LMFDB - Embedded newform 207.8.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [207,8,Mod(1,207)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(207, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("207.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 207 = 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	207.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:	$64.6637002752$
Analytic rank:	$0$
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} - 466x^{4} + 540x^{3} + 48973x^{2} - 77282x - 1061812 $ x^6 - 2x^5 - 466x^4 + 540x^3 + 48973x^2 - 77282*x - 1061812
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{5}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 69)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-17.1241$ of defining polynomial
Character	$\chi$	$=$	207.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-16.1241 q^{2} +131.987 q^{4} +519.327 q^{5} -439.281 q^{7} -64.2798 q^{8} +O(q^{10})$	\(q-16.1241 q^{2} +131.987 q^{4} +519.327 q^{5} -439.281 q^{7} -64.2798 q^{8} -8373.68 q^{10} +1239.00 q^{11} -886.064 q^{13} +7083.01 q^{14} -15857.8 q^{16} +33265.6 q^{17} +24223.0 q^{19} +68544.2 q^{20} -19977.7 q^{22} +12167.0 q^{23} +191576. q^{25} +14287.0 q^{26} -57979.2 q^{28} +26376.0 q^{29} +58381.7 q^{31} +263921. q^{32} -536379. q^{34} -228131. q^{35} +72694.7 q^{37} -390574. q^{38} -33382.2 q^{40} -175132. q^{41} -302259. q^{43} +163531. q^{44} -196182. q^{46} -715309. q^{47} -630575. q^{49} -3.08899e6 q^{50} -116948. q^{52} +1.15458e6 q^{53} +643444. q^{55} +28236.9 q^{56} -425289. q^{58} +1.13651e6 q^{59} +699341. q^{61} -941353. q^{62} -2.22569e6 q^{64} -460157. q^{65} -4.85518e6 q^{67} +4.39062e6 q^{68} +3.67840e6 q^{70} -369628. q^{71} +1.06243e6 q^{73} -1.17214e6 q^{74} +3.19711e6 q^{76} -544267. q^{77} +6.34807e6 q^{79} -8.23540e6 q^{80} +2.82384e6 q^{82} -9.31819e6 q^{83} +1.72758e7 q^{85} +4.87366e6 q^{86} -79642.3 q^{88} +1.25442e7 q^{89} +389231. q^{91} +1.60588e6 q^{92} +1.15337e7 q^{94} +1.25797e7 q^{95} -1.21853e7 q^{97} +1.01675e7 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 8 q^{2} + 178 q^{4} + 372 q^{5} - 1104 q^{7} + 1956 q^{8}+O(q^{10}) $ 6 * q + 8 * q^2 + 178 * q^4 + 372 * q^5 - 1104 * q^7 + 1956 * q^8	\( 6 q + 8 q^{2} + 178 q^{4} + 372 q^{5} - 1104 q^{7} + 1956 q^{8} - 13042 q^{10} + 14824 q^{11} - 756 q^{13} + 3926 q^{14} - 13022 q^{16} + 69484 q^{17} - 43864 q^{19} - 78886 q^{20} + 98204 q^{22} + 73002 q^{23} + 228018 q^{25} + 311956 q^{26} - 545442 q^{28} + 311100 q^{29} - 245248 q^{31} + 390156 q^{32} + 235834 q^{34} + 1331256 q^{35} - 630044 q^{37} - 80910 q^{38} - 2153982 q^{40} + 969204 q^{41} - 1770208 q^{43} + 1749140 q^{44} + 97336 q^{46} + 1400024 q^{47} + 1985598 q^{49} + 956660 q^{50} + 3217272 q^{52} + 1573516 q^{53} - 431296 q^{55} - 7740702 q^{56} + 5987188 q^{58} + 1410320 q^{59} - 942172 q^{61} - 3334412 q^{62} + 1996866 q^{64} + 420944 q^{65} - 452072 q^{67} + 9258254 q^{68} + 21981136 q^{70} - 122928 q^{71} + 16490716 q^{73} + 600104 q^{74} + 7428658 q^{76} - 7239696 q^{77} + 2458408 q^{79} - 19440230 q^{80} + 20510784 q^{82} + 7566456 q^{83} + 5817744 q^{85} + 669666 q^{86} + 14775668 q^{88} + 20368036 q^{89} + 8815576 q^{91} + 2165726 q^{92} + 16952576 q^{94} - 5143832 q^{95} + 12586972 q^{97} + 39164812 q^{98}+O(q^{100}) \) 6 * q + 8 * q^2 + 178 * q^4 + 372 * q^5 - 1104 * q^7 + 1956 * q^8 - 13042 * q^10 + 14824 * q^11 - 756 * q^13 + 3926 * q^14 - 13022 * q^16 + 69484 * q^17 - 43864 * q^19 - 78886 * q^20 + 98204 * q^22 + 73002 * q^23 + 228018 * q^25 + 311956 * q^26 - 545442 * q^28 + 311100 * q^29 - 245248 * q^31 + 390156 * q^32 + 235834 * q^34 + 1331256 * q^35 - 630044 * q^37 - 80910 * q^38 - 2153982 * q^40 + 969204 * q^41 - 1770208 * q^43 + 1749140 * q^44 + 97336 * q^46 + 1400024 * q^47 + 1985598 * q^49 + 956660 * q^50 + 3217272 * q^52 + 1573516 * q^53 - 431296 * q^55 - 7740702 * q^56 + 5987188 * q^58 + 1410320 * q^59 - 942172 * q^61 - 3334412 * q^62 + 1996866 * q^64 + 420944 * q^65 - 452072 * q^67 + 9258254 * q^68 + 21981136 * q^70 - 122928 * q^71 + 16490716 * q^73 + 600104 * q^74 + 7428658 * q^76 - 7239696 * q^77 + 2458408 * q^79 - 19440230 * q^80 + 20510784 * q^82 + 7566456 * q^83 + 5817744 * q^85 + 669666 * q^86 + 14775668 * q^88 + 20368036 * q^89 + 8815576 * q^91 + 2165726 * q^92 + 16952576 * q^94 - 5143832 * q^95 + 12586972 * q^97 + 39164812 * 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 $

$2$	−16.1241	−1.42518	−0.712591	−	0.701579i	$-0.752479\pi$
$2$	−16.1241	−1.42518	−0.712591	+	0.701579i	$0.752479\pi$
$3$	0	0
$3$	0	0
$4$	131.987	1.03115
$5$	519.327	1.85800	0.929001	−	0.370078i	$-0.120669\pi$
$5$	519.327	1.85800	0.929001	+	0.370078i	$0.120669\pi$
$6$	0	0
$7$	−439.281	−0.484060	−0.242030	−	0.970269i	$-0.577813\pi$
$7$	−439.281	−0.484060	−0.242030	+	0.970269i	$0.577813\pi$
$8$	−64.2798	−0.0443874
$9$	0	0
$10$	−8373.68	−2.64799
$11$	1239.00	0.280670	0.140335	−	0.990104i	$-0.455182\pi$
$11$	1239.00	0.280670	0.140335	+	0.990104i	$0.455182\pi$
$12$	0	0
$13$	−886.064	−0.111857	−0.0559285	−	0.998435i	$-0.517812\pi$
$13$	−886.064	−0.111857	−0.0559285	+	0.998435i	$0.517812\pi$
$14$	7083.01	0.689874
$15$	0	0
$16$	−15857.8	−0.967885
$17$	33265.6	1.64219	0.821097	−	0.570788i	$-0.193362\pi$
$17$	33265.6	1.64219	0.821097	+	0.570788i	$0.193362\pi$
$18$	0	0
$19$	24223.0	0.810197	0.405099	−	0.914273i	$-0.367237\pi$
$19$	24223.0	0.810197	0.405099	+	0.914273i	$0.367237\pi$
$20$	68544.2	1.91587
$21$	0	0
$22$	−19977.7	−0.400005
$23$	12167.0	0.208514
$23$	12167.0	0.208514
$24$	0	0
$25$	191576.	2.45217
$26$	14287.0	0.159417
$27$	0	0
$28$	−57979.2	−0.499136
$29$	26376.0	0.200824	0.100412	−	0.994946i	$-0.467984\pi$
