LMFDB - Embedded newform 531.8.a.d.1.7

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			1.7
Root			$4.11298$ 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)

$f(q)$	$=$	$q-2.11298 q^{2} -123.535 q^{4} +537.118 q^{5} +1259.15 q^{7} +531.490 q^{8} +O(q^{10})$	\(q-2.11298 q^{2} -123.535 q^{4} +537.118 q^{5} +1259.15 q^{7} +531.490 q^{8} -1134.92 q^{10} -7730.24 q^{11} -8860.73 q^{13} -2660.56 q^{14} +14689.5 q^{16} -22368.4 q^{17} -24886.1 q^{19} -66353.0 q^{20} +16333.9 q^{22} +26686.2 q^{23} +210371. q^{25} +18722.6 q^{26} -155549. q^{28} -10101.0 q^{29} -265180. q^{31} -99069.4 q^{32} +47264.0 q^{34} +676311. q^{35} +122638. q^{37} +52583.9 q^{38} +285473. q^{40} +741866. q^{41} -166554. q^{43} +954958. q^{44} -56387.4 q^{46} +545699. q^{47} +761910. q^{49} -444510. q^{50} +1.09461e6 q^{52} +1.54083e6 q^{53} -4.15205e6 q^{55} +669225. q^{56} +21343.2 q^{58} +205379. q^{59} +2.74259e6 q^{61} +560320. q^{62} -1.67092e6 q^{64} -4.75926e6 q^{65} -41604.4 q^{67} +2.76328e6 q^{68} -1.42903e6 q^{70} +1.57840e6 q^{71} +5.59479e6 q^{73} -259132. q^{74} +3.07431e6 q^{76} -9.73352e6 q^{77} -3.74825e6 q^{79} +7.88999e6 q^{80} -1.56755e6 q^{82} +3.37715e6 q^{83} -1.20144e7 q^{85} +351926. q^{86} -4.10855e6 q^{88} +5.43486e6 q^{89} -1.11570e7 q^{91} -3.29668e6 q^{92} -1.15305e6 q^{94} -1.33668e7 q^{95} -1.14400e7 q^{97} -1.60990e6 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.11298	−0.186763	−0.0933816	−	0.995630i	$-0.529768\pi$
$2$	−2.11298	−0.186763	−0.0933816	+	0.995630i	$0.529768\pi$
$3$	0	0
$3$	0	0
$4$	−123.535	−0.965120
$5$	537.118	1.92165	0.960826	−	0.277153i	$-0.0893908\pi$
$5$	537.118	1.92165	0.960826	+	0.277153i	$0.0893908\pi$
$6$	0	0
$7$	1259.15	1.38750	0.693751	−	0.720215i	$-0.255957\pi$
$7$	1259.15	1.38750	0.693751	+	0.720215i	$0.255957\pi$
$8$	531.490	0.367012
$9$	0	0
$10$	−1134.92	−0.358894
$11$	−7730.24	−1.75113	−0.875566	−	0.483099i	$-0.839511\pi$
$11$	−7730.24	−1.75113	−0.875566	+	0.483099i	$0.839511\pi$
$12$	0	0
$13$	−8860.73	−1.11858	−0.559291	−	0.828971i	$-0.688927\pi$
$13$	−8860.73	−1.11858	−0.559291	+	0.828971i	$0.688927\pi$
$14$	−2660.56	−0.259134
$15$	0	0
$16$	14689.5	0.896575
$17$	−22368.4	−1.10424	−0.552119	−	0.833765i	$-0.686181\pi$
$17$	−22368.4	−1.10424	−0.552119	+	0.833765i	$0.686181\pi$
$18$	0	0
$19$	−24886.1	−0.832375	−0.416187	−	0.909279i	$-0.636634\pi$
$19$	−24886.1	−0.832375	−0.416187	+	0.909279i	$0.636634\pi$
$20$	−66353.0	−1.85462
$21$	0	0
$22$	16333.9	0.327047
$23$	26686.2	0.457339	0.228670	−	0.973504i	$-0.426562\pi$
$23$	26686.2	0.457339	0.228670	+	0.973504i	$0.426562\pi$
$24$	0	0
$25$	210371.	2.69275
$26$	18722.6	0.208910
$27$	0	0
$28$	−155549.	−1.33911
$29$	−10101.0	−0.0769077	−0.0384539	−	0.999260i	$-0.512243\pi$
$29$	−10101.0	−0.0769077	−0.0384539	+	0.999260i	$0.512243\pi$
$30$	0	0
$31$	−265180.	−1.59873	−0.799363	−	0.600848i	$-0.794830\pi$
$31$	−265180.	−1.59873	−0.799363	+	0.600848i	$0.794830\pi$
$32$	−99069.4	−0.534459
$33$	0	0
$34$	47264.0	0.206231
$35$	676311.	2.66630
$36$	0	0
$37$	122638.	0.398032	0.199016	−	0.979996i	$-0.436225\pi$
$37$	122638.	0.398032	0.199016	+	0.979996i	$0.436225\pi$
$38$	52583.9	0.155457
$39$	0	0
$40$	285473.	0.705269
$41$	741866.	1.68105	0.840527	−	0.541769i	$-0.182245\pi$
$41$	741866.	1.68105	0.840527	+	0.541769i	$0.182245\pi$
$42$	0	0
$43$	−166554.	−0.319459	−0.159730	−	0.987161i	$-0.551062\pi$
$43$	−166554.	−0.319459	−0.159730	+	0.987161i	$0.551062\pi$
$44$	954958.	1.69005
$45$	0	0
$46$	−56387.4	−0.0854142
$47$	545699.	0.766674	0.383337	−	0.923608i	$-0.374775\pi$
$47$	545699.	0.766674	0.383337	+	0.923608i	$0.374775\pi$
$48$	0	0
$49$	761910.	0.925161
$50$	−444510.	−0.502906
$51$	0	0
$52$	1.09461e6	1.07957
$53$	1.54083e6	1.42164	0.710819	−	0.703375i	$-0.248324\pi$
$53$	1.54083e6	1.42164	0.710819	+	0.703375i	$0.248324\pi$
$54$	0	0
$55$	−4.15205e6	−3.36506
$56$	669225.	0.509230
$57$	0	0
$58$	21343.2	0.0143635
$59$	205379.	0.130189
$59$	205379.	0.130189
$60$	0	0
$61$	2.74259e6	1.54706	0.773529	−	0.633761i	$-0.218490\pi$
$61$	2.74259e6	1.54706	0.773529	+	0.633761i	$0.218490\pi$
$62$	560320.	0.298583
$63$	0	0
$64$	−1.67092e6	−0.796758
$65$	−4.75926e6	−2.14952
$66$	0	0
$67$	−41604.4	−0.0168996	−0.00844981	−	0.999964i	$-0.502690\pi$
$67$	−41604.4	−0.0168996	−0.00844981	+	0.999964i	$0.502690\pi$
$68$	2.76328e6	1.06572
$69$	0	0
$70$	−1.42903e6	−0.497966
$71$	1.57840e6	0.523376	0.261688	−	0.965152i	$-0.415721\pi$
$71$	1.57840e6	0.523376	0.261688	+	0.965152i	$0.415721\pi$
$72$	0	0
$73$	5.59479e6	1.68327	0.841635	−	0.540047i	$-0.181594\pi$
$73$	5.59479e6	1.68327	0.841635	+	0.540047i	$0.181594\pi$
$74$	−259132.	−0.0743378
$75$	0	0
$76$	3.07431e6	0.803341
$77$	−9.73352e6	−2.42970
$78$	0	0
$79$	−3.74825e6	−0.855330	−0.427665	−	0.903937i	$-0.640664\pi$
$79$	−3.74825e6	−0.855330	−0.427665	+	0.903937i	$0.640664\pi$
$80$	7.88999e6	1.72291
$81$	0	0
$82$	−1.56755e6	−0.313959
$83$	3.37715e6	0.648302	0.324151	−	0.946005i	$-0.394921\pi$
$83$	3.37715e6	0.648302	0.324151	+	0.946005i	$0.394921\pi$
$84$	0	0
