LMFDB - Embedded newform 6015.2.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6015,2,Mod(1,6015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6015, 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("6015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6015 = 3 \cdot 5 \cdot 401 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6015.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:	$48.0300168158$
Analytic rank:	$1$
Dimension:	$23$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	6015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.62638 q^{2} +1.00000 q^{3} +4.89789 q^{4} +1.00000 q^{5} -2.62638 q^{6} -0.417980 q^{7} -7.61099 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.62638 q^{2} +1.00000 q^{3} +4.89789 q^{4} +1.00000 q^{5} -2.62638 q^{6} -0.417980 q^{7} -7.61099 q^{8} +1.00000 q^{9} -2.62638 q^{10} +0.944706 q^{11} +4.89789 q^{12} +0.996258 q^{13} +1.09777 q^{14} +1.00000 q^{15} +10.1936 q^{16} -1.75609 q^{17} -2.62638 q^{18} -8.64834 q^{19} +4.89789 q^{20} -0.417980 q^{21} -2.48116 q^{22} +5.41203 q^{23} -7.61099 q^{24} +1.00000 q^{25} -2.61656 q^{26} +1.00000 q^{27} -2.04722 q^{28} +0.444247 q^{29} -2.62638 q^{30} -2.08769 q^{31} -11.5503 q^{32} +0.944706 q^{33} +4.61216 q^{34} -0.417980 q^{35} +4.89789 q^{36} +2.35767 q^{37} +22.7139 q^{38} +0.996258 q^{39} -7.61099 q^{40} -1.86420 q^{41} +1.09777 q^{42} -10.9112 q^{43} +4.62707 q^{44} +1.00000 q^{45} -14.2141 q^{46} -6.04478 q^{47} +10.1936 q^{48} -6.82529 q^{49} -2.62638 q^{50} -1.75609 q^{51} +4.87957 q^{52} +9.40146 q^{53} -2.62638 q^{54} +0.944706 q^{55} +3.18124 q^{56} -8.64834 q^{57} -1.16676 q^{58} +0.577394 q^{59} +4.89789 q^{60} -2.21235 q^{61} +5.48307 q^{62} -0.417980 q^{63} +9.94836 q^{64} +0.996258 q^{65} -2.48116 q^{66} +16.3201 q^{67} -8.60112 q^{68} +5.41203 q^{69} +1.09777 q^{70} +1.90782 q^{71} -7.61099 q^{72} -14.1441 q^{73} -6.19216 q^{74} +1.00000 q^{75} -42.3587 q^{76} -0.394868 q^{77} -2.61656 q^{78} -6.00073 q^{79} +10.1936 q^{80} +1.00000 q^{81} +4.89610 q^{82} +5.94837 q^{83} -2.04722 q^{84} -1.75609 q^{85} +28.6570 q^{86} +0.444247 q^{87} -7.19014 q^{88} +2.36348 q^{89} -2.62638 q^{90} -0.416415 q^{91} +26.5076 q^{92} -2.08769 q^{93} +15.8759 q^{94} -8.64834 q^{95} -11.5503 q^{96} +4.24051 q^{97} +17.9258 q^{98} +0.944706 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 23 q - 5 q^{2} + 23 q^{3} + 9 q^{4} + 23 q^{5} - 5 q^{6} - 16 q^{7} - 12 q^{8} + 23 q^{9}+O(q^{10}) $ 23 * q - 5 * q^2 + 23 * q^3 + 9 * q^4 + 23 * q^5 - 5 * q^6 - 16 * q^7 - 12 * q^8 + 23 * q^9	\( 23 q - 5 q^{2} + 23 q^{3} + 9 q^{4} + 23 q^{5} - 5 q^{6} - 16 q^{7} - 12 q^{8} + 23 q^{9} - 5 q^{10} - 13 q^{11} + 9 q^{12} - 18 q^{13} - 6 q^{14} + 23 q^{15} - 11 q^{16} - 34 q^{17} - 5 q^{18} - 35 q^{19} + 9 q^{20} - 16 q^{21} - 11 q^{22} - 14 q^{23} - 12 q^{24} + 23 q^{25} - 6 q^{26} + 23 q^{27} - 26 q^{28} - 43 q^{29} - 5 q^{30} - 21 q^{31} - 14 q^{32} - 13 q^{33} - 12 q^{34} - 16 q^{35} + 9 q^{36} - 18 q^{37} + 6 q^{38} - 18 q^{39} - 12 q^{40} - 45 q^{41} - 6 q^{42} - 43 q^{43} - 11 q^{44} + 23 q^{45} - 29 q^{46} - 14 q^{47} - 11 q^{48} - 25 q^{49} - 5 q^{50} - 34 q^{51} - 20 q^{52} - 3 q^{53} - 5 q^{54} - 13 q^{55} + 3 q^{56} - 35 q^{57} + 10 q^{58} - 9 q^{59} + 9 q^{60} - 67 q^{61} - 7 q^{62} - 16 q^{63} - 8 q^{64} - 18 q^{65} - 11 q^{66} - 32 q^{67} - 24 q^{68} - 14 q^{69} - 6 q^{70} - 8 q^{71} - 12 q^{72} - 39 q^{73} - 16 q^{74} + 23 q^{75} - 48 q^{76} - 26 q^{77} - 6 q^{78} - 59 q^{79} - 11 q^{80} + 23 q^{81} - q^{82} - 23 q^{83} - 26 q^{84} - 34 q^{85} - 7 q^{86} - 43 q^{87} + 17 q^{88} - 51 q^{89} - 5 q^{90} - 37 q^{91} + 11 q^{92} - 21 q^{93} + 8 q^{94} - 35 q^{95} - 14 q^{96} - 29 q^{97} + 32 q^{98} - 13 q^{99}+O(q^{100}) \) 23 * q - 5 * q^2 + 23 * q^3 + 9 * q^4 + 23 * q^5 - 5 * q^6 - 16 * q^7 - 12 * q^8 + 23 * q^9 - 5 * q^10 - 13 * q^11 + 9 * q^12 - 18 * q^13 - 6 * q^14 + 23 * q^15 - 11 * q^16 - 34 * q^17 - 5 * q^18 - 35 * q^19 + 9 * q^20 - 16 * q^21 - 11 * q^22 - 14 * q^23 - 12 * q^24 + 23 * q^25 - 6 * q^26 + 23 * q^27 - 26 * q^28 - 43 * q^29 - 5 * q^30 - 21 * q^31 - 14 * q^32 - 13 * q^33 - 12 * q^34 - 16 * q^35 + 9 * q^36 - 18 * q^37 + 6 * q^38 - 18 * q^39 - 12 * q^40 - 45 * q^41 - 6 * q^42 - 43 * q^43 - 11 * q^44 + 23 * q^45 - 29 * q^46 - 14 * q^47 - 11 * q^48 - 25 * q^49 - 5 * q^50 - 34 * q^51 - 20 * q^52 - 3 * q^53 - 5 * q^54 - 13 * q^55 + 3 * q^56 - 35 * q^57 + 10 * q^58 - 9 * q^59 + 9 * q^60 - 67 * q^61 - 7 * q^62 - 16 * q^63 - 8 * q^64 - 18 * q^65 - 11 * q^66 - 32 * q^67 - 24 * q^68 - 14 * q^69 - 6 * q^70 - 8 * q^71 - 12 * q^72 - 39 * q^73 - 16 * q^74 + 23 * q^75 - 48 * q^76 - 26 * q^77 - 6 * q^78 - 59 * q^79 - 11 * q^80 + 23 * q^81 - q^82 - 23 * q^83 - 26 * q^84 - 34 * q^85 - 7 * q^86 - 43 * q^87 + 17 * q^88 - 51 * q^89 - 5 * q^90 - 37 * q^91 + 11 * q^92 - 21 * q^93 + 8 * q^94 - 35 * q^95 - 14 * q^96 - 29 * q^97 + 32 * q^98 - 13 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.62638	−1.85713	−0.928567	−	0.371165i	$-0.878959\pi$
$2$	−2.62638	−1.85713	−0.928567	+	0.371165i	$0.878959\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	4.89789	2.44895
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−2.62638	−1.07222
$7$	−0.417980	−0.157981	−0.0789907	−	0.996875i	$-0.525170\pi$
$7$	−0.417980	−0.157981	−0.0789907	+	0.996875i	$0.525170\pi$
$8$	−7.61099	−2.69089
$9$	1.00000	0.333333
$10$	−2.62638	−0.830536
$11$	0.944706	0.284839	0.142420	−	0.989806i	$-0.454512\pi$
$11$	0.944706	0.284839	0.142420	+	0.989806i	$0.454512\pi$
$12$	4.89789	1.41390
$13$	0.996258	0.276312	0.138156	−	0.990410i	$-0.455882\pi$
$13$	0.996258	0.276312	0.138156	+	0.990410i	$0.455882\pi$
$14$	1.09777	0.293393
$15$	1.00000	0.258199
$16$	10.1936	2.54840
$17$	−1.75609	−0.425913	−0.212957	−	0.977062i	$-0.568309\pi$
$17$	−1.75609	−0.425913	−0.212957	+	0.977062i	$0.568309\pi$
$18$	−2.62638	−0.619045
$19$	−8.64834	−1.98407	−0.992033	−	0.125981i	$-0.959792\pi$
$19$	−8.64834	−1.98407	−0.992033	+	0.125981i	$0.959792\pi$
$20$	4.89789	1.09520
$21$	−0.417980	−0.0912106
$22$	−2.48116	−0.528985
$23$	5.41203	1.12849	0.564243	−	0.825609i	$-0.309168\pi$
$23$	5.41203	1.12849	0.564243	+	0.825609i	$0.309168\pi$
$24$	−7.61099	−1.55359
$25$	1.00000	0.200000
$26$	−2.61656	−0.513149
$27$	1.00000	0.192450
