LMFDB - Embedded newform 45.22.a.e.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [45,22,Mod(1,45)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(45, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 22, names="a")

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

chi := DirichletCharacter("45.1");

S:= CuspForms(chi, 22);

N := Newforms(S);

Level:	$ N $	$=$	$ 45 = 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 22 $
Character orbit:	$[\chi]$	$=$	45.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:	$125.764804929$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	$\mathbb{Q}[x]/(x^{3} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 125326x + 2416960 $ x^3 - x^2 - 125326*x + 2416960
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{5}\cdot 3^{2}\cdot 5 $
Twist minimal:	no (minimal twist has level 15)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$344.462$ of defining polynomial
Character	$\chi$	$=$	45.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+904.285 q^{2} -1.27942e6 q^{4} -9.76562e6 q^{5} -5.27665e8 q^{7} -3.05338e9 q^{8} +O(q^{10})$	\(q+904.285 q^{2} -1.27942e6 q^{4} -9.76562e6 q^{5} -5.27665e8 q^{7} -3.05338e9 q^{8} -8.83091e9 q^{10} -2.65340e10 q^{11} -2.99119e11 q^{13} -4.77159e11 q^{14} -7.79881e10 q^{16} -5.63375e12 q^{17} -2.99289e13 q^{19} +1.24943e13 q^{20} -2.39943e13 q^{22} -2.68586e14 q^{23} +9.53674e13 q^{25} -2.70489e14 q^{26} +6.75105e14 q^{28} -2.29992e15 q^{29} +9.85582e12 q^{31} +6.33289e15 q^{32} -5.09452e15 q^{34} +5.15297e15 q^{35} -4.70406e16 q^{37} -2.70643e16 q^{38} +2.98182e16 q^{40} +5.27759e16 q^{41} -1.73957e17 q^{43} +3.39482e16 q^{44} -2.42878e17 q^{46} +3.55119e17 q^{47} -2.80116e17 q^{49} +8.62393e16 q^{50} +3.82700e17 q^{52} +1.59624e18 q^{53} +2.59121e17 q^{55} +1.61116e18 q^{56} -2.07978e18 q^{58} +7.01582e17 q^{59} +6.72232e16 q^{61} +8.91247e15 q^{62} +5.89029e18 q^{64} +2.92109e18 q^{65} -1.91979e19 q^{67} +7.20794e18 q^{68} +4.65976e18 q^{70} +3.18707e19 q^{71} +3.26491e19 q^{73} -4.25381e19 q^{74} +3.82917e19 q^{76} +1.40011e19 q^{77} +4.87799e19 q^{79} +7.61602e17 q^{80} +4.77244e19 q^{82} -9.61606e19 q^{83} +5.50171e19 q^{85} -1.57307e20 q^{86} +8.10186e19 q^{88} +1.96348e20 q^{89} +1.57835e20 q^{91} +3.43634e20 q^{92} +3.21129e20 q^{94} +2.92274e20 q^{95} -1.19334e21 q^{97} -2.53305e20 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 2300 q^{2} + 1264400 q^{4} - 29296875 q^{5} + 465666872 q^{7} + 3839876544 q^{8}+O(q^{10}) $ 3 * q + 2300 * q^2 + 1264400 * q^4 - 29296875 * q^5 + 465666872 * q^7 + 3839876544 * q^8	$ 3 q + 2300 q^{2} + 1264400 q^{4} - 29296875 q^{5} + 465666872 q^{7} + 3839876544 q^{8} - 22460937500 q^{10} + 167336332556 q^{11} - 545571033878 q^{13} + 1568858902656 q^{14} + 255267954944 q^{16} + 8104424487194 q^{17} + 3937700740828 q^{19} - 12347656250000 q^{20} + 114198109969712 q^{22} + 156235274730744 q^{23} + 286102294921875 q^{25} - 29\!\cdots\!56 q^{26}+ \cdots + 87\!\cdots\!32 q^{98}+O(q^{100}) $ 3 * q + 2300 * q^2 + 1264400 * q^4 - 29296875 * q^5 + 465666872 * q^7 + 3839876544 * q^8 - 22460937500 * q^10 + 167336332556 * q^11 - 545571033878 * q^13 + 1568858902656 * q^14 + 255267954944 * q^16 + 8104424487194 * q^17 + 3937700740828 * q^19 - 12347656250000 * q^20 + 114198109969712 * q^22 + 156235274730744 * q^23 + 286102294921875 * q^25 - 2972936042645656 * q^26 + 3826676848454144 * q^28 + 930273612785494 * q^29 - 6257709152718928 * q^31 - 4297283007276032 * q^32 - 20587982883981400 * q^34 - 4547528046875000 * q^35 - 22246337613227118 * q^37 + 82202958592557968 * q^38 - 37498794375000000 * q^40 + 186265908060974338 * q^41 - 268609288174096316 * q^43 + 284579440966881088 * q^44 + 375824751838355712 * q^46 + 900034127817222032 * q^47 - 586354193149814837 * q^49 + 219345092773437500 * q^50 - 3462564631549962144 * q^52 + 1269623243180583374 * q^53 - 1634143872617187500 * q^55 + 5236064873787955200 * q^56 - 1091617398834773576 * q^58 + 8551487099411338268 * q^59 - 7181148471323735222 * q^61 + 3050004306382316256 * q^62 - 557099647389855744 * q^64 + 5327842127714843750 * q^65 + 2946635148405656396 * q^67 - 10323921738190858400 * q^68 - 15320887721250000000 * q^70 + 37849731561832987624 * q^71 - 7149058835824826594 * q^73 - 50872537645745842424 * q^74 + 200886445168773700032 * q^76 + 110970090560628236256 * q^77 + 309682369826312504000 * q^79 - 2492851122500000000 * q^80 + 265773545783653420264 * q^82 - 199780825758268631580 * q^83 - 79144770382753906250 * q^85 - 267144820042737104944 * q^86 + 749649166937994283776 * q^88 - 162380735751340085838 * q^89 - 558457704043459369328 * q^91 + 1333721831719821170688 * q^92 - 149583353667227862112 * q^94 - 38454108797148437500 * q^95 - 1208943423358924299354 * q^97 + 876777377902285855132 * 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 $

$2$	904.285	0.624439	0.312220	−	0.950010i	$-0.398927\pi$
$2$	904.285	0.624439	0.312220	+	0.950010i	$0.398927\pi$
$3$	0	0
$3$	0	0
$4$	−1.27942e6	−0.610075
$5$	−9.76562e6	−0.447214
$5$	−9.76562e6	−0.447214
$6$	0	0
$7$	−5.27665e8	−0.706039	−0.353019	−	0.935616i	$-0.614845\pi$
$7$	−5.27665e8	−0.706039	−0.353019	+	0.935616i	$0.614845\pi$
$8$	−3.05338e9	−1.00539
$9$	0	0
$10$	−8.83091e9	−0.279258
$11$	−2.65340e10	−0.308447	−0.154223	−	0.988036i	$-0.549288\pi$
$11$	−2.65340e10	−0.308447	−0.154223	+	0.988036i	$0.549288\pi$
$12$	0	0
$13$	−2.99119e11	−0.601782	−0.300891	−	0.953659i	$-0.597284\pi$
$13$	−2.99119e11	−0.601782	−0.300891	+	0.953659i	$0.597284\pi$
$14$	−4.77159e11	−0.440878
$15$	0	0
$16$	−7.79881e10	−0.0177324
$17$	−5.63375e12	−0.677773	−0.338886	−	0.940827i	$-0.610050\pi$
$17$	−5.63375e12	−0.677773	−0.338886	+	0.940827i	$0.610050\pi$
$18$	0	0
$19$	−2.99289e13	−1.11990	−0.559948	−	0.828527i	$-0.689179\pi$
$19$	−2.99289e13	−1.11990	−0.559948	+	0.828527i	$0.689179\pi$
$20$	1.24943e13	0.272834
$21$	0	0
$22$	−2.39943e13	−0.192606
$23$	−2.68586e14	−1.35189	−0.675944	−	0.736953i	$-0.736264\pi$
