LMFDB - Embedded newform 1617.2.a.y.1.3

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			1.3
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)

$f(q)$	$=$	$q+1.36041 q^{2} +1.00000 q^{3} -0.149286 q^{4} -2.92391 q^{5} +1.36041 q^{6} -2.92391 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.36041 q^{2} +1.00000 q^{3} -0.149286 q^{4} -2.92391 q^{5} +1.36041 q^{6} -2.92391 q^{8} +1.00000 q^{9} -3.97771 q^{10} -1.00000 q^{11} -0.149286 q^{12} +6.54925 q^{13} -2.92391 q^{15} -3.67914 q^{16} +8.05894 q^{17} +1.36041 q^{18} +0.279181 q^{19} +0.436500 q^{20} -1.36041 q^{22} +1.78888 q^{23} -2.92391 q^{24} +3.54925 q^{25} +8.90966 q^{26} +1.00000 q^{27} +3.90452 q^{29} -3.97771 q^{30} -0.617304 q^{31} +0.842681 q^{32} -1.00000 q^{33} +10.9635 q^{34} -0.149286 q^{36} -4.25067 q^{37} +0.379801 q^{38} +6.54925 q^{39} +8.54925 q^{40} +2.88436 q^{41} -4.64473 q^{43} +0.149286 q^{44} -2.92391 q^{45} +2.43361 q^{46} +12.4732 q^{47} -3.67914 q^{48} +4.82843 q^{50} +8.05894 q^{51} -0.977714 q^{52} +7.44573 q^{53} +1.36041 q^{54} +2.92391 q^{55} +0.279181 q^{57} +5.31174 q^{58} +10.7717 q^{59} +0.436500 q^{60} -15.3298 q^{61} -0.839786 q^{62} +8.50467 q^{64} -19.1494 q^{65} -1.36041 q^{66} +4.69564 q^{67} -1.20309 q^{68} +1.78888 q^{69} +9.38571 q^{71} -2.92391 q^{72} -0.847819 q^{73} -5.78266 q^{74} +3.54925 q^{75} -0.0416780 q^{76} +8.90966 q^{78} -5.23461 q^{79} +10.7575 q^{80} +1.00000 q^{81} +3.92391 q^{82} +7.36663 q^{83} -23.5636 q^{85} -6.31873 q^{86} +3.90452 q^{87} +2.92391 q^{88} -6.99088 q^{89} -3.97771 q^{90} -0.267055 q^{92} -0.617304 q^{93} +16.9686 q^{94} -0.816301 q^{95} +0.842681 q^{96} -8.07030 q^{97} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} + 4 q^{3} + 2 q^{4} + 2 q^{6} + 4 q^{9}+O(q^{10}) $ 4 * q + 2 * q^2 + 4 * q^3 + 2 * q^4 + 2 * q^6 + 4 * q^9	$ 4 q + 2 q^{2} + 4 q^{3} + 2 q^{4} + 2 q^{6} + 4 q^{9} - 2 q^{10} - 4 q^{11} + 2 q^{12} + 8 q^{13} - 6 q^{16} + 8 q^{17} + 2 q^{18} + 8 q^{19} + 10 q^{20} - 2 q^{22} + 8 q^{23} - 4 q^{25} + 14 q^{26} + 4 q^{27} + 16 q^{29} - 2 q^{30} + 8 q^{31} + 2 q^{32} - 4 q^{33} + 20 q^{34} + 2 q^{36} - 4 q^{37} - 14 q^{38} + 8 q^{39} + 16 q^{40} + 12 q^{41} - 2 q^{44} - 8 q^{46} + 20 q^{47} - 6 q^{48} + 8 q^{50} + 8 q^{51} + 10 q^{52} + 8 q^{53} + 2 q^{54} + 8 q^{57} - 2 q^{58} + 8 q^{59} + 10 q^{60} - 24 q^{61} + 24 q^{62} - 12 q^{64} - 12 q^{65} - 2 q^{66} - 28 q^{67} + 8 q^{69} + 12 q^{71} + 20 q^{73} - 18 q^{74} - 4 q^{75} - 2 q^{76} + 14 q^{78} - 2 q^{80} + 4 q^{81} + 4 q^{82} + 32 q^{83} - 24 q^{85} - 20 q^{86} + 16 q^{87} + 4 q^{89} - 2 q^{90} - 12 q^{92} + 8 q^{93} + 22 q^{94} + 4 q^{95} + 2 q^{96} + 8 q^{97} - 4 q^{99}+O(q^{100}) $ 4 * q + 2 * q^2 + 4 * q^3 + 2 * q^4 + 2 * q^6 + 4 * q^9 - 2 * q^10 - 4 * q^11 + 2 * q^12 + 8 * q^13 - 6 * q^16 + 8 * q^17 + 2 * q^18 + 8 * q^19 + 10 * q^20 - 2 * q^22 + 8 * q^23 - 4 * q^25 + 14 * q^26 + 4 * q^27 + 16 * q^29 - 2 * q^30 + 8 * q^31 + 2 * q^32 - 4 * q^33 + 20 * q^34 + 2 * q^36 - 4 * q^37 - 14 * q^38 + 8 * q^39 + 16 * q^40 + 12 * q^41 - 2 * q^44 - 8 * q^46 + 20 * q^47 - 6 * q^48 + 8 * q^50 + 8 * q^51 + 10 * q^52 + 8 * q^53 + 2 * q^54 + 8 * q^57 - 2 * q^58 + 8 * q^59 + 10 * q^60 - 24 * q^61 + 24 * q^62 - 12 * q^64 - 12 * q^65 - 2 * q^66 - 28 * q^67 + 8 * q^69 + 12 * q^71 + 20 * q^73 - 18 * q^74 - 4 * q^75 - 2 * q^76 + 14 * q^78 - 2 * q^80 + 4 * q^81 + 4 * q^82 + 32 * q^83 - 24 * q^85 - 20 * q^86 + 16 * q^87 + 4 * q^89 - 2 * q^90 - 12 * q^92 + 8 * q^93 + 22 * q^94 + 4 * q^95 + 2 * q^96 + 8 * 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	$-0.340282\pi$
$2$	1.36041	0.961955	0.480977	+	0.876733i	$0.340282\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−0.149286	−0.0746432
$5$	−2.92391	−1.30761	−0.653806	−	0.756662i	$-0.726829\pi$
$5$	−2.92391	−1.30761	−0.653806	+	0.756662i	$0.726829\pi$
$6$	1.36041	0.555385
$7$	0	0
$7$	0	0
$8$	−2.92391	−1.03376
$9$	1.00000	0.333333
$10$	−3.97771	−1.25786
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−0.149286	−0.0430953
$13$	6.54925	1.81643	0.908217	−	0.418500i	$-0.137444\pi$
$13$	6.54925	1.81643	0.908217	+	0.418500i	$0.137444\pi$
$14$	0	0
$15$	−2.92391	−0.754950
$16$	−3.67914	−0.919785
$17$	8.05894	1.95458	0.977290	−	0.211905i	$-0.0679668\pi$
$17$	8.05894	1.95458	0.977290	+	0.211905i	$0.0679668\pi$
$18$	1.36041	0.320652
$19$	0.279181	0.0640486	0.0320243	−	0.999487i	$-0.489805\pi$
$19$	0.279181	0.0640486	0.0320243	+	0.999487i	$0.489805\pi$
$20$	0.436500	0.0976044
$21$	0	0
$22$	−1.36041	−0.290040
$23$	1.78888	0.373007	0.186503	−	0.982454i	$-0.440284\pi$
$23$	1.78888	0.373007	0.186503	+	0.982454i	$0.440284\pi$
$24$	−2.92391	−0.596840
$25$	3.54925	0.709849
$26$	8.90966	1.74733
$27$	1.00000	0.192450
$28$	0	0
$29$	3.90452	0.725051	0.362525	−	0.931974i	$-0.381915\pi$
$29$	3.90452	0.725051	0.362525	+	0.931974i	$0.381915\pi$
$30$	−3.97771	−0.726228
$31$	−0.617304	−0.110871	−0.0554356	−	0.998462i	$-0.517655\pi$
$31$	−0.617304	−0.110871	−0.0554356	+	0.998462i	$0.517655\pi$
$32$	0.842681	0.148966
$33$	−1.00000	−0.174078
$34$	10.9635	1.88022
$35$	0	0
$36$	−0.149286	−0.0248811
$37$	−4.25067	−0.698806	−0.349403	−	0.936972i	$-0.613616\pi$
$37$	−4.25067	−0.698806	−0.349403	+	0.936972i	$0.613616\pi$
$38$	0.379801	0.0616118
$39$	6.54925	1.04872
$40$	8.54925	1.35175
$41$	2.88436	0.450461	0.225231	−	0.974305i	$-0.427686\pi$
$41$	2.88436	0.450461	0.225231	+	0.974305i	$0.427686\pi$
$42$	0	0
$43$	−4.64473	−0.708314	−0.354157	−	0.935186i	$-0.615232\pi$
$43$	−4.64473	−0.708314	−0.354157	+	0.935186i	$0.615232\pi$
$44$	0.149286	0.0225058
$45$	−2.92391	−0.435871
$46$	2.43361	0.358815
$47$	12.4732	1.81940	0.909698	−	0.415270i	$-0.136313\pi$
$47$	12.4732	1.81940	0.909698	+	0.415270i	$0.136313\pi$
$48$	−3.67914	−0.531038