$28$	−2.04722	−0.386888
$29$	0.444247	0.0824945	0.0412473	−	0.999149i	$-0.486867\pi$
$29$	0.444247	0.0824945	0.0412473	+	0.999149i	$0.486867\pi$
$30$	−2.62638	−0.479510
$31$	−2.08769	−0.374960	−0.187480	−	0.982268i	$-0.560032\pi$
$31$	−2.08769	−0.374960	−0.187480	+	0.982268i	$0.560032\pi$
$32$	−11.5503	−2.04182
$33$	0.944706	0.164452
$34$	4.61216	0.790978
$35$	−0.417980	−0.0706514
$36$	4.89789	0.816316
$37$	2.35767	0.387599	0.193800	−	0.981041i	$-0.437919\pi$
$37$	2.35767	0.387599	0.193800	+	0.981041i	$0.437919\pi$
$38$	22.7139	3.68468
$39$	0.996258	0.159529
$40$	−7.61099	−1.20340
$41$	−1.86420	−0.291139	−0.145570	−	0.989348i	$-0.546501\pi$
$41$	−1.86420	−0.291139	−0.145570	+	0.989348i	$0.546501\pi$
$42$	1.09777	0.169390
$43$	−10.9112	−1.66394	−0.831971	−	0.554819i	$-0.812788\pi$
$43$	−10.9112	−1.66394	−0.831971	+	0.554819i	$0.812788\pi$
$44$	4.62707	0.697557
$45$	1.00000	0.149071
$46$	−14.2141	−2.09575
$47$	−6.04478	−0.881722	−0.440861	−	0.897575i	$-0.645327\pi$
$47$	−6.04478	−0.881722	−0.440861	+	0.897575i	$0.645327\pi$
$48$	10.1936	1.47132
$49$	−6.82529	−0.975042
$50$	−2.62638	−0.371427
$51$	−1.75609	−0.245901
$52$	4.87957	0.676674
$53$	9.40146	1.29139	0.645695	−	0.763596i	$-0.276568\pi$
$53$	9.40146	1.29139	0.645695	+	0.763596i	$0.276568\pi$
$54$	−2.62638	−0.357406
$55$	0.944706	0.127384
$56$	3.18124	0.425111
$57$	−8.64834	−1.14550
$58$	−1.16676	−0.153203
$59$	0.577394	0.0751702	0.0375851	−	0.999293i	$-0.488033\pi$
$59$	0.577394	0.0751702	0.0375851	+	0.999293i	$0.488033\pi$
$60$	4.89789	0.632316
$61$	−2.21235	−0.283262	−0.141631	−	0.989919i	$-0.545235\pi$
$61$	−2.21235	−0.283262	−0.141631	+	0.989919i	$0.545235\pi$
$62$	5.48307	0.696350
$63$	−0.417980	−0.0526605
$64$	9.94836	1.24354
$65$	0.996258	0.123571
$66$	−2.48116	−0.305410
$67$	16.3201	1.99382	0.996911	−	0.0785454i	$-0.0250276\pi$
$67$	16.3201	1.99382	0.996911	+	0.0785454i	$0.0250276\pi$
$68$	−8.60112	−1.04304
$69$	5.41203	0.651532
$70$	1.09777	0.131209
$71$	1.90782	0.226417	0.113209	−	0.993571i	$-0.463887\pi$
$71$	1.90782	0.226417	0.113209	+	0.993571i	$0.463887\pi$
$72$	−7.61099	−0.896963
$73$	−14.1441	−1.65544	−0.827722	−	0.561139i	$-0.810363\pi$
$73$	−14.1441	−1.65544	−0.827722	+	0.561139i	$0.810363\pi$
$74$	−6.19216	−0.719824
$75$	1.00000	0.115470
$76$	−42.3587	−4.85887
$77$	−0.394868	−0.0449993
$78$	−2.61656	−0.296267
$79$	−6.00073	−0.675135	−0.337567	−	0.941301i	$-0.609604\pi$
$79$	−6.00073	−0.675135	−0.337567	+	0.941301i	$0.609604\pi$
$80$	10.1936	1.13968
$81$	1.00000	0.111111
$82$	4.89610	0.540684
$83$	5.94837	0.652918	0.326459	−	0.945211i	$-0.394144\pi$
$83$	5.94837	0.652918	0.326459	+	0.945211i	$0.394144\pi$
$84$	−2.04722	−0.223370
$85$	−1.75609	−0.190474
$86$	28.6570	3.09016
$87$	0.444247	0.0476282
$88$	−7.19014	−0.766472
$89$	2.36348	0.250529	0.125264	−	0.992123i	$-0.460022\pi$
$89$	2.36348	0.250529	0.125264	+	0.992123i	$0.460022\pi$
$90$	−2.62638	−0.276845
$91$	−0.416415	−0.0436522
$92$	26.5076	2.76360
$93$	−2.08769	−0.216483
$94$	15.8759	1.63748
$95$	−8.64834	−0.887301
$96$	−11.5503	−1.17885
$97$	4.24051	0.430559	0.215279	−	0.976552i	$-0.430934\pi$
$97$	4.24051	0.430559	0.215279	+	0.976552i	$0.430934\pi$
$98$	17.9258	1.81078
$99$	0.944706	0.0949465
$100$	4.89789	0.489789
$101$	−13.0397	−1.29750	−0.648749	−	0.761002i	$-0.724708\pi$
$101$	−13.0397	−1.29750	−0.648749	+	0.761002i	$0.724708\pi$
$102$	4.61216	0.456672
$103$	−3.45456	−0.340387	−0.170194	−	0.985411i	$-0.554439\pi$
$103$	−3.45456	−0.340387	−0.170194	+	0.985411i	$0.554439\pi$
$104$	−7.58251	−0.743526
$105$	−0.417980	−0.0407906
$106$	−24.6918	−2.39828
$107$	−3.98588	−0.385330	−0.192665	−	0.981265i	$-0.561713\pi$
$107$	−3.98588	−0.385330	−0.192665	+	0.981265i	$0.561713\pi$
$108$	4.89789	0.471300
$109$	−7.61738	−0.729612	−0.364806	−	0.931083i	$-0.618865\pi$
$109$	−7.61738	−0.729612	−0.364806	+	0.931083i	$0.618865\pi$
$110$	−2.48116	−0.236569
$111$	2.35767	0.223781
$112$	−4.26071	−0.402599
$113$	1.73818	0.163514	0.0817569	−	0.996652i	$-0.473947\pi$
$113$	1.73818	0.163514	0.0817569	+	0.996652i	$0.473947\pi$
$114$	22.7139	2.12735
$115$	5.41203	0.504674
$116$	2.17587	0.202025
$117$	0.996258	0.0921041
$118$	−1.51646	−0.139601
$119$	0.734008	0.0672864
$120$	−7.61099	−0.694785
$121$	−10.1075	−0.918866
$122$	5.81048	0.526056
$123$	−1.86420	−0.168089
$124$	−10.2253	−0.918256
$125$	1.00000	0.0894427
$126$	1.09777	0.0977976
$127$	−2.05365	−0.182232	−0.0911161	−	0.995840i	$-0.529043\pi$
$127$	−2.05365	−0.182232	−0.0911161	+	0.995840i	$0.529043\pi$
$128$	−3.02761	−0.267605
$129$	−10.9112	−0.960678
$130$	−2.61656	−0.229487
$131$	−5.91837	−0.517091	−0.258545	−	0.965999i	$-0.583243\pi$
$131$	−5.91837	−0.517091	−0.258545	+	0.965999i	$0.583243\pi$
$132$	4.62707	0.402735
$133$	3.61483	0.313445
$134$	−42.8629	−3.70279
$135$	1.00000	0.0860663
$136$	13.3655	1.14609
$137$	16.2360	1.38713	0.693565	−	0.720394i	$-0.256039\pi$
$137$	16.2360	1.38713	0.693565	+	0.720394i	$0.256039\pi$
$138$	−14.2141	−1.20998
$139$	−3.92913	−0.333264	−0.166632	−	0.986019i	$-0.553289\pi$
$139$	−3.92913	−0.333264	−0.166632	+	0.986019i	$0.553289\pi$
$140$	−2.04722	−0.173022
$141$	−6.04478	−0.509062
$142$	−5.01068	−0.420487
$143$	0.941171	0.0787046
$144$	10.1936	0.849465
$145$	0.444247	0.0368927
$146$	37.1479	3.07438
$147$	−6.82529	−0.562941
$148$	11.5476	0.949210
$149$	−11.6981	−0.958344	−0.479172	−	0.877721i	$-0.659063\pi$
$149$	−11.6981	−0.958344	−0.479172	+	0.877721i	$0.659063\pi$
$150$	−2.62638	−0.214443
$151$	20.9067	1.70136	0.850681	−	0.525683i	$-0.176190\pi$
$151$	20.9067	1.70136	0.850681	+	0.525683i	$0.176190\pi$
$152$	65.8224	5.33890
$153$	−1.75609	−0.141971
$154$	1.03707	0.0835698
$155$	−2.08769	−0.167687
$156$	4.87957	0.390678
$157$	−20.1915	−1.61145	−0.805727	−	0.592287i	$-0.798225\pi$
$157$	−20.1915	−1.61145	−0.805727	+	0.592287i	$0.798225\pi$
$158$	15.7602	1.25382
$159$	9.40146	0.745584
$160$	−11.5503	−0.913131
$161$	−2.26212	−0.178280
$162$	−2.62638	−0.206348
$163$	16.9422	1.32702	0.663509	−	0.748168i	$-0.269067\pi$
$163$	16.9422	1.32702	0.663509	+	0.748168i	$0.269067\pi$
$164$	−9.13065	−0.712984
$165$	0.944706	0.0735452
$166$	−15.6227	−1.21256
$167$	−16.1622	−1.25067	−0.625333	−	0.780358i	$-0.715037\pi$
$167$	−16.1622	−1.25067	−0.625333	+	0.780358i	$0.715037\pi$
