LMFDB - Embedded newform 4015.2.a.c.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4015,2,Mod(1,4015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4015, 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("4015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4015 = 5 \cdot 11 \cdot 73 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4015.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:	$32.0599364115$
Analytic rank:	$1$
Dimension:	$23$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	4015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.20516 q^{2} +1.14152 q^{3} -0.547593 q^{4} +1.00000 q^{5} +1.37572 q^{6} +3.42329 q^{7} -3.07025 q^{8} -1.69692 q^{9} +O(q^{10})$	\(q+1.20516 q^{2} +1.14152 q^{3} -0.547593 q^{4} +1.00000 q^{5} +1.37572 q^{6} +3.42329 q^{7} -3.07025 q^{8} -1.69692 q^{9} +1.20516 q^{10} -1.00000 q^{11} -0.625091 q^{12} -1.67914 q^{13} +4.12561 q^{14} +1.14152 q^{15} -2.60496 q^{16} -2.55061 q^{17} -2.04506 q^{18} -5.48818 q^{19} -0.547593 q^{20} +3.90777 q^{21} -1.20516 q^{22} -8.58955 q^{23} -3.50477 q^{24} +1.00000 q^{25} -2.02363 q^{26} -5.36165 q^{27} -1.87457 q^{28} -4.02623 q^{29} +1.37572 q^{30} -1.73666 q^{31} +3.00112 q^{32} -1.14152 q^{33} -3.07389 q^{34} +3.42329 q^{35} +0.929222 q^{36} +4.28382 q^{37} -6.61412 q^{38} -1.91678 q^{39} -3.07025 q^{40} -0.338389 q^{41} +4.70948 q^{42} +1.55048 q^{43} +0.547593 q^{44} -1.69692 q^{45} -10.3518 q^{46} +3.34465 q^{47} -2.97362 q^{48} +4.71892 q^{49} +1.20516 q^{50} -2.91158 q^{51} +0.919486 q^{52} -7.45633 q^{53} -6.46164 q^{54} -1.00000 q^{55} -10.5104 q^{56} -6.26489 q^{57} -4.85225 q^{58} -6.24507 q^{59} -0.625091 q^{60} -8.83237 q^{61} -2.09295 q^{62} -5.80906 q^{63} +8.82674 q^{64} -1.67914 q^{65} -1.37572 q^{66} +3.52049 q^{67} +1.39670 q^{68} -9.80518 q^{69} +4.12561 q^{70} +6.15267 q^{71} +5.20998 q^{72} +1.00000 q^{73} +5.16268 q^{74} +1.14152 q^{75} +3.00529 q^{76} -3.42329 q^{77} -2.31003 q^{78} +8.71058 q^{79} -2.60496 q^{80} -1.02969 q^{81} -0.407812 q^{82} -5.48860 q^{83} -2.13987 q^{84} -2.55061 q^{85} +1.86858 q^{86} -4.59604 q^{87} +3.07025 q^{88} -7.72345 q^{89} -2.04506 q^{90} -5.74819 q^{91} +4.70358 q^{92} -1.98244 q^{93} +4.03083 q^{94} -5.48818 q^{95} +3.42585 q^{96} +0.0223558 q^{97} +5.68705 q^{98} +1.69692 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 23 q - 3 q^{2} - 5 q^{3} + 15 q^{4} + 23 q^{5} - 5 q^{6} - 6 q^{8} + 8 q^{9}+O(q^{10}) $ 23 * q - 3 * q^2 - 5 * q^3 + 15 * q^4 + 23 * q^5 - 5 * q^6 - 6 * q^8 + 8 * q^9	\( 23 q - 3 q^{2} - 5 q^{3} + 15 q^{4} + 23 q^{5} - 5 q^{6} - 6 q^{8} + 8 q^{9} - 3 q^{10} - 23 q^{11} - 18 q^{12} - 5 q^{13} - 17 q^{14} - 5 q^{15} - q^{16} - 36 q^{17} + q^{18} + 6 q^{19} + 15 q^{20} - 18 q^{21} + 3 q^{22} - 14 q^{23} - 7 q^{24} + 23 q^{25} - 21 q^{26} - 29 q^{27} + 28 q^{28} - 36 q^{29} - 5 q^{30} - 16 q^{31} - 5 q^{32} + 5 q^{33} - 28 q^{34} - 14 q^{36} - 24 q^{37} + q^{38} - 10 q^{39} - 6 q^{40} - 36 q^{41} - 5 q^{42} + 17 q^{43} - 15 q^{44} + 8 q^{45} - 25 q^{46} - 21 q^{47} - 17 q^{48} - 27 q^{49} - 3 q^{50} + 19 q^{51} - 21 q^{52} - 28 q^{53} - 15 q^{54} - 23 q^{55} - 46 q^{56} - 23 q^{57} - 16 q^{58} - 61 q^{59} - 18 q^{60} - 17 q^{61} - 22 q^{62} - 9 q^{63} - 18 q^{64} - 5 q^{65} + 5 q^{66} + 2 q^{67} - 39 q^{68} - 36 q^{69} - 17 q^{70} - 50 q^{71} + 15 q^{72} + 23 q^{73} + 17 q^{74} - 5 q^{75} - 21 q^{76} + 49 q^{78} - 18 q^{79} - q^{80} - 57 q^{81} + 14 q^{82} - 20 q^{83} - 38 q^{84} - 36 q^{85} - 45 q^{86} + 37 q^{87} + 6 q^{88} - 93 q^{89} + q^{90} - 42 q^{91} - 39 q^{92} - 18 q^{93} - 6 q^{94} + 6 q^{95} - 9 q^{96} - 31 q^{97} - 31 q^{98} - 8 q^{99}+O(q^{100}) \) 23 * q - 3 * q^2 - 5 * q^3 + 15 * q^4 + 23 * q^5 - 5 * q^6 - 6 * q^8 + 8 * q^9 - 3 * q^10 - 23 * q^11 - 18 * q^12 - 5 * q^13 - 17 * q^14 - 5 * q^15 - q^16 - 36 * q^17 + q^18 + 6 * q^19 + 15 * q^20 - 18 * q^21 + 3 * q^22 - 14 * q^23 - 7 * q^24 + 23 * q^25 - 21 * q^26 - 29 * q^27 + 28 * q^28 - 36 * q^29 - 5 * q^30 - 16 * q^31 - 5 * q^32 + 5 * q^33 - 28 * q^34 - 14 * q^36 - 24 * q^37 + q^38 - 10 * q^39 - 6 * q^40 - 36 * q^41 - 5 * q^42 + 17 * q^43 - 15 * q^44 + 8 * q^45 - 25 * q^46 - 21 * q^47 - 17 * q^48 - 27 * q^49 - 3 * q^50 + 19 * q^51 - 21 * q^52 - 28 * q^53 - 15 * q^54 - 23 * q^55 - 46 * q^56 - 23 * q^57 - 16 * q^58 - 61 * q^59 - 18 * q^60 - 17 * q^61 - 22 * q^62 - 9 * q^63 - 18 * q^64 - 5 * q^65 + 5 * q^66 + 2 * q^67 - 39 * q^68 - 36 * q^69 - 17 * q^70 - 50 * q^71 + 15 * q^72 + 23 * q^73 + 17 * q^74 - 5 * q^75 - 21 * q^76 + 49 * q^78 - 18 * q^79 - q^80 - 57 * q^81 + 14 * q^82 - 20 * q^83 - 38 * q^84 - 36 * q^85 - 45 * q^86 + 37 * q^87 + 6 * q^88 - 93 * q^89 + q^90 - 42 * q^91 - 39 * q^92 - 18 * q^93 - 6 * q^94 + 6 * q^95 - 9 * q^96 - 31 * q^97 - 31 * q^98 - 8 * 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 $

$2$	1.20516	0.852176	0.426088	−	0.904682i	$-0.359891\pi$
$2$	1.20516	0.852176	0.426088	+	0.904682i	$0.359891\pi$
$3$	1.14152	0.659059	0.329530	−	0.944145i	$-0.393110\pi$
$3$	1.14152	0.659059	0.329530	+	0.944145i	$0.393110\pi$
$4$	−0.547593	−0.273796
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	1.37572	0.561635
$7$	3.42329	1.29388	0.646941	−	0.762540i	$-0.276048\pi$
$7$	3.42329	1.29388	0.646941	+	0.762540i	$0.276048\pi$
$8$	−3.07025	−1.08550
$9$	−1.69692	−0.565641
$10$	1.20516	0.381105
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−0.625091	−0.180448
$13$	−1.67914	−0.465710	−0.232855	−	0.972511i	$-0.574807\pi$
$13$	−1.67914	−0.465710	−0.232855	+	0.972511i	$0.574807\pi$
$14$	4.12561	1.10262
$15$	1.14152	0.294740
$16$	−2.60496	−0.651239
$17$	−2.55061	−0.618614	−0.309307	−	0.950962i	$-0.600097\pi$
$17$	−2.55061	−0.618614	−0.309307	+	0.950962i	$0.600097\pi$
$18$	−2.04506	−0.482025
$19$	−5.48818	−1.25907	−0.629537	−	0.776970i	$-0.716755\pi$
$19$	−5.48818	−1.25907	−0.629537	+	0.776970i	$0.716755\pi$
$20$	−0.547593	−0.122446
$21$	3.90777	0.852745
$22$	−1.20516	−0.256941
$23$	−8.58955	−1.79105	−0.895523	−	0.445016i	$-0.853198\pi$
$23$	−8.58955	−1.79105	−0.895523	+	0.445016i	$0.853198\pi$
$24$	−3.50477	−0.715408
$25$	1.00000	0.200000
$26$	−2.02363	−0.396867
$27$	−5.36165	−1.03185
$28$	−1.87457	−0.354260
$29$	−4.02623	−0.747653	−0.373826	−	0.927499i	$-0.621954\pi$
