LMFDB - Embedded newform 6019.2.a.e.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6019,2,Mod(1,6019)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6019, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6019.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6019 = 13 \cdot 463 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6019.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$48.0619569766$
Analytic rank:	$0$
Dimension:	$130$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Character	$\chi$	$=$	6019.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.17988 q^{2} -0.326610 q^{3} +2.75186 q^{4} +0.291618 q^{5} +0.711970 q^{6} +2.70764 q^{7} -1.63895 q^{8} -2.89333 q^{9} +O(q^{10})$	\(q-2.17988 q^{2} -0.326610 q^{3} +2.75186 q^{4} +0.291618 q^{5} +0.711970 q^{6} +2.70764 q^{7} -1.63895 q^{8} -2.89333 q^{9} -0.635691 q^{10} +0.168835 q^{11} -0.898785 q^{12} +1.00000 q^{13} -5.90232 q^{14} -0.0952456 q^{15} -1.93100 q^{16} +3.50001 q^{17} +6.30709 q^{18} +7.68699 q^{19} +0.802492 q^{20} -0.884343 q^{21} -0.368040 q^{22} +2.84517 q^{23} +0.535299 q^{24} -4.91496 q^{25} -2.17988 q^{26} +1.92482 q^{27} +7.45104 q^{28} +6.95406 q^{29} +0.207623 q^{30} +9.68368 q^{31} +7.48724 q^{32} -0.0551434 q^{33} -7.62959 q^{34} +0.789597 q^{35} -7.96202 q^{36} +1.54939 q^{37} -16.7567 q^{38} -0.326610 q^{39} -0.477949 q^{40} -5.82149 q^{41} +1.92776 q^{42} -8.32800 q^{43} +0.464611 q^{44} -0.843747 q^{45} -6.20212 q^{46} +8.82116 q^{47} +0.630684 q^{48} +0.331312 q^{49} +10.7140 q^{50} -1.14314 q^{51} +2.75186 q^{52} +6.74630 q^{53} -4.19587 q^{54} +0.0492355 q^{55} -4.43770 q^{56} -2.51065 q^{57} -15.1590 q^{58} -6.51027 q^{59} -0.262102 q^{60} -5.01113 q^{61} -21.1092 q^{62} -7.83408 q^{63} -12.4593 q^{64} +0.291618 q^{65} +0.120206 q^{66} +12.2773 q^{67} +9.63154 q^{68} -0.929262 q^{69} -1.72122 q^{70} +13.8169 q^{71} +4.74203 q^{72} -9.79307 q^{73} -3.37747 q^{74} +1.60528 q^{75} +21.1535 q^{76} +0.457145 q^{77} +0.711970 q^{78} -9.92858 q^{79} -0.563114 q^{80} +8.05131 q^{81} +12.6901 q^{82} -3.56820 q^{83} -2.43359 q^{84} +1.02067 q^{85} +18.1540 q^{86} -2.27127 q^{87} -0.276713 q^{88} -1.79988 q^{89} +1.83926 q^{90} +2.70764 q^{91} +7.82950 q^{92} -3.16279 q^{93} -19.2290 q^{94} +2.24167 q^{95} -2.44541 q^{96} +11.7153 q^{97} -0.722218 q^{98} -0.488496 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 130 q + 10 q^{2} + 11 q^{3} + 146 q^{4} + 40 q^{5} + 4 q^{6} + 8 q^{7} + 24 q^{8} + 181 q^{9}+O(q^{10}) $ 130 * q + 10 * q^2 + 11 * q^3 + 146 * q^4 + 40 * q^5 + 4 * q^6 + 8 * q^7 + 24 * q^8 + 181 * q^9	\( 130 q + 10 q^{2} + 11 q^{3} + 146 q^{4} + 40 q^{5} + 4 q^{6} + 8 q^{7} + 24 q^{8} + 181 q^{9} + 5 q^{10} + 43 q^{11} + 28 q^{12} + 130 q^{13} + 47 q^{14} + 29 q^{15} + 170 q^{16} + 85 q^{17} + 20 q^{18} + 3 q^{19} + 73 q^{20} + 62 q^{21} + 12 q^{22} + 62 q^{23} - 5 q^{24} + 178 q^{25} + 10 q^{26} + 35 q^{27} - q^{28} + 134 q^{29} + 24 q^{30} + 14 q^{31} + 48 q^{32} + 4 q^{33} + 4 q^{34} + 50 q^{35} + 244 q^{36} + 32 q^{37} + 76 q^{38} + 11 q^{39} - 6 q^{40} + 48 q^{41} + 9 q^{42} + 34 q^{43} + 123 q^{44} + 115 q^{45} + 5 q^{46} + 25 q^{47} + 35 q^{48} + 210 q^{49} + 24 q^{50} + 20 q^{51} + 146 q^{52} + 193 q^{53} - 39 q^{54} + 32 q^{55} + 122 q^{56} + 7 q^{57} - 4 q^{58} + 50 q^{59} + 42 q^{60} + 57 q^{61} + 51 q^{62} + 8 q^{63} + 172 q^{64} + 40 q^{65} - 4 q^{66} + 21 q^{67} + 132 q^{68} + 92 q^{69} - 46 q^{70} + 58 q^{71} - 26 q^{72} + 15 q^{73} + 120 q^{74} + 23 q^{75} - 65 q^{76} + 192 q^{77} + 4 q^{78} + 32 q^{79} + 66 q^{80} + 326 q^{81} + 11 q^{82} + 33 q^{83} + 5 q^{84} + 43 q^{85} + 105 q^{86} + 31 q^{87} - 17 q^{88} + 84 q^{89} - 73 q^{90} + 8 q^{91} + 161 q^{92} + 52 q^{93} + 4 q^{94} + 59 q^{95} - 77 q^{96} + 9 q^{97} - 61 q^{98} + 100 q^{99}+O(q^{100}) \) 130 * q + 10 * q^2 + 11 * q^3 + 146 * q^4 + 40 * q^5 + 4 * q^6 + 8 * q^7 + 24 * q^8 + 181 * q^9 + 5 * q^10 + 43 * q^11 + 28 * q^12 + 130 * q^13 + 47 * q^14 + 29 * q^15 + 170 * q^16 + 85 * q^17 + 20 * q^18 + 3 * q^19 + 73 * q^20 + 62 * q^21 + 12 * q^22 + 62 * q^23 - 5 * q^24 + 178 * q^25 + 10 * q^26 + 35 * q^27 - q^28 + 134 * q^29 + 24 * q^30 + 14 * q^31 + 48 * q^32 + 4 * q^33 + 4 * q^34 + 50 * q^35 + 244 * q^36 + 32 * q^37 + 76 * q^38 + 11 * q^39 - 6 * q^40 + 48 * q^41 + 9 * q^42 + 34 * q^43 + 123 * q^44 + 115 * q^45 + 5 * q^46 + 25 * q^47 + 35 * q^48 + 210 * q^49 + 24 * q^50 + 20 * q^51 + 146 * q^52 + 193 * q^53 - 39 * q^54 + 32 * q^55 + 122 * q^56 + 7 * q^57 - 4 * q^58 + 50 * q^59 + 42 * q^60 + 57 * q^61 + 51 * q^62 + 8 * q^63 + 172 * q^64 + 40 * q^65 - 4 * q^66 + 21 * q^67 + 132 * q^68 + 92 * q^69 - 46 * q^70 + 58 * q^71 - 26 * q^72 + 15 * q^73 + 120 * q^74 + 23 * q^75 - 65 * q^76 + 192 * q^77 + 4 * q^78 + 32 * q^79 + 66 * q^80 + 326 * q^81 + 11 * q^82 + 33 * q^83 + 5 * q^84 + 43 * q^85 + 105 * q^86 + 31 * q^87 - 17 * q^88 + 84 * q^89 - 73 * q^90 + 8 * q^91 + 161 * q^92 + 52 * q^93 + 4 * q^94 + 59 * q^95 - 77 * q^96 + 9 * q^97 - 61 * q^98 + 100 * 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 $

$2$	−2.17988	−1.54140	−0.770702	−	0.637195i	$-0.780094\pi$
$2$	−2.17988	−1.54140	−0.770702	+	0.637195i	$0.780094\pi$
$3$	−0.326610	−0.188569	−0.0942843	−	0.995545i	$-0.530056\pi$
$3$	−0.326610	−0.188569	−0.0942843	+	0.995545i	$0.530056\pi$
$4$	2.75186	1.37593
$5$	0.291618	0.130416	0.0652078	−	0.997872i	$-0.479229\pi$
$5$	0.291618	0.130416	0.0652078	+	0.997872i	$0.479229\pi$
$6$	0.711970	0.290661
$7$	2.70764	1.02339	0.511696	−	0.859167i	$-0.329017\pi$
$7$	2.70764	1.02339	0.511696	+	0.859167i	$0.329017\pi$
$8$	−1.63895	−0.579458
$9$	−2.89333	−0.964442
$10$	−0.635691	−0.201023
$11$	0.168835	0.0509058	0.0254529	−	0.999676i	$-0.491897\pi$
$11$	0.168835	0.0509058	0.0254529	+	0.999676i	$0.491897\pi$
$12$	−0.898785	−0.259457
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−5.90232	−1.57746
$15$	−0.0952456	−0.0245923
$16$	−1.93100	−0.482749
$17$	3.50001	0.848878	0.424439	−	0.905457i	$-0.360471\pi$
$17$	3.50001	0.848878	0.424439	+	0.905457i	$0.360471\pi$
$18$	6.30709	1.48660
$19$	7.68699	1.76352	0.881758	−	0.471702i	$-0.156360\pi$
$19$	7.68699	1.76352	0.881758	+	0.471702i	$0.156360\pi$
$20$	0.802492	0.179443
$21$	−0.884343	−0.192980
$22$	−0.368040	−0.0784664
$23$	2.84517	0.593259	0.296630	−	0.954993i	$-0.404137\pi$
