LMFDB - Embedded newform 531.8.a.d.1.6

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:	$0$
Dimension:	$17$
Coefficient field:	$\mathbb{Q}[x]/(x^{17} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{17} - 2 x^{16} - 1639 x^{15} + 1625 x^{14} + 1070274 x^{13} - 274939 x^{12} - 357079564 x^{11} + \cdots - 58\!\cdots\!76 $ x^17 - 2x^16 - 1639x^15 + 1625x^14 + 1070274x^13 - 274939x^12 - 357079564x^11 - 89298188x^10 + 64650816672x^9 + 33122051904x^8 - 6210397064704x^7 - 2735256748800x^6 + 288860762071040x^5 - 34502173230080x^4 - 5633463408885760x^3 + 4719471961341952x^2 + 37636623107620864x - 58321181718347776
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	multiple of $ 2^{10}\cdot 3^{5} $
Twist minimal:	no (minimal twist has level 177)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$7.01814$ 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)

$f(q)$	$=$	$q-5.01814 q^{2} -102.818 q^{4} +77.5687 q^{5} -216.829 q^{7} +1158.28 q^{8} +O(q^{10})$	\(q-5.01814 q^{2} -102.818 q^{4} +77.5687 q^{5} -216.829 q^{7} +1158.28 q^{8} -389.251 q^{10} -3376.21 q^{11} +12448.6 q^{13} +1088.08 q^{14} +7348.33 q^{16} +26362.1 q^{17} +41401.4 q^{19} -7975.48 q^{20} +16942.3 q^{22} +42118.5 q^{23} -72108.1 q^{25} -62468.7 q^{26} +22293.9 q^{28} +151717. q^{29} -239434. q^{31} -185135. q^{32} -132289. q^{34} -16819.1 q^{35} -411153. q^{37} -207758. q^{38} +89846.2 q^{40} +536752. q^{41} +583229. q^{43} +347136. q^{44} -211357. q^{46} +587465. q^{47} -776528. q^{49} +361849. q^{50} -1.27994e6 q^{52} +267710. q^{53} -261889. q^{55} -251148. q^{56} -761339. q^{58} +205379. q^{59} -498824. q^{61} +1.20151e6 q^{62} -11553.8 q^{64} +965620. q^{65} +2.87144e6 q^{67} -2.71050e6 q^{68} +84400.8 q^{70} -1.08176e6 q^{71} -4746.50 q^{73} +2.06322e6 q^{74} -4.25682e6 q^{76} +732060. q^{77} -1.41454e6 q^{79} +570000. q^{80} -2.69350e6 q^{82} -3.72243e6 q^{83} +2.04487e6 q^{85} -2.92672e6 q^{86} -3.91060e6 q^{88} -1.04746e7 q^{89} -2.69921e6 q^{91} -4.33055e6 q^{92} -2.94798e6 q^{94} +3.21145e6 q^{95} -4.51283e6 q^{97} +3.89673e6 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17 q + 32 q^{2} + 1166 q^{4} + 1072 q^{5} - 2407 q^{7} + 6645 q^{8}+O(q^{10}) $ 17 * q + 32 * q^2 + 1166 * q^4 + 1072 * q^5 - 2407 * q^7 + 6645 * q^8	\( 17 q + 32 q^{2} + 1166 q^{4} + 1072 q^{5} - 2407 q^{7} + 6645 q^{8} - 6391 q^{10} + 8888 q^{11} - 12702 q^{13} + 17555 q^{14} + 139226 q^{16} + 36167 q^{17} - 71037 q^{19} + 274883 q^{20} - 325182 q^{22} + 269995 q^{23} + 97329 q^{25} + 336906 q^{26} - 901362 q^{28} + 543825 q^{29} - 633109 q^{31} + 837062 q^{32} - 529288 q^{34} + 287621 q^{35} - 867607 q^{37} + 1727169 q^{38} - 815662 q^{40} + 1428939 q^{41} - 477060 q^{43} + 1667926 q^{44} + 5305549 q^{46} + 1217849 q^{47} + 4350738 q^{49} - 4561369 q^{50} + 4175994 q^{52} + 3487068 q^{53} - 960484 q^{55} + 5363196 q^{56} - 3082906 q^{58} + 3491443 q^{59} + 998917 q^{61} + 5742614 q^{62} + 17531621 q^{64} + 6075816 q^{65} - 356026 q^{67} + 16149231 q^{68} - 548798 q^{70} + 12879428 q^{71} - 6176157 q^{73} + 5971906 q^{74} - 17624580 q^{76} - 239687 q^{77} - 18886490 q^{79} + 70463349 q^{80} - 19351611 q^{82} + 22824893 q^{83} - 7973079 q^{85} + 27502196 q^{86} - 62527651 q^{88} + 30609647 q^{89} - 36301521 q^{91} + 41388548 q^{92} + 1010176 q^{94} + 29303629 q^{95} - 26249806 q^{97} + 93110852 q^{98}+O(q^{100}) \) 17 * q + 32 * q^2 + 1166 * q^4 + 1072 * q^5 - 2407 * q^7 + 6645 * q^8 - 6391 * q^10 + 8888 * q^11 - 12702 * q^13 + 17555 * q^14 + 139226 * q^16 + 36167 * q^17 - 71037 * q^19 + 274883 * q^20 - 325182 * q^22 + 269995 * q^23 + 97329 * q^25 + 336906 * q^26 - 901362 * q^28 + 543825 * q^29 - 633109 * q^31 + 837062 * q^32 - 529288 * q^34 + 287621 * q^35 - 867607 * q^37 + 1727169 * q^38 - 815662 * q^40 + 1428939 * q^41 - 477060 * q^43 + 1667926 * q^44 + 5305549 * q^46 + 1217849 * q^47 + 4350738 * q^49 - 4561369 * q^50 + 4175994 * q^52 + 3487068 * q^53 - 960484 * q^55 + 5363196 * q^56 - 3082906 * q^58 + 3491443 * q^59 + 998917 * q^61 + 5742614 * q^62 + 17531621 * q^64 + 6075816 * q^65 - 356026 * q^67 + 16149231 * q^68 - 548798 * q^70 + 12879428 * q^71 - 6176157 * q^73 + 5971906 * q^74 - 17624580 * q^76 - 239687 * q^77 - 18886490 * q^79 + 70463349 * q^80 - 19351611 * q^82 + 22824893 * q^83 - 7973079 * q^85 + 27502196 * q^86 - 62527651 * q^88 + 30609647 * q^89 - 36301521 * q^91 + 41388548 * q^92 + 1010176 * q^94 + 29303629 * q^95 - 26249806 * q^97 + 93110852 * 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 $

$2$	−5.01814	−0.443545	−0.221773	−	0.975098i	$-0.571184\pi$
$2$	−5.01814	−0.443545	−0.221773	+	0.975098i	$0.571184\pi$
$3$	0	0
$3$	0	0
$4$	−102.818	−0.803268
$5$	77.5687	0.277518	0.138759	−	0.990326i	$-0.455689\pi$
$5$	77.5687	0.277518	0.138759	+	0.990326i	$0.455689\pi$
$6$	0	0
$7$	−216.829	−0.238932	−0.119466	−	0.992838i	$-0.538118\pi$
$7$	−216.829	−0.238932	−0.119466	+	0.992838i	$0.538118\pi$
$8$	1158.28	0.799831
$9$	0	0
$10$	−389.251	−0.123092
$11$	−3376.21	−0.764813	−0.382407	−	0.923994i	$-0.624905\pi$
$11$	−3376.21	−0.764813	−0.382407	+	0.923994i	$0.624905\pi$
$12$	0	0
$13$	12448.6	1.57151	0.785756	−	0.618536i	$-0.212274\pi$
$13$	12448.6	1.57151	0.785756	+	0.618536i	$0.212274\pi$
$14$	1088.08	0.105977
$15$	0	0
$16$	7348.33	0.448506
$17$	26362.1	1.30139	0.650696	−	0.759338i	$-0.274477\pi$
$17$	26362.1	1.30139	0.650696	+	0.759338i	$0.274477\pi$
$18$	0	0
$19$	41401.4	1.38477	0.692384	−	0.721529i	$-0.256560\pi$
$19$	41401.4	1.38477	0.692384	+	0.721529i	$0.256560\pi$
$20$	−7975.48	−0.222921
$21$	0	0
$22$	16942.3	0.339229
$23$	42118.5	0.721815	0.360907	−	0.932602i	$-0.382467\pi$
$23$	42118.5	0.721815	0.360907	+	0.932602i	$0.382467\pi$
$24$	0	0
