LMFDB - Embedded newform 1003.2.a.i.1.16

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:	$0$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 5 x^{17} - 16 x^{16} + 112 x^{15} + 52 x^{14} - 984 x^{13} + 431 x^{12} + 4304 x^{11} + \cdots + 28 $ x^18 - 5x^17 - 16x^16 + 112x^15 + 52x^14 - 984x^13 + 431x^12 + 4304x^11 - 3825x^10 - 9826x^9 + 11533x^8 + 11182x^7 - 15697x^6 - 5604x^5 + 9201x^4 + 1189x^3 - 1952x^2 - 100*x + 28
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Root			$2.45136$ 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)

$f(q)$	$=$	$q+2.45136 q^{2} +2.33620 q^{3} +4.00917 q^{4} -2.57056 q^{5} +5.72687 q^{6} +2.10143 q^{7} +4.92520 q^{8} +2.45783 q^{9} +O(q^{10})$	\(q+2.45136 q^{2} +2.33620 q^{3} +4.00917 q^{4} -2.57056 q^{5} +5.72687 q^{6} +2.10143 q^{7} +4.92520 q^{8} +2.45783 q^{9} -6.30136 q^{10} -0.0953603 q^{11} +9.36622 q^{12} -0.236523 q^{13} +5.15137 q^{14} -6.00534 q^{15} +4.05510 q^{16} +1.00000 q^{17} +6.02504 q^{18} -1.24465 q^{19} -10.3058 q^{20} +4.90937 q^{21} -0.233762 q^{22} -1.18392 q^{23} +11.5062 q^{24} +1.60777 q^{25} -0.579802 q^{26} -1.26661 q^{27} +8.42500 q^{28} +6.97799 q^{29} -14.7213 q^{30} +0.0214154 q^{31} +0.0901072 q^{32} -0.222781 q^{33} +2.45136 q^{34} -5.40186 q^{35} +9.85387 q^{36} -7.55483 q^{37} -3.05108 q^{38} -0.552564 q^{39} -12.6605 q^{40} -0.569103 q^{41} +12.0346 q^{42} -6.07284 q^{43} -0.382315 q^{44} -6.31801 q^{45} -2.90220 q^{46} +2.00378 q^{47} +9.47352 q^{48} -2.58398 q^{49} +3.94122 q^{50} +2.33620 q^{51} -0.948259 q^{52} +2.33241 q^{53} -3.10491 q^{54} +0.245129 q^{55} +10.3500 q^{56} -2.90775 q^{57} +17.1056 q^{58} -1.00000 q^{59} -24.0764 q^{60} +5.06021 q^{61} +0.0524967 q^{62} +5.16498 q^{63} -7.88930 q^{64} +0.607995 q^{65} -0.546116 q^{66} -1.16145 q^{67} +4.00917 q^{68} -2.76587 q^{69} -13.2419 q^{70} -4.37459 q^{71} +12.1053 q^{72} +10.2933 q^{73} -18.5196 q^{74} +3.75607 q^{75} -4.99000 q^{76} -0.200393 q^{77} -1.35453 q^{78} -3.67217 q^{79} -10.4239 q^{80} -10.3326 q^{81} -1.39508 q^{82} +5.62781 q^{83} +19.6825 q^{84} -2.57056 q^{85} -14.8867 q^{86} +16.3020 q^{87} -0.469668 q^{88} -2.91410 q^{89} -15.4877 q^{90} -0.497036 q^{91} -4.74652 q^{92} +0.0500306 q^{93} +4.91199 q^{94} +3.19944 q^{95} +0.210508 q^{96} +7.71938 q^{97} -6.33426 q^{98} -0.234380 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 5 q^{2} + q^{3} + 21 q^{4} + 21 q^{5} + 5 q^{6} - q^{7} + 9 q^{8} + 17 q^{9}+O(q^{10}) $ 18 * q + 5 * q^2 + q^3 + 21 * q^4 + 21 * q^5 + 5 * q^6 - q^7 + 9 * q^8 + 17 * q^9	\( 18 q + 5 q^{2} + q^{3} + 21 q^{4} + 21 q^{5} + 5 q^{6} - q^{7} + 9 q^{8} + 17 q^{9} + 10 q^{10} + 6 q^{11} + 20 q^{12} + 12 q^{13} + 9 q^{14} - q^{15} + 19 q^{16} + 18 q^{17} + 10 q^{18} - 14 q^{19} + 17 q^{20} - 14 q^{21} - 4 q^{22} + 7 q^{23} - 3 q^{24} + 35 q^{25} + 3 q^{26} + 13 q^{27} + q^{28} + 23 q^{29} + 17 q^{30} - q^{31} + 13 q^{32} + 7 q^{33} + 5 q^{34} + 5 q^{35} - 16 q^{36} + 36 q^{37} - 19 q^{38} + 8 q^{39} - 4 q^{40} + 37 q^{41} + 9 q^{42} - 15 q^{43} - 9 q^{44} + 17 q^{45} + q^{46} + 23 q^{47} + 17 q^{48} + 15 q^{49} + 32 q^{50} + q^{51} - 11 q^{52} + 35 q^{53} - 17 q^{54} - 6 q^{55} + 37 q^{56} - 16 q^{57} + 2 q^{58} - 18 q^{59} - 6 q^{60} + 39 q^{61} - q^{62} + 15 q^{63} + 5 q^{64} + 15 q^{65} - 36 q^{66} + 14 q^{67} + 21 q^{68} + 16 q^{69} - 45 q^{70} + 3 q^{71} - 71 q^{72} + 56 q^{73} - 27 q^{74} + 16 q^{75} - q^{76} + 39 q^{77} - 71 q^{78} - 22 q^{79} + 45 q^{80} - 18 q^{81} + 5 q^{82} + 12 q^{83} + 2 q^{84} + 21 q^{85} + 4 q^{86} + 8 q^{87} - 18 q^{88} + 34 q^{89} + 48 q^{90} + 3 q^{91} + 67 q^{92} - 19 q^{93} - 38 q^{94} - 72 q^{95} + 6 q^{96} + 31 q^{97} + 19 q^{98} + 44 q^{99}+O(q^{100}) \) 18 * q + 5 * q^2 + q^3 + 21 * q^4 + 21 * q^5 + 5 * q^6 - q^7 + 9 * q^8 + 17 * q^9 + 10 * q^10 + 6 * q^11 + 20 * q^12 + 12 * q^13 + 9 * q^14 - q^15 + 19 * q^16 + 18 * q^17 + 10 * q^18 - 14 * q^19 + 17 * q^20 - 14 * q^21 - 4 * q^22 + 7 * q^23 - 3 * q^24 + 35 * q^25 + 3 * q^26 + 13 * q^27 + q^28 + 23 * q^29 + 17 * q^30 - q^31 + 13 * q^32 + 7 * q^33 + 5 * q^34 + 5 * q^35 - 16 * q^36 + 36 * q^37 - 19 * q^38 + 8 * q^39 - 4 * q^40 + 37 * q^41 + 9 * q^42 - 15 * q^43 - 9 * q^44 + 17 * q^45 + q^46 + 23 * q^47 + 17 * q^48 + 15 * q^49 + 32 * q^50 + q^51 - 11 * q^52 + 35 * q^53 - 17 * q^54 - 6 * q^55 + 37 * q^56 - 16 * q^57 + 2 * q^58 - 18 * q^59 - 6 * q^60 + 39 * q^61 - q^62 + 15 * q^63 + 5 * q^64 + 15 * q^65 - 36 * q^66 + 14 * q^67 + 21 * q^68 + 16 * q^69 - 45 * q^70 + 3 * q^71 - 71 * q^72 + 56 * q^73 - 27 * q^74 + 16 * q^75 - q^76 + 39 * q^77 - 71 * q^78 - 22 * q^79 + 45 * q^80 - 18 * q^81 + 5 * q^82 + 12 * q^83 + 2 * q^84 + 21 * q^85 + 4 * q^86 + 8 * q^87 - 18 * q^88 + 34 * q^89 + 48 * q^90 + 3 * q^91 + 67 * q^92 - 19 * q^93 - 38 * q^94 - 72 * q^95 + 6 * q^96 + 31 * q^97 + 19 * q^98 + 44 * 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 $

$2$	2.45136	1.73337	0.866687	−	0.498853i	$-0.166245\pi$
$2$	2.45136	1.73337	0.866687	+	0.498853i	$0.166245\pi$
$3$	2.33620	1.34881	0.674403	−	0.738363i	$-0.264401\pi$
$3$	2.33620	1.34881	0.674403	+	0.738363i	$0.264401\pi$
$4$	4.00917	2.00458
$5$	−2.57056	−1.14959	−0.574794	−	0.818298i	$-0.694918\pi$
$5$	−2.57056	−1.14959	−0.574794	+	0.818298i	$0.694918\pi$
$6$	5.72687	2.33799
$7$	2.10143	0.794267	0.397134	−	0.917761i	$-0.370005\pi$
$7$	2.10143	0.794267	0.397134	+	0.917761i	$0.370005\pi$
$8$	4.92520	1.74132
$9$	2.45783	0.819278
$10$	−6.30136	−1.99267
$11$	−0.0953603	−0.0287522	−0.0143761	−	0.999897i	$-0.504576\pi$
$11$	−0.0953603	−0.0287522	−0.0143761	+	0.999897i	$0.504576\pi$
$12$	9.36622	2.70380
$13$	−0.236523	−0.0655996	−0.0327998	−	0.999462i	$-0.510442\pi$
$13$	−0.236523	−0.0655996	−0.0327998	+	0.999462i	$0.510442\pi$
$14$	5.15137	1.37676
$15$	−6.00534	−1.55057
$16$	4.05510	1.01377
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	6.02504	1.42012
$19$	−1.24465	−0.285542	−0.142771	−	0.989756i	$-0.545601\pi$
$19$	−1.24465	−0.285542	−0.142771	+	0.989756i	$0.545601\pi$
$20$	−10.3058	−2.30445
$21$	4.90937	1.07131
$22$	−0.233762	−0.0498383
$23$	−1.18392	−0.246864	−0.123432	−	0.992353i	$-0.539390\pi$
$23$	−1.18392	−0.246864	−0.123432	+	0.992353i	$0.539390\pi$
$24$	11.5062	2.34870
$25$	1.60777	0.321553
$26$	−0.579802	−0.113709
$27$	−1.26661	−0.243759
