−0.581263	+	0.813716i	$0.697441\pi$
$270$	1900.47	0.428367
$271$	−808.391	−0.181204	−0.0906020	−	0.995887i	$-0.528879\pi$
$271$	−808.391	−0.181204	−0.0906020	+	0.995887i	$0.528879\pi$
$272$	4101.10	0.914213
$273$	0	0
$274$	−5076.01	−1.11917
$275$	−1162.20	−0.254849
$276$	134.087	0.0292430
$277$	180.265	0.0391014	0.0195507	−	0.999809i	$-0.493776\pi$
$277$	180.265	0.0391014	0.0195507	+	0.999809i	$0.493776\pi$
$278$	−2494.02	−0.538062
$279$	−2409.93	−0.517129
$280$	0	0
$281$	−3068.29	−0.651384	−0.325692	−	0.945476i	$-0.605597\pi$
$281$	−3068.29	−0.651384	−0.325692	+	0.945476i	$0.605597\pi$
$282$	3065.12	0.647252
$283$	3868.17	0.812506	0.406253	−	0.913761i	$-0.366835\pi$
$283$	3868.17	0.812506	0.406253	+	0.913761i	$0.366835\pi$
$284$	−259.453	−0.0542103
$285$	355.843	0.0739590
$286$	−4158.90	−0.859863
$287$	0	0
$288$	−252.488	−0.0516596
$289$	−1087.38	−0.221326
$290$	2887.14	0.584617
$291$	−67.7854	−0.0136552
$292$	225.276	0.0451482
$293$	1967.79	0.392353	0.196176	−	0.980569i	$-0.437147\pi$
$293$	1967.79	0.392353	0.196176	+	0.980569i	$0.437147\pi$
$294$	0	0
$295$	−3457.45	−0.682374
$296$	−1729.63	−0.339638
$297$	−6133.52	−1.19833
$298$	−8698.01	−1.69081
$299$	4811.52	0.930626
$300$	−21.6350	−0.00416366
$301$	0	0
$302$	−1561.13	−0.297460
$303$	4267.61	0.809135
$304$	−1632.53	−0.308000
$305$	−3482.86	−0.653863
$306$	−3322.26	−0.620657
$307$	−5487.54	−1.02016	−0.510082	−	0.860126i	$-0.670385\pi$
$307$	−5487.54	−1.02016	−0.510082	+	0.860126i	$0.670385\pi$
$308$	0	0
$309$	−2917.82	−0.537180
$310$	1861.83	0.341112
$311$	5172.80	0.943159	0.471579	−	0.881824i	$-0.343684\pi$
$311$	5172.80	0.943159	0.471579	+	0.881824i	$0.343684\pi$
$312$	1991.31	0.361332
$313$	−5762.92	−1.04070	−0.520351	−	0.853953i	$-0.674199\pi$
$313$	−5762.92	−1.04070	−0.520351	+	0.853953i	$0.674199\pi$
$314$	−7450.17	−1.33897
$315$	0	0
$316$	252.323	0.0449186
$317$	3180.88	0.563583	0.281792	−	0.959476i	$-0.409071\pi$
$317$	3180.88	0.563583	0.281792	+	0.959476i	$0.409071\pi$
$318$	−1412.16	−0.249025
$319$	−9317.87	−1.63543
$320$	−2457.16	−0.429248
$321$	−4100.23	−0.712936
$322$	0	0
$323$	−1522.87	−0.262337
$324$	36.5387	0.00626522
$325$	−776.343	−0.132504
$326$	7104.63	1.20702
$327$	2537.47	0.429121
$328$	5223.97	0.879406
$329$	0	0
$330$	1935.58	0.322879
$331$	9233.02	1.53321	0.766606	−	0.642118i	$-0.221944\pi$
$331$	9233.02	1.53321	0.766606	+	0.642118i	$0.221944\pi$
$332$	−432.156	−0.0714387
$333$	1453.67	0.239221
$334$	−1322.38	−0.216638
$335$	−11.6656	−0.00190256
$336$	0	0
$337$	−3259.50	−0.526874	−0.263437	−	0.964677i	$-0.584856\pi$
$337$	−3259.50	−0.526874	−0.263437	+	0.964677i	$0.584856\pi$
$338$	3551.15	0.571470
$339$	4336.11	0.694705
$340$	92.5895	0.0147687
$341$	−6008.79	−0.954236
$342$	1322.50	0.209101
$343$	0	0
$344$	−6175.87	−0.967967
$345$	−2239.31	−0.349451
$346$	12968.1	2.01494
$347$	1851.13	0.286380	0.143190	−	0.989695i	$-0.454264\pi$
$347$	1851.13	0.286380	0.143190	+	0.989695i	$0.454264\pi$
$348$	−173.457	−0.0267192
$349$	−1102.14	−0.169043	−0.0845216	−	0.996422i	$-0.526936\pi$
$349$	−1102.14	−0.169043	−0.0845216	+	0.996422i	$0.526936\pi$
$350$	0	0
$351$	−4097.15	−0.623048
$352$	−629.538	−0.0953252
$353$	−2670.25	−0.402615	−0.201307	−	0.979528i	$-0.564519\pi$
$353$	−2670.25	−0.402615	−0.201307	+	0.979528i	$0.564519\pi$
$354$	5758.18	0.864531
$355$	4333.00	0.647807
$356$	−430.545	−0.0640978
$357$	0	0
$358$	−5646.82	−0.833641
$359$	435.453	0.0640176	0.0320088	−	0.999488i	$-0.489810\pi$
$359$	435.453	0.0640176	0.0320088	+	0.999488i	$0.489810\pi$
$360$	2068.13	0.302778
$361$	−6252.79	−0.911618
$362$	−10502.1	−1.52480
$363$	−2399.54	−0.346951
$364$	0	0
$365$	−3762.22	−0.539516
$366$	5800.51	0.828408
$367$	2474.65	0.351978	0.175989	−	0.984392i	$-0.443688\pi$
$367$	2474.65	0.351978	0.175989	+	0.984392i	$0.443688\pi$
$368$	10273.5	1.45528
$369$	−4390.48	−0.619401
$370$	−1123.05	−0.157796
$371$	0	0
$372$	−111.857	−0.0155901
$373$	5438.18	0.754902	0.377451	−	0.926030i	$-0.376801\pi$
