LMFDB - Embedded newform 3610.2.a.bi.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3610,2,Mod(1,3610)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3610, 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("3610.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3610 = 2 \cdot 5 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3610.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:	$28.8259951297$
Analytic rank:	$0$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 24x^{7} - 6x^{6} + 183x^{5} + 78x^{4} - 455x^{3} - 168x^{2} + 228x - 8 $ x^9 - 24x^7 - 6x^6 + 183x^5 + 78x^4 - 455x^3 - 168x^2 + 228*x - 8
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 190)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$0.0361439$ of defining polynomial
Character	$\chi$	$=$	3610.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +0.0361439 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.0361439 q^{6} +1.83741 q^{7} -1.00000 q^{8} -2.99869 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +0.0361439 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.0361439 q^{6} +1.83741 q^{7} -1.00000 q^{8} -2.99869 q^{9} -1.00000 q^{10} -2.46576 q^{11} +0.0361439 q^{12} +2.39309 q^{13} -1.83741 q^{14} +0.0361439 q^{15} +1.00000 q^{16} +6.74198 q^{17} +2.99869 q^{18} +1.00000 q^{20} +0.0664112 q^{21} +2.46576 q^{22} +1.62092 q^{23} -0.0361439 q^{24} +1.00000 q^{25} -2.39309 q^{26} -0.216816 q^{27} +1.83741 q^{28} +3.30157 q^{29} -0.0361439 q^{30} -3.50384 q^{31} -1.00000 q^{32} -0.0891221 q^{33} -6.74198 q^{34} +1.83741 q^{35} -2.99869 q^{36} -6.00888 q^{37} +0.0864957 q^{39} -1.00000 q^{40} -7.98063 q^{41} -0.0664112 q^{42} +5.71443 q^{43} -2.46576 q^{44} -2.99869 q^{45} -1.62092 q^{46} +12.4926 q^{47} +0.0361439 q^{48} -3.62392 q^{49} -1.00000 q^{50} +0.243682 q^{51} +2.39309 q^{52} -1.92136 q^{53} +0.216816 q^{54} -2.46576 q^{55} -1.83741 q^{56} -3.30157 q^{58} -4.75396 q^{59} +0.0361439 q^{60} +13.6642 q^{61} +3.50384 q^{62} -5.50983 q^{63} +1.00000 q^{64} +2.39309 q^{65} +0.0891221 q^{66} -3.71765 q^{67} +6.74198 q^{68} +0.0585864 q^{69} -1.83741 q^{70} +5.83313 q^{71} +2.99869 q^{72} -0.510408 q^{73} +6.00888 q^{74} +0.0361439 q^{75} -4.53061 q^{77} -0.0864957 q^{78} +12.1354 q^{79} +1.00000 q^{80} +8.98824 q^{81} +7.98063 q^{82} +6.23256 q^{83} +0.0664112 q^{84} +6.74198 q^{85} -5.71443 q^{86} +0.119332 q^{87} +2.46576 q^{88} +17.0020 q^{89} +2.99869 q^{90} +4.39709 q^{91} +1.62092 q^{92} -0.126642 q^{93} -12.4926 q^{94} -0.0361439 q^{96} -13.6598 q^{97} +3.62392 q^{98} +7.39405 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q - 9 q^{2} + 9 q^{4} + 9 q^{5} - 9 q^{8} + 21 q^{9}+O(q^{10}) $ 9 * q - 9 * q^2 + 9 * q^4 + 9 * q^5 - 9 * q^8 + 21 * q^9	$ 9 q - 9 q^{2} + 9 q^{4} + 9 q^{5} - 9 q^{8} + 21 q^{9} - 9 q^{10} + 12 q^{11} - 9 q^{13} + 9 q^{16} + 6 q^{17} - 21 q^{18} + 9 q^{20} - 6 q^{21} - 12 q^{22} + 18 q^{23} + 9 q^{25} + 9 q^{26} + 18 q^{27} + 6 q^{31} - 9 q^{32} - 6 q^{33} - 6 q^{34} + 21 q^{36} - 6 q^{37} + 24 q^{39} - 9 q^{40} + 6 q^{42} + 18 q^{43} + 12 q^{44} + 21 q^{45} - 18 q^{46} - 3 q^{47} + 39 q^{49} - 9 q^{50} + 48 q^{51} - 9 q^{52} - 18 q^{54} + 12 q^{55} - 21 q^{59} + 18 q^{61} - 6 q^{62} - 12 q^{63} + 9 q^{64} - 9 q^{65} + 6 q^{66} + 6 q^{68} + 30 q^{69} - 18 q^{71} - 21 q^{72} - 36 q^{73} + 6 q^{74} + 15 q^{77} - 24 q^{78} + 6 q^{79} + 9 q^{80} + 69 q^{81} - 6 q^{83} - 6 q^{84} + 6 q^{85} - 18 q^{86} - 24 q^{87} - 12 q^{88} + 18 q^{89} - 21 q^{90} + 60 q^{91} + 18 q^{92} + 3 q^{94} - 18 q^{97} - 39 q^{98} + 54 q^{99}+O(q^{100}) $ 9 * q - 9 * q^2 + 9 * q^4 + 9 * q^5 - 9 * q^8 + 21 * q^9 - 9 * q^10 + 12 * q^11 - 9 * q^13 + 9 * q^16 + 6 * q^17 - 21 * q^18 + 9 * q^20 - 6 * q^21 - 12 * q^22 + 18 * q^23 + 9 * q^25 + 9 * q^26 + 18 * q^27 + 6 * q^31 - 9 * q^32 - 6 * q^33 - 6 * q^34 + 21 * q^36 - 6 * q^37 + 24 * q^39 - 9 * q^40 + 6 * q^42 + 18 * q^43 + 12 * q^44 + 21 * q^45 - 18 * q^46 - 3 * q^47 + 39 * q^49 - 9 * q^50 + 48 * q^51 - 9 * q^52 - 18 * q^54 + 12 * q^55 - 21 * q^59 + 18 * q^61 - 6 * q^62 - 12 * q^63 + 9 * q^64 - 9 * q^65 + 6 * q^66 + 6 * q^68 + 30 * q^69 - 18 * q^71 - 21 * q^72 - 36 * q^73 + 6 * q^74 + 15 * q^77 - 24 * q^78 + 6 * q^79 + 9 * q^80 + 69 * q^81 - 6 * q^83 - 6 * q^84 + 6 * q^85 - 18 * q^86 - 24 * q^87 - 12 * q^88 + 18 * q^89 - 21 * q^90 + 60 * q^91 + 18 * q^92 + 3 * q^94 - 18 * q^97 - 39 * q^98 + 54 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	0.0361439	0.0208677	0.0104338	−	0.999946i	$-0.496679\pi$
$3$	0.0361439	0.0208677	0.0104338	+	0.999946i	$0.496679\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−0.0361439	−0.0147557
$7$	1.83741	0.694476	0.347238	−	0.937777i	$-0.387120\pi$
$7$	1.83741	0.694476	0.347238	+	0.937777i	$0.387120\pi$
$8$	−1.00000	−0.353553
$9$	−2.99869	−0.999565
$10$	−1.00000	−0.316228
$11$	−2.46576	−0.743453	−0.371727	−	0.928342i	$-0.621234\pi$
$11$	−2.46576	−0.743453	−0.371727	+	0.928342i	$0.621234\pi$
$12$	0.0361439	0.0104338
$13$	2.39309	0.663724	0.331862	−	0.943328i	$-0.392323\pi$
$13$	2.39309	0.663724	0.331862	+	0.943328i	$0.392323\pi$
$14$	−1.83741	−0.491069
$15$	0.0361439	0.00933232
$16$	1.00000	0.250000
$17$	6.74198	1.63517	0.817586	−	0.575807i	$-0.195312\pi$
$17$	6.74198	1.63517	0.817586	+	0.575807i	$0.195312\pi$
$18$	2.99869	0.706799
$19$	0	0
$19$	0	0
$20$	1.00000	0.223607
$21$	0.0664112	0.0144921
$22$	2.46576	0.525701
$23$	1.62092	0.337985	0.168993	−	0.985617i	$-0.445949\pi$
$23$	1.62092	0.337985	0.168993	+	0.985617i	$0.445949\pi$
$24$	−0.0361439	−0.00737785
$25$	1.00000	0.200000
$26$	−2.39309	−0.469324
$27$	−0.216816	−0.0417263
$28$	1.83741	0.347238
$29$	3.30157	0.613086	0.306543	−	0.951857i	$-0.400828\pi$
$29$	3.30157	0.613086	0.306543	+	0.951857i	$0.400828\pi$
$30$	−0.0361439	−0.00659895
$31$	−3.50384	−0.629308	−0.314654	−	0.949206i	$-0.601889\pi$
$31$	−3.50384	−0.629308	−0.314654	+	0.949206i	$0.601889\pi$
$32$	−1.00000	−0.176777
$33$	−0.0891221	−0.0155142
$34$	−6.74198	−1.15624
$35$	1.83741	0.310579
$36$	−2.99869	−0.499782
$37$	−6.00888	−0.987854	−0.493927	−	0.869503i	$-0.664439\pi$
$37$	−6.00888	−0.987854	−0.493927	+	0.869503i	$0.664439\pi$
