LMFDB - Embedded newform 531.8.a.b.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [531,8,Mod(1,531)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(531, 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("531.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 531 = 3^{2} \cdot 59 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	531.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:	$165.876448532$
Analytic rank:	$1$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6 x^{15} - 1493 x^{14} + 8791 x^{13} + 890490 x^{12} - 5107725 x^{11} - 269092298 x^{10} + \cdots - 23\!\cdots\!32 $ x^16 - 6x^15 - 1493x^14 + 8791x^13 + 890490x^12 - 5107725x^11 - 269092298x^10 + 1488374176x^9 + 42885295136x^8 - 226132003872x^7 - 3353576629440x^6 + 16796366777600x^5 + 99470801612800x^4 - 494039551757568x^3 - 493048066650624x^2 + 3193975642099712*x - 2385018853548032
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{9}\cdot 3^{5} $
Twist minimal:	no (minimal twist has level 177)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Root			$14.7989$ of defining polynomial
Character	$\chi$	$=$	531.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+14.7989 q^{2} +91.0084 q^{4} +296.536 q^{5} -1410.76 q^{7} -547.437 q^{8} +O(q^{10})$	\(q+14.7989 q^{2} +91.0084 q^{4} +296.536 q^{5} -1410.76 q^{7} -547.437 q^{8} +4388.42 q^{10} +7538.45 q^{11} +7066.47 q^{13} -20877.7 q^{14} -19750.5 q^{16} -14832.8 q^{17} -24023.8 q^{19} +26987.3 q^{20} +111561. q^{22} -41590.5 q^{23} +9808.63 q^{25} +104576. q^{26} -128391. q^{28} -15791.6 q^{29} +108246. q^{31} -222215. q^{32} -219509. q^{34} -418341. q^{35} +331221. q^{37} -355527. q^{38} -162335. q^{40} -224396. q^{41} -134226. q^{43} +686063. q^{44} -615494. q^{46} -816259. q^{47} +1.16670e6 q^{49} +145157. q^{50} +643108. q^{52} -1.21786e6 q^{53} +2.23542e6 q^{55} +772301. q^{56} -233699. q^{58} -205379. q^{59} +1.88156e6 q^{61} +1.60193e6 q^{62} -760476. q^{64} +2.09546e6 q^{65} -2.09166e6 q^{67} -1.34991e6 q^{68} -6.19100e6 q^{70} +1.80830e6 q^{71} -4.93066e6 q^{73} +4.90172e6 q^{74} -2.18637e6 q^{76} -1.06349e7 q^{77} -8.26089e6 q^{79} -5.85675e6 q^{80} -3.32083e6 q^{82} +2.95933e6 q^{83} -4.39846e6 q^{85} -1.98640e6 q^{86} -4.12683e6 q^{88} -3.82628e6 q^{89} -9.96908e6 q^{91} -3.78508e6 q^{92} -1.20798e7 q^{94} -7.12393e6 q^{95} -6.24098e6 q^{97} +1.72659e7 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 6 q^{2} + 974 q^{4} + 68 q^{5} - 2343 q^{7} - 819 q^{8}+O(q^{10}) $ 16 * q + 6 * q^2 + 974 * q^4 + 68 * q^5 - 2343 * q^7 - 819 * q^8	\( 16 q + 6 q^{2} + 974 q^{4} + 68 q^{5} - 2343 q^{7} - 819 q^{8} - 3479 q^{10} - 898 q^{11} - 8172 q^{13} + 13315 q^{14} + 3138 q^{16} + 44985 q^{17} - 40137 q^{19} - 130657 q^{20} + 109394 q^{22} + 2833 q^{23} + 285746 q^{25} + 129420 q^{26} + 112890 q^{28} - 144375 q^{29} - 141759 q^{31} + 36224 q^{32} - 341332 q^{34} + 78859 q^{35} - 297971 q^{37} - 329075 q^{38} - 203048 q^{40} - 659077 q^{41} - 1431608 q^{43} - 254916 q^{44} + 873113 q^{46} + 1574073 q^{47} + 1893545 q^{49} - 302533 q^{50} - 4972548 q^{52} - 587736 q^{53} - 4624036 q^{55} + 5798506 q^{56} - 6991380 q^{58} - 3286064 q^{59} - 6117131 q^{61} + 11570258 q^{62} - 19063011 q^{64} + 5335514 q^{65} - 16518710 q^{67} + 17284669 q^{68} - 39189486 q^{70} + 10882582 q^{71} - 21097441 q^{73} + 16717030 q^{74} - 40864952 q^{76} + 3404601 q^{77} - 3784458 q^{79} + 27466195 q^{80} - 24990117 q^{82} + 1951425 q^{83} - 23238675 q^{85} + 35910572 q^{86} - 27843055 q^{88} - 10499443 q^{89} + 699217 q^{91} + 20062766 q^{92} - 59358988 q^{94} + 29236333 q^{95} - 25158976 q^{97} - 2120460 q^{98}+O(q^{100}) \) 16 * q + 6 * q^2 + 974 * q^4 + 68 * q^5 - 2343 * q^7 - 819 * q^8 - 3479 * q^10 - 898 * q^11 - 8172 * q^13 + 13315 * q^14 + 3138 * q^16 + 44985 * q^17 - 40137 * q^19 - 130657 * q^20 + 109394 * q^22 + 2833 * q^23 + 285746 * q^25 + 129420 * q^26 + 112890 * q^28 - 144375 * q^29 - 141759 * q^31 + 36224 * q^32 - 341332 * q^34 + 78859 * q^35 - 297971 * q^37 - 329075 * q^38 - 203048 * q^40 - 659077 * q^41 - 1431608 * q^43 - 254916 * q^44 + 873113 * q^46 + 1574073 * q^47 + 1893545 * q^49 - 302533 * q^50 - 4972548 * q^52 - 587736 * q^53 - 4624036 * q^55 + 5798506 * q^56 - 6991380 * q^58 - 3286064 * q^59 - 6117131 * q^61 + 11570258 * q^62 - 19063011 * q^64 + 5335514 * q^65 - 16518710 * q^67 + 17284669 * q^68 - 39189486 * q^70 + 10882582 * q^71 - 21097441 * q^73 + 16717030 * q^74 - 40864952 * q^76 + 3404601 * q^77 - 3784458 * q^79 + 27466195 * q^80 - 24990117 * q^82 + 1951425 * q^83 - 23238675 * q^85 + 35910572 * q^86 - 27843055 * q^88 - 10499443 * q^89 + 699217 * q^91 + 20062766 * q^92 - 59358988 * q^94 + 29236333 * q^95 - 25158976 * q^97 - 2120460 * 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 $

$2$	14.7989	1.30805	0.654027	−	0.756472i	$-0.273078\pi$
$2$	14.7989	1.30805	0.654027	+	0.756472i	$0.273078\pi$
$3$	0	0
$3$	0	0
$4$	91.0084	0.711003
$5$	296.536	1.06092	0.530460	−	0.847710i	$-0.322019\pi$
$5$	296.536	1.06092	0.530460	+	0.847710i	$0.322019\pi$
$6$	0	0
$7$	−1410.76	−1.55457	−0.777284	−	0.629150i	$-0.783403\pi$
$7$	−1410.76	−1.55457	−0.777284	+	0.629150i	$0.783403\pi$
$8$	−547.437	−0.378024
$9$	0	0
$10$	4388.42	1.38774
$11$	7538.45	1.70769	0.853843	−	0.520531i	$-0.174266\pi$
$11$	7538.45	1.70769	0.853843	+	0.520531i	$0.174266\pi$
$12$	0	0
$13$	7066.47	0.892073	0.446037	−	0.895015i	$-0.352835\pi$
$13$	7066.47	0.892073	0.446037	+	0.895015i	$0.352835\pi$
$14$	−20877.7	−2.03346
$15$	0	0
$16$	−19750.5	−1.20548
$17$	−14832.8	−0.732237	−0.366118	−	0.930568i	$-0.619313\pi$
$17$	−14832.8	−0.732237	−0.366118	+	0.930568i	$0.619313\pi$
$18$	0	0
$19$	−24023.8	−0.803535	−0.401767	−	0.915742i	$-0.631604\pi$
