LMFDB - Embedded newform 325.10.a.h.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [325,10,Mod(1,325)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(325, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("325.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 325 = 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	325.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:	$167.386646753$
Analytic rank:	$1$
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} - x^{16} - 6453 x^{15} - 11965 x^{14} + 16673200 x^{13} + 68278926 x^{12} - 22023799708 x^{11} + \cdots + 22\!\cdots\!80 $ x^17 - x^16 - 6453x^15 - 11965x^14 + 16673200x^13 + 68278926x^12 - 22023799708x^11 - 125071202096x^10 + 15798589803808x^9 + 104438346864256x^8 - 6069247386513920x^7 - 42150961741219840x^6 + 1176708099630112256x^5 + 8192400410671614464x^4 - 105394686485039805440x^3 - 728872183505786896384x^2 + 3347611667766002909184*x + 22946266613430737633280
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{16}\cdot 3^{4}\cdot 5^{8} $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$32.7069$ of defining polynomial
Character	$\chi$	$=$	325.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-30.7069 q^{2} -116.164 q^{3} +430.914 q^{4} +3567.03 q^{6} -1957.66 q^{7} +2489.89 q^{8} -6188.99 q^{9} +27073.5 q^{11} -50056.6 q^{12} -28561.0 q^{13} +60113.8 q^{14} -297085. q^{16} +363224. q^{17} +190045. q^{18} -87100.6 q^{19} +227410. q^{21} -831345. q^{22} -224073. q^{23} -289235. q^{24} +877020. q^{26} +3.00539e6 q^{27} -843585. q^{28} -572339. q^{29} -7.95101e6 q^{31} +7.84774e6 q^{32} -3.14496e6 q^{33} -1.11535e7 q^{34} -2.66692e6 q^{36} +2.65011e6 q^{37} +2.67459e6 q^{38} +3.31775e6 q^{39} +4.68573e6 q^{41} -6.98304e6 q^{42} -2.42200e7 q^{43} +1.16664e7 q^{44} +6.88060e6 q^{46} -2.82299e7 q^{47} +3.45105e7 q^{48} -3.65212e7 q^{49} -4.21934e7 q^{51} -1.23073e7 q^{52} +7.40558e7 q^{53} -9.22861e7 q^{54} -4.87437e6 q^{56} +1.01179e7 q^{57} +1.75748e7 q^{58} +7.09261e7 q^{59} -1.89647e8 q^{61} +2.44151e8 q^{62} +1.21160e7 q^{63} -8.88723e7 q^{64} +9.65721e7 q^{66} -1.70010e7 q^{67} +1.56518e8 q^{68} +2.60292e7 q^{69} -1.52641e7 q^{71} -1.54099e7 q^{72} +3.62458e8 q^{73} -8.13766e7 q^{74} -3.75329e7 q^{76} -5.30009e7 q^{77} -1.01878e8 q^{78} +6.23908e7 q^{79} -2.27299e8 q^{81} -1.43884e8 q^{82} +6.45847e7 q^{83} +9.79940e7 q^{84} +7.43720e8 q^{86} +6.64851e7 q^{87} +6.74102e7 q^{88} +1.99711e8 q^{89} +5.59128e7 q^{91} -9.65564e7 q^{92} +9.23619e8 q^{93} +8.66852e8 q^{94} -9.11622e8 q^{96} +7.09268e8 q^{97} +1.12145e9 q^{98} -1.67558e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17 q + 33 q^{2} - 73 q^{3} + 4267 q^{4} - 1103 q^{6} + 10670 q^{7} - 11481 q^{8} + 47590 q^{9} - 130917 q^{11} - 32239 q^{12} - 485537 q^{13} - 292206 q^{14} + 1064251 q^{16} + 193953 q^{17} + 2026286 q^{18}+ \cdots - 3023832936 q^{99}+O(q^{100}) $ 17 * q + 33 * q^2 - 73 * q^3 + 4267 * q^4 - 1103 * q^6 + 10670 * q^7 - 11481 * q^8 + 47590 * q^9 - 130917 * q^11 - 32239 * q^12 - 485537 * q^13 - 292206 * q^14 + 1064251 * q^16 + 193953 * q^17 + 2026286 * q^18 - 1244111 * q^19 - 115896 * q^21 + 786475 * q^22 + 2599170 * q^23 + 1304331 * q^24 - 942513 * q^26 - 6747967 * q^27 + 14275516 * q^28 - 2247174 * q^29 - 7948896 * q^31 - 23873169 * q^32 + 13542215 * q^33 - 5605153 * q^34 - 25196656 * q^36 - 17455504 * q^37 - 33099219 * q^38 + 2084953 * q^39 - 28253763 * q^41 - 71221836 * q^42 + 28631126 * q^43 - 123980223 * q^44 - 124743136 * q^46 + 41505678 * q^47 - 51624919 * q^48 + 88370777 * q^49 - 97297213 * q^51 - 121869787 * q^52 + 20918940 * q^53 - 279383933 * q^54 - 81987402 * q^56 + 168605047 * q^57 + 533278432 * q^58 - 242672658 * q^59 - 236730546 * q^61 - 630173268 * q^62 + 563712646 * q^63 - 8650957 * q^64 - 247702451 * q^66 - 33870225 * q^67 + 521453709 * q^68 - 16163890 * q^69 - 809145252 * q^71 - 632968230 * q^72 - 460218191 * q^73 + 540389844 * q^74 - 1067090107 * q^76 - 331946328 * q^77 + 31502783 * q^78 - 295742582 * q^79 - 1013246447 * q^81 - 436735349 * q^82 - 298090917 * q^83 - 2574679448 * q^84 - 2183241552 * q^86 - 164038106 * q^87 + 961546625 * q^88 - 448474185 * q^89 - 304745870 * q^91 - 1091742000 * q^92 - 1680564078 * q^93 - 2962970430 * q^94 + 2289126403 * q^96 + 2630881746 * q^97 + 236409993 * q^98 - 3023832936 * q^99

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 $

$2$	−30.7069	−1.35707	−0.678533	−	0.734570i	$-0.737384\pi$
$2$	−30.7069	−1.35707	−0.678533	+	0.734570i	$0.737384\pi$
$3$	−116.164	−0.827990	−0.413995	−	0.910279i	$-0.635867\pi$
$3$	−116.164	−0.827990	−0.413995	+	0.910279i	$0.635867\pi$
$4$	430.914	0.841630
$5$	0	0
$5$	0	0
$6$	3567.03	1.12364
$7$	−1957.66	−0.308175	−0.154087	−	0.988057i	$-0.549244\pi$
$7$	−1957.66	−0.308175	−0.154087	+	0.988057i	$0.549244\pi$
$8$	2489.89	0.214919
$9$	−6188.99	−0.314433
$10$	0	0
$11$	27073.5	0.557543	0.278771	−	0.960358i	$-0.410073\pi$
$11$	27073.5	0.557543	0.278771	+	0.960358i	$0.410073\pi$
$12$	−50056.6	−0.696860
$13$	−28561.0	−0.277350
$13$	−28561.0	−0.277350
$14$	60113.8	0.418214
$15$	0	0
$16$	−297085.	−1.13329
$17$	363224.	1.05476	0.527380	−	0.849629i	$-0.323174\pi$
$17$	363224.	1.05476	0.527380	+	0.849629i	$0.323174\pi$
$18$	190045.	0.426707
$19$	−87100.6	−0.153331	−0.0766655	−	0.997057i	$-0.524427\pi$
$19$	−87100.6	−0.153331	−0.0766655	+	0.997057i	$0.524427\pi$
$20$	0	0
$21$	227410.	0.255165
$22$	−831345.	−0.756622
$23$	−224073.	−0.166961	−0.0834805	−	0.996509i	$-0.526604\pi$
$23$	−224073.	−0.166961	−0.0834805	+	0.996509i	$0.526604\pi$
$24$	−289235.	−0.177951
$25$	0	0
$26$	877020.	0.376383
$27$	3.00539e6	1.08834
$28$	−843585.	−0.259369
$29$	−572339.	−0.150267	−0.0751333	−	0.997173i	$-0.523938\pi$
$29$	−572339.	−0.150267	−0.0751333	+	0.997173i	$0.523938\pi$
$30$	0	0
$31$	−7.95101e6	−1.54630	−0.773151	−	0.634221i	$-0.781321\pi$
$31$	−7.95101e6	−1.54630	−0.773151	+	0.634221i	$0.781321\pi$
$32$	7.84774e6	1.32303
$33$	−3.14496e6	−0.461640
$34$	−1.11535e7	−1.43138
$35$	0	0
$36$	−2.66692e6	−0.264636