$38$	0	0
$39$	0.0864957	0.0138504
$40$	−1.00000	−0.158114
$41$	−7.98063	−1.24637	−0.623183	−	0.782076i	$-0.714161\pi$
$41$	−7.98063	−1.24637	−0.623183	+	0.782076i	$0.714161\pi$
$42$	−0.0664112	−0.0102475
$43$	5.71443	0.871443	0.435721	−	0.900082i	$-0.356493\pi$
$43$	5.71443	0.871443	0.435721	+	0.900082i	$0.356493\pi$
$44$	−2.46576	−0.371727
$45$	−2.99869	−0.447019
$46$	−1.62092	−0.238992
$47$	12.4926	1.82224	0.911120	−	0.412142i	$-0.135219\pi$
$47$	12.4926	1.82224	0.911120	+	0.412142i	$0.135219\pi$
$48$	0.0361439	0.00521692
$49$	−3.62392	−0.517703
$50$	−1.00000	−0.141421
$51$	0.243682	0.0341223
$52$	2.39309	0.331862
$53$	−1.92136	−0.263919	−0.131960	−	0.991255i	$-0.542127\pi$
$53$	−1.92136	−0.263919	−0.131960	+	0.991255i	$0.542127\pi$
$54$	0.216816	0.0295050
$55$	−2.46576	−0.332482
$56$	−1.83741	−0.245534
$57$	0	0
$58$	−3.30157	−0.433518
$59$	−4.75396	−0.618912	−0.309456	−	0.950914i	$-0.600147\pi$
$59$	−4.75396	−0.618912	−0.309456	+	0.950914i	$0.600147\pi$
$60$	0.0361439	0.00466616
$61$	13.6642	1.74952	0.874760	−	0.484556i	$-0.161019\pi$
$61$	13.6642	1.74952	0.874760	+	0.484556i	$0.161019\pi$
$62$	3.50384	0.444988
$63$	−5.50983	−0.694174
$64$	1.00000	0.125000
$65$	2.39309	0.296826
$66$	0.0891221	0.0109702
$67$	−3.71765	−0.454183	−0.227091	−	0.973873i	$-0.572922\pi$
$67$	−3.71765	−0.454183	−0.227091	+	0.973873i	$0.572922\pi$
$68$	6.74198	0.817586
$69$	0.0585864	0.00705297
$70$	−1.83741	−0.219613
$71$	5.83313	0.692265	0.346133	−	0.938186i	$-0.387495\pi$
$71$	5.83313	0.692265	0.346133	+	0.938186i	$0.387495\pi$
$72$	2.99869	0.353399
$73$	−0.510408	−0.0597387	−0.0298694	−	0.999554i	$-0.509509\pi$
$73$	−0.510408	−0.0597387	−0.0298694	+	0.999554i	$0.509509\pi$
$74$	6.00888	0.698519
$75$	0.0361439	0.00417354
$76$	0	0
$77$	−4.53061	−0.516311
$78$	−0.0864957	−0.00979371
$79$	12.1354	1.36534	0.682671	−	0.730726i	$-0.260818\pi$
$79$	12.1354	1.36534	0.682671	+	0.730726i	$0.260818\pi$
$80$	1.00000	0.111803
$81$	8.98824	0.998694
$82$	7.98063	0.881314
$83$	6.23256	0.684112	0.342056	−	0.939680i	$-0.388877\pi$
$83$	6.23256	0.684112	0.342056	+	0.939680i	$0.388877\pi$
$84$	0.0664112	0.00724606
$85$	6.74198	0.731271
$86$	−5.71443	−0.616203
$87$	0.119332	0.0127937
$88$	2.46576	0.262850
$89$	17.0020	1.80220	0.901102	−	0.433607i	$-0.142759\pi$
$89$	17.0020	1.80220	0.901102	+	0.433607i	$0.142759\pi$
$90$	2.99869	0.316090
$91$	4.39709	0.460941
$92$	1.62092	0.168993
$93$	−0.126642	−0.0131322
$94$	−12.4926	−1.28852
$95$	0	0
$96$	−0.0361439	−0.00368892
$97$	−13.6598	−1.38695	−0.693473	−	0.720483i	$-0.743920\pi$
$97$	−13.6598	−1.38695	−0.693473	+	0.720483i	$0.743920\pi$
$98$	3.62392	0.366071
$99$	7.39405	0.743130
$100$	1.00000	0.100000
$101$	−10.6583	−1.06054	−0.530270	−	0.847829i	$-0.677909\pi$
$101$	−10.6583	−1.06054	−0.530270	+	0.847829i	$0.677909\pi$
$102$	−0.243682	−0.0241281
$103$	−9.74930	−0.960627	−0.480313	−	0.877097i	$-0.659477\pi$
$103$	−9.74930	−0.960627	−0.480313	+	0.877097i	$0.659477\pi$
$104$	−2.39309	−0.234662
$105$	0.0664112	0.00648107
$106$	1.92136	0.186619
$107$	13.2857	1.28438	0.642191	−	0.766545i	$-0.278026\pi$
$107$	13.2857	1.28438	0.642191	+	0.766545i	$0.278026\pi$
$108$	−0.216816	−0.0208632
$109$	1.44392	0.138303	0.0691513	−	0.997606i	$-0.477971\pi$
$109$	1.44392	0.138303	0.0691513	+	0.997606i	$0.477971\pi$
$110$	2.46576	0.235101
$111$	−0.217185	−0.0206142
$112$	1.83741	0.173619
$113$	−0.841529	−0.0791644	−0.0395822	−	0.999216i	$-0.512603\pi$
$113$	−0.841529	−0.0791644	−0.0395822	+	0.999216i	$0.512603\pi$
$114$	0	0
$115$	1.62092	0.151151
$116$	3.30157	0.306543
$117$	−7.17615	−0.663435
$118$	4.75396	0.437637
$119$	12.3878	1.13559
$120$	−0.0361439	−0.00329947
$121$	−4.92005	−0.447277
$122$	−13.6642	−1.23710
$123$	−0.288451	−0.0260088
$124$	−3.50384	−0.314654
$125$	1.00000	0.0894427
$126$	5.50983	0.490855
$127$	12.9858	1.15230	0.576152	−	0.817343i	$-0.304554\pi$
$127$	12.9858	1.15230	0.576152	+	0.817343i	$0.304554\pi$
$128$	−1.00000	−0.0883883
$129$	0.206542	0.0181850
$130$	−2.39309	−0.209888
$131$	8.92899	0.780129	0.390065	−	0.920787i	$-0.372453\pi$
$131$	8.92899	0.780129	0.390065	+	0.920787i	$0.372453\pi$
$132$	−0.0891221	−0.00775708
$133$	0	0
$134$	3.71765	0.321156
$135$	−0.216816	−0.0186606
$136$	−6.74198	−0.578120
$137$	4.45359	0.380496	0.190248	−	0.981736i	$-0.439071\pi$
$137$	4.45359	0.380496	0.190248	+	0.981736i	$0.439071\pi$
$138$	−0.0585864	−0.00498720
$139$	−1.21147	−0.102755	−0.0513777	−	0.998679i	$-0.516361\pi$
$139$	−1.21147	−0.102755	−0.0513777	+	0.998679i	$0.516361\pi$
$140$	1.83741	0.155290
$141$	0.451533	0.0380259
$142$	−5.83313	−0.489505
$143$	−5.90078	−0.493448
$144$	−2.99869	−0.249891
$145$	3.30157	0.274181
$146$	0.510408	0.0422416
$147$	−0.130983	−0.0108033
$148$	−6.00888	−0.493927
$149$	9.28405	0.760579	0.380289	−	0.924868i	$-0.375824\pi$
$149$	9.28405	0.760579	0.380289	+	0.924868i	$0.375824\pi$
$150$	−0.0361439	−0.00295114
$151$	−3.34570	−0.272269	−0.136135	−	0.990690i	$-0.543468\pi$
$151$	−3.34570	−0.272269	−0.136135	+	0.990690i	$0.543468\pi$
$152$	0	0
$153$	−20.2171	−1.63446
$154$	4.53061	0.365087
$155$	−3.50384	−0.281435
$156$	0.0864957	0.00692520
$157$	7.05317	0.562904	0.281452	−	0.959575i	$-0.409184\pi$
$157$	7.05317	0.562904	0.281452	+	0.959575i	$0.409184\pi$
$158$	−12.1354	−0.965443
$159$	−0.0694454	−0.00550738
$160$	−1.00000	−0.0790569
$161$	2.97829	0.234723
$162$	−8.98824	−0.706183
$163$	−15.8559	−1.24193	−0.620964	−	0.783839i	$-0.713259\pi$
$163$	−15.8559	−1.24193	−0.620964	+	0.783839i	$0.713259\pi$
$164$	−7.98063	−0.623183
$165$	−0.0891221	−0.00693814
$166$	−6.23256	−0.483740
$167$	−13.6257	−1.05439	−0.527196	−	0.849744i	$-0.676757\pi$
$167$	−13.6257	−1.05439	−0.527196	+	0.849744i	$0.676757\pi$
$168$	−0.0664112	−0.00512374
$169$	−7.27311	−0.559470
$170$	−6.74198	−0.517086
$171$	0	0
$172$	5.71443	0.435721
$173$	12.0395	0.915344	0.457672	−	0.889121i	$-0.348683\pi$
$173$	12.0395	0.915344	0.457672	+	0.889121i	$0.348683\pi$
$174$	−0.119332	−0.00904651
$175$	1.83741	0.138895
$176$	−2.46576	−0.185863
$177$	−0.171827	−0.0129153
$178$	−17.0020	−1.27435
$179$	16.0730	1.20135	0.600675	−	0.799493i	$-0.294898\pi$