$19$	−24023.8	−0.803535	−0.401767	+	0.915742i	$0.631604\pi$
$20$	26987.3	0.754317
$21$	0	0
$22$	111561.	2.23374
$23$	−41590.5	−0.712765	−0.356382	−	0.934340i	$-0.615990\pi$
$23$	−41590.5	−0.712765	−0.356382	+	0.934340i	$0.615990\pi$
$24$	0	0
$25$	9808.63	0.125550
$26$	104576.	1.16688
$27$	0	0
$28$	−128391.	−1.10530
$29$	−15791.6	−0.120235	−0.0601177	−	0.998191i	$-0.519148\pi$
$29$	−15791.6	−0.120235	−0.0601177	+	0.998191i	$0.519148\pi$
$30$	0	0
$31$	108246.	0.652601	0.326300	−	0.945266i	$-0.394198\pi$
$31$	108246.	0.652601	0.326300	+	0.945266i	$0.394198\pi$
$32$	−222215.	−1.19881
$33$	0	0
$34$	−219509.	−0.957805
$35$	−418341.	−1.64927
$36$	0	0
$37$	331221.	1.07501	0.537504	−	0.843261i	$-0.319367\pi$
$37$	331221.	1.07501	0.537504	+	0.843261i	$0.319367\pi$
$38$	−355527.	−1.05107
$39$	0	0
$40$	−162335.	−0.401053
$41$	−224396.	−0.508478	−0.254239	−	0.967141i	$-0.581825\pi$
$41$	−224396.	−0.508478	−0.254239	+	0.967141i	$0.581825\pi$
$42$	0	0
$43$	−134226.	−0.257453	−0.128726	−	0.991680i	$-0.541089\pi$
$43$	−134226.	−0.257453	−0.128726	+	0.991680i	$0.541089\pi$
$44$	686063.	1.21417
$45$	0	0
$46$	−615494.	−0.932334
$47$	−816259.	−1.14679	−0.573397	−	0.819278i	$-0.694375\pi$
$47$	−816259.	−1.14679	−0.573397	+	0.819278i	$0.694375\pi$
$48$	0	0
$49$	1.16670e6	1.41668
$50$	145157.	0.164227
$51$	0	0
$52$	643108.	0.634267
$53$	−1.21786e6	−1.12365	−0.561825	−	0.827256i	$-0.689900\pi$
$53$	−1.21786e6	−1.12365	−0.561825	+	0.827256i	$0.689900\pi$
$54$	0	0
$55$	2.23542e6	1.81172
$56$	772301.	0.587663
$57$	0	0
$58$	−233699.	−0.157274
$59$	−205379.	−0.130189
$59$	−205379.	−0.130189
$60$	0	0
$61$	1.88156e6	1.06136	0.530681	−	0.847571i	$-0.321936\pi$
$61$	1.88156e6	1.06136	0.530681	+	0.847571i	$0.321936\pi$
$62$	1.60193e6	0.853637
$63$	0	0
$64$	−760476.	−0.362623
$65$	2.09546e6	0.946418
$66$	0	0
$67$	−2.09166e6	−0.849627	−0.424814	−	0.905281i	$-0.639660\pi$
$67$	−2.09166e6	−0.849627	−0.424814	+	0.905281i	$0.639660\pi$
$68$	−1.34991e6	−0.520622
$69$	0	0
$70$	−6.19100e6	−2.15734
$71$	1.80830e6	0.599605	0.299802	−	0.954001i	$-0.403079\pi$
$71$	1.80830e6	0.599605	0.299802	+	0.954001i	$0.403079\pi$
$72$	0	0
$73$	−4.93066e6	−1.48346	−0.741729	−	0.670699i	$-0.765994\pi$
$73$	−4.93066e6	−1.48346	−0.741729	+	0.670699i	$0.765994\pi$
$74$	4.90172e6	1.40617
$75$	0	0
$76$	−2.18637e6	−0.571316
$77$	−1.06349e7	−2.65471
$78$	0	0
$79$	−8.26089e6	−1.88509	−0.942545	−	0.334078i	$-0.891575\pi$
$79$	−8.26089e6	−1.88509	−0.942545	+	0.334078i	$0.891575\pi$
$80$	−5.85675e6	−1.27892
$81$	0	0
$82$	−3.32083e6	−0.665116
$83$	2.95933e6	0.568093	0.284047	−	0.958810i	$-0.408323\pi$
$83$	2.95933e6	0.568093	0.284047	+	0.958810i	$0.408323\pi$
$84$	0	0
$85$	−4.39846e6	−0.776844
$86$	−1.98640e6	−0.336762
$87$	0	0
$88$	−4.12683e6	−0.645545
$89$	−3.82628e6	−0.575323	−0.287661	−	0.957732i	$-0.592878\pi$
$89$	−3.82628e6	−0.575323	−0.287661	+	0.957732i	$0.592878\pi$
$90$	0	0
$91$	−9.96908e6	−1.38679
$92$	−3.78508e6	−0.506778
$93$	0	0
$94$	−1.20798e7	−1.50007
$95$	−7.12393e6	−0.852486
$96$	0	0
$97$	−6.24098e6	−0.694308	−0.347154	−	0.937808i	$-0.612852\pi$
$97$	−6.24098e6	−0.694308	−0.347154	+	0.937808i	$0.612852\pi$
$98$	1.72659e7	1.85310
$99$	0	0
$100$	892667.	0.0892667
$101$	−1.50527e7	−1.45375	−0.726873	−	0.686772i	$-0.759027\pi$
$101$	−1.50527e7	−1.45375	−0.726873	+	0.686772i	$0.759027\pi$
$102$	0	0
$103$	1.06416e7	0.959572	0.479786	−	0.877386i	$-0.340714\pi$
$103$	1.06416e7	0.959572	0.479786	+	0.877386i	$0.340714\pi$
$104$	−3.86844e6	−0.337225
$105$	0	0
$106$	−1.80230e7	−1.46979
$107$	1.71933e7	1.35680	0.678402	−	0.734691i	$-0.262673\pi$
$107$	1.71933e7	1.35680	0.678402	+	0.734691i	$0.262673\pi$
$108$	0	0
$109$	−2.61258e7	−1.93231	−0.966154	−	0.257968i	$-0.916947\pi$
$109$	−2.61258e7	−1.93231	−0.966154	+	0.257968i	$0.916947\pi$
$110$	3.30819e7	2.36982
$111$	0	0
$112$	2.78633e7	1.87400
$113$	−1.49158e7	−0.972463	−0.486231	−	0.873830i	$-0.661629\pi$
$113$	−1.49158e7	−0.972463	−0.486231	+	0.873830i	$0.661629\pi$
$114$	0	0
$115$	−1.23331e7	−0.756186
$116$	−1.43717e6	−0.0854878
$117$	0	0
$118$	−3.03939e6	−0.170294
$119$	2.09255e7	1.13831
$120$	0	0
$121$	3.73411e7	1.91619
$122$	2.78451e7	1.38832
$123$	0	0
$124$	9.85133e6	0.464001
$125$	−2.02583e7	−0.927721
$126$	0	0
$127$	−1.99083e7	−0.862426	−0.431213	−	0.902250i	$-0.641914\pi$
$127$	−1.99083e7	−0.862426	−0.431213	+	0.902250i	$0.641914\pi$
$128$	1.71893e7	0.724475
$129$	0	0
$130$	3.10106e7	1.23797
$131$	−2.18462e7	−0.849038	−0.424519	−	0.905419i	$-0.639557\pi$
$131$	−2.18462e7	−0.849038	−0.424519	+	0.905419i	$0.639557\pi$
$132$	0	0
$133$	3.38918e7	1.24915
$134$	−3.09543e7	−1.11136
$135$	0	0
$136$	8.12001e6	0.276803
$137$	1.96904e7	0.654233	0.327117	−	0.944984i	$-0.393923\pi$
$137$	1.96904e7	0.654233	0.327117	+	0.944984i	$0.393923\pi$
$138$	0	0
$139$	2.42247e6	0.0765078	0.0382539	−	0.999268i	$-0.487820\pi$
$139$	2.42247e6	0.0765078	0.0382539	+	0.999268i	$0.487820\pi$
$140$	−3.80725e7	−1.17264
$141$	0	0
$142$	2.67608e7	0.784315
$143$	5.32702e7	1.52338
$144$	0	0
$145$	−4.68277e6	−0.127560
$146$	−7.29686e7	−1.94044
$147$	0	0
$148$	3.01439e7	0.764334
$149$	−2.09513e7	−0.518871	−0.259436	−	0.965760i	$-0.583537\pi$
$149$	−2.09513e7	−0.518871	−0.259436	+	0.965760i	$0.583537\pi$
$150$	0	0
$151$	4.77834e6	0.112943	0.0564713	−	0.998404i	$-0.482015\pi$
$151$	4.77834e6	0.112943	0.0564713	+	0.998404i	$0.482015\pi$
$152$	1.31515e7	0.303755
$153$	0	0
$154$	−1.57386e8	−3.47251
$155$	3.20990e7	0.692357
$156$	0	0
$157$	−6.17818e7	−1.27412	−0.637062	−	0.770813i	$-0.719850\pi$
$157$	−6.17818e7	−1.27412	−0.637062	+	0.770813i	$0.719850\pi$
$158$	−1.22252e8	−2.46580
$159$	0	0
$160$	−6.58948e7	−1.27184
$161$	5.86741e7	1.10804
$162$	0	0
$163$	8.27535e7	1.49668	0.748342	−	0.663313i	$-0.230850\pi$
