LMFDB - Embedded newform 531.8.a.c.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("531.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$165.876448532$
Analytic rank:	$0$
Dimension:	$17$
Coefficient field:	$\mathbb{Q}[x]/(x^{17} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{17} - 2 x^{16} - 1669 x^{15} + 2385 x^{14} + 1108684 x^{13} - 848131 x^{12} - 377920980 x^{11} + \cdots + 24\!\cdots\!16 $ x^17 - 2x^16 - 1669x^15 + 2385x^14 + 1108684x^13 - 848131x^12 - 377920980x^11 + 12724944x^10 + 71331230512x^9 + 50741131904x^8 - 7480805165760x^7 - 10751966150272x^6 + 413177144536320x^5 + 886760582981376x^4 - 10454479722123264x^3 - 29180140031461376x^2 + 79787300207378432x + 248723246810300416
Coefficient ring:	$\Z[a_1, \ldots, a_{31}]$
Coefficient ring index:	multiple of $ 2^{10}\cdot 3^{5} $
Twist minimal:	no (minimal twist has level 177)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$21.5848$ of defining polynomial
Character	$\chi$	$=$	531.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-21.5848 q^{2} +337.903 q^{4} +113.334 q^{5} -647.523 q^{7} -4530.72 q^{8} +O(q^{10})$	\(q-21.5848 q^{2} +337.903 q^{4} +113.334 q^{5} -647.523 q^{7} -4530.72 q^{8} -2446.30 q^{10} -797.052 q^{11} +863.046 q^{13} +13976.6 q^{14} +54543.1 q^{16} -30234.1 q^{17} +36679.8 q^{19} +38296.1 q^{20} +17204.2 q^{22} -55059.3 q^{23} -65280.3 q^{25} -18628.7 q^{26} -218800. q^{28} -201168. q^{29} -17365.2 q^{31} -597369. q^{32} +652597. q^{34} -73386.6 q^{35} -157061. q^{37} -791727. q^{38} -513487. q^{40} -264460. q^{41} +97565.6 q^{43} -269327. q^{44} +1.18844e6 q^{46} -236490. q^{47} -404257. q^{49} +1.40906e6 q^{50} +291626. q^{52} +524092. q^{53} -90333.5 q^{55} +2.93375e6 q^{56} +4.34217e6 q^{58} +205379. q^{59} +2.50976e6 q^{61} +374823. q^{62} +5.91257e6 q^{64} +97812.8 q^{65} -1.86827e6 q^{67} -1.02162e7 q^{68} +1.58404e6 q^{70} +3.17472e6 q^{71} +303181. q^{73} +3.39014e6 q^{74} +1.23942e7 q^{76} +516110. q^{77} +3.54094e6 q^{79} +6.18161e6 q^{80} +5.70830e6 q^{82} -9.87483e6 q^{83} -3.42656e6 q^{85} -2.10593e6 q^{86} +3.61122e6 q^{88} +6.49191e6 q^{89} -558842. q^{91} -1.86047e7 q^{92} +5.10459e6 q^{94} +4.15709e6 q^{95} -8435.50 q^{97} +8.72581e6 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17 q - 2 q^{2} + 1166 q^{4} + 318 q^{5} + 3145 q^{7} - 2355 q^{8}+O(q^{10}) $ 17 * q - 2 * q^2 + 1166 * q^4 + 318 * q^5 + 3145 * q^7 - 2355 * q^8	\( 17 q - 2 q^{2} + 1166 q^{4} + 318 q^{5} + 3145 q^{7} - 2355 q^{8} + 6521 q^{10} + 1764 q^{11} + 18192 q^{13} + 7827 q^{14} + 139226 q^{16} + 15507 q^{17} + 52083 q^{19} - 721 q^{20} - 234434 q^{22} - 63823 q^{23} + 202153 q^{25} + 367956 q^{26} + 182306 q^{28} + 502955 q^{29} + 347531 q^{31} + 243908 q^{32} - 330872 q^{34} - 92641 q^{35} + 447615 q^{37} - 775669 q^{38} + 2203270 q^{40} - 940335 q^{41} + 478562 q^{43} + 596924 q^{44} - 3078663 q^{46} - 703121 q^{47} + 1895082 q^{49} + 876967 q^{50} + 6278296 q^{52} + 1005974 q^{53} + 5212846 q^{55} - 3425294 q^{56} + 6710166 q^{58} + 3491443 q^{59} + 11510749 q^{61} - 5996234 q^{62} + 29496941 q^{64} - 11094180 q^{65} + 14007144 q^{67} - 19688159 q^{68} + 30909708 q^{70} - 5229074 q^{71} + 5452211 q^{73} - 12819662 q^{74} + 41929340 q^{76} - 9930777 q^{77} + 15275654 q^{79} - 36576105 q^{80} + 32025935 q^{82} - 7826609 q^{83} + 11836945 q^{85} - 51649136 q^{86} + 30223741 q^{88} + 6436185 q^{89} + 11633535 q^{91} - 43357972 q^{92} - 4494252 q^{94} - 23741055 q^{95} + 26377540 q^{97} - 26517816 q^{98}+O(q^{100}) \) 17 * q - 2 * q^2 + 1166 * q^4 + 318 * q^5 + 3145 * q^7 - 2355 * q^8 + 6521 * q^10 + 1764 * q^11 + 18192 * q^13 + 7827 * q^14 + 139226 * q^16 + 15507 * q^17 + 52083 * q^19 - 721 * q^20 - 234434 * q^22 - 63823 * q^23 + 202153 * q^25 + 367956 * q^26 + 182306 * q^28 + 502955 * q^29 + 347531 * q^31 + 243908 * q^32 - 330872 * q^34 - 92641 * q^35 + 447615 * q^37 - 775669 * q^38 + 2203270 * q^40 - 940335 * q^41 + 478562 * q^43 + 596924 * q^44 - 3078663 * q^46 - 703121 * q^47 + 1895082 * q^49 + 876967 * q^50 + 6278296 * q^52 + 1005974 * q^53 + 5212846 * q^55 - 3425294 * q^56 + 6710166 * q^58 + 3491443 * q^59 + 11510749 * q^61 - 5996234 * q^62 + 29496941 * q^64 - 11094180 * q^65 + 14007144 * q^67 - 19688159 * q^68 + 30909708 * q^70 - 5229074 * q^71 + 5452211 * q^73 - 12819662 * q^74 + 41929340 * q^76 - 9930777 * q^77 + 15275654 * q^79 - 36576105 * q^80 + 32025935 * q^82 - 7826609 * q^83 + 11836945 * q^85 - 51649136 * q^86 + 30223741 * q^88 + 6436185 * q^89 + 11633535 * q^91 - 43357972 * q^92 - 4494252 * q^94 - 23741055 * q^95 + 26377540 * q^97 - 26517816 * 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 $

$2$	−21.5848	−1.90784	−0.953922	−	0.300054i	$-0.902995\pi$
$2$	−21.5848	−1.90784	−0.953922	+	0.300054i	$0.902995\pi$
$3$	0	0
$3$	0	0
$4$	337.903	2.63987
$5$	113.334	0.405478	0.202739	−	0.979233i	$-0.435016\pi$
$5$	113.334	0.405478	0.202739	+	0.979233i	$0.435016\pi$
$6$	0	0
$7$	−647.523	−0.713530	−0.356765	−	0.934194i	$-0.616120\pi$
$7$	−647.523	−0.713530	−0.356765	+	0.934194i	$0.616120\pi$
$8$	−4530.72	−3.12862
$9$	0	0
$10$	−2446.30	−0.773588
$11$	−797.052	−0.180556	−0.0902781	−	0.995917i	$-0.528776\pi$
$11$	−797.052	−0.180556	−0.0902781	+	0.995917i	$0.528776\pi$
$12$	0	0
$13$	863.046	0.108951	0.0544756	−	0.998515i	$-0.482651\pi$
$13$	863.046	0.108951	0.0544756	+	0.998515i	$0.482651\pi$
$14$	13976.6	1.36130
$15$	0	0
$16$	54543.1	3.32905
$17$	−30234.1	−1.49254	−0.746270	−	0.665644i	$-0.768157\pi$
$17$	−30234.1	−1.49254	−0.746270	+	0.665644i	$0.768157\pi$
$18$	0	0
$19$	36679.8	1.22685	0.613423	−	0.789755i	$-0.289792\pi$
$19$	36679.8	1.22685	0.613423	+	0.789755i	$0.289792\pi$
$20$	38296.1	1.07041
$21$	0	0
$22$	17204.2	0.344473
