LMFDB - Embedded newform 98.6.a.h.1.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [98,6,Mod(1,98)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("98.1"); S:= CuspForms(chi, 6); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(98, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 6, names="a")

Level:	$ N $	$=$	$ 98 = 2 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	98.a (trivial)

Newform invariants

comment:select newform

sage:traces = [2,8,14,32,70,56,0,128,244] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)

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

Self dual:	yes
Analytic conductor:	$15.7176143417$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{79}) $
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 79 $ x^2 - 79
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 14)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-8.88819$ 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)

$f(q)$	$=$	\(q+4.00000 q^{2} -10.7764 q^{3} +16.0000 q^{4} +106.106 q^{5} -43.1056 q^{6} +64.0000 q^{8} -126.869 q^{9} +424.422 q^{10} -93.4347 q^{11} -172.422 q^{12} +661.131 q^{13} -1143.43 q^{15} +256.000 q^{16} +455.919 q^{17} -507.478 q^{18} +1106.28 q^{19} +1697.69 q^{20} -373.739 q^{22} +748.390 q^{23} -689.689 q^{24} +8133.39 q^{25} +2644.52 q^{26} +3985.86 q^{27} +2804.78 q^{29} -4573.74 q^{30} -359.299 q^{31} +1024.00 q^{32} +1006.89 q^{33} +1823.68 q^{34} -2029.91 q^{36} -6812.82 q^{37} +4425.12 q^{38} -7124.60 q^{39} +6790.76 q^{40} +2319.39 q^{41} -19965.7 q^{43} -1494.96 q^{44} -13461.6 q^{45} +2993.56 q^{46} -14209.5 q^{47} -2758.76 q^{48} +32533.6 q^{50} -4913.17 q^{51} +10578.1 q^{52} +26144.2 q^{53} +15943.4 q^{54} -9913.94 q^{55} -11921.7 q^{57} +11219.1 q^{58} +4904.35 q^{59} -18295.0 q^{60} -13203.3 q^{61} -1437.19 q^{62} +4096.00 q^{64} +70149.6 q^{65} +4027.56 q^{66} -59658.1 q^{67} +7294.71 q^{68} -8064.94 q^{69} +8906.43 q^{71} -8119.64 q^{72} -10480.6 q^{73} -27251.3 q^{74} -87648.6 q^{75} +17700.5 q^{76} -28498.4 q^{78} -7230.02 q^{79} +27163.0 q^{80} -12123.9 q^{81} +9277.57 q^{82} -100461. q^{83} +48375.6 q^{85} -79862.9 q^{86} -30225.4 q^{87} -5979.82 q^{88} +20071.8 q^{89} -53846.2 q^{90} +11974.2 q^{92} +3871.94 q^{93} -56838.2 q^{94} +117382. q^{95} -11035.0 q^{96} -23320.9 q^{97} +11854.0 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 8 q^{2} + 14 q^{3} + 32 q^{4} + 70 q^{5} + 56 q^{6} + 128 q^{8} + 244 q^{9} + 280 q^{10} + 62 q^{11} + 224 q^{12} + 1820 q^{13} - 2038 q^{15} + 512 q^{16} + 1694 q^{17} + 976 q^{18} + 826 q^{19} + 1120 q^{20}+ \cdots + 69500 q^{99}+O(q^{100}) $ 2 * q + 8 * q^2 + 14 * q^3 + 32 * q^4 + 70 * q^5 + 56 * q^6 + 128 * q^8 + 244 * q^9 + 280 * q^10 + 62 * q^11 + 224 * q^12 + 1820 * q^13 - 2038 * q^15 + 512 * q^16 + 1694 * q^17 + 976 * q^18 + 826 * q^19 + 1120 * q^20 + 248 * q^22 - 2734 * q^23 + 896 * q^24 + 6312 * q^25 + 7280 * q^26 + 7154 * q^27 - 2852 * q^29 - 8152 * q^30 - 2674 * q^31 + 2048 * q^32 + 4858 * q^33 + 6776 * q^34 + 3904 * q^36 - 9146 * q^37 + 3304 * q^38 + 21588 * q^39 + 4480 * q^40 + 6132 * q^41 - 16040 * q^43 + 992 * q^44 - 26852 * q^45 - 10936 * q^46 - 25326 * q^47 + 3584 * q^48 + 25248 * q^50 + 25762 * q^51 + 29120 * q^52 + 14958 * q^53 + 28616 * q^54 - 15526 * q^55 - 18866 * q^57 - 11408 * q^58 - 1106 * q^59 - 32608 * q^60 - 28042 * q^61 - 10696 * q^62 + 8192 * q^64 + 28308 * q^65 + 19432 * q^66 - 102642 * q^67 + 27104 * q^68 - 94346 * q^69 - 11056 * q^71 + 15616 * q^72 + 35070 * q^73 - 36584 * q^74 - 132776 * q^75 + 13216 * q^76 + 86352 * q^78 + 101762 * q^79 + 17920 * q^80 - 23750 * q^81 + 24528 * q^82 - 44632 * q^83 + 3674 * q^85 - 64160 * q^86 - 170380 * q^87 + 3968 * q^88 - 75474 * q^89 - 107408 * q^90 - 43744 * q^92 - 53478 * q^93 - 101304 * q^94 + 127502 * q^95 + 14336 * q^96 - 8316 * q^97 + 69500 * 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 $

$2$	4.00000	0.707107
$2$	4.00000	0.707107
$3$	−10.7764	−0.691306	−0.345653	−	0.938362i	$-0.612343\pi$
$3$	−10.7764	−0.691306	−0.345653	+	0.938362i	$0.612343\pi$
$4$	16.0000	0.500000
$5$	106.106	1.89807	0.949037	−	0.315165i	$-0.102060\pi$
$5$	106.106	1.89807	0.949037	+	0.315165i	$0.102060\pi$
$6$	−43.1056	−0.488827
$7$	0	0
$7$	0	0
$8$	64.0000	0.353553
$9$	−126.869	−0.522096
$10$	424.422	1.34214
$11$	−93.4347	−0.232823	−0.116412	−	0.993201i	$-0.537139\pi$
$11$	−93.4347	−0.232823	−0.116412	+	0.993201i	$0.537139\pi$
$12$	−172.422	−0.345653
$13$	661.131	1.08500	0.542499	−	0.840057i	$-0.317478\pi$
$13$	661.131	1.08500	0.542499	+	0.840057i	$0.317478\pi$
$14$	0	0
$15$	−1143.43	−1.31215
$16$	256.000	0.250000
$17$	455.919	0.382618	0.191309	−	0.981530i	$-0.438727\pi$
$17$	455.919	0.382618	0.191309	+	0.981530i	$0.438727\pi$
$18$	−507.478	−0.369178
$19$	1106.28	0.703041	0.351521	−	0.936180i	$-0.385665\pi$
$19$	1106.28	0.703041	0.351521	+	0.936180i	$0.385665\pi$
$20$	1697.69	0.949037
$21$	0	0
$22$	−373.739	−0.164631
$23$	748.390	0.294991	0.147495	−	0.989063i	$-0.452879\pi$
$23$	748.390	0.294991	0.147495	+	0.989063i	$0.452879\pi$
$24$	−689.689	−0.244413
$25$	8133.39	2.60268
$26$	2644.52	0.767209
$27$	3985.86	1.05223
$28$	0	0
$29$	2804.78	0.619304	0.309652	−	0.950850i	$-0.399787\pi$
$29$	2804.78	0.619304	0.309652	+	0.950850i	$0.399787\pi$
$30$	−4573.74	−0.927830
$31$	−359.299	−0.0671508	−0.0335754	−	0.999436i	$-0.510689\pi$
$31$	−359.299	−0.0671508	−0.0335754	+	0.999436i	$0.510689\pi$
$32$	1024.00	0.176777
$33$	1006.89	0.160952
$34$	1823.68	0.270552
$35$	0	0
$36$	−2029.91	−0.261048
$37$	−6812.82	−0.818131	−0.409066	−	0.912505i	$-0.634145\pi$
$37$	−6812.82	−0.818131	−0.409066	+	0.912505i	$0.634145\pi$
$38$	4425.12	0.497125
$39$	−7124.60	−0.750065
$40$	6790.76	0.671070
$41$	2319.39	0.215484	0.107742	−	0.994179i	$-0.465638\pi$
$41$	2319.39	0.215484	0.107742	+	0.994179i	$0.465638\pi$
$42$	0	0
$43$	−19965.7	−1.64670	−0.823349	−	0.567535i	$-0.807897\pi$
