LMFDB - Embedded newform 153.10.a.f.1.2

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			1.2
Root			$-34.1532$ 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)

$f(q)$	$=$	$q-34.1532 q^{2} +654.438 q^{4} -195.287 q^{5} -356.628 q^{7} -4864.71 q^{8} +O(q^{10})$	\(q-34.1532 q^{2} +654.438 q^{4} -195.287 q^{5} -356.628 q^{7} -4864.71 q^{8} +6669.66 q^{10} +21467.8 q^{11} -6206.76 q^{13} +12180.0 q^{14} -168927. q^{16} -83521.0 q^{17} +907187. q^{19} -127803. q^{20} -733194. q^{22} +1.23486e6 q^{23} -1.91499e6 q^{25} +211980. q^{26} -233391. q^{28} +3.01596e6 q^{29} -334277. q^{31} +8.26012e6 q^{32} +2.85251e6 q^{34} +69644.7 q^{35} +2.06102e7 q^{37} -3.09833e7 q^{38} +950014. q^{40} -1.47571e7 q^{41} -7.75953e6 q^{43} +1.40494e7 q^{44} -4.21744e7 q^{46} -3.19993e7 q^{47} -4.02264e7 q^{49} +6.54029e7 q^{50} -4.06194e6 q^{52} -9.46750e7 q^{53} -4.19238e6 q^{55} +1.73489e6 q^{56} -1.03005e8 q^{58} -6.01771e7 q^{59} +6.05254e7 q^{61} +1.14166e7 q^{62} -1.95619e8 q^{64} +1.21210e6 q^{65} -1.26316e8 q^{67} -5.46593e7 q^{68} -2.37859e6 q^{70} -3.33917e7 q^{71} +2.85706e8 q^{73} -7.03903e8 q^{74} +5.93698e8 q^{76} -7.65603e6 q^{77} -7.60575e7 q^{79} +3.29892e7 q^{80} +5.04001e8 q^{82} +1.73620e7 q^{83} +1.63105e7 q^{85} +2.65012e8 q^{86} -1.04435e8 q^{88} -3.96876e8 q^{89} +2.21350e6 q^{91} +8.08139e8 q^{92} +1.09288e9 q^{94} -1.77162e8 q^{95} +1.13120e9 q^{97} +1.37386e9 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−34.1532	−1.50937	−0.754685	−	0.656087i	$-0.772210\pi$
$2$	−34.1532	−1.50937	−0.754685	+	0.656087i	$0.772210\pi$
$3$	0	0
$3$	0	0
$4$	654.438	1.27820
$5$	−195.287	−0.139736	−0.0698679	−	0.997556i	$-0.522258\pi$
$5$	−195.287	−0.139736	−0.0698679	+	0.997556i	$0.522258\pi$
$6$	0	0
$7$	−356.628	−0.0561402	−0.0280701	−	0.999606i	$-0.508936\pi$
$7$	−356.628	−0.0561402	−0.0280701	+	0.999606i	$0.508936\pi$
$8$	−4864.71	−0.419906
$9$	0	0
$10$	6669.66	0.210913
$11$	21467.8	0.442101	0.221050	−	0.975262i	$-0.429051\pi$
$11$	21467.8	0.442101	0.221050	+	0.975262i	$0.429051\pi$
$12$	0	0
$13$	−6206.76	−0.0602726	−0.0301363	−	0.999546i	$-0.509594\pi$
$13$	−6206.76	−0.0602726	−0.0301363	+	0.999546i	$0.509594\pi$
$14$	12180.0	0.0847364
$15$	0	0
$16$	−168927.	−0.644406
$17$	−83521.0	−0.242536
$17$	−83521.0	−0.242536
$18$	0	0
$19$	907187.	1.59700	0.798501	−	0.601993i	$-0.205627\pi$
$19$	907187.	1.59700	0.798501	+	0.601993i	$0.205627\pi$
$20$	−127803.	−0.178610
$21$	0	0
$22$	−733194.	−0.667294
$23$	1.23486e6	0.920115	0.460058	−	0.887889i	$-0.347829\pi$
$23$	1.23486e6	0.920115	0.460058	+	0.887889i	$0.347829\pi$
$24$	0	0
$25$	−1.91499e6	−0.980474
$26$	211980.	0.0909737
$27$	0	0
$28$	−233391.	−0.0717584
$29$	3.01596e6	0.791835	0.395917	−	0.918286i	$-0.370427\pi$
$29$	3.01596e6	0.791835	0.395917	+	0.918286i	$0.370427\pi$
$30$	0	0
$31$	−334277.	−0.0650099	−0.0325049	−	0.999472i	$-0.510348\pi$
$31$	−334277.	−0.0650099	−0.0325049	+	0.999472i	$0.510348\pi$
$32$	8.26012e6	1.39255
$33$	0	0
$34$	2.85251e6	0.366076
$35$	69644.7	0.00784481
$36$	0	0
$37$	2.06102e7	1.80790	0.903949	−	0.427640i	$-0.140655\pi$
$37$	2.06102e7	1.80790	0.903949	+	0.427640i	$0.140655\pi$
$38$	−3.09833e7	−2.41047
$39$	0	0
$40$	950014.	0.0586759
$41$	−1.47571e7	−0.815593	−0.407796	−	0.913073i	$-0.633703\pi$
$41$	−1.47571e7	−0.815593	−0.407796	+	0.913073i	$0.633703\pi$
$42$	0	0
$43$	−7.75953e6	−0.346120	−0.173060	−	0.984911i	$-0.555366\pi$
$43$	−7.75953e6	−0.346120	−0.173060	+	0.984911i	$0.555366\pi$
$44$	1.40494e7	0.565093
$45$	0	0
$46$	−4.21744e7	−1.38880
$47$	−3.19993e7	−0.956534	−0.478267	−	0.878214i	$-0.658735\pi$
$47$	−3.19993e7	−0.956534	−0.478267	+	0.878214i	$0.658735\pi$
$48$	0	0
$49$	−4.02264e7	−0.996848
$50$	6.54029e7	1.47990
$51$	0	0
$52$	−4.06194e6	−0.0770404
$53$	−9.46750e7	−1.64814	−0.824070	−	0.566488i	$-0.808302\pi$
$53$	−9.46750e7	−1.64814	−0.824070	+	0.566488i	$0.808302\pi$
$54$	0	0
$55$	−4.19238e6	−0.0617773
$56$	1.73489e6	0.0235736
$57$	0	0
$58$	−1.03005e8	−1.19517
$59$	−6.01771e7	−0.646542	−0.323271	−	0.946306i	$-0.604783\pi$
$59$	−6.01771e7	−0.646542	−0.323271	+	0.946306i	$0.604783\pi$
$60$	0	0
$61$	6.05254e7	0.559698	0.279849	−	0.960044i	$-0.409716\pi$
$61$	6.05254e7	0.559698	0.279849	+	0.960044i	$0.409716\pi$
$62$	1.14166e7	0.0981240
$63$	0	0
$64$	−1.95619e8	−1.45747
$65$	1.21210e6	0.00842224
$66$	0	0
$67$	−1.26316e8	−0.765813	−0.382907	−	0.923787i	$-0.625077\pi$
$67$	−1.26316e8	−0.765813	−0.382907	+	0.923787i	$0.625077\pi$
$68$	−5.46593e7	−0.310009
$69$	0	0
$70$	−2.37859e6	−0.0118407
$71$	−3.33917e7	−0.155947	−0.0779734	−	0.996955i	$-0.524845\pi$
$71$	−3.33917e7	−0.155947	−0.0779734	+	0.996955i	$0.524845\pi$
$72$	0	0
$73$	2.85706e8	1.17752	0.588758	−	0.808309i	$-0.299617\pi$
$73$	2.85706e8	1.17752	0.588758	+	0.808309i	$0.299617\pi$
$74$	−7.03903e8	−2.72879
$75$	0	0
$76$	5.93698e8	2.04129
$77$	−7.65603e6	−0.0248196
$78$	0	0
$79$	−7.60575e7	−0.219695	−0.109848	−	0.993948i	$-0.535036\pi$
$79$	−7.60575e7	−0.219695	−0.109848	+	0.993948i	$0.535036\pi$
$80$	3.29892e7	0.0900466
$81$	0	0
$82$	5.04001e8	1.23103
$83$	1.73620e7	0.0401558	0.0200779	−	0.999798i	$-0.493609\pi$
$83$	1.73620e7	0.0401558	0.0200779	+	0.999798i	$0.493609\pi$