$28$	8.42500	1.59218
$29$	6.97799	1.29578	0.647890	−	0.761734i	$-0.275652\pi$
$29$	6.97799	1.29578	0.647890	+	0.761734i	$0.275652\pi$
$30$	−14.7213	−2.68772
$31$	0.0214154	0.00384631	0.00192316	−	0.999998i	$-0.499388\pi$
$31$	0.0214154	0.00384631	0.00192316	+	0.999998i	$0.499388\pi$
$32$	0.0901072	0.0159289
$33$	−0.222781	−0.0387812
$34$	2.45136	0.420405
$35$	−5.40186	−0.913080
$36$	9.85387	1.64231
$37$	−7.55483	−1.24201	−0.621003	−	0.783808i	$-0.713275\pi$
$37$	−7.55483	−1.24201	−0.621003	+	0.783808i	$0.713275\pi$
$38$	−3.05108	−0.494950
$39$	−0.552564	−0.0884811
$40$	−12.6605	−2.00180
$41$	−0.569103	−0.0888790	−0.0444395	−	0.999012i	$-0.514150\pi$
$41$	−0.569103	−0.0888790	−0.0444395	+	0.999012i	$0.514150\pi$
$42$	12.0346	1.85698
$43$	−6.07284	−0.926099	−0.463050	−	0.886332i	$-0.653245\pi$
$43$	−6.07284	−0.926099	−0.463050	+	0.886332i	$0.653245\pi$
$44$	−0.382315	−0.0576362
$45$	−6.31801	−0.941833
$46$	−2.90220	−0.427907
$47$	2.00378	0.292282	0.146141	−	0.989264i	$-0.453315\pi$
$47$	2.00378	0.292282	0.146141	+	0.989264i	$0.453315\pi$
$48$	9.47352	1.36738
$49$	−2.58398	−0.369140
$50$	3.94122	0.557372
$51$	2.33620	0.327134
$52$	−0.948259	−0.131500
$53$	2.33241	0.320382	0.160191	−	0.987086i	$-0.448789\pi$
$53$	2.33241	0.320382	0.160191	+	0.987086i	$0.448789\pi$
$54$	−3.10491	−0.422525
$55$	0.245129	0.0330532
$56$	10.3500	1.38307
$57$	−2.90775	−0.385140
$58$	17.1056	2.24607
$59$	−1.00000	−0.130189
$59$	−1.00000	−0.130189
$60$	−24.0764	−3.10825
$61$	5.06021	0.647893	0.323947	−	0.946075i	$-0.394990\pi$
$61$	5.06021	0.647893	0.323947	+	0.946075i	$0.394990\pi$
$62$	0.0524967	0.00666709
$63$	5.16498	0.650726
$64$	−7.88930	−0.986163
$65$	0.607995	0.0754125
$66$	−0.546116	−0.0672222
$67$	−1.16145	−0.141893	−0.0709466	−	0.997480i	$-0.522602\pi$
$67$	−1.16145	−0.141893	−0.0709466	+	0.997480i	$0.522602\pi$
$68$	4.00917	0.486183
$69$	−2.76587	−0.332971
$70$	−13.2419	−1.58271
$71$	−4.37459	−0.519169	−0.259584	−	0.965720i	$-0.583586\pi$
$71$	−4.37459	−0.519169	−0.259584	+	0.965720i	$0.583586\pi$
$72$	12.1053	1.42663
$73$	10.2933	1.20474	0.602368	−	0.798218i	$-0.294224\pi$
$73$	10.2933	1.20474	0.602368	+	0.798218i	$0.294224\pi$
$74$	−18.5196	−2.15286
$75$	3.75607	0.433713
$76$	−4.99000	−0.572392
$77$	−0.200393	−0.0228369
$78$	−1.35453	−0.153371
$79$	−3.67217	−0.413151	−0.206575	−	0.978431i	$-0.566232\pi$
$79$	−3.67217	−0.413151	−0.206575	+	0.978431i	$0.566232\pi$
$80$	−10.4239	−1.16542
$81$	−10.3326	−1.14806
$82$	−1.39508	−0.154061
$83$	5.62781	0.617733	0.308866	−	0.951105i	$-0.400050\pi$
$83$	5.62781	0.617733	0.308866	+	0.951105i	$0.400050\pi$
$84$	19.6825	2.14754
$85$	−2.57056	−0.278816
$86$	−14.8867	−1.60528
$87$	16.3020	1.74776
$88$	−0.469668	−0.0500668
$89$	−2.91410	−0.308894	−0.154447	−	0.988001i	$-0.549360\pi$
$89$	−2.91410	−0.308894	−0.154447	+	0.988001i	$0.549360\pi$
$90$	−15.4877	−1.63255
$91$	−0.497036	−0.0521036
$92$	−4.74652	−0.494859
$93$	0.0500306	0.00518793
$94$	4.91199	0.506633
$95$	3.19944	0.328255
$96$	0.210508	0.0214849
$97$	7.71938	0.783784	0.391892	−	0.920011i	$-0.371821\pi$
$97$	7.71938	0.783784	0.391892	+	0.920011i	$0.371821\pi$
$98$	−6.33426	−0.639857
$99$	−0.234380	−0.0235561
$100$	6.44581	0.644581
$101$	4.50148	0.447914	0.223957	−	0.974599i	$-0.428103\pi$
$101$	4.50148	0.447914	0.223957	+	0.974599i	$0.428103\pi$
$102$	5.72687	0.567045
$103$	−3.66614	−0.361236	−0.180618	−	0.983553i	$-0.557810\pi$
$103$	−3.66614	−0.361236	−0.180618	+	0.983553i	$0.557810\pi$
$104$	−1.16492	−0.114230
$105$	−12.6198	−1.23157
$106$	5.71759	0.555341
$107$	14.6256	1.41391	0.706955	−	0.707259i	$-0.250068\pi$
$107$	14.6256	1.41391	0.706955	+	0.707259i	$0.250068\pi$
$108$	−5.07804	−0.488635
$109$	0.254447	0.0243716	0.0121858	−	0.999926i	$-0.496121\pi$
$109$	0.254447	0.0243716	0.0121858	+	0.999926i	$0.496121\pi$
$110$	0.600900	0.0572936
$111$	−17.6496	−1.67523
$112$	8.52151	0.805207
$113$	−11.6625	−1.09712	−0.548559	−	0.836112i	$-0.684823\pi$
$113$	−11.6625	−1.09712	−0.548559	+	0.836112i	$0.684823\pi$
$114$	−7.12793	−0.667592
$115$	3.04332	0.283791
$116$	27.9759	2.59750
$117$	−0.581333	−0.0537443
$118$	−2.45136	−0.225666
$119$	2.10143	0.192638
$120$	−29.5775	−2.70004
$121$	−10.9909	−0.999173
$122$	12.4044	1.12304
$123$	−1.32954	−0.119881
$124$	0.0858578	0.00771025
$125$	8.71993	0.779934
$126$	12.6612	1.12795
$127$	−3.17539	−0.281770	−0.140885	−	0.990026i	$-0.544995\pi$
$127$	−3.17539	−0.281770	−0.140885	+	0.990026i	$0.544995\pi$
$128$	−19.5197	−1.72532
$129$	−14.1874	−1.24913
$130$	1.49041	0.130718
$131$	8.77311	0.766510	0.383255	−	0.923643i	$-0.374803\pi$
$131$	8.77311	0.766510	0.383255	+	0.923643i	$0.374803\pi$
$132$	−0.893166	−0.0777401
$133$	−2.61554	−0.226796
$134$	−2.84712	−0.245954
$135$	3.25589	0.280222
$136$	4.92520	0.422332
$137$	−0.803711	−0.0686657	−0.0343328	−	0.999410i	$-0.510931\pi$
$137$	−0.803711	−0.0686657	−0.0343328	+	0.999410i	$0.510931\pi$
$138$	−6.78013	−0.577163
$139$	5.31708	0.450989	0.225495	−	0.974244i	$-0.427600\pi$
$139$	5.31708	0.450989	0.225495	+	0.974244i	$0.427600\pi$
$140$	−21.6570	−1.83035
$141$	4.68124	0.394231
$142$	−10.7237	−0.899914
$143$	0.0225549	0.00188613
$144$	9.96675	0.830563
$145$	−17.9373	−1.48961
$146$	25.2325	2.08826
$147$	−6.03669	−0.497898
$148$	−30.2886	−2.48971
$149$	−2.82080	−0.231089	−0.115544	−	0.993302i	$-0.536861\pi$
$149$	−2.82080	−0.231089	−0.115544	+	0.993302i	$0.536861\pi$
$150$	9.20747	0.751787
$151$	17.3004	1.40789	0.703943	−	0.710257i	$-0.251421\pi$
$151$	17.3004	1.40789	0.703943	+	0.710257i	$0.251421\pi$
$152$	−6.13013	−0.497219
$153$	2.45783	0.198704
$154$	−0.491236	−0.0395849
$155$	−0.0550494	−0.00442167
$156$	−2.21532	−0.177368
$157$	−10.6508	−0.850029	−0.425014	−	0.905187i	$-0.639731\pi$
$157$	−10.6508	−0.850029	−0.425014	+	0.905187i	$0.639731\pi$
$158$	−9.00180	−0.716145
$159$	5.44899	0.432133
$160$	−0.231626	−0.0183116
$161$	−2.48792	−0.196076
$162$	−25.3288	−1.99002
$163$	−18.7738	−1.47047	−0.735237	−	0.677810i	$-0.762929\pi$
$163$	−18.7738	−1.47047	−0.735237	+	0.677810i	$0.762929\pi$
$164$	−2.28163	−0.178165
$165$	0.572671	0.0445824
$166$	13.7958	1.07076
$167$	12.2742	0.949807	0.474903	−	0.880038i	$-0.342483\pi$
$167$	12.2742	0.949807	0.474903	+	0.880038i	$0.342483\pi$
$168$	24.1796	1.86550