$29$	26376.0	0.200824	0.100412	+	0.994946i	$0.467984\pi$
$30$	0	0
$31$	58381.7	0.351974	0.175987	−	0.984392i	$-0.443688\pi$
$31$	58381.7	0.351974	0.175987	+	0.984392i	$0.443688\pi$
$32$	263921.	1.42380
$33$	0	0
$34$	−536379.	−2.34043
$35$	−228131.	−0.899385
$36$	0	0
$37$	72694.7	0.235937	0.117969	−	0.993017i	$-0.462362\pi$
$37$	72694.7	0.235937	0.117969	+	0.993017i	$0.462362\pi$
$38$	−390574.	−1.15468
$39$	0	0
$40$	−33382.2	−0.0824718
$41$	−175132.	−0.396846	−0.198423	−	0.980117i	$-0.563582\pi$
$41$	−175132.	−0.396846	−0.198423	+	0.980117i	$0.563582\pi$
$42$	0	0
$43$	−302259.	−0.579749	−0.289875	−	0.957065i	$-0.593614\pi$
$43$	−302259.	−0.579749	−0.289875	+	0.957065i	$0.593614\pi$
$44$	163531.	0.289411
$45$	0	0
$46$	−196182.	−0.297171
$47$	−715309.	−1.00497	−0.502483	−	0.864587i	$-0.667580\pi$
$47$	−715309.	−1.00497	−0.502483	+	0.864587i	$0.667580\pi$
$48$	0	0
$49$	−630575.	−0.765686
$50$	−3.08899e6	−3.49479
$51$	0	0
$52$	−116948.	−0.115341
$53$	1.15458e6	1.06526	0.532632	−	0.846347i	$-0.321203\pi$
$53$	1.15458e6	1.06526	0.532632	+	0.846347i	$0.321203\pi$
$54$	0	0
$55$	643444.	0.521484
$56$	28236.9	0.0214862
$57$	0	0
$58$	−425289.	−0.286211
$59$	1.13651e6	0.720429	0.360215	−	0.932869i	$-0.382703\pi$
$59$	1.13651e6	0.720429	0.360215	+	0.932869i	$0.382703\pi$
$60$	0	0
$61$	699341.	0.394489	0.197244	−	0.980354i	$-0.436801\pi$
$61$	699341.	0.394489	0.197244	+	0.980354i	$0.436801\pi$
$62$	−941353.	−0.501628
$63$	0	0
$64$	−2.22569e6	−1.06129
$65$	−460157.	−0.207830
$66$	0	0
$67$	−4.85518e6	−1.97217	−0.986083	−	0.166252i	$-0.946833\pi$
$67$	−4.85518e6	−1.97217	−0.986083	+	0.166252i	$0.946833\pi$
$68$	4.39062e6	1.69334
$69$	0	0
$70$	3.67840e6	1.28179
$71$	−369628.	−0.122563	−0.0612817	−	0.998121i	$-0.519519\pi$
$71$	−369628.	−0.122563	−0.0612817	+	0.998121i	$0.519519\pi$
$72$	0	0
$73$	1.06243e6	0.319646	0.159823	−	0.987146i	$-0.448908\pi$
$73$	1.06243e6	0.319646	0.159823	+	0.987146i	$0.448908\pi$
$74$	−1.17214e6	−0.336254
$75$	0	0
$76$	3.19711e6	0.835431
$77$	−544267.	−0.135861
$78$	0	0
$79$	6.34807e6	1.44860	0.724298	−	0.689487i	$-0.242164\pi$
$79$	6.34807e6	1.44860	0.724298	+	0.689487i	$0.242164\pi$
$80$	−8.23540e6	−1.79833
$81$	0	0
$82$	2.82384e6	0.565577
$83$	−9.31819e6	−1.78879	−0.894393	−	0.447282i	$-0.852392\pi$
$83$	−9.31819e6	−1.78879	−0.894393	+	0.447282i	$0.852392\pi$
$84$	0	0
$85$	1.72758e7	3.05120
$86$	4.87366e6	0.826249
$87$	0	0
$88$	−79642.3	−0.0124582
$89$	1.25442e7	1.88615	0.943077	−	0.332573i	$-0.107917\pi$
$89$	1.25442e7	1.88615	0.943077	+	0.332573i	$0.107917\pi$
$90$	0	0
$91$	389231.	0.0541455
$92$	1.60588e6	0.215009
$93$	0	0
$94$	1.15337e7	1.43226
$95$	1.25797e7	1.50535
$96$	0	0
$97$	−1.21853e7	−1.35562	−0.677808	−	0.735239i	$-0.737070\pi$
$97$	−1.21853e7	−1.35562	−0.677808	+	0.735239i	$0.737070\pi$
$98$	1.01675e7	1.09124
$99$	0	0
$100$	2.52854e7	2.52854
$101$	−4.72794e6	−0.456612	−0.228306	−	0.973589i	$-0.573319\pi$
$101$	−4.72794e6	−0.456612	−0.228306	+	0.973589i	$0.573319\pi$
$102$	0	0
$103$	1.88105e7	1.69617	0.848086	−	0.529859i	$-0.177755\pi$
$103$	1.88105e7	1.69617	0.848086	+	0.529859i	$0.177755\pi$
$104$	56956.0	0.00496504
$105$	0	0
$106$	−1.86165e7	−1.51820
$107$	−6.37897e6	−0.503393	−0.251697	−	0.967806i	$-0.580989\pi$
$107$	−6.37897e6	−0.503393	−0.251697	+	0.967806i	$0.580989\pi$
$108$	0	0
$109$	−2.00961e7	−1.48634	−0.743172	−	0.669101i	$-0.766679\pi$
$109$	−2.00961e7	−1.48634	−0.743172	+	0.669101i	$0.766679\pi$
$110$	−1.03750e7	−0.743210
$111$	0	0
$112$	6.96604e6	0.468515
$113$	2.60610e7	1.69909	0.849545	−	0.527516i	$-0.176877\pi$
$113$	2.60610e7	1.69909	0.849545	+	0.527516i	$0.176877\pi$
$114$	0	0
$115$	6.31865e6	0.387420
$116$	3.48127e6	0.207079
$117$	0	0
$118$	−1.83252e7	−1.02674
$119$	−1.46130e7	−0.794921
$120$	0	0
$121$	−1.79521e7	−0.921225
$122$	−1.12763e7	−0.562219
$123$	0	0
$124$	7.70561e6	0.362937
$125$	5.89180e7	2.69813
$126$	0	0
$127$	2.50989e7	1.08728	0.543640	−	0.839319i	$-0.317046\pi$
$127$	2.50989e7	1.08728	0.543640	+	0.839319i	$0.317046\pi$
$128$	2.10530e6	0.0887317
$129$	0	0
$130$	7.41961e6	0.296196
$131$	3.64373e7	1.41611	0.708055	−	0.706157i	$-0.249573\pi$
$131$	3.64373e7	1.41611	0.708055	+	0.706157i	$0.249573\pi$
$132$	0	0
$133$	−1.06407e7	−0.392184
$134$	7.82854e7	2.81070
$135$	0	0
$136$	−2.13831e6	−0.0728927
$137$	1.69030e7	0.561620	0.280810	−	0.959763i	$-0.409397\pi$
$137$	1.69030e7	0.561620	0.280810	+	0.959763i	$0.409397\pi$
$138$	0	0
$139$	−8.54424e6	−0.269849	−0.134925	−	0.990856i	$-0.543079\pi$
$139$	−8.54424e6	−0.269849	−0.134925	+	0.990856i	$0.543079\pi$
$140$	−3.01102e7	−0.927396
$141$	0	0
$142$	5.95992e6	0.174675
$143$	−1.09783e6	−0.0313948
$144$	0	0
$145$	1.36978e7	0.373131
$146$	−1.71307e7	−0.455554
$147$	0	0
$148$	9.59473e6	0.243286
$149$	3.88029e7	0.960975	0.480487	−	0.877002i	$-0.340460\pi$
$149$	3.88029e7	0.960975	0.480487	+	0.877002i	$0.340460\pi$
$150$	0	0
$151$	−6.01649e7	−1.42208	−0.711040	−	0.703152i	$-0.751775\pi$
$151$	−6.01649e7	−1.42208	−0.711040	+	0.703152i	$0.751775\pi$
$152$	−1.55705e6	−0.0359625
$153$	0	0
$154$	8.77582e6	0.193627
$155$	3.03192e7	0.653969
$156$	0	0
$157$	5.28204e7	1.08931	0.544657	−	0.838659i	$-0.316660\pi$
$157$	5.28204e7	1.08931	0.544657	+	0.838659i	$0.316660\pi$
$158$	−1.02357e8	−2.06451
$159$	0	0
$160$	1.37061e8	2.64542
$161$	−5.34473e6	−0.100934
$162$	0	0
$163$	7.62576e7	1.37920	0.689599	−	0.724192i	$-0.257787\pi$
$163$	7.62576e7	1.37920	0.689599	+	0.724192i	$0.257787\pi$
$164$	−2.31150e7	−0.409205
$165$	0	0
$166$	1.50247e8	2.54935
$167$	3.06894e7	0.509895	0.254947	−	0.966955i	$-0.417942\pi$
$167$	3.06894e7	0.509895	0.254947	+	0.966955i	$0.417942\pi$
$168$	0	0
$169$	−6.19634e7	−0.987488
$170$	−2.78556e8	−4.34852
$171$	0	0