$23$	2.84517	0.593259	0.296630	+	0.954993i	$0.404137\pi$
$24$	0.535299	0.109268
$25$	−4.91496	−0.982992
$26$	−2.17988	−0.427509
$27$	1.92482	0.370432
$28$	7.45104	1.40811
$29$	6.95406	1.29134	0.645668	−	0.763618i	$-0.276579\pi$
$29$	6.95406	1.29134	0.645668	+	0.763618i	$0.276579\pi$
$30$	0.207623	0.0379067
$31$	9.68368	1.73924	0.869620	−	0.493722i	$-0.164364\pi$
$31$	9.68368	1.73924	0.869620	+	0.493722i	$0.164364\pi$
$32$	7.48724	1.32357
$33$	−0.0551434	−0.00959923
$34$	−7.62959	−1.30846
$35$	0.789597	0.133466
$36$	−7.96202	−1.32700
$37$	1.54939	0.254718	0.127359	−	0.991857i	$-0.459350\pi$
$37$	1.54939	0.254718	0.127359	+	0.991857i	$0.459350\pi$
$38$	−16.7567	−2.71829
$39$	−0.326610	−0.0522995
$40$	−0.477949	−0.0755704
$41$	−5.82149	−0.909165	−0.454582	−	0.890705i	$-0.650211\pi$
$41$	−5.82149	−0.909165	−0.454582	+	0.890705i	$0.650211\pi$
$42$	1.92776	0.297460
$43$	−8.32800	−1.27001	−0.635004	−	0.772509i	$-0.719002\pi$
$43$	−8.32800	−1.27001	−0.635004	+	0.772509i	$0.719002\pi$
$44$	0.464611	0.0700427
$45$	−0.843747	−0.125778
$46$	−6.20212	−0.914452
$47$	8.82116	1.28670	0.643349	−	0.765573i	$-0.277544\pi$
$47$	8.82116	1.28670	0.643349	+	0.765573i	$0.277544\pi$
$48$	0.630684	0.0910314
$49$	0.331312	0.0473302
$50$	10.7140	1.51519
$51$	−1.14314	−0.160072
$52$	2.75186	0.381614
$53$	6.74630	0.926676	0.463338	−	0.886182i	$-0.346652\pi$
$53$	6.74630	0.926676	0.463338	+	0.886182i	$0.346652\pi$
$54$	−4.19587	−0.570986
$55$	0.0492355	0.00663891
$56$	−4.43770	−0.593012
$57$	−2.51065	−0.332544
$58$	−15.1590	−1.99047
$59$	−6.51027	−0.847565	−0.423782	−	0.905764i	$-0.639298\pi$
$59$	−6.51027	−0.847565	−0.423782	+	0.905764i	$0.639298\pi$
$60$	−0.262102	−0.0338372
$61$	−5.01113	−0.641609	−0.320804	−	0.947145i	$-0.603953\pi$
$61$	−5.01113	−0.641609	−0.320804	+	0.947145i	$0.603953\pi$
$62$	−21.1092	−2.68087
$63$	−7.83408	−0.987002
$64$	−12.4593	−1.55741
$65$	0.291618	0.0361708
$66$	0.120206	0.0147963
$67$	12.2773	1.49991	0.749956	−	0.661488i	$-0.230075\pi$
$67$	12.2773	1.49991	0.749956	+	0.661488i	$0.230075\pi$
$68$	9.63154	1.16800
$69$	−0.929262	−0.111870
$70$	−1.72122	−0.205726
$71$	13.8169	1.63976	0.819880	−	0.572535i	$-0.194040\pi$
$71$	13.8169	1.63976	0.819880	+	0.572535i	$0.194040\pi$
$72$	4.74203	0.558853
$73$	−9.79307	−1.14619	−0.573096	−	0.819488i	$-0.694258\pi$
$73$	−9.79307	−1.14619	−0.573096	+	0.819488i	$0.694258\pi$
$74$	−3.37747	−0.392623
$75$	1.60528	0.185361
$76$	21.1535	2.42647
$77$	0.457145	0.0520965
$78$	0.711970	0.0806147
$79$	−9.92858	−1.11705	−0.558527	−	0.829487i	$-0.688633\pi$
$79$	−9.92858	−1.11705	−0.558527	+	0.829487i	$0.688633\pi$
$80$	−0.563114	−0.0629581
$81$	8.05131	0.894590
$82$	12.6901	1.40139
$83$	−3.56820	−0.391661	−0.195831	−	0.980638i	$-0.562740\pi$
$83$	−3.56820	−0.391661	−0.195831	+	0.980638i	$0.562740\pi$
$84$	−2.43359	−0.265526
$85$	1.02067	0.110707
$86$	18.1540	1.95760
$87$	−2.27127	−0.243505
$88$	−0.276713	−0.0294978
$89$	−1.79988	−0.190787	−0.0953935	−	0.995440i	$-0.530411\pi$
$89$	−1.79988	−0.190787	−0.0953935	+	0.995440i	$0.530411\pi$
$90$	1.83926	0.193875
$91$	2.70764	0.283838
$92$	7.82950	0.816282
$93$	−3.16279	−0.327966
$94$	−19.2290	−1.98332
$95$	2.24167	0.229990
$96$	−2.44541	−0.249584
$97$	11.7153	1.18951	0.594756	−	0.803906i	$-0.297249\pi$
$97$	11.7153	1.18951	0.594756	+	0.803906i	$0.297249\pi$
$98$	−0.722218	−0.0729551
$99$	−0.488496	−0.0490957
$100$	−13.5253	−1.35253
$101$	3.02445	0.300944	0.150472	−	0.988614i	$-0.451921\pi$
$101$	3.02445	0.300944	0.150472	+	0.988614i	$0.451921\pi$
$102$	2.49190	0.246735
$103$	−2.91522	−0.287245	−0.143623	−	0.989633i	$-0.545875\pi$
$103$	−2.91522	−0.287245	−0.143623	+	0.989633i	$0.545875\pi$
$104$	−1.63895	−0.160713
$105$	−0.257891	−0.0251675
$106$	−14.7061	−1.42838
$107$	8.25646	0.798182	0.399091	−	0.916911i	$-0.369326\pi$
$107$	8.25646	0.798182	0.399091	+	0.916911i	$0.369326\pi$
$108$	5.29683	0.509688
$109$	0.264215	0.0253072	0.0126536	−	0.999920i	$-0.495972\pi$
$109$	0.264215	0.0253072	0.0126536	+	0.999920i	$0.495972\pi$
$110$	−0.107327	−0.0102332
$111$	−0.506046	−0.0480317
$112$	−5.22845	−0.494042
$113$	−4.96955	−0.467496	−0.233748	−	0.972297i	$-0.575099\pi$
$113$	−4.96955	−0.467496	−0.233748	+	0.972297i	$0.575099\pi$
$114$	5.47290	0.512584
$115$	0.829704	0.0773703
$116$	19.1366	1.77679
$117$	−2.89333	−0.267488
$118$	14.1916	1.30644
$119$	9.47677	0.868734
$120$	0.156103	0.0142502
$121$	−10.9715	−0.997409
$122$	10.9236	0.988979
$123$	1.90136	0.171440
$124$	26.6481	2.39307
$125$	−2.89138	−0.258613
$126$	17.0773	1.52137
$127$	15.1998	1.34876	0.674380	−	0.738384i	$-0.264411\pi$
$127$	15.1998	1.34876	0.674380	+	0.738384i	$0.264411\pi$
$128$	12.1852	1.07703
$129$	2.72001	0.239484
$130$	−0.635691	−0.0557538
$131$	6.70859	0.586132	0.293066	−	0.956092i	$-0.405324\pi$
$131$	6.70859	0.586132	0.293066	+	0.956092i	$0.405324\pi$
$132$	−0.151747	−0.0132079
$133$	20.8136	1.80477
$134$	−26.7630	−2.31197
$135$	0.561313	0.0483101
$136$	−5.73636	−0.491889
$137$	−7.93872	−0.678250	−0.339125	−	0.940741i	$-0.610131\pi$
$137$	−7.93872	−0.678250	−0.339125	+	0.940741i	$0.610131\pi$
$138$	2.02568	0.172437
$139$	−12.6949	−1.07677	−0.538385	−	0.842699i	$-0.680965\pi$
$139$	−12.6949	−1.07677	−0.538385	+	0.842699i	$0.680965\pi$
$140$	2.17286	0.183640
$141$	−2.88108	−0.242631
$142$	−30.1190	−2.52753
$143$	0.168835	0.0141187
$144$	5.58700	0.465584
$145$	2.02793	0.168410
$146$	21.3477	1.76675
$147$	−0.108210	−0.00892500
$148$	4.26369	0.350473
$149$	9.32642	0.764050	0.382025	−	0.924152i	$-0.375227\pi$
$149$	9.32642	0.764050	0.382025	+	0.924152i	$0.375227\pi$
$150$	−3.49930	−0.285717
$151$	17.3475	1.41172	0.705860	−	0.708352i	$-0.250561\pi$
$151$	17.3475	1.41172	0.705860	+	0.708352i	$0.250561\pi$
$152$	−12.5986	−1.02188
$153$	−10.1267	−0.818693
$154$	−0.996520	−0.0803019
$155$	2.82394	0.226824
$156$	−0.898785	−0.0719604
$157$	−14.1294	−1.12764	−0.563822	−	0.825896i	$-0.690670\pi$
$157$	−14.1294	−1.12764	−0.563822	+	0.825896i	$0.690670\pi$
$158$	21.6431	1.72183
$159$	−2.20341	−0.174742
$160$	2.18342	0.172614
$161$	7.70370	0.607136
$162$	−17.5509	−1.37893
$163$	1.65487	0.129619	0.0648097	−	0.997898i	$-0.479356\pi$
$163$	1.65487	0.129619	0.0648097	+	0.997898i	$0.479356\pi$
$164$	−16.0199	−1.25095
$165$	−0.0160808	−0.00125189
$166$	7.77824	0.603709