$37$	2.65011e6	0.232464	0.116232	−	0.993222i	$-0.462918\pi$
$37$	2.65011e6	0.232464	0.116232	+	0.993222i	$0.462918\pi$
$38$	2.67459e6	0.208080
$39$	3.31775e6	0.229643
$40$	0	0
$41$	4.68573e6	0.258970	0.129485	−	0.991581i	$-0.458668\pi$
$41$	4.68573e6	0.258970	0.129485	+	0.991581i	$0.458668\pi$
$42$	−6.98304e6	−0.346276
$43$	−2.42200e7	−1.08035	−0.540176	−	0.841552i	$-0.681642\pi$
$43$	−2.42200e7	−1.08035	−0.540176	+	0.841552i	$0.681642\pi$
$44$	1.16664e7	0.469244
$45$	0	0
$46$	6.88060e6	0.226577
$47$	−2.82299e7	−0.843856	−0.421928	−	0.906629i	$-0.638647\pi$
$47$	−2.82299e7	−0.843856	−0.421928	+	0.906629i	$0.638647\pi$
$48$	3.45105e7	0.938352
$49$	−3.65212e7	−0.905028
$50$	0	0
$51$	−4.21934e7	−0.873331
$52$	−1.23073e7	−0.233426
$53$	7.40558e7	1.28919	0.644596	−	0.764524i	$-0.277026\pi$
$53$	7.40558e7	1.28919	0.644596	+	0.764524i	$0.277026\pi$
$54$	−9.22861e7	−1.47695
$55$	0	0
$56$	−4.87437e6	−0.0662327
$57$	1.01179e7	0.126956
$58$	1.75748e7	0.203922
$59$	7.09261e7	0.762030	0.381015	−	0.924569i	$-0.375575\pi$
$59$	7.09261e7	0.762030	0.381015	+	0.924569i	$0.375575\pi$
$60$	0	0
$61$	−1.89647e8	−1.75372	−0.876861	−	0.480743i	$-0.840367\pi$
$61$	−1.89647e8	−1.75372	−0.876861	+	0.480743i	$0.840367\pi$
$62$	2.44151e8	2.09844
$63$	1.21160e7	0.0969004
$64$	−8.88723e7	−0.662150
$65$	0	0
$66$	9.65721e7	0.626476
$67$	−1.70010e7	−0.103071	−0.0515357	−	0.998671i	$-0.516412\pi$
$67$	−1.70010e7	−0.103071	−0.0515357	+	0.998671i	$0.516412\pi$
$68$	1.56518e8	0.887717
$69$	2.60292e7	0.138242
$70$	0	0
$71$	−1.52641e7	−0.0712869	−0.0356435	−	0.999365i	$-0.511348\pi$
$71$	−1.52641e7	−0.0712869	−0.0356435	+	0.999365i	$0.511348\pi$
$72$	−1.54099e7	−0.0675778
$73$	3.62458e8	1.49384	0.746922	−	0.664912i	$-0.231531\pi$
$73$	3.62458e8	1.49384	0.746922	+	0.664912i	$0.231531\pi$
$74$	−8.13766e7	−0.315469
$75$	0	0
$76$	−3.75329e7	−0.129048
$77$	−5.30009e7	−0.171821
$78$	−1.01878e8	−0.311641
$79$	6.23908e7	0.180218	0.0901092	−	0.995932i	$-0.471278\pi$
$79$	6.23908e7	0.180218	0.0901092	+	0.995932i	$0.471278\pi$
$80$	0	0
$81$	−2.27299e8	−0.586699
$82$	−1.43884e8	−0.351440
$83$	6.45847e7	0.149375	0.0746875	−	0.997207i	$-0.476204\pi$
$83$	6.45847e7	0.149375	0.0746875	+	0.997207i	$0.476204\pi$
$84$	9.79940e7	0.214755
$85$	0	0
$86$	7.43720e8	1.46611
$87$	6.64851e7	0.124419
$88$	6.74102e7	0.119827
$89$	1.99711e8	0.337402	0.168701	−	0.985667i	$-0.446043\pi$
$89$	1.99711e8	0.337402	0.168701	+	0.985667i	$0.446043\pi$
$90$	0	0
$91$	5.59128e7	0.0854723
$92$	−9.65564e7	−0.140519
$93$	9.23619e8	1.28032
$94$	8.66852e8	1.14517
$95$	0	0
$96$	−9.11622e8	−1.09545
$97$	7.09268e8	0.813462	0.406731	−	0.913548i	$-0.366669\pi$
$97$	7.09268e8	0.813462	0.406731	+	0.913548i	$0.366669\pi$
$98$	1.12145e9	1.22818
$99$	−1.67558e8	−0.175310
$100$	0	0
$101$	1.34545e9	1.28653	0.643267	−	0.765642i	$-0.277579\pi$
$101$	1.34545e9	1.28653	0.643267	+	0.765642i	$0.277579\pi$
$102$	1.29563e9	1.18517
$103$	−2.61682e8	−0.229090	−0.114545	−	0.993418i	$-0.536541\pi$
$103$	−2.61682e8	−0.229090	−0.114545	+	0.993418i	$0.536541\pi$
$104$	−7.11138e7	−0.0596079
$105$	0	0
$106$	−2.27402e9	−1.74952
$107$	2.56252e9	1.88991	0.944955	−	0.327201i	$-0.106105\pi$
$107$	2.56252e9	1.88991	0.944955	+	0.327201i	$0.106105\pi$
$108$	1.29506e9	0.915977
$109$	1.28736e9	0.873534	0.436767	−	0.899575i	$-0.356124\pi$
$109$	1.28736e9	0.873534	0.436767	+	0.899575i	$0.356124\pi$
$110$	0	0
$111$	−3.07846e8	−0.192478
$112$	5.81593e8	0.349251
$113$	−2.24508e8	−0.129533	−0.0647663	−	0.997900i	$-0.520630\pi$
$113$	−2.24508e8	−0.129533	−0.0647663	+	0.997900i	$0.520630\pi$
$114$	−3.10690e8	−0.172288
$115$	0	0
$116$	−2.46629e8	−0.126469
$117$	1.76764e8	0.0872081
$118$	−2.17792e9	−1.03413
$119$	−7.11070e8	−0.325050
$120$	0	0
$121$	−1.62497e9	−0.689146
$122$	5.82346e9	2.37992
$123$	−5.44312e8	−0.214425
$124$	−3.42620e9	−1.30141
$125$	0	0
$126$	−3.72044e8	−0.131500
$127$	4.03635e9	1.37680	0.688401	−	0.725330i	$-0.258313\pi$
$127$	4.03635e9	1.37680	0.688401	+	0.725330i	$0.258313\pi$
$128$	−1.28905e9	−0.424448
$129$	2.81348e9	0.894520
$130$	0	0
$131$	4.42094e8	0.131158	0.0655789	−	0.997847i	$-0.479111\pi$
$131$	4.42094e8	0.131158	0.0655789	+	0.997847i	$0.479111\pi$
$132$	−1.35521e9	−0.388529
$133$	1.70514e8	0.0472527
$134$	5.22048e8	0.139875
$135$	0	0
$136$	9.04387e8	0.226688
$137$	2.60112e9	0.630839	0.315420	−	0.948952i	$-0.397855\pi$
$137$	2.60112e9	0.630839	0.315420	+	0.948952i	$0.397855\pi$
$138$	−7.99276e8	−0.187603
$139$	1.09708e9	0.249271	0.124635	−	0.992203i	$-0.460224\pi$
$139$	1.09708e9	0.249271	0.124635	+	0.992203i	$0.460224\pi$
$140$	0	0
$141$	3.27929e9	0.698704
$142$	4.68715e8	0.0967411
$143$	−7.73248e8	−0.154635
$144$	1.83866e9	0.356344
$145$	0	0
$146$	−1.11300e10	−2.02725
$147$	4.24243e9	0.749354
$148$	1.14197e9	0.195649
$149$	3.71549e9	0.617558	0.308779	−	0.951134i	$-0.400080\pi$
$149$	3.71549e9	0.617558	0.308779	+	0.951134i	$0.400080\pi$
$150$	0	0
$151$	−6.65481e9	−1.04169	−0.520846	−	0.853651i	$-0.674383\pi$
$151$	−6.65481e9	−1.04169	−0.520846	+	0.853651i	$0.674383\pi$
$152$	−2.16871e8	−0.0329538
$153$	−2.24799e9	−0.331652
$154$	1.62749e9	0.233172
$155$	0	0
$156$	1.42967e9	0.193274
$157$	7.11165e9	0.934162	0.467081	−	0.884215i	$-0.345306\pi$
$157$	7.11165e9	0.934162	0.467081	+	0.884215i	$0.345306\pi$
$158$	−1.91583e9	−0.244568
$159$	−8.60259e9	−1.06744
$160$	0	0
$161$	4.38660e8	0.0514531
$162$	6.97965e9	0.796189
$163$	−5.89815e9	−0.654443	−0.327221	−	0.944948i	$-0.606112\pi$
$163$	−5.89815e9	−0.654443	−0.327221	+	0.944948i	$0.606112\pi$
$164$	2.01915e9	0.217957
$165$	0	0
$166$	−1.98320e9	−0.202712
$167$	4.90068e8	0.0487565	0.0243782	−	0.999703i	$-0.492239\pi$
$167$	4.90068e8	0.0487565	0.0243782	+	0.999703i	$0.492239\pi$
$168$	5.66225e8	0.0548400
$169$	8.15731e8	0.0769231
$170$	0	0
$171$	5.39065e8	0.0482124
$172$	−1.04367e10	−0.909256
$173$	−4.97367e9	−0.422152	−0.211076	−	0.977470i	$-0.567697\pi$
$173$	−4.97367e9	−0.422152	−0.211076	+	0.977470i	$0.567697\pi$
$174$	−2.04155e9	−0.168845
$175$	0	0
$176$	−8.04314e9	−0.631857
