LMFDB - Embedded newform 4007.2.a.a.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4007,2,Mod(1,4007)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4007, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("4007.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4007 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4007.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:	$31.9960560899$
Analytic rank:	$1$
Dimension:	$139$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	4007.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.23150 q^{2} +1.82610 q^{3} +2.97957 q^{4} +2.21560 q^{5} -4.07492 q^{6} +3.73360 q^{7} -2.18591 q^{8} +0.334626 q^{9} +O(q^{10})$	\(q-2.23150 q^{2} +1.82610 q^{3} +2.97957 q^{4} +2.21560 q^{5} -4.07492 q^{6} +3.73360 q^{7} -2.18591 q^{8} +0.334626 q^{9} -4.94411 q^{10} -3.68316 q^{11} +5.44099 q^{12} -3.24566 q^{13} -8.33152 q^{14} +4.04590 q^{15} -1.08129 q^{16} -6.85809 q^{17} -0.746716 q^{18} -0.903543 q^{19} +6.60155 q^{20} +6.81792 q^{21} +8.21895 q^{22} -3.17314 q^{23} -3.99169 q^{24} -0.0911012 q^{25} +7.24267 q^{26} -4.86723 q^{27} +11.1245 q^{28} +4.03844 q^{29} -9.02842 q^{30} -1.31359 q^{31} +6.78472 q^{32} -6.72580 q^{33} +15.3038 q^{34} +8.27218 q^{35} +0.997042 q^{36} -8.64800 q^{37} +2.01625 q^{38} -5.92688 q^{39} -4.84311 q^{40} +4.85883 q^{41} -15.2142 q^{42} -4.13771 q^{43} -10.9742 q^{44} +0.741398 q^{45} +7.08085 q^{46} +7.29694 q^{47} -1.97454 q^{48} +6.93979 q^{49} +0.203292 q^{50} -12.5235 q^{51} -9.67068 q^{52} +2.19910 q^{53} +10.8612 q^{54} -8.16042 q^{55} -8.16133 q^{56} -1.64996 q^{57} -9.01177 q^{58} +1.05949 q^{59} +12.0551 q^{60} -2.14112 q^{61} +2.93127 q^{62} +1.24936 q^{63} -12.9775 q^{64} -7.19109 q^{65} +15.0086 q^{66} -2.21411 q^{67} -20.4342 q^{68} -5.79446 q^{69} -18.4593 q^{70} -0.0868923 q^{71} -0.731463 q^{72} -15.4450 q^{73} +19.2980 q^{74} -0.166359 q^{75} -2.69217 q^{76} -13.7515 q^{77} +13.2258 q^{78} -11.2752 q^{79} -2.39571 q^{80} -9.89190 q^{81} -10.8425 q^{82} -6.73872 q^{83} +20.3145 q^{84} -15.1948 q^{85} +9.23327 q^{86} +7.37458 q^{87} +8.05106 q^{88} +14.5000 q^{89} -1.65443 q^{90} -12.1180 q^{91} -9.45461 q^{92} -2.39874 q^{93} -16.2831 q^{94} -2.00189 q^{95} +12.3896 q^{96} -8.35648 q^{97} -15.4861 q^{98} -1.23248 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 139 q - 13 q^{2} - 22 q^{3} + 113 q^{4} - 16 q^{5} - 15 q^{6} - 44 q^{7} - 36 q^{8} + 87 q^{9}+O(q^{10}) $ 139 * q - 13 * q^2 - 22 * q^3 + 113 * q^4 - 16 * q^5 - 15 * q^6 - 44 * q^7 - 36 * q^8 + 87 * q^9	\( 139 q - 13 q^{2} - 22 q^{3} + 113 q^{4} - 16 q^{5} - 15 q^{6} - 44 q^{7} - 36 q^{8} + 87 q^{9} - 40 q^{10} - 17 q^{11} - 59 q^{12} - 89 q^{13} - 15 q^{14} - 29 q^{15} + 73 q^{16} - 58 q^{17} - 51 q^{18} - 37 q^{19} - 24 q^{20} - 37 q^{21} - 99 q^{22} - 42 q^{23} - 27 q^{24} - 11 q^{25} + 2 q^{26} - 73 q^{27} - 113 q^{28} - 57 q^{29} - 29 q^{30} - 51 q^{31} - 80 q^{32} - 78 q^{33} - 28 q^{34} - 34 q^{35} + 28 q^{36} - 117 q^{37} - 31 q^{38} - 36 q^{39} - 107 q^{40} - 60 q^{41} - 41 q^{42} - 109 q^{43} - 21 q^{44} - 62 q^{45} - 92 q^{46} - 26 q^{47} - 90 q^{48} - 7 q^{49} - 22 q^{50} - 47 q^{51} - 182 q^{52} - 83 q^{53} - 19 q^{54} - 53 q^{55} - 23 q^{56} - 201 q^{57} - 112 q^{58} + 14 q^{59} - 64 q^{60} - 73 q^{61} - 21 q^{62} - 94 q^{63} + 14 q^{64} - 123 q^{65} - 10 q^{66} - 135 q^{67} - 84 q^{68} - 50 q^{69} - 35 q^{70} - 29 q^{71} - 143 q^{72} - 266 q^{73} - 53 q^{74} - 32 q^{75} - 66 q^{76} - 69 q^{77} - 59 q^{78} - 124 q^{79} - 20 q^{80} - 33 q^{81} - 93 q^{82} - 28 q^{83} - 4 q^{84} - 179 q^{85} + 6 q^{86} - 40 q^{87} - 259 q^{88} - 41 q^{89} + 2 q^{90} - 50 q^{91} - 77 q^{92} - 60 q^{93} - 48 q^{94} - 37 q^{95} + 3 q^{96} - 220 q^{97} - 9 q^{98} - 35 q^{99}+O(q^{100}) \) 139 * q - 13 * q^2 - 22 * q^3 + 113 * q^4 - 16 * q^5 - 15 * q^6 - 44 * q^7 - 36 * q^8 + 87 * q^9 - 40 * q^10 - 17 * q^11 - 59 * q^12 - 89 * q^13 - 15 * q^14 - 29 * q^15 + 73 * q^16 - 58 * q^17 - 51 * q^18 - 37 * q^19 - 24 * q^20 - 37 * q^21 - 99 * q^22 - 42 * q^23 - 27 * q^24 - 11 * q^25 + 2 * q^26 - 73 * q^27 - 113 * q^28 - 57 * q^29 - 29 * q^30 - 51 * q^31 - 80 * q^32 - 78 * q^33 - 28 * q^34 - 34 * q^35 + 28 * q^36 - 117 * q^37 - 31 * q^38 - 36 * q^39 - 107 * q^40 - 60 * q^41 - 41 * q^42 - 109 * q^43 - 21 * q^44 - 62 * q^45 - 92 * q^46 - 26 * q^47 - 90 * q^48 - 7 * q^49 - 22 * q^50 - 47 * q^51 - 182 * q^52 - 83 * q^53 - 19 * q^54 - 53 * q^55 - 23 * q^56 - 201 * q^57 - 112 * q^58 + 14 * q^59 - 64 * q^60 - 73 * q^61 - 21 * q^62 - 94 * q^63 + 14 * q^64 - 123 * q^65 - 10 * q^66 - 135 * q^67 - 84 * q^68 - 50 * q^69 - 35 * q^70 - 29 * q^71 - 143 * q^72 - 266 * q^73 - 53 * q^74 - 32 * q^75 - 66 * q^76 - 69 * q^77 - 59 * q^78 - 124 * q^79 - 20 * q^80 - 33 * q^81 - 93 * q^82 - 28 * q^83 - 4 * q^84 - 179 * q^85 + 6 * q^86 - 40 * q^87 - 259 * q^88 - 41 * q^89 + 2 * q^90 - 50 * q^91 - 77 * q^92 - 60 * q^93 - 48 * q^94 - 37 * q^95 + 3 * q^96 - 220 * q^97 - 9 * q^98 - 35 * 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 $

$2$	−2.23150	−1.57791	−0.788953	−	0.614454i	$-0.789376\pi$
$2$	−2.23150	−1.57791	−0.788953	+	0.614454i	$0.789376\pi$
$3$	1.82610	1.05430	0.527148	−	0.849773i	$-0.323261\pi$
$3$	1.82610	1.05430	0.527148	+	0.849773i	$0.323261\pi$
$4$	2.97957	1.48979
$5$	2.21560	0.990848	0.495424	−	0.868651i	$-0.335013\pi$
$5$	2.21560	0.990848	0.495424	+	0.868651i	$0.335013\pi$
$6$	−4.07492	−1.66358
$7$	3.73360	1.41117	0.705585	−	0.708626i	$-0.250684\pi$
$7$	3.73360	1.41117	0.705585	+	0.708626i	$0.250684\pi$
$8$	−2.18591	−0.772837
$9$	0.334626	0.111542
$10$	−4.94411	−1.56346
$11$	−3.68316	−1.11051	−0.555257	−	0.831679i	$-0.687380\pi$
$11$	−3.68316	−1.11051	−0.555257	+	0.831679i	$0.687380\pi$
$12$	5.44099	1.57068
$13$	−3.24566	−0.900184	−0.450092	−	0.892982i	$-0.648609\pi$
$13$	−3.24566	−0.900184	−0.450092	+	0.892982i	$0.648609\pi$
$14$	−8.33152	−2.22669
$15$	4.04590	1.04465
$16$	−1.08129	−0.270323
$17$	−6.85809	−1.66333	−0.831665	−	0.555277i	$-0.812612\pi$
$17$	−6.85809	−1.66333	−0.831665	+	0.555277i	$0.812612\pi$
$18$	−0.746716	−0.176003
$19$	−0.903543	−0.207287	−0.103643	−	0.994615i	$-0.533050\pi$
$19$	−0.903543	−0.207287	−0.103643	+	0.994615i	$0.533050\pi$
$20$	6.60155	1.47615
$21$	6.81792	1.48779
$22$	8.21895	1.75229
