LMFDB - Embedded newform 1502.2.a.c.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1502,2,Mod(1,1502)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1502, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1502.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1502 = 2 \cdot 751 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1502.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:	$11.9935303836$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{10})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 1 $ x^2 - x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-0.618034$ of defining polynomial
Character	$\chi$	$=$	1502.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +2.23607 q^{3} +1.00000 q^{4} -2.61803 q^{5} -2.23607 q^{6} -0.381966 q^{7} -1.00000 q^{8} +2.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +2.23607 q^{3} +1.00000 q^{4} -2.61803 q^{5} -2.23607 q^{6} -0.381966 q^{7} -1.00000 q^{8} +2.00000 q^{9} +2.61803 q^{10} +3.61803 q^{11} +2.23607 q^{12} -1.00000 q^{13} +0.381966 q^{14} -5.85410 q^{15} +1.00000 q^{16} -8.09017 q^{17} -2.00000 q^{18} -6.70820 q^{19} -2.61803 q^{20} -0.854102 q^{21} -3.61803 q^{22} +5.47214 q^{23} -2.23607 q^{24} +1.85410 q^{25} +1.00000 q^{26} -2.23607 q^{27} -0.381966 q^{28} -4.61803 q^{29} +5.85410 q^{30} -6.32624 q^{31} -1.00000 q^{32} +8.09017 q^{33} +8.09017 q^{34} +1.00000 q^{35} +2.00000 q^{36} -0.763932 q^{37} +6.70820 q^{38} -2.23607 q^{39} +2.61803 q^{40} +10.4721 q^{41} +0.854102 q^{42} +2.23607 q^{43} +3.61803 q^{44} -5.23607 q^{45} -5.47214 q^{46} +3.00000 q^{47} +2.23607 q^{48} -6.85410 q^{49} -1.85410 q^{50} -18.0902 q^{51} -1.00000 q^{52} +10.6180 q^{53} +2.23607 q^{54} -9.47214 q^{55} +0.381966 q^{56} -15.0000 q^{57} +4.61803 q^{58} -5.47214 q^{59} -5.85410 q^{60} -7.14590 q^{61} +6.32624 q^{62} -0.763932 q^{63} +1.00000 q^{64} +2.61803 q^{65} -8.09017 q^{66} -15.0902 q^{67} -8.09017 q^{68} +12.2361 q^{69} -1.00000 q^{70} -6.70820 q^{71} -2.00000 q^{72} -7.70820 q^{73} +0.763932 q^{74} +4.14590 q^{75} -6.70820 q^{76} -1.38197 q^{77} +2.23607 q^{78} +8.23607 q^{79} -2.61803 q^{80} -11.0000 q^{81} -10.4721 q^{82} +4.56231 q^{83} -0.854102 q^{84} +21.1803 q^{85} -2.23607 q^{86} -10.3262 q^{87} -3.61803 q^{88} -13.7082 q^{89} +5.23607 q^{90} +0.381966 q^{91} +5.47214 q^{92} -14.1459 q^{93} -3.00000 q^{94} +17.5623 q^{95} -2.23607 q^{96} +9.70820 q^{97} +6.85410 q^{98} +7.23607 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} + 2 q^{4} - 3 q^{5} - 3 q^{7} - 2 q^{8} + 4 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 + 2 * q^4 - 3 * q^5 - 3 * q^7 - 2 * q^8 + 4 * q^9	$ 2 q - 2 q^{2} + 2 q^{4} - 3 q^{5} - 3 q^{7} - 2 q^{8} + 4 q^{9} + 3 q^{10} + 5 q^{11} - 2 q^{13} + 3 q^{14} - 5 q^{15} + 2 q^{16} - 5 q^{17} - 4 q^{18} - 3 q^{20} + 5 q^{21} - 5 q^{22} + 2 q^{23} - 3 q^{25} + 2 q^{26} - 3 q^{28} - 7 q^{29} + 5 q^{30} + 3 q^{31} - 2 q^{32} + 5 q^{33} + 5 q^{34} + 2 q^{35} + 4 q^{36} - 6 q^{37} + 3 q^{40} + 12 q^{41} - 5 q^{42} + 5 q^{44} - 6 q^{45} - 2 q^{46} + 6 q^{47} - 7 q^{49} + 3 q^{50} - 25 q^{51} - 2 q^{52} + 19 q^{53} - 10 q^{55} + 3 q^{56} - 30 q^{57} + 7 q^{58} - 2 q^{59} - 5 q^{60} - 21 q^{61} - 3 q^{62} - 6 q^{63} + 2 q^{64} + 3 q^{65} - 5 q^{66} - 19 q^{67} - 5 q^{68} + 20 q^{69} - 2 q^{70} - 4 q^{72} - 2 q^{73} + 6 q^{74} + 15 q^{75} - 5 q^{77} + 12 q^{79} - 3 q^{80} - 22 q^{81} - 12 q^{82} - 11 q^{83} + 5 q^{84} + 20 q^{85} - 5 q^{87} - 5 q^{88} - 14 q^{89} + 6 q^{90} + 3 q^{91} + 2 q^{92} - 35 q^{93} - 6 q^{94} + 15 q^{95} + 6 q^{97} + 7 q^{98} + 10 q^{99}+O(q^{100}) $ 2 * q - 2 * q^2 + 2 * q^4 - 3 * q^5 - 3 * q^7 - 2 * q^8 + 4 * q^9 + 3 * q^10 + 5 * q^11 - 2 * q^13 + 3 * q^14 - 5 * q^15 + 2 * q^16 - 5 * q^17 - 4 * q^18 - 3 * q^20 + 5 * q^21 - 5 * q^22 + 2 * q^23 - 3 * q^25 + 2 * q^26 - 3 * q^28 - 7 * q^29 + 5 * q^30 + 3 * q^31 - 2 * q^32 + 5 * q^33 + 5 * q^34 + 2 * q^35 + 4 * q^36 - 6 * q^37 + 3 * q^40 + 12 * q^41 - 5 * q^42 + 5 * q^44 - 6 * q^45 - 2 * q^46 + 6 * q^47 - 7 * q^49 + 3 * q^50 - 25 * q^51 - 2 * q^52 + 19 * q^53 - 10 * q^55 + 3 * q^56 - 30 * q^57 + 7 * q^58 - 2 * q^59 - 5 * q^60 - 21 * q^61 - 3 * q^62 - 6 * q^63 + 2 * q^64 + 3 * q^65 - 5 * q^66 - 19 * q^67 - 5 * q^68 + 20 * q^69 - 2 * q^70 - 4 * q^72 - 2 * q^73 + 6 * q^74 + 15 * q^75 - 5 * q^77 + 12 * q^79 - 3 * q^80 - 22 * q^81 - 12 * q^82 - 11 * q^83 + 5 * q^84 + 20 * q^85 - 5 * q^87 - 5 * q^88 - 14 * q^89 + 6 * q^90 + 3 * q^91 + 2 * q^92 - 35 * q^93 - 6 * q^94 + 15 * q^95 + 6 * q^97 + 7 * q^98 + 10 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	2.23607	1.29099	0.645497	−	0.763763i	$-0.276650\pi$
$3$	2.23607	1.29099	0.645497	+	0.763763i	$0.276650\pi$
$4$	1.00000	0.500000
$5$	−2.61803	−1.17082	−0.585410	−	0.810737i	$-0.699067\pi$
$5$	−2.61803	−1.17082	−0.585410	+	0.810737i	$0.699067\pi$
$6$	−2.23607	−0.912871
$7$	−0.381966	−0.144370	−0.0721848	−	0.997391i	$-0.522997\pi$
$7$	−0.381966	−0.144370	−0.0721848	+	0.997391i	$0.522997\pi$
$8$	−1.00000	−0.353553
$9$	2.00000	0.666667
$10$	2.61803	0.827895
$11$	3.61803	1.09088	0.545439	−	0.838150i	$-0.316363\pi$
$11$	3.61803	1.09088	0.545439	+	0.838150i	$0.316363\pi$
$12$	2.23607	0.645497
$13$	−1.00000	−0.277350	−0.138675	−	0.990338i	$-0.544284\pi$
$13$	−1.00000	−0.277350	−0.138675	+	0.990338i	$0.544284\pi$
$14$	0.381966	0.102085
$15$	−5.85410	−1.51152
$16$	1.00000	0.250000
$17$	−8.09017	−1.96215	−0.981077	−	0.193617i	$-0.937978\pi$
$17$	−8.09017	−1.96215	−0.981077	+	0.193617i	$0.937978\pi$
$18$	−2.00000	−0.471405
$19$	−6.70820	−1.53897	−0.769484	−	0.638666i	$-0.779486\pi$
$19$	−6.70820	−1.53897	−0.769484	+	0.638666i	$0.779486\pi$
$20$	−2.61803	−0.585410
$21$	−0.854102	−0.186380
$22$	−3.61803	−0.771367
$23$	5.47214	1.14102	0.570510	−	0.821291i	$-0.306746\pi$
$23$	5.47214	1.14102	0.570510	+	0.821291i	$0.306746\pi$
$24$	−2.23607	−0.456435
$25$	1.85410	0.370820
$26$	1.00000	0.196116
$27$	−2.23607	−0.430331
$28$	−0.381966	−0.0721848
$29$	−4.61803	−0.857547	−0.428774	−	0.903412i	$-0.641054\pi$
$29$	−4.61803	−0.857547	−0.428774	+	0.903412i	$0.641054\pi$
$30$	5.85410	1.06881
$31$	−6.32624	−1.13623	−0.568113	−	0.822951i	$-0.692326\pi$