$163$	8.27535e7	1.49668	0.748342	+	0.663313i	$0.230850\pi$
$164$	−2.04219e7	−0.361529
$165$	0	0
$166$	4.37949e7	0.743096
$167$	1.39381e7	0.231578	0.115789	−	0.993274i	$-0.463060\pi$
$167$	1.39381e7	0.231578	0.115789	+	0.993274i	$0.463060\pi$
$168$	0	0
$169$	−1.28136e7	−0.204205
$170$	−6.50925e7	−1.01615
$171$	0	0
$172$	−1.22157e7	−0.183049
$173$	−9.03037e7	−1.32600	−0.663001	−	0.748618i	$-0.730718\pi$
$173$	−9.03037e7	−1.32600	−0.663001	+	0.748618i	$0.730718\pi$
$174$	0	0
$175$	−1.38376e7	−0.195177
$176$	−1.48889e8	−2.05858
$177$	0	0
$178$	−5.66248e7	−0.752553
$179$	−9.61633e7	−1.25321	−0.626605	−	0.779337i	$-0.715556\pi$
$179$	−9.61633e7	−1.25321	−0.626605	+	0.779337i	$0.715556\pi$
$180$	0	0
$181$	1.27453e8	1.59763	0.798816	−	0.601575i	$-0.205460\pi$
$181$	1.27453e8	1.59763	0.798816	+	0.601575i	$0.205460\pi$
$182$	−1.47532e8	−1.81399
$183$	0	0
$184$	2.27681e7	0.269442
$185$	9.82189e7	1.14050
$186$	0	0
$187$	−1.11816e8	−1.25043
$188$	−7.42864e7	−0.815374
$189$	0	0
$190$	−1.05427e8	−1.11510
$191$	−8.72604e6	−0.0906151	−0.0453075	−	0.998973i	$-0.514427\pi$
$191$	−8.72604e6	−0.0906151	−0.0453075	+	0.998973i	$0.514427\pi$
$192$	0	0
$193$	6.92616e7	0.693492	0.346746	−	0.937959i	$-0.387287\pi$
$193$	6.92616e7	0.693492	0.346746	+	0.937959i	$0.387287\pi$
$194$	−9.23599e7	−0.908191
$195$	0	0
$196$	1.06179e8	1.00726
$197$	−1.99367e7	−0.185790	−0.0928949	−	0.995676i	$-0.529612\pi$
$197$	−1.99367e7	−0.185790	−0.0928949	+	0.995676i	$0.529612\pi$
$198$	0	0
$199$	−1.15995e8	−1.04341	−0.521705	−	0.853126i	$-0.674704\pi$
$199$	−1.15995e8	−1.04341	−0.521705	+	0.853126i	$0.674704\pi$
$200$	−5.36960e6	−0.0474610
$201$	0	0
$202$	−2.22763e8	−1.90158
$203$	2.22781e7	0.186914
$204$	0	0
$205$	−6.65416e7	−0.539454
$206$	1.57485e8	1.25517
$207$	0	0
$208$	−1.39567e8	−1.07537
$209$	−1.81103e8	−1.37218
$210$	0	0
$211$	6.67529e7	0.489195	0.244597	−	0.969625i	$-0.421344\pi$
$211$	6.67529e7	0.489195	0.244597	+	0.969625i	$0.421344\pi$
$212$	−1.10835e8	−0.798918
$213$	0	0
$214$	2.54443e8	1.77477
$215$	−3.98029e7	−0.273136
$216$	0	0
$217$	−1.52710e8	−1.01451
$218$	−3.86633e8	−2.52756
$219$	0	0
$220$	2.03442e8	1.28814
$221$	−1.04815e8	−0.653209
$222$	0	0
$223$	1.76404e8	1.06522	0.532611	−	0.846360i	$-0.321211\pi$
$223$	1.76404e8	1.06522	0.532611	+	0.846360i	$0.321211\pi$
$224$	3.13492e8	1.86362
$225$	0	0
$226$	−2.20738e8	−1.27203
$227$	1.70858e8	0.969491	0.484745	−	0.874655i	$-0.338912\pi$
$227$	1.70858e8	0.969491	0.484745	+	0.874655i	$0.338912\pi$
$228$	0	0
$229$	−1.06631e8	−0.586757	−0.293379	−	0.955996i	$-0.594780\pi$
$229$	−1.06631e8	−0.586757	−0.293379	+	0.955996i	$0.594780\pi$
$230$	−1.82516e8	−0.989132
$231$	0	0
$232$	8.64489e6	0.0454518
$233$	2.36647e8	1.22562	0.612809	−	0.790231i	$-0.290040\pi$
$233$	2.36647e8	1.22562	0.612809	+	0.790231i	$0.290040\pi$
$234$	0	0
$235$	−2.42050e8	−1.21666
$236$	−1.86912e7	−0.0925647
$237$	0	0
$238$	3.09675e8	1.48897
$239$	−4.70420e6	−0.0222891	−0.0111446	−	0.999938i	$-0.503547\pi$
$239$	−4.70420e6	−0.0222891	−0.0111446	+	0.999938i	$0.503547\pi$
$240$	0	0
$241$	−1.57232e8	−0.723573	−0.361786	−	0.932261i	$-0.617833\pi$
$241$	−1.57232e8	−0.723573	−0.361786	+	0.932261i	$0.617833\pi$
$242$	5.52609e8	2.50648
$243$	0	0
$244$	1.71238e8	0.754632
$245$	3.45968e8	1.50299
$246$	0	0
$247$	−1.69764e8	−0.716812
$248$	−5.92581e7	−0.246699
$249$	0	0
$250$	−2.99801e8	−1.21351
$251$	−1.41210e7	−0.0563647	−0.0281823	−	0.999603i	$-0.508972\pi$
$251$	−1.41210e7	−0.0563647	−0.0281823	+	0.999603i	$0.508972\pi$
$252$	0	0
$253$	−3.13528e8	−1.21718
$254$	−2.94622e8	−1.12810
$255$	0	0
$256$	3.51724e8	1.31027
$257$	3.85019e8	1.41487	0.707434	−	0.706780i	$-0.249853\pi$
$257$	3.85019e8	1.41487	0.707434	+	0.706780i	$0.249853\pi$
$258$	0	0
$259$	−4.67273e8	−1.67117
$260$	1.90705e8	0.672906
$261$	0	0
$262$	−3.23301e8	−1.11059
$263$	−1.74319e8	−0.590882	−0.295441	−	0.955361i	$-0.595467\pi$
$263$	−1.74319e8	−0.590882	−0.295441	+	0.955361i	$0.595467\pi$
$264$	0	0
$265$	−3.61138e8	−1.19210
$266$	5.01563e8	1.63395
$267$	0	0
$268$	−1.90358e8	−0.604087
$269$	−2.39784e7	−0.0751083	−0.0375541	−	0.999295i	$-0.511957\pi$
$269$	−2.39784e7	−0.0751083	−0.0375541	+	0.999295i	$0.511957\pi$
$270$	0	0
$271$	5.61954e8	1.71518	0.857588	−	0.514338i	$-0.171962\pi$
$271$	5.61954e8	1.71518	0.857588	+	0.514338i	$0.171962\pi$
$272$	2.92956e8	0.882695
$273$	0	0
$274$	2.91397e8	0.855772
$275$	7.39419e7	0.214401
$276$	0	0
$277$	6.23564e7	0.176280	0.0881398	−	0.996108i	$-0.471908\pi$
$277$	6.23564e7	0.176280	0.0881398	+	0.996108i	$0.471908\pi$
$278$	3.58499e7	0.100076
$279$	0	0
$280$	2.29015e8	0.623463
$281$	−5.33351e8	−1.43397	−0.716986	−	0.697087i	$-0.754479\pi$
$281$	−5.33351e8	−1.43397	−0.716986	+	0.697087i	$0.754479\pi$
$282$	0	0
$283$	−7.38516e8	−1.93690	−0.968450	−	0.249207i	$-0.919830\pi$
$283$	−7.38516e8	−1.93690	−0.968450	+	0.249207i	$0.919830\pi$
$284$	1.64570e8	0.426321
$285$	0	0
$286$	7.88343e8	1.99266
$287$	3.16569e8	0.790464
$288$	0	0
$289$	−1.90327e8	−0.463829
$290$	−6.93001e7	−0.166856
$291$	0	0
$292$	−4.48732e8	−1.05474
$293$	−4.24434e8	−0.985764	−0.492882	−	0.870096i	$-0.664057\pi$
$293$	−4.24434e8	−0.985764	−0.492882	+	0.870096i	$0.664057\pi$
$294$	0	0
$295$	−6.09023e7	−0.138120
$296$	−1.81322e8	−0.406378
$297$	0	0
$298$	−3.10057e8	−0.678711
$299$	−2.93898e8	−0.635839
$300$	0	0
$301$	1.89361e8	0.400227
$302$	7.07143e7	0.147735
$303$	0	0
$304$	4.74484e8	0.968643
$305$	5.57951e8	1.12602
$306$	0	0
$307$	5.81873e8	1.14774	0.573871	−	0.818946i	$-0.305441\pi$
$307$	5.81873e8	1.14774	0.573871	+	0.818946i	$0.305441\pi$
$308$	−9.67869e8	−1.88751
$309$	0	0
$310$	4.75031e8	0.905640
$311$	−4.40429e8	−0.830260	−0.415130	−	0.909762i	$-0.636264\pi$
$311$	−4.40429e8	−0.830260	−0.415130	+	0.909762i	$0.636264\pi$
$312$	0	0
