LMFDB - Embedded newform 162.14.a.h.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [162,14,Mod(1,162)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(162, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 14, names="a")

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

chi := DirichletCharacter("162.1");

S:= CuspForms(chi, 14);

N := Newforms(S);

Level:	$ N $	$=$	$ 162 = 2 \cdot 3^{4} $
Weight:	$ k $	$=$	$ 14 $
Character orbit:	$[\chi]$	$=$	162.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:	$173.714104902$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} - 70055x^{4} - 2462667x^{3} + 809526798x^{2} + 42037623513x + 424360579500 $ x^6 - 2x^5 - 70055x^4 - 2462667x^3 + 809526798x^2 + 42037623513*x + 424360579500
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{8}\cdot 3^{21} $
Twist minimal:	no (minimal twist has level 18)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$255.269$ of defining polynomial
Character	$\chi$	$=$	162.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+64.0000 q^{2} +4096.00 q^{4} -21854.6 q^{5} +292012. q^{7} +262144. q^{8} +O(q^{10})$	\(q+64.0000 q^{2} +4096.00 q^{4} -21854.6 q^{5} +292012. q^{7} +262144. q^{8} -1.39870e6 q^{10} +2.24156e6 q^{11} -1.73866e7 q^{13} +1.86888e7 q^{14} +1.67772e7 q^{16} -1.02646e8 q^{17} +2.84600e8 q^{19} -8.95166e7 q^{20} +1.43460e8 q^{22} -2.58321e8 q^{23} -7.43078e8 q^{25} -1.11274e9 q^{26} +1.19608e9 q^{28} +3.48435e9 q^{29} -8.11402e9 q^{31} +1.07374e9 q^{32} -6.56935e9 q^{34} -6.38182e9 q^{35} -1.28194e10 q^{37} +1.82144e10 q^{38} -5.72906e9 q^{40} +4.71422e9 q^{41} +3.32794e10 q^{43} +9.18142e9 q^{44} -1.65326e10 q^{46} +3.04125e9 q^{47} -1.16178e10 q^{49} -4.75570e10 q^{50} -7.12157e10 q^{52} +5.94638e10 q^{53} -4.89884e10 q^{55} +7.65493e10 q^{56} +2.22998e11 q^{58} +5.78665e11 q^{59} -2.87088e11 q^{61} -5.19297e11 q^{62} +6.87195e10 q^{64} +3.79978e11 q^{65} +8.74840e11 q^{67} -4.20439e11 q^{68} -4.08437e11 q^{70} -1.64422e12 q^{71} -1.62988e12 q^{73} -8.20444e11 q^{74} +1.16572e12 q^{76} +6.54563e11 q^{77} -3.02692e12 q^{79} -3.66660e11 q^{80} +3.01710e11 q^{82} -9.24967e11 q^{83} +2.24329e12 q^{85} +2.12988e12 q^{86} +5.87611e11 q^{88} -6.03750e12 q^{89} -5.07711e12 q^{91} -1.05808e12 q^{92} +1.94640e11 q^{94} -6.21982e12 q^{95} +1.19926e12 q^{97} -7.43538e11 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 384 q^{2} + 24576 q^{4} - 36504 q^{5} - 153942 q^{7} + 1572864 q^{8}+O(q^{10}) $ 6 * q + 384 * q^2 + 24576 * q^4 - 36504 * q^5 - 153942 * q^7 + 1572864 * q^8	\( 6 q + 384 q^{2} + 24576 q^{4} - 36504 q^{5} - 153942 q^{7} + 1572864 q^{8} - 2336256 q^{10} - 1456506 q^{11} - 24033660 q^{13} - 9852288 q^{14} + 100663296 q^{16} + 539766 q^{17} + 168570444 q^{19} - 149520384 q^{20} - 93216384 q^{22} + 445386186 q^{23} + 2193691326 q^{25} - 1538154240 q^{26} - 630546432 q^{28} - 9171393012 q^{29} - 4264851066 q^{31} + 6442450944 q^{32} + 34545024 q^{34} - 2590484706 q^{35} - 24554425344 q^{37} + 10788508416 q^{38} - 9569304576 q^{40} - 15964345782 q^{41} - 78379952838 q^{43} - 5965848576 q^{44} + 28504715904 q^{46} + 94117799358 q^{47} + 15284873538 q^{49} + 140396244864 q^{50} - 98441871360 q^{52} + 296395207632 q^{53} - 554141279106 q^{55} - 40354971648 q^{56} - 586969152768 q^{58} + 46698155010 q^{59} - 928192122600 q^{61} - 272950468224 q^{62} + 412316860416 q^{64} - 1327744890468 q^{65} - 2282039666898 q^{67} + 2210881536 q^{68} - 165791021184 q^{70} - 1180061485344 q^{71} + 677917450614 q^{73} - 1571483222016 q^{74} + 690464538624 q^{76} - 3622976109756 q^{77} - 2457538059750 q^{79} - 612435492864 q^{80} - 1021718130048 q^{82} - 9950916891942 q^{83} + 576987174720 q^{85} - 5016316981632 q^{86} - 381814308864 q^{88} - 11302343348148 q^{89} + 7395764329770 q^{91} + 1824301817856 q^{92} + 6023539158912 q^{94} - 7488669126384 q^{95} - 1124429902242 q^{97} + 978231906432 q^{98}+O(q^{100}) \) 6 * q + 384 * q^2 + 24576 * q^4 - 36504 * q^5 - 153942 * q^7 + 1572864 * q^8 - 2336256 * q^10 - 1456506 * q^11 - 24033660 * q^13 - 9852288 * q^14 + 100663296 * q^16 + 539766 * q^17 + 168570444 * q^19 - 149520384 * q^20 - 93216384 * q^22 + 445386186 * q^23 + 2193691326 * q^25 - 1538154240 * q^26 - 630546432 * q^28 - 9171393012 * q^29 - 4264851066 * q^31 + 6442450944 * q^32 + 34545024 * q^34 - 2590484706 * q^35 - 24554425344 * q^37 + 10788508416 * q^38 - 9569304576 * q^40 - 15964345782 * q^41 - 78379952838 * q^43 - 5965848576 * q^44 + 28504715904 * q^46 + 94117799358 * q^47 + 15284873538 * q^49 + 140396244864 * q^50 - 98441871360 * q^52 + 296395207632 * q^53 - 554141279106 * q^55 - 40354971648 * q^56 - 586969152768 * q^58 + 46698155010 * q^59 - 928192122600 * q^61 - 272950468224 * q^62 + 412316860416 * q^64 - 1327744890468 * q^65 - 2282039666898 * q^67 + 2210881536 * q^68 - 165791021184 * q^70 - 1180061485344 * q^71 + 677917450614 * q^73 - 1571483222016 * q^74 + 690464538624 * q^76 - 3622976109756 * q^77 - 2457538059750 * q^79 - 612435492864 * q^80 - 1021718130048 * q^82 - 9950916891942 * q^83 + 576987174720 * q^85 - 5016316981632 * q^86 - 381814308864 * q^88 - 11302343348148 * q^89 + 7395764329770 * q^91 + 1824301817856 * q^92 + 6023539158912 * q^94 - 7488669126384 * q^95 - 1124429902242 * q^97 + 978231906432 * q^98

Display 100 coefficients 10 coefficients

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 $

$2$	64.0000	0.707107
$2$	64.0000	0.707107
$3$	0	0
$3$	0	0
$4$	4096.00	0.500000
$5$	−21854.6	−0.625516	−0.312758	−	0.949833i	$-0.601253\pi$
$5$	−21854.6	−0.625516	−0.312758	+	0.949833i	$0.601253\pi$
$6$	0	0
$7$	292012.	0.938132	0.469066	−	0.883163i	$-0.344591\pi$
$7$	292012.	0.938132	0.469066	+	0.883163i	$0.344591\pi$
$8$	262144.	0.353553
$9$	0	0
$10$	−1.39870e6	−0.442307
$11$	2.24156e6	0.381503	0.190751	−	0.981638i	$-0.438908\pi$
$11$	2.24156e6	0.381503	0.190751	+	0.981638i	$0.438908\pi$
$12$	0	0
$13$	−1.73866e7	−0.999042	−0.499521	−	0.866302i	$-0.666491\pi$
$13$	−1.73866e7	−0.999042	−0.499521	+	0.866302i	$0.666491\pi$
$14$	1.86888e7	0.663360
