LMFDB - Embedded newform 98.10.a.h.1.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [98,10,Mod(1,98)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(98, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 10, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("98.1"); S:= CuspForms(chi, 10); N := Newforms(S);

Level:	$ N $	$=$	$ 98 = 2 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	98.a (trivial)

Newform invariants

comment:select newform

sage:traces = [3,-48,71] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	yes
Analytic conductor:	$50.4735119441$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	$\mathbb{Q}[x]/(x^{3} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 4037x + 70980 $ x^3 - x^2 - 4037*x + 70980
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{3}\cdot 7 $
Twist minimal:	no (minimal twist has level 14)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-70.5196$ of defining polynomial
Character	$\chi$	$=$	98.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-16.0000 q^{2} +173.458 q^{3} +256.000 q^{4} -2345.55 q^{5} -2775.34 q^{6} -4096.00 q^{8} +10404.8 q^{9} +37528.8 q^{10} -71109.6 q^{11} +44405.4 q^{12} -89420.8 q^{13} -406855. q^{15} +65536.0 q^{16} -32294.5 q^{17} -166477. q^{18} +779068. q^{19} -600460. q^{20} +1.13775e6 q^{22} +1.77284e6 q^{23} -710486. q^{24} +3.54847e6 q^{25} +1.43073e6 q^{26} -1.60938e6 q^{27} -212075. q^{29} +6.50968e6 q^{30} +4.31261e6 q^{31} -1.04858e6 q^{32} -1.23346e7 q^{33} +516712. q^{34} +2.66364e6 q^{36} +6.20102e6 q^{37} -1.24651e7 q^{38} -1.55108e7 q^{39} +9.60736e6 q^{40} -6.40835e6 q^{41} -6.99951e6 q^{43} -1.82041e7 q^{44} -2.44050e7 q^{45} -2.83654e7 q^{46} +3.50844e7 q^{47} +1.13678e7 q^{48} -5.67755e7 q^{50} -5.60175e6 q^{51} -2.28917e7 q^{52} -4.26901e7 q^{53} +2.57500e7 q^{54} +1.66791e8 q^{55} +1.35136e8 q^{57} +3.39320e6 q^{58} +2.90654e7 q^{59} -1.04155e8 q^{60} -6.18781e7 q^{61} -6.90018e7 q^{62} +1.67772e7 q^{64} +2.09741e8 q^{65} +1.97353e8 q^{66} +2.00649e8 q^{67} -8.26739e6 q^{68} +3.07514e8 q^{69} +3.03014e7 q^{71} -4.26182e7 q^{72} +2.91846e8 q^{73} -9.92164e7 q^{74} +6.15512e8 q^{75} +1.99441e8 q^{76} +2.48173e8 q^{78} -1.08871e8 q^{79} -1.53718e8 q^{80} -4.83958e8 q^{81} +1.02534e8 q^{82} -2.16661e8 q^{83} +7.57483e7 q^{85} +1.11992e8 q^{86} -3.67862e7 q^{87} +2.91265e8 q^{88} +1.86505e8 q^{89} +3.90481e8 q^{90} +4.53847e8 q^{92} +7.48059e8 q^{93} -5.61350e8 q^{94} -1.82734e9 q^{95} -1.81884e8 q^{96} +9.53814e8 q^{97} -7.39884e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 48 q^{2} + 71 q^{3} + 768 q^{4} - 1085 q^{5} - 1136 q^{6} - 12288 q^{8} + 9106 q^{9} + 17360 q^{10} - 2555 q^{11} + 18176 q^{12} - 18070 q^{13} - 353073 q^{15} + 196608 q^{16} + 20759 q^{17} - 145696 q^{18}+ \cdots - 1303712634 q^{99}+O(q^{100}) $ 3 * q - 48 * q^2 + 71 * q^3 + 768 * q^4 - 1085 * q^5 - 1136 * q^6 - 12288 * q^8 + 9106 * q^9 + 17360 * q^10 - 2555 * q^11 + 18176 * q^12 - 18070 * q^13 - 353073 * q^15 + 196608 * q^16 + 20759 * q^17 - 145696 * q^18 + 1220649 * q^19 - 277760 * q^20 + 40880 * q^22 + 1960903 * q^23 - 290816 * q^24 + 863572 * q^25 + 289120 * q^26 - 2888659 * q^27 - 2606146 * q^29 + 5649168 * q^30 - 9377989 * q^31 - 3145728 * q^32 - 10778103 * q^33 - 332144 * q^34 + 2331136 * q^36 + 25814913 * q^37 - 19530384 * q^38 - 37990822 * q^39 + 4444160 * q^40 - 209250 * q^41 + 2944308 * q^43 - 654080 * q^44 - 37350558 * q^45 - 31374448 * q^46 + 48391269 * q^47 + 4653056 * q^48 - 13817152 * q^50 + 75441987 * q^51 - 4625920 * q^52 - 102186411 * q^53 + 46218544 * q^54 + 228278701 * q^55 + 43084589 * q^57 + 41698336 * q^58 + 144220135 * q^59 - 90386688 * q^60 + 280936871 * q^61 + 150047824 * q^62 + 50331648 * q^64 + 186819738 * q^65 + 172449648 * q^66 - 170710399 * q^67 + 5314304 * q^68 + 903654171 * q^69 + 469758688 * q^71 - 37298176 * q^72 + 613838539 * q^73 - 413038608 * q^74 + 902254676 * q^75 + 312486144 * q^76 + 607853152 * q^78 - 197445809 * q^79 - 71106560 * q^80 - 887872901 * q^81 + 3348000 * q^82 + 1074181436 * q^83 + 411272519 * q^85 - 47108928 * q^86 + 753428670 * q^87 + 10465280 * q^88 + 805730427 * q^89 + 597608928 * q^90 + 501991168 * q^92 + 1721516327 * q^93 - 774260304 * q^94 - 1799421743 * q^95 - 74448896 * q^96 + 2262918094 * q^97 - 1303712634 * q^99

Coefficient data

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

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

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

$2$	−16.0000	−0.707107
$2$	−16.0000	−0.707107
$3$	173.458	1.23637	0.618187	−	0.786031i	$-0.287867\pi$
$3$	173.458	1.23637	0.618187	+	0.786031i	$0.287867\pi$
$4$	256.000	0.500000
$5$	−2345.55	−1.67834	−0.839169	−	0.543871i	$-0.816958\pi$
$5$	−2345.55	−1.67834	−0.839169	+	0.543871i	$0.816958\pi$
$6$	−2775.34	−0.874248
$7$	0	0
$7$	0	0
$8$	−4096.00	−0.353553
$9$	10404.8	0.528621
$10$	37528.8	1.18676
$11$	−71109.6	−1.46441	−0.732203	−	0.681087i	$-0.761508\pi$
$11$	−71109.6	−1.46441	−0.732203	+	0.681087i	$0.761508\pi$
$12$	44405.4	0.618187
$13$	−89420.8	−0.868347	−0.434174	−	0.900829i	$-0.642960\pi$
$13$	−89420.8	−0.868347	−0.434174	+	0.900829i	$0.642960\pi$
$14$	0	0
$15$	−406855.	−2.07505
$16$	65536.0	0.250000
$17$	−32294.5	−0.0937796	−0.0468898	−	0.998900i	$-0.514931\pi$
$17$	−32294.5	−0.0937796	−0.0468898	+	0.998900i	$0.514931\pi$
$18$	−166477.	−0.373791
$19$	779068.	1.37146	0.685732	−	0.727854i	$-0.259482\pi$
$19$	779068.	1.37146	0.685732	+	0.727854i	$0.259482\pi$
$20$	−600460.	−0.839169
$21$	0	0
$22$	1.13775e6	1.03549
$23$	1.77284e6	1.32097	0.660487	−	0.750837i	$-0.270350\pi$
$23$	1.77284e6	1.32097	0.660487	+	0.750837i	$0.270350\pi$
$24$	−710486.	−0.437124
$25$	3.54847e6	1.81682
$26$	1.43073e6	0.614014
$27$	−1.60938e6	−0.582801
$28$	0	0
$29$	−212075.	−0.0556799	−0.0278399	−	0.999612i	$-0.508863\pi$
$29$	−212075.	−0.0556799	−0.0278399	+	0.999612i	$0.508863\pi$
$30$	6.50968e6	1.46728
$31$	4.31261e6	0.838712	0.419356	−	0.907822i	$-0.362256\pi$
$31$	4.31261e6	0.838712	0.419356	+	0.907822i	$0.362256\pi$
$32$	−1.04858e6	−0.176777
$33$	−1.23346e7	−1.81055
$34$	516712.	0.0663122
$35$	0	0
$36$	2.66364e6	0.264310
$37$	6.20102e6	0.543946	0.271973	−	0.962305i	$-0.412324\pi$
