LMFDB - Embedded newform 4019.2.a.b.1.3

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			1.3
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)

$f(q)$	$=$	$q-2.78390 q^{2} +2.40470 q^{3} +5.75012 q^{4} -2.23828 q^{5} -6.69445 q^{6} -0.0567746 q^{7} -10.4400 q^{8} +2.78257 q^{9} +O(q^{10})$	\(q-2.78390 q^{2} +2.40470 q^{3} +5.75012 q^{4} -2.23828 q^{5} -6.69445 q^{6} -0.0567746 q^{7} -10.4400 q^{8} +2.78257 q^{9} +6.23116 q^{10} +4.46877 q^{11} +13.8273 q^{12} -1.01079 q^{13} +0.158055 q^{14} -5.38239 q^{15} +17.5637 q^{16} -2.51174 q^{17} -7.74642 q^{18} +5.87700 q^{19} -12.8704 q^{20} -0.136526 q^{21} -12.4406 q^{22} -3.02456 q^{23} -25.1050 q^{24} +0.00990820 q^{25} +2.81394 q^{26} -0.522847 q^{27} -0.326461 q^{28} +3.67472 q^{29} +14.9841 q^{30} +1.96933 q^{31} -28.0156 q^{32} +10.7460 q^{33} +6.99244 q^{34} +0.127078 q^{35} +16.0001 q^{36} +8.75339 q^{37} -16.3610 q^{38} -2.43064 q^{39} +23.3676 q^{40} +1.89435 q^{41} +0.380075 q^{42} +5.14850 q^{43} +25.6960 q^{44} -6.22818 q^{45} +8.42007 q^{46} -3.40230 q^{47} +42.2353 q^{48} -6.99678 q^{49} -0.0275835 q^{50} -6.03997 q^{51} -5.81216 q^{52} +3.90647 q^{53} +1.45555 q^{54} -10.0024 q^{55} +0.592726 q^{56} +14.1324 q^{57} -10.2301 q^{58} +2.25947 q^{59} -30.9494 q^{60} +6.85031 q^{61} -5.48243 q^{62} -0.157979 q^{63} +42.8654 q^{64} +2.26243 q^{65} -29.9160 q^{66} -10.1207 q^{67} -14.4428 q^{68} -7.27314 q^{69} -0.353772 q^{70} +0.569963 q^{71} -29.0500 q^{72} -8.05235 q^{73} -24.3686 q^{74} +0.0238262 q^{75} +33.7935 q^{76} -0.253713 q^{77} +6.76668 q^{78} +5.86218 q^{79} -39.3125 q^{80} -9.60501 q^{81} -5.27369 q^{82} -7.74329 q^{83} -0.785040 q^{84} +5.62198 q^{85} -14.3329 q^{86} +8.83659 q^{87} -46.6539 q^{88} +5.19256 q^{89} +17.3387 q^{90} +0.0573871 q^{91} -17.3916 q^{92} +4.73565 q^{93} +9.47167 q^{94} -13.1544 q^{95} -67.3691 q^{96} +14.6535 q^{97} +19.4784 q^{98} +12.4347 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.78390	−1.96852	−0.984259	−	0.176733i	$-0.943447\pi$
$2$	−2.78390	−1.96852	−0.984259	+	0.176733i	$0.943447\pi$
$3$	2.40470	1.38835	0.694177	−	0.719805i	$-0.255769\pi$
$3$	2.40470	1.38835	0.694177	+	0.719805i	$0.255769\pi$
$4$	5.75012	2.87506
$5$	−2.23828	−1.00099	−0.500495	−	0.865739i	$-0.666849\pi$
$5$	−2.23828	−1.00099	−0.500495	+	0.865739i	$0.666849\pi$
$6$	−6.69445	−2.73300
$7$	−0.0567746	−0.0214588	−0.0107294	−	0.999942i	$-0.503415\pi$
$7$	−0.0567746	−0.0214588	−0.0107294	+	0.999942i	$0.503415\pi$
$8$	−10.4400	−3.69109
$9$	2.78257	0.927524
$10$	6.23116	1.97047
$11$	4.46877	1.34739	0.673693	−	0.739012i	$-0.264707\pi$
$11$	4.46877	1.34739	0.673693	+	0.739012i	$0.264707\pi$
$12$	13.8273	3.99160
$13$	−1.01079	−0.280342	−0.140171	−	0.990127i	$-0.544765\pi$
$13$	−1.01079	−0.280342	−0.140171	+	0.990127i	$0.544765\pi$
$14$	0.158055	0.0422420
$15$	−5.38239	−1.38973
$16$	17.5637	4.39092
$17$	−2.51174	−0.609186	−0.304593	−	0.952483i	$-0.598520\pi$
$17$	−2.51174	−0.609186	−0.304593	+	0.952483i	$0.598520\pi$
$18$	−7.74642	−1.82585
$19$	5.87700	1.34828	0.674139	−	0.738605i	$-0.264515\pi$
$19$	5.87700	1.34828	0.674139	+	0.738605i	$0.264515\pi$
$20$	−12.8704	−2.87791
$21$	−0.136526	−0.0297924
$22$	−12.4406	−2.65235
$23$	−3.02456	−0.630663	−0.315332	−	0.948982i	$-0.602116\pi$
$23$	−3.02456	−0.630663	−0.315332	+	0.948982i	$0.602116\pi$
$24$	−25.1050	−5.12454
$25$	0.00990820	0.00198164
$26$	2.81394	0.551859
$27$	−0.522847	−0.100622
$28$	−0.326461	−0.0616953
$29$	3.67472	0.682378	0.341189	−	0.939995i	$-0.389170\pi$
$29$	3.67472	0.682378	0.341189	+	0.939995i	$0.389170\pi$
$30$	14.9841	2.73570
$31$	1.96933	0.353702	0.176851	−	0.984238i	$-0.443409\pi$
$31$	1.96933	0.353702	0.176851	+	0.984238i	$0.443409\pi$
$32$	−28.0156	−4.95251
$33$	10.7460	1.87065
$34$	6.99244	1.19919
$35$	0.127078	0.0214800
$36$	16.0001	2.66669
$37$	8.75339	1.43905	0.719524	−	0.694468i	$-0.244360\pi$
$37$	8.75339	1.43905	0.719524	+	0.694468i	$0.244360\pi$
$38$	−16.3610	−2.65411
$39$	−2.43064	−0.389214
$40$	23.3676	3.69475
$41$	1.89435	0.295848	0.147924	−	0.988999i	$-0.452741\pi$
$41$	1.89435	0.295848	0.147924	+	0.988999i	$0.452741\pi$
$42$	0.380075	0.0586468
$43$	5.14850	0.785138	0.392569	−	0.919722i	$-0.371586\pi$
$43$	5.14850	0.785138	0.392569	+	0.919722i	$0.371586\pi$
$44$	25.6960	3.87382
$45$	−6.22818	−0.928443
$46$	8.42007	1.24147
$47$	−3.40230	−0.496276	−0.248138	−	0.968725i	$-0.579819\pi$
$47$	−3.40230	−0.496276	−0.248138	+	0.968725i	$0.579819\pi$
$48$	42.2353	6.09614
$49$	−6.99678	−0.999540
$50$	−0.0275835	−0.00390089
$51$	−6.03997	−0.845765
$52$	−5.81216	−0.806002
$53$	3.90647	0.536594	0.268297	−	0.963336i	$-0.413539\pi$
$53$	3.90647	0.536594	0.268297	+	0.963336i	$0.413539\pi$
$54$	1.45555	0.198076
$55$	−10.0024	−1.34872
$56$	0.592726	0.0792063
$57$	14.1324	1.87189
$58$	−10.2301	−1.34327
$59$	2.25947	0.294158	0.147079	−	0.989125i	$-0.453013\pi$
$59$	2.25947	0.294158	0.147079	+	0.989125i	$0.453013\pi$
$60$	−30.9494	−3.99555
$61$	6.85031	0.877092	0.438546	−	0.898709i	$-0.355494\pi$
$61$	6.85031	0.877092	0.438546	+	0.898709i	$0.355494\pi$
$62$	−5.48243	−0.696269
$63$	−0.157979	−0.0199035
$64$	42.8654	5.35818
$65$	2.26243	0.280620
$66$	−29.9160	−3.68240
$67$	−10.1207	−1.23643	−0.618217	−	0.786007i	$-0.712145\pi$
$67$	−10.1207	−1.23643	−0.618217	+	0.786007i	$0.712145\pi$
$68$	−14.4428	−1.75145
$69$	−7.27314	−0.875583
$70$	−0.353772	−0.0422838
$71$	0.569963	0.0676422	0.0338211	−	0.999428i	$-0.489232\pi$
$71$	0.569963	0.0676422	0.0338211	+	0.999428i	$0.489232\pi$
$72$	−29.0500	−3.42358
$73$	−8.05235	−0.942456	−0.471228	−	0.882011i	$-0.656189\pi$