$85$	−1.20144e7	−2.12196
$86$	351926.	0.0596632
$87$	0	0
$88$	−4.10855e6	−0.642686
$89$	5.43486e6	0.817191	0.408595	−	0.912716i	$-0.366019\pi$
$89$	5.43486e6	0.817191	0.408595	+	0.912716i	$0.366019\pi$
$90$	0	0
$91$	−1.11570e7	−1.55203
$92$	−3.29668e6	−0.441387
$93$	0	0
$94$	−1.15305e6	−0.143187
$95$	−1.33668e7	−1.59953
$96$	0	0
$97$	−1.14400e7	−1.27270	−0.636349	−	0.771401i	$-0.719556\pi$
$97$	−1.14400e7	−1.27270	−0.636349	+	0.771401i	$0.719556\pi$
$98$	−1.60990e6	−0.172786
$99$	0	0
$100$	−2.59882e7	−2.59882
$101$	1.39505e7	1.34730	0.673652	−	0.739049i	$-0.264725\pi$
$101$	1.39505e7	1.34730	0.673652	+	0.739049i	$0.264725\pi$
$102$	0	0
$103$	−9.43458e6	−0.850731	−0.425366	−	0.905022i	$-0.639855\pi$
$103$	−9.43458e6	−0.850731	−0.425366	+	0.905022i	$0.639855\pi$
$104$	−4.70939e6	−0.410533
$105$	0	0
$106$	−3.25575e6	−0.265510
$107$	−1.19603e7	−0.943844	−0.471922	−	0.881640i	$-0.656440\pi$
$107$	−1.19603e7	−0.943844	−0.471922	+	0.881640i	$0.656440\pi$
$108$	0	0
$109$	2.39265e6	0.176964	0.0884822	−	0.996078i	$-0.471798\pi$
$109$	2.39265e6	0.176964	0.0884822	+	0.996078i	$0.471798\pi$
$110$	8.77322e6	0.628470
$111$	0	0
$112$	1.84962e7	1.24400
$113$	4.09793e6	0.267171	0.133586	−	0.991037i	$-0.457351\pi$
$113$	4.09793e6	0.267171	0.133586	+	0.991037i	$0.457351\pi$
$114$	0	0
$115$	1.43336e7	0.878847
$116$	1.24783e6	0.0742251
$117$	0	0
$118$	−433963.	−0.0243145
$119$	−2.81651e7	−1.53213
$120$	0	0
$121$	4.02695e7	2.06646
$122$	−5.79505e6	−0.288933
$123$	0	0
$124$	3.27590e7	1.54296
$125$	7.10316e7	3.25287
$126$	0	0
$127$	1.95190e7	0.845560	0.422780	−	0.906232i	$-0.361054\pi$
$127$	1.95190e7	0.845560	0.422780	+	0.906232i	$0.361054\pi$
$128$	1.62115e7	0.683264
$129$	0	0
$130$	1.00562e7	0.401452
$131$	3.90620e6	0.151811	0.0759057	−	0.997115i	$-0.475815\pi$
$131$	3.90620e6	0.151811	0.0759057	+	0.997115i	$0.475815\pi$
$132$	0	0
$133$	−3.13352e7	−1.15492
$134$	87909.4	0.00315623
$135$	0	0
$136$	−1.18886e7	−0.405269
$137$	2.53665e7	0.842828	0.421414	−	0.906868i	$-0.361534\pi$
$137$	2.53665e7	0.842828	0.421414	+	0.906868i	$0.361534\pi$
$138$	0	0
$139$	4.42236e7	1.39670	0.698348	−	0.715758i	$-0.253919\pi$
$139$	4.42236e7	1.39670	0.698348	+	0.715758i	$0.253919\pi$
$140$	−8.35483e7	−2.57329
$141$	0	0
$142$	−3.33514e6	−0.0977474
$143$	6.84956e7	1.95878
$144$	0	0
$145$	−5.42541e6	−0.147790
$146$	−1.18217e7	−0.314373
$147$	0	0
$148$	−1.51501e7	−0.384149
$149$	−2.22130e6	−0.0550117	−0.0275059	−	0.999622i	$-0.508756\pi$
$149$	−2.22130e6	−0.0550117	−0.0275059	+	0.999622i	$0.508756\pi$
$150$	0	0
$151$	−4.02533e7	−0.951443	−0.475721	−	0.879596i	$-0.657813\pi$
$151$	−4.02533e7	−0.951443	−0.475721	+	0.879596i	$0.657813\pi$
$152$	−1.32267e7	−0.305491
$153$	0	0
$154$	2.05668e7	0.453778
$155$	−1.42433e8	−3.07220
$156$	0	0
$157$	3.47322e7	0.716281	0.358140	−	0.933668i	$-0.383411\pi$
$157$	3.47322e7	0.716281	0.358140	+	0.933668i	$0.383411\pi$
$158$	7.91999e6	0.159744
$159$	0	0
$160$	−5.32120e7	−1.02704
$161$	3.36018e7	0.634559
$162$	0	0
$163$	−1.15628e7	−0.209126	−0.104563	−	0.994518i	$-0.533344\pi$
$163$	−1.15628e7	−0.209126	−0.104563	+	0.994518i	$0.533344\pi$
$164$	−9.16466e7	−1.62242
$165$	0	0
$166$	−7.13587e6	−0.121079
$167$	1.06887e8	1.77590	0.887949	−	0.459941i	$-0.152130\pi$
$167$	1.06887e8	1.77590	0.887949	+	0.459941i	$0.152130\pi$
$168$	0	0
$169$	1.57640e7	0.251225
$170$	2.53863e7	0.396304
$171$	0	0
$172$	2.05753e7	0.308316
$173$	7.33625e7	1.07724	0.538621	−	0.842548i	$-0.318946\pi$
$173$	7.33625e7	1.07724	0.538621	+	0.842548i	$0.318946\pi$
$174$	0	0
$175$	2.64888e8	3.73619
$176$	−1.13553e8	−1.57002
$177$	0	0
$178$	−1.14838e7	−0.152621
$179$	7.93198e7	1.03370	0.516852	−	0.856075i	$-0.327104\pi$
$179$	7.93198e7	1.03370	0.516852	+	0.856075i	$0.327104\pi$
$180$	0	0
$181$	4.76795e7	0.597663	0.298831	−	0.954306i	$-0.403403\pi$
$181$	4.76795e7	0.597663	0.298831	+	0.954306i	$0.403403\pi$
$182$	2.35745e7	0.289863
$183$	0	0
$184$	1.41834e7	0.167849
$185$	6.58710e7	0.764880
$186$	0	0
$187$	1.72913e8	1.93367
$188$	−6.74131e7	−0.739932
$189$	0	0
$190$	2.82437e7	0.298734
$191$	5.66760e7	0.588549	0.294274	−	0.955721i	$-0.404922\pi$
$191$	5.66760e7	0.588549	0.294274	+	0.955721i	$0.404922\pi$
$192$	0	0
$193$	−1.76636e8	−1.76859	−0.884297	−	0.466924i	$-0.845362\pi$
$193$	−1.76636e8	−1.76859	−0.884297	+	0.466924i	$0.845362\pi$
$194$	2.41726e7	0.237693
$195$	0	0
$196$	−9.41228e7	−0.892891
$197$	−1.27300e8	−1.18630	−0.593151	−	0.805091i	$-0.702116\pi$
$197$	−1.27300e8	−1.18630	−0.593151	+	0.805091i	$0.702116\pi$
$198$	0	0
$199$	1.45827e8	1.31175	0.655877	−	0.754868i	$-0.272299\pi$
$199$	1.45827e8	1.31175	0.655877	+	0.754868i	$0.272299\pi$
$200$	1.11810e8	0.988270
$201$	0	0
$202$	−2.94772e7	−0.251627
$203$	−1.27186e7	−0.106710
$204$	0	0
$205$	3.98469e8	3.23040
$206$	1.99351e7	0.158885
$207$	0	0
$208$	−1.30160e8	−1.00289
$209$	1.92375e8	1.45760
$210$	0	0
$211$	−1.57257e8	−1.15245	−0.576223	−	0.817292i	$-0.695474\pi$
$211$	−1.57257e8	−1.15245	−0.576223	+	0.817292i	$0.695474\pi$
$212$	−1.90347e8	−1.37205
$213$	0	0
$214$	2.52720e7	0.176275