$179$	16.0730	1.20135	0.600675	+	0.799493i	$0.294898\pi$
$180$	−2.99869	−0.223509
$181$	5.75310	0.427625	0.213812	−	0.976875i	$-0.431412\pi$
$181$	5.75310	0.427625	0.213812	+	0.976875i	$0.431412\pi$
$182$	−4.39709	−0.325934
$183$	0.493877	0.0365085
$184$	−1.62092	−0.119496
$185$	−6.00888	−0.441782
$186$	0.126642	0.00928588
$187$	−16.6241	−1.21567
$188$	12.4926	0.911120
$189$	−0.398381	−0.0289779
$190$	0	0
$191$	−20.5460	−1.48666	−0.743329	−	0.668926i	$-0.766754\pi$
$191$	−20.5460	−1.48666	−0.743329	+	0.668926i	$0.766754\pi$
$192$	0.0361439	0.00260846
$193$	−12.5139	−0.900774	−0.450387	−	0.892833i	$-0.648714\pi$
$193$	−12.5139	−0.900774	−0.450387	+	0.892833i	$0.648714\pi$
$194$	13.6598	0.980719
$195$	0.0864957	0.00619408
$196$	−3.62392	−0.258851
$197$	6.02346	0.429154	0.214577	−	0.976707i	$-0.431163\pi$
$197$	6.02346	0.429154	0.214577	+	0.976707i	$0.431163\pi$
$198$	−7.39405	−0.525472
$199$	11.2535	0.797742	0.398871	−	0.917007i	$-0.369402\pi$
$199$	11.2535	0.797742	0.398871	+	0.917007i	$0.369402\pi$
$200$	−1.00000	−0.0707107
$201$	−0.134370	−0.00947775
$202$	10.6583	0.749915
$203$	6.06634	0.425774
$204$	0.243682	0.0170611
$205$	−7.98063	−0.557392
$206$	9.74930	0.679266
$207$	−4.86064	−0.337838
$208$	2.39309	0.165931
$209$	0	0
$210$	−0.0664112	−0.00458281
$211$	14.0676	0.968454	0.484227	−	0.874942i	$-0.339101\pi$
$211$	14.0676	0.968454	0.484227	+	0.874942i	$0.339101\pi$
$212$	−1.92136	−0.131960
$213$	0.210832	0.0144460
$214$	−13.2857	−0.908195
$215$	5.71443	0.389721
$216$	0.216816	0.0147525
$217$	−6.43799	−0.437039
$218$	−1.44392	−0.0977947
$219$	−0.0184481	−0.00124661
$220$	−2.46576	−0.166241
$221$	16.1342	1.08530
$222$	0.217185	0.0145765
$223$	25.3025	1.69438	0.847189	−	0.531291i	$-0.178293\pi$
$223$	25.3025	1.69438	0.847189	+	0.531291i	$0.178293\pi$
$224$	−1.83741	−0.122767
$225$	−2.99869	−0.199913
$226$	0.841529	0.0559777
$227$	22.0111	1.46093	0.730464	−	0.682951i	$-0.239304\pi$
$227$	22.0111	1.46093	0.730464	+	0.682951i	$0.239304\pi$
$228$	0	0
$229$	−5.29529	−0.349923	−0.174961	−	0.984575i	$-0.555980\pi$
$229$	−5.29529	−0.349923	−0.174961	+	0.984575i	$0.555980\pi$
$230$	−1.62092	−0.106880
$231$	−0.163754	−0.0107742
$232$	−3.30157	−0.216759
$233$	20.5518	1.34639	0.673196	−	0.739464i	$-0.264921\pi$
$233$	20.5518	1.34639	0.673196	+	0.739464i	$0.264921\pi$
$234$	7.17615	0.469119
$235$	12.4926	0.814930
$236$	−4.75396	−0.309456
$237$	0.438622	0.0284915
$238$	−12.3878	−0.802981
$239$	0.887170	0.0573863	0.0286931	−	0.999588i	$-0.490865\pi$
$239$	0.887170	0.0573863	0.0286931	+	0.999588i	$0.490865\pi$
$240$	0.0361439	0.00233308
$241$	−4.00142	−0.257754	−0.128877	−	0.991661i	$-0.541137\pi$
$241$	−4.00142	−0.257754	−0.128877	+	0.991661i	$0.541137\pi$
$242$	4.92005	0.316273
$243$	0.975319	0.0625667
$244$	13.6642	0.874760
$245$	−3.62392	−0.231524
$246$	0.288451	0.0183910
$247$	0	0
$248$	3.50384	0.222494
$249$	0.225269	0.0142758
$250$	−1.00000	−0.0632456
$251$	−12.6687	−0.799642	−0.399821	−	0.916593i	$-0.630928\pi$
$251$	−12.6687	−0.799642	−0.399821	+	0.916593i	$0.630928\pi$
$252$	−5.50983	−0.347087
$253$	−3.99679	−0.251276
$254$	−12.9858	−0.814801
$255$	0.243682	0.0152599
$256$	1.00000	0.0625000
$257$	−13.0448	−0.813712	−0.406856	−	0.913492i	$-0.633375\pi$
$257$	−13.0448	−0.813712	−0.406856	+	0.913492i	$0.633375\pi$
$258$	−0.206542	−0.0128587
$259$	−11.0408	−0.686041
$260$	2.39309	0.148413
$261$	−9.90040	−0.612819
$262$	−8.92899	−0.551635
$263$	28.2516	1.74207	0.871033	−	0.491224i	$-0.163450\pi$
$263$	28.2516	1.74207	0.871033	+	0.491224i	$0.163450\pi$
$264$	0.0891221	0.00548508
$265$	−1.92136	−0.118028
$266$	0	0
$267$	0.614517	0.0376079
$268$	−3.71765	−0.227091
$269$	29.5432	1.80128	0.900641	−	0.434563i	$-0.143097\pi$
$269$	29.5432	1.80128	0.900641	+	0.434563i	$0.143097\pi$
$270$	0.216816	0.0131950
$271$	27.0112	1.64081	0.820406	−	0.571782i	$-0.193748\pi$
$271$	27.0112	1.64081	0.820406	+	0.571782i	$0.193748\pi$
$272$	6.74198	0.408793
$273$	0.158928	0.00961877
$274$	−4.45359	−0.269051
$275$	−2.46576	−0.148691
$276$	0.0585864	0.00352648
$277$	−24.1778	−1.45270	−0.726352	−	0.687323i	$-0.758786\pi$
$277$	−24.1778	−1.45270	−0.726352	+	0.687323i	$0.758786\pi$
$278$	1.21147	0.0726591
$279$	10.5069	0.629034
$280$	−1.83741	−0.109806
$281$	2.40101	0.143232	0.0716162	−	0.997432i	$-0.477184\pi$
$281$	2.40101	0.143232	0.0716162	+	0.997432i	$0.477184\pi$
$282$	−0.451533	−0.0268884
$283$	8.15093	0.484523	0.242261	−	0.970211i	$-0.422111\pi$
$283$	8.15093	0.484523	0.242261	+	0.970211i	$0.422111\pi$
$284$	5.83313	0.346133
$285$	0	0
$286$	5.90078	0.348920
$287$	−14.6637	−0.865571
$288$	2.99869	0.176700
$289$	28.4543	1.67378
$290$	−3.30157	−0.193875
$291$	−0.493720	−0.0289424
$292$	−0.510408	−0.0298694
$293$	9.19756	0.537327	0.268664	−	0.963234i	$-0.413418\pi$
$293$	9.19756	0.537327	0.268664	+	0.963234i	$0.413418\pi$
$294$	0.130983	0.00763906
$295$	−4.75396	−0.276786
$296$	6.00888	0.349259
$297$	0.534616	0.0310216
$298$	−9.28405	−0.537811
$299$	3.87901	0.224329
$300$	0.0361439	0.00208677
$301$	10.4998	0.605196
$302$	3.34570	0.192523
$303$	−0.385232	−0.0221310
$304$	0	0
$305$	13.6642	0.782409
$306$	20.2171	1.15574
$307$	−28.3472	−1.61786	−0.808929	−	0.587907i	$-0.799952\pi$
$307$	−28.3472	−1.61786	−0.808929	+	0.587907i	$0.799952\pi$
$308$	−4.53061	−0.258155
$309$	−0.352378	−0.0200461
$310$	3.50384	0.199005
$311$	17.4409	0.988980	0.494490	−	0.869183i	$-0.335355\pi$
$311$	17.4409	0.988980	0.494490	+	0.869183i	$0.335355\pi$
$312$	−0.0864957	−0.00489685
$313$	−13.1983	−0.746012	−0.373006	−	0.927829i	$-0.621673\pi$
$313$	−13.1983	−0.746012	−0.373006	+	0.927829i	$0.621673\pi$
$314$	−7.05317	−0.398034
$315$	−5.50983	−0.310444
$316$	12.1354	0.682671
$317$	−12.2864	−0.690072	−0.345036	−	0.938589i	$-0.612133\pi$
$317$	−12.2864	−0.690072	−0.345036	+	0.938589i	$0.612133\pi$
$318$	0.0694454	0.00389431
$319$	−8.14087	−0.455801
$320$	1.00000	0.0559017
$321$	0.480199	0.0268021
$322$	−2.97829	−0.165974
$323$	0	0
$324$	8.98824	0.499347
$325$	2.39309	0.132745
$326$	15.8559	0.878175
$327$	0.0521890	0.00288606
$328$	7.98063	0.440657
$329$	22.9541	1.26550
$330$	0.0891221	0.00490601
