LMFDB - Embedded newform 4007.2.a.a.1.6

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			1.6
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)

$f(q)$	$=$	$q-2.62057 q^{2} -0.101978 q^{3} +4.86739 q^{4} +0.441388 q^{5} +0.267240 q^{6} +0.132029 q^{7} -7.51419 q^{8} -2.98960 q^{9} +O(q^{10})$	\(q-2.62057 q^{2} -0.101978 q^{3} +4.86739 q^{4} +0.441388 q^{5} +0.267240 q^{6} +0.132029 q^{7} -7.51419 q^{8} -2.98960 q^{9} -1.15669 q^{10} +3.12451 q^{11} -0.496366 q^{12} +5.13253 q^{13} -0.345992 q^{14} -0.0450118 q^{15} +9.95669 q^{16} +2.52799 q^{17} +7.83446 q^{18} -2.43968 q^{19} +2.14841 q^{20} -0.0134641 q^{21} -8.18801 q^{22} -7.28866 q^{23} +0.766281 q^{24} -4.80518 q^{25} -13.4502 q^{26} +0.610807 q^{27} +0.642637 q^{28} +8.24627 q^{29} +0.117957 q^{30} -3.97742 q^{31} -11.0638 q^{32} -0.318631 q^{33} -6.62478 q^{34} +0.0582761 q^{35} -14.5515 q^{36} -7.07808 q^{37} +6.39335 q^{38} -0.523404 q^{39} -3.31667 q^{40} +0.835244 q^{41} +0.0352835 q^{42} -1.92142 q^{43} +15.2082 q^{44} -1.31957 q^{45} +19.1004 q^{46} +0.739888 q^{47} -1.01536 q^{48} -6.98257 q^{49} +12.5923 q^{50} -0.257799 q^{51} +24.9820 q^{52} -4.47754 q^{53} -1.60066 q^{54} +1.37912 q^{55} -0.992093 q^{56} +0.248793 q^{57} -21.6099 q^{58} +6.45865 q^{59} -0.219090 q^{60} -5.59395 q^{61} +10.4231 q^{62} -0.394714 q^{63} +9.08015 q^{64} +2.26544 q^{65} +0.834995 q^{66} -3.64941 q^{67} +12.3047 q^{68} +0.743282 q^{69} -0.152717 q^{70} +2.86339 q^{71} +22.4644 q^{72} +1.69508 q^{73} +18.5486 q^{74} +0.490022 q^{75} -11.8749 q^{76} +0.412527 q^{77} +1.37162 q^{78} +1.93943 q^{79} +4.39477 q^{80} +8.90651 q^{81} -2.18882 q^{82} +5.06979 q^{83} -0.0655348 q^{84} +1.11582 q^{85} +5.03520 q^{86} -0.840937 q^{87} -23.4782 q^{88} -14.4032 q^{89} +3.45804 q^{90} +0.677643 q^{91} -35.4767 q^{92} +0.405609 q^{93} -1.93893 q^{94} -1.07685 q^{95} +1.12827 q^{96} -12.8228 q^{97} +18.2983 q^{98} -9.34104 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.62057	−1.85302	−0.926511	−	0.376266i	$-0.877208\pi$
$2$	−2.62057	−1.85302	−0.926511	+	0.376266i	$0.877208\pi$
$3$	−0.101978	−0.0588769	−0.0294385	−	0.999567i	$-0.509372\pi$
$3$	−0.101978	−0.0588769	−0.0294385	+	0.999567i	$0.509372\pi$
$4$	4.86739	2.43369
$5$	0.441388	0.197395	0.0986974	−	0.995117i	$-0.468532\pi$
$5$	0.441388	0.197395	0.0986974	+	0.995117i	$0.468532\pi$
$6$	0.267240	0.109100
$7$	0.132029	0.0499023	0.0249512	−	0.999689i	$-0.492057\pi$
$7$	0.132029	0.0499023	0.0249512	+	0.999689i	$0.492057\pi$
$8$	−7.51419	−2.65667
$9$	−2.98960	−0.996534
$10$	−1.15669	−0.365777
$11$	3.12451	0.942076	0.471038	−	0.882113i	$-0.343879\pi$
$11$	3.12451	0.942076	0.471038	+	0.882113i	$0.343879\pi$
$12$	−0.496366	−0.143288
$13$	5.13253	1.42351	0.711754	−	0.702429i	$-0.247901\pi$
$13$	5.13253	1.42351	0.711754	+	0.702429i	$0.247901\pi$
$14$	−0.345992	−0.0924702
$15$	−0.0450118	−0.0116220
$16$	9.95669	2.48917
$17$	2.52799	0.613128	0.306564	−	0.951850i	$-0.400821\pi$
$17$	2.52799	0.613128	0.306564	+	0.951850i	$0.400821\pi$
$18$	7.83446	1.84660
$19$	−2.43968	−0.559701	−0.279850	−	0.960044i	$-0.590285\pi$
$19$	−2.43968	−0.559701	−0.279850	+	0.960044i	$0.590285\pi$
$20$	2.14841	0.480398
$21$	−0.0134641	−0.00293810
$22$	−8.18801	−1.74569
$23$	−7.28866	−1.51979	−0.759895	−	0.650045i	$-0.774750\pi$
$23$	−7.28866	−1.51979	−0.759895	+	0.650045i	$0.774750\pi$
$24$	0.766281	0.156417
$25$	−4.80518	−0.961035
$26$	−13.4502	−2.63779
$27$	0.610807	0.117550
$28$	0.642637	0.121447
$29$	8.24627	1.53129	0.765647	−	0.643261i	$-0.222419\pi$
$29$	8.24627	1.53129	0.765647	+	0.643261i	$0.222419\pi$
$30$	0.117957	0.0215358
$31$	−3.97742	−0.714366	−0.357183	−	0.934034i	$-0.616263\pi$
$31$	−3.97742	−0.714366	−0.357183	+	0.934034i	$0.616263\pi$
$32$	−11.0638	−1.95583
$33$	−0.318631	−0.0554666
$34$	−6.62478	−1.13614
$35$	0.0582761	0.00985046
$36$	−14.5515	−2.42526
$37$	−7.07808	−1.16363	−0.581815	−	0.813321i	$-0.697657\pi$
$37$	−7.07808	−1.16363	−0.581815	+	0.813321i	$0.697657\pi$
$38$	6.39335	1.03714
$39$	−0.523404	−0.0838118
$40$	−3.31667	−0.524412
$41$	0.835244	0.130443	0.0652216	−	0.997871i	$-0.479225\pi$
$41$	0.835244	0.130443	0.0652216	+	0.997871i	$0.479225\pi$
$42$	0.0352835	0.00544436
$43$	−1.92142	−0.293013	−0.146507	−	0.989210i	$-0.546803\pi$
$43$	−1.92142	−0.293013	−0.146507	+	0.989210i	$0.546803\pi$
$44$	15.2082	2.29272
$45$	−1.31957	−0.196710
$46$	19.1004	2.81621
$47$	0.739888	0.107924	0.0539619	−	0.998543i	$-0.482815\pi$
$47$	0.739888	0.107924	0.0539619	+	0.998543i	$0.482815\pi$
$48$	−1.01536	−0.146555
$49$	−6.98257	−0.997510
$50$	12.5923	1.78082
$51$	−0.257799	−0.0360991
$52$	24.9820	3.46438
$53$	−4.47754	−0.615037	−0.307519	−	0.951542i	$-0.599499\pi$
$53$	−4.47754	−0.615037	−0.307519	+	0.951542i	$0.599499\pi$
$54$	−1.60066	−0.217822
$55$	1.37912	0.185961
$56$	−0.992093	−0.132574
$57$	0.248793	0.0329535
$58$	−21.6099	−2.83752
$59$	6.45865	0.840845	0.420422	−	0.907328i	$-0.361882\pi$
$59$	6.45865	0.840845	0.420422	+	0.907328i	$0.361882\pi$
$60$	−0.219090	−0.0282844
$61$	−5.59395	−0.716233	−0.358116	−	0.933677i	$-0.616581\pi$
$61$	−5.59395	−0.716233	−0.358116	+	0.933677i	$0.616581\pi$
$62$	10.4231	1.32374
$63$	−0.394714	−0.0497294
$64$	9.08015	1.13502
$65$	2.26544	0.280993
$66$	0.834995	0.102781
$67$	−3.64941	−0.445846	−0.222923	−	0.974836i	$-0.571560\pi$
$67$	−3.64941	−0.445846	−0.222923	+	0.974836i	$0.571560\pi$
$68$	12.3047	1.49217
$69$	0.743282	0.0894806
$70$	−0.152717	−0.0182531
$71$	2.86339	0.339822	0.169911	−	0.985459i	$-0.445652\pi$
$71$	2.86339	0.339822	0.169911	+	0.985459i	$0.445652\pi$
$72$	22.4644	2.64746
$73$	1.69508	0.198394	0.0991970	−	0.995068i	$-0.468373\pi$