$43$	−19965.7	−1.64670	−0.823349	+	0.567535i	$0.807897\pi$
$44$	−1494.96	−0.116412
$45$	−13461.6	−0.990978
$46$	2993.56	0.208590
$47$	−14209.5	−0.938287	−0.469143	−	0.883122i	$-0.655437\pi$
$47$	−14209.5	−0.938287	−0.469143	+	0.883122i	$0.655437\pi$
$48$	−2758.76	−0.172826
$49$	0	0
$50$	32533.6	1.84038
$51$	−4913.17	−0.264506
$52$	10578.1	0.542499
$53$	26144.2	1.27846	0.639228	−	0.769017i	$-0.279254\pi$
$53$	26144.2	1.27846	0.639228	+	0.769017i	$0.279254\pi$
$54$	15943.4	0.744042
$55$	−9913.94	−0.441916
$56$	0	0
$57$	−11921.7	−0.486016
$58$	11219.1	0.437914
$59$	4904.35	0.183422	0.0917110	−	0.995786i	$-0.470766\pi$
$59$	4904.35	0.183422	0.0917110	+	0.995786i	$0.470766\pi$
$60$	−18295.0	−0.656075
$61$	−13203.3	−0.454315	−0.227158	−	0.973858i	$-0.572943\pi$
$61$	−13203.3	−0.454315	−0.227158	+	0.973858i	$0.572943\pi$
$62$	−1437.19	−0.0474828
$63$	0	0
$64$	4096.00	0.125000
$65$	70149.6	2.05941
$66$	4027.56	0.113810
$67$	−59658.1	−1.62361	−0.811807	−	0.583926i	$-0.801516\pi$
$67$	−59658.1	−1.62361	−0.811807	+	0.583926i	$0.801516\pi$
$68$	7294.71	0.191309
$69$	−8064.94	−0.203929
$70$	0	0
$71$	8906.43	0.209680	0.104840	−	0.994489i	$-0.466567\pi$
$71$	8906.43	0.209680	0.104840	+	0.994489i	$0.466567\pi$
$72$	−8119.64	−0.184589
$73$	−10480.6	−0.230186	−0.115093	−	0.993355i	$-0.536717\pi$
$73$	−10480.6	−0.230186	−0.115093	+	0.993355i	$0.536717\pi$
$74$	−27251.3	−0.578506
$75$	−87648.6	−1.79925
$76$	17700.5	0.351521
$77$	0	0
$78$	−28498.4	−0.530376
$79$	−7230.02	−0.130338	−0.0651691	−	0.997874i	$-0.520759\pi$
$79$	−7230.02	−0.130338	−0.0651691	+	0.997874i	$0.520759\pi$
$80$	27163.0	0.474518
$81$	−12123.9	−0.205319
$82$	9277.57	0.152370
$83$	−100461.	−1.60067	−0.800336	−	0.599552i	$-0.795345\pi$
$83$	−100461.	−1.60067	−0.800336	+	0.599552i	$0.795345\pi$
$84$	0	0
$85$	48375.6	0.726238
$86$	−79862.9	−1.16439
$87$	−30225.4	−0.428128
$88$	−5979.82	−0.0823155
$89$	20071.8	0.268603	0.134302	−	0.990940i	$-0.457121\pi$
$89$	20071.8	0.268603	0.134302	+	0.990940i	$0.457121\pi$
$90$	−53846.2	−0.700727
$91$	0	0
$92$	11974.2	0.147495
$93$	3871.94	0.0464217
$94$	−56838.2	−0.663469
$95$	117382.	1.33442
$96$	−11035.0	−0.122207
$97$	−23320.9	−0.251662	−0.125831	−	0.992052i	$-0.540160\pi$
$97$	−23320.9	−0.251662	−0.125831	+	0.992052i	$0.540160\pi$
$98$	0	0
$99$	11854.0	0.121556
$100$	130134.	1.30134
$101$	−68974.1	−0.672795	−0.336398	−	0.941720i	$-0.609209\pi$
$101$	−68974.1	−0.672795	−0.336398	+	0.941720i	$0.609209\pi$
$102$	−19652.7	−0.187034
$103$	113725.	1.05624	0.528121	−	0.849169i	$-0.322897\pi$
$103$	113725.	1.05624	0.528121	+	0.849169i	$0.322897\pi$
$104$	42312.4	0.383605
$105$	0	0
$106$	104577.	0.904005
$107$	−121287.	−1.02413	−0.512066	−	0.858946i	$-0.671120\pi$
$107$	−121287.	−1.02413	−0.512066	+	0.858946i	$0.671120\pi$
$108$	63773.7	0.526117
$109$	−61373.9	−0.494786	−0.247393	−	0.968915i	$-0.579574\pi$
$109$	−61373.9	−0.494786	−0.247393	+	0.968915i	$0.579574\pi$
$110$	−39655.8	−0.312482
$111$	73417.7	0.565579
$112$	0	0
$113$	−242939.	−1.78979	−0.894893	−	0.446281i	$-0.852748\pi$
$113$	−242939.	−1.78979	−0.894893	+	0.446281i	$0.852748\pi$
$114$	−47686.8	−0.343665
$115$	79408.4	0.559914
$116$	44876.5	0.309652
$117$	−83877.3	−0.566474
$118$	19617.4	0.129699
$119$	0	0
$120$	−73179.8	−0.463915
$121$	−152321.	−0.945793
$122$	−52813.1	−0.321249
$123$	−24994.7	−0.148965
$124$	−5748.78	−0.0335754
$125$	531418.	3.04201
$126$	0	0
$127$	201922.	1.11090	0.555448	−	0.831551i	$-0.312547\pi$
$127$	201922.	1.11090	0.555448	+	0.831551i	$0.312547\pi$
$128$	16384.0	0.0883883
$129$	215159.	1.13837
$130$	280598.	1.45622
$131$	283521.	1.44347	0.721734	−	0.692171i	$-0.243345\pi$
$131$	283521.	1.44347	0.721734	+	0.692171i	$0.243345\pi$
$132$	16110.2	0.0804761
$133$	0	0
$134$	−238633.	−1.14807
$135$	422922.	1.99722
$136$	29178.8	0.135276
$137$	188471.	0.857911	0.428955	−	0.903326i	$-0.358882\pi$
$137$	188471.	0.857911	0.428955	+	0.903326i	$0.358882\pi$
$138$	−32259.8	−0.144199
$139$	−211579.	−0.928830	−0.464415	−	0.885618i	$-0.653735\pi$
$139$	−211579.	−0.928830	−0.464415	+	0.885618i	$0.653735\pi$
$140$	0	0
$141$	153128.	0.648643
$142$	35625.7	0.148266
$143$	−61772.5	−0.252613
$144$	−32478.6	−0.130524
$145$	297603.	1.17548
$146$	−41922.4	−0.162766
$147$	0	0
$148$	−109005.	−0.409066
$149$	−293324.	−1.08238	−0.541192	−	0.840899i	$-0.682027\pi$
$149$	−293324.	−1.08238	−0.541192	+	0.840899i	$0.682027\pi$
$150$	−350594.	−1.27226
$151$	−204476.	−0.729794	−0.364897	−	0.931048i	$-0.618896\pi$
$151$	−204476.	−0.729794	−0.364897	+	0.931048i	$0.618896\pi$
$152$	70801.9	0.248563
$153$	−57842.2	−0.199764
$154$	0	0
$155$	−38123.6	−0.127457
$156$	−113994.	−0.375033
$157$	505915.	1.63805	0.819027	−	0.573755i	$-0.194514\pi$
$157$	505915.	1.63805	0.819027	+	0.573755i	$0.194514\pi$
$158$	−28920.1	−0.0921630
$159$	−281740.	−0.883804
$160$	108652.	0.335535
$161$	0	0
$162$	−48495.5	−0.145182
$163$	−284200.	−0.837829	−0.418914	−	0.908026i	$-0.637589\pi$
$163$	−284200.	−0.837829	−0.418914	+	0.908026i	$0.637589\pi$
$164$	37110.3	0.107742
$165$	106837.	0.305499
$166$	−401844.	−1.13185
$167$	−13145.7	−0.0364747	−0.0182373	−	0.999834i	$-0.505805\pi$
$167$	−13145.7	−0.0364747	−0.0182373	+	0.999834i	$0.505805\pi$
$168$	0	0
$169$	65800.6	0.177220
$170$	193502.	0.513528
$171$	−140353.	−0.367055
$172$	−319452.	−0.823349
$173$	51453.0	0.130706	0.0653530	−	0.997862i	$-0.479183\pi$
$173$	51453.0	0.130706	0.0653530	+	0.997862i	$0.479183\pi$
$174$	−120902.	−0.302732
$175$	0	0
$176$	−23919.3	−0.0582058
$177$	−52851.2	−0.126801
$178$	80287.3	0.189931
$179$	−497735.	−1.16109	−0.580544	−	0.814229i	$-0.697160\pi$
$179$	−497735.	−1.16109	−0.580544	+	0.814229i	$0.697160\pi$
$180$	−215385.	−0.495489
$181$	−227120.	−0.515299	−0.257650	−	0.966238i	$-0.582948\pi$
$181$	−227120.	−0.515299	−0.257650	+	0.966238i	$0.582948\pi$
$182$	0	0
$183$	142284.	0.314071
$184$	47897.0	0.104295
$185$	−722879.	−1.55287
$186$	15487.8	0.0328251
$187$	−42598.7	−0.0890825