$331$	0.996594	0.0547778	0.0273889	−	0.999625i	$-0.491281\pi$
$331$	0.996594	0.0547778	0.0273889	+	0.999625i	$0.491281\pi$
$332$	6.23256	0.342056
$333$	18.0188	0.987424
$334$	13.6257	0.745568
$335$	−3.71765	−0.203117
$336$	0.0664112	0.00362303
$337$	8.55919	0.466249	0.233124	−	0.972447i	$-0.425105\pi$
$337$	8.55919	0.466249	0.233124	+	0.972447i	$0.425105\pi$
$338$	7.27311	0.395605
$339$	−0.0304162	−0.00165198
$340$	6.74198	0.365635
$341$	8.63961	0.467861
$342$	0	0
$343$	−19.5205	−1.05401
$344$	−5.71443	−0.308102
$345$	0.0585864	0.00315418
$346$	−12.0395	−0.647246
$347$	−6.63773	−0.356332	−0.178166	−	0.984000i	$-0.557016\pi$
$347$	−6.63773	−0.356332	−0.178166	+	0.984000i	$0.557016\pi$
$348$	0.119332	0.00639685
$349$	31.0443	1.66176	0.830881	−	0.556450i	$-0.187837\pi$
$349$	31.0443	1.66176	0.830881	+	0.556450i	$0.187837\pi$
$350$	−1.83741	−0.0982138
$351$	−0.518861	−0.0276948
$352$	2.46576	0.131425
$353$	17.7629	0.945424	0.472712	−	0.881217i	$-0.343275\pi$
$353$	17.7629	0.945424	0.472712	+	0.881217i	$0.343275\pi$
$354$	0.171827	0.00913248
$355$	5.83313	0.309590
$356$	17.0020	0.901102
$357$	0.447743	0.0236971
$358$	−16.0730	−0.849483
$359$	−5.13615	−0.271076	−0.135538	−	0.990772i	$-0.543276\pi$
$359$	−5.13615	−0.271076	−0.135538	+	0.990772i	$0.543276\pi$
$360$	2.99869	0.158045
$361$	0	0
$362$	−5.75310	−0.302376
$363$	−0.177830	−0.00933364
$364$	4.39709	0.230470
$365$	−0.510408	−0.0267160
$366$	−0.493877	−0.0258154
$367$	−5.74589	−0.299933	−0.149966	−	0.988691i	$-0.547917\pi$
$367$	−5.74589	−0.299933	−0.149966	+	0.988691i	$0.547917\pi$
$368$	1.62092	0.0844963
$369$	23.9315	1.24582
$370$	6.00888	0.312387
$371$	−3.53033	−0.183285
$372$	−0.126642	−0.00656611
$373$	37.7854	1.95645	0.978227	−	0.207539i	$-0.0665455\pi$
$373$	37.7854	1.95645	0.978227	+	0.207539i	$0.0665455\pi$
$374$	16.6241	0.859611
$375$	0.0361439	0.00186646
$376$	−12.4926	−0.644259
$377$	7.90096	0.406920
$378$	0.398381	0.0204905
$379$	−32.2663	−1.65741	−0.828703	−	0.559689i	$-0.810921\pi$
$379$	−32.2663	−1.65741	−0.828703	+	0.559689i	$0.810921\pi$
$380$	0	0
$381$	0.469358	0.0240459
$382$	20.5460	1.05123
$383$	−21.7799	−1.11290	−0.556450	−	0.830881i	$-0.687837\pi$
$383$	−21.7799	−1.11290	−0.556450	+	0.830881i	$0.687837\pi$
$384$	−0.0361439	−0.00184446
$385$	−4.53061	−0.230901
$386$	12.5139	0.636943
$387$	−17.1358	−0.871063
$388$	−13.6598	−0.693473
$389$	9.68485	0.491041	0.245521	−	0.969391i	$-0.421041\pi$
$389$	9.68485	0.491041	0.245521	+	0.969391i	$0.421041\pi$
$390$	−0.0864957	−0.00437988
$391$	10.9282	0.552663
$392$	3.62392	0.183036
$393$	0.322729	0.0162795
$394$	−6.02346	−0.303458
$395$	12.1354	0.610600
$396$	7.39405	0.371565
$397$	−18.3952	−0.923226	−0.461613	−	0.887081i	$-0.652729\pi$
$397$	−18.3952	−0.923226	−0.461613	+	0.887081i	$0.652729\pi$
$398$	−11.2535	−0.564089
$399$	0	0
$400$	1.00000	0.0500000
$401$	−36.5367	−1.82455	−0.912277	−	0.409573i	$-0.865678\pi$
$401$	−36.5367	−1.82455	−0.912277	+	0.409573i	$0.865678\pi$
$402$	0.134370	0.00670178
$403$	−8.38501	−0.417687
$404$	−10.6583	−0.530270
$405$	8.98824	0.446629
$406$	−6.06634	−0.301068
$407$	14.8164	0.734424
$408$	−0.243682	−0.0120640
$409$	36.3063	1.79523	0.897616	−	0.440779i	$-0.145298\pi$
$409$	36.3063	1.79523	0.897616	+	0.440779i	$0.145298\pi$
$410$	7.98063	0.394135
$411$	0.160970	0.00794007
$412$	−9.74930	−0.480313
$413$	−8.73497	−0.429820
$414$	4.86064	0.238887
$415$	6.23256	0.305944
$416$	−2.39309	−0.117331
$417$	−0.0437872	−0.00214427
$418$	0	0
$419$	39.5001	1.92970	0.964852	−	0.262793i	$-0.0846437\pi$
$419$	39.5001	1.92970	0.964852	+	0.262793i	$0.0846437\pi$
$420$	0.0664112	0.00324054
$421$	−14.1005	−0.687217	−0.343609	−	0.939113i	$-0.611649\pi$
$421$	−14.1005	−0.687217	−0.343609	+	0.939113i	$0.611649\pi$
$422$	−14.0676	−0.684800
$423$	−37.4616	−1.82145
$424$	1.92136	0.0933095
$425$	6.74198	0.327034
$426$	−0.210832	−0.0102149
$427$	25.1067	1.21500
$428$	13.2857	0.642191
$429$	−0.213277	−0.0102971
$430$	−5.71443	−0.275574
$431$	21.0431	1.01361	0.506806	−	0.862060i	$-0.330826\pi$
$431$	21.0431	1.01361	0.506806	+	0.862060i	$0.330826\pi$
$432$	−0.216816	−0.0104316
$433$	−5.25769	−0.252669	−0.126334	−	0.991988i	$-0.540321\pi$
$433$	−5.25769	−0.252669	−0.126334	+	0.991988i	$0.540321\pi$
$434$	6.43799	0.309034
$435$	0.119332	0.00572152
$436$	1.44392	0.0691513
$437$	0	0
$438$	0.0184481	0.000881486 0
$439$	36.4838	1.74128	0.870639	−	0.491923i	$-0.163706\pi$
$439$	36.4838	1.74128	0.870639	+	0.491923i	$0.163706\pi$
$440$	2.46576	0.117550
$441$	10.8670	0.517478
$442$	−16.1342	−0.767425
$443$	−9.23069	−0.438564	−0.219282	−	0.975662i	$-0.570371\pi$
$443$	−9.23069	−0.438564	−0.219282	+	0.975662i	$0.570371\pi$
$444$	−0.217185	−0.0103071
$445$	17.0020	0.805970
$446$	−25.3025	−1.19811
$447$	0.335562	0.0158715
$448$	1.83741	0.0868095
$449$	−22.8297	−1.07740	−0.538699	−	0.842498i	$-0.681084\pi$
$449$	−22.8297	−1.07740	−0.538699	+	0.842498i	$0.681084\pi$
$450$	2.99869	0.141360
$451$	19.6783	0.926615
$452$	−0.841529	−0.0395822
$453$	−0.120927	−0.00568163
$454$	−22.0111	−1.03303
$455$	4.39709	0.206139
$456$	0	0
$457$	−7.82515	−0.366045	−0.183022	−	0.983109i	$-0.558588\pi$
$457$	−7.82515	−0.366045	−0.183022	+	0.983109i	$0.558588\pi$
$458$	5.29529	0.247433
$459$	−1.46177	−0.0682296
$460$	1.62092	0.0755757
$461$	−3.93168	−0.183117	−0.0915584	−	0.995800i	$-0.529185\pi$
$461$	−3.93168	−0.183117	−0.0915584	+	0.995800i	$0.529185\pi$
$462$	0.163754	0.00761852
$463$	−17.2964	−0.803832	−0.401916	−	0.915676i	$-0.631656\pi$
$463$	−17.2964	−0.803832	−0.401916	+	0.915676i	$0.631656\pi$
$464$	3.30157	0.153272
$465$	−0.126642	−0.00587290
$466$	−20.5518	−0.952044
$467$	−21.0267	−0.973002	−0.486501	−	0.873680i	$-0.661727\pi$
$467$	−21.0267	−0.973002	−0.486501	+	0.873680i	$0.661727\pi$
$468$	−7.17615	−0.331718
$469$	−6.83084	−0.315419
$470$	−12.4926	−0.576243
$471$	0.254929	0.0117465
$472$	4.75396	0.218819
$473$	−14.0904	−0.647877
$474$	−0.438622	−0.0201466
$475$	0	0
$476$	12.3878	0.567794
$477$	5.76157	0.263804
$478$	−0.887170	−0.0405782
$479$	21.1317	0.965531	0.482766	−	0.875750i	$-0.339632\pi$
$479$	21.1317	0.965531	0.482766	+	0.875750i	$0.339632\pi$
$480$	−0.0361439	−0.00164974