$168$	3.18124	0.245438
$169$	−12.0075	−0.923652
$170$	4.61216	0.353736
$171$	−8.64834	−0.661355
$172$	−53.4419	−4.07491
$173$	−4.42813	−0.336665	−0.168332	−	0.985730i	$-0.553838\pi$
$173$	−4.42813	−0.336665	−0.168332	+	0.985730i	$0.553838\pi$
$174$	−1.16676	−0.0884520
$175$	−0.417980	−0.0315963
$176$	9.62994	0.725884
$177$	0.577394	0.0433996
$178$	−6.20741	−0.465265
$179$	−23.8264	−1.78087	−0.890433	−	0.455114i	$-0.849598\pi$
$179$	−23.8264	−1.78087	−0.890433	+	0.455114i	$0.849598\pi$
$180$	4.89789	0.365068
$181$	5.71363	0.424691	0.212345	−	0.977195i	$-0.431890\pi$
$181$	5.71363	0.424691	0.212345	+	0.977195i	$0.431890\pi$
$182$	1.09367	0.0810680
$183$	−2.21235	−0.163542
$184$	−41.1909	−3.03663
$185$	2.35767	0.173340
$186$	5.48307	0.402038
$187$	−1.65898	−0.121317
$188$	−29.6067	−2.15929
$189$	−0.417980	−0.0304035
$190$	22.7139	1.64784
$191$	4.94518	0.357821	0.178910	−	0.983865i	$-0.442743\pi$
$191$	4.94518	0.357821	0.178910	+	0.983865i	$0.442743\pi$
$192$	9.94836	0.717961
$193$	−20.4116	−1.46926	−0.734629	−	0.678469i	$-0.762644\pi$
$193$	−20.4116	−1.46926	−0.734629	+	0.678469i	$0.762644\pi$
$194$	−11.1372	−0.799606
$195$	0.996258	0.0713435
$196$	−33.4296	−2.38783
$197$	−12.1581	−0.866227	−0.433114	−	0.901339i	$-0.642585\pi$
$197$	−12.1581	−0.866227	−0.433114	+	0.901339i	$0.642585\pi$
$198$	−2.48116	−0.176328
$199$	−9.50655	−0.673901	−0.336951	−	0.941522i	$-0.609396\pi$
$199$	−9.50655	−0.673901	−0.336951	+	0.941522i	$0.609396\pi$
$200$	−7.61099	−0.538178
$201$	16.3201	1.15113
$202$	34.2473	2.40963
$203$	−0.185686	−0.0130326
$204$	−8.60112	−0.602199
$205$	−1.86420	−0.130201
$206$	9.07299	0.632145
$207$	5.41203	0.376162
$208$	10.1554	0.704153
$209$	−8.17014	−0.565140
$210$	1.09777	0.0757537
$211$	−19.1463	−1.31808	−0.659042	−	0.752106i	$-0.729038\pi$
$211$	−19.1463	−1.31808	−0.659042	+	0.752106i	$0.729038\pi$
$212$	46.0474	3.16255
$213$	1.90782	0.130722
$214$	10.4685	0.715610
$215$	−10.9112	−0.744138
$216$	−7.61099	−0.517862
$217$	0.872610	0.0592366
$218$	20.0062	1.35499
$219$	−14.1441	−0.955771
$220$	4.62707	0.311957
$221$	−1.74951	−0.117685
$222$	−6.19216	−0.415591
$223$	−19.3216	−1.29387	−0.646934	−	0.762546i	$-0.723949\pi$
$223$	−19.3216	−1.29387	−0.646934	+	0.762546i	$0.723949\pi$
$224$	4.82779	0.322570
$225$	1.00000	0.0666667
$226$	−4.56512	−0.303667
$227$	18.7595	1.24511	0.622556	−	0.782575i	$-0.286094\pi$
$227$	18.7595	1.24511	0.622556	+	0.782575i	$0.286094\pi$
$228$	−42.3587	−2.80527
$229$	−28.3541	−1.87369	−0.936846	−	0.349741i	$-0.886270\pi$
$229$	−28.3541	−1.87369	−0.936846	+	0.349741i	$0.886270\pi$
$230$	−14.2141	−0.937248
$231$	−0.394868	−0.0259804
$232$	−3.38115	−0.221984
$233$	13.8104	0.904747	0.452373	−	0.891829i	$-0.350577\pi$
$233$	13.8104	0.904747	0.452373	+	0.891829i	$0.350577\pi$
$234$	−2.61656	−0.171050
$235$	−6.04478	−0.394318
$236$	2.82801	0.184088
$237$	−6.00073	−0.389789
$238$	−1.92779	−0.124960
$239$	10.7910	0.698015	0.349007	−	0.937120i	$-0.386519\pi$
$239$	10.7910	0.698015	0.349007	+	0.937120i	$0.386519\pi$
$240$	10.1936	0.657993
$241$	20.3479	1.31072	0.655362	−	0.755315i	$-0.272516\pi$
$241$	20.3479	1.31072	0.655362	+	0.755315i	$0.272516\pi$
$242$	26.5463	1.70646
$243$	1.00000	0.0641500
$244$	−10.8359	−0.693695
$245$	−6.82529	−0.436052
$246$	4.89610	0.312164
$247$	−8.61598	−0.548222
$248$	15.8893	1.00897
$249$	5.94837	0.376963
$250$	−2.62638	−0.166107
$251$	22.7794	1.43782	0.718912	−	0.695101i	$-0.244640\pi$
$251$	22.7794	1.43782	0.718912	+	0.695101i	$0.244640\pi$
$252$	−2.04722	−0.128963
$253$	5.11278	0.321437
$254$	5.39368	0.338430
$255$	−1.75609	−0.109970
$256$	−11.9450	−0.746565
$257$	−30.7671	−1.91920	−0.959599	−	0.281370i	$-0.909211\pi$
$257$	−30.7671	−1.91920	−0.959599	+	0.281370i	$0.909211\pi$
$258$	28.6570	1.78411
$259$	−0.985460	−0.0612335
$260$	4.87957	0.302618
$261$	0.444247	0.0274982
$262$	15.5439	0.960307
$263$	−0.746518	−0.0460323	−0.0230161	−	0.999735i	$-0.507327\pi$
$263$	−0.746518	−0.0460323	−0.0230161	+	0.999735i	$0.507327\pi$
$264$	−7.19014	−0.442523
$265$	9.40146	0.577527
$266$	−9.49393	−0.582110
$267$	2.36348	0.144643
$268$	79.9343	4.88276
$269$	−24.0867	−1.46859	−0.734296	−	0.678829i	$-0.762488\pi$
$269$	−24.0867	−1.46859	−0.734296	+	0.678829i	$0.762488\pi$
$270$	−2.62638	−0.159837
$271$	13.3933	0.813586	0.406793	−	0.913520i	$-0.366647\pi$
$271$	13.3933	0.813586	0.406793	+	0.913520i	$0.366647\pi$
$272$	−17.9008	−1.08540
$273$	−0.416415	−0.0252026
$274$	−42.6418	−2.57609
$275$	0.944706	0.0569679
$276$	26.5076	1.59557
$277$	−2.39246	−0.143749	−0.0718744	−	0.997414i	$-0.522898\pi$
$277$	−2.39246	−0.143749	−0.0718744	+	0.997414i	$0.522898\pi$
$278$	10.3194	0.618917
$279$	−2.08769	−0.124987
$280$	3.18124	0.190115
$281$	4.71640	0.281357	0.140679	−	0.990055i	$-0.455072\pi$
$281$	4.71640	0.281357	0.140679	+	0.990055i	$0.455072\pi$
$282$	15.8759	0.945397
$283$	28.3350	1.68434	0.842169	−	0.539213i	$-0.181278\pi$
$283$	28.3350	1.68434	0.842169	+	0.539213i	$0.181278\pi$
$284$	9.34432	0.554483
$285$	−8.64834	−0.512283
$286$	−2.47188	−0.146165
$287$	0.779197	0.0459946
$288$	−11.5503	−0.680608
$289$	−13.9162	−0.818598
$290$	−1.16676	−0.0685146
$291$	4.24051	0.248583
$292$	−69.2764	−4.05409
$293$	−11.2097	−0.654879	−0.327440	−	0.944872i	$-0.606186\pi$
$293$	−11.2097	−0.654879	−0.327440	+	0.944872i	$0.606186\pi$
$294$	17.9258	1.04546
$295$	0.577394	0.0336171
$296$	−17.9442	−1.04299
$297$	0.944706	0.0548174
$298$	30.7236	1.77977
$299$	5.39178	0.311815
$300$	4.89789	0.282780
$301$	4.56066	0.262872
$302$	−54.9090	−3.15966
$303$	−13.0397	−0.749111
$304$	−88.1576	−5.05618
$305$	−2.21235	−0.126679
$306$	4.61216	0.263659
$307$	17.6309	1.00625	0.503124	−	0.864214i	$-0.332184\pi$
$307$	17.6309	1.00625	0.503124	+	0.864214i	$0.332184\pi$
$308$	−1.93402	−0.110201
$309$	−3.45456	−0.196523
$310$	5.48307	0.311417
$311$	−26.8232	−1.52100	−0.760502	−	0.649336i	$-0.775047\pi$
$311$	−26.8232	−1.52100	−0.760502	+	0.649336i	$0.775047\pi$
$312$	−7.58251	−0.429275
$313$	1.70897	0.0965970	0.0482985	−	0.998833i	$-0.484620\pi$
$313$	1.70897	0.0965970	0.0482985	+	0.998833i	$0.484620\pi$
$314$	53.0305	2.99269
$315$	−0.417980	−0.0235505
$316$	−29.3909	−1.65337
$317$	13.4578	0.755863	0.377931	−	0.925834i	$-0.376636\pi$
$317$	13.4578	0.755863	0.377931	+	0.925834i	$0.376636\pi$