$172$	−3.98942e7	−0.597806
$173$	−9.31796e6	−0.136823	−0.0684116	−	0.997657i	$-0.521793\pi$
$173$	−9.31796e6	−0.136823	−0.0684116	+	0.997657i	$0.521793\pi$
$174$	0	0
$175$	−8.41556e7	−1.18700
$176$	−1.96478e7	−0.271656
$177$	0	0
$178$	−2.02264e8	−2.68811
$179$	−5.74511e7	−0.748708	−0.374354	−	0.927286i	$-0.622135\pi$
$179$	−5.74511e7	−0.748708	−0.374354	+	0.927286i	$0.622135\pi$
$180$	0	0
$181$	−8.31396e7	−1.04216	−0.521078	−	0.853509i	$-0.674470\pi$
$181$	−8.31396e7	−1.04216	−0.521078	+	0.853509i	$0.674470\pi$
$182$	−6.27600e6	−0.0771672
$183$	0	0
$184$	−782092.	−0.00925541
$185$	3.77524e7	0.438372
$186$	0	0
$187$	4.12160e7	0.460914
$188$	−9.44112e7	−1.03627
$189$	0	0
$190$	−2.02836e8	−2.14539
$191$	−1.24826e7	−0.129625	−0.0648124	−	0.997897i	$-0.520645\pi$
$191$	−1.24826e7	−0.129625	−0.0648124	+	0.997897i	$0.520645\pi$
$192$	0	0
$193$	1.10312e8	1.10452	0.552259	−	0.833672i	$-0.313766\pi$
$193$	1.10312e8	1.10452	0.552259	+	0.833672i	$0.313766\pi$
$194$	1.96478e8	1.93200
$195$	0	0
$196$	−8.32274e7	−0.789533
$197$	−7.99268e7	−0.744836	−0.372418	−	0.928065i	$-0.621471\pi$
$197$	−7.99268e7	−0.744836	−0.372418	+	0.928065i	$0.621471\pi$
$198$	0	0
$199$	8.75763e7	0.787773	0.393886	−	0.919159i	$-0.371130\pi$
$199$	8.75763e7	0.787773	0.393886	+	0.919159i	$0.371130\pi$
$200$	−1.23144e7	−0.108845
$201$	0	0
$202$	7.62338e7	0.650756
$203$	−1.15865e7	−0.0972109
$204$	0	0
$205$	−9.09507e7	−0.737340
$206$	−3.03302e8	−2.41735
$207$	0	0
$208$	1.40510e7	0.108265
$209$	3.00122e7	0.227398
$210$	0	0
$211$	−1.01709e8	−0.745366	−0.372683	−	0.927959i	$-0.621562\pi$
$211$	−1.01709e8	−0.745366	−0.372683	+	0.927959i	$0.621562\pi$
$212$	1.52389e8	1.09844
$213$	0	0
$214$	1.02855e8	0.717427
$215$	−1.56972e8	−1.07718
$216$	0	0
$217$	−2.56460e7	−0.170377
$218$	3.24032e8	2.11831
$219$	0	0
$220$	8.49260e7	0.537726
$221$	−2.94755e7	−0.183691
$222$	0	0
$223$	−1.43993e8	−0.869508	−0.434754	−	0.900549i	$-0.643165\pi$
$223$	−1.43993e8	−0.869508	−0.434754	+	0.900549i	$0.643165\pi$
$224$	−1.15936e8	−0.689205
$225$	0	0
$226$	−4.20210e8	−2.42151
$227$	−1.92424e8	−1.09187	−0.545933	−	0.837829i	$-0.683825\pi$
$227$	−1.92424e8	−1.09187	−0.545933	+	0.837829i	$0.683825\pi$
$228$	0	0
$229$	6.02604e7	0.331595	0.165797	−	0.986160i	$-0.446980\pi$
$229$	6.02604e7	0.331595	0.165797	+	0.986160i	$0.446980\pi$
$230$	−1.01883e8	−0.552144
$231$	0	0
$232$	−1.69544e6	−0.00891405
$233$	2.88983e8	1.49667	0.748336	−	0.663320i	$-0.230853\pi$
$233$	2.88983e8	1.49667	0.748336	+	0.663320i	$0.230853\pi$
$234$	0	0
$235$	−3.71480e8	−1.86723
$236$	1.50004e8	0.742867
$237$	0	0
$238$	2.35621e8	1.13291
$239$	−137677.	−0.000652333 0	−0.000326167	−	1.00000i	$-0.500104\pi$
$239$	−137677.	−0.000652333 0	−0.000326167		1.00000i	$0.500104\pi$
$240$	0	0
$241$	3.89474e8	1.79233	0.896167	−	0.443717i	$-0.146340\pi$
$241$	3.89474e8	1.79233	0.896167	+	0.443717i	$0.146340\pi$
$242$	2.89461e8	1.31291
$243$	0	0
$244$	9.23037e7	0.406775
$245$	−3.27475e8	−1.42265
$246$	0	0
$247$	−2.14631e7	−0.0906262
$248$	−3.75277e6	−0.0156232
$249$	0	0
$250$	−9.50000e8	−3.84533
$251$	3.07150e8	1.22600	0.613002	−	0.790081i	$-0.289962\pi$
$251$	3.07150e8	1.22600	0.613002	+	0.790081i	$0.289962\pi$
$252$	0	0
$253$	1.50749e7	0.0585236
$254$	−4.04697e8	−1.54957
$255$	0	0
$256$	2.50942e8	0.934831
$257$	−2.58814e7	−0.0951092	−0.0475546	−	0.998869i	$-0.515143\pi$
$257$	−2.58814e7	−0.0951092	−0.0475546	+	0.998869i	$0.515143\pi$
$258$	0	0
$259$	−3.19334e7	−0.114208
$260$	−6.07345e7	−0.214303
$261$	0	0
$262$	−5.87519e8	−2.01821
$263$	5.03935e8	1.70816	0.854082	−	0.520139i	$-0.174120\pi$
$263$	5.03935e8	1.70816	0.854082	+	0.520139i	$0.174120\pi$
$264$	0	0
$265$	5.99603e8	1.97926
$266$	1.71572e8	0.558934
$267$	0	0
$268$	−6.40819e8	−2.03359
$269$	3.95543e8	1.23897	0.619486	−	0.785008i	$-0.287341\pi$
$269$	3.95543e8	1.23897	0.619486	+	0.785008i	$0.287341\pi$
$270$	0	0
$271$	2.90728e8	0.887348	0.443674	−	0.896188i	$-0.353675\pi$
$271$	2.90728e8	0.887348	0.443674	+	0.896188i	$0.353675\pi$
$272$	−5.27521e8	−1.58946
$273$	0	0
$274$	−2.72546e8	−0.800411
$275$	2.37361e8	0.688249
$276$	0	0
$277$	6.25916e8	1.76944	0.884722	−	0.466120i	$-0.154348\pi$
$277$	6.25916e8	1.76944	0.884722	+	0.466120i	$0.154348\pi$
$278$	1.37768e8	0.384585
$279$	0	0
$280$	1.46642e7	0.0399213
$281$	4.60295e8	1.23755	0.618777	−	0.785566i	$-0.287628\pi$
$281$	4.60295e8	1.23755	0.618777	+	0.785566i	$0.287628\pi$
$282$	0	0
$283$	8.37117e7	0.219550	0.109775	−	0.993956i	$-0.464987\pi$
$283$	8.37117e7	0.219550	0.109775	+	0.993956i	$0.464987\pi$
$284$	−4.87860e7	−0.126381
$285$	0	0
$286$	1.77015e7	0.0447434
$287$	7.69321e7	0.192097
$288$	0	0
$289$	6.96264e8	1.69680
$290$	−2.20864e8	−0.531780
$291$	0	0
$292$	1.40226e8	0.329602
$293$	−5.37739e8	−1.24892	−0.624461	−	0.781056i	$-0.714681\pi$
$293$	−5.37739e8	−1.24892	−0.624461	+	0.781056i	$0.714681\pi$
$294$	0	0
$295$	5.90221e8	1.33856
$296$	−4.67280e6	−0.0104726
$297$	0	0
$298$	−6.25662e8	−1.36956
$299$	−1.07807e7	−0.0233238
$300$	0	0
$301$	1.32777e8	0.280634
$302$	9.70105e8	2.02672
$303$	0	0
$304$	−3.84125e8	−0.784178
$305$	3.63187e8	0.732961
$306$	0	0
$307$	1.42374e7	0.0280832	0.0140416	−	0.999901i	$-0.495530\pi$
$307$	1.42374e7	0.0280832	0.0140416	+	0.999901i	$0.495530\pi$
$308$	−7.18360e7	−0.140092
$309$	0	0
$310$	−4.88870e8	−0.932025
$311$	−2.30383e8	−0.434300	−0.217150	−	0.976138i	$-0.569676\pi$
$311$	−2.30383e8	−0.434300	−0.217150	+	0.976138i	$0.569676\pi$
$312$	0	0
$313$	2.77390e8	0.511312	0.255656	−	0.966768i	$-0.417709\pi$
$313$	2.77390e8	0.511312	0.255656	+	0.966768i	$0.417709\pi$
$314$	−8.51681e8	−1.55247
$315$	0	0
$316$	8.37860e8	1.49371
$317$	6.75974e8	1.19185	0.595926	−	0.803039i	$-0.296785\pi$