$15$	0	0
$16$	1.67772e7	0.250000
$17$	−1.02646e8	−1.03139	−0.515697	−	0.856771i	$-0.672467\pi$
$17$	−1.02646e8	−1.03139	−0.515697	+	0.856771i	$0.672467\pi$
$18$	0	0
$19$	2.84600e8	1.38783	0.693915	−	0.720057i	$-0.255884\pi$
$19$	2.84600e8	1.38783	0.693915	+	0.720057i	$0.255884\pi$
$20$	−8.95166e7	−0.312758
$21$	0	0
$22$	1.43460e8	0.269763
$23$	−2.58321e8	−0.363856	−0.181928	−	0.983312i	$-0.558234\pi$
$23$	−2.58321e8	−0.363856	−0.181928	+	0.983312i	$0.558234\pi$
$24$	0	0
$25$	−7.43078e8	−0.608730
$26$	−1.11274e9	−0.706429
$27$	0	0
$28$	1.19608e9	0.469066
$29$	3.48435e9	1.08776	0.543881	−	0.839162i	$-0.316954\pi$
$29$	3.48435e9	1.08776	0.543881	+	0.839162i	$0.316954\pi$
$30$	0	0
$31$	−8.11402e9	−1.64204	−0.821022	−	0.570896i	$-0.806596\pi$
$31$	−8.11402e9	−1.64204	−0.821022	+	0.570896i	$0.806596\pi$
$32$	1.07374e9	0.176777
$33$	0	0
$34$	−6.56935e9	−0.729306
$35$	−6.38182e9	−0.586817
$36$	0	0
$37$	−1.28194e10	−0.821405	−0.410703	−	0.911769i	$-0.634717\pi$
$37$	−1.28194e10	−0.821405	−0.410703	+	0.911769i	$0.634717\pi$
$38$	1.82144e10	0.981344
$39$	0	0
$40$	−5.72906e9	−0.221153
$41$	4.71422e9	0.154994	0.0774970	−	0.996993i	$-0.475307\pi$
$41$	4.71422e9	0.154994	0.0774970	+	0.996993i	$0.475307\pi$
$42$	0	0
$43$	3.32794e10	0.802844	0.401422	−	0.915893i	$-0.368516\pi$
$43$	3.32794e10	0.802844	0.401422	+	0.915893i	$0.368516\pi$
$44$	9.18142e9	0.190751
$45$	0	0
$46$	−1.65326e10	−0.257285
$47$	3.04125e9	0.0411544	0.0205772	−	0.999788i	$-0.493450\pi$
$47$	3.04125e9	0.0411544	0.0205772	+	0.999788i	$0.493450\pi$
$48$	0	0
$49$	−1.16178e10	−0.119908
$50$	−4.75570e10	−0.430437
$51$	0	0
$52$	−7.12157e10	−0.499521
$53$	5.94638e10	0.368519	0.184259	−	0.982878i	$-0.441011\pi$
$53$	5.94638e10	0.368519	0.184259	+	0.982878i	$0.441011\pi$
$54$	0	0
$55$	−4.89884e10	−0.238636
$56$	7.65493e10	0.331680
$57$	0	0
$58$	2.22998e11	0.769164
$59$	5.78665e11	1.78603	0.893015	−	0.450026i	$-0.148585\pi$
$59$	5.78665e11	1.78603	0.893015	+	0.450026i	$0.148585\pi$
$60$	0	0
$61$	−2.87088e11	−0.713461	−0.356731	−	0.934207i	$-0.616109\pi$
$61$	−2.87088e11	−0.713461	−0.356731	+	0.934207i	$0.616109\pi$
$62$	−5.19297e11	−1.16110
$63$	0	0
$64$	6.87195e10	0.125000
$65$	3.79978e11	0.624917
$66$	0	0
$67$	8.74840e11	1.18152	0.590762	−	0.806846i	$-0.298827\pi$
$67$	8.74840e11	1.18152	0.590762	+	0.806846i	$0.298827\pi$
$68$	−4.20439e11	−0.515697
$69$	0	0
$70$	−4.08437e11	−0.414942
$71$	−1.64422e12	−1.52329	−0.761644	−	0.647996i	$-0.775607\pi$
$71$	−1.64422e12	−1.52329	−0.761644	+	0.647996i	$0.775607\pi$
$72$	0	0
$73$	−1.62988e12	−1.26054	−0.630270	−	0.776376i	$-0.717056\pi$
$73$	−1.62988e12	−1.26054	−0.630270	+	0.776376i	$0.717056\pi$
$74$	−8.20444e11	−0.580821
$75$	0	0
$76$	1.16572e12	0.693915
$77$	6.54563e11	0.357900
$78$	0	0
$79$	−3.02692e12	−1.40096	−0.700478	−	0.713674i	$-0.747030\pi$
$79$	−3.02692e12	−1.40096	−0.700478	+	0.713674i	$0.747030\pi$
$80$	−3.66660e11	−0.156379
$81$	0	0
$82$	3.01710e11	0.109597
$83$	−9.24967e11	−0.310541	−0.155270	−	0.987872i	$-0.549625\pi$
$83$	−9.24967e11	−0.310541	−0.155270	+	0.987872i	$0.549625\pi$
$84$	0	0
$85$	2.24329e12	0.645153
$86$	2.12988e12	0.567696
$87$	0	0
$88$	5.87611e11	0.134882
$89$	−6.03750e12	−1.28772	−0.643861	−	0.765143i	$-0.722668\pi$
$89$	−6.03750e12	−1.28772	−0.643861	+	0.765143i	$0.722668\pi$
$90$	0	0
$91$	−5.07711e12	−0.937233
$92$	−1.05808e12	−0.181928
$93$	0	0
$94$	1.94640e11	0.0291006
$95$	−6.21982e12	−0.868110
$96$	0	0
$97$	1.19926e12	0.146183	0.0730916	−	0.997325i	$-0.476713\pi$
$97$	1.19926e12	0.146183	0.0730916	+	0.997325i	$0.476713\pi$
$98$	−7.43538e11	−0.0847878
$99$	0	0
$100$	−3.04365e12	−0.304365
$101$	1.23215e13	1.15498	0.577490	−	0.816398i	$-0.304032\pi$
$101$	1.23215e13	1.15498	0.577490	+	0.816398i	$0.304032\pi$
$102$	0	0
$103$	3.81865e12	0.315114	0.157557	−	0.987510i	$-0.449638\pi$
$103$	3.81865e12	0.315114	0.157557	+	0.987510i	$0.449638\pi$
$104$	−4.55780e12	−0.353215
$105$	0	0
$106$	3.80569e12	0.260582
$107$	−2.89672e13	−1.86600	−0.933002	−	0.359872i	$-0.882821\pi$
$107$	−2.89672e13	−1.86600	−0.933002	+	0.359872i	$0.882821\pi$
$108$	0	0
$109$	2.01531e13	1.15099	0.575494	−	0.817806i	$-0.304810\pi$
$109$	2.01531e13	1.15099	0.575494	+	0.817806i	$0.304810\pi$
$110$	−3.13526e12	−0.168741
$111$	0	0
$112$	4.89915e12	0.234533
$113$	1.47420e13	0.666113	0.333056	−	0.942907i	$-0.391920\pi$
$113$	1.47420e13	0.666113	0.333056	+	0.942907i	$0.391920\pi$
$114$	0	0
$115$	5.64552e12	0.227598
$116$	1.42719e13	0.543881
$117$	0	0
$118$	3.70345e13	1.26291
$119$	−2.99739e13	−0.967584
$120$	0	0
$121$	−2.94981e13	−0.854456
$122$	−1.83736e13	−0.504493
$123$	0	0
$124$	−3.32350e13	−0.821022
$125$	4.29177e13	1.00629
$126$	0	0
$127$	−6.27677e13	−1.32743	−0.663715	−	0.747985i	$-0.731021\pi$
$127$	−6.27677e13	−1.32743	−0.663715	+	0.747985i	$0.731021\pi$
$128$	4.39805e12	0.0883883
$129$	0	0
$130$	2.43186e13	0.441883
$131$	−5.94046e13	−1.02697	−0.513484	−	0.858099i	$-0.671645\pi$
$131$	−5.94046e13	−1.02697	−0.513484	+	0.858099i	$0.671645\pi$
$132$	0	0
$133$	8.31067e13	1.30197
$134$	5.59898e13	0.835463
$135$	0	0
$136$	−2.69081e13	−0.364653
$137$	−1.34122e14	−1.73307	−0.866535	−	0.499117i	$-0.833658\pi$
$137$	−1.34122e14	−1.73307	−0.866535	+	0.499117i	$0.833658\pi$
$138$	0	0
$139$	−1.48811e14	−1.75000	−0.874999	−	0.484124i	$-0.839138\pi$
$139$	−1.48811e14	−1.75000	−0.874999	+	0.484124i	$0.839138\pi$
$140$	−2.61399e13	−0.293408
$141$	0	0
$142$	−1.05230e14	−1.07713
$143$	−3.89731e13	−0.381137
$144$	0	0
$145$	−7.61491e13	−0.680413
$146$	−1.04312e14	−0.891336
$147$	0	0
$148$	−5.25084e13	−0.410703
$149$	−2.20297e13	−0.164929	−0.0824645	−	0.996594i	$-0.526279\pi$
$149$	−2.20297e13	−0.164929	−0.0824645	+	0.996594i	$0.526279\pi$
$150$	0	0
$151$	4.19006e13	0.287654	0.143827	−	0.989603i	$-0.454059\pi$
$151$	4.19006e13	0.287654	0.143827	+	0.989603i	$0.454059\pi$
$152$	7.46062e13	0.490672
$153$	0	0
$154$	4.18920e13	0.253073
$155$	1.77329e14	1.02712
$156$	0	0
$157$	−1.34874e14	−0.718756	−0.359378	−	0.933192i	$-0.617011\pi$
$157$	−1.34874e14	−0.718756	−0.359378	+	0.933192i	$0.617011\pi$
