LMFDB - Embedded newform 4007.2.a.a.1.7

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			1.7
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)

$f(q)$	$=$	$q-2.60765 q^{2} +2.41443 q^{3} +4.79982 q^{4} +2.62983 q^{5} -6.29599 q^{6} -4.53793 q^{7} -7.30095 q^{8} +2.82948 q^{9} +O(q^{10})$	\(q-2.60765 q^{2} +2.41443 q^{3} +4.79982 q^{4} +2.62983 q^{5} -6.29599 q^{6} -4.53793 q^{7} -7.30095 q^{8} +2.82948 q^{9} -6.85767 q^{10} -0.594314 q^{11} +11.5888 q^{12} -0.829183 q^{13} +11.8333 q^{14} +6.34954 q^{15} +9.43867 q^{16} -1.01063 q^{17} -7.37829 q^{18} +2.67005 q^{19} +12.6227 q^{20} -10.9565 q^{21} +1.54976 q^{22} -2.35649 q^{23} -17.6277 q^{24} +1.91600 q^{25} +2.16222 q^{26} -0.411707 q^{27} -21.7813 q^{28} -0.770927 q^{29} -16.5574 q^{30} +1.79490 q^{31} -10.0108 q^{32} -1.43493 q^{33} +2.63537 q^{34} -11.9340 q^{35} +13.5810 q^{36} -2.01816 q^{37} -6.96254 q^{38} -2.00201 q^{39} -19.2003 q^{40} -5.01310 q^{41} +28.5707 q^{42} -3.60323 q^{43} -2.85260 q^{44} +7.44105 q^{45} +6.14489 q^{46} -7.27998 q^{47} +22.7890 q^{48} +13.5928 q^{49} -4.99626 q^{50} -2.44010 q^{51} -3.97993 q^{52} +0.645219 q^{53} +1.07359 q^{54} -1.56294 q^{55} +33.1312 q^{56} +6.44664 q^{57} +2.01030 q^{58} +6.01596 q^{59} +30.4767 q^{60} -9.31790 q^{61} -4.68046 q^{62} -12.8400 q^{63} +7.22731 q^{64} -2.18061 q^{65} +3.74179 q^{66} +7.99699 q^{67} -4.85084 q^{68} -5.68958 q^{69} +31.1196 q^{70} +10.4817 q^{71} -20.6579 q^{72} -2.49562 q^{73} +5.26265 q^{74} +4.62606 q^{75} +12.8158 q^{76} +2.69695 q^{77} +5.22053 q^{78} +3.87778 q^{79} +24.8221 q^{80} -9.48248 q^{81} +13.0724 q^{82} -14.5201 q^{83} -52.5894 q^{84} -2.65778 q^{85} +9.39595 q^{86} -1.86135 q^{87} +4.33906 q^{88} +4.64917 q^{89} -19.4036 q^{90} +3.76278 q^{91} -11.3107 q^{92} +4.33365 q^{93} +18.9836 q^{94} +7.02176 q^{95} -24.1704 q^{96} -10.8233 q^{97} -35.4452 q^{98} -1.68160 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.60765	−1.84389	−0.921943	−	0.387327i	$-0.873399\pi$
$2$	−2.60765	−1.84389	−0.921943	+	0.387327i	$0.873399\pi$
$3$	2.41443	1.39397	0.696986	−	0.717084i	$-0.254524\pi$
$3$	2.41443	1.39397	0.696986	+	0.717084i	$0.254524\pi$
$4$	4.79982	2.39991
$5$	2.62983	1.17610	0.588048	−	0.808826i	$-0.299897\pi$
$5$	2.62983	1.17610	0.588048	+	0.808826i	$0.299897\pi$
$6$	−6.29599	−2.57033
$7$	−4.53793	−1.71518	−0.857588	−	0.514338i	$-0.828038\pi$
$7$	−4.53793	−1.71518	−0.857588	+	0.514338i	$0.828038\pi$
$8$	−7.30095	−2.58128
$9$	2.82948	0.943160
$10$	−6.85767	−2.16858
$11$	−0.594314	−0.179192	−0.0895961	−	0.995978i	$-0.528558\pi$
$11$	−0.594314	−0.179192	−0.0895961	+	0.995978i	$0.528558\pi$
$12$	11.5888	3.34541
$13$	−0.829183	−0.229974	−0.114987	−	0.993367i	$-0.536683\pi$
$13$	−0.829183	−0.229974	−0.114987	+	0.993367i	$0.536683\pi$
$14$	11.8333	3.16259
$15$	6.34954	1.63945
$16$	9.43867	2.35967
$17$	−1.01063	−0.245114	−0.122557	−	0.992461i	$-0.539109\pi$
$17$	−1.01063	−0.245114	−0.122557	+	0.992461i	$0.539109\pi$
$18$	−7.37829	−1.73908
$19$	2.67005	0.612550	0.306275	−	0.951943i	$-0.400917\pi$
$19$	2.67005	0.612550	0.306275	+	0.951943i	$0.400917\pi$
$20$	12.6227	2.82253
$21$	−10.9565	−2.39091
$22$	1.54976	0.330410
$23$	−2.35649	−0.491362	−0.245681	−	0.969351i	$-0.579012\pi$
$23$	−2.35649	−0.491362	−0.245681	+	0.969351i	$0.579012\pi$
$24$	−17.6277	−3.59823
$25$	1.91600	0.383201
$26$	2.16222	0.424046
$27$	−0.411707	−0.0792331
$28$	−21.7813	−4.11627
$29$	−0.770927	−0.143157	−0.0715787	−	0.997435i	$-0.522804\pi$
$29$	−0.770927	−0.143157	−0.0715787	+	0.997435i	$0.522804\pi$
$30$	−16.5574	−3.02295
$31$	1.79490	0.322373	0.161186	−	0.986924i	$-0.448468\pi$
$31$	1.79490	0.322373	0.161186	+	0.986924i	$0.448468\pi$
$32$	−10.0108	−1.76968
$33$	−1.43493	−0.249789
$34$	2.63537	0.451961
$35$	−11.9340	−2.01721
$36$	13.5810	2.26350
$37$	−2.01816	−0.331784	−0.165892	−	0.986144i	$-0.553050\pi$
$37$	−2.01816	−0.331784	−0.165892	+	0.986144i	$0.553050\pi$
$38$	−6.96254	−1.12947
$39$	−2.00201	−0.320578
$40$	−19.2003	−3.03583
$41$	−5.01310	−0.782914	−0.391457	−	0.920196i	$-0.628029\pi$
$41$	−5.01310	−0.782914	−0.391457	+	0.920196i	$0.628029\pi$
$42$	28.5707	4.40856
$43$	−3.60323	−0.549487	−0.274744	−	0.961518i	$-0.588593\pi$
$43$	−3.60323	−0.549487	−0.274744	+	0.961518i	$0.588593\pi$
$44$	−2.85260	−0.430046
$45$	7.44105	1.10925
$46$	6.14489	0.906015
$47$	−7.27998	−1.06189	−0.530947	−	0.847405i	$-0.678164\pi$
$47$	−7.27998	−1.06189	−0.530947	+	0.847405i	$0.678164\pi$
$48$	22.7890	3.28931
$49$	13.5928	1.94183
$50$	−4.99626	−0.706578
$51$	−2.44010	−0.341682
$52$	−3.97993	−0.551918
$53$	0.645219	0.0886276	0.0443138	−	0.999018i	$-0.485890\pi$
$53$	0.645219	0.0886276	0.0443138	+	0.999018i	$0.485890\pi$
$54$	1.07359	0.146097
$55$	−1.56294	−0.210747
$56$	33.1312	4.42734
$57$	6.44664	0.853879
$58$	2.01030	0.263966
$59$	6.01596	0.783211	0.391606	−	0.920133i	$-0.371920\pi$
$59$	6.01596	0.783211	0.391606	+	0.920133i	$0.371920\pi$
$60$	30.4767	3.93452
$61$	−9.31790	−1.19303	−0.596517	−	0.802600i	$-0.703449\pi$
$61$	−9.31790	−1.19303	−0.596517	+	0.802600i	$0.703449\pi$
$62$	−4.68046	−0.594418
$63$	−12.8400	−1.61769
$64$	7.22731	0.903414
$65$	−2.18061	−0.270472
$66$	3.74179	0.460582
$67$	7.99699	0.976988	0.488494	−	0.872567i	$-0.337547\pi$
$67$	7.99699	0.976988	0.488494	+	0.872567i	$0.337547\pi$
$68$	−4.85084	−0.588251
$69$	−5.68958	−0.684945
$70$	31.1196	3.71950
$71$	10.4817	1.24395	0.621976	−	0.783036i	$-0.286330\pi$
$71$	10.4817	1.24395	0.621976	+	0.783036i	$0.286330\pi$
$72$	−20.6579	−2.43456
$73$	−2.49562	−0.292090	−0.146045	−	0.989278i	$-0.546654\pi$