$29$	−4.02623	−0.747653	−0.373826	+	0.927499i	$0.621954\pi$
$30$	1.37572	0.251171
$31$	−1.73666	−0.311913	−0.155957	−	0.987764i	$-0.549846\pi$
$31$	−1.73666	−0.311913	−0.155957	+	0.987764i	$0.549846\pi$
$32$	3.00112	0.530528
$33$	−1.14152	−0.198714
$34$	−3.07389	−0.527168
$35$	3.42329	0.578642
$36$	0.929222	0.154870
$37$	4.28382	0.704256	0.352128	−	0.935952i	$-0.385458\pi$
$37$	4.28382	0.704256	0.352128	+	0.935952i	$0.385458\pi$
$38$	−6.61412	−1.07295
$39$	−1.91678	−0.306931
$40$	−3.07025	−0.485450
$41$	−0.338389	−0.0528474	−0.0264237	−	0.999651i	$-0.508412\pi$
$41$	−0.338389	−0.0528474	−0.0264237	+	0.999651i	$0.508412\pi$
$42$	4.70948	0.726689
$43$	1.55048	0.236446	0.118223	−	0.992987i	$-0.462280\pi$
$43$	1.55048	0.236446	0.118223	+	0.992987i	$0.462280\pi$
$44$	0.547593	0.0825527
$45$	−1.69692	−0.252962
$46$	−10.3518	−1.52629
$47$	3.34465	0.487867	0.243933	−	0.969792i	$-0.421562\pi$
$47$	3.34465	0.487867	0.243933	+	0.969792i	$0.421562\pi$
$48$	−2.97362	−0.429205
$49$	4.71892	0.674132
$50$	1.20516	0.170435
$51$	−2.91158	−0.407703
$52$	0.919486	0.127510
$53$	−7.45633	−1.02421	−0.512103	−	0.858924i	$-0.671133\pi$
$53$	−7.45633	−1.02421	−0.512103	+	0.858924i	$0.671133\pi$
$54$	−6.46164	−0.879318
$55$	−1.00000	−0.134840
$56$	−10.5104	−1.40451
$57$	−6.26489	−0.829805
$58$	−4.85225	−0.637132
$59$	−6.24507	−0.813039	−0.406519	−	0.913642i	$-0.633258\pi$
$59$	−6.24507	−0.813039	−0.406519	+	0.913642i	$0.633258\pi$
$60$	−0.625091	−0.0806989
$61$	−8.83237	−1.13087	−0.565435	−	0.824793i	$-0.691292\pi$
$61$	−8.83237	−1.13087	−0.565435	+	0.824793i	$0.691292\pi$
$62$	−2.09295	−0.265805
$63$	−5.80906	−0.731872
$64$	8.82674	1.10334
$65$	−1.67914	−0.208272
$66$	−1.37572	−0.169339
$67$	3.52049	0.430096	0.215048	−	0.976603i	$-0.431009\pi$
$67$	3.52049	0.430096	0.215048	+	0.976603i	$0.431009\pi$
$68$	1.39670	0.169374
$69$	−9.80518	−1.18041
$70$	4.12561	0.493105
$71$	6.15267	0.730188	0.365094	−	0.930971i	$-0.381037\pi$
$71$	6.15267	0.730188	0.365094	+	0.930971i	$0.381037\pi$
$72$	5.20998	0.614002
$73$	1.00000	0.117041
$73$	1.00000	0.117041
$74$	5.16268	0.600150
$75$	1.14152	0.131812
$76$	3.00529	0.344730
$77$	−3.42329	−0.390120
$78$	−2.31003	−0.261559
$79$	8.71058	0.980017	0.490009	−	0.871718i	$-0.336994\pi$
$79$	8.71058	0.980017	0.490009	+	0.871718i	$0.336994\pi$
$80$	−2.60496	−0.291243
$81$	−1.02969	−0.114410
$82$	−0.407812	−0.0450353
$83$	−5.48860	−0.602452	−0.301226	−	0.953553i	$-0.597396\pi$
$83$	−5.48860	−0.602452	−0.301226	+	0.953553i	$0.597396\pi$
$84$	−2.13987	−0.233479
$85$	−2.55061	−0.276652
$86$	1.86858	0.201494
$87$	−4.59604	−0.492748
$88$	3.07025	0.327290
$89$	−7.72345	−0.818684	−0.409342	−	0.912381i	$-0.634242\pi$
$89$	−7.72345	−0.818684	−0.409342	+	0.912381i	$0.634242\pi$
$90$	−2.04506	−0.215568
$91$	−5.74819	−0.602574
$92$	4.70358	0.490382
$93$	−1.98244	−0.205569
$94$	4.03083	0.415748
$95$	−5.48818	−0.563075
$96$	3.42585	0.349650
$97$	0.0223558	0.00226989	0.00113494	−	0.999999i	$-0.499639\pi$
$97$	0.0223558	0.00226989	0.00113494	+	0.999999i	$0.499639\pi$
$98$	5.68705	0.574479
$99$	1.69692	0.170547
$100$	−0.547593	−0.0547593
$101$	−1.78198	−0.177313	−0.0886566	−	0.996062i	$-0.528257\pi$
$101$	−1.78198	−0.177313	−0.0886566	+	0.996062i	$0.528257\pi$
$102$	−3.50892	−0.347435
$103$	5.86026	0.577428	0.288714	−	0.957415i	$-0.406772\pi$
$103$	5.86026	0.577428	0.288714	+	0.957415i	$0.406772\pi$
$104$	5.15539	0.505528
$105$	3.90777	0.381359
$106$	−8.98606	−0.872804
$107$	15.9008	1.53719	0.768593	−	0.639738i	$-0.220957\pi$
$107$	15.9008	1.53719	0.768593	+	0.639738i	$0.220957\pi$
$108$	2.93600	0.282517
$109$	19.4336	1.86140	0.930700	−	0.365784i	$-0.119199\pi$
$109$	19.4336	1.86140	0.930700	+	0.365784i	$0.119199\pi$
$110$	−1.20516	−0.114907
$111$	4.89009	0.464147
$112$	−8.91752	−0.842627
$113$	19.1443	1.80094	0.900472	−	0.434913i	$-0.143221\pi$
$113$	19.1443	1.80094	0.900472	+	0.434913i	$0.143221\pi$
$114$	−7.55019	−0.707140
$115$	−8.58955	−0.800980
$116$	2.20474	0.204705
$117$	2.84937	0.263425
$118$	−7.52630	−0.692852
$119$	−8.73148	−0.800413
$120$	−3.50477	−0.319940
$121$	1.00000	0.0909091
$122$	−10.6444	−0.963700
$123$	−0.386279	−0.0348296
$124$	0.950982	0.0854007
$125$	1.00000	0.0894427
$126$	−7.00083	−0.623684
$127$	−4.87168	−0.432292	−0.216146	−	0.976361i	$-0.569349\pi$
$127$	−4.87168	−0.432292	−0.216146	+	0.976361i	$0.569349\pi$
$128$	4.63538	0.409713
$129$	1.76991	0.155832
$130$	−2.02363	−0.177484
$131$	4.32084	0.377514	0.188757	−	0.982024i	$-0.439554\pi$
$131$	4.32084	0.377514	0.188757	+	0.982024i	$0.439554\pi$
$132$	0.625091	0.0544072
$133$	−18.7876	−1.62909
$134$	4.24275	0.366518
$135$	−5.36165	−0.461457
$136$	7.83102	0.671504
$137$	−13.7103	−1.17135	−0.585677	−	0.810545i	$-0.699171\pi$
$137$	−13.7103	−1.17135	−0.585677	+	0.810545i	$0.699171\pi$
$138$	−11.8168	−1.00591
$139$	−11.9495	−1.01355	−0.506773	−	0.862080i	$-0.669162\pi$
$139$	−11.9495	−1.01355	−0.506773	+	0.862080i	$0.669162\pi$
$140$	−1.87457	−0.158430
$141$	3.81799	0.321533
$142$	7.41495	0.622249
$143$	1.67914	0.140417
$144$	4.42041	0.368367
$145$	−4.02623	−0.334360
$146$	1.20516	0.0997396
$147$	5.38676	0.444293
$148$	−2.34579	−0.192823
$149$	−13.0031	−1.06525	−0.532626	−	0.846351i	$-0.678795\pi$
$149$	−13.0031	−1.06525	−0.532626	+	0.846351i	$0.678795\pi$
$150$	1.37572	0.112327
$151$	1.52260	0.123907	0.0619537	−	0.998079i	$-0.480267\pi$
$151$	1.52260	0.123907	0.0619537	+	0.998079i	$0.480267\pi$
$152$	16.8501	1.36672
$153$	4.32819	0.349913
$154$	−4.12561	−0.332451
$155$	−1.73666	−0.139492
$156$	1.04962	0.0840365
$157$	5.12343	0.408894	0.204447	−	0.978878i	$-0.434460\pi$
$157$	5.12343	0.408894	0.204447	+	0.978878i	$0.434460\pi$
$158$	10.4976	0.835147
$159$	−8.51159	−0.675013
$160$	3.00112	0.237259
$161$	−29.4045	−2.31740
$162$	−1.24094	−0.0974975
$163$	−12.4805	−0.977548	−0.488774	−	0.872410i	$-0.662556\pi$
$163$	−12.4805	−0.977548	−0.488774	+	0.872410i	$0.662556\pi$
$164$	0.185299	0.0144694
$165$	−1.14152	−0.0888676
$166$	−6.61464	−0.513395
$167$	−5.34709	−0.413770	−0.206885	−	0.978365i	$-0.566333\pi$
$167$	−5.34709	−0.413770	−0.206885	+	0.978365i	$0.566333\pi$
$168$	−11.9978	−0.925654
$169$	−10.1805	−0.783114
$170$	−3.07389	−0.235757
$171$	9.31301	0.712184
$172$	−0.849034	−0.0647382
