LMFDB - Embedded newform 4019.2.a.b.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4019,2,Mod(1,4019)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4019, 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("4019.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4019 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4019.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:	$32.0918765724$
Analytic rank:	$0$
Dimension:	$186$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	4019.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.59341 q^{2} +1.69325 q^{3} +4.72575 q^{4} -3.22826 q^{5} -4.39129 q^{6} -0.750732 q^{7} -7.06898 q^{8} -0.132895 q^{9} +O(q^{10})$	\(q-2.59341 q^{2} +1.69325 q^{3} +4.72575 q^{4} -3.22826 q^{5} -4.39129 q^{6} -0.750732 q^{7} -7.06898 q^{8} -0.132895 q^{9} +8.37219 q^{10} -1.90047 q^{11} +8.00190 q^{12} +3.93841 q^{13} +1.94695 q^{14} -5.46626 q^{15} +8.88124 q^{16} -5.08204 q^{17} +0.344651 q^{18} -5.14799 q^{19} -15.2560 q^{20} -1.27118 q^{21} +4.92868 q^{22} +0.476522 q^{23} -11.9696 q^{24} +5.42167 q^{25} -10.2139 q^{26} -5.30478 q^{27} -3.54778 q^{28} -8.68999 q^{29} +14.1762 q^{30} +2.91651 q^{31} -8.89469 q^{32} -3.21797 q^{33} +13.1798 q^{34} +2.42356 q^{35} -0.628029 q^{36} -3.88758 q^{37} +13.3508 q^{38} +6.66873 q^{39} +22.8205 q^{40} +3.93068 q^{41} +3.29668 q^{42} +11.6403 q^{43} -8.98114 q^{44} +0.429020 q^{45} -1.23581 q^{46} +6.60193 q^{47} +15.0382 q^{48} -6.43640 q^{49} -14.0606 q^{50} -8.60518 q^{51} +18.6120 q^{52} -12.6826 q^{53} +13.7575 q^{54} +6.13520 q^{55} +5.30691 q^{56} -8.71685 q^{57} +22.5367 q^{58} +1.95762 q^{59} -25.8322 q^{60} -7.61692 q^{61} -7.56369 q^{62} +0.0997685 q^{63} +5.30505 q^{64} -12.7142 q^{65} +8.34551 q^{66} +6.12890 q^{67} -24.0165 q^{68} +0.806872 q^{69} -6.28527 q^{70} +13.0944 q^{71} +0.939432 q^{72} +0.368318 q^{73} +10.0821 q^{74} +9.18025 q^{75} -24.3281 q^{76} +1.42674 q^{77} -17.2947 q^{78} -2.29585 q^{79} -28.6710 q^{80} -8.58365 q^{81} -10.1938 q^{82} +5.89811 q^{83} -6.00728 q^{84} +16.4061 q^{85} -30.1881 q^{86} -14.7144 q^{87} +13.4344 q^{88} -9.35226 q^{89} -1.11262 q^{90} -2.95669 q^{91} +2.25192 q^{92} +4.93839 q^{93} -17.1215 q^{94} +16.6191 q^{95} -15.0610 q^{96} +0.838216 q^{97} +16.6922 q^{98} +0.252563 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 186 q + 6 q^{2} + 10 q^{3} + 212 q^{4} + 38 q^{5} + 47 q^{6} + 32 q^{7} + 15 q^{8} + 216 q^{9}+O(q^{10}) $ 186 * q + 6 * q^2 + 10 * q^3 + 212 * q^4 + 38 * q^5 + 47 * q^6 + 32 * q^7 + 15 * q^8 + 216 * q^9	\( 186 q + 6 q^{2} + 10 q^{3} + 212 q^{4} + 38 q^{5} + 47 q^{6} + 32 q^{7} + 15 q^{8} + 216 q^{9} + 50 q^{10} + 25 q^{11} + 17 q^{12} + 113 q^{13} + 12 q^{14} + 12 q^{15} + 252 q^{16} + 35 q^{17} + 13 q^{18} + 97 q^{19} + 55 q^{20} + 115 q^{21} + 14 q^{22} + 27 q^{23} + 122 q^{24} + 244 q^{25} + 39 q^{26} + 34 q^{27} + 66 q^{28} + 91 q^{29} + 4 q^{30} + 135 q^{31} + 21 q^{32} + 32 q^{33} + 58 q^{34} + 17 q^{35} + 273 q^{36} + 133 q^{37} - 3 q^{38} + 55 q^{39} + 142 q^{40} + 97 q^{41} - 8 q^{42} + 67 q^{43} + 44 q^{44} + 154 q^{45} + 101 q^{46} + 20 q^{47} - 7 q^{48} + 312 q^{49} + 21 q^{50} + 23 q^{51} + 193 q^{52} + 22 q^{53} + 141 q^{54} + 88 q^{55} + 28 q^{56} + 65 q^{57} + 62 q^{58} + 41 q^{59} + q^{60} + 377 q^{61} + 29 q^{62} + 39 q^{63} + 311 q^{64} + 21 q^{65} + 35 q^{66} + 42 q^{67} + 24 q^{68} + 137 q^{69} + 35 q^{70} + 17 q^{71} - 8 q^{72} + 213 q^{73} - 9 q^{74} + 2 q^{75} + 242 q^{76} + 60 q^{77} + 103 q^{79} + 80 q^{80} + 270 q^{81} + 84 q^{82} + 42 q^{83} + 137 q^{84} + 294 q^{85} - 9 q^{86} + 22 q^{87} - 13 q^{88} + 78 q^{89} + 69 q^{90} + 118 q^{91} + 49 q^{92} + 51 q^{93} + 93 q^{94} + 10 q^{95} + 260 q^{96} + 142 q^{97} - 31 q^{98} + 78 q^{99}+O(q^{100}) \) 186 * q + 6 * q^2 + 10 * q^3 + 212 * q^4 + 38 * q^5 + 47 * q^6 + 32 * q^7 + 15 * q^8 + 216 * q^9 + 50 * q^10 + 25 * q^11 + 17 * q^12 + 113 * q^13 + 12 * q^14 + 12 * q^15 + 252 * q^16 + 35 * q^17 + 13 * q^18 + 97 * q^19 + 55 * q^20 + 115 * q^21 + 14 * q^22 + 27 * q^23 + 122 * q^24 + 244 * q^25 + 39 * q^26 + 34 * q^27 + 66 * q^28 + 91 * q^29 + 4 * q^30 + 135 * q^31 + 21 * q^32 + 32 * q^33 + 58 * q^34 + 17 * q^35 + 273 * q^36 + 133 * q^37 - 3 * q^38 + 55 * q^39 + 142 * q^40 + 97 * q^41 - 8 * q^42 + 67 * q^43 + 44 * q^44 + 154 * q^45 + 101 * q^46 + 20 * q^47 - 7 * q^48 + 312 * q^49 + 21 * q^50 + 23 * q^51 + 193 * q^52 + 22 * q^53 + 141 * q^54 + 88 * q^55 + 28 * q^56 + 65 * q^57 + 62 * q^58 + 41 * q^59 + q^60 + 377 * q^61 + 29 * q^62 + 39 * q^63 + 311 * q^64 + 21 * q^65 + 35 * q^66 + 42 * q^67 + 24 * q^68 + 137 * q^69 + 35 * q^70 + 17 * q^71 - 8 * q^72 + 213 * q^73 - 9 * q^74 + 2 * q^75 + 242 * q^76 + 60 * q^77 + 103 * q^79 + 80 * q^80 + 270 * q^81 + 84 * q^82 + 42 * q^83 + 137 * q^84 + 294 * q^85 - 9 * q^86 + 22 * q^87 - 13 * q^88 + 78 * q^89 + 69 * q^90 + 118 * q^91 + 49 * q^92 + 51 * q^93 + 93 * q^94 + 10 * q^95 + 260 * q^96 + 142 * q^97 - 31 * q^98 + 78 * 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 $

$2$	−2.59341	−1.83381	−0.916907	−	0.399100i	$-0.869323\pi$
$2$	−2.59341	−1.83381	−0.916907	+	0.399100i	$0.869323\pi$
$3$	1.69325	0.977600	0.488800	−	0.872396i	$-0.337435\pi$
$3$	1.69325	0.977600	0.488800	+	0.872396i	$0.337435\pi$
$4$	4.72575	2.36288
$5$	−3.22826	−1.44372	−0.721861	−	0.692038i	$-0.756713\pi$
$5$	−3.22826	−1.44372	−0.721861	+	0.692038i	$0.756713\pi$
$6$	−4.39129	−1.79274
$7$	−0.750732	−0.283750	−0.141875	−	0.989885i	$-0.545313\pi$
$7$	−0.750732	−0.283750	−0.141875	+	0.989885i	$0.545313\pi$
$8$	−7.06898	−2.49926
$9$	−0.132895	−0.0442983
$10$	8.37219	2.64752
$11$	−1.90047	−0.573012	−0.286506	−	0.958078i	$-0.592494\pi$
$11$	−1.90047	−0.573012	−0.286506	+	0.958078i	$0.592494\pi$
$12$	8.00190	2.30995
$13$	3.93841	1.09232	0.546160	−	0.837681i	$-0.316089\pi$
$13$	3.93841	1.09232	0.546160	+	0.837681i	$0.316089\pi$
$14$	1.94695	0.520345
$15$	−5.46626	−1.41138
$16$	8.88124	2.22031
$17$	−5.08204	−1.23258	−0.616288	−	0.787521i	$-0.711364\pi$
$17$	−5.08204	−1.23258	−0.616288	+	0.787521i	$0.711364\pi$
$18$	0.344651	0.0812349
$19$	−5.14799	−1.18103	−0.590515	−	0.807027i	$-0.701075\pi$
$19$	−5.14799	−1.18103	−0.590515	+	0.807027i	$0.701075\pi$
$20$	−15.2560	−3.41134
$21$	−1.27118	−0.277394
