LMFDB - Embedded newform 153.10.a.f.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [153,10,Mod(1,153)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(153, 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("153.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 153 = 3^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	153.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:	$78.8004829331$
Analytic rank:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - x^{6} - 2986x^{5} + 8252x^{4} + 2252056x^{3} - 10388768x^{2} - 243559296x - 675998208 $ x^7 - x^6 - 2986x^5 + 8252x^4 + 2252056x^3 - 10388768x^2 - 243559296*x - 675998208
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{10}\cdot 3^{5} $
Twist minimal:	no (minimal twist has level 17)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-5.44491$ of defining polynomial
Character	$\chi$	$=$	153.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-5.44491 q^{2} -482.353 q^{4} -1303.94 q^{5} +9199.27 q^{7} +5414.17 q^{8} +O(q^{10})$	\(q-5.44491 q^{2} -482.353 q^{4} -1303.94 q^{5} +9199.27 q^{7} +5414.17 q^{8} +7099.84 q^{10} -62238.4 q^{11} +141901. q^{13} -50089.2 q^{14} +217485. q^{16} -83521.0 q^{17} -941163. q^{19} +628959. q^{20} +338883. q^{22} -568165. q^{23} -252865. q^{25} -772638. q^{26} -4.43730e6 q^{28} +1.83597e6 q^{29} -7.34903e6 q^{31} -3.95624e6 q^{32} +454765. q^{34} -1.19953e7 q^{35} -8.01674e6 q^{37} +5.12455e6 q^{38} -7.05975e6 q^{40} -1.95674e7 q^{41} +3.46966e7 q^{43} +3.00209e7 q^{44} +3.09361e6 q^{46} +5.63645e7 q^{47} +4.42730e7 q^{49} +1.37683e6 q^{50} -6.84463e7 q^{52} +3.28783e7 q^{53} +8.11551e7 q^{55} +4.98064e7 q^{56} -9.99672e6 q^{58} -1.04852e8 q^{59} +5.69264e7 q^{61} +4.00148e7 q^{62} -8.98109e7 q^{64} -1.85030e8 q^{65} -1.58325e7 q^{67} +4.02866e7 q^{68} +6.53134e7 q^{70} +9.81097e7 q^{71} -6.27365e7 q^{73} +4.36505e7 q^{74} +4.53973e8 q^{76} -5.72548e8 q^{77} -1.38282e8 q^{79} -2.83587e8 q^{80} +1.06543e8 q^{82} +6.69421e8 q^{83} +1.08906e8 q^{85} -1.88920e8 q^{86} -3.36969e8 q^{88} +4.21417e7 q^{89} +1.30538e9 q^{91} +2.74056e8 q^{92} -3.06900e8 q^{94} +1.22722e9 q^{95} -4.11288e8 q^{97} -2.41063e8 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + q^{2} + 2389 q^{4} - 1362 q^{5} + 9388 q^{7} - 16821 q^{8}+O(q^{10}) $ 7 * q + q^2 + 2389 * q^4 - 1362 * q^5 + 9388 * q^7 - 16821 * q^8	\( 7 q + q^{2} + 2389 q^{4} - 1362 q^{5} + 9388 q^{7} - 16821 q^{8} + 154226 q^{10} - 135536 q^{11} + 166122 q^{13} - 447252 q^{14} + 1463585 q^{16} - 584647 q^{17} + 777172 q^{19} + 917162 q^{20} - 1222520 q^{22} - 1357764 q^{23} + 1065785 q^{25} + 14379966 q^{26} - 3328892 q^{28} - 967002 q^{29} + 3546740 q^{31} - 4825461 q^{32} - 83521 q^{34} + 530736 q^{35} + 18296498 q^{37} + 49363020 q^{38} + 127155062 q^{40} - 10285686 q^{41} + 21913204 q^{43} - 96696624 q^{44} - 151509484 q^{46} - 56639800 q^{47} + 27010351 q^{49} + 261150303 q^{50} - 156226378 q^{52} - 121813562 q^{53} + 40793128 q^{55} + 196175436 q^{56} - 236833910 q^{58} - 29222388 q^{59} - 49915846 q^{61} + 73506556 q^{62} + 317922057 q^{64} + 122633668 q^{65} + 301863420 q^{67} - 199531669 q^{68} + 966315960 q^{70} - 652473940 q^{71} + 306656342 q^{73} - 249173874 q^{74} + 128694700 q^{76} + 102442536 q^{77} + 959147884 q^{79} + 692173602 q^{80} + 1046441254 q^{82} + 1512945268 q^{83} + 113755602 q^{85} + 164953236 q^{86} + 1132038848 q^{88} + 1971327114 q^{89} - 1061062864 q^{91} - 901186756 q^{92} + 2534831232 q^{94} + 3249631512 q^{95} + 2006526254 q^{97} + 2170640009 q^{98}+O(q^{100}) \) 7 * q + q^2 + 2389 * q^4 - 1362 * q^5 + 9388 * q^7 - 16821 * q^8 + 154226 * q^10 - 135536 * q^11 + 166122 * q^13 - 447252 * q^14 + 1463585 * q^16 - 584647 * q^17 + 777172 * q^19 + 917162 * q^20 - 1222520 * q^22 - 1357764 * q^23 + 1065785 * q^25 + 14379966 * q^26 - 3328892 * q^28 - 967002 * q^29 + 3546740 * q^31 - 4825461 * q^32 - 83521 * q^34 + 530736 * q^35 + 18296498 * q^37 + 49363020 * q^38 + 127155062 * q^40 - 10285686 * q^41 + 21913204 * q^43 - 96696624 * q^44 - 151509484 * q^46 - 56639800 * q^47 + 27010351 * q^49 + 261150303 * q^50 - 156226378 * q^52 - 121813562 * q^53 + 40793128 * q^55 + 196175436 * q^56 - 236833910 * q^58 - 29222388 * q^59 - 49915846 * q^61 + 73506556 * q^62 + 317922057 * q^64 + 122633668 * q^65 + 301863420 * q^67 - 199531669 * q^68 + 966315960 * q^70 - 652473940 * q^71 + 306656342 * q^73 - 249173874 * q^74 + 128694700 * q^76 + 102442536 * q^77 + 959147884 * q^79 + 692173602 * q^80 + 1046441254 * q^82 + 1512945268 * q^83 + 113755602 * q^85 + 164953236 * q^86 + 1132038848 * q^88 + 1971327114 * q^89 - 1061062864 * q^91 - 901186756 * q^92 + 2534831232 * q^94 + 3249631512 * q^95 + 2006526254 * q^97 + 2170640009 * 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 $

$2$	−5.44491	−0.240633	−0.120317	−	0.992736i	$-0.538391\pi$
$2$	−5.44491	−0.240633	−0.120317	+	0.992736i	$0.538391\pi$
$3$	0	0
$3$	0	0
$4$	−482.353	−0.942096
$5$	−1303.94	−0.933024	−0.466512	−	0.884515i	$-0.654489\pi$
$5$	−1303.94	−0.933024	−0.466512	+	0.884515i	$0.654489\pi$
$6$	0	0
$7$	9199.27	1.44815	0.724073	−	0.689723i	$-0.242268\pi$
$7$	9199.27	1.44815	0.724073	+	0.689723i	$0.242268\pi$
$8$	5414.17	0.467333
$9$	0	0
$10$	7099.84	0.224517
$11$	−62238.4	−1.28171	−0.640857	−	0.767660i	$-0.721421\pi$
$11$	−62238.4	−1.28171	−0.640857	+	0.767660i	$0.721421\pi$
$12$	0	0
$13$	141901.	1.37797	0.688985	−	0.724775i	$-0.258056\pi$
$13$	141901.	1.37797	0.688985	+	0.724775i	$0.258056\pi$
$14$	−50089.2	−0.348472
$15$	0	0
$16$	217485.	0.829640
$17$	−83521.0	−0.242536
$17$	−83521.0	−0.242536
$18$	0	0
$19$	−941163.	−1.65681	−0.828407	−	0.560127i	$-0.810753\pi$
$19$	−941163.	−1.65681	−0.828407	+	0.560127i	$0.810753\pi$
$20$	628959.	0.878997
$21$	0	0
$22$	338883.	0.308423
$23$	−568165.	−0.423349	−0.211675	−	0.977340i	$-0.567892\pi$
