LMFDB - Embedded newform 1502.2.a.h.1.10

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:	$0$
Dimension:	$19$
Coefficient field:	$\mathbb{Q}[x]/(x^{19} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{19} - 6 x^{18} - 23 x^{17} + 190 x^{16} + 128 x^{15} - 2394 x^{14} + 749 x^{13} + 15539 x^{12} + \cdots + 4222 $ x^19 - 6x^18 - 23x^17 + 190x^16 + 128x^15 - 2394x^14 + 749x^13 + 15539x^12 - 11338x^11 - 56744x^10 + 50183x^9 + 120237x^8 - 102992x^7 - 148539x^6 + 99519x^5 + 104388x^4 - 41081x^3 - 35733x^2 + 5542x + 4222
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			1.10
Root			$0.493679$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +0.493679 q^{3} +1.00000 q^{4} +0.378923 q^{5} -0.493679 q^{6} +2.20566 q^{7} -1.00000 q^{8} -2.75628 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +0.493679 q^{3} +1.00000 q^{4} +0.378923 q^{5} -0.493679 q^{6} +2.20566 q^{7} -1.00000 q^{8} -2.75628 q^{9} -0.378923 q^{10} +4.52894 q^{11} +0.493679 q^{12} +1.19798 q^{13} -2.20566 q^{14} +0.187066 q^{15} +1.00000 q^{16} -3.33706 q^{17} +2.75628 q^{18} +4.40722 q^{19} +0.378923 q^{20} +1.08889 q^{21} -4.52894 q^{22} +3.28385 q^{23} -0.493679 q^{24} -4.85642 q^{25} -1.19798 q^{26} -2.84176 q^{27} +2.20566 q^{28} +0.343188 q^{29} -0.187066 q^{30} +8.98560 q^{31} -1.00000 q^{32} +2.23584 q^{33} +3.33706 q^{34} +0.835774 q^{35} -2.75628 q^{36} +5.07170 q^{37} -4.40722 q^{38} +0.591416 q^{39} -0.378923 q^{40} -12.1718 q^{41} -1.08889 q^{42} -0.516108 q^{43} +4.52894 q^{44} -1.04442 q^{45} -3.28385 q^{46} +11.7717 q^{47} +0.493679 q^{48} -2.13508 q^{49} +4.85642 q^{50} -1.64744 q^{51} +1.19798 q^{52} +4.84972 q^{53} +2.84176 q^{54} +1.71612 q^{55} -2.20566 q^{56} +2.17575 q^{57} -0.343188 q^{58} -1.09334 q^{59} +0.187066 q^{60} +6.20793 q^{61} -8.98560 q^{62} -6.07941 q^{63} +1.00000 q^{64} +0.453941 q^{65} -2.23584 q^{66} +8.54831 q^{67} -3.33706 q^{68} +1.62117 q^{69} -0.835774 q^{70} -4.35011 q^{71} +2.75628 q^{72} -5.26126 q^{73} -5.07170 q^{74} -2.39751 q^{75} +4.40722 q^{76} +9.98930 q^{77} -0.591416 q^{78} -0.376445 q^{79} +0.378923 q^{80} +6.86593 q^{81} +12.1718 q^{82} -4.33862 q^{83} +1.08889 q^{84} -1.26449 q^{85} +0.516108 q^{86} +0.169425 q^{87} -4.52894 q^{88} +1.33389 q^{89} +1.04442 q^{90} +2.64233 q^{91} +3.28385 q^{92} +4.43600 q^{93} -11.7717 q^{94} +1.67000 q^{95} -0.493679 q^{96} -1.08771 q^{97} +2.13508 q^{98} -12.4830 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 19 q - 19 q^{2} + 6 q^{3} + 19 q^{4} + 2 q^{5} - 6 q^{6} + 13 q^{7} - 19 q^{8} + 25 q^{9}+O(q^{10}) $ 19 * q - 19 * q^2 + 6 * q^3 + 19 * q^4 + 2 * q^5 - 6 * q^6 + 13 * q^7 - 19 * q^8 + 25 * q^9	\( 19 q - 19 q^{2} + 6 q^{3} + 19 q^{4} + 2 q^{5} - 6 q^{6} + 13 q^{7} - 19 q^{8} + 25 q^{9} - 2 q^{10} - 7 q^{11} + 6 q^{12} + 19 q^{13} - 13 q^{14} + 6 q^{15} + 19 q^{16} + 11 q^{17} - 25 q^{18} + 7 q^{19} + 2 q^{20} + 7 q^{21} + 7 q^{22} + 12 q^{23} - 6 q^{24} + 37 q^{25} - 19 q^{26} + 24 q^{27} + 13 q^{28} - 8 q^{29} - 6 q^{30} + 32 q^{31} - 19 q^{32} + 24 q^{33} - 11 q^{34} - 19 q^{35} + 25 q^{36} + 41 q^{37} - 7 q^{38} - 2 q^{39} - 2 q^{40} + 15 q^{41} - 7 q^{42} + 15 q^{43} - 7 q^{44} + 28 q^{45} - 12 q^{46} - 6 q^{47} + 6 q^{48} + 42 q^{49} - 37 q^{50} + 8 q^{51} + 19 q^{52} + 6 q^{53} - 24 q^{54} + 22 q^{55} - 13 q^{56} + 24 q^{57} + 8 q^{58} - 4 q^{59} + 6 q^{60} + 13 q^{61} - 32 q^{62} + 37 q^{63} + 19 q^{64} + 20 q^{65} - 24 q^{66} + 47 q^{67} + 11 q^{68} + 15 q^{69} + 19 q^{70} - 25 q^{72} + 64 q^{73} - 41 q^{74} - 3 q^{75} + 7 q^{76} - 4 q^{77} + 2 q^{78} + 34 q^{79} + 2 q^{80} + 27 q^{81} - 15 q^{82} + 4 q^{83} + 7 q^{84} + 21 q^{85} - 15 q^{86} + 7 q^{88} + 18 q^{89} - 28 q^{90} + 28 q^{91} + 12 q^{92} + 43 q^{93} + 6 q^{94} - 8 q^{95} - 6 q^{96} + 82 q^{97} - 42 q^{98} - 2 q^{99}+O(q^{100}) \) 19 * q - 19 * q^2 + 6 * q^3 + 19 * q^4 + 2 * q^5 - 6 * q^6 + 13 * q^7 - 19 * q^8 + 25 * q^9 - 2 * q^10 - 7 * q^11 + 6 * q^12 + 19 * q^13 - 13 * q^14 + 6 * q^15 + 19 * q^16 + 11 * q^17 - 25 * q^18 + 7 * q^19 + 2 * q^20 + 7 * q^21 + 7 * q^22 + 12 * q^23 - 6 * q^24 + 37 * q^25 - 19 * q^26 + 24 * q^27 + 13 * q^28 - 8 * q^29 - 6 * q^30 + 32 * q^31 - 19 * q^32 + 24 * q^33 - 11 * q^34 - 19 * q^35 + 25 * q^36 + 41 * q^37 - 7 * q^38 - 2 * q^39 - 2 * q^40 + 15 * q^41 - 7 * q^42 + 15 * q^43 - 7 * q^44 + 28 * q^45 - 12 * q^46 - 6 * q^47 + 6 * q^48 + 42 * q^49 - 37 * q^50 + 8 * q^51 + 19 * q^52 + 6 * q^53 - 24 * q^54 + 22 * q^55 - 13 * q^56 + 24 * q^57 + 8 * q^58 - 4 * q^59 + 6 * q^60 + 13 * q^61 - 32 * q^62 + 37 * q^63 + 19 * q^64 + 20 * q^65 - 24 * q^66 + 47 * q^67 + 11 * q^68 + 15 * q^69 + 19 * q^70 - 25 * q^72 + 64 * q^73 - 41 * q^74 - 3 * q^75 + 7 * q^76 - 4 * q^77 + 2 * q^78 + 34 * q^79 + 2 * q^80 + 27 * q^81 - 15 * q^82 + 4 * q^83 + 7 * q^84 + 21 * q^85 - 15 * q^86 + 7 * q^88 + 18 * q^89 - 28 * q^90 + 28 * q^91 + 12 * q^92 + 43 * q^93 + 6 * q^94 - 8 * q^95 - 6 * q^96 + 82 * q^97 - 42 * q^98 - 2 * 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
$3$	0.493679	0.285026	0.142513	−	0.989793i	$-0.454482\pi$
$3$	0.493679	0.285026	0.142513	+	0.989793i	$0.454482\pi$
$4$	1.00000	0.500000
$5$	0.378923	0.169459	0.0847297	−	0.996404i	$-0.472997\pi$
$5$	0.378923	0.169459	0.0847297	+	0.996404i	$0.472997\pi$
$6$	−0.493679	−0.201544
$7$	2.20566	0.833660	0.416830	−	0.908984i	$-0.363141\pi$
$7$	2.20566	0.833660	0.416830	+	0.908984i	$0.363141\pi$
$8$	−1.00000	−0.353553
$9$	−2.75628	−0.918760
$10$	−0.378923	−0.119826
$11$	4.52894	1.36553	0.682764	−	0.730639i	$-0.260778\pi$
$11$	4.52894	1.36553	0.682764	+	0.730639i	$0.260778\pi$
$12$	0.493679	0.142513
$13$	1.19798	0.332259	0.166130	−	0.986104i	$-0.446873\pi$
$13$	1.19798	0.332259	0.166130	+	0.986104i	$0.446873\pi$
$14$	−2.20566	−0.589487
$15$	0.187066	0.0483003
$16$	1.00000	0.250000
$17$	−3.33706	−0.809355	−0.404678	−	0.914459i	$-0.632616\pi$
$17$	−3.33706	−0.809355	−0.404678	+	0.914459i	$0.632616\pi$
$18$	2.75628	0.649662
$19$	4.40722	1.01109	0.505543	−	0.862802i	$-0.331292\pi$
$19$	4.40722	1.01109	0.505543	+	0.862802i	$0.331292\pi$
$20$	0.378923	0.0847297
$21$	1.08889	0.237615
$22$	−4.52894	−0.965574
$23$	3.28385	0.684730	0.342365	−	0.939567i	$-0.388772\pi$
$23$	3.28385	0.684730	0.342365	+	0.939567i	$0.388772\pi$
$24$	−0.493679	−0.100772
$25$	−4.85642	−0.971283