$73$	1.69508	0.198394	0.0991970	+	0.995068i	$0.468373\pi$
$74$	18.5486	2.15623
$75$	0.490022	0.0565828
$76$	−11.8749	−1.36214
$77$	0.412527	0.0470118
$78$	1.37162	0.155305
$79$	1.93943	0.218202	0.109101	−	0.994031i	$-0.465203\pi$
$79$	1.93943	0.218202	0.109101	+	0.994031i	$0.465203\pi$
$80$	4.39477	0.491350
$81$	8.90651	0.989613
$82$	−2.18882	−0.241714
$83$	5.06979	0.556482	0.278241	−	0.960511i	$-0.410249\pi$
$83$	5.06979	0.556482	0.278241	+	0.960511i	$0.410249\pi$
$84$	−0.0655348	−0.00715043
$85$	1.11582	0.121028
$86$	5.03520	0.542960
$87$	−0.840937	−0.0901579
$88$	−23.4782	−2.50278
$89$	−14.4032	−1.52674	−0.763370	−	0.645961i	$-0.776457\pi$
$89$	−14.4032	−1.52674	−0.763370	+	0.645961i	$0.776457\pi$
$90$	3.45804	0.364509
$91$	0.677643	0.0710363
$92$	−35.4767	−3.69871
$93$	0.405609	0.0420597
$94$	−1.93893	−0.199985
$95$	−1.07685	−0.110482
$96$	1.12827	0.115153
$97$	−12.8228	−1.30196	−0.650978	−	0.759097i	$-0.725641\pi$
$97$	−12.8228	−1.30196	−0.650978	+	0.759097i	$0.725641\pi$
$98$	18.2983	1.84841
$99$	−9.34104	−0.938810
$100$	−23.3887	−2.33887
$101$	−6.59176	−0.655904	−0.327952	−	0.944694i	$-0.606358\pi$
$101$	−6.59176	−0.655904	−0.327952	+	0.944694i	$0.606358\pi$
$102$	0.675580	0.0668924
$103$	−11.1920	−1.10278	−0.551390	−	0.834248i	$-0.685902\pi$
$103$	−11.1920	−1.10278	−0.551390	+	0.834248i	$0.685902\pi$
$104$	−38.5668	−3.78179
$105$	−0.00594287	−0.000579965 0
$106$	11.7337	1.13968
$107$	3.00077	0.290095	0.145048	−	0.989425i	$-0.453666\pi$
$107$	3.00077	0.290095	0.145048	+	0.989425i	$0.453666\pi$
$108$	2.97303	0.286080
$109$	0.000628692 0	6.02178e−5 0	3.01089e−5	−	1.00000i	$-0.499990\pi$
$109$	0.000628692 0	6.02178e−5 0	3.01089e−5		1.00000i	$0.499990\pi$
$110$	−3.61409	−0.344590
$111$	0.721808	0.0685110
$112$	1.31457	0.124216
$113$	6.40332	0.602374	0.301187	−	0.953565i	$-0.402617\pi$
$113$	6.40332	0.602374	0.301187	+	0.953565i	$0.402617\pi$
$114$	−0.651980	−0.0610635
$115$	−3.21713	−0.299999
$116$	40.1378	3.72670
$117$	−15.3442	−1.41857
$118$	−16.9254	−1.55810
$119$	0.333768	0.0305965
$120$	0.338227	0.0308758
$121$	−1.23742	−0.112493
$122$	14.6594	1.32720
$123$	−0.0851764	−0.00768010
$124$	−19.3597	−1.73855
$125$	−4.32789	−0.387098
$126$	1.03438	0.0921496
$127$	7.04852	0.625455	0.312727	−	0.949843i	$-0.398757\pi$
$127$	7.04852	0.625455	0.312727	+	0.949843i	$0.398757\pi$
$128$	−1.66751	−0.147389
$129$	0.195942	0.0172517
$130$	−5.93674	−0.520686
$131$	8.21195	0.717481	0.358741	−	0.933437i	$-0.383206\pi$
$131$	8.21195	0.717481	0.358741	+	0.933437i	$0.383206\pi$
$132$	−1.55090	−0.134989
$133$	−0.322109	−0.0279304
$134$	9.56354	0.826164
$135$	0.269603	0.0232037
$136$	−18.9958	−1.62888
$137$	−8.98130	−0.767324	−0.383662	−	0.923473i	$-0.625337\pi$
$137$	−8.98130	−0.767324	−0.383662	+	0.923473i	$0.625337\pi$
$138$	−1.94782	−0.165810
$139$	−0.961432	−0.0815476	−0.0407738	−	0.999168i	$-0.512982\pi$
$139$	−0.961432	−0.0815476	−0.0407738	+	0.999168i	$0.512982\pi$
$140$	0.283652	0.0239730
$141$	−0.0754522	−0.00635422
$142$	−7.50372	−0.629698
$143$	16.0367	1.34105
$144$	−29.7665	−2.48054
$145$	3.63981	0.302269
$146$	−4.44207	−0.367629
$147$	0.712067	0.0587303
$148$	−34.4518	−2.83192
$149$	5.83559	0.478070	0.239035	−	0.971011i	$-0.423169\pi$
$149$	5.83559	0.478070	0.239035	+	0.971011i	$0.423169\pi$
$150$	−1.28414	−0.104849
$151$	−9.22654	−0.750845	−0.375423	−	0.926854i	$-0.622502\pi$
$151$	−9.22654	−0.750845	−0.375423	+	0.926854i	$0.622502\pi$
$152$	18.3322	1.48694
$153$	−7.55768	−0.611002
$154$	−1.08106	−0.0871139
$155$	−1.75559	−0.141012
$156$	−2.54761	−0.203972
$157$	−4.41795	−0.352591	−0.176295	−	0.984337i	$-0.556411\pi$
$157$	−4.41795	−0.352591	−0.176295	+	0.984337i	$0.556411\pi$
$158$	−5.08240	−0.404334
$159$	0.456610	0.0362115
$160$	−4.88344	−0.386070
$161$	−0.962316	−0.0758411
$162$	−23.3401	−1.83377
$163$	−15.3794	−1.20461	−0.602304	−	0.798266i	$-0.705751\pi$
$163$	−15.3794	−1.20461	−0.602304	+	0.798266i	$0.705751\pi$
$164$	4.06546	0.317459
$165$	−0.140640	−0.0109488
$166$	−13.2857	−1.03117
$167$	10.5422	0.815780	0.407890	−	0.913031i	$-0.366265\pi$
$167$	10.5422	0.815780	0.407890	+	0.913031i	$0.366265\pi$
$168$	0.101171	0.00780555
$169$	13.3428	1.02637
$170$	−2.92410	−0.224268
$171$	7.29367	0.557761
$172$	−9.35227	−0.713104
$173$	−6.30537	−0.479389	−0.239694	−	0.970848i	$-0.577047\pi$
$173$	−6.30537	−0.479389	−0.239694	+	0.970848i	$0.577047\pi$
$174$	2.20373	0.167065
$175$	−0.634423	−0.0479579
$176$	31.1098	2.34499
$177$	−0.658640	−0.0495064
$178$	37.7447	2.82909
$179$	−19.4808	−1.45606	−0.728032	−	0.685543i	$-0.759565\pi$
$179$	−19.4808	−1.45606	−0.728032	+	0.685543i	$0.759565\pi$
$180$	−6.42288	−0.478733
$181$	12.5304	0.931378	0.465689	−	0.884948i	$-0.345807\pi$
$181$	12.5304	0.931378	0.465689	+	0.884948i	$0.345807\pi$
$182$	−1.77581	−0.131632
$183$	0.570460	0.0421696
$184$	54.7684	4.03758
$185$	−3.12418	−0.229694
$186$	−1.06293	−0.0779376
$187$	7.89874	0.577613
$188$	3.60132	0.262653
$189$	0.0806443	0.00586601
$190$	2.82195	0.204726
$191$	−0.363011	−0.0262666	−0.0131333	−	0.999914i	$-0.504181\pi$
$191$	−0.363011	−0.0262666	−0.0131333	+	0.999914i	$0.504181\pi$
$192$	−0.925974	−0.0668264
$193$	12.6886	0.913343	0.456671	−	0.889635i	$-0.349042\pi$
$193$	12.6886	0.913343	0.456671	+	0.889635i	$0.349042\pi$
$194$	33.6030	2.41255
$195$	−0.231024	−0.0165440
$196$	−33.9869	−2.42763
$197$	−20.1707	−1.43710	−0.718552	−	0.695473i	$-0.755195\pi$
$197$	−20.1707	−1.43710	−0.718552	+	0.695473i	$0.755195\pi$
$198$	24.4789	1.73964
$199$	23.8261	1.68899	0.844493	−	0.535566i	$-0.179902\pi$
$199$	23.8261	1.68899	0.844493	+	0.535566i	$0.179902\pi$
$200$	36.1070	2.55315
$201$	0.372159	0.0262501
$202$	17.2742	1.21541
