LMFDB - Embedded newform 1003.2.a.i.1.10

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			1.10
Root			$0.715815$ 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)

$f(q)$	$=$	$q+0.715815 q^{2} +3.10981 q^{3} -1.48761 q^{4} +0.799569 q^{5} +2.22605 q^{6} -0.891306 q^{7} -2.49648 q^{8} +6.67092 q^{9} +O(q^{10})$	\(q+0.715815 q^{2} +3.10981 q^{3} -1.48761 q^{4} +0.799569 q^{5} +2.22605 q^{6} -0.891306 q^{7} -2.49648 q^{8} +6.67092 q^{9} +0.572344 q^{10} +0.790116 q^{11} -4.62618 q^{12} +6.94611 q^{13} -0.638011 q^{14} +2.48651 q^{15} +1.18819 q^{16} +1.00000 q^{17} +4.77515 q^{18} -0.850729 q^{19} -1.18945 q^{20} -2.77179 q^{21} +0.565577 q^{22} -3.83267 q^{23} -7.76359 q^{24} -4.36069 q^{25} +4.97213 q^{26} +11.4159 q^{27} +1.32591 q^{28} +2.63271 q^{29} +1.77988 q^{30} -3.46979 q^{31} +5.84350 q^{32} +2.45711 q^{33} +0.715815 q^{34} -0.712661 q^{35} -9.92372 q^{36} -0.234677 q^{37} -0.608965 q^{38} +21.6011 q^{39} -1.99611 q^{40} +5.91551 q^{41} -1.98409 q^{42} +0.280745 q^{43} -1.17538 q^{44} +5.33387 q^{45} -2.74348 q^{46} -1.88384 q^{47} +3.69506 q^{48} -6.20557 q^{49} -3.12145 q^{50} +3.10981 q^{51} -10.3331 q^{52} +4.91196 q^{53} +8.17166 q^{54} +0.631753 q^{55} +2.22513 q^{56} -2.64561 q^{57} +1.88453 q^{58} -1.00000 q^{59} -3.69895 q^{60} +7.96668 q^{61} -2.48373 q^{62} -5.94583 q^{63} +1.80647 q^{64} +5.55390 q^{65} +1.75884 q^{66} -9.09272 q^{67} -1.48761 q^{68} -11.9189 q^{69} -0.510134 q^{70} -11.8155 q^{71} -16.6539 q^{72} +4.12726 q^{73} -0.167986 q^{74} -13.5609 q^{75} +1.26555 q^{76} -0.704235 q^{77} +15.4624 q^{78} -4.06063 q^{79} +0.950044 q^{80} +15.4885 q^{81} +4.23441 q^{82} -10.4598 q^{83} +4.12334 q^{84} +0.799569 q^{85} +0.200962 q^{86} +8.18723 q^{87} -1.97251 q^{88} +10.6636 q^{89} +3.81806 q^{90} -6.19111 q^{91} +5.70151 q^{92} -10.7904 q^{93} -1.34848 q^{94} -0.680217 q^{95} +18.1722 q^{96} -14.6771 q^{97} -4.44205 q^{98} +5.27081 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.715815	0.506158	0.253079	−	0.967446i	$-0.418557\pi$
$2$	0.715815	0.506158	0.253079	+	0.967446i	$0.418557\pi$
$3$	3.10981	1.79545	0.897725	−	0.440556i	$-0.145219\pi$
$3$	3.10981	1.79545	0.897725	+	0.440556i	$0.145219\pi$
$4$	−1.48761	−0.743804
$5$	0.799569	0.357578	0.178789	−	0.983887i	$-0.442782\pi$
$5$	0.799569	0.357578	0.178789	+	0.983887i	$0.442782\pi$
$6$	2.22605	0.908781
$7$	−0.891306	−0.336882	−0.168441	−	0.985712i	$-0.553873\pi$
$7$	−0.891306	−0.336882	−0.168441	+	0.985712i	$0.553873\pi$
$8$	−2.49648	−0.882640
$9$	6.67092	2.22364
$10$	0.572344	0.180991
$11$	0.790116	0.238229	0.119115	−	0.992881i	$-0.461994\pi$
$11$	0.790116	0.238229	0.119115	+	0.992881i	$0.461994\pi$
$12$	−4.62618	−1.33546
$13$	6.94611	1.92650	0.963252	−	0.268599i	$-0.0865606\pi$
$13$	6.94611	1.92650	0.963252	+	0.268599i	$0.0865606\pi$
$14$	−0.638011	−0.170515
$15$	2.48651	0.642014
$16$	1.18819	0.297049
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	4.77515	1.12551
$19$	−0.850729	−0.195171	−0.0975854	−	0.995227i	$-0.531112\pi$
$19$	−0.850729	−0.195171	−0.0975854	+	0.995227i	$0.531112\pi$
$20$	−1.18945	−0.265968
$21$	−2.77179	−0.604855
$22$	0.565577	0.120582
$23$	−3.83267	−0.799167	−0.399583	−	0.916697i	$-0.630845\pi$
$23$	−3.83267	−0.799167	−0.399583	+	0.916697i	$0.630845\pi$
$24$	−7.76359	−1.58474
$25$	−4.36069	−0.872138
$26$	4.97213	0.975115
$27$	11.4159	2.19699
$28$	1.32591	0.250574
$29$	2.63271	0.488882	0.244441	−	0.969664i	$-0.421396\pi$
$29$	2.63271	0.488882	0.244441	+	0.969664i	$0.421396\pi$
$30$	1.77988	0.324960
$31$	−3.46979	−0.623193	−0.311597	−	0.950214i	$-0.600864\pi$
$31$	−3.46979	−0.623193	−0.311597	+	0.950214i	$0.600864\pi$
$32$	5.84350	1.03299
$33$	2.45711	0.427728
$34$	0.715815	0.122761
$35$	−0.712661	−0.120462
$36$	−9.92372	−1.65395
$37$	−0.234677	−0.0385807	−0.0192904	−	0.999814i	$-0.506141\pi$
$37$	−0.234677	−0.0385807	−0.0192904	+	0.999814i	$0.506141\pi$
$38$	−0.608965	−0.0987872
$39$	21.6011	3.45894
$40$	−1.99611	−0.315613
$41$	5.91551	0.923847	0.461924	−	0.886920i	$-0.347159\pi$
$41$	5.91551	0.923847	0.461924	+	0.886920i	$0.347159\pi$
$42$	−1.98409	−0.306152
$43$	0.280745	0.0428132	0.0214066	−	0.999771i	$-0.493186\pi$
$43$	0.280745	0.0428132	0.0214066	+	0.999771i	$0.493186\pi$
$44$	−1.17538	−0.177196
$45$	5.33387	0.795126
$46$	−2.74348	−0.404505
$47$	−1.88384	−0.274786	−0.137393	−	0.990517i	$-0.543872\pi$
$47$	−1.88384	−0.274786	−0.137393	+	0.990517i	$0.543872\pi$
$48$	3.69506	0.533336
$49$	−6.20557	−0.886511
$50$	−3.12145	−0.441439
$51$	3.10981	0.435461
$52$	−10.3331	−1.43294
$53$	4.91196	0.674710	0.337355	−	0.941378i	$-0.390468\pi$
$53$	4.91196	0.674710	0.337355	+	0.941378i	$0.390468\pi$
$54$	8.17166	1.11202
$55$	0.631753	0.0851855
$56$	2.22513	0.297346
$57$	−2.64561	−0.350419
$58$	1.88453	0.247451
$59$	−1.00000	−0.130189
$59$	−1.00000	−0.130189
$60$	−3.69895	−0.477533
$61$	7.96668	1.02003	0.510014	−	0.860166i	$-0.329640\pi$
$61$	7.96668	1.02003	0.510014	+	0.860166i	$0.329640\pi$
$62$	−2.48373	−0.315434
$63$	−5.94583	−0.749105
$64$	1.80647	0.225809
$65$	5.55390	0.688876
$66$	1.75884	0.216498
$67$	−9.09272	−1.11085	−0.555426	−	0.831566i	$-0.687445\pi$
$67$	−9.09272	−1.11085	−0.555426	+	0.831566i	$0.687445\pi$
$68$	−1.48761	−0.180399
$69$	−11.9189	−1.43486
$70$	−0.510134	−0.0609726
$71$	−11.8155	−1.40224	−0.701122	−	0.713041i	$-0.747317\pi$
$71$	−11.8155	−1.40224	−0.701122	+	0.713041i	$0.747317\pi$
$72$	−16.6539	−1.96268
$73$	4.12726	0.483059	0.241529	−	0.970393i	$-0.422351\pi$
$73$	4.12726	0.483059	0.241529	+	0.970393i	$0.422351\pi$
$74$	−0.167986	−0.0195279
$75$	−13.5609	−1.56588