$173$	−4.98729	−0.379176	−0.189588	−	0.981864i	$-0.560715\pi$
$173$	−4.98729	−0.379176	−0.189588	+	0.981864i	$0.560715\pi$
$174$	−5.53896	−0.419908
$175$	3.42329	0.258776
$176$	2.60496	0.196356
$177$	−7.12890	−0.535841
$178$	−9.30798	−0.697663
$179$	15.6605	1.17052	0.585259	−	0.810846i	$-0.300993\pi$
$179$	15.6605	1.17052	0.585259	+	0.810846i	$0.300993\pi$
$180$	0.929222	0.0692602
$181$	13.7540	1.02233	0.511165	−	0.859483i	$-0.329214\pi$
$181$	13.7540	1.02233	0.511165	+	0.859483i	$0.329214\pi$
$182$	−6.92748	−0.513499
$183$	−10.0824	−0.745310
$184$	26.3721	1.94418
$185$	4.28382	0.314953
$186$	−2.38915	−0.175181
$187$	2.55061	0.186519
$188$	−1.83150	−0.133576
$189$	−18.3545	−1.33509
$190$	−6.61412	−0.479839
$191$	−1.47219	−0.106524	−0.0532620	−	0.998581i	$-0.516962\pi$
$191$	−1.47219	−0.106524	−0.0532620	+	0.998581i	$0.516962\pi$
$192$	10.0759	0.727168
$193$	−17.3317	−1.24756	−0.623782	−	0.781599i	$-0.714405\pi$
$193$	−17.3317	−1.24756	−0.623782	+	0.781599i	$0.714405\pi$
$194$	0.0269423	0.00193434
$195$	−1.91678	−0.137264
$196$	−2.58405	−0.184575
$197$	−7.20705	−0.513481	−0.256741	−	0.966480i	$-0.582649\pi$
$197$	−7.20705	−0.513481	−0.256741	+	0.966480i	$0.582649\pi$
$198$	2.04506	0.145336
$199$	−8.73332	−0.619089	−0.309544	−	0.950885i	$-0.600177\pi$
$199$	−8.73332	−0.619089	−0.309544	+	0.950885i	$0.600177\pi$
$200$	−3.07025	−0.217100
$201$	4.01873	0.283459
$202$	−2.14756	−0.151102
$203$	−13.7830	−0.967375
$204$	1.59436	0.111628
$205$	−0.338389	−0.0236341
$206$	7.06254	0.492070
$207$	14.5758	1.01309
$208$	4.37409	0.303289
$209$	5.48818	0.379625
$210$	4.70948	0.324985
$211$	22.3437	1.53820	0.769100	−	0.639128i	$-0.220705\pi$
$211$	22.3437	1.53820	0.769100	+	0.639128i	$0.220705\pi$
$212$	4.08304	0.280424
$213$	7.02343	0.481237
$214$	19.1629	1.30995
$215$	1.55048	0.105742
$216$	16.4616	1.12007
$217$	−5.94509	−0.403579
$218$	23.4205	1.58624
$219$	1.14152	0.0771371
$220$	0.547593	0.0369187
$221$	4.28283	0.288095
$222$	5.89333	0.395534
$223$	−28.0064	−1.87545	−0.937724	−	0.347382i	$-0.887071\pi$
$223$	−28.0064	−1.87545	−0.937724	+	0.347382i	$0.887071\pi$
$224$	10.2737	0.686441
$225$	−1.69692	−0.113128
$226$	23.0719	1.53472
$227$	−28.5103	−1.89230	−0.946148	−	0.323734i	$-0.895062\pi$
$227$	−28.5103	−1.89230	−0.946148	+	0.323734i	$0.895062\pi$
$228$	3.43061	0.227198
$229$	13.7381	0.907838	0.453919	−	0.891043i	$-0.350025\pi$
$229$	13.7381	0.907838	0.453919	+	0.891043i	$0.350025\pi$
$230$	−10.3518	−0.682576
$231$	−3.90777	−0.257112
$232$	12.3616	0.811576
$233$	0.0797170	0.00522244	0.00261122	−	0.999997i	$-0.499169\pi$
$233$	0.0797170	0.00522244	0.00261122	+	0.999997i	$0.499169\pi$
$234$	3.43394	0.224484
$235$	3.34465	0.218181
$236$	3.41976	0.222607
$237$	9.94334	0.645890
$238$	−10.5228	−0.682093
$239$	4.48207	0.289921	0.144961	−	0.989437i	$-0.453694\pi$
$239$	4.48207	0.289921	0.144961	+	0.989437i	$0.453694\pi$
$240$	−2.97362	−0.191946
$241$	−0.636897	−0.0410261	−0.0205131	−	0.999790i	$-0.506530\pi$
$241$	−0.636897	−0.0410261	−0.0205131	+	0.999790i	$0.506530\pi$
$242$	1.20516	0.0774705
$243$	14.9095	0.956447
$244$	4.83655	0.309628
$245$	4.71892	0.301481
$246$	−0.465527	−0.0296809
$247$	9.21543	0.586364
$248$	5.33198	0.338581
$249$	−6.26537	−0.397052
$250$	1.20516	0.0762209
$251$	−19.1882	−1.21115	−0.605575	−	0.795788i	$-0.707057\pi$
$251$	−19.1882	−1.21115	−0.605575	+	0.795788i	$0.707057\pi$
$252$	3.18100	0.200384
$253$	8.58955	0.540020
$254$	−5.87115	−0.368389
$255$	−2.91158	−0.182330
$256$	−12.0671	−0.754195
$257$	−28.5288	−1.77957	−0.889787	−	0.456375i	$-0.849148\pi$
$257$	−28.5288	−1.77957	−0.889787	+	0.456375i	$0.849148\pi$
$258$	2.13303	0.132796
$259$	14.6648	0.911224
$260$	0.919486	0.0570241
$261$	6.83220	0.422903
$262$	5.20730	0.321708
$263$	−7.06291	−0.435518	−0.217759	−	0.976003i	$-0.569875\pi$
$263$	−7.06291	−0.435518	−0.217759	+	0.976003i	$0.569875\pi$
$264$	3.50477	0.215704
$265$	−7.45633	−0.458039
$266$	−22.6421	−1.38827
$267$	−8.81651	−0.539561
$268$	−1.92780	−0.117759
$269$	0.791360	0.0482501	0.0241250	−	0.999709i	$-0.492320\pi$
$269$	0.791360	0.0482501	0.0241250	+	0.999709i	$0.492320\pi$
$270$	−6.46164	−0.393243
$271$	6.31926	0.383868	0.191934	−	0.981408i	$-0.438524\pi$
$271$	6.31926	0.383868	0.191934	+	0.981408i	$0.438524\pi$
$272$	6.64423	0.402865
$273$	−6.56170	−0.397132
$274$	−16.5231	−0.998199
$275$	−1.00000	−0.0603023
$276$	5.36925	0.323191
$277$	5.96433	0.358362	0.179181	−	0.983816i	$-0.442655\pi$
$277$	5.96433	0.358362	0.179181	+	0.983816i	$0.442655\pi$
$278$	−14.4011	−0.863719
$279$	2.94697	0.176431
$280$	−10.5104	−0.628115
$281$	−8.27251	−0.493496	−0.246748	−	0.969080i	$-0.579362\pi$
$281$	−8.27251	−0.493496	−0.246748	+	0.969080i	$0.579362\pi$
$282$	4.60129	0.274003
$283$	0.661757	0.0393374	0.0196687	−	0.999807i	$-0.493739\pi$
$283$	0.661757	0.0393374	0.0196687	+	0.999807i	$0.493739\pi$
$284$	−3.36916	−0.199923
$285$	−6.26489	−0.371100
$286$	2.02363	0.119660
$287$	−1.15840	−0.0683783
$288$	−5.09267	−0.300088
$289$	−10.4944	−0.617317
$290$	−4.85225	−0.284934
$291$	0.0255197	0.00149599
$292$	−0.547593	−0.0320455
$293$	2.51605	0.146989	0.0734946	−	0.997296i	$-0.476585\pi$
$293$	2.51605	0.146989	0.0734946	+	0.997296i	$0.476585\pi$
$294$	6.49190	0.378616
$295$	−6.24507	−0.363602
$296$	−13.1524	−0.764469
$297$	5.36165	0.311115
$298$	−15.6707	−0.907782
$299$	14.4231	0.834108
$300$	−0.625091	−0.0360896
$301$	5.30775	0.305934
$302$	1.83497	0.105591
$303$	−2.03417	−0.116860
$304$	14.2965	0.819958
$305$	−8.83237	−0.505740
$306$	5.21615	0.298187
$307$	−9.44820	−0.539237	−0.269619	−	0.962967i	$-0.586898\pi$
$307$	−9.44820	−0.539237	−0.269619	+	0.962967i	$0.586898\pi$
$308$	1.87457	0.106814
$309$	6.68963	0.380560
$310$	−2.09295	−0.118872
$311$	−18.8597	−1.06943	−0.534717	−	0.845031i	$-0.679582\pi$
$311$	−18.8597	−1.06943	−0.534717	+	0.845031i	$0.679582\pi$
$312$	5.88500	0.333173
$313$	31.9766	1.80742	0.903711	−	0.428143i	$-0.140832\pi$
$313$	31.9766	1.80742	0.903711	+	0.428143i	$0.140832\pi$
$314$	6.17454	0.348449
$315$	−5.80906	−0.327303
$316$	−4.76985	−0.268325
$317$	22.1496	1.24404	0.622022	−	0.783000i	$-0.286312\pi$
$317$	22.1496	1.24404	0.622022	+	0.783000i	$0.286312\pi$
$318$	−10.2578	−0.575229
$319$	4.02623	0.225426
