LMFDB - Embedded newform 150.10.a.l.1.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [150,10,Mod(1,150)] 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("150.1"); S:= CuspForms(chi, 10); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(150, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 10, names="a")

Level:	$ N $	$=$	$ 150 = 2 \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	150.a (trivial)

Newform invariants

comment:select newform

sage:traces = [2,-32,-162,512,0,2592,-3166] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	yes
Analytic conductor:	$77.2553754246$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{6679}) $
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 6679 $ x^2 - 6679
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{3}\cdot 3\cdot 5 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$81.7251$ 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)

$f(q)$	$=$	\(q-16.0000 q^{2} -81.0000 q^{3} +256.000 q^{4} +1296.00 q^{6} +8224.02 q^{7} -4096.00 q^{8} +6561.00 q^{9} +3734.98 q^{11} -20736.0 q^{12} -113885. q^{13} -131584. q^{14} +65536.0 q^{16} +94341.3 q^{17} -104976. q^{18} -403085. q^{19} -666145. q^{21} -59759.7 q^{22} -1.40996e6 q^{23} +331776. q^{24} +1.82216e6 q^{26} -531441. q^{27} +2.10535e6 q^{28} +4.37774e6 q^{29} +5.54354e6 q^{31} -1.04858e6 q^{32} -302534. q^{33} -1.50946e6 q^{34} +1.67962e6 q^{36} -1.62958e7 q^{37} +6.44936e6 q^{38} +9.22470e6 q^{39} +8.38307e6 q^{41} +1.06583e7 q^{42} -1.61666e7 q^{43} +956155. q^{44} +2.25593e7 q^{46} +3.68255e7 q^{47} -5.30842e6 q^{48} +2.72809e7 q^{49} -7.64165e6 q^{51} -2.91546e7 q^{52} +2.76382e7 q^{53} +8.50306e6 q^{54} -3.36856e7 q^{56} +3.26499e7 q^{57} -7.00438e7 q^{58} +1.21434e8 q^{59} -6.20320e7 q^{61} -8.86966e7 q^{62} +5.39578e7 q^{63} +1.67772e7 q^{64} +4.84054e6 q^{66} -2.35447e8 q^{67} +2.41514e7 q^{68} +1.14207e8 q^{69} -6.28284e7 q^{71} -2.68739e7 q^{72} +2.55855e8 q^{73} +2.60733e8 q^{74} -1.03190e8 q^{76} +3.07166e7 q^{77} -1.47595e8 q^{78} +1.78504e8 q^{79} +4.30467e7 q^{81} -1.34129e8 q^{82} -6.62058e8 q^{83} -1.70533e8 q^{84} +2.58666e8 q^{86} -3.54597e8 q^{87} -1.52985e7 q^{88} -1.29543e8 q^{89} -9.36593e8 q^{91} -3.60949e8 q^{92} -4.49027e8 q^{93} -5.89208e8 q^{94} +8.49347e7 q^{96} +3.64733e8 q^{97} -4.36494e8 q^{98} +2.45052e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 32 q^{2} - 162 q^{3} + 512 q^{4} + 2592 q^{6} - 3166 q^{7} - 8192 q^{8} + 13122 q^{9} + 27084 q^{11} - 41472 q^{12} - 70858 q^{13} + 50656 q^{14} + 131072 q^{16} - 144756 q^{17} - 209952 q^{18} + 115690 q^{19}+ \cdots + 177698124 q^{99}+O(q^{100}) $ 2 * q - 32 * q^2 - 162 * q^3 + 512 * q^4 + 2592 * q^6 - 3166 * q^7 - 8192 * q^8 + 13122 * q^9 + 27084 * q^11 - 41472 * q^12 - 70858 * q^13 + 50656 * q^14 + 131072 * q^16 - 144756 * q^17 - 209952 * q^18 + 115690 * q^19 + 256446 * q^21 - 433344 * q^22 - 799668 * q^23 + 663552 * q^24 + 1133728 * q^26 - 1062882 * q^27 - 810496 * q^28 - 208140 * q^29 + 6360094 * q^31 - 2097152 * q^32 - 2193804 * q^33 + 2316096 * q^34 + 3359232 * q^36 - 1876036 * q^37 - 1851040 * q^38 + 5739498 * q^39 + 38125824 * q^41 - 4103136 * q^42 + 3776162 * q^43 + 6933504 * q^44 + 12794688 * q^46 + 11199924 * q^47 - 10616832 * q^48 + 116659764 * q^49 + 11725236 * q^51 - 18139648 * q^52 + 38780952 * q^53 + 17006112 * q^54 + 12967936 * q^56 - 9370890 * q^57 + 3330240 * q^58 + 286804020 * q^59 - 255752666 * q^61 - 101761504 * q^62 - 20772126 * q^63 + 33554432 * q^64 + 35100864 * q^66 - 208870006 * q^67 - 37057536 * q^68 + 64773108 * q^69 - 277057536 * q^71 - 53747712 * q^72 + 60155132 * q^73 + 30016576 * q^74 + 29616640 * q^76 - 235229172 * q^77 - 91831968 * q^78 + 127287760 * q^79 + 86093442 * q^81 - 610013184 * q^82 - 596984628 * q^83 + 65650176 * q^84 - 60418592 * q^86 + 16859340 * q^87 - 110936064 * q^88 + 940116480 * q^89 - 1426673386 * q^91 - 204715008 * q^92 - 515167614 * q^93 - 179198784 * q^94 + 169869312 * q^96 - 1317925426 * q^97 - 1866556224 * q^98 + 177698124 * q^99

Coefficient data

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

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

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

$2$	−16.0000	−0.707107
$2$	−16.0000	−0.707107
$3$	−81.0000	−0.577350
$3$	−81.0000	−0.577350
$4$	256.000	0.500000
$5$	0	0
$5$	0	0
$6$	1296.00	0.408248
$7$	8224.02	1.29462	0.647311	−	0.762226i	$-0.275894\pi$
$7$	8224.02	1.29462	0.647311	+	0.762226i	$0.275894\pi$
$8$	−4096.00	−0.353553
$9$	6561.00	0.333333
$10$	0	0
$11$	3734.98	0.0769168	0.0384584	−	0.999260i	$-0.487755\pi$
$11$	3734.98	0.0769168	0.0384584	+	0.999260i	$0.487755\pi$
$12$	−20736.0	−0.288675
$13$	−113885.	−1.10592	−0.552958	−	0.833209i	$-0.686501\pi$
$13$	−113885.	−1.10592	−0.552958	+	0.833209i	$0.686501\pi$
$14$	−131584.	−0.915436
$15$	0	0
$16$	65536.0	0.250000
$17$	94341.3	0.273957	0.136978	−	0.990574i	$-0.456261\pi$
$17$	94341.3	0.273957	0.136978	+	0.990574i	$0.456261\pi$
$18$	−104976.	−0.235702
$19$	−403085.	−0.709586	−0.354793	−	0.934945i	$-0.615449\pi$
$19$	−403085.	−0.709586	−0.354793	+	0.934945i	$0.615449\pi$
$20$	0	0
$21$	−666145.	−0.747450
$22$	−59759.7	−0.0543884
$23$	−1.40996e6	−1.05058	−0.525292	−	0.850922i	$-0.676044\pi$
$23$	−1.40996e6	−1.05058	−0.525292	+	0.850922i	$0.676044\pi$
$24$	331776.	0.204124
$25$	0	0
$26$	1.82216e6	0.782000
$27$	−531441.	−0.192450
$28$	2.10535e6	0.647311
$29$	4.37774e6	1.14937	0.574683	−	0.818376i	$-0.305125\pi$
$29$	4.37774e6	1.14937	0.574683	+	0.818376i	$0.305125\pi$
$30$	0	0
$31$	5.54354e6	1.07810	0.539050	−	0.842273i	$-0.318783\pi$
$31$	5.54354e6	1.07810	0.539050	+	0.842273i	$0.318783\pi$
$32$	−1.04858e6	−0.176777
$33$	−302534.	−0.0444080
$34$	−1.50946e6	−0.193717
$35$	0	0
$36$	1.67962e6	0.166667
$37$	−1.62958e7	−1.42945	−0.714724	−	0.699407i	$-0.753448\pi$
$37$	−1.62958e7	−1.42945	−0.714724	+	0.699407i	$0.753448\pi$
$38$	6.44936e6	0.501753
$39$	9.22470e6	0.638501
$40$	0	0
$41$	8.38307e6	0.463314	0.231657	−	0.972797i	$-0.425585\pi$
