LMFDB - Embedded newform 6023.2.a.c.1.17

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:	$0$
Dimension:	$138$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
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)

$f(q)$	$=$	$q-2.24651 q^{2} -2.33680 q^{3} +3.04682 q^{4} +3.03120 q^{5} +5.24966 q^{6} -0.990135 q^{7} -2.35169 q^{8} +2.46065 q^{9} +O(q^{10})$	\(q-2.24651 q^{2} -2.33680 q^{3} +3.04682 q^{4} +3.03120 q^{5} +5.24966 q^{6} -0.990135 q^{7} -2.35169 q^{8} +2.46065 q^{9} -6.80962 q^{10} -4.71761 q^{11} -7.11982 q^{12} +0.982347 q^{13} +2.22435 q^{14} -7.08331 q^{15} -0.810536 q^{16} +1.95999 q^{17} -5.52789 q^{18} +1.00000 q^{19} +9.23550 q^{20} +2.31375 q^{21} +10.5982 q^{22} -7.14721 q^{23} +5.49544 q^{24} +4.18814 q^{25} -2.20685 q^{26} +1.26035 q^{27} -3.01676 q^{28} +4.75205 q^{29} +15.9127 q^{30} -9.35401 q^{31} +6.52426 q^{32} +11.0241 q^{33} -4.40314 q^{34} -3.00129 q^{35} +7.49716 q^{36} -10.7647 q^{37} -2.24651 q^{38} -2.29555 q^{39} -7.12843 q^{40} -7.04437 q^{41} -5.19787 q^{42} -5.79369 q^{43} -14.3737 q^{44} +7.45872 q^{45} +16.0563 q^{46} -5.58364 q^{47} +1.89406 q^{48} -6.01963 q^{49} -9.40872 q^{50} -4.58012 q^{51} +2.99303 q^{52} +1.96479 q^{53} -2.83139 q^{54} -14.3000 q^{55} +2.32849 q^{56} -2.33680 q^{57} -10.6755 q^{58} +6.40016 q^{59} -21.5816 q^{60} +13.2076 q^{61} +21.0139 q^{62} -2.43638 q^{63} -13.0358 q^{64} +2.97768 q^{65} -24.7658 q^{66} +11.2308 q^{67} +5.97174 q^{68} +16.7016 q^{69} +6.74244 q^{70} -6.38919 q^{71} -5.78669 q^{72} +4.18724 q^{73} +24.1830 q^{74} -9.78687 q^{75} +3.04682 q^{76} +4.67107 q^{77} +5.15698 q^{78} -4.55325 q^{79} -2.45689 q^{80} -10.3271 q^{81} +15.8253 q^{82} -9.02474 q^{83} +7.04958 q^{84} +5.94112 q^{85} +13.0156 q^{86} -11.1046 q^{87} +11.0943 q^{88} -14.5015 q^{89} -16.7561 q^{90} -0.972656 q^{91} -21.7763 q^{92} +21.8585 q^{93} +12.5437 q^{94} +3.03120 q^{95} -15.2459 q^{96} +0.636067 q^{97} +13.5232 q^{98} -11.6084 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 138 q + 11 q^{2} + 29 q^{3} + 157 q^{4} + 12 q^{5} + 8 q^{6} + 18 q^{7} + 33 q^{8} + 171 q^{9}+O(q^{10}) $ 138 * q + 11 * q^2 + 29 * q^3 + 157 * q^4 + 12 * q^5 + 8 * q^6 + 18 * q^7 + 33 * q^8 + 171 * q^9	\( 138 q + 11 q^{2} + 29 q^{3} + 157 q^{4} + 12 q^{5} + 8 q^{6} + 18 q^{7} + 33 q^{8} + 171 q^{9} + 40 q^{10} + 4 q^{11} + 69 q^{12} + 72 q^{13} + 3 q^{14} + 30 q^{15} + 191 q^{16} + 31 q^{17} + 31 q^{18} + 138 q^{19} + 16 q^{20} + 16 q^{21} + 95 q^{22} + 34 q^{23} + 3 q^{24} + 244 q^{25} - 13 q^{26} + 107 q^{27} + 43 q^{28} + 30 q^{29} - 14 q^{30} + 60 q^{31} + 62 q^{32} + 77 q^{33} + 36 q^{34} + 2 q^{35} + 205 q^{36} + 142 q^{37} + 11 q^{38} + 20 q^{39} + 76 q^{40} + 46 q^{41} - 21 q^{42} + 69 q^{43} - 7 q^{44} + 30 q^{45} + 39 q^{46} + 8 q^{47} + 116 q^{48} + 236 q^{49} + 34 q^{51} + 165 q^{52} + 49 q^{53} + 6 q^{55} - 33 q^{56} + 29 q^{57} + 75 q^{58} + 8 q^{59} - 24 q^{60} + 38 q^{61} - 10 q^{62} + 2 q^{63} + 251 q^{64} + 72 q^{65} - 15 q^{66} + 158 q^{67} - 19 q^{68} + 33 q^{69} + 48 q^{70} + 23 q^{71} + 88 q^{72} + 134 q^{73} + 4 q^{74} + 118 q^{75} + 157 q^{76} + 13 q^{77} + 12 q^{78} + 78 q^{79} - 48 q^{80} + 254 q^{81} + 89 q^{82} - 27 q^{83} - 15 q^{84} + 37 q^{85} + 66 q^{86} + 43 q^{87} + 224 q^{88} + 26 q^{89} + 38 q^{90} + 108 q^{91} + 113 q^{92} + 83 q^{93} + 48 q^{94} + 12 q^{95} + 40 q^{96} + 254 q^{97} + 47 q^{98} + 11 q^{99}+O(q^{100}) \) 138 * q + 11 * q^2 + 29 * q^3 + 157 * q^4 + 12 * q^5 + 8 * q^6 + 18 * q^7 + 33 * q^8 + 171 * q^9 + 40 * q^10 + 4 * q^11 + 69 * q^12 + 72 * q^13 + 3 * q^14 + 30 * q^15 + 191 * q^16 + 31 * q^17 + 31 * q^18 + 138 * q^19 + 16 * q^20 + 16 * q^21 + 95 * q^22 + 34 * q^23 + 3 * q^24 + 244 * q^25 - 13 * q^26 + 107 * q^27 + 43 * q^28 + 30 * q^29 - 14 * q^30 + 60 * q^31 + 62 * q^32 + 77 * q^33 + 36 * q^34 + 2 * q^35 + 205 * q^36 + 142 * q^37 + 11 * q^38 + 20 * q^39 + 76 * q^40 + 46 * q^41 - 21 * q^42 + 69 * q^43 - 7 * q^44 + 30 * q^45 + 39 * q^46 + 8 * q^47 + 116 * q^48 + 236 * q^49 + 34 * q^51 + 165 * q^52 + 49 * q^53 + 6 * q^55 - 33 * q^56 + 29 * q^57 + 75 * q^58 + 8 * q^59 - 24 * q^60 + 38 * q^61 - 10 * q^62 + 2 * q^63 + 251 * q^64 + 72 * q^65 - 15 * q^66 + 158 * q^67 - 19 * q^68 + 33 * q^69 + 48 * q^70 + 23 * q^71 + 88 * q^72 + 134 * q^73 + 4 * q^74 + 118 * q^75 + 157 * q^76 + 13 * q^77 + 12 * q^78 + 78 * q^79 - 48 * q^80 + 254 * q^81 + 89 * q^82 - 27 * q^83 - 15 * q^84 + 37 * q^85 + 66 * q^86 + 43 * q^87 + 224 * q^88 + 26 * q^89 + 38 * q^90 + 108 * q^91 + 113 * q^92 + 83 * q^93 + 48 * q^94 + 12 * q^95 + 40 * q^96 + 254 * q^97 + 47 * q^98 + 11 * 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 $

$2$	−2.24651	−1.58852	−0.794262	−	0.607575i	$-0.792142\pi$
$2$	−2.24651	−1.58852	−0.794262	+	0.607575i	$0.792142\pi$
$3$	−2.33680	−1.34915	−0.674577	−	0.738204i	$-0.735674\pi$
$3$	−2.33680	−1.34915	−0.674577	+	0.738204i	$0.735674\pi$
$4$	3.04682	1.52341
$5$	3.03120	1.35559	0.677796	−	0.735250i	$-0.262935\pi$
$5$	3.03120	1.35559	0.677796	+	0.735250i	$0.262935\pi$
$6$	5.24966	2.14316
$7$	−0.990135	−0.374236	−0.187118	−	0.982337i	$-0.559915\pi$
$7$	−0.990135	−0.374236	−0.187118	+	0.982337i	$0.559915\pi$
$8$	−2.35169	−0.831448
$9$	2.46065	0.820218
$10$	−6.80962	−2.15339
$11$	−4.71761	−1.42241	−0.711206	−	0.702984i	$-0.751851\pi$
$11$	−4.71761	−1.42241	−0.711206	+	0.702984i	$0.751851\pi$
$12$	−7.11982	−2.05531
$13$	0.982347	0.272454	0.136227	−	0.990678i	$-0.456502\pi$
$13$	0.982347	0.272454	0.136227	+	0.990678i	$0.456502\pi$
$14$	2.22435	0.594483
$15$	−7.08331	−1.82890
$16$	−0.810536	−0.202634
$17$	1.95999	0.475368	0.237684	−	0.971343i	$-0.423612\pi$
$17$	1.95999	0.475368	0.237684	+	0.971343i	$0.423612\pi$
$18$	−5.52789	−1.30294
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	9.23550	2.06512
$21$	2.31375	0.504902
$22$	10.5982	2.25954
$23$	−7.14721	−1.49030	−0.745149	−	0.666898i	$-0.767621\pi$
$23$	−7.14721	−1.49030	−0.745149	+	0.666898i	$0.767621\pi$
$24$	5.49544	1.12175
$25$	4.18814	0.837629
$26$	−2.20685	−0.432800
$27$	1.26035	0.242554
$28$	−3.01676	−0.570114
$29$	4.75205	0.882433	0.441216	−	0.897401i	$-0.354547\pi$
$29$	4.75205	0.882433	0.441216	+	0.897401i	$0.354547\pi$