$73$	−2.49562	−0.292090	−0.146045	+	0.989278i	$0.546654\pi$
$74$	5.26265	0.611771
$75$	4.62606	0.534171
$76$	12.8158	1.47007
$77$	2.69695	0.307346
$78$	5.22053	0.591108
$79$	3.87778	0.436284	0.218142	−	0.975917i	$-0.430000\pi$
$79$	3.87778	0.436284	0.218142	+	0.975917i	$0.430000\pi$
$80$	24.8221	2.77519
$81$	−9.48248	−1.05361
$82$	13.0724	1.44360
$83$	−14.5201	−1.59378	−0.796892	−	0.604121i	$-0.793524\pi$
$83$	−14.5201	−1.59378	−0.796892	+	0.604121i	$0.793524\pi$
$84$	−52.5894	−5.73797
$85$	−2.65778	−0.288277
$86$	9.39595	1.01319
$87$	−1.86135	−0.199558
$88$	4.33906	0.462545
$89$	4.64917	0.492811	0.246405	−	0.969167i	$-0.420751\pi$
$89$	4.64917	0.492811	0.246405	+	0.969167i	$0.420751\pi$
$90$	−19.4036	−2.04532
$91$	3.76278	0.394446
$92$	−11.3107	−1.17923
$93$	4.33365	0.449379
$94$	18.9836	1.95801
$95$	7.02176	0.720418
$96$	−24.1704	−2.46688
$97$	−10.8233	−1.09894	−0.549472	−	0.835512i	$-0.685171\pi$
$97$	−10.8233	−1.09894	−0.549472	+	0.835512i	$0.685171\pi$
$98$	−35.4452	−3.58051
$99$	−1.68160	−0.169007
$100$	9.19648	0.919648
$101$	−16.5500	−1.64678	−0.823391	−	0.567474i	$-0.807921\pi$
$101$	−16.5500	−1.64678	−0.823391	+	0.567474i	$0.807921\pi$
$102$	6.36291	0.630022
$103$	−8.65080	−0.852389	−0.426194	−	0.904632i	$-0.640146\pi$
$103$	−8.65080	−0.852389	−0.426194	+	0.904632i	$0.640146\pi$
$104$	6.05383	0.593627
$105$	−28.8138	−2.81194
$106$	−1.68250	−0.163419
$107$	0.593355	0.0573618	0.0286809	−	0.999589i	$-0.490869\pi$
$107$	0.593355	0.0573618	0.0286809	+	0.999589i	$0.490869\pi$
$108$	−1.97612	−0.190152
$109$	10.3588	0.992189	0.496095	−	0.868268i	$-0.334767\pi$
$109$	10.3588	0.992189	0.496095	+	0.868268i	$0.334767\pi$
$110$	4.07560	0.388594
$111$	−4.87271	−0.462498
$112$	−42.8320	−4.04724
$113$	2.09971	0.197524	0.0987620	−	0.995111i	$-0.468512\pi$
$113$	2.09971	0.197524	0.0987620	+	0.995111i	$0.468512\pi$
$114$	−16.8106	−1.57445
$115$	−6.19716	−0.577888
$116$	−3.70031	−0.343565
$117$	−2.34616	−0.216902
$118$	−15.6875	−1.44415
$119$	4.58616	0.420413
$120$	−46.3577	−4.23186
$121$	−10.6468	−0.967890
$122$	24.2978	2.19982
$123$	−12.1038	−1.09136
$124$	8.61519	0.773666
$125$	−8.11039	−0.725415
$126$	33.4821	2.98283
$127$	0.929189	0.0824522	0.0412261	−	0.999150i	$-0.486874\pi$
$127$	0.929189	0.0824522	0.0412261	+	0.999150i	$0.486874\pi$
$128$	1.17533	0.103886
$129$	−8.69975	−0.765970
$130$	5.68626	0.498718
$131$	−4.55154	−0.397670	−0.198835	−	0.980033i	$-0.563716\pi$
$131$	−4.55154	−0.397670	−0.198835	+	0.980033i	$0.563716\pi$
$132$	−6.88741	−0.599472
$133$	−12.1165	−1.05063
$134$	−20.8533	−1.80145
$135$	−1.08272	−0.0931857
$136$	7.37856	0.632706
$137$	−8.96144	−0.765627	−0.382814	−	0.923826i	$-0.625045\pi$
$137$	−8.96144	−0.765627	−0.382814	+	0.923826i	$0.625045\pi$
$138$	14.8364	1.26296
$139$	−16.9947	−1.44147	−0.720735	−	0.693211i	$-0.756196\pi$
$139$	−16.9947	−1.44147	−0.720735	+	0.693211i	$0.756196\pi$
$140$	−57.2810	−4.84113
$141$	−17.5770	−1.48025
$142$	−27.3326	−2.29370
$143$	0.492795	0.0412096
$144$	26.7065	2.22554
$145$	−2.02741	−0.168367
$146$	6.50769	0.538580
$147$	32.8189	2.70685
$148$	−9.68682	−0.796252
$149$	−2.58663	−0.211905	−0.105952	−	0.994371i	$-0.533789\pi$
$149$	−2.58663	−0.211905	−0.105952	+	0.994371i	$0.533789\pi$
$150$	−12.0631	−0.984950
$151$	−2.75085	−0.223861	−0.111931	−	0.993716i	$-0.535703\pi$
$151$	−2.75085	−0.223861	−0.111931	+	0.993716i	$0.535703\pi$
$152$	−19.4939	−1.58116
$153$	−2.85956	−0.231181
$154$	−7.03270	−0.566711
$155$	4.72027	0.379141
$156$	−9.60928	−0.769358
$157$	−8.98512	−0.717090	−0.358545	−	0.933512i	$-0.616727\pi$
$157$	−8.98512	−0.717090	−0.358545	+	0.933512i	$0.616727\pi$
$158$	−10.1119	−0.804458
$159$	1.55784	0.123544
$160$	−26.3267	−2.08131
$161$	10.6936	0.842772
$162$	24.7270	1.94273
$163$	−19.6728	−1.54089	−0.770447	−	0.637505i	$-0.779967\pi$
$163$	−19.6728	−1.54089	−0.770447	+	0.637505i	$0.779967\pi$
$164$	−24.0620	−1.87893
$165$	−3.77362	−0.293776
$166$	37.8632	2.93876
$167$	7.11554	0.550617	0.275308	−	0.961356i	$-0.411220\pi$
$167$	7.11554	0.550617	0.275308	+	0.961356i	$0.411220\pi$
$168$	79.9930	6.17160
$169$	−12.3125	−0.947112
$170$	6.93056	0.531550
$171$	7.55484	0.577733
$172$	−17.2949	−1.31872
$173$	6.17321	0.469340	0.234670	−	0.972075i	$-0.424599\pi$
$173$	6.17321	0.469340	0.234670	+	0.972075i	$0.424599\pi$
$174$	4.85374	0.367961
$175$	−8.69469	−0.657256
$176$	−5.60953	−0.422834
$177$	14.5251	1.09178
$178$	−12.1234	−0.908686
$179$	0.566466	0.0423397	0.0211698	−	0.999776i	$-0.493261\pi$
$179$	0.566466	0.0423397	0.0211698	+	0.999776i	$0.493261\pi$
$180$	35.7157	2.66209
$181$	9.81047	0.729207	0.364603	−	0.931163i	$-0.381205\pi$
$181$	9.81047	0.729207	0.364603	+	0.931163i	$0.381205\pi$
$182$	−9.81199	−0.727313
$183$	−22.4974	−1.66306
$184$	17.2046	1.26834
$185$	−5.30742	−0.390209
$186$	−11.3006	−0.828603
$187$	0.600631	0.0439225
$188$	−34.9426	−2.54845
$189$	1.86830	0.135899
$190$	−18.3103	−1.32837
$191$	5.62235	0.406819	0.203410	−	0.979094i	$-0.434798\pi$
$191$	5.62235	0.406819	0.203410	+	0.979094i	$0.434798\pi$
$192$	17.4498	1.25933
$193$	−9.70068	−0.698270	−0.349135	−	0.937072i	$-0.613525\pi$
$193$	−9.70068	−0.698270	−0.349135	+	0.937072i	$0.613525\pi$
$194$	28.2234	2.02633
$195$	−5.26494	−0.377030
$196$	65.2430	4.66022
$197$	17.5723	1.25198	0.625988	−	0.779833i	$-0.284696\pi$
$197$	17.5723	1.25198	0.625988	+	0.779833i	$0.284696\pi$
$198$	4.38502	0.311630
$199$	−10.1861	−0.722074	−0.361037	−	0.932552i	$-0.617577\pi$
$199$	−10.1861	−0.722074	−0.361037	+	0.932552i	$0.617577\pi$
