LMFDB - Embedded newform 1815.2.a.r.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1815,2,Mod(1,1815)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1815, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("1815.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1815 = 3 \cdot 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1815.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:	$14.4928479669$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.5725.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 8x^{2} + 6x + 11 $ x^4 - x^3 - 8x^2 + 6x + 11
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 165)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$2.55157$ of defining polynomial
Character	$\chi$	$=$	1815.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.933531 q^{2} -1.00000 q^{3} -1.12852 q^{4} -1.00000 q^{5} -0.933531 q^{6} +2.04108 q^{7} -2.92057 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.933531 q^{2} -1.00000 q^{3} -1.12852 q^{4} -1.00000 q^{5} -0.933531 q^{6} +2.04108 q^{7} -2.92057 q^{8} +1.00000 q^{9} -0.933531 q^{10} +1.12852 q^{12} +1.44843 q^{13} +1.90541 q^{14} +1.00000 q^{15} -0.469405 q^{16} -0.867063 q^{17} +0.933531 q^{18} -3.12852 q^{19} +1.12852 q^{20} -2.04108 q^{21} -4.70547 q^{23} +2.92057 q^{24} +1.00000 q^{25} +1.35216 q^{26} -1.00000 q^{27} -2.30340 q^{28} -2.03835 q^{29} +0.933531 q^{30} +10.6136 q^{31} +5.40294 q^{32} -0.809430 q^{34} -2.04108 q^{35} -1.12852 q^{36} +4.15664 q^{37} -2.92057 q^{38} -1.44843 q^{39} +2.92057 q^{40} +0.805012 q^{41} -1.90541 q^{42} +2.34089 q^{43} -1.00000 q^{45} -4.39271 q^{46} +10.3803 q^{47} +0.469405 q^{48} -2.83399 q^{49} +0.933531 q^{50} +0.867063 q^{51} -1.63459 q^{52} +7.21596 q^{53} -0.933531 q^{54} -5.96112 q^{56} +3.12852 q^{57} -1.90286 q^{58} -8.32351 q^{59} -1.12852 q^{60} +8.76752 q^{61} +9.90814 q^{62} +2.04108 q^{63} +5.98262 q^{64} -1.44843 q^{65} -3.15664 q^{67} +0.978497 q^{68} +4.70547 q^{69} -1.90541 q^{70} +12.8707 q^{71} -2.92057 q^{72} +14.7184 q^{73} +3.88035 q^{74} -1.00000 q^{75} +3.53059 q^{76} -1.35216 q^{78} +16.9992 q^{79} +0.469405 q^{80} +1.00000 q^{81} +0.751504 q^{82} -6.14148 q^{83} +2.30340 q^{84} +0.867063 q^{85} +2.18529 q^{86} +2.03835 q^{87} +3.77194 q^{89} -0.933531 q^{90} +2.95637 q^{91} +5.31022 q^{92} -10.6136 q^{93} +9.69031 q^{94} +3.12852 q^{95} -5.40294 q^{96} -1.93795 q^{97} -2.64562 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{2} - 4 q^{3} + 9 q^{4} - 4 q^{5} + q^{6} + 8 q^{7} - 3 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q - q^2 - 4 * q^3 + 9 * q^4 - 4 * q^5 + q^6 + 8 * q^7 - 3 * q^8 + 4 * q^9	$ 4 q - q^{2} - 4 q^{3} + 9 q^{4} - 4 q^{5} + q^{6} + 8 q^{7} - 3 q^{8} + 4 q^{9} + q^{10} - 9 q^{12} + 15 q^{13} + 7 q^{14} + 4 q^{15} + 7 q^{16} + 6 q^{17} - q^{18} + q^{19} - 9 q^{20} - 8 q^{21} - q^{23} + 3 q^{24} + 4 q^{25} - 18 q^{26} - 4 q^{27} + 31 q^{28} - 17 q^{29} - q^{30} + 15 q^{31} + 8 q^{32} - 35 q^{34} - 8 q^{35} + 9 q^{36} - q^{37} - 3 q^{38} - 15 q^{39} + 3 q^{40} + 12 q^{41} - 7 q^{42} + 14 q^{43} - 4 q^{45} + 9 q^{46} + 14 q^{47} - 7 q^{48} + 20 q^{49} - q^{50} - 6 q^{51} + 39 q^{52} + 2 q^{53} + q^{54} - 12 q^{56} - q^{57} - 11 q^{58} - 11 q^{59} + 9 q^{60} - q^{61} + 30 q^{62} + 8 q^{63} - 3 q^{64} - 15 q^{65} + 5 q^{67} + 19 q^{68} + q^{69} - 7 q^{70} - 3 q^{71} - 3 q^{72} + 45 q^{73} - 29 q^{74} - 4 q^{75} + 23 q^{76} + 18 q^{78} - 7 q^{80} + 4 q^{81} + 11 q^{82} - 15 q^{83} - 31 q^{84} - 6 q^{85} - 10 q^{86} + 17 q^{87} + 2 q^{89} + q^{90} + 16 q^{91} + 34 q^{92} - 15 q^{93} + 29 q^{94} - q^{95} - 8 q^{96} - 26 q^{97} + q^{98}+O(q^{100}) $ 4 * q - q^2 - 4 * q^3 + 9 * q^4 - 4 * q^5 + q^6 + 8 * q^7 - 3 * q^8 + 4 * q^9 + q^10 - 9 * q^12 + 15 * q^13 + 7 * q^14 + 4 * q^15 + 7 * q^16 + 6 * q^17 - q^18 + q^19 - 9 * q^20 - 8 * q^21 - q^23 + 3 * q^24 + 4 * q^25 - 18 * q^26 - 4 * q^27 + 31 * q^28 - 17 * q^29 - q^30 + 15 * q^31 + 8 * q^32 - 35 * q^34 - 8 * q^35 + 9 * q^36 - q^37 - 3 * q^38 - 15 * q^39 + 3 * q^40 + 12 * q^41 - 7 * q^42 + 14 * q^43 - 4 * q^45 + 9 * q^46 + 14 * q^47 - 7 * q^48 + 20 * q^49 - q^50 - 6 * q^51 + 39 * q^52 + 2 * q^53 + q^54 - 12 * q^56 - q^57 - 11 * q^58 - 11 * q^59 + 9 * q^60 - q^61 + 30 * q^62 + 8 * q^63 - 3 * q^64 - 15 * q^65 + 5 * q^67 + 19 * q^68 + q^69 - 7 * q^70 - 3 * q^71 - 3 * q^72 + 45 * q^73 - 29 * q^74 - 4 * q^75 + 23 * q^76 + 18 * q^78 - 7 * q^80 + 4 * q^81 + 11 * q^82 - 15 * q^83 - 31 * q^84 - 6 * q^85 - 10 * q^86 + 17 * q^87 + 2 * q^89 + q^90 + 16 * q^91 + 34 * q^92 - 15 * q^93 + 29 * q^94 - q^95 - 8 * q^96 - 26 * q^97 + q^98

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 $

$2$	0.933531	0.660106	0.330053	−	0.943962i	$-0.392933\pi$
$2$	0.933531	0.660106	0.330053	+	0.943962i	$0.392933\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.12852	−0.564260
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−0.933531	−0.381113
$7$	2.04108	0.771456	0.385728	−	0.922613i	$-0.373950\pi$
$7$	2.04108	0.771456	0.385728	+	0.922613i	$0.373950\pi$
$8$	−2.92057	−1.03258
$9$	1.00000	0.333333
$10$	−0.933531	−0.295209
$11$	0	0
$11$	0	0
$12$	1.12852	0.325775
$13$	1.44843	0.401724	0.200862	−	0.979620i	$-0.435626\pi$
$13$	1.44843	0.401724	0.200862	+	0.979620i	$0.435626\pi$
$14$	1.90541	0.509243
$15$	1.00000	0.258199
$16$	−0.469405	−0.117351
$17$	−0.867063	−0.210294	−0.105147	−	0.994457i	$-0.533531\pi$
$17$	−0.867063	−0.210294	−0.105147	+	0.994457i	$0.533531\pi$
$18$	0.933531	0.220035
$19$	−3.12852	−0.717732	−0.358866	−	0.933389i	$-0.616836\pi$
$19$	−3.12852	−0.717732	−0.358866	+	0.933389i	$0.616836\pi$
$20$	1.12852	0.252345
$21$	−2.04108	−0.445400
$22$	0	0
$23$	−4.70547	−0.981159	−0.490580	−	0.871396i	$-0.663215\pi$
$23$	−4.70547	−0.981159	−0.490580	+	0.871396i	$0.663215\pi$
$24$	2.92057	0.596159
$25$	1.00000	0.200000
$26$	1.35216	0.265180
$27$	−1.00000	−0.192450
$28$	−2.30340	−0.435301
$29$	−2.03835	−0.378512	−0.189256	−	0.981928i	$-0.560608\pi$
$29$	−2.03835	−0.378512	−0.189256	+	0.981928i	$0.560608\pi$
$30$	0.933531	0.170439
$31$	10.6136	1.90626	0.953131	−	0.302558i	$-0.0978407\pi$
