LMFDB - Embedded newform 6015.2.a.d.1.17

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:	$29$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
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)

$f(q)$	$=$	$q+0.242491 q^{2} -1.00000 q^{3} -1.94120 q^{4} +1.00000 q^{5} -0.242491 q^{6} +2.88846 q^{7} -0.955706 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.242491 q^{2} -1.00000 q^{3} -1.94120 q^{4} +1.00000 q^{5} -0.242491 q^{6} +2.88846 q^{7} -0.955706 q^{8} +1.00000 q^{9} +0.242491 q^{10} -5.32228 q^{11} +1.94120 q^{12} +1.78172 q^{13} +0.700426 q^{14} -1.00000 q^{15} +3.65065 q^{16} -4.08727 q^{17} +0.242491 q^{18} -0.811477 q^{19} -1.94120 q^{20} -2.88846 q^{21} -1.29061 q^{22} +3.89770 q^{23} +0.955706 q^{24} +1.00000 q^{25} +0.432051 q^{26} -1.00000 q^{27} -5.60708 q^{28} +1.49902 q^{29} -0.242491 q^{30} +6.63099 q^{31} +2.79666 q^{32} +5.32228 q^{33} -0.991126 q^{34} +2.88846 q^{35} -1.94120 q^{36} +0.231575 q^{37} -0.196776 q^{38} -1.78172 q^{39} -0.955706 q^{40} -11.8231 q^{41} -0.700426 q^{42} -5.72916 q^{43} +10.3316 q^{44} +1.00000 q^{45} +0.945158 q^{46} +1.08092 q^{47} -3.65065 q^{48} +1.34321 q^{49} +0.242491 q^{50} +4.08727 q^{51} -3.45867 q^{52} -3.27834 q^{53} -0.242491 q^{54} -5.32228 q^{55} -2.76052 q^{56} +0.811477 q^{57} +0.363499 q^{58} -13.0272 q^{59} +1.94120 q^{60} +14.0654 q^{61} +1.60796 q^{62} +2.88846 q^{63} -6.62313 q^{64} +1.78172 q^{65} +1.29061 q^{66} +12.8498 q^{67} +7.93420 q^{68} -3.89770 q^{69} +0.700426 q^{70} +7.81391 q^{71} -0.955706 q^{72} -10.4022 q^{73} +0.0561549 q^{74} -1.00000 q^{75} +1.57524 q^{76} -15.3732 q^{77} -0.432051 q^{78} +8.93797 q^{79} +3.65065 q^{80} +1.00000 q^{81} -2.86699 q^{82} -10.5072 q^{83} +5.60708 q^{84} -4.08727 q^{85} -1.38927 q^{86} -1.49902 q^{87} +5.08653 q^{88} -13.4114 q^{89} +0.242491 q^{90} +5.14643 q^{91} -7.56621 q^{92} -6.63099 q^{93} +0.262113 q^{94} -0.811477 q^{95} -2.79666 q^{96} -0.988913 q^{97} +0.325717 q^{98} -5.32228 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 29 q - q^{2} - 29 q^{3} + 27 q^{4} + 29 q^{5} + q^{6} + 2 q^{7} - 6 q^{8} + 29 q^{9}+O(q^{10}) $ 29 * q - q^2 - 29 * q^3 + 27 * q^4 + 29 * q^5 + q^6 + 2 * q^7 - 6 * q^8 + 29 * q^9	\( 29 q - q^{2} - 29 q^{3} + 27 q^{4} + 29 q^{5} + q^{6} + 2 q^{7} - 6 q^{8} + 29 q^{9} - q^{10} - 21 q^{11} - 27 q^{12} - 8 q^{13} - 30 q^{14} - 29 q^{15} + 23 q^{16} - 28 q^{17} - q^{18} - 9 q^{19} + 27 q^{20} - 2 q^{21} - 9 q^{22} + 6 q^{24} + 29 q^{25} - 34 q^{26} - 29 q^{27} + 6 q^{28} - 61 q^{29} + q^{30} - 19 q^{31} - 8 q^{32} + 21 q^{33} - 16 q^{34} + 2 q^{35} + 27 q^{36} - 4 q^{37} + 4 q^{38} + 8 q^{39} - 6 q^{40} - 85 q^{41} + 30 q^{42} + 29 q^{43} - 69 q^{44} + 29 q^{45} - 35 q^{46} - 2 q^{47} - 23 q^{48} + q^{49} - q^{50} + 28 q^{51} - 28 q^{52} - 5 q^{53} + q^{54} - 21 q^{55} - 97 q^{56} + 9 q^{57} + 6 q^{58} - 43 q^{59} - 27 q^{60} - 59 q^{61} - 17 q^{62} + 2 q^{63} - 6 q^{64} - 8 q^{65} + 9 q^{66} + 28 q^{67} - 44 q^{68} - 30 q^{70} - 44 q^{71} - 6 q^{72} - 41 q^{73} - 50 q^{74} - 29 q^{75} - 62 q^{76} - 20 q^{77} + 34 q^{78} - 25 q^{79} + 23 q^{80} + 29 q^{81} - 29 q^{82} - 7 q^{83} - 6 q^{84} - 28 q^{85} - 43 q^{86} + 61 q^{87} - 3 q^{88} - 109 q^{89} - q^{90} - q^{91} - 11 q^{92} + 19 q^{93} - 20 q^{94} - 9 q^{95} + 8 q^{96} - 51 q^{97} - 12 q^{98} - 21 q^{99}+O(q^{100}) \) 29 * q - q^2 - 29 * q^3 + 27 * q^4 + 29 * q^5 + q^6 + 2 * q^7 - 6 * q^8 + 29 * q^9 - q^10 - 21 * q^11 - 27 * q^12 - 8 * q^13 - 30 * q^14 - 29 * q^15 + 23 * q^16 - 28 * q^17 - q^18 - 9 * q^19 + 27 * q^20 - 2 * q^21 - 9 * q^22 + 6 * q^24 + 29 * q^25 - 34 * q^26 - 29 * q^27 + 6 * q^28 - 61 * q^29 + q^30 - 19 * q^31 - 8 * q^32 + 21 * q^33 - 16 * q^34 + 2 * q^35 + 27 * q^36 - 4 * q^37 + 4 * q^38 + 8 * q^39 - 6 * q^40 - 85 * q^41 + 30 * q^42 + 29 * q^43 - 69 * q^44 + 29 * q^45 - 35 * q^46 - 2 * q^47 - 23 * q^48 + q^49 - q^50 + 28 * q^51 - 28 * q^52 - 5 * q^53 + q^54 - 21 * q^55 - 97 * q^56 + 9 * q^57 + 6 * q^58 - 43 * q^59 - 27 * q^60 - 59 * q^61 - 17 * q^62 + 2 * q^63 - 6 * q^64 - 8 * q^65 + 9 * q^66 + 28 * q^67 - 44 * q^68 - 30 * q^70 - 44 * q^71 - 6 * q^72 - 41 * q^73 - 50 * q^74 - 29 * q^75 - 62 * q^76 - 20 * q^77 + 34 * q^78 - 25 * q^79 + 23 * q^80 + 29 * q^81 - 29 * q^82 - 7 * q^83 - 6 * q^84 - 28 * q^85 - 43 * q^86 + 61 * q^87 - 3 * q^88 - 109 * q^89 - q^90 - q^91 - 11 * q^92 + 19 * q^93 - 20 * q^94 - 9 * q^95 + 8 * q^96 - 51 * q^97 - 12 * q^98 - 21 * 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 $

$2$	0.242491	0.171467	0.0857336	−	0.996318i	$-0.472677\pi$
$2$	0.242491	0.171467	0.0857336	+	0.996318i	$0.472677\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.94120	−0.970599
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−0.242491	−0.0989966
$7$	2.88846	1.09174	0.545868	−	0.837871i	$-0.316200\pi$
$7$	2.88846	1.09174	0.545868	+	0.837871i	$0.316200\pi$
$8$	−0.955706	−0.337893
$9$	1.00000	0.333333
$10$	0.242491	0.0766824
$11$	−5.32228	−1.60473	−0.802364	−	0.596835i	$-0.796425\pi$
$11$	−5.32228	−1.60473	−0.802364	+	0.596835i	$0.796425\pi$
$12$	1.94120	0.560376
$13$	1.78172	0.494160	0.247080	−	0.968995i	$-0.420529\pi$
$13$	1.78172	0.494160	0.247080	+	0.968995i	$0.420529\pi$
$14$	0.700426	0.187197
$15$	−1.00000	−0.258199
$16$	3.65065	0.912661
$17$	−4.08727	−0.991308	−0.495654	−	0.868520i	$-0.665072\pi$
$17$	−4.08727	−0.991308	−0.495654	+	0.868520i	$0.665072\pi$
$18$	0.242491	0.0571557
$19$	−0.811477	−0.186165	−0.0930827	−	0.995658i	$-0.529672\pi$
$19$	−0.811477	−0.186165	−0.0930827	+	0.995658i	$0.529672\pi$
$20$	−1.94120	−0.434065
$21$	−2.88846	−0.630314
$22$	−1.29061	−0.275158
$23$	3.89770	0.812727	0.406363	−	0.913712i	$-0.366797\pi$
$23$	3.89770	0.812727	0.406363	+	0.913712i	$0.366797\pi$
$24$	0.955706	0.195083
$25$	1.00000	0.200000
$26$	0.432051	0.0847322
$27$	−1.00000	−0.192450
$28$	−5.60708	−1.05964
$29$	1.49902	0.278361	0.139181	−	0.990267i	$-0.455553\pi$
$29$	1.49902	0.278361	0.139181	+	0.990267i	$0.455553\pi$
$30$	−0.242491	−0.0442726
$31$	6.63099	1.19096	0.595480	−	0.803370i	$-0.296962\pi$
$31$	6.63099	1.19096	0.595480	+	0.803370i	$0.296962\pi$
$32$	2.79666	0.494384
$33$	5.32228	0.926490
$34$	−0.991126	−0.169977
$35$	2.88846	0.488239