$200$	−13.9887	−0.989147
$201$	19.3082	1.36189
$202$	43.1565	3.03648
$203$	3.49841	0.245540
$204$	−11.7120	−0.820006
$205$	−13.1836	−0.920782
$206$	22.5582	1.57171
$207$	−6.66764	−0.463433
$208$	−7.82639	−0.542662
$209$	−1.58684	−0.109764
$210$	75.1362	5.18489
$211$	8.13683	0.560163	0.280081	−	0.959976i	$-0.409639\pi$
$211$	8.13683	0.560163	0.280081	+	0.959976i	$0.409639\pi$
$212$	3.09694	0.212698
$213$	25.3074	1.73404
$214$	−1.54726	−0.105769
$215$	−9.47588	−0.646250
$216$	3.00585	0.204523
$217$	−8.14511	−0.552926
$218$	−27.0120	−1.82948
$219$	−6.02550	−0.407165
$220$	−7.50185	−0.505775
$221$	0.837997	0.0563698
$222$	12.7063	0.852792
$223$	11.6484	0.780031	0.390016	−	0.920808i	$-0.372470\pi$
$223$	11.6484	0.780031	0.390016	+	0.920808i	$0.372470\pi$
$224$	45.4283	3.03531
$225$	5.42129	0.361420
$226$	−5.47530	−0.364212
$227$	18.9056	1.25481	0.627405	−	0.778693i	$-0.284117\pi$
$227$	18.9056	1.25481	0.627405	+	0.778693i	$0.284117\pi$
$228$	30.9428	2.04923
$229$	19.5211	1.28999	0.644994	−	0.764187i	$-0.276860\pi$
$229$	19.5211	1.28999	0.644994	+	0.764187i	$0.276860\pi$
$230$	16.1600	1.06556
$231$	6.51161	0.428432
$232$	5.62850	0.369529
$233$	3.55597	0.232960	0.116480	−	0.993193i	$-0.462839\pi$
$233$	3.55597	0.232960	0.116480	+	0.993193i	$0.462839\pi$
$234$	6.11795	0.399943
$235$	−19.1451	−1.24889
$236$	28.8756	1.87964
$237$	9.36263	0.608168
$238$	−11.9591	−0.775193
$239$	1.42524	0.0921913	0.0460957	−	0.998937i	$-0.485322\pi$
$239$	1.42524	0.0921913	0.0460957	+	0.998937i	$0.485322\pi$
$240$	59.9312	3.86854
$241$	−30.2844	−1.95079	−0.975396	−	0.220461i	$-0.929244\pi$
$241$	−30.2844	−1.95079	−0.975396	+	0.220461i	$0.929244\pi$
$242$	27.7631	1.78468
$243$	−21.6597	−1.38947
$244$	−44.7243	−2.86318
$245$	35.7467	2.28377
$246$	31.5624	2.01234
$247$	−2.21396	−0.140871
$248$	−13.1045	−0.832134
$249$	−35.0577	−2.22169
$250$	21.1490	1.33758
$251$	4.33317	0.273507	0.136754	−	0.990605i	$-0.456333\pi$
$251$	4.33317	0.273507	0.136754	+	0.990605i	$0.456333\pi$
$252$	−61.6297	−3.88230
$253$	1.40049	0.0880482
$254$	−2.42300	−0.152032
$255$	−6.41704	−0.401850
$256$	−17.5195	−1.09497
$257$	−19.9935	−1.24716	−0.623580	−	0.781759i	$-0.714322\pi$
$257$	−19.9935	−1.24716	−0.623580	+	0.781759i	$0.714322\pi$
$258$	22.6859	1.41236
$259$	9.15827	0.569067
$260$	−10.4666	−0.649108
$261$	−2.18132	−0.135020
$262$	11.8688	0.733258
$263$	−19.8907	−1.22651	−0.613256	−	0.789884i	$-0.710141\pi$
$263$	−19.8907	−1.22651	−0.613256	+	0.789884i	$0.710141\pi$
$264$	10.4764	0.644775
$265$	1.69682	0.104235
$266$	31.5955	1.93724
$267$	11.2251	0.686965
$268$	38.3841	2.34468
$269$	8.23458	0.502071	0.251035	−	0.967978i	$-0.419229\pi$
$269$	8.23458	0.502071	0.251035	+	0.967978i	$0.419229\pi$
$270$	2.82335	0.171824
$271$	16.7771	1.01914	0.509568	−	0.860431i	$-0.329805\pi$
$271$	16.7771	1.01914	0.509568	+	0.860431i	$0.329805\pi$
$272$	−9.53899	−0.578386
$273$	9.08496	0.549847
$274$	23.3683	1.41173
$275$	−1.13871	−0.0686666
$276$	−27.3090	−1.64381
$277$	−6.28345	−0.377536	−0.188768	−	0.982022i	$-0.560449\pi$
$277$	−6.28345	−0.377536	−0.188768	+	0.982022i	$0.560449\pi$
$278$	44.3161	2.65790
$279$	5.07862	0.304049
$280$	87.1294	5.20698
$281$	1.08842	0.0649300	0.0324650	−	0.999473i	$-0.489664\pi$
$281$	1.08842	0.0649300	0.0324650	+	0.999473i	$0.489664\pi$
$282$	45.8346	2.72941
$283$	−24.5552	−1.45966	−0.729828	−	0.683630i	$-0.760400\pi$
$283$	−24.5552	−1.45966	−0.729828	+	0.683630i	$0.760400\pi$
$284$	50.3104	2.98538
$285$	16.9536	1.00424
$286$	−1.28504	−0.0759857
$287$	22.7491	1.34284
$288$	−28.3254	−1.66909
$289$	−15.9786	−0.939919
$290$	5.28676	0.310449
$291$	−26.1322	−1.53190
$292$	−11.9785	−0.700990
$293$	23.7187	1.38566	0.692830	−	0.721101i	$-0.256364\pi$
$293$	23.7187	1.38566	0.692830	+	0.721101i	$0.256364\pi$
$294$	−85.5800	−4.99113
$295$	15.8209	0.921131
$296$	14.7345	0.856426
$297$	0.244683	0.0141980
$298$	6.74502	0.390728
$299$	1.95396	0.113001
$300$	22.2043	1.28196
$301$	16.3512	0.942467
$302$	7.17325	0.412774
$303$	−39.9588	−2.29557
$304$	25.2017	1.44541
$305$	−24.5045	−1.40312
$306$	7.45671	0.426272
$307$	−14.6100	−0.833834	−0.416917	−	0.908944i	$-0.636890\pi$
$307$	−14.6100	−0.833834	−0.416917	+	0.908944i	$0.636890\pi$
$308$	12.9449	0.737604
$309$	−20.8868	−1.18821
$310$	−12.3088	−0.699093
$311$	11.9943	0.680135	0.340067	−	0.940401i	$-0.389550\pi$
$311$	11.9943	0.680135	0.340067	+	0.940401i	$0.389550\pi$
$312$	14.6166	0.827500
$313$	−15.8273	−0.894611	−0.447305	−	0.894381i	$-0.647616\pi$
$313$	−15.8273	−0.894611	−0.447305	+	0.894381i	$0.647616\pi$
$314$	23.4300	1.32223
$315$	−33.7670	−1.90255
$316$	18.6126	1.04704
$317$	3.85388	0.216455	0.108228	−	0.994126i	$-0.465482\pi$
$317$	3.85388	0.216455	0.108228	+	0.994126i	$0.465482\pi$
$318$	−4.06229	−0.227802
$319$	0.458172	0.0256527
$320$	19.0066	1.06250
$321$	1.43262	0.0799608
$322$	−27.8851	−1.55397
$323$	−2.69843	−0.150144
$324$	−45.5142	−2.52857
$325$	−1.58872	−0.0881262
$326$	51.2997	2.84123
$327$	25.0105	1.38308
$328$	36.6004	2.02092
$329$	33.0360	1.82133
$330$	9.84027	0.541689
$331$	−12.3675	−0.679782	−0.339891	−	0.940465i	$-0.610390\pi$
$331$	−12.3675	−0.679782	−0.339891	+	0.940465i	$0.610390\pi$
$332$	−69.6938	−3.82494
$333$	−5.71035	−0.312925
$334$	−18.5548	−1.01527
$335$	21.0307	1.14903
$336$	−103.415	−5.64175
$337$	32.0791	1.74746	0.873729	−	0.486413i	$-0.161695\pi$
$337$	32.0791	1.74746	0.873729	+	0.486413i	$0.161695\pi$
$338$	32.1065	1.74637
$339$	5.06960	0.275343
$340$	−12.7569	−0.691840
$341$	−1.06673	−0.0577667
$342$	−19.7004	−1.06527
$343$	−29.9176	−1.61540
