LMFDB - Embedded newform 531.8.a.e.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(531, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 8, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("531.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 531 = 3^{2} \cdot 59 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	531.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$165.876448532$
Analytic rank:	$1$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 6 x^{17} - 1798 x^{16} + 11087 x^{15} + 1326765 x^{14} - 8403720 x^{13} - 518334228 x^{12} + \cdots + 51\!\cdots\!48 $ x^18 - 6x^17 - 1798x^16 + 11087x^15 + 1326765x^14 - 8403720x^13 - 518334228x^12 + 3375594921x^11 + 115310342333x^10 - 774932111214x^9 - 14600047830166x^8 + 102185027148481x^7 + 988557475638619x^6 - 7379206238519716x^5 - 30152342836849520x^4 + 260578770749067175x^3 + 182609347488069978x^2 - 3481290425710753600*x + 5164646074739714048
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{12}\cdot 3^{5} $
Twist minimal:	no (minimal twist has level 177)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$13.6971$ of defining polynomial
Character	$\chi$	$=$	531.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-14.6971 q^{2} +88.0043 q^{4} -457.882 q^{5} +1576.42 q^{7} +587.821 q^{8} +O(q^{10})$	\(q-14.6971 q^{2} +88.0043 q^{4} -457.882 q^{5} +1576.42 q^{7} +587.821 q^{8} +6729.53 q^{10} -6841.63 q^{11} +4116.85 q^{13} -23168.8 q^{14} -19903.8 q^{16} +34857.5 q^{17} -30826.5 q^{19} -40295.5 q^{20} +100552. q^{22} +51444.0 q^{23} +131531. q^{25} -60505.7 q^{26} +138732. q^{28} -106767. q^{29} -236039. q^{31} +217287. q^{32} -512304. q^{34} -721815. q^{35} -320825. q^{37} +453059. q^{38} -269152. q^{40} +227909. q^{41} +156061. q^{43} -602092. q^{44} -756076. q^{46} -902640. q^{47} +1.66156e6 q^{49} -1.93312e6 q^{50} +362300. q^{52} +1.28791e6 q^{53} +3.13266e6 q^{55} +926654. q^{56} +1.56916e6 q^{58} -205379. q^{59} +719101. q^{61} +3.46908e6 q^{62} -645794. q^{64} -1.88503e6 q^{65} -2.73492e6 q^{67} +3.06761e6 q^{68} +1.06086e7 q^{70} -2.81839e6 q^{71} -880677. q^{73} +4.71519e6 q^{74} -2.71286e6 q^{76} -1.07853e7 q^{77} +2.91979e6 q^{79} +9.11359e6 q^{80} -3.34960e6 q^{82} +6.61990e6 q^{83} -1.59606e7 q^{85} -2.29364e6 q^{86} -4.02165e6 q^{88} +6.36510e6 q^{89} +6.48989e6 q^{91} +4.52729e6 q^{92} +1.32662e7 q^{94} +1.41149e7 q^{95} +1.73556e7 q^{97} -2.44201e7 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 24 q^{2} + 1358 q^{4} - 678 q^{5} + 3081 q^{7} - 4107 q^{8}+O(q^{10}) $ 18 * q - 24 * q^2 + 1358 * q^4 - 678 * q^5 + 3081 * q^7 - 4107 * q^8	\( 18 q - 24 q^{2} + 1358 q^{4} - 678 q^{5} + 3081 q^{7} - 4107 q^{8} + 3609 q^{10} - 15070 q^{11} + 13662 q^{13} - 20861 q^{14} + 60482 q^{16} - 71919 q^{17} + 56231 q^{19} - 143053 q^{20} + 274198 q^{22} - 150029 q^{23} + 399672 q^{25} - 182846 q^{26} + 434150 q^{28} - 591285 q^{29} + 426733 q^{31} - 1205630 q^{32} + 403548 q^{34} - 912879 q^{35} + 7703 q^{37} + 417859 q^{38} + 618020 q^{40} - 770959 q^{41} + 793050 q^{43} - 2591274 q^{44} - 4068019 q^{46} - 1410373 q^{47} + 1637427 q^{49} - 1021549 q^{50} - 3749190 q^{52} - 1037934 q^{53} + 331974 q^{55} + 391748 q^{56} + 653724 q^{58} - 3696822 q^{59} - 1374623 q^{61} - 5251718 q^{62} + 5077197 q^{64} - 3257170 q^{65} - 2436904 q^{67} - 14119909 q^{68} + 5185580 q^{70} - 14289172 q^{71} + 5482515 q^{73} - 14934154 q^{74} + 3822912 q^{76} - 23157109 q^{77} + 19786414 q^{79} - 31978143 q^{80} + 9749509 q^{82} - 30227337 q^{83} + 9946981 q^{85} - 44295864 q^{86} + 39970897 q^{88} - 31061677 q^{89} + 26377785 q^{91} - 4719698 q^{92} + 44488296 q^{94} - 15534599 q^{95} + 12084118 q^{97} - 42274744 q^{98}+O(q^{100}) \) 18 * q - 24 * q^2 + 1358 * q^4 - 678 * q^5 + 3081 * q^7 - 4107 * q^8 + 3609 * q^10 - 15070 * q^11 + 13662 * q^13 - 20861 * q^14 + 60482 * q^16 - 71919 * q^17 + 56231 * q^19 - 143053 * q^20 + 274198 * q^22 - 150029 * q^23 + 399672 * q^25 - 182846 * q^26 + 434150 * q^28 - 591285 * q^29 + 426733 * q^31 - 1205630 * q^32 + 403548 * q^34 - 912879 * q^35 + 7703 * q^37 + 417859 * q^38 + 618020 * q^40 - 770959 * q^41 + 793050 * q^43 - 2591274 * q^44 - 4068019 * q^46 - 1410373 * q^47 + 1637427 * q^49 - 1021549 * q^50 - 3749190 * q^52 - 1037934 * q^53 + 331974 * q^55 + 391748 * q^56 + 653724 * q^58 - 3696822 * q^59 - 1374623 * q^61 - 5251718 * q^62 + 5077197 * q^64 - 3257170 * q^65 - 2436904 * q^67 - 14119909 * q^68 + 5185580 * q^70 - 14289172 * q^71 + 5482515 * q^73 - 14934154 * q^74 + 3822912 * q^76 - 23157109 * q^77 + 19786414 * q^79 - 31978143 * q^80 + 9749509 * q^82 - 30227337 * q^83 + 9946981 * q^85 - 44295864 * q^86 + 39970897 * q^88 - 31061677 * q^89 + 26377785 * q^91 - 4719698 * q^92 + 44488296 * q^94 - 15534599 * q^95 + 12084118 * q^97 - 42274744 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−14.6971	−1.29905	−0.649525	−	0.760340i	$-0.725032\pi$
$2$	−14.6971	−1.29905	−0.649525	+	0.760340i	$0.725032\pi$
$3$	0	0
$3$	0	0
$4$	88.0043	0.687533
$5$	−457.882	−1.63817	−0.819084	−	0.573674i	$-0.805518\pi$
$5$	−457.882	−1.63817	−0.819084	+	0.573674i	$0.805518\pi$
$6$	0	0
$7$	1576.42	1.73712	0.868559	−	0.495585i	$-0.165046\pi$
$7$	1576.42	1.73712	0.868559	+	0.495585i	$0.165046\pi$
$8$	587.821	0.405910
$9$	0	0
$10$	6729.53	2.12806
$11$	−6841.63	−1.54983	−0.774917	−	0.632064i	$-0.782208\pi$
$11$	−6841.63	−1.54983	−0.774917	+	0.632064i	$0.782208\pi$
$12$	0	0
$13$	4116.85	0.519713	0.259856	−	0.965647i	$-0.416325\pi$
$13$	4116.85	0.519713	0.259856	+	0.965647i	$0.416325\pi$
$14$	−23168.8	−2.25661
$15$	0	0
$16$	−19903.8	−1.21483
$17$	34857.5	1.72078	0.860389	−	0.509637i	$-0.170220\pi$
$17$	34857.5	1.72078	0.860389	+	0.509637i	$0.170220\pi$
$18$	0	0