$215$	−8.94591e7	−0.613889
$216$	0	0
$217$	−3.33900e8	−2.21824
$218$	−5.05563e6	−0.0330504
$219$	0	0
$220$	5.12925e8	3.24769
$221$	1.98200e8	1.23518
$222$	0	0
$223$	−1.56191e8	−0.943169	−0.471584	−	0.881821i	$-0.656318\pi$
$223$	−1.56191e8	−0.943169	−0.471584	+	0.881821i	$0.656318\pi$
$224$	−1.24743e8	−0.741563
$225$	0	0
$226$	−8.65886e6	−0.0498978
$227$	1.43058e8	0.811748	0.405874	−	0.913929i	$-0.366967\pi$
$227$	1.43058e8	0.811748	0.405874	+	0.913929i	$0.366967\pi$
$228$	0	0
$229$	−9.00963e7	−0.495773	−0.247886	−	0.968789i	$-0.579736\pi$
$229$	−9.00963e7	−0.495773	−0.247886	+	0.968789i	$0.579736\pi$
$230$	−3.02867e7	−0.164136
$231$	0	0
$232$	−5.36856e6	−0.0282261
$233$	−1.58220e8	−0.819437	−0.409718	−	0.912212i	$-0.634373\pi$
$233$	−1.58220e8	−0.819437	−0.409718	+	0.912212i	$0.634373\pi$
$234$	0	0
$235$	2.93105e8	1.47328
$236$	−2.53716e7	−0.125648
$237$	0	0
$238$	5.95123e7	0.286146
$239$	7.78834e7	0.369022	0.184511	−	0.982830i	$-0.440930\pi$
$239$	7.78834e7	0.369022	0.184511	+	0.982830i	$0.440930\pi$
$240$	0	0
$241$	7.51343e7	0.345763	0.172882	−	0.984943i	$-0.444692\pi$
$241$	7.51343e7	0.345763	0.172882	+	0.984943i	$0.444692\pi$
$242$	−8.50887e7	−0.385939
$243$	0	0
$244$	−3.38807e8	−1.49310
$245$	4.09236e8	1.77784
$246$	0	0
$247$	2.20509e8	0.931079
$248$	−1.40940e8	−0.586752
$249$	0	0
$250$	−1.50089e8	−0.607516
$251$	−1.66455e8	−0.664416	−0.332208	−	0.943206i	$-0.607794\pi$
$251$	−1.66455e8	−0.664416	−0.332208	+	0.943206i	$0.607794\pi$
$252$	0	0
$253$	−2.06290e8	−0.800861
$254$	−4.12433e7	−0.157919
$255$	0	0
$256$	1.79623e8	0.669149
$257$	5.67936e7	0.208705	0.104353	−	0.994540i	$-0.466723\pi$
$257$	5.67936e7	0.208705	0.104353	+	0.994540i	$0.466723\pi$
$258$	0	0
$259$	1.54419e8	0.552271
$260$	5.87936e8	2.07455
$261$	0	0
$262$	−8.25373e6	−0.0283528
$263$	1.48859e8	0.504581	0.252291	−	0.967651i	$-0.418816\pi$
$263$	1.48859e8	0.504581	0.252291	+	0.967651i	$0.418816\pi$
$264$	0	0
$265$	8.27608e8	2.73189
$266$	6.62109e7	0.215697
$267$	0	0
$268$	5.13961e6	0.0163102
$269$	3.17458e7	0.0994382	0.0497191	−	0.998763i	$-0.484167\pi$
$269$	3.17458e7	0.0994382	0.0497191	+	0.998763i	$0.484167\pi$
$270$	0	0
$271$	470544.	0.00143618	0.000718089	−	1.00000i	$-0.499771\pi$
$271$	470544.	0.00143618	0.000718089		1.00000i	$0.499771\pi$
$272$	−3.28580e8	−0.990033
$273$	0	0
$274$	−5.35991e7	−0.157409
$275$	−1.62622e9	−4.71535
$276$	0	0
$277$	4.15036e8	1.17329	0.586646	−	0.809843i	$-0.300448\pi$
$277$	4.15036e8	1.17329	0.586646	+	0.809843i	$0.300448\pi$
$278$	−9.34437e7	−0.260851
$279$	0	0
$280$	3.59453e8	0.978562
$281$	−4.91128e8	−1.32045	−0.660226	−	0.751067i	$-0.729539\pi$
$281$	−4.91128e8	−1.32045	−0.660226	+	0.751067i	$0.729539\pi$
$282$	0	0
$283$	−3.10302e8	−0.813827	−0.406914	−	0.913467i	$-0.633395\pi$
$283$	−3.10302e8	−0.813827	−0.406914	+	0.913467i	$0.633395\pi$
$284$	−1.94989e8	−0.505121
$285$	0	0
$286$	−1.44730e8	−0.365829
$287$	9.34119e8	2.33247
$288$	0	0
$289$	9.00046e7	0.219342
$290$	1.14638e7	0.0276017
$291$	0	0
$292$	−6.91154e8	−1.62456
$293$	2.94684e8	0.684415	0.342208	−	0.939624i	$-0.388825\pi$
$293$	2.94684e8	0.684415	0.342208	+	0.939624i	$0.388825\pi$
$294$	0	0
$295$	1.10313e8	0.250178
$296$	6.51808e7	0.146083
$297$	0	0
$298$	4.69357e6	0.0102742
$299$	−2.36459e8	−0.511572
$300$	0	0
$301$	−2.09716e8	−0.443250
$302$	8.50547e7	0.177694
$303$	0	0
$304$	−3.65564e8	−0.746286
$305$	1.47309e9	2.97291
$306$	0	0
$307$	2.26044e8	0.445871	0.222936	−	0.974833i	$-0.428436\pi$
$307$	2.26044e8	0.445871	0.222936	+	0.974833i	$0.428436\pi$
$308$	1.20243e9	2.34495
$309$	0	0
$310$	3.00958e8	0.573773
$311$	4.63267e8	0.873313	0.436656	−	0.899628i	$-0.356163\pi$
$311$	4.63267e8	0.873313	0.436656	+	0.899628i	$0.356163\pi$
$312$	0	0
$313$	6.22167e8	1.14684	0.573418	−	0.819263i	$-0.305617\pi$
$313$	6.22167e8	1.14684	0.573418	+	0.819263i	$0.305617\pi$
$314$	−7.33885e7	−0.133775
$315$	0	0
$316$	4.63041e8	0.825496
$317$	−8.20133e8	−1.44603	−0.723014	−	0.690833i	$-0.757244\pi$
$317$	−8.20133e8	−1.44603	−0.723014	+	0.690833i	$0.757244\pi$
$318$	0	0
$319$	7.80829e7	0.134675
$320$	−8.97483e8	−1.53109
$321$	0	0
$322$	−7.10001e7	−0.118512
$323$	5.56661e8	0.919140
$324$	0	0
$325$	−1.86404e9	−3.01206
$326$	2.44321e7	0.0390570
$327$	0	0
$328$	3.94294e8	0.616967
$329$	6.87116e8	1.06376
$330$	0	0
$331$	−4.99025e8	−0.756352	−0.378176	−	0.925734i	$-0.623449\pi$
$331$	−4.99025e8	−0.756352	−0.378176	+	0.925734i	$0.623449\pi$
$332$	−4.17198e8	−0.625689
$333$	0	0
$334$	−2.25851e8	−0.331672
$335$	−2.23465e7	−0.0324752
$336$	0	0
$337$	−2.16438e8	−0.308056	−0.154028	−	0.988066i	$-0.549225\pi$
$337$	−2.16438e8	−0.308056	−0.154028	+	0.988066i	$0.549225\pi$
$338$	−3.33091e7	−0.0469196
$339$	0	0
$340$	1.48421e9	2.04795
$341$	2.04990e9	2.79958
$342$	0	0
$343$	−7.76048e7	−0.103839
$344$	−8.85218e7	−0.117245
$345$	0	0
$346$	−1.55014e8	−0.201189
$347$	−2.49019e8	−0.319948	−0.159974	−	0.987121i	$-0.551141\pi$
$347$	−2.49019e8	−0.319948	−0.159974	+	0.987121i	$0.551141\pi$
$348$	0	0
$349$	−1.28064e9	−1.61264	−0.806319	−	0.591481i	$-0.798543\pi$