$158$	−1.93723e14	−0.990625
$159$	0	0
$160$	−2.34662e13	−0.110577
$161$	−7.54330e13	−0.341345
$162$	0	0
$163$	1.65656e14	0.691813	0.345907	−	0.938269i	$-0.387571\pi$
$163$	1.65656e14	0.691813	0.345907	+	0.938269i	$0.387571\pi$
$164$	1.93094e13	0.0774970
$165$	0	0
$166$	−5.91979e13	−0.219585
$167$	1.62020e14	0.577980	0.288990	−	0.957332i	$-0.406681\pi$
$167$	1.62020e14	0.577980	0.288990	+	0.957332i	$0.406681\pi$
$168$	0	0
$169$	−5.80027e11	−0.00191507
$170$	1.43571e14	0.456192
$171$	0	0
$172$	1.36313e14	0.401422
$173$	2.67962e14	0.759929	0.379964	−	0.925001i	$-0.375936\pi$
$173$	2.67962e14	0.759929	0.379964	+	0.925001i	$0.375936\pi$
$174$	0	0
$175$	−2.16988e14	−0.571069
$176$	3.76071e13	0.0953756
$177$	0	0
$178$	−3.86400e14	−0.910557
$179$	−8.14358e14	−1.85042	−0.925211	−	0.379454i	$-0.876112\pi$
$179$	−8.14358e14	−1.85042	−0.925211	+	0.379454i	$0.876112\pi$
$180$	0	0
$181$	−6.82572e14	−1.44291	−0.721453	−	0.692464i	$-0.756525\pi$
$181$	−6.82572e14	−1.44291	−0.721453	+	0.692464i	$0.756525\pi$
$182$	−3.24935e14	−0.662724
$183$	0	0
$184$	−6.77174e13	−0.128642
$185$	2.80164e14	0.513802
$186$	0	0
$187$	−2.30087e14	−0.393479
$188$	1.24570e13	0.0205772
$189$	0	0
$190$	−3.98069e14	−0.613846
$191$	5.94242e14	0.885619	0.442809	−	0.896616i	$-0.353982\pi$
$191$	5.94242e14	0.885619	0.442809	+	0.896616i	$0.353982\pi$
$192$	0	0
$193$	8.35528e14	1.16369	0.581847	−	0.813298i	$-0.302330\pi$
$193$	8.35528e14	1.16369	0.581847	+	0.813298i	$0.302330\pi$
$194$	7.67528e13	0.103367
$195$	0	0
$196$	−4.75864e13	−0.0599541
$197$	9.13748e14	1.11377	0.556886	−	0.830589i	$-0.311996\pi$
$197$	9.13748e14	1.11377	0.556886	+	0.830589i	$0.311996\pi$
$198$	0	0
$199$	−5.29824e14	−0.604765	−0.302382	−	0.953187i	$-0.597782\pi$
$199$	−5.29824e14	−0.604765	−0.302382	+	0.953187i	$0.597782\pi$
$200$	−1.94794e14	−0.215218
$201$	0	0
$202$	7.88576e14	0.816694
$203$	1.01747e15	1.02047
$204$	0	0
$205$	−1.03028e14	−0.0969512
$206$	2.44393e14	0.222819
$207$	0	0
$208$	−2.91699e14	−0.249761
$209$	6.37947e14	0.529461
$210$	0	0
$211$	−3.96475e13	−0.0309300	−0.0154650	−	0.999880i	$-0.504923\pi$
$211$	−3.96475e13	−0.0309300	−0.0154650	+	0.999880i	$0.504923\pi$
$212$	2.43564e14	0.184259
$213$	0	0
$214$	−1.85390e15	−1.31946
$215$	−7.27310e14	−0.502192
$216$	0	0
$217$	−2.36939e15	−1.54045
$218$	1.28980e15	0.813871
$219$	0	0
$220$	−2.00657e14	−0.119318
$221$	1.78467e15	1.03041
$222$	0	0
$223$	−3.34360e15	−1.82067	−0.910337	−	0.413867i	$-0.864178\pi$
$223$	−3.34360e15	−1.82067	−0.910337	+	0.413867i	$0.864178\pi$
$224$	3.13546e14	0.165840
$225$	0	0
$226$	9.43490e14	0.471013
$227$	−1.56677e15	−0.760042	−0.380021	−	0.924978i	$-0.624083\pi$
$227$	−1.56677e15	−0.760042	−0.380021	+	0.924978i	$0.624083\pi$
$228$	0	0
$229$	−3.86972e15	−1.77316	−0.886582	−	0.462571i	$-0.846927\pi$
$229$	−3.86972e15	−1.77316	−0.886582	+	0.462571i	$0.846927\pi$
$230$	3.61313e14	0.160936
$231$	0	0
$232$	9.13400e14	0.384582
$233$	−5.09381e14	−0.208559	−0.104280	−	0.994548i	$-0.533254\pi$
$233$	−5.09381e14	−0.208559	−0.104280	+	0.994548i	$0.533254\pi$
$234$	0	0
$235$	−6.64655e13	−0.0257428
$236$	2.37021e15	0.893015
$237$	0	0
$238$	−1.91833e15	−0.684185
$239$	−1.58935e15	−0.551611	−0.275806	−	0.961213i	$-0.588945\pi$
$239$	−1.58935e15	−0.551611	−0.275806	+	0.961213i	$0.588945\pi$
$240$	0	0
$241$	−3.95533e14	−0.130039	−0.0650193	−	0.997884i	$-0.520711\pi$
$241$	−3.95533e14	−0.130039	−0.0650193	+	0.997884i	$0.520711\pi$
$242$	−1.88788e15	−0.604191
$243$	0	0
$244$	−1.17591e15	−0.356731
$245$	2.53902e14	0.0750044
$246$	0	0
$247$	−4.94823e15	−1.38650
$248$	−2.12704e15	−0.580550
$249$	0	0
$250$	2.74673e15	0.711552
$251$	2.94268e15	0.742786	0.371393	−	0.928476i	$-0.378880\pi$
$251$	2.94268e15	0.742786	0.371393	+	0.928476i	$0.378880\pi$
$252$	0	0
$253$	−5.79042e14	−0.138812
$254$	−4.01713e15	−0.938635
$255$	0	0
$256$	2.81475e14	0.0625000
$257$	−8.50231e15	−1.84065	−0.920326	−	0.391152i	$-0.872077\pi$
$257$	−8.50231e15	−1.84065	−0.920326	+	0.391152i	$0.872077\pi$
$258$	0	0
$259$	−3.74343e15	−0.770587
$260$	1.55639e15	0.312458
$261$	0	0
$262$	−3.80190e15	−0.726176
$263$	−8.27094e14	−0.154114	−0.0770570	−	0.997027i	$-0.524552\pi$
$263$	−8.27094e14	−0.154114	−0.0770570	+	0.997027i	$0.524552\pi$
$264$	0	0
$265$	−1.29956e15	−0.230514
$266$	5.31883e15	0.920630
$267$	0	0
$268$	3.58334e15	0.590762
$269$	1.21446e16	1.95431	0.977156	−	0.212521i	$-0.0681674\pi$
$269$	1.21446e16	1.95431	0.977156	+	0.212521i	$0.0681674\pi$
$270$	0	0
$271$	−8.66147e14	−0.132828	−0.0664142	−	0.997792i	$-0.521156\pi$
$271$	−8.66147e14	−0.132828	−0.0664142	+	0.997792i	$0.521156\pi$
$272$	−1.72212e15	−0.257849
$273$	0	0
$274$	−8.58380e15	−1.22547
$275$	−1.66565e15	−0.232232
$276$	0	0
$277$	−2.23397e15	−0.297138	−0.148569	−	0.988902i	$-0.547467\pi$
$277$	−2.23397e15	−0.297138	−0.148569	+	0.988902i	$0.547467\pi$
$278$	−9.52388e15	−1.23744
$279$	0	0
$280$	−1.67296e15	−0.207471
$281$	−4.74770e15	−0.575297	−0.287649	−	0.957736i	$-0.592874\pi$
$281$	−4.74770e15	−0.575297	−0.287649	+	0.957736i	$0.592874\pi$
$282$	0	0
$283$	−6.56052e15	−0.759149	−0.379574	−	0.925161i	$-0.623930\pi$
$283$	−6.56052e15	−0.759149	−0.379574	+	0.925161i	$0.623930\pi$
$284$	−6.73474e15	−0.761644
$285$	0	0
$286$	−2.49428e15	−0.269505
$287$	1.37661e15	0.145405
$288$	0	0
$289$	6.31651e14	0.0637736
$290$	−4.87354e15	−0.481125
$291$	0	0
$292$	−6.67598e15	−0.630270
$293$	1.10611e16	1.02132	0.510658	−	0.859784i	$-0.329402\pi$
$293$	1.10611e16	1.02132	0.510658	+	0.859784i	$0.329402\pi$
$294$	0	0
$295$	−1.26465e16	−1.11719
$296$	−3.36054e15	−0.290411
$297$	0	0
$298$	−1.40990e15	−0.116622
$299$	4.49134e15	0.363507
$300$	0	0
$301$	9.71801e15	0.753174
$302$	2.68164e15	0.203402
$303$	0	0
$304$	4.77479e15	0.346958
$305$	6.27419e15	0.446281
$306$	0	0
$307$	−4.85853e15	−0.331211	−0.165606	−	0.986192i	$-0.552958\pi$
$307$	−4.85853e15	−0.331211	−0.165606	+	0.986192i	$0.552958\pi$
$308$	2.68109e15	0.178950
$309$	0	0
$310$	1.13490e16	0.726287
$311$	−7.76560e15	−0.486667	−0.243334	−	0.969943i	$-0.578241\pi$