$481$	−14.3798	−0.655663
$482$	4.00142	0.182260
$483$	0.107647	0.00489812
$484$	−4.92005	−0.223639
$485$	−13.6598	−0.620261
$486$	−0.975319	−0.0442414
$487$	−17.2003	−0.779420	−0.389710	−	0.920938i	$-0.627425\pi$
$487$	−17.2003	−0.779420	−0.389710	+	0.920938i	$0.627425\pi$
$488$	−13.6642	−0.618549
$489$	−0.573093	−0.0259162
$490$	3.62392	0.163712
$491$	−33.1374	−1.49547	−0.747734	−	0.663998i	$-0.768858\pi$
$491$	−33.1374	−1.49547	−0.747734	+	0.663998i	$0.768858\pi$
$492$	−0.288451	−0.0130044
$493$	22.2591	1.00250
$494$	0	0
$495$	7.39405	0.332338
$496$	−3.50384	−0.157327
$497$	10.7179	0.480762
$498$	−0.225269	−0.0100945
$499$	−31.9699	−1.43117	−0.715584	−	0.698527i	$-0.753839\pi$
$499$	−31.9699	−1.43117	−0.715584	+	0.698527i	$0.753839\pi$
$500$	1.00000	0.0447214
$501$	−0.492488	−0.0220027
$502$	12.6687	0.565432
$503$	−25.2415	−1.12546	−0.562732	−	0.826639i	$-0.690250\pi$
$503$	−25.2415	−1.12546	−0.562732	+	0.826639i	$0.690250\pi$
$504$	5.50983	0.245427
$505$	−10.6583	−0.474288
$506$	3.99679	0.177679
$507$	−0.262879	−0.0116749
$508$	12.9858	0.576152
$509$	−17.0508	−0.755763	−0.377881	−	0.925854i	$-0.623347\pi$
$509$	−17.0508	−0.755763	−0.377881	+	0.925854i	$0.623347\pi$
$510$	−0.243682	−0.0107904
$511$	−0.937829	−0.0414871
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	13.0448	0.575381
$515$	−9.74930	−0.429605
$516$	0.206542	0.00909250
$517$	−30.8038	−1.35475
$518$	11.0408	0.485104
$519$	0.435153	0.0191011
$520$	−2.39309	−0.104944
$521$	−6.80513	−0.298138	−0.149069	−	0.988827i	$-0.547628\pi$
$521$	−6.80513	−0.298138	−0.149069	+	0.988827i	$0.547628\pi$
$522$	9.90040	0.433329
$523$	5.22078	0.228289	0.114144	−	0.993464i	$-0.463587\pi$
$523$	5.22078	0.228289	0.114144	+	0.993464i	$0.463587\pi$
$524$	8.92899	0.390065
$525$	0.0664112	0.00289842
$526$	−28.2516	−1.23183
$527$	−23.6228	−1.02903
$528$	−0.0891221	−0.00387854
$529$	−20.3726	−0.885766
$530$	1.92136	0.0834585
$531$	14.2557	0.618643
$532$	0	0
$533$	−19.0984	−0.827243
$534$	−0.614517	−0.0265928
$535$	13.2857	0.574393
$536$	3.71765	0.160578
$537$	0.580940	0.0250694
$538$	−29.5432	−1.27370
$539$	8.93570	0.384888
$540$	−0.216816	−0.00933029
$541$	−26.1671	−1.12501	−0.562506	−	0.826793i	$-0.690163\pi$
$541$	−26.1671	−1.12501	−0.562506	+	0.826793i	$0.690163\pi$
$542$	−27.0112	−1.16023
$543$	0.207940	0.00892355
$544$	−6.74198	−0.289060
$545$	1.44392	0.0618508
$546$	−0.158928	−0.00680150
$547$	35.5365	1.51943	0.759715	−	0.650256i	$-0.225338\pi$
$547$	35.5365	1.51943	0.759715	+	0.650256i	$0.225338\pi$
$548$	4.45359	0.190248
$549$	−40.9747	−1.74876
$550$	2.46576	0.105140
$551$	0	0
$552$	−0.0585864	−0.00249360
$553$	22.2978	0.948197
$554$	24.1778	1.02722
$555$	−0.217185	−0.00921897
$556$	−1.21147	−0.0513777
$557$	30.6913	1.30043	0.650216	−	0.759749i	$-0.274678\pi$
$557$	30.6913	1.30043	0.650216	+	0.759749i	$0.274678\pi$
$558$	−10.5069	−0.444794
$559$	13.6752	0.578398
$560$	1.83741	0.0776448
$561$	−0.600859	−0.0253683
$562$	−2.40101	−0.101281
$563$	31.2044	1.31511	0.657553	−	0.753408i	$-0.271591\pi$
$563$	31.2044	1.31511	0.657553	+	0.753408i	$0.271591\pi$
$564$	0.451533	0.0190130
$565$	−0.841529	−0.0354034
$566$	−8.15093	−0.342609
$567$	16.5151	0.693569
$568$	−5.83313	−0.244753
$569$	−20.6053	−0.863820	−0.431910	−	0.901917i	$-0.642160\pi$
$569$	−20.6053	−0.863820	−0.431910	+	0.901917i	$0.642160\pi$
$570$	0	0
$571$	4.38785	0.183626	0.0918129	−	0.995776i	$-0.470734\pi$
$571$	4.38785	0.183626	0.0918129	+	0.995776i	$0.470734\pi$
$572$	−5.90078	−0.246724
$573$	−0.742614	−0.0310231
$574$	14.6637	0.612051
$575$	1.62092	0.0675970
$576$	−2.99869	−0.124946
$577$	29.8821	1.24401	0.622004	−	0.783014i	$-0.286319\pi$
$577$	29.8821	1.24401	0.622004	+	0.783014i	$0.286319\pi$
$578$	−28.4543	−1.18354
$579$	−0.452303	−0.0187971
$580$	3.30157	0.137090
$581$	11.4518	0.475100
$582$	0.493720	0.0204653
$583$	4.73760	0.196211
$584$	0.510408	0.0211208
$585$	−7.17615	−0.296697
$586$	−9.19756	−0.379948
$587$	39.3798	1.62538	0.812689	−	0.582698i	$-0.198003\pi$
$587$	39.3798	1.62538	0.812689	+	0.582698i	$0.198003\pi$
$588$	−0.130983	−0.00540163
$589$	0	0
$590$	4.75396	0.195717
$591$	0.217712	0.00895546
$592$	−6.00888	−0.246964
$593$	−40.1118	−1.64719	−0.823597	−	0.567176i	$-0.808036\pi$
$593$	−40.1118	−1.64719	−0.823597	+	0.567176i	$0.808036\pi$
$594$	−0.534616	−0.0219356
$595$	12.3878	0.507850
$596$	9.28405	0.380289
$597$	0.406747	0.0166470
$598$	−3.87901	−0.158624
$599$	31.4596	1.28540	0.642702	−	0.766116i	$-0.277813\pi$
$599$	31.4596	1.28540	0.642702	+	0.766116i	$0.277813\pi$
$600$	−0.0361439	−0.00147557
$601$	−34.4890	−1.40684	−0.703418	−	0.710777i	$-0.748344\pi$
$601$	−34.4890	−1.40684	−0.703418	+	0.710777i	$0.748344\pi$
$602$	−10.4998	−0.427938
$603$	11.1481	0.453985
$604$	−3.34570	−0.136135
$605$	−4.92005	−0.200028
$606$	0.385232	0.0156490
$607$	12.9979	0.527568	0.263784	−	0.964582i	$-0.415029\pi$
$607$	12.9979	0.527568	0.263784	+	0.964582i	$0.415029\pi$
$608$	0	0
$609$	0.219261	0.00888492
$610$	−13.6642	−0.553247
$611$	29.8960	1.20946
$612$	−20.2171	−0.817229
$613$	8.71181	0.351867	0.175933	−	0.984402i	$-0.443706\pi$
$613$	8.71181	0.351867	0.175933	+	0.984402i	$0.443706\pi$
$614$	28.3472	1.14400
$615$	−0.288451	−0.0116315
$616$	4.53061	0.182543
$617$	−24.3566	−0.980559	−0.490279	−	0.871565i	$-0.663105\pi$
$617$	−24.3566	−0.980559	−0.490279	+	0.871565i	$0.663105\pi$
$618$	0.352378	0.0141747
$619$	1.64497	0.0661168	0.0330584	−	0.999453i	$-0.489475\pi$
$619$	1.64497	0.0661168	0.0330584	+	0.999453i	$0.489475\pi$
$620$	−3.50384	−0.140718
$621$	−0.351442	−0.0141029
$622$	−17.4409	−0.699315
$623$	31.2396	1.25159
$624$	0.0864957	0.00346260
$625$	1.00000	0.0400000
$626$	13.1983	0.527510
$627$	0	0
$628$	7.05317	0.281452
$629$	−40.5118	−1.61531
$630$	5.50983	0.219517
$631$	−43.4987	−1.73166	−0.865829	−	0.500341i	$-0.833208\pi$
$631$	−43.4987	−1.73166	−0.865829	+	0.500341i	$0.833208\pi$
$632$	−12.1354	−0.482721
$633$	0.508458	0.0202094
$634$	12.2864	0.487955
$635$	12.9858	0.515326
$636$	−0.0694454	−0.00275369
$637$	−8.67237	−0.343612
$638$	8.14087	0.322300
$639$	−17.4918	−0.691964
$640$	−1.00000	−0.0395285
$641$	−36.8215	−1.45436	−0.727181	−	0.686446i	$-0.759170\pi$
