LMFDB - Embedded newform 6023.2.a.b.1.14

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			1.14
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)

$f(q)$	$=$	$q-2.20648 q^{2} -1.66546 q^{3} +2.86855 q^{4} +2.85921 q^{5} +3.67480 q^{6} -0.996345 q^{7} -1.91643 q^{8} -0.226251 q^{9} +O(q^{10})$	\(q-2.20648 q^{2} -1.66546 q^{3} +2.86855 q^{4} +2.85921 q^{5} +3.67480 q^{6} -0.996345 q^{7} -1.91643 q^{8} -0.226251 q^{9} -6.30878 q^{10} +4.63930 q^{11} -4.77745 q^{12} +1.51057 q^{13} +2.19841 q^{14} -4.76189 q^{15} -1.50853 q^{16} +2.86077 q^{17} +0.499218 q^{18} -1.00000 q^{19} +8.20177 q^{20} +1.65937 q^{21} -10.2365 q^{22} -4.55077 q^{23} +3.19174 q^{24} +3.17506 q^{25} -3.33304 q^{26} +5.37318 q^{27} -2.85806 q^{28} -8.47482 q^{29} +10.5070 q^{30} +9.31539 q^{31} +7.16140 q^{32} -7.72657 q^{33} -6.31222 q^{34} -2.84875 q^{35} -0.649012 q^{36} +3.67526 q^{37} +2.20648 q^{38} -2.51579 q^{39} -5.47948 q^{40} +4.17881 q^{41} -3.66136 q^{42} -10.4376 q^{43} +13.3081 q^{44} -0.646899 q^{45} +10.0412 q^{46} -10.5636 q^{47} +2.51239 q^{48} -6.00730 q^{49} -7.00570 q^{50} -4.76449 q^{51} +4.33314 q^{52} -7.87956 q^{53} -11.8558 q^{54} +13.2647 q^{55} +1.90943 q^{56} +1.66546 q^{57} +18.6995 q^{58} +4.45425 q^{59} -13.6597 q^{60} +0.678642 q^{61} -20.5542 q^{62} +0.225424 q^{63} -12.7844 q^{64} +4.31902 q^{65} +17.0485 q^{66} +10.1411 q^{67} +8.20625 q^{68} +7.57912 q^{69} +6.28572 q^{70} -1.30386 q^{71} +0.433595 q^{72} -5.52882 q^{73} -8.10939 q^{74} -5.28793 q^{75} -2.86855 q^{76} -4.62235 q^{77} +5.55103 q^{78} -9.51275 q^{79} -4.31319 q^{80} -8.27006 q^{81} -9.22046 q^{82} -4.61347 q^{83} +4.75998 q^{84} +8.17952 q^{85} +23.0303 q^{86} +14.1145 q^{87} -8.89092 q^{88} -6.53101 q^{89} +1.42737 q^{90} -1.50505 q^{91} -13.0541 q^{92} -15.5144 q^{93} +23.3085 q^{94} -2.85921 q^{95} -11.9270 q^{96} -3.54978 q^{97} +13.2550 q^{98} -1.04965 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.20648	−1.56022	−0.780108	−	0.625645i	$-0.784836\pi$
$2$	−2.20648	−1.56022	−0.780108	+	0.625645i	$0.784836\pi$
$3$	−1.66546	−0.961552	−0.480776	−	0.876843i	$-0.659645\pi$
$3$	−1.66546	−0.961552	−0.480776	+	0.876843i	$0.659645\pi$
$4$	2.86855	1.43427
$5$	2.85921	1.27868	0.639338	−	0.768926i	$-0.279209\pi$
$5$	2.85921	1.27868	0.639338	+	0.768926i	$0.279209\pi$
$6$	3.67480	1.50023
$7$	−0.996345	−0.376583	−0.188291	−	0.982113i	$-0.560295\pi$
$7$	−0.996345	−0.376583	−0.188291	+	0.982113i	$0.560295\pi$
$8$	−1.91643	−0.677562
$9$	−0.226251	−0.0754171
$10$	−6.30878	−1.99501
$11$	4.63930	1.39880	0.699402	−	0.714729i	$-0.253450\pi$
$11$	4.63930	1.39880	0.699402	+	0.714729i	$0.253450\pi$
$12$	−4.77745	−1.37913
$13$	1.51057	0.418956	0.209478	−	0.977813i	$-0.432824\pi$
$13$	1.51057	0.418956	0.209478	+	0.977813i	$0.432824\pi$
$14$	2.19841	0.587551
$15$	−4.76189	−1.22951
$16$	−1.50853	−0.377131
$17$	2.86077	0.693838	0.346919	−	0.937895i	$-0.387228\pi$
$17$	2.86077	0.693838	0.346919	+	0.937895i	$0.387228\pi$
$18$	0.499218	0.117667
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	8.20177	1.83397
$21$	1.65937	0.362104
$22$	−10.2365	−2.18244
$23$	−4.55077	−0.948902	−0.474451	−	0.880282i	$-0.657353\pi$
$23$	−4.55077	−0.948902	−0.474451	+	0.880282i	$0.657353\pi$
$24$	3.19174	0.651511
$25$	3.17506	0.635012
$26$	−3.33304	−0.653662
$27$	5.37318	1.03407
$28$	−2.85806	−0.540123
$29$	−8.47482	−1.57373	−0.786867	−	0.617122i	$-0.788298\pi$
$29$	−8.47482	−1.57373	−0.786867	+	0.617122i	$0.788298\pi$
$30$	10.5070	1.91831
$31$	9.31539	1.67309	0.836547	−	0.547895i	$-0.184571\pi$
$31$	9.31539	1.67309	0.836547	+	0.547895i	$0.184571\pi$
$32$	7.16140	1.26597
$33$	−7.72657	−1.34502
$34$	−6.31222	−1.08254
$35$	−2.84875	−0.481527
$36$	−0.649012	−0.108169
$37$	3.67526	0.604210	0.302105	−	0.953275i	$-0.402311\pi$
$37$	3.67526	0.604210	0.302105	+	0.953275i	$0.402311\pi$
$38$	2.20648	0.357938
$39$	−2.51579	−0.402848
$40$	−5.47948	−0.866382
$41$	4.17881	0.652621	0.326310	−	0.945263i	$-0.394195\pi$
$41$	4.17881	0.652621	0.326310	+	0.945263i	$0.394195\pi$
$42$	−3.66136	−0.564961
$43$	−10.4376	−1.59171	−0.795857	−	0.605484i	$-0.792980\pi$
$43$	−10.4376	−1.59171	−0.795857	+	0.605484i	$0.792980\pi$
$44$	13.3081	2.00627
$45$	−0.646899	−0.0964340
$46$	10.0412	1.48049
$47$	−10.5636	−1.54087	−0.770433	−	0.637521i	$-0.779960\pi$
$47$	−10.5636	−1.54087	−0.770433	+	0.637521i	$0.779960\pi$
$48$	2.51239	0.362632
$49$	−6.00730	−0.858185
$50$	−7.00570	−0.990756
$51$	−4.76449	−0.667161
$52$	4.33314	0.600898
$53$	−7.87956	−1.08234	−0.541170	−	0.840913i	$-0.682019\pi$
$53$	−7.87956	−1.08234	−0.541170	+	0.840913i	$0.682019\pi$
$54$	−11.8558	−1.61337
$55$	13.2647	1.78862
$56$	1.90943	0.255158
$57$	1.66546	0.220595
$58$	18.6995	2.45537
$59$	4.45425	0.579894	0.289947	−	0.957043i	$-0.406362\pi$
$59$	4.45425	0.579894	0.289947	+	0.957043i	$0.406362\pi$
$60$	−13.6597	−1.76346
$61$	0.678642	0.0868911	0.0434456	−	0.999056i	$-0.486166\pi$
$61$	0.678642	0.0868911	0.0434456	+	0.999056i	$0.486166\pi$
$62$	−20.5542	−2.61039
$63$	0.225424	0.0284008