$344$	26.3070	1.41838
$345$	−14.9626	−0.805561
$346$	−16.0975	−0.865410
$347$	−10.6965	−0.574221	−0.287110	−	0.957898i	$-0.592695\pi$
$347$	−10.6965	−0.574221	−0.287110	+	0.957898i	$0.592695\pi$
$348$	−8.93415	−0.478921
$349$	−7.21644	−0.386287	−0.193143	−	0.981171i	$-0.561868\pi$
$349$	−7.21644	−0.386287	−0.193143	+	0.981171i	$0.561868\pi$
$350$	22.6727	1.21191
$351$	0.341381	0.0182216
$352$	5.94955	0.317112
$353$	−3.43197	−0.182665	−0.0913327	−	0.995820i	$-0.529113\pi$
$353$	−3.43197	−0.182665	−0.0913327	+	0.995820i	$0.529113\pi$
$354$	−37.8764	−2.01311
$355$	27.5652	1.46301
$356$	22.3152	1.18270
$357$	11.0730	0.586044
$358$	−1.47714	−0.0780695
$359$	1.68062	0.0886997	0.0443498	−	0.999016i	$-0.485878\pi$
$359$	1.68062	0.0886997	0.0443498	+	0.999016i	$0.485878\pi$
$360$	−54.3268	−2.86327
$361$	−11.8709	−0.624782
$362$	−25.5823	−1.34457
$363$	−25.7060	−1.34921
$364$	18.0607	0.946636
$365$	−6.56305	−0.343526
$366$	58.6654	3.06649
$367$	3.50896	0.183166	0.0915832	−	0.995797i	$-0.470807\pi$
$367$	3.50896	0.183166	0.0915832	+	0.995797i	$0.470807\pi$
$368$	−22.2421	−1.15945
$369$	−14.1845	−0.738414
$370$	13.8399	0.719501
$371$	−2.92796	−0.152012
$372$	20.8008	1.07847
$373$	−29.9999	−1.55334	−0.776668	−	0.629910i	$-0.783092\pi$
$373$	−29.9999	−1.55334	−0.776668	+	0.629910i	$0.783092\pi$
$374$	−1.56623	−0.0809880
$375$	−19.5820	−1.01121
$376$	53.1508	2.74104
$377$	0.639240	0.0329225
$378$	−4.87186	−0.250581
$379$	−3.79837	−0.195109	−0.0975547	−	0.995230i	$-0.531102\pi$
$379$	−3.79837	−0.195109	−0.0975547	+	0.995230i	$0.531102\pi$
$380$	33.7032	1.72894
$381$	2.24346	0.114936
$382$	−14.6611	−0.750128
$383$	21.5141	1.09932	0.549660	−	0.835388i	$-0.314757\pi$
$383$	21.5141	1.09932	0.549660	+	0.835388i	$0.314757\pi$
$384$	2.83776	0.144814
$385$	7.09252	0.361469
$386$	25.2959	1.28753
$387$	−10.1953	−0.518255
$388$	−51.9501	−2.63737
$389$	−16.4481	−0.833954	−0.416977	−	0.908917i	$-0.636910\pi$
$389$	−16.4481	−0.833954	−0.416977	+	0.908917i	$0.636910\pi$
$390$	13.7291	0.695200
$391$	2.38154	0.120439
$392$	−99.2404	−5.01240
$393$	−10.9894	−0.554341
$394$	−45.8224	−2.30850
$395$	10.1979	0.513112
$396$	−8.07138	−0.405602
$397$	18.2563	0.916256	0.458128	−	0.888886i	$-0.348520\pi$
$397$	18.2563	0.916256	0.458128	+	0.888886i	$0.348520\pi$
$398$	26.5618	1.33142
$399$	−29.2544	−1.46455
$400$	18.0845	0.904226
$401$	17.9524	0.896498	0.448249	−	0.893909i	$-0.352048\pi$
$401$	17.9524	0.896498	0.448249	+	0.893909i	$0.352048\pi$
$402$	−50.3489	−2.51118
$403$	−1.48830	−0.0741374
$404$	−79.4369	−3.95213
$405$	−24.9373	−1.23914
$406$	−9.12262	−0.452748
$407$	1.19942	0.0594531
$408$	17.8150	0.881975
$409$	26.0104	1.28613	0.643065	−	0.765811i	$-0.277662\pi$
$409$	26.0104	1.28613	0.643065	+	0.765811i	$0.277662\pi$
$410$	34.3782	1.69782
$411$	−21.6368	−1.06726
$412$	−41.5223	−2.04566
$413$	−27.3000	−1.34334
$414$	17.3869	0.854517
$415$	−38.1853	−1.87444
$416$	8.30079	0.406980
$417$	−41.0325	−2.00937
$418$	4.13793	0.202393
$419$	13.7257	0.670543	0.335271	−	0.942122i	$-0.391172\pi$
$419$	13.7257	0.670543	0.335271	+	0.942122i	$0.391172\pi$
$420$	−138.301	−6.74840
$421$	9.78121	0.476707	0.238354	−	0.971178i	$-0.423392\pi$
$421$	9.78121	0.476707	0.238354	+	0.971178i	$0.423392\pi$
$422$	−21.2180	−1.03288
$423$	−20.5986	−1.00154
$424$	−4.71071	−0.228772
$425$	−1.93637	−0.0939277
$426$	−65.9928	−3.19736
$427$	42.2840	2.04626
$428$	2.84800	0.137663
$429$	1.18982	0.0574450
$430$	24.7097	1.19161
$431$	20.5653	0.990594	0.495297	−	0.868724i	$-0.335059\pi$
$431$	20.5653	0.990594	0.495297	+	0.868724i	$0.335059\pi$
$432$	−3.88597	−0.186964
$433$	4.74687	0.228120	0.114060	−	0.993474i	$-0.463614\pi$
$433$	4.74687	0.228120	0.114060	+	0.993474i	$0.463614\pi$
$434$	21.2396	1.01953
$435$	−4.89503	−0.234699
$436$	49.7202	2.38117
$437$	−6.29193	−0.300984
$438$	15.7124	0.750766
$439$	18.0359	0.860805	0.430402	−	0.902637i	$-0.358372\pi$
$439$	18.0359	0.860805	0.430402	+	0.902637i	$0.358372\pi$
$440$	11.4110	0.543997
$441$	38.4605	1.83145
$442$	−2.18520	−0.103939
$443$	32.3603	1.53749	0.768743	−	0.639558i	$-0.220883\pi$
$443$	32.3603	1.53749	0.768743	+	0.639558i	$0.220883\pi$
$444$	−23.3882	−1.10995
$445$	12.2265	0.579593
$446$	−30.3748	−1.43829
$447$	−6.24524	−0.295390
$448$	−32.7970	−1.54951
$449$	−5.29302	−0.249793	−0.124896	−	0.992170i	$-0.539860\pi$
$449$	−5.29302	−0.249793	−0.124896	+	0.992170i	$0.539860\pi$
$450$	−14.1368	−0.666416
$451$	2.97935	0.140292
$452$	10.0782	0.474040
$453$	−6.64175	−0.312057
$454$	−49.2992	−2.31373
$455$	9.89546	0.463906
$456$	−47.0666	−2.20410
$457$	−10.1181	−0.473306	−0.236653	−	0.971594i	$-0.576050\pi$
$457$	−10.1181	−0.473306	−0.236653	+	0.971594i	$0.576050\pi$
$458$	−50.9041	−2.37859
$459$	0.416083	0.0194211
$460$	−29.7453	−1.38688
$461$	−5.10605	−0.237813	−0.118906	−	0.992905i	$-0.537939\pi$
$461$	−5.10605	−0.237813	−0.118906	+	0.992905i	$0.537939\pi$
$462$	−16.9800	−0.789980
$463$	−5.07756	−0.235974	−0.117987	−	0.993015i	$-0.537644\pi$
$463$	−5.07756	−0.235974	−0.117987	+	0.993015i	$0.537644\pi$
$464$	−7.27652	−0.337804
$465$	11.3968	0.528513
$466$	−9.27272	−0.429551
$467$	20.8121	0.963068	0.481534	−	0.876427i	$-0.340080\pi$
$467$	20.8121	0.963068	0.481534	+	0.876427i	$0.340080\pi$
$468$	−11.2611	−0.520547
$469$	−36.2898	−1.67571
$470$	49.9237	2.30281
$471$	−21.6939	−0.999604
$472$	−43.9222	−2.02169
$473$	2.14145	0.0984639
$474$	−24.4144	−1.12139
$475$	5.11582	0.234730
$476$	22.0128	1.00895
$477$	1.82563	0.0835900
$478$	−3.71653	−0.169990
$479$	−22.1638	−1.01269	−0.506344	−	0.862331i	$-0.669004\pi$