$169$	−12.9441	−0.995697
$170$	−6.30136	−0.483293
$171$	−3.05914	−0.233938
$172$	−24.3470	−1.85644
$173$	10.5139	0.799356	0.399678	−	0.916656i	$-0.369122\pi$
$173$	10.5139	0.799356	0.399678	+	0.916656i	$0.369122\pi$
$174$	39.9620	3.02951
$175$	3.37862	0.255399
$176$	−0.386695	−0.0291482
$177$	−2.33620	−0.175600
$178$	−7.14350	−0.535428
$179$	10.0293	0.749628	0.374814	−	0.927100i	$-0.377707\pi$
$179$	10.0293	0.749628	0.374814	+	0.927100i	$0.377707\pi$
$180$	−25.3300	−1.88798
$181$	−10.9677	−0.815223	−0.407612	−	0.913155i	$-0.633638\pi$
$181$	−10.9677	−0.815223	−0.407612	+	0.913155i	$0.633638\pi$
$182$	−1.21842	−0.0903150
$183$	11.8217	0.873883
$184$	−5.83102	−0.429868
$185$	19.4201	1.42780
$186$	0.122643	0.00899262
$187$	−0.0953603	−0.00697343
$188$	8.03350	0.585903
$189$	−2.66169	−0.193609
$190$	7.84298	0.568989
$191$	17.5100	1.26698	0.633488	−	0.773753i	$-0.281623\pi$
$191$	17.5100	1.26698	0.633488	+	0.773753i	$0.281623\pi$
$192$	−18.4310	−1.33014
$193$	22.0034	1.58384	0.791920	−	0.610625i	$-0.209082\pi$
$193$	22.0034	1.58384	0.791920	+	0.610625i	$0.209082\pi$
$194$	18.9230	1.35859
$195$	1.42040	0.101717
$196$	−10.3596	−0.739972
$197$	20.6754	1.47306	0.736531	−	0.676404i	$-0.236463\pi$
$197$	20.6754	1.47306	0.736531	+	0.676404i	$0.236463\pi$
$198$	−0.574549	−0.0408315
$199$	−8.23569	−0.583812	−0.291906	−	0.956447i	$-0.594289\pi$
$199$	−8.23569	−0.583812	−0.291906	+	0.956447i	$0.594289\pi$
$200$	7.91857	0.559927
$201$	−2.71337	−0.191386
$202$	11.0347	0.776402
$203$	14.6638	1.02920
$204$	9.36622	0.655767
$205$	1.46291	0.102174
$206$	−8.98704	−0.626157
$207$	−2.90987	−0.202250
$208$	−0.959122	−0.0665031
$209$	0.118690	0.00820995
$210$	−30.9357	−2.13477
$211$	18.3956	1.26640	0.633202	−	0.773986i	$-0.281740\pi$
$211$	18.3956	1.26640	0.633202	+	0.773986i	$0.281740\pi$
$212$	9.35104	0.642232
$213$	−10.2199	−0.700258
$214$	35.8526	2.45083
$215$	15.6106	1.06463
$216$	−6.23829	−0.424462
$217$	0.0450029	0.00305500
$218$	0.623741	0.0422451
$219$	24.0472	1.62496
$220$	0.982764	0.0662579
$221$	−0.236523	−0.0159102
$222$	−43.2655	−2.90379
$223$	27.5139	1.84247	0.921233	−	0.389011i	$-0.127183\pi$
$223$	27.5139	1.84247	0.921233	+	0.389011i	$0.127183\pi$
$224$	0.189354	0.0126518
$225$	3.95163	0.263442
$226$	−28.5890	−1.90171
$227$	20.9087	1.38776	0.693879	−	0.720092i	$-0.255900\pi$
$227$	20.9087	1.38776	0.693879	+	0.720092i	$0.255900\pi$
$228$	−11.6576	−0.772046
$229$	−11.3714	−0.751446	−0.375723	−	0.926732i	$-0.622606\pi$
$229$	−11.3714	−0.751446	−0.375723	+	0.926732i	$0.622606\pi$
$230$	7.46028	0.491917
$231$	−0.468159	−0.0308026
$232$	34.3680	2.25637
$233$	6.51284	0.426670	0.213335	−	0.976979i	$-0.431567\pi$
$233$	6.51284	0.426670	0.213335	+	0.976979i	$0.431567\pi$
$234$	−1.42506	−0.0931590
$235$	−5.15084	−0.336003
$236$	−4.00917	−0.260975
$237$	−8.57892	−0.557260
$238$	5.15137	0.333914
$239$	−4.83338	−0.312646	−0.156323	−	0.987706i	$-0.549964\pi$
$239$	−4.83338	−0.312646	−0.156323	+	0.987706i	$0.549964\pi$
$240$	−24.3522	−1.57193
$241$	−14.1250	−0.909870	−0.454935	−	0.890525i	$-0.650338\pi$
$241$	−14.1250	−0.909870	−0.454935	+	0.890525i	$0.650338\pi$
$242$	−26.9427	−1.73194
$243$	−20.3391	−1.30475
$244$	20.2872	1.29876
$245$	6.64226	0.424359
$246$	−3.25918	−0.207798
$247$	0.294387	0.0187314
$248$	0.105475	0.00669766
$249$	13.1477	0.833202
$250$	21.3757	1.35192
$251$	5.54875	0.350234	0.175117	−	0.984548i	$-0.443970\pi$
$251$	5.54875	0.350234	0.175117	+	0.984548i	$0.443970\pi$
$252$	20.7073	1.30443
$253$	0.112899	0.00709787
$254$	−7.78402	−0.488413
$255$	−6.00534	−0.376069
$256$	−32.0713	−2.00446
$257$	−9.06259	−0.565309	−0.282654	−	0.959222i	$-0.591215\pi$
$257$	−9.06259	−0.565309	−0.282654	+	0.959222i	$0.591215\pi$
$258$	−34.7784	−2.16521
$259$	−15.8760	−0.986485
$260$	2.43755	0.151171
$261$	17.1507	1.06160
$262$	21.5061	1.32865
$263$	−10.6063	−0.654012	−0.327006	−	0.945022i	$-0.606040\pi$
$263$	−10.6063	−0.654012	−0.327006	+	0.945022i	$0.606040\pi$
$264$	−1.09724	−0.0675304
$265$	−5.99561	−0.368307
$266$	−6.41164	−0.393123
$267$	−6.80791	−0.416638
$268$	−4.65643	−0.284437
$269$	29.4842	1.79768	0.898841	−	0.438275i	$-0.144411\pi$
$269$	29.4842	1.79768	0.898841	+	0.438275i	$0.144411\pi$
$270$	7.98135	0.485729
$271$	9.46378	0.574884	0.287442	−	0.957798i	$-0.407195\pi$
$271$	9.46378	0.574884	0.287442	+	0.957798i	$0.407195\pi$
$272$	4.05510	0.245876
$273$	−1.16118	−0.0702776
$274$	−1.97019	−0.119023
$275$	−0.153317	−0.00924537
$276$	−11.0888	−0.667468
$277$	7.79837	0.468559	0.234279	−	0.972169i	$-0.424727\pi$
$277$	7.79837	0.468559	0.234279	+	0.972169i	$0.424727\pi$
$278$	13.0341	0.781732
$279$	0.0526354	0.00315120
$280$	−26.6052	−1.58996
$281$	−25.9956	−1.55077	−0.775385	−	0.631489i	$-0.782444\pi$
$281$	−25.9956	−1.55077	−0.775385	+	0.631489i	$0.782444\pi$
$282$	11.4754	0.683350
$283$	−27.1589	−1.61443	−0.807215	−	0.590258i	$-0.799026\pi$
$283$	−27.1589	−1.61443	−0.807215	+	0.590258i	$0.799026\pi$
$284$	−17.5385	−1.04072
$285$	7.47453	0.442753
$286$	0.0552901	0.00326937
$287$	−1.19593	−0.0705937
$288$	0.221469	0.0130502
$289$	1.00000	0.0588235
$290$	−43.9708	−2.58206
$291$	18.0340	1.05717
$292$	41.2675	2.41500
$293$	−9.52812	−0.556639	−0.278319	−	0.960489i	$-0.589777\pi$
$293$	−9.52812	−0.556639	−0.278319	+	0.960489i	$0.589777\pi$
$294$	−14.7981	−0.863043
$295$	2.57056	0.149664
$296$	−37.2090	−2.16273
$297$	0.120784	0.00700860
$298$	−6.91479	−0.400563
$299$	0.280023	0.0161941
$300$	15.0587	0.869415
$301$	−12.7617	−0.735570
$302$	42.4095	2.44039
$303$	10.5164	0.604149
$304$	−5.04716	−0.289475
$305$	−13.0076	−0.744811
$306$	6.02504	0.344429
$307$	−18.3165	−1.04538	−0.522688	−	0.852524i	$-0.675071\pi$
$307$	−18.3165	−1.04538	−0.522688	+	0.852524i	$0.675071\pi$
$308$	−0.803410	−0.0457786
$309$	−8.56485	−0.487237
$310$	−0.134946	−0.00766441
$311$	10.3469	0.586721	0.293360	−	0.956002i	$-0.405226\pi$
$311$	10.3469	0.586721	0.293360	+	0.956002i	$0.405226\pi$
$312$	−2.72149	−0.154074
$313$	20.0167	1.13141	0.565704	−	0.824608i	$-0.308604\pi$
$313$	20.0167	1.13141	0.565704	+	0.824608i	$0.308604\pi$
$314$	−26.1090	−1.47342
$315$	−13.2769	−0.748067
$316$	−14.7223	−0.828196
$317$	−1.12632	−0.0632603	−0.0316301	−	0.999500i	$-0.510070\pi$
$317$	−1.12632	−0.0632603	−0.0316301	+	0.999500i	$0.510070\pi$
