LMFDB - Embedded newform 6001.2.a.a.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6001,2,Mod(1,6001)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6001, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("6001.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6001 = 17 \cdot 353 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6001.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:	$47.9182262530$
Analytic rank:	$1$
Dimension:	$113$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	6001.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.15299 q^{2} +2.37258 q^{3} +2.63537 q^{4} -0.231510 q^{5} -5.10813 q^{6} +3.32403 q^{7} -1.36794 q^{8} +2.62912 q^{9} +O(q^{10})$	\(q-2.15299 q^{2} +2.37258 q^{3} +2.63537 q^{4} -0.231510 q^{5} -5.10813 q^{6} +3.32403 q^{7} -1.36794 q^{8} +2.62912 q^{9} +0.498439 q^{10} +0.166800 q^{11} +6.25261 q^{12} -4.60039 q^{13} -7.15661 q^{14} -0.549276 q^{15} -2.32558 q^{16} -1.00000 q^{17} -5.66046 q^{18} +4.38750 q^{19} -0.610114 q^{20} +7.88652 q^{21} -0.359120 q^{22} -7.27356 q^{23} -3.24554 q^{24} -4.94640 q^{25} +9.90460 q^{26} -0.879951 q^{27} +8.76004 q^{28} +1.13509 q^{29} +1.18258 q^{30} -5.66107 q^{31} +7.74282 q^{32} +0.395747 q^{33} +2.15299 q^{34} -0.769547 q^{35} +6.92868 q^{36} +7.89040 q^{37} -9.44625 q^{38} -10.9148 q^{39} +0.316692 q^{40} -5.68921 q^{41} -16.9796 q^{42} -5.05389 q^{43} +0.439580 q^{44} -0.608667 q^{45} +15.6599 q^{46} -1.89436 q^{47} -5.51761 q^{48} +4.04919 q^{49} +10.6496 q^{50} -2.37258 q^{51} -12.1237 q^{52} -1.97048 q^{53} +1.89453 q^{54} -0.0386160 q^{55} -4.54707 q^{56} +10.4097 q^{57} -2.44385 q^{58} -0.964051 q^{59} -1.44754 q^{60} -2.03849 q^{61} +12.1882 q^{62} +8.73926 q^{63} -12.0191 q^{64} +1.06504 q^{65} -0.852039 q^{66} -1.05405 q^{67} -2.63537 q^{68} -17.2571 q^{69} +1.65683 q^{70} +11.5884 q^{71} -3.59647 q^{72} -11.7649 q^{73} -16.9880 q^{74} -11.7357 q^{75} +11.5627 q^{76} +0.554450 q^{77} +23.4994 q^{78} +4.45651 q^{79} +0.538395 q^{80} -9.97510 q^{81} +12.2488 q^{82} -14.9303 q^{83} +20.7839 q^{84} +0.231510 q^{85} +10.8810 q^{86} +2.69310 q^{87} -0.228173 q^{88} -5.76793 q^{89} +1.31045 q^{90} -15.2918 q^{91} -19.1685 q^{92} -13.4313 q^{93} +4.07855 q^{94} -1.01575 q^{95} +18.3704 q^{96} +17.2193 q^{97} -8.71786 q^{98} +0.438538 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 113 q - 11 q^{2} - 11 q^{3} + 103 q^{4} - 19 q^{5} - 13 q^{6} + 11 q^{7} - 36 q^{8} + 94 q^{9}+O(q^{10}) $ 113 * q - 11 * q^2 - 11 * q^3 + 103 * q^4 - 19 * q^5 - 13 * q^6 + 11 * q^7 - 36 * q^8 + 94 * q^9	\( 113 q - 11 q^{2} - 11 q^{3} + 103 q^{4} - 19 q^{5} - 13 q^{6} + 11 q^{7} - 36 q^{8} + 94 q^{9} - 5 q^{10} - 40 q^{11} - 19 q^{12} - 18 q^{13} - 48 q^{14} - 63 q^{15} + 79 q^{16} - 113 q^{17} - 32 q^{18} - 46 q^{19} - 56 q^{20} - 46 q^{21} + 14 q^{22} - 35 q^{23} - 42 q^{24} + 88 q^{25} - 89 q^{26} - 41 q^{27} + 20 q^{28} - 51 q^{29} - 18 q^{30} - 57 q^{31} - 93 q^{32} - 40 q^{33} + 11 q^{34} - 69 q^{35} + 18 q^{36} + 16 q^{37} - 74 q^{38} - 51 q^{39} + 2 q^{40} - 87 q^{41} - 23 q^{42} - 32 q^{43} - 110 q^{44} - 17 q^{45} - 17 q^{46} - 161 q^{47} - 36 q^{48} + 56 q^{49} - 69 q^{50} + 11 q^{51} - 49 q^{52} - 48 q^{53} - 38 q^{54} - 79 q^{55} - 171 q^{56} + 20 q^{57} + 13 q^{58} - 174 q^{59} - 146 q^{60} - 34 q^{61} - 34 q^{62} - 14 q^{63} + 62 q^{64} - 22 q^{65} - 60 q^{66} - 50 q^{67} - 103 q^{68} - 59 q^{69} - 58 q^{70} - 189 q^{71} - 123 q^{72} - 4 q^{73} - 24 q^{74} - 106 q^{75} - 92 q^{76} - 78 q^{77} - 42 q^{78} + 8 q^{79} - 150 q^{80} + 13 q^{81} + 6 q^{82} - 109 q^{83} - 114 q^{84} + 19 q^{85} - 116 q^{86} - 106 q^{87} + 54 q^{88} - 170 q^{89} - q^{90} - 43 q^{91} - 94 q^{92} - 69 q^{93} - 35 q^{94} - 78 q^{95} - 44 q^{96} - 3 q^{97} - 68 q^{98} - 119 q^{99}+O(q^{100}) \) 113 * q - 11 * q^2 - 11 * q^3 + 103 * q^4 - 19 * q^5 - 13 * q^6 + 11 * q^7 - 36 * q^8 + 94 * q^9 - 5 * q^10 - 40 * q^11 - 19 * q^12 - 18 * q^13 - 48 * q^14 - 63 * q^15 + 79 * q^16 - 113 * q^17 - 32 * q^18 - 46 * q^19 - 56 * q^20 - 46 * q^21 + 14 * q^22 - 35 * q^23 - 42 * q^24 + 88 * q^25 - 89 * q^26 - 41 * q^27 + 20 * q^28 - 51 * q^29 - 18 * q^30 - 57 * q^31 - 93 * q^32 - 40 * q^33 + 11 * q^34 - 69 * q^35 + 18 * q^36 + 16 * q^37 - 74 * q^38 - 51 * q^39 + 2 * q^40 - 87 * q^41 - 23 * q^42 - 32 * q^43 - 110 * q^44 - 17 * q^45 - 17 * q^46 - 161 * q^47 - 36 * q^48 + 56 * q^49 - 69 * q^50 + 11 * q^51 - 49 * q^52 - 48 * q^53 - 38 * q^54 - 79 * q^55 - 171 * q^56 + 20 * q^57 + 13 * q^58 - 174 * q^59 - 146 * q^60 - 34 * q^61 - 34 * q^62 - 14 * q^63 + 62 * q^64 - 22 * q^65 - 60 * q^66 - 50 * q^67 - 103 * q^68 - 59 * q^69 - 58 * q^70 - 189 * q^71 - 123 * q^72 - 4 * q^73 - 24 * q^74 - 106 * q^75 - 92 * q^76 - 78 * q^77 - 42 * q^78 + 8 * q^79 - 150 * q^80 + 13 * q^81 + 6 * q^82 - 109 * q^83 - 114 * q^84 + 19 * q^85 - 116 * q^86 - 106 * q^87 + 54 * q^88 - 170 * q^89 - q^90 - 43 * q^91 - 94 * q^92 - 69 * q^93 - 35 * q^94 - 78 * q^95 - 44 * q^96 - 3 * q^97 - 68 * q^98 - 119 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.15299	−1.52239	−0.761197	−	0.648521i	$-0.775388\pi$
$2$	−2.15299	−1.52239	−0.761197	+	0.648521i	$0.775388\pi$
$3$	2.37258	1.36981	0.684904	−	0.728634i	$-0.259844\pi$
$3$	2.37258	1.36981	0.684904	+	0.728634i	$0.259844\pi$
$4$	2.63537	1.31768
$5$	−0.231510	−0.103535	−0.0517673	−	0.998659i	$-0.516485\pi$
$5$	−0.231510	−0.103535	−0.0517673	+	0.998659i	$0.516485\pi$
$6$	−5.10813	−2.08539
$7$	3.32403	1.25637	0.628183	−	0.778066i	$-0.283799\pi$
$7$	3.32403	1.25637	0.628183	+	0.778066i	$0.283799\pi$
$8$	−1.36794	−0.483639
$9$	2.62912	0.876372
$10$	0.498439	0.157620
$11$	0.166800	0.0502922	0.0251461	−	0.999684i	$-0.491995\pi$
$11$	0.166800	0.0502922	0.0251461	+	0.999684i	$0.491995\pi$
$12$	6.25261	1.80497
$13$	−4.60039	−1.27592	−0.637960	−	0.770070i	$-0.720221\pi$
$13$	−4.60039	−1.27592	−0.637960	+	0.770070i	$0.720221\pi$
$14$	−7.15661	−1.91268
$15$	−0.549276	−0.141822
$16$	−2.32558	−0.581394
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−5.66046	−1.33418
$19$	4.38750	1.00656	0.503281	−	0.864123i	$-0.332126\pi$
$19$	4.38750	1.00656	0.503281	+	0.864123i	$0.332126\pi$
$20$	−0.610114	−0.136426
$21$	7.88652	1.72098
$22$	−0.359120	−0.0765646
$23$	−7.27356	−1.51664	−0.758321	−	0.651881i	$-0.773980\pi$