$23$	−568165.	−0.423349	−0.211675	+	0.977340i	$0.567892\pi$
$24$	0	0
$25$	−252865.	−0.129467
$26$	−772638.	−0.331586
$27$	0	0
$28$	−4.43730e6	−1.36429
$29$	1.83597e6	0.482032	0.241016	−	0.970521i	$-0.422519\pi$
$29$	1.83597e6	0.482032	0.241016	+	0.970521i	$0.422519\pi$
$30$	0	0
$31$	−7.34903e6	−1.42923	−0.714615	−	0.699518i	$-0.753398\pi$
$31$	−7.34903e6	−1.42923	−0.714615	+	0.699518i	$0.753398\pi$
$32$	−3.95624e6	−0.666972
$33$	0	0
$34$	454765.	0.0583622
$35$	−1.19953e7	−1.35115
$36$	0	0
$37$	−8.01674e6	−0.703218	−0.351609	−	0.936147i	$-0.614365\pi$
$37$	−8.01674e6	−0.703218	−0.351609	+	0.936147i	$0.614365\pi$
$38$	5.12455e6	0.398685
$39$	0	0
$40$	−7.05975e6	−0.436033
$41$	−1.95674e7	−1.08145	−0.540724	−	0.841200i	$-0.681850\pi$
$41$	−1.95674e7	−1.08145	−0.540724	+	0.841200i	$0.681850\pi$
$42$	0	0
$43$	3.46966e7	1.54767	0.773835	−	0.633387i	$-0.218336\pi$
$43$	3.46966e7	1.54767	0.773835	+	0.633387i	$0.218336\pi$
$44$	3.00209e7	1.20750
$45$	0	0
$46$	3.09361e6	0.101872
$47$	5.63645e7	1.68486	0.842432	−	0.538802i	$-0.181123\pi$
$47$	5.63645e7	1.68486	0.842432	+	0.538802i	$0.181123\pi$
$48$	0	0
$49$	4.42730e7	1.09713
$50$	1.37683e6	0.0311541
$51$	0	0
$52$	−6.84463e7	−1.29818
$53$	3.28783e7	0.572359	0.286179	−	0.958176i	$-0.407615\pi$
$53$	3.28783e7	0.572359	0.286179	+	0.958176i	$0.407615\pi$
$54$	0	0
$55$	8.11551e7	1.19587
$56$	4.98064e7	0.676767
$57$	0	0
$58$	−9.99672e6	−0.115993
$59$	−1.04852e8	−1.12653	−0.563267	−	0.826275i	$-0.690456\pi$
$59$	−1.04852e8	−1.12653	−0.563267	+	0.826275i	$0.690456\pi$
$60$	0	0
$61$	5.69264e7	0.526416	0.263208	−	0.964739i	$-0.415219\pi$
$61$	5.69264e7	0.526416	0.263208	+	0.964739i	$0.415219\pi$
$62$	4.00148e7	0.343921
$63$	0	0
$64$	−8.98109e7	−0.669144
$65$	−1.85030e8	−1.28568
$66$	0	0
$67$	−1.58325e7	−0.0959872	−0.0479936	−	0.998848i	$-0.515283\pi$
$67$	−1.58325e7	−0.0959872	−0.0479936	+	0.998848i	$0.515283\pi$
$68$	4.02866e7	0.228492
$69$	0	0
$70$	6.53134e7	0.325133
$71$	9.81097e7	0.458194	0.229097	−	0.973404i	$-0.426423\pi$
$71$	9.81097e7	0.458194	0.229097	+	0.973404i	$0.426423\pi$
$72$	0	0
$73$	−6.27365e7	−0.258564	−0.129282	−	0.991608i	$-0.541267\pi$
$73$	−6.27365e7	−0.258564	−0.129282	+	0.991608i	$0.541267\pi$
$74$	4.36505e7	0.169218
$75$	0	0
$76$	4.53973e8	1.56088
$77$	−5.72548e8	−1.85611
$78$	0	0
$79$	−1.38282e8	−0.399433	−0.199717	−	0.979854i	$-0.564002\pi$
$79$	−1.38282e8	−0.399433	−0.199717	+	0.979854i	$0.564002\pi$
$80$	−2.83587e8	−0.774073
$81$	0	0
$82$	1.06543e8	0.260233
$83$	6.69421e8	1.54827	0.774137	−	0.633018i	$-0.218184\pi$
$83$	6.69421e8	1.54827	0.774137	+	0.633018i	$0.218184\pi$
$84$	0	0
$85$	1.08906e8	0.226291
$86$	−1.88920e8	−0.372421
$87$	0	0
$88$	−3.36969e8	−0.598988
$89$	4.21417e7	0.0711963	0.0355981	−	0.999366i	$-0.488666\pi$
$89$	4.21417e7	0.0711963	0.0355981	+	0.999366i	$0.488666\pi$
$90$	0	0
$91$	1.30538e9	1.99550
$92$	2.74056e8	0.398836
$93$	0	0
$94$	−3.06900e8	−0.405435
$95$	1.22722e9	1.54585
$96$	0	0
$97$	−4.11288e8	−0.471707	−0.235854	−	0.971789i	$-0.575789\pi$
$97$	−4.11288e8	−0.471707	−0.235854	+	0.971789i	$0.575789\pi$
$98$	−2.41063e8	−0.264005
$99$	0	0
$100$	1.21970e8	0.121970
$101$	−1.81470e7	−0.0173524	−0.00867620	−	0.999962i	$-0.502762\pi$
$101$	−1.81470e7	−0.0173524	−0.00867620	+	0.999962i	$0.502762\pi$
$102$	0	0
$103$	7.17681e8	0.628296	0.314148	−	0.949374i	$-0.398281\pi$
$103$	7.17681e8	0.628296	0.314148	+	0.949374i	$0.398281\pi$
$104$	7.68275e8	0.643971
$105$	0	0
$106$	−1.79020e8	−0.137729
$107$	7.18789e8	0.530120	0.265060	−	0.964232i	$-0.414608\pi$
$107$	7.18789e8	0.530120	0.265060	+	0.964232i	$0.414608\pi$
$108$	0	0
$109$	3.41476e8	0.231708	0.115854	−	0.993266i	$-0.463040\pi$
$109$	3.41476e8	0.231708	0.115854	+	0.993266i	$0.463040\pi$
$110$	−4.41883e8	−0.287766
$111$	0	0
$112$	2.00070e9	1.20144
$113$	1.70781e9	0.985339	0.492670	−	0.870216i	$-0.336021\pi$
$113$	1.70781e9	0.985339	0.492670	+	0.870216i	$0.336021\pi$
$114$	0	0
$115$	7.40853e8	0.394995
$116$	−8.85588e8	−0.454120
$117$	0	0
$118$	5.70912e8	0.271082
$119$	−7.68332e8	−0.351227
$120$	0	0
$121$	1.51567e9	0.642792
$122$	−3.09959e8	−0.126673
$123$	0	0
$124$	3.54482e9	1.34647
$125$	2.87648e9	1.05382
$126$	0	0
$127$	1.94335e9	0.662880	0.331440	−	0.943476i	$-0.392466\pi$
$127$	1.94335e9	0.662880	0.331440	+	0.943476i	$0.392466\pi$
$128$	2.51461e9	0.827991
$129$	0	0
$130$	1.00747e9	0.309377
$131$	−3.30692e9	−0.981075	−0.490538	−	0.871420i	$-0.663200\pi$
$131$	−3.30692e9	−0.981075	−0.490538	+	0.871420i	$0.663200\pi$
$132$	0	0
$133$	−8.65802e9	−2.39931
$134$	8.62067e7	0.0230977
$135$	0	0
$136$	−4.52197e8	−0.113345
$137$	4.83938e9	1.17367	0.586836	−	0.809706i	$-0.300373\pi$
$137$	4.83938e9	1.17367	0.586836	+	0.809706i	$0.300373\pi$
$138$	0	0
$139$	3.57524e9	0.812342	0.406171	−	0.913797i	$-0.366864\pi$
$139$	3.57524e9	0.812342	0.406171	+	0.913797i	$0.366864\pi$
$140$	5.78597e9	1.27292
$141$	0	0
$142$	−5.34199e8	−0.110257
$143$	−8.83168e9	−1.76616
$144$	0	0
$145$	−2.39400e9	−0.449747
$146$	3.41595e8	0.0622191
$147$	0	0
$148$	3.86690e9	0.662499
$149$	2.20680e9	0.366796	0.183398	−	0.983039i	$-0.441290\pi$
$149$	2.20680e9	0.366796	0.183398	+	0.983039i	$0.441290\pi$
$150$	0	0
$151$	7.78978e9	1.21935	0.609676	−	0.792651i	$-0.291300\pi$
$151$	7.78978e9	1.21935	0.609676	+	0.792651i	$0.291300\pi$
$152$	−5.09561e9	−0.774284
$153$	0	0
$154$	3.11747e9	0.446642
$155$	9.58269e9	1.33351
$156$	0	0
$157$	5.99611e9	0.787627	0.393814	−	0.919190i	$-0.371155\pi$
$157$	5.99611e9	0.787627	0.393814	+	0.919190i	$0.371155\pi$
$158$	7.52935e8	0.0961171
$159$	0	0
$160$	5.15870e9	0.622301
$161$	−5.22670e9	−0.613072
$162$	0	0
$163$	2.20096e9	0.244212	0.122106	−	0.992517i	$-0.461035\pi$
$163$	2.20096e9	0.244212	0.122106	+	0.992517i	$0.461035\pi$
$164$	9.43839e9	1.01883
$165$	0	0
$166$	−3.64494e9	−0.372567
$167$	1.54378e9	0.153589	0.0767946	−	0.997047i	$-0.475531\pi$
$167$	1.54378e9	0.153589	0.0767946	+	0.997047i	$0.475531\pi$
