LMFDB - Embedded newform 6023.2.a.b.1.3

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			1.3
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)

$f(q)$	$=$	$q-2.63080 q^{2} -0.151619 q^{3} +4.92110 q^{4} -0.321250 q^{5} +0.398879 q^{6} -0.565304 q^{7} -7.68484 q^{8} -2.97701 q^{9} +O(q^{10})$	\(q-2.63080 q^{2} -0.151619 q^{3} +4.92110 q^{4} -0.321250 q^{5} +0.398879 q^{6} -0.565304 q^{7} -7.68484 q^{8} -2.97701 q^{9} +0.845143 q^{10} -4.63699 q^{11} -0.746133 q^{12} -0.0639167 q^{13} +1.48720 q^{14} +0.0487076 q^{15} +10.3751 q^{16} +1.37627 q^{17} +7.83192 q^{18} -1.00000 q^{19} -1.58090 q^{20} +0.0857108 q^{21} +12.1990 q^{22} +6.68613 q^{23} +1.16517 q^{24} -4.89680 q^{25} +0.168152 q^{26} +0.906229 q^{27} -2.78192 q^{28} +1.89444 q^{29} -0.128140 q^{30} -5.91732 q^{31} -11.9250 q^{32} +0.703057 q^{33} -3.62069 q^{34} +0.181604 q^{35} -14.6502 q^{36} -0.0360141 q^{37} +2.63080 q^{38} +0.00969099 q^{39} +2.46875 q^{40} +2.68462 q^{41} -0.225488 q^{42} +2.40508 q^{43} -22.8191 q^{44} +0.956364 q^{45} -17.5899 q^{46} +10.3758 q^{47} -1.57306 q^{48} -6.68043 q^{49} +12.8825 q^{50} -0.208668 q^{51} -0.314541 q^{52} +5.19462 q^{53} -2.38411 q^{54} +1.48963 q^{55} +4.34427 q^{56} +0.151619 q^{57} -4.98388 q^{58} +10.7496 q^{59} +0.239695 q^{60} +14.9701 q^{61} +15.5673 q^{62} +1.68292 q^{63} +10.6222 q^{64} +0.0205332 q^{65} -1.84960 q^{66} +3.00136 q^{67} +6.77276 q^{68} -1.01375 q^{69} -0.477763 q^{70} +6.28821 q^{71} +22.8779 q^{72} +6.93566 q^{73} +0.0947459 q^{74} +0.742448 q^{75} -4.92110 q^{76} +2.62131 q^{77} -0.0254950 q^{78} -12.4370 q^{79} -3.33298 q^{80} +8.79363 q^{81} -7.06270 q^{82} -4.10558 q^{83} +0.421792 q^{84} -0.442126 q^{85} -6.32729 q^{86} -0.287233 q^{87} +35.6346 q^{88} +15.6451 q^{89} -2.51600 q^{90} +0.0361323 q^{91} +32.9031 q^{92} +0.897179 q^{93} -27.2966 q^{94} +0.321250 q^{95} +1.80806 q^{96} -11.8503 q^{97} +17.5749 q^{98} +13.8044 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.63080	−1.86026	−0.930128	−	0.367236i	$-0.880304\pi$
$2$	−2.63080	−1.86026	−0.930128	+	0.367236i	$0.880304\pi$
$3$	−0.151619	−0.0875373	−0.0437687	−	0.999042i	$-0.513936\pi$
$3$	−0.151619	−0.0875373	−0.0437687	+	0.999042i	$0.513936\pi$
$4$	4.92110	2.46055
$5$	−0.321250	−0.143667	−0.0718336	−	0.997417i	$-0.522885\pi$
$5$	−0.321250	−0.143667	−0.0718336	+	0.997417i	$0.522885\pi$
$6$	0.398879	0.162842
$7$	−0.565304	−0.213665	−0.106832	−	0.994277i	$-0.534071\pi$
$7$	−0.565304	−0.213665	−0.106832	+	0.994277i	$0.534071\pi$
$8$	−7.68484	−2.71700
$9$	−2.97701	−0.992337
$10$	0.845143	0.267258
$11$	−4.63699	−1.39811	−0.699053	−	0.715070i	$-0.746395\pi$
$11$	−4.63699	−1.39811	−0.699053	+	0.715070i	$0.746395\pi$
$12$	−0.746133	−0.215390
$13$	−0.0639167	−0.0177273	−0.00886365	−	0.999961i	$-0.502821\pi$
$13$	−0.0639167	−0.0177273	−0.00886365	+	0.999961i	$0.502821\pi$
$14$	1.48720	0.397471
$15$	0.0487076	0.0125762
$16$	10.3751	2.59376
$17$	1.37627	0.333794	0.166897	−	0.985974i	$-0.446625\pi$
$17$	1.37627	0.333794	0.166897	+	0.985974i	$0.446625\pi$
$18$	7.83192	1.84600
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	−1.58090	−0.353501
$21$	0.0857108	0.0187036
$22$	12.1990	2.60084
$23$	6.68613	1.39415	0.697077	−	0.716996i	$-0.254483\pi$
$23$	6.68613	1.39415	0.697077	+	0.716996i	$0.254483\pi$
$24$	1.16517	0.237839
$25$	−4.89680	−0.979360
$26$	0.168152	0.0329773
$27$	0.906229	0.174404
$28$	−2.78192	−0.525733
$29$	1.89444	0.351788	0.175894	−	0.984409i	$-0.443718\pi$
$29$	1.89444	0.351788	0.175894	+	0.984409i	$0.443718\pi$
$30$	−0.128140	−0.0233950
$31$	−5.91732	−1.06278	−0.531391	−	0.847127i	$-0.678331\pi$
$31$	−5.91732	−1.06278	−0.531391	+	0.847127i	$0.678331\pi$
$32$	−11.9250	−2.10806
$33$	0.703057	0.122386
$34$	−3.62069	−0.620942
$35$	0.181604	0.0306966
$36$	−14.6502	−2.44170
$37$	−0.0360141	−0.00592069	−0.00296034	−	0.999996i	$-0.500942\pi$
$37$	−0.0360141	−0.00592069	−0.00296034	+	0.999996i	$0.500942\pi$
$38$	2.63080	0.426772
$39$	0.00969099	0.00155180
$40$	2.46875	0.390344
$41$	2.68462	0.419268	0.209634	−	0.977780i	$-0.432773\pi$
$41$	2.68462	0.419268	0.209634	+	0.977780i	$0.432773\pi$
$42$	−0.225488	−0.0347936
$43$	2.40508	0.366772	0.183386	−	0.983041i	$-0.441294\pi$
$43$	2.40508	0.366772	0.183386	+	0.983041i	$0.441294\pi$
$44$	−22.8191	−3.44011
$45$	0.956364	0.142566
$46$	−17.5899	−2.59348
$47$	10.3758	1.51346	0.756732	−	0.653726i	$-0.226795\pi$
$47$	10.3758	1.51346	0.756732	+	0.653726i	$0.226795\pi$
$48$	−1.57306	−0.227051
$49$	−6.68043	−0.954347
$50$	12.8825	1.82186
$51$	−0.208668	−0.0292194
$52$	−0.314541	−0.0436189
$53$	5.19462	0.713535	0.356768	−	0.934193i	$-0.383879\pi$
$53$	5.19462	0.713535	0.356768	+	0.934193i	$0.383879\pi$
$54$	−2.38411	−0.324436
$55$	1.48963	0.200862
$56$	4.34427	0.580527
$57$	0.151619	0.0200824
$58$	−4.98388	−0.654415
$59$	10.7496	1.39948	0.699741	−	0.714396i	$-0.253299\pi$
$59$	10.7496	1.39948	0.699741	+	0.714396i	$0.253299\pi$
$60$	0.239695	0.0309445
$61$	14.9701	1.91673	0.958365	−	0.285547i	$-0.0921754\pi$
$61$	14.9701	1.91673	0.958365	+	0.285547i	$0.0921754\pi$
$62$	15.5673	1.97705
$63$	1.68292	0.212028
$64$	10.6222	1.32777
$65$	0.0205332	0.00254683
$66$	−1.84960	−0.227670
$67$	3.00136	0.366674	0.183337	−	0.983050i	$-0.441310\pi$
$67$	3.00136	0.366674	0.183337	+	0.983050i	$0.441310\pi$
$68$	6.77276	0.821318
$69$	−1.01375	−0.122041
$70$	−0.477763	−0.0571036
$71$	6.28821	0.746273	0.373136	−	0.927776i	$-0.378282\pi$
$71$	6.28821	0.746273	0.373136	+	0.927776i	$0.378282\pi$
$72$	22.8779	2.69618
$73$	6.93566	0.811758	0.405879	−	0.913927i	$-0.366965\pi$
$73$	6.93566	0.811758	0.405879	+	0.913927i	$0.366965\pi$
$74$	0.0947459	0.0110140