$84$	0	0
$85$	1.63105e7	0.0338909
$86$	2.65012e8	0.522424
$87$	0	0
$88$	−1.04435e8	−0.185641
$89$	−3.96876e8	−0.670501	−0.335251	−	0.942129i	$-0.608821\pi$
$89$	−3.96876e8	−0.670501	−0.335251	+	0.942129i	$0.608821\pi$
$90$	0	0
$91$	2.21350e6	0.00338372
$92$	8.08139e8	1.17609
$93$	0	0
$94$	1.09288e9	1.44376
$95$	−1.77162e8	−0.223159
$96$	0	0
$97$	1.13120e9	1.29737	0.648687	−	0.761055i	$-0.275318\pi$
$97$	1.13120e9	1.29737	0.648687	+	0.761055i	$0.275318\pi$
$98$	1.37386e9	1.50461
$99$	0	0
$100$	−1.25324e9	−1.25324
$101$	1.58638e9	1.51692	0.758458	−	0.651722i	$-0.225953\pi$
$101$	1.58638e9	1.51692	0.758458	+	0.651722i	$0.225953\pi$
$102$	0	0
$103$	−9.77937e8	−0.856137	−0.428068	−	0.903746i	$-0.640806\pi$
$103$	−9.77937e8	−0.856137	−0.428068	+	0.903746i	$0.640806\pi$
$104$	3.01941e7	0.0253088
$105$	0	0
$106$	3.23345e9	2.48765
$107$	1.71253e8	0.126302	0.0631511	−	0.998004i	$-0.479885\pi$
$107$	1.71253e8	0.126302	0.0631511	+	0.998004i	$0.479885\pi$
$108$	0	0
$109$	1.66962e9	1.13292	0.566461	−	0.824089i	$-0.308312\pi$
$109$	1.66962e9	1.13292	0.566461	+	0.824089i	$0.308312\pi$
$110$	1.43183e8	0.0932449
$111$	0	0
$112$	6.02441e7	0.0361771
$113$	2.55660e9	1.47506	0.737531	−	0.675313i	$-0.235992\pi$
$113$	2.55660e9	1.47506	0.737531	+	0.675313i	$0.235992\pi$
$114$	0	0
$115$	−2.41152e8	−0.128573
$116$	1.97376e9	1.01212
$117$	0	0
$118$	2.05524e9	0.975872
$119$	2.97859e7	0.0136160
$120$	0	0
$121$	−1.89708e9	−0.804547
$122$	−2.06713e9	−0.844792
$123$	0	0
$124$	−2.18764e8	−0.0830956
$125$	7.55391e8	0.276743
$126$	0	0
$127$	−1.57297e9	−0.536542	−0.268271	−	0.963344i	$-0.586452\pi$
$127$	−1.57297e9	−0.536542	−0.268271	+	0.963344i	$0.586452\pi$
$128$	2.45181e9	0.807313
$129$	0	0
$130$	−4.13970e7	−0.0127123
$131$	−1.54185e9	−0.457426	−0.228713	−	0.973494i	$-0.573452\pi$
$131$	−1.54185e9	−0.457426	−0.228713	+	0.973494i	$0.573452\pi$
$132$	0	0
$133$	−3.23528e8	−0.0896561
$134$	4.31410e9	1.15590
$135$	0	0
$136$	4.06306e8	0.101842
$137$	7.48495e9	1.81529	0.907646	−	0.419736i	$-0.137877\pi$
$137$	7.48495e9	1.81529	0.907646	+	0.419736i	$0.137877\pi$
$138$	0	0
$139$	4.97076e9	1.12942	0.564711	−	0.825289i	$-0.308988\pi$
$139$	4.97076e9	1.12942	0.564711	+	0.825289i	$0.308988\pi$
$140$	4.55782e7	0.0100272
$141$	0	0
$142$	1.14043e9	0.235382
$143$	−1.33246e8	−0.0266465
$144$	0	0
$145$	−5.88977e8	−0.110648
$146$	−9.75777e9	−1.77731
$147$	0	0
$148$	1.34881e10	2.31085
$149$	2.17167e9	0.360957	0.180479	−	0.983579i	$-0.442235\pi$
$149$	2.17167e9	0.360957	0.180479	+	0.983579i	$0.442235\pi$
$150$	0	0
$151$	5.05353e9	0.791040	0.395520	−	0.918457i	$-0.370564\pi$
$151$	5.05353e9	0.791040	0.395520	+	0.918457i	$0.370564\pi$
$152$	−4.41320e9	−0.670591
$153$	0	0
$154$	2.61478e8	0.0374620
$155$	6.52799e7	0.00908421
$156$	0	0
$157$	−1.14585e10	−1.50515	−0.752577	−	0.658504i	$-0.771190\pi$
$157$	−1.14585e10	−1.50515	−0.752577	+	0.658504i	$0.771190\pi$
$158$	2.59760e9	0.331601
$159$	0	0
$160$	−1.61309e9	−0.194590
$161$	−4.40386e8	−0.0516555
$162$	0	0
$163$	1.58612e10	1.75992	0.879960	−	0.475048i	$-0.157569\pi$
$163$	1.58612e10	1.75992	0.879960	+	0.475048i	$0.157569\pi$
$164$	−9.65760e9	−1.04249
$165$	0	0
$166$	−5.92966e8	−0.0606099
$167$	7.94993e9	0.790932	0.395466	−	0.918481i	$-0.370583\pi$
$167$	7.94993e9	0.790932	0.395466	+	0.918481i	$0.370583\pi$
$168$	0	0
$169$	−1.05660e10	−0.996367
$170$	−5.57057e8	−0.0511540
$171$	0	0
$172$	−5.07813e9	−0.442411
$173$	−4.82389e9	−0.409440	−0.204720	−	0.978821i	$-0.565628\pi$
$173$	−4.82389e9	−0.409440	−0.204720	+	0.978821i	$0.565628\pi$
$174$	0	0
$175$	6.82938e8	0.0550440
$176$	−3.62650e9	−0.284892
$177$	0	0
$178$	1.35546e10	1.01203
$179$	6.50866e9	0.473863	0.236932	−	0.971526i	$-0.423858\pi$
$179$	6.50866e9	0.473863	0.236932	+	0.971526i	$0.423858\pi$
$180$	0	0
$181$	9.87513e9	0.683895	0.341947	−	0.939719i	$-0.388914\pi$
$181$	9.87513e9	0.683895	0.341947	+	0.939719i	$0.388914\pi$
$182$	−7.55982e7	−0.00510728
$183$	0	0
$184$	−6.00724e9	−0.386362
$185$	−4.02490e9	−0.252628
$186$	0	0
$187$	−1.79301e9	−0.107225
$188$	−2.09416e10	−1.22264
$189$	0	0
$190$	6.05063e9	0.336829
$191$	−1.73272e10	−0.942060	−0.471030	−	0.882117i	$-0.656118\pi$
$191$	−1.73272e10	−0.942060	−0.471030	+	0.882117i	$0.656118\pi$
$192$	0	0
$193$	−5.92773e9	−0.307525	−0.153763	−	0.988108i	$-0.549139\pi$
$193$	−5.92773e9	−0.307525	−0.153763	+	0.988108i	$0.549139\pi$
$194$	−3.86339e10	−1.95822
$195$	0	0
$196$	−2.63257e10	−1.27417
$197$	1.61285e10	0.762948	0.381474	−	0.924380i	$-0.375417\pi$
$197$	1.61285e10	0.762948	0.381474	+	0.924380i	$0.375417\pi$
$198$	0	0
$199$	−4.38224e10	−1.98088	−0.990438	−	0.137958i	$-0.955946\pi$
$199$	−4.38224e10	−1.98088	−0.990438	+	0.137958i	$0.955946\pi$
$200$	9.31586e9	0.411707
$201$	0	0
$202$	−5.41800e10	−2.28959
$203$	−1.07558e9	−0.0444538
$204$	0	0
$205$	2.88186e9	0.113968
$206$	3.33996e10	1.29223
$207$	0	0
$208$	1.04849e9	0.0388400
$209$	1.94753e10	0.706036
$210$	0	0
$211$	4.85013e10	1.68454	0.842272	−	0.539053i	$-0.181218\pi$
$211$	4.85013e10	1.68454	0.842272	+	0.539053i	$0.181218\pi$
$212$	−6.19589e10	−2.10665
$213$	0	0
$214$	−5.84883e9	−0.190637
$215$	1.51533e9	0.0483654
$216$	0	0