$30$	15.9127	2.90526
$31$	−9.35401	−1.68003	−0.840015	−	0.542563i	$-0.817454\pi$
$31$	−9.35401	−1.68003	−0.840015	+	0.542563i	$0.817454\pi$
$32$	6.52426	1.15334
$33$	11.0241	1.91905
$34$	−4.40314	−0.755133
$35$	−3.00129	−0.507311
$36$	7.49716	1.24953
$37$	−10.7647	−1.76970	−0.884851	−	0.465873i	$-0.845740\pi$
$37$	−10.7647	−1.76970	−0.884851	+	0.465873i	$0.845740\pi$
$38$	−2.24651	−0.364432
$39$	−2.29555	−0.367582
$40$	−7.12843	−1.12710
$41$	−7.04437	−1.10015	−0.550073	−	0.835116i	$-0.685400\pi$
$41$	−7.04437	−1.10015	−0.550073	+	0.835116i	$0.685400\pi$
$42$	−5.19787	−0.802049
$43$	−5.79369	−0.883529	−0.441765	−	0.897131i	$-0.645647\pi$
$43$	−5.79369	−0.883529	−0.441765	+	0.897131i	$0.645647\pi$
$44$	−14.3737	−2.16692
$45$	7.45872	1.11188
$46$	16.0563	2.36737
$47$	−5.58364	−0.814457	−0.407229	−	0.913326i	$-0.633505\pi$
$47$	−5.58364	−0.814457	−0.407229	+	0.913326i	$0.633505\pi$
$48$	1.89406	0.273385
$49$	−6.01963	−0.859948
$50$	−9.40872	−1.33059
$51$	−4.58012	−0.641344
$52$	2.99303	0.415059
$53$	1.96479	0.269884	0.134942	−	0.990853i	$-0.456915\pi$
$53$	1.96479	0.269884	0.134942	+	0.990853i	$0.456915\pi$
$54$	−2.83139	−0.385303
$55$	−14.3000	−1.92821
$56$	2.32849	0.311158
$57$	−2.33680	−0.309517
$58$	−10.6755	−1.40177
$59$	6.40016	0.833230	0.416615	−	0.909083i	$-0.363216\pi$
$59$	6.40016	0.833230	0.416615	+	0.909083i	$0.363216\pi$
$60$	−21.5816	−2.78617
$61$	13.2076	1.69106	0.845528	−	0.533931i	$-0.179286\pi$
$61$	13.2076	1.69106	0.845528	+	0.533931i	$0.179286\pi$
$62$	21.0139	2.66877
$63$	−2.43638	−0.306955
$64$	−13.0358	−1.62947
$65$	2.97768	0.369336
$66$	−24.7658	−3.04846
$67$	11.2308	1.37206	0.686030	−	0.727573i	$-0.259352\pi$
$67$	11.2308	1.37206	0.686030	+	0.727573i	$0.259352\pi$
$68$	5.97174	0.724179
$69$	16.7016	2.01064
$70$	6.74244	0.805876
$71$	−6.38919	−0.758257	−0.379129	−	0.925344i	$-0.623776\pi$
$71$	−6.38919	−0.758257	−0.379129	+	0.925344i	$0.623776\pi$
$72$	−5.78669	−0.681968
$73$	4.18724	0.490079	0.245040	−	0.969513i	$-0.421199\pi$
$73$	4.18724	0.490079	0.245040	+	0.969513i	$0.421199\pi$
$74$	24.1830	2.81122
$75$	−9.78687	−1.13009
$76$	3.04682	0.349494
$77$	4.67107	0.532318
$78$	5.15698	0.583914
$79$	−4.55325	−0.512281	−0.256140	−	0.966640i	$-0.582451\pi$
$79$	−4.55325	−0.512281	−0.256140	+	0.966640i	$0.582451\pi$
$80$	−2.45689	−0.274689
$81$	−10.3271	−1.14746
$82$	15.8253	1.74761
$83$	−9.02474	−0.990594	−0.495297	−	0.868724i	$-0.664941\pi$
$83$	−9.02474	−0.990594	−0.495297	+	0.868724i	$0.664941\pi$
$84$	7.04958	0.769172
$85$	5.94112	0.644405
$86$	13.0156	1.40351
$87$	−11.1046	−1.19054
$88$	11.0943	1.18266
$89$	−14.5015	−1.53716	−0.768579	−	0.639755i	$-0.779036\pi$
$89$	−14.5015	−1.53716	−0.768579	+	0.639755i	$0.779036\pi$
$90$	−16.7561	−1.76625
$91$	−0.972656	−0.101962
$92$	−21.7763	−2.27033
$93$	21.8585	2.26662
$94$	12.5437	1.29378
$95$	3.03120	0.310994
$96$	−15.2459	−1.55603
$97$	0.636067	0.0645828	0.0322914	−	0.999478i	$-0.489720\pi$
$97$	0.636067	0.0645828	0.0322914	+	0.999478i	$0.489720\pi$
$98$	13.5232	1.36605
$99$	−11.6084	−1.16669
$100$	12.7605	1.27605
$101$	18.0618	1.79721	0.898607	−	0.438755i	$-0.144581\pi$
$101$	18.0618	1.79721	0.898607	+	0.438755i	$0.144581\pi$
$102$	10.2893	1.01879
$103$	10.9746	1.08136	0.540681	−	0.841228i	$-0.318167\pi$
$103$	10.9746	1.08136	0.540681	+	0.841228i	$0.318167\pi$
$104$	−2.31017	−0.226531
$105$	7.01343	0.684441
$106$	−4.41392	−0.428718
$107$	20.0448	1.93781	0.968903	−	0.247442i	$-0.0795901\pi$
$107$	20.0448	1.93781	0.968903	+	0.247442i	$0.0795901\pi$
$108$	3.84005	0.369509
$109$	16.6461	1.59441	0.797206	−	0.603708i	$-0.206311\pi$
$109$	16.6461	1.59441	0.797206	+	0.603708i	$0.206311\pi$
$110$	32.1251	3.06301
$111$	25.1550	2.38760
$112$	0.802540	0.0758329
$113$	−6.70393	−0.630653	−0.315326	−	0.948983i	$-0.602114\pi$
$113$	−6.70393	−0.630653	−0.315326	+	0.948983i	$0.602114\pi$
$114$	5.24966	0.491676
$115$	−21.6646	−2.02023
$116$	14.4786	1.34431
$117$	2.41721	0.223472
$118$	−14.3780	−1.32361
$119$	−1.94066	−0.177900
$120$	16.6577	1.52064
$121$	11.2558	1.02326
$122$	−29.6710	−2.68628
$123$	16.4613	1.48427
$124$	−28.5000	−2.55937
$125$	−2.46089	−0.220109
$126$	5.47335	0.487605
$127$	15.8629	1.40761	0.703803	−	0.710396i	$-0.251484\pi$
$127$	15.8629	1.40761	0.703803	+	0.710396i	$0.251484\pi$
$128$	16.2365	1.43511
$129$	13.5387	1.19202
$130$	−6.68940	−0.586700
$131$	−0.984306	−0.0859993	−0.0429996	−	0.999075i	$-0.513691\pi$
$131$	−0.984306	−0.0859993	−0.0429996	+	0.999075i	$0.513691\pi$
$132$	33.5885	2.92350
$133$	−0.990135	−0.0858556
$134$	−25.2301	−2.17955
$135$	3.82036	0.328804
$136$	−4.60929	−0.395243
$137$	−9.80107	−0.837362	−0.418681	−	0.908133i	$-0.637507\pi$
$137$	−9.80107	−0.837362	−0.418681	+	0.908133i	$0.637507\pi$
$138$	−37.5204	−3.19395
$139$	−1.48104	−0.125620	−0.0628099	−	0.998026i	$-0.520006\pi$
$139$	−1.48104	−0.125620	−0.0628099	+	0.998026i	$0.520006\pi$
$140$	−9.14439	−0.772842
$141$	13.0479	1.09883
$142$	14.3534	1.20451
$143$	−4.63433	−0.387542
$144$	−1.99445	−0.166204
$145$	14.4044	1.19622
$146$	−9.40669	−0.778503
$147$	14.0667	1.16020
$148$	−32.7980	−2.69598
$149$	9.30290	0.762123	0.381062	−	0.924550i	$-0.375559\pi$
$149$	9.30290	0.762123	0.381062	+	0.924550i	$0.375559\pi$
$150$	21.9863	1.79518
$151$	−5.24037	−0.426456	−0.213228	−	0.977003i	$-0.568398\pi$
$151$	−5.24037	−0.426456	−0.213228	+	0.977003i	$0.568398\pi$
$152$	−2.35169	−0.190747
$153$	4.82286	0.389905
$154$	−10.4936	−0.845599
$155$	−28.3538	−2.27743
$156$	−6.99413	−0.559978
$157$	−6.98762	−0.557673	−0.278836	−	0.960339i	$-0.589949\pi$
$157$	−6.98762	−0.557673	−0.278836	+	0.960339i	$0.589949\pi$
$158$	10.2289	0.813770
$159$	−4.59132	−0.364116
$160$	19.7763	1.56345
$161$	7.07671	0.557723
$162$	23.2001	1.82277
$163$	−14.9708	−1.17260	−0.586300	−	0.810094i	$-0.699416\pi$
$163$	−14.9708	−1.17260	−0.586300	+	0.810094i	$0.699416\pi$
$164$	−21.4629	−1.67597
$165$	33.4163	2.60145
$166$	20.2742	1.57358
$167$	−0.920748	−0.0712496	−0.0356248	−	0.999365i	$-0.511342\pi$
$167$	−0.920748	−0.0712496	−0.0356248	+	0.999365i	$0.511342\pi$
$168$	−5.44123	−0.419800
$169$	−12.0350	−0.925769
$170$	−13.3468	−1.02365
$171$	2.46065	0.188171