$318$	13.3574	0.749048
$319$	−0.665423	−0.0372565
$320$	20.2799	1.13368
$321$	34.1683	1.90709
$322$	−6.09879	−0.339872
$323$	−1.24465	−0.0692540
$324$	−41.4249	−2.30139
$325$	−0.380273	−0.0210938
$326$	−46.0213	−2.54888
$327$	0.594439	0.0328726
$328$	−2.80295	−0.154767
$329$	4.21081	0.232150
$330$	1.40382	0.0772779
$331$	−5.90516	−0.324577	−0.162289	−	0.986743i	$-0.551888\pi$
$331$	−5.90516	−0.324577	−0.162289	+	0.986743i	$0.551888\pi$
$332$	22.5628	1.23830
$333$	−18.5685	−1.01755
$334$	30.0885	1.64637
$335$	2.98556	0.163119
$336$	19.9080	1.08607
$337$	−18.3812	−1.00129	−0.500643	−	0.865654i	$-0.666903\pi$
$337$	−18.3812	−1.00129	−0.500643	+	0.865654i	$0.666903\pi$
$338$	−31.7306	−1.72591
$339$	−27.2460	−1.47980
$340$	−10.3058	−0.558910
$341$	−0.00204217	−0.000110590 0
$342$	−7.49905	−0.405502
$343$	−20.1401	−1.08746
$344$	−29.9099	−1.61264
$345$	7.10982	0.382780
$346$	25.7733	1.38558
$347$	−16.1215	−0.865446	−0.432723	−	0.901527i	$-0.642447\pi$
$347$	−16.1215	−0.865446	−0.432723	+	0.901527i	$0.642447\pi$
$348$	65.3574	3.50352
$349$	22.1696	1.18671	0.593356	−	0.804940i	$-0.297803\pi$
$349$	22.1696	1.18671	0.593356	+	0.804940i	$0.297803\pi$
$350$	8.28220	0.442702
$351$	0.299581	0.0159905
$352$	−0.00859265	−0.000457990 0
$353$	−21.3865	−1.13829	−0.569143	−	0.822238i	$-0.692725\pi$
$353$	−21.3865	−1.13829	−0.569143	+	0.822238i	$0.692725\pi$
$354$	−5.72687	−0.304380
$355$	11.2451	0.596830
$356$	−11.6831	−0.619203
$357$	4.90937	0.259831
$358$	24.5855	1.29939
$359$	4.13147	0.218051	0.109025	−	0.994039i	$-0.465227\pi$
$359$	4.13147	0.218051	0.109025	+	0.994039i	$0.465227\pi$
$360$	−31.1174	−1.64003
$361$	−17.4509	−0.918466
$362$	−26.8858	−1.41309
$363$	−25.6770	−1.34769
$364$	−1.99270	−0.104446
$365$	−26.4595	−1.38495
$366$	28.9792	1.51477
$367$	−15.6257	−0.815654	−0.407827	−	0.913059i	$-0.633713\pi$
$367$	−15.6257	−0.815654	−0.407827	+	0.913059i	$0.633713\pi$
$368$	−4.80089	−0.250264
$369$	−1.39876	−0.0728166
$370$	47.6057	2.47490
$371$	4.90141	0.254469
$372$	0.200581	0.0103996
$373$	−8.24848	−0.427090	−0.213545	−	0.976933i	$-0.568501\pi$
$373$	−8.24848	−0.427090	−0.213545	+	0.976933i	$0.568501\pi$
$374$	−0.233762	−0.0120876
$375$	20.3715	1.05198
$376$	9.86902	0.508956
$377$	−1.65045	−0.0850026
$378$	−6.52476	−0.335598
$379$	0.789270	0.0405421	0.0202710	−	0.999795i	$-0.493547\pi$
$379$	0.789270	0.0405421	0.0202710	+	0.999795i	$0.493547\pi$
$380$	12.8271	0.658016
$381$	−7.41835	−0.380053
$382$	42.9232	2.19614
$383$	19.1022	0.976079	0.488039	−	0.872822i	$-0.337712\pi$
$383$	19.1022	0.976079	0.488039	+	0.872822i	$0.337712\pi$
$384$	−45.6020	−2.32712
$385$	0.515123	0.0262531
$386$	53.9383	2.74539
$387$	−14.9260	−0.758733
$388$	30.9483	1.57116
$389$	27.0359	1.37077	0.685387	−	0.728179i	$-0.259633\pi$
$389$	27.0359	1.37077	0.685387	+	0.728179i	$0.259633\pi$
$390$	3.48191	0.176313
$391$	−1.18392	−0.0598732
$392$	−12.7266	−0.642790
$393$	20.4957	1.03387
$394$	50.6829	2.55337
$395$	9.43951	0.474953
$396$	−0.939668	−0.0472201
$397$	33.7073	1.69172	0.845861	−	0.533403i	$-0.179087\pi$
$397$	33.7073	1.69172	0.845861	+	0.533403i	$0.179087\pi$
$398$	−20.1886	−1.01196
$399$	−6.11043	−0.305904
$400$	6.51965	0.325982
$401$	−6.69587	−0.334376	−0.167188	−	0.985925i	$-0.553469\pi$
$401$	−6.69587	−0.334376	−0.167188	+	0.985925i	$0.553469\pi$
$402$	−6.65145	−0.331744
$403$	−0.00506521	−0.000252316 0
$404$	18.0472	0.897881
$405$	26.5604	1.31980
$406$	35.9462	1.78398
$407$	0.720431	0.0357104
$408$	11.5062	0.569644
$409$	14.4367	0.713847	0.356924	−	0.934134i	$-0.383826\pi$
$409$	14.4367	0.713847	0.356924	+	0.934134i	$0.383826\pi$
$410$	3.58613	0.177106
$411$	−1.87763	−0.0926167
$412$	−14.6982	−0.724128
$413$	−2.10143	−0.103405
$414$	−7.13314	−0.350575
$415$	−14.4666	−0.710138
$416$	−0.0213124	−0.00104493
$417$	12.4218	0.608297
$418$	0.290952	0.0142309
$419$	−23.6757	−1.15663	−0.578317	−	0.815812i	$-0.696290\pi$
$419$	−23.6757	−1.15663	−0.578317	+	0.815812i	$0.696290\pi$
$420$	−50.5950	−2.46878
$421$	4.93196	0.240369	0.120184	−	0.992752i	$-0.461651\pi$
$421$	4.93196	0.240369	0.120184	+	0.992752i	$0.461651\pi$
$422$	45.0942	2.19515
$423$	4.92496	0.239460
$424$	11.4876	0.557887
$425$	1.60777	0.0779882
$426$	−25.0527	−1.21381
$427$	10.6337	0.514600
$428$	58.6365	2.83430
$429$	0.0526927	0.00254403
$430$	38.2672	1.84541
$431$	−10.4144	−0.501642	−0.250821	−	0.968033i	$-0.580701\pi$
$431$	−10.4144	−0.501642	−0.250821	+	0.968033i	$0.580701\pi$
$432$	−5.13621	−0.247116
$433$	−18.2458	−0.876836	−0.438418	−	0.898771i	$-0.644461\pi$
$433$	−18.2458	−0.876836	−0.438418	+	0.898771i	$0.644461\pi$
$434$	0.110318	0.00529545
$435$	−41.9052	−2.00920
$436$	1.02012	0.0488549
$437$	1.47356	0.0704898
$438$	58.9483	2.81666
$439$	18.2219	0.869684	0.434842	−	0.900507i	$-0.356804\pi$
$439$	18.2219	0.869684	0.434842	+	0.900507i	$0.356804\pi$
$440$	1.20731	0.0575562
$441$	−6.35099	−0.302428
$442$	−0.579802	−0.0275784
$443$	7.81619	0.371359	0.185679	−	0.982610i	$-0.440551\pi$
$443$	7.81619	0.371359	0.185679	+	0.982610i	$0.440551\pi$
$444$	−70.7602	−3.35813
$445$	7.49085	0.355100
$446$	67.4465	3.19368
$447$	−6.58995	−0.311694
$448$	−16.5788	−0.783277
$449$	−23.1422	−1.09215	−0.546075	−	0.837736i	$-0.683879\pi$
$449$	−23.1422	−1.09215	−0.546075	+	0.837736i	$0.683879\pi$
$450$	9.68686	0.456643
$451$	0.0542699	0.00255547
$452$	−46.7570	−2.19926
$453$	40.4172	1.89896
$454$	51.2547	2.40550
$455$	1.27766	0.0598977
$456$	−14.3212	−0.670653
$457$	−1.88171	−0.0880226	−0.0440113	−	0.999031i	$-0.514014\pi$
$457$	−1.88171	−0.0880226	−0.0440113	+	0.999031i	$0.514014\pi$
$458$	−27.8755	−1.30254
$459$	−1.26661	−0.0591201
$460$	12.2012	0.568884
$461$	22.5569	1.05058	0.525289	−	0.850924i	$-0.323957\pi$
$461$	22.5569	1.05058	0.525289	+	0.850924i	$0.323957\pi$
$462$	−1.14763	−0.0533924
$463$	−29.8477	−1.38714	−0.693570	−	0.720390i	$-0.743963\pi$
$463$	−29.8477	−1.38714	−0.693570	+	0.720390i	$0.743963\pi$
$464$	28.2964	1.31363
$465$	−0.128606	−0.00596398
$466$	15.9653	0.739579
$467$	8.02665	0.371429	0.185715	−	0.982604i	$-0.440540\pi$
$467$	8.02665	0.371429	0.185715	+	0.982604i	$0.440540\pi$
$468$	−2.33066	−0.107735
$469$	−2.44070	−0.112701
$470$	−12.6266	−0.582419
$471$	−24.8825	−1.14652
$472$	−4.92520	−0.226701
