LMFDB - Embedded newform 531.8.a.d.1.3

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			1.3
Root			$17.5255$ 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)

$f(q)$	$=$	$q-15.5255 q^{2} +113.041 q^{4} +141.845 q^{5} +105.285 q^{7} +232.240 q^{8} +O(q^{10})$	\(q-15.5255 q^{2} +113.041 q^{4} +141.845 q^{5} +105.285 q^{7} +232.240 q^{8} -2202.21 q^{10} +555.209 q^{11} -11289.1 q^{13} -1634.61 q^{14} -18074.9 q^{16} +3139.99 q^{17} -21947.5 q^{19} +16034.3 q^{20} -8619.91 q^{22} -28575.9 q^{23} -58005.1 q^{25} +175269. q^{26} +11901.6 q^{28} -160286. q^{29} -163594. q^{31} +250896. q^{32} -48750.0 q^{34} +14934.2 q^{35} -131107. q^{37} +340746. q^{38} +32942.1 q^{40} +277081. q^{41} +621893. q^{43} +62761.6 q^{44} +443655. q^{46} +1.39412e6 q^{47} -812458. q^{49} +900558. q^{50} -1.27614e6 q^{52} -1.49504e6 q^{53} +78753.5 q^{55} +24451.5 q^{56} +2.48851e6 q^{58} +205379. q^{59} -2.41889e6 q^{61} +2.53988e6 q^{62} -1.58169e6 q^{64} -1.60130e6 q^{65} +2.34039e6 q^{67} +354949. q^{68} -231861. q^{70} -52758.6 q^{71} +1.12536e6 q^{73} +2.03550e6 q^{74} -2.48098e6 q^{76} +58455.5 q^{77} +3.33432e6 q^{79} -2.56384e6 q^{80} -4.30183e6 q^{82} +5.69160e6 q^{83} +445391. q^{85} -9.65520e6 q^{86} +128942. q^{88} +5.02101e6 q^{89} -1.18858e6 q^{91} -3.23026e6 q^{92} -2.16444e7 q^{94} -3.11314e6 q^{95} +9.04920e6 q^{97} +1.26138e7 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−15.5255	−1.37227	−0.686137	−	0.727472i	$-0.740695\pi$
$2$	−15.5255	−1.37227	−0.686137	+	0.727472i	$0.740695\pi$
$3$	0	0
$3$	0	0
$4$	113.041	0.883136
$5$	141.845	0.507479	0.253740	−	0.967273i	$-0.418339\pi$
$5$	141.845	0.507479	0.253740	+	0.967273i	$0.418339\pi$
$6$	0	0
$7$	105.285	0.116018	0.0580090	−	0.998316i	$-0.481525\pi$
$7$	105.285	0.116018	0.0580090	+	0.998316i	$0.481525\pi$
$8$	232.240	0.160370
$9$	0	0
$10$	−2202.21	−0.696401
$11$	555.209	0.125772	0.0628858	−	0.998021i	$-0.479970\pi$
$11$	555.209	0.125772	0.0628858	+	0.998021i	$0.479970\pi$
$12$	0	0
$13$	−11289.1	−1.42514	−0.712572	−	0.701599i	$-0.752470\pi$
$13$	−11289.1	−1.42514	−0.712572	+	0.701599i	$0.752470\pi$
$14$	−1634.61	−0.159208
$15$	0	0
$16$	−18074.9	−1.10321
$17$	3139.99	0.155009	0.0775046	−	0.996992i	$-0.475305\pi$
$17$	3139.99	0.155009	0.0775046	+	0.996992i	$0.475305\pi$
$18$	0	0
$19$	−21947.5	−0.734088	−0.367044	−	0.930204i	$-0.619630\pi$
$19$	−21947.5	−0.734088	−0.367044	+	0.930204i	$0.619630\pi$
$20$	16034.3	0.448173
$21$	0	0
$22$	−8619.91	−0.172593
$23$	−28575.9	−0.489725	−0.244863	−	0.969558i	$-0.578743\pi$
$23$	−28575.9	−0.489725	−0.244863	+	0.969558i	$0.578743\pi$
$24$	0	0
$25$	−58005.1	−0.742465
$26$	175269.	1.95569
$27$	0	0
$28$	11901.6	0.102460
$29$	−160286.	−1.22040	−0.610199	−	0.792248i	$-0.708910\pi$
$29$	−160286.	−1.22040	−0.610199	+	0.792248i	$0.708910\pi$
$30$	0	0
$31$	−163594.	−0.986284	−0.493142	−	0.869949i	$-0.664152\pi$
$31$	−163594.	−0.986284	−0.493142	+	0.869949i	$0.664152\pi$
$32$	250896.	1.35353
$33$	0	0
$34$	−48750.0	−0.212715
$35$	14934.2	0.0588767
$36$	0	0
$37$	−131107.	−0.425519	−0.212759	−	0.977105i	$-0.568245\pi$
$37$	−131107.	−0.425519	−0.212759	+	0.977105i	$0.568245\pi$
$38$	340746.	1.00737
$39$	0	0
$40$	32942.1	0.0813843
$41$	277081.	0.627862	0.313931	−	0.949446i	$-0.398354\pi$
$41$	277081.	0.627862	0.313931	+	0.949446i	$0.398354\pi$
$42$	0	0
$43$	621893.	1.19282	0.596411	−	0.802679i	$-0.296593\pi$
$43$	621893.	1.19282	0.596411	+	0.802679i	$0.296593\pi$
$44$	62761.6	0.111073
$45$	0	0
$46$	443655.	0.672037
$47$	1.39412e6	1.95865	0.979325	−	0.202292i	$-0.0648390\pi$
$47$	1.39412e6	1.95865	0.979325	+	0.202292i	$0.0648390\pi$
$48$	0	0
$49$	−812458.	−0.986540
$50$	900558.	1.01887
$51$	0	0
$52$	−1.27614e6	−1.25860
$53$	−1.49504e6	−1.37939	−0.689696	−	0.724099i	$-0.742256\pi$
$53$	−1.49504e6	−1.37939	−0.689696	+	0.724099i	$0.742256\pi$
$54$	0	0
$55$	78753.5	0.0638265
$56$	24451.5	0.0186058
$57$	0	0
$58$	2.48851e6	1.67472
$59$	205379.	0.130189
$59$	205379.	0.130189
$60$	0	0
$61$	−2.41889e6	−1.36446	−0.682230	−	0.731137i	$-0.738990\pi$
$61$	−2.41889e6	−1.36446	−0.682230	+	0.731137i	$0.738990\pi$
$62$	2.53988e6	1.35345
$63$	0	0
$64$	−1.58169e6	−0.754210
$65$	−1.60130e6	−0.723231
$66$	0	0
$67$	2.34039e6	0.950664	0.475332	−	0.879807i	$-0.342328\pi$
$67$	2.34039e6	0.950664	0.475332	+	0.879807i	$0.342328\pi$
$68$	354949.	0.136894
$69$	0	0
$70$	−231861.	−0.0807950
$71$	−52758.6	−0.0174940	−0.00874700	−	0.999962i	$-0.502784\pi$
$71$	−52758.6	−0.0174940	−0.00874700	+	0.999962i	$0.502784\pi$
$72$	0	0
$73$	1.12536e6	0.338581	0.169290	−	0.985566i	$-0.445852\pi$
$73$	1.12536e6	0.338581	0.169290	+	0.985566i	$0.445852\pi$
$74$	2.03550e6	0.583928
$75$	0	0
$76$	−2.48098e6	−0.648299
$77$	58455.5	0.0145918
$78$	0	0
$79$	3.33432e6	0.760873	0.380436	−	0.924807i	$-0.375774\pi$
$79$	3.33432e6	0.760873	0.380436	+	0.924807i	$0.375774\pi$
$80$	−2.56384e6	−0.559855
$81$	0	0
$82$	−4.30183e6	−0.861598
$83$	5.69160e6	1.09260	0.546300	−	0.837590i	$-0.316036\pi$
$83$	5.69160e6	1.09260	0.546300	+	0.837590i	$0.316036\pi$
$84$	0	0