$19$	−30826.5	−1.03107	−0.515533	−	0.856870i	$-0.672406\pi$
$19$	−30826.5	−1.03107	−0.515533	+	0.856870i	$0.672406\pi$
$20$	−40295.5	−1.12629
$21$	0	0
$22$	100552.	2.01331
$23$	51444.0	0.881632	0.440816	−	0.897598i	$-0.354689\pi$
$23$	51444.0	0.881632	0.440816	+	0.897598i	$0.354689\pi$
$24$	0	0
$25$	131531.	1.68359
$26$	−60505.7	−0.675133
$27$	0	0
$28$	138732.	1.19433
$29$	−106767.	−0.812913	−0.406457	−	0.913670i	$-0.633236\pi$
$29$	−106767.	−0.812913	−0.406457	+	0.913670i	$0.633236\pi$
$30$	0	0
$31$	−236039.	−1.42304	−0.711521	−	0.702665i	$-0.751993\pi$
$31$	−236039.	−1.42304	−0.711521	+	0.702665i	$0.751993\pi$
$32$	217287.	1.17222
$33$	0	0
$34$	−512304.	−2.23538
$35$	−721815.	−2.84569
$36$	0	0
$37$	−320825.	−1.04127	−0.520633	−	0.853781i	$-0.674304\pi$
$37$	−320825.	−1.04127	−0.520633	+	0.853781i	$0.674304\pi$
$38$	453059.	1.33941
$39$	0	0
$40$	−269152.	−0.664949
$41$	227909.	0.516439	0.258219	−	0.966086i	$-0.416864\pi$
$41$	227909.	0.516439	0.258219	+	0.966086i	$0.416864\pi$
$42$	0	0
$43$	156061.	0.299333	0.149667	−	0.988737i	$-0.452180\pi$
$43$	156061.	0.299333	0.149667	+	0.988737i	$0.452180\pi$
$44$	−602092.	−1.06556
$45$	0	0
$46$	−756076.	−1.14528
$47$	−902640.	−1.26815	−0.634077	−	0.773270i	$-0.718620\pi$
$47$	−902640.	−1.26815	−0.634077	+	0.773270i	$0.718620\pi$
$48$	0	0
$49$	1.66156e6	2.01758
$50$	−1.93312e6	−2.18707
$51$	0	0
$52$	362300.	0.357320
$53$	1.28791e6	1.18829	0.594143	−	0.804360i	$-0.297491\pi$
$53$	1.28791e6	1.18829	0.594143	+	0.804360i	$0.297491\pi$
$54$	0	0
$55$	3.13266e6	2.53889
$56$	926654.	0.705114
$57$	0	0
$58$	1.56916e6	1.05602
$59$	−205379.	−0.130189
$59$	−205379.	−0.130189
$60$	0	0
$61$	719101.	0.405635	0.202818	−	0.979217i	$-0.434990\pi$
$61$	719101.	0.405635	0.202818	+	0.979217i	$0.434990\pi$
$62$	3.46908e6	1.84860
$63$	0	0
$64$	−645794.	−0.307939
$65$	−1.88503e6	−0.851377
$66$	0	0
$67$	−2.73492e6	−1.11092	−0.555460	−	0.831544i	$-0.687458\pi$
$67$	−2.73492e6	−1.11092	−0.555460	+	0.831544i	$0.687458\pi$
$68$	3.06761e6	1.18309
$69$	0	0
$70$	1.06086e7	3.69670
$71$	−2.81839e6	−0.934538	−0.467269	−	0.884115i	$-0.654762\pi$
$71$	−2.81839e6	−0.934538	−0.467269	+	0.884115i	$0.654762\pi$
$72$	0	0
$73$	−880677.	−0.264964	−0.132482	−	0.991185i	$-0.542295\pi$
$73$	−880677.	−0.264964	−0.132482	+	0.991185i	$0.542295\pi$
$74$	4.71519e6	1.35266
$75$	0	0
$76$	−2.71286e6	−0.708892
$77$	−1.07853e7	−2.69224
$78$	0	0
$79$	2.91979e6	0.666281	0.333140	−	0.942877i	$-0.391892\pi$
$79$	2.91979e6	0.666281	0.333140	+	0.942877i	$0.391892\pi$
$80$	9.11359e6	1.99010
$81$	0	0
$82$	−3.34960e6	−0.670880
$83$	6.61990e6	1.27080	0.635402	−	0.772182i	$-0.280835\pi$
$83$	6.61990e6	1.27080	0.635402	+	0.772182i	$0.280835\pi$
$84$	0	0
$85$	−1.59606e7	−2.81892
$86$	−2.29364e6	−0.388849
$87$	0	0
$88$	−4.02165e6	−0.629093
$89$	6.36510e6	0.957062	0.478531	−	0.878071i	$-0.341169\pi$
$89$	6.36510e6	0.957062	0.478531	+	0.878071i	$0.341169\pi$
$90$	0	0
$91$	6.48989e6	0.902803
$92$	4.52729e6	0.606151
$93$	0	0
$94$	1.32662e7	1.64740
$95$	1.41149e7	1.68906
$96$	0	0
$97$	1.73556e7	1.93081	0.965403	−	0.260764i	$-0.0839744\pi$
$97$	1.73556e7	1.93081	0.965403	+	0.260764i	$0.0839744\pi$
$98$	−2.44201e7	−2.62094
$99$	0	0
$100$	1.15753e7	1.15753
$101$	−1.48075e7	−1.43007	−0.715036	−	0.699087i	$-0.753590\pi$
$101$	−1.48075e7	−1.43007	−0.715036	+	0.699087i	$0.753590\pi$
$102$	0	0
$103$	8.68688e6	0.783310	0.391655	−	0.920112i	$-0.371903\pi$
$103$	8.68688e6	0.783310	0.391655	+	0.920112i	$0.371903\pi$
$104$	2.41997e6	0.210957
$105$	0	0
$106$	−1.89286e7	−1.54364
$107$	1.01246e7	0.798974	0.399487	−	0.916739i	$-0.369188\pi$
$107$	1.01246e7	0.798974	0.399487	+	0.916739i	$0.369188\pi$
$108$	0	0
$109$	−4.44690e6	−0.328900	−0.164450	−	0.986385i	$-0.552585\pi$
$109$	−4.44690e6	−0.328900	−0.164450	+	0.986385i	$0.552585\pi$
$110$	−4.60409e7	−3.29814
$111$	0	0
$112$	−3.13768e7	−2.11031
$113$	2.11640e6	0.137982	0.0689910	−	0.997617i	$-0.478022\pi$
$113$	2.11640e6	0.137982	0.0689910	+	0.997617i	$0.478022\pi$
$114$	0	0
$115$	−2.35553e7	−1.44426
$116$	−9.39595e6	−0.558905
$117$	0	0
$118$	3.01847e6	0.169122
$119$	5.49501e7	2.98920
$120$	0	0
$121$	2.73207e7	1.40198
$122$	−1.05687e7	−0.526941
$123$	0	0
$124$	−2.07724e7	−0.978388
$125$	−2.44535e7	−1.11984
$126$	0	0
$127$	1.43195e7	0.620317	0.310159	−	0.950685i	$-0.399618\pi$
$127$	1.43195e7	0.620317	0.310159	+	0.950685i	$0.399618\pi$
$128$	−1.83214e7	−0.772189
$129$	0	0
$130$	2.77045e7	1.10598
$131$	4.80639e7	1.86797	0.933985	−	0.357312i	$-0.116307\pi$
$131$	4.80639e7	1.86797	0.933985	+	0.357312i	$0.116307\pi$
$132$	0	0
$133$	−4.85956e7	−1.79108
$134$	4.01953e7	1.44314
$135$	0	0
$136$	2.04900e7	0.698482
$137$	1.81664e7	0.603598	0.301799	−	0.953372i	$-0.402413\pi$
$137$	1.81664e7	0.603598	0.301799	+	0.953372i	$0.402413\pi$
$138$	0	0
$139$	2.63273e7	0.831484	0.415742	−	0.909483i	$-0.363522\pi$
$139$	2.63273e7	0.831484	0.415742	+	0.909483i	$0.363522\pi$
$140$	−6.35228e7	−1.95651
$141$	0	0
$142$	4.14221e7	1.21401
$143$	−2.81659e7	−0.805468
$144$	0	0
$145$	4.88867e7	1.33169
$146$	1.29434e7	0.344201
$147$	0	0
$148$	−2.82339e7	−0.715905
$149$	−6.64472e7	−1.64560	−0.822801	−	0.568329i	$-0.807590\pi$
$149$	−6.64472e7	−1.64560	−0.822801	+	0.568329i	$0.807590\pi$
$150$	0	0
$151$	−6.98756e7	−1.65160	−0.825802	−	0.563960i	$-0.809277\pi$
$151$	−6.98756e7	−1.65160	−0.825802	+	0.563960i	$0.809277\pi$
$152$	−1.81205e7	−0.418520
$153$	0	0
$154$	1.58512e8	3.49736
$155$	1.08078e8	2.33118
$156$	0	0
$157$	−2.65494e7	−0.547528	−0.273764	−	0.961797i	$-0.588269\pi$
$157$	−2.65494e7	−0.547528	−0.273764	+	0.961797i	$0.588269\pi$
$158$	−4.29124e7	−0.865533
$159$	0	0
$160$	−9.94916e7	−1.92029
$161$	8.10974e7	1.53150
$162$	0	0
$163$	5.75891e7	1.04156	0.520779	−	0.853691i	$-0.325642\pi$
