LMFDB - Embedded newform 273.2.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(1,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("273.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.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:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{8})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 2 $ x^2 - 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.41421$ of defining polynomial
Character	$\chi$	$=$	273.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.414214 q^{2} -1.00000 q^{3} -1.82843 q^{4} +0.414214 q^{6} +1.00000 q^{7} +1.58579 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.414214 q^{2} -1.00000 q^{3} -1.82843 q^{4} +0.414214 q^{6} +1.00000 q^{7} +1.58579 q^{8} +1.00000 q^{9} +2.00000 q^{11} +1.82843 q^{12} -1.00000 q^{13} -0.414214 q^{14} +3.00000 q^{16} +4.82843 q^{17} -0.414214 q^{18} +5.65685 q^{19} -1.00000 q^{21} -0.828427 q^{22} +6.82843 q^{23} -1.58579 q^{24} -5.00000 q^{25} +0.414214 q^{26} -1.00000 q^{27} -1.82843 q^{28} +7.65685 q^{29} -9.65685 q^{31} -4.41421 q^{32} -2.00000 q^{33} -2.00000 q^{34} -1.82843 q^{36} +3.65685 q^{37} -2.34315 q^{38} +1.00000 q^{39} -5.65685 q^{41} +0.414214 q^{42} -1.65685 q^{43} -3.65685 q^{44} -2.82843 q^{46} +8.82843 q^{47} -3.00000 q^{48} +1.00000 q^{49} +2.07107 q^{50} -4.82843 q^{51} +1.82843 q^{52} -7.65685 q^{53} +0.414214 q^{54} +1.58579 q^{56} -5.65685 q^{57} -3.17157 q^{58} +6.48528 q^{59} -11.6569 q^{61} +4.00000 q^{62} +1.00000 q^{63} -4.17157 q^{64} +0.828427 q^{66} +4.00000 q^{67} -8.82843 q^{68} -6.82843 q^{69} +14.0000 q^{71} +1.58579 q^{72} +3.65685 q^{73} -1.51472 q^{74} +5.00000 q^{75} -10.3431 q^{76} +2.00000 q^{77} -0.414214 q^{78} +11.3137 q^{79} +1.00000 q^{81} +2.34315 q^{82} -12.1421 q^{83} +1.82843 q^{84} +0.686292 q^{86} -7.65685 q^{87} +3.17157 q^{88} -7.31371 q^{89} -1.00000 q^{91} -12.4853 q^{92} +9.65685 q^{93} -3.65685 q^{94} +4.41421 q^{96} -2.00000 q^{97} -0.414214 q^{98} +2.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{6} + 2 q^{7} + 6 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 - 2 * q^6 + 2 * q^7 + 6 * q^8 + 2 * q^9	$ 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{6} + 2 q^{7} + 6 q^{8} + 2 q^{9} + 4 q^{11} - 2 q^{12} - 2 q^{13} + 2 q^{14} + 6 q^{16} + 4 q^{17} + 2 q^{18} - 2 q^{21} + 4 q^{22} + 8 q^{23} - 6 q^{24} - 10 q^{25} - 2 q^{26} - 2 q^{27} + 2 q^{28} + 4 q^{29} - 8 q^{31} - 6 q^{32} - 4 q^{33} - 4 q^{34} + 2 q^{36} - 4 q^{37} - 16 q^{38} + 2 q^{39} - 2 q^{42} + 8 q^{43} + 4 q^{44} + 12 q^{47} - 6 q^{48} + 2 q^{49} - 10 q^{50} - 4 q^{51} - 2 q^{52} - 4 q^{53} - 2 q^{54} + 6 q^{56} - 12 q^{58} - 4 q^{59} - 12 q^{61} + 8 q^{62} + 2 q^{63} - 14 q^{64} - 4 q^{66} + 8 q^{67} - 12 q^{68} - 8 q^{69} + 28 q^{71} + 6 q^{72} - 4 q^{73} - 20 q^{74} + 10 q^{75} - 32 q^{76} + 4 q^{77} + 2 q^{78} + 2 q^{81} + 16 q^{82} + 4 q^{83} - 2 q^{84} + 24 q^{86} - 4 q^{87} + 12 q^{88} + 8 q^{89} - 2 q^{91} - 8 q^{92} + 8 q^{93} + 4 q^{94} + 6 q^{96} - 4 q^{97} + 2 q^{98} + 4 q^{99}+O(q^{100}) $ 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 - 2 * q^6 + 2 * q^7 + 6 * q^8 + 2 * q^9 + 4 * q^11 - 2 * q^12 - 2 * q^13 + 2 * q^14 + 6 * q^16 + 4 * q^17 + 2 * q^18 - 2 * q^21 + 4 * q^22 + 8 * q^23 - 6 * q^24 - 10 * q^25 - 2 * q^26 - 2 * q^27 + 2 * q^28 + 4 * q^29 - 8 * q^31 - 6 * q^32 - 4 * q^33 - 4 * q^34 + 2 * q^36 - 4 * q^37 - 16 * q^38 + 2 * q^39 - 2 * q^42 + 8 * q^43 + 4 * q^44 + 12 * q^47 - 6 * q^48 + 2 * q^49 - 10 * q^50 - 4 * q^51 - 2 * q^52 - 4 * q^53 - 2 * q^54 + 6 * q^56 - 12 * q^58 - 4 * q^59 - 12 * q^61 + 8 * q^62 + 2 * q^63 - 14 * q^64 - 4 * q^66 + 8 * q^67 - 12 * q^68 - 8 * q^69 + 28 * q^71 + 6 * q^72 - 4 * q^73 - 20 * q^74 + 10 * q^75 - 32 * q^76 + 4 * q^77 + 2 * q^78 + 2 * q^81 + 16 * q^82 + 4 * q^83 - 2 * q^84 + 24 * q^86 - 4 * q^87 + 12 * q^88 + 8 * q^89 - 2 * q^91 - 8 * q^92 + 8 * q^93 + 4 * q^94 + 6 * q^96 - 4 * q^97 + 2 * q^98 + 4 * q^99

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 $

$2$	−0.414214	−0.292893	−0.146447	−	0.989219i	$-0.546784\pi$
$2$	−0.414214	−0.292893	−0.146447	+	0.989219i	$0.546784\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.82843	−0.914214
$5$	0	0		−	1.00000i	$-0.5\pi$
$5$	0	0			1.00000i	$0.5\pi$
$6$	0.414214	0.169102
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.58579	0.560660
$9$	1.00000	0.333333
$10$	0	0
$11$	2.00000	0.603023	0.301511	−	0.953463i	$-0.402509\pi$
$11$	2.00000	0.603023	0.301511	+	0.953463i	$0.402509\pi$
$12$	1.82843	0.527821
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−0.414214	−0.110703
$15$	0	0
$16$	3.00000	0.750000
$17$	4.82843	1.17107	0.585533	−	0.810649i	$-0.300885\pi$
$17$	4.82843	1.17107	0.585533	+	0.810649i	$0.300885\pi$
$18$	−0.414214	−0.0976311
$19$	5.65685	1.29777	0.648886	−	0.760886i	$-0.275235\pi$
$19$	5.65685	1.29777	0.648886	+	0.760886i	$0.275235\pi$
$20$	0	0
$21$	−1.00000	−0.218218
$22$	−0.828427	−0.176621
$23$	6.82843	1.42383	0.711913	−	0.702268i	$-0.247829\pi$
$23$	6.82843	1.42383	0.711913	+	0.702268i	$0.247829\pi$
$24$	−1.58579	−0.323697
$25$	−5.00000	−1.00000
$26$	0.414214	0.0812340
$27$	−1.00000	−0.192450
$28$	−1.82843	−0.345540
$29$	7.65685	1.42184	0.710921	−	0.703272i	$-0.248278\pi$
$29$	7.65685	1.42184	0.710921	+	0.703272i	$0.248278\pi$
$30$	0	0
$31$	−9.65685	−1.73442	−0.867211	−	0.497941i	$-0.834090\pi$
$31$	−9.65685	−1.73442	−0.867211	+	0.497941i	$0.834090\pi$
$32$	−4.41421	−0.780330
$33$	−2.00000	−0.348155
$34$	−2.00000	−0.342997
$35$	0	0
$36$	−1.82843	−0.304738
$37$	3.65685	0.601183	0.300592	−	0.953753i	$-0.402816\pi$
$37$	3.65685	0.601183	0.300592	+	0.953753i	$0.402816\pi$
$38$	−2.34315	−0.380108
$39$	1.00000	0.160128
$40$	0	0
$41$	−5.65685	−0.883452	−0.441726	−	0.897150i	$-0.645634\pi$