$23$	−55059.3	−0.943591	−0.471795	−	0.881708i	$-0.656394\pi$
$23$	−55059.3	−0.943591	−0.471795	+	0.881708i	$0.656394\pi$
$24$	0	0
$25$	−65280.3	−0.835588
$26$	−18628.7	−0.207862
$27$	0	0
$28$	−218800.	−1.88363
$29$	−201168.	−1.53167	−0.765836	−	0.643036i	$-0.777675\pi$
$29$	−201168.	−1.53167	−0.765836	+	0.643036i	$0.777675\pi$
$30$	0	0
$31$	−17365.2	−0.104692	−0.0523459	−	0.998629i	$-0.516670\pi$
$31$	−17365.2	−0.104692	−0.0523459	+	0.998629i	$0.516670\pi$
$32$	−597369.	−3.22268
$33$	0	0
$34$	652597.	2.84753
$35$	−73386.6	−0.289320
$36$	0	0
$37$	−157061.	−0.509757	−0.254879	−	0.966973i	$-0.582036\pi$
$37$	−157061.	−0.509757	−0.254879	+	0.966973i	$0.582036\pi$
$38$	−791727.	−2.34063
$39$	0	0
$40$	−513487.	−1.26858
$41$	−264460.	−0.599261	−0.299630	−	0.954055i	$-0.596863\pi$
$41$	−264460.	−0.599261	−0.299630	+	0.954055i	$0.596863\pi$
$42$	0	0
$43$	97565.6	0.187136	0.0935680	−	0.995613i	$-0.470173\pi$
$43$	97565.6	0.187136	0.0935680	+	0.995613i	$0.470173\pi$
$44$	−269327.	−0.476645
$45$	0	0
$46$	1.18844e6	1.80022
$47$	−236490.	−0.332254	−0.166127	−	0.986104i	$-0.553126\pi$
$47$	−236490.	−0.332254	−0.166127	+	0.986104i	$0.553126\pi$
$48$	0	0
$49$	−404257.	−0.490876
$50$	1.40906e6	1.59417
$51$	0	0
$52$	291626.	0.287617
$53$	524092.	0.483551	0.241775	−	0.970332i	$-0.422270\pi$
$53$	524092.	0.483551	0.241775	+	0.970332i	$0.422270\pi$
$54$	0	0
$55$	−90333.5	−0.0732115
$56$	2.93375e6	2.23236
$57$	0	0
$58$	4.34217e6	2.92219
$59$	205379.	0.130189
$59$	205379.	0.130189
$60$	0	0
$61$	2.50976e6	1.41572	0.707860	−	0.706353i	$-0.249661\pi$
$61$	2.50976e6	1.41572	0.707860	+	0.706353i	$0.249661\pi$
$62$	374823.	0.199736
$63$	0	0
$64$	5.91257e6	2.81933
$65$	97812.8	0.0441773
$66$	0	0
$67$	−1.86827e6	−0.758888	−0.379444	−	0.925215i	$-0.623885\pi$
$67$	−1.86827e6	−0.758888	−0.379444	+	0.925215i	$0.623885\pi$
$68$	−1.02162e7	−3.94011
$69$	0	0
$70$	1.58404e6	0.551978
$71$	3.17472e6	1.05269	0.526345	−	0.850271i	$-0.323562\pi$
$71$	3.17472e6	1.05269	0.526345	+	0.850271i	$0.323562\pi$
$72$	0	0
$73$	303181.	0.0912162	0.0456081	−	0.998959i	$-0.485477\pi$
$73$	303181.	0.0912162	0.0456081	+	0.998959i	$0.485477\pi$
$74$	3.39014e6	0.972538
$75$	0	0
$76$	1.23942e7	3.23871
$77$	516110.	0.128832
$78$	0	0
$79$	3.54094e6	0.808023	0.404011	−	0.914754i	$-0.367616\pi$
$79$	3.54094e6	0.808023	0.404011	+	0.914754i	$0.367616\pi$
$80$	6.18161e6	1.34985
$81$	0	0
$82$	5.70830e6	1.14330
$83$	−9.87483e6	−1.89564	−0.947821	−	0.318804i	$-0.896719\pi$
$83$	−9.87483e6	−1.89564	−0.947821	+	0.318804i	$0.896719\pi$
$84$	0	0
$85$	−3.42656e6	−0.605191
$86$	−2.10593e6	−0.357026
$87$	0	0
$88$	3.61122e6	0.564891
$89$	6.49191e6	0.976130	0.488065	−	0.872807i	$-0.337703\pi$
$89$	6.49191e6	0.976130	0.488065	+	0.872807i	$0.337703\pi$
$90$	0	0
$91$	−558842.	−0.0777399
$92$	−1.86047e7	−2.49096
$93$	0	0
$94$	5.10459e6	0.633889
$95$	4.15709e6	0.497458
$96$	0	0
$97$	−8435.50	−0.000938447 0	−0.000469223	−	1.00000i	$-0.500149\pi$
$97$	−8435.50	−0.000938447 0	−0.000469223		1.00000i	$0.500149\pi$
$98$	8.72581e6	0.936514
$99$	0	0
$100$	−2.20584e7	−2.20584
$101$	−3.74750e6	−0.361923	−0.180962	−	0.983490i	$-0.557921\pi$
$101$	−3.74750e6	−0.361923	−0.180962	+	0.983490i	$0.557921\pi$
$102$	0	0
$103$	−7.16189e6	−0.645799	−0.322900	−	0.946433i	$-0.604658\pi$
$103$	−7.16189e6	−0.645799	−0.322900	+	0.946433i	$0.604658\pi$
$104$	−3.91022e6	−0.340867
$105$	0	0
$106$	−1.13124e7	−0.922539
$107$	1.89118e7	1.49242	0.746208	−	0.665712i	$-0.231872\pi$
$107$	1.89118e7	1.49242	0.746208	+	0.665712i	$0.231872\pi$
$108$	0	0
$109$	−1.60040e7	−1.18368	−0.591842	−	0.806054i	$-0.701599\pi$
$109$	−1.60040e7	−1.18368	−0.591842	+	0.806054i	$0.701599\pi$
$110$	1.94983e6	0.139676
$111$	0	0
$112$	−3.53179e7	−2.37537
$113$	4.77754e6	0.311480	0.155740	−	0.987798i	$-0.450224\pi$
$113$	4.77754e6	0.311480	0.155740	+	0.987798i	$0.450224\pi$
$114$	0	0
$115$	−6.24012e6	−0.382605
$116$	−6.79754e7	−4.04342
$117$	0	0
$118$	−4.43306e6	−0.248380
$119$	1.95773e7	1.06497
$120$	0	0
$121$	−1.88519e7	−0.967399
$122$	−5.41726e7	−2.70097
$123$	0	0
$124$	−5.86775e6	−0.276373
$125$	−1.62528e7	−0.744290
$126$	0	0
$127$	2.70787e7	1.17304	0.586522	−	0.809933i	$-0.300497\pi$
$127$	2.70787e7	1.17304	0.586522	+	0.809933i	$0.300497\pi$
$128$	−5.11584e7	−2.15617
$129$	0	0
$130$	−2.11127e6	−0.0842834
$131$	−6.72224e6	−0.261255	−0.130627	−	0.991432i	$-0.541699\pi$
$131$	−6.72224e6	−0.261255	−0.130627	+	0.991432i	$0.541699\pi$
$132$	0	0
$133$	−2.37510e7	−0.875390
$134$	4.03262e7	1.44784
$135$	0	0
$136$	1.36982e8	4.66959
$137$	−4.39105e7	−1.45897	−0.729485	−	0.683997i	$-0.760240\pi$
$137$	−4.39105e7	−1.45897	−0.729485	+	0.683997i	$0.760240\pi$
$138$	0	0
$139$	8.55233e6	0.270105	0.135052	−	0.990838i	$-0.456880\pi$
$139$	8.55233e6	0.270105	0.135052	+	0.990838i	$0.456880\pi$
$140$	−2.47976e7	−0.763768
$141$	0	0
$142$	−6.85256e7	−2.00837
$143$	−687893.	−0.0196718
$144$	0	0
$145$	−2.27993e7	−0.621059
$146$	−6.54410e6	−0.174026
$147$	0	0
$148$	−5.30716e7	−1.34569
$149$	4.40487e7	1.09089	0.545445	−	0.838146i	$-0.316361\pi$
$149$	4.40487e7	1.09089	0.545445	+	0.838146i	$0.316361\pi$
$150$	0	0
$151$	−5.79273e7	−1.36919	−0.684596	−	0.728923i	$-0.740021\pi$
$151$	−5.79273e7	−1.36919	−0.684596	+	0.728923i	$0.740021\pi$
$152$	−1.66186e8	−3.83833
$153$	0	0
$154$	−1.11401e7	−0.245792
$155$	−1.96807e6	−0.0424502
$156$	0	0
$157$	−6.48864e7	−1.33815	−0.669075	−	0.743195i	$-0.733309\pi$
$157$	−6.48864e7	−1.33815	−0.669075	+	0.743195i	$0.733309\pi$
$158$	−7.64304e7	−1.54158
$159$	0	0
$160$	−6.77025e7	−1.30673
$161$	3.56522e7	0.673280
$162$	0	0
$163$	6.81238e7	1.23209	0.616045	−	0.787711i	$-0.288734\pi$
$163$	6.81238e7	1.23209	0.616045	+	0.787711i	$0.288734\pi$
$164$	−8.93618e7	−1.58197