$23$	−2.68586e14	−1.35189	−0.675944	+	0.736953i	$0.736264\pi$
$24$	0	0
$25$	9.53674e13	0.200000
$26$	−2.70489e14	−0.375776
$27$	0	0
$28$	6.75105e14	0.430737
$29$	−2.29992e15	−1.01516	−0.507579	−	0.861605i	$-0.669460\pi$
$29$	−2.29992e15	−1.01516	−0.507579	+	0.861605i	$0.669460\pi$
$30$	0	0
$31$	9.85582e12	0.00215971	0.00107985	−	0.999999i	$-0.499656\pi$
$31$	9.85582e12	0.00215971	0.00107985	+	0.999999i	$0.499656\pi$
$32$	6.33289e15	0.994322
$33$	0	0
$34$	−5.09452e15	−0.423228
$35$	5.15297e15	0.315750
$36$	0	0
$37$	−4.70406e16	−1.60826	−0.804128	−	0.594457i	$-0.797367\pi$
$37$	−4.70406e16	−1.60826	−0.804128	+	0.594457i	$0.797367\pi$
$38$	−2.70643e16	−0.699308
$39$	0	0
$40$	2.98182e16	0.449626
$41$	5.27759e16	0.614052	0.307026	−	0.951701i	$-0.400666\pi$
$41$	5.27759e16	0.614052	0.307026	+	0.951701i	$0.400666\pi$
$42$	0	0
$43$	−1.73957e17	−1.22750	−0.613752	−	0.789499i	$-0.710341\pi$
$43$	−1.73957e17	−1.22750	−0.613752	+	0.789499i	$0.710341\pi$
$44$	3.39482e16	0.188176
$45$	0	0
$46$	−2.42878e17	−0.844173
$47$	3.55119e17	0.984797	0.492399	−	0.870370i	$-0.336120\pi$
$47$	3.55119e17	0.984797	0.492399	+	0.870370i	$0.336120\pi$
$48$	0	0
$49$	−2.80116e17	−0.501509
$50$	8.62393e16	0.124888
$51$	0	0
$52$	3.82700e17	0.367133
$53$	1.59624e18	1.25373	0.626863	−	0.779129i	$-0.284338\pi$
$53$	1.59624e18	1.25373	0.626863	+	0.779129i	$0.284338\pi$
$54$	0	0
$55$	2.59121e17	0.137941
$56$	1.61116e18	0.709847
$57$	0	0
$58$	−2.07978e18	−0.633905
$59$	7.01582e17	0.178703	0.0893516	−	0.996000i	$-0.471521\pi$
$59$	7.01582e17	0.178703	0.0893516	+	0.996000i	$0.471521\pi$
$60$	0	0
$61$	6.72232e16	0.0120658	0.00603290	−	0.999982i	$-0.498080\pi$
$61$	6.72232e16	0.0120658	0.00603290	+	0.999982i	$0.498080\pi$
$62$	8.91247e15	0.00134861
$63$	0	0
$64$	5.89029e18	0.638626
$65$	2.92109e18	0.269125
$66$	0	0
$67$	−1.91979e19	−1.28667	−0.643337	−	0.765583i	$-0.722450\pi$
$67$	−1.91979e19	−1.28667	−0.643337	+	0.765583i	$0.722450\pi$
$68$	7.20794e18	0.413493
$69$	0	0
$70$	4.65976e18	0.197167
$71$	3.18707e19	1.16193	0.580963	−	0.813930i	$-0.302676\pi$
$71$	3.18707e19	1.16193	0.580963	+	0.813930i	$0.302676\pi$
$72$	0	0
$73$	3.26491e19	0.889163	0.444581	−	0.895739i	$-0.353352\pi$
$73$	3.26491e19	0.889163	0.444581	+	0.895739i	$0.353352\pi$
$74$	−4.25381e19	−1.00426
$75$	0	0
$76$	3.82917e19	0.683222
$77$	1.40011e19	0.217775
$78$	0	0
$79$	4.87799e19	0.579638	0.289819	−	0.957082i	$-0.406405\pi$
$79$	4.87799e19	0.579638	0.289819	+	0.957082i	$0.406405\pi$
$80$	7.61602e17	0.00793019
$81$	0	0
$82$	4.77244e19	0.383438
$83$	−9.61606e19	−0.680264	−0.340132	−	0.940378i	$-0.610472\pi$
$83$	−9.61606e19	−0.680264	−0.340132	+	0.940378i	$0.610472\pi$
$84$	0	0
$85$	5.50171e19	0.303109
$86$	−1.57307e20	−0.766502
$87$	0	0
$88$	8.10186e19	0.310110
$89$	1.96348e20	0.667470	0.333735	−	0.942667i	$-0.391691\pi$
$89$	1.96348e20	0.667470	0.333735	+	0.942667i	$0.391691\pi$
$90$	0	0
$91$	1.57835e20	0.424881
$92$	3.43634e20	0.824754
$93$	0	0
$94$	3.21129e20	0.614946
$95$	2.92274e20	0.500833
$96$	0	0
$97$	−1.19334e21	−1.64309	−0.821543	−	0.570147i	$-0.806886\pi$
$97$	−1.19334e21	−1.64309	−0.821543	+	0.570147i	$0.806886\pi$
$98$	−2.53305e20	−0.313162
$99$	0	0
$100$	−1.22015e20	−0.122015
$101$	1.07408e21	0.967525	0.483763	−	0.875199i	$-0.339270\pi$
$101$	1.07408e21	0.967525	0.483763	+	0.875199i	$0.339270\pi$
$102$	0	0
$103$	2.91007e20	0.213359	0.106680	−	0.994293i	$-0.465978\pi$
$103$	2.91007e20	0.213359	0.106680	+	0.994293i	$0.465978\pi$
$104$	9.13326e20	0.605029
$105$	0	0
$106$	1.44346e21	0.782876
$107$	−4.13437e20	−0.203179	−0.101590	−	0.994826i	$-0.532393\pi$
$107$	−4.13437e20	−0.203179	−0.101590	+	0.994826i	$0.532393\pi$
$108$	0	0
$109$	−1.38433e21	−0.560095	−0.280047	−	0.959986i	$-0.590350\pi$
$109$	−1.38433e21	−0.560095	−0.280047	+	0.959986i	$0.590350\pi$
$110$	2.34319e20	0.0861361
$111$	0	0
$112$	4.11516e19	0.0125198
$113$	−4.12215e21	−1.14235	−0.571176	−	0.820828i	$-0.693513\pi$
$113$	−4.12215e21	−1.14235	−0.571176	+	0.820828i	$0.693513\pi$
$114$	0	0
$115$	2.62291e21	0.604583
$116$	2.94257e21	0.619324
$117$	0	0
$118$	6.34430e20	0.111589
$119$	2.97273e21	0.478534
$120$	0	0
$121$	−6.69620e21	−0.904861
$122$	6.07889e19	0.00753436
$123$	0	0
$124$	−1.26097e19	−0.00131758
$125$	−9.31323e20	−0.0894427
$126$	0	0
$127$	9.01466e21	0.732842	0.366421	−	0.930449i	$-0.380583\pi$
$127$	9.01466e21	0.732842	0.366421	+	0.930449i	$0.380583\pi$
$128$	−7.95453e21	−0.595538
$129$	0	0
$130$	2.64150e21	0.168052
$131$	−2.66138e21	−0.156228	−0.0781140	−	0.996944i	$-0.524890\pi$
$131$	−2.66138e21	−0.156228	−0.0781140	+	0.996944i	$0.524890\pi$
$132$	0	0
$133$	1.57924e22	0.790690
$134$	−1.73604e22	−0.803449
$135$	0	0
$136$	1.72020e22	0.681429
$137$	−2.44212e21	−0.0895778	−0.0447889	−	0.998996i	$-0.514262\pi$
$137$	−2.44212e21	−0.0895778	−0.0447889	+	0.998996i	$0.514262\pi$
$138$	0	0
$139$	4.96603e22	1.56442	0.782211	−	0.623014i	$-0.214092\pi$
$139$	4.96603e22	1.56442	0.782211	+	0.623014i	$0.214092\pi$
$140$	−6.59282e21	−0.192631
$141$	0	0
$142$	2.88202e22	0.725553
$143$	7.93684e21	0.185618
$144$	0	0
$145$	2.24602e22	0.453993
$146$	2.95241e22	0.555228
$147$	0	0
$148$	6.01848e22	0.981157
$149$	1.09551e23	1.66403	0.832016	−	0.554752i	$-0.187187\pi$
$149$	1.09551e23	1.66403	0.832016	+	0.554752i	$0.187187\pi$
$150$	0	0
$151$	−6.31612e22	−0.834050	−0.417025	−	0.908895i	$-0.636927\pi$
$151$	−6.31612e22	−0.834050	−0.417025	+	0.908895i	$0.636927\pi$
$152$	9.13844e22	1.12594
$153$	0	0
$154$	1.26609e22	0.135987
$155$	−9.62482e19	−0.000965851 0
$156$	0	0
$157$	1.32747e23	1.16433	0.582167	−	0.813069i	$-0.302205\pi$
$157$	1.32747e23	1.16433	0.582167	+	0.813069i	$0.302205\pi$
$158$	4.41109e22	0.361949
$159$	0	0
$160$	−6.18446e22	−0.444674
$161$	1.41723e23	0.954486
$162$	0	0
$163$	1.55377e23	0.919214	0.459607	−	0.888123i	$-0.347990\pi$
$163$	1.55377e23	0.919214	0.459607	+	0.888123i	$0.347990\pi$
$164$	−6.75226e22	−0.374618
$165$	0	0
$166$	−8.69566e22	−0.424783