$64$	−12.7844	−1.59805
$65$	4.31902	0.535709
$66$	17.0485	2.09853
$67$	10.1411	1.23894	0.619469	−	0.785021i	$-0.287348\pi$
$67$	10.1411	1.23894	0.619469	+	0.785021i	$0.287348\pi$
$68$	8.20625	0.995154
$69$	7.57912	0.912418
$70$	6.28572	0.751287
$71$	−1.30386	−0.154739	−0.0773696	−	0.997002i	$-0.524652\pi$
$71$	−1.30386	−0.154739	−0.0773696	+	0.997002i	$0.524652\pi$
$72$	0.433595	0.0510997
$73$	−5.52882	−0.647100	−0.323550	−	0.946211i	$-0.604876\pi$
$73$	−5.52882	−0.647100	−0.323550	+	0.946211i	$0.604876\pi$
$74$	−8.10939	−0.942698
$75$	−5.28793	−0.610597
$76$	−2.86855	−0.329045
$77$	−4.62235	−0.526765
$78$	5.55103	0.628530
$79$	−9.51275	−1.07027	−0.535134	−	0.844767i	$-0.679739\pi$
$79$	−9.51275	−1.07027	−0.535134	+	0.844767i	$0.679739\pi$
$80$	−4.31319	−0.482229
$81$	−8.27006	−0.918895
$82$	−9.22046	−1.01823
$83$	−4.61347	−0.506394	−0.253197	−	0.967415i	$-0.581482\pi$
$83$	−4.61347	−0.506394	−0.253197	+	0.967415i	$0.581482\pi$
$84$	4.75998	0.519357
$85$	8.17952	0.887194
$86$	23.0303	2.48342
$87$	14.1145	1.51323
$88$	−8.89092	−0.947776
$89$	−6.53101	−0.692286	−0.346143	−	0.938182i	$-0.612509\pi$
$89$	−6.53101	−0.692286	−0.346143	+	0.938182i	$0.612509\pi$
$90$	1.42737	0.150458
$91$	−1.50505	−0.157772
$92$	−13.0541	−1.36099
$93$	−15.5144	−1.60877
$94$	23.3085	2.40408
$95$	−2.85921	−0.293348
$96$	−11.9270	−1.21729
$97$	−3.54978	−0.360425	−0.180213	−	0.983628i	$-0.557679\pi$
$97$	−3.54978	−0.360425	−0.180213	+	0.983628i	$0.557679\pi$
$98$	13.2550	1.33895
$99$	−1.04965	−0.105494
$100$	9.10781	0.910781
$101$	3.19030	0.317447	0.158724	−	0.987323i	$-0.449262\pi$
$101$	3.19030	0.317447	0.158724	+	0.987323i	$0.449262\pi$
$102$	10.5127	1.04092
$103$	−6.81128	−0.671136	−0.335568	−	0.942016i	$-0.608928\pi$
$103$	−6.81128	−0.671136	−0.335568	+	0.942016i	$0.608928\pi$
$104$	−2.89490	−0.283869
$105$	4.74448	0.463014
$106$	17.3861	1.68869
$107$	−9.82688	−0.950000	−0.475000	−	0.879986i	$-0.657552\pi$
$107$	−9.82688	−0.950000	−0.475000	+	0.879986i	$0.657552\pi$
$108$	15.4132	1.48314
$109$	−14.5679	−1.39536	−0.697678	−	0.716411i	$-0.745783\pi$
$109$	−14.5679	−1.39536	−0.697678	+	0.716411i	$0.745783\pi$
$110$	−29.2683	−2.79063
$111$	−6.12100	−0.580979
$112$	1.50301	0.142021
$113$	−5.41146	−0.509067	−0.254533	−	0.967064i	$-0.581922\pi$
$113$	−5.41146	−0.509067	−0.254533	+	0.967064i	$0.581922\pi$
$114$	−3.67480	−0.344176
$115$	−13.0116	−1.21334
$116$	−24.3104	−2.25717
$117$	−0.341768	−0.0315964
$118$	−9.82821	−0.904760
$119$	−2.85031	−0.261287
$120$	9.12584	0.833072
$121$	10.5231	0.956650
$122$	−1.49741	−0.135569
$123$	−6.95963	−0.627529
$124$	26.7217	2.39968
$125$	−5.21788	−0.466702
$126$	−0.497394	−0.0443113
$127$	2.67749	0.237589	0.118795	−	0.992919i	$-0.462097\pi$
$127$	2.67749	0.237589	0.118795	+	0.992919i	$0.462097\pi$
$128$	13.8858	1.22734
$129$	17.3833	1.53052
$130$	−9.52984	−0.835822
$131$	−3.51171	−0.306820	−0.153410	−	0.988163i	$-0.549025\pi$
$131$	−3.51171	−0.306820	−0.153410	+	0.988163i	$0.549025\pi$
$132$	−22.1640	−1.92913
$133$	0.996345	0.0863940
$134$	−22.3762	−1.93301
$135$	15.3630	1.32224
$136$	−5.48247	−0.470118
$137$	−7.90848	−0.675667	−0.337833	−	0.941206i	$-0.609694\pi$
$137$	−7.90848	−0.675667	−0.337833	+	0.941206i	$0.609694\pi$
$138$	−16.7232	−1.42357
$139$	−13.9366	−1.18208	−0.591042	−	0.806641i	$-0.701283\pi$
$139$	−13.9366	−1.18208	−0.591042	+	0.806641i	$0.701283\pi$
$140$	−8.17179	−0.690642
$141$	17.5933	1.48162
$142$	2.87693	0.241427
$143$	7.00798	0.586037
$144$	0.341306	0.0284421
$145$	−24.2313	−2.01230
$146$	12.1992	1.00962
$147$	10.0049	0.825190
$148$	10.5427	0.866602
$149$	1.10069	0.0901718	0.0450859	−	0.998983i	$-0.485644\pi$
$149$	1.10069	0.0901718	0.0450859	+	0.998983i	$0.485644\pi$
$150$	11.6677	0.952663
$151$	22.0629	1.79545	0.897726	−	0.440554i	$-0.145218\pi$
$151$	22.0629	1.79545	0.897726	+	0.440554i	$0.145218\pi$
$152$	1.91643	0.155443
$153$	−0.647252	−0.0523272
$154$	10.1991	0.821868
$155$	26.6346	2.13934
$156$	−7.21666	−0.577795
$157$	−22.8750	−1.82563	−0.912814	−	0.408376i	$-0.866095\pi$
$157$	−22.8750	−1.82563	−0.912814	+	0.408376i	$0.866095\pi$
$158$	20.9897	1.66985
$159$	13.1231	1.04073
$160$	20.4759	1.61876
$161$	4.53414	0.357340
$162$	18.2477	1.43368
$163$	11.6444	0.912060	0.456030	−	0.889965i	$-0.349271\pi$
$163$	11.6444	0.912060	0.456030	+	0.889965i	$0.349271\pi$
$164$	11.9871	0.936037
$165$	−22.0918	−1.71985
$166$	10.1795	0.790083
$167$	−1.69408	−0.131092	−0.0655460	−	0.997850i	$-0.520879\pi$
$167$	−1.69408	−0.131092	−0.0655460	+	0.997850i	$0.520879\pi$
$168$	−3.18007	−0.245348
$169$	−10.7182	−0.824476
$170$	−18.0479	−1.38421
$171$	0.226251	0.0173019
$172$	−29.9407	−2.28296
$173$	−5.03574	−0.382860	−0.191430	−	0.981506i	$-0.561312\pi$
$173$	−5.03574	−0.382860	−0.191430	+	0.981506i	$0.561312\pi$
$174$	−31.1432	−2.36096
$175$	−3.16345	−0.239135
$176$	−6.99851	−0.527533
$177$	−7.41836	−0.557598
$178$	14.4105	1.08012
$179$	11.1998	0.837111	0.418555	−	0.908191i	$-0.362537\pi$
$179$	11.1998	0.837111	0.418555	+	0.908191i	$0.362537\pi$
