LMFDB - Embedded newform 735.2.a.l.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [735,2,Mod(1,735)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(735, 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("735.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 735 = 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	735.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:	$5.86900454856$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{8})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 2 $ x^2 - 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.41421$ of defining polynomial
Character	$\chi$	$=$	735.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.414214 q^{2} -1.00000 q^{3} -1.82843 q^{4} -1.00000 q^{5} +0.414214 q^{6} +1.58579 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.414214 q^{2} -1.00000 q^{3} -1.82843 q^{4} -1.00000 q^{5} +0.414214 q^{6} +1.58579 q^{8} +1.00000 q^{9} +0.414214 q^{10} -2.82843 q^{11} +1.82843 q^{12} -0.828427 q^{13} +1.00000 q^{15} +3.00000 q^{16} -3.65685 q^{17} -0.414214 q^{18} -4.82843 q^{19} +1.82843 q^{20} +1.17157 q^{22} +3.65685 q^{23} -1.58579 q^{24} +1.00000 q^{25} +0.343146 q^{26} -1.00000 q^{27} +6.00000 q^{29} -0.414214 q^{30} +10.4853 q^{31} -4.41421 q^{32} +2.82843 q^{33} +1.51472 q^{34} -1.82843 q^{36} +7.65685 q^{37} +2.00000 q^{38} +0.828427 q^{39} -1.58579 q^{40} -0.343146 q^{41} +8.00000 q^{43} +5.17157 q^{44} -1.00000 q^{45} -1.51472 q^{46} +5.65685 q^{47} -3.00000 q^{48} -0.414214 q^{50} +3.65685 q^{51} +1.51472 q^{52} +8.48528 q^{53} +0.414214 q^{54} +2.82843 q^{55} +4.82843 q^{57} -2.48528 q^{58} -13.6569 q^{59} -1.82843 q^{60} -4.34315 q^{62} -4.17157 q^{64} +0.828427 q^{65} -1.17157 q^{66} +6.68629 q^{68} -3.65685 q^{69} +2.82843 q^{71} +1.58579 q^{72} +16.8284 q^{73} -3.17157 q^{74} -1.00000 q^{75} +8.82843 q^{76} -0.343146 q^{78} -8.00000 q^{79} -3.00000 q^{80} +1.00000 q^{81} +0.142136 q^{82} -9.65685 q^{83} +3.65685 q^{85} -3.31371 q^{86} -6.00000 q^{87} -4.48528 q^{88} -17.3137 q^{89} +0.414214 q^{90} -6.68629 q^{92} -10.4853 q^{93} -2.34315 q^{94} +4.82843 q^{95} +4.41421 q^{96} +10.4853 q^{97} -2.82843 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{5} - 2 q^{6} + 6 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 - 2 * q^5 - 2 * q^6 + 6 * q^8 + 2 * q^9	$ 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{5} - 2 q^{6} + 6 q^{8} + 2 q^{9} - 2 q^{10} - 2 q^{12} + 4 q^{13} + 2 q^{15} + 6 q^{16} + 4 q^{17} + 2 q^{18} - 4 q^{19} - 2 q^{20} + 8 q^{22} - 4 q^{23} - 6 q^{24} + 2 q^{25} + 12 q^{26} - 2 q^{27} + 12 q^{29} + 2 q^{30} + 4 q^{31} - 6 q^{32} + 20 q^{34} + 2 q^{36} + 4 q^{37} + 4 q^{38} - 4 q^{39} - 6 q^{40} - 12 q^{41} + 16 q^{43} + 16 q^{44} - 2 q^{45} - 20 q^{46} - 6 q^{48} + 2 q^{50} - 4 q^{51} + 20 q^{52} - 2 q^{54} + 4 q^{57} + 12 q^{58} - 16 q^{59} + 2 q^{60} - 20 q^{62} - 14 q^{64} - 4 q^{65} - 8 q^{66} + 36 q^{68} + 4 q^{69} + 6 q^{72} + 28 q^{73} - 12 q^{74} - 2 q^{75} + 12 q^{76} - 12 q^{78} - 16 q^{79} - 6 q^{80} + 2 q^{81} - 28 q^{82} - 8 q^{83} - 4 q^{85} + 16 q^{86} - 12 q^{87} + 8 q^{88} - 12 q^{89} - 2 q^{90} - 36 q^{92} - 4 q^{93} - 16 q^{94} + 4 q^{95} + 6 q^{96} + 4 q^{97}+O(q^{100}) $ 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 - 2 * q^5 - 2 * q^6 + 6 * q^8 + 2 * q^9 - 2 * q^10 - 2 * q^12 + 4 * q^13 + 2 * q^15 + 6 * q^16 + 4 * q^17 + 2 * q^18 - 4 * q^19 - 2 * q^20 + 8 * q^22 - 4 * q^23 - 6 * q^24 + 2 * q^25 + 12 * q^26 - 2 * q^27 + 12 * q^29 + 2 * q^30 + 4 * q^31 - 6 * q^32 + 20 * q^34 + 2 * q^36 + 4 * q^37 + 4 * q^38 - 4 * q^39 - 6 * q^40 - 12 * q^41 + 16 * q^43 + 16 * q^44 - 2 * q^45 - 20 * q^46 - 6 * q^48 + 2 * q^50 - 4 * q^51 + 20 * q^52 - 2 * q^54 + 4 * q^57 + 12 * q^58 - 16 * q^59 + 2 * q^60 - 20 * q^62 - 14 * q^64 - 4 * q^65 - 8 * q^66 + 36 * q^68 + 4 * q^69 + 6 * q^72 + 28 * q^73 - 12 * q^74 - 2 * q^75 + 12 * q^76 - 12 * q^78 - 16 * q^79 - 6 * q^80 + 2 * q^81 - 28 * q^82 - 8 * q^83 - 4 * q^85 + 16 * q^86 - 12 * q^87 + 8 * q^88 - 12 * q^89 - 2 * q^90 - 36 * q^92 - 4 * q^93 - 16 * q^94 + 4 * q^95 + 6 * q^96 + 4 * q^97

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−0.414214	−0.292893	−0.146447	−	0.989219i	$-0.546784\pi$
$2$	−0.414214	−0.292893	−0.146447	+	0.989219i	$0.546784\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.82843	−0.914214
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0.414214	0.169102
$7$	0	0
$7$	0	0
$8$	1.58579	0.560660
$9$	1.00000	0.333333
$10$	0.414214	0.130986
$11$	−2.82843	−0.852803	−0.426401	−	0.904534i	$-0.640219\pi$
$11$	−2.82843	−0.852803	−0.426401	+	0.904534i	$0.640219\pi$
$12$	1.82843	0.527821
$13$	−0.828427	−0.229764	−0.114882	−	0.993379i	$-0.536649\pi$
$13$	−0.828427	−0.229764	−0.114882	+	0.993379i	$0.536649\pi$
$14$	0	0
$15$	1.00000	0.258199
$16$	3.00000	0.750000
$17$	−3.65685	−0.886917	−0.443459	−	0.896295i	$-0.646249\pi$
$17$	−3.65685	−0.886917	−0.443459	+	0.896295i	$0.646249\pi$
$18$	−0.414214	−0.0976311
$19$	−4.82843	−1.10772	−0.553859	−	0.832611i	$-0.686845\pi$
$19$	−4.82843	−1.10772	−0.553859	+	0.832611i	$0.686845\pi$
$20$	1.82843	0.408849
$21$	0	0
$22$	1.17157	0.249780
$23$	3.65685	0.762507	0.381253	−	0.924471i	$-0.375493\pi$
$23$	3.65685	0.762507	0.381253	+	0.924471i	$0.375493\pi$
$24$	−1.58579	−0.323697
$25$	1.00000	0.200000
$26$	0.343146	0.0672964
$27$	−1.00000	−0.192450
$28$	0	0
$29$	6.00000	1.11417	0.557086	−	0.830455i	$-0.311919\pi$
$29$	6.00000	1.11417	0.557086	+	0.830455i	$0.311919\pi$
$30$	−0.414214	−0.0756247
$31$	10.4853	1.88321	0.941606	−	0.336717i	$-0.109316\pi$
$31$	10.4853	1.88321	0.941606	+	0.336717i	$0.109316\pi$
$32$	−4.41421	−0.780330
$33$	2.82843	0.492366
$34$	1.51472	0.259772
$35$	0	0
$36$	−1.82843	−0.304738
$37$	7.65685	1.25878	0.629390	−	0.777090i	$-0.283305\pi$