$217$	1.19213e8	0.00364967
$218$	−5.70230e10	−1.71000
$219$	0	0
$220$	−2.74366e9	−0.0789637
$221$	5.18395e8	0.0146182
$222$	0	0
$223$	−1.32607e9	−0.0359082	−0.0179541	−	0.999839i	$-0.505715\pi$
$223$	−1.32607e9	−0.0359082	−0.0179541	+	0.999839i	$0.505715\pi$
$224$	−2.94579e9	−0.0781783
$225$	0	0
$226$	−8.73161e10	−2.22642
$227$	6.30032e10	1.57487	0.787437	−	0.616395i	$-0.211407\pi$
$227$	6.30032e10	1.57487	0.787437	+	0.616395i	$0.211407\pi$
$228$	0	0
$229$	3.36520e10	0.808632	0.404316	−	0.914619i	$-0.367510\pi$
$229$	3.36520e10	0.808632	0.404316	+	0.914619i	$0.367510\pi$
$230$	8.23610e9	0.194064
$231$	0	0
$232$	−1.46718e10	−0.332496
$233$	3.25593e10	0.723724	0.361862	−	0.932232i	$-0.382141\pi$
$233$	3.25593e10	0.723724	0.361862	+	0.932232i	$0.382141\pi$
$234$	0	0
$235$	6.24905e9	0.133662
$236$	−3.93822e10	−0.826410
$237$	0	0
$238$	−1.01728e9	−0.0205516
$239$	−4.25086e10	−0.842725	−0.421363	−	0.906892i	$-0.638448\pi$
$239$	−4.25086e10	−0.842725	−0.421363	+	0.906892i	$0.638448\pi$
$240$	0	0
$241$	−6.46314e10	−1.23415	−0.617074	−	0.786905i	$-0.711682\pi$
$241$	−6.46314e10	−1.23415	−0.617074	+	0.786905i	$0.711682\pi$
$242$	6.47913e10	1.21436
$243$	0	0
$244$	3.96102e10	0.715406
$245$	7.85569e9	0.139295
$246$	0	0
$247$	−5.63069e9	−0.0962555
$248$	1.62616e9	0.0272980
$249$	0	0
$250$	−2.57990e10	−0.417708
$251$	1.00795e11	1.60290	0.801452	−	0.598060i	$-0.204061\pi$
$251$	1.00795e11	1.60290	0.801452	+	0.598060i	$0.204061\pi$
$252$	0	0
$253$	2.65098e10	0.406784
$254$	5.37219e10	0.809840
$255$	0	0
$256$	1.64197e10	0.238938
$257$	7.98430e10	1.14166	0.570831	−	0.821067i	$-0.306621\pi$
$257$	7.98430e10	1.14166	0.570831	+	0.821067i	$0.306621\pi$
$258$	0	0
$259$	−7.35017e9	−0.101496
$260$	7.93243e8	0.0107653
$261$	0	0
$262$	5.26590e10	0.690425
$263$	−9.26392e10	−1.19397	−0.596986	−	0.802252i	$-0.703635\pi$
$263$	−9.26392e10	−1.19397	−0.596986	+	0.802252i	$0.703635\pi$
$264$	0	0
$265$	1.84888e10	0.230304
$266$	1.10495e10	0.135324
$267$	0	0
$268$	−8.26662e10	−0.978862
$269$	6.38400e10	0.743375	0.371687	−	0.928358i	$-0.378779\pi$
$269$	6.38400e10	0.743375	0.371687	+	0.928358i	$0.378779\pi$
$270$	0	0
$271$	1.39281e11	1.56866	0.784331	−	0.620343i	$-0.213007\pi$
$271$	1.39281e11	1.56866	0.784331	+	0.620343i	$0.213007\pi$
$272$	1.41090e10	0.156291
$273$	0	0
$274$	−2.55635e11	−2.73995
$275$	−4.11106e10	−0.433468
$276$	0	0
$277$	1.33421e11	1.36165	0.680826	−	0.732445i	$-0.261621\pi$
$277$	1.33421e11	1.36165	0.680826	+	0.732445i	$0.261621\pi$
$278$	−1.69767e11	−1.70472
$279$	0	0
$280$	−3.38802e8	−0.00329408
$281$	1.22205e11	1.16926	0.584629	−	0.811301i	$-0.301240\pi$
$281$	1.22205e11	1.16926	0.584629	+	0.811301i	$0.301240\pi$
$282$	0	0
$283$	1.48138e11	1.37286	0.686430	−	0.727196i	$-0.259177\pi$
$283$	1.48138e11	1.37286	0.686430	+	0.727196i	$0.259177\pi$
$284$	−2.18528e10	−0.199331
$285$	0	0
$286$	4.55076e9	0.0402195
$287$	5.26279e9	0.0457876
$288$	0	0
$289$	6.97576e9	0.0588235
$290$	2.01154e10	0.167008
$291$	0	0
$292$	1.86977e11	1.50510
$293$	−1.17196e11	−0.928986	−0.464493	−	0.885577i	$-0.653763\pi$
$293$	−1.17196e11	−0.928986	−0.464493	+	0.885577i	$0.653763\pi$
$294$	0	0
$295$	1.17518e10	0.0903452
$296$	−1.00263e11	−0.759147
$297$	0	0
$298$	−7.41694e10	−0.544818
$299$	−7.66448e9	−0.0554577
$300$	0	0
$301$	2.76726e9	0.0194313
$302$	−1.72594e11	−1.19397
$303$	0	0
$304$	−1.53248e11	−1.02912
$305$	−1.18198e10	−0.0782099
$306$	0	0
$307$	−4.33130e10	−0.278288	−0.139144	−	0.990272i	$-0.544435\pi$
$307$	−4.33130e10	−0.278288	−0.139144	+	0.990272i	$0.544435\pi$
$308$	−5.01040e9	−0.0317244
$309$	0	0
$310$	−2.22952e9	−0.0137114
$311$	−1.79166e11	−1.08601	−0.543006	−	0.839729i	$-0.682714\pi$
$311$	−1.79166e11	−1.08601	−0.543006	+	0.839729i	$0.682714\pi$
$312$	0	0
$313$	−6.30182e10	−0.371122	−0.185561	−	0.982633i	$-0.559410\pi$
$313$	−6.30182e10	−0.371122	−0.185561	+	0.982633i	$0.559410\pi$
$314$	3.91346e11	2.27184
$315$	0	0
$316$	−4.97749e10	−0.280814
$317$	−4.25331e10	−0.236570	−0.118285	−	0.992980i	$-0.537740\pi$
$317$	−4.25331e10	−0.236570	−0.118285	+	0.992980i	$0.537740\pi$
$318$	0	0
$319$	6.47461e10	0.350071
$320$	3.82017e10	0.203661
$321$	0	0
$322$	1.50406e10	0.0779673
$323$	−7.57692e10	−0.387330
$324$	0	0
$325$	1.18859e10	0.0590957
$326$	−5.41711e11	−2.65637
$327$	0	0
$328$	7.17890e10	0.342472
$329$	1.14119e10	0.0537001
$330$	0	0
$331$	−1.36038e11	−0.622921	−0.311461	−	0.950259i	$-0.600818\pi$
$331$	−1.36038e11	−0.622921	−0.311461	+	0.950259i	$0.600818\pi$
$332$	1.13623e10	0.0513271
$333$	0	0
$334$	−2.71515e11	−1.19381
$335$	2.46679e10	0.107012
$336$	0	0
$337$	−4.52614e11	−1.91158	−0.955792	−	0.294042i	$-0.904999\pi$
$337$	−4.52614e11	−1.91158	−0.955792	+	0.294042i	$0.904999\pi$
$338$	3.60861e11	1.50389
$339$	0	0
$340$	1.06742e10	0.0433194
$341$	−7.17621e9	−0.0287409
$342$	0	0
$343$	2.87371e10	0.112104
$344$	3.77479e10	0.145338
$345$	0	0
$346$	1.64751e11	0.617996
$347$	2.00653e11	0.742955	0.371478	−	0.928442i	$-0.378851\pi$
$347$	2.00653e11	0.742955	0.371478	+	0.928442i	$0.378851\pi$
$348$	0	0
$349$	1.48945e11	0.537416	0.268708	−	0.963222i	$-0.413403\pi$
$349$	1.48945e11	0.537416	0.268708	+	0.963222i	$0.413403\pi$