$75$	0.742448	0.0857305
$76$	−4.92110	−0.564489
$77$	2.62131	0.298726
$78$	−0.0254950	−0.00288674
$79$	−12.4370	−1.39927	−0.699637	−	0.714499i	$-0.746655\pi$
$79$	−12.4370	−1.39927	−0.699637	+	0.714499i	$0.746655\pi$
$80$	−3.33298	−0.372639
$81$	8.79363	0.977070
$82$	−7.06270	−0.779945
$83$	−4.10558	−0.450646	−0.225323	−	0.974284i	$-0.572344\pi$
$83$	−4.10558	−0.450646	−0.225323	+	0.974284i	$0.572344\pi$
$84$	0.421792	0.0460213
$85$	−0.442126	−0.0479553
$86$	−6.32729	−0.682290
$87$	−0.287233	−0.0307946
$88$	35.6346	3.79866
$89$	15.6451	1.65838	0.829188	−	0.558969i	$-0.188803\pi$
$89$	15.6451	1.65838	0.829188	+	0.558969i	$0.188803\pi$
$90$	−2.51600	−0.265210
$91$	0.0361323	0.00378770
$92$	32.9031	3.43039
$93$	0.897179	0.0930331
$94$	−27.2966	−2.81543
$95$	0.321250	0.0329595
$96$	1.80806	0.184534
$97$	−11.8503	−1.20322	−0.601608	−	0.798792i	$-0.705473\pi$
$97$	−11.8503	−1.20322	−0.601608	+	0.798792i	$0.705473\pi$
$98$	17.5749	1.77533
$99$	13.8044	1.38739
$100$	−24.0977	−2.40977
$101$	−3.53917	−0.352161	−0.176080	−	0.984376i	$-0.556342\pi$
$101$	−3.53917	−0.352161	−0.176080	+	0.984376i	$0.556342\pi$
$102$	0.548965	0.0543556
$103$	−1.50481	−0.148273	−0.0741366	−	0.997248i	$-0.523620\pi$
$103$	−1.50481	−0.148273	−0.0741366	+	0.997248i	$0.523620\pi$
$104$	0.491189	0.0481651
$105$	−0.0275346	−0.00268710
$106$	−13.6660	−1.32736
$107$	6.33333	0.612266	0.306133	−	0.951989i	$-0.400965\pi$
$107$	6.33333	0.612266	0.306133	+	0.951989i	$0.400965\pi$
$108$	4.45965	0.429130
$109$	−6.89780	−0.660689	−0.330345	−	0.943860i	$-0.607165\pi$
$109$	−6.89780	−0.660689	−0.330345	+	0.943860i	$0.607165\pi$
$110$	−3.91892	−0.373655
$111$	0.00546043	0.000518281 0
$112$	−5.86506	−0.554196
$113$	−19.3670	−1.82189	−0.910947	−	0.412523i	$-0.864648\pi$
$113$	−19.3670	−1.82189	−0.910947	+	0.412523i	$0.864648\pi$
$114$	−0.398879	−0.0373585
$115$	−2.14792	−0.200294
$116$	9.32271	0.865592
$117$	0.190281	0.0175915
$118$	−28.2801	−2.60340
$119$	−0.778010	−0.0713200
$120$	−0.374310	−0.0341696
$121$	10.5017	0.954702
$122$	−39.3834	−3.56561
$123$	−0.407040	−0.0367016
$124$	−29.1198	−2.61503
$125$	3.17934	0.284369
$126$	−4.42741	−0.394425
$127$	0.628638	0.0557826	0.0278913	−	0.999611i	$-0.491121\pi$
$127$	0.628638	0.0557826	0.0278913	+	0.999611i	$0.491121\pi$
$128$	−4.09485	−0.361937
$129$	−0.364657	−0.0321062
$130$	−0.0540187	−0.00473776
$131$	−18.9919	−1.65933	−0.829667	−	0.558259i	$-0.811470\pi$
$131$	−18.9919	−1.65933	−0.829667	+	0.558259i	$0.811470\pi$
$132$	3.45982	0.301138
$133$	0.565304	0.0490181
$134$	−7.89596	−0.682107
$135$	−0.291126	−0.0250561
$136$	−10.5764	−0.906919
$137$	8.42134	0.719484	0.359742	−	0.933052i	$-0.382865\pi$
$137$	8.42134	0.719484	0.359742	+	0.933052i	$0.382865\pi$
$138$	2.66696	0.227027
$139$	−1.38780	−0.117712	−0.0588558	−	0.998266i	$-0.518745\pi$
$139$	−1.38780	−0.117712	−0.0588558	+	0.998266i	$0.518745\pi$
$140$	0.893690	0.0755306
$141$	−1.57317	−0.132484
$142$	−16.5430	−1.38826
$143$	0.296381	0.0247846
$144$	−30.8867	−2.57389
$145$	−0.608587	−0.0505404
$146$	−18.2463	−1.51008
$147$	1.01288	0.0835410
$148$	−0.177229	−0.0145682
$149$	12.9671	1.06231	0.531154	−	0.847275i	$-0.321758\pi$
$149$	12.9671	1.06231	0.531154	+	0.847275i	$0.321758\pi$
$150$	−1.95323	−0.159481
$151$	−3.68039	−0.299506	−0.149753	−	0.988723i	$-0.547848\pi$
$151$	−3.68039	−0.299506	−0.149753	+	0.988723i	$0.547848\pi$
$152$	7.68484	0.623323
$153$	−4.09717	−0.331236
$154$	−6.89614	−0.555707
$155$	1.90094	0.152687
$156$	0.0476903	0.00381828
$157$	−16.6159	−1.32609	−0.663046	−	0.748579i	$-0.730737\pi$
$157$	−16.6159	−1.32609	−0.663046	+	0.748579i	$0.730737\pi$
$158$	32.7193	2.60301
$159$	−0.787603	−0.0624610
$160$	3.83091	0.302860
$161$	−3.77970	−0.297882
$162$	−23.1343	−1.81760
$163$	−13.9917	−1.09592	−0.547959	−	0.836505i	$-0.684595\pi$
$163$	−13.9917	−1.09592	−0.547959	+	0.836505i	$0.684595\pi$
$164$	13.2113	1.03163
$165$	−0.225857	−0.0175829
$166$	10.8010	0.838317
$167$	−6.97817	−0.539987	−0.269994	−	0.962862i	$-0.587022\pi$
$167$	−6.97817	−0.539987	−0.269994	+	0.962862i	$0.587022\pi$
$168$	−0.658674	−0.0508178
$169$	−12.9959	−0.999686
$170$	1.16314	0.0892090
$171$	2.97701	0.227658
$172$	11.8357	0.902462
$173$	−1.32835	−0.100992	−0.0504962	−	0.998724i	$-0.516080\pi$
$173$	−1.32835	−0.100992	−0.0504962	+	0.998724i	$0.516080\pi$
$174$	0.755651	0.0572858
$175$	2.76818	0.209255
$176$	−48.1091	−3.62636
$177$	−1.62985	−0.122507
$178$	−41.1591	−3.08501
$179$	6.11145	0.456791	0.228396	−	0.973568i	$-0.426652\pi$
$179$	6.11145	0.456791	0.228396	+	0.973568i	$0.426652\pi$
$180$	4.70637	0.350792
$181$	−1.97349	−0.146688	−0.0733441	−	0.997307i	$-0.523367\pi$
$181$	−1.97349	−0.146688	−0.0733441	+	0.997307i	$0.523367\pi$
$182$	−0.0950569	−0.00704609
$183$	−2.26976	−0.167785
$184$	−51.3818	−3.78792
$185$	0.0115695	0.000850608 0
$186$	−2.36030	−0.173065
$187$	−6.38175	−0.466680
$188$	51.0603	3.72395
$189$	−0.512295	−0.0372640
$190$	−0.845143	−0.0613131
$191$	0.852529	0.0616869	0.0308434	−	0.999524i	$-0.490181\pi$
$191$	0.852529	0.0616869	0.0308434	+	0.999524i	$0.490181\pi$
$192$	−1.61053	−0.116230
$193$	11.1539	0.802876	0.401438	−	0.915886i	$-0.368511\pi$
$193$	11.1539	0.802876	0.401438	+	0.915886i	$0.368511\pi$
$194$	31.1757	2.23829
$195$	−0.00311323	−0.000222943 0
$196$	−32.8751	−2.34822
$197$	−23.0857	−1.64479	−0.822395	−	0.568917i	$-0.807363\pi$
$197$	−23.0857	−1.64479	−0.822395	+	0.568917i	$0.807363\pi$
$198$	−36.3166	−2.58091
$199$	13.4599	0.954151	0.477075	−	0.878862i	$-0.341697\pi$
$199$	13.4599	0.954151	0.477075	+	0.878862i	$0.341697\pi$
$200$	37.6311	2.66092
$201$	−0.455063	−0.0320976
$202$	9.31085	0.655109
