LMFDB - Embedded newform 98.8.a.d.1.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [98,8,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, 8); 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, 8, names="a")

Level:	$ N $	$=$	$ 98 = 2 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	98.a (trivial)

Newform invariants

comment:select newform

sage:traces = [2,-16,-56,128,14,448,0,-1024,-908] 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:	$30.6137324974$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{949}) $
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 237 $ x^2 - x - 237
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			$15.9029$ 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)

$f(q)$	$=$	\(q-8.00000 q^{2} -58.8058 q^{3} +64.0000 q^{4} -424.282 q^{5} +470.447 q^{6} -512.000 q^{8} +1271.13 q^{9} +3394.25 q^{10} +7888.87 q^{11} -3763.57 q^{12} -6717.46 q^{13} +24950.2 q^{15} +4096.00 q^{16} +7075.01 q^{17} -10169.0 q^{18} +26249.2 q^{19} -27154.0 q^{20} -63110.9 q^{22} +12070.5 q^{23} +30108.6 q^{24} +101890. q^{25} +53739.7 q^{26} +53858.7 q^{27} +3061.25 q^{29} -199602. q^{30} +118525. q^{31} -32768.0 q^{32} -463912. q^{33} -56600.1 q^{34} +81352.1 q^{36} -459752. q^{37} -209993. q^{38} +395026. q^{39} +217232. q^{40} -316857. q^{41} -31624.2 q^{43} +504888. q^{44} -539316. q^{45} -96564.3 q^{46} -806553. q^{47} -240869. q^{48} -815120. q^{50} -416052. q^{51} -429917. q^{52} +479328. q^{53} -430869. q^{54} -3.34710e6 q^{55} -1.54360e6 q^{57} -24490.0 q^{58} -674863. q^{59} +1.59682e6 q^{60} +566329. q^{61} -948201. q^{62} +262144. q^{64} +2.85009e6 q^{65} +3.71129e6 q^{66} +1.18470e6 q^{67} +452801. q^{68} -709818. q^{69} +4.61736e6 q^{71} -650817. q^{72} -3.04800e6 q^{73} +3.67801e6 q^{74} -5.99173e6 q^{75} +1.67995e6 q^{76} -3.16021e6 q^{78} -6.90160e6 q^{79} -1.73786e6 q^{80} -5.94716e6 q^{81} +2.53485e6 q^{82} +9.01927e6 q^{83} -3.00180e6 q^{85} +252994. q^{86} -180020. q^{87} -4.03910e6 q^{88} +7.01478e6 q^{89} +4.31453e6 q^{90} +772515. q^{92} -6.96997e6 q^{93} +6.45243e6 q^{94} -1.11370e7 q^{95} +1.92695e6 q^{96} -8.60029e6 q^{97} +1.00278e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 16 q^{2} - 56 q^{3} + 128 q^{4} + 14 q^{5} + 448 q^{6} - 1024 q^{8} - 908 q^{9} - 112 q^{10} + 2408 q^{11} - 3584 q^{12} - 10724 q^{13} + 26180 q^{15} + 8192 q^{16} + 35098 q^{17} + 7264 q^{18} + 2408 q^{19}+ \cdots + 21971264 q^{99}+O(q^{100}) $ 2 * q - 16 * q^2 - 56 * q^3 + 128 * q^4 + 14 * q^5 + 448 * q^6 - 1024 * q^8 - 908 * q^9 - 112 * q^10 + 2408 * q^11 - 3584 * q^12 - 10724 * q^13 + 26180 * q^15 + 8192 * q^16 + 35098 * q^17 + 7264 * q^18 + 2408 * q^19 + 896 * q^20 - 19264 * q^22 - 61684 * q^23 + 28672 * q^24 + 215856 * q^25 + 85792 * q^26 + 41608 * q^27 - 95660 * q^29 - 209440 * q^30 + 166012 * q^31 - 65536 * q^32 - 479290 * q^33 - 280784 * q^34 - 58112 * q^36 - 559814 * q^37 - 19264 * q^38 + 383784 * q^39 - 7168 * q^40 - 805980 * q^41 + 267976 * q^43 + 154112 * q^44 - 1494388 * q^45 + 493472 * q^46 - 1769292 * q^47 - 229376 * q^48 - 1726848 * q^50 - 337424 * q^51 - 686336 * q^52 + 2317194 * q^53 - 332864 * q^54 - 5749268 * q^55 - 1610498 * q^57 + 765280 * q^58 - 660352 * q^59 + 1675520 * q^60 - 1463042 * q^61 - 1328096 * q^62 + 524288 * q^64 + 1094100 * q^65 + 3834320 * q^66 - 1784280 * q^67 + 2246272 * q^68 - 916762 * q^69 + 274400 * q^71 + 464896 * q^72 - 4549062 * q^73 + 4478512 * q^74 - 5671960 * q^75 + 154112 * q^76 - 3070272 * q^78 - 8673964 * q^79 + 57344 * q^80 - 1215782 * q^81 + 6447840 * q^82 + 10594360 * q^83 + 9280166 * q^85 - 2143808 * q^86 - 457016 * q^87 - 1232896 * q^88 - 1779750 * q^89 + 11955104 * q^90 - 3947776 * q^92 - 6836730 * q^93 + 14154336 * q^94 - 21586180 * q^95 + 1835008 * q^96 + 1748964 * q^97 + 21971264 * 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 $

$2$	−8.00000	−0.707107
$2$	−8.00000	−0.707107
$3$	−58.8058	−1.25747	−0.628733	−	0.777621i	$-0.716426\pi$
$3$	−58.8058	−1.25747	−0.628733	+	0.777621i	$0.716426\pi$
$4$	64.0000	0.500000
$5$	−424.282	−1.51796	−0.758978	−	0.651116i	$-0.774301\pi$
$5$	−424.282	−1.51796	−0.758978	+	0.651116i	$0.774301\pi$
$6$	470.447	0.889162
$7$	0	0
$7$	0	0
$8$	−512.000	−0.353553
$9$	1271.13	0.581220
$10$	3394.25	1.07336
$11$	7888.87	1.78706	0.893532	−	0.448999i	$-0.148219\pi$
$11$	7888.87	1.78706	0.893532	+	0.448999i	$0.148219\pi$
$12$	−3763.57	−0.628733
$13$	−6717.46	−0.848014	−0.424007	−	0.905659i	$-0.639377\pi$
$13$	−6717.46	−0.848014	−0.424007	+	0.905659i	$0.639377\pi$
$14$	0	0
$15$	24950.2	1.90878
$16$	4096.00	0.250000
$17$	7075.01	0.349266	0.174633	−	0.984634i	$-0.444126\pi$
$17$	7075.01	0.349266	0.174633	+	0.984634i	$0.444126\pi$
$18$	−10169.0	−0.410984
$19$	26249.2	0.877966	0.438983	−	0.898495i	$-0.355339\pi$
$19$	26249.2	0.877966	0.438983	+	0.898495i	$0.355339\pi$
$20$	−27154.0	−0.758978
$21$	0	0
$22$	−63110.9	−1.26365
$23$	12070.5	0.206861	0.103431	−	0.994637i	$-0.467018\pi$
$23$	12070.5	0.206861	0.103431	+	0.994637i	$0.467018\pi$
$24$	30108.6	0.444581
$25$	101890.	1.30419
$26$	53739.7	0.599637
$27$	53858.7	0.526602
$28$	0	0
$29$	3061.25	0.0233081	0.0116540	−	0.999932i	$-0.496290\pi$
$29$	3061.25	0.0233081	0.0116540	+	0.999932i	$0.496290\pi$
$30$	−199602.	−1.34971
$31$	118525.	0.714570	0.357285	−	0.933995i	$-0.383703\pi$
$31$	118525.	0.714570	0.357285	+	0.933995i	$0.383703\pi$
$32$	−32768.0	−0.176777
$33$	−463912.	−2.24717
$34$	−56600.1	−0.246968
$35$	0	0
$36$	81352.1	0.290610
$37$	−459752.	−1.49217	−0.746083	−	0.665853i	$-0.768068\pi$
$37$	−459752.	−1.49217	−0.746083	+	0.665853i	$0.768068\pi$
$38$	−209993.	−0.620816
$39$	395026.	1.06635
$40$	217232.	0.536679
$41$	−316857.	−0.717992	−0.358996	−	0.933339i	$-0.616881\pi$
$41$	−316857.	−0.717992	−0.358996	+	0.933339i	$0.616881\pi$
$42$	0	0
$43$	−31624.2	−0.0606569	−0.0303284	−	0.999540i	$-0.509655\pi$
$43$	−31624.2	−0.0606569	−0.0303284	+	0.999540i	$0.509655\pi$
$44$	504888.	0.893532
$45$	−539316.	−0.882266
$46$	−96564.3	−0.146273