$188$	−227353.	−0.469143
$189$	0	0
$190$	469529.	0.943580
$191$	502778.	0.997225	0.498612	−	0.866825i	$-0.333843\pi$
$191$	502778.	0.997225	0.498612	+	0.866825i	$0.333843\pi$
$192$	−44140.1	−0.0864132
$193$	140322.	0.271165	0.135582	−	0.990766i	$-0.456709\pi$
$193$	140322.	0.271165	0.135582	+	0.990766i	$0.456709\pi$
$194$	−93283.8	−0.177952
$195$	−755960.	−1.42368
$196$	0	0
$197$	378993.	0.695769	0.347885	−	0.937537i	$-0.386900\pi$
$197$	378993.	0.695769	0.347885	+	0.937537i	$0.386900\pi$
$198$	47416.0	0.0859533
$199$	−461022.	−0.825256	−0.412628	−	0.910900i	$-0.635389\pi$
$199$	−461022.	−0.825256	−0.412628	+	0.910900i	$0.635389\pi$
$200$	520537.	0.920188
$201$	642899.	1.12241
$202$	−275897.	−0.475738
$203$	0	0
$204$	−78610.6	−0.132253
$205$	246100.	0.409004
$206$	454901.	0.746876
$207$	−94947.9	−0.154014
$208$	169249.	0.271249
$209$	−103365.	−0.163684
$210$	0	0
$211$	202139.	0.312567	0.156284	−	0.987712i	$-0.450049\pi$
$211$	202139.	0.312567	0.156284	+	0.987712i	$0.450049\pi$
$212$	418307.	0.639228
$213$	−95979.1	−0.144953
$214$	−485149.	−0.724170
$215$	−2.11848e6	−3.12556
$216$	255095.	0.372021
$217$	0	0
$218$	−245495.	−0.349866
$219$	112943.	0.159129
$220$	−158623.	−0.220958
$221$	301422.	0.415140
$222$	293671.	0.399925
$223$	694340.	0.934997	0.467498	−	0.883994i	$-0.345155\pi$
$223$	694340.	0.934997	0.467498	+	0.883994i	$0.345155\pi$
$224$	0	0
$225$	−1.03188e6	−1.35885
$226$	−971756.	−1.26557
$227$	1.26697e6	1.63194	0.815968	−	0.578096i	$-0.196204\pi$
$227$	1.26697e6	1.63194	0.815968	+	0.578096i	$0.196204\pi$
$228$	−190747.	−0.243008
$229$	856477.	1.07926	0.539631	−	0.841902i	$-0.318564\pi$
$229$	856477.	1.07926	0.539631	+	0.841902i	$0.318564\pi$
$230$	317633.	0.395919
$231$	0	0
$232$	179506.	0.218957
$233$	−284358.	−0.343143	−0.171571	−	0.985172i	$-0.554884\pi$
$233$	−284358.	−0.343143	−0.171571	+	0.985172i	$0.554884\pi$
$234$	−335509.	−0.400557
$235$	−1.50771e6	−1.78094
$236$	78469.6	0.0917110
$237$	77913.5	0.0901035
$238$	0	0
$239$	−427941.	−0.484606	−0.242303	−	0.970201i	$-0.577903\pi$
$239$	−427941.	−0.484606	−0.242303	+	0.970201i	$0.577903\pi$
$240$	−292719.	−0.328037
$241$	809581.	0.897879	0.448940	−	0.893562i	$-0.351802\pi$
$241$	809581.	0.897879	0.448940	+	0.893562i	$0.351802\pi$
$242$	−609284.	−0.668777
$243$	−837912.	−0.910296
$244$	−211253.	−0.227158
$245$	0	0
$246$	−99978.7	−0.105334
$247$	731395.	0.762798
$248$	−22995.1	−0.0237414
$249$	1.08261e6	1.10655
$250$	2.12567e6	2.15103
$251$	−1.26305e6	−1.26542	−0.632711	−	0.774388i	$-0.718058\pi$
$251$	−1.26305e6	−1.26542	−0.632711	+	0.774388i	$0.718058\pi$
$252$	0	0
$253$	−69925.6	−0.0686808
$254$	807687.	0.785523
$255$	−521314.	−0.502052
$256$	65536.0	0.0625000
$257$	56138.2	0.0530183	0.0265091	−	0.999649i	$-0.491561\pi$
$257$	56138.2	0.0530183	0.0265091	+	0.999649i	$0.491561\pi$
$258$	860634.	0.804951
$259$	0	0
$260$	1.12239e6	1.02970
$261$	−355841.	−0.323336
$262$	1.13408e6	1.02069
$263$	1.54275e6	1.37533	0.687664	−	0.726029i	$-0.258636\pi$
$263$	1.54275e6	1.37533	0.687664	+	0.726029i	$0.258636\pi$
$264$	64440.9	0.0569052
$265$	2.77405e6	2.42660
$266$	0	0
$267$	−216302.	−0.185687
$268$	−954530.	−0.811807
$269$	−1.20535e6	−1.01563	−0.507813	−	0.861467i	$-0.669546\pi$
$269$	−1.20535e6	−1.01563	−0.507813	+	0.861467i	$0.669546\pi$
$270$	1.69169e6	1.41225
$271$	1.76489e6	1.45980	0.729900	−	0.683554i	$-0.239567\pi$
$271$	1.76489e6	1.45980	0.729900	+	0.683554i	$0.239567\pi$
$272$	116715.	0.0956546
$273$	0	0
$274$	753882.	0.606634
$275$	−759941.	−0.605966
$276$	−129039.	−0.101964
$277$	1.48319e6	1.16144	0.580719	−	0.814104i	$-0.302771\pi$
$277$	1.48319e6	1.16144	0.580719	+	0.814104i	$0.302771\pi$
$278$	−846317.	−0.656782
$279$	45584.0	0.0350592
$280$	0	0
$281$	−1.26812e6	−0.958061	−0.479031	−	0.877798i	$-0.659012\pi$
$281$	−1.26812e6	−0.958061	−0.479031	+	0.877798i	$0.659012\pi$
$282$	612510.	0.458660
$283$	−1.44657e6	−1.07368	−0.536838	−	0.843685i	$-0.680381\pi$
$283$	−1.44657e6	−1.07368	−0.536838	+	0.843685i	$0.680381\pi$
$284$	142503.	0.104840
$285$	−1.26496e6	−0.922495
$286$	−247090.	−0.178624
$287$	0	0
$288$	−129914.	−0.0922945
$289$	−1.21199e6	−0.853603
$290$	1.19041e6	0.831193
$291$	251316.	0.173975
$292$	−167689.	−0.115093
$293$	367016.	0.249756	0.124878	−	0.992172i	$-0.460146\pi$
$293$	367016.	0.249756	0.124878	+	0.992172i	$0.460146\pi$
$294$	0	0
$295$	520379.	0.348149
$296$	−436021.	−0.289253
$297$	−372417.	−0.244985
$298$	−1.17330e6	−0.765362
$299$	494784.	0.320064
$300$	−1.40238e6	−0.899625
$301$	0	0
$302$	−817905.	−0.516042
$303$	743292.	0.465107
$304$	283207.	0.175760
$305$	−1.40094e6	−0.862324
$306$	−231369.	−0.141254
$307$	−131281.	−0.0794979	−0.0397490	−	0.999210i	$-0.512656\pi$
$307$	−131281.	−0.0794979	−0.0397490	+	0.999210i	$0.512656\pi$
$308$	0	0
$309$	−1.22555e6	−0.730186
$310$	−152494.	−0.0901259
$311$	−2.33471e6	−1.36878	−0.684389	−	0.729118i	$-0.739931\pi$
$311$	−2.33471e6	−1.36878	−0.684389	+	0.729118i	$0.739931\pi$
$312$	−455974.	−0.265188
$313$	−772801.	−0.445869	−0.222934	−	0.974833i	$-0.571564\pi$
$313$	−772801.	−0.445869	−0.222934	+	0.974833i	$0.571564\pi$
$314$	2.02366e6	1.15828
$315$	0	0
$316$	−115680.	−0.0651691
$317$	524336.	0.293063	0.146532	−	0.989206i	$-0.453189\pi$
$317$	524336.	0.293063	0.146532	+	0.989206i	$0.453189\pi$
$318$	−1.12696e6	−0.624944
$319$	−262064.	−0.144188
$320$	434608.	0.237259
$321$	1.30704e6	0.707988
$322$	0	0
$323$	504374.	0.268996
$324$	−193982.	−0.102659
$325$	5.37723e6	2.82391
$326$	−1.13680e6	−0.592434
$327$	661389.	0.342048
$328$	148441.	0.0761850
$329$	0	0
$330$	427346.	0.216020
$331$	631635.	0.316881	0.158440	−	0.987369i	$-0.449353\pi$
$331$	631635.	0.316881	0.158440	+	0.987369i	$0.449353\pi$
$332$	−1.60738e6	−0.800336
$333$	864339.	0.427143
$334$	−52582.7	−0.0257915
$335$	−6.33006e6	−3.08174
$336$	0	0
$337$	3.33479e6	1.59954	0.799768	−	0.600309i	$-0.204956\pi$
$337$	3.33479e6	1.59954	0.799768	+	0.600309i	$0.204956\pi$
