LMFDB - Embedded newform 6019.2.a.d.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("6019.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$48.0619569766$
Analytic rank:	$0$
Dimension:	$123$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	6019.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.49040 q^{2} -2.13188 q^{3} +4.20211 q^{4} -1.49942 q^{5} +5.30925 q^{6} -0.951507 q^{7} -5.48415 q^{8} +1.54493 q^{9} +O(q^{10})$	\(q-2.49040 q^{2} -2.13188 q^{3} +4.20211 q^{4} -1.49942 q^{5} +5.30925 q^{6} -0.951507 q^{7} -5.48415 q^{8} +1.54493 q^{9} +3.73417 q^{10} -1.50536 q^{11} -8.95842 q^{12} -1.00000 q^{13} +2.36964 q^{14} +3.19660 q^{15} +5.25352 q^{16} -6.30395 q^{17} -3.84751 q^{18} +4.62204 q^{19} -6.30075 q^{20} +2.02850 q^{21} +3.74896 q^{22} +8.58376 q^{23} +11.6916 q^{24} -2.75173 q^{25} +2.49040 q^{26} +3.10204 q^{27} -3.99834 q^{28} +3.30171 q^{29} -7.96083 q^{30} -6.10630 q^{31} -2.11509 q^{32} +3.20926 q^{33} +15.6994 q^{34} +1.42671 q^{35} +6.49198 q^{36} -1.19521 q^{37} -11.5107 q^{38} +2.13188 q^{39} +8.22307 q^{40} +2.83840 q^{41} -5.05179 q^{42} -10.2894 q^{43} -6.32570 q^{44} -2.31651 q^{45} -21.3770 q^{46} -4.09093 q^{47} -11.1999 q^{48} -6.09464 q^{49} +6.85291 q^{50} +13.4393 q^{51} -4.20211 q^{52} +3.85736 q^{53} -7.72532 q^{54} +2.25718 q^{55} +5.21820 q^{56} -9.85366 q^{57} -8.22259 q^{58} +2.26387 q^{59} +13.4325 q^{60} -5.68001 q^{61} +15.2071 q^{62} -1.47001 q^{63} -5.23961 q^{64} +1.49942 q^{65} -7.99235 q^{66} -5.57141 q^{67} -26.4899 q^{68} -18.2996 q^{69} -3.55309 q^{70} +14.5648 q^{71} -8.47264 q^{72} -7.50222 q^{73} +2.97656 q^{74} +5.86636 q^{75} +19.4223 q^{76} +1.43236 q^{77} -5.30925 q^{78} +13.2328 q^{79} -7.87725 q^{80} -11.2480 q^{81} -7.06877 q^{82} -5.89209 q^{83} +8.52399 q^{84} +9.45230 q^{85} +25.6249 q^{86} -7.03887 q^{87} +8.25563 q^{88} +12.9550 q^{89} +5.76905 q^{90} +0.951507 q^{91} +36.0699 q^{92} +13.0179 q^{93} +10.1881 q^{94} -6.93040 q^{95} +4.50912 q^{96} -10.3039 q^{97} +15.1781 q^{98} -2.32568 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 123 q + 10 q^{2} + q^{3} + 136 q^{4} + 46 q^{5} + 16 q^{6} + 12 q^{7} + 30 q^{8} + 154 q^{9}+O(q^{10}) $ 123 * q + 10 * q^2 + q^3 + 136 * q^4 + 46 * q^5 + 16 * q^6 + 12 * q^7 + 30 * q^8 + 154 * q^9	\( 123 q + 10 q^{2} + q^{3} + 136 q^{4} + 46 q^{5} + 16 q^{6} + 12 q^{7} + 30 q^{8} + 154 q^{9} + 5 q^{10} + 53 q^{11} - 6 q^{12} - 123 q^{13} + 21 q^{14} + 29 q^{15} + 166 q^{16} - 35 q^{17} + 28 q^{18} + 23 q^{19} + 93 q^{20} + 72 q^{21} + 8 q^{22} + 42 q^{23} + 55 q^{24} + 153 q^{25} - 10 q^{26} + 7 q^{27} + 39 q^{28} + 86 q^{29} + 44 q^{30} + 16 q^{31} + 70 q^{32} + 40 q^{33} + 10 q^{34} + 6 q^{35} + 222 q^{36} + 52 q^{37} + 12 q^{38} - q^{39} + 14 q^{40} + 80 q^{41} + 29 q^{42} + 2 q^{43} + 143 q^{44} + 137 q^{45} + 39 q^{46} + 45 q^{47} - 27 q^{48} + 163 q^{49} + 102 q^{50} + 48 q^{51} - 136 q^{52} + 117 q^{53} + 75 q^{54} + 20 q^{55} + 88 q^{56} + 67 q^{57} + 56 q^{58} + 88 q^{59} + 96 q^{60} + 57 q^{61} - 13 q^{62} + 48 q^{63} + 228 q^{64} - 46 q^{65} + 28 q^{66} + 43 q^{67} - 56 q^{68} + 92 q^{69} + 14 q^{70} + 90 q^{71} + 98 q^{72} + 25 q^{73} + 80 q^{74} + 21 q^{75} + 75 q^{76} + 112 q^{77} - 16 q^{78} + 36 q^{79} + 208 q^{80} + 231 q^{81} - 27 q^{82} + 93 q^{83} + 175 q^{84} + 77 q^{85} + 199 q^{86} + 15 q^{87} + 43 q^{88} + 140 q^{89} + 11 q^{90} - 12 q^{91} + 93 q^{92} + 140 q^{93} + 4 q^{94} + 23 q^{95} + 105 q^{96} + 43 q^{97} + 67 q^{98} + 140 q^{99}+O(q^{100}) \) 123 * q + 10 * q^2 + q^3 + 136 * q^4 + 46 * q^5 + 16 * q^6 + 12 * q^7 + 30 * q^8 + 154 * q^9 + 5 * q^10 + 53 * q^11 - 6 * q^12 - 123 * q^13 + 21 * q^14 + 29 * q^15 + 166 * q^16 - 35 * q^17 + 28 * q^18 + 23 * q^19 + 93 * q^20 + 72 * q^21 + 8 * q^22 + 42 * q^23 + 55 * q^24 + 153 * q^25 - 10 * q^26 + 7 * q^27 + 39 * q^28 + 86 * q^29 + 44 * q^30 + 16 * q^31 + 70 * q^32 + 40 * q^33 + 10 * q^34 + 6 * q^35 + 222 * q^36 + 52 * q^37 + 12 * q^38 - q^39 + 14 * q^40 + 80 * q^41 + 29 * q^42 + 2 * q^43 + 143 * q^44 + 137 * q^45 + 39 * q^46 + 45 * q^47 - 27 * q^48 + 163 * q^49 + 102 * q^50 + 48 * q^51 - 136 * q^52 + 117 * q^53 + 75 * q^54 + 20 * q^55 + 88 * q^56 + 67 * q^57 + 56 * q^58 + 88 * q^59 + 96 * q^60 + 57 * q^61 - 13 * q^62 + 48 * q^63 + 228 * q^64 - 46 * q^65 + 28 * q^66 + 43 * q^67 - 56 * q^68 + 92 * q^69 + 14 * q^70 + 90 * q^71 + 98 * q^72 + 25 * q^73 + 80 * q^74 + 21 * q^75 + 75 * q^76 + 112 * q^77 - 16 * q^78 + 36 * q^79 + 208 * q^80 + 231 * q^81 - 27 * q^82 + 93 * q^83 + 175 * q^84 + 77 * q^85 + 199 * q^86 + 15 * q^87 + 43 * q^88 + 140 * q^89 + 11 * q^90 - 12 * q^91 + 93 * q^92 + 140 * q^93 + 4 * q^94 + 23 * q^95 + 105 * q^96 + 43 * q^97 + 67 * q^98 + 140 * 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 $

$2$	−2.49040	−1.76098	−0.880491	−	0.474063i	$-0.842787\pi$
$2$	−2.49040	−1.76098	−0.880491	+	0.474063i	$0.842787\pi$
$3$	−2.13188	−1.23084	−0.615422	−	0.788198i	$-0.711014\pi$
$3$	−2.13188	−1.23084	−0.615422	+	0.788198i	$0.711014\pi$
$4$	4.20211	2.10106
$5$	−1.49942	−0.670563	−0.335282	−	0.942118i	$-0.608831\pi$
$5$	−1.49942	−0.670563	−0.335282	+	0.942118i	$0.608831\pi$
$6$	5.30925	2.16749
$7$	−0.951507	−0.359636	−0.179818	−	0.983700i	$-0.557551\pi$
$7$	−0.951507	−0.359636	−0.179818	+	0.983700i	$0.557551\pi$
$8$	−5.48415	−1.93894
$9$	1.54493	0.514978
$10$	3.73417	1.18085
$11$	−1.50536	−0.453884	−0.226942	−	0.973908i	$-0.572873\pi$
$11$	−1.50536	−0.453884	−0.226942	+	0.973908i	$0.572873\pi$
$12$	−8.95842	−2.58607
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	2.36964	0.633312
$15$	3.19660	0.825359
$16$	5.25352	1.31338
$17$	−6.30395	−1.52893	−0.764466	−	0.644664i	$-0.776997\pi$
$17$	−6.30395	−1.52893	−0.764466	+	0.644664i	$0.776997\pi$
$18$	−3.84751	−0.906866
$19$	4.62204	1.06037	0.530184	−	0.847882i	$-0.322123\pi$
$19$	4.62204	1.06037	0.530184	+	0.847882i	$0.322123\pi$
$20$	−6.30075	−1.40889
$21$	2.02850	0.442655
$22$	3.74896	0.799281
$23$	8.58376	1.78984	0.894919	−	0.446228i	$-0.147233\pi$
$23$	8.58376	1.78984	0.894919	+	0.446228i	$0.147233\pi$
$24$	11.6916	2.38653
$25$	−2.75173	−0.550345
$26$	2.49040	0.488408
$27$	3.10204	0.596987
$28$	−3.99834	−0.755615
