LMFDB - Embedded newform 6023.2.a.b.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6023,2,Mod(1,6023)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6023, 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("6023.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6023 = 19 \cdot 317 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6023.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:	$48.0938971374$
Analytic rank:	$1$
Dimension:	$99$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Character	$\chi$	$=$	6023.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.33180 q^{2} -3.18012 q^{3} +3.43727 q^{4} +0.827568 q^{5} +7.41539 q^{6} -0.00201560 q^{7} -3.35142 q^{8} +7.11317 q^{9} +O(q^{10})$	\(q-2.33180 q^{2} -3.18012 q^{3} +3.43727 q^{4} +0.827568 q^{5} +7.41539 q^{6} -0.00201560 q^{7} -3.35142 q^{8} +7.11317 q^{9} -1.92972 q^{10} -4.05689 q^{11} -10.9309 q^{12} -2.74850 q^{13} +0.00469996 q^{14} -2.63176 q^{15} +0.940277 q^{16} -4.33812 q^{17} -16.5865 q^{18} -1.00000 q^{19} +2.84457 q^{20} +0.00640985 q^{21} +9.45985 q^{22} +1.63671 q^{23} +10.6579 q^{24} -4.31513 q^{25} +6.40895 q^{26} -13.0804 q^{27} -0.00692815 q^{28} +8.93765 q^{29} +6.13674 q^{30} +8.03527 q^{31} +4.51030 q^{32} +12.9014 q^{33} +10.1156 q^{34} -0.00166804 q^{35} +24.4499 q^{36} -2.00336 q^{37} +2.33180 q^{38} +8.74057 q^{39} -2.77352 q^{40} +2.15390 q^{41} -0.0149464 q^{42} +4.53692 q^{43} -13.9446 q^{44} +5.88663 q^{45} -3.81647 q^{46} -1.81610 q^{47} -2.99019 q^{48} -7.00000 q^{49} +10.0620 q^{50} +13.7957 q^{51} -9.44734 q^{52} -9.98836 q^{53} +30.5008 q^{54} -3.35735 q^{55} +0.00675511 q^{56} +3.18012 q^{57} -20.8408 q^{58} +1.65878 q^{59} -9.04608 q^{60} -5.47696 q^{61} -18.7366 q^{62} -0.0143373 q^{63} -12.3976 q^{64} -2.27457 q^{65} -30.0835 q^{66} +10.1927 q^{67} -14.9113 q^{68} -5.20493 q^{69} +0.00388954 q^{70} +10.4802 q^{71} -23.8392 q^{72} -0.992383 q^{73} +4.67142 q^{74} +13.7226 q^{75} -3.43727 q^{76} +0.00817707 q^{77} -20.3812 q^{78} -0.206703 q^{79} +0.778143 q^{80} +20.2577 q^{81} -5.02245 q^{82} -5.35096 q^{83} +0.0220324 q^{84} -3.59008 q^{85} -10.5792 q^{86} -28.4228 q^{87} +13.5963 q^{88} +8.77864 q^{89} -13.7264 q^{90} +0.00553988 q^{91} +5.62580 q^{92} -25.5531 q^{93} +4.23478 q^{94} -0.827568 q^{95} -14.3433 q^{96} -7.70688 q^{97} +16.3226 q^{98} -28.8574 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 99 q - 4 q^{2} - 3 q^{3} + 80 q^{4} - 15 q^{5} - 12 q^{6} - 19 q^{7} - 12 q^{8} + 58 q^{9}+O(q^{10}) $ 99 * q - 4 * q^2 - 3 * q^3 + 80 * q^4 - 15 * q^5 - 12 * q^6 - 19 * q^7 - 12 * q^8 + 58 * q^9	\( 99 q - 4 q^{2} - 3 q^{3} + 80 q^{4} - 15 q^{5} - 12 q^{6} - 19 q^{7} - 12 q^{8} + 58 q^{9} - 6 q^{10} - 9 q^{11} - 27 q^{12} - 28 q^{13} - 13 q^{14} - 10 q^{15} + 38 q^{16} - 36 q^{17} - 14 q^{18} - 99 q^{19} - 34 q^{20} - 20 q^{21} - 53 q^{22} - 38 q^{23} - 25 q^{24} - 8 q^{25} - 3 q^{26} - 3 q^{27} - 63 q^{28} - 34 q^{29} - 30 q^{30} - 16 q^{31} - 43 q^{32} - 41 q^{33} - 14 q^{34} - 25 q^{35} - 16 q^{36} - 80 q^{37} + 4 q^{38} - 48 q^{39} - 10 q^{40} - 32 q^{41} - 37 q^{42} - 76 q^{43} - 21 q^{44} - 53 q^{45} - 23 q^{46} - 31 q^{47} - 74 q^{48} - 32 q^{49} - 29 q^{50} - 30 q^{51} - 71 q^{52} - 35 q^{53} - 80 q^{54} - 45 q^{55} - 33 q^{56} + 3 q^{57} - 91 q^{58} + 12 q^{59} - 56 q^{60} - 61 q^{61} - 46 q^{62} - 43 q^{63} - 30 q^{64} - 46 q^{65} - 75 q^{66} - 26 q^{67} - 55 q^{68} - 45 q^{69} - 76 q^{70} - 41 q^{71} - 77 q^{72} - 143 q^{73} - 64 q^{74} - 8 q^{75} - 80 q^{76} - 58 q^{77} - 34 q^{78} - 22 q^{79} - 36 q^{80} - 81 q^{81} - 109 q^{82} - 7 q^{83} - 6 q^{84} - 80 q^{85} + 32 q^{86} - 57 q^{87} - 120 q^{88} - 28 q^{89} - 12 q^{90} - 30 q^{91} - 107 q^{92} - 121 q^{93} + 8 q^{94} + 15 q^{95} + 4 q^{96} - 128 q^{97} + 54 q^{98} - 34 q^{99}+O(q^{100}) \) 99 * q - 4 * q^2 - 3 * q^3 + 80 * q^4 - 15 * q^5 - 12 * q^6 - 19 * q^7 - 12 * q^8 + 58 * q^9 - 6 * q^10 - 9 * q^11 - 27 * q^12 - 28 * q^13 - 13 * q^14 - 10 * q^15 + 38 * q^16 - 36 * q^17 - 14 * q^18 - 99 * q^19 - 34 * q^20 - 20 * q^21 - 53 * q^22 - 38 * q^23 - 25 * q^24 - 8 * q^25 - 3 * q^26 - 3 * q^27 - 63 * q^28 - 34 * q^29 - 30 * q^30 - 16 * q^31 - 43 * q^32 - 41 * q^33 - 14 * q^34 - 25 * q^35 - 16 * q^36 - 80 * q^37 + 4 * q^38 - 48 * q^39 - 10 * q^40 - 32 * q^41 - 37 * q^42 - 76 * q^43 - 21 * q^44 - 53 * q^45 - 23 * q^46 - 31 * q^47 - 74 * q^48 - 32 * q^49 - 29 * q^50 - 30 * q^51 - 71 * q^52 - 35 * q^53 - 80 * q^54 - 45 * q^55 - 33 * q^56 + 3 * q^57 - 91 * q^58 + 12 * q^59 - 56 * q^60 - 61 * q^61 - 46 * q^62 - 43 * q^63 - 30 * q^64 - 46 * q^65 - 75 * q^66 - 26 * q^67 - 55 * q^68 - 45 * q^69 - 76 * q^70 - 41 * q^71 - 77 * q^72 - 143 * q^73 - 64 * q^74 - 8 * q^75 - 80 * q^76 - 58 * q^77 - 34 * q^78 - 22 * q^79 - 36 * q^80 - 81 * q^81 - 109 * q^82 - 7 * q^83 - 6 * q^84 - 80 * q^85 + 32 * q^86 - 57 * q^87 - 120 * q^88 - 28 * q^89 - 12 * q^90 - 30 * q^91 - 107 * q^92 - 121 * q^93 + 8 * q^94 + 15 * q^95 + 4 * q^96 - 128 * q^97 + 54 * q^98 - 34 * 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 $

$2$	−2.33180	−1.64883	−0.824414	−	0.565987i	$-0.808495\pi$
$2$	−2.33180	−1.64883	−0.824414	+	0.565987i	$0.808495\pi$
$3$	−3.18012	−1.83604	−0.918022	−	0.396530i	$-0.870214\pi$
$3$	−3.18012	−1.83604	−0.918022	+	0.396530i	$0.870214\pi$
$4$	3.43727	1.71863
$5$	0.827568	0.370099	0.185050	−	0.982729i	$-0.440755\pi$
$5$	0.827568	0.370099	0.185050	+	0.982729i	$0.440755\pi$
$6$	7.41539	3.02732
$7$	−0.00201560	−0.000761824 0	−0.000380912	−	1.00000i	$-0.500121\pi$
$7$	−0.00201560	−0.000761824 0	−0.000380912		1.00000i	$0.500121\pi$
$8$	−3.35142	−1.18490
$9$	7.11317	2.37106
$10$	−1.92972	−0.610230
$11$	−4.05689	−1.22320	−0.611600	−	0.791167i	$-0.709474\pi$
$11$	−4.05689	−1.22320	−0.611600	+	0.791167i	$0.709474\pi$
$12$	−10.9309	−3.15549
$13$	−2.74850	−0.762298	−0.381149	−	0.924514i	$-0.624471\pi$
$13$	−2.74850	−0.762298	−0.381149	+	0.924514i	$0.624471\pi$
$14$	0.00469996	0.00125612
$15$	−2.63176	−0.679519
$16$	0.940277	0.235069
$17$	−4.33812	−1.05215	−0.526074	−	0.850439i	$-0.676336\pi$
$17$	−4.33812	−1.05215	−0.526074	+	0.850439i	$0.676336\pi$
$18$	−16.5865	−3.90946
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	2.84457	0.636066
$21$	0.00640985	0.00139874
$22$	9.45985	2.01685
$23$	1.63671	0.341277	0.170639	−	0.985334i	$-0.445417\pi$
$23$	1.63671	0.341277	0.170639	+	0.985334i	$0.445417\pi$