$73$	−8.05235	−0.942456	−0.471228	+	0.882011i	$0.656189\pi$
$74$	−24.3686	−2.83279
$75$	0.0238262	0.00275121
$76$	33.7935	3.87638
$77$	−0.253713	−0.0289132
$78$	6.76668	0.766175
$79$	5.86218	0.659547	0.329774	−	0.944060i	$-0.393028\pi$
$79$	5.86218	0.659547	0.329774	+	0.944060i	$0.393028\pi$
$80$	−39.3125	−4.39527
$81$	−9.60501	−1.06722
$82$	−5.27369	−0.582382
$83$	−7.74329	−0.849937	−0.424968	−	0.905208i	$-0.639715\pi$
$83$	−7.74329	−0.849937	−0.424968	+	0.905208i	$0.639715\pi$
$84$	−0.785040	−0.0856549
$85$	5.62198	0.609789
$86$	−14.3329	−1.54556
$87$	8.83659	0.947382
$88$	−46.6539	−4.97332
$89$	5.19256	0.550411	0.275205	−	0.961385i	$-0.411254\pi$
$89$	5.19256	0.550411	0.275205	+	0.961385i	$0.411254\pi$
$90$	17.3387	1.82766
$91$	0.0573871	0.00601581
$92$	−17.3916	−1.81320
$93$	4.73565	0.491064
$94$	9.47167	0.976928
$95$	−13.1544	−1.34961
$96$	−67.3691	−6.87583
$97$	14.6535	1.48784	0.743918	−	0.668270i	$-0.232965\pi$
$97$	14.6535	1.48784	0.743918	+	0.668270i	$0.232965\pi$
$98$	19.4784	1.96761
$99$	12.4347	1.24973
$100$	0.0569733	0.00569733
$101$	6.20740	0.617659	0.308830	−	0.951117i	$-0.400063\pi$
$101$	6.20740	0.617659	0.308830	+	0.951117i	$0.400063\pi$
$102$	16.8147	1.66490
$103$	−1.03737	−0.102215	−0.0511073	−	0.998693i	$-0.516275\pi$
$103$	−1.03737	−0.102215	−0.0511073	+	0.998693i	$0.516275\pi$
$104$	10.5526	1.03477
$105$	0.305583	0.0298219
$106$	−10.8752	−1.05630
$107$	−5.23587	−0.506170	−0.253085	−	0.967444i	$-0.581445\pi$
$107$	−5.23587	−0.506170	−0.253085	+	0.967444i	$0.581445\pi$
$108$	−3.00643	−0.289294
$109$	8.82149	0.844946	0.422473	−	0.906376i	$-0.361162\pi$
$109$	8.82149	0.844946	0.422473	+	0.906376i	$0.361162\pi$
$110$	27.8457	2.65498
$111$	21.0493	1.99791
$112$	−0.997170	−0.0942237
$113$	−5.71607	−0.537723	−0.268861	−	0.963179i	$-0.586647\pi$
$113$	−5.71607	−0.537723	−0.268861	+	0.963179i	$0.586647\pi$
$114$	−39.3433	−3.68484
$115$	6.76981	0.631288
$116$	21.1301	1.96188
$117$	−2.81259	−0.260024
$118$	−6.29015	−0.579055
$119$	0.142603	0.0130724
$120$	56.1921	5.12961
$121$	8.96992	0.815448
$122$	−19.0706	−1.72657
$123$	4.55534	0.410742
$124$	11.3239	1.01692
$125$	11.1692	0.999007
$126$	0.439800	0.0391805
$127$	17.5406	1.55648	0.778240	−	0.627967i	$-0.216113\pi$
$127$	17.5406	1.55648	0.778240	+	0.627967i	$0.216113\pi$
$128$	−63.3020	−5.59516
$129$	12.3806	1.09005
$130$	−6.29839	−0.552406
$131$	2.07094	0.180939	0.0904696	−	0.995899i	$-0.471163\pi$
$131$	2.07094	0.180939	0.0904696	+	0.995899i	$0.471163\pi$
$132$	61.7911	5.37822
$133$	−0.333665	−0.0289324
$134$	28.1749	2.43394
$135$	1.17028	0.100722
$136$	26.2225	2.24856
$137$	−8.40350	−0.717959	−0.358980	−	0.933345i	$-0.616875\pi$
$137$	−8.40350	−0.717959	−0.358980	+	0.933345i	$0.616875\pi$
$138$	20.2477	1.72360
$139$	−17.2908	−1.46659	−0.733294	−	0.679912i	$-0.762018\pi$
$139$	−17.2908	−1.46659	−0.733294	+	0.679912i	$0.762018\pi$
$140$	0.730712	0.0617564
$141$	−8.18149	−0.689006
$142$	−1.58672	−0.133155
$143$	−4.51699	−0.377729
$144$	48.8722	4.07268
$145$	−8.22506	−0.683054
$146$	22.4170	1.85524
$147$	−16.8251	−1.38771
$148$	50.3331	4.13735
$149$	7.76103	0.635809	0.317904	−	0.948123i	$-0.397021\pi$
$149$	7.76103	0.635809	0.317904	+	0.948123i	$0.397021\pi$
$150$	−0.0663299	−0.00541581
$151$	18.0287	1.46715	0.733577	−	0.679606i	$-0.237849\pi$
$151$	18.0287	1.46715	0.733577	+	0.679606i	$0.237849\pi$
$152$	−61.3558	−4.97662
$153$	−6.98909	−0.565035
$154$	0.706312	0.0569162
$155$	−4.40792	−0.354053
$156$	−13.9765	−1.11902
$157$	22.0998	1.76376	0.881878	−	0.471477i	$-0.156279\pi$
$157$	22.0998	1.76376	0.881878	+	0.471477i	$0.156279\pi$
$158$	−16.3198	−1.29833
$159$	9.39387	0.744983
$160$	62.7068	4.95741
$161$	0.171718	0.0135333
$162$	26.7394	2.10085
$163$	10.7572	0.842571	0.421285	−	0.906928i	$-0.361579\pi$
$163$	10.7572	0.842571	0.421285	+	0.906928i	$0.361579\pi$
$164$	10.8928	0.850581
$165$	−24.0527	−1.87250
$166$	21.5566	1.67312
$167$	17.4264	1.34850	0.674249	−	0.738504i	$-0.264468\pi$
$167$	17.4264	1.34850	0.674249	+	0.738504i	$0.264468\pi$
$168$	1.42533	0.109966
$169$	−11.9783	−0.921408
$170$	−15.6511	−1.20038
$171$	16.3532	1.25056
$172$	29.6045	2.25732
$173$	−17.0785	−1.29846	−0.649228	−	0.760594i	$-0.724908\pi$
$173$	−17.0785	−1.29846	−0.649228	+	0.760594i	$0.724908\pi$
$174$	−24.6002	−1.86494
$175$	−0.000562534 0	−4.25236e−5 0
$176$	78.4880	5.91626
$177$	5.43334	0.408395
$178$	−14.4556	−1.08349
$179$	18.0292	1.34757	0.673785	−	0.738928i	$-0.264668\pi$
$179$	18.0292	1.34757	0.673785	+	0.738928i	$0.264668\pi$
$180$	−35.8128	−2.66933
$181$	−12.3621	−0.918868	−0.459434	−	0.888212i	$-0.651948\pi$
$181$	−12.3621	−0.918868	−0.459434	+	0.888212i	$0.651948\pi$
$182$	−0.159760	−0.0118422
$183$	16.4729	1.21771
$184$	31.5763	2.32784
$185$	−19.5926	−1.44047
$186$	−13.1836	−0.966668
$187$	−11.2244	−0.820808
$188$	−19.5636	−1.42682
$189$	0.0296844	0.00215922
$190$	36.6206	2.65674
$191$	−11.1927	−0.809872	−0.404936	−	0.914345i	$-0.632706\pi$
$191$	−11.1927	−0.809872	−0.404936	+	0.914345i	$0.632706\pi$
$192$	103.078	7.43904
$193$	0.729995	0.0525462	0.0262731	−	0.999655i	$-0.491636\pi$
$193$	0.729995	0.0525462	0.0262731	+	0.999655i	$0.491636\pi$
$194$	−40.7939	−2.92883
$195$	5.44046	0.389600
$196$	−40.2323	−2.87374
$197$	10.1791	0.725233	0.362616	−	0.931938i	$-0.381884\pi$
$197$	10.1791	0.725233	0.362616	+	0.931938i	$0.381884\pi$
$198$	−34.6170	−2.46012
$199$	26.1440	1.85330	0.926649	−	0.375927i	$-0.122676\pi$
$199$	26.1440	1.85330	0.926649	+	0.375927i	$0.122676\pi$
$200$	−0.103441	−0.00731441
$201$	−24.3371	−1.71661
$202$	−17.2808	−1.21587
