LMFDB - Embedded newform 531.8.a.g.1.19

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			1.19
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)

$f(q)$	$=$	$q+1.65238 q^{2} -125.270 q^{4} +348.169 q^{5} +493.067 q^{7} -418.497 q^{8} +O(q^{10})$	\(q+1.65238 q^{2} -125.270 q^{4} +348.169 q^{5} +493.067 q^{7} -418.497 q^{8} +575.306 q^{10} -3988.70 q^{11} +6108.53 q^{13} +814.733 q^{14} +15343.0 q^{16} -1284.76 q^{17} -1877.22 q^{19} -43615.0 q^{20} -6590.85 q^{22} -56733.2 q^{23} +43096.4 q^{25} +10093.6 q^{26} -61766.3 q^{28} +45249.3 q^{29} -142504. q^{31} +78920.1 q^{32} -2122.92 q^{34} +171670. q^{35} -122399. q^{37} -3101.87 q^{38} -145708. q^{40} -452752. q^{41} +737555. q^{43} +499664. q^{44} -93744.7 q^{46} -95647.8 q^{47} -580428. q^{49} +71211.6 q^{50} -765213. q^{52} +1.39014e6 q^{53} -1.38874e6 q^{55} -206347. q^{56} +74769.0 q^{58} +205379. q^{59} -1.59172e6 q^{61} -235471. q^{62} -1.83350e6 q^{64} +2.12680e6 q^{65} -2.26652e6 q^{67} +160942. q^{68} +283665. q^{70} -1.28325e6 q^{71} -1.27900e6 q^{73} -202250. q^{74} +235158. q^{76} -1.96670e6 q^{77} +5.88841e6 q^{79} +5.34195e6 q^{80} -748118. q^{82} -1.18189e6 q^{83} -447315. q^{85} +1.21872e6 q^{86} +1.66926e6 q^{88} +8.43025e6 q^{89} +3.01191e6 q^{91} +7.10695e6 q^{92} -158046. q^{94} -653588. q^{95} +2.07439e6 q^{97} -959087. q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.65238	0.146051	0.0730255	−	0.997330i	$-0.476735\pi$
$2$	1.65238	0.146051	0.0730255	+	0.997330i	$0.476735\pi$
$3$	0	0
$3$	0	0
$4$	−125.270	−0.978669
$5$	348.169	1.24565	0.622823	−	0.782363i	$-0.285986\pi$
$5$	348.169	1.24565	0.622823	+	0.782363i	$0.285986\pi$
$6$	0	0
$7$	493.067	0.543329	0.271664	−	0.962392i	$-0.412426\pi$
$7$	493.067	0.543329	0.271664	+	0.962392i	$0.412426\pi$
$8$	−418.497	−0.288987
$9$	0	0
$10$	575.306	0.181928
$11$	−3988.70	−0.903561	−0.451780	−	0.892129i	$-0.649211\pi$
$11$	−3988.70	−0.903561	−0.451780	+	0.892129i	$0.649211\pi$
$12$	0	0
$13$	6108.53	0.771143	0.385572	−	0.922678i	$-0.374004\pi$
$13$	6108.53	0.771143	0.385572	+	0.922678i	$0.374004\pi$
$14$	814.733	0.0793537
$15$	0	0
$16$	15343.0	0.936462
$17$	−1284.76	−0.0634238	−0.0317119	−	0.999497i	$-0.510096\pi$
$17$	−1284.76	−0.0634238	−0.0317119	+	0.999497i	$0.510096\pi$
$18$	0	0
$19$	−1877.22	−0.0627880	−0.0313940	−	0.999507i	$-0.509995\pi$
$19$	−1877.22	−0.0627880	−0.0313940	+	0.999507i	$0.509995\pi$
$20$	−43615.0	−1.21908
$21$	0	0
$22$	−6590.85	−0.131966
$23$	−56733.2	−0.972277	−0.486138	−	0.873882i	$-0.661595\pi$
$23$	−56733.2	−0.972277	−0.486138	+	0.873882i	$0.661595\pi$
$24$	0	0
$25$	43096.4	0.551634
$26$	10093.6	0.112626
$27$	0	0
$28$	−61766.3	−0.531739
$29$	45249.3	0.344524	0.172262	−	0.985051i	$-0.444892\pi$
$29$	45249.3	0.344524	0.172262	+	0.985051i	$0.444892\pi$
$30$	0	0
$31$	−142504.	−0.859135	−0.429568	−	0.903035i	$-0.641334\pi$
$31$	−142504.	−0.859135	−0.429568	+	0.903035i	$0.641334\pi$
$32$	78920.1	0.425758
$33$	0	0
$34$	−2122.92	−0.00926311
$35$	171670.	0.676796
$36$	0	0
$37$	−122399.	−0.397259	−0.198629	−	0.980075i	$-0.563649\pi$
$37$	−122399.	−0.397259	−0.198629	+	0.980075i	$0.563649\pi$
$38$	−3101.87	−0.00917025
$39$	0	0
$40$	−145708.	−0.359975
$41$	−452752.	−1.02593	−0.512964	−	0.858410i	$-0.671453\pi$
$41$	−452752.	−1.02593	−0.512964	+	0.858410i	$0.671453\pi$
$42$	0	0
$43$	737555.	1.41467	0.707334	−	0.706879i	$-0.249898\pi$
$43$	737555.	1.41467	0.707334	+	0.706879i	$0.249898\pi$
$44$	499664.	0.884287
$45$	0	0
$46$	−93744.7	−0.142002
$47$	−95647.8	−0.134379	−0.0671896	−	0.997740i	$-0.521403\pi$
$47$	−95647.8	−0.134379	−0.0671896	+	0.997740i	$0.521403\pi$
$48$	0	0
$49$	−580428.	−0.704794
$50$	71211.6	0.0805667
$51$	0	0
$52$	−765213.	−0.754694
$53$	1.39014e6	1.28261	0.641304	−	0.767287i	$-0.278394\pi$
$53$	1.39014e6	1.28261	0.641304	+	0.767287i	$0.278394\pi$
$54$	0	0
$55$	−1.38874e6	−1.12552
$56$	−206347.	−0.157015
$57$	0	0
$58$	74769.0	0.0503181
$59$	205379.	0.130189
$59$	205379.	0.130189
$60$	0	0
$61$	−1.59172e6	−0.897867	−0.448933	−	0.893565i	$-0.648196\pi$
$61$	−1.59172e6	−0.897867	−0.448933	+	0.893565i	$0.648196\pi$
$62$	−235471.	−0.125478
$63$	0	0
$64$	−1.83350e6	−0.874280
$65$	2.12680e6	0.960571
$66$	0	0
$67$	−2.26652e6	−0.920657	−0.460328	−	0.887749i	$-0.652268\pi$
$67$	−2.26652e6	−0.920657	−0.460328	+	0.887749i	$0.652268\pi$
$68$	160942.	0.0620709
$69$	0	0
$70$	283665.	0.0988467
$71$	−1.28325e6	−0.425508	−0.212754	−	0.977106i	$-0.568243\pi$
$71$	−1.28325e6	−0.425508	−0.212754	+	0.977106i	$0.568243\pi$
$72$	0	0
$73$	−1.27900e6	−0.384804	−0.192402	−	0.981316i	$-0.561628\pi$
$73$	−1.27900e6	−0.384804	−0.192402	+	0.981316i	$0.561628\pi$
$74$	−202250.	−0.0580200
$75$	0	0
$76$	235158.	0.0614487
$77$	−1.96670e6	−0.490931
$78$	0	0
$79$	5.88841e6	1.34370	0.671852	−	0.740686i	$-0.265499\pi$
$79$	5.88841e6	1.34370	0.671852	+	0.740686i	$0.265499\pi$
$80$	5.34195e6	1.16650
$81$	0	0
$82$	−748118.	−0.149838
$83$	−1.18189e6	−0.226883	−0.113442	−	0.993545i	$-0.536187\pi$
$83$	−1.18189e6	−0.226883	−0.113442	+	0.993545i	$0.536187\pi$
$84$	0	0
$85$	−447315.	−0.0790036