$338$	263202.	0.125314
$339$	2.61800e6	1.23729
$340$	774009.	0.363119
$341$	33571.0	0.0156343
$342$	−561412.	−0.259547
$343$	0	0
$344$	−1.27781e6	−0.582196
$345$	−855735.	−0.387072
$346$	205812.	0.0924231
$347$	−650351.	−0.289951	−0.144975	−	0.989435i	$-0.546310\pi$
$347$	−650351.	−0.289951	−0.144975	+	0.989435i	$0.546310\pi$
$348$	−483606.	−0.214064
$349$	−601041.	−0.264144	−0.132072	−	0.991240i	$-0.542163\pi$
$349$	−601041.	−0.264144	−0.132072	+	0.991240i	$0.542163\pi$
$350$	0	0
$351$	2.63517e6	1.14167
$352$	−95677.2	−0.0411577
$353$	−2.88889e6	−1.23394	−0.616970	−	0.786987i	$-0.711640\pi$
$353$	−2.88889e6	−1.23394	−0.616970	+	0.786987i	$0.711640\pi$
$354$	−211405.	−0.0896616
$355$	945021.	0.397989
$356$	321149.	0.134302
$357$	0	0
$358$	−1.99094e6	−0.821014
$359$	−97830.5	−0.0400625	−0.0200313	−	0.999799i	$-0.506377\pi$
$359$	−97830.5	−0.0400625	−0.0200313	+	0.999799i	$0.506377\pi$
$360$	−861539.	−0.350364
$361$	−1.25225e6	−0.505733
$362$	−908481.	−0.364371
$363$	1.64147e6	0.653832
$364$	0	0
$365$	−1.11205e6	−0.436910
$366$	569135.	0.222082
$367$	2.14775e6	0.832374	0.416187	−	0.909279i	$-0.363366\pi$
$367$	2.14775e6	0.832374	0.416187	+	0.909279i	$0.363366\pi$
$368$	191588.	0.0737477
$369$	−294260.	−0.112503
$370$	−2.89151e6	−1.09805
$371$	0	0
$372$	61951.1	0.0232109
$373$	4.20458e6	1.56477	0.782386	−	0.622794i	$-0.214003\pi$
$373$	4.20458e6	1.56477	0.782386	+	0.622794i	$0.214003\pi$
$374$	−170395.	−0.0629908
$375$	−5.72677e6	−2.10296
$376$	−909411.	−0.331734
$377$	1.85433e6	0.671943
$378$	0	0
$379$	−535586.	−0.191527	−0.0957637	−	0.995404i	$-0.530529\pi$
$379$	−535586.	−0.191527	−0.0957637	+	0.995404i	$0.530529\pi$
$380$	1.87812e6	0.667212
$381$	−2.17599e6	−0.767969
$382$	2.01111e6	0.705144
$383$	−3.84697e6	−1.34005	−0.670027	−	0.742337i	$-0.733717\pi$
$383$	−3.84697e6	−1.34005	−0.670027	+	0.742337i	$0.733717\pi$
$384$	−176560.	−0.0611034
$385$	0	0
$386$	561289.	0.191742
$387$	2.53304e6	0.859736
$388$	−373135.	−0.125831
$389$	−1.69833e6	−0.569045	−0.284523	−	0.958669i	$-0.591835\pi$
$389$	−1.69833e6	−0.569045	−0.284523	+	0.958669i	$0.591835\pi$
$390$	−3.02384e6	−1.00669
$391$	341206.	0.112869
$392$	0	0
$393$	−3.05533e6	−0.997877
$394$	1.51597e6	0.491983
$395$	−767145.	−0.247391
$396$	189664.	0.0607781
$397$	3.62378e6	1.15394	0.576972	−	0.816764i	$-0.304234\pi$
$397$	3.62378e6	1.15394	0.576972	+	0.816764i	$0.304234\pi$
$398$	−1.84409e6	−0.583544
$399$	0	0
$400$	2.08215e6	0.650671
$401$	−2.79801e6	−0.868937	−0.434469	−	0.900687i	$-0.643064\pi$
$401$	−2.79801e6	−0.868937	−0.434469	+	0.900687i	$0.643064\pi$
$402$	2.57160e6	0.793666
$403$	−237543.	−0.0728585
$404$	−1.10359e6	−0.336398
$405$	−1.28641e6	−0.389710
$406$	0	0
$407$	636554.	0.190480
$408$	−314443.	−0.0935171
$409$	−666281.	−0.196947	−0.0984735	−	0.995140i	$-0.531396\pi$
$409$	−666281.	−0.196947	−0.0984735	+	0.995140i	$0.531396\pi$
$410$	984401.	0.289210
$411$	−2.03103e6	−0.593078
$412$	1.81960e6	0.528121
$413$	0	0
$414$	−379791.	−0.108904
$415$	−1.06595e7	−3.03819
$416$	676998.	0.191802
$417$	2.28006e6	0.642105
$418$	−413460.	−0.115742
$419$	2.89203e6	0.804762	0.402381	−	0.915472i	$-0.368183\pi$
$419$	2.89203e6	0.804762	0.402381	+	0.915472i	$0.368183\pi$
$420$	0	0
$421$	6.72027e6	1.84791	0.923956	−	0.382498i	$-0.124936\pi$
$421$	6.72027e6	1.84791	0.923956	+	0.382498i	$0.124936\pi$
$422$	808555.	0.221018
$423$	1.80276e6	0.489876
$424$	1.67323e6	0.452002
$425$	3.70817e6	0.995835
$426$	−383917.	−0.102497
$427$	0	0
$428$	−1.94060e6	−0.512066
$429$	665685.	0.174633
$430$	−8.47390e6	−2.21010
$431$	4.72298e6	1.22468	0.612341	−	0.790594i	$-0.290228\pi$
$431$	4.72298e6	1.22468	0.612341	+	0.790594i	$0.290228\pi$
$432$	1.02038e6	0.263058
$433$	−5.78136e6	−1.48187	−0.740935	−	0.671577i	$-0.765617\pi$
$433$	−5.78136e6	−1.48187	−0.740935	+	0.671577i	$0.765617\pi$
$434$	0	0
$435$	−3.20708e6	−0.812619
$436$	−981982.	−0.247393
$437$	827929.	0.207391
$438$	451772.	0.112521
$439$	5.36873e6	1.32957	0.664784	−	0.747036i	$-0.268524\pi$
$439$	5.36873e6	1.32957	0.664784	+	0.747036i	$0.268524\pi$
$440$	−634492.	−0.156241
$441$	0	0
$442$	1.20569e6	0.293548
$443$	4.31511e6	1.04468	0.522339	−	0.852738i	$-0.325059\pi$
$443$	4.31511e6	1.04468	0.522339	+	0.852738i	$0.325059\pi$
$444$	1.17468e6	0.282789
$445$	2.12973e6	0.509829
$446$	2.77736e6	0.661143
$447$	3.16097e6	0.748259
$448$	0	0
$449$	4.75292e6	1.11261	0.556307	−	0.830977i	$-0.312218\pi$
$449$	4.75292e6	1.11261	0.556307	+	0.830977i	$0.312218\pi$
$450$	−4.12751e6	−0.960854
$451$	−216712.	−0.0501696
$452$	−3.88702e6	−0.894893
$453$	2.20352e6	0.504511
$454$	5.06790e6	1.15395
$455$	0	0
$456$	−762988.	−0.171833
$457$	2.13728e6	0.478707	0.239354	−	0.970932i	$-0.423064\pi$
$457$	2.13728e6	0.478707	0.239354	+	0.970932i	$0.423064\pi$
$458$	3.42591e6	0.763153
$459$	1.81723e6	0.402604
$460$	1.27053e6	0.279957
$461$	−1.72920e6	−0.378959	−0.189479	−	0.981885i	$-0.560680\pi$
$461$	−1.72920e6	−0.378959	−0.189479	+	0.981885i	$0.560680\pi$
$462$	0	0
$463$	−6.54367e6	−1.41863	−0.709315	−	0.704892i	$-0.750996\pi$
$463$	−6.54367e6	−1.41863	−0.709315	+	0.704892i	$0.750996\pi$
$464$	718024.	0.154826
$465$	410835.	0.0881119
$466$	−1.13743e6	−0.242639
$467$	−1.79419e6	−0.380694	−0.190347	−	0.981717i	$-0.560961\pi$
$467$	−1.79419e6	−0.380694	−0.190347	+	0.981717i	$0.560961\pi$
$468$	−1.34204e6	−0.283237
$469$	0	0
$470$	−6.03085e6	−1.25931
$471$	−5.45194e6	−1.13240
$472$	313878.	0.0648495
$473$	1.86549e6	0.383390
$474$	311654.	0.0637128
$475$	8.99780e6	1.82979
$476$	0	0
$477$	−3.31690e6	−0.667477
$478$	−1.71176e6	−0.342669
$479$	4.09403e6	0.815289	0.407645	−	0.913141i	$-0.366350\pi$
$479$	4.09403e6	0.815289	0.407645	+	0.913141i	$0.366350\pi$
$480$	−1.17088e6	−0.231957
$481$	−4.50417e6	−0.887670
$482$	3.23833e6	0.634897
$483$	0	0
$484$	−2.43714e6	−0.472897
$485$	−2.47448e6	−0.477672
$486$	−3.35165e6	−0.643676
$487$	−4.45210e6	−0.850634	−0.425317	−	0.905045i	$-0.639837\pi$