$37$	7.65685	1.25878	0.629390	+	0.777090i	$0.283305\pi$
$38$	2.00000	0.324443
$39$	0.828427	0.132655
$40$	−1.58579	−0.250735
$41$	−0.343146	−0.0535904	−0.0267952	−	0.999641i	$-0.508530\pi$
$41$	−0.343146	−0.0535904	−0.0267952	+	0.999641i	$0.508530\pi$
$42$	0	0
$43$	8.00000	1.21999	0.609994	−	0.792406i	$-0.291172\pi$
$43$	8.00000	1.21999	0.609994	+	0.792406i	$0.291172\pi$
$44$	5.17157	0.779644
$45$	−1.00000	−0.149071
$46$	−1.51472	−0.223333
$47$	5.65685	0.825137	0.412568	−	0.910927i	$-0.364632\pi$
$47$	5.65685	0.825137	0.412568	+	0.910927i	$0.364632\pi$
$48$	−3.00000	−0.433013
$49$	0	0
$50$	−0.414214	−0.0585786
$51$	3.65685	0.512062
$52$	1.51472	0.210054
$53$	8.48528	1.16554	0.582772	−	0.812636i	$-0.301968\pi$
$53$	8.48528	1.16554	0.582772	+	0.812636i	$0.301968\pi$
$54$	0.414214	0.0563673
$55$	2.82843	0.381385
$56$	0	0
$57$	4.82843	0.639541
$58$	−2.48528	−0.326333
$59$	−13.6569	−1.77797	−0.888985	−	0.457935i	$-0.848589\pi$
$59$	−13.6569	−1.77797	−0.888985	+	0.457935i	$0.848589\pi$
$60$	−1.82843	−0.236049
$61$	0	0		−	1.00000i	$-0.5\pi$
$61$	0	0			1.00000i	$0.5\pi$
$62$	−4.34315	−0.551580
$63$	0	0
$64$	−4.17157	−0.521447
$65$	0.828427	0.102754
$66$	−1.17157	−0.144211
$67$	0	0		−	1.00000i	$-0.5\pi$
$67$	0	0			1.00000i	$0.5\pi$
$68$	6.68629	0.810832
$69$	−3.65685	−0.440234
$70$	0	0
$71$	2.82843	0.335673	0.167836	−	0.985815i	$-0.446322\pi$
$71$	2.82843	0.335673	0.167836	+	0.985815i	$0.446322\pi$
$72$	1.58579	0.186887
$73$	16.8284	1.96962	0.984809	−	0.173640i	$-0.0555529\pi$
$73$	16.8284	1.96962	0.984809	+	0.173640i	$0.0555529\pi$
$74$	−3.17157	−0.368688
$75$	−1.00000	−0.115470
$76$	8.82843	1.01269
$77$	0	0
$78$	−0.343146	−0.0388536
$79$	−8.00000	−0.900070	−0.450035	−	0.893011i	$-0.648589\pi$
$79$	−8.00000	−0.900070	−0.450035	+	0.893011i	$0.648589\pi$
$80$	−3.00000	−0.335410
$81$	1.00000	0.111111
$82$	0.142136	0.0156963
$83$	−9.65685	−1.05998	−0.529989	−	0.848005i	$-0.677804\pi$
$83$	−9.65685	−1.05998	−0.529989	+	0.848005i	$0.677804\pi$
$84$	0	0
$85$	3.65685	0.396642
$86$	−3.31371	−0.357326
$87$	−6.00000	−0.643268
$88$	−4.48528	−0.478133
$89$	−17.3137	−1.83525	−0.917625	−	0.397448i	$-0.869896\pi$
$89$	−17.3137	−1.83525	−0.917625	+	0.397448i	$0.869896\pi$
$90$	0.414214	0.0436619
$91$	0	0
$92$	−6.68629	−0.697094
$93$	−10.4853	−1.08727
$94$	−2.34315	−0.241677
$95$	4.82843	0.495386
$96$	4.41421	0.450524
$97$	10.4853	1.06462	0.532310	−	0.846550i	$-0.321324\pi$
$97$	10.4853	1.06462	0.532310	+	0.846550i	$0.321324\pi$
$98$	0	0
$99$	−2.82843	−0.284268
$100$	−1.82843	−0.182843
$101$	3.65685	0.363871	0.181935	−	0.983311i	$-0.441764\pi$
$101$	3.65685	0.363871	0.181935	+	0.983311i	$0.441764\pi$
$102$	−1.51472	−0.149979
$103$	12.0000	1.18240	0.591198	−	0.806527i	$-0.298655\pi$
$103$	12.0000	1.18240	0.591198	+	0.806527i	$0.298655\pi$
$104$	−1.31371	−0.128820
$105$	0	0
$106$	−3.51472	−0.341380
$107$	−17.3137	−1.67378	−0.836890	−	0.547372i	$-0.815628\pi$
$107$	−17.3137	−1.67378	−0.836890	+	0.547372i	$0.815628\pi$
$108$	1.82843	0.175940
$109$	6.00000	0.574696	0.287348	−	0.957826i	$-0.407226\pi$
$109$	6.00000	0.574696	0.287348	+	0.957826i	$0.407226\pi$
$110$	−1.17157	−0.111705
$111$	−7.65685	−0.726756
$112$	0	0
$113$	−2.82843	−0.266076	−0.133038	−	0.991111i	$-0.542473\pi$
$113$	−2.82843	−0.266076	−0.133038	+	0.991111i	$0.542473\pi$
$114$	−2.00000	−0.187317
$115$	−3.65685	−0.341003
$116$	−10.9706	−1.01859
$117$	−0.828427	−0.0765881
$118$	5.65685	0.520756
$119$	0	0
$120$	1.58579	0.144762
$121$	−3.00000	−0.272727
$122$	0	0
$123$	0.343146	0.0309404
$124$	−19.1716	−1.72166
$125$	−1.00000	−0.0894427
$126$	0	0
$127$	−3.31371	−0.294044	−0.147022	−	0.989133i	$-0.546969\pi$
$127$	−3.31371	−0.294044	−0.147022	+	0.989133i	$0.546969\pi$
$128$	10.5563	0.933058
$129$	−8.00000	−0.704361
$130$	−0.343146	−0.0300959
$131$	5.65685	0.494242	0.247121	−	0.968985i	$-0.420516\pi$
$131$	5.65685	0.494242	0.247121	+	0.968985i	$0.420516\pi$
$132$	−5.17157	−0.450128
$133$	0	0
$134$	0	0
$135$	1.00000	0.0860663
$136$	−5.79899	−0.497259
$137$	18.8284	1.60862	0.804311	−	0.594209i	$-0.202535\pi$
$137$	18.8284	1.60862	0.804311	+	0.594209i	$0.202535\pi$
$138$	1.51472	0.128941
$139$	18.4853	1.56790	0.783951	−	0.620823i	$-0.213202\pi$
$139$	18.4853	1.56790	0.783951	+	0.620823i	$0.213202\pi$
$140$	0	0
$141$	−5.65685	−0.476393
$142$	−1.17157	−0.0983162
$143$	2.34315	0.195944
$144$	3.00000	0.250000
$145$	−6.00000	−0.498273
$146$	−6.97056	−0.576888
$147$	0	0
$148$	−14.0000	−1.15079
$149$	3.65685	0.299581	0.149791	−	0.988718i	$-0.452140\pi$
$149$	3.65685	0.299581	0.149791	+	0.988718i	$0.452140\pi$
$150$	0.414214	0.0338204
$151$	16.9706	1.38104	0.690522	−	0.723311i	$-0.257381\pi$
$151$	16.9706	1.38104	0.690522	+	0.723311i	$0.257381\pi$
$152$	−7.65685	−0.621053
$153$	−3.65685	−0.295639
$154$	0	0
$155$	−10.4853	−0.842198
$156$	−1.51472	−0.121275
$157$	16.1421	1.28828	0.644141	−	0.764906i	$-0.277215\pi$
$157$	16.1421	1.28828	0.644141	+	0.764906i	$0.277215\pi$
$158$	3.31371	0.263624
$159$	−8.48528	−0.672927
$160$	4.41421	0.348974
$161$	0	0
$162$	−0.414214	−0.0325437
$163$	−12.0000	−0.939913	−0.469956	−	0.882690i	$-0.655730\pi$
$163$	−12.0000	−0.939913	−0.469956	+	0.882690i	$0.655730\pi$
$164$	0.627417	0.0489930
$165$	−2.82843	−0.220193
$166$	4.00000	0.310460
$167$	11.3137	0.875481	0.437741	−	0.899101i	$-0.355779\pi$
$167$	11.3137	0.875481	0.437741	+	0.899101i	$0.355779\pi$
$168$	0	0
$169$	−12.3137	−0.947208
$170$	−1.51472	−0.116174
$171$	−4.82843	−0.369239
$172$	−14.6274	−1.11533
$173$	20.6274	1.56827	0.784137	−	0.620588i	$-0.213106\pi$
$173$	20.6274	1.56827	0.784137	+	0.620588i	$0.213106\pi$
$174$	2.48528	0.188409
$175$	0	0
$176$	−8.48528	−0.639602
$177$	13.6569	1.02651
$178$	7.17157	0.537532
$179$	−6.82843	−0.510381	−0.255190	−	0.966891i	$-0.582138\pi$