$167$	2.54123e23	1.16553	0.582763	−	0.812642i	$-0.301972\pi$
$167$	2.54123e23	1.16553	0.582763	+	0.812642i	$0.301972\pi$
$168$	0	0
$169$	−1.57592e23	−0.637858
$170$	4.97511e22	0.189273
$171$	0	0
$172$	2.22564e23	0.748870
$173$	1.55898e23	0.493579	0.246789	−	0.969069i	$-0.420624\pi$
$173$	1.55898e23	0.493579	0.246789	+	0.969069i	$0.420624\pi$
$174$	0	0
$175$	−5.03220e22	−0.141208
$176$	2.06934e21	0.00546951
$177$	0	0
$178$	1.77555e23	0.416795
$179$	−5.96854e23	−1.32103	−0.660513	−	0.750815i	$-0.729661\pi$
$179$	−5.96854e23	−1.32103	−0.660513	+	0.750815i	$0.729661\pi$
$180$	0	0
$181$	9.34668e23	1.84091	0.920454	−	0.390850i	$-0.127819\pi$
$181$	9.34668e23	1.84091	0.920454	+	0.390850i	$0.127819\pi$
$182$	1.42728e23	0.265313
$183$	0	0
$184$	8.20096e23	1.35918
$185$	4.59381e23	0.719234
$186$	0	0
$187$	1.49486e23	0.209057
$188$	−4.54347e23	−0.600801
$189$	0	0
$190$	2.64299e23	0.312740
$191$	3.65829e23	0.409663	0.204832	−	0.978797i	$-0.434335\pi$
$191$	3.65829e23	0.409663	0.204832	+	0.978797i	$0.434335\pi$
$192$	0	0
$193$	−7.82889e23	−0.785866	−0.392933	−	0.919567i	$-0.628540\pi$
$193$	−7.82889e23	−0.785866	−0.392933	+	0.919567i	$0.628540\pi$
$194$	−1.07912e24	−1.02601
$195$	0	0
$196$	3.58386e23	0.305959
$197$	−1.20518e24	−0.975343	−0.487671	−	0.873027i	$-0.662154\pi$
$197$	−1.20518e24	−0.975343	−0.487671	+	0.873027i	$0.662154\pi$
$198$	0	0
$199$	−4.25336e23	−0.309581	−0.154791	−	0.987947i	$-0.549470\pi$
$199$	−4.25336e23	−0.309581	−0.154791	+	0.987947i	$0.549470\pi$
$200$	−2.91193e23	−0.201079
$201$	0	0
$202$	9.71275e23	0.604161
$203$	1.21359e24	0.716741
$204$	0	0
$205$	−5.15389e23	−0.274612
$206$	2.63153e23	0.133230
$207$	0	0
$208$	2.33277e22	0.0106711
$209$	7.94134e23	0.345428
$210$	0	0
$211$	−4.07080e24	−1.60219	−0.801094	−	0.598538i	$-0.795749\pi$
$211$	−4.07080e24	−1.60219	−0.801094	+	0.598538i	$0.795749\pi$
$212$	−2.04227e24	−0.764868
$213$	0	0
$214$	−3.73865e23	−0.126873
$215$	1.69880e24	0.548957
$216$	0	0
$217$	−5.20057e21	−0.00152484
$218$	−1.25183e24	−0.349745
$219$	0	0
$220$	−3.31525e23	−0.0841547
$221$	1.68516e24	0.407872
$222$	0	0
$223$	−5.67983e24	−1.25064	−0.625322	−	0.780366i	$-0.715033\pi$
$223$	−5.67983e24	−1.25064	−0.625322	+	0.780366i	$0.715033\pi$
$224$	−3.34164e24	−0.702030
$225$	0	0
$226$	−3.72760e24	−0.713330
$227$	3.01893e24	0.551546	0.275773	−	0.961223i	$-0.411066\pi$
$227$	3.01893e24	0.551546	0.275773	+	0.961223i	$0.411066\pi$
$228$	0	0
$229$	−5.69538e24	−0.948964	−0.474482	−	0.880265i	$-0.657365\pi$
$229$	−5.69538e24	−0.948964	−0.474482	+	0.880265i	$0.657365\pi$
$230$	2.37186e24	0.377525
$231$	0	0
$232$	7.02254e24	1.02064
$233$	−4.13113e24	−0.573894	−0.286947	−	0.957946i	$-0.592640\pi$
$233$	−4.13113e24	−0.573894	−0.286947	+	0.957946i	$0.592640\pi$
$234$	0	0
$235$	−3.46796e24	−0.440415
$236$	−8.97619e23	−0.109022
$237$	0	0
$238$	2.68820e24	0.298815
$239$	−1.32693e23	−0.0141147	−0.00705734	−	0.999975i	$-0.502246\pi$
$239$	−1.32693e23	−0.0141147	−0.00705734	+	0.999975i	$0.502246\pi$
$240$	0	0
$241$	−1.18800e25	−1.15781	−0.578906	−	0.815394i	$-0.696520\pi$
$241$	−1.18800e25	−1.15781	−0.578906	+	0.815394i	$0.696520\pi$
$242$	−6.05527e24	−0.565031
$243$	0	0
$244$	−8.60068e22	−0.00736104
$245$	2.73551e24	0.224282
$246$	0	0
$247$	8.95232e24	0.673934
$248$	−3.00936e22	−0.00217136
$249$	0	0
$250$	−8.42181e23	−0.0558516
$251$	2.19977e25	1.39895	0.699476	−	0.714656i	$-0.253417\pi$
$251$	2.19977e25	1.39895	0.699476	+	0.714656i	$0.253417\pi$
$252$	0	0
$253$	7.12667e24	0.416985
$254$	8.15182e24	0.457615
$255$	0	0
$256$	−1.95460e25	−1.01050
$257$	−2.99791e25	−1.48772	−0.743859	−	0.668337i	$-0.767007\pi$
$257$	−2.99791e25	−1.48772	−0.743859	+	0.668337i	$0.767007\pi$
$258$	0	0
$259$	2.48217e25	1.13549
$260$	−3.73730e24	−0.164187
$261$	0	0
$262$	−2.40665e24	−0.0975549
$263$	−4.22949e25	−1.64723	−0.823613	−	0.567153i	$-0.808045\pi$
$263$	−4.22949e25	−1.64723	−0.823613	+	0.567153i	$0.808045\pi$
$264$	0	0
$265$	−1.55883e25	−0.560684
$266$	1.42808e25	0.493738
$267$	0	0
$268$	2.45622e25	0.784968
$269$	−6.39643e25	−1.96580	−0.982899	−	0.184147i	$-0.941048\pi$
$269$	−6.39643e25	−1.96580	−0.982899	+	0.184147i	$0.941048\pi$
$270$	0	0
$271$	−6.83795e25	−1.94423	−0.972117	−	0.234498i	$-0.924655\pi$
$271$	−6.83795e25	−1.94423	−0.972117	+	0.234498i	$0.924655\pi$
$272$	4.39366e23	0.0120186
$273$	0	0
$274$	−2.20837e24	−0.0559359
$275$	−2.53048e24	−0.0616893
$276$	0	0
$277$	1.26234e25	0.285193	0.142596	−	0.989781i	$-0.454455\pi$
$277$	1.26234e25	0.285193	0.142596	+	0.989781i	$0.454455\pi$
$278$	4.49071e25	0.976887
$279$	0	0
$280$	−1.57340e25	−0.317453
$281$	4.98345e25	0.968531	0.484265	−	0.874921i	$-0.339087\pi$
$281$	4.98345e25	0.968531	0.484265	+	0.874921i	$0.339087\pi$
$282$	0	0
$283$	−3.37214e25	−0.608343	−0.304171	−	0.952617i	$-0.598380\pi$
$283$	−3.37214e25	−0.608343	−0.304171	+	0.952617i	$0.598380\pi$
$284$	−4.07760e25	−0.708863
$285$	0	0
$286$	7.17716e24	0.115907
$287$	−2.78480e25	−0.433544
$288$	0	0
$289$	−3.73528e25	−0.540624
$290$	2.03104e25	0.283491
$291$	0	0
$292$	−4.17719e25	−0.542456
$293$	6.30480e25	0.789880	0.394940	−	0.918707i	$-0.370765\pi$
$293$	6.30480e25	0.789880	0.394940	+	0.918707i	$0.370765\pi$
$294$	0	0
$295$	−6.85139e24	−0.0799185
$296$	1.43633e26	1.61693
$297$	0	0
$298$	9.90655e25	1.03909
$299$	8.03393e25	0.813543
$300$	0	0
$301$	9.17909e25	0.866665
$302$	−5.71157e25	−0.520814
$303$	0	0
$304$	2.33410e24	0.0198585
$305$	−6.56476e23	−0.00539599
$306$	0	0
$307$	1.96989e26	1.51178	0.755890	−	0.654698i	$-0.227204\pi$
$307$	1.96989e26	1.51178	0.755890	+	0.654698i	$0.227204\pi$
$308$	−1.79133e25	−0.132859
$309$	0	0
$310$	−8.70358e22	−0.000603115 0
$311$	−8.49904e25	−0.569358	−0.284679	−	0.958623i	$-0.591887\pi$
$311$	−8.49904e25	−0.569358	−0.284679	+	0.958623i	$0.591887\pi$
$312$	0	0
$313$	1.73341e26	1.08564	0.542821	−	0.839848i	$-0.317356\pi$
$313$	1.73341e26	1.08564	0.542821	+	0.839848i	$0.317356\pi$
$314$	1.20041e26	0.727056
$315$	0	0