$172$	−17.6523	−1.34598
$173$	20.2945	1.54296	0.771481	−	0.636252i	$-0.219516\pi$
$173$	20.2945	1.54296	0.771481	+	0.636252i	$0.219516\pi$
$174$	24.9466	1.89120
$175$	−4.14683	−0.313471
$176$	3.82379	0.288229
$177$	−14.9559	−1.12416
$178$	32.5778	2.44181
$179$	−21.7633	−1.62666	−0.813332	−	0.581799i	$-0.802349\pi$
$179$	−21.7633	−1.62666	−0.813332	+	0.581799i	$0.802349\pi$
$180$	22.7254	1.69385
$181$	20.3646	1.51369	0.756845	−	0.653594i	$-0.226740\pi$
$181$	20.3646	1.51369	0.756845	+	0.653594i	$0.226740\pi$
$182$	2.18508	0.161969
$183$	−30.8635	−2.28150
$184$	16.8080	1.23910
$185$	−32.6299	−2.39899
$186$	−49.1054	−3.60058
$187$	−9.24647	−0.676169
$188$	−17.0123	−1.24075
$189$	−1.24791	−0.0907724
$190$	−6.80962	−0.494022
$191$	−1.88675	−0.136520	−0.0682601	−	0.997668i	$-0.521745\pi$
$191$	−1.88675	−0.136520	−0.0682601	+	0.997668i	$0.521745\pi$
$192$	30.4620	2.19841
$193$	−10.4251	−0.750415	−0.375207	−	0.926941i	$-0.622428\pi$
$193$	−10.4251	−0.750415	−0.375207	+	0.926941i	$0.622428\pi$
$194$	−1.42893	−0.102591
$195$	−6.95826	−0.498292
$196$	−18.3407	−1.31005
$197$	4.85938	0.346217	0.173108	−	0.984903i	$-0.444619\pi$
$197$	4.85938	0.346217	0.173108	+	0.984903i	$0.444619\pi$
$198$	26.0784	1.85331
$199$	7.32918	0.519552	0.259776	−	0.965669i	$-0.416351\pi$
$199$	7.32918	0.519552	0.259776	+	0.965669i	$0.416351\pi$
$200$	−9.84922	−0.696445
$201$	−26.2442	−1.85112
$202$	−40.5760	−2.85492
$203$	−4.70517	−0.330238
$204$	−13.9548	−0.977030
$205$	−21.3529	−1.49135
$206$	−24.6546	−1.71777
$207$	−17.5868	−1.22237
$208$	−0.796227	−0.0552084
$209$	−4.71761	−0.326324
$210$	−15.7558	−1.08725
$211$	1.68065	0.115701	0.0578503	−	0.998325i	$-0.481575\pi$
$211$	1.68065	0.115701	0.0578503	+	0.998325i	$0.481575\pi$
$212$	5.98635	0.411144
$213$	14.9303	1.02301
$214$	−45.0309	−3.07825
$215$	−17.5618	−1.19771
$216$	−2.96395	−0.201671
$217$	9.26173	0.628727
$218$	−37.3958	−2.53276
$219$	−9.78476	−0.661193
$220$	−43.5695	−2.93745
$221$	1.92539	0.129516
$222$	−56.5109	−3.79276
$223$	7.20359	0.482388	0.241194	−	0.970477i	$-0.422461\pi$
$223$	7.20359	0.482388	0.241194	+	0.970477i	$0.422461\pi$
$224$	−6.45990	−0.431620
$225$	10.3056	0.687038
$226$	15.0605	1.00181
$227$	26.9962	1.79180	0.895901	−	0.444255i	$-0.146531\pi$
$227$	26.9962	1.79180	0.895901	+	0.444255i	$0.146531\pi$
$228$	−7.11982	−0.471521
$229$	−19.5521	−1.29204	−0.646019	−	0.763321i	$-0.723567\pi$
$229$	−19.5521	−1.29204	−0.646019	+	0.763321i	$0.723567\pi$
$230$	48.6698	3.20919
$231$	−10.9154	−0.718179
$232$	−11.1753	−0.733697
$233$	−5.06179	−0.331609	−0.165805	−	0.986159i	$-0.553022\pi$
$233$	−5.06179	−0.331609	−0.165805	+	0.986159i	$0.553022\pi$
$234$	−5.43030	−0.354990
$235$	−16.9251	−1.10407
$236$	19.5001	1.26935
$237$	10.6401	0.691146
$238$	4.35971	0.282598
$239$	−7.81353	−0.505415	−0.252708	−	0.967543i	$-0.581321\pi$
$239$	−7.81353	−0.505415	−0.252708	+	0.967543i	$0.581321\pi$
$240$	5.74128	0.370598
$241$	−7.68831	−0.495248	−0.247624	−	0.968856i	$-0.579650\pi$
$241$	−7.68831	−0.495248	−0.247624	+	0.968856i	$0.579650\pi$
$242$	−25.2863	−1.62547
$243$	20.3515	1.30555
$244$	40.2411	2.57617
$245$	−18.2467	−1.16574
$246$	−36.9806	−2.35779
$247$	0.982347	0.0625052
$248$	21.9977	1.39686
$249$	21.0891	1.33646
$250$	5.52843	0.349649
$251$	12.0524	0.760741	0.380370	−	0.924834i	$-0.375797\pi$
$251$	12.0524	0.760741	0.380370	+	0.924834i	$0.375797\pi$
$252$	−7.42320	−0.467618
$253$	33.7177	2.11982
$254$	−35.6362	−2.23601
$255$	−13.8832	−0.869401
$256$	−10.4039	−0.650245
$257$	1.62358	0.101276	0.0506379	−	0.998717i	$-0.483875\pi$
$257$	1.62358	0.101276	0.0506379	+	0.998717i	$0.483875\pi$
$258$	−30.4149	−1.89355
$259$	10.6585	0.662286
$260$	9.07246	0.562650
$261$	11.6931	0.723787
$262$	2.21126	0.136612
$263$	−3.59961	−0.221961	−0.110981	−	0.993823i	$-0.535399\pi$
$263$	−3.59961	−0.221961	−0.110981	+	0.993823i	$0.535399\pi$
$264$	−25.9253	−1.59559
$265$	5.95566	0.365853
$266$	2.22435	0.136384
$267$	33.8872	2.07386
$268$	34.2182	2.09021
$269$	12.3974	0.755882	0.377941	−	0.925830i	$-0.376632\pi$
$269$	12.3974	0.755882	0.377941	+	0.925830i	$0.376632\pi$
$270$	−8.58249	−0.522313
$271$	−20.7277	−1.25912	−0.629558	−	0.776953i	$-0.716764\pi$
$271$	−20.7277	−1.25912	−0.629558	+	0.776953i	$0.716764\pi$
$272$	−1.58864	−0.0963256
$273$	2.27291	0.137563
$274$	22.0182	1.33017
$275$	−19.7580	−1.19145
$276$	50.8869	3.06303
$277$	16.4598	0.988973	0.494486	−	0.869185i	$-0.335356\pi$
$277$	16.4598	0.988973	0.494486	+	0.869185i	$0.335356\pi$
$278$	3.32717	0.199550
$279$	−23.0170	−1.37799
$280$	7.05811	0.421803
$281$	−23.7608	−1.41745	−0.708725	−	0.705485i	$-0.750729\pi$
$281$	−23.7608	−1.41745	−0.708725	+	0.705485i	$0.750729\pi$
$282$	−29.3122	−1.74552
$283$	−27.1330	−1.61289	−0.806444	−	0.591310i	$-0.798611\pi$
$283$	−27.1330	−1.61289	−0.806444	+	0.591310i	$0.798611\pi$
$284$	−19.4667	−1.15514
$285$	−7.08331	−0.419579
$286$	10.4111	0.615619
$287$	6.97488	0.411714
$288$	16.0539	0.945987
$289$	−13.1584	−0.774026
$290$	−32.3596	−1.90022
$291$	−1.48636	−0.0871321
$292$	12.7578	0.746591
$293$	10.4635	0.611287	0.305644	−	0.952146i	$-0.401128\pi$
$293$	10.4635	0.611287	0.305644	+	0.952146i	$0.401128\pi$
$294$	−31.6010	−1.84301
$295$	19.4001	1.12952
$296$	25.3152	1.47142
$297$	−5.94583	−0.345012
$298$	−20.8991	−1.21065
$299$	−7.02104	−0.406037
$300$	−29.8188	−1.72159
$301$	5.73653	0.330648
$302$	11.7726	0.677435
$303$	−42.2068	−2.42472
$304$	−0.810536	−0.0464874
$305$	40.0347	2.29238
$306$	−10.8346	−0.619374
$307$	21.2390	1.21217	0.606087	−	0.795398i	$-0.292738\pi$
$307$	21.2390	1.21217	0.606087	+	0.795398i	$0.292738\pi$
$308$	14.2319	0.810937
$309$	−25.6455	−1.45892
$310$	63.6972	3.61776
$311$	−8.08881	−0.458674	−0.229337	−	0.973347i	$-0.573656\pi$
$311$	−8.08881	−0.458674	−0.229337	+	0.973347i	$0.573656\pi$
$312$	5.39842	0.305626
$313$	25.2086	1.42487	0.712436	−	0.701737i	$-0.247592\pi$
$313$	25.2086	1.42487	0.712436	+	0.701737i	$0.247592\pi$
$314$	15.6978	0.885877
$315$	−7.38514	−0.416105
$316$	−13.8729	−0.780413
$317$	−1.00000	−0.0561656
$317$	−1.00000	−0.0561656
$318$	10.3145	0.578407
$319$	−22.4183	−1.25518
$320$	−39.5139	−2.20890