$47$	−806553.	−1.13316	−0.566579	−	0.824007i	$-0.691733\pi$
$47$	−806553.	−1.13316	−0.566579	+	0.824007i	$0.691733\pi$
$48$	−240869.	−0.314366
$49$	0	0
$50$	−815120.	−0.922204
$51$	−416052.	−0.439190
$52$	−429917.	−0.424007
$53$	479328.	0.442250	0.221125	−	0.975246i	$-0.429027\pi$
$53$	479328.	0.442250	0.221125	+	0.975246i	$0.429027\pi$
$54$	−430869.	−0.372364
$55$	−3.34710e6	−2.71269
$56$	0	0
$57$	−1.54360e6	−1.10401
$58$	−24490.0	−0.0164813
$59$	−674863.	−0.427793	−0.213896	−	0.976856i	$-0.568615\pi$
$59$	−674863.	−0.427793	−0.213896	+	0.976856i	$0.568615\pi$
$60$	1.59682e6	0.954389
$61$	566329.	0.319459	0.159729	−	0.987161i	$-0.448938\pi$
$61$	566329.	0.319459	0.159729	+	0.987161i	$0.448938\pi$
$62$	−948201.	−0.505277
$63$	0	0
$64$	262144.	0.125000
$65$	2.85009e6	1.28725
$66$	3.71129e6	1.58899
$67$	1.18470e6	0.481222	0.240611	−	0.970622i	$-0.422652\pi$
$67$	1.18470e6	0.481222	0.240611	+	0.970622i	$0.422652\pi$
$68$	452801.	0.174633
$69$	−709818.	−0.260121
$70$	0	0
$71$	4.61736e6	1.53105	0.765524	−	0.643407i	$-0.222480\pi$
$71$	4.61736e6	1.53105	0.765524	+	0.643407i	$0.222480\pi$
$72$	−650817.	−0.205492
$73$	−3.04800e6	−0.917034	−0.458517	−	0.888686i	$-0.651619\pi$
$73$	−3.04800e6	−0.917034	−0.458517	+	0.888686i	$0.651619\pi$
$74$	3.67801e6	1.05512
$75$	−5.99173e6	−1.63998
$76$	1.67995e6	0.438983
$77$	0	0
$78$	−3.16021e6	−0.754022
$79$	−6.90160e6	−1.57491	−0.787454	−	0.616374i	$-0.788601\pi$
$79$	−6.90160e6	−1.57491	−0.787454	+	0.616374i	$0.788601\pi$
$80$	−1.73786e6	−0.379489
$81$	−5.94716e6	−1.24340
$82$	2.53485e6	0.507697
$83$	9.01927e6	1.73140	0.865701	−	0.500562i	$-0.166873\pi$
$83$	9.01927e6	1.73140	0.865701	+	0.500562i	$0.166873\pi$
$84$	0	0
$85$	−3.00180e6	−0.530170
$86$	252994.	0.0428909
$87$	−180020.	−0.0293091
$88$	−4.03910e6	−0.631823
$89$	7.01478e6	1.05475	0.527374	−	0.849633i	$-0.323176\pi$
$89$	7.01478e6	1.05475	0.527374	+	0.849633i	$0.323176\pi$
$90$	4.31453e6	0.623856
$91$	0	0
$92$	772515.	0.103431
$93$	−6.96997e6	−0.898547
$94$	6.45243e6	0.801264
$95$	−1.11370e7	−1.33271
$96$	1.92695e6	0.222291
$97$	−8.60029e6	−0.956779	−0.478390	−	0.878148i	$-0.658779\pi$
$97$	−8.60029e6	−0.956779	−0.478390	+	0.878148i	$0.658779\pi$
$98$	0	0
$99$	1.00278e7	1.03868
$100$	6.52096e6	0.652096
$101$	5.90355e6	0.570149	0.285075	−	0.958505i	$-0.407982\pi$
$101$	5.90355e6	0.570149	0.285075	+	0.958505i	$0.407982\pi$
$102$	3.32842e6	0.310554
$103$	−7.37049e6	−0.664609	−0.332305	−	0.943172i	$-0.607826\pi$
$103$	−7.37049e6	−0.664609	−0.332305	+	0.943172i	$0.607826\pi$
$104$	3.43934e6	0.299818
$105$	0	0
$106$	−3.83463e6	−0.312718
$107$	6.60469e6	0.521206	0.260603	−	0.965446i	$-0.416079\pi$
$107$	6.60469e6	0.521206	0.260603	+	0.965446i	$0.416079\pi$
$108$	3.44695e6	0.263301
$109$	3.14560e6	0.232654	0.116327	−	0.993211i	$-0.462888\pi$
$109$	3.14560e6	0.232654	0.116327	+	0.993211i	$0.462888\pi$
$110$	2.67768e7	1.91816
$111$	2.70361e7	1.87635
$112$	0	0
$113$	2.26100e7	1.47409	0.737047	−	0.675841i	$-0.236220\pi$
$113$	2.26100e7	1.47409	0.737047	+	0.675841i	$0.236220\pi$
$114$	1.23488e7	0.780654
$115$	−5.12131e6	−0.314007
$116$	195920.	0.0116540
$117$	−8.53874e6	−0.492883
$118$	5.39890e6	0.302495
$119$	0	0
$120$	−1.27745e7	−0.674855
$121$	4.27471e7	2.19360
$122$	−4.53063e6	−0.225891
$123$	1.86330e7	0.902850
$124$	7.58561e6	0.357285
$125$	−1.00831e7	−0.461751
$126$	0	0
$127$	−1.76143e7	−0.763047	−0.381524	−	0.924359i	$-0.624601\pi$
$127$	−1.76143e7	−0.763047	−0.381524	+	0.924359i	$0.624601\pi$
$128$	−2.09715e6	−0.0883883
$129$	1.85969e6	0.0762740
$130$	−2.28008e7	−0.910223
$131$	−4.83995e6	−0.188101	−0.0940505	−	0.995567i	$-0.529982\pi$
$131$	−4.83995e6	−0.188101	−0.0940505	+	0.995567i	$0.529982\pi$
$132$	−2.96903e7	−1.12359
$133$	0	0
$134$	−9.47758e6	−0.340276
$135$	−2.28513e7	−0.799359
$136$	−3.62241e6	−0.123484
$137$	−5.46036e7	−1.81426	−0.907130	−	0.420850i	$-0.861732\pi$
$137$	−5.46036e7	−1.81426	−0.907130	+	0.420850i	$0.861732\pi$
$138$	5.67855e6	0.183933
$139$	−5.28540e6	−0.166927	−0.0834633	−	0.996511i	$-0.526598\pi$
$139$	−5.28540e6	−0.166927	−0.0834633	+	0.996511i	$0.526598\pi$
$140$	0	0
$141$	4.74300e7	1.42491
$142$	−3.69388e7	−1.08262
$143$	−5.29931e7	−1.51546
$144$	5.20654e6	0.145305
$145$	−1.29883e6	−0.0353806
$146$	2.43840e7	0.648441
$147$	0	0
$148$	−2.94241e7	−0.746083
$149$	−2.59341e7	−0.642273	−0.321136	−	0.947033i	$-0.604065\pi$
$149$	−2.59341e7	−0.642273	−0.321136	+	0.947033i	$0.604065\pi$
$150$	4.79338e7	1.15964
$151$	−4.59185e7	−1.08535	−0.542673	−	0.839944i	$-0.682588\pi$
$151$	−4.59185e7	−1.08535	−0.542673	+	0.839944i	$0.682588\pi$
$152$	−1.34396e7	−0.310408
$153$	8.99324e6	0.203000
$154$	0	0
$155$	−5.02881e7	−1.08469
$156$	2.52816e7	0.533174
$157$	−7.80083e6	−0.160876	−0.0804381	−	0.996760i	$-0.525632\pi$
$157$	−7.80083e6	−0.160876	−0.0804381	+	0.996760i	$0.525632\pi$
$158$	5.52128e7	1.11363
$159$	−2.81873e7	−0.556114
$160$	1.39029e7	0.268339
$161$	0	0
$162$	4.75773e7	0.879219
$163$	−6.57424e7	−1.18902	−0.594510	−	0.804088i	$-0.702654\pi$
$163$	−6.57424e7	−1.18902	−0.594510	+	0.804088i	$0.702654\pi$
$164$	−2.02788e7	−0.358996
$165$	1.96829e8	3.41111
$166$	−7.21541e7	−1.22429
$167$	−2.42648e7	−0.403152	−0.201576	−	0.979473i	$-0.564606\pi$
$167$	−2.42648e7	−0.403152	−0.201576	+	0.979473i	$0.564606\pi$
$168$	0	0
$169$	−1.76243e7	−0.280872
$170$	2.40144e7	0.374887
$171$	3.33660e7	0.510291
$172$	−2.02395e6	−0.0303284
$173$	3.47849e7	0.510775	0.255388	−	0.966839i	$-0.417797\pi$
$173$	3.47849e7	0.510775	0.255388	+	0.966839i	$0.417797\pi$
$174$	1.44016e6	0.0207247
$175$	0	0
$176$	3.23128e7	0.446766
$177$	3.96859e7	0.537935
$178$	−5.61182e7	−0.745820
$179$	−6.39502e7	−0.833406	−0.416703	−	0.909043i	$-0.636814\pi$
$179$	−6.39502e7	−0.833406	−0.416703	+	0.909043i	$0.636814\pi$
$180$	−3.45162e7	−0.441133
$181$	−1.03303e8	−1.29491	−0.647454	−	0.762104i	$-0.724166\pi$
$181$	−1.03303e8	−1.29491	−0.647454	+	0.762104i	$0.724166\pi$
$182$	0	0
$183$	−3.33035e7	−0.401708
$184$	−6.18012e6	−0.0731365
$185$	1.95064e8	2.26504
$186$	5.57598e7	0.635368