$373$	5438.18	0.754902	0.377451	+	0.926030i	$0.376801\pi$
$374$	−8283.53	−1.14527
$375$	361.315	0.0497553
$376$	8165.74	1.11999
$377$	−6224.28	−0.850309
$378$	0	0
$379$	10597.1	1.43624	0.718122	−	0.695917i	$-0.245002\pi$
$379$	10597.1	1.43624	0.718122	+	0.695917i	$0.245002\pi$
$380$	−36.8572	−0.00497562
$381$	−1204.31	−0.161938
$382$	−7243.78	−0.970221
$383$	4671.36	0.623226	0.311613	−	0.950209i	$-0.399131\pi$
$383$	4671.36	0.623226	0.311613	+	0.950209i	$0.399131\pi$
$384$	4405.40	0.585448
$385$	0	0
$386$	−6307.27	−0.831688
$387$	5190.50	0.681778
$388$	7.02103	0.000918656 0
$389$	3557.69	0.463707	0.231853	−	0.972751i	$-0.425521\pi$
$389$	3557.69	0.463707	0.231853	+	0.972751i	$0.425521\pi$
$390$	1292.95	0.167875
$391$	9583.40	1.23952
$392$	0	0
$393$	1186.55	0.152299
$394$	11196.5	1.43165
$395$	−4213.91	−0.536772
$396$	259.503	0.0329305
$397$	9184.57	1.16111	0.580554	−	0.814221i	$-0.302836\pi$
$397$	9184.57	1.16111	0.580554	+	0.814221i	$0.302836\pi$
$398$	−2792.60	−0.351709
$399$	0	0
$400$	−1657.64	−0.207205
$401$	−9206.52	−1.14651	−0.573256	−	0.819376i	$-0.694320\pi$
$401$	−9206.52	−1.14651	−0.573256	+	0.819376i	$0.694320\pi$
$402$	19.4283	0.00241044
$403$	−4013.83	−0.496137
$404$	−442.027	−0.0544349
$405$	−610.215	−0.0748687
$406$	0	0
$407$	3624.50	0.441424
$408$	3966.21	0.481266
$409$	7653.66	0.925303	0.462652	−	0.886540i	$-0.346898\pi$
$409$	7653.66	0.925303	0.462652	+	0.886540i	$0.346898\pi$
$410$	3391.92	0.408573
$411$	−5093.03	−0.611242
$412$	302.219	0.0361390
$413$	0	0
$414$	−8322.44	−0.987985
$415$	7217.22	0.853686
$416$	−420.527	−0.0495626
$417$	−2502.38	−0.293866
$418$	3297.44	0.385844
$419$	370.864	0.0432408	0.0216204	−	0.999766i	$-0.493117\pi$
$419$	370.864	0.0432408	0.0216204	+	0.999766i	$0.493117\pi$
$420$	0	0
$421$	1221.96	0.141460	0.0707302	−	0.997495i	$-0.477467\pi$
$421$	1221.96	0.141460	0.0707302	+	0.997495i	$0.477467\pi$
$422$	−8872.18	−1.02344
$423$	−6862.89	−0.788854
$424$	−3762.12	−0.430908
$425$	−1546.29	−0.176485
$426$	−7216.35	−0.820736
$427$	0	0
$428$	424.690	0.0479630
$429$	−4172.84	−0.469619
$430$	−4009.99	−0.449718
$431$	−14928.9	−1.66845	−0.834224	−	0.551426i	$-0.814084\pi$
$431$	−14928.9	−1.66845	−0.834224	+	0.551426i	$0.814084\pi$
$432$	−8748.19	−0.974299
$433$	−4544.42	−0.504367	−0.252184	−	0.967679i	$-0.581149\pi$
$433$	−4544.42	−0.504367	−0.252184	+	0.967679i	$0.581149\pi$
$434$	0	0
$435$	2896.82	0.319292
$436$	−262.825	−0.0288693
$437$	−3814.88	−0.417598
$438$	6265.75	0.683537
$439$	−9431.89	−1.02542	−0.512710	−	0.858562i	$-0.671358\pi$
$439$	−9431.89	−1.02542	−0.512710	+	0.858562i	$0.671358\pi$
$440$	5156.55	0.558702
$441$	0	0
$442$	−5533.35	−0.595463
$443$	−5542.61	−0.594441	−0.297220	−	0.954809i	$-0.596060\pi$
$443$	−5542.61	−0.594441	−0.297220	+	0.954809i	$0.596060\pi$
$444$	67.4720	0.00721189
$445$	7190.31	0.765962
$446$	466.708	0.0495500
$447$	−8727.16	−0.923447
$448$	0	0
$449$	16311.6	1.71446	0.857229	−	0.514936i	$-0.172184\pi$
$449$	16311.6	1.71446	0.857229	+	0.514936i	$0.172184\pi$
$450$	1342.83	0.140671
$451$	−10947.0	−1.14295
$452$	−449.122	−0.0467366
$453$	−1566.36	−0.162459
$454$	1094.59	0.113154
$455$	0	0
$456$	−1578.83	−0.162140
$457$	−14231.1	−1.45668	−0.728339	−	0.685217i	$-0.759707\pi$
$457$	−14231.1	−1.45668	−0.728339	+	0.685217i	$0.759707\pi$
$458$	−13774.9	−1.40537
$459$	−8160.55	−0.829852
$460$	231.942	0.0235094
$461$	4960.94	0.501202	0.250601	−	0.968090i	$-0.419372\pi$
$461$	4960.94	0.501202	0.250601	+	0.968090i	$0.419372\pi$
$462$	0	0
$463$	15479.5	1.55377	0.776885	−	0.629642i	$-0.216799\pi$
$463$	15479.5	1.55377	0.776885	+	0.629642i	$0.216799\pi$
$464$	−13290.0	−1.32968
$465$	1868.07	0.186300
$466$	7272.85	0.722979
$467$	14815.6	1.46807	0.734033	−	0.679114i	$-0.237636\pi$
$467$	14815.6	1.46807	0.734033	+	0.679114i	$0.237636\pi$
$468$	173.346	0.0171216
$469$	0	0
$470$	5302.01	0.520348
$471$	−7475.15	−0.731288
$472$	15340.3	1.49596
$473$	12941.7	1.25805
$474$	7018.03	0.680061
$475$	615.534	0.0594582
$476$	0	0
$477$	3161.87	0.303506