$167$	16.7139	1.29336	0.646679	−	0.762762i	$-0.276157\pi$
$167$	16.7139	1.29336	0.646679	+	0.762762i	$0.276157\pi$
$168$	1.44940	0.111823
$169$	1.00000	0.0769231
$170$	−2.22493	−0.170644
$171$	−22.2410	−1.70081
$172$	−22.9175	−1.74744
$173$	−5.82151	−0.442601	−0.221301	−	0.975206i	$-0.571030\pi$
$173$	−5.82151	−0.442601	−0.221301	+	0.975206i	$0.571030\pi$
$174$	4.95108	0.375340
$175$	−13.3079	−1.00599
$176$	−0.326021	−0.0245747
$177$	2.12632	0.159824
$178$	3.92352	0.294080
$179$	14.9430	1.11689	0.558446	−	0.829541i	$-0.311398\pi$
$179$	14.9430	1.11689	0.558446	+	0.829541i	$0.311398\pi$
$180$	−2.32187	−0.173062
$181$	−24.7113	−1.83678	−0.918389	−	0.395679i	$-0.870509\pi$
$181$	−24.7113	−1.83678	−0.918389	+	0.395679i	$0.870509\pi$
$182$	−5.90232	−0.437509
$183$	1.63669	0.120987
$184$	−4.66310	−0.343769
$185$	0.451829	0.0332192
$186$	6.89449	0.505528
$187$	0.590926	0.0432128
$188$	24.2746	1.77041
$189$	5.21172	0.379097
$190$	−4.88655	−0.354508
$191$	−20.0819	−1.45307	−0.726537	−	0.687127i	$-0.758871\pi$
$191$	−20.0819	−1.45307	−0.726537	+	0.687127i	$0.758871\pi$
$192$	4.06932	0.293678
$193$	6.05552	0.435886	0.217943	−	0.975962i	$-0.430065\pi$
$193$	6.05552	0.435886	0.217943	+	0.975962i	$0.430065\pi$
$194$	−25.5380	−1.83352
$195$	−0.0952456	−0.00682068
$196$	0.911722	0.0651230
$197$	−16.1404	−1.14996	−0.574979	−	0.818168i	$-0.694990\pi$
$197$	−16.1404	−1.14996	−0.574979	+	0.818168i	$0.694990\pi$
$198$	1.06486	0.0756763
$199$	−23.6286	−1.67498	−0.837492	−	0.546450i	$-0.815979\pi$
$199$	−23.6286	−1.67498	−0.837492	+	0.546450i	$0.815979\pi$
$200$	8.05539	0.569602
$201$	−4.00990	−0.282836
$202$	−6.59291	−0.463876
$203$	18.8291	1.32154
$204$	−3.14576	−0.220247
$205$	−1.69765	−0.118569
$206$	6.35482	0.442761
$207$	−8.23201	−0.572164
$208$	−1.93100	−0.133891
$209$	1.29784	0.0897731
$210$	0.562169	0.0387934
$211$	6.46260	0.444904	0.222452	−	0.974944i	$-0.428594\pi$
$211$	6.46260	0.444904	0.222452	+	0.974944i	$0.428594\pi$
$212$	18.5649	1.27504
$213$	−4.51273	−0.309207
$214$	−17.9980	−1.23032
$215$	−2.42860	−0.165629
$216$	−3.15469	−0.214650
$217$	26.2199	1.77992
$218$	−0.575955	−0.0390086
$219$	3.19852	0.216136
$220$	0.135489	0.00913467
$221$	3.50001	0.235436
$222$	1.10312	0.0740363
$223$	−4.57954	−0.306669	−0.153334	−	0.988174i	$-0.549001\pi$
$223$	−4.57954	−0.306669	−0.153334	+	0.988174i	$0.549001\pi$
$224$	20.2728	1.35453
$225$	14.2206	0.948038
$226$	10.8330	0.720601
$227$	6.17014	0.409527	0.204763	−	0.978812i	$-0.434358\pi$
$227$	6.17014	0.409527	0.204763	+	0.978812i	$0.434358\pi$
$228$	−6.90895	−0.457556
$229$	−26.7394	−1.76699	−0.883494	−	0.468443i	$-0.844815\pi$
$229$	−26.7394	−1.76699	−0.883494	+	0.468443i	$0.844815\pi$
$230$	−1.80865	−0.119259
$231$	−0.149308	−0.00982377
$232$	−11.3974	−0.748275
$233$	8.40915	0.550902	0.275451	−	0.961315i	$-0.411173\pi$
$233$	8.40915	0.550902	0.275451	+	0.961315i	$0.411173\pi$
$234$	6.30709	0.412307
$235$	2.57241	0.167806
$236$	−17.9153	−1.16619
$237$	3.24278	0.210641
$238$	−20.6582	−1.33907
$239$	−0.882942	−0.0571127	−0.0285564	−	0.999592i	$-0.509091\pi$
$239$	−0.882942	−0.0571127	−0.0285564	+	0.999592i	$0.509091\pi$
$240$	0.183919	0.0118719
$241$	5.97100	0.384626	0.192313	−	0.981334i	$-0.438401\pi$
$241$	5.97100	0.384626	0.192313	+	0.981334i	$0.438401\pi$
$242$	23.9165	1.53741
$243$	−8.40411	−0.539124
$244$	−13.7899	−0.882808
$245$	0.0966165	0.00617260
$246$	−4.14473	−0.264258
$247$	7.68699	0.489111
$248$	−15.8711	−1.00782
$249$	1.16541	0.0738550
$250$	6.30285	0.398628
$251$	20.7812	1.31169	0.655847	−	0.754893i	$-0.272311\pi$
$251$	20.7812	1.31169	0.655847	+	0.754893i	$0.272311\pi$
$252$	−21.5583	−1.35804
$253$	0.480365	0.0302003
$254$	−33.1336	−2.07899
$255$	−0.333361	−0.0208759
$256$	−1.64359	−0.102724
$257$	2.29089	0.142902	0.0714508	−	0.997444i	$-0.477237\pi$
$257$	2.29089	0.142902	0.0714508	+	0.997444i	$0.477237\pi$
$258$	−5.92929	−0.369141
$259$	4.19518	0.260676
$260$	0.802492	0.0497684
$261$	−20.1203	−1.24542
$262$	−14.6239	−0.903467
$263$	−16.5263	−1.01906	−0.509528	−	0.860454i	$-0.670180\pi$
$263$	−16.5263	−1.01906	−0.509528	+	0.860454i	$0.670180\pi$
$264$	0.0903775	0.00556235
$265$	1.96734	0.120853
$266$	−45.3710	−2.78188
$267$	0.587860	0.0359764
$268$	33.7854	2.06377
$269$	3.92007	0.239011	0.119505	−	0.992834i	$-0.461869\pi$
$269$	3.92007	0.239011	0.119505	+	0.992834i	$0.461869\pi$
$270$	−1.22359	−0.0744655
$271$	10.6132	0.644709	0.322354	−	0.946619i	$-0.395526\pi$
$271$	10.6132	0.644709	0.322354	+	0.946619i	$0.395526\pi$
$272$	−6.75852	−0.409795
$273$	−0.884343	−0.0535229
$274$	17.3054	1.04546
$275$	−0.829819	−0.0500400
$276$	−2.55720	−0.153925
$277$	−25.7909	−1.54962	−0.774812	−	0.632192i	$-0.782156\pi$
$277$	−25.7909	−1.54962	−0.774812	+	0.632192i	$0.782156\pi$
$278$	27.6734	1.65974
$279$	−28.0180	−1.67740
$280$	−1.29411	−0.0773381
$281$	−14.8298	−0.884670	−0.442335	−	0.896850i	$-0.645850\pi$
$281$	−14.8298	−0.884670	−0.442335	+	0.896850i	$0.645850\pi$
$282$	6.28040	0.373993
$283$	27.2717	1.62113	0.810566	−	0.585647i	$-0.199160\pi$
$283$	27.2717	1.62113	0.810566	+	0.585647i	$0.199160\pi$
$284$	38.0220	2.25619
$285$	−0.732151	−0.0433689
$286$	−0.368040	−0.0217627
$287$	−15.7625	−0.930431
$288$	−21.6630	−1.27651
$289$	−4.74991	−0.279406
$290$	−4.42063	−0.259589
$291$	−3.82635	−0.224305
$292$	−26.9491	−1.57708
$293$	10.9628	0.640453	0.320226	−	0.947341i	$-0.396241\pi$
$293$	10.9628	0.640453	0.320226	+	0.947341i	$0.396241\pi$
$294$	0.235884	0.0137570
$295$	−1.89851	−0.110536
$296$	−2.53937	−0.147598
$297$	0.324978	0.0188571
$298$	−20.3304	−1.17771
$299$	2.84517	0.164540
$300$	4.41749	0.255044
$301$	−22.5492	−1.29972
$302$	−37.8154	−2.17603
$303$	−0.987815	−0.0567485
$304$	−14.8436	−0.851336
$305$	−1.46134	−0.0836758
$306$	22.0749	1.26194
$307$	−9.37561	−0.535094	−0.267547	−	0.963545i	$-0.586213\pi$
$307$	−9.37561	−0.535094	−0.267547	+	0.963545i	$0.586213\pi$
$308$	1.25800	0.0716811
$309$	0.952142	0.0541654
$310$	−6.15583	−0.349628
$311$	7.81013	0.442872	0.221436	−	0.975175i	$-0.428926\pi$
$311$	7.81013	0.442872	0.221436	+	0.975175i	$0.428926\pi$
$312$	0.535299	0.0303054
$313$	−8.35024	−0.471984	−0.235992	−	0.971755i	$-0.575834\pi$
$313$	−8.35024	−0.471984	−0.235992	+	0.971755i	$0.575834\pi$
$314$	30.8002	1.73816
$315$	−2.28456	−0.128720