$86$	1.21872e6	0.206614
$87$	0	0
$88$	1.66926e6	0.261117
$89$	8.43025e6	1.26758	0.633790	−	0.773505i	$-0.281498\pi$
$89$	8.43025e6	1.26758	0.633790	+	0.773505i	$0.281498\pi$
$90$	0	0
$91$	3.01191e6	0.418984
$92$	7.10695e6	0.951537
$93$	0	0
$94$	−158046.	−0.0196262
$95$	−653588.	−0.0782116
$96$	0	0
$97$	2.07439e6	0.230775	0.115388	−	0.993321i	$-0.463189\pi$
$97$	2.07439e6	0.230775	0.115388	+	0.993321i	$0.463189\pi$
$98$	−959087.	−0.102936
$99$	0	0
$100$	−5.39867e6	−0.539867
$101$	−5.83974e6	−0.563986	−0.281993	−	0.959416i	$-0.590996\pi$
$101$	−5.83974e6	−0.563986	−0.281993	+	0.959416i	$0.590996\pi$
$102$	0	0
$103$	1.02698e7	0.926043	0.463022	−	0.886347i	$-0.346765\pi$
$103$	1.02698e7	0.926043	0.463022	+	0.886347i	$0.346765\pi$
$104$	−2.55640e6	−0.222850
$105$	0	0
$106$	2.29704e6	0.187326
$107$	5.65862e6	0.446547	0.223274	−	0.974756i	$-0.428326\pi$
$107$	5.65862e6	0.446547	0.223274	+	0.974756i	$0.428326\pi$
$108$	0	0
$109$	9.77983e6	0.723333	0.361667	−	0.932307i	$-0.382208\pi$
$109$	9.77983e6	0.723333	0.361667	+	0.932307i	$0.382208\pi$
$110$	−2.29473e6	−0.164383
$111$	0	0
$112$	7.56513e6	0.508807
$113$	−1.24311e7	−0.810469	−0.405234	−	0.914213i	$-0.632810\pi$
$113$	−1.24311e7	−0.810469	−0.405234	+	0.914213i	$0.632810\pi$
$114$	0	0
$115$	−1.97527e7	−1.21111
$116$	−5.66837e6	−0.337175
$117$	0	0
$118$	339364.	0.0190142
$119$	−633475.	−0.0344600
$120$	0	0
$121$	−3.57741e6	−0.183578
$122$	−2.63012e6	−0.131134
$123$	0	0
$124$	1.78514e7	0.840809
$125$	−1.21959e7	−0.558505
$126$	0	0
$127$	−1.62832e7	−0.705385	−0.352692	−	0.935739i	$-0.614734\pi$
$127$	−1.62832e7	−0.705385	−0.352692	+	0.935739i	$0.614734\pi$
$128$	−1.31314e7	−0.553447
$129$	0	0
$130$	3.51428e6	0.140292
$131$	−6.62282e6	−0.257391	−0.128695	−	0.991684i	$-0.541079\pi$
$131$	−6.62282e6	−0.257391	−0.128695	+	0.991684i	$0.541079\pi$
$132$	0	0
$133$	−925593.	−0.0341145
$134$	−3.74515e6	−0.134463
$135$	0	0
$136$	537671.	0.0183286
$137$	−4.52528e7	−1.50357	−0.751785	−	0.659408i	$-0.770807\pi$
$137$	−4.52528e7	−1.50357	−0.751785	+	0.659408i	$0.770807\pi$
$138$	0	0
$139$	1.97696e7	0.624375	0.312187	−	0.950021i	$-0.398938\pi$
$139$	1.97696e7	0.624375	0.312187	+	0.950021i	$0.398938\pi$
$140$	−2.15051e7	−0.662359
$141$	0	0
$142$	−2.12042e6	−0.0621458
$143$	−2.43651e7	−0.696775
$144$	0	0
$145$	1.57544e7	0.429155
$146$	−2.11339e6	−0.0562011
$147$	0	0
$148$	1.53329e7	0.388785
$149$	2.09600e7	0.519086	0.259543	−	0.965732i	$-0.416428\pi$
$149$	2.09600e7	0.519086	0.259543	+	0.965732i	$0.416428\pi$
$150$	0	0
$151$	−3.64919e7	−0.862536	−0.431268	−	0.902224i	$-0.641934\pi$
$151$	−3.64919e7	−0.862536	−0.431268	+	0.902224i	$0.641934\pi$
$152$	785610.	0.0181449
$153$	0	0
$154$	−3.24973e6	−0.0717009
$155$	−4.96155e7	−1.07018
$156$	0	0
$157$	5.15418e6	0.106295	0.0531473	−	0.998587i	$-0.483075\pi$
$157$	5.15418e6	0.106295	0.0531473	+	0.998587i	$0.483075\pi$
$158$	9.72988e6	0.196249
$159$	0	0
$160$	2.74775e7	0.530344
$161$	−2.79733e7	−0.528266
$162$	0	0
$163$	4.76184e6	0.0861228	0.0430614	−	0.999072i	$-0.486289\pi$
$163$	4.76184e6	0.0861228	0.0430614	+	0.999072i	$0.486289\pi$
$164$	5.67161e7	1.00404
$165$	0	0
$166$	−1.95292e6	−0.0331365
$167$	2.87321e6	0.0477376	0.0238688	−	0.999715i	$-0.492402\pi$
$167$	2.87321e6	0.0477376	0.0238688	+	0.999715i	$0.492402\pi$
$168$	0	0
$169$	−2.54344e7	−0.405338
$170$	−739133.	−0.0115386
$171$	0	0
$172$	−9.23932e7	−1.38449
$173$	−9.91625e7	−1.45608	−0.728041	−	0.685533i	$-0.759569\pi$
$173$	−9.91625e7	−1.45608	−0.728041	+	0.685533i	$0.759569\pi$
$174$	0	0
$175$	2.12494e7	0.299719
$176$	−6.11987e7	−0.846151
$177$	0	0
$178$	1.39300e7	0.185131
$179$	−6.37437e7	−0.830714	−0.415357	−	0.909659i	$-0.636343\pi$
$179$	−6.37437e7	−0.830714	−0.415357	+	0.909659i	$0.636343\pi$
$180$	0	0
$181$	−9.53537e7	−1.19526	−0.597630	−	0.801772i	$-0.703891\pi$
$181$	−9.53537e7	−1.19526	−0.597630	+	0.801772i	$0.703891\pi$
$182$	4.97682e6	0.0611931
$183$	0	0
$184$	2.37427e7	0.280975
$185$	−4.26157e7	−0.494844
$186$	0	0
$187$	5.12455e6	0.0573073
$188$	1.19818e7	0.131513
$189$	0	0
$190$	−1.07997e6	−0.0114229
$191$	−2.08867e7	−0.216897	−0.108448	−	0.994102i	$-0.534588\pi$
$191$	−2.08867e7	−0.216897	−0.108448	+	0.994102i	$0.534588\pi$
$192$	0	0
$193$	−8.69620e7	−0.870721	−0.435360	−	0.900256i	$-0.643379\pi$
$193$	−8.69620e7	−0.870721	−0.435360	+	0.900256i	$0.643379\pi$
$194$	3.42767e6	0.0337049
$195$	0	0
$196$	7.27100e7	0.689760
$197$	−2.02725e7	−0.188919	−0.0944594	−	0.995529i	$-0.530112\pi$
$197$	−2.02725e7	−0.188919	−0.0944594	+	0.995529i	$0.530112\pi$
$198$	0	0
$199$	−1.46650e8	−1.31916	−0.659578	−	0.751636i	$-0.729265\pi$
$199$	−1.46650e8	−1.31916	−0.659578	+	0.751636i	$0.729265\pi$
$200$	−1.80357e7	−0.159415
$201$	0	0
$202$	−9.64945e6	−0.0823707
$203$	2.23110e7	0.187190
$204$	0	0
$205$	−1.57634e8	−1.27794
$206$	1.69696e7	0.135250
$207$	0	0
$208$	9.37232e7	0.722146
$209$	7.48766e6	0.0567328
$210$	0	0
$211$	1.05553e8	0.773542	0.386771	−	0.922176i	$-0.373590\pi$
$211$	1.05553e8	0.773542	0.386771	+	0.922176i	$0.373590\pi$
$212$	−1.74143e8	−1.25525
$213$	0	0
$214$	9.35018e6	0.0652187
