LMFDB - Embedded newform 531.8.a.g.1.10

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:	$33$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
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)

$f(q)$	$=$	$q-10.5948 q^{2} -15.7504 q^{4} -27.5110 q^{5} +196.184 q^{7} +1523.01 q^{8} +O(q^{10})$	\(q-10.5948 q^{2} -15.7504 q^{4} -27.5110 q^{5} +196.184 q^{7} +1523.01 q^{8} +291.473 q^{10} -3083.61 q^{11} +15484.9 q^{13} -2078.53 q^{14} -14119.9 q^{16} -4084.57 q^{17} -28228.2 q^{19} +433.310 q^{20} +32670.2 q^{22} +48499.0 q^{23} -77368.1 q^{25} -164059. q^{26} -3089.99 q^{28} -160677. q^{29} +152904. q^{31} -45347.7 q^{32} +43275.1 q^{34} -5397.23 q^{35} -103607. q^{37} +299072. q^{38} -41899.4 q^{40} +488917. q^{41} -130938. q^{43} +48568.2 q^{44} -513837. q^{46} -838180. q^{47} -785055. q^{49} +819699. q^{50} -243893. q^{52} +1.03346e6 q^{53} +84833.2 q^{55} +298790. q^{56} +1.70234e6 q^{58} +205379. q^{59} -1.40927e6 q^{61} -1.61999e6 q^{62} +2.28779e6 q^{64} -426004. q^{65} +4.65907e6 q^{67} +64333.7 q^{68} +57182.5 q^{70} -1.25989e6 q^{71} +3.36535e6 q^{73} +1.09770e6 q^{74} +444606. q^{76} -604956. q^{77} +1.37169e6 q^{79} +388452. q^{80} -5.17997e6 q^{82} -9.21964e6 q^{83} +112371. q^{85} +1.38726e6 q^{86} -4.69635e6 q^{88} -195226. q^{89} +3.03789e6 q^{91} -763880. q^{92} +8.88034e6 q^{94} +776586. q^{95} +1.23409e7 q^{97} +8.31749e6 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 33 q - 24 q^{2} + 1776 q^{4} - 1000 q^{5} + 154 q^{7} - 4608 q^{8}+O(q^{10}) $ 33 * q - 24 * q^2 + 1776 * q^4 - 1000 * q^5 + 154 * q^7 - 4608 * q^8	\( 33 q - 24 q^{2} + 1776 q^{4} - 1000 q^{5} + 154 q^{7} - 4608 q^{8} + 5042 q^{10} - 13310 q^{11} - 14172 q^{13} - 16464 q^{14} + 95772 q^{16} - 39304 q^{17} - 56302 q^{19} + 17936 q^{20} + 152764 q^{22} - 17988 q^{23} + 468523 q^{25} + 27624 q^{26} - 59896 q^{28} - 474564 q^{29} + 188186 q^{31} - 251068 q^{32} + 169888 q^{34} - 514500 q^{35} + 1148200 q^{37} - 446594 q^{38} + 501214 q^{40} - 1246152 q^{41} + 62268 q^{43} - 2555520 q^{44} - 1289942 q^{46} - 1485654 q^{47} + 3829555 q^{49} - 6430160 q^{50} - 2624804 q^{52} - 4086740 q^{53} - 1119118 q^{55} - 8448352 q^{56} + 2966706 q^{58} + 6777507 q^{59} + 2436146 q^{61} - 9005952 q^{62} + 11117562 q^{64} - 16730354 q^{65} - 2652248 q^{67} - 15929124 q^{68} + 3359254 q^{70} - 7356324 q^{71} + 1900454 q^{73} - 25386964 q^{74} - 16047360 q^{76} - 20774826 q^{77} - 5912712 q^{79} - 13568404 q^{80} + 1579434 q^{82} + 1052766 q^{83} + 18372730 q^{85} - 43499960 q^{86} + 18209214 q^{88} - 174788 q^{89} - 18891512 q^{91} - 46033270 q^{92} + 365448 q^{94} - 31505580 q^{95} + 14418540 q^{97} + 15964056 q^{98}+O(q^{100}) \) 33 * q - 24 * q^2 + 1776 * q^4 - 1000 * q^5 + 154 * q^7 - 4608 * q^8 + 5042 * q^10 - 13310 * q^11 - 14172 * q^13 - 16464 * q^14 + 95772 * q^16 - 39304 * q^17 - 56302 * q^19 + 17936 * q^20 + 152764 * q^22 - 17988 * q^23 + 468523 * q^25 + 27624 * q^26 - 59896 * q^28 - 474564 * q^29 + 188186 * q^31 - 251068 * q^32 + 169888 * q^34 - 514500 * q^35 + 1148200 * q^37 - 446594 * q^38 + 501214 * q^40 - 1246152 * q^41 + 62268 * q^43 - 2555520 * q^44 - 1289942 * q^46 - 1485654 * q^47 + 3829555 * q^49 - 6430160 * q^50 - 2624804 * q^52 - 4086740 * q^53 - 1119118 * q^55 - 8448352 * q^56 + 2966706 * q^58 + 6777507 * q^59 + 2436146 * q^61 - 9005952 * q^62 + 11117562 * q^64 - 16730354 * q^65 - 2652248 * q^67 - 15929124 * q^68 + 3359254 * q^70 - 7356324 * q^71 + 1900454 * q^73 - 25386964 * q^74 - 16047360 * q^76 - 20774826 * q^77 - 5912712 * q^79 - 13568404 * q^80 + 1579434 * q^82 + 1052766 * q^83 + 18372730 * q^85 - 43499960 * q^86 + 18209214 * q^88 - 174788 * q^89 - 18891512 * q^91 - 46033270 * q^92 + 365448 * q^94 - 31505580 * q^95 + 14418540 * q^97 + 15964056 * 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 $

$2$	−10.5948	−0.936456	−0.468228	−	0.883608i	$-0.655107\pi$
$2$	−10.5948	−0.936456	−0.468228	+	0.883608i	$0.655107\pi$
$3$	0	0
$3$	0	0
$4$	−15.7504	−0.123050
$5$	−27.5110	−0.0984264	−0.0492132	−	0.998788i	$-0.515671\pi$
$5$	−27.5110	−0.0984264	−0.0492132	+	0.998788i	$0.515671\pi$
$6$	0	0
$7$	196.184	0.216183	0.108091	−	0.994141i	$-0.465526\pi$
$7$	196.184	0.216183	0.108091	+	0.994141i	$0.465526\pi$
$8$	1523.01	1.05169
$9$	0	0
$10$	291.473	0.0921719
$11$	−3083.61	−0.698530	−0.349265	−	0.937024i	$-0.613569\pi$
$11$	−3083.61	−0.698530	−0.349265	+	0.937024i	$0.613569\pi$
$12$	0	0
$13$	15484.9	1.95482	0.977408	−	0.211362i	$-0.0677899\pi$
$13$	15484.9	1.95482	0.977408	+	0.211362i	$0.0677899\pi$
$14$	−2078.53	−0.202446
$15$	0	0
$16$	−14119.9	−0.861808
$17$	−4084.57	−0.201639	−0.100820	−	0.994905i	$-0.532146\pi$
$17$	−4084.57	−0.201639	−0.100820	+	0.994905i	$0.532146\pi$
$18$	0	0
$19$	−28228.2	−0.944159	−0.472080	−	0.881556i	$-0.656497\pi$
$19$	−28228.2	−0.944159	−0.472080	+	0.881556i	$0.656497\pi$
$20$	433.310	0.0121114
$21$	0	0
$22$	32670.2	0.654142
$23$	48499.0	0.831161	0.415581	−	0.909556i	$-0.363578\pi$
$23$	48499.0	0.831161	0.415581	+	0.909556i	$0.363578\pi$
$24$	0	0
$25$	−77368.1	−0.990312
$26$	−164059.	−1.83060
$27$	0	0
$28$	−3089.99	−0.0266014
$29$	−160677.	−1.22338	−0.611689	−	0.791098i	$-0.709510\pi$
$29$	−160677.	−1.22338	−0.611689	+	0.791098i	$0.709510\pi$
$30$	0	0
$31$	152904.	0.921835	0.460918	−	0.887443i	$-0.347520\pi$
$31$	152904.	0.921835	0.460918	+	0.887443i	$0.347520\pi$
$32$	−45347.7	−0.244642
$33$	0	0
$34$	43275.1	0.188826
$35$	−5397.23	−0.0212781
$36$	0	0
$37$	−103607.	−0.336267	−0.168133	−	0.985764i	$-0.553774\pi$
$37$	−103607.	−0.336267	−0.168133	+	0.985764i	$0.553774\pi$
$38$	299072.	0.884164
$39$	0	0
$40$	−41899.4	−0.103514