$179$	−6.82843	−0.510381	−0.255190	+	0.966891i	$0.582138\pi$
$180$	1.82843	0.136283
$181$	−13.6569	−1.01511	−0.507553	−	0.861621i	$-0.669450\pi$
$181$	−13.6569	−1.01511	−0.507553	+	0.861621i	$0.669450\pi$
$182$	0	0
$183$	0	0
$184$	5.79899	0.427507
$185$	−7.65685	−0.562943
$186$	4.34315	0.318455
$187$	10.3431	0.756366
$188$	−10.3431	−0.754351
$189$	0	0
$190$	−2.00000	−0.145095
$191$	−14.8284	−1.07295	−0.536474	−	0.843917i	$-0.680244\pi$
$191$	−14.8284	−1.07295	−0.536474	+	0.843917i	$0.680244\pi$
$192$	4.17157	0.301057
$193$	4.34315	0.312626	0.156313	−	0.987708i	$-0.450039\pi$
$193$	4.34315	0.312626	0.156313	+	0.987708i	$0.450039\pi$
$194$	−4.34315	−0.311820
$195$	−0.828427	−0.0593249
$196$	0	0
$197$	−20.4853	−1.45952	−0.729758	−	0.683706i	$-0.760367\pi$
$197$	−20.4853	−1.45952	−0.729758	+	0.683706i	$0.760367\pi$
$198$	1.17157	0.0832601
$199$	−4.82843	−0.342278	−0.171139	−	0.985247i	$-0.554745\pi$
$199$	−4.82843	−0.342278	−0.171139	+	0.985247i	$0.554745\pi$
$200$	1.58579	0.112132
$201$	0	0
$202$	−1.51472	−0.106575
$203$	0	0
$204$	−6.68629	−0.468134
$205$	0.343146	0.0239663
$206$	−4.97056	−0.346316
$207$	3.65685	0.254169
$208$	−2.48528	−0.172323
$209$	13.6569	0.944664
$210$	0	0
$211$	1.65685	0.114063	0.0570313	−	0.998372i	$-0.481837\pi$
$211$	1.65685	0.114063	0.0570313	+	0.998372i	$0.481837\pi$
$212$	−15.5147	−1.06556
$213$	−2.82843	−0.193801
$214$	7.17157	0.490239
$215$	−8.00000	−0.545595
$216$	−1.58579	−0.107899
$217$	0	0
$218$	−2.48528	−0.168324
$219$	−16.8284	−1.13716
$220$	−5.17157	−0.348667
$221$	3.02944	0.203782
$222$	3.17157	0.212862
$223$	−12.9706	−0.868573	−0.434287	−	0.900775i	$-0.642999\pi$
$223$	−12.9706	−0.868573	−0.434287	+	0.900775i	$0.642999\pi$
$224$	0	0
$225$	1.00000	0.0666667
$226$	1.17157	0.0779319
$227$	4.97056	0.329908	0.164954	−	0.986301i	$-0.447252\pi$
$227$	4.97056	0.329908	0.164954	+	0.986301i	$0.447252\pi$
$228$	−8.82843	−0.584677
$229$	−7.31371	−0.483303	−0.241652	−	0.970363i	$-0.577689\pi$
$229$	−7.31371	−0.483303	−0.241652	+	0.970363i	$0.577689\pi$
$230$	1.51472	0.0998776
$231$	0	0
$232$	9.51472	0.624672
$233$	9.17157	0.600850	0.300425	−	0.953805i	$-0.402872\pi$
$233$	9.17157	0.600850	0.300425	+	0.953805i	$0.402872\pi$
$234$	0.343146	0.0224321
$235$	−5.65685	−0.369012
$236$	24.9706	1.62545
$237$	8.00000	0.519656
$238$	0	0
$239$	26.1421	1.69099	0.845497	−	0.533980i	$-0.179304\pi$
$239$	26.1421	1.69099	0.845497	+	0.533980i	$0.179304\pi$
$240$	3.00000	0.193649
$241$	10.3431	0.666261	0.333130	−	0.942881i	$-0.391895\pi$
$241$	10.3431	0.666261	0.333130	+	0.942881i	$0.391895\pi$
$242$	1.24264	0.0798800
$243$	−1.00000	−0.0641500
$244$	0	0
$245$	0	0
$246$	−0.142136	−0.00906224
$247$	4.00000	0.254514
$248$	16.6274	1.05584
$249$	9.65685	0.611978
$250$	0.414214	0.0261972
$251$	−18.3431	−1.15781	−0.578905	−	0.815395i	$-0.696520\pi$
$251$	−18.3431	−1.15781	−0.578905	+	0.815395i	$0.696520\pi$
$252$	0	0
$253$	−10.3431	−0.650268
$254$	1.37258	0.0861235
$255$	−3.65685	−0.229001
$256$	3.97056	0.248160
$257$	11.6569	0.727135	0.363567	−	0.931568i	$-0.381559\pi$
$257$	11.6569	0.727135	0.363567	+	0.931568i	$0.381559\pi$
$258$	3.31371	0.206302
$259$	0	0
$260$	−1.51472	−0.0939389
$261$	6.00000	0.371391
$262$	−2.34315	−0.144760
$263$	−25.3137	−1.56091	−0.780455	−	0.625212i	$-0.785013\pi$
$263$	−25.3137	−1.56091	−0.780455	+	0.625212i	$0.785013\pi$
$264$	4.48528	0.276050
$265$	−8.48528	−0.521247
$266$	0	0
$267$	17.3137	1.05958
$268$	0	0
$269$	−11.6569	−0.710731	−0.355365	−	0.934727i	$-0.615644\pi$
$269$	−11.6569	−0.710731	−0.355365	+	0.934727i	$0.615644\pi$
$270$	−0.414214	−0.0252082
$271$	5.51472	0.334995	0.167498	−	0.985872i	$-0.446431\pi$
$271$	5.51472	0.334995	0.167498	+	0.985872i	$0.446431\pi$
$272$	−10.9706	−0.665188
$273$	0	0
$274$	−7.79899	−0.471154
$275$	−2.82843	−0.170561
$276$	6.68629	0.402467
$277$	−1.31371	−0.0789331	−0.0394665	−	0.999221i	$-0.512566\pi$
$277$	−1.31371	−0.0789331	−0.0394665	+	0.999221i	$0.512566\pi$
$278$	−7.65685	−0.459228
$279$	10.4853	0.627737
$280$	0	0
$281$	23.6569	1.41125	0.705625	−	0.708586i	$-0.250666\pi$
$281$	23.6569	1.41125	0.705625	+	0.708586i	$0.250666\pi$
$282$	2.34315	0.139532
$283$	0	0		−	1.00000i	$-0.5\pi$
$283$	0	0			1.00000i	$0.5\pi$
$284$	−5.17157	−0.306876
$285$	−4.82843	−0.286011
$286$	−0.970563	−0.0573906
$287$	0	0
$288$	−4.41421	−0.260110
$289$	−3.62742	−0.213377
$290$	2.48528	0.145941
$291$	−10.4853	−0.614658
$292$	−30.7696	−1.80065
$293$	23.6569	1.38205	0.691024	−	0.722832i	$-0.257160\pi$
$293$	23.6569	1.38205	0.691024	+	0.722832i	$0.257160\pi$
$294$	0	0
$295$	13.6569	0.795133
$296$	12.1421	0.705747
$297$	2.82843	0.164122
$298$	−1.51472	−0.0877453
$299$	−3.02944	−0.175197
$300$	1.82843	0.105564
$301$	0	0
$302$	−7.02944	−0.404499
$303$	−3.65685	−0.210081
$304$	−14.4853	−0.830788
$305$	0	0
$306$	1.51472	0.0865907
$307$	−4.97056	−0.283685	−0.141843	−	0.989889i	$-0.545303\pi$
$307$	−4.97056	−0.283685	−0.141843	+	0.989889i	$0.545303\pi$
$308$	0	0
$309$	−12.0000	−0.682656
$310$	4.34315	0.246674
$311$	1.65685	0.0939516	0.0469758	−	0.998896i	$-0.485042\pi$
$311$	1.65685	0.0939516	0.0469758	+	0.998896i	$0.485042\pi$
$312$	1.31371	0.0743741
$313$	14.4853	0.818757	0.409378	−	0.912365i	$-0.365746\pi$
$313$	14.4853	0.818757	0.409378	+	0.912365i	$0.365746\pi$
$314$	−6.68629	−0.377329
$315$	0	0
$316$	14.6274	0.822856
$317$	−6.14214	−0.344977	−0.172488	−	0.985012i	$-0.555181\pi$
$317$	−6.14214	−0.344977	−0.172488	+	0.985012i	$0.555181\pi$
$318$	3.51472	0.197096
$319$	−16.9706	−0.950169
$320$	4.17157	0.233198
$321$	17.3137	0.966357
$322$	0	0
$323$	17.6569	0.982454
$324$	−1.82843	−0.101579
$325$	−0.828427	−0.0459529
$326$	4.97056	0.275294
$327$	−6.00000	−0.331801
$328$	−0.544156	−0.0300460
$329$	0	0
$330$	1.17157	0.0644930