$41$	−5.65685	−0.883452	−0.441726	+	0.897150i	$0.645634\pi$
$42$	0.414214	0.0639145
$43$	−1.65685	−0.252668	−0.126334	−	0.991988i	$-0.540321\pi$
$43$	−1.65685	−0.252668	−0.126334	+	0.991988i	$0.540321\pi$
$44$	−3.65685	−0.551292
$45$	0	0
$46$	−2.82843	−0.417029
$47$	8.82843	1.28776	0.643879	−	0.765127i	$-0.277324\pi$
$47$	8.82843	1.28776	0.643879	+	0.765127i	$0.277324\pi$
$48$	−3.00000	−0.433013
$49$	1.00000	0.142857
$50$	2.07107	0.292893
$51$	−4.82843	−0.676115
$52$	1.82843	0.253557
$53$	−7.65685	−1.05175	−0.525875	−	0.850562i	$-0.676262\pi$
$53$	−7.65685	−1.05175	−0.525875	+	0.850562i	$0.676262\pi$
$54$	0.414214	0.0563673
$55$	0	0
$56$	1.58579	0.211910
$57$	−5.65685	−0.749269
$58$	−3.17157	−0.416448
$59$	6.48528	0.844312	0.422156	−	0.906523i	$-0.361273\pi$
$59$	6.48528	0.844312	0.422156	+	0.906523i	$0.361273\pi$
$60$	0	0
$61$	−11.6569	−1.49251	−0.746254	−	0.665662i	$-0.768149\pi$
$61$	−11.6569	−1.49251	−0.746254	+	0.665662i	$0.768149\pi$
$62$	4.00000	0.508001
$63$	1.00000	0.125988
$64$	−4.17157	−0.521447
$65$	0	0
$66$	0.828427	0.101972
$67$	4.00000	0.488678	0.244339	−	0.969690i	$-0.421429\pi$
$67$	4.00000	0.488678	0.244339	+	0.969690i	$0.421429\pi$
$68$	−8.82843	−1.07060
$69$	−6.82843	−0.822046
$70$	0	0
$71$	14.0000	1.66149	0.830747	−	0.556650i	$-0.187914\pi$
$71$	14.0000	1.66149	0.830747	+	0.556650i	$0.187914\pi$
$72$	1.58579	0.186887
$73$	3.65685	0.428002	0.214001	−	0.976833i	$-0.431350\pi$
$73$	3.65685	0.428002	0.214001	+	0.976833i	$0.431350\pi$
$74$	−1.51472	−0.176082
$75$	5.00000	0.577350
$76$	−10.3431	−1.18644
$77$	2.00000	0.227921
$78$	−0.414214	−0.0469005
$79$	11.3137	1.27289	0.636446	−	0.771321i	$-0.280404\pi$
$79$	11.3137	1.27289	0.636446	+	0.771321i	$0.280404\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	2.34315	0.258757
$83$	−12.1421	−1.33277	−0.666386	−	0.745607i	$-0.732160\pi$
$83$	−12.1421	−1.33277	−0.666386	+	0.745607i	$0.732160\pi$
$84$	1.82843	0.199498
$85$	0	0
$86$	0.686292	0.0740047
$87$	−7.65685	−0.820901
$88$	3.17157	0.338091
$89$	−7.31371	−0.775252	−0.387626	−	0.921817i	$-0.626705\pi$
$89$	−7.31371	−0.775252	−0.387626	+	0.921817i	$0.626705\pi$
$90$	0	0
$91$	−1.00000	−0.104828
$92$	−12.4853	−1.30168
$93$	9.65685	1.00137
$94$	−3.65685	−0.377176
$95$	0	0
$96$	4.41421	0.450524
$97$	−2.00000	−0.203069	−0.101535	−	0.994832i	$-0.532375\pi$
$97$	−2.00000	−0.203069	−0.101535	+	0.994832i	$0.532375\pi$
$98$	−0.414214	−0.0418419
$99$	2.00000	0.201008
$100$	9.14214	0.914214
$101$	−0.828427	−0.0824316	−0.0412158	−	0.999150i	$-0.513123\pi$
$101$	−0.828427	−0.0824316	−0.0412158	+	0.999150i	$0.513123\pi$
$102$	2.00000	0.198030
$103$	2.34315	0.230877	0.115439	−	0.993315i	$-0.463173\pi$
$103$	2.34315	0.230877	0.115439	+	0.993315i	$0.463173\pi$
$104$	−1.58579	−0.155499
$105$	0	0
$106$	3.17157	0.308050
$107$	−2.82843	−0.273434	−0.136717	−	0.990610i	$-0.543655\pi$
$107$	−2.82843	−0.273434	−0.136717	+	0.990610i	$0.543655\pi$
$108$	1.82843	0.175940
$109$	−0.343146	−0.0328674	−0.0164337	−	0.999865i	$-0.505231\pi$
$109$	−0.343146	−0.0328674	−0.0164337	+	0.999865i	$0.505231\pi$
$110$	0	0
$111$	−3.65685	−0.347093
$112$	3.00000	0.283473
$113$	11.6569	1.09658	0.548292	−	0.836287i	$-0.315278\pi$
$113$	11.6569	1.09658	0.548292	+	0.836287i	$0.315278\pi$
$114$	2.34315	0.219456
$115$	0	0
$116$	−14.0000	−1.29987
$117$	−1.00000	−0.0924500
$118$	−2.68629	−0.247293
$119$	4.82843	0.442621
$120$	0	0
$121$	−7.00000	−0.636364
$122$	4.82843	0.437145
$123$	5.65685	0.510061
$124$	17.6569	1.58563
$125$	0	0
$126$	−0.414214	−0.0369011
$127$	16.0000	1.41977	0.709885	−	0.704317i	$-0.248747\pi$
$127$	16.0000	1.41977	0.709885	+	0.704317i	$0.248747\pi$
$128$	10.5563	0.933058
$129$	1.65685	0.145878
$130$	0	0
$131$	−16.9706	−1.48272	−0.741362	−	0.671105i	$-0.765820\pi$
$131$	−16.9706	−1.48272	−0.741362	+	0.671105i	$0.765820\pi$
$132$	3.65685	0.318288
$133$	5.65685	0.490511
$134$	−1.65685	−0.143130
$135$	0	0
$136$	7.65685	0.656570
$137$	6.14214	0.524758	0.262379	−	0.964965i	$-0.415493\pi$
$137$	6.14214	0.524758	0.262379	+	0.964965i	$0.415493\pi$
$138$	2.82843	0.240772
$139$	−6.34315	−0.538019	−0.269009	−	0.963138i	$-0.586696\pi$
$139$	−6.34315	−0.538019	−0.269009	+	0.963138i	$0.586696\pi$
$140$	0	0
$141$	−8.82843	−0.743488
$142$	−5.79899	−0.486640
$143$	−2.00000	−0.167248
$144$	3.00000	0.250000
$145$	0	0
$146$	−1.51472	−0.125359
$147$	−1.00000	−0.0824786
$148$	−6.68629	−0.549610
$149$	−12.4853	−1.02283	−0.511417	−	0.859333i	$-0.670879\pi$
$149$	−12.4853	−1.02283	−0.511417	+	0.859333i	$0.670879\pi$
$150$	−2.07107	−0.169102
$151$	23.3137	1.89724	0.948621	−	0.316414i	$-0.102479\pi$
$151$	23.3137	1.89724	0.948621	+	0.316414i	$0.102479\pi$
$152$	8.97056	0.727609
$153$	4.82843	0.390355
$154$	−0.828427	−0.0667566
$155$	0	0
$156$	−1.82843	−0.146391
$157$	−13.3137	−1.06255	−0.531275	−	0.847200i	$-0.678287\pi$
$157$	−13.3137	−1.06255	−0.531275	+	0.847200i	$0.678287\pi$
$158$	−4.68629	−0.372821
$159$	7.65685	0.607228
$160$	0	0
$161$	6.82843	0.538155
$162$	−0.414214	−0.0325437
$163$	11.3137	0.886158	0.443079	−	0.896483i	$-0.353886\pi$
$163$	11.3137	0.886158	0.443079	+	0.896483i	$0.353886\pi$
$164$	10.3431	0.807664
$165$	0	0
$166$	5.02944	0.390360
$167$	16.8284	1.30222	0.651111	−	0.758982i	$-0.274303\pi$
$167$	16.8284	1.30222	0.651111	+	0.758982i	$0.274303\pi$
$168$	−1.58579	−0.122346
$169$	1.00000	0.0769231
$170$	0	0
$171$	5.65685	0.432590
$172$	3.02944	0.230992
$173$	2.48528	0.188952	0.0944762	−	0.995527i	$-0.469882\pi$
$173$	2.48528	0.188952	0.0944762	+	0.995527i	$0.469882\pi$
$174$	3.17157	0.240436
$175$	−5.00000	−0.377964
$176$	6.00000	0.452267
$177$	−6.48528	−0.487464
$178$	3.02944	0.227066
$179$	−18.1421	−1.35601	−0.678003	−	0.735059i	$-0.737155\pi$
$179$	−18.1421	−1.35601	−0.678003	+	0.735059i	$0.737155\pi$