$478$	−326.839	−0.0312746
$479$	9098.96	0.867938	0.433969	−	0.900928i	$-0.357113\pi$
$479$	9098.96	0.867938	0.433969	+	0.900928i	$0.357113\pi$
$480$	195.716	0.0186108
$481$	2421.14	0.229510
$482$	19374.8	1.83091
$483$	0	0
$484$	248.538	0.0233412
$485$	−117.255	−0.0109778
$486$	11278.8	1.05271
$487$	−14991.4	−1.39492	−0.697461	−	0.716623i	$-0.745687\pi$
$487$	−14991.4	−1.39492	−0.697461	+	0.716623i	$0.745687\pi$
$488$	15453.1	1.43346
$489$	7128.45	0.659222
$490$	0	0
$491$	8243.61	0.757697	0.378848	−	0.925459i	$-0.376320\pi$
$491$	8243.61	0.757697	0.378848	+	0.925459i	$0.376320\pi$
$492$	−203.784	−0.0186733
$493$	−12397.3	−1.13255
$494$	2202.67	0.200613
$495$	−4333.82	−0.393517
$496$	−8570.29	−0.775841
$497$	0	0
$498$	−12019.9	−1.08157
$499$	9227.49	0.827814	0.413907	−	0.910319i	$-0.364164\pi$
$499$	9227.49	0.827814	0.413907	+	0.910319i	$0.364164\pi$
$500$	−37.4241	−0.00334731
$501$	−1326.81	−0.118318
$502$	−10990.5	−0.977152
$503$	13750.9	1.21893	0.609465	−	0.792813i	$-0.291384\pi$
$503$	13750.9	1.21893	0.609465	+	0.792813i	$0.291384\pi$
$504$	0	0
$505$	7382.07	0.650491
$506$	−20750.7	−1.82309
$507$	3563.05	0.312112
$508$	124.739	0.0108945
$509$	−15544.0	−1.35358	−0.676792	−	0.736174i	$-0.736630\pi$
$509$	−15544.0	−1.35358	−0.676792	+	0.736174i	$0.736630\pi$
$510$	2575.26	0.223597
$511$	0	0
$512$	10869.7	0.938236
$513$	3248.48	0.279579
$514$	6343.39	0.544348
$515$	−5047.21	−0.431858
$516$	240.917	0.0205538
$517$	−17111.5	−1.45564
$518$	0	0
$519$	13011.6	1.10047
$520$	3444.54	0.290487
$521$	15247.7	1.28218	0.641089	−	0.767466i	$-0.278483\pi$
$521$	15247.7	1.28218	0.641089	+	0.767466i	$0.278483\pi$
$522$	10766.1	0.902718
$523$	22216.2	1.85745	0.928723	−	0.370773i	$-0.120907\pi$
$523$	22216.2	1.85745	0.928723	+	0.370773i	$0.120907\pi$
$524$	−122.899	−0.0102460
$525$	0	0
$526$	3469.08	0.287565
$527$	−7994.60	−0.660817
$528$	−8909.79	−0.734373
$529$	11839.9	0.973118
$530$	−2442.74	−0.200200
$531$	−12892.7	−1.05367
$532$	0	0
$533$	−7312.50	−0.594258
$534$	−11975.0	−0.970432
$535$	−7092.53	−0.573153
$536$	51.7588	0.00417097
$537$	−5665.74	−0.455298
$538$	14775.9	1.18408
$539$	0	0
$540$	−197.506	−0.0157394
$541$	−12985.3	−1.03194	−0.515972	−	0.856605i	$-0.672569\pi$
$541$	−12985.3	−1.03194	−0.515972	+	0.856605i	$0.672569\pi$
$542$	2328.87	0.184564
$543$	−10537.3	−0.832780
$544$	−837.590	−0.0660136
$545$	4389.30	0.344985
$546$	0	0
$547$	−8226.94	−0.643069	−0.321534	−	0.946898i	$-0.604199\pi$
$547$	−8226.94	−0.643069	−0.321534	+	0.946898i	$0.604199\pi$
$548$	527.522	0.0411215
$549$	−12987.5	−1.00964
$550$	3348.15	0.259574
$551$	4935.00	0.381557
$552$	9935.57	0.766098
$553$	0	0
$554$	−519.320	−0.0398263
$555$	−1126.82	−0.0861814
$556$	259.190	0.0197699
$557$	17841.3	1.35720	0.678599	−	0.734509i	$-0.262588\pi$
$557$	17841.3	1.35720	0.678599	+	0.734509i	$0.262588\pi$
$558$	6942.70	0.526717
$559$	8644.97	0.654103
$560$	0	0
$561$	−8311.30	−0.625496
$562$	8839.34	0.663461
$563$	−1078.40	−0.0807265	−0.0403633	−	0.999185i	$-0.512852\pi$
$563$	−1078.40	−0.0807265	−0.0403633	+	0.999185i	$0.512852\pi$
$564$	−318.541	−0.0237819
$565$	7500.56	0.558497
$566$	−11143.7	−0.827570
$567$	0	0
$568$	−19225.0	−1.42018
$569$	16986.5	1.25151	0.625756	−	0.780019i	$-0.284791\pi$
$569$	16986.5	1.25151	0.625756	+	0.780019i	$0.284791\pi$
$570$	−1025.14	−0.0753302
$571$	−12263.0	−0.898756	−0.449378	−	0.893342i	$-0.648354\pi$
$571$	−12263.0	−0.898756	−0.449378	+	0.893342i	$0.648354\pi$
$572$	432.211	0.0315938
$573$	−7268.07	−0.529891
$574$	0	0
$575$	−3873.54	−0.280935
$576$	−9162.68	−0.662810
$577$	7050.51	0.508694	0.254347	−	0.967113i	$-0.418139\pi$
$577$	7050.51	0.508694	0.254347	+	0.967113i	$0.418139\pi$
$578$	3132.59	0.225430
$579$	−6328.41	−0.454231
$580$	−300.045	−0.0214805
$581$	0	0
$582$	195.281	0.0139083
$583$	7883.63	0.560046
$584$	16692.5	1.18278
$585$	−2894.96	−0.204602
$586$	−5668.93	−0.399627
$587$	20085.3	1.41228	0.706141	−	0.708071i	$-0.250434\pi$
$587$	20085.3	1.41228	0.706141	+	0.708071i	$0.250434\pi$
$588$	0	0