$24$	10.6579	2.17554
$25$	−4.31513	−0.863026
$26$	6.40895	1.25690
$27$	−13.0804	−2.51732
$28$	−0.00692815	−0.00130930
$29$	8.93765	1.65968	0.829840	−	0.558001i	$-0.188432\pi$
$29$	8.93765	1.65968	0.829840	+	0.558001i	$0.188432\pi$
$30$	6.13674	1.12041
$31$	8.03527	1.44318	0.721588	−	0.692322i	$-0.243412\pi$
$31$	8.03527	1.44318	0.721588	+	0.692322i	$0.243412\pi$
$32$	4.51030	0.797315
$33$	12.9014	2.24585
$34$	10.1156	1.73481
$35$	−0.00166804	−0.000281951 0
$36$	24.4499	4.07498
$37$	−2.00336	−0.329350	−0.164675	−	0.986348i	$-0.552657\pi$
$37$	−2.00336	−0.329350	−0.164675	+	0.986348i	$0.552657\pi$
$38$	2.33180	0.378267
$39$	8.74057	1.39961
$40$	−2.77352	−0.438532
$41$	2.15390	0.336383	0.168191	−	0.985754i	$-0.446207\pi$
$41$	2.15390	0.336383	0.168191	+	0.985754i	$0.446207\pi$
$42$	−0.0149464	−0.00230629
$43$	4.53692	0.691875	0.345937	−	0.938258i	$-0.387561\pi$
$43$	4.53692	0.691875	0.345937	+	0.938258i	$0.387561\pi$
$44$	−13.9446	−2.10223
$45$	5.88663	0.877527
$46$	−3.81647	−0.562707
$47$	−1.81610	−0.264906	−0.132453	−	0.991189i	$-0.542285\pi$
$47$	−1.81610	−0.264906	−0.132453	+	0.991189i	$0.542285\pi$
$48$	−2.99019	−0.431597
$49$	−7.00000	−0.999999
$50$	10.0620	1.42298
$51$	13.7957	1.93179
$52$	−9.44734	−1.31011
$53$	−9.98836	−1.37201	−0.686003	−	0.727599i	$-0.740636\pi$
$53$	−9.98836	−1.37201	−0.686003	+	0.727599i	$0.740636\pi$
$54$	30.5008	4.15063
$55$	−3.35735	−0.452706
$56$	0.00675511	0.000902689 0
$57$	3.18012	0.421217
$58$	−20.8408	−2.73653
$59$	1.65878	0.215955	0.107978	−	0.994153i	$-0.465563\pi$
$59$	1.65878	0.215955	0.107978	+	0.994153i	$0.465563\pi$
$60$	−9.04608	−1.16784
$61$	−5.47696	−0.701253	−0.350627	−	0.936515i	$-0.614031\pi$
$61$	−5.47696	−0.701253	−0.350627	+	0.936515i	$0.614031\pi$
$62$	−18.7366	−2.37955
$63$	−0.0143373	−0.00180633
$64$	−12.3976	−1.54971
$65$	−2.27457	−0.282126
$66$	−30.0835	−3.70302
$67$	10.1927	1.24524	0.622618	−	0.782526i	$-0.286069\pi$
$67$	10.1927	1.24524	0.622618	+	0.782526i	$0.286069\pi$
$68$	−14.9113	−1.80826
$69$	−5.20493	−0.626600
$70$	0.00388954	0.000464888 0
$71$	10.4802	1.24377	0.621885	−	0.783108i	$-0.286367\pi$
$71$	10.4802	1.24377	0.621885	+	0.783108i	$0.286367\pi$
$72$	−23.8392	−2.80947
$73$	−0.992383	−0.116150	−0.0580748	−	0.998312i	$-0.518496\pi$
$73$	−0.992383	−0.116150	−0.0580748	+	0.998312i	$0.518496\pi$
$74$	4.67142	0.543041
$75$	13.7226	1.58455
$76$	−3.43727	−0.394282
$77$	0.00817707	0.000931863 0
$78$	−20.3812	−2.30772
$79$	−0.206703	−0.0232559	−0.0116280	−	0.999932i	$-0.503701\pi$
$79$	−0.206703	−0.0232559	−0.0116280	+	0.999932i	$0.503701\pi$
$80$	0.778143	0.0869990
$81$	20.2577	2.25085
$82$	−5.02245	−0.554637
$83$	−5.35096	−0.587344	−0.293672	−	0.955906i	$-0.594877\pi$
$83$	−5.35096	−0.587344	−0.293672	+	0.955906i	$0.594877\pi$
$84$	0.0220324	0.00240393
$85$	−3.59008	−0.389399
$86$	−10.5792	−1.14078
$87$	−28.4228	−3.04725
$88$	13.5963	1.44937
$89$	8.77864	0.930534	0.465267	−	0.885170i	$-0.345958\pi$
$89$	8.77864	0.930534	0.465267	+	0.885170i	$0.345958\pi$
$90$	−13.7264	−1.44689
$91$	0.00553988	0.000580737 0
$92$	5.62580	0.586530
$93$	−25.5531	−2.64974
$94$	4.23478	0.436784
$95$	−0.827568	−0.0849066
$96$	−14.3433	−1.46391
$97$	−7.70688	−0.782515	−0.391258	−	0.920281i	$-0.627960\pi$
$97$	−7.70688	−0.782515	−0.391258	+	0.920281i	$0.627960\pi$
$98$	16.3226	1.64883
$99$	−28.8574	−2.90028
$100$	−14.8323	−1.48323
$101$	0.582809	0.0579917	0.0289958	−	0.999580i	$-0.490769\pi$
$101$	0.582809	0.0579917	0.0289958	+	0.999580i	$0.490769\pi$
$102$	−32.1688	−3.18519
$103$	−1.54942	−0.152669	−0.0763344	−	0.997082i	$-0.524322\pi$
$103$	−1.54942	−0.152669	−0.0763344	+	0.997082i	$0.524322\pi$
$104$	9.21137	0.903250
$105$	0.00530458	0.000517674 0
$106$	23.2908	2.26220
$107$	4.47606	0.432717	0.216358	−	0.976314i	$-0.430582\pi$
$107$	4.47606	0.432717	0.216358	+	0.976314i	$0.430582\pi$
$108$	−44.9608	−4.32635
$109$	−1.62513	−0.155660	−0.0778298	−	0.996967i	$-0.524799\pi$
$109$	−1.62513	−0.155660	−0.0778298	+	0.996967i	$0.524799\pi$
$110$	7.82866	0.746434
$111$	6.37092	0.604701
$112$	−0.00189522	−0.000179081 0
$113$	−2.81778	−0.265075	−0.132537	−	0.991178i	$-0.542312\pi$
$113$	−2.81778	−0.265075	−0.132537	+	0.991178i	$0.542312\pi$
$114$	−7.41539	−0.694515
$115$	1.35449	0.126306
$116$	30.7211	2.85238
$117$	−19.5506	−1.80745
$118$	−3.86794	−0.356073
$119$	0.00874390	0.000801552 0
$120$	8.82014	0.805165
$121$	5.45839	0.496217
$122$	12.7712	1.15625
$123$	−6.84966	−0.617613
$124$	27.6194	2.48029
$125$	−7.70890	−0.689505
$126$	0.0334316	0.00297833
$127$	0.470587	0.0417578	0.0208789	−	0.999782i	$-0.493354\pi$
$127$	0.470587	0.0417578	0.0208789	+	0.999782i	$0.493354\pi$
$128$	19.8882	1.75788
$129$	−14.4280	−1.27031
$130$	5.30384	0.465177
$131$	9.27777	0.810602	0.405301	−	0.914183i	$-0.367167\pi$
$131$	9.27777	0.810602	0.405301	+	0.914183i	$0.367167\pi$
$132$	44.3456	3.85979
$133$	0.00201560	0.000174775 0
$134$	−23.7673	−2.05318
$135$	−10.8249	−0.931659
$136$	14.5388	1.24669
$137$	−2.33737	−0.199695	−0.0998474	−	0.995003i	$-0.531835\pi$
$137$	−2.33737	−0.199695	−0.0998474	+	0.995003i	$0.531835\pi$
$138$	12.1368	1.03315
$139$	10.6382	0.902317	0.451158	−	0.892444i	$-0.351011\pi$
$139$	10.6382	0.902317	0.451158	+	0.892444i	$0.351011\pi$
$140$	−0.00573351	−0.000484570 0
$141$	5.77542	0.486378
$142$	−24.4377	−2.05076
$143$	11.1504	0.932442
$144$	6.68835	0.557362
$145$	7.39651	0.614247
$146$	2.31403	0.191511
$147$	22.2608	1.83604
$148$	−6.88607	−0.566032
$149$	18.5949	1.52335	0.761675	−	0.647959i	$-0.224377\pi$
$149$	18.5949	1.52335	0.761675	+	0.647959i	$0.224377\pi$
$150$	−31.9984	−2.61266
$151$	−8.14825	−0.663095	−0.331548	−	0.943438i	$-0.607571\pi$
$151$	−8.14825	−0.663095	−0.331548	+	0.943438i	$0.607571\pi$
$152$	3.35142	0.271836
$153$	−30.8577	−2.49470
$154$	−0.0190672	−0.00153648
$155$	6.64973	0.534119
$156$	30.0437	2.40542
$157$	17.9009	1.42865	0.714324	−	0.699815i	$-0.246734\pi$
$157$	17.9009	1.42865	0.714324	+	0.699815i	$0.246734\pi$
$158$	0.481989	0.0383450
$159$	31.7642	2.51906
$160$	3.73258	0.295086
$161$	−0.00329894	−0.000259993 0
$162$	−47.2367	−3.71127
$163$	4.52406	0.354352	0.177176	−	0.984179i	$-0.443304\pi$
$163$	4.52406	0.354352	0.177176	+	0.984179i	$0.443304\pi$
$164$	7.40353	0.578119
$165$	10.6768	0.831187
$166$	12.4773	0.968430
$167$	9.81727	0.759683	0.379842	−	0.925052i	$-0.375979\pi$
