LMFDB - Embedded newform 207.8.a.c.1.6

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			1.6
Root			$18.9294$ 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)

$f(q)$	$=$	$q+19.9294 q^{2} +269.181 q^{4} -466.102 q^{5} -1376.23 q^{7} +2813.66 q^{8} +O(q^{10})$	\(q+19.9294 q^{2} +269.181 q^{4} -466.102 q^{5} -1376.23 q^{7} +2813.66 q^{8} -9289.15 q^{10} +6066.56 q^{11} +9371.38 q^{13} -27427.5 q^{14} +21619.3 q^{16} +31738.9 q^{17} -5025.16 q^{19} -125466. q^{20} +120903. q^{22} +12167.0 q^{23} +139126. q^{25} +186766. q^{26} -370455. q^{28} +124306. q^{29} -16099.5 q^{31} +70712.4 q^{32} +632538. q^{34} +641464. q^{35} +101300. q^{37} -100148. q^{38} -1.31145e6 q^{40} +598115. q^{41} -118931. q^{43} +1.63301e6 q^{44} +242481. q^{46} +255226. q^{47} +1.07047e6 q^{49} +2.77271e6 q^{50} +2.52260e6 q^{52} +109847. q^{53} -2.82764e6 q^{55} -3.87224e6 q^{56} +2.47734e6 q^{58} -964886. q^{59} -1.44972e6 q^{61} -320853. q^{62} -1.35802e6 q^{64} -4.36803e6 q^{65} -4.27555e6 q^{67} +8.54353e6 q^{68} +1.27840e7 q^{70} +814451. q^{71} +6.40210e6 q^{73} +2.01884e6 q^{74} -1.35268e6 q^{76} -8.34899e6 q^{77} -6.69183e6 q^{79} -1.00768e7 q^{80} +1.19201e7 q^{82} +7.15533e6 q^{83} -1.47936e7 q^{85} -2.37022e6 q^{86} +1.70692e7 q^{88} +8.17909e6 q^{89} -1.28972e7 q^{91} +3.27513e6 q^{92} +5.08650e6 q^{94} +2.34224e6 q^{95} +1.53893e7 q^{97} +2.13338e7 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	19.9294	1.76153	0.880764	−	0.473556i	$-0.157030\pi$
$2$	19.9294	1.76153	0.880764	+	0.473556i	$0.157030\pi$
$3$	0	0
$3$	0	0
$4$	269.181	2.10298
$5$	−466.102	−1.66758	−0.833789	−	0.552083i	$-0.813833\pi$
$5$	−466.102	−1.66758	−0.833789	+	0.552083i	$0.813833\pi$
$6$	0	0
$7$	−1376.23	−1.51652	−0.758260	−	0.651953i	$-0.773950\pi$
$7$	−1376.23	−1.51652	−0.758260	+	0.651953i	$0.773950\pi$
$8$	2813.66	1.94293
$9$	0	0
$10$	−9289.15	−2.93749
$11$	6066.56	1.37426	0.687129	−	0.726535i	$-0.258871\pi$
$11$	6066.56	1.37426	0.687129	+	0.726535i	$0.258871\pi$
$12$	0	0
$13$	9371.38	1.18305	0.591524	−	0.806288i	$-0.298527\pi$
$13$	9371.38	1.18305	0.591524	+	0.806288i	$0.298527\pi$
$14$	−27427.5	−2.67139
$15$	0	0
$16$	21619.3	1.31954
$17$	31738.9	1.56683	0.783414	−	0.621501i	$-0.213477\pi$
$17$	31738.9	1.56683	0.783414	+	0.621501i	$0.213477\pi$
$18$	0	0
$19$	−5025.16	−0.168079	−0.0840393	−	0.996462i	$-0.526782\pi$
$19$	−5025.16	−0.168079	−0.0840393	+	0.996462i	$0.526782\pi$
$20$	−125466.	−3.50688
$21$	0	0
$22$	120903.	2.42079
$23$	12167.0	0.208514
$23$	12167.0	0.208514
$24$	0	0
$25$	139126.	1.78082
$26$	186766.	2.08397
$27$	0	0
$28$	−370455.	−3.18921
$29$	124306.	0.946449	0.473225	−	0.880942i	$-0.343090\pi$
$29$	124306.	0.946449	0.473225	+	0.880942i	$0.343090\pi$
$30$	0	0
$31$	−16099.5	−0.0970614	−0.0485307	−	0.998822i	$-0.515454\pi$
$31$	−16099.5	−0.0970614	−0.0485307	+	0.998822i	$0.515454\pi$
$32$	70712.4	0.381479
$33$	0	0
$34$	632538.	2.76001
$35$	641464.	2.52892
$36$	0	0
$37$	101300.	0.328778	0.164389	−	0.986396i	$-0.447435\pi$
$37$	101300.	0.328778	0.164389	+	0.986396i	$0.447435\pi$
$38$	−100148.	−0.296075
$39$	0	0
$40$	−1.31145e6	−3.23998
$41$	598115.	1.35532	0.677659	−	0.735377i	$-0.262995\pi$
$41$	598115.	1.35532	0.677659	+	0.735377i	$0.262995\pi$
$42$	0	0
$43$	−118931.	−0.228115	−0.114058	−	0.993474i	$-0.536385\pi$
$43$	−118931.	−0.228115	−0.114058	+	0.993474i	$0.536385\pi$
$44$	1.63301e6	2.89004
$45$	0	0
$46$	242481.	0.367304
$47$	255226.	0.358577	0.179288	−	0.983797i	$-0.442620\pi$
$47$	255226.	0.358577	0.179288	+	0.983797i	$0.442620\pi$
$48$	0	0
$49$	1.07047e6	1.29983
$50$	2.77271e6	3.13696
$51$	0	0
$52$	2.52260e6	2.48792
$53$	109847.	0.101349	0.0506747	−	0.998715i	$-0.483863\pi$
$53$	109847.	0.101349	0.0506747	+	0.998715i	$0.483863\pi$
$54$	0	0
$55$	−2.82764e6	−2.29168
$56$	−3.87224e6	−2.94649
$57$	0	0
$58$	2.47734e6	1.66720
$59$	−964886.	−0.611637	−0.305819	−	0.952090i	$-0.598930\pi$
$59$	−964886.	−0.611637	−0.305819	+	0.952090i	$0.598930\pi$
$60$	0	0
$61$	−1.44972e6	−0.817767	−0.408884	−	0.912587i	$-0.634082\pi$
$61$	−1.44972e6	−0.817767	−0.408884	+	0.912587i	$0.634082\pi$
$62$	−320853.	−0.170976
$63$	0	0
$64$	−1.35802e6	−0.647554
$65$	−4.36803e6	−1.97282
$66$	0	0
$67$	−4.27555e6	−1.73672	−0.868361	−	0.495932i	$-0.834827\pi$
$67$	−4.27555e6	−1.73672	−0.868361	+	0.495932i	$0.834827\pi$
$68$	8.54353e6	3.29500
$69$	0	0
$70$	1.27840e7	4.45475
$71$	814451.	0.270060	0.135030	−	0.990841i	$-0.456887\pi$
$71$	814451.	0.270060	0.135030	+	0.990841i	$0.456887\pi$
$72$	0	0
$73$	6.40210e6	1.92616	0.963080	−	0.269214i	$-0.0867639\pi$
$73$	6.40210e6	1.92616	0.963080	+	0.269214i	$0.0867639\pi$
$74$	2.01884e6	0.579151
$75$	0	0
$76$	−1.35268e6	−0.353466
$77$	−8.34899e6	−2.08409
$78$	0	0
$79$	−6.69183e6	−1.52704	−0.763519	−	0.645785i	$-0.776530\pi$
$79$	−6.69183e6	−1.52704	−0.763519	+	0.645785i	$0.776530\pi$
$80$	−1.00768e7	−2.20044
$81$	0	0
$82$	1.19201e7	2.38743
$83$	7.15533e6	1.37359	0.686793	−	0.726853i	$-0.259018\pi$
$83$	7.15533e6	1.37359	0.686793	+	0.726853i	$0.259018\pi$