$31$	10.6136	1.90626	0.953131	+	0.302558i	$0.0978407\pi$
$32$	5.40294	0.955113
$33$	0	0
$34$	−0.809430	−0.138816
$35$	−2.04108	−0.345005
$36$	−1.12852	−0.188087
$37$	4.15664	0.683347	0.341674	−	0.939819i	$-0.389006\pi$
$37$	4.15664	0.683347	0.341674	+	0.939819i	$0.389006\pi$
$38$	−2.92057	−0.473779
$39$	−1.44843	−0.231935
$40$	2.92057	0.461783
$41$	0.805012	0.125722	0.0628609	−	0.998022i	$-0.479978\pi$
$41$	0.805012	0.125722	0.0628609	+	0.998022i	$0.479978\pi$
$42$	−1.90541	−0.294011
$43$	2.34089	0.356982	0.178491	−	0.983942i	$-0.442878\pi$
$43$	2.34089	0.356982	0.178491	+	0.983942i	$0.442878\pi$
$44$	0	0
$45$	−1.00000	−0.149071
$46$	−4.39271	−0.647669
$47$	10.3803	1.51412	0.757060	−	0.653346i	$-0.226635\pi$
$47$	10.3803	1.51412	0.757060	+	0.653346i	$0.226635\pi$
$48$	0.469405	0.0677528
$49$	−2.83399	−0.404856
$50$	0.933531	0.132021
$51$	0.867063	0.121413
$52$	−1.63459	−0.226676
$53$	7.21596	0.991188	0.495594	−	0.868554i	$-0.334950\pi$
$53$	7.21596	0.991188	0.495594	+	0.868554i	$0.334950\pi$
$54$	−0.933531	−0.127038
$55$	0	0
$56$	−5.96112	−0.796588
$57$	3.12852	0.414383
$58$	−1.90286	−0.249858
$59$	−8.32351	−1.08363	−0.541814	−	0.840498i	$-0.682262\pi$
$59$	−8.32351	−1.08363	−0.541814	+	0.840498i	$0.682262\pi$
$60$	−1.12852	−0.145691
$61$	8.76752	1.12257	0.561283	−	0.827624i	$-0.310308\pi$
$61$	8.76752	1.12257	0.561283	+	0.827624i	$0.310308\pi$
$62$	9.90814	1.25834
$63$	2.04108	0.257152
$64$	5.98262	0.747828
$65$	−1.44843	−0.179656
$66$	0	0
$67$	−3.15664	−0.385645	−0.192822	−	0.981234i	$-0.561764\pi$
$67$	−3.15664	−0.385645	−0.192822	+	0.981234i	$0.561764\pi$
$68$	0.978497	0.118660
$69$	4.70547	0.566472
$70$	−1.90541	−0.227740
$71$	12.8707	1.52747	0.763733	−	0.645532i	$-0.223364\pi$
$71$	12.8707	1.52747	0.763733	+	0.645532i	$0.223364\pi$
$72$	−2.92057	−0.344193
$73$	14.7184	1.72266	0.861331	−	0.508044i	$-0.169631\pi$
$73$	14.7184	1.72266	0.861331	+	0.508044i	$0.169631\pi$
$74$	3.88035	0.451082
$75$	−1.00000	−0.115470
$76$	3.53059	0.404987
$77$	0	0
$78$	−1.35216	−0.153102
$79$	16.9992	1.91256	0.956278	−	0.292458i	$-0.0944733\pi$
$79$	16.9992	1.91256	0.956278	+	0.292458i	$0.0944733\pi$
$80$	0.469405	0.0524811
$81$	1.00000	0.111111
$82$	0.751504	0.0829897
$83$	−6.14148	−0.674115	−0.337058	−	0.941484i	$-0.609432\pi$
$83$	−6.14148	−0.674115	−0.337058	+	0.941484i	$0.609432\pi$
$84$	2.30340	0.251321
$85$	0.867063	0.0940461
$86$	2.18529	0.235646
$87$	2.03835	0.218534
$88$	0	0
$89$	3.77194	0.399825	0.199913	−	0.979814i	$-0.435934\pi$
$89$	3.77194	0.399825	0.199913	+	0.979814i	$0.435934\pi$
$90$	−0.933531	−0.0984028
$91$	2.95637	0.309912
$92$	5.31022	0.553628
$93$	−10.6136	−1.10058
$94$	9.69031	0.999480
$95$	3.12852	0.320979
$96$	−5.40294	−0.551435
$97$	−1.93795	−0.196769	−0.0983845	−	0.995148i	$-0.531367\pi$
$97$	−1.93795	−0.196769	−0.0983845	+	0.995148i	$0.531367\pi$
$98$	−2.64562	−0.267248
$99$	0	0
$100$	−1.12852	−0.112852
$101$	5.25176	0.522570	0.261285	−	0.965262i	$-0.415854\pi$
$101$	5.25176	0.522570	0.261285	+	0.965262i	$0.415854\pi$
$102$	0.809430	0.0801455
$103$	−13.6007	−1.34011	−0.670056	−	0.742310i	$-0.733730\pi$
$103$	−13.6007	−1.34011	−0.670056	+	0.742310i	$0.733730\pi$
$104$	−4.23026	−0.414811
$105$	2.04108	0.199189
$106$	6.73632	0.654290
$107$	9.99063	0.965831	0.482915	−	0.875667i	$-0.339578\pi$
$107$	9.99063	0.965831	0.482915	+	0.875667i	$0.339578\pi$
$108$	1.12852	0.108592
$109$	6.75183	0.646708	0.323354	−	0.946278i	$-0.395189\pi$
$109$	6.75183	0.646708	0.323354	+	0.946278i	$0.395189\pi$
$110$	0	0
$111$	−4.15664	−0.394531
$112$	−0.958094	−0.0905314
$113$	−5.24461	−0.493371	−0.246686	−	0.969096i	$-0.579342\pi$
$113$	−5.24461	−0.493371	−0.246686	+	0.969096i	$0.579342\pi$
$114$	2.92057	0.273537
$115$	4.70547	0.438788
$116$	2.30032	0.213579
$117$	1.44843	0.133908
$118$	−7.77025	−0.715310
$119$	−1.76974	−0.162232
$120$	−2.92057	−0.266610
$121$	0	0
$122$	8.18476	0.741013
$123$	−0.805012	−0.0725855
$124$	−11.9777	−1.07563
$125$	−1.00000	−0.0894427
$126$	1.90541	0.169748
$127$	20.6751	1.83462	0.917311	−	0.398172i	$-0.130355\pi$
$127$	20.6751	1.83462	0.917311	+	0.398172i	$0.130355\pi$
$128$	−5.22091	−0.461468
$129$	−2.34089	−0.206104
$130$	−1.35216	−0.118592
$131$	−20.3089	−1.77439	−0.887197	−	0.461392i	$-0.847350\pi$
$131$	−20.3089	−1.77439	−0.887197	+	0.461392i	$0.847350\pi$
$132$	0	0
$133$	−6.38556	−0.553698
$134$	−2.94682	−0.254567
$135$	1.00000	0.0860663
$136$	2.53232	0.217144
$137$	−3.47982	−0.297301	−0.148650	−	0.988890i	$-0.547493\pi$
$137$	−3.47982	−0.297301	−0.148650	+	0.988890i	$0.547493\pi$
$138$	4.39271	0.373932
$139$	−2.73086	−0.231629	−0.115814	−	0.993271i	$-0.536948\pi$
$139$	−2.73086	−0.231629	−0.115814	+	0.993271i	$0.536948\pi$
$140$	2.30340	0.194673
$141$	−10.3803	−0.874177
$142$	12.0152	1.00829
$143$	0	0
$144$	−0.469405	−0.0391171
$145$	2.03835	0.169276
$146$	13.7401	1.13714
$147$	2.83399	0.233744
$148$	−4.69085	−0.385585
$149$	9.10841	0.746190	0.373095	−	0.927793i	$-0.378297\pi$
$149$	9.10841	0.746190	0.373095	+	0.927793i	$0.378297\pi$
$150$	−0.933531	−0.0762225
$151$	−21.5744	−1.75570	−0.877852	−	0.478933i	$-0.841024\pi$
$151$	−21.5744	−1.75570	−0.877852	+	0.478933i	$0.841024\pi$
$152$	9.13706	0.741114
$153$	−0.867063	−0.0700979
$154$	0	0
$155$	−10.6136	−0.852506
$156$	1.63459	0.130872
$157$	−23.7940	−1.89896	−0.949482	−	0.313821i	$-0.898391\pi$
$157$	−23.7940	−1.89896	−0.949482	+	0.313821i	$0.898391\pi$
$158$	15.8693	1.26249
$159$	−7.21596	−0.572263
$160$	−5.40294	−0.427140
$161$	−9.60425	−0.756921
$162$	0.933531	0.0733451
$163$	−1.80332	−0.141247	−0.0706236	−	0.997503i	$-0.522499\pi$
$163$	−1.80332	−0.141247	−0.0706236	+	0.997503i	$0.522499\pi$
$164$	−0.908472	−0.0709397
$165$	0	0
$166$	−5.73326	−0.444988
$167$	24.5874	1.90263	0.951315	−	0.308220i	$-0.0997333\pi$
$167$	24.5874	1.90263	0.951315	+	0.308220i	$0.0997333\pi$
$168$	5.96112	0.459910
$169$	−10.9020	−0.838618
$170$	0.809430	0.0620804
$171$	−3.12852	−0.239244
$172$	−2.64174	−0.201430
$173$	16.2115	1.23254	0.616270	−	0.787535i	$-0.288643\pi$
$173$	16.2115	1.23254	0.616270	+	0.787535i	$0.288643\pi$
$174$	1.90286	0.144256
$175$	2.04108	0.154291
$176$	0	0