$168$	0	0
$169$	9.53135e9	0.898802
$170$	−5.92986e8	−0.0544533
$171$	0	0
$172$	−1.67360e10	−1.45805
$173$	−1.36568e10	−1.15916	−0.579578	−	0.814917i	$-0.696783\pi$
$173$	−1.36568e10	−1.15916	−0.579578	+	0.814917i	$0.696783\pi$
$174$	0	0
$175$	−2.32618e9	−0.187487
$176$	−1.35359e10	−1.06336
$177$	0	0
$178$	−2.29458e8	−0.0171322
$179$	−7.48481e9	−0.544932	−0.272466	−	0.962165i	$-0.587839\pi$
$179$	−7.48481e9	−0.544932	−0.272466	+	0.962165i	$0.587839\pi$
$180$	0	0
$181$	−1.98188e10	−1.37254	−0.686269	−	0.727348i	$-0.740753\pi$
$181$	−1.98188e10	−1.37254	−0.686269	+	0.727348i	$0.740753\pi$
$182$	−7.10771e9	−0.480185
$183$	0	0
$184$	−3.07614e9	−0.197845
$185$	1.04534e10	0.656119
$186$	0	0
$187$	5.19821e9	0.310861
$188$	−2.71876e10	−1.58730
$189$	0	0
$190$	−6.68211e9	−0.371982
$191$	3.54665e10	1.92827	0.964137	−	0.265405i	$-0.0855056\pi$
$191$	3.54665e10	1.92827	0.964137	+	0.265405i	$0.0855056\pi$
$192$	0	0
$193$	−1.16540e10	−0.604599	−0.302299	−	0.953213i	$-0.597754\pi$
$193$	−1.16540e10	−0.604599	−0.302299	+	0.953213i	$0.597754\pi$
$194$	2.23943e9	0.113509
$195$	0	0
$196$	−2.13552e10	−1.03360
$197$	−4.99943e9	−0.236495	−0.118248	−	0.992984i	$-0.537728\pi$
$197$	−4.99943e9	−0.236495	−0.118248	+	0.992984i	$0.537728\pi$
$198$	0	0
$199$	−1.90482e9	−0.0861026	−0.0430513	−	0.999073i	$-0.513708\pi$
$199$	−1.90482e9	−0.0861026	−0.0430513	+	0.999073i	$0.513708\pi$
$200$	−1.36906e9	−0.0605043
$201$	0	0
$202$	9.88091e7	0.00417557
$203$	1.68896e10	0.698052
$204$	0	0
$205$	2.55147e10	1.00902
$206$	−3.90771e9	−0.151189
$207$	0	0
$208$	3.08613e10	1.14322
$209$	5.85765e10	2.12356
$210$	0	0
$211$	4.45582e10	1.54759	0.773797	−	0.633434i	$-0.218355\pi$
$211$	4.45582e10	1.54759	0.773797	+	0.633434i	$0.218355\pi$
$212$	−1.58590e10	−0.539216
$213$	0	0
$214$	−3.91374e9	−0.127565
$215$	−4.52422e10	−1.44401
$216$	0	0
$217$	−6.76057e10	−2.06973
$218$	−1.85931e9	−0.0557567
$219$	0	0
$220$	−3.91454e10	−1.12662
$221$	−1.18517e10	−0.334207
$222$	0	0
$223$	−1.00748e10	−0.272812	−0.136406	−	0.990653i	$-0.543555\pi$
$223$	−1.00748e10	−0.272812	−0.136406	+	0.990653i	$0.543555\pi$
$224$	−3.63945e10	−0.965873
$225$	0	0
$226$	−9.29886e9	−0.237106
$227$	−7.51701e10	−1.87901	−0.939505	−	0.342536i	$-0.888714\pi$
$227$	−7.51701e10	−1.87901	−0.939505	+	0.342536i	$0.888714\pi$
$228$	0	0
$229$	8.19379e10	1.96891	0.984453	−	0.175647i	$-0.0562016\pi$
$229$	8.19379e10	1.96891	0.984453	+	0.175647i	$0.0562016\pi$
$230$	−4.03388e9	−0.0950490
$231$	0	0
$232$	9.94027e9	0.225269
$233$	4.97304e10	1.10540	0.552701	−	0.833380i	$-0.313597\pi$
$233$	4.97304e10	1.10540	0.552701	+	0.833380i	$0.313597\pi$
$234$	0	0
$235$	−7.34959e10	−1.57202
$236$	5.05759e10	1.06130
$237$	0	0
$238$	4.18350e9	0.0845170
$239$	4.06399e10	0.805680	0.402840	−	0.915270i	$-0.368023\pi$
$239$	4.06399e10	0.805680	0.402840	+	0.915270i	$0.368023\pi$
$240$	0	0
$241$	−3.05939e10	−0.584196	−0.292098	−	0.956388i	$-0.594353\pi$
$241$	−3.05939e10	−0.584196	−0.292098	+	0.956388i	$0.594353\pi$
$242$	−8.25269e9	−0.154677
$243$	0	0
$244$	−2.74586e10	−0.495934
$245$	−5.77293e10	−1.02364
$246$	0	0
$247$	−1.33552e11	−2.28304
$248$	−3.97889e10	−0.667927
$249$	0	0
$250$	−1.56622e10	−0.253584
$251$	−2.05450e10	−0.326719	−0.163359	−	0.986567i	$-0.552233\pi$
$251$	−2.05450e10	−0.326719	−0.163359	+	0.986567i	$0.552233\pi$
$252$	0	0
$253$	3.53617e10	0.542613
$254$	−1.05814e10	−0.159511
$255$	0	0
$256$	3.22914e10	0.469901
$257$	8.98169e10	1.28428	0.642139	−	0.766588i	$-0.278047\pi$
$257$	8.98169e10	1.28428	0.642139	+	0.766588i	$0.278047\pi$
$258$	0	0
$259$	−7.37482e10	−1.01836
$260$	8.92498e10	1.21123
$261$	0	0
$262$	1.80059e10	0.236080
$263$	−1.43373e11	−1.84785	−0.923923	−	0.382577i	$-0.875037\pi$
$263$	−1.43373e11	−1.84785	−0.923923	+	0.382577i	$0.875037\pi$
$264$	0	0
$265$	−4.28714e10	−0.534024
$266$	4.71422e10	0.577354
$267$	0	0
$268$	7.63686e9	0.0904291
$269$	1.67468e11	1.95005	0.975025	−	0.222094i	$-0.0712893\pi$
$269$	1.67468e11	1.95005	0.975025	+	0.222094i	$0.0712893\pi$
$270$	0	0
$271$	4.52996e10	0.510190	0.255095	−	0.966916i	$-0.417893\pi$
$271$	4.52996e10	0.510190	0.255095	+	0.966916i	$0.417893\pi$
$272$	−1.81646e10	−0.201217
$273$	0	0
$274$	−2.63500e10	−0.282425
$275$	1.57379e10	0.165940
$276$	0	0
$277$	1.93194e9	0.0197167	0.00985836	−	0.999951i	$-0.496862\pi$
$277$	1.93194e9	0.0197167	0.00985836	+	0.999951i	$0.496862\pi$
$278$	−1.94669e10	−0.195477
$279$	0	0
$280$	−6.49445e10	−0.631439
$281$	−1.16694e11	−1.11653	−0.558265	−	0.829662i	$-0.688533\pi$
$281$	−1.16694e11	−1.11653	−0.558265	+	0.829662i	$0.688533\pi$
$282$	0	0
$283$	−1.65132e8	−0.00153036	−0.000765180	−	1.00000i	$-0.500244\pi$
$283$	−1.65132e8	−0.00153036	−0.000765180		1.00000i	$0.500244\pi$
$284$	−4.73235e10	−0.431662
$285$	0	0
$286$	4.80877e10	0.424998
$287$	−1.80006e11	−1.56609
$288$	0	0
$289$	6.97576e9	0.0588235
$290$	1.30351e10	0.108224
$291$	0	0
$292$	3.02611e10	0.243592
$293$	−6.45700e10	−0.511831	−0.255915	−	0.966699i	$-0.582377\pi$
$293$	−6.45700e10	−0.511831	−0.255915	+	0.966699i	$0.582377\pi$
$294$	0	0
$295$	1.36721e11	1.05108
$296$	−4.34040e10	−0.328637
$297$	0	0
$298$	−1.20158e10	−0.0882633
$299$	−8.06230e10	−0.583363
$300$	0	0
$301$	3.19183e11	2.24125
$302$	−4.24147e10	−0.293417
$303$	0	0
$304$	−2.04689e11	−1.37456
$305$	−7.42286e10	−0.491159
$306$	0	0
$307$	8.54538e10	0.549046	0.274523	−	0.961581i	$-0.411480\pi$
$307$	8.54538e10	0.549046	0.274523	+	0.961581i	$0.411480\pi$
$308$	2.76170e11	1.74863
$309$	0	0
$310$	−5.21769e10	−0.320886
$311$	7.31980e10	0.443688	0.221844	−	0.975082i	$-0.428792\pi$
$311$	7.31980e10	0.443688	0.221844	+	0.975082i	$0.428792\pi$
$312$	0	0
$313$	1.60425e10	0.0944764	0.0472382	−	0.998884i	$-0.484958\pi$
$313$	1.60425e10	0.0944764	0.0472382	+	0.998884i	$0.484958\pi$
$314$	−3.26483e10	−0.189530
$315$	0	0
$316$	6.67008e10	0.376304