$479$	−22.1638	−1.01269	−0.506344	+	0.862331i	$0.669004\pi$
$480$	−63.5640	−2.90129
$481$	1.67343	0.0763017
$482$	78.9711	3.59704
$483$	25.8189	1.17480
$484$	−51.1027	−2.32285
$485$	−28.4635	−1.29246
$486$	56.4808	2.56202
$487$	−28.0868	−1.27273	−0.636367	−	0.771387i	$-0.719564\pi$
$487$	−28.0868	−1.27273	−0.636367	+	0.771387i	$0.719564\pi$
$488$	68.0296	3.07955
$489$	−47.4986	−2.14796
$490$	−93.2149	−4.21102
$491$	38.0261	1.71609	0.858047	−	0.513571i	$-0.171678\pi$
$491$	38.0261	1.71609	0.858047	+	0.513571i	$0.171678\pi$
$492$	−58.0960	−2.61917
$493$	0.779121	0.0350898
$494$	5.77322	0.259749
$495$	−4.42232	−0.198768
$496$	16.9414	0.760692
$497$	−47.5653	−2.13360
$498$	91.4182	4.09655
$499$	3.74140	0.167488	0.0837441	−	0.996487i	$-0.473312\pi$
$499$	3.74140	0.167488	0.0837441	+	0.996487i	$0.473312\pi$
$500$	−38.9284	−1.74093
$501$	17.1800	0.767545
$502$	−11.2994	−0.504316
$503$	−14.6117	−0.651503	−0.325752	−	0.945455i	$-0.605617\pi$
$503$	−14.6117	−0.651503	−0.325752	+	0.945455i	$0.605617\pi$
$504$	93.7441	4.17569
$505$	−43.5236	−1.93677
$506$	−3.65199	−0.162351
$507$	−29.7276	−1.32025
$508$	4.45994	0.197878
$509$	−11.8894	−0.526988	−0.263494	−	0.964661i	$-0.584875\pi$
$509$	−11.8894	−0.526988	−0.263494	+	0.964661i	$0.584875\pi$
$510$	16.7334	0.740966
$511$	11.3249	0.500985
$512$	43.3339	1.91511
$513$	−1.09928	−0.0485343
$514$	52.1360	2.29962
$515$	−22.7501	−1.00249
$516$	−41.7573	−1.83826
$517$	4.32659	0.190283
$518$	−23.8816	−1.04930
$519$	14.9048	0.654248
$520$	15.9205	0.698162
$521$	−33.8825	−1.48442	−0.742210	−	0.670168i	$-0.766222\pi$
$521$	−33.8825	−1.48442	−0.742210	+	0.670168i	$0.766222\pi$
$522$	5.68812	0.248962
$523$	32.8367	1.43585	0.717924	−	0.696122i	$-0.245093\pi$
$523$	32.8367	1.43585	0.717924	+	0.696122i	$0.245093\pi$
$524$	−21.8466	−0.954373
$525$	−20.9927	−0.916198
$526$	51.8679	2.26155
$527$	−1.81397	−0.0790180
$528$	−13.5438	−0.589419
$529$	−17.4470	−0.758564
$530$	−4.42470	−0.192196
$531$	17.0220	0.738694
$532$	−58.1570	−2.52142
$533$	4.15678	0.180050
$534$	−29.2711	−1.26668
$535$	1.56042	0.0674630
$536$	−58.3856	−2.52188
$537$	1.36769	0.0590203
$538$	−21.4729	−0.925761
$539$	−8.07838	−0.347960
$540$	−5.19686	−0.223637
$541$	0.962887	0.0413977	0.0206989	−	0.999786i	$-0.493411\pi$
$541$	0.962887	0.0413977	0.0206989	+	0.999786i	$0.493411\pi$
$542$	−43.7487	−1.87917
$543$	23.6867	1.01649
$544$	10.1172	0.433772
$545$	27.2418	1.16691
$546$	−23.6904	−1.01385
$547$	−31.6948	−1.35517	−0.677585	−	0.735445i	$-0.736973\pi$
$547$	−31.6948	−1.35517	−0.677585	+	0.735445i	$0.736973\pi$
$548$	−43.0133	−1.83744
$549$	−26.3648	−1.12522
$550$	2.96935	0.126613
$551$	−2.05841	−0.0876912
$552$	41.5394	1.76803
$553$	−17.5971	−0.748304
$554$	16.3850	0.696133
$555$	−12.8144	−0.543941
$556$	−81.5715	−3.45940
$557$	11.6256	0.492594	0.246297	−	0.969194i	$-0.420786\pi$
$557$	11.6256	0.492594	0.246297	+	0.969194i	$0.420786\pi$
$558$	−13.2433	−0.560632
$559$	2.98774	0.126368
$560$	−112.641	−4.75994
$561$	1.45018	0.0612267
$562$	−2.83823	−0.119723
$563$	4.53802	0.191255	0.0956274	−	0.995417i	$-0.469514\pi$
$563$	4.53802	0.191255	0.0956274	+	0.995417i	$0.469514\pi$
$564$	−84.3665	−3.55247
$565$	5.52188	0.232307
$566$	64.0314	2.69144
$567$	43.0308	1.80712
$568$	−76.5266	−3.21099
$569$	−7.13856	−0.299264	−0.149632	−	0.988742i	$-0.547809\pi$
$569$	−7.13856	−0.299264	−0.149632	+	0.988742i	$0.547809\pi$
$570$	−44.2089	−1.85171
$571$	25.1106	1.05085	0.525423	−	0.850841i	$-0.323907\pi$
$571$	25.1106	1.05085	0.525423	+	0.850841i	$0.323907\pi$
$572$	2.36533	0.0988994
$573$	13.5748	0.567095
$574$	−59.3216	−2.47603
$575$	−4.51504	−0.188290
$576$	20.4495	0.852064
$577$	−33.1353	−1.37944	−0.689719	−	0.724077i	$-0.742266\pi$
$577$	−33.1353	−1.37944	−0.689719	+	0.724077i	$0.742266\pi$
$578$	41.6666	1.73310
$579$	−23.4216	−0.973370
$580$	−9.73119	−0.404066
$581$	65.8910	2.73362
$582$	68.1436	2.82464
$583$	−0.383462	−0.0158814
$584$	18.2204	0.753965
$585$	−6.17000	−0.255098
$586$	−61.8500	−2.55500
$587$	29.6817	1.22510	0.612548	−	0.790433i	$-0.290145\pi$
$587$	29.6817	1.22510	0.612548	+	0.790433i	$0.290145\pi$
$588$	157.525	6.49621
$589$	4.79245	0.197470
$590$	−41.2555	−1.69846
$591$	42.4272	1.74522
$592$	−19.0488	−0.782899
$593$	42.3315	1.73835	0.869174	−	0.494506i	$-0.164651\pi$
$593$	42.3315	1.73835	0.869174	+	0.494506i	$0.164651\pi$
$594$	−0.638047	−0.0261794
$595$	12.0608	0.494446
$596$	−12.4154	−0.508553
$597$	−24.5937	−1.00655
$598$	−5.09524	−0.208360
$599$	27.4852	1.12301	0.561507	−	0.827472i	$-0.310222\pi$
$599$	27.4852	1.12301	0.561507	+	0.827472i	$0.310222\pi$
$600$	−33.7746	−1.37884
$601$	25.3698	1.03486	0.517428	−	0.855727i	$-0.326890\pi$
$601$	25.3698	1.03486	0.517428	+	0.855727i	$0.326890\pi$
$602$	−42.6381	−1.73780
$603$	22.6273	0.921456
$604$	−13.2036	−0.537247
$605$	−27.9992	−1.13833
$606$	104.198	4.23277
$607$	9.52289	0.386522	0.193261	−	0.981147i	$-0.438094\pi$
$607$	9.52289	0.386522	0.193261	+	0.981147i	$0.438094\pi$
$608$	−26.7293	−1.08402
$609$	8.44667	0.342276
$610$	63.8991	2.58720
$611$	6.03644	0.244208
$612$	−13.7254	−0.554815
$613$	−13.3540	−0.539362	−0.269681	−	0.962950i	$-0.586918\pi$
$613$	−13.3540	−0.539362	−0.269681	+	0.962950i	$0.586918\pi$
$614$	38.0976	1.53749
$615$	−31.8309	−1.28354
$616$	−19.6903	−0.793346
$617$	16.1269	0.649246	0.324623	−	0.945844i	$-0.394763\pi$
$617$	16.1269	0.649246	0.324623	+	0.945844i	$0.394763\pi$
$618$	54.4653	2.19092
$619$	8.22051	0.330410	0.165205	−	0.986259i	$-0.447171\pi$
