LMFDB - Embedded newform 6015.2.a.b.1.14

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			1.14
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)

$f(q)$	$=$	$q+0.186838 q^{2} +1.00000 q^{3} -1.96509 q^{4} +1.00000 q^{5} +0.186838 q^{6} -4.07485 q^{7} -0.740831 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.186838 q^{2} +1.00000 q^{3} -1.96509 q^{4} +1.00000 q^{5} +0.186838 q^{6} -4.07485 q^{7} -0.740831 q^{8} +1.00000 q^{9} +0.186838 q^{10} +0.161051 q^{11} -1.96509 q^{12} +1.47616 q^{13} -0.761338 q^{14} +1.00000 q^{15} +3.79177 q^{16} -0.638444 q^{17} +0.186838 q^{18} -0.838924 q^{19} -1.96509 q^{20} -4.07485 q^{21} +0.0300904 q^{22} +3.94446 q^{23} -0.740831 q^{24} +1.00000 q^{25} +0.275803 q^{26} +1.00000 q^{27} +8.00745 q^{28} +1.84716 q^{29} +0.186838 q^{30} +2.61862 q^{31} +2.19011 q^{32} +0.161051 q^{33} -0.119286 q^{34} -4.07485 q^{35} -1.96509 q^{36} -6.87973 q^{37} -0.156743 q^{38} +1.47616 q^{39} -0.740831 q^{40} -5.16521 q^{41} -0.761338 q^{42} -7.35526 q^{43} -0.316479 q^{44} +1.00000 q^{45} +0.736976 q^{46} +5.46418 q^{47} +3.79177 q^{48} +9.60440 q^{49} +0.186838 q^{50} -0.638444 q^{51} -2.90078 q^{52} -0.683802 q^{53} +0.186838 q^{54} +0.161051 q^{55} +3.01877 q^{56} -0.838924 q^{57} +0.345120 q^{58} -1.45440 q^{59} -1.96509 q^{60} -10.0127 q^{61} +0.489259 q^{62} -4.07485 q^{63} -7.17434 q^{64} +1.47616 q^{65} +0.0300904 q^{66} +11.7658 q^{67} +1.25460 q^{68} +3.94446 q^{69} -0.761338 q^{70} -3.88712 q^{71} -0.740831 q^{72} +8.35402 q^{73} -1.28540 q^{74} +1.00000 q^{75} +1.64856 q^{76} -0.656258 q^{77} +0.275803 q^{78} +9.06353 q^{79} +3.79177 q^{80} +1.00000 q^{81} -0.965058 q^{82} -12.0792 q^{83} +8.00745 q^{84} -0.638444 q^{85} -1.37424 q^{86} +1.84716 q^{87} -0.119311 q^{88} +17.7140 q^{89} +0.186838 q^{90} -6.01512 q^{91} -7.75123 q^{92} +2.61862 q^{93} +1.02092 q^{94} -0.838924 q^{95} +2.19011 q^{96} -7.34207 q^{97} +1.79447 q^{98} +0.161051 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.186838	0.132115	0.0660573	−	0.997816i	$-0.478958\pi$
$2$	0.186838	0.132115	0.0660573	+	0.997816i	$0.478958\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.96509	−0.982546
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0.186838	0.0762764
$7$	−4.07485	−1.54015	−0.770074	−	0.637954i	$-0.779781\pi$
$7$	−4.07485	−1.54015	−0.770074	+	0.637954i	$0.779781\pi$
$8$	−0.740831	−0.261923
$9$	1.00000	0.333333
$10$	0.186838	0.0590834
$11$	0.161051	0.0485586	0.0242793	−	0.999705i	$-0.492271\pi$
$11$	0.161051	0.0485586	0.0242793	+	0.999705i	$0.492271\pi$
$12$	−1.96509	−0.567273
$13$	1.47616	0.409412	0.204706	−	0.978823i	$-0.434376\pi$
$13$	1.47616	0.409412	0.204706	+	0.978823i	$0.434376\pi$
$14$	−0.761338	−0.203476
$15$	1.00000	0.258199
$16$	3.79177	0.947942
$17$	−0.638444	−0.154845	−0.0774227	−	0.996998i	$-0.524669\pi$
$17$	−0.638444	−0.154845	−0.0774227	+	0.996998i	$0.524669\pi$
$18$	0.186838	0.0440382
$19$	−0.838924	−0.192462	−0.0962312	−	0.995359i	$-0.530679\pi$
$19$	−0.838924	−0.192462	−0.0962312	+	0.995359i	$0.530679\pi$
$20$	−1.96509	−0.439408
$21$	−4.07485	−0.889205
$22$	0.0300904	0.00641530
$23$	3.94446	0.822477	0.411239	−	0.911528i	$-0.365096\pi$
$23$	3.94446	0.822477	0.411239	+	0.911528i	$0.365096\pi$
$24$	−0.740831	−0.151221
$25$	1.00000	0.200000
$26$	0.275803	0.0540893
$27$	1.00000	0.192450
$28$	8.00745	1.51327
$29$	1.84716	0.343009	0.171504	−	0.985183i	$-0.445137\pi$
$29$	1.84716	0.343009	0.171504	+	0.985183i	$0.445137\pi$
$30$	0.186838	0.0341118
$31$	2.61862	0.470318	0.235159	−	0.971957i	$-0.424439\pi$
$31$	2.61862	0.470318	0.235159	+	0.971957i	$0.424439\pi$
$32$	2.19011	0.387160
$33$	0.161051	0.0280353
$34$	−0.119286	−0.0204573
$35$	−4.07485	−0.688775
$36$	−1.96509	−0.327515
$37$	−6.87973	−1.13102	−0.565510	−	0.824741i	$-0.691321\pi$
$37$	−6.87973	−1.13102	−0.565510	+	0.824741i	$0.691321\pi$
$38$	−0.156743	−0.0254271
$39$	1.47616	0.236374
$40$	−0.740831	−0.117136
$41$	−5.16521	−0.806670	−0.403335	−	0.915052i	$-0.632149\pi$
$41$	−5.16521	−0.806670	−0.403335	+	0.915052i	$0.632149\pi$
$42$	−0.761338	−0.117477
$43$	−7.35526	−1.12167	−0.560833	−	0.827929i	$-0.689519\pi$
$43$	−7.35526	−1.12167	−0.560833	+	0.827929i	$0.689519\pi$
$44$	−0.316479	−0.0477111
$45$	1.00000	0.149071
$46$	0.736976	0.108661
$47$	5.46418	0.797032	0.398516	−	0.917161i	$-0.369525\pi$
$47$	5.46418	0.797032	0.398516	+	0.917161i	$0.369525\pi$
$48$	3.79177	0.547294
$49$	9.60440	1.37206
$50$	0.186838	0.0264229
$51$	−0.638444	−0.0894001
$52$	−2.90078	−0.402266
$53$	−0.683802	−0.0939274	−0.0469637	−	0.998897i	$-0.514955\pi$
$53$	−0.683802	−0.0939274	−0.0469637	+	0.998897i	$0.514955\pi$
$54$	0.186838	0.0254255
$55$	0.161051	0.0217161
$56$	3.01877	0.403401
$57$	−0.838924	−0.111118
$58$	0.345120	0.0453164
$59$	−1.45440	−0.189346	−0.0946731	−	0.995508i	$-0.530181\pi$
$59$	−1.45440	−0.189346	−0.0946731	+	0.995508i	$0.530181\pi$
$60$	−1.96509	−0.253692
$61$	−10.0127	−1.28199	−0.640995	−	0.767545i	$-0.721478\pi$
$61$	−10.0127	−1.28199	−0.640995	+	0.767545i	$0.721478\pi$
$62$	0.489259	0.0621359
$63$	−4.07485	−0.513383
$64$	−7.17434	−0.896792
$65$	1.47616	0.183095
$66$	0.0300904	0.00370388
$67$	11.7658	1.43742	0.718710	−	0.695310i	$-0.244733\pi$
$67$	11.7658	1.43742	0.718710	+	0.695310i	$0.244733\pi$
$68$	1.25460	0.152143
$69$	3.94446	0.474857
$70$	−0.761338	−0.0909973
$71$	−3.88712	−0.461317	−0.230658	−	0.973035i	$-0.574088\pi$
$71$	−3.88712	−0.461317	−0.230658	+	0.973035i	$0.574088\pi$
$72$	−0.740831	−0.0873077
$73$	8.35402	0.977764	0.488882	−	0.872350i	$-0.337405\pi$
$73$	8.35402	0.977764	0.488882	+	0.872350i	$0.337405\pi$
$74$	−1.28540	−0.149424
$75$	1.00000	0.115470