$187$	5.58138e7	0.624161
$188$	−5.16194e7	−0.566579
$189$	0	0
$190$	8.90963e7	0.942371
$191$	−8.54456e7	−0.887305	−0.443652	−	0.896199i	$-0.646318\pi$
$191$	−8.54456e7	−0.887305	−0.443652	+	0.896199i	$0.646318\pi$
$192$	−1.54156e7	−0.157183
$193$	4.48641e7	0.449209	0.224605	−	0.974450i	$-0.427891\pi$
$193$	4.48641e7	0.449209	0.224605	+	0.974450i	$0.427891\pi$
$194$	6.88023e7	0.676545
$195$	−1.67602e8	−1.61867
$196$	0	0
$197$	−1.97306e8	−1.83869	−0.919345	−	0.393452i	$-0.871281\pi$
$197$	−1.97306e8	−1.83869	−0.919345	+	0.393452i	$0.871281\pi$
$198$	−8.02220e7	−0.734456
$199$	−5.41099e7	−0.486733	−0.243367	−	0.969934i	$-0.578252\pi$
$199$	−5.41099e7	−0.486733	−0.243367	+	0.969934i	$0.578252\pi$
$200$	−5.21677e7	−0.461102
$201$	−6.96671e7	−0.605120
$202$	−4.72284e7	−0.403156
$203$	0	0
$204$	−2.66273e7	−0.219595
$205$	1.34437e8	1.08988
$206$	5.89639e7	0.469950
$207$	1.53432e7	0.120232
$208$	−2.75147e7	−0.212004
$209$	2.07076e8	1.56898
$210$	0	0
$211$	9.24251e7	0.677331	0.338666	−	0.940907i	$-0.390024\pi$
$211$	9.24251e7	0.677331	0.338666	+	0.940907i	$0.390024\pi$
$212$	3.06770e7	0.221125
$213$	−2.71527e8	−1.92524
$214$	−5.28375e7	−0.368548
$215$	1.34176e7	0.0920745
$216$	−2.75756e7	−0.186182
$217$	0	0
$218$	−2.51648e7	−0.164511
$219$	1.79240e8	1.15314
$220$	−2.14215e8	−1.35634
$221$	−4.75261e7	−0.296182
$222$	−2.16289e8	−1.32678
$223$	3.72959e7	0.225213	0.112607	−	0.993640i	$-0.464080\pi$
$223$	3.72959e7	0.225213	0.112607	+	0.993640i	$0.464080\pi$
$224$	0	0
$225$	1.29515e8	0.758022
$226$	−1.80880e8	−1.04234
$227$	1.14391e8	0.649086	0.324543	−	0.945871i	$-0.394789\pi$
$227$	1.14391e8	0.649086	0.324543	+	0.945871i	$0.394789\pi$
$228$	−9.87906e7	−0.552006
$229$	8.34255e7	0.459065	0.229533	−	0.973301i	$-0.426280\pi$
$229$	8.34255e7	0.459065	0.229533	+	0.973301i	$0.426280\pi$
$230$	4.09705e7	0.222036
$231$	0	0
$232$	−1.56736e6	−0.00824065
$233$	−3.05524e7	−0.158234	−0.0791170	−	0.996865i	$-0.525210\pi$
$233$	−3.05524e7	−0.158234	−0.0791170	+	0.996865i	$0.525210\pi$
$234$	6.83099e7	0.348521
$235$	3.42206e8	1.72008
$236$	−4.31912e7	−0.213896
$237$	4.05854e8	1.98039
$238$	0	0
$239$	5.35396e6	0.0253678	0.0126839	−	0.999920i	$-0.495962\pi$
$239$	5.35396e6	0.0253678	0.0126839	+	0.999920i	$0.495962\pi$
$240$	1.02196e8	0.477195
$241$	1.85524e8	0.853769	0.426884	−	0.904306i	$-0.359611\pi$
$241$	1.85524e8	0.853769	0.426884	+	0.904306i	$0.359611\pi$
$242$	−3.41977e8	−1.55111
$243$	2.31939e8	1.03693
$244$	3.62451e7	0.159729
$245$	0	0
$246$	−1.49064e8	−0.638412
$247$	−1.76328e8	−0.744528
$248$	−6.06849e7	−0.252639
$249$	−5.30386e8	−2.17718
$250$	8.06646e7	0.326508
$251$	−1.50737e6	−0.00601673	−0.00300837	−	0.999995i	$-0.500958\pi$
$251$	−1.50737e6	−0.00601673	−0.00300837	+	0.999995i	$0.500958\pi$
$252$	0	0
$253$	9.52229e7	0.369675
$254$	1.40914e8	0.539556
$255$	1.76523e8	0.666671
$256$	1.67772e7	0.0625000
$257$	3.17375e8	1.16629	0.583145	−	0.812368i	$-0.301822\pi$
$257$	3.17375e8	1.16629	0.583145	+	0.812368i	$0.301822\pi$
$258$	−1.48775e7	−0.0539338
$259$	0	0
$260$	1.82406e8	0.643625
$261$	3.89124e6	0.0135471
$262$	3.87196e7	0.133007
$263$	1.36714e8	0.463413	0.231707	−	0.972786i	$-0.425569\pi$
$263$	1.36714e8	0.463413	0.231707	+	0.972786i	$0.425569\pi$
$264$	2.37523e8	0.794495
$265$	−2.03370e8	−0.671316
$266$	0	0
$267$	−4.12510e8	−1.32631
$268$	7.58206e7	0.240611
$269$	−1.87225e8	−0.586448	−0.293224	−	0.956044i	$-0.594728\pi$
$269$	−1.87225e8	−0.586448	−0.293224	+	0.956044i	$0.594728\pi$
$270$	1.82810e8	0.565232
$271$	−4.55071e8	−1.38895	−0.694475	−	0.719517i	$-0.744363\pi$
$271$	−4.55071e8	−1.38895	−0.694475	+	0.719517i	$0.744363\pi$
$272$	2.89793e7	0.0873164
$273$	0	0
$274$	4.36829e8	1.28288
$275$	8.03797e8	2.33068
$276$	−4.54284e7	−0.130060
$277$	−4.96463e8	−1.40348	−0.701742	−	0.712431i	$-0.747594\pi$
$277$	−4.96463e8	−1.40348	−0.701742	+	0.712431i	$0.747594\pi$
$278$	4.22832e7	0.118035
$279$	1.50661e8	0.415322
$280$	0	0
$281$	−2.68528e7	−0.0721968	−0.0360984	−	0.999348i	$-0.511493\pi$
$281$	−2.68528e7	−0.0721968	−0.0360984	+	0.999348i	$0.511493\pi$
$282$	−3.79440e8	−1.00756
$283$	3.37078e8	0.884053	0.442026	−	0.897002i	$-0.354260\pi$
$283$	3.37078e8	0.884053	0.442026	+	0.897002i	$0.354260\pi$
$284$	2.95511e8	0.765524
$285$	6.54923e8	1.67584
$286$	4.23945e8	1.07159
$287$	0	0
$288$	−4.16523e7	−0.102746
$289$	−3.60283e8	−0.878013
$290$	1.03907e7	0.0250179
$291$	5.05747e8	1.20312
$292$	−1.95072e8	−0.458517
$293$	5.65397e8	1.31316	0.656579	−	0.754258i	$-0.272003\pi$
$293$	5.65397e8	1.31316	0.656579	+	0.754258i	$0.272003\pi$
$294$	0	0
$295$	2.86332e8	0.649371
$296$	2.35393e8	0.527560
$297$	4.24884e8	0.941072
$298$	2.07473e8	0.454156
$299$	−8.10833e7	−0.175421
$300$	−3.83471e8	−0.819989
$301$	0	0
$302$	3.67348e8	0.767456
$303$	−3.47163e8	−0.716943
$304$	1.07517e8	0.219491
$305$	−2.40283e8	−0.484924
$306$	−7.19459e7	−0.143543
$307$	−7.13941e8	−1.40824	−0.704122	−	0.710079i	$-0.748659\pi$
$307$	−7.13941e8	−1.40824	−0.704122	+	0.710079i	$0.748659\pi$
$308$	0	0
$309$	4.33428e8	0.835723
$310$	4.02304e8	0.766989
$311$	−4.56853e8	−0.861221	−0.430611	−	0.902538i	$-0.641702\pi$
$311$	−4.56853e8	−0.861221	−0.430611	+	0.902538i	$0.641702\pi$
$312$	−2.02253e8	−0.377011
$313$	−9.60138e8	−1.76982	−0.884909	−	0.465764i	$-0.845780\pi$
$313$	−9.60138e8	−1.76982	−0.884909	+	0.465764i	$0.845780\pi$
$314$	6.24066e7	0.113757
$315$	0	0
$316$	−4.41702e8	−0.787454
$317$	−5.75883e8	−1.01538	−0.507688	−	0.861541i	$-0.669500\pi$
$317$	−5.75883e8	−1.01538	−0.507688	+	0.861541i	$0.669500\pi$
$318$	2.25498e8	0.393232
$319$	2.41498e7	0.0416530
$320$	−1.11223e8	−0.189745
$321$	−3.88394e8	−0.655398
$322$	0	0
$323$	1.85713e8	0.306643
$324$	−3.80618e8	−0.621702
$325$	−6.84442e8	−1.10597
$326$	5.25940e8	0.840764
$327$	−1.84980e8	−0.292554
$328$	1.62231e8	0.253849
$329$	0	0
$330$	−1.57463e9	−2.41202
$331$	−4.46674e8	−0.677006	−0.338503	−	0.940965i	$-0.609921\pi$
$331$	−4.46674e8	−0.677006	−0.338503	+	0.940965i	$0.609921\pi$
$332$	5.77233e8	0.865701
$333$	−5.84403e8	−0.867276