$215$	2.56793e8	1.76218
$216$	0	0
$217$	−7.02641e7	−0.466793
$218$	1.61600e7	0.105644
$219$	0	0
$220$	1.73967e8	1.10151
$221$	−7.84802e6	−0.0489088
$222$	0	0
$223$	5.78845e6	0.0349539	0.0174769	−	0.999847i	$-0.494437\pi$
$223$	5.78845e6	0.0349539	0.0174769	+	0.999847i	$0.494437\pi$
$224$	3.89129e7	0.231327
$225$	0	0
$226$	−2.05409e7	−0.118370
$227$	2.04717e6	0.0116162	0.00580809	−	0.999983i	$-0.498151\pi$
$227$	2.04717e6	0.0116162	0.00580809	+	0.999983i	$0.498151\pi$
$228$	0	0
$229$	−2.04522e8	−1.12542	−0.562712	−	0.826653i	$-0.690242\pi$
$229$	−2.04522e8	−1.12542	−0.562712	+	0.826653i	$0.690242\pi$
$230$	−3.26390e7	−0.176884
$231$	0	0
$232$	−1.89367e7	−0.0995628
$233$	−2.64333e8	−1.36901	−0.684504	−	0.729009i	$-0.739981\pi$
$233$	−2.64333e8	−1.36901	−0.684504	+	0.729009i	$0.739981\pi$
$234$	0	0
$235$	−3.33016e7	−0.167389
$236$	−2.57278e7	−0.127412
$237$	0	0
$238$	−1.04674e6	−0.00503292
$239$	−2.15692e8	−1.02198	−0.510990	−	0.859587i	$-0.670721\pi$
$239$	−2.15692e8	−1.02198	−0.510990	+	0.859587i	$0.670721\pi$
$240$	0	0
$241$	−1.98569e8	−0.913800	−0.456900	−	0.889518i	$-0.651040\pi$
$241$	−1.98569e8	−0.913800	−0.456900	+	0.889518i	$0.651040\pi$
$242$	−5.91124e6	−0.0268117
$243$	0	0
$244$	1.99394e8	0.878714
$245$	−2.02087e8	−0.877923
$246$	0	0
$247$	−1.14670e7	−0.0484185
$248$	5.96376e7	0.248279
$249$	0	0
$250$	−2.01522e7	−0.0815702
$251$	4.07169e7	0.162524	0.0812619	−	0.996693i	$-0.474105\pi$
$251$	4.07169e7	0.162524	0.0812619	+	0.996693i	$0.474105\pi$
$252$	0	0
$253$	2.26292e8	0.878511
$254$	−2.69060e7	−0.103022
$255$	0	0
$256$	2.12990e8	0.793448
$257$	1.39398e8	0.512261	0.256130	−	0.966642i	$-0.417552\pi$
$257$	1.39398e8	0.512261	0.256130	+	0.966642i	$0.417552\pi$
$258$	0	0
$259$	−6.03511e7	−0.215842
$260$	−2.66423e8	−0.940082
$261$	0	0
$262$	−1.09434e7	−0.0375922
$263$	7.82370e7	0.265196	0.132598	−	0.991170i	$-0.457668\pi$
$263$	7.82370e7	0.265196	0.132598	+	0.991170i	$0.457668\pi$
$264$	0	0
$265$	4.84004e8	1.59767
$266$	−1.52943e6	−0.00498246
$267$	0	0
$268$	2.83926e8	0.901018
$269$	−3.42095e8	−1.07155	−0.535776	−	0.844360i	$-0.679981\pi$
$269$	−3.42095e8	−1.07155	−0.535776	+	0.844360i	$0.679981\pi$
$270$	0	0
$271$	5.29294e8	1.61549	0.807746	−	0.589531i	$-0.200687\pi$
$271$	5.29294e8	1.61549	0.807746	+	0.589531i	$0.200687\pi$
$272$	−1.97121e7	−0.0593940
$273$	0	0
$274$	−7.47748e7	−0.219598
$275$	−1.71899e8	−0.498435
$276$	0	0
$277$	−4.19999e8	−1.18732	−0.593662	−	0.804714i	$-0.702318\pi$
$277$	−4.19999e8	−1.18732	−0.593662	+	0.804714i	$0.702318\pi$
$278$	3.26668e7	0.0911906
$279$	0	0
$280$	−7.18436e7	−0.195585
$281$	−2.80520e8	−0.754209	−0.377105	−	0.926171i	$-0.623080\pi$
$281$	−2.80520e8	−0.754209	−0.377105	+	0.926171i	$0.623080\pi$
$282$	0	0
$283$	2.33565e8	0.612571	0.306285	−	0.951940i	$-0.400914\pi$
$283$	2.33565e8	0.612571	0.306285	+	0.951940i	$0.400914\pi$
$284$	1.60752e8	0.416431
$285$	0	0
$286$	−4.02604e7	−0.101765
$287$	−2.23237e8	−0.557417
$288$	0	0
$289$	−4.08688e8	−0.995977
$290$	2.60322e7	0.0626785
$291$	0	0
$292$	1.60220e8	0.376596
$293$	−2.52513e8	−0.586472	−0.293236	−	0.956040i	$-0.594732\pi$
$293$	−2.52513e8	−0.586472	−0.293236	+	0.956040i	$0.594732\pi$
$294$	0	0
$295$	7.15065e7	0.162169
$296$	5.12238e7	0.114802
$297$	0	0
$298$	3.46339e7	0.0758131
$299$	−3.46556e8	−0.749764
$300$	0	0
$301$	3.63664e8	0.768630
$302$	−6.02985e7	−0.125974
$303$	0	0
$304$	−2.88021e7	−0.0587986
$305$	−5.54187e8	−1.11842
$306$	0	0
$307$	7.44453e8	1.46843	0.734214	−	0.678918i	$-0.237551\pi$
$307$	7.44453e8	1.46843	0.734214	+	0.678918i	$0.237551\pi$
$308$	2.46368e8	0.480459
$309$	0	0
$310$	−8.19836e7	−0.156301
$311$	−5.97272e8	−1.12593	−0.562964	−	0.826481i	$-0.690339\pi$
$311$	−5.97272e8	−1.12593	−0.562964	+	0.826481i	$0.690339\pi$
$312$	0	0
$313$	−4.34394e7	−0.0800716	−0.0400358	−	0.999198i	$-0.512747\pi$
$313$	−4.34394e7	−0.0800716	−0.0400358	+	0.999198i	$0.512747\pi$
$314$	8.51666e6	0.0155244
$315$	0	0
$316$	−7.37639e8	−1.31504
$317$	−2.47054e8	−0.435597	−0.217798	−	0.975994i	$-0.569888\pi$
$317$	−2.47054e8	−0.435597	−0.217798	+	0.975994i	$0.569888\pi$
$318$	0	0
$319$	−1.80486e8	−0.311298
$320$	−6.38367e8	−1.08904
$321$	0	0
$322$	−4.62224e7	−0.0771538
$323$	2.41178e6	0.00398225
$324$	0	0
$325$	2.63256e8	0.425389
$326$	7.86837e6	0.0125783
$327$	0	0
$328$	1.89476e8	0.296480
$329$	−4.71608e7	−0.0730121
$330$	0	0
$331$	2.69917e7	0.0409102	0.0204551	−	0.999791i	$-0.493488\pi$
$331$	2.69917e7	0.0409102	0.0204551	+	0.999791i	$0.493488\pi$
$332$	1.48054e8	0.222043
$333$	0	0
$334$	4.74764e6	0.00697212
$335$	−7.89131e8	−1.14681
$336$	0	0
$337$	7.11679e7	0.101293	0.0506465	−	0.998717i	$-0.483872\pi$
$337$	7.11679e7	0.101293	0.0506465	+	0.998717i	$0.483872\pi$
$338$	−4.20272e7	−0.0592001
$339$	0	0
$340$	5.60350e7	0.0773184
$341$	5.68407e8	0.776281
$342$	0	0
$343$	−6.92252e8	−0.926264
$344$	−3.08665e8	−0.408820
$345$	0	0
$346$	−1.63854e8	−0.212662
$347$	−6.85248e7	−0.0880430	−0.0440215	−	0.999031i	$-0.514017\pi$
$347$	−6.85248e7	−0.0880430	−0.0440215	+	0.999031i	$0.514017\pi$
$348$	0	0
$349$	−5.89340e8	−0.742125	−0.371062	−	0.928608i	$-0.621006\pi$