$36$	−1.94120	−0.323533
$37$	0.231575	0.0380707	0.0190353	−	0.999819i	$-0.493940\pi$
$37$	0.231575	0.0380707	0.0190353	+	0.999819i	$0.493940\pi$
$38$	−0.196776	−0.0319213
$39$	−1.78172	−0.285303
$40$	−0.955706	−0.151110
$41$	−11.8231	−1.84646	−0.923228	−	0.384252i	$-0.874459\pi$
$41$	−11.8231	−1.84646	−0.923228	+	0.384252i	$0.874459\pi$
$42$	−0.700426	−0.108078
$43$	−5.72916	−0.873689	−0.436844	−	0.899537i	$-0.643904\pi$
$43$	−5.72916	−0.873689	−0.436844	+	0.899537i	$0.643904\pi$
$44$	10.3316	1.55755
$45$	1.00000	0.149071
$46$	0.945158	0.139356
$47$	1.08092	0.157668	0.0788340	−	0.996888i	$-0.474880\pi$
$47$	1.08092	0.157668	0.0788340	+	0.996888i	$0.474880\pi$
$48$	−3.65065	−0.526925
$49$	1.34321	0.191887
$50$	0.242491	0.0342934
$51$	4.08727	0.572332
$52$	−3.45867	−0.479631
$53$	−3.27834	−0.450314	−0.225157	−	0.974322i	$-0.572290\pi$
$53$	−3.27834	−0.450314	−0.225157	+	0.974322i	$0.572290\pi$
$54$	−0.242491	−0.0329989
$55$	−5.32228	−0.717656
$56$	−2.76052	−0.368890
$57$	0.811477	0.107483
$58$	0.363499	0.0477298
$59$	−13.0272	−1.69600	−0.848000	−	0.529996i	$-0.822194\pi$
$59$	−13.0272	−1.69600	−0.848000	+	0.529996i	$0.822194\pi$
$60$	1.94120	0.250608
$61$	14.0654	1.80089	0.900445	−	0.434971i	$-0.143241\pi$
$61$	14.0654	1.80089	0.900445	+	0.434971i	$0.143241\pi$
$62$	1.60796	0.204211
$63$	2.88846	0.363912
$64$	−6.62313	−0.827891
$65$	1.78172	0.220995
$66$	1.29061	0.158863
$67$	12.8498	1.56985	0.784926	−	0.619590i	$-0.212701\pi$
$67$	12.8498	1.56985	0.784926	+	0.619590i	$0.212701\pi$
$68$	7.93420	0.962163
$69$	−3.89770	−0.469228
$70$	0.700426	0.0837170
$71$	7.81391	0.927340	0.463670	−	0.886008i	$-0.346532\pi$
$71$	7.81391	0.927340	0.463670	+	0.886008i	$0.346532\pi$
$72$	−0.955706	−0.112631
$73$	−10.4022	−1.21749	−0.608744	−	0.793366i	$-0.708327\pi$
$73$	−10.4022	−1.21749	−0.608744	+	0.793366i	$0.708327\pi$
$74$	0.0561549	0.00652787
$75$	−1.00000	−0.115470
$76$	1.57524	0.180692
$77$	−15.3732	−1.75194
$78$	−0.432051	−0.0489201
$79$	8.93797	1.00560	0.502800	−	0.864403i	$-0.332303\pi$
$79$	8.93797	1.00560	0.502800	+	0.864403i	$0.332303\pi$
$80$	3.65065	0.408155
$81$	1.00000	0.111111
$82$	−2.86699	−0.316607
$83$	−10.5072	−1.15332	−0.576659	−	0.816985i	$-0.695644\pi$
$83$	−10.5072	−1.15332	−0.576659	+	0.816985i	$0.695644\pi$
$84$	5.60708	0.611782
$85$	−4.08727	−0.443326
$86$	−1.38927	−0.149809
$87$	−1.49902	−0.160712
$88$	5.08653	0.542226
$89$	−13.4114	−1.42161	−0.710803	−	0.703391i	$-0.751668\pi$
$89$	−13.4114	−1.42161	−0.710803	+	0.703391i	$0.751668\pi$
$90$	0.242491	0.0255608
$91$	5.14643	0.539492
$92$	−7.56621	−0.788832
$93$	−6.63099	−0.687602
$94$	0.262113	0.0270349
$95$	−0.811477	−0.0832557
$96$	−2.79666	−0.285433
$97$	−0.988913	−0.100409	−0.0502044	−	0.998739i	$-0.515987\pi$
$97$	−0.988913	−0.100409	−0.0502044	+	0.998739i	$0.515987\pi$
$98$	0.325717	0.0329023
$99$	−5.32228	−0.534909
$100$	−1.94120	−0.194120
$101$	3.54537	0.352777	0.176389	−	0.984321i	$-0.443558\pi$
$101$	3.54537	0.352777	0.176389	+	0.984321i	$0.443558\pi$
$102$	0.991126	0.0981361
$103$	2.29267	0.225903	0.112952	−	0.993600i	$-0.463969\pi$
$103$	2.29267	0.225903	0.112952	+	0.993600i	$0.463969\pi$
$104$	−1.70280	−0.166973
$105$	−2.88846	−0.281885
$106$	−0.794968	−0.0772141
$107$	1.24192	0.120060	0.0600302	−	0.998197i	$-0.480880\pi$
$107$	1.24192	0.120060	0.0600302	+	0.998197i	$0.480880\pi$
$108$	1.94120	0.186792
$109$	19.2790	1.84660	0.923299	−	0.384082i	$-0.125482\pi$
$109$	19.2790	1.84660	0.923299	+	0.384082i	$0.125482\pi$
$110$	−1.29061	−0.123054
$111$	−0.231575	−0.0219801
$112$	10.5448	0.996385
$113$	8.97157	0.843974	0.421987	−	0.906602i	$-0.361333\pi$
$113$	8.97157	0.843974	0.421987	+	0.906602i	$0.361333\pi$
$114$	0.196776	0.0184297
$115$	3.89770	0.363462
$116$	−2.90990	−0.270177
$117$	1.78172	0.164720
$118$	−3.15899	−0.290808
$119$	−11.8059	−1.08225
$120$	0.955706	0.0872436
$121$	17.3267	1.57515
$122$	3.41073	0.308793
$123$	11.8231	1.06605
$124$	−12.8721	−1.15595
$125$	1.00000	0.0894427
$126$	0.700426	0.0623989
$127$	−20.1229	−1.78562	−0.892810	−	0.450434i	$-0.851269\pi$
$127$	−20.1229	−1.78562	−0.892810	+	0.450434i	$0.851269\pi$
$128$	−7.19937	−0.636340
$129$	5.72916	0.504424
$130$	0.432051	0.0378934
$131$	−20.3735	−1.78004	−0.890019	−	0.455924i	$-0.849309\pi$
$131$	−20.3735	−1.78004	−0.890019	+	0.455924i	$0.849309\pi$
$132$	−10.3316	−0.899250
$133$	−2.34392	−0.203244
$134$	3.11596	0.269178
$135$	−1.00000	−0.0860663
$136$	3.90622	0.334956
$137$	−1.13502	−0.0969716	−0.0484858	−	0.998824i	$-0.515440\pi$
$137$	−1.13502	−0.0969716	−0.0484858	+	0.998824i	$0.515440\pi$
$138$	−0.945158	−0.0804572
$139$	−6.13512	−0.520374	−0.260187	−	0.965558i	$-0.583784\pi$
$139$	−6.13512	−0.520374	−0.260187	+	0.965558i	$0.583784\pi$
$140$	−5.60708	−0.473884
$141$	−1.08092	−0.0910297
$142$	1.89480	0.159008
$143$	−9.48281	−0.792992
$144$	3.65065	0.304220
$145$	1.49902	0.124487
$146$	−2.52245	−0.208759
$147$	−1.34321	−0.110786
$148$	−0.449533	−0.0369514
$149$	13.0408	1.06834	0.534170	−	0.845377i	$-0.320624\pi$
$149$	13.0408	1.06834	0.534170	+	0.845377i	$0.320624\pi$
$150$	−0.242491	−0.0197993
$151$	−5.47495	−0.445545	−0.222772	−	0.974870i	$-0.571511\pi$
$151$	−5.47495	−0.445545	−0.222772	+	0.974870i	$0.571511\pi$
$152$	0.775533	0.0629040
$153$	−4.08727	−0.330436
$154$	−3.72786	−0.300400
$155$	6.63099	0.532614
$156$	3.45867	0.276915
$157$	−1.32856	−0.106031	−0.0530155	−	0.998594i	$-0.516883\pi$
$157$	−1.32856	−0.106031	−0.0530155	+	0.998594i	$0.516883\pi$
$158$	2.16738	0.172427
$159$	3.27834	0.259989
$160$	2.79666	0.221095
$161$	11.2584	0.887283
$162$	0.242491	0.0190519
$163$	−23.2170	−1.81849	−0.909247	−	0.416257i	$-0.863342\pi$
$163$	−23.2170	−1.81849	−0.909247	+	0.416257i	$0.863342\pi$
$164$	22.9510	1.79217
$165$	5.32228	0.414339
$166$	−2.54791	−0.197756
$167$	−13.1195	−1.01522	−0.507609	−	0.861588i	$-0.669471\pi$
$167$	−13.1195	−1.01522	−0.507609	+	0.861588i	$0.669471\pi$
$168$	2.76052	0.212979
$169$	−9.82548	−0.755806
$170$	−0.991126	−0.0760159
$171$	−0.811477	−0.0620552
$172$	11.1214	0.848001
$173$	18.0339	1.37109	0.685545	−	0.728030i	$-0.259564\pi$
$173$	18.0339	1.37109	0.685545	+	0.728030i	$0.259564\pi$
$174$	−0.363499	−0.0275568
$175$	2.88846	0.218347