$487$	−4.45210e6	−0.850634	−0.425317	+	0.905045i	$0.639837\pi$
$488$	−845010.	−0.160625
$489$	3.06265e6	0.579196
$490$	0	0
$491$	7.09674e6	1.32848	0.664240	−	0.747519i	$-0.268755\pi$
$491$	7.09674e6	1.32848	0.664240	+	0.747519i	$0.268755\pi$
$492$	−399915.	−0.0744826
$493$	1.27875e6	0.236957
$494$	2.92558e6	0.539380
$495$	1.25778e6	0.230723
$496$	−91980.4	−0.0167877
$497$	0	0
$498$	4.33043e6	0.782451
$499$	9.41903e6	1.69338	0.846691	−	0.532085i	$-0.178591\pi$
$499$	9.41903e6	1.69338	0.846691	+	0.532085i	$0.178591\pi$
$500$	8.50269e6	1.52101
$501$	141663.	0.0252152
$502$	−5.05219e6	−0.894789
$503$	957258.	0.168698	0.0843489	−	0.996436i	$-0.473119\pi$
$503$	957258.	0.168698	0.0843489	+	0.996436i	$0.473119\pi$
$504$	0	0
$505$	−7.31854e6	−1.27702
$506$	−279703.	−0.0485646
$507$	−709093.	−0.122513
$508$	3.23075e6	0.555448
$509$	−4.01453e6	−0.686816	−0.343408	−	0.939186i	$-0.611581\pi$
$509$	−4.01453e6	−0.686816	−0.343408	+	0.939186i	$0.611581\pi$
$510$	−2.08526e6	−0.355005
$511$	0	0
$512$	262144.	0.0441942
$513$	4.40947e6	0.739764
$514$	224553.	0.0374896
$515$	1.20669e7	2.00483
$516$	3.44254e6	0.569186
$517$	1.32766e6	0.218455
$518$	0	0
$519$	−554478.	−0.0903578
$520$	4.48958e6	0.728110
$521$	−4.31820e6	−0.696960	−0.348480	−	0.937316i	$-0.613302\pi$
$521$	−4.31820e6	−0.696960	−0.348480	+	0.937316i	$0.613302\pi$
$522$	−1.42336e6	−0.228633
$523$	1.34501e6	0.215017	0.107508	−	0.994204i	$-0.465713\pi$
$523$	1.34501e6	0.215017	0.107508	+	0.994204i	$0.465713\pi$
$524$	4.53634e6	0.721734
$525$	0	0
$526$	6.17100e6	0.972504
$527$	−163811.	−0.0256931
$528$	257764.	0.0402380
$529$	−5.87626e6	−0.912980
$530$	1.10962e7	1.71587
$531$	−622212.	−0.0957640
$532$	0	0
$533$	1.53342e6	0.233799
$534$	−865207.	−0.131301
$535$	−1.28692e7	−1.94388
$536$	−3.81812e6	−0.574034
$537$	5.36378e6	0.802667
$538$	−4.82141e6	−0.718156
$539$	0	0
$540$	6.76675e6	0.998609
$541$	−7.06006e6	−1.03709	−0.518543	−	0.855051i	$-0.673526\pi$
$541$	−7.06006e6	−1.03709	−0.518543	+	0.855051i	$0.673526\pi$
$542$	7.05954e6	1.03223
$543$	2.44754e6	0.356229
$544$	466862.	0.0676380
$545$	−6.51211e6	−0.939140
$546$	0	0
$547$	−1.23520e7	−1.76510	−0.882549	−	0.470221i	$-0.844174\pi$
$547$	−1.23520e7	−1.76510	−0.882549	+	0.470221i	$0.844174\pi$
$548$	3.01553e6	0.428955
$549$	1.67509e6	0.237196
$550$	−3.03976e6	−0.428483
$551$	3.10287e6	0.435396
$552$	−516156.	−0.0720997
$553$	0	0
$554$	5.93275e6	0.821261
$555$	7.79002e6	1.07351
$556$	−3.38527e6	−0.464415
$557$	−1.22251e7	−1.66961	−0.834803	−	0.550549i	$-0.814418\pi$
$557$	−1.22251e7	−1.66961	−0.834803	+	0.550549i	$0.814418\pi$
$558$	182336.	0.0247906
$559$	−1.32000e7	−1.78666
$560$	0	0
$561$	459060.	0.0615832
$562$	−5.07247e6	−0.677452
$563$	−812527.	−0.108036	−0.0540178	−	0.998540i	$-0.517203\pi$
$563$	−812527.	−0.108036	−0.0540178	+	0.998540i	$0.517203\pi$
$564$	2.45004e6	0.324321
$565$	−2.57772e7	−3.39715
$566$	−5.78628e6	−0.759204
$567$	0	0
$568$	570011.	0.0741332
$569$	−8.43881e6	−1.09270	−0.546350	−	0.837557i	$-0.683983\pi$
$569$	−8.43881e6	−1.09270	−0.546350	+	0.837557i	$0.683983\pi$
$570$	−5.05983e6	−0.652302
$571$	3.71511e6	0.476849	0.238425	−	0.971161i	$-0.423369\pi$
$571$	3.71511e6	0.476849	0.238425	+	0.971161i	$0.423369\pi$
$572$	−988361.	−0.126306
$573$	−5.41813e6	−0.689387
$574$	0	0
$575$	6.08695e6	0.767768
$576$	−519657.	−0.0652621
$577$	1.30375e7	1.63025	0.815126	−	0.579284i	$-0.196668\pi$
$577$	1.30375e7	1.63025	0.815126	+	0.579284i	$0.196668\pi$
$578$	−4.84798e6	−0.603589
$579$	−1.51217e6	−0.187458
$580$	4.76164e6	0.587742
$581$	0	0
$582$	1.00526e6	0.123019
$583$	−2.44278e6	−0.297654
$584$	−670758.	−0.0813830
$585$	−8.89984e6	−1.07521
$586$	1.46806e6	0.176604
$587$	1.15227e7	1.38026	0.690128	−	0.723687i	$-0.257554\pi$
$587$	1.15227e7	1.38026	0.690128	+	0.723687i	$0.257554\pi$
$588$	0	0
$589$	−397485.	−0.0472098
$590$	2.08152e6	0.246178
$591$	−4.08417e6	−0.480989
$592$	−1.74408e6	−0.204533
$593$	−1.20103e7	−1.40254	−0.701271	−	0.712895i	$-0.747384\pi$
$593$	−1.20103e7	−1.40254	−0.701271	+	0.712895i	$0.747384\pi$
$594$	−1.48967e6	−0.173230
$595$	0	0
$596$	−4.69318e6	−0.541192
$597$	4.96815e6	0.570504
$598$	1.97913e6	0.226320
$599$	−1.17460e6	−0.133759	−0.0668794	−	0.997761i	$-0.521304\pi$
$599$	−1.17460e6	−0.133759	−0.0668794	+	0.997761i	$0.521304\pi$
$600$	−5.60951e6	−0.636131
$601$	−1.62934e7	−1.84003	−0.920014	−	0.391886i	$-0.871823\pi$
$601$	−1.62934e7	−1.84003	−0.920014	+	0.391886i	$0.871823\pi$
$602$	0	0
$603$	7.56879e6	0.847683
$604$	−3.27162e6	−0.364897
$605$	−1.61621e7	−1.79519
$606$	2.97317e6	0.328880
$607$	−1.82629e6	−0.201186	−0.100593	−	0.994928i	$-0.532074\pi$
$607$	−1.82629e6	−0.201186	−0.100593	+	0.994928i	$0.532074\pi$
$608$	1.13283e6	0.124281
$609$	0	0
$610$	−5.60377e6	−0.609755
$611$	−9.39436e6	−1.01804
$612$	−925476.	−0.0998819
$613$	−5.10271e6	−0.548466	−0.274233	−	0.961663i	$-0.588424\pi$
$613$	−5.10271e6	−0.548466	−0.274233	+	0.961663i	$0.588424\pi$
$614$	−525124.	−0.0562135
$615$	−2.65207e6	−0.282747
$616$	0	0
$617$	−8.03920e6	−0.850158	−0.425079	−	0.905156i	$-0.639754\pi$
$617$	−8.03920e6	−0.850158	−0.425079	+	0.905156i	$0.639754\pi$
$618$	−4.90219e6	−0.516320
$619$	8.60132e6	0.902274	0.451137	−	0.892455i	$-0.351019\pi$
$619$	8.60132e6	0.902274	0.451137	+	0.892455i	$0.351019\pi$
$620$	−609977.	−0.0637286
$621$	2.98298e6	0.310399
$622$	−9.33886e6	−0.967872
$623$	0	0
$624$	−1.82390e6	−0.187516
$625$	3.09695e7	3.17128
$626$	−3.09120e6	−0.315277
$627$	1.11390e6	0.113156
$628$	8.09464e6	0.819027
$629$	−3.10610e6	−0.313032
$630$	0	0
$631$	6.21151e6	0.621046	0.310523	−	0.950566i	$-0.399496\pi$
$631$	6.21151e6	0.621046	0.310523	+	0.950566i	$0.399496\pi$
$632$	−462721.	−0.0460815
$633$	−2.17833e6	−0.216080
$634$	2.09734e6	0.207227
$635$	2.14250e7	2.10856
$636$	−4.50784e6	−0.441902
$637$	0	0
$638$	−1.04826e6	−0.101957
$639$	−1.12995e6	−0.109473
$640$	1.73843e6	0.167768
$641$	4.45143e6	0.427912	0.213956	−	0.976843i	$-0.431365\pi$