$311$	−7.76560e15	−0.486667	−0.243334	+	0.969943i	$0.578241\pi$
$312$	0	0
$313$	−2.49614e16	−1.50048	−0.750241	−	0.661165i	$-0.770062\pi$
$313$	−2.49614e16	−1.50048	−0.750241	+	0.661165i	$0.770062\pi$
$314$	−8.63195e15	−0.508237
$315$	0	0
$316$	−1.23983e16	−0.700478
$317$	−1.07399e15	−0.0594451	−0.0297226	−	0.999558i	$-0.509462\pi$
$317$	−1.07399e15	−0.0594451	−0.0297226	+	0.999558i	$0.509462\pi$
$318$	0	0
$319$	7.81036e15	0.414984
$320$	−1.50184e15	−0.0781895
$321$	0	0
$322$	−4.82771e15	−0.241367
$323$	−2.92131e16	−1.43140
$324$	0	0
$325$	1.29196e16	0.608147
$326$	1.06020e16	0.489186
$327$	0	0
$328$	1.23580e15	0.0547986
$329$	8.88084e14	0.0386083
$330$	0	0
$331$	3.73905e16	1.56271	0.781357	−	0.624085i	$-0.214528\pi$
$331$	3.73905e16	1.56271	0.781357	+	0.624085i	$0.214528\pi$
$332$	−3.78866e15	−0.155270
$333$	0	0
$334$	1.03693e16	0.408693
$335$	−1.91193e16	−0.739062
$336$	0	0
$337$	8.90764e15	0.331259	0.165630	−	0.986188i	$-0.447034\pi$
$337$	8.90764e15	0.331259	0.165630	+	0.986188i	$0.447034\pi$
$338$	−3.71217e13	−0.00135416
$339$	0	0
$340$	9.18853e15	0.322577
$341$	−1.81880e16	−0.626444
$342$	0	0
$343$	−3.16853e16	−1.05062
$344$	8.72401e15	0.283848
$345$	0	0
$346$	1.71495e16	0.537351
$347$	1.77994e16	0.547347	0.273674	−	0.961823i	$-0.411761\pi$
$347$	1.77994e16	0.547347	0.273674	+	0.961823i	$0.411761\pi$
$348$	0	0
$349$	4.05959e16	1.20259	0.601294	−	0.799028i	$-0.294652\pi$
$349$	4.05959e16	1.20259	0.601294	+	0.799028i	$0.294652\pi$
$350$	−1.38872e16	−0.403807
$351$	0	0
$352$	2.40685e15	0.0674408
$353$	5.05425e16	1.39034	0.695170	−	0.718845i	$-0.255329\pi$
$353$	5.05425e16	1.39034	0.695170	+	0.718845i	$0.255329\pi$
$354$	0	0
$355$	3.59339e16	0.952840
$356$	−2.47296e16	−0.643861
$357$	0	0
$358$	−5.21189e16	−1.30845
$359$	4.12005e16	1.01575	0.507877	−	0.861430i	$-0.330430\pi$
$359$	4.12005e16	1.01575	0.507877	+	0.861430i	$0.330430\pi$
$360$	0	0
$361$	3.89441e16	0.926073
$362$	−4.36846e16	−1.02029
$363$	0	0
$364$	−2.07959e16	−0.468617
$365$	3.56204e16	0.788487
$366$	0	0
$367$	−3.84138e16	−0.820650	−0.410325	−	0.911939i	$-0.634585\pi$
$367$	−3.84138e16	−0.820650	−0.410325	+	0.911939i	$0.634585\pi$
$368$	−4.33391e15	−0.0909640
$369$	0	0
$370$	1.79305e16	0.363313
$371$	1.73642e16	0.345719
$372$	0	0
$373$	−5.24759e16	−1.00891	−0.504455	−	0.863438i	$-0.668306\pi$
$373$	−5.24759e16	−1.00891	−0.504455	+	0.863438i	$0.668306\pi$
$374$	−1.47256e16	−0.278232
$375$	0	0
$376$	7.97246e14	0.0145503
$377$	−6.05810e16	−1.08672
$378$	0	0
$379$	−3.80121e16	−0.658820	−0.329410	−	0.944187i	$-0.606850\pi$
$379$	−3.80121e16	−0.658820	−0.329410	+	0.944187i	$0.606850\pi$
$380$	−2.54764e16	−0.434055
$381$	0	0
$382$	3.80315e16	0.626227
$383$	1.91753e16	0.310420	0.155210	−	0.987882i	$-0.450395\pi$
$383$	1.91753e16	0.310420	0.155210	+	0.987882i	$0.450395\pi$
$384$	0	0
$385$	−1.43052e16	−0.223872
$386$	5.34738e16	0.822856
$387$	0	0
$388$	4.91218e15	0.0730916
$389$	7.50350e16	1.09797	0.548987	−	0.835831i	$-0.315014\pi$
$389$	7.50350e16	1.09797	0.548987	+	0.835831i	$0.315014\pi$
$390$	0	0
$391$	2.65157e16	0.375279
$392$	−3.04553e15	−0.0423939
$393$	0	0
$394$	5.84799e16	0.787555
$395$	6.61522e16	0.876320
$396$	0	0
$397$	6.62792e16	0.849647	0.424824	−	0.905276i	$-0.360336\pi$
$397$	6.62792e16	0.849647	0.424824	+	0.905276i	$0.360336\pi$
$398$	−3.39087e16	−0.427633
$399$	0	0
$400$	−1.24668e16	−0.152182
$401$	9.52466e15	0.114396	0.0571980	−	0.998363i	$-0.481783\pi$
$401$	9.52466e15	0.114396	0.0571980	+	0.998363i	$0.481783\pi$
$402$	0	0
$403$	1.41075e17	1.64047
$404$	5.04688e16	0.577490
$405$	0	0
$406$	6.51182e16	0.721578
$407$	−2.87355e16	−0.313368
$408$	0	0
$409$	1.72227e16	0.181928	0.0909639	−	0.995854i	$-0.471005\pi$
$409$	1.72227e16	0.181928	0.0909639	+	0.995854i	$0.471005\pi$
$410$	−6.59376e15	−0.0685548
$411$	0	0
$412$	1.56412e16	0.157557
$413$	1.68977e17	1.67553
$414$	0	0
$415$	2.02148e16	0.194248
$416$	−1.86688e16	−0.176607
$417$	0	0
$418$	4.08286e16	0.374385
$419$	1.42915e17	1.29029	0.645145	−	0.764060i	$-0.276797\pi$
$419$	1.42915e17	1.29029	0.645145	+	0.764060i	$0.276797\pi$
$420$	0	0
$421$	1.06193e17	0.929529	0.464765	−	0.885434i	$-0.346139\pi$
$421$	1.06193e17	0.929529	0.464765	+	0.885434i	$0.346139\pi$
$422$	−2.53744e15	−0.0218708
$423$	0	0
$424$	1.55881e16	0.130291
$425$	7.62741e16	0.627840
$426$	0	0
$427$	−8.38331e16	−0.669321
$428$	−1.18650e17	−0.933002
$429$	0	0
$430$	−4.65478e16	−0.355103
$431$	9.79018e16	0.735679	0.367840	−	0.929889i	$-0.380098\pi$
$431$	9.79018e16	0.735679	0.367840	+	0.929889i	$0.380098\pi$
$432$	0	0
$433$	1.01860e17	0.742736	0.371368	−	0.928486i	$-0.378889\pi$
$433$	1.01860e17	0.742736	0.371368	+	0.928486i	$0.378889\pi$
$434$	−1.51641e17	−1.08927
$435$	0	0
$436$	8.25473e16	0.575494
$437$	−7.35182e16	−0.504970
$438$	0	0
$439$	1.55147e17	1.03448	0.517241	−	0.855840i	$-0.326959\pi$
$439$	1.55147e17	1.03448	0.517241	+	0.855840i	$0.326959\pi$
$440$	−1.28420e16	−0.0843705
$441$	0	0
$442$	1.14219e17	0.728607
$443$	8.21130e15	0.0516164	0.0258082	−	0.999667i	$-0.491784\pi$
$443$	8.21130e15	0.0516164	0.0258082	+	0.999667i	$0.491784\pi$
$444$	0	0
$445$	1.31947e17	0.805490
$446$	−2.13990e17	−1.28741
$447$	0	0
$448$	2.00669e16	0.117267
$449$	2.94000e16	0.169335	0.0846675	−	0.996409i	$-0.473017\pi$
$449$	2.94000e16	0.169335	0.0846675	+	0.996409i	$0.473017\pi$
$450$	0	0
$451$	1.05672e16	0.0591306
$452$	6.03834e16	0.333056
$453$	0	0
$454$	−1.00273e17	−0.537431
$455$	1.10958e17	0.586254
$456$	0	0
$457$	2.55232e17	1.31063	0.655316	−	0.755355i	$-0.272536\pi$
$457$	2.55232e17	1.31063	0.655316	+	0.755355i	$0.272536\pi$
$458$	−2.47662e17	−1.25382
$459$	0	0
$460$	2.31240e16	0.113799
$461$	1.23002e17	0.596839	0.298420	−	0.954435i	$-0.403540\pi$
$461$	1.23002e17	0.596839	0.298420	+	0.954435i	$0.403540\pi$
$462$	0	0
$463$	−5.26525e16	−0.248395	−0.124197	−	0.992258i	$-0.539636\pi$
$463$	−5.26525e16	−0.248395	−0.124197	+	0.992258i	$0.539636\pi$
$464$	5.84576e16	0.271941
$465$	0	0
$466$	−3.26004e16	−0.147474
$467$	−3.35303e17	−1.49581	−0.747907	−	0.663803i	$-0.768941\pi$
