LMFDB - Embedded newform 1617.2.a.u.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1617,2,Mod(1,1617)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1617, 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("1617.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1617 = 3 \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1617.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:	$12.9118100068$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.2624.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 3x^{2} + 2x + 1 $ x^4 - 2x^3 - 3x^2 + 2*x + 1
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			1.2
Root			$-0.360409$ of defining polynomial
Character	$\chi$	$=$	1617.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.36041 q^{2} -1.00000 q^{3} -0.149286 q^{4} -0.923909 q^{5} +1.36041 q^{6} +2.92391 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.36041 q^{2} -1.00000 q^{3} -0.149286 q^{4} -0.923909 q^{5} +1.36041 q^{6} +2.92391 q^{8} +1.00000 q^{9} +1.25689 q^{10} +1.00000 q^{11} +0.149286 q^{12} +3.29857 q^{13} +0.923909 q^{15} -3.67914 q^{16} +3.03955 q^{17} -1.36041 q^{18} +3.52985 q^{19} +0.137927 q^{20} -1.36041 q^{22} -8.88737 q^{23} -2.92391 q^{24} -4.14639 q^{25} -4.48741 q^{26} -1.00000 q^{27} +1.75234 q^{29} -1.25689 q^{30} -2.05894 q^{31} -0.842681 q^{32} -1.00000 q^{33} -4.13503 q^{34} -0.149286 q^{36} -3.40618 q^{37} -4.80205 q^{38} -3.29857 q^{39} -2.70143 q^{40} -5.38571 q^{41} +11.8954 q^{43} -0.149286 q^{44} -0.923909 q^{45} +12.0905 q^{46} +7.37466 q^{47} +3.67914 q^{48} +5.64079 q^{50} -3.03955 q^{51} -0.492432 q^{52} -7.23051 q^{53} +1.36041 q^{54} -0.923909 q^{55} -3.52985 q^{57} -2.38389 q^{58} +3.11487 q^{59} -0.137927 q^{60} +6.86721 q^{61} +2.80100 q^{62} +8.50467 q^{64} -3.04758 q^{65} +1.36041 q^{66} +4.15551 q^{67} -0.453764 q^{68} +8.88737 q^{69} -7.94407 q^{71} +2.92391 q^{72} -1.21522 q^{73} +4.63380 q^{74} +4.14639 q^{75} -0.526959 q^{76} +4.48741 q^{78} +3.57775 q^{79} +3.39919 q^{80} +1.00000 q^{81} +7.32676 q^{82} +8.84859 q^{83} -2.80827 q^{85} -16.1826 q^{86} -1.75234 q^{87} +2.92391 q^{88} -11.5880 q^{89} +1.25689 q^{90} +1.32676 q^{92} +2.05894 q^{93} -10.0326 q^{94} -3.26127 q^{95} +0.842681 q^{96} +2.56563 q^{97} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 4 q^{3} + 2 q^{4} + 8 q^{5} + 2 q^{6} + 4 q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 - 4 * q^3 + 2 * q^4 + 8 * q^5 + 2 * q^6 + 4 * q^9	$ 4 q - 2 q^{2} - 4 q^{3} + 2 q^{4} + 8 q^{5} + 2 q^{6} + 4 q^{9} - 2 q^{10} + 4 q^{11} - 2 q^{12} + 8 q^{13} - 8 q^{15} - 6 q^{16} - 2 q^{18} + 8 q^{19} + 14 q^{20} - 2 q^{22} + 12 q^{25} + 2 q^{26} - 4 q^{27} - 16 q^{29} + 2 q^{30} + 16 q^{31} - 2 q^{32} - 4 q^{33} - 4 q^{34} + 2 q^{36} - 4 q^{37} - 2 q^{38} - 8 q^{39} - 16 q^{40} + 4 q^{41} + 16 q^{43} + 2 q^{44} + 8 q^{45} + 8 q^{46} + 36 q^{47} + 6 q^{48} - 8 q^{50} - 22 q^{52} - 16 q^{53} + 2 q^{54} + 8 q^{55} - 8 q^{57} + 14 q^{58} - 14 q^{60} - 8 q^{61} + 8 q^{62} - 12 q^{64} - 4 q^{65} + 2 q^{66} + 20 q^{67} + 16 q^{68} - 20 q^{71} + 4 q^{73} - 30 q^{74} - 12 q^{75} + 30 q^{76} - 2 q^{78} + 16 q^{79} - 14 q^{80} + 4 q^{81} + 28 q^{82} + 24 q^{83} - 44 q^{86} + 16 q^{87} - 4 q^{89} - 2 q^{90} + 4 q^{92} - 16 q^{93} - 10 q^{94} + 28 q^{95} + 2 q^{96} + 16 q^{97} + 4 q^{99}+O(q^{100}) $ 4 * q - 2 * q^2 - 4 * q^3 + 2 * q^4 + 8 * q^5 + 2 * q^6 + 4 * q^9 - 2 * q^10 + 4 * q^11 - 2 * q^12 + 8 * q^13 - 8 * q^15 - 6 * q^16 - 2 * q^18 + 8 * q^19 + 14 * q^20 - 2 * q^22 + 12 * q^25 + 2 * q^26 - 4 * q^27 - 16 * q^29 + 2 * q^30 + 16 * q^31 - 2 * q^32 - 4 * q^33 - 4 * q^34 + 2 * q^36 - 4 * q^37 - 2 * q^38 - 8 * q^39 - 16 * q^40 + 4 * q^41 + 16 * q^43 + 2 * q^44 + 8 * q^45 + 8 * q^46 + 36 * q^47 + 6 * q^48 - 8 * q^50 - 22 * q^52 - 16 * q^53 + 2 * q^54 + 8 * q^55 - 8 * q^57 + 14 * q^58 - 14 * q^60 - 8 * q^61 + 8 * q^62 - 12 * q^64 - 4 * q^65 + 2 * q^66 + 20 * q^67 + 16 * q^68 - 20 * q^71 + 4 * q^73 - 30 * q^74 - 12 * q^75 + 30 * q^76 - 2 * q^78 + 16 * q^79 - 14 * q^80 + 4 * q^81 + 28 * q^82 + 24 * q^83 - 44 * q^86 + 16 * q^87 - 4 * q^89 - 2 * q^90 + 4 * q^92 - 16 * q^93 - 10 * q^94 + 28 * q^95 + 2 * q^96 + 16 * q^97 + 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 $

$2$	−1.36041	−0.961955	−0.480977	−	0.876733i	$-0.659718\pi$
$2$	−1.36041	−0.961955	−0.480977	+	0.876733i	$0.659718\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−0.149286	−0.0746432
$5$	−0.923909	−0.413185	−0.206592	−	0.978427i	$-0.566237\pi$
$5$	−0.923909	−0.413185	−0.206592	+	0.978427i	$0.566237\pi$
$6$	1.36041	0.555385
$7$	0	0
$7$	0	0
$8$	2.92391	1.03376
$9$	1.00000	0.333333
$10$	1.25689	0.397465
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	0.149286	0.0430953
$13$	3.29857	0.914860	0.457430	−	0.889246i	$-0.348770\pi$
$13$	3.29857	0.914860	0.457430	+	0.889246i	$0.348770\pi$
$14$	0	0
$15$	0.923909	0.238552
$16$	−3.67914	−0.919785
$17$	3.03955	0.737199	0.368600	−	0.929588i	$-0.379837\pi$
$17$	3.03955	0.737199	0.368600	+	0.929588i	$0.379837\pi$
$18$	−1.36041	−0.320652
$19$	3.52985	0.809804	0.404902	−	0.914360i	$-0.367306\pi$
$19$	3.52985	0.809804	0.404902	+	0.914360i	$0.367306\pi$
$20$	0.137927	0.0308414
$21$	0	0
$22$	−1.36041	−0.290040
$23$	−8.88737	−1.85314	−0.926572	−	0.376117i	$-0.877259\pi$
$23$	−8.88737	−1.85314	−0.926572	+	0.376117i	$0.877259\pi$
$24$	−2.92391	−0.596840
$25$	−4.14639	−0.829278
$26$	−4.48741	−0.880053
$27$	−1.00000	−0.192450
$28$	0	0
$29$	1.75234	0.325401	0.162700	−	0.986676i	$-0.447980\pi$
$29$	1.75234	0.325401	0.162700	+	0.986676i	$0.447980\pi$
$30$	−1.25689	−0.229477
$31$	−2.05894	−0.369797	−0.184898	−	0.982758i	$-0.559196\pi$
$31$	−2.05894	−0.369797	−0.184898	+	0.982758i	$0.559196\pi$
$32$	−0.842681	−0.148966
$33$	−1.00000	−0.174078
$34$	−4.13503	−0.709152
$35$	0	0
$36$	−0.149286	−0.0248811