$180$	0	0
$181$	−15.6569	−1.16376	−0.581882	−	0.813273i	$-0.697684\pi$
$181$	−15.6569	−1.16376	−0.581882	+	0.813273i	$0.697684\pi$
$182$	0.414214	0.0307036
$183$	11.6569	0.861699
$184$	10.8284	0.798282
$185$	0	0
$186$	−4.00000	−0.293294
$187$	9.65685	0.706179
$188$	−16.1421	−1.17729
$189$	−1.00000	−0.0727393
$190$	0	0
$191$	−21.1716	−1.53192	−0.765961	−	0.642887i	$-0.777736\pi$
$191$	−21.1716	−1.53192	−0.765961	+	0.642887i	$0.777736\pi$
$192$	4.17157	0.301057
$193$	−6.97056	−0.501752	−0.250876	−	0.968019i	$-0.580719\pi$
$193$	−6.97056	−0.501752	−0.250876	+	0.968019i	$0.580719\pi$
$194$	0.828427	0.0594776
$195$	0	0
$196$	−1.82843	−0.130602
$197$	−2.82843	−0.201517	−0.100759	−	0.994911i	$-0.532127\pi$
$197$	−2.82843	−0.201517	−0.100759	+	0.994911i	$0.532127\pi$
$198$	−0.828427	−0.0588738
$199$	−16.9706	−1.20301	−0.601506	−	0.798869i	$-0.705432\pi$
$199$	−16.9706	−1.20301	−0.601506	+	0.798869i	$0.705432\pi$
$200$	−7.92893	−0.560660
$201$	−4.00000	−0.282138
$202$	0.343146	0.0241437
$203$	7.65685	0.537406
$204$	8.82843	0.618114
$205$	0	0
$206$	−0.970563	−0.0676223
$207$	6.82843	0.474608
$208$	−3.00000	−0.208013
$209$	11.3137	0.782586
$210$	0	0
$211$	−17.6569	−1.21555	−0.607774	−	0.794110i	$-0.707937\pi$
$211$	−17.6569	−1.21555	−0.607774	+	0.794110i	$0.707937\pi$
$212$	14.0000	0.961524
$213$	−14.0000	−0.959264
$214$	1.17157	0.0800871
$215$	0	0
$216$	−1.58579	−0.107899
$217$	−9.65685	−0.655550
$218$	0.142136	0.00962664
$219$	−3.65685	−0.247107
$220$	0	0
$221$	−4.82843	−0.324795
$222$	1.51472	0.101661
$223$	6.34315	0.424768	0.212384	−	0.977186i	$-0.431877\pi$
$223$	6.34315	0.424768	0.212384	+	0.977186i	$0.431877\pi$
$224$	−4.41421	−0.294937
$225$	−5.00000	−0.333333
$226$	−4.82843	−0.321182
$227$	14.4853	0.961422	0.480711	−	0.876879i	$-0.340379\pi$
$227$	14.4853	0.961422	0.480711	+	0.876879i	$0.340379\pi$
$228$	10.3431	0.684992
$229$	−8.34315	−0.551331	−0.275665	−	0.961254i	$-0.588898\pi$
$229$	−8.34315	−0.551331	−0.275665	+	0.961254i	$0.588898\pi$
$230$	0	0
$231$	−2.00000	−0.131590
$232$	12.1421	0.797170
$233$	−21.3137	−1.39631	−0.698154	−	0.715948i	$-0.745995\pi$
$233$	−21.3137	−1.39631	−0.698154	+	0.715948i	$0.745995\pi$
$234$	0.414214	0.0270780
$235$	0	0
$236$	−11.8579	−0.771881
$237$	−11.3137	−0.734904
$238$	−2.00000	−0.129641
$239$	−23.6569	−1.53023	−0.765117	−	0.643891i	$-0.777319\pi$
$239$	−23.6569	−1.53023	−0.765117	+	0.643891i	$0.777319\pi$
$240$	0	0
$241$	−12.3431	−0.795092	−0.397546	−	0.917582i	$-0.630138\pi$
$241$	−12.3431	−0.795092	−0.397546	+	0.917582i	$0.630138\pi$
$242$	2.89949	0.186387
$243$	−1.00000	−0.0641500
$244$	21.3137	1.36447
$245$	0	0
$246$	−2.34315	−0.149394
$247$	−5.65685	−0.359937
$248$	−15.3137	−0.972421
$249$	12.1421	0.769477
$250$	0	0
$251$	22.6274	1.42823	0.714115	−	0.700028i	$-0.246829\pi$
$251$	22.6274	1.42823	0.714115	+	0.700028i	$0.246829\pi$
$252$	−1.82843	−0.115180
$253$	13.6569	0.858599
$254$	−6.62742	−0.415841
$255$	0	0
$256$	3.97056	0.248160
$257$	8.82843	0.550702	0.275351	−	0.961344i	$-0.411206\pi$
$257$	8.82843	0.550702	0.275351	+	0.961344i	$0.411206\pi$
$258$	−0.686292	−0.0427266
$259$	3.65685	0.227226
$260$	0	0
$261$	7.65685	0.473947
$262$	7.02944	0.434280
$263$	−12.4853	−0.769875	−0.384938	−	0.922943i	$-0.625777\pi$
$263$	−12.4853	−0.769875	−0.384938	+	0.922943i	$0.625777\pi$
$264$	−3.17157	−0.195197
$265$	0	0
$266$	−2.34315	−0.143667
$267$	7.31371	0.447592
$268$	−7.31371	−0.446756
$269$	−6.48528	−0.395415	−0.197707	−	0.980261i	$-0.563350\pi$
$269$	−6.48528	−0.395415	−0.197707	+	0.980261i	$0.563350\pi$
$270$	0	0
$271$	−22.6274	−1.37452	−0.687259	−	0.726413i	$-0.741186\pi$
$271$	−22.6274	−1.37452	−0.687259	+	0.726413i	$0.741186\pi$
$272$	14.4853	0.878299
$273$	1.00000	0.0605228
$274$	−2.54416	−0.153698
$275$	−10.0000	−0.603023
$276$	12.4853	0.751526
$277$	−10.0000	−0.600842	−0.300421	−	0.953807i	$-0.597127\pi$
$277$	−10.0000	−0.600842	−0.300421	+	0.953807i	$0.597127\pi$
$278$	2.62742	0.157582
$279$	−9.65685	−0.578141
$280$	0	0
$281$	−0.485281	−0.0289495	−0.0144747	−	0.999895i	$-0.504608\pi$
$281$	−0.485281	−0.0289495	−0.0144747	+	0.999895i	$0.504608\pi$
$282$	3.65685	0.217763
$283$	−14.3431	−0.852612	−0.426306	−	0.904579i	$-0.640185\pi$
$283$	−14.3431	−0.852612	−0.426306	+	0.904579i	$0.640185\pi$
$284$	−25.5980	−1.51896
$285$	0	0
$286$	0.828427	0.0489859
$287$	−5.65685	−0.333914
$288$	−4.41421	−0.260110
$289$	6.31371	0.371395
$290$	0	0
$291$	2.00000	0.117242
$292$	−6.68629	−0.391286
$293$	15.3137	0.894636	0.447318	−	0.894375i	$-0.352379\pi$
$293$	15.3137	0.894636	0.447318	+	0.894375i	$0.352379\pi$
$294$	0.414214	0.0241574
$295$	0	0
$296$	5.79899	0.337059
$297$	−2.00000	−0.116052
$298$	5.17157	0.299581
$299$	−6.82843	−0.394898
$300$	−9.14214	−0.527821
$301$	−1.65685	−0.0954995
$302$	−9.65685	−0.555690
$303$	0.828427	0.0475919
$304$	16.9706	0.973329
$305$	0	0
$306$	−2.00000	−0.114332
$307$	4.00000	0.228292	0.114146	−	0.993464i	$-0.463587\pi$
$307$	4.00000	0.228292	0.114146	+	0.993464i	$0.463587\pi$
$308$	−3.65685	−0.208369
$309$	−2.34315	−0.133297
$310$	0	0
$311$	−8.68629	−0.492554	−0.246277	−	0.969199i	$-0.579207\pi$
$311$	−8.68629	−0.492554	−0.246277	+	0.969199i	$0.579207\pi$
$312$	1.58579	0.0897775
$313$	22.9706	1.29837	0.649186	−	0.760629i	$-0.275109\pi$
$313$	22.9706	1.29837	0.649186	+	0.760629i	$0.275109\pi$
$314$	5.51472	0.311214
$315$	0	0
$316$	−20.6863	−1.16369
$317$	16.4853	0.925906	0.462953	−	0.886383i	$-0.346790\pi$
$317$	16.4853	0.925906	0.462953	+	0.886383i	$0.346790\pi$
$318$	−3.17157	−0.177853
$319$	15.3137	0.857403
$320$	0	0
$321$	2.82843	0.157867
$322$	−2.82843	−0.157622
$323$	27.3137	1.51978
$324$	−1.82843	−0.101579
$325$	5.00000	0.277350
$326$	−4.68629	−0.259550
$327$	0.343146	0.0189760
$328$	−8.97056	−0.495316