$317$	6.75974e8	1.19185	0.595926	+	0.803039i	$0.296785\pi$
$318$	0	0
$319$	3.26797e7	0.0563652
$320$	−1.15586e9	−1.97188
$321$	0	0
$322$	8.61790e7	0.143849
$323$	8.05794e8	1.33050
$324$	0	0
$325$	−1.69748e8	−0.274292
$326$	−1.22958e9	−1.96561
$327$	0	0
$328$	1.12574e7	0.0176149
$329$	3.14222e8	0.486464
$330$	0	0
$331$	−1.06087e9	−1.60792	−0.803958	−	0.594687i	$-0.797276\pi$
$331$	−1.06087e9	−1.60792	−0.803958	+	0.594687i	$0.797276\pi$
$332$	−1.22988e9	−1.84450
$333$	0	0
$334$	−4.94839e8	−0.726693
$335$	−2.52143e9	−3.66429
$336$	0	0
$337$	6.27245e8	0.892755	0.446378	−	0.894845i	$-0.352714\pi$
$337$	6.27245e8	0.892755	0.446378	+	0.894845i	$0.352714\pi$
$338$	9.99104e8	1.40735
$339$	0	0
$340$	2.28017e9	3.14623
$341$	7.23347e7	0.0987885
$342$	0	0
$343$	6.38767e8	0.854698
$344$	1.94292e7	0.0257335
$345$	0	0
$346$	1.50244e8	0.194998
$347$	−2.38728e8	−0.306726	−0.153363	−	0.988170i	$-0.549010\pi$
$347$	−2.38728e8	−0.306726	−0.153363	+	0.988170i	$0.549010\pi$
$348$	0	0
$349$	−4.28787e8	−0.539949	−0.269974	−	0.962867i	$-0.587015\pi$
$349$	−4.28787e8	−0.539949	−0.269974	+	0.962867i	$0.587015\pi$
$350$	1.35693e9	1.69169
$351$	0	0
$352$	3.26997e8	0.399617
$353$	5.91768e8	0.716045	0.358022	−	0.933713i	$-0.383451\pi$
$353$	5.91768e8	0.716045	0.358022	+	0.933713i	$0.383451\pi$
$354$	0	0
$355$	−1.91958e8	−0.227723
$356$	1.65566e9	1.94490
$357$	0	0
$358$	9.26346e8	1.06705
$359$	−3.75613e8	−0.428460	−0.214230	−	0.976783i	$-0.568724\pi$
$359$	−3.75613e8	−0.428460	−0.214230	+	0.976783i	$0.568724\pi$
$360$	0	0
$361$	−3.07117e8	−0.343580
$362$	1.34055e9	1.48526
$363$	0	0
$364$	5.13733e7	0.0558319
$365$	5.51748e8	0.593903
$366$	0	0
$367$	6.77196e8	0.715127	0.357563	−	0.933889i	$-0.383608\pi$
$367$	6.77196e8	0.715127	0.357563	+	0.933889i	$0.383608\pi$
$368$	−1.92942e8	−0.201818
$369$	0	0
$370$	−6.08723e8	−0.624760
$371$	−5.07184e8	−0.515652
$372$	0	0
$373$	−5.35696e8	−0.534488	−0.267244	−	0.963629i	$-0.586113\pi$
$373$	−5.35696e8	−0.534488	−0.267244	+	0.963629i	$0.586113\pi$
$374$	−6.64571e8	−0.656887
$375$	0	0
$376$	4.59799e7	0.0446078
$377$	−2.33708e7	−0.0224636
$378$	0	0
$379$	−2.59380e8	−0.244737	−0.122368	−	0.992485i	$-0.539049\pi$
$379$	−2.59380e8	−0.244737	−0.122368	+	0.992485i	$0.539049\pi$
$380$	1.66035e9	1.55223
$381$	0	0
$382$	2.01271e8	0.184739
$383$	−1.26184e9	−1.14765	−0.573824	−	0.818979i	$-0.694541\pi$
$383$	−1.26184e9	−1.14765	−0.573824	+	0.818979i	$0.694541\pi$
$384$	0	0
$385$	−2.82653e8	−0.252430
$386$	−1.77869e9	−1.57414
$387$	0	0
$388$	−1.60830e9	−1.39784
$389$	−2.21921e9	−1.91150	−0.955749	−	0.294182i	$-0.904953\pi$
$389$	−2.21921e9	−1.91150	−0.955749	+	0.294182i	$0.904953\pi$
$390$	0	0
$391$	4.04743e8	0.342421
$392$	4.05332e7	0.0339868
$393$	0	0
$394$	1.28875e9	1.06153
$395$	3.29673e9	2.69149
$396$	0	0
$397$	−1.73593e9	−1.39241	−0.696203	−	0.717845i	$-0.745129\pi$
$397$	−1.73593e9	−1.39241	−0.696203	+	0.717845i	$0.745129\pi$
$398$	−1.41209e9	−1.12272
$399$	0	0
$400$	−3.03797e9	−2.37342
$401$	−4.16615e8	−0.322648	−0.161324	−	0.986901i	$-0.551576\pi$
$401$	−4.16615e8	−0.322648	−0.161324	+	0.986901i	$0.551576\pi$
$402$	0	0
$403$	−5.17299e7	−0.0393708
$404$	−6.24025e8	−0.470833
$405$	0	0
$406$	1.86821e8	0.138543
$407$	9.00684e7	0.0662205
$408$	0	0
$409$	1.78390e9	1.28925	0.644626	−	0.764498i	$-0.277013\pi$
$409$	1.78390e9	1.28925	0.644626	+	0.764498i	$0.277013\pi$
$410$	1.46650e9	1.05084
$411$	0	0
$412$	2.48273e9	1.74900
$413$	−4.99248e8	−0.348731
$414$	0	0
$415$	−4.83919e9	−3.32357
$416$	−2.33851e8	−0.159262
$417$	0	0
$418$	−4.83920e8	−0.324083
$419$	−2.49057e9	−1.65405	−0.827026	−	0.562163i	$-0.809969\pi$
$419$	−2.49057e9	−1.65405	−0.827026	+	0.562163i	$0.809969\pi$
$420$	0	0
$421$	6.45056e8	0.421318	0.210659	−	0.977560i	$-0.432439\pi$
$421$	6.45056e8	0.421318	0.210659	+	0.977560i	$0.432439\pi$
$422$	1.63996e9	1.06228
$423$	0	0
$424$	−7.42159e7	−0.0472843
$425$	6.37289e9	4.02694
$426$	0	0
$427$	−3.07208e8	−0.190956
$428$	−8.41938e8	−0.519071
$429$	0	0
$430$	2.53102e9	1.53517
$431$	−1.98666e8	−0.119523	−0.0597617	−	0.998213i	$-0.519034\pi$
$431$	−1.98666e8	−0.119523	−0.0597617	+	0.998213i	$0.519034\pi$
$432$	0	0
$433$	−2.95758e8	−0.175077	−0.0875385	−	0.996161i	$-0.527900\pi$
$433$	−2.95758e8	−0.175077	−0.0875385	+	0.996161i	$0.527900\pi$
$434$	4.13519e8	0.242818
$435$	0	0
$436$	−2.65242e9	−1.53264
$437$	2.94722e8	0.168938
$438$	0	0
$439$	−6.11806e6	−0.00345134	−0.00172567	−	0.999999i	$-0.500549\pi$
$439$	−6.11806e6	−0.00345134	−0.00172567	+	0.999999i	$0.500549\pi$
$440$	−4.13604e7	−0.0231473
$441$	0	0
$442$	4.75265e8	0.261793
$443$	−1.76550e9	−0.964841	−0.482421	−	0.875940i	$-0.660242\pi$
$443$	−1.76550e9	−0.964841	−0.482421	+	0.875940i	$0.660242\pi$
$444$	0	0
$445$	6.51453e9	3.50448
$446$	2.32175e9	1.23921
$447$	0	0
$448$	9.77702e8	0.513728
$449$	−3.77930e9	−1.97037	−0.985187	−	0.171484i	$-0.945144\pi$
$449$	−3.77930e9	−1.97037	−0.985187	+	0.171484i	$0.945144\pi$
$450$	0	0
$451$	−2.16988e8	−0.111382
$452$	3.43970e9	1.75201
$453$	0	0
$454$	3.10267e9	1.55611
$455$	2.02138e8	0.100602
$456$	0	0
$457$	1.20572e9	0.590933	0.295467	−	0.955353i	$-0.404525\pi$
$457$	1.20572e9	0.590933	0.295467	+	0.955353i	$0.404525\pi$
$458$	−9.71645e8	−0.472583
$459$	0	0
$460$	8.33977e8	0.399486
$461$	7.73586e8	0.367752	0.183876	−	0.982949i	$-0.441135\pi$
$461$	7.73586e8	0.367752	0.183876	+	0.982949i	$0.441135\pi$
$462$	0	0
$463$	1.53598e8	0.0719204	0.0359602	−	0.999353i	$-0.488551\pi$
$463$	1.53598e8	0.0719204	0.0359602	+	0.999353i	$0.488551\pi$
$464$	−4.18266e8	−0.194375
$465$	0	0
$466$	−4.65959e9	−2.13303
$467$	3.04134e9	1.38184	0.690918	−	0.722933i	$-0.257206\pi$
$467$	3.04134e9	1.38184	0.690918	+	0.722933i	$0.257206\pi$
$468$	0	0
$469$	2.13279e9	0.954647