$41$	8.38307e6	0.463314	0.231657	+	0.972797i	$0.425585\pi$
$42$	1.06583e7	0.528527
$43$	−1.61666e7	−0.721127	−0.360563	−	0.932735i	$-0.617416\pi$
$43$	−1.61666e7	−0.721127	−0.360563	+	0.932735i	$0.617416\pi$
$44$	956155.	0.0384584
$45$	0	0
$46$	2.25593e7	0.742875
$47$	3.68255e7	1.10080	0.550400	−	0.834901i	$-0.314475\pi$
$47$	3.68255e7	1.10080	0.550400	+	0.834901i	$0.314475\pi$
$48$	−5.30842e6	−0.144338
$49$	2.72809e7	0.676045
$50$	0	0
$51$	−7.64165e6	−0.158169
$52$	−2.91546e7	−0.552958
$53$	2.76382e7	0.481136	0.240568	−	0.970632i	$-0.422666\pi$
$53$	2.76382e7	0.481136	0.240568	+	0.970632i	$0.422666\pi$
$54$	8.50306e6	0.136083
$55$	0	0
$56$	−3.36856e7	−0.457718
$57$	3.26499e7	0.409680
$58$	−7.00438e7	−0.812725
$59$	1.21434e8	1.30469	0.652345	−	0.757922i	$-0.273785\pi$
$59$	1.21434e8	1.30469	0.652345	+	0.757922i	$0.273785\pi$
$60$	0	0
$61$	−6.20320e7	−0.573630	−0.286815	−	0.957986i	$-0.592596\pi$
$61$	−6.20320e7	−0.573630	−0.286815	+	0.957986i	$0.592596\pi$
$62$	−8.86966e7	−0.762332
$63$	5.39578e7	0.431541
$64$	1.67772e7	0.125000
$65$	0	0
$66$	4.84054e6	0.0314012
$67$	−2.35447e8	−1.42744	−0.713718	−	0.700433i	$-0.752990\pi$
$67$	−2.35447e8	−1.42744	−0.713718	+	0.700433i	$0.752990\pi$
$68$	2.41514e7	0.136978
$69$	1.14207e8	0.606555
$70$	0	0
$71$	−6.28284e7	−0.293422	−0.146711	−	0.989179i	$-0.546869\pi$
$71$	−6.28284e7	−0.293422	−0.146711	+	0.989179i	$0.546869\pi$
$72$	−2.68739e7	−0.117851
$73$	2.55855e8	1.05449	0.527243	−	0.849715i	$-0.323226\pi$
$73$	2.55855e8	1.05449	0.527243	+	0.849715i	$0.323226\pi$
$74$	2.60733e8	1.01077
$75$	0	0
$76$	−1.03190e8	−0.354793
$77$	3.07166e7	0.0995782
$78$	−1.47595e8	−0.451488
$79$	1.78504e8	0.515615	0.257807	−	0.966196i	$-0.417000\pi$
$79$	1.78504e8	0.515615	0.257807	+	0.966196i	$0.417000\pi$
$80$	0	0
$81$	4.30467e7	0.111111
$82$	−1.34129e8	−0.327613
$83$	−6.62058e8	−1.53124	−0.765622	−	0.643290i	$-0.777569\pi$
$83$	−6.62058e8	−1.53124	−0.765622	+	0.643290i	$0.777569\pi$
$84$	−1.70533e8	−0.373725
$85$	0	0
$86$	2.58666e8	0.509914
$87$	−3.54597e8	−0.663587
$88$	−1.52985e7	−0.0271942
$89$	−1.29543e8	−0.218856	−0.109428	−	0.993995i	$-0.534902\pi$
$89$	−1.29543e8	−0.218856	−0.109428	+	0.993995i	$0.534902\pi$
$90$	0	0
$91$	−9.36593e8	−1.43174
$92$	−3.60949e8	−0.525292
$93$	−4.49027e8	−0.622442
$94$	−5.89208e8	−0.778383
$95$	0	0
$96$	8.49347e7	0.102062
$97$	3.64733e8	0.418314	0.209157	−	0.977882i	$-0.432928\pi$
$97$	3.64733e8	0.418314	0.209157	+	0.977882i	$0.432928\pi$
$98$	−4.36494e8	−0.478036
$99$	2.45052e7	0.0256389
$100$	0	0
$101$	−2.05953e9	−1.96935	−0.984674	−	0.174405i	$-0.944200\pi$
$101$	−2.05953e9	−1.96935	−0.984674	+	0.174405i	$0.944200\pi$
$102$	1.22266e8	0.111842
$103$	−1.93446e9	−1.69353	−0.846766	−	0.531966i	$-0.821453\pi$
$103$	−1.93446e9	−1.69353	−0.846766	+	0.531966i	$0.821453\pi$
$104$	4.66474e8	0.391000
$105$	0	0
$106$	−4.42211e8	−0.340215
$107$	−4.81098e7	−0.0354819	−0.0177409	−	0.999843i	$-0.505647\pi$
$107$	−4.81098e7	−0.0354819	−0.0177409	+	0.999843i	$0.505647\pi$
$108$	−1.36049e8	−0.0962250
$109$	2.04390e9	1.38689	0.693444	−	0.720510i	$-0.256092\pi$
$109$	2.04390e9	1.38689	0.693444	+	0.720510i	$0.256092\pi$
$110$	0	0
$111$	1.31996e9	0.825292
$112$	5.38969e8	0.323655
$113$	−2.39410e9	−1.38130	−0.690652	−	0.723187i	$-0.742676\pi$
$113$	−2.39410e9	−1.38130	−0.690652	+	0.723187i	$0.742676\pi$
$114$	−5.22398e8	−0.289687
$115$	0	0
$116$	1.12070e9	0.574683
$117$	−7.47200e8	−0.368639
$118$	−1.94295e9	−0.922555
$119$	7.75865e8	0.354670
$120$	0	0
$121$	−2.34400e9	−0.994084
$122$	9.92512e8	0.405617
$123$	−6.79029e8	−0.267495
$124$	1.41915e9	0.539050
$125$	0	0
$126$	−8.63325e8	−0.305145
$127$	−2.79320e9	−0.952764	−0.476382	−	0.879239i	$-0.658052\pi$
$127$	−2.79320e9	−0.952764	−0.476382	+	0.879239i	$0.658052\pi$
$128$	−2.68435e8	−0.0883883
$129$	1.30950e9	0.416343
$130$	0	0
$131$	−1.91859e9	−0.569194	−0.284597	−	0.958647i	$-0.591860\pi$
$131$	−1.91859e9	−0.569194	−0.284597	+	0.958647i	$0.591860\pi$
$132$	−7.74486e7	−0.0222040
$133$	−3.31498e9	−0.918646
$134$	3.76715e9	1.00935
$135$	0	0
$136$	−3.86422e8	−0.0968583
$137$	5.36382e9	1.30086	0.650432	−	0.759565i	$-0.274588\pi$
$137$	5.36382e9	1.30086	0.650432	+	0.759565i	$0.274588\pi$
$138$	−1.82730e9	−0.428899
$139$	−7.00655e9	−1.59198	−0.795990	−	0.605310i	$-0.793049\pi$
$139$	−7.00655e9	−1.59198	−0.795990	+	0.605310i	$0.793049\pi$
$140$	0	0
$141$	−2.98287e9	−0.635547
$142$	1.00525e9	0.207481
$143$	−4.25359e8	−0.0850635
$144$	4.29982e8	0.0833333
$145$	0	0
$146$	−4.09368e9	−0.745634
$147$	−2.20975e9	−0.390315
$148$	−4.17173e9	−0.714724
$149$	3.39634e9	0.564512	0.282256	−	0.959339i	$-0.408917\pi$
$149$	3.39634e9	0.564512	0.282256	+	0.959339i	$0.408917\pi$
$150$	0	0
$151$	3.01245e9	0.471545	0.235772	−	0.971808i	$-0.424238\pi$
$151$	3.01245e9	0.471545	0.235772	+	0.971808i	$0.424238\pi$
$152$	1.65104e9	0.250877
$153$	6.18973e8	0.0913189
$154$	−4.91465e8	−0.0704124
$155$	0	0
$156$	2.36152e9	0.319250
$157$	−1.14626e10	−1.50569	−0.752844	−	0.658199i	$-0.771319\pi$
$157$	−1.14626e10	−1.50569	−0.752844	+	0.658199i	$0.771319\pi$
$158$	−2.85606e9	−0.364595
$159$	−2.23869e9	−0.277784
$160$	0	0
$161$	−1.15955e10	−1.36011
$162$	−6.88748e8	−0.0785674
$163$	−1.65677e9	−0.183831	−0.0919154	−	0.995767i	$-0.529299\pi$
$163$	−1.65677e9	−0.183831	−0.0919154	+	0.995767i	$0.529299\pi$
$164$	2.14607e9	0.231657
$165$	0	0
$166$	1.05929e10	1.08275
$167$	−1.46089e10	−1.45343	−0.726716	−	0.686938i	$-0.758954\pi$
$167$	−1.46089e10	−1.45343	−0.726716	+	0.686938i	$0.758954\pi$
$168$	2.72853e9	0.264264
$169$	2.36533e9	0.223049
$170$	0	0
$171$	−2.64464e9	−0.236529
$172$	−4.13866e9	−0.360563
$173$	1.44203e10	1.22396	0.611978	−	0.790875i	$-0.290374\pi$
$173$	1.44203e10	1.22396	0.611978	+	0.790875i	$0.290374\pi$
$174$	5.67355e9	0.469227
$175$	0	0
$176$	2.44776e8	0.0192292
$177$	−9.83618e9	−0.753263
$178$	2.07269e9	0.154755
$179$	2.01766e10	1.46896	0.734480	−	0.678630i	$-0.237426\pi$
$179$	2.01766e10	1.46896	0.734480	+	0.678630i	$0.237426\pi$