$329$	8.82843	0.486727
$330$	0	0
$331$	−18.6274	−1.02386	−0.511928	−	0.859029i	$-0.671068\pi$
$331$	−18.6274	−1.02386	−0.511928	+	0.859029i	$0.671068\pi$
$332$	22.2010	1.21844
$333$	3.65685	0.200394
$334$	−6.97056	−0.381412
$335$	0	0
$336$	−3.00000	−0.163663
$337$	−5.31371	−0.289456	−0.144728	−	0.989471i	$-0.546231\pi$
$337$	−5.31371	−0.289456	−0.144728	+	0.989471i	$0.546231\pi$
$338$	−0.414214	−0.0225302
$339$	−11.6569	−0.633113
$340$	0	0
$341$	−19.3137	−1.04590
$342$	−2.34315	−0.126703
$343$	1.00000	0.0539949
$344$	−2.62742	−0.141661
$345$	0	0
$346$	−1.02944	−0.0553429
$347$	−6.82843	−0.366569	−0.183285	−	0.983060i	$-0.558673\pi$
$347$	−6.82843	−0.366569	−0.183285	+	0.983060i	$0.558673\pi$
$348$	14.0000	0.750479
$349$	9.31371	0.498551	0.249276	−	0.968433i	$-0.419807\pi$
$349$	9.31371	0.498551	0.249276	+	0.968433i	$0.419807\pi$
$350$	2.07107	0.110703
$351$	1.00000	0.0533761
$352$	−8.82843	−0.470557
$353$	−11.3137	−0.602168	−0.301084	−	0.953598i	$-0.597348\pi$
$353$	−11.3137	−0.602168	−0.301084	+	0.953598i	$0.597348\pi$
$354$	2.68629	0.142775
$355$	0	0
$356$	13.3726	0.708745
$357$	−4.82843	−0.255547
$358$	7.51472	0.397165
$359$	2.68629	0.141777	0.0708885	−	0.997484i	$-0.477417\pi$
$359$	2.68629	0.141777	0.0708885	+	0.997484i	$0.477417\pi$
$360$	0	0
$361$	13.0000	0.684211
$362$	6.48528	0.340859
$363$	7.00000	0.367405
$364$	1.82843	0.0958356
$365$	0	0
$366$	−4.82843	−0.252386
$367$	22.6274	1.18114	0.590571	−	0.806986i	$-0.298903\pi$
$367$	22.6274	1.18114	0.590571	+	0.806986i	$0.298903\pi$
$368$	20.4853	1.06787
$369$	−5.65685	−0.294484
$370$	0	0
$371$	−7.65685	−0.397524
$372$	−17.6569	−0.915465
$373$	−2.68629	−0.139091	−0.0695455	−	0.997579i	$-0.522155\pi$
$373$	−2.68629	−0.139091	−0.0695455	+	0.997579i	$0.522155\pi$
$374$	−4.00000	−0.206835
$375$	0	0
$376$	14.0000	0.721995
$377$	−7.65685	−0.394348
$378$	0.414214	0.0213048
$379$	4.68629	0.240719	0.120359	−	0.992730i	$-0.461595\pi$
$379$	4.68629	0.240719	0.120359	+	0.992730i	$0.461595\pi$
$380$	0	0
$381$	−16.0000	−0.819705
$382$	8.76955	0.448689
$383$	20.8284	1.06428	0.532141	−	0.846655i	$-0.321387\pi$
$383$	20.8284	1.06428	0.532141	+	0.846655i	$0.321387\pi$
$384$	−10.5563	−0.538701
$385$	0	0
$386$	2.88730	0.146960
$387$	−1.65685	−0.0842226
$388$	3.65685	0.185649
$389$	22.0000	1.11544	0.557722	−	0.830028i	$-0.311675\pi$
$389$	22.0000	1.11544	0.557722	+	0.830028i	$0.311675\pi$
$390$	0	0
$391$	32.9706	1.66739
$392$	1.58579	0.0800943
$393$	16.9706	0.856052
$394$	1.17157	0.0590230
$395$	0	0
$396$	−3.65685	−0.183764
$397$	−31.6569	−1.58881	−0.794406	−	0.607387i	$-0.792218\pi$
$397$	−31.6569	−1.58881	−0.794406	+	0.607387i	$0.792218\pi$
$398$	7.02944	0.352354
$399$	−5.65685	−0.283197
$400$	−15.0000	−0.750000
$401$	27.1127	1.35394	0.676972	−	0.736009i	$-0.263292\pi$
$401$	27.1127	1.35394	0.676972	+	0.736009i	$0.263292\pi$
$402$	1.65685	0.0826364
$403$	9.65685	0.481042
$404$	1.51472	0.0753601
$405$	0	0
$406$	−3.17157	−0.157403
$407$	7.31371	0.362527
$408$	−7.65685	−0.379071
$409$	−13.3137	−0.658321	−0.329160	−	0.944274i	$-0.606766\pi$
$409$	−13.3137	−0.658321	−0.329160	+	0.944274i	$0.606766\pi$
$410$	0	0
$411$	−6.14214	−0.302969
$412$	−4.28427	−0.211071
$413$	6.48528	0.319120
$414$	−2.82843	−0.139010
$415$	0	0
$416$	4.41421	0.216425
$417$	6.34315	0.310625
$418$	−4.68629	−0.229214
$419$	33.9411	1.65813	0.829066	−	0.559150i	$-0.188873\pi$
$419$	33.9411	1.65813	0.829066	+	0.559150i	$0.188873\pi$
$420$	0	0
$421$	−28.6274	−1.39521	−0.697607	−	0.716480i	$-0.745752\pi$
$421$	−28.6274	−1.39521	−0.697607	+	0.716480i	$0.745752\pi$
$422$	7.31371	0.356026
$423$	8.82843	0.429253
$424$	−12.1421	−0.589674
$425$	−24.1421	−1.17107
$426$	5.79899	0.280962
$427$	−11.6569	−0.564115
$428$	5.17157	0.249977
$429$	2.00000	0.0965609
$430$	0	0
$431$	18.9706	0.913780	0.456890	−	0.889523i	$-0.348963\pi$
$431$	18.9706	0.913780	0.456890	+	0.889523i	$0.348963\pi$
$432$	−3.00000	−0.144338
$433$	8.34315	0.400946	0.200473	−	0.979699i	$-0.435752\pi$
$433$	8.34315	0.400946	0.200473	+	0.979699i	$0.435752\pi$
$434$	4.00000	0.192006
$435$	0	0
$436$	0.627417	0.0300478
$437$	38.6274	1.84780
$438$	1.51472	0.0723761
$439$	19.3137	0.921793	0.460897	−	0.887454i	$-0.347528\pi$
$439$	19.3137	0.921793	0.460897	+	0.887454i	$0.347528\pi$
$440$	0	0
$441$	1.00000	0.0476190
$442$	2.00000	0.0951303
$443$	−9.85786	−0.468361	−0.234181	−	0.972193i	$-0.575241\pi$
$443$	−9.85786	−0.468361	−0.234181	+	0.972193i	$0.575241\pi$
$444$	6.68629	0.317317
$445$	0	0
$446$	−2.62742	−0.124412
$447$	12.4853	0.590534
$448$	−4.17157	−0.197088
$449$	−15.7990	−0.745600	−0.372800	−	0.927912i	$-0.621602\pi$
$449$	−15.7990	−0.745600	−0.372800	+	0.927912i	$0.621602\pi$
$450$	2.07107	0.0976311
$451$	−11.3137	−0.532742
$452$	−21.3137	−1.00251
$453$	−23.3137	−1.09537
$454$	−6.00000	−0.281594
$455$	0	0
$456$	−8.97056	−0.420085
$457$	−14.2843	−0.668190	−0.334095	−	0.942539i	$-0.608431\pi$
$457$	−14.2843	−0.668190	−0.334095	+	0.942539i	$0.608431\pi$
$458$	3.45584	0.161481
$459$	−4.82843	−0.225372
$460$	0	0
$461$	29.6569	1.38126	0.690629	−	0.723210i	$-0.257334\pi$
$461$	29.6569	1.38126	0.690629	+	0.723210i	$0.257334\pi$
$462$	0.828427	0.0385419
$463$	4.68629	0.217790	0.108895	−	0.994053i	$-0.465269\pi$
$463$	4.68629	0.217790	0.108895	+	0.994053i	$0.465269\pi$
$464$	22.9706	1.06638
$465$	0	0
$466$	8.82843	0.408969
$467$	−8.00000	−0.370196	−0.185098	−	0.982720i	$-0.559260\pi$
$467$	−8.00000	−0.370196	−0.185098	+	0.982720i	$0.559260\pi$
$468$	1.82843	0.0845191
$469$	4.00000	0.184703
$470$	0	0
$471$	13.3137	0.613463
$472$	10.2843	0.473372
$473$	−3.31371	−0.152364
$474$	4.68629	0.215248
$475$	−28.2843	−1.29777
$476$	−8.82843	−0.404650
$477$	−7.65685	−0.350583
$478$	9.79899	0.448195
$479$	10.4853	0.479085	0.239542	−	0.970886i	$-0.423003\pi$