$84$	0	0
$85$	−1.47936e7	−2.61281
$86$	−2.37022e6	−0.401831
$87$	0	0
$88$	1.70692e7	2.67008
$89$	8.17909e6	1.22982	0.614908	−	0.788599i	$-0.289193\pi$
$89$	8.17909e6	1.22982	0.614908	+	0.788599i	$0.289193\pi$
$90$	0	0
$91$	−1.28972e7	−1.79411
$92$	3.27513e6	0.438501
$93$	0	0
$94$	5.08650e6	0.631643
$95$	2.34224e6	0.280284
$96$	0	0
$97$	1.53893e7	1.71205	0.856027	−	0.516931i	$-0.172926\pi$
$97$	1.53893e7	1.71205	0.856027	+	0.516931i	$0.172926\pi$
$98$	2.13338e7	2.28969
$99$	0	0
$100$	3.74502e7	3.74502
$101$	7.54010e6	0.728203	0.364101	−	0.931359i	$-0.381376\pi$
$101$	7.54010e6	0.728203	0.364101	+	0.931359i	$0.381376\pi$
$102$	0	0
$103$	−5.04980e6	−0.455348	−0.227674	−	0.973737i	$-0.573112\pi$
$103$	−5.04980e6	−0.455348	−0.227674	+	0.973737i	$0.573112\pi$
$104$	2.63679e7	2.29857
$105$	0	0
$106$	2.18918e6	0.178530
$107$	−9.37807e6	−0.740066	−0.370033	−	0.929019i	$-0.620654\pi$
$107$	−9.37807e6	−0.740066	−0.370033	+	0.929019i	$0.620654\pi$
$108$	0	0
$109$	−2.92944e6	−0.216667	−0.108333	−	0.994115i	$-0.534551\pi$
$109$	−2.92944e6	−0.216667	−0.108333	+	0.994115i	$0.534551\pi$
$110$	−5.63532e7	−4.03686
$111$	0	0
$112$	−2.97532e7	−2.00111
$113$	2.03016e7	1.32360	0.661800	−	0.749681i	$-0.269793\pi$
$113$	2.03016e7	1.32360	0.661800	+	0.749681i	$0.269793\pi$
$114$	0	0
$115$	−5.67107e6	−0.347714
$116$	3.34607e7	1.99036
$117$	0	0
$118$	−1.92296e7	−1.07742
$119$	−4.36801e7	−2.37612
$120$	0	0
$121$	1.73160e7	0.888586
$122$	−2.88921e7	−1.44052
$123$	0	0
$124$	−4.33368e6	−0.204118
$125$	−2.84329e7	−1.30208
$126$	0	0
$127$	−1.35596e7	−0.587400	−0.293700	−	0.955898i	$-0.594887\pi$
$127$	−1.35596e7	−0.587400	−0.293700	+	0.955898i	$0.594887\pi$
$128$	−3.61157e7	−1.52216
$129$	0	0
$130$	−8.70521e7	−3.47518
$131$	−411901.	−0.0160082	−0.00800411	−	0.999968i	$-0.502548\pi$
$131$	−411901.	−0.0160082	−0.00800411	+	0.999968i	$0.502548\pi$
$132$	0	0
$133$	6.91578e6	0.254894
$134$	−8.52092e7	−3.05928
$135$	0	0
$136$	8.93025e7	3.04423
$137$	−5.98529e7	−1.98867	−0.994337	−	0.106274i	$-0.966108\pi$
$137$	−5.98529e7	−1.98867	−0.994337	+	0.106274i	$0.966108\pi$
$138$	0	0
$139$	5.65384e7	1.78563	0.892815	−	0.450423i	$-0.148727\pi$
$139$	5.65384e7	1.78563	0.892815	+	0.450423i	$0.148727\pi$
$140$	1.72670e8	5.31825
$141$	0	0
$142$	1.62315e7	0.475719
$143$	5.68521e7	1.62581
$144$	0	0
$145$	−5.79391e7	−1.57828
$146$	1.27590e8	3.39298
$147$	0	0
$148$	2.72680e7	0.691412
$149$	3.55040e7	0.879275	0.439638	−	0.898175i	$-0.355107\pi$
$149$	3.55040e7	0.879275	0.439638	+	0.898175i	$0.355107\pi$
$150$	0	0
$151$	1.69536e7	0.400721	0.200361	−	0.979722i	$-0.435789\pi$
$151$	1.69536e7	0.400721	0.200361	+	0.979722i	$0.435789\pi$
$152$	−1.41391e7	−0.326564
$153$	0	0
$154$	−1.66390e8	−3.67118
$155$	7.50401e6	0.161857
$156$	0	0
$157$	5.44237e7	1.12238	0.561189	−	0.827688i	$-0.310344\pi$
$157$	5.44237e7	1.12238	0.561189	+	0.827688i	$0.310344\pi$
$158$	−1.33364e8	−2.68992
$159$	0	0
$160$	−3.29592e7	−0.636146
$161$	−1.67446e7	−0.316216
$162$	0	0
$163$	−1.51739e7	−0.274436	−0.137218	−	0.990541i	$-0.543816\pi$
$163$	−1.51739e7	−0.274436	−0.137218	+	0.990541i	$0.543816\pi$
$164$	1.61001e8	2.85020
$165$	0	0
$166$	1.42601e8	2.41961
$167$	2.89893e7	0.481649	0.240824	−	0.970569i	$-0.422582\pi$
$167$	2.89893e7	0.481649	0.240824	+	0.970569i	$0.422582\pi$
$168$	0	0
$169$	2.50743e7	0.399600
$170$	−2.94828e8	−4.60253
$171$	0	0
$172$	−3.20139e7	−0.479721
$173$	−1.52831e7	−0.224413	−0.112207	−	0.993685i	$-0.535792\pi$
$173$	−1.52831e7	−0.224413	−0.112207	+	0.993685i	$0.535792\pi$
$174$	0	0
$175$	−1.91470e8	−2.70065
$176$	1.31155e8	1.81339
$177$	0	0
$178$	1.63004e8	2.16635
$179$	1.01079e8	1.31727	0.658635	−	0.752463i	$-0.271134\pi$
$179$	1.01079e8	1.31727	0.658635	+	0.752463i	$0.271134\pi$
$180$	0	0
$181$	4.91643e6	0.0616276	0.0308138	−	0.999525i	$-0.490190\pi$
$181$	4.91643e6	0.0616276	0.0308138	+	0.999525i	$0.490190\pi$
$182$	−2.57033e8	−3.16038
$183$	0	0
$184$	3.42338e7	0.405128
$185$	−4.72160e7	−0.548263
$186$	0	0
$187$	1.92546e8	2.15323
$188$	6.87020e7	0.754080
$189$	0	0
$190$	4.66794e7	0.493728
$191$	6.54949e7	0.680128	0.340064	−	0.940402i	$-0.389551\pi$
$191$	6.54949e7	0.680128	0.340064	+	0.940402i	$0.389551\pi$
$192$	0	0
$193$	2.61850e7	0.262182	0.131091	−	0.991370i	$-0.458152\pi$
$193$	2.61850e7	0.262182	0.131091	+	0.991370i	$0.458152\pi$
$194$	3.06699e8	3.01583
$195$	0	0
$196$	2.88150e8	2.73352
$197$	−4.80412e7	−0.447695	−0.223848	−	0.974624i	$-0.571862\pi$
$197$	−4.80412e7	−0.447695	−0.223848	+	0.974624i	$0.571862\pi$
$198$	0	0
$199$	1.05462e7	0.0948664	0.0474332	−	0.998874i	$-0.484896\pi$
$199$	1.05462e7	0.0948664	0.0474332	+	0.998874i	$0.484896\pi$
$200$	3.91454e8	3.46000
$201$	0	0
$202$	1.50270e8	1.28275
$203$	−1.71073e8	−1.43531
$204$	0	0
$205$	−2.78783e8	−2.26010
$206$	−1.00639e8	−0.802108
$207$	0	0
$208$	2.02603e8	1.56108
$209$	−3.04854e7	−0.230983
$210$	0	0
$211$	9.30256e7	0.681733	0.340866	−	0.940112i	$-0.389280\pi$
$211$	9.30256e7	0.681733	0.340866	+	0.940112i	$0.389280\pi$
$212$	2.95687e7	0.213136
$213$	0	0