$641$	−36.8215	−1.45436	−0.727181	+	0.686446i	$0.759170\pi$
$642$	−0.480199	−0.0189519
$643$	−14.7356	−0.581117	−0.290558	−	0.956857i	$-0.593841\pi$
$643$	−14.7356	−0.581117	−0.290558	+	0.956857i	$0.593841\pi$
$644$	2.97829	0.117361
$645$	0.206542	0.00813258
$646$	0	0
$647$	−6.04813	−0.237776	−0.118888	−	0.992908i	$-0.537933\pi$
$647$	−6.04813	−0.237776	−0.118888	+	0.992908i	$0.537933\pi$
$648$	−8.98824	−0.353092
$649$	11.7221	0.460132
$650$	−2.39309	−0.0938648
$651$	−0.232694	−0.00912001
$652$	−15.8559	−0.620964
$653$	−2.88867	−0.113043	−0.0565213	−	0.998401i	$-0.518001\pi$
$653$	−2.88867	−0.113043	−0.0565213	+	0.998401i	$0.518001\pi$
$654$	−0.0521890	−0.00204075
$655$	8.92899	0.348884
$656$	−7.98063	−0.311591
$657$	1.53056	0.0597127
$658$	−22.9541	−0.894845
$659$	16.3211	0.635779	0.317889	−	0.948128i	$-0.397026\pi$
$659$	16.3211	0.635779	0.317889	+	0.948128i	$0.397026\pi$
$660$	−0.0891221	−0.00346907
$661$	28.5414	1.11013	0.555066	−	0.831806i	$-0.312693\pi$
$661$	28.5414	1.11013	0.555066	+	0.831806i	$0.312693\pi$
$662$	−0.996594	−0.0387337
$663$	0.583152	0.0226478
$664$	−6.23256	−0.241870
$665$	0	0
$666$	−18.0188	−0.698214
$667$	5.35158	0.207214
$668$	−13.6257	−0.527196
$669$	0.914530	0.0353578
$670$	3.71765	0.143625
$671$	−33.6926	−1.30069
$672$	−0.0664112	−0.00256187
$673$	6.23447	0.240321	0.120161	−	0.992754i	$-0.461659\pi$
$673$	6.23447	0.240321	0.120161	+	0.992754i	$0.461659\pi$
$674$	−8.55919	−0.329688
$675$	−0.216816	−0.00834526
$676$	−7.27311	−0.279735
$677$	−14.6150	−0.561700	−0.280850	−	0.959752i	$-0.590616\pi$
$677$	−14.6150	−0.561700	−0.280850	+	0.959752i	$0.590616\pi$
$678$	0.0304162	0.00116813
$679$	−25.0987	−0.963201
$680$	−6.74198	−0.258543
$681$	0.795568	0.0304862
$682$	−8.63961	−0.330828
$683$	47.0671	1.80097	0.900486	−	0.434885i	$-0.143211\pi$
$683$	47.0671	1.80097	0.900486	+	0.434885i	$0.143211\pi$
$684$	0	0
$685$	4.45359	0.170163
$686$	19.5205	0.745297
$687$	−0.191392	−0.00730208
$688$	5.71443	0.217861
$689$	−4.59799	−0.175169
$690$	−0.0585864	−0.00223034
$691$	−27.3484	−1.04038	−0.520191	−	0.854050i	$-0.674139\pi$
$691$	−27.3484	−1.04038	−0.520191	+	0.854050i	$0.674139\pi$
$692$	12.0395	0.457672
$693$	13.5859	0.516086
$694$	6.63773	0.251965
$695$	−1.21147	−0.0459536
$696$	−0.119332	−0.00452326
$697$	−53.8053	−2.03802
$698$	−31.0443	−1.17504
$699$	0.742822	0.0280961
$700$	1.83741	0.0694476
$701$	19.8319	0.749040	0.374520	−	0.927219i	$-0.377808\pi$
$701$	19.8319	0.749040	0.374520	+	0.927219i	$0.377808\pi$
$702$	0.518861	0.0195831
$703$	0	0
$704$	−2.46576	−0.0929317
$705$	0.451533	0.0170057
$706$	−17.7629	−0.668516
$707$	−19.5837	−0.736519
$708$	−0.171827	−0.00645764
$709$	32.7102	1.22846	0.614230	−	0.789127i	$-0.289467\pi$
$709$	32.7102	1.22846	0.614230	+	0.789127i	$0.289467\pi$
$710$	−5.83313	−0.218913
$711$	−36.3904	−1.36475
$712$	−17.0020	−0.637175
$713$	−5.67944	−0.212697
$714$	−0.447743	−0.0167564
$715$	−5.90078	−0.220677
$716$	16.0730	0.600675
$717$	0.0320658	0.00119752
$718$	5.13615	0.191680
$719$	−3.24776	−0.121121	−0.0605606	−	0.998165i	$-0.519289\pi$
$719$	−3.24776	−0.121121	−0.0605606	+	0.998165i	$0.519289\pi$
$720$	−2.99869	−0.111755
$721$	−17.9135	−0.667132
$722$	0	0
$723$	−0.144627	−0.00537873
$724$	5.75310	0.213812
$725$	3.30157	0.122617
$726$	0.177830	0.00659988
$727$	19.4096	0.719862	0.359931	−	0.932979i	$-0.382800\pi$
$727$	19.4096	0.719862	0.359931	+	0.932979i	$0.382800\pi$
$728$	−4.39709	−0.162967
$729$	−26.9295	−0.997388
$730$	0.510408	0.0188910
$731$	38.5266	1.42496
$732$	0.493877	0.0182542
$733$	12.0753	0.446010	0.223005	−	0.974817i	$-0.428413\pi$
$733$	12.0753	0.446010	0.223005	+	0.974817i	$0.428413\pi$
$734$	5.74589	0.212085
$735$	−0.130983	−0.00483137
$736$	−1.62092	−0.0597479
$737$	9.16681	0.337664
$738$	−23.9315	−0.880930
$739$	3.04613	0.112054	0.0560268	−	0.998429i	$-0.482157\pi$
$739$	3.04613	0.112054	0.0560268	+	0.998429i	$0.482157\pi$
$740$	−6.00888	−0.220891
$741$	0	0
$742$	3.53033	0.129602
$743$	39.7565	1.45853	0.729263	−	0.684234i	$-0.239863\pi$
$743$	39.7565	1.45853	0.729263	+	0.684234i	$0.239863\pi$
$744$	0.126642	0.00464294
$745$	9.28405	0.340141
$746$	−37.7854	−1.38342
$747$	−18.6895	−0.683814
$748$	−16.6241	−0.607837
$749$	24.4114	0.891972
$750$	−0.0361439	−0.00131979
$751$	35.7867	1.30588	0.652938	−	0.757411i	$-0.273536\pi$
$751$	35.7867	1.30588	0.652938	+	0.757411i	$0.273536\pi$
$752$	12.4926	0.455560
$753$	−0.457897	−0.0166867
$754$	−7.90096	−0.287736
$755$	−3.34570	−0.121763
$756$	−0.398381	−0.0144890
$757$	−49.9062	−1.81387	−0.906936	−	0.421267i	$-0.861585\pi$
$757$	−49.9062	−1.81387	−0.906936	+	0.421267i	$0.861585\pi$
$758$	32.2663	1.17196
$759$	−0.144460	−0.00524355
$760$	0	0
$761$	−36.2563	−1.31429	−0.657145	−	0.753764i	$-0.728236\pi$
$761$	−36.2563	−1.31429	−0.657145	+	0.753764i	$0.728236\pi$
$762$	−0.469358	−0.0170030
$763$	2.65308	0.0960478
$764$	−20.5460	−0.743329
$765$	−20.2171	−0.730952
$766$	21.7799	0.786939
$767$	−11.3767	−0.410787
$768$	0.0361439	0.00130423
$769$	−5.51540	−0.198891	−0.0994453	−	0.995043i	$-0.531707\pi$
$769$	−5.51540	−0.198891	−0.0994453	+	0.995043i	$0.531707\pi$
$770$	4.53061	0.163272
$771$	−0.471490	−0.0169803
$772$	−12.5139	−0.450387
$773$	−38.3992	−1.38112	−0.690562	−	0.723273i	$-0.742637\pi$
$773$	−38.3992	−1.38112	−0.690562	+	0.723273i	$0.742637\pi$
$774$	17.1358	0.615935
$775$	−3.50384	−0.125862
$776$	13.6598	0.490359
$777$	−0.399057	−0.0143161
$778$	−9.68485	−0.347219
$779$	0	0
$780$	0.0864957	0.00309704
$781$	−14.3831	−0.514667
$782$	−10.9282	−0.390792
$783$	−0.715834	−0.0255818
$784$	−3.62392	−0.129426
$785$	7.05317	0.251738
$786$	−0.322729	−0.0115113
$787$	3.12058	0.111237	0.0556184	−	0.998452i	$-0.482287\pi$
$787$	3.12058	0.111237	0.0556184	+	0.998452i	$0.482287\pi$
$788$	6.02346	0.214577
$789$	1.02112	0.0363529
$790$	−12.1354	−0.431759
$791$	−1.54624	−0.0549778
$792$	−7.39405	−0.262736
$793$	32.6997	1.16120
$794$	18.3952	0.652819
$795$	−0.0694454	−0.00246298
$796$	11.2535	0.398871
$797$	−0.491495	−0.0174096	−0.00870482	−	0.999962i	$-0.502771\pi$
$797$	−0.491495	−0.0174096	−0.00870482	+	0.999962i	$0.502771\pi$