$49$	0	0
$50$	4.82843	0.682843
$51$	8.05894	1.12848
$52$	−0.977714	−0.135584
$53$	7.44573	1.02275	0.511375	−	0.859358i	$-0.329136\pi$
$53$	7.44573	1.02275	0.511375	+	0.859358i	$0.329136\pi$
$54$	1.36041	0.185128
$55$	2.92391	0.394260
$56$	0	0
$57$	0.279181	0.0369785
$58$	5.31174	0.697466
$59$	10.7717	1.40236	0.701180	−	0.712985i	$-0.252657\pi$
$59$	10.7717	1.40236	0.701180	+	0.712985i	$0.252657\pi$
$60$	0.436500	0.0563519
$61$	−15.3298	−1.96278	−0.981388	−	0.192035i	$-0.938491\pi$
$61$	−15.3298	−1.96278	−0.981388	+	0.192035i	$0.938491\pi$
$62$	−0.839786	−0.106653
$63$	0	0
$64$	8.50467	1.06308
$65$	−19.1494	−2.37519
$66$	−1.36041	−0.167455
$67$	4.69564	0.573663	0.286832	−	0.957981i	$-0.407398\pi$
$67$	4.69564	0.573663	0.286832	+	0.957981i	$0.407398\pi$
$68$	−1.20309	−0.145896
$69$	1.78888	0.215355
$70$	0	0
$71$	9.38571	1.11388	0.556939	−	0.830553i	$-0.311976\pi$
$71$	9.38571	1.11388	0.556939	+	0.830553i	$0.311976\pi$
$72$	−2.92391	−0.344586
$73$	−0.847819	−0.0992297	−0.0496148	−	0.998768i	$-0.515799\pi$
$73$	−0.847819	−0.0992297	−0.0496148	+	0.998768i	$0.515799\pi$
$74$	−5.78266	−0.672220
$75$	3.54925	0.409832
$76$	−0.0416780	−0.00478079
$77$	0	0
$78$	8.90966	1.00882
$79$	−5.23461	−0.588939	−0.294470	−	0.955661i	$-0.595143\pi$
$79$	−5.23461	−0.588939	−0.294470	+	0.955661i	$0.595143\pi$
$80$	10.7575	1.20272
$81$	1.00000	0.111111
$82$	3.92391	0.433323
$83$	7.36663	0.808593	0.404296	−	0.914628i	$-0.367516\pi$
$83$	7.36663	0.808593	0.404296	+	0.914628i	$0.367516\pi$
$84$	0	0
$85$	−23.5636	−2.55583
$86$	−6.31873	−0.681366
$87$	3.90452	0.418608
$88$	2.92391	0.311690
$89$	−6.99088	−0.741032	−0.370516	−	0.928826i	$-0.620819\pi$
$89$	−6.99088	−0.741032	−0.370516	+	0.928826i	$0.620819\pi$
$90$	−3.97771	−0.419288
$91$	0	0
$92$	−0.267055	−0.0278424
$93$	−0.617304	−0.0640115
$94$	16.9686	1.75018
$95$	−0.816301	−0.0837507
$96$	0.842681	0.0860058
$97$	−8.07030	−0.819415	−0.409707	−	0.912217i	$-0.634369\pi$
$97$	−8.07030	−0.819415	−0.409707	+	0.912217i	$0.634369\pi$
$98$	0	0
$99$	−1.00000	−0.100504
$100$	−0.529854	−0.0529854
$101$	12.1220	1.20618	0.603091	−	0.797672i	$-0.293936\pi$
$101$	12.1220	1.20618	0.603091	+	0.797672i	$0.293936\pi$
$102$	10.9635	1.08554
$103$	8.62457	0.849804	0.424902	−	0.905239i	$-0.360309\pi$
$103$	8.62457	0.849804	0.424902	+	0.905239i	$0.360309\pi$
$104$	−19.1494	−1.87775
$105$	0	0
$106$	10.1292	0.983839
$107$	−17.6389	−1.70522	−0.852610	−	0.522547i	$-0.824982\pi$
$107$	−17.6389	−1.70522	−0.852610	+	0.522547i	$0.824982\pi$
$108$	−0.149286	−0.0143651
$109$	−12.6722	−1.21377	−0.606886	−	0.794789i	$-0.707582\pi$
$109$	−12.6722	−1.21377	−0.606886	+	0.794789i	$0.707582\pi$
$110$	3.97771	0.379260
$111$	−4.25067	−0.403456
$112$	0	0
$113$	−11.6009	−1.09132	−0.545661	−	0.838006i	$-0.683722\pi$
$113$	−11.6009	−1.09132	−0.545661	+	0.838006i	$0.683722\pi$
$114$	0.379801	0.0355716
$115$	−5.23051	−0.487748
$116$	−0.582892	−0.0541201
$117$	6.54925	0.605478
$118$	14.6540	1.34901
$119$	0	0
$120$	8.54925	0.780436
$121$	1.00000	0.0909091
$122$	−20.8548	−1.88810
$123$	2.88436	0.260074
$124$	0.0921551	0.00827578
$125$	4.24187	0.379405
$126$	0	0
$127$	−4.03152	−0.357739	−0.178870	−	0.983873i	$-0.557244\pi$
$127$	−4.03152	−0.357739	−0.178870	+	0.983873i	$0.557244\pi$
$128$	9.88447	0.873672
$129$	−4.64473	−0.408945
$130$	−26.0510	−2.28483
$131$	−15.4875	−1.35315	−0.676576	−	0.736373i	$-0.736537\pi$
$131$	−15.4875	−1.35315	−0.676576	+	0.736373i	$0.736537\pi$
$132$	0.149286	0.0129937
$133$	0	0
$134$	6.38799	0.551838
$135$	−2.92391	−0.251650
$136$	−23.5636	−2.02056
$137$	−2.02016	−0.172594	−0.0862969	−	0.996269i	$-0.527503\pi$
$137$	−2.02016	−0.172594	−0.0862969	+	0.996269i	$0.527503\pi$
$138$	2.43361	0.207162
$139$	21.0539	1.78577	0.892885	−	0.450285i	$-0.148678\pi$
$139$	21.0539	1.78577	0.892885	+	0.450285i	$0.148678\pi$
$140$	0	0
$141$	12.4732	1.05043
$142$	12.7684	1.07150
$143$	−6.54925	−0.547675
$144$	−3.67914	−0.306595
$145$	−11.4165	−0.948085
$146$	−1.15338	−0.0954544
$147$	0	0
$148$	0.634568	0.0521612
$149$	6.07942	0.498045	0.249023	−	0.968498i	$-0.419891\pi$
$149$	6.07942	0.498045	0.249023	+	0.968498i	$0.419891\pi$
$150$	4.82843	0.394239
$151$	15.8337	1.28853	0.644263	−	0.764804i	$-0.277164\pi$
$151$	15.8337	1.28853	0.644263	+	0.764804i	$0.277164\pi$
$152$	−0.816301	−0.0662107
$153$	8.05894	0.651527
$154$	0	0
$155$	1.80494	0.144976
$156$	−0.977714	−0.0782797
$157$	−14.3492	−1.14519	−0.572594	−	0.819839i	$-0.694063\pi$
$157$	−14.3492	−1.14519	−0.572594	+	0.819839i	$0.694063\pi$
$158$	−7.12121	−0.566533
$159$	7.44573	0.590485
$160$	−2.46392	−0.194790
$161$	0	0
$162$	1.36041	0.106884
$163$	−9.59715	−0.751706	−0.375853	−	0.926679i	$-0.622650\pi$
$163$	−9.59715	−0.751706	−0.375853	+	0.926679i	$0.622650\pi$
$164$	−0.430596	−0.0336239
$165$	2.92391	0.227626
$166$	10.0216	0.777830
$167$	−4.84705	−0.375076	−0.187538	−	0.982257i	$-0.560051\pi$
$167$	−4.84705	−0.375076	−0.187538	+	0.982257i	$0.560051\pi$
$168$	0	0
$169$	29.8926	2.29943
$170$	−32.0562	−2.45860
$171$	0.279181	0.0213495
$172$	0.693395	0.0528709
$173$	−13.6714	−1.03942	−0.519708	−	0.854344i	$-0.673959\pi$
$173$	−13.6714	−1.03942	−0.519708	+	0.854344i	$0.673959\pi$
$174$	5.31174	0.402682
$175$	0	0
$176$	3.67914	0.277326
$177$	10.7717	0.809653
$178$	−9.51046	−0.712839
$179$	−8.29278	−0.619832	−0.309916	−	0.950764i	$-0.600301\pi$
$179$	−8.29278	−0.619832	−0.309916	+	0.950764i	$0.600301\pi$
$180$	0.436500	0.0325348
$181$	−5.81630	−0.432322	−0.216161	−	0.976358i	$-0.569354\pi$
$181$	−5.81630	−0.432322	−0.216161	+	0.976358i	$0.569354\pi$
$182$	0	0
$183$	−15.3298	−1.13321
$184$	−5.23051	−0.385599
$185$	12.4286	0.913768
$186$	−0.839786	−0.0615761
$187$	−8.05894	−0.589328
$188$	−1.86207	−0.135806
$189$	0	0