$22$	4.92868	1.05080
$23$	0.476522	0.0993616	0.0496808	−	0.998765i	$-0.484180\pi$
$23$	0.476522	0.0993616	0.0496808	+	0.998765i	$0.484180\pi$
$24$	−11.9696	−2.44328
$25$	5.42167	1.08433
$26$	−10.2139	−2.00311
$27$	−5.30478	−1.02091
$28$	−3.54778	−0.670467
$29$	−8.68999	−1.61369	−0.806846	−	0.590762i	$-0.798827\pi$
$29$	−8.68999	−1.61369	−0.806846	+	0.590762i	$0.798827\pi$
$30$	14.1762	2.58821
$31$	2.91651	0.523821	0.261910	−	0.965092i	$-0.415648\pi$
$31$	2.91651	0.523821	0.261910	+	0.965092i	$0.415648\pi$
$32$	−8.89469	−1.57237
$33$	−3.21797	−0.560177
$34$	13.1798	2.26032
$35$	2.42356	0.409656
$36$	−0.628029	−0.104671
$37$	−3.88758	−0.639114	−0.319557	−	0.947567i	$-0.603534\pi$
$37$	−3.88758	−0.639114	−0.319557	+	0.947567i	$0.603534\pi$
$38$	13.3508	2.16579
$39$	6.66873	1.06785
$40$	22.8205	3.60824
$41$	3.93068	0.613869	0.306935	−	0.951731i	$-0.400697\pi$
$41$	3.93068	0.613869	0.306935	+	0.951731i	$0.400697\pi$
$42$	3.29668	0.508689
$43$	11.6403	1.77513	0.887567	−	0.460679i	$-0.152394\pi$
$43$	11.6403	1.77513	0.887567	+	0.460679i	$0.152394\pi$
$44$	−8.98114	−1.35396
$45$	0.429020	0.0639545
$46$	−1.23581	−0.182211
$47$	6.60193	0.962990	0.481495	−	0.876449i	$-0.340094\pi$
$47$	6.60193	0.962990	0.481495	+	0.876449i	$0.340094\pi$
$48$	15.0382	2.17057
$49$	−6.43640	−0.919486
$50$	−14.0606	−1.98847
$51$	−8.60518	−1.20497
$52$	18.6120	2.58102
$53$	−12.6826	−1.74209	−0.871043	−	0.491208i	$-0.836556\pi$
$53$	−12.6826	−1.74209	−0.871043	+	0.491208i	$0.836556\pi$
$54$	13.7575	1.87215
$55$	6.13520	0.827271
$56$	5.30691	0.709166
$57$	−8.71685	−1.15458
$58$	22.5367	2.95921
$59$	1.95762	0.254860	0.127430	−	0.991848i	$-0.459327\pi$
$59$	1.95762	0.254860	0.127430	+	0.991848i	$0.459327\pi$
$60$	−25.8322	−3.33492
$61$	−7.61692	−0.975247	−0.487623	−	0.873054i	$-0.662136\pi$
$61$	−7.61692	−0.975247	−0.487623	+	0.873054i	$0.662136\pi$
$62$	−7.56369	−0.960590
$63$	0.0997685	0.0125697
$64$	5.30505	0.663132
$65$	−12.7142	−1.57701
$66$	8.34551	1.02726
$67$	6.12890	0.748764	0.374382	−	0.927275i	$-0.377855\pi$
$67$	6.12890	0.748764	0.374382	+	0.927275i	$0.377855\pi$
$68$	−24.0165	−2.91242
$69$	0.806872	0.0971359
$70$	−6.28527	−0.751234
$71$	13.0944	1.55401	0.777007	−	0.629492i	$-0.216737\pi$
$71$	13.0944	1.55401	0.777007	+	0.629492i	$0.216737\pi$
$72$	0.939432	0.110713
$73$	0.368318	0.0431084	0.0215542	−	0.999768i	$-0.493139\pi$
$73$	0.368318	0.0431084	0.0215542	+	0.999768i	$0.493139\pi$
$74$	10.0821	1.17202
$75$	9.18025	1.06004
$76$	−24.3281	−2.79063
$77$	1.42674	0.162592
$78$	−17.2947	−1.95824
$79$	−2.29585	−0.258303	−0.129151	−	0.991625i	$-0.541225\pi$
$79$	−2.29585	−0.258303	−0.129151	+	0.991625i	$0.541225\pi$
$80$	−28.6710	−3.20551
$81$	−8.58365	−0.953739
$82$	−10.1938	−1.12572
$83$	5.89811	0.647402	0.323701	−	0.946159i	$-0.395073\pi$
$83$	5.89811	0.647402	0.323701	+	0.946159i	$0.395073\pi$
$84$	−6.00728	−0.655448
$85$	16.4061	1.77950
$86$	−30.1881	−3.25527
$87$	−14.7144	−1.57754
$88$	13.4344	1.43211
$89$	−9.35226	−0.991338	−0.495669	−	0.868512i	$-0.665077\pi$
$89$	−9.35226	−0.991338	−0.495669	+	0.868512i	$0.665077\pi$
$90$	−1.11262	−0.117281
$91$	−2.95669	−0.309946
$92$	2.25192	0.234779
$93$	4.93839	0.512087
$94$	−17.1215	−1.76595
$95$	16.6191	1.70508
$96$	−15.0610	−1.53715
$97$	0.838216	0.0851080	0.0425540	−	0.999094i	$-0.486451\pi$
$97$	0.838216	0.0851080	0.0425540	+	0.999094i	$0.486451\pi$
$98$	16.6922	1.68617
$99$	0.252563	0.0253835
$100$	25.6215	2.56215
$101$	−8.14134	−0.810094	−0.405047	−	0.914296i	$-0.632745\pi$
$101$	−8.14134	−0.810094	−0.405047	+	0.914296i	$0.632745\pi$
$102$	22.3167	2.20968
$103$	−2.23795	−0.220512	−0.110256	−	0.993903i	$-0.535167\pi$
$103$	−2.23795	−0.220512	−0.110256	+	0.993903i	$0.535167\pi$
$104$	−27.8406	−2.72999
$105$	4.10370	0.400480
$106$	32.8911	3.19466
$107$	−1.68194	−0.162599	−0.0812997	−	0.996690i	$-0.525907\pi$
$107$	−1.68194	−0.162599	−0.0812997	+	0.996690i	$0.525907\pi$
$108$	−25.0691	−2.41227
$109$	5.44772	0.521796	0.260898	−	0.965366i	$-0.415981\pi$
$109$	5.44772	0.521796	0.260898	+	0.965366i	$0.415981\pi$
$110$	−15.9111	−1.51706
$111$	−6.58266	−0.624798
$112$	−6.66743	−0.630013
$113$	3.89333	0.366253	0.183127	−	0.983089i	$-0.441378\pi$
$113$	3.89333	0.366253	0.183127	+	0.983089i	$0.441378\pi$
$114$	22.6063	2.11728
$115$	−1.53834	−0.143451
$116$	−41.0668	−3.81295
$117$	−0.523395	−0.0483879
$118$	−5.07689	−0.467366
$119$	3.81525	0.349743
$120$	38.6409	3.52742
$121$	−7.38822	−0.671657
$122$	19.7538	1.78842
$123$	6.65563	0.600118
$124$	13.7827	1.23772
$125$	−1.36125	−0.121754
$126$	−0.258740	−0.0230504
$127$	−11.1026	−0.985195	−0.492597	−	0.870257i	$-0.663952\pi$
$127$	−11.1026	−0.985195	−0.492597	+	0.870257i	$0.663952\pi$
$128$	4.03122	0.356313
$129$	19.7100	1.73537
$130$	32.9732	2.89194
$131$	22.0662	1.92793	0.963967	−	0.266021i	$-0.0857092\pi$
$131$	22.0662	1.92793	0.963967	+	0.266021i	$0.0857092\pi$
$132$	−15.2073	−1.32363
$133$	3.86476	0.335117
$134$	−15.8947	−1.37309
$135$	17.1252	1.47390
$136$	35.9249	3.08053
$137$	−3.02361	−0.258324	−0.129162	−	0.991623i	$-0.541229\pi$
$137$	−3.02361	−0.258324	−0.129162	+	0.991623i	$0.541229\pi$
$138$	−2.09255	−0.178129
$139$	13.0157	1.10397	0.551987	−	0.833853i	$-0.313870\pi$
$139$	13.0157	1.10397	0.551987	+	0.833853i	$0.313870\pi$
$140$	11.4531	0.967967
$141$	11.1787	0.941419
$142$	−33.9590	−2.84977
$143$	−7.48483	−0.625913
$144$	−1.18027	−0.0983560
$145$	28.0536	2.32972
$146$	−0.955199	−0.0790529
$147$	−10.8985	−0.898889
$148$	−18.3718	−1.51015
$149$	12.8203	1.05028	0.525141	−	0.851015i	$-0.324013\pi$
$149$	12.8203	1.05028	0.525141	+	0.851015i	$0.324013\pi$
$150$	−23.8081	−1.94392
$151$	8.05227	0.655284	0.327642	−	0.944802i	$-0.393746\pi$
$151$	8.05227	0.655284	0.327642	+	0.944802i	$0.393746\pi$
$152$	36.3911	2.95171
$153$	0.675377	0.0546010
$154$	−3.70012	−0.298164
$155$	−9.41526	−0.756252
$156$	31.5148	2.52320
$157$	11.1112	0.886767	0.443383	−	0.896332i	$-0.353778\pi$
$157$	11.1112	0.886767	0.443383	+	0.896332i	$0.353778\pi$
$158$	5.95406	0.473679
$159$	−21.4748	−1.70306
$160$	28.7144	2.27007
$161$	−0.357740	−0.0281939
$162$	22.2609	1.74898
$163$	−17.6950	−1.38598	−0.692990	−	0.720947i	$-0.743707\pi$
$163$	−17.6950	−1.38598	−0.692990	+	0.720947i	$0.743707\pi$
$164$	18.5754	1.45050