$203$	1.08875	0.0764151
$204$	−1.25481	−0.0878541
$205$	0.368667	0.0257488
$206$	29.3294	2.04348
$207$	21.7902	1.51452
$208$	51.1030	3.54336
$209$	−7.62281	−0.527281
$210$	0.0155737	0.00107469
$211$	22.8730	1.57464	0.787321	−	0.616543i	$-0.211467\pi$
$211$	22.8730	1.57464	0.787321	+	0.616543i	$0.211467\pi$
$212$	−21.7939	−1.49681
$213$	−0.292002	−0.0200077
$214$	−7.86373	−0.537553
$215$	−0.848090	−0.0578392
$216$	−4.58972	−0.312291
$217$	−0.525136	−0.0356485
$218$	−0.00164753	−0.000111585 0
$219$	−0.172861	−0.0116808
$220$	6.71273	0.452572
$221$	12.9750	0.872792
$222$	−1.89155	−0.126952
$223$	0.647158	0.0433369	0.0216684	−	0.999765i	$-0.493102\pi$
$223$	0.647158	0.0433369	0.0216684	+	0.999765i	$0.493102\pi$
$224$	−1.46075	−0.0976003
$225$	14.3656	0.957704
$226$	−16.7803	−1.11621
$227$	−1.79489	−0.119131	−0.0595656	−	0.998224i	$-0.518972\pi$
$227$	−1.79489	−0.119131	−0.0595656	+	0.998224i	$0.518972\pi$
$228$	1.21097	0.0801987
$229$	−4.02583	−0.266034	−0.133017	−	0.991114i	$-0.542467\pi$
$229$	−4.02583	−0.266034	−0.133017	+	0.991114i	$0.542467\pi$
$230$	8.43071	0.555905
$231$	−0.0420686	−0.00276791
$232$	−61.9641	−4.06814
$233$	26.6026	1.74280	0.871398	−	0.490577i	$-0.163214\pi$
$233$	26.6026	1.74280	0.871398	+	0.490577i	$0.163214\pi$
$234$	40.2106	2.62865
$235$	0.326578	0.0213036
$236$	31.4368	2.04636
$237$	−0.197778	−0.0128471
$238$	−0.874664	−0.0566960
$239$	5.64054	0.364856	0.182428	−	0.983219i	$-0.441604\pi$
$239$	5.64054	0.364856	0.182428	+	0.983219i	$0.441604\pi$
$240$	−0.448169	−0.0289292
$241$	−1.47951	−0.0953033	−0.0476517	−	0.998864i	$-0.515174\pi$
$241$	−1.47951	−0.0953033	−0.0476517	+	0.998864i	$0.515174\pi$
$242$	3.24275	0.208452
$243$	−2.74069	−0.175815
$244$	−27.2279	−1.74309
$245$	−3.08202	−0.196903
$246$	0.223211	0.0142314
$247$	−12.5217	−0.796738
$248$	29.8871	1.89783
$249$	−0.517006	−0.0327639
$250$	11.3415	0.717302
$251$	3.42852	0.216407	0.108203	−	0.994129i	$-0.465490\pi$
$251$	3.42852	0.216407	0.108203	+	0.994129i	$0.465490\pi$
$252$	−1.92123	−0.121026
$253$	−22.7735	−1.43176
$254$	−18.4711	−1.15898
$255$	−0.113789	−0.00712577
$256$	−13.7905	−0.861904
$257$	−3.29679	−0.205648	−0.102824	−	0.994700i	$-0.532788\pi$
$257$	−3.29679	−0.205648	−0.102824	+	0.994700i	$0.532788\pi$
$258$	−0.513479	−0.0319678
$259$	−0.934513	−0.0580678
$260$	11.0268	0.683851
$261$	−24.6531	−1.52599
$262$	−21.5200	−1.32951
$263$	−12.8639	−0.793219	−0.396610	−	0.917987i	$-0.629813\pi$
$263$	−12.8639	−0.793219	−0.396610	+	0.917987i	$0.629813\pi$
$264$	2.39426	0.147356
$265$	−1.97633	−0.121405
$266$	0.844109	0.0517556
$267$	1.46881	0.0898898
$268$	−17.7631	−1.08505
$269$	30.0794	1.83397	0.916986	−	0.398920i	$-0.130615\pi$
$269$	30.0794	1.83397	0.916986	+	0.398920i	$0.130615\pi$
$270$	−0.706513	−0.0429970
$271$	17.4311	1.05886	0.529431	−	0.848353i	$-0.322406\pi$
$271$	17.4311	1.05886	0.529431	+	0.848353i	$0.322406\pi$
$272$	25.1704	1.52618
$273$	−0.0691046	−0.00418240
$274$	23.5361	1.42187
$275$	−15.0138	−0.905368
$276$	3.61784	0.217769
$277$	−14.6830	−0.882214	−0.441107	−	0.897454i	$-0.645414\pi$
$277$	−14.6830	−0.882214	−0.441107	+	0.897454i	$0.645414\pi$
$278$	2.51950	0.151110
$279$	11.8909	0.711890
$280$	−0.437898	−0.0261694
$281$	−13.6451	−0.813996	−0.406998	−	0.913429i	$-0.633424\pi$
$281$	−13.6451	−0.813996	−0.406998	+	0.913429i	$0.633424\pi$
$282$	0.197728	0.0117745
$283$	−13.1236	−0.780119	−0.390060	−	0.920790i	$-0.627546\pi$
$283$	−13.1236	−0.780119	−0.390060	+	0.920790i	$0.627546\pi$
$284$	13.9372	0.827023
$285$	0.109814	0.00650484
$286$	−42.0252	−2.48500
$287$	0.110277	0.00650942
$288$	33.0764	1.94905
$289$	−10.6093	−0.624075
$290$	−9.53837	−0.560112
$291$	1.30764	0.0766552
$292$	8.25061	0.482830
$293$	3.48200	0.203421	0.101710	−	0.994814i	$-0.467569\pi$
$293$	3.48200	0.203421	0.101710	+	0.994814i	$0.467569\pi$
$294$	−1.86602	−0.108829
$295$	2.85077	0.165978
$296$	53.1861	3.09138
$297$	1.90847	0.110741
$298$	−15.2926	−0.885875
$299$	−37.4093	−2.16343
$300$	2.38513	0.137705
$301$	−0.253683	−0.0146220
$302$	24.1788	1.39133
$303$	0.672213	0.0386176
$304$	−24.2911	−1.39319
$305$	−2.46911	−0.141381
$306$	19.8054	1.13220
$307$	−24.0611	−1.37324	−0.686621	−	0.727015i	$-0.740907\pi$
$307$	−24.0611	−1.37324	−0.686621	+	0.727015i	$0.740907\pi$
$308$	2.00793	0.114412
$309$	1.14134	0.0649283
$310$	4.60064	0.261299
$311$	−6.99993	−0.396930	−0.198465	−	0.980108i	$-0.563596\pi$
$311$	−6.99993	−0.396930	−0.198465	+	0.980108i	$0.563596\pi$
$312$	3.93296	0.222660
$313$	15.2908	0.864288	0.432144	−	0.901805i	$-0.357757\pi$
$313$	15.2908	0.864288	0.432144	+	0.901805i	$0.357757\pi$
$314$	11.5775	0.653358
$315$	−0.174222	−0.00981631
$316$	9.43994	0.531038
$317$	−12.3778	−0.695207	−0.347603	−	0.937642i	$-0.613004\pi$
$317$	−12.3778	−0.695207	−0.347603	+	0.937642i	$0.613004\pi$
$318$	−1.19658	−0.0671008
$319$	25.7656	1.44260
$320$	4.00787	0.224047
$321$	−0.306012	−0.0170799
$322$	2.52182	0.140535
$323$	−6.16748	−0.343168
$324$	43.3515	2.40841
$325$	−24.6627	−1.36804
$326$	40.3028	2.23217
$327$	−6.41127e−5 0	−3.54544e−6 0
$328$	−6.27618	−0.346544
$329$	0.0976868	0.00538565
$330$	0.368557	0.0202884
$331$	−8.95634	−0.492285	−0.246143	−	0.969234i	$-0.579163\pi$
$331$	−8.95634	−0.492285	−0.246143	+	0.969234i	$0.579163\pi$
$332$	24.6766	1.35431
$333$	21.1606	1.15960
$334$	−27.6266	−1.51166
$335$	−1.61081	−0.0880077
$336$	−0.134057	−0.00731343
$337$	−21.0505	−1.14669	−0.573347	−	0.819312i	$-0.694355\pi$
$337$	−21.0505	−1.14669	−0.573347	+	0.819312i	$0.694355\pi$
$338$	−34.9659	−1.90189
$339$	−0.652997	−0.0354659
$340$	5.43115	0.294546
$341$	−12.4275	−0.672987
$342$	−19.1136	−1.03354
$343$	−1.84611	−0.0996804
