LMFDB - Embedded newform 1003.2.a.h.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1003,2,Mod(1,1003)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1003, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1003.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1003 = 17 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1003.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:	$8.00899532273$
Analytic rank:	$1$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6 x^{15} - 5 x^{14} + 90 x^{13} - 82 x^{12} - 456 x^{11} + 723 x^{10} + 951 x^{9} - 2105 x^{8} + \cdots - 1 $ x^16 - 6x^15 - 5x^14 + 90x^13 - 82x^12 - 456x^11 + 723x^10 + 951x^9 - 2105x^8 - 695x^7 + 2641x^6 - 151x^5 - 1323x^4 + 301x^3 + 179x^2 - 50*x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$0.431919$ of defining polynomial
Character	$\chi$	$=$	1003.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.431919 q^{2} +0.385290 q^{3} -1.81345 q^{4} -0.726091 q^{5} -0.166414 q^{6} +1.71462 q^{7} +1.64710 q^{8} -2.85155 q^{9} +O(q^{10})$	\(q-0.431919 q^{2} +0.385290 q^{3} -1.81345 q^{4} -0.726091 q^{5} -0.166414 q^{6} +1.71462 q^{7} +1.64710 q^{8} -2.85155 q^{9} +0.313613 q^{10} -1.66392 q^{11} -0.698703 q^{12} +2.26947 q^{13} -0.740577 q^{14} -0.279756 q^{15} +2.91548 q^{16} +1.00000 q^{17} +1.23164 q^{18} +6.41678 q^{19} +1.31673 q^{20} +0.660626 q^{21} +0.718677 q^{22} -7.39172 q^{23} +0.634612 q^{24} -4.47279 q^{25} -0.980226 q^{26} -2.25455 q^{27} -3.10937 q^{28} -4.62644 q^{29} +0.120832 q^{30} -9.94500 q^{31} -4.55345 q^{32} -0.641090 q^{33} -0.431919 q^{34} -1.24497 q^{35} +5.17113 q^{36} -0.591588 q^{37} -2.77153 q^{38} +0.874403 q^{39} -1.19594 q^{40} -0.659431 q^{41} -0.285337 q^{42} +5.75864 q^{43} +3.01742 q^{44} +2.07049 q^{45} +3.19263 q^{46} -8.14609 q^{47} +1.12331 q^{48} -4.06008 q^{49} +1.93188 q^{50} +0.385290 q^{51} -4.11555 q^{52} -0.401204 q^{53} +0.973781 q^{54} +1.20815 q^{55} +2.82415 q^{56} +2.47232 q^{57} +1.99825 q^{58} +1.00000 q^{59} +0.507322 q^{60} +0.400125 q^{61} +4.29543 q^{62} -4.88932 q^{63} -3.86423 q^{64} -1.64784 q^{65} +0.276899 q^{66} +11.3020 q^{67} -1.81345 q^{68} -2.84796 q^{69} +0.537726 q^{70} -13.0408 q^{71} -4.69679 q^{72} -10.7195 q^{73} +0.255518 q^{74} -1.72332 q^{75} -11.6365 q^{76} -2.85298 q^{77} -0.377671 q^{78} -15.2814 q^{79} -2.11690 q^{80} +7.68600 q^{81} +0.284821 q^{82} +2.53437 q^{83} -1.19801 q^{84} -0.726091 q^{85} -2.48727 q^{86} -1.78252 q^{87} -2.74064 q^{88} -13.4826 q^{89} -0.894283 q^{90} +3.89127 q^{91} +13.4045 q^{92} -3.83171 q^{93} +3.51845 q^{94} -4.65917 q^{95} -1.75440 q^{96} +10.5183 q^{97} +1.75363 q^{98} +4.74474 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 6 q^{2} - 7 q^{3} + 14 q^{4} - 21 q^{5} - 5 q^{6} - 11 q^{7} - 12 q^{8} + 17 q^{9}+O(q^{10}) $ 16 * q - 6 * q^2 - 7 * q^3 + 14 * q^4 - 21 * q^5 - 5 * q^6 - 11 * q^7 - 12 * q^8 + 17 * q^9	\( 16 q - 6 q^{2} - 7 q^{3} + 14 q^{4} - 21 q^{5} - 5 q^{6} - 11 q^{7} - 12 q^{8} + 17 q^{9} + 12 q^{10} - 7 q^{11} - 4 q^{12} - 16 q^{13} + 11 q^{14} + 7 q^{15} + 22 q^{16} + 16 q^{17} + 11 q^{18} + q^{19} - 43 q^{20} - 8 q^{21} - 18 q^{22} - 8 q^{23} - 39 q^{24} + 23 q^{25} - 49 q^{26} - 7 q^{27} - 15 q^{28} - 39 q^{29} + q^{30} - 3 q^{31} - 15 q^{33} - 6 q^{34} + 9 q^{35} - 17 q^{36} - 28 q^{37} - 27 q^{38} - 4 q^{39} + 26 q^{40} - 31 q^{41} - 45 q^{42} + 5 q^{43} - 19 q^{44} - 79 q^{45} - 39 q^{46} - 47 q^{47} - 31 q^{48} + 35 q^{49} - 13 q^{50} - 7 q^{51} + 9 q^{52} - 36 q^{53} + 9 q^{54} + 32 q^{55} + 3 q^{56} + 6 q^{57} + 22 q^{58} + 16 q^{59} + 6 q^{60} - 22 q^{61} + q^{62} - 19 q^{63} + 32 q^{64} - 19 q^{65} + 48 q^{66} + 4 q^{67} + 14 q^{68} + 14 q^{69} - 11 q^{70} - 5 q^{71} + 40 q^{72} - 35 q^{73} + 31 q^{74} - 12 q^{75} + q^{76} - 79 q^{77} + 31 q^{78} - 48 q^{79} - 127 q^{80} - 28 q^{81} - 7 q^{82} - 42 q^{83} + 28 q^{84} - 21 q^{85} + 58 q^{86} - 16 q^{87} - 2 q^{88} + 20 q^{89} - 14 q^{90} + 49 q^{91} - 21 q^{92} - 55 q^{93} - 22 q^{95} + 24 q^{96} - 2 q^{97} - 78 q^{98} - 35 q^{99}+O(q^{100}) \) 16 * q - 6 * q^2 - 7 * q^3 + 14 * q^4 - 21 * q^5 - 5 * q^6 - 11 * q^7 - 12 * q^8 + 17 * q^9 + 12 * q^10 - 7 * q^11 - 4 * q^12 - 16 * q^13 + 11 * q^14 + 7 * q^15 + 22 * q^16 + 16 * q^17 + 11 * q^18 + q^19 - 43 * q^20 - 8 * q^21 - 18 * q^22 - 8 * q^23 - 39 * q^24 + 23 * q^25 - 49 * q^26 - 7 * q^27 - 15 * q^28 - 39 * q^29 + q^30 - 3 * q^31 - 15 * q^33 - 6 * q^34 + 9 * q^35 - 17 * q^36 - 28 * q^37 - 27 * q^38 - 4 * q^39 + 26 * q^40 - 31 * q^41 - 45 * q^42 + 5 * q^43 - 19 * q^44 - 79 * q^45 - 39 * q^46 - 47 * q^47 - 31 * q^48 + 35 * q^49 - 13 * q^50 - 7 * q^51 + 9 * q^52 - 36 * q^53 + 9 * q^54 + 32 * q^55 + 3 * q^56 + 6 * q^57 + 22 * q^58 + 16 * q^59 + 6 * q^60 - 22 * q^61 + q^62 - 19 * q^63 + 32 * q^64 - 19 * q^65 + 48 * q^66 + 4 * q^67 + 14 * q^68 + 14 * q^69 - 11 * q^70 - 5 * q^71 + 40 * q^72 - 35 * q^73 + 31 * q^74 - 12 * q^75 + q^76 - 79 * q^77 + 31 * q^78 - 48 * q^79 - 127 * q^80 - 28 * q^81 - 7 * q^82 - 42 * q^83 + 28 * q^84 - 21 * q^85 + 58 * q^86 - 16 * q^87 - 2 * q^88 + 20 * q^89 - 14 * q^90 + 49 * q^91 - 21 * q^92 - 55 * q^93 - 22 * q^95 + 24 * q^96 - 2 * q^97 - 78 * q^98 - 35 * 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 $

$2$	−0.431919	−0.305413	−0.152706	−	0.988272i	$-0.548799\pi$
$2$	−0.431919	−0.305413	−0.152706	+	0.988272i	$0.548799\pi$
$3$	0.385290	0.222447	0.111224	−	0.993795i	$-0.464523\pi$
$3$	0.385290	0.222447	0.111224	+	0.993795i	$0.464523\pi$
$4$	−1.81345	−0.906723
$5$	−0.726091	−0.324718	−0.162359	−	0.986732i	$-0.551910\pi$
$5$	−0.726091	−0.324718	−0.162359	+	0.986732i	$0.551910\pi$
$6$	−0.166414	−0.0679383
$7$	1.71462	0.648065	0.324032	−	0.946046i	$-0.394961\pi$
$7$	1.71462	0.648065	0.324032	+	0.946046i	$0.394961\pi$
$8$	1.64710	0.582338
$9$	−2.85155	−0.950517
$10$	0.313613	0.0991730
$11$	−1.66392	−0.501689	−0.250845	−	0.968027i	$-0.580708\pi$
$11$	−1.66392	−0.501689	−0.250845	+	0.968027i	$0.580708\pi$
$12$	−0.698703	−0.201698
$13$	2.26947	0.629437	0.314718	−	0.949185i	$-0.398090\pi$
$13$	2.26947	0.629437	0.314718	+	0.949185i	$0.398090\pi$
$14$	−0.740577	−0.197927
$15$	−0.279756	−0.0722326
$16$	2.91548	0.728869
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	1.23164	0.290300
$19$	6.41678	1.47211	0.736056	−	0.676921i	$-0.236686\pi$
$19$	6.41678	1.47211	0.736056	+	0.676921i	$0.236686\pi$