$165$	0	0
$166$	2.13146e8	3.61659
$167$	−3.52225e7	−0.585210	−0.292605	−	0.956233i	$-0.594522\pi$
$167$	−3.52225e7	−0.585210	−0.292605	+	0.956233i	$0.594522\pi$
$168$	0	0
$169$	−6.20037e7	−0.988130
$170$	7.39617e7	1.15461
$171$	0	0
$172$	3.29678e7	0.494015
$173$	5.35823e7	0.786792	0.393396	−	0.919369i	$-0.371300\pi$
$173$	5.35823e7	0.786792	0.393396	+	0.919369i	$0.371300\pi$
$174$	0	0
$175$	4.22705e7	0.596217
$176$	−4.34737e7	−0.601080
$177$	0	0
$178$	−1.40127e8	−1.86230
$179$	1.25733e8	1.63857	0.819283	−	0.573390i	$-0.194372\pi$
$179$	1.25733e8	1.63857	0.819283	+	0.573390i	$0.194372\pi$
$180$	0	0
$181$	6.35900e7	0.797102	0.398551	−	0.917146i	$-0.369513\pi$
$181$	6.35900e7	0.797102	0.398551	+	0.917146i	$0.369513\pi$
$182$	1.20625e7	0.148316
$183$	0	0
$184$	2.49459e8	2.95213
$185$	−1.78005e7	−0.206695
$186$	0	0
$187$	2.40982e7	0.269487
$188$	−7.99108e7	−0.877108
$189$	0	0
$190$	−8.97299e7	−0.949073
$191$	−2.21042e7	−0.229540	−0.114770	−	0.993392i	$-0.536613\pi$
$191$	−2.21042e7	−0.229540	−0.114770	+	0.993392i	$0.536613\pi$
$192$	0	0
$193$	−2.73971e6	−0.0274318	−0.0137159	−	0.999906i	$-0.504366\pi$
$193$	−2.73971e6	−0.0274318	−0.0137159	+	0.999906i	$0.504366\pi$
$194$	182078.	0.00179041
$195$	0	0
$196$	−1.36600e8	−1.29585
$197$	−1.45954e7	−0.136014	−0.0680072	−	0.997685i	$-0.521664\pi$
$197$	−1.45954e7	−0.136014	−0.0680072	+	0.997685i	$0.521664\pi$
$198$	0	0
$199$	−1.26330e8	−1.13637	−0.568184	−	0.822901i	$-0.692354\pi$
$199$	−1.26330e8	−1.13637	−0.568184	+	0.822901i	$0.692354\pi$
$200$	2.95767e8	2.61424
$201$	0	0
$202$	8.08890e7	0.690493
$203$	1.30261e8	1.09289
$204$	0	0
$205$	−2.99724e7	−0.242987
$206$	1.54588e8	1.23208
$207$	0	0
$208$	4.70732e7	0.362704
$209$	−2.92357e7	−0.221514
$210$	0	0
$211$	2.01964e8	1.48008	0.740041	−	0.672562i	$-0.234806\pi$
$211$	2.01964e8	1.48008	0.740041	+	0.672562i	$0.234806\pi$
$212$	1.77092e8	1.27651
$213$	0	0
$214$	−4.08208e8	−2.84730
$215$	1.10575e7	0.0758795
$216$	0	0
$217$	1.12443e7	0.0747007
$218$	3.45443e8	2.25829
$219$	0	0
$220$	−3.05240e7	−0.193269
$221$	−2.60934e7	−0.162614
$222$	0	0
$223$	−2.44131e8	−1.47420	−0.737100	−	0.675784i	$-0.763805\pi$
$223$	−2.44131e8	−1.47420	−0.737100	+	0.675784i	$0.763805\pi$
$224$	3.86810e8	2.29948
$225$	0	0
$226$	−1.03122e8	−0.594255
$227$	−6.69826e7	−0.380077	−0.190038	−	0.981777i	$-0.560861\pi$
$227$	−6.69826e7	−0.380077	−0.190038	+	0.981777i	$0.560861\pi$
$228$	0	0
$229$	−5.42627e6	−0.0298591	−0.0149296	−	0.999889i	$-0.504752\pi$
$229$	−5.42627e6	−0.0298591	−0.0149296	+	0.999889i	$0.504752\pi$
$230$	1.34692e8	0.729951
$231$	0	0
$232$	9.11436e8	4.79202
$233$	1.14071e8	0.590784	0.295392	−	0.955376i	$-0.404550\pi$
$233$	1.14071e8	0.590784	0.295392	+	0.955376i	$0.404550\pi$
$234$	0	0
$235$	−2.68025e7	−0.134722
$236$	6.93983e7	0.343682
$237$	0	0
$238$	−4.22571e8	−2.03180
$239$	−2.35111e8	−1.11399	−0.556993	−	0.830517i	$-0.688045\pi$
$239$	−2.35111e8	−1.11399	−0.556993	+	0.830517i	$0.688045\pi$
$240$	0	0
$241$	−2.14221e8	−0.985830	−0.492915	−	0.870078i	$-0.664069\pi$
$241$	−2.14221e8	−0.985830	−0.492915	+	0.870078i	$0.664069\pi$
$242$	4.06914e8	1.84565
$243$	0	0
$244$	8.48055e8	3.73732
$245$	−4.58163e7	−0.199039
$246$	0	0
$247$	3.16564e7	0.133666
$248$	7.86767e7	0.327541
$249$	0	0
$250$	3.50813e8	1.41999
$251$	1.53834e8	0.614036	0.307018	−	0.951704i	$-0.400669\pi$
$251$	1.53834e8	0.614036	0.307018	+	0.951704i	$0.400669\pi$
$252$	0	0
$253$	4.38852e7	0.170371
$254$	−5.84488e8	−2.23799
$255$	0	0
$256$	3.47435e8	1.29430
$257$	−4.74131e8	−1.74234	−0.871169	−	0.490984i	$-0.836637\pi$
$257$	−4.74131e8	−1.74234	−0.871169	+	0.490984i	$0.836637\pi$
$258$	0	0
$259$	1.01701e8	0.363727
$260$	3.30513e7	0.116622
$261$	0	0
$262$	1.45098e8	0.498434
$263$	1.50757e8	0.511014	0.255507	−	0.966807i	$-0.417758\pi$
$263$	1.50757e8	0.511014	0.255507	+	0.966807i	$0.417758\pi$
$264$	0	0
$265$	5.93977e7	0.196069
$266$	5.12661e8	1.67011
$267$	0	0
$268$	−6.31295e8	−2.00337
$269$	−5.50062e8	−1.72297	−0.861486	−	0.507781i	$-0.830466\pi$
$269$	−5.50062e8	−1.72297	−0.861486	+	0.507781i	$0.830466\pi$
$270$	0	0
$271$	4.96505e8	1.51541	0.757707	−	0.652595i	$-0.226319\pi$
$271$	4.96505e8	1.51541	0.757707	+	0.652595i	$0.226319\pi$
$272$	−1.64906e9	−4.96873
$273$	0	0
$274$	9.47799e8	2.78349
$275$	5.20318e7	0.150871
$276$	0	0
$277$	1.08273e8	0.306083	0.153041	−	0.988220i	$-0.451093\pi$
$277$	1.08273e8	0.306083	0.153041	+	0.988220i	$0.451093\pi$
$278$	−1.84600e8	−0.515318
$279$	0	0
$280$	3.32495e8	0.905173
$281$	6.35664e8	1.70905	0.854527	−	0.519407i	$-0.173847\pi$
$281$	6.35664e8	1.70905	0.854527	+	0.519407i	$0.173847\pi$
$282$	0	0
$283$	1.82266e8	0.478027	0.239014	−	0.971016i	$-0.423176\pi$
$283$	1.82266e8	0.478027	0.239014	+	0.971016i	$0.423176\pi$
$284$	1.07275e9	2.77897
$285$	0	0
$286$	1.48480e7	0.0375308
$287$	1.71244e8	0.427590
$288$	0	0
$289$	5.03762e8	1.22767
$290$	4.92117e8	1.18488
$291$	0	0
$292$	1.02446e8	0.240799
$293$	2.94539e8	0.684080	0.342040	−	0.939685i	$-0.388882\pi$
$293$	2.94539e8	0.684080	0.342040	+	0.939685i	$0.388882\pi$
$294$	0	0
$295$	2.32765e7	0.0527887
$296$	7.11602e8	1.59484
$297$	0	0
$298$	−9.50782e8	−2.08125
$299$	−4.75187e7	−0.102805
$300$	0	0
$301$	−6.31760e7	−0.133527
$302$	1.25035e9	2.61220
$303$	0	0
$304$	2.00063e9	4.08422
$305$	2.84442e8	0.574042
$306$	0	0
$307$	−6.80308e8	−1.34190	−0.670952	−	0.741501i	$-0.734114\pi$
$307$	−6.80308e8	−1.34190	−0.670952	+	0.741501i	$0.734114\pi$
$308$	1.74395e8	0.340100
$309$	0	0
$310$	4.24804e7	0.0809884
$311$	1.83957e8	0.346780	0.173390	−	0.984853i	$-0.444528\pi$
$311$	1.83957e8	0.346780	0.173390	+	0.984853i	$0.444528\pi$
$312$	0	0
$313$	−4.45917e8	−0.821956	−0.410978	−	0.911645i	$-0.634813\pi$