$163$	5.75891e7	1.04156	0.520779	+	0.853691i	$0.325642\pi$
$164$	2.00570e7	0.355069
$165$	0	0
$166$	−9.72933e7	−1.65084
$167$	−4.98500e6	−0.0828242	−0.0414121	−	0.999142i	$-0.513186\pi$
$167$	−4.98500e6	−0.0828242	−0.0414121	+	0.999142i	$0.513186\pi$
$168$	0	0
$169$	−4.58001e7	−0.729899
$170$	2.34574e8	3.66193
$171$	0	0
$172$	1.37340e7	0.205801
$173$	−8.44843e7	−1.24055	−0.620276	−	0.784384i	$-0.712979\pi$
$173$	−8.44843e7	−1.24055	−0.620276	+	0.784384i	$0.712979\pi$
$174$	0	0
$175$	2.07348e8	2.92460
$176$	1.36174e8	1.88279
$177$	0	0
$178$	−9.35484e7	−1.24327
$179$	7.90602e6	0.103032	0.0515160	−	0.998672i	$-0.483595\pi$
$179$	7.90602e6	0.103032	0.0515160	+	0.998672i	$0.483595\pi$
$180$	0	0
$181$	4.23307e7	0.530616	0.265308	−	0.964164i	$-0.414526\pi$
$181$	4.23307e7	0.530616	0.265308	+	0.964164i	$0.414526\pi$
$182$	−9.53825e7	−1.17279
$183$	0	0
$184$	3.02398e7	0.357863
$185$	1.46900e8	1.70577
$186$	0	0
$187$	−2.38482e8	−2.66692
$188$	−7.94362e7	−0.871899
$189$	0	0
$190$	−2.07448e8	−2.19417
$191$	8.15774e7	0.847136	0.423568	−	0.905864i	$-0.360777\pi$
$191$	8.15774e7	0.847136	0.423568	+	0.905864i	$0.360777\pi$
$192$	0	0
$193$	3.34817e7	0.335240	0.167620	−	0.985852i	$-0.446392\pi$
$193$	3.34817e7	0.335240	0.167620	+	0.985852i	$0.446392\pi$
$194$	−2.55077e8	−2.50821
$195$	0	0
$196$	1.46225e8	1.38715
$197$	5.69368e7	0.530593	0.265296	−	0.964167i	$-0.414530\pi$
$197$	5.69368e7	0.530593	0.265296	+	0.964167i	$0.414530\pi$
$198$	0	0
$199$	3.68438e7	0.331420	0.165710	−	0.986175i	$-0.447008\pi$
$199$	3.68438e7	0.331420	0.165710	+	0.986175i	$0.447008\pi$
$200$	7.73165e7	0.683388
$201$	0	0
$202$	2.17628e8	1.85774
$203$	−1.68310e8	−1.41213
$204$	0	0
$205$	−1.04356e8	−0.846013
$206$	−1.27672e8	−1.01756
$207$	0	0
$208$	−8.19410e7	−0.631363
$209$	2.10903e8	1.59798
$210$	0	0
$211$	6.42783e6	0.0471059	0.0235530	−	0.999723i	$-0.492502\pi$
$211$	6.42783e6	0.0471059	0.0235530	+	0.999723i	$0.492502\pi$
$212$	1.13342e8	0.816986
$213$	0	0
$214$	−1.48801e8	−1.03791
$215$	−7.14575e7	−0.490358
$216$	0	0
$217$	−3.72097e8	−2.47199
$218$	6.53564e7	0.427258
$219$	0	0
$220$	2.75687e8	1.74557
$221$	1.43503e8	0.894311
$222$	0	0
$223$	−5.93351e7	−0.358298	−0.179149	−	0.983822i	$-0.557334\pi$
$223$	−5.93351e7	−0.358298	−0.179149	+	0.983822i	$0.557334\pi$
$224$	3.42536e8	2.03628
$225$	0	0
$226$	−3.11049e7	−0.179246
$227$	−2.49947e8	−1.41827	−0.709134	−	0.705074i	$-0.750914\pi$
$227$	−2.49947e8	−1.41827	−0.709134	+	0.705074i	$0.750914\pi$
$228$	0	0
$229$	−1.83888e8	−1.01188	−0.505941	−	0.862568i	$-0.668855\pi$
$229$	−1.83888e8	−1.01188	−0.505941	+	0.862568i	$0.668855\pi$
$230$	3.46194e8	1.87617
$231$	0	0
$232$	−6.27599e7	−0.329970
$233$	1.34216e8	0.695120	0.347560	−	0.937658i	$-0.387010\pi$
$233$	1.34216e8	0.695120	0.347560	+	0.937658i	$0.387010\pi$
$234$	0	0
$235$	4.13303e8	2.07745
$236$	−1.80742e7	−0.0895092
$237$	0	0
$238$	−8.07607e8	−3.88312
$239$	3.79885e8	1.79994	0.899972	−	0.435947i	$-0.143587\pi$
$239$	3.79885e8	1.79994	0.899972	+	0.435947i	$0.143587\pi$
$240$	0	0
$241$	−2.48361e7	−0.114294	−0.0571470	−	0.998366i	$-0.518200\pi$
$241$	−2.48361e7	−0.114294	−0.0571470	+	0.998366i	$0.518200\pi$
$242$	−4.01534e8	−1.82125
$243$	0	0
$244$	6.32840e7	0.278888
$245$	−7.60800e8	−3.30514
$246$	0	0
$247$	−1.26908e8	−0.535858
$248$	−1.38749e8	−0.577627
$249$	0	0
$250$	3.59395e8	1.45473
$251$	2.30663e8	0.920705	0.460352	−	0.887736i	$-0.347723\pi$
$251$	2.30663e8	0.920705	0.460352	+	0.887736i	$0.347723\pi$
$252$	0	0
$253$	−3.51960e8	−1.36638
$254$	−2.10454e8	−0.805824
$255$	0	0
$256$	3.51933e8	1.31105
$257$	−2.98007e8	−1.09512	−0.547558	−	0.836768i	$-0.684442\pi$
$257$	−2.98007e8	−1.09512	−0.547558	+	0.836768i	$0.684442\pi$
$258$	0	0
$259$	−5.05755e8	−1.80880
$260$	−1.65891e8	−0.585350
$261$	0	0
$262$	−7.06400e8	−2.42659
$263$	−2.77082e8	−0.939211	−0.469605	−	0.882876i	$-0.655604\pi$
$263$	−2.77082e8	−0.939211	−0.469605	+	0.882876i	$0.655604\pi$
$264$	0	0
$265$	−5.89712e8	−1.94661
$266$	7.14213e8	2.32671
$267$	0	0
$268$	−2.40684e8	−0.763794
$269$	−2.71094e8	−0.849155	−0.424577	−	0.905392i	$-0.639577\pi$
$269$	−2.71094e8	−0.849155	−0.424577	+	0.905392i	$0.639577\pi$
$270$	0	0
$271$	−4.89470e8	−1.49394	−0.746970	−	0.664858i	$-0.768492\pi$
$271$	−4.89470e8	−1.49394	−0.746970	+	0.664858i	$0.768492\pi$
$272$	−6.93797e8	−2.09046
$273$	0	0
$274$	−2.66994e8	−0.784104
$275$	−8.99884e8	−2.60929
$276$	0	0
$277$	−2.76753e8	−0.782371	−0.391186	−	0.920312i	$-0.627935\pi$
$277$	−2.76753e8	−0.782371	−0.391186	+	0.920312i	$0.627935\pi$
$278$	−3.86934e8	−1.08014
$279$	0	0
$280$	−4.24298e8	−1.15510
$281$	−3.28075e8	−0.882065	−0.441032	−	0.897491i	$-0.645388\pi$
$281$	−3.28075e8	−0.882065	−0.441032	+	0.897491i	$0.645388\pi$
$282$	0	0
$283$	2.47479e8	0.649061	0.324531	−	0.945875i	$-0.394794\pi$
$283$	2.47479e8	0.649061	0.324531	+	0.945875i	$0.394794\pi$
$284$	−2.48030e8	−0.642526
$285$	0	0
$286$	4.13957e8	1.04634
$287$	3.59282e8	0.897115
$288$	0	0
$289$	8.04706e8	1.96108
$290$	−7.18492e8	−1.72993
$291$	0	0
$292$	−7.75033e7	−0.182171
$293$	−3.73118e8	−0.866582	−0.433291	−	0.901254i	$-0.642648\pi$
$293$	−3.73118e8	−0.866582	−0.433291	+	0.901254i	$0.642648\pi$
$294$	0	0
$295$	9.40393e7	0.213271
$296$	−1.88587e8	−0.422661
$297$	0	0
$298$	9.76581e8	2.13772
$299$	2.11787e8	0.458195
$300$	0	0
$301$	2.46018e8	0.519977
$302$	1.02697e9	2.14552
$303$	0	0
$304$	6.13564e8	1.25257
$305$	−3.29263e8	−0.664498
$306$	0	0
$307$	−5.11504e8	−1.00894	−0.504469	−	0.863430i	$-0.668312\pi$
$307$	−5.11504e8	−1.00894	−0.504469	+	0.863430i	$0.668312\pi$
$308$	−9.49151e8	−1.85101
$309$	0	0
$310$	−1.58843e9	−3.02832
$311$	−6.07087e6	−0.0114443	−0.00572215	−	0.999984i	$-0.501821\pi$
$311$	−6.07087e6	−0.0114443	−0.00572215	+	0.999984i	$0.501821\pi$
$312$	0	0