$180$	−1.85566	−0.138313
$181$	21.3420	1.58634	0.793168	−	0.609003i	$-0.208430\pi$
$181$	21.3420	1.58634	0.793168	+	0.609003i	$0.208430\pi$
$182$	3.32085	0.246158
$183$	−1.13025	−0.0835504
$184$	8.72126	0.642939
$185$	10.5083	0.772588
$186$	34.2322	2.51003
$187$	13.2720	0.970543
$188$	−30.3023	−2.21002
$189$	−5.35354	−0.389413
$190$	6.30878	0.457687
$191$	−19.8342	−1.43515	−0.717577	−	0.696480i	$-0.754749\pi$
$191$	−19.8342	−1.43515	−0.717577	+	0.696480i	$0.754749\pi$
$192$	21.2919	1.53661
$193$	−8.97106	−0.645751	−0.322876	−	0.946441i	$-0.604650\pi$
$193$	−8.97106	−0.645751	−0.322876	+	0.946441i	$0.604650\pi$
$194$	7.83251	0.562342
$195$	−7.19315	−0.515112
$196$	−17.2322	−1.23087
$197$	−6.82131	−0.485998	−0.242999	−	0.970027i	$-0.578131\pi$
$197$	−6.82131	−0.485998	−0.242999	+	0.970027i	$0.578131\pi$
$198$	2.31603	0.164593
$199$	4.42136	0.313422	0.156711	−	0.987645i	$-0.449911\pi$
$199$	4.42136	0.313422	0.156711	+	0.987645i	$0.449911\pi$
$200$	−6.08479	−0.430260
$201$	−16.8896	−1.19130
$202$	−7.03934	−0.495286
$203$	8.44384	0.592641
$204$	−13.6672	−0.956893
$205$	11.9481	0.834490
$206$	15.0289	1.04712
$207$	1.02962	0.0715634
$208$	−2.27873	−0.158002
$209$	−4.63930	−0.320907
$210$	−10.4686	−0.722402
$211$	9.62297	0.662473	0.331236	−	0.943548i	$-0.392534\pi$
$211$	9.62297	0.662473	0.331236	+	0.943548i	$0.392534\pi$
$212$	−22.6029	−1.55237
$213$	2.17152	0.148790
$214$	21.6828	1.48221
$215$	−29.8432	−2.03529
$216$	−10.2974	−0.700646
$217$	−9.28134	−0.630059
$218$	32.1439	2.17706
$219$	9.20802	0.622220
$220$	38.0505	2.56537
$221$	4.32138	0.290688
$222$	13.5058	0.906453
$223$	−5.62330	−0.376564	−0.188282	−	0.982115i	$-0.560292\pi$
$223$	−5.62330	−0.376564	−0.188282	+	0.982115i	$0.560292\pi$
$224$	−7.13522	−0.476742
$225$	−0.718361	−0.0478907
$226$	11.9403	0.794255
$227$	14.0935	0.935416	0.467708	−	0.883883i	$-0.345080\pi$
$227$	14.0935	0.935416	0.467708	+	0.883883i	$0.345080\pi$
$228$	4.77745	0.316394
$229$	14.4900	0.957525	0.478763	−	0.877944i	$-0.341085\pi$
$229$	14.4900	0.957525	0.478763	+	0.877944i	$0.341085\pi$
$230$	28.7098	1.89307
$231$	7.69832	0.506512
$232$	16.2414	1.06630
$233$	17.1006	1.12030	0.560149	−	0.828392i	$-0.310744\pi$
$233$	17.1006	1.12030	0.560149	+	0.828392i	$0.310744\pi$
$234$	0.754103	0.0492973
$235$	−30.2036	−1.97027
$236$	12.7772	0.831727
$237$	15.8431	1.02912
$238$	6.28915	0.407665
$239$	23.7055	1.53338	0.766692	−	0.642015i	$-0.221901\pi$
$239$	23.7055	1.53338	0.766692	+	0.642015i	$0.221901\pi$
$240$	7.18343	0.463688
$241$	26.0845	1.68025	0.840126	−	0.542391i	$-0.182481\pi$
$241$	26.0845	1.68025	0.840126	+	0.542391i	$0.182481\pi$
$242$	−23.2191	−1.49258
$243$	−2.34612	−0.150504
$244$	1.94672	0.124626
$245$	−17.1761	−1.09734
$246$	15.3563	0.979081
$247$	−1.51057	−0.0961151
$248$	−17.8523	−1.13362
$249$	7.68353	0.486924
$250$	11.5131	0.728155
$251$	4.41109	0.278426	0.139213	−	0.990262i	$-0.455543\pi$
$251$	4.41109	0.278426	0.139213	+	0.990262i	$0.455543\pi$
$252$	0.646640	0.0407345
$253$	−21.1124	−1.32733
$254$	−5.90783	−0.370690
$255$	−13.6226	−0.853083
$256$	−5.06979	−0.316862
$257$	−22.3700	−1.39540	−0.697701	−	0.716389i	$-0.745794\pi$
$257$	−22.3700	−1.39540	−0.697701	+	0.716389i	$0.745794\pi$
$258$	−38.3560	−2.38794
$259$	−3.66183	−0.227535
$260$	12.3893	0.768354
$261$	1.91744	0.118686
$262$	7.74852	0.478705
$263$	−6.67943	−0.411872	−0.205936	−	0.978566i	$-0.566024\pi$
$263$	−6.67943	−0.411872	−0.205936	+	0.978566i	$0.566024\pi$
$264$	14.8075	0.911336
$265$	−22.5293	−1.38396
$266$	−2.19841	−0.134793
$267$	10.8771	0.665669
$268$	29.0904	1.77698
$269$	−5.93768	−0.362027	−0.181014	−	0.983481i	$-0.557938\pi$
$269$	−5.93768	−0.362027	−0.181014	+	0.983481i	$0.557938\pi$
$270$	−33.8982	−2.06298
$271$	−28.2007	−1.71307	−0.856536	−	0.516087i	$-0.827388\pi$
$271$	−28.2007	−1.71307	−0.856536	+	0.516087i	$0.827388\pi$
$272$	−4.31554	−0.261668
$273$	2.50659	0.151706
$274$	17.4499	1.05419
$275$	14.7301	0.888256
$276$	21.7411	1.30866
$277$	11.5208	0.692218	0.346109	−	0.938194i	$-0.387503\pi$
$277$	11.5208	0.692218	0.346109	+	0.938194i	$0.387503\pi$
$278$	30.7507	1.84431
$279$	−2.10762	−0.126180
$280$	5.45945	0.326265
$281$	6.25471	0.373125	0.186562	−	0.982443i	$-0.440265\pi$
$281$	6.25471	0.373125	0.186562	+	0.982443i	$0.440265\pi$
$282$	−38.8193	−2.31165
$283$	26.6041	1.58145	0.790724	−	0.612172i	$-0.209704\pi$
$283$	26.6041	1.58145	0.790724	+	0.612172i	$0.209704\pi$
$284$	−3.74017	−0.221939
$285$	4.76189	0.282070
$286$	−15.4630	−0.914344
$287$	−4.16354	−0.245766
$288$	−1.62027	−0.0954756
$289$	−8.81601	−0.518589
$290$	53.4658	3.13962
$291$	5.91201	0.346568
$292$	−15.8597	−0.928118
$293$	−9.19726	−0.537310	−0.268655	−	0.963236i	$-0.586579\pi$
$293$	−9.19726	−0.537310	−0.268655	+	0.963236i	$0.586579\pi$
$294$	−22.0756	−1.28747
$295$	12.7356	0.741496
$296$	−7.04340	−0.409389
$297$	24.9278	1.44646
$298$	−2.42864	−0.140687
$299$	−6.87425	−0.397548
$300$	−15.1687	−0.875764
$301$	10.3994	0.599413
$302$	−48.6813	−2.80129
$303$	−5.31332	−0.305242