$180$	0	0
$181$	−2.09616e9	−0.145168	−0.0725840	−	0.997362i	$-0.523125\pi$
$181$	−2.09616e9	−0.145168	−0.0725840	+	0.997362i	$0.523125\pi$
$182$	1.49855e10	1.01239
$183$	5.02459e9	0.331185
$184$	5.77518e9	0.371437
$185$	0	0
$186$	7.18443e9	0.440133
$187$	3.52363e8	0.0210719
$188$	9.42733e9	0.550400
$189$	−4.37058e9	−0.249150
$190$	0	0
$191$	−1.52653e9	−0.0829956	−0.0414978	−	0.999139i	$-0.513213\pi$
$191$	−1.52653e9	−0.0829956	−0.0414978	+	0.999139i	$0.513213\pi$
$192$	−1.35895e9	−0.0721688
$193$	−3.59523e9	−0.186517	−0.0932587	−	0.995642i	$-0.529728\pi$
$193$	−3.59523e9	−0.186517	−0.0932587	+	0.995642i	$0.529728\pi$
$194$	−5.83573e9	−0.295793
$195$	0	0
$196$	6.98390e9	0.338023
$197$	6.38747e9	0.302156	0.151078	−	0.988522i	$-0.451726\pi$
$197$	6.38747e9	0.302156	0.151078	+	0.988522i	$0.451726\pi$
$198$	−3.92083e8	−0.0181295
$199$	−2.32330e10	−1.05019	−0.525094	−	0.851044i	$-0.675970\pi$
$199$	−2.32330e10	−1.05019	−0.525094	+	0.851044i	$0.675970\pi$
$200$	0	0
$201$	1.90712e10	0.824130
$202$	3.29525e10	1.39254
$203$	3.60026e10	1.48800
$204$	−1.95626e9	−0.0790845
$205$	0	0
$206$	3.09514e10	1.19751
$207$	−9.25073e9	−0.350194
$208$	−7.46358e9	−0.276479
$209$	−1.50551e9	−0.0545791
$210$	0	0
$211$	−2.29725e10	−0.797878	−0.398939	−	0.916977i	$-0.630621\pi$
$211$	−2.29725e10	−0.797878	−0.398939	+	0.916977i	$0.630621\pi$
$212$	7.07537e9	0.240568
$213$	5.08910e9	0.169408
$214$	7.69756e8	0.0250895
$215$	0	0
$216$	2.17678e9	0.0680414
$217$	4.55902e10	1.39573
$218$	−3.27025e10	−0.980678
$219$	−2.07242e10	−0.608807
$220$	0	0
$221$	−1.07441e10	−0.302973
$222$	−2.11194e10	−0.583569
$223$	5.48275e10	1.48466	0.742329	−	0.670036i	$-0.233721\pi$
$223$	5.48275e10	1.48466	0.742329	+	0.670036i	$0.233721\pi$
$224$	−8.62351e9	−0.228859
$225$	0	0
$226$	3.83056e10	0.976730
$227$	3.42251e10	0.855517	0.427758	−	0.903893i	$-0.359303\pi$
$227$	3.42251e10	0.855517	0.427758	+	0.903893i	$0.359303\pi$
$228$	8.35837e9	0.204840
$229$	−7.66049e10	−1.84076	−0.920379	−	0.391027i	$-0.872120\pi$
$229$	−7.66049e10	−1.84076	−0.920379	+	0.391027i	$0.872120\pi$
$230$	0	0
$231$	−2.48804e9	−0.0574915
$232$	−1.79312e10	−0.406363
$233$	5.69117e10	1.26503	0.632513	−	0.774550i	$-0.282023\pi$
$233$	5.69117e10	1.26503	0.632513	+	0.774550i	$0.282023\pi$
$234$	1.19552e10	0.260667
$235$	0	0
$236$	3.10872e10	0.652345
$237$	−1.44588e10	−0.297690
$238$	−1.24138e10	−0.250790
$239$	−6.35267e9	−0.125941	−0.0629703	−	0.998015i	$-0.520057\pi$
$239$	−6.35267e9	−0.125941	−0.0629703	+	0.998015i	$0.520057\pi$
$240$	0	0
$241$	1.45644e9	0.0278109	0.0139054	−	0.999903i	$-0.495574\pi$
$241$	1.45644e9	0.0278109	0.0139054	+	0.999903i	$0.495574\pi$
$242$	3.75040e10	0.702923
$243$	−3.48678e9	−0.0641500
$244$	−1.58802e10	−0.286815
$245$	0	0
$246$	1.08645e10	0.189147
$247$	4.59054e10	0.784743
$248$	−2.27063e10	−0.381166
$249$	5.36267e10	0.884065
$250$	0	0
$251$	2.51346e10	0.399705	0.199853	−	0.979826i	$-0.435954\pi$
$251$	2.51346e10	0.399705	0.199853	+	0.979826i	$0.435954\pi$
$252$	1.38132e10	0.215770
$253$	−5.26616e9	−0.0808076
$254$	4.46912e10	0.673706
$255$	0	0
$256$	4.29497e9	0.0625000
$257$	−8.89054e10	−1.27124	−0.635622	−	0.772000i	$-0.719256\pi$
$257$	−8.89054e10	−1.27124	−0.635622	+	0.772000i	$0.719256\pi$
$258$	−2.09520e10	−0.294399
$259$	−1.34017e11	−1.85059
$260$	0	0
$261$	2.87223e10	0.383122
$262$	3.06974e10	0.402481
$263$	1.07693e11	1.38799	0.693993	−	0.719982i	$-0.255850\pi$
$263$	1.07693e11	1.38799	0.693993	+	0.719982i	$0.255850\pi$
$264$	1.23918e9	0.0157006
$265$	0	0
$266$	5.30396e10	0.649581
$267$	1.04930e10	0.126357
$268$	−6.02744e10	−0.713718
$269$	−1.00087e11	−1.16544	−0.582722	−	0.812671i	$-0.698013\pi$
$269$	−1.00087e11	−1.16544	−0.582722	+	0.812671i	$0.698013\pi$
$270$	0	0
$271$	−1.11318e11	−1.25373	−0.626867	−	0.779127i	$-0.715663\pi$
$271$	−1.11318e11	−1.25373	−0.626867	+	0.779127i	$0.715663\pi$
$272$	6.18275e9	0.0684891
$273$	7.58641e10	0.826617
$274$	−8.58211e10	−0.919849
$275$	0	0
$276$	2.92369e10	0.303277
$277$	−1.12732e11	−1.15050	−0.575251	−	0.817977i	$-0.695096\pi$
$277$	−1.12732e11	−1.15050	−0.575251	+	0.817977i	$0.695096\pi$
$278$	1.12105e11	1.12570
$279$	3.63712e10	0.359367
$280$	0	0
$281$	−1.44296e11	−1.38062	−0.690311	−	0.723513i	$-0.742526\pi$
$281$	−1.44296e11	−1.38062	−0.690311	+	0.723513i	$0.742526\pi$
$282$	4.77259e10	0.449400
$283$	−1.86409e10	−0.172754	−0.0863768	−	0.996263i	$-0.527529\pi$
$283$	−1.86409e10	−0.172754	−0.0863768	+	0.996263i	$0.527529\pi$
$284$	−1.60841e10	−0.146711
$285$	0	0
$286$	6.80574e9	0.0601490
$287$	6.89425e10	0.599817
$288$	−6.87971e9	−0.0589256
$289$	−1.09688e11	−0.924948
$290$	0	0
$291$	−2.95434e10	−0.241514
$292$	6.54988e10	0.527243
$293$	−1.71380e11	−1.35848	−0.679242	−	0.733914i	$-0.737691\pi$
$293$	−1.71380e11	−1.35848	−0.679242	+	0.733914i	$0.737691\pi$
$294$	3.53560e10	0.275994
$295$	0	0
$296$	6.67476e10	0.505386
$297$	−1.98492e9	−0.0148027
$298$	−5.43415e10	−0.399170
$299$	1.60573e11	1.16186
$300$	0	0
$301$	−1.32955e11	−0.933586
$302$	−4.81991e10	−0.333432
$303$	1.66822e11	1.13700
$304$	−2.64166e10	−0.177397
$305$	0	0
$306$	−9.90357e9	−0.0645722
$307$	2.10696e10	0.135374	0.0676868	−	0.997707i	$-0.478438\pi$
$307$	2.10696e10	0.135374	0.0676868	+	0.997707i	$0.478438\pi$
$308$	7.86344e9	0.0497891
$309$	1.56692e11	0.977761
$310$	0	0
$311$	1.54254e11	0.935005	0.467503	−	0.883992i	$-0.345154\pi$
$311$	1.54254e11	0.935005	0.467503	+	0.883992i	$0.345154\pi$
$312$	−3.77844e10	−0.225744
$313$	−1.09082e11	−0.642397	−0.321198	−	0.947012i	$-0.604086\pi$
$313$	−1.09082e11	−0.642397	−0.321198	+	0.947012i	$0.604086\pi$
$314$	1.83402e11	1.06468
$315$	0	0
$316$	4.56969e10	0.257807
$317$	−2.49559e11	−1.38806	−0.694028	−	0.719948i	$-0.744166\pi$
$317$	−2.49559e11	−1.38806	−0.694028	+	0.719948i	$0.744166\pi$
$318$	3.58191e10	0.196423
$319$	1.63508e10	0.0884057
$320$	0	0
$321$	3.89689e9	0.0204855
$322$	1.85528e11	0.961742
$323$	−3.80275e10	−0.194396
$324$	1.10200e10	0.0555556
$325$	0	0
$326$	2.65083e10	0.129988
$327$	−1.65556e11	−0.800720