$313$	−4.45917e8	−0.821956	−0.410978	+	0.911645i	$0.634813\pi$
$314$	1.40056e9	2.55298
$315$	0	0
$316$	1.19650e9	2.13308
$317$	5.41308e8	0.954414	0.477207	−	0.878791i	$-0.341649\pi$
$317$	5.41308e8	0.954414	0.477207	+	0.878791i	$0.341649\pi$
$318$	0	0
$319$	1.60341e8	0.276553
$320$	6.70098e8	1.14318
$321$	0	0
$322$	−7.69545e8	−1.28451
$323$	−1.10898e9	−1.83111
$324$	0	0
$325$	−5.63399e7	−0.0910383
$326$	−1.47044e9	−2.35063
$327$	0	0
$328$	1.19819e9	1.87486
$329$	1.53133e8	0.237073
$330$	0	0
$331$	3.83779e7	0.0581679	0.0290839	−	0.999577i	$-0.490741\pi$
$331$	3.83779e7	0.0581679	0.0290839	+	0.999577i	$0.490741\pi$
$332$	−3.33674e9	−5.00425
$333$	0	0
$334$	7.60270e8	1.11649
$335$	−2.11739e8	−0.307712
$336$	0	0
$337$	8.56217e8	1.21865	0.609325	−	0.792920i	$-0.291440\pi$
$337$	8.56217e8	1.21865	0.609325	+	0.792920i	$0.291440\pi$
$338$	1.33834e9	1.88520
$339$	0	0
$340$	−1.15785e9	−1.59763
$341$	1.38409e7	0.0189028
$342$	0	0
$343$	7.95029e8	1.06378
$344$	−4.42043e8	−0.585477
$345$	0	0
$346$	−1.15656e9	−1.50108
$347$	2.36529e8	0.303901	0.151950	−	0.988388i	$-0.451445\pi$
$347$	2.36529e8	0.303901	0.151950	+	0.988388i	$0.451445\pi$
$348$	0	0
$349$	−2.69181e8	−0.338966	−0.169483	−	0.985533i	$-0.554210\pi$
$349$	−2.69181e8	−0.338966	−0.169483	+	0.985533i	$0.554210\pi$
$350$	−9.12400e8	−1.13749
$351$	0	0
$352$	4.76134e8	0.581875
$353$	4.00304e8	0.484371	0.242186	−	0.970230i	$-0.422136\pi$
$353$	4.00304e8	0.484371	0.242186	+	0.970230i	$0.422136\pi$
$354$	0	0
$355$	3.59805e8	0.426842
$356$	2.19364e9	2.57686
$357$	0	0
$358$	−2.71392e9	−3.12613
$359$	6.09817e8	0.695615	0.347808	−	0.937566i	$-0.386926\pi$
$359$	6.09817e8	0.695615	0.347808	+	0.937566i	$0.386926\pi$
$360$	0	0
$361$	4.51538e8	0.505149
$362$	−1.37258e9	−1.52075
$363$	0	0
$364$	−1.88835e8	−0.205223
$365$	3.43608e7	0.0369861
$366$	0	0
$367$	−3.65526e8	−0.386000	−0.193000	−	0.981199i	$-0.561822\pi$
$367$	−3.65526e8	−0.386000	−0.193000	+	0.981199i	$0.561822\pi$
$368$	−3.00311e9	−3.14126
$369$	0	0
$370$	3.84219e8	0.394342
$371$	−3.39361e8	−0.345028
$372$	0	0
$373$	−1.64569e9	−1.64198	−0.820990	−	0.570942i	$-0.806578\pi$
$373$	−1.64569e9	−1.64198	−0.820990	+	0.570942i	$0.806578\pi$
$374$	−5.20154e8	−0.514140
$375$	0	0
$376$	1.07147e9	1.03950
$377$	−1.73617e8	−0.166878
$378$	0	0
$379$	1.32916e9	1.25412	0.627062	−	0.778969i	$-0.284257\pi$
$379$	1.32916e9	1.25412	0.627062	+	0.778969i	$0.284257\pi$
$380$	1.40469e9	1.31323
$381$	0	0
$382$	4.77115e8	0.437927
$383$	−1.43631e9	−1.30633	−0.653163	−	0.757217i	$-0.726558\pi$
$383$	−1.43631e9	−1.30633	−0.653163	+	0.757217i	$0.726558\pi$
$384$	0	0
$385$	5.84930e7	0.0522386
$386$	5.91360e7	0.0523355
$387$	0	0
$388$	−2.85038e6	−0.00247738
$389$	−1.62608e9	−1.40062	−0.700309	−	0.713840i	$-0.746954\pi$
$389$	−1.62608e9	−1.40062	−0.700309	+	0.713840i	$0.746954\pi$
$390$	0	0
$391$	1.66467e9	1.40835
$392$	1.83158e9	1.53576
$393$	0	0
$394$	3.15039e8	0.259494
$395$	4.01310e8	0.327635
$396$	0	0
$397$	1.66052e9	1.33192	0.665958	−	0.745989i	$-0.268023\pi$
$397$	1.66052e9	1.33192	0.665958	+	0.745989i	$0.268023\pi$
$398$	2.72680e9	2.16802
$399$	0	0
$400$	−3.56059e9	−2.78171
$401$	−1.65806e9	−1.28409	−0.642045	−	0.766667i	$-0.721914\pi$
$401$	−1.65806e9	−1.28409	−0.642045	+	0.766667i	$0.721914\pi$
$402$	0	0
$403$	−1.49869e7	−0.0114063
$404$	−1.26629e9	−0.955431
$405$	0	0
$406$	−2.81165e9	−2.08507
$407$	1.25186e8	0.0920398
$408$	0	0
$409$	2.60200e9	1.88051	0.940256	−	0.340468i	$-0.110585\pi$
$409$	2.60200e9	1.88051	0.940256	+	0.340468i	$0.110585\pi$
$410$	6.46947e8	0.463581
$411$	0	0
$412$	−2.42003e9	−1.70483
$413$	−1.32988e8	−0.0928936
$414$	0	0
$415$	−1.11916e9	−0.768640
$416$	−5.15557e8	−0.351115
$417$	0	0
$418$	6.31047e8	0.422615
$419$	1.66480e9	1.10564	0.552819	−	0.833302i	$-0.313552\pi$
$419$	1.66480e9	1.10564	0.552819	+	0.833302i	$0.313552\pi$
$420$	0	0
$421$	2.00138e9	1.30720	0.653601	−	0.756839i	$-0.273257\pi$
$421$	2.00138e9	1.30720	0.653601	+	0.756839i	$0.273257\pi$
$422$	−4.35936e9	−2.82377
$423$	0	0
$424$	−2.37451e9	−1.51284
$425$	1.97369e9	1.24715
$426$	0	0
$427$	−1.62512e9	−1.01016
$428$	6.39037e9	3.93979
$429$	0	0
$430$	−2.38675e8	−0.144766
$431$	−4.72430e8	−0.284228	−0.142114	−	0.989850i	$-0.545390\pi$
$431$	−4.72430e8	−0.284228	−0.142114	+	0.989850i	$0.545390\pi$
$432$	0	0
$433$	6.77203e8	0.400877	0.200439	−	0.979706i	$-0.435763\pi$
$433$	6.77203e8	0.400877	0.200439	+	0.979706i	$0.435763\pi$
$434$	−2.42707e8	−0.142517
$435$	0	0
$436$	−5.40781e9	−3.12477
$437$	−2.01957e9	−1.15764
$438$	0	0
$439$	1.96136e9	1.10645	0.553224	−	0.833033i	$-0.313397\pi$
$439$	1.96136e9	1.10645	0.553224	+	0.833033i	$0.313397\pi$
$440$	4.09276e8	0.229051
$441$	0	0
$442$	5.63221e8	0.310242
$443$	−7.15483e7	−0.0391008	−0.0195504	−	0.999809i	$-0.506223\pi$
$443$	−7.15483e7	−0.0391008	−0.0195504	+	0.999809i	$0.506223\pi$
$444$	0	0
$445$	7.35757e8	0.395799
$446$	5.26952e9	2.81254
$447$	0	0
$448$	−3.82853e9	−2.01168
$449$	2.36841e9	1.23479	0.617397	−	0.786652i	$-0.288187\pi$
$449$	2.36841e9	1.23479	0.617397	+	0.786652i	$0.288187\pi$
$450$	0	0
$451$	2.10788e8	0.108200
$452$	1.61435e9	0.822266
$453$	0	0
$454$	1.44580e9	0.725127
$455$	−6.33360e7	−0.0315218
$456$	0	0
$457$	9.23556e8	0.452644	0.226322	−	0.974053i	$-0.427330\pi$
$457$	9.23556e8	0.452644	0.226322	+	0.974053i	$0.427330\pi$
$458$	1.17125e8	0.0569666
$459$	0	0
$460$	−2.10856e9	−1.01003
$461$	2.95040e8	0.140258	0.0701289	−	0.997538i	$-0.477659\pi$
$461$	2.95040e8	0.140258	0.0701289	+	0.997538i	$0.477659\pi$
$462$	0	0
$463$	2.57536e9	1.20588	0.602940	−	0.797787i	$-0.293996\pi$
$463$	2.57536e9	1.20588	0.602940	+	0.797787i	$0.293996\pi$
$464$	−1.09723e10	−5.09901
$465$	0	0
$466$	−2.46219e9	−1.12712
$467$	9.62315e8	0.437228	0.218614	−	0.975811i	$-0.429846\pi$