$313$	1.33282e8	0.245678	0.122839	−	0.992427i	$-0.460800\pi$
$313$	1.33282e8	0.245678	0.122839	+	0.992427i	$0.460800\pi$
$314$	−9.14304e8	−1.66662
$315$	0	0
$316$	−7.51811e8	−1.34031
$317$	5.31810e8	0.937668	0.468834	−	0.883286i	$-0.344674\pi$
$317$	5.31810e8	0.937668	0.468834	+	0.883286i	$0.344674\pi$
$318$	0	0
$319$	−1.19044e8	−0.205324
$320$	−2.25509e8	−0.384714
$321$	0	0
$322$	8.68314e8	1.44938
$323$	3.56340e8	0.588378
$324$	0	0
$325$	6.93123e7	0.112000
$326$	1.22466e9	1.95774
$327$	0	0
$328$	1.22843e8	0.192217
$329$	1.15154e9	1.78277
$330$	0	0
$331$	−1.41095e8	−0.213853	−0.106926	−	0.994267i	$-0.534101\pi$
$331$	−1.41095e8	−0.213853	−0.106926	+	0.994267i	$0.534101\pi$
$332$	2.69323e8	0.403916
$333$	0	0
$334$	2.06269e8	0.302916
$335$	−6.20251e8	−0.901386
$336$	0	0
$337$	−1.15891e9	−1.64948	−0.824739	−	0.565513i	$-0.808678\pi$
$337$	−1.15891e9	−1.64948	−0.824739	+	0.565513i	$0.808678\pi$
$338$	−1.89627e8	−0.267111
$339$	0	0
$340$	−4.00296e8	−0.552339
$341$	8.16011e8	1.11444
$342$	0	0
$343$	−4.84110e8	−0.647760
$344$	7.34802e7	0.0973231
$345$	0	0
$346$	−1.33640e9	−1.73448
$347$	−4.17462e8	−0.536369	−0.268184	−	0.963368i	$-0.586424\pi$
$347$	−4.17462e8	−0.536369	−0.268184	+	0.963368i	$0.586424\pi$
$348$	0	0
$349$	−9.78142e7	−0.123172	−0.0615861	−	0.998102i	$-0.519616\pi$
$349$	−9.78142e7	−0.123172	−0.0615861	+	0.998102i	$0.519616\pi$
$350$	−2.04782e8	−0.255301
$351$	0	0
$352$	−1.67516e9	−2.04718
$353$	1.27204e9	1.53918	0.769590	−	0.638539i	$-0.220461\pi$
$353$	1.27204e9	1.53918	0.769590	+	0.638539i	$0.220461\pi$
$354$	0	0
$355$	5.36225e8	0.636133
$356$	−3.48223e8	−0.409056
$357$	0	0
$358$	−1.42311e9	−1.63927
$359$	2.70429e8	0.308477	0.154238	−	0.988034i	$-0.450708\pi$
$359$	2.70429e8	0.308477	0.154238	+	0.988034i	$0.450708\pi$
$360$	0	0
$361$	−3.16727e8	−0.354332
$362$	1.88618e9	2.08979
$363$	0	0
$364$	−9.07270e8	−0.986011
$365$	−1.46212e9	−1.57383
$366$	0	0
$367$	1.26226e9	1.33296	0.666481	−	0.745522i	$-0.267800\pi$
$367$	1.26226e9	1.33296	0.666481	+	0.745522i	$0.267800\pi$
$368$	8.21434e8	0.859222
$369$	0	0
$370$	1.45354e9	1.49183
$371$	1.71810e9	1.74679
$372$	0	0
$373$	−4.77047e7	−0.0475971	−0.0237985	−	0.999717i	$-0.507576\pi$
$373$	−4.77047e7	−0.0475971	−0.0237985	+	0.999717i	$0.507576\pi$
$374$	−1.65476e9	−1.63563
$375$	0	0
$376$	4.46850e8	0.433515
$377$	−1.11591e8	−0.107259
$378$	0	0
$379$	1.65053e9	1.55735	0.778674	−	0.627429i	$-0.215893\pi$
$379$	1.65053e9	1.55735	0.778674	+	0.627429i	$0.215893\pi$
$380$	−6.48338e8	−0.606120
$381$	0	0
$382$	−1.29136e8	−0.118529
$383$	−4.84522e7	−0.0440674	−0.0220337	−	0.999757i	$-0.507014\pi$
$383$	−4.84522e7	−0.0440674	−0.0220337	+	0.999757i	$0.507014\pi$
$384$	0	0
$385$	−3.15364e9	−2.81644
$386$	1.02500e9	0.907125
$387$	0	0
$388$	−5.67982e8	−0.493655
$389$	−2.13932e9	−1.84269	−0.921345	−	0.388745i	$-0.872909\pi$
$389$	−2.13932e9	−1.84269	−0.921345	+	0.388745i	$0.872909\pi$
$390$	0	0
$391$	6.16902e8	0.521913
$392$	−6.38693e8	−0.535539
$393$	0	0
$394$	−2.95042e8	−0.243023
$395$	−2.44965e9	−1.99993
$396$	0	0
$397$	1.67380e9	1.34257	0.671284	−	0.741200i	$-0.265743\pi$
$397$	1.67380e9	1.34257	0.671284	+	0.741200i	$0.265743\pi$
$398$	−1.71661e9	−1.36484
$399$	0	0
$400$	−1.93726e8	−0.151348
$401$	5.90271e8	0.457137	0.228568	−	0.973528i	$-0.426596\pi$
$401$	5.90271e8	0.457137	0.228568	+	0.973528i	$0.426596\pi$
$402$	0	0
$403$	7.64920e8	0.582168
$404$	−1.36992e9	−1.03362
$405$	0	0
$406$	3.29692e8	0.244494
$407$	2.49689e9	1.83578
$408$	0	0
$409$	−2.01375e8	−0.145537	−0.0727685	−	0.997349i	$-0.523183\pi$
$409$	−2.01375e8	−0.145537	−0.0727685	+	0.997349i	$0.523183\pi$
$410$	−9.84745e8	−0.705635
$411$	0	0
$412$	9.68476e8	0.682258
$413$	2.89740e8	0.202388
$414$	0	0
$415$	8.77547e8	0.602701
$416$	−1.57028e9	−1.06942
$417$	0	0
$418$	−2.68012e9	−1.79489
$419$	−1.53310e9	−1.01817	−0.509086	−	0.860716i	$-0.670017\pi$
$419$	−1.53310e9	−1.01817	−0.509086	+	0.860716i	$0.670017\pi$
$420$	0	0
$421$	1.10242e9	0.720044	0.360022	−	0.932944i	$-0.382769\pi$
$421$	1.10242e9	0.720044	0.360022	+	0.932944i	$0.382769\pi$
$422$	9.87872e8	0.639892
$423$	0	0
$424$	6.66699e8	0.424766
$425$	−1.45489e8	−0.0919326
$426$	0	0
$427$	−2.65443e9	−1.64996
$428$	1.56474e9	0.964691
$429$	0	0
$430$	−5.89040e8	−0.357277
$431$	2.15146e9	1.29438	0.647192	−	0.762327i	$-0.275943\pi$
$431$	2.15146e9	1.29438	0.647192	+	0.762327i	$0.275943\pi$
$432$	0	0
$433$	4.65835e8	0.275756	0.137878	−	0.990449i	$-0.455972\pi$
$433$	4.65835e8	0.275756	0.137878	+	0.990449i	$0.455972\pi$
$434$	−2.25994e9	−1.32704
$435$	0	0
$436$	−2.37766e9	−1.37388
$437$	9.99162e8	0.572732
$438$	0	0
$439$	2.25997e9	1.27490	0.637451	−	0.770491i	$-0.279989\pi$
$439$	2.25997e9	1.27490	0.637451	+	0.770491i	$0.279989\pi$
$440$	−1.22375e9	−0.684872
$441$	0	0
$442$	−1.55116e9	−0.854432
$443$	1.51398e9	0.827383	0.413691	−	0.910417i	$-0.364239\pi$
$443$	1.51398e9	0.827383	0.413691	+	0.910417i	$0.364239\pi$
$444$	0	0
$445$	−1.13463e9	−0.610371
$446$	2.61058e9	1.39337
$447$	0	0
$448$	1.07285e9	0.563723
$449$	2.99785e9	1.56296	0.781480	−	0.623930i	$-0.214465\pi$
$449$	2.99785e9	1.56296	0.781480	+	0.623930i	$0.214465\pi$
$450$	0	0
$451$	−1.69160e9	−0.868321
$452$	−1.35747e9	−0.691424
$453$	0	0
$454$	2.52851e9	1.26815
$455$	−2.95619e9	−1.47127
$456$	0	0
$457$	2.58428e9	1.26658	0.633289	−	0.773915i	$-0.281704\pi$
$457$	2.58428e9	1.26658	0.633289	+	0.773915i	$0.281704\pi$
$458$	−1.57802e9	−0.767510
$459$	0	0
$460$	−1.12241e9	−0.537651
$461$	1.75068e9	0.832247	0.416124	−	0.909308i	$-0.363388\pi$
$461$	1.75068e9	0.832247	0.416124	+	0.909308i	$0.363388\pi$
$462$	0	0
$463$	−3.28077e9	−1.53618	−0.768091	−	0.640341i	$-0.778793\pi$
$463$	−3.28077e9	−1.53618	−0.768091	+	0.640341i	$0.778793\pi$
$464$	3.11892e8	0.144941
