LMFDB - Embedded newform 150.8.a.s.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [150,8,Mod(1,150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(150, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("150.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 150 = 2 \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	150.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	yes
Analytic conductor:	$46.8577538226$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{2641}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 660 $ x^2 - x - 660
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2}\cdot 5 $
Twist minimal:	no (minimal twist has level 30)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-25.1953$ of defining polynomial
Character	$\chi$	$=$	150.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} -216.000 q^{6} +1309.81 q^{7} +512.000 q^{8} +729.000 q^{9} -5457.35 q^{11} -1728.00 q^{12} +5237.72 q^{13} +10478.5 q^{14} +4096.00 q^{16} +4870.92 q^{17} +5832.00 q^{18} +32781.2 q^{19} -35365.0 q^{21} -43658.8 q^{22} -83486.0 q^{23} -13824.0 q^{24} +41901.8 q^{26} -19683.0 q^{27} +83828.0 q^{28} -73409.7 q^{29} +244719. q^{31} +32768.0 q^{32} +147348. q^{33} +38967.3 q^{34} +46656.0 q^{36} +107537. q^{37} +262250. q^{38} -141418. q^{39} +396774. q^{41} -282920. q^{42} +725839. q^{43} -349270. q^{44} -667888. q^{46} +801478. q^{47} -110592. q^{48} +892068. q^{49} -131515. q^{51} +335214. q^{52} -1.22395e6 q^{53} -157464. q^{54} +670624. q^{56} -885092. q^{57} -587278. q^{58} +2.32931e6 q^{59} +2.63553e6 q^{61} +1.95775e6 q^{62} +954854. q^{63} +262144. q^{64} +1.17879e6 q^{66} -209887. q^{67} +311739. q^{68} +2.25412e6 q^{69} +3.76578e6 q^{71} +373248. q^{72} +2.81943e6 q^{73} +860298. q^{74} +2.09800e6 q^{76} -7.14810e6 q^{77} -1.13135e6 q^{78} -8.68583e6 q^{79} +531441. q^{81} +3.17419e6 q^{82} -5.77317e6 q^{83} -2.26336e6 q^{84} +5.80672e6 q^{86} +1.98206e6 q^{87} -2.79416e6 q^{88} +1.02714e7 q^{89} +6.86043e6 q^{91} -5.34310e6 q^{92} -6.60742e6 q^{93} +6.41183e6 q^{94} -884736. q^{96} -5.19683e6 q^{97} +7.13654e6 q^{98} -3.97841e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 16 q^{2} - 54 q^{3} + 128 q^{4} - 432 q^{6} + 564 q^{7} + 1024 q^{8} + 1458 q^{9} - 3720 q^{11} - 3456 q^{12} + 7392 q^{13} + 4512 q^{14} + 8192 q^{16} - 24176 q^{17} + 11664 q^{18} + 34728 q^{19}+ \cdots - 2711880 q^{99}+O(q^{100}) $ 2 * q + 16 * q^2 - 54 * q^3 + 128 * q^4 - 432 * q^6 + 564 * q^7 + 1024 * q^8 + 1458 * q^9 - 3720 * q^11 - 3456 * q^12 + 7392 * q^13 + 4512 * q^14 + 8192 * q^16 - 24176 * q^17 + 11664 * q^18 + 34728 * q^19 - 15228 * q^21 - 29760 * q^22 - 12800 * q^23 - 27648 * q^24 + 59136 * q^26 - 39366 * q^27 + 36096 * q^28 + 186192 * q^29 + 218096 * q^31 + 65536 * q^32 + 100440 * q^33 - 193408 * q^34 + 93312 * q^36 + 382608 * q^37 + 277824 * q^38 - 199584 * q^39 + 304308 * q^41 - 121824 * q^42 + 1048776 * q^43 - 238080 * q^44 - 102400 * q^46 + 351080 * q^47 - 221184 * q^48 + 624762 * q^49 + 652752 * q^51 + 473088 * q^52 + 139104 * q^53 - 314928 * q^54 + 288768 * q^56 - 937656 * q^57 + 1489536 * q^58 + 4558920 * q^59 + 5986420 * q^61 + 1744768 * q^62 + 411156 * q^63 + 524288 * q^64 + 803520 * q^66 + 1968864 * q^67 - 1547264 * q^68 + 345600 * q^69 + 9079440 * q^71 + 746496 * q^72 - 3231168 * q^73 + 3060864 * q^74 + 2222592 * q^76 - 8443840 * q^77 - 1596672 * q^78 - 1979136 * q^79 + 1062882 * q^81 + 2434464 * q^82 - 9881288 * q^83 - 974592 * q^84 + 8390208 * q^86 - 5027184 * q^87 - 1904640 * q^88 + 7793724 * q^89 + 5253744 * q^91 - 819200 * q^92 - 5888592 * q^93 + 2808640 * q^94 - 1769472 * q^96 - 10989792 * q^97 + 4998096 * q^98 - 2711880 * 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
$3$	−27.0000	−0.577350
$3$	−27.0000	−0.577350
$4$	64.0000	0.500000
$5$	0	0
$5$	0	0
$6$	−216.000	−0.408248
$7$	1309.81	1.44333	0.721666	−	0.692241i	$-0.243377\pi$
$7$	1309.81	1.44333	0.721666	+	0.692241i	$0.243377\pi$
$8$	512.000	0.353553
$9$	729.000	0.333333
$10$	0	0
$11$	−5457.35	−1.23625	−0.618126	−	0.786079i	$-0.712108\pi$
$11$	−5457.35	−1.23625	−0.618126	+	0.786079i	$0.712108\pi$
$12$	−1728.00	−0.288675
$13$	5237.72	0.661212	0.330606	−	0.943769i	$-0.392747\pi$
$13$	5237.72	0.661212	0.330606	+	0.943769i	$0.392747\pi$
$14$	10478.5	1.02059
$15$	0	0
$16$	4096.00	0.250000
$17$	4870.92	0.240458	0.120229	−	0.992746i	$-0.461637\pi$
$17$	4870.92	0.240458	0.120229	+	0.992746i	$0.461637\pi$
$18$	5832.00	0.235702
$19$	32781.2	1.09645	0.548223	−	0.836332i	$-0.315305\pi$
$19$	32781.2	1.09645	0.548223	+	0.836332i	$0.315305\pi$
$20$	0	0
$21$	−35365.0	−0.833308
$22$	−43658.8	−0.874162
$23$	−83486.0	−1.43076	−0.715379	−	0.698737i	$-0.753746\pi$
$23$	−83486.0	−1.43076	−0.715379	+	0.698737i	$0.753746\pi$
$24$	−13824.0	−0.204124
$25$	0	0
$26$	41901.8	0.467547
$27$	−19683.0	−0.192450
$28$	83828.0	0.721666
$29$	−73409.7	−0.558934	−0.279467	−	0.960155i	$-0.590158\pi$
$29$	−73409.7	−0.558934	−0.279467	+	0.960155i	$0.590158\pi$
$30$	0	0
$31$	244719.	1.47537	0.737687	−	0.675142i	$-0.235918\pi$
$31$	244719.	1.47537	0.737687	+	0.675142i	$0.235918\pi$
$32$	32768.0	0.176777
$33$	147348.	0.713751
$34$	38967.3	0.170030
$35$	0	0
$36$	46656.0	0.166667
$37$	107537.	0.349022	0.174511	−	0.984655i	$-0.444166\pi$
$37$	107537.	0.349022	0.174511	+	0.984655i	$0.444166\pi$
$38$	262250.	0.775304
$39$	−141418.	−0.381751
$40$	0	0
$41$	396774.	0.899082	0.449541	−	0.893260i	$-0.351588\pi$
$41$	396774.	0.899082	0.449541	+	0.893260i	$0.351588\pi$
$42$	−282920.	−0.589238
$43$	725839.	1.39220	0.696099	−	0.717946i	$-0.254918\pi$
$43$	725839.	1.39220	0.696099	+	0.717946i	$0.254918\pi$
$44$	−349270.	−0.618126
$45$	0	0
$46$	−667888.	−1.01170
$47$	801478.	1.12603	0.563014	−	0.826447i	$-0.309642\pi$
$47$	801478.	1.12603	0.563014	+	0.826447i	$0.309642\pi$
$48$	−110592.	−0.144338
$49$	892068.	1.08321