$349$	−5.89340e8	−0.742125	−0.371062	+	0.928608i	$0.621006\pi$
$350$	3.51121e7	0.0437742
$351$	0	0
$352$	−3.14789e8	−0.384698
$353$	1.03223e9	1.24901	0.624503	−	0.781022i	$-0.285302\pi$
$353$	1.03223e9	1.24901	0.624503	+	0.781022i	$0.285302\pi$
$354$	0	0
$355$	−4.46788e8	−0.530032
$356$	−1.05605e9	−1.24054
$357$	0	0
$358$	−1.05329e8	−0.121327
$359$	−1.52537e9	−1.73998	−0.869991	−	0.493067i	$-0.835876\pi$
$359$	−1.52537e9	−1.73998	−0.869991	+	0.493067i	$0.835876\pi$
$360$	0	0
$361$	−8.90348e8	−0.996058
$362$	−1.57560e8	−0.174569
$363$	0	0
$364$	−3.77302e8	−0.410047
$365$	−4.45307e8	−0.479330
$366$	0	0
$367$	1.60635e8	0.169632	0.0848162	−	0.996397i	$-0.472970\pi$
$367$	1.60635e8	0.169632	0.0848162	+	0.996397i	$0.472970\pi$
$368$	−8.70457e8	−0.910500
$369$	0	0
$370$	−7.04172e7	−0.0722724
$371$	6.85433e8	0.696878
$372$	0	0
$373$	4.18852e8	0.417907	0.208953	−	0.977926i	$-0.432994\pi$
$373$	4.18852e8	0.417907	0.208953	+	0.977926i	$0.432994\pi$
$374$	8.46769e6	0.00836979
$375$	0	0
$376$	4.00283e7	0.0388338
$377$	2.76407e8	0.265677
$378$	0	0
$379$	8.15237e8	0.769213	0.384606	−	0.923081i	$-0.374337\pi$
$379$	8.15237e8	0.769213	0.384606	+	0.923081i	$0.374337\pi$
$380$	8.18747e7	0.0765433
$381$	0	0
$382$	−3.45127e7	−0.0316780
$383$	−1.85492e9	−1.68706	−0.843529	−	0.537084i	$-0.819526\pi$
$383$	−1.85492e9	−1.68706	−0.843529	+	0.537084i	$0.819526\pi$
$384$	0	0
$385$	−6.84743e8	−0.611526
$386$	−1.43694e8	−0.127170
$387$	0	0
$388$	−2.59858e8	−0.225852
$389$	−6.50318e8	−0.560147	−0.280074	−	0.959979i	$-0.590359\pi$
$389$	−6.50318e8	−0.560147	−0.280074	+	0.959979i	$0.590359\pi$
$390$	0	0
$391$	7.28888e7	0.0616655
$392$	2.42908e8	0.203676
$393$	0	0
$394$	−3.34978e7	−0.0275918
$395$	2.05016e9	1.67378
$396$	0	0
$397$	1.44120e9	1.15600	0.577998	−	0.816038i	$-0.303834\pi$
$397$	1.44120e9	1.15600	0.577998	+	0.816038i	$0.303834\pi$
$398$	−2.42321e8	−0.192664
$399$	0	0
$400$	6.61228e8	0.516585
$401$	−4.06152e8	−0.314545	−0.157273	−	0.987555i	$-0.550270\pi$
$401$	−4.06152e8	−0.314545	−0.157273	+	0.987555i	$0.550270\pi$
$402$	0	0
$403$	−8.70491e8	−0.662516
$404$	7.31542e8	0.551956
$405$	0	0
$406$	3.68661e7	0.0273393
$407$	4.88215e8	0.358947
$408$	0	0
$409$	4.38708e8	0.317062	0.158531	−	0.987354i	$-0.449324\pi$
$409$	4.38708e8	0.317062	0.158531	+	0.987354i	$0.449324\pi$
$410$	−2.60471e8	−0.186645
$411$	0	0
$412$	−1.28649e9	−0.906290
$413$	1.01266e8	0.0707354
$414$	0	0
$415$	−4.11496e8	−0.282616
$416$	4.82086e8	0.328320
$417$	0	0
$418$	1.23724e7	0.00828588
$419$	−3.48048e8	−0.231148	−0.115574	−	0.993299i	$-0.536871\pi$
$419$	−3.48048e8	−0.231148	−0.115574	+	0.993299i	$0.536871\pi$
$420$	0	0
$421$	1.83977e9	1.20164	0.600821	−	0.799383i	$-0.294840\pi$
$421$	1.83977e9	1.20164	0.600821	+	0.799383i	$0.294840\pi$
$422$	1.74414e8	0.112977
$423$	0	0
$424$	−5.81771e8	−0.370656
$425$	−5.53688e7	−0.0349867
$426$	0	0
$427$	−7.84824e8	−0.487837
$428$	−7.08853e8	−0.437022
$429$	0	0
$430$	4.24320e8	0.257368
$431$	−1.06970e9	−0.643564	−0.321782	−	0.946814i	$-0.604282\pi$
$431$	−1.06970e9	−0.643564	−0.321782	+	0.946814i	$0.604282\pi$
$432$	0	0
$433$	−6.91926e8	−0.409593	−0.204796	−	0.978805i	$-0.565653\pi$
$433$	−6.91926e8	−0.409593	−0.204796	+	0.978805i	$0.565653\pi$
$434$	−1.16103e8	−0.0681756
$435$	0	0
$436$	−1.22512e9	−0.707904
$437$	1.06500e8	0.0610473
$438$	0	0
$439$	3.71507e8	0.209576	0.104788	−	0.994495i	$-0.466584\pi$
$439$	3.71507e8	0.209576	0.104788	+	0.994495i	$0.466584\pi$
$440$	5.81185e8	0.325259
$441$	0	0
$442$	−1.29679e7	−0.00714319
$443$	3.12047e7	0.0170533	0.00852663	−	0.999964i	$-0.497286\pi$
$443$	3.12047e7	0.0170533	0.00852663	+	0.999964i	$0.497286\pi$
$444$	0	0
$445$	2.93515e9	1.57896
$446$	9.56471e6	0.00510505
$447$	0	0
$448$	−9.04037e8	−0.475022
$449$	1.88655e9	0.983570	0.491785	−	0.870717i	$-0.336345\pi$
$449$	1.88655e9	0.983570	0.491785	+	0.870717i	$0.336345\pi$
$450$	0	0
$451$	1.80589e9	0.926989
$452$	1.55724e9	0.793181
$453$	0	0
$454$	3.38270e6	0.00169656
$455$	1.04865e9	0.521906
$456$	0	0
$457$	−3.08960e9	−1.51424	−0.757122	−	0.653274i	$-0.773395\pi$
$457$	−3.08960e9	−1.51424	−0.757122	+	0.653274i	$0.773395\pi$
$458$	−3.37948e8	−0.164369
$459$	0	0
$460$	2.47442e9	1.18528
$461$	1.72135e9	0.818308	0.409154	−	0.912465i	$-0.365824\pi$
$461$	1.72135e9	0.818308	0.409154	+	0.912465i	$0.365824\pi$
$462$	0	0
$463$	1.48774e9	0.696618	0.348309	−	0.937380i	$-0.386756\pi$
$463$	1.48774e9	0.696618	0.348309	+	0.937380i	$0.386756\pi$
$464$	6.94261e8	0.322634
$465$	0	0
$466$	−4.36778e8	−0.199945
$467$	1.12230e9	0.509919	0.254959	−	0.966952i	$-0.417938\pi$
$467$	1.12230e9	0.509919	0.254959	+	0.966952i	$0.417938\pi$
$468$	0	0
$469$	−1.11755e9	−0.500219
$470$	−5.50268e7	−0.0244473
$471$	0	0
$472$	−8.59506e7	−0.0376229
$473$	−2.94189e9	−1.27824
$474$	0	0
$475$	−8.09013e7	−0.0346360
$476$	7.93552e7	0.0337249
$477$	0	0
$478$	−3.56405e8	−0.149261
$479$	2.84977e9	1.18477	0.592387	−	0.805654i	$-0.298186\pi$
$479$	2.84977e9	1.18477	0.592387	+	0.805654i	$0.298186\pi$
$480$	0	0
$481$	−7.47681e8	−0.306343
$482$	−3.28111e8	−0.133461