$320$	8.82674	0.493430
$321$	18.1511	1.01310
$322$	−35.4371	−1.97483
$323$	13.9982	0.778881
$324$	0.563851	0.0313251
$325$	−1.67914	−0.0931420
$326$	−15.0410	−0.833043
$327$	22.1839	1.22677
$328$	1.03894	0.0573658
$329$	11.4497	0.631242
$330$	−1.37572	−0.0757308
$331$	22.7212	1.24887	0.624435	−	0.781077i	$-0.285329\pi$
$331$	22.7212	1.24887	0.624435	+	0.781077i	$0.285329\pi$
$332$	3.00552	0.164949
$333$	−7.26931	−0.398356
$334$	−6.44409	−0.352605
$335$	3.52049	0.192345
$336$	−10.1796	−0.555341
$337$	5.85539	0.318964	0.159482	−	0.987201i	$-0.449018\pi$
$337$	5.85539	0.318964	0.159482	+	0.987201i	$0.449018\pi$
$338$	−12.2691	−0.667351
$339$	21.8537	1.18693
$340$	1.39670	0.0757465
$341$	1.73666	0.0940454
$342$	11.2237	0.606906
$343$	−7.80880	−0.421635
$344$	−4.76038	−0.256662
$345$	−9.80518	−0.527893
$346$	−6.01047	−0.323125
$347$	11.1179	0.596839	0.298419	−	0.954435i	$-0.403541\pi$
$347$	11.1179	0.596839	0.298419	+	0.954435i	$0.403541\pi$
$348$	2.51676	0.134913
$349$	15.3533	0.821845	0.410922	−	0.911670i	$-0.365207\pi$
$349$	15.3533	0.821845	0.410922	+	0.911670i	$0.365207\pi$
$350$	4.12561	0.220523
$351$	9.00297	0.480543
$352$	−3.00112	−0.159960
$353$	−11.2183	−0.597092	−0.298546	−	0.954395i	$-0.596502\pi$
$353$	−11.2183	−0.597092	−0.298546	+	0.954395i	$0.596502\pi$
$354$	−8.59145	−0.456631
$355$	6.15267	0.326550
$356$	4.22931	0.224153
$357$	−9.96720	−0.527520
$358$	18.8733	0.997487
$359$	11.1829	0.590212	0.295106	−	0.955465i	$-0.404645\pi$
$359$	11.1829	0.590212	0.295106	+	0.955465i	$0.404645\pi$
$360$	5.20998	0.274590
$361$	11.1201	0.585268
$362$	16.5758	0.871205
$363$	1.14152	0.0599145
$364$	3.14767	0.164983
$365$	1.00000	0.0523424
$366$	−12.1509	−0.635135
$367$	−21.7402	−1.13483	−0.567414	−	0.823433i	$-0.692056\pi$
$367$	−21.7402	−1.13483	−0.567414	+	0.823433i	$0.692056\pi$
$368$	22.3754	1.16640
$369$	0.574219	0.0298926
$370$	5.16268	0.268395
$371$	−25.5252	−1.32520
$372$	1.08557	0.0562842
$373$	−32.7674	−1.69663	−0.848315	−	0.529492i	$-0.822382\pi$
$373$	−32.7674	−1.69663	−0.848315	+	0.529492i	$0.822382\pi$
$374$	3.07389	0.158947
$375$	1.14152	0.0589481
$376$	−10.2689	−0.529579
$377$	6.76062	0.348189
$378$	−22.1201	−1.13773
$379$	−11.1865	−0.574609	−0.287305	−	0.957839i	$-0.592759\pi$
$379$	−11.1865	−0.574609	−0.287305	+	0.957839i	$0.592759\pi$
$380$	3.00529	0.154168
$381$	−5.56115	−0.284906
$382$	−1.77422	−0.0907771
$383$	−17.0952	−0.873524	−0.436762	−	0.899577i	$-0.643875\pi$
$383$	−17.0952	−0.873524	−0.436762	+	0.899577i	$0.643875\pi$
$384$	5.29140	0.270025
$385$	−3.42329	−0.174467
$386$	−20.8875	−1.06314
$387$	−2.63105	−0.133744
$388$	−0.0122419	−0.000621487 0
$389$	−2.85510	−0.144759	−0.0723796	−	0.997377i	$-0.523059\pi$
$389$	−2.85510	−0.144759	−0.0723796	+	0.997377i	$0.523059\pi$
$390$	−2.31003	−0.116973
$391$	21.9086	1.10797
$392$	−14.4883	−0.731769
$393$	4.93235	0.248804
$394$	−8.68564	−0.437576
$395$	8.71058	0.438277
$396$	−0.929222	−0.0466952
$397$	1.85471	0.0930852	0.0465426	−	0.998916i	$-0.485180\pi$
$397$	1.85471	0.0930852	0.0465426	+	0.998916i	$0.485180\pi$
$398$	−10.5250	−0.527572
$399$	−21.4465	−1.07367
$400$	−2.60496	−0.130248
$401$	−2.22817	−0.111270	−0.0556348	−	0.998451i	$-0.517718\pi$
$401$	−2.22817	−0.111270	−0.0556348	+	0.998451i	$0.517718\pi$
$402$	4.84320	0.241557
$403$	2.91610	0.145261
$404$	0.975798	0.0485478
$405$	−1.02969	−0.0511657
$406$	−16.6107	−0.824373
$407$	−4.28382	−0.212341
$408$	8.93930	0.442561
$409$	26.4229	1.30653	0.653264	−	0.757131i	$-0.273399\pi$
$409$	26.4229	1.30653	0.653264	+	0.757131i	$0.273399\pi$
$410$	−0.407812	−0.0201404
$411$	−15.6507	−0.771992
$412$	−3.20903	−0.158098
$413$	−21.3787	−1.05198
$414$	17.5661	0.863329
$415$	−5.48860	−0.269425
$416$	−5.03931	−0.247072
$417$	−13.6407	−0.667987
$418$	6.61412	0.323507
$419$	−2.32439	−0.113554	−0.0567769	−	0.998387i	$-0.518082\pi$
$419$	−2.32439	−0.113554	−0.0567769	+	0.998387i	$0.518082\pi$
$420$	−2.13987	−0.104415
$421$	−15.1731	−0.739490	−0.369745	−	0.929133i	$-0.620555\pi$
$421$	−15.1731	−0.739490	−0.369745	+	0.929133i	$0.620555\pi$
$422$	26.9276	1.31082
$423$	−5.67560	−0.275957
$424$	22.8928	1.11177
$425$	−2.55061	−0.123723
$426$	8.46434	0.410099
$427$	−30.2358	−1.46321
$428$	−8.70715	−0.420876
$429$	1.91678	0.0925431
$430$	1.86858	0.0901108
$431$	−37.0186	−1.78312	−0.891561	−	0.452901i	$-0.850389\pi$
$431$	−37.0186	−1.78312	−0.891561	+	0.452901i	$0.850389\pi$
$432$	13.9669	0.671981
$433$	6.58178	0.316300	0.158150	−	0.987415i	$-0.449447\pi$
$433$	6.58178	0.316300	0.158150	+	0.987415i	$0.449447\pi$
$434$	−7.16477	−0.343920
$435$	−4.59604	−0.220363
$436$	−10.6417	−0.509645
$437$	47.1410	2.25506
$438$	1.37572	0.0657343
$439$	10.6649	0.509010	0.254505	−	0.967071i	$-0.418087\pi$
$439$	10.6649	0.509010	0.254505	+	0.967071i	$0.418087\pi$
$440$	3.07025	0.146369
$441$	−8.00764	−0.381316
$442$	5.16149	0.245507
$443$	25.2884	1.20149	0.600745	−	0.799441i	$-0.294871\pi$
$443$	25.2884	1.20149	0.600745	+	0.799441i	$0.294871\pi$
$444$	−2.67778	−0.127082
$445$	−7.72345	−0.366127
$446$	−33.7521	−1.59821
$447$	−14.8433	−0.702065
$448$	30.2165	1.42760
$449$	16.8970	0.797419	0.398709	−	0.917077i	$-0.369458\pi$
$449$	16.8970	0.797419	0.398709	+	0.917077i	$0.369458\pi$
$450$	−2.04506	−0.0964050
$451$	0.338389	0.0159341
$452$	−10.4833	−0.493092
$453$	1.73808	0.0816623
$454$	−34.3594	−1.61257
$455$	−5.74819	−0.269479
$456$	19.2348	0.900752
$457$	23.1308	1.08201	0.541006	−	0.841019i	$-0.318044\pi$
$457$	23.1308	1.08201	0.541006	+	0.841019i	$0.318044\pi$
$458$	16.5566	0.773638
$459$	13.6755	0.638317
$460$	4.70358	0.219305
$461$	−2.26603	−0.105540	−0.0527698	−	0.998607i	$-0.516805\pi$
$461$	−2.26603	−0.105540	−0.0527698	+	0.998607i	$0.516805\pi$
$462$	−4.70948	−0.219105
$463$	14.4701	0.672482	0.336241	−	0.941776i	$-0.390844\pi$
$463$	14.4701	0.672482	0.336241	+	0.941776i	$0.390844\pi$
$464$	10.4882	0.486901
$465$	−1.98244	−0.0919334
$466$	0.0960717	0.00445043
$467$	11.5285	0.533476	0.266738	−	0.963769i	$-0.414054\pi$
$467$	11.5285	0.533476	0.266738	+	0.963769i	$0.414054\pi$
$468$	−1.56030	−0.0721247
$469$	12.0517	0.556494
$470$	4.03083	0.185928
$471$	5.84852	0.269485
$472$	19.1739	0.882552
$473$	−1.55048	−0.0712913
$474$	11.9833	0.550411
$475$	−5.48818	−0.251815