$316$	−6.24100e25	−0.353623
$317$	−2.95504e26	−1.61972	−0.809862	−	0.586621i	$-0.800458\pi$
$317$	−2.95504e26	−1.61972	−0.809862	+	0.586621i	$0.800458\pi$
$318$	0	0
$319$	6.10262e25	0.313122
$320$	−5.75223e25	−0.285602
$321$	0	0
$322$	1.28158e26	0.596019
$323$	1.68612e26	0.759036
$324$	0	0
$325$	−2.85262e25	−0.120356
$326$	1.40505e26	0.573993
$327$	0	0
$328$	−1.61145e26	−0.617364
$329$	−1.87384e26	−0.695305
$330$	0	0
$331$	3.41537e26	1.18917	0.594585	−	0.804033i	$-0.297316\pi$
$331$	3.41537e26	1.18917	0.594585	+	0.804033i	$0.297316\pi$
$332$	1.23030e26	0.415012
$333$	0	0
$334$	2.29800e26	0.727800
$335$	1.87479e26	0.575418
$336$	0	0
$337$	1.87784e26	0.541434	0.270717	−	0.962659i	$-0.412739\pi$
$337$	1.87784e26	0.541434	0.270717	+	0.962659i	$0.412739\pi$
$338$	−1.42508e26	−0.398304
$339$	0	0
$340$	−7.03901e25	−0.184919
$341$	−2.61515e23	−0.000666154 0
$342$	0	0
$343$	4.42532e26	1.06012
$344$	5.31157e26	1.23413
$345$	0	0
$346$	1.40976e26	0.308210
$347$	1.44337e26	0.306138	0.153069	−	0.988216i	$-0.451084\pi$
$347$	1.44337e26	0.306138	0.153069	+	0.988216i	$0.451084\pi$
$348$	0	0
$349$	−3.47715e26	−0.694315	−0.347157	−	0.937807i	$-0.612853\pi$
$349$	−3.47715e26	−0.694315	−0.347157	+	0.937807i	$0.612853\pi$
$350$	−4.55054e25	−0.0881757
$351$	0	0
$352$	−1.68037e26	−0.306695
$353$	6.45150e26	1.14295	0.571474	−	0.820620i	$-0.306372\pi$
$353$	6.45150e26	1.14295	0.571474	+	0.820620i	$0.306372\pi$
$354$	0	0
$355$	−3.11237e26	−0.519629
$356$	−2.51212e26	−0.407207
$357$	0	0
$358$	−5.39726e26	−0.824900
$359$	−7.68850e26	−1.14117	−0.570584	−	0.821239i	$-0.693283\pi$
$359$	−7.68850e26	−1.14117	−0.570584	+	0.821239i	$0.693283\pi$
$360$	0	0
$361$	1.81530e26	0.254169
$362$	8.45206e26	1.14954
$363$	0	0
$364$	−2.01937e26	−0.259210
$365$	−3.18839e26	−0.397646
$366$	0	0
$367$	−6.85612e26	−0.807393	−0.403697	−	0.914893i	$-0.632275\pi$
$367$	−6.85612e26	−0.807393	−0.403697	+	0.914893i	$0.632275\pi$
$368$	2.09465e25	0.0239723
$369$	0	0
$370$	4.15411e26	0.449118
$371$	−8.42282e26	−0.885180
$372$	0	0
$373$	−6.03840e25	−0.0599763	−0.0299881	−	0.999550i	$-0.509547\pi$
$373$	−6.03840e25	−0.0599763	−0.0299881	+	0.999550i	$0.509547\pi$
$374$	1.35178e26	0.130543
$375$	0	0
$376$	−1.08432e27	−0.990110
$377$	6.87951e26	0.610905
$378$	0	0
$379$	−1.51286e27	−1.27082	−0.635412	−	0.772173i	$-0.719170\pi$
$379$	−1.51286e27	−1.27082	−0.635412	+	0.772173i	$0.719170\pi$
$380$	−3.73942e26	−0.305546
$381$	0	0
$382$	3.30813e26	0.255810
$383$	−1.30252e27	−0.979937	−0.489968	−	0.871740i	$-0.662992\pi$
$383$	−1.30252e27	−0.979937	−0.489968	+	0.871740i	$0.662992\pi$
$384$	0	0
$385$	−1.36729e26	−0.0973920
$386$	−7.07954e26	−0.490726
$387$	0	0
$388$	1.52678e27	1.00241
$389$	−1.24558e27	−0.795979	−0.397989	−	0.917390i	$-0.630292\pi$
$389$	−1.24558e27	−0.795979	−0.397989	+	0.917390i	$0.630292\pi$
$390$	0	0
$391$	1.51315e27	0.916273
$392$	8.55302e26	0.504215
$393$	0	0
$394$	−1.08983e27	−0.609042
$395$	−4.76366e26	−0.259222
$396$	0	0
$397$	−3.70376e27	−1.91136	−0.955681	−	0.294405i	$-0.904878\pi$
$397$	−3.70376e27	−1.91136	−0.955681	+	0.294405i	$0.904878\pi$
$398$	−3.84625e26	−0.193315
$399$	0	0
$400$	−7.43752e24	−0.00354649
$401$	−6.07186e26	−0.282037	−0.141018	−	0.990007i	$-0.545038\pi$
$401$	−6.07186e26	−0.282037	−0.141018	+	0.990007i	$0.545038\pi$
$402$	0	0
$403$	−2.94807e24	−0.00129967
$404$	−1.37420e27	−0.590263
$405$	0	0
$406$	1.09743e27	0.447562
$407$	1.24818e27	0.496061
$408$	0	0
$409$	−4.82845e27	−1.82269	−0.911346	−	0.411641i	$-0.864956\pi$
$409$	−4.82845e27	−1.82269	−0.911346	+	0.411641i	$0.864956\pi$
$410$	−4.66059e26	−0.171479
$411$	0	0
$412$	−3.72320e26	−0.130165
$413$	−3.70200e26	−0.126171
$414$	0	0
$415$	9.39068e26	0.304223
$416$	−1.89429e27	−0.598365
$417$	0	0
$418$	7.18124e26	0.215699
$419$	−9.41337e26	−0.275739	−0.137869	−	0.990450i	$-0.544025\pi$
$419$	−9.41337e26	−0.275739	−0.137869	+	0.990450i	$0.544025\pi$
$420$	0	0
$421$	5.72115e27	1.59412	0.797061	−	0.603899i	$-0.206387\pi$
$421$	5.72115e27	1.59412	0.797061	+	0.603899i	$0.206387\pi$
$422$	−3.68116e27	−1.00047
$423$	0	0
$424$	−4.87395e27	−1.26049
$425$	−5.37276e26	−0.135555
$426$	0	0
$427$	−3.54713e25	−0.00851892
$428$	5.28960e26	0.123955
$429$	0	0
$430$	1.53620e27	0.342790
$431$	6.04995e27	1.31747	0.658735	−	0.752375i	$-0.271092\pi$
$431$	6.04995e27	1.31747	0.658735	+	0.752375i	$0.271092\pi$
$432$	0	0
$433$	1.63788e27	0.339749	0.169875	−	0.985466i	$-0.445664\pi$
$433$	1.63788e27	0.339749	0.169875	+	0.985466i	$0.445664\pi$
$434$	−4.70279e24	−0.000952168 0
$435$	0	0
$436$	1.77114e27	0.341700
$437$	8.03848e27	1.51398
$438$	0	0
$439$	−1.11731e26	−0.0200583	−0.0100292	−	0.999950i	$-0.503192\pi$
$439$	−1.11731e26	−0.0200583	−0.0100292	+	0.999950i	$0.503192\pi$
$440$	−7.91197e26	−0.138686
$441$	0	0
$442$	1.52387e27	0.254691
$443$	8.62719e27	1.40809	0.704045	−	0.710156i	$-0.251375\pi$
$443$	8.62719e27	1.40809	0.704045	+	0.710156i	$0.251375\pi$
$444$	0	0
$445$	−1.91746e27	−0.298502
$446$	−5.13618e27	−0.780952
$447$	0	0
$448$	−3.10809e27	−0.450895
$449$	7.30032e27	1.03456	0.517279	−	0.855817i	$-0.326945\pi$
$449$	7.30032e27	1.03456	0.517279	+	0.855817i	$0.326945\pi$
$450$	0	0
$451$	−1.40036e27	−0.189402
$452$	5.27396e27	0.696921
$453$	0	0
$454$	2.72998e27	0.344407
$455$	−1.54135e27	−0.190013
$456$	0	0
$457$	−1.73831e27	−0.204647	−0.102324	−	0.994751i	$-0.532628\pi$
$457$	−1.73831e27	−0.204647	−0.102324	+	0.994751i	$0.532628\pi$
$458$	−5.15024e27	−0.592571
$459$	0	0
$460$	−3.35581e27	−0.368841
$461$	1.51568e27	0.162835	0.0814177	−	0.996680i	$-0.474055\pi$
$461$	1.51568e27	0.162835	0.0814177	+	0.996680i	$0.474055\pi$
$462$	0	0
$463$	2.44187e27	0.250681	0.125341	−	0.992114i	$-0.459998\pi$
$463$	2.44187e27	0.250681	0.125341	+	0.992114i	$0.459998\pi$
$464$	1.79367e26	0.0180012
$465$	0	0
$466$	−3.73572e27	−0.358362
$467$	−2.36192e27	−0.221533	−0.110766	−	0.993846i	$-0.535331\pi$
$467$	−2.36192e27	−0.221533	−0.110766	+	0.993846i	$0.535331\pi$
$468$	0	0
$469$	1.01300e28	0.908441