$473$	0.579108	0.0266274
$474$	−21.0300	−0.965941
$475$	−2.00110	−0.0918169
$476$	8.42500	0.386159
$477$	5.73269	0.262482
$478$	−11.8484	−0.541932
$479$	−13.2273	−0.604369	−0.302185	−	0.953249i	$-0.597716\pi$
$479$	−13.2273	−0.604369	−0.302185	+	0.953249i	$0.597716\pi$
$480$	−0.541124	−0.0246988
$481$	1.78689	0.0814751
$482$	−34.6254	−1.57715
$483$	−5.81228	−0.264468
$484$	−44.0644	−2.00293
$485$	−19.8431	−0.901029
$486$	−49.8585	−2.26163
$487$	20.5736	0.932278	0.466139	−	0.884711i	$-0.345645\pi$
$487$	20.5736	0.932278	0.466139	+	0.884711i	$0.345645\pi$
$488$	24.9225	1.12819
$489$	−43.8593	−1.98339
$490$	16.2826	0.735572
$491$	−31.0637	−1.40189	−0.700943	−	0.713218i	$-0.747237\pi$
$491$	−31.0637	−1.40189	−0.700943	+	0.713218i	$0.747237\pi$
$492$	−5.33035	−0.240311
$493$	6.97799	0.314273
$494$	0.721649	0.0324685
$495$	0.602487	0.0270798
$496$	0.0868413	0.00389929
$497$	−9.19292	−0.412359
$498$	32.2297	1.44425
$499$	3.80976	0.170548	0.0852742	−	0.996358i	$-0.472823\pi$
$499$	3.80976	0.170548	0.0852742	+	0.996358i	$0.472823\pi$
$500$	34.9597	1.56344
$501$	28.6750	1.28111
$502$	13.6020	0.607086
$503$	−6.97575	−0.311033	−0.155517	−	0.987833i	$-0.549704\pi$
$503$	−6.97575	−0.311033	−0.155517	+	0.987833i	$0.549704\pi$
$504$	25.4385	1.13312
$505$	−11.5713	−0.514917
$506$	0.276755	0.0123033
$507$	−30.2399	−1.34300
$508$	−12.7307	−0.564832
$509$	−10.6359	−0.471428	−0.235714	−	0.971822i	$-0.575743\pi$
$509$	−10.6359	−0.471428	−0.235714	+	0.971822i	$0.575743\pi$
$510$	−14.7213	−0.651868
$511$	21.6306	0.956883
$512$	−39.5789	−1.74916
$513$	1.57648	0.0696032
$514$	−22.2157	−0.979891
$515$	9.42404	0.415273
$516$	−56.8796	−2.50398
$517$	−0.191081	−0.00840374
$518$	−38.9177	−1.70995
$519$	24.5625	1.07818
$520$	2.99449	0.131317
$521$	−29.6961	−1.30101	−0.650505	−	0.759502i	$-0.725443\pi$
$521$	−29.6961	−1.30101	−0.650505	+	0.759502i	$0.725443\pi$
$522$	42.0427	1.84016
$523$	−6.49137	−0.283848	−0.141924	−	0.989878i	$-0.545329\pi$
$523$	−6.49137	−0.283848	−0.141924	+	0.989878i	$0.545329\pi$
$524$	35.1729	1.53653
$525$	7.89312	0.344484
$526$	−25.9999	−1.13365
$527$	0.0214154	0.000932867 0
$528$	−0.903397	−0.0393153
$529$	−21.5983	−0.939058
$530$	−14.6974	−0.638414
$531$	−2.45783	−0.106661
$532$	−10.4862	−0.454632
$533$	0.134606	0.00583042
$534$	−16.6887	−0.722189
$535$	−37.5959	−1.62541
$536$	−5.72035	−0.247081
$537$	23.4305	1.01110
$538$	72.2763	3.11605
$539$	0.246409	0.0106136
$540$	13.0534	0.561729
$541$	−25.0971	−1.07901	−0.539503	−	0.841984i	$-0.681388\pi$
$541$	−25.0971	−1.07901	−0.539503	+	0.841984i	$0.681388\pi$
$542$	23.1991	0.996488
$543$	−25.6228	−1.09958
$544$	0.0901072	0.00386331
$545$	−0.654070	−0.0280173
$546$	−2.84646	−0.121817
$547$	19.7311	0.843643	0.421821	−	0.906679i	$-0.361391\pi$
$547$	19.7311	0.843643	0.421821	+	0.906679i	$0.361391\pi$
$548$	−3.22221	−0.137646
$549$	12.4372	0.530805
$550$	−0.375836	−0.0160257
$551$	−8.68513	−0.369999
$552$	−13.6224	−0.579809
$553$	−7.71681	−0.328152
$554$	19.1166	0.812188
$555$	45.3693	1.92582
$556$	21.3171	0.904045
$557$	37.0744	1.57089	0.785447	−	0.618929i	$-0.212433\pi$
$557$	37.0744	1.57089	0.785447	+	0.618929i	$0.212433\pi$
$558$	0.129028	0.00546221
$559$	1.43636	0.0607517
$560$	−21.9050	−0.925657
$561$	−0.222781	−0.00940581
$562$	−63.7247	−2.68806
$563$	−1.70485	−0.0718509	−0.0359255	−	0.999354i	$-0.511438\pi$
$563$	−1.70485	−0.0718509	−0.0359255	+	0.999354i	$0.511438\pi$
$564$	18.7679	0.790270
$565$	29.9792	1.26123
$566$	−66.5763	−2.79841
$567$	−21.7132	−0.911867
$568$	−21.5457	−0.904039
$569$	−44.2902	−1.85674	−0.928371	−	0.371654i	$-0.878791\pi$
$569$	−44.2902	−1.85674	−0.928371	+	0.371654i	$0.878791\pi$
$570$	18.3228	0.767456
$571$	39.1630	1.63892	0.819460	−	0.573136i	$-0.194273\pi$
$571$	39.1630	1.63892	0.819460	+	0.573136i	$0.194273\pi$
$572$	0.0904262	0.00378091
$573$	40.9068	1.70891
$574$	−2.93166	−0.122365
$575$	−1.90346	−0.0793798
$576$	−19.3906	−0.807942
$577$	9.13402	0.380254	0.190127	−	0.981759i	$-0.439110\pi$
$577$	9.13402	0.380254	0.190127	+	0.981759i	$0.439110\pi$
$578$	2.45136	0.101963
$579$	51.4044	2.13629
$580$	−71.9137	−2.98606
$581$	11.8265	0.490645
$582$	44.2079	1.83248
$583$	−0.222420	−0.00921168
$584$	50.6964	2.09783
$585$	1.49435	0.0617838
$586$	−23.3569	−0.964863
$587$	−23.3346	−0.963121	−0.481560	−	0.876413i	$-0.659930\pi$
$587$	−23.3346	−0.963121	−0.481560	+	0.876413i	$0.659930\pi$
$588$	−24.2021	−0.998078
$589$	−0.0266546	−0.00109828
$590$	6.30136	0.259423
$591$	48.3019	1.98687
$592$	−30.6355	−1.25911
$593$	14.2875	0.586715	0.293358	−	0.956003i	$-0.405227\pi$
$593$	14.2875	0.586715	0.293358	+	0.956003i	$0.405227\pi$
$594$	0.296085	0.0121485
$595$	−5.40186	−0.221455
$596$	−11.3091	−0.463237
$597$	−19.2402	−0.787450
$598$	0.686437	0.0280705
$599$	16.5205	0.675010	0.337505	−	0.941324i	$-0.390417\pi$
$599$	16.5205	0.675010	0.337505	+	0.941324i	$0.390417\pi$
$600$	18.4994	0.755233
$601$	23.0039	0.938348	0.469174	−	0.883106i	$-0.344552\pi$
$601$	23.0039	0.938348	0.469174	+	0.883106i	$0.344552\pi$
$602$	−31.2834	−1.27502
$603$	−2.85464	−0.116250
$604$	69.3602	2.82222
$605$	28.2528	1.14864
$606$	25.7794	1.04722
$607$	19.7656	0.802260	0.401130	−	0.916021i	$-0.368618\pi$
$607$	19.7656	0.802260	0.401130	+	0.916021i	$0.368618\pi$
$608$	−0.112152	−0.00454835
$609$	34.2575	1.38819
$610$	−31.8862	−1.29104
$611$	−0.473940	−0.0191735
$612$	9.85387	0.398319
$613$	40.2994	1.62768	0.813838	−	0.581091i	$-0.197374\pi$
$613$	40.2994	1.62768	0.813838	+	0.581091i	$0.197374\pi$
$614$	−44.9002	−1.81203
$615$	3.41766	0.137813
$616$	−0.986976	−0.0397664
$617$	18.8552	0.759080	0.379540	−	0.925175i	$-0.376082\pi$
$617$	18.8552	0.759080	0.379540	+	0.925175i	$0.376082\pi$
$618$	−20.9955	−0.844564
$619$	30.6204	1.23074	0.615370	−	0.788239i	$-0.289007\pi$
$619$	30.6204	1.23074	0.615370	+	0.788239i	$0.289007\pi$
$620$	−0.220702	−0.00886362
$621$	1.49956	0.0601751
$622$	25.3641	1.01701
$623$	−6.12378	−0.245344
$624$	−2.24070	−0.0896998
$625$	−30.4539	−1.21816
$626$	49.0680	1.96115
$627$	0.277284	0.0110736
$628$	−42.7010	−1.70395
$629$	−7.55483	−0.301231
$630$	−32.5464	−1.29668
$631$	−28.3110	−1.12704	−0.563522	−	0.826101i	$-0.690554\pi$
$631$	−28.3110	−1.12704	−0.563522	+	0.826101i	$0.690554\pi$
$632$	−18.0861	−0.719428