$467$	9.62315e8	0.437228	0.218614	+	0.975811i	$0.429846\pi$
$468$	0	0
$469$	1.20975e9	0.541489
$470$	5.78526e8	0.257028
$471$	0	0
$472$	−9.30515e8	−0.407311
$473$	−7.77649e7	−0.0337886
$474$	0	0
$475$	−2.39447e9	−1.02514
$476$	6.61523e9	2.81139
$477$	0	0
$478$	5.07482e9	2.12531
$479$	1.04097e9	0.432777	0.216389	−	0.976307i	$-0.430572\pi$
$479$	1.04097e9	0.432777	0.216389	+	0.976307i	$0.430572\pi$
$480$	0	0
$481$	−1.35551e8	−0.0555387
$482$	4.62391e9	1.88081
$483$	0	0
$484$	−6.37011e9	−2.55381
$485$	−956032.	−0.000380519 0
$486$	0	0
$487$	1.54301e9	0.605365	0.302683	−	0.953091i	$-0.402118\pi$
$487$	1.54301e9	0.605365	0.302683	+	0.953091i	$0.402118\pi$
$488$	−1.13710e10	−4.42924
$489$	0	0
$490$	9.88934e8	0.379736
$491$	−8.27706e8	−0.315566	−0.157783	−	0.987474i	$-0.550435\pi$
$491$	−8.27706e8	−0.315566	−0.157783	+	0.987474i	$0.550435\pi$
$492$	0	0
$493$	6.08213e9	2.28608
$494$	−6.83296e8	−0.255014
$495$	0	0
$496$	−9.47149e8	−0.348524
$497$	−2.05570e9	−0.751126
$498$	0	0
$499$	−5.08912e9	−1.83354	−0.916771	−	0.399413i	$-0.869214\pi$
$499$	−5.08912e9	−1.83354	−0.916771	+	0.399413i	$0.869214\pi$
$500$	−5.49186e9	−1.96483
$501$	0	0
$502$	−3.32047e9	−1.17149
$503$	−1.24283e9	−0.435434	−0.217717	−	0.976012i	$-0.569861\pi$
$503$	−1.24283e9	−0.435434	−0.217717	+	0.976012i	$0.569861\pi$
$504$	0	0
$505$	−4.24721e8	−0.146752
$506$	−9.47252e8	−0.325042
$507$	0	0
$508$	9.14997e9	3.09668
$509$	3.51527e9	1.18154	0.590768	−	0.806842i	$-0.298825\pi$
$509$	3.51527e9	1.18154	0.590768	+	0.806842i	$0.298825\pi$
$510$	0	0
$511$	−1.96317e8	−0.0650854
$512$	−9.51036e8	−0.313150
$513$	0	0
$514$	1.02340e10	3.32411
$515$	−8.11689e8	−0.261857
$516$	0	0
$517$	1.88495e8	0.0599905
$518$	−2.19519e9	−0.693934
$519$	0	0
$520$	−4.43163e8	−0.138214
$521$	4.15959e9	1.28860	0.644301	−	0.764772i	$-0.277148\pi$
$521$	4.15959e9	1.28860	0.644301	+	0.764772i	$0.277148\pi$
$522$	0	0
$523$	−9.27018e8	−0.283356	−0.141678	−	0.989913i	$-0.545250\pi$
$523$	−9.27018e8	−0.283356	−0.141678	+	0.989913i	$0.545250\pi$
$524$	−2.27147e9	−0.689679
$525$	0	0
$526$	−3.25406e9	−0.974936
$527$	5.25020e8	0.156257
$528$	0	0
$529$	−3.73295e8	−0.109637
$530$	−1.28209e9	−0.374069
$531$	0	0
$532$	−8.02555e9	−2.31092
$533$	−2.28241e8	−0.0652902
$534$	0	0
$535$	2.14336e9	0.605142
$536$	8.46461e9	2.37427
$537$	0	0
$538$	1.18730e10	3.28716
$539$	3.22214e8	0.0886306
$540$	0	0
$541$	−6.33596e9	−1.72037	−0.860186	−	0.509981i	$-0.829652\pi$
$541$	−6.33596e9	−1.72037	−0.860186	+	0.509981i	$0.829652\pi$
$542$	−1.07170e10	−2.89118
$543$	0	0
$544$	1.80609e10	4.80998
$545$	−1.81381e9	−0.479958
$546$	0	0
$547$	2.00352e9	0.523406	0.261703	−	0.965148i	$-0.415716\pi$
$547$	2.00352e9	0.523406	0.261703	+	0.965148i	$0.415716\pi$
$548$	−1.48375e10	−3.85149
$549$	0	0
$550$	−1.12310e9	−0.287838
$551$	−7.37881e9	−1.87912
$552$	0	0
$553$	−2.29284e9	−0.576548
$554$	−2.33704e9	−0.583959
$555$	0	0
$556$	2.88986e9	0.713042
$557$	4.93285e9	1.20950	0.604748	−	0.796417i	$-0.293274\pi$
$557$	4.93285e9	1.20950	0.604748	+	0.796417i	$0.293274\pi$
$558$	0	0
$559$	8.42036e7	0.0203887
$560$	−4.00273e9	−0.963160
$561$	0	0
$562$	−1.37207e10	−3.26061
$563$	−4.64054e9	−1.09595	−0.547973	−	0.836496i	$-0.684600\pi$
$563$	−4.64054e9	−1.09595	−0.547973	+	0.836496i	$0.684600\pi$
$564$	0	0
$565$	5.41460e8	0.126298
$566$	−3.93417e9	−0.912001
$567$	0	0
$568$	−1.43838e10	−3.29347
$569$	4.82571e9	1.09817	0.549083	−	0.835768i	$-0.314977\pi$
$569$	4.82571e9	1.09817	0.549083	+	0.835768i	$0.314977\pi$
$570$	0	0
$571$	−6.84565e9	−1.53882	−0.769410	−	0.638755i	$-0.779450\pi$
$571$	−6.84565e9	−1.53882	−0.769410	+	0.638755i	$0.779450\pi$
$572$	−2.32441e8	−0.0519310
$573$	0	0
$574$	−3.69626e9	−0.815775
$575$	3.59429e9	0.788453
$576$	0	0
$577$	−3.78107e9	−0.819407	−0.409704	−	0.912219i	$-0.634368\pi$
$577$	−3.78107e9	−0.819407	−0.409704	+	0.912219i	$0.634368\pi$
$578$	−1.08736e10	−2.34221
$579$	0	0
$580$	−7.70395e9	−1.63951
$581$	6.39418e9	1.35260
$582$	0	0
$583$	−4.17729e8	−0.0873080
$584$	−1.37363e9	−0.285381
$585$	0	0
$586$	−6.35757e9	−1.30512
$587$	−4.65957e9	−0.950852	−0.475426	−	0.879756i	$-0.657706\pi$
$587$	−4.65957e9	−0.950852	−0.475426	+	0.879756i	$0.657706\pi$
$588$	0	0
$589$	−6.36951e8	−0.128441
$590$	−5.02419e8	−0.100713
$591$	0	0
$592$	−8.56661e9	−1.69701
$593$	7.46187e9	1.46945	0.734727	−	0.678363i	$-0.237310\pi$
$593$	7.46187e9	1.46945	0.734727	+	0.678363i	$0.237310\pi$
$594$	0	0
$595$	2.21878e9	0.431822
$596$	1.48842e10	2.87981
$597$	0	0
$598$	1.02568e9	0.196137
$599$	4.56957e9	0.868723	0.434362	−	0.900739i	$-0.356974\pi$
$599$	4.56957e9	0.868723	0.434362	+	0.900739i	$0.356974\pi$
$600$	0	0
$601$	−3.26243e9	−0.613028	−0.306514	−	0.951866i	$-0.599163\pi$
$601$	−3.26243e9	−0.613028	−0.306514	+	0.951866i	$0.599163\pi$
$602$	1.36364e9	0.254749
$603$	0	0
$604$	−1.95738e10	−3.61449
$605$	−2.13657e9	−0.392259
$606$	0	0
$607$	7.83444e9	1.42183	0.710915	−	0.703278i	$-0.248281\pi$
$607$	7.83444e9	1.42183	0.710915	+	0.703278i	$0.248281\pi$
$608$	−2.19114e10	−3.95373
$609$	0	0
$610$	−6.13962e9	−1.09518
$611$	−2.04102e8	−0.0361995
$612$	0	0
$613$	1.83847e9	0.322363	0.161181	−	0.986925i	$-0.448470\pi$
$613$	1.83847e9	0.322363	0.161181	+	0.986925i	$0.448470\pi$
$614$	1.46843e10	2.56014
$615$	0	0
$616$	−2.33835e9	−0.403067
$617$	7.28601e9	1.24880	0.624399	−	0.781106i	$-0.285344\pi$
$617$	7.28601e9	1.24880	0.624399	+	0.781106i	$0.285344\pi$
$618$	0	0
$619$	2.62525e8	0.0444891	0.0222446	−	0.999753i	$-0.492919\pi$
$619$	2.62525e8	0.0444891	0.0222446	+	0.999753i	$0.492919\pi$
$620$	−6.65018e8	−0.112063
$621$	0	0
$622$	−3.97067e9	−0.661603
$623$	−4.20366e9	−0.696497
$624$	0	0
$625$	3.25803e9	0.533795
$626$	9.62502e9	1.56816
$627$	0	0
$628$	−2.19253e10	−3.53254