$316$	−27.3220	−1.53699
$317$	−6.37453	−0.358029	−0.179015	−	0.983846i	$-0.557291\pi$
$317$	−6.37453	−0.358029	−0.179015	+	0.983846i	$0.557291\pi$
$318$	4.80316	0.269348
$319$	1.17409	0.0657365
$320$	−3.63335	−0.203110
$321$	−2.69664	−0.150512
$322$	−16.7931	−0.935843
$323$	26.9046	1.49701
$324$	22.1561	1.23089
$325$	−4.91496	−0.272633
$326$	−3.60741	−0.199796
$327$	−0.0862953	−0.00477214
$328$	9.54116	0.526823
$329$	23.8845	1.31680
$330$	0.0350542	0.00192967
$331$	7.09181	0.389801	0.194900	−	0.980823i	$-0.437562\pi$
$331$	7.09181	0.389801	0.194900	+	0.980823i	$0.437562\pi$
$332$	−9.81919	−0.538898
$333$	−4.48288	−0.245660
$334$	−36.4342	−1.99359
$335$	3.58029	0.195612
$336$	1.70766	0.0931607
$337$	−2.86334	−0.155976	−0.0779881	−	0.996954i	$-0.524850\pi$
$337$	−2.86334	−0.155976	−0.0779881	+	0.996954i	$0.524850\pi$
$338$	−2.17988	−0.118570
$339$	1.62311	0.0881551
$340$	2.80873	0.152325
$341$	1.63495	0.0885374
$342$	48.4825	2.62163
$343$	−18.0564	−0.974954
$344$	13.6492	0.735916
$345$	−0.270990	−0.0145896
$346$	12.6902	0.682228
$347$	7.35668	0.394927	0.197464	−	0.980310i	$-0.436730\pi$
$347$	7.35668	0.394927	0.197464	+	0.980310i	$0.436730\pi$
$348$	−6.25020	−0.335046
$349$	−8.48941	−0.454427	−0.227214	−	0.973845i	$-0.572962\pi$
$349$	−8.48941	−0.454427	−0.227214	+	0.973845i	$0.572962\pi$
$350$	29.0096	1.55063
$351$	1.92482	0.102739
$352$	1.26411	0.0673774
$353$	16.4328	0.874630	0.437315	−	0.899309i	$-0.355930\pi$
$353$	16.4328	0.874630	0.437315	+	0.899309i	$0.355930\pi$
$354$	−4.63511	−0.246354
$355$	4.02925	0.213850
$356$	−4.95302	−0.262509
$357$	−3.09521	−0.163816
$358$	−32.5739	−1.72158
$359$	29.6992	1.56746	0.783732	−	0.621099i	$-0.213314\pi$
$359$	29.6992	1.56746	0.783732	+	0.621099i	$0.213314\pi$
$360$	1.38286	0.0728832
$361$	40.0898	2.10999
$362$	53.8676	2.83122
$363$	3.58340	0.188080
$364$	7.45104	0.390540
$365$	−2.85584	−0.149481
$366$	−3.56777	−0.186490
$367$	−0.00321504	−0.000167824 0	−8.39118e−5	−	1.00000i	$-0.500027\pi$
$367$	−0.00321504	−0.000167824 0	−8.39118e−5		1.00000i	$0.500027\pi$
$368$	−5.49402	−0.286395
$369$	16.8435	0.876836
$370$	−0.984932	−0.0512042
$371$	18.2666	0.948352
$372$	−8.70354	−0.451258
$373$	21.2449	1.10002	0.550009	−	0.835159i	$-0.314624\pi$
$373$	21.2449	1.10002	0.550009	+	0.835159i	$0.314624\pi$
$374$	−1.28815	−0.0666084
$375$	0.944356	0.0487663
$376$	−14.4575	−0.745588
$377$	6.95406	0.358152
$378$	−11.3609	−0.584342
$379$	11.6409	0.597953	0.298976	−	0.954261i	$-0.403355\pi$
$379$	11.6409	0.597953	0.298976	+	0.954261i	$0.403355\pi$
$380$	6.16874	0.316450
$381$	−4.96440	−0.254334
$382$	43.7760	2.23978
$383$	−26.3183	−1.34480	−0.672401	−	0.740187i	$-0.734737\pi$
$383$	−26.3183	−1.34480	−0.672401	+	0.740187i	$0.734737\pi$
$384$	−3.97980	−0.203093
$385$	0.133312	0.00679420
$386$	−13.2003	−0.671876
$387$	24.0956	1.22485
$388$	32.2389	1.63668
$389$	24.3850	1.23637	0.618185	−	0.786032i	$-0.287868\pi$
$389$	24.3850	1.23637	0.618185	+	0.786032i	$0.287868\pi$
$390$	0.207623	0.0105134
$391$	9.95814	0.503605
$392$	−0.543005	−0.0274259
$393$	−2.19109	−0.110526
$394$	35.1841	1.77255
$395$	−2.89536	−0.145681
$396$	−1.34427	−0.0675521
$397$	−4.07064	−0.204300	−0.102150	−	0.994769i	$-0.532572\pi$
$397$	−4.07064	−0.204300	−0.102150	+	0.994769i	$0.532572\pi$
$398$	51.5073	2.58183
$399$	−6.79793	−0.340322
$400$	9.49077	0.474539
$401$	−37.3461	−1.86498	−0.932489	−	0.361199i	$-0.882367\pi$
$401$	−37.3461	−1.86498	−0.932489	+	0.361199i	$0.882367\pi$
$402$	8.74107	0.435965
$403$	9.68368	0.482378
$404$	8.32284	0.414077
$405$	2.34791	0.116669
$406$	−41.0450	−2.03703
$407$	0.261591	0.0129666
$408$	1.87356	0.0927548
$409$	20.1606	0.996876	0.498438	−	0.866925i	$-0.333907\pi$
$409$	20.1606	0.996876	0.498438	+	0.866925i	$0.333907\pi$
$410$	3.70067	0.182763
$411$	2.59287	0.127897
$412$	−8.02227	−0.395229
$413$	−17.6275	−0.867390
$414$	17.9447	0.881936
$415$	−1.04055	−0.0510788
$416$	7.48724	0.367092
$417$	4.14630	0.203045
$418$	−2.82912	−0.138377
$419$	−30.9154	−1.51032	−0.755158	−	0.655543i	$-0.772440\pi$
$419$	−30.9154	−1.51032	−0.755158	+	0.655543i	$0.772440\pi$
$420$	−0.709678	−0.0346287
$421$	−33.2467	−1.62034	−0.810172	−	0.586193i	$-0.800626\pi$
$421$	−33.2467	−1.62034	−0.810172	+	0.586193i	$0.800626\pi$
$422$	−14.0877	−0.685777
$423$	−25.5225	−1.24095
$424$	−11.0569	−0.536970
$425$	−17.2024	−0.834440
$426$	9.83719	0.476614
$427$	−13.5683	−0.656617
$428$	22.7206	1.09824
$429$	−0.0551434	−0.00266235
$430$	5.29404	0.255301
$431$	−17.3805	−0.837187	−0.418594	−	0.908174i	$-0.637477\pi$
$431$	−17.3805	−0.837187	−0.418594	+	0.908174i	$0.637477\pi$
$432$	−3.71683	−0.178826
$433$	26.6625	1.28132	0.640658	−	0.767826i	$-0.278662\pi$
$433$	26.6625	1.28132	0.640658	+	0.767826i	$0.278662\pi$
$434$	−57.1561	−2.74358
$435$	−0.662343	−0.0317569
$436$	0.727081	0.0348209
$437$	21.8708	1.04622
$438$	−6.97237	−0.333153
$439$	32.1940	1.53654	0.768269	−	0.640127i	$-0.221118\pi$
$439$	32.1940	1.53654	0.768269	+	0.640127i	$0.221118\pi$
$440$	−0.0806947	−0.00384697
$441$	−0.958593	−0.0456473
$442$	−7.62959	−0.362903
$443$	−14.4085	−0.684570	−0.342285	−	0.939596i	$-0.611201\pi$
$443$	−14.4085	−0.684570	−0.342285	+	0.939596i	$0.611201\pi$
$444$	−1.39257	−0.0660882
$445$	−0.524878	−0.0248816
$446$	9.98283	0.472701
$447$	−3.04611	−0.144076
$448$	−33.7352	−1.59384
$449$	1.36637	0.0644830	0.0322415	−	0.999480i	$-0.489735\pi$
$449$	1.36637	0.0644830	0.0322415	+	0.999480i	$0.489735\pi$
$450$	−30.9991	−1.46131
$451$	−0.982874	−0.0462817
$452$	−13.6755	−0.643241
$453$	−5.66587	−0.266206
$454$	−13.4501	−0.631246
$455$	0.789597	0.0370169
$456$	4.11484	0.192695
$457$	−22.6456	−1.05932	−0.529658	−	0.848211i	$-0.677680\pi$
$457$	−22.6456	−1.05932	−0.529658	+	0.848211i	$0.677680\pi$
$458$	58.2885	2.72364
$459$	6.73690	0.314452
$460$	2.28323	0.106456
$461$	−36.8876	−1.71802	−0.859012	−	0.511955i	$-0.828922\pi$
$461$	−36.8876	−1.71802	−0.859012	+	0.511955i	$0.828922\pi$
$462$	0.325474	0.0151424
$463$	−1.00000	−0.0464739
$463$	−1.00000	−0.0464739
$464$	−13.4283	−0.623392
$465$	−0.922327	−0.0427719
$466$	−18.3309	−0.849163
$467$	31.4527	1.45546	0.727729	−	0.685864i	$-0.240576\pi$
$467$	31.4527	1.45546	0.727729	+	0.685864i	$0.240576\pi$
$468$	−7.96202	−0.368044
$469$	33.2425	1.53500
$470$	−5.60754	−0.258656
$471$	4.61479	0.212638