$76$	1.64856	0.189103
$77$	−0.656258	−0.0747875
$78$	0.275803	0.0312285
$79$	9.06353	1.01973	0.509863	−	0.860255i	$-0.329696\pi$
$79$	9.06353	1.01973	0.509863	+	0.860255i	$0.329696\pi$
$80$	3.79177	0.423932
$81$	1.00000	0.111111
$82$	−0.965058	−0.106573
$83$	−12.0792	−1.32587	−0.662934	−	0.748678i	$-0.730689\pi$
$83$	−12.0792	−1.32587	−0.662934	+	0.748678i	$0.730689\pi$
$84$	8.00745	0.873685
$85$	−0.638444	−0.0692490
$86$	−1.37424	−0.148189
$87$	1.84716	0.198036
$88$	−0.119311	−0.0127186
$89$	17.7140	1.87769	0.938843	−	0.344346i	$-0.111899\pi$
$89$	17.7140	1.87769	0.938843	+	0.344346i	$0.111899\pi$
$90$	0.186838	0.0196945
$91$	−6.01512	−0.630556
$92$	−7.75123	−0.808121
$93$	2.61862	0.271538
$94$	1.02092	0.105300
$95$	−0.838924	−0.0860718
$96$	2.19011	0.223527
$97$	−7.34207	−0.745474	−0.372737	−	0.927937i	$-0.621581\pi$
$97$	−7.34207	−0.745474	−0.372737	+	0.927937i	$0.621581\pi$
$98$	1.79447	0.181269
$99$	0.161051	0.0161862
$100$	−1.96509	−0.196509
$101$	−19.2666	−1.91709	−0.958547	−	0.284934i	$-0.908028\pi$
$101$	−19.2666	−1.91709	−0.958547	+	0.284934i	$0.908028\pi$
$102$	−0.119286	−0.0118111
$103$	8.82753	0.869802	0.434901	−	0.900478i	$-0.356783\pi$
$103$	8.82753	0.869802	0.434901	+	0.900478i	$0.356783\pi$
$104$	−1.09358	−0.107235
$105$	−4.07485	−0.397665
$106$	−0.127760	−0.0124092
$107$	−14.4835	−1.40017	−0.700087	−	0.714058i	$-0.746855\pi$
$107$	−14.4835	−1.40017	−0.700087	+	0.714058i	$0.746855\pi$
$108$	−1.96509	−0.189091
$109$	−3.96313	−0.379599	−0.189799	−	0.981823i	$-0.560784\pi$
$109$	−3.96313	−0.379599	−0.189799	+	0.981823i	$0.560784\pi$
$110$	0.0300904	0.00286901
$111$	−6.87973	−0.652995
$112$	−15.4509	−1.45997
$113$	−4.40732	−0.414605	−0.207303	−	0.978277i	$-0.566468\pi$
$113$	−4.40732	−0.414605	−0.207303	+	0.978277i	$0.566468\pi$
$114$	−0.156743	−0.0146803
$115$	3.94446	0.367823
$116$	−3.62983	−0.337022
$117$	1.47616	0.136471
$118$	−0.271737	−0.0250154
$119$	2.60156	0.238485
$120$	−0.740831	−0.0676283
$121$	−10.9741	−0.997642
$122$	−1.87075	−0.169370
$123$	−5.16521	−0.465731
$124$	−5.14583	−0.462109
$125$	1.00000	0.0894427
$126$	−0.761338	−0.0678253
$127$	−7.16162	−0.635491	−0.317746	−	0.948176i	$-0.602926\pi$
$127$	−7.16162	−0.635491	−0.317746	+	0.948176i	$0.602926\pi$
$128$	−5.72066	−0.505639
$129$	−7.35526	−0.647595
$130$	0.275803	0.0241895
$131$	−2.76058	−0.241193	−0.120596	−	0.992702i	$-0.538481\pi$
$131$	−2.76058	−0.241193	−0.120596	+	0.992702i	$0.538481\pi$
$132$	−0.316479	−0.0275460
$133$	3.41849	0.296421
$134$	2.19830	0.189904
$135$	1.00000	0.0860663
$136$	0.472979	0.0405576
$137$	−12.9273	−1.10445	−0.552226	−	0.833695i	$-0.686221\pi$
$137$	−12.9273	−1.10445	−0.552226	+	0.833695i	$0.686221\pi$
$138$	0.736976	0.0627356
$139$	−13.0947	−1.11068	−0.555341	−	0.831623i	$-0.687412\pi$
$139$	−13.0947	−1.11068	−0.555341	+	0.831623i	$0.687412\pi$
$140$	8.00745	0.676753
$141$	5.46418	0.460167
$142$	−0.726263	−0.0609467
$143$	0.237736	0.0198805
$144$	3.79177	0.315981
$145$	1.84716	0.153398
$146$	1.56085	0.129177
$147$	9.60440	0.792158
$148$	13.5193	1.11128
$149$	−6.37806	−0.522511	−0.261255	−	0.965270i	$-0.584136\pi$
$149$	−6.37806	−0.522511	−0.261255	+	0.965270i	$0.584136\pi$
$150$	0.186838	0.0152553
$151$	−20.4591	−1.66494	−0.832470	−	0.554070i	$-0.813074\pi$
$151$	−20.4591	−1.66494	−0.832470	+	0.554070i	$0.813074\pi$
$152$	0.621500	0.0504103
$153$	−0.638444	−0.0516152
$154$	−0.122614	−0.00988052
$155$	2.61862	0.210333
$156$	−2.90078	−0.232249
$157$	21.5778	1.72209	0.861047	−	0.508525i	$-0.169809\pi$
$157$	21.5778	1.72209	0.861047	+	0.508525i	$0.169809\pi$
$158$	1.69341	0.134721
$159$	−0.683802	−0.0542290
$160$	2.19011	0.173143
$161$	−16.0731	−1.26674
$162$	0.186838	0.0146794
$163$	23.4843	1.83943	0.919715	−	0.392586i	$-0.128419\pi$
$163$	23.4843	1.83943	0.919715	+	0.392586i	$0.128419\pi$
$164$	10.1501	0.792590
$165$	0.161051	0.0125378
$166$	−2.25686	−0.175166
$167$	−8.71167	−0.674130	−0.337065	−	0.941481i	$-0.609434\pi$
$167$	−8.71167	−0.674130	−0.337065	+	0.941481i	$0.609434\pi$
$168$	3.01877	0.232903
$169$	−10.8210	−0.832381
$170$	−0.119286	−0.00914880
$171$	−0.838924	−0.0641541
$172$	14.4538	1.10209
$173$	−14.6529	−1.11404	−0.557021	−	0.830499i	$-0.688056\pi$
$173$	−14.6529	−1.11404	−0.557021	+	0.830499i	$0.688056\pi$
$174$	0.345120	0.0261635
$175$	−4.07485	−0.308030
$176$	0.610667	0.0460308
$177$	−1.45440	−0.109319
$178$	3.30966	0.248070
$179$	2.21079	0.165242	0.0826212	−	0.996581i	$-0.473671\pi$
$179$	2.21079	0.165242	0.0826212	+	0.996581i	$0.473671\pi$
$180$	−1.96509	−0.146469
$181$	6.58405	0.489388	0.244694	−	0.969600i	$-0.421312\pi$
$181$	6.58405	0.489388	0.244694	+	0.969600i	$0.421312\pi$
$182$	−1.12385	−0.0833056
$183$	−10.0127	−0.740158
$184$	−2.92218	−0.215426
$185$	−6.87973	−0.505807
$186$	0.489259	0.0358742
$187$	−0.102822	−0.00751908
$188$	−10.7376	−0.783121
$189$	−4.07485	−0.296402
$190$	−0.156743	−0.0113713
$191$	−14.3247	−1.03650	−0.518248	−	0.855230i	$-0.673416\pi$
$191$	−14.3247	−1.03650	−0.518248	+	0.855230i	$0.673416\pi$
$192$	−7.17434	−0.517763
$193$	−11.3506	−0.817033	−0.408516	−	0.912751i	$-0.633954\pi$
$193$	−11.3506	−0.817033	−0.408516	+	0.912751i	$0.633954\pi$
$194$	−1.37178	−0.0984880
$195$	1.47616	0.105710
$196$	−18.8735	−1.34811
$197$	−14.1555	−1.00854	−0.504270	−	0.863546i	$-0.668238\pi$
$197$	−14.1555	−1.00854	−0.504270	+	0.863546i	$0.668238\pi$
$198$	0.0300904	0.00213843
$199$	−2.67713	−0.189777	−0.0948884	−	0.995488i	$-0.530249\pi$
$199$	−2.67713	−0.189777	−0.0948884	+	0.995488i	$0.530249\pi$
$200$	−0.740831	−0.0523846
$201$	11.7658	0.829895
$202$	−3.59973	−0.253276
$203$	−7.52689	−0.528284
$204$	1.25460	0.0878397