$321$	−46.8408	−2.61440
$322$	−15.8979	−0.885956
$323$	1.95999	0.109057
$324$	−31.4649	−1.74805
$325$	4.11421	0.228215
$326$	33.6320	1.86270
$327$	−38.8988	−2.15111
$328$	16.5662	0.914714
$329$	5.52855	0.304799
$330$	−75.0701	−4.13247
$331$	−9.98492	−0.548821	−0.274410	−	0.961613i	$-0.588483\pi$
$331$	−9.98492	−0.548821	−0.274410	+	0.961613i	$0.588483\pi$
$332$	−27.4968	−1.50908
$333$	−26.4882	−1.45154
$334$	2.06847	0.113182
$335$	34.0428	1.85995
$336$	−1.87538	−0.102310
$337$	35.6075	1.93966	0.969832	−	0.243772i	$-0.0783850\pi$
$337$	35.6075	1.93966	0.969832	+	0.243772i	$0.0783850\pi$
$338$	27.0368	1.47061
$339$	15.6658	0.850848
$340$	18.1015	0.981692
$341$	44.1286	2.38970
$342$	−5.52789	−0.298914
$343$	12.8912	0.696059
$344$	13.6250	0.734609
$345$	50.6259	2.72561
$346$	−45.5918	−2.45103
$347$	16.7055	0.896801	0.448400	−	0.893833i	$-0.351994\pi$
$347$	16.7055	0.896801	0.448400	+	0.893833i	$0.351994\pi$
$348$	−33.8337	−1.81368
$349$	12.3832	0.662856	0.331428	−	0.943481i	$-0.392470\pi$
$349$	12.3832	0.662856	0.331428	+	0.943481i	$0.392470\pi$
$350$	9.31590	0.497956
$351$	1.23810	0.0660848
$352$	−30.7789	−1.64052
$353$	−18.9665	−1.00948	−0.504742	−	0.863270i	$-0.668412\pi$
$353$	−18.9665	−1.00948	−0.504742	+	0.863270i	$0.668412\pi$
$354$	33.5987	1.78575
$355$	−19.3669	−1.02789
$356$	−44.1835	−2.34172
$357$	4.53493	0.240014
$358$	48.8915	2.58400
$359$	−1.90194	−0.100380	−0.0501902	−	0.998740i	$-0.515983\pi$
$359$	−1.90194	−0.100380	−0.0501902	+	0.998740i	$0.515983\pi$
$360$	−17.5406	−0.924471
$361$	1.00000	0.0526316
$362$	−45.7494	−2.40453
$363$	−26.3026	−1.38053
$364$	−2.96350	−0.155330
$365$	12.6923	0.664348
$366$	69.3353	3.62421
$367$	26.7059	1.39404	0.697018	−	0.717053i	$-0.254510\pi$
$367$	26.7059	1.39404	0.697018	+	0.717053i	$0.254510\pi$
$368$	5.79307	0.301985
$369$	−17.3338	−0.902360
$370$	73.3034	3.81086
$371$	−1.94541	−0.101000
$372$	66.5989	3.45299
$373$	−12.0084	−0.621770	−0.310885	−	0.950448i	$-0.600625\pi$
$373$	−12.0084	−0.621770	−0.310885	+	0.950448i	$0.600625\pi$
$374$	20.7723	1.07411
$375$	5.75063	0.296961
$376$	13.1310	0.677179
$377$	4.66816	0.240422
$378$	2.80345	0.144194
$379$	7.11223	0.365331	0.182665	−	0.983175i	$-0.441528\pi$
$379$	7.11223	0.365331	0.182665	+	0.983175i	$0.441528\pi$
$380$	9.23550	0.473771
$381$	−37.0685	−1.89908
$382$	4.23860	0.216865
$383$	0.255783	0.0130699	0.00653496	−	0.999979i	$-0.497920\pi$
$383$	0.255783	0.0130699	0.00653496	+	0.999979i	$0.497920\pi$
$384$	−37.9415	−1.93619
$385$	14.1589	0.721605
$386$	23.4201	1.19205
$387$	−14.2563	−0.724687
$388$	1.93798	0.0983860
$389$	−17.1331	−0.868682	−0.434341	−	0.900749i	$-0.643019\pi$
$389$	−17.1331	−0.868682	−0.434341	+	0.900749i	$0.643019\pi$
$390$	15.6318	0.791548
$391$	−14.0085	−0.708439
$392$	14.1563	0.715002
$393$	2.30013	0.116026
$394$	−10.9167	−0.549974
$395$	−13.8018	−0.694443
$396$	−35.3687	−1.77734
$397$	−24.5938	−1.23433	−0.617163	−	0.786836i	$-0.711718\pi$
$397$	−24.5938	−1.23433	−0.617163	+	0.786836i	$0.711718\pi$
$398$	−16.4651	−0.825320
$399$	2.31375	0.115832
$400$	−3.39464	−0.169732
$401$	−16.7524	−0.836573	−0.418286	−	0.908315i	$-0.637369\pi$
$401$	−16.7524	−0.836573	−0.418286	+	0.908315i	$0.637369\pi$
$402$	58.9579	2.94055
$403$	−9.18888	−0.457731
$404$	55.0309	2.73789
$405$	−31.3036	−1.55549
$406$	10.5702	0.524591
$407$	50.7835	2.51725
$408$	10.7710	0.533245
$409$	−13.2782	−0.656564	−0.328282	−	0.944580i	$-0.606470\pi$
$409$	−13.2782	−0.656564	−0.328282	+	0.944580i	$0.606470\pi$
$410$	47.9695	2.36904
$411$	22.9032	1.12973
$412$	33.4377	1.64736
$413$	−6.33703	−0.311825
$414$	39.5090	1.94176
$415$	−27.3558	−1.34284
$416$	6.40908	0.314231
$417$	3.46089	0.169481
$418$	10.5982	0.518373
$419$	−29.0375	−1.41858	−0.709288	−	0.704919i	$-0.750983\pi$
$419$	−29.0375	−1.41858	−0.709288	+	0.704919i	$0.750983\pi$
$420$	21.3687	1.04268
$421$	11.5283	0.561856	0.280928	−	0.959729i	$-0.409358\pi$
$421$	11.5283	0.561856	0.280928	+	0.959729i	$0.409358\pi$
$422$	−3.77559	−0.183793
$423$	−13.7394	−0.668032
$424$	−4.62057	−0.224395
$425$	8.20873	0.398182
$426$	−33.5411	−1.62507
$427$	−13.0773	−0.632854
$428$	61.0729	2.95207
$429$	10.8295	0.522854
$430$	39.4528	1.90258
$431$	3.13143	0.150836	0.0754179	−	0.997152i	$-0.475971\pi$
$431$	3.13143	0.150836	0.0754179	+	0.997152i	$0.475971\pi$
$432$	−1.02156	−0.0491497
$433$	19.1899	0.922210	0.461105	−	0.887346i	$-0.347453\pi$
$433$	19.1899	0.922210	0.461105	+	0.887346i	$0.347453\pi$
$434$	−20.8066	−0.998749
$435$	−33.6602	−1.61388
$436$	50.7178	2.42894
$437$	−7.14721	−0.341898
$438$	21.9816	1.05032
$439$	24.2367	1.15675	0.578377	−	0.815770i	$-0.303686\pi$
$439$	24.2367	1.15675	0.578377	+	0.815770i	$0.303686\pi$
$440$	33.6291	1.60321
$441$	−14.8122	−0.705344
$442$	−4.32541	−0.205739
$443$	−15.9253	−0.756636	−0.378318	−	0.925676i	$-0.623497\pi$
$443$	−15.9253	−0.756636	−0.378318	+	0.925676i	$0.623497\pi$
$444$	76.6426	3.63730
$445$	−43.9569	−2.08376
$446$	−16.1830	−0.766285
$447$	−21.7391	−1.02822
$448$	12.9072	0.609806
$449$	−23.4097	−1.10477	−0.552387	−	0.833588i	$-0.686283\pi$
$449$	−23.4097	−1.10477	−0.552387	+	0.833588i	$0.686283\pi$
$450$	−23.1516	−1.09138
$451$	33.2326	1.56486
$452$	−20.4257	−0.960742
$453$	12.2457	0.575354
$454$	−60.6473	−2.84632
$455$	−2.94831	−0.138219
$456$	5.49544	0.257347
$457$	25.3983	1.18808	0.594042	−	0.804434i	$-0.297531\pi$
$457$	25.3983	1.18808	0.594042	+	0.804434i	$0.297531\pi$
$458$	43.9240	2.05243
$459$	2.47027	0.115302
$460$	−66.0081	−3.07764
$461$	6.71653	0.312820	0.156410	−	0.987692i	$-0.450008\pi$
$461$	6.71653	0.312820	0.156410	+	0.987692i	$0.450008\pi$
$462$	24.5215	1.14084
$463$	30.3913	1.41240	0.706201	−	0.708011i	$-0.250407\pi$
$463$	30.3913	1.41240	0.706201	+	0.708011i	$0.250407\pi$
$464$	−3.85170	−0.178811
$465$	66.2574	3.07261
$466$	11.3714	0.526769
$467$	36.8354	1.70454	0.852269	−	0.523104i	$-0.175226\pi$
$467$	36.8354	1.70454	0.852269	+	0.523104i	$0.175226\pi$
$468$	7.36481	0.340439
$469$	−11.1200	−0.513474
$470$	38.0224	1.75384
$471$	16.3287	0.752387
$472$	−15.0512	−0.692788
$473$	27.3324	1.25674
$474$	−23.9030	−1.09790
$475$	4.18814	0.192165
$476$	−5.91283	−0.271014
$477$	4.83466	0.221364