$165$	10.3885	0.808740
$166$	−15.2962	−1.18722
$167$	13.1943	1.02101	0.510504	−	0.859876i	$-0.329459\pi$
$167$	13.1943	1.02101	0.510504	+	0.859876i	$0.329459\pi$
$168$	8.98595	0.693281
$169$	2.51111	0.193162
$170$	−42.5478	−3.26327
$171$	0.684142	0.0523177
$172$	55.0093	4.19442
$173$	−13.3258	−1.01315	−0.506573	−	0.862197i	$-0.669088\pi$
$173$	−13.3258	−1.01315	−0.506573	+	0.862197i	$0.669088\pi$
$174$	38.1603	2.89292
$175$	−4.07022	−0.307680
$176$	−16.8785	−1.27227
$177$	3.31474	0.249151
$178$	24.2542	1.81793
$179$	2.92950	0.218961	0.109481	−	0.993989i	$-0.465081\pi$
$179$	2.92950	0.218961	0.109481	+	0.993989i	$0.465081\pi$
$180$	2.02744	0.151117
$181$	14.5296	1.07997	0.539987	−	0.841673i	$-0.318429\pi$
$181$	14.5296	1.07997	0.539987	+	0.841673i	$0.318429\pi$
$182$	7.66791	0.568383
$183$	−12.8974	−0.953401
$184$	−3.36852	−0.248331
$185$	12.5501	0.922704
$186$	−12.8072	−0.939073
$187$	9.65825	0.706281
$188$	31.1991	2.27543
$189$	3.98247	0.289682
$190$	−43.1000	−3.12680
$191$	10.7150	0.775307	0.387654	−	0.921805i	$-0.373286\pi$
$191$	10.7150	0.775307	0.387654	+	0.921805i	$0.373286\pi$
$192$	8.98279	0.648277
$193$	23.4016	1.68449	0.842243	−	0.539098i	$-0.181235\pi$
$193$	23.4016	1.68449	0.842243	+	0.539098i	$0.181235\pi$
$194$	−2.17383	−0.156072
$195$	−21.5284	−1.54168
$196$	−30.4168	−2.17263
$197$	6.48951	0.462358	0.231179	−	0.972911i	$-0.425742\pi$
$197$	6.48951	0.462358	0.231179	+	0.972911i	$0.425742\pi$
$198$	−0.654997	−0.0465486
$199$	−11.3346	−0.803486	−0.401743	−	0.915753i	$-0.631595\pi$
$199$	−11.3346	−0.803486	−0.401743	+	0.915753i	$0.631595\pi$
$200$	−38.3257	−2.71003
$201$	10.3778	0.731992
$202$	21.1138	1.48556
$203$	6.52386	0.457885
$204$	−40.6659	−2.84719
$205$	−12.6893	−0.886256
$206$	5.80392	0.404378
$207$	−0.0633273	−0.00440155
$208$	34.9780	2.42529
$209$	9.78359	0.676745
$210$	−10.6426	−0.734406
$211$	−1.76338	−0.121396	−0.0606981	−	0.998156i	$-0.519333\pi$
$211$	−1.76338	−0.121396	−0.0606981	+	0.998156i	$0.519333\pi$
$212$	−59.9347	−4.11633
$213$	22.1721	1.51920
$214$	4.36196	0.298177
$215$	−37.5780	−2.56280
$216$	37.4994	2.55151
$217$	−2.18952	−0.148634
$218$	−14.1281	−0.956878
$219$	0.623656	0.0421428
$220$	28.9935	1.95474
$221$	−20.0152	−1.34637
$222$	17.0715	1.14576
$223$	−21.3538	−1.42996	−0.714979	−	0.699146i	$-0.753564\pi$
$223$	−21.3538	−1.42996	−0.714979	+	0.699146i	$0.753564\pi$
$224$	6.67753	0.446161
$225$	−0.720512	−0.0480342
$226$	−10.0970	−0.671641
$227$	−24.7642	−1.64366	−0.821830	−	0.569733i	$-0.807047\pi$
$227$	−24.7642	−1.64366	−0.821830	+	0.569733i	$0.807047\pi$
$228$	−41.1937	−2.72812
$229$	11.6397	0.769174	0.384587	−	0.923089i	$-0.374344\pi$
$229$	11.6397	0.769174	0.384587	+	0.923089i	$0.374344\pi$
$230$	3.98953	0.263062
$231$	2.41583	0.158950
$232$	61.4294	4.03304
$233$	−4.82430	−0.316051	−0.158025	−	0.987435i	$-0.550513\pi$
$233$	−4.82430	−0.316051	−0.158025	+	0.987435i	$0.550513\pi$
$234$	1.35738	0.0887345
$235$	−21.3127	−1.39029
$236$	9.25121	0.602202
$237$	−3.88745	−0.252517
$238$	−9.89449	−0.641365
$239$	−0.764649	−0.0494610	−0.0247305	−	0.999694i	$-0.507873\pi$
$239$	−0.764649	−0.0494610	−0.0247305	+	0.999694i	$0.507873\pi$
$240$	−48.5472	−3.13371
$241$	−14.4360	−0.929906	−0.464953	−	0.885335i	$-0.653929\pi$
$241$	−14.4360	−0.929906	−0.464953	+	0.885335i	$0.653929\pi$
$242$	19.1607	1.23169
$243$	1.38005	0.0885305
$244$	−35.9957	−2.30439
$245$	20.7784	1.32748
$246$	−17.2608	−1.10051
$247$	−20.2749	−1.29006
$248$	−20.6168	−1.30917
$249$	9.98699	0.632900
$250$	3.53028	0.223274
$251$	29.2242	1.84461	0.922307	−	0.386459i	$-0.126302\pi$
$251$	29.2242	1.84461	0.922307	+	0.386459i	$0.126302\pi$
$252$	0.471481	0.0297005
$253$	−0.905614	−0.0569355
$254$	28.7935	1.80666
$255$	27.7798	1.73964
$256$	−21.0647	−1.31654
$257$	−17.3034	−1.07936	−0.539679	−	0.841871i	$-0.681454\pi$
$257$	−17.3034	−1.07936	−0.539679	+	0.841871i	$0.681454\pi$
$258$	−51.1161	−3.18235
$259$	2.91853	0.181349
$260$	−60.0843	−3.72627
$261$	1.15486	0.0714838
$262$	−57.2267	−3.53547
$263$	12.4461	0.767461	0.383730	−	0.923445i	$-0.374639\pi$
$263$	12.4461	0.767461	0.383730	+	0.923445i	$0.374639\pi$
$264$	22.7478	1.40003
$265$	40.9426	2.51509
$266$	−10.0229	−0.614543
$267$	−15.8357	−0.969132
$268$	28.9637	1.76924
$269$	−26.1504	−1.59442	−0.797210	−	0.603702i	$-0.793692\pi$
$269$	−26.1504	−1.59442	−0.797210	+	0.603702i	$0.793692\pi$
$270$	−44.4127	−2.70287
$271$	9.18322	0.557841	0.278920	−	0.960314i	$-0.410023\pi$
$271$	9.18322	0.557841	0.278920	+	0.960314i	$0.410023\pi$
$272$	−45.1348	−2.73670
$273$	−5.00643	−0.303003
$274$	7.84144	0.473719
$275$	−10.3037	−0.621337
$276$	3.81308	0.229520
$277$	−18.0381	−1.08380	−0.541901	−	0.840442i	$-0.682295\pi$
$277$	−18.0381	−1.08380	−0.541901	+	0.840442i	$0.682295\pi$
$278$	−33.7549	−2.02448
$279$	−0.387590	−0.0232044
$280$	−17.1321	−1.02384
$281$	15.2901	0.912128	0.456064	−	0.889947i	$-0.349259\pi$
$281$	15.2901	0.912128	0.456064	+	0.889947i	$0.349259\pi$
$282$	−28.9910	−1.72639
$283$	27.2624	1.62058	0.810291	−	0.586028i	$-0.199309\pi$
$283$	27.2624	1.62058	0.810291	+	0.586028i	$0.199309\pi$
$284$	61.8807	3.67194
$285$	28.1403	1.66689
$286$	19.4112	1.14781
$287$	−2.95089	−0.174185
$288$	1.18206	0.0696535
$289$	8.82712	0.519242
$290$	−72.7543	−4.27228
$291$	1.41931	0.0832015
$292$	1.74058	0.101860
$293$	−12.3434	−0.721109	−0.360554	−	0.932738i	$-0.617412\pi$
$293$	−12.3434	−0.721109	−0.360554	+	0.932738i	$0.617412\pi$
$294$	28.2641	1.64840
$295$	−6.31969	−0.367947
$296$	27.4813	1.59732
$297$	10.0816	0.584992
$298$	−33.2483	−1.92602
$299$	1.87674	0.108535
$300$	43.3836	2.50475
$301$	−8.73877	−0.503694
$302$	−20.8828	−1.20167
$303$	−13.7854	−0.791948
$304$	−45.7205	−2.62225
$305$	24.5894	1.40799
$306$	−1.75153	−0.100128
$307$	11.0014	0.627881	0.313941	−	0.949443i	$-0.398351\pi$
$307$	11.0014	0.627881	0.313941	+	0.949443i	$0.398351\pi$
$308$	6.74243	0.384186
$309$	−3.78942	−0.215572
$310$	24.4176	1.38683
$311$	16.7087	0.947464	0.473732	−	0.880669i	$-0.342907\pi$
$311$	16.7087	0.947464	0.473732	+	0.880669i	$0.342907\pi$
$312$	−47.1412	−2.66884
$313$	16.9364	0.957303	0.478651	−	0.878005i	$-0.341126\pi$
$313$	16.9364	0.957303	0.478651	+	0.878005i	$0.341126\pi$
$314$	−28.8157	−1.62617
$315$	−0.322079	−0.0181471
$316$	−10.8496	−0.610338