$470$	5.98977e9	2.66114
$471$	0	0
$472$	−7.30546e7	−0.0319780
$473$	−3.74498e8	−0.162718
$474$	0	0
$475$	4.64054e9	1.98674
$476$	−1.92872e9	−0.819679
$477$	0	0
$478$	2.21992e6	0.000929694 0
$479$	−2.70620e9	−1.12509	−0.562543	−	0.826768i	$-0.690177\pi$
$479$	−2.70620e9	−1.12509	−0.562543	+	0.826768i	$0.690177\pi$
$480$	0	0
$481$	−6.44122e7	−0.0263913
$482$	−6.27992e9	−2.55440
$483$	0	0
$484$	−2.36943e9	−0.949916
$485$	−6.32818e9	−2.51874
$486$	0	0
$487$	3.18750e8	0.125054	0.0625272	−	0.998043i	$-0.480084\pi$
$487$	3.18750e8	0.125054	0.0625272	+	0.998043i	$0.480084\pi$
$488$	−4.49535e7	−0.0175103
$489$	0	0
$490$	5.28024e9	2.02753
$491$	−1.69191e9	−0.645047	−0.322524	−	0.946561i	$-0.604531\pi$
$491$	−1.69191e9	−0.645047	−0.322524	+	0.946561i	$0.604531\pi$
$492$	0	0
$493$	8.77414e8	0.329792
$494$	3.46074e8	0.129159
$495$	0	0
$496$	−9.25808e8	−0.340671
$497$	1.62371e8	0.0593281
$498$	0	0
$499$	−7.59141e8	−0.273508	−0.136754	−	0.990605i	$-0.543667\pi$
$499$	−7.59141e8	−0.273508	−0.136754	+	0.990605i	$0.543667\pi$
$500$	7.77639e9	2.78217
$501$	0	0
$502$	−4.95251e9	−1.74728
$503$	2.36181e9	0.827477	0.413739	−	0.910396i	$-0.364223\pi$
$503$	2.36181e9	0.827477	0.413739	+	0.910396i	$0.364223\pi$
$504$	0	0
$505$	−2.45535e9	−0.848386
$506$	−2.43068e8	−0.0834069
$507$	0	0
$508$	3.31271e9	1.12114
$509$	−8.81763e8	−0.296374	−0.148187	−	0.988959i	$-0.547344\pi$
$509$	−8.81763e8	−0.296374	−0.148187	+	0.988959i	$0.547344\pi$
$510$	0	0
$511$	−4.66705e8	−0.154728
$512$	−4.31569e9	−1.42104
$513$	0	0
$514$	4.17315e8	0.135548
$515$	9.76880e9	3.15149
$516$	0	0
$517$	−8.86265e8	−0.282063
$518$	5.14898e8	0.162767
$519$	0	0
$520$	2.95788e7	0.00922505
$521$	1.05646e9	0.327281	0.163640	−	0.986520i	$-0.447676\pi$
$521$	1.05646e9	0.327281	0.163640	+	0.986520i	$0.447676\pi$
$522$	0	0
$523$	−3.04696e9	−0.931346	−0.465673	−	0.884957i	$-0.654188\pi$
$523$	−3.04696e9	−0.931346	−0.465673	+	0.884957i	$0.654188\pi$
$524$	4.80924e9	1.46021
$525$	0	0
$526$	−8.12550e9	−2.43444
$527$	1.94211e9	0.578011
$528$	0	0
$529$	1.48036e8	0.0434783
$530$	−9.66806e9	−2.82081
$531$	0	0
$532$	−1.40443e9	−0.404399
$533$	1.55178e8	0.0443900
$534$	0	0
$535$	−3.31277e9	−0.935305
$536$	3.12090e8	0.0875393
$537$	0	0
$538$	−6.37778e9	−1.76576
$539$	−7.81280e8	−0.214905
$540$	0	0
$541$	−4.51721e9	−1.22653	−0.613267	−	0.789875i	$-0.710145\pi$
$541$	−4.51721e9	−1.22653	−0.613267	+	0.789875i	$0.710145\pi$
$542$	−4.68772e9	−1.26463
$543$	0	0
$544$	8.77950e9	2.33816
$545$	−1.04365e10	−2.76163
$546$	0	0
$547$	−3.07485e9	−0.803283	−0.401641	−	0.915797i	$-0.631560\pi$
$547$	−3.07485e9	−0.803283	−0.401641	+	0.915797i	$0.631560\pi$
$548$	2.23097e9	0.579112
$549$	0	0
$550$	−3.82724e9	−0.980881
$551$	6.38906e8	0.162707
$552$	0	0
$553$	−2.78859e9	−0.701207
$554$	−1.00923e10	−2.52178
$555$	0	0
$556$	−1.12772e9	−0.278254
$557$	4.09467e9	1.00398	0.501991	−	0.864873i	$-0.332601\pi$
$557$	4.09467e9	1.00398	0.501991	+	0.864873i	$0.332601\pi$
$558$	0	0
$559$	2.67821e8	0.0648490
$560$	3.61766e9	0.870501
$561$	0	0
$562$	−7.42185e9	−1.76374
$563$	8.37874e8	0.197879	0.0989394	−	0.995093i	$-0.468455\pi$
$563$	8.37874e8	0.197879	0.0989394	+	0.995093i	$0.468455\pi$
$564$	0	0
$565$	1.35342e10	3.15691
$566$	−1.34978e9	−0.312899
$567$	0	0
$568$	2.37596e7	0.00544027
$569$	5.29170e9	1.20421	0.602106	−	0.798417i	$-0.294329\pi$
$569$	5.29170e9	1.20421	0.602106	+	0.798417i	$0.294329\pi$
$570$	0	0
$571$	−2.99442e9	−0.673110	−0.336555	−	0.941664i	$-0.609262\pi$
$571$	−2.99442e9	−0.673110	−0.336555	+	0.941664i	$0.609262\pi$
$572$	−1.44899e8	−0.0323726
$573$	0	0
$574$	−1.24046e9	−0.273774
$575$	2.33090e9	0.511313
$576$	0	0
$577$	−3.24689e9	−0.703642	−0.351821	−	0.936067i	$-0.614437\pi$
$577$	−3.24689e9	−0.703642	−0.351821	+	0.936067i	$0.614437\pi$
$578$	−1.12266e10	−2.41826
$579$	0	0
$580$	1.80792e9	0.384752
$581$	4.09331e9	0.865880
$582$	0	0
$583$	1.43052e9	0.298987
$584$	−6.82927e7	−0.0141883
$585$	0	0
$586$	8.67056e9	1.77994
$587$	3.25912e9	0.665069	0.332534	−	0.943091i	$-0.392096\pi$
$587$	3.25912e9	0.665069	0.332534	+	0.943091i	$0.392096\pi$
$588$	0	0
$589$	1.41418e9	0.285169
$590$	−9.51678e9	−1.90769
$591$	0	0
$592$	−1.15278e9	−0.228360
$593$	−3.83139e9	−0.754510	−0.377255	−	0.926109i	$-0.623132\pi$
$593$	−3.83139e9	−0.754510	−0.377255	+	0.926109i	$0.623132\pi$
$594$	0	0
$595$	−7.58891e9	−1.47696
$596$	5.12146e9	0.990905
$597$	0	0
$598$	1.73830e8	0.0332407
$599$	2.13369e8	0.0405637	0.0202818	−	0.999794i	$-0.493544\pi$
$599$	2.13369e8	0.0405637	0.0202818	+	0.999794i	$0.493544\pi$
$600$	0	0
$601$	−8.28292e9	−1.55641	−0.778203	−	0.628013i	$-0.783869\pi$
$601$	−8.28292e9	−1.55641	−0.778203	+	0.628013i	$0.783869\pi$
$602$	−2.14091e9	−0.399954
$603$	0	0
$604$	−7.94096e9	−1.46637
$605$	−9.32299e9	−1.71164
$606$	0	0
$607$	7.09347e9	1.28735	0.643677	−	0.765297i	$-0.277408\pi$
$607$	7.09347e9	1.28735	0.643677	+	0.765297i	$0.277408\pi$
$608$	6.39296e9	1.15356
$609$	0	0
$610$	−5.85606e9	−1.04460
$611$	6.33809e8	0.112412
$612$	0	0
$613$	−7.47850e9	−1.31130	−0.655651	−	0.755064i	$-0.727606\pi$
$613$	−7.47850e9	−1.31130	−0.655651	+	0.755064i	$0.727606\pi$
$614$	−2.29565e8	−0.0400237
$615$	0	0
$616$	3.49854e7	0.00603051
$617$	−5.98175e9	−1.02525	−0.512626	−	0.858612i	$-0.671327\pi$
$617$	−5.98175e9	−1.02525	−0.512626	+	0.858612i	$0.671327\pi$
$618$	0	0
$619$	4.19998e9	0.711755	0.355877	−	0.934533i	$-0.384182\pi$
$619$	4.19998e9	0.711755	0.355877	+	0.934533i	$0.384182\pi$
$620$	4.00173e9	0.674337
$621$	0	0
$622$	3.71473e9	0.618957
$623$	−5.51042e9	−0.913013
$624$	0	0
$625$	1.56309e10	2.56096
$626$	−4.47267e9	−0.728713
$627$	0	0
$628$	6.97158e9	1.12324
$629$	2.41824e9	0.387455
$630$	0	0
$631$	−1.03015e10	−1.63229	−0.816146	−	0.577845i	$-0.803894\pi$