$214$	−1.86899e8	−1.30365
$215$	5.54339e7	0.380400
$216$	0	0
$217$	2.21566e7	0.147195
$218$	−5.83821e7	−0.381665
$219$	0	0
$220$	−7.61148e8	−4.81936
$221$	2.97438e8	1.85363
$222$	0	0
$223$	−1.33339e8	−0.805176	−0.402588	−	0.915381i	$-0.631889\pi$
$223$	−1.33339e8	−0.805176	−0.402588	+	0.915381i	$0.631889\pi$
$224$	−9.73165e7	−0.578520
$225$	0	0
$226$	4.04600e8	2.33156
$227$	−2.24477e8	−1.27374	−0.636872	−	0.770970i	$-0.719772\pi$
$227$	−2.24477e8	−1.27374	−0.636872	+	0.770970i	$0.719772\pi$
$228$	0	0
$229$	−2.59953e8	−1.43045	−0.715223	−	0.698897i	$-0.753675\pi$
$229$	−2.59953e8	−1.43045	−0.715223	+	0.698897i	$0.753675\pi$
$230$	−1.13021e8	−0.612508
$231$	0	0
$232$	3.49753e8	1.83888
$233$	5.23601e7	0.271178	0.135589	−	0.990765i	$-0.456707\pi$
$233$	5.23601e7	0.271178	0.135589	+	0.990765i	$0.456707\pi$
$234$	0	0
$235$	−1.18961e8	−0.597955
$236$	−2.59729e8	−1.28626
$237$	0	0
$238$	−8.70518e8	−4.18561
$239$	−3.85956e8	−1.82871	−0.914357	−	0.404910i	$-0.867303\pi$
$239$	−3.85956e8	−1.82871	−0.914357	+	0.404910i	$0.867303\pi$
$240$	0	0
$241$	4.72252e7	0.217327	0.108664	−	0.994079i	$-0.465343\pi$
$241$	4.72252e7	0.217327	0.108664	+	0.994079i	$0.465343\pi$
$242$	3.45098e8	1.56527
$243$	0	0
$244$	−3.90237e8	−1.71975
$245$	−4.98947e8	−2.16757
$246$	0	0
$247$	−4.70927e7	−0.198845
$248$	−4.52985e7	−0.188583
$249$	0	0
$250$	−5.66652e8	−2.29364
$251$	−4.32121e7	−0.172484	−0.0862418	−	0.996274i	$-0.527486\pi$
$251$	−4.32121e7	−0.172484	−0.0862418	+	0.996274i	$0.527486\pi$
$252$	0	0
$253$	7.38119e7	0.286553
$254$	−2.70235e8	−1.03472
$255$	0	0
$256$	−5.45938e8	−2.03378
$257$	3.37491e8	1.24021	0.620106	−	0.784518i	$-0.287089\pi$
$257$	3.37491e8	1.24021	0.620106	+	0.784518i	$0.287089\pi$
$258$	0	0
$259$	−1.39412e8	−0.498598
$260$	−1.17579e9	−4.14881
$261$	0	0
$262$	−8.20894e6	−0.0281989
$263$	1.49351e8	0.506249	0.253125	−	0.967434i	$-0.418542\pi$
$263$	1.49351e8	0.506249	0.253125	+	0.967434i	$0.418542\pi$
$264$	0	0
$265$	−5.11998e7	−0.169008
$266$	1.37827e8	0.449003
$267$	0	0
$268$	−1.15090e9	−3.65229
$269$	−3.20872e8	−1.00508	−0.502538	−	0.864555i	$-0.667600\pi$
$269$	−3.20872e8	−1.00508	−0.502538	+	0.864555i	$0.667600\pi$
$270$	0	0
$271$	2.45542e7	0.0749433	0.0374716	−	0.999298i	$-0.488070\pi$
$271$	2.45542e7	0.0749433	0.0374716	+	0.999298i	$0.488070\pi$
$272$	6.86175e8	2.06749
$273$	0	0
$274$	−1.19283e9	−3.50310
$275$	8.44020e8	2.44731
$276$	0	0
$277$	2.99640e8	0.847072	0.423536	−	0.905879i	$-0.360789\pi$
$277$	2.99640e8	0.847072	0.423536	+	0.905879i	$0.360789\pi$
$278$	1.12678e9	3.14544
$279$	0	0
$280$	1.80486e9	4.91350
$281$	−2.26970e8	−0.610235	−0.305117	−	0.952315i	$-0.598696\pi$
$281$	−2.26970e8	−0.610235	−0.305117	+	0.952315i	$0.598696\pi$
$282$	0	0
$283$	7.55768e7	0.198215	0.0991073	−	0.995077i	$-0.468401\pi$
$283$	7.55768e7	0.198215	0.0991073	+	0.995077i	$0.468401\pi$
$284$	2.19235e8	0.567931
$285$	0	0
$286$	1.13303e9	2.86391
$287$	−8.23144e8	−2.05536
$288$	0	0
$289$	5.97021e8	1.45495
$290$	−1.15469e9	−2.78018
$291$	0	0
$292$	1.72333e9	4.05067
$293$	−7.83295e8	−1.81923	−0.909617	−	0.415448i	$-0.863625\pi$
$293$	−7.83295e8	−1.81923	−0.909617	+	0.415448i	$0.863625\pi$
$294$	0	0
$295$	4.49736e8	1.01995
$296$	2.85023e8	0.638791
$297$	0	0
$298$	7.07573e8	1.54887
$299$	1.14022e8	0.246682
$300$	0	0
$301$	1.63676e8	0.345941
$302$	3.37875e8	0.705881
$303$	0	0
$304$	−1.08641e8	−0.221786
$305$	6.75718e8	1.36369
$306$	0	0
$307$	4.64667e7	0.0916554	0.0458277	−	0.998949i	$-0.485407\pi$
$307$	4.64667e7	0.0916554	0.0458277	+	0.998949i	$0.485407\pi$
$308$	−2.24739e9	−4.38279
$309$	0	0
$310$	1.49551e8	0.285116
$311$	−9.79489e7	−0.184645	−0.0923227	−	0.995729i	$-0.529429\pi$
$311$	−9.79489e7	−0.184645	−0.0923227	+	0.995729i	$0.529429\pi$
$312$	0	0
$313$	−7.03146e8	−1.29610	−0.648052	−	0.761596i	$-0.724416\pi$
$313$	−7.03146e8	−1.29610	−0.648052	+	0.761596i	$0.724416\pi$
$314$	1.08463e9	1.97710
$315$	0	0
$316$	−1.80131e9	−3.21133
$317$	−1.51468e8	−0.267064	−0.133532	−	0.991045i	$-0.542632\pi$
$317$	−1.51468e8	−0.267064	−0.133532	+	0.991045i	$0.542632\pi$
$318$	0	0
$319$	7.54107e8	1.30067
$320$	6.32976e8	1.07985
$321$	0	0
$322$	−3.33710e8	−0.557023
$323$	−1.59493e8	−0.263350
$324$	0	0
$325$	1.30381e9	2.10679
$326$	−3.02408e8	−0.483427
$327$	0	0
$328$	1.68289e9	2.63328
$329$	−3.51250e8	−0.543789
$330$	0	0
$331$	−3.67566e8	−0.557105	−0.278552	−	0.960421i	$-0.589855\pi$
$331$	−3.67566e8	−0.557105	−0.278552	+	0.960421i	$0.589855\pi$
$332$	1.92608e9	2.88862
$333$	0	0
$334$	5.77740e8	0.848438
$335$	1.99285e9	2.89612
$336$	0	0
$337$	−3.50623e8	−0.499041	−0.249521	−	0.968370i	$-0.580273\pi$
$337$	−3.50623e8	−0.499041	−0.249521	+	0.968370i	$0.580273\pi$
$338$	4.99716e8	0.703907
$339$	0	0
$340$	−3.98216e9	−5.49468
$341$	−9.76686e7	−0.133387
$342$	0	0
$343$	−3.39824e8	−0.454699
$344$	−3.34630e8	−0.443211
$345$	0	0
$346$	−3.04582e8	−0.395310
$347$	−8.21515e7	−0.105551	−0.0527755	−	0.998606i	$-0.516807\pi$
$347$	−8.21515e7	−0.105551	−0.0527755	+	0.998606i	$0.516807\pi$
$348$	0	0