$29$	3.30171	0.613112	0.306556	−	0.951853i	$-0.400823\pi$
$29$	3.30171	0.613112	0.306556	+	0.951853i	$0.400823\pi$
$30$	−7.96083	−1.45344
$31$	−6.10630	−1.09672	−0.548362	−	0.836241i	$-0.684748\pi$
$31$	−6.10630	−1.09672	−0.548362	+	0.836241i	$0.684748\pi$
$32$	−2.11509	−0.373898
$33$	3.20926	0.558660
$34$	15.6994	2.69242
$35$	1.42671	0.241158
$36$	6.49198	1.08200
$37$	−1.19521	−0.196491	−0.0982457	−	0.995162i	$-0.531323\pi$
$37$	−1.19521	−0.196491	−0.0982457	+	0.995162i	$0.531323\pi$
$38$	−11.5107	−1.86729
$39$	2.13188	0.341375
$40$	8.22307	1.30018
$41$	2.83840	0.443284	0.221642	−	0.975128i	$-0.428858\pi$
$41$	2.83840	0.443284	0.221642	+	0.975128i	$0.428858\pi$
$42$	−5.05179	−0.779508
$43$	−10.2894	−1.56912	−0.784562	−	0.620050i	$-0.787112\pi$
$43$	−10.2894	−1.56912	−0.784562	+	0.620050i	$0.787112\pi$
$44$	−6.32570	−0.953635
$45$	−2.31651	−0.345325
$46$	−21.3770	−3.15187
$47$	−4.09093	−0.596723	−0.298362	−	0.954453i	$-0.596440\pi$
$47$	−4.09093	−0.596723	−0.298362	+	0.954453i	$0.596440\pi$
$48$	−11.1999	−1.61657
$49$	−6.09464	−0.870662
$50$	6.85291	0.969147
$51$	13.4393	1.88188
$52$	−4.20211	−0.582728
$53$	3.85736	0.529849	0.264924	−	0.964269i	$-0.414653\pi$
$53$	3.85736	0.529849	0.264924	+	0.964269i	$0.414653\pi$
$54$	−7.72532	−1.05128
$55$	2.25718	0.304358
$56$	5.21820	0.697312
$57$	−9.85366	−1.30515
$58$	−8.22259	−1.07968
$59$	2.26387	0.294731	0.147365	−	0.989082i	$-0.452921\pi$
$59$	2.26387	0.294731	0.147365	+	0.989082i	$0.452921\pi$
$60$	13.4325	1.73412
$61$	−5.68001	−0.727251	−0.363626	−	0.931545i	$-0.618461\pi$
$61$	−5.68001	−0.727251	−0.363626	+	0.931545i	$0.618461\pi$
$62$	15.2071	1.93131
$63$	−1.47001	−0.185204
$64$	−5.23961	−0.654952
$65$	1.49942	0.185981
$66$	−7.99235	−0.983790
$67$	−5.57141	−0.680656	−0.340328	−	0.940307i	$-0.610538\pi$
$67$	−5.57141	−0.680656	−0.340328	+	0.940307i	$0.610538\pi$
$68$	−26.4899	−3.21237
$69$	−18.2996	−2.20301
$70$	−3.55309	−0.424676
$71$	14.5648	1.72853	0.864264	−	0.503038i	$-0.167784\pi$
$71$	14.5648	1.72853	0.864264	+	0.503038i	$0.167784\pi$
$72$	−8.47264	−0.998510
$73$	−7.50222	−0.878069	−0.439034	−	0.898470i	$-0.644679\pi$
$73$	−7.50222	−0.878069	−0.439034	+	0.898470i	$0.644679\pi$
$74$	2.97656	0.346018
$75$	5.86636	0.677389
$76$	19.4223	2.22789
$77$	1.43236	0.163233
$78$	−5.30925	−0.601155
$79$	13.2328	1.48881	0.744403	−	0.667731i	$-0.232734\pi$
$79$	13.2328	1.48881	0.744403	+	0.667731i	$0.232734\pi$
$80$	−7.87725	−0.880704
$81$	−11.2480	−1.24978
$82$	−7.06877	−0.780615
$83$	−5.89209	−0.646741	−0.323370	−	0.946273i	$-0.604816\pi$
$83$	−5.89209	−0.646741	−0.323370	+	0.946273i	$0.604816\pi$
$84$	8.52399	0.930044
$85$	9.45230	1.02525
$86$	25.6249	2.76320
$87$	−7.03887	−0.754646
$88$	8.25563	0.880053
$89$	12.9550	1.37323	0.686614	−	0.727022i	$-0.259096\pi$
$89$	12.9550	1.37323	0.686614	+	0.727022i	$0.259096\pi$
$90$	5.76905	0.608111
$91$	0.951507	0.0997450
$92$	36.0699	3.76055
$93$	13.0179	1.34990
$94$	10.1881	1.05082
$95$	−6.93040	−0.711044
$96$	4.50912	0.460210
$97$	−10.3039	−1.04620	−0.523099	−	0.852272i	$-0.675224\pi$
$97$	−10.3039	−1.04620	−0.523099	+	0.852272i	$0.675224\pi$
$98$	15.1781	1.53322
$99$	−2.32568	−0.233740
$100$	−11.5631	−1.15631
$101$	−17.1494	−1.70643	−0.853216	−	0.521558i	$-0.825351\pi$
$101$	−17.1494	−1.70643	−0.853216	+	0.521558i	$0.825351\pi$
$102$	−33.4693	−3.31395
$103$	−9.49265	−0.935339	−0.467669	−	0.883903i	$-0.654906\pi$
$103$	−9.49265	−0.935339	−0.467669	+	0.883903i	$0.654906\pi$
$104$	5.48415	0.537765
$105$	−3.04159	−0.296828
$106$	−9.60638	−0.933054
$107$	2.26606	0.219068	0.109534	−	0.993983i	$-0.465064\pi$
$107$	2.26606	0.219068	0.109534	+	0.993983i	$0.465064\pi$
$108$	13.0351	1.25430
$109$	5.97004	0.571826	0.285913	−	0.958256i	$-0.407703\pi$
$109$	5.97004	0.571826	0.285913	+	0.958256i	$0.407703\pi$
$110$	−5.62128	−0.535968
$111$	2.54805	0.241850
$112$	−4.99876	−0.472338
$113$	20.7854	1.95533	0.977665	−	0.210169i	$-0.0674015\pi$
$113$	20.7854	1.95533	0.977665	+	0.210169i	$0.0674015\pi$
$114$	24.5396	2.29834
$115$	−12.8707	−1.20020
$116$	13.8742	1.28818
$117$	−1.54493	−0.142829
$118$	−5.63795	−0.519016
$119$	5.99825	0.549859
$120$	−17.5306	−1.60032
$121$	−8.73388	−0.793989
$122$	14.1455	1.28068
$123$	−6.05115	−0.545614
$124$	−25.6593	−2.30428
$125$	11.6231	1.03960
$126$	3.66093	0.326141
$127$	−12.9639	−1.15036	−0.575180	−	0.818027i	$-0.695068\pi$
$127$	−12.9639	−1.15036	−0.575180	+	0.818027i	$0.695068\pi$
$128$	17.2789	1.52726
$129$	21.9359	1.93135
$130$	−3.73417	−0.327509
$131$	3.15515	0.275667	0.137833	−	0.990455i	$-0.455986\pi$
$131$	3.15515	0.275667	0.137833	+	0.990455i	$0.455986\pi$
$132$	13.4857	1.17378
$133$	−4.39790	−0.381346
$134$	13.8751	1.19862
$135$	−4.65127	−0.400318
$136$	34.5718	2.96451
$137$	−17.2525	−1.47398	−0.736989	−	0.675905i	$-0.763753\pi$
$137$	−17.2525	−1.47398	−0.736989	+	0.675905i	$0.763753\pi$
$138$	45.5734	3.87946
$139$	−15.3946	−1.30576	−0.652878	−	0.757463i	$-0.726438\pi$
$139$	−15.3946	−1.30576	−0.652878	+	0.757463i	$0.726438\pi$
$140$	5.99520	0.506687
$141$	8.72139	0.734473
$142$	−36.2723	−3.04391
$143$	1.50536	0.125885
$144$	8.11633	0.676361
$145$	−4.95067	−0.411131
$146$	18.6836	1.54626
$147$	12.9931	1.07165
$148$	−5.02241	−0.412839
$149$	−16.7191	−1.36968	−0.684842	−	0.728692i	$-0.740129\pi$
$149$	−16.7191	−1.36968	−0.684842	+	0.728692i	$0.740129\pi$
$150$	−14.6096	−1.19287
$151$	16.3365	1.32945	0.664723	−	0.747090i	$-0.268550\pi$
$151$	16.3365	1.32945	0.664723	+	0.747090i	$0.268550\pi$
$152$	−25.3479	−2.05599
$153$	−9.73918	−0.787366
$154$	−3.56716	−0.287450
$155$	9.15593	0.735422
$156$	8.95842	0.717247
$157$	−14.7629	−1.17821	−0.589105	−	0.808057i	$-0.700520\pi$
$157$	−14.7629	−1.17821	−0.589105	+	0.808057i	$0.700520\pi$
$158$	−32.9550	−2.62176
$159$	−8.22344	−0.652161
$160$	3.17141	0.250722
$161$	−8.16751	−0.643690
$162$	28.0120	2.20083
$163$	13.8794	1.08712	0.543558	−	0.839372i	$-0.317077\pi$
$163$	13.8794	1.08712	0.543558	+	0.839372i	$0.317077\pi$
$164$	11.9273	0.931365
$165$	−4.81204	−0.374617
$166$	14.6737	1.13890
$167$	−24.6408	−1.90676	−0.953382	−	0.301768i	$-0.902423\pi$
$167$	−24.6408	−1.90676	−0.953382	+	0.301768i	$0.902423\pi$
$168$	−11.1246	−0.858282