$85$	445391.	0.0786639
$86$	−9.65520e6	−1.63688
$87$	0	0
$88$	128942.	0.0201700
$89$	5.02101e6	0.754963	0.377482	−	0.926017i	$-0.376790\pi$
$89$	5.02101e6	0.754963	0.377482	+	0.926017i	$0.376790\pi$
$90$	0	0
$91$	−1.18858e6	−0.165342
$92$	−3.23026e6	−0.432494
$93$	0	0
$94$	−2.16444e7	−2.68781
$95$	−3.11314e6	−0.372534
$96$	0	0
$97$	9.04920e6	1.00672	0.503361	−	0.864076i	$-0.332097\pi$
$97$	9.04920e6	1.00672	0.503361	+	0.864076i	$0.332097\pi$
$98$	1.26138e7	1.35380
$99$	0	0
$100$	−6.55697e6	−0.655697
$101$	−1.74915e6	−0.168928	−0.0844639	−	0.996427i	$-0.526918\pi$
$101$	−1.74915e6	−0.168928	−0.0844639	+	0.996427i	$0.526918\pi$
$102$	0	0
$103$	1.68825e7	1.52232	0.761160	−	0.648564i	$-0.224630\pi$
$103$	1.68825e7	1.52232	0.761160	+	0.648564i	$0.224630\pi$
$104$	−2.62179e6	−0.228550
$105$	0	0
$106$	2.32113e7	1.89290
$107$	−7.69410e6	−0.607176	−0.303588	−	0.952803i	$-0.598185\pi$
$107$	−7.69410e6	−0.607176	−0.303588	+	0.952803i	$0.598185\pi$
$108$	0	0
$109$	−2.31641e7	−1.71326	−0.856629	−	0.515932i	$-0.827446\pi$
$109$	−2.31641e7	−1.71326	−0.856629	+	0.515932i	$0.827446\pi$
$110$	−1.22269e6	−0.0875874
$111$	0	0
$112$	−1.90303e6	−0.127992
$113$	−2.01725e7	−1.31518	−0.657590	−	0.753376i	$-0.728424\pi$
$113$	−2.01725e7	−1.31518	−0.657590	+	0.753376i	$0.728424\pi$
$114$	0	0
$115$	−4.05334e6	−0.248525
$116$	−1.81189e7	−1.07778
$117$	0	0
$118$	−3.18861e6	−0.178655
$119$	330595.	0.0179838
$120$	0	0
$121$	−1.91789e7	−0.984182
$122$	3.75544e7	1.87241
$123$	0	0
$124$	−1.84929e7	−0.871023
$125$	−1.93093e7	−0.884265
$126$	0	0
$127$	1.39057e6	0.0602395	0.0301197	−	0.999546i	$-0.490411\pi$
$127$	1.39057e6	0.0602395	0.0301197	+	0.999546i	$0.490411\pi$
$128$	−7.55808e6	−0.318549
$129$	0	0
$130$	2.48611e7	0.992471
$131$	4.16332e6	0.161804	0.0809022	−	0.996722i	$-0.474220\pi$
$131$	4.16332e6	0.161804	0.0809022	+	0.996722i	$0.474220\pi$
$132$	0	0
$133$	−2.31075e6	−0.0851673
$134$	−3.63358e7	−1.30457
$135$	0	0
$136$	729232.	0.0248588
$137$	−3.71579e7	−1.23461	−0.617304	−	0.786724i	$-0.711775\pi$
$137$	−3.71579e7	−1.23461	−0.617304	+	0.786724i	$0.711775\pi$
$138$	0	0
$139$	−738784.	−0.0233327	−0.0116664	−	0.999932i	$-0.503714\pi$
$139$	−738784.	−0.0233327	−0.0116664	+	0.999932i	$0.503714\pi$
$140$	1.68818e6	0.0519961
$141$	0	0
$142$	819104.	0.0240066
$143$	−6.26783e6	−0.179243
$144$	0	0
$145$	−2.27357e7	−0.619327
$146$	−1.74718e7	−0.464626
$147$	0	0
$148$	−1.48205e7	−0.375791
$149$	7.16242e7	1.77381	0.886906	−	0.461949i	$-0.152850\pi$
$149$	7.16242e7	1.77381	0.886906	+	0.461949i	$0.152850\pi$
$150$	0	0
$151$	−3.49956e7	−0.827168	−0.413584	−	0.910466i	$-0.635723\pi$
$151$	−3.49956e7	−0.827168	−0.413584	+	0.910466i	$0.635723\pi$
$152$	−5.09710e6	−0.117725
$153$	0	0
$154$	−907551.	−0.0200239
$155$	−2.32050e7	−0.500519
$156$	0	0
$157$	−3.84270e7	−0.792478	−0.396239	−	0.918147i	$-0.629685\pi$
$157$	−3.84270e7	−0.792478	−0.396239	+	0.918147i	$0.629685\pi$
$158$	−5.17669e7	−1.04413
$159$	0	0
$160$	3.55883e7	0.686890
$161$	−3.00863e6	−0.0568169
$162$	0	0
$163$	−4.69770e7	−0.849627	−0.424813	−	0.905281i	$-0.639660\pi$
$163$	−4.69770e7	−0.849627	−0.424813	+	0.905281i	$0.639660\pi$
$164$	3.13217e7	0.554487
$165$	0	0
$166$	−8.83650e7	−1.49935
$167$	−5.23525e7	−0.869820	−0.434910	−	0.900474i	$-0.643220\pi$
$167$	−5.23525e7	−0.869820	−0.434910	+	0.900474i	$0.643220\pi$
$168$	0	0
$169$	6.46959e7	1.03103
$170$	−6.91493e6	−0.107948
$171$	0	0
$172$	7.02996e7	1.05342
$173$	1.05438e8	1.54823	0.774115	−	0.633046i	$-0.218195\pi$
$173$	1.05438e8	1.54823	0.774115	+	0.633046i	$0.218195\pi$
$174$	0	0
$175$	−6.10709e6	−0.0861392
$176$	−1.00354e7	−0.138752
$177$	0	0
$178$	−7.79537e7	−1.03602
$179$	7.74219e7	1.00897	0.504485	−	0.863421i	$-0.331682\pi$
$179$	7.74219e7	1.00897	0.504485	+	0.863421i	$0.331682\pi$
$180$	0	0
$181$	1.44384e8	1.80986	0.904930	−	0.425561i	$-0.139923\pi$
$181$	1.44384e8	1.80986	0.904930	+	0.425561i	$0.139923\pi$
$182$	1.84533e7	0.226895
$183$	0	0
$184$	−6.63647e6	−0.0785371
$185$	−1.85968e7	−0.215942
$186$	0	0
$187$	1.74335e6	0.0194957
$188$	1.57593e8	1.72975
$189$	0	0
$190$	4.83331e7	0.511219
$191$	−1.83193e8	−1.90236	−0.951178	−	0.308642i	$-0.900125\pi$
$191$	−1.83193e8	−1.90236	−0.951178	+	0.308642i	$0.900125\pi$
$192$	0	0
$193$	9.07393e7	0.908542	0.454271	−	0.890864i	$-0.349900\pi$
$193$	9.07393e7	0.908542	0.454271	+	0.890864i	$0.349900\pi$
$194$	−1.40493e8	−1.38150
$195$	0	0
$196$	−9.18414e7	−0.871249
$197$	−9.27275e7	−0.864125	−0.432063	−	0.901844i	$-0.642214\pi$
$197$	−9.27275e7	−0.864125	−0.432063	+	0.901844i	$0.642214\pi$
$198$	0	0
$199$	7.94761e7	0.714909	0.357455	−	0.933931i	$-0.383645\pi$
$199$	7.94761e7	0.714909	0.357455	+	0.933931i	$0.383645\pi$
$200$	−1.34711e7	−0.119069
$201$	0	0
$202$	2.71564e7	0.231815
$203$	−1.68757e7	−0.141588
$204$	0	0
$205$	3.93026e7	0.318627
$206$	−2.62109e8	−2.08904
$207$	0	0
$208$	2.04050e8	1.57223
$209$	−1.21855e7	−0.0923273
$210$	0	0
$211$	1.26710e8	0.928588	0.464294	−	0.885681i	$-0.346308\pi$
$211$	1.26710e8	0.928588	0.464294	+	0.885681i	$0.346308\pi$
$212$	−1.69002e8	−1.21819