$350$	−2.33245e10	−0.0830819
$351$	0	0
$352$	1.77327e11	0.615649
$353$	3.46998e11	1.18944	0.594718	−	0.803934i	$-0.297264\pi$
$353$	3.46998e11	1.18944	0.594718	+	0.803934i	$0.297264\pi$
$354$	0	0
$355$	6.52097e9	0.0217914
$356$	−2.59731e11	−0.857034
$357$	0	0
$358$	−2.22291e11	−0.715235
$359$	5.87619e11	1.86711	0.933556	−	0.358431i	$-0.116688\pi$
$359$	5.87619e11	1.86711	0.933556	+	0.358431i	$0.116688\pi$
$360$	0	0
$361$	5.00300e11	1.55042
$362$	−3.37267e11	−1.03225
$363$	0	0
$364$	1.44860e9	0.00432507
$365$	−5.57947e10	−0.164541
$366$	0	0
$367$	−8.17833e10	−0.235325	−0.117662	−	0.993054i	$-0.537540\pi$
$367$	−8.17833e10	−0.235325	−0.117662	+	0.993054i	$0.537540\pi$
$368$	−2.08601e11	−0.592928
$369$	0	0
$370$	1.37463e11	0.381310
$371$	3.37638e10	0.0925269
$372$	0	0
$373$	3.70187e11	0.990218	0.495109	−	0.868831i	$-0.335128\pi$
$373$	3.70187e11	0.990218	0.495109	+	0.868831i	$0.335128\pi$
$374$	6.12371e10	0.161842
$375$	0	0
$376$	1.55668e11	0.401655
$377$	−1.87193e10	−0.0477259
$378$	0	0
$379$	5.17440e11	1.28820	0.644100	−	0.764941i	$-0.277232\pi$
$379$	5.17440e11	1.28820	0.644100	+	0.764941i	$0.277232\pi$
$380$	−1.15941e11	−0.285241
$381$	0	0
$382$	5.91779e11	1.42192
$383$	−2.03437e11	−0.483099	−0.241549	−	0.970389i	$-0.577656\pi$
$383$	−2.03437e11	−0.483099	−0.241549	+	0.970389i	$0.577656\pi$
$384$	0	0
$385$	1.49512e9	0.00346819
$386$	2.02451e11	0.464170
$387$	0	0
$388$	7.40298e11	1.65830
$389$	−7.76405e11	−1.71916	−0.859578	−	0.511005i	$-0.829273\pi$
$389$	−7.76405e11	−1.71916	−0.859578	+	0.511005i	$0.829273\pi$
$390$	0	0
$391$	−1.03137e11	−0.223161
$392$	1.95690e11	0.418583
$393$	0	0
$394$	−5.50838e11	−1.15157
$395$	1.48530e10	0.0306993
$396$	0	0
$397$	4.33956e11	0.876776	0.438388	−	0.898786i	$-0.355550\pi$
$397$	4.33956e11	0.876776	0.438388	+	0.898786i	$0.355550\pi$
$398$	1.49667e12	2.98988
$399$	0	0
$400$	3.23493e11	0.631823
$401$	−3.07899e11	−0.594645	−0.297323	−	0.954777i	$-0.596094\pi$
$401$	−3.07899e11	−0.594645	−0.297323	+	0.954777i	$0.596094\pi$
$402$	0	0
$403$	2.07478e9	0.00391831
$404$	1.03819e12	1.93892
$405$	0	0
$406$	3.67343e10	0.0670973
$407$	4.42456e11	0.799273
$408$	0	0
$409$	−5.32344e11	−0.940671	−0.470335	−	0.882488i	$-0.655867\pi$
$409$	−5.32344e11	−0.940671	−0.470335	+	0.882488i	$0.655867\pi$
$410$	−9.84248e10	−0.172019
$411$	0	0
$412$	−6.39999e11	−1.09431
$413$	2.14608e10	0.0362970
$414$	0	0
$415$	−3.39057e9	−0.00561120
$416$	−5.12686e10	−0.0839328
$417$	0	0
$418$	−6.65144e11	−1.06567
$419$	1.78965e11	0.283665	0.141833	−	0.989891i	$-0.454701\pi$
$419$	1.78965e11	0.283665	0.141833	+	0.989891i	$0.454701\pi$
$420$	0	0
$421$	1.88185e11	0.291954	0.145977	−	0.989288i	$-0.453367\pi$
$421$	1.88185e11	0.291954	0.145977	+	0.989288i	$0.453367\pi$
$422$	−1.65647e12	−2.54260
$423$	0	0
$424$	4.60567e11	0.692064
$425$	1.59942e11	0.237800
$426$	0	0
$427$	−2.15851e10	−0.0314216
$428$	1.12074e11	0.161439
$429$	0	0
$430$	−5.17534e10	−0.0730014
$431$	6.39015e11	0.891997	0.445998	−	0.895034i	$-0.352849\pi$
$431$	6.39015e11	0.891997	0.445998	+	0.895034i	$0.352849\pi$
$432$	0	0
$433$	3.97400e11	0.543291	0.271645	−	0.962397i	$-0.412432\pi$
$433$	3.97400e11	0.543291	0.271645	+	0.962397i	$0.412432\pi$
$434$	−4.07149e9	−0.00550870
$435$	0	0
$436$	1.09267e12	1.44810
$437$	1.12025e12	1.46943
$438$	0	0
$439$	−1.41931e11	−0.182384	−0.0911918	−	0.995833i	$-0.529068\pi$
$439$	−1.41931e11	−0.182384	−0.0911918	+	0.995833i	$0.529068\pi$
$440$	2.03947e10	0.0259407
$441$	0	0
$442$	−1.77048e10	−0.0220644
$443$	−1.16614e12	−1.43858	−0.719289	−	0.694711i	$-0.755532\pi$
$443$	−1.16614e12	−1.43858	−0.719289	+	0.694711i	$0.755532\pi$
$444$	0	0
$445$	7.75046e10	0.0936931
$446$	4.52893e10	0.0541987
$447$	0	0
$448$	6.97631e10	0.0818229
$449$	−9.04654e11	−1.05045	−0.525223	−	0.850964i	$-0.676018\pi$
$449$	−9.04654e11	−1.05045	−0.525223	+	0.850964i	$0.676018\pi$
$450$	0	0
$451$	−3.16803e11	−0.360574
$452$	1.67314e12	1.88542
$453$	0	0
$454$	−2.15176e12	−2.37707
$455$	−4.32268e8	−0.000472827 0
$456$	0	0
$457$	−2.89019e10	−0.0309959	−0.0154979	−	0.999880i	$-0.504933\pi$
$457$	−2.89019e10	−0.0309959	−0.0154979	+	0.999880i	$0.504933\pi$
$458$	−1.14932e12	−1.22052
$459$	0	0
$460$	−1.57819e11	−0.164342
$461$	3.33362e11	0.343765	0.171883	−	0.985117i	$-0.445015\pi$
$461$	3.33362e11	0.343765	0.171883	+	0.985117i	$0.445015\pi$
$462$	0	0
$463$	9.65145e11	0.976064	0.488032	−	0.872826i	$-0.337715\pi$
$463$	9.65145e11	0.976064	0.488032	+	0.872826i	$0.337715\pi$
$464$	−5.09477e11	−0.510263
$465$	0	0
$466$	−1.11200e12	−1.09237
$467$	7.21341e11	0.701802	0.350901	−	0.936413i	$-0.385875\pi$
$467$	7.21341e11	0.701802	0.350901	+	0.936413i	$0.385875\pi$
$468$	0	0
$469$	4.50479e10	0.0429929
$470$	−2.13425e11	−0.201746
$471$	0	0
$472$	2.92744e11	0.271487
$473$	−1.66580e11	−0.153020
$474$	0	0
$475$	−1.73725e12	−1.56582
$476$	1.94930e10	0.0174040
$477$	0	0
$478$	1.45180e12	1.27198
$479$	−1.57016e12	−1.36281	−0.681403	−	0.731909i	$-0.738630\pi$
$479$	−1.57016e12	−1.36281	−0.681403	+	0.731909i	$0.738630\pi$
$480$	0	0
$481$	−1.27922e11	−0.108967
$482$	2.20737e12	1.86279
$483$	0	0
$484$	−1.24152e12	−1.02837
$485$	−2.20908e11	−0.181290
$486$	0	0