$177$	8.32351	0.625633
$178$	3.52123	0.263927
$179$	16.9697	1.26837	0.634186	−	0.773181i	$-0.281335\pi$
$179$	16.9697	1.26837	0.634186	+	0.773181i	$0.281335\pi$
$180$	1.12852	0.0841149
$181$	18.3508	1.36400	0.682002	−	0.731350i	$-0.261109\pi$
$181$	18.3508	1.36400	0.682002	+	0.731350i	$0.261109\pi$
$182$	2.75986	0.204575
$183$	−8.76752	−0.648114
$184$	13.7427	1.01312
$185$	−4.15664	−0.305602
$186$	−9.90814	−0.726500
$187$	0	0
$188$	−11.7143	−0.854356
$189$	−2.04108	−0.148467
$190$	2.92057	0.211880
$191$	−15.3985	−1.11420	−0.557099	−	0.830446i	$-0.688086\pi$
$191$	−15.3985	−1.11420	−0.557099	+	0.830446i	$0.688086\pi$
$192$	−5.98262	−0.431759
$193$	7.37942	0.531182	0.265591	−	0.964086i	$-0.414433\pi$
$193$	7.37942	0.531182	0.265591	+	0.964086i	$0.414433\pi$
$194$	−1.80914	−0.129888
$195$	1.44843	0.103725
$196$	3.19822	0.228444
$197$	−3.14676	−0.224197	−0.112099	−	0.993697i	$-0.535757\pi$
$197$	−3.14676	−0.224197	−0.112099	+	0.993697i	$0.535757\pi$
$198$	0	0
$199$	−3.25757	−0.230923	−0.115462	−	0.993312i	$-0.536835\pi$
$199$	−3.25757	−0.230923	−0.115462	+	0.993312i	$0.536835\pi$
$200$	−2.92057	−0.206516
$201$	3.15664	0.222652
$202$	4.90268	0.344951
$203$	−4.16043	−0.292005
$204$	−0.978497	−0.0685085
$205$	−0.805012	−0.0562245
$206$	−12.6966	−0.884617
$207$	−4.70547	−0.327053
$208$	−0.679903	−0.0471428
$209$	0	0
$210$	1.90541	0.131486
$211$	−19.9242	−1.37164	−0.685818	−	0.727773i	$-0.740555\pi$
$211$	−19.9242	−1.37164	−0.685818	+	0.727773i	$0.740555\pi$
$212$	−8.14335	−0.559288
$213$	−12.8707	−0.881883
$214$	9.32657	0.637551
$215$	−2.34089	−0.159647
$216$	2.92057	0.198720
$217$	21.6632	1.47060
$218$	6.30305	0.426896
$219$	−14.7184	−0.994580
$220$	0	0
$221$	−1.25588	−0.0844799
$222$	−3.88035	−0.260432
$223$	10.4801	0.701802	0.350901	−	0.936412i	$-0.385875\pi$
$223$	10.4801	0.701802	0.350901	+	0.936412i	$0.385875\pi$
$224$	11.0278	0.736828
$225$	1.00000	0.0666667
$226$	−4.89601	−0.325678
$227$	−17.6731	−1.17301	−0.586503	−	0.809947i	$-0.699496\pi$
$227$	−17.6731	−1.17301	−0.586503	+	0.809947i	$0.699496\pi$
$228$	−3.53059	−0.233819
$229$	4.12967	0.272897	0.136448	−	0.990647i	$-0.456431\pi$
$229$	4.12967	0.272897	0.136448	+	0.990647i	$0.456431\pi$
$230$	4.39271	0.289646
$231$	0	0
$232$	5.95314	0.390843
$233$	−13.5990	−0.890898	−0.445449	−	0.895307i	$-0.646956\pi$
$233$	−13.5990	−0.890898	−0.445449	+	0.895307i	$0.646956\pi$
$234$	1.35216	0.0883934
$235$	−10.3803	−0.677135
$236$	9.39324	0.611448
$237$	−16.9992	−1.10422
$238$	−1.65211	−0.107090
$239$	−8.00632	−0.517886	−0.258943	−	0.965893i	$-0.583374\pi$
$239$	−8.00632	−0.517886	−0.258943	+	0.965893i	$0.583374\pi$
$240$	−0.469405	−0.0303000
$241$	0.501943	0.0323330	0.0161665	−	0.999869i	$-0.494854\pi$
$241$	0.501943	0.0323330	0.0161665	+	0.999869i	$0.494854\pi$
$242$	0	0
$243$	−1.00000	−0.0641500
$244$	−9.89432	−0.633419
$245$	2.83399	0.181057
$246$	−0.751504	−0.0479141
$247$	−4.53146	−0.288330
$248$	−30.9978	−1.96836
$249$	6.14148	0.389200
$250$	−0.933531	−0.0590417
$251$	−18.5405	−1.17027	−0.585133	−	0.810937i	$-0.698958\pi$
$251$	−18.5405	−1.17027	−0.585133	+	0.810937i	$0.698958\pi$
$252$	−2.30340	−0.145100
$253$	0	0
$254$	19.3009	1.21105
$255$	−0.867063	−0.0542976
$256$	−16.8391	−1.05245
$257$	7.38010	0.460358	0.230179	−	0.973148i	$-0.426069\pi$
$257$	7.38010	0.460358	0.230179	+	0.973148i	$0.426069\pi$
$258$	−2.18529	−0.136050
$259$	8.48403	0.527172
$260$	1.63459	0.101373
$261$	−2.03835	−0.126171
$262$	−18.9590	−1.17129
$263$	3.05950	0.188657	0.0943285	−	0.995541i	$-0.469930\pi$
$263$	3.05950	0.188657	0.0943285	+	0.995541i	$0.469930\pi$
$264$	0	0
$265$	−7.21596	−0.443273
$266$	−5.96112	−0.365500
$267$	−3.77194	−0.230839
$268$	3.56233	0.217604
$269$	−17.6801	−1.07797	−0.538987	−	0.842314i	$-0.681193\pi$
$269$	−17.6801	−1.07797	−0.538987	+	0.842314i	$0.681193\pi$
$270$	0.933531	0.0568129
$271$	15.2992	0.929358	0.464679	−	0.885479i	$-0.346170\pi$
$271$	15.2992	0.929358	0.464679	+	0.885479i	$0.346170\pi$
$272$	0.407004	0.0246782
$273$	−2.95637	−0.178928
$274$	−3.24852	−0.196250
$275$	0	0
$276$	−5.31022	−0.319638
$277$	17.8238	1.07093	0.535463	−	0.844559i	$-0.320137\pi$
$277$	17.8238	1.07093	0.535463	+	0.844559i	$0.320137\pi$
$278$	−2.54935	−0.152900
$279$	10.6136	0.635421
$280$	5.96112	0.356245
$281$	17.2990	1.03197	0.515985	−	0.856597i	$-0.327426\pi$
$281$	17.2990	1.03197	0.515985	+	0.856597i	$0.327426\pi$
$282$	−9.69031	−0.577050
$283$	25.7764	1.53225	0.766124	−	0.642693i	$-0.222183\pi$
$283$	25.7764	1.53225	0.766124	+	0.642693i	$0.222183\pi$
$284$	−14.5248	−0.861887
$285$	−3.12852	−0.185317
$286$	0	0
$287$	1.64309	0.0969888
$288$	5.40294	0.318371
$289$	−16.2482	−0.955777
$290$	1.90286	0.111740
$291$	1.93795	0.113605
$292$	−16.6100	−0.972029
$293$	−13.5306	−0.790468	−0.395234	−	0.918581i	$-0.629336\pi$
$293$	−13.5306	−0.790468	−0.395234	+	0.918581i	$0.629336\pi$
$294$	2.64562	0.154296
$295$	8.32351	0.484613
$296$	−12.1398	−0.705609
$297$	0	0
$298$	8.50299	0.492565
$299$	−6.81557	−0.394155
$300$	1.12852	0.0651551
$301$	4.77794	0.275396
$302$	−20.1404	−1.15895
$303$	−5.25176	−0.301706
$304$	1.46854	0.0842268
$305$	−8.76752	−0.502027
$306$	−0.809430	−0.0462720
$307$	13.0268	0.743478	0.371739	−	0.928337i	$-0.378762\pi$
$307$	13.0268	0.743478	0.371739	+	0.928337i	$0.378762\pi$
$308$	0	0
$309$	13.6007	0.773714
$310$	−9.90814	−0.562745
$311$	1.90319	0.107920	0.0539601	−	0.998543i	$-0.482816\pi$
$311$	1.90319	0.107920	0.0539601	+	0.998543i	$0.482816\pi$
$312$	4.23026	0.239491
$313$	10.9324	0.617934	0.308967	−	0.951073i	$-0.400017\pi$
$313$	10.9324	0.617934	0.308967	+	0.951073i	$0.400017\pi$
$314$	−22.2124	−1.25352
$315$	−2.04108	−0.115002
$316$	−19.1839	−1.07918
$317$	−16.0723	−0.902708	−0.451354	−	0.892345i	$-0.649059\pi$
$317$	−16.0723	−0.902708	−0.451354	+	0.892345i	$0.649059\pi$
$318$	−6.73632	−0.377754
$319$	0	0
$320$	−5.98262	−0.334439
$321$	−9.99063	−0.557623
$322$	−8.96587	−0.499648
$323$	2.71262	0.150934
$324$	−1.12852	−0.0626955
$325$	1.44843	0.0803447
$326$	−1.68346	−0.0932382
$327$	−6.75183	−0.373377
$328$	−2.35109	−0.129817
$329$	21.1870	1.16808
$330$	0	0