$328$	−3.43371e10	−0.163806
$329$	3.02854e11	1.42512
$330$	0	0
$331$	−6.11723e10	−0.280110	−0.140055	−	0.990144i	$-0.544728\pi$
$331$	−6.11723e10	−0.280110	−0.140055	+	0.990144i	$0.544728\pi$
$332$	−1.69487e11	−0.765622
$333$	−1.06917e11	−0.476482
$334$	2.33743e11	1.02773
$335$	0	0
$336$	−4.36565e10	−0.186863
$337$	2.69481e11	1.13814	0.569068	−	0.822291i	$-0.307304\pi$
$337$	2.69481e11	1.13814	0.569068	+	0.822291i	$0.307304\pi$
$338$	−3.78452e10	−0.157720
$339$	1.93922e11	0.797496
$340$	0	0
$341$	2.07050e10	0.0829241
$342$	4.23142e10	0.167251
$343$	−1.07510e11	−0.419399
$344$	6.62186e10	0.254957
$345$	0	0
$346$	−2.30724e11	−0.865468
$347$	−4.98526e11	−1.84589	−0.922943	−	0.384937i	$-0.874223\pi$
$347$	−4.98526e11	−1.84589	−0.922943	+	0.384937i	$0.874223\pi$
$348$	−9.07768e10	−0.331794
$349$	1.48163e10	0.0534597	0.0267298	−	0.999643i	$-0.491491\pi$
$349$	1.48163e10	0.0534597	0.0267298	+	0.999643i	$0.491491\pi$
$350$	0	0
$351$	6.05232e10	0.212834
$352$	−3.91641e9	−0.0135971
$353$	−1.65317e11	−0.566673	−0.283336	−	0.959021i	$-0.591441\pi$
$353$	−1.65317e11	−0.566673	−0.283336	+	0.959021i	$0.591441\pi$
$354$	1.57379e11	0.532637
$355$	0	0
$356$	−3.31630e10	−0.109428
$357$	−6.28450e10	−0.204769
$358$	−3.22826e11	−1.03871
$359$	−2.43386e11	−0.773342	−0.386671	−	0.922218i	$-0.626375\pi$
$359$	−2.43386e11	−0.773342	−0.386671	+	0.922218i	$0.626375\pi$
$360$	0	0
$361$	−1.60210e11	−0.496487
$362$	3.35386e10	0.102649
$363$	1.89864e11	0.573935
$364$	−2.39768e11	−0.715871
$365$	0	0
$366$	−8.03935e10	−0.234183
$367$	4.69919e11	1.35215	0.676076	−	0.736832i	$-0.263679\pi$
$367$	4.69919e11	1.35215	0.676076	+	0.736832i	$0.263679\pi$
$368$	−9.24029e10	−0.262646
$369$	5.50013e10	0.154438
$370$	0	0
$371$	2.27297e11	0.622889
$372$	−1.14951e11	−0.311221
$373$	−6.88216e11	−1.84092	−0.920460	−	0.390836i	$-0.872186\pi$
$373$	−6.88216e11	−1.84092	−0.920460	+	0.390836i	$0.872186\pi$
$374$	−5.63781e9	−0.0149001
$375$	0	0
$376$	−1.50837e11	−0.389192
$377$	−4.98559e11	−1.27110
$378$	6.99293e10	0.176176
$379$	−4.12000e11	−1.02570	−0.512851	−	0.858478i	$-0.671411\pi$
$379$	−4.12000e11	−1.02570	−0.512851	+	0.858478i	$0.671411\pi$
$380$	0	0
$381$	2.26249e11	0.550078
$382$	2.44245e10	0.0586868
$383$	−4.78515e11	−1.13632	−0.568160	−	0.822918i	$-0.692345\pi$
$383$	−4.78515e11	−1.13632	−0.568160	+	0.822918i	$0.692345\pi$
$384$	2.17433e10	0.0510310
$385$	0	0
$386$	5.75238e10	0.131888
$387$	−1.06069e11	−0.240376
$388$	9.33717e10	0.209157
$389$	2.29201e11	0.507509	0.253754	−	0.967269i	$-0.418335\pi$
$389$	2.29201e11	0.507509	0.253754	+	0.967269i	$0.418335\pi$
$390$	0	0
$391$	−1.33017e11	−0.287814
$392$	−1.11742e11	−0.239018
$393$	1.55405e11	0.328624
$394$	−1.02200e11	−0.213656
$395$	0	0
$396$	6.27334e9	0.0128195
$397$	8.10866e11	1.63829	0.819147	−	0.573584i	$-0.194447\pi$
$397$	8.10866e11	1.63829	0.819147	+	0.573584i	$0.194447\pi$
$398$	3.71728e11	0.742595
$399$	2.68513e11	0.530380
$400$	0	0
$401$	−7.46341e11	−1.44141	−0.720705	−	0.693242i	$-0.756182\pi$
$401$	−7.46341e11	−1.44141	−0.720705	+	0.693242i	$0.756182\pi$
$402$	−3.05139e11	−0.582748
$403$	−6.31327e11	−1.19229
$404$	−5.27240e11	−0.984674
$405$	0	0
$406$	−5.76041e11	−1.05217
$407$	−6.08646e10	−0.109949
$408$	3.13002e10	0.0559212
$409$	−5.49776e10	−0.0971473	−0.0485737	−	0.998820i	$-0.515468\pi$
$409$	−5.49776e10	−0.0971473	−0.0485737	+	0.998820i	$0.515468\pi$
$410$	0	0
$411$	−4.34469e11	−0.751054
$412$	−4.95223e11	−0.846766
$413$	9.98678e11	1.68908
$414$	1.48012e11	0.247625
$415$	0	0
$416$	1.19417e11	0.195500
$417$	5.67530e11	0.919130
$418$	2.40882e10	0.0385933
$419$	1.20182e12	1.90492	0.952461	−	0.304660i	$-0.0985429\pi$
$419$	1.20182e12	1.90492	0.952461	+	0.304660i	$0.0985429\pi$
$420$	0	0
$421$	−6.30366e10	−0.0977966	−0.0488983	−	0.998804i	$-0.515571\pi$
$421$	−6.30366e10	−0.0977966	−0.0488983	+	0.998804i	$0.515571\pi$
$422$	3.67559e11	0.564185
$423$	2.41612e11	0.366933
$424$	−1.13206e11	−0.170107
$425$	0	0
$426$	−8.14256e10	−0.119789
$427$	−5.10152e11	−0.742633
$428$	−1.23161e10	−0.0177409
$429$	3.44541e10	0.0491115
$430$	0	0
$431$	9.86422e11	1.37694	0.688470	−	0.725265i	$-0.258283\pi$
$431$	9.86422e11	1.37694	0.688470	+	0.725265i	$0.258283\pi$
$432$	−3.48285e10	−0.0481125
$433$	−6.88083e11	−0.940688	−0.470344	−	0.882483i	$-0.655870\pi$
$433$	−6.88083e11	−0.940688	−0.470344	+	0.882483i	$0.655870\pi$
$434$	−7.29443e11	−0.986932
$435$	0	0
$436$	5.23240e11	0.693444
$437$	5.68332e11	0.745480
$438$	3.31588e11	0.430492
$439$	−1.45118e12	−1.86479	−0.932396	−	0.361439i	$-0.882285\pi$
$439$	−1.45118e12	−1.86479	−0.932396	+	0.361439i	$0.882285\pi$
$440$	0	0
$441$	1.78990e11	0.225348
$442$	1.71905e11	0.214234
$443$	−1.26776e12	−1.56394	−0.781971	−	0.623315i	$-0.785785\pi$
$443$	−1.26776e12	−1.56394	−0.781971	+	0.623315i	$0.785785\pi$
$444$	3.37910e11	0.412646
$445$	0	0
$446$	−8.77239e11	−1.04981
$447$	−2.75104e11	−0.325921
$448$	1.37976e11	0.161828
$449$	2.55287e11	0.296429	0.148215	−	0.988955i	$-0.452647\pi$
$449$	2.55287e11	0.296429	0.148215	+	0.988955i	$0.452647\pi$
$450$	0	0
$451$	3.13106e10	0.0356367
$452$	−6.12890e11	−0.690652
$453$	−2.44008e11	−0.272246
$454$	−5.47602e11	−0.604942
$455$	0	0
$456$	−1.33734e11	−0.144844
$457$	1.02881e12	1.10335	0.551674	−	0.834060i	$-0.313989\pi$
$457$	1.02881e12	1.10335	0.551674	+	0.834060i	$0.313989\pi$
$458$	1.22568e12	1.30161
$459$	−5.01368e10	−0.0527230
$460$	0	0
$461$	2.23245e11	0.230211	0.115106	−	0.993353i	$-0.463279\pi$
$461$	2.23245e11	0.230211	0.115106	+	0.993353i	$0.463279\pi$
$462$	3.98087e10	0.0406526
$463$	1.90133e12	1.92284	0.961418	−	0.275091i	$-0.0887081\pi$
$463$	1.90133e12	1.92284	0.961418	+	0.275091i	$0.0887081\pi$
$464$	2.86899e11	0.287342
$465$	0	0
$466$	−9.10587e11	−0.894509
$467$	1.45106e12	1.41175	0.705876	−	0.708336i	$-0.250554\pi$
$467$	1.45106e12	1.41175	0.705876	+	0.708336i	$0.250554\pi$
$468$	−1.91283e11	−0.184319
$469$	−1.93632e12	−1.84799
$470$	0	0
$471$	9.28471e11	0.869310
$472$	−4.97395e11	−0.461278
$473$	−6.03821e10	−0.0554668