$349$	5.47670e8	0.689652	0.344826	−	0.938667i	$-0.387938\pi$
$349$	5.47670e8	0.689652	0.344826	+	0.938667i	$0.387938\pi$
$350$	−3.81589e9	−4.75726
$351$	0	0
$352$	4.28981e8	0.524251
$353$	−7.05195e8	−0.853292	−0.426646	−	0.904419i	$-0.640305\pi$
$353$	−7.05195e8	−0.853292	−0.426646	+	0.904419i	$0.640305\pi$
$354$	0	0
$355$	−3.79618e8	−0.450347
$356$	2.20166e9	2.58628
$357$	0	0
$358$	2.01444e9	2.32041
$359$	6.05279e8	0.690438	0.345219	−	0.938522i	$-0.387805\pi$
$359$	6.05279e8	0.690438	0.345219	+	0.938522i	$0.387805\pi$
$360$	0	0
$361$	−8.68620e8	−0.971750
$362$	9.79816e7	0.108559
$363$	0	0
$364$	−3.47168e9	−3.77298
$365$	−2.98404e9	−3.21202
$366$	0	0
$367$	−4.00347e8	−0.422771	−0.211386	−	0.977403i	$-0.567798\pi$
$367$	−4.00347e8	−0.422771	−0.211386	+	0.977403i	$0.567798\pi$
$368$	2.63043e8	0.275143
$369$	0	0
$370$	−9.40988e8	−0.965779
$371$	−1.51174e8	−0.153698
$372$	0	0
$373$	7.43740e8	0.742063	0.371031	−	0.928620i	$-0.379004\pi$
$373$	7.43740e8	0.742063	0.371031	+	0.928620i	$0.379004\pi$
$374$	3.83733e9	3.79297
$375$	0	0
$376$	7.18119e8	0.696689
$377$	1.16491e9	1.11969
$378$	0	0
$379$	1.08034e9	1.01935	0.509676	−	0.860366i	$-0.329765\pi$
$379$	1.08034e9	1.01935	0.509676	+	0.860366i	$0.329765\pi$
$380$	6.30487e8	0.589432
$381$	0	0
$382$	1.30528e9	1.19806
$383$	−1.83043e9	−1.66478	−0.832389	−	0.554192i	$-0.813027\pi$
$383$	−1.83043e9	−1.66478	−0.832389	+	0.554192i	$0.813027\pi$
$384$	0	0
$385$	3.89148e9	3.47538
$386$	5.21852e8	0.461840
$387$	0	0
$388$	4.14251e9	3.60041
$389$	9.20484e8	0.792853	0.396426	−	0.918066i	$-0.370250\pi$
$389$	9.20484e8	0.792853	0.396426	+	0.918066i	$0.370250\pi$
$390$	0	0
$391$	3.86168e8	0.326706
$392$	3.01193e9	2.52548
$393$	0	0
$394$	−9.57433e8	−0.788627
$395$	3.11908e9	2.54646
$396$	0	0
$397$	1.68258e9	1.34961	0.674807	−	0.737995i	$-0.264227\pi$
$397$	1.68258e9	1.34961	0.674807	+	0.737995i	$0.264227\pi$
$398$	2.10180e8	0.167110
$399$	0	0
$400$	3.00782e9	2.34986
$401$	−1.78289e9	−1.38076	−0.690381	−	0.723446i	$-0.742557\pi$
$401$	−1.78289e9	−1.38076	−0.690381	+	0.723446i	$0.742557\pi$
$402$	0	0
$403$	−1.50875e8	−0.114828
$404$	2.02965e9	1.53139
$405$	0	0
$406$	−3.40938e9	−2.52834
$407$	6.14541e8	0.451825
$408$	0	0
$409$	−1.62476e9	−1.17425	−0.587123	−	0.809498i	$-0.699739\pi$
$409$	−1.62476e9	−1.17425	−0.587123	+	0.809498i	$0.699739\pi$
$410$	−5.55597e9	−3.98123
$411$	0	0
$412$	−1.35931e9	−0.957587
$413$	1.32790e9	0.927559
$414$	0	0
$415$	−3.33512e9	−2.29056
$416$	6.62673e8	0.451308
$417$	0	0
$418$	−6.07557e8	−0.406883
$419$	−2.24799e9	−1.49295	−0.746476	−	0.665412i	$-0.768256\pi$
$419$	−2.24799e9	−1.49295	−0.746476	+	0.665412i	$0.768256\pi$
$420$	0	0
$421$	3.33475e8	0.217809	0.108904	−	0.994052i	$-0.465266\pi$
$421$	3.33475e8	0.217809	0.108904	+	0.994052i	$0.465266\pi$
$422$	1.85395e9	1.20089
$423$	0	0
$424$	3.09071e8	0.196915
$425$	4.41573e9	2.79024
$426$	0	0
$427$	1.99515e9	1.24016
$428$	−2.52440e9	−1.55634
$429$	0	0
$430$	1.10476e9	0.670085
$431$	2.33004e9	1.40182	0.700910	−	0.713249i	$-0.252777\pi$
$431$	2.33004e9	1.40182	0.700910	+	0.713249i	$0.252777\pi$
$432$	0	0
$433$	1.82844e8	0.108237	0.0541183	−	0.998535i	$-0.482765\pi$
$433$	1.82844e8	0.108237	0.0541183	+	0.998535i	$0.482765\pi$
$434$	4.41568e8	0.259289
$435$	0	0
$436$	−7.88551e8	−0.455646
$437$	−6.11411e7	−0.0350468
$438$	0	0
$439$	−1.41207e9	−0.796580	−0.398290	−	0.917260i	$-0.630396\pi$
$439$	−1.41207e9	−0.796580	−0.398290	+	0.917260i	$0.630396\pi$
$440$	−7.95601e9	−4.45257
$441$	0	0
$442$	5.92776e9	3.26522
$443$	−6.88910e8	−0.376487	−0.188243	−	0.982122i	$-0.560279\pi$
$443$	−6.88910e8	−0.376487	−0.188243	+	0.982122i	$0.560279\pi$
$444$	0	0
$445$	−3.81230e9	−2.05082
$446$	−2.65737e9	−1.41834
$447$	0	0
$448$	1.86895e9	0.982029
$449$	6.50678e8	0.339238	0.169619	−	0.985510i	$-0.445746\pi$
$449$	6.50678e8	0.339238	0.169619	+	0.985510i	$0.445746\pi$
$450$	0	0
$451$	3.62850e9	1.86256
$452$	5.46482e9	2.78350
$453$	0	0
$454$	−4.47370e9	−2.24373
$455$	6.01141e9	2.99183
$456$	0	0
$457$	−1.61945e9	−0.793708	−0.396854	−	0.917882i	$-0.629898\pi$
$457$	−1.61945e9	−0.793708	−0.396854	+	0.917882i	$0.629898\pi$
$458$	−5.18072e9	−2.51977
$459$	0	0
$460$	−1.52655e9	−0.731236
$461$	6.21807e8	0.295599	0.147799	−	0.989017i	$-0.452781\pi$
$461$	6.21807e8	0.295599	0.147799	+	0.989017i	$0.452781\pi$
$462$	0	0
$463$	2.85900e9	1.33869	0.669347	−	0.742950i	$-0.266574\pi$
$463$	2.85900e9	1.33869	0.669347	+	0.742950i	$0.266574\pi$
$464$	2.68740e9	1.24888
$465$	0	0
$466$	1.04351e9	0.477688
$467$	−1.28603e9	−0.584309	−0.292154	−	0.956371i	$-0.594372\pi$
$467$	−1.28603e9	−0.584309	−0.292154	+	0.956371i	$0.594372\pi$
$468$	0	0
$469$	5.88415e9	2.63377
$470$	−2.37083e9	−1.05331
$471$	0	0
$472$	−2.71486e9	−1.18837
$473$	−7.21500e8	−0.313489
$474$	0	0
$475$	−6.99133e8	−0.299317
$476$	−1.17579e10	−4.99694
$477$	0	0
$478$	−7.69188e9	−3.22133
$479$	3.90154e9	1.62204	0.811021	−	0.585017i	$-0.198912\pi$
$479$	3.90154e9	1.62204	0.811021	+	0.585017i	$0.198912\pi$
$480$	0	0
$481$	9.49319e8	0.388959
$482$	9.41170e8	0.382828