$487$	1.48730e12	1.19817	0.599084	−	0.800686i	$-0.295532\pi$
$487$	1.48730e12	1.19817	0.599084	+	0.800686i	$0.295532\pi$
$488$	−2.94439e11	−0.235021
$489$	0	0
$490$	−2.68297e11	−0.210248
$491$	−9.71236e11	−0.754150	−0.377075	−	0.926183i	$-0.623070\pi$
$491$	−9.71236e11	−0.754150	−0.377075	+	0.926183i	$0.623070\pi$
$492$	0	0
$493$	−2.51896e11	−0.192048
$494$	1.92306e11	0.145285
$495$	0	0
$496$	5.64685e10	0.0418927
$497$	1.19084e10	0.00875489
$498$	0	0
$499$	1.21621e12	0.878127	0.439064	−	0.898456i	$-0.355310\pi$
$499$	1.21621e12	0.878127	0.439064	+	0.898456i	$0.355310\pi$
$500$	4.94357e11	0.353733
$501$	0	0
$502$	−3.44247e12	−2.41938
$503$	−2.43415e12	−1.69548	−0.847739	−	0.530414i	$-0.822036\pi$
$503$	−2.43415e12	−1.69548	−0.847739	+	0.530414i	$0.822036\pi$
$504$	0	0
$505$	−3.09799e11	−0.211968
$506$	−9.05392e11	−0.613987
$507$	0	0
$508$	−1.02941e12	−0.685807
$509$	2.50151e12	1.65186	0.825930	−	0.563773i	$-0.190651\pi$
$509$	2.50151e12	1.65186	0.825930	+	0.563773i	$0.190651\pi$
$510$	0	0
$511$	−1.01891e11	−0.0661060
$512$	−1.81611e12	−1.16796
$513$	0	0
$514$	−2.72689e12	−1.72319
$515$	1.90978e11	0.119633
$516$	0	0
$517$	−6.86956e11	−0.422884
$518$	2.51031e11	0.153195
$519$	0	0
$520$	−5.89651e9	−0.00353655
$521$	−2.28180e12	−1.35678	−0.678388	−	0.734704i	$-0.737321\pi$
$521$	−2.28180e12	−1.35678	−0.678388	+	0.734704i	$0.737321\pi$
$522$	0	0
$523$	1.67259e12	0.977537	0.488768	−	0.872414i	$-0.337446\pi$
$523$	1.67259e12	0.977537	0.488768	+	0.872414i	$0.337446\pi$
$524$	−1.00904e12	−0.584682
$525$	0	0
$526$	3.16392e12	1.80215
$527$	2.79192e10	0.0157672
$528$	0	0
$529$	−2.76274e11	−0.153388
$530$	−6.31450e11	−0.347614
$531$	0	0
$532$	−2.11729e11	−0.114598
$533$	9.15937e10	0.0491579
$534$	0	0
$535$	−3.34434e10	−0.0176489
$536$	6.14492e11	0.321570
$537$	0	0
$538$	−2.18034e12	−1.12203
$539$	−8.63574e11	−0.440707
$540$	0	0
$541$	−8.84734e11	−0.444043	−0.222021	−	0.975042i	$-0.571265\pi$
$541$	−8.84734e11	−0.444043	−0.222021	+	0.975042i	$0.571265\pi$
$542$	−4.75688e12	−2.36769
$543$	0	0
$544$	−6.89894e11	−0.337744
$545$	−3.26056e11	−0.158310
$546$	0	0
$547$	−2.72146e12	−1.29975	−0.649874	−	0.760042i	$-0.725178\pi$
$547$	−2.72146e12	−1.29975	−0.649874	+	0.760042i	$0.725178\pi$
$548$	4.89844e12	2.32031
$549$	0	0
$550$	1.40406e12	0.654264
$551$	2.73604e12	1.26456
$552$	0	0
$553$	2.71242e10	0.0123337
$554$	−4.55676e12	−2.05524
$555$	0	0
$556$	3.25305e12	1.44363
$557$	2.68557e12	1.18219	0.591096	−	0.806601i	$-0.298695\pi$
$557$	2.68557e12	1.18219	0.591096	+	0.806601i	$0.298695\pi$
$558$	0	0
$559$	4.81615e10	0.0208616
$560$	−1.17649e10	−0.00505524
$561$	0	0
$562$	−4.17369e12	−1.76484
$563$	2.81923e12	1.18261	0.591307	−	0.806446i	$-0.298612\pi$
$563$	2.81923e12	1.18261	0.591307	+	0.806446i	$0.298612\pi$
$564$	0	0
$565$	−4.99271e11	−0.206119
$566$	−5.05936e12	−2.07215
$567$	0	0
$568$	1.62441e11	0.0654830
$569$	−3.57453e11	−0.142960	−0.0714799	−	0.997442i	$-0.522772\pi$
$569$	−3.57453e11	−0.142960	−0.0714799	+	0.997442i	$0.522772\pi$
$570$	0	0
$571$	−3.25953e11	−0.128319	−0.0641596	−	0.997940i	$-0.520437\pi$
$571$	−3.25953e11	−0.128319	−0.0641596	+	0.997940i	$0.520437\pi$
$572$	−8.72010e10	−0.0340596
$573$	0	0
$574$	−1.79741e11	−0.0691104
$575$	−2.36474e12	−0.902149
$576$	0	0
$577$	−2.50107e11	−0.0939365	−0.0469683	−	0.998896i	$-0.514956\pi$
$577$	−2.50107e11	−0.0939365	−0.0469683	+	0.998896i	$0.514956\pi$
$578$	−2.38244e11	−0.0887865
$579$	0	0
$580$	−3.85449e11	−0.141430
$581$	−6.19177e9	−0.00225435
$582$	0	0
$583$	−2.03247e12	−0.728643
$584$	−1.38988e12	−0.494446
$585$	0	0
$586$	4.00262e12	1.40218
$587$	−9.14514e10	−0.0317921	−0.0158960	−	0.999874i	$-0.505060\pi$
$587$	−9.14514e10	−0.0317921	−0.0158960	+	0.999874i	$0.505060\pi$
$588$	0	0
$589$	−3.03252e11	−0.103821
$590$	−4.01361e11	−0.136364
$591$	0	0
$592$	−3.48162e12	−1.16502
$593$	2.60815e12	0.866138	0.433069	−	0.901361i	$-0.357431\pi$
$593$	2.60815e12	0.866138	0.433069	+	0.901361i	$0.357431\pi$
$594$	0	0
$595$	−5.81680e9	−0.00190264
$596$	1.42122e12	0.461376
$597$	0	0
$598$	2.61766e11	0.0837063
$599$	−1.25671e12	−0.398853	−0.199427	−	0.979913i	$-0.563908\pi$
$599$	−1.25671e12	−0.398853	−0.199427	+	0.979913i	$0.563908\pi$
$600$	0	0
$601$	−9.01991e11	−0.282012	−0.141006	−	0.990009i	$-0.545034\pi$
$601$	−9.01991e11	−0.282012	−0.141006	+	0.990009i	$0.545034\pi$
$602$	−9.45108e10	−0.0293290
$603$	0	0
$604$	3.30722e12	1.01111
$605$	3.70475e11	0.112424
$606$	0	0
$607$	4.29234e12	1.28335	0.641675	−	0.766977i	$-0.278240\pi$
$607$	4.29234e12	1.28335	0.641675	+	0.766977i	$0.278240\pi$
$608$	7.49348e12	2.22391
$609$	0	0
$610$	4.03684e11	0.118048
$611$	1.98612e11	0.0576528
$612$	0	0
$613$	3.09808e12	0.886178	0.443089	−	0.896478i	$-0.353883\pi$
$613$	3.09808e12	0.886178	0.443089	+	0.896478i	$0.353883\pi$
$614$	1.47927e12	0.420040
$615$	0	0
$616$	3.72444e10	0.0104219
$617$	2.97483e12	0.826378	0.413189	−	0.910645i	$-0.364415\pi$
$617$	2.97483e12	0.826378	0.413189	+	0.910645i	$0.364415\pi$
$618$	0	0
$619$	−3.10484e10	−0.00850025	−0.00425012	−	0.999991i	$-0.501353\pi$
$619$	−3.10484e10	−0.00850025	−0.00425012	+	0.999991i	$0.501353\pi$
$620$	4.27217e10	0.0116114
$621$	0	0