$203$	−1.07093	−0.0751647
$204$	−1.02688	−0.0718959
$205$	−0.862434	−0.0602350
$206$	3.95885	0.275826
$207$	−19.9047	−1.38347
$208$	−0.663139	−0.0459804
$209$	4.63699	0.320748
$210$	0.0724379	0.00499869
$211$	8.16796	0.562306	0.281153	−	0.959663i	$-0.409283\pi$
$211$	8.16796	0.562306	0.281153	+	0.959663i	$0.409283\pi$
$212$	25.5632	1.75569
$213$	−0.953412	−0.0653267
$214$	−16.6617	−1.13897
$215$	−0.772633	−0.0526931
$216$	−6.96422	−0.473855
$217$	3.34508	0.227079
$218$	18.1467	1.22905
$219$	−1.05158	−0.0710591
$220$	7.33064	0.494231
$221$	−0.0879665	−0.00591727
$222$	−0.0143653	−0.000964135 0
$223$	−14.5992	−0.977637	−0.488819	−	0.872385i	$-0.662572\pi$
$223$	−14.5992	−0.977637	−0.488819	+	0.872385i	$0.662572\pi$
$224$	6.74126	0.450419
$225$	14.5778	0.971855
$226$	50.9507	3.38919
$227$	−20.0319	−1.32957	−0.664783	−	0.747036i	$-0.731476\pi$
$227$	−20.0319	−1.32957	−0.664783	+	0.747036i	$0.731476\pi$
$228$	0.746133	0.0494139
$229$	9.62935	0.636326	0.318163	−	0.948036i	$-0.396934\pi$
$229$	9.62935	0.636326	0.318163	+	0.948036i	$0.396934\pi$
$230$	5.65074	0.372599
$231$	−0.397441	−0.0261497
$232$	−14.5584	−0.955808
$233$	−4.48142	−0.293588	−0.146794	−	0.989167i	$-0.546895\pi$
$233$	−4.48142	−0.293588	−0.146794	+	0.989167i	$0.546895\pi$
$234$	−0.500590	−0.0327246
$235$	−3.33322	−0.217435
$236$	52.9000	3.44350
$237$	1.88569	0.122489
$238$	2.04679	0.132674
$239$	18.2607	1.18119	0.590594	−	0.806969i	$-0.298893\pi$
$239$	18.2607	1.18119	0.590594	+	0.806969i	$0.298893\pi$
$240$	0.505344	0.0326198
$241$	17.6080	1.13423	0.567115	−	0.823639i	$-0.308060\pi$
$241$	17.6080	1.13423	0.567115	+	0.823639i	$0.308060\pi$
$242$	−27.6279	−1.77599
$243$	−4.05197	−0.259934
$244$	73.6696	4.71621
$245$	2.14609	0.137108
$246$	1.07084	0.0682743
$247$	0.0639167	0.00406692
$248$	45.4737	2.88758
$249$	0.622484	0.0394483
$250$	−8.36421	−0.528999
$251$	−11.7241	−0.740021	−0.370010	−	0.929028i	$-0.620646\pi$
$251$	−11.7241	−0.740021	−0.370010	+	0.929028i	$0.620646\pi$
$252$	8.28181	0.521705
$253$	−31.0036	−1.94918
$254$	−1.65382	−0.103770
$255$	0.0670347	0.00419787
$256$	−10.4717	−0.654480
$257$	1.90707	0.118960	0.0594798	−	0.998230i	$-0.481056\pi$
$257$	1.90707	0.118960	0.0594798	+	0.998230i	$0.481056\pi$
$258$	0.959339	0.0597258
$259$	0.0203589	0.00126504
$260$	0.101046	0.00626661
$261$	−5.63976	−0.349092
$262$	49.9640	3.08679
$263$	5.84695	0.360538	0.180269	−	0.983617i	$-0.442303\pi$
$263$	5.84695	0.360538	0.180269	+	0.983617i	$0.442303\pi$
$264$	−5.40288	−0.332524
$265$	−1.66877	−0.102512
$266$	−1.48720	−0.0911861
$267$	−2.37209	−0.145170
$268$	14.7700	0.902220
$269$	−14.3137	−0.872721	−0.436360	−	0.899772i	$-0.643733\pi$
$269$	−14.3137	−0.872721	−0.436360	+	0.899772i	$0.643733\pi$
$270$	0.765893	0.0466108
$271$	−21.8420	−1.32681	−0.663404	−	0.748262i	$-0.730889\pi$
$271$	−21.8420	−1.32681	−0.663404	+	0.748262i	$0.730889\pi$
$272$	14.2789	0.865783
$273$	−0.00547835	−0.000331565 0
$274$	−22.1549	−1.33842
$275$	22.7064	1.36925
$276$	−4.98874	−0.300287
$277$	−20.9533	−1.25896	−0.629480	−	0.777017i	$-0.716732\pi$
$277$	−20.9533	−1.25896	−0.629480	+	0.777017i	$0.716732\pi$
$278$	3.65102	0.218974
$279$	17.6159	1.05464
$280$	−1.39559	−0.0834027
$281$	12.2747	0.732246	0.366123	−	0.930567i	$-0.380685\pi$
$281$	12.2747	0.732246	0.366123	+	0.930567i	$0.380685\pi$
$282$	4.13868	0.246455
$283$	1.24217	0.0738396	0.0369198	−	0.999318i	$-0.488245\pi$
$283$	1.24217	0.0738396	0.0369198	+	0.999318i	$0.488245\pi$
$284$	30.9449	1.83624
$285$	−0.0487076	−0.00288519
$286$	−0.779720	−0.0461058
$287$	−1.51763	−0.0895827
$288$	35.5009	2.09191
$289$	−15.1059	−0.888582
$290$	1.60107	0.0940180
$291$	1.79673	0.105326
$292$	34.1311	1.99737
$293$	−2.87163	−0.167763	−0.0838813	−	0.996476i	$-0.526732\pi$
$293$	−2.87163	−0.167763	−0.0838813	+	0.996476i	$0.526732\pi$
$294$	−2.66469	−0.155408
$295$	−3.45331	−0.201060
$296$	0.276763	0.0160865
$297$	−4.20218	−0.243835
$298$	−34.1139	−1.97617
$299$	−0.427355	−0.0247146
$300$	3.65366	0.210944
$301$	−1.35960	−0.0783663
$302$	9.68236	0.557157
$303$	0.536606	0.0308272
$304$	−10.3751	−0.595050
$305$	−4.80915	−0.275371
$306$	10.7788	0.616184
$307$	24.9696	1.42509	0.712546	−	0.701626i	$-0.247542\pi$
$307$	24.9696	1.42509	0.712546	+	0.701626i	$0.247542\pi$
$308$	12.8997	0.735031
$309$	0.228158	0.0129794
$310$	−5.00098	−0.284037
$311$	−22.1074	−1.25359	−0.626796	−	0.779183i	$-0.715634\pi$
$311$	−22.1074	−1.25359	−0.626796	+	0.779183i	$0.715634\pi$
$312$	−0.0744736	−0.00421624
$313$	−30.8405	−1.74321	−0.871605	−	0.490209i	$-0.836921\pi$
$313$	−30.8405	−1.74321	−0.871605	+	0.490209i	$0.836921\pi$
$314$	43.7130	2.46687
$315$	−0.540636	−0.0304614
$316$	−61.2038	−3.44298
$317$	−1.00000	−0.0561656
$317$	−1.00000	−0.0561656
$318$	2.07203	0.116193
$319$	−8.78449	−0.491837
$320$	−3.41238	−0.190758
$321$	−0.960253	−0.0535961
$322$	9.94362	0.554136
$323$	−1.37627	−0.0765776
$324$	43.2744	2.40413
$325$	0.312987	0.0173614
$326$	36.8095	2.03869
$327$	1.04584	0.0578349
$328$	−20.6309	−1.13915
$329$	−5.86547	−0.323374
$330$	0.594184	0.0327087
$331$	22.8745	1.25730	0.628649	−	0.777689i	$-0.283608\pi$
$331$	22.8745	1.25730	0.628649	+	0.777689i	$0.283608\pi$
$332$	−20.2040	−1.10884
$333$	0.107214	0.00587532
$334$	18.3582	1.00451
$335$	−0.964184	−0.0526790
$336$	0.889255	0.0485128
$337$	28.6553	1.56096	0.780478	−	0.625183i	$-0.214976\pi$
$337$	28.6553	1.56096	0.780478	+	0.625183i	$0.214976\pi$
$338$	34.1896	1.85967
$339$	2.93641	0.159484
$340$	−2.17575	−0.117996
$341$	27.4386	1.48588
$342$	−7.83192	−0.423502
$343$	7.73360	0.417575
$344$	−18.4827	−0.996520
$345$	0.325665	0.0175332
$346$	3.49461	0.187872