$50$	0	0
$51$	−131515.	−0.138829
$52$	335214.	0.330606
$53$	−1.22395e6	−1.12927	−0.564636	−	0.825340i	$-0.690983\pi$
$53$	−1.22395e6	−1.12927	−0.564636	+	0.825340i	$0.690983\pi$
$54$	−157464.	−0.136083
$55$	0	0
$56$	670624.	0.510295
$57$	−885092.	−0.633033
$58$	−587278.	−0.395226
$59$	2.32931e6	1.47654	0.738270	−	0.674506i	$-0.235643\pi$
$59$	2.32931e6	1.47654	0.738270	+	0.674506i	$0.235643\pi$
$60$	0	0
$61$	2.63553e6	1.48667	0.743334	−	0.668921i	$-0.233244\pi$
$61$	2.63553e6	1.48667	0.743334	+	0.668921i	$0.233244\pi$
$62$	1.95775e6	1.04325
$63$	954854.	0.481111
$64$	262144.	0.125000
$65$	0	0
$66$	1.17879e6	0.504698
$67$	−209887.	−0.0852557	−0.0426279	−	0.999091i	$-0.513573\pi$
$67$	−209887.	−0.0852557	−0.0426279	+	0.999091i	$0.513573\pi$
$68$	311739.	0.120229
$69$	2.25412e6	0.826049
$70$	0	0
$71$	3.76578e6	1.24868	0.624339	−	0.781154i	$-0.285368\pi$
$71$	3.76578e6	1.24868	0.624339	+	0.781154i	$0.285368\pi$
$72$	373248.	0.117851
$73$	2.81943e6	0.848265	0.424132	−	0.905600i	$-0.360579\pi$
$73$	2.81943e6	0.848265	0.424132	+	0.905600i	$0.360579\pi$
$74$	860298.	0.246796
$75$	0	0
$76$	2.09800e6	0.548223
$77$	−7.14810e6	−1.78432
$78$	−1.13135e6	−0.269939
$79$	−8.68583e6	−1.98206	−0.991030	−	0.133642i	$-0.957333\pi$
$79$	−8.68583e6	−1.98206	−0.991030	+	0.133642i	$0.957333\pi$
$80$	0	0
$81$	531441.	0.111111
$82$	3.17419e6	0.635747
$83$	−5.77317e6	−1.10826	−0.554129	−	0.832431i	$-0.686949\pi$
$83$	−5.77317e6	−1.10826	−0.554129	+	0.832431i	$0.686949\pi$
$84$	−2.26336e6	−0.416654
$85$	0	0
$86$	5.80672e6	0.984432
$87$	1.98206e6	0.322701
$88$	−2.79416e6	−0.437081
$89$	1.02714e7	1.54441	0.772206	−	0.635373i	$-0.219154\pi$
$89$	1.02714e7	1.54441	0.772206	+	0.635373i	$0.219154\pi$
$90$	0	0
$91$	6.86043e6	0.954348
$92$	−5.34310e6	−0.715379
$93$	−6.60742e6	−0.851808
$94$	6.41183e6	0.796222
$95$	0	0
$96$	−884736.	−0.102062
$97$	−5.19683e6	−0.578146	−0.289073	−	0.957307i	$-0.593347\pi$
$97$	−5.19683e6	−0.578146	−0.289073	+	0.957307i	$0.593347\pi$
$98$	7.13654e6	0.765943
$99$	−3.97841e6	−0.412084
$100$	0	0
$101$	2.84866e6	0.275116	0.137558	−	0.990494i	$-0.456075\pi$
$101$	2.84866e6	0.275116	0.137558	+	0.990494i	$0.456075\pi$
$102$	−1.05212e6	−0.0981666
$103$	−1.49365e7	−1.34685	−0.673423	−	0.739257i	$-0.735177\pi$
$103$	−1.49365e7	−1.34685	−0.673423	+	0.739257i	$0.735177\pi$
$104$	2.68171e6	0.233774
$105$	0	0
$106$	−9.79161e6	−0.798516
$107$	−1.04317e6	−0.0823213	−0.0411606	−	0.999153i	$-0.513106\pi$
$107$	−1.04317e6	−0.0823213	−0.0411606	+	0.999153i	$0.513106\pi$
$108$	−1.25971e6	−0.0962250
$109$	5.23084e6	0.386882	0.193441	−	0.981112i	$-0.438035\pi$
$109$	5.23084e6	0.386882	0.193441	+	0.981112i	$0.438035\pi$
$110$	0	0
$111$	−2.90351e6	−0.201508
$112$	5.36499e6	0.360833
$113$	1.58182e7	1.03130	0.515649	−	0.856800i	$-0.327551\pi$
$113$	1.58182e7	1.03130	0.515649	+	0.856800i	$0.327551\pi$
$114$	−7.08074e6	−0.447622
$115$	0	0
$116$	−4.69822e6	−0.279467
$117$	3.81830e6	0.220404
$118$	1.86345e7	1.04407
$119$	6.37999e6	0.347061
$120$	0	0
$121$	1.02955e7	0.528320
$122$	2.10842e7	1.05123
$123$	−1.07129e7	−0.519085
$124$	1.56620e7	0.737687
$125$	0	0
$126$	7.63883e6	0.340197
$127$	4.24970e6	0.184096	0.0920481	−	0.995755i	$-0.470659\pi$
$127$	4.24970e6	0.184096	0.0920481	+	0.995755i	$0.470659\pi$
$128$	2.09715e6	0.0883883
$129$	−1.95977e7	−0.803786
$130$	0	0
$131$	5.59155e6	0.217312	0.108656	−	0.994079i	$-0.465345\pi$
$131$	5.59155e6	0.217312	0.108656	+	0.994079i	$0.465345\pi$
$132$	9.43029e6	0.356875
$133$	4.29372e7	1.58254
$134$	−1.67910e6	−0.0602849
$135$	0	0
$136$	2.49391e6	0.0850148
$137$	−2.21174e7	−0.734874	−0.367437	−	0.930048i	$-0.619765\pi$
$137$	−2.21174e7	−0.734874	−0.367437	+	0.930048i	$0.619765\pi$
$138$	1.80330e7	0.584105
$139$	−2.55140e7	−0.805799	−0.402900	−	0.915244i	$-0.631998\pi$
$139$	−2.55140e7	−0.805799	−0.402900	+	0.915244i	$0.631998\pi$
$140$	0	0
$141$	−2.16399e7	−0.650113
$142$	3.01262e7	0.882948
$143$	−2.85841e7	−0.817424
$144$	2.98598e6	0.0833333
$145$	0	0
$146$	2.25554e7	0.599814
$147$	−2.40858e7	−0.625390
$148$	6.88238e6	0.174511
$149$	−1.64001e6	−0.0406158	−0.0203079	−	0.999794i	$-0.506465\pi$
$149$	−1.64001e6	−0.0406158	−0.0203079	+	0.999794i	$0.506465\pi$
$150$	0	0
$151$	−4.65795e7	−1.10097	−0.550485	−	0.834845i	$-0.685557\pi$
$151$	−4.65795e7	−1.10097	−0.550485	+	0.834845i	$0.685557\pi$
$152$	1.67840e7	0.387652
$153$	3.55090e6	0.0801527
$154$	−5.71848e7	−1.26171
$155$	0	0
$156$	−9.05078e6	−0.190875
$157$	−6.21860e7	−1.28246	−0.641230	−	0.767349i	$-0.721575\pi$
$157$	−6.21860e7	−1.28246	−0.641230	+	0.767349i	$0.721575\pi$
$158$	−6.94867e7	−1.40153
$159$	3.30467e7	0.651985
$160$	0	0
$161$	−1.09351e8	−2.06506
$162$	4.25153e6	0.0785674
$163$	5.86864e7	1.06140	0.530702	−	0.847558i	$-0.321928\pi$
$163$	5.86864e7	1.06140	0.530702	+	0.847558i	$0.321928\pi$
$164$	2.53935e7	0.449541
$165$	0	0
$166$	−4.61854e7	−0.783657
$167$	2.74875e7	0.456696	0.228348	−	0.973580i	$-0.426668\pi$
$167$	2.74875e7	0.456696	0.228348	+	0.973580i	$0.426668\pi$
$168$	−1.81069e7	−0.294619
$169$	−3.53148e7	−0.562799
$170$	0	0
$171$	2.38975e7	0.365482
$172$	4.64537e7	0.696099
$173$	−6.19491e7	−0.909649	−0.454825	−	0.890581i	$-0.650298\pi$
$173$	−6.19491e7	−0.909649	−0.454825	+	0.890581i	$0.650298\pi$
$174$	1.58565e7	0.228184
$175$	0	0
$176$	−2.23533e7	−0.309063
$177$	−6.28913e7	−0.852480
$178$	8.21709e7	1.09206
$179$	1.04816e7	0.136598	0.0682988	−	0.997665i	$-0.478243\pi$
$179$	1.04816e7	0.136598	0.0682988	+	0.997665i	$0.478243\pi$
$180$	0	0
$181$	−9.64546e7	−1.20906	−0.604530	−	0.796582i	$-0.706639\pi$
$181$	−9.64546e7	−1.20906	−0.604530	+	0.796582i	$0.706639\pi$
$182$	5.48835e7	0.674826
$183$	−7.11593e7	−0.858328
$184$	−4.27448e7	−0.505849
$185$	0	0
$186$	−5.28594e7	−0.602319
$187$	−2.65823e7	−0.297267
$188$	5.12946e7	0.563014
$189$	−2.57811e7	−0.277769
$190$	0	0