$169$	1.00000	0.0769231
$170$	−23.5400	−1.80544
$171$	7.14074	0.546066
$172$	−43.2374	−3.29682
$173$	−0.952976	−0.0724534	−0.0362267	−	0.999344i	$-0.511534\pi$
$173$	−0.952976	−0.0724534	−0.0362267	+	0.999344i	$0.511534\pi$
$174$	17.5296	1.32892
$175$	2.61828	0.197924
$176$	−7.90845	−0.596122
$177$	−4.82631	−0.362768
$178$	−32.2632	−2.41823
$179$	−17.9747	−1.34349	−0.671747	−	0.740781i	$-0.734456\pi$
$179$	−17.9747	−1.34349	−0.671747	+	0.740781i	$0.734456\pi$
$180$	−9.73424	−0.725547
$181$	16.3096	1.21228	0.606140	−	0.795358i	$-0.292717\pi$
$181$	16.3096	1.21228	0.606140	+	0.795358i	$0.292717\pi$
$182$	−2.36964	−0.175649
$183$	12.1091	0.895133
$184$	−47.0746	−3.47039
$185$	1.79213	0.131760
$186$	−32.4199	−2.37714
$187$	9.48973	0.693958
$188$	−17.1905	−1.25375
$189$	−2.95161	−0.214698
$190$	17.2595	1.25214
$191$	4.98373	0.360610	0.180305	−	0.983611i	$-0.442292\pi$
$191$	4.98373	0.360610	0.180305	+	0.983611i	$0.442292\pi$
$192$	11.1703	0.806144
$193$	−1.37207	−0.0987638	−0.0493819	−	0.998780i	$-0.515725\pi$
$193$	−1.37207	−0.0987638	−0.0493819	+	0.998780i	$0.515725\pi$
$194$	25.6608	1.84233
$195$	−3.19660	−0.228913
$196$	−25.6103	−1.82931
$197$	1.29130	0.0920015	0.0460007	−	0.998941i	$-0.485352\pi$
$197$	1.29130	0.0920015	0.0460007	+	0.998941i	$0.485352\pi$
$198$	5.79189	0.411612
$199$	−15.2538	−1.08131	−0.540656	−	0.841244i	$-0.681824\pi$
$199$	−15.2538	−1.08131	−0.540656	+	0.841244i	$0.681824\pi$
$200$	15.0909	1.06709
$201$	11.8776	0.837782
$202$	42.7090	3.00499
$203$	−3.14160	−0.220497
$204$	56.4734	3.95393
$205$	−4.25597	−0.297250
$206$	23.6405	1.64711
$207$	13.2613	0.921727
$208$	−5.25352	−0.364266
$209$	−6.95784	−0.481284
$210$	7.57478	0.522709
$211$	−6.21003	−0.427516	−0.213758	−	0.976887i	$-0.568570\pi$
$211$	−6.21003	−0.427516	−0.213758	+	0.976887i	$0.568570\pi$
$212$	16.2090	1.11324
$213$	−31.0506	−2.12755
$214$	−5.64341	−0.385775
$215$	15.4282	1.05220
$216$	−17.0120	−1.15752
$217$	5.81018	0.394421
$218$	−14.8678	−1.00697
$219$	15.9939	1.08077
$220$	9.48491	0.639473
$221$	6.30395	0.424050
$222$	−6.34568	−0.425894
$223$	−13.7400	−0.920100	−0.460050	−	0.887893i	$-0.652169\pi$
$223$	−13.7400	−0.920100	−0.460050	+	0.887893i	$0.652169\pi$
$224$	2.01252	0.134467
$225$	−4.25123	−0.283415
$226$	−51.7642	−3.44330
$227$	9.01634	0.598436	0.299218	−	0.954185i	$-0.403274\pi$
$227$	9.01634	0.598436	0.299218	+	0.954185i	$0.403274\pi$
$228$	−41.4062	−2.74219
$229$	−17.6843	−1.16861	−0.584307	−	0.811533i	$-0.698634\pi$
$229$	−17.6843	−1.16861	−0.584307	+	0.811533i	$0.698634\pi$
$230$	32.0533	2.11353
$231$	−3.05363	−0.200914
$232$	−18.1071	−1.18879
$233$	−2.15314	−0.141057	−0.0705284	−	0.997510i	$-0.522469\pi$
$233$	−2.15314	−0.141057	−0.0705284	+	0.997510i	$0.522469\pi$
$234$	3.84751	0.251519
$235$	6.13404	0.400141
$236$	9.51304	0.619246
$237$	−28.2108	−1.83249
$238$	−14.9381	−0.968291
$239$	−7.40717	−0.479130	−0.239565	−	0.970880i	$-0.577005\pi$
$239$	−7.40717	−0.479130	−0.239565	+	0.970880i	$0.577005\pi$
$240$	16.7934	1.08401
$241$	16.0190	1.03187	0.515936	−	0.856627i	$-0.327444\pi$
$241$	16.0190	1.03187	0.515936	+	0.856627i	$0.327444\pi$
$242$	21.7509	1.39820
$243$	14.6733	0.941292
$244$	−23.8681	−1.52800
$245$	9.13845	0.583834
$246$	15.0698	0.960816
$247$	−4.62204	−0.294093
$248$	33.4878	2.12648
$249$	12.5613	0.796037
$250$	−28.9463	−1.83072
$251$	−8.39438	−0.529849	−0.264924	−	0.964269i	$-0.585347\pi$
$251$	−8.39438	−0.529849	−0.264924	+	0.964269i	$0.585347\pi$
$252$	−6.17716	−0.389125
$253$	−12.9217	−0.812379
$254$	32.2853	2.02576
$255$	−20.1512	−1.26192
$256$	−32.5523	−2.03452
$257$	−22.4035	−1.39749	−0.698745	−	0.715371i	$-0.746258\pi$
$257$	−22.4035	−1.39749	−0.698745	+	0.715371i	$0.746258\pi$
$258$	−54.6293	−3.40107
$259$	1.13725	0.0706653
$260$	6.30075	0.390756
$261$	5.10092	0.315739
$262$	−7.85761	−0.485444
$263$	−5.57604	−0.343833	−0.171917	−	0.985112i	$-0.554996\pi$
$263$	−5.57604	−0.343833	−0.171917	+	0.985112i	$0.554996\pi$
$264$	−17.6000	−1.08321
$265$	−5.78382	−0.355297
$266$	10.9525	0.671544
$267$	−27.6186	−1.69023
$268$	−23.4117	−1.43010
$269$	−14.3227	−0.873269	−0.436635	−	0.899639i	$-0.643830\pi$
$269$	−14.3227	−0.873269	−0.436635	+	0.899639i	$0.643830\pi$
$270$	11.5835	0.704952
$271$	8.35549	0.507560	0.253780	−	0.967262i	$-0.418326\pi$
$271$	8.35549	0.507560	0.253780	+	0.967262i	$0.418326\pi$
$272$	−33.1179	−2.00807
$273$	−2.02850	−0.122771
$274$	42.9656	2.59565
$275$	4.14234	0.249793
$276$	−76.8969	−4.62865
$277$	−8.92452	−0.536223	−0.268111	−	0.963388i	$-0.586400\pi$
$277$	−8.92452	−0.536223	−0.268111	+	0.963388i	$0.586400\pi$
$278$	38.3388	2.29941
$279$	−9.43382	−0.564788
$280$	−7.82430	−0.467591
$281$	−13.3533	−0.796593	−0.398296	−	0.917257i	$-0.630398\pi$
$281$	−13.3533	−0.796593	−0.398296	+	0.917257i	$0.630398\pi$
$282$	−21.7198	−1.29339
$283$	5.96478	0.354569	0.177285	−	0.984160i	$-0.443269\pi$
$283$	5.96478	0.354569	0.177285	+	0.984160i	$0.443269\pi$
$284$	61.2031	3.63173
$285$	14.7748	0.875185
$286$	−3.74896	−0.221681
$287$	−2.70076	−0.159421
$288$	−3.26767	−0.192549
$289$	22.7398	1.33764
$290$	12.3292	0.723993
$291$	21.9666	1.28771
$292$	−31.5252	−1.84487
$293$	−11.8575	−0.692724	−0.346362	−	0.938101i	$-0.612583\pi$
$293$	−11.8575	−0.692724	−0.346362	+	0.938101i	$0.612583\pi$
$294$	−32.3580	−1.88716
$295$	−3.39450	−0.197636
$296$	6.55471	0.380985
$297$	−4.66969	−0.270963
$298$	41.6374	2.41199
$299$	−8.58376	−0.496412
$300$	24.6511	1.42323
$301$	9.79047	0.564313
$302$	−40.6845	−2.34113
$303$	36.5606	2.10035
$304$	24.2820	1.39267
$305$	8.51675	0.487668
$306$	24.2545	1.38654
$307$	16.3012	0.930359	0.465180	−	0.885216i	$-0.345990\pi$
$307$	16.3012	0.930359	0.465180	+	0.885216i	$0.345990\pi$
$308$	6.01895	0.342961
$309$	20.2372	1.15126
$310$	−22.8020	−1.29507
$311$	21.0236	1.19214	0.596070	−	0.802933i	$-0.296728\pi$
$311$	21.0236	1.19214	0.596070	+	0.802933i	$0.296728\pi$
$312$	−11.6916	−0.661905
$313$	15.2214	0.860367	0.430184	−	0.902741i	$-0.358449\pi$
$313$	15.2214	0.860367	0.430184	+	0.902741i	$0.358449\pi$
$314$	36.7656	2.07481
$315$	2.20417	0.124191
$316$	55.6057	3.12806
$317$	−25.5226	−1.43349	−0.716745	−	0.697336i	$-0.754369\pi$