$26$	−1.19798	−0.234943
$27$	−2.84176	−0.546896
$28$	2.20566	0.416830
$29$	0.343188	0.0637285	0.0318642	−	0.999492i	$-0.489856\pi$
$29$	0.343188	0.0637285	0.0318642	+	0.999492i	$0.489856\pi$
$30$	−0.187066	−0.0341535
$31$	8.98560	1.61386	0.806930	−	0.590647i	$-0.201127\pi$
$31$	8.98560	1.61386	0.806930	+	0.590647i	$0.201127\pi$
$32$	−1.00000	−0.176777
$33$	2.23584	0.389211
$34$	3.33706	0.572301
$35$	0.835774	0.141272
$36$	−2.75628	−0.459380
$37$	5.07170	0.833782	0.416891	−	0.908956i	$-0.363120\pi$
$37$	5.07170	0.833782	0.416891	+	0.908956i	$0.363120\pi$
$38$	−4.40722	−0.714945
$39$	0.591416	0.0947024
$40$	−0.378923	−0.0599130
$41$	−12.1718	−1.90092	−0.950458	−	0.310854i	$-0.899385\pi$
$41$	−12.1718	−1.90092	−0.950458	+	0.310854i	$0.899385\pi$
$42$	−1.08889	−0.168019
$43$	−0.516108	−0.0787057	−0.0393529	−	0.999225i	$-0.512530\pi$
$43$	−0.516108	−0.0787057	−0.0393529	+	0.999225i	$0.512530\pi$
$44$	4.52894	0.682764
$45$	−1.04442	−0.155693
$46$	−3.28385	−0.484177
$47$	11.7717	1.71708	0.858538	−	0.512749i	$-0.171373\pi$
$47$	11.7717	1.71708	0.858538	+	0.512749i	$0.171373\pi$
$48$	0.493679	0.0712564
$49$	−2.13508	−0.305011
$50$	4.85642	0.686801
$51$	−1.64744	−0.230687
$52$	1.19798	0.166130
$53$	4.84972	0.666160	0.333080	−	0.942899i	$-0.391912\pi$
$53$	4.84972	0.666160	0.333080	+	0.942899i	$0.391912\pi$
$54$	2.84176	0.386714
$55$	1.71612	0.231402
$56$	−2.20566	−0.294743
$57$	2.17575	0.288185
$58$	−0.343188	−0.0450628
$59$	−1.09334	−0.142341	−0.0711704	−	0.997464i	$-0.522673\pi$
$59$	−1.09334	−0.142341	−0.0711704	+	0.997464i	$0.522673\pi$
$60$	0.187066	0.0241502
$61$	6.20793	0.794844	0.397422	−	0.917636i	$-0.369905\pi$
$61$	6.20793	0.794844	0.397422	+	0.917636i	$0.369905\pi$
$62$	−8.98560	−1.14117
$63$	−6.07941	−0.765934
$64$	1.00000	0.125000
$65$	0.453941	0.0563045
$66$	−2.23584	−0.275213
$67$	8.54831	1.04434	0.522171	−	0.852841i	$-0.325122\pi$
$67$	8.54831	1.04434	0.522171	+	0.852841i	$0.325122\pi$
$68$	−3.33706	−0.404678
$69$	1.62117	0.195166
$70$	−0.835774	−0.0998941
$71$	−4.35011	−0.516263	−0.258131	−	0.966110i	$-0.583107\pi$
$71$	−4.35011	−0.516263	−0.258131	+	0.966110i	$0.583107\pi$
$72$	2.75628	0.324831
$73$	−5.26126	−0.615784	−0.307892	−	0.951421i	$-0.599624\pi$
$73$	−5.26126	−0.615784	−0.307892	+	0.951421i	$0.599624\pi$
$74$	−5.07170	−0.589573
$75$	−2.39751	−0.276841
$76$	4.40722	0.505543
$77$	9.98930	1.13839
$78$	−0.591416	−0.0669647
$79$	−0.376445	−0.0423534	−0.0211767	−	0.999776i	$-0.506741\pi$
$79$	−0.376445	−0.0423534	−0.0211767	+	0.999776i	$0.506741\pi$
$80$	0.378923	0.0423649
$81$	6.86593	0.762881
$82$	12.1718	1.34415
$83$	−4.33862	−0.476225	−0.238112	−	0.971238i	$-0.576529\pi$
$83$	−4.33862	−0.476225	−0.238112	+	0.971238i	$0.576529\pi$
$84$	1.08889	0.118807
$85$	−1.26449	−0.137153
$86$	0.516108	0.0556533
$87$	0.169425	0.0181643
$88$	−4.52894	−0.482787
$89$	1.33389	0.141392	0.0706961	−	0.997498i	$-0.477478\pi$
$89$	1.33389	0.141392	0.0706961	+	0.997498i	$0.477478\pi$
$90$	1.04442	0.110091
$91$	2.64233	0.276991
$92$	3.28385	0.342365
$93$	4.43600	0.459992
$94$	−11.7717	−1.21416
$95$	1.67000	0.171338
$96$	−0.493679	−0.0503859
$97$	−1.08771	−0.110440	−0.0552202	−	0.998474i	$-0.517586\pi$
$97$	−1.08771	−0.110440	−0.0552202	+	0.998474i	$0.517586\pi$
$98$	2.13508	0.215675
$99$	−12.4830	−1.25459
$100$	−4.85642	−0.485642
$101$	7.91234	0.787307	0.393654	−	0.919259i	$-0.371211\pi$
$101$	7.91234	0.787307	0.393654	+	0.919259i	$0.371211\pi$
$102$	1.64744	0.163120
$103$	−2.07530	−0.204485	−0.102243	−	0.994759i	$-0.532602\pi$
$103$	−2.07530	−0.204485	−0.102243	+	0.994759i	$0.532602\pi$
$104$	−1.19798	−0.117471
$105$	0.412604	0.0402660
$106$	−4.84972	−0.471046
$107$	1.76526	0.170654	0.0853272	−	0.996353i	$-0.472806\pi$
$107$	1.76526	0.170654	0.0853272	+	0.996353i	$0.472806\pi$
$108$	−2.84176	−0.273448
$109$	−0.770447	−0.0737955	−0.0368977	−	0.999319i	$-0.511748\pi$
$109$	−0.770447	−0.0737955	−0.0368977	+	0.999319i	$0.511748\pi$
$110$	−1.71612	−0.163626
$111$	2.50379	0.237649
$112$	2.20566	0.208415
$113$	−3.54563	−0.333545	−0.166772	−	0.985995i	$-0.553335\pi$
$113$	−3.54563	−0.333545	−0.166772	+	0.985995i	$0.553335\pi$
$114$	−2.17575	−0.203778
$115$	1.24433	0.116034
$116$	0.343188	0.0318642
$117$	−3.30196	−0.305267
$118$	1.09334	0.100650
$119$	−7.36040	−0.674727
$120$	−0.187066	−0.0170767
$121$	9.51133	0.864666
$122$	−6.20793	−0.562039
$123$	−6.00896	−0.541810
$124$	8.98560	0.806930
$125$	−3.73482	−0.334053
$126$	6.07941	0.541597
$127$	15.2782	1.35572	0.677861	−	0.735190i	$-0.262907\pi$
$127$	15.2782	1.35572	0.677861	+	0.735190i	$0.262907\pi$
$128$	−1.00000	−0.0883883
$129$	−0.254792	−0.0224332
$130$	−0.453941	−0.0398133
$131$	20.1595	1.76135	0.880673	−	0.473724i	$-0.157091\pi$
$131$	20.1595	1.76135	0.880673	+	0.473724i	$0.157091\pi$
$132$	2.23584	0.194605
$133$	9.72082	0.842902
$134$	−8.54831	−0.738462
$135$	−1.07681	−0.0926767
$136$	3.33706	0.286150
$137$	−0.0864041	−0.00738200	−0.00369100	−	0.999993i	$-0.501175\pi$
$137$	−0.0864041	−0.00738200	−0.00369100	+	0.999993i	$0.501175\pi$
$138$	−1.62117	−0.138003
$139$	14.4212	1.22319	0.611597	−	0.791170i	$-0.290528\pi$
$139$	14.4212	1.22319	0.611597	+	0.791170i	$0.290528\pi$
$140$	0.835774	0.0706358
$141$	5.81143	0.489411
$142$	4.35011	0.365053
$143$	5.42557	0.453709
$144$	−2.75628	−0.229690
$145$	0.130042	0.0107994
$146$	5.26126	0.435425
$147$	−1.05404	−0.0869360
$148$	5.07170	0.416891
$149$	−21.2459	−1.74053	−0.870267	−	0.492581i	$-0.836053\pi$
$149$	−21.2459	−1.74053	−0.870267	+	0.492581i	$0.836053\pi$
$150$	2.39751	0.195756
$151$	4.29494	0.349517	0.174759	−	0.984611i	$-0.444085\pi$
$151$	4.29494	0.349517	0.174759	+	0.984611i	$0.444085\pi$
$152$	−4.40722	−0.357473
$153$	9.19787	0.743603
$154$	−9.98930	−0.804960
$155$	3.40485	0.273484
$156$	0.591416	0.0473512
$157$	18.9281	1.51063	0.755315	−	0.655362i	$-0.227484\pi$
$157$	18.9281	1.51063	0.755315	+	0.655362i	$0.227484\pi$
$158$	0.376445	0.0299484
$159$	2.39420	0.189873
$160$	−0.378923	−0.0299565
$161$	7.24304	0.570832
$162$	−6.86593	−0.539438
$163$	12.6505	0.990866	0.495433	−	0.868646i	$-0.335009\pi$
$163$	12.6505	0.990866	0.495433	+	0.868646i	$0.335009\pi$
$164$	−12.1718	−0.950458
$165$	0.847213	0.0659554
$166$	4.33862	0.336742
$167$	−17.4965	−1.35392	−0.676958	−	0.736021i	$-0.736702\pi$