$205$	−5.16521	−0.360754
$206$	1.64932	0.114913
$207$	3.94446	0.274159
$208$	5.59725	0.388099
$209$	−0.135109	−0.00934571
$210$	−0.761338	−0.0525373
$211$	5.21971	0.359339	0.179670	−	0.983727i	$-0.442497\pi$
$211$	5.21971	0.359339	0.179670	+	0.983727i	$0.442497\pi$
$212$	1.34373	0.0922879
$213$	−3.88712	−0.266341
$214$	−2.70607	−0.184983
$215$	−7.35526	−0.501625
$216$	−0.740831	−0.0504071
$217$	−10.6705	−0.724360
$218$	−0.740463	−0.0501505
$219$	8.35402	0.564512
$220$	−0.316479	−0.0213370
$221$	−0.942444	−0.0633957
$222$	−1.28540	−0.0862701
$223$	9.22363	0.617660	0.308830	−	0.951117i	$-0.400063\pi$
$223$	9.22363	0.617660	0.308830	+	0.951117i	$0.400063\pi$
$224$	−8.92436	−0.596284
$225$	1.00000	0.0666667
$226$	−0.823455	−0.0547754
$227$	17.6807	1.17351	0.586756	−	0.809764i	$-0.300405\pi$
$227$	17.6807	1.17351	0.586756	+	0.809764i	$0.300405\pi$
$228$	1.64856	0.109179
$229$	−4.37590	−0.289168	−0.144584	−	0.989493i	$-0.546184\pi$
$229$	−4.37590	−0.289168	−0.144584	+	0.989493i	$0.546184\pi$
$230$	0.736976	0.0485948
$231$	−0.656258	−0.0431786
$232$	−1.36843	−0.0898419
$233$	19.2585	1.26166	0.630832	−	0.775920i	$-0.282714\pi$
$233$	19.2585	1.26166	0.630832	+	0.775920i	$0.282714\pi$
$234$	0.275803	0.0180298
$235$	5.46418	0.356444
$236$	2.85802	0.186041
$237$	9.06353	0.588740
$238$	0.486072	0.0315073
$239$	−22.1007	−1.42958	−0.714788	−	0.699341i	$-0.753477\pi$
$239$	−22.1007	−1.42958	−0.714788	+	0.699341i	$0.753477\pi$
$240$	3.79177	0.244758
$241$	−11.6031	−0.747423	−0.373711	−	0.927545i	$-0.621915\pi$
$241$	−11.6031	−0.747423	−0.373711	+	0.927545i	$0.621915\pi$
$242$	−2.05037	−0.131803
$243$	1.00000	0.0641500
$244$	19.6758	1.25961
$245$	9.60440	0.613603
$246$	−0.965058	−0.0615298
$247$	−1.23838	−0.0787965
$248$	−1.93996	−0.123187
$249$	−12.0792	−0.765490
$250$	0.186838	0.0118167
$251$	−22.9614	−1.44931	−0.724655	−	0.689112i	$-0.758001\pi$
$251$	−22.9614	−1.44931	−0.724655	+	0.689112i	$0.758001\pi$
$252$	8.00745	0.504422
$253$	0.635258	0.0399384
$254$	−1.33806	−0.0839576
$255$	−0.638444	−0.0399809
$256$	13.2798	0.829990
$257$	−14.1323	−0.881547	−0.440774	−	0.897618i	$-0.645296\pi$
$257$	−14.1323	−0.881547	−0.440774	+	0.897618i	$0.645296\pi$
$258$	−1.37424	−0.0855567
$259$	28.0338	1.74194
$260$	−2.90078	−0.179899
$261$	1.84716	0.114336
$262$	−0.515781	−0.0318651
$263$	−23.7377	−1.46373	−0.731864	−	0.681451i	$-0.761349\pi$
$263$	−23.7377	−1.46373	−0.731864	+	0.681451i	$0.761349\pi$
$264$	−0.119311	−0.00734310
$265$	−0.683802	−0.0420056
$266$	0.638704	0.0391615
$267$	17.7140	1.08408
$268$	−23.1208	−1.41233
$269$	−0.309154	−0.0188494	−0.00942472	−	0.999956i	$-0.503000\pi$
$269$	−0.309154	−0.0188494	−0.00942472	+	0.999956i	$0.503000\pi$
$270$	0.186838	0.0113706
$271$	−14.4718	−0.879102	−0.439551	−	0.898218i	$-0.644862\pi$
$271$	−14.4718	−0.879102	−0.439551	+	0.898218i	$0.644862\pi$
$272$	−2.42083	−0.146785
$273$	−6.01512	−0.364052
$274$	−2.41531	−0.145914
$275$	0.161051	0.00971173
$276$	−7.75123	−0.466569
$277$	13.7450	0.825856	0.412928	−	0.910764i	$-0.364506\pi$
$277$	13.7450	0.825856	0.412928	+	0.910764i	$0.364506\pi$
$278$	−2.44660	−0.146737
$279$	2.61862	0.156773
$280$	3.01877	0.180406
$281$	2.26839	0.135321	0.0676603	−	0.997708i	$-0.478447\pi$
$281$	2.26839	0.135321	0.0676603	+	0.997708i	$0.478447\pi$
$282$	1.02092	0.0607947
$283$	−19.9985	−1.18879	−0.594393	−	0.804174i	$-0.702608\pi$
$283$	−19.9985	−1.18879	−0.594393	+	0.804174i	$0.702608\pi$
$284$	7.63856	0.453265
$285$	−0.838924	−0.0496936
$286$	0.0444182	0.00262650
$287$	21.0474	1.24239
$288$	2.19011	0.129053
$289$	−16.5924	−0.976023
$290$	0.345120	0.0202661
$291$	−7.34207	−0.430400
$292$	−16.4164	−0.960698
$293$	0.763585	0.0446091	0.0223046	−	0.999751i	$-0.492900\pi$
$293$	0.763585	0.0446091	0.0223046	+	0.999751i	$0.492900\pi$
$294$	1.79447	0.104656
$295$	−1.45440	−0.0846782
$296$	5.09671	0.296240
$297$	0.161051	0.00934511
$298$	−1.19166	−0.0690313
$299$	5.82265	0.336732
$300$	−1.96509	−0.113455
$301$	29.9716	1.72753
$302$	−3.82255	−0.219963
$303$	−19.2666	−1.10683
$304$	−3.18100	−0.182443
$305$	−10.0127	−0.573324
$306$	−0.119286	−0.00681911
$307$	−32.9690	−1.88164	−0.940820	−	0.338908i	$-0.889943\pi$
$307$	−32.9690	−1.88164	−0.940820	+	0.338908i	$0.889943\pi$
$308$	1.28961	0.0734821
$309$	8.82753	0.502180
$310$	0.489259	0.0277880
$311$	6.36343	0.360837	0.180418	−	0.983590i	$-0.442255\pi$
$311$	6.36343	0.360837	0.180418	+	0.983590i	$0.442255\pi$
$312$	−1.09358	−0.0619119
$313$	18.8908	1.06777	0.533886	−	0.845556i	$-0.320731\pi$
$313$	18.8908	1.06777	0.533886	+	0.845556i	$0.320731\pi$
$314$	4.03156	0.227514
$315$	−4.07485	−0.229592
$316$	−17.8107	−1.00193
$317$	24.0827	1.35262	0.676308	−	0.736619i	$-0.263579\pi$
$317$	24.0827	1.35262	0.676308	+	0.736619i	$0.263579\pi$
$318$	−0.127760	−0.00716444
$319$	0.297486	0.0166560
$320$	−7.17434	−0.401058
$321$	−14.4835	−0.808390
$322$	−3.00307	−0.167354
$323$	0.535606	0.0298019
$324$	−1.96509	−0.109172
$325$	1.47616	0.0818825
$326$	4.38776	0.243016
$327$	−3.96313	−0.219161
$328$	3.82654	0.211285
$329$	−22.2657	−1.22755
$330$	0.0300904	0.00165642
$331$	12.4552	0.684598	0.342299	−	0.939591i	$-0.388794\pi$
$331$	12.4552	0.684598	0.342299	+	0.939591i	$0.388794\pi$
$332$	23.7368	1.30273
$333$	−6.87973	−0.377007
$334$	−1.62767	−0.0890623
$335$	11.7658	0.642834
$336$	−15.4509	−0.842915
$337$	−35.5018	−1.93390	−0.966952	−	0.254959i	$-0.917938\pi$
$337$	−35.5018	−1.93390	−0.966952	+	0.254959i	$0.917938\pi$
$338$	−2.02177	−0.109970
$339$	−4.40732	−0.239372
$340$	1.25460	0.0680403
$341$	0.421731	0.0228380
$342$	−0.156743	−0.00847569
$343$	−10.6125	−0.573023
$344$	5.44900	0.293790