$331$	1.39579	0.0767195	0.0383597	−	0.999264i	$-0.487787\pi$
$331$	1.39579	0.0767195	0.0383597	+	0.999264i	$0.487787\pi$
$332$	6.93078	0.380376
$333$	4.15664	0.227782
$334$	22.9531	1.25594
$335$	3.15664	0.172466
$336$	0.958094	0.0522683
$337$	2.76340	0.150532	0.0752660	−	0.997163i	$-0.476019\pi$
$337$	2.76340	0.150532	0.0752660	+	0.997163i	$0.476019\pi$
$338$	−10.1774	−0.553577
$339$	5.24461	0.284848
$340$	−0.978497	−0.0530664
$341$	0	0
$342$	−2.92057	−0.157926
$343$	−20.0720	−1.08378
$344$	−6.83672	−0.368611
$345$	−4.70547	−0.253334
$346$	15.1340	0.813608
$347$	3.12683	0.167857	0.0839286	−	0.996472i	$-0.473253\pi$
$347$	3.12683	0.167857	0.0839286	+	0.996472i	$0.473253\pi$
$348$	−2.30032	−0.123310
$349$	−13.1277	−0.702709	−0.351355	−	0.936242i	$-0.614279\pi$
$349$	−13.1277	−0.702709	−0.351355	+	0.936242i	$0.614279\pi$
$350$	1.90541	0.101849
$351$	−1.44843	−0.0773117
$352$	0	0
$353$	10.7984	0.574739	0.287370	−	0.957820i	$-0.407219\pi$
$353$	10.7984	0.574739	0.287370	+	0.957820i	$0.407219\pi$
$354$	7.77025	0.412984
$355$	−12.8707	−0.683103
$356$	−4.25671	−0.225605
$357$	1.76974	0.0936648
$358$	15.8417	0.837260
$359$	−23.9716	−1.26517	−0.632585	−	0.774491i	$-0.718006\pi$
$359$	−23.9716	−1.26517	−0.632585	+	0.774491i	$0.718006\pi$
$360$	2.92057	0.153928
$361$	−9.21237	−0.484861
$362$	17.1310	0.900388
$363$	0	0
$364$	−3.33632	−0.174871
$365$	−14.7184	−0.770398
$366$	−8.18476	−0.427824
$367$	8.87287	0.463160	0.231580	−	0.972816i	$-0.425610\pi$
$367$	8.87287	0.463160	0.231580	+	0.972816i	$0.425610\pi$
$368$	2.20877	0.115140
$369$	0.805012	0.0419072
$370$	−3.88035	−0.201730
$371$	14.7283	0.764658
$372$	11.9777	0.621013
$373$	26.3389	1.36378	0.681888	−	0.731456i	$-0.261159\pi$
$373$	26.3389	1.36378	0.681888	+	0.731456i	$0.261159\pi$
$374$	0	0
$375$	1.00000	0.0516398
$376$	−30.3163	−1.56345
$377$	−2.95242	−0.152057
$378$	−1.90541	−0.0980038
$379$	4.69610	0.241223	0.120611	−	0.992700i	$-0.461515\pi$
$379$	4.69610	0.241223	0.120611	+	0.992700i	$0.461515\pi$
$380$	−3.53059	−0.181116
$381$	−20.6751	−1.05922
$382$	−14.3750	−0.735489
$383$	−6.89931	−0.352538	−0.176269	−	0.984342i	$-0.556403\pi$
$383$	−6.89931	−0.352538	−0.176269	+	0.984342i	$0.556403\pi$
$384$	5.22091	0.266428
$385$	0	0
$386$	6.88892	0.350637
$387$	2.34089	0.118994
$388$	2.18701	0.111029
$389$	2.40462	0.121919	0.0609596	−	0.998140i	$-0.480584\pi$
$389$	2.40462	0.121919	0.0609596	+	0.998140i	$0.480584\pi$
$390$	1.35216	0.0684692
$391$	4.07994	0.206331
$392$	8.27688	0.418045
$393$	20.3089	1.02445
$394$	−2.93760	−0.147994
$395$	−16.9992	−0.855321
$396$	0	0
$397$	37.6715	1.89068	0.945338	−	0.326091i	$-0.105732\pi$
$397$	37.6715	1.89068	0.945338	+	0.326091i	$0.105732\pi$
$398$	−3.04104	−0.152434
$399$	6.38556	0.319678
$400$	−0.469405	−0.0234703
$401$	−12.5168	−0.625060	−0.312530	−	0.949908i	$-0.601176\pi$
$401$	−12.5168	−0.625060	−0.312530	+	0.949908i	$0.601176\pi$
$402$	2.94682	0.146974
$403$	15.3731	0.765790
$404$	−5.92671	−0.294865
$405$	−1.00000	−0.0496904
$406$	−3.88390	−0.192754
$407$	0	0
$408$	−2.53232	−0.125368
$409$	26.4622	1.30847	0.654237	−	0.756290i	$-0.272990\pi$
$409$	26.4622	1.30847	0.654237	+	0.756290i	$0.272990\pi$
$410$	−0.751504	−0.0371141
$411$	3.47982	0.171647
$412$	15.3486	0.756171
$413$	−16.9889	−0.835971
$414$	−4.39271	−0.215890
$415$	6.14148	0.301473
$416$	7.82580	0.383691
$417$	2.73086	0.133731
$418$	0	0
$419$	30.9711	1.51304	0.756518	−	0.653973i	$-0.226899\pi$
$419$	30.9711	1.51304	0.756518	+	0.653973i	$0.226899\pi$
$420$	−2.30340	−0.112394
$421$	18.2435	0.889132	0.444566	−	0.895746i	$-0.353358\pi$
$421$	18.2435	0.889132	0.444566	+	0.895746i	$0.353358\pi$
$422$	−18.5998	−0.905426
$423$	10.3803	0.504706
$424$	−21.0747	−1.02348
$425$	−0.867063	−0.0420587
$426$	−12.0152	−0.582136
$427$	17.8952	0.866010
$428$	−11.2746	−0.544979
$429$	0	0
$430$	−2.18529	−0.105384
$431$	−30.3488	−1.46185	−0.730925	−	0.682458i	$-0.760911\pi$
$431$	−30.3488	−1.46185	−0.730925	+	0.682458i	$0.760911\pi$
$432$	0.469405	0.0225843
$433$	12.7012	0.610382	0.305191	−	0.952291i	$-0.401280\pi$
$433$	12.7012	0.610382	0.305191	+	0.952291i	$0.401280\pi$
$434$	20.2233	0.970750
$435$	−2.03835	−0.0977314
$436$	−7.61957	−0.364911
$437$	14.7212	0.704209
$438$	−13.7401	−0.656528
$439$	25.6564	1.22451	0.612257	−	0.790659i	$-0.290262\pi$
$439$	25.6564	1.22451	0.612257	+	0.790659i	$0.290262\pi$
$440$	0	0
$441$	−2.83399	−0.134952
$442$	−1.17241	−0.0557657
$443$	−26.2148	−1.24550	−0.622751	−	0.782420i	$-0.713985\pi$
$443$	−26.2148	−1.24550	−0.622751	+	0.782420i	$0.713985\pi$
$444$	4.69085	0.222618
$445$	−3.77194	−0.178807
$446$	9.78354	0.463264
$447$	−9.10841	−0.430813
$448$	12.2110	0.576916
$449$	−12.0061	−0.566605	−0.283302	−	0.959031i	$-0.591430\pi$
$449$	−12.0061	−0.566605	−0.283302	+	0.959031i	$0.591430\pi$
$450$	0.933531	0.0440071
$451$	0	0
$452$	5.91864	0.278390
$453$	21.5744	1.01366
$454$	−16.4984	−0.774309
$455$	−2.95637	−0.138597
$456$	−9.13706	−0.427882
$457$	−13.7890	−0.645022	−0.322511	−	0.946566i	$-0.604527\pi$
$457$	−13.7890	−0.645022	−0.322511	+	0.946566i	$0.604527\pi$
$458$	3.85518	0.180141
$459$	0.867063	0.0404710
$460$	−5.31022	−0.247590
$461$	−11.3262	−0.527515	−0.263758	−	0.964589i	$-0.584962\pi$
$461$	−11.3262	−0.527515	−0.263758	+	0.964589i	$0.584962\pi$
$462$	0	0
$463$	6.18784	0.287573	0.143787	−	0.989609i	$-0.454072\pi$
$463$	6.18784	0.287573	0.143787	+	0.989609i	$0.454072\pi$
$464$	0.956812	0.0444189
$465$	10.6136	0.492195
$466$	−12.6951	−0.588087
$467$	8.48288	0.392541	0.196270	−	0.980550i	$-0.437117\pi$
$467$	8.48288	0.392541	0.196270	+	0.980550i	$0.437117\pi$
$468$	−1.63459	−0.0755588
$469$	−6.44295	−0.297508
$470$	−9.69031	−0.446981
$471$	23.7940	1.09637
$472$	24.3094	1.11893
$473$	0	0
$474$	−15.8693	−0.728899
$475$	−3.12852	−0.143546
$476$	1.99719	0.0915411
$477$	7.21596	0.330396
$478$	−7.47415	−0.341860
$479$	−9.23554	−0.421982	−0.210991	−	0.977488i	$-0.567669\pi$
$479$	−9.23554	−0.421982	−0.210991	+	0.977488i	$0.567669\pi$
$480$	5.40294	0.246609
$481$	6.02062	0.274517
$482$	0.468579	0.0213432
$483$	9.60425	0.437008
$484$	0	0
$485$	1.93795	0.0879977
$486$	−0.933531	−0.0423458