$483$	0	0
$484$	4.48141e8	0.179662
$485$	7.22237e8	0.287464
$486$	0	0
$487$	−1.67426e9	−0.656857	−0.328429	−	0.944529i	$-0.606519\pi$
$487$	−1.67426e9	−0.656857	−0.328429	+	0.944529i	$0.606519\pi$
$488$	6.66130e8	0.259471
$489$	0	0
$490$	−3.33924e8	−0.128222
$491$	2.39016e9	0.911257	0.455629	−	0.890170i	$-0.349415\pi$
$491$	2.39016e9	0.911257	0.455629	+	0.890170i	$0.349415\pi$
$492$	0	0
$493$	−5.81348e7	−0.0218510
$494$	−1.89479e7	−0.00707158
$495$	0	0
$496$	−2.18644e9	−0.804548
$497$	−6.32729e8	−0.231191
$498$	0	0
$499$	4.53844e9	1.63514	0.817569	−	0.575830i	$-0.195321\pi$
$499$	4.53844e9	1.63514	0.817569	+	0.575830i	$0.195321\pi$
$500$	1.52777e9	0.546592
$501$	0	0
$502$	6.72798e7	0.0237368
$503$	−2.30217e9	−0.806582	−0.403291	−	0.915072i	$-0.632134\pi$
$503$	−2.30217e9	−0.806582	−0.403291	+	0.915072i	$0.632134\pi$
$504$	0	0
$505$	−2.03321e9	−0.702527
$506$	3.73920e8	0.128307
$507$	0	0
$508$	2.03979e9	0.690338
$509$	−1.36282e9	−0.458064	−0.229032	−	0.973419i	$-0.573556\pi$
$509$	−1.36282e9	−0.458064	−0.229032	+	0.973419i	$0.573556\pi$
$510$	0	0
$511$	−6.30632e8	−0.209075
$512$	2.03276e9	0.669331
$513$	0	0
$514$	2.30338e8	0.0748162
$515$	3.57562e9	1.15352
$516$	0	0
$517$	3.81511e8	0.121420
$518$	−9.97229e7	−0.0315240
$519$	0	0
$520$	−8.90060e8	−0.277592
$521$	−1.45717e8	−0.0451418	−0.0225709	−	0.999745i	$-0.507185\pi$
$521$	−1.45717e8	−0.0451418	−0.0225709	+	0.999745i	$0.507185\pi$
$522$	0	0
$523$	3.76904e9	1.15206	0.576030	−	0.817429i	$-0.304601\pi$
$523$	3.76904e9	1.15206	0.576030	+	0.817429i	$0.304601\pi$
$524$	8.29638e8	0.251901
$525$	0	0
$526$	1.29277e8	0.0387322
$527$	1.83084e8	0.0544896
$528$	0	0
$529$	−1.86170e8	−0.0546782
$530$	7.99758e8	0.233342
$531$	0	0
$532$	1.15949e8	0.0333868
$533$	−2.76565e9	−0.791138
$534$	0	0
$535$	1.97015e9	0.556240
$536$	9.48533e8	0.266057
$537$	0	0
$538$	−5.65270e8	−0.156501
$539$	2.31515e9	0.636824
$540$	0	0
$541$	−5.14043e8	−0.139576	−0.0697878	−	0.997562i	$-0.522232\pi$
$541$	−5.14043e8	−0.139576	−0.0697878	+	0.997562i	$0.522232\pi$
$542$	8.74595e8	0.235944
$543$	0	0
$544$	−1.01394e8	−0.0270032
$545$	3.40503e9	0.901017
$546$	0	0
$547$	3.86857e9	1.01064	0.505319	−	0.862933i	$-0.331375\pi$
$547$	3.86857e9	1.01064	0.505319	+	0.862933i	$0.331375\pi$
$548$	5.66880e9	1.47150
$549$	0	0
$550$	−2.84042e8	−0.0727969
$551$	−8.49428e7	−0.0216320
$552$	0	0
$553$	2.90338e9	0.730073
$554$	−6.93998e8	−0.173410
$555$	0	0
$556$	−2.47653e9	−0.611056
$557$	4.34046e9	1.06425	0.532124	−	0.846667i	$-0.321394\pi$
$557$	4.34046e9	1.06425	0.532124	+	0.846667i	$0.321394\pi$
$558$	0	0
$559$	4.50538e9	1.09091
$560$	2.63394e9	0.633794
$561$	0	0
$562$	−4.63525e8	−0.110153
$563$	−4.90614e9	−1.15867	−0.579336	−	0.815089i	$-0.696688\pi$
$563$	−4.90614e9	−1.15867	−0.579336	+	0.815089i	$0.696688\pi$
$564$	0	0
$565$	−4.32813e9	−1.00956
$566$	3.85939e8	0.0894666
$567$	0	0
$568$	5.37037e8	0.122966
$569$	5.56791e9	1.26707	0.633533	−	0.773716i	$-0.281604\pi$
$569$	5.56791e9	1.26707	0.633533	+	0.773716i	$0.281604\pi$
$570$	0	0
$571$	2.45821e9	0.552578	0.276289	−	0.961075i	$-0.410895\pi$
$571$	2.45821e9	0.552578	0.276289	+	0.961075i	$0.410895\pi$
$572$	3.05221e9	0.681912
$573$	0	0
$574$	−3.68872e8	−0.0814113
$575$	−2.44500e9	−0.536341
$576$	0	0
$577$	−4.96974e9	−1.07701	−0.538504	−	0.842623i	$-0.681010\pi$
$577$	−4.96974e9	−1.07701	−0.538504	+	0.842623i	$0.681010\pi$
$578$	−6.75307e8	−0.145464
$579$	0	0
$580$	−1.97355e9	−0.420000
$581$	−5.82749e8	−0.123272
$582$	0	0
$583$	−5.54486e9	−1.15891
$584$	5.35258e8	0.111203
$585$	0	0
$586$	−4.17247e8	−0.0856548
$587$	6.56154e9	1.33898	0.669488	−	0.742823i	$-0.266514\pi$
$587$	6.56154e9	1.33898	0.669488	+	0.742823i	$0.266514\pi$
$588$	0	0
$589$	2.67511e8	0.0539434
$590$	1.18156e8	0.0236850
$591$	0	0
$592$	−1.87797e9	−0.372018
$593$	1.13756e9	0.224018	0.112009	−	0.993707i	$-0.464271\pi$
$593$	1.13756e9	0.224018	0.112009	+	0.993707i	$0.464271\pi$
$594$	0	0
$595$	−2.20556e8	−0.0429250
$596$	−2.62565e9	−0.508014
$597$	0	0
$598$	−5.72642e8	−0.109504
$599$	−5.33000e9	−1.01329	−0.506644	−	0.862155i	$-0.669114\pi$
$599$	−5.33000e9	−1.01329	−0.506644	+	0.862155i	$0.669114\pi$
$600$	0	0
$601$	−4.73035e9	−0.888859	−0.444430	−	0.895814i	$-0.646594\pi$
$601$	−4.73035e9	−0.888859	−0.444430	+	0.895814i	$0.646594\pi$
$602$	6.00910e8	0.112259
$603$	0	0
$604$	4.57133e9	0.844138
$605$	−1.24554e9	−0.228673
$606$	0	0
$607$	−8.89655e7	−0.0161459	−0.00807293	−	0.999967i	$-0.502570\pi$
$607$	−8.89655e7	−0.0161459	−0.00807293	+	0.999967i	$0.502570\pi$
$608$	−1.48150e8	−0.0267325
$609$	0	0
$610$	−9.15726e8	−0.163347
$611$	−5.84267e8	−0.103626
$612$	0	0
$613$	3.09229e9	0.542210	0.271105	−	0.962550i	$-0.412611\pi$
$613$	3.09229e9	0.542210	0.271105	+	0.962550i	$0.412611\pi$
$614$	1.23012e9	0.214465
$615$	0	0
$616$	8.23058e8	0.141872
$617$	−9.53717e9	−1.63464	−0.817319	−	0.576186i	$-0.804540\pi$
$617$	−9.53717e9	−1.63464	−0.817319	+	0.576186i	$0.804540\pi$
$618$	0	0
$619$	−1.09056e9	−0.184813	−0.0924067	−	0.995721i	$-0.529456\pi$
$619$	−1.09056e9	−0.184813	−0.0924067	+	0.995721i	$0.529456\pi$