$589$	3182.42	0.222631
$590$	9960.45	0.695026
$591$	11234.0	0.781904
$592$	5169.59	0.358900
$593$	18974.3	1.31397	0.656984	−	0.753905i	$-0.271832\pi$
$593$	18974.3	1.31397	0.656984	+	0.753905i	$0.271832\pi$
$594$	17669.9	1.22054
$595$	0	0
$596$	903.936	0.0621252
$597$	−2801.96	−0.192088
$598$	−13861.3	−0.947880
$599$	16795.7	1.14567	0.572834	−	0.819671i	$-0.305844\pi$
$599$	16795.7	1.14567	0.572834	+	0.819671i	$0.305844\pi$
$600$	−1603.11	−0.109078
$601$	13624.3	0.924702	0.462351	−	0.886697i	$-0.347006\pi$
$601$	13624.3	0.924702	0.462351	+	0.886697i	$0.347006\pi$
$602$	0	0
$603$	−43.5006	−0.00293778
$604$	162.240	0.0109295
$605$	−4150.70	−0.278925
$606$	−12294.4	−0.824136
$607$	8399.51	0.561657	0.280828	−	0.959758i	$-0.409391\pi$
$607$	8399.51	0.561657	0.280828	+	0.959758i	$0.409391\pi$
$608$	333.421	0.0222401
$609$	0	0
$610$	10033.7	0.665985
$611$	−11430.4	−0.756832
$612$	345.264	0.0228047
$613$	15520.4	1.02262	0.511308	−	0.859398i	$-0.329161\pi$
$613$	15520.4	1.02262	0.511308	+	0.859398i	$0.329161\pi$
$614$	15808.9	1.03908
$615$	3403.29	0.223144
$616$	0	0
$617$	−26665.1	−1.73987	−0.869933	−	0.493169i	$-0.835838\pi$
$617$	−26665.1	−1.73987	−0.869933	+	0.493169i	$0.835838\pi$
$618$	8405.84	0.547140
$619$	12231.6	0.794229	0.397114	−	0.917769i	$-0.370012\pi$
$619$	12231.6	0.794229	0.397114	+	0.917769i	$0.370012\pi$
$620$	−193.489	−0.0125334
$621$	−20442.6	−1.32099
$622$	−14902.1	−0.960645
$623$	0	0
$624$	−5951.68	−0.381824
$625$	625.000	0.0400000
$626$	16602.2	1.06000
$627$	3308.49	0.210731
$628$	774.255	0.0491977
$629$	4822.34	0.305690
$630$	0	0
$631$	−7237.27	−0.456595	−0.228297	−	0.973591i	$-0.573316\pi$
$631$	−7237.27	−0.456595	−0.228297	+	0.973591i	$0.573316\pi$
$632$	18696.7	1.17676
$633$	−8901.92	−0.558957
$634$	−9163.68	−0.574032
$635$	−2083.20	−0.130188
$636$	146.758	0.00914990
$637$	0	0
$638$	26843.5	1.66575
$639$	16157.6	1.00029
$640$	7620.42	0.470662
$641$	4904.83	0.302230	0.151115	−	0.988516i	$-0.451714\pi$
$641$	4904.83	0.302230	0.151115	+	0.988516i	$0.451714\pi$
$642$	11812.2	0.726154
$643$	8394.46	0.514845	0.257422	−	0.966299i	$-0.417127\pi$
$643$	8394.46	0.514845	0.257422	+	0.966299i	$0.417127\pi$
$644$	0	0
$645$	−4023.43	−0.245616
$646$	4387.19	0.267201
$647$	−9526.45	−0.578861	−0.289431	−	0.957199i	$-0.593466\pi$
$647$	−9526.45	−0.578861	−0.289431	+	0.957199i	$0.593466\pi$
$648$	2707.45	0.164134
$649$	−32146.0	−1.94429
$650$	2236.54	0.134961
$651$	0	0
$652$	−738.345	−0.0443494
$653$	15950.1	0.955856	0.477928	−	0.878399i	$-0.341388\pi$
$653$	15950.1	0.955856	0.477928	+	0.878399i	$0.341388\pi$
$654$	−7310.12	−0.437077
$655$	2052.48	0.122438
$656$	−15613.6	−0.929279
$657$	−14029.2	−0.833077
$658$	0	0
$659$	−3370.65	−0.199244	−0.0996221	−	0.995025i	$-0.531763\pi$
$659$	−3370.65	−0.199244	−0.0996221	+	0.995025i	$0.531763\pi$
$660$	−201.154	−0.0118635
$661$	−24254.0	−1.42719	−0.713594	−	0.700560i	$-0.752934\pi$
$661$	−24254.0	−1.42719	−0.713594	+	0.700560i	$0.752934\pi$
$662$	−26599.1	−1.56164
$663$	−5551.90	−0.325215
$664$	−32022.0	−1.87153
$665$	0	0
$666$	−4187.83	−0.243656
$667$	−31055.9	−1.80283
$668$	137.427	0.00795991
$669$	468.273	0.0270620
$670$	33.6070	0.00193784
$671$	−32382.3	−1.86305
$672$	0	0
$673$	−3510.41	−0.201064	−0.100532	−	0.994934i	$-0.532055\pi$
$673$	−3510.41	−0.201064	−0.100532	+	0.994934i	$0.532055\pi$
$674$	9390.20	0.536642
$675$	3298.44	0.188084
$676$	−369.051	−0.0209974
$677$	−9051.19	−0.513834	−0.256917	−	0.966434i	$-0.582707\pi$
$677$	−9051.19	−0.513834	−0.256917	+	0.966434i	$0.582707\pi$
$678$	−12491.7	−0.707585
$679$	0	0
$680$	6860.71	0.386906
$681$	1098.26	0.0617995
$682$	17310.5	0.971927
$683$	7105.73	0.398087	0.199043	−	0.979991i	$-0.436217\pi$
$683$	7105.73	0.398087	0.199043	+	0.979991i	$0.436217\pi$
$684$	−137.440	−0.00768295
$685$	−8809.87	−0.491398
$686$	0	0
$687$	−13821.0	−0.767548
$688$	18458.6	1.02286
$689$	5266.21	0.291185
$690$	6451.16	0.355930
$691$	12629.4	0.695289	0.347645	−	0.937626i	$-0.386982\pi$