$37$	−3.40618	−0.559973	−0.279986	−	0.960004i	$-0.590330\pi$
$37$	−3.40618	−0.559973	−0.279986	+	0.960004i	$0.590330\pi$
$38$	−4.80205	−0.778995
$39$	−3.29857	−0.528194
$40$	−2.70143	−0.427133
$41$	−5.38571	−0.841106	−0.420553	−	0.907268i	$-0.638164\pi$
$41$	−5.38571	−0.841106	−0.420553	+	0.907268i	$0.638164\pi$
$42$	0	0
$43$	11.8954	1.81403	0.907016	−	0.421097i	$-0.138355\pi$
$43$	11.8954	1.81403	0.907016	+	0.421097i	$0.138355\pi$
$44$	−0.149286	−0.0225058
$45$	−0.923909	−0.137728
$46$	12.0905	1.78264
$47$	7.37466	1.07571	0.537853	−	0.843039i	$-0.319236\pi$
$47$	7.37466	1.07571	0.537853	+	0.843039i	$0.319236\pi$
$48$	3.67914	0.531038
$49$	0	0
$50$	5.64079	0.797728
$51$	−3.03955	−0.425622
$52$	−0.492432	−0.0682881
$53$	−7.23051	−0.993188	−0.496594	−	0.867983i	$-0.665416\pi$
$53$	−7.23051	−0.993188	−0.496594	+	0.867983i	$0.665416\pi$
$54$	1.36041	0.185128
$55$	−0.923909	−0.124580
$56$	0	0
$57$	−3.52985	−0.467541
$58$	−2.38389	−0.313021
$59$	3.11487	0.405522	0.202761	−	0.979228i	$-0.435009\pi$
$59$	3.11487	0.405522	0.202761	+	0.979228i	$0.435009\pi$
$60$	−0.137927	−0.0178063
$61$	6.86721	0.879256	0.439628	−	0.898180i	$-0.355110\pi$
$61$	6.86721	0.879256	0.439628	+	0.898180i	$0.355110\pi$
$62$	2.80100	0.355728
$63$	0	0
$64$	8.50467	1.06308
$65$	−3.04758	−0.378006
$66$	1.36041	0.167455
$67$	4.15551	0.507676	0.253838	−	0.967247i	$-0.418307\pi$
$67$	4.15551	0.507676	0.253838	+	0.967247i	$0.418307\pi$
$68$	−0.453764	−0.0550269
$69$	8.88737	1.06991
$70$	0	0
$71$	−7.94407	−0.942787	−0.471394	−	0.881923i	$-0.656249\pi$
$71$	−7.94407	−0.942787	−0.471394	+	0.881923i	$0.656249\pi$
$72$	2.92391	0.344586
$73$	−1.21522	−0.142230	−0.0711152	−	0.997468i	$-0.522656\pi$
$73$	−1.21522	−0.142230	−0.0711152	+	0.997468i	$0.522656\pi$
$74$	4.63380	0.538668
$75$	4.14639	0.478784
$76$	−0.526959	−0.0604464
$77$	0	0
$78$	4.48741	0.508099
$79$	3.57775	0.402529	0.201264	−	0.979537i	$-0.435495\pi$
$79$	3.57775	0.402529	0.201264	+	0.979537i	$0.435495\pi$
$80$	3.39919	0.380041
$81$	1.00000	0.111111
$82$	7.32676	0.809106
$83$	8.84859	0.971258	0.485629	−	0.874165i	$-0.338591\pi$
$83$	8.84859	0.971258	0.485629	+	0.874165i	$0.338591\pi$
$84$	0	0
$85$	−2.80827	−0.304600
$86$	−16.1826	−1.74502
$87$	−1.75234	−0.187870
$88$	2.92391	0.311690
$89$	−11.5880	−1.22833	−0.614164	−	0.789178i	$-0.710507\pi$
$89$	−11.5880	−1.22833	−0.614164	+	0.789178i	$0.710507\pi$
$90$	1.25689	0.132488
$91$	0	0
$92$	1.32676	0.138325
$93$	2.05894	0.213502
$94$	−10.0326	−1.03478
$95$	−3.26127	−0.334599
$96$	0.842681	0.0860058
$97$	2.56563	0.260500	0.130250	−	0.991481i	$-0.458422\pi$
$97$	2.56563	0.260500	0.130250	+	0.991481i	$0.458422\pi$
$98$	0	0
$99$	1.00000	0.100504
$100$	0.619000	0.0619000
$101$	15.4845	1.54077	0.770383	−	0.637581i	$-0.220065\pi$
$101$	15.4845	1.54077	0.770383	+	0.637581i	$0.220065\pi$
$102$	4.13503	0.409429
$103$	19.1259	1.88453	0.942266	−	0.334865i	$-0.108691\pi$
$103$	19.1259	1.88453	0.942266	+	0.334865i	$0.108691\pi$
$104$	9.64473	0.945743
$105$	0	0
$106$	9.83646	0.955401
$107$	−5.75234	−0.556099	−0.278050	−	0.960567i	$-0.589688\pi$
$107$	−5.75234	−0.556099	−0.278050	+	0.960567i	$0.589688\pi$
$108$	0.149286	0.0143651
$109$	8.46512	0.810812	0.405406	−	0.914137i	$-0.367130\pi$
$109$	8.46512	0.810812	0.405406	+	0.914137i	$0.367130\pi$
$110$	1.25689	0.119840
$111$	3.40618	0.323300
$112$	0	0
$113$	−6.27115	−0.589940	−0.294970	−	0.955507i	$-0.595310\pi$
$113$	−6.27115	−0.589940	−0.294970	+	0.955507i	$0.595310\pi$
$114$	4.80205	0.449753
$115$	8.21112	0.765691
$116$	−0.261600	−0.0242890
$117$	3.29857	0.304953
$118$	−4.23750	−0.390094
$119$	0	0
$120$	2.70143	0.246605
$121$	1.00000	0.0909091
$122$	−9.34222	−0.845805
$123$	5.38571	0.485613
$124$	0.307372	0.0276028
$125$	8.45044	0.755830
$126$	0	0
$127$	−1.25794	−0.111624	−0.0558120	−	0.998441i	$-0.517775\pi$
$127$	−1.25794	−0.111624	−0.0558120	+	0.998441i	$0.517775\pi$
$128$	−9.88447	−0.873672
$129$	−11.8954	−1.04733
$130$	4.14596	0.363625
$131$	0.478178	0.0417786	0.0208893	−	0.999782i	$-0.493350\pi$
$131$	0.478178	0.0417786	0.0208893	+	0.999782i	$0.493350\pi$
$132$	0.149286	0.0129937
$133$	0	0
$134$	−5.65319	−0.488361
$135$	0.923909	0.0795175
$136$	8.88737	0.762086
$137$	−1.76462	−0.150762	−0.0753810	−	0.997155i	$-0.524017\pi$
$137$	−1.76462	−0.150762	−0.0753810	+	0.997155i	$0.524017\pi$
$138$	−12.0905	−1.02921
$139$	−3.91664	−0.332205	−0.166103	−	0.986108i	$-0.553118\pi$
$139$	−3.91664	−0.332205	−0.166103	+	0.986108i	$0.553118\pi$
$140$	0	0
$141$	−7.37466	−0.621059
$142$	10.8072	0.906919
$143$	3.29857	0.275841
$144$	−3.67914	−0.306595
$145$	−1.61900	−0.134451
$146$	1.65319	0.136819
$147$	0	0
$148$	0.508497	0.0417982
$149$	1.61622	0.132406	0.0662029	−	0.997806i	$-0.478912\pi$
$149$	1.61622	0.132406	0.0662029	+	0.997806i	$0.478912\pi$
$150$	−5.64079	−0.460569
$151$	21.9616	1.78721	0.893605	−	0.448854i	$-0.148168\pi$
$151$	21.9616	1.78721	0.893605	+	0.448854i	$0.148168\pi$
$152$	10.3210	0.837142
$153$	3.03955	0.245733
$154$	0	0
$155$	1.90228	0.152794
$156$	0.492432	0.0394261
$157$	7.03546	0.561491	0.280745	−	0.959782i	$-0.409418\pi$
$157$	7.03546	0.561491	0.280745	+	0.959782i	$0.409418\pi$
$158$	−4.86721	−0.387214
$159$	7.23051	0.573417
$160$	0.778561	0.0615507
$161$	0	0
$162$	−1.36041	−0.106884
$163$	20.9496	1.64090	0.820451	−	0.571717i	$-0.193722\pi$
$163$	20.9496	1.64090	0.820451	+	0.571717i	$0.193722\pi$
$164$	0.804013	0.0627828
$165$	0.923909	0.0719262
$166$	−12.0377	−0.934307
$167$	16.2499	1.25746	0.628728	−	0.777626i	$-0.283576\pi$
$167$	16.2499	1.25746	0.628728	+	0.777626i	$0.283576\pi$
$168$	0	0
$169$	−2.11942	−0.163032
$170$	3.82039	0.293011
$171$	3.52985	0.269935
$172$	−1.77582	−0.135405
$173$	−13.2895	−1.01038	−0.505189	−	0.863009i	$-0.668577\pi$
$173$	−13.2895	−1.01038	−0.505189	+	0.863009i	$0.668577\pi$
$174$	2.38389	0.180723
$175$	0	0
$176$	−3.67914	−0.277326