$620$	6.21531e9	1.04735
$621$	0	0
$622$	−9.86919e8	−0.164443
$623$	4.15668e9	0.688713
$624$	0	0
$625$	−7.61312e9	−1.24733
$626$	−7.17784e7	−0.0116945
$627$	0	0
$628$	−6.45662e8	−0.104027
$629$	1.57255e8	0.0251957
$630$	0	0
$631$	8.07693e9	1.27980	0.639902	−	0.768456i	$-0.278975\pi$
$631$	8.07693e9	1.27980	0.639902	+	0.768456i	$0.278975\pi$
$632$	−2.46428e9	−0.388312
$633$	0	0
$634$	−4.08227e8	−0.0636194
$635$	−5.66929e9	−0.878660
$636$	0	0
$637$	−3.54556e9	−0.543497
$638$	−2.98232e8	−0.0454654
$639$	0	0
$640$	−4.57194e9	−0.689400
$641$	5.29976e8	0.0794791	0.0397396	−	0.999210i	$-0.487347\pi$
$641$	5.29976e8	0.0794791	0.0397396	+	0.999210i	$0.487347\pi$
$642$	0	0
$643$	−4.80343e9	−0.712546	−0.356273	−	0.934382i	$-0.615953\pi$
$643$	−4.80343e9	−0.712546	−0.356273	+	0.934382i	$0.615953\pi$
$644$	3.50420e9	0.516998
$645$	0	0
$646$	3.98518e6	0.000581612 0
$647$	−7.16830e9	−1.04052	−0.520261	−	0.854007i	$-0.674165\pi$
$647$	−7.16830e9	−1.04052	−0.520261	+	0.854007i	$0.674165\pi$
$648$	0	0
$649$	−8.19196e8	−0.117634
$650$	4.34998e8	0.0621285
$651$	0	0
$652$	−5.96514e8	−0.0842858
$653$	6.92505e9	0.973255	0.486628	−	0.873609i	$-0.338227\pi$
$653$	6.92505e9	0.973255	0.486628	+	0.873609i	$0.338227\pi$
$654$	0	0
$655$	−2.30586e9	−0.320618
$656$	−6.94658e9	−0.960743
$657$	0	0
$658$	−7.79274e7	−0.0106635
$659$	−1.68761e9	−0.229706	−0.114853	−	0.993383i	$-0.536640\pi$
$659$	−1.68761e9	−0.229706	−0.114853	+	0.993383i	$0.536640\pi$
$660$	0	0
$661$	−3.72084e9	−0.501114	−0.250557	−	0.968102i	$-0.580614\pi$
$661$	−3.72084e9	−0.501114	−0.250557	+	0.968102i	$0.580614\pi$
$662$	4.46004e7	0.00597497
$663$	0	0
$664$	4.94616e8	0.0655662
$665$	−3.22263e8	−0.0424946
$666$	0	0
$667$	−2.56714e9	−0.334972
$668$	−3.59926e8	−0.0467193
$669$	0	0
$670$	−1.30394e9	−0.167493
$671$	6.34889e9	0.811277
$672$	0	0
$673$	1.31632e10	1.66460	0.832299	−	0.554326i	$-0.187024\pi$
$673$	1.31632e10	1.66460	0.832299	+	0.554326i	$0.187024\pi$
$674$	1.17596e8	0.0147940
$675$	0	0
$676$	3.18616e9	0.396692
$677$	−5.57284e9	−0.690265	−0.345133	−	0.938554i	$-0.612166\pi$
$677$	−5.57284e9	−0.690265	−0.345133	+	0.938554i	$0.612166\pi$
$678$	0	0
$679$	1.02281e9	0.125387
$680$	1.87200e8	0.0228310
$681$	0	0
$682$	9.39223e8	0.113377
$683$	−7.37541e9	−0.885755	−0.442877	−	0.896582i	$-0.646042\pi$
$683$	−7.37541e9	−0.885755	−0.442877	+	0.896582i	$0.646042\pi$
$684$	0	0
$685$	−1.57556e10	−1.87292
$686$	−1.14386e9	−0.135282
$687$	0	0
$688$	1.13163e10	1.32478
$689$	8.49172e9	0.989074
$690$	0	0
$691$	1.50339e10	1.73339	0.866697	−	0.498835i	$-0.166239\pi$
$691$	1.50339e10	1.73339	0.866697	+	0.498835i	$0.166239\pi$
$692$	1.24221e10	1.42502
$693$	0	0
$694$	−1.13229e8	−0.0128588
$695$	6.88314e9	0.777750
$696$	0	0
$697$	5.81680e8	0.0650683
$698$	−9.73813e8	−0.108388
$699$	0	0
$700$	−2.66191e9	−0.293326
$701$	1.59887e10	1.75307	0.876534	−	0.481340i	$-0.159850\pi$
$701$	1.59887e10	1.75307	0.876534	+	0.481340i	$0.159850\pi$
$702$	0	0
$703$	2.29770e8	0.0249431
$704$	7.31328e9	0.789965
$705$	0	0
$706$	1.70563e9	0.182419
$707$	−2.87938e9	−0.306430
$708$	0	0
$709$	−5.60546e8	−0.0590676	−0.0295338	−	0.999564i	$-0.509402\pi$
$709$	−5.60546e8	−0.0590676	−0.0295338	+	0.999564i	$0.509402\pi$
$710$	−7.38262e8	−0.0774117
$711$	0	0
$712$	−3.52804e9	−0.366314
$713$	8.08472e9	0.835317
$714$	0	0
$715$	−8.48317e9	−0.867935
$716$	7.98515e9	0.812994
$717$	0	0
$718$	−2.52049e9	−0.254126
$719$	1.63371e9	0.163917	0.0819584	−	0.996636i	$-0.473883\pi$
$719$	1.63371e9	0.163917	0.0819584	+	0.996636i	$0.473883\pi$
$720$	0	0
$721$	5.06369e9	0.503146
$722$	−1.47119e9	−0.145475
$723$	0	0
$724$	1.19449e10	1.16976
$725$	1.95008e9	0.190051
$726$	0	0
$727$	1.42463e9	0.137509	0.0687547	−	0.997634i	$-0.478097\pi$
$727$	1.42463e9	0.137509	0.0687547	+	0.997634i	$0.478097\pi$
$728$	−1.26048e9	−0.121081
$729$	0	0
$730$	−7.35816e8	−0.0700067
$731$	−9.47584e8	−0.0897237
$732$	0	0
$733$	−2.04751e9	−0.192027	−0.0960133	−	0.995380i	$-0.530609\pi$
$733$	−2.04751e9	−0.192027	−0.0960133	+	0.995380i	$0.530609\pi$
$734$	2.65430e8	0.0247750
$735$	0	0
$736$	−4.47739e9	−0.413954
$737$	9.04048e9	0.831869
$738$	0	0
$739$	1.10852e10	1.01038	0.505192	−	0.863007i	$-0.331422\pi$
$739$	1.10852e10	1.01038	0.505192	+	0.863007i	$0.331422\pi$
$740$	5.33845e9	0.484288
$741$	0	0
$742$	1.13260e9	0.101780
$743$	−4.13565e9	−0.369899	−0.184950	−	0.982748i	$-0.559212\pi$
$743$	−4.13565e9	−0.369899	−0.184950	+	0.982748i	$0.559212\pi$
$744$	0	0
$745$	7.29762e9	0.646598
$746$	6.92102e8	0.0610357
$747$	0	0
$748$	−6.41950e8	−0.0560849
$749$	2.79008e9	0.242622
$750$	0	0
$751$	−7.64895e8	−0.0658964	−0.0329482	−	0.999457i	$-0.510490\pi$
$751$	−7.64895e8	−0.0658964	−0.0329482	+	0.999457i	$0.510490\pi$
$752$	−1.46752e9	−0.125841
$753$	0	0
$754$	4.56729e8	0.0388024
$755$	−1.27053e10	−1.07442
$756$	0	0
$757$	6.25169e9	0.523795	0.261898	−	0.965096i	$-0.415652\pi$
$757$	6.25169e9	0.523795	0.261898	+	0.965096i	$0.415652\pi$
$758$	1.34708e9	0.112344
$759$	0	0
$760$	2.73525e8	0.0226021
$761$	1.93548e10	1.59200	0.795999	−	0.605298i	$-0.206946\pi$