$334$	1.94118e8	0.285072
$335$	−5.02646e8	−0.730475
$336$	0	0
$337$	−1.08980e9	−1.55111	−0.775555	−	0.631280i	$-0.782530\pi$
$337$	−1.08980e9	−1.55111	−0.775555	+	0.631280i	$0.782530\pi$
$338$	1.40994e8	0.198606
$339$	−1.32960e9	−1.85362
$340$	−1.92115e8	−0.265085
$341$	9.35029e8	1.27698
$342$	−2.66928e8	−0.360830
$343$	0	0
$344$	1.61916e7	0.0214455
$345$	3.01163e8	0.394852
$346$	−2.78279e8	−0.361173
$347$	1.10080e9	1.41435	0.707175	−	0.707038i	$-0.249969\pi$
$347$	1.10080e9	1.41435	0.707175	+	0.707038i	$0.249969\pi$
$348$	−1.15213e7	−0.0146545
$349$	9.17714e8	1.15563	0.577814	−	0.816168i	$-0.303906\pi$
$349$	9.17714e8	1.15563	0.577814	+	0.816168i	$0.303906\pi$
$350$	0	0
$351$	−3.61793e8	−0.446566
$352$	−2.58502e8	−0.315911
$353$	−2.13361e8	−0.258169	−0.129084	−	0.991634i	$-0.541204\pi$
$353$	−2.13361e8	−0.258169	−0.129084	+	0.991634i	$0.541204\pi$
$354$	−3.17487e8	−0.380377
$355$	−1.95906e9	−2.32407
$356$	4.48946e8	0.527374
$357$	0	0
$358$	5.11602e8	0.589307
$359$	1.18905e8	0.135634	0.0678171	−	0.997698i	$-0.478397\pi$
$359$	1.18905e8	0.135634	0.0678171	+	0.997698i	$0.478397\pi$
$360$	2.76130e8	0.311928
$361$	−2.04854e8	−0.229176
$362$	8.26426e8	0.915638
$363$	−2.51378e9	−2.75838
$364$	0	0
$365$	1.29321e9	1.39202
$366$	2.66428e8	0.284051
$367$	−2.74995e8	−0.290398	−0.145199	−	0.989402i	$-0.546382\pi$
$367$	−2.74995e8	−0.290398	−0.145199	+	0.989402i	$0.546382\pi$
$368$	4.94409e7	0.0517153
$369$	−4.02765e8	−0.417311
$370$	−1.56051e9	−1.60163
$371$	0	0
$372$	−4.46078e8	−0.449273
$373$	8.95753e8	0.893732	0.446866	−	0.894601i	$-0.352540\pi$
$373$	8.95753e8	0.893732	0.446866	+	0.894601i	$0.352540\pi$
$374$	−4.46511e8	−0.441348
$375$	5.92944e8	0.580636
$376$	4.12955e8	0.400632
$377$	−2.05638e7	−0.0197656
$378$	0	0
$379$	1.69750e9	1.60167	0.800833	−	0.598887i	$-0.204390\pi$
$379$	1.69750e9	1.60167	0.800833	+	0.598887i	$0.204390\pi$
$380$	−7.12770e8	−0.666357
$381$	1.03582e9	0.959506
$382$	6.83565e8	0.627419
$383$	−1.24907e9	−1.13603	−0.568014	−	0.823019i	$-0.692288\pi$
$383$	−1.24907e9	−1.13603	−0.568014	+	0.823019i	$0.692288\pi$
$384$	1.23325e8	0.111145
$385$	0	0
$386$	−3.58913e8	−0.317639
$387$	−4.01984e7	−0.0352550
$388$	−5.50418e8	−0.478390
$389$	1.36070e9	1.17203	0.586014	−	0.810301i	$-0.300696\pi$
$389$	1.36070e9	1.17203	0.586014	+	0.810301i	$0.300696\pi$
$390$	1.34082e9	1.14457
$391$	8.53992e7	0.0722496
$392$	0	0
$393$	2.84617e8	0.236531
$394$	1.57845e9	1.30015
$395$	2.92822e9	2.39064
$396$	6.41776e8	0.519339
$397$	−2.06608e9	−1.65722	−0.828610	−	0.559826i	$-0.810868\pi$
$397$	−2.06608e9	−1.65722	−0.828610	+	0.559826i	$0.810868\pi$
$398$	4.32879e8	0.344172
$399$	0	0
$400$	4.17342e8	0.326048
$401$	−1.45920e8	−0.113008	−0.0565040	−	0.998402i	$-0.517995\pi$
$401$	−1.45920e8	−0.113008	−0.0565040	+	0.998402i	$0.517995\pi$
$402$	5.57337e8	0.427885
$403$	−7.96188e8	−0.605965
$404$	3.77827e8	0.285075
$405$	2.52327e9	1.88743
$406$	0	0
$407$	−3.62692e9	−2.66660
$408$	2.13019e8	0.155277
$409$	−1.19190e9	−0.861408	−0.430704	−	0.902493i	$-0.641735\pi$
$409$	−1.19190e9	−0.861408	−0.430704	+	0.902493i	$0.641735\pi$
$410$	−1.07549e9	−0.770662
$411$	3.21101e9	2.28137
$412$	−4.71712e8	−0.332305
$413$	0	0
$414$	−1.22746e8	−0.0850168
$415$	−3.82671e9	−2.62819
$416$	2.20118e8	0.149909
$417$	3.10812e8	0.209905
$418$	−1.65661e9	−1.10944
$419$	−5.89725e8	−0.391652	−0.195826	−	0.980639i	$-0.562739\pi$
$419$	−5.89725e8	−0.391652	−0.195826	+	0.980639i	$0.562739\pi$
$420$	0	0
$421$	2.35971e9	1.54124	0.770622	−	0.637292i	$-0.219946\pi$
$421$	2.35971e9	1.54124	0.770622	+	0.637292i	$0.219946\pi$
$422$	−7.39401e8	−0.478946
$423$	−1.02523e9	−0.658614
$424$	−2.45416e8	−0.156359
$425$	7.20873e8	0.455510
$426$	2.17222e9	1.36135
$427$	0	0
$428$	4.22700e8	0.260603
$429$	3.11631e9	1.90563
$430$	−1.07341e8	−0.0651065
$431$	−2.58646e9	−1.55609	−0.778045	−	0.628209i	$-0.783788\pi$
$431$	−2.58646e9	−1.55609	−0.778045	+	0.628209i	$0.783788\pi$
$432$	2.20605e8	0.131650
$433$	1.48937e9	0.881649	0.440825	−	0.897593i	$-0.354686\pi$
$433$	1.48937e9	0.881649	0.440825	+	0.897593i	$0.354686\pi$
$434$	0	0
$435$	7.63790e7	0.0444899
$436$	2.01318e8	0.116327
$437$	3.16841e8	0.181617
$438$	−1.43392e9	−0.815392
$439$	2.67186e9	1.50726	0.753629	−	0.657300i	$-0.228302\pi$
$439$	2.67186e9	1.50726	0.753629	+	0.657300i	$0.228302\pi$
$440$	1.71372e9	0.959080
$441$	0	0
$442$	3.80209e8	0.209433
$443$	1.38981e8	0.0759524	0.0379762	−	0.999279i	$-0.487909\pi$
$443$	1.38981e8	0.0759524	0.0379762	+	0.999279i	$0.487909\pi$
$444$	1.73031e9	0.938174
$445$	−2.97624e9	−1.60106
$446$	−2.98367e8	−0.159250
$447$	1.52508e9	0.807636
$448$	0	0
$449$	−9.13167e8	−0.476089	−0.238044	−	0.971254i	$-0.576506\pi$
$449$	−9.13167e8	−0.476089	−0.238044	+	0.971254i	$0.576506\pi$
$450$	−1.03612e9	−0.536003
$451$	−2.49964e9	−1.28310
$452$	1.44704e9	0.737047
$453$	2.70028e9	1.36479
$454$	−9.15130e8	−0.458973
$455$	0	0
$456$	7.90325e8	0.390327
$457$	−8.24195e8	−0.403946	−0.201973	−	0.979391i	$-0.564735\pi$
$457$	−8.24195e8	−0.403946	−0.201973	+	0.979391i	$0.564735\pi$
$458$	−6.67404e8	−0.324608
$459$	3.81051e8	0.183924
$460$	−3.27764e8	−0.157003
$461$	−1.64108e9	−0.780147	−0.390073	−	0.920784i	$-0.627550\pi$
$461$	−1.64108e9	−0.780147	−0.390073	+	0.920784i	$0.627550\pi$
$462$	0	0
$463$	2.87188e9	1.34472	0.672361	−	0.740224i	$-0.265280\pi$
$463$	2.87188e9	1.34472	0.672361	+	0.740224i	$0.265280\pi$
$464$	1.25389e7	0.00582702
$465$	2.95723e9	1.36395
$466$	2.44419e8	0.111888
$467$	−2.94390e9	−1.33756	−0.668782	−	0.743459i	$-0.733184\pi$
$467$	−2.94390e9	−1.33756	−0.668782	+	0.743459i	$0.733184\pi$
$468$	−5.46480e8	−0.246441
$469$	0	0
$470$	−2.73765e9	−1.21628
$471$	4.58734e8	0.202296
$472$	3.45530e8	0.151248
$473$	−2.49479e8	−0.108398
$474$	−3.24683e9	−1.40035
$475$	2.67453e9	1.14504
$476$	0	0
$477$	6.09287e8	0.257044
$478$	−4.28317e7	−0.0179377
$479$	−8.38890e8	−0.348763	−0.174382	−	0.984678i	$-0.555793\pi$
$479$	−8.38890e8	−0.348763	−0.174382	+	0.984678i	$0.555793\pi$
$480$	−8.17570e8	−0.337428
$481$	3.08836e9	1.26538