$23$	−7.27356	−1.51664	−0.758321	+	0.651881i	$0.773980\pi$
$24$	−3.24554	−0.662492
$25$	−4.94640	−0.989281
$26$	9.90460	1.94245
$27$	−0.879951	−0.169347
$28$	8.76004	1.65549
$29$	1.13509	0.210782	0.105391	−	0.994431i	$-0.466391\pi$
$29$	1.13509	0.210782	0.105391	+	0.994431i	$0.466391\pi$
$30$	1.18258	0.215909
$31$	−5.66107	−1.01676	−0.508379	−	0.861134i	$-0.669755\pi$
$31$	−5.66107	−1.01676	−0.508379	+	0.861134i	$0.669755\pi$
$32$	7.74282	1.36875
$33$	0.395747	0.0688907
$34$	2.15299	0.369235
$35$	−0.769547	−0.130077
$36$	6.92868	1.15478
$37$	7.89040	1.29717	0.648587	−	0.761140i	$-0.275360\pi$
$37$	7.89040	1.29717	0.648587	+	0.761140i	$0.275360\pi$
$38$	−9.44625	−1.53238
$39$	−10.9148	−1.74776
$40$	0.316692	0.0500733
$41$	−5.68921	−0.888505	−0.444253	−	0.895902i	$-0.646531\pi$
$41$	−5.68921	−0.888505	−0.444253	+	0.895902i	$0.646531\pi$
$42$	−16.9796	−2.62001
$43$	−5.05389	−0.770711	−0.385356	−	0.922768i	$-0.625921\pi$
$43$	−5.05389	−0.770711	−0.385356	+	0.922768i	$0.625921\pi$
$44$	0.439580	0.0662692
$45$	−0.608667	−0.0907348
$46$	15.6599	2.30893
$47$	−1.89436	−0.276321	−0.138161	−	0.990410i	$-0.544119\pi$
$47$	−1.89436	−0.276321	−0.138161	+	0.990410i	$0.544119\pi$
$48$	−5.51761	−0.796398
$49$	4.04919	0.578455
$50$	10.6496	1.50607
$51$	−2.37258	−0.332227
$52$	−12.1237	−1.68126
$53$	−1.97048	−0.270666	−0.135333	−	0.990800i	$-0.543210\pi$
$53$	−1.97048	−0.270666	−0.135333	+	0.990800i	$0.543210\pi$
$54$	1.89453	0.257812
$55$	−0.0386160	−0.00520698
$56$	−4.54707	−0.607627
$57$	10.4097	1.37880
$58$	−2.44385	−0.320893
$59$	−0.964051	−0.125509	−0.0627544	−	0.998029i	$-0.519988\pi$
$59$	−0.964051	−0.125509	−0.0627544	+	0.998029i	$0.519988\pi$
$60$	−1.44754	−0.186877
$61$	−2.03849	−0.261002	−0.130501	−	0.991448i	$-0.541659\pi$
$61$	−2.03849	−0.261002	−0.130501	+	0.991448i	$0.541659\pi$
$62$	12.1882	1.54791
$63$	8.73926	1.10104
$64$	−12.0191	−1.50238
$65$	1.06504	0.132102
$66$	−0.852039	−0.104879
$67$	−1.05405	−0.128772	−0.0643862	−	0.997925i	$-0.520509\pi$
$67$	−1.05405	−0.128772	−0.0643862	+	0.997925i	$0.520509\pi$
$68$	−2.63537	−0.319585
$69$	−17.2571	−2.07751
$70$	1.65683	0.198029
$71$	11.5884	1.37529	0.687647	−	0.726045i	$-0.258644\pi$
$71$	11.5884	1.37529	0.687647	+	0.726045i	$0.258644\pi$
$72$	−3.59647	−0.423848
$73$	−11.7649	−1.37698	−0.688488	−	0.725247i	$-0.741725\pi$
$73$	−11.7649	−1.37698	−0.688488	+	0.725247i	$0.741725\pi$
$74$	−16.9880	−1.97481
$75$	−11.7357	−1.35512
$76$	11.5627	1.32633
$77$	0.554450	0.0631854
$78$	23.4994	2.66078
$79$	4.45651	0.501397	0.250698	−	0.968065i	$-0.419340\pi$
$79$	4.45651	0.501397	0.250698	+	0.968065i	$0.419340\pi$
$80$	0.538395	0.0601944
$81$	−9.97510	−1.10834
$82$	12.2488	1.35265
$83$	−14.9303	−1.63882	−0.819409	−	0.573210i	$-0.805698\pi$
$83$	−14.9303	−1.63882	−0.819409	+	0.573210i	$0.805698\pi$
$84$	20.7839	2.26771
$85$	0.231510	0.0251108
$86$	10.8810	1.17333
$87$	2.69310	0.288730
$88$	−0.228173	−0.0243233
$89$	−5.76793	−0.611400	−0.305700	−	0.952128i	$-0.598890\pi$
$89$	−5.76793	−0.611400	−0.305700	+	0.952128i	$0.598890\pi$
$90$	1.31045	0.138134
$91$	−15.2918	−1.60302
$92$	−19.1685	−1.99845
$93$	−13.4313	−1.39276
$94$	4.07855	0.420670
$95$	−1.01575	−0.104214
$96$	18.3704	1.87492
$97$	17.2193	1.74836	0.874180	−	0.485602i	$-0.161400\pi$
$97$	17.2193	1.74836	0.874180	+	0.485602i	$0.161400\pi$
$98$	−8.71786	−0.880636
$99$	0.438538	0.0440747
$100$	−13.0356	−1.30356
$101$	−13.9955	−1.39260	−0.696300	−	0.717751i	$-0.745172\pi$
$101$	−13.9955	−1.39260	−0.696300	+	0.717751i	$0.745172\pi$
$102$	5.10813	0.505780
$103$	4.24779	0.418547	0.209273	−	0.977857i	$-0.432890\pi$
$103$	4.24779	0.418547	0.209273	+	0.977857i	$0.432890\pi$
$104$	6.29305	0.617084
$105$	−1.82581	−0.178181
$106$	4.24242	0.412060
$107$	−16.0421	−1.55085	−0.775426	−	0.631438i	$-0.782465\pi$
$107$	−16.0421	−1.55085	−0.775426	+	0.631438i	$0.782465\pi$
$108$	−2.31899	−0.223145
$109$	−3.25158	−0.311445	−0.155722	−	0.987801i	$-0.549771\pi$
$109$	−3.25158	−0.311445	−0.155722	+	0.987801i	$0.549771\pi$
$110$	0.0831399	0.00792708
$111$	18.7206	1.77688
$112$	−7.73029	−0.730444
$113$	−12.9044	−1.21394	−0.606971	−	0.794724i	$-0.707615\pi$
$113$	−12.9044	−1.21394	−0.606971	+	0.794724i	$0.707615\pi$
$114$	−22.4119	−2.09907
$115$	1.68390	0.157025
$116$	2.99139	0.277744
$117$	−12.0950	−1.11818
$118$	2.07559	0.191074
$119$	−3.32403	−0.304713
$120$	0.751375	0.0685908
$121$	−10.9722	−0.997471
$122$	4.38886	0.397348
$123$	−13.4981	−1.21708
$124$	−14.9190	−1.33976
$125$	2.30269	0.205959
$126$	−18.8155	−1.67622
$127$	11.8559	1.05204	0.526020	−	0.850472i	$-0.323684\pi$
$127$	11.8559	1.05204	0.526020	+	0.850472i	$0.323684\pi$
$128$	10.3913	0.918468
$129$	−11.9907	−1.05573
$130$	−2.29302	−0.201111
$131$	−18.9244	−1.65343	−0.826715	−	0.562620i	$-0.809793\pi$
$131$	−18.9244	−1.65343	−0.826715	+	0.562620i	$0.809793\pi$
$132$	1.04294	0.0907761
$133$	14.5842	1.26461
$134$	2.26935	0.196042
$135$	0.203718	0.0175332
$136$	1.36794	0.117300
$137$	18.2945	1.56300	0.781501	−	0.623904i	$-0.214454\pi$
$137$	18.2945	1.56300	0.781501	+	0.623904i	$0.214454\pi$
$138$	37.1543	3.16279
$139$	−17.4733	−1.48207	−0.741035	−	0.671466i	$-0.765665\pi$
$139$	−17.4733	−1.48207	−0.741035	+	0.671466i	$0.765665\pi$
$140$	−2.02804	−0.171401
$141$	−4.49452	−0.378507
$142$	−24.9498	−2.09374
$143$	−0.767348	−0.0641688
$144$	−6.11421	−0.509518
$145$	−0.262786	−0.0218232
$146$	25.3297	2.09630
$147$	9.60700	0.792372
$148$	20.7941	1.70926
$149$	13.7066	1.12289	0.561443	−	0.827516i	$-0.310246\pi$
$149$	13.7066	1.12289	0.561443	+	0.827516i	$0.310246\pi$
$150$	25.2669	2.06303
$151$	17.2029	1.39995	0.699976	−	0.714166i	$-0.253194\pi$
$151$	17.2029	1.39995	0.699976	+	0.714166i	$0.253194\pi$
$152$	−6.00183	−0.486813
$153$	−2.62912	−0.212551
$154$	−1.19373	−0.0961931
$155$	1.31059	0.105270
$156$	−28.7644	−2.30300
$157$	19.8714	1.58591	0.792955	−	0.609281i	$-0.208542\pi$
$157$	19.8714	1.58591	0.792955	+	0.609281i	$0.208542\pi$
$158$	−9.59483	−0.763324
$159$	−4.67510	−0.370760
$160$	−1.79254	−0.141713
$161$	−24.1775	−1.90546
$162$	21.4763	1.68734
$163$	1.61401	0.126419	0.0632096	−	0.998000i	$-0.479866\pi$
$163$	1.61401	0.126419	0.0632096	+	0.998000i	$0.479866\pi$
$164$	−14.9932	−1.17077
$165$	−0.0916194	−0.00713256
$166$	32.1449	2.49493