$478$	17.5532	0.802865
$479$	−40.7121	−1.86018	−0.930091	−	0.367330i	$-0.880272\pi$
$479$	−40.7121	−1.86018	−0.930091	+	0.367330i	$0.880272\pi$
$480$	−46.2133	−2.10934
$481$	−10.5746	−0.482163
$482$	17.2719	0.786713
$483$	−16.5369	−0.752454
$484$	34.2944	1.55884
$485$	1.92804	0.0875479
$486$	−45.7198	−2.07389
$487$	32.9772	1.49434	0.747171	−	0.664632i	$-0.231412\pi$
$487$	32.9772	1.49434	0.747171	+	0.664632i	$0.231412\pi$
$488$	−31.0601	−1.40603
$489$	34.9837	1.58202
$490$	40.9914	1.85180
$491$	1.05286	0.0475149	0.0237574	−	0.999718i	$-0.492437\pi$
$491$	1.05286	0.0475149	0.0237574	+	0.999718i	$0.492437\pi$
$492$	50.1547	2.26115
$493$	9.31397	0.419480
$494$	−2.20685	−0.0992910
$495$	−35.1873	−1.58155
$496$	7.58176	0.340431
$497$	6.32616	0.283767
$498$	−47.3768	−2.12301
$499$	−5.20928	−0.233199	−0.116600	−	0.993179i	$-0.537199\pi$
$499$	−5.20928	−0.233199	−0.116600	+	0.993179i	$0.537199\pi$
$500$	−7.49790	−0.335316
$501$	2.15161	0.0961268
$502$	−27.0759	−1.20845
$503$	−19.0458	−0.849209	−0.424605	−	0.905379i	$-0.639587\pi$
$503$	−19.0458	−0.849209	−0.424605	+	0.905379i	$0.639587\pi$
$504$	5.72961	0.255217
$505$	54.7487	2.43629
$506$	−75.7473	−3.36738
$507$	28.1234	1.24901
$508$	48.3314	2.14436
$509$	−42.2038	−1.87065	−0.935324	−	0.353791i	$-0.884892\pi$
$509$	−42.2038	−1.87065	−0.935324	+	0.353791i	$0.884892\pi$
$510$	31.1888	1.38106
$511$	−4.14593	−0.183405
$512$	−9.10040	−0.402185
$513$	1.26035	0.0556457
$514$	−3.64738	−0.160879
$515$	33.2662	1.46588
$516$	41.2500	1.81593
$517$	26.3414	1.15849
$518$	−23.9444	−1.05206
$519$	−47.4243	−2.08169
$520$	−7.00259	−0.307084
$521$	32.9852	1.44511	0.722553	−	0.691315i	$-0.242968\pi$
$521$	32.9852	1.44511	0.722553	+	0.691315i	$0.242968\pi$
$522$	−26.2688	−1.14975
$523$	8.45407	0.369671	0.184835	−	0.982770i	$-0.440825\pi$
$523$	8.45407	0.369671	0.184835	+	0.982770i	$0.440825\pi$
$524$	−2.99900	−0.131012
$525$	9.69032	0.422920
$526$	8.08657	0.352591
$527$	−18.3338	−0.798632
$528$	−8.93545	−0.388865
$529$	28.0827	1.22099
$530$	−13.3795	−0.581166
$531$	15.7486	0.683430
$532$	−3.01676	−0.130793
$533$	−6.92002	−0.299739
$534$	−76.1280	−3.29438
$535$	60.7597	2.62687
$536$	−26.4114	−1.14080
$537$	50.8565	2.19462
$538$	−27.8509	−1.20074
$539$	28.3983	1.22320
$540$	11.6399	0.500903
$541$	−6.78617	−0.291760	−0.145880	−	0.989302i	$-0.546601\pi$
$541$	−6.78617	−0.291760	−0.145880	+	0.989302i	$0.546601\pi$
$542$	46.5650	2.00014
$543$	−47.5881	−2.04220
$544$	12.7875	0.548259
$545$	50.4577	2.16137
$546$	−5.10611	−0.218521
$547$	−13.1790	−0.563492	−0.281746	−	0.959489i	$-0.590913\pi$
$547$	−13.1790	−0.563492	−0.281746	+	0.959489i	$0.590913\pi$
$548$	−29.8621	−1.27564
$549$	32.4993	1.38703
$550$	44.3866	1.89265
$551$	4.75205	0.202444
$552$	−39.2771	−1.67174
$553$	4.50833	0.191714
$554$	−36.9771	−1.57101
$555$	76.2496	3.23661
$556$	−4.51245	−0.191370
$557$	24.2300	1.02666	0.513329	−	0.858192i	$-0.328412\pi$
$557$	24.2300	1.02666	0.513329	+	0.858192i	$0.328412\pi$
$558$	51.7079	2.18897
$559$	−5.69141	−0.240721
$560$	2.43265	0.102798
$561$	21.6072	0.912256
$562$	53.3789	2.25165
$563$	10.2851	0.433466	0.216733	−	0.976231i	$-0.430460\pi$
$563$	10.2851	0.433466	0.216733	+	0.976231i	$0.430460\pi$
$564$	39.7545	1.67397
$565$	−20.3209	−0.854908
$566$	60.9546	2.56211
$567$	10.2253	0.429421
$568$	15.0254	0.630451
$569$	43.1473	1.80883	0.904415	−	0.426653i	$-0.140308\pi$
$569$	43.1473	1.80883	0.904415	+	0.426653i	$0.140308\pi$
$570$	15.9127	0.666511
$571$	−12.2971	−0.514619	−0.257309	−	0.966329i	$-0.582836\pi$
$571$	−12.2971	−0.514619	−0.257309	+	0.966329i	$0.582836\pi$
$572$	−14.1199	−0.590385
$573$	4.40895	0.184187
$574$	−15.6692	−0.654018
$575$	−29.9336	−1.24832
$576$	−32.0765	−1.33652
$577$	−1.92496	−0.0801371	−0.0400686	−	0.999197i	$-0.512758\pi$
$577$	−1.92496	−0.0801371	−0.0400686	+	0.999197i	$0.512758\pi$
$578$	29.5606	1.22956
$579$	24.3614	1.01243
$580$	43.8875	1.82233
$581$	8.93571	0.370716
$582$	3.33913	0.138411
$583$	−9.26910	−0.383887
$584$	−9.84709	−0.407475
$585$	7.32705	0.302936
$586$	−23.5065	−0.971044
$587$	26.8410	1.10785	0.553923	−	0.832568i	$-0.313130\pi$
$587$	26.8410	1.10785	0.553923	+	0.832568i	$0.313130\pi$
$588$	42.8587	1.76746
$589$	−9.35401	−0.385425
$590$	−43.5827	−1.79427
$591$	−11.3554	−0.467100
$592$	8.72516	0.358602
$593$	−27.4962	−1.12913	−0.564567	−	0.825387i	$-0.690957\pi$
$593$	−27.4962	−1.12913	−0.564567	+	0.825387i	$0.690957\pi$
$594$	13.3574	0.548060
$595$	−5.88251	−0.241159
$596$	28.3442	1.16103
$597$	−17.1269	−0.700955
$598$	15.7729	0.645000
$599$	−7.47771	−0.305531	−0.152765	−	0.988262i	$-0.548818\pi$
$599$	−7.47771	−0.305531	−0.152765	+	0.988262i	$0.548818\pi$
$600$	23.0157	0.939611
$601$	37.1015	1.51340	0.756701	−	0.653761i	$-0.226810\pi$
$601$	37.1015	1.51340	0.756701	+	0.653761i	$0.226810\pi$
$602$	−12.8872	−0.525243
$603$	27.6351	1.12539
$604$	−15.9665	−0.649666
$605$	34.1186	1.38712
$606$	94.8181	3.85172
$607$	−36.8264	−1.49474	−0.747369	−	0.664409i	$-0.768683\pi$
$607$	−36.8264	−1.49474	−0.747369	+	0.664409i	$0.768683\pi$
$608$	6.52426	0.264594
$609$	10.9951	0.445542
$610$	−89.9385	−3.64150
$611$	−5.48507	−0.221902
$612$	14.6944	0.593985
$613$	41.2218	1.66493	0.832466	−	0.554077i	$-0.186929\pi$
$613$	41.2218	1.66493	0.832466	+	0.554077i	$0.186929\pi$
$614$	−47.7137	−1.92557
$615$	49.8975	2.01206
$616$	−10.9849	−0.442594
$617$	−19.9554	−0.803374	−0.401687	−	0.915777i	$-0.631576\pi$
$617$	−19.9554	−0.803374	−0.401687	+	0.915777i	$0.631576\pi$
$618$	57.6130	2.31753
$619$	−3.77795	−0.151849	−0.0759243	−	0.997114i	$-0.524191\pi$
$619$	−3.77795	−0.151849	−0.0759243	+	0.997114i	$0.524191\pi$
$620$	−86.3890	−3.46947
$621$	−9.00797	−0.361478
$622$	18.1716	0.728615
$623$	14.3585	0.575260
$624$	1.86063	0.0744847
$625$	−28.4002	−1.13601
$626$	−56.6314	−2.26344
$627$	11.0241	0.440261
$628$	−21.2900	−0.849564
$629$	−21.0987	−0.841260
$630$	16.5908	0.660994
$631$	22.8127	0.908159	0.454080	−	0.890961i	$-0.349968\pi$
$631$	22.8127	0.908159	0.454080	+	0.890961i	$0.349968\pi$
$632$	10.7078	0.425935
$633$	−3.92734	−0.156098
$634$	2.24651	0.0892204
$635$	48.0836	1.90814
$636$	−13.9889	−0.554697
$637$	−5.91337	−0.234296