$476$	4.78130	0.219150
$477$	12.6528	0.579333
$478$	5.40161	0.247064
$479$	0.502455	0.0229578	0.0114789	−	0.999934i	$-0.496346\pi$
$479$	0.502455	0.0229578	0.0114789	+	0.999934i	$0.496346\pi$
$480$	3.42585	0.156368
$481$	−7.19314	−0.327979
$482$	−0.767561	−0.0349615
$483$	−33.5660	−1.52731
$484$	−0.547593	−0.0248906
$485$	0.0223558	0.00101512
$486$	17.9684	0.815061
$487$	−17.6674	−0.800587	−0.400294	−	0.916387i	$-0.631092\pi$
$487$	−17.6674	−0.800587	−0.400294	+	0.916387i	$0.631092\pi$
$488$	27.1176	1.22756
$489$	−14.2468	−0.644263
$490$	5.68705	0.256915
$491$	−9.95490	−0.449258	−0.224629	−	0.974444i	$-0.572117\pi$
$491$	−9.95490	−0.449258	−0.224629	+	0.974444i	$0.572117\pi$
$492$	0.211524	0.00953622
$493$	10.2693	0.462508
$494$	11.1061	0.499685
$495$	1.69692	0.0762710
$496$	4.52392	0.203130
$497$	21.0624	0.944778
$498$	−7.55077	−0.338358
$499$	−21.1367	−0.946207	−0.473103	−	0.881007i	$-0.656866\pi$
$499$	−21.1367	−0.946207	−0.473103	+	0.881007i	$0.656866\pi$
$500$	−0.547593	−0.0244891
$501$	−6.10384	−0.272699
$502$	−23.1249	−1.03211
$503$	10.7941	0.481287	0.240643	−	0.970614i	$-0.422642\pi$
$503$	10.7941	0.481287	0.240643	+	0.970614i	$0.422642\pi$
$504$	17.8353	0.794446
$505$	−1.78198	−0.0792969
$506$	10.3518	0.460192
$507$	−11.6213	−0.516119
$508$	2.66770	0.118360
$509$	−8.99984	−0.398911	−0.199456	−	0.979907i	$-0.563917\pi$
$509$	−8.99984	−0.398911	−0.199456	+	0.979907i	$0.563917\pi$
$510$	−3.50892	−0.155378
$511$	3.42329	0.151437
$512$	−23.8135	−1.05242
$513$	29.4257	1.29918
$514$	−34.3817	−1.51651
$515$	5.86026	0.258234
$516$	−0.969193	−0.0426663
$517$	−3.34465	−0.147097
$518$	17.6734	0.776523
$519$	−5.69311	−0.249900
$520$	5.15539	0.226079
$521$	18.7579	0.821798	0.410899	−	0.911681i	$-0.365215\pi$
$521$	18.7579	0.821798	0.410899	+	0.911681i	$0.365215\pi$
$522$	8.23389	0.360387
$523$	−30.0250	−1.31290	−0.656450	−	0.754370i	$-0.727943\pi$
$523$	−30.0250	−1.31290	−0.656450	+	0.754370i	$0.727943\pi$
$524$	−2.36606	−0.103362
$525$	3.90777	0.170549
$526$	−8.51192	−0.371138
$527$	4.42954	0.192954
$528$	2.97362	0.129410
$529$	50.7804	2.20784
$530$	−8.98606	−0.390330
$531$	10.5974	0.459888
$532$	10.2880	0.446040
$533$	0.568202	0.0246116
$534$	−10.6253	−0.459801
$535$	15.9008	0.687450
$536$	−10.8088	−0.466869
$537$	17.8768	0.771441
$538$	0.953714	0.0411175
$539$	−4.71892	−0.203258
$540$	2.93600	0.126345
$541$	−24.8775	−1.06957	−0.534784	−	0.844989i	$-0.679607\pi$
$541$	−24.8775	−1.06957	−0.534784	+	0.844989i	$0.679607\pi$
$542$	7.61571	0.327123
$543$	15.7006	0.673776
$544$	−7.65469	−0.328192
$545$	19.4336	0.832443
$546$	−7.90789	−0.338426
$547$	−22.8743	−0.978033	−0.489017	−	0.872275i	$-0.662644\pi$
$547$	−22.8743	−0.978033	−0.489017	+	0.872275i	$0.662644\pi$
$548$	7.50769	0.320712
$549$	14.9878	0.639666
$550$	−1.20516	−0.0513881
$551$	22.0967	0.941350
$552$	30.1044	1.28133
$553$	29.8189	1.26803
$554$	7.18797	0.305387
$555$	4.89009	0.207573
$556$	6.54348	0.277505
$557$	−15.4409	−0.654251	−0.327126	−	0.944981i	$-0.606080\pi$
$557$	−15.4409	−0.654251	−0.327126	+	0.944981i	$0.606080\pi$
$558$	3.55157	0.150350
$559$	−2.60348	−0.110115
$560$	−8.91752	−0.376834
$561$	2.91158	0.122927
$562$	−9.96968	−0.420546
$563$	5.79058	0.244044	0.122022	−	0.992527i	$-0.461062\pi$
$563$	5.79058	0.244044	0.122022	+	0.992527i	$0.461062\pi$
$564$	−2.09071	−0.0880346
$565$	19.1443	0.805407
$566$	0.797522	0.0335224
$567$	−3.52493	−0.148033
$568$	−18.8903	−0.792618
$569$	19.2954	0.808904	0.404452	−	0.914559i	$-0.367462\pi$
$569$	19.2954	0.808904	0.404452	+	0.914559i	$0.367462\pi$
$570$	−7.55019	−0.316242
$571$	45.1135	1.88794	0.943971	−	0.330028i	$-0.107058\pi$
$571$	45.1135	1.88794	0.943971	+	0.330028i	$0.107058\pi$
$572$	−0.919486	−0.0384456
$573$	−1.68054	−0.0702056
$574$	−1.39606	−0.0582704
$575$	−8.58955	−0.358209
$576$	−14.9783	−0.624095
$577$	−6.53169	−0.271918	−0.135959	−	0.990714i	$-0.543412\pi$
$577$	−6.53169	−0.271918	−0.135959	+	0.990714i	$0.543412\pi$
$578$	−12.6474	−0.526063
$579$	−19.7846	−0.822219
$580$	2.20474	0.0915467
$581$	−18.7891	−0.779502
$582$	0.0307552	0.00127485
$583$	7.45633	0.308810
$584$	−3.07025	−0.127048
$585$	2.84937	0.117807
$586$	3.03224	0.125261
$587$	10.3243	0.426128	0.213064	−	0.977038i	$-0.431656\pi$
$587$	10.3243	0.426128	0.213064	+	0.977038i	$0.431656\pi$
$588$	−2.94975	−0.121646
$589$	9.53109	0.392722
$590$	−7.52630	−0.309853
$591$	−8.22703	−0.338415
$592$	−11.1592	−0.458639
$593$	−2.21078	−0.0907857	−0.0453929	−	0.998969i	$-0.514454\pi$
$593$	−2.21078	−0.0907857	−0.0453929	+	0.998969i	$0.514454\pi$
$594$	6.46164	0.265124
$595$	−8.73148	−0.357956
$596$	7.12038	0.291662
$597$	−9.96930	−0.408016
$598$	17.3821	0.710806
$599$	15.0406	0.614542	0.307271	−	0.951622i	$-0.400584\pi$
$599$	15.0406	0.614542	0.307271	+	0.951622i	$0.400584\pi$
$600$	−3.50477	−0.143082
$601$	1.79600	0.0732603	0.0366301	−	0.999329i	$-0.488338\pi$
$601$	1.79600	0.0732603	0.0366301	+	0.999329i	$0.488338\pi$
$602$	6.39669	0.260709
$603$	−5.97400	−0.243280
$604$	−0.833764	−0.0339254
$605$	1.00000	0.0406558
$606$	−2.45150	−0.0995853
$607$	−25.7144	−1.04372	−0.521858	−	0.853032i	$-0.674761\pi$
$607$	−25.7144	−1.04372	−0.521858	+	0.853032i	$0.674761\pi$
$608$	−16.4707	−0.667975
$609$	−15.7336	−0.637557
$610$	−10.6444	−0.430980
$611$	−5.61613	−0.227204
$612$	−2.37008	−0.0958050
$613$	47.6633	1.92510	0.962551	−	0.271102i	$-0.0873882\pi$
$613$	47.6633	1.92510	0.962551	+	0.271102i	$0.0873882\pi$
$614$	−11.3866	−0.459525
$615$	−0.386279	−0.0155763
$616$	10.5104	0.423475
$617$	10.3555	0.416896	0.208448	−	0.978034i	$-0.433159\pi$
$617$	10.3555	0.416896	0.208448	+	0.978034i	$0.433159\pi$
$618$	8.06206	0.324304
$619$	−34.3481	−1.38057	−0.690283	−	0.723540i	$-0.742514\pi$
$619$	−34.3481	−1.38057	−0.690283	+	0.723540i	$0.742514\pi$
$620$	0.950982	0.0381924
$621$	46.0542	1.84809
$622$	−22.7289	−0.911346
$623$	−26.4396	−1.05928
$624$	4.99313	0.199885
$625$	1.00000	0.0400000
$626$	38.5368	1.54024
$627$	6.26489	0.250196
$628$	−2.80555	−0.111954
$629$	−10.9264	−0.435662
$630$	−7.00083	−0.278920
$631$	−11.4089	−0.454183	−0.227092	−	0.973873i	$-0.572922\pi$
$631$	−11.4089	−0.454183	−0.227092	+	0.973873i	$0.572922\pi$
$632$	−26.7437	−1.06381
$633$	25.5058	1.01377