$177$	−8.23904e9	−0.630953
$178$	−6.13251e9	−0.457876
$179$	1.86761e10	1.35972	0.679858	−	0.733344i	$-0.262041\pi$
$179$	1.86761e10	1.35972	0.679858	+	0.733344i	$0.262041\pi$
$180$	0	0
$181$	−9.46092e9	−0.655209	−0.327604	−	0.944815i	$-0.606241\pi$
$181$	−9.46092e9	−0.655209	−0.327604	+	0.944815i	$0.606241\pi$
$182$	−1.71691e9	−0.115992
$183$	2.20301e10	1.45206
$184$	−5.57918e8	−0.0358831
$185$	0	0
$186$	−2.83615e10	−1.73748
$187$	9.83375e9	0.588074
$188$	−1.21647e10	−0.710214
$189$	−5.88354e9	−0.335398
$190$	0	0
$191$	1.69581e10	0.921994	0.460997	−	0.887402i	$-0.347492\pi$
$191$	1.69581e10	0.921994	0.460997	+	0.887402i	$0.347492\pi$
$192$	1.03237e10	0.548253
$193$	−1.79066e10	−0.928979	−0.464490	−	0.885579i	$-0.653762\pi$
$193$	−1.79066e10	−0.928979	−0.464490	+	0.885579i	$0.653762\pi$
$194$	−2.17794e10	−1.10392
$195$	0	0
$196$	−1.57375e10	−0.761699
$197$	8.40094e9	0.397402	0.198701	−	0.980060i	$-0.436328\pi$
$197$	8.40094e9	0.397402	0.198701	+	0.980060i	$0.436328\pi$
$198$	5.14519e9	0.237907
$199$	1.27713e10	0.577292	0.288646	−	0.957436i	$-0.406795\pi$
$199$	1.27713e10	0.577292	0.288646	+	0.957436i	$0.406795\pi$
$200$	0	0
$201$	1.97490e9	0.0853420
$202$	−4.13146e10	−1.74591
$203$	1.12045e9	0.0463084
$204$	−1.81817e10	−0.735021
$205$	0	0
$206$	8.03544e9	0.310890
$207$	1.38679e9	0.0524981
$208$	8.48504e9	0.314318
$209$	−2.35812e9	−0.0854886
$210$	0	0
$211$	−2.25817e10	−0.784308	−0.392154	−	0.919900i	$-0.628270\pi$
$211$	−2.25817e10	−0.784308	−0.392154	+	0.919900i	$0.628270\pi$
$212$	3.19117e10	1.08502
$213$	1.77314e9	0.0590248
$214$	−7.86872e10	−2.56473
$215$	0	0
$216$	7.48308e9	0.233905
$217$	1.55654e10	0.476531
$218$	−3.95307e10	−1.18544
$219$	−4.21045e10	−1.23689
$220$	0	0
$221$	−1.03740e10	−0.292538
$222$	9.45301e9	0.261205
$223$	−5.98447e10	−1.62052	−0.810259	−	0.586071i	$-0.800674\pi$
$223$	−5.98447e10	−1.62052	−0.810259	+	0.586071i	$0.800674\pi$
$224$	−1.53632e10	−0.407724
$225$	0	0
$226$	6.89395e9	0.175784
$227$	−5.84969e10	−1.46223	−0.731116	−	0.682253i	$-0.761000\pi$
$227$	−5.84969e10	−1.46223	−0.731116	+	0.682253i	$0.761000\pi$
$228$	4.35996e9	0.106850
$229$	−2.99677e10	−0.720102	−0.360051	−	0.932933i	$-0.617241\pi$
$229$	−2.99677e10	−0.720102	−0.360051	+	0.932933i	$0.617241\pi$
$230$	0	0
$231$	6.15678e9	0.142266
$232$	−1.42506e9	−0.0322952
$233$	2.27856e7	0.000506475 0	0.000253238	−	1.00000i	$-0.499919\pi$
$233$	2.27856e7	0.000506475 0	0.000253238		1.00000i	$0.499919\pi$
$234$	−5.42787e9	−0.118347
$235$	0	0
$236$	3.05631e10	0.641347
$237$	−7.24755e9	−0.149219
$238$	2.18347e10	0.441115
$239$	−6.05149e10	−1.19970	−0.599849	−	0.800114i	$-0.704773\pi$
$239$	−6.05149e10	−1.19970	−0.599849	+	0.800114i	$0.704773\pi$
$240$	0	0
$241$	−2.52017e9	−0.0481231	−0.0240616	−	0.999710i	$-0.507660\pi$
$241$	−2.52017e9	−0.0481231	−0.0240616	+	0.999710i	$0.507660\pi$
$242$	4.98978e10	0.935217
$243$	−3.27511e10	−0.602557
$244$	−8.17215e10	−1.47598
$245$	0	0
$246$	1.67141e10	0.290989
$247$	2.48768e9	0.0425264
$248$	−1.97971e10	−0.332330
$249$	−7.50240e9	−0.123681
$250$	0	0
$251$	3.51793e10	0.559442	0.279721	−	0.960081i	$-0.409758\pi$
$251$	3.51793e10	0.559442	0.279721	+	0.960081i	$0.409758\pi$
$252$	5.22094e9	0.0815542
$253$	−6.06646e9	−0.0930878
$254$	−1.23944e11	−1.86841
$255$	0	0
$256$	8.50853e10	1.23815
$257$	8.55003e10	1.22256	0.611278	−	0.791416i	$-0.290656\pi$
$257$	8.55003e10	1.22256	0.611278	+	0.791416i	$0.290656\pi$
$258$	−8.63933e10	−1.21392
$259$	−5.18802e9	−0.0716395
$260$	0	0
$261$	3.54220e9	0.0472488
$262$	−1.35754e10	−0.177990
$263$	−6.50520e10	−0.838416	−0.419208	−	0.907890i	$-0.637692\pi$
$263$	−6.50520e10	−0.838416	−0.419208	+	0.907890i	$0.637692\pi$
$264$	−7.83062e9	−0.0992152
$265$	0	0
$266$	−5.23595e9	−0.0641251
$267$	−2.31992e10	−0.279365
$268$	−7.32598e9	−0.0867479
$269$	−6.07953e10	−0.707921	−0.353961	−	0.935260i	$-0.615165\pi$
$269$	−6.07953e10	−0.707921	−0.353961	+	0.935260i	$0.615165\pi$
$270$	0	0
$271$	1.47895e11	1.66568	0.832839	−	0.553516i	$-0.186714\pi$
$271$	1.47895e11	1.66568	0.832839	+	0.553516i	$0.186714\pi$
$272$	−1.07908e11	−1.19535
$273$	−6.49504e9	−0.0707702
$274$	−7.98725e10	−0.856091
$275$	0	0
$276$	1.12163e10	0.116348
$277$	4.40418e10	0.449475	0.224738	−	0.974419i	$-0.427848\pi$
$277$	4.40418e10	0.449475	0.224738	+	0.974419i	$0.427848\pi$
$278$	−3.36879e10	−0.338277
$279$	4.92087e10	0.486209
$280$	0	0
$281$	−9.41646e10	−0.900968	−0.450484	−	0.892785i	$-0.648749\pi$
$281$	−9.41646e10	−0.900968	−0.450484	+	0.892785i	$0.648749\pi$
$282$	−1.00697e11	−0.948188
$283$	1.46961e11	1.36196	0.680978	−	0.732304i	$-0.261555\pi$
$283$	1.46961e11	1.36196	0.680978	+	0.732304i	$0.261555\pi$
$284$	−6.57754e9	−0.0599972
$285$	0	0
$286$	2.37440e10	0.209849
$287$	−9.17308e9	−0.0798081
$288$	−4.85696e10	−0.416004
$289$	1.33434e10	0.112519
$290$	0	0
$291$	−8.23912e10	−0.673538
$292$	1.56189e11	1.25726
$293$	3.85762e10	0.305784	0.152892	−	0.988243i	$-0.451141\pi$
$293$	3.85762e10	0.305784	0.152892	+	0.988243i	$0.451141\pi$
$294$	−1.30272e11	−1.01692
$295$	0	0
$296$	6.59848e9	0.0499610
$297$	8.13665e10	0.606794
$298$	−1.14091e11	−0.838068
$299$	6.39976e9	0.0463066
$300$	0	0
$301$	4.74145e10	0.332937
$302$	2.04349e11	1.41365
$303$	−1.56292e11	−1.06524
$304$	2.58763e10	0.173768
$305$	0	0
$306$	6.90287e10	0.450073
$307$	−1.51568e11	−0.973836	−0.486918	−	0.873448i	$-0.661879\pi$
$307$	−1.51568e11	−0.973836	−0.486918	+	0.873448i	$0.661879\pi$
$308$	−2.28388e10	−0.144609
$309$	3.03980e10	0.189684
$310$	0	0
$311$	−1.17012e11	−0.709268	−0.354634	−	0.935005i	$-0.615395\pi$
$311$	−1.17012e11	−0.709268	−0.354634	+	0.935005i	$0.615395\pi$
$312$	8.26084e9	0.0493547
$313$	−1.78793e11	−1.05294	−0.526468	−	0.850195i	$-0.676484\pi$
$313$	−1.78793e11	−1.05294	−0.526468	+	0.850195i	$0.676484\pi$
$314$	−2.18377e11	−1.26772
$315$	0	0
$316$	2.68851e10	0.151677
$317$	−9.91584e10	−0.551522	−0.275761	−	0.961226i	$-0.588930\pi$
$317$	−9.91584e10	−0.551522	−0.275761	+	0.961226i	$0.588930\pi$
$318$	2.64159e11	1.44858
$319$	−1.54953e10	−0.0837801