$345$	3.94446	0.212363
$346$	−2.73773	−0.147181
$347$	10.8716	0.583616	0.291808	−	0.956477i	$-0.405743\pi$
$347$	10.8716	0.583616	0.291808	+	0.956477i	$0.405743\pi$
$348$	−3.62983	−0.194580
$349$	1.08829	0.0582547	0.0291274	−	0.999576i	$-0.490727\pi$
$349$	1.08829	0.0582547	0.0291274	+	0.999576i	$0.490727\pi$
$350$	−0.761338	−0.0406952
$351$	1.47616	0.0787915
$352$	0.352719	0.0188000
$353$	−11.6113	−0.618005	−0.309002	−	0.951061i	$-0.599995\pi$
$353$	−11.6113	−0.618005	−0.309002	+	0.951061i	$0.599995\pi$
$354$	−0.271737	−0.0144426
$355$	−3.88712	−0.206307
$356$	−34.8097	−1.84491
$357$	2.60156	0.137689
$358$	0.413061	0.0218309
$359$	16.1388	0.851771	0.425885	−	0.904777i	$-0.359963\pi$
$359$	16.1388	0.851771	0.425885	+	0.904777i	$0.359963\pi$
$360$	−0.740831	−0.0390452
$361$	−18.2962	−0.962958
$362$	1.23015	0.0646553
$363$	−10.9741	−0.575989
$364$	11.8203	0.619550
$365$	8.35402	0.437269
$366$	−1.87075	−0.0977856
$367$	−12.9802	−0.677558	−0.338779	−	0.940866i	$-0.610014\pi$
$367$	−12.9802	−0.677558	−0.338779	+	0.940866i	$0.610014\pi$
$368$	14.9565	0.779660
$369$	−5.16521	−0.268890
$370$	−1.28540	−0.0668245
$371$	2.78639	0.144662
$372$	−5.14583	−0.266799
$373$	16.4067	0.849505	0.424752	−	0.905310i	$-0.360361\pi$
$373$	16.4067	0.849505	0.424752	+	0.905310i	$0.360361\pi$
$374$	−0.0192111	−0.000993380 0
$375$	1.00000	0.0516398
$376$	−4.04803	−0.208761
$377$	2.72670	0.140432
$378$	−0.761338	−0.0391590
$379$	−2.07847	−0.106764	−0.0533820	−	0.998574i	$-0.517000\pi$
$379$	−2.07847	−0.106764	−0.0533820	+	0.998574i	$0.517000\pi$
$380$	1.64856	0.0845694
$381$	−7.16162	−0.366901
$382$	−2.67639	−0.136936
$383$	−14.7629	−0.754350	−0.377175	−	0.926142i	$-0.623104\pi$
$383$	−14.7629	−0.754350	−0.377175	+	0.926142i	$0.623104\pi$
$384$	−5.72066	−0.291931
$385$	−0.656258	−0.0334460
$386$	−2.12072	−0.107942
$387$	−7.35526	−0.373889
$388$	14.4278	0.732462
$389$	−21.1426	−1.07197	−0.535986	−	0.844227i	$-0.680060\pi$
$389$	−21.1426	−1.07197	−0.535986	+	0.844227i	$0.680060\pi$
$390$	0.275803	0.0139658
$391$	−2.51832	−0.127357
$392$	−7.11523	−0.359374
$393$	−2.76058	−0.139253
$394$	−2.64479	−0.133243
$395$	9.06353	0.456036
$396$	−0.316479	−0.0159037
$397$	7.20188	0.361452	0.180726	−	0.983533i	$-0.442155\pi$
$397$	7.20188	0.361452	0.180726	+	0.983533i	$0.442155\pi$
$398$	−0.500191	−0.0250723
$399$	3.41849	0.171138
$400$	3.79177	0.189588
$401$	−1.00000	−0.0499376
$401$	−1.00000	−0.0499376
$402$	2.19830	0.109641
$403$	3.86550	0.192554
$404$	37.8605	1.88363
$405$	1.00000	0.0496904
$406$	−1.40631	−0.0697940
$407$	−1.10798	−0.0549208
$408$	0.472979	0.0234160
$409$	0.174929	0.00864966	0.00432483	−	0.999991i	$-0.498623\pi$
$409$	0.174929	0.00864966	0.00432483	+	0.999991i	$0.498623\pi$
$410$	−0.965058	−0.0476608
$411$	−12.9273	−0.637655
$412$	−17.3469	−0.854620
$413$	5.92644	0.291621
$414$	0.736976	0.0362204
$415$	−12.0792	−0.592946
$416$	3.23294	0.158508
$417$	−13.0947	−0.641253
$418$	−0.0252436	−0.00123470
$419$	19.4689	0.951120	0.475560	−	0.879683i	$-0.342245\pi$
$419$	19.4689	0.951120	0.475560	+	0.879683i	$0.342245\pi$
$420$	8.00745	0.390724
$421$	11.6190	0.566278	0.283139	−	0.959079i	$-0.408624\pi$
$421$	11.6190	0.566278	0.283139	+	0.959079i	$0.408624\pi$
$422$	0.975241	0.0474740
$423$	5.46418	0.265677
$424$	0.506581	0.0246018
$425$	−0.638444	−0.0309691
$426$	−0.726263	−0.0351876
$427$	40.8001	1.97446
$428$	28.4614	1.37573
$429$	0.237736	0.0114780
$430$	−1.37424	−0.0662719
$431$	29.0334	1.39849	0.699246	−	0.714881i	$-0.253519\pi$
$431$	29.0334	1.39849	0.699246	+	0.714881i	$0.253519\pi$
$432$	3.79177	0.182431
$433$	36.1206	1.73584	0.867922	−	0.496701i	$-0.165455\pi$
$433$	36.1206	1.73584	0.867922	+	0.496701i	$0.165455\pi$
$434$	−1.99366	−0.0956985
$435$	1.84716	0.0885644
$436$	7.78790	0.372973
$437$	−3.30910	−0.158296
$438$	1.56085	0.0745803
$439$	−1.68055	−0.0802081	−0.0401040	−	0.999196i	$-0.512769\pi$
$439$	−1.68055	−0.0802081	−0.0401040	+	0.999196i	$0.512769\pi$
$440$	−0.119311	−0.00568794
$441$	9.60440	0.457352
$442$	−0.176085	−0.00837549
$443$	3.89075	0.184855	0.0924276	−	0.995719i	$-0.470537\pi$
$443$	3.89075	0.184855	0.0924276	+	0.995719i	$0.470537\pi$
$444$	13.5193	0.641597
$445$	17.7140	0.839726
$446$	1.72333	0.0816019
$447$	−6.37806	−0.301672
$448$	29.2344	1.38119
$449$	−24.9164	−1.17588	−0.587939	−	0.808905i	$-0.700060\pi$
$449$	−24.9164	−1.17588	−0.587939	+	0.808905i	$0.700060\pi$
$450$	0.186838	0.00880764
$451$	−0.831860	−0.0391708
$452$	8.66078	0.407369
$453$	−20.4591	−0.961254
$454$	3.30344	0.155038
$455$	−6.01512	−0.281993
$456$	0.621500	0.0291044
$457$	−11.3454	−0.530717	−0.265358	−	0.964150i	$-0.585490\pi$
$457$	−11.3454	−0.530717	−0.265358	+	0.964150i	$0.585490\pi$
$458$	−0.817586	−0.0382033
$459$	−0.638444	−0.0298000
$460$	−7.75123	−0.361403
$461$	−13.5296	−0.630135	−0.315067	−	0.949069i	$-0.602027\pi$
$461$	−13.5296	−0.630135	−0.315067	+	0.949069i	$0.602027\pi$
$462$	−0.122614	−0.00570452
$463$	17.3367	0.805706	0.402853	−	0.915265i	$-0.368019\pi$
$463$	17.3367	0.805706	0.402853	+	0.915265i	$0.368019\pi$
$464$	7.00399	0.325152
$465$	2.61862	0.121436
$466$	3.59821	0.166684
$467$	34.9218	1.61599	0.807993	−	0.589192i	$-0.200554\pi$
$467$	34.9218	1.61599	0.807993	+	0.589192i	$0.200554\pi$
$468$	−2.90078	−0.134089
$469$	−47.9438	−2.21384
$470$	1.02092	0.0470914
$471$	21.5778	0.994252
$472$	1.07746	0.0495941
$473$	−1.18457	−0.0544666
$474$	1.69341	0.0777811
$475$	−0.838924	−0.0384925
$476$	−5.11231	−0.234322
$477$	−0.683802	−0.0313091
$478$	−4.12926	−0.188868
$479$	20.4434	0.934082	0.467041	−	0.884236i	$-0.345320\pi$
$479$	20.4434	0.934082	0.467041	+	0.884236i	$0.345320\pi$