$213$	0	0
$214$	1.19455e8	0.833212
$215$	8.82123e7	0.605333
$216$	0	0
$217$	−1.72241e7	−0.114427
$218$	3.59635e8	2.35106
$219$	0	0
$220$	8.90241e6	0.0563674
$221$	−3.54478e7	−0.220910
$222$	0	0
$223$	1.08372e8	0.654410	0.327205	−	0.944953i	$-0.393893\pi$
$223$	1.08372e8	0.654410	0.327205	+	0.944953i	$0.393893\pi$
$224$	2.64157e7	0.157034
$225$	0	0
$226$	3.13188e8	1.80479
$227$	−1.82593e8	−1.03608	−0.518040	−	0.855356i	$-0.673338\pi$
$227$	−1.82593e8	−1.03608	−0.518040	+	0.855356i	$0.673338\pi$
$228$	0	0
$229$	1.61240e8	0.887256	0.443628	−	0.896211i	$-0.353691\pi$
$229$	1.61240e8	0.887256	0.443628	+	0.896211i	$0.353691\pi$
$230$	6.29302e7	0.341045
$231$	0	0
$232$	−3.72247e7	−0.195715
$233$	1.36205e8	0.705421	0.352711	−	0.935732i	$-0.385260\pi$
$233$	1.36205e8	0.705421	0.352711	+	0.935732i	$0.385260\pi$
$234$	0	0
$235$	1.97748e8	0.993975
$236$	2.32163e7	0.114974
$237$	0	0
$238$	−5.13266e6	−0.0246788
$239$	1.32804e8	0.629241	0.314620	−	0.949218i	$-0.398123\pi$
$239$	1.32804e8	0.629241	0.314620	+	0.949218i	$0.398123\pi$
$240$	0	0
$241$	−1.82912e8	−0.841749	−0.420874	−	0.907119i	$-0.638277\pi$
$241$	−1.82912e8	−0.841749	−0.420874	+	0.907119i	$0.638277\pi$
$242$	2.97762e8	1.35057
$243$	0	0
$244$	−2.73434e8	−1.20500
$245$	−1.15243e8	−0.500649
$246$	0	0
$247$	2.47768e8	1.04618
$248$	−3.79931e7	−0.158170
$249$	0	0
$250$	2.99787e8	1.21345
$251$	3.69029e8	1.47300	0.736500	−	0.676438i	$-0.236477\pi$
$251$	3.69029e8	1.47300	0.736500	+	0.676438i	$0.236477\pi$
$252$	0	0
$253$	−1.58656e7	−0.0615935
$254$	−2.15894e7	−0.0826651
$255$	0	0
$256$	3.19800e8	1.19135
$257$	2.11987e8	0.779010	0.389505	−	0.921024i	$-0.372646\pi$
$257$	2.11987e8	0.779010	0.389505	+	0.921024i	$0.372646\pi$
$258$	0	0
$259$	−1.38036e7	−0.0493678
$260$	−1.81014e8	−0.638711
$261$	0	0
$262$	−6.46377e7	−0.222040
$263$	1.26702e8	0.429476	0.214738	−	0.976672i	$-0.431110\pi$
$263$	1.26702e8	0.429476	0.214738	+	0.976672i	$0.431110\pi$
$264$	0	0
$265$	−2.12064e8	−0.700013
$266$	3.58756e7	0.116873
$267$	0	0
$268$	2.64561e8	0.839565
$269$	2.67421e8	0.837650	0.418825	−	0.908067i	$-0.362442\pi$
$269$	2.67421e8	0.837650	0.418825	+	0.908067i	$0.362442\pi$
$270$	0	0
$271$	−2.12216e7	−0.0647718	−0.0323859	−	0.999475i	$-0.510311\pi$
$271$	−2.12216e7	−0.0647718	−0.0323859	+	0.999475i	$0.510311\pi$
$272$	−5.67552e7	−0.171007
$273$	0	0
$274$	5.76895e8	1.69422
$275$	−3.22050e7	−0.0933809
$276$	0	0
$277$	2.91983e8	0.825425	0.412713	−	0.910861i	$-0.364581\pi$
$277$	2.91983e8	0.825425	0.412713	+	0.910861i	$0.364581\pi$
$278$	1.14700e7	0.0320189
$279$	0	0
$280$	3.46832e6	0.00944204
$281$	−2.59836e8	−0.698597	−0.349298	−	0.937012i	$-0.613580\pi$
$281$	−2.59836e8	−0.698597	−0.349298	+	0.937012i	$0.613580\pi$
$282$	0	0
$283$	3.61529e8	0.948180	0.474090	−	0.880476i	$-0.342777\pi$
$283$	3.61529e8	0.948180	0.474090	+	0.880476i	$0.342777\pi$
$284$	−5.96391e6	−0.0154496
$285$	0	0
$286$	9.73112e7	0.245970
$287$	2.91726e7	0.0728432
$288$	0	0
$289$	−4.00479e8	−0.975972
$290$	3.52983e8	0.849886
$291$	0	0
$292$	1.27213e8	0.299013
$293$	6.52155e8	1.51466	0.757328	−	0.653034i	$-0.226504\pi$
$293$	6.52155e8	1.51466	0.757328	+	0.653034i	$0.226504\pi$
$294$	0	0
$295$	2.91319e7	0.0660682
$296$	−3.04482e7	−0.0682404
$297$	0	0
$298$	−1.11200e9	−2.43416
$299$	3.22597e8	0.697929
$300$	0	0
$301$	6.54763e7	0.138389
$302$	5.43324e8	1.13510
$303$	0	0
$304$	3.96700e8	0.809851
$305$	−3.43106e8	−0.692436
$306$	0	0
$307$	−5.34821e8	−1.05493	−0.527466	−	0.849576i	$-0.676858\pi$
$307$	−5.34821e8	−1.05493	−0.527466	+	0.849576i	$0.676858\pi$
$308$	6.60789e6	0.0128865
$309$	0	0
$310$	3.60269e8	0.686849
$311$	8.03720e8	1.51511	0.757554	−	0.652773i	$-0.226394\pi$
$311$	8.03720e8	1.51511	0.757554	+	0.652773i	$0.226394\pi$
$312$	0	0
$313$	−3.67380e8	−0.677190	−0.338595	−	0.940932i	$-0.609952\pi$
$313$	−3.67380e8	−0.677190	−0.338595	+	0.940932i	$0.609952\pi$
$314$	5.96598e8	1.08750
$315$	0	0
$316$	3.76916e8	0.671954
$317$	6.78407e8	1.19614	0.598071	−	0.801443i	$-0.295934\pi$
$317$	6.78407e8	1.19614	0.598071	+	0.801443i	$0.295934\pi$
$318$	0	0
$319$	−8.89920e7	−0.153491
$320$	−2.24355e8	−0.382746
$321$	0	0
$322$	4.67105e7	0.0779684
$323$	−6.89150e7	−0.113790
$324$	0	0
$325$	6.54827e8	1.05812
$326$	7.29341e8	1.16592
$327$	0	0
$328$	6.43494e7	0.100690
$329$	1.46780e8	0.227239
$330$	0	0
$331$	−1.80151e8	−0.273048	−0.136524	−	0.990637i	$-0.543593\pi$
$331$	−1.80151e8	−0.273048	−0.136524	+	0.990637i	$0.543593\pi$
$332$	6.43386e8	0.964914
$333$	0	0
$334$	8.12799e8	1.19363
$335$	3.31973e8	0.482442
$336$	0	0
$337$	−6.10617e8	−0.869089	−0.434544	−	0.900650i	$-0.643091\pi$
$337$	−6.10617e8	−0.869089	−0.434544	+	0.900650i	$0.643091\pi$
$338$	−1.00444e9	−1.41486
$339$	0	0
$340$	5.03477e7	0.0694709
$341$	−9.08290e7	−0.124046
$342$	0	0
$343$	−1.72247e8	−0.230474
$344$	1.44429e8	0.191293
$345$	0	0
$346$	−1.63698e9	−2.12459
$347$	1.97837e8	0.254188	0.127094	−	0.991891i	$-0.459435\pi$
$347$	1.97837e8	0.254188	0.127094	+	0.991891i	$0.459435\pi$
$348$	0	0
$349$	−9.01885e8	−1.13570	−0.567848	−	0.823133i	$-0.692224\pi$