$320$	0	0
$321$	−2.97672e11	−1.56483
$322$	−1.34699e10	−0.0698253
$323$	−3.16370e10	−0.161727
$324$	−9.79464e10	−0.493783
$325$	0	0
$326$	1.81114e11	0.888122
$327$	−1.49544e11	−0.723277
$328$	1.16670e10	0.0556577
$329$	5.52646e10	0.260055
$330$	0	0
$331$	−2.03975e11	−0.934011	−0.467005	−	0.884255i	$-0.654667\pi$
$331$	−2.03975e11	−0.934011	−0.467005	+	0.884255i	$0.654667\pi$
$332$	2.78305e10	0.125718
$333$	−1.64015e10	−0.0730944
$334$	−1.50485e10	−0.0661658
$335$	0	0
$336$	−6.75600e10	−0.289176
$337$	7.79569e10	0.329246	0.164623	−	0.986357i	$-0.447359\pi$
$337$	7.79569e10	0.329246	0.164623	+	0.986357i	$0.447359\pi$
$338$	−2.50486e10	−0.104390
$339$	2.60797e10	0.107252
$340$	0	0
$341$	−2.15262e11	−0.862130
$342$	−1.65530e10	−0.0654274
$343$	1.50495e11	0.587081
$344$	−6.03051e10	−0.232189
$345$	0	0
$346$	1.52726e11	0.572889
$347$	1.42399e11	0.527260	0.263630	−	0.964624i	$-0.415080\pi$
$347$	1.42399e11	0.527260	0.263630	+	0.964624i	$0.415080\pi$
$348$	2.86494e10	0.104715
$349$	3.21774e11	1.16101	0.580505	−	0.814257i	$-0.302855\pi$
$349$	3.21774e11	1.16101	0.580505	+	0.814257i	$0.302855\pi$
$350$	0	0
$351$	−8.58368e10	−0.301850
$352$	2.12466e11	0.737645
$353$	7.71921e10	0.264598	0.132299	−	0.991210i	$-0.457764\pi$
$353$	7.71921e10	0.264598	0.132299	+	0.991210i	$0.457764\pi$
$354$	2.52995e11	0.856245
$355$	0	0
$356$	8.60584e10	0.283967
$357$	8.26005e10	0.269138
$358$	−5.73486e11	−1.84522
$359$	8.53202e10	0.271098	0.135549	−	0.990771i	$-0.456720\pi$
$359$	8.53202e10	0.271098	0.135549	+	0.990771i	$0.456720\pi$
$360$	0	0
$361$	−3.15101e11	−0.976490
$362$	2.90515e11	0.889162
$363$	1.88763e11	0.570606
$364$	2.40936e10	0.0719360
$365$	0	0
$366$	−6.76475e11	−1.97055
$367$	4.03079e11	1.15983	0.579913	−	0.814678i	$-0.303086\pi$
$367$	4.03079e11	1.15983	0.579913	+	0.814678i	$0.303086\pi$
$368$	6.65688e10	0.189215
$369$	−2.89999e10	−0.0814289
$370$	0	0
$371$	−1.44976e11	−0.397296
$372$	3.98001e11	1.07756
$373$	−2.43635e11	−0.651703	−0.325851	−	0.945421i	$-0.605651\pi$
$373$	−2.43635e11	−0.651703	−0.325851	+	0.945421i	$0.605651\pi$
$374$	−3.01964e11	−0.798055
$375$	0	0
$376$	−7.02893e10	−0.181361
$377$	1.63466e10	0.0416765
$378$	1.80665e11	0.455157
$379$	1.88570e11	0.469458	0.234729	−	0.972061i	$-0.424580\pi$
$379$	1.88570e11	0.469458	0.234729	+	0.972061i	$0.424580\pi$
$380$	0	0
$381$	−4.68877e11	−1.13998
$382$	−5.20732e11	−1.25121
$383$	−1.88684e11	−0.448065	−0.224033	−	0.974582i	$-0.571922\pi$
$383$	−1.88684e11	−0.448065	−0.224033	+	0.974582i	$0.571922\pi$
$384$	1.49741e11	0.351439
$385$	0	0
$386$	5.49857e11	1.26069
$387$	1.49897e11	0.339699
$388$	3.05634e11	0.684634
$389$	−3.57962e11	−0.792618	−0.396309	−	0.918117i	$-0.629709\pi$
$389$	−3.57962e11	−0.792618	−0.396309	+	0.918117i	$0.629709\pi$
$390$	0	0
$391$	−8.13887e10	−0.176104
$392$	−9.09337e10	−0.194508
$393$	−5.13553e10	−0.108597
$394$	−2.57967e11	−0.539301
$395$	0	0
$396$	−7.22031e10	−0.147546
$397$	2.60956e11	0.527242	0.263621	−	0.964626i	$-0.415083\pi$
$397$	2.60956e11	0.527242	0.263621	+	0.964626i	$0.415083\pi$
$398$	−3.92167e11	−0.783424
$399$	−1.98075e10	−0.0391248
$400$	0	0
$401$	−6.13426e11	−1.18471	−0.592355	−	0.805677i	$-0.701802\pi$
$401$	−6.13426e11	−1.18471	−0.592355	+	0.805677i	$0.701802\pi$
$402$	−6.06431e10	−0.115815
$403$	2.27089e11	0.428867
$404$	5.79774e11	1.08279
$405$	0	0
$406$	−3.44055e10	−0.0628435
$407$	7.17478e10	0.129609
$408$	−1.05057e11	−0.187696
$409$	4.44382e11	0.785238	0.392619	−	0.919701i	$-0.371569\pi$
$409$	4.44382e11	0.785238	0.392619	+	0.919701i	$0.371569\pi$
$410$	0	0
$411$	−3.02156e11	−0.522328
$412$	−1.12763e11	−0.192809
$413$	−1.38849e11	−0.234838
$414$	−4.25839e10	−0.0712434
$415$	0	0
$416$	−2.24139e11	−0.366942
$417$	−1.27441e11	−0.206393
$418$	7.24107e10	0.116014
$419$	9.07812e11	1.43891	0.719454	−	0.694541i	$-0.244392\pi$
$419$	9.07812e11	1.43891	0.719454	+	0.694541i	$0.244392\pi$
$420$	0	0
$421$	7.68297e11	1.19195	0.595977	−	0.803001i	$-0.296765\pi$
$421$	7.68297e11	1.19195	0.595977	+	0.803001i	$0.296765\pi$
$422$	6.93416e11	1.06436
$423$	1.74714e11	0.265336
$424$	1.84391e11	0.277072
$425$	0	0
$426$	−5.44477e10	−0.0801006
$427$	3.71264e11	0.540453
$428$	1.10423e12	1.59060
$429$	8.98233e10	0.128036
$430$	0	0
$431$	6.60645e11	0.922190	0.461095	−	0.887351i	$-0.347457\pi$
$431$	6.60645e11	0.922190	0.461095	+	0.887351i	$0.347457\pi$
$432$	−8.92855e11	−1.23340
$433$	7.19098e8	0.000983089 0	0.000491544	−	1.00000i	$-0.499844\pi$
$433$	7.19098e8	0.000983089 0	0.000491544		1.00000i	$0.499844\pi$
$434$	−4.77965e11	−0.646685
$435$	0	0
$436$	5.54740e11	0.735192
$437$	1.95169e10	0.0256003
$438$	1.29290e12	1.67854
$439$	3.93610e11	0.505797	0.252898	−	0.967493i	$-0.418616\pi$
$439$	3.93610e11	0.505797	0.252898	+	0.967493i	$0.418616\pi$
$440$	0	0
$441$	2.26029e11	0.284571
$442$	3.18554e11	0.396993
$443$	−4.99039e11	−0.615628	−0.307814	−	0.951447i	$-0.599597\pi$
$443$	−4.99039e11	−0.615628	−0.307814	+	0.951447i	$0.599597\pi$
$444$	−1.32655e11	−0.161995
$445$	0	0
$446$	1.83765e12	2.19915
$447$	−4.31605e11	−0.511332
$448$	1.73982e11	0.204058
$449$	1.05750e12	1.22793	0.613963	−	0.789335i	$-0.289574\pi$
$449$	1.05750e12	1.22793	0.613963	+	0.789335i	$0.289574\pi$
$450$	0	0
$451$	1.26859e11	0.144387
$452$	−9.67438e10	−0.109018
$453$	7.73047e11	0.862510
$454$	1.79626e12	1.98435
$455$	0	0
$456$	2.51925e10	0.0272854
$457$	−1.14326e12	−1.22609	−0.613046	−	0.790047i	$-0.710056\pi$
$457$	−1.14326e12	−1.22609	−0.613046	+	0.790047i	$0.710056\pi$
$458$	9.20216e11	0.977226
$459$	1.09163e12	1.14793
$460$	0	0
$461$	6.86468e11	0.707890	0.353945	−	0.935266i	$-0.384840\pi$
$461$	6.86468e11	0.707890	0.353945	+	0.935266i	$0.384840\pi$
$462$	−1.89056e11	−0.193064
$463$	2.80081e10	0.0283250	0.0141625	−	0.999900i	$-0.495492\pi$
$463$	2.80081e10	0.0283250	0.0141625	+	0.999900i	$0.495492\pi$
$464$	1.70033e11	0.170296
$465$	0	0
$466$	−6.99675e8	−0.000687321 0
$467$	1.60767e12	1.56412	0.782061	−	0.623202i	$-0.214168\pi$
$467$	1.60767e12	1.56412	0.782061	+	0.623202i	$0.214168\pi$