$167$	9.81727	0.759683	0.379842	+	0.925052i	$0.375979\pi$
$168$	−0.0214821	−0.00165738
$169$	−5.44573	−0.418902
$170$	8.37134	0.642052
$171$	−7.11317	−0.543958
$172$	15.5946	1.18908
$173$	23.5554	1.79089	0.895443	−	0.445175i	$-0.146859\pi$
$173$	23.5554	1.79089	0.895443	+	0.445175i	$0.146859\pi$
$174$	66.2762	5.02438
$175$	0.00869757	0.000657475 0
$176$	−3.81460	−0.287537
$177$	−5.27513	−0.396503
$178$	−20.4700	−1.53429
$179$	12.4215	0.928425	0.464213	−	0.885724i	$-0.346337\pi$
$179$	12.4215	0.928425	0.464213	+	0.885724i	$0.346337\pi$
$180$	20.2339	1.50815
$181$	1.65180	0.122777	0.0613885	−	0.998114i	$-0.480447\pi$
$181$	1.65180	0.122777	0.0613885	+	0.998114i	$0.480447\pi$
$182$	−0.0129179	−0.000957535 0
$183$	17.4174	1.28753
$184$	−5.48529	−0.404381
$185$	−1.65791	−0.121892
$186$	59.5846	4.36896
$187$	17.5993	1.28699
$188$	−6.24243	−0.455276
$189$	0.0263648	0.00191776
$190$	1.92972	0.139996
$191$	−18.9683	−1.37250	−0.686248	−	0.727368i	$-0.740743\pi$
$191$	−18.9683	−1.37250	−0.686248	+	0.727368i	$0.740743\pi$
$192$	39.4260	2.84533
$193$	−0.794447	−0.0571855	−0.0285928	−	0.999591i	$-0.509103\pi$
$193$	−0.794447	−0.0571855	−0.0285928	+	0.999591i	$0.509103\pi$
$194$	17.9709	1.29023
$195$	7.23341	0.517995
$196$	−24.0609	−1.71863
$197$	−8.99506	−0.640871	−0.320436	−	0.947270i	$-0.603829\pi$
$197$	−8.99506	−0.640871	−0.320436	+	0.947270i	$0.603829\pi$
$198$	67.2895	4.78206
$199$	−24.2584	−1.71964	−0.859818	−	0.510601i	$-0.829423\pi$
$199$	−24.2584	−1.71964	−0.859818	+	0.510601i	$0.829423\pi$
$200$	14.4618	1.02260
$201$	−32.4140	−2.28631
$202$	−1.35899	−0.0956183
$203$	−0.0180147	−0.00126439
$204$	47.4196	3.32004
$205$	1.78250	0.124495
$206$	3.61293	0.251725
$207$	11.6422	0.809187
$208$	−2.58435	−0.179193
$209$	4.05689	0.280621
$210$	−0.0123692	−0.000853556 0
$211$	−7.02109	−0.483352	−0.241676	−	0.970357i	$-0.577697\pi$
$211$	−7.02109	−0.483352	−0.241676	+	0.970357i	$0.577697\pi$
$212$	−34.3327	−2.35798
$213$	−33.3283	−2.28362
$214$	−10.4372	−0.713476
$215$	3.75461	0.256062
$216$	43.8378	2.98278
$217$	−0.0161959	−0.00109945
$218$	3.78948	0.256656
$219$	3.15590	0.213256
$220$	−11.5401	−0.778035
$221$	11.9233	0.802049
$222$	−14.8557	−0.997047
$223$	−5.77160	−0.386495	−0.193247	−	0.981150i	$-0.561902\pi$
$223$	−5.77160	−0.386495	−0.193247	+	0.981150i	$0.561902\pi$
$224$	−0.00909095	−0.000607414 0
$225$	−30.6943	−2.04628
$226$	6.57049	0.437062
$227$	5.43681	0.360854	0.180427	−	0.983588i	$-0.442252\pi$
$227$	5.43681	0.360854	0.180427	+	0.983588i	$0.442252\pi$
$228$	10.9309	0.723918
$229$	21.7057	1.43435	0.717176	−	0.696892i	$-0.245435\pi$
$229$	21.7057	1.43435	0.717176	+	0.696892i	$0.245435\pi$
$230$	−3.15838	−0.208258
$231$	−0.0260041	−0.00171094
$232$	−29.9538	−1.96656
$233$	−10.3642	−0.678984	−0.339492	−	0.940609i	$-0.610255\pi$
$233$	−10.3642	−0.678984	−0.339492	+	0.940609i	$0.610255\pi$
$234$	45.5879	2.98017
$235$	−1.50295	−0.0980415
$236$	5.70168	0.371148
$237$	0.657341	0.0426989
$238$	−0.0203890	−0.00132162
$239$	4.02776	0.260534	0.130267	−	0.991479i	$-0.458417\pi$
$239$	4.02776	0.260534	0.130267	+	0.991479i	$0.458417\pi$
$240$	−2.47459	−0.159734
$241$	−30.3531	−1.95522	−0.977608	−	0.210433i	$-0.932513\pi$
$241$	−30.3531	−1.95522	−0.977608	+	0.210433i	$0.932513\pi$
$242$	−12.7279	−0.818177
$243$	−25.1807	−1.61534
$244$	−18.8258	−1.20520
$245$	−5.79297	−0.370099
$246$	15.9720	1.01834
$247$	2.74850	0.174883
$248$	−26.9295	−1.71003
$249$	17.0167	1.07839
$250$	17.9756	1.13688
$251$	17.6655	1.11504	0.557520	−	0.830164i	$-0.311753\pi$
$251$	17.6655	1.11504	0.557520	+	0.830164i	$0.311753\pi$
$252$	−0.0492811	−0.00310442
$253$	−6.63995	−0.417450
$254$	−1.09731	−0.0688515
$255$	11.4169	0.714954
$256$	−21.5798	−1.34874
$257$	−5.52698	−0.344764	−0.172382	−	0.985030i	$-0.555146\pi$
$257$	−5.52698	−0.344764	−0.172382	+	0.985030i	$0.555146\pi$
$258$	33.6431	2.09453
$259$	0.00403796	0.000250907 0
$260$	−7.81831	−0.484871
$261$	63.5750	3.93520
$262$	−21.6339	−1.33654
$263$	−11.4711	−0.707341	−0.353670	−	0.935370i	$-0.615067\pi$
$263$	−11.4711	−0.707341	−0.353670	+	0.935370i	$0.615067\pi$
$264$	−43.2380	−2.66111
$265$	−8.26604	−0.507779
$266$	−0.00469996	−0.000288173 0
$267$	−27.9171	−1.70850
$268$	35.0350	2.14011
$269$	24.6020	1.50001	0.750006	−	0.661431i	$-0.230051\pi$
$269$	24.6020	1.50001	0.750006	+	0.661431i	$0.230051\pi$
$270$	25.2414	1.53614
$271$	8.29400	0.503825	0.251912	−	0.967750i	$-0.418941\pi$
$271$	8.29400	0.503825	0.251912	+	0.967750i	$0.418941\pi$
$272$	−4.07903	−0.247327
$273$	−0.0176175	−0.00106626
$274$	5.45026	0.329262
$275$	17.5060	1.05565
$276$	−17.8907	−1.07690
$277$	−18.4444	−1.10821	−0.554107	−	0.832445i	$-0.686940\pi$
$277$	−18.4444	−1.10821	−0.554107	+	0.832445i	$0.686940\pi$
$278$	−24.8060	−1.48777
$279$	57.1562	3.42185
$280$	0.00559031	0.000334085 0
$281$	−31.9354	−1.90511	−0.952553	−	0.304373i	$-0.901553\pi$
$281$	−31.9354	−1.90511	−0.952553	+	0.304373i	$0.901553\pi$
$282$	−13.4671	−0.801954
$283$	14.6555	0.871181	0.435591	−	0.900145i	$-0.356540\pi$
$283$	14.6555	0.871181	0.435591	+	0.900145i	$0.356540\pi$
$284$	36.0232	2.13759
$285$	2.63176	0.155892
$286$	−26.0004	−1.53744
$287$	−0.00434140	−0.000256264 0
$288$	32.0825	1.89048
$289$	1.81925	0.107014
$290$	−17.2471	−1.01279
$291$	24.5088	1.43673
$292$	−3.41109	−0.199619
$293$	2.12337	0.124049	0.0620243	−	0.998075i	$-0.480244\pi$
$293$	2.12337	0.124049	0.0620243	+	0.998075i	$0.480244\pi$
$294$	−51.9077	−3.02732
$295$	1.37275	0.0799249
$296$	6.71408	0.390248
$297$	53.0657	3.07918
$298$	−43.3594	−2.51174
$299$	−4.49849	−0.260155
$300$	47.1684	2.72327
$301$	−0.00914462	−0.000527087 0
$302$	19.0001	1.09333
$303$	−1.85340	−0.106475
$304$	−0.940277	−0.0539286
$305$	−4.53256	−0.259533
$306$	71.9539	4.11333
$307$	5.93479	0.338716	0.169358	−	0.985555i	$-0.445831\pi$
$307$	5.93479	0.338716	0.169358	+	0.985555i	$0.445831\pi$
$308$	0.0281068	0.00160153
$309$	4.92734	0.280306
$310$	−15.5058	−0.880670
$311$	32.0456	1.81714	0.908568	−	0.417736i	$-0.137176\pi$
$311$	32.0456	1.81714	0.908568	+	0.417736i	$0.137176\pi$
$312$	−29.2933	−1.65841
$313$	−2.18698	−0.123616	−0.0618078	−	0.998088i	$-0.519687\pi$
$313$	−2.18698	−0.123616	−0.0618078	+	0.998088i	$0.519687\pi$
$314$	−41.7412	−2.35559
$315$	−0.0118651	−0.000668521 0
$316$	−0.710494	−0.0399684
$317$	−1.00000	−0.0561656