$465$	0	0
$466$	3.50212e9	1.60317
$467$	−2.15325e9	−0.978329	−0.489164	−	0.872192i	$-0.662698\pi$
$467$	−2.15325e9	−0.978329	−0.489164	+	0.872192i	$0.662698\pi$
$468$	0	0
$469$	2.95082e9	1.32080
$470$	−3.58208e9	−1.59145
$471$	0	0
$472$	1.12432e8	0.0492145
$473$	−1.01186e9	−0.439648
$474$	0	0
$475$	−2.35641e8	−0.100884
$476$	1.90439e9	0.809343
$477$	0	0
$478$	−6.96171e7	−0.0291554
$479$	4.22659e9	1.75718	0.878589	−	0.477578i	$-0.158485\pi$
$479$	4.22659e9	1.75718	0.878589	+	0.477578i	$0.158485\pi$
$480$	0	0
$481$	2.34056e9	0.958986
$482$	−2.32687e9	−0.946471
$483$	0	0
$484$	3.39836e9	1.36242
$485$	−1.85068e9	−0.736605
$486$	0	0
$487$	−3.71716e9	−1.45835	−0.729173	−	0.684330i	$-0.760095\pi$
$487$	−3.71716e9	−1.45835	−0.729173	+	0.684330i	$0.760095\pi$
$488$	−1.03004e9	−0.401220
$489$	0	0
$490$	5.11996e9	1.96599
$491$	−3.64965e9	−1.39144	−0.695722	−	0.718311i	$-0.744915\pi$
$491$	−3.64965e9	−1.39144	−0.695722	+	0.718311i	$0.744915\pi$
$492$	0	0
$493$	2.34233e8	0.0880409
$494$	−2.51232e9	−0.937628
$495$	0	0
$496$	−2.13793e9	−0.786696
$497$	−2.55107e9	−0.932127
$498$	0	0
$499$	−8.31205e8	−0.299472	−0.149736	−	0.988726i	$-0.547842\pi$
$499$	−8.31205e8	−0.299472	−0.149736	+	0.988726i	$0.547842\pi$
$500$	−1.84367e9	−0.659612
$501$	0	0
$502$	−2.08976e8	−0.0737280
$503$	3.38642e9	1.18646	0.593230	−	0.805033i	$-0.297853\pi$
$503$	3.38642e9	1.18646	0.593230	+	0.805033i	$0.297853\pi$
$504$	0	0
$505$	−4.46366e9	−1.54231
$506$	−4.63988e9	−1.59213
$507$	0	0
$508$	−1.81183e9	−0.613188
$509$	2.52186e9	0.847633	0.423817	−	0.905748i	$-0.360690\pi$
$509$	2.52186e9	0.847633	0.423817	+	0.905748i	$0.360690\pi$
$510$	0	0
$511$	6.95598e9	2.30614
$512$	3.00491e9	0.989434
$513$	0	0
$514$	5.69786e9	1.85072
$515$	3.15562e9	1.01803
$516$	0	0
$517$	−6.15333e9	−1.95836
$518$	−6.91514e9	−2.18598
$519$	0	0
$520$	−1.14713e9	−0.357768
$521$	−4.55029e9	−1.40964	−0.704818	−	0.709388i	$-0.748971\pi$
$521$	−4.55029e9	−1.40964	−0.704818	+	0.709388i	$0.748971\pi$
$522$	0	0
$523$	−1.39010e9	−0.424903	−0.212451	−	0.977172i	$-0.568145\pi$
$523$	−1.39010e9	−0.424903	−0.212451	+	0.977172i	$0.568145\pi$
$524$	−1.98819e9	−0.603668
$525$	0	0
$526$	−2.57974e9	−0.772905
$527$	−1.60560e9	−0.477858
$528$	0	0
$529$	−1.67506e9	−0.491966
$530$	−5.34446e9	−1.55933
$531$	0	0
$532$	3.08444e9	0.888149
$533$	−1.58569e9	−0.453600
$534$	0	0
$535$	5.09844e9	1.43946
$536$	1.14505e9	0.321179
$537$	0	0
$538$	−3.54855e8	−0.0982456
$539$	8.79510e9	2.41925
$540$	0	0
$541$	3.45589e9	0.938360	0.469180	−	0.883103i	$-0.344550\pi$
$541$	3.45589e9	0.938360	0.469180	+	0.883103i	$0.344550\pi$
$542$	8.31632e9	2.24354
$543$	0	0
$544$	3.29607e9	0.877809
$545$	−7.74723e9	−2.05002
$546$	0	0
$547$	5.69696e9	1.48829	0.744145	−	0.668018i	$-0.232857\pi$
$547$	5.69696e9	1.48829	0.744145	+	0.668018i	$0.232857\pi$
$548$	1.79199e9	0.465162
$549$	0	0
$550$	1.09426e9	0.280447
$551$	3.79374e8	0.0966134
$552$	0	0
$553$	1.16541e10	2.93050
$554$	9.22809e8	0.230583
$555$	0	0
$556$	2.20465e8	0.0543973
$557$	7.56400e9	1.85464	0.927318	−	0.374275i	$-0.122108\pi$
$557$	7.56400e9	1.85464	0.927318	+	0.374275i	$0.122108\pi$
$558$	0	0
$559$	−9.48504e8	−0.229667
$560$	8.26246e9	1.98816
$561$	0	0
$562$	−7.89302e9	−1.87571
$563$	5.67154e9	1.33943	0.669717	−	0.742616i	$-0.266415\pi$
$563$	5.67154e9	1.33943	0.669717	+	0.742616i	$0.266415\pi$
$564$	0	0
$565$	−4.42308e9	−1.03170
$566$	−1.09292e10	−2.53357
$567$	0	0
$568$	−9.89927e8	−0.226665
$569$	−1.36290e9	−0.310149	−0.155074	−	0.987903i	$-0.549562\pi$
$569$	−1.36290e9	−0.310149	−0.155074	+	0.987903i	$0.549562\pi$
$570$	0	0
$571$	−2.64928e9	−0.595528	−0.297764	−	0.954640i	$-0.596241\pi$
$571$	−2.64928e9	−0.595528	−0.297764	+	0.954640i	$0.596241\pi$
$572$	4.84804e9	1.08313
$573$	0	0
$574$	4.68489e9	1.03397
$575$	−4.07945e8	−0.0894880
$576$	0	0
$577$	7.60073e9	1.64718	0.823588	−	0.567188i	$-0.191969\pi$
$577$	7.60073e9	1.64718	0.823588	+	0.567188i	$0.191969\pi$
$578$	−2.81664e9	−0.606713
$579$	0	0
$580$	−4.26172e8	−0.0906957
$581$	−4.17490e9	−0.883139
$582$	0	0
$583$	−9.18076e9	−1.91884
$584$	2.69923e9	0.560782
$585$	0	0
$586$	−6.28116e9	−1.28943
$587$	3.30015e9	0.673443	0.336721	−	0.941604i	$-0.390682\pi$
$587$	3.30015e9	0.673443	0.336721	+	0.941604i	$0.390682\pi$
$588$	0	0
$589$	−2.60049e9	−0.524388
$590$	−9.01289e8	−0.180668
$591$	0	0
$592$	−6.54179e9	−1.29590
$593$	−5.80009e9	−1.14220	−0.571102	−	0.820879i	$-0.693484\pi$
$593$	−5.80009e9	−1.14220	−0.571102	+	0.820879i	$0.693484\pi$
$594$	0	0
$595$	6.20516e9	1.20766
$596$	−1.90675e9	−0.368919
$597$	0	0
$598$	−4.34937e9	−0.831711
$599$	−3.53769e9	−0.672551	−0.336276	−	0.941764i	$-0.609167\pi$
$599$	−3.53769e9	−0.672551	−0.336276	+	0.941764i	$0.609167\pi$
$600$	0	0
$601$	−7.08661e9	−1.33161	−0.665806	−	0.746125i	$-0.731912\pi$
$601$	−7.08661e9	−1.33161	−0.665806	+	0.746125i	$0.731912\pi$
$602$	2.80233e9	0.523519
$603$	0	0
$604$	4.34869e8	0.0803025
$605$	1.10730e10	2.03292
$606$	0	0
$607$	−9.13138e8	−0.165720	−0.0828602	−	0.996561i	$-0.526406\pi$
$607$	−9.13138e8	−0.165720	−0.0828602	+	0.996561i	$0.526406\pi$
$608$	5.33846e9	0.963282
$609$	0	0
$610$	8.25707e9	1.47289
$611$	−5.76807e9	−1.02302
$612$	0	0
$613$	6.24314e8	0.109469	0.0547346	−	0.998501i	$-0.482569\pi$
$613$	6.24314e8	0.109469	0.0547346	+	0.998501i	$0.482569\pi$
$614$	8.61110e9	1.50131
$615$	0	0
$616$	5.82196e9	1.00354
$617$	1.00319e10	1.71943	0.859714	−	0.510775i	$-0.170642\pi$
$617$	1.00319e10	1.71943	0.859714	+	0.510775i	$0.170642\pi$
$618$	0	0
$619$	−1.02470e10	−1.73652	−0.868258	−	0.496114i	$-0.834760\pi$
$619$	−1.02470e10	−1.73652	−0.868258	+	0.496114i	$0.834760\pi$
$620$	2.92128e9	0.492268
$621$	0	0
$622$	−6.51787e9	−1.08602
$623$	5.39796e9	0.894378
$624$	0	0
$625$	−6.77361e9	−1.10979
$626$	1.97243e9	0.321360