$25$	−72108.1	−0.922984
$26$	−62468.7	−0.697037
$27$	0	0
$28$	22293.9	0.191926
$29$	151717.	1.15516	0.577580	−	0.816334i	$-0.303997\pi$
$29$	151717.	1.15516	0.577580	+	0.816334i	$0.303997\pi$
$30$	0	0
$31$	−239434.	−1.44351	−0.721754	−	0.692149i	$-0.756664\pi$
$31$	−239434.	−1.44351	−0.721754	+	0.692149i	$0.756664\pi$
$32$	−185135.	−0.998764
$33$	0	0
$34$	−132289.	−0.577226
$35$	−16819.1	−0.0663079
$36$	0	0
$37$	−411153.	−1.33444	−0.667218	−	0.744863i	$-0.732515\pi$
$37$	−411153.	−1.33444	−0.667218	+	0.744863i	$0.732515\pi$
$38$	−207758.	−0.614208
$39$	0	0
$40$	89846.2	0.221968
$41$	536752.	1.21627	0.608135	−	0.793834i	$-0.291918\pi$
$41$	536752.	1.21627	0.608135	+	0.793834i	$0.291918\pi$
$42$	0	0
$43$	583229.	1.11866	0.559331	−	0.828944i	$-0.311058\pi$
$43$	583229.	1.11866	0.559331	+	0.828944i	$0.311058\pi$
$44$	347136.	0.614350
$45$	0	0
$46$	−211357.	−0.320158
$47$	587465.	0.825353	0.412677	−	0.910878i	$-0.364594\pi$
$47$	587465.	0.825353	0.412677	+	0.910878i	$0.364594\pi$
$48$	0	0
$49$	−776528.	−0.942912
$50$	361849.	0.409385
$51$	0	0
$52$	−1.27994e6	−1.26234
$53$	267710.	0.247001	0.123501	−	0.992344i	$-0.460588\pi$
$53$	267710.	0.247001	0.123501	+	0.992344i	$0.460588\pi$
$54$	0	0
$55$	−261889.	−0.212250
$56$	−251148.	−0.191105
$57$	0	0
$58$	−761339.	−0.512366
$59$	205379.	0.130189
$59$	205379.	0.130189
$60$	0	0
$61$	−498824.	−0.281380	−0.140690	−	0.990054i	$-0.544932\pi$
$61$	−498824.	−0.281380	−0.140690	+	0.990054i	$0.544932\pi$
$62$	1.20151e6	0.640261
$63$	0	0
$64$	−11553.8	−0.00550929
$65$	965620.	0.436124
$66$	0	0
$67$	2.87144e6	1.16637	0.583187	−	0.812338i	$-0.301805\pi$
$67$	2.87144e6	1.16637	0.583187	+	0.812338i	$0.301805\pi$
$68$	−2.71050e6	−1.04537
$69$	0	0
$70$	84400.8	0.0294106
$71$	−1.08176e6	−0.358697	−0.179349	−	0.983786i	$-0.557399\pi$
$71$	−1.08176e6	−0.358697	−0.179349	+	0.983786i	$0.557399\pi$
$72$	0	0
$73$	−4746.50	−0.00142805	−0.000714025	−	1.00000i	$-0.500227\pi$
$73$	−4746.50	−0.00142805	−0.000714025		1.00000i	$0.500227\pi$
$74$	2.06322e6	0.591883
$75$	0	0
$76$	−4.25682e6	−1.11234
$77$	732060.	0.182738
$78$	0	0
$79$	−1.41454e6	−0.322791	−0.161396	−	0.986890i	$-0.551600\pi$
$79$	−1.41454e6	−0.322791	−0.161396	+	0.986890i	$0.551600\pi$
$80$	570000.	0.124469
$81$	0	0
$82$	−2.69350e6	−0.539471
$83$	−3.72243e6	−0.714583	−0.357292	−	0.933993i	$-0.616300\pi$
$83$	−3.72243e6	−0.714583	−0.357292	+	0.933993i	$0.616300\pi$
$84$	0	0
$85$	2.04487e6	0.361160
$86$	−2.92672e6	−0.496178
$87$	0	0
$88$	−3.91060e6	−0.611721
$89$	−1.04746e7	−1.57497	−0.787484	−	0.616336i	$-0.788616\pi$
$89$	−1.04746e7	−1.57497	−0.787484	+	0.616336i	$0.788616\pi$
$90$	0	0
$91$	−2.69921e6	−0.375484
$92$	−4.33055e6	−0.579810
$93$	0	0
$94$	−2.94798e6	−0.366081
$95$	3.21145e6	0.384299
$96$	0	0
$97$	−4.51283e6	−0.502051	−0.251025	−	0.967980i	$-0.580768\pi$
$97$	−4.51283e6	−0.502051	−0.251025	+	0.967980i	$0.580768\pi$
$98$	3.89673e6	0.418224
$99$	0	0
$100$	7.41403e6	0.741403
$101$	1.70633e7	1.64793	0.823963	−	0.566644i	$-0.191758\pi$
$101$	1.70633e7	1.64793	0.823963	+	0.566644i	$0.191758\pi$
$102$	0	0
$103$	−4.18892e6	−0.377721	−0.188861	−	0.982004i	$-0.560479\pi$
$103$	−4.18892e6	−0.377721	−0.188861	+	0.982004i	$0.560479\pi$
$104$	1.44189e7	1.25694
$105$	0	0
$106$	−1.34341e6	−0.109556
$107$	1.20271e7	0.949116	0.474558	−	0.880224i	$-0.342608\pi$
$107$	1.20271e7	0.949116	0.474558	+	0.880224i	$0.342608\pi$
$108$	0	0
$109$	−1.96024e7	−1.44983	−0.724913	−	0.688840i	$-0.758120\pi$
$109$	−1.96024e7	−1.44983	−0.724913	+	0.688840i	$0.758120\pi$
$110$	1.31419e6	0.0941424
$111$	0	0
$112$	−1.59333e6	−0.107162
$113$	7.54916e6	0.492180	0.246090	−	0.969247i	$-0.420854\pi$
$113$	7.54916e6	0.492180	0.246090	+	0.969247i	$0.420854\pi$
$114$	0	0
$115$	3.26708e6	0.200317
$116$	−1.55993e7	−0.927903
$117$	0	0
$118$	−1.03062e6	−0.0577447
$119$	−5.71605e6	−0.310944
$120$	0	0
$121$	−8.08835e6	−0.415060
$122$	2.50317e6	0.124805
$123$	0	0
$124$	2.46182e7	1.15952
$125$	−1.16534e7	−0.533663
$126$	0	0
$127$	−1.36062e7	−0.589417	−0.294709	−	0.955587i	$-0.595223\pi$
$127$	−1.36062e7	−0.589417	−0.294709	+	0.955587i	$0.595223\pi$
$128$	2.37552e7	1.00121
$129$	0	0
$130$	−4.84562e6	−0.193441
$131$	1.29419e7	0.502978	0.251489	−	0.967860i	$-0.419080\pi$
$131$	1.29419e7	0.502978	0.251489	+	0.967860i	$0.419080\pi$
$132$	0	0
$133$	−8.97700e6	−0.330865
$134$	−1.44093e7	−0.517340
$135$	0	0
$136$	3.05346e7	1.04089
$137$	7.65865e6	0.254466	0.127233	−	0.991873i	$-0.459390\pi$
$137$	7.65865e6	0.254466	0.127233	+	0.991873i	$0.459390\pi$
$138$	0	0
$139$	4.87660e6	0.154016	0.0770080	−	0.997030i	$-0.475463\pi$
$139$	4.87660e6	0.154016	0.0770080	+	0.997030i	$0.475463\pi$
$140$	1.72931e6	0.0532630
$141$	0	0
$142$	5.42844e6	0.159098
$143$	−4.20290e7	−1.20191
$144$	0	0
$145$	1.17685e7	0.320578
$146$	23818.6	0.000633405 0
$147$	0	0
$148$	4.22740e7	1.07191
$149$	−1.05059e6	−0.0260186	−0.0130093	−	0.999915i	$-0.504141\pi$
$149$	−1.05059e6	−0.0260186	−0.0130093	+	0.999915i	$0.504141\pi$
$150$	0	0
$151$	5.81661e7	1.37484	0.687418	−	0.726262i	$-0.258744\pi$
$151$	5.81661e7	1.37484	0.687418	+	0.726262i	$0.258744\pi$
$152$	4.79543e7	1.10758
$153$	0	0
$154$	−3.67358e6	−0.0810526
$155$	−1.85726e7	−0.400600
$156$	0	0
$157$	4.08109e7	0.841642	0.420821	−	0.907144i	$-0.361742\pi$
$157$	4.08109e7	0.841642	0.420821	+	0.907144i	$0.361742\pi$
$158$	7.09838e6	0.143173
$159$	0	0
$160$	−1.43607e7	−0.277175
$161$	−9.13250e6	−0.172464
$162$	0	0
$163$	−7.46918e7	−1.35088	−0.675439	−	0.737416i	$-0.736046\pi$
$163$	−7.46918e7	−1.35088	−0.675439	+	0.737416i	$0.736046\pi$
$164$	−5.51879e7	−0.976990
$165$	0	0
$166$	1.86797e7	0.316950
$167$	5.71426e7	0.949407	0.474704	−	0.880146i	$-0.342555\pi$
$167$	5.71426e7	0.949407	0.474704	+	0.880146i	$0.342555\pi$