$479$	10.4853	0.479085	0.239542	+	0.970886i	$0.423003\pi$
$480$	0	0
$481$	−3.65685	−0.166738
$482$	5.11270	0.232877
$483$	−6.82843	−0.310704
$484$	12.7990	0.581772
$485$	0	0
$486$	0.414214	0.0187891
$487$	8.68629	0.393613	0.196807	−	0.980442i	$-0.436943\pi$
$487$	8.68629	0.393613	0.196807	+	0.980442i	$0.436943\pi$
$488$	−18.4853	−0.836789
$489$	−11.3137	−0.511624
$490$	0	0
$491$	−40.4853	−1.82708	−0.913538	−	0.406754i	$-0.866661\pi$
$491$	−40.4853	−1.82708	−0.913538	+	0.406754i	$0.866661\pi$
$492$	−10.3431	−0.466305
$493$	36.9706	1.66507
$494$	2.34315	0.105423
$495$	0	0
$496$	−28.9706	−1.30082
$497$	14.0000	0.627986
$498$	−5.02944	−0.225374
$499$	15.3137	0.685536	0.342768	−	0.939420i	$-0.388636\pi$
$499$	15.3137	0.685536	0.342768	+	0.939420i	$0.388636\pi$
$500$	0	0
$501$	−16.8284	−0.751839
$502$	−9.37258	−0.418319
$503$	−16.2843	−0.726080	−0.363040	−	0.931774i	$-0.618261\pi$
$503$	−16.2843	−0.726080	−0.363040	+	0.931774i	$0.618261\pi$
$504$	1.58579	0.0706365
$505$	0	0
$506$	−5.65685	−0.251478
$507$	−1.00000	−0.0444116
$508$	−29.2548	−1.29797
$509$	−8.00000	−0.354594	−0.177297	−	0.984157i	$-0.556735\pi$
$509$	−8.00000	−0.354594	−0.177297	+	0.984157i	$0.556735\pi$
$510$	0	0
$511$	3.65685	0.161770
$512$	−22.7574	−1.00574
$513$	−5.65685	−0.249756
$514$	−3.65685	−0.161297
$515$	0	0
$516$	−3.02944	−0.133364
$517$	17.6569	0.776548
$518$	−1.51472	−0.0665529
$519$	−2.48528	−0.109092
$520$	0	0
$521$	33.7990	1.48076	0.740380	−	0.672188i	$-0.234645\pi$
$521$	33.7990	1.48076	0.740380	+	0.672188i	$0.234645\pi$
$522$	−3.17157	−0.138816
$523$	−9.65685	−0.422265	−0.211132	−	0.977457i	$-0.567715\pi$
$523$	−9.65685	−0.422265	−0.211132	+	0.977457i	$0.567715\pi$
$524$	31.0294	1.35553
$525$	5.00000	0.218218
$526$	5.17157	0.225491
$527$	−46.6274	−2.03112
$528$	−6.00000	−0.261116
$529$	23.6274	1.02728
$530$	0	0
$531$	6.48528	0.281437
$532$	−10.3431	−0.448432
$533$	5.65685	0.245026
$534$	−3.02944	−0.131097
$535$	0	0
$536$	6.34315	0.273982
$537$	18.1421	0.782891
$538$	2.68629	0.115814
$539$	2.00000	0.0861461
$540$	0	0
$541$	−17.3137	−0.744374	−0.372187	−	0.928158i	$-0.621392\pi$
$541$	−17.3137	−0.744374	−0.372187	+	0.928158i	$0.621392\pi$
$542$	9.37258	0.402587
$543$	15.6569	0.671900
$544$	−21.3137	−0.913818
$545$	0	0
$546$	−0.414214	−0.0177267
$547$	−4.00000	−0.171028	−0.0855138	−	0.996337i	$-0.527253\pi$
$547$	−4.00000	−0.171028	−0.0855138	+	0.996337i	$0.527253\pi$
$548$	−11.2304	−0.479741
$549$	−11.6569	−0.497502
$550$	4.14214	0.176621
$551$	43.3137	1.84523
$552$	−10.8284	−0.460888
$553$	11.3137	0.481108
$554$	4.14214	0.175982
$555$	0	0
$556$	11.5980	0.491864
$557$	27.5147	1.16584	0.582918	−	0.812531i	$-0.301911\pi$
$557$	27.5147	1.16584	0.582918	+	0.812531i	$0.301911\pi$
$558$	4.00000	0.169334
$559$	1.65685	0.0700775
$560$	0	0
$561$	−9.65685	−0.407713
$562$	0.201010	0.00847910
$563$	−17.6569	−0.744148	−0.372074	−	0.928203i	$-0.621353\pi$
$563$	−17.6569	−0.744148	−0.372074	+	0.928203i	$0.621353\pi$
$564$	16.1421	0.679707
$565$	0	0
$566$	5.94113	0.249724
$567$	1.00000	0.0419961
$568$	22.2010	0.931534
$569$	−21.3137	−0.893517	−0.446759	−	0.894655i	$-0.647422\pi$
$569$	−21.3137	−0.893517	−0.446759	+	0.894655i	$0.647422\pi$
$570$	0	0
$571$	−34.6274	−1.44911	−0.724556	−	0.689216i	$-0.757955\pi$
$571$	−34.6274	−1.44911	−0.724556	+	0.689216i	$0.757955\pi$
$572$	3.65685	0.152901
$573$	21.1716	0.884455
$574$	2.34315	0.0978010
$575$	−34.1421	−1.42383
$576$	−4.17157	−0.173816
$577$	−22.9706	−0.956277	−0.478139	−	0.878284i	$-0.658688\pi$
$577$	−22.9706	−0.956277	−0.478139	+	0.878284i	$0.658688\pi$
$578$	−2.61522	−0.108779
$579$	6.97056	0.289687
$580$	0	0
$581$	−12.1421	−0.503741
$582$	−0.828427	−0.0343394
$583$	−15.3137	−0.634229
$584$	5.79899	0.239964
$585$	0	0
$586$	−6.34315	−0.262033
$587$	−37.1127	−1.53180	−0.765902	−	0.642957i	$-0.777707\pi$
$587$	−37.1127	−1.53180	−0.765902	+	0.642957i	$0.777707\pi$
$588$	1.82843	0.0754031
$589$	−54.6274	−2.25088
$590$	0	0
$591$	2.82843	0.116346
$592$	10.9706	0.450887
$593$	−14.3431	−0.589002	−0.294501	−	0.955651i	$-0.595153\pi$
$593$	−14.3431	−0.589002	−0.294501	+	0.955651i	$0.595153\pi$
$594$	0.828427	0.0339908
$595$	0	0
$596$	22.8284	0.935089
$597$	16.9706	0.694559
$598$	2.82843	0.115663
$599$	−3.51472	−0.143608	−0.0718038	−	0.997419i	$-0.522876\pi$
$599$	−3.51472	−0.143608	−0.0718038	+	0.997419i	$0.522876\pi$
$600$	7.92893	0.323697
$601$	22.9706	0.936989	0.468494	−	0.883466i	$-0.344797\pi$
$601$	22.9706	0.936989	0.468494	+	0.883466i	$0.344797\pi$
$602$	0.686292	0.0279712
$603$	4.00000	0.162893
$604$	−42.6274	−1.73448
$605$	0	0
$606$	−0.343146	−0.0139393
$607$	22.6274	0.918419	0.459209	−	0.888328i	$-0.348133\pi$
$607$	22.6274	0.918419	0.459209	+	0.888328i	$0.348133\pi$
$608$	−24.9706	−1.01269
$609$	−7.65685	−0.310271
$610$	0	0
$611$	−8.82843	−0.357160
$612$	−8.82843	−0.356868
$613$	33.3137	1.34553	0.672764	−	0.739857i	$-0.265107\pi$
$613$	33.3137	1.34553	0.672764	+	0.739857i	$0.265107\pi$
$614$	−1.65685	−0.0668652
$615$	0	0
$616$	3.17157	0.127786
$617$	36.7696	1.48029	0.740143	−	0.672449i	$-0.234758\pi$
$617$	36.7696	1.48029	0.740143	+	0.672449i	$0.234758\pi$
$618$	0.970563	0.0390418
$619$	−36.0000	−1.44696	−0.723481	−	0.690344i	$-0.757459\pi$
$619$	−36.0000	−1.44696	−0.723481	+	0.690344i	$0.757459\pi$
$620$	0	0
$621$	−6.82843	−0.274015
$622$	3.59798	0.144266
$623$	−7.31371	−0.293018
$624$	3.00000	0.120096
$625$	25.0000	1.00000
$626$	−9.51472	−0.380285
$627$	−11.3137	−0.451826
$628$	24.3431	0.971397
$629$	17.6569	0.704025
$630$	0	0
$631$	44.0000	1.75161	0.875806	−	0.482663i	$-0.160330\pi$
$631$	44.0000	1.75161	0.875806	+	0.482663i	$0.160330\pi$
$632$	17.9411	0.713660
$633$	17.6569	0.701797
$634$	−6.82843	−0.271191
$635$	0	0
$636$	−14.0000	−0.555136
$637$	−1.00000	−0.0396214