$482$	−1.48419e9	−0.603706
$483$	0	0
$484$	2.73581e9	1.09680
$485$	3.64895e9	1.45235
$486$	−1.85551e9	−0.733224
$487$	2.45337e8	0.0962523	0.0481261	−	0.998841i	$-0.484675\pi$
$487$	2.45337e8	0.0962523	0.0481261	+	0.998841i	$0.484675\pi$
$488$	−2.89961e8	−0.112946
$489$	3.86604e9	1.49515
$490$	0	0
$491$	−4.86528e9	−1.85491	−0.927455	−	0.373936i	$-0.878008\pi$
$491$	−4.86528e9	−1.85491	−0.927455	+	0.373936i	$0.878008\pi$
$492$	1.19251e9	0.451425
$493$	2.16584e7	0.00814071
$494$	1.41062e9	0.526461
$495$	−4.25459e9	−1.57667
$496$	4.85479e8	0.178642
$497$	0	0
$498$	4.24308e9	1.53950
$499$	1.88308e9	0.678447	0.339223	−	0.940706i	$-0.389836\pi$
$499$	1.88308e9	0.678447	0.339223	+	0.940706i	$0.389836\pi$
$500$	−6.45317e8	−0.230876
$501$	1.42691e9	0.506950
$502$	1.20589e7	0.00425447
$503$	−4.05510e9	−1.42074	−0.710369	−	0.703830i	$-0.751472\pi$
$503$	−4.05510e9	−1.42074	−0.710369	+	0.703830i	$0.751472\pi$
$504$	0	0
$505$	−2.50477e9	−0.865462
$506$	−7.61783e8	−0.261399
$507$	1.03641e9	0.353187
$508$	−1.12731e9	−0.381524
$509$	5.88473e9	1.97794	0.988972	−	0.148101i	$-0.0473161\pi$
$509$	5.88473e9	1.97794	0.988972	+	0.148101i	$0.0473161\pi$
$510$	−1.41219e9	−0.471408
$511$	0	0
$512$	−1.34218e8	−0.0441942
$513$	1.41374e9	0.462339
$514$	−2.53900e9	−0.824692
$515$	3.12717e9	1.00885
$516$	1.19020e8	0.0381370
$517$	−6.36279e9	−2.02503
$518$	0	0
$519$	−2.04556e9	−0.642282
$520$	−1.45925e9	−0.455111
$521$	3.64769e9	1.13002	0.565009	−	0.825084i	$-0.308873\pi$
$521$	3.64769e9	1.13002	0.565009	+	0.825084i	$0.308873\pi$
$522$	−3.11299e7	−0.00957925
$523$	−2.35550e9	−0.719992	−0.359996	−	0.932954i	$-0.617222\pi$
$523$	−2.35550e9	−0.719992	−0.359996	+	0.932954i	$0.617222\pi$
$524$	−3.09757e8	−0.0940505
$525$	0	0
$526$	−1.09371e9	−0.327683
$527$	8.38567e8	0.249575
$528$	−1.90018e9	−0.561793
$529$	−3.25913e9	−0.957208
$530$	1.62696e9	0.474692
$531$	−8.57836e8	−0.248641
$532$	0	0
$533$	2.12847e9	0.608867
$534$	3.30008e9	0.937843
$535$	−2.80225e9	−0.791168
$536$	−6.06565e8	−0.170138
$537$	3.76065e9	1.04798
$538$	1.49780e9	0.414682
$539$	0	0
$540$	−1.46248e9	−0.399679
$541$	−5.48786e8	−0.149009	−0.0745045	−	0.997221i	$-0.523738\pi$
$541$	−5.48786e8	−0.149009	−0.0745045	+	0.997221i	$0.523738\pi$
$542$	3.64057e9	0.982136
$543$	6.07483e9	1.62830
$544$	−2.31834e8	−0.0617420
$545$	−1.33462e9	−0.353159
$546$	0	0
$547$	1.19987e8	0.0313457	0.0156729	−	0.999877i	$-0.495011\pi$
$547$	1.19987e8	0.0313457	0.0156729	+	0.999877i	$0.495011\pi$
$548$	−3.49463e9	−0.907130
$549$	7.19876e8	0.185676
$550$	−6.43038e9	−1.64804
$551$	8.03553e7	0.0204637
$552$	3.63427e8	0.0919667
$553$	0	0
$554$	3.97170e9	0.992413
$555$	−1.14709e10	−2.84821
$556$	−3.38265e8	−0.0834633
$557$	−3.07592e8	−0.0754191	−0.0377096	−	0.999289i	$-0.512006\pi$
$557$	−3.07592e8	−0.0754191	−0.0377096	+	0.999289i	$0.512006\pi$
$558$	−1.20528e9	−0.293677
$559$	2.12434e8	0.0514379
$560$	0	0
$561$	−3.28218e9	−0.784860
$562$	2.14823e8	0.0510508
$563$	−1.33820e9	−0.316040	−0.158020	−	0.987436i	$-0.550511\pi$
$563$	−1.33820e9	−0.316040	−0.158020	+	0.987436i	$0.550511\pi$
$564$	3.03552e9	0.712454
$565$	−9.59299e9	−2.23761
$566$	−2.69663e9	−0.625120
$567$	0	0
$568$	−2.36409e9	−0.541308
$569$	−6.48887e9	−1.47664	−0.738322	−	0.674448i	$-0.764382\pi$
$569$	−6.48887e9	−1.47664	−0.738322	+	0.674448i	$0.764382\pi$
$570$	−5.23938e9	−1.18500
$571$	6.97192e9	1.56721	0.783603	−	0.621262i	$-0.213380\pi$
$571$	6.97192e9	1.56721	0.783603	+	0.621262i	$0.213380\pi$
$572$	−3.39156e9	−0.757728
$573$	5.02470e9	1.11576
$574$	0	0
$575$	1.22987e9	0.269787
$576$	3.33218e8	0.0726524
$577$	4.53578e9	0.982962	0.491481	−	0.870888i	$-0.336456\pi$
$577$	4.53578e9	0.982962	0.491481	+	0.870888i	$0.336456\pi$
$578$	2.88226e9	0.620849
$579$	−2.63827e9	−0.564865
$580$	−8.31254e7	−0.0176903
$581$	0	0
$582$	−4.04598e9	−0.850732
$583$	3.78136e9	0.790329
$584$	1.56058e9	0.324221
$585$	3.62283e9	0.748174
$586$	−4.52318e9	−0.928542
$587$	5.05375e9	1.03129	0.515644	−	0.856803i	$-0.327553\pi$
$587$	5.05375e9	1.03129	0.515644	+	0.856803i	$0.327553\pi$
$588$	0	0
$589$	3.11118e9	0.627368
$590$	−2.29066e9	−0.459174
$591$	1.16027e10	2.31209
$592$	−1.88314e9	−0.373041
$593$	−3.81936e8	−0.0752140	−0.0376070	−	0.999293i	$-0.511974\pi$
$593$	−3.81936e8	−0.0752140	−0.0376070	+	0.999293i	$0.511974\pi$
$594$	−3.39907e9	−0.665438
$595$	0	0
$596$	−1.65978e9	−0.321136
$597$	3.18198e9	0.612050
$598$	6.48667e8	0.124042
$599$	1.78946e9	0.340195	0.170097	−	0.985427i	$-0.445592\pi$
$599$	1.78946e9	0.340195	0.170097	+	0.985427i	$0.445592\pi$
$600$	3.06777e9	0.579820
$601$	3.92179e8	0.0736925	0.0368463	−	0.999321i	$-0.488269\pi$
$601$	3.92179e8	0.0736925	0.0368463	+	0.999321i	$0.488269\pi$
$602$	0	0
$603$	1.50590e9	0.279696
$604$	−2.93878e9	−0.542673
$605$	−1.81368e10	−3.32979
$606$	2.77731e9	0.506955
$607$	1.11903e9	0.203086	0.101543	−	0.994831i	$-0.467622\pi$
$607$	1.11903e9	0.203086	0.101543	+	0.994831i	$0.467622\pi$
$608$	−8.60132e8	−0.155204
$609$	0	0
$610$	1.92227e9	0.342893
$611$	5.41799e9	0.960934
$612$	5.75567e8	0.101500
$613$	−4.45618e9	−0.781360	−0.390680	−	0.920527i	$-0.627760\pi$
$613$	−4.45618e9	−0.781360	−0.390680	+	0.920527i	$0.627760\pi$
$614$	5.71153e9	0.995779
$615$	−7.90566e9	−1.37049
$616$	0	0
$617$	−2.50707e9	−0.429704	−0.214852	−	0.976647i	$-0.568927\pi$
$617$	−2.50707e9	−0.429704	−0.214852	+	0.976647i	$0.568927\pi$
$618$	−3.46742e9	−0.590945
$619$	1.48446e8	0.0251566	0.0125783	−	0.999921i	$-0.495996\pi$
$619$	1.48446e8	0.0251566	0.0125783	+	0.999921i	$0.495996\pi$
$620$	−3.21844e9	−0.542343
$621$	6.50103e8	0.108934
$622$	3.65482e9	0.608975
$623$	0	0
$624$	1.61803e9	0.266587
$625$	−3.68209e9	−0.603274
$626$	7.68111e9	1.25145
$627$	−1.21773e10	−1.97294
$628$	−4.99253e8	−0.0804381
$629$	−3.25275e9	−0.521163
$630$	0	0
$631$	6.90977e9	1.09487	0.547433	−	0.836850i	$-0.315605\pi$
$631$	6.90977e9	1.09487	0.547433	+	0.836850i	$0.315605\pi$
$632$	3.53362e9	0.556814
$633$	−5.43513e9	−0.851721
$634$	4.60707e9	0.717980
$635$	7.47341e9	1.15827
$636$	−1.80399e9	−0.278057