$177$	−3.11487	−0.234128
$178$	15.7645	1.18160
$179$	−22.4122	−1.67517	−0.837583	−	0.546310i	$-0.816032\pi$
$179$	−22.4122	−1.67517	−0.837583	+	0.546310i	$0.816032\pi$
$180$	0.137927	0.0102805
$181$	4.00727	0.297858	0.148929	−	0.988848i	$-0.452417\pi$
$181$	4.00727	0.297858	0.148929	+	0.988848i	$0.452417\pi$
$182$	0	0
$183$	−6.86721	−0.507639
$184$	−25.9859	−1.91570
$185$	3.14700	0.231372
$186$	−2.80100	−0.205380
$187$	3.03955	0.222274
$188$	−1.10094	−0.0802941
$189$	0	0
$190$	4.43666	0.321869
$191$	22.4640	1.62544	0.812720	−	0.582654i	$-0.197986\pi$
$191$	22.4640	1.62544	0.812720	+	0.582654i	$0.197986\pi$
$192$	−8.50467	−0.613772
$193$	10.4651	0.753296	0.376648	−	0.926356i	$-0.377077\pi$
$193$	10.4651	0.753296	0.376648	+	0.926356i	$0.377077\pi$
$194$	−3.49030	−0.250589
$195$	3.04758	0.218242
$196$	0	0
$197$	−5.74174	−0.409082	−0.204541	−	0.978858i	$-0.565570\pi$
$197$	−5.74174	−0.409082	−0.204541	+	0.978858i	$0.565570\pi$
$198$	−1.36041	−0.0966801
$199$	5.85662	0.415165	0.207582	−	0.978218i	$-0.433441\pi$
$199$	5.85662	0.415165	0.207582	+	0.978218i	$0.433441\pi$
$200$	−12.1237	−0.857273
$201$	−4.15551	−0.293107
$202$	−21.0653	−1.48215
$203$	0	0
$204$	0.453764	0.0317698
$205$	4.97590	0.347532
$206$	−26.0191	−1.81283
$207$	−8.88737	−0.617715
$208$	−12.1359	−0.841474
$209$	3.52985	0.244165
$210$	0	0
$211$	−20.4122	−1.40523	−0.702617	−	0.711568i	$-0.747985\pi$
$211$	−20.4122	−1.40523	−0.702617	+	0.711568i	$0.747985\pi$
$212$	1.07942	0.0741347
$213$	7.94407	0.544319
$214$	7.82553	0.534942
$215$	−10.9903	−0.749530
$216$	−2.92391	−0.198947
$217$	0	0
$218$	−11.5160	−0.779964
$219$	1.21522	0.0821167
$220$	0.137927	0.00929905
$221$	10.0262	0.674434
$222$	−4.63380	−0.311000
$223$	−19.8926	−1.33211	−0.666054	−	0.745903i	$-0.732018\pi$
$223$	−19.8926	−1.33211	−0.666054	+	0.745903i	$0.732018\pi$
$224$	0	0
$225$	−4.14639	−0.276426
$226$	8.53133	0.567496
$227$	27.7415	1.84127	0.920635	−	0.390425i	$-0.127672\pi$
$227$	27.7415	1.84127	0.920635	+	0.390425i	$0.127672\pi$
$228$	0.526959	0.0348987
$229$	21.1187	1.39556	0.697780	−	0.716312i	$-0.254171\pi$
$229$	21.1187	1.39556	0.697780	+	0.716312i	$0.254171\pi$
$230$	−11.1705	−0.736560
$231$	0	0
$232$	5.12367	0.336386
$233$	8.22549	0.538870	0.269435	−	0.963019i	$-0.413163\pi$
$233$	8.22549	0.538870	0.269435	+	0.963019i	$0.413163\pi$
$234$	−4.48741	−0.293351
$235$	−6.81352	−0.444465
$236$	−0.465008	−0.0302695
$237$	−3.57775	−0.232400
$238$	0	0
$239$	−4.05517	−0.262307	−0.131153	−	0.991362i	$-0.541868\pi$
$239$	−4.05517	−0.262307	−0.131153	+	0.991362i	$0.541868\pi$
$240$	−3.39919	−0.219417
$241$	5.56864	0.358707	0.179354	−	0.983785i	$-0.442599\pi$
$241$	5.56864	0.358707	0.179354	+	0.983785i	$0.442599\pi$
$242$	−1.36041	−0.0874504
$243$	−1.00000	−0.0641500
$244$	−1.02518	−0.0656305
$245$	0	0
$246$	−7.32676	−0.467137
$247$	11.6435	0.740857
$248$	−6.02016	−0.382280
$249$	−8.84859	−0.560756
$250$	−11.4961	−0.727074
$251$	−9.94483	−0.627712	−0.313856	−	0.949471i	$-0.601621\pi$
$251$	−9.94483	−0.627712	−0.313856	+	0.949471i	$0.601621\pi$
$252$	0	0
$253$	−8.88737	−0.558744
$254$	1.71131	0.107377
$255$	2.80827	0.175861
$256$	−3.56242	−0.222651
$257$	23.3279	1.45516	0.727578	−	0.686025i	$-0.240646\pi$
$257$	23.3279	1.45516	0.727578	+	0.686025i	$0.240646\pi$
$258$	16.1826	1.00749
$259$	0	0
$260$	0.454963	0.0282156
$261$	1.75234	0.108467
$262$	−0.650518	−0.0401891
$263$	14.9972	0.924768	0.462384	−	0.886680i	$-0.346994\pi$
$263$	14.9972	0.924768	0.462384	+	0.886680i	$0.346994\pi$
$264$	−2.92391	−0.179954
$265$	6.68034	0.410370
$266$	0	0
$267$	11.5880	0.709176
$268$	−0.620361	−0.0378946
$269$	18.0630	1.10132	0.550661	−	0.834729i	$-0.314376\pi$
$269$	18.0630	1.10132	0.550661	+	0.834729i	$0.314376\pi$
$270$	−1.25689	−0.0764922
$271$	28.8538	1.75275	0.876373	−	0.481633i	$-0.159956\pi$
$271$	28.8538	1.75275	0.876373	+	0.481633i	$0.159956\pi$
$272$	−11.1829	−0.678065
$273$	0	0
$274$	2.40061	0.145026
$275$	−4.14639	−0.250037
$276$	−1.32676	−0.0798618
$277$	16.5288	0.993118	0.496559	−	0.868003i	$-0.334597\pi$
$277$	16.5288	0.993118	0.496559	+	0.868003i	$0.334597\pi$
$278$	5.32824	0.319567
$279$	−2.05894	−0.123266
$280$	0	0
$281$	6.04272	0.360479	0.180239	−	0.983623i	$-0.442313\pi$
$281$	6.04272	0.360479	0.180239	+	0.983623i	$0.442313\pi$
$282$	10.0326	0.597430
$283$	−12.9027	−0.766984	−0.383492	−	0.923544i	$-0.625279\pi$
$283$	−12.9027	−0.766984	−0.383492	+	0.923544i	$0.625279\pi$
$284$	1.18594	0.0703727
$285$	3.26127	0.193181
$286$	−4.48741	−0.265346
$287$	0	0
$288$	−0.842681	−0.0496555
$289$	−7.76114	−0.456537
$290$	2.20250	0.129335
$291$	−2.56563	−0.150400
$292$	0.181415	0.0106165
$293$	−11.4256	−0.667489	−0.333745	−	0.942664i	$-0.608312\pi$
$293$	−11.4256	−0.667489	−0.333745	+	0.942664i	$0.608312\pi$
$294$	0	0
$295$	−2.87786	−0.167556
$296$	−9.95937	−0.578876
$297$	−1.00000	−0.0580259
$298$	−2.19872	−0.127368
$299$	−29.3156	−1.69537
$300$	−0.619000	−0.0357380
$301$	0	0
$302$	−29.8768	−1.71922
$303$	−15.4845	−0.889562
$304$	−12.9868	−0.744846
$305$	−6.34468	−0.363295
$306$	−4.13503	−0.236384
$307$	3.71170	0.211838	0.105919	−	0.994375i	$-0.466222\pi$
$307$	3.71170	0.211838	0.105919	+	0.994375i	$0.466222\pi$
$308$	0	0
$309$	−19.1259	−1.08804
$310$	−2.58787	−0.146981
$311$	−5.89239	−0.334127	−0.167063	−	0.985946i	$-0.553428\pi$
$311$	−5.89239	−0.334127	−0.167063	+	0.985946i	$0.553428\pi$
$312$	−9.64473	−0.546025
$313$	−19.1735	−1.08375	−0.541875	−	0.840459i	$-0.682285\pi$
$313$	−19.1735	−1.08375	−0.541875	+	0.840459i	$0.682285\pi$
$314$	−9.57110	−0.540128
$315$	0	0
$316$	−0.534110	−0.0300460
$317$	3.29247	0.184923	0.0924616	−	0.995716i	$-0.470526\pi$
$317$	3.29247	0.184923	0.0924616	+	0.995716i	$0.470526\pi$
$318$	−9.83646	−0.551601
$319$	1.75234	0.0981120
$320$	−7.85755	−0.439250
$321$	5.75234	0.321064
$322$	0	0
$323$	10.7292	0.596987