$331$	−9.65685	−0.530789	−0.265394	−	0.964140i	$-0.585502\pi$
$331$	−9.65685	−0.530789	−0.265394	+	0.964140i	$0.585502\pi$
$332$	17.6569	0.969046
$333$	7.65685	0.419593
$334$	−4.68629	−0.256422
$335$	0	0
$336$	0	0
$337$	26.9706	1.46918	0.734590	−	0.678511i	$-0.237374\pi$
$337$	26.9706	1.46918	0.734590	+	0.678511i	$0.237374\pi$
$338$	5.10051	0.277431
$339$	2.82843	0.153619
$340$	−6.68629	−0.362615
$341$	−29.6569	−1.60601
$342$	2.00000	0.108148
$343$	0	0
$344$	12.6863	0.683999
$345$	3.65685	0.196878
$346$	−8.54416	−0.459337
$347$	10.9706	0.588931	0.294465	−	0.955662i	$-0.404858\pi$
$347$	10.9706	0.588931	0.294465	+	0.955662i	$0.404858\pi$
$348$	10.9706	0.588084
$349$	−16.0000	−0.856460	−0.428230	−	0.903670i	$-0.640863\pi$
$349$	−16.0000	−0.856460	−0.428230	+	0.903670i	$0.640863\pi$
$350$	0	0
$351$	0.828427	0.0442182
$352$	12.4853	0.665468
$353$	2.68629	0.142977	0.0714884	−	0.997441i	$-0.477225\pi$
$353$	2.68629	0.142977	0.0714884	+	0.997441i	$0.477225\pi$
$354$	−5.65685	−0.300658
$355$	−2.82843	−0.150117
$356$	31.6569	1.67781
$357$	0	0
$358$	2.82843	0.149487
$359$	23.7990	1.25606	0.628031	−	0.778188i	$-0.283861\pi$
$359$	23.7990	1.25606	0.628031	+	0.778188i	$0.283861\pi$
$360$	−1.58579	−0.0835783
$361$	4.31371	0.227037
$362$	5.65685	0.297318
$363$	3.00000	0.157459
$364$	0	0
$365$	−16.8284	−0.880840
$366$	0	0
$367$	−20.9706	−1.09465	−0.547327	−	0.836919i	$-0.684355\pi$
$367$	−20.9706	−1.09465	−0.547327	+	0.836919i	$0.684355\pi$
$368$	10.9706	0.571880
$369$	−0.343146	−0.0178635
$370$	3.17157	0.164882
$371$	0	0
$372$	19.1716	0.994000
$373$	20.6274	1.06805	0.534024	−	0.845470i	$-0.320679\pi$
$373$	20.6274	1.06805	0.534024	+	0.845470i	$0.320679\pi$
$374$	−4.28427	−0.221534
$375$	1.00000	0.0516398
$376$	8.97056	0.462621
$377$	−4.97056	−0.255997
$378$	0	0
$379$	12.9706	0.666253	0.333127	−	0.942882i	$-0.391896\pi$
$379$	12.9706	0.666253	0.333127	+	0.942882i	$0.391896\pi$
$380$	−8.82843	−0.452889
$381$	3.31371	0.169766
$382$	6.14214	0.314259
$383$	0	0		−	1.00000i	$-0.5\pi$
$383$	0	0			1.00000i	$0.5\pi$
$384$	−10.5563	−0.538701
$385$	0	0
$386$	−1.79899	−0.0915662
$387$	8.00000	0.406663
$388$	−19.1716	−0.973289
$389$	−0.343146	−0.0173982	−0.00869909	−	0.999962i	$-0.502769\pi$
$389$	−0.343146	−0.0173982	−0.00869909	+	0.999962i	$0.502769\pi$
$390$	0.343146	0.0173759
$391$	−13.3726	−0.676281
$392$	0	0
$393$	−5.65685	−0.285351
$394$	8.48528	0.427482
$395$	8.00000	0.402524
$396$	5.17157	0.259881
$397$	19.1716	0.962194	0.481097	−	0.876667i	$-0.340239\pi$
$397$	19.1716	0.962194	0.481097	+	0.876667i	$0.340239\pi$
$398$	2.00000	0.100251
$399$	0	0
$400$	3.00000	0.150000
$401$	30.0000	1.49813	0.749064	−	0.662497i	$-0.230503\pi$
$401$	30.0000	1.49813	0.749064	+	0.662497i	$0.230503\pi$
$402$	0	0
$403$	−8.68629	−0.432695
$404$	−6.68629	−0.332655
$405$	−1.00000	−0.0496904
$406$	0	0
$407$	−21.6569	−1.07349
$408$	5.79899	0.287093
$409$	−12.0000	−0.593362	−0.296681	−	0.954977i	$-0.595880\pi$
$409$	−12.0000	−0.593362	−0.296681	+	0.954977i	$0.595880\pi$
$410$	−0.142136	−0.00701958
$411$	−18.8284	−0.928738
$412$	−21.9411	−1.08096
$413$	0	0
$414$	−1.51472	−0.0744444
$415$	9.65685	0.474036
$416$	3.65685	0.179292
$417$	−18.4853	−0.905228
$418$	−5.65685	−0.276686
$419$	23.3137	1.13895	0.569475	−	0.822009i	$-0.307147\pi$
$419$	23.3137	1.13895	0.569475	+	0.822009i	$0.307147\pi$
$420$	0	0
$421$	−6.00000	−0.292422	−0.146211	−	0.989253i	$-0.546708\pi$
$421$	−6.00000	−0.292422	−0.146211	+	0.989253i	$0.546708\pi$
$422$	−0.686292	−0.0334081
$423$	5.65685	0.275046
$424$	13.4558	0.653474
$425$	−3.65685	−0.177383
$426$	1.17157	0.0567629
$427$	0	0
$428$	31.6569	1.53019
$429$	−2.34315	−0.113128
$430$	3.31371	0.159801
$431$	−5.17157	−0.249106	−0.124553	−	0.992213i	$-0.539750\pi$
$431$	−5.17157	−0.249106	−0.124553	+	0.992213i	$0.539750\pi$
$432$	−3.00000	−0.144338
$433$	−12.8284	−0.616495	−0.308247	−	0.951306i	$-0.599742\pi$
$433$	−12.8284	−0.616495	−0.308247	+	0.951306i	$0.599742\pi$
$434$	0	0
$435$	6.00000	0.287678
$436$	−10.9706	−0.525395
$437$	−17.6569	−0.844642
$438$	6.97056	0.333066
$439$	30.4853	1.45498	0.727492	−	0.686117i	$-0.240686\pi$
$439$	30.4853	1.45498	0.727492	+	0.686117i	$0.240686\pi$
$440$	4.48528	0.213827
$441$	0	0
$442$	−1.25483	−0.0596864
$443$	12.3431	0.586441	0.293220	−	0.956045i	$-0.405273\pi$
$443$	12.3431	0.586441	0.293220	+	0.956045i	$0.405273\pi$
$444$	14.0000	0.664411
$445$	17.3137	0.820748
$446$	5.37258	0.254399
$447$	−3.65685	−0.172963
$448$	0	0
$449$	32.6274	1.53978	0.769892	−	0.638175i	$-0.220310\pi$
$449$	32.6274	1.53978	0.769892	+	0.638175i	$0.220310\pi$
$450$	−0.414214	−0.0195262
$451$	0.970563	0.0457020
$452$	5.17157	0.243250
$453$	−16.9706	−0.797347
$454$	−2.05887	−0.0966278
$455$	0	0
$456$	7.65685	0.358565
$457$	27.6569	1.29373	0.646867	−	0.762603i	$-0.276079\pi$
$457$	27.6569	1.29373	0.646867	+	0.762603i	$0.276079\pi$
$458$	3.02944	0.141556
$459$	3.65685	0.170687
$460$	6.68629	0.311750
$461$	9.31371	0.433783	0.216891	−	0.976196i	$-0.430408\pi$
$461$	9.31371	0.433783	0.216891	+	0.976196i	$0.430408\pi$
$462$	0	0
$463$	−6.62742	−0.308002	−0.154001	−	0.988071i	$-0.549216\pi$
$463$	−6.62742	−0.308002	−0.154001	+	0.988071i	$0.549216\pi$
$464$	18.0000	0.835629
$465$	10.4853	0.486243
$466$	−3.79899	−0.175985
$467$	−32.2843	−1.49394	−0.746969	−	0.664859i	$-0.768492\pi$
$467$	−32.2843	−1.49394	−0.746969	+	0.664859i	$0.768492\pi$
$468$	1.51472	0.0700179
$469$	0	0
$470$	2.34315	0.108081
$471$	−16.1421	−0.743790
$472$	−21.6569	−0.996838
$473$	−22.6274	−1.04041
$474$	−3.31371	−0.152204
$475$	−4.82843	−0.221543
$476$	0	0
$477$	8.48528	0.388514
$478$	−10.8284	−0.495281
$479$	25.6569	1.17229	0.586146	−	0.810206i	$-0.300645\pi$
$479$	25.6569	1.17229	0.586146	+	0.810206i	$0.300645\pi$
$480$	−4.41421	−0.201480