$349$	−9.01885e8	−1.13570	−0.567848	+	0.823133i	$0.692224\pi$
$350$	9.48156e7	0.118207
$351$	0	0
$352$	1.39300e8	0.170236
$353$	8.58268e8	1.03851	0.519256	−	0.854619i	$-0.326209\pi$
$353$	8.58268e8	1.03851	0.519256	+	0.854619i	$0.326209\pi$
$354$	0	0
$355$	−7.48353e6	−0.00887784
$356$	5.67582e8	0.666735
$357$	0	0
$358$	−1.20201e9	−1.38458
$359$	4.75915e8	0.542874	0.271437	−	0.962456i	$-0.412501\pi$
$359$	4.75915e8	0.542874	0.271437	+	0.962456i	$0.412501\pi$
$360$	0	0
$361$	−4.12178e8	−0.461115
$362$	−2.24164e9	−2.48362
$363$	0	0
$364$	−1.34359e8	−0.146020
$365$	1.59627e8	0.171823
$366$	0	0
$367$	7.17854e8	0.758062	0.379031	−	0.925384i	$-0.376257\pi$
$367$	7.17854e8	0.758062	0.379031	+	0.925384i	$0.376257\pi$
$368$	5.16508e8	0.540268
$369$	0	0
$370$	2.88725e8	0.296332
$371$	−1.57406e8	−0.160034
$372$	0	0
$373$	−5.85967e8	−0.584645	−0.292322	−	0.956320i	$-0.594428\pi$
$373$	−5.85967e8	−0.584645	−0.292322	+	0.956320i	$0.594428\pi$
$374$	−2.70664e7	−0.0267535
$375$	0	0
$376$	3.23770e8	0.314108
$377$	1.80948e9	1.73924
$378$	0	0
$379$	1.74459e8	0.164610	0.0823050	−	0.996607i	$-0.473772\pi$
$379$	1.74459e8	0.164610	0.0823050	+	0.996607i	$0.473772\pi$
$380$	−3.51914e8	−0.328998
$381$	0	0
$382$	2.84416e9	2.61055
$383$	6.24930e8	0.568376	0.284188	−	0.958769i	$-0.408276\pi$
$383$	6.24930e8	0.568376	0.284188	+	0.958769i	$0.408276\pi$
$384$	0	0
$385$	8.29160e6	0.00740501
$386$	−1.40877e9	−1.24677
$387$	0	0
$388$	1.02293e9	0.889071
$389$	2.05004e8	0.176579	0.0882896	−	0.996095i	$-0.471860\pi$
$389$	2.05004e8	0.176579	0.0882896	+	0.996095i	$0.471860\pi$
$390$	0	0
$391$	−8.97281e7	−0.0759119
$392$	−1.88685e8	−0.158211
$393$	0	0
$394$	1.43964e9	1.18582
$395$	4.72955e8	0.386127
$396$	0	0
$397$	−1.96710e9	−1.57783	−0.788915	−	0.614502i	$-0.789357\pi$
$397$	−1.96710e9	−1.57783	−0.788915	+	0.614502i	$0.789357\pi$
$398$	−1.23391e9	−0.981051
$399$	0	0
$400$	1.04844e9	0.819092
$401$	2.09175e9	1.61996	0.809979	−	0.586458i	$-0.199478\pi$
$401$	2.09175e9	1.61996	0.809979	+	0.586458i	$0.199478\pi$
$402$	0	0
$403$	1.84684e9	1.40560
$404$	−1.97726e8	−0.149186
$405$	0	0
$406$	2.62004e8	0.194298
$407$	−7.27917e7	−0.0535182
$408$	0	0
$409$	3.66808e8	0.265099	0.132549	−	0.991176i	$-0.457684\pi$
$409$	3.66808e8	0.265099	0.132549	+	0.991176i	$0.457684\pi$
$410$	−6.10192e8	−0.437243
$411$	0	0
$412$	1.90842e9	1.34441
$413$	2.16234e7	0.0151042
$414$	0	0
$415$	8.07324e8	0.554472
$416$	−2.83240e9	−1.92898
$417$	0	0
$418$	1.89186e8	0.126698
$419$	−1.27304e9	−0.845463	−0.422731	−	0.906255i	$-0.638929\pi$
$419$	−1.27304e9	−0.845463	−0.422731	+	0.906255i	$0.638929\pi$
$420$	0	0
$421$	−6.98288e8	−0.456087	−0.228043	−	0.973651i	$-0.573233\pi$
$421$	−6.98288e8	−0.456087	−0.228043	+	0.973651i	$0.573233\pi$
$422$	−1.96724e9	−1.27428
$423$	0	0
$424$	−3.47209e8	−0.221213
$425$	−1.82135e8	−0.115089
$426$	0	0
$427$	−2.54674e8	−0.158302
$428$	−8.69752e8	−0.536219
$429$	0	0
$430$	−1.36954e9	−0.830683
$431$	−2.63872e8	−0.158753	−0.0793765	−	0.996845i	$-0.525293\pi$
$431$	−2.63872e8	−0.158753	−0.0793765	+	0.996845i	$0.525293\pi$
$432$	0	0
$433$	2.13875e9	1.26606	0.633028	−	0.774128i	$-0.281812\pi$
$433$	2.13875e9	1.26606	0.633028	+	0.774128i	$0.281812\pi$
$434$	2.67413e8	0.157025
$435$	0	0
$436$	−2.61850e9	−1.51304
$437$	6.27170e8	0.359501
$438$	0	0
$439$	2.80384e9	1.58171	0.790856	−	0.612003i	$-0.209636\pi$
$439$	2.80384e9	1.58171	0.790856	+	0.612003i	$0.209636\pi$
$440$	1.82897e7	0.0102358
$441$	0	0
$442$	5.50345e8	0.303149
$443$	−2.51161e9	−1.37259	−0.686293	−	0.727326i	$-0.740763\pi$
$443$	−2.51161e9	−1.37259	−0.686293	+	0.727326i	$0.740763\pi$
$444$	0	0
$445$	7.12204e8	0.383128
$446$	−1.68253e9	−0.898030
$447$	0	0
$448$	−1.66529e8	−0.0875019
$449$	−2.93296e9	−1.52913	−0.764564	−	0.644548i	$-0.777045\pi$
$449$	−2.93296e9	−1.52913	−0.764564	+	0.644548i	$0.777045\pi$
$450$	0	0
$451$	1.53838e8	0.0789671
$452$	−2.28033e9	−1.16148
$453$	0	0
$454$	2.83485e9	1.42179
$455$	−1.68594e8	−0.0839078
$456$	0	0
$457$	−3.30374e9	−1.61920	−0.809598	−	0.586984i	$-0.800315\pi$
$457$	−3.30374e9	−1.61920	−0.809598	+	0.586984i	$0.800315\pi$
$458$	−2.50333e9	−1.21756
$459$	0	0
$460$	−4.58195e8	−0.219482
$461$	−6.28637e7	−0.0298845	−0.0149423	−	0.999888i	$-0.504756\pi$
$461$	−6.28637e7	−0.0298845	−0.0149423	+	0.999888i	$0.504756\pi$
$462$	0	0
$463$	−2.07437e9	−0.971300	−0.485650	−	0.874153i	$-0.661417\pi$
$463$	−2.07437e9	−0.971300	−0.485650	+	0.874153i	$0.661417\pi$
$464$	2.89715e9	1.34635
$465$	0	0
$466$	−2.11466e9	−0.968031
$467$	1.86804e9	0.848743	0.424372	−	0.905488i	$-0.360495\pi$
$467$	1.86804e9	0.848743	0.424372	+	0.905488i	$0.360495\pi$
$468$	0	0
$469$	2.46409e8	0.110294
$470$	−3.07014e9	−1.36401
$471$	0	0
$472$	4.76973e7	0.0208784
$473$	3.45281e8	0.150023
$474$	0	0
$475$	1.27307e9	0.545034
$476$	3.73710e7	0.0158822
$477$	0	0
$478$	−2.06184e9	−0.863491
$479$	−7.39665e8	−0.307511	−0.153755	−	0.988109i	$-0.549137\pi$
$479$	−7.39665e8	−0.307511	−0.153755	+	0.988109i	$0.549137\pi$
$480$	0	0
$481$	1.48008e9	0.606426
$482$	2.83980e9	1.15511
$483$	0	0