$37$	6.20102e6	0.543946	0.271973	+	0.962305i	$0.412324\pi$
$38$	−1.24651e7	−0.969771
$39$	−1.55108e7	−1.07360
$40$	9.60736e6	0.593382
$41$	−6.40835e6	−0.354176	−0.177088	−	0.984195i	$-0.556668\pi$
$41$	−6.40835e6	−0.354176	−0.177088	+	0.984195i	$0.556668\pi$
$42$	0	0
$43$	−6.99951e6	−0.312219	−0.156110	−	0.987740i	$-0.549895\pi$
$43$	−6.99951e6	−0.312219	−0.156110	+	0.987740i	$0.549895\pi$
$44$	−1.82041e7	−0.732203
$45$	−2.44050e7	−0.887204
$46$	−2.83654e7	−0.934070
$47$	3.50844e7	1.04875	0.524377	−	0.851486i	$-0.324298\pi$
$47$	3.50844e7	1.04875	0.524377	+	0.851486i	$0.324298\pi$
$48$	1.13678e7	0.309093
$49$	0	0
$50$	−5.67755e7	−1.28468
$51$	−5.60175e6	−0.115947
$52$	−2.28917e7	−0.434174
$53$	−4.26901e7	−0.743166	−0.371583	−	0.928400i	$-0.621185\pi$
$53$	−4.26901e7	−0.743166	−0.371583	+	0.928400i	$0.621185\pi$
$54$	2.57500e7	0.412103
$55$	1.66791e8	2.45777
$56$	0	0
$57$	1.35136e8	1.69564
$58$	3.39320e6	0.0393716
$59$	2.90654e7	0.312279	0.156139	−	0.987735i	$-0.450095\pi$
$59$	2.90654e7	0.312279	0.156139	+	0.987735i	$0.450095\pi$
$60$	−1.04155e8	−1.03753
$61$	−6.18781e7	−0.572207	−0.286103	−	0.958199i	$-0.592360\pi$
$61$	−6.18781e7	−0.572207	−0.286103	+	0.958199i	$0.592360\pi$
$62$	−6.90018e7	−0.593059
$63$	0	0
$64$	1.67772e7	0.125000
$65$	2.09741e8	1.45738
$66$	1.97353e8	1.28025
$67$	2.00649e8	1.21647	0.608234	−	0.793758i	$-0.291878\pi$
$67$	2.00649e8	1.21647	0.608234	+	0.793758i	$0.291878\pi$
$68$	−8.26739e6	−0.0468898
$69$	3.07514e8	1.63322
$70$	0	0
$71$	3.03014e7	0.141514	0.0707571	−	0.997494i	$-0.477458\pi$
$71$	3.03014e7	0.141514	0.0707571	+	0.997494i	$0.477458\pi$
$72$	−4.26182e7	−0.186896
$73$	2.91846e8	1.20282	0.601411	−	0.798940i	$-0.294606\pi$
$73$	2.91846e8	1.20282	0.601411	+	0.798940i	$0.294606\pi$
$74$	−9.92164e7	−0.384628
$75$	6.15512e8	2.24626
$76$	1.99441e8	0.685732
$77$	0	0
$78$	2.48173e8	0.759151
$79$	−1.08871e8	−0.314479	−0.157240	−	0.987560i	$-0.550260\pi$
$79$	−1.08871e8	−0.314479	−0.157240	+	0.987560i	$0.550260\pi$
$80$	−1.53718e8	−0.419584
$81$	−4.83958e8	−1.24918
$82$	1.02534e8	0.250440
$83$	−2.16661e8	−0.501106	−0.250553	−	0.968103i	$-0.580612\pi$
$83$	−2.16661e8	−0.501106	−0.250553	+	0.968103i	$0.580612\pi$
$84$	0	0
$85$	7.57483e7	0.157394
$86$	1.11992e8	0.220772
$87$	−3.67862e7	−0.0688412
$88$	2.91265e8	0.517746
$89$	1.86505e8	0.315090	0.157545	−	0.987512i	$-0.449642\pi$
$89$	1.86505e8	0.315090	0.157545	+	0.987512i	$0.449642\pi$
$90$	3.90481e8	0.627348
$91$	0	0
$92$	4.53847e8	0.660487
$93$	7.48059e8	1.03696
$94$	−5.61350e8	−0.741581
$95$	−1.82734e9	−2.30178
$96$	−1.81884e8	−0.218562
$97$	9.53814e8	1.09393	0.546966	−	0.837155i	$-0.315783\pi$
$97$	9.53814e8	1.09393	0.546966	+	0.837155i	$0.315783\pi$
$98$	0	0
$99$	−7.39884e8	−0.774115
$100$	9.08408e8	0.908408
$101$	1.94749e9	1.86221	0.931105	−	0.364750i	$-0.118846\pi$
$101$	1.94749e9	1.86221	0.931105	+	0.364750i	$0.118846\pi$
$102$	8.96281e7	0.0819867
$103$	1.38319e9	1.21092	0.605458	−	0.795877i	$-0.292990\pi$
$103$	1.38319e9	1.21092	0.605458	+	0.795877i	$0.292990\pi$
$104$	3.66268e8	0.307007
$105$	0	0
$106$	6.83042e8	0.525498
$107$	−1.91831e9	−1.41479	−0.707396	−	0.706817i	$-0.750130\pi$
$107$	−1.91831e9	−1.41479	−0.707396	+	0.706817i	$0.750130\pi$
$108$	−4.12000e8	−0.291401
$109$	1.88505e9	1.27910	0.639548	−	0.768751i	$-0.279121\pi$
$109$	1.88505e9	1.27910	0.639548	+	0.768751i	$0.279121\pi$
$110$	−2.66866e9	−1.73790
$111$	1.07562e9	0.672520
$112$	0	0
$113$	−1.65917e9	−0.957277	−0.478639	−	0.878012i	$-0.658870\pi$
$113$	−1.65917e9	−0.957277	−0.478639	+	0.878012i	$0.658870\pi$
$114$	−2.16218e9	−1.19900
$115$	−4.15828e9	−2.21704
$116$	−5.42912e7	−0.0278399
$117$	−9.30409e8	−0.459026
$118$	−4.65046e8	−0.220814
$119$	0	0
$120$	1.66648e9	0.733642
$121$	2.69863e9	1.14448
$122$	9.90050e8	0.404611
$123$	−1.11158e9	−0.437893
$124$	1.10403e9	0.419356
$125$	−3.74196e9	−1.37089
$126$	0	0
$127$	−2.50752e9	−0.855319	−0.427659	−	0.903940i	$-0.640662\pi$
$127$	−2.50752e9	−0.855319	−0.427659	+	0.903940i	$0.640662\pi$
$128$	−2.68435e8	−0.0883883
$129$	−1.21412e9	−0.386020
$130$	−3.35585e9	−1.03052
$131$	3.05147e9	0.905290	0.452645	−	0.891691i	$-0.350480\pi$
$131$	3.05147e9	0.905290	0.452645	+	0.891691i	$0.350480\pi$
$132$	−3.15765e9	−0.905277
$133$	0	0
$134$	−3.21039e9	−0.860173
$135$	3.77487e9	0.978137
$136$	1.32278e8	0.0331561
$137$	7.30548e9	1.77176	0.885882	−	0.463910i	$-0.153554\pi$
$137$	7.30548e9	1.77176	0.885882	+	0.463910i	$0.153554\pi$
$138$	−4.92023e9	−1.15486
$139$	−2.79289e9	−0.634581	−0.317290	−	0.948328i	$-0.602773\pi$
$139$	−2.79289e9	−0.634581	−0.317290	+	0.948328i	$0.602773\pi$
$140$	0	0
$141$	6.08569e9	1.29665
$142$	−4.84822e8	−0.100066
$143$	6.35868e9	1.27161
$144$	6.81892e8	0.132155
$145$	4.97432e8	0.0934496
$146$	−4.66954e9	−0.850523
$147$	0	0
$148$	1.58746e9	0.271973
$149$	−2.53425e9	−0.421223	−0.210611	−	0.977570i	$-0.567545\pi$
$149$	−2.53425e9	−0.421223	−0.210611	+	0.977570i	$0.567545\pi$
$150$	−9.84819e9	−1.58835
$151$	3.10856e9	0.486591	0.243295	−	0.969952i	$-0.421772\pi$
$151$	3.10856e9	0.486591	0.243295	+	0.969952i	$0.421772\pi$
$152$	−3.19106e9	−0.484886
$153$	−3.36019e8	−0.0495738
$154$	0	0
$155$	−1.01154e10	−1.40764
$156$	−3.97076e9	−0.536801
$157$	1.16398e10	1.52896	0.764481	−	0.644646i	$-0.222995\pi$
$157$	1.16398e10	1.52896	0.764481	+	0.644646i	$0.222995\pi$
$158$	1.74194e9	0.222370
$159$	−7.40496e9	−0.918831
$160$	2.45949e9	0.296691
$161$	0	0
$162$	7.74333e9	0.883304
$163$	−1.23726e10	−1.37283	−0.686417	−	0.727208i	$-0.740818\pi$
$163$	−1.23726e10	−1.37283	−0.686417	+	0.727208i	$0.740818\pi$
$164$	−1.64054e9	−0.177088
$165$	2.89313e10	3.03872
$166$	3.46658e9	0.354336
$167$	−6.26181e9	−0.622982	−0.311491	−	0.950249i	$-0.600828\pi$
$167$	−6.26181e9	−0.622982	−0.311491	+	0.950249i	$0.600828\pi$
$168$	0	0
$169$	−2.60842e9	−0.245973
$170$	−1.21197e9	−0.111294
$171$	8.10608e9	0.724984
$172$	−1.79187e9	−0.156110
$173$	8.79129e8	0.0746183	0.0373091	−	0.999304i	$-0.488121\pi$
$173$	8.79129e8	0.0746183	0.0373091	+	0.999304i	$0.488121\pi$
$174$	5.88579e8	0.0486780
$175$	0	0
$176$	−4.66024e9	−0.366101
$177$	5.04164e9	0.386093
$178$	−2.98407e9	−0.222802
$179$	−1.67343e10	−1.21834	−0.609170	−	0.793039i	$-0.708497\pi$