$691$	12629.4	0.695289	0.347645	+	0.937626i	$0.386982\pi$
$692$	−1347.70	−0.0740346
$693$	0	0
$694$	−5332.86	−0.291690
$695$	−4328.59	−0.236249
$696$	−12852.9	−0.699981
$697$	−14564.8	−0.791506
$698$	3175.11	0.172177
$699$	7297.23	0.394859
$700$	0	0
$701$	−912.952	−0.0491893	−0.0245947	−	0.999698i	$-0.507830\pi$
$701$	−912.952	−0.0491893	−0.0245947	+	0.999698i	$0.507830\pi$
$702$	11803.4	0.634599
$703$	−1919.63	−0.102988
$704$	−22845.7	−1.22305
$705$	5319.78	0.284191
$706$	7692.63	0.410079
$707$	0	0
$708$	−598.416	−0.0317653
$709$	−20710.5	−1.09704	−0.548518	−	0.836139i	$-0.684808\pi$
$709$	−20710.5	−1.09704	−0.548518	+	0.836139i	$0.684808\pi$
$710$	−12482.8	−0.659818
$711$	−15713.6	−0.828840
$712$	−31902.6	−1.67921
$713$	−20026.9	−1.05191
$714$	0	0
$715$	−7218.14	−0.377543
$716$	586.842	0.0306303
$717$	−327.934	−0.0170808
$718$	−1254.48	−0.0652045
$719$	−2469.76	−0.128104	−0.0640518	−	0.997947i	$-0.520402\pi$
$719$	−2469.76	−0.128104	−0.0640518	+	0.997947i	$0.520402\pi$
$720$	−6181.29	−0.319949
$721$	0	0
$722$	18013.4	0.928520
$723$	19439.8	0.999962
$724$	1091.43	0.0560256
$725$	5010.89	0.256690
$726$	6912.75	0.353383
$727$	−10893.4	−0.555729	−0.277865	−	0.960620i	$-0.589627\pi$
$727$	−10893.4	−0.555729	−0.277865	+	0.960620i	$0.589627\pi$
$728$	0	0
$729$	8021.48	0.407533
$730$	10838.4	0.549519
$731$	17218.7	0.871214
$732$	−602.814	−0.0304381
$733$	−26259.9	−1.32324	−0.661619	−	0.749840i	$-0.730130\pi$
$733$	−26259.9	−1.32324	−0.661619	+	0.749840i	$0.730130\pi$
$734$	−7129.14	−0.358503
$735$	0	0
$736$	−2098.21	−0.105083
$737$	−108.462	−0.00542096
$738$	12648.4	0.630885
$739$	−1840.83	−0.0916319	−0.0458160	−	0.998950i	$-0.514589\pi$
$739$	−1840.83	−0.0916319	−0.0458160	+	0.998950i	$0.514589\pi$
$740$	116.712	0.00579788
$741$	2210.05	0.109566
$742$	0	0
$743$	4022.25	0.198603	0.0993015	−	0.995057i	$-0.468339\pi$
$743$	4022.25	0.198603	0.0993015	+	0.995057i	$0.468339\pi$
$744$	−8288.40	−0.408424
$745$	−15096.2	−0.742390
$746$	−15666.7	−0.768898
$747$	26912.8	1.31819
$748$	860.862	0.0420805
$749$	0	0
$750$	−1040.90	−0.0506778
$751$	25725.3	1.24997	0.624986	−	0.780636i	$-0.285105\pi$
$751$	25725.3	1.24997	0.624986	+	0.780636i	$0.285105\pi$
$752$	−24406.0	−1.18351
$753$	−11027.4	−0.533677
$754$	17931.3	0.866074
$755$	−2709.48	−0.130607
$756$	0	0
$757$	11359.2	0.545385	0.272692	−	0.962101i	$-0.412086\pi$
$757$	11359.2	0.545385	0.272692	+	0.962101i	$0.412086\pi$
$758$	−30528.8	−1.46287
$759$	−20820.3	−0.995689
$760$	−2731.05	−0.130350
$761$	−7843.37	−0.373616	−0.186808	−	0.982396i	$-0.559814\pi$
$761$	−7843.37	−0.373616	−0.186808	+	0.982396i	$0.559814\pi$
$762$	3469.45	0.164941
$763$	0	0
$764$	752.806	0.0356487
$765$	−5766.08	−0.272514
$766$	−13457.6	−0.634781
$767$	−21473.3	−1.01090
$768$	−1327.42	−0.0623685
$769$	−29007.8	−1.36027	−0.680136	−	0.733086i	$-0.738079\pi$
$769$	−29007.8	−1.36027	−0.680136	+	0.733086i	$0.738079\pi$
$770$	0	0
$771$	6364.65	0.297299
$772$	655.479	0.0305586
$773$	679.160	0.0316012	0.0158006	−	0.999875i	$-0.494970\pi$
$773$	679.160	0.0316012	0.0158006	+	0.999875i	$0.494970\pi$
$774$	−14953.1	−0.694418
$775$	3231.36	0.149773
$776$	520.245	0.0240666
$777$	0	0
$778$	−10249.2	−0.472304
$779$	5797.81	0.266660
$780$	−134.370	−0.00616821
$781$	40286.5	1.84579
$782$	−27608.5	−1.26250
$783$	26445.0	1.20698
$784$	0	0
$785$	−12930.4	−0.587907
$786$	−3418.29	−0.155122
$787$	24329.0	1.10195	0.550976	−	0.834521i	$-0.314256\pi$
$787$	24329.0	1.10195	0.550976	+	0.834521i	$0.314256\pi$
$788$	−1163.59	−0.0526029
$789$	3480.71	0.157055
$790$	12139.7	0.546724
$791$	0	0
$792$	19228.7	0.862703
$793$	−21631.2	−0.968657
$794$	−26459.5	−1.18264
$795$	−2450.93	−0.109340
$796$	290.219	0.0129228
$797$	−2791.24	−0.124054	−0.0620269	−	0.998074i	$-0.519756\pi$
$797$	−2791.24	−0.124054	−0.0620269	+	0.998074i	$0.519756\pi$
$798$	0	0
$799$	−22766.6	−1.00804
$800$	338.548	0.0149619
$801$	26812.5	1.18274
$802$	26522.7	1.16777
$803$	−34979.6	−1.53724
$804$	−2.01908	−8.85664e−5 0
$805$	0	0
$806$	11563.3	0.505336