$168$	0	0
$169$	9.22184e7	1.46965
$170$	−1.02615e7	−0.160191
$171$	0	0
$172$	−5.99665e7	−0.898585
$173$	−6.74021e7	−0.989720	−0.494860	−	0.868973i	$-0.664781\pi$
$173$	−6.74021e7	−0.989720	−0.494860	+	0.868973i	$0.664781\pi$
$174$	0	0
$175$	1.56351e7	0.220530
$176$	−2.48095e7	−0.343024
$177$	0	0
$178$	5.25629e7	0.698569
$179$	−5.40298e7	−0.704122	−0.352061	−	0.935977i	$-0.614519\pi$
$179$	−5.40298e7	−0.704122	−0.352061	+	0.935977i	$0.614519\pi$
$180$	0	0
$181$	−2.98190e7	−0.373782	−0.186891	−	0.982381i	$-0.559841\pi$
$181$	−2.98190e7	−0.373782	−0.186891	+	0.982381i	$0.559841\pi$
$182$	1.35450e7	0.166544
$183$	0	0
$184$	4.87850e7	0.577330
$185$	−3.18926e7	−0.370330
$186$	0	0
$187$	−8.90040e7	−0.995322
$188$	−6.04022e7	−0.662979
$189$	0	0
$190$	−1.61155e7	−0.170454
$191$	1.03129e8	1.07093	0.535466	−	0.844557i	$-0.320136\pi$
$191$	1.03129e8	1.07093	0.535466	+	0.844557i	$0.320136\pi$
$192$	0	0
$193$	1.72283e8	1.72501	0.862506	−	0.506047i	$-0.168894\pi$
$193$	1.72283e8	1.72501	0.862506	+	0.506047i	$0.168894\pi$
$194$	2.26460e7	0.222682
$195$	0	0
$196$	7.98413e7	0.757410
$197$	1.27602e8	1.18912	0.594562	−	0.804050i	$-0.297326\pi$
$197$	1.27602e8	1.18912	0.594562	+	0.804050i	$0.297326\pi$
$198$	0	0
$199$	−6.47395e7	−0.582349	−0.291175	−	0.956670i	$-0.594046\pi$
$199$	−6.47395e7	−0.582349	−0.291175	+	0.956670i	$0.594046\pi$
$200$	−8.35213e7	−0.738231
$201$	0	0
$202$	−8.56260e7	−0.730930
$203$	−3.28967e7	−0.276004
$204$	0	0
$205$	4.16351e7	0.337537
$206$	2.10206e7	0.167536
$207$	0	0
$208$	9.14762e7	0.704833
$209$	−1.39780e8	−1.05909
$210$	0	0
$211$	1.42567e8	1.04479	0.522395	−	0.852704i	$-0.325039\pi$
$211$	1.42567e8	1.04479	0.522395	+	0.852704i	$0.325039\pi$
$212$	−2.75255e7	−0.198408
$213$	0	0
$214$	−6.03539e7	−0.420976
$215$	4.52403e7	0.310449
$216$	0	0
$217$	5.19161e7	0.344900
$218$	9.83675e7	0.643064
$219$	0	0
$220$	2.69269e7	0.170493
$221$	3.28170e8	2.04515
$222$	0	0
$223$	2.35480e8	1.42196	0.710979	−	0.703213i	$-0.248252\pi$
$223$	2.35480e8	1.42196	0.710979	+	0.703213i	$0.248252\pi$
$224$	4.01425e7	0.238636
$225$	0	0
$226$	−3.78828e7	−0.218304
$227$	−3.35151e8	−1.90174	−0.950868	−	0.309598i	$-0.899806\pi$
$227$	−3.35151e8	−1.90174	−0.950868	+	0.309598i	$0.899806\pi$
$228$	0	0
$229$	−1.68231e8	−0.925727	−0.462864	−	0.886430i	$-0.653178\pi$
$229$	−1.68231e8	−0.925727	−0.462864	+	0.886430i	$0.653178\pi$
$230$	−1.63947e7	−0.0888496
$231$	0	0
$232$	1.75731e8	0.923933
$233$	2.76156e8	1.43024	0.715120	−	0.699002i	$-0.246372\pi$
$233$	2.76156e8	1.43024	0.715120	+	0.699002i	$0.246372\pi$
$234$	0	0
$235$	4.55689e7	0.229051
$236$	−2.11167e7	−0.104577
$237$	0	0
$238$	2.86840e7	0.137918
$239$	−1.64969e8	−0.781647	−0.390824	−	0.920466i	$-0.627810\pi$
$239$	−1.64969e8	−0.781647	−0.390824	+	0.920466i	$0.627810\pi$
$240$	0	0
$241$	2.19804e8	1.01152	0.505761	−	0.862674i	$-0.331212\pi$
$241$	2.19804e8	1.01152	0.505761	+	0.862674i	$0.331212\pi$
$242$	4.05885e7	0.184098
$243$	0	0
$244$	5.12882e7	0.226023
$245$	−6.02343e7	−0.261675
$246$	0	0
$247$	5.15388e8	2.17618
$248$	−2.77331e8	−1.15456
$249$	0	0
$250$	5.84784e7	0.236704
$251$	2.64722e8	1.05665	0.528327	−	0.849041i	$-0.322820\pi$
$251$	2.64722e8	1.05665	0.528327	+	0.849041i	$0.322820\pi$
$252$	0	0
$253$	−1.42201e8	−0.552054
$254$	6.82777e7	0.261433
$255$	0	0
$256$	−1.17728e8	−0.438572
$257$	2.39775e8	0.881125	0.440563	−	0.897722i	$-0.354779\pi$
$257$	2.39775e8	0.881125	0.440563	+	0.897722i	$0.354779\pi$
$258$	0	0
$259$	8.91498e7	0.318839
$260$	−9.92834e7	−0.350324
$261$	0	0
$262$	−6.49444e7	−0.223094
$263$	−1.27661e8	−0.432727	−0.216364	−	0.976313i	$-0.569420\pi$
$263$	−1.27661e8	−0.432727	−0.216364	+	0.976313i	$0.569420\pi$
$264$	0	0
$265$	2.07659e7	0.0685474
$266$	4.50479e7	0.146754
$267$	0	0
$268$	−2.95236e8	−0.936910
$269$	−1.98210e8	−0.620858	−0.310429	−	0.950597i	$-0.600473\pi$
$269$	−1.98210e8	−0.620858	−0.310429	+	0.950597i	$0.600473\pi$
$270$	0	0
$271$	1.17159e8	0.357587	0.178794	−	0.983887i	$-0.442781\pi$
$271$	1.17159e8	0.357587	0.178794	+	0.983887i	$0.442781\pi$
$272$	1.93717e8	0.583683
$273$	0	0
$274$	−3.84322e7	−0.112867
$275$	2.43452e8	0.705910
$276$	0	0
$277$	2.80002e8	0.791555	0.395778	−	0.918346i	$-0.370475\pi$
$277$	2.80002e8	0.791555	0.395778	+	0.918346i	$0.370475\pi$
$278$	−2.44715e7	−0.0683131
$279$	0	0
$280$	−1.94812e7	−0.0530351
$281$	6.16699e7	0.165806	0.0829032	−	0.996558i	$-0.473581\pi$
$281$	6.16699e7	0.165806	0.0829032	+	0.996558i	$0.473581\pi$
$282$	0	0
$283$	−6.20410e8	−1.62715	−0.813573	−	0.581463i	$-0.802481\pi$
$283$	−6.20410e8	−1.62715	−0.813573	+	0.581463i	$0.802481\pi$
$284$	1.11225e8	0.288130
$285$	0	0
$286$	2.10908e8	0.533103
$287$	−1.16383e8	−0.290605
$288$	0	0
$289$	2.84620e8	0.693622
$290$	−5.90561e7	−0.142191
$291$	0	0
$292$	488027.	0.00114711
$293$	7.47133e8	1.73525	0.867623	−	0.497222i	$-0.165647\pi$
$293$	7.47133e8	1.73525	0.867623	+	0.497222i	$0.165647\pi$
$294$	0	0
$295$	1.59310e7	0.0361298
$296$	−4.76230e8	−1.06732
$297$	0	0
$298$	5.27203e6	0.0115404
$299$	5.24316e8	1.13434
$300$	0	0
$301$	−1.26461e8	−0.267284
$302$	−2.91886e8	−0.609802
$303$	0	0
$304$	3.04231e8	0.621077
$305$	−3.86932e7	−0.0780881
$306$	0	0
$307$	6.94608e8	1.37011	0.685056	−	0.728491i	$-0.259778\pi$
$307$	6.94608e8	1.37011	0.685056	+	0.728491i	$0.259778\pi$
$308$	−7.52691e7	−0.146788
$309$	0	0
$310$	9.31998e7	0.177684
$311$	−1.27745e8	−0.240815	−0.120407	−	0.992725i	$-0.538420\pi$
$311$	−1.27745e8	−0.240815	−0.120407	+	0.992725i	$0.538420\pi$
$312$	0	0
$313$	−9.74255e8	−1.79584	−0.897920	−	0.440159i	$-0.854922\pi$
$313$	−9.74255e8	−1.79584	−0.897920	+	0.440159i	$0.854922\pi$
$314$	−2.04795e8	−0.373306
$315$	0	0
$316$	1.45441e8	0.259288