$347$	−32.5024	−1.74482	−0.872409	−	0.488777i	$-0.837443\pi$
$347$	−32.5024	−1.74482	−0.872409	+	0.488777i	$0.837443\pi$
$348$	−1.41350	−0.0757716
$349$	−11.4728	−0.614123	−0.307062	−	0.951690i	$-0.599346\pi$
$349$	−11.4728	−0.614123	−0.307062	+	0.951690i	$0.599346\pi$
$350$	−7.28252	−0.389267
$351$	−0.0579231	−0.00309171
$352$	55.2962	2.94730
$353$	16.1913	0.861776	0.430888	−	0.902405i	$-0.358200\pi$
$353$	16.1913	0.861776	0.430888	+	0.902405i	$0.358200\pi$
$354$	4.28780	0.227894
$355$	−2.02008	−0.107215
$356$	76.9911	4.08052
$357$	0.117961	0.00624316
$358$	−16.0780	−0.849749
$359$	−25.2772	−1.33408	−0.667040	−	0.745022i	$-0.732439\pi$
$359$	−25.2772	−1.33408	−0.667040	+	0.745022i	$0.732439\pi$
$360$	−7.34950	−0.387353
$361$	1.00000	0.0526316
$362$	5.19185	0.272878
$363$	−1.59226	−0.0835720
$364$	0.177811	0.00931983
$365$	−2.22808	−0.116623
$366$	5.97128	0.312124
$367$	29.3420	1.53164	0.765820	−	0.643055i	$-0.222333\pi$
$367$	29.3420	1.53164	0.765820	+	0.643055i	$0.222333\pi$
$368$	69.3690	3.61611
$369$	−7.99215	−0.416055
$370$	−0.0304371	−0.00158235
$371$	−2.93654	−0.152457
$372$	4.41511	0.228913
$373$	6.89509	0.357014	0.178507	−	0.983939i	$-0.442873\pi$
$373$	6.89509	0.357014	0.178507	+	0.983939i	$0.442873\pi$
$374$	16.7891	0.868144
$375$	−0.482049	−0.0248929
$376$	−79.7362	−4.11208
$377$	−0.121086	−0.00623625
$378$	1.34774	0.0693205
$379$	−10.7299	−0.551157	−0.275579	−	0.961279i	$-0.588869\pi$
$379$	−10.7299	−0.551157	−0.275579	+	0.961279i	$0.588869\pi$
$380$	1.58090	0.0810986
$381$	−0.0953134	−0.00488306
$382$	−2.24283	−0.114753
$383$	13.6852	0.699283	0.349642	−	0.936884i	$-0.386303\pi$
$383$	13.6852	0.699283	0.349642	+	0.936884i	$0.386303\pi$
$384$	0.620857	0.0316830
$385$	−0.842095	−0.0429171
$386$	−29.3437	−1.49355
$387$	−7.15997	−0.363962
$388$	−58.3165	−2.96057
$389$	−37.8353	−1.91832	−0.959162	−	0.282858i	$-0.908718\pi$
$389$	−37.8353	−1.91832	−0.959162	+	0.282858i	$0.908718\pi$
$390$	0.00819027	0.000414730 0
$391$	9.20191	0.465361
$392$	51.3380	2.59296
$393$	2.87954	0.145254
$394$	60.7339	3.05973
$395$	3.99539	0.201030
$396$	67.9328	3.41375
$397$	−5.80187	−0.291187	−0.145594	−	0.989344i	$-0.546509\pi$
$397$	−5.80187	−0.291187	−0.145594	+	0.989344i	$0.546509\pi$
$398$	−35.4104	−1.77496
$399$	−0.0857108	−0.00429091
$400$	−50.8046	−2.54023
$401$	−0.140898	−0.00703612	−0.00351806	−	0.999994i	$-0.501120\pi$
$401$	−0.140898	−0.00703612	−0.00351806	+	0.999994i	$0.501120\pi$
$402$	1.19718	0.0597098
$403$	0.378215	0.0188403
$404$	−17.4166	−0.866510
$405$	−2.82495	−0.140373
$406$	2.81741	0.139826
$407$	0.166997	0.00827775
$408$	1.60358	0.0793892
$409$	32.7166	1.61773	0.808865	−	0.587995i	$-0.200082\pi$
$409$	32.7166	1.61773	0.808865	+	0.587995i	$0.200082\pi$
$410$	2.26889	0.112053
$411$	−1.27684	−0.0629817
$412$	−7.40532	−0.364834
$413$	−6.07681	−0.299020
$414$	52.3652	2.57361
$415$	1.31892	0.0647431
$416$	0.762207	0.0373703
$417$	0.210417	0.0103042
$418$	−12.1990	−0.596673
$419$	16.7990	0.820686	0.410343	−	0.911931i	$-0.365409\pi$
$419$	16.7990	0.820686	0.410343	+	0.911931i	$0.365409\pi$
$420$	−0.135501	−0.00661175
$421$	31.9117	1.55528	0.777640	−	0.628710i	$-0.216417\pi$
$421$	31.9117	1.55528	0.777640	+	0.628710i	$0.216417\pi$
$422$	−21.4883	−1.04603
$423$	−30.8888	−1.50187
$424$	−39.9198	−1.93868
$425$	−6.73931	−0.326904
$426$	2.50824	0.121524
$427$	−8.46267	−0.409538
$428$	31.1670	1.50651
$429$	−0.0449370	−0.00216958
$430$	2.03264	0.0980227
$431$	4.56161	0.219725	0.109863	−	0.993947i	$-0.464959\pi$
$431$	4.56161	0.219725	0.109863	+	0.993947i	$0.464959\pi$
$432$	9.40218	0.452362
$433$	−24.2816	−1.16690	−0.583449	−	0.812150i	$-0.698297\pi$
$433$	−24.2816	−1.16690	−0.583449	+	0.812150i	$0.698297\pi$
$434$	−8.80025	−0.422425
$435$	0.0922733	0.00442417
$436$	−33.9448	−1.62566
$437$	−6.68613	−0.319841
$438$	2.76649	0.132188
$439$	4.66088	0.222452	0.111226	−	0.993795i	$-0.464522\pi$
$439$	4.66088	0.222452	0.111226	+	0.993795i	$0.464522\pi$
$440$	−11.4476	−0.545742
$441$	19.8877	0.947034
$442$	0.231422	0.0110076
$443$	−27.2262	−1.29355	−0.646777	−	0.762679i	$-0.723883\pi$
$443$	−27.2262	−1.29355	−0.646777	+	0.762679i	$0.723883\pi$
$444$	0.0268713	0.00127526
$445$	−5.02598	−0.238254
$446$	38.4077	1.81866
$447$	−1.96606	−0.0929916
$448$	−6.00477	−0.283699
$449$	−10.9118	−0.514960	−0.257480	−	0.966284i	$-0.582892\pi$
$449$	−10.9118	−0.514960	−0.257480	+	0.966284i	$0.582892\pi$
$450$	−38.3513	−1.80790
$451$	−12.4486	−0.586181
$452$	−95.3070	−4.48287
$453$	0.558017	0.0262179
$454$	52.7000	2.47333
$455$	−0.0116075	−0.000544168 0
$456$	−1.16517	−0.0545640
$457$	−31.3364	−1.46585	−0.732927	−	0.680307i	$-0.761846\pi$
$457$	−31.3364	−1.46585	−0.732927	+	0.680307i	$0.761846\pi$
$458$	−25.3329	−1.18373
$459$	1.24721	0.0582150
$460$	−10.5701	−0.492835
$461$	11.5167	0.536385	0.268192	−	0.963365i	$-0.413574\pi$
$461$	11.5167	0.536385	0.268192	+	0.963365i	$0.413574\pi$
$462$	1.04559	0.0486451
$463$	9.94675	0.462265	0.231132	−	0.972922i	$-0.425757\pi$
$463$	9.94675	0.462265	0.231132	+	0.972922i	$0.425757\pi$
$464$	19.6549	0.912455
$465$	−0.288218	−0.0133658
$466$	11.7897	0.546148
$467$	1.04001	0.0481257	0.0240629	−	0.999710i	$-0.492340\pi$
$467$	1.04001	0.0481257	0.0240629	+	0.999710i	$0.492340\pi$
$468$	0.936391	0.0432847
$469$	−1.69668	−0.0783453
$470$	8.76902	0.404485
$471$	2.51928	0.116082
$472$	−82.6092	−3.80239
$473$	−11.1524	−0.512786
$474$	−4.96087	−0.227860
$475$	4.89680	0.224681
$476$	−3.82867	−0.175487
$477$	−15.4644	−0.708068
$478$	−48.0403	−2.19731
$479$	29.6099	1.35291	0.676456	−	0.736483i	$-0.263515\pi$
$479$	29.6099	1.35291	0.676456	+	0.736483i	$0.263515\pi$