$190$	−1.11050	−0.0805644
$191$	22.5841	1.63413	0.817064	−	0.576547i	$-0.195600\pi$
$191$	22.5841	1.63413	0.817064	+	0.576547i	$0.195600\pi$
$192$	8.50467	0.613772
$193$	−8.98317	−0.646623	−0.323311	−	0.946293i	$-0.604796\pi$
$193$	−8.98317	−0.646623	−0.323311	+	0.946293i	$0.604796\pi$
$194$	−10.9789	−0.788240
$195$	−19.1494	−1.37132
$196$	0	0
$197$	11.3180	0.806372	0.403186	−	0.915118i	$-0.367903\pi$
$197$	11.3180	0.806372	0.403186	+	0.915118i	$0.367903\pi$
$198$	−1.36041	−0.0966801
$199$	−17.7820	−1.26053	−0.630266	−	0.776379i	$-0.717054\pi$
$199$	−17.7820	−1.26053	−0.630266	+	0.776379i	$0.717054\pi$
$200$	−10.3777	−0.733812
$201$	4.69564	0.331205
$202$	16.4909	1.16029
$203$	0	0
$204$	−1.20309	−0.0842332
$205$	−8.43361	−0.589029
$206$	11.7329	0.817473
$207$	1.78888	0.124336
$208$	−24.0956	−1.67073
$209$	−0.279181	−0.0193114
$210$	0	0
$211$	1.40285	0.0965765	0.0482882	−	0.998833i	$-0.484623\pi$
$211$	1.40285	0.0965765	0.0482882	+	0.998833i	$0.484623\pi$
$212$	−1.11155	−0.0763413
$213$	9.38571	0.643098
$214$	−23.9962	−1.64034
$215$	13.5808	0.926200
$216$	−2.92391	−0.198947
$217$	0	0
$218$	−17.2393	−1.16759
$219$	−0.847819	−0.0572903
$220$	−0.436500	−0.0294288
$221$	52.7800	3.55037
$222$	−5.78266	−0.388106
$223$	9.61807	0.644074	0.322037	−	0.946727i	$-0.395633\pi$
$223$	9.61807	0.644074	0.322037	+	0.946727i	$0.395633\pi$
$224$	0	0
$225$	3.54925	0.236616
$226$	−15.7820	−1.04980
$227$	−7.23352	−0.480106	−0.240053	−	0.970760i	$-0.577165\pi$
$227$	−7.23352	−0.480106	−0.240053	+	0.970760i	$0.577165\pi$
$228$	−0.0416780	−0.00276019
$229$	10.5603	0.697843	0.348922	−	0.937152i	$-0.386548\pi$
$229$	10.5603	0.697843	0.348922	+	0.937152i	$0.386548\pi$
$230$	−7.11564	−0.469191
$231$	0	0
$232$	−11.4165	−0.749527
$233$	3.93271	0.257640	0.128820	−	0.991668i	$-0.458881\pi$
$233$	3.93271	0.257640	0.128820	+	0.991668i	$0.458881\pi$
$234$	8.90966	0.582442
$235$	−36.4704	−2.37906
$236$	−1.60807	−0.104677
$237$	−5.23461	−0.340024
$238$	0	0
$239$	−11.6405	−0.752960	−0.376480	−	0.926425i	$-0.622866\pi$
$239$	−11.6405	−0.752960	−0.376480	+	0.926425i	$0.622866\pi$
$240$	10.7575	0.694392
$241$	13.9360	0.897699	0.448849	−	0.893607i	$-0.351834\pi$
$241$	13.9360	0.897699	0.448849	+	0.893607i	$0.351834\pi$
$242$	1.36041	0.0874504
$243$	1.00000	0.0641500
$244$	2.28853	0.146508
$245$	0	0
$246$	3.92391	0.250179
$247$	1.82843	0.116340
$248$	1.80494	0.114614
$249$	7.36663	0.466841
$250$	5.77068	0.364970
$251$	−4.32676	−0.273103	−0.136551	−	0.990633i	$-0.543602\pi$
$251$	−4.32676	−0.273103	−0.136551	+	0.990633i	$0.543602\pi$
$252$	0	0
$253$	−1.78888	−0.112466
$254$	−5.48451	−0.344129
$255$	−23.5636	−1.47561
$256$	−3.56242	−0.222651
$257$	−21.4092	−1.33547	−0.667734	−	0.744400i	$-0.732736\pi$
$257$	−21.4092	−1.33547	−0.667734	+	0.744400i	$0.732736\pi$
$258$	−6.31873	−0.393387
$259$	0	0
$260$	2.85875	0.177292
$261$	3.90452	0.241684
$262$	−21.0694	−1.30167
$263$	2.43284	0.150015	0.0750076	−	0.997183i	$-0.476102\pi$
$263$	2.43284	0.150015	0.0750076	+	0.997183i	$0.476102\pi$
$264$	2.92391	0.179954
$265$	−21.7706	−1.33736
$266$	0	0
$267$	−6.99088	−0.427835
$268$	−0.700995	−0.0428201
$269$	−27.2573	−1.66191	−0.830954	−	0.556341i	$-0.812205\pi$
$269$	−27.2573	−1.66191	−0.830954	+	0.556341i	$0.812205\pi$
$270$	−3.97771	−0.242076
$271$	17.1727	1.04317	0.521585	−	0.853200i	$-0.325341\pi$
$271$	17.1727	1.04317	0.521585	+	0.853200i	$0.325341\pi$
$272$	−29.6500	−1.79779
$273$	0	0
$274$	−2.74824	−0.166027
$275$	−3.54925	−0.214028
$276$	−0.267055	−0.0160748
$277$	14.3202	0.860418	0.430209	−	0.902729i	$-0.358440\pi$
$277$	14.3202	0.860418	0.430209	+	0.902729i	$0.358440\pi$
$278$	28.6419	1.71783
$279$	−0.617304	−0.0369570
$280$	0	0
$281$	−7.74808	−0.462212	−0.231106	−	0.972929i	$-0.574234\pi$
$281$	−7.74808	−0.462212	−0.231106	+	0.972929i	$0.574234\pi$
$282$	16.9686	1.01047
$283$	17.5811	1.04509	0.522543	−	0.852613i	$-0.324983\pi$
$283$	17.5811	1.04509	0.522543	+	0.852613i	$0.324983\pi$
$284$	−1.40116	−0.0831435
$285$	−0.816301	−0.0483535
$286$	−8.90966	−0.526839
$287$	0	0
$288$	0.842681	0.0496555
$289$	47.9465	2.82038
$290$	−15.5311	−0.912015
$291$	−8.07030	−0.473089
$292$	0.126568	0.00740682
$293$	−6.19915	−0.362158	−0.181079	−	0.983469i	$-0.557959\pi$
$293$	−6.19915	−0.362158	−0.181079	+	0.983469i	$0.557959\pi$
$294$	0	0
$295$	−31.4956	−1.83374
$296$	12.4286	0.722397
$297$	−1.00000	−0.0580259
$298$	8.27050	0.479097
$299$	11.7158	0.677542
$300$	−0.529854	−0.0305911
$301$	0	0
$302$	21.5403	1.23950
$303$	12.1220	0.696389
$304$	−1.02715	−0.0589109
$305$	44.8229	2.56655
$306$	10.9635	0.626739
$307$	5.29099	0.301973	0.150986	−	0.988536i	$-0.451755\pi$
$307$	5.29099	0.301973	0.150986	+	0.988536i	$0.451755\pi$
$308$	0	0
$309$	8.62457	0.490635
$310$	2.45546	0.139461
$311$	13.8924	0.787765	0.393883	−	0.919161i	$-0.371132\pi$
$311$	13.8924	0.787765	0.393883	+	0.919161i	$0.371132\pi$
$312$	−19.1494	−1.08412
$313$	8.16076	0.461273	0.230637	−	0.973040i	$-0.425919\pi$
$313$	8.16076	0.461273	0.230637	+	0.973040i	$0.425919\pi$
$314$	−19.5207	−1.10162
$315$	0	0
$316$	0.781456	0.0439603
$317$	7.44465	0.418133	0.209067	−	0.977901i	$-0.432957\pi$
$317$	7.44465	0.418133	0.209067	+	0.977901i	$0.432957\pi$
$318$	10.1292	0.568020
$319$	−3.90452	−0.218611
$320$	−24.8669	−1.39010
$321$	−17.6389	−0.984510
$322$	0	0
$323$	2.24991	0.125188
$324$	−0.149286	−0.00829369
$325$	23.2449	1.28939
$326$	−13.0560	−0.723108
$327$	−12.6722	−0.700772
$328$	−8.43361	−0.465668
$329$	0	0
$330$	3.97771	0.218966
$331$	11.1067	0.610478	0.305239	−	0.952276i	$-0.401264\pi$
$331$	11.1067	0.610478	0.305239	+	0.952276i	$0.401264\pi$
$332$	−1.09974	−0.0603560
$333$	−4.25067	−0.232935
$334$	−6.59397	−0.360806
$335$	−13.7296	−0.750129
$336$	0	0