$633$	42.9758	1.70813
$634$	−2.76101	−0.109654
$635$	8.16252	0.323920
$636$	21.8459	0.866247
$637$	0.611169	0.0242154
$638$	−1.63119	−0.0645795
$639$	−10.7520	−0.425344
$640$	50.1766	1.98341
$641$	41.7276	1.64814	0.824070	−	0.566488i	$-0.191698\pi$
$641$	41.7276	1.64814	0.824070	+	0.566488i	$0.191698\pi$
$642$	83.7589	3.30570
$643$	−23.1222	−0.911851	−0.455925	−	0.890018i	$-0.650692\pi$
$643$	−23.1222	−0.911851	−0.455925	+	0.890018i	$0.650692\pi$
$644$	−9.97449	−0.393050
$645$	36.4695	1.43598
$646$	−3.05108	−0.120043
$647$	−13.0974	−0.514912	−0.257456	−	0.966290i	$-0.582884\pi$
$647$	−13.0974	−0.514912	−0.257456	+	0.966290i	$0.582884\pi$
$648$	−50.8898	−1.99914
$649$	0.0953603	0.00374322
$650$	−0.932187	−0.0365634
$651$	0.105136	0.00412060
$652$	−75.2672	−2.94769
$653$	−31.2919	−1.22455	−0.612274	−	0.790646i	$-0.709745\pi$
$653$	−31.2919	−1.22455	−0.612274	+	0.790646i	$0.709745\pi$
$654$	1.45718	0.0569804
$655$	−22.5518	−0.881171
$656$	−2.30777	−0.0901032
$657$	25.2992	0.987015
$658$	10.3222	0.402402
$659$	−4.79778	−0.186895	−0.0934474	−	0.995624i	$-0.529789\pi$
$659$	−4.79778	−0.186895	−0.0934474	+	0.995624i	$0.529789\pi$
$660$	2.29593	0.0893691
$661$	9.43286	0.366896	0.183448	−	0.983029i	$-0.441274\pi$
$661$	9.43286	0.366896	0.183448	+	0.983029i	$0.441274\pi$
$662$	−14.4757	−0.562613
$663$	−0.552564	−0.0214598
$664$	27.7181	1.07567
$665$	6.72341	0.260722
$666$	−45.5181	−1.76379
$667$	−8.26135	−0.319881
$668$	49.2094	1.90397
$669$	64.2780	2.48513
$670$	7.31869	0.282746
$671$	−0.482543	−0.0186284
$672$	0.442370	0.0170648
$673$	−27.0039	−1.04092	−0.520462	−	0.853885i	$-0.674240\pi$
$673$	−27.0039	−1.04092	−0.520462	+	0.853885i	$0.674240\pi$
$674$	−45.0589	−1.73560
$675$	−2.03641	−0.0783814
$676$	−51.8949	−1.99596
$677$	17.3166	0.665532	0.332766	−	0.943009i	$-0.392018\pi$
$677$	17.3166	0.665532	0.332766	+	0.943009i	$0.392018\pi$
$678$	−66.7897	−2.56504
$679$	16.2218	0.622534
$680$	−12.6605	−0.485508
$681$	48.8469	1.87182
$682$	−0.00500611	−0.000191694 0
$683$	−10.4974	−0.401672	−0.200836	−	0.979625i	$-0.564366\pi$
$683$	−10.4974	−0.401672	−0.200836	+	0.979625i	$0.564366\pi$
$684$	−12.2646	−0.468949
$685$	2.06599	0.0789373
$686$	−49.3706	−1.88498
$687$	−26.5660	−1.01355
$688$	−24.6259	−0.938855
$689$	−0.551669	−0.0210169
$690$	17.4287	0.663500
$691$	−13.7064	−0.521416	−0.260708	−	0.965418i	$-0.583956\pi$
$691$	−13.7064	−0.521416	−0.260708	+	0.965418i	$0.583956\pi$
$692$	42.1519	1.60238
$693$	−0.492534	−0.0187098
$694$	−39.5196	−1.50014
$695$	−13.6679	−0.518452
$696$	80.2905	3.04340
$697$	−0.569103	−0.0215563
$698$	54.3457	2.05702
$699$	15.2153	0.575496
$700$	13.5454	0.511969
$701$	−5.19097	−0.196060	−0.0980301	−	0.995183i	$-0.531254\pi$
$701$	−5.19097	−0.196060	−0.0980301	+	0.995183i	$0.531254\pi$
$702$	0.734381	0.0277174
$703$	9.40310	0.354644
$704$	0.752326	0.0283544
$705$	−12.0334	−0.453204
$706$	−52.4259	−1.97308
$707$	9.45956	0.355763
$708$	−9.36622	−0.352004
$709$	−12.1378	−0.455846	−0.227923	−	0.973679i	$-0.573193\pi$
$709$	−12.1378	−0.455846	−0.227923	+	0.973679i	$0.573193\pi$
$710$	27.5659	1.03453
$711$	−9.02558	−0.338486
$712$	−14.3525	−0.537882
$713$	−0.0253540	−0.000949514 0
$714$	12.0346	0.450385
$715$	−0.0579786	−0.00216828
$716$	40.2093	1.50269
$717$	−11.2918	−0.421698
$718$	10.1277	0.377963
$719$	−29.6012	−1.10394	−0.551969	−	0.833865i	$-0.686123\pi$
$719$	−29.6012	−1.10394	−0.551969	+	0.833865i	$0.686123\pi$
$720$	−25.6201	−0.954805
$721$	−7.70416	−0.286918
$722$	−42.7783	−1.59204
$723$	−32.9988	−1.22724
$724$	−43.9714	−1.63418
$725$	11.2190	0.416662
$726$	−62.9435	−2.33605
$727$	−1.52667	−0.0566212	−0.0283106	−	0.999599i	$-0.509013\pi$
$727$	−1.52667	−0.0566212	−0.0283106	+	0.999599i	$0.509013\pi$
$728$	−2.44800	−0.0907290
$729$	−16.5186	−0.611799
$730$	−64.8617	−2.40064
$731$	−6.07284	−0.224612
$732$	47.3950	1.75177
$733$	−34.9832	−1.29213	−0.646067	−	0.763281i	$-0.723587\pi$
$733$	−34.9832	−1.29213	−0.646067	+	0.763281i	$0.723587\pi$
$734$	−38.3042	−1.41383
$735$	15.5177	0.572378
$736$	−0.106679	−0.00393225
$737$	0.110756	0.00407974
$738$	−3.42887	−0.126218
$739$	18.0353	0.663439	0.331719	−	0.943378i	$-0.392371\pi$
$739$	18.0353	0.663439	0.331719	+	0.943378i	$0.392371\pi$
$740$	77.8585	2.86214
$741$	0.687748	0.0252650
$742$	12.0151	0.441089
$743$	26.9869	0.990055	0.495027	−	0.868877i	$-0.335158\pi$
$743$	26.9869	0.990055	0.495027	+	0.868877i	$0.335158\pi$
$744$	0.246410	0.00903384
$745$	7.25102	0.265657
$746$	−20.2200	−0.740307
$747$	13.8322	0.506095
$748$	−0.382315	−0.0139788
$749$	30.7347	1.12302
$750$	49.9379	1.82347
$751$	−9.25323	−0.337655	−0.168828	−	0.985646i	$-0.553998\pi$
$751$	−9.25323	−0.337655	−0.168828	+	0.985646i	$0.553998\pi$
$752$	8.12552	0.296307
$753$	12.9630	0.472397
$754$	−4.04585	−0.147341
$755$	−44.4716	−1.61849
$756$	−10.6712	−0.388106
$757$	−26.0356	−0.946279	−0.473139	−	0.880988i	$-0.656879\pi$
$757$	−26.0356	−0.946279	−0.473139	+	0.880988i	$0.656879\pi$
$758$	1.93478	0.0702745
$759$	0.263754	0.00957365
$760$	15.7579	0.571598
$761$	23.8982	0.866308	0.433154	−	0.901320i	$-0.357401\pi$
$761$	23.8982	0.866308	0.433154	+	0.901320i	$0.357401\pi$
$762$	−18.1850	−0.658775
$763$	0.534703	0.0193576
$764$	70.2004	2.53976
$765$	−6.31801	−0.228428
$766$	46.8265	1.69191
$767$	0.236523	0.00854034
$768$	−74.9251	−2.70363
$769$	−4.51410	−0.162783	−0.0813913	−	0.996682i	$-0.525936\pi$
$769$	−4.51410	−0.162783	−0.0813913	+	0.996682i	$0.525936\pi$
$770$	1.26275	0.0455064
$771$	−21.1720	−0.762492
$772$	88.2154	3.17494
$773$	−21.0181	−0.755968	−0.377984	−	0.925812i	$-0.623383\pi$
$773$	−21.0181	−0.755968	−0.377984	+	0.925812i	$0.623383\pi$
$774$	−36.5891	−1.31517
$775$	0.0344309	0.00123679
$776$	38.0195	1.36482
$777$	−37.0895	−1.33058
$778$	66.2747	2.37606
$779$	0.708333	0.0253787
$780$	5.69462	0.203900
$781$	0.417163	0.0149272
$782$	−2.90220	−0.103783
$783$	−8.83837	−0.315857
$784$	−10.4783	−0.374224
$785$	27.3786	0.977183
$786$	50.2425	1.79209
$787$	2.33308	0.0831653	0.0415826	−	0.999135i	$-0.486760\pi$
$787$	2.33308	0.0831653	0.0415826	+	0.999135i	$0.486760\pi$
$788$	82.8912	2.95288
$789$	−24.7784	−0.882136
$790$	23.1396	0.823272
$791$	−24.5080	−0.871404
$792$	−1.15437	−0.0410186
$793$	−1.19685	−0.0425015
$794$	82.6288	2.93239