$480$	−0.580838	−0.0265115
$481$	0.00230190	0.000104958 0
$482$	−46.3231	−2.10996
$483$	0.573074	0.0260758
$484$	51.6801	2.34909
$485$	3.80690	0.172863
$486$	10.6599	0.483544
$487$	32.1482	1.45677	0.728387	−	0.685166i	$-0.240270\pi$
$487$	32.1482	1.45677	0.728387	+	0.685166i	$0.240270\pi$
$488$	−115.043	−5.20775
$489$	2.12142	0.0959337
$490$	−5.64592	−0.255057
$491$	22.4433	1.01285	0.506426	−	0.862283i	$-0.330966\pi$
$491$	22.4433	1.01285	0.506426	+	0.862283i	$0.330966\pi$
$492$	−2.00309	−0.0903061
$493$	2.60725	0.117425
$494$	−0.168152	−0.00756551
$495$	−4.43465	−0.199323
$496$	−61.3925	−2.75661
$497$	−3.55475	−0.159452
$498$	−1.63763	−0.0733840
$499$	−0.137035	−0.00613454	−0.00306727	−	0.999995i	$-0.500976\pi$
$499$	−0.137035	−0.00613454	−0.00306727	+	0.999995i	$0.500976\pi$
$500$	15.6459	0.699705
$501$	1.05802	0.0472690
$502$	30.8438	1.37663
$503$	−41.9990	−1.87264	−0.936321	−	0.351144i	$-0.885793\pi$
$503$	−41.9990	−1.87264	−0.936321	+	0.351144i	$0.885793\pi$
$504$	−12.9329	−0.576079
$505$	1.13696	0.0505940
$506$	81.5641	3.62597
$507$	1.97043	0.0875098
$508$	3.09359	0.137256
$509$	−13.6595	−0.605445	−0.302722	−	0.953079i	$-0.597895\pi$
$509$	−13.6595	−0.605445	−0.302722	+	0.953079i	$0.597895\pi$
$510$	−0.176355	−0.00780912
$511$	−3.92076	−0.173444
$512$	35.7386	1.57944
$513$	−0.906229	−0.0400110
$514$	−5.01711	−0.221295
$515$	0.483419	0.0213020
$516$	−1.79451	−0.0789991
$517$	−48.1124	−2.11598
$518$	−0.0535602	−0.00235330
$519$	0.201403	0.00884060
$520$	−0.157794	−0.00691974
$521$	−17.9553	−0.786635	−0.393318	−	0.919403i	$-0.628673\pi$
$521$	−17.9553	−0.786635	−0.393318	+	0.919403i	$0.628673\pi$
$522$	14.8371	0.649401
$523$	−9.07837	−0.396970	−0.198485	−	0.980104i	$-0.563602\pi$
$523$	−9.07837	−0.396970	−0.198485	+	0.980104i	$0.563602\pi$
$524$	−93.4613	−4.08288
$525$	−0.419709	−0.0183176
$526$	−15.3821	−0.670693
$527$	−8.14382	−0.354750
$528$	7.29425	0.317442
$529$	21.7044	0.943668
$530$	4.39019	0.190698
$531$	−32.0018	−1.38876
$532$	2.78192	0.120611
$533$	−0.171592	−0.00743248
$534$	6.24050	0.270053
$535$	−2.03458	−0.0879625
$536$	−23.0649	−0.996253
$537$	−0.926613	−0.0399863
$538$	37.6564	1.62348
$539$	30.9771	1.33428
$540$	−1.43266	−0.0616519
$541$	8.70935	0.374444	0.187222	−	0.982318i	$-0.440052\pi$
$541$	8.70935	0.374444	0.187222	+	0.982318i	$0.440052\pi$
$542$	57.4619	2.46820
$543$	0.299218	0.0128407
$544$	−16.4120	−0.703659
$545$	2.21591	0.0949193
$546$	0.0144124	0.000616796 0
$547$	−19.0164	−0.813082	−0.406541	−	0.913632i	$-0.633265\pi$
$547$	−19.0164	−0.813082	−0.406541	+	0.913632i	$0.633265\pi$
$548$	41.4423	1.77033
$549$	−44.5663	−1.90204
$550$	−59.7361	−2.54715
$551$	−1.89444	−0.0807057
$552$	7.79047	0.331584
$553$	7.03069	0.298975
$554$	55.1238	2.34199
$555$	−0.00175416	−7.44600e−5 0
$556$	−6.82950	−0.289635
$557$	−33.4093	−1.41560	−0.707799	−	0.706413i	$-0.750312\pi$
$557$	−33.4093	−1.41560	−0.707799	+	0.706413i	$0.750312\pi$
$558$	−46.3440	−1.96190
$559$	−0.153725	−0.00650188
$560$	1.88415	0.0796198
$561$	0.967595	0.0408519
$562$	−32.2922	−1.36216
$563$	33.5164	1.41255	0.706274	−	0.707939i	$-0.250375\pi$
$563$	33.5164	1.41255	0.706274	+	0.707939i	$0.250375\pi$
$564$	−7.74171	−0.325985
$565$	6.22164	0.261746
$566$	−3.26791	−0.137361
$567$	−4.97108	−0.208766
$568$	−48.3238	−2.02762
$569$	37.6232	1.57725	0.788624	−	0.614875i	$-0.210794\pi$
$569$	37.6232	1.57725	0.788624	+	0.614875i	$0.210794\pi$
$570$	0.128140	0.00536719
$571$	−1.05810	−0.0442800	−0.0221400	−	0.999755i	$-0.507048\pi$
$571$	−1.05810	−0.0442800	−0.0221400	+	0.999755i	$0.507048\pi$
$572$	1.45852	0.0609839
$573$	−0.129260	−0.00539990
$574$	3.99257	0.166647
$575$	−32.7406	−1.36538
$576$	−31.6224	−1.31760
$577$	−21.0600	−0.876738	−0.438369	−	0.898795i	$-0.644444\pi$
$577$	−21.0600	−0.876738	−0.438369	+	0.898795i	$0.644444\pi$
$578$	39.7406	1.65299
$579$	−1.69114	−0.0702816
$580$	−2.99492	−0.124357
$581$	2.32090	0.0962872
$582$	−4.72684	−0.195934
$583$	−24.0874	−0.997599
$584$	−53.2994	−2.20555
$585$	−0.0611276	−0.00252731
$586$	7.55469	0.312082
$587$	3.34088	0.137893	0.0689465	−	0.997620i	$-0.478036\pi$
$587$	3.34088	0.137893	0.0689465	+	0.997620i	$0.478036\pi$
$588$	4.98449	0.205557
$589$	5.91732	0.243819
$590$	9.08498	0.374023
$591$	3.50024	0.143980
$592$	−0.373649	−0.0153569
$593$	−16.7838	−0.689228	−0.344614	−	0.938744i	$-0.611990\pi$
$593$	−16.7838	−0.689228	−0.344614	+	0.938744i	$0.611990\pi$
$594$	11.0551	0.453596
$595$	0.249935	0.0102463
$596$	63.8126	2.61387
$597$	−2.04078	−0.0835238
$598$	1.12429	0.0459755
$599$	5.98907	0.244707	0.122353	−	0.992487i	$-0.460956\pi$
$599$	5.98907	0.244707	0.122353	+	0.992487i	$0.460956\pi$
$600$	−5.70559	−0.232930
$601$	9.32877	0.380529	0.190264	−	0.981733i	$-0.439066\pi$
$601$	9.32877	0.380529	0.190264	+	0.981733i	$0.439066\pi$
$602$	3.57684	0.145781
$603$	−8.93507	−0.363864
$604$	−18.1116	−0.736949
$605$	−3.37367	−0.137159
$606$	−1.41170	−0.0573465
$607$	−17.6969	−0.718293	−0.359147	−	0.933281i	$-0.616932\pi$
$607$	−17.6969	−0.718293	−0.359147	+	0.933281i	$0.616932\pi$
$608$	11.9250	0.483623
$609$	0.162374	0.00657971
$610$	12.6519	0.512261
$611$	−0.663185	−0.0268296
$612$	−20.1626	−0.815024
$613$	11.5002	0.464490	0.232245	−	0.972657i	$-0.425393\pi$
$613$	11.5002	0.464490	0.232245	+	0.972657i	$0.425393\pi$
$614$	−65.6901	−2.65103
$615$	0.130761	0.00527281
$616$	−20.1444	−0.811639
$617$	35.8428	1.44298	0.721489	−	0.692426i	$-0.243458\pi$
$617$	35.8428	1.44298	0.721489	+	0.692426i	$0.243458\pi$
$618$	−0.600237	−0.0241451
$619$	41.6671	1.67474	0.837372	−	0.546634i	$-0.184091\pi$
$619$	41.6671	1.67474	0.837372	+	0.546634i	$0.184091\pi$
$620$	9.35471	0.375694