$622$	6.11910e12	1.63920
$623$	1.41537e11	0.0376421
$624$	0	0
$625$	3.59269e12	0.941803
$626$	2.15227e12	0.560160
$627$	0	0
$628$	−7.49891e12	−1.92389
$629$	−1.72138e12	−0.438480
$630$	0	0
$631$	5.20764e12	1.30770	0.653851	−	0.756623i	$-0.273152\pi$
$631$	5.20764e12	1.30770	0.653851	+	0.756623i	$0.273152\pi$
$632$	3.69998e11	0.0922513
$633$	0	0
$634$	1.45264e12	0.357072
$635$	3.07180e11	0.0749741
$636$	0	0
$637$	2.49676e11	0.0600826
$638$	−2.21128e12	−0.528386
$639$	0	0
$640$	−4.78806e11	−0.112811
$641$	−2.80533e12	−0.656330	−0.328165	−	0.944620i	$-0.606430\pi$
$641$	−2.80533e12	−0.656330	−0.328165	+	0.944620i	$0.606430\pi$
$642$	0	0
$643$	2.80520e12	0.647164	0.323582	−	0.946200i	$-0.395113\pi$
$643$	2.80520e12	0.647164	0.323582	+	0.946200i	$0.395113\pi$
$644$	−2.88205e11	−0.0660260
$645$	0	0
$646$	2.58776e12	0.584624
$647$	−4.72530e12	−1.06013	−0.530066	−	0.847956i	$-0.677833\pi$
$647$	−4.72530e12	−1.06013	−0.530066	+	0.847956i	$0.677833\pi$
$648$	0	0
$649$	−1.29187e12	−0.285837
$650$	−4.05940e11	−0.0891973
$651$	0	0
$652$	1.03802e13	2.24953
$653$	7.04467e12	1.51618	0.758091	−	0.652149i	$-0.226132\pi$
$653$	7.04467e12	1.51618	0.758091	+	0.652149i	$0.226132\pi$
$654$	0	0
$655$	3.01103e11	0.0639188
$656$	2.49287e12	0.525572
$657$	0	0
$658$	−3.89751e11	−0.0810533
$659$	2.93823e12	0.606879	0.303439	−	0.952851i	$-0.401865\pi$
$659$	2.93823e12	0.606879	0.303439	+	0.952851i	$0.401865\pi$
$660$	0	0
$661$	−7.72453e11	−0.157386	−0.0786929	−	0.996899i	$-0.525075\pi$
$661$	−7.72453e11	−0.157386	−0.0786929	+	0.996899i	$0.525075\pi$
$662$	4.64611e12	0.940219
$663$	0	0
$664$	−8.44610e10	−0.0168616
$665$	6.31808e10	0.0125282
$666$	0	0
$667$	3.72429e12	0.728580
$668$	5.20274e12	1.01097
$669$	0	0
$670$	−8.42487e11	−0.161520
$671$	1.29935e12	0.247443
$672$	0	0
$673$	2.83634e12	0.532954	0.266477	−	0.963841i	$-0.414140\pi$
$673$	2.83634e12	0.532954	0.266477	+	0.963841i	$0.414140\pi$
$674$	1.54582e13	2.88529
$675$	0	0
$676$	−6.91478e12	−1.27356
$677$	2.65986e12	0.486642	0.243321	−	0.969946i	$-0.421763\pi$
$677$	2.65986e12	0.486642	0.243321	+	0.969946i	$0.421763\pi$
$678$	0	0
$679$	−4.03416e11	−0.0728349
$680$	−7.93461e10	−0.0142310
$681$	0	0
$682$	2.45090e11	0.0433807
$683$	2.44022e12	0.429078	0.214539	−	0.976715i	$-0.431175\pi$
$683$	2.44022e12	0.429078	0.214539	+	0.976715i	$0.431175\pi$
$684$	0	0
$685$	−1.46171e12	−0.253661
$686$	−9.81463e11	−0.169206
$687$	0	0
$688$	1.31079e12	0.223042
$689$	5.87625e11	0.0993376
$690$	0	0
$691$	5.13446e12	0.856730	0.428365	−	0.903606i	$-0.359090\pi$
$691$	5.13446e12	0.856730	0.428365	+	0.903606i	$0.359090\pi$
$692$	−3.15694e12	−0.523345
$693$	0	0
$694$	−6.85293e12	−1.12139
$695$	−9.70724e11	−0.157821
$696$	0	0
$697$	1.23253e12	0.197810
$698$	−5.08693e12	−0.811159
$699$	0	0
$700$	4.46941e11	0.0703573
$701$	4.00510e12	0.626444	0.313222	−	0.949680i	$-0.398592\pi$
$701$	4.00510e12	0.626444	0.313222	+	0.949680i	$0.398592\pi$
$702$	0	0
$703$	1.86973e13	2.88722
$704$	−4.19951e12	−0.644350
$705$	0	0
$706$	−1.18511e13	−1.79530
$707$	−5.65748e11	−0.0851600
$708$	0	0
$709$	−7.18171e12	−1.06738	−0.533691	−	0.845680i	$-0.679195\pi$
$709$	−7.18171e12	−1.06738	−0.533691	+	0.845680i	$0.679195\pi$
$710$	−2.22712e11	−0.0328912
$711$	0	0
$712$	1.93069e12	0.281548
$713$	−4.12785e11	−0.0598166
$714$	0	0
$715$	2.60211e10	0.00372348
$716$	4.25951e12	0.605691
$717$	0	0
$718$	−2.00690e13	−2.81816
$719$	−2.19372e10	−0.00306127	−0.00153063	−	0.999999i	$-0.500487\pi$
$719$	−2.19372e10	−0.00306127	−0.00153063	+	0.999999i	$0.500487\pi$
$720$	0	0
$721$	3.48760e11	0.0480637
$722$	−1.70868e13	−2.34015
$723$	0	0
$724$	6.46266e12	0.874154
$725$	−5.77553e12	−0.776373
$726$	0	0
$727$	3.47360e11	0.0461185	0.0230593	−	0.999734i	$-0.492659\pi$
$727$	3.47360e11	0.0461185	0.0230593	+	0.999734i	$0.492659\pi$
$728$	−1.07681e10	−0.00142084
$729$	0	0
$730$	1.90556e12	0.248354
$731$	6.48083e11	0.0839465
$732$	0	0
$733$	3.58285e11	0.0458417	0.0229208	−	0.999737i	$-0.492703\pi$
$733$	3.58285e11	0.0458417	0.0229208	+	0.999737i	$0.492703\pi$
$734$	2.79316e12	0.355192
$735$	0	0
$736$	1.02001e13	1.28131
$737$	−2.71174e12	−0.338566
$738$	0	0
$739$	−2.16274e12	−0.266750	−0.133375	−	0.991066i	$-0.542581\pi$
$739$	−2.16274e12	−0.266750	−0.133375	+	0.991066i	$0.542581\pi$
$740$	−2.63405e12	−0.322909
$741$	0	0
$742$	−1.15314e12	−0.139657
$743$	−6.42105e12	−0.772959	−0.386479	−	0.922298i	$-0.626309\pi$
$743$	−6.42105e12	−0.772959	−0.386479	+	0.922298i	$0.626309\pi$
$744$	0	0
$745$	−4.24099e11	−0.0504387
$746$	−1.26430e13	−1.49461
$747$	0	0
$748$	−1.17342e12	−0.137055
$749$	−6.10736e10	−0.00709064
$750$	0	0
$751$	−1.15069e13	−1.32002	−0.660010	−	0.751257i	$-0.729448\pi$
$751$	−1.15069e13	−1.32002	−0.660010	+	0.751257i	$0.729448\pi$
$752$	5.40555e12	0.616396
$753$	0	0
$754$	6.39325e11	0.0720361
$755$	−9.86888e11	−0.110537
$756$	0	0
$757$	−7.80850e12	−0.864243	−0.432122	−	0.901815i	$-0.642235\pi$
$757$	−7.80850e12	−0.864243	−0.432122	+	0.901815i	$0.642235\pi$
$758$	−1.76722e13	−1.94437
$759$	0	0
$760$	8.61840e11	0.0937056
$761$	6.58284e12	0.711512	0.355756	−	0.934579i	$-0.384223\pi$
$761$	6.58284e12	0.711512	0.355756	+	0.934579i	$0.384223\pi$