$41$	488917.	1.10788	0.553938	−	0.832558i	$-0.313124\pi$
$41$	488917.	1.10788	0.553938	+	0.832558i	$0.313124\pi$
$42$	0	0
$43$	−130938.	−0.251146	−0.125573	−	0.992084i	$-0.540077\pi$
$43$	−130938.	−0.251146	−0.125573	+	0.992084i	$0.540077\pi$
$44$	48568.2	0.0859543
$45$	0	0
$46$	−513837.	−0.778346
$47$	−838180.	−1.17759	−0.588796	−	0.808282i	$-0.700398\pi$
$47$	−838180.	−1.17759	−0.588796	+	0.808282i	$0.700398\pi$
$48$	0	0
$49$	−785055.	−0.953265
$50$	819699.	0.927384
$51$	0	0
$52$	−243893.	−0.240541
$53$	1.03346e6	0.953517	0.476759	−	0.879034i	$-0.341812\pi$
$53$	1.03346e6	0.953517	0.476759	+	0.879034i	$0.341812\pi$
$54$	0	0
$55$	84833.2	0.0687537
$56$	298790.	0.227357
$57$	0	0
$58$	1.70234e6	1.14564
$59$	205379.	0.130189
$59$	205379.	0.130189
$60$	0	0
$61$	−1.40927e6	−0.794950	−0.397475	−	0.917613i	$-0.630114\pi$
$61$	−1.40927e6	−0.794950	−0.397475	+	0.917613i	$0.630114\pi$
$62$	−1.61999e6	−0.863258
$63$	0	0
$64$	2.28779e6	1.09090
$65$	−426004.	−0.192405
$66$	0	0
$67$	4.65907e6	1.89251	0.946253	−	0.323428i	$-0.104835\pi$
$67$	4.65907e6	1.89251	0.946253	+	0.323428i	$0.104835\pi$
$68$	64333.7	0.0248118
$69$	0	0
$70$	57182.5	0.0199260
$71$	−1.25989e6	−0.417761	−0.208881	−	0.977941i	$-0.566982\pi$
$71$	−1.25989e6	−0.417761	−0.208881	+	0.977941i	$0.566982\pi$
$72$	0	0
$73$	3.36535e6	1.01251	0.506256	−	0.862383i	$-0.331029\pi$
$73$	3.36535e6	1.01251	0.506256	+	0.862383i	$0.331029\pi$
$74$	1.09770e6	0.314899
$75$	0	0
$76$	444606.	0.116179
$77$	−604956.	−0.151010
$78$	0	0
$79$	1.37169e6	0.313012	0.156506	−	0.987677i	$-0.449977\pi$
$79$	1.37169e6	0.313012	0.156506	+	0.987677i	$0.449977\pi$
$80$	388452.	0.0848247
$81$	0	0
$82$	−5.17997e6	−1.03748
$83$	−9.21964e6	−1.76987	−0.884934	−	0.465717i	$-0.845797\pi$
$83$	−9.21964e6	−1.76987	−0.884934	+	0.465717i	$0.845797\pi$
$84$	0	0
$85$	112371.	0.0198466
$86$	1.38726e6	0.235187
$87$	0	0
$88$	−4.69635e6	−0.734635
$89$	−195226.	−0.0293544	−0.0146772	−	0.999892i	$-0.504672\pi$
$89$	−195226.	−0.0293544	−0.0146772	+	0.999892i	$0.504672\pi$
$90$	0	0
$91$	3.03789e6	0.422598
$92$	−763880.	−0.102275
$93$	0	0
$94$	8.88034e6	1.10276
$95$	776586.	0.0929302
$96$	0	0
$97$	1.23409e7	1.37293	0.686463	−	0.727165i	$-0.259162\pi$
$97$	1.23409e7	1.37293	0.686463	+	0.727165i	$0.259162\pi$
$98$	8.31749e6	0.892691
$99$	0	0
$100$	1.21858e6	0.121858
$101$	−6.66494e6	−0.643682	−0.321841	−	0.946794i	$-0.604302\pi$
$101$	−6.66494e6	−0.643682	−0.321841	+	0.946794i	$0.604302\pi$
$102$	0	0
$103$	5.74650e6	0.518171	0.259086	−	0.965854i	$-0.416579\pi$
$103$	5.74650e6	0.518171	0.259086	+	0.965854i	$0.416579\pi$
$104$	2.35835e7	2.05585
$105$	0	0
$106$	−1.09493e7	−0.892927
$107$	−1.37238e7	−1.08301	−0.541505	−	0.840697i	$-0.682145\pi$
$107$	−1.37238e7	−1.08301	−0.541505	+	0.840697i	$0.682145\pi$
$108$	0	0
$109$	1.03389e7	0.764680	0.382340	−	0.924022i	$-0.375118\pi$
$109$	1.03389e7	0.764680	0.382340	+	0.924022i	$0.375118\pi$
$110$	−898790.	−0.0643848
$111$	0	0
$112$	−2.77010e6	−0.186308
$113$	9.97154e6	0.650111	0.325056	−	0.945695i	$-0.394617\pi$
$113$	9.97154e6	0.650111	0.325056	+	0.945695i	$0.394617\pi$
$114$	0	0
$115$	−1.33426e6	−0.0818082
$116$	2.53073e6	0.150537
$117$	0	0
$118$	−2.17595e6	−0.121916
$119$	−801329.	−0.0435909
$120$	0	0
$121$	−9.97853e6	−0.512056
$122$	1.49309e7	0.744436
$123$	0	0
$124$	−2.40831e6	−0.113432
$125$	4.27777e6	0.195899
$126$	0	0
$127$	2.27374e7	0.984983	0.492491	−	0.870317i	$-0.336086\pi$
$127$	2.27374e7	0.984983	0.492491	+	0.870317i	$0.336086\pi$
$128$	−1.84342e7	−0.776942
$129$	0	0
$130$	4.51343e6	0.180179
$131$	5.47974e6	0.212966	0.106483	−	0.994315i	$-0.466041\pi$
$131$	5.47974e6	0.212966	0.106483	+	0.994315i	$0.466041\pi$
$132$	0	0
$133$	−5.53793e6	−0.204111
$134$	−4.93618e7	−1.77225
$135$	0	0
$136$	−6.22082e6	−0.212061
$137$	−2.12817e7	−0.707106	−0.353553	−	0.935414i	$-0.615027\pi$
$137$	−2.12817e7	−0.707106	−0.353553	+	0.935414i	$0.615027\pi$
$138$	0	0
$139$	3.15095e6	0.0995153	0.0497577	−	0.998761i	$-0.484155\pi$
$139$	3.15095e6	0.0995153	0.0497577	+	0.998761i	$0.484155\pi$
$140$	85008.7	0.00261828
$141$	0	0
$142$	1.33483e7	0.391215
$143$	−4.77493e7	−1.36550
$144$	0	0
$145$	4.42038e6	0.120413
$146$	−3.56552e7	−0.948172
$147$	0	0
$148$	1.63186e6	0.0413777
$149$	−1.39408e7	−0.345251	−0.172626	−	0.984988i	$-0.555225\pi$
$149$	−1.39408e7	−0.345251	−0.172626	+	0.984988i	$0.555225\pi$
$150$	0	0
$151$	1.25413e6	0.0296430	0.0148215	−	0.999890i	$-0.495282\pi$
$151$	1.25413e6	0.0296430	0.0148215	+	0.999890i	$0.495282\pi$
$152$	−4.29917e7	−0.992960
$153$	0	0
$154$	6.40938e6	0.141414
$155$	−4.20655e6	−0.0907329
$156$	0	0
$157$	4.53152e7	0.934534	0.467267	−	0.884116i	$-0.345239\pi$
$157$	4.53152e7	0.934534	0.467267	+	0.884116i	$0.345239\pi$
$158$	−1.45328e7	−0.293122
$159$	0	0
$160$	1.24756e6	0.0240792
$161$	9.51475e6	0.179683
$162$	0	0
$163$	−3.26923e7	−0.591275	−0.295637	−	0.955300i	$-0.595532\pi$
$163$	−3.26923e7	−0.591275	−0.295637	+	0.955300i	$0.595532\pi$
$164$	−7.70065e6	−0.136325
$165$	0	0
$166$	9.76802e7	1.65740
$167$	7.97741e7	1.32542	0.662711	−	0.748875i	$-0.269406\pi$
$167$	7.97741e7	1.32542	0.662711	+	0.748875i	$0.269406\pi$
$168$	0	0
$169$	1.77033e8	2.82130
$170$	−1.19054e6	−0.0185855
$171$	0	0
$172$	2.06233e6	0.0309036
$173$	−5.77567e7	−0.848089	−0.424044	−	0.905641i	$-0.639390\pi$
$173$	−5.77567e7	−0.848089	−0.424044	+	0.905641i	$0.639390\pi$
$174$	0	0
$175$	−1.51784e7	−0.214089
$176$	4.35401e7	0.601999
$177$	0	0
$178$	2.06838e6	0.0274891
$179$	1.26896e8	1.65373	0.826863	−	0.562404i	$-0.190123\pi$
$179$	1.26896e8	1.65373	0.826863	+	0.562404i	$0.190123\pi$
$180$	0	0
$181$	4.52103e7	0.566713	0.283356	−	0.959015i	$-0.408552\pi$