$317$	8.99019e8	1.58512	0.792559	−	0.609795i	$-0.208748\pi$
$317$	8.99019e8	1.58512	0.792559	+	0.609795i	$0.208748\pi$
$318$	0	0
$319$	−5.12230e8	−0.883482
$320$	−896215.	−0.00152893
$321$	0	0
$322$	4.58282e7	0.0764957
$323$	1.09143e9	1.80213
$324$	0	0
$325$	−8.97643e8	−1.45048
$326$	3.74814e8	0.599176
$327$	0	0
$328$	6.21708e8	0.972810
$329$	−1.27379e8	−0.197203
$330$	0	0
$331$	−1.16605e9	−1.76733	−0.883666	−	0.468119i	$-0.844932\pi$
$331$	−1.16605e9	−1.76733	−0.883666	+	0.468119i	$0.844932\pi$
$332$	3.82733e8	0.574002
$333$	0	0
$334$	−2.86750e8	−0.421105
$335$	2.22734e8	0.323690
$336$	0	0
$337$	1.23311e9	1.75509	0.877544	−	0.479496i	$-0.159181\pi$
$337$	1.23311e9	1.75509	0.877544	+	0.479496i	$0.159181\pi$
$338$	−4.62765e8	−0.651857
$339$	0	0
$340$	−2.10250e8	−0.290108
$341$	8.08379e8	1.10401
$342$	0	0
$343$	3.46941e8	0.464223
$344$	6.75541e8	0.894741
$345$	0	0
$346$	3.38233e8	0.438986
$347$	5.89436e8	0.757327	0.378664	−	0.925534i	$-0.376384\pi$
$347$	5.89436e8	0.757327	0.378664	+	0.925534i	$0.376384\pi$
$348$	0	0
$349$	1.15878e9	1.45919	0.729596	−	0.683878i	$-0.239708\pi$
$349$	1.15878e9	1.45919	0.729596	+	0.683878i	$0.239708\pi$
$350$	−7.84592e7	−0.0978150
$351$	0	0
$352$	6.25054e8	0.763868
$353$	5.26080e8	0.636561	0.318281	−	0.947997i	$-0.396895\pi$
$353$	5.26080e8	0.636561	0.318281	+	0.947997i	$0.396895\pi$
$354$	0	0
$355$	−8.39110e7	−0.0995450
$356$	1.07698e9	1.26512
$357$	0	0
$358$	2.71129e8	0.312310
$359$	−1.09995e9	−1.25470	−0.627351	−	0.778737i	$-0.715861\pi$
$359$	−1.09995e9	−1.25470	−0.627351	+	0.778737i	$0.715861\pi$
$360$	0	0
$361$	8.20202e8	0.917583
$362$	1.49636e8	0.165789
$363$	0	0
$364$	2.77528e8	0.301614
$365$	−368180.	−0.000396310 0
$366$	0	0
$367$	1.21755e9	1.28575	0.642874	−	0.765972i	$-0.277742\pi$
$367$	1.21755e9	1.28575	0.642874	+	0.765972i	$0.277742\pi$
$368$	3.09501e8	0.323738
$369$	0	0
$370$	1.60042e8	0.164258
$371$	−5.80473e7	−0.0590164
$372$	0	0
$373$	5.53595e8	0.552346	0.276173	−	0.961108i	$-0.410934\pi$
$373$	5.53595e8	0.552346	0.276173	+	0.961108i	$0.410934\pi$
$374$	4.46635e8	0.441471
$375$	0	0
$376$	6.80449e8	0.660143
$377$	1.88866e9	1.81535
$378$	0	0
$379$	−2.47132e8	−0.233180	−0.116590	−	0.993180i	$-0.537196\pi$
$379$	−2.47132e8	−0.233180	−0.116590	+	0.993180i	$0.537196\pi$
$380$	−3.30196e8	−0.308695
$381$	0	0
$382$	−5.17514e8	−0.475007
$383$	599846.	0.000545562 0	0.000272781	−	1.00000i	$-0.499913\pi$
$383$	599846.	0.000545562 0	0.000272781		1.00000i	$0.499913\pi$
$384$	0	0
$385$	5.67850e7	0.0507132
$386$	−8.64541e8	−0.765121
$387$	0	0
$388$	4.64001e8	0.403281
$389$	8.92101e8	0.768406	0.384203	−	0.923249i	$-0.374476\pi$
$389$	8.92101e8	0.768406	0.384203	+	0.923249i	$0.374476\pi$
$390$	0	0
$391$	1.11033e9	0.939364
$392$	−8.99436e8	−0.754170
$393$	0	0
$394$	−6.40327e8	−0.527430
$395$	−1.09724e8	−0.0895805
$396$	0	0
$397$	−9.58791e8	−0.769055	−0.384527	−	0.923114i	$-0.625636\pi$
$397$	−9.58791e8	−0.769055	−0.384527	+	0.923114i	$0.625636\pi$
$398$	3.24872e8	0.258298
$399$	0	0
$400$	−5.29874e8	−0.413964
$401$	−1.82830e9	−1.41593	−0.707966	−	0.706247i	$-0.750387\pi$
$401$	−1.82830e9	−1.41593	−0.707966	+	0.706247i	$0.750387\pi$
$402$	0	0
$403$	−2.98061e9	−2.26849
$404$	−1.75442e9	−1.32373
$405$	0	0
$406$	1.65080e8	0.122420
$407$	1.38814e9	1.02059
$408$	0	0
$409$	−7.15047e8	−0.516776	−0.258388	−	0.966041i	$-0.583191\pi$
$409$	−7.15047e8	−0.516776	−0.258388	+	0.966041i	$0.583191\pi$
$410$	−2.08931e8	−0.149713
$411$	0	0
$412$	4.30697e8	0.303411
$413$	−4.45320e7	−0.0311062
$414$	0	0
$415$	−2.88744e8	−0.198310
$416$	−2.30466e9	−1.56957
$417$	0	0
$418$	7.01435e8	0.469754
$419$	−2.22875e9	−1.48017	−0.740086	−	0.672513i	$-0.765215\pi$
$419$	−2.22875e9	−1.48017	−0.740086	+	0.672513i	$0.765215\pi$
$420$	0	0
$421$	1.49109e9	0.973906	0.486953	−	0.873428i	$-0.338108\pi$
$421$	1.49109e9	0.973906	0.486953	+	0.873428i	$0.338108\pi$
$422$	−7.15419e8	−0.463412
$423$	0	0
$424$	3.10083e8	0.197559
$425$	−1.90092e9	−1.20116
$426$	0	0
$427$	1.08159e8	0.0672306
$428$	−1.23661e9	−0.762394
$429$	0	0
$430$	−2.27022e8	−0.137698
$431$	−2.66273e9	−1.60198	−0.800988	−	0.598680i	$-0.795692\pi$
$431$	−2.66273e9	−1.60198	−0.800988	+	0.598680i	$0.795692\pi$
$432$	0	0
$433$	7.09435e7	0.0419957	0.0209979	−	0.999780i	$-0.493316\pi$
$433$	7.09435e7	0.0419957	0.0209979	+	0.999780i	$0.493316\pi$
$434$	−2.60522e8	−0.152979
$435$	0	0
$436$	2.01548e9	1.16460
$437$	1.74376e9	0.999546
$438$	0	0
$439$	6.26733e7	0.0353555	0.0176777	−	0.999844i	$-0.494373\pi$
$439$	6.26733e7	0.0353555	0.0176777	+	0.999844i	$0.494373\pi$
$440$	−3.03340e8	−0.169764
$441$	0	0
$442$	−1.64680e9	−0.907119
$443$	6.41984e8	0.350842	0.175421	−	0.984494i	$-0.443871\pi$
$443$	6.41984e8	0.350842	0.175421	+	0.984494i	$0.443871\pi$
$444$	0	0
$445$	−8.12500e8	−0.437082
$446$	−1.18167e9	−0.630703
$447$	0	0
$448$	2.50520e6	0.00131634
$449$	2.77507e9	1.44681	0.723406	−	0.690423i	$-0.242575\pi$
$449$	2.77507e9	1.44681	0.723406	+	0.690423i	$0.242575\pi$
$450$	0	0
$451$	−1.81219e9	−0.930219
$452$	−7.76191e8	−0.395352
$453$	0	0
$454$	1.68184e9	0.843506
$455$	−2.09374e8	−0.104204
$456$	0	0
$457$	3.79393e9	1.85944	0.929721	−	0.368266i	$-0.120048\pi$
$457$	3.79393e9	1.85944	0.929721	+	0.368266i	$0.120048\pi$
$458$	8.44209e8	0.410602
$459$	0	0
$460$	−3.35916e8	−0.160908
$461$	3.74187e9	1.77884	0.889418	−	0.457095i	$-0.151110\pi$
$461$	3.74187e9	1.77884	0.889418	+	0.457095i	$0.151110\pi$
$462$	0	0
$463$	1.68652e9	0.789691	0.394846	−	0.918748i	$-0.370798\pi$
$463$	1.68652e9	0.789691	0.394846	+	0.918748i	$0.370798\pi$
$464$	1.11487e9	0.518097
$465$	0	0
$466$	−1.38579e9	−0.634376
$467$	1.90310e8	0.0864675	0.0432338	−	0.999065i	$-0.486234\pi$
$467$	1.90310e8	0.0864675	0.0432338	+	0.999065i	$0.486234\pi$
$468$	0	0