$631$	−1.03015e10	−1.63229	−0.816146	+	0.577845i	$0.803894\pi$
$632$	−4.08053e8	−0.0642993
$633$	0	0
$634$	−1.08995e10	−1.69861
$635$	1.30345e10	2.02017
$636$	0	0
$637$	5.58730e8	0.0856473
$638$	−5.26931e8	−0.0803307
$639$	0	0
$640$	1.09334e9	0.164864
$641$	1.07358e9	0.161003	0.0805013	−	0.996755i	$-0.474348\pi$
$641$	1.07358e9	0.161003	0.0805013	+	0.996755i	$0.474348\pi$
$642$	0	0
$643$	−3.34469e8	−0.0496155	−0.0248078	−	0.999692i	$-0.507897\pi$
$643$	−3.34469e8	−0.0496155	−0.0248078	+	0.999692i	$0.507897\pi$
$644$	−7.05433e8	−0.104077
$645$	0	0
$646$	−1.29927e10	−1.89621
$647$	6.21703e9	0.902440	0.451220	−	0.892413i	$-0.350989\pi$
$647$	6.21703e9	0.902440	0.451220	+	0.892413i	$0.350989\pi$
$648$	0	0
$649$	1.40813e9	0.202203
$650$	2.73704e9	0.390916
$651$	0	0
$652$	1.00650e10	1.42215
$653$	−1.19060e10	−1.67329	−0.836645	−	0.547745i	$-0.815486\pi$
$653$	−1.19060e10	−1.67329	−0.836645	+	0.547745i	$0.815486\pi$
$654$	0	0
$655$	1.89229e10	2.63113
$656$	2.77721e9	0.384101
$657$	0	0
$658$	−5.06654e9	−0.693300
$659$	9.67726e9	1.31721	0.658603	−	0.752491i	$-0.271148\pi$
$659$	9.67726e9	1.31721	0.658603	+	0.752491i	$0.271148\pi$
$660$	0	0
$661$	6.44298e9	0.867724	0.433862	−	0.900979i	$-0.357151\pi$
$661$	6.44298e9	0.867724	0.433862	+	0.900979i	$0.357151\pi$
$662$	1.71055e10	2.29157
$663$	0	0
$664$	5.98971e8	0.0793995
$665$	−5.52601e9	−0.728679
$666$	0	0
$667$	3.20917e8	0.0418747
$668$	4.05059e9	0.525775
$669$	0	0
$670$	4.06557e10	5.22228
$671$	8.66481e8	0.110721
$672$	0	0
$673$	−4.78618e9	−0.605252	−0.302626	−	0.953109i	$-0.597863\pi$
$673$	−4.78618e9	−0.605252	−0.302626	+	0.953109i	$0.597863\pi$
$674$	−1.01138e10	−1.27234
$675$	0	0
$676$	−8.17834e9	−1.01824
$677$	2.69329e9	0.333598	0.166799	−	0.985991i	$-0.446657\pi$
$677$	2.69329e9	0.333598	0.166799	+	0.985991i	$0.446657\pi$
$678$	0	0
$679$	5.35279e9	0.656200
$680$	−1.11048e9	−0.135435
$681$	0	0
$682$	−1.16633e9	−0.140792
$683$	5.44458e9	0.653871	0.326935	−	0.945047i	$-0.393984\pi$
$683$	5.44458e9	0.653871	0.326935	+	0.945047i	$0.393984\pi$
$684$	0	0
$685$	8.77820e9	1.04349
$686$	−1.02995e10	−1.21810
$687$	0	0
$688$	4.79318e9	0.561131
$689$	−1.02303e9	−0.119157
$690$	0	0
$691$	−1.35606e10	−1.56353	−0.781763	−	0.623576i	$-0.785679\pi$
$691$	−1.35606e10	−1.56353	−0.781763	+	0.623576i	$0.785679\pi$
$692$	−1.22985e9	−0.141084
$693$	0	0
$694$	3.84927e9	0.437140
$695$	−4.43725e9	−0.501381
$696$	0	0
$697$	−5.82587e9	−0.651698
$698$	6.91380e9	0.769526
$699$	0	0
$700$	−1.11074e10	−1.22397
$701$	1.21383e10	1.33090	0.665450	−	0.746443i	$-0.268240\pi$
$701$	1.21383e10	1.33090	0.665450	+	0.746443i	$0.268240\pi$
$702$	0	0
$703$	1.76089e9	0.191156
$704$	−2.75761e9	−0.297872
$705$	0	0
$706$	−9.54173e9	−1.02049
$707$	2.07690e9	0.221028
$708$	0	0
$709$	−3.91398e9	−0.412436	−0.206218	−	0.978506i	$-0.566116\pi$
$709$	−3.91398e9	−0.412436	−0.206218	+	0.978506i	$0.566116\pi$
$710$	3.09515e9	0.324547
$711$	0	0
$712$	−8.06337e8	−0.0837214
$713$	7.10331e8	0.0733918
$714$	0	0
$715$	−5.70132e8	−0.0583317
$716$	−7.58277e9	−0.772026
$717$	0	0
$718$	6.05642e9	0.610634
$719$	−8.59067e8	−0.0861938	−0.0430969	−	0.999071i	$-0.513722\pi$
$719$	−8.59067e8	−0.0861938	−0.0430969	+	0.999071i	$0.513722\pi$
$720$	0	0
$721$	−8.26309e9	−0.821049
$722$	4.95198e9	0.489665
$723$	0	0
$724$	−1.09733e10	−1.07461
$725$	5.05300e9	0.492454
$726$	0	0
$727$	3.24989e9	0.313688	0.156844	−	0.987623i	$-0.449868\pi$
$727$	3.24989e9	0.313688	0.156844	+	0.987623i	$0.449868\pi$
$728$	−2.50197e7	−0.00240338
$729$	0	0
$730$	−8.89644e9	−0.846421
$731$	−1.00549e10	−0.952062
$732$	0	0
$733$	−1.31932e9	−0.123733	−0.0618666	−	0.998084i	$-0.519705\pi$
$733$	−1.31932e9	−0.123733	−0.0618666	+	0.998084i	$0.519705\pi$
$734$	−1.09192e10	−1.01919
$735$	0	0
$736$	3.21113e9	0.296883
$737$	−6.01555e9	−0.553527
$738$	0	0
$739$	6.75718e9	0.615900	0.307950	−	0.951403i	$-0.400357\pi$
$739$	6.75718e9	0.615900	0.307950	+	0.951403i	$0.400357\pi$
$740$	4.98280e9	0.452025
$741$	0	0
$742$	8.17788e9	0.734898
$743$	−8.31567e8	−0.0743766	−0.0371883	−	0.999308i	$-0.511840\pi$
$743$	−8.31567e8	−0.0743766	−0.0371883	+	0.999308i	$0.511840\pi$
$744$	0	0
$745$	2.01514e10	1.78549
$746$	8.63762e9	0.761743
$747$	0	0
$748$	5.43996e9	0.475269
$749$	2.80216e9	0.243673
$750$	0	0
$751$	−1.24613e10	−1.07355	−0.536777	−	0.843724i	$-0.680358\pi$
$751$	−1.24613e10	−1.07355	−0.536777	+	0.843724i	$0.680358\pi$
$752$	1.13433e10	0.972691
$753$	0	0
$754$	3.76833e8	0.0320147
$755$	−3.12453e10	−2.64223
$756$	0	0
$757$	1.69129e10	1.41704	0.708520	−	0.705691i	$-0.249363\pi$
$757$	1.69129e10	1.41704	0.708520	+	0.705691i	$0.249363\pi$
$758$	4.18227e9	0.348795
$759$	0	0
$760$	−8.08619e8	−0.0668184
$761$	4.92489e9	0.405089	0.202544	−	0.979273i	$-0.435079\pi$
$761$	4.92489e9	0.405089	0.202544	+	0.979273i	$0.435079\pi$
$762$	0	0
$763$	8.82784e9	0.719480
$764$	−1.64754e9	−0.133662
$765$	0	0
$766$	2.03460e10	1.63561
$767$	−1.00702e9	−0.0805851
$768$	0	0
$769$	1.38388e10	1.09737	0.548687	−	0.836028i	$-0.315128\pi$
$769$	1.38388e10	1.09737	0.548687	+	0.836028i	$0.315128\pi$
$770$	4.55752e9	0.359759
$771$	0	0
$772$	1.45597e10	1.13892
$773$	7.78161e8	0.0605956	0.0302978	−	0.999541i	$-0.490354\pi$
$773$	7.78161e8	0.0605956	0.0302978	+	0.999541i	$0.490354\pi$
$774$	0	0
$775$	1.11845e10	0.863101
$776$	7.83271e8	0.0601722
$777$	0	0
$778$	3.57827e10	2.72423
$779$	−4.24222e9	−0.321523
$780$	0	0
$781$	−4.57968e8	−0.0343998
$782$	−6.52612e9	−0.488013
$783$	0	0
$784$	9.99955e9	0.741096
$785$	2.74311e10	2.02395
$786$	0	0
$787$	1.34125e10	0.980839	0.490420	−	0.871486i	$-0.336844\pi$
$787$	1.34125e10	0.980839	0.490420	+	0.871486i	$0.336844\pi$
$788$	−1.05493e10	−0.768034
$789$	0	0