$324$	−0.149286	−0.00829369
$325$	−13.6772	−0.758673
$326$	−28.5001	−1.57847
$327$	−8.46512	−0.468122
$328$	−15.7473	−0.869500
$329$	0	0
$330$	−1.25689	−0.0691898
$331$	3.82510	0.210247	0.105123	−	0.994459i	$-0.466476\pi$
$331$	3.82510	0.210247	0.105123	+	0.994459i	$0.466476\pi$
$332$	−1.32097	−0.0724979
$333$	−3.40618	−0.186658
$334$	−22.1065	−1.20962
$335$	−3.83931	−0.209764
$336$	0	0
$337$	34.0634	1.85555	0.927777	−	0.373136i	$-0.121718\pi$
$337$	34.0634	1.85555	0.927777	+	0.373136i	$0.121718\pi$
$338$	2.88327	0.156829
$339$	6.27115	0.340602
$340$	0.419236	0.0227363
$341$	−2.05894	−0.111498
$342$	−4.80205	−0.259665
$343$	0	0
$344$	34.7811	1.87527
$345$	−8.21112	−0.442072
$346$	18.0791	0.971938
$347$	−22.6377	−1.21525	−0.607627	−	0.794222i	$-0.707879\pi$
$347$	−22.6377	−1.21525	−0.607627	+	0.794222i	$0.707879\pi$
$348$	0.261600	0.0140232
$349$	−33.1406	−1.77398	−0.886988	−	0.461793i	$-0.847206\pi$
$349$	−33.1406	−1.77398	−0.886988	+	0.461793i	$0.847206\pi$
$350$	0	0
$351$	−3.29857	−0.176065
$352$	−0.842681	−0.0449151
$353$	−21.2833	−1.13280	−0.566399	−	0.824131i	$-0.691664\pi$
$353$	−21.2833	−1.13280	−0.566399	+	0.824131i	$0.691664\pi$
$354$	4.23750	0.225221
$355$	7.33960	0.389545
$356$	1.72994	0.0916864
$357$	0	0
$358$	30.4898	1.61143
$359$	12.8387	0.677601	0.338800	−	0.940858i	$-0.389979\pi$
$359$	12.8387	0.677601	0.338800	+	0.940858i	$0.389979\pi$
$360$	−2.70143	−0.142378
$361$	−6.54013	−0.344217
$362$	−5.45152	−0.286526
$363$	−1.00000	−0.0524864
$364$	0	0
$365$	1.12275	0.0587674
$366$	9.34222	0.488325
$367$	36.1970	1.88947	0.944734	−	0.327839i	$-0.106320\pi$
$367$	36.1970	1.88947	0.944734	+	0.327839i	$0.106320\pi$
$368$	32.6979	1.70449
$369$	−5.38571	−0.280369
$370$	−4.28121	−0.222570
$371$	0	0
$372$	−0.307372	−0.0159365
$373$	17.7372	0.918397	0.459199	−	0.888334i	$-0.348137\pi$
$373$	17.7372	0.918397	0.459199	+	0.888334i	$0.348137\pi$
$374$	−4.13503	−0.213817
$375$	−8.45044	−0.436379
$376$	21.5628	1.11202
$377$	5.78021	0.297696
$378$	0	0
$379$	−31.2315	−1.60425	−0.802127	−	0.597153i	$-0.796299\pi$
$379$	−31.2315	−1.60425	−0.802127	+	0.597153i	$0.796299\pi$
$380$	0.486863	0.0249755
$381$	1.25794	0.0644461
$382$	−30.5603	−1.56360
$383$	3.71749	0.189955	0.0949775	−	0.995479i	$-0.469722\pi$
$383$	3.71749	0.189955	0.0949775	+	0.995479i	$0.469722\pi$
$384$	9.88447	0.504415
$385$	0	0
$386$	−14.2369	−0.724637
$387$	11.8954	0.604677
$388$	−0.383013	−0.0194446
$389$	−0.421161	−0.0213537	−0.0106769	−	0.999943i	$-0.503399\pi$
$389$	−0.421161	−0.0213537	−0.0106769	+	0.999943i	$0.503399\pi$
$390$	−4.14596	−0.209939
$391$	−27.0136	−1.36614
$392$	0	0
$393$	−0.478178	−0.0241209
$394$	7.81112	0.393519
$395$	−3.30552	−0.166319
$396$	−0.149286	−0.00750193
$397$	−36.1265	−1.81314	−0.906568	−	0.422061i	$-0.861307\pi$
$397$	−36.1265	−1.81314	−0.906568	+	0.422061i	$0.861307\pi$
$398$	−7.96740	−0.399370
$399$	0	0
$400$	15.2552	0.762758
$401$	14.6405	0.731110	0.365555	−	0.930790i	$-0.380879\pi$
$401$	14.6405	0.731110	0.365555	+	0.930790i	$0.380879\pi$
$402$	5.65319	0.281956
$403$	−6.79157	−0.338312
$404$	−2.31163	−0.115008
$405$	−0.923909	−0.0459094
$406$	0	0
$407$	−3.40618	−0.168838
$408$	−8.88737	−0.439990
$409$	−40.2703	−1.99124	−0.995619	−	0.0935037i	$-0.970193\pi$
$409$	−40.2703	−1.99124	−0.995619	+	0.0935037i	$0.970193\pi$
$410$	−6.76927	−0.334310
$411$	1.76462	0.0870425
$412$	−2.85524	−0.140668
$413$	0	0
$414$	12.0905	0.594214
$415$	−8.17529	−0.401309
$416$	−2.77965	−0.136283
$417$	3.91664	0.191799
$418$	−4.80205	−0.234876
$419$	−6.68235	−0.326454	−0.163227	−	0.986589i	$-0.552190\pi$
$419$	−6.68235	−0.326454	−0.163227	+	0.986589i	$0.552190\pi$
$420$	0	0
$421$	−1.31889	−0.0642789	−0.0321395	−	0.999483i	$-0.510232\pi$
$421$	−1.31889	−0.0642789	−0.0321395	+	0.999483i	$0.510232\pi$
$422$	27.7689	1.35177
$423$	7.37466	0.358568
$424$	−21.1414	−1.02672
$425$	−12.6032	−0.611343
$426$	−10.8072	−0.523610
$427$	0	0
$428$	0.858746	0.0415090
$429$	−3.29857	−0.159257
$430$	14.9513	0.721014
$431$	31.4928	1.51695	0.758477	−	0.651700i	$-0.225944\pi$
$431$	31.4928	1.51695	0.758477	+	0.651700i	$0.225944\pi$
$432$	3.67914	0.177013
$433$	30.8168	1.48096	0.740482	−	0.672077i	$-0.234597\pi$
$433$	30.8168	1.48096	0.740482	+	0.672077i	$0.234597\pi$
$434$	0	0
$435$	1.61900	0.0776251
$436$	−1.26373	−0.0605216
$437$	−31.3711	−1.50068
$438$	−1.65319	−0.0789926
$439$	−17.1163	−0.816919	−0.408459	−	0.912776i	$-0.633934\pi$
$439$	−17.1163	−0.816919	−0.408459	+	0.912776i	$0.633934\pi$
$440$	−2.70143	−0.128785
$441$	0	0
$442$	−13.6397	−0.648775
$443$	23.7979	1.13067	0.565336	−	0.824861i	$-0.308746\pi$
$443$	23.7979	1.13067	0.565336	+	0.824861i	$0.308746\pi$
$444$	−0.508497	−0.0241322
$445$	10.7063	0.507527
$446$	27.0621	1.28143
$447$	−1.61622	−0.0764446
$448$	0	0
$449$	−7.45879	−0.352002	−0.176001	−	0.984390i	$-0.556316\pi$
$449$	−7.45879	−0.352002	−0.176001	+	0.984390i	$0.556316\pi$
$450$	5.64079	0.265909
$451$	−5.38571	−0.253603
$452$	0.936197	0.0440350
$453$	−21.9616	−1.03185
$454$	−37.7398	−1.77122
$455$	0	0
$456$	−10.3210	−0.483324
$457$	10.2902	0.481356	0.240678	−	0.970605i	$-0.422630\pi$
$457$	10.2902	0.481356	0.240678	+	0.970605i	$0.422630\pi$
$458$	−28.7300	−1.34247
$459$	−3.03955	−0.141874
$460$	−1.22581	−0.0571537
$461$	30.1235	1.40299	0.701495	−	0.712675i	$-0.252516\pi$
$461$	30.1235	1.40299	0.701495	+	0.712675i	$0.252516\pi$
$462$	0	0
$463$	10.2937	0.478389	0.239195	−	0.970972i	$-0.423117\pi$
$463$	10.2937	0.478389	0.239195	+	0.970972i	$0.423117\pi$
$464$	−6.44709	−0.299299
$465$	−1.90228	−0.0882159
$466$	−11.1900	−0.518368
$467$	22.8508	1.05741	0.528705	−	0.848806i	$-0.322678\pi$
$467$	22.8508	1.05741	0.528705	+	0.848806i	$0.322678\pi$
$468$	−0.492432	−0.0227627
$469$	0	0
$470$	9.26918	0.427555
$471$	−7.03546	−0.324177
$472$	9.10761	0.419212
$473$	11.8954	0.546951
$474$	4.86721	0.223558