$317$	−25.5226	−1.43349	−0.716745	+	0.697336i	$0.754369\pi$
$318$	20.4797	1.14844
$319$	−4.97027	−0.278282
$320$	7.85641	0.439186
$321$	−4.83098	−0.269639
$322$	20.3404	1.13353
$323$	−29.1371	−1.62123
$324$	−47.2653	−2.62585
$325$	2.75173	0.152638
$326$	−34.5652	−1.91439
$327$	−12.7274	−0.703829
$328$	−15.5662	−0.859501
$329$	3.89255	0.214603
$330$	11.9839	0.659694
$331$	2.45050	0.134692	0.0673459	−	0.997730i	$-0.478547\pi$
$331$	2.45050	0.134692	0.0673459	+	0.997730i	$0.478547\pi$
$332$	−24.7592	−1.35884
$333$	−1.84652	−0.101189
$334$	61.3656	3.35777
$335$	8.35391	0.456423
$336$	10.6568	0.581375
$337$	−14.3202	−0.780072	−0.390036	−	0.920800i	$-0.627538\pi$
$337$	−14.3202	−0.780072	−0.390036	+	0.920800i	$0.627538\pi$
$338$	−2.49040	−0.135460
$339$	−44.3122	−2.40671
$340$	39.7196	2.15410
$341$	9.19219	0.497785
$342$	−17.7833	−0.961612
$343$	12.4596	0.672757
$344$	56.4288	3.04244
$345$	27.4389	1.47726
$346$	2.37329	0.127589
$347$	−20.8352	−1.11849	−0.559247	−	0.829001i	$-0.688910\pi$
$347$	−20.8352	−1.11849	−0.559247	+	0.829001i	$0.688910\pi$
$348$	−29.5781	−1.58555
$349$	3.26766	0.174914	0.0874568	−	0.996168i	$-0.472126\pi$
$349$	3.26766	0.174914	0.0874568	+	0.996168i	$0.472126\pi$
$350$	−6.52059	−0.348540
$351$	−3.10204	−0.165574
$352$	3.18397	0.169706
$353$	6.84198	0.364162	0.182081	−	0.983284i	$-0.441717\pi$
$353$	6.84198	0.364162	0.182081	+	0.983284i	$0.441717\pi$
$354$	12.0195	0.638827
$355$	−21.8389	−1.15909
$356$	54.4384	2.88523
$357$	−12.7876	−0.676791
$358$	44.7643	2.36587
$359$	−14.3376	−0.756708	−0.378354	−	0.925661i	$-0.623510\pi$
$359$	−14.3376	−0.756708	−0.378354	+	0.925661i	$0.623510\pi$
$360$	12.7041	0.669564
$361$	2.36325	0.124382
$362$	−40.6174	−2.13480
$363$	18.6196	0.977277
$364$	3.99834	0.209570
$365$	11.2490	0.588801
$366$	−30.1566	−1.57631
$367$	−34.8530	−1.81931	−0.909655	−	0.415365i	$-0.863654\pi$
$367$	−34.8530	−1.81931	−0.909655	+	0.415365i	$0.863654\pi$
$368$	45.0949	2.35074
$369$	4.38514	0.228281
$370$	−4.46312	−0.232027
$371$	−3.67030	−0.190553
$372$	54.7028	2.83621
$373$	16.4248	0.850442	0.425221	−	0.905090i	$-0.360196\pi$
$373$	16.4248	0.850442	0.425221	+	0.905090i	$0.360196\pi$
$374$	−23.6333	−1.22205
$375$	−24.7792	−1.27959
$376$	22.4353	1.15701
$377$	−3.30171	−0.170047
$378$	7.35069	0.378079
$379$	25.0874	1.28865	0.644325	−	0.764751i	$-0.277138\pi$
$379$	25.0874	1.28865	0.644325	+	0.764751i	$0.277138\pi$
$380$	−29.1223	−1.49394
$381$	27.6375	1.41591
$382$	−12.4115	−0.635028
$383$	3.50111	0.178898	0.0894492	−	0.995991i	$-0.471489\pi$
$383$	3.50111	0.178898	0.0894492	+	0.995991i	$0.471489\pi$
$384$	−36.8367	−1.87981
$385$	−2.14772	−0.109458
$386$	3.41701	0.173921
$387$	−15.8965	−0.808064
$388$	−43.2979	−2.19812
$389$	37.4573	1.89916	0.949579	−	0.313527i	$-0.101510\pi$
$389$	37.4573	1.89916	0.949579	+	0.313527i	$0.101510\pi$
$390$	7.96083	0.403112
$391$	−54.1116	−2.73654
$392$	33.4239	1.68816
$393$	−6.72642	−0.339303
$394$	−3.21586	−0.162013
$395$	−19.8416	−0.998338
$396$	−9.77278	−0.491101
$397$	−25.6008	−1.28487	−0.642433	−	0.766342i	$-0.722075\pi$
$397$	−25.6008	−1.28487	−0.642433	+	0.766342i	$0.722075\pi$
$398$	37.9881	1.90417
$399$	9.37582	0.469378
$400$	−14.4562	−0.722812
$401$	−5.21046	−0.260198	−0.130099	−	0.991501i	$-0.541530\pi$
$401$	−5.21046	−0.260198	−0.130099	+	0.991501i	$0.541530\pi$
$402$	−29.5800	−1.47532
$403$	6.10630	0.304176
$404$	−72.0638	−3.58531
$405$	16.8655	0.838053
$406$	7.82385	0.388291
$407$	1.79923	0.0891843
$408$	−73.7031	−3.64885
$409$	21.4084	1.05858	0.529289	−	0.848441i	$-0.322459\pi$
$409$	21.4084	1.05858	0.529289	+	0.848441i	$0.322459\pi$
$410$	10.5991	0.523452
$411$	36.7803	1.81424
$412$	−39.8892	−1.96520
$413$	−2.15409	−0.105996
$414$	−33.0261	−1.62314
$415$	8.83474	0.433680
$416$	2.11509	0.103701
$417$	32.8196	1.60718
$418$	17.3278	0.847533
$419$	22.1734	1.08324	0.541621	−	0.840623i	$-0.317811\pi$
$419$	22.1734	1.08324	0.541621	+	0.840623i	$0.317811\pi$
$420$	−12.7811	−0.623653
$421$	−18.6809	−0.910451	−0.455225	−	0.890376i	$-0.650441\pi$
$421$	−18.6809	−0.910451	−0.455225	+	0.890376i	$0.650441\pi$
$422$	15.4655	0.752848
$423$	−6.32021	−0.307299
$424$	−21.1543	−1.02734
$425$	17.3467	0.841441
$426$	77.3284	3.74658
$427$	5.40457	0.261546
$428$	9.52224	0.460275
$429$	−3.20926	−0.154944
$430$	−38.4225	−1.85290
$431$	−16.7465	−0.806652	−0.403326	−	0.915056i	$-0.632146\pi$
$431$	−16.7465	−0.806652	−0.403326	+	0.915056i	$0.632146\pi$
$432$	16.2966	0.784071
$433$	−1.88641	−0.0906550	−0.0453275	−	0.998972i	$-0.514433\pi$
$433$	−1.88641	−0.0906550	−0.0453275	+	0.998972i	$0.514433\pi$
$434$	−14.4697	−0.694568
$435$	10.5543	0.506038
$436$	25.0868	1.20144
$437$	39.6745	1.89789
$438$	−39.8312	−1.90321
$439$	−24.9834	−1.19239	−0.596197	−	0.802838i	$-0.703322\pi$
$439$	−24.9834	−1.19239	−0.596197	+	0.802838i	$0.703322\pi$
$440$	−12.3787	−0.590131
$441$	−9.41580	−0.448372
$442$	−15.6994	−0.746744
$443$	10.5094	0.499315	0.249658	−	0.968334i	$-0.419682\pi$
$443$	10.5094	0.499315	0.249658	+	0.968334i	$0.419682\pi$
$444$	10.7072	0.508141
$445$	−19.4251	−0.920837
$446$	34.2182	1.62028
$447$	35.6433	1.68587
$448$	4.98553	0.235544
$449$	40.4293	1.90798	0.953988	−	0.299843i	$-0.0969344\pi$
$449$	40.4293	1.90798	0.953988	+	0.299843i	$0.0969344\pi$
$450$	10.5873	0.499089
$451$	−4.27283	−0.201200
$452$	87.3428	4.10826
$453$	−34.8275	−1.63634
$454$	−22.4543	−1.05383
$455$	−1.42671	−0.0668853
$456$	54.0389	2.53060
$457$	−1.52686	−0.0714237	−0.0357118	−	0.999362i	$-0.511370\pi$
$457$	−1.52686	−0.0714237	−0.0357118	+	0.999362i	$0.511370\pi$
$458$	44.0412	2.05791
$459$	−19.5551	−0.912753
$460$	−54.0841	−2.52169
$461$	−2.89814	−0.134980	−0.0674899	−	0.997720i	$-0.521499\pi$
$461$	−2.89814	−0.134980	−0.0674899	+	0.997720i	$0.521499\pi$
$462$	7.60477	0.353806
$463$	1.00000	0.0464739
$463$	1.00000	0.0464739
$464$	17.3456	0.805249
$465$	−19.5194	−0.905190
$466$	5.36219	0.248398
$467$	−7.85648	−0.363555	−0.181777	−	0.983340i	$-0.558185\pi$
$467$	−7.85648	−0.363555	−0.181777	+	0.983340i	$0.558185\pi$
$468$	−6.49198	−0.300092
$469$	5.30124	0.244788
$470$	−15.2762	−0.704640
$471$	31.4729	1.45019
$472$	−12.4154	−0.571465
$473$	15.4893	0.712200
$474$	70.2563	3.22698