$317$	11.3436	0.637118	0.318559	−	0.947903i	$-0.396801\pi$
$317$	11.3436	0.637118	0.318559	+	0.947903i	$0.396801\pi$
$318$	55.6929	3.12310
$319$	16.5150	0.924665
$320$	−17.1261	−0.957378
$321$	−2.84795	−0.158957
$322$	0.927765	0.0517023
$323$	26.1623	1.45571
$324$	−40.5642	−2.25357
$325$	21.3528	1.18444
$326$	45.8904	2.54163
$327$	9.22436	0.510108
$328$	−27.7859	−1.53422
$329$	−4.95628	−0.273249
$330$	−26.9415	−1.48308
$331$	31.8616	1.75127	0.875635	−	0.482974i	$-0.160443\pi$
$331$	31.8616	1.75127	0.875635	+	0.482974i	$0.160443\pi$
$332$	27.8730	1.52973
$333$	0.516640	0.0283117
$334$	−34.2182	−1.87234
$335$	−19.7857	−1.08101
$336$	−11.2896	−0.615901
$337$	−13.7083	−0.746741	−0.373370	−	0.927682i	$-0.621798\pi$
$337$	−13.7083	−0.746741	−0.373370	+	0.927682i	$0.621798\pi$
$338$	−6.51233	−0.354224
$339$	6.59239	0.358049
$340$	77.5314	4.20473
$341$	−5.54273	−0.300156
$342$	−1.77426	−0.0959409
$343$	10.0871	0.544654
$344$	−82.2853	−4.43653
$345$	−2.60479	−0.140237
$346$	34.5593	1.85792
$347$	34.3853	1.84590	0.922949	−	0.384923i	$-0.125772\pi$
$347$	34.3853	1.84590	0.922949	+	0.384923i	$0.125772\pi$
$348$	−69.5364	−3.72754
$349$	−19.1978	−1.02763	−0.513817	−	0.857900i	$-0.671769\pi$
$349$	−19.1978	−1.02763	−0.513817	+	0.857900i	$0.671769\pi$
$350$	10.5557	0.564228
$351$	−20.8924	−1.11516
$352$	16.9041	0.900989
$353$	23.1527	1.23230	0.616148	−	0.787631i	$-0.288692\pi$
$353$	23.1527	1.23230	0.616148	+	0.787631i	$0.288692\pi$
$354$	−8.59646	−0.456897
$355$	−42.2720	−2.24356
$356$	−44.1965	−2.34241
$357$	6.46018	0.341909
$358$	−7.59739	−0.401535
$359$	−4.55174	−0.240232	−0.120116	−	0.992760i	$-0.538327\pi$
$359$	−4.55174	−0.240232	−0.120116	+	0.992760i	$0.538327\pi$
$360$	−3.03273	−0.159839
$361$	7.50181	0.394832
$362$	−37.6811	−1.98047
$363$	−12.5101	−0.656612
$364$	−13.9726	−0.732364
$365$	−1.18903	−0.0622366
$366$	33.4481	1.74836
$367$	9.77515	0.510259	0.255129	−	0.966907i	$-0.417882\pi$
$367$	9.77515	0.510259	0.255129	+	0.966907i	$0.417882\pi$
$368$	4.23210	0.220614
$369$	−0.522368	−0.0271934
$370$	−32.5476	−1.69207
$371$	9.52121	0.494317
$372$	23.3376	1.21000
$373$	10.6942	0.553724	0.276862	−	0.960910i	$-0.410706\pi$
$373$	10.6942	0.553724	0.276862	+	0.960910i	$0.410706\pi$
$374$	−25.0478	−1.29519
$375$	−2.30494	−0.119027
$376$	−46.6689	−2.40677
$377$	−34.2248	−1.76267
$378$	−10.3282	−0.531223
$379$	−10.4880	−0.538735	−0.269367	−	0.963037i	$-0.586815\pi$
$379$	−10.4880	−0.538735	−0.269367	+	0.963037i	$0.586815\pi$
$380$	78.5376	4.02889
$381$	−18.7995	−0.963126
$382$	−27.7882	−1.42177
$383$	−18.8764	−0.964540	−0.482270	−	0.876023i	$-0.660188\pi$
$383$	−18.8764	−0.964540	−0.482270	+	0.876023i	$0.660188\pi$
$384$	6.82587	0.348331
$385$	−4.60590	−0.234738
$386$	−60.6899	−3.08904
$387$	−1.54694	−0.0786354
$388$	3.96120	0.201100
$389$	37.3675	1.89461	0.947303	−	0.320340i	$-0.103797\pi$
$389$	37.3675	1.89461	0.947303	+	0.320340i	$0.103797\pi$
$390$	55.8319	2.82716
$391$	−2.42170	−0.122471
$392$	45.4988	2.29804
$393$	37.3637	1.88475
$394$	−16.8299	−0.847879
$395$	7.41159	0.372917
$396$	1.19355	0.0599781
$397$	−0.903344	−0.0453376	−0.0226688	−	0.999743i	$-0.507216\pi$
$397$	−0.903344	−0.0453376	−0.0226688	+	0.999743i	$0.507216\pi$
$398$	29.3951	1.47344
$399$	6.54402	0.327611
$400$	48.1511	2.40756
$401$	−26.8156	−1.33911	−0.669555	−	0.742763i	$-0.733515\pi$
$401$	−26.8156	−1.33911	−0.669555	+	0.742763i	$0.733515\pi$
$402$	−26.9138	−1.34234
$403$	11.4864	0.572180
$404$	−38.4740	−1.91415
$405$	27.7103	1.37693
$406$	−16.9190	−0.839676
$407$	7.38822	0.366221
$408$	60.8299	3.01153
$409$	−12.5241	−0.619275	−0.309637	−	0.950855i	$-0.600208\pi$
$409$	−12.5241	−0.619275	−0.309637	+	0.950855i	$0.600208\pi$
$410$	32.9084	1.62523
$411$	−5.11973	−0.252538
$412$	−10.5760	−0.521043
$413$	−1.46964	−0.0723165
$414$	0.164233	0.00807163
$415$	−19.0406	−0.934668
$416$	−35.0310	−1.71753
$417$	22.0388	1.07924
$418$	−25.3728	−1.24103
$419$	27.6385	1.35023	0.675114	−	0.737713i	$-0.264094\pi$
$419$	27.6385	1.35023	0.675114	+	0.737713i	$0.264094\pi$
$420$	19.3931	0.946285
$421$	23.0022	1.12106	0.560530	−	0.828134i	$-0.310597\pi$
$421$	23.0022	1.12106	0.560530	+	0.828134i	$0.310597\pi$
$422$	4.57316	0.222618
$423$	−0.877363	−0.0426589
$424$	89.6529	4.35393
$425$	−27.5531	−1.33652
$426$	−57.5011	−2.78594
$427$	5.71827	0.276726
$428$	−7.94844	−0.384202
$429$	−12.6737	−0.611892
$430$	97.4550	4.69970
$431$	11.5806	0.557816	0.278908	−	0.960318i	$-0.410028\pi$
$431$	11.5806	0.557816	0.278908	+	0.960318i	$0.410028\pi$
$432$	−47.1130	−2.26673
$433$	−18.0607	−0.867943	−0.433972	−	0.900926i	$-0.642888\pi$
$433$	−18.0607	−0.867943	−0.433972	+	0.900926i	$0.642888\pi$
$434$	5.67831	0.272568
$435$	47.5018	2.27754
$436$	25.7446	1.23294
$437$	−2.45313	−0.117349
$438$	−1.61739	−0.0772821
$439$	27.9317	1.33311	0.666554	−	0.745457i	$-0.267769\pi$
$439$	27.9317	1.33311	0.666554	+	0.745457i	$0.267769\pi$
$440$	−43.3697	−2.06757
$441$	0.855365	0.0407317
$442$	51.9075	2.46899
$443$	−32.5806	−1.54795	−0.773975	−	0.633216i	$-0.781735\pi$
$443$	−32.5806	−1.54795	−0.773975	+	0.633216i	$0.781735\pi$
$444$	−31.1080	−1.47632
$445$	30.1915	1.43122
$446$	55.3792	2.62228
$447$	21.7080	1.02676
$448$	−3.98267	−0.188164
$449$	−14.7323	−0.695261	−0.347630	−	0.937632i	$-0.613014\pi$
$449$	−14.7323	−0.695261	−0.347630	+	0.937632i	$0.613014\pi$
$450$	1.86858	0.0880857
$451$	−7.47013	−0.351755
$452$	18.3989	0.865412
$453$	13.6345	0.640606
$454$	64.2237	3.01417
$455$	9.54498	0.447476
$456$	61.6193	2.88559
$457$	−10.5137	−0.491811	−0.245906	−	0.969294i	$-0.579085\pi$
$457$	−10.5137	−0.491811	−0.245906	+	0.969294i	$0.579085\pi$
$458$	−30.1865	−1.41052
$459$	26.9591	1.25834
$460$	−7.26980	−0.338956
$461$	−0.897127	−0.0417834	−0.0208917	−	0.999782i	$-0.506651\pi$
$461$	−0.897127	−0.0417834	−0.0208917	+	0.999782i	$0.506651\pi$
$462$	−6.26524	−0.291485
$463$	32.7247	1.52085	0.760423	−	0.649428i	$-0.224992\pi$
$463$	32.7247	1.52085	0.760423	+	0.649428i	$0.224992\pi$
$464$	−77.1779	−3.58289
$465$	−15.9424	−0.739311
$466$	12.5114	0.579578
$467$	−31.8393	−1.47335	−0.736675	−	0.676247i	$-0.763605\pi$
$467$	−31.8393	−1.47335	−0.736675	+	0.676247i	$0.763605\pi$
$468$	−2.47344	−0.114335
$469$	−4.60116	−0.212462
$470$	55.2726	2.54954