$337$	−32.2802	−1.75841	−0.879207	−	0.476441i	$-0.841927\pi$
$337$	−32.2802	−1.75841	−0.879207	+	0.476441i	$0.841927\pi$
$338$	40.6662	2.21195
$339$	−11.6009	−0.630076
$340$	3.51773	0.190776
$341$	0.617304	0.0334289
$342$	0.379801	0.0205373
$343$	0	0
$344$	13.5808	0.732226
$345$	−5.23051	−0.281601
$346$	−18.5987	−0.999871
$347$	0.664437	0.0356689	0.0178344	−	0.999841i	$-0.494323\pi$
$347$	0.664437	0.0356689	0.0178344	+	0.999841i	$0.494323\pi$
$348$	−0.582892	−0.0312463
$349$	13.8833	0.743155	0.371577	−	0.928402i	$-0.378817\pi$
$349$	13.8833	0.743155	0.371577	+	0.928402i	$0.378817\pi$
$350$	0	0
$351$	6.54925	0.349573
$352$	−0.842681	−0.0449151
$353$	17.2452	0.917869	0.458935	−	0.888470i	$-0.348231\pi$
$353$	17.2452	0.917869	0.458935	+	0.888470i	$0.348231\pi$
$354$	14.6540	0.778849
$355$	−27.4430	−1.45652
$356$	1.04364	0.0553130
$357$	0	0
$358$	−11.2816	−0.596250
$359$	26.4385	1.39537	0.697686	−	0.716403i	$-0.254213\pi$
$359$	26.4385	1.39537	0.697686	+	0.716403i	$0.254213\pi$
$360$	8.54925	0.450585
$361$	−18.9221	−0.995898
$362$	−7.91255	−0.415874
$363$	1.00000	0.0524864
$364$	0	0
$365$	2.47894	0.129754
$366$	−20.8548	−1.09010
$367$	27.8926	1.45598	0.727991	−	0.685586i	$-0.240454\pi$
$367$	27.8926	1.45598	0.727991	+	0.685586i	$0.240454\pi$
$368$	−6.58153	−0.343086
$369$	2.88436	0.150154
$370$	16.9080	0.879003
$371$	0	0
$372$	0.0921551	0.00477802
$373$	9.51347	0.492589	0.246294	−	0.969195i	$-0.420787\pi$
$373$	9.51347	0.492589	0.246294	+	0.969195i	$0.420787\pi$
$374$	−10.9635	−0.566907
$375$	4.24187	0.219049
$376$	−36.4704	−1.88082
$377$	25.5716	1.31701
$378$	0	0
$379$	−6.48468	−0.333095	−0.166548	−	0.986033i	$-0.553262\pi$
$379$	−6.48468	−0.333095	−0.166548	+	0.986033i	$0.553262\pi$
$380$	0.121863	0.00625142
$381$	−4.03152	−0.206541
$382$	30.7236	1.57196
$383$	30.5116	1.55907	0.779535	−	0.626358i	$-0.215455\pi$
$383$	30.5116	1.55907	0.779535	+	0.626358i	$0.215455\pi$
$384$	9.88447	0.504415
$385$	0	0
$386$	−12.2208	−0.622022
$387$	−4.64473	−0.236105
$388$	1.20479	0.0611638
$389$	−2.10073	−0.106511	−0.0532557	−	0.998581i	$-0.516960\pi$
$389$	−2.10073	−0.106511	−0.0532557	+	0.998581i	$0.516960\pi$
$390$	−26.0510	−1.31914
$391$	14.4165	0.729072
$392$	0	0
$393$	−15.4875	−0.781242
$394$	15.3971	0.775693
$395$	15.3055	0.770104
$396$	0.149286	0.00750193
$397$	−21.3645	−1.07225	−0.536126	−	0.844138i	$-0.680113\pi$
$397$	−21.3645	−1.07225	−0.536126	+	0.844138i	$0.680113\pi$
$398$	−24.1908	−1.21258
$399$	0	0
$400$	−13.0582	−0.652909
$401$	25.2909	1.26297	0.631484	−	0.775389i	$-0.282446\pi$
$401$	25.2909	1.26297	0.631484	+	0.775389i	$0.282446\pi$
$402$	6.38799	0.318604
$403$	−4.04288	−0.201390
$404$	−1.80965	−0.0900333
$405$	−2.92391	−0.145290
$406$	0	0
$407$	4.25067	0.210698
$408$	−23.5636	−1.16657
$409$	−19.8763	−0.982821	−0.491411	−	0.870928i	$-0.663519\pi$
$409$	−19.8763	−0.982821	−0.491411	+	0.870928i	$0.663519\pi$
$410$	−11.4732	−0.566619
$411$	−2.02016	−0.0996471
$412$	−1.28753	−0.0634321
$413$	0	0
$414$	2.43361	0.119605
$415$	−21.5394	−1.05733
$416$	5.51893	0.270588
$417$	21.0539	1.03101
$418$	−0.379801	−0.0185767
$419$	18.1118	0.884818	0.442409	−	0.896813i	$-0.354124\pi$
$419$	18.1118	0.884818	0.442409	+	0.896813i	$0.354124\pi$
$420$	0	0
$421$	−14.3380	−0.698789	−0.349395	−	0.936976i	$-0.613613\pi$
$421$	−14.3380	−0.698789	−0.349395	+	0.936976i	$0.613613\pi$
$422$	1.90846	0.0929022
$423$	12.4732	0.606466
$424$	−21.7706	−1.05728
$425$	28.6032	1.38746
$426$	12.7684	0.618631
$427$	0	0
$428$	2.63325	0.127283
$429$	−6.54925	−0.316201
$430$	18.4754	0.890963
$431$	−28.9139	−1.39273	−0.696366	−	0.717687i	$-0.745201\pi$
$431$	−28.9139	−1.39273	−0.696366	+	0.717687i	$0.745201\pi$
$432$	−3.67914	−0.177013
$433$	−1.81722	−0.0873302	−0.0436651	−	0.999046i	$-0.513903\pi$
$433$	−1.81722	−0.0873302	−0.0436651	+	0.999046i	$0.513903\pi$
$434$	0	0
$435$	−11.4165	−0.547377
$436$	1.89178	0.0905998
$437$	0.499421	0.0238906
$438$	−1.15338	−0.0551106
$439$	31.2115	1.48964	0.744822	−	0.667263i	$-0.232534\pi$
$439$	31.2115	1.48964	0.744822	+	0.667263i	$0.232534\pi$
$440$	−8.54925	−0.407569
$441$	0	0
$442$	71.8024	3.41529
$443$	2.46813	0.117265	0.0586323	−	0.998280i	$-0.481326\pi$
$443$	2.46813	0.117265	0.0586323	+	0.998280i	$0.481326\pi$
$444$	0.634568	0.0301153
$445$	20.4407	0.968983
$446$	13.0845	0.619570
$447$	6.07942	0.287547
$448$	0	0
$449$	−11.0996	−0.523821	−0.261911	−	0.965092i	$-0.584353\pi$
$449$	−11.0996	−0.523821	−0.261911	+	0.965092i	$0.584353\pi$
$450$	4.82843	0.227614
$451$	−2.88436	−0.135819
$452$	1.73186	0.0814599
$453$	15.8337	0.743931
$454$	−9.84055	−0.461840
$455$	0	0
$456$	−0.816301	−0.0382268
$457$	−4.26814	−0.199655	−0.0998276	−	0.995005i	$-0.531829\pi$
$457$	−4.26814	−0.199655	−0.0998276	+	0.995005i	$0.531829\pi$
$458$	14.3663	0.671294
$459$	8.05894	0.376159
$460$	0.780845	0.0364071
$461$	10.1578	0.473094	0.236547	−	0.971620i	$-0.423984\pi$
$461$	10.1578	0.473094	0.236547	+	0.971620i	$0.423984\pi$
$462$	0	0
$463$	−38.0517	−1.76841	−0.884207	−	0.467095i	$-0.845301\pi$
$463$	−38.0517	−1.76841	−0.884207	+	0.467095i	$0.845301\pi$
$464$	−14.3653	−0.666891
$465$	1.80494	0.0837022
$466$	5.35009	0.247838
$467$	−36.7374	−1.70001	−0.850003	−	0.526778i	$-0.823400\pi$
$467$	−36.7374	−1.70001	−0.850003	+	0.526778i	$0.823400\pi$
$468$	−0.977714	−0.0451948
$469$	0	0
$470$	−49.6146	−2.28855
$471$	−14.3492	−0.661175
$472$	−31.4956	−1.44970
$473$	4.64473	0.213565
$474$	−7.12121	−0.327088
$475$	0.990883	0.0454648
$476$	0	0
$477$	7.44573	0.340917
$478$	−15.8358	−0.724313
$479$	−25.6886	−1.17374	−0.586871	−	0.809680i	$-0.699640\pi$
$479$	−25.6886	−1.17374	−0.586871	+	0.809680i	$0.699640\pi$
$480$	−2.46392	−0.112462
$481$	−27.8387	−1.26934
$482$	18.9587	0.863546
$483$	0	0
$484$	−0.149286	−0.00678575