$468$	7.61700e10	0.0733969
$469$	3.32823e10	0.0317640
$470$	0	0
$471$	−8.26116e11	−0.773476
$472$	1.76598e11	0.163775
$473$	−6.55720e11	−0.602342
$474$	2.22550e11	0.202500
$475$	0	0
$476$	−3.06410e11	−0.273572
$477$	−4.58330e11	−0.405365
$478$	1.85822e12	1.62807
$479$	−4.86376e11	−0.422145	−0.211073	−	0.977470i	$-0.567696\pi$
$479$	−4.86376e11	−0.422145	−0.211073	+	0.977470i	$0.567696\pi$
$480$	0	0
$481$	−7.56897e10	−0.0644739
$482$	7.73867e10	0.0653063
$483$	−5.09564e10	−0.0426027
$484$	−7.00223e11	−0.580006
$485$	0	0
$486$	1.00569e12	0.817710
$487$	−4.44103e11	−0.357769	−0.178885	−	0.983870i	$-0.557249\pi$
$487$	−4.44103e11	−0.357769	−0.178885	+	0.983870i	$0.557249\pi$
$488$	−4.72200e11	−0.376909
$489$	6.85151e11	0.541872
$490$	0	0
$491$	3.58783e11	0.278590	0.139295	−	0.990251i	$-0.455516\pi$
$491$	3.58783e11	0.278590	0.139295	+	0.990251i	$0.455516\pi$
$492$	−2.34552e11	−0.180466
$493$	−2.07887e11	−0.158495
$494$	−7.63890e10	−0.0577111
$495$	0	0
$496$	2.36213e12	1.75241
$497$	2.98821e10	0.0219688
$498$	2.30375e11	0.167843
$499$	2.87985e11	0.207930	0.103965	−	0.994581i	$-0.466847\pi$
$499$	2.87985e11	0.207930	0.103965	+	0.994581i	$0.466847\pi$
$500$	0	0
$501$	−5.69281e10	−0.0403699
$502$	−1.08025e12	−0.759200
$503$	−2.11191e12	−1.47103	−0.735513	−	0.677511i	$-0.763059\pi$
$503$	−2.11191e12	−1.47103	−0.735513	+	0.677511i	$0.763059\pi$
$504$	3.01674e10	0.0208258
$505$	0	0
$506$	1.86282e11	0.126326
$507$	−9.47583e10	−0.0636915
$508$	1.73932e12	1.15876
$509$	−2.39142e12	−1.57916	−0.789581	−	0.613646i	$-0.789702\pi$
$509$	−2.39142e12	−1.57916	−0.789581	+	0.613646i	$0.789702\pi$
$510$	0	0
$511$	−7.09572e11	−0.460365
$512$	−1.95271e12	−1.25581
$513$	−2.61771e11	−0.166876
$514$	−2.62545e12	−1.65909
$515$	0	0
$516$	1.21237e12	0.752855
$517$	−7.64283e11	−0.470486
$518$	1.59308e11	0.0972196
$519$	5.77760e11	0.349538
$520$	0	0
$521$	−1.83163e12	−1.08910	−0.544549	−	0.838729i	$-0.683299\pi$
$521$	−1.83163e12	−1.08910	−0.544549	+	0.838729i	$0.683299\pi$
$522$	−1.08770e11	−0.0641198
$523$	−1.97276e12	−1.15297	−0.576483	−	0.817109i	$-0.695575\pi$
$523$	−1.97276e12	−1.15297	−0.576483	+	0.817109i	$0.695575\pi$
$524$	1.90505e11	0.110386
$525$	0	0
$526$	1.99755e12	1.13779
$527$	−2.88799e12	−1.63098
$528$	9.34322e11	0.523171
$529$	−1.75094e12	−0.972124
$530$	0	0
$531$	−4.38961e11	−0.239607
$532$	7.34768e10	0.0397693
$533$	−1.33829e11	−0.0718254
$534$	7.12375e11	0.379117
$535$	0	0
$536$	−4.23307e10	−0.0221520
$537$	−2.16949e12	−1.12583
$538$	1.86684e12	0.960696
$539$	−9.88757e11	−0.504592
$540$	0	0
$541$	2.73309e12	1.37172	0.685862	−	0.727731i	$-0.259425\pi$
$541$	2.73309e12	1.37172	0.685862	+	0.727731i	$0.259425\pi$
$542$	−4.54139e12	−2.26044
$543$	1.09902e12	0.542506
$544$	2.85048e12	1.39548
$545$	0	0
$546$	1.99443e11	0.0960398
$547$	−3.61895e12	−1.72838	−0.864192	−	0.503163i	$-0.832170\pi$
$547$	−3.61895e12	−1.72838	−0.864192	+	0.503163i	$0.832170\pi$
$548$	1.12086e12	0.530933
$549$	1.17372e12	0.551429
$550$	0	0
$551$	4.98511e10	0.0230405
$552$	6.48098e10	0.0297109
$553$	−1.22140e11	−0.0555387
$554$	−1.35239e12	−0.609968
$555$	0	0
$556$	4.72747e11	0.209794
$557$	2.72407e12	1.19914	0.599570	−	0.800322i	$-0.295338\pi$
$557$	2.72407e12	1.19914	0.599570	+	0.800322i	$0.295338\pi$
$558$	−1.51105e12	−0.659818
$559$	6.91746e11	0.299636
$560$	0	0
$561$	−1.14232e12	−0.486919
$562$	2.89150e12	1.22267
$563$	−1.23357e12	−0.517457	−0.258729	−	0.965950i	$-0.583304\pi$
$563$	−1.23357e12	−0.517457	−0.258729	+	0.965950i	$0.583304\pi$
$564$	1.41309e12	0.588050
$565$	0	0
$566$	−4.51272e12	−1.84827
$567$	4.44975e11	0.180806
$568$	−3.80061e10	−0.0153209
$569$	−1.70088e11	−0.0680250	−0.0340125	−	0.999421i	$-0.510829\pi$
$569$	−1.70088e11	−0.0680250	−0.0340125	+	0.999421i	$0.510829\pi$
$570$	0	0
$571$	1.02034e12	0.401684	0.200842	−	0.979624i	$-0.435632\pi$
$571$	1.02034e12	0.401684	0.200842	+	0.979624i	$0.435632\pi$
$572$	−3.33203e11	−0.130145
$573$	−1.96992e12	−0.763401
$574$	2.81677e11	0.108305
$575$	0	0
$576$	5.50029e11	0.208202
$577$	−1.54010e12	−0.578438	−0.289219	−	0.957263i	$-0.593396\pi$
$577$	−1.54010e12	−0.578438	−0.289219	+	0.957263i	$0.593396\pi$
$578$	−4.09736e11	−0.152696
$579$	2.08010e12	0.769185
$580$	0	0
$581$	−1.26435e11	−0.0460336
$582$	2.52998e12	0.914036
$583$	2.00495e12	0.718779
$584$	9.02482e11	0.321056
$585$	0	0
$586$	−1.18455e12	−0.414969
$587$	−2.72445e12	−0.947126	−0.473563	−	0.880760i	$-0.657032\pi$
$587$	−2.72445e12	−0.947126	−0.473563	+	0.880760i	$0.657032\pi$
$588$	1.82813e12	0.630679
$589$	6.92538e11	0.237096
$590$	0	0
$591$	−9.75885e11	−0.329045
$592$	−7.87307e11	−0.263449
$593$	−1.50341e12	−0.499266	−0.249633	−	0.968341i	$-0.580310\pi$
$593$	−1.50341e12	−0.499266	−0.249633	+	0.968341i	$0.580310\pi$
$594$	−2.49851e12	−0.823460
$595$	0	0
$596$	1.60106e12	0.519755
$597$	−1.48356e12	−0.477992
$598$	−1.96517e11	−0.0628412
$599$	1.53971e12	0.488672	0.244336	−	0.969691i	$-0.421430\pi$
$599$	1.53971e12	0.488672	0.244336	+	0.969691i	$0.421430\pi$
$600$	0	0
$601$	−4.93363e12	−1.54252	−0.771261	−	0.636519i	$-0.780374\pi$
$601$	−4.93363e12	−1.54252	−0.771261	+	0.636519i	$0.780374\pi$
$602$	−1.45595e12	−0.451818
$603$	1.05219e11	0.0324091
$604$	−2.86765e12	−0.876719
$605$	0	0
$606$	4.79926e12	1.44560
$607$	−5.30962e12	−1.58750	−0.793751	−	0.608243i	$-0.791875\pi$
$607$	−5.30962e12	−1.58750	−0.793751	+	0.608243i	$0.791875\pi$
$608$	−6.83543e11	−0.202861
$609$	−1.30155e11	−0.0383428
$610$	0	0
$611$	8.06273e11	0.234044
$612$	−9.68690e11	−0.279128
$613$	−2.24135e12	−0.641116	−0.320558	−	0.947229i	$-0.603870\pi$
$613$	−2.24135e12	−0.641116	−0.320558	+	0.947229i	$0.603870\pi$
$614$	4.65420e12	1.32156
$615$	0	0
$616$	−1.31966e11	−0.0369275
$617$	−3.06345e12	−0.850995	−0.425497	−	0.904960i	$-0.639901\pi$
$617$	−3.06345e12	−0.850995	−0.425497	+	0.904960i	$0.639901\pi$
$618$	−9.33427e11	−0.257414
$619$	1.59329e12	0.436202	0.218101	−	0.975926i	$-0.430014\pi$
$619$	1.59329e12	0.436202	0.218101	+	0.975926i	$0.430014\pi$
$620$	0	0
$621$	−6.73427e11	−0.181710