$470$	−3.13603e27	−0.275012
$471$	0	0
$472$	−2.14220e27	−0.179667
$473$	4.61578e27	0.378619
$474$	0	0
$475$	−2.85424e27	−0.223979
$476$	−3.80337e27	−0.291942
$477$	0	0
$478$	−1.19993e26	−0.00881376
$479$	−7.29552e27	−0.524244	−0.262122	−	0.965035i	$-0.584422\pi$
$479$	−7.29552e27	−0.524244	−0.262122	+	0.965035i	$0.584422\pi$
$480$	0	0
$481$	1.40708e28	0.967819
$482$	−1.07429e28	−0.722984
$483$	0	0
$484$	8.56725e27	0.552033
$485$	1.16537e28	0.734810
$486$	0	0
$487$	2.80625e28	1.69462	0.847309	−	0.531100i	$-0.178221\pi$
$487$	2.80625e28	1.69462	0.847309	+	0.531100i	$0.178221\pi$
$488$	−2.05258e26	−0.0121309
$489$	0	0
$490$	2.47368e27	0.140050
$491$	−3.13375e26	−0.0173663	−0.00868317	−	0.999962i	$-0.502764\pi$
$491$	−3.13375e26	−0.0173663	−0.00868317	+	0.999962i	$0.502764\pi$
$492$	0	0
$493$	1.29572e28	0.688047
$494$	8.09544e27	0.420831
$495$	0	0
$496$	−7.68637e23	−3.82969e−5 0
$497$	−1.68170e28	−0.820365
$498$	0	0
$499$	1.60375e28	0.750035	0.375018	−	0.927018i	$-0.377637\pi$
$499$	1.60375e28	0.750035	0.375018	+	0.927018i	$0.377637\pi$
$500$	1.19155e27	0.0545668
$501$	0	0
$502$	1.98922e28	0.873560
$503$	−2.67063e28	−1.14855	−0.574274	−	0.818663i	$-0.694716\pi$
$503$	−2.67063e28	−1.14855	−0.574274	+	0.818663i	$0.694716\pi$
$504$	0	0
$505$	−1.04891e28	−0.432690
$506$	6.44454e27	0.260382
$507$	0	0
$508$	−1.15335e28	−0.447089
$509$	−3.93582e27	−0.149451	−0.0747254	−	0.997204i	$-0.523808\pi$
$509$	−3.93582e27	−0.149451	−0.0747254	+	0.997204i	$0.523808\pi$
$510$	0	0
$511$	−1.72278e28	−0.627783
$512$	−9.93279e26	−0.0354598
$513$	0	0
$514$	−2.71096e28	−0.928990
$515$	−2.84186e27	−0.0954173
$516$	0	0
$517$	−9.42275e27	−0.303757
$518$	2.24459e28	0.709045
$519$	0	0
$520$	−8.91920e27	−0.270577
$521$	5.72374e28	1.70170	0.850852	−	0.525406i	$-0.176087\pi$
$521$	5.72374e28	1.70170	0.850852	+	0.525406i	$0.176087\pi$
$522$	0	0
$523$	4.82136e28	1.37690	0.688450	−	0.725284i	$-0.258292\pi$
$523$	4.82136e28	1.37690	0.688450	+	0.725284i	$0.258292\pi$
$524$	3.40503e27	0.0953108
$525$	0	0
$526$	−3.82467e28	−1.02859
$527$	−5.55253e25	−0.00146379
$528$	0	0
$529$	3.26668e28	0.827604
$530$	−1.40963e28	−0.350113
$531$	0	0
$532$	−2.02052e28	−0.482381
$533$	−1.57863e28	−0.369525
$534$	0	0
$535$	4.03747e27	0.0908646
$536$	5.86185e28	1.29361
$537$	0	0
$538$	−5.78420e28	−1.22752
$539$	7.43260e27	0.154689
$540$	0	0
$541$	3.94366e28	0.789456	0.394728	−	0.918798i	$-0.370839\pi$
$541$	3.94366e28	0.789456	0.394728	+	0.918798i	$0.370839\pi$
$542$	−6.18345e28	−1.21406
$543$	0	0
$544$	−3.56779e28	−0.673924
$545$	1.35189e28	0.250482
$546$	0	0
$547$	−2.44331e28	−0.435624	−0.217812	−	0.975991i	$-0.569892\pi$
$547$	−2.44331e28	−0.435624	−0.217812	+	0.975991i	$0.569892\pi$
$548$	3.12450e27	0.0546492
$549$	0	0
$550$	−2.28828e27	−0.0385212
$551$	6.88341e28	1.13687
$552$	0	0
$553$	−2.57394e28	−0.409247
$554$	1.14151e28	0.178086
$555$	0	0
$556$	−6.35364e28	−0.954416
$557$	1.71274e28	0.252471	0.126236	−	0.992000i	$-0.459710\pi$
$557$	1.71274e28	0.252471	0.126236	+	0.992000i	$0.459710\pi$
$558$	0	0
$559$	5.20339e28	0.738690
$560$	−4.01871e26	−0.00559902
$561$	0	0
$562$	4.50645e28	0.604789
$563$	−9.43070e28	−1.24224	−0.621120	−	0.783715i	$-0.713322\pi$
$563$	−9.43070e28	−1.24224	−0.621120	+	0.783715i	$0.713322\pi$
$564$	0	0
$565$	4.02554e28	0.510875
$566$	−3.04938e28	−0.379873
$567$	0	0
$568$	−9.73134e28	−1.16819
$569$	−6.29445e28	−0.741786	−0.370893	−	0.928676i	$-0.620948\pi$
$569$	−6.29445e28	−0.741786	−0.370893	+	0.928676i	$0.620948\pi$
$570$	0	0
$571$	−1.34257e29	−1.52495	−0.762477	−	0.647015i	$-0.776017\pi$
$571$	−1.34257e29	−1.52495	−0.762477	+	0.647015i	$0.776017\pi$
$572$	−1.01546e28	−0.113241
$573$	0	0
$574$	−2.51825e28	−0.270722
$575$	−2.56144e28	−0.270378
$576$	0	0
$577$	8.85922e28	0.901674	0.450837	−	0.892606i	$-0.351126\pi$
$577$	8.85922e28	0.901674	0.450837	+	0.892606i	$0.351126\pi$
$578$	−3.37775e28	−0.337587
$579$	0	0
$580$	−2.87360e28	−0.276970
$581$	5.07405e28	0.480292
$582$	0	0
$583$	−4.23548e28	−0.386708
$584$	−9.96902e28	−0.893959
$585$	0	0
$586$	5.70133e28	0.493232
$587$	4.65958e28	0.395956	0.197978	−	0.980206i	$-0.436563\pi$
$587$	4.65958e28	0.395956	0.197978	+	0.980206i	$0.436563\pi$
$588$	0	0
$589$	−2.94974e26	−0.00241865
$590$	−6.19560e27	−0.0499043
$591$	0	0
$592$	3.66861e27	0.0285183
$593$	−1.61981e29	−1.23705	−0.618527	−	0.785764i	$-0.712270\pi$
$593$	−1.61981e29	−1.23705	−0.618527	+	0.785764i	$0.712270\pi$
$594$	0	0
$595$	−2.90306e28	−0.214007
$596$	−1.40162e29	−1.01518
$597$	0	0
$598$	7.26496e28	0.508008
$599$	1.42044e28	0.0975979	0.0487990	−	0.998809i	$-0.484461\pi$
$599$	1.42044e28	0.0975979	0.0487990	+	0.998809i	$0.484461\pi$
$600$	0	0
$601$	1.90701e26	0.00126523	0.000632616	−	1.00000i	$-0.499799\pi$
$601$	1.90701e26	0.00126523	0.000632616		1.00000i	$0.499799\pi$
$602$	8.30051e28	0.541180
$603$	0	0
$604$	8.08098e28	0.508834
$605$	6.53925e28	0.404666
$606$	0	0
$607$	−1.39059e29	−0.831225	−0.415613	−	0.909542i	$-0.636433\pi$
$607$	−1.39059e29	−0.831225	−0.415613	+	0.909542i	$0.636433\pi$
$608$	−1.89536e29	−1.11354
$609$	0	0
$610$	−5.93642e26	−0.00336947
$611$	−1.06223e29	−0.592634
$612$	0	0
$613$	−1.30877e29	−0.705550	−0.352775	−	0.935708i	$-0.614762\pi$
$613$	−1.30877e29	−0.705550	−0.352775	+	0.935708i	$0.614762\pi$
$614$	1.78134e29	0.944015
$615$	0	0
$616$	−4.27506e28	−0.218950
$617$	2.68479e29	1.35181	0.675905	−	0.736989i	$-0.263753\pi$
$617$	2.68479e29	1.35181	0.675905	+	0.736989i	$0.263753\pi$
$618$	0	0
$619$	2.72311e29	1.32530	0.662648	−	0.748931i	$-0.269432\pi$
$619$	2.72311e29	1.32530	0.662648	+	0.748931i	$0.269432\pi$
$620$	1.23142e26	0.000589242 0
$621$	0	0
$622$	−7.68555e28	−0.355530
$623$	−1.03606e29	−0.471260
$624$	0	0
$625$	9.09495e27	0.0400000
$626$	1.56750e29	0.677918
$627$	0	0
$628$	−1.69839e29	−0.710331
$629$	2.65015e29	1.09003
$630$	0	0
$631$	3.13479e29	1.24710	0.623548	−	0.781785i	$-0.285691\pi$
$631$	3.13479e29	1.24710	0.623548	+	0.781785i	$0.285691\pi$