$191$	9.71449e7	1.00880	0.504398	−	0.863471i	$-0.331714\pi$
$191$	9.71449e7	1.00880	0.504398	+	0.863471i	$0.331714\pi$
$192$	−7.07789e6	−0.0721688
$193$	−5.17514e7	−0.518169	−0.259085	−	0.965855i	$-0.583421\pi$
$193$	−5.17514e7	−0.518169	−0.259085	+	0.965855i	$0.583421\pi$
$194$	−4.15746e7	−0.408811
$195$	0	0
$196$	5.70923e7	0.541604
$197$	−1.55737e8	−1.45131	−0.725657	−	0.688057i	$-0.758464\pi$
$197$	−1.55737e8	−1.45131	−0.725657	+	0.688057i	$0.758464\pi$
$198$	−3.18272e7	−0.291387
$199$	1.49558e8	1.34532	0.672658	−	0.739954i	$-0.265153\pi$
$199$	1.49558e8	1.34532	0.672658	+	0.739954i	$0.265153\pi$
$200$	0	0
$201$	5.66695e6	0.0492224
$202$	2.27892e7	0.194536
$203$	−9.61530e7	−0.806728
$204$	−8.41695e6	−0.0694143
$205$	0	0
$206$	−1.19492e8	−0.952364
$207$	−6.08613e7	−0.476919
$208$	2.14537e7	0.165303
$209$	−1.78898e8	−1.35548
$210$	0	0
$211$	−4.83513e6	−0.0354340	−0.0177170	−	0.999843i	$-0.505640\pi$
$211$	−4.83513e6	−0.0354340	−0.0177170	+	0.999843i	$0.505640\pi$
$212$	−7.83329e7	−0.564636
$213$	−1.01676e8	−0.720924
$214$	−8.34536e6	−0.0582099
$215$	0	0
$216$	−1.00777e7	−0.0680414
$217$	3.20537e8	2.12946
$218$	4.18467e7	0.273567
$219$	−7.61246e7	−0.489746
$220$	0	0
$221$	2.55125e7	0.158994
$222$	−2.32280e7	−0.142488
$223$	2.61843e8	1.58116	0.790578	−	0.612361i	$-0.209780\pi$
$223$	2.61843e8	1.58116	0.790578	+	0.612361i	$0.209780\pi$
$224$	4.29200e7	0.255147
$225$	0	0
$226$	1.26546e8	0.729237
$227$	−1.28619e8	−0.729820	−0.364910	−	0.931043i	$-0.618900\pi$
$227$	−1.28619e8	−0.729820	−0.364910	+	0.931043i	$0.618900\pi$
$228$	−5.66459e7	−0.316517
$229$	1.01465e8	0.558330	0.279165	−	0.960243i	$-0.409942\pi$
$229$	1.01465e8	0.558330	0.279165	+	0.960243i	$0.409942\pi$
$230$	0	0
$231$	1.92999e8	1.03018
$232$	−3.75858e7	−0.197613
$233$	−2.74718e8	−1.42279	−0.711397	−	0.702791i	$-0.751937\pi$
$233$	−2.74718e8	−1.42279	−0.711397	+	0.702791i	$0.751937\pi$
$234$	3.05464e7	0.155849
$235$	0	0
$236$	1.49076e8	0.738270
$237$	2.34518e8	1.14434
$238$	5.10399e7	0.245409
$239$	−3.77861e7	−0.179035	−0.0895177	−	0.995985i	$-0.528533\pi$
$239$	−3.77861e7	−0.179035	−0.0895177	+	0.995985i	$0.528533\pi$
$240$	0	0
$241$	1.70494e8	0.784600	0.392300	−	0.919837i	$-0.371680\pi$
$241$	1.70494e8	0.784600	0.392300	+	0.919837i	$0.371680\pi$
$242$	8.23637e7	0.373578
$243$	−1.43489e7	−0.0641500
$244$	1.68674e8	0.743334
$245$	0	0
$246$	−8.57031e7	−0.367049
$247$	1.71699e8	0.724983
$248$	1.25296e8	0.521624
$249$	1.55876e8	0.639854
$250$	0	0
$251$	−3.41080e8	−1.36144	−0.680719	−	0.732544i	$-0.738333\pi$
$251$	−3.41080e8	−1.36144	−0.680719	+	0.732544i	$0.738333\pi$
$252$	6.11106e7	0.240555
$253$	4.55612e8	1.76878
$254$	3.39976e7	0.130176
$255$	0	0
$256$	1.67772e7	0.0625000
$257$	−1.94713e8	−0.715530	−0.357765	−	0.933812i	$-0.616461\pi$
$257$	−1.94713e8	−0.715530	−0.357765	+	0.933812i	$0.616461\pi$
$258$	−1.56781e8	−0.568362
$259$	1.40854e8	0.503755
$260$	0	0
$261$	−5.35157e7	−0.186311
$262$	4.47324e7	0.153663
$263$	4.85601e8	1.64602	0.823009	−	0.568029i	$-0.192294\pi$
$263$	4.85601e8	1.64602	0.823009	+	0.568029i	$0.192294\pi$
$264$	7.54424e7	0.252349
$265$	0	0
$266$	3.43498e8	1.11902
$267$	−2.77327e8	−0.891666
$268$	−1.34328e7	−0.0426279
$269$	−2.89744e7	−0.0907572	−0.0453786	−	0.998970i	$-0.514449\pi$
$269$	−2.89744e7	−0.0907572	−0.0453786	+	0.998970i	$0.514449\pi$
$270$	0	0
$271$	3.02460e8	0.923156	0.461578	−	0.887100i	$-0.347283\pi$
$271$	3.02460e8	0.923156	0.461578	+	0.887100i	$0.347283\pi$
$272$	1.99513e7	0.0601146
$273$	−1.85232e8	−0.550993
$274$	−1.76939e8	−0.519634
$275$	0	0
$276$	1.44264e8	0.413024
$277$	−1.78252e8	−0.503912	−0.251956	−	0.967739i	$-0.581074\pi$
$277$	−1.78252e8	−0.503912	−0.251956	+	0.967739i	$0.581074\pi$
$278$	−2.04112e8	−0.569786
$279$	1.78400e8	0.491792
$280$	0	0
$281$	2.21487e7	0.0595492	0.0297746	−	0.999557i	$-0.490521\pi$
$281$	2.21487e7	0.0595492	0.0297746	+	0.999557i	$0.490521\pi$
$282$	−1.73119e8	−0.459699
$283$	1.08099e8	0.283511	0.141756	−	0.989902i	$-0.454725\pi$
$283$	1.08099e8	0.283511	0.141756	+	0.989902i	$0.454725\pi$
$284$	2.41010e8	0.624339
$285$	0	0
$286$	−2.28672e8	−0.578006
$287$	5.19699e8	1.29767
$288$	2.38879e7	0.0589256
$289$	−3.86613e8	−0.942180
$290$	0	0
$291$	1.40314e8	0.333793
$292$	1.80444e8	0.424132
$293$	−5.08345e8	−1.18065	−0.590326	−	0.807165i	$-0.701001\pi$
$293$	−5.08345e8	−1.18065	−0.590326	+	0.807165i	$0.701001\pi$
$294$	−1.92687e8	−0.442217
$295$	0	0
$296$	5.50591e7	0.123398
$297$	1.07417e8	0.237917
$298$	−1.31201e7	−0.0287197
$299$	−4.37276e8	−0.946034
$300$	0	0
$301$	9.50714e8	2.00940
$302$	−3.72636e8	−0.778503
$303$	−7.69137e7	−0.158838
$304$	1.34272e8	0.274111
$305$	0	0
$306$	2.84072e7	0.0566765
$307$	−4.60852e8	−0.909027	−0.454514	−	0.890740i	$-0.650187\pi$
$307$	−4.60852e8	−0.909027	−0.454514	+	0.890740i	$0.650187\pi$
$308$	−4.57479e8	−0.892161
$309$	4.03285e8	0.777602
$310$	0	0
$311$	7.63906e8	1.44005	0.720027	−	0.693946i	$-0.244129\pi$
$311$	7.63906e8	1.44005	0.720027	+	0.693946i	$0.244129\pi$
$312$	−7.24062e7	−0.134969
$313$	4.96971e8	0.916064	0.458032	−	0.888936i	$-0.348554\pi$
$313$	4.96971e8	0.916064	0.458032	+	0.888936i	$0.348554\pi$
$314$	−4.97488e8	−0.906836
$315$	0	0
$316$	−5.55893e8	−0.991030
$317$	4.18865e8	0.738528	0.369264	−	0.929325i	$-0.379610\pi$
$317$	4.18865e8	0.738528	0.369264	+	0.929325i	$0.379610\pi$
$318$	2.64373e8	0.461023
$319$	4.00622e8	0.690984
$320$	0	0
$321$	2.81656e7	0.0475282
$322$	−8.74808e8	−1.46022
$323$	1.59675e8	0.263649
$324$	3.40122e7	0.0555556
$325$	0	0
$326$	4.69491e8	0.750527
$327$	−1.41233e8	−0.223366
$328$	2.03148e8	0.317873
$329$	1.04979e9	1.62523
$330$	0	0
$331$	−8.00262e8	−1.21293	−0.606463	−	0.795112i	$-0.707412\pi$
$331$	−8.00262e8	−1.21293	−0.606463	+	0.795112i	$0.707412\pi$
$332$	−3.69483e8	−0.554129
$333$	7.83946e7	0.116341
$334$	2.19900e8	0.322933
$335$	0	0
$336$	−1.44855e8	−0.208327