$313$	9.00976e6	0.0166076	0.00830382	−	0.999966i	$-0.497357\pi$
$313$	9.00976e6	0.0166076	0.00830382	+	0.999966i	$0.497357\pi$
$314$	3.90199e8	0.711266
$315$	0	0
$316$	2.56954e8	0.458090
$317$	−1.54129e8	−0.271755	−0.135878	−	0.990726i	$-0.543385\pi$
$317$	−1.54129e8	−0.271755	−0.135878	+	0.990726i	$0.543385\pi$
$318$	0	0
$319$	7.30460e8	1.25988
$320$	2.95698e8	0.504455
$321$	0	0
$322$	−1.19190e9	−1.98949
$323$	−1.07453e9	−1.77424
$324$	0	0
$325$	5.41492e8	0.874985
$326$	−8.46391e8	−1.35304
$327$	0	0
$328$	1.33970e8	0.209628
$329$	−1.42294e9	−2.20294
$330$	0	0
$331$	6.66857e8	1.01073	0.505365	−	0.862906i	$-0.331358\pi$
$331$	6.66857e8	1.01073	0.505365	+	0.862906i	$0.331358\pi$
$332$	5.82580e8	0.873719
$333$	0	0
$334$	7.32649e7	0.107593
$335$	1.25227e9	1.81987
$336$	0	0
$337$	7.12103e8	1.01353	0.506767	−	0.862083i	$-0.330840\pi$
$337$	7.12103e8	1.01353	0.506767	+	0.862083i	$0.330840\pi$
$338$	6.73127e8	0.948176
$339$	0	0
$340$	−1.40460e9	−1.93810
$341$	1.61489e9	2.20548
$342$	0	0
$343$	1.32108e9	1.76766
$344$	9.17359e7	0.121502
$345$	0	0
$346$	1.24167e9	1.61154
$347$	−6.85187e8	−0.880351	−0.440175	−	0.897912i	$-0.645084\pi$
$347$	−6.85187e8	−0.880351	−0.440175	+	0.897912i	$0.645084\pi$
$348$	0	0
$349$	−4.10968e8	−0.517511	−0.258755	−	0.965943i	$-0.583312\pi$
$349$	−4.10968e8	−0.517511	−0.258755	+	0.965943i	$0.583312\pi$
$350$	−3.04741e9	−3.79921
$351$	0	0
$352$	−1.48659e9	−1.81674
$353$	−7.36899e8	−0.891654	−0.445827	−	0.895119i	$-0.647090\pi$
$353$	−7.36899e8	−0.891654	−0.445827	+	0.895119i	$0.647090\pi$
$354$	0	0
$355$	1.29049e9	1.53093
$356$	5.60156e8	0.658012
$357$	0	0
$358$	−1.16195e8	−0.133844
$359$	−1.53809e9	−1.75449	−0.877246	−	0.480041i	$-0.840622\pi$
$359$	−1.53809e9	−1.75449	−0.877246	+	0.480041i	$0.840622\pi$
$360$	0	0
$361$	5.64007e7	0.0630971
$362$	−6.22138e8	−0.689298
$363$	0	0
$364$	5.71138e8	0.620707
$365$	4.03246e8	0.434055
$366$	0	0
$367$	−9.99795e8	−1.05580	−0.527898	−	0.849308i	$-0.677020\pi$
$367$	−9.99795e8	−1.05580	−0.527898	+	0.849308i	$0.677020\pi$
$368$	−1.02393e9	−1.07103
$369$	0	0
$370$	−2.15900e9	−2.21588
$371$	2.03029e9	2.06419
$372$	0	0
$373$	−9.19979e8	−0.917903	−0.458952	−	0.888461i	$-0.651775\pi$
$373$	−9.19979e8	−0.917903	−0.458952	+	0.888461i	$0.651775\pi$
$374$	3.50499e9	3.46446
$375$	0	0
$376$	−5.30591e8	−0.514757
$377$	−4.39544e8	−0.422481
$378$	0	0
$379$	1.21564e9	1.14701	0.573505	−	0.819202i	$-0.305583\pi$
$379$	1.21564e9	1.14701	0.573505	+	0.819202i	$0.305583\pi$
$380$	1.24217e9	1.16128
$381$	0	0
$382$	−1.19895e9	−1.10047
$383$	−3.85577e8	−0.350683	−0.175342	−	0.984508i	$-0.556103\pi$
$383$	−3.85577e8	−0.350683	−0.175342	+	0.984508i	$0.556103\pi$
$384$	0	0
$385$	4.93839e9	4.41035
$386$	−4.92083e8	−0.435494
$387$	0	0
$388$	1.52737e9	1.32749
$389$	1.39089e9	1.19804	0.599019	−	0.800735i	$-0.295557\pi$
$389$	1.39089e9	1.19804	0.599019	+	0.800735i	$0.295557\pi$
$390$	0	0
$391$	1.79321e9	1.51709
$392$	9.76702e8	0.818957
$393$	0	0
$394$	−8.36805e8	−0.689267
$395$	−1.33692e9	−1.09148
$396$	0	0
$397$	−1.34669e8	−0.108019	−0.0540096	−	0.998540i	$-0.517200\pi$
$397$	−1.34669e8	−0.108019	−0.0540096	+	0.998540i	$0.517200\pi$
$398$	−5.41497e8	−0.430532
$399$	0	0
$400$	−2.61796e9	−2.04528
$401$	−7.92234e8	−0.613547	−0.306774	−	0.951782i	$-0.599249\pi$
$401$	−7.92234e8	−0.613547	−0.306774	+	0.951782i	$0.599249\pi$
$402$	0	0
$403$	−9.71737e8	−0.739573
$404$	−1.30313e9	−0.983223
$405$	0	0
$406$	2.47367e9	1.83442
$407$	2.19496e9	1.61379
$408$	0	0
$409$	−1.98450e9	−1.43424	−0.717118	−	0.696952i	$-0.754539\pi$
$409$	−1.98450e9	−1.43424	−0.717118	+	0.696952i	$0.754539\pi$
$410$	1.53372e9	1.09901
$411$	0	0
$412$	7.64482e8	0.538551
$413$	−3.23764e8	−0.226154
$414$	0	0
$415$	−3.03113e9	−2.08179
$416$	8.94537e8	0.609216
$417$	0	0
$418$	−3.09966e9	−2.07586
$419$	−1.12010e9	−0.743886	−0.371943	−	0.928256i	$-0.621308\pi$
$419$	−1.12010e9	−0.743886	−0.371943	+	0.928256i	$0.621308\pi$
$420$	0	0
$421$	1.60154e9	1.04605	0.523024	−	0.852318i	$-0.324804\pi$
$421$	1.60154e9	1.04605	0.523024	+	0.852318i	$0.324804\pi$
$422$	−9.44703e7	−0.0611930
$423$	0	0
$424$	7.57062e8	0.482337
$425$	4.58483e9	2.89709
$426$	0	0
$427$	1.13361e9	0.704636
$428$	8.91004e8	0.549321
$429$	0	0
$430$	1.05022e9	0.637000
$431$	1.42222e9	0.855648	0.427824	−	0.903862i	$-0.359280\pi$
$431$	1.42222e9	0.855648	0.427824	+	0.903862i	$0.359280\pi$
$432$	0	0
$433$	1.13304e9	0.670713	0.335356	−	0.942091i	$-0.391143\pi$
$433$	1.13304e9	0.670713	0.335356	+	0.942091i	$0.391143\pi$
$434$	5.46874e9	3.21124
$435$	0	0
$436$	−3.91346e8	−0.226130
$437$	−1.58584e9	−0.909020
$438$	0	0
$439$	−1.92938e9	−1.08841	−0.544204	−	0.838953i	$-0.683168\pi$
$439$	−1.92938e9	−1.08841	−0.544204	+	0.838953i	$0.683168\pi$
$440$	1.84144e9	1.03056
$441$	0	0
$442$	−2.10908e9	−1.16175
$443$	8.33711e7	0.0455620	0.0227810	−	0.999740i	$-0.492748\pi$
$443$	8.33711e7	0.0455620	0.0227810	+	0.999740i	$0.492748\pi$
$444$	0	0
$445$	−2.91446e9	−1.56783
$446$	8.72053e8	0.465448
$447$	0	0
$448$	−1.01804e9	−0.534926
$449$	−2.88898e9	−1.50620	−0.753099	−	0.657907i	$-0.771442\pi$
$449$	−2.88898e9	−1.50620	−0.753099	+	0.657907i	$0.771442\pi$
$450$	0	0
$451$	−1.55927e9	−0.800394
$452$	1.86252e8	0.0948673
$453$	0	0
$454$	3.67350e9	1.84240
$455$	−2.97160e9	−1.47894
$456$	0	0
$457$	−2.23596e9	−1.09587	−0.547933	−	0.836522i	$-0.684585\pi$
$457$	−2.23596e9	−1.09587	−0.547933	+	0.836522i	$0.684585\pi$
$458$	2.70262e9	1.31449
$459$	0	0
$460$	−2.07296e9	−0.992977
$461$	1.26440e9	0.601077	0.300539	−	0.953770i	$-0.402834\pi$
$461$	1.26440e9	0.601077	0.300539	+	0.953770i	$0.402834\pi$
$462$	0	0
$463$	2.39212e9	1.12008	0.560041	−	0.828465i	$-0.310785\pi$
$463$	2.39212e9	1.12008	0.560041	+	0.828465i	$0.310785\pi$
$464$	2.12507e9	0.987553
$465$	0	0