$634$	26.6937	1.06014
$635$	−4.87168	−0.193327
$636$	4.66088	0.184816
$637$	−7.92374	−0.313950
$638$	4.85225	0.192102
$639$	−10.4406	−0.413024
$640$	4.63538	0.183229
$641$	20.2576	0.800128	0.400064	−	0.916487i	$-0.368988\pi$
$641$	20.2576	0.800128	0.400064	+	0.916487i	$0.368988\pi$
$642$	21.8750	0.863336
$643$	−1.27864	−0.0504248	−0.0252124	−	0.999682i	$-0.508026\pi$
$643$	−1.27864	−0.0504248	−0.0252124	+	0.999682i	$0.508026\pi$
$644$	16.1017	0.634496
$645$	1.76991	0.0696903
$646$	16.8701	0.663743
$647$	−40.9208	−1.60876	−0.804381	−	0.594114i	$-0.797503\pi$
$647$	−40.9208	−1.60876	−0.804381	+	0.594114i	$0.797503\pi$
$648$	3.16141	0.124192
$649$	6.24507	0.245140
$650$	−2.02363	−0.0793734
$651$	−6.78646	−0.265983
$652$	6.83424	0.267649
$653$	−41.9998	−1.64358	−0.821789	−	0.569791i	$-0.807024\pi$
$653$	−41.9998	−1.64358	−0.821789	+	0.569791i	$0.807024\pi$
$654$	26.7351	1.04543
$655$	4.32084	0.168829
$656$	0.881487	0.0344163
$657$	−1.69692	−0.0662032
$658$	13.7987	0.537929
$659$	18.9097	0.736619	0.368309	−	0.929703i	$-0.379937\pi$
$659$	18.9097	0.736619	0.368309	+	0.929703i	$0.379937\pi$
$660$	0.625091	0.0243316
$661$	23.8726	0.928536	0.464268	−	0.885695i	$-0.346318\pi$
$661$	23.8726	0.928536	0.464268	+	0.885695i	$0.346318\pi$
$662$	27.3826	1.06426
$663$	4.88896	0.189872
$664$	16.8514	0.653961
$665$	−18.7876	−0.728553
$666$	−8.76067	−0.339469
$667$	34.5835	1.33908
$668$	2.92803	0.113289
$669$	−31.9700	−1.23603
$670$	4.24275	0.163912
$671$	8.83237	0.340970
$672$	11.7277	0.452406
$673$	8.53607	0.329041	0.164521	−	0.986374i	$-0.447392\pi$
$673$	8.53607	0.329041	0.164521	+	0.986374i	$0.447392\pi$
$674$	7.05668	0.271813
$675$	−5.36165	−0.206370
$676$	5.57476	0.214414
$677$	33.5013	1.28756	0.643780	−	0.765211i	$-0.277365\pi$
$677$	33.5013	1.28756	0.643780	+	0.765211i	$0.277365\pi$
$678$	26.3372	1.01147
$679$	0.0765303	0.00293696
$680$	7.83102	0.300306
$681$	−32.5452	−1.24714
$682$	2.09295	0.0801432
$683$	26.3043	1.00650	0.503252	−	0.864140i	$-0.332137\pi$
$683$	26.3043	1.00650	0.503252	+	0.864140i	$0.332137\pi$
$684$	−5.09974	−0.194993
$685$	−13.7103	−0.523845
$686$	−9.41084	−0.359307
$687$	15.6824	0.598319
$688$	−4.03894	−0.153983
$689$	12.5202	0.476983
$690$	−11.8168	−0.449858
$691$	33.0270	1.25641	0.628204	−	0.778049i	$-0.283790\pi$
$691$	33.0270	1.25641	0.628204	+	0.778049i	$0.283790\pi$
$692$	2.73100	0.103817
$693$	5.80906	0.220668
$694$	13.3988	0.508611
$695$	−11.9495	−0.453271
$696$	14.1110	0.534877
$697$	0.863097	0.0326921
$698$	18.5032	0.700356
$699$	0.0909990	0.00344190
$700$	−1.87457	−0.0708521
$701$	−44.5139	−1.68127	−0.840634	−	0.541604i	$-0.817817\pi$
$701$	−44.5139	−1.68127	−0.840634	+	0.541604i	$0.817817\pi$
$702$	10.8500	0.409507
$703$	−23.5104	−0.886711
$704$	−8.82674	−0.332670
$705$	3.81799	0.143794
$706$	−13.5199	−0.508827
$707$	−6.10022	−0.229423
$708$	3.90374	0.146711
$709$	−9.95015	−0.373686	−0.186843	−	0.982390i	$-0.559826\pi$
$709$	−9.95015	−0.373686	−0.186843	+	0.982390i	$0.559826\pi$
$710$	7.41495	0.278278
$711$	−14.7812	−0.554337
$712$	23.7129	0.888680
$713$	14.9171	0.558651
$714$	−12.0121	−0.449540
$715$	1.67914	0.0627963
$716$	−8.57556	−0.320484
$717$	5.11639	0.191075
$718$	13.4772	0.502964
$719$	17.6755	0.659183	0.329592	−	0.944124i	$-0.393089\pi$
$719$	17.6755	0.659183	0.329592	+	0.944124i	$0.393089\pi$
$720$	4.42041	0.164739
$721$	20.0614	0.747124
$722$	13.4015	0.498752
$723$	−0.727033	−0.0270387
$724$	−7.53161	−0.279910
$725$	−4.02623	−0.149531
$726$	1.37572	0.0510577
$727$	40.9793	1.51984	0.759918	−	0.650019i	$-0.225239\pi$
$727$	40.9793	1.51984	0.759918	+	0.650019i	$0.225239\pi$
$728$	17.6484	0.654093
$729$	20.1087	0.744766
$730$	1.20516	0.0446049
$731$	−3.95468	−0.146269
$732$	5.52103	0.204063
$733$	−19.6994	−0.727616	−0.363808	−	0.931474i	$-0.618524\pi$
$733$	−19.6994	−0.727616	−0.363808	+	0.931474i	$0.618524\pi$
$734$	−26.2004	−0.967073
$735$	5.38676	0.198694
$736$	−25.7783	−0.950200
$737$	−3.52049	−0.129679
$738$	0.692025	0.0254738
$739$	−29.2463	−1.07584	−0.537922	−	0.842995i	$-0.680791\pi$
$739$	−29.2463	−1.07584	−0.537922	+	0.842995i	$0.680791\pi$
$740$	−2.34579	−0.0862330
$741$	10.5196	0.386449
$742$	−30.7619	−1.12931
$743$	−48.1379	−1.76601	−0.883004	−	0.469365i	$-0.844483\pi$
$743$	−48.1379	−1.76601	−0.883004	+	0.469365i	$0.844483\pi$
$744$	6.08659	0.223145
$745$	−13.0031	−0.476395
$746$	−39.4899	−1.44583
$747$	9.31373	0.340772
$748$	−1.39670	−0.0510683
$749$	54.4330	1.98894
$750$	1.37572	0.0502341
$751$	26.1150	0.952949	0.476474	−	0.879188i	$-0.341915\pi$
$751$	26.1150	0.952949	0.476474	+	0.879188i	$0.341915\pi$
$752$	−8.71265	−0.317718
$753$	−21.9038	−0.798220
$754$	8.14761	0.296719
$755$	1.52260	0.0554130
$756$	10.0508	0.365544
$757$	−8.39550	−0.305140	−0.152570	−	0.988293i	$-0.548755\pi$
$757$	−8.39550	−0.305140	−0.152570	+	0.988293i	$0.548755\pi$
$758$	−13.4814	−0.489668
$759$	9.80518	0.355906
$760$	16.8501	0.611217
$761$	−9.62743	−0.348994	−0.174497	−	0.984658i	$-0.555830\pi$
$761$	−9.62743	−0.348994	−0.174497	+	0.984658i	$0.555830\pi$
$762$	−6.70206	−0.242790
$763$	66.5268	2.40843
$764$	0.806161	0.0291659
$765$	4.32819	0.156486
$766$	−20.6024	−0.744396
$767$	10.4864	0.378640
$768$	−13.7749	−0.497059
$769$	−21.9276	−0.790729	−0.395365	−	0.918524i	$-0.629382\pi$
$769$	−21.9276	−0.790729	−0.395365	+	0.918524i	$0.629382\pi$
$770$	−4.12561	−0.148677
$771$	−32.5663	−1.17285
$772$	9.49072	0.341578
$773$	30.1811	1.08554	0.542769	−	0.839882i	$-0.317376\pi$
$773$	30.1811	1.08554	0.542769	+	0.839882i	$0.317376\pi$
$774$	−3.17083	−0.113973
$775$	−1.73666	−0.0623826
$776$	−0.0686379	−0.00246396
$777$	16.7402	0.600551
$778$	−3.44085	−0.123360
$779$	1.85714	0.0665388
$780$	1.04962	0.0375823
$781$	−6.15267	−0.220160
$782$	26.4033	0.944181
$783$	21.5873	0.771466
$784$	−12.2926	−0.439021
$785$	5.12343	0.182863
$786$	5.94426	0.212025
$787$	43.0183	1.53344	0.766718	−	0.641984i	$-0.221888\pi$
$787$	43.0183	1.53344	0.766718	+	0.641984i	$0.221888\pi$
$788$	3.94653	0.140589
$789$	−8.06248	−0.287032
$790$	10.4976	0.373489
$791$	65.5365	2.33021
$792$	−5.20998	−0.185129
$793$	14.8308	0.526657
$794$	2.23522	0.0793249
$795$	−8.51159	−0.301875
$796$	4.78230	0.169504
$797$	−41.0353	−1.45354	−0.726772	−	0.686879i	$-0.758980\pi$