$475$	−14.6362	−0.671553
$476$	0	0
$477$	−7.23051	−0.331063
$478$	5.51668	0.252327
$479$	−32.2409	−1.47313	−0.736563	−	0.676369i	$-0.763553\pi$
$479$	−32.2409	−1.47313	−0.736563	+	0.676369i	$0.763553\pi$
$480$	−0.778561	−0.0355363
$481$	−11.2355	−0.512296
$482$	−7.57563	−0.345060
$483$	0	0
$484$	−0.149286	−0.00678575
$485$	−2.37041	−0.107635
$486$	1.36041	0.0617094
$487$	−35.1030	−1.59067	−0.795334	−	0.606172i	$-0.792704\pi$
$487$	−35.1030	−1.59067	−0.795334	+	0.606172i	$0.792704\pi$
$488$	20.0791	0.908938
$489$	−20.9496	−0.947375
$490$	0	0
$491$	3.27307	0.147712	0.0738559	−	0.997269i	$-0.476470\pi$
$491$	3.27307	0.147712	0.0738559	+	0.997269i	$0.476470\pi$
$492$	−0.804013	−0.0362477
$493$	5.32631	0.239885
$494$	−15.8399	−0.712671
$495$	−0.923909	−0.0415266
$496$	7.57514	0.340134
$497$	0	0
$498$	12.0377	0.539422
$499$	10.3480	0.463240	0.231620	−	0.972806i	$-0.425597\pi$
$499$	10.3480	0.463240	0.231620	+	0.972806i	$0.425597\pi$
$500$	−1.26154	−0.0564176
$501$	−16.2499	−0.725992
$502$	13.5290	0.603831
$503$	21.0612	0.939072	0.469536	−	0.882913i	$-0.344421\pi$
$503$	21.0612	0.939072	0.469536	+	0.882913i	$0.344421\pi$
$504$	0	0
$505$	−14.3063	−0.636621
$506$	12.0905	0.537486
$507$	2.11942	0.0941266
$508$	0.187793	0.00833197
$509$	−17.9472	−0.795497	−0.397749	−	0.917494i	$-0.630208\pi$
$509$	−17.9472	−0.795497	−0.397749	+	0.917494i	$0.630208\pi$
$510$	−3.82039	−0.169170
$511$	0	0
$512$	24.6153	1.08785
$513$	−3.52985	−0.155847
$514$	−31.7355	−1.39979
$515$	−17.6706	−0.778660
$516$	1.77582	0.0781762
$517$	7.37466	0.324337
$518$	0	0
$519$	13.2895	0.583342
$520$	−8.91085	−0.390767
$521$	−24.4507	−1.07120	−0.535602	−	0.844471i	$-0.679915\pi$
$521$	−24.4507	−1.07120	−0.535602	+	0.844471i	$0.679915\pi$
$522$	−2.38389	−0.104340
$523$	−0.334029	−0.0146061	−0.00730303	−	0.999973i	$-0.502325\pi$
$523$	−0.334029	−0.0146061	−0.00730303	+	0.999973i	$0.502325\pi$
$524$	−0.0713855	−0.00311849
$525$	0	0
$526$	−20.4024	−0.889585
$527$	−6.25826	−0.272614
$528$	3.67914	0.160114
$529$	55.9853	2.43414
$530$	−9.08800	−0.394757
$531$	3.11487	0.135174
$532$	0	0
$533$	−17.7651	−0.769494
$534$	−15.7645	−0.682195
$535$	5.31464	0.229772
$536$	12.1503	0.524814
$537$	22.4122	0.967158
$538$	−24.5731	−1.05942
$539$	0	0
$540$	−0.137927	−0.00593544
$541$	−15.5466	−0.668402	−0.334201	−	0.942502i	$-0.608466\pi$
$541$	−15.5466	−0.668402	−0.334201	+	0.942502i	$0.608466\pi$
$542$	−39.2530	−1.68606
$543$	−4.00727	−0.171968
$544$	−2.56137	−0.109818
$545$	−7.82101	−0.335015
$546$	0	0
$547$	33.4042	1.42826	0.714130	−	0.700014i	$-0.246823\pi$
$547$	33.4042	1.42826	0.714130	+	0.700014i	$0.246823\pi$
$548$	0.263435	0.0112534
$549$	6.86721	0.293085
$550$	5.64079	0.240524
$551$	6.18549	0.263511
$552$	25.9859	1.10603
$553$	0	0
$554$	−22.4859	−0.955334
$555$	−3.14700	−0.133583
$556$	0.584702	0.0247969
$557$	−13.4077	−0.568101	−0.284050	−	0.958809i	$-0.591678\pi$
$557$	−13.4077	−0.568101	−0.284050	+	0.958809i	$0.591678\pi$
$558$	2.80100	0.118576
$559$	39.2378	1.65958
$560$	0	0
$561$	−3.03955	−0.128330
$562$	−8.22057	−0.346764
$563$	38.2015	1.61000	0.805001	−	0.593273i	$-0.202165\pi$
$563$	38.2015	1.61000	0.805001	+	0.593273i	$0.202165\pi$
$564$	1.10094	0.0463578
$565$	5.79397	0.243754
$566$	17.5529	0.737804
$567$	0	0
$568$	−23.2277	−0.974614
$569$	−38.1972	−1.60131	−0.800655	−	0.599125i	$-0.795515\pi$
$569$	−38.1972	−1.60131	−0.800655	+	0.599125i	$0.795515\pi$
$570$	−4.43666	−0.185831
$571$	−2.31419	−0.0968458	−0.0484229	−	0.998827i	$-0.515420\pi$
$571$	−2.31419	−0.0968458	−0.0484229	+	0.998827i	$0.515420\pi$
$572$	−0.492432	−0.0205896
$573$	−22.4640	−0.938449
$574$	0	0
$575$	36.8505	1.53677
$576$	8.50467	0.354361
$577$	42.3744	1.76407	0.882036	−	0.471183i	$-0.156173\pi$
$577$	42.3744	1.76407	0.882036	+	0.471183i	$0.156173\pi$
$578$	10.5583	0.439168
$579$	−10.4651	−0.434916
$580$	0.241695	0.0100358
$581$	0	0
$582$	3.49030	0.144678
$583$	−7.23051	−0.299457
$584$	−3.55318	−0.147032
$585$	−3.04758	−0.126002
$586$	15.5435	0.642094
$587$	12.2091	0.503924	0.251962	−	0.967737i	$-0.418924\pi$
$587$	12.2091	0.503924	0.251962	+	0.967737i	$0.418924\pi$
$588$	0	0
$589$	−7.26776	−0.299463
$590$	3.91507	0.161181
$591$	5.74174	0.236184
$592$	12.5318	0.515055
$593$	−35.6397	−1.46355	−0.731774	−	0.681548i	$-0.761307\pi$
$593$	−35.6397	−1.46355	−0.731774	+	0.681548i	$0.761307\pi$
$594$	1.36041	0.0558183
$595$	0	0
$596$	−0.241280	−0.00988320
$597$	−5.85662	−0.239695
$598$	39.8813	1.63087
$599$	8.34763	0.341075	0.170537	−	0.985351i	$-0.445450\pi$
$599$	8.34763	0.341075	0.170537	+	0.985351i	$0.445450\pi$
$600$	12.1237	0.494947
$601$	8.58956	0.350376	0.175188	−	0.984535i	$-0.443947\pi$
$601$	8.58956	0.350376	0.175188	+	0.984535i	$0.443947\pi$
$602$	0	0
$603$	4.15551	0.169225
$604$	−3.27857	−0.133403
$605$	−0.923909	−0.0375623
$606$	21.0653	0.855718
$607$	45.2097	1.83500	0.917502	−	0.397732i	$-0.130203\pi$
$607$	45.2097	1.83500	0.917502	+	0.397732i	$0.130203\pi$
$608$	−2.97454	−0.120634
$609$	0	0
$610$	8.63136	0.349474
$611$	24.3259	0.984119
$612$	−0.453764	−0.0183423
$613$	12.2840	0.496145	0.248073	−	0.968741i	$-0.420203\pi$
$613$	12.2840	0.496145	0.248073	+	0.968741i	$0.420203\pi$
$614$	−5.04943	−0.203779
$615$	−4.97590	−0.200648
$616$	0	0
$617$	−29.5580	−1.18996	−0.594980	−	0.803741i	$-0.702840\pi$
$617$	−29.5580	−1.18996	−0.594980	+	0.803741i	$0.702840\pi$
$618$	26.0191	1.04664
$619$	−45.0796	−1.81190	−0.905952	−	0.423380i	$-0.860843\pi$
$619$	−45.0796	−1.81190	−0.905952	+	0.423380i	$0.860843\pi$
$620$	−0.283984	−0.0114051
$621$	8.88737	0.356638
$622$	8.01606	0.321415
$623$	0	0
$624$	12.1359	0.485825
$625$	12.9245	0.516981
$626$	26.0838	1.04252
$627$	−3.52985	−0.140969
$628$	−1.05030	−0.0419115
$629$	−10.3533	−0.412811
$630$	0	0
$631$	−10.5956	−0.421805	−0.210902	−	0.977507i	$-0.567640\pi$