$181$	4.52103e7	0.566713	0.283356	+	0.959015i	$0.408552\pi$
$182$	−3.21858e7	−0.395744
$183$	0	0
$184$	7.38642e7	0.874121
$185$	2.85034e6	0.0330975
$186$	0	0
$187$	1.25952e7	0.140851
$188$	1.32017e7	0.144903
$189$	0	0
$190$	−8.22776e6	−0.0870250
$191$	2.92519e6	0.0303765	0.0151882	−	0.999885i	$-0.495165\pi$
$191$	2.92519e6	0.0303765	0.0151882	+	0.999885i	$0.495165\pi$
$192$	0	0
$193$	−1.20823e8	−1.20976	−0.604879	−	0.796317i	$-0.706779\pi$
$193$	−1.20823e8	−1.20976	−0.604879	+	0.796317i	$0.706779\pi$
$194$	−1.30750e8	−1.28568
$195$	0	0
$196$	1.23650e7	0.117300
$197$	−5.56016e7	−0.518150	−0.259075	−	0.965857i	$-0.583418\pi$
$197$	−5.56016e7	−0.518150	−0.259075	+	0.965857i	$0.583418\pi$
$198$	0	0
$199$	−7.38051e7	−0.663897	−0.331948	−	0.943298i	$-0.607706\pi$
$199$	−7.38051e7	−0.663897	−0.331948	+	0.943298i	$0.607706\pi$
$200$	−1.17832e8	−1.04150
$201$	0	0
$202$	7.06136e7	0.602780
$203$	−3.15223e7	−0.264473
$204$	0	0
$205$	−1.34506e7	−0.109044
$206$	−6.08830e7	−0.485244
$207$	0	0
$208$	−2.18644e8	−1.68468
$209$	8.70447e7	0.659523
$210$	0	0
$211$	−1.88105e8	−1.37852	−0.689259	−	0.724515i	$-0.742064\pi$
$211$	−1.88105e8	−1.37852	−0.689259	+	0.724515i	$0.742064\pi$
$212$	−1.62775e7	−0.117331
$213$	0	0
$214$	1.45401e8	1.01419
$215$	3.60224e6	0.0247194
$216$	0	0
$217$	2.99974e7	0.199285
$218$	−1.09538e8	−0.716089
$219$	0	0
$220$	−1.33616e6	−0.00846017
$221$	−6.32490e7	−0.394167
$222$	0	0
$223$	2.36378e8	1.42738	0.713691	−	0.700460i	$-0.247022\pi$
$223$	2.36378e8	1.42738	0.713691	+	0.700460i	$0.247022\pi$
$224$	−8.89651e6	−0.0528873
$225$	0	0
$226$	−1.05646e8	−0.608801
$227$	−1.74041e8	−0.987552	−0.493776	−	0.869589i	$-0.664384\pi$
$227$	−1.74041e8	−0.987552	−0.493776	+	0.869589i	$0.664384\pi$
$228$	0	0
$229$	8.64382e7	0.475644	0.237822	−	0.971309i	$-0.423567\pi$
$229$	8.64382e7	0.475644	0.237822	+	0.971309i	$0.423567\pi$
$230$	1.41362e7	0.0766097
$231$	0	0
$232$	−2.44712e8	−1.28661
$233$	−3.12725e8	−1.61963	−0.809816	−	0.586683i	$-0.800433\pi$
$233$	−3.12725e8	−1.61963	−0.809816	+	0.586683i	$0.800433\pi$
$234$	0	0
$235$	2.30592e7	0.115906
$236$	−3.23481e6	−0.0160198
$237$	0	0
$238$	8.48991e6	0.0408210
$239$	−3.16008e8	−1.49729	−0.748644	−	0.662972i	$-0.769295\pi$
$239$	−3.16008e8	−1.49729	−0.748644	+	0.662972i	$0.769295\pi$
$240$	0	0
$241$	7.11836e7	0.327582	0.163791	−	0.986495i	$-0.447628\pi$
$241$	7.11836e7	0.327582	0.163791	+	0.986495i	$0.447628\pi$
$242$	1.05720e8	0.479518
$243$	0	0
$244$	2.21966e7	0.0978189
$245$	2.15976e7	0.0938264
$246$	0	0
$247$	−4.37110e8	−1.84566
$248$	2.32874e8	0.969482
$249$	0	0
$250$	−4.53221e7	−0.183451
$251$	−1.25489e8	−0.500896	−0.250448	−	0.968130i	$-0.580578\pi$
$251$	−1.25489e8	−0.500896	−0.250448	+	0.968130i	$0.580578\pi$
$252$	0	0
$253$	−1.49552e8	−0.580591
$254$	−2.40898e8	−0.922393
$255$	0	0
$256$	−9.75312e7	−0.363332
$257$	−9.74331e7	−0.358047	−0.179024	−	0.983845i	$-0.557294\pi$
$257$	−9.74331e7	−0.358047	−0.179024	+	0.983845i	$0.557294\pi$
$258$	0	0
$259$	−2.03261e7	−0.0726951
$260$	6.70975e6	0.0236755
$261$	0	0
$262$	−5.80567e7	−0.199433
$263$	−7.50373e7	−0.254350	−0.127175	−	0.991880i	$-0.540591\pi$
$263$	−7.50373e7	−0.254350	−0.127175	+	0.991880i	$0.540591\pi$
$264$	0	0
$265$	−2.84315e7	−0.0938512
$266$	5.86732e7	0.191141
$267$	0	0
$268$	−7.33823e7	−0.232873
$269$	−5.08532e8	−1.59289	−0.796444	−	0.604713i	$-0.793288\pi$
$269$	−5.08532e8	−1.59289	−0.796444	+	0.604713i	$0.793288\pi$
$270$	0	0
$271$	−3.78696e7	−0.115584	−0.0577921	−	0.998329i	$-0.518406\pi$
$271$	−3.78696e7	−0.115584	−0.0577921	+	0.998329i	$0.518406\pi$
$272$	5.76736e7	0.173774
$273$	0	0
$274$	2.25475e8	0.662174
$275$	2.38573e8	0.691762
$276$	0	0
$277$	−2.19980e8	−0.621875	−0.310938	−	0.950430i	$-0.600643\pi$
$277$	−2.19980e8	−0.621875	−0.310938	+	0.950430i	$0.600643\pi$
$278$	−3.33837e7	−0.0931917
$279$	0	0
$280$	−8.22001e6	−0.0223779
$281$	−5.30057e8	−1.42512	−0.712559	−	0.701612i	$-0.752464\pi$
$281$	−5.30057e8	−1.42512	−0.712559	+	0.701612i	$0.752464\pi$
$282$	0	0
$283$	−2.41217e8	−0.632639	−0.316320	−	0.948653i	$-0.602447\pi$
$283$	−2.41217e8	−0.632639	−0.316320	+	0.948653i	$0.602447\pi$
$284$	1.98438e7	0.0514056
$285$	0	0
$286$	5.05894e8	1.27873
$287$	9.59178e7	0.239504
$288$	0	0
$289$	−3.93655e8	−0.959342
$290$	−4.68330e7	−0.112761
$291$	0	0
$292$	−5.30057e7	−0.124590
$293$	−5.96366e8	−1.38508	−0.692542	−	0.721378i	$-0.743509\pi$
$293$	−5.96366e8	−1.38508	−0.692542	+	0.721378i	$0.743509\pi$
$294$	0	0
$295$	−5.65018e6	−0.0128140
$296$	−1.57794e8	−0.353647
$297$	0	0
$298$	1.47700e8	0.323312
$299$	7.51000e8	1.62477
$300$	0	0
$301$	−2.56880e7	−0.0542935
$302$	−1.32872e7	−0.0277594
$303$	0	0
$304$	3.98578e8	0.813684
$305$	3.87705e7	0.0782441
$306$	0	0
$307$	−1.31027e8	−0.258451	−0.129225	−	0.991615i	$-0.541249\pi$
$307$	−1.31027e8	−0.258451	−0.129225	+	0.991615i	$0.541249\pi$
$308$	9.52832e6	0.0185819
$309$	0	0
$310$	4.45675e7	0.0849673
$311$	9.14764e7	0.172444	0.0862219	−	0.996276i	$-0.472521\pi$
$311$	9.14764e7	0.172444	0.0862219	+	0.996276i	$0.472521\pi$
$312$	0	0
$313$	−2.09166e8	−0.385555	−0.192778	−	0.981242i	$-0.561750\pi$
$313$	−2.09166e8	−0.385555	−0.192778	+	0.981242i	$0.561750\pi$
$314$	−4.80105e8	−0.875150
$315$	0	0
$316$	−2.16047e7	−0.0385162
$317$	−6.38188e8	−1.12523	−0.562615	−	0.826719i	$-0.690204\pi$
$317$	−6.38188e8	−1.12523	−0.562615	+	0.826719i	$0.690204\pi$
$318$	0	0
$319$	4.95465e8	0.854566
$320$	−6.29395e7	−0.107374
$321$	0	0
$322$	−1.00807e8	−0.168265
$323$	1.15300e8	0.190379
$324$	0	0
$325$	−1.19804e9	−1.93588
$326$	3.46368e8	0.553703
$327$	0	0
$328$	7.44623e8	1.16514
$329$	−1.64438e8	−0.254575
$330$	0	0
$331$	6.30420e8	0.955503	0.477751	−	0.878495i	$-0.341452\pi$