$472$	10.6700	0.491128
$473$	−1.40606	−0.0646508
$474$	−7.06885	−0.324683
$475$	−37.7812	−1.73352
$476$	26.0787	1.19532
$477$	−19.5193	−0.893725
$478$	1.92470	0.0880338
$479$	14.2575	0.651443	0.325722	−	0.945466i	$-0.394393\pi$
$479$	14.2575	0.651443	0.325722	+	0.945466i	$0.394393\pi$
$480$	−0.713127	−0.0325496
$481$	1.54939	0.0706459
$482$	−13.0160	−0.592864
$483$	−2.51611	−0.114487
$484$	−30.1920	−1.37236
$485$	3.41640	0.155131
$486$	18.3199	0.831008
$487$	14.2083	0.643842	0.321921	−	0.946767i	$-0.395672\pi$
$487$	14.2083	0.643842	0.321921	+	0.946767i	$0.395672\pi$
$488$	8.21301	0.371785
$489$	−0.540498	−0.0244421
$490$	−0.210612	−0.00951448
$491$	22.3791	1.00995	0.504977	−	0.863133i	$-0.331501\pi$
$491$	22.3791	1.00995	0.504977	+	0.863133i	$0.331501\pi$
$492$	5.23227	0.235889
$493$	24.3393	1.09619
$494$	−16.7567	−0.753918
$495$	−0.142454	−0.00640284
$496$	−18.6992	−0.839617
$497$	37.4111	1.67812
$498$	−2.54045	−0.113840
$499$	38.0238	1.70218	0.851090	−	0.525020i	$-0.175942\pi$
$499$	38.0238	1.70218	0.851090	+	0.525020i	$0.175942\pi$
$500$	−7.95667	−0.355833
$501$	−5.45892	−0.243887
$502$	−45.3003	−2.02185
$503$	17.2494	0.769112	0.384556	−	0.923102i	$-0.374354\pi$
$503$	17.2494	0.769112	0.384556	+	0.923102i	$0.374354\pi$
$504$	12.8397	0.571926
$505$	0.881983	0.0392477
$506$	−1.04714	−0.0465509
$507$	−0.326610	−0.0145053
$508$	41.8276	1.85580
$509$	24.5379	1.08763	0.543813	−	0.839207i	$-0.316980\pi$
$509$	24.5379	1.08763	0.543813	+	0.839207i	$0.316980\pi$
$510$	0.726685	0.0321781
$511$	−26.5161	−1.17300
$512$	−20.7875	−0.918686
$513$	14.7961	0.653263
$514$	−4.99384	−0.220269
$515$	−0.850132	−0.0374613
$516$	7.48508	0.329512
$517$	1.48932	0.0655004
$518$	−9.14497	−0.401807
$519$	1.90137	0.0834607
$520$	−0.477949	−0.0209594
$521$	2.83634	0.124262	0.0621312	−	0.998068i	$-0.480210\pi$
$521$	2.83634	0.124262	0.0621312	+	0.998068i	$0.480210\pi$
$522$	43.8599	1.91969
$523$	3.53266	0.154472	0.0772362	−	0.997013i	$-0.475390\pi$
$523$	3.53266	0.154472	0.0772362	+	0.997013i	$0.475390\pi$
$524$	18.4611	0.806476
$525$	4.34651	0.189697
$526$	36.0253	1.57078
$527$	33.8930	1.47640
$528$	0.106482	0.00463402
$529$	−14.9050	−0.648044
$530$	−4.28857	−0.186283
$531$	18.8363	0.817427
$532$	57.2760	2.48323
$533$	−5.82149	−0.252157
$534$	−1.28146	−0.0554543
$535$	2.40773	0.104095
$536$	−20.1219	−0.869136
$537$	−4.88054	−0.210611
$538$	−8.54527	−0.368413
$539$	0.0559371	0.00240938
$540$	1.54465	0.0664713
$541$	−24.5108	−1.05380	−0.526901	−	0.849927i	$-0.676646\pi$
$541$	−24.5108	−1.05380	−0.526901	+	0.849927i	$0.676646\pi$
$542$	−23.1355	−0.993757
$543$	8.07097	0.346359
$544$	26.2054	1.12355
$545$	0.0770498	0.00330045
$546$	1.92776	0.0825004
$547$	5.45482	0.233231	0.116616	−	0.993177i	$-0.462795\pi$
$547$	5.45482	0.233231	0.116616	+	0.993177i	$0.462795\pi$
$548$	−21.8462	−0.933224
$549$	14.4988	0.618795
$550$	1.80890	0.0771318
$551$	53.4557	2.27729
$552$	1.52302	0.0648240
$553$	−26.8830	−1.14318
$554$	56.2209	2.38860
$555$	−0.147572	−0.00626409
$556$	−34.9346	−1.48156
$557$	21.5938	0.914958	0.457479	−	0.889220i	$-0.348752\pi$
$557$	21.5938	0.914958	0.457479	+	0.889220i	$0.348752\pi$
$558$	61.0758	2.58555
$559$	−8.32800	−0.352237
$560$	−1.52471	−0.0644308
$561$	−0.193003	−0.00814858
$562$	32.3271	1.36363
$563$	−16.2200	−0.683590	−0.341795	−	0.939775i	$-0.611035\pi$
$563$	−16.2200	−0.683590	−0.341795	+	0.939775i	$0.611035\pi$
$564$	−7.92833	−0.333843
$565$	−1.44921	−0.0609688
$566$	−59.4488	−2.49882
$567$	21.8000	0.915516
$568$	−22.6452	−0.950172
$569$	29.0467	1.21770	0.608850	−	0.793286i	$-0.291631\pi$
$569$	29.0467	1.21770	0.608850	+	0.793286i	$0.291631\pi$
$570$	1.59600	0.0668490
$571$	−3.69878	−0.154789	−0.0773946	−	0.997001i	$-0.524660\pi$
$571$	−3.69878	−0.154789	−0.0773946	+	0.997001i	$0.524660\pi$
$572$	0.464611	0.0194264
$573$	6.55895	0.274004
$574$	34.3603	1.43417
$575$	−13.9839	−0.583169
$576$	36.0487	1.50203
$577$	8.32690	0.346654	0.173327	−	0.984864i	$-0.444548\pi$
$577$	8.32690	0.346654	0.173327	+	0.984864i	$0.444548\pi$
$578$	10.3542	0.430678
$579$	−1.97779	−0.0821943
$580$	5.58057	0.231721
$581$	−9.66141	−0.400823
$582$	8.34096	0.345744
$583$	1.13901	0.0471732
$584$	16.0504	0.664170
$585$	−0.843747	−0.0348846
$586$	−23.8975	−0.987197
$587$	4.51395	0.186310	0.0931552	−	0.995652i	$-0.470305\pi$
$587$	4.51395	0.186310	0.0931552	+	0.995652i	$0.470305\pi$
$588$	−0.297778	−0.0122802
$589$	74.4383	3.06718
$590$	4.13852	0.170380
$591$	5.27163	0.216846
$592$	−2.99186	−0.122965
$593$	28.6319	1.17577	0.587886	−	0.808944i	$-0.299960\pi$
$593$	28.6319	1.17577	0.587886	+	0.808944i	$0.299960\pi$
$594$	−0.708411	−0.0290665
$595$	2.76360	0.113297
$596$	25.6650	1.05128
$597$	7.71733	0.315849
$598$	−6.20212	−0.253623
$599$	16.1038	0.657985	0.328992	−	0.944333i	$-0.393291\pi$
$599$	16.1038	0.657985	0.328992	+	0.944333i	$0.393291\pi$
$600$	−2.63097	−0.107409
$601$	34.4758	1.40630	0.703149	−	0.711042i	$-0.251776\pi$
$601$	34.4758	1.40630	0.703149	+	0.711042i	$0.251776\pi$
$602$	49.1545	2.00339
$603$	−35.5222	−1.44658
$604$	47.7378	1.94243
$605$	−3.19949	−0.130078
$606$	2.15331	0.0874724
$607$	−11.3308	−0.459905	−0.229952	−	0.973202i	$-0.573857\pi$
$607$	−11.3308	−0.459905	−0.229952	+	0.973202i	$0.573857\pi$
$608$	57.5543	2.33414
$609$	−6.14977	−0.249201
$610$	3.18553	0.128978
$611$	8.82116	0.356866
$612$	−27.8672	−1.12646
$613$	−25.2170	−1.01851	−0.509253	−	0.860617i	$-0.670078\pi$
$613$	−25.2170	−1.01851	−0.509253	+	0.860617i	$0.670078\pi$
$614$	20.4377	0.824797
$615$	0.554471	0.0223584
$616$	−0.749240	−0.0301878
$617$	7.10053	0.285857	0.142928	−	0.989733i	$-0.454348\pi$
$617$	7.10053	0.285857	0.142928	+	0.989733i	$0.454348\pi$
$618$	−2.07555	−0.0834909
$619$	−14.5074	−0.583103	−0.291551	−	0.956555i	$-0.594171\pi$
$619$	−14.5074	−0.583103	−0.291551	+	0.956555i	$0.594171\pi$
$620$	7.77107	0.312094
$621$	5.47645	0.219762
$622$	−17.0251	−0.682644
$623$	−4.87343	−0.195250
$624$	0.630684	0.0252476
$625$	23.7316	0.949265
$626$	18.2025	0.727518
$627$	−0.423886	−0.0169284
$628$	−38.8820	−1.55156
$629$	5.42287	0.216224
$630$	4.98006	0.198410
$631$	47.3458	1.88481	0.942403	−	0.334479i	$-0.108560\pi$
$631$	47.3458	1.88481	0.942403	+	0.334479i	$0.108560\pi$
$632$	16.2725	0.647285
$633$	−2.11075	−0.0838949
$634$	13.8957	0.551868