$176$	−19.4298	−1.46457
$177$	13.0272	0.979186
$178$	−3.25215	−0.243759
$179$	12.0559	0.901101	0.450551	−	0.892751i	$-0.351228\pi$
$179$	12.0559	0.901101	0.450551	+	0.892751i	$0.351228\pi$
$180$	−1.94120	−0.144688
$181$	−13.9628	−1.03784	−0.518922	−	0.854822i	$-0.673667\pi$
$181$	−13.9628	−1.03784	−0.518922	+	0.854822i	$0.673667\pi$
$182$	1.24796	0.0925052
$183$	−14.0654	−1.03974
$184$	−3.72505	−0.274615
$185$	0.231575	0.0170257
$186$	−1.60796	−0.117901
$187$	21.7536	1.59078
$188$	−2.09828	−0.153032
$189$	−2.88846	−0.210105
$190$	−0.196776	−0.0142756
$191$	−4.07175	−0.294621	−0.147311	−	0.989090i	$-0.547062\pi$
$191$	−4.07175	−0.294621	−0.147311	+	0.989090i	$0.547062\pi$
$192$	6.62313	0.477983
$193$	−0.0141951	−0.00102178	−0.000510891	−	1.00000i	$-0.500163\pi$
$193$	−0.0141951	−0.00102178	−0.000510891		1.00000i	$0.500163\pi$
$194$	−0.239803	−0.0172168
$195$	−1.78172	−0.127592
$196$	−2.60744	−0.186246
$197$	0.486831	0.0346852	0.0173426	−	0.999850i	$-0.494479\pi$
$197$	0.486831	0.0346852	0.0173426	+	0.999850i	$0.494479\pi$
$198$	−1.29061	−0.0917193
$199$	14.3360	1.01626	0.508128	−	0.861282i	$-0.330338\pi$
$199$	14.3360	1.01626	0.508128	+	0.861282i	$0.330338\pi$
$200$	−0.955706	−0.0675786
$201$	−12.8498	−0.906354
$202$	0.859720	0.0604897
$203$	4.32987	0.303897
$204$	−7.93420	−0.555505
$205$	−11.8231	−0.825760
$206$	0.555952	0.0387350
$207$	3.89770	0.270909
$208$	6.50443	0.451001
$209$	4.31890	0.298745
$210$	−0.700426	−0.0483340
$211$	16.6939	1.14925	0.574627	−	0.818416i	$-0.305147\pi$
$211$	16.6939	1.14925	0.574627	+	0.818416i	$0.305147\pi$
$212$	6.36390	0.437075
$213$	−7.81391	−0.535400
$214$	0.301153	0.0205864
$215$	−5.72916	−0.390725
$216$	0.955706	0.0650275
$217$	19.1534	1.30021
$218$	4.67500	0.316631
$219$	10.4022	0.702918
$220$	10.3316	0.696556
$221$	−7.28236	−0.489865
$222$	−0.0561549	−0.00376887
$223$	−24.7595	−1.65802	−0.829008	−	0.559236i	$-0.811095\pi$
$223$	−24.7595	−1.65802	−0.829008	+	0.559236i	$0.811095\pi$
$224$	8.07805	0.539737
$225$	1.00000	0.0666667
$226$	2.17553	0.144714
$227$	17.9985	1.19460	0.597301	−	0.802017i	$-0.296240\pi$
$227$	17.9985	1.19460	0.597301	+	0.802017i	$0.296240\pi$
$228$	−1.57524	−0.104323
$229$	−28.7312	−1.89861	−0.949304	−	0.314359i	$-0.898211\pi$
$229$	−28.7312	−1.89861	−0.949304	+	0.314359i	$0.898211\pi$
$230$	0.945158	0.0623219
$231$	15.3732	1.01148
$232$	−1.43262	−0.0940563
$233$	−11.0161	−0.721691	−0.360846	−	0.932626i	$-0.617512\pi$
$233$	−11.0161	−0.721691	−0.360846	+	0.932626i	$0.617512\pi$
$234$	0.432051	0.0282441
$235$	1.08092	0.0705113
$236$	25.2884	1.64614
$237$	−8.93797	−0.580583
$238$	−2.86283	−0.185570
$239$	11.6824	0.755669	0.377835	−	0.925873i	$-0.376669\pi$
$239$	11.6824	0.755669	0.377835	+	0.925873i	$0.376669\pi$
$240$	−3.65065	−0.235648
$241$	−2.67838	−0.172529	−0.0862647	−	0.996272i	$-0.527493\pi$
$241$	−2.67838	−0.172529	−0.0862647	+	0.996272i	$0.527493\pi$
$242$	4.20156	0.270087
$243$	−1.00000	−0.0641500
$244$	−27.3037	−1.74794
$245$	1.34321	0.0858146
$246$	2.86699	0.182793
$247$	−1.44582	−0.0919955
$248$	−6.33727	−0.402417
$249$	10.5072	0.665869
$250$	0.242491	0.0153365
$251$	−14.5562	−0.918778	−0.459389	−	0.888235i	$-0.651932\pi$
$251$	−14.5562	−0.918778	−0.459389	+	0.888235i	$0.651932\pi$
$252$	−5.60708	−0.353213
$253$	−20.7447	−1.30421
$254$	−4.87963	−0.306175
$255$	4.08727	0.255955
$256$	11.5005	0.718779
$257$	−27.6638	−1.72562	−0.862811	−	0.505526i	$-0.831298\pi$
$257$	−27.6638	−1.72562	−0.862811	+	0.505526i	$0.831298\pi$
$258$	1.38927	0.0864922
$259$	0.668895	0.0415631
$260$	−3.45867	−0.214498
$261$	1.49902	0.0927871
$262$	−4.94038	−0.305218
$263$	−18.5870	−1.14612	−0.573061	−	0.819512i	$-0.694244\pi$
$263$	−18.5870	−1.14612	−0.573061	+	0.819512i	$0.694244\pi$
$264$	−5.08653	−0.313054
$265$	−3.27834	−0.201387
$266$	−0.568380	−0.0348496
$267$	13.4114	0.820765
$268$	−24.9440	−1.52370
$269$	−9.64395	−0.588002	−0.294001	−	0.955805i	$-0.594987\pi$
$269$	−9.64395	−0.588002	−0.294001	+	0.955805i	$0.594987\pi$
$270$	−0.242491	−0.0147575
$271$	−18.3114	−1.11234	−0.556169	−	0.831069i	$-0.687729\pi$
$271$	−18.3114	−1.11234	−0.556169	+	0.831069i	$0.687729\pi$
$272$	−14.9212	−0.904729
$273$	−5.14643	−0.311476
$274$	−0.275233	−0.0166274
$275$	−5.32228	−0.320946
$276$	7.56621	0.455432
$277$	−15.6506	−0.940356	−0.470178	−	0.882572i	$-0.655810\pi$
$277$	−15.6506	−0.940356	−0.470178	+	0.882572i	$0.655810\pi$
$278$	−1.48771	−0.0892270
$279$	6.63099	0.396987
$280$	−2.76052	−0.164973
$281$	−19.4171	−1.15833	−0.579164	−	0.815211i	$-0.696621\pi$
$281$	−19.4171	−1.15833	−0.579164	+	0.815211i	$0.696621\pi$
$282$	−0.262113	−0.0156086
$283$	−29.7782	−1.77013	−0.885065	−	0.465467i	$-0.845886\pi$
$283$	−29.7782	−1.77013	−0.885065	+	0.465467i	$0.845886\pi$
$284$	−15.1683	−0.900075
$285$	0.811477	0.0480677
$286$	−2.29950	−0.135972
$287$	−34.1505	−2.01584
$288$	2.79666	0.164795
$289$	−0.294245	−0.0173085
$290$	0.363499	0.0213454
$291$	0.988913	0.0579711
$292$	20.1928	1.18169
$293$	2.09310	0.122280	0.0611402	−	0.998129i	$-0.480526\pi$
$293$	2.09310	0.122280	0.0611402	+	0.998129i	$0.480526\pi$
$294$	−0.325717	−0.0189962
$295$	−13.0272	−0.758475
$296$	−0.221318	−0.0128638
$297$	5.32228	0.308830
$298$	3.16227	0.183185
$299$	6.94461	0.401617
$300$	1.94120	0.112075
$301$	−16.5485	−0.953837
$302$	−1.32763	−0.0763963
$303$	−3.54537	−0.203676
$304$	−2.96241	−0.169906
$305$	14.0654	0.805382
$306$	−0.991126	−0.0566589
$307$	23.7725	1.35677	0.678383	−	0.734709i	$-0.262681\pi$
$307$	23.7725	1.35677	0.678383	+	0.734709i	$0.262681\pi$
$308$	29.8424	1.70043
$309$	−2.29267	−0.130425
$310$	1.60796	0.0913258
$311$	27.7733	1.57488	0.787439	−	0.616393i	$-0.211407\pi$
$311$	27.7733	1.57488	0.787439	+	0.616393i	$0.211407\pi$
$312$	1.70280	0.0964020
$313$	1.44622	0.0817450	0.0408725	−	0.999164i	$-0.486986\pi$
$313$	1.44622	0.0817450	0.0408725	+	0.999164i	$0.486986\pi$
$314$	−0.322165	−0.0181808
$315$	2.88846	0.162746
$316$	−17.3504	−0.976034
$317$	12.8696	0.722827	0.361414	−	0.932406i	$-0.382294\pi$
$317$	12.8696	0.722827	0.361414	+	0.932406i	$0.382294\pi$
$318$	0.794968	0.0445796
$319$	−7.97821	−0.446694
$320$	−6.62313	−0.370244
$321$	−1.24192	−0.0693169
$322$	2.73005	0.152140
$323$	3.31672	0.184547