$331$	6.30420e8	0.955503	0.477751	+	0.878495i	$0.341452\pi$
$332$	1.45213e8	0.217783
$333$	0	0
$334$	−8.45190e8	−1.24120
$335$	−1.28176e8	−0.186272
$336$	0	0
$337$	−1.07346e9	−1.52785	−0.763927	−	0.645302i	$-0.776731\pi$
$337$	−1.07346e9	−1.52785	−0.763927	+	0.645302i	$0.776731\pi$
$338$	−1.87562e9	−2.64203
$339$	0	0
$340$	−1.76989e6	−0.00244213
$341$	−4.71496e8	−0.643929
$342$	0	0
$343$	−3.15582e8	−0.422263
$344$	−1.99419e8	−0.264127
$345$	0	0
$346$	6.11920e8	0.794198
$347$	−7.32544e8	−0.941198	−0.470599	−	0.882347i	$-0.655962\pi$
$347$	−7.32544e8	−0.941198	−0.470599	+	0.882347i	$0.655962\pi$
$348$	0	0
$349$	9.30370e7	0.117157	0.0585783	−	0.998283i	$-0.481343\pi$
$349$	9.30370e7	0.117157	0.0585783	+	0.998283i	$0.481343\pi$
$350$	1.60812e8	0.200485
$351$	0	0
$352$	1.39835e8	0.170889
$353$	−4.21720e8	−0.510284	−0.255142	−	0.966904i	$-0.582122\pi$
$353$	−4.21720e8	−0.510284	−0.255142	+	0.966904i	$0.582122\pi$
$354$	0	0
$355$	3.46608e7	0.0411187
$356$	3.07490e6	0.00361206
$357$	0	0
$358$	−1.34444e9	−1.54864
$359$	1.55427e9	1.77295	0.886475	−	0.462776i	$-0.153147\pi$
$359$	1.55427e9	1.77295	0.886475	+	0.462776i	$0.153147\pi$
$360$	0	0
$361$	−9.70415e7	−0.108563
$362$	−4.78994e8	−0.530701
$363$	0	0
$364$	−4.78481e7	−0.0520008
$365$	−9.25841e7	−0.0996578
$366$	0	0
$367$	−3.61547e8	−0.381798	−0.190899	−	0.981610i	$-0.561140\pi$
$367$	−3.61547e8	−0.381798	−0.190899	+	0.981610i	$0.561140\pi$
$368$	−6.84799e8	−0.716302
$369$	0	0
$370$	−3.01987e7	−0.0309943
$371$	2.02749e8	0.206134
$372$	0	0
$373$	−3.99379e8	−0.398478	−0.199239	−	0.979951i	$-0.563847\pi$
$373$	−3.99379e8	−0.398478	−0.199239	+	0.979951i	$0.563847\pi$
$374$	−1.33444e8	−0.131901
$375$	0	0
$376$	−1.27655e9	−1.23846
$377$	−2.48806e9	−2.39148
$378$	0	0
$379$	1.14227e9	1.07779	0.538894	−	0.842374i	$-0.318842\pi$
$379$	1.14227e9	1.07779	0.538894	+	0.842374i	$0.318842\pi$
$380$	−1.22316e7	−0.0114351
$381$	0	0
$382$	−3.09918e7	−0.0284463
$383$	−9.82584e8	−0.893663	−0.446832	−	0.894618i	$-0.647448\pi$
$383$	−9.82584e8	−0.893663	−0.446832	+	0.894618i	$0.647448\pi$
$384$	0	0
$385$	1.66429e7	0.0148634
$386$	1.28009e9	1.13289
$387$	0	0
$388$	−1.94375e8	−0.168939
$389$	2.12534e9	1.83065	0.915326	−	0.402714i	$-0.131933\pi$
$389$	2.12534e9	1.83065	0.915326	+	0.402714i	$0.131933\pi$
$390$	0	0
$391$	−1.98097e8	−0.167595
$392$	−1.19564e9	−1.00254
$393$	0	0
$394$	5.89088e8	0.485225
$395$	−3.77365e7	−0.0308086
$396$	0	0
$397$	−5.12670e8	−0.411217	−0.205608	−	0.978634i	$-0.565917\pi$
$397$	−5.12670e8	−0.411217	−0.205608	+	0.978634i	$0.565917\pi$
$398$	7.81950e8	0.621710
$399$	0	0
$400$	1.09243e9	0.853459
$401$	8.46442e8	0.655529	0.327764	−	0.944760i	$-0.393705\pi$
$401$	8.46442e8	0.655529	0.327764	+	0.944760i	$0.393705\pi$
$402$	0	0
$403$	2.36770e9	1.80202
$404$	1.04976e8	0.0792053
$405$	0	0
$406$	3.33972e8	0.247668
$407$	3.19484e8	0.234892
$408$	0	0
$409$	1.16951e9	0.845222	0.422611	−	0.906311i	$-0.361114\pi$
$409$	1.16951e9	0.845222	0.422611	+	0.906311i	$0.361114\pi$
$410$	1.42506e8	0.102115
$411$	0	0
$412$	−9.05099e7	−0.0637611
$413$	4.02922e7	0.0281446
$414$	0	0
$415$	2.53642e8	0.174202
$416$	−7.02203e8	−0.478229
$417$	0	0
$418$	−9.22220e8	−0.617615
$419$	1.98068e9	1.31542	0.657710	−	0.753272i	$-0.271525\pi$
$419$	1.98068e9	1.31542	0.657710	+	0.753272i	$0.271525\pi$
$420$	0	0
$421$	−1.57680e9	−1.02989	−0.514944	−	0.857224i	$-0.672187\pi$
$421$	−1.57680e9	−1.02989	−0.514944	+	0.857224i	$0.672187\pi$
$422$	1.99294e9	1.29092
$423$	0	0
$424$	1.57397e9	1.00280
$425$	3.16015e8	0.199686
$426$	0	0
$427$	−2.76477e8	−0.171855
$428$	2.16157e8	0.133265
$429$	0	0
$430$	−3.81650e7	−0.0231486
$431$	2.24461e9	1.35042	0.675211	−	0.737625i	$-0.264053\pi$
$431$	2.24461e9	1.35042	0.675211	+	0.737625i	$0.264053\pi$
$432$	0	0
$433$	1.11989e9	0.662931	0.331466	−	0.943467i	$-0.392457\pi$
$433$	1.11989e9	0.662931	0.331466	+	0.943467i	$0.392457\pi$
$434$	−3.17816e8	−0.186622
$435$	0	0
$436$	−1.62842e8	−0.0940941
$437$	−1.36904e9	−0.784749
$438$	0	0
$439$	−9.51929e7	−0.0537005	−0.0268503	−	0.999639i	$-0.508548\pi$
$439$	−9.51929e7	−0.0537005	−0.0268503	+	0.999639i	$0.508548\pi$
$440$	1.29201e8	0.0723074
$441$	0	0
$442$	6.70110e8	0.369120
$443$	−1.40712e9	−0.768987	−0.384494	−	0.923128i	$-0.625624\pi$
$443$	−1.40712e9	−0.768987	−0.384494	+	0.923128i	$0.625624\pi$
$444$	0	0
$445$	5.37087e6	0.00288924
$446$	−2.50438e9	−1.33668
$447$	0	0
$448$	4.48829e8	0.235835
$449$	−1.13774e9	−0.593173	−0.296586	−	0.955006i	$-0.595848\pi$
$449$	−1.13774e9	−0.593173	−0.296586	+	0.955006i	$0.595848\pi$
$450$	0	0
$451$	−1.50763e9	−0.773885
$452$	−1.57056e8	−0.0799964
$453$	0	0
$454$	1.84392e9	0.924799
$455$	−8.35754e7	−0.0415948
$456$	0	0
$457$	9.71859e8	0.476318	0.238159	−	0.971226i	$-0.423456\pi$
$457$	9.71859e8	0.476318	0.238159	+	0.971226i	$0.423456\pi$
$458$	−9.15795e8	−0.445419
$459$	0	0
$460$	2.10151e7	0.0100665
$461$	−3.38981e7	−0.0161147	−0.00805735	−	0.999968i	$-0.502565\pi$
$461$	−3.38981e7	−0.0161147	−0.00805735	+	0.999968i	$0.502565\pi$
$462$	0	0
$463$	−3.22900e9	−1.51194	−0.755970	−	0.654606i	$-0.772835\pi$
$463$	−3.22900e9	−1.51194	−0.755970	+	0.654606i	$0.772835\pi$
$464$	2.26874e9	1.05432
$465$	0	0
$466$	3.31325e9	1.51671
$467$	−1.78458e9	−0.810823	−0.405412	−	0.914134i	$-0.632872\pi$
$467$	−1.78458e9	−0.810823	−0.405412	+	0.914134i	$0.632872\pi$
$468$	0	0
$469$	9.14037e8	0.409127
$470$	−2.44307e8	−0.108541
$471$	0	0
$472$	3.12793e8	0.136918
$473$	4.03762e8	0.175433
$474$	0	0
$475$	2.18396e9	0.935013
$476$	1.26213e7	0.00536388
$477$	0	0
$478$	3.34804e9	1.40214
$479$	2.69912e9	1.12214	0.561072	−	0.827767i	$-0.310389\pi$