$23$	−3.17314	−0.661646	−0.330823	−	0.943693i	$-0.607326\pi$
$23$	−3.17314	−0.661646	−0.330823	+	0.943693i	$0.607326\pi$
$24$	−3.99169	−0.814799
$25$	−0.0911012	−0.0182202
$26$	7.24267	1.42040
$27$	−4.86723	−0.936699
$28$	11.1245	2.10234
$29$	4.03844	0.749920	0.374960	−	0.927041i	$-0.377656\pi$
$29$	4.03844	0.749920	0.374960	+	0.927041i	$0.377656\pi$
$30$	−9.02842	−1.64836
$31$	−1.31359	−0.235928	−0.117964	−	0.993018i	$-0.537637\pi$
$31$	−1.31359	−0.235928	−0.117964	+	0.993018i	$0.537637\pi$
$32$	6.78472	1.19938
$33$	−6.72580	−1.17081
$34$	15.3038	2.62458
$35$	8.27218	1.39825
$36$	0.997042	0.166174
$37$	−8.64800	−1.42172	−0.710861	−	0.703332i	$-0.751695\pi$
$37$	−8.64800	−1.42172	−0.710861	+	0.703332i	$0.751695\pi$
$38$	2.01625	0.327079
$39$	−5.92688	−0.949061
$40$	−4.84311	−0.765764
$41$	4.85883	0.758822	0.379411	−	0.925228i	$-0.376127\pi$
$41$	4.85883	0.758822	0.379411	+	0.925228i	$0.376127\pi$
$42$	−15.2142	−2.34759
$43$	−4.13771	−0.630994	−0.315497	−	0.948927i	$-0.602171\pi$
$43$	−4.13771	−0.630994	−0.315497	+	0.948927i	$0.602171\pi$
$44$	−10.9742	−1.65443
$45$	0.741398	0.110521
$46$	7.08085	1.04401
$47$	7.29694	1.06437	0.532184	−	0.846629i	$-0.321372\pi$
$47$	7.29694	1.06437	0.532184	+	0.846629i	$0.321372\pi$
$48$	−1.97454	−0.285001
$49$	6.93979	0.991399
$50$	0.203292	0.0287498
$51$	−12.5235	−1.75364
$52$	−9.67068	−1.34108
$53$	2.19910	0.302070	0.151035	−	0.988528i	$-0.451739\pi$
$53$	2.19910	0.302070	0.151035	+	0.988528i	$0.451739\pi$
$54$	10.8612	1.47802
$55$	−8.16042	−1.10035
$56$	−8.16133	−1.09060
$57$	−1.64996	−0.218542
$58$	−9.01177	−1.18330
$59$	1.05949	0.137934	0.0689670	−	0.997619i	$-0.478030\pi$
$59$	1.05949	0.137934	0.0689670	+	0.997619i	$0.478030\pi$
$60$	12.0551	1.55630
$61$	−2.14112	−0.274142	−0.137071	−	0.990561i	$-0.543769\pi$
$61$	−2.14112	−0.274142	−0.137071	+	0.990561i	$0.543769\pi$
$62$	2.93127	0.372272
$63$	1.24936	0.157405
$64$	−12.9775	−1.62219
$65$	−7.19109	−0.891945
$66$	15.0086	1.84743
$67$	−2.21411	−0.270496	−0.135248	−	0.990812i	$-0.543183\pi$
$67$	−2.21411	−0.270496	−0.135248	+	0.990812i	$0.543183\pi$
$68$	−20.4342	−2.47801
$69$	−5.79446	−0.697571
$70$	−18.4593	−2.20631
$71$	−0.0868923	−0.0103122	−0.00515611	−	0.999987i	$-0.501641\pi$
$71$	−0.0868923	−0.0103122	−0.00515611	+	0.999987i	$0.501641\pi$
$72$	−0.731463	−0.0862037
$73$	−15.4450	−1.80770	−0.903850	−	0.427849i	$-0.859271\pi$
$73$	−15.4450	−1.80770	−0.903850	+	0.427849i	$0.859271\pi$
$74$	19.2980	2.24334
$75$	−0.166359	−0.0192095
$76$	−2.69217	−0.308813
$77$	−13.7515	−1.56712
$78$	13.2258	1.49753
$79$	−11.2752	−1.26856	−0.634278	−	0.773105i	$-0.718702\pi$
$79$	−11.2752	−1.26856	−0.634278	+	0.773105i	$0.718702\pi$
$80$	−2.39571	−0.267849
$81$	−9.89190	−1.09910
$82$	−10.8425	−1.19735
$83$	−6.73872	−0.739670	−0.369835	−	0.929097i	$-0.620586\pi$
$83$	−6.73872	−0.739670	−0.369835	+	0.929097i	$0.620586\pi$
$84$	20.3145	2.21649
$85$	−15.1948	−1.64811
$86$	9.23327	0.995649
$87$	7.37458	0.790638
$88$	8.05106	0.858246
$89$	14.5000	1.53700	0.768499	−	0.639851i	$-0.221004\pi$
$89$	14.5000	1.53700	0.768499	+	0.639851i	$0.221004\pi$
$90$	−1.65443	−0.174392
$91$	−12.1180	−1.27031
$92$	−9.45461	−0.985711
$93$	−2.39874	−0.248738
$94$	−16.2831	−1.67947
$95$	−2.00189	−0.205390
$96$	12.3896	1.26450
$97$	−8.35648	−0.848472	−0.424236	−	0.905552i	$-0.639457\pi$
$97$	−8.35648	−0.848472	−0.424236	+	0.905552i	$0.639457\pi$
$98$	−15.4861	−1.56433
$99$	−1.23248	−0.123869
$100$	−0.271443	−0.0271443
$101$	6.29069	0.625947	0.312973	−	0.949762i	$-0.398675\pi$
$101$	6.29069	0.625947	0.312973	+	0.949762i	$0.398675\pi$
$102$	27.9462	2.76709
$103$	4.94125	0.486876	0.243438	−	0.969917i	$-0.421725\pi$
$103$	4.94125	0.486876	0.243438	+	0.969917i	$0.421725\pi$
$104$	7.09472	0.695695
$105$	15.1058	1.47418
$106$	−4.90729	−0.476638
$107$	4.00147	0.386837	0.193418	−	0.981116i	$-0.438043\pi$
$107$	4.00147	0.386837	0.193418	+	0.981116i	$0.438043\pi$
$108$	−14.5023	−1.39548
$109$	−0.105208	−0.0100771	−0.00503855	−	0.999987i	$-0.501604\pi$
$109$	−0.105208	−0.0100771	−0.00503855	+	0.999987i	$0.501604\pi$
$110$	18.2099	1.73625
$111$	−15.7921	−1.49892
$112$	−4.03712	−0.381472
$113$	6.99386	0.657927	0.328964	−	0.944343i	$-0.393301\pi$
$113$	6.99386	0.657927	0.328964	+	0.944343i	$0.393301\pi$
$114$	3.68187	0.344839
$115$	−7.03043	−0.655591
$116$	12.0328	1.11722
$117$	−1.08608	−0.100408
$118$	−2.36425	−0.217647
$119$	−25.6054	−2.34724
$120$	−8.84399	−0.807342
$121$	2.56566	0.233242
$122$	4.77790	0.432571
$123$	8.87269	0.800023
$124$	−3.91394	−0.351482
$125$	−11.2799	−1.00890
$126$	−2.78794	−0.248370
$127$	5.85702	0.519727	0.259863	−	0.965645i	$-0.416322\pi$
$127$	5.85702	0.519727	0.259863	+	0.965645i	$0.416322\pi$
$128$	15.3898	1.36028
$129$	−7.55585	−0.665255
$130$	16.0469	1.40741
$131$	−7.84578	−0.685489	−0.342744	−	0.939429i	$-0.611356\pi$
$131$	−7.84578	−0.685489	−0.342744	+	0.939429i	$0.611356\pi$
$132$	−20.0400	−1.74426
$133$	−3.37347	−0.292517
$134$	4.94077	0.426817
$135$	−10.7838	−0.928126
$136$	14.9912	1.28548
$137$	−11.2281	−0.959283	−0.479641	−	0.877465i	$-0.659233\pi$
$137$	−11.2281	−0.959283	−0.479641	+	0.877465i	$0.659233\pi$
$138$	12.9303	1.10070
$139$	−4.21036	−0.357118	−0.178559	−	0.983929i	$-0.557144\pi$
$139$	−4.21036	−0.357118	−0.178559	+	0.983929i	$0.557144\pi$
$140$	24.6476	2.08310
$141$	13.3249	1.12216
$142$	0.193900	0.0162717
$143$	11.9543	0.999667
$144$	−0.361828	−0.0301524
$145$	8.94759	0.743057
$146$	34.4654	2.85238
$147$	12.6727	1.04523
$148$	−25.7673	−2.11806
$149$	−3.33818	−0.273474	−0.136737	−	0.990607i	$-0.543662\pi$
$149$	−3.33818	−0.273474	−0.136737	+	0.990607i	$0.543662\pi$
$150$	0.371230	0.0303108
$151$	−2.55255	−0.207723	−0.103862	−	0.994592i	$-0.533120\pi$
$151$	−2.55255	−0.207723	−0.103862	+	0.994592i	$0.533120\pi$
$152$	1.97507	0.160199
$153$	−2.29489	−0.185531
$154$	30.6863	2.47277
$155$	−2.91040	−0.233769
$156$	−17.6596	−1.41390
$157$	16.7725	1.33859	0.669294	−	0.742998i	$-0.266597\pi$
$157$	16.7725	1.33859	0.669294	+	0.742998i	$0.266597\pi$
$158$	25.1605	2.00166
$159$	4.01577	0.318471
$160$	15.0323	1.18840
$161$	−11.8473	−0.933694
$162$	22.0737	1.73428
$163$	−1.66917	−0.130740	−0.0653699	−	0.997861i	$-0.520823\pi$
$163$	−1.66917	−0.130740	−0.0653699	+	0.997861i	$0.520823\pi$
$164$	14.4772	1.13048