$167$	−6.38449	−0.494047	−0.247023	−	0.969010i	$-0.579452\pi$
$167$	−6.38449	−0.494047	−0.247023	+	0.969010i	$0.579452\pi$
$168$	−10.7883	−0.832332
$169$	8.16361	0.627970
$170$	−0.498439	−0.0382285
$171$	11.5353	0.882123
$172$	−13.3189	−1.01555
$173$	13.5564	1.03068	0.515338	−	0.856987i	$-0.327666\pi$
$173$	13.5564	1.03068	0.515338	+	0.856987i	$0.327666\pi$
$174$	−5.79821	−0.439562
$175$	−16.4420	−1.24290
$176$	−0.387907	−0.0292396
$177$	−2.28728	−0.171923
$178$	12.4183	0.930791
$179$	5.35766	0.400451	0.200225	−	0.979750i	$-0.435833\pi$
$179$	5.35766	0.400451	0.200225	+	0.979750i	$0.435833\pi$
$180$	−1.60406	−0.119560
$181$	−13.1858	−0.980093	−0.490046	−	0.871696i	$-0.663020\pi$
$181$	−13.1858	−0.980093	−0.490046	+	0.871696i	$0.663020\pi$
$182$	32.9232	2.44043
$183$	−4.83648	−0.357523
$184$	9.94978	0.733507
$185$	−1.82671	−0.134302
$186$	28.9175	2.12033
$187$	−0.166800	−0.0121977
$188$	−4.99234	−0.364104
$189$	−2.92498	−0.212761
$190$	2.18690	0.158655
$191$	−22.7433	−1.64565	−0.822824	−	0.568296i	$-0.807603\pi$
$191$	−22.7433	−1.64565	−0.822824	+	0.568296i	$0.807603\pi$
$192$	−28.5161	−2.05797
$193$	20.0822	1.44554	0.722772	−	0.691086i	$-0.242867\pi$
$193$	20.0822	1.44554	0.722772	+	0.691086i	$0.242867\pi$
$194$	−37.0731	−2.66169
$195$	2.52688	0.180954
$196$	10.6711	0.762221
$197$	−8.13900	−0.579880	−0.289940	−	0.957045i	$-0.593635\pi$
$197$	−8.13900	−0.579880	−0.289940	+	0.957045i	$0.593635\pi$
$198$	−0.944168	−0.0670991
$199$	−10.4322	−0.739516	−0.369758	−	0.929128i	$-0.620559\pi$
$199$	−10.4322	−0.739516	−0.369758	+	0.929128i	$0.620559\pi$
$200$	6.76637	0.478455
$201$	−2.50081	−0.176393
$202$	30.1321	2.12009
$203$	3.77309	0.264819
$204$	−6.25261	−0.437770
$205$	1.31711	0.0919910
$206$	−9.14544	−0.637193
$207$	−19.1230	−1.32914
$208$	10.6986	0.741812
$209$	0.731838	0.0506223
$210$	3.93095	0.271261
$211$	18.1560	1.24991	0.624956	−	0.780660i	$-0.285117\pi$
$211$	18.1560	1.24991	0.624956	+	0.780660i	$0.285117\pi$
$212$	−5.19293	−0.356652
$213$	27.4944	1.88389
$214$	34.5386	2.36101
$215$	1.17003	0.0797952
$216$	1.20372	0.0819026
$217$	−18.8176	−1.27742
$218$	7.00062	0.474142
$219$	−27.9131	−1.88619
$220$	−0.101767	−0.00686115
$221$	4.60039	0.309456
$222$	−40.3052	−2.70511
$223$	−20.3960	−1.36582	−0.682910	−	0.730503i	$-0.739286\pi$
$223$	−20.3960	−1.36582	−0.682910	+	0.730503i	$0.739286\pi$
$224$	25.7374	1.71965
$225$	−13.0047	−0.866978
$226$	27.7830	1.84810
$227$	−0.497714	−0.0330344	−0.0165172	−	0.999864i	$-0.505258\pi$
$227$	−0.497714	−0.0330344	−0.0165172	+	0.999864i	$0.505258\pi$
$228$	27.4333	1.81682
$229$	−4.61779	−0.305152	−0.152576	−	0.988292i	$-0.548757\pi$
$229$	−4.61779	−0.305152	−0.152576	+	0.988292i	$0.548757\pi$
$230$	−3.62543	−0.239054
$231$	1.31547	0.0865519
$232$	−1.55274	−0.101942
$233$	−5.40264	−0.353938	−0.176969	−	0.984216i	$-0.556629\pi$
$233$	−5.40264	−0.353938	−0.176969	+	0.984216i	$0.556629\pi$
$234$	26.0403	1.70231
$235$	0.438565	0.0286088
$236$	−2.54063	−0.165381
$237$	10.5734	0.686817
$238$	7.15661	0.463894
$239$	−17.8280	−1.15320	−0.576599	−	0.817027i	$-0.695621\pi$
$239$	−17.8280	−1.15320	−0.576599	+	0.817027i	$0.695621\pi$
$240$	1.27738	0.0824547
$241$	20.2107	1.30188	0.650942	−	0.759128i	$-0.274374\pi$
$241$	20.2107	1.30188	0.650942	+	0.759128i	$0.274374\pi$
$242$	23.6230	1.51854
$243$	−21.0268	−1.34887
$244$	−5.37218	−0.343918
$245$	−0.937428	−0.0598901
$246$	29.0612	1.85288
$247$	−20.1842	−1.28429
$248$	7.74398	0.491744
$249$	−35.4234	−2.24486
$250$	−4.95768	−0.313551
$251$	11.9148	0.752053	0.376027	−	0.926609i	$-0.377290\pi$
$251$	11.9148	0.752053	0.376027	+	0.926609i	$0.377290\pi$
$252$	23.0312	1.45083
$253$	−1.21323	−0.0762753
$254$	−25.5256	−1.60162
$255$	0.549276	0.0343970
$256$	1.66580	0.104113
$257$	−5.42416	−0.338350	−0.169175	−	0.985586i	$-0.554110\pi$
$257$	−5.42416	−0.338350	−0.169175	+	0.985586i	$0.554110\pi$
$258$	25.8160	1.60723
$259$	26.2279	1.62973
$260$	2.80676	0.174068
$261$	2.98430	0.184723
$262$	40.7440	2.51717
$263$	1.17215	0.0722779	0.0361390	−	0.999347i	$-0.488494\pi$
$263$	1.17215	0.0722779	0.0361390	+	0.999347i	$0.488494\pi$
$264$	−0.541357	−0.0333182
$265$	0.456185	0.0280233
$266$	−31.3996	−1.92523
$267$	−13.6849	−0.837500
$268$	−2.77780	−0.169681
$269$	13.1893	0.804165	0.402083	−	0.915603i	$-0.368286\pi$
$269$	13.1893	0.804165	0.402083	+	0.915603i	$0.368286\pi$
$270$	−0.438602	−0.0266925
$271$	−19.2080	−1.16680	−0.583401	−	0.812184i	$-0.698278\pi$
$271$	−19.2080	−1.16680	−0.583401	+	0.812184i	$0.698278\pi$
$272$	2.32558	0.141009
$273$	−36.2811	−2.19583
$274$	−39.3878	−2.37951
$275$	−0.825062	−0.0497531
$276$	−45.4787	−2.73750
$277$	4.14506	0.249052	0.124526	−	0.992216i	$-0.460259\pi$
$277$	4.14506	0.249052	0.124526	+	0.992216i	$0.460259\pi$
$278$	37.6199	2.25629
$279$	−14.8836	−0.891058
$280$	1.05269	0.0629104
$281$	23.1718	1.38232	0.691158	−	0.722704i	$-0.257101\pi$
$281$	23.1718	1.38232	0.691158	+	0.722704i	$0.257101\pi$
$282$	9.67666	0.576237
$283$	21.7699	1.29409	0.647043	−	0.762454i	$-0.276006\pi$
$283$	21.7699	1.29409	0.647043	+	0.762454i	$0.276006\pi$
$284$	30.5398	1.81220
$285$	−2.40995	−0.142753
$286$	1.65209	0.0976902
$287$	−18.9111	−1.11629
$288$	20.3568	1.19953
$289$	1.00000	0.0588235
$290$	0.565776	0.0332235
$291$	40.8542	2.39492
$292$	−31.0048	−1.81442
$293$	−26.0898	−1.52418	−0.762090	−	0.647471i	$-0.775827\pi$
$293$	−26.0898	−1.52418	−0.762090	+	0.647471i	$0.775827\pi$
$294$	−20.6838	−1.20630
$295$	0.223188	0.0129945
$296$	−10.7936	−0.627364
$297$	−0.146776	−0.00851682
$298$	−29.5101	−1.70947
$299$	33.4612	1.93511
$300$	−30.9279	−1.78562
$301$	−16.7993	−0.968295
$302$	−37.0377	−2.13128
$303$	−33.2053	−1.90759
$304$	−10.2035	−0.585209
$305$	0.471932	0.0270227
$306$	5.66046	0.323587
$307$	17.9211	1.02281	0.511405	−	0.859340i	$-0.329125\pi$
$307$	17.9211	1.02281	0.511405	+	0.859340i	$0.329125\pi$
$308$	1.46118	0.0832584
$309$	10.0782	0.573329
$310$	−2.82170	−0.160262
$311$	−28.5664	−1.61985	−0.809925	−	0.586533i	$-0.800492\pi$
$311$	−28.5664	−1.61985	−0.809925	+	0.586533i	$0.800492\pi$
$312$	14.9307	0.845286
$313$	−27.2791	−1.54191	−0.770953	−	0.636892i	$-0.780220\pi$
$313$	−27.2791	−1.54191	−0.770953	+	0.636892i	$0.780220\pi$
$314$	−42.7829	−2.41438
$315$	−2.02323	−0.113996