$619$	8.22051	0.330410	0.165205	+	0.986259i	$0.447171\pi$
$620$	22.6565	0.909906
$621$	0.970183	0.0389321
$622$	−31.2769	−1.25409
$623$	−21.0976	−0.845257
$624$	−18.8963	−0.756456
$625$	−30.9089	−1.23636
$626$	41.2720	1.64956
$627$	−3.83133	−0.153008
$628$	−43.1270	−1.72095
$629$	2.03961	0.0813247
$630$	88.0523	3.50809
$631$	42.1930	1.67968	0.839839	−	0.542836i	$-0.182649\pi$
$631$	42.1930	1.67968	0.839839	+	0.542836i	$0.182649\pi$
$632$	−28.3115	−1.12617
$633$	19.6458	0.780852
$634$	−10.0495	−0.399119
$635$	2.44361	0.0969716
$636$	7.47734	0.296496
$637$	−11.2709	−0.446570
$638$	−1.19475	−0.0473007
$639$	29.6578	1.17325
$640$	3.09092	0.122179
$641$	4.46092	0.176196	0.0880979	−	0.996112i	$-0.471921\pi$
$641$	4.46092	0.176196	0.0880979	+	0.996112i	$0.471921\pi$
$642$	−3.73576	−0.147439
$643$	−21.8852	−0.863068	−0.431534	−	0.902097i	$-0.642028\pi$
$643$	−21.8852	−0.863068	−0.431534	+	0.902097i	$0.642028\pi$
$644$	51.3273	2.02258
$645$	−22.8789	−0.900854
$646$	7.03654	0.276849
$647$	−28.1504	−1.10671	−0.553353	−	0.832947i	$-0.686652\pi$
$647$	−28.1504	−1.10671	−0.553353	+	0.832947i	$0.686652\pi$
$648$	69.2312	2.71966
$649$	−3.57537	−0.140345
$650$	4.14282	0.162495
$651$	−19.6658	−0.770764
$652$	−94.4260	−3.69801
$653$	39.1484	1.53200	0.765999	−	0.642842i	$-0.222245\pi$
$653$	39.1484	1.53200	0.765999	+	0.642842i	$0.222245\pi$
$654$	−65.2186	−2.55025
$655$	−11.9698	−0.467698
$656$	−47.3169	−1.84742
$657$	−7.06130	−0.275488
$658$	−86.1463	−3.35833
$659$	15.0866	0.587690	0.293845	−	0.955853i	$-0.405065\pi$
$659$	15.0866	0.587690	0.293845	+	0.955853i	$0.405065\pi$
$660$	−18.1127	−0.705036
$661$	−21.9281	−0.852904	−0.426452	−	0.904510i	$-0.640237\pi$
$661$	−21.9281	−0.852904	−0.426452	+	0.904510i	$0.640237\pi$
$662$	32.2502	1.25344
$663$	2.02329	0.0785780
$664$	106.010	4.11400
$665$	−31.8643	−1.23564
$666$	14.8906	0.576998
$667$	1.81668	0.0703421
$668$	34.1533	1.32143
$669$	28.1241	1.08734
$670$	−54.8407	−2.11868
$671$	5.53775	0.213783
$672$	109.684	4.23113
$673$	18.3366	0.706824	0.353412	−	0.935468i	$-0.385021\pi$
$673$	18.3366	0.706824	0.353412	+	0.935468i	$0.385021\pi$
$674$	−83.6509	−3.22211
$675$	−0.788832	−0.0303622
$676$	−59.0976	−2.27299
$677$	−28.0480	−1.07797	−0.538986	−	0.842315i	$-0.681192\pi$
$677$	−28.0480	−1.07797	−0.538986	+	0.842315i	$0.681192\pi$
$678$	−13.2197	−0.507701
$679$	49.1155	1.88488
$680$	19.4044	0.744123
$681$	45.6463	1.74917
$682$	2.78166	0.106515
$683$	28.9695	1.10849	0.554244	−	0.832354i	$-0.313008\pi$
$683$	28.9695	1.10849	0.554244	+	0.832354i	$0.313008\pi$
$684$	36.2619	1.38651
$685$	−23.5670	−0.900451
$686$	78.0146	2.97861
$687$	47.1323	1.79821
$688$	−34.0097	−1.29661
$689$	−0.535005	−0.0203821
$690$	39.0173	1.48536
$691$	−45.7338	−1.73980	−0.869899	−	0.493231i	$-0.835816\pi$
$691$	−45.7338	−1.73980	−0.869899	+	0.493231i	$0.835816\pi$
$692$	29.6303	1.12638
$693$	7.63097	0.289877
$694$	27.8928	1.05880
$695$	−44.6931	−1.69531
$696$	13.5896	0.515114
$697$	5.06638	0.191903
$698$	18.8179	0.712269
$699$	8.58565	0.324739
$700$	−41.7330	−1.57736
$701$	−33.1944	−1.25373	−0.626867	−	0.779126i	$-0.715663\pi$
$701$	−33.1944	−1.25373	−0.626867	+	0.779126i	$0.715663\pi$
$702$	−0.890200	−0.0335985
$703$	−5.38858	−0.203234
$704$	−4.29529	−0.161885
$705$	−46.2245	−1.74092
$706$	8.94937	0.336814
$707$	75.1025	2.82452
$708$	69.7180	2.62016
$709$	−8.09949	−0.304183	−0.152091	−	0.988366i	$-0.548601\pi$
$709$	−8.09949	−0.304183	−0.152091	+	0.988366i	$0.548601\pi$
$710$	−71.8802	−2.69762
$711$	10.9721	0.411486
$712$	−33.9434	−1.27208
$713$	−4.22965	−0.158402
$714$	−28.8744	−1.08060
$715$	1.29597	0.0484664
$716$	2.71894	0.101611
$717$	3.44115	0.128512
$718$	−4.38246	−0.163552
$719$	38.1190	1.42160	0.710800	−	0.703394i	$-0.248333\pi$
$719$	38.1190	1.42160	0.710800	+	0.703394i	$0.248333\pi$
$720$	70.2336	2.61745
$721$	39.2567	1.46200
$722$	30.9550	1.15203
$723$	−73.1197	−2.71935
$724$	47.0886	1.75003
$725$	−1.47710	−0.0548580
$726$	67.0321	2.48779
$727$	33.1782	1.23051	0.615256	−	0.788328i	$-0.289053\pi$
$727$	33.1782	1.23051	0.615256	+	0.788328i	$0.289053\pi$
$728$	−27.4718	−1.01817
$729$	−23.8484	−0.883273
$730$	17.1141	0.633422
$731$	3.64153	0.134687
$732$	−107.984	−3.99119
$733$	25.6741	0.948296	0.474148	−	0.880445i	$-0.342756\pi$
$733$	25.6741	0.948296	0.474148	+	0.880445i	$0.342756\pi$
$734$	−9.15014	−0.337738
$735$	86.3080	3.18352
$736$	23.5903	0.869552
$737$	−4.75272	−0.175069
$738$	36.9881	1.36155
$739$	34.9507	1.28568	0.642842	−	0.765999i	$-0.277755\pi$
$739$	34.9507	1.28568	0.642842	+	0.765999i	$0.277755\pi$
$740$	−25.4747	−0.936468
$741$	−5.34545	−0.196370
$742$	7.63508	0.280292
$743$	−15.3428	−0.562873	−0.281437	−	0.959580i	$-0.590811\pi$
$743$	−15.3428	−0.562873	−0.281437	+	0.959580i	$0.590811\pi$
$744$	−31.6398	−1.15997
$745$	−6.80239	−0.249220
$746$	78.2292	2.86417
$747$	−41.0843	−1.50319
$748$	2.88292	0.105410
$749$	−2.69260	−0.0983856
$750$	51.0629	1.86455
$751$	−6.88451	−0.251219	−0.125610	−	0.992080i	$-0.540089\pi$
$751$	−6.88451	−0.251219	−0.125610	+	0.992080i	$0.540089\pi$
$752$	−68.7133	−2.50571
$753$	10.4621	0.381262
$754$	−1.66691	−0.0607053
$755$	−7.23427	−0.263282
$756$	8.96750	0.326145
$757$	−5.28301	−0.192014	−0.0960071	−	0.995381i	$-0.530607\pi$
$757$	−5.28301	−0.192014	−0.0960071	+	0.995381i	$0.530607\pi$
$758$	9.90482	0.359759
$759$	3.38140	0.122737
$760$	−51.2656	−1.85960
$761$	12.3751	0.448598	0.224299	−	0.974520i	$-0.427991\pi$
$761$	12.3751	0.448598	0.224299	+	0.974520i	$0.427991\pi$
$762$	−5.85016	−0.211929
$763$	−47.0073	−1.70178
$764$	26.9863	0.976330