$31$	−6.32624	−1.13623	−0.568113	+	0.822951i	$0.692326\pi$
$32$	−1.00000	−0.176777
$33$	8.09017	1.40832
$34$	8.09017	1.38745
$35$	1.00000	0.169031
$36$	2.00000	0.333333
$37$	−0.763932	−0.125590	−0.0627948	−	0.998026i	$-0.520001\pi$
$37$	−0.763932	−0.125590	−0.0627948	+	0.998026i	$0.520001\pi$
$38$	6.70820	1.08821
$39$	−2.23607	−0.358057
$40$	2.61803	0.413948
$41$	10.4721	1.63547	0.817736	−	0.575593i	$-0.195229\pi$
$41$	10.4721	1.63547	0.817736	+	0.575593i	$0.195229\pi$
$42$	0.854102	0.131791
$43$	2.23607	0.340997	0.170499	−	0.985358i	$-0.445462\pi$
$43$	2.23607	0.340997	0.170499	+	0.985358i	$0.445462\pi$
$44$	3.61803	0.545439
$45$	−5.23607	−0.780547
$46$	−5.47214	−0.806822
$47$	3.00000	0.437595	0.218797	−	0.975770i	$-0.429787\pi$
$47$	3.00000	0.437595	0.218797	+	0.975770i	$0.429787\pi$
$48$	2.23607	0.322749
$49$	−6.85410	−0.979157
$50$	−1.85410	−0.262210
$51$	−18.0902	−2.53313
$52$	−1.00000	−0.138675
$53$	10.6180	1.45850	0.729250	−	0.684248i	$-0.239869\pi$
$53$	10.6180	1.45850	0.729250	+	0.684248i	$0.239869\pi$
$54$	2.23607	0.304290
$55$	−9.47214	−1.27722
$56$	0.381966	0.0510424
$57$	−15.0000	−1.98680
$58$	4.61803	0.606378
$59$	−5.47214	−0.712411	−0.356206	−	0.934408i	$-0.615930\pi$
$59$	−5.47214	−0.712411	−0.356206	+	0.934408i	$0.615930\pi$
$60$	−5.85410	−0.755761
$61$	−7.14590	−0.914938	−0.457469	−	0.889225i	$-0.651244\pi$
$61$	−7.14590	−0.914938	−0.457469	+	0.889225i	$0.651244\pi$
$62$	6.32624	0.803433
$63$	−0.763932	−0.0962464
$64$	1.00000	0.125000
$65$	2.61803	0.324727
$66$	−8.09017	−0.995831
$67$	−15.0902	−1.84356	−0.921779	−	0.387716i	$-0.873264\pi$
$67$	−15.0902	−1.84356	−0.921779	+	0.387716i	$0.873264\pi$
$68$	−8.09017	−0.981077
$69$	12.2361	1.47305
$70$	−1.00000	−0.119523
$71$	−6.70820	−0.796117	−0.398059	−	0.917360i	$-0.630316\pi$
$71$	−6.70820	−0.796117	−0.398059	+	0.917360i	$0.630316\pi$
$72$	−2.00000	−0.235702
$73$	−7.70820	−0.902177	−0.451089	−	0.892479i	$-0.648964\pi$
$73$	−7.70820	−0.902177	−0.451089	+	0.892479i	$0.648964\pi$
$74$	0.763932	0.0888053
$75$	4.14590	0.478727
$76$	−6.70820	−0.769484
$77$	−1.38197	−0.157490
$78$	2.23607	0.253185
$79$	8.23607	0.926630	0.463315	−	0.886194i	$-0.346660\pi$
$79$	8.23607	0.926630	0.463315	+	0.886194i	$0.346660\pi$
$80$	−2.61803	−0.292705
$81$	−11.0000	−1.22222
$82$	−10.4721	−1.15645
$83$	4.56231	0.500778	0.250389	−	0.968145i	$-0.419441\pi$
$83$	4.56231	0.500778	0.250389	+	0.968145i	$0.419441\pi$
$84$	−0.854102	−0.0931902
$85$	21.1803	2.29733
$86$	−2.23607	−0.241121
$87$	−10.3262	−1.10709
$88$	−3.61803	−0.385684
$89$	−13.7082	−1.45307	−0.726533	−	0.687131i	$-0.758870\pi$
$89$	−13.7082	−1.45307	−0.726533	+	0.687131i	$0.758870\pi$
$90$	5.23607	0.551930
$91$	0.381966	0.0400409
$92$	5.47214	0.570510
$93$	−14.1459	−1.46686
$94$	−3.00000	−0.309426
$95$	17.5623	1.80185
$96$	−2.23607	−0.228218
$97$	9.70820	0.985719	0.492859	−	0.870109i	$-0.335952\pi$
$97$	9.70820	0.985719	0.492859	+	0.870109i	$0.335952\pi$
$98$	6.85410	0.692369
$99$	7.23607	0.727252
$100$	1.85410	0.185410
$101$	17.8885	1.77998	0.889988	−	0.455983i	$-0.150712\pi$
$101$	17.8885	1.77998	0.889988	+	0.455983i	$0.150712\pi$
$102$	18.0902	1.79119
$103$	−17.2361	−1.69832	−0.849160	−	0.528135i	$-0.822891\pi$
$103$	−17.2361	−1.69832	−0.849160	+	0.528135i	$0.822891\pi$
$104$	1.00000	0.0980581
$105$	2.23607	0.218218
$106$	−10.6180	−1.03131
$107$	−13.7984	−1.33394	−0.666970	−	0.745085i	$-0.732409\pi$
$107$	−13.7984	−1.33394	−0.666970	+	0.745085i	$0.732409\pi$
$108$	−2.23607	−0.215166
$109$	2.85410	0.273373	0.136687	−	0.990614i	$-0.456355\pi$
$109$	2.85410	0.273373	0.136687	+	0.990614i	$0.456355\pi$
$110$	9.47214	0.903133
$111$	−1.70820	−0.162136
$112$	−0.381966	−0.0360924
$113$	−12.7639	−1.20073	−0.600365	−	0.799726i	$-0.704978\pi$
$113$	−12.7639	−1.20073	−0.600365	+	0.799726i	$0.704978\pi$
$114$	15.0000	1.40488
$115$	−14.3262	−1.33593
$116$	−4.61803	−0.428774
$117$	−2.00000	−0.184900
$118$	5.47214	0.503751
$119$	3.09017	0.283275
$120$	5.85410	0.534404
$121$	2.09017	0.190015
$122$	7.14590	0.646959
$123$	23.4164	2.11139
$124$	−6.32624	−0.568113
$125$	8.23607	0.736656
$126$	0.763932	0.0680565
$127$	5.61803	0.498520	0.249260	−	0.968437i	$-0.419813\pi$
$127$	5.61803	0.498520	0.249260	+	0.968437i	$0.419813\pi$
$128$	−1.00000	−0.0883883
$129$	5.00000	0.440225
$130$	−2.61803	−0.229617
$131$	10.7082	0.935580	0.467790	−	0.883840i	$-0.345050\pi$
$131$	10.7082	0.935580	0.467790	+	0.883840i	$0.345050\pi$
$132$	8.09017	0.704159
$133$	2.56231	0.222180
$134$	15.0902	1.30359
$135$	5.85410	0.503841
$136$	8.09017	0.693726
$137$	−0.437694	−0.0373947	−0.0186974	−	0.999825i	$-0.505952\pi$
$137$	−0.437694	−0.0373947	−0.0186974	+	0.999825i	$0.505952\pi$
$138$	−12.2361	−1.04160
$139$	3.32624	0.282128	0.141064	−	0.990000i	$-0.454948\pi$
$139$	3.32624	0.282128	0.141064	+	0.990000i	$0.454948\pi$
$140$	1.00000	0.0845154
$141$	6.70820	0.564933
$142$	6.70820	0.562940
$143$	−3.61803	−0.302555
$144$	2.00000	0.166667
$145$	12.0902	1.00403
$146$	7.70820	0.637935
$147$	−15.3262	−1.26409
$148$	−0.763932	−0.0627948
$149$	0.673762	0.0551967	0.0275984	−	0.999619i	$-0.491214\pi$
$149$	0.673762	0.0551967	0.0275984	+	0.999619i	$0.491214\pi$
$150$	−4.14590	−0.338511
$151$	18.2361	1.48403	0.742015	−	0.670383i	$-0.233870\pi$
$151$	18.2361	1.48403	0.742015	+	0.670383i	$0.233870\pi$
$152$	6.70820	0.544107
$153$	−16.1803	−1.30810
$154$	1.38197	0.111362
$155$	16.5623	1.33032
$156$	−2.23607	−0.179029
$157$	1.23607	0.0986490	0.0493245	−	0.998783i	$-0.484293\pi$
$157$	1.23607	0.0986490	0.0493245	+	0.998783i	$0.484293\pi$
$158$	−8.23607	−0.655226
$159$	23.7426	1.88291
$160$	2.61803	0.206974
$161$	−2.09017	−0.164728
$162$	11.0000	0.864242
$163$	−23.0902	−1.80856	−0.904281	−	0.426938i	$-0.859592\pi$
$163$	−23.0902	−1.80856	−0.904281	+	0.426938i	$0.859592\pi$
$164$	10.4721	0.817736
$165$	−21.1803	−1.64889
$166$	−4.56231	−0.354104
$167$	−18.6180	−1.44071	−0.720353	−	0.693607i	$-0.756020\pi$
$167$	−18.6180	−1.44071	−0.720353	+	0.693607i	$0.756020\pi$
$168$	0.854102	0.0658954
$169$	−12.0000	−0.923077
$170$	−21.1803	−1.62446
$171$	−13.4164	−1.02598