$807$	14825.4	0.646692
$808$	−32753.4	−1.42607
$809$	15695.9	0.682126	0.341063	−	0.940040i	$-0.389213\pi$
$809$	15695.9	0.682126	0.341063	+	0.940040i	$0.389213\pi$
$810$	1757.95	0.0762568
$811$	9580.84	0.414832	0.207416	−	0.978253i	$-0.433495\pi$
$811$	9580.84	0.414832	0.207416	+	0.978253i	$0.433495\pi$
$812$	0	0
$813$	2336.67	0.100800
$814$	−10441.7	−0.449608
$815$	12330.7	0.529971
$816$	−11854.3	−0.508560
$817$	−6854.28	−0.293514
$818$	−22049.2	−0.942458
$819$	0	0
$820$	−352.503	−0.0150121
$821$	27541.0	1.17075	0.585376	−	0.810762i	$-0.300947\pi$
$821$	27541.0	1.17075	0.585376	+	0.810762i	$0.300947\pi$
$822$	14672.3	0.622575
$823$	−11746.5	−0.497516	−0.248758	−	0.968566i	$-0.580022\pi$
$823$	−11746.5	−0.497516	−0.248758	+	0.968566i	$0.580022\pi$
$824$	22393.9	0.946757
$825$	3359.37	0.141768
$826$	0	0
$827$	−20831.7	−0.875924	−0.437962	−	0.898994i	$-0.644300\pi$
$827$	−20831.7	−0.875924	−0.437962	+	0.898994i	$0.644300\pi$
$828$	864.905	0.0363014
$829$	3590.00	0.150405	0.0752027	−	0.997168i	$-0.476040\pi$
$829$	3590.00	0.150405	0.0752027	+	0.997168i	$0.476040\pi$
$830$	−20791.9	−0.869513
$831$	−521.061	−0.0217514
$832$	−15260.8	−0.635904
$833$	0	0
$834$	7209.02	0.299314
$835$	−2295.10	−0.0951201
$836$	−342.684	−0.0141770
$837$	17053.5	0.704249
$838$	−1068.41	−0.0440425
$839$	−10917.2	−0.449229	−0.224614	−	0.974448i	$-0.572112\pi$
$839$	−10917.2	−0.449229	−0.224614	+	0.974448i	$0.572112\pi$
$840$	0	0
$841$	15785.5	0.647239
$842$	−3520.31	−0.144083
$843$	8868.97	0.362353
$844$	922.036	0.0376040
$845$	6163.33	0.250917
$846$	19771.1	0.803479
$847$	0	0
$848$	11244.4	0.455345
$849$	−11181.0	−0.451982
$850$	4454.66	0.179757
$851$	12080.2	0.486609
$852$	749.956	0.0301562
$853$	35912.9	1.44154	0.720770	−	0.693175i	$-0.243789\pi$
$853$	35912.9	1.44154	0.720770	+	0.693175i	$0.243789\pi$
$854$	0	0
$855$	2295.31	0.0918105
$856$	31468.8	1.25652
$857$	−39353.3	−1.56859	−0.784295	−	0.620388i	$-0.786975\pi$
$857$	−39353.3	−1.56859	−0.784295	+	0.620388i	$0.786975\pi$
$858$	12021.4	0.478326
$859$	32234.7	1.28037	0.640183	−	0.768222i	$-0.278858\pi$
$859$	32234.7	1.28037	0.640183	+	0.768222i	$0.278858\pi$
$860$	416.736	0.0165239
$861$	0	0
$862$	43008.2	1.69938
$863$	43811.4	1.72811	0.864053	−	0.503401i	$-0.167918\pi$
$863$	43811.4	1.72811	0.864053	+	0.503401i	$0.167918\pi$
$864$	1786.69	0.0703523
$865$	22507.3	0.884706
$866$	13091.9	0.513718
$867$	3143.09	0.123120
$868$	0	0
$869$	−39179.3	−1.52942
$870$	−8345.36	−0.325212
$871$	−72.4519	−0.00281853
$872$	−19474.8	−0.756308
$873$	−437.239	−0.0169511
$874$	10990.1	0.425340
$875$	0	0
$876$	−651.165	−0.0251151
$877$	−9140.68	−0.351948	−0.175974	−	0.984395i	$-0.556308\pi$
$877$	−9140.68	−0.351948	−0.175974	+	0.984395i	$0.556308\pi$
$878$	27172.0	1.04443
$879$	−5687.94	−0.218259
$880$	−15412.1	−0.590387
$881$	23013.1	0.880058	0.440029	−	0.897984i	$-0.354968\pi$
$881$	23013.1	0.880058	0.440029	+	0.897984i	$0.354968\pi$
$882$	0	0
$883$	7448.15	0.283862	0.141931	−	0.989877i	$-0.454669\pi$
$883$	7448.15	0.283862	0.141931	+	0.989877i	$0.454669\pi$
$884$	575.050	0.0218790
$885$	9993.83	0.379592
$886$	15967.5	0.605462
$887$	46061.1	1.74361	0.871803	−	0.489856i	$-0.162951\pi$
$887$	46061.1	1.74361	0.871803	+	0.489856i	$0.162951\pi$
$888$	4999.55	0.188935
$889$	0	0
$890$	−20714.3	−0.780163
$891$	−5673.54	−0.213323
$892$	−48.5024	−0.00182061
$893$	9062.74	0.339612
$894$	25141.8	0.940568
$895$	−9800.55	−0.366029
$896$	0	0
$897$	−13907.8	−0.517690
$898$	−46991.5	−1.74624
$899$	25907.2	0.961129
$900$	−139.553	−0.00516864
$901$	10489.0	0.387837
$902$	31536.7	1.16414
$903$	0	0
$904$	−33279.1	−1.22439
$905$	−18227.3	−0.669500
$906$	4512.48	0.165472
$907$	38496.1	1.40931	0.704653	−	0.709552i	$-0.251103\pi$
$907$	38496.1	1.40931	0.704653	+	0.709552i	$0.251103\pi$
$908$	−113.755	−0.00415758
$909$	27527.6	1.00444
$910$	0	0
$911$	−18329.1	−0.666596	−0.333298	−	0.942822i	$-0.608162\pi$
$911$	−18329.1	−0.666596	−0.333298	+	0.942822i	$0.608162\pi$
$912$	4718.87	0.171335