$638$	−6.34315	−0.251128
$639$	14.0000	0.553831
$640$	0	0
$641$	−8.34315	−0.329534	−0.164767	−	0.986332i	$-0.552687\pi$
$641$	−8.34315	−0.329534	−0.164767	+	0.986332i	$0.552687\pi$
$642$	−1.17157	−0.0462383
$643$	−15.3137	−0.603914	−0.301957	−	0.953322i	$-0.597640\pi$
$643$	−15.3137	−0.603914	−0.301957	+	0.953322i	$0.597640\pi$
$644$	−12.4853	−0.491989
$645$	0	0
$646$	−11.3137	−0.445132
$647$	−44.2843	−1.74099	−0.870497	−	0.492173i	$-0.836203\pi$
$647$	−44.2843	−1.74099	−0.870497	+	0.492173i	$0.836203\pi$
$648$	1.58579	0.0622956
$649$	12.9706	0.509139
$650$	−2.07107	−0.0812340
$651$	9.65685	0.378482
$652$	−20.6863	−0.810138
$653$	−37.5980	−1.47132	−0.735661	−	0.677350i	$-0.763128\pi$
$653$	−37.5980	−1.47132	−0.735661	+	0.677350i	$0.763128\pi$
$654$	−0.142136	−0.00555794
$655$	0	0
$656$	−16.9706	−0.662589
$657$	3.65685	0.142667
$658$	−3.65685	−0.142559
$659$	21.4558	0.835801	0.417901	−	0.908493i	$-0.362766\pi$
$659$	21.4558	0.835801	0.417901	+	0.908493i	$0.362766\pi$
$660$	0	0
$661$	−13.3137	−0.517843	−0.258922	−	0.965898i	$-0.583367\pi$
$661$	−13.3137	−0.517843	−0.258922	+	0.965898i	$0.583367\pi$
$662$	7.71573	0.299880
$663$	4.82843	0.187521
$664$	−19.2548	−0.747232
$665$	0	0
$666$	−1.51472	−0.0586942
$667$	52.2843	2.02446
$668$	−30.7696	−1.19051
$669$	−6.34315	−0.245240
$670$	0	0
$671$	−23.3137	−0.900016
$672$	4.41421	0.170282
$673$	−44.6274	−1.72026	−0.860130	−	0.510074i	$-0.829618\pi$
$673$	−44.6274	−1.72026	−0.860130	+	0.510074i	$0.829618\pi$
$674$	2.20101	0.0847797
$675$	5.00000	0.192450
$676$	−1.82843	−0.0703241
$677$	−2.48528	−0.0955171	−0.0477586	−	0.998859i	$-0.515208\pi$
$677$	−2.48528	−0.0955171	−0.0477586	+	0.998859i	$0.515208\pi$
$678$	4.82843	0.185435
$679$	−2.00000	−0.0767530
$680$	0	0
$681$	−14.4853	−0.555077
$682$	8.00000	0.306336
$683$	−35.6569	−1.36437	−0.682186	−	0.731179i	$-0.738970\pi$
$683$	−35.6569	−1.36437	−0.682186	+	0.731179i	$0.738970\pi$
$684$	−10.3431	−0.395480
$685$	0	0
$686$	−0.414214	−0.0158147
$687$	8.34315	0.318311
$688$	−4.97056	−0.189501
$689$	7.65685	0.291703
$690$	0	0
$691$	−0.686292	−0.0261078	−0.0130539	−	0.999915i	$-0.504155\pi$
$691$	−0.686292	−0.0261078	−0.0130539	+	0.999915i	$0.504155\pi$
$692$	−4.54416	−0.172743
$693$	2.00000	0.0759737
$694$	2.82843	0.107366
$695$	0	0
$696$	−12.1421	−0.460246
$697$	−27.3137	−1.03458
$698$	−3.85786	−0.146022
$699$	21.3137	0.806158
$700$	9.14214	0.345540
$701$	44.6274	1.68555	0.842777	−	0.538263i	$-0.180919\pi$
$701$	44.6274	1.68555	0.842777	+	0.538263i	$0.180919\pi$
$702$	−0.414214	−0.0156335
$703$	20.6863	0.780198
$704$	−8.34315	−0.314444
$705$	0	0
$706$	4.68629	0.176371
$707$	−0.828427	−0.0311562
$708$	11.8579	0.445646
$709$	−30.9706	−1.16312	−0.581562	−	0.813502i	$-0.697558\pi$
$709$	−30.9706	−1.16312	−0.581562	+	0.813502i	$0.697558\pi$
$710$	0	0
$711$	11.3137	0.424297
$712$	−11.5980	−0.434653
$713$	−65.9411	−2.46951
$714$	2.00000	0.0748481
$715$	0	0
$716$	33.1716	1.23968
$717$	23.6569	0.883481
$718$	−1.11270	−0.0415255
$719$	41.6569	1.55354	0.776769	−	0.629785i	$-0.216857\pi$
$719$	41.6569	1.55354	0.776769	+	0.629785i	$0.216857\pi$
$720$	0	0
$721$	2.34315	0.0872633
$722$	−5.38478	−0.200401
$723$	12.3431	0.459047
$724$	28.6274	1.06393
$725$	−38.2843	−1.42184
$726$	−2.89949	−0.107610
$727$	14.6274	0.542501	0.271250	−	0.962509i	$-0.412563\pi$
$727$	14.6274	0.542501	0.271250	+	0.962509i	$0.412563\pi$
$728$	−1.58579	−0.0587732
$729$	1.00000	0.0370370
$730$	0	0
$731$	−8.00000	−0.295891
$732$	−21.3137	−0.787777
$733$	38.2843	1.41406	0.707031	−	0.707183i	$-0.250034\pi$
$733$	38.2843	1.41406	0.707031	+	0.707183i	$0.250034\pi$
$734$	−9.37258	−0.345948
$735$	0	0
$736$	−30.1421	−1.11105
$737$	8.00000	0.294684
$738$	2.34315	0.0862524
$739$	12.0000	0.441427	0.220714	−	0.975339i	$-0.429161\pi$
$739$	12.0000	0.441427	0.220714	+	0.975339i	$0.429161\pi$
$740$	0	0
$741$	5.65685	0.207810
$742$	3.17157	0.116432
$743$	20.6274	0.756747	0.378373	−	0.925653i	$-0.376484\pi$
$743$	20.6274	0.756747	0.378373	+	0.925653i	$0.376484\pi$
$744$	15.3137	0.561428
$745$	0	0
$746$	1.11270	0.0407388
$747$	−12.1421	−0.444258
$748$	−17.6569	−0.645599
$749$	−2.82843	−0.103348
$750$	0	0
$751$	−28.2843	−1.03211	−0.516054	−	0.856556i	$-0.672600\pi$
$751$	−28.2843	−1.03211	−0.516054	+	0.856556i	$0.672600\pi$
$752$	26.4853	0.965819
$753$	−22.6274	−0.824589
$754$	3.17157	0.115502
$755$	0	0
$756$	1.82843	0.0664993
$757$	24.6274	0.895099	0.447549	−	0.894259i	$-0.352297\pi$
$757$	24.6274	0.895099	0.447549	+	0.894259i	$0.352297\pi$
$758$	−1.94113	−0.0705049
$759$	−13.6569	−0.495712
$760$	0	0
$761$	−15.0294	−0.544817	−0.272408	−	0.962182i	$-0.587820\pi$
$761$	−15.0294	−0.544817	−0.272408	+	0.962182i	$0.587820\pi$
$762$	6.62742	0.240086
$763$	−0.343146	−0.0124227
$764$	38.7107	1.40050
$765$	0	0
$766$	−8.62742	−0.311721
$767$	−6.48528	−0.234170
$768$	−3.97056	−0.143275
$769$	27.9411	1.00758	0.503791	−	0.863825i	$-0.331938\pi$
$769$	27.9411	1.00758	0.503791	+	0.863825i	$0.331938\pi$
$770$	0	0
$771$	−8.82843	−0.317948
$772$	12.7452	0.458709
$773$	20.0000	0.719350	0.359675	−	0.933078i	$-0.382888\pi$
$773$	20.0000	0.719350	0.359675	+	0.933078i	$0.382888\pi$
$774$	0.686292	0.0246682
$775$	48.2843	1.73442
$776$	−3.17157	−0.113853
$777$	−3.65685	−0.131189
$778$	−9.11270	−0.326706
$779$	−32.0000	−1.14652
$780$	0	0
$781$	28.0000	1.00192
$782$	−13.6569	−0.488368
$783$	−7.65685	−0.273634
$784$	3.00000	0.107143
$785$	0	0
$786$	−7.02944	−0.250732
$787$	15.3137	0.545875	0.272937	−	0.962032i	$-0.412005\pi$
$787$	15.3137	0.545875	0.272937	+	0.962032i	$0.412005\pi$
$788$	5.17157	0.184230
$789$	12.4853	0.444488
$790$	0	0
$791$	11.6569	0.414470
$792$	3.17157	0.112697
$793$	11.6569	0.413947
$794$	13.1127	0.465352
$795$	0	0
$796$	31.0294	1.09981
$797$	12.1421	0.430097	0.215048	−	0.976603i	$-0.431009\pi$