$76$	1.26555	0.145169
$77$	−0.704235	−0.0802551
$78$	15.4624	1.75077
$79$	−4.06063	−0.456857	−0.228428	−	0.973561i	$-0.573359\pi$
$79$	−4.06063	−0.456857	−0.228428	+	0.973561i	$0.573359\pi$
$80$	0.950044	0.106218
$81$	15.4885	1.72094
$82$	4.23441	0.467613
$83$	−10.4598	−1.14812	−0.574059	−	0.818814i	$-0.694632\pi$
$83$	−10.4598	−1.14812	−0.574059	+	0.818814i	$0.694632\pi$
$84$	4.12334	0.449893
$85$	0.799569	0.0867255
$86$	0.200962	0.0216703
$87$	8.18723	0.877763
$88$	−1.97251	−0.210271
$89$	10.6636	1.13034	0.565169	−	0.824975i	$-0.308811\pi$
$89$	10.6636	1.13034	0.565169	+	0.824975i	$0.308811\pi$
$90$	3.81806	0.402459
$91$	−6.19111	−0.649004
$92$	5.70151	0.594424
$93$	−10.7904	−1.11891
$94$	−1.34848	−0.139085
$95$	−0.680217	−0.0697888
$96$	18.1722	1.85469
$97$	−14.6771	−1.49024	−0.745119	−	0.666932i	$-0.767607\pi$
$97$	−14.6771	−1.49024	−0.745119	+	0.666932i	$0.767607\pi$
$98$	−4.44205	−0.448714
$99$	5.27081	0.529736
$100$	6.48700	0.648700
$101$	−19.4512	−1.93546	−0.967732	−	0.251980i	$-0.918918\pi$
$101$	−19.4512	−1.93546	−0.967732	+	0.251980i	$0.918918\pi$
$102$	2.22605	0.220412
$103$	5.50413	0.542338	0.271169	−	0.962532i	$-0.412590\pi$
$103$	5.50413	0.542338	0.271169	+	0.962532i	$0.412590\pi$
$104$	−17.3409	−1.70041
$105$	−2.21624	−0.216283
$106$	3.51606	0.341510
$107$	−6.33435	−0.612364	−0.306182	−	0.951973i	$-0.599052\pi$
$107$	−6.33435	−0.612364	−0.306182	+	0.951973i	$0.599052\pi$
$108$	−16.9824	−1.63413
$109$	16.4229	1.57302	0.786512	−	0.617575i	$-0.211885\pi$
$109$	16.4229	1.57302	0.786512	+	0.617575i	$0.211885\pi$
$110$	0.452218	0.0431173
$111$	−0.729802	−0.0692698
$112$	−1.05905	−0.100070
$113$	−6.31664	−0.594219	−0.297110	−	0.954843i	$-0.596023\pi$
$113$	−6.31664	−0.594219	−0.297110	+	0.954843i	$0.596023\pi$
$114$	−1.89377	−0.177368
$115$	−3.06449	−0.285765
$116$	−3.91644	−0.363632
$117$	46.3370	4.28385
$118$	−0.715815	−0.0658962
$119$	−0.891306	−0.0817059
$120$	−6.20753	−0.566667
$121$	−10.3757	−0.943247
$122$	5.70267	0.516295
$123$	18.3961	1.65872
$124$	5.16169	0.463534
$125$	−7.48452	−0.669436
$126$	−4.25612	−0.379165
$127$	−15.9169	−1.41239	−0.706197	−	0.708015i	$-0.749591\pi$
$127$	−15.9169	−1.41239	−0.706197	+	0.708015i	$0.749591\pi$
$128$	−10.3939	−0.918699
$129$	0.873065	0.0768691
$130$	3.97556	0.348680
$131$	−10.4847	−0.916050	−0.458025	−	0.888939i	$-0.651443\pi$
$131$	−10.4847	−0.916050	−0.458025	+	0.888939i	$0.651443\pi$
$132$	−3.65522	−0.318146
$133$	0.758260	0.0657495
$134$	−6.50871	−0.562267
$135$	9.12779	0.785595
$136$	−2.49648	−0.214072
$137$	−2.36251	−0.201843	−0.100921	−	0.994894i	$-0.532179\pi$
$137$	−2.36251	−0.201843	−0.100921	+	0.994894i	$0.532179\pi$
$138$	−8.53172	−0.726268
$139$	−14.6302	−1.24091	−0.620457	−	0.784241i	$-0.713053\pi$
$139$	−14.6302	−1.24091	−0.620457	+	0.784241i	$0.713053\pi$
$140$	1.06016	0.0895999
$141$	−5.85838	−0.493364
$142$	−8.45773	−0.709757
$143$	5.48823	0.458949
$144$	7.92636	0.660530
$145$	2.10503	0.174814
$146$	2.95435	0.244504
$147$	−19.2982	−1.59169
$148$	0.349108	0.0286965
$149$	0.821269	0.0672810	0.0336405	−	0.999434i	$-0.489290\pi$
$149$	0.821269	0.0672810	0.0336405	+	0.999434i	$0.489290\pi$
$150$	−9.70711	−0.792583
$151$	−4.59418	−0.373869	−0.186934	−	0.982372i	$-0.559855\pi$
$151$	−4.59418	−0.373869	−0.186934	+	0.982372i	$0.559855\pi$
$152$	2.12383	0.172266
$153$	6.67092	0.539312
$154$	−0.504103	−0.0406217
$155$	−2.77434	−0.222840
$156$	−32.1340	−2.57278
$157$	14.9689	1.19465	0.597325	−	0.801999i	$-0.296230\pi$
$157$	14.9689	1.19465	0.597325	+	0.801999i	$0.296230\pi$
$158$	−2.90666	−0.231242
$159$	15.2753	1.21141
$160$	4.67228	0.369376
$161$	3.41608	0.269225
$162$	11.0869	0.871067
$163$	15.3919	1.20559	0.602794	−	0.797897i	$-0.294054\pi$
$163$	15.3919	1.20559	0.602794	+	0.797897i	$0.294054\pi$
$164$	−8.79996	−0.687161
$165$	1.96463	0.152946
$166$	−7.48732	−0.581129
$167$	17.0407	1.31865	0.659326	−	0.751857i	$-0.270842\pi$
$167$	17.0407	1.31865	0.659326	+	0.751857i	$0.270842\pi$
$168$	6.91974	0.533869
$169$	35.2484	2.71142
$170$	0.572344	0.0438968
$171$	−5.67515	−0.433990
$172$	−0.417639	−0.0318447
$173$	15.9730	1.21441	0.607203	−	0.794547i	$-0.292292\pi$
$173$	15.9730	1.21441	0.607203	+	0.794547i	$0.292292\pi$
$174$	5.86054	0.444287
$175$	3.88671	0.293807
$176$	0.938812	0.0707656
$177$	−3.10981	−0.233748
$178$	7.63315	0.572129
$179$	−7.27446	−0.543719	−0.271859	−	0.962337i	$-0.587639\pi$
$179$	−7.27446	−0.543719	−0.271859	+	0.962337i	$0.587639\pi$
$180$	−7.93470	−0.591418
$181$	−16.4972	−1.22623	−0.613114	−	0.789994i	$-0.710083\pi$
$181$	−16.4972	−1.22623	−0.613114	+	0.789994i	$0.710083\pi$
$182$	−4.43169	−0.328499
$183$	24.7749	1.83141
$184$	9.56820	0.705377
$185$	−0.187641	−0.0137956
$186$	−7.72394	−0.566347
$187$	0.790116	0.0577790
$188$	2.80241	0.204387
$189$	−10.1750	−0.740125
$190$	−0.486910	−0.0353242
$191$	20.4131	1.47704	0.738520	−	0.674232i	$-0.235525\pi$
$191$	20.4131	1.47704	0.738520	+	0.674232i	$0.235525\pi$
$192$	5.61780	0.405429
$193$	15.0468	1.08309	0.541545	−	0.840672i	$-0.317840\pi$
$193$	15.0468	1.08309	0.541545	+	0.840672i	$0.317840\pi$
$194$	−10.5061	−0.754295
$195$	17.2716	1.23684
$196$	9.23146	0.659390
$197$	−23.3199	−1.66148	−0.830738	−	0.556664i	$-0.812081\pi$
$197$	−23.3199	−1.66148	−0.830738	+	0.556664i	$0.812081\pi$
$198$	3.77292	0.268130
$199$	−1.36639	−0.0968607	−0.0484303	−	0.998827i	$-0.515422\pi$
$199$	−1.36639	−0.0968607	−0.0484303	+	0.998827i	$0.515422\pi$
$200$	10.8864	0.769784
$201$	−28.2766	−1.99448
$202$	−13.9235	−0.979651
$203$	−2.34655	−0.164695
$204$	−4.62618	−0.323897
$205$	4.72986	0.330348