$317$	−8.53822e10	−0.474899	−0.237449	−	0.971400i	$-0.576311\pi$
$317$	−8.53822e10	−0.474899	−0.237449	+	0.971400i	$0.576311\pi$
$318$	0	0
$319$	−1.14268e11	−0.617827
$320$	1.17108e11	0.624327
$321$	0	0
$322$	2.84589e10	0.147526
$323$	7.86069e10	0.401836
$324$	0	0
$325$	−3.58818e10	−0.178402
$326$	−1.19840e10	−0.0587656
$327$	0	0
$328$	−1.05941e11	−0.505397
$329$	5.18512e11	2.43993
$330$	0	0
$331$	5.68636e10	0.260380	0.130190	−	0.991489i	$-0.458441\pi$
$331$	5.68636e10	0.260380	0.130190	+	0.991489i	$0.458441\pi$
$332$	−3.22897e11	−1.45862
$333$	0	0
$334$	−8.40574e9	−0.0369587
$335$	2.06447e10	0.0895583
$336$	0	0
$337$	3.07106e11	1.29704	0.648521	−	0.761197i	$-0.275388\pi$
$337$	3.07106e11	1.29704	0.648521	+	0.761197i	$0.275388\pi$
$338$	−5.18974e10	−0.216282
$339$	0	0
$340$	−5.25313e10	−0.213188
$341$	4.57392e11	1.83187
$342$	0	0
$343$	3.60556e10	0.140653
$344$	1.87853e11	0.723278
$345$	0	0
$346$	7.43602e10	0.278932
$347$	−3.34687e10	−0.123924	−0.0619621	−	0.998079i	$-0.519736\pi$
$347$	−3.34687e10	−0.123924	−0.0619621	+	0.998079i	$0.519736\pi$
$348$	0	0
$349$	−3.80974e11	−1.37462	−0.687308	−	0.726366i	$-0.741208\pi$
$349$	−3.80974e11	−1.37462	−0.687308	+	0.726366i	$0.741208\pi$
$350$	1.26658e10	0.0451157
$351$	0	0
$352$	2.46230e11	0.854868
$353$	−2.09902e11	−0.719499	−0.359750	−	0.933049i	$-0.617138\pi$
$353$	−2.09902e11	−0.719499	−0.359750	+	0.933049i	$0.617138\pi$
$354$	0	0
$355$	−1.27929e11	−0.427506
$356$	−2.03272e10	−0.0670737
$357$	0	0
$358$	4.07542e10	0.131129
$359$	−3.14148e11	−0.998181	−0.499091	−	0.866550i	$-0.666332\pi$
$359$	−3.14148e11	−0.998181	−0.499091	+	0.866550i	$0.666332\pi$
$360$	0	0
$361$	5.63101e11	1.74503
$362$	1.07912e11	0.330279
$363$	0	0
$364$	−6.29656e11	−1.87995
$365$	8.18047e10	0.241246
$366$	0	0
$367$	2.40379e11	0.691671	0.345835	−	0.938295i	$-0.387596\pi$
$367$	2.40379e11	0.691671	0.345835	+	0.938295i	$0.387596\pi$
$368$	−1.23567e11	−0.351227
$369$	0	0
$370$	−5.69176e10	−0.157884
$371$	3.02457e11	0.828859
$372$	0	0
$373$	2.93908e11	0.786179	0.393089	−	0.919500i	$-0.371406\pi$
$373$	2.93908e11	0.786179	0.393089	+	0.919500i	$0.371406\pi$
$374$	−2.83038e10	−0.0748037
$375$	0	0
$376$	3.05167e11	0.787393
$377$	2.60526e11	0.664225
$378$	0	0
$379$	3.76034e11	0.936161	0.468081	−	0.883686i	$-0.344946\pi$
$379$	3.76034e11	0.936161	0.468081	+	0.883686i	$0.344946\pi$
$380$	−5.91953e11	−1.45634
$381$	0	0
$382$	−1.93112e11	−0.464007
$383$	−3.73836e11	−0.887741	−0.443870	−	0.896091i	$-0.646395\pi$
$383$	−3.73836e11	−0.887741	−0.443870	+	0.896091i	$0.646395\pi$
$384$	0	0
$385$	7.46568e11	1.73179
$386$	6.34550e10	0.145487
$387$	0	0
$388$	1.98386e11	0.444394
$389$	4.62613e10	0.102434	0.0512171	−	0.998688i	$-0.483690\pi$
$389$	4.62613e10	0.102434	0.0512171	+	0.998688i	$0.483690\pi$
$390$	0	0
$391$	4.74537e10	0.102677
$392$	2.39701e11	0.512724
$393$	0	0
$394$	2.72215e10	0.0569087
$395$	1.80312e11	0.372681
$396$	0	0
$397$	−3.36827e11	−0.680534	−0.340267	−	0.940329i	$-0.610517\pi$
$397$	−3.36827e11	−0.680534	−0.340267	+	0.940329i	$0.610517\pi$
$398$	1.03716e10	0.0207192
$399$	0	0
$400$	−5.49944e10	−0.107411
$401$	9.81350e11	1.89528	0.947642	−	0.319335i	$-0.103459\pi$
$401$	9.81350e11	1.89528	0.947642	+	0.319335i	$0.103459\pi$
$402$	0	0
$403$	−1.04283e12	−1.96944
$404$	8.75328e9	0.0163476
$405$	0	0
$406$	−9.19626e10	−0.167975
$407$	4.98949e11	0.901325
$408$	0	0
$409$	8.17703e11	1.44491	0.722455	−	0.691418i	$-0.243014\pi$
$409$	8.17703e11	1.44491	0.722455	+	0.691418i	$0.243014\pi$
$410$	−1.38925e11	−0.242803
$411$	0	0
$412$	−3.46176e11	−0.591915
$413$	−9.64566e11	−1.63139
$414$	0	0
$415$	−8.72885e11	−1.44458
$416$	−5.61394e11	−0.919068
$417$	0	0
$418$	−3.18944e11	−0.511000
$419$	4.18196e11	0.662852	0.331426	−	0.943481i	$-0.392470\pi$
$419$	4.18196e11	0.662852	0.331426	+	0.943481i	$0.392470\pi$
$420$	0	0
$421$	3.11784e11	0.483709	0.241855	−	0.970313i	$-0.422244\pi$
$421$	3.11784e11	0.483709	0.241855	+	0.970313i	$0.422244\pi$
$422$	−2.42616e11	−0.372403
$423$	0	0
$424$	1.78009e11	0.267482
$425$	2.11196e10	0.0314004
$426$	0	0
$427$	5.23681e11	0.762328
$428$	−3.46710e11	−0.499424
$429$	0	0
$430$	2.46340e11	0.347478
$431$	−8.66540e11	−1.20960	−0.604799	−	0.796378i	$-0.706747\pi$
$431$	−8.66540e11	−1.20960	−0.604799	+	0.796378i	$0.706747\pi$
$432$	0	0
$433$	2.95119e11	0.403461	0.201730	−	0.979441i	$-0.435344\pi$
$433$	2.95119e11	0.403461	0.201730	+	0.979441i	$0.435344\pi$
$434$	3.68107e11	0.498047
$435$	0	0
$436$	−1.64712e11	−0.218291
$437$	5.34736e11	0.701411
$438$	0	0
$439$	5.48786e11	0.705201	0.352600	−	0.935774i	$-0.385297\pi$
$439$	5.48786e11	0.705201	0.352600	+	0.935774i	$0.385297\pi$
$440$	4.39387e11	0.558870
$441$	0	0
$442$	6.45315e10	0.0804214
$443$	1.03597e12	1.27800	0.638999	−	0.769207i	$-0.279349\pi$
$443$	1.03597e12	1.27800	0.638999	+	0.769207i	$0.279349\pi$
$444$	0	0
$445$	−5.49503e10	−0.0664278
$446$	5.48562e10	0.0656476
$447$	0	0
$448$	−8.26195e11	−0.969018
$449$	1.04924e12	1.21833	0.609167	−	0.793042i	$-0.291504\pi$
$449$	1.04924e12	1.21833	0.609167	+	0.793042i	$0.291504\pi$
$450$	0	0
$451$	1.21784e12	1.38611
$452$	−8.23766e11	−0.928284
$453$	0	0
$454$	4.09295e11	0.452153
$455$	−1.70214e12	−1.86185
$456$	0	0
$457$	1.13929e11	0.122183	0.0610917	−	0.998132i	$-0.480542\pi$
$457$	1.13929e11	0.122183	0.0610917	+	0.998132i	$0.480542\pi$
$458$	−4.46145e11	−0.473785
$459$	0	0
$460$	−3.57352e11	−0.372123
$461$	−1.04783e12	−1.08053	−0.540264	−	0.841496i	$-0.681675\pi$
$461$	−1.04783e12	−1.08053	−0.540264	+	0.841496i	$0.681675\pi$
$462$	0	0
$463$	1.26218e11	0.127646	0.0638231	−	0.997961i	$-0.479671\pi$
$463$	1.26218e11	0.127646	0.0638231	+	0.997961i	$0.479671\pi$
$464$	3.99297e11	0.399913
$465$	0	0
$466$	−2.70778e11	−0.265997
$467$	1.20765e12	1.17494	0.587470	−	0.809246i	$-0.300124\pi$
$467$	1.20765e12	1.17494	0.587470	+	0.809246i	$0.300124\pi$
$468$	0	0
$469$	−1.45648e11	−0.139003