$621$	6.05917	0.243146
$622$	58.1600	2.33200
$623$	−8.84423	−0.354337
$624$	0.100545	0.00402500
$625$	23.4626	0.938505
$626$	81.1353	3.24282
$627$	−0.703057	−0.0280774
$628$	−81.7685	−3.26292
$629$	−0.0495651	−0.00197629
$630$	1.42231	0.0566660
$631$	−33.9208	−1.35036	−0.675182	−	0.737651i	$-0.735935\pi$
$631$	−33.9208	−1.35036	−0.675182	+	0.737651i	$0.735935\pi$
$632$	95.5764	3.80183
$633$	−1.23842	−0.0492227
$634$	2.63080	0.104482
$635$	−0.201950	−0.00801412
$636$	−3.87588	−0.153688
$637$	0.426991	0.0169180
$638$	23.1102	0.914942
$639$	−18.7201	−0.740554
$640$	1.31547	0.0519985
$641$	−40.6684	−1.60631	−0.803153	−	0.595773i	$-0.796846\pi$
$641$	−40.6684	−1.60631	−0.803153	+	0.595773i	$0.796846\pi$
$642$	2.52623	0.0997025
$643$	−9.39786	−0.370616	−0.185308	−	0.982681i	$-0.559328\pi$
$643$	−9.39786	−0.370616	−0.185308	+	0.982681i	$0.559328\pi$
$644$	−18.6003	−0.732954
$645$	0.117146	0.00461261
$646$	3.62069	0.142454
$647$	−29.3762	−1.15490	−0.577449	−	0.816427i	$-0.695952\pi$
$647$	−29.3762	−1.15490	−0.577449	+	0.816427i	$0.695952\pi$
$648$	−67.5776	−2.65470
$649$	−49.8460	−1.95663
$650$	−0.823406	−0.0322966
$651$	−0.507179	−0.0198779
$652$	−68.8549	−2.69656
$653$	1.63436	0.0639576	0.0319788	−	0.999489i	$-0.489819\pi$
$653$	1.63436	0.0639576	0.0319788	+	0.999489i	$0.489819\pi$
$654$	−2.75139	−0.107588
$655$	6.10116	0.238392
$656$	27.8531	1.08748
$657$	−20.6475	−0.805537
$658$	15.4309	0.601558
$659$	8.51844	0.331831	0.165916	−	0.986140i	$-0.446942\pi$
$659$	8.51844	0.331831	0.165916	+	0.986140i	$0.446942\pi$
$660$	−1.11146	−0.0432637
$661$	−35.6124	−1.38516	−0.692581	−	0.721340i	$-0.743526\pi$
$661$	−35.6124	−1.38516	−0.692581	+	0.721340i	$0.743526\pi$
$662$	−60.1783	−2.33890
$663$	0.0133374	0.000517982 0
$664$	31.5507	1.22441
$665$	−0.181604	−0.00704229
$666$	−0.282060	−0.0109296
$667$	12.6664	0.490447
$668$	−34.3403	−1.32867
$669$	2.21352	0.0855797
$670$	2.53658	0.0979964
$671$	−69.4164	−2.67979
$672$	−1.02210	−0.0394285
$673$	−12.2901	−0.473748	−0.236874	−	0.971540i	$-0.576123\pi$
$673$	−12.2901	−0.473748	−0.236874	+	0.971540i	$0.576123\pi$
$674$	−75.3864	−2.90378
$675$	−4.43762	−0.170804
$676$	−63.9542	−2.45978
$677$	−32.1509	−1.23566	−0.617829	−	0.786312i	$-0.711988\pi$
$677$	−32.1509	−1.23566	−0.617829	+	0.786312i	$0.711988\pi$
$678$	−7.72510	−0.296681
$679$	6.69902	0.257085
$680$	3.39766	0.130294
$681$	3.03722	0.116387
$682$	−72.1854	−2.76412
$683$	39.7068	1.51934	0.759669	−	0.650309i	$-0.225361\pi$
$683$	39.7068	1.51934	0.759669	+	0.650309i	$0.225361\pi$
$684$	14.6502	0.560164
$685$	−2.70535	−0.103366
$686$	−20.3456	−0.776797
$687$	−1.45999	−0.0557022
$688$	24.9529	0.951320
$689$	−0.332023	−0.0126491
$690$	−0.856760	−0.0326163
$691$	5.49492	0.209037	0.104518	−	0.994523i	$-0.466670\pi$
$691$	5.49492	0.209037	0.104518	+	0.994523i	$0.466670\pi$
$692$	−6.53693	−0.248497
$693$	−7.80367	−0.296437
$694$	85.5072	3.24581
$695$	0.445830	0.0169113
$696$	2.20734	0.0836688
$697$	3.69476	0.139949
$698$	30.1826	1.14243
$699$	0.679469	0.0256999
$700$	13.6225	0.514882
$701$	11.5975	0.438032	0.219016	−	0.975721i	$-0.429715\pi$
$701$	11.5975	0.438032	0.219016	+	0.975721i	$0.429715\pi$
$702$	0.152384	0.00575137
$703$	0.0360141	0.00135830
$704$	−49.2551	−1.85637
$705$	0.505379	0.0190337
$706$	−42.5960	−1.60312
$707$	2.00071	0.0752444
$708$	−8.02066	−0.301435
$709$	17.7056	0.664949	0.332475	−	0.943112i	$-0.392116\pi$
$709$	17.7056	0.664949	0.332475	+	0.943112i	$0.392116\pi$
$710$	5.31443	0.199447
$711$	37.0251	1.38855
$712$	−120.230	−4.50581
$713$	−39.5640	−1.48168
$714$	−0.310332	−0.0116139
$715$	−0.0952124	−0.00356074
$716$	30.0751	1.12396
$717$	−2.76867	−0.103398
$718$	66.4993	2.48173
$719$	−23.4975	−0.876309	−0.438154	−	0.898900i	$-0.644368\pi$
$719$	−23.4975	−0.876309	−0.438154	+	0.898900i	$0.644368\pi$
$720$	9.92233	0.369783
$721$	0.850675	0.0316808
$722$	−2.63080	−0.0979082
$723$	−2.66971	−0.0992874
$724$	−9.71174	−0.360934
$725$	−9.27667	−0.344527
$726$	4.18892	0.155465
$727$	29.2908	1.08634	0.543168	−	0.839624i	$-0.317225\pi$
$727$	29.2908	1.08634	0.543168	+	0.839624i	$0.317225\pi$
$728$	−0.277671	−0.0102912
$729$	−25.7665	−0.954316
$730$	5.86163	0.216949
$731$	3.31004	0.122426
$732$	−11.1697	−0.412844
$733$	−18.3142	−0.676449	−0.338224	−	0.941065i	$-0.609826\pi$
$733$	−18.3142	−0.676449	−0.338224	+	0.941065i	$0.609826\pi$
$734$	−77.1929	−2.84924
$735$	−0.325388	−0.0120021
$736$	−79.7322	−2.93897
$737$	−13.9173	−0.512649
$738$	21.0257	0.773968
$739$	−0.866860	−0.0318880	−0.0159440	−	0.999873i	$-0.505075\pi$
$739$	−0.866860	−0.0318880	−0.0159440	+	0.999873i	$0.505075\pi$
$740$	0.0569348	0.00209297
$741$	−0.00969099	−0.000356007 0
$742$	7.72544	0.283610
$743$	12.6859	0.465400	0.232700	−	0.972549i	$-0.425244\pi$
$743$	12.6859	0.465400	0.232700	+	0.972549i	$0.425244\pi$
$744$	−6.89467	−0.252771
$745$	−4.16569	−0.152619
$746$	−18.1396	−0.664138
$747$	12.2224	0.447193
$748$	−31.4052	−1.14829
$749$	−3.58025	−0.130820
$750$	1.26817	0.0463072
$751$	−25.8972	−0.945001	−0.472501	−	0.881330i	$-0.656649\pi$
$751$	−25.8972	−0.945001	−0.472501	+	0.881330i	$0.656649\pi$
$752$	107.649	3.92557
$753$	1.77760	0.0647794
$754$	0.318553	0.0116010
$755$	1.18232	0.0430291
$756$	−2.52106	−0.0916899
$757$	−7.65024	−0.278053	−0.139026	−	0.990289i	$-0.544397\pi$
$757$	−7.65024	−0.278053	−0.139026	+	0.990289i	$0.544397\pi$
$758$	28.2282	1.02529
$759$	4.70073	0.170626
$760$	−2.46875	−0.0895510
$761$	14.0560	0.509530	0.254765	−	0.967003i	$-0.418002\pi$
$761$	14.0560	0.509530	0.254765	+	0.967003i	$0.418002\pi$
$762$	0.250751	0.00908373
$763$	3.89935	0.141166
$764$	4.19538	0.151784
$765$	1.31621	0.0475878