$797$	−41.0353	−1.45354	−0.726772	+	0.686879i	$0.758980\pi$
$798$	−25.8465	−0.914956
$799$	−8.53089	−0.301801
$800$	3.00112	0.106106
$801$	13.1061	0.463081
$802$	−2.68530	−0.0948212
$803$	−1.00000	−0.0352892
$804$	−2.20063	−0.0776101
$805$	−29.4045	−1.03637
$806$	3.51436	0.123788
$807$	0.903357	0.0317997
$808$	5.47112	0.192473
$809$	13.5644	0.476900	0.238450	−	0.971155i	$-0.423361\pi$
$809$	13.5644	0.476900	0.238450	+	0.971155i	$0.423361\pi$
$810$	−1.24094	−0.0436022
$811$	41.0959	1.44307	0.721535	−	0.692378i	$-0.243437\pi$
$811$	41.0959	1.44307	0.721535	+	0.692378i	$0.243437\pi$
$812$	7.54746	0.264864
$813$	7.21359	0.252992
$814$	−5.16268	−0.180952
$815$	−12.4805	−0.437173
$816$	7.58455	0.265512
$817$	−8.50933	−0.297704
$818$	31.8438	1.11339
$819$	9.75423	0.340840
$820$	0.185299	0.00647093
$821$	−17.9637	−0.626937	−0.313468	−	0.949599i	$-0.601491\pi$
$821$	−17.9637	−0.626937	−0.313468	+	0.949599i	$0.601491\pi$
$822$	−18.8616	−0.657872
$823$	−49.1625	−1.71370	−0.856848	−	0.515569i	$-0.827580\pi$
$823$	−49.1625	−1.71370	−0.856848	+	0.515569i	$0.827580\pi$
$824$	−17.9925	−0.626797
$825$	−1.14152	−0.0397428
$826$	−25.7647	−0.896469
$827$	28.8135	1.00194	0.500972	−	0.865463i	$-0.332976\pi$
$827$	28.8135	1.00194	0.500972	+	0.865463i	$0.332976\pi$
$828$	−7.98160	−0.277380
$829$	−5.61809	−0.195124	−0.0975622	−	0.995229i	$-0.531105\pi$
$829$	−5.61809	−0.195124	−0.0975622	+	0.995229i	$0.531105\pi$
$830$	−6.61464	−0.229597
$831$	6.80843	0.236182
$832$	−14.8213	−0.513838
$833$	−12.0361	−0.417027
$834$	−16.4392	−0.569242
$835$	−5.34709	−0.185044
$836$	−3.00529	−0.103940
$837$	9.31136	0.321848
$838$	−2.80126	−0.0967678
$839$	6.55241	0.226214	0.113107	−	0.993583i	$-0.463920\pi$
$839$	6.55241	0.226214	0.113107	+	0.993583i	$0.463920\pi$
$840$	−11.9978	−0.413965
$841$	−12.7894	−0.441015
$842$	−18.2860	−0.630175
$843$	−9.44327	−0.325244
$844$	−12.2352	−0.421154
$845$	−10.1805	−0.350219
$846$	−6.84000	−0.235164
$847$	3.42329	0.117626
$848$	19.4234	0.667003
$849$	0.755412	0.0259257
$850$	−3.07389	−0.105434
$851$	−36.7961	−1.26135
$852$	−3.84598	−0.131761
$853$	−35.4497	−1.21377	−0.606887	−	0.794788i	$-0.707582\pi$
$853$	−35.4497	−1.21377	−0.606887	+	0.794788i	$0.707582\pi$
$854$	−36.4389	−1.24691
$855$	9.31301	0.318498
$856$	−48.8194	−1.66861
$857$	−3.42456	−0.116981	−0.0584903	−	0.998288i	$-0.518629\pi$
$857$	−3.42456	−0.116981	−0.0584903	+	0.998288i	$0.518629\pi$
$858$	2.31003	0.0788630
$859$	−31.4758	−1.07394	−0.536970	−	0.843601i	$-0.680431\pi$
$859$	−31.4758	−1.07394	−0.536970	+	0.843601i	$0.680431\pi$
$860$	−0.849034	−0.0289518
$861$	−1.32234	−0.0450654
$862$	−44.6132	−1.51953
$863$	31.9695	1.08826	0.544128	−	0.839002i	$-0.316861\pi$
$863$	31.9695	1.08826	0.544128	+	0.839002i	$0.316861\pi$
$864$	−16.0910	−0.547426
$865$	−4.98729	−0.169573
$866$	7.93209	0.269543
$867$	−11.9796	−0.406849
$868$	3.25549	0.110498
$869$	−8.71058	−0.295486
$870$	−5.53896	−0.187788
$871$	−5.91140	−0.200300
$872$	−59.6660	−2.02055
$873$	−0.0379360	−0.00128394
$874$	56.8124	1.92171
$875$	3.42329	0.115728
$876$	−0.625091	−0.0211199
$877$	22.6400	0.764499	0.382250	−	0.924059i	$-0.375149\pi$
$877$	22.6400	0.764499	0.382250	+	0.924059i	$0.375149\pi$
$878$	12.8529	0.433766
$879$	2.87213	0.0968746
$880$	2.60496	0.0878131
$881$	−35.4408	−1.19403	−0.597015	−	0.802230i	$-0.703647\pi$
$881$	−35.4408	−1.19403	−0.597015	+	0.802230i	$0.703647\pi$
$882$	−9.65048	−0.324948
$883$	−0.390760	−0.0131501	−0.00657506	−	0.999978i	$-0.502093\pi$
$883$	−0.390760	−0.0131501	−0.00657506	+	0.999978i	$0.502093\pi$
$884$	−2.34525	−0.0788793
$885$	−7.12890	−0.239635
$886$	30.4766	1.02388
$887$	−36.6227	−1.22967	−0.614835	−	0.788655i	$-0.710778\pi$
$887$	−36.6227	−1.22967	−0.614835	+	0.788655i	$0.710778\pi$
$888$	−15.0138	−0.503830
$889$	−16.6772	−0.559335
$890$	−9.30798	−0.312004
$891$	1.02969	0.0344959
$892$	15.3361	0.513491
$893$	−18.3560	−0.614260
$894$	−17.8885	−0.598282
$895$	15.6605	0.523472
$896$	15.8682	0.530121
$897$	16.4643	0.549727
$898$	20.3636	0.679541
$899$	6.99219	0.233203
$900$	0.929222	0.0309741
$901$	19.0182	0.633588
$902$	0.407812	0.0135786
$903$	6.05893	0.201629
$904$	−58.7779	−1.95492
$905$	13.7540	0.457200
$906$	2.09467	0.0695906
$907$	−2.22586	−0.0739084	−0.0369542	−	0.999317i	$-0.511766\pi$
$907$	−2.22586	−0.0739084	−0.0369542	+	0.999317i	$0.511766\pi$
$908$	15.6120	0.518104
$909$	3.02387	0.100296
$910$	−6.92748	−0.229644
$911$	−17.0813	−0.565928	−0.282964	−	0.959131i	$-0.591318\pi$
$911$	−17.0813	−0.565928	−0.282964	+	0.959131i	$0.591318\pi$
$912$	16.3198	0.540401
$913$	5.48860	0.181646
$914$	27.8763	0.922065
$915$	−10.0824	−0.333313
$916$	−7.52288	−0.248563
$917$	14.7915	0.488458
$918$	16.4811	0.543958
$919$	26.3498	0.869198	0.434599	−	0.900624i	$-0.356890\pi$
$919$	26.3498	0.869198	0.434599	+	0.900624i	$0.356890\pi$
$920$	26.3721	0.869462
$921$	−10.7853	−0.355389
$922$	−2.73093	−0.0899384
$923$	−10.3312	−0.340056
$924$	2.13987	0.0703965
$925$	4.28382	0.140851
$926$	17.4388	0.573073
$927$	−9.94440	−0.326617
$928$	−12.0832	−0.396651
$929$	1.09809	0.0360272	0.0180136	−	0.999838i	$-0.494266\pi$
$929$	1.09809	0.0360272	0.0180136	+	0.999838i	$0.494266\pi$
$930$	−2.38915	−0.0783434
$931$	−25.8983	−0.848782
$932$	−0.0436525	−0.00142988
$933$	−21.5288	−0.704821
$934$	13.8937	0.454615
$935$	2.55061	0.0834139
$936$	−8.74829	−0.285947
$937$	−17.9579	−0.586659	−0.293329	−	0.956011i	$-0.594763\pi$
$937$	−17.9579	−0.586659	−0.293329	+	0.956011i	$0.594763\pi$
$938$	14.5242	0.474231
$939$	36.5020	1.19120
$940$	−1.83150	−0.0597371
$941$	59.1419	1.92797	0.963986	−	0.265955i	$-0.0856871\pi$
$941$	59.1419	1.92797	0.963986	+	0.265955i	$0.0856871\pi$
$942$	7.04839	0.229649
$943$	2.90661	0.0946521
$944$	16.2681	0.529483
$945$	−18.3545	−0.597072
$946$	−1.86858	−0.0607527
$947$	46.4748	1.51023	0.755114	−	0.655594i	$-0.227582\pi$
$947$	46.4748	1.51023	0.755114	+	0.655594i	$0.227582\pi$
$948$	−5.44490	−0.176842
$949$	−1.67914	−0.0545072
$950$	−6.61412	−0.214591
$951$	25.2843	0.819898
$952$	26.8079	0.868848
$953$	−18.1667	−0.588479	−0.294239	−	0.955732i	$-0.595066\pi$
$953$	−18.1667	−0.588479	−0.294239	+	0.955732i	$0.595066\pi$
$954$	15.2486	0.493693
$955$	−1.47219	−0.0476389