$206$	3.93994	0.274509
$207$	−25.5674	−1.77706
$208$	8.25333	0.572266
$209$	−0.672175	−0.0464953
$210$	−1.58642	−0.109473
$211$	−12.4662	−0.858207	−0.429103	−	0.903255i	$-0.641170\pi$
$211$	−12.4662	−0.858207	−0.429103	+	0.903255i	$0.641170\pi$
$212$	−7.30707	−0.501852
$213$	−36.7440	−2.51766
$214$	−4.53422	−0.309953
$215$	0.224475	0.0153091
$216$	−28.4996	−1.93915
$217$	3.09265	0.209943
$218$	11.7557	0.796199
$219$	12.8350	0.867308
$220$	−0.939801	−0.0633613
$221$	6.94611	0.467246
$222$	−0.522404	−0.0350614
$223$	5.64293	0.377878	0.188939	−	0.981989i	$-0.439495\pi$
$223$	5.64293	0.377878	0.188939	+	0.981989i	$0.439495\pi$
$224$	−5.20834	−0.347997
$225$	−29.0898	−1.93932
$226$	−4.52155	−0.300769
$227$	12.7965	0.849336	0.424668	−	0.905349i	$-0.360391\pi$
$227$	12.7965	0.849336	0.424668	+	0.905349i	$0.360391\pi$
$228$	3.93563	0.260643
$229$	2.45284	0.162088	0.0810442	−	0.996711i	$-0.474174\pi$
$229$	2.45284	0.162088	0.0810442	+	0.996711i	$0.474174\pi$
$230$	−2.19361	−0.144642
$231$	−2.19004	−0.144094
$232$	−6.57252	−0.431507
$233$	3.71566	0.243421	0.121711	−	0.992566i	$-0.461162\pi$
$233$	3.71566	0.243421	0.121711	+	0.992566i	$0.461162\pi$
$234$	33.1687	2.16831
$235$	−1.50626	−0.0982575
$236$	1.48761	0.0968350
$237$	−12.6278	−0.820264
$238$	−0.638011	−0.0413561
$239$	26.8098	1.73418	0.867092	−	0.498148i	$-0.165987\pi$
$239$	26.8098	1.73418	0.867092	+	0.498148i	$0.165987\pi$
$240$	2.95446	0.190709
$241$	−27.6081	−1.77839	−0.889197	−	0.457524i	$-0.848736\pi$
$241$	−27.6081	−1.77839	−0.889197	+	0.457524i	$0.848736\pi$
$242$	−7.42710	−0.477432
$243$	13.9185	0.892874
$244$	−11.8513	−0.758701
$245$	−4.96179	−0.316997
$246$	13.1682	0.839575
$247$	−5.90926	−0.375997
$248$	8.66228	0.550056
$249$	−32.5281	−2.06139
$250$	−5.35753	−0.338840
$251$	14.1831	0.895230	0.447615	−	0.894226i	$-0.352274\pi$
$251$	14.1831	0.895230	0.447615	+	0.894226i	$0.352274\pi$
$252$	8.84507	0.557187
$253$	−3.02825	−0.190385
$254$	−11.3935	−0.714894
$255$	2.48651	0.155711
$256$	−11.0531	−0.690816
$257$	3.78188	0.235907	0.117954	−	0.993019i	$-0.462367\pi$
$257$	3.78188	0.235907	0.117954	+	0.993019i	$0.462367\pi$
$258$	0.624953	0.0389079
$259$	0.209169	0.0129971
$260$	−8.26202	−0.512389
$261$	17.5626	1.08710
$262$	−7.50509	−0.463666
$263$	4.18224	0.257888	0.128944	−	0.991652i	$-0.458841\pi$
$263$	4.18224	0.257888	0.128944	+	0.991652i	$0.458841\pi$
$264$	−6.13414	−0.377530
$265$	3.92745	0.241262
$266$	0.542774	0.0332796
$267$	33.1617	2.02946
$268$	13.5264	0.826256
$269$	20.4299	1.24563	0.622815	−	0.782369i	$-0.285989\pi$
$269$	20.4299	1.24563	0.622815	+	0.782369i	$0.285989\pi$
$270$	6.53381	0.397635
$271$	7.62188	0.462996	0.231498	−	0.972835i	$-0.425637\pi$
$271$	7.62188	0.462996	0.231498	+	0.972835i	$0.425637\pi$
$272$	1.18819	0.0720449
$273$	−19.2532	−1.16526
$274$	−1.69112	−0.102164
$275$	−3.44545	−0.207769
$276$	17.7306	1.06726
$277$	14.2686	0.857316	0.428658	−	0.903467i	$-0.358986\pi$
$277$	14.2686	0.857316	0.428658	+	0.903467i	$0.358986\pi$
$278$	−10.4725	−0.628098
$279$	−23.1467	−1.38576
$280$	1.77915	0.106324
$281$	9.32831	0.556480	0.278240	−	0.960512i	$-0.410249\pi$
$281$	9.32831	0.556480	0.278240	+	0.960512i	$0.410249\pi$
$282$	−4.19352	−0.249720
$283$	2.42555	0.144184	0.0720920	−	0.997398i	$-0.477032\pi$
$283$	2.42555	0.144184	0.0720920	+	0.997398i	$0.477032\pi$
$284$	17.5769	1.04299
$285$	−2.11535	−0.125302
$286$	3.92856	0.232301
$287$	−5.27253	−0.311228
$288$	38.9815	2.29701
$289$	1.00000	0.0588235
$290$	1.50682	0.0884833
$291$	−45.6431	−2.67565
$292$	−6.13974	−0.359301
$293$	−21.7269	−1.26930	−0.634651	−	0.772799i	$-0.718856\pi$
$293$	−21.7269	−1.26930	−0.634651	+	0.772799i	$0.718856\pi$
$294$	−13.8139	−0.805644
$295$	−0.799569	−0.0465527
$296$	0.585868	0.0340529
$297$	9.01987	0.523386
$298$	0.587877	0.0340548
$299$	−26.6221	−1.53960
$300$	20.1733	1.16471
$301$	−0.250230	−0.0144230
$302$	−3.28858	−0.189237
$303$	−60.4895	−3.47503
$304$	−1.01083	−0.0579752
$305$	6.36991	0.364740
$306$	4.77515	0.272977
$307$	6.86604	0.391866	0.195933	−	0.980617i	$-0.437227\pi$
$307$	6.86604	0.391866	0.195933	+	0.980617i	$0.437227\pi$
$308$	1.04763	0.0596940
$309$	17.1168	0.973741
$310$	−1.98592	−0.112792
$311$	15.3732	0.871736	0.435868	−	0.900011i	$-0.356441\pi$
$311$	15.3732	0.871736	0.435868	+	0.900011i	$0.356441\pi$
$312$	−53.9268	−3.05300
$313$	−7.41153	−0.418924	−0.209462	−	0.977817i	$-0.567171\pi$
$313$	−7.41153	−0.418924	−0.209462	+	0.977817i	$0.567171\pi$
$314$	10.7150	0.604682
$315$	−4.75411	−0.267864
$316$	6.04063	0.339812
$317$	0.820916	0.0461072	0.0230536	−	0.999734i	$-0.492661\pi$
$317$	0.820916	0.0461072	0.0230536	+	0.999734i	$0.492661\pi$
$318$	10.9343	0.613164
$319$	2.08015	0.116466
$320$	1.44440	0.0807445
$321$	−19.6986	−1.09947
$322$	2.44528	0.136270
$323$	−0.850729	−0.0473358
$324$	−23.0408	−1.28004
$325$	−30.2898	−1.68018
$326$	11.0178	0.610218
$327$	51.0720	2.82429
$328$	−14.7680	−0.815425
$329$	1.67907	0.0925704
$330$	1.40631	0.0774150
$331$	−2.09064	−0.114912	−0.0574559	−	0.998348i	$-0.518299\pi$
$331$	−2.09064	−0.114912	−0.0574559	+	0.998348i	$0.518299\pi$
$332$	15.5602	0.853974
$333$	−1.56551	−0.0857897
$334$	12.1980	0.667446
$335$	−7.27026	−0.397217
$336$	−3.29343	−0.179671
$337$	−23.3746	−1.27329	−0.636647	−	0.771155i	$-0.719679\pi$
$337$	−23.3746	−1.27329	−0.636647	+	0.771155i	$0.719679\pi$
$338$	25.2314	1.37241
$339$	−19.6435	−1.06689
$340$	−1.18945	−0.0645068
$341$	−2.74154	−0.148463
$342$	−4.06236	−0.219667
$343$	11.7702	0.635531
$344$	−0.700876	−0.0377887
$345$	−9.52997	−0.513076
$346$	11.4337	0.614681