$172$	2.23607	0.170499
$173$	11.6180	0.883303	0.441651	−	0.897187i	$-0.354393\pi$
$173$	11.6180	0.883303	0.441651	+	0.897187i	$0.354393\pi$
$174$	10.3262	0.782830
$175$	−0.708204	−0.0535352
$176$	3.61803	0.272720
$177$	−12.2361	−0.919719
$178$	13.7082	1.02747
$179$	−15.6180	−1.16735	−0.583673	−	0.811989i	$-0.698385\pi$
$179$	−15.6180	−1.16735	−0.583673	+	0.811989i	$0.698385\pi$
$180$	−5.23607	−0.390273
$181$	11.3820	0.846015	0.423007	−	0.906126i	$-0.360974\pi$
$181$	11.3820	0.846015	0.423007	+	0.906126i	$0.360974\pi$
$182$	−0.381966	−0.0283132
$183$	−15.9787	−1.18118
$184$	−5.47214	−0.403411
$185$	2.00000	0.147043
$186$	14.1459	1.03723
$187$	−29.2705	−2.14047
$188$	3.00000	0.218797
$189$	0.854102	0.0621268
$190$	−17.5623	−1.27410
$191$	1.29180	0.0934711	0.0467355	−	0.998907i	$-0.485118\pi$
$191$	1.29180	0.0934711	0.0467355	+	0.998907i	$0.485118\pi$
$192$	2.23607	0.161374
$193$	23.3607	1.68154	0.840769	−	0.541394i	$-0.182103\pi$
$193$	23.3607	1.68154	0.840769	+	0.541394i	$0.182103\pi$
$194$	−9.70820	−0.697008
$195$	5.85410	0.419221
$196$	−6.85410	−0.489579
$197$	−6.79837	−0.484364	−0.242182	−	0.970231i	$-0.577863\pi$
$197$	−6.79837	−0.484364	−0.242182	+	0.970231i	$0.577863\pi$
$198$	−7.23607	−0.514245
$199$	3.18034	0.225448	0.112724	−	0.993626i	$-0.464042\pi$
$199$	3.18034	0.225448	0.112724	+	0.993626i	$0.464042\pi$
$200$	−1.85410	−0.131105
$201$	−33.7426	−2.38002
$202$	−17.8885	−1.25863
$203$	1.76393	0.123804
$204$	−18.0902	−1.26657
$205$	−27.4164	−1.91484
$206$	17.2361	1.20089
$207$	10.9443	0.760679
$208$	−1.00000	−0.0693375
$209$	−24.2705	−1.67883
$210$	−2.23607	−0.154303
$211$	3.41641	0.235195	0.117598	−	0.993061i	$-0.462481\pi$
$211$	3.41641	0.235195	0.117598	+	0.993061i	$0.462481\pi$
$212$	10.6180	0.729250
$213$	−15.0000	−1.02778
$214$	13.7984	0.943237
$215$	−5.85410	−0.399246
$216$	2.23607	0.152145
$217$	2.41641	0.164036
$218$	−2.85410	−0.193304
$219$	−17.2361	−1.16471
$220$	−9.47214	−0.638611
$221$	8.09017	0.544204
$222$	1.70820	0.114647
$223$	−23.4164	−1.56808	−0.784039	−	0.620711i	$-0.786844\pi$
$223$	−23.4164	−1.56808	−0.784039	+	0.620711i	$0.786844\pi$
$224$	0.381966	0.0255212
$225$	3.70820	0.247214
$226$	12.7639	0.849044
$227$	15.9443	1.05826	0.529129	−	0.848541i	$-0.322519\pi$
$227$	15.9443	1.05826	0.529129	+	0.848541i	$0.322519\pi$
$228$	−15.0000	−0.993399
$229$	−2.47214	−0.163363	−0.0816817	−	0.996658i	$-0.526029\pi$
$229$	−2.47214	−0.163363	−0.0816817	+	0.996658i	$0.526029\pi$
$230$	14.3262	0.944644
$231$	−3.09017	−0.203318
$232$	4.61803	0.303189
$233$	12.2361	0.801611	0.400806	−	0.916163i	$-0.368730\pi$
$233$	12.2361	0.801611	0.400806	+	0.916163i	$0.368730\pi$
$234$	2.00000	0.130744
$235$	−7.85410	−0.512345
$236$	−5.47214	−0.356206
$237$	18.4164	1.19627
$238$	−3.09017	−0.200306
$239$	23.6180	1.52772	0.763862	−	0.645380i	$-0.223301\pi$
$239$	23.6180	1.52772	0.763862	+	0.645380i	$0.223301\pi$
$240$	−5.85410	−0.377881
$241$	3.94427	0.254073	0.127036	−	0.991898i	$-0.459453\pi$
$241$	3.94427	0.254073	0.127036	+	0.991898i	$0.459453\pi$
$242$	−2.09017	−0.134361
$243$	−17.8885	−1.14755
$244$	−7.14590	−0.457469
$245$	17.9443	1.14642
$246$	−23.4164	−1.49298
$247$	6.70820	0.426833
$248$	6.32624	0.401717
$249$	10.2016	0.646502
$250$	−8.23607	−0.520895
$251$	18.2361	1.15105	0.575525	−	0.817784i	$-0.304798\pi$
$251$	18.2361	1.15105	0.575525	+	0.817784i	$0.304798\pi$
$252$	−0.763932	−0.0481232
$253$	19.7984	1.24471
$254$	−5.61803	−0.352507
$255$	47.3607	2.96584
$256$	1.00000	0.0625000
$257$	16.0902	1.00368	0.501839	−	0.864961i	$-0.332657\pi$
$257$	16.0902	1.00368	0.501839	+	0.864961i	$0.332657\pi$
$258$	−5.00000	−0.311286
$259$	0.291796	0.0181313
$260$	2.61803	0.162364
$261$	−9.23607	−0.571698
$262$	−10.7082	−0.661555
$263$	10.5279	0.649176	0.324588	−	0.945856i	$-0.394774\pi$
$263$	10.5279	0.649176	0.324588	+	0.945856i	$0.394774\pi$
$264$	−8.09017	−0.497916
$265$	−27.7984	−1.70764
$266$	−2.56231	−0.157105
$267$	−30.6525	−1.87590
$268$	−15.0902	−0.921779
$269$	−24.1246	−1.47090	−0.735452	−	0.677577i	$-0.763030\pi$
$269$	−24.1246	−1.47090	−0.735452	+	0.677577i	$0.763030\pi$
$270$	−5.85410	−0.356269
$271$	−24.8541	−1.50978	−0.754890	−	0.655852i	$-0.772310\pi$
$271$	−24.8541	−1.50978	−0.754890	+	0.655852i	$0.772310\pi$
$272$	−8.09017	−0.490539
$273$	0.854102	0.0516926
$274$	0.437694	0.0264421
$275$	6.70820	0.404520
$276$	12.2361	0.736525
$277$	8.70820	0.523225	0.261613	−	0.965173i	$-0.415746\pi$
$277$	8.70820	0.523225	0.261613	+	0.965173i	$0.415746\pi$
$278$	−3.32624	−0.199494
$279$	−12.6525	−0.757484
$280$	−1.00000	−0.0597614
$281$	22.1246	1.31984	0.659922	−	0.751334i	$-0.270589\pi$
$281$	22.1246	1.31984	0.659922	+	0.751334i	$0.270589\pi$
$282$	−6.70820	−0.399468
$283$	23.4164	1.39196	0.695980	−	0.718061i	$-0.254970\pi$
$283$	23.4164	1.39196	0.695980	+	0.718061i	$0.254970\pi$
$284$	−6.70820	−0.398059
$285$	39.2705	2.32618
$286$	3.61803	0.213939
$287$	−4.00000	−0.236113
$288$	−2.00000	−0.117851
$289$	48.4508	2.85005
$290$	−12.0902	−0.709959
$291$	21.7082	1.27256
$292$	−7.70820	−0.451089
$293$	2.81966	0.164726	0.0823632	−	0.996602i	$-0.473753\pi$
$293$	2.81966	0.164726	0.0823632	+	0.996602i	$0.473753\pi$
$294$	15.3262	0.893844
$295$	14.3262	0.834106
$296$	0.763932	0.0444026
$297$	−8.09017	−0.469439
$298$	−0.673762	−0.0390300
$299$	−5.47214	−0.316462
$300$	4.14590	0.239364
$301$	−0.854102	−0.0492296
$302$	−18.2361	−1.04937
$303$	40.0000	2.29794
$304$	−6.70820	−0.384742
$305$	18.7082	1.07123
$306$	16.1803	0.924968
$307$	−27.0344	−1.54294	−0.771469	−	0.636267i	$-0.780477\pi$
$307$	−27.0344	−1.54294	−0.771469	+	0.636267i	$0.780477\pi$
$308$	−1.38197	−0.0787448
$309$	−38.5410	−2.19252
$310$	−16.5623	−0.940676
$311$	20.1246	1.14116	0.570581	−	0.821241i	$-0.306718\pi$
$311$	20.1246	1.14116	0.570581	+	0.821241i	$0.306718\pi$
$312$	2.23607	0.126592
$313$	10.0000	0.565233	0.282617	−	0.959233i	$-0.408798\pi$
$313$	10.0000	0.565233	0.282617	+	0.959233i	$0.408798\pi$
$314$	−1.23607	−0.0697554
$315$	2.00000	0.112687
$316$	8.23607	0.463315
$317$	−18.5066	−1.03943	−0.519716	−	0.854339i	$-0.673962\pi$
$317$	−18.5066	−1.03943	−0.519716	+	0.854339i	$0.673962\pi$