$165$	−14.9017	−1.16010
$166$	15.0374	1.16713
$167$	−4.24272	−0.328311	−0.164156	−	0.986434i	$-0.552490\pi$
$167$	−4.24272	−0.328311	−0.164156	+	0.986434i	$0.552490\pi$
$168$	−14.9034	−1.14982
$169$	−2.46570	−0.189669
$170$	33.9071	2.60056
$171$	−0.302349	−0.0231212
$172$	−12.3286	−0.940047
$173$	3.40965	0.259231	0.129615	−	0.991564i	$-0.458626\pi$
$173$	3.40965	0.259231	0.129615	+	0.991564i	$0.458626\pi$
$174$	−16.4563	−1.24755
$175$	−0.340136	−0.0257118
$176$	3.98257	0.300198
$177$	1.93473	0.145423
$178$	−32.3567	−2.42524
$179$	2.26432	0.169243	0.0846217	−	0.996413i	$-0.473032\pi$
$179$	2.26432	0.169243	0.0846217	+	0.996413i	$0.473032\pi$
$180$	2.20905	0.164653
$181$	−12.1103	−0.900152	−0.450076	−	0.892990i	$-0.648603\pi$
$181$	−12.1103	−0.900152	−0.450076	+	0.892990i	$0.648603\pi$
$182$	27.0413	2.00443
$183$	−3.90989	−0.289027
$184$	6.93621	0.511344
$185$	−19.1605	−1.40871
$186$	5.35278	0.392485
$187$	25.2594	1.84715
$188$	21.7418	1.58568
$189$	−18.1723	−1.32184
$190$	4.46721	0.324086
$191$	−2.78777	−0.201716	−0.100858	−	0.994901i	$-0.532159\pi$
$191$	−2.78777	−0.201716	−0.100858	+	0.994901i	$0.532159\pi$
$192$	−23.6981	−1.71027
$193$	8.98442	0.646713	0.323356	−	0.946277i	$-0.395189\pi$
$193$	8.98442	0.646713	0.323356	+	0.946277i	$0.395189\pi$
$194$	18.6474	1.33881
$195$	−13.1316	−0.940375
$196$	20.6776	1.47697
$197$	−23.1796	−1.65148	−0.825740	−	0.564051i	$-0.809242\pi$
$197$	−23.1796	−1.65148	−0.825740	+	0.564051i	$0.809242\pi$
$198$	2.75028	0.195454
$199$	14.8718	1.05424	0.527119	−	0.849792i	$-0.323272\pi$
$199$	14.8718	1.05424	0.527119	+	0.849792i	$0.323272\pi$
$200$	0.199139	0.0140813
$201$	−4.04317	−0.285183
$202$	−14.0376	−0.987685
$203$	15.0779	1.05826
$204$	−37.3148	−2.61256
$205$	10.7652	0.751877
$206$	−11.0264	−0.768244
$207$	−1.06182	−0.0738013
$208$	3.50950	0.243340
$209$	3.32789	0.230195
$210$	−33.7085	−2.32611
$211$	3.16770	0.218073	0.109037	−	0.994038i	$-0.465223\pi$
$211$	3.16770	0.218073	0.109037	+	0.994038i	$0.465223\pi$
$212$	6.55239	0.450020
$213$	−0.158674	−0.0108721
$214$	−8.92926	−0.610392
$215$	−9.16752	−0.625219
$216$	10.6393	0.723915
$217$	−4.90443	−0.332934
$218$	0.234771	0.0159007
$219$	−28.2040	−1.90585
$220$	−24.3146	−1.63929
$221$	22.2590	1.49730
$222$	35.2400	2.36515
$223$	−24.9493	−1.67073	−0.835365	−	0.549695i	$-0.814744\pi$
$223$	−24.9493	−1.67073	−0.835365	+	0.549695i	$0.814744\pi$
$224$	25.3315	1.69253
$225$	−0.0304848	−0.00203232
$226$	−15.6068	−1.03815
$227$	8.54520	0.567165	0.283583	−	0.958948i	$-0.408477\pi$
$227$	8.54520	0.567165	0.283583	+	0.958948i	$0.408477\pi$
$228$	−4.91616	−0.325581
$229$	18.9649	1.25323	0.626617	−	0.779328i	$-0.284439\pi$
$229$	18.9649	1.25323	0.626617	+	0.779328i	$0.284439\pi$
$230$	15.6884	1.03446
$231$	−25.1115	−1.65221
$232$	−8.82768	−0.579566
$233$	22.5443	1.47693	0.738464	−	0.674293i	$-0.235552\pi$
$233$	22.5443	1.47693	0.738464	+	0.674293i	$0.235552\pi$
$234$	2.42359	0.158435
$235$	16.1671	1.05463
$236$	3.15683	0.205492
$237$	−20.5895	−1.33743
$238$	57.1383	3.70373
$239$	−3.00720	−0.194519	−0.0972597	−	0.995259i	$-0.531008\pi$
$239$	−3.00720	−0.194519	−0.0972597	+	0.995259i	$0.531008\pi$
$240$	−4.37480	−0.282392
$241$	−5.46321	−0.351916	−0.175958	−	0.984398i	$-0.556302\pi$
$241$	−5.46321	−0.351916	−0.175958	+	0.984398i	$0.556302\pi$
$242$	−5.72526	−0.368034
$243$	−3.46188	−0.222080
$244$	−6.37962	−0.408414
$245$	15.3758	0.982326
$246$	−19.7994	−1.26236
$247$	2.93259	0.186596
$248$	2.87139	0.182334
$249$	−12.3055	−0.779832
$250$	25.1710	1.59195
$251$	−20.3217	−1.28269	−0.641347	−	0.767251i	$-0.721624\pi$
$251$	−20.3217	−1.28269	−0.641347	+	0.767251i	$0.721624\pi$
$252$	3.72256	0.234499
$253$	11.6872	0.734767
$254$	−13.0699	−0.820080
$255$	−27.7472	−1.73760
$256$	−8.38723	−0.524202
$257$	6.85753	0.427761	0.213881	−	0.976860i	$-0.431390\pi$
$257$	6.85753	0.427761	0.213881	+	0.976860i	$0.431390\pi$
$258$	16.8608	1.04971
$259$	−32.2882	−2.00629
$260$	−21.4264	−1.32881
$261$	1.35137	0.0836476
$262$	17.5078	1.08164
$263$	−26.7279	−1.64812	−0.824058	−	0.566506i	$-0.808295\pi$
$263$	−26.7279	−1.64812	−0.824058	+	0.566506i	$0.808295\pi$
$264$	14.7020	0.904846
$265$	4.87234	0.299305
$266$	7.52788	0.461564
$267$	26.4784	1.62045
$268$	−6.59709	−0.402981
$269$	−1.74671	−0.106499	−0.0532495	−	0.998581i	$-0.516958\pi$
$269$	−1.74671	−0.106499	−0.0532495	+	0.998581i	$0.516958\pi$
$270$	24.0641	1.46450
$271$	6.98161	0.424103	0.212051	−	0.977259i	$-0.431986\pi$
$271$	6.98161	0.424103	0.212051	+	0.977259i	$0.431986\pi$
$272$	7.41560	0.449637
$273$	−22.1286	−1.33929
$274$	25.0555	1.51366
$275$	0.335540	0.0202338
$276$	−17.2650	−1.03923
$277$	26.5550	1.59553	0.797767	−	0.602965i	$-0.206014\pi$
$277$	26.5550	1.59553	0.797767	+	0.602965i	$0.206014\pi$
$278$	9.39539	0.563498
$279$	−0.439562	−0.0263159
$280$	−18.0823	−1.08062
$281$	−13.5845	−0.810381	−0.405191	−	0.914232i	$-0.632795\pi$
$281$	−13.5845	−0.810381	−0.405191	+	0.914232i	$0.632795\pi$
$282$	−29.7345	−1.77066
$283$	13.3166	0.791589	0.395795	−	0.918339i	$-0.370469\pi$
$283$	13.3166	0.791589	0.395795	+	0.918339i	$0.370469\pi$
$284$	−0.258902	−0.0153630
$285$	−3.65565	−0.216542
$286$	−26.6759	−1.57738
$287$	18.1409	1.07083
$288$	2.27034	0.133781
$289$	30.0334	1.76667
$290$	−19.9665	−1.17247
$291$	−15.2597	−0.894541
$292$	−46.0195	−2.69309
$293$	1.81360	0.105951	0.0529757	−	0.998596i	$-0.483129\pi$
$293$	1.81360	0.105951	0.0529757	+	0.998596i	$0.483129\pi$
$294$	−28.2791	−1.64927
$295$	2.34741	0.136672
$296$	18.9038	1.09876
$297$	17.9268	1.04022
$298$	7.44914	0.431517
$299$	10.2989	0.595603
$300$	−0.495680	−0.0286181
$301$	−15.4486	−0.890440
$302$	5.69600	0.327768
$303$	11.4874	0.659934
$304$	0.976994	0.0560344
$305$	−4.74387	−0.271633
$306$	5.12105	0.292751
$307$	8.22235	0.469274	0.234637	−	0.972083i	$-0.424610\pi$
$307$	8.22235	0.469274	0.234637	+	0.972083i	$0.424610\pi$
$308$	−40.9735	−2.33468
$309$	9.02319	0.513311
$310$	6.49454	0.368865
$311$	28.9015	1.63885	0.819426	−	0.573185i	$-0.194292\pi$
$311$	28.9015	1.63885	0.819426	+	0.573185i	$0.194292\pi$
$312$	12.9556	0.733469
$313$	−2.37024	−0.133974	−0.0669869	−	0.997754i	$-0.521339\pi$
$313$	−2.37024	−0.133974	−0.0669869	+	0.997754i	$0.521339\pi$
$314$	−37.4277	−2.11217
$315$	2.76809	0.155964
$316$	−33.5952	−1.88988