$483$	0	0
$484$	4.66115e9	1.86868
$485$	−7.17299e9	−2.85499
$486$	0	0
$487$	−2.21345e9	−0.868397	−0.434199	−	0.900817i	$-0.642968\pi$
$487$	−2.21345e9	−0.868397	−0.434199	+	0.900817i	$0.642968\pi$
$488$	−4.07902e9	−1.58886
$489$	0	0
$490$	−9.94372e9	−3.81823
$491$	4.33060e9	1.65106	0.825530	−	0.564358i	$-0.190876\pi$
$491$	4.33060e9	1.65106	0.825530	+	0.564358i	$0.190876\pi$
$492$	0	0
$493$	3.94532e9	1.48292
$494$	−9.38530e8	−0.350271
$495$	0	0
$496$	−3.48061e8	−0.128076
$497$	−1.12087e9	−0.409552
$498$	0	0
$499$	−1.11601e9	−0.402085	−0.201042	−	0.979583i	$-0.564433\pi$
$499$	−1.11601e9	−0.402085	−0.201042	+	0.979583i	$0.564433\pi$
$500$	−7.65362e9	−2.73824
$501$	0	0
$502$	−8.61192e8	−0.303834
$503$	5.61394e9	1.96689	0.983444	−	0.181212i	$-0.0580019\pi$
$503$	5.61394e9	1.96689	0.983444	+	0.181212i	$0.0580019\pi$
$504$	0	0
$505$	−3.51446e9	−1.21434
$506$	1.47103e9	0.504770
$507$	0	0
$508$	−3.64999e9	−1.23529
$509$	−9.54298e8	−0.320754	−0.160377	−	0.987056i	$-0.551271\pi$
$509$	−9.54298e8	−0.320754	−0.160377	+	0.987056i	$0.551271\pi$
$510$	0	0
$511$	−8.81077e9	−2.92106
$512$	−6.25741e9	−2.06039
$513$	0	0
$514$	6.72600e9	2.18467
$515$	2.35372e9	0.759329
$516$	0	0
$517$	1.54834e9	0.492777
$518$	−2.77839e9	−0.878293
$519$	0	0
$520$	−1.22901e10	−3.83305
$521$	3.27349e9	1.01409	0.507047	−	0.861918i	$-0.330737\pi$
$521$	3.27349e9	1.01409	0.507047	+	0.861918i	$0.330737\pi$
$522$	0	0
$523$	3.35615e9	1.02585	0.512927	−	0.858432i	$-0.328561\pi$
$523$	3.35615e9	1.02585	0.512927	+	0.858432i	$0.328561\pi$
$524$	−1.10876e8	−0.0336649
$525$	0	0
$526$	2.97649e9	0.891772
$527$	−5.10981e8	−0.152078
$528$	0	0
$529$	1.48036e8	0.0434783
$530$	−1.02038e9	−0.297713
$531$	0	0
$532$	1.86160e9	0.536037
$533$	5.60516e9	1.60340
$534$	0	0
$535$	4.37114e9	1.23412
$536$	−1.20299e10	−3.37433
$537$	0	0
$538$	−6.39479e9	−1.77047
$539$	6.49405e9	1.78630
$540$	0	0
$541$	−2.62460e9	−0.712643	−0.356321	−	0.934363i	$-0.615969\pi$
$541$	−2.62460e9	−0.712643	−0.356321	+	0.934363i	$0.615969\pi$
$542$	4.89350e8	0.132015
$543$	0	0
$544$	2.24434e9	0.597712
$545$	1.36542e9	0.361309
$546$	0	0
$547$	1.01462e9	0.265063	0.132532	−	0.991179i	$-0.457689\pi$
$547$	1.01462e9	0.265063	0.132532	+	0.991179i	$0.457689\pi$
$548$	−1.61113e10	−4.18214
$549$	0	0
$550$	1.68208e10	4.31100
$551$	−6.24655e8	−0.159078
$552$	0	0
$553$	9.20949e9	2.31578
$554$	5.97164e9	1.49214
$555$	0	0
$556$	1.52191e10	3.75514
$557$	−2.67923e9	−0.656926	−0.328463	−	0.944517i	$-0.606531\pi$
$557$	−2.67923e9	−0.656926	−0.328463	+	0.944517i	$0.606531\pi$
$558$	0	0
$559$	−1.11454e9	−0.269871
$560$	1.38680e10	3.33700
$561$	0	0
$562$	−4.52338e9	−1.07494
$563$	−3.37265e9	−0.796512	−0.398256	−	0.917274i	$-0.630384\pi$
$563$	−3.37265e9	−0.796512	−0.398256	+	0.917274i	$0.630384\pi$
$564$	0	0
$565$	−9.46264e9	−2.20721
$566$	1.50620e9	0.349161
$567$	0	0
$568$	2.29159e9	0.524707
$569$	−5.59018e9	−1.27213	−0.636067	−	0.771634i	$-0.719440\pi$
$569$	−5.59018e9	−1.27213	−0.636067	+	0.771634i	$0.719440\pi$
$570$	0	0
$571$	−1.53052e9	−0.344043	−0.172022	−	0.985093i	$-0.555030\pi$
$571$	−1.53052e9	−0.344043	−0.172022	+	0.985093i	$0.555030\pi$
$572$	1.53035e10	3.41905
$573$	0	0
$574$	−1.64048e10	−3.62058
$575$	1.69275e9	0.371326
$576$	0	0
$577$	−2.33744e9	−0.506554	−0.253277	−	0.967394i	$-0.581508\pi$
$577$	−2.33744e9	−0.506554	−0.253277	+	0.967394i	$0.581508\pi$
$578$	1.18983e10	2.56293
$579$	0	0
$580$	−1.55961e10	−3.31909
$581$	−9.84738e9	−2.08307
$582$	0	0
$583$	6.66392e8	0.139280
$584$	1.80133e10	3.74239
$585$	0	0
$586$	−1.56106e10	−3.20463
$587$	3.31061e9	0.675578	0.337789	−	0.941222i	$-0.390321\pi$
$587$	3.31061e9	0.675578	0.337789	+	0.941222i	$0.390321\pi$
$588$	0	0
$589$	8.09025e7	0.0163139
$590$	8.96296e9	1.79668
$591$	0	0
$592$	2.19003e9	0.433835
$593$	−8.44516e8	−0.166309	−0.0831546	−	0.996537i	$-0.526500\pi$
$593$	−8.44516e8	−0.166309	−0.0831546	+	0.996537i	$0.526500\pi$
$594$	0	0
$595$	2.03594e10	3.96237
$596$	9.55700e9	1.84910
$597$	0	0
$598$	2.27238e9	0.434538
$599$	−5.48397e9	−1.04256	−0.521280	−	0.853386i	$-0.674545\pi$
$599$	−5.48397e9	−1.04256	−0.521280	+	0.853386i	$0.674545\pi$
$600$	0	0
$601$	−1.01235e10	−1.90225	−0.951127	−	0.308801i	$-0.900072\pi$
$601$	−1.01235e10	−1.90225	−0.951127	+	0.308801i	$0.900072\pi$
$602$	3.26196e9	0.609385
$603$	0	0
$604$	4.56359e9	0.842708
$605$	−8.07104e9	−1.48179
$606$	0	0
$607$	−6.01963e9	−1.09247	−0.546235	−	0.837632i	$-0.683939\pi$
$607$	−6.01963e9	−1.09247	−0.546235	+	0.837632i	$0.683939\pi$
$608$	−3.55341e8	−0.0641184
$609$	0	0
$610$	1.34667e10	2.40218
$611$	2.39182e9	0.424213
$612$	0	0
$613$	1.95203e9	0.342274	0.171137	−	0.985247i	$-0.445256\pi$
$613$	1.95203e9	0.342274	0.171137	+	0.985247i	$0.445256\pi$
$614$	9.26055e8	0.161453
$615$	0	0
$616$	−2.34912e10	−4.04923
$617$	−9.76165e8	−0.167311	−0.0836556	−	0.996495i	$-0.526660\pi$
$617$	−9.76165e8	−0.167311	−0.0836556	+	0.996495i	$0.526660\pi$
$618$	0	0
$619$	−2.48694e9	−0.421452	−0.210726	−	0.977545i	$-0.567583\pi$