$179$	−1.67343e10	−1.21834	−0.609170	+	0.793039i	$0.708497\pi$
$180$	−6.24769e9	−0.443602
$181$	3.33844e9	0.231201	0.115601	−	0.993296i	$-0.463121\pi$
$181$	3.33844e9	0.231201	0.115601	+	0.993296i	$0.463121\pi$
$182$	0	0
$183$	−1.07333e10	−0.707462
$184$	−7.26155e9	−0.467035
$185$	−1.45448e10	−0.912924
$186$	−1.19689e10	−0.733243
$187$	2.29645e9	0.137331
$188$	8.98161e9	0.524377
$189$	0	0
$190$	2.92375e10	1.62760
$191$	−1.17806e10	−0.640498	−0.320249	−	0.947333i	$-0.603767\pi$
$191$	−1.17806e10	−0.640498	−0.320249	+	0.947333i	$0.603767\pi$
$192$	2.91015e9	0.154547
$193$	−3.21873e10	−1.66985	−0.834923	−	0.550367i	$-0.814488\pi$
$193$	−3.21873e10	−1.66985	−0.834923	+	0.550367i	$0.814488\pi$
$194$	−1.52610e10	−0.773527
$195$	3.63813e10	1.80187
$196$	0	0
$197$	−2.41075e10	−1.14039	−0.570195	−	0.821509i	$-0.693132\pi$
$197$	−2.41075e10	−1.14039	−0.570195	+	0.821509i	$0.693132\pi$
$198$	1.18382e10	0.547382
$199$	−1.14558e10	−0.517828	−0.258914	−	0.965900i	$-0.583365\pi$
$199$	−1.14558e10	−0.517828	−0.258914	+	0.965900i	$0.583365\pi$
$200$	−1.45345e10	−0.642342
$201$	3.48043e10	1.50401
$202$	−3.11598e10	−1.31678
$203$	0	0
$204$	−1.43405e9	−0.0579733
$205$	1.50311e10	0.594426
$206$	−2.21310e10	−0.856247
$207$	1.84461e10	0.698294
$208$	−5.86028e9	−0.217087
$209$	−5.53993e10	−2.00838
$210$	0	0
$211$	2.03945e10	0.708339	0.354169	−	0.935181i	$-0.384764\pi$
$211$	2.03945e10	0.708339	0.354169	+	0.935181i	$0.384764\pi$
$212$	−1.09287e10	−0.371583
$213$	5.25603e9	0.174964
$214$	3.06930e10	1.00041
$215$	1.64177e10	0.524009
$216$	6.59200e9	0.206051
$217$	0	0
$218$	−3.01608e10	−0.904458
$219$	5.06232e10	1.48714
$220$	4.26985e10	1.22888
$221$	2.88780e9	0.0814332
$222$	−1.72099e10	−0.475544
$223$	5.72310e10	1.54974	0.774871	−	0.632119i	$-0.217815\pi$
$223$	5.72310e10	1.54974	0.774871	+	0.632119i	$0.217815\pi$
$224$	0	0
$225$	3.69213e10	0.960407
$226$	2.65467e10	0.676897
$227$	−1.52497e10	−0.381193	−0.190596	−	0.981669i	$-0.561042\pi$
$227$	−1.52497e10	−0.381193	−0.190596	+	0.981669i	$0.561042\pi$
$228$	3.45948e10	0.847821
$229$	3.48029e10	0.836287	0.418144	−	0.908381i	$-0.362681\pi$
$229$	3.48029e10	0.836287	0.418144	+	0.908381i	$0.362681\pi$
$230$	6.65325e10	1.56768
$231$	0	0
$232$	8.68659e8	0.0196858
$233$	7.42782e10	1.65105	0.825524	−	0.564367i	$-0.190880\pi$
$233$	7.42782e10	1.65105	0.825524	+	0.564367i	$0.190880\pi$
$234$	1.48865e10	0.324580
$235$	−8.22921e10	−1.76016
$236$	7.44074e9	0.156139
$237$	−1.88847e10	−0.388814
$238$	0	0
$239$	6.12890e10	1.21504	0.607522	−	0.794303i	$-0.292164\pi$
$239$	6.12890e10	1.21504	0.607522	+	0.794303i	$0.292164\pi$
$240$	−2.66637e10	−0.518763
$241$	4.28739e10	0.818683	0.409342	−	0.912381i	$-0.365758\pi$
$241$	4.28739e10	0.818683	0.409342	+	0.912381i	$0.365758\pi$
$242$	−4.31781e10	−0.809273
$243$	−5.22693e10	−0.961653
$244$	−1.58408e10	−0.286103
$245$	0	0
$246$	1.77853e10	0.309637
$247$	−6.96649e10	−1.19091
$248$	−1.76645e10	−0.296529
$249$	−3.75817e10	−0.619555
$250$	5.98713e10	0.969368
$251$	2.70921e10	0.430835	0.215417	−	0.976522i	$-0.430889\pi$
$251$	2.70921e10	0.430835	0.215417	+	0.976522i	$0.430889\pi$
$252$	0	0
$253$	−1.26066e11	−1.93444
$254$	4.01204e10	0.604802
$255$	1.31392e10	0.194598
$256$	4.29497e9	0.0625000
$257$	8.34743e10	1.19359	0.596793	−	0.802395i	$-0.296441\pi$
$257$	8.34743e10	1.19359	0.596793	+	0.802395i	$0.296441\pi$
$258$	1.94260e10	0.272957
$259$	0	0
$260$	5.36936e10	0.728690
$261$	−2.20661e9	−0.0294335
$262$	−4.88235e10	−0.640137
$263$	5.03326e10	0.648707	0.324354	−	0.945936i	$-0.394853\pi$
$263$	5.03326e10	0.648707	0.324354	+	0.945936i	$0.394853\pi$
$264$	5.05224e10	0.640127
$265$	1.00132e11	1.24728
$266$	0	0
$267$	3.23508e10	0.389569
$268$	5.13662e10	0.608234
$269$	−3.29687e10	−0.383898	−0.191949	−	0.981405i	$-0.561481\pi$
$269$	−3.29687e10	−0.383898	−0.191949	+	0.981405i	$0.561481\pi$
$270$	−6.03979e10	−0.691647
$271$	−2.37345e10	−0.267312	−0.133656	−	0.991028i	$-0.542672\pi$
$271$	−2.37345e10	−0.267312	−0.133656	+	0.991028i	$0.542672\pi$
$272$	−2.11645e9	−0.0234449
$273$	0	0
$274$	−1.16888e11	−1.25283
$275$	−2.52330e11	−2.66056
$276$	7.87236e10	0.816609
$277$	−8.31501e10	−0.848602	−0.424301	−	0.905521i	$-0.639480\pi$
$277$	−8.31501e10	−0.848602	−0.424301	+	0.905521i	$0.639480\pi$
$278$	4.46862e10	0.448716
$279$	4.48720e10	0.443360
$280$	0	0
$281$	1.48862e11	1.42431	0.712154	−	0.702023i	$-0.247720\pi$
$281$	1.48862e11	1.42431	0.712154	+	0.702023i	$0.247720\pi$
$282$	−9.73710e10	−0.916872
$283$	−5.93552e10	−0.550072	−0.275036	−	0.961434i	$-0.588690\pi$
$283$	−5.93552e10	−0.550072	−0.275036	+	0.961434i	$0.588690\pi$
$284$	7.75715e9	0.0707571
$285$	−3.16968e11	−2.84586
$286$	−1.01739e11	−0.899166
$287$	0	0
$288$	−1.09103e10	−0.0934478
$289$	−1.17545e11	−0.991205
$290$	−7.95891e9	−0.0660789
$291$	1.65447e11	1.35251
$292$	7.47126e10	0.601411
$293$	−9.10565e10	−0.721783	−0.360892	−	0.932608i	$-0.617528\pi$
$293$	−9.10565e10	−0.721783	−0.360892	+	0.932608i	$0.617528\pi$
$294$	0	0
$295$	−6.81743e10	−0.524109
$296$	−2.53994e10	−0.192314
$297$	1.14442e11	0.853458
$298$	4.05480e10	0.297849
$299$	−1.58529e11	−1.14706
$300$	1.57571e11	1.12313
$301$	0	0
$302$	−4.97370e10	−0.344071
$303$	3.37808e11	2.30239
$304$	5.10570e10	0.342866
$305$	1.45138e11	0.960356
$306$	5.37630e9	0.0350540
$307$	−6.61649e10	−0.425114	−0.212557	−	0.977149i	$-0.568179\pi$
$307$	−6.61649e10	−0.425114	−0.212557	+	0.977149i	$0.568179\pi$
$308$	0	0
$309$	2.39926e11	1.49714
$310$	1.61847e11	0.995353
$311$	−8.84316e9	−0.0536026	−0.0268013	−	0.999641i	$-0.508532\pi$
$311$	−8.84316e9	−0.0536026	−0.0268013	+	0.999641i	$0.508532\pi$
$312$	6.35322e10	0.379576
$313$	−1.58157e10	−0.0931406	−0.0465703	−	0.998915i	$-0.514829\pi$
$313$	−1.58157e10	−0.0931406	−0.0465703	+	0.998915i	$0.514829\pi$
$314$	−1.86237e11	−1.08114
$315$	0	0
$316$	−2.78711e10	−0.157240
$317$	2.15403e11	1.19808	0.599039	−	0.800720i	$-0.295550\pi$
$317$	2.15403e11	1.19808	0.599039	+	0.800720i	$0.295550\pi$
$318$	1.18479e11	0.649712
$319$	1.50806e10	0.0815379
$320$	−3.93518e10	−0.209792
$321$	−3.32748e11	−1.74921
$322$	0	0
$323$	−2.51596e10	−0.128615
$324$	−1.23893e11	−0.624590
$325$	−3.17307e11	−1.57763
$326$	1.97962e11	0.970741
$327$	3.26978e11	1.58144
$328$	2.62486e10	0.125220