$487$	20.1708	0.914024	0.457012	−	0.889460i	$-0.348920\pi$
$487$	20.1708	0.914024	0.457012	+	0.889460i	$0.348920\pi$
$488$	−25.6062	−1.15914
$489$	1.80332	0.0815491
$490$	2.64562	0.119517
$491$	5.33594	0.240807	0.120404	−	0.992725i	$-0.461581\pi$
$491$	5.33594	0.240807	0.120404	+	0.992725i	$0.461581\pi$
$492$	0.908472	0.0409571
$493$	1.76738	0.0795986
$494$	−4.23026	−0.190328
$495$	0	0
$496$	−4.98209	−0.223702
$497$	26.2700	1.17837
$498$	5.73326	0.256914
$499$	−39.2816	−1.75849	−0.879243	−	0.476374i	$-0.841951\pi$
$499$	−39.2816	−1.75849	−0.879243	+	0.476374i	$0.841951\pi$
$500$	1.12852	0.0504689
$501$	−24.5874	−1.09848
$502$	−17.3081	−0.772500
$503$	−32.4181	−1.44545	−0.722727	−	0.691134i	$-0.757111\pi$
$503$	−32.4181	−1.44545	−0.722727	+	0.691134i	$0.757111\pi$
$504$	−5.96112	−0.265529
$505$	−5.25176	−0.233700
$506$	0	0
$507$	10.9020	0.484176
$508$	−23.3323	−1.03520
$509$	−17.0656	−0.756421	−0.378211	−	0.925720i	$-0.623461\pi$
$509$	−17.0656	−0.756421	−0.378211	+	0.925720i	$0.623461\pi$
$510$	−0.809430	−0.0358422
$511$	30.0415	1.32896
$512$	−5.27803	−0.233258
$513$	3.12852	0.138128
$514$	6.88955	0.303885
$515$	13.6007	0.599316
$516$	2.64174	0.116296
$517$	0	0
$518$	7.92011	0.347990
$519$	−16.2115	−0.711608
$520$	4.23026	0.185509
$521$	−15.0471	−0.659224	−0.329612	−	0.944116i	$-0.606918\pi$
$521$	−15.0471	−0.659224	−0.329612	+	0.944116i	$0.606918\pi$
$522$	−1.90286	−0.0832860
$523$	37.0416	1.61972	0.809859	−	0.586624i	$-0.199544\pi$
$523$	37.0416	1.61972	0.809859	+	0.586624i	$0.199544\pi$
$524$	22.9189	1.00122
$525$	−2.04108	−0.0890800
$526$	2.85614	0.124534
$527$	−9.20267	−0.400875
$528$	0	0
$529$	−0.858520	−0.0373270
$530$	−6.73632	−0.292607
$531$	−8.32351	−0.361209
$532$	7.20623	0.312430
$533$	1.16601	0.0505054
$534$	−3.52123	−0.152378
$535$	−9.99063	−0.431933
$536$	9.21919	0.398208
$537$	−16.9697	−0.732295
$538$	−16.5049	−0.711577
$539$	0	0
$540$	−1.12852	−0.0485637
$541$	−0.177099	−0.00761407	−0.00380704	−	0.999993i	$-0.501212\pi$
$541$	−0.177099	−0.00761407	−0.00380704	+	0.999993i	$0.501212\pi$
$542$	14.2822	0.613475
$543$	−18.3508	−0.787508
$544$	−4.68468	−0.200854
$545$	−6.75183	−0.289217
$546$	−2.75986	−0.118111
$547$	−1.21270	−0.0518511	−0.0259256	−	0.999664i	$-0.508253\pi$
$547$	−1.21270	−0.0518511	−0.0259256	+	0.999664i	$0.508253\pi$
$548$	3.92704	0.167755
$549$	8.76752	0.374189
$550$	0	0
$551$	6.37702	0.271670
$552$	−13.7427	−0.584927
$553$	34.6967	1.47545
$554$	16.6390	0.706925
$555$	4.15664	0.176439
$556$	3.08183	0.130699
$557$	−1.93846	−0.0821352	−0.0410676	−	0.999156i	$-0.513076\pi$
$557$	−1.93846	−0.0821352	−0.0410676	+	0.999156i	$0.513076\pi$
$558$	9.90814	0.419445
$559$	3.39062	0.143408
$560$	0.958094	0.0404869
$561$	0	0
$562$	16.1491	0.681210
$563$	20.9958	0.884866	0.442433	−	0.896802i	$-0.354115\pi$
$563$	20.9958	0.884866	0.442433	+	0.896802i	$0.354115\pi$
$564$	11.7143	0.493263
$565$	5.24461	0.220642
$566$	24.0631	1.01145
$567$	2.04108	0.0857173
$568$	−37.5897	−1.57723
$569$	39.3757	1.65071	0.825357	−	0.564612i	$-0.190974\pi$
$569$	39.3757	1.65071	0.825357	+	0.564612i	$0.190974\pi$
$570$	−2.92057	−0.122329
$571$	−30.6796	−1.28390	−0.641950	−	0.766746i	$-0.721874\pi$
$571$	−30.6796	−1.28390	−0.641950	+	0.766746i	$0.721874\pi$
$572$	0	0
$573$	15.3985	0.643282
$574$	1.53388	0.0640229
$575$	−4.70547	−0.196232
$576$	5.98262	0.249276
$577$	−34.7038	−1.44474	−0.722369	−	0.691508i	$-0.756947\pi$
$577$	−34.7038	−1.44474	−0.722369	+	0.691508i	$0.756947\pi$
$578$	−15.1682	−0.630914
$579$	−7.37942	−0.306678
$580$	−2.30032	−0.0955155
$581$	−12.5353	−0.520050
$582$	1.80914	0.0749911
$583$	0	0
$584$	−42.9862	−1.77878
$585$	−1.44843	−0.0598854
$586$	−12.6313	−0.521793
$587$	8.05710	0.332552	0.166276	−	0.986079i	$-0.446826\pi$
$587$	8.05710	0.332552	0.166276	+	0.986079i	$0.446826\pi$
$588$	−3.19822	−0.131892
$589$	−33.2049	−1.36818
$590$	7.77025	0.319896
$591$	3.14676	0.129440
$592$	−1.95115	−0.0801917
$593$	28.1409	1.15561	0.577805	−	0.816175i	$-0.303909\pi$
$593$	28.1409	1.15561	0.577805	+	0.816175i	$0.303909\pi$
$594$	0	0
$595$	1.76974	0.0725524
$596$	−10.2790	−0.421045
$597$	3.25757	0.133324
$598$	−6.36255	−0.260184
$599$	−28.5988	−1.16851	−0.584257	−	0.811568i	$-0.698614\pi$
$599$	−28.5988	−1.16851	−0.584257	+	0.811568i	$0.698614\pi$
$600$	2.92057	0.119232
$601$	7.27610	0.296799	0.148399	−	0.988928i	$-0.452588\pi$
$601$	7.27610	0.296799	0.148399	+	0.988928i	$0.452588\pi$
$602$	4.46035	0.181790
$603$	−3.15664	−0.128548
$604$	24.3472	0.990672
$605$	0	0
$606$	−4.90268	−0.199158
$607$	5.34785	0.217063	0.108531	−	0.994093i	$-0.465385\pi$
$607$	5.34785	0.217063	0.108531	+	0.994093i	$0.465385\pi$
$608$	−16.9032	−0.685515
$609$	4.16043	0.168589
$610$	−8.18476	−0.331391
$611$	15.0352	0.608257
$612$	0.978497	0.0395534
$613$	4.64099	0.187448	0.0937238	−	0.995598i	$-0.470123\pi$
$613$	4.64099	0.187448	0.0937238	+	0.995598i	$0.470123\pi$
$614$	12.1609	0.490774
$615$	0.805012	0.0324612
$616$	0	0
$617$	24.5843	0.989727	0.494864	−	0.868971i	$-0.335218\pi$
$617$	24.5843	0.989727	0.494864	+	0.868971i	$0.335218\pi$
$618$	12.6966	0.510734
$619$	−6.13789	−0.246703	−0.123351	−	0.992363i	$-0.539364\pi$
$619$	−6.13789	−0.246703	−0.123351	+	0.992363i	$0.539364\pi$
$620$	11.9777	0.481035
$621$	4.70547	0.188824
$622$	1.77669	0.0712387
$623$	7.69884	0.308447
$624$	0.679903	0.0272179
$625$	1.00000	0.0400000
$626$	10.2057	0.407902
$627$	0	0
$628$	26.8519	1.07151
$629$	−3.60407	−0.143704
$630$	−1.90541	−0.0759134
$631$	−17.7085	−0.704966	−0.352483	−	0.935818i	$-0.614662\pi$
$631$	−17.7085	−0.704966	−0.352483	+	0.935818i	$0.614662\pi$
$632$	−49.6473	−1.97486
$633$	19.9242	0.791914
$634$	−15.0040	−0.595883
$635$	−20.6751	−0.820468
$636$	8.14335	0.322905
$637$	−4.10485	−0.162640
$638$	0	0
$639$	12.8707	0.509155
$640$	5.22091	0.206375
$641$	39.8621	1.57446	0.787230	−	0.616659i	$-0.211514\pi$
$641$	39.8621	1.57446	0.787230	+	0.616659i	$0.211514\pi$
$642$	−9.32657	−0.368090
$643$	−17.8662	−0.704576	−0.352288	−	0.935892i	$-0.614596\pi$
$643$	−17.8662	−0.704576	−0.352288	+	0.935892i	$0.614596\pi$
$644$	10.8386	0.427100
$645$	2.34089	0.0921723