$485$	23.5968	1.07148
$486$	1.36041	0.0617094
$487$	−33.3686	−1.51207	−0.756037	−	0.654529i	$-0.772867\pi$
$487$	−33.3686	−1.51207	−0.756037	+	0.654529i	$0.772867\pi$
$488$	44.8229	2.02904
$489$	−9.59715	−0.433998
$490$	0	0
$491$	−5.20216	−0.234770	−0.117385	−	0.993086i	$-0.537451\pi$
$491$	−5.20216	−0.234770	−0.117385	+	0.993086i	$0.537451\pi$
$492$	−0.430596	−0.0194128
$493$	31.4663	1.41717
$494$	2.48741	0.111914
$495$	2.92391	0.131420
$496$	2.27115	0.101978
$497$	0	0
$498$	10.0216	0.449080
$499$	−19.6132	−0.878008	−0.439004	−	0.898485i	$-0.644669\pi$
$499$	−19.6132	−0.878008	−0.439004	+	0.898485i	$0.644669\pi$
$500$	−0.633254	−0.0283200
$501$	−4.84705	−0.216550
$502$	−5.88617	−0.262713
$503$	15.2316	0.679143	0.339572	−	0.940580i	$-0.389718\pi$
$503$	15.2316	0.679143	0.339572	+	0.940580i	$0.389718\pi$
$504$	0	0
$505$	−35.4436	−1.57722
$506$	−2.43361	−0.108187
$507$	29.8926	1.32758
$508$	0.601851	0.0267028
$509$	−12.5541	−0.556451	−0.278225	−	0.960516i	$-0.589746\pi$
$509$	−12.5541	−0.556451	−0.278225	+	0.960516i	$0.589746\pi$
$510$	−32.0562	−1.41947
$511$	0	0
$512$	−24.6153	−1.08785
$513$	0.279181	0.0123262
$514$	−29.1253	−1.28466
$515$	−25.2175	−1.11121
$516$	0.693395	0.0305250
$517$	−12.4732	−0.548569
$518$	0	0
$519$	−13.6714	−0.600107
$520$	55.9911	2.45537
$521$	−14.1828	−0.621358	−0.310679	−	0.950515i	$-0.600556\pi$
$521$	−14.1828	−0.621358	−0.310679	+	0.950515i	$0.600556\pi$
$522$	5.31174	0.232489
$523$	−22.2897	−0.974660	−0.487330	−	0.873218i	$-0.662029\pi$
$523$	−22.2897	−0.974660	−0.487330	+	0.873218i	$0.662029\pi$
$524$	2.31208	0.101004
$525$	0	0
$526$	3.30966	0.144308
$527$	−4.97482	−0.216707
$528$	3.67914	0.160114
$529$	−19.7999	−0.860866
$530$	−29.6170	−1.28648
$531$	10.7717	0.467453
$532$	0	0
$533$	18.8904	0.818233
$534$	−9.51046	−0.411558
$535$	51.5747	2.22977
$536$	−13.7296	−0.593029
$537$	−8.29278	−0.357860
$538$	−37.0811	−1.59868
$539$	0	0
$540$	0.436500	0.0187840
$541$	−28.6870	−1.23335	−0.616675	−	0.787218i	$-0.711521\pi$
$541$	−28.6870	−1.23335	−0.616675	+	0.787218i	$0.711521\pi$
$542$	23.3619	1.00348
$543$	−5.81630	−0.249601
$544$	6.79112	0.291167
$545$	37.0522	1.58714
$546$	0	0
$547$	−3.93981	−0.168454	−0.0842271	−	0.996447i	$-0.526842\pi$
$547$	−3.93981	−0.168454	−0.0842271	+	0.996447i	$0.526842\pi$
$548$	0.301582	0.0128830
$549$	−15.3298	−0.654259
$550$	−4.82843	−0.205885
$551$	1.09007	0.0464385
$552$	−5.23051	−0.222625
$553$	0	0
$554$	19.4813	0.827683
$555$	12.4286	0.527564
$556$	−3.14306	−0.133296
$557$	−16.7541	−0.709895	−0.354948	−	0.934886i	$-0.615501\pi$
$557$	−16.7541	−0.709895	−0.354948	+	0.934886i	$0.615501\pi$
$558$	−0.839786	−0.0355510
$559$	−30.4195	−1.28661
$560$	0	0
$561$	−8.05894	−0.340249
$562$	−10.5406	−0.444627
$563$	−41.1388	−1.73379	−0.866896	−	0.498489i	$-0.833888\pi$
$563$	−41.1388	−1.73379	−0.866896	+	0.498489i	$0.833888\pi$
$564$	−1.86207	−0.0784074
$565$	33.9200	1.42703
$566$	23.9175	1.00533
$567$	0	0
$568$	−27.4430	−1.15148
$569$	−22.0185	−0.923062	−0.461531	−	0.887124i	$-0.652700\pi$
$569$	−22.0185	−0.923062	−0.461531	+	0.887124i	$0.652700\pi$
$570$	−1.11050	−0.0465139
$571$	−8.26689	−0.345959	−0.172979	−	0.984925i	$-0.555339\pi$
$571$	−8.26689	−0.345959	−0.172979	+	0.984925i	$0.555339\pi$
$572$	0.977714	0.0408803
$573$	22.5841	0.943464
$574$	0	0
$575$	6.34916	0.264778
$576$	8.50467	0.354361
$577$	−27.7303	−1.15443	−0.577214	−	0.816593i	$-0.695860\pi$
$577$	−27.7303	−1.15443	−0.577214	+	0.816593i	$0.695860\pi$
$578$	65.2269	2.71308
$579$	−8.98317	−0.373328
$580$	1.70432	0.0707681
$581$	0	0
$582$	−10.9789	−0.455091
$583$	−7.44573	−0.308371
$584$	2.47894	0.102579
$585$	−19.1494	−0.791730
$586$	−8.43338	−0.348380
$587$	−4.55289	−0.187918	−0.0939590	−	0.995576i	$-0.529952\pi$
$587$	−4.55289	−0.187918	−0.0939590	+	0.995576i	$0.529952\pi$
$588$	0	0
$589$	−0.172340	−0.00710114
$590$	−42.8468	−1.76398
$591$	11.3180	0.465559
$592$	15.6388	0.642752
$593$	25.7106	1.05581	0.527904	−	0.849304i	$-0.322978\pi$
$593$	25.7106	1.05581	0.527904	+	0.849304i	$0.322978\pi$
$594$	−1.36041	−0.0558183
$595$	0	0
$596$	−0.907575	−0.0371757
$597$	−17.7820	−0.727769
$598$	15.9383	0.651765
$599$	−25.7808	−1.05337	−0.526687	−	0.850060i	$-0.676566\pi$
$599$	−25.7808	−1.05337	−0.526687	+	0.850060i	$0.676566\pi$
$600$	−10.3777	−0.423667
$601$	−18.6731	−0.761694	−0.380847	−	0.924638i	$-0.624367\pi$
$601$	−18.6731	−0.761694	−0.380847	+	0.924638i	$0.624367\pi$
$602$	0	0
$603$	4.69564	0.191221
$604$	−2.36375	−0.0961798
$605$	−2.92391	−0.118874
$606$	16.4909	0.669895
$607$	−7.83291	−0.317928	−0.158964	−	0.987284i	$-0.550815\pi$
$607$	−7.83291	−0.317928	−0.158964	+	0.987284i	$0.550815\pi$
$608$	0.235261	0.00954109
$609$	0	0
$610$	60.9774	2.46890
$611$	81.6898	3.30481
$612$	−1.20309	−0.0486321
$613$	15.6008	0.630109	0.315054	−	0.949074i	$-0.397977\pi$
$613$	15.6008	0.630109	0.315054	+	0.949074i	$0.397977\pi$
$614$	7.19791	0.290484
$615$	−8.43361	−0.340076
$616$	0	0
$617$	10.5196	0.423502	0.211751	−	0.977324i	$-0.432083\pi$
$617$	10.5196	0.423502	0.211751	+	0.977324i	$0.432083\pi$
$618$	11.7329	0.471968
$619$	48.6552	1.95562	0.977809	−	0.209496i	$-0.0671824\pi$
$619$	48.6552	1.95562	0.977809	+	0.209496i	$0.0671824\pi$
$620$	−0.269453	−0.0108215
$621$	1.78888	0.0717852
$622$	18.8993	0.757794
$623$	0	0
$624$	−24.0956	−0.964596
$625$	−30.1491	−1.20596
$626$	11.1020	0.443724
$627$	−0.279181	−0.0111494
$628$	2.14214	0.0854805
$629$	−34.2559	−1.36587
$630$	0	0
$631$	33.7632	1.34409	0.672045	−	0.740510i	$-0.265416\pi$
$631$	33.7632	1.34409	0.672045	+	0.740510i	$0.265416\pi$
$632$	15.3055	0.608821
$633$	1.40285	0.0557585
$634$	10.1278	0.402225
$635$	11.7878	0.467784
$636$	−1.11155	−0.0440757
$637$	0	0
$638$	−5.31174	−0.210294