$337$	1.38535e9	1.97177	0.985883	−	0.167437i	$-0.0535491\pi$
$337$	1.38535e9	1.97177	0.985883	+	0.167437i	$0.0535491\pi$
$338$	−2.82518e8	−0.397959
$339$	−4.27093e8	−0.595420
$340$	0	0
$341$	−1.33552e9	−1.82394
$342$	1.91180e8	0.258435
$343$	8.97545e7	0.120096
$344$	3.71630e8	0.492216
$345$	0	0
$346$	−4.95593e8	−0.643219
$347$	9.62881e8	1.23714	0.618571	−	0.785729i	$-0.287712\pi$
$347$	9.62881e8	1.23714	0.618571	+	0.785729i	$0.287712\pi$
$348$	1.26852e8	0.161350
$349$	−5.40052e8	−0.680058	−0.340029	−	0.940415i	$-0.610437\pi$
$349$	−5.40052e8	−0.680058	−0.340029	+	0.940415i	$0.610437\pi$
$350$	0	0
$351$	−1.03094e8	−0.127250
$352$	−1.78826e8	−0.218541
$353$	−1.02599e9	−1.24145	−0.620727	−	0.784027i	$-0.713163\pi$
$353$	−1.02599e9	−1.24145	−0.620727	+	0.784027i	$0.713163\pi$
$354$	−5.03131e8	−0.602795
$355$	0	0
$356$	6.57367e8	0.772206
$357$	−1.72260e8	−0.200376
$358$	8.38530e7	0.0965891
$359$	−7.47383e8	−0.852536	−0.426268	−	0.904597i	$-0.640172\pi$
$359$	−7.47383e8	−0.852536	−0.426268	+	0.904597i	$0.640172\pi$
$360$	0	0
$361$	1.80735e8	0.202194
$362$	−7.71637e8	−0.854935
$363$	−2.77977e8	−0.305026
$364$	4.39068e8	0.477174
$365$	0	0
$366$	−5.69275e8	−0.606929
$367$	4.77968e8	0.504740	0.252370	−	0.967631i	$-0.418790\pi$
$367$	4.77968e8	0.504740	0.252370	+	0.967631i	$0.418790\pi$
$368$	−3.41959e8	−0.357689
$369$	2.89248e8	0.299694
$370$	0	0
$371$	−1.60315e9	−1.62991
$372$	−4.22875e8	−0.425904
$373$	−1.41621e9	−1.41302	−0.706509	−	0.707704i	$-0.749731\pi$
$373$	−1.41621e9	−1.41302	−0.706509	+	0.707704i	$0.749731\pi$
$374$	−2.12658e8	−0.210200
$375$	0	0
$376$	4.10357e8	0.398111
$377$	−3.84500e8	−0.369574
$378$	−2.06248e8	−0.196413
$379$	4.23809e8	0.399883	0.199941	−	0.979808i	$-0.435925\pi$
$379$	4.23809e8	0.399883	0.199941	+	0.979808i	$0.435925\pi$
$380$	0	0
$381$	−1.14742e8	−0.106288
$382$	7.77159e8	0.713327
$383$	8.56505e8	0.778994	0.389497	−	0.921028i	$-0.372649\pi$
$383$	8.56505e8	0.778994	0.389497	+	0.921028i	$0.372649\pi$
$384$	−5.66231e7	−0.0510310
$385$	0	0
$386$	−4.14011e8	−0.366401
$387$	5.29137e8	0.464066
$388$	−3.32597e8	−0.289073
$389$	−1.08932e8	−0.0938282	−0.0469141	−	0.998899i	$-0.514939\pi$
$389$	−1.08932e8	−0.0938282	−0.0469141	+	0.998899i	$0.514939\pi$
$390$	0	0
$391$	−4.06653e8	−0.344037
$392$	4.56739e8	0.382972
$393$	−1.50972e8	−0.125465
$394$	−1.24590e9	−1.02623
$395$	0	0
$396$	−2.54618e8	−0.206042
$397$	−2.13997e9	−1.71649	−0.858245	−	0.513239i	$-0.828445\pi$
$397$	−2.13997e9	−1.71649	−0.858245	+	0.513239i	$0.828445\pi$
$398$	1.19646e9	0.951281
$399$	−1.15931e9	−0.913677
$400$	0	0
$401$	−9.00462e8	−0.697365	−0.348682	−	0.937241i	$-0.613371\pi$
$401$	−9.00462e8	−0.697365	−0.348682	+	0.937241i	$0.613371\pi$
$402$	4.53356e7	0.0348055
$403$	1.28177e9	0.975535
$404$	1.82314e8	0.137558
$405$	0	0
$406$	−7.69224e8	−0.570443
$407$	−5.86868e8	−0.431479
$408$	−6.73356e7	−0.0490833
$409$	−2.15143e9	−1.55487	−0.777436	−	0.628962i	$-0.783480\pi$
$409$	−2.15143e9	−1.55487	−0.777436	+	0.628962i	$0.783480\pi$
$410$	0	0
$411$	5.97171e8	0.424279
$412$	−9.55935e8	−0.673423
$413$	3.05096e9	2.13114
$414$	−4.86890e8	−0.337233
$415$	0	0
$416$	1.71630e8	0.116887
$417$	6.88878e8	0.465228
$418$	−1.43119e9	−0.958472
$419$	7.96072e7	0.0528693	0.0264346	−	0.999651i	$-0.491585\pi$
$419$	7.96072e7	0.0528693	0.0264346	+	0.999651i	$0.491585\pi$
$420$	0	0
$421$	3.29700e8	0.215344	0.107672	−	0.994186i	$-0.465660\pi$
$421$	3.29700e8	0.215344	0.107672	+	0.994186i	$0.465660\pi$
$422$	−3.86810e7	−0.0250556
$423$	5.84278e8	0.375343
$424$	−6.26663e8	−0.399258
$425$	0	0
$426$	−8.13408e8	−0.509771
$427$	3.45205e9	2.14575
$428$	−6.67629e7	−0.0411606
$429$	7.71769e8	0.471940
$430$	0	0
$431$	5.57393e8	0.335345	0.167672	−	0.985843i	$-0.446375\pi$
$431$	5.57393e8	0.335345	0.167672	+	0.985843i	$0.446375\pi$
$432$	−8.06216e7	−0.0481125
$433$	−1.00562e9	−0.595287	−0.297644	−	0.954677i	$-0.596201\pi$
$433$	−1.00562e9	−0.595287	−0.297644	+	0.954677i	$0.596201\pi$
$434$	2.56429e9	1.50575
$435$	0	0
$436$	3.34774e8	0.193441
$437$	−2.73677e9	−1.56875
$438$	−6.08997e8	−0.346303
$439$	2.43906e9	1.37593	0.687967	−	0.725742i	$-0.258504\pi$
$439$	2.43906e9	1.37593	0.687967	+	0.725742i	$0.258504\pi$
$440$	0	0
$441$	6.50317e8	0.361069
$442$	2.04100e8	0.112426
$443$	1.15960e9	0.633715	0.316858	−	0.948473i	$-0.397372\pi$
$443$	1.15960e9	0.633715	0.316858	+	0.948473i	$0.397372\pi$
$444$	−1.85824e8	−0.100754
$445$	0	0
$446$	2.09475e9	1.11805
$447$	4.42804e7	0.0234496
$448$	3.43360e8	0.180416
$449$	6.32037e8	0.329519	0.164759	−	0.986334i	$-0.447315\pi$
$449$	6.32037e8	0.329519	0.164759	+	0.986334i	$0.447315\pi$
$450$	0	0
$451$	−2.16533e9	−1.11149
$452$	1.01237e9	0.515649
$453$	1.25765e9	0.635645
$454$	−1.02895e9	−0.516061
$455$	0	0
$456$	−4.53167e8	−0.223811
$457$	−1.78534e9	−0.875015	−0.437507	−	0.899215i	$-0.644139\pi$
$457$	−1.78534e9	−0.875015	−0.437507	+	0.899215i	$0.644139\pi$
$458$	8.11718e8	0.394799
$459$	−9.58743e7	−0.0462762
$460$	0	0
$461$	−1.23239e9	−0.585862	−0.292931	−	0.956134i	$-0.594631\pi$
$461$	−1.23239e9	−0.585862	−0.292931	+	0.956134i	$0.594631\pi$
$462$	1.54399e9	0.728447
$463$	−3.27184e9	−1.53200	−0.766000	−	0.642841i	$-0.777756\pi$
$463$	−3.27184e9	−1.53200	−0.766000	+	0.642841i	$0.777756\pi$
$464$	−3.00686e8	−0.139734
$465$	0	0
$466$	−2.19775e9	−1.00607
$467$	4.20893e8	0.191233	0.0956165	−	0.995418i	$-0.469518\pi$
$467$	4.20893e8	0.191233	0.0956165	+	0.995418i	$0.469518\pi$
$468$	2.44371e8	0.110202
$469$	−2.74913e8	−0.123052
$470$	0	0
$471$	1.67902e9	0.740428
$472$	1.19261e9	0.522036
$473$	−3.96116e9	−1.72111
$474$	1.87614e9	0.809172
$475$	0	0
$476$	4.08320e8	0.173531
$477$	−8.92260e8	−0.376424
$478$	−3.02288e8	−0.126597
$479$	−2.91500e7	−0.0121189	−0.00605946	−	0.999982i	$-0.501929\pi$
$479$	−2.91500e7	−0.0121189	−0.00605946	+	0.999982i	$0.501929\pi$
$480$	0	0
$481$	5.63250e8	0.230777
$482$	1.36395e9	0.554796