$467$	−3.35303e17	−1.49581	−0.747907	+	0.663803i	$0.768941\pi$
$468$	0	0
$469$	2.55464e17	1.10843
$470$	−4.25379e15	−0.0182029
$471$	0	0
$472$	1.51694e17	0.631457
$473$	7.45978e16	0.306287
$474$	0	0
$475$	−2.11480e17	−0.844814
$476$	−1.22773e17	−0.483792
$477$	0	0
$478$	−1.01718e17	−0.390048
$479$	2.57408e17	0.973738	0.486869	−	0.873475i	$-0.338139\pi$
$479$	2.57408e17	0.973738	0.486869	+	0.873475i	$0.338139\pi$
$480$	0	0
$481$	2.22887e17	0.820618
$482$	−2.53141e16	−0.0919512
$483$	0	0
$484$	−1.20824e17	−0.427228
$485$	−2.62094e16	−0.0914400
$486$	0	0
$487$	−1.57963e17	−0.536560	−0.268280	−	0.963341i	$-0.586455\pi$
$487$	−1.57963e17	−0.536560	−0.268280	+	0.963341i	$0.586455\pi$
$488$	−7.52583e16	−0.252247
$489$	0	0
$490$	1.62497e16	0.0530362
$491$	1.93601e17	0.623560	0.311780	−	0.950154i	$-0.399075\pi$
$491$	1.93601e17	0.623560	0.311780	+	0.950154i	$0.399075\pi$
$492$	0	0
$493$	−3.57655e17	−1.12191
$494$	−3.16687e17	−0.980404
$495$	0	0
$496$	−1.36131e17	−0.410511
$497$	−4.80134e17	−1.42904
$498$	0	0
$499$	4.07577e17	1.18183	0.590917	−	0.806732i	$-0.298766\pi$
$499$	4.07577e17	1.18183	0.590917	+	0.806732i	$0.298766\pi$
$500$	1.75791e17	0.503143
$501$	0	0
$502$	1.88331e17	0.525229
$503$	3.41866e17	0.941162	0.470581	−	0.882357i	$-0.344044\pi$
$503$	3.41866e17	0.941162	0.470581	+	0.882357i	$0.344044\pi$
$504$	0	0
$505$	−2.69282e17	−0.722458
$506$	−3.70587e16	−0.0981549
$507$	0	0
$508$	−2.57096e17	−0.663715
$509$	−6.61539e17	−1.68612	−0.843062	−	0.537816i	$-0.819249\pi$
$509$	−6.61539e17	−1.68612	−0.843062	+	0.537816i	$0.819249\pi$
$510$	0	0
$511$	−4.75944e17	−1.18255
$512$	1.80144e16	0.0441942
$513$	0	0
$514$	−5.44148e17	−1.30154
$515$	−8.34551e16	−0.197109
$516$	0	0
$517$	6.81715e15	0.0157005
$518$	−2.39580e17	−0.544887
$519$	0	0
$520$	9.96091e16	0.220941
$521$	−1.27627e17	−0.279575	−0.139787	−	0.990182i	$-0.544642\pi$
$521$	−1.27627e17	−0.279575	−0.139787	+	0.990182i	$0.544642\pi$
$522$	0	0
$523$	−1.90574e17	−0.407196	−0.203598	−	0.979055i	$-0.565264\pi$
$523$	−1.90574e17	−0.407196	−0.203598	+	0.979055i	$0.565264\pi$
$524$	−2.43321e17	−0.513484
$525$	0	0
$526$	−5.29340e16	−0.108975
$527$	8.32872e17	1.69359
$528$	0	0
$529$	−4.37306e17	−0.867609
$530$	−8.31718e16	−0.162998
$531$	0	0
$532$	3.40405e17	0.650984
$533$	−8.19644e16	−0.154845
$534$	0	0
$535$	6.33068e17	1.16722
$536$	2.29334e17	0.417732
$537$	0	0
$538$	7.77256e17	1.38191
$539$	−2.60419e16	−0.0457453
$540$	0	0
$541$	6.46355e17	1.10838	0.554191	−	0.832390i	$-0.313028\pi$
$541$	6.46355e17	1.10838	0.554191	+	0.832390i	$0.313028\pi$
$542$	−5.54334e16	−0.0939239
$543$	0	0
$544$	−1.10215e17	−0.182326
$545$	−4.40440e17	−0.719961
$546$	0	0
$547$	3.59802e17	0.574310	0.287155	−	0.957884i	$-0.407291\pi$
$547$	3.59802e17	0.574310	0.287155	+	0.957884i	$0.407291\pi$
$548$	−5.49363e17	−0.866535
$549$	0	0
$550$	−1.06602e17	−0.164213
$551$	9.91644e17	1.50963
$552$	0	0
$553$	−8.83897e17	−1.31428
$554$	−1.42974e17	−0.210108
$555$	0	0
$556$	−6.09528e17	−0.874999
$557$	1.20436e18	1.70883	0.854413	−	0.519595i	$-0.173917\pi$
$557$	1.20436e18	1.70883	0.854413	+	0.519595i	$0.173917\pi$
$558$	0	0
$559$	−5.78617e17	−0.802075
$560$	−1.07069e17	−0.146704
$561$	0	0
$562$	−3.03853e17	−0.406797
$563$	−1.49848e16	−0.0198310	−0.00991551	−	0.999951i	$-0.503156\pi$
$563$	−1.49848e16	−0.0198310	−0.00991551	+	0.999951i	$0.503156\pi$
$564$	0	0
$565$	−3.22182e17	−0.416664
$566$	−4.19874e17	−0.536799
$567$	0	0
$568$	−4.31024e17	−0.538563
$569$	7.94289e17	0.981180	0.490590	−	0.871390i	$-0.336781\pi$
$569$	7.94289e17	0.981180	0.490590	+	0.871390i	$0.336781\pi$
$570$	0	0
$571$	−9.50018e17	−1.14709	−0.573545	−	0.819174i	$-0.694432\pi$
$571$	−9.50018e17	−1.14709	−0.573545	+	0.819174i	$0.694432\pi$
$572$	−1.59634e17	−0.190569
$573$	0	0
$574$	8.81031e16	0.102817
$575$	1.91953e17	0.221490
$576$	0	0
$577$	2.58846e17	0.292011	0.146005	−	0.989284i	$-0.453358\pi$
$577$	2.58846e17	0.292011	0.146005	+	0.989284i	$0.453358\pi$
$578$	4.04257e16	0.0450948
$579$	0	0
$580$	−3.11907e17	−0.340206
$581$	−2.70102e17	−0.291328
$582$	0	0
$583$	1.33292e17	0.140591
$584$	−4.27263e17	−0.445668
$585$	0	0
$586$	7.07913e17	0.722180
$587$	−1.30036e18	−1.31195	−0.655973	−	0.754785i	$-0.727741\pi$
$587$	−1.30036e18	−1.31195	−0.655973	+	0.754785i	$0.727741\pi$
$588$	0	0
$589$	−2.30925e18	−2.27888
$590$	−8.09376e17	−0.789973
$591$	0	0
$592$	−2.15074e17	−0.205351
$593$	1.53388e18	1.44855	0.724277	−	0.689509i	$-0.242174\pi$
$593$	1.53388e18	1.44855	0.724277	+	0.689509i	$0.242174\pi$
$594$	0	0
$595$	6.55069e17	0.605239
$596$	−9.02335e16	−0.0824645
$597$	0	0
$598$	2.87446e17	0.257039
$599$	8.31693e17	0.735680	0.367840	−	0.929889i	$-0.380097\pi$
$599$	8.31693e17	0.735680	0.367840	+	0.929889i	$0.380097\pi$
$600$	0	0
$601$	−7.38765e17	−0.639473	−0.319737	−	0.947506i	$-0.603594\pi$
$601$	−7.38765e17	−0.639473	−0.319737	+	0.947506i	$0.603594\pi$
$602$	6.21953e17	0.532574
$603$	0	0
$604$	1.71625e17	0.143827
$605$	6.44671e17	0.534476
$606$	0	0
$607$	−1.93200e17	−0.156776	−0.0783880	−	0.996923i	$-0.524977\pi$
$607$	−1.93200e17	−0.156776	−0.0783880	+	0.996923i	$0.524977\pi$
$608$	3.05587e17	0.245336
$609$	0	0
$610$	4.01548e17	0.315569
$611$	−5.28772e16	−0.0411150
$612$	0	0
$613$	−1.81666e18	−1.38286	−0.691432	−	0.722441i	$-0.743020\pi$
$613$	−1.81666e18	−1.38286	−0.691432	+	0.722441i	$0.743020\pi$
$614$	−3.10946e17	−0.234202
$615$	0	0
$616$	1.71590e17	0.126537
$617$	3.92736e17	0.286581	0.143290	−	0.989681i	$-0.454232\pi$
$617$	3.92736e17	0.286581	0.143290	+	0.989681i	$0.454232\pi$
$618$	0	0
$619$	2.31716e17	0.165564	0.0827822	−	0.996568i	$-0.473619\pi$
$619$	2.31716e17	0.165564	0.0827822	+	0.996568i	$0.473619\pi$
$620$	7.26339e17	0.513562
$621$	0	0
$622$	−4.96998e17	−0.344126
$623$	−1.76302e18	−1.20805
$624$	0	0
$625$	−3.08727e16	−0.0207183
$626$	−1.59753e18	−1.06100
$627$	0	0
$628$	−5.52445e17	−0.359378
$629$	1.31586e18	0.847193
$630$	0	0
$631$	−3.03856e18	−1.91636	−0.958180	−	0.286165i	$-0.907620\pi$
$631$	−3.03856e18	−1.91636	−0.958180	+	0.286165i	$0.907620\pi$
$632$	−7.93488e17	−0.495313
$633$	0	0