$646$	2.53232	0.0996327
$647$	5.04075	0.198172	0.0990862	−	0.995079i	$-0.468408\pi$
$647$	5.04075	0.198172	0.0990862	+	0.995079i	$0.468408\pi$
$648$	−2.92057	−0.114731
$649$	0	0
$650$	1.35216	0.0530360
$651$	−21.6632	−0.849049
$652$	2.03509	0.0797001
$653$	40.7212	1.59354	0.796771	−	0.604281i	$-0.206540\pi$
$653$	40.7212	1.59354	0.796771	+	0.604281i	$0.206540\pi$
$654$	−6.30305	−0.246469
$655$	20.3089	0.793533
$656$	−0.377877	−0.0147536
$657$	14.7184	0.574221
$658$	19.7787	0.771054
$659$	−48.7556	−1.89925	−0.949624	−	0.313390i	$-0.898535\pi$
$659$	−48.7556	−1.89925	−0.949624	+	0.313390i	$0.898535\pi$
$660$	0	0
$661$	−41.0061	−1.59495	−0.797477	−	0.603350i	$-0.793832\pi$
$661$	−41.0061	−1.59495	−0.797477	+	0.603350i	$0.793832\pi$
$662$	1.30301	0.0506430
$663$	1.25588	0.0487745
$664$	17.9366	0.696076
$665$	6.38556	0.247621
$666$	3.88035	0.150361
$667$	9.59140	0.371380
$668$	−27.7474	−1.07358
$669$	−10.4801	−0.405186
$670$	2.94682	0.113846
$671$	0	0
$672$	−11.0278	−0.425408
$673$	30.4936	1.17544	0.587722	−	0.809063i	$-0.300025\pi$
$673$	30.4936	1.17544	0.587722	+	0.809063i	$0.300025\pi$
$674$	2.57972	0.0993671
$675$	−1.00000	−0.0384900
$676$	12.3032	0.473198
$677$	43.4424	1.66963	0.834813	−	0.550534i	$-0.185576\pi$
$677$	43.4424	1.66963	0.834813	+	0.550534i	$0.185576\pi$
$678$	4.89601	0.188030
$679$	−3.95551	−0.151799
$680$	−2.53232	−0.0971099
$681$	17.6731	0.677235
$682$	0	0
$683$	−43.5970	−1.66819	−0.834096	−	0.551619i	$-0.814010\pi$
$683$	−43.5970	−1.66819	−0.834096	+	0.551619i	$0.814010\pi$
$684$	3.53059	0.134996
$685$	3.47982	0.132957
$686$	−18.7378	−0.715413
$687$	−4.12967	−0.157557
$688$	−1.09882	−0.0418923
$689$	10.4518	0.398184
$690$	−4.39271	−0.167227
$691$	−8.30897	−0.316088	−0.158044	−	0.987432i	$-0.550519\pi$
$691$	−8.30897	−0.316088	−0.158044	+	0.987432i	$0.550519\pi$
$692$	−18.2950	−0.695473
$693$	0	0
$694$	2.91900	0.110804
$695$	2.73086	0.103588
$696$	−5.95314	−0.225653
$697$	−0.697996	−0.0264385
$698$	−12.2551	−0.463863
$699$	13.5990	0.514360
$700$	−2.30340	−0.0870603
$701$	−9.08744	−0.343228	−0.171614	−	0.985164i	$-0.554898\pi$
$701$	−9.08744	−0.343228	−0.171614	+	0.985164i	$0.554898\pi$
$702$	−1.35216	−0.0510340
$703$	−13.0041	−0.490460
$704$	0	0
$705$	10.3803	0.390944
$706$	10.0806	0.379389
$707$	10.7193	0.403139
$708$	−9.39324	−0.353020
$709$	−4.85568	−0.182359	−0.0911794	−	0.995834i	$-0.529064\pi$
$709$	−4.85568	−0.182359	−0.0911794	+	0.995834i	$0.529064\pi$
$710$	−12.0152	−0.450921
$711$	16.9992	0.637519
$712$	−11.0162	−0.412850
$713$	−49.9421	−1.87035
$714$	1.65211	0.0618287
$715$	0	0
$716$	−19.1506	−0.715691
$717$	8.00632	0.299002
$718$	−22.3782	−0.835147
$719$	23.9034	0.891448	0.445724	−	0.895171i	$-0.352946\pi$
$719$	23.9034	0.891448	0.445724	+	0.895171i	$0.352946\pi$
$720$	0.469405	0.0174937
$721$	−27.7600	−1.03384
$722$	−8.60003	−0.320060
$723$	−0.501943	−0.0186675
$724$	−20.7092	−0.769653
$725$	−2.03835	−0.0757024
$726$	0	0
$727$	−11.3674	−0.421592	−0.210796	−	0.977530i	$-0.567606\pi$
$727$	−11.3674	−0.421592	−0.210796	+	0.977530i	$0.567606\pi$
$728$	−8.63429	−0.320008
$729$	1.00000	0.0370370
$730$	−13.7401	−0.508545
$731$	−2.02969	−0.0750710
$732$	9.89432	0.365705
$733$	34.1178	1.26017	0.630085	−	0.776526i	$-0.283020\pi$
$733$	34.1178	1.26017	0.630085	+	0.776526i	$0.283020\pi$
$734$	8.28311	0.305735
$735$	−2.83399	−0.104533
$736$	−25.4234	−0.937118
$737$	0	0
$738$	0.751504	0.0276632
$739$	−2.33848	−0.0860225	−0.0430113	−	0.999075i	$-0.513695\pi$
$739$	−2.33848	−0.0860225	−0.0430113	+	0.999075i	$0.513695\pi$
$740$	4.69085	0.172439
$741$	4.53146	0.166467
$742$	13.7494	0.504755
$743$	−14.4885	−0.531533	−0.265767	−	0.964037i	$-0.585625\pi$
$743$	−14.4885	−0.531533	−0.265767	+	0.964037i	$0.585625\pi$
$744$	30.9978	1.13644
$745$	−9.10841	−0.333706
$746$	24.5882	0.900238
$747$	−6.14148	−0.224705
$748$	0	0
$749$	20.3917	0.745096
$750$	0.933531	0.0340877
$751$	33.3203	1.21587	0.607937	−	0.793985i	$-0.291997\pi$
$751$	33.3203	1.21587	0.607937	+	0.793985i	$0.291997\pi$
$752$	−4.87256	−0.177684
$753$	18.5405	0.675654
$754$	−2.75617	−0.100374
$755$	21.5744	0.785174
$756$	2.30340	0.0837738
$757$	40.3778	1.46755	0.733777	−	0.679390i	$-0.237756\pi$
$757$	40.3778	1.46755	0.733777	+	0.679390i	$0.237756\pi$
$758$	4.38396	0.159233
$759$	0	0
$760$	−9.13706	−0.331436
$761$	49.8971	1.80877	0.904384	−	0.426720i	$-0.140331\pi$
$761$	49.8971	1.80877	0.904384	+	0.426720i	$0.140331\pi$
$762$	−19.3009	−0.699197
$763$	13.7810	0.498907
$764$	17.3775	0.628697
$765$	0.867063	0.0313487
$766$	−6.44072	−0.232713
$767$	−12.0561	−0.435319
$768$	16.8391	0.607630
$769$	−4.93932	−0.178116	−0.0890582	−	0.996026i	$-0.528386\pi$
$769$	−4.93932	−0.178116	−0.0890582	+	0.996026i	$0.528386\pi$
$770$	0	0
$771$	−7.38010	−0.265788
$772$	−8.32781	−0.299725
$773$	−33.4710	−1.20387	−0.601934	−	0.798546i	$-0.705603\pi$
$773$	−33.4710	−1.20387	−0.601934	+	0.798546i	$0.705603\pi$
$774$	2.18529	0.0785486
$775$	10.6136	0.381252
$776$	5.65992	0.203179
$777$	−8.48403	−0.304363
$778$	2.24479	0.0804797
$779$	−2.51850	−0.0902345
$780$	−1.63459	−0.0585276
$781$	0	0
$782$	3.80875	0.136201
$783$	2.03835	0.0728447
$784$	1.33029	0.0475104
$785$	23.7940	0.849243
$786$	18.9590	0.676244
$787$	−25.9400	−0.924661	−0.462331	−	0.886708i	$-0.652987\pi$
$787$	−25.9400	−0.924661	−0.462331	+	0.886708i	$0.652987\pi$
$788$	3.55118	0.126506
$789$	−3.05950	−0.108921
$790$	−15.8693	−0.564603
$791$	−10.7047	−0.380614
$792$	0	0
$793$	12.6992	0.450961
$794$	35.1675	1.24805
$795$	7.21596	0.255924
$796$	3.67623	0.130301
$797$	9.86264	0.349353	0.174676	−	0.984626i	$-0.444112\pi$
$797$	9.86264	0.349353	0.174676	+	0.984626i	$0.444112\pi$
$798$	5.96112	0.211021
$799$	−9.00035	−0.318410
$800$	5.40294	0.191023
$801$	3.77194	0.133275
$802$	−11.6848	−0.412606
$803$	0	0
$804$	−3.56233	−0.125634
$805$	9.60425	0.338505
$806$	14.3513	0.505503
$807$	17.6801	0.622368
$808$	−15.3381	−0.539594
$809$	33.0590	1.16229	0.581146	−	0.813799i	$-0.302604\pi$
$809$	33.0590	1.16229	0.581146	+	0.813799i	$0.302604\pi$
$810$	−0.933531	−0.0328009
$811$	−5.21312	−0.183057	−0.0915286	−	0.995802i	$-0.529175\pi$