$483$	2.95248e9	1.19226
$484$	6.58909e8	0.264160
$485$	0	0
$486$	−1.14791e8	−0.0453609
$487$	−2.58798e9	−1.01534	−0.507668	−	0.861553i	$-0.669492\pi$
$487$	−2.58798e9	−1.01534	−0.507668	+	0.861553i	$0.669492\pi$
$488$	1.34939e9	0.525616
$489$	−1.58453e9	−0.612802
$490$	0	0
$491$	−2.01157e9	−0.766918	−0.383459	−	0.923558i	$-0.625267\pi$
$491$	−2.01157e9	−0.766918	−0.383459	+	0.923558i	$0.625267\pi$
$492$	−6.85625e8	−0.259543
$493$	−3.57573e8	−0.134400
$494$	1.37359e9	0.512640
$495$	0	0
$496$	1.00237e9	0.368844
$497$	4.93246e9	1.80226
$498$	1.24701e9	0.452445
$499$	−6.31261e8	−0.227435	−0.113717	−	0.993513i	$-0.536276\pi$
$499$	−6.31261e8	−0.227435	−0.113717	+	0.993513i	$0.536276\pi$
$500$	0	0
$501$	−7.42162e8	−0.263674
$502$	−2.72864e9	−0.962682
$503$	−1.57252e9	−0.550944	−0.275472	−	0.961309i	$-0.588834\pi$
$503$	−1.57252e9	−0.550944	−0.275472	+	0.961309i	$0.588834\pi$
$504$	4.88885e8	0.170098
$505$	0	0
$506$	3.64490e9	1.25071
$507$	9.53500e8	0.324932
$508$	2.71981e8	0.0920481
$509$	−2.18665e9	−0.734965	−0.367482	−	0.930031i	$-0.619780\pi$
$509$	−2.18665e9	−0.734965	−0.367482	+	0.930031i	$0.619780\pi$
$510$	0	0
$511$	3.69293e9	1.22433
$512$	1.34218e8	0.0441942
$513$	−6.45232e8	−0.211011
$514$	−1.55770e9	−0.505956
$515$	0	0
$516$	−1.25425e9	−0.401893
$517$	−4.37394e9	−1.39205
$518$	1.12683e9	0.356208
$519$	1.67263e9	0.525186
$520$	0	0
$521$	5.81389e9	1.80109	0.900543	−	0.434766i	$-0.143169\pi$
$521$	5.81389e9	1.80109	0.900543	+	0.434766i	$0.143169\pi$
$522$	−4.28126e8	−0.131742
$523$	−2.36475e9	−0.722819	−0.361409	−	0.932407i	$-0.617704\pi$
$523$	−2.36475e9	−0.722819	−0.361409	+	0.932407i	$0.617704\pi$
$524$	3.57859e8	0.108656
$525$	0	0
$526$	3.88481e9	1.16391
$527$	1.19201e9	0.354766
$528$	6.03539e8	0.178438
$529$	3.56509e9	1.04707
$530$	0	0
$531$	1.69807e9	0.492180
$532$	2.74798e9	0.791268
$533$	2.07819e9	0.594483
$534$	−2.21861e9	−0.630503
$535$	0	0
$536$	−1.07462e8	−0.0301425
$537$	−2.83004e8	−0.0788647
$538$	−2.31795e8	−0.0641751
$539$	−4.86832e9	−1.33912
$540$	0	0
$541$	5.64040e9	1.53151	0.765754	−	0.643134i	$-0.222366\pi$
$541$	5.64040e9	1.53151	0.765754	+	0.643134i	$0.222366\pi$
$542$	2.41968e9	0.652770
$543$	2.60428e9	0.698051
$544$	1.59610e8	0.0425074
$545$	0	0
$546$	−1.48185e9	−0.389611
$547$	−1.78063e9	−0.465177	−0.232589	−	0.972575i	$-0.574720\pi$
$547$	−1.78063e9	−0.465177	−0.232589	+	0.972575i	$0.574720\pi$
$548$	−1.41552e9	−0.367437
$549$	1.92130e9	0.495556
$550$	0	0
$551$	−2.40646e9	−0.612841
$552$	1.15411e9	0.292052
$553$	−1.13768e10	−2.86077
$554$	−1.42602e9	−0.356320
$555$	0	0
$556$	−1.63290e9	−0.402900
$557$	−1.56532e9	−0.383805	−0.191902	−	0.981414i	$-0.561466\pi$
$557$	−1.56532e9	−0.383805	−0.191902	+	0.981414i	$0.561466\pi$
$558$	1.42720e9	0.347749
$559$	3.80174e9	0.920537
$560$	0	0
$561$	7.17722e8	0.171627
$562$	1.77190e8	0.0421077
$563$	2.73932e9	0.646939	0.323470	−	0.946239i	$-0.395151\pi$
$563$	2.73932e9	0.646939	0.323470	+	0.946239i	$0.395151\pi$
$564$	−1.38495e9	−0.325056
$565$	0	0
$566$	8.64794e8	0.200473
$567$	6.96088e8	0.160370
$568$	1.92808e9	0.441474
$569$	7.38630e8	0.168087	0.0840435	−	0.996462i	$-0.473217\pi$
$569$	7.38630e8	0.168087	0.0840435	+	0.996462i	$0.473217\pi$
$570$	0	0
$571$	3.23235e9	0.726594	0.363297	−	0.931673i	$-0.381651\pi$
$571$	3.23235e9	0.726594	0.363297	+	0.931673i	$0.381651\pi$
$572$	−1.82938e9	−0.408712
$573$	−2.62291e9	−0.582429
$574$	4.15759e9	0.917594
$575$	0	0
$576$	1.91103e8	0.0416667
$577$	−2.65831e9	−0.576090	−0.288045	−	0.957617i	$-0.593005\pi$
$577$	−2.65831e9	−0.576090	−0.288045	+	0.957617i	$0.593005\pi$
$578$	−3.09290e9	−0.666222
$579$	1.39729e9	0.299165
$580$	0	0
$581$	−7.56178e9	−1.59959
$582$	1.12252e9	0.236027
$583$	6.67952e9	1.39606
$584$	1.44355e9	0.299907
$585$	0	0
$586$	−4.06676e9	−0.834848
$587$	−9.42375e9	−1.92305	−0.961524	−	0.274720i	$-0.911415\pi$
$587$	−9.42375e9	−1.92305	−0.961524	+	0.274720i	$0.911415\pi$
$588$	−1.54149e9	−0.312695
$589$	8.02219e9	1.61767
$590$	0	0
$591$	4.20491e9	0.837916
$592$	4.40472e8	0.0872555
$593$	−2.34902e9	−0.462589	−0.231294	−	0.972884i	$-0.574296\pi$
$593$	−2.34902e9	−0.462589	−0.231294	+	0.972884i	$0.574296\pi$
$594$	8.59336e8	0.168233
$595$	0	0
$596$	−1.04961e8	−0.0203079
$597$	−4.03807e9	−0.776718
$598$	−3.49821e9	−0.668947
$599$	2.66914e9	0.507431	0.253715	−	0.967279i	$-0.418347\pi$
$599$	2.66914e9	0.507431	0.253715	+	0.967279i	$0.418347\pi$
$600$	0	0
$601$	−1.24294e9	−0.233555	−0.116777	−	0.993158i	$-0.537256\pi$
$601$	−1.24294e9	−0.233555	−0.116777	+	0.993158i	$0.537256\pi$
$602$	7.60571e9	1.42086
$603$	−1.53008e8	−0.0284186
$604$	−2.98109e9	−0.550485
$605$	0	0
$606$	−6.15310e8	−0.112315
$607$	−1.29515e9	−0.235050	−0.117525	−	0.993070i	$-0.537496\pi$
$607$	−1.29515e9	−0.235050	−0.117525	+	0.993070i	$0.537496\pi$
$608$	1.07417e9	0.193826
$609$	2.59613e9	0.465764
$610$	0	0
$611$	4.19792e9	0.744543
$612$	2.27258e8	0.0400764
$613$	−5.13495e9	−0.900377	−0.450188	−	0.892934i	$-0.648643\pi$
$613$	−5.13495e9	−0.900377	−0.450188	+	0.892934i	$0.648643\pi$
$614$	−3.68681e9	−0.642779
$615$	0	0
$616$	−3.65983e9	−0.630853
$617$	1.20368e9	0.206306	0.103153	−	0.994665i	$-0.467107\pi$
$617$	1.20368e9	0.206306	0.103153	+	0.994665i	$0.467107\pi$
$618$	3.22628e9	0.549848
$619$	−9.74534e9	−1.65150	−0.825752	−	0.564034i	$-0.809249\pi$
$619$	−9.74534e9	−1.65150	−0.825752	+	0.564034i	$0.809249\pi$
$620$	0	0
$621$	1.64325e9	0.275350
$622$	6.11125e9	1.01827
$623$	1.34536e10	2.22910
$624$	−5.79250e8	−0.0954377
$625$	0	0
$626$	3.97577e9	0.647755
$627$	4.83026e9	0.782589
$628$	−3.97990e9	−0.641230
$629$	5.23805e8	0.0839252
$630$	0	0
$631$	−9.82029e9	−1.55604	−0.778021	−	0.628238i	$-0.783776\pi$
$631$	−9.82029e9	−1.55604	−0.778021	+	0.628238i	$0.783776\pi$
$632$	−4.44715e9	−0.700764
$633$	1.30549e8	0.0204578
$634$	3.35092e9	0.522218
$635$	0	0
$636$	2.11499e9	0.325993