$637$	0	0
$638$	−1.93199e8	−0.0294531
$639$	5.86925e9	0.889876
$640$	8.89783e8	0.134170
$641$	−1.56699e9	−0.234997	−0.117498	−	0.993073i	$-0.537487\pi$
$641$	−1.56699e9	−0.234997	−0.117498	+	0.993073i	$0.537487\pi$
$642$	3.10716e9	0.463437
$643$	−7.91354e9	−1.17390	−0.586952	−	0.809622i	$-0.699672\pi$
$643$	−7.91354e9	−1.17390	−0.586952	+	0.809622i	$0.699672\pi$
$644$	0	0
$645$	−7.89032e8	−0.115781
$646$	−1.48570e9	−0.216830
$647$	−3.86852e9	−0.561538	−0.280769	−	0.959775i	$-0.590590\pi$
$647$	−3.86852e9	−0.561538	−0.280769	+	0.959775i	$0.590590\pi$
$648$	3.04495e9	0.439609
$649$	−5.32390e9	−0.764493
$650$	5.47554e9	0.782042
$651$	0	0
$652$	−4.20752e9	−0.594510
$653$	6.69429e9	0.940824	0.470412	−	0.882447i	$-0.344105\pi$
$653$	6.69429e9	0.940824	0.470412	+	0.882447i	$0.344105\pi$
$654$	1.47984e9	0.206867
$655$	2.05350e9	0.285529
$656$	−1.29785e9	−0.179498
$657$	−3.87440e9	−0.532998
$658$	0	0
$659$	−4.20015e9	−0.571696	−0.285848	−	0.958275i	$-0.592275\pi$
$659$	−4.20015e9	−0.571696	−0.285848	+	0.958275i	$0.592275\pi$
$660$	1.25971e10	1.70556
$661$	9.00673e9	1.21300	0.606502	−	0.795082i	$-0.292572\pi$
$661$	9.00673e9	1.21300	0.606502	+	0.795082i	$0.292572\pi$
$662$	3.57339e9	0.478716
$663$	2.79481e9	0.372439
$664$	−4.61786e9	−0.612143
$665$	0	0
$666$	4.67522e9	0.613257
$667$	3.69510e7	0.00482154
$668$	−1.55295e9	−0.201576
$669$	−2.19322e9	−0.283198
$670$	4.02116e9	0.516523
$671$	4.46770e9	0.570893
$672$	0	0
$673$	−6.02502e9	−0.761913	−0.380957	−	0.924593i	$-0.624405\pi$
$673$	−6.02502e9	−0.761913	−0.380957	+	0.924593i	$0.624405\pi$
$674$	8.71841e9	1.09680
$675$	5.48766e9	0.686790
$676$	−1.12795e9	−0.140436
$677$	7.77545e9	0.963086	0.481543	−	0.876422i	$-0.340077\pi$
$677$	7.77545e9	0.963086	0.481543	+	0.876422i	$0.340077\pi$
$678$	1.06368e10	1.31071
$679$	0	0
$680$	1.53692e9	0.187444
$681$	−6.72688e9	−0.816204
$682$	−7.48023e9	−0.902963
$683$	−7.60072e9	−0.912814	−0.456407	−	0.889771i	$-0.650864\pi$
$683$	−7.60072e9	−0.912814	−0.456407	+	0.889771i	$0.650864\pi$
$684$	2.13542e9	0.255145
$685$	2.31673e10	2.75397
$686$	0	0
$687$	−4.90590e9	−0.577259
$688$	−1.29533e8	−0.0151642
$689$	−3.21987e9	−0.375034
$690$	−2.40930e9	−0.279203
$691$	5.02861e9	0.579796	0.289898	−	0.957058i	$-0.406379\pi$
$691$	5.02861e9	0.579796	0.289898	+	0.957058i	$0.406379\pi$
$692$	2.22624e9	0.255388
$693$	0	0
$694$	−8.80644e9	−1.00010
$695$	2.24250e9	0.253387
$696$	9.21700e7	0.0103623
$697$	−2.24177e9	−0.250770
$698$	−7.34171e9	−0.817153
$699$	1.79666e9	0.198974
$700$	0	0
$701$	1.07254e10	1.17598	0.587989	−	0.808869i	$-0.299920\pi$
$701$	1.07254e10	1.17598	0.587989	+	0.808869i	$0.299920\pi$
$702$	2.89435e9	0.315770
$703$	−1.20681e10	−1.31007
$704$	2.06802e9	0.223383
$705$	−2.01237e10	−2.16295
$706$	1.70689e9	0.182553
$707$	0	0
$708$	2.53990e9	0.268967
$709$	−1.47683e10	−1.55621	−0.778105	−	0.628134i	$-0.783819\pi$
$709$	−1.47683e10	−1.55621	−0.778105	+	0.628134i	$0.783819\pi$
$710$	1.56725e10	1.64336
$711$	−8.77281e9	−0.915367
$712$	−3.59157e9	−0.372910
$713$	1.43066e9	0.147817
$714$	0	0
$715$	2.24840e10	2.30040
$716$	−4.09281e9	−0.416703
$717$	−3.14844e8	−0.0318991
$718$	−9.51239e8	−0.0959078
$719$	−1.23958e10	−1.24372	−0.621859	−	0.783129i	$-0.713622\pi$
$719$	−1.23958e10	−1.24372	−0.621859	+	0.783129i	$0.713622\pi$
$720$	−2.20904e9	−0.220567
$721$	0	0
$722$	1.63883e9	0.162052
$723$	−1.09099e10	−1.07358
$724$	−6.61141e9	−0.647454
$725$	3.11911e8	0.0303982
$726$	2.01102e10	1.95047
$727$	−1.18455e10	−1.14336	−0.571681	−	0.820476i	$-0.693709\pi$
$727$	−1.18455e10	−1.14336	−0.571681	+	0.820476i	$0.693709\pi$
$728$	0	0
$729$	−6.32921e8	−0.0605066
$730$	−1.03457e10	−0.984306
$731$	−2.23742e8	−0.0211854
$732$	−2.13142e9	−0.200854
$733$	7.39982e9	0.693997	0.346998	−	0.937866i	$-0.387201\pi$
$733$	7.39982e9	0.693997	0.346998	+	0.937866i	$0.387201\pi$
$734$	2.19996e9	0.205343
$735$	0	0
$736$	−3.95527e8	−0.0365683
$737$	9.34592e9	0.859975
$738$	3.22212e9	0.295083
$739$	−1.18491e10	−1.08002	−0.540009	−	0.841659i	$-0.681579\pi$
$739$	−1.18491e10	−1.08002	−0.540009	+	0.841659i	$0.681579\pi$
$740$	1.24841e10	1.13252
$741$	1.03691e10	0.936218
$742$	0	0
$743$	4.53308e9	0.405446	0.202723	−	0.979236i	$-0.435021\pi$
$743$	4.53308e9	0.405446	0.202723	+	0.979236i	$0.435021\pi$
$744$	3.56863e9	0.317684
$745$	1.10034e10	0.974942
$746$	−7.16602e9	−0.631964
$747$	1.14646e10	1.00632
$748$	3.57209e9	0.312080
$749$	0	0
$750$	−4.74355e9	−0.410572
$751$	2.17673e10	1.87528	0.937638	−	0.347614i	$-0.113008\pi$
$751$	2.17673e10	1.87528	0.937638	+	0.347614i	$0.113008\pi$
$752$	−3.30364e9	−0.283290
$753$	8.86419e7	0.00756583
$754$	1.64511e8	0.0139764
$755$	1.94824e10	1.64751
$756$	0	0
$757$	2.03442e9	0.170453	0.0852266	−	0.996362i	$-0.472839\pi$
$757$	2.03442e9	0.170453	0.0852266	+	0.996362i	$0.472839\pi$
$758$	−1.35800e10	−1.13255
$759$	−5.59966e9	−0.464853
$760$	5.70216e9	0.471186
$761$	−1.26095e10	−1.03717	−0.518587	−	0.855025i	$-0.673542\pi$
$761$	−1.26095e10	−1.03717	−0.518587	+	0.855025i	$0.673542\pi$
$762$	−8.28657e9	−0.678473
$763$	0	0
$764$	−5.46852e9	−0.443652
$765$	−3.81567e9	−0.308145
$766$	9.99252e9	0.803294
$767$	4.53336e9	0.362774
$768$	−9.86598e8	−0.0785916
$769$	−1.47113e10	−1.16657	−0.583284	−	0.812268i	$-0.698232\pi$
$769$	−1.47113e10	−1.16657	−0.583284	+	0.812268i	$0.698232\pi$
$770$	0	0
$771$	−1.86635e10	−1.46657
$772$	2.87131e9	0.224605
$773$	−5.78606e8	−0.0450562	−0.0225281	−	0.999746i	$-0.507172\pi$
$773$	−5.78606e8	−0.0450562	−0.0225281	+	0.999746i	$0.507172\pi$
$774$	3.21587e8	0.0249290
$775$	1.20765e10	0.931936
$776$	4.40335e9	0.338273
$777$	0	0
$778$	−1.08856e10	−0.828749
$779$	−8.31722e9	−0.630373
$780$	−1.07265e10	−0.809336
$781$	3.64257e10	2.73608
$782$	−6.83194e8	−0.0510882
$783$	1.64875e8	0.0122741
$784$	0	0
$785$	3.30975e9	0.244203
$786$	−2.27694e9	−0.167252
$787$	−3.33278e9	−0.243722	−0.121861	−	0.992547i	$-0.538886\pi$
$787$	−3.33278e9	−0.243722	−0.121861	+	0.992547i	$0.538886\pi$
$788$	−1.26276e10	−0.919345
$789$	−8.03959e9	−0.582726
$790$	−2.34258e10	−1.69044