$619$	−2.48694e9	−0.421452	−0.210726	+	0.977545i	$0.567583\pi$
$620$	2.01994e9	0.340383
$621$	0	0
$622$	−1.95206e9	−0.325258
$623$	−1.12563e10	−1.86504
$624$	0	0
$625$	2.38341e9	0.390498
$626$	−1.40133e10	−2.28312
$627$	0	0
$628$	1.46498e10	2.36034
$629$	3.21515e9	0.515138
$630$	0	0
$631$	3.03958e9	0.481627	0.240813	−	0.970571i	$-0.422586\pi$
$631$	3.03958e9	0.481627	0.240813	+	0.970571i	$0.422586\pi$
$632$	−1.88285e10	−2.96692
$633$	0	0
$634$	−3.01868e9	−0.470440
$635$	6.32016e9	0.979536
$636$	0	0
$637$	1.00318e10	1.53776
$638$	1.50289e10	2.29116
$639$	0	0
$640$	1.68336e10	2.53833
$641$	1.19765e10	1.79609	0.898046	−	0.439902i	$-0.144987\pi$
$641$	1.19765e10	1.79609	0.898046	+	0.439902i	$0.144987\pi$
$642$	0	0
$643$	4.75355e9	0.705146	0.352573	−	0.935784i	$-0.385307\pi$
$643$	4.75355e9	0.705146	0.352573	+	0.935784i	$0.385307\pi$
$644$	−4.50733e9	−0.664996
$645$	0	0
$646$	−3.17860e9	−0.463898
$647$	−2.68173e9	−0.389269	−0.194635	−	0.980876i	$-0.562352\pi$
$647$	−2.68173e9	−0.389269	−0.194635	+	0.980876i	$0.562352\pi$
$648$	0	0
$649$	−5.85354e9	−0.840547
$650$	2.59841e10	3.71117
$651$	0	0
$652$	−4.08454e9	−0.577134
$653$	−2.10661e9	−0.296065	−0.148033	−	0.988982i	$-0.547294\pi$
$653$	−2.10661e9	−0.296065	−0.148033	+	0.988982i	$0.547294\pi$
$654$	0	0
$655$	1.91988e8	0.0266950
$656$	1.29308e10	1.78840
$657$	0	0
$658$	−7.00020e9	−0.957899
$659$	−1.10631e10	−1.50583	−0.752916	−	0.658117i	$-0.771353\pi$
$659$	−1.10631e10	−1.50583	−0.752916	+	0.658117i	$0.771353\pi$
$660$	0	0
$661$	−1.11027e10	−1.49528	−0.747641	−	0.664103i	$-0.768814\pi$
$661$	−1.11027e10	−1.49528	−0.747641	+	0.664103i	$0.768814\pi$
$662$	−7.32537e9	−0.981356
$663$	0	0
$664$	2.01326e10	2.66878
$665$	−3.22346e9	−0.425056
$666$	0	0
$667$	1.51243e9	0.197348
$668$	7.80338e9	1.01290
$669$	0	0
$670$	3.97162e10	5.10160
$671$	−8.79482e9	−1.12382
$672$	0	0
$673$	2.54772e9	0.322180	0.161090	−	0.986940i	$-0.448499\pi$
$673$	2.54772e9	0.322180	0.161090	+	0.986940i	$0.448499\pi$
$674$	−6.98772e9	−0.879074
$675$	0	0
$676$	6.74954e9	0.840351
$677$	1.21766e10	1.50822	0.754112	−	0.656745i	$-0.228067\pi$
$677$	1.21766e10	1.50822	0.754112	+	0.656745i	$0.228067\pi$
$678$	0	0
$679$	−2.11792e10	−2.59636
$680$	−4.16241e10	−5.07649
$681$	0	0
$682$	−1.94648e9	−0.234965
$683$	9.17376e9	1.10173	0.550864	−	0.834595i	$-0.314298\pi$
$683$	9.17376e9	1.10173	0.550864	+	0.834595i	$0.314298\pi$
$684$	0	0
$685$	2.78976e10	3.31627
$686$	−6.77248e9	−0.800965
$687$	0	0
$688$	−2.57120e9	−0.301007
$689$	1.02942e9	0.119901
$690$	0	0
$691$	2.31775e8	0.0267235	0.0133617	−	0.999911i	$-0.495747\pi$
$691$	2.31775e8	0.0267235	0.0133617	+	0.999911i	$0.495747\pi$
$692$	−4.11391e9	−0.471936
$693$	0	0
$694$	−1.63723e9	−0.185931
$695$	−2.63527e10	−2.97768
$696$	0	0
$697$	1.89835e10	2.12355
$698$	1.09147e10	1.21484
$699$	0	0
$700$	−5.15402e10	−5.67940
$701$	5.45607e9	0.598228	0.299114	−	0.954217i	$-0.403309\pi$
$701$	5.45607e9	0.598228	0.299114	+	0.954217i	$0.403309\pi$
$702$	0	0
$703$	−5.09047e8	−0.0552604
$704$	−8.23851e9	−0.889907
$705$	0	0
$706$	−1.40541e10	−1.50310
$707$	−1.03769e10	−1.10433
$708$	0	0
$709$	−1.56400e9	−0.164807	−0.0824034	−	0.996599i	$-0.526260\pi$
$709$	−1.56400e9	−0.164807	−0.0824034	+	0.996599i	$0.526260\pi$
$710$	−7.56556e9	−0.793298
$711$	0	0
$712$	2.30132e10	2.38944
$713$	−1.95883e8	−0.0202387
$714$	0	0
$715$	−2.64989e10	−2.71117
$716$	2.72085e10	2.77019
$717$	0	0
$718$	1.20628e10	1.21623
$719$	1.01004e9	0.101341	0.0506706	−	0.998715i	$-0.483864\pi$
$719$	1.01004e9	0.101341	0.0506706	+	0.998715i	$0.483864\pi$
$720$	0	0
$721$	6.94968e9	0.690544
$722$	−1.73111e10	−1.71176
$723$	0	0
$724$	1.32341e9	0.129601
$725$	1.72942e10	1.68546
$726$	0	0
$727$	2.06395e8	0.0199218	0.00996091	−	0.999950i	$-0.496829\pi$
$727$	2.06395e8	0.0199218	0.00996091	+	0.999950i	$0.496829\pi$
$728$	−3.62883e10	−3.48583
$729$	0	0
$730$	−5.94700e10	−5.65807
$731$	−3.77473e9	−0.357417
$732$	0	0
$733$	−1.37499e10	−1.28954	−0.644772	−	0.764375i	$-0.723048\pi$
$733$	−1.37499e10	−1.28954	−0.644772	+	0.764375i	$0.723048\pi$
$734$	−7.97868e9	−0.744723
$735$	0	0
$736$	8.60358e8	0.0795439
$737$	−2.59379e10	−2.38671
$738$	0	0
$739$	−1.08060e10	−0.984937	−0.492469	−	0.870330i	$-0.663905\pi$
$739$	−1.08060e10	−0.984937	−0.492469	+	0.870330i	$0.663905\pi$
$740$	−1.27097e10	−1.15298
$741$	0	0
$742$	−3.01282e9	−0.270744
$743$	6.51922e9	0.583088	0.291544	−	0.956557i	$-0.405831\pi$
$743$	6.51922e9	0.583088	0.291544	+	0.956557i	$0.405831\pi$
$744$	0	0
$745$	−1.65485e10	−1.46626
$746$	1.48223e10	1.30716
$747$	0	0
$748$	5.18298e10	4.52819
$749$	1.29064e10	1.12232
$750$	0	0
$751$	−4.66797e9	−0.402150	−0.201075	−	0.979576i	$-0.564443\pi$
$751$	−4.66797e9	−0.402150	−0.201075	+	0.979576i	$0.564443\pi$
$752$	5.51782e9	0.473157
$753$	0	0
$754$	2.32161e10	1.97237
$755$	−7.90211e9	−0.668234
$756$	0	0
$757$	1.84301e10	1.54416	0.772079	−	0.635526i	$-0.219217\pi$
$757$	1.84301e10	1.54416	0.772079	+	0.635526i	$0.219217\pi$
$758$	2.15306e10	1.79562
$759$	0	0
$760$	6.59026e9	0.544572