$631$	−10.5956	−0.421805	−0.210902	+	0.977507i	$0.567640\pi$
$632$	10.4610	0.416117
$633$	20.4122	0.811312
$634$	−4.47910	−0.177888
$635$	1.16222	0.0461213
$636$	−1.07942	−0.0428017
$637$	0	0
$638$	−2.38389	−0.0943793
$639$	−7.94407	−0.314262
$640$	9.13236	0.360988
$641$	19.6976	0.778007	0.389003	−	0.921236i	$-0.372819\pi$
$641$	19.6976	0.778007	0.389003	+	0.921236i	$0.372819\pi$
$642$	−7.82553	−0.308849
$643$	26.2695	1.03597	0.517983	−	0.855391i	$-0.326683\pi$
$643$	26.2695	1.03597	0.517983	+	0.855391i	$0.326683\pi$
$644$	0	0
$645$	10.9903	0.432742
$646$	−14.5961	−0.574274
$647$	47.5716	1.87023	0.935117	−	0.354339i	$-0.115294\pi$
$647$	47.5716	1.87023	0.935117	+	0.354339i	$0.115294\pi$
$648$	2.92391	0.114862
$649$	3.11487	0.122269
$650$	18.6066	0.729809
$651$	0	0
$652$	−3.12750	−0.122482
$653$	8.72661	0.341499	0.170749	−	0.985315i	$-0.445381\pi$
$653$	8.72661	0.341499	0.170749	+	0.985315i	$0.445381\pi$
$654$	11.5160	0.450312
$655$	−0.441793	−0.0172623
$656$	19.8148	0.773637
$657$	−1.21522	−0.0474101
$658$	0	0
$659$	1.69749	0.0661248	0.0330624	−	0.999453i	$-0.489474\pi$
$659$	1.69749	0.0661248	0.0330624	+	0.999453i	$0.489474\pi$
$660$	−0.137927	−0.00536881
$661$	−16.6561	−0.647847	−0.323923	−	0.946083i	$-0.605002\pi$
$661$	−16.6561	−0.647847	−0.323923	+	0.946083i	$0.605002\pi$
$662$	−5.20370	−0.202248
$663$	−10.0262	−0.389384
$664$	25.8725	1.00405
$665$	0	0
$666$	4.63380	0.179556
$667$	−15.5737	−0.603015
$668$	−2.42589	−0.0938605
$669$	19.8926	0.769093
$670$	5.22304	0.201784
$671$	6.86721	0.265106
$672$	0	0
$673$	−46.9656	−1.81039	−0.905196	−	0.424995i	$-0.860276\pi$
$673$	−46.9656	−1.81039	−0.905196	+	0.424995i	$0.860276\pi$
$674$	−46.3402	−1.78496
$675$	4.14639	0.159595
$676$	0.316400	0.0121692
$677$	−18.4864	−0.710489	−0.355244	−	0.934773i	$-0.615602\pi$
$677$	−18.4864	−0.710489	−0.355244	+	0.934773i	$0.615602\pi$
$678$	−8.53133	−0.327644
$679$	0	0
$680$	−8.21112	−0.314882
$681$	−27.7415	−1.06306
$682$	2.80100	0.107256
$683$	37.7374	1.44398	0.721991	−	0.691902i	$-0.243227\pi$
$683$	37.7374	1.44398	0.721991	+	0.691902i	$0.243227\pi$
$684$	−0.526959	−0.0201488
$685$	1.63035	0.0622926
$686$	0	0
$687$	−21.1187	−0.805727
$688$	−43.7649	−1.66852
$689$	−23.8504	−0.908627
$690$	11.1705	0.425253
$691$	6.86938	0.261324	0.130662	−	0.991427i	$-0.458290\pi$
$691$	6.86938	0.261324	0.130662	+	0.991427i	$0.458290\pi$
$692$	1.98394	0.0754179
$693$	0	0
$694$	30.7965	1.16902
$695$	3.61862	0.137262
$696$	−5.12367	−0.194212
$697$	−16.3701	−0.620063
$698$	45.0848	1.70648
$699$	−8.22549	−0.311117
$700$	0	0
$701$	27.2324	1.02856	0.514278	−	0.857624i	$-0.328060\pi$
$701$	27.2324	1.02856	0.514278	+	0.857624i	$0.328060\pi$
$702$	4.48741	0.169366
$703$	−12.0233	−0.453468
$704$	8.50467	0.320532
$705$	6.81352	0.256612
$706$	28.9541	1.08970
$707$	0	0
$708$	0.465008	0.0174761
$709$	10.1700	0.381944	0.190972	−	0.981596i	$-0.438836\pi$
$709$	10.1700	0.381944	0.190972	+	0.981596i	$0.438836\pi$
$710$	−9.98486	−0.374725
$711$	3.57775	0.134176
$712$	−33.8823	−1.26979
$713$	18.2986	0.685287
$714$	0	0
$715$	−3.04758	−0.113973
$716$	3.34584	0.125040
$717$	4.05517	0.151443
$718$	−17.4659	−0.651821
$719$	23.7911	0.887259	0.443630	−	0.896210i	$-0.353691\pi$
$719$	23.7911	0.887259	0.443630	+	0.896210i	$0.353691\pi$
$720$	3.39919	0.126680
$721$	0	0
$722$	8.89725	0.331121
$723$	−5.56864	−0.207100
$724$	−0.598230	−0.0222331
$725$	−7.26587	−0.269848
$726$	1.36041	0.0504895
$727$	−20.9643	−0.777523	−0.388761	−	0.921338i	$-0.627097\pi$
$727$	−20.9643	−0.777523	−0.388761	+	0.921338i	$0.627097\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−1.52740	−0.0565316
$731$	36.1567	1.33730
$732$	1.02518	0.0378918
$733$	−34.7941	−1.28515	−0.642575	−	0.766223i	$-0.722134\pi$
$733$	−34.7941	−1.28515	−0.642575	+	0.766223i	$0.722134\pi$
$734$	−49.2427	−1.81758
$735$	0	0
$736$	7.48922	0.276056
$737$	4.15551	0.153070
$738$	7.32676	0.269702
$739$	2.21778	0.0815822	0.0407911	−	0.999168i	$-0.487012\pi$
$739$	2.21778	0.0815822	0.0407911	+	0.999168i	$0.487012\pi$
$740$	−0.469805	−0.0172704
$741$	−11.6435	−0.427734
$742$	0	0
$743$	0.418308	0.0153462	0.00767311	−	0.999971i	$-0.497558\pi$
$743$	0.418308	0.0153462	0.00767311	+	0.999971i	$0.497558\pi$
$744$	6.02016	0.220710
$745$	−1.49324	−0.0547081
$746$	−24.1299	−0.883457
$747$	8.84859	0.323753
$748$	−0.453764	−0.0165912
$749$	0	0
$750$	11.4961	0.419776
$751$	−2.02093	−0.0737446	−0.0368723	−	0.999320i	$-0.511739\pi$
$751$	−2.02093	−0.0737446	−0.0368723	+	0.999320i	$0.511739\pi$
$752$	−27.1324	−0.989418
$753$	9.94483	0.362410
$754$	−7.86345	−0.286370
$755$	−20.2905	−0.738448
$756$	0	0
$757$	28.9630	1.05268	0.526339	−	0.850275i	$-0.323564\pi$
$757$	28.9630	1.05268	0.526339	+	0.850275i	$0.323564\pi$
$758$	42.4876	1.54322
$759$	8.88737	0.322591
$760$	−9.53564	−0.345894
$761$	−20.3073	−0.736140	−0.368070	−	0.929798i	$-0.619981\pi$
$761$	−20.3073	−0.736140	−0.368070	+	0.929798i	$0.619981\pi$
$762$	−1.71131	−0.0619943
$763$	0	0
$764$	−3.35358	−0.121328
$765$	−2.80827	−0.101533
$766$	−5.05731	−0.182728
$767$	10.2746	0.370996
$768$	3.56242	0.128548
$769$	45.5301	1.64186	0.820928	−	0.571031i	$-0.193456\pi$
$769$	45.5301	1.64186	0.820928	+	0.571031i	$0.193456\pi$
$770$	0	0
$771$	−23.3279	−0.840135
$772$	−1.56230	−0.0562284
$773$	44.2766	1.59252	0.796260	−	0.604955i	$-0.206809\pi$
$773$	44.2766	1.59252	0.796260	+	0.604955i	$0.206809\pi$
$774$	−16.1826	−0.581672
$775$	8.53718	0.306664
$776$	7.50166	0.269294
$777$	0	0
$778$	0.572952	0.0205413
$779$	−19.0108	−0.681131
$780$	−0.454963	−0.0162903
$781$	−7.94407	−0.284261
$782$	36.7496	1.31416
$783$	−1.75234	−0.0626234
$784$	0	0
$785$	−6.50012	−0.231999
$786$	0.650518	0.0232032
$787$	5.55683	0.198080	0.0990398	−	0.995083i	$-0.468423\pi$
$787$	5.55683	0.198080	0.0990398	+	0.995083i	$0.468423\pi$
$788$	0.857165	0.0305352
$789$	−14.9972	−0.533915
$790$	4.49686	0.159991