$484$	−2.16801e9	−0.869166
$485$	1.28358e9	0.510890
$486$	0	0
$487$	−3.16893e9	−1.24326	−0.621629	−	0.783312i	$-0.713529\pi$
$487$	−3.16893e9	−1.24326	−0.621629	+	0.783312i	$0.713529\pi$
$488$	−5.61763e8	−0.218818
$489$	0	0
$490$	1.78920e9	0.687027
$491$	1.78015e9	0.678692	0.339346	−	0.940662i	$-0.389794\pi$
$491$	1.78015e9	0.678692	0.339346	+	0.940662i	$0.389794\pi$
$492$	0	0
$493$	−5.03295e8	−0.189173
$494$	−3.84673e9	−1.43565
$495$	0	0
$496$	2.95696e9	1.08808
$497$	−5.55471e6	−0.00202962
$498$	0	0
$499$	−1.30086e9	−0.468684	−0.234342	−	0.972154i	$-0.575294\pi$
$499$	−1.30086e9	−0.468684	−0.234342	+	0.972154i	$0.575294\pi$
$500$	−2.18275e9	−0.780926
$501$	0	0
$502$	−5.72937e9	−2.02136
$503$	1.92822e9	0.675569	0.337784	−	0.941224i	$-0.390323\pi$
$503$	1.92822e9	0.675569	0.337784	+	0.941224i	$0.390323\pi$
$504$	0	0
$505$	−2.48107e8	−0.0857274
$506$	2.46322e8	0.0845232
$507$	0	0
$508$	1.57192e8	0.0531996
$509$	3.91015e9	1.31426	0.657129	−	0.753778i	$-0.271771\pi$
$509$	3.91015e9	1.31426	0.657129	+	0.753778i	$0.271771\pi$
$510$	0	0
$511$	1.18484e8	0.0392815
$512$	−3.99762e9	−1.31631
$513$	0	0
$514$	−3.29120e9	−1.06902
$515$	2.39469e9	0.772546
$516$	0	0
$517$	7.74027e8	0.246343
$518$	2.14308e8	0.0677462
$519$	0	0
$520$	−3.71887e8	−0.115984
$521$	−3.14164e9	−0.973251	−0.486626	−	0.873611i	$-0.661772\pi$
$521$	−3.14164e9	−0.973251	−0.486626	+	0.873611i	$0.661772\pi$
$522$	0	0
$523$	−3.32735e8	−0.101705	−0.0508525	−	0.998706i	$-0.516194\pi$
$523$	−3.32735e8	−0.101705	−0.0508525	+	0.998706i	$0.516194\pi$
$524$	4.70627e8	0.142895
$525$	0	0
$526$	−1.96712e9	−0.589359
$527$	−5.13684e8	−0.152883
$528$	0	0
$529$	−2.58824e9	−0.760169
$530$	3.29240e9	0.960610
$531$	0	0
$532$	−2.61211e8	−0.0752143
$533$	−3.12801e9	−0.894793
$534$	0	0
$535$	−1.09137e9	−0.308129
$536$	5.43533e8	0.152458
$537$	0	0
$538$	−4.15185e9	−1.14949
$539$	−4.51084e8	−0.124079
$540$	0	0
$541$	3.91262e9	1.06237	0.531187	−	0.847255i	$-0.321746\pi$
$541$	3.91262e9	1.06237	0.531187	+	0.847255i	$0.321746\pi$
$542$	3.29476e8	0.0888847
$543$	0	0
$544$	7.87811e8	0.209810
$545$	−3.28571e9	−0.869443
$546$	0	0
$547$	−2.61916e9	−0.684237	−0.342118	−	0.939657i	$-0.611144\pi$
$547$	−2.61916e9	−0.684237	−0.342118	+	0.939657i	$0.611144\pi$
$548$	−4.20038e9	−1.09033
$549$	0	0
$550$	4.99998e8	0.128144
$551$	3.51787e9	0.895879
$552$	0	0
$553$	3.51055e8	0.0882749
$554$	−4.53318e9	−1.13271
$555$	0	0
$556$	−8.35131e7	−0.0206060
$557$	4.99537e9	1.22483	0.612413	−	0.790538i	$-0.290199\pi$
$557$	4.99537e9	1.22483	0.612413	+	0.790538i	$0.290199\pi$
$558$	0	0
$559$	−7.02063e9	−1.69994
$560$	−2.69935e8	−0.0649532
$561$	0	0
$562$	4.03408e9	0.958666
$563$	−1.65832e9	−0.391643	−0.195821	−	0.980640i	$-0.562737\pi$
$563$	−1.65832e9	−0.391643	−0.195821	+	0.980640i	$0.562737\pi$
$564$	0	0
$565$	−2.86137e9	−0.667427
$566$	−5.61292e9	−1.30116
$567$	0	0
$568$	−1.22527e7	−0.00280551
$569$	−6.06474e9	−1.38013	−0.690064	−	0.723748i	$-0.742418\pi$
$569$	−6.06474e9	−1.38013	−0.690064	+	0.723748i	$0.742418\pi$
$570$	0	0
$571$	7.56971e9	1.70158	0.850791	−	0.525504i	$-0.176123\pi$
$571$	7.56971e9	1.70158	0.850791	+	0.525504i	$0.176123\pi$
$572$	−7.08524e8	−0.158295
$573$	0	0
$574$	−4.52920e8	−0.0999608
$575$	1.65755e9	0.363604
$576$	0	0
$577$	4.65513e9	1.00883	0.504413	−	0.863462i	$-0.331709\pi$
$577$	4.65513e9	1.00883	0.504413	+	0.863462i	$0.331709\pi$
$578$	6.21764e9	1.33930
$579$	0	0
$580$	−2.57007e9	−0.546949
$581$	5.99243e8	0.126761
$582$	0	0
$583$	−8.30062e8	−0.173488
$584$	2.61354e8	0.0542981
$585$	0	0
$586$	−1.01250e10	−2.07852
$587$	4.59010e9	0.936675	0.468337	−	0.883550i	$-0.344853\pi$
$587$	4.59010e9	0.936675	0.468337	+	0.883550i	$0.344853\pi$
$588$	0	0
$589$	3.59049e9	0.724019
$590$	−4.52288e8	−0.0906636
$591$	0	0
$592$	2.36975e9	0.469435
$593$	3.99474e9	0.786679	0.393339	−	0.919393i	$-0.371320\pi$
$593$	3.99474e9	0.786679	0.393339	+	0.919393i	$0.371320\pi$
$594$	0	0
$595$	4.68932e7	0.00912643
$596$	8.09650e9	1.56652
$597$	0	0
$598$	−5.00848e9	−0.957750
$599$	7.94405e9	1.51025	0.755124	−	0.655582i	$-0.227577\pi$
$599$	7.94405e9	1.51025	0.755124	+	0.655582i	$0.227577\pi$
$600$	0	0
$601$	2.34327e9	0.440313	0.220157	−	0.975465i	$-0.429343\pi$
$601$	2.34327e9	0.440313	0.220157	+	0.975465i	$0.429343\pi$
$602$	−1.01655e9	−0.189907
$603$	0	0
$604$	−3.95595e9	−0.730502
$605$	−2.72043e9	−0.499452
$606$	0	0
$607$	4.14140e9	0.751600	0.375800	−	0.926701i	$-0.377368\pi$
$607$	4.14140e9	0.751600	0.375800	+	0.926701i	$0.377368\pi$
$608$	−5.50654e9	−0.993611
$609$	0	0
$610$	5.32690e9	0.950211
$611$	−1.57384e10	−2.79136
$612$	0	0
$613$	−8.67426e9	−1.52097	−0.760485	−	0.649355i	$-0.775039\pi$
$613$	−8.67426e9	−1.52097	−0.760485	+	0.649355i	$0.775039\pi$
$614$	8.30337e9	1.44766
$615$	0	0
$616$	1.35757e7	0.00234008
$617$	−6.63163e9	−1.13664	−0.568319	−	0.822808i	$-0.692406\pi$
$617$	−6.63163e9	−1.13664	−0.568319	+	0.822808i	$0.692406\pi$
$618$	0	0
$619$	1.16526e9	0.197473	0.0987364	−	0.995114i	$-0.468520\pi$
$619$	1.16526e9	0.197473	0.0987364	+	0.995114i	$0.468520\pi$
$620$	−2.62312e9	−0.442026