$479$	2.69912e9	1.12214	0.561072	+	0.827767i	$0.310389\pi$
$480$	0	0
$481$	−1.60434e9	−0.657339
$482$	−7.54175e8	−0.306766
$483$	0	0
$484$	1.57166e8	0.0630087
$485$	−3.39512e8	−0.135132
$486$	0	0
$487$	1.26270e9	0.495391	0.247695	−	0.968838i	$-0.420327\pi$
$487$	1.26270e9	0.495391	0.247695	+	0.968838i	$0.420327\pi$
$488$	−2.14633e9	−0.836039
$489$	0	0
$490$	−2.28822e8	−0.0878643
$491$	−4.51620e9	−1.72182	−0.860911	−	0.508756i	$-0.830105\pi$
$491$	−4.51620e9	−1.72182	−0.860911	+	0.508756i	$0.830105\pi$
$492$	0	0
$493$	6.56296e8	0.246681
$494$	4.63109e9	1.72838
$495$	0	0
$496$	−2.15899e9	−0.794445
$497$	−2.47171e8	−0.0903129
$498$	0	0
$499$	−7.08115e8	−0.255124	−0.127562	−	0.991831i	$-0.540715\pi$
$499$	−7.08115e8	−0.255124	−0.127562	+	0.991831i	$0.540715\pi$
$500$	−6.73768e7	−0.0241054
$501$	0	0
$502$	1.32953e9	0.469067
$503$	−2.56658e9	−0.899222	−0.449611	−	0.893225i	$-0.648437\pi$
$503$	−2.56658e9	−0.899222	−0.449611	+	0.893225i	$0.648437\pi$
$504$	0	0
$505$	1.83359e8	0.0633553
$506$	1.58447e9	0.543698
$507$	0	0
$508$	−3.58125e8	−0.121202
$509$	4.19019e9	1.40839	0.704193	−	0.710008i	$-0.251309\pi$
$509$	4.19019e9	1.40839	0.704193	+	0.710008i	$0.251309\pi$
$510$	0	0
$511$	6.60229e8	0.218888
$512$	3.39290e9	1.11719
$513$	0	0
$514$	1.03228e9	0.335295
$515$	−1.58092e8	−0.0510017
$516$	0	0
$517$	2.58462e9	0.822583
$518$	2.15351e8	0.0680758
$519$	0	0
$520$	−6.48807e8	−0.202350
$521$	1.37031e9	0.424510	0.212255	−	0.977214i	$-0.431919\pi$
$521$	1.37031e9	0.424510	0.212255	+	0.977214i	$0.431919\pi$
$522$	0	0
$523$	−1.23138e8	−0.0376387	−0.0188193	−	0.999823i	$-0.505991\pi$
$523$	−1.23138e8	−0.0376387	−0.0188193	+	0.999823i	$0.505991\pi$
$524$	−8.63083e7	−0.0262055
$525$	0	0
$526$	7.95004e8	0.238188
$527$	−6.24547e8	−0.185878
$528$	0	0
$529$	−1.05267e9	−0.309171
$530$	3.01226e8	0.0878875
$531$	0	0
$532$	8.72248e7	0.0251159
$533$	7.57081e9	2.16569
$534$	0	0
$535$	3.77557e8	0.106597
$536$	7.09579e9	1.99032
$537$	0	0
$538$	5.38779e9	1.49167
$539$	2.42080e9	0.665884
$540$	0	0
$541$	−2.51384e9	−0.682571	−0.341285	−	0.939960i	$-0.610862\pi$
$541$	−2.51384e9	−0.682571	−0.341285	+	0.939960i	$0.610862\pi$
$542$	4.01221e8	0.108240
$543$	0	0
$544$	1.85226e8	0.0493293
$545$	−2.84432e8	−0.0752647
$546$	0	0
$547$	−5.46833e9	−1.42856	−0.714281	−	0.699859i	$-0.753246\pi$
$547$	−5.46833e9	−1.42856	−0.714281	+	0.699859i	$0.753246\pi$
$548$	3.35196e8	0.0870096
$549$	0	0
$550$	−2.52763e9	−0.647805
$551$	4.53562e9	1.15506
$552$	0	0
$553$	2.69104e8	0.0676678
$554$	2.33064e9	0.582359
$555$	0	0
$556$	−4.96289e7	−0.0122454
$557$	6.02940e9	1.47836	0.739181	−	0.673507i	$-0.235213\pi$
$557$	6.02940e9	1.47836	0.739181	+	0.673507i	$0.235213\pi$
$558$	0	0
$559$	−2.02756e9	−0.490944
$560$	7.62082e7	0.0183376
$561$	0	0
$562$	5.61585e9	1.33456
$563$	−4.27414e9	−1.00941	−0.504707	−	0.863291i	$-0.668399\pi$
$563$	−4.27414e9	−1.00941	−0.504707	+	0.863291i	$0.668399\pi$
$564$	0	0
$565$	−2.74327e8	−0.0639881
$566$	2.55565e9	0.592439
$567$	0	0
$568$	−1.91882e9	−0.439354
$569$	−5.96971e9	−1.35850	−0.679252	−	0.733906i	$-0.737695\pi$
$569$	−5.96971e9	−1.35850	−0.679252	+	0.733906i	$0.737695\pi$
$570$	0	0
$571$	−4.48628e9	−1.00846	−0.504231	−	0.863569i	$-0.668224\pi$
$571$	−4.48628e9	−1.00846	−0.504231	+	0.863569i	$0.668224\pi$
$572$	7.52072e8	0.168025
$573$	0	0
$574$	−1.01623e9	−0.224285
$575$	−3.75228e9	−0.823109
$576$	0	0
$577$	3.94552e8	0.0855044	0.0427522	−	0.999086i	$-0.486387\pi$
$577$	3.94552e8	0.0855044	0.0427522	+	0.999086i	$0.486387\pi$
$578$	4.17069e9	0.898381
$579$	0	0
$580$	−6.96230e7	−0.0148168
$581$	−1.80875e9	−0.382615
$582$	0	0
$583$	−3.18679e9	−0.666060
$584$	5.12544e9	1.06485
$585$	0	0
$586$	6.31837e9	1.29707
$587$	−3.79803e9	−0.775042	−0.387521	−	0.921861i	$-0.626668\pi$
$587$	−3.79803e9	−0.775042	−0.387521	+	0.921861i	$0.626668\pi$
$588$	0	0
$589$	−4.31621e9	−0.870359
$590$	5.98625e7	0.0119998
$591$	0	0
$592$	1.46292e9	0.289797
$593$	−6.35572e9	−1.25162	−0.625811	−	0.779974i	$-0.715232\pi$
$593$	−6.35572e9	−1.25162	−0.625811	+	0.779974i	$0.715232\pi$
$594$	0	0
$595$	2.20454e7	0.00429050
$596$	2.19573e8	0.0424832
$597$	0	0
$598$	−7.95669e9	−1.52152
$599$	6.72234e9	1.27799	0.638994	−	0.769212i	$-0.279351\pi$
$599$	6.72234e9	1.27799	0.638994	+	0.769212i	$0.279351\pi$
$600$	0	0
$601$	8.40583e9	1.57950	0.789750	−	0.613428i	$-0.210210\pi$
$601$	8.40583e9	1.57950	0.789750	+	0.613428i	$0.210210\pi$
$602$	2.72159e8	0.0508435
$603$	0	0
$604$	−1.97530e7	−0.00364758
$605$	2.74519e8	0.0503998
$606$	0	0
$607$	9.50798e9	1.72555	0.862775	−	0.505588i	$-0.168724\pi$
$607$	9.50798e9	1.72555	0.862775	+	0.505588i	$0.168724\pi$
$608$	1.28008e9	0.230981
$609$	0	0
$610$	−4.10765e8	−0.0732721
$611$	−1.29791e10	−2.30198
$612$	0	0
$613$	−5.92010e9	−1.03805	−0.519024	−	0.854760i	$-0.673704\pi$
$613$	−5.92010e9	−1.03805	−0.519024	+	0.854760i	$0.673704\pi$
$614$	1.38821e9	0.242028
$615$	0	0
$616$	−9.21352e8	−0.158816
$617$	9.90280e9	1.69731	0.848653	−	0.528950i	$-0.177414\pi$
$617$	9.90280e9	1.69731	0.848653	+	0.528950i	$0.177414\pi$
$618$	0	0
$619$	−4.78191e9	−0.810371	−0.405185	−	0.914235i	$-0.632793\pi$
$619$	−4.78191e9	−0.810371	−0.405185	+	0.914235i	$0.632793\pi$
$620$	6.62549e7	0.0111647
$621$	0	0
$622$	−9.69173e8	−0.161486
$623$	−3.83003e7	−0.00634592
$624$	0	0
$625$	5.92670e9	0.971031
$626$	2.21607e9	0.361055
$627$	0	0
$628$	−7.13734e8	−0.114995
$629$	4.23190e8	0.0678045
$630$	0	0
$631$	5.89153e9	0.933523	0.466761	−	0.884383i	$-0.345421\pi$
$631$	5.89153e9	0.933523	0.466761	+	0.884383i	$0.345421\pi$
$632$	2.08909e9	0.329190
$633$	0	0
$634$	6.76146e9	1.05373
$635$	−6.25530e8	−0.0969483
$636$	0	0
$637$	−1.21565e10	−1.86346