$347$	7.25195	0.389305	0.194653	−	0.980872i	$-0.437642\pi$
$347$	7.25195	0.389305	0.194653	+	0.980872i	$0.437642\pi$
$348$	−12.1794	−0.652884
$349$	−21.4735	−1.14945	−0.574725	−	0.818347i	$-0.694891\pi$
$349$	−21.4735	−1.14945	−0.574725	+	0.818347i	$0.694891\pi$
$350$	2.78217	0.148713
$351$	79.2959	4.23250
$352$	4.61704	0.246089
$353$	25.3164	1.34746	0.673728	−	0.738979i	$-0.264692\pi$
$353$	25.3164	1.34746	0.673728	+	0.738979i	$0.264692\pi$
$354$	−2.22605	−0.118313
$355$	−9.44732	−0.501412
$356$	−15.8632	−0.840749
$357$	−2.77179	−0.146699
$358$	−5.20717	−0.275207
$359$	−2.29751	−0.121258	−0.0606288	−	0.998160i	$-0.519311\pi$
$359$	−2.29751	−0.121258	−0.0606288	+	0.998160i	$0.519311\pi$
$360$	−13.3159	−0.701810
$361$	−18.2763	−0.961908
$362$	−11.8090	−0.620665
$363$	−32.2665	−1.69355
$364$	9.20994	0.482732
$365$	3.30003	0.172731
$366$	17.7342	0.926983
$367$	0.940489	0.0490931	0.0245466	−	0.999699i	$-0.492186\pi$
$367$	0.940489	0.0490931	0.0245466	+	0.999699i	$0.492186\pi$
$368$	−4.55396	−0.237391
$369$	39.4619	2.05431
$370$	−0.134316	−0.00698277
$371$	−4.37806	−0.227298
$372$	16.0519	0.832252
$373$	−24.1158	−1.24867	−0.624336	−	0.781156i	$-0.714630\pi$
$373$	−24.1158	−1.24867	−0.624336	+	0.781156i	$0.714630\pi$
$374$	0.565577	0.0292453
$375$	−23.2754	−1.20194
$376$	4.70297	0.242537
$377$	18.2871	0.941833
$378$	−7.28345	−0.374620
$379$	−7.43821	−0.382075	−0.191037	−	0.981583i	$-0.561185\pi$
$379$	−7.43821	−0.382075	−0.191037	+	0.981583i	$0.561185\pi$
$380$	1.01190	0.0519092
$381$	−49.4985	−2.53588
$382$	14.6120	0.747615
$383$	−36.7702	−1.87887	−0.939435	−	0.342728i	$-0.888649\pi$
$383$	−36.7702	−1.87887	−0.939435	+	0.342728i	$0.888649\pi$
$384$	−32.3230	−1.64948
$385$	−0.563085	−0.0286975
$386$	10.7707	0.548214
$387$	1.87283	0.0952013
$388$	21.8338	1.10844
$389$	20.9619	1.06281	0.531406	−	0.847117i	$-0.321664\pi$
$389$	20.9619	1.06281	0.531406	+	0.847117i	$0.321664\pi$
$390$	12.3633	0.626038
$391$	−3.83267	−0.193826
$392$	15.4921	0.782470
$393$	−32.6053	−1.64472
$394$	−16.6928	−0.840969
$395$	−3.24676	−0.163362
$396$	−7.84089	−0.394020
$397$	31.8689	1.59945	0.799727	−	0.600363i	$-0.204977\pi$
$397$	31.8689	1.59945	0.799727	+	0.600363i	$0.204977\pi$
$398$	−0.978082	−0.0490268
$399$	2.35805	0.118050
$400$	−5.18135	−0.259067
$401$	20.2974	1.01360	0.506802	−	0.862062i	$-0.330827\pi$
$401$	20.2974	1.01360	0.506802	+	0.862062i	$0.330827\pi$
$402$	−20.2408	−1.00952
$403$	−24.1016	−1.20058
$404$	28.9357	1.43961
$405$	12.3841	0.615371
$406$	−1.67970	−0.0833619
$407$	−0.185422	−0.00919105
$408$	−7.76359	−0.384355
$409$	−7.30974	−0.361444	−0.180722	−	0.983534i	$-0.557843\pi$
$409$	−7.30974	−0.361444	−0.180722	+	0.983534i	$0.557843\pi$
$410$	3.38571	0.167208
$411$	−7.34696	−0.362399
$412$	−8.18799	−0.403393
$413$	0.891306	0.0438583
$414$	−18.3016	−0.899473
$415$	−8.36337	−0.410542
$416$	40.5896	1.99007
$417$	−45.4970	−2.22800
$418$	−0.481153	−0.0235340
$419$	15.0943	0.737404	0.368702	−	0.929548i	$-0.379802\pi$
$419$	15.0943	0.737404	0.368702	+	0.929548i	$0.379802\pi$
$420$	3.29690	0.160872
$421$	25.9622	1.26532	0.632659	−	0.774430i	$-0.281963\pi$
$421$	25.9622	1.26532	0.632659	+	0.774430i	$0.281963\pi$
$422$	−8.92348	−0.434388
$423$	−12.5669	−0.611025
$424$	−12.2626	−0.595526
$425$	−4.36069	−0.211524
$426$	−26.3019	−1.27433
$427$	−7.10074	−0.343629
$428$	9.42303	0.455479
$429$	17.0674	0.824020
$430$	0.160683	0.00774882
$431$	25.7473	1.24020	0.620102	−	0.784521i	$-0.287091\pi$
$431$	25.7473	1.24020	0.620102	+	0.784521i	$0.287091\pi$
$432$	13.5643	0.652612
$433$	−3.64574	−0.175203	−0.0876015	−	0.996156i	$-0.527920\pi$
$433$	−3.64574	−0.175203	−0.0876015	+	0.996156i	$0.527920\pi$
$434$	2.21376	0.106264
$435$	6.54626	0.313869
$436$	−24.4308	−1.17002
$437$	3.26056	0.155974
$438$	9.18749	0.438995
$439$	15.6504	0.746953	0.373477	−	0.927640i	$-0.378166\pi$
$439$	15.6504	0.746953	0.373477	+	0.927640i	$0.378166\pi$
$440$	−1.57716	−0.0751882
$441$	−41.3969	−1.97128
$442$	4.97213	0.236500
$443$	5.49462	0.261057	0.130529	−	0.991445i	$-0.458333\pi$
$443$	5.49462	0.261057	0.130529	+	0.991445i	$0.458333\pi$
$444$	1.08566	0.0515231
$445$	8.52627	0.404184
$446$	4.03929	0.191266
$447$	2.55399	0.120800
$448$	−1.61012	−0.0760711
$449$	25.1710	1.18789	0.593945	−	0.804505i	$-0.297570\pi$
$449$	25.1710	1.18789	0.593945	+	0.804505i	$0.297570\pi$
$450$	−20.8229	−0.981603
$451$	4.67394	0.220087
$452$	9.39668	0.441983
$453$	−14.2870	−0.671263
$454$	9.15996	0.429898
$455$	−4.95022	−0.232070
$456$	6.60472	0.309294
$457$	−24.9340	−1.16636	−0.583182	−	0.812342i	$-0.698192\pi$
$457$	−24.9340	−1.16636	−0.583182	+	0.812342i	$0.698192\pi$
$458$	1.75578	0.0820424
$459$	11.4159	0.532848
$460$	4.55875	0.212553
$461$	−1.34109	−0.0624607	−0.0312303	−	0.999512i	$-0.509943\pi$
$461$	−1.34109	−0.0624607	−0.0312303	+	0.999512i	$0.509943\pi$
$462$	−1.56766	−0.0729343
$463$	22.6773	1.05390	0.526952	−	0.849895i	$-0.323335\pi$
$463$	22.6773	1.05390	0.526952	+	0.849895i	$0.323335\pi$
$464$	3.12817	0.145222
$465$	−8.62768	−0.400099
$466$	2.65973	0.123210
$467$	−13.0318	−0.603039	−0.301520	−	0.953460i	$-0.597494\pi$
$467$	−13.0318	−0.603039	−0.301520	+	0.953460i	$0.597494\pi$
$468$	−68.9313	−3.18635
$469$	8.10439	0.374226
$470$	−1.07820	−0.0497338
$471$	46.5505	2.14494
$472$	2.49648	0.114910
$473$	0.221821	0.0101994
$474$	−9.03917	−0.415183
$475$	3.70977	0.170216
$476$	1.32591	0.0607732
$477$	32.7673	1.50031
$478$	19.1909	0.877771
$479$	7.68206	0.351003	0.175501	−	0.984479i	$-0.443845\pi$
$479$	7.68206	0.351003	0.175501	+	0.984479i	$0.443845\pi$
$480$	14.5299	0.663197