$761$	−6.60838e9	−0.543561	−0.271781	−	0.962359i	$-0.587613\pi$
$761$	−6.60838e9	−0.543561	−0.271781	+	0.962359i	$0.587613\pi$
$762$	0	0
$763$	4.03159e9	0.328579
$764$	1.76300e10	1.43030
$765$	0	0
$766$	−3.64793e10	−2.93255
$767$	−9.04231e9	−0.723595
$768$	0	0
$769$	1.51293e10	1.19971	0.599857	−	0.800107i	$-0.295224\pi$
$769$	1.51293e10	1.19971	0.599857	+	0.800107i	$0.295224\pi$
$770$	7.75550e10	6.12198
$771$	0	0
$772$	7.04851e9	0.551362
$773$	1.46251e10	1.13886	0.569432	−	0.822039i	$-0.307163\pi$
$773$	1.46251e10	1.13886	0.569432	+	0.822039i	$0.307163\pi$
$774$	0	0
$775$	−2.23987e9	−0.172849
$776$	4.33002e10	3.32640
$777$	0	0
$778$	1.83447e10	1.39663
$779$	−3.00562e9	−0.227800
$780$	0	0
$781$	4.94092e9	0.371133
$782$	7.69609e9	0.575502
$783$	0	0
$784$	2.31428e10	1.71518
$785$	−2.53670e10	−1.87165
$786$	0	0
$787$	−7.19809e9	−0.526387	−0.263194	−	0.964743i	$-0.584776\pi$
$787$	−7.19809e9	−0.526387	−0.263194	+	0.964743i	$0.584776\pi$
$788$	−1.29318e10	−0.941493
$789$	0	0
$790$	6.21613e10	4.48565
$791$	−2.79397e10	−2.00726
$792$	0	0
$793$	−1.35859e10	−0.967457
$794$	3.35328e10	2.37738
$795$	0	0
$796$	2.83885e9	0.199502
$797$	8.60373e9	0.601981	0.300990	−	0.953627i	$-0.402683\pi$
$797$	8.60373e9	0.601981	0.300990	+	0.953627i	$0.402683\pi$
$798$	0	0
$799$	8.10060e9	0.561828
$800$	9.83797e9	0.679345
$801$	0	0
$802$	−3.55319e10	−2.43225
$803$	3.88388e10	2.64704
$804$	0	0
$805$	7.80470e9	0.527315
$806$	−3.00684e9	−0.202273
$807$	0	0
$808$	2.12153e10	1.41484
$809$	−2.23111e10	−1.48150	−0.740748	−	0.671783i	$-0.765529\pi$
$809$	−2.23111e10	−1.48150	−0.740748	+	0.671783i	$0.765529\pi$
$810$	0	0
$811$	6.50028e9	0.427917	0.213958	−	0.976843i	$-0.431364\pi$
$811$	6.50028e9	0.427917	0.213958	+	0.976843i	$0.431364\pi$
$812$	−4.60496e10	−3.01842
$813$	0	0
$814$	1.22474e10	0.795903
$815$	7.07261e9	0.457644
$816$	0	0
$817$	5.97646e8	0.0383413
$818$	−3.23806e10	−2.06846
$819$	0	0
$820$	−7.50431e10	−4.75294
$821$	−7.01294e9	−0.442282	−0.221141	−	0.975242i	$-0.570978\pi$
$821$	−7.01294e9	−0.442282	−0.221141	+	0.975242i	$0.570978\pi$
$822$	0	0
$823$	−1.67931e10	−1.05010	−0.525051	−	0.851071i	$-0.675954\pi$
$823$	−1.67931e10	−1.05010	−0.525051	+	0.851071i	$0.675954\pi$
$824$	−1.42084e10	−0.884708
$825$	0	0
$826$	2.64644e10	1.63392
$827$	−5.65627e9	−0.347745	−0.173872	−	0.984768i	$-0.555628\pi$
$827$	−5.65627e9	−0.347745	−0.173872	+	0.984768i	$0.555628\pi$
$828$	0	0
$829$	8.59914e9	0.524220	0.262110	−	0.965038i	$-0.415582\pi$
$829$	8.59914e9	0.524220	0.262110	+	0.965038i	$0.415582\pi$
$830$	−6.64669e10	−4.03489
$831$	0	0
$832$	−1.27265e10	−0.766087
$833$	3.39755e10	2.03661
$834$	0	0
$835$	−1.35120e10	−0.803187
$836$	−8.20611e9	−0.485753
$837$	0	0
$838$	−4.48012e10	−2.62988
$839$	1.50648e10	0.880636	0.440318	−	0.897842i	$-0.354866\pi$
$839$	1.50648e10	0.880636	0.440318	+	0.897842i	$0.354866\pi$
$840$	0	0
$841$	−1.79802e9	−0.104234
$842$	6.64595e9	0.383676
$843$	0	0
$844$	2.50408e10	1.43367
$845$	−1.16872e10	−0.666365
$846$	0	0
$847$	−2.38308e10	−1.34756
$848$	2.37481e9	0.133735
$849$	0	0
$850$	8.80028e10	4.91508
$851$	1.23251e9	0.0685549
$852$	0	0
$853$	−1.71226e10	−0.944598	−0.472299	−	0.881438i	$-0.656576\pi$
$853$	−1.71226e10	−0.944598	−0.472299	+	0.881438i	$0.656576\pi$
$854$	3.97621e10	2.18458
$855$	0	0
$856$	−2.63867e10	−1.43789
$857$	2.12967e10	1.15579	0.577897	−	0.816110i	$-0.303874\pi$
$857$	2.12967e10	1.15579	0.577897	+	0.816110i	$0.303874\pi$
$858$	0	0
$859$	−1.57530e10	−0.847981	−0.423990	−	0.905667i	$-0.639371\pi$
$859$	−1.57530e10	−0.847981	−0.423990	+	0.905667i	$0.639371\pi$
$860$	1.49218e10	0.799973
$861$	0	0
$862$	4.64363e10	2.46935
$863$	−2.32739e10	−1.23263	−0.616313	−	0.787501i	$-0.711374\pi$
$863$	−2.32739e10	−1.23263	−0.616313	+	0.787501i	$0.711374\pi$
$864$	0	0
$865$	7.12347e9	0.374227
$866$	3.64398e9	0.190662
$867$	0	0
$868$	5.96414e9	0.309549
$869$	−4.05964e10	−2.09854
$870$	0	0
$871$	−4.00679e10	−2.05462
$872$	−8.24245e9	−0.420968
$873$	0	0
$874$	−1.21851e9	−0.0617359
$875$	3.91303e10	1.97463
$876$	0	0
$877$	−9.84011e9	−0.492608	−0.246304	−	0.969193i	$-0.579216\pi$
$877$	−9.84011e9	−0.492608	−0.246304	+	0.969193i	$0.579216\pi$
$878$	−2.81416e10	−1.40320
$879$	0	0
$880$	−6.11317e10	−3.02397
$881$	2.40556e10	1.18522	0.592611	−	0.805489i	$-0.298097\pi$
$881$	2.40556e10	1.18522	0.592611	+	0.805489i	$0.298097\pi$
$882$	0	0
$883$	4.99537e9	0.244177	0.122089	−	0.992519i	$-0.461041\pi$
$883$	4.99537e9	0.244177	0.122089	+	0.992519i	$0.461041\pi$
$884$	8.00647e10	3.89814
$885$	0	0
$886$	−1.37296e10	−0.663192
$887$	4.68695e9	0.225506	0.112753	−	0.993623i	$-0.464033\pi$
$887$	4.68695e9	0.225506	0.112753	+	0.993623i	$0.464033\pi$
$888$	0	0
$889$	1.86611e10	0.890803
$890$	−7.59768e10	−3.61257
$891$	0	0
$892$	−3.58924e10	−1.69327
$893$	−1.28255e9	−0.0602691
$894$	0	0
$895$	−4.71131e10	−2.19665
$896$	4.97035e10	2.30839
$897$	0	0
$898$	1.29676e10	0.597577
$899$	−2.00126e9	−0.0918637
$900$	0	0
$901$	3.48642e9	0.158797
$902$	7.23139e10	3.28094
$903$	0	0
$904$	5.71219e10	2.57166