$324$	−1.94120	−0.107844
$325$	1.78172	0.0988320
$326$	−5.62991	−0.311812
$327$	−19.2790	−1.06613
$328$	11.2994	0.623905
$329$	3.12219	0.172132
$330$	1.29061	0.0710455
$331$	6.18629	0.340029	0.170015	−	0.985442i	$-0.445619\pi$
$331$	6.18629	0.340029	0.170015	+	0.985442i	$0.445619\pi$
$332$	20.3966	1.11941
$333$	0.231575	0.0126902
$334$	−3.18136	−0.174077
$335$	12.8498	0.702059
$336$	−10.5448	−0.575263
$337$	9.61825	0.523940	0.261970	−	0.965076i	$-0.415628\pi$
$337$	9.61825	0.523940	0.261970	+	0.965076i	$0.415628\pi$
$338$	−2.38259	−0.129596
$339$	−8.97157	−0.487269
$340$	7.93420	0.430292
$341$	−35.2920	−1.91117
$342$	−0.196776	−0.0106404
$343$	−16.3394	−0.882246
$344$	5.47539	0.295213
$345$	−3.89770	−0.209845
$346$	4.37305	0.235097
$347$	33.3739	1.79161	0.895803	−	0.444451i	$-0.146601\pi$
$347$	33.3739	1.79161	0.895803	+	0.444451i	$0.146601\pi$
$348$	2.90990	0.155987
$349$	−11.1367	−0.596134	−0.298067	−	0.954545i	$-0.596342\pi$
$349$	−11.1367	−0.596134	−0.298067	+	0.954545i	$0.596342\pi$
$350$	0.700426	0.0374394
$351$	−1.78172	−0.0951011
$352$	−14.8846	−0.793352
$353$	−25.8246	−1.37451	−0.687253	−	0.726418i	$-0.741184\pi$
$353$	−25.8246	−1.37451	−0.687253	+	0.726418i	$0.741184\pi$
$354$	3.15899	0.167898
$355$	7.81391	0.414719
$356$	26.0342	1.37981
$357$	11.8059	0.624835
$358$	2.92345	0.154509
$359$	9.42760	0.497570	0.248785	−	0.968559i	$-0.419969\pi$
$359$	9.42760	0.497570	0.248785	+	0.968559i	$0.419969\pi$
$360$	−0.955706	−0.0503701
$361$	−18.3415	−0.965342
$362$	−3.38585	−0.177956
$363$	−17.3267	−0.909414
$364$	−9.99023	−0.523631
$365$	−10.4022	−0.544478
$366$	−3.41073	−0.178282
$367$	−9.64655	−0.503546	−0.251773	−	0.967786i	$-0.581014\pi$
$367$	−9.64655	−0.503546	−0.251773	+	0.967786i	$0.581014\pi$
$368$	14.2291	0.741745
$369$	−11.8231	−0.615485
$370$	0.0561549	0.00291935
$371$	−9.46935	−0.491624
$372$	12.8721	0.667385
$373$	−13.4357	−0.695676	−0.347838	−	0.937555i	$-0.613084\pi$
$373$	−13.4357	−0.695676	−0.347838	+	0.937555i	$0.613084\pi$
$374$	5.27505	0.272766
$375$	−1.00000	−0.0516398
$376$	−1.03304	−0.0532749
$377$	2.67083	0.137555
$378$	−0.700426	−0.0360260
$379$	32.7940	1.68451	0.842257	−	0.539077i	$-0.181227\pi$
$379$	32.7940	1.68451	0.842257	+	0.539077i	$0.181227\pi$
$380$	1.57524	0.0808079
$381$	20.1229	1.03093
$382$	−0.987363	−0.0505179
$383$	−18.0958	−0.924655	−0.462327	−	0.886709i	$-0.652985\pi$
$383$	−18.0958	−0.924655	−0.462327	+	0.886709i	$0.652985\pi$
$384$	7.19937	0.367391
$385$	−15.3732	−0.783491
$386$	−0.00344218	−0.000175202 0
$387$	−5.72916	−0.291230
$388$	1.91968	0.0974568
$389$	−26.0098	−1.31875	−0.659374	−	0.751816i	$-0.729178\pi$
$389$	−26.0098	−1.31875	−0.659374	+	0.751816i	$0.729178\pi$
$390$	−0.432051	−0.0218778
$391$	−15.9309	−0.805663
$392$	−1.28371	−0.0648373
$393$	20.3735	1.02770
$394$	0.118052	0.00594738
$395$	8.93797	0.449718
$396$	10.3316	0.519182
$397$	−32.1333	−1.61272	−0.806361	−	0.591423i	$-0.798566\pi$
$397$	−32.1333	−1.61272	−0.806361	+	0.591423i	$0.798566\pi$
$398$	3.47636	0.174254
$399$	2.34392	0.117343
$400$	3.65065	0.182532
$401$	1.00000	0.0499376
$401$	1.00000	0.0499376
$402$	−3.11596	−0.155410
$403$	11.8146	0.588525
$404$	−6.88226	−0.342405
$405$	1.00000	0.0496904
$406$	1.04995	0.0521083
$407$	−1.23251	−0.0610931
$408$	−3.90622	−0.193387
$409$	−39.3615	−1.94630	−0.973150	−	0.230171i	$-0.926071\pi$
$409$	−39.3615	−1.94630	−0.973150	+	0.230171i	$0.926071\pi$
$410$	−2.86699	−0.141591
$411$	1.13502	0.0559866
$412$	−4.45052	−0.219262
$413$	−37.6286	−1.85158
$414$	0.945158	0.0464520
$415$	−10.5072	−0.515780
$416$	4.98286	0.244305
$417$	6.13512	0.300438
$418$	1.04730	0.0512249
$419$	4.75540	0.232317	0.116158	−	0.993231i	$-0.462942\pi$
$419$	4.75540	0.232317	0.116158	+	0.993231i	$0.462942\pi$
$420$	5.60708	0.273597
$421$	−10.5599	−0.514660	−0.257330	−	0.966324i	$-0.582843\pi$
$421$	−10.5599	−0.514660	−0.257330	+	0.966324i	$0.582843\pi$
$422$	4.04812	0.197059
$423$	1.08092	0.0525560
$424$	3.13313	0.152158
$425$	−4.08727	−0.198262
$426$	−1.89480	−0.0918035
$427$	40.6273	1.96610
$428$	−2.41080	−0.116531
$429$	9.48281	0.457834
$430$	−1.38927	−0.0669966
$431$	−24.3985	−1.17524	−0.587618	−	0.809138i	$-0.699934\pi$
$431$	−24.3985	−1.17524	−0.587618	+	0.809138i	$0.699934\pi$
$432$	−3.65065	−0.175642
$433$	−20.1213	−0.966968	−0.483484	−	0.875353i	$-0.660629\pi$
$433$	−20.1213	−0.966968	−0.483484	+	0.875353i	$0.660629\pi$
$434$	4.64452	0.222944
$435$	−1.49902	−0.0718726
$436$	−37.4244	−1.79231
$437$	−3.16289	−0.151302
$438$	2.52245	0.120527
$439$	39.4327	1.88202	0.941011	−	0.338376i	$-0.109878\pi$
$439$	39.4327	1.88202	0.941011	+	0.338376i	$0.109878\pi$
$440$	5.08653	0.242491
$441$	1.34321	0.0639624
$442$	−1.76591	−0.0839957
$443$	−5.06467	−0.240630	−0.120315	−	0.992736i	$-0.538390\pi$
$443$	−5.06467	−0.240630	−0.120315	+	0.992736i	$0.538390\pi$
$444$	0.449533	0.0213339
$445$	−13.4114	−0.635762
$446$	−6.00395	−0.284295
$447$	−13.0408	−0.616806
$448$	−19.1306	−0.903838
$449$	−31.6717	−1.49468	−0.747340	−	0.664442i	$-0.768669\pi$
$449$	−31.6717	−1.49468	−0.747340	+	0.664442i	$0.768669\pi$
$450$	0.242491	0.0114311
$451$	62.9258	2.96306
$452$	−17.4156	−0.819160
$453$	5.47495	0.257236
$454$	4.36448	0.204835
$455$	5.14643	0.241268
$456$	−0.775533	−0.0363176
$457$	10.9241	0.511007	0.255503	−	0.966808i	$-0.417759\pi$
$457$	10.9241	0.511007	0.255503	+	0.966808i	$0.417759\pi$
$458$	−6.96705	−0.325549
$459$	4.08727	0.190777
$460$	−7.56621	−0.352776
$461$	16.9538	0.789615	0.394808	−	0.918764i	$-0.370811\pi$
$461$	16.9538	0.789615	0.394808	+	0.918764i	$0.370811\pi$
$462$	3.72786	0.173436
$463$	−4.43973	−0.206332	−0.103166	−	0.994664i	$-0.532897\pi$
$463$	−4.43973	−0.206332	−0.103166	+	0.994664i	$0.532897\pi$
$464$	5.47240	0.254050
$465$	−6.63099	−0.307505
$466$	−2.67132	−0.123746
$467$	−19.5787	−0.905996	−0.452998	−	0.891512i	$-0.649646\pi$
$467$	−19.5787	−0.905996	−0.452998	+	0.891512i	$0.649646\pi$
$468$	−3.45867	−0.159877
$469$	37.1161	1.71386
$470$	0.262113	0.0120904
$471$	1.32856	0.0612170
$472$	12.4502	0.573067
$473$	30.4922	1.40203
$474$	−2.16738	−0.0995510
$475$	−0.811477	−0.0372331
$476$	22.9176	1.05043
$477$	−3.27834	−0.150105
$478$	2.83287	0.129572