$639$	9.38571	0.371293
$640$	−28.9013	−1.14242
$641$	14.5230	0.573626	0.286813	−	0.957987i	$-0.407404\pi$
$641$	14.5230	0.573626	0.286813	+	0.957987i	$0.407404\pi$
$642$	−23.9962	−0.947054
$643$	2.08637	0.0822782	0.0411391	−	0.999153i	$-0.486901\pi$
$643$	2.08637	0.0822782	0.0411391	+	0.999153i	$0.486901\pi$
$644$	0	0
$645$	13.5808	0.534742
$646$	3.06079	0.120425
$647$	−13.2225	−0.519829	−0.259915	−	0.965632i	$-0.583694\pi$
$647$	−13.2225	−0.519829	−0.259915	+	0.965632i	$0.583694\pi$
$648$	−2.92391	−0.114862
$649$	−10.7717	−0.422827
$650$	31.6226	1.24034
$651$	0	0
$652$	1.43272	0.0561098
$653$	41.7262	1.63287	0.816437	−	0.577435i	$-0.195946\pi$
$653$	41.7262	1.63287	0.816437	+	0.577435i	$0.195946\pi$
$654$	−17.2393	−0.674111
$655$	45.2841	1.76940
$656$	−10.6120	−0.414328
$657$	−0.847819	−0.0330766
$658$	0	0
$659$	13.4701	0.524719	0.262359	−	0.964970i	$-0.415499\pi$
$659$	13.4701	0.524719	0.262359	+	0.964970i	$0.415499\pi$
$660$	−0.436500	−0.0169907
$661$	−26.9877	−1.04970	−0.524849	−	0.851195i	$-0.675878\pi$
$661$	−26.9877	−1.04970	−0.524849	+	0.851195i	$0.675878\pi$
$662$	15.1096	0.587252
$663$	52.7800	2.04980
$664$	−21.5394	−0.835889
$665$	0	0
$666$	−5.78266	−0.224073
$667$	6.98470	0.270449
$668$	0.723599	0.0279969
$669$	9.61807	0.371856
$670$	−18.6779	−0.721590
$671$	15.3298	0.591799
$672$	0	0
$673$	44.8638	1.72937	0.864686	−	0.502313i	$-0.167517\pi$
$673$	44.8638	1.72937	0.864686	+	0.502313i	$0.167517\pi$
$674$	−43.9143	−1.69151
$675$	3.54925	0.136611
$676$	−4.46256	−0.171637
$677$	11.4891	0.441560	0.220780	−	0.975324i	$-0.429140\pi$
$677$	11.4891	0.441560	0.220780	+	0.975324i	$0.429140\pi$
$678$	−15.7820	−0.606104
$679$	0	0
$680$	68.8979	2.64211
$681$	−7.23352	−0.277189
$682$	0.839786	0.0321571
$683$	−40.5886	−1.55308	−0.776539	−	0.630069i	$-0.783027\pi$
$683$	−40.5886	−1.55308	−0.776539	+	0.630069i	$0.783027\pi$
$684$	−0.0416780	−0.00159360
$685$	5.90676	0.225686
$686$	0	0
$687$	10.5603	0.402900
$688$	17.0886	0.651497
$689$	48.7639	1.85776
$690$	−7.11564	−0.270888
$691$	35.7228	1.35896	0.679480	−	0.733694i	$-0.262205\pi$
$691$	35.7228	1.35896	0.679480	+	0.733694i	$0.262205\pi$
$692$	2.04095	0.0775854
$693$	0	0
$694$	0.903907	0.0343118
$695$	−61.5597	−2.33509
$696$	−11.4165	−0.432740
$697$	23.2449	0.880463
$698$	18.8869	0.714881
$699$	3.93271	0.148749
$700$	0	0
$701$	−23.2809	−0.879309	−0.439655	−	0.898167i	$-0.644899\pi$
$701$	−23.2809	−0.879309	−0.439655	+	0.898167i	$0.644899\pi$
$702$	8.90966	0.336273
$703$	−1.18671	−0.0447576
$704$	−8.50467	−0.320532
$705$	−36.4704	−1.37355
$706$	23.4605	0.882949
$707$	0	0
$708$	−1.60807	−0.0604351
$709$	−41.6838	−1.56547	−0.782734	−	0.622356i	$-0.786175\pi$
$709$	−41.6838	−1.56547	−0.782734	+	0.622356i	$0.786175\pi$
$710$	−37.3336	−1.40111
$711$	−5.23461	−0.196313
$712$	20.4407	0.766048
$713$	−1.10428	−0.0413557
$714$	0	0
$715$	19.1494	0.716147
$716$	1.23800	0.0462662
$717$	−11.6405	−0.434721
$718$	35.9672	1.34229
$719$	32.2149	1.20141	0.600707	−	0.799470i	$-0.294886\pi$
$719$	32.2149	1.20141	0.600707	+	0.799470i	$0.294886\pi$
$720$	10.7575	0.400907
$721$	0	0
$722$	−25.7417	−0.958009
$723$	13.9360	0.518287
$724$	0.868295	0.0322699
$725$	13.8581	0.514677
$726$	1.36041	0.0504895
$727$	−38.9139	−1.44324	−0.721619	−	0.692290i	$-0.756602\pi$
$727$	−38.9139	−1.44324	−0.721619	+	0.692290i	$0.756602\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	3.37238	0.124817
$731$	−37.4316	−1.38446
$732$	2.28853	0.0845864
$733$	28.8329	1.06497	0.532484	−	0.846440i	$-0.321259\pi$
$733$	28.8329	1.06497	0.532484	+	0.846440i	$0.321259\pi$
$734$	37.9454	1.40059
$735$	0	0
$736$	1.50745	0.0555655
$737$	−4.69564	−0.172966
$738$	3.92391	0.144441
$739$	−49.7506	−1.83010	−0.915052	−	0.403336i	$-0.867850\pi$
$739$	−49.7506	−1.83010	−0.915052	+	0.403336i	$0.867850\pi$
$740$	−1.85542	−0.0682065
$741$	1.82843	0.0671689
$742$	0	0
$743$	34.6365	1.27069	0.635345	−	0.772229i	$-0.280858\pi$
$743$	34.6365	1.27069	0.635345	+	0.772229i	$0.280858\pi$
$744$	1.80494	0.0661724
$745$	−17.7757	−0.651250
$746$	12.9422	0.473848
$747$	7.36663	0.269531
$748$	1.20309	0.0439894
$749$	0	0
$750$	5.77068	0.210716
$751$	−20.4901	−0.747696	−0.373848	−	0.927490i	$-0.621962\pi$
$751$	−20.4901	−0.747696	−0.373848	+	0.927490i	$0.621962\pi$
$752$	−45.8905	−1.67345
$753$	−4.32676	−0.157676
$754$	34.7879	1.26690
$755$	−46.2962	−1.68489
$756$	0	0
$757$	−17.0103	−0.618249	−0.309124	−	0.951022i	$-0.600036\pi$
$757$	−17.0103	−0.618249	−0.309124	+	0.951022i	$0.600036\pi$
$758$	−8.82181	−0.320423
$759$	−1.78888	−0.0649321
$760$	2.38679	0.0865780
$761$	−29.2809	−1.06143	−0.530717	−	0.847549i	$-0.678077\pi$
$761$	−29.2809	−1.06143	−0.530717	+	0.847549i	$0.678077\pi$
$762$	−5.48451	−0.198683
$763$	0	0
$764$	−3.37150	−0.121977
$765$	−23.5636	−0.851944
$766$	41.5083	1.49976
$767$	70.5467	2.54729
$768$	−3.56242	−0.128548
$769$	−21.0142	−0.757792	−0.378896	−	0.925439i	$-0.623696\pi$
$769$	−21.0142	−0.757792	−0.378896	+	0.925439i	$0.623696\pi$
$770$	0	0
$771$	−21.4092	−0.771033
$772$	1.34107	0.0482660
$773$	−23.5389	−0.846635	−0.423317	−	0.905981i	$-0.639134\pi$
$773$	−23.5389	−0.846635	−0.423317	+	0.905981i	$0.639134\pi$
$774$	−6.31873	−0.227122
$775$	−2.19096	−0.0787018
$776$	23.5968	0.847077
$777$	0	0
$778$	−2.85786	−0.102459
$779$	0.805259	0.0288514
$780$	2.85875	0.102360
$781$	−9.38571	−0.335847
$782$	19.6123	0.701334
$783$	3.90452	0.139536
$784$	0	0
$785$	41.9557	1.49746
$786$	−21.0694	−0.751520
$787$	45.3961	1.61820	0.809099	−	0.587673i	$-0.199956\pi$
$787$	45.3961	1.61820	0.809099	+	0.587673i	$0.199956\pi$
$788$	−1.68962	−0.0601902
$789$	2.43284	0.0866113
$790$	20.8218	0.740805
$791$	0	0
$792$	2.92391	0.103897
$793$	−100.398	−3.56525
$794$	−29.0644	−1.03146
$795$	−21.7706	−0.772125