$318$	−23.7426	−1.33142
$319$	−16.7082	−0.935480
$320$	−2.61803	−0.146353
$321$	−30.8541	−1.72211
$322$	2.09017	0.116481
$323$	54.2705	3.01969
$324$	−11.0000	−0.611111
$325$	−1.85410	−0.102847
$326$	23.0902	1.27885
$327$	6.38197	0.352924
$328$	−10.4721	−0.578227
$329$	−1.14590	−0.0631754
$330$	21.1803	1.16594
$331$	7.76393	0.426744	0.213372	−	0.976971i	$-0.431555\pi$
$331$	7.76393	0.426744	0.213372	+	0.976971i	$0.431555\pi$
$332$	4.56231	0.250389
$333$	−1.52786	−0.0837264
$334$	18.6180	1.01873
$335$	39.5066	2.15847
$336$	−0.854102	−0.0465951
$337$	12.0344	0.655558	0.327779	−	0.944754i	$-0.393700\pi$
$337$	12.0344	0.655558	0.327779	+	0.944754i	$0.393700\pi$
$338$	12.0000	0.652714
$339$	−28.5410	−1.55014
$340$	21.1803	1.14867
$341$	−22.8885	−1.23948
$342$	13.4164	0.725476
$343$	5.29180	0.285730
$344$	−2.23607	−0.120561
$345$	−32.0344	−1.72468
$346$	−11.6180	−0.624589
$347$	−34.1246	−1.83191	−0.915953	−	0.401287i	$-0.868563\pi$
$347$	−34.1246	−1.83191	−0.915953	+	0.401287i	$0.868563\pi$
$348$	−10.3262	−0.553544
$349$	−5.65248	−0.302570	−0.151285	−	0.988490i	$-0.548341\pi$
$349$	−5.65248	−0.302570	−0.151285	+	0.988490i	$0.548341\pi$
$350$	0.708204	0.0378551
$351$	2.23607	0.119352
$352$	−3.61803	−0.192842
$353$	−21.8541	−1.16318	−0.581588	−	0.813483i	$-0.697568\pi$
$353$	−21.8541	−1.16318	−0.581588	+	0.813483i	$0.697568\pi$
$354$	12.2361	0.650340
$355$	17.5623	0.932110
$356$	−13.7082	−0.726533
$357$	6.90983	0.365707
$358$	15.6180	0.825439
$359$	19.4721	1.02770	0.513850	−	0.857880i	$-0.328219\pi$
$359$	19.4721	1.02770	0.513850	+	0.857880i	$0.328219\pi$
$360$	5.23607	0.275965
$361$	26.0000	1.36842
$362$	−11.3820	−0.598223
$363$	4.67376	0.245309
$364$	0.381966	0.0200205
$365$	20.1803	1.05629
$366$	15.9787	0.835221
$367$	19.3262	1.00882	0.504411	−	0.863464i	$-0.331710\pi$
$367$	19.3262	1.00882	0.504411	+	0.863464i	$0.331710\pi$
$368$	5.47214	0.285255
$369$	20.9443	1.09032
$370$	−2.00000	−0.103975
$371$	−4.05573	−0.210563
$372$	−14.1459	−0.733431
$373$	19.3607	1.00246	0.501229	−	0.865315i	$-0.332881\pi$
$373$	19.3607	1.00246	0.501229	+	0.865315i	$0.332881\pi$
$374$	29.2705	1.51354
$375$	18.4164	0.951019
$376$	−3.00000	−0.154713
$377$	4.61803	0.237841
$378$	−0.854102	−0.0439303
$379$	17.0344	0.875001	0.437500	−	0.899218i	$-0.355864\pi$
$379$	17.0344	0.875001	0.437500	+	0.899218i	$0.355864\pi$
$380$	17.5623	0.900927
$381$	12.5623	0.643586
$382$	−1.29180	−0.0660940
$383$	−32.5623	−1.66386	−0.831928	−	0.554884i	$-0.812763\pi$
$383$	−32.5623	−1.66386	−0.831928	+	0.554884i	$0.812763\pi$
$384$	−2.23607	−0.114109
$385$	3.61803	0.184392
$386$	−23.3607	−1.18903
$387$	4.47214	0.227331
$388$	9.70820	0.492859
$389$	9.94427	0.504195	0.252097	−	0.967702i	$-0.418880\pi$
$389$	9.94427	0.504195	0.252097	+	0.967702i	$0.418880\pi$
$390$	−5.85410	−0.296434
$391$	−44.2705	−2.23886
$392$	6.85410	0.346184
$393$	23.9443	1.20783
$394$	6.79837	0.342497
$395$	−21.5623	−1.08492
$396$	7.23607	0.363626
$397$	−4.52786	−0.227247	−0.113623	−	0.993524i	$-0.536246\pi$
$397$	−4.52786	−0.227247	−0.113623	+	0.993524i	$0.536246\pi$
$398$	−3.18034	−0.159416
$399$	5.72949	0.286833
$400$	1.85410	0.0927051
$401$	5.58359	0.278831	0.139416	−	0.990234i	$-0.455478\pi$
$401$	5.58359	0.278831	0.139416	+	0.990234i	$0.455478\pi$
$402$	33.7426	1.68293
$403$	6.32624	0.315132
$404$	17.8885	0.889988
$405$	28.7984	1.43100
$406$	−1.76393	−0.0875425
$407$	−2.76393	−0.137003
$408$	18.0902	0.895597
$409$	−20.2361	−1.00061	−0.500305	−	0.865849i	$-0.666779\pi$
$409$	−20.2361	−1.00061	−0.500305	+	0.865849i	$0.666779\pi$
$410$	27.4164	1.35400
$411$	−0.978714	−0.0482764
$412$	−17.2361	−0.849160
$413$	2.09017	0.102851
$414$	−10.9443	−0.537882
$415$	−11.9443	−0.586321
$416$	1.00000	0.0490290
$417$	7.43769	0.364225
$418$	24.2705	1.18711
$419$	8.67376	0.423741	0.211871	−	0.977298i	$-0.432044\pi$
$419$	8.67376	0.423741	0.211871	+	0.977298i	$0.432044\pi$
$420$	2.23607	0.109109
$421$	−21.8541	−1.06510	−0.532552	−	0.846397i	$-0.678767\pi$
$421$	−21.8541	−1.06510	−0.532552	+	0.846397i	$0.678767\pi$
$422$	−3.41641	−0.166308
$423$	6.00000	0.291730
$424$	−10.6180	−0.515657
$425$	−15.0000	−0.727607
$426$	15.0000	0.726752
$427$	2.72949	0.132089
$428$	−13.7984	−0.666970
$429$	−8.09017	−0.390597
$430$	5.85410	0.282310
$431$	28.8328	1.38883	0.694414	−	0.719576i	$-0.255664\pi$
$431$	28.8328	1.38883	0.694414	+	0.719576i	$0.255664\pi$
$432$	−2.23607	−0.107583
$433$	−15.9098	−0.764578	−0.382289	−	0.924043i	$-0.624864\pi$
$433$	−15.9098	−0.764578	−0.382289	+	0.924043i	$0.624864\pi$
$434$	−2.41641	−0.115991
$435$	27.0344	1.29620
$436$	2.85410	0.136687
$437$	−36.7082	−1.75599
$438$	17.2361	0.823571
$439$	15.2148	0.726162	0.363081	−	0.931758i	$-0.381725\pi$
$439$	15.2148	0.726162	0.363081	+	0.931758i	$0.381725\pi$
$440$	9.47214	0.451566
$441$	−13.7082	−0.652772
$442$	−8.09017	−0.384810
$443$	−25.6525	−1.21879	−0.609393	−	0.792868i	$-0.708587\pi$
$443$	−25.6525	−1.21879	−0.609393	+	0.792868i	$0.708587\pi$
$444$	−1.70820	−0.0810678
$445$	35.8885	1.70128
$446$	23.4164	1.10880
$447$	1.50658	0.0712587
$448$	−0.381966	−0.0180462
$449$	−30.9098	−1.45873	−0.729363	−	0.684127i	$-0.760183\pi$
$449$	−30.9098	−1.45873	−0.729363	+	0.684127i	$0.760183\pi$
$450$	−3.70820	−0.174806
$451$	37.8885	1.78410
$452$	−12.7639	−0.600365
$453$	40.7771	1.91587
$454$	−15.9443	−0.748302
$455$	−1.00000	−0.0468807
$456$	15.0000	0.702439
$457$	11.4377	0.535033	0.267516	−	0.963553i	$-0.413797\pi$
$457$	11.4377	0.535033	0.267516	+	0.963553i	$0.413797\pi$
$458$	2.47214	0.115515
$459$	18.0902	0.844377
$460$	−14.3262	−0.667964
$461$	−31.9443	−1.48779	−0.743897	−	0.668295i	$-0.767024\pi$
$461$	−31.9443	−1.48779	−0.743897	+	0.668295i	$0.767024\pi$
$462$	3.09017	0.143768
$463$	−33.3607	−1.55040	−0.775201	−	0.631714i	$-0.782352\pi$
$463$	−33.3607	−1.55040	−0.775201	+	0.631714i	$0.782352\pi$
$464$	−4.61803	−0.214387
$465$	37.0344	1.71743
$466$	−12.2361	−0.566825
$467$	25.1246	1.16263	0.581314	−	0.813679i	$-0.302539\pi$
$467$	25.1246	1.16263	0.581314	+	0.813679i	$0.302539\pi$
$468$	−2.00000	−0.0924500
$469$	5.76393	0.266154
$470$	7.85410	0.362283