$329$	0	0
$330$	−4.62901e11	−2.14870
$331$	−4.03133e10	−0.184596	−0.0922980	−	0.995731i	$-0.529421\pi$
$331$	−4.03133e10	−0.184596	−0.0922980	+	0.995731i	$0.529421\pi$
$332$	−5.54653e10	−0.250553
$333$	6.45206e10	0.287541
$334$	1.00189e11	0.440515
$335$	−4.70632e11	−2.04164
$336$	0	0
$337$	−1.47587e11	−0.623324	−0.311662	−	0.950193i	$-0.600886\pi$
$337$	−1.47587e11	−0.623324	−0.311662	+	0.950193i	$0.600886\pi$
$338$	4.17348e10	0.173929
$339$	−2.87797e11	−1.18355
$340$	1.93916e10	0.0786969
$341$	−3.06668e11	−1.22821
$342$	−1.29697e11	−0.512641
$343$	0	0
$344$	2.86700e10	0.110386
$345$	−7.21289e11	−2.74109
$346$	−1.40661e10	−0.0527631
$347$	−3.90127e11	−1.44452	−0.722259	−	0.691623i	$-0.756896\pi$
$347$	−3.90127e11	−1.44452	−0.722259	+	0.691623i	$0.756896\pi$
$348$	−9.41726e9	−0.0344206
$349$	2.60554e10	0.0940119	0.0470059	−	0.998895i	$-0.485032\pi$
$349$	2.60554e10	0.0940119	0.0470059	+	0.998895i	$0.485032\pi$
$350$	0	0
$351$	1.43912e11	0.506074
$352$	7.45639e10	0.258873
$353$	−7.51585e10	−0.257627	−0.128814	−	0.991669i	$-0.541117\pi$
$353$	−7.51585e10	−0.257627	−0.128814	+	0.991669i	$0.541117\pi$
$354$	−8.06662e10	−0.273009
$355$	−7.10733e10	−0.237508
$356$	4.77452e10	0.157545
$357$	0	0
$358$	2.67749e11	0.861497
$359$	2.87238e11	0.912676	0.456338	−	0.889807i	$-0.349161\pi$
$359$	2.87238e11	0.912676	0.456338	+	0.889807i	$0.349161\pi$
$360$	9.99631e10	0.313674
$361$	2.84259e11	0.880912
$362$	−5.34151e10	−0.163484
$363$	4.68101e11	1.41501
$364$	0	0
$365$	−6.84539e11	−2.01874
$366$	1.71733e11	0.500251
$367$	5.08906e11	1.46434	0.732168	−	0.681124i	$-0.238509\pi$
$367$	5.08906e11	1.46434	0.732168	+	0.681124i	$0.238509\pi$
$368$	1.16185e11	0.330244
$369$	−6.66778e10	−0.187224
$370$	2.32717e11	0.645535
$371$	0	0
$372$	1.91503e11	0.518481
$373$	1.03452e11	0.276726	0.138363	−	0.990382i	$-0.455816\pi$
$373$	1.03452e11	0.276726	0.138363	+	0.990382i	$0.455816\pi$
$374$	−3.67432e10	−0.0971080
$375$	−6.49074e11	−1.69494
$376$	−1.43706e11	−0.370791
$377$	1.89639e10	0.0483495
$378$	0	0
$379$	1.10894e11	0.276078	0.138039	−	0.990427i	$-0.455920\pi$
$379$	1.10894e11	0.276078	0.138039	+	0.990427i	$0.455920\pi$
$380$	−4.67799e11	−1.15089
$381$	−4.34951e11	−1.05749
$382$	1.88490e11	0.452901
$383$	−2.59944e11	−0.617284	−0.308642	−	0.951178i	$-0.599875\pi$
$383$	−2.59944e11	−0.617284	−0.308642	+	0.951178i	$0.599875\pi$
$384$	−4.65624e10	−0.109281
$385$	0	0
$386$	5.14997e11	1.18076
$387$	−7.28288e10	−0.165045
$388$	2.44176e11	0.546966
$389$	5.82556e11	1.28993	0.644963	−	0.764214i	$-0.276873\pi$
$389$	5.82556e11	1.28993	0.644963	+	0.764214i	$0.276873\pi$
$390$	−5.82101e11	−1.27411
$391$	−5.72530e10	−0.123880
$392$	0	0
$393$	5.29303e11	1.11928
$394$	3.85719e11	0.806377
$395$	2.55363e11	0.527802
$396$	−1.89410e11	−0.387058
$397$	1.87073e11	0.377967	0.188983	−	0.981980i	$-0.439481\pi$
$397$	1.87073e11	0.377967	0.188983	+	0.981980i	$0.439481\pi$
$398$	1.83292e11	0.366159
$399$	0	0
$400$	2.32553e11	0.454204
$401$	−8.82741e11	−1.70484	−0.852420	−	0.522857i	$-0.824866\pi$
$401$	−8.82741e11	−1.70484	−0.852420	+	0.522857i	$0.824866\pi$
$402$	−5.56869e11	−1.06350
$403$	−3.85637e11	−0.728293
$404$	4.98557e11	0.931105
$405$	1.13515e12	2.09655
$406$	0	0
$407$	−4.40953e11	−0.796557
$408$	2.29448e10	0.0409933
$409$	3.94325e11	0.696785	0.348393	−	0.937349i	$-0.386728\pi$
$409$	3.94325e11	0.696785	0.348393	+	0.937349i	$0.386728\pi$
$410$	−2.40497e11	−0.420323
$411$	1.26720e12	2.19056
$412$	3.54096e11	0.605458
$413$	0	0
$414$	−2.95138e11	−0.493769
$415$	5.08189e11	0.841025
$416$	9.37645e10	0.153504
$417$	−4.84450e11	−0.784579
$418$	8.86388e11	1.42014
$419$	1.77960e11	0.282072	0.141036	−	0.990004i	$-0.454957\pi$
$419$	1.77960e11	0.282072	0.141036	+	0.990004i	$0.454957\pi$
$420$	0	0
$421$	3.94445e11	0.611952	0.305976	−	0.952039i	$-0.401017\pi$
$421$	3.94445e11	0.611952	0.305976	+	0.952039i	$0.401017\pi$
$422$	−3.26311e11	−0.500871
$423$	3.65048e11	0.554393
$424$	1.74859e11	0.262749
$425$	−1.14596e11	−0.170380
$426$	−8.40965e10	−0.123719
$427$	0	0
$428$	−4.91088e11	−0.707396
$429$	1.10297e12	1.57219
$430$	−2.62683e11	−0.370530
$431$	8.07791e11	1.12759	0.563795	−	0.825915i	$-0.309341\pi$
$431$	8.07791e11	1.12759	0.563795	+	0.825915i	$0.309341\pi$
$432$	−1.05472e11	−0.145700
$433$	−5.77686e11	−0.789763	−0.394881	−	0.918732i	$-0.629214\pi$
$433$	−5.77686e11	−0.789763	−0.394881	+	0.918732i	$0.629214\pi$
$434$	0	0
$435$	8.62838e10	0.115539
$436$	4.82573e11	0.639548
$437$	1.38116e12	1.81167
$438$	−8.09971e11	−1.05156
$439$	1.32828e12	1.70687	0.853436	−	0.521198i	$-0.174515\pi$
$439$	1.32828e12	1.70687	0.853436	+	0.521198i	$0.174515\pi$
$440$	−6.83176e11	−0.868952
$441$	0	0
$442$	−4.62048e10	−0.0575820
$443$	4.99467e11	0.616155	0.308077	−	0.951361i	$-0.400314\pi$
$443$	4.99467e11	0.616155	0.308077	+	0.951361i	$0.400314\pi$
$444$	2.75359e11	0.336260
$445$	−4.37455e11	−0.528827
$446$	−9.15696e11	−1.09583
$447$	−4.39588e11	−0.520789
$448$	0	0
$449$	−4.51211e10	−0.0523927	−0.0261964	−	0.999657i	$-0.508340\pi$
$449$	−4.51211e10	−0.0523927	−0.0261964	+	0.999657i	$0.508340\pi$
$450$	−5.90740e11	−0.679110
$451$	4.55695e11	0.518657
$452$	−4.24747e11	−0.478639
$453$	5.39207e11	0.601608
$454$	2.43995e11	0.269544
$455$	0	0
$456$	−5.53517e11	−0.599500
$457$	6.35220e11	0.681242	0.340621	−	0.940201i	$-0.389363\pi$
$457$	6.35220e11	0.681242	0.340621	+	0.940201i	$0.389363\pi$
$458$	−5.56846e11	−0.591344
$459$	5.19740e10	0.0546549
$460$	−1.06452e12	−1.10852
$461$	1.21010e12	1.24786	0.623932	−	0.781479i	$-0.285534\pi$
$461$	1.21010e12	1.24786	0.623932	+	0.781479i	$0.285534\pi$
$462$	0	0
$463$	9.73087e11	0.984095	0.492047	−	0.870568i	$-0.336249\pi$
$463$	9.73087e11	0.984095	0.492047	+	0.870568i	$0.336249\pi$
$464$	−1.38985e10	−0.0139200
$465$	−1.75461e12	−1.74037
$466$	−1.18845e12	−1.16747
$467$	−1.68306e12	−1.63747	−0.818735	−	0.574171i	$-0.805324\pi$
$467$	−1.68306e12	−1.63747	−0.818735	+	0.574171i	$0.805324\pi$
$468$	−2.38185e11	−0.229513
$469$	0	0
$470$	1.31667e12	1.24462
$471$	2.01902e12	1.89037
$472$	−1.19052e11	−0.110407
$473$	4.97733e11	0.457215
$474$	3.02155e11	0.274933
$475$	2.76450e12	2.49170
$476$	0	0
$477$	−4.44184e11	−0.392853
$478$	−9.80624e11	−0.859165