$761$	1.93548e10	1.59200	0.795999	+	0.605298i	$0.206946\pi$
$762$	0	0
$763$	4.82211e9	0.393008
$764$	2.61647e9	0.212270
$765$	0	0
$766$	−3.06503e9	−0.246397
$767$	1.25456e9	0.100394
$768$	0	0
$769$	2.15998e10	1.71281	0.856403	−	0.516308i	$-0.172694\pi$
$769$	2.15998e10	1.71281	0.856403	+	0.516308i	$0.172694\pi$
$770$	−1.13145e9	−0.0893140
$771$	0	0
$772$	1.08937e10	0.852147
$773$	−1.04145e10	−0.810977	−0.405489	−	0.914100i	$-0.632899\pi$
$773$	−1.04145e10	−0.810977	−0.405489	+	0.914100i	$0.632899\pi$
$774$	0	0
$775$	−6.14142e9	−0.473928
$776$	−8.68126e8	−0.0666909
$777$	0	0
$778$	−1.07457e9	−0.0818100
$779$	8.49914e8	0.0644160
$780$	0	0
$781$	5.11851e9	0.384472
$782$	1.20440e8	0.00900631
$783$	0	0
$784$	−8.90550e9	−0.660013
$785$	1.79452e9	0.132405
$786$	0	0
$787$	−1.48715e9	−0.108753	−0.0543766	−	0.998520i	$-0.517317\pi$
$787$	−1.48715e9	−0.108753	−0.0543766	+	0.998520i	$0.517317\pi$
$788$	2.53953e9	0.184889
$789$	0	0
$790$	3.38764e9	0.244457
$791$	−6.12938e9	−0.440351
$792$	0	0
$793$	−9.72306e9	−0.692384
$794$	2.38140e9	0.168834
$795$	0	0
$796$	1.83708e10	1.29102
$797$	−7.05171e9	−0.493390	−0.246695	−	0.969093i	$-0.579345\pi$
$797$	−7.05171e9	−0.493390	−0.246695	+	0.969093i	$0.579345\pi$
$798$	0	0
$799$	1.22885e8	0.00852285
$800$	3.40117e9	0.234863
$801$	0	0
$802$	−6.71117e8	−0.0459397
$803$	5.10155e9	0.347694
$804$	0	0
$805$	−9.73942e9	−0.658032
$806$	−1.43838e9	−0.0967612
$807$	0	0
$808$	2.44391e9	0.162984
$809$	−2.75982e10	−1.83257	−0.916285	−	0.400527i	$-0.868827\pi$
$809$	−2.75982e10	−1.83257	−0.916285	+	0.400527i	$0.868827\pi$
$810$	0	0
$811$	6.33683e9	0.417157	0.208578	−	0.978006i	$-0.433116\pi$
$811$	6.33683e9	0.417157	0.208578	+	0.978006i	$0.433116\pi$
$812$	−2.79489e9	−0.183197
$813$	0	0
$814$	8.06716e8	0.0524246
$815$	1.65792e9	0.107279
$816$	0	0
$817$	−1.38455e9	−0.0888242
$818$	7.24912e8	0.0463072
$819$	0	0
$820$	1.97468e10	1.25068
$821$	1.25736e10	0.792974	0.396487	−	0.918040i	$-0.370229\pi$
$821$	1.25736e10	0.792974	0.396487	+	0.918040i	$0.370229\pi$
$822$	0	0
$823$	8.14145e9	0.509099	0.254549	−	0.967060i	$-0.418073\pi$
$823$	8.14145e9	0.509099	0.254549	+	0.967060i	$0.418073\pi$
$824$	−4.29788e9	−0.267614
$825$	0	0
$826$	1.67329e8	0.0103310
$827$	−3.01027e10	−1.85070	−0.925351	−	0.379111i	$-0.876230\pi$
$827$	−3.01027e10	−1.85070	−0.925351	+	0.379111i	$0.876230\pi$
$828$	0	0
$829$	−1.24726e10	−0.760354	−0.380177	−	0.924914i	$-0.624137\pi$
$829$	−1.24726e10	−0.760354	−0.380177	+	0.924914i	$0.624137\pi$
$830$	−6.79946e8	−0.0412764
$831$	0	0
$832$	−1.12000e10	−0.674195
$833$	7.45713e8	0.0447007
$834$	0	0
$835$	1.00036e9	0.0594641
$836$	−9.37976e8	−0.0555226
$837$	0	0
$838$	−5.75107e8	−0.0337594
$839$	2.55936e10	1.49611	0.748056	−	0.663636i	$-0.230987\pi$
$839$	2.55936e10	1.49611	0.748056	+	0.663636i	$0.230987\pi$
$840$	0	0
$841$	−1.52024e10	−0.881303
$842$	3.03999e9	0.175501
$843$	0	0
$844$	−1.32226e10	−0.757042
$845$	−8.85545e9	−0.504908
$846$	0	0
$847$	−1.76390e9	−0.0997432
$848$	2.13289e10	1.20111
$849$	0	0
$850$	−9.14901e7	−0.00510985
$851$	6.94411e9	0.386245
$852$	0	0
$853$	−4.79390e9	−0.264465	−0.132232	−	0.991219i	$-0.542214\pi$
$853$	−4.79390e9	−0.264465	−0.132232	+	0.991219i	$0.542214\pi$
$854$	−1.29683e9	−0.0712491
$855$	0	0
$856$	−2.36812e9	−0.129046
$857$	−2.39828e10	−1.30157	−0.650784	−	0.759263i	$-0.725560\pi$
$857$	−2.39828e10	−1.30157	−0.650784	+	0.759263i	$0.725560\pi$
$858$	0	0
$859$	−1.01440e10	−0.546051	−0.273026	−	0.962007i	$-0.588024\pi$
$859$	−1.01440e10	−0.546051	−0.273026	+	0.962007i	$0.588024\pi$
$860$	−3.21684e10	−1.72459
$861$	0	0
$862$	−1.76755e9	−0.0939931
$863$	−1.90673e10	−1.00984	−0.504918	−	0.863168i	$-0.668477\pi$
$863$	−1.90673e10	−1.00984	−0.504918	+	0.863168i	$0.668477\pi$
$864$	0	0
$865$	−3.45253e10	−1.81376
$866$	−1.14332e9	−0.0598214
$867$	0	0
$868$	8.80196e9	0.456836
$869$	−2.34871e10	−1.21412
$870$	0	0
$871$	−1.38451e10	−0.709958
$872$	−4.09283e9	−0.209034
$873$	0	0
$874$	1.75979e8	0.00891602
$875$	−6.01337e9	−0.303452
$876$	0	0
$877$	9.47943e8	0.0474552	0.0237276	−	0.999718i	$-0.492447\pi$
$877$	9.47943e8	0.0474552	0.0237276	+	0.999718i	$0.492447\pi$
$878$	6.13870e8	0.0306087
$879$	0	0
$880$	−2.13075e10	−1.05400
$881$	1.71902e10	0.846967	0.423483	−	0.905904i	$-0.360807\pi$
$881$	1.71902e10	0.846967	0.423483	+	0.905904i	$0.360807\pi$
$882$	0	0
$883$	−2.18303e10	−1.06708	−0.533541	−	0.845774i	$-0.679139\pi$
$883$	−2.18303e10	−1.06708	−0.533541	+	0.845774i	$0.679139\pi$
$884$	9.83119e8	0.0478656
$885$	0	0
$886$	5.15620e7	0.00249065
$887$	−1.14245e10	−0.549675	−0.274837	−	0.961491i	$-0.588624\pi$
$887$	−1.14245e10	−0.549675	−0.274837	+	0.961491i	$0.588624\pi$
$888$	0	0
$889$	−8.02870e9	−0.383256
$890$	4.84998e9	0.230608
$891$	0	0
$892$	−7.25117e8	−0.0342083
$893$	1.79551e8	0.00843741
$894$	0	0
$895$	−2.21935e10	−1.03478
$896$	−6.47466e9	−0.300704
$897$	0	0
$898$	3.11729e9	0.143651
$899$	−6.44822e9	−0.295993
$900$	0	0
$901$	−1.78601e9	−0.0813478
$902$	2.98402e9	0.135388
$903$	0	0
$904$	5.20240e9	0.234215
$905$	−3.31992e10	−1.48887
$906$	0	0
$907$	5.60191e9	0.249293	0.124647	−	0.992201i	$-0.460220\pi$