$471$	2.76393	0.127355
$472$	5.47214	0.251875
$473$	8.09017	0.371986
$474$	−18.4164	−0.845894
$475$	−12.4377	−0.570681
$476$	3.09017	0.141638
$477$	21.2361	0.972333
$478$	−23.6180	−1.08026
$479$	−23.2361	−1.06168	−0.530842	−	0.847471i	$-0.678124\pi$
$479$	−23.2361	−1.06168	−0.530842	+	0.847471i	$0.678124\pi$
$480$	5.85410	0.267202
$481$	0.763932	0.0348323
$482$	−3.94427	−0.179657
$483$	−4.67376	−0.212664
$484$	2.09017	0.0950077
$485$	−25.4164	−1.15410
$486$	17.8885	0.811441
$487$	23.8885	1.08249	0.541247	−	0.840864i	$-0.317953\pi$
$487$	23.8885	1.08249	0.541247	+	0.840864i	$0.317953\pi$
$488$	7.14590	0.323480
$489$	−51.6312	−2.33484
$490$	−17.9443	−0.810640
$491$	40.5967	1.83211	0.916053	−	0.401058i	$-0.131357\pi$
$491$	40.5967	1.83211	0.916053	+	0.401058i	$0.131357\pi$
$492$	23.4164	1.05569
$493$	37.3607	1.68264
$494$	−6.70820	−0.301816
$495$	−18.9443	−0.851482
$496$	−6.32624	−0.284056
$497$	2.56231	0.114935
$498$	−10.2016	−0.457146
$499$	−18.9443	−0.848062	−0.424031	−	0.905648i	$-0.639385\pi$
$499$	−18.9443	−0.848062	−0.424031	+	0.905648i	$0.639385\pi$
$500$	8.23607	0.368328
$501$	−41.6312	−1.85994
$502$	−18.2361	−0.813916
$503$	16.2361	0.723930	0.361965	−	0.932192i	$-0.382106\pi$
$503$	16.2361	0.723930	0.361965	+	0.932192i	$0.382106\pi$
$504$	0.763932	0.0340282
$505$	−46.8328	−2.08403
$506$	−19.7984	−0.880145
$507$	−26.8328	−1.19169
$508$	5.61803	0.249260
$509$	41.7082	1.84868	0.924342	−	0.381565i	$-0.124615\pi$
$509$	41.7082	1.84868	0.924342	+	0.381565i	$0.124615\pi$
$510$	−47.3607	−2.09717
$511$	2.94427	0.130247
$512$	−1.00000	−0.0441942
$513$	15.0000	0.662266
$514$	−16.0902	−0.709707
$515$	45.1246	1.98843
$516$	5.00000	0.220113
$517$	10.8541	0.477363
$518$	−0.291796	−0.0128208
$519$	25.9787	1.14034
$520$	−2.61803	−0.114808
$521$	−22.5279	−0.986964	−0.493482	−	0.869756i	$-0.664276\pi$
$521$	−22.5279	−0.986964	−0.493482	+	0.869756i	$0.664276\pi$
$522$	9.23607	0.404252
$523$	−37.4721	−1.63854	−0.819271	−	0.573406i	$-0.805622\pi$
$523$	−37.4721	−1.63854	−0.819271	+	0.573406i	$0.805622\pi$
$524$	10.7082	0.467790
$525$	−1.58359	−0.0691136
$526$	−10.5279	−0.459037
$527$	51.1803	2.22945
$528$	8.09017	0.352079
$529$	6.94427	0.301925
$530$	27.7984	1.20748
$531$	−10.9443	−0.474941
$532$	2.56231	0.111090
$533$	−10.4721	−0.453599
$534$	30.6525	1.32646
$535$	36.1246	1.56180
$536$	15.0902	0.651796
$537$	−34.9230	−1.50704
$538$	24.1246	1.04009
$539$	−24.7984	−1.06814
$540$	5.85410	0.251920
$541$	−15.5967	−0.670557	−0.335278	−	0.942119i	$-0.608830\pi$
$541$	−15.5967	−0.670557	−0.335278	+	0.942119i	$0.608830\pi$
$542$	24.8541	1.06758
$543$	25.4508	1.09220
$544$	8.09017	0.346863
$545$	−7.47214	−0.320071
$546$	−0.854102	−0.0365522
$547$	0.201626	0.00862091	0.00431046	−	0.999991i	$-0.498628\pi$
$547$	0.201626	0.00862091	0.00431046	+	0.999991i	$0.498628\pi$
$548$	−0.437694	−0.0186974
$549$	−14.2918	−0.609959
$550$	−6.70820	−0.286039
$551$	30.9787	1.31974
$552$	−12.2361	−0.520802
$553$	−3.14590	−0.133777
$554$	−8.70820	−0.369976
$555$	4.47214	0.189832
$556$	3.32624	0.141064
$557$	3.00000	0.127114	0.0635570	−	0.997978i	$-0.479756\pi$
$557$	3.00000	0.127114	0.0635570	+	0.997978i	$0.479756\pi$
$558$	12.6525	0.535622
$559$	−2.23607	−0.0945756
$560$	1.00000	0.0422577
$561$	−65.4508	−2.76334
$562$	−22.1246	−0.933270
$563$	16.2361	0.684269	0.342134	−	0.939651i	$-0.388850\pi$
$563$	16.2361	0.684269	0.342134	+	0.939651i	$0.388850\pi$
$564$	6.70820	0.282466
$565$	33.4164	1.40584
$566$	−23.4164	−0.984265
$567$	4.20163	0.176452
$568$	6.70820	0.281470
$569$	−41.1803	−1.72637	−0.863185	−	0.504888i	$-0.831534\pi$
$569$	−41.1803	−1.72637	−0.863185	+	0.504888i	$0.831534\pi$
$570$	−39.2705	−1.64486
$571$	−12.7639	−0.534154	−0.267077	−	0.963675i	$-0.586058\pi$
$571$	−12.7639	−0.534154	−0.267077	+	0.963675i	$0.586058\pi$
$572$	−3.61803	−0.151278
$573$	2.88854	0.120671
$574$	4.00000	0.166957
$575$	10.1459	0.423113
$576$	2.00000	0.0833333
$577$	20.7984	0.865848	0.432924	−	0.901431i	$-0.357482\pi$
$577$	20.7984	0.865848	0.432924	+	0.901431i	$0.357482\pi$
$578$	−48.4508	−2.01529
$579$	52.2361	2.17086
$580$	12.0902	0.502017
$581$	−1.74265	−0.0722971
$582$	−21.7082	−0.899834
$583$	38.4164	1.59105
$584$	7.70820	0.318968
$585$	5.23607	0.216485
$586$	−2.81966	−0.116479
$587$	−12.6525	−0.522224	−0.261112	−	0.965309i	$-0.584089\pi$
$587$	−12.6525	−0.522224	−0.261112	+	0.965309i	$0.584089\pi$
$588$	−15.3262	−0.632043
$589$	42.4377	1.74861
$590$	−14.3262	−0.589802
$591$	−15.2016	−0.625311
$592$	−0.763932	−0.0313974
$593$	−34.0902	−1.39992	−0.699958	−	0.714184i	$-0.746798\pi$
$593$	−34.0902	−1.39992	−0.699958	+	0.714184i	$0.746798\pi$
$594$	8.09017	0.331944
$595$	−8.09017	−0.331665
$596$	0.673762	0.0275984
$597$	7.11146	0.291053
$598$	5.47214	0.223772
$599$	−5.03444	−0.205702	−0.102851	−	0.994697i	$-0.532796\pi$
$599$	−5.03444	−0.205702	−0.102851	+	0.994697i	$0.532796\pi$
$600$	−4.14590	−0.169256
$601$	−14.8541	−0.605911	−0.302956	−	0.953005i	$-0.597973\pi$
$601$	−14.8541	−0.605911	−0.302956	+	0.953005i	$0.597973\pi$
$602$	0.854102	0.0348106
$603$	−30.1803	−1.22904
$604$	18.2361	0.742015
$605$	−5.47214	−0.222474
$606$	−40.0000	−1.62489
$607$	−14.5836	−0.591930	−0.295965	−	0.955199i	$-0.595641\pi$
$607$	−14.5836	−0.591930	−0.295965	+	0.955199i	$0.595641\pi$
$608$	6.70820	0.272054
$609$	3.94427	0.159830
$610$	−18.7082	−0.757473
$611$	−3.00000	−0.121367
$612$	−16.1803	−0.654051
$613$	−19.9787	−0.806933	−0.403466	−	0.914994i	$-0.632195\pi$
$613$	−19.9787	−0.806933	−0.403466	+	0.914994i	$0.632195\pi$
$614$	27.0344	1.09102
$615$	−61.3050	−2.47205
$616$	1.38197	0.0556810
$617$	−7.52786	−0.303060	−0.151530	−	0.988453i	$-0.548420\pi$
$617$	−7.52786	−0.303060	−0.151530	+	0.988453i	$0.548420\pi$
$618$	38.5410	1.55035
$619$	13.6738	0.549595	0.274797	−	0.961502i	$-0.411389\pi$
$619$	13.6738	0.549595	0.274797	+	0.961502i	$0.411389\pi$
$620$	16.5623	0.665158
$621$	−12.2361	−0.491016
$622$	−20.1246	−0.806923
$623$	5.23607	0.209779
$624$	−2.23607	−0.0895144
$625$	−30.8328	−1.23331
$626$	−10.0000	−0.399680
$627$	−54.2705	−2.16736
$628$	1.23607	0.0493245
$629$	6.18034	0.246426
$630$	−2.00000	−0.0796819