$470$	4.00179e11	0.378280
$471$	0	0
$472$	−5.67688e11	−0.526467
$473$	−2.15946e12	−1.98367
$474$	0	0
$475$	2.37988e11	0.214503
$476$	3.70607e11	0.330889
$477$	0	0
$478$	−2.21281e11	−0.193874
$479$	1.58750e12	1.37786	0.688930	−	0.724828i	$-0.258081\pi$
$479$	1.58750e12	1.37786	0.688930	+	0.724828i	$0.258081\pi$
$480$	0	0
$481$	−1.13758e12	−0.969014
$482$	1.66581e11	0.140577
$483$	0	0
$484$	−7.31088e11	−0.605572
$485$	5.36294e11	0.440114
$486$	0	0
$487$	9.39880e11	0.757167	0.378584	−	0.925567i	$-0.376411\pi$
$487$	9.39880e11	0.757167	0.378584	+	0.925567i	$0.376411\pi$
$488$	3.08209e11	0.246012
$489$	0	0
$490$	3.14331e11	0.246323
$491$	−9.66438e11	−0.750425	−0.375213	−	0.926939i	$-0.622430\pi$
$491$	−9.66438e11	−0.750425	−0.375213	+	0.926939i	$0.622430\pi$
$492$	0	0
$493$	−1.53342e11	−0.116910
$494$	7.27178e11	0.549376
$495$	0	0
$496$	−1.59830e12	−1.18575
$497$	9.02538e11	0.663532
$498$	0	0
$499$	−1.22995e12	−0.888045	−0.444022	−	0.896016i	$-0.646449\pi$
$499$	−1.22995e12	−0.888045	−0.444022	+	0.896016i	$0.646449\pi$
$500$	−1.38748e12	−0.992799
$501$	0	0
$502$	1.11866e11	0.0786195
$503$	1.98521e12	1.38277	0.691386	−	0.722485i	$-0.257000\pi$
$503$	1.98521e12	1.38277	0.691386	+	0.722485i	$0.257000\pi$
$504$	0	0
$505$	2.36626e10	0.0161902
$506$	−1.92541e11	−0.130571
$507$	0	0
$508$	−9.37382e11	−0.624496
$509$	−2.25974e12	−1.49221	−0.746104	−	0.665830i	$-0.768078\pi$
$509$	−2.25974e12	−1.49221	−0.746104	+	0.665830i	$0.768078\pi$
$510$	0	0
$511$	−5.77130e11	−0.374438
$512$	−1.46330e12	−0.941065
$513$	0	0
$514$	−4.89045e11	−0.309040
$515$	−9.35813e11	−0.586215
$516$	0	0
$517$	−3.50803e12	−2.15952
$518$	4.01553e11	0.245052
$519$	0	0
$520$	−1.00178e12	−0.600840
$521$	−4.78832e11	−0.284717	−0.142358	−	0.989815i	$-0.545469\pi$
$521$	−4.78832e11	−0.284717	−0.142358	+	0.989815i	$0.545469\pi$
$522$	0	0
$523$	−9.37326e11	−0.547814	−0.273907	−	0.961756i	$-0.588316\pi$
$523$	−9.37326e11	−0.547814	−0.273907	+	0.961756i	$0.588316\pi$
$524$	1.59510e12	0.924267
$525$	0	0
$526$	7.80653e11	0.444654
$527$	6.13798e11	0.346639
$528$	0	0
$529$	−1.47834e12	−0.820775
$530$	2.33431e11	0.128504
$531$	0	0
$532$	4.17622e12	2.26038
$533$	−2.77663e12	−1.49020
$534$	0	0
$535$	−9.37257e11	−0.494614
$536$	−8.57199e10	−0.0448580
$537$	0	0
$538$	−9.11847e11	−0.469247
$539$	−2.75548e12	−1.40620
$540$	0	0
$541$	−3.44109e12	−1.72706	−0.863532	−	0.504293i	$-0.831753\pi$
$541$	−3.44109e12	−1.72706	−0.863532	+	0.504293i	$0.831753\pi$
$542$	−2.46652e11	−0.122769
$543$	0	0
$544$	3.30429e11	0.161765
$545$	−4.45264e11	−0.216189
$546$	0	0
$547$	8.05238e11	0.384575	0.192288	−	0.981339i	$-0.438409\pi$
$547$	8.05238e11	0.384575	0.192288	+	0.981339i	$0.438409\pi$
$548$	−2.33429e12	−1.10571
$549$	0	0
$550$	−8.56917e10	−0.0399307
$551$	−1.72795e12	−0.798637
$552$	0	0
$553$	−1.27210e12	−0.578438
$554$	−1.05192e10	−0.00474450
$555$	0	0
$556$	−1.72453e12	−0.765304
$557$	2.13503e11	0.0939842	0.0469921	−	0.998895i	$-0.485036\pi$
$557$	2.13503e11	0.0939842	0.0469921	+	0.998895i	$0.485036\pi$
$558$	0	0
$559$	4.92347e12	2.13264
$560$	−2.60880e12	−1.12097
$561$	0	0
$562$	6.35390e11	0.268675
$563$	1.94290e12	0.815010	0.407505	−	0.913203i	$-0.366399\pi$
$563$	1.94290e12	0.815010	0.407505	+	0.913203i	$0.366399\pi$
$564$	0	0
$565$	−2.22688e12	−0.919345
$566$	8.99132e8	0.000368256 0
$567$	0	0
$568$	5.31182e11	0.214129
$569$	9.66618e11	0.386589	0.193295	−	0.981141i	$-0.438083\pi$
$569$	9.66618e11	0.386589	0.193295	+	0.981141i	$0.438083\pi$
$570$	0	0
$571$	3.96159e12	1.55958	0.779788	−	0.626043i	$-0.215327\pi$
$571$	3.96159e12	1.55958	0.779788	+	0.626043i	$0.215327\pi$
$572$	4.25999e12	1.66390
$573$	0	0
$574$	9.80116e11	0.376855
$575$	1.43669e11	0.0548098
$576$	0	0
$577$	2.21488e12	0.831876	0.415938	−	0.909393i	$-0.363453\pi$
$577$	2.21488e12	0.831876	0.415938	+	0.909393i	$0.363453\pi$
$578$	−3.79824e10	−0.0141549
$579$	0	0
$580$	1.15475e12	0.423705
$581$	6.15819e12	2.24213
$582$	0	0
$583$	−2.04629e12	−0.733600
$584$	−3.39666e11	−0.120835
$585$	0	0
$586$	3.51578e11	0.123164
$587$	6.70503e11	0.233093	0.116546	−	0.993185i	$-0.462818\pi$
$587$	6.70503e11	0.233093	0.116546	+	0.993185i	$0.462818\pi$
$588$	0	0
$589$	6.91664e12	2.36797
$590$	−7.44435e11	−0.252926
$591$	0	0
$592$	−1.74352e12	−0.583418
$593$	4.14332e12	1.37595	0.687975	−	0.725735i	$-0.258500\pi$
$593$	4.14332e12	1.37595	0.687975	+	0.725735i	$0.258500\pi$
$594$	0	0
$595$	1.00186e12	0.327703
$596$	−1.06445e12	−0.345556
$597$	0	0
$598$	4.38986e11	0.140377
$599$	−2.11940e12	−0.672653	−0.336327	−	0.941745i	$-0.609185\pi$
$599$	−2.11940e12	−0.672653	−0.336327	+	0.941745i	$0.609185\pi$
$600$	0	0
$601$	4.44856e12	1.39086	0.695431	−	0.718593i	$-0.255213\pi$
$601$	4.44856e12	1.39086	0.695431	+	0.718593i	$0.255213\pi$
$602$	−1.73792e12	−0.539320
$603$	0	0
$604$	−3.75742e12	−1.14875
$605$	−1.97634e12	−0.599740
$606$	0	0
$607$	8.59588e11	0.257005	0.128502	−	0.991709i	$-0.458983\pi$
$607$	8.59588e11	0.257005	0.128502	+	0.991709i	$0.458983\pi$
$608$	3.72347e12	1.10505
$609$	0	0
$610$	4.04168e11	0.118189
$611$	7.99816e12	2.32169
$612$	0	0
$613$	−5.43289e12	−1.55403	−0.777013	−	0.629484i	$-0.783266\pi$
$613$	−5.43289e12	−1.55403	−0.777013	+	0.629484i	$0.783266\pi$
$614$	−4.65289e11	−0.132119
$615$	0	0
$616$	−3.09987e12	−0.867422
$617$	1.22774e12	0.341053	0.170527	−	0.985353i	$-0.445453\pi$
$617$	1.22774e12	0.341053	0.170527	+	0.985353i	$0.445453\pi$
$618$	0	0
$619$	4.33143e12	1.18583	0.592917	−	0.805264i	$-0.297976\pi$
$619$	4.33143e12	1.18583	0.592917	+	0.805264i	$0.297976\pi$
$620$	−4.62224e12	−1.25629
$621$	0	0
$622$	−3.98557e11	−0.106766
$623$	3.87673e11	0.103103
$624$	0	0
$625$	−3.25688e12	−0.853771
$626$	−8.73502e10	−0.0227342
$627$	0	0
$628$	−2.89224e12	−0.742020
$629$	6.69566e11	0.170555
$630$	0	0
$631$	1.79967e12	0.451919	0.225959	−	0.974137i	$-0.427448\pi$
$631$	1.79967e12	0.451919	0.225959	+	0.974137i	$0.427448\pi$