$641$	4.45143e6	0.427912	0.213956	+	0.976843i	$0.431365\pi$
$642$	5.22815e6	0.500623
$643$	1.58708e7	1.51381	0.756907	−	0.653523i	$-0.226710\pi$
$643$	1.58708e7	1.51381	0.756907	+	0.653523i	$0.226710\pi$
$644$	0	0
$645$	2.28295e7	2.16071
$646$	2.01750e6	0.190209
$647$	−3.65619e6	−0.343375	−0.171687	−	0.985151i	$-0.554922\pi$
$647$	−3.65619e6	−0.343375	−0.171687	+	0.985151i	$0.554922\pi$
$648$	−775928.	−0.0725912
$649$	−458237.	−0.0427049
$650$	2.15089e7	1.99680
$651$	0	0
$652$	−4.54720e6	−0.418914
$653$	−4.15039e6	−0.380896	−0.190448	−	0.981697i	$-0.560994\pi$
$653$	−4.15039e6	−0.380896	−0.190448	+	0.981697i	$0.560994\pi$
$654$	2.64555e6	0.241865
$655$	3.00832e7	2.73981
$656$	593764.	0.0538709
$657$	1.32967e6	0.120179
$658$	0	0
$659$	−1.33739e7	−1.19962	−0.599810	−	0.800143i	$-0.704757\pi$
$659$	−1.33739e7	−1.19962	−0.599810	+	0.800143i	$0.704757\pi$
$660$	1.70938e6	0.152750
$661$	−9.82641e6	−0.874764	−0.437382	−	0.899276i	$-0.644094\pi$
$661$	−9.82641e6	−0.874764	−0.437382	+	0.899276i	$0.644094\pi$
$662$	2.52654e6	0.224069
$663$	−3.24824e6	−0.286989
$664$	−6.42950e6	−0.565923
$665$	0	0
$666$	3.45736e6	0.302036
$667$	2.09907e6	0.182689
$668$	−210331.	−0.0182373
$669$	−7.48248e6	−0.646369
$670$	−2.53202e7	−2.17912
$671$	1.23365e6	0.105775
$672$	0	0
$673$	401148.	0.0341403	0.0170702	−	0.999854i	$-0.494566\pi$
$673$	401148.	0.0341403	0.0170702	+	0.999854i	$0.494566\pi$
$674$	1.33392e7	1.13104
$675$	3.24185e7	2.73863
$676$	1.05281e6	0.0886101
$677$	2.07302e7	1.73833	0.869164	−	0.494524i	$-0.164657\pi$
$677$	2.07302e7	1.73833	0.869164	+	0.494524i	$0.164657\pi$
$678$	1.04720e7	0.874896
$679$	0	0
$680$	3.09604e6	0.256764
$681$	−1.36534e7	−1.12817
$682$	134284.	0.0110551
$683$	−1.91996e7	−1.57485	−0.787427	−	0.616409i	$-0.788587\pi$
$683$	−1.91996e7	−1.57485	−0.787427	+	0.616409i	$0.788587\pi$
$684$	−2.24565e6	−0.183528
$685$	1.99978e7	1.62838
$686$	0	0
$687$	−9.22972e6	−0.746100
$688$	−5.11123e6	−0.411675
$689$	1.72847e7	1.38712
$690$	−3.42294e6	−0.273701
$691$	−1.13093e7	−0.901033	−0.450517	−	0.892768i	$-0.648760\pi$
$691$	−1.13093e7	−0.901033	−0.450517	+	0.892768i	$0.648760\pi$
$692$	823248.	0.0653530
$693$	0	0
$694$	−2.60140e6	−0.205026
$695$	−2.24497e7	−1.76299
$696$	−1.93443e6	−0.151366
$697$	1.05746e6	0.0824480
$698$	−2.40417e6	−0.186778
$699$	3.06435e6	0.237217
$700$	0	0
$701$	−1.92159e7	−1.47695	−0.738473	−	0.674283i	$-0.764453\pi$
$701$	−1.92159e7	−1.47695	−0.738473	+	0.674283i	$0.764453\pi$
$702$	1.05407e7	0.807284
$703$	−7.53689e6	−0.575180
$704$	−382709.	−0.0291029
$705$	1.62477e7	1.23117
$706$	−1.15555e7	−0.872527
$707$	0	0
$708$	−845619.	−0.0634004
$709$	5.64480e6	0.421729	0.210864	−	0.977515i	$-0.432372\pi$
$709$	5.64480e6	0.421729	0.210864	+	0.977515i	$0.432372\pi$
$710$	3.78009e6	0.281421
$711$	917268.	0.0680491
$712$	1.28460e6	0.0949657
$713$	−268896.	−0.0198089
$714$	0	0
$715$	−6.55441e6	−0.479478
$716$	−7.96376e6	−0.580544
$717$	4.61166e6	0.335011
$718$	−391322.	−0.0283285
$719$	4.42077e6	0.318916	0.159458	−	0.987205i	$-0.449025\pi$
$719$	4.42077e6	0.318916	0.159458	+	0.987205i	$0.449025\pi$
$720$	−3.44616e6	−0.247744
$721$	0	0
$722$	−5.00898e6	−0.357607
$723$	−8.72436e6	−0.620709
$724$	−3.63392e6	−0.257650
$725$	2.28124e7	1.61185
$726$	6.56588e6	0.462329
$727$	1.92503e7	1.35083	0.675416	−	0.737437i	$-0.263964\pi$
$727$	1.92503e7	1.35083	0.675416	+	0.737437i	$0.263964\pi$
$728$	0	0
$729$	1.19758e7	0.834611
$730$	−4.44819e6	−0.308942
$731$	−9.10277e6	−0.630057
$732$	2.27654e6	0.157035
$733$	1.30187e7	0.894966	0.447483	−	0.894292i	$-0.352320\pi$
$733$	1.30187e7	0.894966	0.447483	+	0.894292i	$0.352320\pi$
$734$	8.59100e6	0.588577
$735$	0	0
$736$	766352.	0.0521475
$737$	5.57414e6	0.378015
$738$	−1.17704e6	−0.0795518
$739$	−1.70955e7	−1.15152	−0.575758	−	0.817620i	$-0.695293\pi$
$739$	−1.70955e7	−1.15152	−0.575758	+	0.817620i	$0.695293\pi$
$740$	−1.15661e7	−0.776437
$741$	−7.88180e6	−0.527327
$742$	0	0
$743$	2.36546e7	1.57197	0.785984	−	0.618247i	$-0.212157\pi$
$743$	2.36546e7	1.57197	0.785984	+	0.618247i	$0.212157\pi$
$744$	247804.	0.0164126
$745$	−3.11233e7	−2.05445
$746$	1.68183e7	1.10646
$747$	1.27454e7	0.835705
$748$	−681579.	−0.0445413
$749$	0	0
$750$	−2.29071e7	−1.48702
$751$	−166564.	−0.0107766	−0.00538828	−	0.999985i	$-0.501715\pi$
$751$	−166564.	−0.0107766	−0.00538828	+	0.999985i	$0.501715\pi$
$752$	−3.63764e6	−0.234572
$753$	1.36111e7	0.874794
$754$	7.41730e6	0.475136
$755$	−2.16961e7	−1.38520
$756$	0	0
$757$	−4.63842e6	−0.294192	−0.147096	−	0.989122i	$-0.546993\pi$
$757$	−4.63842e6	−0.294192	−0.147096	+	0.989122i	$0.546993\pi$
$758$	−2.14234e6	−0.135430
$759$	753546.	0.0474794
$760$	7.51247e6	0.471790
$761$	−6.96999e6	−0.436285	−0.218143	−	0.975917i	$-0.570000\pi$
$761$	−6.96999e6	−0.436285	−0.218143	+	0.975917i	$0.570000\pi$
$762$	−8.70395e6	−0.543036
$763$	0	0
$764$	8.04445e6	0.498612
$765$	−6.13738e6	−0.379166
$766$	−1.53879e7	−0.947561
$767$	3.24242e6	0.199013
$768$	−706241.	−0.0432066
$769$	3.02590e6	0.184518	0.0922590	−	0.995735i	$-0.470591\pi$
$769$	3.02590e6	0.184518	0.0922590	+	0.995735i	$0.470591\pi$
$770$	0	0
$771$	−604967.	−0.0366518
$772$	2.24516e6	0.135582
$773$	2.78539e7	1.67663	0.838314	−	0.545188i	$-0.183542\pi$
$773$	2.78539e7	1.67663	0.838314	+	0.545188i	$0.183542\pi$
$774$	1.01322e7	0.607925
$775$	−2.92232e6	−0.174772
$776$	−1.49254e6	−0.0889758
$777$	0	0
$778$	−6.79330e6	−0.402376
$779$	2.56589e6	0.151494
$780$	−1.20954e7	−0.711839
$781$	−832170.	−0.0488185
$782$	1.36482e6	0.0798104
$783$	1.11795e7	0.651653
$784$	0	0
$785$	5.36804e7	3.10915
$786$	−1.22213e7	−0.705606
$787$	2.87913e7	1.65701	0.828503	−	0.559985i	$-0.189193\pi$
$787$	2.87913e7	1.65701	0.828503	+	0.559985i	$0.189193\pi$
$788$	6.06388e6	0.347885
$789$	−1.66253e7	−0.950773
$790$	−3.06858e6	−0.174932
$791$	0	0
$792$	758657.	0.0429766
$793$	−8.72910e6	−0.492931
$794$	1.44951e7	0.815962
$795$	−2.98942e7	−1.67753
$796$	−7.37635e6	−0.412628