$481$	−1.63009	−0.0743259
$482$	−19.7623	−0.900149
$483$	10.6234	0.483380
$484$	15.4350	0.701591
$485$	−11.7354	−0.532876
$486$	9.96310	0.451935
$487$	38.2571	1.73359	0.866797	−	0.498661i	$-0.166175\pi$
$487$	38.2571	1.73359	0.866797	+	0.498661i	$0.166175\pi$
$488$	−19.8887	−0.900318
$489$	47.8659	2.16457
$490$	−3.55172	−0.160451
$491$	25.5145	1.15145	0.575727	−	0.817642i	$-0.304719\pi$
$491$	25.5145	1.15145	0.575727	+	0.817642i	$0.304719\pi$
$492$	−27.3662	−1.23376
$493$	2.63271	0.118571
$494$	−4.22994	−0.190314
$495$	4.21437	0.189422
$496$	−4.12279	−0.185119
$497$	10.5312	0.472391
$498$	−23.2841	−1.04339
$499$	12.9521	0.579814	0.289907	−	0.957055i	$-0.406376\pi$
$499$	12.9521	0.579814	0.289907	+	0.957055i	$0.406376\pi$
$500$	11.1340	0.497929
$501$	52.9935	2.36757
$502$	10.1525	0.453128
$503$	−35.4930	−1.58256	−0.791278	−	0.611457i	$-0.790584\pi$
$503$	−35.4930	−1.58256	−0.791278	+	0.611457i	$0.790584\pi$
$504$	14.8437	0.661190
$505$	−15.5526	−0.692080
$506$	−2.16767	−0.0963648
$507$	109.616	4.86822
$508$	23.6781	1.05054
$509$	12.6517	0.560777	0.280388	−	0.959887i	$-0.409537\pi$
$509$	12.6517	0.560777	0.280388	+	0.959887i	$0.409537\pi$
$510$	1.77988	0.0788145
$511$	−3.67865	−0.162734
$512$	12.8758	0.569037
$513$	−9.71182	−0.428788
$514$	2.70713	0.119406
$515$	4.40093	0.193928
$516$	−1.29878	−0.0571755
$517$	−1.48845	−0.0654620
$518$	0.149727	0.00657861
$519$	49.6731	2.18041
$520$	−13.8652	−0.608030
$521$	−30.5330	−1.33767	−0.668837	−	0.743409i	$-0.733208\pi$
$521$	−30.5330	−1.33767	−0.668837	+	0.743409i	$0.733208\pi$
$522$	12.5716	0.550243
$523$	14.7528	0.645094	0.322547	−	0.946554i	$-0.395461\pi$
$523$	14.7528	0.645094	0.322547	+	0.946554i	$0.395461\pi$
$524$	15.5971	0.681362
$525$	12.0869	0.527517
$526$	2.99372	0.130532
$527$	−3.46979	−0.151147
$528$	2.91953	0.127056
$529$	−8.31064	−0.361332
$530$	2.81133	0.122116
$531$	−6.67092	−0.289493
$532$	−1.12799	−0.0489047
$533$	41.0898	1.77980
$534$	23.7377	1.02723
$535$	−5.06475	−0.218968
$536$	22.6998	0.980483
$537$	−22.6222	−0.976220
$538$	14.6240	0.630486
$539$	−4.90313	−0.211193
$540$	−13.5786	−0.584329
$541$	28.0775	1.20715	0.603573	−	0.797307i	$-0.293743\pi$
$541$	28.0775	1.20715	0.603573	+	0.797307i	$0.293743\pi$
$542$	5.45586	0.234349
$543$	−51.3032	−2.20163
$544$	5.84350	0.250538
$545$	13.1312	0.562479
$546$	−13.7817	−0.589803
$547$	−12.7368	−0.544585	−0.272292	−	0.962215i	$-0.587782\pi$
$547$	−12.7368	−0.544585	−0.272292	+	0.962215i	$0.587782\pi$
$548$	3.51449	0.150132
$549$	53.1451	2.26818
$550$	−2.46631	−0.105164
$551$	−2.23972	−0.0954154
$552$	29.7553	1.26647
$553$	3.61927	0.153907
$554$	10.2137	0.433938
$555$	−0.583527	−0.0247694
$556$	21.7639	0.922996
$557$	3.73776	0.158374	0.0791870	−	0.996860i	$-0.474768\pi$
$557$	3.73776	0.158374	0.0791870	+	0.996860i	$0.474768\pi$
$558$	−16.5688	−0.701413
$559$	1.95009	0.0824799
$560$	−0.846780	−0.0357830
$561$	2.45711	0.103739
$562$	6.67735	0.281667
$563$	−27.4474	−1.15677	−0.578386	−	0.815763i	$-0.696317\pi$
$563$	−27.4474	−1.15677	−0.578386	+	0.815763i	$0.696317\pi$
$564$	8.71497	0.366966
$565$	−5.05059	−0.212480
$566$	1.73625	0.0729799
$567$	−13.8050	−0.579753
$568$	29.4972	1.23768
$569$	30.4921	1.27830	0.639148	−	0.769084i	$-0.279287\pi$
$569$	30.4921	1.27830	0.639148	+	0.769084i	$0.279287\pi$
$570$	−1.51420	−0.0634228
$571$	−22.8460	−0.956076	−0.478038	−	0.878339i	$-0.658652\pi$
$571$	−22.8460	−0.956076	−0.478038	+	0.878339i	$0.658652\pi$
$572$	−8.16434	−0.341368
$573$	63.4809	2.65195
$574$	−3.77416	−0.157530
$575$	16.7131	0.696984
$576$	12.0509	0.502119
$577$	−46.1756	−1.92232	−0.961158	−	0.275998i	$-0.910992\pi$
$577$	−46.1756	−1.92232	−0.961158	+	0.275998i	$0.910992\pi$
$578$	0.715815	0.0297740
$579$	46.7926	1.94463
$580$	−3.13147	−0.130027
$581$	9.32292	0.386780
$582$	−32.6720	−1.35430
$583$	3.88102	0.160735
$584$	−10.3036	−0.426367
$585$	37.0496	1.53181
$586$	−15.5525	−0.642467
$587$	9.81827	0.405243	0.202622	−	0.979257i	$-0.435054\pi$
$587$	9.81827	0.405243	0.202622	+	0.979257i	$0.435054\pi$
$588$	28.7081	1.18390
$589$	2.95186	0.121629
$590$	−0.572344	−0.0235630
$591$	−72.5206	−2.98310
$592$	−0.278842	−0.0114604
$593$	−2.65979	−0.109225	−0.0546123	−	0.998508i	$-0.517392\pi$
$593$	−2.65979	−0.109225	−0.0546123	+	0.998508i	$0.517392\pi$
$594$	6.45656	0.264916
$595$	−0.712661	−0.0292162
$596$	−1.22173	−0.0500439
$597$	−4.24921	−0.173909
$598$	−19.0565	−0.779280
$599$	36.6206	1.49628	0.748139	−	0.663542i	$-0.230948\pi$
$599$	36.6206	1.49628	0.748139	+	0.663542i	$0.230948\pi$
$600$	33.8546	1.38211
$601$	15.8491	0.646499	0.323249	−	0.946314i	$-0.395225\pi$
$601$	15.8491	0.646499	0.323249	+	0.946314i	$0.395225\pi$
$602$	−0.179118	−0.00730032
$603$	−60.6568	−2.47014
$604$	6.83434	0.278085
$605$	−8.29610	−0.337285
$606$	−43.2993	−1.75891
$607$	−10.9358	−0.443870	−0.221935	−	0.975061i	$-0.571237\pi$
$607$	−10.9358	−0.443870	−0.221935	+	0.975061i	$0.571237\pi$
$608$	−4.97123	−0.201610
$609$	−7.29732	−0.295703
$610$	4.55968	0.184616
$611$	−13.0853	−0.529376
$612$	−9.92372	−0.401143
$613$	−12.6890	−0.512504	−0.256252	−	0.966610i	$-0.582488\pi$
$613$	−12.6890	−0.512504	−0.256252	+	0.966610i	$0.582488\pi$
$614$	4.91482	0.198346
$615$	14.7090	0.593123
$616$	1.75811	0.0708364
$617$	22.6233	0.910782	0.455391	−	0.890292i	$-0.349500\pi$
$617$	22.6233	0.910782	0.455391	+	0.890292i	$0.349500\pi$
$618$	12.2525	0.492867
$619$	−44.0689	−1.77128	−0.885640	−	0.464372i	$-0.846280\pi$
$619$	−44.0689	−1.77128	−0.885640	+	0.464372i	$0.846280\pi$
$620$	4.12713	0.165750
$621$	−43.7533	−1.75576
$622$	11.0044	0.441236