$317$	−1.00000	−0.0561656
$318$	−74.0676	−4.15350
$319$	−36.2591	−2.03012
$320$	−10.2599	−0.573545
$321$	−14.2344	−0.794487
$322$	0.00769246	0.000428684 0
$323$	4.33812	0.241379
$324$	69.6310	3.86839
$325$	11.8602	0.657883
$326$	−10.5492	−0.584265
$327$	5.16812	0.285798
$328$	−7.21861	−0.398581
$329$	0.00366053	0.000201812 0
$330$	−24.8961	−1.37048
$331$	−1.40645	−0.0773057	−0.0386528	−	0.999253i	$-0.512307\pi$
$331$	−1.40645	−0.0773057	−0.0386528	+	0.999253i	$0.512307\pi$
$332$	−18.3927	−1.00943
$333$	−14.2502	−0.780907
$334$	−22.8919	−1.25259
$335$	8.43514	0.460861
$336$	0.00602703	0.000328801 0
$337$	−5.17619	−0.281965	−0.140982	−	0.990012i	$-0.545026\pi$
$337$	−5.17619	−0.281965	−0.140982	+	0.990012i	$0.545026\pi$
$338$	12.6983	0.690698
$339$	8.96088	0.486688
$340$	−12.3401	−0.669235
$341$	−32.5982	−1.76529
$342$	16.5865	0.896893
$343$	0.0282184	0.00152365
$344$	−15.2051	−0.819805
$345$	−4.30743	−0.231904
$346$	−54.9265	−2.95286
$347$	−2.52961	−0.135796	−0.0678982	−	0.997692i	$-0.521629\pi$
$347$	−2.52961	−0.135796	−0.0678982	+	0.997692i	$0.521629\pi$
$348$	−97.6968	−5.23710
$349$	−1.63079	−0.0872939	−0.0436470	−	0.999047i	$-0.513898\pi$
$349$	−1.63079	−0.0872939	−0.0436470	+	0.999047i	$0.513898\pi$
$350$	−0.0202810	−0.00108406
$351$	35.9514	1.91895
$352$	−18.2978	−0.975276
$353$	5.37407	0.286033	0.143016	−	0.989720i	$-0.454320\pi$
$353$	5.37407	0.286033	0.143016	+	0.989720i	$0.454320\pi$
$354$	12.3005	0.653765
$355$	8.67307	0.460319
$356$	30.1745	1.59925
$357$	−0.0278067	−0.00147168
$358$	−28.9644	−1.53081
$359$	33.1690	1.75059	0.875297	−	0.483586i	$-0.160666\pi$
$359$	33.1690	1.75059	0.875297	+	0.483586i	$0.160666\pi$
$360$	−19.7285	−1.03979
$361$	1.00000	0.0526316
$362$	−3.85165	−0.202438
$363$	−17.3583	−0.911077
$364$	0.0190420	0.000998074 0
$365$	−0.821264	−0.0429869
$366$	−40.6138	−2.12292
$367$	7.16564	0.374043	0.187022	−	0.982356i	$-0.440117\pi$
$367$	7.16564	0.374043	0.187022	+	0.982356i	$0.440117\pi$
$368$	1.53896	0.0802237
$369$	15.3211	0.797582
$370$	3.86591	0.200979
$371$	0.0201325	0.00104523
$372$	−87.8329	−4.55393
$373$	6.19041	0.320527	0.160264	−	0.987074i	$-0.448766\pi$
$373$	6.19041	0.320527	0.160264	+	0.987074i	$0.448766\pi$
$374$	−41.0379	−2.12202
$375$	24.5152	1.26596
$376$	6.08651	0.313888
$377$	−24.5652	−1.26517
$378$	−0.0614773	−0.00316205
$379$	2.72449	0.139948	0.0699738	−	0.997549i	$-0.477708\pi$
$379$	2.72449	0.139948	0.0699738	+	0.997549i	$0.477708\pi$
$380$	−2.84457	−0.145923
$381$	−1.49652	−0.0766692
$382$	44.2301	2.26301
$383$	−11.8848	−0.607283	−0.303642	−	0.952786i	$-0.598203\pi$
$383$	−11.8848	−0.607283	−0.303642	+	0.952786i	$0.598203\pi$
$384$	−63.2468	−3.22755
$385$	0.00676708	0.000344882 0
$386$	1.85249	0.0942891
$387$	32.2719	1.64047
$388$	−26.4906	−1.34486
$389$	−0.457178	−0.0231798	−0.0115899	−	0.999933i	$-0.503689\pi$
$389$	−0.457178	−0.0231798	−0.0115899	+	0.999933i	$0.503689\pi$
$390$	−16.8668	−0.854086
$391$	−7.10022	−0.359074
$392$	23.4599	1.18490
$393$	−29.5044	−1.48830
$394$	20.9746	1.05669
$395$	−0.171061	−0.00860700
$396$	−99.1905	−4.98451
$397$	8.49801	0.426503	0.213251	−	0.976997i	$-0.431595\pi$
$397$	8.49801	0.426503	0.213251	+	0.976997i	$0.431595\pi$
$398$	56.5657	2.83538
$399$	−0.00640985	−0.000320894 0
$400$	−4.05742	−0.202871
$401$	19.1177	0.954693	0.477347	−	0.878715i	$-0.341599\pi$
$401$	19.1177	0.954693	0.477347	+	0.878715i	$0.341599\pi$
$402$	75.5828	3.76973
$403$	−22.0850	−1.10013
$404$	2.00327	0.0996665
$405$	16.7646	0.833039
$406$	0.0420066	0.00208475
$407$	8.12741	0.402861
$408$	−46.2352	−2.28898
$409$	−5.95756	−0.294582	−0.147291	−	0.989093i	$-0.547055\pi$
$409$	−5.95756	−0.294582	−0.147291	+	0.989093i	$0.547055\pi$
$410$	−4.15642	−0.205271
$411$	7.43311	0.366648
$412$	−5.32577	−0.262382
$413$	−0.00334344	−0.000164520 0
$414$	−27.1472	−1.33421
$415$	−4.42828	−0.217376
$416$	−12.3966	−0.607792
$417$	−33.8306	−1.65669
$418$	−9.45985	−0.462696
$419$	17.8748	0.873243	0.436621	−	0.899645i	$-0.356175\pi$
$419$	17.8748	0.873243	0.436621	+	0.899645i	$0.356175\pi$
$420$	0.0182333	0.000889692 0
$421$	21.6663	1.05595	0.527976	−	0.849259i	$-0.322951\pi$
$421$	21.6663	1.05595	0.527976	+	0.849259i	$0.322951\pi$
$422$	16.3717	0.796964
$423$	−12.9182	−0.628106
$424$	33.4751	1.62570
$425$	18.7195	0.908031
$426$	77.7148	3.76529
$427$	0.0110394	0.000534232 0
$428$	15.3854	0.743682
$429$	−35.4596	−1.71200
$430$	−8.75499	−0.422203
$431$	−25.6505	−1.23554	−0.617770	−	0.786359i	$-0.711964\pi$
$431$	−25.6505	−1.23554	−0.617770	+	0.786359i	$0.711964\pi$
$432$	−12.2992	−0.591744
$433$	5.37919	0.258508	0.129254	−	0.991612i	$-0.458742\pi$
$433$	5.37919	0.258508	0.129254	+	0.991612i	$0.458742\pi$
$434$	0.0377654	0.00181280
$435$	−23.5218	−1.12778
$436$	−5.58602	−0.267522
$437$	−1.63671	−0.0782943
$438$	−7.35891	−0.351622
$439$	26.6127	1.27015	0.635077	−	0.772449i	$-0.280968\pi$
$439$	26.6127	1.27015	0.635077	+	0.772449i	$0.280968\pi$
$440$	11.2519	0.536413
$441$	−49.7922	−2.37105
$442$	−27.8027	−1.32244
$443$	7.78093	0.369683	0.184842	−	0.982768i	$-0.440823\pi$
$443$	7.78093	0.369683	0.184842	+	0.982768i	$0.440823\pi$
$444$	21.8985	1.03926
$445$	7.26492	0.344390
$446$	13.4582	0.637264
$447$	−59.1339	−2.79694
$448$	0.0249887	0.00118060
$449$	−6.85465	−0.323491	−0.161746	−	0.986832i	$-0.551712\pi$
$449$	−6.85465	−0.323491	−0.161746	+	0.986832i	$0.551712\pi$
$450$	71.5727	3.37397
$451$	−8.73814	−0.411463
$452$	−9.68547	−0.455566
$453$	25.9124	1.21747
$454$	−12.6775	−0.594986
$455$	0.00458462	0.000214930 0
$456$	−10.6579	−0.499102
$457$	−37.7910	−1.76779	−0.883893	−	0.467689i	$-0.845087\pi$
$457$	−37.7910	−1.76779	−0.883893	+	0.467689i	$0.845087\pi$
$458$	−50.6132	−2.36500
$459$	56.7442	2.64859
$460$	4.65573	0.217075
$461$	−41.0479	−1.91179	−0.955896	−	0.293706i	$-0.905111\pi$
$461$	−41.0479	−1.91179	−0.955896	+	0.293706i	$0.905111\pi$
$462$	0.0606362	0.00282105
$463$	23.5339	1.09371	0.546857	−	0.837226i	$-0.315824\pi$
$463$	23.5339	1.09371	0.546857	+	0.837226i	$0.315824\pi$
$464$	8.40387	0.390140
$465$	−21.1469	−0.980666
$466$	24.1673	1.11953
$467$	3.20274	0.148205	0.0741027	−	0.997251i	$-0.476391\pi$
$467$	3.20274	0.148205	0.0741027	+	0.997251i	$0.476391\pi$
$468$	−67.2005	−3.10635
$469$	−0.0205444	−0.000948651 0
$470$	3.50456	0.161654
$471$	−56.9270	−2.62306
$472$	−5.55927	−0.255886
$473$	−18.4058	−0.846301