$797$	−3.67489e6	−0.204927	−0.102463	−	0.994737i	$-0.532672\pi$
$797$	−3.67489e6	−0.204927	−0.102463	+	0.994737i	$0.532672\pi$
$798$	0	0
$799$	−6.47841e6	−0.359006
$800$	8.32859e6	0.460094
$801$	−2.54650e6	−0.140237
$802$	−1.11920e7	−0.614431
$803$	979251.	0.0535926
$804$	1.02864e7	0.561207
$805$	0	0
$806$	−950173.	−0.0515187
$807$	1.29894e7	0.702108
$808$	−4.41435e6	−0.237869
$809$	−1.04012e7	−0.558744	−0.279372	−	0.960183i	$-0.590126\pi$
$809$	−1.04012e7	−0.558744	−0.279372	+	0.960183i	$0.590126\pi$
$810$	−5.14564e6	−0.275567
$811$	−1.53749e7	−0.820844	−0.410422	−	0.911896i	$-0.634619\pi$
$811$	−1.53749e7	−0.820844	−0.410422	+	0.911896i	$0.634619\pi$
$812$	0	0
$813$	−1.90191e7	−1.00917
$814$	2.54622e6	0.134690
$815$	−3.01552e7	−1.59026
$816$	−1.25777e6	−0.0661266
$817$	−2.20877e7	−1.15770
$818$	−2.66513e6	−0.139263
$819$	0	0
$820$	3.93761e6	0.204502
$821$	1.91243e7	0.990209	0.495104	−	0.868834i	$-0.335130\pi$
$821$	1.91243e7	0.990209	0.495104	+	0.868834i	$0.335130\pi$
$822$	−8.12413e6	−0.419370
$823$	2.88895e6	0.148676	0.0743381	−	0.997233i	$-0.476316\pi$
$823$	2.88895e6	0.148676	0.0743381	+	0.997233i	$0.476316\pi$
$824$	7.27841e6	0.373438
$825$	8.18942e6	0.418908
$826$	0	0
$827$	−1.99201e7	−1.01281	−0.506406	−	0.862295i	$-0.669026\pi$
$827$	−1.99201e7	−1.01281	−0.506406	+	0.862295i	$0.669026\pi$
$828$	−1.51917e6	−0.0770068
$829$	−1.19726e7	−0.605065	−0.302532	−	0.953139i	$-0.597832\pi$
$829$	−1.19726e7	−0.605065	−0.302532	+	0.953139i	$0.597832\pi$
$830$	−4.26379e7	−2.14833
$831$	−1.59834e7	−0.802909
$832$	2.70799e6	0.135625
$833$	0	0
$834$	9.12024e6	0.454037
$835$	−1.39483e6	−0.0692316
$836$	−1.65384e6	−0.0818422
$837$	−1.43211e6	−0.0706584
$838$	1.15681e7	0.569053
$839$	−1.43453e7	−0.703568	−0.351784	−	0.936081i	$-0.614425\pi$
$839$	−1.43453e7	−0.703568	−0.351784	+	0.936081i	$0.614425\pi$
$840$	0	0
$841$	−1.26444e7	−0.616463
$842$	2.68811e7	1.30667
$843$	1.36657e7	0.662313
$844$	3.23422e6	0.156284
$845$	6.98181e6	0.336377
$846$	7.21103e6	0.346395
$847$	0	0
$848$	6.69292e6	0.319614
$849$	1.55888e7	0.742239
$850$	1.48327e7	0.704162
$851$	−5.09865e6	−0.241341
$852$	−1.53567e6	−0.0724766
$853$	−1.41859e7	−0.667551	−0.333776	−	0.942653i	$-0.608323\pi$
$853$	−1.41859e7	−0.667551	−0.333776	+	0.942653i	$0.608323\pi$
$854$	0	0
$855$	−1.48922e7	−0.696698
$856$	−7.76238e6	−0.362085
$857$	2.41394e7	1.12273	0.561363	−	0.827570i	$-0.310277\pi$
$857$	2.41394e7	1.12273	0.561363	+	0.827570i	$0.310277\pi$
$858$	2.66274e6	0.123484
$859$	1.37343e7	0.635071	0.317536	−	0.948246i	$-0.397145\pi$
$859$	1.37343e7	0.635071	0.317536	+	0.948246i	$0.397145\pi$
$860$	−3.38956e7	−1.56278
$861$	0	0
$862$	1.88919e7	0.865981
$863$	1.74905e7	0.799419	0.399709	−	0.916642i	$-0.369111\pi$
$863$	1.74905e7	0.799419	0.399709	+	0.916642i	$0.369111\pi$
$864$	4.08152e6	0.186010
$865$	5.45945e6	0.248090
$866$	−2.31254e7	−1.04784
$867$	1.30609e7	0.590101
$868$	0	0
$869$	675534.	0.0303458
$870$	−1.28283e7	−0.574609
$871$	−3.94418e7	−1.76162
$872$	−3.92793e6	−0.174933
$873$	2.95872e6	0.131392
$874$	3.31171e6	0.146647
$875$	0	0
$876$	1.80709e6	0.0795644
$877$	−3.51221e7	−1.54199	−0.770995	−	0.636842i	$-0.780241\pi$
$877$	−3.51221e7	−1.54199	−0.770995	+	0.636842i	$0.780241\pi$
$878$	2.14749e7	0.940146
$879$	−3.95510e6	−0.172658
$880$	−2.53797e6	−0.110479
$881$	−8.78528e6	−0.381343	−0.190672	−	0.981654i	$-0.561067\pi$
$881$	−8.78528e6	−0.381343	−0.190672	+	0.981654i	$0.561067\pi$
$882$	0	0
$883$	1.87501e7	0.809287	0.404643	−	0.914475i	$-0.367396\pi$
$883$	1.87501e7	0.809287	0.404643	+	0.914475i	$0.367396\pi$
$884$	4.82276e6	0.207570
$885$	−5.60781e6	−0.240677
$886$	1.72605e7	0.738700
$887$	−2.72434e7	−1.16266	−0.581330	−	0.813668i	$-0.697468\pi$
$887$	−2.72434e7	−1.16266	−0.581330	+	0.813668i	$0.697468\pi$
$888$	4.69873e6	0.199962
$889$	0	0
$890$	8.51892e6	0.360504
$891$	1.13279e6	0.0478030
$892$	1.11094e7	0.467498
$893$	−1.57197e7	−0.659654
$894$	1.26439e7	0.529099
$895$	−5.28124e7	−2.20383
$896$	0	0
$897$	−5.33198e6	−0.221262
$898$	1.90117e7	0.786737
$899$	−1.00775e6	−0.0415868
$900$	−1.65101e7	−0.679426
$901$	1.19197e7	0.489161
$902$	−866847.	−0.0354753
$903$	0	0
$904$	−1.55481e7	−0.632785
$905$	−2.40987e7	−0.978076
$906$	8.81406e6	0.356743
$907$	2.90420e7	1.17222	0.586110	−	0.810232i	$-0.300659\pi$
$907$	2.90420e7	1.17222	0.586110	+	0.810232i	$0.300659\pi$
$908$	2.02716e7	0.815968
$909$	8.75071e6	0.351264
$910$	0	0
$911$	4.12057e7	1.64498	0.822491	−	0.568778i	$-0.192583\pi$
$911$	4.12057e7	1.64498	0.822491	+	0.568778i	$0.192583\pi$
$912$	−3.05195e6	−0.121504
$913$	9.38655e6	0.372674
$914$	8.54910e6	0.338497
$915$	1.50971e7	0.596130
$916$	1.37036e7	0.539631
$917$	0	0
$918$	7.26892e6	0.284684
$919$	3.04768e7	1.19037	0.595184	−	0.803589i	$-0.297079\pi$
$919$	3.04768e7	1.19037	0.595184	+	0.803589i	$0.297079\pi$
$920$	5.08214e6	0.197960
$921$	1.41473e6	0.0549574
$922$	−6.91679e6	−0.267964
$923$	5.88831e6	0.227503
$924$	0	0
$925$	−5.54114e7	−2.12934
$926$	−2.61747e7	−1.00312
$927$	−1.44283e7	−0.551460
$928$	2.87210e6	0.109479
$929$	−3.60640e7	−1.37099	−0.685495	−	0.728077i	$-0.740414\pi$
$929$	−3.60640e7	−1.37099	−0.685495	+	0.728077i	$0.740414\pi$
$930$	1.64334e6	0.0623045
$931$	0	0
$932$	−4.54972e6	−0.171571
$933$	2.51598e7	0.946243
$934$	−7.17676e6	−0.269191
$935$	−4.51996e6	−0.169085
$936$	−5.36815e6	−0.200279
$937$	4.80602e7	1.78828	0.894141	−	0.447785i	$-0.147787\pi$
$937$	4.80602e7	1.78828	0.894141	+	0.447785i	$0.147787\pi$
$938$	0	0
$939$	8.32800e6	0.308231
$940$	−2.41234e7	−0.890469
$941$	−4.28577e7	−1.57781	−0.788906	−	0.614514i	$-0.789352\pi$
$941$	−4.28577e7	−1.57781	−0.788906	+	0.614514i	$0.789352\pi$
$942$	−2.18077e7	−0.800725
$943$	1.73581e6	0.0635657
$944$	1.25551e6	0.0458555
$945$	0	0
$946$	7.46197e6	0.271098
$947$	4.32432e7	1.56690	0.783452	−	0.621452i	$-0.213457\pi$
$947$	4.32432e7	1.56690	0.783452	+	0.621452i	$0.213457\pi$
$948$	1.24662e6	0.0450517