$20$	1.31673	0.294429
$21$	0.660626	0.144160
$22$	0.718677	0.153222
$23$	−7.39172	−1.54128	−0.770640	−	0.637271i	$-0.780063\pi$
$23$	−7.39172	−1.54128	−0.770640	+	0.637271i	$0.780063\pi$
$24$	0.634612	0.129540
$25$	−4.47279	−0.894558
$26$	−0.980226	−0.192238
$27$	−2.25455	−0.433887
$28$	−3.10937	−0.587615
$29$	−4.62644	−0.859109	−0.429554	−	0.903041i	$-0.641329\pi$
$29$	−4.62644	−0.859109	−0.429554	+	0.903041i	$0.641329\pi$
$30$	0.120832	0.0220608
$31$	−9.94500	−1.78617	−0.893087	−	0.449884i	$-0.851465\pi$
$31$	−9.94500	−1.78617	−0.893087	+	0.449884i	$0.851465\pi$
$32$	−4.55345	−0.804944
$33$	−0.641090	−0.111600
$34$	−0.431919	−0.0740735
$35$	−1.24497	−0.210438
$36$	5.17113	0.861856
$37$	−0.591588	−0.0972565	−0.0486282	−	0.998817i	$-0.515485\pi$
$37$	−0.591588	−0.0972565	−0.0486282	+	0.998817i	$0.515485\pi$
$38$	−2.77153	−0.449602
$39$	0.874403	0.140017
$40$	−1.19594	−0.189095
$41$	−0.659431	−0.102986	−0.0514929	−	0.998673i	$-0.516398\pi$
$41$	−0.659431	−0.102986	−0.0514929	+	0.998673i	$0.516398\pi$
$42$	−0.285337	−0.0440284
$43$	5.75864	0.878184	0.439092	−	0.898442i	$-0.355300\pi$
$43$	5.75864	0.878184	0.439092	+	0.898442i	$0.355300\pi$
$44$	3.01742	0.454893
$45$	2.07049	0.308650
$46$	3.19263	0.470727
$47$	−8.14609	−1.18823	−0.594115	−	0.804380i	$-0.702498\pi$
$47$	−8.14609	−1.18823	−0.594115	+	0.804380i	$0.702498\pi$
$48$	1.12331	0.162135
$49$	−4.06008	−0.580012
$50$	1.93188	0.273210
$51$	0.385290	0.0539514
$52$	−4.11555	−0.570725
$53$	−0.401204	−0.0551096	−0.0275548	−	0.999620i	$-0.508772\pi$
$53$	−0.401204	−0.0551096	−0.0275548	+	0.999620i	$0.508772\pi$
$54$	0.973781	0.132515
$55$	1.20815	0.162907
$56$	2.82415	0.377393
$57$	2.47232	0.327467
$58$	1.99825	0.262383
$59$	1.00000	0.130189
$59$	1.00000	0.130189
$60$	0.507322	0.0654950
$61$	0.400125	0.0512307	0.0256154	−	0.999672i	$-0.491845\pi$
$61$	0.400125	0.0512307	0.0256154	+	0.999672i	$0.491845\pi$
$62$	4.29543	0.545521
$63$	−4.88932	−0.615997
$64$	−3.86423	−0.483029
$65$	−1.64784	−0.204389
$66$	0.276899	0.0340839
$67$	11.3020	1.38076	0.690380	−	0.723447i	$-0.257444\pi$
$67$	11.3020	1.38076	0.690380	+	0.723447i	$0.257444\pi$
$68$	−1.81345	−0.219913
$69$	−2.84796	−0.342854
$70$	0.537726	0.0642706
$71$	−13.0408	−1.54766	−0.773830	−	0.633394i	$-0.781661\pi$
$71$	−13.0408	−1.54766	−0.773830	+	0.633394i	$0.781661\pi$
$72$	−4.69679	−0.553522
$73$	−10.7195	−1.25462	−0.627312	−	0.778768i	$-0.715845\pi$
$73$	−10.7195	−1.25462	−0.627312	+	0.778768i	$0.715845\pi$
$74$	0.255518	0.0297034
$75$	−1.72332	−0.198992
$76$	−11.6365	−1.33480
$77$	−2.85298	−0.325127
$78$	−0.377671	−0.0427629
$79$	−15.2814	−1.71929	−0.859647	−	0.510889i	$-0.829316\pi$
$79$	−15.2814	−1.71929	−0.859647	+	0.510889i	$0.829316\pi$
$80$	−2.11690	−0.236677
$81$	7.68600	0.854000
$82$	0.284821	0.0314532
$83$	2.53437	0.278183	0.139092	−	0.990279i	$-0.455582\pi$
$83$	2.53437	0.278183	0.139092	+	0.990279i	$0.455582\pi$
$84$	−1.19801	−0.130714
$85$	−0.726091	−0.0787556
$86$	−2.48727	−0.268209
$87$	−1.78252	−0.191106
$88$	−2.74064	−0.292153
$89$	−13.4826	−1.42915	−0.714575	−	0.699559i	$-0.753380\pi$
$89$	−13.4826	−1.42915	−0.714575	+	0.699559i	$0.753380\pi$
$90$	−0.894283	−0.0942657
$91$	3.89127	0.407916
$92$	13.4045	1.39751
$93$	−3.83171	−0.397330
$94$	3.51845	0.362901
$95$	−4.65917	−0.478021
$96$	−1.75440	−0.179058
$97$	10.5183	1.06798	0.533988	−	0.845492i	$-0.320693\pi$
$97$	10.5183	1.06798	0.533988	+	0.845492i	$0.320693\pi$
$98$	1.75363	0.177143
$99$	4.74474	0.476864
$100$	8.11117	0.811117
$101$	16.6060	1.65236	0.826181	−	0.563404i	$-0.190509\pi$
$101$	16.6060	1.65236	0.826181	+	0.563404i	$0.190509\pi$
$102$	−0.166414	−0.0164775
$103$	4.42859	0.436362	0.218181	−	0.975908i	$-0.429988\pi$
$103$	4.42859	0.436362	0.218181	+	0.975908i	$0.429988\pi$
$104$	3.73804	0.366545
$105$	−0.479675	−0.0468114
$106$	0.173288	0.0168312
$107$	−12.5594	−1.21417	−0.607084	−	0.794638i	$-0.707661\pi$
$107$	−12.5594	−1.21417	−0.607084	+	0.794638i	$0.707661\pi$
$108$	4.08850	0.393416
$109$	−12.8128	−1.22724	−0.613620	−	0.789602i	$-0.710287\pi$
$109$	−12.8128	−1.22724	−0.613620	+	0.789602i	$0.710287\pi$
$110$	−0.521825	−0.0497541
$111$	−0.227933	−0.0216344
$112$	4.99893	0.472355
$113$	11.3286	1.06570	0.532851	−	0.846209i	$-0.321121\pi$
$113$	11.3286	1.06570	0.532851	+	0.846209i	$0.321121\pi$
$114$	−1.06784	−0.100013
$115$	5.36706	0.500481
$116$	8.38980	0.778973
$117$	−6.47150	−0.598290
$118$	−0.431919	−0.0397614
$119$	1.71462	0.157179
$120$	−0.460786	−0.0420638
$121$	−8.23139	−0.748308
$122$	−0.172822	−0.0156465
$123$	−0.254072	−0.0229089
$124$	18.0347	1.61957
$125$	6.87811	0.615197
$126$	2.11179	0.188133
$127$	−13.7000	−1.21568	−0.607839	−	0.794061i	$-0.707963\pi$
$127$	−13.7000	−1.21568	−0.607839	+	0.794061i	$0.707963\pi$
$128$	10.7759	0.952467
$129$	2.21875	0.195350
$130$	0.711733	0.0624231
$131$	−1.36833	−0.119552	−0.0597758	−	0.998212i	$-0.519039\pi$
$131$	−1.36833	−0.119552	−0.0597758	+	0.998212i	$0.519039\pi$
$132$	1.16258	0.101190
$133$	11.0023	0.954024
$134$	−4.88155	−0.421702
$135$	1.63701	0.140891
$136$	1.64710	0.141238
$137$	1.35289	0.115585	0.0577926	−	0.998329i	$-0.481594\pi$
$137$	1.35289	0.115585	0.0577926	+	0.998329i	$0.481594\pi$
$138$	1.23009	0.104712
$139$	0.609409	0.0516894	0.0258447	−	0.999666i	$-0.491772\pi$
$139$	0.609409	0.0516894	0.0258447	+	0.999666i	$0.491772\pi$
$140$	2.25768	0.190809
$141$	−3.13861	−0.264319
$142$	5.63258	0.472675
$143$	−3.77620	−0.315782
$144$	−8.31363	−0.692803
$145$	3.35922	0.278968
$146$	4.62996	0.383179
$147$	−1.56431	−0.129022
$148$	1.07281	0.0881847
$149$	−11.9518	−0.979127	−0.489564	−	0.871968i	$-0.662844\pi$
$149$	−11.9518	−0.979127	−0.489564	+	0.871968i	$0.662844\pi$
$150$	0.744336	0.0607748
$151$	19.4366	1.58173	0.790864	−	0.611992i	$-0.209631\pi$
$151$	19.4366	1.58173	0.790864	+	0.611992i	$0.209631\pi$
$152$	10.5691	0.857266
$153$	−2.85155	−0.230534
$154$	1.23226	0.0992981
$155$	7.22097	0.580003
$156$	−1.58568	−0.126956
$157$	0.839065	0.0669647	0.0334823	−	0.999439i	$-0.489340\pi$
$157$	0.839065	0.0669647	0.0334823	+	0.999439i	$0.489340\pi$
$158$	6.60033	0.525094
$159$	−0.154580	−0.0122590
$160$	3.30622	0.261380
$161$	−12.6740	−0.998850
$162$	−3.31973	−0.260823
$163$	−7.35197	−0.575851	−0.287925	−	0.957653i	$-0.592966\pi$
$163$	−7.35197	−0.575851	−0.287925	+	0.957653i	$0.592966\pi$