$765$	−7.52015	−0.271891
$766$	−56.1013	−2.02702
$767$	−4.98833	−0.180118
$768$	−42.2996	−1.52635
$769$	−9.70012	−0.349795	−0.174898	−	0.984587i	$-0.555959\pi$
$769$	−9.70012	−0.349795	−0.174898	+	0.984587i	$0.555959\pi$
$770$	−18.4948	−0.666506
$771$	−48.2729	−1.73851
$772$	−46.5616	−1.67579
$773$	−4.88819	−0.175816	−0.0879079	−	0.996129i	$-0.528018\pi$
$773$	−4.88819	−0.175816	−0.0879079	+	0.996129i	$0.528018\pi$
$774$	26.5857	0.955602
$775$	3.43903	0.123533
$776$	79.0207	2.83668
$777$	22.1120	0.793265
$778$	42.8910	1.53772
$779$	−13.3852	−0.479574
$780$	−25.2708	−0.904839
$781$	−6.22943	−0.222907
$782$	−6.21021	−0.222077
$783$	0.317396	0.0113428
$784$	128.298	4.58207
$785$	−23.6293	−0.843367
$786$	28.6564	1.02214
$787$	41.9897	1.49677	0.748385	−	0.663265i	$-0.230830\pi$
$787$	41.9897	1.49677	0.748385	+	0.663265i	$0.230830\pi$
$788$	84.3440	3.00463
$789$	−48.0247	−1.70972
$790$	−26.5925	−0.946119
$791$	−9.52833	−0.338788
$792$	12.2773	0.436254
$793$	7.72625	0.274367
$794$	−47.6059	−1.68947
$795$	4.09684	0.145300
$796$	−48.8915	−1.73291
$797$	8.60848	0.304928	0.152464	−	0.988309i	$-0.451279\pi$
$797$	8.60848	0.304928	0.152464	+	0.988309i	$0.451279\pi$
$798$	76.2852	2.70047
$799$	7.35736	0.260285
$800$	−19.1807	−0.678141
$801$	13.1547	0.464800
$802$	−46.8134	−1.65304
$803$	1.48318	0.0523402
$804$	92.6759	3.26843
$805$	28.1223	0.991180
$806$	3.88096	0.136701
$807$	19.8818	0.699873
$808$	120.831	4.25080
$809$	−48.1882	−1.69421	−0.847103	−	0.531428i	$-0.821656\pi$
$809$	−48.1882	−1.69421	−0.847103	+	0.531428i	$0.821656\pi$
$810$	65.0277	2.28484
$811$	28.3311	0.994841	0.497420	−	0.867510i	$-0.334281\pi$
$811$	28.3311	0.994841	0.497420	+	0.867510i	$0.334281\pi$
$812$	16.7918	0.589275
$813$	40.5071	1.42065
$814$	−3.12767	−0.109625
$815$	−51.7361	−1.81224
$816$	−23.0312	−0.806255
$817$	−9.62079	−0.336589
$818$	−67.8259	−2.37148
$819$	10.6467	0.372026
$820$	−63.2789	−2.20980
$821$	−33.0175	−1.15232	−0.576160	−	0.817337i	$-0.695449\pi$
$821$	−33.0175	−1.15232	−0.576160	+	0.817337i	$0.695449\pi$
$822$	56.4211	1.96791
$823$	−20.3263	−0.708529	−0.354265	−	0.935145i	$-0.615269\pi$
$823$	−20.3263	−0.708529	−0.354265	+	0.935145i	$0.615269\pi$
$824$	63.1591	2.20025
$825$	−2.74933	−0.0957194
$826$	71.1888	2.47697
$827$	−21.0485	−0.731927	−0.365964	−	0.930629i	$-0.619261\pi$
$827$	−21.0485	−0.731927	−0.365964	+	0.930629i	$0.619261\pi$
$828$	−32.0035	−1.11220
$829$	−11.4022	−0.396014	−0.198007	−	0.980201i	$-0.563447\pi$
$829$	−11.4022	−0.396014	−0.198007	+	0.980201i	$0.563447\pi$
$830$	99.5738	3.45626
$831$	−15.1710	−0.526275
$832$	−5.99277	−0.207762
$833$	−13.7373	−0.475968
$834$	106.998	3.70505
$835$	18.7126	0.647578
$836$	−7.61657	−0.263425
$837$	−0.738971	−0.0255426
$838$	−35.7917	−1.23640
$839$	13.4920	0.465795	0.232898	−	0.972501i	$-0.425179\pi$
$839$	13.4920	0.465795	0.232898	+	0.972501i	$0.425179\pi$
$840$	210.368	7.25839
$841$	−28.4057	−0.979506
$842$	−25.5060	−0.878993
$843$	2.62793	0.0905106
$844$	39.0554	1.34434
$845$	−32.3797	−1.11389
$846$	53.7138	1.84672
$847$	48.3144	1.66010
$848$	6.09000	0.209132
$849$	−59.2869	−2.03472
$850$	5.04937	0.173192
$851$	4.75578	0.163026
$852$	121.471	4.16153
$853$	−28.3141	−0.969455	−0.484728	−	0.874665i	$-0.661081\pi$
$853$	−28.3141	−0.969455	−0.484728	+	0.874665i	$0.661081\pi$
$854$	−110.262	−3.77308
$855$	19.8679	0.679469
$856$	−4.33206	−0.148067
$857$	24.1554	0.825134	0.412567	−	0.910927i	$-0.364632\pi$
$857$	24.1554	0.825134	0.412567	+	0.910927i	$0.364632\pi$
$858$	−3.10263	−0.105922
$859$	16.5520	0.564746	0.282373	−	0.959305i	$-0.408878\pi$
$859$	16.5520	0.564746	0.282373	+	0.959305i	$0.408878\pi$
$860$	−45.4826	−1.55094
$861$	54.9261	1.87188
$862$	−53.6269	−1.82654
$863$	31.6185	1.07631	0.538154	−	0.842847i	$-0.319122\pi$
$863$	31.6185	1.07631	0.538154	+	0.842847i	$0.319122\pi$
$864$	4.12152	0.140217
$865$	16.2345	0.551989
$866$	−12.3782	−0.420627
$867$	−38.5793	−1.31022
$868$	−39.0951	−1.32697
$869$	−2.30462	−0.0781787
$870$	12.7645	0.432758
$871$	−6.63097	−0.224682
$872$	−75.6288	−2.56112
$873$	−30.6244	−1.03648
$874$	16.4071	0.554980
$875$	36.8043	1.24421
$876$	−28.9213	−0.977161
$877$	−42.7661	−1.44411	−0.722053	−	0.691837i	$-0.756802\pi$
$877$	−42.7661	−1.44411	−0.722053	+	0.691837i	$0.756802\pi$
$878$	−47.0312	−1.58722
$879$	57.2671	1.93157
$880$	−14.7521	−0.497293
$881$	−45.6028	−1.53640	−0.768199	−	0.640211i	$-0.778847\pi$
$881$	−45.6028	−1.53640	−0.768199	+	0.640211i	$0.778847\pi$
$882$	−100.292	−3.37699
$883$	−13.6025	−0.457759	−0.228880	−	0.973455i	$-0.573506\pi$
$883$	−13.6025	−0.457759	−0.228880	+	0.973455i	$0.573506\pi$
$884$	4.02224	0.135283
$885$	38.1986	1.28403
$886$	−84.3843	−2.83495
$887$	−21.5089	−0.722198	−0.361099	−	0.932528i	$-0.617598\pi$
$887$	−21.5089	−0.722198	−0.361099	+	0.932528i	$0.617598\pi$
$888$	35.5755	1.19383
$889$	−4.21659	−0.141420
$890$	−31.8824	−1.06870
$891$	5.63557	0.188799
$892$	55.9100	1.87201
$893$	−19.4379	−0.650463
$894$	16.2854	0.544665
$895$	1.48971	0.0497955
$896$	−5.33357	−0.178182
$897$	4.71771	0.157520
$898$	13.8023	0.460590
$899$	−1.38373	−0.0461501
$900$	26.0213	0.867375
$901$	−0.652077	−0.0217238
$902$	−7.76910	−0.258683
$903$	39.4788	1.31377
$904$	−15.3299	−0.509864
$905$	25.7999	0.857617
$906$	17.3193	0.575396
$907$	−24.2978	−0.806795	−0.403397	−	0.915025i	$-0.632171\pi$
$907$	−24.2978	−0.806795	−0.403397	+	0.915025i	$0.632171\pi$
$908$	90.7437	3.01143
$909$	−46.8278	−1.55318
$910$	−25.8039	−0.855390
$911$	19.5850	0.648879	0.324439	−	0.945907i	$-0.394824\pi$