$474$	2.31341e11	0.210499
$475$	0	0
$476$	1.98621e11	0.177335
$477$	1.81334e11	0.160379
$478$	1.01643e11	0.0890534
$479$	5.35569e11	0.464842	0.232421	−	0.972615i	$-0.425335\pi$
$479$	5.35569e11	0.464842	0.232421	+	0.972615i	$0.425335\pi$
$480$	0	0
$481$	1.85585e12	1.58085
$482$	−2.33030e10	−0.0196653
$483$	9.39236e11	0.785259
$484$	−6.00063e11	−0.497042
$485$	0	0
$486$	5.57886e10	0.0453609
$487$	6.30916e11	0.508266	0.254133	−	0.967169i	$-0.418210\pi$
$487$	6.30916e11	0.508266	0.254133	+	0.967169i	$0.418210\pi$
$488$	2.54083e11	0.202809
$489$	1.34198e11	0.106135
$490$	0	0
$491$	7.42654e11	0.576660	0.288330	−	0.957531i	$-0.406900\pi$
$491$	7.42654e11	0.576660	0.288330	+	0.957531i	$0.406900\pi$
$492$	−1.73831e11	−0.133747
$493$	4.13001e11	0.314877
$494$	−7.34486e11	−0.554897
$495$	0	0
$496$	3.63301e11	0.269525
$497$	−5.16702e11	−0.379871
$498$	−8.58027e11	−0.625128
$499$	1.47516e12	1.06509	0.532544	−	0.846402i	$-0.321236\pi$
$499$	1.47516e12	1.06509	0.532544	+	0.846402i	$0.321236\pi$
$500$	0	0
$501$	1.18332e12	0.839139
$502$	−4.02153e11	−0.282634
$503$	2.29676e12	1.59978	0.799891	−	0.600146i	$-0.204891\pi$
$503$	2.29676e12	1.59978	0.799891	+	0.600146i	$0.204891\pi$
$504$	−2.21011e11	−0.152573
$505$	0	0
$506$	8.42586e10	0.0571396
$507$	−1.91591e11	−0.128778
$508$	−7.15059e11	−0.476382
$509$	1.05824e12	0.698803	0.349402	−	0.936973i	$-0.386385\pi$
$509$	1.05824e12	0.698803	0.349402	+	0.936973i	$0.386385\pi$
$510$	0	0
$511$	2.10415e12	1.36516
$512$	−6.87195e10	−0.0441942
$513$	2.14216e11	0.136560
$514$	1.42249e12	0.898905
$515$	0	0
$516$	3.35231e11	0.208171
$517$	1.37543e11	0.0846700
$518$	2.14427e12	1.30857
$519$	−1.16804e12	−0.706652
$520$	0	0
$521$	1.88235e12	1.11926	0.559628	−	0.828744i	$-0.310944\pi$
$521$	1.88235e12	1.11926	0.559628	+	0.828744i	$0.310944\pi$
$522$	−4.59557e11	−0.270908
$523$	4.89479e11	0.286073	0.143036	−	0.989717i	$-0.454313\pi$
$523$	4.89479e11	0.286073	0.143036	+	0.989717i	$0.454313\pi$
$524$	−4.91158e11	−0.284597
$525$	0	0
$526$	−1.72308e12	−0.981454
$527$	5.22985e11	0.295353
$528$	−1.98268e10	−0.0111020
$529$	1.86826e11	0.103726
$530$	0	0
$531$	7.96730e11	0.434897
$532$	−8.48634e11	−0.459323
$533$	−9.54707e11	−0.512387
$534$	−1.67888e11	−0.0893476
$535$	0	0
$536$	9.64391e11	0.504675
$537$	−1.63431e12	−0.848105
$538$	1.60139e12	0.824094
$539$	1.01894e11	0.0519993
$540$	0	0
$541$	−8.00915e11	−0.401975	−0.200987	−	0.979594i	$-0.564415\pi$
$541$	−8.00915e11	−0.401975	−0.200987	+	0.979594i	$0.564415\pi$
$542$	1.78109e12	0.886523
$543$	1.69789e11	0.0838128
$544$	−9.89240e10	−0.0484291
$545$	0	0
$546$	−1.21383e12	−0.584506
$547$	−1.39381e12	−0.665673	−0.332837	−	0.942985i	$-0.608006\pi$
$547$	−1.39381e12	−0.665673	−0.332837	+	0.942985i	$0.608006\pi$
$548$	1.37314e12	0.650432
$549$	−4.06992e11	−0.191210
$550$	0	0
$551$	−1.76460e12	−0.815575
$552$	−4.67790e11	−0.214449
$553$	1.46802e12	0.667526
$554$	1.80371e12	0.813528
$555$	0	0
$556$	−1.79368e12	−0.795990
$557$	7.96649e11	0.350686	0.175343	−	0.984507i	$-0.443897\pi$
$557$	7.96649e11	0.350686	0.175343	+	0.984507i	$0.443897\pi$
$558$	−5.81938e11	−0.254111
$559$	1.84114e12	0.797505
$560$	0	0
$561$	−2.85414e10	−0.0121659
$562$	2.30873e12	0.976247
$563$	−3.20673e12	−1.34516	−0.672580	−	0.740024i	$-0.734814\pi$
$563$	−3.20673e12	−1.34516	−0.672580	+	0.740024i	$0.734814\pi$
$564$	−7.63614e11	−0.317774
$565$	0	0
$566$	2.98254e11	0.122155
$567$	3.54017e11	0.143847
$568$	2.57345e11	0.103741
$569$	−4.14631e12	−1.65828	−0.829138	−	0.559043i	$-0.811168\pi$
$569$	−4.14631e12	−1.65828	−0.829138	+	0.559043i	$0.811168\pi$
$570$	0	0
$571$	−1.26421e12	−0.497687	−0.248844	−	0.968544i	$-0.580051\pi$
$571$	−1.26421e12	−0.497687	−0.248844	+	0.968544i	$0.580051\pi$
$572$	−1.08892e11	−0.0425318
$573$	1.23649e11	0.0479175
$574$	−1.10308e12	−0.424134
$575$	0	0
$576$	1.10075e11	0.0416667
$577$	−8.08451e11	−0.303643	−0.151821	−	0.988408i	$-0.548514\pi$
$577$	−8.08451e11	−0.303643	−0.151821	+	0.988408i	$0.548514\pi$
$578$	1.75500e12	0.654037
$579$	2.91214e11	0.107686
$580$	0	0
$581$	−5.44478e12	−1.98238
$582$	4.72694e11	0.170776
$583$	1.03228e11	0.0370075
$584$	−1.04798e12	−0.372817
$585$	0	0
$586$	2.74207e12	0.960593
$587$	8.37879e11	0.291280	0.145640	−	0.989338i	$-0.453476\pi$
$587$	8.37879e11	0.291280	0.145640	+	0.989338i	$0.453476\pi$
$588$	−5.65696e11	−0.195157
$589$	−2.23452e12	−0.765006
$590$	0	0
$591$	−5.17385e11	−0.174450
$592$	−1.06796e12	−0.357362
$593$	−3.13947e12	−1.04258	−0.521291	−	0.853379i	$-0.674549\pi$
$593$	−3.13947e12	−1.04258	−0.521291	+	0.853379i	$0.674549\pi$
$594$	3.17588e10	0.0104671
$595$	0	0
$596$	8.69464e11	0.282256
$597$	1.88188e12	0.606326
$598$	−2.56917e12	−0.821557
$599$	3.79611e12	1.20481	0.602404	−	0.798191i	$-0.294209\pi$
$599$	3.79611e12	1.20481	0.602404	+	0.798191i	$0.294209\pi$
$600$	0	0
$601$	4.10001e12	1.28189	0.640943	−	0.767589i	$-0.278544\pi$
$601$	4.10001e12	1.28189	0.640943	+	0.767589i	$0.278544\pi$
$602$	2.12728e12	0.660145
$603$	−1.54477e12	−0.475812
$604$	7.71186e11	0.235772
$605$	0	0
$606$	−2.66915e12	−0.803983
$607$	−1.01349e12	−0.303020	−0.151510	−	0.988456i	$-0.548414\pi$
$607$	−1.01349e12	−0.303020	−0.151510	+	0.988456i	$0.548414\pi$
$608$	4.22665e11	0.125438
$609$	−2.91621e12	−0.859094
$610$	0	0
$611$	−4.19388e12	−1.21739
$612$	1.58457e11	0.0456594
$613$	1.01720e12	0.290960	0.145480	−	0.989361i	$-0.453527\pi$
$613$	1.01720e12	0.290960	0.145480	+	0.989361i	$0.453527\pi$
$614$	−3.37114e11	−0.0957236
$615$	0	0
$616$	−1.25815e11	−0.0352062
$617$	−2.71258e11	−0.0753529	−0.0376764	−	0.999290i	$-0.511996\pi$
$617$	−2.71258e11	−0.0753529	−0.0376764	+	0.999290i	$0.511996\pi$
$618$	−2.50707e12	−0.691381
$619$	4.15719e12	1.13813	0.569065	−	0.822293i	$-0.307305\pi$
$619$	4.15719e12	1.13813	0.569065	+	0.822293i	$0.307305\pi$
$620$	0	0
$621$	7.49309e11	0.202185
$622$	−2.46806e12	−0.661149
$623$	−1.06536e12	−0.283336
$624$	6.04550e11	0.159625
$625$	0	0
$626$	1.74531e12	0.454243
$627$	1.21947e11	0.0315113
$628$	−2.93443e12	−0.752844