$791$	0	0
$792$	2.92391	0.103897
$793$	22.6520	0.804396
$794$	49.1468	1.74415
$795$	−6.68034	−0.236927
$796$	−0.874314	−0.0309892
$797$	16.7372	0.592862	0.296431	−	0.955054i	$-0.404204\pi$
$797$	16.7372	0.592862	0.296431	+	0.955054i	$0.404204\pi$
$798$	0	0
$799$	22.4157	0.793009
$800$	3.49409	0.123535
$801$	−11.5880	−0.409443
$802$	−19.9170	−0.703295
$803$	−1.21522	−0.0428841
$804$	0.620361	0.0218784
$805$	0	0
$806$	9.23931	0.325441
$807$	−18.0630	−0.635849
$808$	45.2753	1.59278
$809$	34.1930	1.20216	0.601082	−	0.799188i	$-0.294737\pi$
$809$	34.1930	1.20216	0.601082	+	0.799188i	$0.294737\pi$
$810$	1.25689	0.0441628
$811$	−9.97273	−0.350190	−0.175095	−	0.984552i	$-0.556023\pi$
$811$	−9.97273	−0.350190	−0.175095	+	0.984552i	$0.556023\pi$
$812$	0	0
$813$	−28.8538	−1.01195
$814$	4.63380	0.162415
$815$	−19.3556	−0.677996
$816$	11.1829	0.391481
$817$	41.9890	1.46901
$818$	54.7841	1.91548
$819$	0	0
$820$	−0.742835	−0.0259409
$821$	−44.8348	−1.56474	−0.782372	−	0.622811i	$-0.785990\pi$
$821$	−44.8348	−1.56474	−0.782372	+	0.622811i	$0.785990\pi$
$822$	−2.40061	−0.0837310
$823$	1.16911	0.0407526	0.0203763	−	0.999792i	$-0.493514\pi$
$823$	1.16911	0.0407526	0.0203763	+	0.999792i	$0.493514\pi$
$824$	55.9224	1.94815
$825$	4.14639	0.144359
$826$	0	0
$827$	−20.7220	−0.720576	−0.360288	−	0.932841i	$-0.617322\pi$
$827$	−20.7220	−0.720576	−0.360288	+	0.932841i	$0.617322\pi$
$828$	1.32676	0.0461082
$829$	−11.0582	−0.384066	−0.192033	−	0.981388i	$-0.561508\pi$
$829$	−11.0582	−0.384066	−0.192033	+	0.981388i	$0.561508\pi$
$830$	11.1217	0.386041
$831$	−16.5288	−0.573377
$832$	28.0533	0.972573
$833$	0	0
$834$	−5.32824	−0.184502
$835$	−15.0134	−0.519562
$836$	−0.526959	−0.0182253
$837$	2.05894	0.0711674
$838$	9.09074	0.314034
$839$	17.8887	0.617586	0.308793	−	0.951129i	$-0.400075\pi$
$839$	17.8887	0.617586	0.308793	+	0.951129i	$0.400075\pi$
$840$	0	0
$841$	−25.9293	−0.894114
$842$	1.79423	0.0618334
$843$	−6.04272	−0.208122
$844$	3.04726	0.104891
$845$	1.95815	0.0673624
$846$	−10.0326	−0.344927
$847$	0	0
$848$	26.6021	0.913519
$849$	12.9027	0.442818
$850$	17.1455	0.588085
$851$	30.2720	1.03771
$852$	−1.18594	−0.0406297
$853$	−10.8590	−0.371806	−0.185903	−	0.982568i	$-0.559521\pi$
$853$	−10.8590	−0.371806	−0.185903	+	0.982568i	$0.559521\pi$
$854$	0	0
$855$	−3.26127	−0.111533
$856$	−16.8193	−0.574872
$857$	2.90536	0.0992451	0.0496226	−	0.998768i	$-0.484198\pi$
$857$	2.90536	0.0992451	0.0496226	+	0.998768i	$0.484198\pi$
$858$	4.48741	0.153198
$859$	−51.5070	−1.75740	−0.878698	−	0.477378i	$-0.841587\pi$
$859$	−51.5070	−1.75740	−0.878698	+	0.477378i	$0.841587\pi$
$860$	1.64070	0.0559474
$861$	0	0
$862$	−42.8431	−1.45924
$863$	14.0660	0.478814	0.239407	−	0.970919i	$-0.423047\pi$
$863$	14.0660	0.478814	0.239407	+	0.970919i	$0.423047\pi$
$864$	0.842681	0.0286686
$865$	12.2783	0.417473
$866$	−41.9235	−1.42462
$867$	7.76114	0.263582
$868$	0	0
$869$	3.57775	0.121367
$870$	−2.20250	−0.0746718
$871$	13.7072	0.464452
$872$	24.7513	0.838183
$873$	2.56563	0.0868334
$874$	42.6776	1.44359
$875$	0	0
$876$	−0.181415	−0.00612946
$877$	−34.2455	−1.15639	−0.578194	−	0.815899i	$-0.696242\pi$
$877$	−34.2455	−1.15639	−0.578194	+	0.815899i	$0.696242\pi$
$878$	23.2852	0.785839
$879$	11.4256	0.385375
$880$	3.39919	0.114587
$881$	−17.3580	−0.584805	−0.292402	−	0.956295i	$-0.594455\pi$
$881$	−17.3580	−0.584805	−0.292402	+	0.956295i	$0.594455\pi$
$882$	0	0
$883$	−32.8178	−1.10441	−0.552203	−	0.833710i	$-0.686213\pi$
$883$	−32.8178	−1.10441	−0.552203	+	0.833710i	$0.686213\pi$
$884$	−1.49677	−0.0503419
$885$	2.87786	0.0967382
$886$	−32.3749	−1.08766
$887$	32.1839	1.08063	0.540315	−	0.841463i	$-0.318305\pi$
$887$	32.1839	1.08063	0.540315	+	0.841463i	$0.318305\pi$
$888$	9.95937	0.334214
$889$	0	0
$890$	−14.5649	−0.488218
$891$	1.00000	0.0335013
$892$	2.96970	0.0994329
$893$	26.0315	0.871111
$894$	2.19872	0.0735362
$895$	20.7068	0.692153
$896$	0	0
$897$	29.3156	0.978821
$898$	10.1470	0.338610
$899$	−3.60796	−0.120332
$900$	0.619000	0.0206333
$901$	−21.9775	−0.732177
$902$	7.32676	0.243955
$903$	0	0
$904$	−18.3363	−0.609855
$905$	−3.70235	−0.123070
$906$	29.8768	0.992589
$907$	14.9036	0.494866	0.247433	−	0.968905i	$-0.420413\pi$
$907$	14.9036	0.494866	0.247433	+	0.968905i	$0.420413\pi$
$908$	−4.14143	−0.137438
$909$	15.4845	0.513589
$910$	0	0
$911$	30.4345	1.00834	0.504169	−	0.863605i	$-0.331799\pi$
$911$	30.4345	1.00834	0.504169	+	0.863605i	$0.331799\pi$
$912$	12.9868	0.430037
$913$	8.84859	0.292845
$914$	−13.9989	−0.463043
$915$	6.34468	0.209749
$916$	−3.15273	−0.104169
$917$	0	0
$918$	4.13503	0.136476
$919$	−42.1098	−1.38907	−0.694536	−	0.719458i	$-0.744390\pi$
$919$	−42.1098	−1.38907	−0.694536	+	0.719458i	$0.744390\pi$
$920$	24.0086	0.791539
$921$	−3.71170	−0.122305
$922$	−40.9802	−1.34961
$923$	−26.2041	−0.862518
$924$	0	0
$925$	14.1234	0.464373
$926$	−14.0037	−0.460189
$927$	19.1259	0.628177
$928$	−1.47666	−0.0484738
$929$	−29.5146	−0.968344	−0.484172	−	0.874973i	$-0.660879\pi$
$929$	−29.5146	−0.968344	−0.484172	+	0.874973i	$0.660879\pi$
$930$	2.58787	0.0848597
$931$	0	0
$932$	−1.22795	−0.0402230
$933$	5.89239	0.192908
$934$	−31.0865	−1.01718
$935$	−2.80827	−0.0918402
$936$	9.64473	0.315248
$937$	5.74383	0.187643	0.0938214	−	0.995589i	$-0.470092\pi$
$937$	5.74383	0.187643	0.0938214	+	0.995589i	$0.470092\pi$
$938$	0	0
$939$	19.1735	0.625703
$940$	1.01717	0.0331763
$941$	−28.1664	−0.918198	−0.459099	−	0.888385i	$-0.651828\pi$
$941$	−28.1664	−0.918198	−0.459099	+	0.888385i	$0.651828\pi$
$942$	9.57110	0.311843
$943$	47.8647	1.55869
$944$	−11.4601	−0.372993
$945$	0	0
$946$	−16.1826	−0.526142
$947$	17.9336	0.582763	0.291381	−	0.956607i	$-0.405885\pi$
$947$	17.9336	0.582763	0.291381	+	0.956607i	$0.405885\pi$
$948$	0.534110	0.0173471
$949$	−4.00848	−0.130121
$950$	19.9112	0.646004
$951$	−3.29247	−0.106766