$344$	14.4379	0.778439
$345$	0.328076	0.0176630
$346$	16.5237	0.888318
$347$	−6.70775	−0.360091	−0.180045	−	0.983658i	$-0.557624\pi$
$347$	−6.70775	−0.360091	−0.180045	+	0.983658i	$0.557624\pi$
$348$	−4.09317	−0.219417
$349$	−28.0734	−1.50273	−0.751367	−	0.659884i	$-0.770605\pi$
$349$	−28.0734	−1.50273	−0.751367	+	0.659884i	$0.770605\pi$
$350$	1.66255	0.0888671
$351$	3.13498	0.167333
$352$	−34.5691	−1.84254
$353$	−7.65480	−0.407424	−0.203712	−	0.979031i	$-0.565301\pi$
$353$	−7.65480	−0.407424	−0.203712	+	0.979031i	$0.565301\pi$
$354$	1.72601	0.0917365
$355$	1.26387	0.0670791
$356$	−70.1062	−3.71562
$357$	−0.0340370	−0.00180143
$358$	51.0508	2.69812
$359$	10.6200	0.560500	0.280250	−	0.959927i	$-0.409583\pi$
$359$	10.6200	0.560500	0.280250	+	0.959927i	$0.409583\pi$
$360$	9.91553	0.522594
$361$	−13.0480	−0.686735
$362$	−32.8368	−1.72586
$363$	0.126189	0.00662323
$364$	3.29835	0.172881
$365$	0.748188	0.0391619
$366$	−1.49493	−0.0781412
$367$	−25.3560	−1.32357	−0.661786	−	0.749693i	$-0.730201\pi$
$367$	−25.3560	−1.32357	−0.661786	+	0.749693i	$0.730201\pi$
$368$	−72.5709	−3.78302
$369$	−2.49705	−0.129991
$370$	8.18714	0.425629
$371$	−0.591166	−0.0306918
$372$	1.97426	0.102360
$373$	−20.9890	−1.08677	−0.543384	−	0.839485i	$-0.682857\pi$
$373$	−20.9890	−1.08677	−0.543384	+	0.839485i	$0.682857\pi$
$374$	−20.6992	−1.07033
$375$	0.441349	0.0227912
$376$	−5.55966	−0.286718
$377$	42.3242	2.17981
$378$	−0.211334	−0.0108699
$379$	11.5161	0.591541	0.295771	−	0.955259i	$-0.404424\pi$
$379$	11.5161	0.591541	0.295771	+	0.955259i	$0.404424\pi$
$380$	−5.24142	−0.268879
$381$	−0.718793	−0.0368249
$382$	0.951297	0.0486726
$383$	−31.4218	−1.60558	−0.802790	−	0.596262i	$-0.796652\pi$
$383$	−31.4218	−1.60558	−0.802790	+	0.596262i	$0.796652\pi$
$384$	0.170049	0.00867780
$385$	0.182084	0.00927988
$386$	−33.2513	−1.69244
$387$	5.74426	0.291997
$388$	−62.4134	−3.16856
$389$	−36.4097	−1.84605	−0.923023	−	0.384744i	$-0.874290\pi$
$389$	−36.4097	−1.84605	−0.923023	+	0.384744i	$0.874290\pi$
$390$	0.605416	0.0306564
$391$	−18.4257	−0.931826
$392$	52.4684	2.65005
$393$	−0.837437	−0.0422431
$394$	52.8588	2.66299
$395$	0.856039	0.0430720
$396$	−45.4665	−2.28478
$397$	15.4754	0.776689	0.388344	−	0.921514i	$-0.373047\pi$
$397$	15.4754	0.776689	0.388344	+	0.921514i	$0.373047\pi$
$398$	−62.4379	−3.12973
$399$	0.0328480	0.00164446
$400$	−47.8437	−2.39218
$401$	−10.0375	−0.501251	−0.250625	−	0.968084i	$-0.580636\pi$
$401$	−10.0375	−0.501251	−0.250625	+	0.968084i	$0.580636\pi$
$402$	−0.975269	−0.0486420
$403$	−20.4142	−1.01691
$404$	−32.0846	−1.59627
$405$	3.93123	0.195344
$406$	−2.85314	−0.141599
$407$	−22.1156	−1.09623
$408$	1.93715	0.0959033
$409$	9.04992	0.447490	0.223745	−	0.974648i	$-0.428172\pi$
$409$	9.04992	0.447490	0.223745	+	0.974648i	$0.428172\pi$
$410$	−0.966117	−0.0477131
$411$	0.915894	0.0451777
$412$	−54.4758	−2.68383
$413$	0.852731	0.0419601
$414$	−57.1027	−2.80644
$415$	2.23774	0.109847
$416$	−56.7854	−2.78413
$417$	0.0980448	0.00480127
$418$	19.9761	0.977063
$419$	−1.74656	−0.0853249	−0.0426624	−	0.999090i	$-0.513584\pi$
$419$	−1.74656	−0.0853249	−0.0426624	+	0.999090i	$0.513584\pi$
$420$	−0.0289263	−0.00141146
$421$	8.00195	0.389991	0.194996	−	0.980804i	$-0.437531\pi$
$421$	8.00195	0.389991	0.194996	+	0.980804i	$0.437531\pi$
$422$	−59.9403	−2.91785
$423$	−2.21197	−0.107550
$424$	33.6451	1.63395
$425$	−12.1474	−0.589237
$426$	0.765213	0.0370747
$427$	−0.738565	−0.0357417
$428$	14.6059	0.706003
$429$	−1.63538	−0.0789570
$430$	2.22248	0.107177
$431$	17.3806	0.837193	0.418597	−	0.908172i	$-0.362522\pi$
$431$	17.3806	0.837193	0.418597	+	0.908172i	$0.362522\pi$
$432$	6.08161	0.292602
$433$	−6.35112	−0.305216	−0.152608	−	0.988287i	$-0.548767\pi$
$433$	−6.35112	−0.305216	−0.152608	+	0.988287i	$0.548767\pi$
$434$	1.37615	0.0660575
$435$	−0.371180	−0.0177967
$436$	0.00306009	0.000146552 0
$437$	17.7820	0.850628
$438$	0.452993	0.0216449
$439$	−24.1826	−1.15417	−0.577087	−	0.816683i	$-0.695811\pi$
$439$	−24.1826	−1.15417	−0.577087	+	0.816683i	$0.695811\pi$
$440$	−10.3630	−0.494036
$441$	20.8751	0.994052
$442$	−34.0018	−1.61730
$443$	−25.0523	−1.19027	−0.595136	−	0.803625i	$-0.702902\pi$
$443$	−25.0523	−1.19027	−0.595136	+	0.803625i	$0.702902\pi$
$444$	3.51332	0.166735
$445$	−6.35742	−0.301371
$446$	−1.69592	−0.0803043
$447$	−0.595101	−0.0281473
$448$	1.19884	0.0566401
$449$	26.2293	1.23784	0.618919	−	0.785455i	$-0.287571\pi$
$449$	26.2293	1.23784	0.618919	+	0.785455i	$0.287571\pi$
$450$	−37.6460	−1.77465
$451$	2.60973	0.122887
$452$	31.1674	1.46599
$453$	0.940903	0.0442075
$454$	4.70364	0.220753
$455$	0.299104	0.0140222
$456$	−1.86948	−0.0875464
$457$	−24.4887	−1.14554	−0.572768	−	0.819718i	$-0.694130\pi$
$457$	−24.4887	−1.14554	−0.572768	+	0.819718i	$0.694130\pi$
$458$	10.5500	0.492968
$459$	1.54411	0.0720730
$460$	−15.6590	−0.730105
$461$	−24.5364	−1.14277	−0.571386	−	0.820681i	$-0.693594\pi$
$461$	−24.5364	−1.14277	−0.571386	+	0.820681i	$0.693594\pi$
$462$	0.110244	0.00512900
$463$	14.3318	0.666055	0.333027	−	0.942917i	$-0.391930\pi$
$463$	14.3318	0.666055	0.333027	+	0.942917i	$0.391930\pi$
$464$	82.1056	3.81166
$465$	0.179031	0.00830236
$466$	−69.7140	−3.22944
$467$	2.03318	0.0940845	0.0470422	−	0.998893i	$-0.485020\pi$
$467$	2.03318	0.0940845	0.0470422	+	0.998893i	$0.485020\pi$
$468$	−74.6862	−3.45237
$469$	−0.481829	−0.0222488
$470$	−0.855820	−0.0394760
$471$	0.450533	0.0207595
$472$	−48.5316	−2.23385
$473$	−6.00349	−0.276041
$474$	0.518292	0.0238060
$475$	11.7231	0.537892
$476$	1.62458	0.0744625
$477$	13.3861	0.612905
$478$	−14.7814	−0.676087
$479$	30.7404	1.40457	0.702283	−	0.711898i	$-0.252164\pi$