$471$	18.8140	0.866903
$472$	−13.8384	−0.636962
$473$	−22.1221	−1.01717
$474$	10.0817	0.463069
$475$	−27.9107	−1.28063
$476$	18.0299	0.826401
$477$	1.68545	0.0771714
$478$	1.98304	0.0907023
$479$	13.6228	0.622442	0.311221	−	0.950338i	$-0.399262\pi$
$479$	13.6228	0.622442	0.311221	+	0.950338i	$0.399262\pi$
$480$	48.6207	2.21922
$481$	−15.3109	−0.698117
$482$	37.4385	1.70528
$483$	−0.605745	−0.0275623
$484$	−34.9149	−1.58704
$485$	−2.70598	−0.122872
$486$	−3.57904	−0.162348
$487$	−20.2084	−0.915732	−0.457866	−	0.889021i	$-0.651386\pi$
$487$	−20.2084	−0.915732	−0.457866	+	0.889021i	$0.651386\pi$
$488$	53.8439	2.43740
$489$	−29.9621	−1.35493
$490$	−53.8868	−2.43436
$491$	−1.34490	−0.0606947	−0.0303473	−	0.999539i	$-0.509661\pi$
$491$	−1.34490	−0.0606947	−0.0303473	+	0.999539i	$0.509661\pi$
$492$	31.4529	1.41801
$493$	44.1629	1.98900
$494$	52.5811	2.36574
$495$	−0.815338	−0.0366467
$496$	25.9022	1.16304
$497$	−9.83035	−0.440952
$498$	−25.9003	−1.16062
$499$	14.3490	0.642350	0.321175	−	0.947020i	$-0.395922\pi$
$499$	14.3490	0.642350	0.321175	+	0.947020i	$0.395922\pi$
$500$	−6.43294	−0.287690
$501$	22.3413	0.998137
$502$	−75.7901	−3.38268
$503$	−3.24888	−0.144860	−0.0724301	−	0.997373i	$-0.523075\pi$
$503$	−3.24888	−0.144860	−0.0724301	+	0.997373i	$0.523075\pi$
$504$	−0.705262	−0.0314149
$505$	26.2824	1.16955
$506$	2.34862	0.104409
$507$	4.25194	0.188835
$508$	−52.4681	−2.32789
$509$	6.33035	0.280588	0.140294	−	0.990110i	$-0.455195\pi$
$509$	6.33035	0.280588	0.140294	+	0.990110i	$0.455195\pi$
$510$	−72.0442	−3.19017
$511$	−0.276509	−0.0122320
$512$	46.5668	2.05798
$513$	27.3090	1.20572
$514$	44.8748	1.97934
$515$	7.22469	0.318358
$516$	93.1447	4.10047
$517$	−12.5468	−0.551805
$518$	−7.56894	−0.332560
$519$	−22.5640	−0.990451
$520$	89.8767	3.94135
$521$	−2.89812	−0.126969	−0.0634844	−	0.997983i	$-0.520221\pi$
$521$	−2.89812	−0.126969	−0.0634844	+	0.997983i	$0.520221\pi$
$522$	−2.99501	−0.131088
$523$	−32.0569	−1.40175	−0.700875	−	0.713284i	$-0.747207\pi$
$523$	−32.0569	−1.40175	−0.700875	+	0.713284i	$0.747207\pi$
$524$	104.279	4.55547
$525$	−6.89191	−0.300788
$526$	−32.2778	−1.40738
$527$	−14.8218	−0.645649
$528$	−28.5796	−1.24377
$529$	−22.7729	−0.990127
$530$	−106.181	−4.61220
$531$	−0.260157	−0.0112899
$532$	18.2639	0.791841
$533$	15.4806	0.670541
$534$	41.0685	1.77721
$535$	5.42975	0.234748
$536$	−43.3251	−1.87136
$537$	4.96039	0.214057
$538$	67.8187	2.92387
$539$	12.2322	0.526877
$540$	80.9296	3.48265
$541$	45.6333	1.96193	0.980964	−	0.194190i	$-0.0622079\pi$
$541$	45.6333	1.96193	0.980964	+	0.194190i	$0.0622079\pi$
$542$	−23.8158	−1.02298
$543$	24.6022	1.05578
$544$	45.2031	1.93807
$545$	−17.5866	−0.753329
$546$	12.9837	0.555651
$547$	14.3464	0.613407	0.306704	−	0.951805i	$-0.400774\pi$
$547$	14.3464	0.613407	0.306704	+	0.951805i	$0.400774\pi$
$548$	−14.2888	−0.610388
$549$	1.01225	0.0432018
$550$	26.7217	1.13942
$551$	44.7360	1.90582
$552$	−5.70376	−0.242768
$553$	1.72357	0.0732934
$554$	46.7800	1.98749
$555$	21.2505	0.902035
$556$	61.5088	2.60855
$557$	4.44027	0.188140	0.0940702	−	0.995566i	$-0.470012\pi$
$557$	4.44027	0.188140	0.0940702	+	0.995566i	$0.470012\pi$
$558$	1.00518	0.0425525
$559$	45.8444	1.93901
$560$	21.5242	0.909564
$561$	16.3539	0.690460
$562$	−39.6533	−1.67267
$563$	37.2623	1.57042	0.785209	−	0.619231i	$-0.212555\pi$
$563$	37.2623	1.57042	0.785209	+	0.619231i	$0.212555\pi$
$564$	52.8279	2.22446
$565$	−12.5687	−0.528768
$566$	−70.7025	−2.97185
$567$	6.44403	0.270624
$568$	−92.5638	−3.88389
$569$	25.5184	1.06978	0.534892	−	0.844920i	$-0.320352\pi$
$569$	25.5184	1.06978	0.534892	+	0.844920i	$0.320352\pi$
$570$	−72.9791	−3.05676
$571$	−13.8242	−0.578526	−0.289263	−	0.957250i	$-0.593410\pi$
$571$	−13.8242	−0.578526	−0.289263	+	0.957250i	$0.593410\pi$
$572$	−35.3715	−1.47895
$573$	18.1431	0.757940
$574$	7.65285	0.319424
$575$	2.58354	0.107741
$576$	−0.705015	−0.0293756
$577$	24.5403	1.02163	0.510813	−	0.859692i	$-0.329344\pi$
$577$	24.5403	1.02163	0.510813	+	0.859692i	$0.329344\pi$
$578$	−22.8923	−0.952194
$579$	39.6249	1.64675
$580$	132.574	5.50485
$581$	−4.42790	−0.183700
$582$	−3.68085	−0.152576
$583$	24.1028	0.998236
$584$	−2.60364	−0.107739
$585$	1.68966	0.0698587
$586$	32.0114	1.32238
$587$	−10.6040	−0.437675	−0.218838	−	0.975761i	$-0.570227\pi$
$587$	−10.6040	−0.437675	−0.218838	+	0.975761i	$0.570227\pi$
$588$	−51.5034	−2.12396
$589$	−15.0142	−0.618648
$590$	16.3895	0.674746
$591$	10.9884	0.452001
$592$	−34.5265	−1.41903
$593$	−19.6125	−0.805388	−0.402694	−	0.915335i	$-0.631926\pi$
$593$	−19.6125	−0.805388	−0.402694	+	0.915335i	$0.631926\pi$
$594$	−26.1456	−1.07277
$595$	−12.3166	−0.504932
$596$	60.5857	2.48169
$597$	−19.1923	−0.785488
$598$	−4.86715	−0.199033
$599$	−22.1832	−0.906379	−0.453190	−	0.891414i	$-0.649714\pi$
$599$	−22.1832	−0.906379	−0.453190	+	0.891414i	$0.649714\pi$
$600$	−64.8951	−2.64933
$601$	−16.5455	−0.674905	−0.337453	−	0.941343i	$-0.609565\pi$
$601$	−16.5455	−0.674905	−0.337453	+	0.941343i	$0.609565\pi$
$602$	22.6632	0.923682
$603$	−0.814500	−0.0331690
$604$	38.0530	1.54836
$605$	23.8511	0.969686
$606$	35.7510	1.45229
$607$	21.1646	0.859044	0.429522	−	0.903056i	$-0.358682\pi$
$607$	21.1646	0.859044	0.429522	+	0.903056i	$0.358682\pi$
$608$	45.7898	1.85702
$609$	11.0465	0.447628
$610$	−63.7703	−2.58198
$611$	26.0011	1.05189
$612$	3.19167	0.129015
$613$	43.8957	1.77293	0.886464	−	0.462797i	$-0.153154\pi$
$613$	43.8957	1.77293	0.886464	+	0.462797i	$0.153154\pi$
$614$	−28.5310	−1.15142
$615$	−21.4861	−0.866404
$616$	−10.0856	−0.406361
$617$	−35.8634	−1.44381	−0.721904	−	0.691993i	$-0.756733\pi$
$617$	−35.8634	−1.44381	−0.721904	+	0.691993i	$0.756733\pi$
$618$	9.82750	0.395320
$619$	−1.70051	−0.0683494	−0.0341747	−	0.999416i	$-0.510880\pi$
$619$	−1.70051	−0.0683494	−0.0341747	+	0.999416i	$0.510880\pi$
$620$	−44.4942	−1.78693
$621$	−2.52784	−0.101439
$622$	−43.3325	−1.73747
$623$	7.02104	0.281292
$624$	59.2266	2.37096
$625$	−22.7139	−0.908554
$626$	−43.9230	−1.75552
$627$	16.5661	0.661586
$628$	52.5086	2.09532
$629$	19.7568	0.787757
$630$	0.835281	0.0332784
$631$	11.5062	0.458053	0.229026	−	0.973420i	$-0.426446\pi$
$631$	11.5062	0.458053	0.229026	+	0.973420i	$0.426446\pi$
$632$	16.2293	0.645567
$633$	−2.98585	−0.118677