$475$	−12.7186	−0.583569
$476$	25.2053	1.15528
$477$	5.95936	0.272860
$478$	18.4469	0.843740
$479$	−5.56621	−0.254327	−0.127163	−	0.991882i	$-0.540587\pi$
$479$	−5.56621	−0.254327	−0.127163	+	0.991882i	$0.540587\pi$
$480$	−6.76109	−0.308600
$481$	1.19521	0.0544969
$482$	−39.8937	−1.81711
$483$	17.4122	0.792282
$484$	−36.7008	−1.66822
$485$	15.4499	0.701542
$486$	−36.5424	−1.65760
$487$	32.3355	1.46526	0.732632	−	0.680625i	$-0.238292\pi$
$487$	32.3355	1.46526	0.732632	+	0.680625i	$0.238292\pi$
$488$	31.1500	1.41010
$489$	−29.5892	−1.33807
$490$	−22.7584	−1.02812
$491$	−33.3989	−1.50727	−0.753637	−	0.657291i	$-0.771702\pi$
$491$	−33.3989	−1.50727	−0.753637	+	0.657291i	$0.771702\pi$
$492$	−25.4276	−1.14636
$493$	−20.8138	−0.937408
$494$	11.5107	0.517893
$495$	3.48719	0.156737
$496$	−32.0795	−1.44041
$497$	−13.8585	−0.621641
$498$	−31.2826	−1.40181
$499$	38.4264	1.72020	0.860102	−	0.510123i	$-0.170400\pi$
$499$	38.4264	1.72020	0.860102	+	0.510123i	$0.170400\pi$
$500$	48.8417	2.18427
$501$	52.5314	2.34693
$502$	20.9054	0.933054
$503$	−18.6774	−0.832784	−0.416392	−	0.909185i	$-0.636706\pi$
$503$	−18.6774	−0.832784	−0.416392	+	0.909185i	$0.636706\pi$
$504$	8.06177	0.359100
$505$	25.7143	1.14427
$506$	32.1802	1.43058
$507$	−2.13188	−0.0946803
$508$	−54.4757	−2.41697
$509$	0.125456	0.00556072	0.00278036	−	0.999996i	$-0.499115\pi$
$509$	0.125456	0.00556072	0.00278036	+	0.999996i	$0.499115\pi$
$510$	50.1847	2.22221
$511$	7.13841	0.315785
$512$	46.5105	2.05549
$513$	14.3377	0.633026
$514$	55.7937	2.46095
$515$	14.2335	0.627204
$516$	92.1771	4.05787
$517$	6.15833	0.270843
$518$	−2.83221	−0.124440
$519$	2.03163	0.0891788
$520$	−8.22307	−0.360605
$521$	12.2411	0.536292	0.268146	−	0.963378i	$-0.413589\pi$
$521$	12.2411	0.536292	0.268146	+	0.963378i	$0.413589\pi$
$522$	−12.7034	−0.556011
$523$	−34.0264	−1.48787	−0.743936	−	0.668251i	$-0.767043\pi$
$523$	−34.0264	−1.48787	−0.743936	+	0.668251i	$0.767043\pi$
$524$	13.2583	0.579192
$525$	−5.58188	−0.243613
$526$	13.8866	0.605484
$527$	38.4938	1.67682
$528$	16.8599	0.733733
$529$	50.6810	2.20352
$530$	14.4040	0.625672
$531$	3.49753	0.151780
$532$	−18.4805	−0.801230
$533$	−2.83840	−0.122945
$534$	68.7815	2.97647
$535$	−3.39779	−0.146899
$536$	30.5544	1.31975
$537$	38.3200	1.65363
$538$	35.6693	1.53781
$539$	9.17463	0.395179
$540$	−19.5452	−0.841089
$541$	22.6644	0.974419	0.487209	−	0.873285i	$-0.338015\pi$
$541$	22.6644	0.974419	0.487209	+	0.873285i	$0.338015\pi$
$542$	−20.8085	−0.893804
$543$	−34.7701	−1.49213
$544$	13.3334	0.571665
$545$	−8.95162	−0.383445
$546$	5.05179	0.216197
$547$	40.6886	1.73972	0.869861	−	0.493298i	$-0.164209\pi$
$547$	40.6886	1.73972	0.869861	+	0.493298i	$0.164209\pi$
$548$	−72.4968	−3.09691
$549$	−8.77524	−0.374518
$550$	−10.3161	−0.439880
$551$	15.2606	0.650125
$552$	100.358	4.27151
$553$	−12.5911	−0.535428
$554$	22.2257	0.944278
$555$	−3.82061	−0.162176
$556$	−64.6900	−2.74347
$557$	8.77619	0.371859	0.185930	−	0.982563i	$-0.440470\pi$
$557$	8.77619	0.371859	0.185930	+	0.982563i	$0.440470\pi$
$558$	23.4940	0.994581
$559$	10.2894	0.435197
$560$	7.49526	0.316733
$561$	−20.2310	−0.854154
$562$	33.2552	1.40279
$563$	45.5022	1.91769	0.958844	−	0.283935i	$-0.0916399\pi$
$563$	45.5022	1.91769	0.958844	+	0.283935i	$0.0916399\pi$
$564$	36.6482	1.54317
$565$	−31.1662	−1.31117
$566$	−14.8547	−0.624390
$567$	10.7025	0.449464
$568$	−79.8757	−3.35151
$569$	−10.2302	−0.428873	−0.214437	−	0.976738i	$-0.568792\pi$
$569$	−10.2302	−0.428873	−0.214437	+	0.976738i	$0.568792\pi$
$570$	−36.7953	−1.54118
$571$	−29.7381	−1.24450	−0.622250	−	0.782819i	$-0.713781\pi$
$571$	−29.7381	−1.24450	−0.622250	+	0.782819i	$0.713781\pi$
$572$	6.32570	0.264491
$573$	−10.6247	−0.443855
$574$	6.72598	0.280737
$575$	−23.6202	−0.985029
$576$	−8.09485	−0.337285
$577$	17.0400	0.709385	0.354692	−	0.934983i	$-0.384586\pi$
$577$	17.0400	0.709385	0.354692	+	0.934983i	$0.384586\pi$
$578$	−56.6313	−2.35555
$579$	2.92510	0.121563
$580$	−20.8033	−0.863808
$581$	5.60636	0.232591
$582$	−54.7058	−2.26763
$583$	−5.80672	−0.240490
$584$	41.1433	1.70252
$585$	2.31651	0.0957759
$586$	29.5300	1.21987
$587$	−29.2950	−1.20914	−0.604568	−	0.796554i	$-0.706654\pi$
$587$	−29.2950	−1.20914	−0.604568	+	0.796554i	$0.706654\pi$
$588$	54.5983	2.25160
$589$	−28.2236	−1.16293
$590$	8.45369	0.348033
$591$	−2.75291	−0.113239
$592$	−6.27906	−0.258068
$593$	32.3809	1.32973	0.664863	−	0.746966i	$-0.268490\pi$
$593$	32.3809	1.32973	0.664863	+	0.746966i	$0.268490\pi$
$594$	11.6294	0.477160
$595$	−8.99393	−0.368715
$596$	−70.2556	−2.87778
$597$	32.5193	1.33093
$598$	21.3770	0.874172
$599$	−37.3755	−1.52712	−0.763561	−	0.645735i	$-0.776551\pi$
$599$	−37.3755	−1.52712	−0.763561	+	0.645735i	$0.776551\pi$
$600$	−32.1720	−1.31342
$601$	−41.7597	−1.70341	−0.851706	−	0.524019i	$-0.824432\pi$
$601$	−41.7597	−1.70341	−0.851706	+	0.524019i	$0.824432\pi$
$602$	−24.3822	−0.993745
$603$	−8.60746	−0.350523
$604$	68.6478	2.79324
$605$	13.0958	0.532420
$606$	−91.0507	−3.69868
$607$	23.6389	0.959474	0.479737	−	0.877412i	$-0.340732\pi$
$607$	23.6389	0.959474	0.479737	+	0.877412i	$0.340732\pi$
$608$	−9.77602	−0.396470
$609$	6.69753	0.271398
$610$	−21.2102	−0.858774
$611$	4.09093	0.165501
$612$	−40.9251	−1.65430
$613$	40.4241	1.63271	0.816356	−	0.577549i	$-0.195991\pi$
$613$	40.4241	1.63271	0.816356	+	0.577549i	$0.195991\pi$
$614$	−40.5966	−1.63834
$615$	9.07324	0.365868
$616$	−7.85528	−0.316498
$617$	−15.7638	−0.634625	−0.317313	−	0.948321i	$-0.602780\pi$
$617$	−15.7638	−0.634625	−0.317313	+	0.948321i	$0.602780\pi$
$618$	−50.3989	−2.02734
$619$	20.8358	0.837463	0.418731	−	0.908110i	$-0.362475\pi$
$619$	20.8358	0.837463	0.418731	+	0.908110i	$0.362475\pi$
$620$	38.4743	1.54516
$621$	26.6271	1.06851
$622$	−52.3573	−2.09934
$623$	−12.3268	−0.493862
$624$	11.1999	0.448355
$625$	−3.66938	−0.146775
$626$	−37.9076	−1.51509
$627$	14.8333	0.592386
$628$	−62.0355	−2.47548
$629$	7.53455	0.300422
$630$	−5.48929	−0.218698
$631$	11.8070	0.470030	0.235015	−	0.971992i	$-0.424486\pi$
$631$	11.8070	0.470030	0.235015	+	0.971992i	$0.424486\pi$
$632$	−72.5706	−2.88670
$633$	13.2391	0.526206
$634$	63.5615	2.52435
$635$	19.4384	0.771389