$635$	4.43253	0.175900
$636$	−6.06348	−0.240432
$637$	0.331312	0.0131270
$638$	−2.55937	−0.101326
$639$	−39.9767	−1.58145
$640$	3.55341	0.140461
$641$	5.32982	0.210515	0.105258	−	0.994445i	$-0.466433\pi$
$641$	5.32982	0.210515	0.105258	+	0.994445i	$0.466433\pi$
$642$	5.87835	0.232000
$643$	−17.5454	−0.691921	−0.345961	−	0.938249i	$-0.612447\pi$
$643$	−17.5454	−0.691921	−0.345961	+	0.938249i	$0.612447\pi$
$644$	21.1995	0.835376
$645$	0.793205	0.0312324
$646$	−58.6486	−2.30750
$647$	−29.4645	−1.15837	−0.579185	−	0.815196i	$-0.696629\pi$
$647$	−29.4645	−1.15837	−0.579185	+	0.815196i	$0.696629\pi$
$648$	−13.1957	−0.518377
$649$	−1.09916	−0.0431459
$650$	10.7140	0.420238
$651$	−8.56369	−0.335638
$652$	4.55396	0.178347
$653$	−11.0939	−0.434136	−0.217068	−	0.976156i	$-0.569649\pi$
$653$	−11.0939	−0.434136	−0.217068	+	0.976156i	$0.569649\pi$
$654$	0.188113	0.00735580
$655$	1.95635	0.0764408
$656$	11.2413	0.438899
$657$	28.3346	1.10544
$658$	−52.0653	−2.02972
$659$	33.4967	1.30485	0.652423	−	0.757855i	$-0.273753\pi$
$659$	33.4967	1.30485	0.652423	+	0.757855i	$0.273753\pi$
$660$	−0.0442521	−0.00172251
$661$	27.6118	1.07397	0.536987	−	0.843591i	$-0.319562\pi$
$661$	27.6118	1.07397	0.536987	+	0.843591i	$0.319562\pi$
$662$	−15.4593	−0.600841
$663$	−1.14314	−0.0443959
$664$	5.84812	0.226951
$665$	6.06962	0.235370
$666$	9.77212	0.378662
$667$	19.7855	0.766097
$668$	45.9942	1.77957
$669$	1.49573	0.0578281
$670$	−7.80458	−0.301517
$671$	−0.846055	−0.0326616
$672$	−6.62129	−0.255422
$673$	−20.3307	−0.783691	−0.391845	−	0.920031i	$-0.628163\pi$
$673$	−20.3307	−0.783691	−0.391845	+	0.920031i	$0.628163\pi$
$674$	6.24173	0.240423
$675$	−9.46042	−0.364132
$676$	2.75186	0.105841
$677$	3.46907	0.133327	0.0666635	−	0.997776i	$-0.478765\pi$
$677$	3.46907	0.133327	0.0666635	+	0.997776i	$0.478765\pi$
$678$	−3.53817	−0.135883
$679$	31.7209	1.21734
$680$	−1.67283	−0.0641500
$681$	−2.01523	−0.0772238
$682$	−3.56398	−0.136472
$683$	5.65848	0.216516	0.108258	−	0.994123i	$-0.465473\pi$
$683$	5.65848	0.216516	0.108258	+	0.994123i	$0.465473\pi$
$684$	−61.2039	−2.34019
$685$	−2.31507	−0.0884545
$686$	39.3607	1.50280
$687$	8.73336	0.333198
$688$	16.0813	0.613096
$689$	6.74630	0.257014
$690$	0.590724	0.0224885
$691$	2.11003	0.0802695	0.0401347	−	0.999194i	$-0.487221\pi$
$691$	2.11003	0.0802695	0.0401347	+	0.999194i	$0.487221\pi$
$692$	−16.0200	−0.608988
$693$	−1.32267	−0.0502441
$694$	−16.0366	−0.608743
$695$	−3.70207	−0.140428
$696$	3.72250	0.141101
$697$	−20.3753	−0.771770
$698$	18.5058	0.700457
$699$	−2.74652	−0.103883
$700$	−36.6215	−1.38416
$701$	20.5301	0.775413	0.387706	−	0.921783i	$-0.373267\pi$
$701$	20.5301	0.775413	0.387706	+	0.921783i	$0.373267\pi$
$702$	−4.19587	−0.158363
$703$	11.9101	0.449198
$704$	−2.10356	−0.0792810
$705$	−0.840177	−0.0316429
$706$	−35.8214	−1.34816
$707$	8.18911	0.307983
$708$	5.85133	0.219906
$709$	16.0353	0.602220	0.301110	−	0.953589i	$-0.402643\pi$
$709$	16.0353	0.602220	0.301110	+	0.953589i	$0.402643\pi$
$710$	−8.78326	−0.329630
$711$	28.7266	1.07733
$712$	2.94992	0.110553
$713$	27.5517	1.03182
$714$	6.74718	0.252507
$715$	0.0492355	0.00184130
$716$	41.1210	1.53676
$717$	0.288378	0.0107697
$718$	−64.7406	−2.41610
$719$	−9.11783	−0.340038	−0.170019	−	0.985441i	$-0.554383\pi$
$719$	−9.11783	−0.340038	−0.170019	+	0.985441i	$0.554383\pi$
$720$	1.62927	0.0607194
$721$	−7.89337	−0.293964
$722$	−87.3907	−3.25235
$723$	−1.95019	−0.0725283
$724$	−68.0020	−2.52728
$725$	−34.1789	−1.26937
$726$	−7.81137	−0.289907
$727$	−20.4399	−0.758076	−0.379038	−	0.925381i	$-0.623745\pi$
$727$	−20.4399	−0.758076	−0.379038	+	0.925381i	$0.623745\pi$
$728$	−4.43770	−0.164472
$729$	−21.4091	−0.792928
$730$	6.22537	0.230411
$731$	−29.1481	−1.07808
$732$	4.50393	0.166470
$733$	38.4202	1.41908	0.709542	−	0.704663i	$-0.248902\pi$
$733$	38.4202	1.41908	0.709542	+	0.704663i	$0.248902\pi$
$734$	0.00700838	0.000258684 0
$735$	−0.0315560	−0.00116396
$736$	21.3025	0.785220
$737$	2.07284	0.0763542
$738$	−36.7167	−1.35156
$739$	4.92646	0.181223	0.0906114	−	0.995886i	$-0.471118\pi$
$739$	4.92646	0.181223	0.0906114	+	0.995886i	$0.471118\pi$
$740$	1.24337	0.0457072
$741$	−2.51065	−0.0922310
$742$	−39.8188	−1.46179
$743$	−7.15125	−0.262354	−0.131177	−	0.991359i	$-0.541876\pi$
$743$	−7.15125	−0.262354	−0.131177	+	0.991359i	$0.541876\pi$
$744$	5.18367	0.190042
$745$	2.71975	0.0996441
$746$	−46.3112	−1.69557
$747$	10.3240	0.377735
$748$	1.62614	0.0594577
$749$	22.3555	0.816852
$750$	−2.05858	−0.0751686
$751$	−36.4619	−1.33051	−0.665256	−	0.746615i	$-0.731678\pi$
$751$	−36.4619	−1.33051	−0.665256	+	0.746615i	$0.731678\pi$
$752$	−17.0336	−0.621153
$753$	−6.78734	−0.247344
$754$	−15.1590	−0.552057
$755$	5.05885	0.184110
$756$	14.3419	0.521610
$757$	−9.10343	−0.330870	−0.165435	−	0.986221i	$-0.552903\pi$
$757$	−9.10343	−0.330870	−0.165435	+	0.986221i	$0.552903\pi$
$758$	−25.3757	−0.921687
$759$	−0.156892	−0.00569483
$760$	−3.67399	−0.133270
$761$	18.3635	0.665676	0.332838	−	0.942984i	$-0.391994\pi$
$761$	18.3635	0.665676	0.332838	+	0.942984i	$0.391994\pi$
$762$	10.8218	0.392032
$763$	0.715398	0.0258992
$764$	−55.2625	−1.99933
$765$	−2.95312	−0.106770
$766$	57.3706	2.07289
$767$	−6.51027	−0.235072
$768$	0.536814	0.0193706
$769$	40.4451	1.45849	0.729245	−	0.684253i	$-0.239872\pi$
$769$	40.4451	1.45849	0.729245	+	0.684253i	$0.239872\pi$
$770$	−0.290603	−0.0104726
$771$	−0.748227	−0.0269467
$772$	16.6639	0.599747
$773$	−34.4022	−1.23736	−0.618681	−	0.785642i	$-0.712333\pi$
$773$	−34.4022	−1.23736	−0.618681	+	0.785642i	$0.712333\pi$
$774$	−52.5254	−1.88799
$775$	−47.5949	−1.70966
$776$	−19.2009	−0.689272
$777$	−1.37019	−0.0491553
$778$	−53.1564	−1.90575
$779$	−44.7497	−1.60333
$780$	−0.262102	−0.00938476
$781$	2.33278	0.0834733
$782$	−21.7075	−0.776258
$783$	13.3853	0.478352
$784$	−0.639762	−0.0228486
$785$	−4.12038	−0.147063
$786$	4.77631	0.170365
$787$	−41.4548	−1.47771	−0.738853	−	0.673867i	$-0.764632\pi$
$787$	−41.4548	−1.47771	−0.738853	+	0.673867i	$0.764632\pi$
$788$	−44.4161	−1.58226
$789$	5.39767	0.192162
$790$	6.31152	0.224554
$791$	−13.4558	−0.478431
$792$	0.800622	0.0284489
$793$	−5.01113	−0.177950
$794$	8.87349	0.314908
$795$	−0.642555	−0.0227891
$796$	−65.0224	−2.30466
$797$	10.1920	0.361020	0.180510	−	0.983573i	$-0.442225\pi$