$481$	−6.34315	−0.289223
$482$	−4.28427	−0.195143
$483$	0	0
$484$	5.48528	0.249331
$485$	−10.4853	−0.476112
$486$	0.414214	0.0187891
$487$	−37.9411	−1.71928	−0.859638	−	0.510903i	$-0.829311\pi$
$487$	−37.9411	−1.71928	−0.859638	+	0.510903i	$0.829311\pi$
$488$	0	0
$489$	12.0000	0.542659
$490$	0	0
$491$	−10.1421	−0.457708	−0.228854	−	0.973461i	$-0.573498\pi$
$491$	−10.1421	−0.457708	−0.228854	+	0.973461i	$0.573498\pi$
$492$	−0.627417	−0.0282861
$493$	−21.9411	−0.988179
$494$	−1.65685	−0.0745454
$495$	2.82843	0.127128
$496$	31.4558	1.41241
$497$	0	0
$498$	−4.00000	−0.179244
$499$	−28.9706	−1.29690	−0.648450	−	0.761257i	$-0.724583\pi$
$499$	−28.9706	−1.29690	−0.648450	+	0.761257i	$0.724583\pi$
$500$	1.82843	0.0817697
$501$	−11.3137	−0.505459
$502$	7.59798	0.339114
$503$	−27.3137	−1.21786	−0.608929	−	0.793225i	$-0.708401\pi$
$503$	−27.3137	−1.21786	−0.608929	+	0.793225i	$0.708401\pi$
$504$	0	0
$505$	−3.65685	−0.162728
$506$	4.28427	0.190459
$507$	12.3137	0.546871
$508$	6.05887	0.268819
$509$	39.6569	1.75776	0.878880	−	0.477044i	$-0.158292\pi$
$509$	39.6569	1.75776	0.878880	+	0.477044i	$0.158292\pi$
$510$	1.51472	0.0670729
$511$	0	0
$512$	−22.7574	−1.00574
$513$	4.82843	0.213180
$514$	−4.82843	−0.212973
$515$	−12.0000	−0.528783
$516$	14.6274	0.643936
$517$	−16.0000	−0.703679
$518$	0	0
$519$	−20.6274	−0.905443
$520$	1.31371	0.0576099
$521$	34.2843	1.50202	0.751011	−	0.660290i	$-0.229567\pi$
$521$	34.2843	1.50202	0.751011	+	0.660290i	$0.229567\pi$
$522$	−2.48528	−0.108778
$523$	20.2843	0.886969	0.443485	−	0.896282i	$-0.353742\pi$
$523$	20.2843	0.886969	0.443485	+	0.896282i	$0.353742\pi$
$524$	−10.3431	−0.451842
$525$	0	0
$526$	10.4853	0.457180
$527$	−38.3431	−1.67025
$528$	8.48528	0.369274
$529$	−9.62742	−0.418583
$530$	3.51472	0.152670
$531$	−13.6569	−0.592657
$532$	0	0
$533$	0.284271	0.0123132
$534$	−7.17157	−0.310344
$535$	17.3137	0.748537
$536$	0	0
$537$	6.82843	0.294668
$538$	4.82843	0.208168
$539$	0	0
$540$	−1.82843	−0.0786830
$541$	18.0000	0.773880	0.386940	−	0.922105i	$-0.373532\pi$
$541$	18.0000	0.773880	0.386940	+	0.922105i	$0.373532\pi$
$542$	−2.28427	−0.0981179
$543$	13.6569	0.586072
$544$	16.1421	0.692088
$545$	−6.00000	−0.257012
$546$	0	0
$547$	−4.68629	−0.200371	−0.100186	−	0.994969i	$-0.531944\pi$
$547$	−4.68629	−0.200371	−0.100186	+	0.994969i	$0.531944\pi$
$548$	−34.4264	−1.47062
$549$	0	0
$550$	1.17157	0.0499560
$551$	−28.9706	−1.23419
$552$	−5.79899	−0.246821
$553$	0	0
$554$	0.544156	0.0231190
$555$	7.65685	0.325015
$556$	−33.7990	−1.43340
$557$	21.1716	0.897068	0.448534	−	0.893766i	$-0.351946\pi$
$557$	21.1716	0.897068	0.448534	+	0.893766i	$0.351946\pi$
$558$	−4.34315	−0.183860
$559$	−6.62742	−0.280310
$560$	0	0
$561$	−10.3431	−0.436688
$562$	−9.79899	−0.413345
$563$	−31.3137	−1.31972	−0.659858	−	0.751391i	$-0.729383\pi$
$563$	−31.3137	−1.31972	−0.659858	+	0.751391i	$0.729383\pi$
$564$	10.3431	0.435525
$565$	2.82843	0.118993
$566$	0	0
$567$	0	0
$568$	4.48528	0.188198
$569$	33.3137	1.39658	0.698292	−	0.715813i	$-0.253944\pi$
$569$	33.3137	1.39658	0.698292	+	0.715813i	$0.253944\pi$
$570$	2.00000	0.0837708
$571$	−39.3137	−1.64523	−0.822614	−	0.568601i	$-0.807485\pi$
$571$	−39.3137	−1.64523	−0.822614	+	0.568601i	$0.807485\pi$
$572$	−4.28427	−0.179134
$573$	14.8284	0.619466
$574$	0	0
$575$	3.65685	0.152501
$576$	−4.17157	−0.173816
$577$	−1.51472	−0.0630586	−0.0315293	−	0.999503i	$-0.510038\pi$
$577$	−1.51472	−0.0630586	−0.0315293	+	0.999503i	$0.510038\pi$
$578$	1.50253	0.0624968
$579$	−4.34315	−0.180495
$580$	10.9706	0.455528
$581$	0	0
$582$	4.34315	0.180029
$583$	−24.0000	−0.993978
$584$	26.6863	1.10429
$585$	0.828427	0.0342512
$586$	−9.79899	−0.404793
$587$	31.3137	1.29246	0.646228	−	0.763145i	$-0.276346\pi$
$587$	31.3137	1.29246	0.646228	+	0.763145i	$0.276346\pi$
$588$	0	0
$589$	−50.6274	−2.08607
$590$	−5.65685	−0.232889
$591$	20.4853	0.842652
$592$	22.9706	0.944084
$593$	−40.6274	−1.66837	−0.834184	−	0.551486i	$-0.814061\pi$
$593$	−40.6274	−1.66837	−0.834184	+	0.551486i	$0.814061\pi$
$594$	−1.17157	−0.0480702
$595$	0	0
$596$	−6.68629	−0.273881
$597$	4.82843	0.197614
$598$	1.25483	0.0513140
$599$	−27.5147	−1.12422	−0.562110	−	0.827062i	$-0.690010\pi$
$599$	−27.5147	−1.12422	−0.562110	+	0.827062i	$0.690010\pi$
$600$	−1.58579	−0.0647395
$601$	−22.3431	−0.911396	−0.455698	−	0.890134i	$-0.650610\pi$
$601$	−22.3431	−0.911396	−0.455698	+	0.890134i	$0.650610\pi$
$602$	0	0
$603$	0	0
$604$	−31.0294	−1.26257
$605$	3.00000	0.121967
$606$	1.51472	0.0615312
$607$	36.9706	1.50059	0.750294	−	0.661104i	$-0.229912\pi$
$607$	36.9706	1.50059	0.750294	+	0.661104i	$0.229912\pi$
$608$	21.3137	0.864385
$609$	0	0
$610$	0	0
$611$	−4.68629	−0.189587
$612$	6.68629	0.270277
$613$	43.9411	1.77477	0.887383	−	0.461034i	$-0.152521\pi$
$613$	43.9411	1.77477	0.887383	+	0.461034i	$0.152521\pi$
$614$	2.05887	0.0830894
$615$	−0.343146	−0.0138370
$616$	0	0
$617$	−37.4558	−1.50792	−0.753958	−	0.656923i	$-0.771858\pi$
$617$	−37.4558	−1.50792	−0.753958	+	0.656923i	$0.771858\pi$
$618$	4.97056	0.199945
$619$	19.8579	0.798155	0.399077	−	0.916917i	$-0.369330\pi$
$619$	19.8579	0.798155	0.399077	+	0.916917i	$0.369330\pi$
$620$	19.1716	0.769949
$621$	−3.65685	−0.146745
$622$	−0.686292	−0.0275178
$623$	0	0
$624$	2.48528	0.0994909
$625$	1.00000	0.0400000
$626$	−6.00000	−0.239808
$627$	−13.6569	−0.545402
$628$	−29.5147	−1.17777
$629$	−28.0000	−1.11643
$630$	0	0
$631$	−19.3137	−0.768867	−0.384433	−	0.923153i	$-0.625603\pi$
$631$	−19.3137	−0.768867	−0.384433	+	0.923153i	$0.625603\pi$
$632$	−12.6863	−0.504634
$633$	−1.65685	−0.0658540
$634$	2.54416	0.101041
$635$	3.31371	0.131501
$636$	15.5147	0.615199
$637$	0	0
$638$	7.02944	0.278298
$639$	2.82843	0.111891
$640$	−10.5563	−0.417276
$641$	22.2843	0.880176	0.440088	−	0.897955i	$-0.354947\pi$