$762$	0	0
$763$	−5.95435e11	−0.0636025
$764$	−1.13396e13	−1.20414
$765$	0	0
$766$	6.94803e12	0.729175
$767$	3.73505e11	0.0389688
$768$	0	0
$769$	−1.27459e13	−1.31433	−0.657163	−	0.753748i	$-0.728244\pi$
$769$	−1.27459e13	−1.31433	−0.657163	+	0.753748i	$0.728244\pi$
$770$	−5.10631e10	−0.00523479
$771$	0	0
$772$	−3.87933e12	−0.393079
$773$	1.07389e13	1.08181	0.540907	−	0.841083i	$-0.318081\pi$
$773$	1.07389e13	1.08181	0.540907	+	0.841083i	$0.318081\pi$
$774$	0	0
$775$	6.40137e11	0.0637405
$776$	−5.50294e12	−0.544775
$777$	0	0
$778$	2.65167e13	2.59484
$779$	−1.33874e13	−1.30250
$780$	0	0
$781$	−7.16848e11	−0.0689442
$782$	3.52244e12	0.336832
$783$	0	0
$784$	6.79533e12	0.642375
$785$	2.23770e12	0.210324
$786$	0	0
$787$	3.76105e12	0.349481	0.174740	−	0.984615i	$-0.444091\pi$
$787$	3.76105e12	0.349481	0.174740	+	0.984615i	$0.444091\pi$
$788$	1.05551e13	0.975200
$789$	0	0
$790$	−5.07278e11	−0.0463366
$791$	−9.11756e11	−0.0828103
$792$	0	0
$793$	−3.75667e11	−0.0337344
$794$	−1.48210e13	−1.32338
$795$	0	0
$796$	−2.86790e13	−2.53195
$797$	−2.18200e13	−1.91555	−0.957773	−	0.287524i	$-0.907168\pi$
$797$	−2.18200e13	−1.91555	−0.957773	+	0.287524i	$0.907168\pi$
$798$	0	0
$799$	2.67262e12	0.231994
$800$	−1.58180e13	−1.36536
$801$	0	0
$802$	1.05157e13	0.897540
$803$	6.13349e12	0.520581
$804$	0	0
$805$	8.60015e10	0.00721813
$806$	−7.08602e10	−0.00591418
$807$	0	0
$808$	−7.71729e12	−0.636962
$809$	1.90714e13	1.56536	0.782681	−	0.622423i	$-0.213852\pi$
$809$	1.90714e13	1.56536	0.782681	+	0.622423i	$0.213852\pi$
$810$	0	0
$811$	−1.86624e13	−1.51486	−0.757430	−	0.652916i	$-0.773546\pi$
$811$	−1.86624e13	−1.51486	−0.757430	+	0.652916i	$0.773546\pi$
$812$	−7.03898e11	−0.0568208
$813$	0	0
$814$	−1.51113e13	−1.20640
$815$	−3.09749e12	−0.245924
$816$	0	0
$817$	−7.03934e12	−0.552755
$818$	1.81812e13	1.41982
$819$	0	0
$820$	1.88600e12	0.145673
$821$	4.79906e12	0.368648	0.184324	−	0.982866i	$-0.440990\pi$
$821$	4.79906e12	0.368648	0.184324	+	0.982866i	$0.440990\pi$
$822$	0	0
$823$	2.14502e13	1.62979	0.814895	−	0.579609i	$-0.196795\pi$
$823$	2.14502e13	1.62979	0.814895	+	0.579609i	$0.196795\pi$
$824$	4.75738e12	0.359497
$825$	0	0
$826$	−7.32955e11	−0.0547857
$827$	1.32157e13	0.982463	0.491231	−	0.871029i	$-0.336547\pi$
$827$	1.32157e13	0.982463	0.491231	+	0.871029i	$0.336547\pi$
$828$	0	0
$829$	−7.78893e12	−0.572773	−0.286386	−	0.958114i	$-0.592454\pi$
$829$	−7.78893e12	−0.572773	−0.286386	+	0.958114i	$0.592454\pi$
$830$	1.15799e11	0.00846938
$831$	0	0
$832$	1.21416e12	0.0878456
$833$	3.35975e12	0.241771
$834$	0	0
$835$	−1.55252e12	−0.110522
$836$	1.27454e13	0.902454
$837$	0	0
$838$	−6.11223e12	−0.428156
$839$	9.65976e12	0.673035	0.336517	−	0.941677i	$-0.390751\pi$
$839$	9.65976e12	0.673035	0.336517	+	0.941677i	$0.390751\pi$
$840$	0	0
$841$	−5.41113e12	−0.372997
$842$	−6.42710e12	−0.440667
$843$	0	0
$844$	3.17411e13	2.15318
$845$	2.06340e12	0.139228
$846$	0	0
$847$	6.76552e11	0.0451675
$848$	1.59932e13	1.06207
$849$	0	0
$850$	−5.46251e12	−0.358928
$851$	2.54507e13	1.66348
$852$	0	0
$853$	2.43508e13	1.57486	0.787430	−	0.616404i	$-0.211411\pi$
$853$	2.43508e13	1.57486	0.787430	+	0.616404i	$0.211411\pi$
$854$	7.37198e11	0.0474268
$855$	0	0
$856$	−8.33096e11	−0.0530351
$857$	−2.45424e13	−1.55419	−0.777095	−	0.629383i	$-0.783308\pi$
$857$	−2.45424e13	−1.55419	−0.777095	+	0.629383i	$0.783308\pi$
$858$	0	0
$859$	−2.12084e13	−1.32904	−0.664521	−	0.747270i	$-0.731364\pi$
$859$	−2.12084e13	−1.32904	−0.664521	+	0.747270i	$0.731364\pi$
$860$	9.91692e11	0.0618207
$861$	0	0
$862$	−2.18244e13	−1.34635
$863$	−1.64190e13	−1.00762	−0.503811	−	0.863814i	$-0.668069\pi$
$863$	−1.64190e13	−1.00762	−0.503811	+	0.863814i	$0.668069\pi$
$864$	0	0
$865$	9.42042e11	0.0572134
$866$	−1.35725e13	−0.820027
$867$	0	0
$868$	7.80173e10	0.00466500
$869$	−1.63279e12	−0.0971273
$870$	0	0
$871$	7.84015e11	0.0461575
$872$	−8.12224e12	−0.475720
$873$	0	0
$874$	−3.82600e13	−2.21791
$875$	−2.69394e11	−0.0155364
$876$	0	0
$877$	7.74986e12	0.442380	0.221190	−	0.975231i	$-0.429006\pi$
$877$	7.74986e12	0.442380	0.221190	+	0.975231i	$0.429006\pi$
$878$	4.84738e12	0.275285
$879$	0	0
$880$	7.08207e11	0.0398096
$881$	−1.47006e12	−0.0822135	−0.0411068	−	0.999155i	$-0.513088\pi$
$881$	−1.47006e12	−0.0822135	−0.0411068	+	0.999155i	$0.513088\pi$
$882$	0	0
$883$	−2.27229e13	−1.25788	−0.628941	−	0.777453i	$-0.716511\pi$
$883$	−2.27229e13	−1.25788	−0.628941	+	0.777453i	$0.716511\pi$
$884$	3.39257e11	0.0186850
$885$	0	0
$886$	3.98273e13	2.17135
$887$	2.54193e13	1.37882	0.689411	−	0.724371i	$-0.257870\pi$
$887$	2.54193e13	1.37882	0.689411	+	0.724371i	$0.257870\pi$
$888$	0	0
$889$	5.60965e11	0.0301216
$890$	−2.64703e12	−0.141418
$891$	0	0
$892$	−8.67828e11	−0.0458978
$893$	−2.90294e13	−1.52759
$894$	0	0
$895$	−1.27106e12	−0.0662157
$896$	−8.74385e11	−0.0453228
$897$	0	0
$898$	3.08968e13	1.58551
$899$	−1.00817e12	−0.0514771
$900$	0	0
$901$	7.90735e12	0.399733
$902$	1.08198e13	0.544240
$903$	0	0
$904$	−1.24371e13	−0.619387
$905$	−1.92848e12	−0.0955646
$906$	0	0
$907$	2.33059e13	1.14349	0.571745	−	0.820431i	$-0.306267\pi$
$907$	2.33059e13	1.14349	0.571745	+	0.820431i	$0.306267\pi$