$167$	−17.4965	−1.35392	−0.676958	+	0.736021i	$0.736702\pi$
$168$	−1.08889	−0.0840094
$169$	−11.5649	−0.889604
$170$	1.26449	0.0969818
$171$	−12.1475	−0.928945
$172$	−0.516108	−0.0393529
$173$	4.07643	0.309925	0.154963	−	0.987920i	$-0.450474\pi$
$173$	4.07643	0.309925	0.154963	+	0.987920i	$0.450474\pi$
$174$	−0.169425	−0.0128441
$175$	−10.7116	−0.809720
$176$	4.52894	0.341382
$177$	−0.539759	−0.0405708
$178$	−1.33389	−0.0999793
$179$	−0.464862	−0.0347455	−0.0173727	−	0.999849i	$-0.505530\pi$
$179$	−0.464862	−0.0347455	−0.0173727	+	0.999849i	$0.505530\pi$
$180$	−1.04442	−0.0778463
$181$	5.67513	0.421829	0.210914	−	0.977505i	$-0.432356\pi$
$181$	5.67513	0.421829	0.210914	+	0.977505i	$0.432356\pi$
$182$	−2.64233	−0.195862
$183$	3.06472	0.226551
$184$	−3.28385	−0.242089
$185$	1.92178	0.141292
$186$	−4.43600	−0.325263
$187$	−15.1133	−1.10520
$188$	11.7717	0.858538
$189$	−6.26794	−0.455925
$190$	−1.67000	−0.121154
$191$	−16.6979	−1.20821	−0.604107	−	0.796903i	$-0.706470\pi$
$191$	−16.6979	−1.20821	−0.604107	+	0.796903i	$0.706470\pi$
$192$	0.493679	0.0356282
$193$	11.1394	0.801830	0.400915	−	0.916115i	$-0.368692\pi$
$193$	11.1394	0.801830	0.400915	+	0.916115i	$0.368692\pi$
$194$	1.08771	0.0780932
$195$	0.224101	0.0160482
$196$	−2.13508	−0.152505
$197$	14.1905	1.01103	0.505517	−	0.862817i	$-0.331302\pi$
$197$	14.1905	1.01103	0.505517	+	0.862817i	$0.331302\pi$
$198$	12.4830	0.887131
$199$	−0.220598	−0.0156378	−0.00781888	−	0.999969i	$-0.502489\pi$
$199$	−0.220598	−0.0156378	−0.00781888	+	0.999969i	$0.502489\pi$
$200$	4.85642	0.343401
$201$	4.22012	0.297665
$202$	−7.91234	−0.556710
$203$	0.756956	0.0531279
$204$	−1.64744	−0.115344
$205$	−4.61217	−0.322128
$206$	2.07530	0.144593
$207$	−9.05121	−0.629102
$208$	1.19798	0.0830648
$209$	19.9600	1.38067
$210$	−0.412604	−0.0284724
$211$	10.0385	0.691076	0.345538	−	0.938405i	$-0.387696\pi$
$211$	10.0385	0.691076	0.345538	+	0.938405i	$0.387696\pi$
$212$	4.84972	0.333080
$213$	−2.14756	−0.147148
$214$	−1.76526	−0.120671
$215$	−0.195565	−0.0133374
$216$	2.84176	0.193357
$217$	19.8191	1.34541
$218$	0.770447	0.0521813
$219$	−2.59737	−0.175514
$220$	1.71612	0.115701
$221$	−3.99772	−0.268916
$222$	−2.50379	−0.168044
$223$	−9.58476	−0.641843	−0.320921	−	0.947106i	$-0.603993\pi$
$223$	−9.58476	−0.641843	−0.320921	+	0.947106i	$0.603993\pi$
$224$	−2.20566	−0.147372
$225$	13.3857	0.892377
$226$	3.54563	0.235852
$227$	−4.15878	−0.276028	−0.138014	−	0.990430i	$-0.544072\pi$
$227$	−4.15878	−0.276028	−0.138014	+	0.990430i	$0.544072\pi$
$228$	2.17575	0.144093
$229$	−7.92129	−0.523454	−0.261727	−	0.965142i	$-0.584292\pi$
$229$	−7.92129	−0.523454	−0.261727	+	0.965142i	$0.584292\pi$
$230$	−1.24433	−0.0820484
$231$	4.93151	0.324469
$232$	−0.343188	−0.0225314
$233$	−11.5057	−0.753767	−0.376883	−	0.926261i	$-0.623004\pi$
$233$	−11.5057	−0.753767	−0.376883	+	0.926261i	$0.623004\pi$
$234$	3.30196	0.215856
$235$	4.46056	0.290975
$236$	−1.09334	−0.0711704
$237$	−0.185843	−0.0120718
$238$	7.36040	0.477104
$239$	9.59934	0.620929	0.310465	−	0.950585i	$-0.399515\pi$
$239$	9.59934	0.620929	0.310465	+	0.950585i	$0.399515\pi$
$240$	0.187066	0.0120751
$241$	−6.95169	−0.447798	−0.223899	−	0.974612i	$-0.571879\pi$
$241$	−6.95169	−0.447798	−0.223899	+	0.974612i	$0.571879\pi$
$242$	−9.51133	−0.611411
$243$	11.9148	0.764337
$244$	6.20793	0.397422
$245$	−0.809030	−0.0516870
$246$	6.00896	0.383117
$247$	5.27975	0.335942
$248$	−8.98560	−0.570586
$249$	−2.14188	−0.135736
$250$	3.73482	0.236211
$251$	−14.9830	−0.945716	−0.472858	−	0.881139i	$-0.656778\pi$
$251$	−14.9830	−0.945716	−0.472858	+	0.881139i	$0.656778\pi$
$252$	−6.07941	−0.382967
$253$	14.8724	0.935017
$254$	−15.2782	−0.958640
$255$	−0.624251	−0.0390921
$256$	1.00000	0.0625000
$257$	−23.0498	−1.43781	−0.718903	−	0.695110i	$-0.755356\pi$
$257$	−23.0498	−1.43781	−0.718903	+	0.695110i	$0.755356\pi$
$258$	0.254792	0.0158626
$259$	11.1864	0.695091
$260$	0.453941	0.0281522
$261$	−0.945923	−0.0585512
$262$	−20.1595	−1.24546
$263$	−6.46048	−0.398370	−0.199185	−	0.979962i	$-0.563830\pi$
$263$	−6.46048	−0.398370	−0.199185	+	0.979962i	$0.563830\pi$
$264$	−2.23584	−0.137607
$265$	1.83767	0.112887
$266$	−9.72082	−0.596021
$267$	0.658514	0.0403004
$268$	8.54831	0.522171
$269$	9.75199	0.594589	0.297295	−	0.954786i	$-0.403916\pi$
$269$	9.75199	0.594589	0.297295	+	0.954786i	$0.403916\pi$
$270$	1.07681	0.0655324
$271$	−13.8096	−0.838875	−0.419438	−	0.907784i	$-0.637773\pi$
$271$	−13.8096	−0.838875	−0.419438	+	0.907784i	$0.637773\pi$
$272$	−3.33706	−0.202339
$273$	1.30446	0.0789496
$274$	0.0864041	0.00521986
$275$	−21.9944	−1.32631
$276$	1.62117	0.0975828
$277$	5.20674	0.312843	0.156421	−	0.987690i	$-0.450004\pi$
$277$	5.20674	0.312843	0.156421	+	0.987690i	$0.450004\pi$
$278$	−14.4212	−0.864928
$279$	−24.7668	−1.48275
$280$	−0.835774	−0.0499471
$281$	−1.52952	−0.0912434	−0.0456217	−	0.998959i	$-0.514527\pi$
$281$	−1.52952	−0.0912434	−0.0456217	+	0.998959i	$0.514527\pi$
$282$	−5.81143	−0.346066
$283$	−27.9108	−1.65913	−0.829563	−	0.558413i	$-0.811411\pi$
$283$	−27.9108	−1.65913	−0.829563	+	0.558413i	$0.811411\pi$
$284$	−4.35011	−0.258131
$285$	0.824442	0.0488358
$286$	−5.42557	−0.320821
$287$	−26.8468	−1.58472
$288$	2.75628	0.162415
$289$	−5.86405	−0.344944
$290$	−0.130042	−0.00763633
$291$	−0.536981	−0.0314784
$292$	−5.26126	−0.307892
$293$	−17.2365	−1.00697	−0.503483	−	0.864005i	$-0.667949\pi$
$293$	−17.2365	−1.00697	−0.503483	+	0.864005i	$0.667949\pi$
$294$	1.05404	0.0614730
$295$	−0.414292	−0.0241210
$296$	−5.07170	−0.294787
$297$	−12.8702	−0.746802
$298$	21.2459	1.23074
$299$	3.93398	0.227508
$300$	−2.39751	−0.138420
$301$	−1.13836	−0.0656138
$302$	−4.29494	−0.247146
$303$	3.90616	0.224403
$304$	4.40722	0.252771
$305$	2.35233	0.134694
$306$	−9.19787	−0.525807
$307$	18.7704	1.07129	0.535643	−	0.844445i	$-0.320069\pi$
$307$	18.7704	1.07129	0.535643	+	0.844445i	$0.320069\pi$
$308$	9.98930	0.569193
$309$	−1.02453	−0.0582836
$310$	−3.40485	−0.193382
$311$	−7.45086	−0.422500	−0.211250	−	0.977432i	$-0.567753\pi$
$311$	−7.45086	−0.422500	−0.211250	+	0.977432i	$0.567753\pi$
$312$	−0.591416	−0.0334824
$313$	−1.23816	−0.0699848	−0.0349924	−	0.999388i	$-0.511141\pi$
$313$	−1.23816	−0.0699848	−0.0349924	+	0.999388i	$0.511141\pi$
$314$	−18.9281	−1.06818