$949$	−6.92904e6	−0.249751
$950$	3.59912e7	1.29386
$951$	−5.65045e6	−0.202596
$952$	0	0
$953$	−2.81115e7	−1.00265	−0.501327	−	0.865258i	$-0.667155\pi$
$953$	−2.81115e7	−1.00265	−0.501327	+	0.865258i	$0.667155\pi$
$954$	−1.32676e7	−0.471978
$955$	5.33476e7	1.89281
$956$	−6.84706e6	−0.242303
$957$	2.82410e6	0.0996783
$958$	1.63761e7	0.576497
$959$	0	0
$960$	−4.68351e6	−0.164019
$961$	−2.85001e7	−0.995491
$962$	−1.80167e7	−0.627678
$963$	1.53876e7	0.534695
$964$	1.29533e7	0.448940
$965$	1.48890e7	0.514691
$966$	0	0
$967$	3.70437e7	1.27394	0.636968	−	0.770890i	$-0.280188\pi$
$967$	3.70437e7	1.27394	0.636968	+	0.770890i	$0.280188\pi$
$968$	−9.74854e6	−0.334388
$969$	−5.43533e6	−0.185959
$970$	−9.89793e6	−0.337765
$971$	−4.58140e7	−1.55937	−0.779686	−	0.626170i	$-0.784621\pi$
$971$	−4.58140e7	−1.55937	−0.779686	+	0.626170i	$0.784621\pi$
$972$	−1.34066e7	−0.455148
$973$	0	0
$974$	−1.78084e7	−0.601489
$975$	−5.79471e7	−1.95218
$976$	−3.38004e6	−0.113579
$977$	1.17497e6	0.0393812	0.0196906	−	0.999806i	$-0.493732\pi$
$977$	1.17497e6	0.0393812	0.0196906	+	0.999806i	$0.493732\pi$
$978$	1.22506e7	0.409553
$979$	−1.87540e6	−0.0625372
$980$	0	0
$981$	7.78647e6	0.258326
$982$	2.83870e7	0.939377
$983$	−2.63520e7	−0.869822	−0.434911	−	0.900474i	$-0.643220\pi$
$983$	−2.63520e7	−0.869822	−0.434911	+	0.900474i	$0.643220\pi$
$984$	−1.59966e6	−0.0526671
$985$	4.02132e7	1.32062
$986$	5.11502e6	0.167554
$987$	0	0
$988$	1.17023e7	0.381399
$989$	−1.49422e7	−0.485761
$990$	5.03111e6	0.163146
$991$	3.82424e7	1.23697	0.618487	−	0.785795i	$-0.287746\pi$
$991$	3.82424e7	1.23697	0.618487	+	0.785795i	$0.287746\pi$
$992$	−367922.	−0.0118707
$993$	−6.80674e6	−0.219062
$994$	0	0
$995$	−4.89170e7	−1.56640
$996$	1.73217e7	0.553277
$997$	4.36919e7	1.39208	0.696038	−	0.718005i	$-0.254945\pi$
$997$	4.36919e7	1.39208	0.696038	+	0.718005i	$0.254945\pi$
$998$	3.76761e7	1.19740
$999$	−2.71549e7	−0.860865

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	98.6.a.h.1.1		2
3.2	odd	2		882.6.a.ba.1.1		2
4.3	odd	2		784.6.a.s.1.2		2
7.2	even	3		14.6.c.a.11.2	yes	4
7.3	odd	6		98.6.c.e.79.1		4
7.4	even	3		14.6.c.a.9.2	✓	4
7.5	odd	6		98.6.c.e.67.1		4
7.6	odd	2		98.6.a.g.1.2		2
21.2	odd	6		126.6.g.j.109.2		4
21.11	odd	6		126.6.g.j.37.2		4
21.20	even	2		882.6.a.bi.1.2		2
28.11	odd	6		112.6.i.d.65.1		4
28.23	odd	6		112.6.i.d.81.1		4
28.27	even	2		784.6.a.bb.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.6.c.a.9.2	✓	4	7.4	even	3
14.6.c.a.11.2	yes	4	7.2	even	3
98.6.a.g.1.2		2	7.6	odd	2
98.6.a.h.1.1		2	1.1	even	1	trivial
98.6.c.e.67.1		4	7.5	odd	6
98.6.c.e.79.1		4	7.3	odd	6
112.6.i.d.65.1		4	28.11	odd	6
112.6.i.d.81.1		4	28.23	odd	6
126.6.g.j.37.2		4	21.11	odd	6
126.6.g.j.109.2		4	21.2	odd	6
784.6.a.s.1.2		2	4.3	odd	2
784.6.a.bb.1.1		2	28.27	even	2
882.6.a.ba.1.1		2	3.2	odd	2
882.6.a.bi.1.2		2	21.20	even	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 98 = 2 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	98.a (trivial)

\(f(q)\)	\(=\)	\(q+4.00000 q^{2} -10.7764 q^{3} +16.0000 q^{4} +106.106 q^{5} -43.1056 q^{6} +64.0000 q^{8} -126.869 q^{9} +424.422 q^{10} -93.4347 q^{11} -172.422 q^{12} +661.131 q^{13} -1143.43 q^{15} +256.000 q^{16} +455.919 q^{17} -507.478 q^{18} +1106.28 q^{19} +1697.69 q^{20} -373.739 q^{22} +748.390 q^{23} -689.689 q^{24} +8133.39 q^{25} +2644.52 q^{26} +3985.86 q^{27} +2804.78 q^{29} -4573.74 q^{30} -359.299 q^{31} +1024.00 q^{32} +1006.89 q^{33} +1823.68 q^{34} -2029.91 q^{36} -6812.82 q^{37} +4425.12 q^{38} -7124.60 q^{39} +6790.76 q^{40} +2319.39 q^{41} -19965.7 q^{43} -1494.96 q^{44} -13461.6 q^{45} +2993.56 q^{46} -14209.5 q^{47} -2758.76 q^{48} +32533.6 q^{50} -4913.17 q^{51} +10578.1 q^{52} +26144.2 q^{53} +15943.4 q^{54} -9913.94 q^{55} -11921.7 q^{57} +11219.1 q^{58} +4904.35 q^{59} -18295.0 q^{60} -13203.3 q^{61} -1437.19 q^{62} +4096.00 q^{64} +70149.6 q^{65} +4027.56 q^{66} -59658.1 q^{67} +7294.71 q^{68} -8064.94 q^{69} +8906.43 q^{71} -8119.64 q^{72} -10480.6 q^{73} -27251.3 q^{74} -87648.6 q^{75} +17700.5 q^{76} -28498.4 q^{78} -7230.02 q^{79} +27163.0 q^{80} -12123.9 q^{81} +9277.57 q^{82} -100461. q^{83} +48375.6 q^{85} -79862.9 q^{86} -30225.4 q^{87} -5979.82 q^{88} +20071.8 q^{89} -53846.2 q^{90} +11974.2 q^{92} +3871.94 q^{93} -56838.2 q^{94} +117382. q^{95} -11035.0 q^{96} -23320.9 q^{97} +11854.0 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 8 q^{2} + 14 q^{3} + 32 q^{4} + 70 q^{5} + 56 q^{6} + 128 q^{8} + 244 q^{9} + 280 q^{10} + 62 q^{11} + 224 q^{12} + 1820 q^{13} - 2038 q^{15} + 512 q^{16} + 1694 q^{17} + 976 q^{18} + 826 q^{19} + 1120 q^{20}+ \cdots + 69500 q^{99}+O(q^{100}) \) 2 * q + 8 * q^2 + 14 * q^3 + 32 * q^4 + 70 * q^5 + 56 * q^6 + 128 * q^8 + 244 * q^9 + 280 * q^10 + 62 * q^11 + 224 * q^12 + 1820 * q^13 - 2038 * q^15 + 512 * q^16 + 1694 * q^17 + 976 * q^18 + 826 * q^19 + 1120 * q^20 + 248 * q^22 - 2734 * q^23 + 896 * q^24 + 6312 * q^25 + 7280 * q^26 + 7154 * q^27 - 2852 * q^29 - 8152 * q^30 - 2674 * q^31 + 2048 * q^32 + 4858 * q^33 + 6776 * q^34 + 3904 * q^36 - 9146 * q^37 + 3304 * q^38 + 21588 * q^39 + 4480 * q^40 + 6132 * q^41 - 16040 * q^43 + 992 * q^44 - 26852 * q^45 - 10936 * q^46 - 25326 * q^47 + 3584 * q^48 + 25248 * q^50 + 25762 * q^51 + 29120 * q^52 + 14958 * q^53 + 28616 * q^54 - 15526 * q^55 - 18866 * q^57 - 11408 * q^58 - 1106 * q^59 - 32608 * q^60 - 28042 * q^61 - 10696 * q^62 + 8192 * q^64 + 28308 * q^65 + 19432 * q^66 - 102642 * q^67 + 27104 * q^68 - 94346 * q^69 - 11056 * q^71 + 15616 * q^72 + 35070 * q^73 - 36584 * q^74 - 132776 * q^75 + 13216 * q^76 + 86352 * q^78 + 101762 * q^79 + 17920 * q^80 - 23750 * q^81 + 24528 * q^82 - 44632 * q^83 + 3674 * q^85 - 64160 * q^86 - 170380 * q^87 + 3968 * q^88 - 75474 * q^89 - 107408 * q^90 - 43744 * q^92 - 53478 * q^93 - 101304 * q^94 + 127502 * q^95 + 14336 * q^96 - 8316 * q^97 + 69500 * q^99

Introduction

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