$479$	−1.16467e12	−1.01086	−0.505432	−	0.862866i	$-0.668667\pi$
$479$	−1.16467e12	−1.01086	−0.505432	+	0.862866i	$0.668667\pi$
$480$	4.26619e11	0.366821
$481$	−5.54500e11	−0.472334
$482$	−6.85982e11	−0.578897
$483$	0	0
$484$	6.90850e11	0.572242
$485$	−2.23722e12	−1.83599
$486$	8.36309e11	0.679992
$487$	2.24154e12	1.80578	0.902891	−	0.429869i	$-0.141440\pi$
$487$	2.24154e12	1.80578	0.902891	+	0.429869i	$0.141440\pi$
$488$	2.53453e11	0.202306
$489$	−2.14614e12	−1.69734
$490$	0	0
$491$	1.65508e11	0.128515	0.0642573	−	0.997933i	$-0.479532\pi$
$491$	1.65508e11	0.128515	0.0642573	+	0.997933i	$0.479532\pi$
$492$	−2.84565e11	−0.218947
$493$	6.84885e9	0.00522164
$494$	1.11464e12	0.842098
$495$	1.73543e12	1.29923
$496$	2.82631e11	0.209678
$497$	0	0
$498$	6.01307e11	0.438091
$499$	−1.21355e12	−0.876200	−0.438100	−	0.898926i	$-0.644348\pi$
$499$	−1.21355e12	−0.876200	−0.438100	+	0.898926i	$0.644348\pi$
$500$	−9.57941e11	−0.685447
$501$	−1.08616e12	−0.770239
$502$	−4.33473e11	−0.304646
$503$	−8.95258e10	−0.0623580	−0.0311790	−	0.999514i	$-0.509926\pi$
$503$	−8.95258e10	−0.0623580	−0.0311790	+	0.999514i	$0.509926\pi$
$504$	0	0
$505$	−4.56793e12	−3.12542
$506$	2.01706e12	1.36786
$507$	−4.52453e11	−0.304115
$508$	−6.41926e11	−0.427659
$509$	−1.33391e12	−0.880838	−0.440419	−	0.897792i	$-0.645170\pi$
$509$	−1.33391e12	−0.880838	−0.440419	+	0.897792i	$0.645170\pi$
$510$	−2.10227e11	−0.137601
$511$	0	0
$512$	−6.87195e10	−0.0441942
$513$	−1.25381e12	−0.799291
$514$	−1.33559e12	−0.843993
$515$	−3.24434e12	−2.03233
$516$	−3.10816e11	−0.193010
$517$	−2.49484e12	−1.53580
$518$	0	0
$519$	1.52492e11	0.0922561
$520$	−8.59098e11	−0.515261
$521$	5.72090e11	0.340169	0.170084	−	0.985430i	$-0.445596\pi$
$521$	5.72090e11	0.340169	0.170084	+	0.985430i	$0.445596\pi$
$522$	3.53057e10	0.0208127
$523$	2.50016e12	1.46120	0.730602	−	0.682804i	$-0.239240\pi$
$523$	2.50016e12	1.46120	0.730602	+	0.682804i	$0.239240\pi$
$524$	7.81175e11	0.452645
$525$	0	0
$526$	−8.05322e11	−0.458705
$527$	−1.39274e11	−0.0786541
$528$	−8.08358e11	−0.452638
$529$	1.34181e12	0.744973
$530$	−1.60211e12	−0.881962
$531$	3.02421e11	0.165077
$532$	0	0
$533$	5.73039e11	0.307547
$534$	−5.17613e11	−0.275467
$535$	4.49950e12	2.37450
$536$	−8.21859e11	−0.430087
$537$	−2.90271e12	−1.50632
$538$	5.27499e11	0.271457
$539$	0	0
$540$	9.66366e11	0.489069
$541$	1.04831e12	0.526140	0.263070	−	0.964777i	$-0.415265\pi$
$541$	1.04831e12	0.526140	0.263070	+	0.964777i	$0.415265\pi$
$542$	3.79752e11	0.189018
$543$	5.79081e11	0.285851
$544$	3.38632e10	0.0165780
$545$	−4.42147e12	−2.14676
$546$	0	0
$547$	−3.50622e12	−1.67454	−0.837272	−	0.546786i	$-0.815851\pi$
$547$	−3.50622e12	−1.67454	−0.837272	+	0.546786i	$0.815851\pi$
$548$	1.87020e12	0.885882
$549$	−6.43832e11	−0.302480
$550$	4.03729e12	1.88130
$551$	−1.65221e11	−0.0763629
$552$	−1.25958e12	−0.577430
$553$	0	0
$554$	1.33040e12	0.600052
$555$	−2.52292e12	−1.12872
$556$	−7.14979e11	−0.317290
$557$	2.24275e12	0.987262	0.493631	−	0.869671i	$-0.335669\pi$
$557$	2.24275e12	0.987262	0.493631	+	0.869671i	$0.335669\pi$
$558$	−7.17953e11	−0.313503
$559$	6.25901e11	0.271115
$560$	0	0
$561$	3.98339e11	0.169793
$562$	−2.38178e12	−1.00714
$563$	−2.03846e12	−0.855094	−0.427547	−	0.903993i	$-0.640622\pi$
$563$	−2.03846e12	−0.855094	−0.427547	+	0.903993i	$0.640622\pi$
$564$	1.55794e12	0.648326
$565$	3.89166e12	1.60663
$566$	9.49683e11	0.388960
$567$	0	0
$568$	−1.24114e11	−0.0500328
$569$	1.24872e12	0.499414	0.249707	−	0.968321i	$-0.419666\pi$
$569$	1.24872e12	0.499414	0.249707	+	0.968321i	$0.419666\pi$
$570$	5.07149e12	2.01233
$571$	2.28673e12	0.900226	0.450113	−	0.892972i	$-0.351384\pi$
$571$	2.28673e12	0.900226	0.450113	+	0.892972i	$0.351384\pi$
$572$	1.62782e12	0.635806
$573$	−2.04345e12	−0.791896
$574$	0	0
$575$	6.29087e12	2.39997
$576$	1.74564e11	0.0660776
$577$	2.61597e12	0.982521	0.491260	−	0.871013i	$-0.336536\pi$
$577$	2.61597e12	0.982521	0.491260	+	0.871013i	$0.336536\pi$
$578$	1.88072e12	0.700888
$579$	−5.58316e12	−2.06455
$580$	1.27343e11	0.0467248
$581$	0	0
$582$	−2.64715e12	−0.956369
$583$	3.03568e12	1.08830
$584$	−1.19540e12	−0.425262
$585$	2.18232e12	0.770401
$586$	1.45690e12	0.510378
$587$	3.09779e12	1.07691	0.538457	−	0.842653i	$-0.319007\pi$
$587$	3.09779e12	1.07691	0.538457	+	0.842653i	$0.319007\pi$
$588$	0	0
$589$	3.35982e12	1.15026
$590$	1.09079e12	0.370601
$591$	−4.18164e12	−1.40995
$592$	4.06390e11	0.135986
$593$	2.63952e12	0.876556	0.438278	−	0.898839i	$-0.355589\pi$
$593$	2.63952e12	0.876556	0.438278	+	0.898839i	$0.355589\pi$
$594$	−1.83107e12	−0.603486
$595$	0	0
$596$	−6.48769e11	−0.210611
$597$	−1.98710e12	−0.640229
$598$	2.53646e12	0.811097
$599$	−3.78448e12	−1.20112	−0.600558	−	0.799581i	$-0.705055\pi$
$599$	−3.78448e12	−1.20112	−0.600558	+	0.799581i	$0.705055\pi$
$600$	−2.52114e12	−0.794175
$601$	5.10190e11	0.159513	0.0797567	−	0.996814i	$-0.474586\pi$
$601$	5.10190e11	0.159513	0.0797567	+	0.996814i	$0.474586\pi$
$602$	0	0
$603$	2.08772e12	0.643050
$604$	7.95793e11	0.243295
$605$	−6.32978e12	−1.92083
$606$	−5.40494e12	−1.62803
$607$	−4.89855e12	−1.46460	−0.732299	−	0.680984i	$-0.761552\pi$
$607$	−4.89855e12	−1.46460	−0.732299	+	0.680984i	$0.761552\pi$
$608$	−8.16912e11	−0.242443
$609$	0	0
$610$	−2.32221e12	−0.679074
$611$	−3.13727e12	−0.910683
$612$	−8.60209e10	−0.0247869
$613$	4.36492e12	1.24854	0.624272	−	0.781207i	$-0.285396\pi$
$613$	4.36492e12	1.24854	0.624272	+	0.781207i	$0.285396\pi$
$614$	1.05864e12	0.300601
$615$	2.60727e12	0.734933
$616$	0	0
$617$	−3.81081e12	−1.05861	−0.529303	−	0.848433i	$-0.677547\pi$
$617$	−3.81081e12	−1.05861	−0.529303	+	0.848433i	$0.677547\pi$
$618$	−3.83881e12	−1.05864
$619$	1.52564e12	0.417680	0.208840	−	0.977950i	$-0.433031\pi$
$619$	1.52564e12	0.417680	0.208840	+	0.977950i	$0.433031\pi$
$620$	−2.58955e12	−0.703821
$621$	−2.85317e12	−0.769865
$622$	1.41491e11	0.0379028
$623$	0	0
$624$	−1.01652e12	−0.268400
$625$	1.84634e12	0.484006
$626$	2.53051e11	0.0658603
$627$	−9.60947e12	−2.48311
$628$	2.97979e12	0.764481
$629$	−2.00259e11	−0.0510110
$630$	0	0
$631$	−6.08153e12	−1.52715	−0.763573	−	0.645721i	$-0.776557\pi$
$631$	−6.08153e12	−1.52715	−0.763573	+	0.645721i	$0.776557\pi$
$632$	4.45937e11	0.111185