$629$	4.74861e9	0.760833
$630$	0	0
$631$	1.62131e9	0.256899	0.128450	−	0.991716i	$-0.459000\pi$
$631$	1.62131e9	0.256899	0.128450	+	0.991716i	$0.459000\pi$
$632$	−1.60430e10	−2.52799
$633$	0	0
$634$	−1.16840e10	−1.82087
$635$	3.06895e9	0.475643
$636$	0	0
$637$	−3.48892e8	−0.0534815
$638$	−3.46094e9	−0.527620
$639$	0	0
$640$	−5.79801e9	−0.874277
$641$	−1.50371e9	−0.225508	−0.112754	−	0.993623i	$-0.535967\pi$
$641$	−1.50371e9	−0.225508	−0.112754	+	0.993623i	$0.535967\pi$
$642$	0	0
$643$	7.26580e9	1.07782	0.538908	−	0.842365i	$-0.318837\pi$
$643$	7.26580e9	1.07782	0.538908	+	0.842365i	$0.318837\pi$
$644$	1.20470e10	1.77737
$645$	0	0
$646$	2.39371e10	3.49348
$647$	1.31988e10	1.91588	0.957942	−	0.286962i	$-0.0926454\pi$
$647$	1.31988e10	1.91588	0.957942	+	0.286962i	$0.0926454\pi$
$648$	0	0
$649$	−1.63698e8	−0.0235064
$650$	1.21609e9	0.173687
$651$	0	0
$652$	2.30193e10	3.25256
$653$	1.08050e10	1.51855	0.759276	−	0.650768i	$-0.225553\pi$
$653$	1.08050e10	1.51855	0.759276	+	0.650768i	$0.225553\pi$
$654$	0	0
$655$	−7.61861e8	−0.105933
$656$	−1.44244e10	−1.99497
$657$	0	0
$658$	−3.30534e9	−0.452299
$659$	1.38422e10	1.88411	0.942053	−	0.335464i	$-0.108893\pi$
$659$	1.38422e10	1.88411	0.942053	+	0.335464i	$0.108893\pi$
$660$	0	0
$661$	1.08222e10	1.45751	0.728756	−	0.684773i	$-0.240099\pi$
$661$	1.08222e10	1.45751	0.728756	+	0.684773i	$0.240099\pi$
$662$	−8.28379e8	−0.110975
$663$	0	0
$664$	4.47401e10	5.93074
$665$	−2.69181e9	−0.354951
$666$	0	0
$667$	1.10762e10	1.44527
$668$	−1.19018e10	−1.54488
$669$	0	0
$670$	4.57035e9	0.587067
$671$	−2.00041e9	−0.255617
$672$	0	0
$673$	−7.77779e9	−0.983566	−0.491783	−	0.870718i	$-0.663655\pi$
$673$	−7.77779e9	−0.983566	−0.491783	+	0.870718i	$0.663655\pi$
$674$	−1.84813e10	−2.32500
$675$	0	0
$676$	−2.09513e10	−2.60853
$677$	9.88602e9	1.22451	0.612253	−	0.790662i	$-0.290263\pi$
$677$	9.88602e9	1.22451	0.612253	+	0.790662i	$0.290263\pi$
$678$	0	0
$679$	5.46218e6	0.000669610 0
$680$	1.55248e10	1.89341
$681$	0	0
$682$	−2.98754e8	−0.0360635
$683$	−1.44552e10	−1.73601	−0.868003	−	0.496559i	$-0.834597\pi$
$683$	−1.44552e10	−1.73601	−0.868003	+	0.496559i	$0.834597\pi$
$684$	0	0
$685$	−4.97657e9	−0.591580
$686$	−1.71605e10	−2.02953
$687$	0	0
$688$	5.32153e9	0.622984
$689$	4.52315e8	0.0526834
$690$	0	0
$691$	−9.78421e9	−1.12811	−0.564056	−	0.825736i	$-0.690760\pi$
$691$	−9.78421e9	−1.12811	−0.564056	+	0.825736i	$0.690760\pi$
$692$	1.81056e10	2.07703
$693$	0	0
$694$	−5.10544e9	−0.579795
$695$	9.69273e8	0.109521
$696$	0	0
$697$	7.99570e9	0.894420
$698$	5.81022e9	0.646694
$699$	0	0
$700$	1.42833e10	1.57393
$701$	1.39642e7	0.00153110	0.000765548	−	1.00000i	$-0.499756\pi$
$701$	1.39642e7	0.00153110	0.000765548		1.00000i	$0.499756\pi$
$702$	0	0
$703$	−5.76099e9	−0.625393
$704$	−4.71263e9	−0.509048
$705$	0	0
$706$	−8.64047e9	−0.924105
$707$	2.42659e9	0.258243
$708$	0	0
$709$	1.10083e10	1.16000	0.580002	−	0.814615i	$-0.303052\pi$
$709$	1.10083e10	1.16000	0.580002	+	0.814615i	$0.303052\pi$
$710$	−7.76631e9	−0.814349
$711$	0	0
$712$	−2.94130e10	−3.05394
$713$	9.56114e8	0.0987862
$714$	0	0
$715$	−7.79619e7	−0.00797648
$716$	4.24856e10	4.32560
$717$	0	0
$718$	−1.31628e10	−1.32713
$719$	1.00251e10	1.00586	0.502932	−	0.864326i	$-0.332254\pi$
$719$	1.00251e10	1.00586	0.502932	+	0.864326i	$0.332254\pi$
$720$	0	0
$721$	4.63749e9	0.460797
$722$	−9.74636e9	−0.963745
$723$	0	0
$724$	2.14873e10	2.10425
$725$	1.31323e10	1.27985
$726$	0	0
$727$	1.36958e9	0.132195	0.0660977	−	0.997813i	$-0.478945\pi$
$727$	1.36958e9	0.132195	0.0660977	+	0.997813i	$0.478945\pi$
$728$	2.53196e9	0.243219
$729$	0	0
$730$	−7.41672e8	−0.0705637
$731$	−2.94981e9	−0.279308
$732$	0	0
$733$	−2.47923e9	−0.232516	−0.116258	−	0.993219i	$-0.537090\pi$
$733$	−2.47923e9	−0.232516	−0.116258	+	0.993219i	$0.537090\pi$
$734$	7.88981e9	0.736428
$735$	0	0
$736$	3.28907e10	3.04089
$737$	1.48911e9	0.137022
$738$	0	0
$739$	−4.61946e9	−0.421052	−0.210526	−	0.977588i	$-0.567518\pi$
$739$	−4.61946e9	−0.421052	−0.210526	+	0.977588i	$0.567518\pi$
$740$	−6.01484e9	−0.545649
$741$	0	0
$742$	7.32505e9	0.658259
$743$	1.55272e10	1.38878	0.694389	−	0.719600i	$-0.255675\pi$
$743$	1.55272e10	1.38878	0.694389	+	0.719600i	$0.255675\pi$
$744$	0	0
$745$	4.99224e9	0.442332
$746$	3.55220e10	3.13264
$747$	0	0
$748$	8.14285e9	0.711411
$749$	−1.22458e10	−1.06488
$750$	0	0
$751$	−5.50391e9	−0.474167	−0.237084	−	0.971489i	$-0.576192\pi$
$751$	−5.50391e9	−0.474167	−0.237084	+	0.971489i	$0.576192\pi$
$752$	−1.28989e10	−1.10609
$753$	0	0
$754$	3.74749e9	0.318376
$755$	−6.56516e9	−0.555177
$756$	0	0
$757$	−1.57056e10	−1.31589	−0.657946	−	0.753065i	$-0.728574\pi$
$757$	−1.57056e10	−1.31589	−0.657946	+	0.753065i	$0.728574\pi$
$758$	−2.86897e10	−2.39268
$759$	0	0
$760$	−1.88346e10	−1.55636
$761$	1.80765e10	1.48685	0.743427	−	0.668817i	$-0.233199\pi$
$761$	1.80765e10	1.48685	0.743427	+	0.668817i	$0.233199\pi$
$762$	0	0
$763$	1.03630e10	0.844594
$764$	−7.46910e9	−0.605956
$765$	0	0
$766$	3.10024e10	2.49227
$767$	1.77251e8	0.0141842
$768$	0	0
$769$	−1.35958e10	−1.07811	−0.539053	−	0.842272i	$-0.681218\pi$
$769$	−1.35958e10	−1.07811	−0.539053	+	0.842272i	$0.681218\pi$
$770$	−1.26256e9	−0.0996630
$771$	0	0
$772$	−9.25757e8	−0.0724163
$773$	−1.25983e9	−0.0981032	−0.0490516	−	0.998796i	$-0.515620\pi$
$773$	−1.25983e9	−0.0981032	−0.0490516	+	0.998796i	$0.515620\pi$
$774$	0	0
$775$	1.13360e9	0.0874792
$776$	3.82189e7	0.00293604
$777$	0	0
$778$	3.50987e10	2.67216
$779$	−9.70033e9	−0.735200
$780$	0	0
$781$	−2.53041e9	−0.190070
$782$	−3.59316e10	−2.68691
$783$	0	0
$784$	−2.20494e10	−1.63415
$785$	−7.35386e9	−0.542590
$786$	0	0
$787$	1.93512e10	1.41513	0.707566	−	0.706647i	$-0.249793\pi$