$164$	1.19584	0.0933795
$165$	0.465490	0.0362384
$166$	−1.09464	−0.0849608
$167$	23.7254	1.83593	0.917963	−	0.396667i	$-0.129833\pi$
$167$	23.7254	1.83593	0.917963	+	0.396667i	$0.129833\pi$
$168$	1.08812	0.0839500
$169$	−7.84953	−0.603810
$170$	0.313613	0.0240530
$171$	−18.2978	−1.39927
$172$	−10.4430	−0.796270
$173$	16.5411	1.25759	0.628797	−	0.777569i	$-0.283548\pi$
$173$	16.5411	1.25759	0.628797	+	0.777569i	$0.283548\pi$
$174$	0.769906	0.0583664
$175$	−7.66913	−0.579732
$176$	−4.85111	−0.365666
$177$	0.385290	0.0289602
$178$	5.82338	0.436481
$179$	−24.1573	−1.80560	−0.902801	−	0.430059i	$-0.858493\pi$
$179$	−24.1573	−1.80560	−0.902801	+	0.430059i	$0.858493\pi$
$180$	−3.75471	−0.279860
$181$	19.8736	1.47720	0.738598	−	0.674146i	$-0.235488\pi$
$181$	19.8736	1.47720	0.738598	+	0.674146i	$0.235488\pi$
$182$	−1.68071	−0.124583
$183$	0.154164	0.0113961
$184$	−12.1749	−0.897546
$185$	0.429547	0.0315809
$186$	1.65499	0.121350
$187$	−1.66392	−0.121678
$188$	14.7725	1.07739
$189$	−3.86569	−0.281187
$190$	2.01238	0.145994
$191$	1.47771	0.106924	0.0534619	−	0.998570i	$-0.482974\pi$
$191$	1.47771	0.106924	0.0534619	+	0.998570i	$0.482974\pi$
$192$	−1.48885	−0.107449
$193$	15.7160	1.13126	0.565630	−	0.824659i	$-0.308633\pi$
$193$	15.7160	1.13126	0.565630	+	0.824659i	$0.308633\pi$
$194$	−4.54307	−0.326174
$195$	−0.634896	−0.0454659
$196$	7.36274	0.525910
$197$	−0.0318413	−0.00226860	−0.00113430	−	0.999999i	$-0.500361\pi$
$197$	−0.0318413	−0.00226860	−0.00113430	+	0.999999i	$0.500361\pi$
$198$	−2.04934	−0.145641
$199$	17.5701	1.24551	0.622757	−	0.782415i	$-0.286013\pi$
$199$	17.5701	1.24551	0.622757	+	0.782415i	$0.286013\pi$
$200$	−7.36714	−0.520935
$201$	4.35455	0.307146
$202$	−7.17247	−0.504653
$203$	−7.93258	−0.556758
$204$	−0.698703	−0.0489190
$205$	0.478807	0.0334413
$206$	−1.91279	−0.133271
$207$	21.0779	1.46501
$208$	6.61658	0.458777
$209$	−10.6770	−0.738543
$210$	0.207181	0.0142968
$211$	−9.53181	−0.656197	−0.328098	−	0.944644i	$-0.606408\pi$
$211$	−9.53181	−0.656197	−0.328098	+	0.944644i	$0.606408\pi$
$212$	0.727561	0.0499691
$213$	−5.02450	−0.344273
$214$	5.42466	0.370822
$215$	−4.18130	−0.285162
$216$	−3.71346	−0.252669
$217$	−17.0519	−1.15756
$218$	5.53407	0.374815
$219$	−4.13012	−0.279088
$220$	−2.19092	−0.147712
$221$	2.26947	0.152661
$222$	0.0984486	0.00660744
$223$	24.1917	1.62000	0.809999	−	0.586431i	$-0.199468\pi$
$223$	24.1917	1.62000	0.809999	+	0.586431i	$0.199468\pi$
$224$	−7.80743	−0.521656
$225$	12.7544	0.850293
$226$	−4.89302	−0.325479
$227$	17.8855	1.18710	0.593550	−	0.804797i	$-0.297726\pi$
$227$	17.8855	1.18710	0.593550	+	0.804797i	$0.297726\pi$
$228$	−4.48343	−0.296922
$229$	−4.41432	−0.291706	−0.145853	−	0.989306i	$-0.546593\pi$
$229$	−4.41432	−0.291706	−0.145853	+	0.989306i	$0.546593\pi$
$230$	−2.31814	−0.152853
$231$	−1.09923	−0.0723237
$232$	−7.62021	−0.500291
$233$	−11.7301	−0.768467	−0.384233	−	0.923236i	$-0.625534\pi$
$233$	−11.7301	−0.768467	−0.384233	+	0.923236i	$0.625534\pi$
$234$	2.79516	0.182726
$235$	5.91481	0.385839
$236$	−1.81345	−0.118045
$237$	−5.88778	−0.382452
$238$	−0.740577	−0.0480044
$239$	−17.7376	−1.14735	−0.573676	−	0.819082i	$-0.694483\pi$
$239$	−17.7376	−1.14735	−0.573676	+	0.819082i	$0.694483\pi$
$240$	−0.815622	−0.0526482
$241$	6.04217	0.389210	0.194605	−	0.980882i	$-0.437657\pi$
$241$	6.04217	0.389210	0.194605	+	0.980882i	$0.437657\pi$
$242$	3.55529	0.228543
$243$	9.72498	0.623858
$244$	−0.725605	−0.0464521
$245$	2.94799	0.188340
$246$	0.109739	0.00699668
$247$	14.5627	0.926600
$248$	−16.3804	−1.04016
$249$	0.976469	0.0618812
$250$	−2.97079	−0.187889
$251$	16.2690	1.02689	0.513444	−	0.858123i	$-0.328369\pi$
$251$	16.2690	1.02689	0.513444	+	0.858123i	$0.328369\pi$
$252$	8.86652	0.558538
$253$	12.2992	0.773244
$254$	5.91729	0.371284
$255$	−0.279756	−0.0175190
$256$	3.07413	0.192133
$257$	5.03686	0.314191	0.157095	−	0.987583i	$-0.449787\pi$
$257$	5.03686	0.314191	0.157095	+	0.987583i	$0.449787\pi$
$258$	−0.958320	−0.0596624
$259$	−1.01435	−0.0630285
$260$	2.98827	0.185324
$261$	13.1925	0.816597
$262$	0.591008	0.0365126
$263$	−28.0282	−1.72829	−0.864146	−	0.503241i	$-0.832141\pi$
$263$	−28.0282	−1.72829	−0.864146	+	0.503241i	$0.832141\pi$
$264$	−1.05594	−0.0649886
$265$	0.291310	0.0178951
$266$	−4.75212	−0.291371
$267$	−5.19470	−0.317911
$268$	−20.4956	−1.25197
$269$	−31.5245	−1.92208	−0.961042	−	0.276402i	$-0.910858\pi$
$269$	−31.5245	−1.92208	−0.961042	+	0.276402i	$0.910858\pi$
$270$	−0.707054	−0.0430299
$271$	26.8012	1.62806	0.814029	−	0.580824i	$-0.197270\pi$
$271$	26.8012	1.62806	0.814029	+	0.580824i	$0.197270\pi$
$272$	2.91548	0.176777
$273$	1.49927	0.0907398
$274$	−0.584339	−0.0353012
$275$	7.44235	0.448790
$276$	5.16462	0.310873
$277$	−17.3265	−1.04105	−0.520525	−	0.853846i	$-0.674264\pi$
$277$	−17.3265	−1.04105	−0.520525	+	0.853846i	$0.674264\pi$
$278$	−0.263215	−0.0157866
$279$	28.3587	1.69779
$280$	−2.05059	−0.122546
$281$	6.29330	0.375427	0.187713	−	0.982224i	$-0.439892\pi$
$281$	6.29330	0.375427	0.187713	+	0.982224i	$0.439892\pi$
$282$	1.35563	0.0807263
$283$	−16.1267	−0.958631	−0.479315	−	0.877643i	$-0.659115\pi$
$283$	−16.1267	−0.958631	−0.479315	+	0.877643i	$0.659115\pi$
$284$	23.6488	1.40330
$285$	−1.79513	−0.106334
$286$	1.63101	0.0964438
$287$	−1.13067	−0.0667415
$288$	12.9844	0.765113
$289$	1.00000	0.0588235
$290$	−1.45091	−0.0852004
$291$	4.05261	0.237568
$292$	19.4393	1.13760
$293$	−8.02343	−0.468734	−0.234367	−	0.972148i	$-0.575302\pi$
$293$	−8.02343	−0.468734	−0.234367	+	0.972148i	$0.575302\pi$
$294$	0.675655	0.0394050
$295$	−0.726091	−0.0422747
$296$	−0.974405	−0.0566361
$297$	3.75137	0.217677
$298$	5.16220	0.299038
$299$	−16.7753	−0.970138
$300$	3.12515	0.180431
$301$	9.87387	0.569121
$302$	−8.39504	−0.483080
$303$	6.39814	0.367564
$304$	18.7080	1.07298
$305$	−0.290527	−0.0166355
$306$	1.23164	0.0704081
$307$	18.6738	1.06577	0.532885	−	0.846187i	$-0.321108\pi$
$307$	18.6738	1.06577	0.532885	+	0.846187i	$0.321108\pi$
$308$	5.17373	0.294800
$309$	1.70629	0.0970676
$310$	−3.11888	−0.177140
$311$	−31.2511	−1.77209	−0.886045	−	0.463600i	$-0.846557\pi$
$311$	−31.2511	−1.77209	−0.886045	+	0.463600i	$0.846557\pi$
$312$	1.44023	0.0815369
$313$	22.0236	1.24484	0.622422	−	0.782681i	$-0.286149\pi$
$313$	22.0236	1.24484	0.622422	+	0.782681i	$0.286149\pi$