$633$	3.53759e12	0.875772
$634$	−3.44645e12	−0.847169
$635$	5.88151e12	1.43551
$636$	−1.89567e12	−0.459415
$637$	0	0
$638$	−2.41289e11	−0.0576560
$639$	3.15281e11	0.0748073
$640$	6.29628e11	0.148345
$641$	−1.36816e12	−0.320093	−0.160047	−	0.987109i	$-0.551164\pi$
$641$	−1.36816e12	−0.320093	−0.160047	+	0.987109i	$0.551164\pi$
$642$	5.32396e12	1.23688
$643$	2.94301e12	0.678958	0.339479	−	0.940614i	$-0.389749\pi$
$643$	2.94301e12	0.678958	0.339479	+	0.940614i	$0.389749\pi$
$644$	0	0
$645$	2.84779e12	0.647871
$646$	4.02554e11	0.0909447
$647$	4.40334e12	0.987901	0.493951	−	0.869490i	$-0.335552\pi$
$647$	4.40334e12	0.987901	0.493951	+	0.869490i	$0.335552\pi$
$648$	1.98229e12	0.441652
$649$	−2.06683e12	−0.457303
$650$	5.07691e12	1.11555
$651$	0	0
$652$	−3.16740e12	−0.686417
$653$	6.87439e11	0.147953	0.0739767	−	0.997260i	$-0.476431\pi$
$653$	6.87439e11	0.147953	0.0739767	+	0.997260i	$0.476431\pi$
$654$	−5.23164e12	−1.11825
$655$	−7.15736e12	−1.51938
$656$	−4.19977e11	−0.0885439
$657$	3.03661e12	0.635836
$658$	0	0
$659$	7.48190e12	1.54535	0.772676	−	0.634800i	$-0.218918\pi$
$659$	7.48190e12	1.54535	0.772676	+	0.634800i	$0.218918\pi$
$660$	7.40642e12	1.51936
$661$	−8.28772e12	−1.68861	−0.844303	−	0.535866i	$-0.819985\pi$
$661$	−8.28772e12	−1.68861	−0.844303	+	0.535866i	$0.819985\pi$
$662$	6.45012e11	0.130529
$663$	5.00913e11	0.100682
$664$	8.87444e11	0.177168
$665$	0	0
$666$	−1.03233e12	−0.203322
$667$	−3.75975e11	−0.0735517
$668$	−1.60302e12	−0.311491
$669$	9.92721e12	1.91606
$670$	7.53012e12	1.44366
$671$	4.40013e12	0.837943
$672$	0	0
$673$	−2.54077e11	−0.0477416	−0.0238708	−	0.999715i	$-0.507599\pi$
$673$	−2.54077e11	−0.0477416	−0.0238708	+	0.999715i	$0.507599\pi$
$674$	2.36139e12	0.440757
$675$	−5.71082e12	−1.05884
$676$	−6.67757e11	−0.122987
$677$	−9.71804e12	−1.77799	−0.888995	−	0.457916i	$-0.848596\pi$
$677$	−9.71804e12	−1.77799	−0.888995	+	0.457916i	$0.848596\pi$
$678$	4.60475e12	0.836898
$679$	0	0
$680$	−3.10265e11	−0.0556471
$681$	−2.64519e12	−0.471297
$682$	4.90669e12	0.868479
$683$	−7.54116e12	−1.32601	−0.663003	−	0.748617i	$-0.730718\pi$
$683$	−7.54116e12	−1.32601	−0.663003	+	0.748617i	$0.730718\pi$
$684$	2.07516e12	0.362492
$685$	−1.71353e13	−2.97362
$686$	0	0
$687$	6.03685e12	1.03396
$688$	−4.58720e11	−0.0780548
$689$	3.81738e12	0.645326
$690$	1.15406e13	1.93824
$691$	1.02932e13	1.71752	0.858758	−	0.512382i	$-0.171237\pi$
$691$	1.02932e13	1.71752	0.858758	+	0.512382i	$0.171237\pi$
$692$	2.25057e11	0.0373091
$693$	0	0
$694$	6.24203e12	1.02143
$695$	6.55085e12	1.06504
$696$	1.50676e11	0.0243390
$697$	2.06954e11	0.0332144
$698$	−4.16886e11	−0.0664764
$699$	1.28842e13	2.04131
$700$	0	0
$701$	9.10623e12	1.42432	0.712160	−	0.702017i	$-0.247717\pi$
$701$	9.10623e12	1.42432	0.712160	+	0.702017i	$0.247717\pi$
$702$	−2.30259e12	−0.357848
$703$	4.83102e12	0.746002
$704$	−1.19302e12	−0.183051
$705$	−1.42743e13	−2.17622
$706$	1.20254e12	0.182170
$707$	0	0
$708$	1.29066e12	0.193047
$709$	6.52973e12	0.970481	0.485240	−	0.874381i	$-0.338732\pi$
$709$	6.52973e12	0.970481	0.485240	+	0.874381i	$0.338732\pi$
$710$	1.13717e12	0.167944
$711$	−1.13279e12	−0.166240
$712$	−7.63923e11	−0.111401
$713$	7.64557e12	1.10792
$714$	0	0
$715$	−1.49146e13	−2.13419
$716$	−4.28398e12	−0.609170
$717$	1.06311e13	1.50225
$718$	−4.59580e12	−0.645359
$719$	1.04951e13	1.46455	0.732276	−	0.681007i	$-0.238458\pi$
$719$	1.04951e13	1.46455	0.732276	+	0.681007i	$0.238458\pi$
$720$	−1.59941e12	−0.221801
$721$	0	0
$722$	−4.54815e12	−0.622899
$723$	7.43684e12	1.01220
$724$	8.54641e11	0.115601
$725$	−7.52541e11	−0.101160
$726$	−7.48961e12	−1.00056
$727$	−3.77271e12	−0.500898	−0.250449	−	0.968130i	$-0.580578\pi$
$727$	−3.77271e12	−0.500898	−0.250449	+	0.968130i	$0.580578\pi$
$728$	0	0
$729$	4.59195e11	0.0602176
$730$	1.09526e13	1.42746
$731$	2.26046e11	0.0292798
$732$	−2.74772e12	−0.353731
$733$	1.38609e13	1.77347	0.886737	−	0.462275i	$-0.152967\pi$
$733$	1.38609e13	1.77347	0.886737	+	0.462275i	$0.152967\pi$
$734$	−8.14250e12	−1.03544
$735$	0	0
$736$	−1.85896e12	−0.233517
$737$	−1.42681e13	−1.78140
$738$	1.06684e12	0.132388
$739$	−1.46859e12	−0.181135	−0.0905673	−	0.995890i	$-0.528868\pi$
$739$	−1.46859e12	−0.181135	−0.0905673	+	0.995890i	$0.528868\pi$
$740$	−3.72347e12	−0.456462
$741$	−1.20840e13	−1.47241
$742$	0	0
$743$	−4.86883e12	−0.586104	−0.293052	−	0.956096i	$-0.594671\pi$
$743$	−4.86883e12	−0.586104	−0.293052	+	0.956096i	$0.594671\pi$
$744$	−3.06405e12	−0.366621
$745$	5.94421e12	0.706954
$746$	−1.65523e12	−0.195674
$747$	−2.25432e12	−0.264895
$748$	5.87891e11	0.0686657
$749$	0	0
$750$	1.03852e13	1.19850
$751$	−1.14272e13	−1.31087	−0.655435	−	0.755252i	$-0.727515\pi$
$751$	−1.14272e13	−1.31087	−0.655435	+	0.755252i	$0.727515\pi$
$752$	2.29929e12	0.262189
$753$	4.69935e12	0.532673
$754$	−3.03422e11	−0.0341882
$755$	−7.29129e12	−0.816663
$756$	0	0
$757$	4.87971e12	0.540085	0.270043	−	0.962848i	$-0.412962\pi$
$757$	4.87971e12	0.540085	0.270043	+	0.962848i	$0.412962\pi$
$758$	−1.77430e12	−0.195217
$759$	−2.18672e13	−2.39169
$760$	7.48479e12	0.813802
$761$	−1.12567e13	−1.21669	−0.608343	−	0.793674i	$-0.708166\pi$
$761$	−1.12567e13	−1.21669	−0.608343	+	0.793674i	$0.708166\pi$
$762$	6.95922e12	0.747761
$763$	0	0
$764$	−3.01584e12	−0.320249
$765$	7.88149e11	0.0832016
$766$	4.15910e12	0.436486
$767$	−2.59905e12	−0.271166
$768$	7.44998e11	0.0772734
$769$	1.61412e13	1.66444	0.832220	−	0.554446i	$-0.187070\pi$
$769$	1.61412e13	1.66444	0.832220	+	0.554446i	$0.187070\pi$
$770$	0	0
$771$	1.44793e13	1.47572
$772$	−8.23995e12	−0.834923
$773$	−1.40382e13	−1.41418	−0.707089	−	0.707125i	$-0.749992\pi$
$773$	−1.40382e13	−1.41418	−0.707089	+	0.707125i	$0.749992\pi$
$774$	1.16526e12	0.116705
$775$	1.53032e13	1.52379
$776$	−3.90682e12	−0.386764
$777$	0	0
$778$	−9.32090e12	−0.912115
$779$	−4.99254e12	−0.485739
$780$	9.31361e12	0.900933
$781$	−2.15472e12	−0.207234
$782$	9.16048e11	0.0875967
$783$	3.41308e11	0.0324503
$784$	0	0
$785$	−2.73017e13	−2.56612
$786$	−8.46884e12	−0.791448
$787$	−1.34428e12	−0.124912	−0.0624560	−	0.998048i	$-0.519893\pi$
$787$	−1.34428e12	−0.124912	−0.0624560	+	0.998048i	$0.519893\pi$
$788$	−6.17151e12	−0.570195
$789$	8.73062e12	0.802045