$315$	−2.30363	−0.129795
$316$	−0.376445	−0.0211767
$317$	3.68521	0.206982	0.103491	−	0.994630i	$-0.466999\pi$
$317$	3.68521	0.206982	0.103491	+	0.994630i	$0.466999\pi$
$318$	−2.39420	−0.134260
$319$	1.55428	0.0870230
$320$	0.378923	0.0211824
$321$	0.871473	0.0486409
$322$	−7.24304	−0.403639
$323$	−14.7071	−0.818327
$324$	6.86593	0.381440
$325$	−5.81788	−0.322718
$326$	−12.6505	−0.700648
$327$	−0.380354	−0.0210336
$328$	12.1718	0.672075
$329$	25.9643	1.43146
$330$	−0.847213	−0.0466375
$331$	1.88330	0.103516	0.0517579	−	0.998660i	$-0.483518\pi$
$331$	1.88330	0.103516	0.0517579	+	0.998660i	$0.483518\pi$
$332$	−4.33862	−0.238112
$333$	−13.9790	−0.766046
$334$	17.4965	0.957364
$335$	3.23915	0.176974
$336$	1.08889	0.0594036
$337$	−1.69944	−0.0925742	−0.0462871	−	0.998928i	$-0.514739\pi$
$337$	−1.69944	−0.0925742	−0.0462871	+	0.998928i	$0.514739\pi$
$338$	11.5649	0.629045
$339$	−1.75040	−0.0950689
$340$	−1.26449	−0.0685765
$341$	40.6953	2.20377
$342$	12.1475	0.656864
$343$	−20.1488	−1.08794
$344$	0.516108	0.0278267
$345$	0.614298	0.0330727
$346$	−4.07643	−0.219150
$347$	−26.1314	−1.40281	−0.701403	−	0.712765i	$-0.747442\pi$
$347$	−26.1314	−1.40281	−0.701403	+	0.712765i	$0.747442\pi$
$348$	0.169425	0.00908213
$349$	−26.6534	−1.42672	−0.713362	−	0.700796i	$-0.752829\pi$
$349$	−26.6534	−1.42672	−0.713362	+	0.700796i	$0.752829\pi$
$350$	10.7116	0.572559
$351$	−3.40436	−0.181711
$352$	−4.52894	−0.241393
$353$	1.38683	0.0738134	0.0369067	−	0.999319i	$-0.488250\pi$
$353$	1.38683	0.0738134	0.0369067	+	0.999319i	$0.488250\pi$
$354$	0.539759	0.0286879
$355$	−1.64836	−0.0874856
$356$	1.33389	0.0706961
$357$	−3.63368	−0.192315
$358$	0.464862	0.0245687
$359$	−21.1312	−1.11526	−0.557631	−	0.830089i	$-0.688289\pi$
$359$	−21.1312	−1.11526	−0.557631	+	0.830089i	$0.688289\pi$
$360$	1.04442	0.0550457
$361$	0.423586	0.0222940
$362$	−5.67513	−0.298278
$363$	4.69554	0.246452
$364$	2.64233	0.138496
$365$	−1.99361	−0.104350
$366$	−3.06472	−0.160196
$367$	5.76933	0.301156	0.150578	−	0.988598i	$-0.451886\pi$
$367$	5.76933	0.301156	0.150578	+	0.988598i	$0.451886\pi$
$368$	3.28385	0.171182
$369$	33.5489	1.74649
$370$	−1.92178	−0.0999087
$371$	10.6968	0.555351
$372$	4.43600	0.229996
$373$	−13.3645	−0.691985	−0.345993	−	0.938237i	$-0.612458\pi$
$373$	−13.3645	−0.691985	−0.345993	+	0.938237i	$0.612458\pi$
$374$	15.1133	0.781492
$375$	−1.84380	−0.0952136
$376$	−11.7717	−0.607078
$377$	0.411132	0.0211744
$378$	6.26794	0.322388
$379$	12.8926	0.662248	0.331124	−	0.943587i	$-0.392572\pi$
$379$	12.8926	0.662248	0.331124	+	0.943587i	$0.392572\pi$
$380$	1.67000	0.0856690
$381$	7.54253	0.386416
$382$	16.6979	0.854337
$383$	1.04266	0.0532774	0.0266387	−	0.999645i	$-0.491520\pi$
$383$	1.04266	0.0532774	0.0266387	+	0.999645i	$0.491520\pi$
$384$	−0.493679	−0.0251930
$385$	3.78517	0.192910
$386$	−11.1394	−0.566979
$387$	1.42254	0.0723117
$388$	−1.08771	−0.0552202
$389$	−26.7800	−1.35780	−0.678899	−	0.734231i	$-0.737543\pi$
$389$	−26.7800	−1.35780	−0.678899	+	0.734231i	$0.737543\pi$
$390$	−0.224101	−0.0113478
$391$	−10.9584	−0.554190
$392$	2.13508	0.107838
$393$	9.95234	0.502029
$394$	−14.1905	−0.714908
$395$	−0.142644	−0.00717718
$396$	−12.4830	−0.627296
$397$	−26.6517	−1.33761	−0.668806	−	0.743437i	$-0.733195\pi$
$397$	−26.6517	−1.33761	−0.668806	+	0.743437i	$0.733195\pi$
$398$	0.220598	0.0110576
$399$	4.79896	0.240249
$400$	−4.85642	−0.242821
$401$	−30.6978	−1.53297	−0.766487	−	0.642259i	$-0.777997\pi$
$401$	−30.6978	−1.53297	−0.766487	+	0.642259i	$0.777997\pi$
$402$	−4.22012	−0.210481
$403$	10.7645	0.536220
$404$	7.91234	0.393654
$405$	2.60166	0.129277
$406$	−0.756956	−0.0375671
$407$	22.9694	1.13855
$408$	1.64744	0.0815602
$409$	−19.1486	−0.946839	−0.473420	−	0.880837i	$-0.656981\pi$
$409$	−19.1486	−0.946839	−0.473420	+	0.880837i	$0.656981\pi$
$410$	4.61217	0.227779
$411$	−0.0426559	−0.00210406
$412$	−2.07530	−0.102243
$413$	−2.41153	−0.118664
$414$	9.05121	0.444843
$415$	−1.64400	−0.0807008
$416$	−1.19798	−0.0587357
$417$	7.11946	0.348642
$418$	−19.9600	−0.976278
$419$	25.5262	1.24704	0.623519	−	0.781808i	$-0.285702\pi$
$419$	25.5262	1.24704	0.623519	+	0.781808i	$0.285702\pi$
$420$	0.412604	0.0201330
$421$	14.5424	0.708753	0.354377	−	0.935103i	$-0.384693\pi$
$421$	14.5424	0.708753	0.354377	+	0.935103i	$0.384693\pi$
$422$	−10.0385	−0.488664
$423$	−32.4461	−1.57758
$424$	−4.84972	−0.235523
$425$	16.2061	0.786113
$426$	2.14756	0.104049
$427$	13.6926	0.662629
$428$	1.76526	0.0853272
$429$	2.67849	0.129319
$430$	0.195565	0.00943099
$431$	−4.64412	−0.223699	−0.111850	−	0.993725i	$-0.535678\pi$
$431$	−4.64412	−0.223699	−0.111850	+	0.993725i	$0.535678\pi$
$432$	−2.84176	−0.136724
$433$	14.1278	0.678939	0.339470	−	0.940617i	$-0.389752\pi$
$433$	14.1278	0.678939	0.339470	+	0.940617i	$0.389752\pi$
$434$	−19.8191	−0.951349
$435$	0.0641990	0.00307811
$436$	−0.770447	−0.0368977
$437$	14.4726	0.692320
$438$	2.59737	0.124107
$439$	−12.2960	−0.586858	−0.293429	−	0.955981i	$-0.594796\pi$
$439$	−12.2960	−0.586858	−0.293429	+	0.955981i	$0.594796\pi$
$440$	−1.71612	−0.0818128
$441$	5.88487	0.280232
$442$	3.99772	0.190152
$443$	−21.4055	−1.01700	−0.508502	−	0.861061i	$-0.669801\pi$
$443$	−21.4055	−1.01700	−0.508502	+	0.861061i	$0.669801\pi$
$444$	2.50379	0.118825
$445$	0.505442	0.0239602
$446$	9.58476	0.453851
$447$	−10.4887	−0.496097
$448$	2.20566	0.104208
$449$	−28.7035	−1.35460	−0.677302	−	0.735705i	$-0.736851\pi$
$449$	−28.7035	−1.35460	−0.677302	+	0.735705i	$0.736851\pi$
$450$	−13.3857	−0.631006
$451$	−55.1254	−2.59575
$452$	−3.54563	−0.166772
$453$	2.12032	0.0996215
$454$	4.15878	0.195181
$455$	1.00124	0.0469388
$456$	−2.17575	−0.101889
$457$	−15.7557	−0.737020	−0.368510	−	0.929624i	$-0.620132\pi$
$457$	−15.7557	−0.737020	−0.368510	+	0.929624i	$0.620132\pi$
$458$	7.92129	0.370138
$459$	9.48310	0.442633
$460$	1.24433	0.0580170
$461$	−9.76537	−0.454819	−0.227409	−	0.973799i	$-0.573026\pi$
$461$	−9.76537	−0.454819	−0.227409	+	0.973799i	$0.573026\pi$
$462$	−4.93151	−0.229434
$463$	27.3179	1.26957	0.634786	−	0.772688i	$-0.281088\pi$
$463$	27.3179	1.26957	0.634786	+	0.772688i	$0.281088\pi$
$464$	0.343188	0.0159321
$465$	1.68090	0.0779500
$466$	11.5057	0.532994
$467$	−10.4388	−0.483050	−0.241525	−	0.970395i	$-0.577648\pi$