$474$	−1.53278	−0.0704031
$475$	4.31513	0.197992
$476$	0.0300551	0.00137757
$477$	−71.0489	−3.25310
$478$	−9.39190	−0.429576
$479$	21.0787	0.963112	0.481556	−	0.876415i	$-0.340072\pi$
$479$	21.0787	0.963112	0.481556	+	0.876415i	$0.340072\pi$
$480$	−11.8700	−0.541791
$481$	5.50623	0.251063
$482$	70.7773	3.22382
$483$	0.0104910	0.000477359 0
$484$	18.7620	0.852816
$485$	−6.37797	−0.289609
$486$	58.7162	2.66342
$487$	−27.8917	−1.26389	−0.631947	−	0.775011i	$-0.717744\pi$
$487$	−27.8917	−1.26389	−0.631947	+	0.775011i	$0.717744\pi$
$488$	18.3556	0.830918
$489$	−14.3871	−0.650605
$490$	13.5080	0.610230
$491$	1.94346	0.0877072	0.0438536	−	0.999038i	$-0.486036\pi$
$491$	1.94346	0.0877072	0.0438536	+	0.999038i	$0.486036\pi$
$492$	−23.5441	−1.06145
$493$	−38.7726	−1.74623
$494$	−6.40895	−0.288352
$495$	−23.8814	−1.07339
$496$	7.55538	0.339246
$497$	−0.0211239	−0.000947535 0
$498$	−39.6795	−1.77808
$499$	−20.6892	−0.926178	−0.463089	−	0.886312i	$-0.653259\pi$
$499$	−20.6892	−0.926178	−0.463089	+	0.886312i	$0.653259\pi$
$500$	−26.4976	−1.18501
$501$	−31.2201	−1.39481
$502$	−41.1924	−1.83851
$503$	34.6230	1.54376	0.771882	−	0.635765i	$-0.219315\pi$
$503$	34.6230	1.54376	0.771882	+	0.635765i	$0.219315\pi$
$504$	0.0480502	0.00214033
$505$	0.482314	0.0214627
$506$	15.4830	0.688303
$507$	17.3181	0.769123
$508$	1.61753	0.0717664
$509$	36.8624	1.63390	0.816949	−	0.576709i	$-0.195663\pi$
$509$	36.8624	1.63390	0.816949	+	0.576709i	$0.195663\pi$
$510$	−26.6219	−1.17884
$511$	0.00200025	8.84856e−5 0
$512$	10.5434	0.465959
$513$	13.0804	0.577513
$514$	12.8878	0.568456
$515$	−1.28225	−0.0565026
$516$	−49.5928	−2.18320
$517$	7.36773	0.324033
$518$	−0.00941570	−0.000413702 0
$519$	−74.9091	−3.28815
$520$	7.62303	0.334292
$521$	15.6930	0.687521	0.343760	−	0.939057i	$-0.388299\pi$
$521$	15.6930	0.687521	0.343760	+	0.939057i	$0.388299\pi$
$522$	−148.244	−6.48846
$523$	27.1603	1.18764	0.593819	−	0.804599i	$-0.297620\pi$
$523$	27.1603	1.18764	0.593819	+	0.804599i	$0.297620\pi$
$524$	31.8902	1.39313
$525$	−0.0276593	−0.00120715
$526$	26.7483	1.16628
$527$	−34.8579	−1.51843
$528$	12.1309	0.527930
$529$	−20.3212	−0.883530
$530$	19.2747	0.837240
$531$	11.7992	0.512042
$532$	0.00692815	0.000300373 0
$533$	−5.92000	−0.256424
$534$	65.0971	2.81703
$535$	3.70424	0.160148
$536$	−34.1600	−1.47549
$537$	−39.5018	−1.70463
$538$	−57.3669	−2.47326
$539$	28.3982	1.22320
$540$	−37.2081	−1.60118
$541$	9.23382	0.396993	0.198496	−	0.980102i	$-0.436394\pi$
$541$	9.23382	0.396993	0.198496	+	0.980102i	$0.436394\pi$
$542$	−19.3399	−0.830721
$543$	−5.25291	−0.225424
$544$	−19.5662	−0.838894
$545$	−1.34491	−0.0576095
$546$	0.0410804	0.00175808
$547$	−14.9271	−0.638238	−0.319119	−	0.947715i	$-0.603387\pi$
$547$	−14.9271	−0.638238	−0.319119	+	0.947715i	$0.603387\pi$
$548$	−8.03416	−0.343202
$549$	−38.9586	−1.66271
$550$	−40.8205	−1.74059
$551$	−8.93765	−0.380757
$552$	17.4439	0.742460
$553$	0.000416631 0	1.77169e−5 0
$554$	43.0085	1.82726
$555$	5.27236	0.223799
$556$	36.5662	1.55075
$557$	−30.6559	−1.29893	−0.649466	−	0.760391i	$-0.725007\pi$
$557$	−30.6559	−1.29893	−0.649466	+	0.760391i	$0.725007\pi$
$558$	−133.277	−5.64205
$559$	−12.4698	−0.527414
$560$	−0.00156842	−6.62780e−5 0
$561$	−55.9678	−2.36296
$562$	74.4668	3.14119
$563$	0.0412890	0.00174012	0.000870061	−	1.00000i	$-0.499723\pi$
$563$	0.0412890	0.00174012	0.000870061		1.00000i	$0.499723\pi$
$564$	19.8517	0.835907
$565$	−2.33190	−0.0981039
$566$	−34.1737	−1.43643
$567$	−0.0408313	−0.00171475
$568$	−35.1235	−1.47375
$569$	−17.0592	−0.715157	−0.357579	−	0.933883i	$-0.616398\pi$
$569$	−17.0592	−0.715157	−0.357579	+	0.933883i	$0.616398\pi$
$570$	−6.13674	−0.257040
$571$	3.11814	0.130490	0.0652452	−	0.997869i	$-0.479217\pi$
$571$	3.11814	0.130490	0.0652452	+	0.997869i	$0.479217\pi$
$572$	38.3269	1.60253
$573$	60.3214	2.51996
$574$	0.0101232	0.000422536 0
$575$	−7.06261	−0.294531
$576$	−88.1865	−3.67444
$577$	−26.2736	−1.09378	−0.546891	−	0.837204i	$-0.684189\pi$
$577$	−26.2736	−1.09378	−0.546891	+	0.837204i	$0.684189\pi$
$578$	−4.24211	−0.176448
$579$	2.52644	0.104995
$580$	25.4238	1.05567
$581$	0.0107854	0.000447453 0
$582$	−57.1495	−2.36892
$583$	40.5217	1.67824
$584$	3.32589	0.137626
$585$	−16.1794	−0.668936
$586$	−4.95127	−0.204535
$587$	34.4625	1.42242	0.711211	−	0.702979i	$-0.248147\pi$
$587$	34.4625	1.42242	0.711211	+	0.702979i	$0.248147\pi$
$588$	76.5165	3.15549
$589$	−8.03527	−0.331087
$590$	−3.20098	−0.131782
$591$	28.6054	1.17667
$592$	−1.88371	−0.0774200
$593$	−17.0831	−0.701518	−0.350759	−	0.936466i	$-0.614076\pi$
$593$	−17.0831	−0.701518	−0.350759	+	0.936466i	$0.614076\pi$
$594$	−123.738	−5.07705
$595$	0.00723617	0.000296654 0
$596$	63.9155	2.61808
$597$	77.1448	3.15733
$598$	10.4896	0.428950
$599$	−1.59196	−0.0650456	−0.0325228	−	0.999471i	$-0.510354\pi$
$599$	−1.59196	−0.0650456	−0.0325228	+	0.999471i	$0.510354\pi$
$600$	−45.9903	−1.87754
$601$	16.6771	0.680274	0.340137	−	0.940376i	$-0.389527\pi$
$601$	16.6771	0.680274	0.340137	+	0.940376i	$0.389527\pi$
$602$	0.0213234	0.000869076 0
$603$	72.5024	2.95252
$604$	−28.0077	−1.13962
$605$	4.51719	0.183650
$606$	4.32176	0.175559
$607$	3.69644	0.150034	0.0750170	−	0.997182i	$-0.476099\pi$
$607$	3.69644	0.150034	0.0750170	+	0.997182i	$0.476099\pi$
$608$	−4.51030	−0.182917
$609$	0.0572890	0.00232147
$610$	10.5690	0.427926
$611$	4.99156	0.201937
$612$	−106.066	−4.28748
$613$	−13.8680	−0.560123	−0.280062	−	0.959982i	$-0.590355\pi$
$613$	−13.8680	−0.560123	−0.280062	+	0.959982i	$0.590355\pi$
$614$	−13.8387	−0.558485
$615$	−5.66856	−0.228578
$616$	−0.0274048	−0.00110417
$617$	−36.0640	−1.45188	−0.725941	−	0.687757i	$-0.758596\pi$
$617$	−36.0640	−1.45188	−0.725941	+	0.687757i	$0.758596\pi$
$618$	−11.4895	−0.462177
$619$	−21.5245	−0.865142	−0.432571	−	0.901600i	$-0.642394\pi$
$619$	−21.5245	−0.865142	−0.432571	+	0.901600i	$0.642394\pi$
$620$	22.8569	0.917955
$621$	−21.4087	−0.859103
$622$	−74.7237	−2.99615
$623$	−0.0176942	−0.000708904 0
$624$	8.21856	0.329006
$625$	15.1960	0.607841
$626$	5.09959	0.203821
$627$	−12.9014	−0.515233
$628$	61.5302	2.45532
$629$	8.69079	0.346525
$630$	0.0276669	0.00110228
$631$	−21.9135	−0.872365	−0.436182	−	0.899858i	$-0.643670\pi$
$631$	−21.9135	−0.872365	−0.436182	+	0.899858i	$0.643670\pi$
$632$	0.692748	0.0275560
$633$	22.3279	0.887455
$634$	2.33180	0.0926074