$480$	2.19011	0.0999643
$481$	−10.1556	−0.463054
$482$	−2.16791	−0.0987454
$483$	−16.0731	−0.731351
$484$	21.5650	0.980229
$485$	−7.34207	−0.333386
$486$	0.186838	0.00847515
$487$	15.5064	0.702663	0.351332	−	0.936251i	$-0.385729\pi$
$487$	15.5064	0.702663	0.351332	+	0.936251i	$0.385729\pi$
$488$	7.41769	0.335783
$489$	23.4843	1.06200
$490$	1.79447	0.0810658
$491$	20.7080	0.934540	0.467270	−	0.884115i	$-0.345238\pi$
$491$	20.7080	0.934540	0.467270	+	0.884115i	$0.345238\pi$
$492$	10.1501	0.457602
$493$	−1.17931	−0.0531133
$494$	−0.231377	−0.0104102
$495$	0.161051	0.00723869
$496$	9.92921	0.445835
$497$	15.8395	0.710496
$498$	−2.25686	−0.101132
$499$	26.7800	1.19884	0.599419	−	0.800436i	$-0.295398\pi$
$499$	26.7800	1.19884	0.599419	+	0.800436i	$0.295398\pi$
$500$	−1.96509	−0.0878816
$501$	−8.71167	−0.389209
$502$	−4.29006	−0.191475
$503$	13.5111	0.602430	0.301215	−	0.953556i	$-0.402608\pi$
$503$	13.5111	0.602430	0.301215	+	0.953556i	$0.402608\pi$
$504$	3.01877	0.134467
$505$	−19.2666	−0.857351
$506$	0.118691	0.00527644
$507$	−10.8210	−0.480576
$508$	14.0732	0.624399
$509$	24.8585	1.10183	0.550917	−	0.834560i	$-0.314278\pi$
$509$	24.8585	1.10183	0.550917	+	0.834560i	$0.314278\pi$
$510$	−0.119286	−0.00528206
$511$	−34.0414	−1.50590
$512$	13.9225	0.615293
$513$	−0.838924	−0.0370394
$514$	−2.64045	−0.116465
$515$	8.82753	0.388987
$516$	14.4538	0.636291
$517$	0.880010	0.0387028
$518$	5.23779	0.230135
$519$	−14.6529	−0.643192
$520$	−1.09358	−0.0479568
$521$	17.3999	0.762305	0.381153	−	0.924512i	$-0.375527\pi$
$521$	17.3999	0.762305	0.381153	+	0.924512i	$0.375527\pi$
$522$	0.345120	0.0151055
$523$	−34.3651	−1.50268	−0.751340	−	0.659916i	$-0.770592\pi$
$523$	−34.3651	−1.50268	−0.751340	+	0.659916i	$0.770592\pi$
$524$	5.42479	0.236983
$525$	−4.07485	−0.177841
$526$	−4.43511	−0.193380
$527$	−1.67184	−0.0728267
$528$	0.610667	0.0265759
$529$	−7.44122	−0.323531
$530$	−0.127760	−0.00554955
$531$	−1.45440	−0.0631154
$532$	−6.71764	−0.291247
$533$	−7.62466	−0.330261
$534$	3.30966	0.143223
$535$	−14.4835	−0.626176
$536$	−8.71646	−0.376494
$537$	2.21079	0.0954028
$538$	−0.0577617	−0.00249028
$539$	1.54680	0.0666252
$540$	−1.96509	−0.0845641
$541$	−29.6237	−1.27362	−0.636811	−	0.771020i	$-0.719747\pi$
$541$	−29.6237	−1.27362	−0.636811	+	0.771020i	$0.719747\pi$
$542$	−2.70389	−0.116142
$543$	6.58405	0.282548
$544$	−1.39826	−0.0599500
$545$	−3.96313	−0.169762
$546$	−1.12385	−0.0480965
$547$	22.8564	0.977269	0.488634	−	0.872489i	$-0.337495\pi$
$547$	22.8564	0.977269	0.488634	+	0.872489i	$0.337495\pi$
$548$	25.4033	1.08517
$549$	−10.0127	−0.427330
$550$	0.0300904	0.00128306
$551$	−1.54962	−0.0660162
$552$	−2.92218	−0.124376
$553$	−36.9325	−1.57053
$554$	2.56809	0.109108
$555$	−6.87973	−0.292028
$556$	25.7324	1.09130
$557$	−11.4144	−0.483642	−0.241821	−	0.970321i	$-0.577745\pi$
$557$	−11.4144	−0.483642	−0.241821	+	0.970321i	$0.577745\pi$
$558$	0.489259	0.0207120
$559$	−10.8575	−0.459224
$560$	−15.4509	−0.652919
$561$	−0.102822	−0.00434114
$562$	0.423821	0.0178778
$563$	11.7599	0.495622	0.247811	−	0.968808i	$-0.420289\pi$
$563$	11.7599	0.495622	0.247811	+	0.968808i	$0.420289\pi$
$564$	−10.7376	−0.452135
$565$	−4.40732	−0.185417
$566$	−3.73648	−0.157056
$567$	−4.07485	−0.171128
$568$	2.87970	0.120830
$569$	27.9293	1.17086	0.585428	−	0.810724i	$-0.300926\pi$
$569$	27.9293	1.17086	0.585428	+	0.810724i	$0.300926\pi$
$570$	−0.156743	−0.00656524
$571$	9.77730	0.409167	0.204584	−	0.978849i	$-0.434416\pi$
$571$	9.77730	0.409167	0.204584	+	0.978849i	$0.434416\pi$
$572$	−0.467173	−0.0195335
$573$	−14.3247	−0.598421
$574$	3.93247	0.164138
$575$	3.94446	0.164495
$576$	−7.17434	−0.298931
$577$	−39.1243	−1.62877	−0.814383	−	0.580327i	$-0.802925\pi$
$577$	−39.1243	−1.62877	−0.814383	+	0.580327i	$0.802925\pi$
$578$	−3.10009	−0.128947
$579$	−11.3506	−0.471714
$580$	−3.62983	−0.150721
$581$	49.2211	2.04203
$582$	−1.37178	−0.0568620
$583$	−0.110127	−0.00456098
$584$	−6.18891	−0.256099
$585$	1.47616	0.0610316
$586$	0.142667	0.00589351
$587$	3.18924	0.131634	0.0658170	−	0.997832i	$-0.479035\pi$
$587$	3.18924	0.131634	0.0658170	+	0.997832i	$0.479035\pi$
$588$	−18.8735	−0.778331
$589$	−2.19682	−0.0905186
$590$	−0.271737	−0.0111872
$591$	−14.1555	−0.582281
$592$	−26.0863	−1.07214
$593$	−37.2749	−1.53070	−0.765348	−	0.643616i	$-0.777433\pi$
$593$	−37.2749	−1.53070	−0.765348	+	0.643616i	$0.777433\pi$
$594$	0.0300904	0.00123463
$595$	2.60156	0.106654
$596$	12.5335	0.513391
$597$	−2.67713	−0.109568
$598$	1.08789	0.0444872
$599$	−7.63675	−0.312029	−0.156015	−	0.987755i	$-0.549865\pi$
$599$	−7.63675	−0.312029	−0.156015	+	0.987755i	$0.549865\pi$
$600$	−0.740831	−0.0302443
$601$	31.0443	1.26632	0.633161	−	0.774020i	$-0.281757\pi$
$601$	31.0443	1.26632	0.633161	+	0.774020i	$0.281757\pi$
$602$	5.59984	0.228232
$603$	11.7658	0.479140
$604$	40.2041	1.63588
$605$	−10.9741	−0.446159
$606$	−3.59973	−0.146229
$607$	−2.95854	−0.120083	−0.0600417	−	0.998196i	$-0.519123\pi$
$607$	−2.95854	−0.120083	−0.0600417	+	0.998196i	$0.519123\pi$
$608$	−1.83733	−0.0745137
$609$	−7.52689	−0.305005
$610$	−1.87075	−0.0757444
$611$	8.06599	0.326315
$612$	1.25460	0.0507143
$613$	−18.9845	−0.766776	−0.383388	−	0.923587i	$-0.625243\pi$
$613$	−18.9845	−0.766776	−0.383388	+	0.923587i	$0.625243\pi$
$614$	−6.15987	−0.248592
$615$	−5.16521	−0.208281
$616$	0.486176	0.0195886
$617$	−41.4291	−1.66787	−0.833937	−	0.551860i	$-0.813918\pi$
$617$	−41.4291	−1.66787	−0.833937	+	0.551860i	$0.813918\pi$
$618$	1.64932	0.0663453
$619$	−11.3268	−0.455263	−0.227632	−	0.973747i	$-0.573098\pi$
$619$	−11.3268	−0.455263	−0.227632	+	0.973747i	$0.573098\pi$
$620$	−5.14583	−0.206662