$766$	−36.0031	−1.30085
$767$	−0.687081	−0.0248090
$768$	1.58771	0.0572914
$769$	−16.8386	−0.607214	−0.303607	−	0.952797i	$-0.598191\pi$
$769$	−16.8386	−0.607214	−0.303607	+	0.952797i	$0.598191\pi$
$770$	2.21538	0.0798369
$771$	−0.289148	−0.0104134
$772$	54.8895	1.97552
$773$	−3.71644	−0.133671	−0.0668355	−	0.997764i	$-0.521290\pi$
$773$	−3.71644	−0.133671	−0.0668355	+	0.997764i	$0.521290\pi$
$774$	18.8364	0.677062
$775$	28.9759	1.04085
$776$	91.0676	3.26914
$777$	−0.00308680	−0.000110738 0
$778$	99.5370	3.56857
$779$	−2.68462	−0.0961866
$780$	−0.0153205	−0.000548562 0
$781$	−29.1584	−1.04337
$782$	−24.2084	−0.865690
$783$	1.71679	0.0613531
$784$	−69.3098	−2.47535
$785$	5.33785	0.190516
$786$	−7.57549	−0.270209
$787$	0.0309705	0.00110398	0.000551989	−	1.00000i	$-0.499824\pi$
$787$	0.0309705	0.00110398	0.000551989		1.00000i	$0.499824\pi$
$788$	−113.607	−4.04709
$789$	−0.886509	−0.0315605
$790$	−10.5111	−0.373967
$791$	10.9482	0.389275
$792$	−106.084	−3.76955
$793$	−0.956841	−0.0339784
$794$	15.2635	0.541683
$795$	0.253017	0.00897359
$796$	66.2378	2.34774
$797$	−12.2109	−0.432531	−0.216265	−	0.976335i	$-0.569388\pi$
$797$	−12.2109	−0.432531	−0.216265	+	0.976335i	$0.569388\pi$
$798$	0.225488	0.00798219
$799$	14.2799	0.505185
$800$	58.3944	2.06455
$801$	−46.5756	−1.64567
$802$	0.370675	0.0130890
$803$	−32.1606	−1.13492
$804$	−2.23941	−0.0789779
$805$	1.21423	0.0427958
$806$	−0.995009	−0.0350477
$807$	2.17023	0.0763956
$808$	27.1980	0.956821
$809$	16.7603	0.589262	0.294631	−	0.955611i	$-0.404803\pi$
$809$	16.7603	0.589262	0.294631	+	0.955611i	$0.404803\pi$
$810$	7.43188	0.261130
$811$	−5.39693	−0.189512	−0.0947559	−	0.995501i	$-0.530207\pi$
$811$	−5.39693	−0.189512	−0.0947559	+	0.995501i	$0.530207\pi$
$812$	−5.27017	−0.184947
$813$	3.31166	0.116145
$814$	−0.439336	−0.0153987
$815$	4.49484	0.157448
$816$	−2.16495	−0.0757883
$817$	−2.40508	−0.0841433
$818$	−86.0707	−3.00939
$819$	−0.107566	−0.00375867
$820$	−4.24413	−0.148211
$821$	−16.8878	−0.589389	−0.294694	−	0.955592i	$-0.595218\pi$
$821$	−16.8878	−0.589389	−0.294694	+	0.955592i	$0.595218\pi$
$822$	3.35910	0.117162
$823$	37.1374	1.29453	0.647265	−	0.762265i	$-0.275913\pi$
$823$	37.1374	1.29453	0.647265	+	0.762265i	$0.275913\pi$
$824$	11.5642	0.402859
$825$	−3.44273	−0.119860
$826$	15.9869	0.556254
$827$	−43.2715	−1.50470	−0.752349	−	0.658765i	$-0.771079\pi$
$827$	−43.2715	−1.50470	−0.752349	+	0.658765i	$0.771079\pi$
$828$	−97.9531	−3.40410
$829$	51.3812	1.78454	0.892271	−	0.451501i	$-0.149111\pi$
$829$	51.3812	1.78454	0.892271	+	0.451501i	$0.149111\pi$
$830$	−3.46980	−0.120439
$831$	3.17691	0.110206
$832$	−0.678936	−0.0235379
$833$	−9.19407	−0.318555
$834$	−0.553564	−0.0191684
$835$	2.24174	0.0775785
$836$	22.8191	0.789216
$837$	−5.36245	−0.185353
$838$	−44.1949	−1.52669
$839$	22.2169	0.767013	0.383506	−	0.923538i	$-0.374716\pi$
$839$	22.2169	0.767013	0.383506	+	0.923538i	$0.374716\pi$
$840$	0.211599	0.00730085
$841$	−25.4111	−0.876245
$842$	−83.9532	−2.89322
$843$	−1.86107	−0.0640988
$844$	40.1954	1.38358
$845$	4.17493	0.143622
$846$	81.2623	2.79385
$847$	−5.93666	−0.203986
$848$	53.8944	1.85074
$849$	−0.188337	−0.00646372
$850$	17.7298	0.608126
$851$	−0.240795	−0.00825435
$852$	−4.69184	−0.160740
$853$	−35.8616	−1.22788	−0.613939	−	0.789353i	$-0.710416\pi$
$853$	−35.8616	−1.22788	−0.613939	+	0.789353i	$0.710416\pi$
$854$	22.2636	0.761845
$855$	−0.956364	−0.0327070
$856$	−48.6706	−1.66353
$857$	36.4588	1.24541	0.622704	−	0.782457i	$-0.286034\pi$
$857$	36.4588	1.24541	0.622704	+	0.782457i	$0.286034\pi$
$858$	0.118220	0.00403598
$859$	−8.92090	−0.304377	−0.152189	−	0.988351i	$-0.548632\pi$
$859$	−8.92090	−0.304377	−0.152189	+	0.988351i	$0.548632\pi$
$860$	−3.80221	−0.129654
$861$	0.230101	0.00784183
$862$	−12.0007	−0.408745
$863$	−4.50948	−0.153505	−0.0767523	−	0.997050i	$-0.524455\pi$
$863$	−4.50948	−0.153505	−0.0767523	+	0.997050i	$0.524455\pi$
$864$	−10.8068	−0.367654
$865$	0.426731	0.0145093
$866$	63.8799	2.17073
$867$	2.29034	0.0777840
$868$	16.4615	0.558740
$869$	57.6704	1.95633
$870$	−0.242753	−0.00823008
$871$	−0.191837	−0.00650014
$872$	53.0084	1.79509
$873$	35.2785	1.19400
$874$	17.5899	0.594986
$875$	−1.79729	−0.0607597
$876$	−5.17493	−0.174845
$877$	−49.7290	−1.67923	−0.839615	−	0.543182i	$-0.817219\pi$
$877$	−49.7290	−1.67923	−0.839615	+	0.543182i	$0.817219\pi$
$878$	−12.2618	−0.413817
$879$	0.435395	0.0146855
$880$	15.4550	0.520989
$881$	−33.5212	−1.12936	−0.564678	−	0.825311i	$-0.691000\pi$
$881$	−33.5212	−1.12936	−0.564678	+	0.825311i	$0.691000\pi$
$882$	−52.3206	−1.76173
$883$	−36.6933	−1.23483	−0.617414	−	0.786638i	$-0.711820\pi$
$883$	−36.6933	−1.23483	−0.617414	+	0.786638i	$0.711820\pi$
$884$	−0.432892	−0.0145597
$885$	0.523588	0.0176002
$886$	71.6265	2.40634
$887$	−45.1876	−1.51725	−0.758625	−	0.651528i	$-0.774128\pi$
$887$	−45.1876	−1.51725	−0.758625	+	0.651528i	$0.774128\pi$
$888$	−0.0419625	−0.00140817
$889$	−0.355371	−0.0119188
$890$	13.2223	0.443214
$891$	−40.7760	−1.36605
$892$	−71.8444	−2.40553
$893$	−10.3758	−0.347212
$894$	5.17232	0.172988
$895$	−1.96330	−0.0656259
$896$	2.31483	0.0773332
$897$	0.0647952	0.00216345
$898$	28.7067	0.957957
$899$	−11.2100	−0.373874
$900$	71.7390	2.39130
$901$	7.14919	0.238174
$902$	32.7497	1.09045
$903$	0.206142	0.00685997
$904$	148.832	4.95009
$905$	0.633982	0.0210743
$906$	−1.46803	−0.0487720
$907$	38.4521	1.27678	0.638390	−	0.769713i	$-0.279601\pi$
$907$	38.4521	1.27678	0.638390	+	0.769713i	$0.279601\pi$
$908$	−98.5792	−3.27147
$909$	10.5362	0.349462
$910$	0.0305370	0.00101229
$911$	−49.4790	−1.63931	−0.819655	−	0.572857i	$-0.805835\pi$