$317$	33.6012	1.88723	0.943615	−	0.331046i	$-0.107402\pi$
$317$	33.6012	1.88723	0.943615	+	0.331046i	$0.107402\pi$
$318$	−8.96118	−0.502518
$319$	−14.8742	−0.832797
$320$	−28.7530	−1.60734
$321$	7.30707	0.407841
$322$	26.4371	1.47328
$323$	6.19658	0.344787
$324$	−29.4736	−1.63742
$325$	0.295683	0.0164016
$326$	3.72475	0.206295
$327$	−0.192120	−0.0106243
$328$	−10.6210	−0.586445
$329$	27.2439	1.50200
$330$	33.2531	1.83052
$331$	8.94770	0.491810	0.245905	−	0.969294i	$-0.420915\pi$
$331$	8.94770	0.491810	0.245905	+	0.969294i	$0.420915\pi$
$332$	−20.0785	−1.10195
$333$	−2.89385	−0.158582
$334$	9.46760	0.518044
$335$	−4.90558	−0.268020
$336$	−7.37216	−0.402184
$337$	3.10797	0.169302	0.0846509	−	0.996411i	$-0.473022\pi$
$337$	3.10797	0.169302	0.0846509	+	0.996411i	$0.473022\pi$
$338$	5.50220	0.299280
$339$	12.7715	0.693651
$340$	−45.2740	−2.45533
$341$	4.83816	0.262001
$342$	0.674690	0.0364831
$343$	−0.224792	−0.0121376
$344$	9.04466	0.487655
$345$	−12.8382	−0.691187
$346$	−7.60861	−0.409041
$347$	24.3645	1.30795	0.653977	−	0.756514i	$-0.273099\pi$
$347$	24.3645	1.30795	0.653977	+	0.756514i	$0.273099\pi$
$348$	21.9731	1.17788
$349$	−13.5319	−0.724344	−0.362172	−	0.932111i	$-0.617965\pi$
$349$	−13.5319	−0.724344	−0.362172	+	0.932111i	$0.617965\pi$
$350$	0.759011	0.0405708
$351$	15.7974	0.843201
$352$	−24.9892	−1.33193
$353$	−13.0791	−0.696129	−0.348064	−	0.937471i	$-0.613161\pi$
$353$	−13.0791	−0.696129	−0.348064	+	0.937471i	$0.613161\pi$
$354$	−4.31735	−0.229464
$355$	−0.192519	−0.0102178
$356$	43.2038	2.28980
$357$	−46.7579	−2.47469
$358$	−5.05283	−0.267050
$359$	4.71500	0.248848	0.124424	−	0.992229i	$-0.460292\pi$
$359$	4.71500	0.248848	0.124424	+	0.992229i	$0.460292\pi$
$360$	−1.62063	−0.0854148
$361$	−18.1836	−0.957032
$362$	27.0241	1.42035
$363$	4.68514	0.245906
$364$	−36.1065	−1.89249
$365$	−34.2200	−1.79116
$366$	8.72490	0.456058
$367$	−15.5967	−0.814141	−0.407070	−	0.913397i	$-0.633450\pi$
$367$	−15.5967	−0.814141	−0.407070	+	0.913397i	$0.633450\pi$
$368$	3.43109	0.178858
$369$	1.62589	0.0846405
$370$	42.7567	2.22281
$371$	8.21058	0.426272
$372$	−7.14723	−0.370566
$373$	−27.7173	−1.43515	−0.717574	−	0.696482i	$-0.754747\pi$
$373$	−27.7173	−1.43515	−0.717574	+	0.696482i	$0.754747\pi$
$374$	−56.3663	−2.91463
$375$	−20.5981	−1.06368
$376$	−15.9505	−0.822582
$377$	−13.1074	−0.675066
$378$	40.5514	2.08574
$379$	2.50600	0.128725	0.0643623	−	0.997927i	$-0.479499\pi$
$379$	2.50600	0.128725	0.0643623	+	0.997927i	$0.479499\pi$
$380$	−5.96478	−0.305987
$381$	10.6955	0.547946
$382$	6.22090	0.318289
$383$	−36.9563	−1.88838	−0.944189	−	0.329405i	$-0.893152\pi$
$383$	−36.9563	−1.88838	−0.944189	+	0.329405i	$0.893152\pi$
$384$	28.1032	1.43414
$385$	−30.4678	−1.55278
$386$	−20.0487	−1.02045
$387$	−1.38458	−0.0703824
$388$	−24.8987	−1.26404
$389$	2.45130	0.124286	0.0621428	−	0.998067i	$-0.480207\pi$
$389$	2.45130	0.124286	0.0621428	+	0.998067i	$0.480207\pi$
$390$	29.3032	1.48382
$391$	21.7617	1.10054
$392$	−15.1698	−0.766189
$393$	−14.3271	−0.722709
$394$	51.7252	2.60588
$395$	−24.9813	−1.25695
$396$	−3.67227	−0.184538
$397$	−0.435792	−0.0218718	−0.0109359	−	0.999940i	$-0.503481\pi$
$397$	−0.435792	−0.0218718	−0.0109359	+	0.999940i	$0.503481\pi$
$398$	−33.1865	−1.66349
$399$	−6.16028	−0.308400
$400$	0.0985070	0.00492535
$401$	31.1900	1.55756	0.778778	−	0.627300i	$-0.215840\pi$
$401$	31.1900	1.55756	0.778778	+	0.627300i	$0.215840\pi$
$402$	9.02231	0.449992
$403$	4.26347	0.212378
$404$	18.7436	0.932527
$405$	−21.9165	−1.08904
$406$	−33.6464	−1.66984
$407$	31.8520	1.57884
$408$	27.3753	1.35528
$409$	−4.66893	−0.230864	−0.115432	−	0.993315i	$-0.536825\pi$
$409$	−4.66893	−0.230864	−0.115432	+	0.993315i	$0.536825\pi$
$410$	−24.0226	−1.18639
$411$	−20.5036	−1.01137
$412$	14.7228	0.725340
$413$	3.95572	0.194648
$414$	2.36944	0.116452
$415$	−14.9303	−0.732901
$416$	−22.0209	−1.07966
$417$	−7.68851	−0.376508
$418$	−7.42618	−0.363226
$419$	−6.77896	−0.331174	−0.165587	−	0.986195i	$-0.552952\pi$
$419$	−6.77896	−0.331174	−0.165587	+	0.986195i	$0.552952\pi$
$420$	45.0088	2.19621
$421$	−29.9711	−1.46070	−0.730351	−	0.683072i	$-0.760643\pi$
$421$	−29.9711	−1.46070	−0.730351	+	0.683072i	$0.760643\pi$
$422$	−7.06870	−0.344099
$423$	2.44174	0.118722
$424$	−4.80704	−0.233451
$425$	0.624780	0.0303063
$426$	0.354080	0.0171552
$427$	−7.99409	−0.386861
$428$	11.9227	0.576304
$429$	21.8297	1.05395
$430$	20.4573	0.986537
$431$	24.0973	1.16072	0.580362	−	0.814358i	$-0.302911\pi$
$431$	24.0973	1.16072	0.580362	+	0.814358i	$0.302911\pi$
$432$	5.26290	0.253211
$433$	36.2720	1.74312	0.871560	−	0.490288i	$-0.163109\pi$
$433$	36.2720	1.74312	0.871560	+	0.490288i	$0.163109\pi$
$434$	10.9442	0.525339
$435$	16.3392	0.783402
$436$	−0.313475	−0.0150127
$437$	2.86707	0.137151
$438$	62.9372	3.00726
$439$	−38.5184	−1.83838	−0.919191	−	0.393812i	$-0.871156\pi$
$439$	−38.5184	−1.83838	−0.919191	+	0.393812i	$0.871156\pi$
$440$	17.8380	0.850391
$441$	2.32223	0.110583
$442$	−49.6709	−2.36260
$443$	17.0581	0.810457	0.405228	−	0.914216i	$-0.367192\pi$
$443$	17.0581	0.810457	0.405228	+	0.914216i	$0.367192\pi$
$444$	−47.0536	−2.23307
$445$	32.1263	1.52293
$446$	55.6743	2.63626
$447$	−6.09584	−0.288323
$448$	−48.4528	−2.28918
$449$	33.7872	1.59452	0.797259	−	0.603638i	$-0.206283\pi$
$449$	33.7872	1.59452	0.797259	+	0.603638i	$0.206283\pi$
$450$	0.0680267	0.00320681
$451$	−17.8958	−0.842682
$452$	20.8387	0.980171
$453$	−4.66119	−0.219002
$454$	−19.0686	−0.894933
$455$	−26.8487	−1.25869
$456$	3.60666	0.168897
$457$	−7.30550	−0.341737	−0.170869	−	0.985294i	$-0.554657\pi$
$457$	−7.30550	−0.341737	−0.170869	+	0.985294i	$0.554657\pi$
$458$	−42.3200	−1.97748
$459$	33.3799	1.55804
$460$	−20.9477	−0.976690
$461$	18.2154	0.848375	0.424188	−	0.905574i	$-0.360560\pi$
$461$	18.2154	0.848375	0.424188	+	0.905574i	$0.360560\pi$
$462$	56.0361	2.60704
$463$	−19.7125	−0.916116	−0.458058	−	0.888922i	$-0.651455\pi$
$463$	−19.7125	−0.916116	−0.458058	+	0.888922i	$0.651455\pi$
$464$	−4.36674	−0.202721
$465$	−5.31466	−0.246462
$466$	−50.3075	−2.33045
$467$	−25.6379	−1.18638	−0.593190	−	0.805062i	$-0.702132\pi$
$467$	−25.6379	−1.18638	−0.593190	+	0.805062i	$0.702132\pi$
$468$	−3.23606	−0.149587
$469$	−8.26659	−0.381716
$470$	−36.0769	−1.66410