$634$	−29.4185	−1.16836
$635$	35.8420	1.42235
$636$	−101.485	−4.02413
$637$	−25.3492	−1.00437
$638$	−42.8302	−1.69566
$639$	−1.74017	−0.0688402
$640$	−13.0138	−0.514417
$641$	25.4406	1.00484	0.502421	−	0.864623i	$-0.332443\pi$
$641$	25.4406	1.00484	0.502421	+	0.864623i	$0.332443\pi$
$642$	7.38590	0.291498
$643$	18.2160	0.718367	0.359183	−	0.933267i	$-0.383055\pi$
$643$	18.2160	0.718367	0.359183	+	0.933267i	$0.383055\pi$
$644$	−1.69059	−0.0666187
$645$	−63.6291	−2.50539
$646$	−67.8494	−2.66950
$647$	30.0129	1.17993	0.589964	−	0.807430i	$-0.299142\pi$
$647$	30.0129	1.17993	0.589964	+	0.807430i	$0.299142\pi$
$648$	60.6777	2.38365
$649$	−3.72038	−0.146038
$650$	−55.3764	−2.17204
$651$	−3.70741	−0.145305
$652$	−83.6223	−3.27490
$653$	0.146955	0.00575079	0.00287540	−	0.999996i	$-0.499085\pi$
$653$	0.146955	0.00575079	0.00287540	+	0.999996i	$0.499085\pi$
$654$	−23.9225	−0.935444
$655$	−71.2355	−2.78340
$656$	34.9093	1.36298
$657$	−0.0489477	−0.00190963
$658$	12.8536	0.501087
$659$	20.0542	0.781199	0.390600	−	0.920561i	$-0.372268\pi$
$659$	20.0542	0.781199	0.390600	+	0.920561i	$0.372268\pi$
$660$	49.0933	1.91095
$661$	11.5108	0.447717	0.223858	−	0.974622i	$-0.428135\pi$
$661$	11.5108	0.447717	0.223858	+	0.974622i	$0.428135\pi$
$662$	−82.6299	−3.21150
$663$	−33.8908	−1.31621
$664$	−41.6937	−1.61803
$665$	−12.4765	−0.483816
$666$	−1.33986	−0.0519184
$667$	−4.14097	−0.160339
$668$	62.3531	2.41252
$669$	−36.1574	−1.39793
$670$	51.3123	1.98237
$671$	14.4757	0.558829
$672$	11.3067	0.436167
$673$	−6.35746	−0.245062	−0.122531	−	0.992465i	$-0.539101\pi$
$673$	−6.35746	−0.245062	−0.122531	+	0.992465i	$0.539101\pi$
$674$	35.5513	1.36938
$675$	−28.7608	−1.10700
$676$	11.8669	0.456419
$677$	28.0154	1.07672	0.538360	−	0.842715i	$-0.319044\pi$
$677$	28.0154	1.07672	0.538360	+	0.842715i	$0.319044\pi$
$678$	−17.0967	−0.656596
$679$	−0.629276	−0.0241494
$680$	−115.975	−4.44743
$681$	−41.9321	−1.60684
$682$	14.3746	0.550430
$683$	51.6176	1.97509	0.987547	−	0.157325i	$-0.0502869\pi$
$683$	51.6176	1.97509	0.987547	+	0.157325i	$0.0502869\pi$
$684$	3.23309	0.123620
$685$	9.76099	0.372948
$686$	−26.1600	−0.998795
$687$	19.7090	0.751945
$688$	103.381	3.94135
$689$	−49.9492	−1.90291
$690$	6.75528	0.257169
$691$	9.58150	0.364497	0.182249	−	0.983252i	$-0.441662\pi$
$691$	9.58150	0.364497	0.182249	+	0.983252i	$0.441662\pi$
$692$	−62.9747	−2.39394
$693$	−0.189607	−0.00720257
$694$	−89.1749	−3.38503
$695$	−42.0179	−1.59383
$696$	104.016	3.94270
$697$	−19.9759	−0.756640
$698$	49.7877	1.88449
$699$	−8.16876	−0.308971
$700$	−19.2349	−0.727009
$701$	9.19586	0.347323	0.173661	−	0.984805i	$-0.444440\pi$
$701$	9.19586	0.347323	0.173661	+	0.984805i	$0.444440\pi$
$702$	54.1826	2.04499
$703$	20.0132	0.754813
$704$	−10.0821	−0.379983
$705$	−36.0879	−1.35915
$706$	−60.0444	−2.25980
$707$	6.11197	0.229864
$708$	15.6646	0.588713
$709$	−37.4936	−1.40810	−0.704051	−	0.710149i	$-0.748628\pi$
$709$	−37.4936	−1.40810	−0.704051	+	0.710149i	$0.748628\pi$
$710$	109.628	4.11428
$711$	0.305106	0.0114424
$712$	66.1110	2.47761
$713$	1.38978	0.0520477
$714$	−16.7539	−0.626998
$715$	24.1630	0.903644
$716$	13.8441	0.517379
$717$	−1.29474	−0.0483531
$718$	11.8045	0.440540
$719$	5.12401	0.191093	0.0955466	−	0.995425i	$-0.469540\pi$
$719$	5.12401	0.191093	0.0955466	+	0.995425i	$0.469540\pi$
$720$	3.81023	0.141999
$721$	1.68010	0.0625703
$722$	−19.4552	−0.724049
$723$	−24.4438	−0.909077
$724$	68.6632	2.55185
$725$	−47.1143	−1.74978
$726$	32.4438	1.20410
$727$	−2.64598	−0.0981341	−0.0490671	−	0.998795i	$-0.515625\pi$
$727$	−2.64598	−0.0981341	−0.0490671	+	0.998795i	$0.515625\pi$
$728$	20.9008	0.774636
$729$	28.0877	1.04029
$730$	3.08363	0.114130
$731$	−59.1566	−2.18799
$732$	−60.9498	−2.25277
$733$	−30.7659	−1.13637	−0.568183	−	0.822902i	$-0.692353\pi$
$733$	−30.7659	−1.13637	−0.568183	+	0.822902i	$0.692353\pi$
$734$	−25.3509	−0.935720
$735$	35.1831	1.29775
$736$	−4.23851	−0.156234
$737$	−11.6478	−0.429051
$738$	1.35471	0.0498676
$739$	24.4851	0.900699	0.450350	−	0.892852i	$-0.351299\pi$
$739$	24.4851	0.900699	0.450350	+	0.892852i	$0.351299\pi$
$740$	59.3088	2.18023
$741$	−34.3306	−1.26117
$742$	−24.6924	−0.906485
$743$	8.46018	0.310374	0.155187	−	0.987885i	$-0.450402\pi$
$743$	8.46018	0.310374	0.155187	+	0.987885i	$0.450402\pi$
$744$	−34.9094	−1.27984
$745$	−41.3873	−1.51632
$746$	−27.7344	−1.01543
$747$	−0.783829	−0.0286788
$748$	45.6425	1.66886
$749$	1.26269	0.0461376
$750$	5.97765	0.218273
$751$	−42.8284	−1.56283	−0.781415	−	0.624012i	$-0.785502\pi$
$751$	−42.8284	−1.56283	−0.781415	+	0.624012i	$0.785502\pi$
$752$	58.6333	2.13814
$753$	49.4839	1.80329
$754$	88.7588	3.23240
$755$	−25.9948	−0.946048
$756$	18.8202	0.684483
$757$	−53.6680	−1.95060	−0.975298	−	0.220894i	$-0.929103\pi$
$757$	−53.6680	−1.95060	−0.975298	+	0.220894i	$0.929103\pi$
$758$	27.1998	0.987940
$759$	−1.53343	−0.0556601
$760$	−117.480	−4.26144
$761$	6.35272	0.230286	0.115143	−	0.993349i	$-0.463267\pi$
$761$	6.35272	0.230286	0.115143	+	0.993349i	$0.463267\pi$
$762$	48.7547	1.76620
$763$	−4.08978	−0.148060
$764$	50.6363	1.83196
$765$	−2.18029	−0.0788287
$766$	48.9542	1.76879
$767$	7.70990	0.278388
$768$	−35.6678	−1.28705
$769$	−8.05600	−0.290507	−0.145253	−	0.989394i	$-0.546400\pi$
$769$	−8.05600	−0.290507	−0.145253	+	0.989394i	$0.546400\pi$
$770$	11.9450	0.430466
$771$	−29.2991	−1.05518
$772$	110.590	3.98023
$773$	−13.5121	−0.485997	−0.242998	−	0.970027i	$-0.578131\pi$
$773$	−13.5121	−0.485997	−0.242998	+	0.970027i	$0.578131\pi$
$774$	4.01184	0.144203
$775$	15.8123	0.567996
$776$	−5.92534	−0.212707
$777$	4.94181	0.177287
$778$	−96.9090	−3.47436
$779$	−20.2351	−0.724998
$780$	−101.738	−3.64280
$781$	−24.8854	−0.890469
$782$	6.28046	0.224589
$783$	46.0985	1.64743
$784$	−57.1632	−2.04154
$785$	−35.8697	−1.28024
$786$	−96.8992	−3.45628
$787$	26.2460	0.935569	0.467784	−	0.883843i	$-0.345052\pi$
$787$	26.2460	0.935569	0.467784	+	0.883843i	$0.345052\pi$
$788$	30.6678	1.09250
$789$	21.0744	0.750270
$790$	−19.2213	−0.683862
$791$	−2.92285	−0.103924
$792$	−1.78536	−0.0634400
$793$	−29.9986	−1.06528
$794$	2.34274	0.0831407
$795$	69.3262	2.45875
$796$	−53.5643	−1.89854
$797$	−35.9770	−1.27437	−0.637185	−	0.770711i	$-0.719901\pi$