$905$	−2.29156e9	−0.102769
$906$	0	0
$907$	2.14893e10	0.956304	0.478152	−	0.878277i	$-0.341307\pi$
$907$	2.14893e10	0.956304	0.478152	+	0.878277i	$0.341307\pi$
$908$	−6.04251e10	−2.67865
$909$	0	0
$910$	1.19804e11	5.27018
$911$	−3.15925e10	−1.38443	−0.692214	−	0.721693i	$-0.743364\pi$
$911$	−3.15925e10	−1.38443	−0.692214	+	0.721693i	$0.743364\pi$
$912$	0	0
$913$	4.34082e10	1.88766
$914$	−3.22747e10	−1.39814
$915$	0	0
$916$	−6.99746e10	−3.00820
$917$	5.66870e8	0.0242768
$918$	0	0
$919$	−1.58869e10	−0.675205	−0.337603	−	0.941289i	$-0.609616\pi$
$919$	−1.58869e10	−0.675205	−0.337603	+	0.941289i	$0.609616\pi$
$920$	−1.59564e10	−0.675583
$921$	0	0
$922$	1.23922e10	0.520705
$923$	7.63254e9	0.319494
$924$	0	0
$925$	1.40935e10	0.585493
$926$	5.69782e10	2.35815
$927$	0	0
$928$	8.78994e9	0.361051
$929$	4.25155e10	1.73977	0.869886	−	0.493253i	$-0.164192\pi$
$929$	4.25155e10	1.73977	0.869886	+	0.493253i	$0.164192\pi$
$930$	0	0
$931$	−5.37927e9	−0.218474
$932$	1.40944e10	0.570282
$933$	0	0
$934$	−2.56298e10	−1.02928
$935$	−8.97463e10	−3.59067
$936$	0	0
$937$	−1.52382e9	−0.0605126	−0.0302563	−	0.999542i	$-0.509632\pi$
$937$	−1.52382e9	−0.0605126	−0.0302563	+	0.999542i	$0.509632\pi$
$938$	1.17268e11	4.63946
$939$	0	0
$940$	−3.20222e10	−1.25749
$941$	−3.98090e10	−1.55746	−0.778732	−	0.627357i	$-0.784137\pi$
$941$	−3.98090e10	−1.55746	−0.778732	+	0.627357i	$0.784137\pi$
$942$	0	0
$943$	7.27726e9	0.282603
$944$	−2.08602e10	−0.807080
$945$	0	0
$946$	−1.43791e10	−0.552220
$947$	−1.71695e9	−0.0656949	−0.0328475	−	0.999460i	$-0.510458\pi$
$947$	−1.71695e9	−0.0656949	−0.0328475	+	0.999460i	$0.510458\pi$
$948$	0	0
$949$	5.99966e10	2.27874
$950$	−1.39333e10	−0.527256
$951$	0	0
$952$	−1.22901e11	−4.61663
$953$	2.93461e10	1.09831	0.549155	−	0.835721i	$-0.314950\pi$
$953$	2.93461e10	1.09831	0.549155	+	0.835721i	$0.314950\pi$
$954$	0	0
$955$	−3.05274e10	−1.13417
$956$	−1.03892e11	−3.84574
$957$	0	0
$958$	7.77554e10	2.85727
$959$	8.23714e10	3.01586
$960$	0	0
$961$	−2.72534e10	−0.990579
$962$	1.89194e10	0.685163
$963$	0	0
$964$	1.27121e10	0.457034
$965$	−1.22049e10	−0.437209
$966$	0	0
$967$	1.69145e10	0.601543	0.300771	−	0.953696i	$-0.402756\pi$
$967$	1.69145e10	0.601543	0.300771	+	0.953696i	$0.402756\pi$
$968$	4.87214e10	1.72646
$969$	0	0
$970$	−1.42953e11	−5.02913
$971$	3.82953e9	0.134239	0.0671195	−	0.997745i	$-0.478619\pi$
$971$	3.82953e9	0.134239	0.0671195	+	0.997745i	$0.478619\pi$
$972$	0	0
$973$	−7.78098e10	−2.70794
$974$	−4.41127e10	−1.52971
$975$	0	0
$976$	−3.13420e10	−1.07908
$977$	3.33271e10	1.14332	0.571658	−	0.820492i	$-0.306300\pi$
$977$	3.33271e10	1.14332	0.571658	+	0.820492i	$0.306300\pi$
$978$	0	0
$979$	4.96190e10	1.69008
$980$	−1.34307e11	−4.55835
$981$	0	0
$982$	8.63063e10	2.90839
$983$	−1.71429e10	−0.575634	−0.287817	−	0.957685i	$-0.592930\pi$
$983$	−1.71429e10	−0.575634	−0.287817	+	0.957685i	$0.592930\pi$
$984$	0	0
$985$	2.23921e10	0.746567
$986$	7.86280e10	2.61221
$987$	0	0
$988$	−1.26765e10	−0.418166
$989$	−1.44703e9	−0.0475653
$990$	0	0
$991$	4.73510e10	1.54551	0.772755	−	0.634705i	$-0.218878\pi$
$991$	4.73510e10	1.54551	0.772755	+	0.634705i	$0.218878\pi$
$992$	−1.13843e9	−0.0370269
$993$	0	0
$994$	−2.23383e10	−0.721437
$995$	−4.91563e9	−0.158197
$996$	0	0
$997$	−2.46977e10	−0.789267	−0.394634	−	0.918839i	$-0.629128\pi$
$997$	−2.46977e10	−0.789267	−0.394634	+	0.918839i	$0.629128\pi$
$998$	−2.22415e10	−0.708283
$999$	0	0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.8.a.b.1.1	✓	6	3.2	odd	2
207.8.a.c.1.6		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)

\(f(q)\)	\(=\)	\(q+19.9294 q^{2} +269.181 q^{4} -466.102 q^{5} -1376.23 q^{7} +2813.66 q^{8} +O(q^{10})\)	\(q+19.9294 q^{2} +269.181 q^{4} -466.102 q^{5} -1376.23 q^{7} +2813.66 q^{8} -9289.15 q^{10} +6066.56 q^{11} +9371.38 q^{13} -27427.5 q^{14} +21619.3 q^{16} +31738.9 q^{17} -5025.16 q^{19} -125466. q^{20} +120903. q^{22} +12167.0 q^{23} +139126. q^{25} +186766. q^{26} -370455. q^{28} +124306. q^{29} -16099.5 q^{31} +70712.4 q^{32} +632538. q^{34} +641464. q^{35} +101300. q^{37} -100148. q^{38} -1.31145e6 q^{40} +598115. q^{41} -118931. q^{43} +1.63301e6 q^{44} +242481. q^{46} +255226. q^{47} +1.07047e6 q^{49} +2.77271e6 q^{50} +2.52260e6 q^{52} +109847. q^{53} -2.82764e6 q^{55} -3.87224e6 q^{56} +2.47734e6 q^{58} -964886. q^{59} -1.44972e6 q^{61} -320853. q^{62} -1.35802e6 q^{64} -4.36803e6 q^{65} -4.27555e6 q^{67} +8.54353e6 q^{68} +1.27840e7 q^{70} +814451. q^{71} +6.40210e6 q^{73} +2.01884e6 q^{74} -1.35268e6 q^{76} -8.34899e6 q^{77} -6.69183e6 q^{79} -1.00768e7 q^{80} +1.19201e7 q^{82} +7.15533e6 q^{83} -1.47936e7 q^{85} -2.37022e6 q^{86} +1.70692e7 q^{88} +8.17909e6 q^{89} -1.28972e7 q^{91} +3.27513e6 q^{92} +5.08650e6 q^{94} +2.34224e6 q^{95} +1.53893e7 q^{97} +2.13338e7 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 8 q^{2} + 178 q^{4} + 372 q^{5} - 1104 q^{7} + 1956 q^{8}+O(q^{10}) \) 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

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