$629$	−1.53737e12	−0.391606
$630$	0	0
$631$	9.66429e11	0.242682	0.121341	−	0.992611i	$-0.461281\pi$
$631$	9.66429e11	0.242682	0.121341	+	0.992611i	$0.461281\pi$
$632$	−7.31151e11	−0.182297
$633$	1.86077e12	0.460655
$634$	3.99295e12	0.981504
$635$	0	0
$636$	−5.73105e11	−0.138892
$637$	−3.10689e12	−0.747649
$638$	−2.61612e11	−0.0625123
$639$	−4.12217e11	−0.0978075
$640$	0	0
$641$	−5.26532e12	−1.23187	−0.615934	−	0.787798i	$-0.711221\pi$
$641$	−5.26532e12	−1.23187	−0.615934	+	0.787798i	$0.711221\pi$
$642$	−6.23503e10	−0.0144854
$643$	−1.46647e12	−0.338317	−0.169158	−	0.985589i	$-0.554105\pi$
$643$	−1.46647e12	−0.338317	−0.169158	+	0.985589i	$0.554105\pi$
$644$	−2.96845e12	−0.680054
$645$	0	0
$646$	6.08441e11	0.137459
$647$	−4.68611e12	−1.05134	−0.525670	−	0.850689i	$-0.676185\pi$
$647$	−4.68611e12	−1.05134	−0.525670	+	0.850689i	$0.676185\pi$
$648$	−1.76319e11	−0.0392837
$649$	4.53555e11	0.100353
$650$	0	0
$651$	−3.69280e12	−0.805827
$652$	−4.24133e11	−0.0919154
$653$	−6.00529e12	−1.29248	−0.646242	−	0.763133i	$-0.723660\pi$
$653$	−6.00529e12	−1.29248	−0.646242	+	0.763133i	$0.723660\pi$
$654$	2.64890e12	0.566195
$655$	0	0
$656$	5.49393e11	0.115829
$657$	1.67866e12	0.351495
$658$	−4.84566e12	−1.00771
$659$	4.76526e12	0.984243	0.492122	−	0.870526i	$-0.336221\pi$
$659$	4.76526e12	0.984243	0.492122	+	0.870526i	$0.336221\pi$
$660$	0	0
$661$	1.09459e12	0.223021	0.111510	−	0.993763i	$-0.464431\pi$
$661$	1.09459e12	0.223021	0.111510	+	0.993763i	$0.464431\pi$
$662$	9.78757e11	0.198068
$663$	8.70270e11	0.174921
$664$	2.71179e12	0.541377
$665$	0	0
$666$	1.71067e12	0.336924
$667$	−6.17242e12	−1.20751
$668$	−3.73989e12	−0.726716
$669$	−4.44102e12	−0.857167
$670$	0	0
$671$	−2.31688e11	−0.0441218
$672$	6.98504e11	0.132132
$673$	−6.96795e10	−0.0130929	−0.00654647	−	0.999979i	$-0.502084\pi$
$673$	−6.96795e10	−0.0130929	−0.00654647	+	0.999979i	$0.502084\pi$
$674$	−4.31170e12	−0.804783
$675$	0	0
$676$	6.05524e11	0.111525
$677$	7.19055e12	1.31557	0.657784	−	0.753207i	$-0.271494\pi$
$677$	7.19055e12	1.31557	0.657784	+	0.753207i	$0.271494\pi$
$678$	−3.10275e12	−0.563915
$679$	2.99957e12	0.541558
$680$	0	0
$681$	−2.77223e12	−0.493933
$682$	−3.31280e11	−0.0586362
$683$	−7.36932e12	−1.29579	−0.647894	−	0.761730i	$-0.724350\pi$
$683$	−7.36932e12	−1.29579	−0.647894	+	0.761730i	$0.724350\pi$
$684$	−6.77028e11	−0.118264
$685$	0	0
$686$	1.72017e12	0.296560
$687$	6.20499e12	1.06276
$688$	−1.05950e12	−0.180282
$689$	−3.14758e12	−0.532096
$690$	0	0
$691$	−2.34206e12	−0.390793	−0.195397	−	0.980724i	$-0.562599\pi$
$691$	−2.34206e12	−0.390793	−0.195397	+	0.980724i	$0.562599\pi$
$692$	3.69159e12	0.611978
$693$	2.01531e11	0.0331927
$694$	7.97641e12	1.30524
$695$	0	0
$696$	1.45243e12	0.234614
$697$	7.90870e11	0.126928
$698$	−2.37061e11	−0.0378017
$699$	−4.60984e12	−0.730363
$700$	0	0
$701$	−1.50522e12	−0.235434	−0.117717	−	0.993047i	$-0.537557\pi$
$701$	−1.50522e12	−0.235434	−0.117717	+	0.993047i	$0.537557\pi$
$702$	−9.68372e11	−0.150496
$703$	6.56859e12	1.01432
$704$	6.26626e10	0.00961461
$705$	0	0
$706$	2.64508e12	0.400698
$707$	−1.69376e13	−2.54956
$708$	−2.51806e12	−0.376632
$709$	1.14340e13	1.69937	0.849687	−	0.527288i	$-0.176791\pi$
$709$	1.14340e13	1.69937	0.849687	+	0.527288i	$0.176791\pi$
$710$	0	0
$711$	1.17116e12	0.171872
$712$	5.30607e11	0.0773773
$713$	−7.81615e12	−1.13264
$714$	1.00552e12	0.144793
$715$	0	0
$716$	5.16522e12	0.734480
$717$	5.14566e11	0.0727118
$718$	3.89418e12	0.546835
$719$	3.25896e12	0.454777	0.227388	−	0.973804i	$-0.426981\pi$
$719$	3.25896e12	0.454777	0.227388	+	0.973804i	$0.426981\pi$
$720$	0	0
$721$	−1.59091e13	−2.19248
$722$	2.56336e12	0.351069
$723$	−1.17971e11	−0.0160566
$724$	−5.36617e11	−0.0725840
$725$	0	0
$726$	−3.03782e12	−0.405833
$727$	4.92968e12	0.654506	0.327253	−	0.944937i	$-0.393877\pi$
$727$	4.92968e12	0.654506	0.327253	+	0.944937i	$0.393877\pi$
$728$	3.83629e12	0.506197
$729$	2.82430e11	0.0370370
$730$	0	0
$731$	−1.52518e12	−0.197557
$732$	1.28630e12	0.165593
$733$	1.41175e13	1.80629	0.903147	−	0.429331i	$-0.141251\pi$
$733$	1.41175e13	1.80629	0.903147	+	0.429331i	$0.141251\pi$
$734$	−7.51870e12	−0.956116
$735$	0	0
$736$	1.47845e12	0.185719
$737$	−8.79390e11	−0.109794
$738$	−8.80021e11	−0.109204
$739$	8.11730e12	1.00118	0.500589	−	0.865685i	$-0.333117\pi$
$739$	8.11730e12	1.00118	0.500589	+	0.865685i	$0.333117\pi$
$740$	0	0
$741$	−3.71834e12	−0.453071
$742$	−3.63675e12	−0.440449
$743$	1.28296e13	1.54441	0.772204	−	0.635375i	$-0.219155\pi$
$743$	1.28296e13	1.54441	0.772204	+	0.635375i	$0.219155\pi$
$744$	1.83921e12	0.220066
$745$	0	0
$746$	1.10115e13	1.30173
$747$	−4.34376e12	−0.510415
$748$	9.02049e10	0.0105359
$749$	−3.95656e11	−0.0459356
$750$	0	0
$751$	5.54959e12	0.636621	0.318310	−	0.947987i	$-0.396885\pi$
$751$	5.54959e12	0.636621	0.318310	+	0.947987i	$0.396885\pi$
$752$	2.41340e12	0.275200
$753$	−2.03590e12	−0.230770
$754$	7.97695e12	0.898805
$755$	0	0
$756$	−1.11887e12	−0.124575
$757$	−1.19519e12	−0.132283	−0.0661416	−	0.997810i	$-0.521069\pi$
$757$	−1.19519e12	−0.132283	−0.0661416	+	0.997810i	$0.521069\pi$
$758$	6.59200e12	0.725281
$759$	4.26559e11	0.0466543
$760$	0	0
$761$	3.31600e12	0.358413	0.179206	−	0.983812i	$-0.442647\pi$
$761$	3.31600e12	0.358413	0.179206	+	0.983812i	$0.442647\pi$
$762$	−3.61999e12	−0.388964
$763$	1.68091e13	1.79550
$764$	−3.90792e11	−0.0414978
$765$	0	0
$766$	7.65623e12	0.803500
$767$	−1.38296e13	−1.44288
$768$	−3.47892e11	−0.0360844
$769$	−5.79888e12	−0.597965	−0.298982	−	0.954259i	$-0.596647\pi$
$769$	−5.79888e12	−0.597965	−0.298982	+	0.954259i	$0.596647\pi$
$770$	0	0
$771$	7.20133e12	0.733953
$772$	−9.20380e11	−0.0932587
$773$	−1.11447e13	−1.12269	−0.561344	−	0.827582i	$-0.689716\pi$
$773$	−1.11447e13	−1.12269	−0.561344	+	0.827582i	$0.689716\pi$
$774$	1.69711e12	0.169971
$775$	0	0
$776$	−1.49395e12	−0.147896
$777$	1.08554e13	1.06844
$778$	−3.66722e12	−0.358863
$779$	−3.37909e12	−0.328762
$780$	0	0
$781$	−2.34663e11	−0.0225691
$782$	2.12827e12	0.203515