$790$	−4.08581e12	−0.373213
$791$	0	0
$792$	3.03057e12	0.273691
$793$	5.53319e12	0.496874
$794$	−2.99317e12	−0.267263
$795$	1.73687e13	1.54211
$796$	−2.93268e12	−0.258914
$797$	9.34992e12	0.820815	0.410408	−	0.911902i	$-0.365386\pi$
$797$	9.34992e12	0.820815	0.410408	+	0.911902i	$0.365386\pi$
$798$	0	0
$799$	−1.13303e12	−0.0983517
$800$	−3.72084e12	−0.321171
$801$	1.94055e12	0.166563
$802$	1.41239e13	1.20550
$803$	−2.07531e13	−1.76142
$804$	8.90990e12	0.752005
$805$	0	0
$806$	6.17019e12	0.514981
$807$	−5.71869e12	−0.474642
$808$	−7.97691e12	−0.658391
$809$	−5.46916e12	−0.448902	−0.224451	−	0.974485i	$-0.572059\pi$
$809$	−5.46916e12	−0.448902	−0.224451	+	0.974485i	$0.572059\pi$
$810$	−1.81624e13	−1.48248
$811$	−6.82318e12	−0.553851	−0.276925	−	0.960891i	$-0.589315\pi$
$811$	−6.82318e12	−0.553851	−0.276925	+	0.960891i	$0.589315\pi$
$812$	0	0
$813$	−4.11695e12	−0.330498
$814$	7.05524e12	0.563251
$815$	2.90206e13	2.30408
$816$	−3.67117e11	−0.0289867
$817$	−5.45309e12	−0.428197
$818$	−6.30919e12	−0.492702
$819$	0	0
$820$	3.84796e12	0.297213
$821$	2.27679e12	0.174896	0.0874479	−	0.996169i	$-0.472129\pi$
$821$	2.27679e12	0.174896	0.0874479	+	0.996169i	$0.472129\pi$
$822$	−2.02752e13	−1.54896
$823$	2.17924e13	1.65579	0.827897	−	0.560879i	$-0.189537\pi$
$823$	2.17924e13	1.65579	0.827897	+	0.560879i	$0.189537\pi$
$824$	−5.66554e12	−0.428123
$825$	−4.37689e13	−3.28944
$826$	0	0
$827$	1.32468e13	0.984772	0.492386	−	0.870377i	$-0.336125\pi$
$827$	1.32468e13	0.984772	0.492386	+	0.870377i	$0.336125\pi$
$828$	4.72221e12	0.349147
$829$	−6.43837e12	−0.473457	−0.236729	−	0.971576i	$-0.576075\pi$
$829$	−6.43837e12	−0.473457	−0.236729	+	0.971576i	$0.576075\pi$
$830$	−8.13103e12	−0.594695
$831$	−1.44231e13	−1.04919
$832$	−1.50023e12	−0.108543
$833$	0	0
$834$	7.75120e12	0.554781
$835$	1.46874e13	1.04557
$836$	−1.41822e13	−1.00419
$837$	−6.94061e12	−0.488802
$838$	−2.84736e12	−0.199455
$839$	−2.25634e12	−0.157208	−0.0786041	−	0.996906i	$-0.525046\pi$
$839$	−2.25634e12	−0.157208	−0.0786041	+	0.996906i	$0.525046\pi$
$840$	0	0
$841$	−1.44622e13	−0.996900
$842$	−6.31112e12	−0.432715
$843$	2.58213e13	1.76098
$844$	5.22098e12	0.354169
$845$	6.11818e12	0.412826
$846$	−5.84076e12	−0.392015
$847$	0	0
$848$	−2.79774e12	−0.185791
$849$	−1.02957e13	−0.680095
$850$	1.83354e12	0.120477
$851$	1.09934e13	0.718538
$852$	1.34554e12	0.0874822
$853$	2.07580e13	1.34250	0.671252	−	0.741229i	$-0.265757\pi$
$853$	2.07580e13	1.34250	0.671252	+	0.741229i	$0.265757\pi$
$854$	0	0
$855$	−1.90132e13	−1.21677
$856$	7.85741e12	0.500205
$857$	−3.17253e12	−0.200906	−0.100453	−	0.994942i	$-0.532029\pi$
$857$	−3.17253e12	−0.200906	−0.100453	+	0.994942i	$0.532029\pi$
$858$	−1.76475e13	−1.11171
$859$	2.93119e11	0.0183685	0.00918426	−	0.999958i	$-0.497077\pi$
$859$	2.93119e11	0.0183685	0.00918426	+	0.999958i	$0.497077\pi$
$860$	4.20293e12	0.262005
$861$	0	0
$862$	−1.29247e13	−0.797326
$863$	1.21943e13	0.748355	0.374178	−	0.927357i	$-0.377925\pi$
$863$	1.21943e13	0.748355	0.374178	+	0.927357i	$0.377925\pi$
$864$	1.68755e12	0.103026
$865$	−2.06204e12	−0.125235
$866$	9.24298e12	0.558447
$867$	−2.03892e13	−1.22550
$868$	0	0
$869$	7.74181e12	0.460525
$870$	−1.38054e12	−0.0816982
$871$	−1.79422e13	−1.05632
$872$	−7.72116e12	−0.452229
$873$	9.92428e12	0.578275
$874$	−2.20986e13	−1.28104
$875$	0	0
$876$	1.29595e13	0.743568
$877$	−1.84735e13	−1.05451	−0.527255	−	0.849707i	$-0.676779\pi$
$877$	−1.84735e13	−1.05451	−0.527255	+	0.849707i	$0.676779\pi$
$878$	−2.12526e13	−1.20694
$879$	−1.57945e13	−0.892394
$880$	1.09308e13	0.614442
$881$	−2.16016e13	−1.20808	−0.604039	−	0.796955i	$-0.706443\pi$
$881$	−2.16016e13	−1.20808	−0.604039	+	0.796955i	$0.706443\pi$
$882$	0	0
$883$	−1.00085e13	−0.554043	−0.277022	−	0.960864i	$-0.589347\pi$
$883$	−1.00085e13	−0.554043	−0.277022	+	0.960864i	$0.589347\pi$
$884$	7.39277e11	0.0407166
$885$	−1.18254e13	−0.647995
$886$	−7.99147e12	−0.435687
$887$	1.50548e13	0.816615	0.408307	−	0.912844i	$-0.366119\pi$
$887$	1.50548e13	0.816615	0.408307	+	0.912844i	$0.366119\pi$
$888$	−4.40574e12	−0.237772
$889$	0	0
$890$	6.99929e12	0.373937
$891$	3.44141e13	1.82931
$892$	1.46511e13	0.774871
$893$	2.73331e13	1.43833
$894$	7.03340e12	0.368253
$895$	3.92511e13	2.04479
$896$	0	0
$897$	−2.74982e13	−1.41820
$898$	7.21938e11	0.0370473
$899$	−9.14597e11	−0.0466994
$900$	9.45184e12	0.480203
$901$	1.37866e12	0.0696938
$902$	−7.29112e12	−0.366746
$903$	0	0
$904$	6.79596e12	0.338449
$905$	−7.83048e12	−0.388034
$906$	−8.62731e12	−0.425401
$907$	2.29359e13	1.12534	0.562668	−	0.826683i	$-0.309775\pi$
$907$	2.29359e13	1.12534	0.562668	+	0.826683i	$0.309775\pi$
$908$	−3.90392e12	−0.190596
$909$	2.02633e13	0.984403
$910$	0	0
$911$	4.04241e13	1.94450	0.972248	−	0.233952i	$-0.0751657\pi$
$911$	4.04241e13	1.94450	0.972248	+	0.233952i	$0.0751657\pi$
$912$	8.85627e12	0.423910
$913$	1.54067e13	0.733823
$914$	−1.01635e13	−0.481711
$915$	2.51754e13	1.18736
$916$	8.90954e12	0.418144
$917$	0	0
$918$	−8.31584e11	−0.0386468
$919$	4.18997e12	0.193772	0.0968859	−	0.995295i	$-0.469112\pi$
$919$	4.18997e12	0.193772	0.0968859	+	0.995295i	$0.469112\pi$
$920$	1.70323e13	0.783842
$921$	−1.14769e13	−0.525599
$922$	−1.93616e13	−0.882373
$923$	−2.70957e12	−0.122883
$924$	0	0
$925$	2.20041e13	0.988250
$926$	−1.55694e13	−0.695860
$927$	1.43919e13	0.640115
$928$	2.22377e11	0.00984291
$929$	−4.83610e12	−0.213022	−0.106511	−	0.994312i	$-0.533968\pi$
$929$	−4.83610e12	−0.213022	−0.106511	+	0.994312i	$0.533968\pi$
$930$	2.80737e13	1.23063
$931$	0	0
$932$	1.90152e13	0.825524
$933$	−1.53392e12	−0.0662729
$934$	2.69290e13	1.15787
$935$	−5.38643e12	−0.230488
$936$	3.81095e12	0.162290
$937$	1.70190e12	0.0721282	0.0360641	−	0.999349i	$-0.488518\pi$
$937$	1.70190e12	0.0721282	0.0360641	+	0.999349i	$0.488518\pi$
$938$	0	0
$939$	−2.74337e12	−0.115157
$940$	−2.10668e13	−0.880082
$941$	−2.82987e12	−0.117656	−0.0588278	−	0.998268i	$-0.518736\pi$
$941$	−2.82987e12	−0.117656	−0.0588278	+	0.998268i	$0.518736\pi$
$942$	−3.23043e13	−1.33669
$943$	−1.13610e13	−0.467857
$944$	1.90483e12	0.0780697
$945$	0	0
$946$	−7.96372e12	−0.323300
$947$	3.70636e13	1.49752	0.748761	−	0.662840i	$-0.230649\pi$
$947$	3.70636e13	1.49752	0.748761	+	0.662840i	$0.230649\pi$