$466$	−1.97259e9	−0.902996
$467$	−5.83299e8	−0.265022	−0.132511	−	0.991182i	$-0.542304\pi$
$467$	−5.83299e8	−0.265022	−0.132511	+	0.991182i	$0.542304\pi$
$468$	0	0
$469$	−4.31138e9	−1.92980
$470$	−6.07434e9	−2.69871
$471$	0	0
$472$	−1.20726e8	−0.0528450
$473$	−1.06771e9	−0.463916
$474$	0	0
$475$	−4.05463e9	−1.73590
$476$	4.83585e9	2.05517
$477$	0	0
$478$	−5.58320e9	−2.33822
$479$	−3.79366e9	−1.57719	−0.788595	−	0.614913i	$-0.789191\pi$
$479$	−3.79366e9	−1.57719	−0.788595	+	0.614913i	$0.789191\pi$
$480$	0	0
$481$	−1.32079e9	−0.541159
$482$	3.65018e8	0.148474
$483$	0	0
$484$	2.40434e9	0.963909
$485$	−7.94681e9	−3.16298
$486$	0	0
$487$	−2.39967e9	−0.941455	−0.470728	−	0.882279i	$-0.656009\pi$
$487$	−2.39967e9	−0.941455	−0.470728	+	0.882279i	$0.656009\pi$
$488$	4.22703e8	0.164651
$489$	0	0
$490$	1.11815e10	4.29354
$491$	−4.01253e9	−1.52979	−0.764897	−	0.644152i	$-0.777210\pi$
$491$	−4.01253e9	−1.52979	−0.764897	+	0.644152i	$0.777210\pi$
$492$	0	0
$493$	−3.72163e9	−1.39884
$494$	1.86518e9	0.696107
$495$	0	0
$496$	4.69807e9	1.72876
$497$	−4.44297e9	−1.62340
$498$	0	0
$499$	2.58807e9	0.932445	0.466223	−	0.884667i	$-0.345615\pi$
$499$	2.58807e9	0.932445	0.466223	+	0.884667i	$0.345615\pi$
$500$	−2.15201e9	−0.769928
$501$	0	0
$502$	−3.39008e9	−1.19604
$503$	5.50700e9	1.92942	0.964712	−	0.263309i	$-0.0848138\pi$
$503$	5.50700e9	1.92942	0.964712	+	0.263309i	$0.0848138\pi$
$504$	0	0
$505$	6.78010e9	2.34270
$506$	5.17279e9	1.77500
$507$	0	0
$508$	1.26017e9	0.426489
$509$	−1.30017e9	−0.437007	−0.218503	−	0.975836i	$-0.570117\pi$
$509$	−1.30017e9	−0.437007	−0.218503	+	0.975836i	$0.570117\pi$
$510$	0	0
$511$	−1.38832e9	−0.460273
$512$	−2.82725e9	−0.930934
$513$	0	0
$514$	4.37983e9	1.42261
$515$	−3.97756e9	−1.28319
$516$	0	0
$517$	6.17553e9	1.96543
$518$	7.43313e9	2.34973
$519$	0	0
$520$	−1.10806e9	−0.345582
$521$	4.64043e9	1.43756	0.718780	−	0.695238i	$-0.244701\pi$
$521$	4.64043e9	1.43756	0.718780	+	0.695238i	$0.244701\pi$
$522$	0	0
$523$	6.14798e9	1.87922	0.939608	−	0.342254i	$-0.111190\pi$
$523$	6.14798e9	1.87922	0.939608	+	0.342254i	$0.111190\pi$
$524$	4.22983e9	1.28429
$525$	0	0
$526$	4.07230e9	1.22008
$527$	−8.22772e9	−2.44874
$528$	0	0
$529$	−7.58342e8	−0.222726
$530$	8.66704e9	2.52875
$531$	0	0
$532$	−4.27662e9	−1.23143
$533$	9.38269e8	0.268400
$534$	0	0
$535$	−4.63585e9	−1.30885
$536$	−1.60764e9	−0.450933
$537$	0	0
$538$	3.98429e9	1.10310
$539$	−1.13678e10	−3.12691
$540$	0	0
$541$	−1.05096e9	−0.285362	−0.142681	−	0.989769i	$-0.545572\pi$
$541$	−1.05096e9	−0.285362	−0.142681	+	0.989769i	$0.545572\pi$
$542$	7.19377e9	1.94070
$543$	0	0
$544$	7.57407e9	2.01713
$545$	2.03615e9	0.538794
$546$	0	0
$547$	5.58405e9	1.45879	0.729396	−	0.684092i	$-0.239801\pi$
$547$	5.58405e9	1.45879	0.729396	+	0.684092i	$0.239801\pi$
$548$	1.59872e9	0.414994
$549$	0	0
$550$	1.32257e10	3.38960
$551$	3.29125e9	0.838167
$552$	0	0
$553$	4.60283e9	1.15741
$554$	4.06746e9	1.01634
$555$	0	0
$556$	2.31691e9	0.571673
$557$	2.32229e7	0.00569408	0.00284704	−	0.999996i	$-0.499094\pi$
$557$	2.32229e7	0.00569408	0.00284704	+	0.999996i	$0.499094\pi$
$558$	0	0
$559$	6.42480e8	0.155567
$560$	1.43669e10	3.45703
$561$	0	0
$562$	4.82174e9	1.14585
$563$	−4.34065e9	−1.02512	−0.512561	−	0.858651i	$-0.671303\pi$
$563$	−4.34065e9	−1.02512	−0.512561	+	0.858651i	$0.671303\pi$
$564$	0	0
$565$	−9.69060e8	−0.226038
$566$	−3.63722e9	−0.843163
$567$	0	0
$568$	−1.65671e9	−0.379338
$569$	1.25447e9	0.285474	0.142737	−	0.989761i	$-0.454410\pi$
$569$	1.25447e9	0.285474	0.142737	+	0.989761i	$0.454410\pi$
$570$	0	0
$571$	−7.73775e9	−1.73936	−0.869678	−	0.493620i	$-0.835673\pi$
$571$	−7.73775e9	−1.73936	−0.869678	+	0.493620i	$0.835673\pi$
$572$	−2.47872e9	−0.553786
$573$	0	0
$574$	−5.28039e9	−1.16540
$575$	6.76646e9	1.48431
$576$	0	0
$577$	6.30012e9	1.36532	0.682658	−	0.730738i	$-0.260824\pi$
$577$	6.30012e9	1.36532	0.682658	+	0.730738i	$0.260824\pi$
$578$	−1.18268e10	−2.54754
$579$	0	0
$580$	4.30224e9	0.915580
$581$	1.04358e10	2.20754
$582$	0	0
$583$	−8.81142e9	−1.84164
$584$	−5.17680e8	−0.107551
$585$	0	0
$586$	5.48375e9	1.12573
$587$	2.77083e9	0.565426	0.282713	−	0.959204i	$-0.408766\pi$
$587$	2.77083e9	0.565426	0.282713	+	0.959204i	$0.408766\pi$
$588$	0	0
$589$	7.27625e9	1.46725
$590$	−1.38210e9	−0.277050
$591$	0	0
$592$	6.38563e9	1.26496
$593$	5.31671e9	1.04701	0.523506	−	0.852022i	$-0.324624\pi$
$593$	5.31671e9	1.04701	0.523506	+	0.852022i	$0.324624\pi$
$594$	0	0
$595$	−2.51607e10	−4.89680
$596$	−5.84764e9	−1.13141
$597$	0	0
$598$	−3.11265e9	−0.595219
$599$	5.08449e9	0.966616	0.483308	−	0.875450i	$-0.339435\pi$
$599$	5.08449e9	0.966616	0.483308	+	0.875450i	$0.339435\pi$
$600$	0	0
$601$	−5.61219e9	−1.05456	−0.527280	−	0.849691i	$-0.676788\pi$
$601$	−5.61219e9	−1.05456	−0.527280	+	0.849691i	$0.676788\pi$
$602$	−3.61575e9	−0.675477
$603$	0	0
$604$	−6.14935e9	−1.13553
$605$	−1.25096e10	−2.29668
$606$	0	0
$607$	6.49781e9	1.17925	0.589626	−	0.807677i	$-0.299275\pi$
$607$	6.49781e9	1.17925	0.589626	+	0.807677i	$0.299275\pi$
$608$	−6.69819e9	−1.20863
$609$	0	0
$610$	4.83921e9	0.863217
$611$	−3.71604e9	−0.659076
$612$	0	0
$613$	3.54849e9	0.622203	0.311102	−	0.950377i	$-0.399302\pi$
$613$	3.54849e9	0.622203	0.311102	+	0.950377i	$0.399302\pi$
$614$	7.51762e9	1.31066
$615$	0	0
$616$	−6.33982e9	−1.09281
$617$	8.10427e9	1.38904	0.694522	−	0.719472i	$-0.255616\pi$
$617$	8.10427e9	1.38904	0.694522	+	0.719472i	$0.255616\pi$
$618$	0	0
$619$	−4.62805e9	−0.784298	−0.392149	−	0.919902i	$-0.628268\pi$
$619$	−4.62805e9	−0.784298	−0.392149	+	0.919902i	$0.628268\pi$
$620$	9.51131e9	1.60276
$621$	0	0
$622$	8.92240e7	0.0148667
$623$	1.00341e10	1.66253
$624$	0	0
$625$	9.20980e8	0.150893
$626$	−1.32417e8	−0.0215742
$627$	0	0
$628$	−2.33646e9	−0.376443