$479$	−0.853690	−0.0390061	−0.0195030	−	0.999810i	$-0.506208\pi$
$479$	−0.853690	−0.0390061	−0.0195030	+	0.999810i	$0.506208\pi$
$480$	−2.79666	−0.127649
$481$	0.412602	0.0188130
$482$	−0.649483	−0.0295831
$483$	−11.2584	−0.512273
$484$	−33.6345	−1.52884
$485$	−0.988913	−0.0449042
$486$	−0.242491	−0.0109996
$487$	34.6145	1.56853	0.784266	−	0.620425i	$-0.213040\pi$
$487$	34.6145	1.56853	0.784266	+	0.620425i	$0.213040\pi$
$488$	−13.4424	−0.608508
$489$	23.2170	1.04991
$490$	0.325717	0.0147144
$491$	−10.4033	−0.469495	−0.234747	−	0.972056i	$-0.575426\pi$
$491$	−10.4033	−0.469495	−0.234747	+	0.972056i	$0.575426\pi$
$492$	−22.9510	−1.03471
$493$	−6.12690	−0.275942
$494$	−0.350599	−0.0157742
$495$	−5.32228	−0.239219
$496$	24.2074	1.08694
$497$	22.5702	1.01241
$498$	2.54791	0.114175
$499$	−26.6663	−1.19375	−0.596875	−	0.802334i	$-0.703591\pi$
$499$	−26.6663	−1.19375	−0.596875	+	0.802334i	$0.703591\pi$
$500$	−1.94120	−0.0868130
$501$	13.1195	0.586136
$502$	−3.52974	−0.157540
$503$	−4.38320	−0.195437	−0.0977185	−	0.995214i	$-0.531154\pi$
$503$	−4.38320	−0.195437	−0.0977185	+	0.995214i	$0.531154\pi$
$504$	−2.76052	−0.122963
$505$	3.54537	0.157767
$506$	−5.03039	−0.223628
$507$	9.82548	0.436365
$508$	39.0626	1.73312
$509$	−43.0346	−1.90747	−0.953737	−	0.300642i	$-0.902799\pi$
$509$	−43.0346	−1.90747	−0.953737	+	0.300642i	$0.902799\pi$
$510$	0.991126	0.0438878
$511$	−30.0464	−1.32918
$512$	17.1875	0.759587
$513$	0.811477	0.0358276
$514$	−6.70823	−0.295888
$515$	2.29267	0.101027
$516$	−11.1214	−0.489594
$517$	−5.75295	−0.253014
$518$	0.162201	0.00712671
$519$	−18.0339	−0.791599
$520$	−1.70280	−0.0746727
$521$	−29.9391	−1.31165	−0.655827	−	0.754911i	$-0.727680\pi$
$521$	−29.9391	−1.31165	−0.655827	+	0.754911i	$0.727680\pi$
$522$	0.363499	0.0159099
$523$	13.3097	0.581994	0.290997	−	0.956724i	$-0.406013\pi$
$523$	13.3097	0.581994	0.290997	+	0.956724i	$0.406013\pi$
$524$	39.5489	1.72770
$525$	−2.88846	−0.126063
$526$	−4.50718	−0.196522
$527$	−27.1026	−1.18061
$528$	19.4298	0.845572
$529$	−7.80793	−0.339475
$530$	−0.794968	−0.0345312
$531$	−13.0272	−0.565334
$532$	4.55001	0.197268
$533$	−21.0654	−0.912445
$534$	3.25215	0.140734
$535$	1.24192	0.0536927
$536$	−12.2806	−0.530442
$537$	−12.0559	−0.520251
$538$	−2.33857	−0.100823
$539$	−7.14894	−0.307927
$540$	1.94120	0.0835359
$541$	−29.9021	−1.28559	−0.642796	−	0.766037i	$-0.722226\pi$
$541$	−29.9021	−1.28559	−0.642796	+	0.766037i	$0.722226\pi$
$542$	−4.44035	−0.190729
$543$	13.9628	0.599200
$544$	−11.4307	−0.490087
$545$	19.2790	0.825824
$546$	−1.24796	−0.0534079
$547$	−13.9405	−0.596051	−0.298026	−	0.954558i	$-0.596328\pi$
$547$	−13.9405	−0.596051	−0.298026	+	0.954558i	$0.596328\pi$
$548$	2.20330	0.0941205
$549$	14.0654	0.600296
$550$	−1.29061	−0.0550316
$551$	−1.21642	−0.0518213
$552$	3.72505	0.158549
$553$	25.8170	1.09785
$554$	−3.79514	−0.161240
$555$	−0.231575	−0.00982981
$556$	11.9095	0.505075
$557$	13.3462	0.565495	0.282747	−	0.959194i	$-0.408754\pi$
$557$	13.3462	0.565495	0.282747	+	0.959194i	$0.408754\pi$
$558$	1.60796	0.0680702
$559$	−10.2078	−0.431742
$560$	10.5448	0.445597
$561$	−21.7536	−0.918437
$562$	−4.70848	−0.198615
$563$	−37.1959	−1.56762	−0.783809	−	0.621002i	$-0.786726\pi$
$563$	−37.1959	−1.56762	−0.783809	+	0.621002i	$0.786726\pi$
$564$	2.09828	0.0883533
$565$	8.97157	0.377437
$566$	−7.22095	−0.303519
$567$	2.88846	0.121304
$568$	−7.46779	−0.313342
$569$	−8.88231	−0.372366	−0.186183	−	0.982515i	$-0.559612\pi$
$569$	−8.88231	−0.372366	−0.186183	+	0.982515i	$0.559612\pi$
$570$	0.196776	0.00824203
$571$	−40.4257	−1.69176	−0.845882	−	0.533370i	$-0.820925\pi$
$571$	−40.4257	−1.69176	−0.845882	+	0.533370i	$0.820925\pi$
$572$	18.4080	0.769677
$573$	4.07175	0.170100
$574$	−8.28120	−0.345651
$575$	3.89770	0.162545
$576$	−6.62313	−0.275964
$577$	8.55505	0.356151	0.178076	−	0.984017i	$-0.443013\pi$
$577$	8.55505	0.356151	0.178076	+	0.984017i	$0.443013\pi$
$578$	−0.0713518	−0.00296784
$579$	0.0141951	0.000589927 0
$580$	−2.90990	−0.120827
$581$	−30.3497	−1.25912
$582$	0.239803	0.00994014
$583$	17.4482	0.722632
$584$	9.94147	0.411381
$585$	1.78172	0.0736650
$586$	0.507559	0.0209671
$587$	45.2259	1.86667	0.933335	−	0.359005i	$-0.116884\pi$
$587$	45.2259	1.86667	0.933335	+	0.359005i	$0.116884\pi$
$588$	2.60744	0.107529
$589$	−5.38089	−0.221716
$590$	−3.15899	−0.130053
$591$	−0.486831	−0.0200255
$592$	0.845398	0.0347457
$593$	−31.5166	−1.29423	−0.647116	−	0.762392i	$-0.724025\pi$
$593$	−31.5166	−1.29423	−0.647116	+	0.762392i	$0.724025\pi$
$594$	1.29061	0.0529542
$595$	−11.8059	−0.483995
$596$	−25.3147	−1.03693
$597$	−14.3360	−0.586735
$598$	1.68401	0.0688641
$599$	33.3299	1.36182	0.680912	−	0.732365i	$-0.261584\pi$
$599$	33.3299	1.36182	0.680912	+	0.732365i	$0.261584\pi$
$600$	0.955706	0.0390165
$601$	−31.4775	−1.28399	−0.641997	−	0.766707i	$-0.721894\pi$
$601$	−31.4775	−1.28399	−0.641997	+	0.766707i	$0.721894\pi$
$602$	−4.01285	−0.163552
$603$	12.8498	0.523284
$604$	10.6280	0.432446
$605$	17.3267	0.704429
$606$	−0.859720	−0.0349237
$607$	20.8110	0.844693	0.422346	−	0.906434i	$-0.361207\pi$
$607$	20.8110	0.844693	0.422346	+	0.906434i	$0.361207\pi$
$608$	−2.26942	−0.0920373
$609$	−4.32987	−0.175455
$610$	3.41073	0.138097
$611$	1.92589	0.0779132
$612$	7.93420	0.320721
$613$	32.8124	1.32528	0.662641	−	0.748938i	$-0.269436\pi$
$613$	32.8124	1.32528	0.662641	+	0.748938i	$0.269436\pi$
$614$	5.76461	0.232641
$615$	11.8231	0.476753
$616$	14.6923	0.591968
$617$	10.1473	0.408514	0.204257	−	0.978917i	$-0.434522\pi$
$617$	10.1473	0.408514	0.204257	+	0.978917i	$0.434522\pi$
$618$	−0.555952	−0.0223637
$619$	−1.88700	−0.0758448	−0.0379224	−	0.999281i	$-0.512074\pi$
$619$	−1.88700	−0.0758448	−0.0379224	+	0.999281i	$0.512074\pi$
$620$	−12.8721	−0.516955
$621$	−3.89770	−0.156409
$622$	6.73477	0.270040
$623$	−38.7383	−1.55202
$624$	−6.50443	−0.260385
$625$	1.00000	0.0400000
$626$	0.350695	0.0140166
$627$	−4.31890	−0.172480
$628$	2.57901	0.102914
$629$	−0.946509	−0.0377398
$630$	0.700426	0.0279057
$631$	−40.7977	−1.62413	−0.812066	−	0.583566i	$-0.801657\pi$
$631$	−40.7977	−1.62413	−0.812066	+	0.583566i	$0.801657\pi$
$632$	−8.54207	−0.339785
$633$	−16.6939	−0.663522
$634$	3.12076	0.123941