$797$	12.1421	0.430097	0.215048	+	0.976603i	$0.431009\pi$
$798$	2.34315	0.0829465
$799$	42.6274	1.50805
$800$	22.0711	0.780330
$801$	−7.31371	−0.258417
$802$	−11.2304	−0.396561
$803$	7.31371	0.258095
$804$	7.31371	0.257935
$805$	0	0
$806$	−4.00000	−0.140894
$807$	6.48528	0.228293
$808$	−1.31371	−0.0462161
$809$	30.9706	1.08887	0.544433	−	0.838804i	$-0.316745\pi$
$809$	30.9706	1.08887	0.544433	+	0.838804i	$0.316745\pi$
$810$	0	0
$811$	28.2843	0.993195	0.496598	−	0.867981i	$-0.334583\pi$
$811$	28.2843	0.993195	0.496598	+	0.867981i	$0.334583\pi$
$812$	−14.0000	−0.491304
$813$	22.6274	0.793578
$814$	−3.02944	−0.106182
$815$	0	0
$816$	−14.4853	−0.507086
$817$	−9.37258	−0.327905
$818$	5.51472	0.192818
$819$	−1.00000	−0.0349428
$820$	0	0
$821$	29.4558	1.02802	0.514008	−	0.857785i	$-0.328160\pi$
$821$	29.4558	1.02802	0.514008	+	0.857785i	$0.328160\pi$
$822$	2.54416	0.0887376
$823$	−22.6274	−0.788742	−0.394371	−	0.918951i	$-0.629038\pi$
$823$	−22.6274	−0.788742	−0.394371	+	0.918951i	$0.629038\pi$
$824$	3.71573	0.129444
$825$	10.0000	0.348155
$826$	−2.68629	−0.0934680
$827$	−22.0000	−0.765015	−0.382507	−	0.923952i	$-0.624939\pi$
$827$	−22.0000	−0.765015	−0.382507	+	0.923952i	$0.624939\pi$
$828$	−12.4853	−0.433894
$829$	−18.6863	−0.649002	−0.324501	−	0.945885i	$-0.605196\pi$
$829$	−18.6863	−0.649002	−0.324501	+	0.945885i	$0.605196\pi$
$830$	0	0
$831$	10.0000	0.346896
$832$	4.17157	0.144623
$833$	4.82843	0.167295
$834$	−2.62742	−0.0909800
$835$	0	0
$836$	−20.6863	−0.715450
$837$	9.65685	0.333790
$838$	−14.0589	−0.485656
$839$	−10.2010	−0.352178	−0.176089	−	0.984374i	$-0.556345\pi$
$839$	−10.2010	−0.352178	−0.176089	+	0.984374i	$0.556345\pi$
$840$	0	0
$841$	29.6274	1.02164
$842$	11.8579	0.408649
$843$	0.485281	0.0167140
$844$	32.2843	1.11127
$845$	0	0
$846$	−3.65685	−0.125725
$847$	−7.00000	−0.240523
$848$	−22.9706	−0.788812
$849$	14.3431	0.492255
$850$	10.0000	0.342997
$851$	24.9706	0.855980
$852$	25.5980	0.876972
$853$	−26.9706	−0.923454	−0.461727	−	0.887022i	$-0.652770\pi$
$853$	−26.9706	−0.923454	−0.461727	+	0.887022i	$0.652770\pi$
$854$	4.82843	0.165225
$855$	0	0
$856$	−4.48528	−0.153304
$857$	−25.1127	−0.857833	−0.428917	−	0.903344i	$-0.641105\pi$
$857$	−25.1127	−0.857833	−0.428917	+	0.903344i	$0.641105\pi$
$858$	−0.828427	−0.0282820
$859$	4.97056	0.169593	0.0847967	−	0.996398i	$-0.472976\pi$
$859$	4.97056	0.169593	0.0847967	+	0.996398i	$0.472976\pi$
$860$	0	0
$861$	5.65685	0.192785
$862$	−7.85786	−0.267640
$863$	47.2548	1.60857	0.804287	−	0.594242i	$-0.202548\pi$
$863$	47.2548	1.60857	0.804287	+	0.594242i	$0.202548\pi$
$864$	4.41421	0.150175
$865$	0	0
$866$	−3.45584	−0.117434
$867$	−6.31371	−0.214425
$868$	17.6569	0.599313
$869$	22.6274	0.767583
$870$	0	0
$871$	−4.00000	−0.135535
$872$	−0.544156	−0.0184274
$873$	−2.00000	−0.0676897
$874$	−16.0000	−0.541208
$875$	0	0
$876$	6.68629	0.225909
$877$	41.3137	1.39506	0.697532	−	0.716553i	$-0.254281\pi$
$877$	41.3137	1.39506	0.697532	+	0.716553i	$0.254281\pi$
$878$	−8.00000	−0.269987
$879$	−15.3137	−0.516519
$880$	0	0
$881$	−38.7696	−1.30618	−0.653090	−	0.757281i	$-0.726528\pi$
$881$	−38.7696	−1.30618	−0.653090	+	0.757281i	$0.726528\pi$
$882$	−0.414214	−0.0139473
$883$	48.2843	1.62490	0.812448	−	0.583034i	$-0.198135\pi$
$883$	48.2843	1.62490	0.812448	+	0.583034i	$0.198135\pi$
$884$	8.82843	0.296932
$885$	0	0
$886$	4.08326	0.137180
$887$	15.0294	0.504639	0.252320	−	0.967644i	$-0.418807\pi$
$887$	15.0294	0.504639	0.252320	+	0.967644i	$0.418807\pi$
$888$	−5.79899	−0.194601
$889$	16.0000	0.536623
$890$	0	0
$891$	2.00000	0.0670025
$892$	−11.5980	−0.388329
$893$	49.9411	1.67122
$894$	−5.17157	−0.172963
$895$	0	0
$896$	10.5563	0.352663
$897$	6.82843	0.227995
$898$	6.54416	0.218381
$899$	−73.9411	−2.46607
$900$	9.14214	0.304738
$901$	−36.9706	−1.23167
$902$	4.68629	0.156036
$903$	1.65685	0.0551367
$904$	18.4853	0.614811
$905$	0	0
$906$	9.65685	0.320827
$907$	−38.3431	−1.27316	−0.636582	−	0.771209i	$-0.719652\pi$
$907$	−38.3431	−1.27316	−0.636582	+	0.771209i	$0.719652\pi$
$908$	−26.4853	−0.878945
$909$	−0.828427	−0.0274772
$910$	0	0
$911$	−55.1127	−1.82597	−0.912983	−	0.407999i	$-0.866227\pi$
$911$	−55.1127	−1.82597	−0.912983	+	0.407999i	$0.866227\pi$
$912$	−16.9706	−0.561951
$913$	−24.2843	−0.803692
$914$	5.91674	0.195708
$915$	0	0
$916$	15.2548	0.504034
$917$	−16.9706	−0.560417
$918$	2.00000	0.0660098
$919$	−7.02944	−0.231880	−0.115940	−	0.993256i	$-0.536988\pi$
$919$	−7.02944	−0.231880	−0.115940	+	0.993256i	$0.536988\pi$
$920$	0	0
$921$	−4.00000	−0.131804
$922$	−12.2843	−0.404561
$923$	−14.0000	−0.460816
$924$	3.65685	0.120302
$925$	−18.2843	−0.601183
$926$	−1.94113	−0.0637893
$927$	2.34315	0.0769590
$928$	−33.7990	−1.10951
$929$	−32.9706	−1.08173	−0.540865	−	0.841110i	$-0.681903\pi$
$929$	−32.9706	−1.08173	−0.540865	+	0.841110i	$0.681903\pi$
$930$	0	0
$931$	5.65685	0.185396
$932$	38.9706	1.27652
$933$	8.68629	0.284376
$934$	3.31371	0.108428
$935$	0	0
$936$	−1.58579	−0.0518331
$937$	−18.9706	−0.619741	−0.309871	−	0.950779i	$-0.600286\pi$
$937$	−18.9706	−0.619741	−0.309871	+	0.950779i	$0.600286\pi$
$938$	−1.65685	−0.0540982
$939$	−22.9706	−0.749616
$940$	0	0
$941$	30.3431	0.989158	0.494579	−	0.869133i	$-0.335322\pi$
$941$	30.3431	0.989158	0.494579	+	0.869133i	$0.335322\pi$
$942$	−5.51472	−0.179679
$943$	−38.6274	−1.25788
$944$	19.4558	0.633234
$945$	0	0
$946$	1.37258	0.0446265
$947$	−26.9706	−0.876426	−0.438213	−	0.898871i	$-0.644388\pi$
$947$	−26.9706	−0.876426	−0.438213	+	0.898871i	$0.644388\pi$
$948$	20.6863	0.671860
$949$	−3.65685	−0.118707
$950$	11.7157	0.380108
$951$	−16.4853	−0.534572
$952$	7.65685	0.248160
$953$	−39.6569	−1.28461	−0.642306	−	0.766449i	$-0.722022\pi$
$953$	−39.6569	−1.28461	−0.642306	+	0.766449i	$0.722022\pi$