$627$	0	0
$628$	−5.62266e9	−0.905906
$629$	−4.91293e9	−0.787160
$630$	0	0
$631$	3.58757e9	0.568457	0.284228	−	0.958757i	$-0.408263\pi$
$631$	3.58757e9	0.568457	0.284228	+	0.958757i	$0.408263\pi$
$632$	4.52232e9	0.712609
$633$	0	0
$634$	7.87022e9	1.22652
$635$	−5.90354e9	−0.914965
$636$	0	0
$637$	8.24444e9	1.26378
$638$	−1.76173e9	−0.268575
$639$	0	0
$640$	5.09725e9	0.768609
$641$	2.92622e9	0.438837	0.219419	−	0.975631i	$-0.429584\pi$
$641$	2.92622e9	0.438837	0.219419	+	0.975631i	$0.429584\pi$
$642$	0	0
$643$	5.85273e9	0.868200	0.434100	−	0.900865i	$-0.357066\pi$
$643$	5.85273e9	0.868200	0.434100	+	0.900865i	$0.357066\pi$
$644$	5.33984e9	0.787821
$645$	0	0
$646$	5.27346e9	0.769629
$647$	7.40954e9	1.07554	0.537770	−	0.843092i	$-0.319267\pi$
$647$	7.40954e9	1.07554	0.537770	+	0.843092i	$0.319267\pi$
$648$	0	0
$649$	−1.54824e9	−0.222322
$650$	1.02575e9	0.146502
$651$	0	0
$652$	7.53127e9	1.06415
$653$	4.89548e9	0.688018	0.344009	−	0.938966i	$-0.388215\pi$
$653$	4.89548e9	0.688018	0.344009	+	0.938966i	$0.388215\pi$
$654$	0	0
$655$	−6.47820e9	−0.900761
$656$	4.43195e9	0.612959
$657$	0	0
$658$	1.70416e10	2.33196
$659$	1.26032e10	1.71547	0.857736	−	0.514091i	$-0.171871\pi$
$659$	1.26032e10	1.71547	0.857736	+	0.514091i	$0.171871\pi$
$660$	0	0
$661$	3.60198e8	0.0485106	0.0242553	−	0.999706i	$-0.492279\pi$
$661$	3.60198e8	0.0485106	0.0242553	+	0.999706i	$0.492279\pi$
$662$	−2.08806e9	−0.279731
$663$	0	0
$664$	−1.62004e9	−0.214753
$665$	1.00502e10	1.32525
$666$	0	0
$667$	6.56779e8	0.0856996
$668$	1.26849e9	0.164652
$669$	0	0
$670$	−9.17906e9	−1.17906
$671$	1.41841e10	1.81247
$672$	0	0
$673$	1.40565e9	0.177756	0.0888782	−	0.996043i	$-0.471672\pi$
$673$	1.40565e9	0.177756	0.0888782	+	0.996043i	$0.471672\pi$
$674$	−1.71507e10	−2.15761
$675$	0	0
$676$	−1.16614e9	−0.145190
$677$	−5.12306e9	−0.634555	−0.317278	−	0.948333i	$-0.602769\pi$
$677$	−5.12306e9	−0.634555	−0.317278	+	0.948333i	$0.602769\pi$
$678$	0	0
$679$	8.80452e9	1.07935
$680$	2.40788e9	0.293665
$681$	0	0
$682$	1.20761e10	1.45774
$683$	1.70981e9	0.205341	0.102671	−	0.994715i	$-0.467261\pi$
$683$	1.70981e9	0.205341	0.102671	+	0.994715i	$0.467261\pi$
$684$	0	0
$685$	5.83891e9	0.694089
$686$	−7.16431e9	−0.847305
$687$	0	0
$688$	2.65104e9	0.310353
$689$	−8.60594e9	−1.00238
$690$	0	0
$691$	−1.38466e10	−1.59651	−0.798253	−	0.602323i	$-0.794242\pi$
$691$	−1.38466e10	−1.59651	−0.798253	+	0.602323i	$0.794242\pi$
$692$	−8.21839e9	−0.942791
$693$	0	0
$694$	−6.17799e9	−0.701599
$695$	7.18348e8	0.0811686
$696$	0	0
$697$	3.32842e9	0.372326
$698$	−1.44755e9	−0.161116
$699$	0	0
$700$	−1.25934e9	−0.138771
$701$	1.16579e10	1.27823	0.639115	−	0.769111i	$-0.279301\pi$
$701$	1.16579e10	1.27823	0.639115	+	0.769111i	$0.279301\pi$
$702$	0	0
$703$	−7.95720e9	−0.863806
$704$	−5.73282e9	−0.619247
$705$	0	0
$706$	1.88248e10	2.01333
$707$	2.12357e10	2.25995
$708$	0	0
$709$	−1.12659e10	−1.18714	−0.593572	−	0.804781i	$-0.702283\pi$
$709$	−1.12659e10	−1.18714	−0.593572	+	0.804781i	$0.702283\pi$
$710$	7.93555e9	0.832095
$711$	0	0
$712$	2.09464e9	0.217486
$713$	−4.50202e9	−0.465151
$714$	0	0
$715$	1.57965e10	1.61618
$716$	−8.75167e9	−0.891036
$717$	0	0
$718$	4.00206e9	0.403504
$719$	9.57915e9	0.961116	0.480558	−	0.876963i	$-0.340434\pi$
$719$	9.57915e9	0.961116	0.480558	+	0.876963i	$0.340434\pi$
$720$	0	0
$721$	−1.50128e10	−1.49172
$722$	−4.68722e9	−0.463485
$723$	0	0
$724$	1.15993e10	1.13592
$725$	−1.54894e8	−0.0150956
$726$	0	0
$727$	1.06396e10	1.02697	0.513484	−	0.858099i	$-0.328355\pi$
$727$	1.06396e10	1.02697	0.513484	+	0.858099i	$0.328355\pi$
$728$	5.45744e9	0.524239
$729$	0	0
$730$	−2.16378e10	−2.05865
$731$	1.99095e9	0.188516
$732$	0	0
$733$	−1.85210e10	−1.73700	−0.868500	−	0.495689i	$-0.834916\pi$
$733$	−1.85210e10	−1.73700	−0.868500	+	0.495689i	$0.834916\pi$
$734$	1.86801e10	1.74359
$735$	0	0
$736$	9.24203e9	0.854467
$737$	−1.57679e10	−1.45090
$738$	0	0
$739$	2.17412e9	0.198166	0.0990828	−	0.995079i	$-0.468409\pi$
$739$	2.17412e9	0.198166	0.0990828	+	0.995079i	$0.468409\pi$
$740$	8.93875e9	0.810897
$741$	0	0
$742$	2.54261e10	2.28489
$743$	−1.86262e10	−1.66595	−0.832977	−	0.553307i	$-0.813366\pi$
$743$	−1.86262e10	−1.66595	−0.832977	+	0.553307i	$0.813366\pi$
$744$	0	0
$745$	−6.21282e9	−0.550481
$746$	−7.05979e8	−0.0622595
$747$	0	0
$748$	−1.01762e10	−0.889060
$749$	−2.42557e10	−2.10924
$750$	0	0
$751$	−2.24532e9	−0.193437	−0.0967185	−	0.995312i	$-0.530835\pi$
$751$	−2.24532e9	−0.193437	−0.0967185	+	0.995312i	$0.530835\pi$
$752$	1.61216e10	1.38243
$753$	0	0
$754$	−1.65142e9	−0.140300
$755$	1.41695e9	0.119823
$756$	0	0
$757$	1.91646e10	1.60570	0.802852	−	0.596179i	$-0.203315\pi$
$757$	1.91646e10	1.60570	0.802852	+	0.596179i	$0.203315\pi$
$758$	2.44260e10	2.03709
$759$	0	0
$760$	3.89990e9	0.322260
$761$	−1.33554e10	−1.09853	−0.549265	−	0.835648i	$-0.685092\pi$
$761$	−1.33554e10	−1.09853	−0.549265	+	0.835648i	$0.685092\pi$
$762$	0	0
$763$	3.68572e10	3.00390
$764$	−7.94143e8	−0.0644276
$765$	0	0
$766$	−7.17041e8	−0.0576426
$767$	−1.45130e9	−0.116138
$768$	0	0
$769$	−5.20020e9	−0.412361	−0.206181	−	0.978514i	$-0.566103\pi$
$769$	−5.20020e9	−0.412361	−0.206181	+	0.978514i	$0.566103\pi$
$770$	−4.66706e10	−3.68405
$771$	0	0
$772$	6.30338e9	0.493075
$773$	−2.37920e10	−1.85269	−0.926347	−	0.376672i	$-0.877068\pi$
$773$	−2.37920e10	−1.85269	−0.926347	+	0.376672i	$0.877068\pi$
$774$	0	0
$775$	1.06175e9	0.0819343
$776$	3.41654e9	0.262465
$777$	0	0
$778$	−3.16597e10	−2.41034
$779$	5.39086e9	0.408580
$780$	0	0
$781$	1.36318e10	1.02394
$782$	9.12950e9	0.682690
$783$	0	0
$784$	−2.30429e10	−1.70778
$785$	−1.83205e10	−1.35174
$786$	0	0
$787$	5.45988e9	0.399275	0.199637	−	0.979870i	$-0.436024\pi$
$787$	5.45988e9	0.399275	0.199637	+	0.979870i	$0.436024\pi$