$621$	3.94446	0.158286
$622$	1.18893	0.0476718
$623$	−72.1821	−2.89191
$624$	5.59725	0.224069
$625$	1.00000	0.0400000
$626$	3.52953	0.141068
$627$	−0.135109	−0.00539575
$628$	−42.4023	−1.69204
$629$	4.39232	0.175133
$630$	−0.761338	−0.0303324
$631$	−37.7049	−1.50101	−0.750504	−	0.660866i	$-0.770189\pi$
$631$	−37.7049	−1.50101	−0.750504	+	0.660866i	$0.770189\pi$
$632$	−6.71454	−0.267090
$633$	5.21971	0.207465
$634$	4.49956	0.178700
$635$	−7.16162	−0.284200
$636$	1.34373	0.0532825
$637$	14.1776	0.561737
$638$	0.0555818	0.00220050
$639$	−3.88712	−0.153772
$640$	−5.72066	−0.226129
$641$	−15.5405	−0.613814	−0.306907	−	0.951739i	$-0.599294\pi$
$641$	−15.5405	−0.613814	−0.306907	+	0.951739i	$0.599294\pi$
$642$	−2.70607	−0.106800
$643$	−9.68217	−0.381828	−0.190914	−	0.981607i	$-0.561145\pi$
$643$	−9.68217	−0.381828	−0.190914	+	0.981607i	$0.561145\pi$
$644$	31.5851	1.24463
$645$	−7.35526	−0.289613
$646$	0.100072	0.00393727
$647$	29.9306	1.17669	0.588346	−	0.808609i	$-0.299779\pi$
$647$	29.9306	1.17669	0.588346	+	0.808609i	$0.299779\pi$
$648$	−0.740831	−0.0291026
$649$	−0.234231	−0.00919439
$650$	0.275803	0.0108179
$651$	−10.6705	−0.418210
$652$	−46.1488	−1.80732
$653$	10.6737	0.417694	0.208847	−	0.977948i	$-0.433029\pi$
$653$	10.6737	0.417694	0.208847	+	0.977948i	$0.433029\pi$
$654$	−0.740463	−0.0289544
$655$	−2.76058	−0.107865
$656$	−19.5853	−0.764676
$657$	8.35402	0.325921
$658$	−4.16008	−0.162177
$659$	44.9561	1.75124	0.875620	−	0.483001i	$-0.160453\pi$
$659$	44.9561	1.75124	0.875620	+	0.483001i	$0.160453\pi$
$660$	−0.316479	−0.0123189
$661$	1.73712	0.0675660	0.0337830	−	0.999429i	$-0.489244\pi$
$661$	1.73712	0.0675660	0.0337830	+	0.999429i	$0.489244\pi$
$662$	2.32710	0.0904453
$663$	−0.942444	−0.0366015
$664$	8.94867	0.347276
$665$	3.41849	0.132563
$666$	−1.28540	−0.0498081
$667$	7.28604	0.282117
$668$	17.1192	0.662363
$669$	9.22363	0.356606
$670$	2.19830	0.0849277
$671$	−1.61255	−0.0622517
$672$	−8.92436	−0.344265
$673$	−0.618892	−0.0238565	−0.0119283	−	0.999929i	$-0.503797\pi$
$673$	−0.618892	−0.0238565	−0.0119283	+	0.999929i	$0.503797\pi$
$674$	−6.63308	−0.255497
$675$	1.00000	0.0384900
$676$	21.2642	0.817853
$677$	−28.3427	−1.08930	−0.544649	−	0.838664i	$-0.683337\pi$
$677$	−28.3427	−1.08930	−0.544649	+	0.838664i	$0.683337\pi$
$678$	−0.823455	−0.0316246
$679$	29.9178	1.14814
$680$	0.472979	0.0181379
$681$	17.6807	0.677527
$682$	0.0787955	0.00301723
$683$	1.60999	0.0616044	0.0308022	−	0.999525i	$-0.490194\pi$
$683$	1.60999	0.0616044	0.0308022	+	0.999525i	$0.490194\pi$
$684$	1.64856	0.0630343
$685$	−12.9273	−0.493926
$686$	−1.98283	−0.0757047
$687$	−4.37590	−0.166951
$688$	−27.8894	−1.06327
$689$	−1.00940	−0.0384550
$690$	0.736976	0.0280562
$691$	−32.9745	−1.25441	−0.627204	−	0.778855i	$-0.715801\pi$
$691$	−32.9745	−1.25441	−0.627204	+	0.778855i	$0.715801\pi$
$692$	28.7943	1.09460
$693$	−0.656258	−0.0249292
$694$	2.03122	0.0771042
$695$	−13.0947	−0.496712
$696$	−1.36843	−0.0518702
$697$	3.29770	0.124909
$698$	0.203334	0.00769630
$699$	19.2585	0.728422
$700$	8.00745	0.302653
$701$	−37.1558	−1.40336	−0.701678	−	0.712494i	$-0.747566\pi$
$701$	−37.1558	−1.40336	−0.701678	+	0.712494i	$0.747566\pi$
$702$	0.275803	0.0104095
$703$	5.77157	0.217679
$704$	−1.15543	−0.0435470
$705$	5.46418	0.205793
$706$	−2.16943	−0.0816475
$707$	78.5083	2.95261
$708$	2.85802	0.107411
$709$	18.4787	0.693983	0.346992	−	0.937868i	$-0.387203\pi$
$709$	18.4787	0.693983	0.346992	+	0.937868i	$0.387203\pi$
$710$	−0.726263	−0.0272562
$711$	9.06353	0.339909
$712$	−13.1231	−0.491809
$713$	10.3291	0.386826
$714$	0.486072	0.0181908
$715$	0.237736	0.00889083
$716$	−4.34441	−0.162358
$717$	−22.1007	−0.825366
$718$	3.01534	0.112531
$719$	23.1482	0.863282	0.431641	−	0.902045i	$-0.357935\pi$
$719$	23.1482	0.863282	0.431641	+	0.902045i	$0.357935\pi$
$720$	3.79177	0.141311
$721$	−35.9708	−1.33962
$722$	−3.41843	−0.127221
$723$	−11.6031	−0.431525
$724$	−12.9383	−0.480846
$725$	1.84716	0.0686017
$726$	−2.05037	−0.0760965
$727$	16.8719	0.625742	0.312871	−	0.949796i	$-0.398709\pi$
$727$	16.8719	0.625742	0.312871	+	0.949796i	$0.398709\pi$
$728$	4.45618	0.165157
$729$	1.00000	0.0370370
$730$	1.56085	0.0577696
$731$	4.69592	0.173685
$732$	19.6758	0.727239
$733$	−15.0158	−0.554620	−0.277310	−	0.960780i	$-0.589443\pi$
$733$	−15.0158	−0.554620	−0.277310	+	0.960780i	$0.589443\pi$
$734$	−2.42519	−0.0895153
$735$	9.60440	0.354264
$736$	8.63880	0.318430
$737$	1.89489	0.0697991
$738$	−0.965058	−0.0355243
$739$	−35.4996	−1.30587	−0.652937	−	0.757413i	$-0.726463\pi$
$739$	−35.4996	−1.30587	−0.652937	+	0.757413i	$0.726463\pi$
$740$	13.5193	0.496979
$741$	−1.23838	−0.0454932
$742$	0.520604	0.0191120
$743$	41.3382	1.51655	0.758276	−	0.651934i	$-0.226042\pi$
$743$	41.3382	1.51655	0.758276	+	0.651934i	$0.226042\pi$
$744$	−1.93996	−0.0711222
$745$	−6.37806	−0.233674
$746$	3.06539	0.112232
$747$	−12.0792	−0.441956
$748$	0.202054	0.00738784
$749$	59.0181	2.15647
$750$	0.186838	0.00682237
$751$	−19.2682	−0.703105	−0.351552	−	0.936168i	$-0.614346\pi$
$751$	−19.2682	−0.703105	−0.351552	+	0.936168i	$0.614346\pi$
$752$	20.7189	0.755540
$753$	−22.9614	−0.836759
$754$	0.509451	0.0185531
$755$	−20.4591	−0.744584
$756$	8.00745	0.291228
$757$	0.506386	0.0184049	0.00920246	−	0.999958i	$-0.497071\pi$
$757$	0.506386	0.0184049	0.00920246	+	0.999958i	$0.497071\pi$
$758$	−0.388338	−0.0141051
$759$	0.635258	0.0230584
$760$	0.621500	0.0225442
$761$	26.2824	0.952735	0.476368	−	0.879246i	$-0.341953\pi$
$761$	26.2824	0.952735	0.476368	+	0.879246i	$0.341953\pi$
$762$	−1.33806	−0.0484730
$763$	16.1491	0.584638
$764$	28.1493	1.01841
$765$	−0.638444	−0.0230830