$314$	−0.362408	−0.0204519
$315$	3.55009	0.200025
$316$	27.7120	1.55892
$317$	11.0525	0.620772	0.310386	−	0.950611i	$-0.399542\pi$
$317$	11.0525	0.620772	0.310386	+	0.950611i	$0.399542\pi$
$318$	0.0667660	0.00374405
$319$	7.69801	0.431006
$320$	2.80579	0.156848
$321$	−4.83903	−0.270088
$322$	5.47413	0.305062
$323$	6.41678	0.357039
$324$	−13.9381	−0.774341
$325$	−10.1508	−0.563068
$326$	3.17546	0.175872
$327$	−4.93663	−0.272996
$328$	−1.08615	−0.0599725
$329$	−13.9674	−0.770050
$330$	−0.201054	−0.0110677
$331$	34.8243	1.91412	0.957059	−	0.289892i	$-0.0936194\pi$
$331$	34.8243	1.91412	0.957059	+	0.289892i	$0.0936194\pi$
$332$	−4.59595	−0.252235
$333$	1.68694	0.0924439
$334$	−10.2474	−0.560715
$335$	−8.20628	−0.448357
$336$	1.92604	0.105074
$337$	−24.3011	−1.32377	−0.661883	−	0.749607i	$-0.730243\pi$
$337$	−24.3011	−1.32377	−0.661883	+	0.749607i	$0.730243\pi$
$338$	3.39036	0.184411
$339$	4.36478	0.237062
$340$	1.31673	0.0714096
$341$	16.5476	0.896105
$342$	7.90316	0.427354
$343$	−18.9638	−1.02395
$344$	9.48506	0.511400
$345$	2.06788	0.111331
$346$	−7.14441	−0.384086
$347$	−10.0184	−0.537815	−0.268908	−	0.963166i	$-0.586663\pi$
$347$	−10.0184	−0.537815	−0.268908	+	0.963166i	$0.586663\pi$
$348$	3.23251	0.173281
$349$	−6.26283	−0.335242	−0.167621	−	0.985852i	$-0.553608\pi$
$349$	−6.26283	−0.335242	−0.167621	+	0.985852i	$0.553608\pi$
$350$	3.31244	0.177058
$351$	−5.11661	−0.273105
$352$	7.57656	0.403832
$353$	−1.63136	−0.0868283	−0.0434142	−	0.999057i	$-0.513824\pi$
$353$	−1.63136	−0.0868283	−0.0434142	+	0.999057i	$0.513824\pi$
$354$	−0.166414	−0.00884482
$355$	9.46882	0.502553
$356$	24.4499	1.29584
$357$	0.660626	0.0349640
$358$	10.4340	0.551454
$359$	21.2803	1.12313	0.561565	−	0.827433i	$-0.310199\pi$
$359$	21.2803	1.12313	0.561565	+	0.827433i	$0.310199\pi$
$360$	3.41030	0.179739
$361$	22.1751	1.16711
$362$	−8.58381	−0.451155
$363$	−3.17147	−0.166459
$364$	−7.05660	−0.369867
$365$	7.78335	0.407399
$366$	−0.0665865	−0.00348053
$367$	12.5048	0.652744	0.326372	−	0.945241i	$-0.394174\pi$
$367$	12.5048	0.652744	0.326372	+	0.945241i	$0.394174\pi$
$368$	−21.5504	−1.12339
$369$	1.88040	0.0978897
$370$	−0.185529	−0.00964522
$371$	−0.687911	−0.0357146
$372$	6.94860	0.360268
$373$	−24.3340	−1.25997	−0.629983	−	0.776609i	$-0.716938\pi$
$373$	−24.3340	−1.25997	−0.629983	+	0.776609i	$0.716938\pi$
$374$	0.718677	0.0371619
$375$	2.65007	0.136849
$376$	−13.4174	−0.691951
$377$	−10.4995	−0.540754
$378$	1.66966	0.0858782
$379$	−16.4902	−0.847042	−0.423521	−	0.905886i	$-0.639206\pi$
$379$	−16.4902	−0.847042	−0.423521	+	0.905886i	$0.639206\pi$
$380$	8.44915	0.433432
$381$	−5.27847	−0.270424
$382$	−0.638253	−0.0326559
$383$	−18.2410	−0.932073	−0.466036	−	0.884766i	$-0.654318\pi$
$383$	−18.2410	−0.932073	−0.466036	+	0.884766i	$0.654318\pi$
$384$	4.15186	0.211874
$385$	2.07152	0.105575
$386$	−6.78802	−0.345501
$387$	−16.4211	−0.834729
$388$	−19.0744	−0.968358
$389$	−33.3039	−1.68857	−0.844287	−	0.535891i	$-0.819976\pi$
$389$	−33.3039	−1.68857	−0.844287	+	0.535891i	$0.819976\pi$
$390$	0.274224	0.0138859
$391$	−7.39172	−0.373815
$392$	−6.68736	−0.337763
$393$	−0.527204	−0.0265939
$394$	0.0137529	0.000692860 0
$395$	11.0957	0.558285
$396$	−8.60433	−0.432384
$397$	23.1340	1.16106	0.580530	−	0.814239i	$-0.302845\pi$
$397$	23.1340	1.16106	0.580530	+	0.814239i	$0.302845\pi$
$398$	−7.58888	−0.380396
$399$	4.23909	0.212220
$400$	−13.0403	−0.652016
$401$	−24.3570	−1.21633	−0.608166	−	0.793810i	$-0.708094\pi$
$401$	−24.3570	−1.21633	−0.608166	+	0.793810i	$0.708094\pi$
$402$	−1.88081	−0.0938064
$403$	−22.5698	−1.12428
$404$	−30.1142	−1.49824
$405$	−5.58074	−0.277309
$406$	3.42623	0.170041
$407$	0.984352	0.0487925
$408$	0.634612	0.0314180
$409$	−11.2571	−0.556629	−0.278314	−	0.960490i	$-0.589776\pi$
$409$	−11.2571	−0.556629	−0.278314	+	0.960490i	$0.589776\pi$
$410$	−0.206806	−0.0102134
$411$	0.521255	0.0257116
$412$	−8.03101	−0.395660
$413$	1.71462	0.0843709
$414$	−9.10393	−0.447434
$415$	−1.84019	−0.0903311
$416$	−10.3339	−0.506661
$417$	0.234799	0.0114982
$418$	4.61159	0.225560
$419$	13.6268	0.665713	0.332857	−	0.942977i	$-0.391987\pi$
$419$	13.6268	0.665713	0.332857	+	0.942977i	$0.391987\pi$
$420$	0.869864	0.0424450
$421$	−26.5384	−1.29340	−0.646702	−	0.762743i	$-0.723852\pi$
$421$	−26.5384	−1.29340	−0.646702	+	0.762743i	$0.723852\pi$
$422$	4.11697	0.200411
$423$	23.2290	1.12943
$424$	−0.660823	−0.0320924
$425$	−4.47279	−0.216962
$426$	2.17018	0.105145
$427$	0.686061	0.0332008
$428$	22.7759	1.10091
$429$	−1.45493	−0.0702448
$430$	1.80598	0.0870922
$431$	24.3608	1.17342	0.586709	−	0.809798i	$-0.300423\pi$
$431$	24.3608	1.17342	0.586709	+	0.809798i	$0.300423\pi$
$432$	−6.57308	−0.316247
$433$	6.24829	0.300274	0.150137	−	0.988665i	$-0.452029\pi$
$433$	6.24829	0.300274	0.150137	+	0.988665i	$0.452029\pi$
$434$	7.36503	0.353533
$435$	1.29427	0.0620557
$436$	23.2352	1.11277
$437$	−47.4311	−2.26894
$438$	1.78388	0.0852371
$439$	−0.375330	−0.0179135	−0.00895676	−	0.999960i	$-0.502851\pi$
$439$	−0.375330	−0.0179135	−0.00895676	+	0.999960i	$0.502851\pi$
$440$	1.98995	0.0948672
$441$	11.5775	0.551311
$442$	−0.980226	−0.0466246
$443$	22.8160	1.08402	0.542011	−	0.840371i	$-0.317663\pi$
$443$	22.8160	1.08402	0.542011	+	0.840371i	$0.317663\pi$
$444$	0.413344	0.0196164
$445$	9.78957	0.464070
$446$	−10.4489	−0.494768
$447$	−4.60490	−0.217804
$448$	−6.62569	−0.313034
$449$	13.8145	0.651945	0.325972	−	0.945379i	$-0.394308\pi$
$449$	13.8145	0.651945	0.325972	+	0.945379i	$0.394308\pi$
$450$	−5.50887	−0.259690
$451$	1.09724	0.0516669
$452$	−20.5437	−0.966296
$453$	7.48873	0.351851
$454$	−7.72508	−0.362556
$455$	−2.82542	−0.132458
$456$	4.07216	0.190697
$457$	−16.8364	−0.787574	−0.393787	−	0.919202i	$-0.628835\pi$
$457$	−16.8364	−0.787574	−0.393787	+	0.919202i	$0.628835\pi$
$458$	1.90663	0.0890909
$459$	−2.25455	−0.105233
$460$	−9.73288	−0.453798
$461$	−18.3575	−0.854994	−0.427497	−	0.904017i	$-0.640605\pi$
$461$	−18.3575	−0.854994	−0.427497	+	0.904017i	$0.640605\pi$
$462$	0.474776	0.0220886
$463$	28.8569	1.34110	0.670548	−	0.741866i	$-0.266059\pi$
$463$	28.8569	1.34110	0.670548	+	0.741866i	$0.266059\pi$
$464$	−13.4883	−0.626178
$465$	2.78217	0.129020
$466$	5.06647	0.234700
$467$	−17.5037	−0.809975	−0.404988	−	0.914322i	$-0.632724\pi$
$467$	−17.5037	−0.809975	−0.404988	+	0.914322i	$0.632724\pi$