$796$	2.65461	0.0940902
$797$	−15.0379	−0.532668	−0.266334	−	0.963881i	$-0.585812\pi$
$797$	−15.0379	−0.532668	−0.266334	+	0.963881i	$0.585812\pi$
$798$	0	0
$799$	100.520	3.55616
$800$	2.99088	0.105744
$801$	−6.99088	−0.247011
$802$	34.4060	1.21492
$803$	0.847819	0.0299189
$804$	−0.700995	−0.0247222
$805$	0	0
$806$	−5.49997	−0.193728
$807$	−27.2573	−0.959503
$808$	−35.4436	−1.24690
$809$	−46.4609	−1.63348	−0.816740	−	0.577006i	$-0.804221\pi$
$809$	−46.4609	−1.63348	−0.816740	+	0.577006i	$0.804221\pi$
$810$	−3.97771	−0.139763
$811$	29.7217	1.04367	0.521835	−	0.853047i	$-0.325248\pi$
$811$	29.7217	1.04367	0.521835	+	0.853047i	$0.325248\pi$
$812$	0	0
$813$	17.1727	0.602274
$814$	5.78266	0.202682
$815$	28.0612	0.982940
$816$	−29.6500	−1.03796
$817$	−1.29672	−0.0453665
$818$	−27.0399	−0.945429
$819$	0	0
$820$	1.25902	0.0439670
$821$	−2.98694	−0.104245	−0.0521225	−	0.998641i	$-0.516599\pi$
$821$	−2.98694	−0.104245	−0.0521225	+	0.998641i	$0.516599\pi$
$822$	−2.74824	−0.0958560
$823$	28.4374	0.991265	0.495632	−	0.868532i	$-0.334936\pi$
$823$	28.4374	0.991265	0.495632	+	0.868532i	$0.334936\pi$
$824$	−25.2175	−0.878492
$825$	−3.54925	−0.123569
$826$	0	0
$827$	−23.8502	−0.829354	−0.414677	−	0.909969i	$-0.636105\pi$
$827$	−23.8502	−0.829354	−0.414677	+	0.909969i	$0.636105\pi$
$828$	−0.267055	−0.00928081
$829$	40.7271	1.41451	0.707255	−	0.706959i	$-0.249933\pi$
$829$	40.7271	1.41451	0.707255	+	0.706959i	$0.249933\pi$
$830$	−29.3023	−1.01710
$831$	14.3202	0.496762
$832$	55.6992	1.93102
$833$	0	0
$834$	28.6419	0.991790
$835$	14.1723	0.490454
$836$	0.0416780	0.00144146
$837$	−0.617304	−0.0213372
$838$	24.6394	0.851155
$839$	−34.6131	−1.19498	−0.597489	−	0.801877i	$-0.703835\pi$
$839$	−34.6131	−1.19498	−0.597489	+	0.801877i	$0.703835\pi$
$840$	0	0
$841$	−13.7547	−0.474301
$842$	−19.5055	−0.672204
$843$	−7.74808	−0.266858
$844$	−0.209427	−0.00720878
$845$	−87.4033	−3.00677
$846$	16.9686	0.583392
$847$	0	0
$848$	−27.3939	−0.940710
$849$	17.5811	0.603381
$850$	38.9120	1.33467
$851$	−7.60393	−0.260659
$852$	−1.40116	−0.0480029
$853$	−0.101819	−0.00348620	−0.00174310	−	0.999998i	$-0.500555\pi$
$853$	−0.101819	−0.00348620	−0.00174310	+	0.999998i	$0.500555\pi$
$854$	0	0
$855$	−0.816301	−0.0279169
$856$	51.5747	1.76279
$857$	−11.4013	−0.389462	−0.194731	−	0.980857i	$-0.562383\pi$
$857$	−11.4013	−0.389462	−0.194731	+	0.980857i	$0.562383\pi$
$858$	−8.90966	−0.304171
$859$	−11.0840	−0.378180	−0.189090	−	0.981960i	$-0.560554\pi$
$859$	−11.0840	−0.378180	−0.189090	+	0.981960i	$0.560554\pi$
$860$	−2.02742	−0.0691346
$861$	0	0
$862$	−39.3347	−1.33974
$863$	−14.5286	−0.494560	−0.247280	−	0.968944i	$-0.579537\pi$
$863$	−14.5286	−0.494560	−0.247280	+	0.968944i	$0.579537\pi$
$864$	0.842681	0.0286686
$865$	39.9739	1.35915
$866$	−2.47217	−0.0840077
$867$	47.9465	1.62835
$868$	0	0
$869$	5.23461	0.177572
$870$	−15.5311	−0.526552
$871$	30.7529	1.04202
$872$	37.0522	1.25475
$873$	−8.07030	−0.273138
$874$	0.679417	0.0229816
$875$	0	0
$876$	0.126568	0.00427633
$877$	19.1876	0.647920	0.323960	−	0.946071i	$-0.394986\pi$
$877$	19.1876	0.647920	0.323960	+	0.946071i	$0.394986\pi$
$878$	42.4604	1.43297
$879$	−6.19915	−0.209092
$880$	−10.7575	−0.362634
$881$	27.7071	0.933477	0.466738	−	0.884395i	$-0.345429\pi$
$881$	27.7071	0.933477	0.466738	+	0.884395i	$0.345429\pi$
$882$	0	0
$883$	−10.8275	−0.364374	−0.182187	−	0.983264i	$-0.558318\pi$
$883$	−10.8275	−0.364374	−0.182187	+	0.983264i	$0.558318\pi$
$884$	−7.87934	−0.265011
$885$	−31.4956	−1.05871
$886$	3.35767	0.112803
$887$	−21.2758	−0.714370	−0.357185	−	0.934034i	$-0.616263\pi$
$887$	−21.2758	−0.714370	−0.357185	+	0.934034i	$0.616263\pi$
$888$	12.4286	0.417076
$889$	0	0
$890$	27.8077	0.932117
$891$	−1.00000	−0.0335013
$892$	−1.43585	−0.0480757
$893$	3.48227	0.116530
$894$	8.27050	0.276607
$895$	24.2473	0.810499
$896$	0	0
$897$	11.7158	0.391179
$898$	−15.1000	−0.503892
$899$	−2.41028	−0.0803872
$900$	−0.529854	−0.0176618
$901$	60.0047	1.99905
$902$	−3.92391	−0.130652
$903$	0	0
$904$	33.9200	1.12816
$905$	17.0063	0.565310
$906$	21.5403	0.715628
$907$	−26.1767	−0.869182	−0.434591	−	0.900628i	$-0.643107\pi$
$907$	−26.1767	−0.869182	−0.434591	+	0.900628i	$0.643107\pi$
$908$	1.07987	0.0358366
$909$	12.1220	0.402061
$910$	0	0
$911$	42.2202	1.39882	0.699408	−	0.714723i	$-0.253447\pi$
$911$	42.2202	1.39882	0.699408	+	0.714723i	$0.253447\pi$
$912$	−1.02715	−0.0340122
$913$	−7.36663	−0.243800
$914$	−5.80642	−0.192059
$915$	44.8229	1.48180
$916$	−1.57651	−0.0520893
$917$	0	0
$918$	10.9635	0.361848
$919$	48.3234	1.59404	0.797022	−	0.603951i	$-0.206408\pi$
$919$	48.3234	1.59404	0.797022	+	0.603951i	$0.206408\pi$
$920$	15.2936	0.504213
$921$	5.29099	0.174344
$922$	13.8187	0.455095
$923$	61.4693	2.02329
$924$	0	0
$925$	−15.0867	−0.496047
$926$	−51.7660	−1.70113
$927$	8.62457	0.283268
$928$	3.29026	0.108008
$929$	43.4012	1.42395	0.711974	−	0.702206i	$-0.247801\pi$
$929$	43.4012	1.42395	0.711974	+	0.702206i	$0.247801\pi$
$930$	2.45546	0.0805177
$931$	0	0
$932$	−0.587100	−0.0192311
$933$	13.8924	0.454816
$934$	−49.9779	−1.63533
$935$	23.5636	0.770613
$936$	−19.1494	−0.625918
$937$	6.13907	0.200555	0.100277	−	0.994960i	$-0.468027\pi$
$937$	6.13907	0.200555	0.100277	+	0.994960i	$0.468027\pi$
$938$	0	0
$939$	8.16076	0.266316
$940$	5.44453	0.177581
$941$	14.8108	0.482819	0.241410	−	0.970423i	$-0.422390\pi$
$941$	14.8108	0.482819	0.241410	+	0.970423i	$0.422390\pi$
$942$	−19.5207	−0.636020
$943$	5.15976	0.168025
$944$	−39.6307	−1.28987
$945$	0	0
$946$	6.31873	0.205440
$947$	−6.03430	−0.196088	−0.0980442	−	0.995182i	$-0.531259\pi$
$947$	−6.03430	−0.196088	−0.0980442	+	0.995182i	$0.531259\pi$
$948$	0.781456	0.0253805
$949$	−5.55257	−0.180244
$950$	1.34801	0.0437351