$638$	−5.24935e9	−0.800263
$639$	0	0
$640$	5.07143e8	0.0764716
$641$	−4.61318e9	−0.691826	−0.345913	−	0.938267i	$-0.612431\pi$
$641$	−4.61318e9	−0.691826	−0.345913	+	0.938267i	$0.612431\pi$
$642$	0	0
$643$	5.44438e9	0.807625	0.403812	−	0.914842i	$-0.367685\pi$
$643$	5.44438e9	0.807625	0.403812	+	0.914842i	$0.367685\pi$
$644$	−1.49861e8	−0.0221100
$645$	0	0
$646$	−1.22158e9	−0.178282
$647$	3.87507e9	0.562490	0.281245	−	0.959636i	$-0.409253\pi$
$647$	3.87507e9	0.562490	0.281245	+	0.959636i	$0.409253\pi$
$648$	0	0
$649$	−6.33308e8	−0.0909408
$650$	1.26929e10	1.81286
$651$	0	0
$652$	5.14918e8	0.0727565
$653$	7.85551e9	1.10402	0.552012	−	0.833836i	$-0.313860\pi$
$653$	7.85551e9	1.10402	0.552012	+	0.833836i	$0.313860\pi$
$654$	0	0
$655$	−1.50753e8	−0.0209615
$656$	−6.90344e9	−0.954777
$657$	0	0
$658$	1.74219e9	0.238399
$659$	−5.65831e8	−0.0770172	−0.0385086	−	0.999258i	$-0.512261\pi$
$659$	−5.65831e8	−0.0770172	−0.0385086	+	0.999258i	$0.512261\pi$
$660$	0	0
$661$	−1.43598e10	−1.93394	−0.966972	−	0.254884i	$-0.917963\pi$
$661$	−1.43598e10	−1.93394	−0.966972	+	0.254884i	$0.917963\pi$
$662$	−6.67916e9	−0.894786
$663$	0	0
$664$	−1.40416e10	−1.86135
$665$	1.52354e8	0.0200899
$666$	0	0
$667$	−7.79267e9	−1.01682
$668$	−1.25648e9	−0.163094
$669$	0	0
$670$	1.35799e9	0.174436
$671$	4.34564e9	0.555296
$672$	0	0
$673$	−1.67001e9	−0.211186	−0.105593	−	0.994409i	$-0.533674\pi$
$673$	−1.67001e9	−0.211186	−0.105593	+	0.994409i	$0.533674\pi$
$674$	1.13731e10	1.43077
$675$	0	0
$676$	−2.78834e9	−0.347162
$677$	−3.35024e9	−0.414968	−0.207484	−	0.978238i	$-0.566528\pi$
$677$	−3.35024e9	−0.414968	−0.207484	+	0.978238i	$0.566528\pi$
$678$	0	0
$679$	2.42110e9	0.296803
$680$	1.71141e8	0.0208724
$681$	0	0
$682$	4.99541e9	0.603011
$683$	9.06577e9	1.08876	0.544380	−	0.838839i	$-0.316765\pi$
$683$	9.06577e9	1.08876	0.544380	+	0.838839i	$0.316765\pi$
$684$	0	0
$685$	5.85481e8	0.0695979
$686$	3.34352e9	0.395430
$687$	0	0
$688$	1.84883e9	0.216440
$689$	1.60030e10	1.86395
$690$	0	0
$691$	−1.48221e10	−1.70898	−0.854492	−	0.519464i	$-0.826131\pi$
$691$	−1.48221e10	−1.70898	−0.854492	+	0.519464i	$0.826131\pi$
$692$	9.09694e8	0.104358
$693$	0	0
$694$	7.76115e9	0.881390
$695$	−8.66858e7	−0.00979493
$696$	0	0
$697$	−1.99701e9	−0.223391
$698$	−9.85708e8	−0.109712
$699$	0	0
$700$	2.39067e8	0.0263437
$701$	−5.34153e9	−0.585669	−0.292835	−	0.956163i	$-0.594599\pi$
$701$	−5.34153e9	−0.585669	−0.292835	+	0.956163i	$0.594599\pi$
$702$	0	0
$703$	2.92464e9	0.317489
$704$	−7.05466e9	−0.762029
$705$	0	0
$706$	4.46803e9	0.477859
$707$	−1.30756e9	−0.139153
$708$	0	0
$709$	8.91904e9	0.939845	0.469922	−	0.882708i	$-0.344282\pi$
$709$	8.91904e9	0.939845	0.469922	+	0.882708i	$0.344282\pi$
$710$	−3.67224e8	−0.0385059
$711$	0	0
$712$	−2.97330e8	−0.0308716
$713$	7.41569e9	0.766194
$714$	0	0
$715$	1.31363e9	0.134401
$716$	−1.99867e9	−0.203491
$717$	0	0
$718$	−1.64672e10	−1.66029
$719$	−6.48440e9	−0.650607	−0.325304	−	0.945610i	$-0.605467\pi$
$719$	−6.48440e9	−0.650607	−0.325304	+	0.945610i	$0.605467\pi$
$720$	0	0
$721$	1.12737e9	0.112020
$722$	1.02813e9	0.101665
$723$	0	0
$724$	−7.12083e8	−0.0697341
$725$	1.24313e10	1.21153
$726$	0	0
$727$	−1.05746e10	−1.02069	−0.510343	−	0.859971i	$-0.670482\pi$
$727$	−1.05746e10	−1.02069	−0.510343	+	0.859971i	$0.670482\pi$
$728$	4.62672e9	0.444441
$729$	0	0
$730$	9.80909e8	0.0933252
$731$	5.34825e8	0.0506409
$732$	0	0
$733$	1.27477e10	1.19555	0.597777	−	0.801663i	$-0.296051\pi$
$733$	1.27477e10	1.19555	0.597777	+	0.801663i	$0.296051\pi$
$734$	3.83051e9	0.357537
$735$	0	0
$736$	−2.19932e9	−0.203337
$737$	−1.43667e10	−1.32197
$738$	0	0
$739$	−1.87173e9	−0.170603	−0.0853015	−	0.996355i	$-0.527185\pi$
$739$	−1.87173e9	−0.170603	−0.0853015	+	0.996355i	$0.527185\pi$
$740$	−4.48941e7	−0.00407266
$741$	0	0
$742$	−2.14808e9	−0.193036
$743$	−1.17688e10	−1.05262	−0.526310	−	0.850293i	$-0.676425\pi$
$743$	−1.17688e10	−1.05262	−0.526310	+	0.850293i	$0.676425\pi$
$744$	0	0
$745$	3.83525e8	0.0339818
$746$	4.23134e9	0.373157
$747$	0	0
$748$	−1.98380e8	−0.0173317
$749$	−2.69241e9	−0.234128
$750$	0	0
$751$	−6.61690e9	−0.570053	−0.285026	−	0.958520i	$-0.592002\pi$
$751$	−6.61690e9	−0.570053	−0.285026	+	0.958520i	$0.592002\pi$
$752$	1.18350e10	1.01486
$753$	0	0
$754$	2.63605e10	2.23951
$755$	−3.45023e7	−0.00291765
$756$	0	0
$757$	−1.29360e10	−1.08384	−0.541919	−	0.840431i	$-0.682302\pi$
$757$	−1.29360e10	−1.08384	−0.541919	+	0.840431i	$0.682302\pi$
$758$	−1.21022e10	−1.00930
$759$	0	0
$760$	1.18274e9	0.0977335
$761$	−1.20040e9	−0.0987370	−0.0493685	−	0.998781i	$-0.515721\pi$
$761$	−1.20040e9	−0.0987370	−0.0493685	+	0.998781i	$0.515721\pi$
$762$	0	0
$763$	2.02832e9	0.165311
$764$	−4.60731e7	−0.00373784
$765$	0	0
$766$	1.04103e10	0.836876
$767$	3.18027e9	0.254495
$768$	0	0
$769$	−2.02392e9	−0.160491	−0.0802455	−	0.996775i	$-0.525570\pi$
$769$	−2.02392e9	−0.160491	−0.0802455	+	0.996775i	$0.525570\pi$
$770$	−1.76329e8	−0.0139189
$771$	0	0
$772$	1.90301e9	0.148861
$773$	1.99538e10	1.55381	0.776904	−	0.629619i	$-0.216789\pi$
$773$	1.99538e10	1.55381	0.776904	+	0.629619i	$0.216789\pi$
$774$	0	0
$775$	−1.18299e10	−0.912905
$776$	1.87953e10	1.44389
$777$	0	0
$778$	−2.25176e10	−1.71432
$779$	−1.38012e10	−1.04601
$780$	0	0
$781$	3.88501e9	0.291819
$782$	2.09880e9	0.156945
$783$	0	0
$784$	1.10849e10	0.821532
$785$	−1.24667e9	−0.0919828
$786$	0	0
$787$	−1.73330e10	−1.26754	−0.633771	−	0.773521i	$-0.718494\pi$
$787$	−1.73330e10	−1.26754	−0.633771	+	0.773521i	$0.718494\pi$
$788$	8.75750e8	0.0637585
$789$	0	0
$790$	3.99811e8	0.0288509
$791$	1.95626e9	0.140543
$792$	0	0
$793$	−2.18224e10	−1.55398
$794$	5.43163e9	0.385086
$795$	0	0