$623$	−9.50451	−0.380790
$624$	25.6663	1.02747
$625$	15.8191	0.632762
$626$	−5.30529	−0.212042
$627$	−2.09034	−0.0834800
$628$	−22.2679	−0.888586
$629$	−0.234677	−0.00935720
$630$	−3.40306	−0.135581
$631$	14.9403	0.594763	0.297382	−	0.954759i	$-0.403887\pi$
$631$	14.9403	0.594763	0.297382	+	0.954759i	$0.403887\pi$
$632$	10.1373	0.403240
$633$	−38.7674	−1.54087
$634$	0.587624	0.0233375
$635$	−12.7266	−0.505041
$636$	−22.7236	−0.901050
$637$	−43.1046	−1.70787
$638$	1.48900	0.0589501
$639$	−78.8204	−3.11809
$640$	−8.31064	−0.328507
$641$	25.9747	1.02594	0.512969	−	0.858407i	$-0.328546\pi$
$641$	25.9747	1.02594	0.512969	+	0.858407i	$0.328546\pi$
$642$	−14.1006	−0.556505
$643$	15.9245	0.628003	0.314001	−	0.949423i	$-0.398330\pi$
$643$	15.9245	0.628003	0.314001	+	0.949423i	$0.398330\pi$
$644$	−5.08179	−0.200251
$645$	0.698076	0.0274867
$646$	−0.608965	−0.0239594
$647$	−1.39182	−0.0547179	−0.0273590	−	0.999626i	$-0.508710\pi$
$647$	−1.39182	−0.0547179	−0.0273590	+	0.999626i	$0.508710\pi$
$648$	−38.6667	−1.51897
$649$	−0.790116	−0.0310148
$650$	−21.6819	−0.850435
$651$	9.61755	0.376941
$652$	−22.8971	−0.896721
$653$	−11.2631	−0.440758	−0.220379	−	0.975414i	$-0.570729\pi$
$653$	−11.2631	−0.440758	−0.220379	+	0.975414i	$0.570729\pi$
$654$	36.5581	1.42953
$655$	−8.38322	−0.327560
$656$	7.02878	0.274428
$657$	27.5326	1.07415
$658$	1.20191	0.0468552
$659$	32.5692	1.26872	0.634359	−	0.773039i	$-0.281264\pi$
$659$	32.5692	1.26872	0.634359	+	0.773039i	$0.281264\pi$
$660$	−2.92260	−0.113762
$661$	−2.40477	−0.0935347	−0.0467673	−	0.998906i	$-0.514892\pi$
$661$	−2.40477	−0.0935347	−0.0467673	+	0.998906i	$0.514892\pi$
$662$	−1.49651	−0.0581635
$663$	21.6011	0.838917
$664$	26.1128	1.01337
$665$	0.606282	0.0235106
$666$	−1.12062	−0.0434231
$667$	−10.0903	−0.390698
$668$	−25.3499	−0.980818
$669$	17.5484	0.678462
$670$	−5.20416	−0.201054
$671$	6.29460	0.243000
$672$	−16.1970	−0.624811
$673$	2.19677	0.0846794	0.0423397	−	0.999103i	$-0.486519\pi$
$673$	2.19677	0.0846794	0.0423397	+	0.999103i	$0.486519\pi$
$674$	−16.7319	−0.644488
$675$	−49.7811	−1.91608
$676$	−52.4359	−2.01676
$677$	−13.8425	−0.532012	−0.266006	−	0.963971i	$-0.585704\pi$
$677$	−13.8425	−0.532012	−0.266006	+	0.963971i	$0.585704\pi$
$678$	−14.0612	−0.540015
$679$	13.0818	0.502034
$680$	−1.99611	−0.0765474
$681$	39.7948	1.52494
$682$	−1.96244	−0.0751456
$683$	−3.40731	−0.130377	−0.0651886	−	0.997873i	$-0.520765\pi$
$683$	−3.40731	−0.130377	−0.0651886	+	0.997873i	$0.520765\pi$
$684$	8.44240	0.322803
$685$	−1.88899	−0.0721746
$686$	8.42529	0.321679
$687$	7.62788	0.291022
$688$	0.333580	0.0127176
$689$	34.1190	1.29983
$690$	−6.82170	−0.259698
$691$	5.80499	0.220832	0.110416	−	0.993885i	$-0.464782\pi$
$691$	5.80499	0.220832	0.110416	+	0.993885i	$0.464782\pi$
$692$	−23.7616	−0.903280
$693$	−4.69790	−0.178458
$694$	5.19106	0.197050
$695$	−11.6978	−0.443724
$696$	−20.4393	−0.774749
$697$	5.91551	0.224066
$698$	−15.3711	−0.581803
$699$	11.5550	0.437051
$700$	−5.78190	−0.218535
$701$	−50.8512	−1.92062	−0.960311	−	0.278931i	$-0.910020\pi$
$701$	−50.8512	−1.92062	−0.960311	+	0.278931i	$0.910020\pi$
$702$	56.7613	2.14232
$703$	0.199647	0.00752983
$704$	1.42733	0.0537943
$705$	−4.68418	−0.176416
$706$	18.1219	0.682026
$707$	17.3370	0.652023
$708$	4.62618	0.173863
$709$	−28.8897	−1.08498	−0.542488	−	0.840064i	$-0.682518\pi$
$709$	−28.8897	−1.08498	−0.542488	+	0.840064i	$0.682518\pi$
$710$	−6.76254	−0.253794
$711$	−27.0882	−1.01589
$712$	−26.6215	−0.997681
$713$	13.2986	0.498035
$714$	−1.98409	−0.0742528
$715$	4.38822	0.164110
$716$	10.8215	0.404420
$717$	83.3735	3.11364
$718$	−1.64459	−0.0613755
$719$	−2.32635	−0.0867583	−0.0433792	−	0.999059i	$-0.513812\pi$
$719$	−2.32635	−0.0867583	−0.0433792	+	0.999059i	$0.513812\pi$
$720$	6.33767	0.236191
$721$	−4.90586	−0.182704
$722$	−13.0824	−0.486878
$723$	−85.8560	−3.19302
$724$	24.5414	0.912073
$725$	−11.4804	−0.426372
$726$	−23.0969	−0.857205
$727$	−12.0056	−0.445261	−0.222631	−	0.974903i	$-0.571464\pi$
$727$	−12.0056	−0.445261	−0.222631	+	0.974903i	$0.571464\pi$
$728$	15.4560	0.572838
$729$	−3.18138	−0.117829
$730$	2.36221	0.0874294
$731$	0.280745	0.0103837
$732$	−36.8553	−1.36221
$733$	−8.13720	−0.300554	−0.150277	−	0.988644i	$-0.548017\pi$
$733$	−8.13720	−0.300554	−0.150277	+	0.988644i	$0.548017\pi$
$734$	0.673216	0.0248489
$735$	−15.4302	−0.569152
$736$	−22.3962	−0.825535
$737$	−7.18430	−0.264637
$738$	28.2474	1.03980
$739$	−41.8009	−1.53767	−0.768835	−	0.639447i	$-0.779163\pi$
$739$	−41.8009	−1.53767	−0.768835	+	0.639447i	$0.779163\pi$
$740$	0.279136	0.0102612
$741$	−18.3767	−0.675084
$742$	−3.13388	−0.115048
$743$	−36.1795	−1.32730	−0.663648	−	0.748045i	$-0.730993\pi$
$743$	−36.1795	−1.32730	−0.663648	+	0.748045i	$0.730993\pi$
$744$	26.9381	0.987597
$745$	0.656662	0.0240582
$746$	−17.2625	−0.632025
$747$	−69.7768	−2.55300
$748$	−1.17538	−0.0429763
$749$	5.64584	0.206295
$750$	−16.6609	−0.608371
$751$	45.4698	1.65922	0.829608	−	0.558346i	$-0.188564\pi$
$751$	45.4698	1.65922	0.829608	+	0.558346i	$0.188564\pi$
$752$	−2.23837	−0.0816248
$753$	44.1068	1.60734
$754$	13.0902	0.476716
$755$	−3.67336	−0.133687
$756$	15.1365	0.550508
$757$	42.3508	1.53926	0.769632	−	0.638488i	$-0.220440\pi$
$757$	42.3508	1.53926	0.769632	+	0.638488i	$0.220440\pi$
$758$	−5.32438	−0.193390
$759$	−9.41730	−0.341826
$760$	1.69815	0.0615984
$761$	−18.6990	−0.677838	−0.338919	−	0.940816i	$-0.610061\pi$
$761$	−18.6990	−0.677838	−0.338919	+	0.940816i	$0.610061\pi$
$762$	−35.4318	−1.28356
$763$	−14.6378	−0.529923
$764$	−30.3667	−1.09863
$765$	5.33387	0.192846