$632$	−7.48683e11	−0.186669
$633$	0	0
$634$	4.64899e11	0.114277
$635$	−2.53402e12	−0.618483
$636$	0	0
$637$	6.28238e12	1.51181
$638$	6.22180e11	0.148670
$639$	0	0
$640$	−3.27890e12	−0.772535
$641$	−5.02365e12	−1.17532	−0.587662	−	0.809106i	$-0.699952\pi$
$641$	−5.02365e12	−1.17532	−0.587662	+	0.809106i	$0.699952\pi$
$642$	0	0
$643$	4.60458e12	1.06229	0.531143	−	0.847283i	$-0.321763\pi$
$643$	4.60458e12	1.06229	0.531143	+	0.847283i	$0.321763\pi$
$644$	2.52111e12	0.577572
$645$	0	0
$646$	−4.28008e11	−0.0966953
$647$	−4.15507e12	−0.932201	−0.466100	−	0.884732i	$-0.654341\pi$
$647$	−4.15507e12	−0.932201	−0.466100	+	0.884732i	$0.654341\pi$
$648$	0	0
$649$	6.52584e12	1.44390
$650$	1.95373e11	0.0429295
$651$	0	0
$652$	−1.06164e12	−0.230071
$653$	−3.43743e11	−0.0739817	−0.0369909	−	0.999316i	$-0.511777\pi$
$653$	−3.43743e11	−0.0739817	−0.0369909	+	0.999316i	$0.511777\pi$
$654$	0	0
$655$	4.31202e12	0.915367
$656$	−4.25562e12	−0.897212
$657$	0	0
$658$	−2.82325e12	−0.587129
$659$	−2.39727e12	−0.495145	−0.247572	−	0.968869i	$-0.579633\pi$
$659$	−2.39727e12	−0.495145	−0.247572	+	0.968869i	$0.579633\pi$
$660$	0	0
$661$	−2.09899e12	−0.427665	−0.213833	−	0.976870i	$-0.568595\pi$
$661$	−2.09899e12	−0.427665	−0.213833	+	0.976870i	$0.568595\pi$
$662$	−3.09617e11	−0.0626563
$663$	0	0
$664$	3.62436e12	0.723560
$665$	1.12895e13	2.23861
$666$	0	0
$667$	−1.04314e12	−0.204068
$668$	−7.44646e11	−0.144696
$669$	0	0
$670$	−1.12408e11	−0.0215507
$671$	−3.54301e12	−0.674715
$672$	0	0
$673$	−1.61276e12	−0.303042	−0.151521	−	0.988454i	$-0.548417\pi$
$673$	−1.61276e12	−0.303042	−0.151521	+	0.988454i	$0.548417\pi$
$674$	−1.67217e12	−0.312112
$675$	0	0
$676$	−4.59747e12	−0.846758
$677$	−2.64830e12	−0.484527	−0.242264	−	0.970210i	$-0.577890\pi$
$677$	−2.64830e12	−0.484527	−0.242264	+	0.970210i	$0.577890\pi$
$678$	0	0
$679$	−3.78355e12	−0.683101
$680$	5.89637e11	0.105754
$681$	0	0
$682$	−2.49046e12	−0.440808
$683$	9.69821e12	1.70529	0.852645	−	0.522491i	$-0.174997\pi$
$683$	9.69821e12	1.70529	0.852645	+	0.522491i	$0.174997\pi$
$684$	0	0
$685$	−6.31026e12	−1.09506
$686$	−1.96320e11	−0.0338458
$687$	0	0
$688$	7.54598e12	1.28401
$689$	4.66546e12	0.788693
$690$	0	0
$691$	−7.85953e12	−1.31143	−0.655715	−	0.755008i	$-0.727633\pi$
$691$	−7.85953e12	−1.31143	−0.655715	+	0.755008i	$0.727633\pi$
$692$	6.58740e12	1.09204
$693$	0	0
$694$	1.82234e11	0.0298203
$695$	−4.66190e12	−0.757934
$696$	0	0
$697$	1.63429e12	0.262290
$698$	2.07437e12	0.330779
$699$	0	0
$700$	1.12204e12	0.176631
$701$	−1.35808e12	−0.212419	−0.106210	−	0.994344i	$-0.533871\pi$
$701$	−1.35808e12	−0.212419	−0.106210	+	0.994344i	$0.533871\pi$
$702$	0	0
$703$	7.54506e12	1.16510
$704$	5.58969e12	0.857651
$705$	0	0
$706$	1.14290e12	0.173136
$707$	−1.66940e11	−0.0251288
$708$	0	0
$709$	8.38924e12	1.24685	0.623426	−	0.781883i	$-0.285740\pi$
$709$	8.38924e12	1.24685	0.623426	+	0.781883i	$0.285740\pi$
$710$	6.96563e11	0.102872
$711$	0	0
$712$	2.28162e11	0.0332724
$713$	4.17546e12	0.605064
$714$	0	0
$715$	1.15160e13	1.64787
$716$	3.61032e12	0.513378
$717$	0	0
$718$	1.71051e12	0.240196
$719$	−1.05644e12	−0.147423	−0.0737117	−	0.997280i	$-0.523484\pi$
$719$	−1.05644e12	−0.147423	−0.0737117	+	0.997280i	$0.523484\pi$
$720$	0	0
$721$	6.60214e12	0.909864
$722$	−3.06604e12	−0.419913
$723$	0	0
$724$	9.55967e12	1.29306
$725$	−4.64254e11	−0.0624072
$726$	0	0
$727$	1.20219e12	0.159614	0.0798068	−	0.996810i	$-0.474570\pi$
$727$	1.20219e12	0.159614	0.0798068	+	0.996810i	$0.474570\pi$
$728$	7.06757e12	0.932564
$729$	0	0
$730$	−4.45419e11	−0.0580519
$731$	−2.89789e12	−0.375365
$732$	0	0
$733$	−1.38044e13	−1.76624	−0.883121	−	0.469146i	$-0.844562\pi$
$733$	−1.38044e13	−1.76624	−0.883121	+	0.469146i	$0.844562\pi$
$734$	−1.30884e12	−0.166439
$735$	0	0
$736$	2.24780e12	0.282362
$737$	9.85390e11	0.123028
$738$	0	0
$739$	−1.03973e13	−1.28240	−0.641198	−	0.767375i	$-0.721562\pi$
$739$	−1.03973e13	−1.28240	−0.641198	+	0.767375i	$0.721562\pi$
$740$	−5.04220e12	−0.618127
$741$	0	0
$742$	−1.64685e12	−0.199451
$743$	−7.06440e12	−0.850405	−0.425202	−	0.905098i	$-0.639797\pi$
$743$	−7.06440e12	−0.850405	−0.425202	+	0.905098i	$0.639797\pi$
$744$	0	0
$745$	−2.87753e12	−0.342229
$746$	−1.60030e12	−0.189181
$747$	0	0
$748$	−2.50737e12	−0.292861
$749$	6.61233e12	0.767691
$750$	0	0
$751$	5.52292e12	0.633562	0.316781	−	0.948499i	$-0.397398\pi$
$751$	5.52292e12	0.633562	0.316781	+	0.948499i	$0.397398\pi$
$752$	1.22584e13	1.39783
$753$	0	0
$754$	−1.41854e12	−0.159835
$755$	−1.01574e13	−1.13768
$756$	0	0
$757$	−5.93646e12	−0.657046	−0.328523	−	0.944496i	$-0.606551\pi$
$757$	−5.93646e12	−0.657046	−0.328523	+	0.944496i	$0.606551\pi$
$758$	−2.04747e12	−0.225272
$759$	0	0
$760$	6.64438e12	0.722425
$761$	1.16527e13	1.25949	0.629745	−	0.776802i	$-0.283160\pi$
$761$	1.16527e13	1.25949	0.629745	+	0.776802i	$0.283160\pi$
$762$	0	0
$763$	3.14133e12	0.335547
$764$	−1.71074e13	−1.81662
$765$	0	0
$766$	2.03550e12	0.213620
$767$	−1.48786e13	−1.55233
$768$	0	0
$769$	−3.13586e12	−0.323361	−0.161681	−	0.986843i	$-0.551691\pi$
$769$	−3.13586e12	−0.323361	−0.161681	+	0.986843i	$0.551691\pi$
$770$	−4.06500e12	−0.416728
$771$	0	0
$772$	5.62134e12	0.569590
$773$	−1.41981e13	−1.43029	−0.715143	−	0.698979i	$-0.753638\pi$
$773$	−1.41981e13	−1.43029	−0.715143	+	0.698979i	$0.753638\pi$
$774$	0	0
$775$	1.85831e12	0.185038
$776$	−2.22678e12	−0.220445
$777$	0	0
$778$	−2.51889e11	−0.0246491
$779$	1.84161e13	1.79176
$780$	0	0
$781$	−6.10619e12	−0.587274
$782$	−2.58381e11	−0.0247076
$783$	0	0
$784$	9.62871e12	0.910219
$785$	−7.81856e12	−0.734875
$786$	0	0
$787$	−7.60742e12	−0.706889	−0.353444	−	0.935456i	$-0.614990\pi$
$787$	−7.60742e12	−0.706889	−0.353444	+	0.935456i	$0.614990\pi$
$788$	2.41149e12	0.222801
$789$	0	0
$790$	−9.81782e11	−0.0896795
$791$	1.57106e13	1.42691
$792$	0	0
$793$	8.07790e12	0.725386
$794$	1.83399e12	0.163759