$304$	1.50853	0.0865199
$305$	1.94038	0.111106
$306$	1.42815	0.0816418
$307$	25.2512	1.44116	0.720582	−	0.693370i	$-0.243875\pi$
$307$	25.2512	1.44116	0.720582	+	0.693370i	$0.243875\pi$
$308$	−13.2594	−0.755526
$309$	11.3439	0.645332
$310$	−58.7687	−3.33784
$311$	19.0851	1.08222	0.541109	−	0.840953i	$-0.318005\pi$
$311$	19.0851	1.08222	0.541109	+	0.840953i	$0.318005\pi$
$312$	4.82134	0.272955
$313$	−1.50541	−0.0850907	−0.0425453	−	0.999095i	$-0.513547\pi$
$313$	−1.50541	−0.0850907	−0.0425453	+	0.999095i	$0.513547\pi$
$314$	50.4733	2.84837
$315$	0.644534	0.0363154
$316$	−27.2878	−1.53506
$317$	−1.00000	−0.0561656
$317$	−1.00000	−0.0561656
$318$	−28.9558	−1.62376
$319$	−39.3173	−2.20134
$320$	−36.5533	−2.04339
$321$	16.3663	0.913475
$322$	−10.0045	−0.557528
$323$	−2.86077	−0.159177
$324$	−23.7231	−1.31795
$325$	4.79614	0.266042
$326$	−25.6931	−1.42301
$327$	24.2623	1.34171
$328$	−8.00842	−0.442191
$329$	10.5250	0.580264
$330$	48.7452	2.68333
$331$	−26.1955	−1.43984	−0.719918	−	0.694059i	$-0.755821\pi$
$331$	−26.1955	−1.43984	−0.719918	+	0.694059i	$0.755821\pi$
$332$	−13.2339	−0.726307
$333$	−0.831533	−0.0455677
$334$	3.73795	0.204532
$335$	28.9956	1.58420
$336$	−2.50320	−0.136561
$337$	33.3015	1.81405	0.907024	−	0.421080i	$-0.138349\pi$
$337$	33.3015	1.81405	0.907024	+	0.421080i	$0.138349\pi$
$338$	23.6494	1.28636
$339$	9.01255	0.489495
$340$	23.4634	1.27248
$341$	43.2170	2.34033
$342$	−0.499218	−0.0269946
$343$	12.9598	0.699761
$344$	20.0029	1.07849
$345$	21.6703	1.16669
$346$	11.1112	0.597344
$347$	−1.93502	−0.103877	−0.0519387	−	0.998650i	$-0.516540\pi$
$347$	−1.93502	−0.103877	−0.0519387	+	0.998650i	$0.516540\pi$
$348$	40.4880	2.17038
$349$	−8.13301	−0.435350	−0.217675	−	0.976021i	$-0.569847\pi$
$349$	−8.13301	−0.435350	−0.217675	+	0.976021i	$0.569847\pi$
$350$	6.98009	0.373102
$351$	8.11656	0.433230
$352$	33.2239	1.77084
$353$	12.7288	0.677488	0.338744	−	0.940879i	$-0.389998\pi$
$353$	12.7288	0.677488	0.338744	+	0.940879i	$0.389998\pi$
$354$	16.3685	0.869974
$355$	−3.72799	−0.197861
$356$	−18.7345	−0.992927
$357$	4.74707	0.251242
$358$	−24.7121	−1.30607
$359$	25.0364	1.32137	0.660686	−	0.750663i	$-0.270266\pi$
$359$	25.0364	1.32137	0.660686	+	0.750663i	$0.270266\pi$
$360$	1.23974	0.0653400
$361$	1.00000	0.0526316
$362$	−47.0906	−2.47503
$363$	−17.5259	−0.919869
$364$	−4.31730	−0.226288
$365$	−15.8080	−0.827431
$366$	2.49387	0.130357
$367$	−32.2111	−1.68141	−0.840704	−	0.541495i	$-0.817859\pi$
$367$	−32.2111	−1.68141	−0.840704	+	0.541495i	$0.817859\pi$
$368$	6.86496	0.357861
$369$	−0.945461	−0.0492187
$370$	−23.1864	−1.20540
$371$	7.85076	0.407591
$372$	−44.5038	−2.30741
$373$	−33.9916	−1.76002	−0.880010	−	0.474955i	$-0.842464\pi$
$373$	−33.9916	−1.76002	−0.880010	+	0.474955i	$0.842464\pi$
$374$	−29.2843	−1.51426
$375$	8.69016	0.448758
$376$	20.2445	1.04403
$377$	−12.8018	−0.659326
$378$	11.8125	0.607568
$379$	−20.7053	−1.06356	−0.531779	−	0.846883i	$-0.678476\pi$
$379$	−20.7053	−1.06356	−0.531779	+	0.846883i	$0.678476\pi$
$380$	−8.20177	−0.420742
$381$	−4.45925	−0.228454
$382$	43.7638	2.23915
$383$	−3.48169	−0.177906	−0.0889531	−	0.996036i	$-0.528352\pi$
$383$	−3.48169	−0.177906	−0.0889531	+	0.996036i	$0.528352\pi$
$384$	−23.1261	−1.18015
$385$	−13.2162	−0.673562
$386$	19.7945	1.00751
$387$	2.36151	0.120042
$388$	−10.1827	−0.516949
$389$	34.3179	1.73999	0.869993	−	0.493064i	$-0.164123\pi$
$389$	34.3179	1.73999	0.869993	+	0.493064i	$0.164123\pi$
$390$	15.8715	0.803686
$391$	−13.0187	−0.658384
$392$	11.5126	0.581474
$393$	5.84861	0.295023
$394$	15.0511	0.758262
$395$	−27.1989	−1.36853
$396$	−3.01097	−0.151307
$397$	−18.9587	−0.951509	−0.475755	−	0.879578i	$-0.657825\pi$
$397$	−18.9587	−0.951509	−0.475755	+	0.879578i	$0.657825\pi$
$398$	−9.75563	−0.489006
$399$	−1.65937	−0.0830724
$400$	−4.78966	−0.239483
$401$	−11.1614	−0.557374	−0.278687	−	0.960382i	$-0.589899\pi$
$401$	−11.1614	−0.557374	−0.278687	+	0.960382i	$0.589899\pi$
$402$	37.2667	1.85869
$403$	14.0715	0.700953
$404$	9.15154	0.455306
$405$	−23.6458	−1.17497
$406$	−18.6312	−0.924649
$407$	17.0507	0.845170
$408$	9.13082	0.452043
$409$	−32.2735	−1.59582	−0.797910	−	0.602776i	$-0.794061\pi$
$409$	−32.2735	−1.59582	−0.797910	+	0.602776i	$0.794061\pi$
$410$	−26.3632	−1.30199
$411$	13.1712	0.649689
$412$	−19.5385	−0.962593
$413$	−4.43797	−0.218378
$414$	−2.27183	−0.111654
$415$	−13.1908	−0.647513
$416$	10.8178	0.530385
$417$	23.2107	1.13663
$418$	10.2365	0.500685
$419$	18.5806	0.907721	0.453861	−	0.891073i	$-0.350046\pi$
$419$	18.5806	0.907721	0.453861	+	0.891073i	$0.350046\pi$
$420$	13.6098	0.664089
$421$	20.2117	0.985057	0.492528	−	0.870296i	$-0.336073\pi$
$421$	20.2117	0.985057	0.492528	+	0.870296i	$0.336073\pi$
$422$	−21.2329	−1.03360
$423$	2.39004	0.116208
$424$	15.1007	0.733353
$425$	9.08310	0.440595
$426$	−4.79141	−0.232144
$427$	−0.676161	−0.0327217
$428$	−28.1889	−1.36256
$429$	−11.6715	−0.563505
$430$	65.8483	3.17549
$431$	20.6809	0.996162	0.498081	−	0.867130i	$-0.334038\pi$