$471$	30.6281	1.41127
$472$	−2.31595	−0.106600
$473$	15.2398	0.700728
$474$	45.9455	2.11035
$475$	0.0823138	0.00377682
$476$	−76.2931	−3.49689
$477$	0.735877	0.0336935
$478$	6.71054	0.306933
$479$	−31.0290	−1.41775	−0.708876	−	0.705333i	$-0.750798\pi$
$479$	−31.0290	−1.41775	−0.708876	+	0.705333i	$0.750798\pi$
$480$	27.4503	1.25293
$481$	28.0685	1.27981
$482$	12.1911	0.555290
$483$	−21.6342	−0.984391
$484$	7.64457	0.347481
$485$	−18.5146	−0.840706
$486$	7.72517	0.350421
$487$	−0.383475	−0.0173769	−0.00868846	−	0.999962i	$-0.502766\pi$
$487$	−0.383475	−0.0173769	−0.00868846	+	0.999962i	$0.502766\pi$
$488$	4.68030	0.211867
$489$	−3.04807	−0.137838
$490$	−34.3111	−1.55002
$491$	−24.9379	−1.12543	−0.562715	−	0.826651i	$-0.690243\pi$
$491$	−24.9379	−1.12543	−0.562715	+	0.826651i	$0.690243\pi$
$492$	26.4368	1.19186
$493$	−27.6960	−1.24736
$494$	−6.54406	−0.294431
$495$	−2.73069	−0.122735
$496$	1.42038	0.0637767
$497$	−0.324421	−0.0145523
$498$	27.4598	1.23050
$499$	−43.1603	−1.93212	−0.966059	−	0.258320i	$-0.916831\pi$
$499$	−43.1603	−1.93212	−0.966059	+	0.258320i	$0.916831\pi$
$500$	−33.6092	−1.50305
$501$	−7.74760	−0.346137
$502$	45.3478	2.02397
$503$	16.8289	0.750365	0.375183	−	0.926951i	$-0.377580\pi$
$503$	16.8289	0.750365	0.375183	+	0.926951i	$0.377580\pi$
$504$	−2.73099	−0.121648
$505$	13.9377	0.620218
$506$	−26.0799	−1.15939
$507$	−4.50261	−0.199968
$508$	17.4514	0.774282
$509$	−17.1420	−0.759805	−0.379902	−	0.925027i	$-0.624042\pi$
$509$	−17.1420	−0.759805	−0.379902	+	0.925027i	$0.624042\pi$
$510$	61.9177	2.74176
$511$	−57.6655	−2.55097
$512$	−12.0635	−0.533136
$513$	4.39775	0.194165
$514$	−15.3026	−0.674967
$515$	10.9478	0.482420
$516$	−22.5132	−0.991088
$517$	−26.8758	−1.18200
$518$	72.0510	3.16574
$519$	6.22634	0.273306
$520$	15.7191	0.689328
$521$	32.8416	1.43882	0.719408	−	0.694588i	$-0.244413\pi$
$521$	32.8416	1.43882	0.719408	+	0.694588i	$0.244413\pi$
$522$	−3.01557	−0.131988
$523$	−35.3539	−1.54592	−0.772959	−	0.634456i	$-0.781224\pi$
$523$	−35.3539	−1.54592	−0.772959	+	0.634456i	$0.781224\pi$
$524$	−23.3771	−1.02123
$525$	−0.621120	−0.0271079
$526$	59.6433	2.60057
$527$	9.00872	0.392426
$528$	7.27256	0.316497
$529$	−12.9312	−0.562225
$530$	−10.8726	−0.472276
$531$	0.354533	0.0153854
$532$	−10.0515	−0.435788
$533$	−15.7701	−0.683079
$534$	−59.0865	−2.55692
$535$	8.86567	0.383296
$536$	4.83984	0.209049
$537$	4.13487	0.178433
$538$	3.89778	0.168045
$539$	−25.5604	−1.10096
$540$	−32.1313	−1.38271
$541$	1.24606	0.0535725	0.0267862	−	0.999641i	$-0.491473\pi$
$541$	1.24606	0.0535725	0.0267862	+	0.999641i	$0.491473\pi$
$542$	−15.5794	−0.669194
$543$	−22.1146	−0.949027
$544$	−46.5302	−1.99497
$545$	−0.233099	−0.00998487
$546$	49.3799	2.11327
$547$	27.7288	1.18560	0.592798	−	0.805351i	$-0.298023\pi$
$547$	27.7288	1.18560	0.592798	+	0.805351i	$0.298023\pi$
$548$	−33.4550	−1.42913
$549$	−0.716474	−0.0305784
$550$	−0.748756	−0.0319271
$551$	−3.64891	−0.155449
$552$	12.6662	0.539109
$553$	−42.0970	−1.79015
$554$	−59.2573	−2.51760
$555$	−34.9890	−1.48520
$556$	−12.5451	−0.532029
$557$	−27.0275	−1.14519	−0.572596	−	0.819838i	$-0.694064\pi$
$557$	−27.0275	−1.14519	−0.572596	+	0.819838i	$0.694064\pi$
$558$	0.980880	0.0415240
$559$	13.4296	0.568011
$560$	−8.94465	−0.377980
$561$	46.1261	1.94745
$562$	30.3137	1.27871
$563$	17.8317	0.751515	0.375758	−	0.926718i	$-0.377383\pi$
$563$	17.8317	0.751515	0.375758	+	0.926718i	$0.377383\pi$
$564$	39.7025	1.67178
$565$	15.4956	0.651906
$566$	−29.7159	−1.24905
$567$	−36.9324	−1.55102
$568$	0.189939	0.00796966
$569$	21.5877	0.905004	0.452502	−	0.891763i	$-0.350532\pi$
$569$	21.5877	0.905004	0.452502	+	0.891763i	$0.350532\pi$
$570$	8.15756	0.341683
$571$	20.3052	0.849745	0.424873	−	0.905253i	$-0.360319\pi$
$571$	20.3052	0.849745	0.424873	+	0.905253i	$0.360319\pi$
$572$	35.6186	1.48929
$573$	−5.09074	−0.212669
$574$	−40.4814	−1.68966
$575$	0.289077	0.0120553
$576$	−4.34261	−0.180942
$577$	−13.3291	−0.554897	−0.277449	−	0.960740i	$-0.589489\pi$
$577$	−13.3291	−0.554897	−0.277449	+	0.960740i	$0.589489\pi$
$578$	−67.0193	−2.78764
$579$	16.4064	0.681827
$580$	26.6600	1.10700
$581$	−25.1597	−1.04380
$582$	34.0520	1.41150
$583$	−8.09964	−0.335453
$584$	33.7614	1.39706
$585$	−2.40633	−0.0994893
$586$	−4.04703	−0.167181
$587$	−0.226346	−0.00934228	−0.00467114	−	0.999989i	$-0.501487\pi$
$587$	−0.226346	−0.00934228	−0.00467114	+	0.999989i	$0.501487\pi$
$588$	37.7593	1.55717
$589$	1.18689	0.0489048
$590$	−5.23824	−0.215655
$591$	−42.3282	−1.74115
$592$	9.35101	0.384324
$593$	−9.76312	−0.400923	−0.200462	−	0.979702i	$-0.564244\pi$
$593$	−9.76312	−0.400923	−0.200462	+	0.979702i	$0.564244\pi$
$594$	−40.0035	−1.64136
$595$	−56.7314	−2.32576
$596$	−9.94635	−0.407418
$597$	27.1574	1.11148
$598$	−22.9820	−0.939805
$599$	−25.2291	−1.03083	−0.515417	−	0.856939i	$-0.672363\pi$
$599$	−25.2291	−1.03083	−0.515417	+	0.856939i	$0.672363\pi$
$600$	0.363647	0.0148458
$601$	24.8200	1.01243	0.506215	−	0.862407i	$-0.331044\pi$
$601$	24.8200	1.01243	0.506215	+	0.862407i	$0.331044\pi$
$602$	34.4734	1.40503
$603$	−0.740897	−0.0301717
$604$	−7.60550	−0.309463
$605$	5.68449	0.231107
$606$	−25.6341	−1.04131
$607$	−18.2097	−0.739109	−0.369554	−	0.929209i	$-0.620490\pi$
$607$	−18.2097	−0.739109	−0.369554	+	0.929209i	$0.620490\pi$
$608$	−6.13029	−0.248616
$609$	27.5338	1.11572
$610$	10.5859	0.428612
$611$	−23.6834	−0.958126
$612$	−6.83780	−0.276402
$613$	42.1708	1.70326	0.851630	−	0.524143i	$-0.175614\pi$
$613$	42.1708	1.70326	0.851630	+	0.524143i	$0.175614\pi$
$614$	−18.3481	−0.740470
$615$	19.6584	0.792702
$616$	30.0595	1.21113
$617$	−26.1645	−1.05335	−0.526673	−	0.850068i	$-0.676561\pi$
$617$	−26.1645	−1.05335	−0.526673	+	0.850068i	$0.676561\pi$
$618$	−20.1352	−0.809957
$619$	12.1981	0.490284	0.245142	−	0.969487i	$-0.421165\pi$
$619$	12.1981	0.490284	0.245142	+	0.969487i	$0.421165\pi$
$620$	−8.67174	−0.348265
$621$	15.4444	0.619763
$622$	−64.4935	−2.58595
$623$	54.1373	2.16897
$624$	6.40869	0.256553
$625$	−24.5362	−0.981448
$626$	5.28918	0.211398
$627$	6.07705	0.242694
$628$	49.9748	1.99421
$629$	59.3088	2.36479
$630$	−6.17698	−0.246097
$631$	29.6209	1.17919	0.589595	−	0.807699i	$-0.299287\pi$
$631$	29.6209	1.17919	0.589595	+	0.807699i	$0.299287\pi$
$632$	24.6465	0.980386