$811$	−5.21312	−0.183057	−0.0915286	+	0.995802i	$0.529175\pi$
$812$	4.69513	0.164767
$813$	−15.2992	−0.536565
$814$	0	0
$815$	1.80332	0.0631677
$816$	−0.407004	−0.0142480
$817$	−7.32351	−0.256217
$818$	24.7033	0.863731
$819$	2.95637	0.103304
$820$	0.908472	0.0317252
$821$	1.63933	0.0572131	0.0286066	−	0.999591i	$-0.490893\pi$
$821$	1.63933	0.0572131	0.0286066	+	0.999591i	$0.490893\pi$
$822$	3.24852	0.113305
$823$	−17.8894	−0.623586	−0.311793	−	0.950150i	$-0.600930\pi$
$823$	−17.8894	−0.623586	−0.311793	+	0.950150i	$0.600930\pi$
$824$	39.7217	1.38377
$825$	0	0
$826$	−15.8597	−0.551830
$827$	−35.5449	−1.23602	−0.618009	−	0.786171i	$-0.712061\pi$
$827$	−35.5449	−1.23602	−0.618009	+	0.786171i	$0.712061\pi$
$828$	5.31022	0.184543
$829$	−26.9512	−0.936053	−0.468026	−	0.883715i	$-0.655035\pi$
$829$	−26.9512	−0.936053	−0.468026	+	0.883715i	$0.655035\pi$
$830$	5.73326	0.199004
$831$	−17.8238	−0.618299
$832$	8.66544	0.300420
$833$	2.45725	0.0851386
$834$	2.54935	0.0882766
$835$	−24.5874	−0.850882
$836$	0	0
$837$	−10.6136	−0.366860
$838$	28.9124	0.998764
$839$	−11.8373	−0.408667	−0.204334	−	0.978901i	$-0.565503\pi$
$839$	−11.8373	−0.408667	−0.204334	+	0.978901i	$0.565503\pi$
$840$	−5.96112	−0.205678
$841$	−24.8451	−0.856729
$842$	17.0308	0.586921
$843$	−17.2990	−0.595809
$844$	22.4848	0.773959
$845$	10.9020	0.375041
$846$	9.69031	0.333160
$847$	0	0
$848$	−3.38721	−0.116317
$849$	−25.7764	−0.884644
$850$	−0.809430	−0.0277632
$851$	−19.5590	−0.670472
$852$	14.5248	0.497611
$853$	30.3043	1.03760	0.518799	−	0.854896i	$-0.326379\pi$
$853$	30.3043	1.03760	0.518799	+	0.854896i	$0.326379\pi$
$854$	16.7057	0.571659
$855$	3.12852	0.106993
$856$	−29.1783	−0.997295
$857$	29.2318	0.998540	0.499270	−	0.866446i	$-0.333602\pi$
$857$	29.2318	0.998540	0.499270	+	0.866446i	$0.333602\pi$
$858$	0	0
$859$	−36.7151	−1.25270	−0.626351	−	0.779541i	$-0.715452\pi$
$859$	−36.7151	−1.25270	−0.626351	+	0.779541i	$0.715452\pi$
$860$	2.64174	0.0900824
$861$	−1.64309	−0.0559965
$862$	−28.3315	−0.964976
$863$	43.5758	1.48334	0.741669	−	0.670766i	$-0.234034\pi$
$863$	43.5758	1.48334	0.741669	+	0.670766i	$0.234034\pi$
$864$	−5.40294	−0.183812
$865$	−16.2115	−0.551209
$866$	11.8570	0.402917
$867$	16.2482	0.551818
$868$	−24.4474	−0.829798
$869$	0	0
$870$	−1.90286	−0.0645131
$871$	−4.57219	−0.154923
$872$	−19.7192	−0.667777
$873$	−1.93795	−0.0655896
$874$	13.7427	0.464853
$875$	−2.04108	−0.0690011
$876$	16.6100	0.561201
$877$	11.1173	0.375404	0.187702	−	0.982226i	$-0.439896\pi$
$877$	11.1173	0.375404	0.187702	+	0.982226i	$0.439896\pi$
$878$	23.9511	0.808309
$879$	13.5306	0.456377
$880$	0	0
$881$	−39.1155	−1.31783	−0.658917	−	0.752216i	$-0.728985\pi$
$881$	−39.1155	−1.31783	−0.658917	+	0.752216i	$0.728985\pi$
$882$	−2.64562	−0.0890827
$883$	19.5187	0.656857	0.328428	−	0.944529i	$-0.393481\pi$
$883$	19.5187	0.656857	0.328428	+	0.944529i	$0.393481\pi$
$884$	1.41729	0.0476686
$885$	−8.32351	−0.279792
$886$	−24.4723	−0.822164
$887$	5.19108	0.174299	0.0871497	−	0.996195i	$-0.472224\pi$
$887$	5.19108	0.174299	0.0871497	+	0.996195i	$0.472224\pi$
$888$	12.1398	0.407384
$889$	42.1996	1.41533
$890$	−3.52123	−0.118032
$891$	0	0
$892$	−11.8270	−0.395999
$893$	−32.4749	−1.08673
$894$	−8.50299	−0.284382
$895$	−16.9697	−0.567233
$896$	−10.6563	−0.356002
$897$	6.81557	0.227565
$898$	−11.2081	−0.374019
$899$	−21.6343	−0.721543
$900$	−1.12852	−0.0376173
$901$	−6.25669	−0.208440
$902$	0	0
$903$	−4.77794	−0.159000
$904$	15.3173	0.509444
$905$	−18.3508	−0.610001
$906$	20.1404	0.669120
$907$	−42.4379	−1.40913	−0.704563	−	0.709641i	$-0.748857\pi$
$907$	−42.4379	−1.40913	−0.704563	+	0.709641i	$0.748857\pi$
$908$	19.9445	0.661880
$909$	5.25176	0.174190
$910$	−2.75986	−0.0914886
$911$	−19.7499	−0.654344	−0.327172	−	0.944965i	$-0.606096\pi$
$911$	−19.7499	−0.654344	−0.327172	+	0.944965i	$0.606096\pi$
$912$	−1.46854	−0.0486283
$913$	0	0
$914$	−12.8725	−0.425783
$915$	8.76752	0.289845
$916$	−4.66042	−0.153985
$917$	−41.4520	−1.36887
$918$	0.809430	0.0267152
$919$	24.4853	0.807696	0.403848	−	0.914826i	$-0.367672\pi$
$919$	24.4853	0.807696	0.403848	+	0.914826i	$0.367672\pi$
$920$	−13.7427	−0.453082
$921$	−13.0268	−0.429247
$922$	−10.5734	−0.348216
$923$	18.6423	0.613619
$924$	0	0
$925$	4.15664	0.136669
$926$	5.77654	0.189829
$927$	−13.6007	−0.446704
$928$	−11.0131	−0.361522
$929$	−6.05289	−0.198589	−0.0992944	−	0.995058i	$-0.531659\pi$
$929$	−6.05289	−0.198589	−0.0992944	+	0.995058i	$0.531659\pi$
$930$	9.90814	0.324901
$931$	8.86620	0.290578
$932$	15.3467	0.502698
$933$	−1.90319	−0.0623077
$934$	7.91903	0.259119
$935$	0	0
$936$	−4.23026	−0.138270
$937$	−6.83865	−0.223409	−0.111704	−	0.993741i	$-0.535631\pi$
$937$	−6.83865	−0.223409	−0.111704	+	0.993741i	$0.535631\pi$
$938$	−6.01470	−0.196387
$939$	−10.9324	−0.356765
$940$	11.7143	0.382080
$941$	3.95417	0.128902	0.0644512	−	0.997921i	$-0.479470\pi$
$941$	3.95417	0.128902	0.0644512	+	0.997921i	$0.479470\pi$
$942$	22.2124	0.723719
$943$	−3.78796	−0.123353
$944$	3.90710	0.127165
$945$	2.04108	0.0663963
$946$	0	0
$947$	−40.1742	−1.30549	−0.652743	−	0.757579i	$-0.726382\pi$
$947$	−40.1742	−1.30549	−0.652743	+	0.757579i	$0.726382\pi$
$948$	19.1839	0.623064
$949$	21.3187	0.692034
$950$	−2.92057	−0.0947558
$951$	16.0723	0.521179
$952$	5.16866	0.167517
$953$	41.2470	1.33612	0.668061	−	0.744106i	$-0.267124\pi$
$953$	41.2470	1.33612	0.668061	+	0.744106i	$0.267124\pi$
$954$	6.73632	0.218097
$955$	15.3985	0.498284
$956$	9.03529	0.292222
$957$	0	0
$958$	−8.62166	−0.278553
$959$	−7.10258	−0.229354
$960$	5.98262	0.193088
$961$	81.6488	2.63383
$962$	5.62044	0.181210
$963$	9.99063	0.321944
$964$	−0.566452	−0.0182442
$965$	−7.37942	−0.237552
$966$	8.96587	0.288472
$967$	−9.16826	−0.294831	−0.147416	−	0.989075i	$-0.547096\pi$
$967$	−9.16826	−0.294831	−0.147416	+	0.989075i	$0.547096\pi$
$968$	0	0
$969$	−2.71262	−0.0871420
$970$	1.80914	0.0580879
$971$	−3.71264	−0.119144	−0.0595722	−	0.998224i	$-0.518974\pi$
$971$	−3.71264	−0.119144	−0.0595722	+	0.998224i	$0.518974\pi$
$972$	1.12852	0.0361973
$973$	−5.57391	−0.178691
$974$	18.8300	0.603353
$975$	−1.44843	−0.0463870