$203$	−0.208631	−0.0146430
$204$	−34.7306	−2.43163
$205$	−4.24009	−0.296141
$206$	2.88793	0.201211
$207$	−8.41605	−0.584956
$208$	−17.7532	−1.23096
$209$	26.2630	1.81665
$210$	−0.850714	−0.0587049
$211$	−8.53671	−0.587691	−0.293846	−	0.955853i	$-0.594935\pi$
$211$	−8.53671	−0.587691	−0.293846	+	0.955853i	$0.594935\pi$
$212$	22.4627	1.54274
$213$	1.37059	0.0939112
$214$	14.5762	0.996405
$215$	−11.5238	−0.785916
$216$	5.45851	0.371405
$217$	−0.111808	−0.00759002
$218$	−24.5582	−1.66329
$219$	−19.3635	−1.30846
$220$	−57.5149	−3.87765
$221$	2.53884	0.170781
$222$	−58.5991	−3.93291
$223$	−1.05085	−0.0703702	−0.0351851	−	0.999381i	$-0.511202\pi$
$223$	−1.05085	−0.0703702	−0.0351851	+	0.999381i	$0.511202\pi$
$224$	1.59057	0.106275
$225$	0.0275703	0.00183802
$226$	15.9130	1.05852
$227$	6.64009	0.440718	0.220359	−	0.975419i	$-0.429277\pi$
$227$	6.64009	0.440718	0.220359	+	0.975419i	$0.429277\pi$
$228$	81.2632	5.38178
$229$	−13.1696	−0.870274	−0.435137	−	0.900364i	$-0.643300\pi$
$229$	−13.1696	−0.870274	−0.435137	+	0.900364i	$0.643300\pi$
$230$	−18.8465	−1.24270
$231$	−0.610102	−0.0401418
$232$	−38.3640	−2.51872
$233$	19.2115	1.25858	0.629292	−	0.777169i	$-0.283345\pi$
$233$	19.2115	1.25858	0.629292	+	0.777169i	$0.283345\pi$
$234$	7.82999	0.511863
$235$	7.61530	0.496767
$236$	12.9922	0.845722
$237$	14.0968	0.915685
$238$	−0.396993	−0.0257332
$239$	14.2038	0.918768	0.459384	−	0.888238i	$-0.348070\pi$
$239$	14.2038	0.918768	0.459384	+	0.888238i	$0.348070\pi$
$240$	−94.5346	−6.10218
$241$	14.7231	0.948401	0.474200	−	0.880417i	$-0.342737\pi$
$241$	14.7231	0.948401	0.474200	+	0.880417i	$0.342737\pi$
$242$	−24.9714	−1.60522
$243$	−21.5286	−1.38106
$244$	39.3901	2.52169
$245$	15.6608	1.00053
$246$	−12.6816	−0.808552
$247$	−5.94041	−0.377979
$248$	−20.5598	−1.30555
$249$	−18.6203	−1.18001
$250$	−31.0941	−1.96656
$251$	18.4452	1.16425	0.582124	−	0.813100i	$-0.302222\pi$
$251$	18.4452	1.16425	0.582124	+	0.813100i	$0.302222\pi$
$252$	−0.908401	−0.0572239
$253$	−13.5160	−0.849747
$254$	−48.8315	−3.06396
$255$	13.5192	0.846603
$256$	90.4960	5.65600
$257$	1.10325	0.0688190	0.0344095	−	0.999408i	$-0.489045\pi$
$257$	1.10325	0.0688190	0.0344095	+	0.999408i	$0.489045\pi$
$258$	−34.4664	−2.14578
$259$	−0.496970	−0.0308802
$260$	13.0093	0.806800
$261$	10.2252	0.632923
$262$	−5.76531	−0.356182
$263$	3.75153	0.231329	0.115665	−	0.993288i	$-0.463100\pi$
$263$	3.75153	0.231329	0.115665	+	0.993288i	$0.463100\pi$
$264$	−112.189	−6.90473
$265$	−8.74378	−0.537126
$266$	0.928890	0.0569539
$267$	12.4866	0.764164
$268$	−58.1950	−3.55482
$269$	−17.3095	−1.05538	−0.527690	−	0.849437i	$-0.676942\pi$
$269$	−17.3095	−1.05538	−0.527690	+	0.849437i	$0.676942\pi$
$270$	−3.25794	−0.198272
$271$	10.5614	0.641560	0.320780	−	0.947154i	$-0.396055\pi$
$271$	10.5614	0.641560	0.320780	+	0.947154i	$0.396055\pi$
$272$	−44.1153	−2.67489
$273$	0.137999	0.00835206
$274$	23.3945	1.41332
$275$	0.0442775	0.00267003
$276$	−41.8215	−2.51736
$277$	−27.4220	−1.64763	−0.823815	−	0.566859i	$-0.808158\pi$
$277$	−27.4220	−1.64763	−0.823815	+	0.566859i	$0.808158\pi$
$278$	48.1360	2.88700
$279$	5.47981	0.328068
$280$	−1.32669	−0.0792848
$281$	4.46092	0.266116	0.133058	−	0.991108i	$-0.457520\pi$
$281$	4.46092	0.266116	0.133058	+	0.991108i	$0.457520\pi$
$282$	22.7765	1.35632
$283$	−8.18035	−0.486272	−0.243136	−	0.969992i	$-0.578176\pi$
$283$	−8.18035	−0.486272	−0.243136	+	0.969992i	$0.578176\pi$
$284$	3.27736	0.194475
$285$	−31.6324	−1.87374
$286$	12.5749	0.743567
$287$	−0.107551	−0.00634854
$288$	−77.9555	−4.59357
$289$	−10.6912	−0.628893
$290$	22.8978	1.34460
$291$	35.2372	2.06564
$292$	−46.3020	−2.70962
$293$	20.1651	1.17806	0.589030	−	0.808111i	$-0.299510\pi$
$293$	20.1651	1.17806	0.589030	+	0.808111i	$0.299510\pi$
$294$	46.8396	2.73174
$295$	−5.05733	−0.294449
$296$	−91.3852	−5.31166
$297$	−2.33648	−0.135576
$298$	−21.6060	−1.25160
$299$	3.05719	0.176802
$300$	0.137004	0.00790991
$301$	−0.292304	−0.0168481
$302$	−50.1902	−2.88812
$303$	14.9269	0.857529
$304$	103.222	5.92017
$305$	−15.3329	−0.877961
$306$	19.4570	1.11228
$307$	19.2709	1.09985	0.549924	−	0.835215i	$-0.314657\pi$
$307$	19.2709	1.09985	0.549924	+	0.835215i	$0.314657\pi$
$308$	−1.45888	−0.0831274
$309$	−2.49455	−0.141910
$310$	12.2712	0.696959
$311$	−14.8811	−0.843829	−0.421914	−	0.906636i	$-0.638642\pi$
$311$	−14.8811	−0.843829	−0.421914	+	0.906636i	$0.638642\pi$
$312$	25.3759	1.43663
$313$	7.69713	0.435068	0.217534	−	0.976053i	$-0.430199\pi$
$313$	7.69713	0.435068	0.217534	+	0.976053i	$0.430199\pi$
$314$	−61.5237	−3.47199
$315$	0.353603	0.0199232
$316$	33.7083	1.89624
$317$	8.39183	0.471332	0.235666	−	0.971834i	$-0.424273\pi$
$317$	8.39183	0.471332	0.235666	+	0.971834i	$0.424273\pi$
$318$	−26.1516	−1.46651
$319$	16.4215	0.919427
$320$	−95.9449	−5.36349
$321$	−12.5907	−0.702743
$322$	−0.478046	−0.0266405
$323$	−14.7615	−0.821352
$324$	−55.2300	−3.06833
$325$	−0.0100151	−0.000555538 0
$326$	−29.9471	−1.65862
$327$	21.2130	1.17308
$328$	−19.7770	−1.09200
$329$	0.193164	0.0106495
$330$	66.9604	3.68605
$331$	−31.0620	−1.70732	−0.853662	−	0.520827i	$-0.825624\pi$
$331$	−31.0620	−1.70732	−0.853662	+	0.520827i	$0.825624\pi$
$332$	−44.5249	−2.44362
$333$	24.3569	1.33475
$334$	−48.5135	−2.65454
$335$	22.6529	1.23766
$336$	−2.39789	−0.130816
$337$	6.34005	0.345364	0.172682	−	0.984978i	$-0.444757\pi$
$337$	6.34005	0.345364	0.172682	+	0.984978i	$0.444757\pi$
$338$	33.3465	1.81381
$339$	−13.7454	−0.746549
$340$	32.3271	1.75318
$341$	8.80049	0.476573
$342$	−45.5257	−2.46175
$343$	0.794661	0.0429077
$344$	−53.7502	−2.89802