$637$	4.67240e9	0.716229
$638$	3.20498e9	0.488599
$639$	2.74525e9	0.416226
$640$	0	0
$641$	−5.05603e9	−0.758240	−0.379120	−	0.925347i	$-0.623773\pi$
$641$	−5.05603e9	−0.758240	−0.379120	+	0.925347i	$0.623773\pi$
$642$	2.25325e8	0.0336075
$643$	1.13650e10	1.68590	0.842951	−	0.537990i	$-0.180816\pi$
$643$	1.13650e10	1.68590	0.842951	+	0.537990i	$0.180816\pi$
$644$	−6.99847e9	−1.03253
$645$	0	0
$646$	1.27740e9	0.186428
$647$	−1.08126e8	−0.0156952	−0.00784758	−	0.999969i	$-0.502498\pi$
$647$	−1.08126e8	−0.0156952	−0.00784758	+	0.999969i	$0.502498\pi$
$648$	2.72098e8	0.0392837
$649$	−1.27118e10	−1.82538
$650$	0	0
$651$	−8.65449e9	−1.22944
$652$	3.75593e9	0.530702
$653$	−3.37806e9	−0.474757	−0.237378	−	0.971417i	$-0.576288\pi$
$653$	−3.37806e9	−0.474757	−0.237378	+	0.971417i	$0.576288\pi$
$654$	−1.12986e9	−0.157944
$655$	0	0
$656$	1.62518e9	0.224770
$657$	2.05536e9	0.282755
$658$	8.39829e9	1.14921
$659$	−2.43494e9	−0.331428	−0.165714	−	0.986174i	$-0.552993\pi$
$659$	−2.43494e9	−0.331428	−0.165714	+	0.986174i	$0.552993\pi$
$660$	0	0
$661$	6.61695e9	0.891154	0.445577	−	0.895244i	$-0.352999\pi$
$661$	6.61695e9	0.891154	0.445577	+	0.895244i	$0.352999\pi$
$662$	−6.40210e9	−0.857668
$663$	−6.88838e8	−0.0917951
$664$	−2.95586e9	−0.391829
$665$	0	0
$666$	6.27157e8	0.0822653
$667$	6.12868e9	0.799700
$668$	1.75920e9	0.228348
$669$	−7.06977e9	−0.912881
$670$	0	0
$671$	−1.43830e10	−1.83790
$672$	−1.15884e9	−0.147309
$673$	−4.76258e9	−0.602267	−0.301134	−	0.953582i	$-0.597365\pi$
$673$	−4.76258e9	−0.602267	−0.301134	+	0.953582i	$0.597365\pi$
$674$	1.10828e10	1.39425
$675$	0	0
$676$	−2.26015e9	−0.281400
$677$	2.85988e9	0.354232	0.177116	−	0.984190i	$-0.443323\pi$
$677$	2.85988e9	0.354232	0.177116	+	0.984190i	$0.443323\pi$
$678$	−3.41674e9	−0.421025
$679$	−6.80688e9	−0.834456
$680$	0	0
$681$	3.47272e9	0.421362
$682$	−1.06841e10	−1.28972
$683$	5.11045e9	0.613744	0.306872	−	0.951751i	$-0.400718\pi$
$683$	5.11045e9	0.613744	0.306872	+	0.951751i	$0.400718\pi$
$684$	1.52944e9	0.182741
$685$	0	0
$686$	7.18036e8	0.0849204
$687$	−2.73955e9	−0.322352
$688$	2.97304e9	0.348049
$689$	−6.41071e9	−0.746688
$690$	0	0
$691$	9.23300e9	1.06456	0.532279	−	0.846569i	$-0.321336\pi$
$691$	9.23300e9	1.06456	0.532279	+	0.846569i	$0.321336\pi$
$692$	−3.96475e9	−0.454825
$693$	−5.21097e9	−0.594774
$694$	7.70304e9	0.874791
$695$	0	0
$696$	1.01482e9	0.114092
$697$	1.93265e9	0.216192
$698$	−4.32041e9	−0.480874
$699$	7.41739e9	0.821450
$700$	0	0
$701$	−4.27775e9	−0.469031	−0.234516	−	0.972112i	$-0.575350\pi$
$701$	−4.27775e9	−0.469031	−0.234516	+	0.972112i	$0.575350\pi$
$702$	−8.24752e8	−0.0899795
$703$	3.52520e9	0.382684
$704$	−1.43061e9	−0.154532
$705$	0	0
$706$	−8.20790e9	−0.877841
$707$	3.73121e9	0.397083
$708$	−4.02505e9	−0.426240
$709$	6.00248e9	0.632512	0.316256	−	0.948674i	$-0.397574\pi$
$709$	6.00248e9	0.632512	0.316256	+	0.948674i	$0.397574\pi$
$710$	0	0
$711$	−6.33197e9	−0.660686
$712$	5.25894e9	0.546032
$713$	−2.04306e10	−2.11090
$714$	−1.37808e9	−0.141687
$715$	0	0
$716$	6.70824e8	0.0682988
$717$	1.02022e9	0.103366
$718$	−5.97907e9	−0.602834
$719$	1.01189e9	0.101527	0.0507634	−	0.998711i	$-0.483835\pi$
$719$	1.01189e9	0.101527	0.0507634	+	0.998711i	$0.483835\pi$
$720$	0	0
$721$	−1.95640e10	−1.94395
$722$	1.44588e9	0.142973
$723$	−4.60333e9	−0.452989
$724$	−6.17310e9	−0.604530
$725$	0	0
$726$	−2.22382e9	−0.215686
$727$	1.27391e10	1.22961	0.614807	−	0.788678i	$-0.289234\pi$
$727$	1.27391e10	1.22961	0.614807	+	0.788678i	$0.289234\pi$
$728$	3.51254e9	0.337413
$729$	3.87420e8	0.0370370
$730$	0	0
$731$	3.53550e9	0.334765
$732$	−4.55420e9	−0.429164
$733$	1.02714e10	0.963314	0.481657	−	0.876360i	$-0.340035\pi$
$733$	1.02714e10	0.963314	0.481657	+	0.876360i	$0.340035\pi$
$734$	3.82374e9	0.356905
$735$	0	0
$736$	−2.73567e9	−0.252925
$737$	1.14543e9	0.105398
$738$	2.31398e9	0.211916
$739$	7.46828e9	0.680714	0.340357	−	0.940296i	$-0.389452\pi$
$739$	7.46828e9	0.680714	0.340357	+	0.940296i	$0.389452\pi$
$740$	0	0
$741$	−4.63587e9	−0.418569
$742$	−1.28252e10	−1.15252
$743$	−1.13615e10	−1.01619	−0.508093	−	0.861302i	$-0.669649\pi$
$743$	−1.13615e10	−1.01619	−0.508093	+	0.861302i	$0.669649\pi$
$744$	−3.38300e9	−0.301160
$745$	0	0
$746$	−1.13297e10	−0.999155
$747$	−4.20864e9	−0.369420
$748$	−1.70127e9	−0.148634
$749$	−1.36636e9	−0.118817
$750$	0	0
$751$	9.08552e9	0.782726	0.391363	−	0.920236i	$-0.372004\pi$
$751$	9.08552e9	0.782726	0.391363	+	0.920236i	$0.372004\pi$
$752$	3.28285e9	0.281507
$753$	9.20916e9	0.786027
$754$	−3.07600e9	−0.261328
$755$	0	0
$756$	−1.64999e9	−0.138885
$757$	−1.00537e10	−0.842348	−0.421174	−	0.906980i	$-0.638382\pi$
$757$	−1.00537e10	−0.842348	−0.421174	+	0.906980i	$0.638382\pi$
$758$	3.39047e9	0.282760
$759$	−1.23015e10	−1.02120
$760$	0	0
$761$	1.04527e9	0.0859768	0.0429884	−	0.999076i	$-0.486312\pi$
$761$	1.04527e9	0.0859768	0.0429884	+	0.999076i	$0.486312\pi$
$762$	−9.17934e8	−0.0751570
$763$	6.85142e9	0.558399
$764$	6.21728e9	0.504398
$765$	0	0
$766$	6.85204e9	0.550832
$767$	1.22003e10	0.976305
$768$	−4.52985e8	−0.0360844
$769$	1.24461e10	0.986939	0.493470	−	0.869763i	$-0.335728\pi$
$769$	1.24461e10	0.986939	0.493470	+	0.869763i	$0.335728\pi$
$770$	0	0
$771$	5.25724e9	0.413112
$772$	−3.31209e9	−0.259085
$773$	−2.86975e9	−0.223469	−0.111734	−	0.993738i	$-0.535641\pi$
$773$	−2.86975e9	−0.223469	−0.111734	+	0.993738i	$0.535641\pi$
$774$	4.23310e9	0.328144
$775$	0	0
$776$	−2.66078e9	−0.204405
$777$	−3.80305e9	−0.290843
$778$	−8.71459e8	−0.0663465
$779$	1.30067e10	0.985795
$780$	0	0
$781$	−2.05511e10	−1.54368
$782$	−3.25323e9	−0.243271
$783$	1.44492e9	0.107567
$784$	3.65391e9	0.270802
$785$	0	0
$786$	−1.20778e9	−0.0887171
$787$	−1.10693e10	−0.809487	−0.404743	−	0.914430i	$-0.632639\pi$
$787$	−1.10693e10	−0.809487	−0.404743	+	0.914430i	$0.632639\pi$
$788$	−9.96719e9	−0.725657
$789$	−1.31112e10	−0.950329