$787$	1.93512e10	1.41513	0.707566	+	0.706647i	$0.249793\pi$
$788$	−4.93184e9	−0.359060
$789$	0	0
$790$	−8.66220e9	−0.625077
$791$	−3.09357e9	−0.222250
$792$	0	0
$793$	2.16603e9	0.154244
$794$	−3.58420e10	−2.54109
$795$	0	0
$796$	−4.26872e10	−2.99987
$797$	−1.07925e10	−0.755122	−0.377561	−	0.925985i	$-0.623237\pi$
$797$	−1.07925e10	−0.755122	−0.377561	+	0.925985i	$0.623237\pi$
$798$	0	0
$799$	7.15006e9	0.495902
$800$	3.89964e10	2.69284
$801$	0	0
$802$	3.57890e10	2.44985
$803$	−2.41651e8	−0.0164696
$804$	0	0
$805$	4.04062e9	0.273000
$806$	3.23490e8	0.0217615
$807$	0	0
$808$	1.69789e10	1.13232
$809$	4.14105e9	0.274973	0.137487	−	0.990504i	$-0.456098\pi$
$809$	4.14105e9	0.274973	0.137487	+	0.990504i	$0.456098\pi$
$810$	0	0
$811$	3.15148e9	0.207463	0.103732	−	0.994605i	$-0.466922\pi$
$811$	3.15148e9	0.207463	0.103732	+	0.994605i	$0.466922\pi$
$812$	4.40156e10	2.88510
$813$	0	0
$814$	−2.70212e9	−0.175598
$815$	7.72077e9	0.499585
$816$	0	0
$817$	3.57869e9	0.229587
$818$	−5.61637e10	−3.58773
$819$	0	0
$820$	−1.01278e10	−0.641454
$821$	3.16518e10	1.99617	0.998085	−	0.0618543i	$-0.0197014\pi$
$821$	3.16518e10	1.99617	0.998085	+	0.0618543i	$0.0197014\pi$
$822$	0	0
$823$	−2.99731e9	−0.187427	−0.0937135	−	0.995599i	$-0.529874\pi$
$823$	−2.99731e9	−0.187427	−0.0937135	+	0.995599i	$0.529874\pi$
$824$	3.24485e10	2.02046
$825$	0	0
$826$	2.87051e9	0.177227
$827$	6.29398e9	0.386951	0.193475	−	0.981105i	$-0.438024\pi$
$827$	6.29398e9	0.386951	0.193475	+	0.981105i	$0.438024\pi$
$828$	0	0
$829$	1.29264e10	0.788018	0.394009	−	0.919107i	$-0.371088\pi$
$829$	1.29264e10	0.788018	0.394009	+	0.919107i	$0.371088\pi$
$830$	2.41568e10	1.46645
$831$	0	0
$832$	5.10282e9	0.307170
$833$	1.22223e10	0.732651
$834$	0	0
$835$	−3.99192e9	−0.237290
$836$	−9.87886e9	−0.584769
$837$	0	0
$838$	−3.59343e10	−2.10938
$839$	−2.72788e9	−0.159462	−0.0797312	−	0.996816i	$-0.525406\pi$
$839$	−2.72788e9	−0.159462	−0.0797312	+	0.996816i	$0.525406\pi$
$840$	0	0
$841$	2.32187e10	1.34602
$842$	−4.31994e10	−2.49394
$843$	0	0
$844$	6.82444e10	3.90722
$845$	−7.02715e9	−0.400664
$846$	0	0
$847$	1.22070e10	0.690268
$848$	2.85856e10	1.60976
$849$	0	0
$850$	−4.26017e10	−2.37936
$851$	8.64770e9	0.481002
$852$	0	0
$853$	−1.22649e10	−0.676618	−0.338309	−	0.941035i	$-0.609855\pi$
$853$	−1.22649e10	−0.676618	−0.338309	+	0.941035i	$0.609855\pi$
$854$	3.50780e10	1.92722
$855$	0	0
$856$	−8.56842e10	−4.66920
$857$	3.61684e10	1.96289	0.981447	−	0.191732i	$-0.0614106\pi$
$857$	3.61684e10	1.96289	0.981447	+	0.191732i	$0.0614106\pi$
$858$	0	0
$859$	−9.13867e9	−0.491934	−0.245967	−	0.969278i	$-0.579106\pi$
$859$	−9.13867e9	−0.491934	−0.245967	+	0.969278i	$0.579106\pi$
$860$	3.73638e9	0.200312
$861$	0	0
$862$	1.01973e10	0.542262
$863$	−2.82611e10	−1.49676	−0.748378	−	0.663272i	$-0.769167\pi$
$863$	−2.82611e10	−1.49676	−0.748378	+	0.663272i	$0.769167\pi$
$864$	0	0
$865$	6.07272e9	0.319027
$866$	−1.46173e10	−0.764811
$867$	0	0
$868$	3.79950e9	0.197200
$869$	−2.82231e9	−0.145893
$870$	0	0
$871$	−1.61240e9	−0.0826818
$872$	7.25097e10	3.70330
$873$	0	0
$874$	4.35919e10	2.20860
$875$	1.05240e10	0.531073
$876$	0	0
$877$	−8.41638e9	−0.421334	−0.210667	−	0.977558i	$-0.567564\pi$
$877$	−8.41638e9	−0.421334	−0.210667	+	0.977558i	$0.567564\pi$
$878$	−4.23355e10	−2.11093
$879$	0	0
$880$	−4.92707e9	−0.243724
$881$	−2.07127e10	−1.02052	−0.510259	−	0.860021i	$-0.670450\pi$
$881$	−2.07127e10	−1.02052	−0.510259	+	0.860021i	$0.670450\pi$
$882$	0	0
$883$	−1.60168e10	−0.782910	−0.391455	−	0.920197i	$-0.628028\pi$
$883$	−1.60168e10	−0.782910	−0.391455	+	0.920197i	$0.628028\pi$
$884$	−8.81705e9	−0.429280
$885$	0	0
$886$	1.54435e9	0.0745983
$887$	−2.24851e10	−1.08184	−0.540920	−	0.841074i	$-0.681924\pi$
$887$	−2.24851e10	−1.08184	−0.540920	+	0.841074i	$0.681924\pi$
$888$	0	0
$889$	−1.75341e10	−0.837002
$890$	−1.58812e10	−0.755122
$891$	0	0
$892$	−8.24928e10	−3.89170
$893$	−8.67441e9	−0.407624
$894$	0	0
$895$	1.42499e10	0.664402
$896$	3.31263e10	1.53849
$897$	0	0
$898$	−5.11216e10	−2.35580
$899$	3.49331e9	0.160354
$900$	0	0
$901$	−1.58454e10	−0.721718
$902$	−4.54982e9	−0.206429
$903$	0	0
$904$	−2.16457e10	−0.974501
$905$	7.20694e9	0.323207
$906$	0	0
$907$	1.63521e10	0.727693	0.363847	−	0.931459i	$-0.381463\pi$
$907$	1.63521e10	0.727693	0.363847	+	0.931459i	$0.381463\pi$
$908$	−2.26336e10	−1.00335
$909$	0	0
$910$	1.36710e9	0.0601387
$911$	−5.02950e9	−0.220399	−0.110200	−	0.993909i	$-0.535149\pi$
$911$	−5.02950e9	−0.220399	−0.110200	+	0.993909i	$0.535149\pi$
$912$	0	0
$913$	7.87075e9	0.342270
$914$	−1.99348e10	−0.863574
$915$	0	0
$916$	−1.83356e9	−0.0788243
$917$	4.35280e9	0.186413
$918$	0	0
$919$	−2.98229e10	−1.26749	−0.633746	−	0.773541i	$-0.718483\pi$
$919$	−2.98229e10	−1.26749	−0.633746	+	0.773541i	$0.718483\pi$
$920$	2.82723e10	1.19702
$921$	0	0
$922$	−6.36837e9	−0.267590
$923$	2.73993e9	0.114692
$924$	0	0
$925$	1.02530e10	0.425947
$926$	−5.55885e10	−2.30063
$927$	0	0
$928$	1.20172e11	4.93610
$929$	−1.92466e10	−0.787589	−0.393794	−	0.919199i	$-0.628838\pi$
$929$	−1.92466e10	−0.787589	−0.393794	+	0.919199i	$0.628838\pi$
$930$	0	0
$931$	−1.48281e10	−0.602228
$932$	3.85449e10	1.55959
$933$	0	0
$934$	−2.07714e10	−0.834164
$935$	2.73115e9	0.109271
$936$	0	0
$937$	2.73206e10	1.08493	0.542465	−	0.840078i	$-0.317491\pi$
$937$	2.73206e10	1.08493	0.542465	+	0.840078i	$0.317491\pi$
$938$	−2.61121e10	−1.03308
$939$	0	0
$940$	−9.05664e9	−0.355648
$941$	−4.38771e10	−1.71662	−0.858309	−	0.513132i	$-0.828485\pi$
$941$	−4.38771e10	−1.71662	−0.858309	+	0.513132i	$0.828485\pi$
$942$	0	0
$943$	1.45610e10	0.565457
$944$	1.12020e10	0.433405
$945$	0	0
$946$	1.67854e9	0.0644633
$947$	7.76685e9	0.297180	0.148590	−	0.988899i	$-0.452526\pi$
$947$	7.76685e9	0.297180	0.148590	+	0.988899i	$0.452526\pi$