$635$	−20.1229	−0.798553
$636$	−6.36390	−0.252345
$637$	2.39322	0.0948230
$638$	−1.93465	−0.0765933
$639$	7.81391	0.309113
$640$	−7.19937	−0.284580
$641$	14.1424	0.558591	0.279295	−	0.960205i	$-0.409899\pi$
$641$	14.1424	0.558591	0.279295	+	0.960205i	$0.409899\pi$
$642$	−0.301153	−0.0118856
$643$	11.3107	0.446049	0.223024	−	0.974813i	$-0.428407\pi$
$643$	11.3107	0.446049	0.223024	+	0.974813i	$0.428407\pi$
$644$	−21.8547	−0.861196
$645$	5.72916	0.225585
$646$	0.804276	0.0316438
$647$	−29.2195	−1.14874	−0.574369	−	0.818597i	$-0.694752\pi$
$647$	−29.2195	−1.14874	−0.574369	+	0.818597i	$0.694752\pi$
$648$	−0.955706	−0.0375437
$649$	69.3345	2.72162
$650$	0.432051	0.0169464
$651$	−19.1534	−0.750679
$652$	45.0687	1.76503
$653$	40.5711	1.58767	0.793835	−	0.608133i	$-0.208081\pi$
$653$	40.5711	1.58767	0.793835	+	0.608133i	$0.208081\pi$
$654$	−4.67500	−0.182807
$655$	−20.3735	−0.796057
$656$	−43.1619	−1.68519
$657$	−10.4022	−0.405830
$658$	0.757103	0.0295150
$659$	12.3339	0.480462	0.240231	−	0.970716i	$-0.422777\pi$
$659$	12.3339	0.480462	0.240231	+	0.970716i	$0.422777\pi$
$660$	−10.3316	−0.402157
$661$	33.8082	1.31499	0.657494	−	0.753460i	$-0.271616\pi$
$661$	33.8082	1.31499	0.657494	+	0.753460i	$0.271616\pi$
$662$	1.50012	0.0583038
$663$	7.28236	0.282824
$664$	10.0418	0.389698
$665$	−2.34392	−0.0908933
$666$	0.0561549	0.00217596
$667$	5.84274	0.226232
$668$	25.4676	0.985370
$669$	24.7595	0.957257
$670$	3.11596	0.120380
$671$	−74.8600	−2.88994
$672$	−8.07805	−0.311617
$673$	−6.92031	−0.266758	−0.133379	−	0.991065i	$-0.542583\pi$
$673$	−6.92031	−0.266758	−0.133379	+	0.991065i	$0.542583\pi$
$674$	2.33234	0.0898384
$675$	−1.00000	−0.0384900
$676$	19.0732	0.733585
$677$	41.4244	1.59207	0.796035	−	0.605251i	$-0.206927\pi$
$677$	41.4244	1.59207	0.796035	+	0.605251i	$0.206927\pi$
$678$	−2.17553	−0.0835506
$679$	−2.85644	−0.109620
$680$	3.90622	0.149797
$681$	−17.9985	−0.689704
$682$	−8.55799	−0.327702
$683$	−8.69720	−0.332789	−0.166394	−	0.986059i	$-0.553213\pi$
$683$	−8.69720	−0.332789	−0.166394	+	0.986059i	$0.553213\pi$
$684$	1.57524	0.0602307
$685$	−1.13502	−0.0433670
$686$	−3.96216	−0.151276
$687$	28.7312	1.09616
$688$	−20.9151	−0.797382
$689$	−5.84108	−0.222527
$690$	−0.945158	−0.0359815
$691$	13.6727	0.520135	0.260067	−	0.965590i	$-0.416255\pi$
$691$	13.6727	0.520135	0.260067	+	0.965590i	$0.416255\pi$
$692$	−35.0073	−1.33078
$693$	−15.3732	−0.583980
$694$	8.09288	0.307202
$695$	−6.13512	−0.232718
$696$	1.43262	0.0543034
$697$	48.3241	1.83041
$698$	−2.70055	−0.102217
$699$	11.0161	0.416669
$700$	−5.60708	−0.211928
$701$	−3.75865	−0.141962	−0.0709811	−	0.997478i	$-0.522613\pi$
$701$	−3.75865	−0.141962	−0.0709811	+	0.997478i	$0.522613\pi$
$702$	−0.432051	−0.0163067
$703$	−0.187918	−0.00708745
$704$	35.2501	1.32854
$705$	−1.08092	−0.0407097
$706$	−6.26224	−0.235683
$707$	10.2407	0.385139
$708$	−25.2884	−0.950397
$709$	20.3225	0.763229	0.381614	−	0.924322i	$-0.375368\pi$
$709$	20.3225	0.763229	0.381614	+	0.924322i	$0.375368\pi$
$710$	1.89480	0.0711107
$711$	8.93797	0.335200
$712$	12.8174	0.480351
$713$	25.8456	0.967926
$714$	2.86283	0.107139
$715$	−9.48281	−0.354637
$716$	−23.4029	−0.874608
$717$	−11.6824	−0.436286
$718$	2.28611	0.0853169
$719$	1.97662	0.0737156	0.0368578	−	0.999321i	$-0.488265\pi$
$719$	1.97662	0.0737156	0.0368578	+	0.999321i	$0.488265\pi$
$720$	3.65065	0.136052
$721$	6.62229	0.246627
$722$	−4.44765	−0.165524
$723$	2.67838	0.0996099
$724$	27.1045	1.00733
$725$	1.49902	0.0556723
$726$	−4.20156	−0.155935
$727$	24.2598	0.899745	0.449873	−	0.893093i	$-0.351469\pi$
$727$	24.2598	0.899745	0.449873	+	0.893093i	$0.351469\pi$
$728$	−4.91847	−0.182291
$729$	1.00000	0.0370370
$730$	−2.52245	−0.0933600
$731$	23.4166	0.866094
$732$	27.3037	1.00917
$733$	28.8675	1.06625	0.533123	−	0.846038i	$-0.321018\pi$
$733$	28.8675	1.06625	0.533123	+	0.846038i	$0.321018\pi$
$734$	−2.33920	−0.0863415
$735$	−1.34321	−0.0495451
$736$	10.9005	0.401799
$737$	−68.3902	−2.51918
$738$	−2.86699	−0.105536
$739$	−17.6086	−0.647744	−0.323872	−	0.946101i	$-0.604985\pi$
$739$	−17.6086	−0.647744	−0.323872	+	0.946101i	$0.604985\pi$
$740$	−0.449533	−0.0165252
$741$	1.44582	0.0531136
$742$	−2.29623	−0.0842974
$743$	−13.1702	−0.483169	−0.241585	−	0.970380i	$-0.577667\pi$
$743$	−13.1702	−0.483169	−0.241585	+	0.970380i	$0.577667\pi$
$744$	6.33727	0.232336
$745$	13.0408	0.477776
$746$	−3.25805	−0.119286
$747$	−10.5072	−0.384439
$748$	−42.2280	−1.54401
$749$	3.58722	0.131074
$750$	−0.242491	−0.00885452
$751$	−2.50996	−0.0915896	−0.0457948	−	0.998951i	$-0.514582\pi$
$751$	−2.50996	−0.0915896	−0.0457948	+	0.998951i	$0.514582\pi$
$752$	3.94605	0.143898
$753$	14.5562	0.530457
$754$	0.647654	0.0235862
$755$	−5.47495	−0.199254
$756$	5.60708	0.203927
$757$	−27.1563	−0.987014	−0.493507	−	0.869742i	$-0.664285\pi$
$757$	−27.1563	−0.987014	−0.493507	+	0.869742i	$0.664285\pi$
$758$	7.95225	0.288839
$759$	20.7447	0.752983
$760$	0.775533	0.0281315
$761$	40.4583	1.46661	0.733306	−	0.679898i	$-0.237976\pi$
$761$	40.4583	1.46661	0.733306	+	0.679898i	$0.237976\pi$
$762$	4.87963	0.176770
$763$	55.6868	2.01600
$764$	7.90407	0.285959
$765$	−4.08727	−0.147775
$766$	−4.38808	−0.158548
$767$	−23.2109	−0.838096
$768$	−11.5005	−0.414987
$769$	32.7590	1.18132	0.590661	−	0.806920i	$-0.298867\pi$
$769$	32.7590	1.18132	0.590661	+	0.806920i	$0.298867\pi$
$770$	−3.72786	−0.134343
$771$	27.6638	0.996289
$772$	0.0275554	0.000991741 0
$773$	−4.29324	−0.154417	−0.0772085	−	0.997015i	$-0.524601\pi$
$773$	−4.29324	−0.154417	−0.0772085	+	0.997015i	$0.524601\pi$
$774$	−1.38927	−0.0499363
$775$	6.63099	0.238192
$776$	0.945109	0.0339274
$777$	−0.668895	−0.0239965
$778$	−6.30714	−0.226122
$779$	9.59416	0.343746
$780$	3.45867	0.123840
$781$	−41.5878	−1.48813
$782$	−3.86311	−0.138145
$783$	−1.49902	−0.0535707
$784$	4.90359	0.175128
$785$	−1.32856	−0.0474185
$786$	4.94038	0.176218
$787$	38.4608	1.37098	0.685490	−	0.728082i	$-0.259588\pi$
$787$	38.4608	1.37098	0.685490	+	0.728082i	$0.259588\pi$
$788$	−0.945035	−0.0336655
$789$	18.5870	0.661714
$790$	2.16738	0.0771118
$791$	25.9140	0.921397
$792$	5.08653	0.180742
$793$	25.0606	0.889927
$794$	−7.79203	−0.276529
$795$	3.27834	0.116271
$796$	−27.8291	−0.986376