$468$	11.7357	0.542483
$469$	19.3786	0.894822
$470$	−2.55472	−0.117840
$471$	0.323284	0.0148961
$472$	1.64710	0.0758139
$473$	−9.58189	−0.440576
$474$	2.54304	0.116806
$475$	−28.7009	−1.31689
$476$	−3.10937	−0.142518
$477$	1.14405	0.0523826
$478$	7.66122	0.350416
$479$	12.1841	0.556706	0.278353	−	0.960479i	$-0.410211\pi$
$479$	12.1841	0.556706	0.278353	+	0.960479i	$0.410211\pi$
$480$	1.27385	0.0581432
$481$	−1.34259	−0.0612168
$482$	−2.60973	−0.118870
$483$	−4.88316	−0.222192
$484$	14.9272	0.678508
$485$	−7.63728	−0.346791
$486$	−4.20040	−0.190534
$487$	−18.4393	−0.835566	−0.417783	−	0.908547i	$-0.637193\pi$
$487$	−18.4393	−0.835566	−0.417783	+	0.908547i	$0.637193\pi$
$488$	0.659046	0.0298336
$489$	−2.83264	−0.128097
$490$	−1.27329	−0.0575215
$491$	7.92654	0.357720	0.178860	−	0.983875i	$-0.442759\pi$
$491$	7.92654	0.357720	0.178860	+	0.983875i	$0.442759\pi$
$492$	0.460746	0.0207720
$493$	−4.62644	−0.208364
$494$	−6.28990	−0.282996
$495$	−3.44511	−0.154846
$496$	−28.9944	−1.30189
$497$	−22.3600	−1.00298
$498$	−0.421756	−0.0188993
$499$	5.99049	0.268171	0.134086	−	0.990970i	$-0.457190\pi$
$499$	5.99049	0.268171	0.134086	+	0.990970i	$0.457190\pi$
$500$	−12.4731	−0.557813
$501$	9.14116	0.408397
$502$	−7.02688	−0.313625
$503$	6.25385	0.278845	0.139423	−	0.990233i	$-0.455475\pi$
$503$	6.25385	0.278845	0.139423	+	0.990233i	$0.455475\pi$
$504$	−8.05321	−0.358718
$505$	−12.0575	−0.536552
$506$	−5.31226	−0.236159
$507$	−3.02435	−0.134316
$508$	24.8442	1.10228
$509$	9.91739	0.439580	0.219790	−	0.975547i	$-0.429463\pi$
$509$	9.91739	0.439580	0.219790	+	0.975547i	$0.429463\pi$
$510$	0.120832	0.00535053
$511$	−18.3799	−0.813078
$512$	−22.8797	−1.01115
$513$	−14.4669	−0.638731
$514$	−2.17552	−0.0959579
$515$	−3.21556	−0.141695
$516$	−4.02358	−0.177128
$517$	13.5544	0.596122
$518$	0.438116	0.0192497
$519$	6.37311	0.279749
$520$	−2.71416	−0.119024
$521$	−11.0022	−0.482016	−0.241008	−	0.970523i	$-0.577478\pi$
$521$	−11.0022	−0.482016	−0.241008	+	0.970523i	$0.577478\pi$
$522$	−5.69811	−0.249399
$523$	−43.4949	−1.90190	−0.950949	−	0.309347i	$-0.899889\pi$
$523$	−43.4949	−1.90190	−0.950949	+	0.309347i	$0.899889\pi$
$524$	2.48139	0.108400
$525$	−2.95484	−0.128960
$526$	12.1059	0.527843
$527$	−9.94500	−0.433211
$528$	−1.86908	−0.0813415
$529$	31.6375	1.37554
$530$	−0.125823	−0.00546538
$531$	−2.85155	−0.123747
$532$	−19.9521	−0.865035
$533$	−1.49656	−0.0648230
$534$	2.24369	0.0970940
$535$	9.11930	0.394262
$536$	18.6155	0.804068
$537$	−9.30757	−0.401651
$538$	13.6160	0.587029
$539$	6.75563	0.290986
$540$	−2.96862	−0.127749
$541$	−6.32253	−0.271827	−0.135913	−	0.990721i	$-0.543397\pi$
$541$	−6.32253	−0.271827	−0.135913	+	0.990721i	$0.543397\pi$
$542$	−11.5760	−0.497230
$543$	7.65712	0.328599
$544$	−4.55345	−0.195228
$545$	9.30323	0.398506
$546$	−0.647562	−0.0277131
$547$	15.5196	0.663569	0.331784	−	0.943355i	$-0.392349\pi$
$547$	15.5196	0.663569	0.331784	+	0.943355i	$0.392349\pi$
$548$	−2.45339	−0.104804
$549$	−1.14098	−0.0486957
$550$	−3.21449	−0.137066
$551$	−29.6869	−1.26470
$552$	−4.69087	−0.199657
$553$	−26.2018	−1.11421
$554$	7.48366	0.317950
$555$	0.165500	0.00702509
$556$	−1.10513	−0.0468679
$557$	16.1518	0.684374	0.342187	−	0.939632i	$-0.388832\pi$
$557$	16.1518	0.684374	0.342187	+	0.939632i	$0.388832\pi$
$558$	−12.2487	−0.518527
$559$	13.0690	0.552761
$560$	−3.62968	−0.153382
$561$	−0.641090	−0.0270669
$562$	−2.71820	−0.114660
$563$	−2.16778	−0.0913610	−0.0456805	−	0.998956i	$-0.514546\pi$
$563$	−2.16778	−0.0913610	−0.0456805	+	0.998956i	$0.514546\pi$
$564$	5.69170	0.239664
$565$	−8.22557	−0.346052
$566$	6.96542	0.292778
$567$	13.1786	0.553447
$568$	−21.4795	−0.901261
$569$	11.5103	0.482538	0.241269	−	0.970458i	$-0.422436\pi$
$569$	11.5103	0.482538	0.241269	+	0.970458i	$0.422436\pi$
$570$	0.775352	0.0324759
$571$	−0.920427	−0.0385187	−0.0192593	−	0.999815i	$-0.506131\pi$
$571$	−0.920427	−0.0385187	−0.0192593	+	0.999815i	$0.506131\pi$
$572$	6.84793	0.286326
$573$	0.569349	0.0237849
$574$	0.488359	0.0203837
$575$	33.0616	1.37876
$576$	11.0191	0.459127
$577$	−21.9480	−0.913706	−0.456853	−	0.889542i	$-0.651024\pi$
$577$	−21.9480	−0.913706	−0.456853	+	0.889542i	$0.651024\pi$
$578$	−0.431919	−0.0179655
$579$	6.05521	0.251646
$580$	−6.09176	−0.252947
$581$	4.34548	0.180281
$582$	−1.75040	−0.0725565
$583$	0.667569	0.0276479
$584$	−17.6561	−0.730615
$585$	4.69890	0.194276
$586$	3.46547	0.143157
$587$	27.9487	1.15357	0.576783	−	0.816897i	$-0.304308\pi$
$587$	27.9487	1.15357	0.576783	+	0.816897i	$0.304308\pi$
$588$	2.83679	0.116987
$589$	−63.8149	−2.62945
$590$	0.313613	0.0129112
$591$	−0.0122681	−0.000504644 0
$592$	−1.72476	−0.0708873
$593$	−5.45449	−0.223989	−0.111995	−	0.993709i	$-0.535724\pi$
$593$	−5.45449	−0.223989	−0.111995	+	0.993709i	$0.535724\pi$
$594$	−1.62029	−0.0664813
$595$	−1.24497	−0.0510388
$596$	21.6739	0.887797
$597$	6.76960	0.277061
$598$	7.24555	0.296293
$599$	15.7878	0.645071	0.322536	−	0.946557i	$-0.395465\pi$
$599$	15.7878	0.645071	0.322536	+	0.946557i	$0.395465\pi$
$600$	−2.83849	−0.115881
$601$	43.3259	1.76730	0.883649	−	0.468149i	$-0.155079\pi$
$601$	43.3259	1.76730	0.883649	+	0.468149i	$0.155079\pi$
$602$	−4.26471	−0.173817
$603$	−32.2282	−1.31244
$604$	−35.2472	−1.43419
$605$	5.97674	0.242989
$606$	−2.76348	−0.112259
$607$	24.9044	1.01084	0.505418	−	0.862874i	$-0.331338\pi$
$607$	24.9044	1.01084	0.505418	+	0.862874i	$0.331338\pi$
$608$	−29.2185	−1.18497
$609$	−3.05635	−0.123849
$610$	0.125484	0.00508071
$611$	−18.4873	−0.747915
$612$	5.17113	0.209031
$613$	23.9207	0.966148	0.483074	−	0.875579i	$-0.339520\pi$
$613$	23.9207	0.966148	0.483074	+	0.875579i	$0.339520\pi$
$614$	−8.06558	−0.325500
$615$	0.184480	0.00743893
$616$	−4.69914	−0.189334
$617$	−47.4025	−1.90835	−0.954177	−	0.299242i	$-0.903266\pi$
$617$	−47.4025	−1.90835	−0.954177	+	0.299242i	$0.903266\pi$
$618$	−0.736981	−0.0296457
$619$	33.4463	1.34432	0.672159	−	0.740407i	$-0.265367\pi$
$619$	33.4463	1.34432	0.672159	+	0.740407i	$0.265367\pi$
$620$	−13.0948	−0.525902
$621$	16.6650	0.668742
$622$	13.4980	0.541219
$623$	−23.1175	−0.926181
$624$	2.54930	0.102054
$625$	17.3698	0.694793
$626$	−9.51239	−0.380192
$627$	−4.11374	−0.164287
$628$	−1.52160	−0.0607184
$629$	−0.591588	−0.0235882
$630$	−1.53335	−0.0610903
$631$	40.8680	1.62693	0.813465	−	0.581614i	$-0.197579\pi$