$795$	0	0
$796$	9.18798e11	0.0811169
$797$	−8.82832e11	−0.0775025	−0.0387513	−	0.999249i	$-0.512338\pi$
$797$	−8.82832e11	−0.0775025	−0.0387513	+	0.999249i	$0.512338\pi$
$798$	0	0
$799$	−4.70762e12	−0.408640
$800$	1.00040e12	0.0863510
$801$	0	0
$802$	−5.34337e12	−0.456069
$803$	3.90462e12	0.331405
$804$	0	0
$805$	6.81530e12	0.572010
$806$	5.67814e12	0.473913
$807$	0	0
$808$	−9.82511e10	−0.00810935
$809$	−1.36683e13	−1.12188	−0.560940	−	0.827856i	$-0.689560\pi$
$809$	−1.36683e13	−1.12188	−0.560940	+	0.827856i	$0.689560\pi$
$810$	0	0
$811$	−1.63530e13	−1.32741	−0.663703	−	0.747996i	$-0.731016\pi$
$811$	−1.63530e13	−1.32741	−0.663703	+	0.747996i	$0.731016\pi$
$812$	−8.14676e12	−0.657632
$813$	0	0
$814$	−2.71674e12	−0.216889
$815$	−2.86992e12	−0.227856
$816$	0	0
$817$	−3.26551e13	−2.56420
$818$	−4.45232e12	−0.347694
$819$	0	0
$820$	−1.23071e13	−0.950590
$821$	4.83235e12	0.371206	0.185603	−	0.982625i	$-0.440576\pi$
$821$	4.83235e12	0.371206	0.185603	+	0.982625i	$0.440576\pi$
$822$	0	0
$823$	−1.61695e13	−1.22856	−0.614282	−	0.789087i	$-0.710554\pi$
$823$	−1.61695e13	−1.22856	−0.614282	+	0.789087i	$0.710554\pi$
$824$	3.88565e12	0.293623
$825$	0	0
$826$	5.25198e12	0.392566
$827$	−1.37247e13	−1.02030	−0.510149	−	0.860086i	$-0.670410\pi$
$827$	−1.37247e13	−1.02030	−0.510149	+	0.860086i	$0.670410\pi$
$828$	0	0
$829$	2.58304e13	1.89949	0.949743	−	0.313031i	$-0.101344\pi$
$829$	2.58304e13	1.89949	0.949743	+	0.313031i	$0.101344\pi$
$830$	4.75278e12	0.347613
$831$	0	0
$832$	−1.27442e13	−0.922060
$833$	−3.69773e12	−0.266092
$834$	0	0
$835$	−2.01299e12	−0.143302
$836$	−2.82545e13	−2.00060
$837$	0	0
$838$	−2.27704e12	−0.159504
$839$	5.42716e11	0.0378132	0.0189066	−	0.999821i	$-0.493981\pi$
$839$	5.42716e11	0.0378132	0.0189066	+	0.999821i	$0.493981\pi$
$840$	0	0
$841$	−1.11363e13	−0.767645
$842$	−1.69764e12	−0.116397
$843$	0	0
$844$	−2.14928e13	−1.45798
$845$	−1.24283e13	−0.838604
$846$	0	0
$847$	1.39431e13	0.930857
$848$	7.15054e12	0.474851
$849$	0	0
$850$	−1.14994e11	−0.00755598
$851$	4.55483e12	0.297707
$852$	0	0
$853$	−1.71048e13	−1.10623	−0.553116	−	0.833104i	$-0.686561\pi$
$853$	−1.71048e13	−1.10623	−0.553116	+	0.833104i	$0.686561\pi$
$854$	−2.85140e12	−0.183442
$855$	0	0
$856$	3.89164e12	0.247743
$857$	6.06810e12	0.384272	0.192136	−	0.981368i	$-0.438458\pi$
$857$	6.06810e12	0.384272	0.192136	+	0.981368i	$0.438458\pi$
$858$	0	0
$859$	−1.87986e13	−1.17803	−0.589016	−	0.808122i	$-0.700484\pi$
$859$	−1.87986e13	−1.17803	−0.589016	+	0.808122i	$0.700484\pi$
$860$	2.18227e13	1.36040
$861$	0	0
$862$	4.71824e12	0.291070
$863$	6.53337e12	0.400949	0.200474	−	0.979699i	$-0.435752\pi$
$863$	6.53337e12	0.400949	0.200474	+	0.979699i	$0.435752\pi$
$864$	0	0
$865$	1.78077e13	1.08152
$866$	−1.60690e12	−0.0970862
$867$	0	0
$868$	3.26098e13	1.94989
$869$	8.60646e12	0.511960
$870$	0	0
$871$	−2.24665e12	−0.132268
$872$	1.84881e12	0.108285
$873$	0	0
$874$	−2.91159e12	−0.168783
$875$	2.64615e13	1.52608
$876$	0	0
$877$	−1.60851e13	−0.918178	−0.459089	−	0.888390i	$-0.651824\pi$
$877$	−1.60851e13	−0.918178	−0.459089	+	0.888390i	$0.651824\pi$
$878$	−2.98809e12	−0.169695
$879$	0	0
$880$	1.76500e13	0.992141
$881$	−3.30698e13	−1.84944	−0.924720	−	0.380647i	$-0.875701\pi$
$881$	−3.30698e13	−1.84944	−0.924720	+	0.380647i	$0.875701\pi$
$882$	0	0
$883$	−7.25465e12	−0.401599	−0.200800	−	0.979632i	$-0.564354\pi$
$883$	−7.25465e12	−0.401599	−0.200800	+	0.979632i	$0.564354\pi$
$884$	5.71670e12	0.314855
$885$	0	0
$886$	−5.64077e12	−0.307529
$887$	1.13226e13	0.614170	0.307085	−	0.951682i	$-0.400646\pi$
$887$	1.13226e13	0.614170	0.307085	+	0.951682i	$0.400646\pi$
$888$	0	0
$889$	1.78774e13	0.959947
$890$	2.99200e11	0.0159848
$891$	0	0
$892$	4.85959e12	0.257015
$893$	−5.30482e13	−2.79151
$894$	0	0
$895$	9.75974e12	0.508434
$896$	2.31326e13	1.19905
$897$	0	0
$898$	−5.71303e12	−0.293172
$899$	−1.34926e13	−0.688934
$900$	0	0
$901$	−2.74603e12	−0.138817
$902$	−6.63105e12	−0.333544
$903$	0	0
$904$	9.24635e12	0.460482
$905$	2.58426e13	1.28061
$906$	0	0
$907$	3.43776e13	1.68672	0.843360	−	0.537348i	$-0.180574\pi$
$907$	3.43776e13	1.68672	0.843360	+	0.537348i	$0.180574\pi$
$908$	3.62585e13	1.77021
$909$	0	0
$910$	9.26802e12	0.448024
$911$	1.18306e13	0.569082	0.284541	−	0.958664i	$-0.408159\pi$
$911$	1.18306e13	0.569082	0.284541	+	0.958664i	$0.408159\pi$
$912$	0	0
$913$	−4.16637e13	−1.98445
$914$	−6.20334e11	−0.0294014
$915$	0	0
$916$	−3.95230e13	−1.85490
$917$	−3.04212e13	−1.42074
$918$	0	0
$919$	−2.68999e13	−1.24403	−0.622015	−	0.783005i	$-0.713686\pi$
$919$	−2.68999e13	−1.24403	−0.622015	+	0.783005i	$0.713686\pi$
$920$	4.01110e12	0.184594
$921$	0	0
$922$	5.70533e12	0.260011
$923$	1.39218e13	0.631378
$924$	0	0
$925$	2.02716e12	0.0910436
$926$	−6.87248e11	−0.0307160
$927$	0	0
$928$	−7.26356e12	−0.321502
$929$	9.83481e12	0.433207	0.216603	−	0.976260i	$-0.430502\pi$
$929$	9.83481e12	0.433207	0.216603	+	0.976260i	$0.430502\pi$
$930$	0	0
$931$	−4.16681e13	−1.81773
$932$	−2.39876e13	−1.04139
$933$	0	0
$934$	−6.57556e12	−0.282730
$935$	−6.77816e12	−0.290041
$936$	0	0
$937$	9.23144e12	0.391238	0.195619	−	0.980680i	$-0.437328\pi$
$937$	9.23144e12	0.391238	0.195619	+	0.980680i	$0.437328\pi$
$938$	7.93039e11	0.0334489
$939$	0	0
$940$	3.54509e13	1.48099
$941$	1.00553e13	0.418062	0.209031	−	0.977909i	$-0.432969\pi$
$941$	1.00553e13	0.418062	0.209031	+	0.977909i	$0.432969\pi$
$942$	0	0
$943$	1.11175e13	0.457830
$944$	−2.28038e13	−0.934617
$945$	0	0
$946$	1.17581e13	0.477338
$947$	−3.28956e13	−1.32912	−0.664558	−	0.747237i	$-0.731380\pi$
$947$	−3.28956e13	−1.32912	−0.664558	+	0.747237i	$0.731380\pi$
$948$	0	0
$949$	−8.90236e12	−0.356293
$950$	−1.29582e12	−0.0516166
$951$	0	0
$952$	−4.15988e12	−0.164140
$953$	2.79353e13	1.09707	0.548537	−	0.836126i	$-0.315185\pi$
$953$	2.79353e13	1.09707	0.548537	+	0.836126i	$0.315185\pi$
$954$	0	0