$631$	−7.47214	−0.297461	−0.148731	−	0.988878i	$-0.547519\pi$
$631$	−7.47214	−0.297461	−0.148731	+	0.988878i	$0.547519\pi$
$632$	−8.23607	−0.327613
$633$	7.63932	0.303636
$634$	18.5066	0.734990
$635$	−14.7082	−0.583677
$636$	23.7426	0.941457
$637$	6.85410	0.271569
$638$	16.7082	0.661484
$639$	−13.4164	−0.530745
$640$	2.61803	0.103487
$641$	3.52786	0.139342	0.0696711	−	0.997570i	$-0.477805\pi$
$641$	3.52786	0.139342	0.0696711	+	0.997570i	$0.477805\pi$
$642$	30.8541	1.21771
$643$	−4.96556	−0.195822	−0.0979112	−	0.995195i	$-0.531216\pi$
$643$	−4.96556	−0.195822	−0.0979112	+	0.995195i	$0.531216\pi$
$644$	−2.09017	−0.0823642
$645$	−13.0902	−0.515425
$646$	−54.2705	−2.13524
$647$	22.4164	0.881280	0.440640	−	0.897684i	$-0.354752\pi$
$647$	22.4164	0.881280	0.440640	+	0.897684i	$0.354752\pi$
$648$	11.0000	0.432121
$649$	−19.7984	−0.777154
$650$	1.85410	0.0727239
$651$	5.40325	0.211770
$652$	−23.0902	−0.904281
$653$	−3.47214	−0.135875	−0.0679376	−	0.997690i	$-0.521642\pi$
$653$	−3.47214	−0.135875	−0.0679376	+	0.997690i	$0.521642\pi$
$654$	−6.38197	−0.249555
$655$	−28.0344	−1.09540
$656$	10.4721	0.408868
$657$	−15.4164	−0.601451
$658$	1.14590	0.0446718
$659$	13.0000	0.506408	0.253204	−	0.967413i	$-0.418516\pi$
$659$	13.0000	0.506408	0.253204	+	0.967413i	$0.418516\pi$
$660$	−21.1803	−0.824444
$661$	−7.03444	−0.273608	−0.136804	−	0.990598i	$-0.543683\pi$
$661$	−7.03444	−0.273608	−0.136804	+	0.990598i	$0.543683\pi$
$662$	−7.76393	−0.301754
$663$	18.0902	0.702564
$664$	−4.56231	−0.177052
$665$	−6.70820	−0.260133
$666$	1.52786	0.0592035
$667$	−25.2705	−0.978478
$668$	−18.6180	−0.720353
$669$	−52.3607	−2.02438
$670$	−39.5066	−1.52627
$671$	−25.8541	−0.998087
$672$	0.854102	0.0329477
$673$	−0.639320	−0.0246440	−0.0123220	−	0.999924i	$-0.503922\pi$
$673$	−0.639320	−0.0246440	−0.0123220	+	0.999924i	$0.503922\pi$
$674$	−12.0344	−0.463549
$675$	−4.14590	−0.159576
$676$	−12.0000	−0.461538
$677$	−43.7426	−1.68117	−0.840583	−	0.541682i	$-0.817788\pi$
$677$	−43.7426	−1.68117	−0.840583	+	0.541682i	$0.817788\pi$
$678$	28.5410	1.09611
$679$	−3.70820	−0.142308
$680$	−21.1803	−0.812229
$681$	35.6525	1.36621
$682$	22.8885	0.876448
$683$	0	0		−	1.00000i	$-0.5\pi$
$683$	0	0			1.00000i	$0.5\pi$
$684$	−13.4164	−0.512989
$685$	1.14590	0.0437825
$686$	−5.29180	−0.202042
$687$	−5.52786	−0.210901
$688$	2.23607	0.0852493
$689$	−10.6180	−0.404515
$690$	32.0344	1.21953
$691$	28.7082	1.09211	0.546056	−	0.837749i	$-0.316129\pi$
$691$	28.7082	1.09211	0.546056	+	0.837749i	$0.316129\pi$
$692$	11.6180	0.441651
$693$	−2.76393	−0.104993
$694$	34.1246	1.29535
$695$	−8.70820	−0.330321
$696$	10.3262	0.391415
$697$	−84.7214	−3.20905
$698$	5.65248	0.213949
$699$	27.3607	1.03488
$700$	−0.708204	−0.0267676
$701$	47.2492	1.78458	0.892289	−	0.451464i	$-0.149098\pi$
$701$	47.2492	1.78458	0.892289	+	0.451464i	$0.149098\pi$
$702$	−2.23607	−0.0843949
$703$	5.12461	0.193278
$704$	3.61803	0.136360
$705$	−17.5623	−0.661435
$706$	21.8541	0.822490
$707$	−6.83282	−0.256974
$708$	−12.2361	−0.459860
$709$	21.1459	0.794151	0.397075	−	0.917786i	$-0.370025\pi$
$709$	21.1459	0.794151	0.397075	+	0.917786i	$0.370025\pi$
$710$	−17.5623	−0.659102
$711$	16.4721	0.617753
$712$	13.7082	0.513737
$713$	−34.6180	−1.29646
$714$	−6.90983	−0.258594
$715$	9.47214	0.354238
$716$	−15.6180	−0.583673
$717$	52.8115	1.97228
$718$	−19.4721	−0.726694
$719$	5.61803	0.209517	0.104759	−	0.994498i	$-0.466593\pi$
$719$	5.61803	0.209517	0.104759	+	0.994498i	$0.466593\pi$
$720$	−5.23607	−0.195137
$721$	6.58359	0.245186
$722$	−26.0000	−0.967620
$723$	8.81966	0.328007
$724$	11.3820	0.423007
$725$	−8.56231	−0.317996
$726$	−4.67376	−0.173460
$727$	−33.6525	−1.24810	−0.624051	−	0.781384i	$-0.714514\pi$
$727$	−33.6525	−1.24810	−0.624051	+	0.781384i	$0.714514\pi$
$728$	−0.381966	−0.0141566
$729$	−7.00000	−0.259259
$730$	−20.1803	−0.746908
$731$	−18.0902	−0.669089
$732$	−15.9787	−0.590590
$733$	−16.5279	−0.610471	−0.305235	−	0.952277i	$-0.598735\pi$
$733$	−16.5279	−0.610471	−0.305235	+	0.952277i	$0.598735\pi$
$734$	−19.3262	−0.713344
$735$	40.1246	1.48002
$736$	−5.47214	−0.201706
$737$	−54.5967	−2.01110
$738$	−20.9443	−0.770969
$739$	−6.70820	−0.246765	−0.123383	−	0.992359i	$-0.539374\pi$
$739$	−6.70820	−0.246765	−0.123383	+	0.992359i	$0.539374\pi$
$740$	2.00000	0.0735215
$741$	15.0000	0.551039
$742$	4.05573	0.148890
$743$	27.9787	1.02644	0.513220	−	0.858257i	$-0.328453\pi$
$743$	27.9787	1.02644	0.513220	+	0.858257i	$0.328453\pi$
$744$	14.1459	0.518614
$745$	−1.76393	−0.0646255
$746$	−19.3607	−0.708845
$747$	9.12461	0.333852
$748$	−29.2705	−1.07024
$749$	5.27051	0.192580
$750$	−18.4164	−0.672472
$751$	−1.00000	−0.0364905
$751$	−1.00000	−0.0364905
$752$	3.00000	0.109399
$753$	40.7771	1.48600
$754$	−4.61803	−0.168179
$755$	−47.7426	−1.73753
$756$	0.854102	0.0310634
$757$	37.8328	1.37506	0.687529	−	0.726157i	$-0.258696\pi$
$757$	37.8328	1.37506	0.687529	+	0.726157i	$0.258696\pi$
$758$	−17.0344	−0.618719
$759$	44.2705	1.60692
$760$	−17.5623	−0.637052
$761$	−6.25735	−0.226829	−0.113414	−	0.993548i	$-0.536179\pi$
$761$	−6.25735	−0.226829	−0.113414	+	0.993548i	$0.536179\pi$
$762$	−12.5623	−0.455084
$763$	−1.09017	−0.0394668
$764$	1.29180	0.0467355
$765$	42.3607	1.53155
$766$	32.5623	1.17652
$767$	5.47214	0.197587
$768$	2.23607	0.0806872
$769$	−49.8541	−1.79778	−0.898892	−	0.438169i	$-0.855627\pi$
$769$	−49.8541	−1.79778	−0.898892	+	0.438169i	$0.855627\pi$
$770$	−3.61803	−0.130385
$771$	35.9787	1.29574
$772$	23.3607	0.840769
$773$	15.1246	0.543994	0.271997	−	0.962298i	$-0.412316\pi$
$773$	15.1246	0.543994	0.271997	+	0.962298i	$0.412316\pi$
$774$	−4.47214	−0.160748
$775$	−11.7295	−0.421336
$776$	−9.70820	−0.348504
$777$	0.652476	0.0234074
$778$	−9.94427	−0.356519
$779$	−70.2492	−2.51694
$780$	5.85410	0.209610
$781$	−24.2705	−0.868467
$782$	44.2705	1.58311
$783$	10.3262	0.369030
$784$	−6.85410	−0.244789
$785$	−3.23607	−0.115500
$786$	−23.9443	−0.854064
$787$	5.03444	0.179458	0.0897292	−	0.995966i	$-0.471400\pi$
$787$	5.03444	0.179458	0.0897292	+	0.995966i	$0.471400\pi$
$788$	−6.79837	−0.242182
$789$	23.5410	0.838082
$790$	21.5623	0.767152