$636$	−34.5558	−1.37023
$637$	6.09464	0.241478
$638$	12.3780	0.490049
$639$	22.5017	0.890153
$640$	−25.9085	−1.02412
$641$	−7.99921	−0.315950	−0.157975	−	0.987443i	$-0.550496\pi$
$641$	−7.99921	−0.315950	−0.157975	+	0.987443i	$0.550496\pi$
$642$	12.0311	0.474829
$643$	41.5394	1.63816	0.819078	−	0.573683i	$-0.194486\pi$
$643$	41.5394	1.63816	0.819078	+	0.573683i	$0.194486\pi$
$644$	−34.3208	−1.35243
$645$	−32.8912	−1.29509
$646$	72.5632	2.85496
$647$	29.0831	1.14338	0.571688	−	0.820471i	$-0.306289\pi$
$647$	29.0831	1.14338	0.571688	+	0.820471i	$0.306289\pi$
$648$	61.6856	2.42324
$649$	−3.40795	−0.133774
$650$	−6.85291	−0.268793
$651$	−12.3866	−0.485471
$652$	58.3227	2.28409
$653$	−19.7185	−0.771644	−0.385822	−	0.922573i	$-0.626082\pi$
$653$	−19.7185	−0.771644	−0.385822	+	0.922573i	$0.626082\pi$
$654$	31.6965	1.23943
$655$	−4.73091	−0.184852
$656$	14.9116	0.582200
$657$	−11.5904	−0.452186
$658$	−9.69401	−0.377912
$659$	48.1530	1.87578	0.937888	−	0.346938i	$-0.112779\pi$
$659$	48.1530	1.87578	0.937888	+	0.346938i	$0.112779\pi$
$660$	−20.2207	−0.787091
$661$	−2.79792	−0.108826	−0.0544132	−	0.998519i	$-0.517329\pi$
$661$	−2.79792	−0.108826	−0.0544132	+	0.998519i	$0.517329\pi$
$662$	−6.10274	−0.237190
$663$	−13.4393	−0.521939
$664$	32.3131	1.25399
$665$	6.59432	0.255717
$666$	4.59858	0.178191
$667$	28.3411	1.09737
$668$	−103.543	−4.00622
$669$	29.2921	1.13250
$670$	−20.8046	−0.803753
$671$	8.55048	0.330088
$672$	−4.29046	−0.165508
$673$	47.8608	1.84490	0.922450	−	0.386118i	$-0.126184\pi$
$673$	47.8608	1.84490	0.922450	+	0.386118i	$0.126184\pi$
$674$	35.6632	1.37369
$675$	−8.53595	−0.328549
$676$	4.20211	0.161620
$677$	−1.04147	−0.0400268	−0.0200134	−	0.999800i	$-0.506371\pi$
$677$	−1.04147	−0.0400268	−0.0200134	+	0.999800i	$0.506371\pi$
$678$	110.355	4.23817
$679$	9.80418	0.376250
$680$	−51.8378	−1.98789
$681$	−19.2218	−0.736581
$682$	−22.8923	−0.876590
$683$	−21.3420	−0.816627	−0.408314	−	0.912842i	$-0.633883\pi$
$683$	−21.3420	−0.816627	−0.408314	+	0.912842i	$0.633883\pi$
$684$	30.0062	1.14732
$685$	25.8688	0.988395
$686$	−31.0295	−1.18471
$687$	37.7010	1.43838
$688$	−54.0558	−2.06086
$689$	−3.85736	−0.146954
$690$	−68.3338	−2.60143
$691$	40.8617	1.55445	0.777227	−	0.629220i	$-0.216626\pi$
$691$	40.8617	1.55445	0.777227	+	0.629220i	$0.216626\pi$
$692$	−4.00451	−0.152229
$693$	2.21290	0.0840612
$694$	51.8882	1.96965
$695$	23.0831	0.875592
$696$	38.6022	1.46321
$697$	−17.8932	−0.677752
$698$	−8.13779	−0.308020
$699$	4.59025	0.173619
$700$	11.0023	0.415849
$701$	35.5016	1.34088	0.670438	−	0.741966i	$-0.266106\pi$
$701$	35.5016	1.34088	0.670438	+	0.741966i	$0.266106\pi$
$702$	7.72532	0.291573
$703$	−5.52431	−0.208353
$704$	7.88752	0.297272
$705$	−13.0771	−0.492511
$706$	−17.0393	−0.641283
$707$	16.3178	0.613694
$708$	−20.2807	−0.762195
$709$	28.6275	1.07513	0.537565	−	0.843222i	$-0.319344\pi$
$709$	28.6275	1.07513	0.537565	+	0.843222i	$0.319344\pi$
$710$	54.3876	2.04113
$711$	20.4438	0.766702
$712$	−71.0472	−2.66261
$713$	−52.4150	−1.96296
$714$	31.8462	1.19182
$715$	−2.25718	−0.0844137
$716$	−75.5318	−2.82275
$717$	15.7912	0.589735
$718$	35.7063	1.33255
$719$	18.3137	0.682987	0.341494	−	0.939884i	$-0.389067\pi$
$719$	18.3137	0.682987	0.341494	+	0.939884i	$0.389067\pi$
$720$	−12.1698	−0.453543
$721$	9.03232	0.336381
$722$	−5.88545	−0.219034
$723$	−34.1506	−1.27007
$724$	68.5346	2.54707
$725$	−9.08540	−0.337423
$726$	−46.3704	−1.72097
$727$	−25.4472	−0.943785	−0.471892	−	0.881656i	$-0.656429\pi$
$727$	−25.4472	−0.943785	−0.471892	+	0.881656i	$0.656429\pi$
$728$	−5.21820	−0.193399
$729$	2.46217	0.0911916
$730$	−28.0146	−1.03687
$731$	64.8641	2.39909
$732$	50.8839	1.88072
$733$	−30.4529	−1.12480	−0.562402	−	0.826864i	$-0.690123\pi$
$733$	−30.4529	−1.12480	−0.562402	+	0.826864i	$0.690123\pi$
$734$	86.7980	3.20377
$735$	−19.4821	−0.718609
$736$	−18.1554	−0.669217
$737$	8.38699	0.308939
$738$	−10.9208	−0.401999
$739$	−30.0120	−1.10401	−0.552004	−	0.833841i	$-0.686137\pi$
$739$	−30.0120	−1.10401	−0.552004	+	0.833841i	$0.686137\pi$
$740$	7.53072	0.276835
$741$	9.85366	0.361983
$742$	9.14053	0.335560
$743$	−43.1603	−1.58340	−0.791699	−	0.610911i	$-0.790803\pi$
$743$	−43.1603	−1.58340	−0.791699	+	0.610911i	$0.790803\pi$
$744$	−71.3922	−2.61737
$745$	25.0691	0.918460
$746$	−40.9043	−1.49761
$747$	−9.10288	−0.333057
$748$	39.8769	1.45804
$749$	−2.15617	−0.0787848
$750$	61.7101	2.25334
$751$	−24.7121	−0.901756	−0.450878	−	0.892586i	$-0.648889\pi$
$751$	−24.7121	−0.901756	−0.450878	+	0.892586i	$0.648889\pi$
$752$	−21.4918	−0.783724
$753$	17.8959	0.652161
$754$	8.22259	0.299449
$755$	−24.4954	−0.891477
$756$	−12.4030	−0.451092
$757$	40.1591	1.45961	0.729803	−	0.683658i	$-0.239612\pi$
$757$	40.1591	1.45961	0.729803	+	0.683658i	$0.239612\pi$
$758$	−62.4776	−2.26929
$759$	27.5475	0.999912
$760$	38.0073	1.37867
$761$	51.1616	1.85461	0.927303	−	0.374311i	$-0.122121\pi$
$761$	51.1616	1.85461	0.927303	+	0.374311i	$0.122121\pi$
$762$	−68.8286	−2.49340
$763$	−5.68053	−0.205649
$764$	20.9422	0.757662
$765$	14.6032	0.527979
$766$	−8.71918	−0.315037
$767$	−2.26387	−0.0817436
$768$	69.3977	2.50417
$769$	32.9454	1.18804	0.594020	−	0.804450i	$-0.297540\pi$
$769$	32.9454	1.18804	0.594020	+	0.804450i	$0.297540\pi$
$770$	5.34869	0.192753
$771$	47.7616	1.72009
$772$	−5.76559	−0.207508
$773$	38.1326	1.37153	0.685766	−	0.727822i	$-0.259467\pi$
$773$	38.1326	1.37153	0.685766	+	0.727822i	$0.259467\pi$
$774$	39.5887	1.42299
$775$	16.8029	0.603576
$776$	56.5078	2.02851
$777$	−2.42449	−0.0869780
$778$	−93.2837	−3.34438
$779$	13.1192	0.470045
$780$	−13.4325	−0.480960
$781$	−21.9254	−0.784551
$782$	134.760	4.81900
$783$	10.2420	0.366020
$784$	−32.0183	−1.14351
$785$	22.1359	0.790064
$786$	16.7515	0.597507
$787$	−8.30357	−0.295990	−0.147995	−	0.988988i	$-0.547282\pi$
$787$	−8.30357	−0.295990	−0.147995	+	0.988988i	$0.547282\pi$
$788$	5.42620	0.193300
$789$	11.8875	0.423205
$790$	49.4135	1.75806
$791$	−19.7775	−0.703206
$792$	12.7544	0.453208
$793$	5.68001	0.201703
$794$	63.7563	2.26263
$795$	12.3304	0.437315
$796$	−64.0981	−2.27190
$797$	−12.5259	−0.443689	−0.221844	−	0.975082i	$-0.571208\pi$
$797$	−12.5259	−0.443689	−0.221844	+	0.975082i	$0.571208\pi$