$638$	50.3630	1.99389
$639$	−15.7216	−0.621936
$640$	49.2159	1.94543
$641$	−3.41041	−0.134703	−0.0673515	−	0.997729i	$-0.521455\pi$
$641$	−3.41041	−0.134703	−0.0673515	+	0.997729i	$0.521455\pi$
$642$	105.228	4.15304
$643$	36.0005	1.41972	0.709861	−	0.704342i	$-0.248758\pi$
$643$	36.0005	1.41972	0.709861	+	0.704342i	$0.248758\pi$
$644$	21.5614	0.849640
$645$	41.0385	1.61589
$646$	−4.40314	−0.173239
$647$	37.1509	1.46055	0.730277	−	0.683152i	$-0.239391\pi$
$647$	37.1509	1.46055	0.730277	+	0.683152i	$0.239391\pi$
$648$	24.2862	0.954054
$649$	−30.1935	−1.18520
$650$	−9.24262	−0.362525
$651$	−21.6429	−0.848250
$652$	−45.6132	−1.78635
$653$	0.196865	0.00770392	0.00385196	−	0.999993i	$-0.498774\pi$
$653$	0.196865	0.00770392	0.00385196	+	0.999993i	$0.498774\pi$
$654$	87.3866	3.41708
$655$	−2.98362	−0.116580
$656$	5.70972	0.222927
$657$	10.3033	0.401972
$658$	−12.4200	−0.484181
$659$	−43.5634	−1.69699	−0.848494	−	0.529206i	$-0.822490\pi$
$659$	−43.5634	−1.69699	−0.848494	+	0.529206i	$0.822490\pi$
$660$	101.813	3.96308
$661$	−20.0380	−0.779389	−0.389694	−	0.920944i	$-0.627419\pi$
$661$	−20.0380	−0.779389	−0.389694	+	0.920944i	$0.627419\pi$
$662$	22.4313	0.871815
$663$	−4.49926	−0.174737
$664$	21.2234	0.823628
$665$	−3.00129	−0.116385
$666$	59.5060	2.30581
$667$	−33.9639	−1.31509
$668$	−2.80535	−0.108542
$669$	−16.8334	−0.650816
$670$	−76.4775	−2.95458
$671$	−62.3082	−2.40538
$672$	15.0955	0.582322
$673$	−7.27714	−0.280513	−0.140257	−	0.990115i	$-0.544793\pi$
$673$	−7.27714	−0.280513	−0.140257	+	0.990115i	$0.544793\pi$
$674$	−79.9927	−3.08120
$675$	5.27852	0.203170
$676$	−36.6684	−1.41032
$677$	48.7398	1.87322	0.936611	−	0.350371i	$-0.113945\pi$
$677$	48.7398	1.87322	0.936611	+	0.350371i	$0.113945\pi$
$678$	−35.1934	−1.35159
$679$	−0.629792	−0.0241692
$680$	−13.9717	−0.535789
$681$	−63.0848	−2.41742
$682$	−99.1354	−3.79609
$683$	−27.8611	−1.06608	−0.533038	−	0.846091i	$-0.678950\pi$
$683$	−27.8611	−1.06608	−0.533038	+	0.846091i	$0.678950\pi$
$684$	7.49716	0.286661
$685$	−29.7090	−1.13512
$686$	−28.9602	−1.10571
$687$	45.6894	1.74316
$688$	4.69599	0.179033
$689$	1.93010	0.0735311
$690$	−113.732	−4.32969
$691$	10.2521	0.390008	0.195004	−	0.980802i	$-0.437528\pi$
$691$	10.2521	0.390008	0.195004	+	0.980802i	$0.437528\pi$
$692$	61.8336	2.35056
$693$	11.4939	0.436616
$694$	−37.5292	−1.42459
$695$	−4.48931	−0.170289
$696$	26.1146	0.989870
$697$	−13.8069	−0.522974
$698$	−27.8189	−1.05296
$699$	11.8284	0.447392
$700$	−12.6346	−0.477544
$701$	−35.6918	−1.34806	−0.674030	−	0.738704i	$-0.735438\pi$
$701$	−35.6918	−1.34806	−0.674030	+	0.738704i	$0.735438\pi$
$702$	−2.78140	−0.104977
$703$	−10.7647	−0.405998
$704$	61.4976	2.31778
$705$	39.5506	1.48956
$706$	42.6084	1.60359
$707$	−17.8836	−0.672582
$708$	−45.5680	−1.71255
$709$	7.35713	0.276303	0.138151	−	0.990411i	$-0.455884\pi$
$709$	7.35713	0.276303	0.138151	+	0.990411i	$0.455884\pi$
$710$	43.5079	1.63282
$711$	−11.2040	−0.420182
$712$	34.1031	1.27807
$713$	66.8551	2.50374
$714$	−10.1878	−0.381268
$715$	−14.0475	−0.525348
$716$	−66.3088	−2.47808
$717$	18.2587	0.681884
$718$	4.27273	0.159457
$719$	47.4234	1.76860	0.884298	−	0.466923i	$-0.154638\pi$
$719$	47.4234	1.76860	0.884298	+	0.466923i	$0.154638\pi$
$720$	−6.04556	−0.225305
$721$	−10.8664	−0.404684
$722$	−2.24651	−0.0836065
$723$	17.9661	0.668166
$724$	62.0473	2.30597
$725$	19.9022	0.739151
$726$	59.0892	2.19301
$727$	41.7898	1.54990	0.774948	−	0.632024i	$-0.217776\pi$
$727$	41.7898	1.54990	0.774948	+	0.632024i	$0.217776\pi$
$728$	2.28738	0.0847761
$729$	−16.5760	−0.613925
$730$	−28.5135	−1.05533
$731$	−11.3556	−0.420001
$732$	−94.0355	−3.47565
$733$	11.3085	0.417690	0.208845	−	0.977949i	$-0.433030\pi$
$733$	11.3085	0.417690	0.208845	+	0.977949i	$0.433030\pi$
$734$	−59.9952	−2.21446
$735$	42.6389	1.57276
$736$	−46.6303	−1.71881
$737$	−52.9825	−1.95164
$738$	38.9405	1.43342
$739$	32.7113	1.20330	0.601652	−	0.798759i	$-0.294510\pi$
$739$	32.7113	1.20330	0.601652	+	0.798759i	$0.294510\pi$
$740$	−99.4172	−3.65465
$741$	−2.29555	−0.0843292
$742$	4.37038	0.160442
$743$	−30.1176	−1.10491	−0.552454	−	0.833543i	$-0.686309\pi$
$743$	−30.1176	−1.10491	−0.552454	+	0.833543i	$0.686309\pi$
$744$	−51.4044	−1.88458
$745$	28.1989	1.03313
$746$	26.9769	0.987696
$747$	−22.2068	−0.812503
$748$	−28.1723	−1.03008
$749$	−19.8471	−0.725196
$750$	−12.9189	−0.471730
$751$	41.3929	1.51045	0.755223	−	0.655468i	$-0.227528\pi$
$751$	41.3929	1.51045	0.755223	+	0.655468i	$0.227528\pi$
$752$	4.52574	0.165037
$753$	−28.1641	−1.02636
$754$	−10.4871	−0.381917
$755$	−15.8846	−0.578100
$756$	−3.80217	−0.138284
$757$	23.5140	0.854632	0.427316	−	0.904102i	$-0.359459\pi$
$757$	23.5140	0.854632	0.427316	+	0.904102i	$0.359459\pi$
$758$	−15.9777	−0.580336
$759$	−78.7918	−2.85996
$760$	−7.12843	−0.258575
$761$	−33.0173	−1.19688	−0.598438	−	0.801169i	$-0.704212\pi$
$761$	−33.0173	−1.19688	−0.598438	+	0.801169i	$0.704212\pi$
$762$	83.2748	3.01673
$763$	−16.4819	−0.596686
$764$	−5.74857	−0.207976
$765$	14.6190	0.528552
$766$	−0.574620	−0.0207619
$767$	6.28718	0.227017
$768$	24.3119	0.877281
$769$	31.2121	1.12554	0.562769	−	0.826614i	$-0.309736\pi$
$769$	31.2121	1.12554	0.562769	+	0.826614i	$0.309736\pi$
$770$	−31.8082	−1.14629
$771$	−3.79398	−0.136637
$772$	−31.7634	−1.14319
$773$	49.9478	1.79650	0.898248	−	0.439488i	$-0.144840\pi$
$773$	49.9478	1.79650	0.898248	+	0.439488i	$0.144840\pi$
$774$	32.0269	1.15118
$775$	−39.1760	−1.40724
$776$	−1.49583	−0.0536972
$777$	−24.9068	−0.893526
$778$	38.4897	1.37992
$779$	−7.04437	−0.252391
$780$	−21.2006	−0.759102
$781$	30.1417	1.07855
$782$	31.4702	1.12537
$783$	5.98923	0.214038
$784$	4.87913	0.174255
$785$	−21.1808	−0.755977
$786$	−5.16727	−0.184311
$787$	26.2294	0.934975	0.467488	−	0.884000i	$-0.345159\pi$
$787$	26.2294	0.934975	0.467488	+	0.884000i	$0.345159\pi$
$788$	14.8057	0.527430
$789$	8.41158	0.299460
$790$	31.0059	1.10314
$791$	6.63780	0.236013
$792$	27.2993	0.970040
$793$	12.9744	0.460735
$794$	55.2502	1.96076
$795$	−13.9172	−0.493592
$796$	22.3307	0.791490
$797$	−5.66490	−0.200661	−0.100331	−	0.994954i	$-0.531990\pi$
$797$	−5.66490	−0.200661	−0.100331	+	0.994954i	$0.531990\pi$