$641$	22.2843	0.880176	0.440088	+	0.897955i	$0.354947\pi$
$642$	−7.17157	−0.283039
$643$	28.9706	1.14249	0.571244	−	0.820780i	$-0.306461\pi$
$643$	28.9706	1.14249	0.571244	+	0.820780i	$0.306461\pi$
$644$	0	0
$645$	8.00000	0.315000
$646$	−7.31371	−0.287754
$647$	−3.31371	−0.130275	−0.0651377	−	0.997876i	$-0.520749\pi$
$647$	−3.31371	−0.130275	−0.0651377	+	0.997876i	$0.520749\pi$
$648$	1.58579	0.0622956
$649$	38.6274	1.51626
$650$	0.343146	0.0134593
$651$	0	0
$652$	21.9411	0.859281
$653$	−19.7990	−0.774794	−0.387397	−	0.921913i	$-0.626626\pi$
$653$	−19.7990	−0.774794	−0.387397	+	0.921913i	$0.626626\pi$
$654$	2.48528	0.0971822
$655$	−5.65685	−0.221032
$656$	−1.02944	−0.0401928
$657$	16.8284	0.656539
$658$	0	0
$659$	−19.1127	−0.744525	−0.372263	−	0.928127i	$-0.621418\pi$
$659$	−19.1127	−0.744525	−0.372263	+	0.928127i	$0.621418\pi$
$660$	5.17157	0.201303
$661$	−3.31371	−0.128888	−0.0644442	−	0.997921i	$-0.520527\pi$
$661$	−3.31371	−0.128888	−0.0644442	+	0.997921i	$0.520527\pi$
$662$	4.00000	0.155464
$663$	−3.02944	−0.117654
$664$	−15.3137	−0.594287
$665$	0	0
$666$	−3.17157	−0.122896
$667$	21.9411	0.849564
$668$	−20.6863	−0.800377
$669$	12.9706	0.501471
$670$	0	0
$671$	0	0
$672$	0	0
$673$	−10.9706	−0.422884	−0.211442	−	0.977391i	$-0.567816\pi$
$673$	−10.9706	−0.422884	−0.211442	+	0.977391i	$0.567816\pi$
$674$	−11.1716	−0.430313
$675$	−1.00000	−0.0384900
$676$	22.5147	0.865951
$677$	4.34315	0.166921	0.0834603	−	0.996511i	$-0.473403\pi$
$677$	4.34315	0.166921	0.0834603	+	0.996511i	$0.473403\pi$
$678$	−1.17157	−0.0449940
$679$	0	0
$680$	5.79899	0.222381
$681$	−4.97056	−0.190472
$682$	12.2843	0.470389
$683$	−27.6569	−1.05826	−0.529130	−	0.848541i	$-0.677482\pi$
$683$	−27.6569	−1.05826	−0.529130	+	0.848541i	$0.677482\pi$
$684$	8.82843	0.337563
$685$	−18.8284	−0.719397
$686$	0	0
$687$	7.31371	0.279035
$688$	24.0000	0.914991
$689$	−7.02944	−0.267800
$690$	−1.51472	−0.0576644
$691$	−10.4853	−0.398879	−0.199439	−	0.979910i	$-0.563912\pi$
$691$	−10.4853	−0.398879	−0.199439	+	0.979910i	$0.563912\pi$
$692$	−37.7157	−1.43374
$693$	0	0
$694$	−4.54416	−0.172494
$695$	−18.4853	−0.701187
$696$	−9.51472	−0.360654
$697$	1.25483	0.0475302
$698$	6.62742	0.250851
$699$	−9.17157	−0.346901
$700$	0	0
$701$	−32.6274	−1.23232	−0.616160	−	0.787621i	$-0.711313\pi$
$701$	−32.6274	−1.23232	−0.616160	+	0.787621i	$0.711313\pi$
$702$	−0.343146	−0.0129512
$703$	−36.9706	−1.39437
$704$	11.7990	0.444691
$705$	5.65685	0.213049
$706$	−1.11270	−0.0418770
$707$	0	0
$708$	−24.9706	−0.938451
$709$	2.00000	0.0751116	0.0375558	−	0.999295i	$-0.488043\pi$
$709$	2.00000	0.0751116	0.0375558	+	0.999295i	$0.488043\pi$
$710$	1.17157	0.0439683
$711$	−8.00000	−0.300023
$712$	−27.4558	−1.02895
$713$	38.3431	1.43596
$714$	0	0
$715$	−2.34315	−0.0876287
$716$	12.4853	0.466597
$717$	−26.1421	−0.976296
$718$	−9.85786	−0.367892
$719$	−1.65685	−0.0617902	−0.0308951	−	0.999523i	$-0.509836\pi$
$719$	−1.65685	−0.0617902	−0.0308951	+	0.999523i	$0.509836\pi$
$720$	−3.00000	−0.111803
$721$	0	0
$722$	−1.78680	−0.0664977
$723$	−10.3431	−0.384666
$724$	24.9706	0.928024
$725$	6.00000	0.222834
$726$	−1.24264	−0.0461187
$727$	21.6569	0.803208	0.401604	−	0.915813i	$-0.368453\pi$
$727$	21.6569	0.803208	0.401604	+	0.915813i	$0.368453\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	6.97056	0.257992
$731$	−29.2548	−1.08203
$732$	0	0
$733$	−47.4558	−1.75282	−0.876411	−	0.481564i	$-0.840069\pi$
$733$	−47.4558	−1.75282	−0.876411	+	0.481564i	$0.840069\pi$
$734$	8.68629	0.320617
$735$	0	0
$736$	−16.1421	−0.595007
$737$	0	0
$738$	0.142136	0.00523208
$739$	37.9411	1.39569	0.697843	−	0.716250i	$-0.254143\pi$
$739$	37.9411	1.39569	0.697843	+	0.716250i	$0.254143\pi$
$740$	14.0000	0.514650
$741$	−4.00000	−0.146944
$742$	0	0
$743$	−6.68629	−0.245296	−0.122648	−	0.992450i	$-0.539139\pi$
$743$	−6.68629	−0.245296	−0.122648	+	0.992450i	$0.539139\pi$
$744$	−16.6274	−0.609591
$745$	−3.65685	−0.133977
$746$	−8.54416	−0.312824
$747$	−9.65685	−0.353326
$748$	−18.9117	−0.691480
$749$	0	0
$750$	−0.414214	−0.0151249
$751$	−26.3431	−0.961275	−0.480638	−	0.876919i	$-0.659595\pi$
$751$	−26.3431	−0.961275	−0.480638	+	0.876919i	$0.659595\pi$
$752$	16.9706	0.618853
$753$	18.3431	0.668461
$754$	2.05887	0.0749798
$755$	−16.9706	−0.617622
$756$	0	0
$757$	−15.6569	−0.569058	−0.284529	−	0.958667i	$-0.591837\pi$
$757$	−15.6569	−0.569058	−0.284529	+	0.958667i	$0.591837\pi$
$758$	−5.37258	−0.195141
$759$	10.3431	0.375432
$760$	7.65685	0.277743
$761$	13.3137	0.482622	0.241311	−	0.970448i	$-0.422423\pi$
$761$	13.3137	0.482622	0.241311	+	0.970448i	$0.422423\pi$
$762$	−1.37258	−0.0497234
$763$	0	0
$764$	27.1127	0.980903
$765$	3.65685	0.132214
$766$	0	0
$767$	11.3137	0.408514
$768$	−3.97056	−0.143275
$769$	−36.9706	−1.33319	−0.666596	−	0.745419i	$-0.732249\pi$
$769$	−36.9706	−1.33319	−0.666596	+	0.745419i	$0.732249\pi$
$770$	0	0
$771$	−11.6569	−0.419811
$772$	−7.94113	−0.285807
$773$	12.6274	0.454177	0.227088	−	0.973874i	$-0.427079\pi$
$773$	12.6274	0.454177	0.227088	+	0.973874i	$0.427079\pi$
$774$	−3.31371	−0.119109
$775$	10.4853	0.376642
$776$	16.6274	0.596889
$777$	0	0
$778$	0.142136	0.00509581
$779$	1.65685	0.0593630
$780$	1.51472	0.0542356
$781$	−8.00000	−0.286263
$782$	5.53911	0.198078
$783$	−6.00000	−0.214423
$784$	0	0
$785$	−16.1421	−0.576138
$786$	2.34315	0.0835772
$787$	−2.34315	−0.0835241	−0.0417621	−	0.999128i	$-0.513297\pi$
$787$	−2.34315	−0.0835241	−0.0417621	+	0.999128i	$0.513297\pi$
$788$	37.4558	1.33431
$789$	25.3137	0.901192
$790$	−3.31371	−0.117896
$791$	0	0
$792$	−4.48528	−0.159378
$793$	0	0
$794$	−7.94113	−0.281820
$795$	8.48528	0.300942
$796$	8.82843	0.312915
$797$	52.6274	1.86416	0.932079	−	0.362254i	$-0.117993\pi$
$797$	52.6274	1.86416	0.932079	+	0.362254i	$0.117993\pi$