$318$	−24.6918	−1.38465
$319$	0.419682	0.0234977
$320$	9.94836	0.556130
$321$	−3.98588	−0.222470
$322$	5.94119	0.331090
$323$	15.1872	0.845040
$324$	4.89789	0.272105
$325$	0.996258	0.0552625
$326$	−44.4968	−2.46445
$327$	−7.61738	−0.421242
$328$	14.1884	0.783423
$329$	2.52660	0.139296
$330$	−2.48116	−0.136583
$331$	0.0446578	0.00245461	0.00122731	−	0.999999i	$-0.499609\pi$
$331$	0.0446578	0.00245461	0.00122731	+	0.999999i	$0.499609\pi$
$332$	29.1345	1.59896
$333$	2.35767	0.129200
$334$	42.4481	2.32265
$335$	16.3201	0.891664
$336$	−4.26071	−0.232441
$337$	22.4365	1.22220	0.611098	−	0.791555i	$-0.290728\pi$
$337$	22.4365	1.22220	0.611098	+	0.791555i	$0.290728\pi$
$338$	31.5362	1.71534
$339$	1.73818	0.0944048
$340$	−8.60112	−0.466461
$341$	−1.97225	−0.106803
$342$	22.7139	1.22823
$343$	5.77869	0.312020
$344$	83.0450	4.47749
$345$	5.41203	0.291374
$346$	11.6300	0.625231
$347$	28.6905	1.54019	0.770093	−	0.637932i	$-0.220210\pi$
$347$	28.6905	1.54019	0.770093	+	0.637932i	$0.220210\pi$
$348$	2.17587	0.116639
$349$	3.12541	0.167299	0.0836497	−	0.996495i	$-0.473342\pi$
$349$	3.12541	0.167299	0.0836497	+	0.996495i	$0.473342\pi$
$350$	1.09777	0.0586785
$351$	0.996258	0.0531763
$352$	−10.9116	−0.581592
$353$	21.8170	1.16120	0.580601	−	0.814188i	$-0.302818\pi$
$353$	21.8170	1.16120	0.580601	+	0.814188i	$0.302818\pi$
$354$	−1.51646	−0.0805988
$355$	1.90782	0.101257
$356$	11.5761	0.613531
$357$	0.734008	0.0388478
$358$	62.5772	3.30731
$359$	16.0464	0.846898	0.423449	−	0.905920i	$-0.360819\pi$
$359$	16.0464	0.846898	0.423449	+	0.905920i	$0.360819\pi$
$360$	−7.61099	−0.401134
$361$	55.7938	2.93652
$362$	−15.0062	−0.788707
$363$	−10.1075	−0.530508
$364$	−2.03956	−0.106902
$365$	−14.1441	−0.740337
$366$	5.81048	0.303719
$367$	−19.0854	−0.996248	−0.498124	−	0.867106i	$-0.665978\pi$
$367$	−19.0854	−0.996248	−0.498124	+	0.867106i	$0.665978\pi$
$368$	55.1680	2.87583
$369$	−1.86420	−0.0970463
$370$	−6.19216	−0.321915
$371$	−3.92962	−0.204016
$372$	−10.2253	−0.530155
$373$	−7.39399	−0.382846	−0.191423	−	0.981508i	$-0.561310\pi$
$373$	−7.39399	−0.382846	−0.191423	+	0.981508i	$0.561310\pi$
$374$	4.35713	0.225302
$375$	1.00000	0.0516398
$376$	46.0068	2.37262
$377$	0.442584	0.0227942
$378$	1.09777	0.0564635
$379$	−2.22404	−0.114241	−0.0571207	−	0.998367i	$-0.518192\pi$
$379$	−2.22404	−0.114241	−0.0571207	+	0.998367i	$0.518192\pi$
$380$	−42.3587	−2.17295
$381$	−2.05365	−0.105212
$382$	−12.9879	−0.664521
$383$	20.6322	1.05425	0.527127	−	0.849787i	$-0.323269\pi$
$383$	20.6322	1.05425	0.527127	+	0.849787i	$0.323269\pi$
$384$	−3.02761	−0.154502
$385$	−0.394868	−0.0201243
$386$	53.6087	2.72861
$387$	−10.9112	−0.554648
$388$	20.7696	1.05442
$389$	−2.51831	−0.127684	−0.0638418	−	0.997960i	$-0.520335\pi$
$389$	−2.51831	−0.127684	−0.0638418	+	0.997960i	$0.520335\pi$
$390$	−2.61656	−0.132494
$391$	−9.50399	−0.480637
$392$	51.9472	2.62373
$393$	−5.91837	−0.298542
$394$	31.9318	1.60870
$395$	−6.00073	−0.301930
$396$	4.62707	0.232519
$397$	−24.8558	−1.24748	−0.623739	−	0.781633i	$-0.714387\pi$
$397$	−24.8558	−1.24748	−0.623739	+	0.781633i	$0.714387\pi$
$398$	24.9678	1.25152
$399$	3.61483	0.180968
$400$	10.1936	0.509679
$401$	−1.00000	−0.0499376
$401$	−1.00000	−0.0499376
$402$	−42.8629	−2.13781
$403$	−2.07987	−0.103606
$404$	−63.8671	−3.17751
$405$	1.00000	0.0496904
$406$	0.487683	0.0242033
$407$	2.22731	0.110404
$408$	13.3655	0.661693
$409$	22.5689	1.11596	0.557981	−	0.829854i	$-0.311576\pi$
$409$	22.5689	1.11596	0.557981	+	0.829854i	$0.311576\pi$
$410$	4.89610	0.241801
$411$	16.2360	0.800860
$412$	−16.9200	−0.833591
$413$	−0.241339	−0.0118755
$414$	−14.2141	−0.698583
$415$	5.94837	0.291994
$416$	−11.5071	−0.564181
$417$	−3.92913	−0.192410
$418$	21.4579	1.04954
$419$	13.8673	0.677464	0.338732	−	0.940883i	$-0.390002\pi$
$419$	13.8673	0.677464	0.338732	+	0.940883i	$0.390002\pi$
$420$	−2.04722	−0.0998941
$421$	−2.21630	−0.108016	−0.0540078	−	0.998541i	$-0.517200\pi$
$421$	−2.21630	−0.108016	−0.0540078	+	0.998541i	$0.517200\pi$
$422$	50.2855	2.44786
$423$	−6.04478	−0.293907
$424$	−71.5544	−3.47499
$425$	−1.75609	−0.0851827
$426$	−5.01068	−0.242768
$427$	0.924717	0.0447502
$428$	−19.5224	−0.943653
$429$	0.941171	0.0454401
$430$	28.6570	1.38196
$431$	40.5777	1.95456	0.977279	−	0.211955i	$-0.0679830\pi$
$431$	40.5777	1.95456	0.977279	+	0.211955i	$0.0679830\pi$
$432$	10.1936	0.490439
$433$	35.0044	1.68220	0.841101	−	0.540878i	$-0.181908\pi$
$433$	35.0044	1.68220	0.841101	+	0.540878i	$0.181908\pi$
$434$	−2.29181	−0.110010
$435$	0.444247	0.0213000
$436$	−37.3091	−1.78678
$437$	−46.8051	−2.23899
$438$	37.1479	1.77499
$439$	−25.3064	−1.20781	−0.603905	−	0.797057i	$-0.706389\pi$
$439$	−25.3064	−1.20781	−0.603905	+	0.797057i	$0.706389\pi$
$440$	−7.19014	−0.342777
$441$	−6.82529	−0.325014
$442$	4.59490	0.218557
$443$	−24.1592	−1.14784	−0.573919	−	0.818912i	$-0.694578\pi$
$443$	−24.1592	−1.14784	−0.573919	+	0.818912i	$0.694578\pi$
$444$	11.5476	0.548027
$445$	2.36348	0.112040
$446$	50.7458	2.40289
$447$	−11.6981	−0.553300
$448$	−4.15821	−0.196457
$449$	−12.9333	−0.610359	−0.305179	−	0.952295i	$-0.598716\pi$
$449$	−12.9333	−0.610359	−0.305179	+	0.952295i	$0.598716\pi$
$450$	−2.62638	−0.123809
$451$	−1.76112	−0.0829279
$452$	8.51340	0.400437
$453$	20.9067	0.982281
$454$	−49.2697	−2.31234
$455$	−0.416415	−0.0195219
$456$	65.8224	3.08242
$457$	0.712406	0.0333249	0.0166625	−	0.999861i	$-0.494696\pi$
$457$	0.712406	0.0333249	0.0166625	+	0.999861i	$0.494696\pi$
$458$	74.4688	3.47970
$459$	−1.75609	−0.0819671
$460$	26.5076	1.23592
$461$	11.2467	0.523809	0.261905	−	0.965094i	$-0.415649\pi$
$461$	11.2467	0.523809	0.261905	+	0.965094i	$0.415649\pi$
$462$	1.03707	0.0482491
$463$	−26.1661	−1.21604	−0.608021	−	0.793921i	$-0.708036\pi$
$463$	−26.1661	−1.21604	−0.608021	+	0.793921i	$0.708036\pi$
$464$	4.52846	0.210229
$465$	−2.08769	−0.0968141
$466$	−36.2713	−1.68024
$467$	−8.21041	−0.379933	−0.189966	−	0.981791i	$-0.560838\pi$
$467$	−8.21041	−0.379933	−0.189966	+	0.981791i	$0.560838\pi$
$468$	4.87957	0.225558
$469$	−6.82148	−0.314987
$470$	15.8759	0.732302
$471$	−20.1915	−0.930374
$472$	−4.39453	−0.202275
$473$	−10.3079	−0.473957
$474$	15.7602	0.723891
$475$	−8.64834	−0.396813
$476$	3.59509	0.164781