$629$	−1.11831e10	−1.79179
$630$	0	0
$631$	−2.22522e9	−0.352590	−0.176295	−	0.984337i	$-0.556411\pi$
$631$	−2.22522e9	−0.352590	−0.176295	+	0.984337i	$0.556411\pi$
$632$	1.71632e9	0.270450
$633$	0	0
$634$	2.26525e9	0.353024
$635$	−6.55663e9	−1.01618
$636$	0	0
$637$	6.84041e9	1.04856
$638$	−1.07356e10	−1.63665
$639$	0	0
$640$	8.38904e9	1.26498
$641$	3.74794e9	0.562069	0.281034	−	0.959698i	$-0.409323\pi$
$641$	3.74794e9	0.562069	0.281034	+	0.959698i	$0.409323\pi$
$642$	0	0
$643$	−6.50343e9	−0.964726	−0.482363	−	0.875971i	$-0.660221\pi$
$643$	−6.50343e9	−0.964726	−0.482363	+	0.875971i	$0.660221\pi$
$644$	7.13692e9	1.05296
$645$	0	0
$646$	1.57925e10	2.30482
$647$	4.25390e9	0.617479	0.308740	−	0.951147i	$-0.400093\pi$
$647$	4.25390e9	0.617479	0.308740	+	0.951147i	$0.400093\pi$
$648$	0	0
$649$	1.40513e9	0.201771
$650$	−7.95836e9	−1.13665
$651$	0	0
$652$	5.06808e9	0.716106
$653$	−3.65504e9	−0.513684	−0.256842	−	0.966453i	$-0.582682\pi$
$653$	−3.65504e9	−0.513684	−0.256842	+	0.966453i	$0.582682\pi$
$654$	0	0
$655$	−2.20076e10	−3.06005
$656$	−4.53626e9	−0.627386
$657$	0	0
$658$	2.09131e10	2.86173
$659$	9.45163e9	1.28649	0.643247	−	0.765659i	$-0.277587\pi$
$659$	9.45163e9	1.28649	0.643247	+	0.765659i	$0.277587\pi$
$660$	0	0
$661$	−4.38475e9	−0.590527	−0.295264	−	0.955416i	$-0.595407\pi$
$661$	−4.38475e9	−0.590527	−0.295264	+	0.955416i	$0.595407\pi$
$662$	−9.80086e9	−1.31299
$663$	0	0
$664$	3.89132e9	0.515832
$665$	2.22510e10	2.93410
$666$	0	0
$667$	−5.49252e9	−0.716690
$668$	−4.38701e8	−0.0569444
$669$	0	0
$670$	−1.84047e10	−2.36411
$671$	−4.91982e9	−0.628667
$672$	0	0
$673$	−1.06771e10	−1.35020	−0.675102	−	0.737724i	$-0.735900\pi$
$673$	−1.06771e10	−1.35020	−0.675102	+	0.737724i	$0.735900\pi$
$674$	−1.04658e10	−1.31663
$675$	0	0
$676$	−4.03060e9	−0.501830
$677$	−5.43224e8	−0.0672851	−0.0336426	−	0.999434i	$-0.510711\pi$
$677$	−5.43224e8	−0.0672851	−0.0336426	+	0.999434i	$0.510711\pi$
$678$	0	0
$679$	2.73597e10	3.35404
$680$	−9.38198e9	−1.14423
$681$	0	0
$682$	−2.37342e10	−2.86503
$683$	9.65996e8	0.116012	0.0580060	−	0.998316i	$-0.481526\pi$
$683$	9.65996e8	0.116012	0.0580060	+	0.998316i	$0.481526\pi$
$684$	0	0
$685$	−8.31808e9	−0.988794
$686$	−1.94160e10	−2.29628
$687$	0	0
$688$	−3.10621e9	−0.363639
$689$	5.30214e9	0.617567
$690$	0	0
$691$	−6.65558e9	−0.767384	−0.383692	−	0.923461i	$-0.625348\pi$
$691$	−6.65558e9	−0.767384	−0.383692	+	0.923461i	$0.625348\pi$
$692$	−7.43498e9	−0.852920
$693$	0	0
$694$	1.00702e10	1.14362
$695$	−1.20548e10	−1.36211
$696$	0	0
$697$	7.94435e9	0.888677
$698$	6.04004e9	0.672273
$699$	0	0
$700$	1.82475e10	2.01076
$701$	7.59130e9	0.832345	0.416172	−	0.909286i	$-0.363371\pi$
$701$	7.59130e9	0.832345	0.416172	+	0.909286i	$0.363371\pi$
$702$	0	0
$703$	9.88990e9	1.07361
$704$	4.41828e9	0.477254
$705$	0	0
$706$	1.08303e10	1.15830
$707$	−2.33429e10	−2.48421
$708$	0	0
$709$	−7.76529e9	−0.818268	−0.409134	−	0.912474i	$-0.634169\pi$
$709$	−7.76529e9	−0.818268	−0.409134	+	0.912474i	$0.634169\pi$
$710$	−1.89664e10	−1.98876
$711$	0	0
$712$	3.74154e9	0.388481
$713$	−1.21428e10	−1.25460
$714$	0	0
$715$	1.28967e10	1.31949
$716$	6.95763e8	0.0708380
$717$	0	0
$718$	2.26054e10	2.27917
$719$	−2.04713e9	−0.205398	−0.102699	−	0.994713i	$-0.532748\pi$
$719$	−2.04713e9	−0.205398	−0.102699	+	0.994713i	$0.532748\pi$
$720$	0	0
$721$	1.36942e10	1.36070
$722$	−8.28926e8	−0.0819664
$723$	0	0
$724$	3.72528e9	0.364816
$725$	−1.40431e10	−1.36862
$726$	0	0
$727$	−7.27546e9	−0.702247	−0.351124	−	0.936329i	$-0.614200\pi$
$727$	−7.27546e9	−0.702247	−0.351124	+	0.936329i	$0.614200\pi$
$728$	3.81490e9	0.366457
$729$	0	0
$730$	−5.92654e9	−0.563860
$731$	5.43990e9	0.515086
$732$	0	0
$733$	1.92809e9	0.180827	0.0904135	−	0.995904i	$-0.471181\pi$
$733$	1.92809e9	0.180827	0.0904135	+	0.995904i	$0.471181\pi$
$734$	1.46941e10	1.37153
$735$	0	0
$736$	1.11781e10	1.03346
$737$	1.87113e10	1.72174
$738$	0	0
$739$	−1.32836e9	−0.121077	−0.0605385	−	0.998166i	$-0.519282\pi$
$739$	−1.32836e9	−0.121077	−0.0605385	+	0.998166i	$0.519282\pi$
$740$	1.29278e10	1.17277
$741$	0	0
$742$	−2.98394e10	−2.68149
$743$	−2.02673e10	−1.81273	−0.906367	−	0.422490i	$-0.861156\pi$
$743$	−2.02673e10	−1.81273	−0.906367	+	0.422490i	$0.861156\pi$
$744$	0	0
$745$	3.04250e10	2.69577
$746$	1.35210e10	1.19240
$747$	0	0
$748$	−2.09874e10	−1.83360
$749$	1.59606e10	1.38791
$750$	0	0
$751$	−7.01982e9	−0.604764	−0.302382	−	0.953187i	$-0.597782\pi$
$751$	−7.01982e9	−0.604764	−0.302382	+	0.953187i	$0.597782\pi$
$752$	1.79660e10	1.54059
$753$	0	0
$754$	6.46001e9	0.548825
$755$	3.19947e10	2.70560
$756$	0	0
$757$	−1.56061e10	−1.30755	−0.653774	−	0.756690i	$-0.726815\pi$
$757$	−1.56061e10	−1.30755	−0.653774	+	0.756690i	$0.726815\pi$
$758$	−1.78664e10	−1.49003
$759$	0	0
$760$	8.29703e9	0.685606
$761$	−1.06411e8	−0.00875264	−0.00437632	−	0.999990i	$-0.501393\pi$
$761$	−1.06411e8	−0.00875264	−0.00437632	+	0.999990i	$0.501393\pi$
$762$	0	0
$763$	−7.01018e9	−0.571339
$764$	7.17916e9	0.582434
$765$	0	0
$766$	5.66685e9	0.455556
$767$	−8.45515e8	−0.0676608
$768$	0	0
$769$	1.40421e9	0.111350	0.0556750	−	0.998449i	$-0.482269\pi$
$769$	1.40421e9	0.111350	0.0556750	+	0.998449i	$0.482269\pi$
$770$	−7.25799e10	−5.72926
$771$	0	0
$772$	2.94653e9	0.230489
$773$	−1.70826e10	−1.33022	−0.665112	−	0.746744i	$-0.731616\pi$
$773$	−1.70826e10	−1.33022	−0.665112	+	0.746744i	$0.731616\pi$
$774$	0	0
$775$	−3.10464e10	−2.39582
$776$	1.02020e10	0.783734
$777$	0	0
$778$	−2.04421e10	−1.55631
$779$	−7.02565e9	−0.532483
$780$	0	0
$781$	1.92824e10	1.44838
$782$	−2.63549e10	−1.97078
$783$	0	0
$784$	−3.30714e10	−2.45102
$785$	1.21565e10	0.896942
$786$	0	0
$787$	−9.46350e9	−0.692054	−0.346027	−	0.938224i	$-0.612470\pi$
$787$	−9.46350e9	−0.692054	−0.346027	+	0.938224i	$0.612470\pi$