$631$	40.8680	1.62693	0.813465	+	0.581614i	$0.197579\pi$
$632$	−25.1700	−1.00121
$633$	−3.67251	−0.145969
$634$	−4.77380	−0.189592
$635$	9.94744	0.394752
$636$	0.280322	0.0111155
$637$	−9.21422	−0.365081
$638$	−3.32492	−0.131635
$639$	37.1865	1.47108
$640$	−7.82431	−0.309283
$641$	−29.0732	−1.14832	−0.574161	−	0.818742i	$-0.694672\pi$
$641$	−29.0732	−1.14832	−0.574161	+	0.818742i	$0.694672\pi$
$642$	2.09007	0.0824885
$643$	4.65001	0.183378	0.0916891	−	0.995788i	$-0.470773\pi$
$643$	4.65001	0.183378	0.0916891	+	0.995788i	$0.470773\pi$
$644$	22.9836	0.905680
$645$	−1.61101	−0.0634336
$646$	−2.77153	−0.109044
$647$	−32.0901	−1.26159	−0.630795	−	0.775949i	$-0.717271\pi$
$647$	−32.0901	−1.26159	−0.630795	+	0.775949i	$0.717271\pi$
$648$	12.6596	0.497317
$649$	−1.66392	−0.0653144
$650$	4.38434	0.171968
$651$	−6.56992	−0.257496
$652$	13.3324	0.522137
$653$	−24.7941	−0.970268	−0.485134	−	0.874440i	$-0.661229\pi$
$653$	−24.7941	−0.970268	−0.485134	+	0.874440i	$0.661229\pi$
$654$	2.13222	0.0833766
$655$	0.993532	0.0388205
$656$	−1.92256	−0.0750632
$657$	30.5673	1.19254
$658$	6.03280	0.235183
$659$	8.17979	0.318639	0.159320	−	0.987227i	$-0.449070\pi$
$659$	8.17979	0.318639	0.159320	+	0.987227i	$0.449070\pi$
$660$	−0.844141	−0.0328581
$661$	−42.3639	−1.64776	−0.823882	−	0.566761i	$-0.808196\pi$
$661$	−42.3639	−1.64776	−0.823882	+	0.566761i	$0.808196\pi$
$662$	−15.0413	−0.584597
$663$	0.874403	0.0339590
$664$	4.17436	0.161997
$665$	−7.98870	−0.309788
$666$	−0.728623	−0.0282336
$667$	34.1974	1.32413
$668$	−43.0247	−1.66468
$669$	9.32083	0.360364
$670$	3.54445	0.136934
$671$	−0.665774	−0.0257019
$672$	−3.00813	−0.116041
$673$	−24.3973	−0.940447	−0.470223	−	0.882547i	$-0.655827\pi$
$673$	−24.3973	−0.940447	−0.470223	+	0.882547i	$0.655827\pi$
$674$	10.4961	0.404295
$675$	10.0841	0.388138
$676$	14.2347	0.547488
$677$	−41.0916	−1.57928	−0.789640	−	0.613570i	$-0.789733\pi$
$677$	−41.0916	−1.57928	−0.789640	+	0.613570i	$0.789733\pi$
$678$	−1.88523	−0.0724019
$679$	18.0349	0.692118
$680$	−1.19594	−0.0458624
$681$	6.89110	0.264067
$682$	−7.14724	−0.273682
$683$	−32.1963	−1.23196	−0.615978	−	0.787763i	$-0.711239\pi$
$683$	−32.1963	−1.23196	−0.615978	+	0.787763i	$0.711239\pi$
$684$	33.1820	1.26875
$685$	−0.982321	−0.0375326
$686$	8.19084	0.312728
$687$	−1.70079	−0.0648894
$688$	16.7892	0.640082
$689$	−0.910518	−0.0346880
$690$	−0.893155	−0.0340018
$691$	3.53471	0.134467	0.0672334	−	0.997737i	$-0.478583\pi$
$691$	3.53471	0.134467	0.0672334	+	0.997737i	$0.478583\pi$
$692$	−29.9963	−1.14029
$693$	8.13542	0.309039
$694$	4.32713	0.164256
$695$	−0.442486	−0.0167845
$696$	−2.93599	−0.111289
$697$	−0.659431	−0.0249777
$698$	2.70504	0.102387
$699$	−4.51951	−0.170943
$700$	13.9076	0.525656
$701$	41.6373	1.57262	0.786309	−	0.617833i	$-0.211989\pi$
$701$	41.6373	1.57262	0.786309	+	0.617833i	$0.211989\pi$
$702$	2.20996	0.0834097
$703$	−3.79609	−0.143172
$704$	6.42976	0.242331
$705$	2.27892	0.0858290
$706$	0.704614	0.0265185
$707$	28.4730	1.07084
$708$	−0.698703	−0.0262589
$709$	−15.0992	−0.567061	−0.283531	−	0.958963i	$-0.591506\pi$
$709$	−15.0992	−0.567061	−0.283531	+	0.958963i	$0.591506\pi$
$710$	−4.08976	−0.153486
$711$	43.5757	1.63422
$712$	−22.2071	−0.832248
$713$	73.5106	2.75299
$714$	−0.285337	−0.0106785
$715$	2.74186	0.102540
$716$	43.8080	1.63718
$717$	−6.83414	−0.255225
$718$	−9.19136	−0.343019
$719$	−23.9707	−0.893957	−0.446979	−	0.894545i	$-0.647500\pi$
$719$	−23.9707	−0.893957	−0.446979	+	0.894545i	$0.647500\pi$
$720$	6.03646	0.224965
$721$	7.59335	0.282791
$722$	−9.57785	−0.356451
$723$	2.32799	0.0865788
$724$	−36.0398	−1.33941
$725$	20.6931	0.768523
$726$	1.36982	0.0508388
$727$	4.58619	0.170093	0.0850463	−	0.996377i	$-0.472896\pi$
$727$	4.58619	0.170093	0.0850463	+	0.996377i	$0.472896\pi$
$728$	6.40931	0.237545
$729$	−19.3111	−0.715225
$730$	−3.36178	−0.124425
$731$	5.75864	0.212991
$732$	−0.279568	−0.0103331
$733$	−45.9595	−1.69755	−0.848776	−	0.528752i	$-0.822660\pi$
$733$	−45.9595	−1.69755	−0.848776	+	0.528752i	$0.822660\pi$
$734$	−5.40105	−0.199356
$735$	1.13583	0.0418958
$736$	33.6578	1.24064
$737$	−18.8056	−0.692712
$738$	−0.812181	−0.0298968
$739$	34.0895	1.25400	0.627002	−	0.779018i	$-0.284282\pi$
$739$	34.0895	1.25400	0.627002	+	0.779018i	$0.284282\pi$
$740$	−0.778960	−0.0286351
$741$	5.61085	0.206120
$742$	0.297122	0.0109077
$743$	12.2949	0.451056	0.225528	−	0.974237i	$-0.427589\pi$
$743$	12.2949	0.451056	0.225528	+	0.974237i	$0.427589\pi$
$744$	−6.31121	−0.231380
$745$	8.67807	0.317940
$746$	10.5103	0.384810
$747$	−7.22689	−0.264418
$748$	3.01742	0.110328
$749$	−21.5347	−0.786859
$750$	−1.14462	−0.0417954
$751$	−35.2703	−1.28703	−0.643516	−	0.765433i	$-0.722525\pi$
$751$	−35.2703	−1.28703	−0.643516	+	0.765433i	$0.722525\pi$
$752$	−23.7497	−0.866064
$753$	6.26828	0.228429
$754$	4.53496	0.165153
$755$	−14.1127	−0.513615
$756$	7.01021	0.254959
$757$	11.3964	0.414210	0.207105	−	0.978319i	$-0.433596\pi$
$757$	11.3964	0.414210	0.207105	+	0.978319i	$0.433596\pi$
$758$	7.12241	0.258698
$759$	4.73876	0.172006
$760$	−7.67412	−0.278370
$761$	24.9957	0.906095	0.453047	−	0.891487i	$-0.350337\pi$
$761$	24.9957	0.906095	0.453047	+	0.891487i	$0.350337\pi$
$762$	2.27987	0.0825911
$763$	−21.9690	−0.795331
$764$	−2.67976	−0.0969502
$765$	2.07049	0.0748586
$766$	7.87865	0.284667
$767$	2.26947	0.0819457
$768$	1.18443	0.0427395
$769$	29.9210	1.07898	0.539489	−	0.841993i	$-0.318618\pi$
$769$	29.9210	1.07898	0.539489	+	0.841993i	$0.318618\pi$
$770$	−0.894731	−0.0322439
$771$	1.94065	0.0698909
$772$	−28.5000	−1.02574
$773$	−48.3407	−1.73869	−0.869347	−	0.494203i	$-0.835460\pi$
$773$	−48.3407	−1.73869	−0.869347	+	0.494203i	$0.835460\pi$
$774$	7.09257	0.254937
$775$	44.4819	1.59784
$776$	17.3248	0.621923
$777$	−0.390818	−0.0140205
$778$	14.3846	0.515712
$779$	−4.23142	−0.151606
$780$	1.15135	0.0412249
$781$	21.6988	0.776444
$782$	3.19263	0.114168
$783$	10.4305	0.372756
$784$	−11.8371	−0.422753
$785$	−0.609238	−0.0217446
$786$	0.227709	0.00812213
$787$	−4.29384	−0.153059	−0.0765294	−	0.997067i	$-0.524384\pi$
$787$	−4.29384	−0.153059	−0.0765294	+	0.997067i	$0.524384\pi$
$788$	0.0577425	0.00205699
$789$	−10.7990	−0.384454
$790$	−4.79244	−0.170508
$791$	19.4242	0.690644
$792$	7.81506	0.277696
$793$	0.908070	0.0322465
$794$	−9.99200	−0.354603