$797$	10.1920	0.361020	0.180510	+	0.983573i	$0.442225\pi$
$798$	14.8187	0.524575
$799$	30.8742	1.09225
$800$	−36.7995	−1.30106
$801$	5.20764	0.184003
$802$	81.4099	2.87468
$803$	−1.65342	−0.0583478
$804$	−11.0347	−0.389162
$805$	2.24654	0.0791801
$806$	−21.1092	−0.743540
$807$	−1.28034	−0.0450700
$808$	−4.95693	−0.174384
$809$	4.35354	0.153062	0.0765311	−	0.997067i	$-0.475616\pi$
$809$	4.35354	0.153062	0.0765311	+	0.997067i	$0.475616\pi$
$810$	−5.11815	−0.179833
$811$	−6.85412	−0.240681	−0.120340	−	0.992733i	$-0.538399\pi$
$811$	−6.85412	−0.240681	−0.120340	+	0.992733i	$0.538399\pi$
$812$	51.8149	1.81835
$813$	−3.46640	−0.121572
$814$	−0.570236	−0.0199868
$815$	0.482590	0.0169044
$816$	2.20740	0.0772745
$817$	−64.0172	−2.23968
$818$	−43.9475	−1.53659
$819$	−7.83408	−0.273745
$820$	−4.67170	−0.163143
$821$	−6.23411	−0.217572	−0.108786	−	0.994065i	$-0.534696\pi$
$821$	−6.23411	−0.217572	−0.108786	+	0.994065i	$0.534696\pi$
$822$	−5.65213	−0.197141
$823$	34.2162	1.19270	0.596351	−	0.802724i	$-0.296617\pi$
$823$	34.2162	1.19270	0.596351	+	0.802724i	$0.296617\pi$
$824$	4.77791	0.166447
$825$	0.271027	0.00943597
$826$	38.4257	1.33700
$827$	−17.0563	−0.593104	−0.296552	−	0.955017i	$-0.595837\pi$
$827$	−17.0563	−0.593104	−0.296552	+	0.955017i	$0.595837\pi$
$828$	−22.6533	−0.787257
$829$	14.2766	0.495846	0.247923	−	0.968780i	$-0.420252\pi$
$829$	14.2766	0.495846	0.247923	+	0.968780i	$0.420252\pi$
$830$	2.26828	0.0787330
$831$	8.42357	0.292210
$832$	−12.4593	−0.431947
$833$	1.15960	0.0401776
$834$	−9.03841	−0.312974
$835$	4.87407	0.168674
$836$	3.57146	0.123521
$837$	18.6393	0.644270
$838$	67.3917	2.32801
$839$	22.2095	0.766758	0.383379	−	0.923591i	$-0.374760\pi$
$839$	22.2095	0.766758	0.383379	+	0.923591i	$0.374760\pi$
$840$	0.422671	0.0145835
$841$	19.3589	0.667548
$842$	72.4736	2.49760
$843$	4.84356	0.166821
$844$	17.7842	0.612156
$845$	0.291618	0.0100320
$846$	55.6359	1.91280
$847$	−29.7069	−1.02074
$848$	−13.0271	−0.447352
$849$	−8.90721	−0.305695
$850$	37.4991	1.28621
$851$	4.40827	0.151114
$852$	−12.4184	−0.425447
$853$	3.50891	0.120143	0.0600715	−	0.998194i	$-0.480867\pi$
$853$	3.50891	0.120143	0.0600715	+	0.998194i	$0.480867\pi$
$854$	29.5773	1.01211
$855$	−6.48587	−0.221812
$856$	−13.5320	−0.462513
$857$	17.6296	0.602215	0.301107	−	0.953590i	$-0.402644\pi$
$857$	17.6296	0.602215	0.301107	+	0.953590i	$0.402644\pi$
$858$	0.120206	0.00410376
$859$	22.6444	0.772616	0.386308	−	0.922370i	$-0.373750\pi$
$859$	22.6444	0.772616	0.386308	+	0.922370i	$0.373750\pi$
$860$	−6.68315	−0.227894
$861$	5.14820	0.175450
$862$	37.8872	1.29044
$863$	17.4816	0.595082	0.297541	−	0.954709i	$-0.403834\pi$
$863$	17.4816	0.595082	0.297541	+	0.954709i	$0.403834\pi$
$864$	14.4116	0.490293
$865$	−1.69766	−0.0577222
$866$	−58.1209	−1.97503
$867$	1.55137	0.0526873
$868$	72.1534	2.44905
$869$	−1.67630	−0.0568645
$870$	1.44382	0.0489503
$871$	12.2773	0.416001
$872$	−0.433036	−0.0146644
$873$	−33.8963	−1.14721
$874$	−47.6756	−1.61265
$875$	−7.82882	−0.264663
$876$	8.80187	0.297388
$877$	10.0910	0.340748	0.170374	−	0.985379i	$-0.445502\pi$
$877$	10.0910	0.340748	0.170374	+	0.985379i	$0.445502\pi$
$878$	−70.1790	−2.36843
$879$	−3.58056	−0.120769
$880$	−0.0950736	−0.00320493
$881$	54.2913	1.82912	0.914561	−	0.404448i	$-0.132536\pi$
$881$	54.2913	1.82912	0.914561	+	0.404448i	$0.132536\pi$
$882$	2.08961	0.0703609
$883$	−3.54795	−0.119398	−0.0596989	−	0.998216i	$-0.519014\pi$
$883$	−3.54795	−0.119398	−0.0596989	+	0.998216i	$0.519014\pi$
$884$	9.63154	0.323944
$885$	0.620074	0.0208436
$886$	31.4088	1.05520
$887$	40.1171	1.34700	0.673500	−	0.739187i	$-0.264790\pi$
$887$	40.1171	1.34700	0.673500	+	0.739187i	$0.264790\pi$
$888$	0.829386	0.0278324
$889$	41.1555	1.38031
$890$	1.14417	0.0383526
$891$	1.35935	0.0455398
$892$	−12.6022	−0.421954
$893$	67.8082	2.26911
$894$	6.64013	0.222079
$895$	4.35765	0.145660
$896$	32.9930	1.10222
$897$	−0.929262	−0.0310272
$898$	−2.97852	−0.0993945
$899$	67.3408	2.24594
$900$	39.1330	1.30443
$901$	23.6121	0.786635
$902$	2.14254	0.0713389
$903$	7.36481	0.245086
$904$	8.14487	0.270894
$905$	−7.20627	−0.239545
$906$	12.3509	0.410331
$907$	−12.9984	−0.431605	−0.215802	−	0.976437i	$-0.569237\pi$
$907$	−12.9984	−0.431605	−0.215802	+	0.976437i	$0.569237\pi$
$908$	16.9793	0.563479
$909$	−8.75071	−0.290243
$910$	−1.72122	−0.0570580
$911$	8.63660	0.286143	0.143072	−	0.989712i	$-0.454302\pi$
$911$	8.63660	0.286143	0.143072	+	0.989712i	$0.454302\pi$
$912$	4.84806	0.160535
$913$	−0.602439	−0.0199378
$914$	49.3646	1.63283
$915$	0.477287	0.0157786
$916$	−73.5829	−2.43125
$917$	18.1644	0.599843
$918$	−14.6856	−0.484697
$919$	−44.9298	−1.48210	−0.741048	−	0.671452i	$-0.765671\pi$
$919$	−44.9298	−1.48210	−0.741048	+	0.671452i	$0.765671\pi$
$920$	−1.35985	−0.0448328
$921$	3.06217	0.100902
$922$	80.4103	2.64817
$923$	13.8169	0.454788
$924$	−0.410875	−0.0135168
$925$	−7.61517	−0.250385
$926$	2.17988	0.0716352
$927$	8.43468	0.277031
$928$	52.0667	1.70917
$929$	−51.6750	−1.69540	−0.847700	−	0.530476i	$-0.822013\pi$
$929$	−51.6750	−1.69540	−0.847700	+	0.530476i	$0.822013\pi$
$930$	2.01056	0.0659288
$931$	2.54679	0.0834676
$932$	23.1408	0.758002
$933$	−2.55087	−0.0835117
$934$	−68.5630	−2.24345
$935$	0.172325	0.00563562
$936$	4.74203	0.154998
$937$	−6.39325	−0.208858	−0.104429	−	0.994532i	$-0.533302\pi$
$937$	−6.39325	−0.208858	−0.104429	+	0.994532i	$0.533302\pi$
$938$	−72.4645	−2.36605
$939$	2.72728	0.0890013
$940$	7.07891	0.230889
$941$	44.3523	1.44584	0.722921	−	0.690931i	$-0.242799\pi$
$941$	44.3523	1.44584	0.722921	+	0.690931i	$0.242799\pi$
$942$	−10.0597	−0.327762
$943$	−16.5631	−0.539370
$944$	12.5713	0.409161
$945$	1.51983	0.0494402
$946$	3.06504	0.0996530
$947$	37.1363	1.20677	0.603384	−	0.797450i	$-0.293818\pi$
$947$	37.1363	1.20677	0.603384	+	0.797450i	$0.293818\pi$
$948$	8.92366	0.289827
$949$	−9.79307	−0.317897
$950$	82.3584	2.67206
$951$	2.08199	0.0675130
$952$	−15.5320	−0.503395
$953$	−58.4326	−1.89282	−0.946409	−	0.322970i	$-0.895319\pi$
$953$	−58.4326	−1.89282	−0.946409	+	0.322970i	$0.895319\pi$
$954$	42.5495	1.37759
$955$	−5.85624	−0.189504
$956$	−2.42973	−0.0785830
$957$	−0.383470	−0.0123958
$958$	−31.0796	−1.00414
$959$	−21.4952	−0.694116
$960$	1.18669	0.0383002
$961$	62.7736	2.02496
$962$	−3.37747	−0.108894