$796$	1.16246e9	0.0816927
$797$	−2.74452e10	−1.92027	−0.960135	−	0.279537i	$-0.909819\pi$
$797$	−2.74452e10	−1.92027	−0.960135	+	0.279537i	$0.909819\pi$
$798$	0	0
$799$	3.42360e9	0.237449
$800$	3.50847e9	0.242272
$801$	0	0
$802$	−8.96787e9	−0.613874
$803$	−1.03774e10	−0.707269
$804$	0	0
$805$	−2.61760e8	−0.0176855
$806$	−2.50853e10	−1.68751
$807$	0	0
$808$	−1.01507e10	−0.676952
$809$	−1.52422e10	−1.01211	−0.506053	−	0.862502i	$-0.668896\pi$
$809$	−1.52422e10	−1.01211	−0.506053	+	0.862502i	$0.668896\pi$
$810$	0	0
$811$	−2.23041e10	−1.46829	−0.734146	−	0.678992i	$-0.762417\pi$
$811$	−2.23041e10	−1.46829	−0.734146	+	0.678992i	$0.762417\pi$
$812$	4.96490e8	0.0325435
$813$	0	0
$814$	−3.38487e9	−0.219966
$815$	8.99399e8	0.0581970
$816$	0	0
$817$	3.69614e9	0.237122
$818$	−1.23907e10	−0.791513
$819$	0	0
$820$	2.11853e8	0.0134179
$821$	−2.03331e9	−0.128234	−0.0641170	−	0.997942i	$-0.520423\pi$
$821$	−2.03331e9	−0.128234	−0.0641170	+	0.997942i	$0.520423\pi$
$822$	0	0
$823$	2.44002e10	1.52579	0.762894	−	0.646524i	$-0.223778\pi$
$823$	2.44002e10	1.52579	0.762894	+	0.646524i	$0.223778\pi$
$824$	8.75195e9	0.544954
$825$	0	0
$826$	−4.26887e8	−0.0263562
$827$	1.03623e10	0.637073	0.318536	−	0.947911i	$-0.396809\pi$
$827$	1.03623e10	0.637073	0.318536	+	0.947911i	$0.396809\pi$
$828$	0	0
$829$	2.02624e10	1.23524	0.617619	−	0.786477i	$-0.288097\pi$
$829$	2.02624e10	1.23524	0.617619	+	0.786477i	$0.288097\pi$
$830$	−2.68728e9	−0.163132
$831$	0	0
$832$	3.54262e10	2.13252
$833$	3.20661e9	0.192216
$834$	0	0
$835$	−2.19467e9	−0.130457
$836$	−1.37099e9	−0.0811545
$837$	0	0
$838$	−2.09848e10	−1.23183
$839$	−2.01465e10	−1.17770	−0.588848	−	0.808244i	$-0.700418\pi$
$839$	−2.01465e10	−1.17770	−0.588848	+	0.808244i	$0.700418\pi$
$840$	0	0
$841$	8.56721e9	0.496653
$842$	1.67059e10	0.964444
$843$	0	0
$844$	2.96274e9	0.169627
$845$	−4.87035e9	−0.277691
$846$	0	0
$847$	−1.95763e9	−0.110698
$848$	−1.45923e10	−0.821749
$849$	0	0
$850$	−3.34812e9	−0.186997
$851$	−5.02484e9	−0.279492
$852$	0	0
$853$	−1.22421e10	−0.675361	−0.337680	−	0.941261i	$-0.609642\pi$
$853$	−1.22421e10	−0.675361	−0.337680	+	0.941261i	$0.609642\pi$
$854$	2.92922e9	0.160934
$855$	0	0
$856$	−2.09015e10	−1.13899
$857$	3.02381e9	0.164105	0.0820524	−	0.996628i	$-0.473852\pi$
$857$	3.02381e9	0.164105	0.0820524	+	0.996628i	$0.473852\pi$
$858$	0	0
$859$	2.27114e9	0.122255	0.0611276	−	0.998130i	$-0.480530\pi$
$859$	2.27114e9	0.122255	0.0611276	+	0.998130i	$0.480530\pi$
$860$	−5.67368e7	−0.00304173
$861$	0	0
$862$	−2.37811e10	−1.26461
$863$	6.87351e9	0.364033	0.182016	−	0.983295i	$-0.441738\pi$
$863$	6.87351e9	0.364033	0.182016	+	0.983295i	$0.441738\pi$
$864$	0	0
$865$	1.58895e9	0.0834743
$866$	−1.18650e10	−0.620806
$867$	0	0
$868$	−4.72472e8	−0.0245221
$869$	−4.22975e9	−0.218648
$870$	0	0
$871$	7.21450e10	3.69950
$872$	1.57461e10	0.804204
$873$	0	0
$874$	1.45047e10	0.734882
$875$	8.39232e8	0.0423501
$876$	0	0
$877$	1.64472e10	0.823369	0.411684	−	0.911326i	$-0.364941\pi$
$877$	1.64472e10	0.823369	0.411684	+	0.911326i	$0.364941\pi$
$878$	1.00855e9	0.0502882
$879$	0	0
$880$	−1.19783e9	−0.0592525
$881$	−2.86625e10	−1.41221	−0.706104	−	0.708108i	$-0.749549\pi$
$881$	−2.86625e10	−1.41221	−0.706104	+	0.708108i	$0.749549\pi$
$882$	0	0
$883$	1.47898e10	0.722934	0.361467	−	0.932385i	$-0.382276\pi$
$883$	1.47898e10	0.722934	0.361467	+	0.932385i	$0.382276\pi$
$884$	9.96199e8	0.0485024
$885$	0	0
$886$	1.49082e10	0.720123
$887$	−2.03041e10	−0.976904	−0.488452	−	0.872591i	$-0.662438\pi$
$887$	−2.03041e10	−0.976904	−0.488452	+	0.872591i	$0.662438\pi$
$888$	0	0
$889$	4.46073e9	0.212937
$890$	−5.69032e7	−0.00270565
$891$	0	0
$892$	−3.72306e9	−0.175640
$893$	2.36603e10	1.11183
$894$	0	0
$895$	−3.49104e9	−0.162770
$896$	−3.61650e9	−0.167962
$897$	0	0
$898$	1.20541e10	0.555480
$899$	−2.45682e10	−1.12775
$900$	0	0
$901$	−4.22124e9	−0.192266
$902$	1.59730e10	0.724709
$903$	0	0
$904$	1.51867e10	0.683714
$905$	−1.24378e9	−0.0557794
$906$	0	0
$907$	2.27424e9	0.101207	0.0506034	−	0.998719i	$-0.483886\pi$
$907$	2.27424e9	0.101207	0.0506034	+	0.998719i	$0.483886\pi$
$908$	2.74121e9	0.121519
$909$	0	0
$910$	8.85464e8	0.0389517
$911$	3.93967e9	0.172642	0.0863209	−	0.996267i	$-0.472489\pi$
$911$	3.93967e9	0.172642	0.0863209	+	0.996267i	$0.472489\pi$
$912$	0	0
$913$	2.84298e10	1.23631
$914$	−1.02966e10	−0.446050
$915$	0	0
$916$	−1.36144e9	−0.0585281
$917$	1.07504e9	0.0460397
$918$	0	0
$919$	−4.52534e10	−1.92330	−0.961650	−	0.274281i	$-0.911560\pi$
$919$	−4.52534e10	−1.92330	−0.961650	+	0.274281i	$0.911560\pi$
$920$	−2.03208e9	−0.0860366
$921$	0	0
$922$	3.59143e8	0.0150907
$923$	−1.95092e10	−0.816646
$924$	0	0
$925$	8.01589e9	0.333009
$926$	3.42106e10	1.41587
$927$	0	0
$928$	7.28633e9	0.299289
$929$	−3.82732e10	−1.56617	−0.783086	−	0.621914i	$-0.786356\pi$
$929$	−3.82732e10	−1.56617	−0.783086	+	0.621914i	$0.786356\pi$
$930$	0	0
$931$	2.21607e10	0.900034
$932$	4.92555e9	0.199296
$933$	0	0
$934$	1.89072e10	0.759300
$935$	−3.46507e8	−0.0138634
$936$	0	0
$937$	−3.29616e10	−1.30894	−0.654470	−	0.756088i	$-0.727108\pi$
$937$	−3.29616e10	−1.30894	−0.654470	+	0.756088i	$0.727108\pi$
$938$	−9.68403e9	−0.383130
$939$	0	0
$940$	−3.63192e8	−0.0142623
$941$	−1.04089e10	−0.407232	−0.203616	−	0.979051i	$-0.565269\pi$
$941$	−1.04089e10	−0.407232	−0.203616	+	0.979051i	$0.565269\pi$
$942$	0	0
$943$	2.37120e10	0.920824
$944$	−2.89992e9	−0.112198
$945$	0	0
$946$	−4.27777e9	−0.164285
$947$	4.76656e9	0.182381	0.0911906	−	0.995833i	$-0.470933\pi$
$947$	4.76656e9	0.182381	0.0911906	+	0.995833i	$0.470933\pi$
$948$	0	0
$949$	5.21120e10	1.97927
$950$	−2.31386e10	−0.875598
$951$	0	0