$316$	11.7445	0.660682
$317$	4.70026	0.263993	0.131996	−	0.991250i	$-0.457861\pi$
$317$	4.70026	0.263993	0.131996	+	0.991250i	$0.457861\pi$
$318$	10.0655	0.564443
$319$	0.189334	0.0106007
$320$	2.78254	0.155548
$321$	−38.0612	−2.12437
$322$	52.0540	2.90086
$323$	−4.38750	−0.244127
$324$	−26.2880	−1.46045
$325$	22.7554	1.26224
$326$	−3.47495	−0.192460
$327$	−7.71462	−0.426619
$328$	7.78248	0.429716
$329$	−6.29693	−0.347161
$330$	0.197256	0.0108586
$331$	12.6196	0.693634	0.346817	−	0.937933i	$-0.387262\pi$
$331$	12.6196	0.693634	0.346817	+	0.937933i	$0.387262\pi$
$332$	−39.3469	−2.15944
$333$	20.7448	1.13681
$334$	13.7457	0.752134
$335$	0.244023	0.0133324
$336$	−18.3407	−1.00057
$337$	13.1473	0.716180	0.358090	−	0.933687i	$-0.383428\pi$
$337$	13.1473	0.716180	0.358090	+	0.933687i	$0.383428\pi$
$338$	−17.5762	−0.956018
$339$	−30.6166	−1.66287
$340$	0.610114	0.0330881
$341$	−0.944269	−0.0511350
$342$	−24.8353	−1.34294
$343$	−9.80860	−0.529615
$344$	6.91341	0.372746
$345$	3.99519	0.215094
$346$	−29.1869	−1.56910
$347$	−0.630670	−0.0338562	−0.0169281	−	0.999857i	$-0.505389\pi$
$347$	−0.630670	−0.0338562	−0.0169281	+	0.999857i	$0.505389\pi$
$348$	7.09730	0.380455
$349$	24.6507	1.31952	0.659762	−	0.751475i	$-0.270657\pi$
$349$	24.6507	1.31952	0.659762	+	0.751475i	$0.270657\pi$
$350$	35.3995	1.89218
$351$	4.04812	0.216073
$352$	1.29151	0.0688375
$353$	−1.00000	−0.0532246
$353$	−1.00000	−0.0532246
$354$	4.92450	0.261734
$355$	−2.68284	−0.142390
$356$	−15.2006	−0.805631
$357$	−7.88652	−0.417399
$358$	−11.5350	−0.609644
$359$	29.7496	1.57012	0.785062	−	0.619417i	$-0.212631\pi$
$359$	29.7496	1.57012	0.785062	+	0.619417i	$0.212631\pi$
$360$	0.832619	0.0438829
$361$	0.250180	0.0131674
$362$	28.3889	1.49209
$363$	−26.0323	−1.36634
$364$	−40.2996	−2.11227
$365$	2.72369	0.142565
$366$	10.4129	0.544291
$367$	7.30592	0.381366	0.190683	−	0.981652i	$-0.438930\pi$
$367$	7.30592	0.381366	0.190683	+	0.981652i	$0.438930\pi$
$368$	16.9152	0.881767
$369$	−14.9576	−0.778661
$370$	3.93289	0.204461
$371$	−6.54993	−0.340055
$372$	−35.3964	−1.83522
$373$	−36.5990	−1.89502	−0.947511	−	0.319722i	$-0.896411\pi$
$373$	−36.5990	−1.89502	−0.947511	+	0.319722i	$0.896411\pi$
$374$	0.359120	0.0185696
$375$	5.46332	0.282124
$376$	2.59137	0.133640
$377$	−5.22188	−0.268941
$378$	6.29746	0.323906
$379$	37.4323	1.92277	0.961385	−	0.275208i	$-0.0887466\pi$
$379$	37.4323	1.92277	0.961385	+	0.275208i	$0.0887466\pi$
$380$	−2.67688	−0.137321
$381$	28.1290	1.44109
$382$	48.9661	2.50533
$383$	6.07657	0.310498	0.155249	−	0.987875i	$-0.450382\pi$
$383$	6.07657	0.310498	0.155249	+	0.987875i	$0.450382\pi$
$384$	24.6541	1.25812
$385$	−0.128361	−0.00654188
$386$	−43.2367	−2.20069
$387$	−13.2873	−0.675430
$388$	45.3793	2.30378
$389$	−33.3558	−1.69120	−0.845602	−	0.533814i	$-0.820758\pi$
$389$	−33.3558	−1.69120	−0.845602	+	0.533814i	$0.820758\pi$
$390$	−5.44035	−0.275483
$391$	7.27356	0.367840
$392$	−5.53903	−0.279763
$393$	−44.8995	−2.26488
$394$	17.5232	0.882806
$395$	−1.03173	−0.0519119
$396$	1.15571	0.0580765
$397$	23.4349	1.17617	0.588083	−	0.808801i	$-0.299883\pi$
$397$	23.4349	1.17617	0.588083	+	0.808801i	$0.299883\pi$
$398$	22.4603	1.12584
$399$	34.6021	1.73227
$400$	11.5032	0.575162
$401$	21.3364	1.06549	0.532744	−	0.846277i	$-0.321161\pi$
$401$	21.3364	1.06549	0.532744	+	0.846277i	$0.321161\pi$
$402$	5.38421	0.268540
$403$	26.0431	1.29730
$404$	−36.8831	−1.83500
$405$	2.30934	0.114752
$406$	−8.12343	−0.403159
$407$	1.31612	0.0652378
$408$	3.24554	0.160678
$409$	−13.1725	−0.651339	−0.325670	−	0.945484i	$-0.605590\pi$
$409$	−13.1725	−0.651339	−0.325670	+	0.945484i	$0.605590\pi$
$410$	−2.83573	−0.140046
$411$	43.4050	2.14101
$412$	11.1945	0.551512
$413$	−3.20454	−0.157685
$414$	41.1717	2.02348
$415$	3.45653	0.169674
$416$	−35.6200	−1.74641
$417$	−41.4568	−2.03015
$418$	−1.57564	−0.0770670
$419$	1.62227	0.0792533	0.0396266	−	0.999215i	$-0.487383\pi$
$419$	1.62227	0.0792533	0.0396266	+	0.999215i	$0.487383\pi$
$420$	−4.81168	−0.234786
$421$	37.1761	1.81185	0.905926	−	0.423436i	$-0.139176\pi$
$421$	37.1761	1.81185	0.905926	+	0.423436i	$0.139176\pi$
$422$	−39.0898	−1.90286
$423$	−4.98050	−0.242160
$424$	2.69549	0.130904
$425$	4.94640	0.239936
$426$	−59.1953	−2.86802
$427$	−6.77602	−0.327914
$428$	−42.2769	−2.04353
$429$	−1.82059	−0.0878989
$430$	−2.51906	−0.121480
$431$	36.1617	1.74185	0.870925	−	0.491417i	$-0.163521\pi$
$431$	36.1617	1.74185	0.870925	+	0.491417i	$0.163521\pi$
$432$	2.04639	0.0984571
$433$	−11.7307	−0.563743	−0.281872	−	0.959452i	$-0.590955\pi$
$433$	−11.7307	−0.563743	−0.281872	+	0.959452i	$0.590955\pi$
$434$	40.5140	1.94474
$435$	−0.623480	−0.0298936
$436$	−8.56910	−0.410386
$437$	−31.9128	−1.52659
$438$	60.0966	2.87153
$439$	−23.3460	−1.11424	−0.557121	−	0.830431i	$-0.688094\pi$
$439$	−23.3460	−1.11424	−0.557121	+	0.830431i	$0.688094\pi$
$440$	0.0528243	0.00251830
$441$	10.6458	0.506942
$442$	−9.90460	−0.471114
$443$	−10.8278	−0.514445	−0.257222	−	0.966352i	$-0.582807\pi$
$443$	−10.8278	−0.514445	−0.257222	+	0.966352i	$0.582807\pi$
$444$	49.3356	2.34136
$445$	1.33534	0.0633010
$446$	43.9124	2.07931
$447$	32.5199	1.53814
$448$	−39.9517	−1.88754
$449$	−16.3991	−0.773924	−0.386962	−	0.922096i	$-0.626475\pi$
$449$	−16.3991	−0.773924	−0.386962	+	0.922096i	$0.626475\pi$
$450$	27.9989	1.31988
$451$	−0.948963	−0.0446849
$452$	−34.0078	−1.59959
$453$	40.8152	1.91766
$454$	1.07157	0.0502914
$455$	3.54022	0.165968
$456$	−14.2398	−0.666839
$457$	36.5468	1.70959	0.854794	−	0.518968i	$-0.173683\pi$
$457$	36.5468	1.70959	0.854794	+	0.518968i	$0.173683\pi$
$458$	9.94205	0.464562
$459$	0.879951	0.0410726
$460$	4.43770	0.206909
$461$	−4.00238	−0.186410	−0.0932048	−	0.995647i	$-0.529711\pi$
$461$	−4.00238	−0.186410	−0.0932048	+	0.995647i	$0.529711\pi$
$462$	−2.83220	−0.131766
$463$	21.3189	0.990776	0.495388	−	0.868672i	$-0.335026\pi$
$463$	21.3189	0.990776	0.495388	+	0.868672i	$0.335026\pi$
$464$	−2.63975	−0.122547
$465$	3.10949	0.144199
$466$	11.6318	0.538834
$467$	36.0353	1.66752	0.833758	−	0.552130i	$-0.186185\pi$
$467$	36.0353	1.66752	0.833758	+	0.552130i	$0.186185\pi$
$468$	−31.8747	−1.47341
$469$	−3.50369	−0.161785
$470$	−0.944225	−0.0435539
$471$	47.1464	2.17239
$472$	1.31876	0.0607009
$473$	−0.842992	−0.0387608