$349$	−1.28064e9	−1.61264	−0.806319	+	0.591481i	$0.798543\pi$
$350$	−5.59704e8	−0.697783
$351$	0	0
$352$	7.65830e8	0.935908
$353$	−1.01386e8	−0.122678	−0.0613390	−	0.998117i	$-0.519537\pi$
$353$	−1.01386e8	−0.122678	−0.0613390	+	0.998117i	$0.519537\pi$
$354$	0	0
$355$	8.47790e8	1.00575
$356$	−6.71397e8	−0.788687
$357$	0	0
$358$	−1.67601e8	−0.193058
$359$	9.38042e8	1.07002	0.535010	−	0.844846i	$-0.320308\pi$
$359$	9.38042e8	1.07002	0.535010	+	0.844846i	$0.320308\pi$
$360$	0	0
$361$	−2.74555e8	−0.307153
$362$	−1.00746e8	−0.111621
$363$	0	0
$364$	1.37828e9	1.49790
$365$	3.00506e9	3.23466
$366$	0	0
$367$	7.40350e8	0.781818	0.390909	−	0.920429i	$-0.372161\pi$
$367$	7.40350e8	0.781818	0.390909	+	0.920429i	$0.372161\pi$
$368$	3.92006e8	0.410039
$369$	0	0
$370$	−1.39184e8	−0.142851
$371$	1.94013e9	1.97253
$372$	0	0
$373$	1.05390e9	1.05152	0.525761	−	0.850632i	$-0.323781\pi$
$373$	1.05390e9	1.05152	0.525761	+	0.850632i	$0.323781\pi$
$374$	−3.65362e8	−0.361138
$375$	0	0
$376$	2.90034e8	0.281379
$377$	8.95019e7	0.0860276
$378$	0	0
$379$	1.16570e9	1.09989	0.549947	−	0.835199i	$-0.314648\pi$
$379$	1.16570e9	1.09989	0.549947	+	0.835199i	$0.314648\pi$
$380$	1.65127e9	1.54374
$381$	0	0
$382$	−1.19755e8	−0.109919
$383$	1.70280e7	0.0154870	0.00774349	−	0.999970i	$-0.497535\pi$
$383$	1.70280e7	0.0154870	0.00774349	+	0.999970i	$0.497535\pi$
$384$	0	0
$385$	−5.22805e9	−4.66903
$386$	3.73229e8	0.330308
$387$	0	0
$388$	1.41325e9	1.22831
$389$	−3.59169e8	−0.309368	−0.154684	−	0.987964i	$-0.549436\pi$
$389$	−3.59169e8	−0.309368	−0.154684	+	0.987964i	$0.549436\pi$
$390$	0	0
$391$	−5.96925e8	−0.505012
$392$	4.04948e8	0.339545
$393$	0	0
$394$	2.68982e8	0.221558
$395$	−2.01325e9	−1.64365
$396$	0	0
$397$	−1.33556e9	−1.07127	−0.535634	−	0.844450i	$-0.679927\pi$
$397$	−1.33556e9	−1.07127	−0.535634	+	0.844450i	$0.679927\pi$
$398$	−3.08130e8	−0.244987
$399$	0	0
$400$	3.09024e9	2.41425
$401$	−2.22573e9	−1.72372	−0.861862	−	0.507143i	$-0.830702\pi$
$401$	−2.22573e9	−1.72372	−0.861862	+	0.507143i	$0.830702\pi$
$402$	0	0
$403$	2.34968e9	1.78831
$404$	−1.72338e9	−1.30031
$405$	0	0
$406$	2.68742e7	0.0199294
$407$	−9.48020e8	−0.697007
$408$	0	0
$409$	1.44669e9	1.04555	0.522774	−	0.852471i	$-0.324897\pi$
$409$	1.44669e9	1.04555	0.522774	+	0.852471i	$0.324897\pi$
$410$	−8.41960e8	−0.603320
$411$	0	0
$412$	1.16550e9	0.821057
$413$	2.58603e8	0.180637
$414$	0	0
$415$	1.81393e9	1.24581
$416$	8.77827e8	0.597836
$417$	0	0
$418$	−4.06486e8	−0.272225
$419$	1.91705e9	1.27316	0.636581	−	0.771210i	$-0.280348\pi$
$419$	1.91705e9	1.27316	0.636581	+	0.771210i	$0.280348\pi$
$420$	0	0
$421$	−1.78027e9	−1.16278	−0.581392	−	0.813623i	$-0.697492\pi$
$421$	−1.78027e9	−1.16278	−0.581392	+	0.813623i	$0.697492\pi$
$422$	3.32281e8	0.215235
$423$	0	0
$424$	8.18936e8	0.521758
$425$	−4.70565e9	−2.97343
$426$	0	0
$427$	3.45333e9	2.14655
$428$	1.47752e9	0.910923
$429$	0	0
$430$	1.89026e8	0.114652
$431$	−3.29923e8	−0.198492	−0.0992458	−	0.995063i	$-0.531643\pi$
$431$	−3.29923e8	−0.198492	−0.0992458	+	0.995063i	$0.531643\pi$
$432$	0	0
$433$	−4.75888e7	−0.0281707	−0.0140853	−	0.999901i	$-0.504484\pi$
$433$	−4.75888e7	−0.0281707	−0.0140853	+	0.999901i	$0.504484\pi$
$434$	7.05526e8	0.414285
$435$	0	0
$436$	−2.95576e8	−0.170792
$437$	−6.64114e8	−0.380678
$438$	0	0
$439$	−3.04664e8	−0.171868	−0.0859342	−	0.996301i	$-0.527387\pi$
$439$	−3.04664e8	−0.171868	−0.0859342	+	0.996301i	$0.527387\pi$
$440$	−2.20677e9	−1.23502
$441$	0	0
$442$	−4.18793e8	−0.230686
$443$	−2.92263e9	−1.59721	−0.798603	−	0.601858i	$-0.794427\pi$
$443$	−2.92263e9	−1.59721	−0.798603	+	0.601858i	$0.794427\pi$
$444$	0	0
$445$	2.91916e9	1.57036
$446$	3.30029e8	0.176149
$447$	0	0
$448$	−2.10394e9	−1.10550
$449$	3.10711e9	1.61993	0.809963	−	0.586481i	$-0.199487\pi$
$449$	3.10711e9	1.61993	0.809963	+	0.586481i	$0.199487\pi$
$450$	0	0
$451$	−5.73480e9	−2.94375
$452$	−5.06239e8	−0.257852
$453$	0	0
$454$	−3.02279e8	−0.151605
$455$	−5.99261e9	−2.98247
$456$	0	0
$457$	−1.02063e8	−0.0500221	−0.0250110	−	0.999687i	$-0.507962\pi$
$457$	−1.02063e8	−0.0500221	−0.0250110	+	0.999687i	$0.507962\pi$
$458$	1.90372e8	0.0925921
$459$	0	0
$460$	−1.77071e9	−0.848192
$461$	1.96777e9	0.935452	0.467726	−	0.883873i	$-0.345073\pi$
$461$	1.96777e9	0.935452	0.467726	+	0.883873i	$0.345073\pi$
$462$	0	0
$463$	1.67779e9	0.785604	0.392802	−	0.919623i	$-0.371506\pi$
$463$	1.67779e9	0.785604	0.392802	+	0.919623i	$0.371506\pi$
$464$	−1.48378e8	−0.0689536
$465$	0	0
$466$	3.34316e8	0.153041
$467$	1.19888e9	0.544709	0.272355	−	0.962197i	$-0.412198\pi$
$467$	1.19888e9	0.544709	0.272355	+	0.962197i	$0.412198\pi$
$468$	0	0
$469$	−5.23860e7	−0.0234483
$470$	−6.19326e8	−0.275155
$471$	0	0
$472$	1.09157e8	0.0477809
$473$	1.28750e9	0.559415
$474$	0	0
$475$	−5.23530e9	−2.24137
$476$	3.47938e9	1.47869
$477$	0	0
$478$	−1.64566e8	−0.0689197
$479$	3.41930e9	1.42155	0.710777	−	0.703418i	$-0.248344\pi$
$479$	3.41930e9	1.42155	0.710777	+	0.703418i	$0.248344\pi$
$480$	0	0
$481$	−1.08666e9	−0.445232
$482$	−1.58758e8	−0.0645758