$622$	3.59309e12	0.962524
$623$	−3.90967e11	−0.103979
$624$	−9.85654e11	−0.260252
$625$	0	0
$626$	5.49019e12	1.42890
$627$	2.73928e11	0.0707836
$628$	3.06451e12	0.786218
$629$	9.62582e11	0.245194
$630$	0	0
$631$	1.22287e12	0.307077	0.153538	−	0.988143i	$-0.450933\pi$
$631$	1.22287e12	0.307077	0.153538	+	0.988143i	$0.450933\pi$
$632$	1.55346e11	0.0387324
$633$	2.62318e12	0.649398
$634$	3.04485e12	0.748452
$635$	0	0
$636$	−3.70698e12	−0.898387
$637$	1.04308e12	0.251010
$638$	4.75811e11	0.113695
$639$	9.44696e10	0.0224150
$640$	0	0
$641$	−1.17908e12	−0.275856	−0.137928	−	0.990442i	$-0.544044\pi$
$641$	−1.17908e12	−0.275856	−0.137928	+	0.990442i	$0.544044\pi$
$642$	9.14060e12	2.12357
$643$	−4.45678e12	−1.02819	−0.514093	−	0.857734i	$-0.671871\pi$
$643$	−4.45678e12	−1.02819	−0.514093	+	0.857734i	$0.671871\pi$
$644$	1.89025e11	0.0433045
$645$	0	0
$646$	9.71474e11	0.219475
$647$	3.56755e12	0.800389	0.400194	−	0.916430i	$-0.368943\pi$
$647$	3.56755e12	0.800389	0.400194	+	0.916430i	$0.368943\pi$
$648$	−5.65950e11	−0.126093
$649$	1.92022e12	0.424864
$650$	0	0
$651$	−1.80813e12	−0.394563
$652$	−2.54160e12	−0.550798
$653$	−1.21320e12	−0.261109	−0.130554	−	0.991441i	$-0.541676\pi$
$653$	−1.21320e12	−0.261109	−0.130554	+	0.991441i	$0.541676\pi$
$654$	4.59204e12	0.981535
$655$	0	0
$656$	−1.39206e12	−0.293488
$657$	−2.24325e12	−0.469714
$658$	−1.69700e12	−0.352912
$659$	−7.70957e12	−1.59238	−0.796188	−	0.605049i	$-0.793154\pi$
$659$	−7.70957e12	−1.59238	−0.796188	+	0.605049i	$0.793154\pi$
$660$	0	0
$661$	1.79581e12	0.365892	0.182946	−	0.983123i	$-0.441437\pi$
$661$	1.79581e12	0.365892	0.182946	+	0.983123i	$0.441437\pi$
$662$	6.26345e12	1.26751
$663$	1.20509e12	0.242218
$664$	1.60809e11	0.0321036
$665$	0	0
$666$	5.03639e11	0.0991940
$667$	1.28246e11	0.0250887
$668$	2.11177e11	0.0410349
$669$	6.95179e12	1.34177
$670$	0	0
$671$	−5.13441e12	−0.977775
$672$	1.78465e12	0.337591
$673$	8.00387e12	1.50395	0.751973	−	0.659194i	$-0.229102\pi$
$673$	8.00387e12	1.50395	0.751973	+	0.659194i	$0.229102\pi$
$674$	−2.39382e12	−0.446808
$675$	0	0
$676$	3.51510e11	0.0647407
$677$	6.40368e12	1.17160	0.585802	−	0.810454i	$-0.300780\pi$
$677$	6.40368e12	1.17160	0.585802	+	0.810454i	$0.300780\pi$
$678$	−8.00827e11	−0.145548
$679$	−1.38851e12	−0.250688
$680$	0	0
$681$	6.79522e12	1.21071
$682$	6.61003e12	1.16997
$683$	−9.26091e12	−1.62840	−0.814199	−	0.580587i	$-0.802823\pi$
$683$	−9.26091e12	−1.62840	−0.814199	+	0.580587i	$0.802823\pi$
$684$	2.32291e11	0.0405769
$685$	0	0
$686$	−4.62123e12	−0.796709
$687$	3.48116e12	0.596237
$688$	7.19539e12	1.22435
$689$	−2.11511e12	−0.357557
$690$	0	0
$691$	1.32532e12	0.221142	0.110571	−	0.993868i	$-0.464732\pi$
$691$	1.32532e12	0.221142	0.110571	+	0.993868i	$0.464732\pi$
$692$	−2.14322e12	−0.355296
$693$	3.28022e11	0.0540261
$694$	−4.37264e12	−0.715527
$695$	0	0
$696$	1.65541e11	0.0267401
$697$	1.70197e12	0.273152
$698$	−9.88067e12	−1.57557
$699$	−2.64686e9	−0.000419356 0
$700$	0	0
$701$	−1.04308e13	−1.63149	−0.815747	−	0.578409i	$-0.803674\pi$
$701$	−1.04308e13	−1.63149	−0.815747	+	0.578409i	$0.803674\pi$
$702$	2.63578e12	0.409631
$703$	−2.30826e11	−0.0356440
$704$	−2.40609e12	−0.369177
$705$	0	0
$706$	−2.37033e12	−0.359077
$707$	−2.63394e12	−0.396477
$708$	−3.55032e12	−0.531028
$709$	1.48226e12	0.220301	0.110150	−	0.993915i	$-0.464867\pi$
$709$	1.48226e12	0.220301	0.110150	+	0.993915i	$0.464867\pi$
$710$	0	0
$711$	−3.86136e11	−0.0566666
$712$	4.97259e11	0.0725141
$713$	1.78161e12	0.258172
$714$	−2.53641e12	−0.365239
$715$	0	0
$716$	8.04781e12	1.14438
$717$	7.02963e12	0.993337
$718$	−2.61992e12	−0.367898
$719$	−3.56718e12	−0.497788	−0.248894	−	0.968531i	$-0.580067\pi$
$719$	−3.56718e12	−0.497788	−0.248894	+	0.968531i	$0.580067\pi$
$720$	0	0
$721$	5.12285e11	0.0705998
$722$	9.67578e12	1.32516
$723$	2.92753e11	0.0398454
$724$	−4.07684e12	−0.551443
$725$	0	0
$726$	−5.79632e12	−0.774350
$727$	1.65301e12	0.219468	0.109734	−	0.993961i	$-0.465000\pi$
$727$	1.65301e12	0.219468	0.109734	+	0.993961i	$0.465000\pi$
$728$	1.39217e11	0.0183696
$729$	8.27842e12	1.08561
$730$	0	0
$731$	−8.79726e12	−1.13951
$732$	9.49307e12	1.22210
$733$	9.83874e12	1.25884	0.629421	−	0.777064i	$-0.283292\pi$
$733$	9.83874e12	1.25884	0.629421	+	0.777064i	$0.283292\pi$
$734$	−1.23773e13	−1.57396
$735$	0	0
$736$	−1.75847e12	−0.220894
$737$	−4.60278e11	−0.0574667
$738$	8.90498e11	0.110504
$739$	−1.45950e13	−1.80014	−0.900068	−	0.435749i	$-0.856484\pi$
$739$	−1.45950e13	−1.80014	−0.900068	+	0.435749i	$0.856484\pi$
$740$	0	0
$741$	−2.88978e11	−0.0352114
$742$	4.45177e12	0.539157
$743$	2.18759e12	0.263340	0.131670	−	0.991294i	$-0.457966\pi$
$743$	2.18759e12	0.263340	0.131670	+	0.991294i	$0.457966\pi$
$744$	2.29971e12	0.275166
$745$	0	0
$746$	7.48127e12	0.884404
$747$	−3.99714e11	−0.0469685
$748$	4.23750e12	0.494940
$749$	−5.01656e12	−0.582422
$750$	0	0
$751$	−2.92254e12	−0.335259	−0.167630	−	0.985850i	$-0.553611\pi$
$751$	−2.92254e12	−0.335259	−0.167630	+	0.985850i	$0.553611\pi$
$752$	8.38667e12	0.956333
$753$	−4.08656e12	−0.463212
$754$	−5.01953e11	−0.0565577
$755$	0	0
$756$	−2.53530e12	−0.282281
$757$	1.25903e11	0.0139350	0.00696748	−	0.999976i	$-0.497782\pi$
$757$	1.25903e11	0.0139350	0.00696748	+	0.999976i	$0.497782\pi$
$758$	−5.79041e12	−0.637085
$759$	7.04702e11	0.0770758
$760$	0	0
$761$	−1.56609e13	−1.69272	−0.846361	−	0.532610i	$-0.821211\pi$
$761$	−1.56609e13	−1.69272	−0.846361	+	0.532610i	$0.821211\pi$
$762$	1.43978e13	1.54703
$763$	−2.52021e12	−0.269201
$764$	7.30750e12	0.775977
$765$	0	0
$766$	5.79391e12	0.608055
$767$	−2.02572e12	−0.211349
$768$	−9.88383e12	−1.02518
$769$	−1.36642e13	−1.40902	−0.704508	−	0.709696i	$-0.748832\pi$
$769$	−1.36642e13	−1.40902	−0.704508	+	0.709696i	$0.748832\pi$
$770$	0	0
$771$	−9.93203e12	−1.01226
$772$	−7.71622e12	−0.781856
$773$	1.13099e13	1.13933	0.569665	−	0.821877i	$-0.307073\pi$
$773$	1.13099e13	1.13933	0.569665	+	0.821877i	$0.307073\pi$
$774$	−4.60288e12	−0.460994
$775$	0	0
$776$	1.76600e12	0.174829
$777$	6.02660e11	0.0593168