$477$	9.40146	0.430463
$478$	−28.3414	−1.29631
$479$	37.0499	1.69285	0.846426	−	0.532506i	$-0.178750\pi$
$479$	37.0499	1.69285	0.846426	+	0.532506i	$0.178750\pi$
$480$	−11.5503	−0.527197
$481$	2.34885	0.107098
$482$	−53.4414	−2.43419
$483$	−2.26212	−0.102930
$484$	−49.5056	−2.25026
$485$	4.24051	0.192552
$486$	−2.62638	−0.119135
$487$	−38.0066	−1.72224	−0.861121	−	0.508400i	$-0.830237\pi$
$487$	−38.0066	−1.72224	−0.861121	+	0.508400i	$0.830237\pi$
$488$	16.8382	0.762228
$489$	16.9422	0.766154
$490$	17.9258	0.809807
$491$	−32.6921	−1.47538	−0.737688	−	0.675142i	$-0.764082\pi$
$491$	−32.6921	−1.47538	−0.737688	+	0.675142i	$0.764082\pi$
$492$	−9.13065	−0.411642
$493$	−0.780135	−0.0351355
$494$	22.6289	1.01812
$495$	0.944706	0.0424614
$496$	−21.2810	−0.955545
$497$	−0.797431	−0.0357697
$498$	−15.6227	−0.700070
$499$	−19.6649	−0.880323	−0.440161	−	0.897919i	$-0.645079\pi$
$499$	−19.6649	−0.880323	−0.440161	+	0.897919i	$0.645079\pi$
$500$	4.89789	0.219041
$501$	−16.1622	−0.722072
$502$	−59.8275	−2.67023
$503$	−28.6259	−1.27637	−0.638184	−	0.769884i	$-0.720314\pi$
$503$	−28.6259	−1.27637	−0.638184	+	0.769884i	$0.720314\pi$
$504$	3.18124	0.141704
$505$	−13.0397	−0.580259
$506$	−13.4281	−0.596952
$507$	−12.0075	−0.533270
$508$	−10.0586	−0.446277
$509$	−31.9435	−1.41587	−0.707935	−	0.706278i	$-0.750373\pi$
$509$	−31.9435	−1.41587	−0.707935	+	0.706278i	$0.750373\pi$
$510$	4.61216	0.204230
$511$	5.91195	0.261529
$512$	37.4275	1.65408
$513$	−8.64834	−0.381834
$514$	80.8062	3.56421
$515$	−3.45456	−0.152226
$516$	−53.4419	−2.35265
$517$	−5.71054	−0.251149
$518$	2.58820	0.113719
$519$	−4.42813	−0.194373
$520$	−7.58251	−0.332515
$521$	−35.6080	−1.56001	−0.780007	−	0.625770i	$-0.784785\pi$
$521$	−35.6080	−1.56001	−0.780007	+	0.625770i	$0.784785\pi$
$522$	−1.16676	−0.0510678
$523$	−15.9663	−0.698156	−0.349078	−	0.937094i	$-0.613505\pi$
$523$	−15.9663	−0.698156	−0.349078	+	0.937094i	$0.613505\pi$
$524$	−28.9876	−1.26633
$525$	−0.417980	−0.0182421
$526$	1.96064	0.0854881
$527$	3.66616	0.159700
$528$	9.62994	0.419089
$529$	6.29007	0.273481
$530$	−24.6918	−1.07255
$531$	0.577394	0.0250567
$532$	17.7051	0.767611
$533$	−1.85722	−0.0804453
$534$	−6.20741	−0.268621
$535$	−3.98588	−0.172325
$536$	−124.212	−5.36515
$537$	−23.8264	−1.02818
$538$	63.2610	2.72737
$539$	−6.44789	−0.277730
$540$	4.89789	0.210772
$541$	24.5310	1.05467	0.527335	−	0.849657i	$-0.323191\pi$
$541$	24.5310	1.05467	0.527335	+	0.849657i	$0.323191\pi$
$542$	−35.1760	−1.51094
$543$	5.71363	0.245195
$544$	20.2833	0.869640
$545$	−7.61738	−0.326293
$546$	1.09367	0.0468046
$547$	17.3444	0.741591	0.370796	−	0.928714i	$-0.379085\pi$
$547$	17.3444	0.741591	0.370796	+	0.928714i	$0.379085\pi$
$548$	79.5220	3.39701
$549$	−2.21235	−0.0944208
$550$	−2.48116	−0.105797
$551$	−3.84200	−0.163674
$552$	−41.1909	−1.75320
$553$	2.50818	0.106659
$554$	6.28351	0.266961
$555$	2.35767	0.100078
$556$	−19.2445	−0.816147
$557$	16.1427	0.683988	0.341994	−	0.939702i	$-0.388898\pi$
$557$	16.1427	0.683988	0.341994	+	0.939702i	$0.388898\pi$
$558$	5.48307	0.232117
$559$	−10.8704	−0.459768
$560$	−4.26071	−0.180048
$561$	−1.65898	−0.0700424
$562$	−12.3871	−0.522518
$563$	−12.6557	−0.533373	−0.266686	−	0.963783i	$-0.585929\pi$
$563$	−12.6557	−0.533373	−0.266686	+	0.963783i	$0.585929\pi$
$564$	−29.6067	−1.24667
$565$	1.73818	0.0731256
$566$	−74.4185	−3.12804
$567$	−0.417980	−0.0175535
$568$	−14.5204	−0.609263
$569$	−13.2513	−0.555522	−0.277761	−	0.960650i	$-0.589592\pi$
$569$	−13.2513	−0.555522	−0.277761	+	0.960650i	$0.589592\pi$
$570$	22.7139	0.951379
$571$	1.63826	0.0685592	0.0342796	−	0.999412i	$-0.489086\pi$
$571$	1.63826	0.0685592	0.0342796	+	0.999412i	$0.489086\pi$
$572$	4.60975	0.192744
$573$	4.94518	0.206588
$574$	−2.04647	−0.0854181
$575$	5.41203	0.225697
$576$	9.94836	0.414515
$577$	1.32509	0.0551644	0.0275822	−	0.999620i	$-0.491219\pi$
$577$	1.32509	0.0551644	0.0275822	+	0.999620i	$0.491219\pi$
$578$	36.5492	1.52025
$579$	−20.4116	−0.848277
$580$	2.17587	0.0903482
$581$	−2.48630	−0.103149
$582$	−11.1372	−0.461653
$583$	8.88161	0.367839
$584$	107.651	4.45462
$585$	0.996258	0.0411902
$586$	29.4411	1.21620
$587$	−16.6044	−0.685335	−0.342668	−	0.939457i	$-0.611330\pi$
$587$	−16.6044	−0.685335	−0.342668	+	0.939457i	$0.611330\pi$
$588$	−33.4296	−1.37861
$589$	18.0550	0.743944
$590$	−1.51646	−0.0624316
$591$	−12.1581	−0.500117
$592$	24.0332	0.987757
$593$	−21.2913	−0.874330	−0.437165	−	0.899381i	$-0.644017\pi$
$593$	−21.2913	−0.874330	−0.437165	+	0.899381i	$0.644017\pi$
$594$	−2.48116	−0.101803
$595$	0.734008	0.0300914
$596$	−57.2959	−2.34693
$597$	−9.50655	−0.389077
$598$	−14.1609	−0.579082
$599$	−11.1285	−0.454697	−0.227348	−	0.973813i	$-0.573006\pi$
$599$	−11.1285	−0.454697	−0.227348	+	0.973813i	$0.573006\pi$
$600$	−7.61099	−0.310717
$601$	−18.0114	−0.734699	−0.367349	−	0.930083i	$-0.619735\pi$
$601$	−18.0114	−0.734699	−0.367349	+	0.930083i	$0.619735\pi$
$602$	−11.9780	−0.488189
$603$	16.3201	0.664607
$604$	102.399	4.16654
$605$	−10.1075	−0.410930
$606$	34.2473	1.39120
$607$	−17.9770	−0.729662	−0.364831	−	0.931074i	$-0.618873\pi$
$607$	−17.9770	−0.729662	−0.364831	+	0.931074i	$0.618873\pi$
$608$	99.8909	4.05111
$609$	−0.185686	−0.00752438
$610$	5.81048	0.235259
$611$	−6.02216	−0.243631
$612$	−8.60112	−0.347680
$613$	14.2906	0.577190	0.288595	−	0.957451i	$-0.406812\pi$
$613$	14.2906	0.577190	0.288595	+	0.957451i	$0.406812\pi$
$614$	−46.3055	−1.86874
$615$	−1.86420	−0.0751718
$616$	3.00533	0.121088
$617$	−30.6890	−1.23549	−0.617745	−	0.786378i	$-0.711954\pi$
$617$	−30.6890	−1.23549	−0.617745	+	0.786378i	$0.711954\pi$
$618$	9.07299	0.364969
$619$	23.4651	0.943141	0.471570	−	0.881828i	$-0.343687\pi$
$619$	23.4651	0.943141	0.471570	+	0.881828i	$0.343687\pi$
$620$	−10.2253	−0.410657
$621$	5.41203	0.217177
$622$	70.4480	2.82471
$623$	−0.987887	−0.0395789
$624$	10.1554	0.406543
$625$	1.00000	0.0400000
$626$	−4.48842	−0.179394
$627$	−8.17014	−0.326284
$628$	−98.8957	−3.94637
$629$	−4.14028	−0.165084
$630$	1.09777	0.0437364
$631$	36.6681	1.45973	0.729867	−	0.683589i	$-0.239582\pi$
$631$	36.6681	1.45973	0.729867	+	0.683589i	$0.239582\pi$
$632$	45.6715	1.81671
$633$	−19.1463	−0.760996
$634$	−35.3452	−1.40374
$635$	−2.05365	−0.0814968
$636$	46.0474	1.82590