$483$	0	0
$484$	−4.97470e9	−1.99438
$485$	−6.14464e9	−2.44568
$486$	0	0
$487$	−1.02116e9	−0.400628	−0.200314	−	0.979732i	$-0.564196\pi$
$487$	−1.02116e9	−0.400628	−0.200314	+	0.979732i	$0.564196\pi$
$488$	1.45766e9	0.567789
$489$	0	0
$490$	−8.64709e8	−0.332035
$491$	−3.59695e9	−1.37135	−0.685677	−	0.727906i	$-0.740494\pi$
$491$	−3.59695e9	−1.37135	−0.685677	+	0.727906i	$0.740494\pi$
$492$	0	0
$493$	2.25942e8	0.0849245
$494$	−4.65932e8	−0.173891
$495$	0	0
$496$	−3.89535e9	−1.43338
$497$	1.98744e9	0.726186
$498$	0	0
$499$	−1.17064e9	−0.421765	−0.210883	−	0.977511i	$-0.567634\pi$
$499$	−1.17064e9	−0.421765	−0.210883	+	0.977511i	$0.567634\pi$
$500$	−8.77491e9	−3.13941
$501$	0	0
$502$	3.51718e8	0.124088
$503$	1.37007e9	0.480014	0.240007	−	0.970771i	$-0.422850\pi$
$503$	1.37007e9	0.480014	0.240007	+	0.970771i	$0.422850\pi$
$504$	0	0
$505$	7.49308e9	2.58905
$506$	4.35888e8	0.149571
$507$	0	0
$508$	−2.41129e9	−0.816067
$509$	6.94286e8	0.233360	0.116680	−	0.993170i	$-0.462775\pi$
$509$	6.94286e8	0.233360	0.116680	+	0.993170i	$0.462775\pi$
$510$	0	0
$511$	7.04466e9	2.33554
$512$	−2.45462e9	−0.808237
$513$	0	0
$514$	−1.20004e8	−0.0389785
$515$	−5.06748e9	−1.63481
$516$	0	0
$517$	−4.21839e9	−1.34255
$518$	−3.26285e8	−0.103144
$519$	0	0
$520$	−2.52950e9	−0.788901
$521$	3.26480e9	1.01140	0.505702	−	0.862708i	$-0.331233\pi$
$521$	3.26480e9	1.01140	0.505702	+	0.862708i	$0.331233\pi$
$522$	0	0
$523$	1.44867e9	0.442806	0.221403	−	0.975182i	$-0.428936\pi$
$523$	1.44867e9	0.442806	0.221403	+	0.975182i	$0.428936\pi$
$524$	−4.82553e8	−0.146516
$525$	0	0
$526$	−3.14538e8	−0.0942372
$527$	5.93163e9	1.76537
$528$	0	0
$529$	−2.69267e9	−0.790841
$530$	−1.74872e9	−0.510217
$531$	0	0
$532$	3.87101e9	1.11464
$533$	−6.57347e9	−1.88040
$534$	0	0
$535$	−6.42412e9	−1.81374
$536$	−2.21123e7	−0.00620237
$537$	0	0
$538$	−6.70784e7	−0.0185714
$539$	−5.88975e9	−1.62008
$540$	0	0
$541$	5.30499e9	1.44044	0.720218	−	0.693748i	$-0.244042\pi$
$541$	5.30499e9	1.44044	0.720218	+	0.693748i	$0.244042\pi$
$542$	−994253.	−0.000268225 0
$543$	0	0
$544$	2.21602e9	0.590170
$545$	1.28513e9	0.340064
$546$	0	0
$547$	2.77315e9	0.724465	0.362232	−	0.932088i	$-0.382015\pi$
$547$	2.77315e9	0.724465	0.362232	+	0.932088i	$0.382015\pi$
$548$	−3.13366e9	−0.813430
$549$	0	0
$550$	3.43617e9	0.880654
$551$	2.51373e8	0.0640160
$552$	0	0
$553$	−4.71960e9	−1.18677
$554$	−8.76964e8	−0.219128
$555$	0	0
$556$	−5.46317e9	−1.34798
$557$	2.33572e9	0.572701	0.286350	−	0.958125i	$-0.407558\pi$
$557$	2.33572e9	0.572701	0.286350	+	0.958125i	$0.407558\pi$
$558$	0	0
$559$	1.47579e9	0.357341
$560$	9.93466e9	2.39053
$561$	0	0
$562$	1.03775e9	0.246612
$563$	−5.53231e9	−1.30655	−0.653276	−	0.757120i	$-0.726606\pi$
$563$	−5.53231e9	−1.30655	−0.653276	+	0.757120i	$0.726606\pi$
$564$	0	0
$565$	2.20107e9	0.513411
$566$	6.55663e8	0.151993
$567$	0	0
$568$	8.38906e8	0.192085
$569$	−5.01743e8	−0.114180	−0.0570898	−	0.998369i	$-0.518182\pi$
$569$	−5.01743e8	−0.114180	−0.0570898	+	0.998369i	$0.518182\pi$
$570$	0	0
$571$	−1.45684e9	−0.327481	−0.163741	−	0.986503i	$-0.552356\pi$
$571$	−1.45684e9	−0.327481	−0.163741	+	0.986503i	$0.552356\pi$
$572$	−8.46162e9	−1.89046
$573$	0	0
$574$	−1.97378e9	−0.435619
$575$	5.61399e9	1.23150
$576$	0	0
$577$	−5.26247e9	−1.14044	−0.570222	−	0.821490i	$-0.693143\pi$
$577$	−5.26247e9	−1.14044	−0.570222	+	0.821490i	$0.693143\pi$
$578$	−1.90178e8	−0.0409650
$579$	0	0
$580$	6.70230e8	0.142635
$581$	4.25234e9	0.899521
$582$	0	0
$583$	−1.19110e10	−2.48948
$584$	2.97357e9	0.617780
$585$	0	0
$586$	−6.22662e8	−0.127824
$587$	3.91337e9	0.798579	0.399290	−	0.916825i	$-0.369257\pi$
$587$	3.91337e9	0.798579	0.399290	+	0.916825i	$0.369257\pi$
$588$	0	0
$589$	6.59928e9	1.33074
$590$	−2.33089e8	−0.0467240
$591$	0	0
$592$	1.80149e9	0.356866
$593$	−6.52849e9	−1.28564	−0.642822	−	0.766015i	$-0.722237\pi$
$593$	−6.52849e9	−1.28564	−0.642822	+	0.766015i	$0.722237\pi$
$594$	0	0
$595$	−1.51280e10	−2.94423
$596$	2.74409e8	0.0530929
$597$	0	0
$598$	4.99634e8	0.0955427
$599$	−8.24579e9	−1.56761	−0.783805	−	0.621007i	$-0.786724\pi$
$599$	−8.24579e9	−1.56761	−0.783805	+	0.621007i	$0.786724\pi$
$600$	0	0
$601$	−6.15461e9	−1.15648	−0.578242	−	0.815865i	$-0.696261\pi$
$601$	−6.15461e9	−1.15648	−0.578242	+	0.815865i	$0.696261\pi$
$602$	4.43127e8	0.0827828
$603$	0	0
$604$	4.97271e9	0.918256
$605$	2.16295e10	3.97102
$606$	0	0
$607$	7.75348e6	0.00140714	0.000703569	−	1.00000i	$-0.499776\pi$
$607$	7.75348e6	0.00140714	0.000703569		1.00000i	$0.499776\pi$
$608$	2.46545e9	0.444870
$609$	0	0
$610$	−3.11263e9	−0.555230
$611$	−4.83529e9	−0.857588
$612$	0	0
$613$	5.41748e9	0.949917	0.474958	−	0.880008i	$-0.342463\pi$
$613$	5.41748e9	0.949917	0.474958	+	0.880008i	$0.342463\pi$
$614$	−4.77628e8	−0.0832723
$615$	0	0
$616$	−5.17327e9	−0.891728
$617$	1.53588e9	0.263245	0.131622	−	0.991300i	$-0.457981\pi$
$617$	1.53588e9	0.263245	0.131622	+	0.991300i	$0.457981\pi$
$618$	0	0
$619$	−1.24887e9	−0.211641	−0.105821	−	0.994385i	$-0.533747\pi$
$619$	−1.24887e9	−0.211641	−0.105821	+	0.994385i	$0.533747\pi$