$798$	−5.19787	−0.184003
$799$	−10.9439	−0.387167
$800$	27.3245	0.966068
$801$	−35.6832	−1.26080
$802$	37.6344	1.32892
$803$	−19.7538	−0.697095
$804$	−79.9613	−2.82002
$805$	21.4509	0.756044
$806$	20.6429	0.727116
$807$	−28.9703	−1.01980
$808$	−42.4757	−1.49429
$809$	41.5516	1.46088	0.730438	−	0.682979i	$-0.239316\pi$
$809$	41.5516	1.46088	0.730438	+	0.682979i	$0.239316\pi$
$810$	70.3239	2.47093
$811$	18.2169	0.639680	0.319840	−	0.947472i	$-0.396371\pi$
$811$	18.2169	0.639680	0.319840	+	0.947472i	$0.396371\pi$
$812$	−14.3358	−0.503087
$813$	48.4365	1.69874
$814$	−114.086	−3.99871
$815$	−45.3793	−1.58957
$816$	3.71235	0.129958
$817$	−5.79369	−0.202696
$818$	29.8296	1.04297
$819$	−2.39337	−0.0836311
$820$	−65.0583	−2.27194
$821$	−37.8805	−1.32204	−0.661019	−	0.750369i	$-0.729876\pi$
$821$	−37.8805	−1.32204	−0.661019	+	0.750369i	$0.729876\pi$
$822$	−51.4523	−1.79460
$823$	11.7544	0.409732	0.204866	−	0.978790i	$-0.434324\pi$
$823$	11.7544	0.409732	0.204866	+	0.978790i	$0.434324\pi$
$824$	−25.8089	−0.899095
$825$	46.1706	1.60745
$826$	14.2362	0.495341
$827$	−49.7491	−1.72994	−0.864972	−	0.501819i	$-0.832664\pi$
$827$	−49.7491	−1.72994	−0.864972	+	0.501819i	$0.832664\pi$
$828$	−53.5838	−1.86217
$829$	9.21493	0.320048	0.160024	−	0.987113i	$-0.448843\pi$
$829$	9.21493	0.320048	0.160024	+	0.987113i	$0.448843\pi$
$830$	61.4551	2.13314
$831$	−38.4633	−1.33428
$832$	−12.8056	−0.443955
$833$	−11.7984	−0.408791
$834$	−7.77494	−0.269224
$835$	−2.79097	−0.0965854
$836$	−14.3737	−0.497125
$837$	−11.7893	−0.407498
$838$	65.2332	2.25344
$839$	53.7185	1.85457	0.927284	−	0.374358i	$-0.122137\pi$
$839$	53.7185	1.85457	0.927284	+	0.374358i	$0.122137\pi$
$840$	−16.4934	−0.569077
$841$	−6.41807	−0.221313
$842$	−25.8985	−0.892522
$843$	55.5243	1.91236
$844$	5.12063	0.176259
$845$	−36.4804	−1.25496
$846$	30.8657	1.06119
$847$	−11.1448	−0.382939
$848$	−1.59253	−0.0546877
$849$	63.4044	2.17604
$850$	−18.4410	−0.632521
$851$	76.9375	2.63738
$852$	45.4898	1.55846
$853$	18.6109	0.637225	0.318612	−	0.947885i	$-0.396783\pi$
$853$	18.6109	0.637225	0.318612	+	0.947885i	$0.396783\pi$
$854$	29.3783	1.00530
$855$	7.45872	0.255083
$856$	−47.1392	−1.61118
$857$	−39.2833	−1.34189	−0.670946	−	0.741506i	$-0.734112\pi$
$857$	−39.2833	−1.34189	−0.670946	+	0.741506i	$0.734112\pi$
$858$	−24.3286	−0.830566
$859$	26.4755	0.903332	0.451666	−	0.892187i	$-0.350830\pi$
$859$	26.4755	0.903332	0.451666	+	0.892187i	$0.350830\pi$
$860$	−53.5076	−1.82459
$861$	−16.2989	−0.555466
$862$	−7.03481	−0.239606
$863$	−45.5458	−1.55040	−0.775198	−	0.631719i	$-0.782350\pi$
$863$	−45.5458	−1.55040	−0.775198	+	0.631719i	$0.782350\pi$
$864$	8.22283	0.279746
$865$	61.5166	2.09163
$866$	−43.1104	−1.46495
$867$	30.7487	1.04428
$868$	28.2188	0.957809
$869$	21.4804	0.728674
$870$	75.6181	2.56369
$871$	11.0325	0.373823
$872$	−39.1466	−1.32567
$873$	1.56514	0.0529719
$874$	16.0563	0.543113
$875$	2.43662	0.0823727
$876$	−29.8124	−1.00727
$877$	−35.4241	−1.19619	−0.598093	−	0.801427i	$-0.704075\pi$
$877$	−35.4241	−1.19619	−0.598093	+	0.801427i	$0.704075\pi$
$878$	−54.4480	−1.83753
$879$	−24.4513	−0.824721
$880$	11.5907	0.390721
$881$	−30.6880	−1.03390	−0.516952	−	0.856014i	$-0.672933\pi$
$881$	−30.6880	−1.03390	−0.516952	+	0.856014i	$0.672933\pi$
$882$	33.2759	1.12046
$883$	−27.2736	−0.917830	−0.458915	−	0.888480i	$-0.651762\pi$
$883$	−27.2736	−0.917830	−0.458915	+	0.888480i	$0.651762\pi$
$884$	5.86632	0.197306
$885$	−45.3343	−1.52390
$886$	35.7765	1.20193
$887$	−43.1044	−1.44730	−0.723652	−	0.690165i	$-0.757538\pi$
$887$	−43.1044	−1.44730	−0.723652	+	0.690165i	$0.757538\pi$
$888$	−59.1566	−1.98517
$889$	−15.7064	−0.526776
$890$	98.7498	3.31010
$891$	48.7194	1.63216
$892$	21.9480	0.734874
$893$	−5.58364	−0.186849
$894$	48.8371	1.63336
$895$	−65.9688	−2.20509
$896$	−16.0763	−0.537071
$897$	16.4068	0.547807
$898$	52.5903	1.75496
$899$	−44.4507	−1.48251
$900$	31.3992	1.04664
$901$	3.85097	0.128294
$902$	−74.6574	−2.48582
$903$	−13.4052	−0.446096
$904$	15.7656	0.524355
$905$	61.7291	2.05195
$906$	−27.5102	−0.913964
$907$	13.3421	0.443019	0.221509	−	0.975158i	$-0.428902\pi$
$907$	13.3421	0.443019	0.221509	+	0.975158i	$0.428902\pi$
$908$	82.2525	2.72965
$909$	44.4437	1.47411
$910$	6.62341	0.219564
$911$	11.3142	0.374855	0.187427	−	0.982278i	$-0.439985\pi$
$911$	11.3142	0.374855	0.187427	+	0.982278i	$0.439985\pi$
$912$	1.89406	0.0627187
$913$	42.5752	1.40903
$914$	−57.0577	−1.88730
$915$	−93.5533	−3.09278
$916$	−59.5717	−1.96830
$917$	0.974596	0.0321840
$918$	−5.54949	−0.183161
$919$	−5.07988	−0.167570	−0.0837848	−	0.996484i	$-0.526701\pi$
$919$	−5.07988	−0.167570	−0.0837848	+	0.996484i	$0.526701\pi$
$920$	50.9484	1.67972
$921$	−49.6314	−1.63541
$922$	−15.0888	−0.496922
$923$	−6.27640	−0.206590
$924$	−33.2571	−1.09408
$925$	−45.0840	−1.48235
$926$	−68.2744	−2.24364
$927$	27.0047	0.886952
$928$	31.0036	1.01774
$929$	18.3022	0.600475	0.300238	−	0.953864i	$-0.402934\pi$
$929$	18.3022	0.600475	0.300238	+	0.953864i	$0.402934\pi$
$930$	−148.848	−4.88092
$931$	−6.01963	−0.197285
$932$	−15.4224	−0.505176
$933$	18.9020	0.618823
$934$	−82.7511	−2.70770
$935$	−28.0279	−0.916609
$936$	−5.68454	−0.185805
$937$	18.6708	0.609947	0.304974	−	0.952361i	$-0.401352\pi$
$937$	18.6708	0.609947	0.304974	+	0.952361i	$0.401352\pi$
$938$	24.9812	0.815666
$939$	−58.9075	−1.92237
$940$	−51.5677	−1.68195
$941$	−1.26325	−0.0411807	−0.0205903	−	0.999788i	$-0.506555\pi$
$941$	−1.26325	−0.0411807	−0.0205903	+	0.999788i	$0.506555\pi$
$942$	−36.6826	−1.19518
$943$	50.3477	1.63955
$944$	−5.18756	−0.168841
$945$	−3.78267	−0.123050
$946$	−61.4025	−1.99637
$947$	−56.6561	−1.84108	−0.920538	−	0.390653i	$-0.872249\pi$
$947$	−56.6561	−1.84108	−0.920538	+	0.390653i	$0.872249\pi$
$948$	32.4183	1.05290
$949$	4.11332	0.133524
$950$	−9.40872	−0.305259
$951$	2.33680	0.0757761
$952$	4.56382	0.147914
$953$	14.9498	0.484271	0.242136	−	0.970242i	$-0.422152\pi$
$953$	14.9498	0.484271	0.242136	+	0.970242i	$0.422152\pi$
$954$	−10.8611	−0.351642
$955$	−5.71909	−0.185066
$956$	−23.8064	−0.769954
$957$	52.3871	1.69344
$958$	91.4601	2.95494
$959$	9.70438	0.313371
$960$	92.3363	2.98014