$634$	−6.87355e16	−0.0420340
$635$	1.37176e18	0.830329
$636$	0	0
$637$	2.01994e17	0.119793
$638$	4.99863e17	0.293438
$639$	0	0
$640$	−9.61177e16	−0.0552883
$641$	2.95356e18	1.68177	0.840887	−	0.541210i	$-0.182034\pi$
$641$	2.95356e18	1.68177	0.840887	+	0.541210i	$0.182034\pi$
$642$	0	0
$643$	1.19223e18	0.665256	0.332628	−	0.943058i	$-0.392065\pi$
$643$	1.19223e18	0.665256	0.332628	+	0.943058i	$0.392065\pi$
$644$	−3.08974e17	−0.170672
$645$	0	0
$646$	−1.86964e18	−1.01215
$647$	−2.23653e18	−1.19866	−0.599331	−	0.800502i	$-0.704567\pi$
$647$	−2.23653e18	−1.19866	−0.599331	+	0.800502i	$0.704567\pi$
$648$	0	0
$649$	1.29711e18	0.681375
$650$	8.26856e17	0.430025
$651$	0	0
$652$	6.78529e17	0.345907
$653$	4.38457e17	0.221305	0.110653	−	0.993859i	$-0.464706\pi$
$653$	4.38457e17	0.221305	0.110653	+	0.993859i	$0.464706\pi$
$654$	0	0
$655$	1.29827e18	0.642385
$656$	7.90915e16	0.0387485
$657$	0	0
$658$	5.68374e16	0.0273002
$659$	−1.32988e18	−0.632497	−0.316248	−	0.948676i	$-0.602423\pi$
$659$	−1.32988e18	−0.632497	−0.316248	+	0.948676i	$0.602423\pi$
$660$	0	0
$661$	5.14630e17	0.239986	0.119993	−	0.992775i	$-0.461713\pi$
$661$	5.14630e17	0.239986	0.119993	+	0.992775i	$0.461713\pi$
$662$	2.39299e18	1.10501
$663$	0	0
$664$	−2.42475e17	−0.109793
$665$	−1.81627e18	−0.814402
$666$	0	0
$667$	−9.00081e17	−0.395789
$668$	6.63636e17	0.288990
$669$	0	0
$670$	−1.22364e18	−0.522596
$671$	−6.43523e17	−0.272187
$672$	0	0
$673$	−3.78144e18	−1.56877	−0.784384	−	0.620275i	$-0.787021\pi$
$673$	−3.78144e18	−1.56877	−0.784384	+	0.620275i	$0.787021\pi$
$674$	5.70089e17	0.234236
$675$	0	0
$676$	−2.37579e15	−0.000957534 0
$677$	1.69577e18	0.676926	0.338463	−	0.940980i	$-0.390093\pi$
$677$	1.69577e18	0.676926	0.338463	+	0.940980i	$0.390093\pi$
$678$	0	0
$679$	3.50199e17	0.137139
$680$	5.88066e17	0.228096
$681$	0	0
$682$	−1.16403e18	−0.442963
$683$	−3.06899e18	−1.15681	−0.578404	−	0.815750i	$-0.696324\pi$
$683$	−3.06899e18	−1.15681	−0.578404	+	0.815750i	$0.696324\pi$
$684$	0	0
$685$	2.93118e18	1.08406
$686$	−2.02786e18	−0.742902
$687$	0	0
$688$	5.58336e17	0.200711
$689$	−1.03388e18	−0.368166
$690$	0	0
$691$	−5.73998e17	−0.200587	−0.100294	−	0.994958i	$-0.531978\pi$
$691$	−5.73998e17	−0.200587	−0.100294	+	0.994958i	$0.531978\pi$
$692$	1.09757e18	0.379964
$693$	0	0
$694$	1.13916e18	0.387033
$695$	3.25220e18	1.09465
$696$	0	0
$697$	−4.83896e17	−0.159860
$698$	2.59814e18	0.850358
$699$	0	0
$700$	−8.88783e17	−0.285534
$701$	−5.78307e18	−1.84073	−0.920367	−	0.391056i	$-0.872110\pi$
$701$	−5.78307e18	−1.84073	−0.920367	+	0.391056i	$0.872110\pi$
$702$	0	0
$703$	−3.64841e18	−1.13997
$704$	1.54039e17	0.0476878
$705$	0	0
$706$	3.23472e18	0.983119
$707$	3.59803e18	1.08352
$708$	0	0
$709$	2.09151e18	0.618386	0.309193	−	0.950999i	$-0.399941\pi$
$709$	2.09151e18	0.618386	0.309193	+	0.950999i	$0.399941\pi$
$710$	2.29977e18	0.673760
$711$	0	0
$712$	−1.58269e18	−0.455278
$713$	2.09602e18	0.597468
$714$	0	0
$715$	8.51744e17	0.238407
$716$	−3.33561e18	−0.925211
$717$	0	0
$718$	2.63683e18	0.718247
$719$	2.54253e18	0.686321	0.343161	−	0.939277i	$-0.388502\pi$
$719$	2.54253e18	0.686321	0.343161	+	0.939277i	$0.388502\pi$
$720$	0	0
$721$	1.11509e18	0.295618
$722$	2.49242e18	0.654832
$723$	0	0
$724$	−2.79582e18	−0.721453
$725$	−2.58914e18	−0.662154
$726$	0	0
$727$	5.34941e18	1.34379	0.671897	−	0.740645i	$-0.265480\pi$
$727$	5.34941e18	1.34379	0.671897	+	0.740645i	$0.265480\pi$
$728$	−1.33093e18	−0.331362
$729$	0	0
$730$	2.27970e18	0.557545
$731$	−3.41601e18	−0.828048
$732$	0	0
$733$	−1.01505e18	−0.241720	−0.120860	−	0.992670i	$-0.538565\pi$
$733$	−1.01505e18	−0.241720	−0.120860	+	0.992670i	$0.538565\pi$
$734$	−2.45848e18	−0.580287
$735$	0	0
$736$	−2.77370e17	−0.0643212
$737$	1.96100e18	0.450754
$738$	0	0
$739$	−4.21697e18	−0.952384	−0.476192	−	0.879341i	$-0.657983\pi$
$739$	−4.21697e18	−0.952384	−0.476192	+	0.879341i	$0.657983\pi$
$740$	1.14755e18	0.256901
$741$	0	0
$742$	1.11131e18	0.244461
$743$	−1.25531e18	−0.273731	−0.136865	−	0.990590i	$-0.543703\pi$
$743$	−1.25531e18	−0.273731	−0.136865	+	0.990590i	$0.543703\pi$
$744$	0	0
$745$	4.81450e17	0.103166
$746$	−3.35846e18	−0.713407
$747$	0	0
$748$	−9.42437e17	−0.196740
$749$	−8.45879e18	−1.75056
$750$	0	0
$751$	9.53400e18	1.93917	0.969584	−	0.244758i	$-0.0787085\pi$
$751$	9.53400e18	1.93917	0.969584	+	0.244758i	$0.0787085\pi$
$752$	5.10238e16	0.0102886
$753$	0	0
$754$	−3.87719e18	−0.768428
$755$	−9.15722e17	−0.179932
$756$	0	0
$757$	8.60869e18	1.66270	0.831350	−	0.555749i	$-0.187569\pi$
$757$	8.60869e18	1.66270	0.831350	+	0.555749i	$0.187569\pi$
$758$	−2.43277e18	−0.465856
$759$	0	0
$760$	−1.63049e18	−0.306923
$761$	−5.18301e18	−0.967345	−0.483673	−	0.875249i	$-0.660697\pi$
$761$	−5.18301e18	−0.967345	−0.483673	+	0.875249i	$0.660697\pi$
$762$	0	0
$763$	5.88497e18	1.07978
$764$	2.43402e18	0.442809
$765$	0	0
$766$	1.22722e18	0.219500
$767$	−1.00610e19	−1.78432
$768$	0	0
$769$	−4.05903e18	−0.707784	−0.353892	−	0.935286i	$-0.615142\pi$
$769$	−4.05903e18	−0.707784	−0.353892	+	0.935286i	$0.615142\pi$
$770$	−9.15534e17	−0.158301
$771$	0	0
$772$	3.42232e18	0.581847
$773$	−1.51385e18	−0.255221	−0.127610	−	0.991824i	$-0.540731\pi$
$773$	−1.51385e18	−0.255221	−0.127610	+	0.991824i	$0.540731\pi$
$774$	0	0
$775$	6.02935e18	0.999561
$776$	3.14379e17	0.0516836
$777$	0	0
$778$	4.80224e18	0.776384
$779$	1.34167e18	0.215105
$780$	0	0
$781$	−3.68562e18	−0.581138
$782$	1.69700e18	0.265362
$783$	0	0
$784$	−1.94914e17	−0.0299770
$785$	2.94763e18	0.449593
$786$	0	0
$787$	−5.11397e18	−0.767224	−0.383612	−	0.923494i	$-0.625320\pi$
$787$	−5.11397e18	−0.767224	−0.383612	+	0.923494i	$0.625320\pi$
$788$	3.74271e18	0.556886
$789$	0	0
$790$	4.23374e18	0.619652
$791$	4.30486e18	0.624902
$792$	0	0
$793$	4.99149e18	0.712778
$794$	4.24187e18	0.600791
$795$	0	0
$796$	−2.17016e18	−0.302382
$797$	−1.10867e19	−1.53223	−0.766115	−	0.642703i	$-0.777813\pi$
$797$	−1.10867e19	−1.53223	−0.766115	+	0.642703i	$0.777813\pi$
$798$	0	0
$799$	−3.12173e17	−0.0424464
$800$	−7.97874e17	−0.107609
$801$	0	0
$802$	6.09578e17	0.0808902