$798$	0	0
$799$	84.2252	2.97967
$800$	−1.00000	−0.0353553
$801$	−50.9837	−1.80142
$802$	36.5367	1.29015
$803$	1.25854	0.0444129
$804$	−0.134370	−0.00473887
$805$	2.97829	0.104971
$806$	8.38501	0.295349
$807$	1.06781	0.0375886
$808$	10.6583	0.374957
$809$	33.6552	1.18326	0.591628	−	0.806211i	$-0.298486\pi$
$809$	33.6552	1.18326	0.591628	+	0.806211i	$0.298486\pi$
$810$	−8.98824	−0.315815
$811$	−48.1108	−1.68940	−0.844699	−	0.535242i	$-0.820220\pi$
$811$	−48.1108	−1.68940	−0.844699	+	0.535242i	$0.820220\pi$
$812$	6.06634	0.212887
$813$	0.976289	0.0342400
$814$	−14.8164	−0.519316
$815$	−15.8559	−0.555407
$816$	0.243682	0.00853056
$817$	0	0
$818$	−36.3063	−1.26942
$819$	−13.1855	−0.460740
$820$	−7.98063	−0.278696
$821$	−1.89435	−0.0661131	−0.0330566	−	0.999453i	$-0.510524\pi$
$821$	−1.89435	−0.0661131	−0.0330566	+	0.999453i	$0.510524\pi$
$822$	−0.160970	−0.00561448
$823$	−26.5567	−0.925707	−0.462853	−	0.886435i	$-0.653174\pi$
$823$	−26.5567	−0.925707	−0.462853	+	0.886435i	$0.653174\pi$
$824$	9.74930	0.339633
$825$	−0.0891221	−0.00310283
$826$	8.73497	0.303929
$827$	25.7977	0.897075	0.448537	−	0.893764i	$-0.351945\pi$
$827$	25.7977	0.897075	0.448537	+	0.893764i	$0.351945\pi$
$828$	−4.86064	−0.168919
$829$	−27.9638	−0.971221	−0.485611	−	0.874175i	$-0.661403\pi$
$829$	−27.9638	−0.971221	−0.485611	+	0.874175i	$0.661403\pi$
$830$	−6.23256	−0.216335
$831$	−0.873881	−0.0303146
$832$	2.39309	0.0829655
$833$	−24.4324	−0.846533
$834$	0.0437872	0.00151623
$835$	−13.6257	−0.471539
$836$	0	0
$837$	0.759689	0.0262587
$838$	−39.5001	−1.36451
$839$	49.9183	1.72337	0.861685	−	0.507443i	$-0.169409\pi$
$839$	49.9183	1.72337	0.861685	+	0.507443i	$0.169409\pi$
$840$	−0.0664112	−0.00229140
$841$	−18.0996	−0.624125
$842$	14.1005	0.485936
$843$	0.0867820	0.00298893
$844$	14.0676	0.484227
$845$	−7.27311	−0.250203
$846$	37.4616	1.28796
$847$	−9.04015	−0.310623
$848$	−1.92136	−0.0659798
$849$	0.294607	0.0101109
$850$	−6.74198	−0.231248
$851$	−9.73991	−0.333880
$852$	0.210832	0.00722299
$853$	−7.95618	−0.272415	−0.136207	−	0.990680i	$-0.543491\pi$
$853$	−7.95618	−0.272415	−0.136207	+	0.990680i	$0.543491\pi$
$854$	−25.1067	−0.859135
$855$	0	0
$856$	−13.2857	−0.454097
$857$	−25.1550	−0.859277	−0.429638	−	0.903001i	$-0.641359\pi$
$857$	−25.1550	−0.859277	−0.429638	+	0.903001i	$0.641359\pi$
$858$	0.213277	0.00728116
$859$	3.46880	0.118354	0.0591769	−	0.998248i	$-0.481152\pi$
$859$	3.46880	0.118354	0.0591769	+	0.998248i	$0.481152\pi$
$860$	5.71443	0.194861
$861$	−0.530004	−0.0180625
$862$	−21.0431	−0.716732
$863$	−40.9708	−1.39466	−0.697331	−	0.716750i	$-0.745629\pi$
$863$	−40.9708	−1.39466	−0.697331	+	0.716750i	$0.745629\pi$
$864$	0.216816	0.00737624
$865$	12.0395	0.409354
$866$	5.25769	0.178664
$867$	1.02845	0.0349280
$868$	−6.43799	−0.218520
$869$	−29.9230	−1.01507
$870$	−0.119332	−0.00404572
$871$	−8.89666	−0.301452
$872$	−1.44392	−0.0488973
$873$	40.9616	1.38634
$874$	0	0
$875$	1.83741	0.0621158
$876$	−0.0184481	−0.000623305 0
$877$	−24.8602	−0.839469	−0.419735	−	0.907647i	$-0.637877\pi$
$877$	−24.8602	−0.839469	−0.419735	+	0.907647i	$0.637877\pi$
$878$	−36.4838	−1.23127
$879$	0.332436	0.0112128
$880$	−2.46576	−0.0831206
$881$	−15.7411	−0.530332	−0.265166	−	0.964203i	$-0.585427\pi$
$881$	−15.7411	−0.530332	−0.265166	+	0.964203i	$0.585427\pi$
$882$	−10.8670	−0.365912
$883$	−7.75970	−0.261135	−0.130567	−	0.991439i	$-0.541680\pi$
$883$	−7.75970	−0.261135	−0.130567	+	0.991439i	$0.541680\pi$
$884$	16.1342	0.542651
$885$	−0.171827	−0.00577589
$886$	9.23069	0.310111
$887$	34.0594	1.14360	0.571802	−	0.820392i	$-0.306245\pi$
$887$	34.0594	1.14360	0.571802	+	0.820392i	$0.306245\pi$
$888$	0.217185	0.00728824
$889$	23.8603	0.800247
$890$	−17.0020	−0.569907
$891$	−22.1628	−0.742482
$892$	25.3025	0.847189
$893$	0	0
$894$	−0.335562	−0.0112229
$895$	16.0730	0.537260
$896$	−1.83741	−0.0613836
$897$	0.140203	0.00468123
$898$	22.8297	0.761836
$899$	−11.5682	−0.385820
$900$	−2.99869	−0.0999565
$901$	−12.9538	−0.431553
$902$	−19.6783	−0.655216
$903$	0.379503	0.0126291
$904$	0.841529	0.0279888
$905$	5.75310	0.191240
$906$	0.120927	0.00401752
$907$	4.80756	0.159633	0.0798163	−	0.996810i	$-0.474567\pi$
$907$	4.80756	0.159633	0.0798163	+	0.996810i	$0.474567\pi$
$908$	22.0111	0.730464
$909$	31.9609	1.06008
$910$	−4.39709	−0.145762
$911$	9.14462	0.302975	0.151487	−	0.988459i	$-0.451594\pi$
$911$	9.14462	0.302975	0.151487	+	0.988459i	$0.451594\pi$
$912$	0	0
$913$	−15.3680	−0.508606
$914$	7.82515	0.258833
$915$	0.493877	0.0163271
$916$	−5.29529	−0.174961
$917$	16.4062	0.541781
$918$	1.46177	0.0482456
$919$	−21.0816	−0.695419	−0.347709	−	0.937602i	$-0.613040\pi$
$919$	−21.0816	−0.695419	−0.347709	+	0.937602i	$0.613040\pi$
$920$	−1.62092	−0.0534401
$921$	−1.02458	−0.0337610
$922$	3.93168	0.129483
$923$	13.9592	0.459473
$924$	−0.163754	−0.00538711
$925$	−6.00888	−0.197571
$926$	17.2964	0.568395
$927$	29.2352	0.960209
$928$	−3.30157	−0.108379
$929$	18.8119	0.617200	0.308600	−	0.951192i	$-0.400140\pi$
$929$	18.8119	0.617200	0.308600	+	0.951192i	$0.400140\pi$
$930$	0.126642	0.00415277
$931$	0	0
$932$	20.5518	0.673196
$933$	0.630381	0.0206377
$934$	21.0267	0.688016
$935$	−16.6241	−0.543666
$936$	7.17615	0.234560
$937$	−19.2143	−0.627704	−0.313852	−	0.949472i	$-0.601620\pi$
$937$	−19.2143	−0.627704	−0.313852	+	0.949472i	$0.601620\pi$
$938$	6.83084	0.223035
$939$	−0.477038	−0.0155676
$940$	12.4926	0.407465
$941$	15.5583	0.507185	0.253593	−	0.967311i	$-0.418388\pi$
$941$	15.5583	0.507185	0.253593	+	0.967311i	$0.418388\pi$
$942$	−0.254929	−0.00830604
$943$	−12.9360	−0.421253
$944$	−4.75396	−0.154728
$945$	−0.398381	−0.0129593
$946$	14.0904	0.458118
$947$	−22.1758	−0.720618	−0.360309	−	0.932833i	$-0.617329\pi$
$947$	−22.1758	−0.720618	−0.360309	+	0.932833i	$0.617329\pi$
$948$	0.438622	0.0142458
$949$	−1.22145	−0.0396500
$950$	0	0
$951$	−0.444078	−0.0144002
$952$	−12.3878	−0.401491
$953$	−4.95575	−0.160532	−0.0802662	−	0.996773i	$-0.525577\pi$
$953$	−4.95575	−0.160532	−0.0802662	+	0.996773i	$0.525577\pi$
$954$	−5.76157	−0.186538
$955$	−20.5460	−0.664854
$956$	0.887170	0.0286931
$957$	−0.294243	−0.00951152
$958$	−21.1317	−0.682734