$790$	−5.31567e10	−3.83587
$791$	−1.14481e10	−0.822462
$792$	0	0
$793$	−6.19661e8	−0.0441263
$794$	2.79903e10	1.98443
$795$	0	0
$796$	1.15589e10	0.812308
$797$	2.23182e10	1.56155	0.780775	−	0.624813i	$-0.214825\pi$
$797$	2.23182e10	1.56155	0.780775	+	0.624813i	$0.214825\pi$
$798$	0	0
$799$	−2.37952e10	−1.65035
$800$	5.05608e10	3.49140
$801$	0	0
$802$	6.71754e9	0.459833
$803$	1.31634e9	0.0897150
$804$	0	0
$805$	−2.77567e9	−0.187535
$806$	8.34099e8	0.0561106
$807$	0	0
$808$	3.03911e8	0.0202678
$809$	−2.62752e10	−1.74472	−0.872360	−	0.488864i	$-0.837411\pi$
$809$	−2.62752e10	−1.74472	−0.872360	+	0.488864i	$0.837411\pi$
$810$	0	0
$811$	−7.12447e9	−0.469008	−0.234504	−	0.972115i	$-0.575347\pi$
$811$	−7.12447e9	−0.469008	−0.234504	+	0.972115i	$0.575347\pi$
$812$	−1.52926e9	−0.100239
$813$	0	0
$814$	−1.45227e9	−0.0943762
$815$	3.96026e10	2.56255
$816$	0	0
$817$	−7.32164e9	−0.469711
$818$	−2.87637e10	−1.83742
$819$	0	0
$820$	−1.20043e10	−0.760304
$821$	1.18524e10	0.747492	0.373746	−	0.927531i	$-0.378073\pi$
$821$	1.18524e10	0.747492	0.373746	+	0.927531i	$0.378073\pi$
$822$	0	0
$823$	−1.39730e10	−0.873755	−0.436877	−	0.899521i	$-0.643916\pi$
$823$	−1.39730e10	−0.873755	−0.436877	+	0.899521i	$0.643916\pi$
$824$	−1.20913e9	−0.0752886
$825$	0	0
$826$	8.04992e9	0.497006
$827$	2.17594e10	1.33776	0.668879	−	0.743371i	$-0.266774\pi$
$827$	2.17594e10	1.33776	0.668879	+	0.743371i	$0.266774\pi$
$828$	0	0
$829$	−1.90784e10	−1.16306	−0.581528	−	0.813527i	$-0.697545\pi$
$829$	−1.90784e10	−1.16306	−0.581528	+	0.813527i	$0.697545\pi$
$830$	7.80276e10	4.73669
$831$	0	0
$832$	1.97210e9	0.118713
$833$	−2.09765e10	−1.25741
$834$	0	0
$835$	1.59378e10	0.947385
$836$	3.96121e9	0.234480
$837$	0	0
$838$	4.01582e10	2.35733
$839$	7.66588e9	0.448121	0.224060	−	0.974575i	$-0.428069\pi$
$839$	7.66588e9	0.448121	0.224060	+	0.974575i	$0.428069\pi$
$840$	0	0
$841$	−1.65542e10	−0.959670
$842$	−1.04010e10	−0.600456
$843$	0	0
$844$	−1.34242e10	−0.768581
$845$	−3.21793e10	−1.83475
$846$	0	0
$847$	7.88600e9	0.445928
$848$	−1.83091e10	−1.03105
$849$	0	0
$850$	−1.02757e11	−5.73912
$851$	8.84477e8	0.0491964
$852$	0	0
$853$	−4.17913e9	−0.230549	−0.115275	−	0.993334i	$-0.536775\pi$
$853$	−4.17913e9	−0.230549	−0.115275	+	0.993334i	$0.536775\pi$
$854$	4.95344e9	0.272148
$855$	0	0
$856$	4.10039e8	0.0223443
$857$	−2.49437e10	−1.35372	−0.676859	−	0.736112i	$-0.736659\pi$
$857$	−2.49437e10	−1.35372	−0.676859	+	0.736112i	$0.736659\pi$
$858$	0	0
$859$	−2.11511e10	−1.13856	−0.569280	−	0.822144i	$-0.692778\pi$
$859$	−2.11511e10	−1.13856	−0.569280	+	0.822144i	$0.692778\pi$
$860$	−2.07181e10	−1.11072
$861$	0	0
$862$	3.20331e9	0.170343
$863$	−2.03614e10	−1.07838	−0.539189	−	0.842185i	$-0.681269\pi$
$863$	−2.03614e10	−1.07838	−0.539189	+	0.842185i	$0.681269\pi$
$864$	0	0
$865$	−4.83907e9	−0.254218
$866$	4.76883e9	0.249517
$867$	0	0
$868$	−3.38493e9	−0.175683
$869$	7.86523e9	0.406577
$870$	0	0
$871$	4.30200e9	0.220601
$872$	1.29177e9	0.0659749
$873$	0	0
$874$	−4.75212e9	−0.240767
$875$	−2.58816e10	−1.30606
$876$	0	0
$877$	8.64182e9	0.432620	0.216310	−	0.976325i	$-0.430598\pi$
$877$	8.64182e9	0.432620	0.216310	+	0.976325i	$0.430598\pi$
$878$	9.86482e7	0.00491879
$879$	0	0
$880$	−1.02036e10	−0.504737
$881$	−2.32377e10	−1.14493	−0.572464	−	0.819930i	$-0.694012\pi$
$881$	−2.32377e10	−1.14493	−0.572464	+	0.819930i	$0.694012\pi$
$882$	0	0
$883$	−1.80558e10	−0.882582	−0.441291	−	0.897364i	$-0.645479\pi$
$883$	−1.80558e10	−0.882582	−0.441291	+	0.897364i	$0.645479\pi$
$884$	−3.89037e9	−0.189412
$885$	0	0
$886$	2.84672e10	1.37507
$887$	1.68574e9	0.0811067	0.0405534	−	0.999177i	$-0.487088\pi$
$887$	1.68574e9	0.0811067	0.0405534	+	0.999177i	$0.487088\pi$
$888$	0	0
$889$	−1.10255e10	−0.526309
$890$	−1.05041e11	−4.99452
$891$	0	0
$892$	−1.90051e10	−0.896589
$893$	−1.73270e10	−0.814221
$894$	0	0
$895$	−2.98359e10	−1.39110
$896$	−9.24818e8	−0.0429515
$897$	0	0
$898$	6.09377e10	2.80814
$899$	1.53988e9	0.0706849
$900$	0	0
$901$	3.84077e10	1.74937
$902$	3.49873e9	0.158740
$903$	0	0
$904$	−1.67519e9	−0.0754181
$905$	−4.31766e10	−1.93633
$906$	0	0
$907$	3.69615e10	1.64484	0.822422	−	0.568878i	$-0.192622\pi$
$907$	3.69615e10	1.64484	0.822422	+	0.568878i	$0.192622\pi$
$908$	−2.53974e10	−1.12587
$909$	0	0
$910$	−3.25930e9	−0.143377
$911$	2.56946e10	1.12597	0.562986	−	0.826466i	$-0.309652\pi$
$911$	2.56946e10	1.12597	0.562986	+	0.826466i	$0.309652\pi$
$912$	0	0
$913$	−1.15452e10	−0.502058
$914$	−1.94411e10	−0.842187
$915$	0	0
$916$	7.95356e9	0.341922
$917$	−1.60062e10	−0.685482
$918$	0	0
$919$	−3.71651e10	−1.57954	−0.789772	−	0.613401i	$-0.789801\pi$
$919$	−3.71651e10	−1.57954	−0.789772	+	0.613401i	$0.789801\pi$
$920$	−4.06162e8	−0.0171966
$921$	0	0
$922$	−1.24734e10	−0.524114
$923$	3.27514e8	0.0137096
$924$	0	0
$925$	1.39265e10	0.578559
$926$	−2.47663e9	−0.102500
$927$	0	0
$928$	6.96117e9	0.285933
$929$	1.03012e10	0.421536	0.210768	−	0.977536i	$-0.432404\pi$
$929$	1.03012e10	0.421536	0.210768	+	0.977536i	$0.432404\pi$
$930$	0	0
$931$	−1.52744e10	−0.620356
$932$	3.81419e10	1.54329
$933$	0	0
$934$	−4.90389e10	−1.96937
$935$	2.14046e10	0.856379
$936$	0	0
$937$	−1.80935e10	−0.718511	−0.359255	−	0.933239i	$-0.616969\pi$
$937$	−1.80935e10	−0.718511	−0.359255	+	0.933239i	$0.616969\pi$
$938$	−3.43893e10	−1.36055
$939$	0	0
$940$	−4.90303e10	−1.92538
$941$	9.79964e9	0.383395	0.191698	−	0.981454i	$-0.438601\pi$
$941$	9.79964e9	0.383395	0.191698	+	0.981454i	$0.438601\pi$
$942$	0	0
$943$	−2.13083e9	−0.0827480
$944$	−1.80226e10	−0.697293
$945$	0	0
$946$	6.03844e9	0.231903
$947$	2.14911e10	0.822307	0.411153	−	0.911566i	$-0.365126\pi$
$947$	2.14911e10	0.822307	0.411153	+	0.911566i	$0.365126\pi$
$948$	0	0
$949$	−9.41379e8	−0.0357547