$620$	1.75955e10	2.96504
$621$	0	0
$622$	−9.78875e8	−0.163103
$623$	6.84329e9	1.13385
$624$	0	0
$625$	2.17171e10	3.55813
$626$	−1.31463e9	−0.214187
$627$	0	0
$628$	−4.29065e9	−0.691296
$629$	−2.74321e9	−0.439523
$630$	0	0
$631$	−8.97235e9	−1.42169	−0.710843	−	0.703351i	$-0.751686\pi$
$631$	−8.97235e9	−1.42169	−0.710843	+	0.703351i	$0.751686\pi$
$632$	−1.99216e9	−0.313916
$633$	0	0
$634$	1.73293e9	0.270065
$635$	1.04840e10	1.62487
$636$	0	0
$637$	−6.75108e9	−1.03487
$638$	−1.64988e8	−0.0251524
$639$	0	0
$640$	8.70750e9	1.31300
$641$	5.94956e9	0.892240	0.446120	−	0.894973i	$-0.352805\pi$
$641$	5.94956e9	0.892240	0.446120	+	0.894973i	$0.352805\pi$
$642$	0	0
$643$	8.03210e9	1.19149	0.595745	−	0.803173i	$-0.296857\pi$
$643$	8.03210e9	1.19149	0.595745	+	0.803173i	$0.296857\pi$
$644$	−4.15101e9	−0.612426
$645$	0	0
$646$	−1.17621e9	−0.171661
$647$	8.88936e9	1.29034	0.645172	−	0.764038i	$-0.276786\pi$
$647$	8.88936e9	1.29034	0.645172	+	0.764038i	$0.276786\pi$
$648$	0	0
$649$	−1.58763e9	−0.227978
$650$	3.93868e9	0.562541
$651$	0	0
$652$	1.42842e9	0.201831
$653$	1.14448e10	1.60846	0.804231	−	0.594316i	$-0.202577\pi$
$653$	1.14448e10	1.60846	0.804231	+	0.594316i	$0.202577\pi$
$654$	0	0
$655$	2.09809e9	0.291729
$656$	1.08976e10	1.50719
$657$	0	0
$658$	−1.45187e9	−0.198672
$659$	−9.40014e9	−1.27949	−0.639743	−	0.768589i	$-0.720959\pi$
$659$	−9.40014e9	−1.27949	−0.639743	+	0.768589i	$0.720959\pi$
$660$	0	0
$661$	1.37618e9	0.185341	0.0926704	−	0.995697i	$-0.470460\pi$
$661$	1.37618e9	0.185341	0.0926704	+	0.995697i	$0.470460\pi$
$662$	1.05443e9	0.141259
$663$	0	0
$664$	1.79492e9	0.237935
$665$	−1.68307e10	−2.21936
$666$	0	0
$667$	−2.69556e8	−0.0351729
$668$	−1.32043e10	−1.71395
$669$	0	0
$670$	4.72177e7	0.00606517
$671$	−2.12009e10	−2.70910
$672$	0	0
$673$	9.13119e9	1.15471	0.577357	−	0.816492i	$-0.304084\pi$
$673$	9.13119e9	1.15471	0.577357	+	0.816492i	$0.304084\pi$
$674$	4.57331e8	0.0575335
$675$	0	0
$676$	−1.94741e9	−0.242462
$677$	−6.14968e9	−0.761715	−0.380857	−	0.924634i	$-0.624371\pi$
$677$	−6.14968e9	−0.761715	−0.380857	+	0.924634i	$0.624371\pi$
$678$	0	0
$679$	−1.44047e10	−1.76587
$680$	−6.38556e9	−0.778785
$681$	0	0
$682$	−4.33141e9	−0.522858
$683$	1.15096e10	1.38225	0.691127	−	0.722734i	$-0.257115\pi$
$683$	1.15096e10	1.38225	0.691127	+	0.722734i	$0.257115\pi$
$684$	0	0
$685$	1.36248e10	1.61962
$686$	1.63978e8	0.0193932
$687$	0	0
$688$	−2.44659e9	−0.286419
$689$	−1.36529e10	−1.59022
$690$	0	0
$691$	−6.76616e9	−0.780134	−0.390067	−	0.920786i	$-0.627548\pi$
$691$	−6.76616e9	−0.780134	−0.390067	+	0.920786i	$0.627548\pi$
$692$	−9.06286e9	−1.03967
$693$	0	0
$694$	5.26173e8	0.0597545
$695$	2.37533e10	2.68396
$696$	0	0
$697$	−1.65943e10	−1.85628
$698$	2.70596e9	0.301181
$699$	0	0
$700$	−3.27230e10	−3.60587
$701$	−2.85225e9	−0.312734	−0.156367	−	0.987699i	$-0.549978\pi$
$701$	−2.85225e9	−0.312734	−0.156367	+	0.987699i	$0.549978\pi$
$702$	0	0
$703$	−3.05197e9	−0.331312
$704$	1.29166e10	1.39523
$705$	0	0
$706$	2.14227e8	0.0229117
$707$	1.75658e10	1.86939
$708$	0	0
$709$	1.72710e10	1.81994	0.909969	−	0.414676i	$-0.136105\pi$
$709$	1.72710e10	1.81994	0.909969	+	0.414676i	$0.136105\pi$
$710$	−1.79137e9	−0.187837
$711$	0	0
$712$	2.88858e9	0.299919
$713$	−7.07662e9	−0.731161
$714$	0	0
$715$	3.67902e10	3.76410
$716$	−9.79879e9	−0.997647
$717$	0	0
$718$	−1.98207e9	−0.199840
$719$	−6.37828e9	−0.639959	−0.319980	−	0.947424i	$-0.603676\pi$
$719$	−6.37828e9	−0.639959	−0.319980	+	0.947424i	$0.603676\pi$
$720$	0	0
$721$	−1.18795e10	−1.18039
$722$	5.80130e8	0.0573648
$723$	0	0
$724$	−5.89010e9	−0.576816
$725$	−2.12495e9	−0.207093
$726$	0	0
$727$	1.75274e10	1.69179	0.845895	−	0.533350i	$-0.179067\pi$
$727$	1.75274e10	1.69179	0.845895	+	0.533350i	$0.179067\pi$
$728$	−5.92982e9	−0.569615
$729$	0	0
$730$	−6.34965e9	−0.604115
$731$	3.72554e9	0.352759
$732$	0	0
$733$	6.90854e9	0.647922	0.323961	−	0.946070i	$-0.394985\pi$
$733$	6.90854e9	0.647922	0.323961	+	0.946070i	$0.394985\pi$
$734$	−1.56435e9	−0.146015
$735$	0	0
$736$	−2.64378e9	−0.244429
$737$	3.21612e8	0.0295935
$738$	0	0
$739$	1.05720e10	0.963610	0.481805	−	0.876278i	$-0.339981\pi$
$739$	1.05720e10	0.963610	0.481805	+	0.876278i	$0.339981\pi$
$740$	−8.13739e9	−0.738200
$741$	0	0
$742$	−4.09947e9	−0.368395
$743$	−1.14806e10	−1.02685	−0.513423	−	0.858136i	$-0.671623\pi$
$743$	−1.14806e10	−1.02685	−0.513423	+	0.858136i	$0.671623\pi$
$744$	0	0
$745$	−1.19310e9	−0.105713
$746$	−2.22687e9	−0.196386
$747$	0	0
$748$	−2.13608e10	−1.86622
$749$	−1.50598e10	−1.30959
$750$	0	0
$751$	−6.77468e9	−0.583645	−0.291823	−	0.956472i	$-0.594262\pi$
$751$	−6.77468e9	−0.583645	−0.291823	+	0.956472i	$0.594262\pi$
$752$	8.01604e9	0.687381
$753$	0	0
$754$	−1.89116e8	−0.0160668
$755$	−2.16208e10	−1.82834
$756$	0	0
$757$	−1.20655e10	−1.01090	−0.505451	−	0.862855i	$-0.668674\pi$
$757$	−1.20655e10	−1.01090	−0.505451	+	0.862855i	$0.668674\pi$
$758$	−2.46311e9	−0.205420
$759$	0	0
$760$	−7.10430e9	−0.587048
$761$	6.97304e9	0.573556	0.286778	−	0.957997i	$-0.407416\pi$