$621$	0	0
$622$	−1.24782e10	−2.07914
$623$	5.28639e8	0.0875893
$624$	0	0
$625$	1.79272e9	0.293719
$626$	5.70376e9	0.929290
$627$	0	0
$628$	−4.34384e9	−0.699866
$629$	−4.11674e8	−0.0659593
$630$	0	0
$631$	−5.61888e9	−0.890322	−0.445161	−	0.895450i	$-0.646854\pi$
$631$	−5.61888e9	−0.890322	−0.445161	+	0.895450i	$0.646854\pi$
$632$	7.74362e8	0.122021
$633$	0	0
$634$	−1.05326e10	−1.64144
$635$	1.97246e8	0.0305703
$636$	0	0
$637$	9.17194e9	1.40596
$638$	1.38165e9	0.210632
$639$	0	0
$640$	−1.07207e9	−0.161657
$641$	−9.83028e8	−0.147422	−0.0737111	−	0.997280i	$-0.523484\pi$
$641$	−9.83028e8	−0.147422	−0.0737111	+	0.997280i	$0.523484\pi$
$642$	0	0
$643$	7.69653e9	1.14171	0.570856	−	0.821050i	$-0.306612\pi$
$643$	7.69653e9	1.14171	0.570856	+	0.821050i	$0.306612\pi$
$644$	−3.40099e8	−0.0501771
$645$	0	0
$646$	1.06994e9	0.156151
$647$	4.42661e9	0.642549	0.321275	−	0.946986i	$-0.395889\pi$
$647$	4.42661e9	0.642549	0.321275	+	0.946986i	$0.395889\pi$
$648$	0	0
$649$	1.14028e8	0.0163741
$650$	−1.01665e10	−1.45203
$651$	0	0
$652$	−5.31034e9	−0.750336
$653$	3.99185e7	0.00561020	0.00280510	−	0.999996i	$-0.499107\pi$
$653$	3.99185e7	0.00561020	0.00280510	+	0.999996i	$0.499107\pi$
$654$	0	0
$655$	5.90545e8	0.0821124
$656$	−5.00823e9	−0.692661
$657$	0	0
$658$	−2.27884e9	−0.311834
$659$	−2.06680e9	−0.281319	−0.140660	−	0.990058i	$-0.544922\pi$
$659$	−2.06680e9	−0.281319	−0.140660	+	0.990058i	$0.544922\pi$
$660$	0	0
$661$	−5.72369e8	−0.0770853	−0.0385426	−	0.999257i	$-0.512272\pi$
$661$	−5.72369e8	−0.0770853	−0.0385426	+	0.999257i	$0.512272\pi$
$662$	2.79694e9	0.374697
$663$	0	0
$664$	1.32182e9	0.175220
$665$	−3.27768e8	−0.0432207
$666$	0	0
$667$	4.58030e9	0.597660
$668$	−5.91800e9	−0.768170
$669$	0	0
$670$	−5.15404e9	−0.662043
$671$	−1.34299e9	−0.171610
$672$	0	0
$673$	−5.59964e9	−0.708121	−0.354060	−	0.935223i	$-0.615199\pi$
$673$	−5.59964e9	−0.708121	−0.354060	+	0.935223i	$0.615199\pi$
$674$	9.48014e9	1.19263
$675$	0	0
$676$	7.31331e9	0.910543
$677$	−2.66208e9	−0.329731	−0.164866	−	0.986316i	$-0.552719\pi$
$677$	−2.66208e9	−0.329731	−0.164866	+	0.986316i	$0.552719\pi$
$678$	0	0
$679$	9.52749e8	0.116798
$680$	1.03438e8	0.0126153
$681$	0	0
$682$	1.41017e9	0.170226
$683$	3.08492e9	0.370485	0.185243	−	0.982693i	$-0.440693\pi$
$683$	3.08492e9	0.370485	0.185243	+	0.982693i	$0.440693\pi$
$684$	0	0
$685$	−5.27065e9	−0.626538
$686$	2.67422e9	0.316274
$687$	0	0
$688$	−1.12407e10	−1.31593
$689$	1.68777e10	1.96583
$690$	0	0
$691$	1.50276e9	0.173267	0.0866336	−	0.996240i	$-0.472389\pi$
$691$	1.50276e9	0.173267	0.0866336	+	0.996240i	$0.472389\pi$
$692$	1.19188e10	1.36730
$693$	0	0
$694$	−3.07152e9	−0.348815
$695$	−1.04793e8	−0.0118409
$696$	0	0
$697$	8.70033e8	0.0973243
$698$	1.40022e10	1.55849
$699$	0	0
$700$	−6.90354e8	−0.0760726
$701$	8.60128e9	0.943083	0.471541	−	0.881844i	$-0.343698\pi$
$701$	8.60128e9	0.943083	0.471541	+	0.881844i	$0.343698\pi$
$702$	0	0
$703$	2.87747e9	0.312368
$704$	−8.78171e8	−0.0948582
$705$	0	0
$706$	−1.33251e10	−1.42512
$707$	−1.84160e8	−0.0195987
$708$	0	0
$709$	1.22113e10	1.28677	0.643384	−	0.765544i	$-0.277530\pi$
$709$	1.22113e10	1.28677	0.643384	+	0.765544i	$0.277530\pi$
$710$	1.16186e8	0.0121828
$711$	0	0
$712$	1.16608e9	0.121073
$713$	4.67485e9	0.483008
$714$	0	0
$715$	−8.89059e8	−0.0909619
$716$	8.75188e9	0.891057
$717$	0	0
$718$	−7.38882e9	−0.744972
$719$	−3.71959e9	−0.373202	−0.186601	−	0.982436i	$-0.559747\pi$
$719$	−3.71959e9	−0.373202	−0.186601	+	0.982436i	$0.559747\pi$
$720$	0	0
$721$	1.77748e9	0.176616
$722$	6.39927e9	0.632777
$723$	0	0
$724$	1.63214e10	1.59835
$725$	9.29737e9	0.906102
$726$	0	0
$727$	1.15890e10	1.11861	0.559303	−	0.828963i	$-0.311069\pi$
$727$	1.15890e10	1.11861	0.559303	+	0.828963i	$0.311069\pi$
$728$	−2.76036e8	−0.0265159
$729$	0	0
$730$	−2.47829e9	−0.235788
$731$	1.95274e9	0.184898
$732$	0	0
$733$	1.55996e10	1.46302	0.731510	−	0.681830i	$-0.238816\pi$
$733$	1.55996e10	1.46302	0.731510	+	0.681830i	$0.238816\pi$
$734$	−1.11450e10	−1.04027
$735$	0	0
$736$	−7.16958e9	−0.662859
$737$	1.29941e9	0.119566
$738$	0	0
$739$	−1.06655e10	−0.972137	−0.486069	−	0.873921i	$-0.661569\pi$
$739$	−1.06655e10	−0.972137	−0.486069	+	0.873921i	$0.661569\pi$
$740$	−2.10221e9	−0.190706
$741$	0	0
$742$	2.44381e9	0.219611
$743$	7.49599e9	0.670453	0.335226	−	0.942138i	$-0.391187\pi$
$743$	7.49599e9	0.670453	0.335226	+	0.942138i	$0.391187\pi$
$744$	0	0
$745$	1.01595e10	0.900173
$746$	9.09743e9	0.802292
$747$	0	0
$748$	1.97071e8	0.0172174
$749$	−8.10077e8	−0.0704433
$750$	0	0
$751$	1.56605e10	1.34916	0.674582	−	0.738200i	$-0.264324\pi$
$751$	1.56605e10	1.34916	0.674582	+	0.738200i	$0.264324\pi$
$752$	−2.51986e10	−2.16080
$753$	0	0
$754$	−2.80932e10	−2.38672
$755$	−4.96394e9	−0.419771
$756$	0	0
$757$	2.02856e10	1.69962	0.849810	−	0.527090i	$-0.176717\pi$
$757$	2.02856e10	1.69962	0.849810	+	0.527090i	$0.176717\pi$
$758$	−2.70857e9	−0.225890
$759$	0	0
$760$	−7.22997e8	−0.0597432
$761$	1.72538e10	1.41919	0.709594	−	0.704611i	$-0.248879\pi$
$761$	1.72538e10	1.41919	0.709594	+	0.704611i	$0.248879\pi$