$797$	28.2398	1.00031	0.500153	−	0.865937i	$-0.333277\pi$
$797$	28.2398	1.00031	0.500153	+	0.865937i	$0.333277\pi$
$798$	0.568380	0.0201204
$799$	−4.41800	−0.156298
$800$	2.79666	0.0988769
$801$	−13.4114	−0.473869
$802$	0.242491	0.00856266
$803$	55.3636	1.95374
$804$	24.9440	0.879707
$805$	11.2584	0.396805
$806$	2.86493	0.100913
$807$	9.64395	0.339483
$808$	−3.38833	−0.119201
$809$	38.8395	1.36552	0.682762	−	0.730641i	$-0.260779\pi$
$809$	38.8395	1.36552	0.682762	+	0.730641i	$0.260779\pi$
$810$	0.242491	0.00852027
$811$	3.10601	0.109067	0.0545335	−	0.998512i	$-0.482633\pi$
$811$	3.10601	0.109067	0.0545335	+	0.998512i	$0.482633\pi$
$812$	−8.40513	−0.294962
$813$	18.3114	0.642208
$814$	−0.298872	−0.0104755
$815$	−23.2170	−0.813255
$816$	14.9212	0.522345
$817$	4.64908	0.162651
$818$	−9.54481	−0.333726
$819$	5.14643	0.179831
$820$	22.9510	0.801482
$821$	7.84141	0.273667	0.136834	−	0.990594i	$-0.456307\pi$
$821$	7.84141	0.273667	0.136834	+	0.990594i	$0.456307\pi$
$822$	0.275233	0.00959985
$823$	23.7138	0.826612	0.413306	−	0.910592i	$-0.364374\pi$
$823$	23.7138	0.826612	0.413306	+	0.910592i	$0.364374\pi$
$824$	−2.19112	−0.0763312
$825$	5.32228	0.185298
$826$	−9.12461	−0.317486
$827$	30.9738	1.07706	0.538532	−	0.842605i	$-0.318979\pi$
$827$	30.9738	1.07706	0.538532	+	0.842605i	$0.318979\pi$
$828$	−7.56621	−0.262944
$829$	17.9312	0.622775	0.311387	−	0.950283i	$-0.399206\pi$
$829$	17.9312	0.622775	0.311387	+	0.950283i	$0.399206\pi$
$830$	−2.54791	−0.0884392
$831$	15.6506	0.542915
$832$	−11.8006	−0.409110
$833$	−5.49006	−0.190219
$834$	1.48771	0.0515153
$835$	−13.1195	−0.454019
$836$	−8.38385	−0.289961
$837$	−6.63099	−0.229201
$838$	1.15314	0.0398347
$839$	38.0252	1.31278	0.656389	−	0.754423i	$-0.272083\pi$
$839$	38.0252	1.31278	0.656389	+	0.754423i	$0.272083\pi$
$840$	2.76052	0.0952469
$841$	−26.7529	−0.922515
$842$	−2.56069	−0.0882473
$843$	19.4171	0.668761
$844$	−32.4061	−1.11546
$845$	−9.82548	−0.338007
$846$	0.262113	0.00901163
$847$	50.0474	1.71965
$848$	−11.9680	−0.410984
$849$	29.7782	1.02199
$850$	−0.991126	−0.0339953
$851$	0.902610	0.0309411
$852$	15.1683	0.519659
$853$	55.4484	1.89852	0.949259	−	0.314495i	$-0.101835\pi$
$853$	55.4484	1.89852	0.949259	+	0.314495i	$0.101835\pi$
$854$	9.85177	0.337121
$855$	−0.811477	−0.0277519
$856$	−1.18691	−0.0405676
$857$	−24.2576	−0.828623	−0.414311	−	0.910135i	$-0.635978\pi$
$857$	−24.2576	−0.828623	−0.414311	+	0.910135i	$0.635978\pi$
$858$	2.29950	0.0785035
$859$	−9.90320	−0.337893	−0.168946	−	0.985625i	$-0.554037\pi$
$859$	−9.90320	−0.337893	−0.168946	+	0.985625i	$0.554037\pi$
$860$	11.1214	0.379238
$861$	34.1505	1.16385
$862$	−5.91643	−0.201514
$863$	35.2076	1.19848	0.599240	−	0.800569i	$-0.295469\pi$
$863$	35.2076	1.19848	0.599240	+	0.800569i	$0.295469\pi$
$864$	−2.79666	−0.0951443
$865$	18.0339	0.613170
$866$	−4.87924	−0.165803
$867$	0.294245	0.00999308
$868$	−37.1805	−1.26199
$869$	−47.5704	−1.61371
$870$	−0.363499	−0.0123238
$871$	22.8947	0.775758
$872$	−18.4251	−0.623952
$873$	−0.988913	−0.0334696
$874$	−0.766973	−0.0259433
$875$	2.88846	0.0976478
$876$	−20.1928	−0.682251
$877$	20.1535	0.680535	0.340268	−	0.940329i	$-0.389482\pi$
$877$	20.1535	0.680535	0.340268	+	0.940329i	$0.389482\pi$
$878$	9.56209	0.322705
$879$	−2.09310	−0.0705986
$880$	−19.4298	−0.654977
$881$	−14.5353	−0.489708	−0.244854	−	0.969560i	$-0.578740\pi$
$881$	−14.5353	−0.489708	−0.244854	+	0.969560i	$0.578740\pi$
$882$	0.325717	0.0109674
$883$	−3.25718	−0.109613	−0.0548065	−	0.998497i	$-0.517454\pi$
$883$	−3.25718	−0.109613	−0.0548065	+	0.998497i	$0.517454\pi$
$884$	14.1365	0.475462
$885$	13.0272	0.437905
$886$	−1.22814	−0.0412601
$887$	4.87548	0.163702	0.0818512	−	0.996645i	$-0.473917\pi$
$887$	4.87548	0.163702	0.0818512	+	0.996645i	$0.473917\pi$
$888$	0.221318	0.00742693
$889$	−58.1243	−1.94942
$890$	−3.25215	−0.109012
$891$	−5.32228	−0.178303
$892$	48.0630	1.60927
$893$	−0.877139	−0.0293523
$894$	−3.16227	−0.105762
$895$	12.0559	0.402985
$896$	−20.7951	−0.694716
$897$	−6.94461	−0.231874
$898$	−7.68011	−0.256289
$899$	9.93999	0.331517
$900$	−1.94120	−0.0647066
$901$	13.3994	0.446400
$902$	15.2589	0.508067
$903$	16.5485	0.550698
$904$	−8.57418	−0.285173
$905$	−13.9628	−0.464138
$906$	1.32763	0.0441074
$907$	32.0388	1.06383	0.531916	−	0.846797i	$-0.321472\pi$
$907$	32.0388	1.06383	0.531916	+	0.846797i	$0.321472\pi$
$908$	−34.9386	−1.15948
$909$	3.54537	0.117592
$910$	1.24796	0.0413696
$911$	−43.7360	−1.44904	−0.724518	−	0.689255i	$-0.757938\pi$
$911$	−43.7360	−1.44904	−0.724518	+	0.689255i	$0.757938\pi$
$912$	2.96241	0.0980953
$913$	55.9224	1.85076
$914$	2.64899	0.0876208
$915$	−14.0654	−0.464988
$916$	55.7729	1.84279
$917$	−58.8479	−1.94333
$918$	0.991126	0.0327120
$919$	37.9391	1.25150	0.625748	−	0.780025i	$-0.284794\pi$
$919$	37.9391	1.25150	0.625748	+	0.780025i	$0.284794\pi$
$920$	−3.72505	−0.122811
$921$	−23.7725	−0.783329
$922$	4.11114	0.135393
$923$	13.9222	0.458254
$924$	−29.8424	−0.981744
$925$	0.231575	0.00761414
$926$	−1.07659	−0.0353791
$927$	2.29267	0.0753011
$928$	4.19225	0.137617
$929$	−31.3521	−1.02863	−0.514314	−	0.857602i	$-0.671954\pi$
$929$	−31.3521	−1.02863	−0.514314	+	0.857602i	$0.671954\pi$
$930$	−1.60796	−0.0527270
$931$	−1.08998	−0.0357228
$932$	21.3845	0.700473
$933$	−27.7733	−0.909256
$934$	−4.74767	−0.155349
$935$	21.7536	0.711418
$936$	−1.70280	−0.0556577
$937$	34.2182	1.11786	0.558931	−	0.829214i	$-0.311212\pi$
$937$	34.2182	1.11786	0.558931	+	0.829214i	$0.311212\pi$
$938$	9.00033	0.293871
$939$	−1.44622	−0.0471955
$940$	−2.09828	−0.0684382
$941$	−50.0725	−1.63232	−0.816158	−	0.577829i	$-0.803900\pi$
$941$	−50.0725	−1.63232	−0.816158	+	0.577829i	$0.803900\pi$
$942$	0.322165	0.0104967
$943$	−46.0829	−1.50066
$944$	−47.5578	−1.54787
$945$	−2.88846	−0.0939617
$946$	7.39408	0.240402
$947$	41.6684	1.35404	0.677020	−	0.735964i	$-0.263271\pi$
$947$	41.6684	1.35404	0.677020	+	0.735964i	$0.263271\pi$
$948$	17.3504	0.563514
$949$	−18.5339	−0.601634
$950$	−0.196776	−0.00638425
$951$	−12.8696	−0.417325
$952$	11.2830	0.365683
$953$	42.4903	1.37640	0.688198	−	0.725523i	$-0.258402\pi$
$953$	42.4903	1.37640	0.688198	+	0.725523i	$0.258402\pi$
$954$	−0.794968	−0.0257380