$431$	20.6809	0.996162	0.498081	+	0.867130i	$0.334038\pi$
$432$	−8.10559	−0.389980
$433$	−34.2036	−1.64372	−0.821861	−	0.569688i	$-0.807064\pi$
$433$	−34.2036	−1.64372	−0.821861	+	0.569688i	$0.807064\pi$
$434$	20.4791	0.983028
$435$	40.3561	1.93493
$436$	−41.7889	−2.00132
$437$	4.55077	0.217693
$438$	−20.3173	−0.970798
$439$	4.94993	0.236247	0.118124	−	0.992999i	$-0.462312\pi$
$439$	4.94993	0.236247	0.118124	+	0.992999i	$0.462312\pi$
$440$	−25.4210	−1.21190
$441$	1.35916	0.0647218
$442$	−9.53504	−0.453536
$443$	15.1771	0.721086	0.360543	−	0.932743i	$-0.382591\pi$
$443$	15.1771	0.721086	0.360543	+	0.932743i	$0.382591\pi$
$444$	−17.5584	−0.833284
$445$	−18.6735	−0.885209
$446$	12.4077	0.587521
$447$	−1.83315	−0.0867049
$448$	12.7377	0.601799
$449$	15.6330	0.737767	0.368884	−	0.929476i	$-0.379740\pi$
$449$	15.6330	0.737767	0.368884	+	0.929476i	$0.379740\pi$
$450$	1.58505	0.0747199
$451$	19.3868	0.912888
$452$	−15.5230	−0.730142
$453$	−36.7448	−1.72642
$454$	−31.0969	−1.45945
$455$	−4.30324	−0.201739
$456$	−3.19174	−0.149467
$457$	−19.6187	−0.917726	−0.458863	−	0.888507i	$-0.651743\pi$
$457$	−19.6187	−0.917726	−0.458863	+	0.888507i	$0.651743\pi$
$458$	−31.9719	−1.49395
$459$	15.3714	0.717477
$460$	−37.3244	−1.74026
$461$	−19.2375	−0.895980	−0.447990	−	0.894038i	$-0.647860\pi$
$461$	−19.2375	−0.895980	−0.447990	+	0.894038i	$0.647860\pi$
$462$	−16.9862	−0.790269
$463$	32.2853	1.50043	0.750213	−	0.661196i	$-0.229951\pi$
$463$	32.2853	1.50043	0.750213	+	0.661196i	$0.229951\pi$
$464$	12.7845	0.593505
$465$	−44.3588	−2.05709
$466$	−37.7321	−1.74791
$467$	−21.9740	−1.01683	−0.508417	−	0.861111i	$-0.669769\pi$
$467$	−21.9740	−1.01683	−0.508417	+	0.861111i	$0.669769\pi$
$468$	−0.980377	−0.0453180
$469$	−10.1041	−0.466563
$470$	66.6437	3.07404
$471$	38.0974	1.75544
$472$	−8.53628	−0.392914
$473$	−48.4231	−2.22650
$474$	−34.9574	−1.60565
$475$	−3.17506	−0.145682
$476$	−8.17625	−0.374758
$477$	1.78276	0.0816270
$478$	−52.3058	−2.39241
$479$	−0.636927	−0.0291020	−0.0145510	−	0.999894i	$-0.504632\pi$
$479$	−0.636927	−0.0291020	−0.0145510	+	0.999894i	$0.504632\pi$
$480$	−34.1018	−1.55653
$481$	5.55174	0.253137
$482$	−57.5550	−2.62156
$483$	−7.55141	−0.343601
$484$	30.1862	1.37210
$485$	−10.1495	−0.460867
$486$	5.17667	0.234819
$487$	−21.5537	−0.976693	−0.488346	−	0.872650i	$-0.662400\pi$
$487$	−21.5537	−0.976693	−0.488346	+	0.872650i	$0.662400\pi$
$488$	−1.30057	−0.0588741
$489$	−19.3932	−0.876993
$490$	37.8987	1.71209
$491$	14.1894	0.640359	0.320180	−	0.947357i	$-0.396257\pi$
$491$	14.1894	0.640359	0.320180	+	0.947357i	$0.396257\pi$
$492$	−19.9640	−0.900049
$493$	−24.2445	−1.09192
$494$	3.33304	0.149960
$495$	−3.00116	−0.134892
$496$	−14.0525	−0.630976
$497$	1.29909	0.0582722
$498$	−16.9535	−0.759707
$499$	−9.38643	−0.420194	−0.210097	−	0.977681i	$-0.567378\pi$
$499$	−9.38643	−0.420194	−0.210097	+	0.977681i	$0.567378\pi$
$500$	−14.9678	−0.669378
$501$	2.82142	0.126052
$502$	−9.73298	−0.434404
$503$	−24.5717	−1.09560	−0.547800	−	0.836609i	$-0.684535\pi$
$503$	−24.5717	−1.09560	−0.547800	+	0.836609i	$0.684535\pi$
$504$	−0.432011	−0.0192433
$505$	9.12174	0.405912
$506$	46.5841	2.07092
$507$	17.8507	0.792777
$508$	7.68052	0.340768
$509$	12.6386	0.560197	0.280099	−	0.959971i	$-0.409633\pi$
$509$	12.6386	0.560197	0.280099	+	0.959971i	$0.409633\pi$
$510$	30.0581	1.33099
$511$	5.50861	0.243687
$512$	−16.5851	−0.732966
$513$	−5.37318	−0.237232
$514$	49.3589	2.17713
$515$	−19.4749	−0.858165
$516$	49.8649	2.19518
$517$	−49.0080	−2.15537
$518$	8.07975	0.355004
$519$	8.38681	0.368140
$520$	−8.27713	−0.362976
$521$	0.204005	0.00893761	0.00446880	−	0.999990i	$-0.498578\pi$
$521$	0.204005	0.00893761	0.00446880	+	0.999990i	$0.498578\pi$
$522$	−4.23079	−0.185176
$523$	−10.9746	−0.479885	−0.239943	−	0.970787i	$-0.577129\pi$
$523$	−10.9746	−0.479885	−0.239943	+	0.970787i	$0.577129\pi$
$524$	−10.0735	−0.440064
$525$	5.26860	0.229940
$526$	14.7380	0.642609
$527$	26.6492	1.16086
$528$	11.6557	0.507250
$529$	−2.29048	−0.0995859
$530$	49.7104	2.15928
$531$	−1.00778	−0.0437339
$532$	2.85806	0.123913
$533$	6.31238	0.273419
$534$	−24.0001	−1.03859
$535$	−28.0971	−1.21474
$536$	−19.4348	−0.839457
$537$	−18.6528	−0.804926
$538$	13.1014	0.564840
$539$	−27.8697	−1.20043
$540$	44.0696	1.89645
$541$	−32.5754	−1.40053	−0.700263	−	0.713885i	$-0.746934\pi$
$541$	−32.5754	−1.40053	−0.700263	+	0.713885i	$0.746934\pi$
$542$	62.2243	2.67276
$543$	−35.5441	−1.52535
$544$	20.4871	0.878377
$545$	−41.6528	−1.78421
$546$	−5.53074	−0.236694
$547$	−16.9940	−0.726612	−0.363306	−	0.931670i	$-0.618352\pi$
$547$	−16.9940	−0.726612	−0.363306	+	0.931670i	$0.618352\pi$
$548$	−22.6858	−0.969091
$549$	−0.153543	−0.00655307
$550$	−32.5016	−1.38587
$551$	8.47482	0.361039
$552$	−14.5249	−0.618220
$553$	9.47797	0.403044
$554$	−25.4204	−1.08001
$555$	−17.5012	−0.742884
$556$	−39.9777	−1.69543
$557$	−6.23451	−0.264165	−0.132082	−	0.991239i	$-0.542166\pi$
$557$	−6.23451	−0.264165	−0.132082	+	0.991239i	$0.542166\pi$
$558$	4.65042	0.196868