$959$	8.18308	0.264245
$960$	0.0361439	0.00116654
$961$	−18.7231	−0.603971
$962$	14.3798	0.463624
$963$	−39.8399	−1.28382
$964$	−4.00142	−0.128877
$965$	−12.5139	−0.402838
$966$	−0.107647	−0.00346349
$967$	−17.2293	−0.554056	−0.277028	−	0.960862i	$-0.589349\pi$
$967$	−17.2293	−0.554056	−0.277028	+	0.960862i	$0.589349\pi$
$968$	4.92005	0.158136
$969$	0	0
$970$	13.6598	0.438591
$971$	−3.80331	−0.122054	−0.0610270	−	0.998136i	$-0.519438\pi$
$971$	−3.80331	−0.122054	−0.0610270	+	0.998136i	$0.519438\pi$
$972$	0.975319	0.0312834
$973$	−2.22597	−0.0713612
$974$	17.2003	0.551133
$975$	0.0864957	0.00277008
$976$	13.6642	0.437380
$977$	−61.7916	−1.97689	−0.988445	−	0.151582i	$-0.951563\pi$
$977$	−61.7916	−1.97689	−0.988445	+	0.151582i	$0.951563\pi$
$978$	0.573093	0.0183255
$979$	−41.9227	−1.33985
$980$	−3.62392	−0.115762
$981$	−4.32988	−0.138242
$982$	33.1374	1.05746
$983$	−11.9175	−0.380109	−0.190055	−	0.981774i	$-0.560867\pi$
$983$	−11.9175	−0.380109	−0.190055	+	0.981774i	$0.560867\pi$
$984$	0.288451	0.00919549
$985$	6.02346	0.191924
$986$	−22.2591	−0.708875
$987$	0.829652	0.0264081
$988$	0	0
$989$	9.26263	0.294535
$990$	−7.39405	−0.234998
$991$	16.1454	0.512874	0.256437	−	0.966561i	$-0.417451\pi$
$991$	16.1454	0.512874	0.256437	+	0.966561i	$0.417451\pi$
$992$	3.50384	0.111247
$993$	0.0360208	0.00114309
$994$	−10.7179	−0.339950
$995$	11.2535	0.356761
$996$	0.225269	0.00713792
$997$	−42.5330	−1.34703	−0.673517	−	0.739172i	$-0.735217\pi$
$997$	−42.5330	−1.34703	−0.673517	+	0.739172i	$0.735217\pi$
$998$	31.9699	1.01199
$999$	1.30282	0.0412195

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3610.2.a.bi.1.5		9
19.9	even	9		190.2.k.d.81.2	yes	18
19.17	even	9		190.2.k.d.61.2	✓	18
19.18	odd	2		3610.2.a.bj.1.5		9
95.9	even	18		950.2.l.i.651.2		18
95.17	odd	36		950.2.u.g.99.2		36
95.28	odd	36		950.2.u.g.499.2		36
95.47	odd	36		950.2.u.g.499.5		36
95.74	even	18		950.2.l.i.251.2		18
95.93	odd	36		950.2.u.g.99.5		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.k.d.61.2	✓	18	19.17	even	9
190.2.k.d.81.2	yes	18	19.9	even	9
950.2.l.i.251.2		18	95.74	even	18
950.2.l.i.651.2		18	95.9	even	18
950.2.u.g.99.2		36	95.17	odd	36
950.2.u.g.99.5		36	95.93	odd	36
950.2.u.g.499.2		36	95.28	odd	36
950.2.u.g.499.5		36	95.47	odd	36
3610.2.a.bi.1.5		9	1.1	even	1	trivial
3610.2.a.bj.1.5		9	19.18	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:	\( N \)	\(=\)	\( 3610 = 2 \cdot 5 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3610.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +0.0361439 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.0361439 q^{6} +1.83741 q^{7} -1.00000 q^{8} -2.99869 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +0.0361439 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.0361439 q^{6} +1.83741 q^{7} -1.00000 q^{8} -2.99869 q^{9} -1.00000 q^{10} -2.46576 q^{11} +0.0361439 q^{12} +2.39309 q^{13} -1.83741 q^{14} +0.0361439 q^{15} +1.00000 q^{16} +6.74198 q^{17} +2.99869 q^{18} +1.00000 q^{20} +0.0664112 q^{21} +2.46576 q^{22} +1.62092 q^{23} -0.0361439 q^{24} +1.00000 q^{25} -2.39309 q^{26} -0.216816 q^{27} +1.83741 q^{28} +3.30157 q^{29} -0.0361439 q^{30} -3.50384 q^{31} -1.00000 q^{32} -0.0891221 q^{33} -6.74198 q^{34} +1.83741 q^{35} -2.99869 q^{36} -6.00888 q^{37} +0.0864957 q^{39} -1.00000 q^{40} -7.98063 q^{41} -0.0664112 q^{42} +5.71443 q^{43} -2.46576 q^{44} -2.99869 q^{45} -1.62092 q^{46} +12.4926 q^{47} +0.0361439 q^{48} -3.62392 q^{49} -1.00000 q^{50} +0.243682 q^{51} +2.39309 q^{52} -1.92136 q^{53} +0.216816 q^{54} -2.46576 q^{55} -1.83741 q^{56} -3.30157 q^{58} -4.75396 q^{59} +0.0361439 q^{60} +13.6642 q^{61} +3.50384 q^{62} -5.50983 q^{63} +1.00000 q^{64} +2.39309 q^{65} +0.0891221 q^{66} -3.71765 q^{67} +6.74198 q^{68} +0.0585864 q^{69} -1.83741 q^{70} +5.83313 q^{71} +2.99869 q^{72} -0.510408 q^{73} +6.00888 q^{74} +0.0361439 q^{75} -4.53061 q^{77} -0.0864957 q^{78} +12.1354 q^{79} +1.00000 q^{80} +8.98824 q^{81} +7.98063 q^{82} +6.23256 q^{83} +0.0664112 q^{84} +6.74198 q^{85} -5.71443 q^{86} +0.119332 q^{87} +2.46576 q^{88} +17.0020 q^{89} +2.99869 q^{90} +4.39709 q^{91} +1.62092 q^{92} -0.126642 q^{93} -12.4926 q^{94} -0.0361439 q^{96} -13.6598 q^{97} +3.62392 q^{98} +7.39405 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q - 9 q^{2} + 9 q^{4} + 9 q^{5} - 9 q^{8} + 21 q^{9}+O(q^{10}) \) 9 * q - 9 * q^2 + 9 * q^4 + 9 * q^5 - 9 * q^8 + 21 * q^9	\( 9 q - 9 q^{2} + 9 q^{4} + 9 q^{5} - 9 q^{8} + 21 q^{9} - 9 q^{10} + 12 q^{11} - 9 q^{13} + 9 q^{16} + 6 q^{17} - 21 q^{18} + 9 q^{20} - 6 q^{21} - 12 q^{22} + 18 q^{23} + 9 q^{25} + 9 q^{26} + 18 q^{27} + 6 q^{31} - 9 q^{32} - 6 q^{33} - 6 q^{34} + 21 q^{36} - 6 q^{37} + 24 q^{39} - 9 q^{40} + 6 q^{42} + 18 q^{43} + 12 q^{44} + 21 q^{45} - 18 q^{46} - 3 q^{47} + 39 q^{49} - 9 q^{50} + 48 q^{51} - 9 q^{52} - 18 q^{54} + 12 q^{55} - 21 q^{59} + 18 q^{61} - 6 q^{62} - 12 q^{63} + 9 q^{64} - 9 q^{65} + 6 q^{66} + 6 q^{68} + 30 q^{69} - 18 q^{71} - 21 q^{72} - 36 q^{73} + 6 q^{74} + 15 q^{77} - 24 q^{78} + 6 q^{79} + 9 q^{80} + 69 q^{81} - 6 q^{83} - 6 q^{84} + 6 q^{85} - 18 q^{86} - 24 q^{87} - 12 q^{88} + 18 q^{89} - 21 q^{90} + 60 q^{91} + 18 q^{92} + 3 q^{94} - 18 q^{97} - 39 q^{98} + 54 q^{99}+O(q^{100}) \) 9 * q - 9 * q^2 + 9 * q^4 + 9 * q^5 - 9 * q^8 + 21 * q^9 - 9 * q^10 + 12 * q^11 - 9 * q^13 + 9 * q^16 + 6 * q^17 - 21 * q^18 + 9 * q^20 - 6 * q^21 - 12 * q^22 + 18 * q^23 + 9 * q^25 + 9 * q^26 + 18 * q^27 + 6 * q^31 - 9 * q^32 - 6 * q^33 - 6 * q^34 + 21 * q^36 - 6 * q^37 + 24 * q^39 - 9 * q^40 + 6 * q^42 + 18 * q^43 + 12 * q^44 + 21 * q^45 - 18 * q^46 - 3 * q^47 + 39 * q^49 - 9 * q^50 + 48 * q^51 - 9 * q^52 - 18 * q^54 + 12 * q^55 - 21 * q^59 + 18 * q^61 - 6 * q^62 - 12 * q^63 + 9 * q^64 - 9 * q^65 + 6 * q^66 + 6 * q^68 + 30 * q^69 - 18 * q^71 - 21 * q^72 - 36 * q^73 + 6 * q^74 + 15 * q^77 - 24 * q^78 + 6 * q^79 + 9 * q^80 + 69 * q^81 - 6 * q^83 - 6 * q^84 + 6 * q^85 - 18 * q^86 - 24 * q^87 - 12 * q^88 + 18 * q^89 - 21 * q^90 + 60 * q^91 + 18 * q^92 + 3 * q^94 - 18 * q^97 - 39 * q^98 + 54 * q^99

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