$632$	−1.48944e29	−0.582764
$633$	0	0
$634$	−2.67220e29	−1.01142
$635$	−8.80338e28	−0.327737
$636$	0	0
$637$	8.37881e28	0.301799
$638$	5.51850e28	0.195526
$639$	0	0
$640$	7.76809e28	0.266333
$641$	−4.55378e28	−0.153590	−0.0767949	−	0.997047i	$-0.524469\pi$
$641$	−4.55378e28	−0.153590	−0.0767949	+	0.997047i	$0.524469\pi$
$642$	0	0
$643$	−3.71338e29	−1.21214	−0.606071	−	0.795410i	$-0.707255\pi$
$643$	−3.71338e29	−1.21214	−0.606071	+	0.795410i	$0.707255\pi$
$644$	−1.81324e29	−0.582308
$645$	0	0
$646$	1.52473e29	0.473972
$647$	1.55664e29	0.476095	0.238048	−	0.971254i	$-0.423493\pi$
$647$	1.55664e29	0.476095	0.238048	+	0.971254i	$0.423493\pi$
$648$	0	0
$649$	−1.86158e28	−0.0551204
$650$	−2.57959e28	−0.0751553
$651$	0	0
$652$	−1.98792e29	−0.560790
$653$	3.07859e29	0.854601	0.427300	−	0.904110i	$-0.359465\pi$
$653$	3.07859e29	0.854601	0.427300	+	0.904110i	$0.359465\pi$
$654$	0	0
$655$	2.59901e28	0.0698673
$656$	−4.11589e27	−0.0108886
$657$	0	0
$658$	−1.69448e29	−0.434176
$659$	5.66902e29	1.42959	0.714795	−	0.699335i	$-0.246520\pi$
$659$	5.66902e29	1.42959	0.714795	+	0.699335i	$0.246520\pi$
$660$	0	0
$661$	6.30797e29	1.54090	0.770449	−	0.637501i	$-0.220032\pi$
$661$	6.30797e29	1.54090	0.770449	+	0.637501i	$0.220032\pi$
$662$	3.08847e29	0.742565
$663$	0	0
$664$	2.93615e29	0.683933
$665$	−1.54223e29	−0.353608
$666$	0	0
$667$	6.17727e29	1.37238
$668$	−3.25131e29	−0.711058
$669$	0	0
$670$	1.69535e29	0.359313
$671$	−1.78370e27	−0.00372165
$672$	0	0
$673$	−5.33313e28	−0.107851	−0.0539255	−	0.998545i	$-0.517173\pi$
$673$	−5.33313e28	−0.107851	−0.0539255	+	0.998545i	$0.517173\pi$
$674$	1.69811e29	0.338093
$675$	0	0
$676$	2.01627e29	0.389142
$677$	8.40719e29	1.59761	0.798804	−	0.601592i	$-0.205467\pi$
$677$	8.40719e29	1.59761	0.798804	+	0.601592i	$0.205467\pi$
$678$	0	0
$679$	6.29682e29	1.16008
$680$	−1.67988e29	−0.304744
$681$	0	0
$682$	−2.36484e26	−0.000415973 0
$683$	−6.27856e29	−1.08753	−0.543767	−	0.839236i	$-0.683002\pi$
$683$	−6.27856e29	−1.08753	−0.543767	+	0.839236i	$0.683002\pi$
$684$	0	0
$685$	2.38488e28	0.0400604
$686$	4.00175e29	0.661983
$687$	0	0
$688$	1.35666e28	0.0217666
$689$	−4.77468e29	−0.754470
$690$	0	0
$691$	1.00537e30	1.54101	0.770503	−	0.637436i	$-0.220005\pi$
$691$	1.00537e30	1.54101	0.770503	+	0.637436i	$0.220005\pi$
$692$	−1.99459e29	−0.301120
$693$	0	0
$694$	1.30521e29	0.191164
$695$	−4.84964e29	−0.699631
$696$	0	0
$697$	−2.97326e29	−0.416188
$698$	−3.14433e29	−0.433557
$699$	0	0
$700$	6.43830e28	0.0861474
$701$	4.71398e29	0.621368	0.310684	−	0.950513i	$-0.399442\pi$
$701$	4.71398e29	0.621368	0.310684	+	0.950513i	$0.399442\pi$
$702$	0	0
$703$	1.40787e30	1.80108
$704$	−1.56293e29	−0.196982
$705$	0	0
$706$	5.83399e29	0.713702
$707$	−5.66754e29	−0.683110
$708$	0	0
$709$	−1.53346e30	−1.79427	−0.897133	−	0.441761i	$-0.854354\pi$
$709$	−1.53346e30	−1.79427	−0.897133	+	0.441761i	$0.854354\pi$
$710$	−2.81447e29	−0.324477
$711$	0	0
$712$	−5.99527e29	−0.671071
$713$	−2.64713e27	−0.00291969
$714$	0	0
$715$	−7.75082e28	−0.0830107
$716$	7.63627e29	0.805925
$717$	0	0
$718$	−6.95259e29	−0.712591
$719$	1.32240e30	1.33571	0.667853	−	0.744294i	$-0.267214\pi$
$719$	1.32240e30	1.33571	0.667853	+	0.744294i	$0.267214\pi$
$720$	0	0
$721$	−1.53554e29	−0.150640
$722$	1.64155e29	0.158713
$723$	0	0
$724$	−1.19583e30	−1.12309
$725$	−2.19338e29	−0.203032
$726$	0	0
$727$	−8.19191e29	−0.736672	−0.368336	−	0.929693i	$-0.620072\pi$
$727$	−8.19191e29	−0.736672	−0.368336	+	0.929693i	$0.620072\pi$
$728$	−4.81930e29	−0.427174
$729$	0	0
$730$	−2.88321e29	−0.248306
$731$	9.80030e29	0.831969
$732$	0	0
$733$	−1.75132e30	−1.44469	−0.722344	−	0.691534i	$-0.756935\pi$
$733$	−1.75132e30	−1.44469	−0.722344	+	0.691534i	$0.756935\pi$
$734$	−6.19989e29	−0.504168
$735$	0	0
$736$	−1.70092e30	−1.34421
$737$	5.09397e29	0.396870
$738$	0	0
$739$	1.34607e30	1.01930	0.509649	−	0.860382i	$-0.329775\pi$
$739$	1.34607e30	1.01930	0.509649	+	0.860382i	$0.329775\pi$
$740$	−5.87742e29	−0.438787
$741$	0	0
$742$	−7.61663e29	−0.552741
$743$	−2.45921e30	−1.75960	−0.879798	−	0.475348i	$-0.842322\pi$
$743$	−2.45921e30	−1.75960	−0.879798	+	0.475348i	$0.842322\pi$
$744$	0	0
$745$	−1.06984e30	−0.744177
$746$	−5.46044e28	−0.0374515
$747$	0	0
$748$	−1.91256e29	−0.127540
$749$	2.18156e29	0.143453
$750$	0	0
$751$	−1.99438e29	−0.127523	−0.0637615	−	0.997965i	$-0.520310\pi$
$751$	−1.99438e29	−0.127523	−0.0637615	+	0.997965i	$0.520310\pi$
$752$	−2.76951e28	−0.0174629
$753$	0	0
$754$	6.22104e29	0.381473
$755$	6.16808e29	0.372999
$756$	0	0
$757$	1.74236e30	1.02478	0.512390	−	0.858753i	$-0.328760\pi$
$757$	1.74236e30	1.02478	0.512390	+	0.858753i	$0.328760\pi$
$758$	−1.36805e30	−0.793553
$759$	0	0
$760$	−8.92426e29	−0.503535
$761$	1.65011e29	0.0918279	0.0459139	−	0.998945i	$-0.485380\pi$
$761$	1.65011e29	0.0918279	0.0459139	+	0.998945i	$0.485380\pi$
$762$	0	0
$763$	7.30462e29	0.395449
$764$	−4.68049e29	−0.249926
$765$	0	0
$766$	−1.17785e30	−0.611911
$767$	−2.09857e29	−0.107540
$768$	0	0
$769$	−5.92785e29	−0.295577	−0.147789	−	0.989019i	$-0.547216\pi$
$769$	−5.92785e29	−0.295577	−0.147789	+	0.989019i	$0.547216\pi$
$770$	−1.23642e29	−0.0608154
$771$	0	0
$772$	1.00164e30	0.479437
$773$	−3.26388e30	−1.54117	−0.770583	−	0.637340i	$-0.780035\pi$
$773$	−3.26388e30	−1.54117	−0.770583	+	0.637340i	$0.780035\pi$
$774$	0	0
$775$	9.39924e26	0.000431942 0
$776$	3.64372e30	1.65195
$777$	0	0
$778$	−1.12636e30	−0.497041
$779$	−1.57952e30	−0.687675
$780$	0	0
$781$	−8.45658e29	−0.358392
$782$	1.36832e30	0.572157
$783$	0	0
$784$	2.18457e28	0.00889299
$785$	−1.29635e30	−0.520706
$786$	0	0
$787$	3.74851e30	1.46597	0.732984	−	0.680246i	$-0.238127\pi$
$787$	3.74851e30	1.46597	0.732984	+	0.680246i	$0.238127\pi$
$788$	1.54194e30	0.595033
$789$	0	0
$790$	−4.30771e29	−0.161868
$791$	2.17511e30	0.806545
$792$	0	0
$793$	−2.01078e28	−0.00726098
$794$	−3.34926e30	−1.19353
$795$	0	0
$796$	5.44183e29	0.188868
$797$	7.49034e29	0.256560	0.128280	−	0.991738i	$-0.459054\pi$