$345$	16.2793	0.876451
$346$	47.5449	2.55603
$347$	−24.9725	−1.34060	−0.670298	−	0.742092i	$-0.733834\pi$
$347$	−24.9725	−1.34060	−0.670298	+	0.742092i	$0.733834\pi$
$348$	50.8115	2.72378
$349$	−1.90366	−0.101900	−0.0509502	−	0.998701i	$-0.516225\pi$
$349$	−1.90366	−0.101900	−0.0509502	+	0.998701i	$0.516225\pi$
$350$	0.00156604	8.37084e−5 0
$351$	0.528488	0.0282086
$352$	−125.195	−6.67294
$353$	4.32797	0.230354	0.115177	−	0.993345i	$-0.463256\pi$
$353$	4.32797	0.230354	0.115177	+	0.993345i	$0.463256\pi$
$354$	−15.1259	−0.803933
$355$	−1.27574	−0.0677092
$356$	29.8579	1.58246
$357$	0.342917	0.0181491
$358$	−50.1917	−2.65271
$359$	16.4668	0.869084	0.434542	−	0.900651i	$-0.356910\pi$
$359$	16.4668	0.869084	0.434542	+	0.900651i	$0.356910\pi$
$360$	65.0221	3.42697
$361$	15.5392	0.817852
$362$	34.4149	1.80881
$363$	21.5700	1.13213
$364$	0.329983	0.0172958
$365$	18.0234	0.943389
$366$	−45.8590	−2.39709
$367$	−13.1276	−0.685255	−0.342627	−	0.939471i	$-0.611317\pi$
$367$	−13.1276	−0.685255	−0.342627	+	0.939471i	$0.611317\pi$
$368$	−53.1223	−2.76919
$369$	5.27117	0.274406
$370$	54.5438	2.83560
$371$	−0.221788	−0.0115147
$372$	27.2306	1.41184
$373$	15.6166	0.808594	0.404297	−	0.914628i	$-0.367516\pi$
$373$	15.6166	0.808594	0.404297	+	0.914628i	$0.367516\pi$
$374$	31.2476	1.61578
$375$	26.8586	1.38697
$376$	35.5199	1.83180
$377$	−3.71437	−0.191300
$378$	−0.0826385	−0.00425047
$379$	17.2449	0.885811	0.442905	−	0.896568i	$-0.353948\pi$
$379$	17.2449	0.885811	0.442905	+	0.896568i	$0.353948\pi$
$380$	−75.6394	−3.88022
$381$	42.1799	2.16094
$382$	31.1593	1.59425
$383$	7.85704	0.401476	0.200738	−	0.979645i	$-0.435666\pi$
$383$	7.85704	0.401476	0.200738	+	0.979645i	$0.435666\pi$
$384$	−152.222	−7.76806
$385$	0.567881	0.0289419
$386$	−2.03224	−0.103438
$387$	14.3261	0.728235
$388$	84.2594	4.27762
$389$	−35.5138	−1.80062	−0.900310	−	0.435250i	$-0.856660\pi$
$389$	−35.5138	−1.80062	−0.900310	+	0.435250i	$0.856660\pi$
$390$	−15.1457	−0.766934
$391$	7.59689	0.384191
$392$	73.0462	3.68939
$393$	4.97999	0.251207
$394$	−28.3377	−1.42763
$395$	−13.1212	−0.660200
$396$	71.5010	3.59306
$397$	7.95230	0.399115	0.199557	−	0.979886i	$-0.436050\pi$
$397$	7.95230	0.399115	0.199557	+	0.979886i	$0.436050\pi$
$398$	−72.7824	−3.64825
$399$	−0.802363	−0.0401684
$400$	0.174024	0.00870121
$401$	1.36633	0.0682310	0.0341155	−	0.999418i	$-0.489139\pi$
$401$	1.36633	0.0682310	0.0341155	+	0.999418i	$0.489139\pi$
$402$	67.7522	3.37917
$403$	−1.99058	−0.0991578
$404$	35.6933	1.77581
$405$	21.4987	1.06828
$406$	0.580808	0.0288250
$407$	39.1169	1.93895
$408$	63.0572	3.12180
$409$	15.7814	0.780340	0.390170	−	0.920743i	$-0.372416\pi$
$409$	15.7814	0.780340	0.390170	+	0.920743i	$0.372416\pi$
$410$	11.8040	0.582959
$411$	−20.2079	−0.996781
$412$	−5.96498	−0.293874
$413$	−0.128280	−0.00631227
$414$	23.4295	1.15150
$415$	17.3317	0.850779
$416$	28.3179	1.38840
$417$	−41.5792	−2.03614
$418$	−73.1137	−3.57611
$419$	17.3206	0.846166	0.423083	−	0.906091i	$-0.360948\pi$
$419$	17.3206	0.846166	0.423083	+	0.906091i	$0.360948\pi$
$420$	1.75714	0.0857397
$421$	23.6432	1.15230	0.576150	−	0.817344i	$-0.304554\pi$
$421$	23.6432	1.15230	0.576150	+	0.817344i	$0.304554\pi$
$422$	23.7654	1.15688
$423$	−9.46714	−0.460308
$424$	−40.7835	−1.98062
$425$	−0.0248868	−0.00120719
$426$	−3.81559	−0.184866
$427$	−0.388923	−0.0188213
$428$	−30.1069	−1.45527
$429$	−10.8620	−0.524422
$430$	32.0811	1.54709
$431$	26.2928	1.26648	0.633240	−	0.773955i	$-0.281724\pi$
$431$	26.2928	1.26648	0.633240	+	0.773955i	$0.281724\pi$
$432$	−9.18310	−0.441822
$433$	13.8904	0.667529	0.333765	−	0.942656i	$-0.391681\pi$
$433$	13.8904	0.667529	0.333765	+	0.942656i	$0.391681\pi$
$434$	0.311263	0.0149411
$435$	−19.7788	−0.948320
$436$	50.7247	2.42927
$437$	−17.7753	−0.850309
$438$	53.9060	2.57573
$439$	−8.88645	−0.424127	−0.212063	−	0.977256i	$-0.568018\pi$
$439$	−8.88645	−0.424127	−0.212063	+	0.977256i	$0.568018\pi$
$440$	104.425	4.97825
$441$	−19.4690	−0.927097
$442$	−7.06788	−0.336185
$443$	37.5090	1.78211	0.891054	−	0.453897i	$-0.149967\pi$
$443$	37.5090	1.78211	0.891054	+	0.453897i	$0.149967\pi$
$444$	121.036	5.74410
$445$	−11.6224	−0.550956
$446$	2.92547	0.138525
$447$	18.6629	0.882727
$448$	−2.43367	−0.114980
$449$	−24.6199	−1.16188	−0.580942	−	0.813945i	$-0.697316\pi$
$449$	−24.6199	−1.16188	−0.580942	+	0.813945i	$0.697316\pi$
$450$	−0.0767530	−0.00361817
$451$	8.46543	0.398621
$452$	−32.8681	−1.54599
$453$	43.3536	2.03693
$454$	−18.4854	−0.867562
$455$	−0.128449	−0.00602176
$456$	−147.542	−6.90930
$457$	5.64598	0.264108	0.132054	−	0.991243i	$-0.457843\pi$
$457$	5.64598	0.264108	0.132054	+	0.991243i	$0.457843\pi$
$458$	36.6630	1.71315
$459$	1.31325	0.0612974
$460$	38.9272	1.81499
$461$	34.3504	1.59986	0.799929	−	0.600094i	$-0.204870\pi$
$461$	34.3504	1.59986	0.799929	+	0.600094i	$0.204870\pi$
$462$	1.69847	0.0790198
$463$	10.2102	0.474507	0.237253	−	0.971448i	$-0.423753\pi$
$463$	10.2102	0.474507	0.237253	+	0.971448i	$0.423753\pi$
$464$	64.5416	2.99627
$465$	−10.5997	−0.491550
$466$	−53.4829	−2.47755
$467$	−29.2100	−1.35168	−0.675839	−	0.737049i	$-0.736219\pi$
$467$	−29.2100	−1.35168	−0.675839	+	0.737049i	$0.736219\pi$
$468$	−16.1728	−0.747586
$469$	0.574596	0.0265324
$470$	−21.2003	−0.977895
$471$	53.1434	2.44872
$472$	−23.5888	−1.08576
$473$	23.0075	1.05788
$474$	−39.2441	−1.80254
$475$	0.0582305	0.00267180
$476$	0.819984	0.0375839
$477$	10.8700	0.497704
$478$	−39.5420	−1.80861
$479$	31.7894	1.45250	0.726248	−	0.687433i	$-0.241263\pi$
$479$	31.7894	1.45250	0.726248	+	0.687433i	$0.241263\pi$