$637$	−6.79975	−0.269416
$638$	−1.10225	−0.0436384
$639$	1.90782	0.0754723
$640$	−3.02761	−0.119677
$641$	−18.0901	−0.714516	−0.357258	−	0.934006i	$-0.616288\pi$
$641$	−18.0901	−0.714516	−0.357258	+	0.934006i	$0.616288\pi$
$642$	10.4685	0.413157
$643$	−12.6640	−0.499420	−0.249710	−	0.968321i	$-0.580335\pi$
$643$	−12.6640	−0.499420	−0.249710	+	0.968321i	$0.580335\pi$
$644$	−11.0796	−0.436598
$645$	−10.9112	−0.429628
$646$	−39.8875	−1.56935
$647$	15.1873	0.597073	0.298537	−	0.954398i	$-0.403502\pi$
$647$	15.1873	0.597073	0.298537	+	0.954398i	$0.403502\pi$
$648$	−7.61099	−0.298988
$649$	0.545467	0.0214114
$650$	−2.61656	−0.102630
$651$	0.872610	0.0342003
$652$	82.9812	3.24980
$653$	45.0030	1.76110	0.880552	−	0.473949i	$-0.157172\pi$
$653$	45.0030	1.76110	0.880552	+	0.473949i	$0.157172\pi$
$654$	20.0062	0.782303
$655$	−5.91837	−0.231250
$656$	−19.0029	−0.741938
$657$	−14.1441	−0.551814
$658$	−6.63581	−0.258691
$659$	−23.4862	−0.914892	−0.457446	−	0.889237i	$-0.651236\pi$
$659$	−23.4862	−0.914892	−0.457446	+	0.889237i	$0.651236\pi$
$660$	4.62707	0.180108
$661$	−10.0479	−0.390817	−0.195408	−	0.980722i	$-0.562603\pi$
$661$	−10.0479	−0.390817	−0.195408	+	0.980722i	$0.562603\pi$
$662$	−0.117288	−0.00455855
$663$	−1.74951	−0.0679455
$664$	−45.2730	−1.75693
$665$	3.61483	0.140177
$666$	−6.19216	−0.239941
$667$	2.40428	0.0930939
$668$	−79.1606	−3.06281
$669$	−19.3216	−0.747015
$670$	−42.8629	−1.65594
$671$	−2.09002	−0.0806843
$672$	4.82779	0.186236
$673$	−8.93439	−0.344395	−0.172198	−	0.985062i	$-0.555087\pi$
$673$	−8.93439	−0.344395	−0.172198	+	0.985062i	$0.555087\pi$
$674$	−58.9270	−2.26978
$675$	1.00000	0.0384900
$676$	−58.8113	−2.26197
$677$	−14.5703	−0.559983	−0.279992	−	0.960002i	$-0.590332\pi$
$677$	−14.5703	−0.559983	−0.279992	+	0.960002i	$0.590332\pi$
$678$	−4.56512	−0.175322
$679$	−1.77245	−0.0680203
$680$	13.3655	0.512545
$681$	18.7595	0.718866
$682$	5.17988	0.198348
$683$	0.0461210	0.00176477	0.000882385	−	1.00000i	$-0.499719\pi$
$683$	0.0461210	0.00176477	0.000882385		1.00000i	$0.499719\pi$
$684$	−42.3587	−1.61962
$685$	16.2360	0.620344
$686$	−15.1771	−0.579463
$687$	−28.3541	−1.08178
$688$	−111.224	−4.24038
$689$	9.36628	0.356827
$690$	−14.2141	−0.541120
$691$	5.83285	0.221892	0.110946	−	0.993826i	$-0.464612\pi$
$691$	5.83285	0.221892	0.110946	+	0.993826i	$0.464612\pi$
$692$	−21.6885	−0.824474
$693$	−0.394868	−0.0149998
$694$	−75.3522	−2.86033
$695$	−3.92913	−0.149040
$696$	−3.38115	−0.128162
$697$	3.27369	0.124000
$698$	−8.20853	−0.310698
$699$	13.8104	0.522356
$700$	−2.04722	−0.0773776
$701$	4.27842	0.161594	0.0807969	−	0.996731i	$-0.474253\pi$
$701$	4.27842	0.161594	0.0807969	+	0.996731i	$0.474253\pi$
$702$	−2.61656	−0.0987556
$703$	−20.3900	−0.769022
$704$	9.39827	0.354211
$705$	−6.04478	−0.227660
$706$	−57.2999	−2.15651
$707$	5.45033	0.204981
$708$	2.82801	0.106283
$709$	−13.4623	−0.505589	−0.252794	−	0.967520i	$-0.581350\pi$
$709$	−13.4623	−0.505589	−0.252794	+	0.967520i	$0.581350\pi$
$710$	−5.01068	−0.188047
$711$	−6.00073	−0.225045
$712$	−17.9884	−0.674145
$713$	−11.2986	−0.423137
$714$	−1.92779	−0.0721456
$715$	0.941171	0.0351978
$716$	−116.699	−4.36125
$717$	10.7910	0.402999
$718$	−42.1441	−1.57280
$719$	8.32658	0.310529	0.155264	−	0.987873i	$-0.450377\pi$
$719$	8.32658	0.310529	0.155264	+	0.987873i	$0.450377\pi$
$720$	10.1936	0.379892
$721$	1.44393	0.0537749
$722$	−146.536	−5.45350
$723$	20.3479	0.756746
$724$	27.9847	1.04004
$725$	0.444247	0.0164989
$726$	26.5463	0.985224
$727$	−13.4619	−0.499274	−0.249637	−	0.968339i	$-0.580311\pi$
$727$	−13.4619	−0.499274	−0.249637	+	0.968339i	$0.580311\pi$
$728$	3.16933	0.117463
$729$	1.00000	0.0370370
$730$	37.1479	1.37490
$731$	19.1610	0.708695
$732$	−10.8359	−0.400505
$733$	−3.93017	−0.145164	−0.0725821	−	0.997362i	$-0.523124\pi$
$733$	−3.93017	−0.145164	−0.0725821	+	0.997362i	$0.523124\pi$
$734$	50.1255	1.85017
$735$	−6.82529	−0.251755
$736$	−62.5106	−2.30417
$737$	15.4177	0.567919
$738$	4.89610	0.180228
$739$	−32.5226	−1.19636	−0.598182	−	0.801360i	$-0.704110\pi$
$739$	−32.5226	−1.19636	−0.598182	+	0.801360i	$0.704110\pi$
$740$	11.5476	0.424500
$741$	−8.61598	−0.316516
$742$	10.3207	0.378884
$743$	−12.8499	−0.471417	−0.235708	−	0.971824i	$-0.575741\pi$
$743$	−12.8499	−0.471417	−0.235708	+	0.971824i	$0.575741\pi$
$744$	15.8893	0.582532
$745$	−11.6981	−0.428584
$746$	19.4195	0.710997
$747$	5.94837	0.217639
$748$	−8.12553	−0.297099
$749$	1.66602	0.0608750
$750$	−2.62638	−0.0959020
$751$	−2.91509	−0.106373	−0.0531866	−	0.998585i	$-0.516938\pi$
$751$	−2.91509	−0.106373	−0.0531866	+	0.998585i	$0.516938\pi$
$752$	−61.6180	−2.24698
$753$	22.7794	0.830128
$754$	−1.16240	−0.0423320
$755$	20.9067	0.760872
$756$	−2.04722	−0.0744567
$757$	−43.1268	−1.56747	−0.783736	−	0.621094i	$-0.786688\pi$
$757$	−43.1268	−1.56747	−0.783736	+	0.621094i	$0.786688\pi$
$758$	5.84119	0.212162
$759$	5.11278	0.185582
$760$	65.8224	2.38763
$761$	4.25696	0.154315	0.0771574	−	0.997019i	$-0.475416\pi$
$761$	4.25696	0.154315	0.0771574	+	0.997019i	$0.475416\pi$
$762$	5.39368	0.195393
$763$	3.18391	0.115265
$764$	24.2210	0.876284
$765$	−1.75609	−0.0634914
$766$	−54.1880	−1.95789
$767$	0.575233	0.0207705
$768$	−11.9450	−0.431030
$769$	−16.0777	−0.579777	−0.289889	−	0.957060i	$-0.593618\pi$
$769$	−16.0777	−0.579777	−0.289889	+	0.957060i	$0.593618\pi$
$770$	1.03707	0.0373736
$771$	−30.7671	−1.10805
$772$	−99.9738	−3.59814
$773$	−16.7137	−0.601151	−0.300575	−	0.953758i	$-0.597179\pi$
$773$	−16.7137	−0.601151	−0.300575	+	0.953758i	$0.597179\pi$
$774$	28.6570	1.03005
$775$	−2.08769	−0.0749919
$776$	−32.2745	−1.15859
$777$	−0.985460	−0.0353532
$778$	6.61406	0.237126
$779$	16.1222	0.577639
$780$	4.87957	0.174717
$781$	1.80233	0.0644925
$782$	24.9611	0.892608
$783$	0.444247	0.0158761
$784$	−69.5742	−2.48479
$785$	−20.1915	−0.720664
$786$	15.5439	0.554433
$787$	10.7916	0.384679	0.192339	−	0.981328i	$-0.438393\pi$
$787$	10.7916	0.384679	0.192339	+	0.981328i	$0.438393\pi$
$788$	−59.5490	−2.12135
$789$	−0.746518	−0.0265767
$790$	15.7602	0.560724
$791$	−0.726522	−0.0258322
$792$	−7.19014	−0.255491
$793$	−2.20407	−0.0782689
$794$	65.2810	2.31673
$795$	9.40146	0.333435
$796$	−46.5621	−1.65035
$797$	1.58127	0.0560115	0.0280058	−	0.999608i	$-0.491084\pi$