$469$	−6.22610e8	−0.278684
$470$	−2.28671e8	−0.101594
$471$	0	0
$472$	2.37886e8	0.104129
$473$	−1.96910e9	−0.855568
$474$	0	0
$475$	−2.98537e9	−1.27812
$476$	5.87714e8	0.249771
$477$	0	0
$478$	8.27840e8	0.346696
$479$	−1.04486e9	−0.434395	−0.217197	−	0.976128i	$-0.569692\pi$
$479$	−1.04486e9	−0.434395	−0.217197	+	0.976128i	$0.569692\pi$
$480$	0	0
$481$	−5.11827e9	−2.09708
$482$	−1.10301e9	−0.448656
$483$	0	0
$484$	8.31630e8	0.333404
$485$	−3.50054e8	−0.139328
$486$	0	0
$487$	−4.52457e9	−1.77511	−0.887557	−	0.460697i	$-0.847599\pi$
$487$	−4.52457e9	−1.77511	−0.887557	+	0.460697i	$0.847599\pi$
$488$	−5.77778e8	−0.225056
$489$	0	0
$490$	3.02264e8	0.116065
$491$	−1.28164e9	−0.488630	−0.244315	−	0.969696i	$-0.578563\pi$
$491$	−1.28164e9	−0.488630	−0.244315	+	0.969696i	$0.578563\pi$
$492$	0	0
$493$	3.99958e9	1.50332
$494$	−2.58629e9	−0.965235
$495$	0	0
$496$	−1.75944e9	−0.647423
$497$	2.34557e8	0.0857041
$498$	0	0
$499$	−3.26234e9	−1.17538	−0.587689	−	0.809087i	$-0.699962\pi$
$499$	−3.26234e9	−1.17538	−0.587689	+	0.809087i	$0.699962\pi$
$500$	1.19818e9	0.428674
$501$	0	0
$502$	−1.32841e9	−0.468674
$503$	−5.11806e8	−0.179315	−0.0896577	−	0.995973i	$-0.528577\pi$
$503$	−5.11806e8	−0.179315	−0.0896577	+	0.995973i	$0.528577\pi$
$504$	0	0
$505$	1.32358e9	0.457330
$506$	7.13586e8	0.244861
$507$	0	0
$508$	1.39896e9	0.473460
$509$	−5.38317e9	−1.80936	−0.904682	−	0.426088i	$-0.859892\pi$
$509$	−5.38317e9	−1.80936	−0.904682	+	0.426088i	$0.859892\pi$
$510$	0	0
$511$	1.02918e6	0.000341206 0
$512$	−2.44989e9	−0.806681
$513$	0	0
$514$	−1.20322e9	−0.390819
$515$	−3.24929e8	−0.104825
$516$	0	0
$517$	−1.98341e9	−0.631241
$518$	−4.47366e8	−0.141419
$519$	0	0
$520$	1.11846e9	0.348825
$521$	−1.92620e9	−0.596720	−0.298360	−	0.954453i	$-0.596440\pi$
$521$	−1.92620e9	−0.596720	−0.298360	+	0.954453i	$0.596440\pi$
$522$	0	0
$523$	3.47164e9	1.06115	0.530577	−	0.847637i	$-0.321975\pi$
$523$	3.47164e9	1.06115	0.530577	+	0.847637i	$0.321975\pi$
$524$	−1.33067e9	−0.404026
$525$	0	0
$526$	6.40623e8	0.191934
$527$	−6.31197e9	−1.87857
$528$	0	0
$529$	−1.63086e9	−0.478984
$530$	−1.04206e8	−0.0304039
$531$	0	0
$532$	9.23000e8	0.265773
$533$	6.68179e9	1.91138
$534$	0	0
$535$	9.32930e8	0.263397
$536$	3.32593e9	0.932902
$537$	0	0
$538$	9.94645e8	0.275379
$539$	2.62173e9	0.721152
$540$	0	0
$541$	−1.13960e9	−0.309430	−0.154715	−	0.987959i	$-0.549446\pi$
$541$	−1.13960e9	−0.309430	−0.154715	+	0.987959i	$0.549446\pi$
$542$	−5.87919e8	−0.158606
$543$	0	0
$544$	−4.88053e9	−1.29978
$545$	−1.52053e9	−0.402353
$546$	0	0
$547$	−3.40030e9	−0.888303	−0.444152	−	0.895952i	$-0.646495\pi$
$547$	−3.40030e9	−0.888303	−0.444152	+	0.895952i	$0.646495\pi$
$548$	−7.87449e8	−0.204405
$549$	0	0
$550$	−1.22168e9	−0.313103
$551$	6.28131e9	1.59963
$552$	0	0
$553$	3.06714e8	0.0771250
$554$	−1.40509e9	−0.351091
$555$	0	0
$556$	−5.01404e8	−0.123716
$557$	−1.94268e9	−0.476331	−0.238165	−	0.971225i	$-0.576546\pi$
$557$	−1.94268e9	−0.476331	−0.238165	+	0.971225i	$0.576546\pi$
$558$	0	0
$559$	7.26036e9	1.75799
$560$	−1.23592e8	−0.0297395
$561$	0	0
$562$	−3.09468e8	−0.0735427
$563$	−6.16858e9	−1.45682	−0.728410	−	0.685142i	$-0.759740\pi$
$563$	−6.16858e9	−1.45682	−0.728410	+	0.685142i	$0.759740\pi$
$564$	0	0
$565$	5.85579e8	0.136589
$566$	3.11331e9	0.721713
$567$	0	0
$568$	−1.25298e9	−0.286897
$569$	5.43476e9	1.23677	0.618383	−	0.785877i	$-0.287788\pi$
$569$	5.43476e9	1.23677	0.618383	+	0.785877i	$0.287788\pi$
$570$	0	0
$571$	−5.20959e9	−1.17105	−0.585527	−	0.810653i	$-0.699112\pi$
$571$	−5.20959e9	−1.17105	−0.585527	+	0.810653i	$0.699112\pi$
$572$	4.32135e9	0.965458
$573$	0	0
$574$	5.84027e8	0.128897
$575$	−3.03709e9	−0.666223
$576$	0	0
$577$	2.67350e9	0.579381	0.289691	−	0.957120i	$-0.406448\pi$
$577$	2.67350e9	0.579381	0.289691	+	0.957120i	$0.406448\pi$
$578$	−1.42826e9	−0.307653
$579$	0	0
$580$	−1.21002e9	−0.257510
$581$	8.07129e8	0.170737
$582$	0	0
$583$	−9.03847e8	−0.188910
$584$	−5.49777e6	−0.00114220
$585$	0	0
$586$	−3.74922e9	−0.769660
$587$	−4.23836e9	−0.864898	−0.432449	−	0.901658i	$-0.642350\pi$
$587$	−4.23836e9	−0.864898	−0.432449	+	0.901658i	$0.642350\pi$
$588$	0	0
$589$	−9.91288e9	−1.99892
$590$	−7.99440e7	−0.0160252
$591$	0	0
$592$	−3.02129e9	−0.598503
$593$	5.59276e9	1.10137	0.550687	−	0.834712i	$-0.314366\pi$
$593$	5.59276e9	1.10137	0.550687	+	0.834712i	$0.314366\pi$
$594$	0	0
$595$	−4.43387e8	−0.0862926
$596$	1.08020e8	0.0208999
$597$	0	0
$598$	−2.63109e9	−0.503132
$599$	2.76072e9	0.524842	0.262421	−	0.964953i	$-0.415479\pi$
$599$	2.76072e9	0.524842	0.262421	+	0.964953i	$0.415479\pi$
$600$	0	0
$601$	−3.38464e9	−0.635992	−0.317996	−	0.948092i	$-0.603010\pi$
$601$	−3.38464e9	−0.635992	−0.317996	+	0.948092i	$0.603010\pi$
$602$	6.34598e8	0.118552
$603$	0	0
$604$	−5.98054e9	−1.10436
$605$	−6.27403e8	−0.115187
$606$	0	0
$607$	3.57949e9	0.649622	0.324811	−	0.945779i	$-0.394699\pi$
$607$	3.57949e9	0.649622	0.324811	+	0.945779i	$0.394699\pi$
$608$	−7.66483e9	−1.38306
$609$	0	0
$610$	1.94168e8	0.0346356
$611$	7.31310e9	1.29705
$612$	0	0
$613$	9.92114e9	1.73960	0.869801	−	0.493403i	$-0.164247\pi$
$613$	9.92114e9	1.73960	0.869801	+	0.493403i	$0.164247\pi$
$614$	−3.48564e9	−0.607706
$615$	0	0
$616$	8.47929e8	0.146160
$617$	2.67237e9	0.458034	0.229017	−	0.973422i	$-0.426449\pi$
$617$	2.67237e9	0.458034	0.229017	+	0.973422i	$0.426449\pi$
$618$	0	0
$619$	5.77104e9	0.977996	0.488998	−	0.872285i	$-0.337363\pi$
$619$	5.77104e9	0.977996	0.488998	+	0.872285i	$0.337363\pi$
$620$	1.90960e9	0.321789
$621$	0	0
$622$	6.41044e8	0.106812
$623$	2.27119e9	0.376309
$624$	0	0
$625$	4.72951e9	0.774882
$626$	4.88895e9	0.796536
$627$	0	0
$628$	−4.19610e9	−0.676064
$629$	−1.08388e10	−1.73662
$630$	0	0