$480$	150.791	6.88264
$481$	−8.84783	−0.403426
$482$	−40.9878	−1.86694
$483$	0.412930	0.0187890
$484$	51.5782	2.34446
$485$	−32.7987	−1.48931
$486$	59.9336	2.71864
$487$	3.65311	0.165538	0.0827692	−	0.996569i	$-0.473624\pi$
$487$	3.65311	0.165538	0.0827692	+	0.996569i	$0.473624\pi$
$488$	−71.5171	−3.23743
$489$	25.8679	1.16979
$490$	−43.5981	−1.96956
$491$	−38.0504	−1.71719	−0.858595	−	0.512655i	$-0.828662\pi$
$491$	−38.0504	−1.71719	−0.858595	+	0.512655i	$0.828662\pi$
$492$	26.1938	1.18091
$493$	−9.22993	−0.415695
$494$	16.5375	0.744059
$495$	−27.8323	−1.25097
$496$	34.5887	1.55308
$497$	−0.0323594	−0.00145152
$498$	51.8371	2.32288
$499$	8.21311	0.367669	0.183835	−	0.982957i	$-0.441149\pi$
$499$	8.21311	0.367669	0.183835	+	0.982957i	$0.441149\pi$
$500$	64.2245	2.87221
$501$	41.9053	1.87219
$502$	−51.3496	−2.29184
$503$	41.8858	1.86760	0.933799	−	0.357799i	$-0.116473\pi$
$503$	41.8858	1.86760	0.933799	+	0.357799i	$0.116473\pi$
$504$	1.64930	0.0734658
$505$	−13.8939	−0.618271
$506$	37.6274	1.67274
$507$	−28.8042	−1.27924
$508$	100.861	4.47498
$509$	−36.1271	−1.60131	−0.800653	−	0.599129i	$-0.795514\pi$
$509$	−36.1271	−1.60131	−0.800653	+	0.599129i	$0.795514\pi$
$510$	−37.6361	−1.66655
$511$	0.457169	0.0202240
$512$	−125.328	−5.53877
$513$	−3.07277	−0.135666
$514$	−3.07135	−0.135471
$515$	2.32192	0.102316
$516$	71.1899	3.13396
$517$	−15.2041	−0.668675
$518$	1.38352	0.0607882
$519$	−41.0687	−1.80271
$520$	−23.6197	−1.03579
$521$	−13.3411	−0.584482	−0.292241	−	0.956345i	$-0.594401\pi$
$521$	−13.3411	−0.584482	−0.292241	+	0.956345i	$0.594401\pi$
$522$	−28.4659	−1.24592
$523$	22.7016	0.992670	0.496335	−	0.868131i	$-0.334679\pi$
$523$	22.7016	0.992670	0.496335	+	0.868131i	$0.334679\pi$
$524$	11.9082	0.520211
$525$	−0.00135272	−5.90377e−5 0
$526$	−10.4439	−0.455376
$527$	−4.94644	−0.215471
$528$	188.740	8.21386
$529$	−13.8521	−0.602264
$530$	24.3418	1.05734
$531$	6.28714	0.272839
$532$	−1.91861	−0.0831824
$533$	−1.91479	−0.0829388
$534$	−34.7614	−1.50427
$535$	11.7193	0.506672
$536$	105.659	4.56379
$537$	43.3549	1.87090
$538$	48.1880	2.07753
$539$	−31.2670	−1.34677
$540$	6.72924	0.289581
$541$	−37.2425	−1.60118	−0.800591	−	0.599212i	$-0.795481\pi$
$541$	−37.2425	−1.60118	−0.800591	+	0.599212i	$0.795481\pi$
$542$	−29.4020	−1.26292
$543$	−29.7271	−1.27571
$544$	70.3679	3.01700
$545$	−19.7450	−0.845783
$546$	−0.384175	−0.0164412
$547$	−24.5951	−1.05161	−0.525804	−	0.850605i	$-0.676236\pi$
$547$	−24.5951	−1.05161	−0.525804	+	0.850605i	$0.676236\pi$
$548$	−48.3212	−2.06418
$549$	19.0615	0.813524
$550$	−0.123264	−0.00525600
$551$	21.5964	0.920035
$552$	75.9315	3.23186
$553$	−0.332823	−0.0141531
$554$	76.3403	3.24339
$555$	−47.1142	−1.99989
$556$	−99.4243	−4.21653
$557$	−23.7094	−1.00460	−0.502300	−	0.864694i	$-0.667513\pi$
$557$	−23.7094	−1.00460	−0.502300	+	0.864694i	$0.667513\pi$
$558$	−15.2553	−0.645807
$559$	−5.20404	−0.220108
$560$	2.23195	0.0943170
$561$	−26.9913	−1.13957
$562$	−12.4188	−0.523855
$563$	−26.8891	−1.13324	−0.566620	−	0.823979i	$-0.691749\pi$
$563$	−26.8891	−1.13324	−0.566620	+	0.823979i	$0.691749\pi$
$564$	−47.0446	−1.98094
$565$	12.7942	0.538255
$566$	22.7733	0.957234
$567$	0.545320	0.0229013
$568$	−5.95041	−0.249673
$569$	−3.35316	−0.140572	−0.0702859	−	0.997527i	$-0.522391\pi$
$569$	−3.35316	−0.140572	−0.0702859	+	0.997527i	$0.522391\pi$
$570$	88.0614	3.68849
$571$	16.6016	0.694757	0.347378	−	0.937725i	$-0.387072\pi$
$571$	16.6016	0.694757	0.347378	+	0.937725i	$0.387072\pi$
$572$	−25.9732	−1.08600
$573$	−26.9150	−1.12439
$574$	0.299412	0.0124972
$575$	−0.0299679	−0.00124975
$576$	119.276	4.96984
$577$	−41.9998	−1.74847	−0.874237	−	0.485500i	$-0.838638\pi$
$577$	−41.9998	−1.74847	−0.874237	+	0.485500i	$0.838638\pi$
$578$	29.7632	1.23799
$579$	1.75542	0.0729526
$580$	−47.2951	−1.96382
$581$	0.439622	0.0182386
$582$	−98.0971	−4.06625
$583$	17.4571	0.723000
$584$	84.0664	3.47869
$585$	6.29538	0.260282
$586$	−56.1378	−2.31903
$587$	−19.1794	−0.791617	−0.395808	−	0.918333i	$-0.629536\pi$
$587$	−19.1794	−0.791617	−0.395808	+	0.918333i	$0.629536\pi$
$588$	−96.7466	−3.98976
$589$	11.5738	0.476889
$590$	14.0791	0.579628
$591$	24.4777	1.00688
$592$	153.742	6.31874
$593$	46.0608	1.89149	0.945745	−	0.324909i	$-0.105334\pi$
$593$	46.0608	1.89149	0.945745	+	0.324909i	$0.105334\pi$
$594$	6.50454	0.266885
$595$	−0.319186	−0.0130853
$596$	44.6269	1.82799
$597$	62.8684	2.57303
$598$	−8.51092	−0.348037
$599$	−3.92338	−0.160305	−0.0801524	−	0.996783i	$-0.525541\pi$
$599$	−3.92338	−0.160305	−0.0801524	+	0.996783i	$0.525541\pi$
$600$	−0.248745	−0.0101550
$601$	−44.3363	−1.80851	−0.904257	−	0.426989i	$-0.859574\pi$
$601$	−44.3363	−1.80851	−0.904257	+	0.426989i	$0.859574\pi$
$602$	0.813746	0.0331658
$603$	−28.1614	−1.14682
$604$	103.667	4.21816
$605$	−20.0772	−0.816255
$606$	−41.5551	−1.68806
$607$	33.5928	1.36349	0.681745	−	0.731590i	$-0.261221\pi$
$607$	33.5928	1.36349	0.681745	+	0.731590i	$0.261221\pi$
$608$	−164.648	−6.67735
$609$	−0.501694	−0.0203297
$610$	42.6854	1.72828
$611$	3.43900	0.139127
$612$	−40.1881	−1.62451
$613$	38.2029	1.54300	0.771500	−	0.636229i	$-0.219507\pi$
$613$	38.2029	1.54300	0.771500	+	0.636229i	$0.219507\pi$
$614$	−53.6483	−2.16507
$615$	−10.1961	−0.411148
$616$	2.64876	0.106721
$617$	−17.0650	−0.687012	−0.343506	−	0.939151i	$-0.611615\pi$
$617$	−17.0650	−0.687012	−0.343506	+	0.939151i	$0.611615\pi$
$618$	6.94459	0.279353
$619$	38.0997	1.53136	0.765678	−	0.643224i	$-0.222403\pi$
$619$	38.0997	1.53136	0.765678	+	0.643224i	$0.222403\pi$
$620$	−25.3461	−1.01792
$621$	1.58138	0.0634585