$474$	−22.7645	−1.04561
$475$	−21.7024	−0.995772
$476$	−8.76004	−0.401516
$477$	−5.18061	−0.237204
$478$	38.3835	1.75562
$479$	7.92259	0.361992	0.180996	−	0.983484i	$-0.442068\pi$
$479$	7.92259	0.361992	0.180996	+	0.983484i	$0.442068\pi$
$480$	−4.25294	−0.194119
$481$	−36.2989	−1.65509
$482$	−43.5134	−1.98198
$483$	−57.3631	−2.61011
$484$	−28.9157	−1.31435
$485$	−3.98645	−0.181016
$486$	45.2705	2.05351
$487$	43.4449	1.96868	0.984339	−	0.176285i	$-0.0564079\pi$
$487$	43.4449	1.96868	0.984339	+	0.176285i	$0.0564079\pi$
$488$	2.78853	0.126231
$489$	3.82936	0.173170
$490$	2.01827	0.0911763
$491$	1.29635	0.0585037	0.0292518	−	0.999572i	$-0.490688\pi$
$491$	1.29635	0.0585037	0.0292518	+	0.999572i	$0.490688\pi$
$492$	−35.5724	−1.60373
$493$	−1.13509	−0.0511221
$494$	43.4565	1.95520
$495$	−0.101526	−0.00456325
$496$	13.1652	0.591137
$497$	38.5203	1.72787
$498$	76.2661	3.41757
$499$	−25.1639	−1.12649	−0.563245	−	0.826290i	$-0.690447\pi$
$499$	−25.1639	−1.12649	−0.563245	+	0.826290i	$0.690447\pi$
$500$	6.06844	0.271389
$501$	−15.1477	−0.676749
$502$	−25.6524	−1.14492
$503$	18.9336	0.844207	0.422104	−	0.906548i	$-0.361292\pi$
$503$	18.9336	0.844207	0.422104	+	0.906548i	$0.361292\pi$
$504$	−11.9548	−0.532508
$505$	3.24009	0.144182
$506$	2.61208	0.116121
$507$	19.3688	0.860198
$508$	31.2446	1.38625
$509$	−33.7601	−1.49639	−0.748195	−	0.663479i	$-0.769079\pi$
$509$	−33.7601	−1.49639	−0.748195	+	0.663479i	$0.769079\pi$
$510$	−1.18258	−0.0523657
$511$	−39.1069	−1.72999
$512$	−24.3690	−1.07697
$513$	−3.86079	−0.170458
$514$	11.6782	0.515102
$515$	−0.983406	−0.0433341
$516$	−31.6000	−1.39111
$517$	−0.315981	−0.0138968
$518$	−56.4685	−2.48108
$519$	32.1637	1.41183
$520$	−1.45691	−0.0638895
$521$	3.62713	0.158907	0.0794537	−	0.996839i	$-0.474682\pi$
$521$	3.62713	0.158907	0.0794537	+	0.996839i	$0.474682\pi$
$522$	−6.42516	−0.281222
$523$	9.17173	0.401052	0.200526	−	0.979688i	$-0.435735\pi$
$523$	9.17173	0.401052	0.200526	+	0.979688i	$0.435735\pi$
$524$	−49.8727	−2.17870
$525$	−39.0099	−1.70253
$526$	−2.52363	−0.110035
$527$	5.66107	0.246600
$528$	−0.920340	−0.0400526
$529$	29.9047	1.30020
$530$	−0.982163	−0.0426624
$531$	−2.53460	−0.109992
$532$	38.4347	1.66636
$533$	26.1726	1.13366
$534$	29.4634	1.27500
$535$	3.71392	0.160567
$536$	1.44187	0.0622793
$537$	12.7115	0.548540
$538$	−28.3964	−1.22426
$539$	0.675406	0.0290918
$540$	0.536870	0.0231032
$541$	−32.4885	−1.39679	−0.698396	−	0.715712i	$-0.746102\pi$
$541$	−32.4885	−1.39679	−0.698396	+	0.715712i	$0.746102\pi$
$542$	41.3546	1.77633
$543$	−31.2843	−1.34254
$544$	−7.74282	−0.331971
$545$	0.752774	0.0322453
$546$	78.1128	3.34292
$547$	−15.7409	−0.673030	−0.336515	−	0.941678i	$-0.609248\pi$
$547$	−15.7409	−0.673030	−0.336515	+	0.941678i	$0.609248\pi$
$548$	48.2126	2.05954
$549$	−5.35943	−0.228735
$550$	1.77635	0.0757439
$551$	4.98023	0.212165
$552$	23.6066	1.00476
$553$	14.8136	0.629938
$554$	−8.92427	−0.379156
$555$	−4.33401	−0.183968
$556$	−46.0487	−1.95290
$557$	−31.5621	−1.33733	−0.668665	−	0.743563i	$-0.733134\pi$
$557$	−31.5621	−1.33733	−0.668665	+	0.743563i	$0.733134\pi$
$558$	32.0442	1.35654
$559$	23.2499	0.983366
$560$	1.78964	0.0756262
$561$	−0.395747	−0.0167084
$562$	−49.8887	−2.10443
$563$	24.3882	1.02784	0.513921	−	0.857838i	$-0.328193\pi$
$563$	24.3882	1.02784	0.513921	+	0.857838i	$0.328193\pi$
$564$	−11.8447	−0.498752
$565$	2.98749	0.125685
$566$	−46.8703	−1.97011
$567$	−33.1575	−1.39249
$568$	−15.8523	−0.665146
$569$	6.93166	0.290590	0.145295	−	0.989388i	$-0.453587\pi$
$569$	6.93166	0.290590	0.145295	+	0.989388i	$0.453587\pi$
$570$	5.18859	0.217326
$571$	−19.0202	−0.795972	−0.397986	−	0.917392i	$-0.630291\pi$
$571$	−19.0202	−0.795972	−0.397986	+	0.917392i	$0.630291\pi$
$572$	−2.02224	−0.0845542
$573$	−53.9602	−2.25422
$574$	40.7154	1.69943
$575$	35.9780	1.50038
$576$	−31.5995	−1.31665
$577$	−36.9961	−1.54017	−0.770084	−	0.637943i	$-0.779786\pi$
$577$	−36.9961	−1.54017	−0.770084	+	0.637943i	$0.779786\pi$
$578$	−2.15299	−0.0895526
$579$	47.6464	1.98012
$580$	−0.692538	−0.0287561
$581$	−49.6289	−2.05895
$582$	−87.9587	−3.64601
$583$	−0.328676	−0.0136124
$584$	16.0936	0.665959
$585$	2.80011	0.115770
$586$	56.1710	2.32040
$587$	−40.8382	−1.68557	−0.842787	−	0.538248i	$-0.819086\pi$
$587$	−40.8382	−1.68557	−0.842787	+	0.538248i	$0.819086\pi$
$588$	25.3180	1.04410
$589$	−24.8379	−1.02343
$590$	−0.480521	−0.0197827
$591$	−19.3104	−0.794324
$592$	−18.3497	−0.754170
$593$	−40.3841	−1.65838	−0.829189	−	0.558968i	$-0.811197\pi$
$593$	−40.3841	−1.65838	−0.829189	+	0.558968i	$0.811197\pi$
$594$	0.316008	0.0129660
$595$	0.769547	0.0315484
$596$	36.1218	1.47961
$597$	−24.7511	−1.01299
$598$	−72.0417	−2.94600
$599$	−3.11250	−0.127173	−0.0635867	−	0.997976i	$-0.520254\pi$
$599$	−3.11250	−0.127173	−0.0635867	+	0.997976i	$0.520254\pi$
$600$	16.0537	0.655391
$601$	−10.1295	−0.413193	−0.206596	−	0.978426i	$-0.566239\pi$
$601$	−10.1295	−0.413193	−0.206596	+	0.978426i	$0.566239\pi$
$602$	36.1687	1.47413
$603$	−2.77121	−0.112852
$604$	45.3359	1.84469
$605$	2.54017	0.103273
$606$	71.4906	2.90411
$607$	−41.9372	−1.70218	−0.851089	−	0.525021i	$-0.824058\pi$
$607$	−41.9372	−1.70218	−0.851089	+	0.525021i	$0.824058\pi$
$608$	33.9716	1.37773
$609$	8.95194	0.362751
$610$	−1.01606	−0.0411393
$611$	8.71482	0.352564
$612$	−6.92868	−0.280075
$613$	−41.0240	−1.65694	−0.828472	−	0.560030i	$-0.810789\pi$
$613$	−41.0240	−1.65694	−0.828472	+	0.560030i	$0.810789\pi$
$614$	−38.5839	−1.55712
$615$	3.12494	0.126010
$616$	−0.758453	−0.0305589
$617$	5.77073	0.232321	0.116160	−	0.993230i	$-0.462941\pi$
$617$	5.77073	0.232321	0.116160	+	0.993230i	$0.462941\pi$
$618$	−21.6983	−0.872832
$619$	−35.9610	−1.44540	−0.722698	−	0.691164i	$-0.757098\pi$
$619$	−35.9610	−1.44540	−0.722698	+	0.691164i	$0.757098\pi$
$620$	3.45390	0.138712
$621$	6.40038	0.256838
$622$	61.5031	2.46605
$623$	−19.1728	−0.768142
$624$	25.3832	1.01614
$625$	24.1989	0.967957
$626$	58.7316	2.34739
$627$	1.73634	0.0693427
$628$	52.3684	2.08973
$629$	−7.89040	−0.314611
$630$	4.35599	0.173547
$631$	32.4862	1.29325	0.646627	−	0.762807i	$-0.276179\pi$
$631$	32.4862	1.29325	0.646627	+	0.762807i	$0.276179\pi$
$632$	−6.09623	−0.242495
$633$	43.0766	1.71214
$634$	−10.1196	−0.401901
$635$	−2.74476	−0.108922