$791$	0	0
$792$	−5.13421e9	−0.367228
$793$	−3.80429e9	−0.270905
$794$	1.65286e10	1.17183
$795$	1.19594e10	0.844156
$796$	−3.46303e9	−0.243367
$797$	−1.88465e10	−1.31864	−0.659322	−	0.751861i	$-0.729157\pi$
$797$	−1.88465e10	−1.31864	−0.659322	+	0.751861i	$0.729157\pi$
$798$	0	0
$799$	−5.70637e9	−0.395773
$800$	−3.33873e9	−0.230551
$801$	8.91668e9	0.613041
$802$	1.16736e9	0.0799087
$803$	−2.40453e10	−1.63880
$804$	−4.45870e9	−0.302560
$805$	0	0
$806$	6.36950e9	0.428482
$807$	1.10099e10	0.737439
$808$	−3.02262e9	−0.201578
$809$	9.38809e8	0.0623386	0.0311693	−	0.999514i	$-0.490077\pi$
$809$	9.38809e8	0.0623386	0.0311693	+	0.999514i	$0.490077\pi$
$810$	−2.01862e10	−1.33462
$811$	2.78193e10	1.83136	0.915679	−	0.401910i	$-0.131654\pi$
$811$	2.78193e10	1.83136	0.915679	+	0.401910i	$0.131654\pi$
$812$	0	0
$813$	2.67608e10	1.74656
$814$	2.90154e10	1.88557
$815$	2.78933e10	1.80488
$816$	−1.70415e9	−0.109797
$817$	−8.30109e8	−0.0532547
$818$	9.53521e9	0.609107
$819$	0	0
$820$	8.60394e9	0.544940
$821$	−8.54990e9	−0.539212	−0.269606	−	0.962971i	$-0.586894\pi$
$821$	−8.54990e9	−0.539212	−0.269606	+	0.962971i	$0.586894\pi$
$822$	−2.56881e10	−1.61317
$823$	1.28951e10	0.806355	0.403177	−	0.915122i	$-0.367906\pi$
$823$	1.28951e10	0.806355	0.403177	+	0.915122i	$0.367906\pi$
$824$	3.77369e9	0.234975
$825$	−4.72680e10	−2.93075
$826$	0	0
$827$	4.73751e9	0.291260	0.145630	−	0.989339i	$-0.453479\pi$
$827$	4.73751e9	0.291260	0.145630	+	0.989339i	$0.453479\pi$
$828$	9.81964e8	0.0601159
$829$	−1.40766e10	−0.858137	−0.429069	−	0.903272i	$-0.641158\pi$
$829$	−1.40766e10	−0.858137	−0.429069	+	0.903272i	$0.641158\pi$
$830$	3.06137e10	1.85841
$831$	2.91949e10	1.76483
$832$	−1.76094e9	−0.106002
$833$	0	0
$834$	−2.48650e9	−0.148425
$835$	1.02951e10	0.611967
$836$	1.32529e10	0.784491
$837$	6.38361e9	0.376294
$838$	4.71780e9	0.276940
$839$	−1.66762e10	−0.974833	−0.487416	−	0.873170i	$-0.662061\pi$
$839$	−1.66762e10	−0.974833	−0.487416	+	0.873170i	$0.662061\pi$
$840$	0	0
$841$	−1.72405e10	−0.999457
$842$	−1.88777e10	−1.08982
$843$	1.57910e9	0.0907849
$844$	5.91521e9	0.338666
$845$	7.47766e9	0.426351
$846$	8.20185e9	0.465710
$847$	0	0
$848$	1.96333e9	0.110562
$849$	−1.98222e10	−1.11167
$850$	−5.76699e9	−0.322094
$851$	−5.54945e9	−0.308671
$852$	−1.73778e10	−0.962621
$853$	−2.75175e10	−1.51805	−0.759027	−	0.651060i	$-0.774325\pi$
$853$	−2.75175e10	−1.51805	−0.759027	+	0.651060i	$0.774325\pi$
$854$	0	0
$855$	−1.41566e10	−0.774600
$856$	−3.38160e9	−0.184274
$857$	−3.56045e10	−1.93229	−0.966144	−	0.258003i	$-0.916935\pi$
$857$	−3.56045e10	−1.93229	−0.966144	+	0.258003i	$0.916935\pi$
$858$	−2.49304e10	−1.34749
$859$	−1.45758e10	−0.784614	−0.392307	−	0.919834i	$-0.628323\pi$
$859$	−1.45758e10	−0.784614	−0.392307	+	0.919834i	$0.628323\pi$
$860$	8.58725e8	0.0460373
$861$	0	0
$862$	2.06917e10	1.10032
$863$	6.52547e9	0.345600	0.172800	−	0.984957i	$-0.444719\pi$
$863$	6.52547e9	0.345600	0.172800	+	0.984957i	$0.444719\pi$
$864$	−1.76484e9	−0.0930910
$865$	−1.47586e10	−0.775335
$866$	−1.19150e10	−0.623420
$867$	2.11867e10	1.10407
$868$	0	0
$869$	−5.44458e10	−2.81446
$870$	−6.11032e8	−0.0314591
$871$	−7.95816e9	−0.408083
$872$	−1.61055e9	−0.0822556
$873$	−1.09321e10	−0.556099
$874$	−2.53473e9	−0.128423
$875$	0	0
$876$	1.14714e10	0.576569
$877$	3.76944e9	0.188703	0.0943514	−	0.995539i	$-0.469922\pi$
$877$	3.76944e9	0.188703	0.0943514	+	0.995539i	$0.469922\pi$
$878$	−2.13749e10	−1.06579
$879$	−3.32486e10	−1.65125
$880$	−1.37097e10	−0.678172
$881$	6.65654e9	0.327969	0.163985	−	0.986463i	$-0.447565\pi$
$881$	6.65654e9	0.327969	0.163985	+	0.986463i	$0.447565\pi$
$882$	0	0
$883$	−2.18423e10	−1.06767	−0.533834	−	0.845590i	$-0.679249\pi$
$883$	−2.18423e10	−1.06767	−0.533834	+	0.845590i	$0.679249\pi$
$884$	−3.04167e9	−0.148091
$885$	−1.68380e10	−0.816561
$886$	−1.11185e9	−0.0537064
$887$	9.10415e9	0.438033	0.219017	−	0.975721i	$-0.429715\pi$
$887$	9.10415e9	0.438033	0.219017	+	0.975721i	$0.429715\pi$
$888$	−1.38425e10	−0.663389
$889$	0	0
$890$	2.38100e10	1.13212
$891$	−4.69164e10	−2.22204
$892$	2.38694e9	0.112607
$893$	−2.11713e10	−0.994874
$894$	−1.22006e10	−0.571085
$895$	2.71329e10	1.26507
$896$	0	0
$897$	4.76817e9	0.220586
$898$	7.30533e9	0.336646
$899$	3.62836e8	0.0166552
$900$	8.28897e9	0.379011
$901$	3.39125e9	0.154463
$902$	1.99971e10	0.907287
$903$	0	0
$904$	−1.15763e10	−0.521171
$905$	4.38297e10	1.96561
$906$	−2.16022e10	−0.965050
$907$	1.51718e10	0.675167	0.337583	−	0.941296i	$-0.390390\pi$
$907$	1.51718e10	0.675167	0.337583	+	0.941296i	$0.390390\pi$
$908$	7.32104e9	0.324543
$909$	7.50416e9	0.331382
$910$	0	0
$911$	1.48713e10	0.651679	0.325839	−	0.945425i	$-0.394353\pi$
$911$	1.48713e10	0.651679	0.325839	+	0.945425i	$0.394353\pi$
$912$	−6.32260e9	−0.276003
$913$	7.11518e10	3.09413
$914$	6.59356e9	0.285633
$915$	1.41301e10	0.609776
$916$	5.33923e9	0.229533
$917$	0	0
$918$	−3.04841e9	−0.130054
$919$	−3.10812e10	−1.32097	−0.660486	−	0.750838i	$-0.729650\pi$
$919$	−3.10812e10	−1.32097	−0.660486	+	0.750838i	$0.729650\pi$
$920$	2.62211e9	0.111018
$921$	4.19839e10	1.77082
$922$	1.31286e10	0.551647
$923$	−3.10169e10	−1.29835
$924$	0	0
$925$	−4.68441e10	−1.94607
$926$	−2.29750e10	−0.950862
$927$	−9.36883e9	−0.386284
$928$	−1.00311e8	−0.00412032
$929$	2.99578e10	1.22590	0.612950	−	0.790121i	$-0.289983\pi$
$929$	2.99578e10	1.22590	0.612950	+	0.790121i	$0.289983\pi$
$930$	−2.36579e10	−0.964462
$931$	0	0
$932$	−1.95535e9	−0.0791170
$933$	2.68656e10	1.08296
$934$	2.35512e10	0.945800
$935$	−2.36808e10	−0.947449
$936$	4.37184e9	0.174260
$937$	1.75637e10	0.697473	0.348736	−	0.937221i	$-0.386611\pi$
$937$	1.75637e10	0.697473	0.348736	+	0.937221i	$0.386611\pi$
$938$	0	0
$939$	5.64618e10	2.22549
$940$	2.19012e10	0.860042
$941$	1.73824e10	0.680059	0.340029	−	0.940415i	$-0.389563\pi$
$941$	1.73824e10	0.680059	0.340029	+	0.940415i	$0.389563\pi$
$942$	−3.66988e9	−0.143045
$943$	−3.82463e9	−0.148525
$944$	−2.76424e9	−0.106948
$945$	0	0
$946$	1.99583e9	0.0766488
$947$	4.01637e10	1.53677	0.768385	−	0.639988i	$-0.221061\pi$