$913$	67102.9	2.43240
$914$	40997.8	1.48368
$915$	10067.3	0.363732
$916$	1431.55	0.0516371
$917$	0	0
$918$	23509.5	0.845237
$919$	−37448.4	−1.34419	−0.672094	−	0.740466i	$-0.734605\pi$
$919$	−37448.4	−1.34419	−0.672094	+	0.740466i	$0.734605\pi$
$920$	17186.5	0.615892
$921$	15861.9	0.567498
$922$	−14291.8	−0.510494
$923$	26911.1	0.959686
$924$	0	0
$925$	−1949.15	−0.0692841
$926$	−44594.5	−1.58258
$927$	−18820.9	−0.666839
$928$	2714.29	0.0960138
$929$	−2946.34	−0.104054	−0.0520271	−	0.998646i	$-0.516568\pi$
$929$	−2946.34	−0.104054	−0.0520271	+	0.998646i	$0.516568\pi$
$930$	−5381.65	−0.189754
$931$	0	0
$932$	−755.827	−0.0265643
$933$	−14952.1	−0.524662
$934$	−42681.9	−1.49528
$935$	−14376.8	−0.502858
$936$	12844.6	0.448547
$937$	48870.0	1.70386	0.851928	−	0.523659i	$-0.175434\pi$
$937$	48870.0	1.70386	0.851928	+	0.523659i	$0.175434\pi$
$938$	0	0
$939$	16657.9	0.578923
$940$	−551.009	−0.0191191
$941$	20661.0	0.715758	0.357879	−	0.933768i	$-0.383500\pi$
$941$	20661.0	0.715758	0.357879	+	0.933768i	$0.383500\pi$
$942$	21534.9	0.744846
$943$	−36485.5	−1.25995
$944$	−45849.6	−1.58080
$945$	0	0
$946$	−37283.3	−1.28138
$947$	13130.3	0.450557	0.225279	−	0.974294i	$-0.427671\pi$
$947$	13130.3	0.450557	0.225279	+	0.974294i	$0.427671\pi$
$948$	−729.345	−0.0249874
$949$	−23366.2	−0.799260
$950$	−1773.27	−0.0605605
$951$	−9194.40	−0.313511
$952$	0	0
$953$	16098.9	0.547214	0.273607	−	0.961842i	$-0.411783\pi$
$953$	16098.9	0.547214	0.273607	+	0.961842i	$0.411783\pi$
$954$	−9108.93	−0.309133
$955$	−12572.2	−0.425998
$956$	33.9665	0.00114912
$957$	26933.5	0.909757
$958$	−26212.9	−0.884030
$959$	0	0
$960$	7102.47	0.238783
$961$	−13084.3	−0.439202
$962$	−6974.98	−0.233766
$963$	−26447.9	−0.885017
$964$	−2013.52	−0.0672728
$965$	−10946.8	−0.365172
$966$	0	0
$967$	15916.9	0.529320	0.264660	−	0.964342i	$-0.414740\pi$
$967$	15916.9	0.529320	0.264660	+	0.964342i	$0.414740\pi$
$968$	18416.2	0.611486
$969$	4401.89	0.145933
$970$	337.795	0.0111814
$971$	−675.909	−0.0223388	−0.0111694	−	0.999938i	$-0.503555\pi$
$971$	−675.909	−0.0223388	−0.0111694	+	0.999938i	$0.503555\pi$
$972$	−1172.15	−0.0386796
$973$	0	0
$974$	43188.3	1.42078
$975$	2244.04	0.0737095
$976$	−46186.6	−1.51475
$977$	−46169.3	−1.51186	−0.755931	−	0.654652i	$-0.772815\pi$
$977$	−46169.3	−1.51186	−0.755931	+	0.654652i	$0.772815\pi$
$978$	−20536.1	−0.671444
$979$	66852.7	2.18245
$980$	0	0
$981$	16367.6	0.532698
$982$	−23748.8	−0.771745
$983$	50336.2	1.63324	0.816620	−	0.577175i	$-0.195845\pi$
$983$	50336.2	1.63324	0.816620	+	0.577175i	$0.195845\pi$
$984$	−15100.0	−0.489197
$985$	19432.5	0.628599
$986$	35714.9	1.15354
$987$	0	0
$988$	−228.911	−0.00737108
$989$	43133.8	1.38683
$990$	12485.2	0.400812
$991$	40186.9	1.28817	0.644087	−	0.764953i	$-0.277238\pi$
$991$	40186.9	1.28817	0.644087	+	0.764953i	$0.277238\pi$
$992$	1750.36	0.0560220
$993$	−26688.3	−0.852897
$994$	0	0
$995$	−4846.80	−0.154426
$996$	1249.16	0.0397401
$997$	−17750.2	−0.563846	−0.281923	−	0.959437i	$-0.590972\pi$
$997$	−17750.2	−0.563846	−0.281923	+	0.959437i	$0.590972\pi$
$998$	−26583.2	−0.843162
$999$	−10286.7	−0.325782

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	245.4.a.p.1.2	yes	6
3.2	odd	2		2205.4.a.ca.1.5		6
5.4	even	2		1225.4.a.bi.1.5		6
7.2	even	3		245.4.e.p.116.5		12
7.3	odd	6		245.4.e.q.226.5		12
7.4	even	3		245.4.e.p.226.5		12
7.5	odd	6		245.4.e.q.116.5		12
7.6	odd	2		245.4.a.o.1.2	✓	6
21.20	even	2		2205.4.a.bz.1.5		6
35.34	odd	2		1225.4.a.bj.1.5		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
245.4.a.o.1.2	✓	6	7.6	odd	2
245.4.a.p.1.2	yes	6	1.1	even	1	trivial
245.4.e.p.116.5		12	7.2	even	3
245.4.e.p.226.5		12	7.4	even	3
245.4.e.q.116.5		12	7.5	odd	6
245.4.e.q.226.5		12	7.3	odd	6
1225.4.a.bi.1.5		6	5.4	even	2
1225.4.a.bj.1.5		6	35.34	odd	2
2205.4.a.bz.1.5		6	21.20	even	2
2205.4.a.ca.1.5		6	3.2	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:	\( N \)	\(=\)	\( 245 = 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	245.a (trivial)