$797$	7.49034e29	0.256560	0.128280	+	0.991738i	$0.459054\pi$
$798$	0	0
$799$	−2.00065e30	−0.667469
$800$	6.03951e29	0.198864
$801$	0	0
$802$	−5.49069e29	−0.176115
$803$	−8.66312e29	−0.274259
$804$	0	0
$805$	−1.38402e30	−0.426859
$806$	−2.66589e27	−0.000811567 0
$807$	0	0
$808$	−3.27958e30	−0.972745
$809$	4.28318e30	1.25403	0.627013	−	0.779008i	$-0.284277\pi$
$809$	4.28318e30	1.25403	0.627013	+	0.779008i	$0.284277\pi$
$810$	0	0
$811$	5.96489e30	1.70170	0.850851	−	0.525407i	$-0.176087\pi$
$811$	5.96489e30	1.70170	0.850851	+	0.525407i	$0.176087\pi$
$812$	−1.55269e30	−0.437266
$813$	0	0
$814$	1.12871e30	0.309760
$815$	−1.51735e30	−0.411085
$816$	0	0
$817$	5.20634e30	1.37468
$818$	−4.36630e30	−1.13816
$819$	0	0
$820$	6.59400e29	0.167534
$821$	7.09264e30	1.77912	0.889559	−	0.456820i	$-0.151012\pi$
$821$	7.09264e30	1.77912	0.889559	+	0.456820i	$0.151012\pi$
$822$	0	0
$823$	−2.35723e30	−0.576374	−0.288187	−	0.957574i	$-0.593052\pi$
$823$	−2.35723e30	−0.576374	−0.288187	+	0.957574i	$0.593052\pi$
$824$	−8.88555e29	−0.214510
$825$	0	0
$826$	−3.34766e29	−0.0787864
$827$	−7.09467e30	−1.64863	−0.824317	−	0.566129i	$-0.808440\pi$
$827$	−7.09467e30	−1.64863	−0.824317	+	0.566129i	$0.808440\pi$
$828$	0	0
$829$	−3.28171e30	−0.743494	−0.371747	−	0.928334i	$-0.621241\pi$
$829$	−3.28171e30	−0.743494	−0.371747	+	0.928334i	$0.621241\pi$
$830$	8.49185e29	0.189969
$831$	0	0
$832$	−1.76190e30	−0.384314
$833$	1.57810e30	0.339909
$834$	0	0
$835$	−2.48167e30	−0.521239
$836$	−1.01603e30	−0.210737
$837$	0	0
$838$	−8.51236e29	−0.172182
$839$	−2.41416e30	−0.482242	−0.241121	−	0.970495i	$-0.577515\pi$
$839$	−2.41416e30	−0.482242	−0.241121	+	0.970495i	$0.577515\pi$
$840$	0	0
$841$	1.56797e29	0.0305477
$842$	5.17355e30	0.995433
$843$	0	0
$844$	5.20826e30	0.977456
$845$	1.53899e30	0.285259
$846$	0	0
$847$	3.53334e30	0.638867
$848$	−1.24488e29	−0.0222316
$849$	0	0
$850$	−4.85851e29	−0.0846456
$851$	1.26344e31	2.17418
$852$	0	0
$853$	5.84642e30	0.981580	0.490790	−	0.871278i	$-0.336708\pi$
$853$	5.84642e30	0.981580	0.490790	+	0.871278i	$0.336708\pi$
$854$	−3.20762e28	−0.00531955
$855$	0	0
$856$	1.26238e30	0.204276
$857$	8.39671e30	1.34218	0.671090	−	0.741376i	$-0.265827\pi$
$857$	8.39671e30	1.34218	0.671090	+	0.741376i	$0.265827\pi$
$858$	0	0
$859$	−9.63711e30	−1.50321	−0.751603	−	0.659616i	$-0.770719\pi$
$859$	−9.63711e30	−1.50321	−0.751603	+	0.659616i	$0.770719\pi$
$860$	−2.17348e30	−0.334905
$861$	0	0
$862$	5.47088e30	0.822680
$863$	−9.02677e30	−1.34097	−0.670485	−	0.741923i	$-0.733914\pi$
$863$	−9.02677e30	−1.34097	−0.670485	+	0.741923i	$0.733914\pi$
$864$	0	0
$865$	−1.52244e30	−0.220735
$866$	1.48111e30	0.212153
$867$	0	0
$868$	6.65371e27	0.000930266 0
$869$	−1.29433e30	−0.178787
$870$	0	0
$871$	5.74246e30	0.774297
$872$	4.22689e30	0.563116
$873$	0	0
$874$	7.26908e30	0.945386
$875$	4.91426e29	0.0631500
$876$	0	0
$877$	−1.09983e31	−1.37985	−0.689925	−	0.723881i	$-0.742356\pi$
$877$	−1.09983e31	−1.37985	−0.689925	+	0.723881i	$0.742356\pi$
$878$	−1.01036e29	−0.0125252
$879$	0	0
$880$	−2.02084e28	−0.00244604
$881$	4.12022e30	0.492803	0.246401	−	0.969168i	$-0.420752\pi$
$881$	4.12022e30	0.492803	0.246401	+	0.969168i	$0.420752\pi$
$882$	0	0
$883$	−2.19772e30	−0.256676	−0.128338	−	0.991730i	$-0.540964\pi$
$883$	−2.19772e30	−0.256676	−0.128338	+	0.991730i	$0.540964\pi$
$884$	−2.15603e30	−0.248832
$885$	0	0
$886$	7.80144e30	0.879267
$887$	4.93141e30	0.549253	0.274627	−	0.961551i	$-0.411446\pi$
$887$	4.93141e30	0.549253	0.274627	+	0.961551i	$0.411446\pi$
$888$	0	0
$889$	−4.75671e30	−0.517415
$890$	−1.73393e30	−0.186396
$891$	0	0
$892$	7.26689e30	0.762988
$893$	−1.06283e31	−1.10287
$894$	0	0
$895$	5.82865e30	0.590780
$896$	4.19732e30	0.420473
$897$	0	0
$898$	6.60156e30	0.646019
$899$	−2.26676e28	−0.00219245
$900$	0	0
$901$	−8.99285e30	−0.849742
$902$	−1.26632e30	−0.118270
$903$	0	0
$904$	1.25865e31	1.14851
$905$	−9.12762e30	−0.823279
$906$	0	0
$907$	−5.86988e29	−0.0517313	−0.0258656	−	0.999665i	$-0.508234\pi$
$907$	−5.86988e29	−0.0517313	−0.0258656	+	0.999665i	$0.508234\pi$
$908$	−3.86249e30	−0.336485
$909$	0	0
$910$	−1.39382e30	−0.118651
$911$	−1.68034e31	−1.41402	−0.707009	−	0.707205i	$-0.749956\pi$
$911$	−1.68034e31	−1.41402	−0.707009	+	0.707205i	$0.749956\pi$
$912$	0	0
$913$	2.55153e30	0.209825
$914$	−1.57192e30	−0.127790
$915$	0	0
$916$	7.28678e30	0.578940
$917$	1.40432e30	0.110303
$918$	0	0
$919$	6.44289e30	0.494616	0.247308	−	0.968937i	$-0.420454\pi$
$919$	6.44289e30	0.494616	0.247308	+	0.968937i	$0.420454\pi$
$920$	−8.00875e30	−0.607845
$921$	0	0
$922$	1.37061e30	0.101681
$923$	−9.53314e30	−0.699227
$924$	0	0
$925$	−4.48614e30	−0.321651
$926$	2.20814e30	0.156535
$927$	0	0
$928$	−1.45651e31	−1.00939
$929$	2.72877e31	1.86983	0.934915	−	0.354871i	$-0.115475\pi$
$929$	2.72877e31	1.86983	0.934915	+	0.354871i	$0.115475\pi$
$930$	0	0
$931$	8.38357e30	0.561639
$932$	5.28546e30	0.350119
$933$	0	0
$934$	−2.13585e30	−0.138334
$935$	−1.45983e30	−0.0934930
$936$	0	0
$937$	−9.61874e30	−0.602355	−0.301177	−	0.953568i	$-0.597380\pi$
$937$	−9.61874e30	−0.602355	−0.301177	+	0.953568i	$0.597380\pi$
$938$	9.16045e30	0.567266
$939$	0	0
$940$	4.43698e30	0.268686
$941$	−2.69319e30	−0.161278	−0.0806392	−	0.996743i	$-0.525696\pi$
$941$	−2.69319e30	−0.161278	−0.0806392	+	0.996743i	$0.525696\pi$
$942$	0	0
$943$	−1.41749e31	−0.830130
$944$	−5.47150e28	−0.00316884
$945$	0	0
$946$	4.17398e30	0.236425
$947$	1.36082e31	0.762299	0.381149	−	0.924513i	$-0.375528\pi$
$947$	1.36082e31	0.762299	0.381149	+	0.924513i	$0.375528\pi$
$948$	0	0
$949$	−9.76598e30	−0.535082
$950$	−2.58105e30	−0.139862
$951$	0	0
$952$	−9.07689e30	−0.481115
$953$	−2.51424e31	−1.31805	−0.659025	−	0.752121i	$-0.729031\pi$
$953$	−2.51424e31	−1.31805	−0.659025	+	0.752121i	$0.729031\pi$
$954$	0	0
$955$	−3.57254e30	−0.183207
$956$	1.69771e29	0.00861102
$957$	0	0
$958$	−6.59723e30	−0.327359
$959$	1.28862e30	0.0632454
$960$	0	0
$961$	−2.08254e31	−0.999995
$962$	1.27240e31	0.604344
$963$	0	0