$622$	41.4275	1.66109
$623$	−0.294806	−0.0118111
$624$	−42.6910	−1.70901
$625$	−25.0494	−1.00198
$626$	−21.4281	−0.856438
$627$	63.1546	2.52215
$628$	127.077	5.07091
$629$	−21.9862	−0.876648
$630$	−0.984396	−0.0392193
$631$	−25.3340	−1.00853	−0.504265	−	0.863549i	$-0.668237\pi$
$631$	−25.3340	−1.00853	−0.504265	+	0.863549i	$0.668237\pi$
$632$	−61.2011	−2.43445
$633$	−20.5282	−0.815923
$634$	−23.3621	−0.927826
$635$	−39.2609	−1.55802
$636$	54.0159	2.14187
$637$	7.07227	0.280213
$638$	−45.7159	−1.80991
$639$	1.58596	0.0627398
$640$	141.688	5.60070
$641$	−9.05500	−0.357651	−0.178825	−	0.983881i	$-0.557230\pi$
$641$	−9.05500	−0.357651	−0.178825	+	0.983881i	$0.557230\pi$
$642$	35.0512	1.38336
$643$	7.79552	0.307425	0.153713	−	0.988116i	$-0.450877\pi$
$643$	7.79552	0.307425	0.153713	+	0.988116i	$0.450877\pi$
$644$	0.987399	0.0389090
$645$	−27.7112	−1.09113
$646$	41.0946	1.61685
$647$	36.4734	1.43392	0.716959	−	0.697116i	$-0.245534\pi$
$647$	36.4734	1.43392	0.716959	+	0.697116i	$0.245534\pi$
$648$	100.276	3.93922
$649$	10.0971	0.396344
$650$	0.0278811	0.00109359
$651$	−0.268864	−0.0105376
$652$	61.8554	2.42244
$653$	47.4205	1.85571	0.927855	−	0.372942i	$-0.121651\pi$
$653$	47.4205	1.85571	0.927855	+	0.372942i	$0.121651\pi$
$654$	−59.0550	−2.30923
$655$	−4.63536	−0.181118
$656$	33.2718	1.29904
$657$	−22.4062	−0.874151
$658$	−0.537750	−0.0209637
$659$	1.74351	0.0679177	0.0339588	−	0.999423i	$-0.489188\pi$
$659$	1.74351	0.0679177	0.0339588	+	0.999423i	$0.489188\pi$
$660$	−138.306	−5.38355
$661$	25.1401	0.977836	0.488918	−	0.872330i	$-0.337392\pi$
$661$	25.1401	0.977836	0.488918	+	0.872330i	$0.337392\pi$
$662$	86.4738	3.36090
$663$	6.10514	0.237104
$664$	80.8399	3.13720
$665$	0.746836	0.0289610
$666$	−67.8074	−2.62748
$667$	−11.1144	−0.430351
$668$	100.204	3.87701
$669$	−2.52698	−0.0976986
$670$	−63.0634	−2.43635
$671$	30.6125	1.18178
$672$	3.82485	0.147547
$673$	46.2881	1.78428	0.892138	−	0.451763i	$-0.149205\pi$
$673$	46.2881	1.78428	0.892138	+	0.451763i	$0.149205\pi$
$674$	−17.6501	−0.679856
$675$	−0.00518047	−0.000199396 0
$676$	−68.8767	−2.64911
$677$	−33.3594	−1.28211	−0.641053	−	0.767497i	$-0.721502\pi$
$677$	−33.3594	−1.28211	−0.641053	+	0.767497i	$0.721502\pi$
$678$	38.2660	1.46960
$679$	−0.831946	−0.0319272
$680$	−58.6934	−2.25079
$681$	15.9674	0.611873
$682$	−24.4997	−0.938143
$683$	11.8600	0.453812	0.226906	−	0.973917i	$-0.427139\pi$
$683$	11.8600	0.453812	0.226906	+	0.973917i	$0.427139\pi$
$684$	94.0329	3.59544
$685$	18.8094	0.718670
$686$	−2.21226	−0.0844645
$687$	−31.6690	−1.20825
$688$	90.4265	3.44748
$689$	−3.94861	−0.150430
$690$	−45.3201	−1.72531
$691$	−18.6628	−0.709966	−0.354983	−	0.934873i	$-0.615513\pi$
$691$	−18.6628	−0.709966	−0.354983	+	0.934873i	$0.615513\pi$
$692$	−98.2036	−3.73314
$693$	−0.705974	−0.0268177
$694$	69.5211	2.63899
$695$	38.7017	1.46804
$696$	−92.2539	−3.49687
$697$	−4.75812	−0.180226
$698$	5.29959	0.200593
$699$	46.1978	1.74736
$700$	−0.00323464	−0.000122258 0
$701$	6.71903	0.253774	0.126887	−	0.991917i	$-0.459501\pi$
$701$	6.71903	0.253774	0.126887	+	0.991917i	$0.459501\pi$
$702$	−1.47126	−0.0555291
$703$	51.4437	1.94024
$704$	191.556	7.21953
$705$	18.3125	0.689689
$706$	−12.0486	−0.453457
$707$	−0.352423	−0.0132542
$708$	31.2424	1.17416
$709$	−45.6265	−1.71354	−0.856769	−	0.515701i	$-0.827532\pi$
$709$	−45.6265	−1.71354	−0.856769	+	0.515701i	$0.827532\pi$
$710$	3.55153	0.133287
$711$	16.3120	0.611746
$712$	−54.2103	−2.03162
$713$	−5.95635	−0.223067
$714$	−0.954648	−0.0357268
$715$	10.1103	0.378103
$716$	103.670	3.87434
$717$	34.1559	1.27557
$718$	−45.8420	−1.71081
$719$	13.2163	0.492883	0.246442	−	0.969158i	$-0.420739\pi$
$719$	13.2163	0.492883	0.246442	+	0.969158i	$0.420739\pi$
$720$	−109.390	−4.07672
$721$	0.0588960	0.00219340
$722$	−43.2596	−1.60996
$723$	35.4047	1.31672
$724$	−71.0836	−2.64180
$725$	0.0364099	0.00135223
$726$	−60.0487	−2.22862
$727$	−40.0931	−1.48697	−0.743486	−	0.668752i	$-0.766829\pi$
$727$	−40.0931	−1.48697	−0.743486	+	0.668752i	$0.766829\pi$
$728$	−0.599121	−0.0222049
$729$	−22.9548	−0.850177
$730$	−50.1755	−1.85708
$731$	−12.9317	−0.478295
$732$	94.7213	3.50100
$733$	−14.6344	−0.540535	−0.270267	−	0.962785i	$-0.587112\pi$
$733$	−14.6344	−0.540535	−0.270267	+	0.962785i	$0.587112\pi$
$734$	36.5460	1.34894
$735$	37.6594	1.38909
$736$	84.7348	3.12336
$737$	−45.2269	−1.66595
$738$	−14.6744	−0.540174
$739$	−48.2744	−1.77580	−0.887900	−	0.460036i	$-0.847837\pi$
$739$	−48.2744	−1.77580	−0.887900	+	0.460036i	$0.847837\pi$
$740$	−112.660	−4.14145
$741$	−14.2849	−0.524769
$742$	0.617437	0.0226668
$743$	−25.2529	−0.926437	−0.463219	−	0.886244i	$-0.653306\pi$
$743$	−25.2529	−0.926437	−0.463219	+	0.886244i	$0.653306\pi$
$744$	−49.4401	−1.81256
$745$	−17.3714	−0.636438
$746$	−43.4750	−1.59173
$747$	−21.5463	−0.788337
$748$	−64.5416	−2.35987
$749$	0.297264	0.0108618
$750$	−74.7719	−2.73028
$751$	−15.0796	−0.550261	−0.275131	−	0.961407i	$-0.588721\pi$
$751$	−15.0796	−0.550261	−0.275131	+	0.961407i	$0.588721\pi$
$752$	−59.7568	−2.17911
$753$	44.3550	1.61639
$754$	10.3404	0.376577
$755$	−40.3533	−1.46861
$756$	0.170689	0.00620790
$757$	36.7887	1.33711	0.668553	−	0.743664i	$-0.266914\pi$
$757$	36.7887	1.33711	0.668553	+	0.743664i	$0.266914\pi$
$758$	−48.0081	−1.74373
$759$	−32.5020	−1.17975
$760$	137.332	4.98154
$761$	30.8702	1.11904	0.559521	−	0.828816i	$-0.310985\pi$
$761$	30.8702	1.11904	0.559521	+	0.828816i	$0.310985\pi$
$762$	−117.425	−4.25386
$763$	−0.500837	−0.0181315
$764$	−64.3591	−2.32843
$765$	15.6436	0.565594
$766$	−21.8732	−0.790313