$631$	−1.33017e9	−0.210768	−0.105384	−	0.994432i	$-0.533607\pi$
$631$	−1.33017e9	−0.210768	−0.105384	+	0.994432i	$0.533607\pi$
$632$	−1.63844e9	−0.258178
$633$	0	0
$634$	−4.51141e9	−0.703072
$635$	−1.05541e9	−0.163574
$636$	0	0
$637$	−9.66667e9	−1.48180
$638$	2.57044e9	0.391864
$639$	0	0
$640$	1.84266e9	0.277853
$641$	−8.97295e8	−0.134565	−0.0672825	−	0.997734i	$-0.521433\pi$
$641$	−8.97295e8	−0.134565	−0.0672825	+	0.997734i	$0.521433\pi$
$642$	0	0
$643$	7.92605e9	1.17576	0.587879	−	0.808949i	$-0.299963\pi$
$643$	7.92605e9	1.17576	0.587879	+	0.808949i	$0.299963\pi$
$644$	9.38988e8	0.138535
$645$	0	0
$646$	−5.47693e9	−0.799325
$647$	9.72853e9	1.41215	0.706077	−	0.708135i	$-0.250463\pi$
$647$	9.72853e9	1.41215	0.706077	+	0.708135i	$0.250463\pi$
$648$	0	0
$649$	−6.93403e8	−0.0995702
$650$	4.50450e9	0.643354
$651$	0	0
$652$	7.67968e9	1.08512
$653$	4.58349e9	0.644170	0.322085	−	0.946711i	$-0.395616\pi$
$653$	4.58349e9	0.644170	0.322085	+	0.946711i	$0.395616\pi$
$654$	0	0
$655$	1.00389e9	0.139586
$656$	3.94423e9	0.545505
$657$	0	0
$658$	6.39208e8	0.0874684
$659$	1.15331e9	0.156982	0.0784908	−	0.996915i	$-0.474990\pi$
$659$	1.15331e9	0.156982	0.0784908	+	0.996915i	$0.474990\pi$
$660$	0	0
$661$	−1.03408e8	−0.0139267	−0.00696334	−	0.999976i	$-0.502217\pi$
$661$	−1.03408e8	−0.0139267	−0.00696334	+	0.999976i	$0.502217\pi$
$662$	5.85139e9	0.783892
$663$	0	0
$664$	−4.31161e9	−0.571546
$665$	−6.96335e8	−0.0918211
$666$	0	0
$667$	6.39011e9	0.833812
$668$	−5.87530e9	−0.762628
$669$	0	0
$670$	−1.11771e9	−0.143571
$671$	1.68414e9	0.215203
$672$	0	0
$673$	−8.65901e9	−1.09500	−0.547502	−	0.836804i	$-0.684421\pi$
$673$	−8.65901e9	−1.09500	−0.547502	+	0.836804i	$0.684421\pi$
$674$	−6.18795e9	−0.778461
$675$	0	0
$676$	−9.48174e9	−1.18052
$677$	−1.41759e10	−1.75586	−0.877930	−	0.478789i	$-0.841076\pi$
$677$	−1.41759e10	−1.75586	−0.877930	+	0.478789i	$0.841076\pi$
$678$	0	0
$679$	9.78511e8	0.119956
$680$	2.36853e9	0.288867
$681$	0	0
$682$	−4.05656e9	−0.489681
$683$	−2.10450e9	−0.252742	−0.126371	−	0.991983i	$-0.540333\pi$
$683$	−2.10450e9	−0.252742	−0.126371	+	0.991983i	$0.540333\pi$
$684$	0	0
$685$	5.94072e8	0.0706191
$686$	−1.74100e9	−0.205904
$687$	0	0
$688$	4.28575e9	0.501727
$689$	3.33261e9	0.388166
$690$	0	0
$691$	8.19673e9	0.945078	0.472539	−	0.881310i	$-0.343338\pi$
$691$	8.19673e9	0.945078	0.472539	+	0.881310i	$0.343338\pi$
$692$	6.93017e9	0.795010
$693$	0	0
$694$	−2.95787e9	−0.335909
$695$	3.78272e8	0.0427423
$696$	0	0
$697$	1.41499e10	1.58284
$698$	−5.81493e9	−0.647218
$699$	0	0
$700$	−1.60757e9	−0.177145
$701$	1.58794e9	0.174109	0.0870547	−	0.996204i	$-0.472255\pi$
$701$	1.58794e9	0.174109	0.0870547	+	0.996204i	$0.472255\pi$
$702$	0	0
$703$	−1.70223e10	−1.84788
$704$	3.90082e7	0.00421358
$705$	0	0
$706$	−2.63994e9	−0.282344
$707$	−3.69981e9	−0.393741
$708$	0	0
$709$	−1.39994e10	−1.47519	−0.737596	−	0.675242i	$-0.764039\pi$
$709$	−1.39994e10	−1.47519	−0.737596	+	0.675242i	$0.764039\pi$
$710$	4.21077e8	0.0441527
$711$	0	0
$712$	−1.21325e10	−1.25971
$713$	−1.00846e10	−1.04195
$714$	0	0
$715$	−3.26014e9	−0.333553
$716$	5.55525e9	0.565598
$717$	0	0
$718$	5.51968e9	0.556517
$719$	3.63177e8	0.0364391	0.0182195	−	0.999834i	$-0.494200\pi$
$719$	3.63177e8	0.0364391	0.0182195	+	0.999834i	$0.494200\pi$
$720$	0	0
$721$	9.08277e8	0.0902495
$722$	−4.11589e9	−0.406990
$723$	0	0
$724$	3.06594e9	0.300247
$725$	−1.09401e10	−1.06619
$726$	0	0
$727$	−7.18128e9	−0.693157	−0.346578	−	0.938021i	$-0.612657\pi$
$727$	−7.18128e9	−0.693157	−0.346578	+	0.938021i	$0.612657\pi$
$728$	−3.12643e9	−0.300324
$729$	0	0
$730$	1.84758e6	0.000175782 0
$731$	1.53751e10	1.45582
$732$	0	0
$733$	1.12100e10	1.05133	0.525667	−	0.850691i	$-0.323816\pi$
$733$	1.12100e10	1.05133	0.525667	+	0.850691i	$0.323816\pi$
$734$	−6.10985e9	−0.570288
$735$	0	0
$736$	−7.79760e9	−0.720922
$737$	−9.69459e9	−0.892059
$738$	0	0
$739$	−2.61736e9	−0.238566	−0.119283	−	0.992860i	$-0.538060\pi$
$739$	−2.61736e9	−0.238566	−0.119283	+	0.992860i	$0.538060\pi$
$740$	3.27914e9	0.297474
$741$	0	0
$742$	2.91289e8	0.0261765
$743$	2.16513e10	1.93653	0.968264	−	0.249930i	$-0.0804075\pi$
$743$	2.16513e10	1.93653	0.968264	+	0.249930i	$0.0804075\pi$
$744$	0	0
$745$	−8.14933e7	−0.00722063
$746$	−2.77802e9	−0.244991
$747$	0	0
$748$	9.15123e9	0.799510
$749$	−2.60783e9	−0.226774
$750$	0	0
$751$	−1.23735e10	−1.06599	−0.532995	−	0.846118i	$-0.678934\pi$
$751$	−1.23735e10	−1.06599	−0.532995	+	0.846118i	$0.678934\pi$
$752$	4.31689e9	0.370176
$753$	0	0
$754$	−9.47759e9	−0.805190
$755$	4.51187e9	0.381542
$756$	0	0
$757$	−1.68097e9	−0.140840	−0.0704198	−	0.997517i	$-0.522434\pi$
$757$	−1.68097e9	−0.140840	−0.0704198	+	0.997517i	$0.522434\pi$
$758$	1.24014e9	0.103426
$759$	0	0
$760$	3.71976e9	0.307374
$761$	−1.31161e10	−1.07884	−0.539421	−	0.842036i	$-0.681357\pi$
$761$	−1.31161e10	−1.07884	−0.539421	+	0.842036i	$0.681357\pi$
$762$	0	0
$763$	4.25036e9	0.346409
$764$	−1.06035e10	−0.860246
$765$	0	0
$766$	−3.01011e6	−0.000241981 0
$767$	2.55668e9	0.204593
$768$	0	0
$769$	1.42811e10	1.13245	0.566224	−	0.824251i	$-0.308404\pi$
$769$	1.42811e10	1.13245	0.566224	+	0.824251i	$0.308404\pi$
$770$	−2.84955e8	−0.0224936
$771$	0	0
$772$	−1.77138e10	−1.38565
$773$	8.34783e9	0.650048	0.325024	−	0.945706i	$-0.394628\pi$
$773$	8.34783e9	0.650048	0.325024	+	0.945706i	$0.394628\pi$
$774$	0	0
$775$	1.72651e10	1.33233
$776$	−5.22711e9	−0.401556
$777$	0	0
$778$	−4.47669e9	−0.340823
$779$	2.22223e10	1.68425
$780$	0	0
$781$	3.65226e9	0.274336
$782$	−5.57180e9	−0.416651
$783$	0	0
$784$	−5.70618e9	−0.422902
$785$	3.16565e9	0.233571
$786$	0	0
$787$	1.47026e10	1.07518	0.537591	−	0.843206i	$-0.319334\pi$
$787$	1.47026e10	1.07518	0.537591	+	0.843206i	$0.319334\pi$