$964$	1.51996e31	0.706353
$965$	7.64540e30	0.351450
$966$	0	0
$967$	−2.28373e31	−1.02723	−0.513615	−	0.858021i	$-0.671694\pi$
$967$	−2.28373e31	−1.02723	−0.513615	+	0.858021i	$0.671694\pi$
$968$	2.04461e31	0.909742
$969$	0	0
$970$	1.05383e31	0.458844
$971$	−9.39665e30	−0.404735	−0.202368	−	0.979310i	$-0.564864\pi$
$971$	−9.39665e30	−0.404735	−0.202368	+	0.979310i	$0.564864\pi$
$972$	0	0
$973$	−2.62040e31	−1.10454
$974$	2.53765e31	1.05819
$975$	0	0
$976$	−5.24261e27	−0.000213956 0
$977$	−1.88387e31	−0.760601	−0.380300	−	0.924863i	$-0.624179\pi$
$977$	−1.88387e31	−0.760601	−0.380300	+	0.924863i	$0.624179\pi$
$978$	0	0
$979$	−5.20991e30	−0.205879
$980$	−3.49987e30	−0.136829
$981$	0	0
$982$	−2.83380e29	−0.0108442
$983$	−3.20724e31	−1.21428	−0.607142	−	0.794593i	$-0.707684\pi$
$983$	−3.20724e31	−1.21428	−0.607142	+	0.794593i	$0.707684\pi$
$984$	0	0
$985$	1.17694e31	0.436187
$986$	1.17170e31	0.429644
$987$	0	0
$988$	−1.14538e31	−0.411151
$989$	4.67224e31	1.65945
$990$	0	0
$991$	4.08742e31	1.42127	0.710635	−	0.703561i	$-0.248408\pi$
$991$	4.08742e31	1.42127	0.710635	+	0.703561i	$0.248408\pi$
$992$	6.24158e28	0.00214744
$993$	0	0
$994$	−1.52074e31	−0.512268
$995$	4.15367e30	0.138449
$996$	0	0
$997$	−2.22134e31	−0.724963	−0.362481	−	0.931991i	$-0.618070\pi$
$997$	−2.22134e31	−0.724963	−0.362481	+	0.931991i	$0.618070\pi$
$998$	1.45025e31	0.468352
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	45.22.a.e.1.2		3
3.2	odd	2		15.22.a.b.1.2	✓	3
15.2	even	4		75.22.b.g.49.3		6
15.8	even	4		75.22.b.g.49.4		6
15.14	odd	2		75.22.a.g.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.22.a.b.1.2	✓	3	3.2	odd	2
45.22.a.e.1.2		3	1.1	even	1	trivial
75.22.a.g.1.2		3	15.14	odd	2
75.22.b.g.49.3		6	15.2	even	4
75.22.b.g.49.4		6	15.8	even	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 45 = 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 22 \)
Character orbit:	\([\chi]\)	\(=\)	45.a (trivial)

\(f(q)\)	\(=\)	\(q+904.285 q^{2} -1.27942e6 q^{4} -9.76562e6 q^{5} -5.27665e8 q^{7} -3.05338e9 q^{8} +O(q^{10})\)	\(q+904.285 q^{2} -1.27942e6 q^{4} -9.76562e6 q^{5} -5.27665e8 q^{7} -3.05338e9 q^{8} -8.83091e9 q^{10} -2.65340e10 q^{11} -2.99119e11 q^{13} -4.77159e11 q^{14} -7.79881e10 q^{16} -5.63375e12 q^{17} -2.99289e13 q^{19} +1.24943e13 q^{20} -2.39943e13 q^{22} -2.68586e14 q^{23} +9.53674e13 q^{25} -2.70489e14 q^{26} +6.75105e14 q^{28} -2.29992e15 q^{29} +9.85582e12 q^{31} +6.33289e15 q^{32} -5.09452e15 q^{34} +5.15297e15 q^{35} -4.70406e16 q^{37} -2.70643e16 q^{38} +2.98182e16 q^{40} +5.27759e16 q^{41} -1.73957e17 q^{43} +3.39482e16 q^{44} -2.42878e17 q^{46} +3.55119e17 q^{47} -2.80116e17 q^{49} +8.62393e16 q^{50} +3.82700e17 q^{52} +1.59624e18 q^{53} +2.59121e17 q^{55} +1.61116e18 q^{56} -2.07978e18 q^{58} +7.01582e17 q^{59} +6.72232e16 q^{61} +8.91247e15 q^{62} +5.89029e18 q^{64} +2.92109e18 q^{65} -1.91979e19 q^{67} +7.20794e18 q^{68} +4.65976e18 q^{70} +3.18707e19 q^{71} +3.26491e19 q^{73} -4.25381e19 q^{74} +3.82917e19 q^{76} +1.40011e19 q^{77} +4.87799e19 q^{79} +7.61602e17 q^{80} +4.77244e19 q^{82} -9.61606e19 q^{83} +5.50171e19 q^{85} -1.57307e20 q^{86} +8.10186e19 q^{88} +1.96348e20 q^{89} +1.57835e20 q^{91} +3.43634e20 q^{92} +3.21129e20 q^{94} +2.92274e20 q^{95} -1.19334e21 q^{97} -2.53305e20 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 2300 q^{2} + 1264400 q^{4} - 29296875 q^{5} + 465666872 q^{7} + 3839876544 q^{8}+O(q^{10}) \) 3 * q + 2300 * q^2 + 1264400 * q^4 - 29296875 * q^5 + 465666872 * q^7 + 3839876544 * q^8	\( 3 q + 2300 q^{2} + 1264400 q^{4} - 29296875 q^{5} + 465666872 q^{7} + 3839876544 q^{8} - 22460937500 q^{10} + 167336332556 q^{11} - 545571033878 q^{13} + 1568858902656 q^{14} + 255267954944 q^{16} + 8104424487194 q^{17} + 3937700740828 q^{19} - 12347656250000 q^{20} + 114198109969712 q^{22} + 156235274730744 q^{23} + 286102294921875 q^{25} - 29\!\cdots\!56 q^{26}+ \cdots + 87\!\cdots\!32 q^{98}+O(q^{100}) \) 3 * q + 2300 * q^2 + 1264400 * q^4 - 29296875 * q^5 + 465666872 * q^7 + 3839876544 * q^8 - 22460937500 * q^10 + 167336332556 * q^11 - 545571033878 * q^13 + 1568858902656 * q^14 + 255267954944 * q^16 + 8104424487194 * q^17 + 3937700740828 * q^19 - 12347656250000 * q^20 + 114198109969712 * q^22 + 156235274730744 * q^23 + 286102294921875 * q^25 - 2972936042645656 * q^26 + 3826676848454144 * q^28 + 930273612785494 * q^29 - 6257709152718928 * q^31 - 4297283007276032 * q^32 - 20587982883981400 * q^34 - 4547528046875000 * q^35 - 22246337613227118 * q^37 + 82202958592557968 * q^38 - 37498794375000000 * q^40 + 186265908060974338 * q^41 - 268609288174096316 * q^43 + 284579440966881088 * q^44 + 375824751838355712 * q^46 + 900034127817222032 * q^47 - 586354193149814837 * q^49 + 219345092773437500 * q^50 - 3462564631549962144 * q^52 + 1269623243180583374 * q^53 - 1634143872617187500 * q^55 + 5236064873787955200 * q^56 - 1091617398834773576 * q^58 + 8551487099411338268 * q^59 - 7181148471323735222 * q^61 + 3050004306382316256 * q^62 - 557099647389855744 * q^64 + 5327842127714843750 * q^65 + 2946635148405656396 * q^67 - 10323921738190858400 * q^68 - 15320887721250000000 * q^70 + 37849731561832987624 * q^71 - 7149058835824826594 * q^73 - 50872537645745842424 * q^74 + 200886445168773700032 * q^76 + 110970090560628236256 * q^77 + 309682369826312504000 * q^79 - 2492851122500000000 * q^80 + 265773545783653420264 * q^82 - 199780825758268631580 * q^83 - 79144770382753906250 * q^85 - 267144820042737104944 * q^86 + 749649166937994283776 * q^88 - 162380735751340085838 * q^89 - 558457704043459369328 * q^91 + 1333721831719821170688 * q^92 - 149583353667227862112 * q^94 - 38454108797148437500 * q^95 - 1208943423358924299354 * q^97 + 876777377902285855132 * q^98

Introduction

L-functions

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Varieties

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Database

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