$636$	−12.3206	−0.488544
$637$	−18.6278	−0.738062
$638$	−0.407635	−0.0161384
$639$	30.4673	1.20527
$640$	−2.40569	−0.0950931
$641$	26.1012	1.03093	0.515467	−	0.856909i	$-0.327618\pi$
$641$	26.1012	1.03093	0.515467	+	0.856909i	$0.327618\pi$
$642$	81.9454	3.23413
$643$	17.9757	0.708891	0.354446	−	0.935077i	$-0.384670\pi$
$643$	17.9757	0.708891	0.354446	+	0.935077i	$0.384670\pi$
$644$	−63.7167	−2.51079
$645$	2.77598	0.109304
$646$	9.44625	0.371658
$647$	−35.7823	−1.40675	−0.703374	−	0.710820i	$-0.748324\pi$
$647$	−35.7823	−1.40675	−0.703374	+	0.710820i	$0.748324\pi$
$648$	13.6453	0.536038
$649$	−0.160804	−0.00631212
$650$	−48.9921	−1.92163
$651$	−44.6461	−1.74982
$652$	4.25351	0.166580
$653$	2.64965	0.103689	0.0518445	−	0.998655i	$-0.483490\pi$
$653$	2.64965	0.103689	0.0518445	+	0.998655i	$0.483490\pi$
$654$	16.6095	0.649483
$655$	4.38119	0.171187
$656$	13.2307	0.516572
$657$	−30.9313	−1.20674
$658$	13.5572	0.528515
$659$	6.55100	0.255191	0.127595	−	0.991826i	$-0.459274\pi$
$659$	6.55100	0.255191	0.127595	+	0.991826i	$0.459274\pi$
$660$	−0.241451	−0.00939846
$661$	−13.4027	−0.521306	−0.260653	−	0.965433i	$-0.583938\pi$
$661$	−13.4027	−0.521306	−0.260653	+	0.965433i	$0.583938\pi$
$662$	−27.1698	−1.05598
$663$	10.9148	0.423895
$664$	20.4238	0.792596
$665$	−3.37639	−0.130931
$666$	−44.6633	−1.73067
$667$	−8.25618	−0.319681
$668$	−16.8255	−0.650997
$669$	−48.3911	−1.87091
$670$	−0.525378	−0.0202971
$671$	−0.340022	−0.0131264
$672$	61.0639	2.35559
$673$	35.8617	1.38237	0.691183	−	0.722680i	$-0.257090\pi$
$673$	35.8617	1.38237	0.691183	+	0.722680i	$0.257090\pi$
$674$	−28.3060	−1.09031
$675$	4.35259	0.167531
$676$	21.5141	0.827465
$677$	−20.6341	−0.793032	−0.396516	−	0.918028i	$-0.629781\pi$
$677$	−20.6341	−0.793032	−0.396516	+	0.918028i	$0.629781\pi$
$678$	65.9173	2.53154
$679$	57.2376	2.19658
$680$	−0.316692	−0.0121446
$681$	−1.18086	−0.0452508
$682$	2.03300	0.0778476
$683$	21.0832	0.806725	0.403362	−	0.915040i	$-0.367841\pi$
$683$	21.0832	0.806725	0.403362	+	0.915040i	$0.367841\pi$
$684$	30.3996	1.16236
$685$	−4.23536	−0.161825
$686$	21.1178	0.806282
$687$	−10.9561	−0.417999
$688$	11.7532	0.448087
$689$	9.06497	0.345348
$690$	−8.60160	−0.327457
$691$	17.3165	0.658751	0.329375	−	0.944199i	$-0.393162\pi$
$691$	17.3165	0.658751	0.329375	+	0.944199i	$0.393162\pi$
$692$	35.7262	1.35811
$693$	1.45771	0.0553740
$694$	1.35783	0.0515424
$695$	4.04526	0.153445
$696$	−3.68399	−0.139641
$697$	5.68921	0.215494
$698$	−53.0728	−2.00883
$699$	−12.8182	−0.484827
$700$	−43.3307	−1.63775
$701$	−22.8407	−0.862680	−0.431340	−	0.902189i	$-0.641959\pi$
$701$	−22.8407	−0.862680	−0.431340	+	0.902189i	$0.641959\pi$
$702$	−8.71556	−0.328948
$703$	34.6192	1.30569
$704$	−2.00478	−0.0755582
$705$	1.04053	0.0391885
$706$	2.15299	0.0810289
$707$	−46.5213	−1.74961
$708$	−6.02783	−0.226540
$709$	−8.13183	−0.305397	−0.152699	−	0.988273i	$-0.548796\pi$
$709$	−8.13183	−0.305397	−0.152699	+	0.988273i	$0.548796\pi$
$710$	5.77613	0.216774
$711$	11.7167	0.439410
$712$	7.89017	0.295697
$713$	41.1761	1.54206
$714$	16.9796	0.635445
$715$	0.177649	0.00664369
$716$	14.1194	0.527667
$717$	−42.2983	−1.57966
$718$	−64.0506	−2.39035
$719$	2.68629	0.100182	0.0500909	−	0.998745i	$-0.484049\pi$
$719$	2.68629	0.100182	0.0500909	+	0.998745i	$0.484049\pi$
$720$	1.41550	0.0527527
$721$	14.1198	0.525848
$722$	−0.538635	−0.0200459
$723$	47.9514	1.78333
$724$	−34.7494	−1.29145
$725$	−5.61464	−0.208522
$726$	56.0473	2.08011
$727$	−32.8391	−1.21794	−0.608968	−	0.793195i	$-0.708416\pi$
$727$	−32.8391	−1.21794	−0.608968	+	0.793195i	$0.708416\pi$
$728$	20.9183	0.775283
$729$	−19.9624	−0.739350
$730$	−5.86408	−0.217040
$731$	5.05389	0.186925
$732$	−12.7459	−0.471102
$733$	−35.1651	−1.29885	−0.649427	−	0.760424i	$-0.724991\pi$
$733$	−35.1651	−1.29885	−0.649427	+	0.760424i	$0.724991\pi$
$734$	−15.7296	−0.580589
$735$	−2.22412	−0.0820379
$736$	−56.3179	−2.07590
$737$	−0.175816	−0.00647625
$738$	32.2035	1.18543
$739$	43.4357	1.59781	0.798905	−	0.601458i	$-0.205413\pi$
$739$	43.4357	1.59781	0.798905	+	0.601458i	$0.205413\pi$
$740$	−4.81405	−0.176968
$741$	−47.8886	−1.75923
$742$	14.1019	0.517698
$743$	−3.10926	−0.114068	−0.0570339	−	0.998372i	$-0.518164\pi$
$743$	−3.10926	−0.114068	−0.0570339	+	0.998372i	$0.518164\pi$
$744$	18.3732	0.673594
$745$	−3.17321	−0.116257
$746$	78.7972	2.88497
$747$	−39.2536	−1.43621
$748$	−0.439580	−0.0160726
$749$	−53.3246	−1.94844
$750$	−11.7625	−0.429505
$751$	−51.0892	−1.86427	−0.932136	−	0.362109i	$-0.882057\pi$
$751$	−51.0892	−1.86427	−0.932136	+	0.362109i	$0.882057\pi$
$752$	4.40549	0.160652
$753$	28.2687	1.03017
$754$	11.2427	0.409433
$755$	−3.98265	−0.144943
$756$	−7.70840	−0.280352
$757$	4.76152	0.173060	0.0865301	−	0.996249i	$-0.472422\pi$
$757$	4.76152	0.173060	0.0865301	+	0.996249i	$0.472422\pi$
$758$	−80.5914	−2.92721
$759$	−2.87849	−0.104483
$760$	1.38948	0.0504019
$761$	20.4826	0.742493	0.371246	−	0.928534i	$-0.378931\pi$
$761$	20.4826	0.742493	0.371246	+	0.928534i	$0.378931\pi$
$762$	−60.5614	−2.19391
$763$	−10.8084	−0.391289
$764$	−59.9370	−2.16844
$765$	0.608667	0.0220064
$766$	−13.0828	−0.472700
$767$	4.43501	0.160139
$768$	3.95224	0.142614
$769$	22.7381	0.819956	0.409978	−	0.912095i	$-0.365536\pi$
$769$	22.7381	0.819956	0.409978	+	0.912095i	$0.365536\pi$
$770$	0.276360	0.00995931
$771$	−12.8692	−0.463474
$772$	52.9238	1.90477
$773$	−43.5579	−1.56667	−0.783334	−	0.621601i	$-0.786482\pi$
$773$	−43.5579	−1.56667	−0.783334	+	0.621601i	$0.786482\pi$
$774$	28.6074	1.02827
$775$	28.0019	1.00586
$776$	−23.5550	−0.845575
$777$	62.2278	2.23241
$778$	71.8146	2.57468
$779$	−24.9614	−0.894336
$780$	6.65926	0.238440
$781$	1.93296	0.0691666
$782$	−15.6599	−0.559997
$783$	−0.998827	−0.0356952
$784$	−9.41669	−0.336310
$785$	−4.60043	−0.164196
$786$	96.6682	3.44804
$787$	−32.5692	−1.16097	−0.580483	−	0.814272i	$-0.697136\pi$
$787$	−32.5692	−1.16097	−0.580483	+	0.814272i	$0.697136\pi$
$788$	−21.4492	−0.764098
$789$	2.78102	0.0990068
$790$	2.22130	0.0790303
$791$	−42.8945	−1.52515
$792$	−0.599892	−0.0213162
$793$	9.37787	0.333018
$794$	−50.4552	−1.79059
$795$	1.08233	0.0383865
$796$	−27.4926	−0.974448
$797$	−12.4740	−0.441850	−0.220925	−	0.975291i	$-0.570908\pi$
$797$	−12.4740	−0.441850	−0.220925	+	0.975291i	$0.570908\pi$