$467$	−10.4388	−0.483050	−0.241525	+	0.970395i	$0.577648\pi$
$468$	−3.30196	−0.152633
$469$	18.8546	0.870627
$470$	−4.46056	−0.205750
$471$	9.34443	0.430569
$472$	1.09334	0.0503250
$473$	−2.33742	−0.107475
$474$	0.185843	0.00853606
$475$	−21.4033	−0.982051
$476$	−7.36040	−0.337364
$477$	−13.3672	−0.612041
$478$	−9.59934	−0.439063
$479$	2.59231	0.118445	0.0592227	−	0.998245i	$-0.481138\pi$
$479$	2.59231	0.118445	0.0592227	+	0.998245i	$0.481138\pi$
$480$	−0.187066	−0.00853837
$481$	6.07578	0.277032
$482$	6.95169	0.316641
$483$	3.57574	0.162702
$484$	9.51133	0.432333
$485$	−0.412159	−0.0187152
$486$	−11.9148	−0.540468
$487$	−32.0210	−1.45101	−0.725505	−	0.688217i	$-0.758394\pi$
$487$	−32.0210	−1.45101	−0.725505	+	0.688217i	$0.758394\pi$
$488$	−6.20793	−0.281020
$489$	6.24530	0.282422
$490$	0.809030	0.0365482
$491$	−8.82878	−0.398437	−0.199219	−	0.979955i	$-0.563840\pi$
$491$	−8.82878	−0.398437	−0.199219	+	0.979955i	$0.563840\pi$
$492$	−6.00896	−0.270905
$493$	−1.14524	−0.0515790
$494$	−5.27975	−0.237547
$495$	−4.73011	−0.212603
$496$	8.98560	0.403465
$497$	−9.59484	−0.430388
$498$	2.14188	0.0959801
$499$	−6.49254	−0.290646	−0.145323	−	0.989384i	$-0.546422\pi$
$499$	−6.49254	−0.290646	−0.145323	+	0.989384i	$0.546422\pi$
$500$	−3.73482	−0.167026
$501$	−8.63764	−0.385901
$502$	14.9830	0.668722
$503$	16.0962	0.717696	0.358848	−	0.933396i	$-0.383170\pi$
$503$	16.0962	0.717696	0.358848	+	0.933396i	$0.383170\pi$
$504$	6.07941	0.270798
$505$	2.99817	0.133417
$506$	−14.8724	−0.661157
$507$	−5.70932	−0.253560
$508$	15.2782	0.677861
$509$	−24.5862	−1.08977	−0.544883	−	0.838512i	$-0.683426\pi$
$509$	−24.5862	−1.08977	−0.544883	+	0.838512i	$0.683426\pi$
$510$	0.624251	0.0276423
$511$	−11.6045	−0.513355
$512$	−1.00000	−0.0441942
$513$	−12.5242	−0.552959
$514$	23.0498	1.01668
$515$	−0.786379	−0.0346520
$516$	−0.254792	−0.0112166
$517$	53.3133	2.34472
$518$	−11.1864	−0.491503
$519$	2.01245	0.0883366
$520$	−0.453941	−0.0199066
$521$	3.96895	0.173883	0.0869415	−	0.996213i	$-0.472291\pi$
$521$	3.96895	0.173883	0.0869415	+	0.996213i	$0.472291\pi$
$522$	0.945923	0.0414019
$523$	2.53282	0.110752	0.0553762	−	0.998466i	$-0.482364\pi$
$523$	2.53282	0.110752	0.0553762	+	0.998466i	$0.482364\pi$
$524$	20.1595	0.880673
$525$	−5.28809	−0.230791
$526$	6.46048	0.281690
$527$	−29.9854	−1.30619
$528$	2.23584	0.0973027
$529$	−12.2163	−0.531145
$530$	−1.83767	−0.0798233
$531$	3.01355	0.130777
$532$	9.72082	0.421451
$533$	−14.5815	−0.631597
$534$	−0.658514	−0.0284967
$535$	0.668898	0.0289190
$536$	−8.54831	−0.369231
$537$	−0.229493	−0.00990335
$538$	−9.75199	−0.420438
$539$	−9.66964	−0.416501
$540$	−1.07681	−0.0463384
$541$	−26.3821	−1.13426	−0.567128	−	0.823630i	$-0.691945\pi$
$541$	−26.3821	−1.13426	−0.567128	+	0.823630i	$0.691945\pi$
$542$	13.8096	0.593174
$543$	2.80169	0.120232
$544$	3.33706	0.143075
$545$	−0.291940	−0.0125053
$546$	−1.30446	−0.0558258
$547$	10.8855	0.465431	0.232716	−	0.972545i	$-0.425239\pi$
$547$	10.8855	0.465431	0.232716	+	0.972545i	$0.425239\pi$
$548$	−0.0864041	−0.00369100
$549$	−17.1108	−0.730271
$550$	21.9944	0.937846
$551$	1.51251	0.0644349
$552$	−1.62117	−0.0690015
$553$	−0.830309	−0.0353083
$554$	−5.20674	−0.221213
$555$	0.948744	0.0402719
$556$	14.4212	0.611597
$557$	22.4480	0.951153	0.475577	−	0.879674i	$-0.342239\pi$
$557$	22.4480	0.951153	0.475577	+	0.879674i	$0.342239\pi$
$558$	24.7668	1.04846
$559$	−0.618286	−0.0261507
$560$	0.835774	0.0353179
$561$	−7.46114	−0.315010
$562$	1.52952	0.0645188
$563$	−33.0641	−1.39349	−0.696744	−	0.717320i	$-0.745368\pi$
$563$	−33.0641	−1.39349	−0.696744	+	0.717320i	$0.745368\pi$
$564$	5.81143	0.244706
$565$	−1.34352	−0.0565224
$566$	27.9108	1.17318
$567$	15.1439	0.635983
$568$	4.35011	0.182526
$569$	−4.39648	−0.184310	−0.0921551	−	0.995745i	$-0.529376\pi$
$569$	−4.39648	−0.184310	−0.0921551	+	0.995745i	$0.529376\pi$
$570$	−0.824442	−0.0345321
$571$	−6.97167	−0.291755	−0.145878	−	0.989303i	$-0.546601\pi$
$571$	−6.97167	−0.291755	−0.145878	+	0.989303i	$0.546601\pi$
$572$	5.42557	0.226855
$573$	−8.24338	−0.344372
$574$	26.8468	1.12056
$575$	−15.9477	−0.665067
$576$	−2.75628	−0.114845
$577$	7.69642	0.320406	0.160203	−	0.987084i	$-0.448785\pi$
$577$	7.69642	0.320406	0.160203	+	0.987084i	$0.448785\pi$
$578$	5.86405	0.243912
$579$	5.49928	0.228542
$580$	0.130042	0.00539970
$581$	−9.56950	−0.397010
$582$	0.536981	0.0222586
$583$	21.9641	0.909660
$584$	5.26126	0.217713
$585$	−1.25119	−0.0517303
$586$	17.2365	0.712033
$587$	−17.3298	−0.715276	−0.357638	−	0.933860i	$-0.616418\pi$
$587$	−17.3298	−0.715276	−0.357638	+	0.933860i	$0.616418\pi$
$588$	−1.05404	−0.0434680
$589$	39.6015	1.63175
$590$	0.414292	0.0170561
$591$	7.00557	0.288171
$592$	5.07170	0.208446
$593$	24.9464	1.02442	0.512212	−	0.858859i	$-0.328826\pi$
$593$	24.9464	1.02442	0.512212	+	0.858859i	$0.328826\pi$
$594$	12.8702	0.528069
$595$	−2.78903	−0.114339
$596$	−21.2459	−0.870267
$597$	−0.108905	−0.00445717
$598$	−3.93398	−0.160872
$599$	−18.8771	−0.771299	−0.385649	−	0.922645i	$-0.626023\pi$
$599$	−18.8771	−0.771299	−0.385649	+	0.922645i	$0.626023\pi$
$600$	2.39751	0.0978780
$601$	30.5403	1.24577	0.622883	−	0.782315i	$-0.285961\pi$
$601$	30.5403	1.24577	0.622883	+	0.782315i	$0.285961\pi$
$602$	1.13836	0.0463960
$603$	−23.5615	−0.959500
$604$	4.29494	0.174759
$605$	3.60406	0.146526
$606$	−3.90616	−0.158677
$607$	34.9164	1.41721	0.708606	−	0.705604i	$-0.249324\pi$
$607$	34.9164	1.41721	0.708606	+	0.705604i	$0.249324\pi$
$608$	−4.40722	−0.178736
$609$	0.373693	0.0151428
$610$	−2.35233	−0.0952429
$611$	14.1022	0.570514
$612$	9.19787	0.371802
$613$	43.8014	1.76912	0.884561	−	0.466424i	$-0.154458\pi$
$613$	43.8014	1.76912	0.884561	+	0.466424i	$0.154458\pi$
$614$	−18.7704	−0.757513
$615$	−2.27693	−0.0918148
$616$	−9.98930	−0.402480
$617$	40.8724	1.64546	0.822730	−	0.568432i	$-0.192450\pi$
$617$	40.8724	1.64546	0.822730	+	0.568432i	$0.192450\pi$
$618$	1.02453	0.0412127
$619$	−32.6363	−1.31177	−0.655883	−	0.754863i	$-0.727703\pi$
$619$	−32.6363	−1.31177	−0.655883	+	0.754863i	$0.727703\pi$
$620$	3.40485	0.136742
$621$	−9.33189	−0.374476
$622$	7.45086	0.298752
$623$	2.94210	0.117873
$624$	0.591416	0.0236756
$625$	22.8669	0.914675
$626$	1.23816	0.0494867
$627$	9.85386	0.393525
$628$	18.9281	0.755315
$629$	−16.9245	−0.674826
$630$	2.30363	0.0917787