$635$	0.389443	0.0154546
$636$	109.182	4.32935
$637$	19.2395	0.762297
$638$	84.5488	3.34732
$639$	74.5474	2.94905
$640$	16.4588	0.650591
$641$	−2.31263	−0.0913434	−0.0456717	−	0.998957i	$-0.514543\pi$
$641$	−2.31263	−0.0913434	−0.0456717	+	0.998957i	$0.514543\pi$
$642$	33.1917	1.30997
$643$	−43.2236	−1.70457	−0.852287	−	0.523075i	$-0.824785\pi$
$643$	−43.2236	−1.70457	−0.852287	+	0.523075i	$0.824785\pi$
$644$	−0.0113394	−0.000446833 0
$645$	−11.9401	−0.470142
$646$	−10.1156	−0.397993
$647$	−16.5179	−0.649385	−0.324693	−	0.945820i	$-0.605261\pi$
$647$	−16.5179	−0.649385	−0.324693	+	0.945820i	$0.605261\pi$
$648$	−67.8918	−2.66704
$649$	−6.72951	−0.264156
$650$	−27.6554	−1.08474
$651$	0.0515048	0.00201863
$652$	15.5504	0.609001
$653$	26.9470	1.05452	0.527258	−	0.849705i	$-0.323220\pi$
$653$	26.9470	1.05452	0.527258	+	0.849705i	$0.323220\pi$
$654$	−12.0510	−0.471231
$655$	7.67798	0.300004
$656$	2.02526	0.0790732
$657$	−7.05899	−0.275397
$658$	−0.00853561	−0.000332753 0
$659$	−14.1584	−0.551532	−0.275766	−	0.961225i	$-0.588932\pi$
$659$	−14.1584	−0.551532	−0.275766	+	0.961225i	$0.588932\pi$
$660$	36.6990	1.42851
$661$	−46.0427	−1.79085	−0.895426	−	0.445210i	$-0.853129\pi$
$661$	−46.0427	−1.79085	−0.895426	+	0.445210i	$0.853129\pi$
$662$	3.27956	0.127464
$663$	−37.9176	−1.47260
$664$	17.9333	0.695947
$665$	0.00166804	6.46840e−5 0
$666$	33.2286	1.28758
$667$	14.6283	0.566411
$668$	33.7446	1.30562
$669$	18.3544	0.709622
$670$	−19.6690	−0.759881
$671$	22.2195	0.857773
$672$	0.0289103	0.00111524
$673$	28.3368	1.09230	0.546151	−	0.837687i	$-0.316092\pi$
$673$	28.3368	1.09230	0.546151	+	0.837687i	$0.316092\pi$
$674$	12.0698	0.464912
$675$	56.4435	2.17251
$676$	−18.7184	−0.719940
$677$	−11.3945	−0.437924	−0.218962	−	0.975733i	$-0.570267\pi$
$677$	−11.3945	−0.437924	−0.218962	+	0.975733i	$0.570267\pi$
$678$	−20.8949	−0.802465
$679$	0.0155340	0.000596139 0
$680$	12.0319	0.461401
$681$	−17.2897	−0.662544
$682$	76.0124	2.91066
$683$	−24.1339	−0.923460	−0.461730	−	0.887021i	$-0.652771\pi$
$683$	−24.1339	−0.923460	−0.461730	+	0.887021i	$0.652771\pi$
$684$	−24.4499	−0.934864
$685$	−1.93433	−0.0739069
$686$	−0.0657994	−0.00251223
$687$	−69.0267	−2.63353
$688$	4.26597	0.162638
$689$	27.4530	1.04588
$690$	10.0440	0.382370
$691$	−22.7535	−0.865585	−0.432793	−	0.901494i	$-0.642472\pi$
$691$	−22.7535	−0.865585	−0.432793	+	0.901494i	$0.642472\pi$
$692$	80.9664	3.07788
$693$	0.0581649	0.00220950
$694$	5.89853	0.223905
$695$	8.80379	0.333947
$696$	95.2566	3.61069
$697$	−9.34386	−0.353924
$698$	3.80266	0.143933
$699$	32.9595	1.24664
$700$	0.0298959	0.00112996
$701$	24.6133	0.929630	0.464815	−	0.885408i	$-0.346121\pi$
$701$	24.6133	0.929630	0.464815	+	0.885408i	$0.346121\pi$
$702$	−83.8314	−3.16401
$703$	2.00336	0.0755580
$704$	50.2959	1.89560
$705$	4.77955	0.180008
$706$	−12.5312	−0.471619
$707$	−0.00117471	−4.41795e−5 0
$708$	−18.1320	−0.681444
$709$	21.2668	0.798692	0.399346	−	0.916800i	$-0.369237\pi$
$709$	21.2668	0.798692	0.399346	+	0.916800i	$0.369237\pi$
$710$	−20.2238	−0.758987
$711$	−1.47031	−0.0551411
$712$	−29.4209	−1.10259
$713$	13.1514	0.492523
$714$	0.0648394	0.00242655
$715$	9.22770	0.345096
$716$	42.6960	1.59562
$717$	−12.8088	−0.478352
$718$	−77.3434	−2.88643
$719$	0.878476	0.0327616	0.0163808	−	0.999866i	$-0.494786\pi$
$719$	0.878476	0.0327616	0.0163808	+	0.999866i	$0.494786\pi$
$720$	5.53506	0.206280
$721$	0.00312301	0.000116307 0
$722$	−2.33180	−0.0867804
$723$	96.5266	3.58986
$724$	5.67766	0.211009
$725$	−38.5671	−1.43235
$726$	40.4761	1.50221
$727$	−8.41128	−0.311957	−0.155979	−	0.987760i	$-0.549853\pi$
$727$	−8.41128	−0.311957	−0.155979	+	0.987760i	$0.549853\pi$
$728$	−0.0185664	−0.000688118 0
$729$	19.3047	0.714988
$730$	1.91502	0.0708780
$731$	−19.6817	−0.727954
$732$	59.8683	2.21280
$733$	−10.4213	−0.384918	−0.192459	−	0.981305i	$-0.561646\pi$
$733$	−10.4213	−0.384918	−0.192459	+	0.981305i	$0.561646\pi$
$734$	−16.7088	−0.616733
$735$	18.4223	0.679518
$736$	7.38204	0.272105
$737$	−41.3507	−1.52317
$738$	−35.7256	−1.31508
$739$	−34.8685	−1.28266	−0.641329	−	0.767266i	$-0.721617\pi$
$739$	−34.8685	−1.28266	−0.641329	+	0.767266i	$0.721617\pi$
$740$	−5.69869	−0.209488
$741$	−8.74057	−0.321093
$742$	−0.0469449	−0.00172340
$743$	−28.4787	−1.04478	−0.522392	−	0.852706i	$-0.674960\pi$
$743$	−28.4787	−1.04478	−0.522392	+	0.852706i	$0.674960\pi$
$744$	85.6391	3.13968
$745$	15.3885	0.563791
$746$	−14.4348	−0.528494
$747$	−38.0623	−1.39263
$748$	60.4934	2.21186
$749$	−0.00902193	−0.000329654 0
$750$	−57.1645	−2.08735
$751$	17.2874	0.630828	0.315414	−	0.948954i	$-0.397857\pi$
$751$	17.2874	0.630828	0.315414	+	0.948954i	$0.397857\pi$
$752$	−1.70764	−0.0622712
$753$	−56.1786	−2.04726
$754$	57.2809	2.08605
$755$	−6.74323	−0.245411
$756$	0.0906228	0.00329592
$757$	−25.4403	−0.924643	−0.462322	−	0.886712i	$-0.652983\pi$
$757$	−25.4403	−0.924643	−0.462322	+	0.886712i	$0.652983\pi$
$758$	−6.35295	−0.230749
$759$	21.1158	0.766456
$760$	2.77352	0.100606
$761$	−15.0480	−0.545490	−0.272745	−	0.962086i	$-0.587932\pi$
$761$	−15.0480	−0.545490	−0.272745	+	0.962086i	$0.587932\pi$
$762$	3.48959	0.126414
$763$	0.00327562	0.000118585 0
$764$	−65.1990	−2.35882
$765$	−25.5369	−0.923288
$766$	27.7128	1.00131
$767$	−4.55917	−0.164622
$768$	68.6265	2.47635
$769$	21.5857	0.778401	0.389201	−	0.921153i	$-0.372751\pi$
$769$	21.5857	0.778401	0.389201	+	0.921153i	$0.372751\pi$
$770$	−0.0157794	−0.000568651 0
$771$	17.5765	0.633001
$772$	−2.73073	−0.0982810
$773$	−41.4298	−1.49013	−0.745063	−	0.666994i	$-0.767581\pi$
$773$	−41.4298	−1.49013	−0.745063	+	0.666994i	$0.767581\pi$
$774$	−75.2515	−2.70486
$775$	−34.6732	−1.24550
$776$	25.8290	0.927206
$777$	−0.0128412	−0.000460676 0
$778$	1.06605	0.0382196
$779$	−2.15390	−0.0771715
$780$	24.8632	0.890245
$781$	−42.5171	−1.52138
$782$	16.5563	0.592051
$783$	−116.908	−4.17795
$784$	−6.58193	−0.235069
$785$	14.8142	0.528742
$786$	68.7983	2.45395
$787$	−6.40974	−0.228482	−0.114241	−	0.993453i	$-0.536444\pi$
$787$	−6.40974	−0.228482	−0.114241	+	0.993453i	$0.536444\pi$
$788$	−30.9184	−1.10142
$789$	36.4796	1.29871
$790$	0.398879	0.0141915
$791$	0.00567951	0.000201940 0
$792$	96.7130	3.43655
$793$	15.0534	0.534564
$794$	−19.8156	−0.703230
$795$	26.2870	0.932304
$796$	−83.3828	−2.95542
$797$	−23.0604	−0.816841	−0.408421	−	0.912794i	$-0.633920\pi$