$952$	0	0
$953$	19.6302	0.635884	0.317942	−	0.948110i	$-0.397008\pi$
$953$	19.6302	0.635884	0.317942	+	0.948110i	$0.397008\pi$
$954$	9.83646	0.318467
$955$	−20.7547	−0.671607
$956$	0.605381	0.0195794
$957$	−1.75234	−0.0566450
$958$	43.8609	1.41708
$959$	0	0
$960$	7.85755	0.253601
$961$	−26.7608	−0.863250
$962$	15.2849	0.492806
$963$	−5.75234	−0.185366
$964$	−0.831322	−0.0267751
$965$	−9.66882	−0.311250
$966$	0	0
$967$	9.18742	0.295447	0.147724	−	0.989029i	$-0.452805\pi$
$967$	9.18742	0.295447	0.147724	+	0.989029i	$0.452805\pi$
$968$	2.92391	0.0939780
$969$	−10.7292	−0.344671
$970$	3.22472	0.103540
$971$	−29.9645	−0.961606	−0.480803	−	0.876829i	$-0.659655\pi$
$971$	−29.9645	−0.961606	−0.480803	+	0.876829i	$0.659655\pi$
$972$	0.149286	0.00478836
$973$	0	0
$974$	47.7544	1.53015
$975$	13.6772	0.438020
$976$	−25.2654	−0.808727
$977$	−10.9810	−0.351313	−0.175657	−	0.984451i	$-0.556205\pi$
$977$	−10.9810	−0.351313	−0.175657	+	0.984451i	$0.556205\pi$
$978$	28.5001	0.911332
$979$	−11.5880	−0.370355
$980$	0	0
$981$	8.46512	0.270271
$982$	−4.45272	−0.142092
$983$	35.0379	1.11753	0.558767	−	0.829325i	$-0.311275\pi$
$983$	35.0379	1.11753	0.558767	+	0.829325i	$0.311275\pi$
$984$	15.7473	0.502006
$985$	5.30485	0.169027
$986$	−7.24597	−0.230759
$987$	0	0
$988$	−1.73821	−0.0552999
$989$	−105.719	−3.36166
$990$	1.25689	0.0399467
$991$	−56.2288	−1.78617	−0.893084	−	0.449891i	$-0.851463\pi$
$991$	−56.2288	−1.78617	−0.893084	+	0.449891i	$0.851463\pi$
$992$	1.73503	0.0550873
$993$	−3.82510	−0.121386
$994$	0	0
$995$	−5.41098	−0.171540
$996$	1.32097	0.0418567
$997$	−46.8211	−1.48284	−0.741420	−	0.671042i	$-0.765847\pi$
$997$	−46.8211	−1.48284	−0.741420	+	0.671042i	$0.765847\pi$
$998$	−14.0775	−0.445616
$999$	3.40618	0.107767

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1617.2.a.u.1.2	✓	4
3.2	odd	2		4851.2.a.bx.1.3		4
7.6	odd	2		1617.2.a.v.1.2	yes	4
21.20	even	2		4851.2.a.by.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1617.2.a.u.1.2	✓	4	1.1	even	1	trivial
1617.2.a.v.1.2	yes	4	7.6	odd	2
4851.2.a.bx.1.3		4	3.2	odd	2
4851.2.a.by.1.3		4	21.20	even	2

Overview	Random
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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:	\( N \)	\(=\)	\( 1617 = 3 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1617.a (trivial)

\(f(q)\)	\(=\)	\(q-1.36041 q^{2} -1.00000 q^{3} -0.149286 q^{4} -0.923909 q^{5} +1.36041 q^{6} +2.92391 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.36041 q^{2} -1.00000 q^{3} -0.149286 q^{4} -0.923909 q^{5} +1.36041 q^{6} +2.92391 q^{8} +1.00000 q^{9} +1.25689 q^{10} +1.00000 q^{11} +0.149286 q^{12} +3.29857 q^{13} +0.923909 q^{15} -3.67914 q^{16} +3.03955 q^{17} -1.36041 q^{18} +3.52985 q^{19} +0.137927 q^{20} -1.36041 q^{22} -8.88737 q^{23} -2.92391 q^{24} -4.14639 q^{25} -4.48741 q^{26} -1.00000 q^{27} +1.75234 q^{29} -1.25689 q^{30} -2.05894 q^{31} -0.842681 q^{32} -1.00000 q^{33} -4.13503 q^{34} -0.149286 q^{36} -3.40618 q^{37} -4.80205 q^{38} -3.29857 q^{39} -2.70143 q^{40} -5.38571 q^{41} +11.8954 q^{43} -0.149286 q^{44} -0.923909 q^{45} +12.0905 q^{46} +7.37466 q^{47} +3.67914 q^{48} +5.64079 q^{50} -3.03955 q^{51} -0.492432 q^{52} -7.23051 q^{53} +1.36041 q^{54} -0.923909 q^{55} -3.52985 q^{57} -2.38389 q^{58} +3.11487 q^{59} -0.137927 q^{60} +6.86721 q^{61} +2.80100 q^{62} +8.50467 q^{64} -3.04758 q^{65} +1.36041 q^{66} +4.15551 q^{67} -0.453764 q^{68} +8.88737 q^{69} -7.94407 q^{71} +2.92391 q^{72} -1.21522 q^{73} +4.63380 q^{74} +4.14639 q^{75} -0.526959 q^{76} +4.48741 q^{78} +3.57775 q^{79} +3.39919 q^{80} +1.00000 q^{81} +7.32676 q^{82} +8.84859 q^{83} -2.80827 q^{85} -16.1826 q^{86} -1.75234 q^{87} +2.92391 q^{88} -11.5880 q^{89} +1.25689 q^{90} +1.32676 q^{92} +2.05894 q^{93} -10.0326 q^{94} -3.26127 q^{95} +0.842681 q^{96} +2.56563 q^{97} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 4 q^{3} + 2 q^{4} + 8 q^{5} + 2 q^{6} + 4 q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 - 4 * q^3 + 2 * q^4 + 8 * q^5 + 2 * q^6 + 4 * q^9	\( 4 q - 2 q^{2} - 4 q^{3} + 2 q^{4} + 8 q^{5} + 2 q^{6} + 4 q^{9} - 2 q^{10} + 4 q^{11} - 2 q^{12} + 8 q^{13} - 8 q^{15} - 6 q^{16} - 2 q^{18} + 8 q^{19} + 14 q^{20} - 2 q^{22} + 12 q^{25} + 2 q^{26} - 4 q^{27} - 16 q^{29} + 2 q^{30} + 16 q^{31} - 2 q^{32} - 4 q^{33} - 4 q^{34} + 2 q^{36} - 4 q^{37} - 2 q^{38} - 8 q^{39} - 16 q^{40} + 4 q^{41} + 16 q^{43} + 2 q^{44} + 8 q^{45} + 8 q^{46} + 36 q^{47} + 6 q^{48} - 8 q^{50} - 22 q^{52} - 16 q^{53} + 2 q^{54} + 8 q^{55} - 8 q^{57} + 14 q^{58} - 14 q^{60} - 8 q^{61} + 8 q^{62} - 12 q^{64} - 4 q^{65} + 2 q^{66} + 20 q^{67} + 16 q^{68} - 20 q^{71} + 4 q^{73} - 30 q^{74} - 12 q^{75} + 30 q^{76} - 2 q^{78} + 16 q^{79} - 14 q^{80} + 4 q^{81} + 28 q^{82} + 24 q^{83} - 44 q^{86} + 16 q^{87} - 4 q^{89} - 2 q^{90} + 4 q^{92} - 16 q^{93} - 10 q^{94} + 28 q^{95} + 2 q^{96} + 16 q^{97} + 4 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 - 4 * q^3 + 2 * q^4 + 8 * q^5 + 2 * q^6 + 4 * q^9 - 2 * q^10 + 4 * q^11 - 2 * q^12 + 8 * q^13 - 8 * q^15 - 6 * q^16 - 2 * q^18 + 8 * q^19 + 14 * q^20 - 2 * q^22 + 12 * q^25 + 2 * q^26 - 4 * q^27 - 16 * q^29 + 2 * q^30 + 16 * q^31 - 2 * q^32 - 4 * q^33 - 4 * q^34 + 2 * q^36 - 4 * q^37 - 2 * q^38 - 8 * q^39 - 16 * q^40 + 4 * q^41 + 16 * q^43 + 2 * q^44 + 8 * q^45 + 8 * q^46 + 36 * q^47 + 6 * q^48 - 8 * q^50 - 22 * q^52 - 16 * q^53 + 2 * q^54 + 8 * q^55 - 8 * q^57 + 14 * q^58 - 14 * q^60 - 8 * q^61 + 8 * q^62 - 12 * q^64 - 4 * q^65 + 2 * q^66 + 20 * q^67 + 16 * q^68 - 20 * q^71 + 4 * q^73 - 30 * q^74 - 12 * q^75 + 30 * q^76 - 2 * q^78 + 16 * q^79 - 14 * q^80 + 4 * q^81 + 28 * q^82 + 24 * q^83 - 44 * q^86 + 16 * q^87 - 4 * q^89 - 2 * q^90 + 4 * q^92 - 16 * q^93 - 10 * q^94 + 28 * q^95 + 2 * q^96 + 16 * q^97 + 4 * q^99

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