$788$	5.01068e9	0.364800
$789$	0	0
$790$	1.96488e10	1.41789
$791$	3.33634e9	0.239691
$792$	0	0
$793$	2.96043e9	0.210814
$794$	1.97924e9	0.140322
$795$	0	0
$796$	3.24241e9	0.227862
$797$	1.05899e10	0.740949	0.370474	−	0.928843i	$-0.379195\pi$
$797$	1.05899e10	0.740949	0.370474	+	0.928843i	$0.379195\pi$
$798$	0	0
$799$	−3.14638e10	−2.18221
$800$	2.85799e10	1.97354
$801$	0	0
$802$	1.16435e10	0.797029
$803$	6.02526e9	0.410650
$804$	0	0
$805$	−3.71330e10	−2.50885
$806$	1.42817e10	0.960743
$807$	0	0
$808$	−8.70418e9	−0.580481
$809$	−1.90523e10	−1.26511	−0.632555	−	0.774516i	$-0.717994\pi$
$809$	−1.90523e10	−1.26511	−0.632555	+	0.774516i	$0.717994\pi$
$810$	0	0
$811$	1.62908e10	1.07243	0.536217	−	0.844080i	$-0.319853\pi$
$811$	1.62908e10	1.07243	0.536217	+	0.844080i	$0.319853\pi$
$812$	−1.48120e10	−0.970884
$813$	0	0
$814$	−3.22595e10	−2.09639
$815$	−2.63690e10	−1.70625
$816$	0	0
$817$	−4.81081e9	−0.308632
$818$	2.91664e10	1.86314
$819$	0	0
$820$	−9.18374e9	−0.581662
$821$	−1.60953e9	−0.101508	−0.0507539	−	0.998711i	$-0.516162\pi$
$821$	−1.60953e9	−0.101508	−0.0507539	+	0.998711i	$0.516162\pi$
$822$	0	0
$823$	−1.20942e10	−0.756272	−0.378136	−	0.925750i	$-0.623435\pi$
$823$	−1.20942e10	−0.756272	−0.378136	+	0.925750i	$0.623435\pi$
$824$	5.10633e9	0.317953
$825$	0	0
$826$	4.75839e9	0.293785
$827$	−9.39665e9	−0.577702	−0.288851	−	0.957374i	$-0.593273\pi$
$827$	−9.39665e9	−0.577702	−0.288851	+	0.957374i	$0.593273\pi$
$828$	0	0
$829$	1.58388e10	0.965563	0.482781	−	0.875741i	$-0.339627\pi$
$829$	1.58388e10	0.965563	0.482781	+	0.875741i	$0.339627\pi$
$830$	4.45488e10	2.70435
$831$	0	0
$832$	−2.65864e9	−0.160040
$833$	5.79180e10	3.47181
$834$	0	0
$835$	2.28254e9	0.135680
$836$	1.85604e10	1.09866
$837$	0	0
$838$	1.64622e10	0.966346
$839$	−3.24355e10	−1.89607	−0.948034	−	0.318170i	$-0.896932\pi$
$839$	−3.24355e10	−1.89607	−0.948034	+	0.318170i	$0.896932\pi$
$840$	0	0
$841$	−5.85067e9	−0.339172
$842$	−2.35380e10	−1.35887
$843$	0	0
$844$	5.65676e8	0.0323869
$845$	2.09710e10	1.19570
$846$	0	0
$847$	4.30689e10	2.43541
$848$	−2.56343e10	−1.44357
$849$	0	0
$850$	−6.73837e10	−3.76347
$851$	−1.65045e10	−0.918013
$852$	0	0
$853$	4.28375e9	0.236321	0.118161	−	0.992995i	$-0.462300\pi$
$853$	4.28375e9	0.236321	0.118161	+	0.992995i	$0.462300\pi$
$854$	−1.66607e10	−0.915358
$855$	0	0
$856$	5.95142e9	0.324312
$857$	2.60684e9	0.141475	0.0707377	−	0.997495i	$-0.477465\pi$
$857$	2.60684e9	0.141475	0.0707377	+	0.997495i	$0.477465\pi$
$858$	0	0
$859$	7.87750e8	0.0424046	0.0212023	−	0.999775i	$-0.493251\pi$
$859$	7.87750e8	0.0424046	0.0212023	+	0.999775i	$0.493251\pi$
$860$	−6.28856e9	−0.337137
$861$	0	0
$862$	−2.09024e10	−1.11153
$863$	1.69537e10	0.897896	0.448948	−	0.893558i	$-0.351799\pi$
$863$	1.69537e10	0.897896	0.448948	+	0.893558i	$0.351799\pi$
$864$	0	0
$865$	3.86838e10	2.03223
$866$	−1.66523e10	−0.871290
$867$	0	0
$868$	−3.27461e10	−1.69958
$869$	−1.99761e10	−1.03262
$870$	0	0
$871$	−1.12592e10	−0.577359
$872$	−2.61398e9	−0.133504
$873$	0	0
$874$	2.33072e10	1.18086
$875$	−3.85491e10	−1.94530
$876$	0	0
$877$	−1.67825e10	−0.840153	−0.420076	−	0.907489i	$-0.637997\pi$
$877$	−1.67825e10	−0.840153	−0.420076	+	0.907489i	$0.637997\pi$
$878$	2.83562e10	1.41390
$879$	0	0
$880$	−6.23517e10	−3.08432
$881$	−3.74442e10	−1.84488	−0.922442	−	0.386135i	$-0.873810\pi$
$881$	−3.74442e10	−1.84488	−0.922442	+	0.386135i	$0.873810\pi$
$882$	0	0
$883$	2.15204e10	1.05193	0.525967	−	0.850505i	$-0.323703\pi$
$883$	2.15204e10	1.05193	0.525967	+	0.850505i	$0.323703\pi$
$884$	1.26289e10	0.614868
$885$	0	0
$886$	−1.22531e9	−0.0591873
$887$	1.11581e10	0.536857	0.268429	−	0.963300i	$-0.413496\pi$
$887$	1.11581e10	0.536857	0.268429	+	0.963300i	$0.413496\pi$
$888$	0	0
$889$	2.25735e10	1.07756
$890$	4.28341e10	2.03669
$891$	0	0
$892$	−5.22174e9	−0.246342
$893$	2.78252e10	1.30755
$894$	0	0
$895$	−3.62002e9	−0.168784
$896$	−2.88823e10	−1.34138
$897$	0	0
$898$	4.24596e10	1.95663
$899$	2.52012e10	1.15681
$900$	0	0
$901$	4.48934e10	2.04478
$902$	2.29167e10	1.03975
$903$	0	0
$904$	1.24406e9	0.0560083
$905$	−1.93825e10	−0.869238
$906$	0	0
$907$	7.89855e9	0.351497	0.175749	−	0.984435i	$-0.443765\pi$
$907$	7.89855e9	0.351497	0.175749	+	0.984435i	$0.443765\pi$
$908$	−2.19964e10	−0.975106
$909$	0	0
$910$	4.36739e10	1.92122
$911$	−1.68370e10	−0.737821	−0.368911	−	0.929465i	$-0.620269\pi$
$911$	−1.68370e10	−0.737821	−0.368911	+	0.929465i	$0.620269\pi$
$912$	0	0
$913$	−4.52909e10	−1.96953
$914$	3.28621e10	1.42359
$915$	0	0
$916$	−1.61829e10	−0.695702
$917$	7.57691e10	3.24489
$918$	0	0
$919$	2.78362e10	1.18306	0.591529	−	0.806284i	$-0.298525\pi$
$919$	2.78362e10	1.18306	0.591529	+	0.806284i	$0.298525\pi$
$920$	−1.38463e10	−0.586240
$921$	0	0
$922$	−1.85830e10	−0.780830
$923$	−1.16029e10	−0.485691
$924$	0	0
$925$	−4.21983e10	−1.75307
$926$	−3.51572e10	−1.45504
$927$	0	0
$928$	−2.31991e10	−0.952911
$929$	−2.25578e10	−0.923083	−0.461542	−	0.887119i	$-0.652704\pi$
$929$	−2.25578e10	−0.923083	−0.461542	+	0.887119i	$0.652704\pi$
$930$	0	0
$931$	−5.12202e10	−2.08026
$932$	1.18116e10	0.477918
$933$	0	0
$934$	8.57279e9	0.344277
$935$	1.09197e11	4.36886
$936$	0	0
$937$	−2.56679e10	−1.01930	−0.509649	−	0.860382i	$-0.670225\pi$
$937$	−2.56679e10	−1.01930	−0.509649	+	0.860382i	$0.670225\pi$
$938$	6.33648e10	2.50691
$939$	0	0
$940$	3.63724e10	1.42832
$941$	−7.37013e9	−0.288344	−0.144172	−	0.989553i	$-0.546052\pi$
$941$	−7.37013e9	−0.288344	−0.144172	+	0.989553i	$0.546052\pi$
$942$	0	0
$943$	1.17246e10	0.455309
$944$	4.08782e9	0.158158
$945$	0	0
$946$	1.56922e10	0.602651
$947$	−4.90023e10	−1.87496	−0.937479	−	0.348042i	$-0.886847\pi$
$947$	−4.90023e10	−1.87496	−0.937479	+	0.348042i	$0.886847\pi$
$948$	0	0
$949$	−3.62561e9	−0.137705