$797$	−23.0604	−0.816841	−0.408421	+	0.912794i	$0.633920\pi$
$798$	0.0149464	0.000529098 0
$799$	7.87846	0.278720
$800$	−19.4625	−0.688104
$801$	62.4440	2.20635
$802$	−44.5786	−1.57412
$803$	4.02599	0.142074
$804$	−111.416	−3.92933
$805$	−0.00273010	−9.62233e−5 0
$806$	51.4976	1.81393
$807$	−78.2374	−2.75409
$808$	−1.95324	−0.0687146
$809$	26.7526	0.940572	0.470286	−	0.882514i	$-0.344151\pi$
$809$	26.7526	0.940572	0.470286	+	0.882514i	$0.344151\pi$
$810$	−39.0916	−1.37354
$811$	−50.8350	−1.78506	−0.892530	−	0.450989i	$-0.851071\pi$
$811$	−50.8350	−1.78506	−0.892530	+	0.450989i	$0.851071\pi$
$812$	−0.0619214	−0.00217302
$813$	−26.3759	−0.925044
$814$	−18.9514	−0.664248
$815$	3.74397	0.131145
$816$	12.9718	0.454104
$817$	−4.53692	−0.158727
$818$	13.8918	0.485715
$819$	0.0394061	0.00137696
$820$	6.12692	0.213961
$821$	−12.0830	−0.421699	−0.210850	−	0.977519i	$-0.567623\pi$
$821$	−12.0830	−0.421699	−0.210850	+	0.977519i	$0.567623\pi$
$822$	−17.3325	−0.604540
$823$	−6.46816	−0.225466	−0.112733	−	0.993625i	$-0.535960\pi$
$823$	−6.46816	−0.225466	−0.112733	+	0.993625i	$0.535960\pi$
$824$	5.19274	0.180898
$825$	−55.6713	−1.93823
$826$	0.00779622	0.000271265 0
$827$	38.1714	1.32735	0.663675	−	0.748021i	$-0.268996\pi$
$827$	38.1714	1.32735	0.663675	+	0.748021i	$0.268996\pi$
$828$	40.0173	1.39070
$829$	20.4881	0.711581	0.355790	−	0.934566i	$-0.384212\pi$
$829$	20.4881	0.711581	0.355790	+	0.934566i	$0.384212\pi$
$830$	10.3258	0.358415
$831$	58.6553	2.03473
$832$	34.0750	1.18134
$833$	30.3668	1.05215
$834$	78.8861	2.73160
$835$	8.12445	0.281158
$836$	13.9446	0.482285
$837$	−105.104	−3.63294
$838$	−41.6804	−1.43983
$839$	−47.0709	−1.62507	−0.812534	−	0.582914i	$-0.801912\pi$
$839$	−47.0709	−1.62507	−0.812534	+	0.582914i	$0.801912\pi$
$840$	−0.0177779	−0.000613394 0
$841$	50.8816	1.75454
$842$	−50.5214	−1.74108
$843$	101.558	3.49786
$844$	−24.1334	−0.830704
$845$	−4.50671	−0.155036
$846$	30.1227	1.03564
$847$	−0.0110019	−0.000378031 0
$848$	−9.39182	−0.322516
$849$	−46.6064	−1.59953
$850$	−43.6501	−1.49719
$851$	−3.27891	−0.112400
$852$	−114.558	−3.92470
$853$	−11.8014	−0.404073	−0.202036	−	0.979378i	$-0.564756\pi$
$853$	−11.8014	−0.404073	−0.202036	+	0.979378i	$0.564756\pi$
$854$	−0.0257415	−0.000880857 0
$855$	−5.88663	−0.201318
$856$	−15.0011	−0.512728
$857$	−28.6238	−0.977769	−0.488885	−	0.872348i	$-0.662596\pi$
$857$	−28.6238	−0.977769	−0.488885	+	0.872348i	$0.662596\pi$
$858$	82.6845	2.82280
$859$	−37.6687	−1.28524	−0.642619	−	0.766186i	$-0.722152\pi$
$859$	−37.6687	−1.28524	−0.642619	+	0.766186i	$0.722152\pi$
$860$	12.9056	0.440078
$861$	0.0138062	0.000470513 0
$862$	59.8117	2.03719
$863$	−27.8120	−0.946732	−0.473366	−	0.880866i	$-0.656961\pi$
$863$	−27.8120	−0.946732	−0.473366	+	0.880866i	$0.656961\pi$
$864$	−58.9964	−2.00710
$865$	19.4937	0.662806
$866$	−12.5432	−0.426234
$867$	−5.78542	−0.196483
$868$	−0.0556695	−0.00188955
$869$	0.838573	0.0284466
$870$	54.8480	1.85952
$871$	−28.0147	−0.949240
$872$	5.44650	0.184442
$873$	−54.8204	−1.85539
$874$	3.81647	0.129094
$875$	0.0155380	0.000525282 0
$876$	10.8477	0.366509
$877$	−19.5619	−0.660557	−0.330278	−	0.943884i	$-0.607143\pi$
$877$	−19.5619	−0.660557	−0.330278	+	0.943884i	$0.607143\pi$
$878$	−62.0553	−2.09427
$879$	−6.75258	−0.227759
$880$	−3.15684	−0.106417
$881$	38.5665	1.29934	0.649669	−	0.760217i	$-0.274907\pi$
$881$	38.5665	1.29934	0.649669	+	0.760217i	$0.274907\pi$
$882$	116.105	3.90946
$883$	−47.2299	−1.58941	−0.794706	−	0.606995i	$-0.792375\pi$
$883$	−47.2299	−1.58941	−0.794706	+	0.606995i	$0.792375\pi$
$884$	40.9837	1.37843
$885$	−4.36553	−0.146746
$886$	−18.1435	−0.609544
$887$	−35.5561	−1.19386	−0.596928	−	0.802295i	$-0.703612\pi$
$887$	−35.5561	−1.19386	−0.596928	+	0.802295i	$0.703612\pi$
$888$	−21.3516	−0.716512
$889$	−0.000948514 0	−3.18121e−5 0
$890$	−16.9403	−0.567840
$891$	−82.1832	−2.75324
$892$	−19.8385	−0.664243
$893$	1.81610	0.0607735
$894$	137.888	4.61167
$895$	10.2796	0.343610
$896$	−0.0400866	−0.00133920
$897$	14.3058	0.477655
$898$	15.9836	0.533381
$899$	71.8164	2.39521
$900$	−105.504	−3.51681
$901$	43.3306	1.44355
$902$	20.3756	0.678432
$903$	0.0290810	0.000967755 0
$904$	9.44355	0.314088
$905$	1.36697	0.0454397
$906$	−60.4225	−2.00740
$907$	−7.90809	−0.262584	−0.131292	−	0.991344i	$-0.541913\pi$
$907$	−7.90809	−0.262584	−0.131292	+	0.991344i	$0.541913\pi$
$908$	18.6878	0.620176
$909$	4.14562	0.137502
$910$	−0.0106904	−0.000354383 0
$911$	−18.5754	−0.615430	−0.307715	−	0.951479i	$-0.599564\pi$
$911$	−18.5754	−0.615430	−0.307715	+	0.951479i	$0.599564\pi$
$912$	2.99019	0.0990152
$913$	21.7083	0.718439
$914$	88.1208	2.91478
$915$	14.4141	0.476515
$916$	74.6082	2.46513
$917$	−0.0187003	−0.000617537 0
$918$	−132.316	−4.36707
$919$	−56.8714	−1.87601	−0.938007	−	0.346616i	$-0.887331\pi$
$919$	−56.8714	−1.87601	−0.938007	+	0.346616i	$0.887331\pi$
$920$	−4.53944	−0.149661
$921$	−18.8733	−0.621898
$922$	95.7153	3.15222
$923$	−28.8049	−0.948123
$924$	−0.0893830	−0.00294048
$925$	8.64475	0.284238
$926$	−54.8763	−1.80335
$927$	−11.0213	−0.361986
$928$	40.3115	1.32329
$929$	37.4640	1.22915	0.614576	−	0.788857i	$-0.289327\pi$
$929$	37.4640	1.22915	0.614576	+	0.788857i	$0.289327\pi$
$930$	49.3103	1.61695
$931$	7.00000	0.229416
$932$	−35.6247	−1.16692
$933$	−101.909	−3.33634
$934$	−7.46814	−0.244365
$935$	14.5646	0.476313
$936$	65.5221	2.14166
$937$	30.3303	0.990849	0.495424	−	0.868651i	$-0.335013\pi$
$937$	30.3303	0.990849	0.495424	+	0.868651i	$0.335013\pi$
$938$	0.0479053	0.00156416
$939$	6.95487	0.226964
$940$	−5.16603	−0.168497
$941$	14.5932	0.475723	0.237862	−	0.971299i	$-0.423553\pi$
$941$	14.5932	0.475723	0.237862	+	0.971299i	$0.423553\pi$
$942$	132.742	4.32497
$943$	3.52530	0.114800
$944$	1.55972	0.0507644
$945$	0.0218186	0.000709760 0
$946$	42.9186	1.39540
$947$	54.6702	1.77654	0.888271	−	0.459320i	$-0.151907\pi$
$947$	54.6702	1.77654	0.888271	+	0.459320i	$0.151907\pi$
$948$	2.25946	0.0733838
$949$	2.72757	0.0885406
$950$	−10.0620	−0.326454
$951$	3.18012	0.103122
$952$	−0.0293044	−0.000949762 0
$953$	−1.81395	−0.0587597	−0.0293799	−	0.999568i	$-0.509353\pi$
$953$	−1.81395	−0.0587597	−0.0293799	+	0.999568i	$0.509353\pi$
$954$	165.671	5.36381
$955$	−15.6975	−0.507960
$956$	13.8445	0.447762
$957$	115.308	3.72739
$958$	−49.1513	−1.58801
$959$	0.00471119	0.000152132 0