$633$	5.78452	0.229914
$634$	−74.9808	−2.97787
$635$	12.9768	0.514970
$636$	11.9653	0.474454
$637$	−22.5242	−0.892441
$638$	33.1918	1.31407
$639$	−0.0290764	−0.00115025
$640$	34.0976	1.34783
$641$	6.77864	0.267740	0.133870	−	0.990999i	$-0.457260\pi$
$641$	6.77864	0.267740	0.133870	+	0.990999i	$0.457260\pi$
$642$	−16.3057	−0.643534
$643$	16.2942	0.642581	0.321290	−	0.946981i	$-0.395883\pi$
$643$	16.2942	0.642581	0.321290	+	0.946981i	$0.395883\pi$
$644$	−35.2998	−1.39101
$645$	−16.7408	−0.659167
$646$	−13.8276	−0.544041
$647$	−15.6756	−0.616271	−0.308135	−	0.951343i	$-0.599705\pi$
$647$	−15.6756	−0.616271	−0.308135	+	0.951343i	$0.599705\pi$
$648$	21.6228	0.849425
$649$	−3.90227	−0.153178
$650$	−0.659816	−0.0258801
$651$	−8.95595	−0.351011
$652$	−4.97342	−0.194774
$653$	−1.15748	−0.0452957	−0.0226478	−	0.999744i	$-0.507210\pi$
$653$	−1.15748	−0.0452957	−0.0226478	+	0.999744i	$0.507210\pi$
$654$	0.428715	0.0167641
$655$	−17.3831	−0.679215
$656$	−5.25381	−0.205127
$657$	−5.16830	−0.201635
$658$	−60.7946	−2.37002
$659$	−14.3810	−0.560205	−0.280102	−	0.959970i	$-0.590368\pi$
$659$	−14.3810	−0.560205	−0.280102	+	0.959970i	$0.590368\pi$
$660$	−44.4007	−1.72830
$661$	15.8556	0.616710	0.308355	−	0.951271i	$-0.400222\pi$
$661$	15.8556	0.616710	0.308355	+	0.951271i	$0.400222\pi$
$662$	−19.9667	−0.776030
$663$	40.6471	1.57860
$664$	14.7302	0.571644
$665$	−7.47427	−0.289840
$666$	6.45760	0.250227
$667$	−12.8146	−0.496181
$668$	−12.6415	−0.489113
$669$	−45.5599	−1.76145
$670$	10.9468	0.422911
$671$	7.88609	0.304439
$672$	46.2577	1.78443
$673$	−2.97111	−0.114528	−0.0572639	−	0.998359i	$-0.518238\pi$
$673$	−2.97111	−0.114528	−0.0572639	+	0.998359i	$0.518238\pi$
$674$	−6.93542	−0.267142
$675$	0.443410	0.0170669
$676$	−7.34674	−0.282567
$677$	−42.0277	−1.61526	−0.807628	−	0.589692i	$-0.799249\pi$
$677$	−42.0277	−1.61526	−0.807628	+	0.589692i	$0.799249\pi$
$678$	−28.4995	−1.09452
$679$	−31.1998	−1.19734
$680$	33.2145	1.27372
$681$	15.6044	0.597960
$682$	−10.7963	−0.413413
$683$	47.4416	1.81530	0.907650	−	0.419727i	$-0.137874\pi$
$683$	47.4416	1.81530	0.907650	+	0.419727i	$0.137874\pi$
$684$	−0.900871	−0.0344456
$685$	−24.8771	−0.950503
$686$	0.501623	0.0191520
$687$	34.6316	1.32128
$688$	4.47407	0.170572
$689$	−7.13754	−0.271918
$690$	28.6485	1.09063
$691$	46.2732	1.76032	0.880158	−	0.474680i	$-0.157436\pi$
$691$	46.2732	1.76032	0.880158	+	0.474680i	$0.157436\pi$
$692$	10.1593	0.386198
$693$	−4.60159	−0.174800
$694$	−54.3692	−2.06383
$695$	−9.32848	−0.353849
$696$	−16.1202	−0.611034
$697$	−33.3223	−1.26217
$698$	30.1963	1.14295
$699$	41.1681	1.55712
$700$	−1.01346	−0.0383051
$701$	−25.0791	−0.947223	−0.473612	−	0.880734i	$-0.657050\pi$
$701$	−25.0791	−0.947223	−0.473612	+	0.880734i	$0.657050\pi$
$702$	−35.2517	−1.33049
$703$	7.81384	0.294705
$704$	47.7982	1.80146
$705$	29.5227	1.11189
$706$	29.1859	1.09843
$707$	23.4869	0.883317
$708$	5.76468	0.216650
$709$	−14.2784	−0.536235	−0.268118	−	0.963386i	$-0.586402\pi$
$709$	−14.2784	−0.536235	−0.268118	+	0.963386i	$0.586402\pi$
$710$	0.429605	0.0161228
$711$	−3.77296	−0.141497
$712$	−31.6958	−1.18785
$713$	4.16821	0.156101
$714$	104.340	3.90483
$715$	26.4859	0.990518
$716$	6.74672	0.252137
$717$	−5.49143	−0.205081
$718$	−10.5215	−0.392659
$719$	−2.75961	−0.102916	−0.0514580	−	0.998675i	$-0.516387\pi$
$719$	−2.75961	−0.102916	−0.0514580	+	0.998675i	$0.516387\pi$
$720$	−0.801668	−0.0298764
$721$	18.4487	0.687064
$722$	40.5766	1.51011
$723$	−9.97634	−0.371024
$724$	−36.0835	−1.34103
$725$	−0.367907	−0.0136637
$726$	−10.4549	−0.388017
$727$	5.76358	0.213759	0.106880	−	0.994272i	$-0.465914\pi$
$727$	5.76358	0.213759	0.106880	+	0.994272i	$0.465914\pi$
$728$	26.4889	0.981743
$729$	23.3540	0.864963
$730$	76.3618	2.82628
$731$	28.3768	1.04955
$732$	−11.6498	−0.430589
$733$	−6.45023	−0.238245	−0.119122	−	0.992880i	$-0.538008\pi$
$733$	−6.45023	−0.238245	−0.119122	+	0.992880i	$0.538008\pi$
$734$	34.8040	1.28464
$735$	28.0777	1.03566
$736$	−21.5289	−0.793566
$737$	8.15490	0.300390
$738$	−3.62817	−0.133555
$739$	26.4216	0.971933	0.485966	−	0.873978i	$-0.338468\pi$
$739$	26.4216	0.971933	0.485966	+	0.873978i	$0.338468\pi$
$740$	−57.0902	−2.09868
$741$	5.35519	0.196728
$742$	−18.3219	−0.672617
$743$	31.7006	1.16298	0.581491	−	0.813553i	$-0.302470\pi$
$743$	31.7006	1.16298	0.581491	+	0.813553i	$0.302470\pi$
$744$	5.24344	0.192234
$745$	−7.39608	−0.270972
$746$	61.8510	2.26453
$747$	−2.25495	−0.0825043
$748$	75.2623	2.75186
$749$	14.9399	0.545892
$750$	45.9646	1.67839
$751$	26.5158	0.967574	0.483787	−	0.875186i	$-0.339261\pi$
$751$	26.5158	0.967574	0.483787	+	0.875186i	$0.339261\pi$
$752$	−7.89012	−0.287723
$753$	−37.1093	−1.35234
$754$	29.2491	1.06519
$755$	−5.65543	−0.205822
$756$	−54.1457	−1.96926
$757$	30.5754	1.11128	0.555640	−	0.831423i	$-0.312473\pi$
$757$	30.5754	1.11128	0.555640	+	0.831423i	$0.312473\pi$
$758$	−5.59213	−0.203115
$759$	21.3419	0.774663
$760$	4.37596	0.158733
$761$	−4.46454	−0.161840	−0.0809198	−	0.996721i	$-0.525786\pi$
$761$	−4.46454	−0.161840	−0.0809198	+	0.996721i	$0.525786\pi$
$762$	−23.8669	−0.864608
$763$	−0.392805	−0.0142205
$764$	−8.30637	−0.300514
$765$	−5.08458	−0.183833
$766$	82.4678	2.97968
$767$	−3.43875	−0.124166
$768$	−15.3159	−0.552665
$769$	29.6261	1.06834	0.534172	−	0.845376i	$-0.320624\pi$
$769$	29.6261	1.06834	0.534172	+	0.845376i	$0.320624\pi$
$770$	67.9887	2.45014
$771$	12.5225	0.450987
$772$	26.7697	0.963464
$773$	9.96480	0.358409	0.179204	−	0.983812i	$-0.442648\pi$
$773$	9.96480	0.358409	0.179204	+	0.983812i	$0.442648\pi$
$774$	3.08969	0.111057
$775$	0.119670	0.00429866
$776$	18.2665	0.655730
$777$	−58.9614	−2.11523
$778$	−5.47006	−0.196111
$779$	−4.39016	−0.157294
$780$	−39.1266	−1.40096
$781$	0.320038	0.0114519
$782$	−48.5611	−1.73654
$783$	−19.6560	−0.702449
$784$	−7.50394	−0.267998
$785$	37.1611	1.32634
$786$	31.9709	1.14037
$787$	−3.89223	−0.138743	−0.0693715	−	0.997591i	$-0.522099\pi$
$787$	−3.89223	−0.138743	−0.0693715	+	0.997591i	$0.522099\pi$
$788$	−69.0654	−2.46035
$789$	−48.8078	−1.73760
$790$	55.7457	1.98334
$791$	26.1123	0.928447
$792$	2.69409	0.0957305
$793$	6.94935	0.246778
$794$	0.972468	0.0345116
$795$	8.89736	0.315557
$796$	44.3117	1.57059
$797$	−1.05110	−0.0372317	−0.0186159	−	0.999827i	$-0.505926\pi$