$778$	1.09919e13	1.07564
$779$	−4.08130e11	−0.0397082
$780$	0	0
$781$	−4.13255e11	−0.0397455
$782$	2.49920e12	0.238985
$783$	−1.72010e12	−0.163541
$784$	1.08499e13	1.02566
$785$	0	0
$786$	1.57696e12	0.147374
$787$	−1.23575e13	−1.14827	−0.574133	−	0.818762i	$-0.694661\pi$
$787$	−1.23575e13	−1.14827	−0.574133	+	0.818762i	$0.694661\pi$
$788$	3.62009e12	0.334465
$789$	7.55668e12	0.694200
$790$	0	0
$791$	4.39511e11	0.0399187
$792$	−4.17201e11	−0.0376775
$793$	5.41650e12	0.486395
$794$	−8.01315e12	−0.715502
$795$	0	0
$796$	5.50333e12	0.485866
$797$	−1.28829e13	−1.13097	−0.565485	−	0.824758i	$-0.691311\pi$
$797$	−1.28829e13	−1.13097	−0.565485	+	0.824758i	$0.691311\pi$
$798$	6.08227e11	0.0530949
$799$	−1.02538e13	−0.890066
$800$	0	0
$801$	−1.23601e12	−0.106090
$802$	1.88364e13	1.60773
$803$	9.81303e12	0.832882
$804$	8.51013e11	0.0718264
$805$	0	0
$806$	−6.97319e12	−0.582001
$807$	7.06221e12	0.586152
$808$	3.35002e12	0.276501
$809$	2.53503e12	0.208072	0.104036	−	0.994574i	$-0.466824\pi$
$809$	2.53503e12	0.208072	0.104036	+	0.994574i	$0.466824\pi$
$810$	0	0
$811$	−2.05903e12	−0.167135	−0.0835677	−	0.996502i	$-0.526631\pi$
$811$	−2.05903e12	−0.167135	−0.0835677	+	0.996502i	$0.526631\pi$
$812$	4.82817e11	0.0389745
$813$	−1.71800e13	−1.37916
$814$	−2.20315e12	−0.175888
$815$	0	0
$816$	1.25350e13	0.989736
$817$	2.10957e12	0.165651
$818$	−1.36456e13	−1.06562
$819$	−3.46044e11	−0.0268753
$820$	0	0
$821$	3.30701e12	0.254034	0.127017	−	0.991901i	$-0.459460\pi$
$821$	3.30701e12	0.254034	0.127017	+	0.991901i	$0.459460\pi$
$822$	9.27829e12	0.708834
$823$	7.30832e11	0.0555288	0.0277644	−	0.999614i	$-0.491161\pi$
$823$	7.30832e11	0.0555288	0.0277644	+	0.999614i	$0.491161\pi$
$824$	−6.51560e11	−0.0492359
$825$	0	0
$826$	4.26364e12	0.318691
$827$	−9.77172e12	−0.726434	−0.363217	−	0.931705i	$-0.618322\pi$
$827$	−9.77172e12	−0.726434	−0.363217	+	0.931705i	$0.618322\pi$
$828$	5.97586e11	0.0441839
$829$	−2.50861e13	−1.84475	−0.922374	−	0.386299i	$-0.873753\pi$
$829$	−2.50861e13	−1.84475	−0.922374	+	0.386299i	$0.873753\pi$
$830$	0	0
$831$	−5.11606e12	−0.372161
$832$	2.53828e12	0.183647
$833$	−1.32653e13	−0.954588
$834$	3.91331e12	0.280090
$835$	0	0
$836$	−1.01615e12	−0.0719497
$837$	−2.38959e13	−1.68290
$838$	−2.78761e13	−1.95269
$839$	−1.88412e12	−0.131274	−0.0656370	−	0.997844i	$-0.520908\pi$
$839$	−1.88412e12	−0.131274	−0.0656370	+	0.997844i	$0.520908\pi$
$840$	0	0
$841$	−1.41796e13	−0.977420
$842$	−2.35920e13	−1.61756
$843$	1.09385e13	0.745992
$844$	−9.73080e12	−0.660096
$845$	0	0
$846$	−5.36494e12	−0.360079
$847$	3.18115e12	0.212377
$848$	−2.20009e13	−1.46103
$849$	−1.70715e13	−1.12769
$850$	0	0
$851$	−5.93819e11	−0.0388124
$852$	7.64071e11	0.0496771
$853$	2.94969e13	1.90768	0.953842	−	0.300309i	$-0.0970899\pi$
$853$	2.94969e13	1.90768	0.953842	+	0.300309i	$0.0970899\pi$
$854$	−1.14004e13	−0.733431
$855$	0	0
$856$	6.38041e12	0.406178
$857$	−2.50876e12	−0.158871	−0.0794356	−	0.996840i	$-0.525312\pi$
$857$	−2.50876e12	−0.158871	−0.0794356	+	0.996840i	$0.525312\pi$
$858$	−2.75820e12	−0.173753
$859$	1.92591e13	1.20689	0.603444	−	0.797405i	$-0.293795\pi$
$859$	1.92591e13	1.20689	0.603444	+	0.797405i	$0.293795\pi$
$860$	0	0
$861$	1.06558e12	0.0660802
$862$	−2.02864e13	−1.25147
$863$	2.06285e13	1.26596	0.632980	−	0.774168i	$-0.281831\pi$
$863$	2.06285e13	1.26596	0.632980	+	0.774168i	$0.281831\pi$
$864$	2.35855e13	1.43990
$865$	0	0
$866$	−2.20813e10	−0.00133412
$867$	−1.55002e12	−0.0931649
$868$	6.70735e12	0.401063
$869$	1.68914e12	0.100479
$870$	0	0
$871$	4.85566e11	0.0285869
$872$	3.20538e12	0.187739
$873$	−4.38965e12	−0.255779
$874$	−5.99304e11	−0.0347413
$875$	0	0
$876$	−1.81434e13	−1.04100
$877$	3.02157e13	1.72478	0.862390	−	0.506244i	$-0.168966\pi$
$877$	3.02157e13	1.72478	0.862390	+	0.506244i	$0.168966\pi$
$878$	−1.20865e13	−0.686400
$879$	−4.48115e12	−0.253186
$880$	0	0
$881$	1.85017e13	1.03471	0.517356	−	0.855770i	$-0.326916\pi$
$881$	1.85017e13	1.03471	0.517356	+	0.855770i	$0.326916\pi$
$882$	−6.94065e12	−0.386182
$883$	−1.38720e13	−0.767921	−0.383961	−	0.923349i	$-0.625440\pi$
$883$	−1.38720e13	−0.767921	−0.383961	+	0.923349i	$0.625440\pi$
$884$	−4.47032e12	−0.246209
$885$	0	0
$886$	1.53240e13	0.835448
$887$	−2.20852e13	−1.19797	−0.598984	−	0.800761i	$-0.704429\pi$
$887$	−2.20852e13	−1.19797	−0.598984	+	0.800761i	$0.704429\pi$
$888$	−7.66504e11	−0.0413672
$889$	−7.90181e12	−0.424296
$890$	0	0
$891$	−6.15379e12	−0.327109
$892$	−2.57880e13	−1.36388
$893$	2.45884e12	0.129389
$894$	1.32533e13	0.693911
$895$	0	0
$896$	2.52352e12	0.130804
$897$	−7.43420e11	−0.0383414
$898$	−3.24726e13	−1.66638
$899$	4.55067e12	0.232358
$900$	0	0
$901$	2.68988e13	1.35979
$902$	−3.89546e12	−0.195943
$903$	−5.50785e12	−0.275668
$904$	−5.59001e11	−0.0278391
$905$	0	0
$906$	−2.37379e13	−1.17048
$907$	1.50279e13	0.737336	0.368668	−	0.929561i	$-0.379814\pi$
$907$	1.50279e13	0.737336	0.368668	+	0.929561i	$0.379814\pi$
$908$	−2.52071e13	−1.23066
$909$	−8.32697e12	−0.404529
$910$	0	0
$911$	2.02336e13	0.973288	0.486644	−	0.873600i	$-0.338221\pi$
$911$	2.02336e13	0.973288	0.486644	+	0.873600i	$0.338221\pi$
$912$	−3.00589e12	−0.143878
$913$	1.74854e12	0.0832830
$914$	3.51061e13	1.66389
$915$	0	0
$916$	−1.29135e13	−0.606059
$917$	−8.65472e11	−0.0404195
$918$	−3.35205e13	−1.55782
$919$	−2.10036e13	−0.971347	−0.485673	−	0.874140i	$-0.661426\pi$
$919$	−2.10036e13	−0.971347	−0.485673	+	0.874140i	$0.661426\pi$
$920$	0	0
$921$	1.76068e13	0.806326
$922$	−2.10793e13	−0.960654
$923$	4.35959e11	0.0197714
$924$	2.65305e12	0.119735
$925$	0	0
$926$	−8.60043e11	−0.0384389
$927$	1.61955e12	0.0720335
$928$	−4.49157e12	−0.198807
$929$	−2.02768e13	−0.893159	−0.446580	−	0.894744i	$-0.647358\pi$
$929$	−2.02768e13	−0.893159	−0.446580	+	0.894744i	$0.647358\pi$
$930$	0	0
$931$	3.18102e12	0.138769
$932$	9.81863e9	0.000426265 0
$933$	1.35926e13	0.587267
$934$	−4.93665e13	−2.12262
$935$	0	0
$936$	4.40122e11	0.0187427
$937$	−3.63175e13	−1.53917	−0.769587	−	0.638542i	$-0.779538\pi$