$559$	−15.7667	−0.666859
$560$	4.29742	0.181599
$561$	−22.1039	−0.933227
$562$	−13.8009	−0.582155
$563$	−21.3677	−0.900540	−0.450270	−	0.892892i	$-0.648672\pi$
$563$	−21.3677	−0.900540	−0.450270	+	0.892892i	$0.648672\pi$
$564$	50.4673	2.12505
$565$	−15.4725	−0.650932
$566$	−58.7013	−2.46740
$567$	8.23983	0.346040
$568$	2.49875	0.104845
$569$	−25.5911	−1.07283	−0.536417	−	0.843953i	$-0.680223\pi$
$569$	−25.5911	−1.07283	−0.536417	+	0.843953i	$0.680223\pi$
$570$	−10.5070	−0.440090
$571$	−25.0555	−1.04854	−0.524271	−	0.851552i	$-0.675662\pi$
$571$	−25.0555	−1.04854	−0.524271	+	0.851552i	$0.675662\pi$
$572$	20.1027	0.840538
$573$	33.0330	1.37997
$574$	9.18675	0.383448
$575$	−14.4490	−0.602564
$576$	2.89249	0.120520
$577$	−11.0713	−0.460906	−0.230453	−	0.973083i	$-0.574021\pi$
$577$	−11.0713	−0.460906	−0.230453	+	0.973083i	$0.574021\pi$
$578$	19.4523	0.809111
$579$	14.9409	0.620923
$580$	−69.5085	−2.88618
$581$	4.59660	0.190699
$582$	−13.0447	−0.540721
$583$	−36.5557	−1.51398
$584$	10.5956	0.438450
$585$	−0.977184	−0.0404016
$586$	20.2936	0.838319
$587$	−15.4232	−0.636582	−0.318291	−	0.947993i	$-0.603109\pi$
$587$	−15.4232	−0.636582	−0.318291	+	0.947993i	$0.603109\pi$
$588$	28.6995	1.18355
$589$	−9.31539	−0.383834
$590$	−28.1009	−1.15689
$591$	11.3606	0.467313
$592$	−5.54423	−0.227866
$593$	−35.7808	−1.46934	−0.734670	−	0.678425i	$-0.762663\pi$
$593$	−35.7808	−1.46934	−0.734670	+	0.678425i	$0.762663\pi$
$594$	−55.0027	−2.25679
$595$	−8.14962	−0.334102
$596$	3.15737	0.129331
$597$	−7.36358	−0.301371
$598$	15.1679	0.620261
$599$	26.4128	1.07920	0.539598	−	0.841923i	$-0.318576\pi$
$599$	26.4128	1.07920	0.539598	+	0.841923i	$0.318576\pi$
$600$	10.1340	0.413717
$601$	9.40049	0.383454	0.191727	−	0.981448i	$-0.438591\pi$
$601$	9.40049	0.383454	0.191727	+	0.981448i	$0.438591\pi$
$602$	−22.9461	−0.935213
$603$	−2.29445	−0.0934371
$604$	63.2885	2.57517
$605$	30.0878	1.22325
$606$	11.7237	0.476244
$607$	37.0366	1.50327	0.751634	−	0.659580i	$-0.229266\pi$
$607$	37.0366	1.50327	0.751634	+	0.659580i	$0.229266\pi$
$608$	−7.16140	−0.290433
$609$	−14.0629	−0.569856
$610$	−4.28140	−0.173349
$611$	−15.9571	−0.645555
$612$	−1.85667	−0.0750516
$613$	−14.8900	−0.601400	−0.300700	−	0.953719i	$-0.597220\pi$
$613$	−14.8900	−0.601400	−0.300700	+	0.953719i	$0.597220\pi$
$614$	−55.7163	−2.24853
$615$	−19.8990	−0.802406
$616$	8.85842	0.356916
$617$	0.394863	0.0158966	0.00794830	−	0.999968i	$-0.497470\pi$
$617$	0.394863	0.0158966	0.00794830	+	0.999968i	$0.497470\pi$
$618$	−25.0301	−1.00686
$619$	−25.5070	−1.02521	−0.512607	−	0.858623i	$-0.671320\pi$
$619$	−25.5070	−1.02521	−0.512607	+	0.858623i	$0.671320\pi$
$620$	76.4027	3.06841
$621$	−24.4521	−0.981230
$622$	−42.1109	−1.68849
$623$	6.50714	0.260703
$624$	3.79513	0.151927
$625$	−30.7943	−1.23177
$626$	3.32165	0.132760
$627$	7.72657	0.308569
$628$	−65.6182	−2.61845
$629$	10.5141	0.419224
$630$	−1.42215	−0.0566598
$631$	−20.9015	−0.832075	−0.416038	−	0.909347i	$-0.636581\pi$
$631$	−20.9015	−0.832075	−0.416038	+	0.909347i	$0.636581\pi$
$632$	18.2306	0.725172
$633$	−16.0267	−0.637002
$634$	2.20648	0.0876305
$635$	7.65551	0.303799
$636$	37.6442	1.49269
$637$	−9.07443	−0.359542
$638$	86.7527	3.43457
$639$	0.294999	0.0116700
$640$	39.7023	1.56937
$641$	−4.44033	−0.175383	−0.0876913	−	0.996148i	$-0.527949\pi$
$641$	−4.44033	−0.175383	−0.0876913	+	0.996148i	$0.527949\pi$
$642$	−36.1118	−1.42522
$643$	−37.3499	−1.47294	−0.736468	−	0.676472i	$-0.763508\pi$
$643$	−37.3499	−1.47294	−0.736468	+	0.676472i	$0.763508\pi$
$644$	13.0064	0.512524
$645$	49.7025	1.95704
$646$	6.31222	0.248351
$647$	39.7561	1.56297	0.781487	−	0.623921i	$-0.214461\pi$
$647$	39.7561	1.56297	0.781487	+	0.623921i	$0.214461\pi$
$648$	15.8490	0.622608
$649$	20.6646	0.811157
$650$	−10.5826	−0.415083
$651$	15.4577	0.605834
$652$	33.4025	1.30814
$653$	16.2165	0.634603	0.317301	−	0.948325i	$-0.397223\pi$
$653$	16.2165	0.634603	0.317301	+	0.948325i	$0.397223\pi$
$654$	−53.5342	−2.09335
$655$	−10.0407	−0.392323
$656$	−6.30384	−0.246124
$657$	1.25090	0.0488023
$658$	−23.2233	−0.905337
$659$	−1.23004	−0.0479155	−0.0239577	−	0.999713i	$-0.507627\pi$
$659$	−1.23004	−0.0479155	−0.0239577	+	0.999713i	$0.507627\pi$
$660$	−63.3715	−2.46673
$661$	−7.46481	−0.290347	−0.145174	−	0.989406i	$-0.546374\pi$
$661$	−7.46481	−0.290347	−0.145174	+	0.989406i	$0.546374\pi$
$662$	57.7999	2.24646
$663$	−7.19708	−0.279511
$664$	8.84140	0.343113
$665$	2.84875	0.110470
$666$	1.83476	0.0710955
$667$	38.5670	1.49332
$668$	−4.85955	−0.188022
$669$	9.36537	0.362086
$670$	−63.9782	−2.47169
$671$	3.14842	0.121544
$672$	11.8834	0.458412
$673$	−37.0945	−1.42989	−0.714943	−	0.699183i	$-0.753547\pi$
$673$	−37.0945	−1.42989	−0.714943	+	0.699183i	$0.753547\pi$
$674$	−73.4790	−2.83031
$675$	17.0602	0.656647
$676$	−30.7456	−1.18252
$677$	−6.67528	−0.256552	−0.128276	−	0.991739i	$-0.540944\pi$
$677$	−6.67528	−0.256552	−0.128276	+	0.991739i	$0.540944\pi$
$678$	−19.8860	−0.763717
$679$	3.53680	0.135730
$680$	−15.6755	−0.601129