$479$	30.7404	1.40457	0.702283	+	0.711898i	$0.252164\pi$
$480$	0.498003	0.0227306
$481$	−36.3285	−1.65644
$482$	3.87715	0.176599
$483$	0.0981349	0.00446529
$484$	−6.02300	−0.273773
$485$	−5.65982	−0.256999
$486$	7.18216	0.325790
$487$	7.36486	0.333734	0.166867	−	0.985979i	$-0.446635\pi$
$487$	7.36486	0.333734	0.166867	+	0.985979i	$0.446635\pi$
$488$	42.0341	1.90279
$489$	1.56836	0.0709237
$490$	8.07666	0.364866
$491$	5.96760	0.269314	0.134657	−	0.990892i	$-0.457007\pi$
$491$	5.96760	0.269314	0.134657	+	0.990892i	$0.457007\pi$
$492$	−0.414587	−0.0186910
$493$	20.8465	0.938879
$494$	32.8141	1.47637
$495$	−4.12303	−0.185316
$496$	−39.6020	−1.77818
$497$	0.378051	0.0169579
$498$	1.35485	0.0607123
$499$	−1.04892	−0.0469561	−0.0234781	−	0.999724i	$-0.507474\pi$
$499$	−1.04892	−0.0469561	−0.0234781	+	0.999724i	$0.507474\pi$
$500$	−21.0655	−0.942078
$501$	−1.07507	−0.0480306
$502$	−8.98469	−0.401006
$503$	−34.4832	−1.53753	−0.768764	−	0.639533i	$-0.779128\pi$
$503$	−34.4832	−1.53753	−0.768764	+	0.639533i	$0.779128\pi$
$504$	2.96596	0.132114
$505$	−2.90952	−0.129472
$506$	59.6796	2.65308
$507$	−1.36067	−0.0604297
$508$	34.3079	1.52217
$509$	−0.663447	−0.0294068	−0.0147034	−	0.999892i	$-0.504680\pi$
$509$	−0.663447	−0.0294068	−0.0147034	+	0.999892i	$0.504680\pi$
$510$	0.298193	0.0132042
$511$	0.223800	0.00990033
$512$	39.4739	1.74452
$513$	−1.49017	−0.0657927
$514$	8.63947	0.381071
$515$	−4.94001	−0.217683
$516$	0.953725	0.0419854
$517$	2.31179	0.101672
$518$	2.44896	0.107601
$519$	0.643008	0.0282249
$520$	−17.0229	−0.746505
$521$	−1.97156	−0.0863758	−0.0431879	−	0.999067i	$-0.513751\pi$
$521$	−1.97156	−0.0863758	−0.0431879	+	0.999067i	$0.513751\pi$
$522$	64.6051	2.82769
$523$	−4.49425	−0.196520	−0.0982599	−	0.995161i	$-0.531328\pi$
$523$	−4.49425	−0.196520	−0.0982599	+	0.995161i	$0.531328\pi$
$524$	39.9707	1.74613
$525$	0.0646972	0.00282362
$526$	33.7106	1.46985
$527$	−10.0549	−0.437997
$528$	−3.17251	−0.138066
$529$	30.1246	1.30976
$530$	5.17912	0.224966
$531$	−19.3088	−0.837930
$532$	−1.56783	−0.0679740
$533$	4.28691	0.185687
$534$	−3.84912	−0.166568
$535$	1.32450	0.0572633
$536$	27.4224	1.18447
$537$	1.98661	0.0857286
$538$	−78.8251	−3.39839
$539$	−21.8171	−0.939730
$540$	1.31226	0.0564707
$541$	11.4957	0.494239	0.247120	−	0.968985i	$-0.420516\pi$
$541$	11.4957	0.494239	0.247120	+	0.968985i	$0.420516\pi$
$542$	−45.6793	−1.96209
$543$	−1.27782	−0.0548367
$544$	−27.9692	−1.19917
$545$	0.000277497 0	1.18867e−5 0
$546$	0.181094	0.00775009
$547$	32.2998	1.38104	0.690519	−	0.723314i	$-0.257382\pi$
$547$	32.2998	1.38104	0.690519	+	0.723314i	$0.257382\pi$
$548$	−43.7155	−1.86743
$549$	16.7237	0.713750
$550$	39.3448	1.67767
$551$	−20.1183	−0.857066
$552$	−5.58516	−0.237720
$553$	0.256061	0.0108888
$554$	38.4778	1.63476
$555$	0.318597	0.0135237
$556$	−4.67966	−0.198462
$557$	−16.7448	−0.709502	−0.354751	−	0.934961i	$-0.615434\pi$
$557$	−16.7448	−0.709502	−0.354751	+	0.934961i	$0.615434\pi$
$558$	−31.1609	−1.31915
$559$	−9.86172	−0.417106
$560$	0.580237	0.0245195
$561$	−0.805496	−0.0340081
$562$	35.7578	1.50835
$563$	18.2958	0.771075	0.385537	−	0.922692i	$-0.374016\pi$
$563$	18.2958	0.771075	0.385537	+	0.922692i	$0.374016\pi$
$564$	−0.367255	−0.0154642
$565$	2.82635	0.118905
$566$	34.3914	1.44558
$567$	1.17592	0.0493840
$568$	−21.5161	−0.902794
$569$	9.06084	0.379850	0.189925	−	0.981799i	$-0.439176\pi$
$569$	9.06084	0.379850	0.189925	+	0.981799i	$0.439176\pi$
$570$	−0.287776	−0.0120536
$571$	−3.60957	−0.151056	−0.0755280	−	0.997144i	$-0.524064\pi$
$571$	−3.60957	−0.151056	−0.0755280	+	0.997144i	$0.524064\pi$
$572$	78.0566	3.26371
$573$	0.0370191	0.00154650
$574$	−0.288988	−0.0120621
$575$	35.0233	1.46057
$576$	−27.1460	−1.13108
$577$	−11.0761	−0.461105	−0.230552	−	0.973060i	$-0.574053\pi$
$577$	−11.0761	−0.461105	−0.230552	+	0.973060i	$0.574053\pi$
$578$	27.8023	1.15642
$579$	−1.29395	−0.0537748
$580$	17.7163	0.735631
$581$	0.669360	0.0277697
$582$	−3.42676	−0.142044
$583$	−13.9901	−0.579412
$584$	−12.7372	−0.527067
$585$	−6.77275	−0.280019
$586$	−9.12482	−0.376943
$587$	−11.8527	−0.489212	−0.244606	−	0.969623i	$-0.578659\pi$
$587$	−11.8527	−0.489212	−0.244606	+	0.969623i	$0.578659\pi$
$588$	3.46591	0.142932
$589$	9.70363	0.399831
$590$	−7.47065	−0.307562
$591$	2.05697	0.0846123
$592$	−70.4743	−2.89648
$593$	−7.00961	−0.287850	−0.143925	−	0.989589i	$-0.545972\pi$
$593$	−7.00961	−0.287850	−0.143925	+	0.989589i	$0.545972\pi$
$594$	−5.00129	−0.205205
$595$	0.147321	0.00603959
$596$	28.4041	1.16348
$597$	−2.42973	−0.0994424
$598$	98.0336	4.00889
$599$	−27.7312	−1.13307	−0.566534	−	0.824038i	$-0.691716\pi$
$599$	−27.7312	−1.13307	−0.566534	+	0.824038i	$0.691716\pi$
$600$	−3.68212	−0.150322
$601$	−6.34988	−0.259017	−0.129509	−	0.991578i	$-0.541340\pi$
$601$	−6.34988	−0.259017	−0.129509	+	0.991578i	$0.541340\pi$
$602$	0.664794	0.0270950
$603$	10.9103	0.444301
$604$	−44.9092	−1.82733
$605$	−0.546182	−0.0222055
$606$	−1.76158	−0.0715594
$607$	−39.7937	−1.61518	−0.807589	−	0.589746i	$-0.799228\pi$
$607$	−39.7937	−1.61518	−0.807589	+	0.589746i	$0.799228\pi$
$608$	26.9922	1.09468
$609$	−0.111028	−0.00449909
$610$	6.47046	0.261981
$611$	3.79749	0.153630
$612$	−36.7862	−1.48699
$613$	−16.3497	−0.660358	−0.330179	−	0.943918i	$-0.607109\pi$
$613$	−16.3497	−0.660358	−0.330179	+	0.943918i	$0.607109\pi$
$614$	63.0539	2.54465
$615$	−0.0375958	−0.00151601
$616$	−3.09981	−0.124895
$617$	5.14855	0.207273	0.103636	−	0.994615i	$-0.466952\pi$
$617$	5.14855	0.207273	0.103636	+	0.994615i	$0.466952\pi$
$618$	−2.99095	−0.120314
$619$	7.12427	0.286348	0.143174	−	0.989698i	$-0.454269\pi$
$619$	7.12427	0.286348	0.143174	+	0.989698i	$0.454269\pi$