$798$	0	0
$799$	−20.6863	−0.731828
$800$	−4.41421	−0.156066
$801$	−17.3137	−0.611750
$802$	−12.4264	−0.438792
$803$	−47.5980	−1.67970
$804$	0	0
$805$	0	0
$806$	3.59798	0.126733
$807$	11.6569	0.410341
$808$	5.79899	0.204008
$809$	−7.65685	−0.269201	−0.134600	−	0.990900i	$-0.542975\pi$
$809$	−7.65685	−0.269201	−0.134600	+	0.990900i	$0.542975\pi$
$810$	0.414214	0.0145540
$811$	−7.45584	−0.261810	−0.130905	−	0.991395i	$-0.541788\pi$
$811$	−7.45584	−0.261810	−0.130905	+	0.991395i	$0.541788\pi$
$812$	0	0
$813$	−5.51472	−0.193410
$814$	8.97056	0.314418
$815$	12.0000	0.420342
$816$	10.9706	0.384047
$817$	−38.6274	−1.35140
$818$	4.97056	0.173792
$819$	0	0
$820$	−0.627417	−0.0219104
$821$	0.627417	0.0218970	0.0109485	−	0.999940i	$-0.496515\pi$
$821$	0.627417	0.0218970	0.0109485	+	0.999940i	$0.496515\pi$
$822$	7.79899	0.272021
$823$	25.9411	0.904251	0.452125	−	0.891954i	$-0.350666\pi$
$823$	25.9411	0.904251	0.452125	+	0.891954i	$0.350666\pi$
$824$	19.0294	0.662922
$825$	2.82843	0.0984732
$826$	0	0
$827$	−17.3137	−0.602057	−0.301028	−	0.953615i	$-0.597330\pi$
$827$	−17.3137	−0.602057	−0.301028	+	0.953615i	$0.597330\pi$
$828$	−6.68629	−0.232365
$829$	31.5980	1.09744	0.548722	−	0.836005i	$-0.315115\pi$
$829$	31.5980	1.09744	0.548722	+	0.836005i	$0.315115\pi$
$830$	−4.00000	−0.138842
$831$	1.31371	0.0455720
$832$	3.45584	0.119810
$833$	0	0
$834$	7.65685	0.265135
$835$	−11.3137	−0.391527
$836$	−24.9706	−0.863625
$837$	−10.4853	−0.362424
$838$	−9.65685	−0.333590
$839$	1.37258	0.0473868	0.0236934	−	0.999719i	$-0.492457\pi$
$839$	1.37258	0.0473868	0.0236934	+	0.999719i	$0.492457\pi$
$840$	0	0
$841$	7.00000	0.241379
$842$	2.48528	0.0856485
$843$	−23.6569	−0.814785
$844$	−3.02944	−0.104278
$845$	12.3137	0.423604
$846$	−2.34315	−0.0805590
$847$	0	0
$848$	25.4558	0.874157
$849$	0	0
$850$	1.51472	0.0519544
$851$	28.0000	0.959828
$852$	5.17157	0.177175
$853$	6.48528	0.222052	0.111026	−	0.993818i	$-0.464586\pi$
$853$	6.48528	0.222052	0.111026	+	0.993818i	$0.464586\pi$
$854$	0	0
$855$	4.82843	0.165129
$856$	−27.4558	−0.938421
$857$	0.627417	0.0214322	0.0107161	−	0.999943i	$-0.496589\pi$
$857$	0.627417	0.0214322	0.0107161	+	0.999943i	$0.496589\pi$
$858$	0.970563	0.0331345
$859$	6.20101	0.211576	0.105788	−	0.994389i	$-0.466264\pi$
$859$	6.20101	0.211576	0.105788	+	0.994389i	$0.466264\pi$
$860$	14.6274	0.498791
$861$	0	0
$862$	2.14214	0.0729614
$863$	13.0294	0.443527	0.221764	−	0.975100i	$-0.428819\pi$
$863$	13.0294	0.443527	0.221764	+	0.975100i	$0.428819\pi$
$864$	4.41421	0.150175
$865$	−20.6274	−0.701353
$866$	5.31371	0.180567
$867$	3.62742	0.123194
$868$	0	0
$869$	22.6274	0.767583
$870$	−2.48528	−0.0842589
$871$	0	0
$872$	9.51472	0.322209
$873$	10.4853	0.354873
$874$	7.31371	0.247390
$875$	0	0
$876$	30.7696	1.03961
$877$	−39.9411	−1.34872	−0.674358	−	0.738405i	$-0.735580\pi$
$877$	−39.9411	−1.34872	−0.674358	+	0.738405i	$0.735580\pi$
$878$	−12.6274	−0.426155
$879$	−23.6569	−0.797926
$880$	8.48528	0.286039
$881$	−47.2548	−1.59206	−0.796028	−	0.605260i	$-0.793069\pi$
$881$	−47.2548	−1.59206	−0.796028	+	0.605260i	$0.793069\pi$
$882$	0	0
$883$	28.0000	0.942275	0.471138	−	0.882060i	$-0.343844\pi$
$883$	28.0000	0.942275	0.471138	+	0.882060i	$0.343844\pi$
$884$	−5.53911	−0.186300
$885$	−13.6569	−0.459070
$886$	−5.11270	−0.171764
$887$	40.9706	1.37566	0.687828	−	0.725873i	$-0.258564\pi$
$887$	40.9706	1.37566	0.687828	+	0.725873i	$0.258564\pi$
$888$	−12.1421	−0.407463
$889$	0	0
$890$	−7.17157	−0.240392
$891$	−2.82843	−0.0947559
$892$	23.7157	0.794061
$893$	−27.3137	−0.914018
$894$	1.51472	0.0506598
$895$	6.82843	0.228249
$896$	0	0
$897$	3.02944	0.101150
$898$	−13.5147	−0.450992
$899$	62.9117	2.09822
$900$	−1.82843	−0.0609476
$901$	−31.0294	−1.03374
$902$	−0.402020	−0.0133858
$903$	0	0
$904$	−4.48528	−0.149178
$905$	13.6569	0.453969
$906$	7.02944	0.233537
$907$	−16.6863	−0.554059	−0.277030	−	0.960861i	$-0.589350\pi$
$907$	−16.6863	−0.554059	−0.277030	+	0.960861i	$0.589350\pi$
$908$	−9.08831	−0.301606
$909$	3.65685	0.121290
$910$	0	0
$911$	31.7990	1.05355	0.526774	−	0.850006i	$-0.323402\pi$
$911$	31.7990	1.05355	0.526774	+	0.850006i	$0.323402\pi$
$912$	14.4853	0.479656
$913$	27.3137	0.903952
$914$	−11.4558	−0.378926
$915$	0	0
$916$	13.3726	0.441843
$917$	0	0
$918$	−1.51472	−0.0499932
$919$	−12.2843	−0.405221	−0.202610	−	0.979259i	$-0.564942\pi$
$919$	−12.2843	−0.405221	−0.202610	+	0.979259i	$0.564942\pi$
$920$	−5.79899	−0.191187
$921$	4.97056	0.163786
$922$	−3.85786	−0.127052
$923$	−2.34315	−0.0771256
$924$	0	0
$925$	7.65685	0.251756
$926$	2.74517	0.0902118
$927$	12.0000	0.394132
$928$	−26.4853	−0.869422
$929$	42.0000	1.37798	0.688988	−	0.724773i	$-0.258055\pi$
$929$	42.0000	1.37798	0.688988	+	0.724773i	$0.258055\pi$
$930$	−4.34315	−0.142417
$931$	0	0
$932$	−16.7696	−0.549305
$933$	−1.65685	−0.0542430
$934$	13.3726	0.437564
$935$	−10.3431	−0.338257
$936$	−1.31371	−0.0429399
$937$	35.4558	1.15829	0.579146	−	0.815224i	$-0.303386\pi$
$937$	35.4558	1.15829	0.579146	+	0.815224i	$0.303386\pi$
$938$	0	0
$939$	−14.4853	−0.472709
$940$	10.3431	0.337356
$941$	−44.6274	−1.45481	−0.727406	−	0.686207i	$-0.759274\pi$
$941$	−44.6274	−1.45481	−0.727406	+	0.686207i	$0.759274\pi$
$942$	6.68629	0.217851
$943$	−1.25483	−0.0408630
$944$	−40.9706	−1.33348
$945$	0	0
$946$	9.37258	0.304729
$947$	−23.6569	−0.768744	−0.384372	−	0.923178i	$-0.625582\pi$
$947$	−23.6569	−0.768744	−0.384372	+	0.923178i	$0.625582\pi$
$948$	−14.6274	−0.475076
$949$	−13.9411	−0.452548
$950$	2.00000	0.0648886
$951$	6.14214	0.199172
$952$	0	0
$953$	−22.1421	−0.717254	−0.358627	−	0.933481i	$-0.616755\pi$
$953$	−22.1421	−0.717254	−0.358627	+	0.933481i	$0.616755\pi$
$954$	−3.51472	−0.113793
$955$	14.8284	0.479837
$956$	−47.7990	−1.54593
$957$	16.9706	0.548580