$907$	5.60191e9	0.249293	0.124647	+	0.992201i	$0.460220\pi$
$908$	−2.56448e8	−0.0113684
$909$	0	0
$910$	1.73277e9	0.0762249
$911$	−3.71793e10	−1.62925	−0.814623	−	0.579990i	$-0.803056\pi$
$911$	−3.71793e10	−1.62925	−0.814623	+	0.579990i	$0.803056\pi$
$912$	0	0
$913$	4.71419e9	0.205003
$914$	−5.10519e9	−0.221157
$915$	0	0
$916$	2.56204e10	1.10142
$917$	−3.26549e9	−0.139848
$918$	0	0
$919$	2.00291e9	0.0851251	0.0425626	−	0.999094i	$-0.486448\pi$
$919$	2.00291e9	0.0851251	0.0425626	+	0.999094i	$0.486448\pi$
$920$	8.26646e9	0.349995
$921$	0	0
$922$	2.84433e9	0.119515
$923$	−7.83878e9	−0.328127
$924$	0	0
$925$	−5.27498e9	−0.219141
$926$	2.45832e9	0.101742
$927$	0	0
$928$	3.57108e9	0.146684
$929$	−9.73670e9	−0.398434	−0.199217	−	0.979955i	$-0.563840\pi$
$929$	−9.73670e9	−0.398434	−0.199217	+	0.979955i	$0.563840\pi$
$930$	0	0
$931$	1.08959e9	0.0442526
$932$	3.31129e10	1.33981
$933$	0	0
$934$	1.85447e9	0.0744742
$935$	1.78421e9	0.0713846
$936$	0	0
$937$	1.30317e10	0.517504	0.258752	−	0.965944i	$-0.416689\pi$
$937$	1.30317e10	0.517504	0.258752	+	0.965944i	$0.416689\pi$
$938$	−1.84661e9	−0.0730576
$939$	0	0
$940$	4.17167e9	0.163818
$941$	−8.01351e9	−0.313516	−0.156758	−	0.987637i	$-0.550104\pi$
$941$	−8.01351e9	−0.313516	−0.156758	+	0.987637i	$0.550104\pi$
$942$	0	0
$943$	2.56861e10	0.997486
$944$	3.15113e9	0.121917
$945$	0	0
$946$	−4.86111e9	−0.186688
$947$	−2.06839e10	−0.791423	−0.395711	−	0.918375i	$-0.629502\pi$
$947$	−2.06839e10	−0.791423	−0.395711	+	0.918375i	$0.629502\pi$
$948$	0	0
$949$	−7.81280e9	−0.296739
$950$	−1.33680e8	−0.00505862
$951$	0	0
$952$	2.65108e8	0.00995848
$953$	−1.62010e10	−0.606339	−0.303169	−	0.952937i	$-0.598045\pi$
$953$	−1.62010e10	−0.606339	−0.303169	+	0.952937i	$0.598045\pi$
$954$	0	0
$955$	−7.27209e9	−0.270176
$956$	2.70197e10	1.00018
$957$	0	0
$958$	4.70890e9	0.173037
$959$	−2.23127e10	−0.816933
$960$	0	0
$961$	−7.20518e9	−0.261886
$962$	−1.23545e9	−0.0447418
$963$	0	0
$964$	2.48746e10	0.894308
$965$	−3.02774e10	−1.08461
$966$	0	0
$967$	−1.30620e10	−0.464533	−0.232266	−	0.972652i	$-0.574614\pi$
$967$	−1.30620e10	−0.464533	−0.232266	+	0.972652i	$0.574614\pi$
$968$	1.49714e9	0.0530515
$969$	0	0
$970$	1.19341e9	0.0419844
$971$	−2.52039e10	−0.883489	−0.441744	−	0.897141i	$-0.645640\pi$
$971$	−2.52039e10	−0.883489	−0.441744	+	0.897141i	$0.645640\pi$
$972$	0	0
$973$	9.74772e9	0.339241
$974$	−2.76651e9	−0.0959347
$975$	0	0
$976$	−2.44217e10	−0.840818
$977$	−3.47488e10	−1.19209	−0.596045	−	0.802951i	$-0.703262\pi$
$977$	−3.47488e10	−1.19209	−0.596045	+	0.802951i	$0.703262\pi$
$978$	0	0
$979$	−3.36258e10	−1.14534
$980$	2.53153e10	0.859197
$981$	0	0
$982$	3.94944e9	0.133090
$983$	−1.96316e10	−0.659203	−0.329602	−	0.944120i	$-0.606914\pi$
$983$	−1.96316e10	−0.659203	−0.329602	+	0.944120i	$0.606914\pi$
$984$	0	0
$985$	−7.05824e9	−0.235326
$986$	−9.60606e7	−0.00319136
$987$	0	0
$988$	1.43647e9	0.0473857
$989$	−4.18438e10	−1.37545
$990$	0	0
$991$	2.05111e10	0.669469	0.334734	−	0.942313i	$-0.391353\pi$
$991$	2.05111e10	0.669469	0.334734	+	0.942313i	$0.391353\pi$
$992$	−1.12464e10	−0.365784
$993$	0	0
$994$	−1.04551e9	−0.0337656
$995$	−5.10589e10	−1.64320
$996$	0	0
$997$	3.29464e10	1.05287	0.526436	−	0.850215i	$-0.323528\pi$
$997$	3.29464e10	1.05287	0.526436	+	0.850215i	$0.323528\pi$
$998$	7.49922e9	0.238814
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	531.8.a.g.1.19	✓	33
3.2	odd	2		531.8.a.h.1.15	yes	33

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
531.8.a.g.1.19	✓	33	1.1	even	1	trivial
531.8.a.h.1.15	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)

\(f(q)\)	\(=\)	\(q+1.65238 q^{2} -125.270 q^{4} +348.169 q^{5} +493.067 q^{7} -418.497 q^{8} +O(q^{10})\)	\(q+1.65238 q^{2} -125.270 q^{4} +348.169 q^{5} +493.067 q^{7} -418.497 q^{8} +575.306 q^{10} -3988.70 q^{11} +6108.53 q^{13} +814.733 q^{14} +15343.0 q^{16} -1284.76 q^{17} -1877.22 q^{19} -43615.0 q^{20} -6590.85 q^{22} -56733.2 q^{23} +43096.4 q^{25} +10093.6 q^{26} -61766.3 q^{28} +45249.3 q^{29} -142504. q^{31} +78920.1 q^{32} -2122.92 q^{34} +171670. q^{35} -122399. q^{37} -3101.87 q^{38} -145708. q^{40} -452752. q^{41} +737555. q^{43} +499664. q^{44} -93744.7 q^{46} -95647.8 q^{47} -580428. q^{49} +71211.6 q^{50} -765213. q^{52} +1.39014e6 q^{53} -1.38874e6 q^{55} -206347. q^{56} +74769.0 q^{58} +205379. q^{59} -1.59172e6 q^{61} -235471. q^{62} -1.83350e6 q^{64} +2.12680e6 q^{65} -2.26652e6 q^{67} +160942. q^{68} +283665. q^{70} -1.28325e6 q^{71} -1.27900e6 q^{73} -202250. q^{74} +235158. q^{76} -1.96670e6 q^{77} +5.88841e6 q^{79} +5.34195e6 q^{80} -748118. q^{82} -1.18189e6 q^{83} -447315. q^{85} +1.21872e6 q^{86} +1.66926e6 q^{88} +8.43025e6 q^{89} +3.01191e6 q^{91} +7.10695e6 q^{92} -158046. q^{94} -653588. q^{95} +2.07439e6 q^{97} -959087. q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 33 q - 24 q^{2} + 1776 q^{4} - 1000 q^{5} + 154 q^{7} - 4608 q^{8}+O(q^{10}) \) 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

L-functions

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