$798$	−74.4980	−2.63720
$799$	1.89436	0.0670178
$800$	−38.2991	−1.35408
$801$	−15.1646	−0.535814
$802$	−45.9370	−1.62209
$803$	−1.96239	−0.0692512
$804$	−6.59054	−0.232430
$805$	5.59735	0.197281
$806$	−56.0706	−1.97500
$807$	31.2926	1.10155
$808$	19.1449	0.673515
$809$	−5.21970	−0.183515	−0.0917574	−	0.995781i	$-0.529248\pi$
$809$	−5.21970	−0.183515	−0.0917574	+	0.995781i	$0.529248\pi$
$810$	−4.97198	−0.174698
$811$	0.696970	0.0244739	0.0122370	−	0.999925i	$-0.496105\pi$
$811$	0.696970	0.0244739	0.0122370	+	0.999925i	$0.496105\pi$
$812$	9.94348	0.348948
$813$	−45.5724	−1.59829
$814$	−2.83360	−0.0993176
$815$	−0.373660	−0.0130887
$816$	5.51761	0.193155
$817$	−22.1740	−0.775769
$818$	28.3603	0.991595
$819$	−40.2040	−1.40484
$820$	3.47107	0.121215
$821$	7.27960	0.254060	0.127030	−	0.991899i	$-0.459456\pi$
$821$	7.27960	0.254060	0.127030	+	0.991899i	$0.459456\pi$
$822$	−93.4506	−3.25946
$823$	31.2983	1.09099	0.545496	−	0.838114i	$-0.316341\pi$
$823$	31.2983	1.09099	0.545496	+	0.838114i	$0.316341\pi$
$824$	−5.81071	−0.202426
$825$	−1.95752	−0.0681522
$826$	6.89934	0.240059
$827$	44.2323	1.53811	0.769054	−	0.639183i	$-0.220727\pi$
$827$	44.2323	1.53811	0.769054	+	0.639183i	$0.220727\pi$
$828$	−50.3962	−1.75139
$829$	−10.9857	−0.381550	−0.190775	−	0.981634i	$-0.561100\pi$
$829$	−10.9857	−0.381550	−0.190775	+	0.981634i	$0.561100\pi$
$830$	−7.44187	−0.258311
$831$	9.83447	0.341154
$832$	55.2924	1.91692
$833$	−4.04919	−0.140296
$834$	89.2562	3.09069
$835$	1.47807	0.0511509
$836$	1.92866	0.0667041
$837$	4.98146	0.172184
$838$	−3.49274	−0.120655
$839$	−23.9988	−0.828531	−0.414266	−	0.910156i	$-0.635962\pi$
$839$	−23.9988	−0.828531	−0.414266	+	0.910156i	$0.635962\pi$
$840$	2.49759	0.0861751
$841$	−27.7116	−0.955571
$842$	−80.0397	−2.75835
$843$	54.9769	1.89351
$844$	47.8478	1.64699
$845$	−1.88996	−0.0650166
$846$	10.7230	0.368663
$847$	−36.4719	−1.25319
$848$	4.58249	0.157364
$849$	51.6507	1.77265
$850$	−10.6496	−0.365277
$851$	−57.3913	−1.96735
$852$	72.4579	2.48237
$853$	7.72174	0.264387	0.132194	−	0.991224i	$-0.457798\pi$
$853$	7.72174	0.264387	0.132194	+	0.991224i	$0.457798\pi$
$854$	14.5887	0.499215
$855$	−2.67053	−0.0913302
$856$	21.9446	0.750052
$857$	−9.78747	−0.334334	−0.167167	−	0.985929i	$-0.553462\pi$
$857$	−9.78747	−0.334334	−0.167167	+	0.985929i	$0.553462\pi$
$858$	3.91971	0.133817
$859$	35.0175	1.19478	0.597391	−	0.801950i	$-0.296204\pi$
$859$	35.0175	1.19478	0.597391	+	0.801950i	$0.296204\pi$
$860$	3.08345	0.105145
$861$	−44.8680	−1.52910
$862$	−77.8558	−2.65178
$863$	−40.5657	−1.38087	−0.690436	−	0.723394i	$-0.742581\pi$
$863$	−40.5657	−1.38087	−0.690436	+	0.723394i	$0.742581\pi$
$864$	−6.81330	−0.231793
$865$	−3.13845	−0.106711
$866$	25.2562	0.858239
$867$	2.37258	0.0805769
$868$	−49.5912	−1.68323
$869$	0.743349	0.0252164
$870$	1.34235	0.0455098
$871$	4.84903	0.164303
$872$	4.44796	0.150627
$873$	45.2717	1.53221
$874$	68.7079	2.32408
$875$	7.65423	0.258760
$876$	−73.5612	−2.48540
$877$	13.1839	0.445189	0.222594	−	0.974911i	$-0.428547\pi$
$877$	13.1839	0.445189	0.222594	+	0.974911i	$0.428547\pi$
$878$	50.2636	1.69632
$879$	−61.8999	−2.08783
$880$	0.0898045	0.00302731
$881$	−49.3846	−1.66381	−0.831904	−	0.554920i	$-0.812749\pi$
$881$	−49.3846	−1.66381	−0.831904	+	0.554920i	$0.812749\pi$
$882$	−22.9203	−0.771765
$883$	51.8863	1.74611	0.873057	−	0.487618i	$-0.162134\pi$
$883$	51.8863	1.74611	0.873057	+	0.487618i	$0.162134\pi$
$884$	12.1237	0.407765
$885$	0.529530	0.0178000
$886$	23.3122	0.783188
$887$	36.8221	1.23637	0.618183	−	0.786035i	$-0.287869\pi$
$887$	36.8221	1.23637	0.618183	+	0.786035i	$0.287869\pi$
$888$	−25.6086	−0.859368
$889$	39.4093	1.32175
$890$	−2.87496	−0.0963690
$891$	−1.66385	−0.0557411
$892$	−53.7510	−1.79972
$893$	−8.31153	−0.278135
$894$	−70.0150	−2.34165
$895$	−1.24035	−0.0414605
$896$	34.5409	1.15393
$897$	79.3893	2.65073
$898$	35.3072	1.17822
$899$	−6.42585	−0.214314
$900$	−34.2721	−1.14240
$901$	1.97048	0.0656461
$902$	2.04311	0.0680280
$903$	−39.8576	−1.32638
$904$	17.6524	0.587109
$905$	3.05265	0.101473
$906$	−87.8747	−2.91944
$907$	14.1041	0.468318	0.234159	−	0.972198i	$-0.424766\pi$
$907$	14.1041	0.468318	0.234159	+	0.972198i	$0.424766\pi$
$908$	−1.31166	−0.0435289
$909$	−36.7957	−1.22044
$910$	−7.62206	−0.252669
$911$	−31.9027	−1.05698	−0.528492	−	0.848938i	$-0.677242\pi$
$911$	−31.9027	−1.05698	−0.528492	+	0.848938i	$0.677242\pi$
$912$	−24.2085	−0.801624
$913$	−2.49039	−0.0824198
$914$	−78.6849	−2.60267
$915$	1.11969	0.0370160
$916$	−12.1696	−0.402094
$917$	−62.9052	−2.07731
$918$	−1.89453	−0.0625286
$919$	30.1570	0.994787	0.497393	−	0.867525i	$-0.334291\pi$
$919$	30.1570	0.994787	0.497393	+	0.867525i	$0.334291\pi$
$920$	−2.30348	−0.0759433
$921$	42.5191	1.40105
$922$	8.61710	0.283789
$923$	−53.3113	−1.75476
$924$	3.46676	0.114048
$925$	−39.0291	−1.28327
$926$	−45.8995	−1.50835
$927$	11.1679	0.366803
$928$	8.78883	0.288508
$929$	10.9313	0.358644	0.179322	−	0.983790i	$-0.442610\pi$
$929$	10.9313	0.358644	0.179322	+	0.983790i	$0.442610\pi$
$930$	−6.69469	−0.219528
$931$	17.7658	0.582251
$932$	−14.2379	−0.466379
$933$	−67.7759	−2.21888
$934$	−77.5837	−2.53862
$935$	0.0386160	0.00126288
$936$	16.5452	0.540795
$937$	−5.49875	−0.179636	−0.0898182	−	0.995958i	$-0.528629\pi$
$937$	−5.49875	−0.179636	−0.0898182	+	0.995958i	$0.528629\pi$
$938$	7.54340	0.246301
$939$	−64.7217	−2.11211
$940$	1.15578	0.0376973
$941$	2.00151	0.0652473	0.0326236	−	0.999468i	$-0.489614\pi$
$941$	2.00151	0.0652473	0.0326236	+	0.999468i	$0.489614\pi$
$942$	−101.506	−3.30723
$943$	41.3808	1.34754
$944$	2.24198	0.0729701
$945$	0.677164	0.0220281
$946$	1.81495	0.0590092
$947$	−52.9012	−1.71906	−0.859529	−	0.511087i	$-0.829243\pi$
$947$	−52.9012	−1.71906	−0.859529	+	0.511087i	$0.829243\pi$
$948$	27.8648	0.905007
$949$	54.1231	1.75691
$950$	46.7250	1.51596
$951$	11.1517	0.361619
$952$	4.54707	0.147371
$953$	−27.0439	−0.876039	−0.438020	−	0.898965i	$-0.644320\pi$
$953$	−27.0439	−0.876039	−0.438020	+	0.898965i	$0.644320\pi$
$954$	11.1538	0.361118
$955$	5.26531	0.170381
$956$	−46.9833	−1.51955
$957$	0.449210	0.0145209
$958$	−17.0572	−0.551095
$959$	60.8114	1.96370
$960$	6.60178	0.213071
$961$	1.04767	0.0337960
$962$	78.1513	2.51970
$963$	−42.1766	−1.35912