$951$	7.44465	0.241409
$952$	0	0
$953$	−53.9047	−1.74615	−0.873073	−	0.487589i	$-0.837876\pi$
$953$	−53.9047	−1.74615	−0.873073	+	0.487589i	$0.837876\pi$
$954$	10.1292	0.327946
$955$	−66.0338	−2.13680
$956$	1.73776	0.0562033
$957$	−3.90452	−0.126215
$958$	−34.9470	−1.12909
$959$	0	0
$960$	−24.8669	−0.802576
$961$	−30.6189	−0.987708
$962$	−37.8720	−1.22104
$963$	−17.6389	−0.568407
$964$	−2.08046	−0.0670071
$965$	26.2660	0.845532
$966$	0	0
$967$	27.4445	0.882555	0.441278	−	0.897371i	$-0.354525\pi$
$967$	27.4445	0.882555	0.441278	+	0.897371i	$0.354525\pi$
$968$	−2.92391	−0.0939780
$969$	2.24991	0.0722774
$970$	32.1013	1.03071
$971$	0.462880	0.0148545	0.00742727	−	0.999972i	$-0.497636\pi$
$971$	0.462880	0.0148545	0.00742727	+	0.999972i	$0.497636\pi$
$972$	−0.149286	−0.00478836
$973$	0	0
$974$	−45.3949	−1.45455
$975$	23.2449	0.744432
$976$	56.4004	1.80533
$977$	−34.6479	−1.10848	−0.554242	−	0.832355i	$-0.686992\pi$
$977$	−34.6479	−1.10848	−0.554242	+	0.832355i	$0.686992\pi$
$978$	−13.0560	−0.417486
$979$	6.99088	0.223430
$980$	0	0
$981$	−12.6722	−0.404591
$982$	−7.07707	−0.225838
$983$	−32.4710	−1.03566	−0.517832	−	0.855483i	$-0.673261\pi$
$983$	−32.4710	−1.03566	−0.517832	+	0.855483i	$0.673261\pi$
$984$	−8.43361	−0.268854
$985$	−33.0927	−1.05442
$986$	42.8070	1.36325
$987$	0	0
$988$	−0.272959	−0.00868399
$989$	−8.30885	−0.264206
$990$	3.97771	0.126420
$991$	−29.6456	−0.941723	−0.470861	−	0.882207i	$-0.656057\pi$
$991$	−29.6456	−0.941723	−0.470861	+	0.882207i	$0.656057\pi$
$992$	−0.520191	−0.0165161
$993$	11.1067	0.352460
$994$	0	0
$995$	51.9930	1.64829
$996$	−1.09974	−0.0348465
$997$	−56.7168	−1.79624	−0.898119	−	0.439752i	$-0.855066\pi$
$997$	−56.7168	−1.79624	−0.898119	+	0.439752i	$0.855066\pi$
$998$	−26.6820	−0.844604
$999$	−4.25067	−0.134485

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1617.2.a.y.1.3	yes	4
3.2	odd	2		4851.2.a.br.1.2		4
7.6	odd	2		1617.2.a.w.1.3	✓	4
21.20	even	2		4851.2.a.bs.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1617.2.a.w.1.3	✓	4	7.6	odd	2
1617.2.a.y.1.3	yes	4	1.1	even	1	trivial
4851.2.a.br.1.2		4	3.2	odd	2
4851.2.a.bs.1.2		4	21.20	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:	\( N \)	\(=\)	\( 1617 = 3 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1617.a (trivial)

\(f(q)\)	\(=\)	\(q+1.36041 q^{2} +1.00000 q^{3} -0.149286 q^{4} -2.92391 q^{5} +1.36041 q^{6} -2.92391 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.36041 q^{2} +1.00000 q^{3} -0.149286 q^{4} -2.92391 q^{5} +1.36041 q^{6} -2.92391 q^{8} +1.00000 q^{9} -3.97771 q^{10} -1.00000 q^{11} -0.149286 q^{12} +6.54925 q^{13} -2.92391 q^{15} -3.67914 q^{16} +8.05894 q^{17} +1.36041 q^{18} +0.279181 q^{19} +0.436500 q^{20} -1.36041 q^{22} +1.78888 q^{23} -2.92391 q^{24} +3.54925 q^{25} +8.90966 q^{26} +1.00000 q^{27} +3.90452 q^{29} -3.97771 q^{30} -0.617304 q^{31} +0.842681 q^{32} -1.00000 q^{33} +10.9635 q^{34} -0.149286 q^{36} -4.25067 q^{37} +0.379801 q^{38} +6.54925 q^{39} +8.54925 q^{40} +2.88436 q^{41} -4.64473 q^{43} +0.149286 q^{44} -2.92391 q^{45} +2.43361 q^{46} +12.4732 q^{47} -3.67914 q^{48} +4.82843 q^{50} +8.05894 q^{51} -0.977714 q^{52} +7.44573 q^{53} +1.36041 q^{54} +2.92391 q^{55} +0.279181 q^{57} +5.31174 q^{58} +10.7717 q^{59} +0.436500 q^{60} -15.3298 q^{61} -0.839786 q^{62} +8.50467 q^{64} -19.1494 q^{65} -1.36041 q^{66} +4.69564 q^{67} -1.20309 q^{68} +1.78888 q^{69} +9.38571 q^{71} -2.92391 q^{72} -0.847819 q^{73} -5.78266 q^{74} +3.54925 q^{75} -0.0416780 q^{76} +8.90966 q^{78} -5.23461 q^{79} +10.7575 q^{80} +1.00000 q^{81} +3.92391 q^{82} +7.36663 q^{83} -23.5636 q^{85} -6.31873 q^{86} +3.90452 q^{87} +2.92391 q^{88} -6.99088 q^{89} -3.97771 q^{90} -0.267055 q^{92} -0.617304 q^{93} +16.9686 q^{94} -0.816301 q^{95} +0.842681 q^{96} -8.07030 q^{97} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} + 4 q^{3} + 2 q^{4} + 2 q^{6} + 4 q^{9}+O(q^{10}) \) 4 * q + 2 * q^2 + 4 * q^3 + 2 * q^4 + 2 * q^6 + 4 * q^9	\( 4 q + 2 q^{2} + 4 q^{3} + 2 q^{4} + 2 q^{6} + 4 q^{9} - 2 q^{10} - 4 q^{11} + 2 q^{12} + 8 q^{13} - 6 q^{16} + 8 q^{17} + 2 q^{18} + 8 q^{19} + 10 q^{20} - 2 q^{22} + 8 q^{23} - 4 q^{25} + 14 q^{26} + 4 q^{27} + 16 q^{29} - 2 q^{30} + 8 q^{31} + 2 q^{32} - 4 q^{33} + 20 q^{34} + 2 q^{36} - 4 q^{37} - 14 q^{38} + 8 q^{39} + 16 q^{40} + 12 q^{41} - 2 q^{44} - 8 q^{46} + 20 q^{47} - 6 q^{48} + 8 q^{50} + 8 q^{51} + 10 q^{52} + 8 q^{53} + 2 q^{54} + 8 q^{57} - 2 q^{58} + 8 q^{59} + 10 q^{60} - 24 q^{61} + 24 q^{62} - 12 q^{64} - 12 q^{65} - 2 q^{66} - 28 q^{67} + 8 q^{69} + 12 q^{71} + 20 q^{73} - 18 q^{74} - 4 q^{75} - 2 q^{76} + 14 q^{78} - 2 q^{80} + 4 q^{81} + 4 q^{82} + 32 q^{83} - 24 q^{85} - 20 q^{86} + 16 q^{87} + 4 q^{89} - 2 q^{90} - 12 q^{92} + 8 q^{93} + 22 q^{94} + 4 q^{95} + 2 q^{96} + 8 q^{97} - 4 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 + 4 * q^3 + 2 * q^4 + 2 * q^6 + 4 * q^9 - 2 * q^10 - 4 * q^11 + 2 * q^12 + 8 * q^13 - 6 * q^16 + 8 * q^17 + 2 * q^18 + 8 * q^19 + 10 * q^20 - 2 * q^22 + 8 * q^23 - 4 * q^25 + 14 * q^26 + 4 * q^27 + 16 * q^29 - 2 * q^30 + 8 * q^31 + 2 * q^32 - 4 * q^33 + 20 * q^34 + 2 * q^36 - 4 * q^37 - 14 * q^38 + 8 * q^39 + 16 * q^40 + 12 * q^41 - 2 * q^44 - 8 * q^46 + 20 * q^47 - 6 * q^48 + 8 * q^50 + 8 * q^51 + 10 * q^52 + 8 * q^53 + 2 * q^54 + 8 * q^57 - 2 * q^58 + 8 * q^59 + 10 * q^60 - 24 * q^61 + 24 * q^62 - 12 * q^64 - 12 * q^65 - 2 * q^66 - 28 * q^67 + 8 * q^69 + 12 * q^71 + 20 * q^73 - 18 * q^74 - 4 * q^75 - 2 * q^76 + 14 * q^78 - 2 * q^80 + 4 * q^81 + 4 * q^82 + 32 * q^83 - 24 * q^85 - 20 * q^86 + 16 * q^87 + 4 * q^89 - 2 * q^90 - 12 * q^92 + 8 * q^93 + 22 * q^94 + 4 * q^95 + 2 * q^96 + 8 * q^97 - 4 * q^99

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