$908$	4.12317e13	2.01300
$909$	0	0
$910$	1.47633e10	0.000713671 0
$911$	6.19635e12	0.298060	0.149030	−	0.988833i	$-0.452385\pi$
$911$	6.19635e12	0.298060	0.149030	+	0.988833i	$0.452385\pi$
$912$	0	0
$913$	3.72724e11	0.0177529
$914$	9.87092e11	0.0467842
$915$	0	0
$916$	2.20231e13	1.03359
$917$	5.49866e11	0.0256800
$918$	0	0
$919$	−2.57602e13	−1.19132	−0.595661	−	0.803236i	$-0.703110\pi$
$919$	−2.57602e13	−1.19132	−0.595661	+	0.803236i	$0.703110\pi$
$920$	1.17313e12	0.0539886
$921$	0	0
$922$	−1.13854e13	−0.518869
$923$	2.07255e11	0.00939932
$924$	0	0
$925$	−3.94682e13	−1.77260
$926$	−3.29628e13	−1.47324
$927$	0	0
$928$	2.49122e13	1.10267
$929$	−1.87578e13	−0.826251	−0.413126	−	0.910674i	$-0.635563\pi$
$929$	−1.87578e13	−0.826251	−0.413126	+	0.910674i	$0.635563\pi$
$930$	0	0
$931$	−3.64929e13	−1.59197
$932$	2.13080e13	0.925064
$933$	0	0
$934$	−2.46361e13	−1.05928
$935$	3.50152e11	0.0149832
$936$	0	0
$937$	5.64054e12	0.239052	0.119526	−	0.992831i	$-0.461863\pi$
$937$	5.64054e12	0.239052	0.119526	+	0.992831i	$0.461863\pi$
$938$	−1.53853e12	−0.0648923
$939$	0	0
$940$	4.08962e12	0.170847
$941$	−2.26889e13	−0.943321	−0.471660	−	0.881780i	$-0.656345\pi$
$941$	−2.26889e13	−0.943321	−0.471660	+	0.881780i	$0.656345\pi$
$942$	0	0
$943$	−1.82229e13	−0.750439
$944$	1.01655e13	0.416636
$945$	0	0
$946$	5.68924e12	0.230964
$947$	1.49881e13	0.605582	0.302791	−	0.953057i	$-0.402082\pi$
$947$	1.49881e13	0.605582	0.302791	+	0.953057i	$0.402082\pi$
$948$	0	0
$949$	−1.77331e12	−0.0709719
$950$	5.93326e13	2.36340
$951$	0	0
$952$	−1.44900e11	−0.00571744
$953$	4.04272e13	1.58765	0.793827	−	0.608143i	$-0.208085\pi$
$953$	4.04272e13	1.58765	0.793827	+	0.608143i	$0.208085\pi$
$954$	0	0
$955$	3.38377e12	0.131640
$956$	−2.78192e13	−1.07717
$957$	0	0
$958$	5.36259e13	2.05698
$959$	−2.66934e12	−0.101911
$960$	0	0
$961$	−2.63279e13	−0.995774
$962$	4.36895e12	0.164471
$963$	0	0
$964$	−4.22973e13	−1.57749
$965$	1.15761e12	0.0429723
$966$	0	0
$967$	−7.15269e12	−0.263057	−0.131529	−	0.991312i	$-0.541989\pi$
$967$	−7.15269e12	−0.263057	−0.131529	+	0.991312i	$0.541989\pi$
$968$	9.22875e12	0.337834
$969$	0	0
$970$	7.54470e12	0.273633
$971$	−2.34500e13	−0.846556	−0.423278	−	0.906000i	$-0.639121\pi$
$971$	−2.34500e13	−0.846556	−0.423278	+	0.906000i	$0.639121\pi$
$972$	0	0
$973$	−1.77271e12	−0.0634060
$974$	−5.07959e13	−1.80848
$975$	0	0
$976$	−1.02244e13	−0.360673
$977$	−3.75171e13	−1.31736	−0.658678	−	0.752425i	$-0.728884\pi$
$977$	−3.75171e13	−1.31736	−0.658678	+	0.752425i	$0.728884\pi$
$978$	0	0
$979$	−8.52006e12	−0.296429
$980$	5.14106e12	0.178047
$981$	0	0
$982$	3.31708e13	1.13829
$983$	−5.31777e13	−1.81651	−0.908256	−	0.418414i	$-0.862586\pi$
$983$	−5.31777e13	−1.81651	−0.908256	+	0.418414i	$0.862586\pi$
$984$	0	0
$985$	−3.14968e12	−0.106611
$986$	8.60304e12	0.289872
$987$	0	0
$988$	−3.68494e12	−0.123034
$989$	−9.58193e12	−0.318471
$990$	0	0
$991$	3.41823e13	1.12582	0.562912	−	0.826517i	$-0.309681\pi$
$991$	3.41823e13	1.12582	0.562912	+	0.826517i	$0.309681\pi$
$992$	−2.76117e12	−0.0905297
$993$	0	0
$994$	−4.06711e11	−0.0132144
$995$	8.55794e12	0.276799
$996$	0	0
$997$	4.83269e13	1.54903	0.774517	−	0.632553i	$-0.217993\pi$
$997$	4.83269e13	1.54903	0.774517	+	0.632553i	$0.217993\pi$
$998$	−4.15375e13	−1.32542
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	153.10.a.f.1.2		7
3.2	odd	2		17.10.a.b.1.6	✓	7
12.11	even	2		272.10.a.g.1.2		7
51.50	odd	2		289.10.a.b.1.6		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.10.a.b.1.6	✓	7	3.2	odd	2
153.10.a.f.1.2		7	1.1	even	1	trivial
272.10.a.g.1.2		7	12.11	even	2
289.10.a.b.1.6		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)

\(f(q)\)	\(=\)	\(q-34.1532 q^{2} +654.438 q^{4} -195.287 q^{5} -356.628 q^{7} -4864.71 q^{8} +O(q^{10})\)	\(q-34.1532 q^{2} +654.438 q^{4} -195.287 q^{5} -356.628 q^{7} -4864.71 q^{8} +6669.66 q^{10} +21467.8 q^{11} -6206.76 q^{13} +12180.0 q^{14} -168927. q^{16} -83521.0 q^{17} +907187. q^{19} -127803. q^{20} -733194. q^{22} +1.23486e6 q^{23} -1.91499e6 q^{25} +211980. q^{26} -233391. q^{28} +3.01596e6 q^{29} -334277. q^{31} +8.26012e6 q^{32} +2.85251e6 q^{34} +69644.7 q^{35} +2.06102e7 q^{37} -3.09833e7 q^{38} +950014. q^{40} -1.47571e7 q^{41} -7.75953e6 q^{43} +1.40494e7 q^{44} -4.21744e7 q^{46} -3.19993e7 q^{47} -4.02264e7 q^{49} +6.54029e7 q^{50} -4.06194e6 q^{52} -9.46750e7 q^{53} -4.19238e6 q^{55} +1.73489e6 q^{56} -1.03005e8 q^{58} -6.01771e7 q^{59} +6.05254e7 q^{61} +1.14166e7 q^{62} -1.95619e8 q^{64} +1.21210e6 q^{65} -1.26316e8 q^{67} -5.46593e7 q^{68} -2.37859e6 q^{70} -3.33917e7 q^{71} +2.85706e8 q^{73} -7.03903e8 q^{74} +5.93698e8 q^{76} -7.65603e6 q^{77} -7.60575e7 q^{79} +3.29892e7 q^{80} +5.04001e8 q^{82} +1.73620e7 q^{83} +1.63105e7 q^{85} +2.65012e8 q^{86} -1.04435e8 q^{88} -3.96876e8 q^{89} +2.21350e6 q^{91} +8.08139e8 q^{92} +1.09288e9 q^{94} -1.77162e8 q^{95} +1.13120e9 q^{97} +1.37386e9 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + q^{2} + 2389 q^{4} - 1362 q^{5} + 9388 q^{7} - 16821 q^{8}+O(q^{10}) \) 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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