$947$	4.01637e10	1.53677	0.768385	+	0.639988i	$0.221061\pi$
$948$	2.59747e10	0.990196
$949$	2.04748e10	0.777658
$950$	−2.13962e10	−0.809663
$951$	3.38653e10	1.27680
$952$	0	0
$953$	3.96693e10	1.48467	0.742335	−	0.670029i	$-0.233718\pi$
$953$	3.96693e10	1.48467	0.742335	+	0.670029i	$0.233718\pi$
$954$	−4.87430e9	−0.181758
$955$	3.62530e10	1.34689
$956$	3.42654e8	0.0126839
$957$	−1.42015e9	−0.0523773
$958$	6.71112e9	0.246613
$959$	0	0
$960$	6.54056e9	0.238597
$961$	−1.34644e10	−0.489390
$962$	−2.47069e10	−0.894757
$963$	8.39540e9	0.302935
$964$	1.18735e10	0.426884
$965$	−1.90350e10	−0.681880
$966$	0	0
$967$	3.37872e10	1.20160	0.600800	−	0.799400i	$-0.294849\pi$
$967$	3.37872e10	1.20160	0.600800	+	0.799400i	$0.294849\pi$
$968$	−2.18865e10	−0.775555
$969$	−1.09210e10	−0.385594
$970$	−2.91916e10	−1.02697
$971$	1.55541e10	0.545227	0.272613	−	0.962124i	$-0.412112\pi$
$971$	1.55541e10	0.545227	0.272613	+	0.962124i	$0.412112\pi$
$972$	1.48441e10	0.518467
$973$	0	0
$974$	−1.96269e9	−0.0680606
$975$	4.02492e10	1.39072
$976$	2.31968e9	0.0798646
$977$	−2.02929e8	−0.00696167	−0.00348083	−	0.999994i	$-0.501108\pi$
$977$	−2.02929e8	−0.00696167	−0.00348083	+	0.999994i	$0.501108\pi$
$978$	−3.09283e10	−1.05723
$979$	5.53387e10	1.88490
$980$	0	0
$981$	3.99846e9	0.135223
$982$	3.89222e10	1.31162
$983$	−4.56894e10	−1.53418	−0.767092	−	0.641537i	$-0.778297\pi$
$983$	−4.56894e10	−1.53418	−0.767092	+	0.641537i	$0.778297\pi$
$984$	−9.54011e9	−0.319206
$985$	8.37134e10	2.79105
$986$	−1.73267e8	−0.00575635
$987$	0	0
$988$	−1.12850e10	−0.372264
$989$	−3.81721e8	−0.0125476
$990$	3.40368e10	1.11487
$991$	−1.11948e10	−0.365393	−0.182696	−	0.983169i	$-0.558482\pi$
$991$	−1.11948e10	−0.365393	−0.182696	+	0.983169i	$0.558482\pi$
$992$	−3.88383e9	−0.126319
$993$	2.62670e10	0.851312
$994$	0	0
$995$	2.29579e10	0.738840
$996$	−3.39447e10	−1.08859
$997$	−1.81656e10	−0.580518	−0.290259	−	0.956948i	$-0.593742\pi$
$997$	−1.81656e10	−0.580518	−0.290259	+	0.956948i	$0.593742\pi$
$998$	−1.50646e10	−0.479734
$999$	−2.47616e10	−0.785777

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	98.8.a.d.1.1		2
7.2	even	3		98.8.c.m.67.2		4
7.3	odd	6		14.8.c.b.9.1	✓	4
7.4	even	3		98.8.c.m.79.2		4
7.5	odd	6		14.8.c.b.11.1	yes	4
7.6	odd	2		98.8.a.f.1.2		2
21.5	even	6		126.8.g.d.109.2		4
21.17	even	6		126.8.g.d.37.2		4
28.3	even	6		112.8.i.b.65.2		4
28.19	even	6		112.8.i.b.81.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.8.c.b.9.1	✓	4	7.3	odd	6
14.8.c.b.11.1	yes	4	7.5	odd	6
98.8.a.d.1.1		2	1.1	even	1	trivial
98.8.a.f.1.2		2	7.6	odd	2
98.8.c.m.67.2		4	7.2	even	3
98.8.c.m.79.2		4	7.4	even	3
112.8.i.b.65.2		4	28.3	even	6
112.8.i.b.81.2		4	28.19	even	6
126.8.g.d.37.2		4	21.17	even	6
126.8.g.d.109.2		4	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:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	98.a (trivial)

\(f(q)\)	\(=\)	\(q-8.00000 q^{2} -58.8058 q^{3} +64.0000 q^{4} -424.282 q^{5} +470.447 q^{6} -512.000 q^{8} +1271.13 q^{9} +3394.25 q^{10} +7888.87 q^{11} -3763.57 q^{12} -6717.46 q^{13} +24950.2 q^{15} +4096.00 q^{16} +7075.01 q^{17} -10169.0 q^{18} +26249.2 q^{19} -27154.0 q^{20} -63110.9 q^{22} +12070.5 q^{23} +30108.6 q^{24} +101890. q^{25} +53739.7 q^{26} +53858.7 q^{27} +3061.25 q^{29} -199602. q^{30} +118525. q^{31} -32768.0 q^{32} -463912. q^{33} -56600.1 q^{34} +81352.1 q^{36} -459752. q^{37} -209993. q^{38} +395026. q^{39} +217232. q^{40} -316857. q^{41} -31624.2 q^{43} +504888. q^{44} -539316. q^{45} -96564.3 q^{46} -806553. q^{47} -240869. q^{48} -815120. q^{50} -416052. q^{51} -429917. q^{52} +479328. q^{53} -430869. q^{54} -3.34710e6 q^{55} -1.54360e6 q^{57} -24490.0 q^{58} -674863. q^{59} +1.59682e6 q^{60} +566329. q^{61} -948201. q^{62} +262144. q^{64} +2.85009e6 q^{65} +3.71129e6 q^{66} +1.18470e6 q^{67} +452801. q^{68} -709818. q^{69} +4.61736e6 q^{71} -650817. q^{72} -3.04800e6 q^{73} +3.67801e6 q^{74} -5.99173e6 q^{75} +1.67995e6 q^{76} -3.16021e6 q^{78} -6.90160e6 q^{79} -1.73786e6 q^{80} -5.94716e6 q^{81} +2.53485e6 q^{82} +9.01927e6 q^{83} -3.00180e6 q^{85} +252994. q^{86} -180020. q^{87} -4.03910e6 q^{88} +7.01478e6 q^{89} +4.31453e6 q^{90} +772515. q^{92} -6.96997e6 q^{93} +6.45243e6 q^{94} -1.11370e7 q^{95} +1.92695e6 q^{96} -8.60029e6 q^{97} +1.00278e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 16 q^{2} - 56 q^{3} + 128 q^{4} + 14 q^{5} + 448 q^{6} - 1024 q^{8} - 908 q^{9} - 112 q^{10} + 2408 q^{11} - 3584 q^{12} - 10724 q^{13} + 26180 q^{15} + 8192 q^{16} + 35098 q^{17} + 7264 q^{18} + 2408 q^{19}+ \cdots + 21971264 q^{99}+O(q^{100}) \) 2 * q - 16 * q^2 - 56 * q^3 + 128 * q^4 + 14 * q^5 + 448 * q^6 - 1024 * q^8 - 908 * q^9 - 112 * q^10 + 2408 * q^11 - 3584 * q^12 - 10724 * q^13 + 26180 * q^15 + 8192 * q^16 + 35098 * q^17 + 7264 * q^18 + 2408 * q^19 + 896 * q^20 - 19264 * q^22 - 61684 * q^23 + 28672 * q^24 + 215856 * q^25 + 85792 * q^26 + 41608 * q^27 - 95660 * q^29 - 209440 * q^30 + 166012 * q^31 - 65536 * q^32 - 479290 * q^33 - 280784 * q^34 - 58112 * q^36 - 559814 * q^37 - 19264 * q^38 + 383784 * q^39 - 7168 * q^40 - 805980 * q^41 + 267976 * q^43 + 154112 * q^44 - 1494388 * q^45 + 493472 * q^46 - 1769292 * q^47 - 229376 * q^48 - 1726848 * q^50 - 337424 * q^51 - 686336 * q^52 + 2317194 * q^53 - 332864 * q^54 - 5749268 * q^55 - 1610498 * q^57 + 765280 * q^58 - 660352 * q^59 + 1675520 * q^60 - 1463042 * q^61 - 1328096 * q^62 + 524288 * q^64 + 1094100 * q^65 + 3834320 * q^66 - 1784280 * q^67 + 2246272 * q^68 - 916762 * q^69 + 274400 * q^71 + 464896 * q^72 - 4549062 * q^73 + 4478512 * q^74 - 5671960 * q^75 + 154112 * q^76 - 3070272 * q^78 - 8673964 * q^79 + 57344 * q^80 - 1215782 * q^81 + 6447840 * q^82 + 10594360 * q^83 + 9280166 * q^85 - 2143808 * q^86 - 457016 * q^87 - 1232896 * q^88 - 1779750 * q^89 + 11955104 * q^90 - 3947776 * q^92 - 6836730 * q^93 + 14154336 * q^94 - 21586180 * q^95 + 1835008 * q^96 + 1748964 * q^97 + 21971264 * q^99

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