$766$	−26.3207	−0.951005
$767$	−6.94611	−0.250809
$768$	−34.3729	−1.24033
$769$	−7.99058	−0.288148	−0.144074	−	0.989567i	$-0.546020\pi$
$769$	−7.99058	−0.288148	−0.144074	+	0.989567i	$0.546020\pi$
$770$	−0.403065	−0.0145255
$771$	11.7609	0.423560
$772$	−22.3837	−0.805607
$773$	35.8990	1.29120	0.645599	−	0.763677i	$-0.276608\pi$
$773$	35.8990	1.29120	0.645599	+	0.763677i	$0.276608\pi$
$774$	1.34060	0.0481869
$775$	15.1307	0.543510
$776$	36.6412	1.31534
$777$	0.650477	0.0233357
$778$	15.0049	0.537951
$779$	−5.03250	−0.180308
$780$	−25.6933	−0.919969
$781$	−9.33563	−0.334055
$782$	−2.74348	−0.0981068
$783$	30.0547	1.07407
$784$	−7.37343	−0.263337
$785$	11.9687	0.427181
$786$	−23.3394	−0.832489
$787$	−34.7580	−1.23899	−0.619494	−	0.785002i	$-0.712662\pi$
$787$	−34.7580	−1.23899	−0.619494	+	0.785002i	$0.712662\pi$
$788$	34.6909	1.23581
$789$	13.0060	0.463026
$790$	−2.32408	−0.0826870
$791$	5.63005	0.200182
$792$	−13.1585	−0.467566
$793$	55.3374	1.96509
$794$	22.8123	0.809577
$795$	12.2136	0.433173
$796$	2.03265	0.0720454
$797$	−48.4969	−1.71785	−0.858925	−	0.512102i	$-0.828867\pi$
$797$	−48.4969	−1.71785	−0.858925	+	0.512102i	$0.828867\pi$
$798$	1.68793	0.0597519
$799$	−1.88384	−0.0666454
$800$	−25.4817	−0.900913
$801$	71.1359	2.51346
$802$	14.5292	0.513044
$803$	3.26101	0.115079
$804$	42.0645	1.48350
$805$	2.73139	0.0962690
$806$	−17.2523	−0.607685
$807$	63.5330	2.23647
$808$	48.5596	1.70832
$809$	17.0653	0.599985	0.299992	−	0.953942i	$-0.403016\pi$
$809$	17.0653	0.599985	0.299992	+	0.953942i	$0.403016\pi$
$810$	8.86473	0.311475
$811$	−27.7125	−0.973119	−0.486559	−	0.873648i	$-0.661748\pi$
$811$	−27.7125	−0.973119	−0.486559	+	0.873648i	$0.661748\pi$
$812$	3.49075	0.122501
$813$	23.7026	0.831286
$814$	−0.132728	−0.00465212
$815$	12.3069	0.431092
$816$	3.69506	0.129353
$817$	−0.238838	−0.00835589
$818$	−5.23243	−0.182948
$819$	−41.3004	−1.44315
$820$	−7.03618	−0.245714
$821$	−2.90597	−0.101419	−0.0507095	−	0.998713i	$-0.516148\pi$
$821$	−2.90597	−0.101419	−0.0507095	+	0.998713i	$0.516148\pi$
$822$	−5.25907	−0.183431
$823$	23.5490	0.820867	0.410433	−	0.911891i	$-0.365377\pi$
$823$	23.5490	0.820867	0.410433	+	0.911891i	$0.365377\pi$
$824$	−13.7410	−0.478689
$825$	−10.7147	−0.373038
$826$	0.638011	0.0221992
$827$	17.0705	0.593600	0.296800	−	0.954940i	$-0.404080\pi$
$827$	17.0705	0.593600	0.296800	+	0.954940i	$0.404080\pi$
$828$	38.0343	1.32178
$829$	−33.4324	−1.16116	−0.580578	−	0.814205i	$-0.697173\pi$
$829$	−33.4324	−1.16116	−0.580578	+	0.814205i	$0.697173\pi$
$830$	−5.98663	−0.207799
$831$	44.3726	1.53927
$832$	12.5480	0.435023
$833$	−6.20557	−0.215010
$834$	−32.5675	−1.12772
$835$	13.6252	0.471521
$836$	0.999933	0.0345834
$837$	−39.6107	−1.36915
$838$	10.8047	0.373243
$839$	−11.6884	−0.403528	−0.201764	−	0.979434i	$-0.564667\pi$
$839$	−11.6884	−0.403528	−0.201764	+	0.979434i	$0.564667\pi$
$840$	5.53281	0.190900
$841$	−22.0688	−0.760995
$842$	18.5841	0.640451
$843$	29.0093	0.999132
$844$	18.5448	0.638338
$845$	28.1836	0.969544
$846$	−8.99560	−0.309275
$847$	9.24794	0.317763
$848$	5.83637	0.200422
$849$	7.54300	0.258875
$850$	−3.12145	−0.107065
$851$	0.899441	0.0308324
$852$	54.6607	1.87265
$853$	−26.8548	−0.919490	−0.459745	−	0.888051i	$-0.652059\pi$
$853$	−26.8548	−0.919490	−0.459745	+	0.888051i	$0.652059\pi$
$854$	−5.08282	−0.173931
$855$	−4.53768	−0.155185
$856$	15.8136	0.540498
$857$	55.1307	1.88323	0.941615	−	0.336692i	$-0.109308\pi$
$857$	55.1307	1.88323	0.941615	+	0.336692i	$0.109308\pi$
$858$	12.2171	0.417084
$859$	44.2264	1.50898	0.754492	−	0.656309i	$-0.227883\pi$
$859$	44.2264	1.50898	0.754492	+	0.656309i	$0.227883\pi$
$860$	−0.333931	−0.0113870
$861$	−16.3966	−0.558793
$862$	18.4303	0.627739
$863$	35.4084	1.20532	0.602658	−	0.798000i	$-0.294108\pi$
$863$	35.4084	1.20532	0.602658	+	0.798000i	$0.294108\pi$
$864$	66.7086	2.26947
$865$	12.7715	0.434245
$866$	−2.60967	−0.0886803
$867$	3.10981	0.105615
$868$	−4.60065	−0.156156
$869$	−3.20837	−0.108837
$870$	4.68591	0.158867
$871$	−63.1590	−2.14006
$872$	−40.9994	−1.38841
$873$	−97.9100	−3.31375
$874$	2.33396	0.0789475
$875$	6.67100	0.225521
$876$	−19.0934	−0.645108
$877$	13.6997	0.462607	0.231304	−	0.972882i	$-0.425701\pi$
$877$	13.6997	0.462607	0.231304	+	0.972882i	$0.425701\pi$
$878$	11.2028	0.378076
$879$	−67.5667	−2.27897
$880$	0.750645	0.0253043
$881$	1.46429	0.0493332	0.0246666	−	0.999696i	$-0.492148\pi$
$881$	1.46429	0.0493332	0.0246666	+	0.999696i	$0.492148\pi$
$882$	−29.6325	−0.997780
$883$	−4.32189	−0.145443	−0.0727216	−	0.997352i	$-0.523168\pi$
$883$	−4.32189	−0.145443	−0.0727216	+	0.997352i	$0.523168\pi$
$884$	−10.3331	−0.347539
$885$	−2.48651	−0.0835831
$886$	3.93313	0.132136
$887$	−35.5692	−1.19430	−0.597149	−	0.802131i	$-0.703700\pi$
$887$	−35.5692	−1.19430	−0.597149	+	0.802131i	$0.703700\pi$
$888$	1.82194	0.0611403
$889$	14.1868	0.475810
$890$	6.10324	0.204581
$891$	12.2377	0.409978
$892$	−8.39447	−0.281067
$893$	1.60264	0.0536302
$894$	1.82819	0.0611437
$895$	−5.81643	−0.194422
$896$	9.26413	0.309493
$897$	−82.7898	−2.76427
$898$	18.0178	0.601260
$899$	−9.13496	−0.304668
$900$	43.2743	1.44248
$901$	4.91196	0.163641
$902$	3.34568	0.111399
$903$	−0.778168	−0.0258958
$904$	15.7694	0.524482
$905$	−13.1907	−0.438473
$906$	−10.2269	−0.339765
$907$	−57.0712	−1.89502	−0.947509	−	0.319728i	$-0.896409\pi$
$907$	−57.0712	−1.89502	−0.947509	+	0.319728i	$0.896409\pi$
$908$	−19.0362	−0.631740
$909$	−129.757	−4.30378
$910$	−3.54344	−0.117464
$911$	−53.1533	−1.76105	−0.880524	−	0.474001i	$-0.842809\pi$
$911$	−53.1533	−1.76105	−0.880524	+	0.474001i	$0.842809\pi$