$767$	−2.28385	−0.0824649
$768$	217.616	7.85252
$769$	29.9751	1.08093	0.540464	−	0.841367i	$-0.318249\pi$
$769$	29.9751	1.08093	0.540464	+	0.841367i	$0.318249\pi$
$770$	−1.58093	−0.0569726
$771$	2.65299	0.0955451
$772$	4.19756	0.151073
$773$	−3.31481	−0.119225	−0.0596127	−	0.998222i	$-0.518987\pi$
$773$	−3.31481	−0.119225	−0.0596127	+	0.998222i	$0.518987\pi$
$774$	−39.8824	−1.43354
$775$	0.0195125	0.000700911 0
$776$	−152.982	−5.49174
$777$	−1.19506	−0.0428726
$778$	98.8669	3.54455
$779$	11.1331	0.398885
$780$	31.2833	1.12012
$781$	2.54704	0.0911401
$782$	−21.1490	−0.756287
$783$	−1.92131	−0.0686622
$784$	−122.889	−4.38890
$785$	−49.4656	−1.76550
$786$	−13.8638	−0.494506
$787$	51.0005	1.81797	0.908986	−	0.416826i	$-0.136858\pi$
$787$	51.0005	1.81797	0.908986	+	0.416826i	$0.136858\pi$
$788$	58.5312	2.08509
$789$	9.02130	0.321167
$790$	36.5282	1.29962
$791$	0.324528	0.0115389
$792$	−129.818	−4.61288
$793$	−6.92422	−0.245886
$794$	−22.1384	−0.785664
$795$	−21.0261	−0.745720
$796$	150.331	5.32835
$797$	−3.27665	−0.116065	−0.0580325	−	0.998315i	$-0.518483\pi$
$797$	−3.27665	−0.116065	−0.0580325	+	0.998315i	$0.518483\pi$
$798$	2.23370	0.0790721
$799$	8.54568	0.302324
$800$	−0.277584	−0.00981408
$801$	14.4487	0.510519
$802$	−3.80372	−0.134314
$803$	−35.9841	−1.26985
$804$	−139.941	−4.93535
$805$	−0.384353	−0.0135467
$806$	5.54158	0.195194
$807$	−41.6241	−1.46524
$808$	−64.8052	−2.27984
$809$	−32.8470	−1.15484	−0.577420	−	0.816447i	$-0.695941\pi$
$809$	−32.8470	−1.15484	−0.577420	+	0.816447i	$0.695941\pi$
$810$	−59.8504	−2.10293
$811$	−14.6067	−0.512910	−0.256455	−	0.966556i	$-0.582555\pi$
$811$	−14.6067	−0.512910	−0.256455	+	0.966556i	$0.582555\pi$
$812$	−1.19965	−0.0420996
$813$	25.3970	0.890712
$814$	−108.898	−3.81686
$815$	−24.0777	−0.843405
$816$	−106.084	−3.71368
$817$	30.2577	1.05858
$818$	−43.9339	−1.53611
$819$	0.159684	0.00557981
$820$	−24.3811	−0.851424
$821$	−31.2432	−1.09039	−0.545197	−	0.838308i	$-0.683545\pi$
$821$	−31.2432	−1.09039	−0.545197	+	0.838308i	$0.683545\pi$
$822$	56.2568	1.96218
$823$	−20.0259	−0.698058	−0.349029	−	0.937112i	$-0.613488\pi$
$823$	−20.0259	−0.698058	−0.349029	+	0.937112i	$0.613488\pi$
$824$	10.8301	0.377284
$825$	0.106474	0.00370695
$826$	0.357121	0.0124258
$827$	−4.55756	−0.158482	−0.0792409	−	0.996855i	$-0.525250\pi$
$827$	−4.55756	−0.158482	−0.0792409	+	0.996855i	$0.525250\pi$
$828$	−48.3933	−1.68178
$829$	−45.9058	−1.59437	−0.797187	−	0.603733i	$-0.793679\pi$
$829$	−45.9058	−1.59437	−0.797187	+	0.603733i	$0.793679\pi$
$830$	−48.2497	−1.67477
$831$	−65.9417	−2.28749
$832$	−43.3279	−1.50213
$833$	17.5741	0.608905
$834$	115.752	4.00818
$835$	−39.0053	−1.34983
$836$	151.015	5.22298
$837$	−1.02966	−0.0355902
$838$	−48.2188	−1.66569
$839$	21.0535	0.726848	0.363424	−	0.931624i	$-0.381608\pi$
$839$	21.0535	0.726848	0.363424	+	0.931624i	$0.381608\pi$
$840$	−3.19028	−0.110075
$841$	−15.4964	−0.534360
$842$	−65.8205	−2.26832
$843$	10.7272	0.369463
$844$	−49.0871	−1.68965
$845$	26.8108	0.922321
$846$	26.3556	0.906124
$847$	−0.509264	−0.0174985
$848$	68.6119	2.35614
$849$	−19.6713	−0.675117
$850$	0.0692824	0.00237637
$851$	−26.4751	−0.907555
$852$	7.88106	0.270001
$853$	2.19428	0.0751307	0.0375653	−	0.999294i	$-0.488040\pi$
$853$	2.19428	0.0751307	0.0375653	+	0.999294i	$0.488040\pi$
$854$	1.08273	0.0370501
$855$	−36.6031	−1.25180
$856$	54.6624	1.86832
$857$	−22.9582	−0.784237	−0.392119	−	0.919915i	$-0.628258\pi$
$857$	−22.9582	−0.784237	−0.392119	+	0.919915i	$0.628258\pi$
$858$	30.2387	1.03233
$859$	−28.8325	−0.983752	−0.491876	−	0.870665i	$-0.663689\pi$
$859$	−28.8325	−0.983752	−0.491876	+	0.870665i	$0.663689\pi$
$860$	−66.2632	−2.25956
$861$	−0.258628	−0.00881401
$862$	−73.1967	−2.49309
$863$	20.3072	0.691265	0.345633	−	0.938370i	$-0.387664\pi$
$863$	20.3072	0.691265	0.345633	+	0.938370i	$0.387664\pi$
$864$	14.6479	0.498330
$865$	38.2265	1.29974
$866$	−38.6695	−1.31404
$867$	−25.7090	−0.873125
$868$	−0.642910	−0.0218218
$869$	26.1968	0.888664
$870$	55.0623	1.86679
$871$	10.2298	0.346625
$872$	−92.0962	−3.11877
$873$	40.7744	1.38000
$874$	49.4848	1.67385
$875$	−0.634129	−0.0214375
$876$	−111.342	−3.76191
$877$	−4.45487	−0.150430	−0.0752152	−	0.997167i	$-0.523964\pi$
$877$	−4.45487	−0.150430	−0.0752152	+	0.997167i	$0.523964\pi$
$878$	24.7390	0.834901
$879$	48.4910	1.63556
$880$	−175.678	−5.92212
$881$	39.7804	1.34024	0.670118	−	0.742255i	$-0.266244\pi$
$881$	39.7804	1.34024	0.670118	+	0.742255i	$0.266244\pi$
$882$	54.1999	1.82501
$883$	−10.3635	−0.348758	−0.174379	−	0.984679i	$-0.555792\pi$
$883$	−10.3635	−0.348758	−0.174379	+	0.984679i	$0.555792\pi$
$884$	14.5986	0.491005
$885$	−12.1614	−0.408799
$886$	−104.422	−3.50811
$887$	20.4859	0.687849	0.343924	−	0.938997i	$-0.388244\pi$
$887$	20.4859	0.687849	0.343924	+	0.938997i	$0.388244\pi$
$888$	−219.754	−7.37446
$889$	−0.995863	−0.0334002
$890$	32.3557	1.08457
$891$	−42.9226	−1.43796
$892$	−6.04252	−0.202319
$893$	−19.9953	−0.669118
$894$	−51.9559	−1.73766
$895$	−40.3545	−1.34890
$896$	3.59395	0.120065
$897$	7.35161	0.245463
$898$	68.5394	2.28719
$899$	7.23674	0.241359
$900$	0.158532	0.00528442
$901$	−9.81202	−0.326886
$902$	−23.5669	−0.784693
$903$	−0.702902	−0.0233911
$904$	59.6757	1.98478
$905$	27.6699	0.919778
$906$	−120.692	−4.00973
$907$	39.2596	1.30359	0.651796	−	0.758394i	$-0.274016\pi$
$907$	39.2596	1.30359	0.651796	+	0.758394i	$0.274016\pi$
$908$	38.1814	1.26709
$909$	17.2725	0.572894
$910$	0.357589	0.0118539
$911$	25.0309	0.829310	0.414655	−	0.909979i	$-0.363902\pi$
$911$	25.0309	0.829310	0.414655	+	0.909979i	$0.363902\pi$