$631$	42.3403	1.68554	0.842770	−	0.538274i	$-0.180923\pi$
$631$	42.3403	1.68554	0.842770	+	0.538274i	$0.180923\pi$
$632$	0.376445	0.0149742
$633$	4.95578	0.196974
$634$	−3.68521	−0.146358
$635$	5.78926	0.229740
$636$	2.39420	0.0949364
$637$	−2.55777	−0.101343
$638$	−1.55428	−0.0615346
$639$	11.9901	0.474322
$640$	−0.378923	−0.0149782
$641$	39.3102	1.55266	0.776330	−	0.630327i	$-0.217079\pi$
$641$	39.3102	1.55266	0.776330	+	0.630327i	$0.217079\pi$
$642$	−0.871473	−0.0343943
$643$	−8.63600	−0.340570	−0.170285	−	0.985395i	$-0.554469\pi$
$643$	−8.63600	−0.340570	−0.170285	+	0.985395i	$0.554469\pi$
$644$	7.24304	0.285416
$645$	−0.0965464	−0.00380151
$646$	14.7071	0.578645
$647$	2.82952	0.111240	0.0556199	−	0.998452i	$-0.482286\pi$
$647$	2.82952	0.111240	0.0556199	+	0.998452i	$0.482286\pi$
$648$	−6.86593	−0.269719
$649$	−4.95167	−0.194370
$650$	5.81788	0.228196
$651$	9.78430	0.383477
$652$	12.6505	0.495433
$653$	2.83152	0.110806	0.0554030	−	0.998464i	$-0.482356\pi$
$653$	2.83152	0.110806	0.0554030	+	0.998464i	$0.482356\pi$
$654$	0.380354	0.0148730
$655$	7.63891	0.298477
$656$	−12.1718	−0.475229
$657$	14.5015	0.565758
$658$	−25.9643	−1.01219
$659$	17.6426	0.687257	0.343628	−	0.939106i	$-0.388344\pi$
$659$	17.6426	0.687257	0.343628	+	0.939106i	$0.388344\pi$
$660$	0.847213	0.0329777
$661$	−12.7103	−0.494372	−0.247186	−	0.968968i	$-0.579506\pi$
$661$	−12.7103	−0.494372	−0.247186	+	0.968968i	$0.579506\pi$
$662$	−1.88330	−0.0731967
$663$	−1.97359	−0.0766479
$664$	4.33862	0.168371
$665$	3.68344	0.142838
$666$	13.9790	0.541676
$667$	1.12698	0.0436368
$668$	−17.4965	−0.676958
$669$	−4.73179	−0.182942
$670$	−3.23915	−0.125139
$671$	28.1153	1.08538
$672$	−1.08889	−0.0420047
$673$	−35.2568	−1.35905	−0.679526	−	0.733652i	$-0.737814\pi$
$673$	−35.2568	−1.35905	−0.679526	+	0.733652i	$0.737814\pi$
$674$	1.69944	0.0654599
$675$	13.8008	0.531191
$676$	−11.5649	−0.444802
$677$	−21.4779	−0.825462	−0.412731	−	0.910853i	$-0.635425\pi$
$677$	−21.4779	−0.825462	−0.412731	+	0.910853i	$0.635425\pi$
$678$	1.75040	0.0672239
$679$	−2.39912	−0.0920698
$680$	1.26449	0.0484909
$681$	−2.05310	−0.0786750
$682$	−40.6953	−1.55830
$683$	37.7651	1.44504	0.722521	−	0.691349i	$-0.242983\pi$
$683$	37.7651	1.44504	0.722521	+	0.691349i	$0.242983\pi$
$684$	−12.1475	−0.464473
$685$	−0.0327405	−0.00125095
$686$	20.1488	0.769287
$687$	−3.91058	−0.149198
$688$	−0.516108	−0.0196764
$689$	5.80985	0.221338
$690$	−0.614298	−0.0233859
$691$	−4.41019	−0.167772	−0.0838858	−	0.996475i	$-0.526733\pi$
$691$	−4.41019	−0.167772	−0.0838858	+	0.996475i	$0.526733\pi$
$692$	4.07643	0.154963
$693$	−27.5333	−1.04590
$694$	26.1314	0.991933
$695$	5.46454	0.207282
$696$	−0.169425	−0.00642203
$697$	40.6180	1.53852
$698$	26.6534	1.00885
$699$	−5.68015	−0.214843
$700$	−10.7116	−0.404860
$701$	−3.74769	−0.141548	−0.0707741	−	0.997492i	$-0.522547\pi$
$701$	−3.74769	−0.141548	−0.0707741	+	0.997492i	$0.522547\pi$
$702$	3.40436	0.128489
$703$	22.3521	0.843025
$704$	4.52894	0.170691
$705$	2.20209	0.0829354
$706$	−1.38683	−0.0521940
$707$	17.4519	0.656346
$708$	−0.539759	−0.0202854
$709$	6.58339	0.247244	0.123622	−	0.992329i	$-0.460549\pi$
$709$	6.58339	0.247244	0.123622	+	0.992329i	$0.460549\pi$
$710$	1.64836	0.0618617
$711$	1.03759	0.0389126
$712$	−1.33389	−0.0499897
$713$	29.5073	1.10506
$714$	3.63368	0.135987
$715$	2.05587	0.0768853
$716$	−0.464862	−0.0173727
$717$	4.73899	0.176981
$718$	21.1312	0.788609
$719$	29.7745	1.11040	0.555201	−	0.831716i	$-0.312641\pi$
$719$	29.7745	1.11040	0.555201	+	0.831716i	$0.312641\pi$
$720$	−1.04442	−0.0389232
$721$	−4.57740	−0.170471
$722$	−0.423586	−0.0157642
$723$	−3.43190	−0.127634
$724$	5.67513	0.210914
$725$	−1.66667	−0.0618984
$726$	−4.69554	−0.174268
$727$	49.1477	1.82279	0.911394	−	0.411535i	$-0.135007\pi$
$727$	49.1477	1.82279	0.911394	+	0.411535i	$0.135007\pi$
$728$	−2.64233	−0.0979312
$729$	−14.7157	−0.545025
$730$	1.99361	0.0737869
$731$	1.72228	0.0637009
$732$	3.06472	0.113275
$733$	32.3580	1.19517	0.597585	−	0.801806i	$-0.296127\pi$
$733$	32.3580	1.19517	0.597585	+	0.801806i	$0.296127\pi$
$734$	−5.76933	−0.212950
$735$	−0.399401	−0.0147321
$736$	−3.28385	−0.121044
$737$	38.7148	1.42608
$738$	−33.5489	−1.23495
$739$	−49.5908	−1.82423	−0.912113	−	0.409938i	$-0.865550\pi$
$739$	−49.5908	−1.82423	−0.912113	+	0.409938i	$0.865550\pi$
$740$	1.92178	0.0706462
$741$	2.60650	0.0957523
$742$	−10.6968	−0.392692
$743$	24.9010	0.913529	0.456764	−	0.889588i	$-0.349008\pi$
$743$	24.9010	0.913529	0.456764	+	0.889588i	$0.349008\pi$
$744$	−4.43600	−0.162632
$745$	−8.05056	−0.294950
$746$	13.3645	0.489307
$747$	11.9584	0.437537
$748$	−15.1133	−0.552598
$749$	3.89356	0.142268
$750$	1.84380	0.0673262
$751$	1.00000	0.0364905
$751$	1.00000	0.0364905
$752$	11.7717	0.429269
$753$	−7.39677	−0.269553
$754$	−0.411132	−0.0149725
$755$	1.62745	0.0592291
$756$	−6.26794	−0.227963
$757$	−15.5074	−0.563624	−0.281812	−	0.959470i	$-0.590936\pi$
$757$	−15.5074	−0.563624	−0.281812	+	0.959470i	$0.590936\pi$
$758$	−12.8926	−0.468280
$759$	7.34217	0.266504
$760$	−1.67000	−0.0605771
$761$	11.0406	0.400221	0.200110	−	0.979773i	$-0.435870\pi$
$761$	11.0406	0.400221	0.200110	+	0.979773i	$0.435870\pi$
$762$	−7.54253	−0.273237
$763$	−1.69934	−0.0615203
$764$	−16.6979	−0.604107
$765$	3.48528	0.126011
$766$	−1.04266	−0.0376728
$767$	−1.30980	−0.0472940
$768$	0.493679	0.0178141
$769$	−21.1278	−0.761888	−0.380944	−	0.924598i	$-0.624401\pi$
$769$	−21.1278	−0.761888	−0.380944	+	0.924598i	$0.624401\pi$
$770$	−3.78517	−0.136408
$771$	−11.3792	−0.409812
$772$	11.1394	0.400915
$773$	0.232597	0.00836595	0.00418297	−	0.999991i	$-0.498669\pi$
$773$	0.232597	0.00836595	0.00418297	+	0.999991i	$0.498669\pi$
$774$	−1.42254	−0.0511321
$775$	−43.6378	−1.56752
$776$	1.08771	0.0390466
$777$	5.52251	0.198119
$778$	26.7800	0.960109
$779$	−53.6438	−1.92199
$780$	0.224101	0.00802411
$781$	−19.7014	−0.704971
$782$	10.9584	0.391871
$783$	−0.975257	−0.0348529
$784$	−2.13508	−0.0762527
$785$	7.17231	0.255991
$786$	−9.95234	−0.354988
$787$	−4.31225	−0.153715	−0.0768575	−	0.997042i	$-0.524489\pi$
$787$	−4.31225	−0.153715	−0.0768575	+	0.997042i	$0.524489\pi$
$788$	14.1905	0.505517
$789$	−3.18941	−0.113546
$790$	0.142644	0.00507503
$791$	−7.82045	−0.278063
$792$	12.4830	0.443566