$795$	0.112239	0.00398071
$796$	−31.8625	−1.12934
$797$	35.8142	1.26860	0.634302	−	0.773085i	$-0.281287\pi$
$797$	35.8142	1.26860	0.634302	+	0.773085i	$0.281287\pi$
$798$	−1.83095	−0.0648148
$799$	−8.14609	−0.288188
$800$	20.3666	0.720069
$801$	38.4462	1.35843
$802$	10.5203	0.371483
$803$	17.8364	0.629432
$804$	−7.89674	−0.278497
$805$	9.20247	0.324344
$806$	9.74834	0.343371
$807$	−12.1461	−0.427563
$808$	27.3518	0.962233
$809$	9.38668	0.330018	0.165009	−	0.986292i	$-0.447235\pi$
$809$	9.38668	0.330018	0.165009	+	0.986292i	$0.447235\pi$
$810$	2.41043	0.0846938
$811$	13.4151	0.471066	0.235533	−	0.971866i	$-0.424316\pi$
$811$	13.4151	0.471066	0.235533	+	0.971866i	$0.424316\pi$
$812$	14.3853	0.504825
$813$	10.3262	0.362157
$814$	−0.425161	−0.0149019
$815$	5.33820	0.186989
$816$	1.12331	0.0393235
$817$	36.9519	1.29278
$818$	4.86217	0.170002
$819$	−11.0962	−0.387731
$820$	−0.868290	−0.0303220
$821$	−13.8056	−0.481820	−0.240910	−	0.970547i	$-0.577446\pi$
$821$	−13.8056	−0.481820	−0.240910	+	0.970547i	$0.577446\pi$
$822$	−0.225140	−0.00785266
$823$	−0.666009	−0.0232156	−0.0116078	−	0.999933i	$-0.503695\pi$
$823$	−0.666009	−0.0232156	−0.0116078	+	0.999933i	$0.503695\pi$
$824$	7.29434	0.254110
$825$	2.86746	0.0998323
$826$	−0.740577	−0.0257680
$827$	−7.97048	−0.277161	−0.138580	−	0.990351i	$-0.544254\pi$
$827$	−7.97048	−0.277161	−0.138580	+	0.990351i	$0.544254\pi$
$828$	−38.2236	−1.32836
$829$	−34.6757	−1.20434	−0.602168	−	0.798370i	$-0.705696\pi$
$829$	−34.6757	−1.20434	−0.602168	+	0.798370i	$0.705696\pi$
$830$	0.794811	0.0275883
$831$	−6.67575	−0.231579
$832$	−8.76974	−0.304036
$833$	−4.06008	−0.140674
$834$	−0.101414	−0.00351169
$835$	−17.2268	−0.596158
$836$	19.3621	0.669653
$837$	22.4214	0.774999
$838$	−5.88568	−0.203317
$839$	12.9303	0.446403	0.223202	−	0.974772i	$-0.428349\pi$
$839$	12.9303	0.446403	0.223202	+	0.974772i	$0.428349\pi$
$840$	−0.790072	−0.0272601
$841$	−7.59604	−0.261933
$842$	11.4624	0.395022
$843$	2.42475	0.0835127
$844$	17.2854	0.594988
$845$	5.69947	0.196068
$846$	−10.0330	−0.344943
$847$	−14.1137	−0.484952
$848$	−1.16970	−0.0401677
$849$	−6.21345	−0.213245
$850$	1.93188	0.0662631
$851$	4.37285	0.149899
$852$	9.11165	0.312160
$853$	−15.1434	−0.518500	−0.259250	−	0.965810i	$-0.583475\pi$
$853$	−15.1434	−0.518500	−0.259250	+	0.965810i	$0.583475\pi$
$854$	−0.296323	−0.0101400
$855$	13.2859	0.454367
$856$	−20.6867	−0.707055
$857$	40.1226	1.37056	0.685281	−	0.728278i	$-0.259679\pi$
$857$	40.1226	1.37056	0.685281	+	0.728278i	$0.259679\pi$
$858$	0.628413	0.0214537
$859$	35.5062	1.21146	0.605728	−	0.795672i	$-0.292882\pi$
$859$	35.5062	1.21146	0.605728	+	0.795672i	$0.292882\pi$
$860$	7.58256	0.258563
$861$	−0.435637	−0.0148465
$862$	−10.5219	−0.358377
$863$	32.5228	1.10709	0.553544	−	0.832820i	$-0.313275\pi$
$863$	32.5228	1.10709	0.553544	+	0.832820i	$0.313275\pi$
$864$	10.2660	0.349255
$865$	−12.0103	−0.408363
$866$	−2.69876	−0.0917075
$867$	0.385290	0.0130851
$868$	30.9227	1.04958
$869$	25.4270	0.862551
$870$	−0.559022	−0.0189526
$871$	25.6495	0.869100
$872$	−21.1039	−0.714668
$873$	−29.9936	−1.01513
$874$	20.4864	0.692962
$875$	11.7933	0.398688
$876$	7.48976	0.253055
$877$	9.81574	0.331454	0.165727	−	0.986172i	$-0.447003\pi$
$877$	9.81574	0.331454	0.165727	+	0.986172i	$0.447003\pi$
$878$	0.162112	0.00547102
$879$	−3.09135	−0.104269
$880$	3.52235	0.118738
$881$	−12.5243	−0.421953	−0.210977	−	0.977491i	$-0.567664\pi$
$881$	−12.5243	−0.421953	−0.210977	+	0.977491i	$0.567664\pi$
$882$	−5.00056	−0.168378
$883$	49.4333	1.66356	0.831782	−	0.555102i	$-0.187321\pi$
$883$	49.4333	1.66356	0.831782	+	0.555102i	$0.187321\pi$
$884$	−4.11555	−0.138421
$885$	−0.279756	−0.00940389
$886$	−9.85468	−0.331074
$887$	15.7203	0.527837	0.263918	−	0.964545i	$-0.414985\pi$
$887$	15.7203	0.527837	0.263918	+	0.964545i	$0.414985\pi$
$888$	−0.375429	−0.0125986
$889$	−23.4903	−0.787838
$890$	−4.22830	−0.141733
$891$	−12.7889	−0.428443
$892$	−43.8704	−1.46889
$893$	−52.2717	−1.74921
$894$	1.98894	0.0665202
$895$	17.5404	0.586311
$896$	18.4766	0.617261
$897$	−6.46334	−0.215805
$898$	−5.96673	−0.199112
$899$	46.0099	1.53452
$900$	−23.1294	−0.770980
$901$	−0.401204	−0.0133660
$902$	−0.473918	−0.0157797
$903$	3.80431	0.126599
$904$	18.6593	0.620598
$905$	−14.4301	−0.479672
$906$	−3.23453	−0.107460
$907$	−30.0606	−0.998145	−0.499073	−	0.866560i	$-0.666326\pi$
$907$	−30.0606	−0.998145	−0.499073	+	0.866560i	$0.666326\pi$
$908$	−32.4343	−1.07637
$909$	−47.3530	−1.57060
$910$	1.22035	0.0404542
$911$	26.4713	0.877034	0.438517	−	0.898723i	$-0.355504\pi$
$911$	26.4713	0.877034	0.438517	+	0.898723i	$0.355504\pi$
$912$	7.20800	0.238681
$913$	−4.21698	−0.139562
$914$	7.27197	0.240535
$915$	−0.111937	−0.00370053
$916$	8.00513	0.264497
$917$	−2.34616	−0.0774771
$918$	0.973781	0.0321396
$919$	−44.1020	−1.45479	−0.727395	−	0.686219i	$-0.759269\pi$
$919$	−44.1020	−1.45479	−0.727395	+	0.686219i	$0.759269\pi$
$920$	8.84009	0.291449
$921$	7.19484	0.237078
$922$	7.92896	0.261126
$923$	−29.5957	−0.974154
$924$	1.99339	0.0655776
$925$	2.64605	0.0870016
$926$	−12.4639	−0.409588
$927$	−12.6284	−0.414770
$928$	21.0663	0.691534
$929$	2.98303	0.0978701	0.0489350	−	0.998802i	$-0.484417\pi$
$929$	2.98303	0.0978701	0.0489350	+	0.998802i	$0.484417\pi$
$930$	−1.20167	−0.0394044
$931$	−26.0527	−0.853842
$932$	21.2720	0.696786
$933$	−12.0408	−0.394197
$934$	7.56019	0.247377
$935$	1.20815	0.0395109
$936$	−10.6592	−0.348407
$937$	5.38934	0.176062	0.0880310	−	0.996118i	$-0.471943\pi$
$937$	5.38934	0.176062	0.0880310	+	0.996118i	$0.471943\pi$
$938$	−8.37000	−0.273290
$939$	8.48546	0.276913
$940$	−10.7262	−0.349849
$941$	25.8561	0.842886	0.421443	−	0.906855i	$-0.361524\pi$
$941$	25.8561	0.842886	0.421443	+	0.906855i	$0.361524\pi$
$942$	−0.139632	−0.00454947
$943$	4.87433	0.158730
$944$	2.91548	0.0948907
$945$	2.80684	0.0913065
$946$	4.13860	0.134558
$947$	55.8247	1.81406	0.907029	−	0.421068i	$-0.138345\pi$
$947$	55.8247	1.81406	0.907029	+	0.421068i	$0.138345\pi$
$948$	10.6772	0.346778
$949$	−24.3276	−0.789706
$950$	12.3965	0.402195
$951$	4.25843	0.138089
$952$	2.82415	0.0915312
$953$	−39.4341	−1.27740	−0.638698	−	0.769457i	$-0.720527\pi$
$953$	−39.4341	−1.27740	−0.638698	+	0.769457i	$0.720527\pi$
$954$	−0.494138	−0.0159983
$955$	−1.07296	−0.0347200
$956$	32.1662	1.04033