$788$	−1.81441e9	−0.132097
$789$	0	0
$790$	−3.62522e10	−2.61601
$791$	2.10427e10	1.51176
$792$	0	0
$793$	1.32960e10	0.946814
$794$	2.47704e10	1.75615
$795$	0	0
$796$	−1.05566e10	−0.741868
$797$	4.12638e9	0.288712	0.144356	−	0.989526i	$-0.453889\pi$
$797$	4.12638e9	0.288712	0.144356	+	0.989526i	$0.453889\pi$
$798$	0	0
$799$	1.21074e10	0.839725
$800$	−2.17963e9	−0.150511
$801$	0	0
$802$	8.73538e9	0.597959
$803$	−3.71696e10	−2.53328
$804$	0	0
$805$	1.73990e10	1.17554
$806$	1.13200e10	0.761507
$807$	0	0
$808$	8.24037e9	0.549550
$809$	−4.36775e9	−0.290027	−0.145013	−	0.989430i	$-0.546322\pi$
$809$	−4.36775e9	−0.290027	−0.145013	+	0.989430i	$0.546322\pi$
$810$	0	0
$811$	−1.81321e10	−1.19364	−0.596822	−	0.802374i	$-0.703570\pi$
$811$	−1.81321e10	−1.19364	−0.596822	+	0.802374i	$0.703570\pi$
$812$	2.02750e9	0.132897
$813$	0	0
$814$	3.69514e10	2.40129
$815$	2.45394e10	1.58786
$816$	0	0
$817$	3.22462e9	0.206872
$818$	−2.98013e9	−0.190370
$819$	0	0
$820$	−6.05584e9	−0.383554
$821$	−1.18439e10	−0.746951	−0.373475	−	0.927640i	$-0.621834\pi$
$821$	−1.18439e10	−0.746951	−0.373475	+	0.927640i	$0.621834\pi$
$822$	0	0
$823$	7.82921e8	0.0489574	0.0244787	−	0.999700i	$-0.492207\pi$
$823$	7.82921e8	0.0489574	0.0244787	+	0.999700i	$0.492207\pi$
$824$	−5.82561e9	−0.362741
$825$	0	0
$826$	4.28785e9	0.264734
$827$	1.09138e10	0.670974	0.335487	−	0.942045i	$-0.391099\pi$
$827$	1.09138e10	0.670974	0.335487	+	0.942045i	$0.391099\pi$
$828$	0	0
$829$	−2.91147e10	−1.77489	−0.887446	−	0.460911i	$-0.847523\pi$
$829$	−2.91147e10	−1.77489	−0.887446	+	0.460911i	$0.847523\pi$
$830$	1.29868e10	0.788365
$831$	0	0
$832$	−5.37388e9	−0.323487
$833$	−1.73054e10	−1.03735
$834$	0	0
$835$	4.13316e9	0.245685
$836$	−1.64819e10	−0.975628
$837$	0	0
$838$	−2.26882e10	−1.33182
$839$	3.47596e9	0.203193	0.101596	−	0.994826i	$-0.467605\pi$
$839$	3.47596e9	0.203193	0.101596	+	0.994826i	$0.467605\pi$
$840$	0	0
$841$	−1.70005e10	−0.985543
$842$	1.63146e10	0.941855
$843$	0	0
$844$	6.07507e9	0.347819
$845$	−3.79969e9	−0.216645
$846$	0	0
$847$	−5.26793e10	−2.97885
$848$	2.40533e10	1.35453
$849$	0	0
$850$	−2.15309e9	−0.120253
$851$	−1.37756e10	−0.766228
$852$	0	0
$853$	−2.90613e10	−1.60322	−0.801610	−	0.597847i	$-0.796023\pi$
$853$	−2.90613e10	−1.60322	−0.801610	+	0.597847i	$0.796023\pi$
$854$	−3.92827e10	−2.15824
$855$	0	0
$856$	−9.41226e9	−0.512904
$857$	−3.15674e10	−1.71319	−0.856597	−	0.515987i	$-0.827425\pi$
$857$	−3.15674e10	−1.71319	−0.856597	+	0.515987i	$0.827425\pi$
$858$	0	0
$859$	4.24010e9	0.228244	0.114122	−	0.993467i	$-0.463594\pi$
$859$	4.24010e9	0.228244	0.114122	+	0.993467i	$0.463594\pi$
$860$	−3.62239e9	−0.194201
$861$	0	0
$862$	3.18393e10	1.69312
$863$	2.94013e9	0.155715	0.0778573	−	0.996965i	$-0.475192\pi$
$863$	2.94013e9	0.155715	0.0778573	+	0.996965i	$0.475192\pi$
$864$	0	0
$865$	−2.67783e10	−1.40678
$866$	6.89387e9	0.360703
$867$	0	0
$868$	−1.38979e10	−0.721321
$869$	−6.22744e10	−3.21914
$870$	0	0
$871$	−1.47806e10	−0.757930
$872$	1.43022e10	0.730458
$873$	0	0
$874$	1.47865e10	0.749163
$875$	2.85795e10	1.44220
$876$	0	0
$877$	2.78040e10	1.39190	0.695952	−	0.718088i	$-0.254983\pi$
$877$	2.78040e10	1.39190	0.695952	+	0.718088i	$0.254983\pi$
$878$	3.34451e10	1.66764
$879$	0	0
$880$	−4.41508e10	−2.18398
$881$	−2.13975e10	−1.05426	−0.527131	−	0.849784i	$-0.676732\pi$
$881$	−2.13975e10	−1.05426	−0.527131	+	0.849784i	$0.676732\pi$
$882$	0	0
$883$	2.73260e10	1.33572	0.667858	−	0.744289i	$-0.267211\pi$
$883$	2.73260e10	1.33572	0.667858	+	0.744289i	$0.267211\pi$
$884$	−9.53908e9	−0.464433
$885$	0	0
$886$	2.24053e10	1.08226
$887$	−2.35865e10	−1.13483	−0.567416	−	0.823431i	$-0.692057\pi$
$887$	−2.35865e10	−1.13483	−0.567416	+	0.823431i	$0.692057\pi$
$888$	0	0
$889$	2.80859e10	1.34070
$890$	−1.67913e10	−0.798398
$891$	0	0
$892$	1.60542e10	0.757376
$893$	1.96097e10	0.921489
$894$	0	0
$895$	−2.85159e10	−1.32955
$896$	−2.42500e10	−1.12625
$897$	0	0
$898$	4.43650e10	2.04444
$899$	−1.70938e9	−0.0784658
$900$	0	0
$901$	1.80642e10	0.822777
$902$	−2.50339e10	−1.13581
$903$	0	0
$904$	8.16547e9	0.367614
$905$	3.77946e10	1.69496
$906$	0	0
$907$	−1.48021e9	−0.0658716	−0.0329358	−	0.999457i	$-0.510486\pi$
$907$	−1.48021e9	−0.0658716	−0.0329358	+	0.999457i	$0.510486\pi$
$908$	1.55495e10	0.689311
$909$	0	0
$910$	−4.37485e10	−1.92450
$911$	−1.06953e10	−0.468681	−0.234341	−	0.972155i	$-0.575293\pi$
$911$	−1.06953e10	−0.468681	−0.234341	+	0.972155i	$0.575293\pi$
$912$	0	0
$913$	2.23087e10	0.970124
$914$	3.82445e10	1.65675
$915$	0	0
$916$	−9.70430e9	−0.417186
$917$	3.08198e10	1.31989
$918$	0	0
$919$	−3.15248e9	−0.133983	−0.0669913	−	0.997754i	$-0.521340\pi$
$919$	−3.15248e9	−0.133983	−0.0669913	+	0.997754i	$0.521340\pi$
$920$	6.75157e9	0.285856
$921$	0	0
$922$	2.59081e10	1.08862
$923$	1.27783e10	0.534892
$924$	0	0
$925$	3.24882e9	0.134968
$926$	−4.85519e10	−2.00941
$927$	0	0
$928$	3.50913e9	0.144139
$929$	−4.53386e10	−1.85529	−0.927647	−	0.373458i	$-0.878172\pi$
$929$	−4.53386e10	−1.85529	−0.927647	+	0.373458i	$0.878172\pi$
$930$	0	0
$931$	−2.80286e10	−1.13835
$932$	2.15368e10	0.871418
$933$	0	0
$934$	−3.18658e10	−1.27971
$935$	−3.31576e10	−1.32661
$936$	0	0
$937$	4.84194e9	0.192279	0.0961393	−	0.995368i	$-0.469351\pi$
$937$	4.84194e9	0.192279	0.0961393	+	0.995368i	$0.469351\pi$
$938$	4.36690e10	1.72768
$939$	0	0
$940$	−2.20286e10	−0.865046
$941$	8.67653e9	0.339455	0.169728	−	0.985491i	$-0.445711\pi$
$941$	8.67653e9	0.339455	0.169728	+	0.985491i	$0.445711\pi$
$942$	0	0
$943$	9.33275e9	0.362425
$944$	4.05635e9	0.156940
$945$	0	0
$946$	−1.49744e10	−0.575083
$947$	−1.85330e10	−0.709121	−0.354561	−	0.935033i	$-0.615370\pi$
$947$	−1.85330e10	−0.709121	−0.354561	+	0.935033i	$0.615370\pi$
$948$	0	0
$949$	−3.48424e10	−1.32335