$950$	−7.48246e10	−2.83147
$951$	0	0
$952$	9.39318e8	0.0352845
$953$	4.88212e10	1.82719	0.913593	−	0.406629i	$-0.133296\pi$
$953$	4.88212e10	1.82719	0.913593	+	0.406629i	$0.133296\pi$
$954$	0	0
$955$	−6.48255e9	−0.240843
$956$	−1.81715e7	−0.000672650 0
$957$	0	0
$958$	4.36350e10	1.60345
$959$	−7.42518e9	−0.271858
$960$	0	0
$961$	−2.41042e10	−0.876114
$962$	1.03859e9	0.0376124
$963$	0	0
$964$	5.14054e10	1.84816
$965$	5.72881e10	2.05220
$966$	0	0
$967$	−1.44801e10	−0.514967	−0.257483	−	0.966283i	$-0.582893\pi$
$967$	−1.44801e10	−0.514967	−0.257483	+	0.966283i	$0.582893\pi$
$968$	1.15395e9	0.0408907
$969$	0	0
$970$	1.02036e11	3.58966
$971$	−1.52131e10	−0.533274	−0.266637	−	0.963797i	$-0.585913\pi$
$971$	−1.52131e10	−0.533274	−0.266637	+	0.963797i	$0.585913\pi$
$972$	0	0
$973$	3.75332e9	0.130623
$974$	−5.13956e9	−0.178225
$975$	0	0
$976$	−1.10900e10	−0.381820
$977$	7.61072e9	0.261093	0.130546	−	0.991442i	$-0.458327\pi$
$977$	7.61072e9	0.261093	0.130546	+	0.991442i	$0.458327\pi$
$978$	0	0
$979$	1.55422e10	0.529386
$980$	−4.32223e10	−1.46695
$981$	0	0
$982$	2.72805e10	0.919310
$983$	−5.78044e10	−1.94099	−0.970495	−	0.241121i	$-0.922485\pi$
$983$	−5.78044e10	−1.94099	−0.970495	+	0.241121i	$0.922485\pi$
$984$	0	0
$985$	−4.15081e10	−1.38391
$986$	−1.41475e10	−0.470014
$987$	0	0
$988$	−2.83285e9	−0.0934488
$989$	−3.67759e9	−0.120886
$990$	0	0
$991$	−9.60474e9	−0.313493	−0.156747	−	0.987639i	$-0.550101\pi$
$991$	−9.60474e9	−0.313493	−0.156747	+	0.987639i	$0.550101\pi$
$992$	1.54082e10	0.501141
$993$	0	0
$994$	−2.61808e9	−0.0845534
$995$	4.54808e10	1.46368
$996$	0	0
$997$	−5.00503e10	−1.59946	−0.799730	−	0.600360i	$-0.795024\pi$
$997$	−5.00503e10	−1.59946	−0.799730	+	0.600360i	$0.795024\pi$
$998$	1.22405e10	0.389799
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	207.8.a.c.1.1		6
3.2	odd	2		69.8.a.b.1.6	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.8.a.b.1.6	✓	6	3.2	odd	2
207.8.a.c.1.1		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:	\( N \)	\(=\)	\( 207 = 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	207.a (trivial)

\(f(q)\)	\(=\)	\(q-16.1241 q^{2} +131.987 q^{4} +519.327 q^{5} -439.281 q^{7} -64.2798 q^{8} +O(q^{10})\)	\(q-16.1241 q^{2} +131.987 q^{4} +519.327 q^{5} -439.281 q^{7} -64.2798 q^{8} -8373.68 q^{10} +1239.00 q^{11} -886.064 q^{13} +7083.01 q^{14} -15857.8 q^{16} +33265.6 q^{17} +24223.0 q^{19} +68544.2 q^{20} -19977.7 q^{22} +12167.0 q^{23} +191576. q^{25} +14287.0 q^{26} -57979.2 q^{28} +26376.0 q^{29} +58381.7 q^{31} +263921. q^{32} -536379. q^{34} -228131. q^{35} +72694.7 q^{37} -390574. q^{38} -33382.2 q^{40} -175132. q^{41} -302259. q^{43} +163531. q^{44} -196182. q^{46} -715309. q^{47} -630575. q^{49} -3.08899e6 q^{50} -116948. q^{52} +1.15458e6 q^{53} +643444. q^{55} +28236.9 q^{56} -425289. q^{58} +1.13651e6 q^{59} +699341. q^{61} -941353. q^{62} -2.22569e6 q^{64} -460157. q^{65} -4.85518e6 q^{67} +4.39062e6 q^{68} +3.67840e6 q^{70} -369628. q^{71} +1.06243e6 q^{73} -1.17214e6 q^{74} +3.19711e6 q^{76} -544267. q^{77} +6.34807e6 q^{79} -8.23540e6 q^{80} +2.82384e6 q^{82} -9.31819e6 q^{83} +1.72758e7 q^{85} +4.87366e6 q^{86} -79642.3 q^{88} +1.25442e7 q^{89} +389231. q^{91} +1.60588e6 q^{92} +1.15337e7 q^{94} +1.25797e7 q^{95} -1.21853e7 q^{97} +1.01675e7 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 8 q^{2} + 178 q^{4} + 372 q^{5} - 1104 q^{7} + 1956 q^{8}+O(q^{10}) \) 6 * q + 8 * q^2 + 178 * q^4 + 372 * q^5 - 1104 * q^7 + 1956 * q^8	\( 6 q + 8 q^{2} + 178 q^{4} + 372 q^{5} - 1104 q^{7} + 1956 q^{8} - 13042 q^{10} + 14824 q^{11} - 756 q^{13} + 3926 q^{14} - 13022 q^{16} + 69484 q^{17} - 43864 q^{19} - 78886 q^{20} + 98204 q^{22} + 73002 q^{23} + 228018 q^{25} + 311956 q^{26} - 545442 q^{28} + 311100 q^{29} - 245248 q^{31} + 390156 q^{32} + 235834 q^{34} + 1331256 q^{35} - 630044 q^{37} - 80910 q^{38} - 2153982 q^{40} + 969204 q^{41} - 1770208 q^{43} + 1749140 q^{44} + 97336 q^{46} + 1400024 q^{47} + 1985598 q^{49} + 956660 q^{50} + 3217272 q^{52} + 1573516 q^{53} - 431296 q^{55} - 7740702 q^{56} + 5987188 q^{58} + 1410320 q^{59} - 942172 q^{61} - 3334412 q^{62} + 1996866 q^{64} + 420944 q^{65} - 452072 q^{67} + 9258254 q^{68} + 21981136 q^{70} - 122928 q^{71} + 16490716 q^{73} + 600104 q^{74} + 7428658 q^{76} - 7239696 q^{77} + 2458408 q^{79} - 19440230 q^{80} + 20510784 q^{82} + 7566456 q^{83} + 5817744 q^{85} + 669666 q^{86} + 14775668 q^{88} + 20368036 q^{89} + 8815576 q^{91} + 2165726 q^{92} + 16952576 q^{94} - 5143832 q^{95} + 12586972 q^{97} + 39164812 q^{98}+O(q^{100}) \) 6 * q + 8 * q^2 + 178 * q^4 + 372 * q^5 - 1104 * q^7 + 1956 * q^8 - 13042 * q^10 + 14824 * q^11 - 756 * q^13 + 3926 * q^14 - 13022 * q^16 + 69484 * q^17 - 43864 * q^19 - 78886 * q^20 + 98204 * q^22 + 73002 * q^23 + 228018 * q^25 + 311956 * q^26 - 545442 * q^28 + 311100 * q^29 - 245248 * q^31 + 390156 * q^32 + 235834 * q^34 + 1331256 * q^35 - 630044 * q^37 - 80910 * q^38 - 2153982 * q^40 + 969204 * q^41 - 1770208 * q^43 + 1749140 * q^44 + 97336 * q^46 + 1400024 * q^47 + 1985598 * q^49 + 956660 * q^50 + 3217272 * q^52 + 1573516 * q^53 - 431296 * q^55 - 7740702 * q^56 + 5987188 * q^58 + 1410320 * q^59 - 942172 * q^61 - 3334412 * q^62 + 1996866 * q^64 + 420944 * q^65 - 452072 * q^67 + 9258254 * q^68 + 21981136 * q^70 - 122928 * q^71 + 16490716 * q^73 + 600104 * q^74 + 7428658 * q^76 - 7239696 * q^77 + 2458408 * q^79 - 19440230 * q^80 + 20510784 * q^82 + 7566456 * q^83 + 5817744 * q^85 + 669666 * q^86 + 14775668 * q^88 + 20368036 * q^89 + 8815576 * q^91 + 2165726 * q^92 + 16952576 * q^94 - 5143832 * q^95 + 12586972 * q^97 + 39164812 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more