$964$	53.2625	1.71547
$965$	−4.64922	−0.149664
$966$	123.502	3.97362
$967$	−56.0711	−1.80313	−0.901563	−	0.432648i	$-0.857579\pi$
$967$	−56.0711	−1.80313	−0.901563	+	0.432648i	$0.857579\pi$
$968$	15.0093	0.482416
$969$	−10.4097	−0.334407
$970$	8.58280	0.275577
$971$	13.8124	0.443260	0.221630	−	0.975131i	$-0.428862\pi$
$971$	13.8124	0.443260	0.221630	+	0.975131i	$0.428862\pi$
$972$	−55.4134	−1.77738
$973$	−58.0820	−1.86202
$974$	−93.5365	−2.99710
$975$	53.9889	1.72903
$976$	4.74067	0.151745
$977$	22.6691	0.725250	0.362625	−	0.931935i	$-0.381881\pi$
$977$	22.6691	0.725250	0.362625	+	0.931935i	$0.381881\pi$
$978$	−8.24458	−0.263633
$979$	−0.962094	−0.0307487
$980$	−2.47047	−0.0789161
$981$	−8.54878	−0.272942
$982$	−2.79104	−0.0890656
$983$	−16.0878	−0.513122	−0.256561	−	0.966528i	$-0.582589\pi$
$983$	−16.0878	−0.513122	−0.256561	+	0.966528i	$0.582589\pi$
$984$	18.4645	0.588628
$985$	1.88426	0.0600376
$986$	2.44385	0.0778280
$987$	−14.9399	−0.475543
$988$	−53.1928	−1.69229
$989$	36.7598	1.16889
$990$	0.218584	0.00694707
$991$	−18.2076	−0.578384	−0.289192	−	0.957271i	$-0.593387\pi$
$991$	−18.2076	−0.578384	−0.289192	+	0.957271i	$0.593387\pi$
$992$	−43.8326	−1.39169
$993$	29.9409	0.950145
$994$	−82.9339	−2.63050
$995$	2.41515	0.0765655
$996$	−93.3535	−2.95802
$997$	10.2114	0.323397	0.161699	−	0.986840i	$-0.448303\pi$
$997$	10.2114	0.323397	0.161699	+	0.986840i	$0.448303\pi$
$998$	54.1776	1.71496
$999$	−6.94316	−0.219672

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6001.2.a.a.1.18	✓	113

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6001.2.a.a.1.18	✓	113	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:	\( N \)	\(=\)	\( 6001 = 17 \cdot 353 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6001.a (trivial)

\(f(q)\)	\(=\)	\(q-2.15299 q^{2} +2.37258 q^{3} +2.63537 q^{4} -0.231510 q^{5} -5.10813 q^{6} +3.32403 q^{7} -1.36794 q^{8} +2.62912 q^{9} +O(q^{10})\)	\(q-2.15299 q^{2} +2.37258 q^{3} +2.63537 q^{4} -0.231510 q^{5} -5.10813 q^{6} +3.32403 q^{7} -1.36794 q^{8} +2.62912 q^{9} +0.498439 q^{10} +0.166800 q^{11} +6.25261 q^{12} -4.60039 q^{13} -7.15661 q^{14} -0.549276 q^{15} -2.32558 q^{16} -1.00000 q^{17} -5.66046 q^{18} +4.38750 q^{19} -0.610114 q^{20} +7.88652 q^{21} -0.359120 q^{22} -7.27356 q^{23} -3.24554 q^{24} -4.94640 q^{25} +9.90460 q^{26} -0.879951 q^{27} +8.76004 q^{28} +1.13509 q^{29} +1.18258 q^{30} -5.66107 q^{31} +7.74282 q^{32} +0.395747 q^{33} +2.15299 q^{34} -0.769547 q^{35} +6.92868 q^{36} +7.89040 q^{37} -9.44625 q^{38} -10.9148 q^{39} +0.316692 q^{40} -5.68921 q^{41} -16.9796 q^{42} -5.05389 q^{43} +0.439580 q^{44} -0.608667 q^{45} +15.6599 q^{46} -1.89436 q^{47} -5.51761 q^{48} +4.04919 q^{49} +10.6496 q^{50} -2.37258 q^{51} -12.1237 q^{52} -1.97048 q^{53} +1.89453 q^{54} -0.0386160 q^{55} -4.54707 q^{56} +10.4097 q^{57} -2.44385 q^{58} -0.964051 q^{59} -1.44754 q^{60} -2.03849 q^{61} +12.1882 q^{62} +8.73926 q^{63} -12.0191 q^{64} +1.06504 q^{65} -0.852039 q^{66} -1.05405 q^{67} -2.63537 q^{68} -17.2571 q^{69} +1.65683 q^{70} +11.5884 q^{71} -3.59647 q^{72} -11.7649 q^{73} -16.9880 q^{74} -11.7357 q^{75} +11.5627 q^{76} +0.554450 q^{77} +23.4994 q^{78} +4.45651 q^{79} +0.538395 q^{80} -9.97510 q^{81} +12.2488 q^{82} -14.9303 q^{83} +20.7839 q^{84} +0.231510 q^{85} +10.8810 q^{86} +2.69310 q^{87} -0.228173 q^{88} -5.76793 q^{89} +1.31045 q^{90} -15.2918 q^{91} -19.1685 q^{92} -13.4313 q^{93} +4.07855 q^{94} -1.01575 q^{95} +18.3704 q^{96} +17.2193 q^{97} -8.71786 q^{98} +0.438538 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 113 q - 11 q^{2} - 11 q^{3} + 103 q^{4} - 19 q^{5} - 13 q^{6} + 11 q^{7} - 36 q^{8} + 94 q^{9}+O(q^{10}) \) 113 * q - 11 * q^2 - 11 * q^3 + 103 * q^4 - 19 * q^5 - 13 * q^6 + 11 * q^7 - 36 * q^8 + 94 * q^9	\( 113 q - 11 q^{2} - 11 q^{3} + 103 q^{4} - 19 q^{5} - 13 q^{6} + 11 q^{7} - 36 q^{8} + 94 q^{9} - 5 q^{10} - 40 q^{11} - 19 q^{12} - 18 q^{13} - 48 q^{14} - 63 q^{15} + 79 q^{16} - 113 q^{17} - 32 q^{18} - 46 q^{19} - 56 q^{20} - 46 q^{21} + 14 q^{22} - 35 q^{23} - 42 q^{24} + 88 q^{25} - 89 q^{26} - 41 q^{27} + 20 q^{28} - 51 q^{29} - 18 q^{30} - 57 q^{31} - 93 q^{32} - 40 q^{33} + 11 q^{34} - 69 q^{35} + 18 q^{36} + 16 q^{37} - 74 q^{38} - 51 q^{39} + 2 q^{40} - 87 q^{41} - 23 q^{42} - 32 q^{43} - 110 q^{44} - 17 q^{45} - 17 q^{46} - 161 q^{47} - 36 q^{48} + 56 q^{49} - 69 q^{50} + 11 q^{51} - 49 q^{52} - 48 q^{53} - 38 q^{54} - 79 q^{55} - 171 q^{56} + 20 q^{57} + 13 q^{58} - 174 q^{59} - 146 q^{60} - 34 q^{61} - 34 q^{62} - 14 q^{63} + 62 q^{64} - 22 q^{65} - 60 q^{66} - 50 q^{67} - 103 q^{68} - 59 q^{69} - 58 q^{70} - 189 q^{71} - 123 q^{72} - 4 q^{73} - 24 q^{74} - 106 q^{75} - 92 q^{76} - 78 q^{77} - 42 q^{78} + 8 q^{79} - 150 q^{80} + 13 q^{81} + 6 q^{82} - 109 q^{83} - 114 q^{84} + 19 q^{85} - 116 q^{86} - 106 q^{87} + 54 q^{88} - 170 q^{89} - q^{90} - 43 q^{91} - 94 q^{92} - 69 q^{93} - 35 q^{94} - 78 q^{95} - 44 q^{96} - 3 q^{97} - 68 q^{98} - 119 q^{99}+O(q^{100}) \) 113 * q - 11 * q^2 - 11 * q^3 + 103 * q^4 - 19 * q^5 - 13 * q^6 + 11 * q^7 - 36 * q^8 + 94 * q^9 - 5 * q^10 - 40 * q^11 - 19 * q^12 - 18 * q^13 - 48 * q^14 - 63 * q^15 + 79 * q^16 - 113 * q^17 - 32 * q^18 - 46 * q^19 - 56 * q^20 - 46 * q^21 + 14 * q^22 - 35 * q^23 - 42 * q^24 + 88 * q^25 - 89 * q^26 - 41 * q^27 + 20 * q^28 - 51 * q^29 - 18 * q^30 - 57 * q^31 - 93 * q^32 - 40 * q^33 + 11 * q^34 - 69 * q^35 + 18 * q^36 + 16 * q^37 - 74 * q^38 - 51 * q^39 + 2 * q^40 - 87 * q^41 - 23 * q^42 - 32 * q^43 - 110 * q^44 - 17 * q^45 - 17 * q^46 - 161 * q^47 - 36 * q^48 + 56 * q^49 - 69 * q^50 + 11 * q^51 - 49 * q^52 - 48 * q^53 - 38 * q^54 - 79 * q^55 - 171 * q^56 + 20 * q^57 + 13 * q^58 - 174 * q^59 - 146 * q^60 - 34 * q^61 - 34 * q^62 - 14 * q^63 + 62 * q^64 - 22 * q^65 - 60 * q^66 - 50 * q^67 - 103 * q^68 - 59 * q^69 - 58 * q^70 - 189 * q^71 - 123 * q^72 - 4 * q^73 - 24 * q^74 - 106 * q^75 - 92 * q^76 - 78 * q^77 - 42 * q^78 + 8 * q^79 - 150 * q^80 + 13 * q^81 + 6 * q^82 - 109 * q^83 - 114 * q^84 + 19 * q^85 - 116 * q^86 - 106 * q^87 + 54 * q^88 - 170 * q^89 - q^90 - 43 * q^91 - 94 * q^92 - 69 * q^93 - 35 * q^94 - 78 * q^95 - 44 * q^96 - 3 * q^97 - 68 * q^98 - 119 * q^99

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