$798$	−23.3496	−0.826566
$799$	25.7890	0.912350
$800$	5.82014	0.205773
$801$	20.0146	0.707182
$802$	12.9762	0.458204
$803$	11.2936	0.398541
$804$	49.9110	1.76023
$805$	12.2466	0.431635
$806$	−15.2071	−0.535649
$807$	30.5343	1.07486
$808$	94.0500	3.30867
$809$	22.1303	0.778061	0.389030	−	0.921225i	$-0.372810\pi$
$809$	22.1303	0.778061	0.389030	+	0.921225i	$0.372810\pi$
$810$	−42.0019	−1.47580
$811$	13.1593	0.462085	0.231043	−	0.972944i	$-0.425786\pi$
$811$	13.1593	0.462085	0.231043	+	0.972944i	$0.425786\pi$
$812$	−13.2014	−0.463277
$813$	−17.8129	−0.624727
$814$	−4.48080	−0.157052
$815$	−20.8111	−0.728980
$816$	70.6036	2.47162
$817$	−47.5582	−1.66385
$818$	−53.3156	−1.86414
$819$	1.47001	0.0513664
$820$	−17.8841	−0.624539
$821$	−7.30311	−0.254880	−0.127440	−	0.991846i	$-0.540676\pi$
$821$	−7.30311	−0.254880	−0.127440	+	0.991846i	$0.540676\pi$
$822$	−91.5977	−3.19484
$823$	−39.1386	−1.36429	−0.682143	−	0.731219i	$-0.738952\pi$
$823$	−39.1386	−1.36429	−0.682143	+	0.731219i	$0.738952\pi$
$824$	52.0591	1.81357
$825$	−8.83100	−0.307456
$826$	5.36455	0.186657
$827$	30.5074	1.06084	0.530422	−	0.847734i	$-0.322033\pi$
$827$	30.5074	1.06084	0.530422	+	0.847734i	$0.322033\pi$
$828$	55.7256	1.93660
$829$	53.8442	1.87009	0.935043	−	0.354534i	$-0.115360\pi$
$829$	53.8442	1.87009	0.935043	+	0.354534i	$0.115360\pi$
$830$	−22.0021	−0.763703
$831$	19.0261	0.660007
$832$	5.23961	0.181651
$833$	38.4203	1.33118
$834$	−81.7340	−2.83022
$835$	36.9470	1.27861
$836$	−29.2376	−1.01120
$837$	−18.9420	−0.654730
$838$	−55.2207	−1.90757
$839$	−27.5700	−0.951822	−0.475911	−	0.879494i	$-0.657881\pi$
$839$	−27.5700	−0.951822	−0.475911	+	0.879494i	$0.657881\pi$
$840$	16.6805	0.575532
$841$	−18.0987	−0.624093
$842$	46.5230	1.60329
$843$	28.4678	0.980482
$844$	−26.0952	−0.898235
$845$	−1.49942	−0.0515818
$846$	15.7399	0.541148
$847$	8.31035	0.285547
$848$	20.2647	0.695893
$849$	−12.7162	−0.436420
$850$	−43.2004	−1.48176
$851$	−10.2594	−0.351688
$852$	−130.478	−4.47010
$853$	25.2780	0.865501	0.432751	−	0.901514i	$-0.357543\pi$
$853$	25.2780	0.865501	0.432751	+	0.901514i	$0.357543\pi$
$854$	−13.4596	−0.460577
$855$	−10.7070	−0.366172
$856$	−12.4274	−0.424760
$857$	−27.8901	−0.952709	−0.476354	−	0.879253i	$-0.658042\pi$
$857$	−27.8901	−0.952709	−0.476354	+	0.879253i	$0.658042\pi$
$858$	7.99235	0.272854
$859$	−23.2656	−0.793813	−0.396906	−	0.917859i	$-0.629916\pi$
$859$	−23.2656	−0.793813	−0.396906	+	0.917859i	$0.629916\pi$
$860$	64.8312	2.21073
$861$	5.75771	0.196222
$862$	41.7056	1.42050
$863$	40.7670	1.38772	0.693862	−	0.720108i	$-0.255908\pi$
$863$	40.7670	1.38772	0.693862	+	0.720108i	$0.255908\pi$
$864$	−6.56108	−0.223212
$865$	1.42892	0.0485846
$866$	4.69792	0.159642
$867$	−48.4786	−1.64642
$868$	24.4150	0.828700
$869$	−19.9202	−0.675745
$870$	−26.2844	−0.891123
$871$	5.57141	0.188780
$872$	−32.7406	−1.10874
$873$	−15.9188	−0.538768
$874$	−98.8055	−3.34215
$875$	−11.0595	−0.373879
$876$	67.2080	2.27075
$877$	−1.32556	−0.0447611	−0.0223805	−	0.999750i	$-0.507125\pi$
$877$	−1.32556	−0.0447611	−0.0223805	+	0.999750i	$0.507125\pi$
$878$	62.2188	2.09978
$879$	25.2789	0.852635
$880$	11.8581	0.399737
$881$	−29.6085	−0.997534	−0.498767	−	0.866736i	$-0.666214\pi$
$881$	−29.6085	−0.997534	−0.498767	+	0.866736i	$0.666214\pi$
$882$	23.4491	0.789574
$883$	−41.0282	−1.38071	−0.690355	−	0.723471i	$-0.742546\pi$
$883$	−41.0282	−1.38071	−0.690355	+	0.723471i	$0.742546\pi$
$884$	26.4899	0.890952
$885$	7.23669	0.243259
$886$	−26.1726	−0.879285
$887$	−4.68721	−0.157381	−0.0786905	−	0.996899i	$-0.525074\pi$
$887$	−4.68721	−0.157381	−0.0786905	+	0.996899i	$0.525074\pi$
$888$	−13.9739	−0.468933
$889$	12.3352	0.413710
$890$	48.3763	1.62158
$891$	16.9323	0.567253
$892$	−57.7371	−1.93318
$893$	−18.9084	−0.632747
$894$	−88.7661	−2.96878
$895$	26.9517	0.900897
$896$	−16.4410	−0.549256
$897$	18.2996	0.611006
$898$	−100.685	−3.35991
$899$	−20.1612	−0.672415
$900$	−17.8641	−0.595472
$901$	−24.3166	−0.810103
$902$	10.6411	0.354309
$903$	−20.8722	−0.694582
$904$	−113.990	−3.79127
$905$	−24.4550	−0.812910
$906$	86.7346	2.88157
$907$	−9.20036	−0.305493	−0.152746	−	0.988265i	$-0.548812\pi$
$907$	−9.20036	−0.305493	−0.152746	+	0.988265i	$0.548812\pi$
$908$	37.8877	1.25735
$909$	−26.4947	−0.878774
$910$	3.55309	0.117784
$911$	25.4578	0.843455	0.421727	−	0.906723i	$-0.361424\pi$
$911$	25.4578	0.843455	0.421727	+	0.906723i	$0.361424\pi$
$912$	−51.7664	−1.71416
$913$	8.86973	0.293545
$914$	3.80251	0.125776
$915$	−18.1567	−0.600243
$916$	−74.3116	−2.45532
$917$	−3.00215	−0.0991397
$918$	48.7001	1.60734
$919$	−34.8100	−1.14828	−0.574138	−	0.818758i	$-0.694663\pi$
$919$	−34.8100	−1.14828	−0.574138	+	0.818758i	$0.694663\pi$
$920$	70.5848	2.32711
$921$	−34.7523	−1.14513
$922$	7.21754	0.237697
$923$	−14.5648	−0.479408
$924$	−12.8317	−0.422132
$925$	3.28889	0.108138
$926$	−2.49040	−0.0818397
$927$	−14.6655	−0.481679
$928$	−6.98341	−0.229242
$929$	46.6531	1.53064	0.765320	−	0.643650i	$-0.222581\pi$
$929$	46.6531	1.53064	0.765320	+	0.643650i	$0.222581\pi$
$930$	48.6112	1.59402
$931$	−28.1696	−0.923223
$932$	−9.04773	−0.296368
$933$	−44.8199	−1.46734
$934$	19.5658	0.640213
$935$	−14.2291	−0.465343
$936$	8.47264	0.276937
$937$	32.8448	1.07299	0.536497	−	0.843903i	$-0.319747\pi$
$937$	32.8448	1.07299	0.536497	+	0.843903i	$0.319747\pi$
$938$	−13.2022	−0.431068
$939$	−32.4504	−1.05898
$940$	25.7759	0.840718
$941$	37.7471	1.23052	0.615261	−	0.788324i	$-0.289051\pi$
$941$	37.7471	1.23052	0.615261	+	0.788324i	$0.289051\pi$
$942$	−78.3801	−2.55376
$943$	24.3642	0.793407
$944$	11.8933	0.387093
$945$	4.42571	0.143968
$946$	−38.5747	−1.25417
$947$	−28.2516	−0.918053	−0.459027	−	0.888422i	$-0.651802\pi$
$947$	−28.2516	−0.918053	−0.459027	+	0.888422i	$0.651802\pi$
$948$	−118.545	−3.85016
$949$	7.50222	0.243532
$950$	31.6744	1.02765
$951$	54.4111	1.76440
$952$	−32.8953	−1.06614
$953$	31.9491	1.03493	0.517467	−	0.855703i	$-0.326875\pi$
$953$	31.9491	1.03493	0.517467	+	0.855703i	$0.326875\pi$
$954$	−14.8412	−0.480502
$955$	−7.47273	−0.241812
$956$	−31.1258	−1.00668
$957$	10.5960	0.342522
$958$	13.8621	0.447864
$959$	16.4158	0.530095
$960$	−16.7490	−0.540570