$797$	−35.9770	−1.27437	−0.637185	+	0.770711i	$0.719901\pi$
$798$	−16.9713	−0.600778
$799$	−33.5513	−1.18696
$800$	−48.2240	−1.70498
$801$	1.24287	0.0439146
$802$	69.5438	2.45568
$803$	−0.699977	−0.0247017
$804$	49.0428	1.72961
$805$	1.15488	0.0407041
$806$	−29.7890	−1.04927
$807$	−44.2793	−1.55871
$808$	57.5510	2.02464
$809$	15.6571	0.550473	0.275236	−	0.961377i	$-0.411244\pi$
$809$	15.6571	0.550473	0.275236	+	0.961377i	$0.411244\pi$
$810$	−71.8640	−2.52504
$811$	5.90148	0.207229	0.103614	−	0.994618i	$-0.466959\pi$
$811$	5.90148	0.207229	0.103614	+	0.994618i	$0.466959\pi$
$812$	30.8301	1.08193
$813$	15.5495	0.545345
$814$	−19.1607	−0.671581
$815$	57.1241	2.00097
$816$	−76.4246	−2.67540
$817$	−59.9243	−2.09649
$818$	32.4800	1.13564
$819$	0.392930	0.0137301
$820$	−59.9663	−2.09411
$821$	31.0639	1.08414	0.542068	−	0.840335i	$-0.317641\pi$
$821$	31.0639	1.08414	0.542068	+	0.840335i	$0.317641\pi$
$822$	13.2775	0.463107
$823$	27.1781	0.947369	0.473685	−	0.880695i	$-0.342924\pi$
$823$	27.1781	0.947369	0.473685	+	0.880695i	$0.342924\pi$
$824$	15.8200	0.551117
$825$	−17.4468	−0.607419
$826$	3.81139	0.132615
$827$	−53.9201	−1.87499	−0.937493	−	0.348004i	$-0.886859\pi$
$827$	−53.9201	−1.87499	−0.937493	+	0.348004i	$0.886859\pi$
$828$	−0.299269	−0.0104003
$829$	51.5068	1.78890	0.894452	−	0.447164i	$-0.147566\pi$
$829$	51.5068	1.78890	0.894452	+	0.447164i	$0.147566\pi$
$830$	49.3801	1.71401
$831$	−30.5430	−1.05953
$832$	20.8935	0.724352
$833$	32.7100	1.13334
$834$	−57.1555	−1.97913
$835$	−42.5947	−1.47405
$836$	46.2348	1.59907
$837$	−15.4715	−0.534772
$838$	−71.6778	−2.47607
$839$	−23.2282	−0.801926	−0.400963	−	0.916094i	$-0.631324\pi$
$839$	−23.2282	−0.801926	−0.400963	+	0.916094i	$0.631324\pi$
$840$	−29.0090	−1.00090
$841$	46.5160	1.60400
$842$	−59.6541	−2.05582
$843$	25.8899	0.891697
$844$	−8.33331	−0.286844
$845$	−8.10652	−0.278873
$846$	2.27536	0.0782284
$847$	5.54658	0.190583
$848$	−112.637	−3.86797
$849$	46.1621	1.58428
$850$	71.4564	2.45094
$851$	−1.85252	−0.0635035
$852$	104.780	3.58969
$853$	10.3715	0.355114	0.177557	−	0.984111i	$-0.443181\pi$
$853$	10.3715	0.355114	0.177557	+	0.984111i	$0.443181\pi$
$854$	−14.8298	−0.507465
$855$	−2.20859	−0.0755322
$856$	11.8896	0.406379
$857$	6.06354	0.207126	0.103563	−	0.994623i	$-0.466976\pi$
$857$	6.06354	0.207126	0.103563	+	0.994623i	$0.466976\pi$
$858$	32.8681	1.12210
$859$	−41.1329	−1.40344	−0.701718	−	0.712455i	$-0.747583\pi$
$859$	−41.1329	−1.40344	−0.701718	+	0.712455i	$0.747583\pi$
$860$	−177.584	−6.05558
$861$	−4.99660	−0.170284
$862$	−30.0331	−1.02293
$863$	26.8911	0.915383	0.457691	−	0.889111i	$-0.348676\pi$
$863$	26.8911	0.915383	0.457691	+	0.889111i	$0.348676\pi$
$864$	47.1844	1.60525
$865$	43.0193	1.46270
$866$	46.8388	1.59165
$867$	14.9465	0.507611
$868$	−10.3471	−0.351204
$869$	4.36318	0.148011
$870$	−123.191	−4.17658
$871$	24.1381	0.817890
$872$	−38.5098	−1.30411
$873$	−0.111395	−0.00377014
$874$	6.36196	0.215197
$875$	1.02194	0.0345477
$876$	2.94725	0.0995782
$877$	−16.9538	−0.572488	−0.286244	−	0.958157i	$-0.592407\pi$
$877$	−16.9538	−0.572488	−0.286244	+	0.958157i	$0.592407\pi$
$878$	−72.4382	−2.44467
$879$	−20.9005	−0.704956
$880$	54.4882	1.83680
$881$	−38.7528	−1.30561	−0.652807	−	0.757524i	$-0.726409\pi$
$881$	−38.7528	−1.30561	−0.652807	+	0.757524i	$0.726409\pi$
$882$	−2.21831	−0.0746944
$883$	−20.7850	−0.699471	−0.349736	−	0.936848i	$-0.613729\pi$
$883$	−20.7850	−0.699471	−0.349736	+	0.936848i	$0.613729\pi$
$884$	−94.5868	−3.18130
$885$	−10.7008	−0.359705
$886$	84.4947	2.83866
$887$	−24.8321	−0.833782	−0.416891	−	0.908957i	$-0.636880\pi$
$887$	−24.8321	−0.833782	−0.416891	+	0.908957i	$0.636880\pi$
$888$	46.5327	1.56154
$889$	8.33506	0.279549
$890$	−78.2989	−2.62459
$891$	16.3130	0.546505
$892$	−100.913	−3.37882
$893$	−33.9867	−1.13732
$894$	−56.2978	−1.88288
$895$	−9.45720	−0.316119
$896$	−3.02637	−0.101104
$897$	3.17780	0.106103
$898$	38.2069	1.27498
$899$	−25.3445	−0.845285
$900$	−3.40496	−0.113499
$901$	64.4533	2.14725
$902$	19.3731	0.645053
$903$	−14.7969	−0.492411
$904$	−27.5219	−0.915364
$905$	−46.9053	−1.55918
$906$	−35.3599	−1.17475
$907$	−24.4876	−0.813099	−0.406549	−	0.913629i	$-0.633268\pi$
$907$	−24.4876	−0.813099	−0.406549	+	0.913629i	$0.633268\pi$
$908$	−117.030	−3.88377
$909$	1.08194	0.0358858
$910$	−24.7540	−0.820587
$911$	19.4839	0.645530	0.322765	−	0.946479i	$-0.395388\pi$
$911$	19.4839	0.645530	0.322765	+	0.946479i	$0.395388\pi$
$912$	−77.4164	−2.56351
$913$	−11.2092	−0.370969
$914$	27.2664	0.901891
$915$	41.6361	1.37645
$916$	55.0065	1.81746
$917$	−16.5658	−0.547052
$918$	−69.9159	−2.30757
$919$	−23.7854	−0.784609	−0.392305	−	0.919835i	$-0.628322\pi$
$919$	−23.7854	−0.784609	−0.392305	+	0.919835i	$0.628322\pi$
$920$	10.8745	0.358521
$921$	18.6281	0.613816
$922$	2.32661	0.0766229
$923$	51.5710	1.69748
$924$	11.4166	0.375580
$925$	−21.0772	−0.693013
$926$	−84.8685	−2.78895
$927$	0.297413	0.00976831
$928$	77.2948	2.53732
$929$	−21.4773	−0.704649	−0.352324	−	0.935878i	$-0.614609\pi$
$929$	−21.4773	−0.704649	−0.352324	+	0.935878i	$0.614609\pi$
$930$	41.3451	1.35576
$931$	33.1345	1.08594
$932$	−22.7985	−0.746789
$933$	28.2921	0.926241
$934$	82.5723	2.70185
$935$	−31.1793	−1.01967
$936$	3.69987	0.120934
$937$	−28.1170	−0.918544	−0.459272	−	0.888296i	$-0.651890\pi$
$937$	−28.1170	−0.918544	−0.459272	+	0.888296i	$0.651890\pi$
$938$	11.9327	0.389616
$939$	28.6776	0.935859
$940$	−100.719	−3.28508
$941$	20.7050	0.674962	0.337481	−	0.941332i	$-0.390425\pi$
$941$	20.7050	0.674962	0.337481	+	0.941332i	$0.390425\pi$
$942$	−48.7923	−1.58974
$943$	1.87305	0.0609950
$944$	17.3860	0.565868
$945$	−12.8565	−0.418221
$946$	57.3715	1.86531
$947$	−31.1915	−1.01359	−0.506794	−	0.862067i	$-0.669169\pi$
$947$	−31.1915	−1.01359	−0.506794	+	0.862067i	$0.669169\pi$
$948$	−18.3711	−0.596666
$949$	1.45059	0.0470882
$950$	72.3838	2.34844
$951$	19.2075	0.622847
$952$	−26.9699	−0.874101
$953$	−45.7916	−1.48334	−0.741668	−	0.670767i	$-0.765965\pi$
$953$	−45.7916	−1.48334	−0.741668	+	0.670767i	$0.765965\pi$
$954$	−4.37106	−0.141518
$955$	−34.5907	−1.11933
$956$	−3.61354	−0.116870
$957$	27.9642	0.903953
$958$	−35.3295	−1.14144
$959$	2.26992	0.0732995
$960$	−28.9988	−0.935932
$961$	−22.4940	−0.725612
$962$	39.7074	1.28022