$950$	−3.48723e9	−0.131962
$951$	0	0
$952$	−1.14554e10	−0.430309
$953$	−1.33156e10	−0.498352	−0.249176	−	0.968458i	$-0.580160\pi$
$953$	−1.33156e10	−0.498352	−0.249176	+	0.968458i	$0.580160\pi$
$954$	0	0
$955$	−2.58759e9	−0.0961353
$956$	−4.28122e8	−0.0158476
$957$	0	0
$958$	6.25490e10	2.29848
$959$	−2.77784e10	−1.01705
$960$	0	0
$961$	−1.57953e10	−0.574112
$962$	3.46378e10	1.25440
$963$	0	0
$964$	−1.43095e10	−0.514462
$965$	2.05385e10	0.735740
$966$	0	0
$967$	1.13617e10	0.404064	0.202032	−	0.979379i	$-0.435246\pi$
$967$	1.13617e10	0.404064	0.202032	+	0.979379i	$0.435246\pi$
$968$	−2.04419e10	−0.724365
$969$	0	0
$970$	−2.73880e10	−0.963518
$971$	−1.97070e10	−0.690802	−0.345401	−	0.938455i	$-0.612257\pi$
$971$	−1.97070e10	−0.690802	−0.345401	+	0.938455i	$0.612257\pi$
$972$	0	0
$973$	−3.41751e9	−0.118937
$974$	−5.50100e10	−1.90759
$975$	0	0
$976$	−3.71619e10	−1.27945
$977$	4.83923e10	1.66014	0.830072	−	0.557657i	$-0.188299\pi$
$977$	4.83923e10	1.66014	0.830072	+	0.557657i	$0.188299\pi$
$978$	0	0
$979$	−2.88442e10	−0.982470
$980$	3.14860e10	1.06863
$981$	0	0
$982$	−5.40109e10	−1.82008
$983$	−2.12104e10	−0.712214	−0.356107	−	0.934445i	$-0.615896\pi$
$983$	−2.12104e10	−0.712214	−0.356107	+	0.934445i	$0.615896\pi$
$984$	0	0
$985$	−5.91196e9	−0.197108
$986$	3.46640e9	0.115162
$987$	0	0
$988$	−1.54499e10	−0.509655
$989$	5.58252e9	0.183503
$990$	0	0
$991$	3.64631e10	1.19013	0.595067	−	0.803676i	$-0.297125\pi$
$991$	3.64631e10	1.19013	0.595067	+	0.803676i	$0.297125\pi$
$992$	−2.40540e10	−0.782342
$993$	0	0
$994$	−3.77531e10	−1.21927
$995$	−3.43968e10	−1.10697
$996$	0	0
$997$	−3.41980e10	−1.09287	−0.546434	−	0.837502i	$-0.684015\pi$
$997$	−3.41980e10	−1.09287	−0.546434	+	0.837502i	$0.684015\pi$
$998$	−1.23009e10	−0.391725
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	531.8.a.b.1.12		16
3.2	odd	2		177.8.a.a.1.5	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.8.a.a.1.5	✓	16	3.2	odd	2
531.8.a.b.1.12		16	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:	\( N \)	\(=\)	\( 531 = 3^{2} \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	531.a (trivial)

\(f(q)\)	\(=\)	\(q+14.7989 q^{2} +91.0084 q^{4} +296.536 q^{5} -1410.76 q^{7} -547.437 q^{8} +O(q^{10})\)	\(q+14.7989 q^{2} +91.0084 q^{4} +296.536 q^{5} -1410.76 q^{7} -547.437 q^{8} +4388.42 q^{10} +7538.45 q^{11} +7066.47 q^{13} -20877.7 q^{14} -19750.5 q^{16} -14832.8 q^{17} -24023.8 q^{19} +26987.3 q^{20} +111561. q^{22} -41590.5 q^{23} +9808.63 q^{25} +104576. q^{26} -128391. q^{28} -15791.6 q^{29} +108246. q^{31} -222215. q^{32} -219509. q^{34} -418341. q^{35} +331221. q^{37} -355527. q^{38} -162335. q^{40} -224396. q^{41} -134226. q^{43} +686063. q^{44} -615494. q^{46} -816259. q^{47} +1.16670e6 q^{49} +145157. q^{50} +643108. q^{52} -1.21786e6 q^{53} +2.23542e6 q^{55} +772301. q^{56} -233699. q^{58} -205379. q^{59} +1.88156e6 q^{61} +1.60193e6 q^{62} -760476. q^{64} +2.09546e6 q^{65} -2.09166e6 q^{67} -1.34991e6 q^{68} -6.19100e6 q^{70} +1.80830e6 q^{71} -4.93066e6 q^{73} +4.90172e6 q^{74} -2.18637e6 q^{76} -1.06349e7 q^{77} -8.26089e6 q^{79} -5.85675e6 q^{80} -3.32083e6 q^{82} +2.95933e6 q^{83} -4.39846e6 q^{85} -1.98640e6 q^{86} -4.12683e6 q^{88} -3.82628e6 q^{89} -9.96908e6 q^{91} -3.78508e6 q^{92} -1.20798e7 q^{94} -7.12393e6 q^{95} -6.24098e6 q^{97} +1.72659e7 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 6 q^{2} + 974 q^{4} + 68 q^{5} - 2343 q^{7} - 819 q^{8}+O(q^{10}) \) 16 * q + 6 * q^2 + 974 * q^4 + 68 * q^5 - 2343 * q^7 - 819 * q^8	\( 16 q + 6 q^{2} + 974 q^{4} + 68 q^{5} - 2343 q^{7} - 819 q^{8} - 3479 q^{10} - 898 q^{11} - 8172 q^{13} + 13315 q^{14} + 3138 q^{16} + 44985 q^{17} - 40137 q^{19} - 130657 q^{20} + 109394 q^{22} + 2833 q^{23} + 285746 q^{25} + 129420 q^{26} + 112890 q^{28} - 144375 q^{29} - 141759 q^{31} + 36224 q^{32} - 341332 q^{34} + 78859 q^{35} - 297971 q^{37} - 329075 q^{38} - 203048 q^{40} - 659077 q^{41} - 1431608 q^{43} - 254916 q^{44} + 873113 q^{46} + 1574073 q^{47} + 1893545 q^{49} - 302533 q^{50} - 4972548 q^{52} - 587736 q^{53} - 4624036 q^{55} + 5798506 q^{56} - 6991380 q^{58} - 3286064 q^{59} - 6117131 q^{61} + 11570258 q^{62} - 19063011 q^{64} + 5335514 q^{65} - 16518710 q^{67} + 17284669 q^{68} - 39189486 q^{70} + 10882582 q^{71} - 21097441 q^{73} + 16717030 q^{74} - 40864952 q^{76} + 3404601 q^{77} - 3784458 q^{79} + 27466195 q^{80} - 24990117 q^{82} + 1951425 q^{83} - 23238675 q^{85} + 35910572 q^{86} - 27843055 q^{88} - 10499443 q^{89} + 699217 q^{91} + 20062766 q^{92} - 59358988 q^{94} + 29236333 q^{95} - 25158976 q^{97} - 2120460 q^{98}+O(q^{100}) \) 16 * q + 6 * q^2 + 974 * q^4 + 68 * q^5 - 2343 * q^7 - 819 * q^8 - 3479 * q^10 - 898 * q^11 - 8172 * q^13 + 13315 * q^14 + 3138 * q^16 + 44985 * q^17 - 40137 * q^19 - 130657 * q^20 + 109394 * q^22 + 2833 * q^23 + 285746 * q^25 + 129420 * q^26 + 112890 * q^28 - 144375 * q^29 - 141759 * q^31 + 36224 * q^32 - 341332 * q^34 + 78859 * q^35 - 297971 * q^37 - 329075 * q^38 - 203048 * q^40 - 659077 * q^41 - 1431608 * q^43 - 254916 * q^44 + 873113 * q^46 + 1574073 * q^47 + 1893545 * q^49 - 302533 * q^50 - 4972548 * q^52 - 587736 * q^53 - 4624036 * q^55 + 5798506 * q^56 - 6991380 * q^58 - 3286064 * q^59 - 6117131 * q^61 + 11570258 * q^62 - 19063011 * q^64 + 5335514 * q^65 - 16518710 * q^67 + 17284669 * q^68 - 39189486 * q^70 + 10882582 * q^71 - 21097441 * q^73 + 16717030 * q^74 - 40864952 * q^76 + 3404601 * q^77 - 3784458 * q^79 + 27466195 * q^80 - 24990117 * q^82 + 1951425 * q^83 - 23238675 * q^85 + 35910572 * q^86 - 27843055 * q^88 - 10499443 * q^89 + 699217 * q^91 + 20062766 * q^92 - 59358988 * q^94 + 29236333 * q^95 - 25158976 * q^97 - 2120460 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more