$955$	−4.07175	−0.131759
$956$	−22.6778	−0.733452
$957$	7.97821	0.257899
$958$	−0.207012	−0.00668826
$959$	−3.27847	−0.105867
$960$	6.62313	0.213760
$961$	12.9700	0.418388
$962$	0.100052	0.00322581
$963$	1.24192	0.0400202
$964$	5.19926	0.167457
$965$	−0.0141951	−0.000456955 0
$966$	−2.73005	−0.0878380
$967$	−58.5057	−1.88142	−0.940708	−	0.339219i	$-0.889837\pi$
$967$	−58.5057	−1.88142	−0.940708	+	0.339219i	$0.889837\pi$
$968$	−16.5592	−0.532232
$969$	−3.31672	−0.106548
$970$	−0.239803	−0.00769960
$971$	−7.26266	−0.233070	−0.116535	−	0.993187i	$-0.537179\pi$
$971$	−7.26266	−0.233070	−0.116535	+	0.993187i	$0.537179\pi$
$972$	1.94120	0.0622640
$973$	−17.7211	−0.568111
$974$	8.39371	0.268952
$975$	−1.78172	−0.0570607
$976$	51.3478	1.64360
$977$	−36.8183	−1.17792	−0.588961	−	0.808162i	$-0.700463\pi$
$977$	−36.8183	−1.17792	−0.588961	+	0.808162i	$0.700463\pi$
$978$	5.62991	0.180025
$979$	71.3793	2.28129
$980$	−2.60744	−0.0832915
$981$	19.2790	0.615533
$982$	−2.52271	−0.0805029
$983$	40.7583	1.29999	0.649994	−	0.759940i	$-0.274772\pi$
$983$	40.7583	1.29999	0.649994	+	0.759940i	$0.274772\pi$
$984$	−11.2994	−0.360211
$985$	0.486831	0.0155117
$986$	−1.48572	−0.0473149
$987$	−3.12219	−0.0993804
$988$	2.80663	0.0892908
$989$	−22.3305	−0.710070
$990$	−1.29061	−0.0410181
$991$	44.2384	1.40528	0.702640	−	0.711546i	$-0.252004\pi$
$991$	44.2384	1.40528	0.702640	+	0.711546i	$0.252004\pi$
$992$	18.5446	0.588792
$993$	−6.18629	−0.196316
$994$	5.47306	0.173595
$995$	14.3360	0.454483
$996$	−20.3966	−0.646291
$997$	−51.0938	−1.61816	−0.809079	−	0.587700i	$-0.800034\pi$
$997$	−51.0938	−1.61816	−0.809079	+	0.587700i	$0.800034\pi$
$998$	−6.46635	−0.204689
$999$	−0.231575	−0.00732671

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6015.2.a.d.1.17	✓	29

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6015.2.a.d.1.17	✓	29	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)

\(f(q)\)	\(=\)	\(q+0.242491 q^{2} -1.00000 q^{3} -1.94120 q^{4} +1.00000 q^{5} -0.242491 q^{6} +2.88846 q^{7} -0.955706 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.242491 q^{2} -1.00000 q^{3} -1.94120 q^{4} +1.00000 q^{5} -0.242491 q^{6} +2.88846 q^{7} -0.955706 q^{8} +1.00000 q^{9} +0.242491 q^{10} -5.32228 q^{11} +1.94120 q^{12} +1.78172 q^{13} +0.700426 q^{14} -1.00000 q^{15} +3.65065 q^{16} -4.08727 q^{17} +0.242491 q^{18} -0.811477 q^{19} -1.94120 q^{20} -2.88846 q^{21} -1.29061 q^{22} +3.89770 q^{23} +0.955706 q^{24} +1.00000 q^{25} +0.432051 q^{26} -1.00000 q^{27} -5.60708 q^{28} +1.49902 q^{29} -0.242491 q^{30} +6.63099 q^{31} +2.79666 q^{32} +5.32228 q^{33} -0.991126 q^{34} +2.88846 q^{35} -1.94120 q^{36} +0.231575 q^{37} -0.196776 q^{38} -1.78172 q^{39} -0.955706 q^{40} -11.8231 q^{41} -0.700426 q^{42} -5.72916 q^{43} +10.3316 q^{44} +1.00000 q^{45} +0.945158 q^{46} +1.08092 q^{47} -3.65065 q^{48} +1.34321 q^{49} +0.242491 q^{50} +4.08727 q^{51} -3.45867 q^{52} -3.27834 q^{53} -0.242491 q^{54} -5.32228 q^{55} -2.76052 q^{56} +0.811477 q^{57} +0.363499 q^{58} -13.0272 q^{59} +1.94120 q^{60} +14.0654 q^{61} +1.60796 q^{62} +2.88846 q^{63} -6.62313 q^{64} +1.78172 q^{65} +1.29061 q^{66} +12.8498 q^{67} +7.93420 q^{68} -3.89770 q^{69} +0.700426 q^{70} +7.81391 q^{71} -0.955706 q^{72} -10.4022 q^{73} +0.0561549 q^{74} -1.00000 q^{75} +1.57524 q^{76} -15.3732 q^{77} -0.432051 q^{78} +8.93797 q^{79} +3.65065 q^{80} +1.00000 q^{81} -2.86699 q^{82} -10.5072 q^{83} +5.60708 q^{84} -4.08727 q^{85} -1.38927 q^{86} -1.49902 q^{87} +5.08653 q^{88} -13.4114 q^{89} +0.242491 q^{90} +5.14643 q^{91} -7.56621 q^{92} -6.63099 q^{93} +0.262113 q^{94} -0.811477 q^{95} -2.79666 q^{96} -0.988913 q^{97} +0.325717 q^{98} -5.32228 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 29 q - q^{2} - 29 q^{3} + 27 q^{4} + 29 q^{5} + q^{6} + 2 q^{7} - 6 q^{8} + 29 q^{9}+O(q^{10}) \) 29 * q - q^2 - 29 * q^3 + 27 * q^4 + 29 * q^5 + q^6 + 2 * q^7 - 6 * q^8 + 29 * q^9	\( 29 q - q^{2} - 29 q^{3} + 27 q^{4} + 29 q^{5} + q^{6} + 2 q^{7} - 6 q^{8} + 29 q^{9} - q^{10} - 21 q^{11} - 27 q^{12} - 8 q^{13} - 30 q^{14} - 29 q^{15} + 23 q^{16} - 28 q^{17} - q^{18} - 9 q^{19} + 27 q^{20} - 2 q^{21} - 9 q^{22} + 6 q^{24} + 29 q^{25} - 34 q^{26} - 29 q^{27} + 6 q^{28} - 61 q^{29} + q^{30} - 19 q^{31} - 8 q^{32} + 21 q^{33} - 16 q^{34} + 2 q^{35} + 27 q^{36} - 4 q^{37} + 4 q^{38} + 8 q^{39} - 6 q^{40} - 85 q^{41} + 30 q^{42} + 29 q^{43} - 69 q^{44} + 29 q^{45} - 35 q^{46} - 2 q^{47} - 23 q^{48} + q^{49} - q^{50} + 28 q^{51} - 28 q^{52} - 5 q^{53} + q^{54} - 21 q^{55} - 97 q^{56} + 9 q^{57} + 6 q^{58} - 43 q^{59} - 27 q^{60} - 59 q^{61} - 17 q^{62} + 2 q^{63} - 6 q^{64} - 8 q^{65} + 9 q^{66} + 28 q^{67} - 44 q^{68} - 30 q^{70} - 44 q^{71} - 6 q^{72} - 41 q^{73} - 50 q^{74} - 29 q^{75} - 62 q^{76} - 20 q^{77} + 34 q^{78} - 25 q^{79} + 23 q^{80} + 29 q^{81} - 29 q^{82} - 7 q^{83} - 6 q^{84} - 28 q^{85} - 43 q^{86} + 61 q^{87} - 3 q^{88} - 109 q^{89} - q^{90} - q^{91} - 11 q^{92} + 19 q^{93} - 20 q^{94} - 9 q^{95} + 8 q^{96} - 51 q^{97} - 12 q^{98} - 21 q^{99}+O(q^{100}) \) 29 * q - q^2 - 29 * q^3 + 27 * q^4 + 29 * q^5 + q^6 + 2 * q^7 - 6 * q^8 + 29 * q^9 - q^10 - 21 * q^11 - 27 * q^12 - 8 * q^13 - 30 * q^14 - 29 * q^15 + 23 * q^16 - 28 * q^17 - q^18 - 9 * q^19 + 27 * q^20 - 2 * q^21 - 9 * q^22 + 6 * q^24 + 29 * q^25 - 34 * q^26 - 29 * q^27 + 6 * q^28 - 61 * q^29 + q^30 - 19 * q^31 - 8 * q^32 + 21 * q^33 - 16 * q^34 + 2 * q^35 + 27 * q^36 - 4 * q^37 + 4 * q^38 + 8 * q^39 - 6 * q^40 - 85 * q^41 + 30 * q^42 + 29 * q^43 - 69 * q^44 + 29 * q^45 - 35 * q^46 - 2 * q^47 - 23 * q^48 + q^49 - q^50 + 28 * q^51 - 28 * q^52 - 5 * q^53 + q^54 - 21 * q^55 - 97 * q^56 + 9 * q^57 + 6 * q^58 - 43 * q^59 - 27 * q^60 - 59 * q^61 - 17 * q^62 + 2 * q^63 - 6 * q^64 - 8 * q^65 + 9 * q^66 + 28 * q^67 - 44 * q^68 - 30 * q^70 - 44 * q^71 - 6 * q^72 - 41 * q^73 - 50 * q^74 - 29 * q^75 - 62 * q^76 - 20 * q^77 + 34 * q^78 - 25 * q^79 + 23 * q^80 + 29 * q^81 - 29 * q^82 - 7 * q^83 - 6 * q^84 - 28 * q^85 - 43 * q^86 + 61 * q^87 - 3 * q^88 - 109 * q^89 - q^90 - q^91 - 11 * q^92 + 19 * q^93 - 20 * q^94 - 9 * q^95 + 8 * q^96 - 51 * q^97 - 12 * q^98 - 21 * q^99

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