$788$	−1.31199e10	−0.955184
$789$	0	0
$790$	5.50613e8	0.0397330
$791$	−1.63687e9	−0.117597
$792$	0	0
$793$	−6.20965e9	−0.442192
$794$	4.81135e9	0.341111
$795$	0	0
$796$	6.65640e9	0.467782
$797$	−3.94070e9	−0.275721	−0.137860	−	0.990452i	$-0.544023\pi$
$797$	−3.94070e9	−0.275721	−0.137860	+	0.990452i	$0.544023\pi$
$798$	0	0
$799$	1.54868e10	1.07411
$800$	1.33497e10	0.921843
$801$	0	0
$802$	9.17467e9	0.628030
$803$	1.60252e7	0.00109219
$804$	0	0
$805$	−7.08397e8	−0.0478620
$806$	1.49571e10	1.00618
$807$	0	0
$808$	1.97640e10	1.31806
$809$	−2.12121e10	−1.40852	−0.704260	−	0.709942i	$-0.748721\pi$
$809$	−2.12121e10	−1.40852	−0.704260	+	0.709942i	$0.748721\pi$
$810$	0	0
$811$	4.13209e9	0.272018	0.136009	−	0.990708i	$-0.456572\pi$
$811$	4.13209e9	0.272018	0.136009	+	0.990708i	$0.456572\pi$
$812$	3.38238e9	0.221705
$813$	0	0
$814$	−6.96589e9	−0.452680
$815$	−5.79375e9	−0.374893
$816$	0	0
$817$	2.41465e10	1.54909
$818$	3.58821e9	0.229214
$819$	0	0
$820$	−4.28085e9	−0.271133
$821$	−4.99283e9	−0.314880	−0.157440	−	0.987529i	$-0.550324\pi$
$821$	−4.99283e9	−0.314880	−0.157440	+	0.987529i	$0.550324\pi$
$822$	0	0
$823$	8.56606e9	0.535650	0.267825	−	0.963468i	$-0.413695\pi$
$823$	8.56606e9	0.535650	0.267825	+	0.963468i	$0.413695\pi$
$824$	−4.85193e9	−0.302113
$825$	0	0
$826$	2.23468e8	0.0137970
$827$	−2.19884e10	−1.35184	−0.675920	−	0.736975i	$-0.736253\pi$
$827$	−2.19884e10	−1.35184	−0.675920	+	0.736975i	$0.736253\pi$
$828$	0	0
$829$	−1.74819e9	−0.106573	−0.0532867	−	0.998579i	$-0.516970\pi$
$829$	−1.74819e9	−0.106573	−0.0532867	+	0.998579i	$0.516970\pi$
$830$	1.44896e9	0.0879595
$831$	0	0
$832$	−1.43829e8	−0.00865792
$833$	−2.04709e10	−1.22710
$834$	0	0
$835$	4.43248e9	0.263478
$836$	1.43719e10	0.850732
$837$	0	0
$838$	1.11842e10	0.656523
$839$	−7.57544e8	−0.0442834	−0.0221417	−	0.999755i	$-0.507048\pi$
$839$	−7.57544e8	−0.0442834	−0.0221417	+	0.999755i	$0.507048\pi$
$840$	0	0
$841$	5.76829e9	0.334396
$842$	−7.48251e9	−0.431972
$843$	0	0
$844$	−1.46584e10	−0.839246
$845$	7.15327e9	0.407855
$846$	0	0
$847$	1.75379e9	0.0991710
$848$	1.96722e9	0.110782
$849$	0	0
$850$	9.53908e9	0.532771
$851$	−1.73172e10	−0.963215
$852$	0	0
$853$	−1.72683e9	−0.0952636	−0.0476318	−	0.998865i	$-0.515167\pi$
$853$	−1.72683e9	−0.0952636	−0.0476318	+	0.998865i	$0.515167\pi$
$854$	−5.42759e8	−0.0298198
$855$	0	0
$856$	1.39308e10	0.759132
$857$	3.43055e10	1.86179	0.930895	−	0.365286i	$-0.119029\pi$
$857$	3.43055e10	1.86179	0.930895	+	0.365286i	$0.119029\pi$
$858$	0	0
$859$	−1.16013e10	−0.624499	−0.312249	−	0.950000i	$-0.601082\pi$
$859$	−1.16013e10	−0.624499	−0.312249	+	0.950000i	$0.601082\pi$
$860$	−4.65153e9	−0.249374
$861$	0	0
$862$	1.33619e10	0.710549
$863$	−1.06656e10	−0.564870	−0.282435	−	0.959286i	$-0.591142\pi$
$863$	−1.06656e10	−0.564870	−0.282435	+	0.959286i	$0.591142\pi$
$864$	0	0
$865$	−5.22830e9	−0.274665
$866$	−3.56005e8	−0.0186270
$867$	0	0
$868$	−5.33792e9	−0.277047
$869$	4.77580e9	0.246875
$870$	0	0
$871$	3.57453e10	1.83297
$872$	−2.27050e10	−1.15962
$873$	0	0
$874$	−8.75046e9	−0.443344
$875$	2.52679e9	0.127509
$876$	0	0
$877$	−5.25940e9	−0.263292	−0.131646	−	0.991297i	$-0.542026\pi$
$877$	−5.25940e9	−0.263292	−0.131646	+	0.991297i	$0.542026\pi$
$878$	−3.14503e8	−0.0156817
$879$	0	0
$880$	−1.92444e9	−0.0951954
$881$	2.79482e10	1.37701	0.688507	−	0.725230i	$-0.258266\pi$
$881$	2.79482e10	1.37701	0.688507	+	0.725230i	$0.258266\pi$
$882$	0	0
$883$	3.72423e9	0.182043	0.0910214	−	0.995849i	$-0.470987\pi$
$883$	3.72423e9	0.182043	0.0910214	+	0.995849i	$0.470987\pi$
$884$	−3.37419e10	−1.64281
$885$	0	0
$886$	−3.22157e9	−0.155614
$887$	−6.26596e9	−0.301477	−0.150739	−	0.988574i	$-0.548165\pi$
$887$	−6.26596e9	−0.301477	−0.150739	+	0.988574i	$0.548165\pi$
$888$	0	0
$889$	2.95021e9	0.140830
$890$	4.07724e9	0.193866
$891$	0	0
$892$	−2.42116e10	−1.14221
$893$	2.43219e10	1.14292
$894$	0	0
$895$	−4.19102e9	−0.195407
$896$	−5.15081e9	−0.239220
$897$	0	0
$898$	−1.39257e10	−0.641727
$899$	−3.63263e10	−1.66748
$900$	0	0
$901$	7.05740e9	0.321446
$902$	9.09382e9	0.412594
$903$	0	0
$904$	8.74403e9	0.393661
$905$	−2.31302e9	−0.103731
$906$	0	0
$907$	8.21053e9	0.365381	0.182690	−	0.983170i	$-0.441519\pi$
$907$	8.21053e9	0.365381	0.182690	+	0.983170i	$0.441519\pi$
$908$	3.44596e10	1.52760
$909$	0	0
$910$	1.05067e9	0.0462191
$911$	1.57505e10	0.690207	0.345103	−	0.938565i	$-0.387844\pi$
$911$	1.57505e10	0.690207	0.345103	+	0.938565i	$0.387844\pi$
$912$	0	0
$913$	1.25677e10	0.546523
$914$	−1.90385e10	−0.824746
$915$	0	0
$916$	1.72973e10	0.743607
$917$	−2.80618e9	−0.120177
$918$	0	0
$919$	−6.94140e9	−0.295014	−0.147507	−	0.989061i	$-0.547125\pi$
$919$	−6.94140e9	−0.295014	−0.147507	+	0.989061i	$0.547125\pi$
$920$	3.78419e9	0.160220
$921$	0	0
$922$	−1.87773e10	−0.788994
$923$	−1.34664e10	−0.563697
$924$	0	0
$925$	2.96475e10	1.23166
$926$	−8.46318e9	−0.350264
$927$	0	0
$928$	−2.80881e10	−1.15373
$929$	1.64084e9	0.0671448	0.0335724	−	0.999436i	$-0.489312\pi$
$929$	1.64084e9	0.0671448	0.0335724	+	0.999436i	$0.489312\pi$
$930$	0	0
$931$	−3.21493e10	−1.30571
$932$	−2.83939e10	−1.14887
$933$	0	0
$934$	−9.55004e8	−0.0383523
$935$	−6.90393e9	−0.276220
$936$	0	0
$937$	3.84565e10	1.52715	0.763575	−	0.645719i	$-0.223442\pi$
$937$	3.84565e10	1.52715	0.763575	+	0.645719i	$0.223442\pi$
$938$	3.12435e9	0.123609
$939$	0	0
$940$	−4.68532e9	−0.183989
$941$	−3.13483e10	−1.22645	−0.613226	−	0.789907i	$-0.710129\pi$
$941$	−3.13483e10	−1.22645	−0.613226	+	0.789907i	$0.710129\pi$
$942$	0	0
$943$	2.26072e10	0.877921
$944$	1.50919e9	0.0583905
$945$	0	0
$946$	9.88124e9	0.379483
$947$	4.56816e10	1.74790	0.873950	−	0.486016i	$-0.161550\pi$
$947$	4.56816e10	1.74790	0.873950	+	0.486016i	$0.161550\pi$
$948$	0	0