$790$	0	0
$791$	2.07189e10	1.48850
$792$	−2.03694e9	−0.145694
$793$	1.38042e10	0.983002
$794$	−1.71198e10	−1.21374
$795$	0	0
$796$	9.57172e9	0.672658
$797$	−9.16190e9	−0.641034	−0.320517	−	0.947243i	$-0.603857\pi$
$797$	−9.16190e9	−0.641034	−0.320517	+	0.947243i	$0.603857\pi$
$798$	−9.27445e9	−0.646067
$799$	3.90393e9	0.270763
$800$	0	0
$801$	7.48782e9	0.514804
$802$	−7.20369e9	−0.493111
$803$	−1.53866e10	−1.04867
$804$	3.62685e8	0.0246112
$805$	0	0
$806$	1.02542e10	0.689807
$807$	7.82308e8	0.0523987
$808$	1.45851e9	0.0972681
$809$	−7.65555e9	−0.508343	−0.254171	−	0.967159i	$-0.581803\pi$
$809$	−7.65555e9	−0.508343	−0.254171	+	0.967159i	$0.581803\pi$
$810$	0	0
$811$	1.37797e10	0.907121	0.453561	−	0.891225i	$-0.350154\pi$
$811$	1.37797e10	0.907121	0.453561	+	0.891225i	$0.350154\pi$
$812$	−6.15380e9	−0.403364
$813$	−8.16641e9	−0.532984
$814$	−4.69494e9	−0.305102
$815$	0	0
$816$	−5.38685e8	−0.0347072
$817$	2.37939e10	1.52647
$818$	−1.72114e10	−1.09946
$819$	5.00126e9	0.318116
$820$	0	0
$821$	3.07675e10	1.94040	0.970200	−	0.242304i	$-0.0779032\pi$
$821$	3.07675e10	1.94040	0.970200	+	0.242304i	$0.0779032\pi$
$822$	4.77736e9	0.300011
$823$	2.78795e10	1.74335	0.871677	−	0.490081i	$-0.163033\pi$
$823$	2.78795e10	1.74335	0.871677	+	0.490081i	$0.163033\pi$
$824$	−7.64748e9	−0.476182
$825$	0	0
$826$	2.44077e10	1.50694
$827$	1.30484e10	0.802211	0.401105	−	0.916032i	$-0.368626\pi$
$827$	1.30484e10	0.802211	0.401105	+	0.916032i	$0.368626\pi$
$828$	−3.89512e9	−0.238460
$829$	−2.37741e10	−1.44932	−0.724659	−	0.689108i	$-0.758003\pi$
$829$	−2.37741e10	−1.44932	−0.724659	+	0.689108i	$0.758003\pi$
$830$	0	0
$831$	4.81280e9	0.290934
$832$	1.37304e9	0.0826515
$833$	4.34519e9	0.260466
$834$	5.51103e9	0.328966
$835$	0	0
$836$	−1.14495e10	−0.677742
$837$	−4.81681e9	−0.283936
$838$	6.36858e8	0.0373842
$839$	1.02523e10	0.599315	0.299658	−	0.954047i	$-0.403128\pi$
$839$	1.02523e10	0.599315	0.299658	+	0.954047i	$0.403128\pi$
$840$	0	0
$841$	−1.18609e10	−0.687593
$842$	2.63760e9	0.152271
$843$	−5.98015e8	−0.0343808
$844$	−3.09448e8	−0.0177170
$845$	0	0
$846$	4.67422e9	0.265407
$847$	1.34851e10	0.762541
$848$	−5.01330e9	−0.282318
$849$	−2.91868e9	−0.163685
$850$	0	0
$851$	−8.97785e9	−0.499366
$852$	−6.50726e9	−0.360462
$853$	−1.30152e10	−0.718008	−0.359004	−	0.933336i	$-0.616884\pi$
$853$	−1.30152e10	−0.718008	−0.359004	+	0.933336i	$0.616884\pi$
$854$	2.76164e10	1.51728
$855$	0	0
$856$	−5.34103e8	−0.0291050
$857$	−3.47955e10	−1.88838	−0.944192	−	0.329396i	$-0.893155\pi$
$857$	−3.47955e10	−1.88838	−0.944192	+	0.329396i	$0.893155\pi$
$858$	6.17415e9	0.333712
$859$	−2.22903e9	−0.119989	−0.0599943	−	0.998199i	$-0.519108\pi$
$859$	−2.22903e9	−0.119989	−0.0599943	+	0.998199i	$0.519108\pi$
$860$	0	0
$861$	−1.40319e10	−0.749212
$862$	4.45915e9	0.237124
$863$	2.28044e10	1.20776	0.603880	−	0.797075i	$-0.293621\pi$
$863$	2.28044e10	1.20776	0.603880	+	0.797075i	$0.293621\pi$
$864$	−6.44973e8	−0.0340207
$865$	0	0
$866$	−8.04497e9	−0.420932
$867$	1.04385e10	0.543968
$868$	2.05143e10	1.06473
$869$	4.74016e10	2.45033
$870$	0	0
$871$	−1.09933e9	−0.0563721
$872$	2.67819e9	0.136783
$873$	−3.78849e9	−0.192715
$874$	−2.18942e10	−1.10927
$875$	0	0
$876$	−4.87198e9	−0.244873
$877$	4.21151e9	0.210833	0.105417	−	0.994428i	$-0.466382\pi$
$877$	4.21151e9	0.210833	0.105417	+	0.994428i	$0.466382\pi$
$878$	1.95125e10	0.972932
$879$	1.37253e10	0.681650
$880$	0	0
$881$	2.60856e10	1.28524	0.642622	−	0.766184i	$-0.277847\pi$
$881$	2.60856e10	1.28524	0.642622	+	0.766184i	$0.277847\pi$
$882$	5.20254e9	0.255314
$883$	1.24090e9	0.0606560	0.0303280	−	0.999540i	$-0.490345\pi$
$883$	1.24090e9	0.0606560	0.0303280	+	0.999540i	$0.490345\pi$
$884$	1.63280e9	0.0794969
$885$	0	0
$886$	9.27678e9	0.448104
$887$	2.74043e10	1.31852	0.659260	−	0.751915i	$-0.270870\pi$
$887$	2.74043e10	1.31852	0.659260	+	0.751915i	$0.270870\pi$
$888$	−1.48659e9	−0.0712438
$889$	5.56631e9	0.265712
$890$	0	0
$891$	−2.90026e9	−0.137361
$892$	1.67580e10	0.790578
$893$	2.62734e10	1.23463
$894$	3.54243e8	0.0165813
$895$	0	0
$896$	2.74688e9	0.127574
$897$	1.18065e10	0.546193
$898$	5.05629e9	0.233005
$899$	−1.79648e10	−0.824637
$900$	0	0
$901$	−5.96176e9	−0.271543
$902$	−1.73226e10	−0.785943
$903$	−2.56693e10	−1.16013
$904$	8.09894e9	0.364619
$905$	0	0
$906$	1.00612e10	0.449469
$907$	1.54071e10	0.685638	0.342819	−	0.939402i	$-0.388618\pi$
$907$	1.54071e10	0.685638	0.342819	+	0.939402i	$0.388618\pi$
$908$	−8.23163e9	−0.364910
$909$	2.07667e9	0.0917052
$910$	0	0
$911$	1.20985e9	0.0530171	0.0265085	−	0.999649i	$-0.491561\pi$
$911$	1.20985e9	0.0530171	0.0265085	+	0.999649i	$0.491561\pi$
$912$	−3.62534e9	−0.158258
$913$	3.15062e10	1.37009
$914$	−1.42828e10	−0.618729
$915$	0	0
$916$	6.49374e9	0.279165
$917$	7.32389e9	0.313653
$918$	−7.66994e8	−0.0327222
$919$	1.95758e10	0.831986	0.415993	−	0.909368i	$-0.363434\pi$
$919$	1.95758e10	0.831986	0.415993	+	0.909368i	$0.363434\pi$
$920$	0	0
$921$	1.24430e10	0.524827
$922$	−9.85913e9	−0.414267
$923$	1.97241e10	0.825640
$924$	1.23519e10	0.515090
$925$	0	0
$926$	−2.61747e10	−1.08329
$927$	−1.08887e10	−0.448949
$928$	−2.40549e9	−0.0988065
$929$	2.43152e10	0.994999	0.497500	−	0.867464i	$-0.334252\pi$
$929$	2.43152e10	0.994999	0.497500	+	0.867464i	$0.334252\pi$
$930$	0	0
$931$	2.92430e10	1.18768
$932$	−1.75820e10	−0.711397
$933$	−2.06255e10	−0.831416
$934$	3.36714e9	0.135222
$935$	0	0
$936$	1.95497e9	0.0779245
$937$	2.87271e9	0.114078	0.0570391	−	0.998372i	$-0.481834\pi$
$937$	2.87271e9	0.114078	0.0570391	+	0.998372i	$0.481834\pi$
$938$	−2.19930e9	−0.0870111
$939$	−1.34182e10	−0.528890
$940$	0	0
$941$	3.33166e10	1.30346	0.651729	−	0.758452i	$-0.274044\pi$
$941$	3.33166e10	1.30346	0.651729	+	0.758452i	$0.274044\pi$
$942$	1.34322e10	0.523562
$943$	−3.31250e10	−1.28637
$944$	9.54085e9	0.369135
$945$	0	0
$946$	−3.16893e10	−1.21701