$783$	−2.32651e12	−0.221196
$784$	1.78788e12	0.169011
$785$	0	0
$786$	−2.48649e12	−0.232372
$787$	−1.05424e13	−0.979606	−0.489803	−	0.871833i	$-0.662931\pi$
$787$	−1.05424e13	−0.979606	−0.489803	+	0.871833i	$0.662931\pi$
$788$	1.63519e12	0.151078
$789$	−8.72310e12	−0.801354
$790$	0	0
$791$	−1.96891e13	−1.78827
$792$	−1.00373e11	−0.00906474
$793$	7.06452e12	0.634386
$794$	−1.29739e13	−1.15845
$795$	0	0
$796$	−5.94765e12	−0.525094
$797$	−2.96440e12	−0.260240	−0.130120	−	0.991498i	$-0.541536\pi$
$797$	−2.96440e12	−0.260240	−0.130120	+	0.991498i	$0.541536\pi$
$798$	−4.29621e12	−0.375036
$799$	3.47417e12	0.301571
$800$	0	0
$801$	−8.49931e11	−0.0729520
$802$	1.19415e13	1.01923
$803$	9.55613e11	0.0811077
$804$	4.88223e12	0.412065
$805$	0	0
$806$	1.01012e13	0.843075
$807$	8.10704e12	0.672870
$808$	8.43585e12	0.696270
$809$	−1.20187e13	−0.986485	−0.493243	−	0.869892i	$-0.664189\pi$
$809$	−1.20187e13	−0.986485	−0.493243	+	0.869892i	$0.664189\pi$
$810$	0	0
$811$	1.67172e13	1.35697	0.678484	−	0.734615i	$-0.262637\pi$
$811$	1.67172e13	1.35697	0.678484	+	0.734615i	$0.262637\pi$
$812$	9.21666e12	0.743998
$813$	9.01679e12	0.723843
$814$	9.73833e11	0.0777454
$815$	0	0
$816$	−5.00803e11	−0.0395422
$817$	6.51653e12	0.511702
$818$	8.79642e11	0.0686935
$819$	−6.14499e12	−0.477247
$820$	0	0
$821$	8.93150e12	0.686089	0.343044	−	0.939319i	$-0.388542\pi$
$821$	8.93150e12	0.686089	0.343044	+	0.939319i	$0.388542\pi$
$822$	6.95151e12	0.531075
$823$	6.33020e12	0.480970	0.240485	−	0.970653i	$-0.422693\pi$
$823$	6.33020e12	0.480970	0.240485	+	0.970653i	$0.422693\pi$
$824$	7.92357e12	0.598754
$825$	0	0
$826$	−1.59788e13	−1.19436
$827$	6.72193e12	0.499711	0.249856	−	0.968283i	$-0.419617\pi$
$827$	6.72193e12	0.499711	0.249856	+	0.968283i	$0.419617\pi$
$828$	−2.36819e12	−0.175097
$829$	−2.56009e13	−1.88261	−0.941303	−	0.337563i	$-0.890397\pi$
$829$	−2.56009e13	−1.88261	−0.941303	+	0.337563i	$0.890397\pi$
$830$	0	0
$831$	9.13128e12	0.664243
$832$	−1.91068e12	−0.138239
$833$	2.57371e12	0.185207
$834$	−9.08049e12	−0.649923
$835$	0	0
$836$	−3.85412e11	−0.0272896
$837$	−2.94606e12	−0.207481
$838$	−1.92292e13	−1.34698
$839$	−1.79495e13	−1.25061	−0.625306	−	0.780379i	$-0.715026\pi$
$839$	−1.79495e13	−1.25061	−0.625306	+	0.780379i	$0.715026\pi$
$840$	0	0
$841$	4.65744e12	0.321044
$842$	1.00859e12	0.0691526
$843$	1.16879e13	0.797102
$844$	−5.88095e12	−0.398939
$845$	0	0
$846$	−3.86579e12	−0.259461
$847$	−1.92771e13	−1.28696
$848$	1.81130e12	0.120284
$849$	1.50991e12	0.0997394
$850$	0	0
$851$	2.29764e13	1.50175
$852$	1.30281e12	0.0847038
$853$	−1.47770e13	−0.955688	−0.477844	−	0.878445i	$-0.658582\pi$
$853$	−1.47770e13	−0.955688	−0.477844	+	0.878445i	$0.658582\pi$
$854$	8.16244e12	0.525121
$855$	0	0
$856$	1.97058e11	0.0125447
$857$	2.96640e13	1.87852	0.939261	−	0.343204i	$-0.111512\pi$
$857$	2.96640e13	1.87852	0.939261	+	0.343204i	$0.111512\pi$
$858$	−5.51265e11	−0.0347270
$859$	2.71397e12	0.170073	0.0850366	−	0.996378i	$-0.472899\pi$
$859$	2.71397e12	0.170073	0.0850366	+	0.996378i	$0.472899\pi$
$860$	0	0
$861$	−5.58434e12	−0.346304
$862$	−1.57828e13	−0.973644
$863$	−4.43572e12	−0.272217	−0.136109	−	0.990694i	$-0.543460\pi$
$863$	−4.43572e12	−0.272217	−0.136109	+	0.990694i	$0.543460\pi$
$864$	5.57256e11	0.0340207
$865$	0	0
$866$	1.10093e13	0.665167
$867$	8.88470e12	0.534019
$868$	1.16711e13	0.697866
$869$	6.66708e11	0.0396595
$870$	0	0
$871$	2.68139e13	1.57862
$872$	−8.37183e12	−0.490339
$873$	2.39301e12	0.139438
$874$	−9.09332e12	−0.527134
$875$	0	0
$876$	−5.30540e12	−0.304404
$877$	1.78251e13	1.01750	0.508749	−	0.860915i	$-0.330108\pi$
$877$	1.78251e13	1.01750	0.508749	+	0.860915i	$0.330108\pi$
$878$	2.32188e13	1.31861
$879$	1.38817e13	0.784321
$880$	0	0
$881$	−1.12118e13	−0.627021	−0.313511	−	0.949585i	$-0.601505\pi$
$881$	−1.12118e13	−0.627021	−0.313511	+	0.949585i	$0.601505\pi$
$882$	−2.86384e12	−0.159345
$883$	1.69399e13	0.937754	0.468877	−	0.883263i	$-0.344659\pi$
$883$	1.69399e13	0.937754	0.468877	+	0.883263i	$0.344659\pi$
$884$	−2.75048e12	−0.151486
$885$	0	0
$886$	2.02842e13	1.10587
$887$	1.38745e13	0.752595	0.376297	−	0.926499i	$-0.377197\pi$
$887$	1.38745e13	0.752595	0.376297	+	0.926499i	$0.377197\pi$
$888$	−5.40656e12	−0.291785
$889$	−2.29713e13	−1.23347
$890$	0	0
$891$	1.60779e11	0.00854632
$892$	1.40358e13	0.742329
$893$	−1.48438e13	−0.781113
$894$	4.40166e12	0.230461
$895$	0	0
$896$	−2.20762e12	−0.114429
$897$	−1.30064e13	−0.670798
$898$	−4.08460e12	−0.209607
$899$	2.42682e13	1.23913
$900$	0	0
$901$	2.60742e12	0.131810
$902$	−5.00970e11	−0.0251989
$903$	1.07693e13	0.539006
$904$	9.80624e12	0.488365
$905$	0	0
$906$	3.90413e12	0.192507
$907$	2.71558e13	1.33239	0.666193	−	0.745779i	$-0.267923\pi$
$907$	2.71558e13	1.33239	0.666193	+	0.745779i	$0.267923\pi$
$908$	8.76163e12	0.427758
$909$	−1.35126e13	−0.656449
$910$	0	0
$911$	−2.46750e13	−1.18693	−0.593464	−	0.804861i	$-0.702240\pi$
$911$	−2.46750e13	−1.18693	−0.593464	+	0.804861i	$0.702240\pi$
$912$	2.13974e12	0.102420
$913$	−2.47278e12	−0.117779
$914$	−1.64610e13	−0.780184
$915$	0	0
$916$	−1.96108e13	−0.920379
$917$	−1.57785e13	−0.736891
$918$	8.02189e11	0.0372808
$919$	3.20842e13	1.48379	0.741894	−	0.670518i	$-0.233928\pi$
$919$	3.20842e13	1.48379	0.741894	+	0.670518i	$0.233928\pi$
$920$	0	0
$921$	−1.70664e12	−0.0781580
$922$	−3.57191e12	−0.162784
$923$	7.15522e12	0.324501
$924$	−6.36939e11	−0.0287458
$925$	0	0
$926$	−3.04212e13	−1.35965
$927$	−1.26920e13	−0.564511
$928$	−4.59039e12	−0.203181
$929$	3.59157e11	0.0158203	0.00791014	−	0.999969i	$-0.497482\pi$
$929$	3.59157e11	0.0158203	0.00791014	+	0.999969i	$0.497482\pi$
$930$	0	0
$931$	−1.09965e13	−0.479712
$932$	1.45694e13	0.632513
$933$	−1.24946e13	−0.539826
$934$	−2.32169e13	−0.998259
$935$	0	0
$936$	3.06053e12	0.130333
$937$	−2.54992e12	−0.108068	−0.0540342	−	0.998539i	$-0.517208\pi$
$937$	−2.54992e12	−0.108068	−0.0540342	+	0.998539i	$0.517208\pi$
$938$	3.09811e13	1.30673
$939$	8.83564e12	0.370888
$940$	0	0