$797$	1.58127	0.0560115	0.0280058	+	0.999608i	$0.491084\pi$
$798$	−9.49393	−0.336082
$799$	10.6152	0.375537
$800$	−11.5503	−0.408365
$801$	2.36348	0.0835095
$802$	2.62638	0.0927409
$803$	−13.3620	−0.471536
$804$	79.9343	2.81906
$805$	−2.26212	−0.0797292
$806$	5.46255	0.192410
$807$	−24.0867	−0.847892
$808$	99.2450	3.49143
$809$	−10.2444	−0.360173	−0.180087	−	0.983651i	$-0.557638\pi$
$809$	−10.2444	−0.360173	−0.180087	+	0.983651i	$0.557638\pi$
$810$	−2.62638	−0.0922817
$811$	−45.9553	−1.61371	−0.806855	−	0.590750i	$-0.798832\pi$
$811$	−45.9553	−1.61371	−0.806855	+	0.590750i	$0.798832\pi$
$812$	−0.909470	−0.0319162
$813$	13.3933	0.469724
$814$	−5.84977	−0.205034
$815$	16.9422	0.593460
$816$	−17.9008	−0.626654
$817$	94.3638	3.30137
$818$	−59.2747	−2.07249
$819$	−0.416415	−0.0145507
$820$	−9.13065	−0.318856
$821$	2.50012	0.0872548	0.0436274	−	0.999048i	$-0.486109\pi$
$821$	2.50012	0.0872548	0.0436274	+	0.999048i	$0.486109\pi$
$822$	−42.6418	−1.48731
$823$	40.7198	1.41940	0.709702	−	0.704502i	$-0.248830\pi$
$823$	40.7198	1.41940	0.709702	+	0.704502i	$0.248830\pi$
$824$	26.2926	0.915945
$825$	0.944706	0.0328904
$826$	0.633848	0.0220544
$827$	56.2416	1.95571	0.977856	−	0.209281i	$-0.0671122\pi$
$827$	56.2416	1.95571	0.977856	+	0.209281i	$0.0671122\pi$
$828$	26.5076	0.921201
$829$	31.4040	1.09071	0.545353	−	0.838206i	$-0.316395\pi$
$829$	31.4040	1.09071	0.545353	+	0.838206i	$0.316395\pi$
$830$	−15.6227	−0.542272
$831$	−2.39246	−0.0829934
$832$	9.91113	0.343607
$833$	11.9858	0.415283
$834$	10.3194	0.357332
$835$	−16.1622	−0.559315
$836$	−40.0165	−1.38400
$837$	−2.08769	−0.0721610
$838$	−36.4209	−1.25814
$839$	17.3225	0.598041	0.299020	−	0.954247i	$-0.403340\pi$
$839$	17.3225	0.598041	0.299020	+	0.954247i	$0.403340\pi$
$840$	3.18124	0.109763
$841$	−28.8026	−0.993195
$842$	5.82084	0.200599
$843$	4.71640	0.162442
$844$	−93.7764	−3.22792
$845$	−12.0075	−0.413070
$846$	15.8759	0.545825
$847$	4.22474	0.145164
$848$	95.8346	3.29097
$849$	28.3350	0.972453
$850$	4.61216	0.158196
$851$	12.7598	0.437401
$852$	9.34432	0.320131
$853$	0.0422306	0.00144595	0.000722975	−	1.00000i	$-0.499770\pi$
$853$	0.0422306	0.00144595	0.000722975		1.00000i	$0.499770\pi$
$854$	−2.42866	−0.0831071
$855$	−8.64834	−0.295767
$856$	30.3365	1.03688
$857$	−16.7023	−0.570540	−0.285270	−	0.958447i	$-0.592083\pi$
$857$	−16.7023	−0.570540	−0.285270	+	0.958447i	$0.592083\pi$
$858$	−2.47188	−0.0843884
$859$	32.1011	1.09527	0.547637	−	0.836716i	$-0.315527\pi$
$859$	32.1011	1.09527	0.547637	+	0.836716i	$0.315527\pi$
$860$	−53.4419	−1.82235
$861$	0.779197	0.0265550
$862$	−106.573	−3.62988
$863$	−7.94786	−0.270548	−0.135274	−	0.990808i	$-0.543192\pi$
$863$	−7.94786	−0.270548	−0.135274	+	0.990808i	$0.543192\pi$
$864$	−11.5503	−0.392949
$865$	−4.42813	−0.150561
$866$	−91.9349	−3.12408
$867$	−13.9162	−0.472618
$868$	4.27395	0.145067
$869$	−5.66892	−0.192305
$870$	−1.16676	−0.0395569
$871$	16.2591	0.550917
$872$	57.9757	1.96331
$873$	4.24051	0.143520
$874$	122.928	4.15811
$875$	−0.417980	−0.0141303
$876$	−69.2764	−2.34063
$877$	−5.53503	−0.186905	−0.0934524	−	0.995624i	$-0.529790\pi$
$877$	−5.53503	−0.186905	−0.0934524	+	0.995624i	$0.529790\pi$
$878$	66.4644	2.24306
$879$	−11.2097	−0.378095
$880$	9.62994	0.324625
$881$	−18.8794	−0.636065	−0.318032	−	0.948080i	$-0.603022\pi$
$881$	−18.8794	−0.636065	−0.318032	+	0.948080i	$0.603022\pi$
$882$	17.9258	0.603595
$883$	−32.4790	−1.09300	−0.546502	−	0.837458i	$-0.684041\pi$
$883$	−32.4790	−1.09300	−0.546502	+	0.837458i	$0.684041\pi$
$884$	−8.56894	−0.288205
$885$	0.577394	0.0194089
$886$	63.4513	2.13169
$887$	38.2429	1.28407	0.642035	−	0.766675i	$-0.278090\pi$
$887$	38.2429	1.28407	0.642035	+	0.766675i	$0.278090\pi$
$888$	−17.9442	−0.602169
$889$	0.858385	0.0287893
$890$	−6.20741	−0.208073
$891$	0.944706	0.0316488
$892$	−94.6350	−3.16861
$893$	52.2773	1.74939
$894$	30.7236	1.02755
$895$	−23.8264	−0.796427
$896$	1.26548	0.0422767
$897$	5.39178	0.180026
$898$	33.9677	1.13352
$899$	−0.927447	−0.0309321
$900$	4.89789	0.163263
$901$	−16.5098	−0.550020
$902$	4.62538	0.154008
$903$	4.56066	0.151769
$904$	−13.2292	−0.439998
$905$	5.71363	0.189927
$906$	−54.9090	−1.82423
$907$	−31.2455	−1.03749	−0.518746	−	0.854929i	$-0.673601\pi$
$907$	−31.2455	−1.03749	−0.518746	+	0.854929i	$0.673601\pi$
$908$	91.8821	3.04921
$909$	−13.0397	−0.432500
$910$	1.09367	0.0362547
$911$	−23.0039	−0.762152	−0.381076	−	0.924544i	$-0.624446\pi$
$911$	−23.0039	−0.762152	−0.381076	+	0.924544i	$0.624446\pi$
$912$	−88.1576	−2.91919
$913$	5.61946	0.185977
$914$	−1.87105	−0.0618889
$915$	−2.21235	−0.0731380
$916$	−138.875	−4.58858
$917$	2.47376	0.0816907
$918$	4.61216	0.152224
$919$	−26.4070	−0.871087	−0.435544	−	0.900168i	$-0.643444\pi$
$919$	−26.4070	−0.871087	−0.435544	+	0.900168i	$0.643444\pi$
$920$	−41.1909	−1.35802
$921$	17.6309	0.580957
$922$	−29.5381	−0.972784
$923$	1.90068	0.0625618
$924$	−1.93402	−0.0636246
$925$	2.35767	0.0775199
$926$	68.7222	2.25835
$927$	−3.45456	−0.113462
$928$	−5.13118	−0.168439
$929$	−22.5764	−0.740706	−0.370353	−	0.928891i	$-0.620763\pi$
$929$	−22.5764	−0.740706	−0.370353	+	0.928891i	$0.620763\pi$
$930$	5.48307	0.179797
$931$	59.0275	1.93455
$932$	67.6417	2.21568
$933$	−26.8232	−0.878152
$934$	21.5637	0.705586
$935$	−1.65898	−0.0542546
$936$	−7.58251	−0.247842
$937$	−22.3069	−0.728734	−0.364367	−	0.931255i	$-0.618715\pi$
$937$	−22.3069	−0.728734	−0.364367	+	0.931255i	$0.618715\pi$
$938$	17.9158	0.584973
$939$	1.70897	0.0557703
$940$	−29.6067	−0.965664
$941$	−27.2463	−0.888203	−0.444102	−	0.895976i	$-0.646477\pi$
$941$	−27.2463	−0.888203	−0.444102	+	0.895976i	$0.646477\pi$
$942$	53.0305	1.72783
$943$	−10.0891	−0.328546
$944$	5.88571	0.191564
$945$	−0.417980	−0.0135969
$946$	27.0724	0.880201
$947$	−42.9483	−1.39563	−0.697817	−	0.716276i	$-0.745845\pi$
$947$	−42.9483	−1.39563	−0.697817	+	0.716276i	$0.745845\pi$
$948$	−29.3909	−0.954574
$949$	−14.0912	−0.457419
$950$	22.7139	0.736935
$951$	13.4578	0.436398
$952$	−5.58652	−0.181060
$953$	−9.41333	−0.304928	−0.152464	−	0.988309i	$-0.548721\pi$
$953$	−9.41333	−0.304928	−0.152464	+	0.988309i	$0.548721\pi$
$954$	−24.6918	−0.799428
$955$	4.94518	0.160022
$956$	52.8534	1.70940
$957$	0.419682	0.0135664
$958$	−97.3073	−3.14385
$959$	−6.78630	−0.219141