$960$	32.6277	1.05305
$961$	33.5655	1.08276
$962$	−12.8394	−0.413959
$963$	31.8390	1.02600
$964$	−104.332	−3.36030
$965$	−0.657458	−0.0211643
$966$	−0.0244630	−0.000787083 0
$967$	−45.3912	−1.45968	−0.729841	−	0.683617i	$-0.760406\pi$
$967$	−45.3912	−1.45968	−0.729841	+	0.683617i	$0.760406\pi$
$968$	−18.2933	−0.587970
$969$	−13.7957	−0.443183
$970$	14.8721	0.477515
$971$	34.0361	1.09227	0.546135	−	0.837697i	$-0.316098\pi$
$971$	34.0361	1.09227	0.546135	+	0.837697i	$0.316098\pi$
$972$	−86.5528	−2.77618
$973$	−0.0214422	−0.000687407 0
$974$	65.0378	2.08394
$975$	−37.7167	−1.20790
$976$	−5.14986	−0.164843
$977$	17.2891	0.553126	0.276563	−	0.960996i	$-0.410804\pi$
$977$	17.2891	0.553126	0.276563	+	0.960996i	$0.410804\pi$
$978$	33.5477	1.07274
$979$	−35.6140	−1.13823
$980$	−19.9120	−0.636065
$981$	−11.5598	−0.369078
$982$	−4.53175	−0.144614
$983$	−28.9745	−0.924142	−0.462071	−	0.886843i	$-0.652893\pi$
$983$	−28.9745	−0.924142	−0.462071	+	0.886843i	$0.652893\pi$
$984$	22.9561	0.731812
$985$	−7.44402	−0.237186
$986$	90.4097	2.87923
$987$	−0.0116409	−0.000370535 0
$988$	9.44734	0.300560
$989$	7.42562	0.236121
$990$	55.6866	1.76984
$991$	37.3319	1.18589	0.592943	−	0.805244i	$-0.297966\pi$
$991$	37.3319	1.18589	0.592943	+	0.805244i	$0.297966\pi$
$992$	36.2414	1.15067
$993$	4.47269	0.141937
$994$	0.0492565	0.00156232
$995$	−20.0755	−0.636436
$996$	58.4910	1.85336
$997$	10.7772	0.341316	0.170658	−	0.985330i	$-0.445411\pi$
$997$	10.7772	0.341316	0.170658	+	0.985330i	$0.445411\pi$
$998$	48.2431	1.52711
$999$	26.2047	0.829079

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6023.2.a.b.1.8	✓	99

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6023.2.a.b.1.8	✓	99	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:	\( N \)	\(=\)	\( 6023 = 19 \cdot 317 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6023.a (trivial)

\(f(q)\)	\(=\)	\(q-2.33180 q^{2} -3.18012 q^{3} +3.43727 q^{4} +0.827568 q^{5} +7.41539 q^{6} -0.00201560 q^{7} -3.35142 q^{8} +7.11317 q^{9} +O(q^{10})\)	\(q-2.33180 q^{2} -3.18012 q^{3} +3.43727 q^{4} +0.827568 q^{5} +7.41539 q^{6} -0.00201560 q^{7} -3.35142 q^{8} +7.11317 q^{9} -1.92972 q^{10} -4.05689 q^{11} -10.9309 q^{12} -2.74850 q^{13} +0.00469996 q^{14} -2.63176 q^{15} +0.940277 q^{16} -4.33812 q^{17} -16.5865 q^{18} -1.00000 q^{19} +2.84457 q^{20} +0.00640985 q^{21} +9.45985 q^{22} +1.63671 q^{23} +10.6579 q^{24} -4.31513 q^{25} +6.40895 q^{26} -13.0804 q^{27} -0.00692815 q^{28} +8.93765 q^{29} +6.13674 q^{30} +8.03527 q^{31} +4.51030 q^{32} +12.9014 q^{33} +10.1156 q^{34} -0.00166804 q^{35} +24.4499 q^{36} -2.00336 q^{37} +2.33180 q^{38} +8.74057 q^{39} -2.77352 q^{40} +2.15390 q^{41} -0.0149464 q^{42} +4.53692 q^{43} -13.9446 q^{44} +5.88663 q^{45} -3.81647 q^{46} -1.81610 q^{47} -2.99019 q^{48} -7.00000 q^{49} +10.0620 q^{50} +13.7957 q^{51} -9.44734 q^{52} -9.98836 q^{53} +30.5008 q^{54} -3.35735 q^{55} +0.00675511 q^{56} +3.18012 q^{57} -20.8408 q^{58} +1.65878 q^{59} -9.04608 q^{60} -5.47696 q^{61} -18.7366 q^{62} -0.0143373 q^{63} -12.3976 q^{64} -2.27457 q^{65} -30.0835 q^{66} +10.1927 q^{67} -14.9113 q^{68} -5.20493 q^{69} +0.00388954 q^{70} +10.4802 q^{71} -23.8392 q^{72} -0.992383 q^{73} +4.67142 q^{74} +13.7226 q^{75} -3.43727 q^{76} +0.00817707 q^{77} -20.3812 q^{78} -0.206703 q^{79} +0.778143 q^{80} +20.2577 q^{81} -5.02245 q^{82} -5.35096 q^{83} +0.0220324 q^{84} -3.59008 q^{85} -10.5792 q^{86} -28.4228 q^{87} +13.5963 q^{88} +8.77864 q^{89} -13.7264 q^{90} +0.00553988 q^{91} +5.62580 q^{92} -25.5531 q^{93} +4.23478 q^{94} -0.827568 q^{95} -14.3433 q^{96} -7.70688 q^{97} +16.3226 q^{98} -28.8574 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 99 q - 4 q^{2} - 3 q^{3} + 80 q^{4} - 15 q^{5} - 12 q^{6} - 19 q^{7} - 12 q^{8} + 58 q^{9}+O(q^{10}) \) 99 * q - 4 * q^2 - 3 * q^3 + 80 * q^4 - 15 * q^5 - 12 * q^6 - 19 * q^7 - 12 * q^8 + 58 * q^9	\( 99 q - 4 q^{2} - 3 q^{3} + 80 q^{4} - 15 q^{5} - 12 q^{6} - 19 q^{7} - 12 q^{8} + 58 q^{9} - 6 q^{10} - 9 q^{11} - 27 q^{12} - 28 q^{13} - 13 q^{14} - 10 q^{15} + 38 q^{16} - 36 q^{17} - 14 q^{18} - 99 q^{19} - 34 q^{20} - 20 q^{21} - 53 q^{22} - 38 q^{23} - 25 q^{24} - 8 q^{25} - 3 q^{26} - 3 q^{27} - 63 q^{28} - 34 q^{29} - 30 q^{30} - 16 q^{31} - 43 q^{32} - 41 q^{33} - 14 q^{34} - 25 q^{35} - 16 q^{36} - 80 q^{37} + 4 q^{38} - 48 q^{39} - 10 q^{40} - 32 q^{41} - 37 q^{42} - 76 q^{43} - 21 q^{44} - 53 q^{45} - 23 q^{46} - 31 q^{47} - 74 q^{48} - 32 q^{49} - 29 q^{50} - 30 q^{51} - 71 q^{52} - 35 q^{53} - 80 q^{54} - 45 q^{55} - 33 q^{56} + 3 q^{57} - 91 q^{58} + 12 q^{59} - 56 q^{60} - 61 q^{61} - 46 q^{62} - 43 q^{63} - 30 q^{64} - 46 q^{65} - 75 q^{66} - 26 q^{67} - 55 q^{68} - 45 q^{69} - 76 q^{70} - 41 q^{71} - 77 q^{72} - 143 q^{73} - 64 q^{74} - 8 q^{75} - 80 q^{76} - 58 q^{77} - 34 q^{78} - 22 q^{79} - 36 q^{80} - 81 q^{81} - 109 q^{82} - 7 q^{83} - 6 q^{84} - 80 q^{85} + 32 q^{86} - 57 q^{87} - 120 q^{88} - 28 q^{89} - 12 q^{90} - 30 q^{91} - 107 q^{92} - 121 q^{93} + 8 q^{94} + 15 q^{95} + 4 q^{96} - 128 q^{97} + 54 q^{98} - 34 q^{99}+O(q^{100}) \) 99 * q - 4 * q^2 - 3 * q^3 + 80 * q^4 - 15 * q^5 - 12 * q^6 - 19 * q^7 - 12 * q^8 + 58 * q^9 - 6 * q^10 - 9 * q^11 - 27 * q^12 - 28 * q^13 - 13 * q^14 - 10 * q^15 + 38 * q^16 - 36 * q^17 - 14 * q^18 - 99 * q^19 - 34 * q^20 - 20 * q^21 - 53 * q^22 - 38 * q^23 - 25 * q^24 - 8 * q^25 - 3 * q^26 - 3 * q^27 - 63 * q^28 - 34 * q^29 - 30 * q^30 - 16 * q^31 - 43 * q^32 - 41 * q^33 - 14 * q^34 - 25 * q^35 - 16 * q^36 - 80 * q^37 + 4 * q^38 - 48 * q^39 - 10 * q^40 - 32 * q^41 - 37 * q^42 - 76 * q^43 - 21 * q^44 - 53 * q^45 - 23 * q^46 - 31 * q^47 - 74 * q^48 - 32 * q^49 - 29 * q^50 - 30 * q^51 - 71 * q^52 - 35 * q^53 - 80 * q^54 - 45 * q^55 - 33 * q^56 + 3 * q^57 - 91 * q^58 + 12 * q^59 - 56 * q^60 - 61 * q^61 - 46 * q^62 - 43 * q^63 - 30 * q^64 - 46 * q^65 - 75 * q^66 - 26 * q^67 - 55 * q^68 - 45 * q^69 - 76 * q^70 - 41 * q^71 - 77 * q^72 - 143 * q^73 - 64 * q^74 - 8 * q^75 - 80 * q^76 - 58 * q^77 - 34 * q^78 - 22 * q^79 - 36 * q^80 - 81 * q^81 - 109 * q^82 - 7 * q^83 - 6 * q^84 - 80 * q^85 + 32 * q^86 - 57 * q^87 - 120 * q^88 - 28 * q^89 - 12 * q^90 - 30 * q^91 - 107 * q^92 - 121 * q^93 + 8 * q^94 + 15 * q^95 + 4 * q^96 - 128 * q^97 + 54 * q^98 - 34 * q^99

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