$976$	−4.11552	−0.131735
$977$	12.3932	0.396495	0.198247	−	0.980152i	$-0.436475\pi$
$977$	12.3932	0.396495	0.198247	+	0.980152i	$0.436475\pi$
$978$	1.68346	0.0538311
$979$	0	0
$980$	−3.19822	−0.102163
$981$	6.75183	0.215569
$982$	4.98126	0.158958
$983$	23.2949	0.742992	0.371496	−	0.928435i	$-0.378845\pi$
$983$	23.2949	0.742992	0.371496	+	0.928435i	$0.378845\pi$
$984$	2.35109	0.0749501
$985$	3.14676	0.100264
$986$	1.64990	0.0525436
$987$	−21.1870	−0.674389
$988$	5.11384	0.162693
$989$	−11.0150	−0.350256
$990$	0	0
$991$	−37.7826	−1.20020	−0.600101	−	0.799924i	$-0.704873\pi$
$991$	−37.7826	−1.20020	−0.600101	+	0.799924i	$0.704873\pi$
$992$	57.3447	1.82070
$993$	−1.39579	−0.0442940
$994$	24.5239	0.777851
$995$	3.25757	0.103272
$996$	−6.93078	−0.219610
$997$	−7.87590	−0.249432	−0.124716	−	0.992192i	$-0.539802\pi$
$997$	−7.87590	−0.249432	−0.124716	+	0.992192i	$0.539802\pi$
$998$	−36.6706	−1.16079
$999$	−4.15664	−0.131510

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1815.2.a.r.1.3		4
3.2	odd	2		5445.2.a.br.1.2		4
5.4	even	2		9075.2.a.dg.1.2		4
11.7	odd	10		165.2.m.b.16.1	✓	8
11.8	odd	10		165.2.m.b.31.1	yes	8
11.10	odd	2		1815.2.a.v.1.2		4
33.8	even	10		495.2.n.b.361.2		8
33.29	even	10		495.2.n.b.181.2		8
33.32	even	2		5445.2.a.bk.1.3		4
55.7	even	20		825.2.bx.g.49.3		16
55.8	even	20		825.2.bx.g.724.3		16
55.18	even	20		825.2.bx.g.49.2		16
55.19	odd	10		825.2.n.i.526.2		8
55.29	odd	10		825.2.n.i.676.2		8
55.52	even	20		825.2.bx.g.724.2		16
55.54	odd	2		9075.2.a.cq.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.2.m.b.16.1	✓	8	11.7	odd	10
165.2.m.b.31.1	yes	8	11.8	odd	10
495.2.n.b.181.2		8	33.29	even	10
495.2.n.b.361.2		8	33.8	even	10
825.2.n.i.526.2		8	55.19	odd	10
825.2.n.i.676.2		8	55.29	odd	10
825.2.bx.g.49.2		16	55.18	even	20
825.2.bx.g.49.3		16	55.7	even	20
825.2.bx.g.724.2		16	55.52	even	20
825.2.bx.g.724.3		16	55.8	even	20
1815.2.a.r.1.3		4	1.1	even	1	trivial
1815.2.a.v.1.2		4	11.10	odd	2
5445.2.a.bk.1.3		4	33.32	even	2
5445.2.a.br.1.2		4	3.2	odd	2
9075.2.a.cq.1.3		4	55.54	odd	2
9075.2.a.dg.1.2		4	5.4	even	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:	\( N \)	\(=\)	\( 1815 = 3 \cdot 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1815.a (trivial)

\(f(q)\)	\(=\)	\(q+0.933531 q^{2} -1.00000 q^{3} -1.12852 q^{4} -1.00000 q^{5} -0.933531 q^{6} +2.04108 q^{7} -2.92057 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.933531 q^{2} -1.00000 q^{3} -1.12852 q^{4} -1.00000 q^{5} -0.933531 q^{6} +2.04108 q^{7} -2.92057 q^{8} +1.00000 q^{9} -0.933531 q^{10} +1.12852 q^{12} +1.44843 q^{13} +1.90541 q^{14} +1.00000 q^{15} -0.469405 q^{16} -0.867063 q^{17} +0.933531 q^{18} -3.12852 q^{19} +1.12852 q^{20} -2.04108 q^{21} -4.70547 q^{23} +2.92057 q^{24} +1.00000 q^{25} +1.35216 q^{26} -1.00000 q^{27} -2.30340 q^{28} -2.03835 q^{29} +0.933531 q^{30} +10.6136 q^{31} +5.40294 q^{32} -0.809430 q^{34} -2.04108 q^{35} -1.12852 q^{36} +4.15664 q^{37} -2.92057 q^{38} -1.44843 q^{39} +2.92057 q^{40} +0.805012 q^{41} -1.90541 q^{42} +2.34089 q^{43} -1.00000 q^{45} -4.39271 q^{46} +10.3803 q^{47} +0.469405 q^{48} -2.83399 q^{49} +0.933531 q^{50} +0.867063 q^{51} -1.63459 q^{52} +7.21596 q^{53} -0.933531 q^{54} -5.96112 q^{56} +3.12852 q^{57} -1.90286 q^{58} -8.32351 q^{59} -1.12852 q^{60} +8.76752 q^{61} +9.90814 q^{62} +2.04108 q^{63} +5.98262 q^{64} -1.44843 q^{65} -3.15664 q^{67} +0.978497 q^{68} +4.70547 q^{69} -1.90541 q^{70} +12.8707 q^{71} -2.92057 q^{72} +14.7184 q^{73} +3.88035 q^{74} -1.00000 q^{75} +3.53059 q^{76} -1.35216 q^{78} +16.9992 q^{79} +0.469405 q^{80} +1.00000 q^{81} +0.751504 q^{82} -6.14148 q^{83} +2.30340 q^{84} +0.867063 q^{85} +2.18529 q^{86} +2.03835 q^{87} +3.77194 q^{89} -0.933531 q^{90} +2.95637 q^{91} +5.31022 q^{92} -10.6136 q^{93} +9.69031 q^{94} +3.12852 q^{95} -5.40294 q^{96} -1.93795 q^{97} -2.64562 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{2} - 4 q^{3} + 9 q^{4} - 4 q^{5} + q^{6} + 8 q^{7} - 3 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q - q^2 - 4 * q^3 + 9 * q^4 - 4 * q^5 + q^6 + 8 * q^7 - 3 * q^8 + 4 * q^9	\( 4 q - q^{2} - 4 q^{3} + 9 q^{4} - 4 q^{5} + q^{6} + 8 q^{7} - 3 q^{8} + 4 q^{9} + q^{10} - 9 q^{12} + 15 q^{13} + 7 q^{14} + 4 q^{15} + 7 q^{16} + 6 q^{17} - q^{18} + q^{19} - 9 q^{20} - 8 q^{21} - q^{23} + 3 q^{24} + 4 q^{25} - 18 q^{26} - 4 q^{27} + 31 q^{28} - 17 q^{29} - q^{30} + 15 q^{31} + 8 q^{32} - 35 q^{34} - 8 q^{35} + 9 q^{36} - q^{37} - 3 q^{38} - 15 q^{39} + 3 q^{40} + 12 q^{41} - 7 q^{42} + 14 q^{43} - 4 q^{45} + 9 q^{46} + 14 q^{47} - 7 q^{48} + 20 q^{49} - q^{50} - 6 q^{51} + 39 q^{52} + 2 q^{53} + q^{54} - 12 q^{56} - q^{57} - 11 q^{58} - 11 q^{59} + 9 q^{60} - q^{61} + 30 q^{62} + 8 q^{63} - 3 q^{64} - 15 q^{65} + 5 q^{67} + 19 q^{68} + q^{69} - 7 q^{70} - 3 q^{71} - 3 q^{72} + 45 q^{73} - 29 q^{74} - 4 q^{75} + 23 q^{76} + 18 q^{78} - 7 q^{80} + 4 q^{81} + 11 q^{82} - 15 q^{83} - 31 q^{84} - 6 q^{85} - 10 q^{86} + 17 q^{87} + 2 q^{89} + q^{90} + 16 q^{91} + 34 q^{92} - 15 q^{93} + 29 q^{94} - q^{95} - 8 q^{96} - 26 q^{97} + q^{98}+O(q^{100}) \) 4 * q - q^2 - 4 * q^3 + 9 * q^4 - 4 * q^5 + q^6 + 8 * q^7 - 3 * q^8 + 4 * q^9 + q^10 - 9 * q^12 + 15 * q^13 + 7 * q^14 + 4 * q^15 + 7 * q^16 + 6 * q^17 - q^18 + q^19 - 9 * q^20 - 8 * q^21 - q^23 + 3 * q^24 + 4 * q^25 - 18 * q^26 - 4 * q^27 + 31 * q^28 - 17 * q^29 - q^30 + 15 * q^31 + 8 * q^32 - 35 * q^34 - 8 * q^35 + 9 * q^36 - q^37 - 3 * q^38 - 15 * q^39 + 3 * q^40 + 12 * q^41 - 7 * q^42 + 14 * q^43 - 4 * q^45 + 9 * q^46 + 14 * q^47 - 7 * q^48 + 20 * q^49 - q^50 - 6 * q^51 + 39 * q^52 + 2 * q^53 + q^54 - 12 * q^56 - q^57 - 11 * q^58 - 11 * q^59 + 9 * q^60 - q^61 + 30 * q^62 + 8 * q^63 - 3 * q^64 - 15 * q^65 + 5 * q^67 + 19 * q^68 + q^69 - 7 * q^70 - 3 * q^71 - 3 * q^72 + 45 * q^73 - 29 * q^74 - 4 * q^75 + 23 * q^76 + 18 * q^78 - 7 * q^80 + 4 * q^81 + 11 * q^82 - 15 * q^83 - 31 * q^84 - 6 * q^85 - 10 * q^86 + 17 * q^87 + 2 * q^89 + q^90 + 16 * q^91 + 34 * q^92 - 15 * q^93 + 29 * q^94 - q^95 - 8 * q^96 - 26 * q^97 + q^98

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