$960$	9.94836	0.321082
$961$	−26.6416	−0.859405
$962$	−6.16899	−0.198896
$963$	−3.98588	−0.128443
$964$	99.6619	3.20989
$965$	−20.4116	−0.657072
$966$	5.94119	0.191155
$967$	42.4943	1.36652	0.683262	−	0.730174i	$-0.260561\pi$
$967$	42.4943	1.36652	0.683262	+	0.730174i	$0.260561\pi$
$968$	76.9283	2.47257
$969$	15.1872	0.487884
$970$	−11.1372	−0.357595
$971$	37.4491	1.20180	0.600900	−	0.799324i	$-0.294809\pi$
$971$	37.4491	1.20180	0.600900	+	0.799324i	$0.294809\pi$
$972$	4.89789	0.157100
$973$	1.64230	0.0526496
$974$	99.8199	3.19843
$975$	0.996258	0.0319058
$976$	−22.5518	−0.721865
$977$	30.3623	0.971377	0.485688	−	0.874132i	$-0.338569\pi$
$977$	30.3623	0.971377	0.485688	+	0.874132i	$0.338569\pi$
$978$	−44.4968	−1.42285
$979$	2.23279	0.0713604
$980$	−33.4296	−1.06787
$981$	−7.61738	−0.243204
$982$	85.8621	2.73997
$983$	−19.8339	−0.632602	−0.316301	−	0.948659i	$-0.602441\pi$
$983$	−19.8339	−0.632602	−0.316301	+	0.948659i	$0.602441\pi$
$984$	14.1884	0.452310
$985$	−12.1581	−0.387389
$986$	2.04893	0.0652514
$987$	2.52660	0.0804224
$988$	−42.2002	−1.34257
$989$	−59.0517	−1.87774
$990$	−2.48116	−0.0788564
$991$	−18.3936	−0.584291	−0.292146	−	0.956374i	$-0.594369\pi$
$991$	−18.3936	−0.584291	−0.292146	+	0.956374i	$0.594369\pi$
$992$	24.1134	0.765601
$993$	0.0446578	0.00141717
$994$	2.09436	0.0664291
$995$	−9.50655	−0.301378
$996$	29.1345	0.923162
$997$	61.8339	1.95830	0.979149	−	0.203143i	$-0.0651157\pi$
$997$	61.8339	1.95830	0.979149	+	0.203143i	$0.0651157\pi$
$998$	51.6476	1.63488
$999$	2.35767	0.0745935

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6015.2.a.b.1.1	✓	23

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6015.2.a.b.1.1	✓	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:	\( N \)	\(=\)	\( 6015 = 3 \cdot 5 \cdot 401 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6015.a (trivial)

\(f(q)\)	\(=\)	\(q-2.62638 q^{2} +1.00000 q^{3} +4.89789 q^{4} +1.00000 q^{5} -2.62638 q^{6} -0.417980 q^{7} -7.61099 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.62638 q^{2} +1.00000 q^{3} +4.89789 q^{4} +1.00000 q^{5} -2.62638 q^{6} -0.417980 q^{7} -7.61099 q^{8} +1.00000 q^{9} -2.62638 q^{10} +0.944706 q^{11} +4.89789 q^{12} +0.996258 q^{13} +1.09777 q^{14} +1.00000 q^{15} +10.1936 q^{16} -1.75609 q^{17} -2.62638 q^{18} -8.64834 q^{19} +4.89789 q^{20} -0.417980 q^{21} -2.48116 q^{22} +5.41203 q^{23} -7.61099 q^{24} +1.00000 q^{25} -2.61656 q^{26} +1.00000 q^{27} -2.04722 q^{28} +0.444247 q^{29} -2.62638 q^{30} -2.08769 q^{31} -11.5503 q^{32} +0.944706 q^{33} +4.61216 q^{34} -0.417980 q^{35} +4.89789 q^{36} +2.35767 q^{37} +22.7139 q^{38} +0.996258 q^{39} -7.61099 q^{40} -1.86420 q^{41} +1.09777 q^{42} -10.9112 q^{43} +4.62707 q^{44} +1.00000 q^{45} -14.2141 q^{46} -6.04478 q^{47} +10.1936 q^{48} -6.82529 q^{49} -2.62638 q^{50} -1.75609 q^{51} +4.87957 q^{52} +9.40146 q^{53} -2.62638 q^{54} +0.944706 q^{55} +3.18124 q^{56} -8.64834 q^{57} -1.16676 q^{58} +0.577394 q^{59} +4.89789 q^{60} -2.21235 q^{61} +5.48307 q^{62} -0.417980 q^{63} +9.94836 q^{64} +0.996258 q^{65} -2.48116 q^{66} +16.3201 q^{67} -8.60112 q^{68} +5.41203 q^{69} +1.09777 q^{70} +1.90782 q^{71} -7.61099 q^{72} -14.1441 q^{73} -6.19216 q^{74} +1.00000 q^{75} -42.3587 q^{76} -0.394868 q^{77} -2.61656 q^{78} -6.00073 q^{79} +10.1936 q^{80} +1.00000 q^{81} +4.89610 q^{82} +5.94837 q^{83} -2.04722 q^{84} -1.75609 q^{85} +28.6570 q^{86} +0.444247 q^{87} -7.19014 q^{88} +2.36348 q^{89} -2.62638 q^{90} -0.416415 q^{91} +26.5076 q^{92} -2.08769 q^{93} +15.8759 q^{94} -8.64834 q^{95} -11.5503 q^{96} +4.24051 q^{97} +17.9258 q^{98} +0.944706 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 23 q - 5 q^{2} + 23 q^{3} + 9 q^{4} + 23 q^{5} - 5 q^{6} - 16 q^{7} - 12 q^{8} + 23 q^{9}+O(q^{10}) \) 23 * q - 5 * q^2 + 23 * q^3 + 9 * q^4 + 23 * q^5 - 5 * q^6 - 16 * q^7 - 12 * q^8 + 23 * q^9	\( 23 q - 5 q^{2} + 23 q^{3} + 9 q^{4} + 23 q^{5} - 5 q^{6} - 16 q^{7} - 12 q^{8} + 23 q^{9} - 5 q^{10} - 13 q^{11} + 9 q^{12} - 18 q^{13} - 6 q^{14} + 23 q^{15} - 11 q^{16} - 34 q^{17} - 5 q^{18} - 35 q^{19} + 9 q^{20} - 16 q^{21} - 11 q^{22} - 14 q^{23} - 12 q^{24} + 23 q^{25} - 6 q^{26} + 23 q^{27} - 26 q^{28} - 43 q^{29} - 5 q^{30} - 21 q^{31} - 14 q^{32} - 13 q^{33} - 12 q^{34} - 16 q^{35} + 9 q^{36} - 18 q^{37} + 6 q^{38} - 18 q^{39} - 12 q^{40} - 45 q^{41} - 6 q^{42} - 43 q^{43} - 11 q^{44} + 23 q^{45} - 29 q^{46} - 14 q^{47} - 11 q^{48} - 25 q^{49} - 5 q^{50} - 34 q^{51} - 20 q^{52} - 3 q^{53} - 5 q^{54} - 13 q^{55} + 3 q^{56} - 35 q^{57} + 10 q^{58} - 9 q^{59} + 9 q^{60} - 67 q^{61} - 7 q^{62} - 16 q^{63} - 8 q^{64} - 18 q^{65} - 11 q^{66} - 32 q^{67} - 24 q^{68} - 14 q^{69} - 6 q^{70} - 8 q^{71} - 12 q^{72} - 39 q^{73} - 16 q^{74} + 23 q^{75} - 48 q^{76} - 26 q^{77} - 6 q^{78} - 59 q^{79} - 11 q^{80} + 23 q^{81} - q^{82} - 23 q^{83} - 26 q^{84} - 34 q^{85} - 7 q^{86} - 43 q^{87} + 17 q^{88} - 51 q^{89} - 5 q^{90} - 37 q^{91} + 11 q^{92} - 21 q^{93} + 8 q^{94} - 35 q^{95} - 14 q^{96} - 29 q^{97} + 32 q^{98} - 13 q^{99}+O(q^{100}) \) 23 * q - 5 * q^2 + 23 * q^3 + 9 * q^4 + 23 * q^5 - 5 * q^6 - 16 * q^7 - 12 * q^8 + 23 * q^9 - 5 * q^10 - 13 * q^11 + 9 * q^12 - 18 * q^13 - 6 * q^14 + 23 * q^15 - 11 * q^16 - 34 * q^17 - 5 * q^18 - 35 * q^19 + 9 * q^20 - 16 * q^21 - 11 * q^22 - 14 * q^23 - 12 * q^24 + 23 * q^25 - 6 * q^26 + 23 * q^27 - 26 * q^28 - 43 * q^29 - 5 * q^30 - 21 * q^31 - 14 * q^32 - 13 * q^33 - 12 * q^34 - 16 * q^35 + 9 * q^36 - 18 * q^37 + 6 * q^38 - 18 * q^39 - 12 * q^40 - 45 * q^41 - 6 * q^42 - 43 * q^43 - 11 * q^44 + 23 * q^45 - 29 * q^46 - 14 * q^47 - 11 * q^48 - 25 * q^49 - 5 * q^50 - 34 * q^51 - 20 * q^52 - 3 * q^53 - 5 * q^54 - 13 * q^55 + 3 * q^56 - 35 * q^57 + 10 * q^58 - 9 * q^59 + 9 * q^60 - 67 * q^61 - 7 * q^62 - 16 * q^63 - 8 * q^64 - 18 * q^65 - 11 * q^66 - 32 * q^67 - 24 * q^68 - 14 * q^69 - 6 * q^70 - 8 * q^71 - 12 * q^72 - 39 * q^73 - 16 * q^74 + 23 * q^75 - 48 * q^76 - 26 * q^77 - 6 * q^78 - 59 * q^79 - 11 * q^80 + 23 * q^81 - q^82 - 23 * q^83 - 26 * q^84 - 34 * q^85 - 7 * q^86 - 43 * q^87 + 17 * q^88 - 51 * q^89 - 5 * q^90 - 37 * q^91 + 11 * q^92 - 21 * q^93 + 8 * q^94 - 35 * q^95 - 14 * q^96 - 29 * q^97 + 32 * q^98 - 13 * q^99

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