$766$	−2.75828	−0.0996606
$767$	−2.14692	−0.0775207
$768$	13.2798	0.479195
$769$	44.7648	1.61426	0.807131	−	0.590373i	$-0.201019\pi$
$769$	44.7648	1.61426	0.807131	+	0.590373i	$0.201019\pi$
$770$	−0.122614	−0.00441870
$771$	−14.1323	−0.508961
$772$	22.3049	0.802772
$773$	−32.1880	−1.15772	−0.578861	−	0.815426i	$-0.696503\pi$
$773$	−32.1880	−1.15772	−0.578861	+	0.815426i	$0.696503\pi$
$774$	−1.37424	−0.0493962
$775$	2.61862	0.0940637
$776$	5.43923	0.195257
$777$	28.0338	1.00571
$778$	−3.95024	−0.141623
$779$	4.33321	0.155254
$780$	−2.90078	−0.103865
$781$	−0.626024	−0.0224009
$782$	−0.470518	−0.0168257
$783$	1.84716	0.0660120
$784$	36.4177	1.30063
$785$	21.5778	0.770144
$786$	−0.515781	−0.0183973
$787$	−27.0196	−0.963146	−0.481573	−	0.876406i	$-0.659934\pi$
$787$	−27.0196	−0.963146	−0.481573	+	0.876406i	$0.659934\pi$
$788$	27.8169	0.990936
$789$	−23.7377	−0.845084
$790$	1.69341	0.0602490
$791$	17.9591	0.638554
$792$	−0.119311	−0.00423954
$793$	−14.7803	−0.524863
$794$	1.34559	0.0477531
$795$	−0.683802	−0.0242519
$796$	5.26081	0.186464
$797$	−4.02251	−0.142485	−0.0712423	−	0.997459i	$-0.522696\pi$
$797$	−4.02251	−0.142485	−0.0712423	+	0.997459i	$0.522696\pi$
$798$	0.638704	0.0226099
$799$	−3.48857	−0.123417
$800$	2.19011	0.0774320
$801$	17.7140	0.625895
$802$	−0.186838	−0.00659749
$803$	1.34542	0.0474789
$804$	−23.1208	−0.815409
$805$	−16.0731	−0.566502
$806$	0.722223	0.0254392
$807$	−0.309154	−0.0108827
$808$	14.2733	0.502131
$809$	5.95768	0.209461	0.104730	−	0.994501i	$-0.466602\pi$
$809$	5.95768	0.209461	0.104730	+	0.994501i	$0.466602\pi$
$810$	0.186838	0.00656483
$811$	40.6926	1.42891	0.714456	−	0.699681i	$-0.246674\pi$
$811$	40.6926	1.42891	0.714456	+	0.699681i	$0.246674\pi$
$812$	14.7910	0.519063
$813$	−14.4718	−0.507550
$814$	−0.207014	−0.00725583
$815$	23.4843	0.822618
$816$	−2.42083	−0.0847461
$817$	6.17050	0.215879
$818$	0.0326833	0.00114275
$819$	−6.01512	−0.210185
$820$	10.1501	0.354457
$821$	4.46788	0.155930	0.0779651	−	0.996956i	$-0.475158\pi$
$821$	4.46788	0.155930	0.0779651	+	0.996956i	$0.475158\pi$
$822$	−2.41531	−0.0842436
$823$	3.39588	0.118373	0.0591865	−	0.998247i	$-0.481149\pi$
$823$	3.39588	0.118373	0.0591865	+	0.998247i	$0.481149\pi$
$824$	−6.53970	−0.227821
$825$	0.161051	0.00560707
$826$	1.10729	0.0385274
$827$	38.1782	1.32758	0.663792	−	0.747917i	$-0.268946\pi$
$827$	38.1782	1.32758	0.663792	+	0.747917i	$0.268946\pi$
$828$	−7.75123	−0.269374
$829$	−31.7346	−1.10219	−0.551093	−	0.834444i	$-0.685789\pi$
$829$	−31.7346	−1.10219	−0.551093	+	0.834444i	$0.685789\pi$
$830$	−2.25686	−0.0783368
$831$	13.7450	0.476808
$832$	−10.5905	−0.367158
$833$	−6.13187	−0.212457
$834$	−2.44660	−0.0847188
$835$	−8.71167	−0.301480
$836$	0.265502	0.00918258
$837$	2.61862	0.0905128
$838$	3.63754	0.125657
$839$	−10.4093	−0.359370	−0.179685	−	0.983724i	$-0.557508\pi$
$839$	−10.4093	−0.359370	−0.179685	+	0.983724i	$0.557508\pi$
$840$	3.01877	0.104158
$841$	−25.5880	−0.882345
$842$	2.17088	0.0748135
$843$	2.26839	0.0781274
$844$	−10.2572	−0.353067
$845$	−10.8210	−0.372252
$846$	1.02092	0.0350999
$847$	44.7177	1.53652
$848$	−2.59282	−0.0890377
$849$	−19.9985	−0.686346
$850$	−0.119286	−0.00409147
$851$	−27.1368	−0.930238
$852$	7.63856	0.261693
$853$	18.7292	0.641275	0.320638	−	0.947202i	$-0.396103\pi$
$853$	18.7292	0.641275	0.320638	+	0.947202i	$0.396103\pi$
$854$	7.62302	0.260854
$855$	−0.838924	−0.0286906
$856$	10.7298	0.366738
$857$	−7.25881	−0.247956	−0.123978	−	0.992285i	$-0.539565\pi$
$857$	−7.25881	−0.247956	−0.123978	+	0.992285i	$0.539565\pi$
$858$	0.0444182	0.00151641
$859$	−49.0696	−1.67423	−0.837116	−	0.547026i	$-0.815760\pi$
$859$	−49.0696	−1.67423	−0.837116	+	0.547026i	$0.815760\pi$
$860$	14.4538	0.492869
$861$	21.0474	0.717295
$862$	5.42456	0.184761
$863$	27.7303	0.943949	0.471974	−	0.881612i	$-0.343541\pi$
$863$	27.7303	0.943949	0.471974	+	0.881612i	$0.343541\pi$
$864$	2.19011	0.0745090
$865$	−14.6529	−0.498214
$866$	6.74870	0.229330
$867$	−16.5924	−0.563507
$868$	20.9685	0.711717
$869$	1.45969	0.0495165
$870$	0.345120	0.0117007
$871$	17.3682	0.588497
$872$	2.93600	0.0994257
$873$	−7.34207	−0.248491
$874$	−0.618267	−0.0209132
$875$	−4.07485	−0.137755
$876$	−16.4164	−0.554659
$877$	−9.11052	−0.307640	−0.153820	−	0.988099i	$-0.549158\pi$
$877$	−9.11052	−0.307640	−0.153820	+	0.988099i	$0.549158\pi$
$878$	−0.313990	−0.0105967
$879$	0.763585	0.0257551
$880$	0.610667	0.0205856
$881$	10.3742	0.349516	0.174758	−	0.984611i	$-0.444086\pi$
$881$	10.3742	0.349516	0.174758	+	0.984611i	$0.444086\pi$
$882$	1.79447	0.0604229
$883$	−49.6235	−1.66996	−0.834982	−	0.550277i	$-0.814522\pi$
$883$	−49.6235	−1.66996	−0.834982	+	0.550277i	$0.814522\pi$
$884$	1.85199	0.0622891
$885$	−1.45440	−0.0488890
$886$	0.726941	0.0244221
$887$	17.3905	0.583918	0.291959	−	0.956431i	$-0.405693\pi$
$887$	17.3905	0.583918	0.291959	+	0.956431i	$0.405693\pi$
$888$	5.09671	0.171034
$889$	29.1825	0.978751
$890$	3.30966	0.110940
$891$	0.161051	0.00539540
$892$	−18.1253	−0.606879
$893$	−4.58403	−0.153399
$894$	−1.19166	−0.0398552
$895$	2.21079	0.0738987
$896$	23.3108	0.778760
$897$	5.82265	0.194412
$898$	−4.65534	−0.155351
$899$	4.83701	0.161323
$900$	−1.96509	−0.0655030
$901$	0.436569	0.0145442
$902$	−0.155423	−0.00517503
$903$	29.9716	0.997392
$904$	3.26507	0.108595
$905$	6.58405	0.218861
$906$	−3.82255	−0.126996
$907$	19.5937	0.650598	0.325299	−	0.945611i	$-0.394535\pi$
$907$	19.5937	0.650598	0.325299	+	0.945611i	$0.394535\pi$
$908$	−34.7443	−1.15303
$909$	−19.2666	−0.639031
$910$	−1.12385	−0.0372554
$911$	−1.26388	−0.0418742	−0.0209371	−	0.999781i	$-0.506665\pi$
$911$	−1.26388	−0.0418742	−0.0209371	+	0.999781i	$0.506665\pi$