$791$	4.87539	0.173349
$792$	−7.23607	−0.257122
$793$	7.14590	0.253758
$794$	4.52786	0.160688
$795$	−62.1591	−2.20455
$796$	3.18034	0.112724
$797$	−11.5836	−0.410312	−0.205156	−	0.978729i	$-0.565770\pi$
$797$	−11.5836	−0.410312	−0.205156	+	0.978729i	$0.565770\pi$
$798$	−5.72949	−0.202822
$799$	−24.2705	−0.858629
$800$	−1.85410	−0.0655524
$801$	−27.4164	−0.968711
$802$	−5.58359	−0.197163
$803$	−27.8885	−0.984165
$804$	−33.7426	−1.19001
$805$	5.47214	0.192867
$806$	−6.32624	−0.222832
$807$	−53.9443	−1.89893
$808$	−17.8885	−0.629317
$809$	12.2574	0.430946	0.215473	−	0.976510i	$-0.430871\pi$
$809$	12.2574	0.430946	0.215473	+	0.976510i	$0.430871\pi$
$810$	−28.7984	−1.01187
$811$	−17.3607	−0.609616	−0.304808	−	0.952414i	$-0.598592\pi$
$811$	−17.3607	−0.609616	−0.304808	+	0.952414i	$0.598592\pi$
$812$	1.76393	0.0619019
$813$	−55.5755	−1.94912
$814$	2.76393	0.0968758
$815$	60.4508	2.11750
$816$	−18.0902	−0.633283
$817$	−15.0000	−0.524784
$818$	20.2361	0.707538
$819$	0.763932	0.0266939
$820$	−27.4164	−0.957422
$821$	−0.0557281	−0.00194492	−0.000972462	−	1.00000i	$-0.500310\pi$
$821$	−0.0557281	−0.00194492	−0.000972462		1.00000i	$0.500310\pi$
$822$	0.978714	0.0341366
$823$	13.4721	0.469609	0.234805	−	0.972043i	$-0.424555\pi$
$823$	13.4721	0.469609	0.234805	+	0.972043i	$0.424555\pi$
$824$	17.2361	0.600447
$825$	15.0000	0.522233
$826$	−2.09017	−0.0727263
$827$	15.1246	0.525934	0.262967	−	0.964805i	$-0.415299\pi$
$827$	15.1246	0.525934	0.262967	+	0.964805i	$0.415299\pi$
$828$	10.9443	0.380340
$829$	37.3050	1.29565	0.647827	−	0.761787i	$-0.275678\pi$
$829$	37.3050	1.29565	0.647827	+	0.761787i	$0.275678\pi$
$830$	11.9443	0.414592
$831$	19.4721	0.675481
$832$	−1.00000	−0.0346688
$833$	55.4508	1.92126
$834$	−7.43769	−0.257546
$835$	48.7426	1.68681
$836$	−24.2705	−0.839413
$837$	14.1459	0.488954
$838$	−8.67376	−0.299630
$839$	−25.1803	−0.869322	−0.434661	−	0.900594i	$-0.643132\pi$
$839$	−25.1803	−0.869322	−0.434661	+	0.900594i	$0.643132\pi$
$840$	−2.23607	−0.0771517
$841$	−7.67376	−0.264612
$842$	21.8541	0.753142
$843$	49.4721	1.70391
$844$	3.41641	0.117598
$845$	31.4164	1.08076
$846$	−6.00000	−0.206284
$847$	−0.798374	−0.0274325
$848$	10.6180	0.364625
$849$	52.3607	1.79701
$850$	15.0000	0.514496
$851$	−4.18034	−0.143300
$852$	−15.0000	−0.513892
$853$	−37.2361	−1.27494	−0.637469	−	0.770476i	$-0.720019\pi$
$853$	−37.2361	−1.27494	−0.637469	+	0.770476i	$0.720019\pi$
$854$	−2.72949	−0.0934012
$855$	35.1246	1.20124
$856$	13.7984	0.471619
$857$	−55.7426	−1.90413	−0.952066	−	0.305892i	$-0.901045\pi$
$857$	−55.7426	−1.90413	−0.952066	+	0.305892i	$0.901045\pi$
$858$	8.09017	0.276194
$859$	37.7984	1.28966	0.644832	−	0.764324i	$-0.276927\pi$
$859$	37.7984	1.28966	0.644832	+	0.764324i	$0.276927\pi$
$860$	−5.85410	−0.199623
$861$	−8.94427	−0.304820
$862$	−28.8328	−0.982050
$863$	−41.0132	−1.39610	−0.698052	−	0.716047i	$-0.745950\pi$
$863$	−41.0132	−1.39610	−0.698052	+	0.716047i	$0.745950\pi$
$864$	2.23607	0.0760726
$865$	−30.4164	−1.03419
$866$	15.9098	0.540638
$867$	108.339	3.67940
$868$	2.41641	0.0820182
$869$	29.7984	1.01084
$870$	−27.0344	−0.916553
$871$	15.0902	0.511311
$872$	−2.85410	−0.0966521
$873$	19.4164	0.657146
$874$	36.7082	1.24167
$875$	−3.14590	−0.106351
$876$	−17.2361	−0.582353
$877$	−26.6869	−0.901153	−0.450577	−	0.892738i	$-0.648782\pi$
$877$	−26.6869	−0.901153	−0.450577	+	0.892738i	$0.648782\pi$
$878$	−15.2148	−0.513474
$879$	6.30495	0.212661
$880$	−9.47214	−0.319306
$881$	4.88854	0.164699	0.0823496	−	0.996604i	$-0.473758\pi$
$881$	4.88854	0.164699	0.0823496	+	0.996604i	$0.473758\pi$
$882$	13.7082	0.461579
$883$	−24.7639	−0.833373	−0.416686	−	0.909050i	$-0.636809\pi$
$883$	−24.7639	−0.833373	−0.416686	+	0.909050i	$0.636809\pi$
$884$	8.09017	0.272102
$885$	32.0344	1.07683
$886$	25.6525	0.861812
$887$	−16.7984	−0.564034	−0.282017	−	0.959409i	$-0.591003\pi$
$887$	−16.7984	−0.564034	−0.282017	+	0.959409i	$0.591003\pi$
$888$	1.70820	0.0573236
$889$	−2.14590	−0.0719711
$890$	−35.8885	−1.20299
$891$	−39.7984	−1.33330
$892$	−23.4164	−0.784039
$893$	−20.1246	−0.673444
$894$	−1.50658	−0.0503875
$895$	40.8885	1.36675
$896$	0.381966	0.0127606
$897$	−12.2361	−0.408550
$898$	30.9098	1.03147
$899$	29.2148	0.974368
$900$	3.70820	0.123607
$901$	−85.9017	−2.86180
$902$	−37.8885	−1.26155
$903$	−1.90983	−0.0635552
$904$	12.7639	0.424522
$905$	−29.7984	−0.990531
$906$	−40.7771	−1.35473
$907$	39.1803	1.30096	0.650481	−	0.759523i	$-0.274567\pi$
$907$	39.1803	1.30096	0.650481	+	0.759523i	$0.274567\pi$
$908$	15.9443	0.529129
$909$	35.7771	1.18665
$910$	1.00000	0.0331497
$911$	−16.9656	−0.562094	−0.281047	−	0.959694i	$-0.590682\pi$
$911$	−16.9656	−0.562094	−0.281047	+	0.959694i	$0.590682\pi$
$912$	−15.0000	−0.496700
$913$	16.5066	0.546288
$914$	−11.4377	−0.378325
$915$	41.8328	1.38295
$916$	−2.47214	−0.0816817
$917$	−4.09017	−0.135069
$918$	−18.0902	−0.597065
$919$	−29.1033	−0.960030	−0.480015	−	0.877260i	$-0.659369\pi$
$919$	−29.1033	−0.960030	−0.480015	+	0.877260i	$0.659369\pi$
$920$	14.3262	0.472322
$921$	−60.4508	−1.99192
$922$	31.9443	1.05203
$923$	6.70820	0.220803
$924$	−3.09017	−0.101659
$925$	−1.41641	−0.0465712
$926$	33.3607	1.09630
$927$	−34.4721	−1.13221
$928$	4.61803	0.151594
$929$	−1.23607	−0.0405541	−0.0202770	−	0.999794i	$-0.506455\pi$
$929$	−1.23607	−0.0405541	−0.0202770	+	0.999794i	$0.506455\pi$
$930$	−37.0344	−1.21441
$931$	45.9787	1.50689
$932$	12.2361	0.400806
$933$	45.0000	1.47323
$934$	−25.1246	−0.822102
$935$	76.6312	2.50611
$936$	2.00000	0.0653720
$937$	5.58359	0.182408	0.0912040	−	0.995832i	$-0.470928\pi$
$937$	5.58359	0.182408	0.0912040	+	0.995832i	$0.470928\pi$
$938$	−5.76393	−0.188199
$939$	22.3607	0.729713
$940$	−7.85410	−0.256173
$941$	−41.8885	−1.36553	−0.682764	−	0.730639i	$-0.739222\pi$
$941$	−41.8885	−1.36553	−0.682764	+	0.730639i	$0.739222\pi$
$942$	−2.76393	−0.0900538
$943$	57.3050	1.86611
$944$	−5.47214	−0.178103
$945$	−2.23607	−0.0727393
$946$	−8.09017	−0.263034
$947$	−21.9230	−0.712401	−0.356201	−	0.934409i	$-0.615928\pi$
$947$	−21.9230	−0.712401	−0.356201	+	0.934409i	$0.615928\pi$
$948$	18.4164	0.598137
$949$	7.70820	0.250219