$937$	−3.63175e13	−1.53917	−0.769587	+	0.638542i	$0.779538\pi$
$938$	−1.02200e12	−0.0431058
$939$	2.07693e13	0.871819
$940$	0	0
$941$	−8.42040e12	−0.350090	−0.175045	−	0.984560i	$-0.556007\pi$
$941$	−8.42040e12	−0.350090	−0.175045	+	0.984560i	$0.556007\pi$
$942$	2.53675e13	1.04966
$943$	−1.04995e12	−0.0432379
$944$	−2.10711e13	−0.863600
$945$	0	0
$946$	2.01351e13	0.817419
$947$	3.79409e12	0.153297	0.0766484	−	0.997058i	$-0.475578\pi$
$947$	3.79409e12	0.153297	0.0766484	+	0.997058i	$0.475578\pi$
$948$	−3.12307e12	−0.125587
$949$	−1.03522e13	−0.414318
$950$	0	0
$951$	1.15186e13	0.456655
$952$	−1.77049e12	−0.0698596
$953$	−9.45158e11	−0.0371182	−0.0185591	−	0.999828i	$-0.505908\pi$
$953$	−9.45158e11	−0.0371182	−0.0185591	+	0.999828i	$0.505908\pi$
$954$	1.40739e13	0.550107
$955$	0	0
$956$	−2.60767e13	−1.00970
$957$	1.79999e12	0.0693690
$958$	1.49351e13	0.572879
$959$	−5.09213e12	−0.194409
$960$	0	0
$961$	3.67789e13	1.39105
$962$	2.32420e12	0.0874954
$963$	−1.58594e13	−0.594250
$964$	−1.08598e12	−0.0405018
$965$	0	0
$966$	1.56471e12	0.0578146
$967$	1.49914e13	0.551344	0.275672	−	0.961252i	$-0.411100\pi$
$967$	1.49914e13	0.551344	0.275672	+	0.961252i	$0.411100\pi$
$968$	−4.04600e12	−0.148111
$969$	3.67507e12	0.133909
$970$	0	0
$971$	−2.36113e13	−0.852381	−0.426191	−	0.904633i	$-0.640145\pi$
$971$	−2.36113e13	−0.852381	−0.426191	+	0.904633i	$0.640145\pi$
$972$	−1.41129e13	−0.507130
$973$	−2.14771e12	−0.0768189
$974$	1.36370e13	0.485517
$975$	0	0
$976$	5.63412e13	1.98748
$977$	3.20135e13	1.12411	0.562053	−	0.827101i	$-0.310012\pi$
$977$	3.20135e13	1.12411	0.562053	+	0.827101i	$0.310012\pi$
$978$	−2.10389e13	−0.735356
$979$	5.40689e12	0.188116
$980$	0	0
$981$	−7.96744e12	−0.274668
$982$	−1.10171e13	−0.378065
$983$	−8.83785e12	−0.301895	−0.150948	−	0.988542i	$-0.548232\pi$
$983$	−8.83785e12	−0.301895	−0.150948	+	0.988542i	$0.548232\pi$
$984$	−1.35528e12	−0.0460840
$985$	0	0
$986$	6.38357e12	0.215089
$987$	−6.41974e12	−0.215323
$988$	1.07198e12	0.0357914
$989$	5.42705e12	0.180377
$990$	0	0
$991$	−1.68042e12	−0.0553459	−0.0276729	−	0.999617i	$-0.508810\pi$
$991$	−1.68042e12	−0.0553459	−0.0276729	+	0.999617i	$0.508810\pi$
$992$	−6.23974e13	−2.04580
$993$	2.36945e13	0.773351
$994$	−9.17586e11	−0.0298132
$995$	0	0
$996$	−3.23289e12	−0.104094
$997$	3.62155e13	1.16082	0.580412	−	0.814323i	$-0.302892\pi$
$997$	3.62155e13	1.16082	0.580412	+	0.814323i	$0.302892\pi$
$998$	−8.84314e12	−0.282175
$999$	7.96460e12	0.252999

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	325.10.a.h.1.3	yes	17
5.4	even	2		325.10.a.g.1.15	✓	17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
325.10.a.g.1.15	✓	17	5.4	even	2
325.10.a.h.1.3	yes	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:	\( N \)	\(=\)	\( 325 = 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	325.a (trivial)

\(f(q)\)	\(=\)	\(q-30.7069 q^{2} -116.164 q^{3} +430.914 q^{4} +3567.03 q^{6} -1957.66 q^{7} +2489.89 q^{8} -6188.99 q^{9} +27073.5 q^{11} -50056.6 q^{12} -28561.0 q^{13} +60113.8 q^{14} -297085. q^{16} +363224. q^{17} +190045. q^{18} -87100.6 q^{19} +227410. q^{21} -831345. q^{22} -224073. q^{23} -289235. q^{24} +877020. q^{26} +3.00539e6 q^{27} -843585. q^{28} -572339. q^{29} -7.95101e6 q^{31} +7.84774e6 q^{32} -3.14496e6 q^{33} -1.11535e7 q^{34} -2.66692e6 q^{36} +2.65011e6 q^{37} +2.67459e6 q^{38} +3.31775e6 q^{39} +4.68573e6 q^{41} -6.98304e6 q^{42} -2.42200e7 q^{43} +1.16664e7 q^{44} +6.88060e6 q^{46} -2.82299e7 q^{47} +3.45105e7 q^{48} -3.65212e7 q^{49} -4.21934e7 q^{51} -1.23073e7 q^{52} +7.40558e7 q^{53} -9.22861e7 q^{54} -4.87437e6 q^{56} +1.01179e7 q^{57} +1.75748e7 q^{58} +7.09261e7 q^{59} -1.89647e8 q^{61} +2.44151e8 q^{62} +1.21160e7 q^{63} -8.88723e7 q^{64} +9.65721e7 q^{66} -1.70010e7 q^{67} +1.56518e8 q^{68} +2.60292e7 q^{69} -1.52641e7 q^{71} -1.54099e7 q^{72} +3.62458e8 q^{73} -8.13766e7 q^{74} -3.75329e7 q^{76} -5.30009e7 q^{77} -1.01878e8 q^{78} +6.23908e7 q^{79} -2.27299e8 q^{81} -1.43884e8 q^{82} +6.45847e7 q^{83} +9.79940e7 q^{84} +7.43720e8 q^{86} +6.64851e7 q^{87} +6.74102e7 q^{88} +1.99711e8 q^{89} +5.59128e7 q^{91} -9.65564e7 q^{92} +9.23619e8 q^{93} +8.66852e8 q^{94} -9.11622e8 q^{96} +7.09268e8 q^{97} +1.12145e9 q^{98} -1.67558e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q + 33 q^{2} - 73 q^{3} + 4267 q^{4} - 1103 q^{6} + 10670 q^{7} - 11481 q^{8} + 47590 q^{9} - 130917 q^{11} - 32239 q^{12} - 485537 q^{13} - 292206 q^{14} + 1064251 q^{16} + 193953 q^{17} + 2026286 q^{18}+ \cdots - 3023832936 q^{99}+O(q^{100}) \) 17 * q + 33 * q^2 - 73 * q^3 + 4267 * q^4 - 1103 * q^6 + 10670 * q^7 - 11481 * q^8 + 47590 * q^9 - 130917 * q^11 - 32239 * q^12 - 485537 * q^13 - 292206 * q^14 + 1064251 * q^16 + 193953 * q^17 + 2026286 * q^18 - 1244111 * q^19 - 115896 * q^21 + 786475 * q^22 + 2599170 * q^23 + 1304331 * q^24 - 942513 * q^26 - 6747967 * q^27 + 14275516 * q^28 - 2247174 * q^29 - 7948896 * q^31 - 23873169 * q^32 + 13542215 * q^33 - 5605153 * q^34 - 25196656 * q^36 - 17455504 * q^37 - 33099219 * q^38 + 2084953 * q^39 - 28253763 * q^41 - 71221836 * q^42 + 28631126 * q^43 - 123980223 * q^44 - 124743136 * q^46 + 41505678 * q^47 - 51624919 * q^48 + 88370777 * q^49 - 97297213 * q^51 - 121869787 * q^52 + 20918940 * q^53 - 279383933 * q^54 - 81987402 * q^56 + 168605047 * q^57 + 533278432 * q^58 - 242672658 * q^59 - 236730546 * q^61 - 630173268 * q^62 + 563712646 * q^63 - 8650957 * q^64 - 247702451 * q^66 - 33870225 * q^67 + 521453709 * q^68 - 16163890 * q^69 - 809145252 * q^71 - 632968230 * q^72 - 460218191 * q^73 + 540389844 * q^74 - 1067090107 * q^76 - 331946328 * q^77 + 31502783 * q^78 - 295742582 * q^79 - 1013246447 * q^81 - 436735349 * q^82 - 298090917 * q^83 - 2574679448 * q^84 - 2183241552 * q^86 - 164038106 * q^87 + 961546625 * q^88 - 448474185 * q^89 - 304745870 * q^91 - 1091742000 * q^92 - 1680564078 * q^93 - 2962970430 * q^94 + 2289126403 * q^96 + 2630881746 * q^97 + 236409993 * q^98 - 3023832936 * q^99

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