$911$	−49.4790	−1.63931	−0.819655	+	0.572857i	$0.805835\pi$
$912$	1.57306	0.0520891
$913$	19.0376	0.630051
$914$	82.4397	2.72686
$915$	0.729159	0.0241052
$916$	47.3870	1.56571
$917$	10.7362	0.354541
$918$	−3.28117	−0.108295
$919$	−31.2817	−1.03189	−0.515944	−	0.856622i	$-0.672559\pi$
$919$	−31.2817	−1.03189	−0.515944	+	0.856622i	$0.672559\pi$
$920$	16.5064	0.544200
$921$	−3.78587	−0.124749
$922$	−30.2980	−0.997813
$923$	−0.401921	−0.0132294
$924$	−1.95585	−0.0643427
$925$	0.176354	0.00579848
$926$	−26.1679	−0.859930
$927$	4.47984	0.147137
$928$	−22.5912	−0.741591
$929$	−45.2490	−1.48457	−0.742286	−	0.670083i	$-0.766258\pi$
$929$	−45.2490	−1.48457	−0.742286	+	0.670083i	$0.766258\pi$
$930$	0.758244	0.0248638
$931$	6.68043	0.218942
$932$	−22.0535	−0.722387
$933$	3.35190	0.109736
$934$	−2.73605	−0.0895262
$935$	2.05013	0.0670466
$936$	−1.46228	−0.0477960
$937$	−33.0824	−1.08076	−0.540378	−	0.841422i	$-0.681719\pi$
$937$	−33.0824	−1.08076	−0.540378	+	0.841422i	$0.681719\pi$
$938$	4.46362	0.145742
$939$	4.67601	0.152596
$940$	−16.4031	−0.535010
$941$	−41.1036	−1.33994	−0.669970	−	0.742388i	$-0.733693\pi$
$941$	−41.1036	−1.33994	−0.669970	+	0.742388i	$0.733693\pi$
$942$	−6.62773	−0.215943
$943$	17.9497	0.584524
$944$	111.528	3.62993
$945$	0.164574	0.00535361
$946$	29.3396	0.953914
$947$	45.8518	1.48998	0.744992	−	0.667074i	$-0.232453\pi$
$947$	45.8518	1.48998	0.744992	+	0.667074i	$0.232453\pi$
$948$	9.27967	0.301390
$949$	−0.443304	−0.0143903
$950$	−12.8825	−0.417963
$951$	0.151619	0.00491659
$952$	5.97888	0.193777
$953$	22.9627	0.743834	0.371917	−	0.928266i	$-0.378701\pi$
$953$	22.9627	0.743834	0.371917	+	0.928266i	$0.378701\pi$
$954$	40.6838	1.31719
$955$	−0.273875	−0.00886238
$956$	89.8629	2.90637
$957$	1.33190	0.0430541
$958$	−77.8978	−2.51676
$959$	−4.76062	−0.153728
$960$	0.517381	0.0166984
$961$	4.01469	0.129506
$962$	−0.00605584	−0.000195248 0
$963$	−18.8544	−0.607574
$964$	86.6507	2.79083
$965$	−3.58319	−0.115347
$966$	−1.50764	−0.0485076
$967$	29.0541	0.934317	0.467158	−	0.884174i	$-0.345278\pi$
$967$	29.0541	0.934317	0.467158	+	0.884174i	$0.345278\pi$
$968$	−80.7040	−2.59393
$969$	0.208668	0.00670340
$970$	−10.0152	−0.321569
$971$	−17.3161	−0.555702	−0.277851	−	0.960624i	$-0.589622\pi$
$971$	−17.3161	−0.555702	−0.277851	+	0.960624i	$0.589622\pi$
$972$	−19.9402	−0.639581
$973$	0.784528	0.0251508
$974$	−84.5755	−2.70997
$975$	−0.0474548	−0.00151977
$976$	155.316	4.97154
$977$	19.5146	0.624328	0.312164	−	0.950028i	$-0.398946\pi$
$977$	19.5146	0.624328	0.312164	+	0.950028i	$0.398946\pi$
$978$	−5.58102	−0.178461
$979$	−72.5462	−2.31859
$980$	10.5611	0.337362
$981$	20.5348	0.655626
$982$	−59.0439	−1.88416
$983$	−15.8203	−0.504591	−0.252295	−	0.967650i	$-0.581185\pi$
$983$	−15.8203	−0.504591	−0.252295	+	0.967650i	$0.581185\pi$
$984$	3.12804	0.0997181
$985$	7.41628	0.236302
$986$	−6.85915	−0.218440
$987$	0.889317	0.0283073
$988$	0.314541	0.0100069
$989$	16.0807	0.511337
$990$	11.6667	0.370792
$991$	−15.0747	−0.478862	−0.239431	−	0.970913i	$-0.576961\pi$
$991$	−15.0747	−0.478862	−0.239431	+	0.970913i	$0.576961\pi$
$992$	70.5641	2.24041
$993$	−3.46821	−0.110060
$994$	9.35183	0.296622
$995$	−4.32400	−0.137080
$996$	3.06331	0.0970647
$997$	−42.2096	−1.33679	−0.668396	−	0.743805i	$-0.733019\pi$
$997$	−42.2096	−1.33679	−0.668396	+	0.743805i	$0.733019\pi$
$998$	0.360512	0.0114118
$999$	−0.0326370	−0.00103259

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6023.2.a.b.1.3	✓	99

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6023.2.a.b.1.3	✓	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)

\(f(q)\)	\(=\)	\(q-2.63080 q^{2} -0.151619 q^{3} +4.92110 q^{4} -0.321250 q^{5} +0.398879 q^{6} -0.565304 q^{7} -7.68484 q^{8} -2.97701 q^{9} +O(q^{10})\)	\(q-2.63080 q^{2} -0.151619 q^{3} +4.92110 q^{4} -0.321250 q^{5} +0.398879 q^{6} -0.565304 q^{7} -7.68484 q^{8} -2.97701 q^{9} +0.845143 q^{10} -4.63699 q^{11} -0.746133 q^{12} -0.0639167 q^{13} +1.48720 q^{14} +0.0487076 q^{15} +10.3751 q^{16} +1.37627 q^{17} +7.83192 q^{18} -1.00000 q^{19} -1.58090 q^{20} +0.0857108 q^{21} +12.1990 q^{22} +6.68613 q^{23} +1.16517 q^{24} -4.89680 q^{25} +0.168152 q^{26} +0.906229 q^{27} -2.78192 q^{28} +1.89444 q^{29} -0.128140 q^{30} -5.91732 q^{31} -11.9250 q^{32} +0.703057 q^{33} -3.62069 q^{34} +0.181604 q^{35} -14.6502 q^{36} -0.0360141 q^{37} +2.63080 q^{38} +0.00969099 q^{39} +2.46875 q^{40} +2.68462 q^{41} -0.225488 q^{42} +2.40508 q^{43} -22.8191 q^{44} +0.956364 q^{45} -17.5899 q^{46} +10.3758 q^{47} -1.57306 q^{48} -6.68043 q^{49} +12.8825 q^{50} -0.208668 q^{51} -0.314541 q^{52} +5.19462 q^{53} -2.38411 q^{54} +1.48963 q^{55} +4.34427 q^{56} +0.151619 q^{57} -4.98388 q^{58} +10.7496 q^{59} +0.239695 q^{60} +14.9701 q^{61} +15.5673 q^{62} +1.68292 q^{63} +10.6222 q^{64} +0.0205332 q^{65} -1.84960 q^{66} +3.00136 q^{67} +6.77276 q^{68} -1.01375 q^{69} -0.477763 q^{70} +6.28821 q^{71} +22.8779 q^{72} +6.93566 q^{73} +0.0947459 q^{74} +0.742448 q^{75} -4.92110 q^{76} +2.62131 q^{77} -0.0254950 q^{78} -12.4370 q^{79} -3.33298 q^{80} +8.79363 q^{81} -7.06270 q^{82} -4.10558 q^{83} +0.421792 q^{84} -0.442126 q^{85} -6.32729 q^{86} -0.287233 q^{87} +35.6346 q^{88} +15.6451 q^{89} -2.51600 q^{90} +0.0361323 q^{91} +32.9031 q^{92} +0.897179 q^{93} -27.2966 q^{94} +0.321250 q^{95} +1.80806 q^{96} -11.8503 q^{97} +17.5749 q^{98} +13.8044 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 99 q - 4 q^{2} - 3 q^{3} + 80 q^{4} - 15 q^{5} - 12 q^{6} - 19 q^{7} - 12 q^{8} + 58 q^{9}+O(q^{10}) \) 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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