$956$	−2.45435	−0.0793794
$957$	4.59604	0.148569
$958$	0.605538	0.0195640
$959$	−46.9345	−1.51559
$960$	10.0759	0.325200
$961$	−27.9840	−0.902710
$962$	−8.66888	−0.279496
$963$	−26.9824	−0.869495
$964$	0.348760	0.0112328
$965$	−17.3317	−0.557927
$966$	−40.4523	−1.30153
$967$	−14.0773	−0.452697	−0.226348	−	0.974046i	$-0.572679\pi$
$967$	−14.0773	−0.452697	−0.226348	+	0.974046i	$0.572679\pi$
$968$	−3.07025	−0.0986817
$969$	15.9793	0.513329
$970$	0.0269423	0.000865064 0
$971$	10.1606	0.326070	0.163035	−	0.986620i	$-0.447872\pi$
$971$	10.1606	0.326070	0.163035	+	0.986620i	$0.447872\pi$
$972$	−8.16436	−0.261872
$973$	−40.9067	−1.31141
$974$	−21.2920	−0.682241
$975$	−1.91678	−0.0613861
$976$	23.0079	0.736466
$977$	6.49503	0.207794	0.103897	−	0.994588i	$-0.466869\pi$
$977$	6.49503	0.207794	0.103897	+	0.994588i	$0.466869\pi$
$978$	−17.1697	−0.549025
$979$	7.72345	0.246842
$980$	−2.58405	−0.0825444
$981$	−32.9773	−1.05288
$982$	−11.9972	−0.382847
$983$	−20.1832	−0.643743	−0.321872	−	0.946783i	$-0.604312\pi$
$983$	−20.1832	−0.643743	−0.321872	+	0.946783i	$0.604312\pi$
$984$	1.18597	0.0378075
$985$	−7.20705	−0.229636
$986$	12.3762	0.394138
$987$	13.0701	0.416026
$988$	−5.04630	−0.160544
$989$	−13.3180	−0.423486
$990$	2.04506	0.0649963
$991$	−4.34035	−0.137876	−0.0689379	−	0.997621i	$-0.521961\pi$
$991$	−4.34035	−0.137876	−0.0689379	+	0.997621i	$0.521961\pi$
$992$	−5.21192	−0.165479
$993$	25.9368	0.823079
$994$	25.3835	0.805117
$995$	−8.73332	−0.276865
$996$	3.43087	0.108711
$997$	−41.0136	−1.29891	−0.649456	−	0.760399i	$-0.725003\pi$
$997$	−41.0136	−1.29891	−0.649456	+	0.760399i	$0.725003\pi$
$998$	−25.4730	−0.806334
$999$	−22.9684	−0.726687

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4015.2.a.c.1.17	✓	23

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4015.2.a.c.1.17	✓	23	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 4015 = 5 \cdot 11 \cdot 73 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4015.a (trivial)

\(f(q)\)	\(=\)	\(q+1.20516 q^{2} +1.14152 q^{3} -0.547593 q^{4} +1.00000 q^{5} +1.37572 q^{6} +3.42329 q^{7} -3.07025 q^{8} -1.69692 q^{9} +O(q^{10})\)	\(q+1.20516 q^{2} +1.14152 q^{3} -0.547593 q^{4} +1.00000 q^{5} +1.37572 q^{6} +3.42329 q^{7} -3.07025 q^{8} -1.69692 q^{9} +1.20516 q^{10} -1.00000 q^{11} -0.625091 q^{12} -1.67914 q^{13} +4.12561 q^{14} +1.14152 q^{15} -2.60496 q^{16} -2.55061 q^{17} -2.04506 q^{18} -5.48818 q^{19} -0.547593 q^{20} +3.90777 q^{21} -1.20516 q^{22} -8.58955 q^{23} -3.50477 q^{24} +1.00000 q^{25} -2.02363 q^{26} -5.36165 q^{27} -1.87457 q^{28} -4.02623 q^{29} +1.37572 q^{30} -1.73666 q^{31} +3.00112 q^{32} -1.14152 q^{33} -3.07389 q^{34} +3.42329 q^{35} +0.929222 q^{36} +4.28382 q^{37} -6.61412 q^{38} -1.91678 q^{39} -3.07025 q^{40} -0.338389 q^{41} +4.70948 q^{42} +1.55048 q^{43} +0.547593 q^{44} -1.69692 q^{45} -10.3518 q^{46} +3.34465 q^{47} -2.97362 q^{48} +4.71892 q^{49} +1.20516 q^{50} -2.91158 q^{51} +0.919486 q^{52} -7.45633 q^{53} -6.46164 q^{54} -1.00000 q^{55} -10.5104 q^{56} -6.26489 q^{57} -4.85225 q^{58} -6.24507 q^{59} -0.625091 q^{60} -8.83237 q^{61} -2.09295 q^{62} -5.80906 q^{63} +8.82674 q^{64} -1.67914 q^{65} -1.37572 q^{66} +3.52049 q^{67} +1.39670 q^{68} -9.80518 q^{69} +4.12561 q^{70} +6.15267 q^{71} +5.20998 q^{72} +1.00000 q^{73} +5.16268 q^{74} +1.14152 q^{75} +3.00529 q^{76} -3.42329 q^{77} -2.31003 q^{78} +8.71058 q^{79} -2.60496 q^{80} -1.02969 q^{81} -0.407812 q^{82} -5.48860 q^{83} -2.13987 q^{84} -2.55061 q^{85} +1.86858 q^{86} -4.59604 q^{87} +3.07025 q^{88} -7.72345 q^{89} -2.04506 q^{90} -5.74819 q^{91} +4.70358 q^{92} -1.98244 q^{93} +4.03083 q^{94} -5.48818 q^{95} +3.42585 q^{96} +0.0223558 q^{97} +5.68705 q^{98} +1.69692 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 23 q - 3 q^{2} - 5 q^{3} + 15 q^{4} + 23 q^{5} - 5 q^{6} - 6 q^{8} + 8 q^{9}+O(q^{10}) \) 23 * q - 3 * q^2 - 5 * q^3 + 15 * q^4 + 23 * q^5 - 5 * q^6 - 6 * q^8 + 8 * q^9	\( 23 q - 3 q^{2} - 5 q^{3} + 15 q^{4} + 23 q^{5} - 5 q^{6} - 6 q^{8} + 8 q^{9} - 3 q^{10} - 23 q^{11} - 18 q^{12} - 5 q^{13} - 17 q^{14} - 5 q^{15} - q^{16} - 36 q^{17} + q^{18} + 6 q^{19} + 15 q^{20} - 18 q^{21} + 3 q^{22} - 14 q^{23} - 7 q^{24} + 23 q^{25} - 21 q^{26} - 29 q^{27} + 28 q^{28} - 36 q^{29} - 5 q^{30} - 16 q^{31} - 5 q^{32} + 5 q^{33} - 28 q^{34} - 14 q^{36} - 24 q^{37} + q^{38} - 10 q^{39} - 6 q^{40} - 36 q^{41} - 5 q^{42} + 17 q^{43} - 15 q^{44} + 8 q^{45} - 25 q^{46} - 21 q^{47} - 17 q^{48} - 27 q^{49} - 3 q^{50} + 19 q^{51} - 21 q^{52} - 28 q^{53} - 15 q^{54} - 23 q^{55} - 46 q^{56} - 23 q^{57} - 16 q^{58} - 61 q^{59} - 18 q^{60} - 17 q^{61} - 22 q^{62} - 9 q^{63} - 18 q^{64} - 5 q^{65} + 5 q^{66} + 2 q^{67} - 39 q^{68} - 36 q^{69} - 17 q^{70} - 50 q^{71} + 15 q^{72} + 23 q^{73} + 17 q^{74} - 5 q^{75} - 21 q^{76} + 49 q^{78} - 18 q^{79} - q^{80} - 57 q^{81} + 14 q^{82} - 20 q^{83} - 38 q^{84} - 36 q^{85} - 45 q^{86} + 37 q^{87} + 6 q^{88} - 93 q^{89} + q^{90} - 42 q^{91} - 39 q^{92} - 18 q^{93} - 6 q^{94} + 6 q^{95} - 9 q^{96} - 31 q^{97} - 31 q^{98} - 8 q^{99}+O(q^{100}) \) 23 * q - 3 * q^2 - 5 * q^3 + 15 * q^4 + 23 * q^5 - 5 * q^6 - 6 * q^8 + 8 * q^9 - 3 * q^10 - 23 * q^11 - 18 * q^12 - 5 * q^13 - 17 * q^14 - 5 * q^15 - q^16 - 36 * q^17 + q^18 + 6 * q^19 + 15 * q^20 - 18 * q^21 + 3 * q^22 - 14 * q^23 - 7 * q^24 + 23 * q^25 - 21 * q^26 - 29 * q^27 + 28 * q^28 - 36 * q^29 - 5 * q^30 - 16 * q^31 - 5 * q^32 + 5 * q^33 - 28 * q^34 - 14 * q^36 - 24 * q^37 + q^38 - 10 * q^39 - 6 * q^40 - 36 * q^41 - 5 * q^42 + 17 * q^43 - 15 * q^44 + 8 * q^45 - 25 * q^46 - 21 * q^47 - 17 * q^48 - 27 * q^49 - 3 * q^50 + 19 * q^51 - 21 * q^52 - 28 * q^53 - 15 * q^54 - 23 * q^55 - 46 * q^56 - 23 * q^57 - 16 * q^58 - 61 * q^59 - 18 * q^60 - 17 * q^61 - 22 * q^62 - 9 * q^63 - 18 * q^64 - 5 * q^65 + 5 * q^66 + 2 * q^67 - 39 * q^68 - 36 * q^69 - 17 * q^70 - 50 * q^71 + 15 * q^72 + 23 * q^73 + 17 * q^74 - 5 * q^75 - 21 * q^76 + 49 * q^78 - 18 * q^79 - q^80 - 57 * q^81 + 14 * q^82 - 20 * q^83 - 38 * q^84 - 36 * q^85 - 45 * q^86 + 37 * q^87 + 6 * q^88 - 93 * q^89 + q^90 - 42 * q^91 - 39 * q^92 - 18 * q^93 - 6 * q^94 + 6 * q^95 - 9 * q^96 - 31 * q^97 - 31 * q^98 - 8 * q^99

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