$793$	7.43696	0.264094
$794$	26.6517	0.945835
$795$	0.907219	0.0321757
$796$	−0.220598	−0.00781888
$797$	48.6351	1.72274	0.861372	−	0.507975i	$-0.169606\pi$
$797$	48.6351	1.72274	0.861372	+	0.507975i	$0.169606\pi$
$798$	−4.79896	−0.169881
$799$	−39.2828	−1.38972
$800$	4.85642	0.171700
$801$	−3.67658	−0.129905
$802$	30.6978	1.08398
$803$	−23.8280	−0.840870
$804$	4.22012	0.148832
$805$	2.74456	0.0967329
$806$	−10.7645	−0.379165
$807$	4.81435	0.169473
$808$	−7.91234	−0.278355
$809$	−39.0505	−1.37294	−0.686472	−	0.727156i	$-0.740841\pi$
$809$	−39.0505	−1.37294	−0.686472	+	0.727156i	$0.740841\pi$
$810$	−2.60166	−0.0914129
$811$	36.4183	1.27882	0.639410	−	0.768866i	$-0.279179\pi$
$811$	36.4183	1.27882	0.639410	+	0.768866i	$0.279179\pi$
$812$	0.756956	0.0265639
$813$	−6.81752	−0.239101
$814$	−22.9694	−0.805078
$815$	4.79358	0.167912
$816$	−1.64744	−0.0576718
$817$	−2.27460	−0.0795782
$818$	19.1486	0.669517
$819$	−7.28300	−0.254488
$820$	−4.61217	−0.161064
$821$	−33.1598	−1.15728	−0.578642	−	0.815582i	$-0.696417\pi$
$821$	−33.1598	−1.15728	−0.578642	+	0.815582i	$0.696417\pi$
$822$	0.0426559	0.00148780
$823$	3.12045	0.108772	0.0543860	−	0.998520i	$-0.482680\pi$
$823$	3.12045	0.108772	0.0543860	+	0.998520i	$0.482680\pi$
$824$	2.07530	0.0722965
$825$	−10.8582	−0.378034
$826$	2.41153	0.0839080
$827$	18.5662	0.645612	0.322806	−	0.946465i	$-0.395374\pi$
$827$	18.5662	0.645612	0.322806	+	0.946465i	$0.395374\pi$
$828$	−9.05121	−0.314551
$829$	−46.5156	−1.61555	−0.807776	−	0.589489i	$-0.799329\pi$
$829$	−46.5156	−1.61555	−0.807776	+	0.589489i	$0.799329\pi$
$830$	1.64400	0.0570641
$831$	2.57046	0.0891683
$832$	1.19798	0.0415324
$833$	7.12487	0.246862
$834$	−7.11946	−0.246527
$835$	−6.62981	−0.229434
$836$	19.9600	0.690333
$837$	−25.5349	−0.882614
$838$	−25.5262	−0.881789
$839$	30.4070	1.04977	0.524883	−	0.851174i	$-0.324109\pi$
$839$	30.4070	1.04977	0.524883	+	0.851174i	$0.324109\pi$
$840$	−0.412604	−0.0142362
$841$	−28.8822	−0.995939
$842$	−14.5424	−0.501164
$843$	−0.755091	−0.0260067
$844$	10.0385	0.345538
$845$	−4.38219	−0.150752
$846$	32.4461	1.11552
$847$	20.9787	0.720838
$848$	4.84972	0.166540
$849$	−13.7790	−0.472894
$850$	−16.2061	−0.555866
$851$	16.6547	0.570915
$852$	−2.14756	−0.0735741
$853$	18.8902	0.646789	0.323394	−	0.946264i	$-0.395176\pi$
$853$	18.8902	0.646789	0.323394	+	0.946264i	$0.395176\pi$
$854$	−13.6926	−0.468550
$855$	−4.60298	−0.157419
$856$	−1.76526	−0.0603354
$857$	20.8048	0.710680	0.355340	−	0.934737i	$-0.384365\pi$
$857$	20.8048	0.710680	0.355340	+	0.934737i	$0.384365\pi$
$858$	−2.67849	−0.0914422
$859$	27.8722	0.950987	0.475494	−	0.879719i	$-0.342270\pi$
$859$	27.8722	0.950987	0.475494	+	0.879719i	$0.342270\pi$
$860$	−0.195565	−0.00666871
$861$	−13.2537	−0.451685
$862$	4.64412	0.158179
$863$	35.9977	1.22538	0.612689	−	0.790324i	$-0.290088\pi$
$863$	35.9977	1.22538	0.612689	+	0.790324i	$0.290088\pi$
$864$	2.84176	0.0966785
$865$	1.54465	0.0525198
$866$	−14.1278	−0.480083
$867$	−2.89496	−0.0983180
$868$	19.8191	0.672706
$869$	−1.70490	−0.0578347
$870$	−0.0641990	−0.00217655
$871$	10.2407	0.346992
$872$	0.770447	0.0260906
$873$	2.99804	0.101468
$874$	−14.4726	−0.489544
$875$	−8.23774	−0.278486
$876$	−2.59737	−0.0877572
$877$	12.3413	0.416735	0.208367	−	0.978051i	$-0.433185\pi$
$877$	12.3413	0.416735	0.208367	+	0.978051i	$0.433185\pi$
$878$	12.2960	0.414971
$879$	−8.50930	−0.287012
$880$	1.71612	0.0578504
$881$	−25.5982	−0.862426	−0.431213	−	0.902250i	$-0.641914\pi$
$881$	−25.5982	−0.862426	−0.431213	+	0.902250i	$0.641914\pi$
$882$	−5.88487	−0.198154
$883$	−25.8989	−0.871566	−0.435783	−	0.900052i	$-0.643528\pi$
$883$	−25.8989	−0.871566	−0.435783	+	0.900052i	$0.643528\pi$
$884$	−3.99772	−0.134458
$885$	−0.204527	−0.00687510
$886$	21.4055	0.719130
$887$	−11.2279	−0.376996	−0.188498	−	0.982074i	$-0.560362\pi$
$887$	−11.2279	−0.376996	−0.188498	+	0.982074i	$0.560362\pi$
$888$	−2.50379	−0.0840218
$889$	33.6985	1.13021
$890$	−0.505442	−0.0169424
$891$	31.0954	1.04173
$892$	−9.58476	−0.320921
$893$	51.8804	1.73611
$894$	10.4887	0.350793
$895$	−0.176147	−0.00588795
$896$	−2.20566	−0.0736858
$897$	1.94212	0.0648456
$898$	28.7035	0.957850
$899$	3.08375	0.102849
$900$	13.3857	0.446188
$901$	−16.1838	−0.539160
$902$	55.1254	1.83547
$903$	−0.561983	−0.0187016
$904$	3.54563	0.117926
$905$	2.15044	0.0714829
$906$	−2.12032	−0.0704430
$907$	−28.7544	−0.954775	−0.477388	−	0.878693i	$-0.658416\pi$
$907$	−28.7544	−0.954775	−0.477388	+	0.878693i	$0.658416\pi$
$908$	−4.15878	−0.138014
$909$	−21.8086	−0.723346
$910$	−1.00124	−0.0331907
$911$	−16.5614	−0.548703	−0.274351	−	0.961630i	$-0.588463\pi$
$911$	−16.5614	−0.548703	−0.274351	+	0.961630i	$0.588463\pi$
$912$	2.17575	0.0720464
$913$	−19.6493	−0.650298
$914$	15.7557	0.521152
$915$	1.16129	0.0383912
$916$	−7.92129	−0.261727
$917$	44.4650	1.46836
$918$	−9.48310	−0.312989
$919$	−50.9888	−1.68196	−0.840982	−	0.541063i	$-0.818022\pi$
$919$	−50.9888	−1.68196	−0.840982	+	0.541063i	$0.818022\pi$
$920$	−1.24433	−0.0410242
$921$	9.26657	0.305344
$922$	9.76537	0.321605
$923$	−5.21133	−0.171533
$924$	4.93151	0.162235
$925$	−24.6303	−0.809839
$926$	−27.3179	−0.897723
$927$	5.72011	0.187873
$928$	−0.343188	−0.0112657
$929$	−28.7033	−0.941724	−0.470862	−	0.882207i	$-0.656057\pi$
$929$	−28.7033	−0.941724	−0.470862	+	0.882207i	$0.656057\pi$
$930$	−1.68090	−0.0551190
$931$	−9.40975	−0.308392
$932$	−11.5057	−0.376883
$933$	−3.67834	−0.120423
$934$	10.4388	0.341568
$935$	−5.72679	−0.187286
$936$	3.30196	0.107928
$937$	28.4458	0.929282	0.464641	−	0.885499i	$-0.346183\pi$
$937$	28.4458	0.929282	0.464641	+	0.885499i	$0.346183\pi$
$938$	−18.8546	−0.615626
$939$	−0.611252	−0.0199475
$940$	4.46056	0.145487
$941$	−39.1989	−1.27785	−0.638924	−	0.769270i	$-0.720620\pi$
$941$	−39.1989	−1.27785	−0.638924	+	0.769270i	$0.720620\pi$
$942$	−9.34443	−0.304458
$943$	−39.9703	−1.30161
$944$	−1.09334	−0.0355852
$945$	−2.37507	−0.0772609
$946$	2.33742	0.0759962
$947$	36.9876	1.20194	0.600968	−	0.799273i	$-0.294782\pi$
$947$	36.9876	1.20194	0.600968	+	0.799273i	$0.294782\pi$
$948$	−0.185843	−0.00603590
$949$	−6.30287	−0.204600
$950$	21.4033	0.694415
$951$	1.81931	0.0589952
$952$	7.36040	0.238552
$953$	−27.9575	−0.905634	−0.452817	−	0.891604i	$-0.649581\pi$