$912$	−3.18100	−0.105334
$913$	−1.94537	−0.0643823
$914$	−2.11976	−0.0701154
$915$	−10.0127	−0.331009
$916$	8.59905	0.284121
$917$	11.2489	0.371473
$918$	−0.119286	−0.00393702
$919$	15.9558	0.526332	0.263166	−	0.964751i	$-0.415233\pi$
$919$	15.9558	0.526332	0.263166	+	0.964751i	$0.415233\pi$
$920$	−2.92218	−0.0963413
$921$	−32.9690	−1.08636
$922$	−2.52784	−0.0832500
$923$	−5.73801	−0.188869
$924$	1.28961	0.0424249
$925$	−6.87973	−0.226204
$926$	3.23916	0.106446
$927$	8.82753	0.289934
$928$	4.04548	0.132799
$929$	−25.9743	−0.852190	−0.426095	−	0.904679i	$-0.640111\pi$
$929$	−25.9743	−0.852190	−0.426095	+	0.904679i	$0.640111\pi$
$930$	0.489259	0.0160434
$931$	−8.05736	−0.264069
$932$	−37.8446	−1.23964
$933$	6.36343	0.208329
$934$	6.52472	0.213495
$935$	−0.102822	−0.00336264
$936$	−1.09358	−0.0357449
$937$	−40.7537	−1.33136	−0.665682	−	0.746236i	$-0.731859\pi$
$937$	−40.7537	−1.33136	−0.665682	+	0.746236i	$0.731859\pi$
$938$	−8.95774	−0.292480
$939$	18.8908	0.616479
$940$	−10.7376	−0.350222
$941$	−49.1907	−1.60357	−0.801785	−	0.597613i	$-0.796116\pi$
$941$	−49.1907	−1.60357	−0.801785	+	0.597613i	$0.796116\pi$
$942$	4.03156	0.131355
$943$	−20.3740	−0.663467
$944$	−5.51473	−0.179489
$945$	−4.07485	−0.132555
$946$	−0.221323	−0.00719583
$947$	−39.3060	−1.27727	−0.638636	−	0.769509i	$-0.720501\pi$
$947$	−39.3060	−1.27727	−0.638636	+	0.769509i	$0.720501\pi$
$948$	−17.8107	−0.578464
$949$	12.3318	0.400309
$950$	−0.156743	−0.00508542
$951$	24.0827	0.780934
$952$	−1.92732	−0.0624648
$953$	−3.32160	−0.107597	−0.0537985	−	0.998552i	$-0.517133\pi$
$953$	−3.32160	−0.107597	−0.0537985	+	0.998552i	$0.517133\pi$
$954$	−0.127760	−0.00413639
$955$	−14.3247	−0.463535
$956$	43.4299	1.40462
$957$	0.297486	0.00961636
$958$	3.81960	0.123406
$959$	52.6767	1.70102
$960$	−7.17434	−0.231551
$961$	−24.1428	−0.778801
$962$	−1.89745	−0.0611761
$963$	−14.4835	−0.466724
$964$	22.8012	0.734377
$965$	−11.3506	−0.365388
$966$	−3.00307	−0.0966221
$967$	12.3935	0.398549	0.199275	−	0.979944i	$-0.436141\pi$
$967$	12.3935	0.398549	0.199275	+	0.979944i	$0.436141\pi$
$968$	8.12992	0.261306
$969$	0.535606	0.0172061
$970$	−1.37178	−0.0440452
$971$	13.4921	0.432981	0.216490	−	0.976285i	$-0.430539\pi$
$971$	13.4921	0.432981	0.216490	+	0.976285i	$0.430539\pi$
$972$	−1.96509	−0.0630303
$973$	53.3591	1.71062
$974$	2.89719	0.0928321
$975$	1.47616	0.0472749
$976$	−37.9657	−1.21525
$977$	39.1778	1.25341	0.626704	−	0.779257i	$-0.284404\pi$
$977$	39.1778	1.25341	0.626704	+	0.779257i	$0.284404\pi$
$978$	4.38776	0.140305
$979$	2.85286	0.0911778
$980$	−18.8735	−0.602893
$981$	−3.96313	−0.126533
$982$	3.86905	0.123466
$983$	−23.8976	−0.762216	−0.381108	−	0.924531i	$-0.624457\pi$
$983$	−23.8976	−0.762216	−0.381108	+	0.924531i	$0.624457\pi$
$984$	3.82654	0.121986
$985$	−14.1555	−0.451033
$986$	−0.220340	−0.00701704
$987$	−22.2657	−0.708725
$988$	2.43354	0.0774211
$989$	−29.0125	−0.922545
$990$	0.0300904	0.000956337 0
$991$	27.0814	0.860269	0.430134	−	0.902765i	$-0.358466\pi$
$991$	27.0814	0.860269	0.430134	+	0.902765i	$0.358466\pi$
$992$	5.73507	0.182089
$993$	12.4552	0.395253
$994$	2.95941	0.0938669
$995$	−2.67713	−0.0848708
$996$	23.7368	0.752129
$997$	16.3928	0.519166	0.259583	−	0.965721i	$-0.416415\pi$
$997$	16.3928	0.519166	0.259583	+	0.965721i	$0.416415\pi$
$998$	5.00353	0.158384
$999$	−6.87973	−0.217665

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6015.2.a.b.1.14	✓	23

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6015.2.a.b.1.14	✓	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)

\(f(q)\)	\(=\)	\(q+0.186838 q^{2} +1.00000 q^{3} -1.96509 q^{4} +1.00000 q^{5} +0.186838 q^{6} -4.07485 q^{7} -0.740831 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.186838 q^{2} +1.00000 q^{3} -1.96509 q^{4} +1.00000 q^{5} +0.186838 q^{6} -4.07485 q^{7} -0.740831 q^{8} +1.00000 q^{9} +0.186838 q^{10} +0.161051 q^{11} -1.96509 q^{12} +1.47616 q^{13} -0.761338 q^{14} +1.00000 q^{15} +3.79177 q^{16} -0.638444 q^{17} +0.186838 q^{18} -0.838924 q^{19} -1.96509 q^{20} -4.07485 q^{21} +0.0300904 q^{22} +3.94446 q^{23} -0.740831 q^{24} +1.00000 q^{25} +0.275803 q^{26} +1.00000 q^{27} +8.00745 q^{28} +1.84716 q^{29} +0.186838 q^{30} +2.61862 q^{31} +2.19011 q^{32} +0.161051 q^{33} -0.119286 q^{34} -4.07485 q^{35} -1.96509 q^{36} -6.87973 q^{37} -0.156743 q^{38} +1.47616 q^{39} -0.740831 q^{40} -5.16521 q^{41} -0.761338 q^{42} -7.35526 q^{43} -0.316479 q^{44} +1.00000 q^{45} +0.736976 q^{46} +5.46418 q^{47} +3.79177 q^{48} +9.60440 q^{49} +0.186838 q^{50} -0.638444 q^{51} -2.90078 q^{52} -0.683802 q^{53} +0.186838 q^{54} +0.161051 q^{55} +3.01877 q^{56} -0.838924 q^{57} +0.345120 q^{58} -1.45440 q^{59} -1.96509 q^{60} -10.0127 q^{61} +0.489259 q^{62} -4.07485 q^{63} -7.17434 q^{64} +1.47616 q^{65} +0.0300904 q^{66} +11.7658 q^{67} +1.25460 q^{68} +3.94446 q^{69} -0.761338 q^{70} -3.88712 q^{71} -0.740831 q^{72} +8.35402 q^{73} -1.28540 q^{74} +1.00000 q^{75} +1.64856 q^{76} -0.656258 q^{77} +0.275803 q^{78} +9.06353 q^{79} +3.79177 q^{80} +1.00000 q^{81} -0.965058 q^{82} -12.0792 q^{83} +8.00745 q^{84} -0.638444 q^{85} -1.37424 q^{86} +1.84716 q^{87} -0.119311 q^{88} +17.7140 q^{89} +0.186838 q^{90} -6.01512 q^{91} -7.75123 q^{92} +2.61862 q^{93} +1.02092 q^{94} -0.838924 q^{95} +2.19011 q^{96} -7.34207 q^{97} +1.79447 q^{98} +0.161051 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 23 q - 5 q^{2} + 23 q^{3} + 9 q^{4} + 23 q^{5} - 5 q^{6} - 16 q^{7} - 12 q^{8} + 23 q^{9}+O(q^{10}) \) 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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