$961$	56.4975	1.82250
$962$	23.7561	0.765927
$963$	49.3233	1.58942
$964$	−23.4249	−0.754465
$965$	−31.6005	−1.01726
$966$	37.1503	1.19529
$967$	41.5686	1.33676	0.668379	−	0.743821i	$-0.266989\pi$
$967$	41.5686	1.33676	0.668379	+	0.743821i	$0.266989\pi$
$968$	−26.4702	−0.850784
$969$	−4.58012	−0.147135
$970$	−4.33137	−0.139072
$971$	61.2844	1.96671	0.983355	−	0.181693i	$-0.0581576\pi$
$971$	61.2844	1.96671	0.983355	+	0.181693i	$0.0581576\pi$
$972$	62.0072	1.98888
$973$	1.46643	0.0470115
$974$	−74.0838	−2.37380
$975$	−9.61410	−0.307898
$976$	−10.7052	−0.342666
$977$	24.1750	0.773428	0.386714	−	0.922200i	$-0.373610\pi$
$977$	24.1750	0.773428	0.386714	+	0.922200i	$0.373610\pi$
$978$	−78.5914	−2.51308
$979$	68.4125	2.18647
$980$	−55.5943	−1.77590
$981$	40.9604	1.30776
$982$	−2.36526	−0.0754785
$983$	13.1607	0.419761	0.209881	−	0.977727i	$-0.432692\pi$
$983$	13.1607	0.419761	0.209881	+	0.977727i	$0.432692\pi$
$984$	−38.7119	−1.23409
$985$	14.7297	0.469329
$986$	−20.9239	−0.666354
$987$	−12.9191	−0.411221
$988$	2.99303	0.0952210
$989$	41.4087	1.31672
$990$	79.0487	2.51233
$991$	−19.9981	−0.635261	−0.317631	−	0.948215i	$-0.602887\pi$
$991$	−19.9981	−0.635261	−0.317631	+	0.948215i	$0.602887\pi$
$992$	−61.0280	−1.93764
$993$	23.3328	0.740444
$994$	−14.2118	−0.450771
$995$	22.2162	0.704300
$996$	64.2545	2.03598
$997$	21.4858	0.680461	0.340230	−	0.940342i	$-0.389495\pi$
$997$	21.4858	0.680461	0.340230	+	0.940342i	$0.389495\pi$
$998$	11.7027	0.370443
$999$	−13.5672	−0.429249

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6023.2.a.c.1.17	✓	138

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6023.2.a.c.1.17	✓	138	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)

\(f(q)\)	\(=\)	\(q-2.24651 q^{2} -2.33680 q^{3} +3.04682 q^{4} +3.03120 q^{5} +5.24966 q^{6} -0.990135 q^{7} -2.35169 q^{8} +2.46065 q^{9} +O(q^{10})\)	\(q-2.24651 q^{2} -2.33680 q^{3} +3.04682 q^{4} +3.03120 q^{5} +5.24966 q^{6} -0.990135 q^{7} -2.35169 q^{8} +2.46065 q^{9} -6.80962 q^{10} -4.71761 q^{11} -7.11982 q^{12} +0.982347 q^{13} +2.22435 q^{14} -7.08331 q^{15} -0.810536 q^{16} +1.95999 q^{17} -5.52789 q^{18} +1.00000 q^{19} +9.23550 q^{20} +2.31375 q^{21} +10.5982 q^{22} -7.14721 q^{23} +5.49544 q^{24} +4.18814 q^{25} -2.20685 q^{26} +1.26035 q^{27} -3.01676 q^{28} +4.75205 q^{29} +15.9127 q^{30} -9.35401 q^{31} +6.52426 q^{32} +11.0241 q^{33} -4.40314 q^{34} -3.00129 q^{35} +7.49716 q^{36} -10.7647 q^{37} -2.24651 q^{38} -2.29555 q^{39} -7.12843 q^{40} -7.04437 q^{41} -5.19787 q^{42} -5.79369 q^{43} -14.3737 q^{44} +7.45872 q^{45} +16.0563 q^{46} -5.58364 q^{47} +1.89406 q^{48} -6.01963 q^{49} -9.40872 q^{50} -4.58012 q^{51} +2.99303 q^{52} +1.96479 q^{53} -2.83139 q^{54} -14.3000 q^{55} +2.32849 q^{56} -2.33680 q^{57} -10.6755 q^{58} +6.40016 q^{59} -21.5816 q^{60} +13.2076 q^{61} +21.0139 q^{62} -2.43638 q^{63} -13.0358 q^{64} +2.97768 q^{65} -24.7658 q^{66} +11.2308 q^{67} +5.97174 q^{68} +16.7016 q^{69} +6.74244 q^{70} -6.38919 q^{71} -5.78669 q^{72} +4.18724 q^{73} +24.1830 q^{74} -9.78687 q^{75} +3.04682 q^{76} +4.67107 q^{77} +5.15698 q^{78} -4.55325 q^{79} -2.45689 q^{80} -10.3271 q^{81} +15.8253 q^{82} -9.02474 q^{83} +7.04958 q^{84} +5.94112 q^{85} +13.0156 q^{86} -11.1046 q^{87} +11.0943 q^{88} -14.5015 q^{89} -16.7561 q^{90} -0.972656 q^{91} -21.7763 q^{92} +21.8585 q^{93} +12.5437 q^{94} +3.03120 q^{95} -15.2459 q^{96} +0.636067 q^{97} +13.5232 q^{98} -11.6084 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 138 q + 11 q^{2} + 29 q^{3} + 157 q^{4} + 12 q^{5} + 8 q^{6} + 18 q^{7} + 33 q^{8} + 171 q^{9}+O(q^{10}) \) 138 * q + 11 * q^2 + 29 * q^3 + 157 * q^4 + 12 * q^5 + 8 * q^6 + 18 * q^7 + 33 * q^8 + 171 * q^9	\( 138 q + 11 q^{2} + 29 q^{3} + 157 q^{4} + 12 q^{5} + 8 q^{6} + 18 q^{7} + 33 q^{8} + 171 q^{9} + 40 q^{10} + 4 q^{11} + 69 q^{12} + 72 q^{13} + 3 q^{14} + 30 q^{15} + 191 q^{16} + 31 q^{17} + 31 q^{18} + 138 q^{19} + 16 q^{20} + 16 q^{21} + 95 q^{22} + 34 q^{23} + 3 q^{24} + 244 q^{25} - 13 q^{26} + 107 q^{27} + 43 q^{28} + 30 q^{29} - 14 q^{30} + 60 q^{31} + 62 q^{32} + 77 q^{33} + 36 q^{34} + 2 q^{35} + 205 q^{36} + 142 q^{37} + 11 q^{38} + 20 q^{39} + 76 q^{40} + 46 q^{41} - 21 q^{42} + 69 q^{43} - 7 q^{44} + 30 q^{45} + 39 q^{46} + 8 q^{47} + 116 q^{48} + 236 q^{49} + 34 q^{51} + 165 q^{52} + 49 q^{53} + 6 q^{55} - 33 q^{56} + 29 q^{57} + 75 q^{58} + 8 q^{59} - 24 q^{60} + 38 q^{61} - 10 q^{62} + 2 q^{63} + 251 q^{64} + 72 q^{65} - 15 q^{66} + 158 q^{67} - 19 q^{68} + 33 q^{69} + 48 q^{70} + 23 q^{71} + 88 q^{72} + 134 q^{73} + 4 q^{74} + 118 q^{75} + 157 q^{76} + 13 q^{77} + 12 q^{78} + 78 q^{79} - 48 q^{80} + 254 q^{81} + 89 q^{82} - 27 q^{83} - 15 q^{84} + 37 q^{85} + 66 q^{86} + 43 q^{87} + 224 q^{88} + 26 q^{89} + 38 q^{90} + 108 q^{91} + 113 q^{92} + 83 q^{93} + 48 q^{94} + 12 q^{95} + 40 q^{96} + 254 q^{97} + 47 q^{98} + 11 q^{99}+O(q^{100}) \) 138 * q + 11 * q^2 + 29 * q^3 + 157 * q^4 + 12 * q^5 + 8 * q^6 + 18 * q^7 + 33 * q^8 + 171 * q^9 + 40 * q^10 + 4 * q^11 + 69 * q^12 + 72 * q^13 + 3 * q^14 + 30 * q^15 + 191 * q^16 + 31 * q^17 + 31 * q^18 + 138 * q^19 + 16 * q^20 + 16 * q^21 + 95 * q^22 + 34 * q^23 + 3 * q^24 + 244 * q^25 - 13 * q^26 + 107 * q^27 + 43 * q^28 + 30 * q^29 - 14 * q^30 + 60 * q^31 + 62 * q^32 + 77 * q^33 + 36 * q^34 + 2 * q^35 + 205 * q^36 + 142 * q^37 + 11 * q^38 + 20 * q^39 + 76 * q^40 + 46 * q^41 - 21 * q^42 + 69 * q^43 - 7 * q^44 + 30 * q^45 + 39 * q^46 + 8 * q^47 + 116 * q^48 + 236 * q^49 + 34 * q^51 + 165 * q^52 + 49 * q^53 + 6 * q^55 - 33 * q^56 + 29 * q^57 + 75 * q^58 + 8 * q^59 - 24 * q^60 + 38 * q^61 - 10 * q^62 + 2 * q^63 + 251 * q^64 + 72 * q^65 - 15 * q^66 + 158 * q^67 - 19 * q^68 + 33 * q^69 + 48 * q^70 + 23 * q^71 + 88 * q^72 + 134 * q^73 + 4 * q^74 + 118 * q^75 + 157 * q^76 + 13 * q^77 + 12 * q^78 + 78 * q^79 - 48 * q^80 + 254 * q^81 + 89 * q^82 - 27 * q^83 - 15 * q^84 + 37 * q^85 + 66 * q^86 + 43 * q^87 + 224 * q^88 + 26 * q^89 + 38 * q^90 + 108 * q^91 + 113 * q^92 + 83 * q^93 + 48 * q^94 + 12 * q^95 + 40 * q^96 + 254 * q^97 + 47 * q^98 + 11 * q^99

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