$949$	−5.90871e7	−0.00224420
$950$	1.49810e10	0.566903
$951$	0	0
$952$	−6.62078e9	−0.248702
$953$	2.57557e10	0.963937	0.481968	−	0.876189i	$-0.339922\pi$
$953$	2.57557e10	0.963937	0.481968	+	0.876189i	$0.339922\pi$
$954$	0	0
$955$	7.99955e9	0.297204
$956$	1.69619e10	0.627872
$957$	0	0
$958$	5.24327e9	0.192674
$959$	−1.66061e9	−0.0608000
$960$	0	0
$961$	2.98159e10	1.08372
$962$	2.56842e10	0.930151
$963$	0	0
$964$	−2.25998e10	−0.812522
$965$	1.33638e10	0.478723
$966$	0	0
$967$	2.61784e10	0.931002	0.465501	−	0.885047i	$-0.345874\pi$
$967$	2.61784e10	0.931002	0.465501	+	0.885047i	$0.345874\pi$
$968$	−9.36857e9	−0.331978
$969$	0	0
$970$	1.75662e9	0.0617984
$971$	7.63541e9	0.267648	0.133824	−	0.991005i	$-0.457274\pi$
$971$	7.63541e9	0.267648	0.133824	+	0.991005i	$0.457274\pi$
$972$	0	0
$973$	−1.05739e9	−0.0367993
$974$	2.27050e10	0.787344
$975$	0	0
$976$	−3.66552e9	−0.126201
$977$	1.18991e10	0.408211	0.204105	−	0.978949i	$-0.434571\pi$
$977$	1.18991e10	0.408211	0.204105	+	0.978949i	$0.434571\pi$
$978$	0	0
$979$	3.53644e10	1.20456
$980$	6.19319e9	0.210195
$981$	0	0
$982$	6.43144e9	0.216729
$983$	3.88296e10	1.30384	0.651921	−	0.758287i	$-0.273963\pi$
$983$	3.88296e10	1.30384	0.651921	+	0.758287i	$0.273963\pi$
$984$	0	0
$985$	9.89796e9	0.330004
$986$	−2.00705e10	−0.666789
$987$	0	0
$988$	−5.29913e10	−1.74806
$989$	2.45647e10	0.807467
$990$	0	0
$991$	−4.18861e10	−1.36714	−0.683569	−	0.729886i	$-0.739573\pi$
$991$	−4.18861e10	−1.36714	−0.683569	+	0.729886i	$0.739573\pi$
$992$	4.43275e10	1.44172
$993$	0	0
$994$	−1.17704e9	−0.0380136
$995$	−5.02176e9	−0.161613
$996$	0	0
$997$	−2.75354e10	−0.879950	−0.439975	−	0.898010i	$-0.645013\pi$
$997$	−2.75354e10	−0.879950	−0.439975	+	0.898010i	$0.645013\pi$
$998$	1.63709e10	0.521333
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	531.8.a.d.1.6		17
3.2	odd	2		177.8.a.b.1.12	✓	17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.8.a.b.1.12	✓	17	3.2	odd	2
531.8.a.d.1.6		17	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)

\(f(q)\)	\(=\)	\(q-5.01814 q^{2} -102.818 q^{4} +77.5687 q^{5} -216.829 q^{7} +1158.28 q^{8} +O(q^{10})\)	\(q-5.01814 q^{2} -102.818 q^{4} +77.5687 q^{5} -216.829 q^{7} +1158.28 q^{8} -389.251 q^{10} -3376.21 q^{11} +12448.6 q^{13} +1088.08 q^{14} +7348.33 q^{16} +26362.1 q^{17} +41401.4 q^{19} -7975.48 q^{20} +16942.3 q^{22} +42118.5 q^{23} -72108.1 q^{25} -62468.7 q^{26} +22293.9 q^{28} +151717. q^{29} -239434. q^{31} -185135. q^{32} -132289. q^{34} -16819.1 q^{35} -411153. q^{37} -207758. q^{38} +89846.2 q^{40} +536752. q^{41} +583229. q^{43} +347136. q^{44} -211357. q^{46} +587465. q^{47} -776528. q^{49} +361849. q^{50} -1.27994e6 q^{52} +267710. q^{53} -261889. q^{55} -251148. q^{56} -761339. q^{58} +205379. q^{59} -498824. q^{61} +1.20151e6 q^{62} -11553.8 q^{64} +965620. q^{65} +2.87144e6 q^{67} -2.71050e6 q^{68} +84400.8 q^{70} -1.08176e6 q^{71} -4746.50 q^{73} +2.06322e6 q^{74} -4.25682e6 q^{76} +732060. q^{77} -1.41454e6 q^{79} +570000. q^{80} -2.69350e6 q^{82} -3.72243e6 q^{83} +2.04487e6 q^{85} -2.92672e6 q^{86} -3.91060e6 q^{88} -1.04746e7 q^{89} -2.69921e6 q^{91} -4.33055e6 q^{92} -2.94798e6 q^{94} +3.21145e6 q^{95} -4.51283e6 q^{97} +3.89673e6 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q + 32 q^{2} + 1166 q^{4} + 1072 q^{5} - 2407 q^{7} + 6645 q^{8}+O(q^{10}) \) 17 * q + 32 * q^2 + 1166 * q^4 + 1072 * q^5 - 2407 * q^7 + 6645 * q^8	\( 17 q + 32 q^{2} + 1166 q^{4} + 1072 q^{5} - 2407 q^{7} + 6645 q^{8} - 6391 q^{10} + 8888 q^{11} - 12702 q^{13} + 17555 q^{14} + 139226 q^{16} + 36167 q^{17} - 71037 q^{19} + 274883 q^{20} - 325182 q^{22} + 269995 q^{23} + 97329 q^{25} + 336906 q^{26} - 901362 q^{28} + 543825 q^{29} - 633109 q^{31} + 837062 q^{32} - 529288 q^{34} + 287621 q^{35} - 867607 q^{37} + 1727169 q^{38} - 815662 q^{40} + 1428939 q^{41} - 477060 q^{43} + 1667926 q^{44} + 5305549 q^{46} + 1217849 q^{47} + 4350738 q^{49} - 4561369 q^{50} + 4175994 q^{52} + 3487068 q^{53} - 960484 q^{55} + 5363196 q^{56} - 3082906 q^{58} + 3491443 q^{59} + 998917 q^{61} + 5742614 q^{62} + 17531621 q^{64} + 6075816 q^{65} - 356026 q^{67} + 16149231 q^{68} - 548798 q^{70} + 12879428 q^{71} - 6176157 q^{73} + 5971906 q^{74} - 17624580 q^{76} - 239687 q^{77} - 18886490 q^{79} + 70463349 q^{80} - 19351611 q^{82} + 22824893 q^{83} - 7973079 q^{85} + 27502196 q^{86} - 62527651 q^{88} + 30609647 q^{89} - 36301521 q^{91} + 41388548 q^{92} + 1010176 q^{94} + 29303629 q^{95} - 26249806 q^{97} + 93110852 q^{98}+O(q^{100}) \) 17 * q + 32 * q^2 + 1166 * q^4 + 1072 * q^5 - 2407 * q^7 + 6645 * q^8 - 6391 * q^10 + 8888 * q^11 - 12702 * q^13 + 17555 * q^14 + 139226 * q^16 + 36167 * q^17 - 71037 * q^19 + 274883 * q^20 - 325182 * q^22 + 269995 * q^23 + 97329 * q^25 + 336906 * q^26 - 901362 * q^28 + 543825 * q^29 - 633109 * q^31 + 837062 * q^32 - 529288 * q^34 + 287621 * q^35 - 867607 * q^37 + 1727169 * q^38 - 815662 * q^40 + 1428939 * q^41 - 477060 * q^43 + 1667926 * q^44 + 5305549 * q^46 + 1217849 * q^47 + 4350738 * q^49 - 4561369 * q^50 + 4175994 * q^52 + 3487068 * q^53 - 960484 * q^55 + 5363196 * q^56 - 3082906 * q^58 + 3491443 * q^59 + 998917 * q^61 + 5742614 * q^62 + 17531621 * q^64 + 6075816 * q^65 - 356026 * q^67 + 16149231 * q^68 - 548798 * q^70 + 12879428 * q^71 - 6176157 * q^73 + 5971906 * q^74 - 17624580 * q^76 - 239687 * q^77 - 18886490 * q^79 + 70463349 * q^80 - 19351611 * q^82 + 22824893 * q^83 - 7973079 * q^85 + 27502196 * q^86 - 62527651 * q^88 + 30609647 * q^89 - 36301521 * q^91 + 41388548 * q^92 + 1010176 * q^94 + 29303629 * q^95 - 26249806 * q^97 + 93110852 * q^98

Introduction

L-functions

Modular forms

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