$797$	−1.05110	−0.0372317	−0.0186159	+	0.999827i	$0.505926\pi$
$798$	13.7466	0.486626
$799$	−50.0430	−1.77040
$800$	−0.618096	−0.0218530
$801$	4.85208	0.171440
$802$	−69.6004	−2.45768
$803$	56.8864	2.00748
$804$	−12.0469	−0.424862
$805$	−26.2488	−0.925149
$806$	−9.51391	−0.335113
$807$	−3.18967	−0.112282
$808$	−13.7509	−0.483755
$809$	−31.3594	−1.10254	−0.551269	−	0.834327i	$-0.685856\pi$
$809$	−31.3594	−1.10254	−0.551269	+	0.834327i	$0.685856\pi$
$810$	48.9067	1.71840
$811$	−21.0665	−0.739746	−0.369873	−	0.929082i	$-0.620599\pi$
$811$	−21.0665	−0.739746	−0.369873	+	0.929082i	$0.620599\pi$
$812$	44.9258	1.57659
$813$	12.7491	0.447130
$814$	−71.0775	−2.49127
$815$	−3.69823	−0.129543
$816$	13.5416	0.474050
$817$	3.73859	0.130797
$818$	10.4187	0.364282
$819$	−4.05500	−0.141693
$820$	32.0758	1.12014
$821$	−49.8418	−1.73949	−0.869746	−	0.493500i	$-0.835717\pi$
$821$	−49.8418	−1.73949	−0.869746	+	0.493500i	$0.835717\pi$
$822$	45.7537	1.59584
$823$	42.2657	1.47329	0.736644	−	0.676281i	$-0.236409\pi$
$823$	42.2657	1.47329	0.736644	+	0.676281i	$0.236409\pi$
$824$	−10.8011	−0.376275
$825$	0.612728	0.0213325
$826$	−8.82717	−0.307137
$827$	−25.8486	−0.898843	−0.449421	−	0.893320i	$-0.648370\pi$
$827$	−25.8486	−0.898843	−0.449421	+	0.893320i	$0.648370\pi$
$828$	−3.16376	−0.109948
$829$	−2.99859	−0.104145	−0.0520726	−	0.998643i	$-0.516583\pi$
$829$	−2.99859	−0.104145	−0.0520726	+	0.998643i	$0.516583\pi$
$830$	33.3170	1.15645
$831$	48.4920	1.68217
$832$	42.1205	1.46027
$833$	−47.5937	−1.64902
$834$	17.1569	0.594094
$835$	−9.40017	−0.325306
$836$	9.91570	0.342942
$837$	6.39355	0.220993
$838$	15.1272	0.522561
$839$	28.6082	0.987665	0.493833	−	0.869557i	$-0.335596\pi$
$839$	28.6082	0.987665	0.493833	+	0.869557i	$0.335596\pi$
$840$	−33.0200	−1.13930
$841$	−12.6910	−0.437620
$842$	66.8804	2.30485
$843$	−24.8065	−0.854382
$844$	9.43839	0.324883
$845$	−5.46302	−0.187933
$846$	−5.44874	−0.187332
$847$	9.57916	0.329144
$848$	−2.37787	−0.0816565
$849$	24.3174	0.834570
$850$	−1.39419	−0.0478204
$851$	27.4413	0.940677
$852$	−0.472780	−0.0161972
$853$	−34.1576	−1.16953	−0.584766	−	0.811202i	$-0.698814\pi$
$853$	−34.1576	−1.16953	−0.584766	+	0.811202i	$0.698814\pi$
$854$	17.8388	0.610431
$855$	−0.669885	−0.0229096
$856$	−8.74686	−0.298962
$857$	−19.6377	−0.670811	−0.335406	−	0.942074i	$-0.608873\pi$
$857$	−19.6377	−0.670811	−0.335406	+	0.942074i	$0.608873\pi$
$858$	−48.7128	−1.66303
$859$	25.8085	0.880576	0.440288	−	0.897857i	$-0.354876\pi$
$859$	25.8085	0.880576	0.440288	+	0.897857i	$0.354876\pi$
$860$	−27.3153	−0.931443
$861$	33.1271	1.12897
$862$	−53.7730	−1.83151
$863$	−19.7877	−0.673582	−0.336791	−	0.941579i	$-0.609342\pi$
$863$	−19.7877	−0.673582	−0.336791	+	0.941579i	$0.609342\pi$
$864$	−33.0228	−1.12346
$865$	7.55442	0.256858
$866$	−80.9408	−2.75048
$867$	54.8438	1.86259
$868$	−14.6131	−0.496001
$869$	41.5282	1.40875
$870$	−36.4607	−1.23613
$871$	7.18623	0.243496
$872$	0.229975	0.00778795
$873$	−2.79629	−0.0946402
$874$	−6.39785	−0.216411
$875$	−42.1145	−1.42373
$876$	−84.0360	−2.83931
$877$	−3.48989	−0.117845	−0.0589227	−	0.998263i	$-0.518767\pi$
$877$	−3.48989	−0.117845	−0.0589227	+	0.998263i	$0.518767\pi$
$878$	85.9536	2.90079
$879$	3.31180	0.111704
$880$	8.82380	0.297450
$881$	11.8881	0.400519	0.200260	−	0.979743i	$-0.435821\pi$
$881$	11.8881	0.400519	0.200260	+	0.979743i	$0.435821\pi$
$882$	−5.18206	−0.174489
$883$	−55.0706	−1.85327	−0.926636	−	0.375959i	$-0.877313\pi$
$883$	−55.0706	−1.85327	−0.926636	+	0.375959i	$0.877313\pi$
$884$	66.3223	2.23066
$885$	4.28660	0.144092
$886$	−38.0652	−1.27882
$887$	−45.5396	−1.52907	−0.764536	−	0.644581i	$-0.777032\pi$
$887$	−45.5396	−1.52907	−0.764536	+	0.644581i	$0.777032\pi$
$888$	34.5201	1.15842
$889$	21.8678	0.733422
$890$	−71.6897	−2.40304
$891$	36.4335	1.22057
$892$	−74.3383	−2.48903
$893$	−6.59309	−0.220630
$894$	13.6028	0.454947
$895$	5.01684	0.167695
$896$	57.4593	1.91958
$897$	18.8068	0.627942
$898$	−75.3960	−2.51600
$899$	−5.30486	−0.176927
$900$	−0.0908317	−0.00302772
$901$	−15.0816	−0.502442
$902$	39.9345	1.32967
$903$	−28.2105	−0.938788
$904$	−15.2880	−0.508470
$905$	−26.8316	−0.891914
$906$	10.4014	0.345565
$907$	52.2904	1.73627	0.868137	−	0.496325i	$-0.165318\pi$
$907$	52.2904	1.73627	0.868137	+	0.496325i	$0.165318\pi$
$908$	25.4611	0.844955
$909$	2.10503	0.0698193
$910$	59.9127	1.98609
$911$	21.8431	0.723693	0.361847	−	0.932238i	$-0.382146\pi$
$911$	21.8431	0.723693	0.361847	+	0.932238i	$0.382146\pi$
$912$	1.78408	0.0590769
$913$	24.8198	0.821414
$914$	16.3022	0.539229
$915$	−8.66277	−0.286382
$916$	56.5072	1.86705
$917$	−29.2930	−0.967341
$918$	−74.4871	−2.45844
$919$	−50.0865	−1.65220	−0.826101	−	0.563523i	$-0.809446\pi$
$919$	−50.0865	−1.65220	−0.826101	+	0.563523i	$0.809446\pi$
$920$	15.3679	0.506664
$921$	15.0148	0.494754
$922$	−40.6476	−1.33866
$923$	0.282023	0.00928289
$924$	−74.8215	−2.46145
$925$	0.787843	0.0259041
$926$	43.9883	1.44555
$927$	1.65347	0.0543071
$928$	27.3997	0.899440
$929$	35.4047	1.16159	0.580795	−	0.814050i	$-0.302742\pi$
$929$	35.4047	1.16159	0.580795	+	0.814050i	$0.302742\pi$
$930$	11.8596	0.388893
$931$	−6.27040	−0.205504
$932$	67.1724	2.20031
$933$	52.7769	1.72784
$934$	57.2109	1.87200
$935$	55.9649	1.83025
$936$	2.37408	0.0775992
$937$	−26.6098	−0.869303	−0.434652	−	0.900599i	$-0.643128\pi$
$937$	−26.6098	−0.869303	−0.434652	+	0.900599i	$0.643128\pi$
$938$	18.4469	0.602311
$939$	−4.32828	−0.141248
$940$	48.1711	1.57117
$941$	17.2123	0.561106	0.280553	−	0.959838i	$-0.409482\pi$
$941$	17.2123	0.561106	0.280553	+	0.959838i	$0.409482\pi$
$942$	−68.3465	−2.22685
$943$	−15.4178	−0.502071
$944$	−1.14562	−0.0372867
$945$	−40.2626	−1.30974
$946$	−34.0076	−1.10568
$947$	4.00334	0.130091	0.0650455	−	0.997882i	$-0.479281\pi$
$947$	4.00334	0.130091	0.0650455	+	0.997882i	$0.479281\pi$
$948$	−61.3480	−1.99249
$949$	50.1292	1.62726
$950$	−0.183683	−0.00595946
$951$	61.3589	1.98970
$952$	55.9711	1.81403
$953$	19.9496	0.646230	0.323115	−	0.946360i	$-0.395270\pi$
$953$	19.9496	0.646230	0.323115	+	0.946360i	$0.395270\pi$
$954$	−1.64211	−0.0531651
$955$	−6.17660	−0.199870
$956$	−8.96016	−0.289792
$957$	−27.1618	−0.878015
$958$	69.2411	2.23708
$959$	−41.9213	−1.35371
$960$	−52.5057	−1.69461
$961$	−29.2745	−0.944338