$620$	−8.54512	−0.343180
$621$	−4.45196	−0.178651
$622$	18.3438	0.735520
$623$	−1.90165	−0.0761879
$624$	−5.21137	−0.208622
$625$	22.1156	0.884624
$626$	−40.0706	−1.60155
$627$	0.777358	0.0310447
$628$	−21.5039	−0.858098
$629$	−17.8933	−0.713453
$630$	0.456562	0.0181899
$631$	−21.8705	−0.870652	−0.435326	−	0.900273i	$-0.643367\pi$
$631$	−21.8705	−0.870652	−0.435326	+	0.900273i	$0.643367\pi$
$632$	−14.5732	−0.579691
$633$	−2.33254	−0.0927101
$634$	32.4369	1.28823
$635$	3.11113	0.123462
$636$	2.22250	0.0881277
$637$	−35.8382	−1.41996
$638$	−67.5205	−2.67316
$639$	−8.56040	−0.338644
$640$	−0.736020	−0.0290938
$641$	−10.1702	−0.401699	−0.200849	−	0.979622i	$-0.564370\pi$
$641$	−10.1702	−0.401699	−0.200849	+	0.979622i	$0.564370\pi$
$642$	0.801926	0.0316495
$643$	−7.92988	−0.312724	−0.156362	−	0.987700i	$-0.549977\pi$
$643$	−7.92988	−0.312724	−0.156362	+	0.987700i	$0.549977\pi$
$644$	−4.68396	−0.184574
$645$	0.0864864	0.00340540
$646$	16.1623	0.635898
$647$	31.8072	1.25047	0.625234	−	0.780437i	$-0.285003\pi$
$647$	31.8072	1.25047	0.625234	+	0.780437i	$0.285003\pi$
$648$	−66.9252	−2.62907
$649$	20.1801	0.792140
$650$	64.6303	2.53501
$651$	0.0535522	0.00209888
$652$	−74.8576	−2.93165
$653$	−19.9997	−0.782649	−0.391325	−	0.920253i	$-0.627983\pi$
$653$	−19.9997	−0.782649	−0.391325	+	0.920253i	$0.627983\pi$
$654$	0.000168012 0	6.56978e−6 0
$655$	3.62466	0.141627
$656$	8.31627	0.324696
$657$	−5.06761	−0.197706
$658$	−0.255995	−0.00997973
$659$	16.5548	0.644883	0.322442	−	0.946589i	$-0.395496\pi$
$659$	16.5548	0.644883	0.322442	+	0.946589i	$0.395496\pi$
$660$	−0.684549	−0.0266460
$661$	41.4304	1.61146	0.805728	−	0.592285i	$-0.201774\pi$
$661$	41.4304	1.61146	0.805728	+	0.592285i	$0.201774\pi$
$662$	23.4707	0.912216
$663$	−1.32316	−0.0513873
$664$	−38.0954	−1.47839
$665$	−0.142175	−0.00551331
$666$	−55.4529	−2.14876
$667$	−60.1043	−2.32725
$668$	51.3130	1.98536
$669$	−0.0659958	−0.00255154
$670$	4.22123	0.163080
$671$	−17.4784	−0.674745
$672$	0.148964	0.00574641
$673$	41.9546	1.61723	0.808616	−	0.588337i	$-0.200217\pi$
$673$	41.9546	1.61723	0.808616	+	0.588337i	$0.200217\pi$
$674$	55.1643	2.12485
$675$	−2.93503	−0.112970
$676$	64.9448	2.49788
$677$	−30.9091	−1.18793	−0.593967	−	0.804489i	$-0.702439\pi$
$677$	−30.9091	−1.18793	−0.593967	+	0.804489i	$0.702439\pi$
$678$	1.71122	0.0657192
$679$	−1.69298	−0.0649706
$680$	−8.38452	−0.321532
$681$	0.183039	0.00701408
$682$	32.5671	1.24706
$683$	−31.2750	−1.19670	−0.598352	−	0.801233i	$-0.704177\pi$
$683$	−31.2750	−1.19670	−0.598352	+	0.801233i	$0.704177\pi$
$684$	35.5011	1.35742
$685$	−3.96424	−0.151466
$686$	4.83785	0.184710
$687$	0.410546	0.0156633
$688$	−19.1309	−0.729360
$689$	−22.9811	−0.875510
$690$	−0.859746	−0.0327300
$691$	−4.57116	−0.173895	−0.0869475	−	0.996213i	$-0.527711\pi$
$691$	−4.57116	−0.173895	−0.0869475	+	0.996213i	$0.527711\pi$
$692$	−30.6907	−1.16668
$693$	−1.23329	−0.0468488
$694$	17.5781	0.667256
$695$	−0.424365	−0.0160971
$696$	6.31896	0.239520
$697$	2.11149	0.0799783
$698$	73.5683	2.78460
$699$	−2.71288	−0.102610
$700$	−3.08799	−0.116715
$701$	38.9005	1.46925	0.734626	−	0.678472i	$-0.237358\pi$
$701$	38.9005	1.46925	0.734626	+	0.678472i	$0.237358\pi$
$702$	−8.21544	−0.310072
$703$	17.2682	0.651284
$704$	28.3710	1.06927
$705$	−0.0333037	−0.00125429
$706$	20.0599	0.754965
$707$	−0.870304	−0.0327312
$708$	−3.20585	−0.120483
$709$	6.47613	0.243216	0.121608	−	0.992578i	$-0.461195\pi$
$709$	6.47613	0.243216	0.121608	+	0.992578i	$0.461195\pi$
$710$	−3.31205	−0.124299
$711$	−5.79811	−0.217446
$712$	108.229	4.05604
$713$	28.9901	1.08569
$714$	0.0891963	0.00333809
$715$	7.07839	0.264717
$716$	−94.8206	−3.54361
$717$	−0.575210	−0.0214816
$718$	−27.8304	−1.03862
$719$	−6.77978	−0.252843	−0.126422	−	0.991977i	$-0.540349\pi$
$719$	−6.77978	−0.252843	−0.126422	+	0.991977i	$0.540349\pi$
$720$	−13.1386	−0.489646
$721$	−1.47767	−0.0550313
$722$	34.1931	1.27254
$723$	0.150877	0.00561117
$724$	60.9904	2.26669
$725$	−39.6248	−1.47163
$726$	−0.330688	−0.0122730
$727$	1.60517	0.0595326	0.0297663	−	0.999557i	$-0.490524\pi$
$727$	1.60517	0.0595326	0.0297663	+	0.999557i	$0.490524\pi$
$728$	−5.09194	−0.188720
$729$	−26.4400	−0.979261
$730$	−1.96068	−0.0725680
$731$	−4.85732	−0.179654
$732$	2.77665	0.102628
$733$	−15.5754	−0.575291	−0.287646	−	0.957737i	$-0.592873\pi$
$733$	−15.5754	−0.575291	−0.287646	+	0.957737i	$0.592873\pi$
$734$	66.4472	2.45261
$735$	0.314298	0.0115931
$736$	80.6405	2.97245
$737$	−11.4026	−0.420021
$738$	6.54368	0.240876
$739$	−45.5199	−1.67448	−0.837239	−	0.546838i	$-0.815831\pi$
$739$	−45.5199	−1.67448	−0.837239	+	0.546838i	$0.815831\pi$
$740$	−15.2066	−0.559006
$741$	1.27694	0.0469095
$742$	1.54919	0.0568726
$743$	1.55980	0.0572234	0.0286117	−	0.999591i	$-0.490891\pi$
$743$	1.55980	0.0572234	0.0286117	+	0.999591i	$0.490891\pi$
$744$	−3.04782	−0.111739
$745$	2.57576	0.0943686
$746$	55.0030	2.01380
$747$	−15.1566	−0.554553
$748$	38.4462	1.40573
$749$	0.396189	0.0144764
$750$	−1.15659	−0.0422325
$751$	25.9677	0.947575	0.473788	−	0.880639i	$-0.342886\pi$
$751$	25.9677	0.947575	0.473788	+	0.880639i	$0.342886\pi$
$752$	7.36683	0.268641
$753$	−0.349634	−0.0127414
$754$	−110.914	−4.03923
$755$	−4.07249	−0.148213
$756$	0.392527	0.0142761
$757$	−44.6929	−1.62439	−0.812195	−	0.583385i	$-0.801728\pi$
$757$	−44.6929	−1.62439	−0.812195	+	0.583385i	$0.801728\pi$
$758$	−30.1787	−1.09614
$759$	2.32239	0.0842976
$760$	8.09162	0.293514
$761$	−10.7663	−0.390278	−0.195139	−	0.980776i	$-0.562516\pi$
$761$	−10.7663	−0.390278	−0.195139	+	0.980776i	$0.562516\pi$
$762$	1.88365	0.0682373
$763$	8.30057e−5 0	3.00501e−6 0