$948$	−4.83448e12	−0.194407
$949$	−2.60971e13	−1.04447
$950$	−4.42320e13	−1.76190
$951$	3.73635e13	1.48127
$952$	0	0
$953$	−1.53995e12	−0.0604768	−0.0302384	−	0.999543i	$-0.509627\pi$
$953$	−1.53995e12	−0.0604768	−0.0302384	+	0.999543i	$0.509627\pi$
$954$	7.10694e12	0.277789
$955$	2.76320e13	1.07497
$956$	1.56900e13	0.607522
$957$	2.61585e12	0.100811
$958$	1.86347e13	0.714789
$959$	0	0
$960$	−6.82590e12	−0.259382
$961$	−7.84100e12	−0.296562
$962$	8.87200e12	0.333990
$963$	−1.99597e13	−0.747888
$964$	1.09757e13	0.409342
$965$	7.54968e13	2.80257
$966$	0	0
$967$	−1.09919e13	−0.404254	−0.202127	−	0.979359i	$-0.564785\pi$
$967$	−1.09919e13	−0.404254	−0.202127	+	0.979359i	$0.564785\pi$
$968$	−1.10536e13	−0.404636
$969$	−4.36415e12	−0.159017
$970$	3.57954e13	1.29824
$971$	1.32559e12	0.0478544	0.0239272	−	0.999714i	$-0.492383\pi$
$971$	1.32559e12	0.0478544	0.0239272	+	0.999714i	$0.492383\pi$
$972$	−1.33809e13	−0.480827
$973$	0	0
$974$	−3.58646e13	−1.27688
$975$	−5.50396e13	−1.95054
$976$	−4.05525e12	−0.143052
$977$	−2.73317e12	−0.0959711	−0.0479856	−	0.998848i	$-0.515280\pi$
$977$	−2.73317e12	−0.0959711	−0.0479856	+	0.998848i	$0.515280\pi$
$978$	3.43382e13	1.20020
$979$	−1.32623e13	−0.461419
$980$	0	0
$981$	1.96136e13	0.676157
$982$	−2.64813e12	−0.0908736
$983$	−6.48654e11	−0.0221576	−0.0110788	−	0.999939i	$-0.503527\pi$
$983$	−6.48654e11	−0.0221576	−0.0110788	+	0.999939i	$0.503527\pi$
$984$	4.55304e12	0.154819
$985$	5.65452e13	1.91396
$986$	−1.09582e11	−0.00369226
$987$	0	0
$988$	−1.78342e13	−0.595453
$989$	−1.24090e13	−0.412433
$990$	−2.77669e13	−0.918692
$991$	−3.95845e13	−1.30375	−0.651874	−	0.758327i	$-0.726017\pi$
$991$	−3.95845e13	−1.30375	−0.651874	+	0.758327i	$0.726017\pi$
$992$	−4.52210e12	−0.148265
$993$	−6.99268e12	−0.228230
$994$	0	0
$995$	2.68700e13	0.869090
$996$	−9.62092e12	−0.309777
$997$	−2.11249e13	−0.677121	−0.338560	−	0.940945i	$-0.609940\pi$
$997$	−2.11249e13	−0.677121	−0.338560	+	0.940945i	$0.609940\pi$
$998$	1.94167e13	0.619567
$999$	−9.97977e12	−0.317012

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	98.10.a.h.1.3		3
7.2	even	3		98.10.c.l.67.1		6
7.3	odd	6		14.10.c.b.9.3	✓	6
7.4	even	3		98.10.c.l.79.1		6
7.5	odd	6		14.10.c.b.11.3	yes	6
7.6	odd	2		98.10.a.g.1.1		3
21.5	even	6		126.10.g.e.109.3		6
21.17	even	6		126.10.g.e.37.3		6
28.3	even	6		112.10.i.a.65.1		6
28.19	even	6		112.10.i.a.81.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.10.c.b.9.3	✓	6	7.3	odd	6
14.10.c.b.11.3	yes	6	7.5	odd	6
98.10.a.g.1.1		3	7.6	odd	2
98.10.a.h.1.3		3	1.1	even	1	trivial
98.10.c.l.67.1		6	7.2	even	3
98.10.c.l.79.1		6	7.4	even	3
112.10.i.a.65.1		6	28.3	even	6
112.10.i.a.81.1		6	28.19	even	6
126.10.g.e.37.3		6	21.17	even	6
126.10.g.e.109.3		6	21.5	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 98 = 2 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	98.a (trivial)

\(f(q)\)	\(=\)	\(q-16.0000 q^{2} +173.458 q^{3} +256.000 q^{4} -2345.55 q^{5} -2775.34 q^{6} -4096.00 q^{8} +10404.8 q^{9} +37528.8 q^{10} -71109.6 q^{11} +44405.4 q^{12} -89420.8 q^{13} -406855. q^{15} +65536.0 q^{16} -32294.5 q^{17} -166477. q^{18} +779068. q^{19} -600460. q^{20} +1.13775e6 q^{22} +1.77284e6 q^{23} -710486. q^{24} +3.54847e6 q^{25} +1.43073e6 q^{26} -1.60938e6 q^{27} -212075. q^{29} +6.50968e6 q^{30} +4.31261e6 q^{31} -1.04858e6 q^{32} -1.23346e7 q^{33} +516712. q^{34} +2.66364e6 q^{36} +6.20102e6 q^{37} -1.24651e7 q^{38} -1.55108e7 q^{39} +9.60736e6 q^{40} -6.40835e6 q^{41} -6.99951e6 q^{43} -1.82041e7 q^{44} -2.44050e7 q^{45} -2.83654e7 q^{46} +3.50844e7 q^{47} +1.13678e7 q^{48} -5.67755e7 q^{50} -5.60175e6 q^{51} -2.28917e7 q^{52} -4.26901e7 q^{53} +2.57500e7 q^{54} +1.66791e8 q^{55} +1.35136e8 q^{57} +3.39320e6 q^{58} +2.90654e7 q^{59} -1.04155e8 q^{60} -6.18781e7 q^{61} -6.90018e7 q^{62} +1.67772e7 q^{64} +2.09741e8 q^{65} +1.97353e8 q^{66} +2.00649e8 q^{67} -8.26739e6 q^{68} +3.07514e8 q^{69} +3.03014e7 q^{71} -4.26182e7 q^{72} +2.91846e8 q^{73} -9.92164e7 q^{74} +6.15512e8 q^{75} +1.99441e8 q^{76} +2.48173e8 q^{78} -1.08871e8 q^{79} -1.53718e8 q^{80} -4.83958e8 q^{81} +1.02534e8 q^{82} -2.16661e8 q^{83} +7.57483e7 q^{85} +1.11992e8 q^{86} -3.67862e7 q^{87} +2.91265e8 q^{88} +1.86505e8 q^{89} +3.90481e8 q^{90} +4.53847e8 q^{92} +7.48059e8 q^{93} -5.61350e8 q^{94} -1.82734e9 q^{95} -1.81884e8 q^{96} +9.53814e8 q^{97} -7.39884e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 48 q^{2} + 71 q^{3} + 768 q^{4} - 1085 q^{5} - 1136 q^{6} - 12288 q^{8} + 9106 q^{9} + 17360 q^{10} - 2555 q^{11} + 18176 q^{12} - 18070 q^{13} - 353073 q^{15} + 196608 q^{16} + 20759 q^{17} - 145696 q^{18}+ \cdots - 1303712634 q^{99}+O(q^{100}) \) 3 * q - 48 * q^2 + 71 * q^3 + 768 * q^4 - 1085 * q^5 - 1136 * q^6 - 12288 * q^8 + 9106 * q^9 + 17360 * q^10 - 2555 * q^11 + 18176 * q^12 - 18070 * q^13 - 353073 * q^15 + 196608 * q^16 + 20759 * q^17 - 145696 * q^18 + 1220649 * q^19 - 277760 * q^20 + 40880 * q^22 + 1960903 * q^23 - 290816 * q^24 + 863572 * q^25 + 289120 * q^26 - 2888659 * q^27 - 2606146 * q^29 + 5649168 * q^30 - 9377989 * q^31 - 3145728 * q^32 - 10778103 * q^33 - 332144 * q^34 + 2331136 * q^36 + 25814913 * q^37 - 19530384 * q^38 - 37990822 * q^39 + 4444160 * q^40 - 209250 * q^41 + 2944308 * q^43 - 654080 * q^44 - 37350558 * q^45 - 31374448 * q^46 + 48391269 * q^47 + 4653056 * q^48 - 13817152 * q^50 + 75441987 * q^51 - 4625920 * q^52 - 102186411 * q^53 + 46218544 * q^54 + 228278701 * q^55 + 43084589 * q^57 + 41698336 * q^58 + 144220135 * q^59 - 90386688 * q^60 + 280936871 * q^61 + 150047824 * q^62 + 50331648 * q^64 + 186819738 * q^65 + 172449648 * q^66 - 170710399 * q^67 + 5314304 * q^68 + 903654171 * q^69 + 469758688 * q^71 - 37298176 * q^72 + 613838539 * q^73 - 413038608 * q^74 + 902254676 * q^75 + 312486144 * q^76 + 607853152 * q^78 - 197445809 * q^79 - 71106560 * q^80 - 887872901 * q^81 + 3348000 * q^82 + 1074181436 * q^83 + 411272519 * q^85 - 47108928 * q^86 + 753428670 * q^87 + 10465280 * q^88 + 805730427 * q^89 + 597608928 * q^90 + 501991168 * q^92 + 1721516327 * q^93 - 774260304 * q^94 - 1799421743 * q^95 - 74448896 * q^96 + 2262918094 * q^97 - 1303712634 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more