$761$	6.97304e9	0.573556	0.286778	+	0.957997i	$0.407416\pi$
$762$	0	0
$763$	3.01270e9	0.245539
$764$	−7.00149e9	−0.568020
$765$	0	0
$766$	−3.59798e7	−0.00289240
$767$	−1.81981e9	−0.145627
$768$	0	0
$769$	−6.18686e9	−0.490600	−0.245300	−	0.969447i	$-0.578887\pi$
$769$	−6.18686e9	−0.490600	−0.245300	+	0.969447i	$0.578887\pi$
$770$	1.10468e10	0.872003
$771$	0	0
$772$	2.18208e10	1.70691
$773$	−9.77041e9	−0.760825	−0.380412	−	0.924817i	$-0.624218\pi$
$773$	−9.77041e9	−0.760825	−0.380412	+	0.924817i	$0.624218\pi$
$774$	0	0
$775$	−5.57860e10	−4.30496
$776$	−6.08025e9	−0.467096
$777$	0	0
$778$	7.58918e8	0.0577785
$779$	−1.84621e10	−1.39927
$780$	0	0
$781$	−1.22014e10	−0.916501
$782$	1.26129e9	0.0943176
$783$	0	0
$784$	1.11921e10	0.829477
$785$	1.86553e10	1.37644
$786$	0	0
$787$	−3.17612e9	−0.232266	−0.116133	−	0.993234i	$-0.537050\pi$
$787$	−3.17612e9	−0.232266	−0.116133	+	0.993234i	$0.537050\pi$
$788$	1.57260e10	1.14492
$789$	0	0
$790$	4.25397e9	0.306973
$791$	5.15990e9	0.370701
$792$	0	0
$793$	−2.43014e10	−1.73051
$794$	2.82203e9	0.200073
$795$	0	0
$796$	−1.80148e10	−1.26600
$797$	1.64367e10	1.15003	0.575016	−	0.818142i	$-0.304996\pi$
$797$	1.64367e10	1.15003	0.575016	+	0.818142i	$0.304996\pi$
$798$	0	0
$799$	−1.22064e10	−0.846591
$800$	−2.08413e10	−1.43916
$801$	0	0
$802$	4.70294e9	0.321928
$803$	−4.32491e10	−2.94762
$804$	0	0
$805$	1.80481e10	1.21940
$806$	−4.96485e9	−0.333990
$807$	0	0
$808$	7.41457e9	0.494477
$809$	−6.28475e9	−0.417319	−0.208659	−	0.977988i	$-0.566910\pi$
$809$	−6.28475e9	−0.417319	−0.208659	+	0.977988i	$0.566910\pi$
$810$	0	0
$811$	2.31027e10	1.52086	0.760432	−	0.649418i	$-0.224987\pi$
$811$	2.31027e10	1.52086	0.760432	+	0.649418i	$0.224987\pi$
$812$	1.57120e9	0.102988
$813$	0	0
$814$	2.00315e9	0.130175
$815$	−6.21060e9	−0.401866
$816$	0	0
$817$	4.14487e9	0.265910
$818$	−3.05683e9	−0.195270
$819$	0	0
$820$	−4.92250e10	−3.11772
$821$	2.91799e10	1.84027	0.920137	−	0.391597i	$-0.128077\pi$
$821$	2.91799e10	1.84027	0.920137	+	0.391597i	$0.128077\pi$
$822$	0	0
$823$	2.76539e10	1.72925	0.864624	−	0.502419i	$-0.167557\pi$
$823$	2.76539e10	1.72925	0.864624	+	0.502419i	$0.167557\pi$
$824$	−5.01439e9	−0.312229
$825$	0	0
$826$	−5.46423e8	−0.0337364
$827$	5.03285e9	0.309417	0.154709	−	0.987960i	$-0.450556\pi$
$827$	5.03285e9	0.309417	0.154709	+	0.987960i	$0.450556\pi$
$828$	0	0
$829$	1.94317e10	1.18459	0.592296	−	0.805720i	$-0.298222\pi$
$829$	1.94317e10	1.18459	0.592296	+	0.805720i	$0.298222\pi$
$830$	−3.83281e9	−0.232672
$831$	0	0
$832$	1.48056e10	0.891239
$833$	−1.70427e10	−1.02160
$834$	0	0
$835$	5.74111e10	3.41266
$836$	−2.37651e10	−1.40676
$837$	0	0
$838$	−4.05069e9	−0.237780
$839$	−1.03412e10	−0.604509	−0.302255	−	0.953227i	$-0.597739\pi$
$839$	−1.03412e10	−0.604509	−0.302255	+	0.953227i	$0.597739\pi$
$840$	0	0
$841$	−1.71478e10	−0.994085
$842$	3.76169e9	0.217165
$843$	0	0
$844$	1.94268e10	1.11225
$845$	8.46713e9	0.482767
$846$	0	0
$847$	5.07052e10	2.86722
$848$	2.26340e10	1.27461
$849$	0	0
$850$	9.94296e9	0.555328
$851$	3.27273e9	0.182036
$852$	0	0
$853$	2.35292e10	1.29803	0.649016	−	0.760775i	$-0.275181\pi$
$853$	2.35292e10	1.29803	0.649016	+	0.760775i	$0.275181\pi$
$854$	−7.29683e9	−0.400896
$855$	0	0
$856$	−6.35680e9	−0.346402
$857$	2.62808e10	1.42628	0.713142	−	0.701020i	$-0.247272\pi$
$857$	2.62808e10	1.42628	0.713142	+	0.701020i	$0.247272\pi$
$858$	0	0
$859$	1.11154e9	0.0598339	0.0299170	−	0.999552i	$-0.490476\pi$
$859$	1.11154e9	0.0598339	0.0299170	+	0.999552i	$0.490476\pi$
$860$	1.10514e10	0.592476
$861$	0	0
$862$	6.97122e8	0.0370709
$863$	1.39838e10	0.740604	0.370302	−	0.928911i	$-0.379254\pi$
$863$	1.39838e10	0.740604	0.370302	+	0.928911i	$0.379254\pi$
$864$	0	0
$865$	3.94043e10	2.07008
$866$	1.00554e8	0.00526125
$867$	0	0
$868$	4.12485e10	2.14086
$869$	2.89749e10	1.49780
$870$	0	0
$871$	3.68645e8	0.0189036
$872$	1.27167e9	0.0649481
$873$	0	0
$874$	1.40326e9	0.0710966
$875$	8.94392e10	4.51336
$876$	0	0
$877$	3.43482e10	1.71951	0.859756	−	0.510705i	$-0.170615\pi$
$877$	3.43482e10	1.71951	0.859756	+	0.510705i	$0.170615\pi$
$878$	6.43751e8	0.0320987
$879$	0	0
$880$	−6.09915e10	−3.01703
$881$	−3.32281e10	−1.63715	−0.818576	−	0.574398i	$-0.805236\pi$
$881$	−3.32281e10	−1.63715	−0.818576	+	0.574398i	$0.805236\pi$
$882$	0	0
$883$	−2.10543e10	−1.02915	−0.514576	−	0.857445i	$-0.672051\pi$
$883$	−2.10543e10	−1.02915	−0.514576	+	0.857445i	$0.672051\pi$
$884$	−2.44847e10	−1.19210
$885$	0	0
$886$	6.17547e9	0.298299
$887$	−1.23601e10	−0.594688	−0.297344	−	0.954770i	$-0.596101\pi$
$887$	−1.23601e10	−0.594688	−0.297344	+	0.954770i	$0.596101\pi$
$888$	0	0
$889$	2.45773e10	1.17322
$890$	−6.16814e9	−0.293285
$891$	0	0
$892$	1.92951e10	0.910271
$893$	−1.35803e10	−0.638160
$894$	0	0
$895$	4.26041e10	1.98642
$896$	2.04127e10	0.948030
$897$	0	0
$898$	−6.56528e9	−0.302542
$899$	2.67857e9	0.122954
$900$	0	0
$901$	−3.44658e10	−1.56983
$902$	1.21175e10	0.549784
$903$	0	0
$904$	2.17801e9	0.0980551
$905$	2.56095e10	1.14850
$906$	0	0
$907$	1.40907e10	0.627058	0.313529	−	0.949579i	$-0.398489\pi$