$950$	12.4377	0.403532
$951$	−41.3820	−1.34190
$952$	−3.09017	−0.100153
$953$	−4.41641	−0.143061	−0.0715307	−	0.997438i	$-0.522788\pi$
$953$	−4.41641	−0.143061	−0.0715307	+	0.997438i	$0.522788\pi$
$954$	−21.2361	−0.687543
$955$	−3.38197	−0.109438
$956$	23.6180	0.763862
$957$	−37.3607	−1.20770
$958$	23.2361	0.750723
$959$	0.167184	0.00539866
$960$	−5.85410	−0.188940
$961$	9.02129	0.291009
$962$	−0.763932	−0.0246302
$963$	−27.5967	−0.889293
$964$	3.94427	0.127036
$965$	−61.1591	−1.96878
$966$	4.67376	0.150376
$967$	31.8885	1.02547	0.512733	−	0.858548i	$-0.328633\pi$
$967$	31.8885	1.02547	0.512733	+	0.858548i	$0.328633\pi$
$968$	−2.09017	−0.0671806
$969$	121.353	3.89841
$970$	25.4164	0.816072
$971$	−7.70820	−0.247368	−0.123684	−	0.992322i	$-0.539471\pi$
$971$	−7.70820	−0.247368	−0.123684	+	0.992322i	$0.539471\pi$
$972$	−17.8885	−0.573775
$973$	−1.27051	−0.0407307
$974$	−23.8885	−0.765438
$975$	−4.14590	−0.132775
$976$	−7.14590	−0.228735
$977$	−38.0132	−1.21615	−0.608074	−	0.793880i	$-0.708058\pi$
$977$	−38.0132	−1.21615	−0.608074	+	0.793880i	$0.708058\pi$
$978$	51.6312	1.65098
$979$	−49.5967	−1.58512
$980$	17.9443	0.573209
$981$	5.70820	0.182249
$982$	−40.5967	−1.29549
$983$	−20.3820	−0.650084	−0.325042	−	0.945700i	$-0.605378\pi$
$983$	−20.3820	−0.650084	−0.325042	+	0.945700i	$0.605378\pi$
$984$	−23.4164	−0.746488
$985$	17.7984	0.567103
$986$	−37.3607	−1.18981
$987$	−2.56231	−0.0815591
$988$	6.70820	0.213416
$989$	12.2361	0.389084
$990$	18.9443	0.602088
$991$	33.2492	1.05620	0.528098	−	0.849183i	$-0.322905\pi$
$991$	33.2492	1.05620	0.528098	+	0.849183i	$0.322905\pi$
$992$	6.32624	0.200858
$993$	17.3607	0.550925
$994$	−2.56231	−0.0812714
$995$	−8.32624	−0.263959
$996$	10.2016	0.323251
$997$	−50.8673	−1.61098	−0.805491	−	0.592608i	$-0.798098\pi$
$997$	−50.8673	−1.61098	−0.805491	+	0.592608i	$0.798098\pi$
$998$	18.9443	0.599670
$999$	1.70820	0.0540452

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1502.2.a.c.1.2	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1502.2.a.c.1.2	✓	2	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1502 = 2 \cdot 751 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1502.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +2.23607 q^{3} +1.00000 q^{4} -2.61803 q^{5} -2.23607 q^{6} -0.381966 q^{7} -1.00000 q^{8} +2.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +2.23607 q^{3} +1.00000 q^{4} -2.61803 q^{5} -2.23607 q^{6} -0.381966 q^{7} -1.00000 q^{8} +2.00000 q^{9} +2.61803 q^{10} +3.61803 q^{11} +2.23607 q^{12} -1.00000 q^{13} +0.381966 q^{14} -5.85410 q^{15} +1.00000 q^{16} -8.09017 q^{17} -2.00000 q^{18} -6.70820 q^{19} -2.61803 q^{20} -0.854102 q^{21} -3.61803 q^{22} +5.47214 q^{23} -2.23607 q^{24} +1.85410 q^{25} +1.00000 q^{26} -2.23607 q^{27} -0.381966 q^{28} -4.61803 q^{29} +5.85410 q^{30} -6.32624 q^{31} -1.00000 q^{32} +8.09017 q^{33} +8.09017 q^{34} +1.00000 q^{35} +2.00000 q^{36} -0.763932 q^{37} +6.70820 q^{38} -2.23607 q^{39} +2.61803 q^{40} +10.4721 q^{41} +0.854102 q^{42} +2.23607 q^{43} +3.61803 q^{44} -5.23607 q^{45} -5.47214 q^{46} +3.00000 q^{47} +2.23607 q^{48} -6.85410 q^{49} -1.85410 q^{50} -18.0902 q^{51} -1.00000 q^{52} +10.6180 q^{53} +2.23607 q^{54} -9.47214 q^{55} +0.381966 q^{56} -15.0000 q^{57} +4.61803 q^{58} -5.47214 q^{59} -5.85410 q^{60} -7.14590 q^{61} +6.32624 q^{62} -0.763932 q^{63} +1.00000 q^{64} +2.61803 q^{65} -8.09017 q^{66} -15.0902 q^{67} -8.09017 q^{68} +12.2361 q^{69} -1.00000 q^{70} -6.70820 q^{71} -2.00000 q^{72} -7.70820 q^{73} +0.763932 q^{74} +4.14590 q^{75} -6.70820 q^{76} -1.38197 q^{77} +2.23607 q^{78} +8.23607 q^{79} -2.61803 q^{80} -11.0000 q^{81} -10.4721 q^{82} +4.56231 q^{83} -0.854102 q^{84} +21.1803 q^{85} -2.23607 q^{86} -10.3262 q^{87} -3.61803 q^{88} -13.7082 q^{89} +5.23607 q^{90} +0.381966 q^{91} +5.47214 q^{92} -14.1459 q^{93} -3.00000 q^{94} +17.5623 q^{95} -2.23607 q^{96} +9.70820 q^{97} +6.85410 q^{98} +7.23607 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + 2 q^{4} - 3 q^{5} - 3 q^{7} - 2 q^{8} + 4 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 + 2 * q^4 - 3 * q^5 - 3 * q^7 - 2 * q^8 + 4 * q^9	\( 2 q - 2 q^{2} + 2 q^{4} - 3 q^{5} - 3 q^{7} - 2 q^{8} + 4 q^{9} + 3 q^{10} + 5 q^{11} - 2 q^{13} + 3 q^{14} - 5 q^{15} + 2 q^{16} - 5 q^{17} - 4 q^{18} - 3 q^{20} + 5 q^{21} - 5 q^{22} + 2 q^{23} - 3 q^{25} + 2 q^{26} - 3 q^{28} - 7 q^{29} + 5 q^{30} + 3 q^{31} - 2 q^{32} + 5 q^{33} + 5 q^{34} + 2 q^{35} + 4 q^{36} - 6 q^{37} + 3 q^{40} + 12 q^{41} - 5 q^{42} + 5 q^{44} - 6 q^{45} - 2 q^{46} + 6 q^{47} - 7 q^{49} + 3 q^{50} - 25 q^{51} - 2 q^{52} + 19 q^{53} - 10 q^{55} + 3 q^{56} - 30 q^{57} + 7 q^{58} - 2 q^{59} - 5 q^{60} - 21 q^{61} - 3 q^{62} - 6 q^{63} + 2 q^{64} + 3 q^{65} - 5 q^{66} - 19 q^{67} - 5 q^{68} + 20 q^{69} - 2 q^{70} - 4 q^{72} - 2 q^{73} + 6 q^{74} + 15 q^{75} - 5 q^{77} + 12 q^{79} - 3 q^{80} - 22 q^{81} - 12 q^{82} - 11 q^{83} + 5 q^{84} + 20 q^{85} - 5 q^{87} - 5 q^{88} - 14 q^{89} + 6 q^{90} + 3 q^{91} + 2 q^{92} - 35 q^{93} - 6 q^{94} + 15 q^{95} + 6 q^{97} + 7 q^{98} + 10 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 + 2 * q^4 - 3 * q^5 - 3 * q^7 - 2 * q^8 + 4 * q^9 + 3 * q^10 + 5 * q^11 - 2 * q^13 + 3 * q^14 - 5 * q^15 + 2 * q^16 - 5 * q^17 - 4 * q^18 - 3 * q^20 + 5 * q^21 - 5 * q^22 + 2 * q^23 - 3 * q^25 + 2 * q^26 - 3 * q^28 - 7 * q^29 + 5 * q^30 + 3 * q^31 - 2 * q^32 + 5 * q^33 + 5 * q^34 + 2 * q^35 + 4 * q^36 - 6 * q^37 + 3 * q^40 + 12 * q^41 - 5 * q^42 + 5 * q^44 - 6 * q^45 - 2 * q^46 + 6 * q^47 - 7 * q^49 + 3 * q^50 - 25 * q^51 - 2 * q^52 + 19 * q^53 - 10 * q^55 + 3 * q^56 - 30 * q^57 + 7 * q^58 - 2 * q^59 - 5 * q^60 - 21 * q^61 - 3 * q^62 - 6 * q^63 + 2 * q^64 + 3 * q^65 - 5 * q^66 - 19 * q^67 - 5 * q^68 + 20 * q^69 - 2 * q^70 - 4 * q^72 - 2 * q^73 + 6 * q^74 + 15 * q^75 - 5 * q^77 + 12 * q^79 - 3 * q^80 - 22 * q^81 - 12 * q^82 - 11 * q^83 + 5 * q^84 + 20 * q^85 - 5 * q^87 - 5 * q^88 - 14 * q^89 + 6 * q^90 + 3 * q^91 + 2 * q^92 - 35 * q^93 - 6 * q^94 + 15 * q^95 + 6 * q^97 + 7 * q^98 + 10 * q^99

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