$681$	−23.4721	−0.899452
$682$	−95.3573	−3.65142
$683$	15.0637	0.576398	0.288199	−	0.957571i	$-0.406944\pi$
$683$	15.0637	0.576398	0.288199	+	0.957571i	$0.406944\pi$
$684$	0.649012	0.0248156
$685$	−22.6120	−0.863959
$686$	−28.5954	−1.09178
$687$	−24.1325	−0.920711
$688$	15.7453	0.600286
$689$	−11.9026	−0.453453
$690$	−47.8150	−1.82028
$691$	−44.5274	−1.69390	−0.846951	−	0.531671i	$-0.821564\pi$
$691$	−44.5274	−1.69390	−0.846951	+	0.531671i	$0.821564\pi$
$692$	−14.4453	−0.549126
$693$	1.04581	0.0397271
$694$	4.26958	0.162071
$695$	−39.8475	−1.51150
$696$	−27.0494	−1.02531
$697$	11.9546	0.452813
$698$	17.9453	0.679240
$699$	−28.4803	−1.07723
$700$	−9.07452	−0.342985
$701$	−0.767459	−0.0289865	−0.0144933	−	0.999895i	$-0.504614\pi$
$701$	−0.767459	−0.0289865	−0.0144933	+	0.999895i	$0.504614\pi$
$702$	−17.9090	−0.675932
$703$	−3.67526	−0.138615
$704$	−59.3108	−2.23536
$705$	50.3029	1.89452
$706$	−28.0859	−1.05703
$707$	−3.17864	−0.119545
$708$	−21.2799	−0.799749
$709$	38.0543	1.42916	0.714580	−	0.699553i	$-0.246618\pi$
$709$	38.0543	1.42916	0.714580	+	0.699553i	$0.246618\pi$
$710$	8.22574	0.308706
$711$	2.15227	0.0807164
$712$	12.5162	0.469066
$713$	−42.3922	−1.58760
$714$	−10.4743	−0.391991
$715$	20.0373	0.749351
$716$	32.1271	1.20065
$717$	−39.4806	−1.47443
$718$	−55.2423	−2.06163
$719$	24.9985	0.932288	0.466144	−	0.884709i	$-0.345643\pi$
$719$	24.9985	0.932288	0.466144	+	0.884709i	$0.345643\pi$
$720$	0.975863	0.0363683
$721$	6.78638	0.252738
$722$	−2.20648	−0.0821166
$723$	−43.4427	−1.61565
$724$	61.2205	2.27524
$725$	−26.9081	−0.999340
$726$	38.6704	1.43519
$727$	−14.8519	−0.550827	−0.275413	−	0.961326i	$-0.588815\pi$
$727$	−14.8519	−0.550827	−0.275413	+	0.961326i	$0.588815\pi$
$728$	2.88432	0.106900
$729$	28.7175	1.06361
$730$	34.8801	1.29097
$731$	−29.8595	−1.10439
$732$	−3.24217	−0.119834
$733$	−28.9854	−1.07060	−0.535300	−	0.844662i	$-0.679801\pi$
$733$	−28.9854	−1.07060	−0.535300	+	0.844662i	$0.679801\pi$
$734$	71.0732	2.62336
$735$	28.6061	1.05515
$736$	−32.5899	−1.20128
$737$	47.0479	1.73303
$738$	2.08614	0.0767919
$739$	−9.66230	−0.355434	−0.177717	−	0.984082i	$-0.556871\pi$
$739$	−9.66230	−0.355434	−0.177717	+	0.984082i	$0.556871\pi$
$740$	30.1437	1.10810
$741$	2.51579	0.0924197
$742$	−17.3225	−0.635930
$743$	43.4995	1.59584	0.797922	−	0.602761i	$-0.205933\pi$
$743$	43.4995	1.59584	0.797922	+	0.602761i	$0.205933\pi$
$744$	29.7323	1.09004
$745$	3.14709	0.115300
$746$	75.0018	2.74601
$747$	1.04380	0.0381907
$748$	38.0713	1.39202
$749$	9.79096	0.357754
$750$	−19.1747	−0.700160
$751$	22.0101	0.803159	0.401580	−	0.915824i	$-0.368461\pi$
$751$	22.0101	0.803159	0.401580	+	0.915824i	$0.368461\pi$
$752$	15.9355	0.581109
$753$	−7.34649	−0.267721
$754$	28.2469	1.02869
$755$	63.0823	2.29580
$756$	−15.3569	−0.558525
$757$	−26.2899	−0.955521	−0.477761	−	0.878490i	$-0.658551\pi$
$757$	−26.2899	−0.955521	−0.477761	+	0.878490i	$0.658551\pi$
$758$	45.6857	1.65938
$759$	35.1618	1.27629
$760$	5.47948	0.198762
$761$	48.1510	1.74547	0.872736	−	0.488193i	$-0.162344\pi$
$761$	48.1510	1.74547	0.872736	+	0.488193i	$0.162344\pi$
$762$	9.83925	0.356438
$763$	14.5147	0.525467
$764$	−56.8954	−2.05840
$765$	−1.85063	−0.0669095
$766$	7.68228	0.277572
$767$	6.72844	0.242950
$768$	8.44352	0.304679
$769$	−0.670309	−0.0241720	−0.0120860	−	0.999927i	$-0.503847\pi$
$769$	−0.670309	−0.0241720	−0.0120860	+	0.999927i	$0.503847\pi$
$770$	29.1614	1.05090
$771$	37.2563	1.34175
$772$	−25.7339	−0.926184
$773$	−26.1415	−0.940243	−0.470122	−	0.882602i	$-0.655790\pi$
$773$	−26.1415	−0.940243	−0.470122	+	0.882602i	$0.655790\pi$
$774$	−5.21063	−0.187292
$775$	29.5769	1.06243
$776$	6.80292	0.244211
$777$	6.09862	0.218787
$778$	−75.7217	−2.71476
$779$	−4.17881	−0.149721
$780$	−20.6339	−0.738812
$781$	−6.04899	−0.216450
$782$	28.7255	1.02722
$783$	−45.5368	−1.62735
$784$	9.06216	0.323649
$785$	−65.4045	−2.33439
$786$	−12.9048	−0.460300
$787$	21.9967	0.784097	0.392049	−	0.919945i	$-0.371767\pi$
$787$	21.9967	0.784097	0.392049	+	0.919945i	$0.371767\pi$
$788$	−19.5673	−0.697055
$789$	11.1243	0.396036
$790$	60.0138	2.13520
$791$	5.39168	0.191706
$792$	2.01158	0.0714784
$793$	1.02513	0.0364036
$794$	41.8319	1.48456
$795$	37.5216	1.33075
$796$	12.6829	0.449533
$797$	−17.2647	−0.611548	−0.305774	−	0.952104i	$-0.598915\pi$
$797$	−17.2647	−0.611548	−0.305774	+	0.952104i	$0.598915\pi$
$798$	3.66136	0.129611
$799$	−30.2201	−1.06911
$800$	22.7379	0.803905
$801$	1.47765	0.0522101
$802$	24.6274	0.869623
$803$	−25.6499	−0.905165
$804$	−48.4488	−1.70866
$805$	12.9640	0.456922
$806$	−31.0485	−1.09364
$807$	9.88896	0.348108
$808$	−6.11401	−0.215090
$809$	44.4877	1.56411	0.782053	−	0.623212i	$-0.214173\pi$
$809$	44.4877	1.56411	0.782053	+	0.623212i	$0.214173\pi$
$810$	52.1739	1.83321
$811$	−40.3191	−1.41580	−0.707898	−	0.706315i	$-0.750356\pi$
$811$	−40.3191	−1.41580	−0.707898	+	0.706315i	$0.750356\pi$
$812$	24.2216	0.850010
$813$	46.9671	1.64721
$814$	−37.6219	−1.31865
$815$	33.2937	1.16623
$816$	7.18735	0.251608