$762$	0	0
$763$	−2.43884e9	−0.198769
$764$	−2.07084e10	−1.68004
$765$	0	0
$766$	−9.70235e9	−0.779967
$767$	−2.31855e9	−0.185538
$768$	0	0
$769$	2.62229e9	0.207940	0.103970	−	0.994580i	$-0.466845\pi$
$769$	2.62229e9	0.207940	0.103970	+	0.994580i	$0.466845\pi$
$770$	−1.28731e8	−0.0101617
$771$	0	0
$772$	1.02573e10	0.802366
$773$	1.36251e10	1.06099	0.530497	−	0.847687i	$-0.322005\pi$
$773$	1.36251e10	1.06099	0.530497	+	0.847687i	$0.322005\pi$
$774$	0	0
$775$	9.48929e9	0.732281
$776$	2.10159e9	0.161448
$777$	0	0
$778$	−3.18280e9	−0.242315
$779$	−6.08125e9	−0.460905
$780$	0	0
$781$	−2.92921e7	−0.00220025
$782$	1.39307e9	0.104172
$783$	0	0
$784$	1.46851e10	1.08836
$785$	−5.45067e9	−0.402166
$786$	0	0
$787$	−1.27830e9	−0.0934803	−0.0467402	−	0.998907i	$-0.514883\pi$
$787$	−1.27830e9	−0.0934803	−0.0467402	+	0.998907i	$0.514883\pi$
$788$	−1.04820e10	−0.763140
$789$	0	0
$790$	−7.34287e9	−0.529872
$791$	−2.12387e9	−0.152585
$792$	0	0
$793$	2.73071e10	1.94455
$794$	3.05403e10	2.16522
$795$	0	0
$796$	8.98409e9	0.631362
$797$	1.05141e10	0.735642	0.367821	−	0.929897i	$-0.380104\pi$
$797$	1.05141e10	0.735642	0.367821	+	0.929897i	$0.380104\pi$
$798$	0	0
$799$	4.37752e9	0.303609
$800$	−1.45532e10	−1.00495
$801$	0	0
$802$	−3.24754e10	−2.22303
$803$	6.24812e8	0.0425838
$804$	0	0
$805$	−4.26758e8	−0.0288334
$806$	−2.86731e10	−1.92886
$807$	0	0
$808$	−4.06222e8	−0.0270909
$809$	6.76915e7	0.00449484	0.00224742	−	0.999997i	$-0.499285\pi$
$809$	6.76915e7	0.00449484	0.00224742	+	0.999997i	$0.499285\pi$
$810$	0	0
$811$	−1.33239e10	−0.877121	−0.438560	−	0.898702i	$-0.644511\pi$
$811$	−1.33239e10	−0.877121	−0.438560	+	0.898702i	$0.644511\pi$
$812$	−1.90766e9	−0.125041
$813$	0	0
$814$	1.13013e9	0.0734416
$815$	−6.66343e9	−0.431168
$816$	0	0
$817$	−1.36490e10	−0.875637
$818$	−5.69488e9	−0.363788
$819$	0	0
$820$	4.44281e9	0.281391
$821$	−1.93379e10	−1.21957	−0.609787	−	0.792565i	$-0.708745\pi$
$821$	−1.93379e10	−1.21957	−0.609787	+	0.792565i	$0.708745\pi$
$822$	0	0
$823$	−1.01992e10	−0.637774	−0.318887	−	0.947793i	$-0.603309\pi$
$823$	−1.01992e10	−0.637774	−0.318887	+	0.947793i	$0.603309\pi$
$824$	3.92079e9	0.244134
$825$	0	0
$826$	−3.35715e8	−0.0207272
$827$	2.20862e9	0.135785	0.0678925	−	0.997693i	$-0.478372\pi$
$827$	2.20862e9	0.135785	0.0678925	+	0.997693i	$0.478372\pi$
$828$	0	0
$829$	5.49783e9	0.335159	0.167579	−	0.985859i	$-0.446405\pi$
$829$	5.49783e9	0.335159	0.167579	+	0.985859i	$0.446405\pi$
$830$	−1.25341e10	−0.760887
$831$	0	0
$832$	1.78559e10	1.07486
$833$	−2.55111e9	−0.152923
$834$	0	0
$835$	−7.42593e9	−0.441416
$836$	−1.37746e9	−0.0815376
$837$	0	0
$838$	1.97647e10	1.16021
$839$	−4.86845e9	−0.284593	−0.142297	−	0.989824i	$-0.545449\pi$
$839$	−4.86845e9	−0.284593	−0.142297	+	0.989824i	$0.545449\pi$
$840$	0	0
$841$	8.44158e9	0.489371
$842$	1.08413e10	0.625876
$843$	0	0
$844$	1.43235e10	0.820070
$845$	9.17677e9	0.523229
$846$	0	0
$847$	−2.01926e9	−0.114183
$848$	2.70228e10	1.52176
$849$	0	0
$850$	2.82774e9	0.157933
$851$	3.74649e9	0.208387
$852$	0	0
$853$	2.22806e10	1.22915	0.614577	−	0.788857i	$-0.289327\pi$
$853$	2.22806e10	1.22915	0.614577	+	0.788857i	$0.289327\pi$
$854$	3.95394e9	0.217234
$855$	0	0
$856$	−1.78688e9	−0.0973727
$857$	−3.09258e10	−1.67837	−0.839186	−	0.543844i	$-0.816968\pi$
$857$	−3.09258e10	−1.67837	−0.839186	+	0.543844i	$0.816968\pi$
$858$	0	0
$859$	6.06715e9	0.326594	0.163297	−	0.986577i	$-0.447787\pi$
$859$	6.06715e9	0.326594	0.163297	+	0.986577i	$0.447787\pi$
$860$	9.97163e9	0.534591
$861$	0	0
$862$	4.09674e9	0.217853
$863$	5.47212e8	0.0289813	0.0144906	−	0.999895i	$-0.495387\pi$
$863$	5.47212e8	0.0289813	0.0144906	+	0.999895i	$0.495387\pi$
$864$	0	0
$865$	1.49558e10	0.785694
$866$	−3.32052e10	−1.73738
$867$	0	0
$868$	−1.94703e9	−0.101054
$869$	1.85124e9	0.0956961
$870$	0	0
$871$	−2.64210e10	−1.35483
$872$	−5.37964e9	−0.274755
$873$	0	0
$874$	−9.73714e9	−0.493334
$875$	−2.03299e9	−0.102591
$876$	0	0
$877$	−1.05471e10	−0.528001	−0.264001	−	0.964523i	$-0.585042\pi$
$877$	−1.05471e10	−0.528001	−0.264001	+	0.964523i	$0.585042\pi$
$878$	−4.35310e10	−2.17054
$879$	0	0
$880$	−1.42347e9	−0.0704138
$881$	2.80065e10	1.37989	0.689943	−	0.723864i	$-0.257636\pi$
$881$	2.80065e10	1.37989	0.689943	+	0.723864i	$0.257636\pi$
$882$	0	0
$883$	−1.61306e10	−0.788477	−0.394238	−	0.919008i	$-0.628992\pi$
$883$	−1.61306e10	−0.788477	−0.394238	+	0.919008i	$0.628992\pi$
$884$	−4.00706e9	−0.195094
$885$	0	0
$886$	3.89940e10	1.88356
$887$	−8.47554e9	−0.407788	−0.203894	−	0.978993i	$-0.565360\pi$
$887$	−8.47554e9	−0.407788	−0.203894	+	0.978993i	$0.565360\pi$
$888$	0	0
$889$	1.46407e8	0.00698886
$890$	−1.10573e10	−0.525757
$891$	0	0
$892$	1.22505e10	0.577933
$893$	−3.05974e10	−1.43782
$894$	0	0
$895$	1.09819e10	0.512031
$896$	−7.95756e8	−0.0369574
$897$	0	0
$898$	4.55357e10	2.09838
$899$	2.62218e10	1.20366
$900$	0	0
$901$	−4.69442e9	−0.213818
$902$	−2.38842e9	−0.108365
$903$	0	0
$904$	−4.68487e9	−0.210915
$905$	2.04802e10	0.918466
$906$	0	0
$907$	1.59071e10	0.707892	0.353946	−	0.935266i	$-0.384840\pi$