$952$	−1.22043e9	−0.0458440
$953$	−3.61082e10	−1.35139	−0.675694	−	0.737182i	$-0.736156\pi$
$953$	−3.61082e10	−1.35139	−0.675694	+	0.737182i	$0.736156\pi$
$954$	0	0
$955$	−8.04750e7	−0.00298985
$956$	4.97727e9	0.184242
$957$	0	0
$958$	−2.85966e10	−1.05084
$959$	−4.17514e9	−0.152864
$960$	0	0
$961$	−4.13295e9	−0.150220
$962$	1.69977e10	0.615569
$963$	0	0
$964$	−1.12117e9	−0.0403091
$965$	3.32396e9	0.119072
$966$	0	0
$967$	−4.25656e10	−1.51379	−0.756896	−	0.653536i	$-0.773285\pi$
$967$	−4.25656e10	−1.51379	−0.756896	+	0.653536i	$0.773285\pi$
$968$	−1.51974e10	−0.538523
$969$	0	0
$970$	3.59705e9	0.126545
$971$	−3.62745e10	−1.27155	−0.635777	−	0.771873i	$-0.719320\pi$
$971$	−3.62745e10	−1.27155	−0.635777	+	0.771873i	$0.719320\pi$
$972$	0	0
$973$	6.18168e8	0.0215135
$974$	−1.33780e10	−0.463912
$975$	0	0
$976$	1.98987e10	0.685095
$977$	−2.66535e10	−0.914372	−0.457186	−	0.889371i	$-0.651143\pi$
$977$	−2.66535e10	−0.914372	−0.457186	+	0.889371i	$0.651143\pi$
$978$	0	0
$979$	6.02001e8	0.0205049
$980$	−3.40172e8	−0.0115454
$981$	0	0
$982$	4.78482e10	1.61241
$983$	3.42147e10	1.14888	0.574441	−	0.818546i	$-0.305220\pi$
$983$	3.42147e10	1.14888	0.574441	+	0.818546i	$0.305220\pi$
$984$	0	0
$985$	1.52966e9	0.0509996
$986$	−6.95332e9	−0.231006
$987$	0	0
$988$	6.88467e9	0.227109
$989$	−6.35036e9	−0.208743
$990$	0	0
$991$	−2.61325e10	−0.852948	−0.426474	−	0.904500i	$-0.640244\pi$
$991$	−2.61325e10	−0.852948	−0.426474	+	0.904500i	$0.640244\pi$
$992$	−6.93385e9	−0.225519
$993$	0	0
$994$	2.61872e9	0.0845740
$995$	2.03045e9	0.0653450
$996$	0	0
$997$	9.42638e9	0.301240	0.150620	−	0.988592i	$-0.451873\pi$
$997$	9.42638e9	0.301240	0.150620	+	0.988592i	$0.451873\pi$
$998$	7.50233e9	0.238913
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	531.8.a.g.1.10	✓	33
3.2	odd	2		531.8.a.h.1.24	yes	33

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
531.8.a.g.1.10	✓	33	1.1	even	1	trivial
531.8.a.h.1.24	yes	33	3.2	odd	2

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)

\(f(q)\)	\(=\)	\(q-10.5948 q^{2} -15.7504 q^{4} -27.5110 q^{5} +196.184 q^{7} +1523.01 q^{8} +O(q^{10})\)	\(q-10.5948 q^{2} -15.7504 q^{4} -27.5110 q^{5} +196.184 q^{7} +1523.01 q^{8} +291.473 q^{10} -3083.61 q^{11} +15484.9 q^{13} -2078.53 q^{14} -14119.9 q^{16} -4084.57 q^{17} -28228.2 q^{19} +433.310 q^{20} +32670.2 q^{22} +48499.0 q^{23} -77368.1 q^{25} -164059. q^{26} -3089.99 q^{28} -160677. q^{29} +152904. q^{31} -45347.7 q^{32} +43275.1 q^{34} -5397.23 q^{35} -103607. q^{37} +299072. q^{38} -41899.4 q^{40} +488917. q^{41} -130938. q^{43} +48568.2 q^{44} -513837. q^{46} -838180. q^{47} -785055. q^{49} +819699. q^{50} -243893. q^{52} +1.03346e6 q^{53} +84833.2 q^{55} +298790. q^{56} +1.70234e6 q^{58} +205379. q^{59} -1.40927e6 q^{61} -1.61999e6 q^{62} +2.28779e6 q^{64} -426004. q^{65} +4.65907e6 q^{67} +64333.7 q^{68} +57182.5 q^{70} -1.25989e6 q^{71} +3.36535e6 q^{73} +1.09770e6 q^{74} +444606. q^{76} -604956. q^{77} +1.37169e6 q^{79} +388452. q^{80} -5.17997e6 q^{82} -9.21964e6 q^{83} +112371. q^{85} +1.38726e6 q^{86} -4.69635e6 q^{88} -195226. q^{89} +3.03789e6 q^{91} -763880. q^{92} +8.88034e6 q^{94} +776586. q^{95} +1.23409e7 q^{97} +8.31749e6 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 33 q - 24 q^{2} + 1776 q^{4} - 1000 q^{5} + 154 q^{7} - 4608 q^{8}+O(q^{10}) \) 33 * q - 24 * q^2 + 1776 * q^4 - 1000 * q^5 + 154 * q^7 - 4608 * q^8	\( 33 q - 24 q^{2} + 1776 q^{4} - 1000 q^{5} + 154 q^{7} - 4608 q^{8} + 5042 q^{10} - 13310 q^{11} - 14172 q^{13} - 16464 q^{14} + 95772 q^{16} - 39304 q^{17} - 56302 q^{19} + 17936 q^{20} + 152764 q^{22} - 17988 q^{23} + 468523 q^{25} + 27624 q^{26} - 59896 q^{28} - 474564 q^{29} + 188186 q^{31} - 251068 q^{32} + 169888 q^{34} - 514500 q^{35} + 1148200 q^{37} - 446594 q^{38} + 501214 q^{40} - 1246152 q^{41} + 62268 q^{43} - 2555520 q^{44} - 1289942 q^{46} - 1485654 q^{47} + 3829555 q^{49} - 6430160 q^{50} - 2624804 q^{52} - 4086740 q^{53} - 1119118 q^{55} - 8448352 q^{56} + 2966706 q^{58} + 6777507 q^{59} + 2436146 q^{61} - 9005952 q^{62} + 11117562 q^{64} - 16730354 q^{65} - 2652248 q^{67} - 15929124 q^{68} + 3359254 q^{70} - 7356324 q^{71} + 1900454 q^{73} - 25386964 q^{74} - 16047360 q^{76} - 20774826 q^{77} - 5912712 q^{79} - 13568404 q^{80} + 1579434 q^{82} + 1052766 q^{83} + 18372730 q^{85} - 43499960 q^{86} + 18209214 q^{88} - 174788 q^{89} - 18891512 q^{91} - 46033270 q^{92} + 365448 q^{94} - 31505580 q^{95} + 14418540 q^{97} + 15964056 q^{98}+O(q^{100}) \) 33 * q - 24 * q^2 + 1776 * q^4 - 1000 * q^5 + 154 * q^7 - 4608 * q^8 + 5042 * q^10 - 13310 * q^11 - 14172 * q^13 - 16464 * q^14 + 95772 * q^16 - 39304 * q^17 - 56302 * q^19 + 17936 * q^20 + 152764 * q^22 - 17988 * q^23 + 468523 * q^25 + 27624 * q^26 - 59896 * q^28 - 474564 * q^29 + 188186 * q^31 - 251068 * q^32 + 169888 * q^34 - 514500 * q^35 + 1148200 * q^37 - 446594 * q^38 + 501214 * q^40 - 1246152 * q^41 + 62268 * q^43 - 2555520 * q^44 - 1289942 * q^46 - 1485654 * q^47 + 3829555 * q^49 - 6430160 * q^50 - 2624804 * q^52 - 4086740 * q^53 - 1119118 * q^55 - 8448352 * q^56 + 2966706 * q^58 + 6777507 * q^59 + 2436146 * q^61 - 9005952 * q^62 + 11117562 * q^64 - 16730354 * q^65 - 2652248 * q^67 - 15929124 * q^68 + 3359254 * q^70 - 7356324 * q^71 + 1900454 * q^73 - 25386964 * q^74 - 16047360 * q^76 - 20774826 * q^77 - 5912712 * q^79 - 13568404 * q^80 + 1579434 * q^82 + 1052766 * q^83 + 18372730 * q^85 - 43499960 * q^86 + 18209214 * q^88 - 174788 * q^89 - 18891512 * q^91 - 46033270 * q^92 + 365448 * q^94 - 31505580 * q^95 + 14418540 * q^97 + 15964056 * q^98

Introduction

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