$950$	5.95912e10	2.25502
$951$	0	0
$952$	3.23008e10	1.21335
$953$	2.07767e10	0.777590	0.388795	−	0.921324i	$-0.372891\pi$
$953$	2.07767e10	0.777590	0.388795	+	0.921324i	$0.372891\pi$
$954$	0	0
$955$	−3.73528e10	−1.38775
$956$	3.34315e10	1.23752
$957$	0	0
$958$	5.57557e10	2.04885
$959$	2.86380e10	1.04852
$960$	0	0
$961$	2.82017e10	1.02505
$962$	1.94117e10	0.702993
$963$	0	0
$964$	−2.18568e9	−0.0785809
$965$	−1.53306e10	−0.549180
$966$	0	0
$967$	−1.99822e10	−0.710642	−0.355321	−	0.934744i	$-0.615628\pi$
$967$	−1.99822e10	−0.710642	−0.355321	+	0.934744i	$0.615628\pi$
$968$	1.60597e10	0.569079
$969$	0	0
$970$	1.16795e11	4.10888
$971$	1.36752e9	0.0479365	0.0239683	−	0.999713i	$-0.492370\pi$
$971$	1.36752e9	0.0479365	0.0239683	+	0.999713i	$0.492370\pi$
$972$	0	0
$973$	4.15029e10	1.44439
$974$	3.52681e10	1.22300
$975$	0	0
$976$	−1.43128e10	−0.492778
$977$	2.85359e10	0.978951	0.489475	−	0.872017i	$-0.337188\pi$
$977$	2.85359e10	0.978951	0.489475	+	0.872017i	$0.337188\pi$
$978$	0	0
$979$	−4.35476e10	−1.48329
$980$	−6.69536e10	−2.27239
$981$	0	0
$982$	5.89725e10	1.98728
$983$	−1.22389e10	−0.410965	−0.205483	−	0.978661i	$-0.565876\pi$
$983$	−1.22389e10	−0.410965	−0.205483	+	0.978661i	$0.565876\pi$
$984$	0	0
$985$	−2.60703e10	−0.869200
$986$	5.46971e10	1.81717
$987$	0	0
$988$	−1.11684e10	−0.368420
$989$	8.02840e9	0.263902
$990$	0	0
$991$	−3.67813e10	−1.20052	−0.600260	−	0.799805i	$-0.704936\pi$
$991$	−3.67813e10	−1.20052	−0.600260	+	0.799805i	$0.704936\pi$
$992$	−5.12881e10	−1.66811
$993$	0	0
$994$	6.52987e10	2.10888
$995$	−1.68701e10	−0.542922
$996$	0	0
$997$	−6.04917e10	−1.93314	−0.966569	−	0.256405i	$-0.917462\pi$
$997$	−6.04917e10	−1.93314	−0.966569	+	0.256405i	$0.917462\pi$
$998$	−3.80370e10	−1.21129
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	531.8.a.e.1.5		18
3.2	odd	2		177.8.a.d.1.14	✓	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.8.a.d.1.14	✓	18	3.2	odd	2
531.8.a.e.1.5		18	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 531 = 3^{2} \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	531.a (trivial)

\(f(q)\)	\(=\)	\(q-14.6971 q^{2} +88.0043 q^{4} -457.882 q^{5} +1576.42 q^{7} +587.821 q^{8} +O(q^{10})\)	\(q-14.6971 q^{2} +88.0043 q^{4} -457.882 q^{5} +1576.42 q^{7} +587.821 q^{8} +6729.53 q^{10} -6841.63 q^{11} +4116.85 q^{13} -23168.8 q^{14} -19903.8 q^{16} +34857.5 q^{17} -30826.5 q^{19} -40295.5 q^{20} +100552. q^{22} +51444.0 q^{23} +131531. q^{25} -60505.7 q^{26} +138732. q^{28} -106767. q^{29} -236039. q^{31} +217287. q^{32} -512304. q^{34} -721815. q^{35} -320825. q^{37} +453059. q^{38} -269152. q^{40} +227909. q^{41} +156061. q^{43} -602092. q^{44} -756076. q^{46} -902640. q^{47} +1.66156e6 q^{49} -1.93312e6 q^{50} +362300. q^{52} +1.28791e6 q^{53} +3.13266e6 q^{55} +926654. q^{56} +1.56916e6 q^{58} -205379. q^{59} +719101. q^{61} +3.46908e6 q^{62} -645794. q^{64} -1.88503e6 q^{65} -2.73492e6 q^{67} +3.06761e6 q^{68} +1.06086e7 q^{70} -2.81839e6 q^{71} -880677. q^{73} +4.71519e6 q^{74} -2.71286e6 q^{76} -1.07853e7 q^{77} +2.91979e6 q^{79} +9.11359e6 q^{80} -3.34960e6 q^{82} +6.61990e6 q^{83} -1.59606e7 q^{85} -2.29364e6 q^{86} -4.02165e6 q^{88} +6.36510e6 q^{89} +6.48989e6 q^{91} +4.52729e6 q^{92} +1.32662e7 q^{94} +1.41149e7 q^{95} +1.73556e7 q^{97} -2.44201e7 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 24 q^{2} + 1358 q^{4} - 678 q^{5} + 3081 q^{7} - 4107 q^{8}+O(q^{10}) \) 18 * q - 24 * q^2 + 1358 * q^4 - 678 * q^5 + 3081 * q^7 - 4107 * q^8	\( 18 q - 24 q^{2} + 1358 q^{4} - 678 q^{5} + 3081 q^{7} - 4107 q^{8} + 3609 q^{10} - 15070 q^{11} + 13662 q^{13} - 20861 q^{14} + 60482 q^{16} - 71919 q^{17} + 56231 q^{19} - 143053 q^{20} + 274198 q^{22} - 150029 q^{23} + 399672 q^{25} - 182846 q^{26} + 434150 q^{28} - 591285 q^{29} + 426733 q^{31} - 1205630 q^{32} + 403548 q^{34} - 912879 q^{35} + 7703 q^{37} + 417859 q^{38} + 618020 q^{40} - 770959 q^{41} + 793050 q^{43} - 2591274 q^{44} - 4068019 q^{46} - 1410373 q^{47} + 1637427 q^{49} - 1021549 q^{50} - 3749190 q^{52} - 1037934 q^{53} + 331974 q^{55} + 391748 q^{56} + 653724 q^{58} - 3696822 q^{59} - 1374623 q^{61} - 5251718 q^{62} + 5077197 q^{64} - 3257170 q^{65} - 2436904 q^{67} - 14119909 q^{68} + 5185580 q^{70} - 14289172 q^{71} + 5482515 q^{73} - 14934154 q^{74} + 3822912 q^{76} - 23157109 q^{77} + 19786414 q^{79} - 31978143 q^{80} + 9749509 q^{82} - 30227337 q^{83} + 9946981 q^{85} - 44295864 q^{86} + 39970897 q^{88} - 31061677 q^{89} + 26377785 q^{91} - 4719698 q^{92} + 44488296 q^{94} - 15534599 q^{95} + 12084118 q^{97} - 42274744 q^{98}+O(q^{100}) \) 18 * q - 24 * q^2 + 1358 * q^4 - 678 * q^5 + 3081 * q^7 - 4107 * q^8 + 3609 * q^10 - 15070 * q^11 + 13662 * q^13 - 20861 * q^14 + 60482 * q^16 - 71919 * q^17 + 56231 * q^19 - 143053 * q^20 + 274198 * q^22 - 150029 * q^23 + 399672 * q^25 - 182846 * q^26 + 434150 * q^28 - 591285 * q^29 + 426733 * q^31 - 1205630 * q^32 + 403548 * q^34 - 912879 * q^35 + 7703 * q^37 + 417859 * q^38 + 618020 * q^40 - 770959 * q^41 + 793050 * q^43 - 2591274 * q^44 - 4068019 * q^46 - 1410373 * q^47 + 1637427 * q^49 - 1021549 * q^50 - 3749190 * q^52 - 1037934 * q^53 + 331974 * q^55 + 391748 * q^56 + 653724 * q^58 - 3696822 * q^59 - 1374623 * q^61 - 5251718 * q^62 + 5077197 * q^64 - 3257170 * q^65 - 2436904 * q^67 - 14119909 * q^68 + 5185580 * q^70 - 14289172 * q^71 + 5482515 * q^73 - 14934154 * q^74 + 3822912 * q^76 - 23157109 * q^77 + 19786414 * q^79 - 31978143 * q^80 + 9749509 * q^82 - 30227337 * q^83 + 9946981 * q^85 - 44295864 * q^86 + 39970897 * q^88 - 31061677 * q^89 + 26377785 * q^91 - 4719698 * q^92 + 44488296 * q^94 - 15534599 * q^95 + 12084118 * q^97 - 42274744 * q^98

Introduction

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