$941$	−5.31550e12	−0.220999	−0.110500	−	0.993876i	$-0.535245\pi$
$941$	−5.31550e12	−0.220999	−0.110500	+	0.993876i	$0.535245\pi$
$942$	−1.48555e13	−0.614695
$943$	−1.18198e13	−0.486750
$944$	7.95832e12	0.326172
$945$	0	0
$946$	9.66114e11	0.0392210
$947$	−1.17412e13	−0.474394	−0.237197	−	0.971462i	$-0.576229\pi$
$947$	−1.17412e13	−0.474394	−0.237197	+	0.971462i	$0.576229\pi$
$948$	−3.70145e12	−0.148845
$949$	−2.91381e13	−1.16617
$950$	0	0
$951$	2.02143e13	0.801394
$952$	−3.17794e12	−0.125395
$953$	−4.31292e13	−1.69377	−0.846884	−	0.531778i	$-0.821524\pi$
$953$	−4.31292e13	−1.69377	−0.846884	+	0.531778i	$0.821524\pi$
$954$	−2.90135e12	−0.113405
$955$	0	0
$956$	−1.62628e12	−0.0629703
$957$	−1.32441e12	−0.0510410
$958$	−8.56910e12	−0.328693
$959$	4.41122e13	1.68413
$960$	0	0
$961$	4.29119e12	0.162302
$962$	−2.96936e13	−1.11783
$963$	−3.15648e11	−0.0118273
$964$	3.72848e11	0.0139054
$965$	0	0
$966$	−1.50278e13	−0.555262
$967$	1.62737e13	0.598505	0.299252	−	0.954174i	$-0.403263\pi$
$967$	1.62737e13	0.598505	0.299252	+	0.954174i	$0.403263\pi$
$968$	9.60101e12	0.351462
$969$	3.08023e12	0.112234
$970$	0	0
$971$	2.35398e13	0.849799	0.424900	−	0.905241i	$-0.360309\pi$
$971$	2.35398e13	0.849799	0.424900	+	0.905241i	$0.360309\pi$
$972$	−8.92617e11	−0.0320750
$973$	−5.76220e13	−2.06101
$974$	−1.00947e13	−0.359398
$975$	0	0
$976$	−4.06533e12	−0.143407
$977$	1.49259e13	0.524103	0.262051	−	0.965054i	$-0.415601\pi$
$977$	1.49259e13	0.524103	0.262051	+	0.965054i	$0.415601\pi$
$978$	−2.14717e12	−0.0750486
$979$	−4.83840e11	−0.0168337
$980$	0	0
$981$	1.34101e13	0.462296
$982$	−1.18825e13	−0.407760
$983$	7.14011e12	0.243901	0.121951	−	0.992536i	$-0.461085\pi$
$983$	7.14011e12	0.243901	0.121951	+	0.992536i	$0.461085\pi$
$984$	2.78130e12	0.0945736
$985$	0	0
$986$	−6.60802e12	−0.222651
$987$	−2.45311e13	−0.822793
$988$	1.17518e13	0.392371
$989$	2.27943e13	0.757604
$990$	0	0
$991$	−3.31522e13	−1.09189	−0.545947	−	0.837819i	$-0.683830\pi$
$991$	−3.31522e13	−1.09189	−0.545947	+	0.837819i	$0.683830\pi$
$992$	−5.81282e12	−0.190583
$993$	4.95496e12	0.161722
$994$	8.26723e12	0.268609
$995$	0	0
$996$	1.37284e13	0.442032
$997$	5.60870e12	0.179777	0.0898884	−	0.995952i	$-0.471349\pi$
$997$	5.60870e12	0.179777	0.0898884	+	0.995952i	$0.471349\pi$
$998$	−2.36025e13	−0.753131
$999$	8.66026e12	0.275097

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	150.10.a.l.1.2	✓	2
5.2	odd	4		150.10.c.k.49.2		4
5.3	odd	4		150.10.c.k.49.3		4
5.4	even	2		150.10.a.q.1.1	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.10.a.l.1.2	✓	2	1.1	even	1	trivial
150.10.a.q.1.1	yes	2	5.4	even	2
150.10.c.k.49.2		4	5.2	odd	4
150.10.c.k.49.3		4	5.3	odd	4

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:	\( N \)	\(=\)	\( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	150.a (trivial)

\(f(q)\)	\(=\)	\(q-16.0000 q^{2} -81.0000 q^{3} +256.000 q^{4} +1296.00 q^{6} +8224.02 q^{7} -4096.00 q^{8} +6561.00 q^{9} +3734.98 q^{11} -20736.0 q^{12} -113885. q^{13} -131584. q^{14} +65536.0 q^{16} +94341.3 q^{17} -104976. q^{18} -403085. q^{19} -666145. q^{21} -59759.7 q^{22} -1.40996e6 q^{23} +331776. q^{24} +1.82216e6 q^{26} -531441. q^{27} +2.10535e6 q^{28} +4.37774e6 q^{29} +5.54354e6 q^{31} -1.04858e6 q^{32} -302534. q^{33} -1.50946e6 q^{34} +1.67962e6 q^{36} -1.62958e7 q^{37} +6.44936e6 q^{38} +9.22470e6 q^{39} +8.38307e6 q^{41} +1.06583e7 q^{42} -1.61666e7 q^{43} +956155. q^{44} +2.25593e7 q^{46} +3.68255e7 q^{47} -5.30842e6 q^{48} +2.72809e7 q^{49} -7.64165e6 q^{51} -2.91546e7 q^{52} +2.76382e7 q^{53} +8.50306e6 q^{54} -3.36856e7 q^{56} +3.26499e7 q^{57} -7.00438e7 q^{58} +1.21434e8 q^{59} -6.20320e7 q^{61} -8.86966e7 q^{62} +5.39578e7 q^{63} +1.67772e7 q^{64} +4.84054e6 q^{66} -2.35447e8 q^{67} +2.41514e7 q^{68} +1.14207e8 q^{69} -6.28284e7 q^{71} -2.68739e7 q^{72} +2.55855e8 q^{73} +2.60733e8 q^{74} -1.03190e8 q^{76} +3.07166e7 q^{77} -1.47595e8 q^{78} +1.78504e8 q^{79} +4.30467e7 q^{81} -1.34129e8 q^{82} -6.62058e8 q^{83} -1.70533e8 q^{84} +2.58666e8 q^{86} -3.54597e8 q^{87} -1.52985e7 q^{88} -1.29543e8 q^{89} -9.36593e8 q^{91} -3.60949e8 q^{92} -4.49027e8 q^{93} -5.89208e8 q^{94} +8.49347e7 q^{96} +3.64733e8 q^{97} -4.36494e8 q^{98} +2.45052e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 32 q^{2} - 162 q^{3} + 512 q^{4} + 2592 q^{6} - 3166 q^{7} - 8192 q^{8} + 13122 q^{9} + 27084 q^{11} - 41472 q^{12} - 70858 q^{13} + 50656 q^{14} + 131072 q^{16} - 144756 q^{17} - 209952 q^{18} + 115690 q^{19}+ \cdots + 177698124 q^{99}+O(q^{100}) \) 2 * q - 32 * q^2 - 162 * q^3 + 512 * q^4 + 2592 * q^6 - 3166 * q^7 - 8192 * q^8 + 13122 * q^9 + 27084 * q^11 - 41472 * q^12 - 70858 * q^13 + 50656 * q^14 + 131072 * q^16 - 144756 * q^17 - 209952 * q^18 + 115690 * q^19 + 256446 * q^21 - 433344 * q^22 - 799668 * q^23 + 663552 * q^24 + 1133728 * q^26 - 1062882 * q^27 - 810496 * q^28 - 208140 * q^29 + 6360094 * q^31 - 2097152 * q^32 - 2193804 * q^33 + 2316096 * q^34 + 3359232 * q^36 - 1876036 * q^37 - 1851040 * q^38 + 5739498 * q^39 + 38125824 * q^41 - 4103136 * q^42 + 3776162 * q^43 + 6933504 * q^44 + 12794688 * q^46 + 11199924 * q^47 - 10616832 * q^48 + 116659764 * q^49 + 11725236 * q^51 - 18139648 * q^52 + 38780952 * q^53 + 17006112 * q^54 + 12967936 * q^56 - 9370890 * q^57 + 3330240 * q^58 + 286804020 * q^59 - 255752666 * q^61 - 101761504 * q^62 - 20772126 * q^63 + 33554432 * q^64 + 35100864 * q^66 - 208870006 * q^67 - 37057536 * q^68 + 64773108 * q^69 - 277057536 * q^71 - 53747712 * q^72 + 60155132 * q^73 + 30016576 * q^74 + 29616640 * q^76 - 235229172 * q^77 - 91831968 * q^78 + 127287760 * q^79 + 86093442 * q^81 - 610013184 * q^82 - 596984628 * q^83 + 65650176 * q^84 - 60418592 * q^86 + 16859340 * q^87 - 110936064 * q^88 + 940116480 * q^89 - 1426673386 * q^91 - 204715008 * q^92 - 515167614 * q^93 - 179198784 * q^94 + 169869312 * q^96 - 1317925426 * q^97 - 1866556224 * q^98 + 177698124 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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