$962$	−62.6346	−2.01942
$963$	1.33900	0.0431485
$964$	−16.2780	−0.524280
$965$	19.9059	0.640794
$966$	48.2767	1.55328
$967$	−34.5930	−1.11244	−0.556218	−	0.831036i	$-0.687748\pi$
$967$	−34.5930	−1.11244	−0.556218	+	0.831036i	$0.687748\pi$
$968$	−5.60831	−0.180258
$969$	11.3155	0.363508
$970$	41.3153	1.32656
$971$	13.2869	0.426397	0.213199	−	0.977009i	$-0.431612\pi$
$971$	13.2869	0.426397	0.213199	+	0.977009i	$0.431612\pi$
$972$	−10.3149	−0.330851
$973$	−15.7198	−0.503954
$974$	0.855724	0.0274192
$975$	0.539946	0.0172921
$976$	2.31518	0.0741070
$977$	20.4191	0.653265	0.326632	−	0.945151i	$-0.394086\pi$
$977$	20.4191	0.653265	0.326632	+	0.945151i	$0.394086\pi$
$978$	6.80175	0.217496
$979$	−53.4059	−1.70686
$980$	45.8134	1.46346
$981$	−0.0352053	−0.00112402
$982$	55.6487	1.77582
$983$	2.61528	0.0834144	0.0417072	−	0.999130i	$-0.486720\pi$
$983$	2.61528	0.0834144	0.0417072	+	0.999130i	$0.486720\pi$
$984$	−19.3949	−0.618287
$985$	−51.3569	−1.63637
$986$	61.8035	1.96822
$987$	49.7499	1.58356
$988$	8.73787	0.277989
$989$	13.1295	0.417495
$990$	6.09352	0.193665
$991$	−41.4661	−1.31722	−0.658608	−	0.752487i	$-0.728854\pi$
$991$	−41.4661	−1.31722	−0.658608	+	0.752487i	$0.728854\pi$
$992$	−8.91235	−0.282967
$993$	16.3394	0.518514
$994$	0.723945	0.0229621
$995$	32.9501	1.04459
$996$	−36.6653	−1.16178
$997$	23.8928	0.756692	0.378346	−	0.925664i	$-0.376493\pi$
$997$	23.8928	0.756692	0.378346	+	0.925664i	$0.376493\pi$
$998$	96.3119	3.04870
$999$	42.0918	1.33173

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4007.2.a.a.1.18	✓	139

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4007.2.a.a.1.18	✓	139	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:	\( N \)	\(=\)	\( 4007 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4007.a (trivial)

\(f(q)\)	\(=\)	\(q-2.23150 q^{2} +1.82610 q^{3} +2.97957 q^{4} +2.21560 q^{5} -4.07492 q^{6} +3.73360 q^{7} -2.18591 q^{8} +0.334626 q^{9} +O(q^{10})\)	\(q-2.23150 q^{2} +1.82610 q^{3} +2.97957 q^{4} +2.21560 q^{5} -4.07492 q^{6} +3.73360 q^{7} -2.18591 q^{8} +0.334626 q^{9} -4.94411 q^{10} -3.68316 q^{11} +5.44099 q^{12} -3.24566 q^{13} -8.33152 q^{14} +4.04590 q^{15} -1.08129 q^{16} -6.85809 q^{17} -0.746716 q^{18} -0.903543 q^{19} +6.60155 q^{20} +6.81792 q^{21} +8.21895 q^{22} -3.17314 q^{23} -3.99169 q^{24} -0.0911012 q^{25} +7.24267 q^{26} -4.86723 q^{27} +11.1245 q^{28} +4.03844 q^{29} -9.02842 q^{30} -1.31359 q^{31} +6.78472 q^{32} -6.72580 q^{33} +15.3038 q^{34} +8.27218 q^{35} +0.997042 q^{36} -8.64800 q^{37} +2.01625 q^{38} -5.92688 q^{39} -4.84311 q^{40} +4.85883 q^{41} -15.2142 q^{42} -4.13771 q^{43} -10.9742 q^{44} +0.741398 q^{45} +7.08085 q^{46} +7.29694 q^{47} -1.97454 q^{48} +6.93979 q^{49} +0.203292 q^{50} -12.5235 q^{51} -9.67068 q^{52} +2.19910 q^{53} +10.8612 q^{54} -8.16042 q^{55} -8.16133 q^{56} -1.64996 q^{57} -9.01177 q^{58} +1.05949 q^{59} +12.0551 q^{60} -2.14112 q^{61} +2.93127 q^{62} +1.24936 q^{63} -12.9775 q^{64} -7.19109 q^{65} +15.0086 q^{66} -2.21411 q^{67} -20.4342 q^{68} -5.79446 q^{69} -18.4593 q^{70} -0.0868923 q^{71} -0.731463 q^{72} -15.4450 q^{73} +19.2980 q^{74} -0.166359 q^{75} -2.69217 q^{76} -13.7515 q^{77} +13.2258 q^{78} -11.2752 q^{79} -2.39571 q^{80} -9.89190 q^{81} -10.8425 q^{82} -6.73872 q^{83} +20.3145 q^{84} -15.1948 q^{85} +9.23327 q^{86} +7.37458 q^{87} +8.05106 q^{88} +14.5000 q^{89} -1.65443 q^{90} -12.1180 q^{91} -9.45461 q^{92} -2.39874 q^{93} -16.2831 q^{94} -2.00189 q^{95} +12.3896 q^{96} -8.35648 q^{97} -15.4861 q^{98} -1.23248 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 139 q - 13 q^{2} - 22 q^{3} + 113 q^{4} - 16 q^{5} - 15 q^{6} - 44 q^{7} - 36 q^{8} + 87 q^{9}+O(q^{10}) \) 139 * q - 13 * q^2 - 22 * q^3 + 113 * q^4 - 16 * q^5 - 15 * q^6 - 44 * q^7 - 36 * q^8 + 87 * q^9	\( 139 q - 13 q^{2} - 22 q^{3} + 113 q^{4} - 16 q^{5} - 15 q^{6} - 44 q^{7} - 36 q^{8} + 87 q^{9} - 40 q^{10} - 17 q^{11} - 59 q^{12} - 89 q^{13} - 15 q^{14} - 29 q^{15} + 73 q^{16} - 58 q^{17} - 51 q^{18} - 37 q^{19} - 24 q^{20} - 37 q^{21} - 99 q^{22} - 42 q^{23} - 27 q^{24} - 11 q^{25} + 2 q^{26} - 73 q^{27} - 113 q^{28} - 57 q^{29} - 29 q^{30} - 51 q^{31} - 80 q^{32} - 78 q^{33} - 28 q^{34} - 34 q^{35} + 28 q^{36} - 117 q^{37} - 31 q^{38} - 36 q^{39} - 107 q^{40} - 60 q^{41} - 41 q^{42} - 109 q^{43} - 21 q^{44} - 62 q^{45} - 92 q^{46} - 26 q^{47} - 90 q^{48} - 7 q^{49} - 22 q^{50} - 47 q^{51} - 182 q^{52} - 83 q^{53} - 19 q^{54} - 53 q^{55} - 23 q^{56} - 201 q^{57} - 112 q^{58} + 14 q^{59} - 64 q^{60} - 73 q^{61} - 21 q^{62} - 94 q^{63} + 14 q^{64} - 123 q^{65} - 10 q^{66} - 135 q^{67} - 84 q^{68} - 50 q^{69} - 35 q^{70} - 29 q^{71} - 143 q^{72} - 266 q^{73} - 53 q^{74} - 32 q^{75} - 66 q^{76} - 69 q^{77} - 59 q^{78} - 124 q^{79} - 20 q^{80} - 33 q^{81} - 93 q^{82} - 28 q^{83} - 4 q^{84} - 179 q^{85} + 6 q^{86} - 40 q^{87} - 259 q^{88} - 41 q^{89} + 2 q^{90} - 50 q^{91} - 77 q^{92} - 60 q^{93} - 48 q^{94} - 37 q^{95} + 3 q^{96} - 220 q^{97} - 9 q^{98} - 35 q^{99}+O(q^{100}) \) 139 * q - 13 * q^2 - 22 * q^3 + 113 * q^4 - 16 * q^5 - 15 * q^6 - 44 * q^7 - 36 * q^8 + 87 * q^9 - 40 * q^10 - 17 * q^11 - 59 * q^12 - 89 * q^13 - 15 * q^14 - 29 * q^15 + 73 * q^16 - 58 * q^17 - 51 * q^18 - 37 * q^19 - 24 * q^20 - 37 * q^21 - 99 * q^22 - 42 * q^23 - 27 * q^24 - 11 * q^25 + 2 * q^26 - 73 * q^27 - 113 * q^28 - 57 * q^29 - 29 * q^30 - 51 * q^31 - 80 * q^32 - 78 * q^33 - 28 * q^34 - 34 * q^35 + 28 * q^36 - 117 * q^37 - 31 * q^38 - 36 * q^39 - 107 * q^40 - 60 * q^41 - 41 * q^42 - 109 * q^43 - 21 * q^44 - 62 * q^45 - 92 * q^46 - 26 * q^47 - 90 * q^48 - 7 * q^49 - 22 * q^50 - 47 * q^51 - 182 * q^52 - 83 * q^53 - 19 * q^54 - 53 * q^55 - 23 * q^56 - 201 * q^57 - 112 * q^58 + 14 * q^59 - 64 * q^60 - 73 * q^61 - 21 * q^62 - 94 * q^63 + 14 * q^64 - 123 * q^65 - 10 * q^66 - 135 * q^67 - 84 * q^68 - 50 * q^69 - 35 * q^70 - 29 * q^71 - 143 * q^72 - 266 * q^73 - 53 * q^74 - 32 * q^75 - 66 * q^76 - 69 * q^77 - 59 * q^78 - 124 * q^79 - 20 * q^80 - 33 * q^81 - 93 * q^82 - 28 * q^83 - 4 * q^84 - 179 * q^85 + 6 * q^86 - 40 * q^87 - 259 * q^88 - 41 * q^89 + 2 * q^90 - 50 * q^91 - 77 * q^92 - 60 * q^93 - 48 * q^94 - 37 * q^95 + 3 * q^96 - 220 * q^97 - 9 * q^98 - 35 * q^99

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