$911$	19.5850	0.648879	0.324439	+	0.945907i	$0.394824\pi$
$912$	60.8477	2.01487
$913$	8.62947	0.285594
$914$	26.3845	0.872721
$915$	−59.1644	−1.95592
$916$	93.6977	3.09586
$917$	20.6546	0.682074
$918$	−1.08500	−0.0358103
$919$	−39.8409	−1.31423	−0.657115	−	0.753790i	$-0.728223\pi$
$919$	−39.8409	−1.31423	−0.657115	+	0.753790i	$0.728223\pi$
$920$	45.2452	1.49169
$921$	−35.2747	−1.16234
$922$	13.3148	0.438499
$923$	−8.69127	−0.286077
$924$	31.2546	1.02820
$925$	−3.86680	−0.127140
$926$	13.2405	0.435109
$927$	−24.4773	−0.803939
$928$	7.71759	0.253342
$929$	−8.70538	−0.285614	−0.142807	−	0.989751i	$-0.545613\pi$
$929$	−8.70538	−0.285614	−0.142807	+	0.989751i	$0.545613\pi$
$930$	−29.7188	−0.974516
$931$	36.2934	1.18947
$932$	17.0680	0.559082
$933$	28.9594	0.948089
$934$	−54.2705	−1.77579
$935$	1.57956	0.0516570
$936$	17.1292	0.559885
$937$	−47.2073	−1.54220	−0.771098	−	0.636717i	$-0.780292\pi$
$937$	−47.2073	−1.54220	−0.771098	+	0.636717i	$0.780292\pi$
$938$	94.6309	3.08981
$939$	−38.2139	−1.24706
$940$	−91.8931	−2.99722
$941$	2.84270	0.0926693	0.0463347	−	0.998926i	$-0.485246\pi$
$941$	2.84270	0.0926693	0.0463347	+	0.998926i	$0.485246\pi$
$942$	56.5702	1.84316
$943$	11.8133	0.384694
$944$	56.7826	1.84812
$945$	4.91330	0.159830
$946$	−5.58414	−0.181556
$947$	−40.0365	−1.30101	−0.650506	−	0.759501i	$-0.725443\pi$
$947$	−40.0365	−1.30101	−0.650506	+	0.759501i	$0.725443\pi$
$948$	44.9390	1.45955
$949$	2.06932	0.0671731
$950$	−13.3402	−0.432815
$951$	9.30492	0.301733
$952$	−33.4834	−1.08520
$953$	−28.4649	−0.922067	−0.461034	−	0.887383i	$-0.652521\pi$
$953$	−28.4649	−0.922067	−0.461034	+	0.887383i	$0.652521\pi$
$954$	−4.76061	−0.154130
$955$	14.7858	0.478458
$956$	6.84092	0.221251
$957$	1.10623	0.0357592
$958$	57.7953	1.86728
$959$	40.6664	1.31318
$960$	45.8901	1.48110
$961$	−27.7783	−0.896076
$962$	−4.36371	−0.140692
$963$	1.67889	0.0541014
$964$	−145.360	−4.68173
$965$	−25.5111	−0.821232
$966$	−67.3266	−2.16620
$967$	−12.7040	−0.408532	−0.204266	−	0.978915i	$-0.565481\pi$
$967$	−12.7040	−0.408532	−0.204266	+	0.978915i	$0.565481\pi$
$968$	77.7317	2.49839
$969$	−6.51517	−0.209297
$970$	74.2228	2.38315
$971$	17.5978	0.564741	0.282371	−	0.959305i	$-0.408879\pi$
$971$	17.5978	0.564741	0.282371	+	0.959305i	$0.408879\pi$
$972$	−103.963	−3.33460
$973$	77.1206	2.47237
$974$	73.2404	2.34677
$975$	−3.83585	−0.122846
$976$	−87.9485	−2.81516
$977$	10.6457	0.340586	0.170293	−	0.985393i	$-0.445529\pi$
$977$	10.6457	0.340586	0.170293	+	0.985393i	$0.445529\pi$
$978$	123.860	3.96060
$979$	−2.76306	−0.0883079
$980$	171.578	5.48086
$981$	29.3099	0.935794
$982$	−99.1587	−3.16428
$983$	−49.7836	−1.58785	−0.793925	−	0.608016i	$-0.791966\pi$
$983$	−49.7836	−1.58785	−0.793925	+	0.608016i	$0.791966\pi$
$984$	88.3692	2.81711
$985$	46.2122	1.47244
$986$	−2.03167	−0.0647016
$987$	79.7632	2.53889
$988$	−10.6266	−0.338077
$989$	8.49097	0.269997
$990$	11.5318	0.366506
$991$	42.6700	1.35546	0.677728	−	0.735312i	$-0.262964\pi$
$991$	42.6700	1.35546	0.677728	+	0.735312i	$0.262964\pi$
$992$	−17.9683	−0.570496
$993$	−29.8606	−0.947597
$994$	124.034	3.93411
$995$	−26.7877	−0.849228
$996$	−168.271	−5.33187
$997$	47.6167	1.50804	0.754018	−	0.656854i	$-0.228113\pi$
$997$	47.6167	1.50804	0.754018	+	0.656854i	$0.228113\pi$
$998$	−9.75626	−0.308829
$999$	0.830892	0.0262882

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4007.2.a.a.1.7	✓	139

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4007.2.a.a.1.7	✓	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)

\(f(q)\)	\(=\)	\(q-2.60765 q^{2} +2.41443 q^{3} +4.79982 q^{4} +2.62983 q^{5} -6.29599 q^{6} -4.53793 q^{7} -7.30095 q^{8} +2.82948 q^{9} +O(q^{10})\)	\(q-2.60765 q^{2} +2.41443 q^{3} +4.79982 q^{4} +2.62983 q^{5} -6.29599 q^{6} -4.53793 q^{7} -7.30095 q^{8} +2.82948 q^{9} -6.85767 q^{10} -0.594314 q^{11} +11.5888 q^{12} -0.829183 q^{13} +11.8333 q^{14} +6.34954 q^{15} +9.43867 q^{16} -1.01063 q^{17} -7.37829 q^{18} +2.67005 q^{19} +12.6227 q^{20} -10.9565 q^{21} +1.54976 q^{22} -2.35649 q^{23} -17.6277 q^{24} +1.91600 q^{25} +2.16222 q^{26} -0.411707 q^{27} -21.7813 q^{28} -0.770927 q^{29} -16.5574 q^{30} +1.79490 q^{31} -10.0108 q^{32} -1.43493 q^{33} +2.63537 q^{34} -11.9340 q^{35} +13.5810 q^{36} -2.01816 q^{37} -6.96254 q^{38} -2.00201 q^{39} -19.2003 q^{40} -5.01310 q^{41} +28.5707 q^{42} -3.60323 q^{43} -2.85260 q^{44} +7.44105 q^{45} +6.14489 q^{46} -7.27998 q^{47} +22.7890 q^{48} +13.5928 q^{49} -4.99626 q^{50} -2.44010 q^{51} -3.97993 q^{52} +0.645219 q^{53} +1.07359 q^{54} -1.56294 q^{55} +33.1312 q^{56} +6.44664 q^{57} +2.01030 q^{58} +6.01596 q^{59} +30.4767 q^{60} -9.31790 q^{61} -4.68046 q^{62} -12.8400 q^{63} +7.22731 q^{64} -2.18061 q^{65} +3.74179 q^{66} +7.99699 q^{67} -4.85084 q^{68} -5.68958 q^{69} +31.1196 q^{70} +10.4817 q^{71} -20.6579 q^{72} -2.49562 q^{73} +5.26265 q^{74} +4.62606 q^{75} +12.8158 q^{76} +2.69695 q^{77} +5.22053 q^{78} +3.87778 q^{79} +24.8221 q^{80} -9.48248 q^{81} +13.0724 q^{82} -14.5201 q^{83} -52.5894 q^{84} -2.65778 q^{85} +9.39595 q^{86} -1.86135 q^{87} +4.33906 q^{88} +4.64917 q^{89} -19.4036 q^{90} +3.76278 q^{91} -11.3107 q^{92} +4.33365 q^{93} +18.9836 q^{94} +7.02176 q^{95} -24.1704 q^{96} -10.8233 q^{97} -35.4452 q^{98} -1.68160 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 139 q - 13 q^{2} - 22 q^{3} + 113 q^{4} - 16 q^{5} - 15 q^{6} - 44 q^{7} - 36 q^{8} + 87 q^{9}+O(q^{10}) \) 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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