$954$	3.17157	0.102683
$955$	0	0
$956$	43.2548	1.39896
$957$	−15.3137	−0.495022
$958$	−4.34315	−0.140321
$959$	6.14214	0.198340
$960$	0	0
$961$	62.2548	2.00822
$962$	1.51472	0.0488365
$963$	−2.82843	−0.0911448
$964$	22.5685	0.726884
$965$	0	0
$966$	2.82843	0.0910032
$967$	−61.9411	−1.99189	−0.995946	−	0.0899514i	$-0.971329\pi$
$967$	−61.9411	−1.99189	−0.995946	+	0.0899514i	$0.971329\pi$
$968$	−11.1005	−0.356784
$969$	−27.3137	−0.877443
$970$	0	0
$971$	−12.0000	−0.385098	−0.192549	−	0.981287i	$-0.561675\pi$
$971$	−12.0000	−0.385098	−0.192549	+	0.981287i	$0.561675\pi$
$972$	1.82843	0.0586468
$973$	−6.34315	−0.203352
$974$	−3.59798	−0.115287
$975$	−5.00000	−0.160128
$976$	−34.9706	−1.11938
$977$	13.8579	0.443352	0.221676	−	0.975120i	$-0.428847\pi$
$977$	13.8579	0.443352	0.221676	+	0.975120i	$0.428847\pi$
$978$	4.68629	0.149851
$979$	−14.6274	−0.467494
$980$	0	0
$981$	−0.343146	−0.0109558
$982$	16.7696	0.535138
$983$	−13.1127	−0.418230	−0.209115	−	0.977891i	$-0.567058\pi$
$983$	−13.1127	−0.418230	−0.209115	+	0.977891i	$0.567058\pi$
$984$	8.97056	0.285971
$985$	0	0
$986$	−15.3137	−0.487688
$987$	−8.82843	−0.281012
$988$	10.3431	0.329059
$989$	−11.3137	−0.359755
$990$	0	0
$991$	−42.3431	−1.34507	−0.672537	−	0.740063i	$-0.734795\pi$
$991$	−42.3431	−1.34507	−0.672537	+	0.740063i	$0.734795\pi$
$992$	42.6274	1.35342
$993$	18.6274	0.591123
$994$	−5.79899	−0.183933
$995$	0	0
$996$	−22.2010	−0.703466
$997$	33.3137	1.05506	0.527528	−	0.849538i	$-0.323119\pi$
$997$	33.3137	1.05506	0.527528	+	0.849538i	$0.323119\pi$
$998$	−6.34315	−0.200789
$999$	−3.65685	−0.115698

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.a.c.1.1	✓	2
3.2	odd	2		819.2.a.g.1.2		2
4.3	odd	2		4368.2.a.bj.1.2		2
5.4	even	2		6825.2.a.m.1.2		2
7.6	odd	2		1911.2.a.k.1.1		2
13.12	even	2		3549.2.a.f.1.2		2
21.20	even	2		5733.2.a.n.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.a.c.1.1	✓	2	1.1	even	1	trivial
819.2.a.g.1.2		2	3.2	odd	2
1911.2.a.k.1.1		2	7.6	odd	2
3549.2.a.f.1.2		2	13.12	even	2
4368.2.a.bj.1.2		2	4.3	odd	2
5733.2.a.n.1.2		2	21.20	even	2
6825.2.a.m.1.2		2	5.4	even	2

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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:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.a (trivial)

\(f(q)\)	\(=\)	\(q-0.414214 q^{2} -1.00000 q^{3} -1.82843 q^{4} +0.414214 q^{6} +1.00000 q^{7} +1.58579 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.414214 q^{2} -1.00000 q^{3} -1.82843 q^{4} +0.414214 q^{6} +1.00000 q^{7} +1.58579 q^{8} +1.00000 q^{9} +2.00000 q^{11} +1.82843 q^{12} -1.00000 q^{13} -0.414214 q^{14} +3.00000 q^{16} +4.82843 q^{17} -0.414214 q^{18} +5.65685 q^{19} -1.00000 q^{21} -0.828427 q^{22} +6.82843 q^{23} -1.58579 q^{24} -5.00000 q^{25} +0.414214 q^{26} -1.00000 q^{27} -1.82843 q^{28} +7.65685 q^{29} -9.65685 q^{31} -4.41421 q^{32} -2.00000 q^{33} -2.00000 q^{34} -1.82843 q^{36} +3.65685 q^{37} -2.34315 q^{38} +1.00000 q^{39} -5.65685 q^{41} +0.414214 q^{42} -1.65685 q^{43} -3.65685 q^{44} -2.82843 q^{46} +8.82843 q^{47} -3.00000 q^{48} +1.00000 q^{49} +2.07107 q^{50} -4.82843 q^{51} +1.82843 q^{52} -7.65685 q^{53} +0.414214 q^{54} +1.58579 q^{56} -5.65685 q^{57} -3.17157 q^{58} +6.48528 q^{59} -11.6569 q^{61} +4.00000 q^{62} +1.00000 q^{63} -4.17157 q^{64} +0.828427 q^{66} +4.00000 q^{67} -8.82843 q^{68} -6.82843 q^{69} +14.0000 q^{71} +1.58579 q^{72} +3.65685 q^{73} -1.51472 q^{74} +5.00000 q^{75} -10.3431 q^{76} +2.00000 q^{77} -0.414214 q^{78} +11.3137 q^{79} +1.00000 q^{81} +2.34315 q^{82} -12.1421 q^{83} +1.82843 q^{84} +0.686292 q^{86} -7.65685 q^{87} +3.17157 q^{88} -7.31371 q^{89} -1.00000 q^{91} -12.4853 q^{92} +9.65685 q^{93} -3.65685 q^{94} +4.41421 q^{96} -2.00000 q^{97} -0.414214 q^{98} +2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{6} + 2 q^{7} + 6 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 - 2 * q^6 + 2 * q^7 + 6 * q^8 + 2 * q^9	\( 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{6} + 2 q^{7} + 6 q^{8} + 2 q^{9} + 4 q^{11} - 2 q^{12} - 2 q^{13} + 2 q^{14} + 6 q^{16} + 4 q^{17} + 2 q^{18} - 2 q^{21} + 4 q^{22} + 8 q^{23} - 6 q^{24} - 10 q^{25} - 2 q^{26} - 2 q^{27} + 2 q^{28} + 4 q^{29} - 8 q^{31} - 6 q^{32} - 4 q^{33} - 4 q^{34} + 2 q^{36} - 4 q^{37} - 16 q^{38} + 2 q^{39} - 2 q^{42} + 8 q^{43} + 4 q^{44} + 12 q^{47} - 6 q^{48} + 2 q^{49} - 10 q^{50} - 4 q^{51} - 2 q^{52} - 4 q^{53} - 2 q^{54} + 6 q^{56} - 12 q^{58} - 4 q^{59} - 12 q^{61} + 8 q^{62} + 2 q^{63} - 14 q^{64} - 4 q^{66} + 8 q^{67} - 12 q^{68} - 8 q^{69} + 28 q^{71} + 6 q^{72} - 4 q^{73} - 20 q^{74} + 10 q^{75} - 32 q^{76} + 4 q^{77} + 2 q^{78} + 2 q^{81} + 16 q^{82} + 4 q^{83} - 2 q^{84} + 24 q^{86} - 4 q^{87} + 12 q^{88} + 8 q^{89} - 2 q^{91} - 8 q^{92} + 8 q^{93} + 4 q^{94} + 6 q^{96} - 4 q^{97} + 2 q^{98} + 4 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 - 2 * q^6 + 2 * q^7 + 6 * q^8 + 2 * q^9 + 4 * q^11 - 2 * q^12 - 2 * q^13 + 2 * q^14 + 6 * q^16 + 4 * q^17 + 2 * q^18 - 2 * q^21 + 4 * q^22 + 8 * q^23 - 6 * q^24 - 10 * q^25 - 2 * q^26 - 2 * q^27 + 2 * q^28 + 4 * q^29 - 8 * q^31 - 6 * q^32 - 4 * q^33 - 4 * q^34 + 2 * q^36 - 4 * q^37 - 16 * q^38 + 2 * q^39 - 2 * q^42 + 8 * q^43 + 4 * q^44 + 12 * q^47 - 6 * q^48 + 2 * q^49 - 10 * q^50 - 4 * q^51 - 2 * q^52 - 4 * q^53 - 2 * q^54 + 6 * q^56 - 12 * q^58 - 4 * q^59 - 12 * q^61 + 8 * q^62 + 2 * q^63 - 14 * q^64 - 4 * q^66 + 8 * q^67 - 12 * q^68 - 8 * q^69 + 28 * q^71 + 6 * q^72 - 4 * q^73 - 20 * q^74 + 10 * q^75 - 32 * q^76 + 4 * q^77 + 2 * q^78 + 2 * q^81 + 16 * q^82 + 4 * q^83 - 2 * q^84 + 24 * q^86 - 4 * q^87 + 12 * q^88 + 8 * q^89 - 2 * q^91 - 8 * q^92 + 8 * q^93 + 4 * q^94 + 6 * q^96 - 4 * q^97 + 2 * q^98 + 4 * q^99

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