$958$	−10.6274	−0.343356
$959$	0	0
$960$	−4.17157	−0.134637
$961$	78.9411	2.54649
$962$	2.62742	0.0847113
$963$	−17.3137	−0.557926
$964$	−18.9117	−0.609104
$965$	−4.34315	−0.139811
$966$	0	0
$967$	50.6274	1.62807	0.814034	−	0.580817i	$-0.197267\pi$
$967$	50.6274	1.62807	0.814034	+	0.580817i	$0.197267\pi$
$968$	−4.75736	−0.152907
$969$	−17.6569	−0.567220
$970$	4.34315	0.139450
$971$	−16.6863	−0.535489	−0.267744	−	0.963490i	$-0.586278\pi$
$971$	−16.6863	−0.535489	−0.267744	+	0.963490i	$0.586278\pi$
$972$	1.82843	0.0586468
$973$	0	0
$974$	15.7157	0.503564
$975$	0.828427	0.0265309
$976$	0	0
$977$	−3.51472	−0.112446	−0.0562229	−	0.998418i	$-0.517906\pi$
$977$	−3.51472	−0.112446	−0.0562229	+	0.998418i	$0.517906\pi$
$978$	−4.97056	−0.158941
$979$	48.9706	1.56511
$980$	0	0
$981$	6.00000	0.191565
$982$	4.20101	0.134060
$983$	−10.3431	−0.329895	−0.164948	−	0.986302i	$-0.552745\pi$
$983$	−10.3431	−0.329895	−0.164948	+	0.986302i	$0.552745\pi$
$984$	0.544156	0.0173471
$985$	20.4853	0.652715
$986$	9.08831	0.289431
$987$	0	0
$988$	−7.31371	−0.232680
$989$	29.2548	0.930250
$990$	−1.17157	−0.0372350
$991$	−16.9706	−0.539088	−0.269544	−	0.962988i	$-0.586873\pi$
$991$	−16.9706	−0.539088	−0.269544	+	0.962988i	$0.586873\pi$
$992$	−46.2843	−1.46953
$993$	9.65685	0.306451
$994$	0	0
$995$	4.82843	0.153071
$996$	−17.6569	−0.559479
$997$	4.54416	0.143915	0.0719574	−	0.997408i	$-0.477075\pi$
$997$	4.54416	0.143915	0.0719574	+	0.997408i	$0.477075\pi$
$998$	12.0000	0.379853
$999$	−7.65685	−0.242252

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	735.2.a.l.1.1	✓	2
3.2	odd	2		2205.2.a.r.1.2		2
5.4	even	2		3675.2.a.t.1.2		2
7.2	even	3		735.2.i.h.361.2		4
7.3	odd	6		735.2.i.g.226.2		4
7.4	even	3		735.2.i.h.226.2		4
7.5	odd	6		735.2.i.g.361.2		4
7.6	odd	2		735.2.a.m.1.1	yes	2
21.20	even	2		2205.2.a.o.1.2		2
35.34	odd	2		3675.2.a.s.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
735.2.a.l.1.1	✓	2	1.1	even	1	trivial
735.2.a.m.1.1	yes	2	7.6	odd	2
735.2.i.g.226.2		4	7.3	odd	6
735.2.i.g.361.2		4	7.5	odd	6
735.2.i.h.226.2		4	7.4	even	3
735.2.i.h.361.2		4	7.2	even	3
2205.2.a.o.1.2		2	21.20	even	2
2205.2.a.r.1.2		2	3.2	odd	2
3675.2.a.s.1.2		2	35.34	odd	2
3675.2.a.t.1.2		2	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	735.a (trivial)

\(f(q)\)	\(=\)	\(q-0.414214 q^{2} -1.00000 q^{3} -1.82843 q^{4} -1.00000 q^{5} +0.414214 q^{6} +1.58579 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.414214 q^{2} -1.00000 q^{3} -1.82843 q^{4} -1.00000 q^{5} +0.414214 q^{6} +1.58579 q^{8} +1.00000 q^{9} +0.414214 q^{10} -2.82843 q^{11} +1.82843 q^{12} -0.828427 q^{13} +1.00000 q^{15} +3.00000 q^{16} -3.65685 q^{17} -0.414214 q^{18} -4.82843 q^{19} +1.82843 q^{20} +1.17157 q^{22} +3.65685 q^{23} -1.58579 q^{24} +1.00000 q^{25} +0.343146 q^{26} -1.00000 q^{27} +6.00000 q^{29} -0.414214 q^{30} +10.4853 q^{31} -4.41421 q^{32} +2.82843 q^{33} +1.51472 q^{34} -1.82843 q^{36} +7.65685 q^{37} +2.00000 q^{38} +0.828427 q^{39} -1.58579 q^{40} -0.343146 q^{41} +8.00000 q^{43} +5.17157 q^{44} -1.00000 q^{45} -1.51472 q^{46} +5.65685 q^{47} -3.00000 q^{48} -0.414214 q^{50} +3.65685 q^{51} +1.51472 q^{52} +8.48528 q^{53} +0.414214 q^{54} +2.82843 q^{55} +4.82843 q^{57} -2.48528 q^{58} -13.6569 q^{59} -1.82843 q^{60} -4.34315 q^{62} -4.17157 q^{64} +0.828427 q^{65} -1.17157 q^{66} +6.68629 q^{68} -3.65685 q^{69} +2.82843 q^{71} +1.58579 q^{72} +16.8284 q^{73} -3.17157 q^{74} -1.00000 q^{75} +8.82843 q^{76} -0.343146 q^{78} -8.00000 q^{79} -3.00000 q^{80} +1.00000 q^{81} +0.142136 q^{82} -9.65685 q^{83} +3.65685 q^{85} -3.31371 q^{86} -6.00000 q^{87} -4.48528 q^{88} -17.3137 q^{89} +0.414214 q^{90} -6.68629 q^{92} -10.4853 q^{93} -2.34315 q^{94} +4.82843 q^{95} +4.41421 q^{96} +10.4853 q^{97} -2.82843 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{5} - 2 q^{6} + 6 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 - 2 * q^5 - 2 * q^6 + 6 * q^8 + 2 * q^9	\( 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{5} - 2 q^{6} + 6 q^{8} + 2 q^{9} - 2 q^{10} - 2 q^{12} + 4 q^{13} + 2 q^{15} + 6 q^{16} + 4 q^{17} + 2 q^{18} - 4 q^{19} - 2 q^{20} + 8 q^{22} - 4 q^{23} - 6 q^{24} + 2 q^{25} + 12 q^{26} - 2 q^{27} + 12 q^{29} + 2 q^{30} + 4 q^{31} - 6 q^{32} + 20 q^{34} + 2 q^{36} + 4 q^{37} + 4 q^{38} - 4 q^{39} - 6 q^{40} - 12 q^{41} + 16 q^{43} + 16 q^{44} - 2 q^{45} - 20 q^{46} - 6 q^{48} + 2 q^{50} - 4 q^{51} + 20 q^{52} - 2 q^{54} + 4 q^{57} + 12 q^{58} - 16 q^{59} + 2 q^{60} - 20 q^{62} - 14 q^{64} - 4 q^{65} - 8 q^{66} + 36 q^{68} + 4 q^{69} + 6 q^{72} + 28 q^{73} - 12 q^{74} - 2 q^{75} + 12 q^{76} - 12 q^{78} - 16 q^{79} - 6 q^{80} + 2 q^{81} - 28 q^{82} - 8 q^{83} - 4 q^{85} + 16 q^{86} - 12 q^{87} + 8 q^{88} - 12 q^{89} - 2 q^{90} - 36 q^{92} - 4 q^{93} - 16 q^{94} + 4 q^{95} + 6 q^{96} + 4 q^{97}+O(q^{100}) \) 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 - 2 * q^5 - 2 * q^6 + 6 * q^8 + 2 * q^9 - 2 * q^10 - 2 * q^12 + 4 * q^13 + 2 * q^15 + 6 * q^16 + 4 * q^17 + 2 * q^18 - 4 * q^19 - 2 * q^20 + 8 * q^22 - 4 * q^23 - 6 * q^24 + 2 * q^25 + 12 * q^26 - 2 * q^27 + 12 * q^29 + 2 * q^30 + 4 * q^31 - 6 * q^32 + 20 * q^34 + 2 * q^36 + 4 * q^37 + 4 * q^38 - 4 * q^39 - 6 * q^40 - 12 * q^41 + 16 * q^43 + 16 * q^44 - 2 * q^45 - 20 * q^46 - 6 * q^48 + 2 * q^50 - 4 * q^51 + 20 * q^52 - 2 * q^54 + 4 * q^57 + 12 * q^58 - 16 * q^59 + 2 * q^60 - 20 * q^62 - 14 * q^64 - 4 * q^65 - 8 * q^66 + 36 * q^68 + 4 * q^69 + 6 * q^72 + 28 * q^73 - 12 * q^74 - 2 * q^75 + 12 * q^76 - 12 * q^78 - 16 * q^79 - 6 * q^80 + 2 * q^81 - 28 * q^82 - 8 * q^83 - 4 * q^85 + 16 * q^86 - 12 * q^87 + 8 * q^88 - 12 * q^89 - 2 * q^90 - 36 * q^92 - 4 * q^93 - 16 * q^94 + 4 * q^95 + 6 * q^96 + 4 * q^97

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