$963$	0.223522	0.00720288
$964$	−68.2211	−2.19725
$965$	−75.5466	−2.43193
$966$	1.57094	0.0505442
$967$	5.94135	0.191061	0.0955304	−	0.995427i	$-0.469545\pi$
$967$	5.94135	0.191061	0.0955304	+	0.995427i	$0.469545\pi$
$968$	52.2272	1.67865
$969$	44.2994	1.42310
$970$	7.01771	0.225325
$971$	−15.4255	−0.495027	−0.247513	−	0.968884i	$-0.579613\pi$
$971$	−15.4255	−0.495027	−0.247513	+	0.968884i	$0.579613\pi$
$972$	6.52179	0.209187
$973$	−9.77127	−0.313253
$974$	52.4087	1.67928
$975$	36.1556	1.15791
$976$	−67.6477	−2.16535
$977$	−12.2469	−0.391812	−0.195906	−	0.980623i	$-0.562765\pi$
$977$	−12.2469	−0.391812	−0.195906	+	0.980623i	$0.562765\pi$
$978$	77.7040	2.48470
$979$	17.7737	0.568049
$980$	98.1935	3.13668
$981$	−0.723974	−0.0231147
$982$	3.48788	0.111303
$983$	−29.3212	−0.935202	−0.467601	−	0.883940i	$-0.654882\pi$
$983$	−29.3212	−0.935202	−0.467601	+	0.883940i	$0.654882\pi$
$984$	−47.0486	−1.49985
$985$	−20.9498	−0.667517
$986$	−114.532	−3.64745
$987$	−8.39224	−0.267128
$988$	−95.8143	−3.04826
$989$	5.54687	0.176380
$990$	2.11450	0.0672033
$991$	16.4889	0.523788	0.261894	−	0.965097i	$-0.415653\pi$
$991$	16.4889	0.523788	0.261894	+	0.965097i	$0.415653\pi$
$992$	−25.9414	−0.823642
$993$	53.9497	1.71204
$994$	25.4941	0.808624
$995$	36.5909	1.16001
$996$	47.1961	1.49546
$997$	−38.7685	−1.22781	−0.613905	−	0.789380i	$-0.710402\pi$
$997$	−38.7685	−1.22781	−0.613905	+	0.789380i	$0.710402\pi$
$998$	−37.2128	−1.17795
$999$	20.6228	0.652476

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4019.2.a.b.1.11	✓	186

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4019.2.a.b.1.11	✓	186	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:	\( N \)	\(=\)	\( 4019 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4019.a (trivial)

\(f(q)\)	\(=\)	\(q-2.59341 q^{2} +1.69325 q^{3} +4.72575 q^{4} -3.22826 q^{5} -4.39129 q^{6} -0.750732 q^{7} -7.06898 q^{8} -0.132895 q^{9} +O(q^{10})\)	\(q-2.59341 q^{2} +1.69325 q^{3} +4.72575 q^{4} -3.22826 q^{5} -4.39129 q^{6} -0.750732 q^{7} -7.06898 q^{8} -0.132895 q^{9} +8.37219 q^{10} -1.90047 q^{11} +8.00190 q^{12} +3.93841 q^{13} +1.94695 q^{14} -5.46626 q^{15} +8.88124 q^{16} -5.08204 q^{17} +0.344651 q^{18} -5.14799 q^{19} -15.2560 q^{20} -1.27118 q^{21} +4.92868 q^{22} +0.476522 q^{23} -11.9696 q^{24} +5.42167 q^{25} -10.2139 q^{26} -5.30478 q^{27} -3.54778 q^{28} -8.68999 q^{29} +14.1762 q^{30} +2.91651 q^{31} -8.89469 q^{32} -3.21797 q^{33} +13.1798 q^{34} +2.42356 q^{35} -0.628029 q^{36} -3.88758 q^{37} +13.3508 q^{38} +6.66873 q^{39} +22.8205 q^{40} +3.93068 q^{41} +3.29668 q^{42} +11.6403 q^{43} -8.98114 q^{44} +0.429020 q^{45} -1.23581 q^{46} +6.60193 q^{47} +15.0382 q^{48} -6.43640 q^{49} -14.0606 q^{50} -8.60518 q^{51} +18.6120 q^{52} -12.6826 q^{53} +13.7575 q^{54} +6.13520 q^{55} +5.30691 q^{56} -8.71685 q^{57} +22.5367 q^{58} +1.95762 q^{59} -25.8322 q^{60} -7.61692 q^{61} -7.56369 q^{62} +0.0997685 q^{63} +5.30505 q^{64} -12.7142 q^{65} +8.34551 q^{66} +6.12890 q^{67} -24.0165 q^{68} +0.806872 q^{69} -6.28527 q^{70} +13.0944 q^{71} +0.939432 q^{72} +0.368318 q^{73} +10.0821 q^{74} +9.18025 q^{75} -24.3281 q^{76} +1.42674 q^{77} -17.2947 q^{78} -2.29585 q^{79} -28.6710 q^{80} -8.58365 q^{81} -10.1938 q^{82} +5.89811 q^{83} -6.00728 q^{84} +16.4061 q^{85} -30.1881 q^{86} -14.7144 q^{87} +13.4344 q^{88} -9.35226 q^{89} -1.11262 q^{90} -2.95669 q^{91} +2.25192 q^{92} +4.93839 q^{93} -17.1215 q^{94} +16.6191 q^{95} -15.0610 q^{96} +0.838216 q^{97} +16.6922 q^{98} +0.252563 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 186 q + 6 q^{2} + 10 q^{3} + 212 q^{4} + 38 q^{5} + 47 q^{6} + 32 q^{7} + 15 q^{8} + 216 q^{9}+O(q^{10}) \) 186 * q + 6 * q^2 + 10 * q^3 + 212 * q^4 + 38 * q^5 + 47 * q^6 + 32 * q^7 + 15 * q^8 + 216 * q^9	\( 186 q + 6 q^{2} + 10 q^{3} + 212 q^{4} + 38 q^{5} + 47 q^{6} + 32 q^{7} + 15 q^{8} + 216 q^{9} + 50 q^{10} + 25 q^{11} + 17 q^{12} + 113 q^{13} + 12 q^{14} + 12 q^{15} + 252 q^{16} + 35 q^{17} + 13 q^{18} + 97 q^{19} + 55 q^{20} + 115 q^{21} + 14 q^{22} + 27 q^{23} + 122 q^{24} + 244 q^{25} + 39 q^{26} + 34 q^{27} + 66 q^{28} + 91 q^{29} + 4 q^{30} + 135 q^{31} + 21 q^{32} + 32 q^{33} + 58 q^{34} + 17 q^{35} + 273 q^{36} + 133 q^{37} - 3 q^{38} + 55 q^{39} + 142 q^{40} + 97 q^{41} - 8 q^{42} + 67 q^{43} + 44 q^{44} + 154 q^{45} + 101 q^{46} + 20 q^{47} - 7 q^{48} + 312 q^{49} + 21 q^{50} + 23 q^{51} + 193 q^{52} + 22 q^{53} + 141 q^{54} + 88 q^{55} + 28 q^{56} + 65 q^{57} + 62 q^{58} + 41 q^{59} + q^{60} + 377 q^{61} + 29 q^{62} + 39 q^{63} + 311 q^{64} + 21 q^{65} + 35 q^{66} + 42 q^{67} + 24 q^{68} + 137 q^{69} + 35 q^{70} + 17 q^{71} - 8 q^{72} + 213 q^{73} - 9 q^{74} + 2 q^{75} + 242 q^{76} + 60 q^{77} + 103 q^{79} + 80 q^{80} + 270 q^{81} + 84 q^{82} + 42 q^{83} + 137 q^{84} + 294 q^{85} - 9 q^{86} + 22 q^{87} - 13 q^{88} + 78 q^{89} + 69 q^{90} + 118 q^{91} + 49 q^{92} + 51 q^{93} + 93 q^{94} + 10 q^{95} + 260 q^{96} + 142 q^{97} - 31 q^{98} + 78 q^{99}+O(q^{100}) \) 186 * q + 6 * q^2 + 10 * q^3 + 212 * q^4 + 38 * q^5 + 47 * q^6 + 32 * q^7 + 15 * q^8 + 216 * q^9 + 50 * q^10 + 25 * q^11 + 17 * q^12 + 113 * q^13 + 12 * q^14 + 12 * q^15 + 252 * q^16 + 35 * q^17 + 13 * q^18 + 97 * q^19 + 55 * q^20 + 115 * q^21 + 14 * q^22 + 27 * q^23 + 122 * q^24 + 244 * q^25 + 39 * q^26 + 34 * q^27 + 66 * q^28 + 91 * q^29 + 4 * q^30 + 135 * q^31 + 21 * q^32 + 32 * q^33 + 58 * q^34 + 17 * q^35 + 273 * q^36 + 133 * q^37 - 3 * q^38 + 55 * q^39 + 142 * q^40 + 97 * q^41 - 8 * q^42 + 67 * q^43 + 44 * q^44 + 154 * q^45 + 101 * q^46 + 20 * q^47 - 7 * q^48 + 312 * q^49 + 21 * q^50 + 23 * q^51 + 193 * q^52 + 22 * q^53 + 141 * q^54 + 88 * q^55 + 28 * q^56 + 65 * q^57 + 62 * q^58 + 41 * q^59 + q^60 + 377 * q^61 + 29 * q^62 + 39 * q^63 + 311 * q^64 + 21 * q^65 + 35 * q^66 + 42 * q^67 + 24 * q^68 + 137 * q^69 + 35 * q^70 + 17 * q^71 - 8 * q^72 + 213 * q^73 - 9 * q^74 + 2 * q^75 + 242 * q^76 + 60 * q^77 + 103 * q^79 + 80 * q^80 + 270 * q^81 + 84 * q^82 + 42 * q^83 + 137 * q^84 + 294 * q^85 - 9 * q^86 + 22 * q^87 - 13 * q^88 + 78 * q^89 + 69 * q^90 + 118 * q^91 + 49 * q^92 + 51 * q^93 + 93 * q^94 + 10 * q^95 + 260 * q^96 + 142 * q^97 - 31 * q^98 + 78 * q^99

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