$764$	−1.76692	−0.0639248
$765$	−3.33587	−0.120609
$766$	82.3431	2.97518
$767$	33.1492	1.19695
$768$	1.40632	0.0507463
$769$	10.3293	0.372485	0.186243	−	0.982504i	$-0.440369\pi$
$769$	10.3293	0.372485	0.186243	+	0.982504i	$0.440369\pi$
$770$	−0.477165	−0.0171958
$771$	0.336200	0.0121079
$772$	61.7602	2.22280
$773$	−14.7801	−0.531605	−0.265802	−	0.964028i	$-0.585637\pi$
$773$	−14.7801	−0.531605	−0.265802	+	0.964028i	$0.585637\pi$
$774$	−15.0532	−0.541078
$775$	19.1122	0.686531
$776$	96.3528	3.45886
$777$	0.0952997	0.00341886
$778$	95.4143	3.42077
$779$	−2.03773	−0.0730092
$780$	−1.12449	−0.0402630
$781$	8.94670	0.320138
$782$	48.2857	1.72669
$783$	5.03688	0.180003
$784$	−69.5233	−2.48297
$785$	−1.95003	−0.0695995
$786$	2.19456	0.0782774
$787$	−46.8380	−1.66960	−0.834798	−	0.550557i	$-0.814415\pi$
$787$	−46.8380	−1.66960	−0.834798	+	0.550557i	$0.814415\pi$
$788$	−98.1788	−3.49747
$789$	1.31183	0.0467023
$790$	−2.24331	−0.0798134
$791$	0.845425	0.0300599
$792$	70.1904	2.49411
$793$	−28.7111	−1.01956
$794$	−40.5544	−1.43922
$795$	0.201542	0.00714796
$796$	115.971	4.11048
$797$	−52.4024	−1.85619	−0.928094	−	0.372346i	$-0.878554\pi$
$797$	−52.4024	−1.85619	−0.928094	+	0.372346i	$0.878554\pi$
$798$	−0.0860804	−0.00304721
$799$	1.87043	0.0661710
$800$	53.1636	1.87962
$801$	43.0599	1.52145
$802$	26.3041	0.928829
$803$	5.29630	0.186902
$804$	1.81144	0.0638846
$805$	−0.424755	−0.0149706
$806$	53.4969	1.88435
$807$	−3.06743	−0.107979
$808$	49.5317	1.74252
$809$	3.23455	0.113721	0.0568604	−	0.998382i	$-0.481891\pi$
$809$	3.23455	0.113721	0.0568604	+	0.998382i	$0.481891\pi$
$810$	−10.3021	−0.361978
$811$	−33.0582	−1.16083	−0.580415	−	0.814321i	$-0.697110\pi$
$811$	−33.0582	−1.16083	−0.580415	+	0.814321i	$0.697110\pi$
$812$	5.29936	0.185971
$813$	−1.77758	−0.0623425
$814$	57.9554	2.03133
$815$	−6.78829	−0.237783
$816$	−2.56683	−0.0898569
$817$	4.68764	0.164000
$818$	−23.7159	−0.829208
$819$	−2.02588	−0.0707901
$820$	1.79444	0.0626647
$821$	38.2559	1.33514	0.667570	−	0.744547i	$-0.267335\pi$
$821$	38.2559	1.33514	0.667570	+	0.744547i	$0.267335\pi$
$822$	−2.40016	−0.0837154
$823$	−10.3868	−0.362059	−0.181030	−	0.983478i	$-0.557943\pi$
$823$	−10.3868	−0.362059	−0.181030	+	0.983478i	$0.557943\pi$
$824$	84.0988	2.92972
$825$	1.53108	0.0533053
$826$	−2.23464	−0.0777531
$827$	−7.28524	−0.253333	−0.126666	−	0.991945i	$-0.540428\pi$
$827$	−7.28524	−0.253333	−0.126666	+	0.991945i	$0.540428\pi$
$828$	106.061	3.68588
$829$	−29.6680	−1.03041	−0.515207	−	0.857066i	$-0.672285\pi$
$829$	−29.6680	−1.03041	−0.515207	+	0.857066i	$0.672285\pi$
$830$	−5.86417	−0.203548
$831$	1.49734	0.0519421
$832$	46.6041	1.61571
$833$	−17.6519	−0.611601
$834$	−0.256933	−0.00889687
$835$	4.65320	0.161031
$836$	−37.1032	−1.28324
$837$	−2.42944	−0.0839736
$838$	4.57697	0.158109
$839$	−5.57662	−0.192526	−0.0962632	−	0.995356i	$-0.530689\pi$
$839$	−5.57662	−0.192526	−0.0962632	+	0.995356i	$0.530689\pi$
$840$	0.0446559	0.00154077
$841$	39.0010	1.34486
$842$	−20.9697	−0.722663
$843$	1.39149	0.0479256
$844$	111.332	3.83220
$845$	5.88937	0.202601
$846$	5.79662	0.199292
$847$	−0.163376	−0.00561365
$848$	−44.5815	−1.53093
$849$	1.33832	0.0459310
$850$	31.8332	1.09187
$851$	51.5897	1.76847
$852$	−1.42129	−0.0486926
$853$	6.99449	0.239487	0.119743	−	0.992805i	$-0.461793\pi$
$853$	6.99449	0.239487	0.119743	+	0.992805i	$0.461793\pi$
$854$	1.93546	0.0662301
$855$	3.21934	0.110099
$856$	−22.5484	−0.770687
$857$	42.2914	1.44465	0.722323	−	0.691556i	$-0.243074\pi$
$857$	42.2914	1.44465	0.722323	+	0.691556i	$0.243074\pi$
$858$	4.28564	0.146309
$859$	−17.0741	−0.582560	−0.291280	−	0.956638i	$-0.594081\pi$
$859$	−17.0741	−0.582560	−0.291280	+	0.956638i	$0.594081\pi$
$860$	−4.12798	−0.140763
$861$	−0.0112458	−0.000383255 0
$862$	−45.5470	−1.55134
$863$	−18.0840	−0.615588	−0.307794	−	0.951453i	$-0.599591\pi$
$863$	−18.0840	−0.615588	−0.307794	+	0.951453i	$0.599591\pi$
$864$	−6.75786	−0.229907
$865$	−2.78312	−0.0946288
$866$	16.6436	0.565571
$867$	1.08191	0.0367436
$868$	−2.55604	−0.0867576
$869$	6.05976	0.205563
$870$	0.972702	0.0329777
$871$	−18.7307	−0.634666
$872$	−0.00472411	−0.000159979 0
$873$	38.3350	1.29744
$874$	−46.5990	−1.57623
$875$	−0.571408	−0.0193171
$876$	−0.841380	−0.0284276
$877$	−32.3366	−1.09193	−0.545965	−	0.837808i	$-0.683837\pi$
$877$	−32.3366	−1.09193	−0.545965	+	0.837808i	$0.683837\pi$
$878$	63.3723	2.13871
$879$	−0.355087	−0.0119768
$880$	13.7315	0.462889
$881$	3.89811	0.131331	0.0656653	−	0.997842i	$-0.479083\pi$
$881$	3.89811	0.131331	0.0656653	+	0.997842i	$0.479083\pi$
$882$	−54.7046	−1.84200
$883$	−14.3985	−0.484548	−0.242274	−	0.970208i	$-0.577893\pi$
$883$	−14.3985	−0.484548	−0.242274	+	0.970208i	$0.577893\pi$
$884$	63.1543	2.12411
$885$	−0.290716	−0.00977230
$886$	65.6514	2.20560
$887$	17.4870	0.587157	0.293579	−	0.955935i	$-0.405154\pi$
$887$	17.4870	0.587157	0.293579	+	0.955935i	$0.405154\pi$
$888$	−5.42380	−0.182011
$889$	0.930610	0.0312117
$890$	16.6601	0.558447
$891$	27.8285	0.932290
$892$	3.14997	0.105469
$893$	−1.80509	−0.0604050
$894$	1.55950	0.0521576
$895$	−8.59859	−0.287419
$896$	−0.220160	−0.00735504
$897$	3.81492	0.127376
$898$	−68.7357	−2.29374
$899$	−32.7989	−1.09390
$900$	69.9227	2.33076
$901$	−11.3192	−0.377096
$902$	−6.83898	−0.227713
$903$	0.0258700	0.000860901 0
$904$	−48.1158	−1.60031
$905$	5.53077	0.183849
$906$	−2.46570	−0.0819175
$907$	46.7463	1.55219	0.776093	−	0.630619i	$-0.217199\pi$
$907$	46.7463	1.55219	0.776093	+	0.630619i	$0.217199\pi$
$908$	−8.73644	−0.289929
$909$	19.7067	0.653631
$910$	−0.783822	−0.0259835
$911$	26.1831	0.867483	0.433742	−	0.901037i	$-0.357193\pi$
$911$	26.1831	0.867483	0.433742	+	0.901037i	$0.357193\pi$