$961$	6.28688	0.202803
$962$	−2.97656	−0.0959681
$963$	3.50091	0.112815
$964$	67.3134	2.16802
$965$	2.05732	0.0662273
$966$	−43.3634	−1.39519
$967$	−26.6766	−0.857862	−0.428931	−	0.903337i	$-0.641110\pi$
$967$	−26.6766	−0.857862	−0.428931	+	0.903337i	$0.641110\pi$
$968$	47.8979	1.53950
$969$	62.1170	1.99548
$970$	−38.4764	−1.23540
$971$	−35.1191	−1.12702	−0.563512	−	0.826108i	$-0.690550\pi$
$971$	−35.1191	−1.12702	−0.563512	+	0.826108i	$0.690550\pi$
$972$	61.6588	1.97771
$973$	14.6481	0.469596
$974$	−80.5286	−2.58030
$975$	−5.86636	−0.187874
$976$	−29.8401	−0.955157
$977$	−3.71231	−0.118767	−0.0593837	−	0.998235i	$-0.518914\pi$
$977$	−3.71231	−0.118767	−0.0593837	+	0.998235i	$0.518914\pi$
$978$	73.6891	2.35632
$979$	−19.5020	−0.623286
$980$	38.4008	1.22667
$981$	9.22331	0.294478
$982$	83.1769	2.65428
$983$	6.09679	0.194457	0.0972286	−	0.995262i	$-0.469002\pi$
$983$	6.09679	0.194457	0.0972286	+	0.995262i	$0.469002\pi$
$984$	33.1854	1.05791
$985$	−1.93621	−0.0616928
$986$	51.8348	1.65076
$987$	−8.29846	−0.264143
$988$	−19.4223	−0.617907
$989$	−88.3221	−2.80848
$990$	−8.68451	−0.276012
$991$	26.2694	0.834475	0.417238	−	0.908797i	$-0.362998\pi$
$991$	26.2694	0.834475	0.417238	+	0.908797i	$0.362998\pi$
$992$	12.9154	0.410063
$993$	−5.22419	−0.165785
$994$	34.5134	1.09470
$995$	22.8719	0.725088
$996$	52.7838	1.67252
$997$	25.8756	0.819489	0.409744	−	0.912200i	$-0.365618\pi$
$997$	25.8756	0.819489	0.409744	+	0.912200i	$0.365618\pi$
$998$	−95.6973	−3.02925
$999$	−3.70759	−0.117303

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6019.2.a.d.1.10	✓	123

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6019.2.a.d.1.10	✓	123	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q-2.49040 q^{2} -2.13188 q^{3} +4.20211 q^{4} -1.49942 q^{5} +5.30925 q^{6} -0.951507 q^{7} -5.48415 q^{8} +1.54493 q^{9} +O(q^{10})\)	\(q-2.49040 q^{2} -2.13188 q^{3} +4.20211 q^{4} -1.49942 q^{5} +5.30925 q^{6} -0.951507 q^{7} -5.48415 q^{8} +1.54493 q^{9} +3.73417 q^{10} -1.50536 q^{11} -8.95842 q^{12} -1.00000 q^{13} +2.36964 q^{14} +3.19660 q^{15} +5.25352 q^{16} -6.30395 q^{17} -3.84751 q^{18} +4.62204 q^{19} -6.30075 q^{20} +2.02850 q^{21} +3.74896 q^{22} +8.58376 q^{23} +11.6916 q^{24} -2.75173 q^{25} +2.49040 q^{26} +3.10204 q^{27} -3.99834 q^{28} +3.30171 q^{29} -7.96083 q^{30} -6.10630 q^{31} -2.11509 q^{32} +3.20926 q^{33} +15.6994 q^{34} +1.42671 q^{35} +6.49198 q^{36} -1.19521 q^{37} -11.5107 q^{38} +2.13188 q^{39} +8.22307 q^{40} +2.83840 q^{41} -5.05179 q^{42} -10.2894 q^{43} -6.32570 q^{44} -2.31651 q^{45} -21.3770 q^{46} -4.09093 q^{47} -11.1999 q^{48} -6.09464 q^{49} +6.85291 q^{50} +13.4393 q^{51} -4.20211 q^{52} +3.85736 q^{53} -7.72532 q^{54} +2.25718 q^{55} +5.21820 q^{56} -9.85366 q^{57} -8.22259 q^{58} +2.26387 q^{59} +13.4325 q^{60} -5.68001 q^{61} +15.2071 q^{62} -1.47001 q^{63} -5.23961 q^{64} +1.49942 q^{65} -7.99235 q^{66} -5.57141 q^{67} -26.4899 q^{68} -18.2996 q^{69} -3.55309 q^{70} +14.5648 q^{71} -8.47264 q^{72} -7.50222 q^{73} +2.97656 q^{74} +5.86636 q^{75} +19.4223 q^{76} +1.43236 q^{77} -5.30925 q^{78} +13.2328 q^{79} -7.87725 q^{80} -11.2480 q^{81} -7.06877 q^{82} -5.89209 q^{83} +8.52399 q^{84} +9.45230 q^{85} +25.6249 q^{86} -7.03887 q^{87} +8.25563 q^{88} +12.9550 q^{89} +5.76905 q^{90} +0.951507 q^{91} +36.0699 q^{92} +13.0179 q^{93} +10.1881 q^{94} -6.93040 q^{95} +4.50912 q^{96} -10.3039 q^{97} +15.1781 q^{98} -2.32568 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 123 q + 10 q^{2} + q^{3} + 136 q^{4} + 46 q^{5} + 16 q^{6} + 12 q^{7} + 30 q^{8} + 154 q^{9}+O(q^{10}) \) 123 * q + 10 * q^2 + q^3 + 136 * q^4 + 46 * q^5 + 16 * q^6 + 12 * q^7 + 30 * q^8 + 154 * q^9	\( 123 q + 10 q^{2} + q^{3} + 136 q^{4} + 46 q^{5} + 16 q^{6} + 12 q^{7} + 30 q^{8} + 154 q^{9} + 5 q^{10} + 53 q^{11} - 6 q^{12} - 123 q^{13} + 21 q^{14} + 29 q^{15} + 166 q^{16} - 35 q^{17} + 28 q^{18} + 23 q^{19} + 93 q^{20} + 72 q^{21} + 8 q^{22} + 42 q^{23} + 55 q^{24} + 153 q^{25} - 10 q^{26} + 7 q^{27} + 39 q^{28} + 86 q^{29} + 44 q^{30} + 16 q^{31} + 70 q^{32} + 40 q^{33} + 10 q^{34} + 6 q^{35} + 222 q^{36} + 52 q^{37} + 12 q^{38} - q^{39} + 14 q^{40} + 80 q^{41} + 29 q^{42} + 2 q^{43} + 143 q^{44} + 137 q^{45} + 39 q^{46} + 45 q^{47} - 27 q^{48} + 163 q^{49} + 102 q^{50} + 48 q^{51} - 136 q^{52} + 117 q^{53} + 75 q^{54} + 20 q^{55} + 88 q^{56} + 67 q^{57} + 56 q^{58} + 88 q^{59} + 96 q^{60} + 57 q^{61} - 13 q^{62} + 48 q^{63} + 228 q^{64} - 46 q^{65} + 28 q^{66} + 43 q^{67} - 56 q^{68} + 92 q^{69} + 14 q^{70} + 90 q^{71} + 98 q^{72} + 25 q^{73} + 80 q^{74} + 21 q^{75} + 75 q^{76} + 112 q^{77} - 16 q^{78} + 36 q^{79} + 208 q^{80} + 231 q^{81} - 27 q^{82} + 93 q^{83} + 175 q^{84} + 77 q^{85} + 199 q^{86} + 15 q^{87} + 43 q^{88} + 140 q^{89} + 11 q^{90} - 12 q^{91} + 93 q^{92} + 140 q^{93} + 4 q^{94} + 23 q^{95} + 105 q^{96} + 43 q^{97} + 67 q^{98} + 140 q^{99}+O(q^{100}) \) 123 * q + 10 * q^2 + q^3 + 136 * q^4 + 46 * q^5 + 16 * q^6 + 12 * q^7 + 30 * q^8 + 154 * q^9 + 5 * q^10 + 53 * q^11 - 6 * q^12 - 123 * q^13 + 21 * q^14 + 29 * q^15 + 166 * q^16 - 35 * q^17 + 28 * q^18 + 23 * q^19 + 93 * q^20 + 72 * q^21 + 8 * q^22 + 42 * q^23 + 55 * q^24 + 153 * q^25 - 10 * q^26 + 7 * q^27 + 39 * q^28 + 86 * q^29 + 44 * q^30 + 16 * q^31 + 70 * q^32 + 40 * q^33 + 10 * q^34 + 6 * q^35 + 222 * q^36 + 52 * q^37 + 12 * q^38 - q^39 + 14 * q^40 + 80 * q^41 + 29 * q^42 + 2 * q^43 + 143 * q^44 + 137 * q^45 + 39 * q^46 + 45 * q^47 - 27 * q^48 + 163 * q^49 + 102 * q^50 + 48 * q^51 - 136 * q^52 + 117 * q^53 + 75 * q^54 + 20 * q^55 + 88 * q^56 + 67 * q^57 + 56 * q^58 + 88 * q^59 + 96 * q^60 + 57 * q^61 - 13 * q^62 + 48 * q^63 + 228 * q^64 - 46 * q^65 + 28 * q^66 + 43 * q^67 - 56 * q^68 + 92 * q^69 + 14 * q^70 + 90 * q^71 + 98 * q^72 + 25 * q^73 + 80 * q^74 + 21 * q^75 + 75 * q^76 + 112 * q^77 - 16 * q^78 + 36 * q^79 + 208 * q^80 + 231 * q^81 - 27 * q^82 + 93 * q^83 + 175 * q^84 + 77 * q^85 + 199 * q^86 + 15 * q^87 + 43 * q^88 + 140 * q^89 + 11 * q^90 - 12 * q^91 + 93 * q^92 + 140 * q^93 + 4 * q^94 + 23 * q^95 + 105 * q^96 + 43 * q^97 + 67 * q^98 + 140 * q^99

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