$955$	−4.62463e13	−1.79913
$956$	−1.96028e13	−0.759027
$957$	0	0
$958$	−8.64382e12	−0.331559
$959$	4.45187e13	1.69965
$960$	0	0
$961$	2.75686e13	1.04270
$962$	6.19404e12	0.233177
$963$	0	0
$964$	1.47571e13	0.550368
$965$	1.51961e13	0.564105
$966$	0	0
$967$	3.57620e13	1.31523	0.657617	−	0.753352i	$-0.271565\pi$
$967$	3.57620e13	1.31523	0.657617	+	0.753352i	$0.271565\pi$
$968$	8.20609e12	0.300398
$969$	0	0
$970$	−2.92008e12	−0.105906
$971$	5.49737e12	0.198458	0.0992290	−	0.995065i	$-0.468362\pi$
$971$	5.49737e12	0.198458	0.0992290	+	0.995065i	$0.468362\pi$
$972$	0	0
$973$	3.28896e13	1.17639
$974$	−5.11756e12	−0.182200
$975$	0	0
$976$	1.23806e13	0.436736
$977$	1.41757e13	0.497759	0.248879	−	0.968534i	$-0.419938\pi$
$977$	1.41757e13	0.497759	0.248879	+	0.968534i	$0.419938\pi$
$978$	0	0
$979$	−2.62283e12	−0.0912533
$980$	2.78459e13	0.964371
$981$	0	0
$982$	5.26217e12	0.180577
$983$	−4.48632e13	−1.53250	−0.766248	−	0.642545i	$-0.777879\pi$
$983$	−4.48632e13	−1.53250	−0.766248	+	0.642545i	$0.777879\pi$
$984$	0	0
$985$	6.51896e12	0.220656
$986$	8.34936e11	0.0281324
$987$	0	0
$988$	6.44191e13	2.15084
$989$	−1.97134e13	−0.655205
$990$	0	0
$991$	2.93025e13	0.965101	0.482550	−	0.875868i	$-0.339711\pi$
$991$	2.93025e13	0.965101	0.482550	+	0.875868i	$0.339711\pi$
$992$	2.90745e13	0.953257
$993$	0	0
$994$	−4.91424e12	−0.159668
$995$	2.48378e12	0.0803357
$996$	0	0
$997$	1.15625e13	0.370616	0.185308	−	0.982680i	$-0.440672\pi$
$997$	1.15625e13	0.370616	0.185308	+	0.982680i	$0.440672\pi$
$998$	6.69697e12	0.213693
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	153.10.a.f.1.3		7
3.2	odd	2		17.10.a.b.1.5	✓	7
12.11	even	2		272.10.a.g.1.4		7
51.50	odd	2		289.10.a.b.1.5		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.10.a.b.1.5	✓	7	3.2	odd	2
153.10.a.f.1.3		7	1.1	even	1	trivial
272.10.a.g.1.4		7	12.11	even	2
289.10.a.b.1.5		7	51.50	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 153 = 3^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	153.a (trivial)

\(f(q)\)	\(=\)	\(q-5.44491 q^{2} -482.353 q^{4} -1303.94 q^{5} +9199.27 q^{7} +5414.17 q^{8} +O(q^{10})\)	\(q-5.44491 q^{2} -482.353 q^{4} -1303.94 q^{5} +9199.27 q^{7} +5414.17 q^{8} +7099.84 q^{10} -62238.4 q^{11} +141901. q^{13} -50089.2 q^{14} +217485. q^{16} -83521.0 q^{17} -941163. q^{19} +628959. q^{20} +338883. q^{22} -568165. q^{23} -252865. q^{25} -772638. q^{26} -4.43730e6 q^{28} +1.83597e6 q^{29} -7.34903e6 q^{31} -3.95624e6 q^{32} +454765. q^{34} -1.19953e7 q^{35} -8.01674e6 q^{37} +5.12455e6 q^{38} -7.05975e6 q^{40} -1.95674e7 q^{41} +3.46966e7 q^{43} +3.00209e7 q^{44} +3.09361e6 q^{46} +5.63645e7 q^{47} +4.42730e7 q^{49} +1.37683e6 q^{50} -6.84463e7 q^{52} +3.28783e7 q^{53} +8.11551e7 q^{55} +4.98064e7 q^{56} -9.99672e6 q^{58} -1.04852e8 q^{59} +5.69264e7 q^{61} +4.00148e7 q^{62} -8.98109e7 q^{64} -1.85030e8 q^{65} -1.58325e7 q^{67} +4.02866e7 q^{68} +6.53134e7 q^{70} +9.81097e7 q^{71} -6.27365e7 q^{73} +4.36505e7 q^{74} +4.53973e8 q^{76} -5.72548e8 q^{77} -1.38282e8 q^{79} -2.83587e8 q^{80} +1.06543e8 q^{82} +6.69421e8 q^{83} +1.08906e8 q^{85} -1.88920e8 q^{86} -3.36969e8 q^{88} +4.21417e7 q^{89} +1.30538e9 q^{91} +2.74056e8 q^{92} -3.06900e8 q^{94} +1.22722e9 q^{95} -4.11288e8 q^{97} -2.41063e8 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + q^{2} + 2389 q^{4} - 1362 q^{5} + 9388 q^{7} - 16821 q^{8}+O(q^{10}) \) 7 * q + q^2 + 2389 * q^4 - 1362 * q^5 + 9388 * q^7 - 16821 * q^8	\( 7 q + q^{2} + 2389 q^{4} - 1362 q^{5} + 9388 q^{7} - 16821 q^{8} + 154226 q^{10} - 135536 q^{11} + 166122 q^{13} - 447252 q^{14} + 1463585 q^{16} - 584647 q^{17} + 777172 q^{19} + 917162 q^{20} - 1222520 q^{22} - 1357764 q^{23} + 1065785 q^{25} + 14379966 q^{26} - 3328892 q^{28} - 967002 q^{29} + 3546740 q^{31} - 4825461 q^{32} - 83521 q^{34} + 530736 q^{35} + 18296498 q^{37} + 49363020 q^{38} + 127155062 q^{40} - 10285686 q^{41} + 21913204 q^{43} - 96696624 q^{44} - 151509484 q^{46} - 56639800 q^{47} + 27010351 q^{49} + 261150303 q^{50} - 156226378 q^{52} - 121813562 q^{53} + 40793128 q^{55} + 196175436 q^{56} - 236833910 q^{58} - 29222388 q^{59} - 49915846 q^{61} + 73506556 q^{62} + 317922057 q^{64} + 122633668 q^{65} + 301863420 q^{67} - 199531669 q^{68} + 966315960 q^{70} - 652473940 q^{71} + 306656342 q^{73} - 249173874 q^{74} + 128694700 q^{76} + 102442536 q^{77} + 959147884 q^{79} + 692173602 q^{80} + 1046441254 q^{82} + 1512945268 q^{83} + 113755602 q^{85} + 164953236 q^{86} + 1132038848 q^{88} + 1971327114 q^{89} - 1061062864 q^{91} - 901186756 q^{92} + 2534831232 q^{94} + 3249631512 q^{95} + 2006526254 q^{97} + 2170640009 q^{98}+O(q^{100}) \) 7 * q + q^2 + 2389 * q^4 - 1362 * q^5 + 9388 * q^7 - 16821 * q^8 + 154226 * q^10 - 135536 * q^11 + 166122 * q^13 - 447252 * q^14 + 1463585 * q^16 - 584647 * q^17 + 777172 * q^19 + 917162 * q^20 - 1222520 * q^22 - 1357764 * q^23 + 1065785 * q^25 + 14379966 * q^26 - 3328892 * q^28 - 967002 * q^29 + 3546740 * q^31 - 4825461 * q^32 - 83521 * q^34 + 530736 * q^35 + 18296498 * q^37 + 49363020 * q^38 + 127155062 * q^40 - 10285686 * q^41 + 21913204 * q^43 - 96696624 * q^44 - 151509484 * q^46 - 56639800 * q^47 + 27010351 * q^49 + 261150303 * q^50 - 156226378 * q^52 - 121813562 * q^53 + 40793128 * q^55 + 196175436 * q^56 - 236833910 * q^58 - 29222388 * q^59 - 49915846 * q^61 + 73506556 * q^62 + 317922057 * q^64 + 122633668 * q^65 + 301863420 * q^67 - 199531669 * q^68 + 966315960 * q^70 - 652473940 * q^71 + 306656342 * q^73 - 249173874 * q^74 + 128694700 * q^76 + 102442536 * q^77 + 959147884 * q^79 + 692173602 * q^80 + 1046441254 * q^82 + 1512945268 * q^83 + 113755602 * q^85 + 164953236 * q^86 + 1132038848 * q^88 + 1971327114 * q^89 - 1061062864 * q^91 - 901186756 * q^92 + 2534831232 * q^94 + 3249631512 * q^95 + 2006526254 * q^97 + 2170640009 * q^98

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