$795$	−14.0069	−0.496775
$796$	−33.0183	−1.17030
$797$	52.0933	1.84524	0.922619	−	0.385712i	$-0.126044\pi$
$797$	52.0933	1.84524	0.922619	+	0.385712i	$0.126044\pi$
$798$	−14.9789	−0.530247
$799$	2.00378	0.0708887
$800$	0.144871	0.00512198
$801$	−7.16237	−0.253070
$802$	−16.4140	−0.579598
$803$	−0.981570	−0.0346388
$804$	−10.8784	−0.383650
$805$	6.39534	0.225406
$806$	−0.0124167	−0.000437358 0
$807$	68.8809	2.42472
$808$	22.1707	0.779961
$809$	41.5539	1.46096	0.730479	−	0.682935i	$-0.239297\pi$
$809$	41.5539	1.46096	0.730479	+	0.682935i	$0.239297\pi$
$810$	65.1092	2.28770
$811$	33.0699	1.16124	0.580621	−	0.814174i	$-0.302810\pi$
$811$	33.0699	1.16124	0.580621	+	0.814174i	$0.302810\pi$
$812$	58.7896	2.06311
$813$	22.1093	0.775407
$814$	1.76604	0.0618995
$815$	48.2590	1.69044
$816$	9.47352	0.331639
$817$	7.55854	0.264440
$818$	35.3895	1.23736
$819$	−1.22163	−0.0426873
$820$	5.86506	0.204817
$821$	31.8745	1.11243	0.556215	−	0.831039i	$-0.312253\pi$
$821$	31.8745	1.11243	0.556215	+	0.831039i	$0.312253\pi$
$822$	−4.60275	−0.160539
$823$	−34.5590	−1.20465	−0.602326	−	0.798250i	$-0.705759\pi$
$823$	−34.5590	−1.20465	−0.602326	+	0.798250i	$0.705759\pi$
$824$	−18.0565	−0.629027
$825$	−0.358180	−0.0124702
$826$	−5.15137	−0.179239
$827$	−39.5458	−1.37514	−0.687570	−	0.726118i	$-0.741323\pi$
$827$	−39.5458	−1.37514	−0.687570	+	0.726118i	$0.741323\pi$
$828$	−11.6662	−0.405427
$829$	−1.12482	−0.0390665	−0.0195333	−	0.999809i	$-0.506218\pi$
$829$	−1.12482	−0.0390665	−0.0195333	+	0.999809i	$0.506218\pi$
$830$	−35.4629	−1.23093
$831$	18.2186	0.631995
$832$	1.86600	0.0646919
$833$	−2.58398	−0.0895295
$834$	30.4502	1.05441
$835$	−31.5516	−1.09189
$836$	0.475848	0.0164575
$837$	−0.0271248	−0.000937571 0
$838$	−58.0377	−2.00488
$839$	−48.0309	−1.65821	−0.829105	−	0.559093i	$-0.811149\pi$
$839$	−48.0309	−1.65821	−0.829105	+	0.559093i	$0.811149\pi$
$840$	−62.1551	−2.14455
$841$	19.6923	0.679045
$842$	12.0900	0.416649
$843$	−60.7310	−2.09169
$844$	73.7510	2.53862
$845$	33.2734	1.14464
$846$	12.0729	0.415073
$847$	−23.0967	−0.793611
$848$	9.45816	0.324795
$849$	−63.4487	−2.17755
$850$	3.94122	0.135183
$851$	8.94428	0.306606
$852$	−40.9734	−1.40373
$853$	−28.9784	−0.992203	−0.496101	−	0.868265i	$-0.665236\pi$
$853$	−28.9784	−0.992203	−0.496101	+	0.868265i	$0.665236\pi$
$854$	26.0670	0.891995
$855$	7.86369	0.268932
$856$	72.0339	2.46207
$857$	19.2241	0.656682	0.328341	−	0.944559i	$-0.393510\pi$
$857$	19.2241	0.656682	0.328341	+	0.944559i	$0.393510\pi$
$858$	0.129169	0.00440975
$859$	−33.2665	−1.13504	−0.567519	−	0.823361i	$-0.692097\pi$
$859$	−33.2665	−1.13504	−0.567519	+	0.823361i	$0.692097\pi$
$860$	62.5855	2.13415
$861$	−2.79394	−0.0952172
$862$	−25.5294	−0.869534
$863$	−42.8673	−1.45922	−0.729610	−	0.683864i	$-0.760298\pi$
$863$	−42.8673	−1.45922	−0.729610	+	0.683864i	$0.760298\pi$
$864$	−0.114130	−0.00388279
$865$	−27.0265	−0.918930
$866$	−44.7270	−1.51988
$867$	2.33620	0.0793415
$868$	0.180424	0.00612400
$869$	0.350179	0.0118790
$870$	−102.725	−3.48269
$871$	0.274708	0.00930813
$872$	1.25320	0.0424387
$873$	18.9730	0.642137
$874$	3.61222	0.122185
$875$	18.3244	0.619476
$876$	96.4091	3.25736
$877$	−13.0362	−0.440202	−0.220101	−	0.975477i	$-0.570639\pi$
$877$	−13.0362	−0.440202	−0.220101	+	0.975477i	$0.570639\pi$
$878$	44.6684	1.50749
$879$	−22.2596	−0.750798
$880$	0.994022	0.0335085
$881$	−32.7490	−1.10334	−0.551671	−	0.834062i	$-0.686009\pi$
$881$	−32.7490	−1.10334	−0.551671	+	0.834062i	$0.686009\pi$
$882$	−15.5686	−0.524221
$883$	−46.1766	−1.55397	−0.776984	−	0.629520i	$-0.783251\pi$
$883$	−46.1766	−1.55397	−0.776984	+	0.629520i	$0.783251\pi$
$884$	−0.948259	−0.0318934
$885$	6.00534	0.201867
$886$	19.1603	0.643703
$887$	34.1912	1.14803	0.574014	−	0.818845i	$-0.305385\pi$
$887$	34.1912	1.14803	0.574014	+	0.818845i	$0.305385\pi$
$888$	−86.9277	−2.91710
$889$	−6.67287	−0.223801
$890$	18.3628	0.615522
$891$	0.985315	0.0330093
$892$	110.308	3.69338
$893$	−2.49400	−0.0834586
$894$	−16.1543	−0.540282
$895$	−25.7810	−0.861764
$896$	−41.0194	−1.37036
$897$	0.654190	0.0218428
$898$	−56.7300	−1.89310
$899$	0.149436	0.00498397
$900$	15.8427	0.528091
$901$	2.33241	0.0777040
$902$	0.133035	0.00442958
$903$	−29.8138	−0.992142
$904$	−57.4402	−1.91043
$905$	28.1931	0.937171
$906$	99.0771	3.29162
$907$	−52.0629	−1.72872	−0.864360	−	0.502874i	$-0.832276\pi$
$907$	−52.0629	−1.72872	−0.864360	+	0.502874i	$0.832276\pi$
$908$	83.8264	2.78188
$909$	11.0639	0.366966
$910$	3.13201	0.103825
$911$	11.4600	0.379685	0.189843	−	0.981815i	$-0.439202\pi$
$911$	11.4600	0.379685	0.189843	+	0.981815i	$0.439202\pi$
$912$	−11.7912	−0.390445
$913$	−0.536670	−0.0177612
$914$	−4.61274	−0.152576
$915$	−30.3883	−1.00461
$916$	−45.5900	−1.50634
$917$	18.4361	0.608814
$918$	−3.10491	−0.102477
$919$	53.1698	1.75391	0.876955	−	0.480572i	$-0.159571\pi$
$919$	53.1698	1.75391	0.876955	+	0.480572i	$0.159571\pi$
$920$	14.9890	0.494172
$921$	−42.7909	−1.41001
$922$	55.2950	1.82104
$923$	1.03469	0.0340572
$924$	−1.87693	−0.0617464
$925$	−12.1464	−0.399371
$926$	−73.1674	−2.40443
$927$	−9.01078	−0.295953
$928$	0.628767	0.0206403
$929$	−45.8047	−1.50280	−0.751401	−	0.659846i	$-0.770622\pi$
$929$	−45.8047	−1.50280	−0.751401	+	0.659846i	$0.770622\pi$
$930$	−0.315261	−0.0103378
$931$	3.21614	0.105405
$932$	26.1111	0.855297
$933$	24.1725	0.791373
$934$	19.6762	0.643826
$935$	0.245129	0.00801658
$936$	−2.86318	−0.0935860
$937$	41.4148	1.35296	0.676480	−	0.736461i	$-0.263504\pi$
$937$	41.4148	1.35296	0.676480	+	0.736461i	$0.263504\pi$
$938$	−5.98304	−0.195353
$939$	46.7629	1.52605
$940$	−20.6506	−0.673547
$941$	29.9153	0.975211	0.487606	−	0.873064i	$-0.337870\pi$
$941$	29.9153	0.975211	0.487606	+	0.873064i	$0.337870\pi$
$942$	−60.9959	−1.98736
$943$	0.673770	0.0219410
$944$	−4.05510	−0.131982
$945$	6.84203	0.222571
$946$	1.41960	0.0461552
$947$	20.5767	0.668653	0.334326	−	0.942457i	$-0.391491\pi$
$947$	20.5767	0.668653	0.334326	+	0.942457i	$0.391491\pi$
$948$	−34.3943	−1.11708
$949$	−2.43459	−0.0790302
$950$	−4.90542	−0.159153
$951$	−2.63130	−0.0853259
$952$	10.3500	0.335445
$953$	−51.2589	−1.66044	−0.830219	−	0.557437i	$-0.811785\pi$
$953$	−51.2589	−1.66044	−0.830219	+	0.557437i	$0.811785\pi$
$954$	14.0529	0.454979
$955$	−45.0104	−1.45650