$907$	1.40907e10	0.627058	0.313529	+	0.949579i	$0.398489\pi$
$908$	−1.76727e10	−0.783433
$909$	0	0
$910$	1.26623e10	0.557015
$911$	−2.85261e10	−1.25005	−0.625027	−	0.780603i	$-0.714912\pi$
$911$	−2.85261e10	−1.25005	−0.625027	+	0.780603i	$0.714912\pi$
$912$	0	0
$913$	−2.61062e10	−1.13526
$914$	2.15657e8	0.00934228
$915$	0	0
$916$	1.11301e10	0.478480
$917$	4.91848e9	0.210639
$918$	0	0
$919$	−1.21759e10	−0.517485	−0.258742	−	0.965946i	$-0.583308\pi$
$919$	−1.21759e10	−0.517485	−0.258742	+	0.965946i	$0.583308\pi$
$920$	7.61817e9	0.322547
$921$	0	0
$922$	−4.15787e9	−0.174708
$923$	−1.39858e10	−0.585439
$924$	0	0
$925$	2.57994e10	1.07180
$926$	−3.54514e9	−0.146722
$927$	0	0
$928$	1.00070e9	0.0411040
$929$	4.26915e9	0.174697	0.0873487	−	0.996178i	$-0.472161\pi$
$929$	4.26915e9	0.174697	0.0873487	+	0.996178i	$0.472161\pi$
$930$	0	0
$931$	−1.89610e10	−0.770081
$932$	1.95457e10	0.790854
$933$	0	0
$934$	−2.53320e9	−0.101732
$935$	9.28746e10	3.71583
$936$	0	0
$937$	1.52673e10	0.606282	0.303141	−	0.952946i	$-0.401965\pi$
$937$	1.52673e10	0.606282	0.303141	+	0.952946i	$0.401965\pi$
$938$	1.10691e8	0.00437927
$939$	0	0
$940$	−3.62088e10	−1.42189
$941$	−3.60621e10	−1.41087	−0.705435	−	0.708775i	$-0.749248\pi$
$941$	−3.60621e10	−1.41087	−0.705435	+	0.708775i	$0.749248\pi$
$942$	0	0
$943$	1.97975e10	0.768813
$944$	3.01691e9	0.116724
$945$	0	0
$946$	−2.72047e9	−0.104478
$947$	−1.21747e10	−0.465836	−0.232918	−	0.972496i	$-0.574827\pi$
$947$	−1.21747e10	−0.465836	−0.232918	+	0.972496i	$0.574827\pi$
$948$	0	0
$949$	−4.95739e10	−1.88287
$950$	1.10621e10	0.418606
$951$	0	0
$952$	−1.49695e10	−0.562311
$953$	2.94721e10	1.10303	0.551514	−	0.834166i	$-0.314050\pi$
$953$	2.94721e10	1.10303	0.551514	+	0.834166i	$0.314050\pi$
$954$	0	0
$955$	3.04417e10	1.13099
$956$	−9.62135e9	−0.356150
$957$	0	0
$958$	−7.22493e9	−0.265494
$959$	3.19402e10	1.16943
$960$	0	0
$961$	4.28076e10	1.55593
$962$	2.29610e9	0.0831529
$963$	0	0
$964$	−9.28174e9	−0.333703
$965$	−9.48743e10	−3.39862
$966$	0	0
$967$	−3.39812e10	−1.20850	−0.604250	−	0.796795i	$-0.706527\pi$
$967$	−3.39812e10	−1.20850	−0.604250	+	0.796795i	$0.706527\pi$
$968$	2.14028e10	0.758415
$969$	0	0
$970$	1.29835e10	0.456764
$971$	1.42757e9	0.0500415	0.0250208	−	0.999687i	$-0.492035\pi$
$971$	1.42757e9	0.0500415	0.0250208	+	0.999687i	$0.492035\pi$
$972$	0	0
$973$	5.56840e10	1.93792
$974$	2.15769e9	0.0748226
$975$	0	0
$976$	4.02873e10	1.38705
$977$	−2.69567e10	−0.924775	−0.462388	−	0.886678i	$-0.653007\pi$
$977$	−2.69567e10	−0.924775	−0.462388	+	0.886678i	$0.653007\pi$
$978$	0	0
$979$	−4.20128e10	−1.43101
$980$	−5.05551e10	−1.71583
$981$	0	0
$982$	7.60030e9	0.256118
$983$	1.23730e10	0.415469	0.207735	−	0.978185i	$-0.433391\pi$
$983$	1.23730e10	0.415469	0.207735	+	0.978185i	$0.433391\pi$
$984$	0	0
$985$	−6.83749e10	−2.27966
$986$	−4.77412e8	−0.0158608
$987$	0	0
$988$	−2.72406e10	−0.898602
$989$	−4.44468e9	−0.146101
$990$	0	0
$991$	−6.08067e10	−1.98470	−0.992348	−	0.123474i	$-0.960597\pi$
$991$	−6.08067e10	−1.98470	−0.992348	+	0.123474i	$0.960597\pi$
$992$	2.62712e10	0.854454
$993$	0	0
$994$	−4.19944e9	−0.135625
$995$	7.83264e10	2.52074
$996$	0	0
$997$	4.42391e10	1.41375	0.706876	−	0.707338i	$-0.250104\pi$
$997$	4.42391e10	1.41375	0.706876	+	0.707338i	$0.250104\pi$
$998$	2.47354e9	0.0787702
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	531.8.a.d.1.7		17
3.2	odd	2		177.8.a.b.1.11	✓	17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.8.a.b.1.11	✓	17	3.2	odd	2
531.8.a.d.1.7		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)

\(f(q)\)	\(=\)	\(q-2.11298 q^{2} -123.535 q^{4} +537.118 q^{5} +1259.15 q^{7} +531.490 q^{8} +O(q^{10})\)	\(q-2.11298 q^{2} -123.535 q^{4} +537.118 q^{5} +1259.15 q^{7} +531.490 q^{8} -1134.92 q^{10} -7730.24 q^{11} -8860.73 q^{13} -2660.56 q^{14} +14689.5 q^{16} -22368.4 q^{17} -24886.1 q^{19} -66353.0 q^{20} +16333.9 q^{22} +26686.2 q^{23} +210371. q^{25} +18722.6 q^{26} -155549. q^{28} -10101.0 q^{29} -265180. q^{31} -99069.4 q^{32} +47264.0 q^{34} +676311. q^{35} +122638. q^{37} +52583.9 q^{38} +285473. q^{40} +741866. q^{41} -166554. q^{43} +954958. q^{44} -56387.4 q^{46} +545699. q^{47} +761910. q^{49} -444510. q^{50} +1.09461e6 q^{52} +1.54083e6 q^{53} -4.15205e6 q^{55} +669225. q^{56} +21343.2 q^{58} +205379. q^{59} +2.74259e6 q^{61} +560320. q^{62} -1.67092e6 q^{64} -4.75926e6 q^{65} -41604.4 q^{67} +2.76328e6 q^{68} -1.42903e6 q^{70} +1.57840e6 q^{71} +5.59479e6 q^{73} -259132. q^{74} +3.07431e6 q^{76} -9.73352e6 q^{77} -3.74825e6 q^{79} +7.88999e6 q^{80} -1.56755e6 q^{82} +3.37715e6 q^{83} -1.20144e7 q^{85} +351926. q^{86} -4.10855e6 q^{88} +5.43486e6 q^{89} -1.11570e7 q^{91} -3.29668e6 q^{92} -1.15305e6 q^{94} -1.33668e7 q^{95} -1.14400e7 q^{97} -1.60990e6 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q + 32 q^{2} + 1166 q^{4} + 1072 q^{5} - 2407 q^{7} + 6645 q^{8}+O(q^{10}) \) 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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