$803$	−3.65346e18	−0.480899
$804$	0	0
$805$	1.64856e18	0.213517
$806$	9.02883e18	1.15999
$807$	0	0
$808$	3.23001e18	0.408347
$809$	1.01551e19	1.27356	0.636778	−	0.771047i	$-0.280267\pi$
$809$	1.01551e19	1.27356	0.636778	+	0.771047i	$0.280267\pi$
$810$	0	0
$811$	8.70589e18	1.07443	0.537214	−	0.843446i	$-0.319477\pi$
$811$	8.70589e18	1.07443	0.537214	+	0.843446i	$0.319477\pi$
$812$	4.16757e18	0.510233
$813$	0	0
$814$	−1.83907e18	−0.221585
$815$	−3.62036e18	−0.432740
$816$	0	0
$817$	9.47132e18	1.11421
$818$	1.10225e18	0.128642
$819$	0	0
$820$	−4.22001e17	−0.0484756
$821$	−7.15045e17	−0.0814897	−0.0407448	−	0.999170i	$-0.512973\pi$
$821$	−7.15045e17	−0.0814897	−0.0407448	+	0.999170i	$0.512973\pi$
$822$	0	0
$823$	1.24490e19	1.39649	0.698244	−	0.715860i	$-0.253965\pi$
$823$	1.24490e19	1.39649	0.698244	+	0.715860i	$0.253965\pi$
$824$	1.00103e18	0.111410
$825$	0	0
$826$	1.08145e19	1.18478
$827$	−4.42505e18	−0.480986	−0.240493	−	0.970651i	$-0.577309\pi$
$827$	−4.42505e18	−0.480986	−0.240493	+	0.970651i	$0.577309\pi$
$828$	0	0
$829$	1.96050e18	0.209779	0.104890	−	0.994484i	$-0.466551\pi$
$829$	1.96050e18	0.209779	0.104890	+	0.994484i	$0.466551\pi$
$830$	1.29375e18	0.137354
$831$	0	0
$832$	−1.19480e18	−0.124880
$833$	1.19252e18	0.123673
$834$	0	0
$835$	−3.54090e18	−0.361536
$836$	2.61303e18	0.264730
$837$	0	0
$838$	9.14658e18	0.912373
$839$	9.76000e18	0.966044	0.483022	−	0.875608i	$-0.339539\pi$
$839$	9.76000e18	0.966044	0.483022	+	0.875608i	$0.339539\pi$
$840$	0	0
$841$	1.88003e18	0.183228
$842$	6.79636e18	0.657276
$843$	0	0
$844$	−1.62396e17	−0.0154650
$845$	1.26763e16	0.00119791
$846$	0	0
$847$	−8.61382e18	−0.801592
$848$	9.97638e17	0.0921297
$849$	0	0
$850$	4.88154e18	0.443950
$851$	3.31153e18	0.298873
$852$	0	0
$853$	−2.34492e18	−0.208430	−0.104215	−	0.994555i	$-0.533233\pi$
$853$	−2.34492e18	−0.208430	−0.104215	+	0.994555i	$0.533233\pi$
$854$	−5.36532e18	−0.473281
$855$	0	0
$856$	−7.59359e18	−0.659732
$857$	−1.06772e19	−0.920625	−0.460313	−	0.887757i	$-0.652263\pi$
$857$	−1.06772e19	−0.920625	−0.460313	+	0.887757i	$0.652263\pi$
$858$	0	0
$859$	−1.72041e19	−1.46109	−0.730546	−	0.682864i	$-0.760734\pi$
$859$	−1.72041e19	−1.46109	−0.730546	+	0.682864i	$0.760734\pi$
$860$	−2.97906e18	−0.251096
$861$	0	0
$862$	6.26572e18	0.520204
$863$	1.42851e18	0.117710	0.0588548	−	0.998267i	$-0.481255\pi$
$863$	1.42851e18	0.117710	0.0588548	+	0.998267i	$0.481255\pi$
$864$	0	0
$865$	−5.85620e18	−0.475348
$866$	6.51907e18	0.525193
$867$	0	0
$868$	−9.70504e18	−0.770227
$869$	−6.78501e18	−0.534468
$870$	0	0
$871$	−1.52105e19	−1.18039
$872$	5.28303e18	0.406936
$873$	0	0
$874$	−4.70517e18	−0.357068
$875$	1.25325e19	0.944029
$876$	0	0
$877$	1.24560e19	0.924447	0.462223	−	0.886764i	$-0.347052\pi$
$877$	1.24560e19	0.924447	0.462223	+	0.886764i	$0.347052\pi$
$878$	9.92938e18	0.731489
$879$	0	0
$880$	−8.21889e17	−0.0596590
$881$	3.63494e18	0.261911	0.130956	−	0.991388i	$-0.458195\pi$
$881$	3.63494e18	0.261911	0.130956	+	0.991388i	$0.458195\pi$
$882$	0	0
$883$	−1.55878e18	−0.110673	−0.0553364	−	0.998468i	$-0.517623\pi$
$883$	−1.55878e18	−0.110673	−0.0553364	+	0.998468i	$0.517623\pi$
$884$	7.31001e18	0.515203
$885$	0	0
$886$	5.25523e17	0.0364983
$887$	−8.56709e18	−0.590649	−0.295325	−	0.955397i	$-0.595428\pi$
$887$	−8.56709e18	−0.590649	−0.295325	+	0.955397i	$0.595428\pi$
$888$	0	0
$889$	−1.83289e19	−1.24531
$890$	8.44462e18	0.569568
$891$	0	0
$892$	−1.36954e19	−0.910337
$893$	8.65541e17	0.0571154
$894$	0	0
$895$	1.77975e19	1.15747
$896$	1.28428e18	0.0829199
$897$	0	0
$898$	1.88160e18	0.119738
$899$	−2.82720e19	−1.78615
$900$	0	0
$901$	−6.10373e18	−0.380088
$902$	6.76300e17	0.0418116
$903$	0	0
$904$	3.86454e18	0.235506
$905$	1.49174e19	0.902560
$906$	0	0
$907$	6.83830e18	0.407850	0.203925	−	0.978986i	$-0.434630\pi$
$907$	6.83830e18	0.407850	0.203925	+	0.978986i	$0.434630\pi$
$908$	−6.41749e18	−0.380021
$909$	0	0
$910$	7.10134e18	0.414545
$911$	−5.35839e18	−0.310574	−0.155287	−	0.987869i	$-0.549630\pi$
$911$	−5.35839e18	−0.310574	−0.155287	+	0.987869i	$0.549630\pi$
$912$	0	0
$913$	−2.07337e18	−0.118472
$914$	1.63349e19	0.926756
$915$	0	0
$916$	−1.58504e19	−0.886582
$917$	−1.73469e19	−0.963432
$918$	0	0
$919$	2.65287e19	1.45266	0.726332	−	0.687344i	$-0.241224\pi$
$919$	2.65287e19	1.45266	0.726332	+	0.687344i	$0.241224\pi$
$920$	1.47994e18	0.0804679
$921$	0	0
$922$	7.87215e18	0.422029
$923$	2.85875e19	1.52183
$924$	0	0
$925$	9.52584e18	0.500014
$926$	−3.36976e18	−0.175642
$927$	0	0
$928$	3.74129e18	0.192291
$929$	−2.23601e18	−0.114123	−0.0570613	−	0.998371i	$-0.518173\pi$
$929$	−2.23601e18	−0.114123	−0.0570613	+	0.998371i	$0.518173\pi$
$930$	0	0
$931$	−3.30642e18	−0.166412
$932$	−2.08642e18	−0.104280
$933$	0	0
$934$	−2.14594e19	−1.05770
$935$	5.02847e18	0.246128
$936$	0	0
$937$	−9.93409e18	−0.479536	−0.239768	−	0.970830i	$-0.577071\pi$
$937$	−9.93409e18	−0.479536	−0.239768	+	0.970830i	$0.577071\pi$
$938$	1.63497e19	0.783775
$939$	0	0
$940$	−2.72243e17	−0.0128714
$941$	−2.74187e18	−0.128740	−0.0643700	−	0.997926i	$-0.520504\pi$
$941$	−2.74187e18	−0.128740	−0.0643700	+	0.997926i	$0.520504\pi$
$942$	0	0
$943$	−1.21778e18	−0.0563955
$944$	9.70838e18	0.446508
$945$	0	0
$946$	4.77426e18	0.216578
$947$	−1.30411e19	−0.587544	−0.293772	−	0.955876i	$-0.594911\pi$
$947$	−1.30411e19	−0.587544	−0.293772	+	0.955876i	$0.594911\pi$
$948$	0	0
$949$	2.83381e19	1.25933
$950$	−1.35347e19	−0.597373
$951$	0	0
$952$	−7.85749e18	−0.342093
$953$	−1.23319e19	−0.533243	−0.266621	−	0.963801i	$-0.585907\pi$
$953$	−1.23319e19	−0.533243	−0.266621	+	0.963801i	$0.585907\pi$
$954$	0	0
$955$	−1.29869e19	−0.553969
$956$	−6.50998e18	−0.275806
$957$	0	0
$958$	1.64741e19	0.688537
$959$	−3.91653e19	−1.62585
$960$	0	0
$961$	4.14197e19	1.69631
$962$	1.42648e19	0.580265
$963$	0	0
$964$	−1.62010e18	−0.0650193
$965$	−1.82602e19	−0.727909
$966$	0	0
$967$	−3.07735e19	−1.21033	−0.605167	−	0.796098i	$-0.706894\pi$
$967$	−3.07735e19	−1.21033	−0.605167	+	0.796098i	$0.706894\pi$
$968$	−7.73276e18	−0.302096
$969$	0	0
$970$	−1.67740e18	−0.0646578