$912$	−3.14350	−0.104092
$913$	−8.26450	−0.273515
$914$	−17.8481	−0.590364
$915$	19.8092	0.654872
$916$	−3.64887	−0.120562
$917$	9.34505	0.308601
$918$	8.17166	0.269705
$919$	−53.0861	−1.75115	−0.875574	−	0.483085i	$-0.839516\pi$
$919$	−53.0861	−1.75115	−0.875574	+	0.483085i	$0.839516\pi$
$920$	7.65044	0.252227
$921$	21.3521	0.703575
$922$	−0.959971	−0.0316150
$923$	−82.0719	−2.70143
$924$	3.25792	0.107178
$925$	1.02335	0.0336477
$926$	16.2328	0.533441
$927$	36.7176	1.20596
$928$	15.3842	0.505012
$929$	27.6780	0.908085	0.454042	−	0.890980i	$-0.349982\pi$
$929$	27.6780	0.908085	0.454042	+	0.890980i	$0.349982\pi$
$930$	−6.17582	−0.202513
$931$	5.27926	0.173021
$932$	−5.52745	−0.181058
$933$	47.8079	1.56516
$934$	−9.32836	−0.305233
$935$	0.631753	0.0206605
$936$	−115.679	−3.78110
$937$	−59.4736	−1.94292	−0.971459	−	0.237210i	$-0.923767\pi$
$937$	−59.4736	−1.94292	−0.971459	+	0.237210i	$0.923767\pi$
$938$	5.80125	0.189417
$939$	−23.0485	−0.752158
$940$	2.24072	0.0730843
$941$	40.9723	1.33566	0.667830	−	0.744314i	$-0.267223\pi$
$941$	40.9723	1.33566	0.667830	+	0.744314i	$0.267223\pi$
$942$	33.3216	1.08568
$943$	−22.6722	−0.738308
$944$	−1.18819	−0.0386724
$945$	−8.13565	−0.264653
$946$	0.158783	0.00516249
$947$	−22.1080	−0.718413	−0.359207	−	0.933258i	$-0.616953\pi$
$947$	−22.1080	−0.718413	−0.359207	+	0.933258i	$0.616953\pi$
$948$	18.7852	0.610116
$949$	28.6684	0.930615
$950$	2.65551	0.0861561
$951$	2.55289	0.0827832
$952$	2.22513	0.0721169
$953$	39.6897	1.28568	0.642838	−	0.766003i	$-0.277757\pi$
$953$	39.6897	1.28568	0.642838	+	0.766003i	$0.277757\pi$
$954$	23.4554	0.759395
$955$	16.3217	0.528157
$956$	−39.8825	−1.28989
$957$	6.46886	0.209109
$958$	5.49894	0.177663
$959$	2.10572	0.0679972
$960$	4.49182	0.144973
$961$	−18.9605	−0.611630
$962$	−1.16685	−0.0376207
$963$	−42.2559	−1.36168
$964$	41.0701	1.32278
$965$	12.0309	0.387289
$966$	7.60437	0.244667
$967$	0.779501	0.0250670	0.0125335	−	0.999921i	$-0.496010\pi$
$967$	0.779501	0.0250670	0.0125335	+	0.999921i	$0.496010\pi$
$968$	25.9028	0.832548
$969$	−2.64561	−0.0849892
$970$	−8.40037	−0.269720
$971$	−41.7108	−1.33856	−0.669282	−	0.743008i	$-0.733398\pi$
$971$	−41.7108	−1.33856	−0.669282	+	0.743008i	$0.733398\pi$
$972$	−20.7053	−0.664123
$973$	13.0399	0.418041
$974$	27.3850	0.877473
$975$	−94.1956	−3.01667
$976$	9.46596	0.302998
$977$	39.1788	1.25344	0.626720	−	0.779245i	$-0.284397\pi$
$977$	39.1788	1.25344	0.626720	+	0.779245i	$0.284397\pi$
$978$	34.2632	1.09562
$979$	8.42547	0.269279
$980$	7.38119	0.235784
$981$	109.556	3.49784
$982$	18.2637	0.582817
$983$	37.7820	1.20506	0.602530	−	0.798096i	$-0.294159\pi$
$983$	37.7820	1.20506	0.602530	+	0.798096i	$0.294159\pi$
$984$	−45.9256	−1.46405
$985$	−18.6459	−0.594108
$986$	1.88453	0.0600158
$987$	5.22161	0.166206
$988$	8.79066	0.279668
$989$	−1.07600	−0.0342149
$990$	3.01671	0.0958775
$991$	58.2792	1.85130	0.925650	−	0.378381i	$-0.123519\pi$
$991$	58.2792	1.85130	0.925650	+	0.378381i	$0.123519\pi$
$992$	−20.2757	−0.643755
$993$	−6.50148	−0.206318
$994$	7.53842	0.239104
$995$	−1.09252	−0.0346353
$996$	48.3891	1.53327
$997$	28.9808	0.917832	0.458916	−	0.888480i	$-0.348238\pi$
$997$	28.9808	0.917832	0.458916	+	0.888480i	$0.348238\pi$
$998$	9.27128	0.293477
$999$	−2.67905	−0.0847613

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1003.2.a.i.1.10	✓	18
3.2	odd	2		9027.2.a.q.1.9		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1003.2.a.i.1.10	✓	18	1.1	even	1	trivial
9027.2.a.q.1.9		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)

\(f(q)\)	\(=\)	\(q+0.715815 q^{2} +3.10981 q^{3} -1.48761 q^{4} +0.799569 q^{5} +2.22605 q^{6} -0.891306 q^{7} -2.49648 q^{8} +6.67092 q^{9} +O(q^{10})\)	\(q+0.715815 q^{2} +3.10981 q^{3} -1.48761 q^{4} +0.799569 q^{5} +2.22605 q^{6} -0.891306 q^{7} -2.49648 q^{8} +6.67092 q^{9} +0.572344 q^{10} +0.790116 q^{11} -4.62618 q^{12} +6.94611 q^{13} -0.638011 q^{14} +2.48651 q^{15} +1.18819 q^{16} +1.00000 q^{17} +4.77515 q^{18} -0.850729 q^{19} -1.18945 q^{20} -2.77179 q^{21} +0.565577 q^{22} -3.83267 q^{23} -7.76359 q^{24} -4.36069 q^{25} +4.97213 q^{26} +11.4159 q^{27} +1.32591 q^{28} +2.63271 q^{29} +1.77988 q^{30} -3.46979 q^{31} +5.84350 q^{32} +2.45711 q^{33} +0.715815 q^{34} -0.712661 q^{35} -9.92372 q^{36} -0.234677 q^{37} -0.608965 q^{38} +21.6011 q^{39} -1.99611 q^{40} +5.91551 q^{41} -1.98409 q^{42} +0.280745 q^{43} -1.17538 q^{44} +5.33387 q^{45} -2.74348 q^{46} -1.88384 q^{47} +3.69506 q^{48} -6.20557 q^{49} -3.12145 q^{50} +3.10981 q^{51} -10.3331 q^{52} +4.91196 q^{53} +8.17166 q^{54} +0.631753 q^{55} +2.22513 q^{56} -2.64561 q^{57} +1.88453 q^{58} -1.00000 q^{59} -3.69895 q^{60} +7.96668 q^{61} -2.48373 q^{62} -5.94583 q^{63} +1.80647 q^{64} +5.55390 q^{65} +1.75884 q^{66} -9.09272 q^{67} -1.48761 q^{68} -11.9189 q^{69} -0.510134 q^{70} -11.8155 q^{71} -16.6539 q^{72} +4.12726 q^{73} -0.167986 q^{74} -13.5609 q^{75} +1.26555 q^{76} -0.704235 q^{77} +15.4624 q^{78} -4.06063 q^{79} +0.950044 q^{80} +15.4885 q^{81} +4.23441 q^{82} -10.4598 q^{83} +4.12334 q^{84} +0.799569 q^{85} +0.200962 q^{86} +8.18723 q^{87} -1.97251 q^{88} +10.6636 q^{89} +3.81806 q^{90} -6.19111 q^{91} +5.70151 q^{92} -10.7904 q^{93} -1.34848 q^{94} -0.680217 q^{95} +18.1722 q^{96} -14.6771 q^{97} -4.44205 q^{98} +5.27081 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 5 q^{2} + q^{3} + 21 q^{4} + 21 q^{5} + 5 q^{6} - q^{7} + 9 q^{8} + 17 q^{9}+O(q^{10}) \) 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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