$912$	248.217	8.21929
$913$	−34.6030	−1.14519
$914$	−15.7179	−0.519901
$915$	−36.8710	−1.21892
$916$	−75.7270	−2.50209
$917$	−0.117577	−0.00388273
$918$	−3.65597	−0.120665
$919$	−29.4287	−0.970763	−0.485381	−	0.874303i	$-0.661319\pi$
$919$	−29.4287	−0.970763	−0.485381	+	0.874303i	$0.661319\pi$
$920$	−70.6767	−2.33014
$921$	46.3407	1.52698
$922$	−95.6283	−3.14935
$923$	−0.576112	−0.0189630
$924$	−3.50816	−0.115410
$925$	0.0867303	0.00285167
$926$	−28.4241	−0.934075
$927$	−2.88655	−0.0948066
$928$	−102.950	−3.37948
$929$	27.2482	0.893984	0.446992	−	0.894538i	$-0.352495\pi$
$929$	27.2482	0.893984	0.446992	+	0.894538i	$0.352495\pi$
$930$	29.5086	0.967625
$931$	−41.1201	−1.34766
$932$	110.468	3.61851
$933$	−35.7845	−1.17153
$934$	81.3179	2.66080
$935$	25.1233	0.821621
$936$	29.3634	0.959774
$937$	−26.6447	−0.870445	−0.435222	−	0.900323i	$-0.643330\pi$
$937$	−26.6447	−0.870445	−0.435222	+	0.900323i	$0.643330\pi$
$938$	−1.59962	−0.0522294
$939$	18.5093	0.604027
$940$	43.7889	1.42824
$941$	41.2145	1.34355	0.671777	−	0.740753i	$-0.265531\pi$
$941$	41.2145	1.34355	0.671777	+	0.740753i	$0.265531\pi$
$942$	−147.946	−4.82034
$943$	−5.72957	−0.186581
$944$	39.6846	1.29162
$945$	−0.0664421	−0.00216136
$946$	−64.0506	−2.08246
$947$	22.1283	0.719072	0.359536	−	0.933131i	$-0.382935\pi$
$947$	22.1283	0.719072	0.359536	+	0.933131i	$0.382935\pi$
$948$	81.0582	2.63265
$949$	8.13923	0.264210
$950$	−0.162108	−0.00525948
$951$	20.1798	0.654376
$952$	−1.48877	−0.0482514
$953$	44.0188	1.42591	0.712954	−	0.701211i	$-0.247357\pi$
$953$	44.0188	1.42591	0.712954	+	0.701211i	$0.247357\pi$
$954$	−30.2611	−0.979740
$955$	25.0523	0.810674
$956$	81.6736	2.64151
$957$	39.4887	1.27649
$958$	−88.4987	−2.85926
$959$	0.477105	0.0154065
$960$	−230.719	−7.44641
$961$	−27.1217	−0.874895
$962$	24.6315	0.794152
$963$	−14.5692	−0.469485
$964$	84.6599	2.72671
$965$	−1.63393	−0.0525982
$966$	−1.14956	−0.0369864
$967$	−57.7420	−1.85686	−0.928429	−	0.371510i	$-0.878840\pi$
$967$	−57.7420	−1.85686	−0.928429	+	0.371510i	$0.878840\pi$
$968$	−93.6459	−3.00989
$969$	−35.4969	−1.14033
$970$	91.3083	2.93173
$971$	6.71945	0.215638	0.107819	−	0.994171i	$-0.465613\pi$
$971$	6.71945	0.215638	0.107819	+	0.994171i	$0.465613\pi$
$972$	−123.792	−3.97063
$973$	0.981679	0.0314712
$974$	−10.1699	−0.325865
$975$	−0.0240833	−0.000771282 0
$976$	120.317	3.85124
$977$	−58.3875	−1.86798	−0.933991	−	0.357297i	$-0.883698\pi$
$977$	−58.3875	−1.86798	−0.933991	+	0.357297i	$0.883698\pi$
$978$	−72.0137	−2.30274
$979$	23.2044	0.741615
$980$	90.0513	2.87658
$981$	24.5464	0.783708
$982$	105.929	3.38032
$983$	−25.2729	−0.806081	−0.403041	−	0.915182i	$-0.632047\pi$
$983$	−25.2729	−0.806081	−0.403041	+	0.915182i	$0.632047\pi$
$984$	−47.5577	−1.51608
$985$	−22.7838	−0.725951
$986$	25.6953	0.818304
$987$	0.464501	0.0147852
$988$	−34.1581	−1.08671
$989$	−15.5719	−0.495158
$990$	77.4826	2.46256
$991$	−21.3350	−0.677727	−0.338864	−	0.940835i	$-0.610043\pi$
$991$	−21.3350	−0.677727	−0.338864	+	0.940835i	$0.610043\pi$
$992$	−55.1720	−1.75171
$993$	−74.6948	−2.37037
$994$	0.0900855	0.00285734
$995$	−58.5176	−1.85513
$996$	−107.069	−3.39261
$997$	−23.5253	−0.745054	−0.372527	−	0.928021i	$-0.621509\pi$
$997$	−23.5253	−0.745054	−0.372527	+	0.928021i	$0.621509\pi$
$998$	−22.8645	−0.723763
$999$	−4.57668	−0.144800

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4019.2.a.b.1.3	✓	186

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4019.2.a.b.1.3	✓	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)

\(f(q)\)	\(=\)	\(q-2.78390 q^{2} +2.40470 q^{3} +5.75012 q^{4} -2.23828 q^{5} -6.69445 q^{6} -0.0567746 q^{7} -10.4400 q^{8} +2.78257 q^{9} +O(q^{10})\)	\(q-2.78390 q^{2} +2.40470 q^{3} +5.75012 q^{4} -2.23828 q^{5} -6.69445 q^{6} -0.0567746 q^{7} -10.4400 q^{8} +2.78257 q^{9} +6.23116 q^{10} +4.46877 q^{11} +13.8273 q^{12} -1.01079 q^{13} +0.158055 q^{14} -5.38239 q^{15} +17.5637 q^{16} -2.51174 q^{17} -7.74642 q^{18} +5.87700 q^{19} -12.8704 q^{20} -0.136526 q^{21} -12.4406 q^{22} -3.02456 q^{23} -25.1050 q^{24} +0.00990820 q^{25} +2.81394 q^{26} -0.522847 q^{27} -0.326461 q^{28} +3.67472 q^{29} +14.9841 q^{30} +1.96933 q^{31} -28.0156 q^{32} +10.7460 q^{33} +6.99244 q^{34} +0.127078 q^{35} +16.0001 q^{36} +8.75339 q^{37} -16.3610 q^{38} -2.43064 q^{39} +23.3676 q^{40} +1.89435 q^{41} +0.380075 q^{42} +5.14850 q^{43} +25.6960 q^{44} -6.22818 q^{45} +8.42007 q^{46} -3.40230 q^{47} +42.2353 q^{48} -6.99678 q^{49} -0.0275835 q^{50} -6.03997 q^{51} -5.81216 q^{52} +3.90647 q^{53} +1.45555 q^{54} -10.0024 q^{55} +0.592726 q^{56} +14.1324 q^{57} -10.2301 q^{58} +2.25947 q^{59} -30.9494 q^{60} +6.85031 q^{61} -5.48243 q^{62} -0.157979 q^{63} +42.8654 q^{64} +2.26243 q^{65} -29.9160 q^{66} -10.1207 q^{67} -14.4428 q^{68} -7.27314 q^{69} -0.353772 q^{70} +0.569963 q^{71} -29.0500 q^{72} -8.05235 q^{73} -24.3686 q^{74} +0.0238262 q^{75} +33.7935 q^{76} -0.253713 q^{77} +6.76668 q^{78} +5.86218 q^{79} -39.3125 q^{80} -9.60501 q^{81} -5.27369 q^{82} -7.74329 q^{83} -0.785040 q^{84} +5.62198 q^{85} -14.3329 q^{86} +8.83659 q^{87} -46.6539 q^{88} +5.19256 q^{89} +17.3387 q^{90} +0.0573871 q^{91} -17.3916 q^{92} +4.73565 q^{93} +9.47167 q^{94} -13.1544 q^{95} -67.3691 q^{96} +14.6535 q^{97} +19.4784 q^{98} +12.4347 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 186 q + 6 q^{2} + 10 q^{3} + 212 q^{4} + 38 q^{5} + 47 q^{6} + 32 q^{7} + 15 q^{8} + 216 q^{9}+O(q^{10}) \) 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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