$957$	2.96597	0.0958761
$958$	−5.26255	−0.170025
$959$	2.31969	0.0749067
$960$	1.08104	0.0348905
$961$	67.9030	2.19042
$962$	0.579890	0.0186964
$963$	35.8139	1.15409
$964$	−10.9571	−0.352906
$965$	−11.4112	−0.367340
$966$	2.10913	0.0678602
$967$	−34.3072	−1.10324	−0.551622	−	0.834094i	$-0.685991\pi$
$967$	−34.3072	−1.10324	−0.551622	+	0.834094i	$0.685991\pi$
$968$	−13.5579	−0.435768
$969$	2.47232	0.0794225
$970$	3.29869	0.105914
$971$	−5.32558	−0.170906	−0.0854529	−	0.996342i	$-0.527234\pi$
$971$	−5.32558	−0.170906	−0.0854529	+	0.996342i	$0.527234\pi$
$972$	−17.6357	−0.565666
$973$	1.04490	0.0334981
$974$	7.96430	0.255193
$975$	−3.91102	−0.125253
$976$	1.16655	0.0373405
$977$	−2.84601	−0.0910519	−0.0455260	−	0.998963i	$-0.514496\pi$
$977$	−2.84601	−0.0910519	−0.0455260	+	0.998963i	$0.514496\pi$
$978$	1.22347	0.0391223
$979$	22.4339	0.716989
$980$	−5.34602	−0.170772
$981$	36.5362	1.16651
$982$	−3.42362	−0.109252
$983$	−45.7072	−1.45783	−0.728917	−	0.684602i	$-0.759976\pi$
$983$	−45.7072	−1.45783	−0.728917	+	0.684602i	$0.759976\pi$
$984$	−0.418482	−0.0133407
$985$	0.0231197	0.000736655 0
$986$	1.99825	0.0636372
$987$	−5.38152	−0.171296
$988$	−26.4086	−0.840170
$989$	−42.5663	−1.35353
$990$	1.48801	0.0472921
$991$	53.4081	1.69657	0.848283	−	0.529544i	$-0.177637\pi$
$991$	53.4081	1.69657	0.848283	+	0.529544i	$0.177637\pi$
$992$	45.2841	1.43777
$993$	13.4175	0.425791
$994$	9.65772	0.306324
$995$	−12.7575	−0.404441
$996$	−1.77077	−0.0561091
$997$	30.4373	0.963959	0.481980	−	0.876182i	$-0.339918\pi$
$997$	30.4373	0.963959	0.481980	+	0.876182i	$0.339918\pi$
$998$	−2.58741	−0.0819030
$999$	1.33376	0.0421984

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1003.2.a.h.1.8	✓	16
3.2	odd	2		9027.2.a.n.1.9		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1003.2.a.h.1.8	✓	16	1.1	even	1	trivial
9027.2.a.n.1.9		16	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1003 = 17 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1003.a (trivial)

\(f(q)\)	\(=\)	\(q-0.431919 q^{2} +0.385290 q^{3} -1.81345 q^{4} -0.726091 q^{5} -0.166414 q^{6} +1.71462 q^{7} +1.64710 q^{8} -2.85155 q^{9} +O(q^{10})\)	\(q-0.431919 q^{2} +0.385290 q^{3} -1.81345 q^{4} -0.726091 q^{5} -0.166414 q^{6} +1.71462 q^{7} +1.64710 q^{8} -2.85155 q^{9} +0.313613 q^{10} -1.66392 q^{11} -0.698703 q^{12} +2.26947 q^{13} -0.740577 q^{14} -0.279756 q^{15} +2.91548 q^{16} +1.00000 q^{17} +1.23164 q^{18} +6.41678 q^{19} +1.31673 q^{20} +0.660626 q^{21} +0.718677 q^{22} -7.39172 q^{23} +0.634612 q^{24} -4.47279 q^{25} -0.980226 q^{26} -2.25455 q^{27} -3.10937 q^{28} -4.62644 q^{29} +0.120832 q^{30} -9.94500 q^{31} -4.55345 q^{32} -0.641090 q^{33} -0.431919 q^{34} -1.24497 q^{35} +5.17113 q^{36} -0.591588 q^{37} -2.77153 q^{38} +0.874403 q^{39} -1.19594 q^{40} -0.659431 q^{41} -0.285337 q^{42} +5.75864 q^{43} +3.01742 q^{44} +2.07049 q^{45} +3.19263 q^{46} -8.14609 q^{47} +1.12331 q^{48} -4.06008 q^{49} +1.93188 q^{50} +0.385290 q^{51} -4.11555 q^{52} -0.401204 q^{53} +0.973781 q^{54} +1.20815 q^{55} +2.82415 q^{56} +2.47232 q^{57} +1.99825 q^{58} +1.00000 q^{59} +0.507322 q^{60} +0.400125 q^{61} +4.29543 q^{62} -4.88932 q^{63} -3.86423 q^{64} -1.64784 q^{65} +0.276899 q^{66} +11.3020 q^{67} -1.81345 q^{68} -2.84796 q^{69} +0.537726 q^{70} -13.0408 q^{71} -4.69679 q^{72} -10.7195 q^{73} +0.255518 q^{74} -1.72332 q^{75} -11.6365 q^{76} -2.85298 q^{77} -0.377671 q^{78} -15.2814 q^{79} -2.11690 q^{80} +7.68600 q^{81} +0.284821 q^{82} +2.53437 q^{83} -1.19801 q^{84} -0.726091 q^{85} -2.48727 q^{86} -1.78252 q^{87} -2.74064 q^{88} -13.4826 q^{89} -0.894283 q^{90} +3.89127 q^{91} +13.4045 q^{92} -3.83171 q^{93} +3.51845 q^{94} -4.65917 q^{95} -1.75440 q^{96} +10.5183 q^{97} +1.75363 q^{98} +4.74474 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{2} - 7 q^{3} + 14 q^{4} - 21 q^{5} - 5 q^{6} - 11 q^{7} - 12 q^{8} + 17 q^{9}+O(q^{10}) \) 16 * q - 6 * q^2 - 7 * q^3 + 14 * q^4 - 21 * q^5 - 5 * q^6 - 11 * q^7 - 12 * q^8 + 17 * q^9	\( 16 q - 6 q^{2} - 7 q^{3} + 14 q^{4} - 21 q^{5} - 5 q^{6} - 11 q^{7} - 12 q^{8} + 17 q^{9} + 12 q^{10} - 7 q^{11} - 4 q^{12} - 16 q^{13} + 11 q^{14} + 7 q^{15} + 22 q^{16} + 16 q^{17} + 11 q^{18} + q^{19} - 43 q^{20} - 8 q^{21} - 18 q^{22} - 8 q^{23} - 39 q^{24} + 23 q^{25} - 49 q^{26} - 7 q^{27} - 15 q^{28} - 39 q^{29} + q^{30} - 3 q^{31} - 15 q^{33} - 6 q^{34} + 9 q^{35} - 17 q^{36} - 28 q^{37} - 27 q^{38} - 4 q^{39} + 26 q^{40} - 31 q^{41} - 45 q^{42} + 5 q^{43} - 19 q^{44} - 79 q^{45} - 39 q^{46} - 47 q^{47} - 31 q^{48} + 35 q^{49} - 13 q^{50} - 7 q^{51} + 9 q^{52} - 36 q^{53} + 9 q^{54} + 32 q^{55} + 3 q^{56} + 6 q^{57} + 22 q^{58} + 16 q^{59} + 6 q^{60} - 22 q^{61} + q^{62} - 19 q^{63} + 32 q^{64} - 19 q^{65} + 48 q^{66} + 4 q^{67} + 14 q^{68} + 14 q^{69} - 11 q^{70} - 5 q^{71} + 40 q^{72} - 35 q^{73} + 31 q^{74} - 12 q^{75} + q^{76} - 79 q^{77} + 31 q^{78} - 48 q^{79} - 127 q^{80} - 28 q^{81} - 7 q^{82} - 42 q^{83} + 28 q^{84} - 21 q^{85} + 58 q^{86} - 16 q^{87} - 2 q^{88} + 20 q^{89} - 14 q^{90} + 49 q^{91} - 21 q^{92} - 55 q^{93} - 22 q^{95} + 24 q^{96} - 2 q^{97} - 78 q^{98} - 35 q^{99}+O(q^{100}) \) 16 * q - 6 * q^2 - 7 * q^3 + 14 * q^4 - 21 * q^5 - 5 * q^6 - 11 * q^7 - 12 * q^8 + 17 * q^9 + 12 * q^10 - 7 * q^11 - 4 * q^12 - 16 * q^13 + 11 * q^14 + 7 * q^15 + 22 * q^16 + 16 * q^17 + 11 * q^18 + q^19 - 43 * q^20 - 8 * q^21 - 18 * q^22 - 8 * q^23 - 39 * q^24 + 23 * q^25 - 49 * q^26 - 7 * q^27 - 15 * q^28 - 39 * q^29 + q^30 - 3 * q^31 - 15 * q^33 - 6 * q^34 + 9 * q^35 - 17 * q^36 - 28 * q^37 - 27 * q^38 - 4 * q^39 + 26 * q^40 - 31 * q^41 - 45 * q^42 + 5 * q^43 - 19 * q^44 - 79 * q^45 - 39 * q^46 - 47 * q^47 - 31 * q^48 + 35 * q^49 - 13 * q^50 - 7 * q^51 + 9 * q^52 - 36 * q^53 + 9 * q^54 + 32 * q^55 + 3 * q^56 + 6 * q^57 + 22 * q^58 + 16 * q^59 + 6 * q^60 - 22 * q^61 + q^62 - 19 * q^63 + 32 * q^64 - 19 * q^65 + 48 * q^66 + 4 * q^67 + 14 * q^68 + 14 * q^69 - 11 * q^70 - 5 * q^71 + 40 * q^72 - 35 * q^73 + 31 * q^74 - 12 * q^75 + q^76 - 79 * q^77 + 31 * q^78 - 48 * q^79 - 127 * q^80 - 28 * q^81 - 7 * q^82 - 42 * q^83 + 28 * q^84 - 21 * q^85 + 58 * q^86 - 16 * q^87 - 2 * q^88 + 20 * q^89 - 14 * q^90 + 49 * q^91 - 21 * q^92 - 55 * q^93 - 22 * q^95 + 24 * q^96 - 2 * q^97 - 78 * q^98 - 35 * q^99

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