$907$	1.59071e10	0.707892	0.353946	+	0.935266i	$0.384840\pi$
$908$	−2.06406e10	−0.914999
$909$	0	0
$910$	2.61751e9	0.115144
$911$	7.44930e9	0.326438	0.163219	−	0.986590i	$-0.447812\pi$
$911$	7.44930e9	0.326438	0.163219	+	0.986590i	$0.447812\pi$
$912$	0	0
$913$	3.16003e9	0.137418
$914$	5.12923e10	2.22198
$915$	0	0
$916$	1.82268e10	0.783567
$917$	4.38337e8	0.0187722
$918$	0	0
$919$	−2.63715e10	−1.12080	−0.560402	−	0.828221i	$-0.689353\pi$
$919$	−2.63715e10	−1.12080	−0.560402	+	0.828221i	$0.689353\pi$
$920$	−9.41349e8	−0.0398560
$921$	0	0
$922$	9.75990e8	0.0410098
$923$	5.95599e8	0.0249315
$924$	0	0
$925$	7.60485e9	0.315933
$926$	3.22057e10	1.33289
$927$	0	0
$928$	−4.02150e10	−1.65185
$929$	−1.48686e9	−0.0608437	−0.0304219	−	0.999537i	$-0.509685\pi$
$929$	−1.48686e9	−0.0608437	−0.0304219	+	0.999537i	$0.509685\pi$
$930$	0	0
$931$	1.78314e10	0.724207
$932$	1.53968e10	0.622983
$933$	0	0
$934$	−2.90022e10	−1.16471
$935$	2.47285e8	0.00989368
$936$	0	0
$937$	1.58188e10	0.628182	0.314091	−	0.949393i	$-0.398300\pi$
$937$	1.58188e10	0.628182	0.314091	+	0.949393i	$0.398300\pi$
$938$	−3.82563e9	−0.151354
$939$	0	0
$940$	2.23537e10	0.877814
$941$	7.02941e9	0.275014	0.137507	−	0.990501i	$-0.456091\pi$
$941$	7.02941e9	0.275014	0.137507	+	0.990501i	$0.456091\pi$
$942$	0	0
$943$	−7.91785e9	−0.307480
$944$	−3.71221e9	−0.143625
$945$	0	0
$946$	−5.36066e9	−0.205873
$947$	−4.03890e10	−1.54539	−0.772695	−	0.634778i	$-0.781092\pi$
$947$	−4.03890e10	−1.54539	−0.772695	+	0.634778i	$0.781092\pi$
$948$	0	0
$949$	−1.27044e10	−0.482526
$950$	−1.97650e10	−0.747936
$951$	0	0
$952$	7.67775e7	0.00288406
$953$	−2.02572e10	−0.758148	−0.379074	−	0.925366i	$-0.623757\pi$
$953$	−2.02572e10	−0.758148	−0.379074	+	0.925366i	$0.623757\pi$
$954$	0	0
$955$	−2.59850e10	−0.965406
$956$	1.50123e10	0.555705
$957$	0	0
$958$	1.14837e10	0.421989
$959$	−3.91219e9	−0.143237
$960$	0	0
$961$	−7.49560e8	−0.0272442
$962$	−2.29790e10	−0.832182
$963$	0	0
$964$	−2.06766e10	−0.743378
$965$	1.28709e10	0.461066
$966$	0	0
$967$	1.14238e10	0.406273	0.203137	−	0.979150i	$-0.434886\pi$
$967$	1.14238e10	0.406273	0.203137	+	0.979150i	$0.434886\pi$
$968$	−4.45411e9	−0.157833
$969$	0	0
$970$	−1.99283e10	−0.701081
$971$	−2.91162e10	−1.02063	−0.510314	−	0.859988i	$-0.670471\pi$
$971$	−2.91162e10	−1.02063	−0.510314	+	0.859988i	$0.670471\pi$
$972$	0	0
$973$	−7.77832e7	−0.00270701
$974$	4.91992e10	1.70609
$975$	0	0
$976$	4.37212e10	1.50528
$977$	−4.46068e10	−1.53028	−0.765139	−	0.643865i	$-0.777330\pi$
$977$	−4.46068e10	−1.53028	−0.765139	+	0.643865i	$0.777330\pi$
$978$	0	0
$979$	2.78771e9	0.0949529
$980$	−1.30272e10	−0.442141
$981$	0	0
$982$	−2.76378e10	−0.931351
$983$	6.33957e9	0.212874	0.106437	−	0.994319i	$-0.466056\pi$
$983$	6.33957e9	0.212874	0.106437	+	0.994319i	$0.466056\pi$
$984$	0	0
$985$	−1.31529e10	−0.438526
$986$	7.81391e9	0.259597
$987$	0	0
$988$	2.80081e10	0.923919
$989$	−1.77712e10	−0.584156
$990$	0	0
$991$	−2.38700e10	−0.779103	−0.389551	−	0.921005i	$-0.627370\pi$
$991$	−2.38700e10	−0.779103	−0.389551	+	0.921005i	$0.627370\pi$
$992$	−4.10451e10	−1.33497
$993$	0	0
$994$	8.62397e7	0.00278519
$995$	1.12733e10	0.362802
$996$	0	0
$997$	−1.70894e9	−0.0546127	−0.0273063	−	0.999627i	$-0.508693\pi$
$997$	−1.70894e9	−0.0546127	−0.0273063	+	0.999627i	$0.508693\pi$
$998$	2.01966e10	0.643163
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	531.8.a.d.1.3		17
3.2	odd	2		177.8.a.b.1.15	✓	17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.8.a.b.1.15	✓	17	3.2	odd	2
531.8.a.d.1.3		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)

\(f(q)\)	\(=\)	\(q-15.5255 q^{2} +113.041 q^{4} +141.845 q^{5} +105.285 q^{7} +232.240 q^{8} +O(q^{10})\)	\(q-15.5255 q^{2} +113.041 q^{4} +141.845 q^{5} +105.285 q^{7} +232.240 q^{8} -2202.21 q^{10} +555.209 q^{11} -11289.1 q^{13} -1634.61 q^{14} -18074.9 q^{16} +3139.99 q^{17} -21947.5 q^{19} +16034.3 q^{20} -8619.91 q^{22} -28575.9 q^{23} -58005.1 q^{25} +175269. q^{26} +11901.6 q^{28} -160286. q^{29} -163594. q^{31} +250896. q^{32} -48750.0 q^{34} +14934.2 q^{35} -131107. q^{37} +340746. q^{38} +32942.1 q^{40} +277081. q^{41} +621893. q^{43} +62761.6 q^{44} +443655. q^{46} +1.39412e6 q^{47} -812458. q^{49} +900558. q^{50} -1.27614e6 q^{52} -1.49504e6 q^{53} +78753.5 q^{55} +24451.5 q^{56} +2.48851e6 q^{58} +205379. q^{59} -2.41889e6 q^{61} +2.53988e6 q^{62} -1.58169e6 q^{64} -1.60130e6 q^{65} +2.34039e6 q^{67} +354949. q^{68} -231861. q^{70} -52758.6 q^{71} +1.12536e6 q^{73} +2.03550e6 q^{74} -2.48098e6 q^{76} +58455.5 q^{77} +3.33432e6 q^{79} -2.56384e6 q^{80} -4.30183e6 q^{82} +5.69160e6 q^{83} +445391. q^{85} -9.65520e6 q^{86} +128942. q^{88} +5.02101e6 q^{89} -1.18858e6 q^{91} -3.23026e6 q^{92} -2.16444e7 q^{94} -3.11314e6 q^{95} +9.04920e6 q^{97} +1.26138e7 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q + 32 q^{2} + 1166 q^{4} + 1072 q^{5} - 2407 q^{7} + 6645 q^{8}+O(q^{10}) \) 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

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