$971$	2.27430e19	0.870809	0.435404	−	0.900235i	$-0.356605\pi$
$971$	2.27430e19	0.870809	0.435404	+	0.900235i	$0.356605\pi$
$972$	0	0
$973$	−4.34545e19	−1.64173
$974$	−1.01097e19	−0.379405
$975$	0	0
$976$	−4.81653e18	−0.178365
$977$	2.71859e18	0.100007	0.0500033	−	0.998749i	$-0.484077\pi$
$977$	2.71859e18	0.100007	0.0500033	+	0.998749i	$0.484077\pi$
$978$	0	0
$979$	−1.35334e19	−0.491269
$980$	1.03998e18	0.0375022
$981$	0	0
$982$	1.23905e19	0.440924
$983$	2.11540e19	0.747815	0.373908	−	0.927466i	$-0.378018\pi$
$983$	2.11540e19	0.747815	0.373908	+	0.927466i	$0.378018\pi$
$984$	0	0
$985$	−1.99696e19	−0.696682
$986$	−2.28899e19	−0.793312
$987$	0	0
$988$	−2.02680e19	−0.693250
$989$	−8.59679e18	−0.292119
$990$	0	0
$991$	−2.51495e19	−0.843434	−0.421717	−	0.906727i	$-0.638572\pi$
$991$	−2.51495e19	−0.843434	−0.421717	+	0.906727i	$0.638572\pi$
$992$	−8.71236e18	−0.290275
$993$	0	0
$994$	−3.07286e19	−1.01049
$995$	1.15791e19	0.378290
$996$	0	0
$997$	−4.70615e18	−0.151757	−0.0758783	−	0.997117i	$-0.524176\pi$
$997$	−4.70615e18	−0.151757	−0.0758783	+	0.997117i	$0.524176\pi$
$998$	2.60849e19	0.835683
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.14.a.h.1.3		6
3.2	odd	2		162.14.a.e.1.4		6
9.2	odd	6		18.14.c.a.13.1	yes	12
9.4	even	3		54.14.c.a.19.4		12
9.5	odd	6		18.14.c.a.7.1	✓	12
9.7	even	3		54.14.c.a.37.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
18.14.c.a.7.1	✓	12	9.5	odd	6
18.14.c.a.13.1	yes	12	9.2	odd	6
54.14.c.a.19.4		12	9.4	even	3
54.14.c.a.37.4		12	9.7	even	3
162.14.a.e.1.4		6	3.2	odd	2
162.14.a.h.1.3		6	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	162.a (trivial)

\(f(q)\)	\(=\)	\(q+64.0000 q^{2} +4096.00 q^{4} -21854.6 q^{5} +292012. q^{7} +262144. q^{8} +O(q^{10})\)	\(q+64.0000 q^{2} +4096.00 q^{4} -21854.6 q^{5} +292012. q^{7} +262144. q^{8} -1.39870e6 q^{10} +2.24156e6 q^{11} -1.73866e7 q^{13} +1.86888e7 q^{14} +1.67772e7 q^{16} -1.02646e8 q^{17} +2.84600e8 q^{19} -8.95166e7 q^{20} +1.43460e8 q^{22} -2.58321e8 q^{23} -7.43078e8 q^{25} -1.11274e9 q^{26} +1.19608e9 q^{28} +3.48435e9 q^{29} -8.11402e9 q^{31} +1.07374e9 q^{32} -6.56935e9 q^{34} -6.38182e9 q^{35} -1.28194e10 q^{37} +1.82144e10 q^{38} -5.72906e9 q^{40} +4.71422e9 q^{41} +3.32794e10 q^{43} +9.18142e9 q^{44} -1.65326e10 q^{46} +3.04125e9 q^{47} -1.16178e10 q^{49} -4.75570e10 q^{50} -7.12157e10 q^{52} +5.94638e10 q^{53} -4.89884e10 q^{55} +7.65493e10 q^{56} +2.22998e11 q^{58} +5.78665e11 q^{59} -2.87088e11 q^{61} -5.19297e11 q^{62} +6.87195e10 q^{64} +3.79978e11 q^{65} +8.74840e11 q^{67} -4.20439e11 q^{68} -4.08437e11 q^{70} -1.64422e12 q^{71} -1.62988e12 q^{73} -8.20444e11 q^{74} +1.16572e12 q^{76} +6.54563e11 q^{77} -3.02692e12 q^{79} -3.66660e11 q^{80} +3.01710e11 q^{82} -9.24967e11 q^{83} +2.24329e12 q^{85} +2.12988e12 q^{86} +5.87611e11 q^{88} -6.03750e12 q^{89} -5.07711e12 q^{91} -1.05808e12 q^{92} +1.94640e11 q^{94} -6.21982e12 q^{95} +1.19926e12 q^{97} -7.43538e11 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 384 q^{2} + 24576 q^{4} - 36504 q^{5} - 153942 q^{7} + 1572864 q^{8}+O(q^{10}) \) 6 * q + 384 * q^2 + 24576 * q^4 - 36504 * q^5 - 153942 * q^7 + 1572864 * q^8	\( 6 q + 384 q^{2} + 24576 q^{4} - 36504 q^{5} - 153942 q^{7} + 1572864 q^{8} - 2336256 q^{10} - 1456506 q^{11} - 24033660 q^{13} - 9852288 q^{14} + 100663296 q^{16} + 539766 q^{17} + 168570444 q^{19} - 149520384 q^{20} - 93216384 q^{22} + 445386186 q^{23} + 2193691326 q^{25} - 1538154240 q^{26} - 630546432 q^{28} - 9171393012 q^{29} - 4264851066 q^{31} + 6442450944 q^{32} + 34545024 q^{34} - 2590484706 q^{35} - 24554425344 q^{37} + 10788508416 q^{38} - 9569304576 q^{40} - 15964345782 q^{41} - 78379952838 q^{43} - 5965848576 q^{44} + 28504715904 q^{46} + 94117799358 q^{47} + 15284873538 q^{49} + 140396244864 q^{50} - 98441871360 q^{52} + 296395207632 q^{53} - 554141279106 q^{55} - 40354971648 q^{56} - 586969152768 q^{58} + 46698155010 q^{59} - 928192122600 q^{61} - 272950468224 q^{62} + 412316860416 q^{64} - 1327744890468 q^{65} - 2282039666898 q^{67} + 2210881536 q^{68} - 165791021184 q^{70} - 1180061485344 q^{71} + 677917450614 q^{73} - 1571483222016 q^{74} + 690464538624 q^{76} - 3622976109756 q^{77} - 2457538059750 q^{79} - 612435492864 q^{80} - 1021718130048 q^{82} - 9950916891942 q^{83} + 576987174720 q^{85} - 5016316981632 q^{86} - 381814308864 q^{88} - 11302343348148 q^{89} + 7395764329770 q^{91} + 1824301817856 q^{92} + 6023539158912 q^{94} - 7488669126384 q^{95} - 1124429902242 q^{97} + 978231906432 q^{98}+O(q^{100}) \) 6 * q + 384 * q^2 + 24576 * q^4 - 36504 * q^5 - 153942 * q^7 + 1572864 * q^8 - 2336256 * q^10 - 1456506 * q^11 - 24033660 * q^13 - 9852288 * q^14 + 100663296 * q^16 + 539766 * q^17 + 168570444 * q^19 - 149520384 * q^20 - 93216384 * q^22 + 445386186 * q^23 + 2193691326 * q^25 - 1538154240 * q^26 - 630546432 * q^28 - 9171393012 * q^29 - 4264851066 * q^31 + 6442450944 * q^32 + 34545024 * q^34 - 2590484706 * q^35 - 24554425344 * q^37 + 10788508416 * q^38 - 9569304576 * q^40 - 15964345782 * q^41 - 78379952838 * q^43 - 5965848576 * q^44 + 28504715904 * q^46 + 94117799358 * q^47 + 15284873538 * q^49 + 140396244864 * q^50 - 98441871360 * q^52 + 296395207632 * q^53 - 554141279106 * q^55 - 40354971648 * q^56 - 586969152768 * q^58 + 46698155010 * q^59 - 928192122600 * q^61 - 272950468224 * q^62 + 412316860416 * q^64 - 1327744890468 * q^65 - 2282039666898 * q^67 + 2210881536 * q^68 - 165791021184 * q^70 - 1180061485344 * q^71 + 677917450614 * q^73 - 1571483222016 * q^74 + 690464538624 * q^76 - 3622976109756 * q^77 - 2457538059750 * q^79 - 612435492864 * q^80 - 1021718130048 * q^82 - 9950916891942 * q^83 + 576987174720 * q^85 - 5016316981632 * q^86 - 381814308864 * q^88 - 11302343348148 * q^89 + 7395764329770 * q^91 + 1824301817856 * q^92 + 6023539158912 * q^94 - 7488669126384 * q^95 - 1124429902242 * q^97 + 978231906432 * q^98

Introduction

L-functions

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Database

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