$956$	−19.3778	−0.626724
$957$	−1.55456	−0.0502518
$958$	−32.4248	−1.04760
$959$	−1.68895	−0.0545389
$960$	47.3780	1.52912
$961$	−30.9995	−0.999985
$962$	4.38031	0.141227
$963$	35.9473	1.15839
$964$	−56.6295	−1.82391
$965$	−56.5610	−1.82076
$966$	−14.2480	−0.458422
$967$	−23.5516	−0.757368	−0.378684	−	0.925526i	$-0.623623\pi$
$967$	−23.5516	−0.757368	−0.378684	+	0.925526i	$0.623623\pi$
$968$	−54.1324	−1.73988
$969$	−2.90775	−0.0934103
$970$	−48.6426	−1.56182
$971$	−31.8986	−1.02367	−0.511837	−	0.859082i	$-0.671035\pi$
$971$	−31.8986	−1.02367	−0.511837	+	0.859082i	$0.671035\pi$
$972$	−81.5429	−2.61549
$973$	11.1735	0.358206
$974$	50.4333	1.61599
$975$	−0.888395	−0.0284514
$976$	20.5196	0.656817
$977$	39.9529	1.27821	0.639104	−	0.769120i	$-0.279305\pi$
$977$	39.9529	1.27821	0.639104	+	0.769120i	$0.279305\pi$
$978$	−107.515	−3.43795
$979$	0.277889	0.00888137
$980$	26.6300	0.850663
$981$	0.625388	0.0199671
$982$	−76.1483	−2.42999
$983$	−29.1081	−0.928405	−0.464203	−	0.885729i	$-0.653659\pi$
$983$	−29.1081	−0.928405	−0.464203	+	0.885729i	$0.653659\pi$
$984$	−6.54824	−0.208750
$985$	−53.1473	−1.69341
$986$	17.1056	0.544752
$987$	9.83730	0.313125
$988$	1.18025	0.0375487
$989$	7.18973	0.228620
$990$	1.47691	0.0469394
$991$	27.1080	0.861115	0.430558	−	0.902563i	$-0.358317\pi$
$991$	27.1080	0.861115	0.430558	+	0.902563i	$0.358317\pi$
$992$	0.00192968	6.12673e−5 0
$993$	−13.7956	−0.437792
$994$	−22.5352	−0.714772
$995$	21.1703	0.671144
$996$	52.7113	1.67022
$997$	−49.8389	−1.57841	−0.789207	−	0.614128i	$-0.789508\pi$
$997$	−49.8389	−1.57841	−0.789207	+	0.614128i	$0.789508\pi$
$998$	9.33910	0.295624
$999$	9.56900	0.302750

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1003.2.a.i.1.16	✓	18
3.2	odd	2		9027.2.a.q.1.3		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1003.2.a.i.1.16	✓	18	1.1	even	1	trivial
9027.2.a.q.1.3		18	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)

\(f(q)\)	\(=\)	\(q+2.45136 q^{2} +2.33620 q^{3} +4.00917 q^{4} -2.57056 q^{5} +5.72687 q^{6} +2.10143 q^{7} +4.92520 q^{8} +2.45783 q^{9} +O(q^{10})\)	\(q+2.45136 q^{2} +2.33620 q^{3} +4.00917 q^{4} -2.57056 q^{5} +5.72687 q^{6} +2.10143 q^{7} +4.92520 q^{8} +2.45783 q^{9} -6.30136 q^{10} -0.0953603 q^{11} +9.36622 q^{12} -0.236523 q^{13} +5.15137 q^{14} -6.00534 q^{15} +4.05510 q^{16} +1.00000 q^{17} +6.02504 q^{18} -1.24465 q^{19} -10.3058 q^{20} +4.90937 q^{21} -0.233762 q^{22} -1.18392 q^{23} +11.5062 q^{24} +1.60777 q^{25} -0.579802 q^{26} -1.26661 q^{27} +8.42500 q^{28} +6.97799 q^{29} -14.7213 q^{30} +0.0214154 q^{31} +0.0901072 q^{32} -0.222781 q^{33} +2.45136 q^{34} -5.40186 q^{35} +9.85387 q^{36} -7.55483 q^{37} -3.05108 q^{38} -0.552564 q^{39} -12.6605 q^{40} -0.569103 q^{41} +12.0346 q^{42} -6.07284 q^{43} -0.382315 q^{44} -6.31801 q^{45} -2.90220 q^{46} +2.00378 q^{47} +9.47352 q^{48} -2.58398 q^{49} +3.94122 q^{50} +2.33620 q^{51} -0.948259 q^{52} +2.33241 q^{53} -3.10491 q^{54} +0.245129 q^{55} +10.3500 q^{56} -2.90775 q^{57} +17.1056 q^{58} -1.00000 q^{59} -24.0764 q^{60} +5.06021 q^{61} +0.0524967 q^{62} +5.16498 q^{63} -7.88930 q^{64} +0.607995 q^{65} -0.546116 q^{66} -1.16145 q^{67} +4.00917 q^{68} -2.76587 q^{69} -13.2419 q^{70} -4.37459 q^{71} +12.1053 q^{72} +10.2933 q^{73} -18.5196 q^{74} +3.75607 q^{75} -4.99000 q^{76} -0.200393 q^{77} -1.35453 q^{78} -3.67217 q^{79} -10.4239 q^{80} -10.3326 q^{81} -1.39508 q^{82} +5.62781 q^{83} +19.6825 q^{84} -2.57056 q^{85} -14.8867 q^{86} +16.3020 q^{87} -0.469668 q^{88} -2.91410 q^{89} -15.4877 q^{90} -0.497036 q^{91} -4.74652 q^{92} +0.0500306 q^{93} +4.91199 q^{94} +3.19944 q^{95} +0.210508 q^{96} +7.71938 q^{97} -6.33426 q^{98} -0.234380 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 5 q^{2} + q^{3} + 21 q^{4} + 21 q^{5} + 5 q^{6} - q^{7} + 9 q^{8} + 17 q^{9}+O(q^{10}) \) 18 * q + 5 * q^2 + q^3 + 21 * q^4 + 21 * q^5 + 5 * q^6 - q^7 + 9 * q^8 + 17 * q^9	\( 18 q + 5 q^{2} + q^{3} + 21 q^{4} + 21 q^{5} + 5 q^{6} - q^{7} + 9 q^{8} + 17 q^{9} + 10 q^{10} + 6 q^{11} + 20 q^{12} + 12 q^{13} + 9 q^{14} - q^{15} + 19 q^{16} + 18 q^{17} + 10 q^{18} - 14 q^{19} + 17 q^{20} - 14 q^{21} - 4 q^{22} + 7 q^{23} - 3 q^{24} + 35 q^{25} + 3 q^{26} + 13 q^{27} + q^{28} + 23 q^{29} + 17 q^{30} - q^{31} + 13 q^{32} + 7 q^{33} + 5 q^{34} + 5 q^{35} - 16 q^{36} + 36 q^{37} - 19 q^{38} + 8 q^{39} - 4 q^{40} + 37 q^{41} + 9 q^{42} - 15 q^{43} - 9 q^{44} + 17 q^{45} + q^{46} + 23 q^{47} + 17 q^{48} + 15 q^{49} + 32 q^{50} + q^{51} - 11 q^{52} + 35 q^{53} - 17 q^{54} - 6 q^{55} + 37 q^{56} - 16 q^{57} + 2 q^{58} - 18 q^{59} - 6 q^{60} + 39 q^{61} - q^{62} + 15 q^{63} + 5 q^{64} + 15 q^{65} - 36 q^{66} + 14 q^{67} + 21 q^{68} + 16 q^{69} - 45 q^{70} + 3 q^{71} - 71 q^{72} + 56 q^{73} - 27 q^{74} + 16 q^{75} - q^{76} + 39 q^{77} - 71 q^{78} - 22 q^{79} + 45 q^{80} - 18 q^{81} + 5 q^{82} + 12 q^{83} + 2 q^{84} + 21 q^{85} + 4 q^{86} + 8 q^{87} - 18 q^{88} + 34 q^{89} + 48 q^{90} + 3 q^{91} + 67 q^{92} - 19 q^{93} - 38 q^{94} - 72 q^{95} + 6 q^{96} + 31 q^{97} + 19 q^{98} + 44 q^{99}+O(q^{100}) \) 18 * q + 5 * q^2 + q^3 + 21 * q^4 + 21 * q^5 + 5 * q^6 - q^7 + 9 * q^8 + 17 * q^9 + 10 * q^10 + 6 * q^11 + 20 * q^12 + 12 * q^13 + 9 * q^14 - q^15 + 19 * q^16 + 18 * q^17 + 10 * q^18 - 14 * q^19 + 17 * q^20 - 14 * q^21 - 4 * q^22 + 7 * q^23 - 3 * q^24 + 35 * q^25 + 3 * q^26 + 13 * q^27 + q^28 + 23 * q^29 + 17 * q^30 - q^31 + 13 * q^32 + 7 * q^33 + 5 * q^34 + 5 * q^35 - 16 * q^36 + 36 * q^37 - 19 * q^38 + 8 * q^39 - 4 * q^40 + 37 * q^41 + 9 * q^42 - 15 * q^43 - 9 * q^44 + 17 * q^45 + q^46 + 23 * q^47 + 17 * q^48 + 15 * q^49 + 32 * q^50 + q^51 - 11 * q^52 + 35 * q^53 - 17 * q^54 - 6 * q^55 + 37 * q^56 - 16 * q^57 + 2 * q^58 - 18 * q^59 - 6 * q^60 + 39 * q^61 - q^62 + 15 * q^63 + 5 * q^64 + 15 * q^65 - 36 * q^66 + 14 * q^67 + 21 * q^68 + 16 * q^69 - 45 * q^70 + 3 * q^71 - 71 * q^72 + 56 * q^73 - 27 * q^74 + 16 * q^75 - q^76 + 39 * q^77 - 71 * q^78 - 22 * q^79 + 45 * q^80 - 18 * q^81 + 5 * q^82 + 12 * q^83 + 2 * q^84 + 21 * q^85 + 4 * q^86 + 8 * q^87 - 18 * q^88 + 34 * q^89 + 48 * q^90 + 3 * q^91 + 67 * q^92 - 19 * q^93 - 38 * q^94 - 72 * q^95 + 6 * q^96 + 31 * q^97 + 19 * q^98 + 44 * q^99

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