$948$	0	0
$949$	2.61659e8	0.00993811
$950$	5.16842e10	1.95580
$951$	0	0
$952$	−8.86992e10	−3.33189
$953$	8.96167e9	0.335401	0.167700	−	0.985838i	$-0.446366\pi$
$953$	8.96167e9	0.335401	0.167700	+	0.985838i	$0.446366\pi$
$954$	0	0
$955$	−2.50517e9	−0.0930734
$956$	−7.94448e10	−2.94078
$957$	0	0
$958$	−2.24692e10	−0.825672
$959$	2.84331e10	1.04102
$960$	0	0
$961$	−2.72111e10	−0.989040
$962$	2.92585e9	0.105959
$963$	0	0
$964$	−7.23859e10	−2.60246
$965$	−3.10503e8	−0.0111230
$966$	0	0
$967$	3.13646e10	1.11544	0.557721	−	0.830029i	$-0.311676\pi$
$967$	3.13646e10	1.11544	0.557721	+	0.830029i	$0.311676\pi$
$968$	8.54126e10	3.02662
$969$	0	0
$970$	2.06358e7	0.000725971 0
$971$	3.71209e10	1.30122	0.650611	−	0.759411i	$-0.274513\pi$
$971$	3.71209e10	1.30122	0.650611	+	0.759411i	$0.274513\pi$
$972$	0	0
$973$	−5.53783e9	−0.192728
$974$	−3.33056e10	−1.15494
$975$	0	0
$976$	1.36890e11	4.71299
$977$	−3.64354e10	−1.24995	−0.624975	−	0.780644i	$-0.714891\pi$
$977$	−3.64354e10	−1.24995	−0.624975	+	0.780644i	$0.714891\pi$
$978$	0	0
$979$	−5.17439e9	−0.176246
$980$	−1.54815e10	−0.525437
$981$	0	0
$982$	1.78659e10	0.602052
$983$	4.88356e9	0.163983	0.0819915	−	0.996633i	$-0.473872\pi$
$983$	4.88356e9	0.163983	0.0819915	+	0.996633i	$0.473872\pi$
$984$	0	0
$985$	−1.65416e9	−0.0551508
$986$	−1.31282e11	−4.36149
$987$	0	0
$988$	1.06968e10	0.352862
$989$	−5.37190e9	−0.176580
$990$	0	0
$991$	2.89018e10	0.943336	0.471668	−	0.881776i	$-0.343652\pi$
$991$	2.89018e10	0.943336	0.471668	+	0.881776i	$0.343652\pi$
$992$	1.03734e10	0.337389
$993$	0	0
$994$	4.43719e10	1.43303
$995$	−1.43175e10	−0.460772
$996$	0	0
$997$	−8.79812e9	−0.281162	−0.140581	−	0.990069i	$-0.544897\pi$
$997$	−8.79812e9	−0.281162	−0.140581	+	0.990069i	$0.544897\pi$
$998$	1.09848e11	3.49811
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	531.8.a.c.1.2		17
3.2	odd	2		177.8.a.c.1.16	✓	17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.8.a.c.1.16	✓	17	3.2	odd	2
531.8.a.c.1.2		17	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-21.5848 q^{2} +337.903 q^{4} +113.334 q^{5} -647.523 q^{7} -4530.72 q^{8} +O(q^{10})\)	\(q-21.5848 q^{2} +337.903 q^{4} +113.334 q^{5} -647.523 q^{7} -4530.72 q^{8} -2446.30 q^{10} -797.052 q^{11} +863.046 q^{13} +13976.6 q^{14} +54543.1 q^{16} -30234.1 q^{17} +36679.8 q^{19} +38296.1 q^{20} +17204.2 q^{22} -55059.3 q^{23} -65280.3 q^{25} -18628.7 q^{26} -218800. q^{28} -201168. q^{29} -17365.2 q^{31} -597369. q^{32} +652597. q^{34} -73386.6 q^{35} -157061. q^{37} -791727. q^{38} -513487. q^{40} -264460. q^{41} +97565.6 q^{43} -269327. q^{44} +1.18844e6 q^{46} -236490. q^{47} -404257. q^{49} +1.40906e6 q^{50} +291626. q^{52} +524092. q^{53} -90333.5 q^{55} +2.93375e6 q^{56} +4.34217e6 q^{58} +205379. q^{59} +2.50976e6 q^{61} +374823. q^{62} +5.91257e6 q^{64} +97812.8 q^{65} -1.86827e6 q^{67} -1.02162e7 q^{68} +1.58404e6 q^{70} +3.17472e6 q^{71} +303181. q^{73} +3.39014e6 q^{74} +1.23942e7 q^{76} +516110. q^{77} +3.54094e6 q^{79} +6.18161e6 q^{80} +5.70830e6 q^{82} -9.87483e6 q^{83} -3.42656e6 q^{85} -2.10593e6 q^{86} +3.61122e6 q^{88} +6.49191e6 q^{89} -558842. q^{91} -1.86047e7 q^{92} +5.10459e6 q^{94} +4.15709e6 q^{95} -8435.50 q^{97} +8.72581e6 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q - 2 q^{2} + 1166 q^{4} + 318 q^{5} + 3145 q^{7} - 2355 q^{8}+O(q^{10}) \) 17 * q - 2 * q^2 + 1166 * q^4 + 318 * q^5 + 3145 * q^7 - 2355 * q^8	\( 17 q - 2 q^{2} + 1166 q^{4} + 318 q^{5} + 3145 q^{7} - 2355 q^{8} + 6521 q^{10} + 1764 q^{11} + 18192 q^{13} + 7827 q^{14} + 139226 q^{16} + 15507 q^{17} + 52083 q^{19} - 721 q^{20} - 234434 q^{22} - 63823 q^{23} + 202153 q^{25} + 367956 q^{26} + 182306 q^{28} + 502955 q^{29} + 347531 q^{31} + 243908 q^{32} - 330872 q^{34} - 92641 q^{35} + 447615 q^{37} - 775669 q^{38} + 2203270 q^{40} - 940335 q^{41} + 478562 q^{43} + 596924 q^{44} - 3078663 q^{46} - 703121 q^{47} + 1895082 q^{49} + 876967 q^{50} + 6278296 q^{52} + 1005974 q^{53} + 5212846 q^{55} - 3425294 q^{56} + 6710166 q^{58} + 3491443 q^{59} + 11510749 q^{61} - 5996234 q^{62} + 29496941 q^{64} - 11094180 q^{65} + 14007144 q^{67} - 19688159 q^{68} + 30909708 q^{70} - 5229074 q^{71} + 5452211 q^{73} - 12819662 q^{74} + 41929340 q^{76} - 9930777 q^{77} + 15275654 q^{79} - 36576105 q^{80} + 32025935 q^{82} - 7826609 q^{83} + 11836945 q^{85} - 51649136 q^{86} + 30223741 q^{88} + 6436185 q^{89} + 11633535 q^{91} - 43357972 q^{92} - 4494252 q^{94} - 23741055 q^{95} + 26377540 q^{97} - 26517816 q^{98}+O(q^{100}) \) 17 * q - 2 * q^2 + 1166 * q^4 + 318 * q^5 + 3145 * q^7 - 2355 * q^8 + 6521 * q^10 + 1764 * q^11 + 18192 * q^13 + 7827 * q^14 + 139226 * q^16 + 15507 * q^17 + 52083 * q^19 - 721 * q^20 - 234434 * q^22 - 63823 * q^23 + 202153 * q^25 + 367956 * q^26 + 182306 * q^28 + 502955 * q^29 + 347531 * q^31 + 243908 * q^32 - 330872 * q^34 - 92641 * q^35 + 447615 * q^37 - 775669 * q^38 + 2203270 * q^40 - 940335 * q^41 + 478562 * q^43 + 596924 * q^44 - 3078663 * q^46 - 703121 * q^47 + 1895082 * q^49 + 876967 * q^50 + 6278296 * q^52 + 1005974 * q^53 + 5212846 * q^55 - 3425294 * q^56 + 6710166 * q^58 + 3491443 * q^59 + 11510749 * q^61 - 5996234 * q^62 + 29496941 * q^64 - 11094180 * q^65 + 14007144 * q^67 - 19688159 * q^68 + 30909708 * q^70 - 5229074 * q^71 + 5452211 * q^73 - 12819662 * q^74 + 41929340 * q^76 - 9930777 * q^77 + 15275654 * q^79 - 36576105 * q^80 + 32025935 * q^82 - 7826609 * q^83 + 11836945 * q^85 - 51649136 * q^86 + 30223741 * q^88 + 6436185 * q^89 + 11633535 * q^91 - 43357972 * q^92 - 4494252 * q^94 - 23741055 * q^95 + 26377540 * q^97 - 26517816 * q^98

Introduction

L-functions

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