$912$	2.47716	0.0820269
$913$	15.8406	0.524248
$914$	64.1745	2.12270
$915$	0.251794	0.00832405
$916$	−19.5953	−0.647447
$917$	1.08422	0.0358040
$918$	−4.04646	−0.133553
$919$	−30.0504	−0.991273	−0.495636	−	0.868530i	$-0.665065\pi$
$919$	−30.0504	−0.991273	−0.495636	+	0.868530i	$0.665065\pi$
$920$	24.1741	0.796997
$921$	2.45370	0.0808523
$922$	64.2993	2.11758
$923$	14.6964	0.483739
$924$	−0.204764	−0.00673625
$925$	34.0114	1.11829
$926$	−37.5575	−1.23421
$927$	33.4596	1.09896
$928$	−91.2353	−2.99495
$929$	−5.18353	−0.170066	−0.0850330	−	0.996378i	$-0.527100\pi$
$929$	−5.18353	−0.170066	−0.0850330	+	0.996378i	$0.527100\pi$
$930$	−0.469163	−0.0153845
$931$	17.0352	0.558307
$932$	129.485	4.24143
$933$	0.713838	0.0233700
$934$	−5.32810	−0.174341
$935$	3.48641	0.114018
$936$	115.299	3.76868
$937$	−50.0447	−1.63489	−0.817445	−	0.576007i	$-0.804610\pi$
$937$	−50.0447	−1.63489	−0.817445	+	0.576007i	$0.804610\pi$
$938$	1.26267	0.0412275
$939$	−1.55932	−0.0508866
$940$	1.58958	0.0518464
$941$	−15.1265	−0.493111	−0.246556	−	0.969129i	$-0.579299\pi$
$941$	−15.1265	−0.493111	−0.246556	+	0.969129i	$0.579299\pi$
$942$	−1.18065	−0.0384677
$943$	−6.08781	−0.198246
$944$	64.3068	2.09301
$945$	0.0355954	0.00115792
$946$	15.7326	0.511510
$947$	57.6410	1.87308	0.936541	−	0.350558i	$-0.114008\pi$
$947$	57.6410	1.87308	0.936541	+	0.350558i	$0.114008\pi$
$948$	−0.962665	−0.0312659
$949$	8.70004	0.282415
$950$	−30.7212	−0.996727
$951$	1.26226	0.0409317
$952$	−2.50800	−0.0812847
$953$	0.813305	0.0263455	0.0131728	−	0.999913i	$-0.495807\pi$
$953$	0.813305	0.0263455	0.0131728	+	0.999913i	$0.495807\pi$
$954$	−35.0791	−1.13573
$955$	−0.160229	−0.00518488
$956$	27.4547	0.887948
$957$	−2.62752	−0.0849356
$958$	−80.5574	−2.60269
$959$	−1.18579	−0.0382913
$960$	−0.408714	−0.0131912
$961$	−15.1801	−0.489681
$962$	95.2013	3.06941
$963$	−8.97110	−0.289090
$964$	−7.20133	−0.231939
$965$	5.60058	0.180289
$966$	−0.257169	−0.00827429
$967$	8.27797	0.266202	0.133101	−	0.991103i	$-0.457507\pi$
$967$	8.27797	0.266202	0.133101	+	0.991103i	$0.457507\pi$
$968$	9.29821	0.298856
$969$	0.628947	0.0202047
$970$	14.8320	0.476225
$971$	−31.8997	−1.02371	−0.511855	−	0.859072i	$-0.671042\pi$
$971$	−31.8997	−1.02371	−0.511855	+	0.859072i	$0.671042\pi$
$972$	−13.3400	−0.427880
$973$	−0.126937	−0.00406942
$974$	−19.3001	−0.618416
$975$	2.51505	0.0805461
$976$	−55.6973	−1.78283
$977$	−31.0871	−0.994563	−0.497282	−	0.867589i	$-0.665668\pi$
$977$	−31.0871	−0.994563	−0.497282	+	0.867589i	$0.665668\pi$
$978$	−4.11000	−0.131423
$979$	−45.0031	−1.43831
$980$	−15.0014	−0.479202
$981$	−0.00187954	−6.00090e−5 0
$982$	−15.6385	−0.499045
$983$	−16.1716	−0.515793	−0.257896	−	0.966173i	$-0.583029\pi$
$983$	−16.1716	−0.515793	−0.257896	+	0.966173i	$0.583029\pi$
$984$	0.640032	0.0204035
$985$	−8.90312	−0.283677
$986$	−54.6297	−1.73976
$987$	−0.00996189	−0.000317090 0
$988$	−60.9481	−1.93902
$989$	14.0045	0.445319
$990$	10.8047	0.343395
$991$	−1.12799	−0.0358317	−0.0179159	−	0.999839i	$-0.505703\pi$
$991$	−1.12799	−0.0358317	−0.0179159	+	0.999839i	$0.505703\pi$
$992$	44.0055	1.39718
$993$	0.913349	0.0289842
$994$	−0.990710	−0.0314234
$995$	10.5166	0.333397
$996$	−2.51647	−0.0797374
$997$	−26.0257	−0.824242	−0.412121	−	0.911129i	$-0.635212\pi$
$997$	−26.0257	−0.824242	−0.412121	+	0.911129i	$0.635212\pi$
$998$	2.74877	0.0870108
$999$	−4.32334	−0.136784

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4007.2.a.a.1.6	✓	139

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4007.2.a.a.1.6	✓	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)

\(f(q)\)	\(=\)	\(q-2.62057 q^{2} -0.101978 q^{3} +4.86739 q^{4} +0.441388 q^{5} +0.267240 q^{6} +0.132029 q^{7} -7.51419 q^{8} -2.98960 q^{9} +O(q^{10})\)	\(q-2.62057 q^{2} -0.101978 q^{3} +4.86739 q^{4} +0.441388 q^{5} +0.267240 q^{6} +0.132029 q^{7} -7.51419 q^{8} -2.98960 q^{9} -1.15669 q^{10} +3.12451 q^{11} -0.496366 q^{12} +5.13253 q^{13} -0.345992 q^{14} -0.0450118 q^{15} +9.95669 q^{16} +2.52799 q^{17} +7.83446 q^{18} -2.43968 q^{19} +2.14841 q^{20} -0.0134641 q^{21} -8.18801 q^{22} -7.28866 q^{23} +0.766281 q^{24} -4.80518 q^{25} -13.4502 q^{26} +0.610807 q^{27} +0.642637 q^{28} +8.24627 q^{29} +0.117957 q^{30} -3.97742 q^{31} -11.0638 q^{32} -0.318631 q^{33} -6.62478 q^{34} +0.0582761 q^{35} -14.5515 q^{36} -7.07808 q^{37} +6.39335 q^{38} -0.523404 q^{39} -3.31667 q^{40} +0.835244 q^{41} +0.0352835 q^{42} -1.92142 q^{43} +15.2082 q^{44} -1.31957 q^{45} +19.1004 q^{46} +0.739888 q^{47} -1.01536 q^{48} -6.98257 q^{49} +12.5923 q^{50} -0.257799 q^{51} +24.9820 q^{52} -4.47754 q^{53} -1.60066 q^{54} +1.37912 q^{55} -0.992093 q^{56} +0.248793 q^{57} -21.6099 q^{58} +6.45865 q^{59} -0.219090 q^{60} -5.59395 q^{61} +10.4231 q^{62} -0.394714 q^{63} +9.08015 q^{64} +2.26544 q^{65} +0.834995 q^{66} -3.64941 q^{67} +12.3047 q^{68} +0.743282 q^{69} -0.152717 q^{70} +2.86339 q^{71} +22.4644 q^{72} +1.69508 q^{73} +18.5486 q^{74} +0.490022 q^{75} -11.8749 q^{76} +0.412527 q^{77} +1.37162 q^{78} +1.93943 q^{79} +4.39477 q^{80} +8.90651 q^{81} -2.18882 q^{82} +5.06979 q^{83} -0.0655348 q^{84} +1.11582 q^{85} +5.03520 q^{86} -0.840937 q^{87} -23.4782 q^{88} -14.4032 q^{89} +3.45804 q^{90} +0.677643 q^{91} -35.4767 q^{92} +0.405609 q^{93} -1.93893 q^{94} -1.07685 q^{95} +1.12827 q^{96} -12.8228 q^{97} +18.2983 q^{98} -9.34104 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 139 q - 13 q^{2} - 22 q^{3} + 113 q^{4} - 16 q^{5} - 15 q^{6} - 44 q^{7} - 36 q^{8} + 87 q^{9}+O(q^{10}) \) 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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