$953$	−27.9575	−0.905634	−0.452817	+	0.891604i	$0.649581\pi$
$954$	13.3672	0.432779
$955$	−6.32720	−0.204743
$956$	9.59934	0.310465
$957$	0.767316	0.0248038
$958$	−2.59231	−0.0837536
$959$	−0.190578	−0.00615408
$960$	0.187066	0.00603754
$961$	49.7409	1.60455
$962$	−6.07578	−0.195891
$963$	−4.86556	−0.156790
$964$	−6.95169	−0.223899
$965$	4.22096	0.135878
$966$	−3.57574	−0.115048
$967$	11.9895	0.385555	0.192778	−	0.981242i	$-0.438250\pi$
$967$	11.9895	0.385555	0.192778	+	0.981242i	$0.438250\pi$
$968$	−9.51133	−0.305706
$969$	−7.26061	−0.233244
$970$	0.412159	0.0132336
$971$	3.77934	0.121285	0.0606425	−	0.998160i	$-0.480685\pi$
$971$	3.77934	0.121285	0.0606425	+	0.998160i	$0.480685\pi$
$972$	11.9148	0.382168
$973$	31.8083	1.01973
$974$	32.0210	1.02602
$975$	−2.87217	−0.0919829
$976$	6.20793	0.198711
$977$	13.1933	0.422090	0.211045	−	0.977476i	$-0.432313\pi$
$977$	13.1933	0.422090	0.211045	+	0.977476i	$0.432313\pi$
$978$	−6.24530	−0.199703
$979$	6.04111	0.193075
$980$	−0.809030	−0.0258435
$981$	2.12357	0.0678004
$982$	8.82878	0.281738
$983$	−58.5935	−1.86884	−0.934421	−	0.356171i	$-0.884082\pi$
$983$	−58.5935	−1.86884	−0.934421	+	0.356171i	$0.884082\pi$
$984$	6.00896	0.191559
$985$	5.37712	0.171329
$986$	1.14524	0.0364718
$987$	12.8180	0.408002
$988$	5.27975	0.167971
$989$	−1.69482	−0.0538921
$990$	4.73011	0.150333
$991$	−16.5626	−0.526129	−0.263064	−	0.964778i	$-0.584733\pi$
$991$	−16.5626	−0.526129	−0.263064	+	0.964778i	$0.584733\pi$
$992$	−8.98560	−0.285293
$993$	0.929748	0.0295047
$994$	9.59484	0.304330
$995$	−0.0835896	−0.00264997
$996$	−2.14188	−0.0678682
$997$	22.0758	0.699147	0.349574	−	0.936909i	$-0.386326\pi$
$997$	22.0758	0.699147	0.349574	+	0.936909i	$0.386326\pi$
$998$	6.49254	0.205518
$999$	−14.4125	−0.455992

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1502.2.a.h.1.10	✓	19

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1502.2.a.h.1.10	✓	19	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +0.493679 q^{3} +1.00000 q^{4} +0.378923 q^{5} -0.493679 q^{6} +2.20566 q^{7} -1.00000 q^{8} -2.75628 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +0.493679 q^{3} +1.00000 q^{4} +0.378923 q^{5} -0.493679 q^{6} +2.20566 q^{7} -1.00000 q^{8} -2.75628 q^{9} -0.378923 q^{10} +4.52894 q^{11} +0.493679 q^{12} +1.19798 q^{13} -2.20566 q^{14} +0.187066 q^{15} +1.00000 q^{16} -3.33706 q^{17} +2.75628 q^{18} +4.40722 q^{19} +0.378923 q^{20} +1.08889 q^{21} -4.52894 q^{22} +3.28385 q^{23} -0.493679 q^{24} -4.85642 q^{25} -1.19798 q^{26} -2.84176 q^{27} +2.20566 q^{28} +0.343188 q^{29} -0.187066 q^{30} +8.98560 q^{31} -1.00000 q^{32} +2.23584 q^{33} +3.33706 q^{34} +0.835774 q^{35} -2.75628 q^{36} +5.07170 q^{37} -4.40722 q^{38} +0.591416 q^{39} -0.378923 q^{40} -12.1718 q^{41} -1.08889 q^{42} -0.516108 q^{43} +4.52894 q^{44} -1.04442 q^{45} -3.28385 q^{46} +11.7717 q^{47} +0.493679 q^{48} -2.13508 q^{49} +4.85642 q^{50} -1.64744 q^{51} +1.19798 q^{52} +4.84972 q^{53} +2.84176 q^{54} +1.71612 q^{55} -2.20566 q^{56} +2.17575 q^{57} -0.343188 q^{58} -1.09334 q^{59} +0.187066 q^{60} +6.20793 q^{61} -8.98560 q^{62} -6.07941 q^{63} +1.00000 q^{64} +0.453941 q^{65} -2.23584 q^{66} +8.54831 q^{67} -3.33706 q^{68} +1.62117 q^{69} -0.835774 q^{70} -4.35011 q^{71} +2.75628 q^{72} -5.26126 q^{73} -5.07170 q^{74} -2.39751 q^{75} +4.40722 q^{76} +9.98930 q^{77} -0.591416 q^{78} -0.376445 q^{79} +0.378923 q^{80} +6.86593 q^{81} +12.1718 q^{82} -4.33862 q^{83} +1.08889 q^{84} -1.26449 q^{85} +0.516108 q^{86} +0.169425 q^{87} -4.52894 q^{88} +1.33389 q^{89} +1.04442 q^{90} +2.64233 q^{91} +3.28385 q^{92} +4.43600 q^{93} -11.7717 q^{94} +1.67000 q^{95} -0.493679 q^{96} -1.08771 q^{97} +2.13508 q^{98} -12.4830 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 19 q - 19 q^{2} + 6 q^{3} + 19 q^{4} + 2 q^{5} - 6 q^{6} + 13 q^{7} - 19 q^{8} + 25 q^{9}+O(q^{10}) \) 19 * q - 19 * q^2 + 6 * q^3 + 19 * q^4 + 2 * q^5 - 6 * q^6 + 13 * q^7 - 19 * q^8 + 25 * q^9	\( 19 q - 19 q^{2} + 6 q^{3} + 19 q^{4} + 2 q^{5} - 6 q^{6} + 13 q^{7} - 19 q^{8} + 25 q^{9} - 2 q^{10} - 7 q^{11} + 6 q^{12} + 19 q^{13} - 13 q^{14} + 6 q^{15} + 19 q^{16} + 11 q^{17} - 25 q^{18} + 7 q^{19} + 2 q^{20} + 7 q^{21} + 7 q^{22} + 12 q^{23} - 6 q^{24} + 37 q^{25} - 19 q^{26} + 24 q^{27} + 13 q^{28} - 8 q^{29} - 6 q^{30} + 32 q^{31} - 19 q^{32} + 24 q^{33} - 11 q^{34} - 19 q^{35} + 25 q^{36} + 41 q^{37} - 7 q^{38} - 2 q^{39} - 2 q^{40} + 15 q^{41} - 7 q^{42} + 15 q^{43} - 7 q^{44} + 28 q^{45} - 12 q^{46} - 6 q^{47} + 6 q^{48} + 42 q^{49} - 37 q^{50} + 8 q^{51} + 19 q^{52} + 6 q^{53} - 24 q^{54} + 22 q^{55} - 13 q^{56} + 24 q^{57} + 8 q^{58} - 4 q^{59} + 6 q^{60} + 13 q^{61} - 32 q^{62} + 37 q^{63} + 19 q^{64} + 20 q^{65} - 24 q^{66} + 47 q^{67} + 11 q^{68} + 15 q^{69} + 19 q^{70} - 25 q^{72} + 64 q^{73} - 41 q^{74} - 3 q^{75} + 7 q^{76} - 4 q^{77} + 2 q^{78} + 34 q^{79} + 2 q^{80} + 27 q^{81} - 15 q^{82} + 4 q^{83} + 7 q^{84} + 21 q^{85} - 15 q^{86} + 7 q^{88} + 18 q^{89} - 28 q^{90} + 28 q^{91} + 12 q^{92} + 43 q^{93} + 6 q^{94} - 8 q^{95} - 6 q^{96} + 82 q^{97} - 42 q^{98} - 2 q^{99}+O(q^{100}) \) 19 * q - 19 * q^2 + 6 * q^3 + 19 * q^4 + 2 * q^5 - 6 * q^6 + 13 * q^7 - 19 * q^8 + 25 * q^9 - 2 * q^10 - 7 * q^11 + 6 * q^12 + 19 * q^13 - 13 * q^14 + 6 * q^15 + 19 * q^16 + 11 * q^17 - 25 * q^18 + 7 * q^19 + 2 * q^20 + 7 * q^21 + 7 * q^22 + 12 * q^23 - 6 * q^24 + 37 * q^25 - 19 * q^26 + 24 * q^27 + 13 * q^28 - 8 * q^29 - 6 * q^30 + 32 * q^31 - 19 * q^32 + 24 * q^33 - 11 * q^34 - 19 * q^35 + 25 * q^36 + 41 * q^37 - 7 * q^38 - 2 * q^39 - 2 * q^40 + 15 * q^41 - 7 * q^42 + 15 * q^43 - 7 * q^44 + 28 * q^45 - 12 * q^46 - 6 * q^47 + 6 * q^48 + 42 * q^49 - 37 * q^50 + 8 * q^51 + 19 * q^52 + 6 * q^53 - 24 * q^54 + 22 * q^55 - 13 * q^56 + 24 * q^57 + 8 * q^58 - 4 * q^59 + 6 * q^60 + 13 * q^61 - 32 * q^62 + 37 * q^63 + 19 * q^64 + 20 * q^65 - 24 * q^66 + 47 * q^67 + 11 * q^68 + 15 * q^69 + 19 * q^70 - 25 * q^72 + 64 * q^73 - 41 * q^74 - 3 * q^75 + 7 * q^76 - 4 * q^77 + 2 * q^78 + 34 * q^79 + 2 * q^80 + 27 * q^81 - 15 * q^82 + 4 * q^83 + 7 * q^84 + 21 * q^85 - 15 * q^86 + 7 * q^88 + 18 * q^89 - 28 * q^90 + 28 * q^91 + 12 * q^92 + 43 * q^93 + 6 * q^94 - 8 * q^95 - 6 * q^96 + 82 * q^97 - 42 * q^98 - 2 * q^99

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