\(f(q)\)	\(=\)	\(q-2.88087 q^{2} -2.89052 q^{3} +0.299392 q^{4} -5.00000 q^{5} +8.32721 q^{6} +22.1844 q^{8} -18.6449 q^{9} +O(q^{10})\)	\(q-2.88087 q^{2} -2.89052 q^{3} +0.299392 q^{4} -5.00000 q^{5} +8.32721 q^{6} +22.1844 q^{8} -18.6449 q^{9} +14.4043 q^{10} -46.4881 q^{11} -0.865401 q^{12} -31.0537 q^{13} +14.4526 q^{15} -66.3055 q^{16} -61.8516 q^{17} +53.7134 q^{18} +24.6214 q^{19} -1.49696 q^{20} +133.926 q^{22} -154.942 q^{23} -64.1246 q^{24} +25.0000 q^{25} +89.4616 q^{26} +131.938 q^{27} +200.436 q^{29} -41.6361 q^{30} +129.255 q^{31} +13.5419 q^{32} +134.375 q^{33} +178.186 q^{34} -5.58213 q^{36} -77.9662 q^{37} -70.9309 q^{38} +89.7615 q^{39} -110.922 q^{40} +235.479 q^{41} -278.388 q^{43} -13.9182 q^{44} +93.2244 q^{45} +446.366 q^{46} +368.085 q^{47} +191.658 q^{48} -72.0217 q^{50} +178.784 q^{51} -9.29725 q^{52} -169.584 q^{53} -380.095 q^{54} +232.440 q^{55} -71.1686 q^{57} -577.429 q^{58} +691.490 q^{59} +4.32700 q^{60} +696.572 q^{61} -372.365 q^{62} +491.432 q^{64} +155.269 q^{65} -387.116 q^{66} +2.33311 q^{67} -18.5179 q^{68} +447.863 q^{69} -866.599 q^{71} -413.626 q^{72} +752.443 q^{73} +224.610 q^{74} -72.2631 q^{75} +7.37145 q^{76} -258.591 q^{78} +842.783 q^{79} +331.528 q^{80} +122.043 q^{81} -678.384 q^{82} -1443.44 q^{83} +309.258 q^{85} +801.998 q^{86} -579.364 q^{87} -1031.31 q^{88} -1438.06 q^{89} -268.567 q^{90} -46.3884 q^{92} -373.613 q^{93} -1060.40 q^{94} -123.107 q^{95} -39.1433 q^{96} +23.4509 q^{97} +866.764 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 2 q^{2} + 16 q^{3} + 14 q^{4} - 30 q^{5} + 24 q^{6} - 66 q^{8} + 70 q^{9}+O(q^{10}) \) 6 * q - 2 * q^2 + 16 * q^3 + 14 * q^4 - 30 * q^5 + 24 * q^6 - 66 * q^8 + 70 * q^9	\( 6 q - 2 q^{2} + 16 q^{3} + 14 q^{4} - 30 q^{5} + 24 q^{6} - 66 q^{8} + 70 q^{9} + 10 q^{10} - 16 q^{11} + 160 q^{12} + 168 q^{13} - 80 q^{15} + 298 q^{16} - 4 q^{17} + 354 q^{18} + 308 q^{19} - 70 q^{20} - 236 q^{22} - 336 q^{23} - 92 q^{24} + 150 q^{25} + 56 q^{26} + 964 q^{27} + 176 q^{29} - 120 q^{30} + 392 q^{31} - 770 q^{32} + 188 q^{33} + 812 q^{34} + 230 q^{36} - 140 q^{37} + 20 q^{38} + 140 q^{39} + 330 q^{40} + 656 q^{41} - 388 q^{43} - 160 q^{44} - 350 q^{45} - 388 q^{46} + 628 q^{47} + 1396 q^{48} - 50 q^{50} + 744 q^{51} + 1520 q^{52} - 676 q^{53} + 2284 q^{54} + 80 q^{55} + 1468 q^{57} - 2012 q^{58} + 996 q^{59} - 800 q^{60} + 740 q^{61} - 364 q^{62} + 1426 q^{64} - 840 q^{65} - 3620 q^{66} + 1768 q^{67} - 2940 q^{68} - 1048 q^{69} - 224 q^{71} + 2858 q^{72} + 2640 q^{73} + 928 q^{74} + 400 q^{75} - 1340 q^{76} + 8 q^{78} + 1636 q^{79} - 1490 q^{80} + 4442 q^{81} - 1756 q^{82} + 140 q^{83} + 20 q^{85} + 1180 q^{86} + 1940 q^{87} - 5652 q^{88} - 1904 q^{89} - 1770 q^{90} - 1952 q^{92} - 1592 q^{93} - 3332 q^{94} - 1540 q^{95} - 6460 q^{96} + 516 q^{97} - 2804 q^{99}+O(q^{100}) \) 6 * q - 2 * q^2 + 16 * q^3 + 14 * q^4 - 30 * q^5 + 24 * q^6 - 66 * q^8 + 70 * q^9 + 10 * q^10 - 16 * q^11 + 160 * q^12 + 168 * q^13 - 80 * q^15 + 298 * q^16 - 4 * q^17 + 354 * q^18 + 308 * q^19 - 70 * q^20 - 236 * q^22 - 336 * q^23 - 92 * q^24 + 150 * q^25 + 56 * q^26 + 964 * q^27 + 176 * q^29 - 120 * q^30 + 392 * q^31 - 770 * q^32 + 188 * q^33 + 812 * q^34 + 230 * q^36 - 140 * q^37 + 20 * q^38 + 140 * q^39 + 330 * q^40 + 656 * q^41 - 388 * q^43 - 160 * q^44 - 350 * q^45 - 388 * q^46 + 628 * q^47 + 1396 * q^48 - 50 * q^50 + 744 * q^51 + 1520 * q^52 - 676 * q^53 + 2284 * q^54 + 80 * q^55 + 1468 * q^57 - 2012 * q^58 + 996 * q^59 - 800 * q^60 + 740 * q^61 - 364 * q^62 + 1426 * q^64 - 840 * q^65 - 3620 * q^66 + 1768 * q^67 - 2940 * q^68 - 1048 * q^69 - 224 * q^71 + 2858 * q^72 + 2640 * q^73 + 928 * q^74 + 400 * q^75 - 1340 * q^76 + 8 * q^78 + 1636 * q^79 - 1490 * q^80 + 4442 * q^81 - 1756 * q^82 + 140 * q^83 + 20 * q^85 + 1180 * q^86 + 1940 * q^87 - 5652 * q^88 - 1904 * q^89 - 1770 * q^90 - 1952 * q^92 - 1592 * q^93 - 3332 * q^94 - 1540 * q^95 - 6460 * q^96 + 516 * q^97 - 2804 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more