$947$	−5.07496e9	−0.194182	−0.0970908	−	0.995276i	$-0.530954\pi$
$947$	−5.07496e9	−0.194182	−0.0970908	+	0.995276i	$0.530954\pi$
$948$	1.50091e10	0.572171
$949$	1.47674e10	0.560882
$950$	0	0
$951$	−1.13094e10	−0.426389
$952$	3.26656e9	0.122705
$953$	−2.69161e10	−1.00737	−0.503683	−	0.863889i	$-0.668022\pi$
$953$	−2.69161e10	−1.00737	−0.503683	+	0.863889i	$0.668022\pi$
$954$	−7.13808e9	−0.266172
$955$	0	0
$956$	−2.41831e9	−0.0895177
$957$	−1.08168e10	−0.398940
$958$	−2.33200e8	−0.00856937
$959$	−2.89697e10	−1.06067
$960$	0	0
$961$	3.23749e10	1.17673
$962$	4.50600e9	0.163184
$963$	−7.60471e8	−0.0274404
$964$	1.09116e10	0.392300
$965$	0	0
$966$	2.36198e10	0.843057
$967$	−1.62053e10	−0.576320	−0.288160	−	0.957582i	$-0.593043\pi$
$967$	−1.62053e10	−0.576320	−0.288160	+	0.957582i	$0.593043\pi$
$968$	5.27127e9	0.186789
$969$	−4.31121e9	−0.152218
$970$	0	0
$971$	−1.58919e10	−0.557068	−0.278534	−	0.960426i	$-0.589848\pi$
$971$	−1.58919e10	−0.557068	−0.278534	+	0.960426i	$0.589848\pi$
$972$	−9.18330e8	−0.0320750
$973$	−3.34186e10	−1.16304
$974$	−2.07039e10	−0.717951
$975$	0	0
$976$	1.07951e10	0.371667
$977$	−2.98228e10	−1.02310	−0.511549	−	0.859254i	$-0.670928\pi$
$977$	−2.98228e10	−1.02310	−0.511549	+	0.859254i	$0.670928\pi$
$978$	−1.26763e10	−0.433317
$979$	−5.60544e10	−1.90928
$980$	0	0
$981$	3.81328e9	0.128961
$982$	−1.60925e10	−0.542293
$983$	−3.04567e10	−1.02270	−0.511348	−	0.859374i	$-0.670854\pi$
$983$	−3.04567e10	−1.02270	−0.511348	+	0.859374i	$0.670854\pi$
$984$	−5.48500e9	−0.183524
$985$	0	0
$986$	−2.86058e9	−0.0950354
$987$	−2.83442e10	−0.938328
$988$	1.09887e10	0.362491
$989$	−6.05974e10	−1.99190
$990$	0	0
$991$	−4.03364e10	−1.31656	−0.658278	−	0.752775i	$-0.728715\pi$
$991$	−4.03364e10	−1.31656	−0.658278	+	0.752775i	$0.728715\pi$
$992$	8.01896e9	0.260812
$993$	2.16071e10	0.700283
$994$	3.94597e10	1.27439
$995$	0	0
$996$	9.97604e9	0.319927
$997$	1.00858e10	0.322312	0.161156	−	0.986929i	$-0.448478\pi$
$997$	1.00858e10	0.322312	0.161156	+	0.986929i	$0.448478\pi$
$998$	−5.05009e9	−0.160821
$999$	−2.11666e9	−0.0671693

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	150.8.a.s.1.2		2
3.2	odd	2		450.8.a.be.1.2		2
5.2	odd	4		30.8.c.b.19.4	yes	4
5.3	odd	4		30.8.c.b.19.2	✓	4
5.4	even	2		150.8.a.r.1.1		2
15.2	even	4		90.8.c.b.19.1		4
15.8	even	4		90.8.c.b.19.3		4
15.14	odd	2		450.8.a.bh.1.1		2
20.3	even	4		240.8.f.d.49.4		4
20.7	even	4		240.8.f.d.49.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
30.8.c.b.19.2	✓	4	5.3	odd	4
30.8.c.b.19.4	yes	4	5.2	odd	4
90.8.c.b.19.1		4	15.2	even	4
90.8.c.b.19.3		4	15.8	even	4
150.8.a.r.1.1		2	5.4	even	2
150.8.a.s.1.2		2	1.1	even	1	trivial
240.8.f.d.49.2		4	20.7	even	4
240.8.f.d.49.4		4	20.3	even	4
450.8.a.be.1.2		2	3.2	odd	2
450.8.a.bh.1.1		2	15.14	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	150.a (trivial)

\(f(q)\)	\(=\)	\(q+8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} -216.000 q^{6} +1309.81 q^{7} +512.000 q^{8} +729.000 q^{9} -5457.35 q^{11} -1728.00 q^{12} +5237.72 q^{13} +10478.5 q^{14} +4096.00 q^{16} +4870.92 q^{17} +5832.00 q^{18} +32781.2 q^{19} -35365.0 q^{21} -43658.8 q^{22} -83486.0 q^{23} -13824.0 q^{24} +41901.8 q^{26} -19683.0 q^{27} +83828.0 q^{28} -73409.7 q^{29} +244719. q^{31} +32768.0 q^{32} +147348. q^{33} +38967.3 q^{34} +46656.0 q^{36} +107537. q^{37} +262250. q^{38} -141418. q^{39} +396774. q^{41} -282920. q^{42} +725839. q^{43} -349270. q^{44} -667888. q^{46} +801478. q^{47} -110592. q^{48} +892068. q^{49} -131515. q^{51} +335214. q^{52} -1.22395e6 q^{53} -157464. q^{54} +670624. q^{56} -885092. q^{57} -587278. q^{58} +2.32931e6 q^{59} +2.63553e6 q^{61} +1.95775e6 q^{62} +954854. q^{63} +262144. q^{64} +1.17879e6 q^{66} -209887. q^{67} +311739. q^{68} +2.25412e6 q^{69} +3.76578e6 q^{71} +373248. q^{72} +2.81943e6 q^{73} +860298. q^{74} +2.09800e6 q^{76} -7.14810e6 q^{77} -1.13135e6 q^{78} -8.68583e6 q^{79} +531441. q^{81} +3.17419e6 q^{82} -5.77317e6 q^{83} -2.26336e6 q^{84} +5.80672e6 q^{86} +1.98206e6 q^{87} -2.79416e6 q^{88} +1.02714e7 q^{89} +6.86043e6 q^{91} -5.34310e6 q^{92} -6.60742e6 q^{93} +6.41183e6 q^{94} -884736. q^{96} -5.19683e6 q^{97} +7.13654e6 q^{98} -3.97841e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 16 q^{2} - 54 q^{3} + 128 q^{4} - 432 q^{6} + 564 q^{7} + 1024 q^{8} + 1458 q^{9} - 3720 q^{11} - 3456 q^{12} + 7392 q^{13} + 4512 q^{14} + 8192 q^{16} - 24176 q^{17} + 11664 q^{18} + 34728 q^{19}+ \cdots - 2711880 q^{99}+O(q^{100}) \) 2 * q + 16 * q^2 - 54 * q^3 + 128 * q^4 - 432 * q^6 + 564 * q^7 + 1024 * q^8 + 1458 * q^9 - 3720 * q^11 - 3456 * q^12 + 7392 * q^13 + 4512 * q^14 + 8192 * q^16 - 24176 * q^17 + 11664 * q^18 + 34728 * q^19 - 15228 * q^21 - 29760 * q^22 - 12800 * q^23 - 27648 * q^24 + 59136 * q^26 - 39366 * q^27 + 36096 * q^28 + 186192 * q^29 + 218096 * q^31 + 65536 * q^32 + 100440 * q^33 - 193408 * q^34 + 93312 * q^36 + 382608 * q^37 + 277824 * q^38 - 199584 * q^39 + 304308 * q^41 - 121824 * q^42 + 1048776 * q^43 - 238080 * q^44 - 102400 * q^46 + 351080 * q^47 - 221184 * q^48 + 624762 * q^49 + 652752 * q^51 + 473088 * q^52 + 139104 * q^53 - 314928 * q^54 + 288768 * q^56 - 937656 * q^57 + 1489536 * q^58 + 4558920 * q^59 + 5986420 * q^61 + 1744768 * q^62 + 411156 * q^63 + 524288 * q^64 + 803520 * q^66 + 1968864 * q^67 - 1547264 * q^68 + 345600 * q^69 + 9079440 * q^71 + 746496 * q^72 - 3231168 * q^73 + 3060864 * q^74 + 2222592 * q^76 - 8443840 * q^77 - 1596672 * q^78 - 1979136 * q^79 + 1062882 * q^81 + 2434464 * q^82 - 9881288 * q^83 - 974592 * q^84 + 8390208 * q^86 - 5027184 * q^87 - 1904640 * q^88 + 7793724 * q^89 + 5253744 * q^91 - 819200 * q^92 - 5888592 * q^93 + 2808640 * q^94 - 1769472 * q^96 - 10989792 * q^97 + 4998096 * q^98 - 2711880 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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