$963$	−23.8886	−0.769800
$964$	16.4313	0.529217
$965$	1.76590	0.0568463
$966$	5.48480	0.176471
$967$	−19.8739	−0.639102	−0.319551	−	0.947569i	$-0.603532\pi$
$967$	−19.8739	−0.639102	−0.319551	+	0.947569i	$0.603532\pi$
$968$	17.9818	0.577956
$969$	−8.78731	−0.282289
$970$	−7.44734	−0.239120
$971$	47.5671	1.52650	0.763250	−	0.646103i	$-0.223602\pi$
$971$	47.5671	1.52650	0.763250	+	0.646103i	$0.223602\pi$
$972$	−23.1269	−0.741796
$973$	−34.3733	−1.10196
$974$	−30.9724	−0.992421
$975$	1.60528	0.0514100
$976$	9.67647	0.309736
$977$	−0.345350	−0.0110487	−0.00552436	−	0.999985i	$-0.501758\pi$
$977$	−0.345350	−0.0110487	−0.00552436	+	0.999985i	$0.501758\pi$
$978$	1.17822	0.0376752
$979$	−0.303884	−0.00971216
$980$	0.265875	0.00849306
$981$	−0.764459	−0.0244073
$982$	−48.7836	−1.55675
$983$	50.1414	1.59926	0.799632	−	0.600491i	$-0.205028\pi$
$983$	50.1414	1.59926	0.799632	+	0.600491i	$0.205028\pi$
$984$	−3.11624	−0.0993422
$985$	−4.70684	−0.149973
$986$	−53.0566	−1.68967
$987$	−7.80094	−0.248307
$988$	21.1535	0.672982
$989$	−23.6946	−0.753444
$990$	0.310533	0.00986937
$991$	26.1433	0.830469	0.415234	−	0.909714i	$-0.363700\pi$
$991$	26.1433	0.830469	0.415234	+	0.909714i	$0.363700\pi$
$992$	72.5040	2.30201
$993$	−2.31626	−0.0735042
$994$	−81.5515	−2.58666
$995$	−6.89052	−0.218444
$996$	3.20705	0.101619
$997$	−36.1390	−1.14453	−0.572267	−	0.820067i	$-0.693936\pi$
$997$	−36.1390	−1.14453	−0.572267	+	0.820067i	$0.693936\pi$
$998$	−82.8872	−2.62375
$999$	2.98229	0.0943556

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6019.2.a.e.1.19	✓	130

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6019.2.a.e.1.19	✓	130	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:	\( N \)	\(=\)	\( 6019 = 13 \cdot 463 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6019.a (trivial)

\(f(q)\)	\(=\)	\(q-2.17988 q^{2} -0.326610 q^{3} +2.75186 q^{4} +0.291618 q^{5} +0.711970 q^{6} +2.70764 q^{7} -1.63895 q^{8} -2.89333 q^{9} +O(q^{10})\)	\(q-2.17988 q^{2} -0.326610 q^{3} +2.75186 q^{4} +0.291618 q^{5} +0.711970 q^{6} +2.70764 q^{7} -1.63895 q^{8} -2.89333 q^{9} -0.635691 q^{10} +0.168835 q^{11} -0.898785 q^{12} +1.00000 q^{13} -5.90232 q^{14} -0.0952456 q^{15} -1.93100 q^{16} +3.50001 q^{17} +6.30709 q^{18} +7.68699 q^{19} +0.802492 q^{20} -0.884343 q^{21} -0.368040 q^{22} +2.84517 q^{23} +0.535299 q^{24} -4.91496 q^{25} -2.17988 q^{26} +1.92482 q^{27} +7.45104 q^{28} +6.95406 q^{29} +0.207623 q^{30} +9.68368 q^{31} +7.48724 q^{32} -0.0551434 q^{33} -7.62959 q^{34} +0.789597 q^{35} -7.96202 q^{36} +1.54939 q^{37} -16.7567 q^{38} -0.326610 q^{39} -0.477949 q^{40} -5.82149 q^{41} +1.92776 q^{42} -8.32800 q^{43} +0.464611 q^{44} -0.843747 q^{45} -6.20212 q^{46} +8.82116 q^{47} +0.630684 q^{48} +0.331312 q^{49} +10.7140 q^{50} -1.14314 q^{51} +2.75186 q^{52} +6.74630 q^{53} -4.19587 q^{54} +0.0492355 q^{55} -4.43770 q^{56} -2.51065 q^{57} -15.1590 q^{58} -6.51027 q^{59} -0.262102 q^{60} -5.01113 q^{61} -21.1092 q^{62} -7.83408 q^{63} -12.4593 q^{64} +0.291618 q^{65} +0.120206 q^{66} +12.2773 q^{67} +9.63154 q^{68} -0.929262 q^{69} -1.72122 q^{70} +13.8169 q^{71} +4.74203 q^{72} -9.79307 q^{73} -3.37747 q^{74} +1.60528 q^{75} +21.1535 q^{76} +0.457145 q^{77} +0.711970 q^{78} -9.92858 q^{79} -0.563114 q^{80} +8.05131 q^{81} +12.6901 q^{82} -3.56820 q^{83} -2.43359 q^{84} +1.02067 q^{85} +18.1540 q^{86} -2.27127 q^{87} -0.276713 q^{88} -1.79988 q^{89} +1.83926 q^{90} +2.70764 q^{91} +7.82950 q^{92} -3.16279 q^{93} -19.2290 q^{94} +2.24167 q^{95} -2.44541 q^{96} +11.7153 q^{97} -0.722218 q^{98} -0.488496 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 130 q + 10 q^{2} + 11 q^{3} + 146 q^{4} + 40 q^{5} + 4 q^{6} + 8 q^{7} + 24 q^{8} + 181 q^{9}+O(q^{10}) \) 130 * q + 10 * q^2 + 11 * q^3 + 146 * q^4 + 40 * q^5 + 4 * q^6 + 8 * q^7 + 24 * q^8 + 181 * q^9	\( 130 q + 10 q^{2} + 11 q^{3} + 146 q^{4} + 40 q^{5} + 4 q^{6} + 8 q^{7} + 24 q^{8} + 181 q^{9} + 5 q^{10} + 43 q^{11} + 28 q^{12} + 130 q^{13} + 47 q^{14} + 29 q^{15} + 170 q^{16} + 85 q^{17} + 20 q^{18} + 3 q^{19} + 73 q^{20} + 62 q^{21} + 12 q^{22} + 62 q^{23} - 5 q^{24} + 178 q^{25} + 10 q^{26} + 35 q^{27} - q^{28} + 134 q^{29} + 24 q^{30} + 14 q^{31} + 48 q^{32} + 4 q^{33} + 4 q^{34} + 50 q^{35} + 244 q^{36} + 32 q^{37} + 76 q^{38} + 11 q^{39} - 6 q^{40} + 48 q^{41} + 9 q^{42} + 34 q^{43} + 123 q^{44} + 115 q^{45} + 5 q^{46} + 25 q^{47} + 35 q^{48} + 210 q^{49} + 24 q^{50} + 20 q^{51} + 146 q^{52} + 193 q^{53} - 39 q^{54} + 32 q^{55} + 122 q^{56} + 7 q^{57} - 4 q^{58} + 50 q^{59} + 42 q^{60} + 57 q^{61} + 51 q^{62} + 8 q^{63} + 172 q^{64} + 40 q^{65} - 4 q^{66} + 21 q^{67} + 132 q^{68} + 92 q^{69} - 46 q^{70} + 58 q^{71} - 26 q^{72} + 15 q^{73} + 120 q^{74} + 23 q^{75} - 65 q^{76} + 192 q^{77} + 4 q^{78} + 32 q^{79} + 66 q^{80} + 326 q^{81} + 11 q^{82} + 33 q^{83} + 5 q^{84} + 43 q^{85} + 105 q^{86} + 31 q^{87} - 17 q^{88} + 84 q^{89} - 73 q^{90} + 8 q^{91} + 161 q^{92} + 52 q^{93} + 4 q^{94} + 59 q^{95} - 77 q^{96} + 9 q^{97} - 61 q^{98} + 100 q^{99}+O(q^{100}) \) 130 * q + 10 * q^2 + 11 * q^3 + 146 * q^4 + 40 * q^5 + 4 * q^6 + 8 * q^7 + 24 * q^8 + 181 * q^9 + 5 * q^10 + 43 * q^11 + 28 * q^12 + 130 * q^13 + 47 * q^14 + 29 * q^15 + 170 * q^16 + 85 * q^17 + 20 * q^18 + 3 * q^19 + 73 * q^20 + 62 * q^21 + 12 * q^22 + 62 * q^23 - 5 * q^24 + 178 * q^25 + 10 * q^26 + 35 * q^27 - q^28 + 134 * q^29 + 24 * q^30 + 14 * q^31 + 48 * q^32 + 4 * q^33 + 4 * q^34 + 50 * q^35 + 244 * q^36 + 32 * q^37 + 76 * q^38 + 11 * q^39 - 6 * q^40 + 48 * q^41 + 9 * q^42 + 34 * q^43 + 123 * q^44 + 115 * q^45 + 5 * q^46 + 25 * q^47 + 35 * q^48 + 210 * q^49 + 24 * q^50 + 20 * q^51 + 146 * q^52 + 193 * q^53 - 39 * q^54 + 32 * q^55 + 122 * q^56 + 7 * q^57 - 4 * q^58 + 50 * q^59 + 42 * q^60 + 57 * q^61 + 51 * q^62 + 8 * q^63 + 172 * q^64 + 40 * q^65 - 4 * q^66 + 21 * q^67 + 132 * q^68 + 92 * q^69 - 46 * q^70 + 58 * q^71 - 26 * q^72 + 15 * q^73 + 120 * q^74 + 23 * q^75 - 65 * q^76 + 192 * q^77 + 4 * q^78 + 32 * q^79 + 66 * q^80 + 326 * q^81 + 11 * q^82 + 33 * q^83 + 5 * q^84 + 43 * q^85 + 105 * q^86 + 31 * q^87 - 17 * q^88 + 84 * q^89 - 73 * q^90 + 8 * q^91 + 161 * q^92 + 52 * q^93 + 4 * q^94 + 59 * q^95 - 77 * q^96 + 9 * q^97 - 61 * q^98 + 100 * q^99

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