$817$	10.4376	0.365164
$818$	71.2107	2.48982
$819$	0.340518	0.0118987
$820$	34.2737	1.19689
$821$	3.49194	0.121869	0.0609347	−	0.998142i	$-0.480592\pi$
$821$	3.49194	0.121869	0.0609347	+	0.998142i	$0.480592\pi$
$822$	−29.0620	−1.01366
$823$	−11.3787	−0.396636	−0.198318	−	0.980138i	$-0.563548\pi$
$823$	−11.3787	−0.396636	−0.198318	+	0.980138i	$0.563548\pi$
$824$	13.0534	0.454736
$825$	−24.5323	−0.854105
$826$	9.79228	0.340717
$827$	−25.2499	−0.878025	−0.439012	−	0.898481i	$-0.644672\pi$
$827$	−25.2499	−0.878025	−0.439012	+	0.898481i	$0.644672\pi$
$828$	2.95351	0.102641
$829$	−25.8734	−0.898620	−0.449310	−	0.893376i	$-0.648330\pi$
$829$	−25.8734	−0.898620	−0.449310	+	0.893376i	$0.648330\pi$
$830$	29.1053	1.01026
$831$	−19.1874	−0.665604
$832$	−19.3117	−0.669514
$833$	−17.1855	−0.595442
$834$	−51.2140	−1.77340
$835$	−4.84373	−0.167624
$836$	−13.3081	−0.460269
$837$	50.0533	1.73010
$838$	−40.9977	−1.41624
$839$	48.0672	1.65946	0.829732	−	0.558162i	$-0.188493\pi$
$839$	48.0672	1.65946	0.829732	+	0.558162i	$0.188493\pi$
$840$	−9.09248	−0.313720
$841$	42.8226	1.47664
$842$	−44.5966	−1.53690
$843$	−10.4170	−0.358779
$844$	27.6040	0.950168
$845$	−30.6455	−1.05424
$846$	−5.27357	−0.181309
$847$	−10.4847	−0.360258
$848$	11.8865	0.408185
$849$	−44.3080	−1.52065
$850$	−20.0417	−0.687424
$851$	−16.7253	−0.573335
$852$	6.22910	0.213406
$853$	−4.01704	−0.137541	−0.0687704	−	0.997633i	$-0.521908\pi$
$853$	−4.01704	−0.137541	−0.0687704	+	0.997633i	$0.521908\pi$
$854$	1.49193	0.0510530
$855$	0.646899	0.0221235
$856$	18.8326	0.643684
$857$	5.40918	0.184774	0.0923870	−	0.995723i	$-0.470550\pi$
$857$	5.40918	0.184774	0.0923870	+	0.995723i	$0.470550\pi$
$858$	25.7529	0.879190
$859$	34.5560	1.17904	0.589518	−	0.807755i	$-0.299318\pi$
$859$	34.5560	1.17904	0.589518	+	0.807755i	$0.299318\pi$
$860$	−85.6066	−2.91916
$861$	6.93419	0.236317
$862$	−45.6319	−1.55423
$863$	19.5155	0.664316	0.332158	−	0.943224i	$-0.392223\pi$
$863$	19.5155	0.664316	0.332158	+	0.943224i	$0.392223\pi$
$864$	38.4795	1.30910
$865$	−14.3982	−0.489554
$866$	75.4696	2.56456
$867$	14.6827	0.498650
$868$	−26.6240	−0.903677
$869$	−44.1325	−1.49709
$870$	−89.0449	−3.01891
$871$	15.3189	0.519061
$872$	27.9185	0.945440
$873$	0.803142	0.0271822
$874$	−10.0412	−0.339648
$875$	5.19881	0.175752
$876$	26.4136	0.892434
$877$	9.27680	0.313255	0.156628	−	0.987658i	$-0.449938\pi$
$877$	9.27680	0.313255	0.156628	+	0.987658i	$0.449938\pi$
$878$	−10.9219	−0.368596
$879$	15.3176	0.516651
$880$	−20.0102	−0.674543
$881$	−12.5957	−0.424359	−0.212179	−	0.977231i	$-0.568056\pi$
$881$	−12.5957	−0.424359	−0.212179	+	0.977231i	$0.568056\pi$
$882$	−2.99895	−0.100980
$883$	−22.2634	−0.749224	−0.374612	−	0.927182i	$-0.622224\pi$
$883$	−22.2634	−0.749224	−0.374612	+	0.927182i	$0.622224\pi$
$884$	12.3961	0.416926
$885$	−21.2106	−0.712987
$886$	−33.4880	−1.12505
$887$	−25.6123	−0.859978	−0.429989	−	0.902834i	$-0.641483\pi$
$887$	−25.6123	−0.859978	−0.429989	+	0.902834i	$0.641483\pi$
$888$	11.7305	0.393649
$889$	−2.66771	−0.0894720
$890$	41.2027	1.38112
$891$	−38.3673	−1.28535
$892$	−16.1307	−0.540096
$893$	10.5636	0.353499
$894$	4.04480	0.135278
$895$	32.0225	1.07039
$896$	−13.8350	−0.462195
$897$	11.4488	0.382263
$898$	−34.4939	−1.15108
$899$	−78.9463	−2.63301
$900$	−2.06065	−0.0686884
$901$	−22.5416	−0.750969
$902$	−42.7765	−1.42430
$903$	−17.3198	−0.576367
$904$	10.3707	0.344924
$905$	61.0211	2.02841
$906$	81.0766	2.69359
$907$	11.8235	0.392594	0.196297	−	0.980544i	$-0.437108\pi$
$907$	11.8235	0.392594	0.196297	+	0.980544i	$0.437108\pi$
$908$	40.4278	1.34164
$909$	−0.721810	−0.0239409
$910$	9.49500	0.314756
$911$	−33.8940	−1.12296	−0.561479	−	0.827491i	$-0.689767\pi$
$911$	−33.8940	−1.12296	−0.561479	+	0.827491i	$0.689767\pi$
$912$	−2.51239	−0.0831934
$913$	−21.4033	−0.708345
$914$	43.2883	1.43185
$915$	−3.23161	−0.106834
$916$	41.5652	1.37335
$917$	3.49888	0.115543
$918$	−33.9167	−1.11942
$919$	49.0190	1.61699	0.808493	−	0.588505i	$-0.200283\pi$
$919$	49.0190	1.61699	0.808493	+	0.588505i	$0.200283\pi$
$920$	24.9359	0.822111
$921$	−42.0548	−1.38575
$922$	42.4472	1.39792
$923$	−1.96956	−0.0648290
$924$	22.0830	0.726478
$925$	11.6692	0.383680
$926$	−71.2369	−2.34099
$927$	1.54106	0.0506151
$928$	−60.6916	−1.99230
$929$	−34.9824	−1.14774	−0.573868	−	0.818948i	$-0.694558\pi$
$929$	−34.9824	−1.14774	−0.573868	+	0.818948i	$0.694558\pi$
$930$	97.8769	3.20951
$931$	6.00730	0.196881
$932$	49.0539	1.60681
$933$	−31.7855	−1.04061
$934$	48.4851	1.58648
$935$	37.9473	1.24101
$936$	0.654975	0.0214085
$937$	60.6607	1.98170	0.990849	−	0.134973i	$-0.0430946\pi$
$937$	60.6607	1.98170	0.990849	+	0.134973i	$0.0430946\pi$
$938$	22.2944	0.727939
$939$	2.50719	0.0818192
$940$	−86.6406	−2.82591
$941$	−25.9431	−0.845722	−0.422861	−	0.906194i	$-0.638974\pi$
$941$	−25.9431	−0.845722	−0.422861	+	0.906194i	$0.638974\pi$
$942$	−84.0611	−2.73886
$943$	−19.0168	−0.619273
$944$	−6.71935	−0.218696
$945$	−15.3069	−0.497933
$946$	106.844	3.47381
$947$	5.97264	0.194085	0.0970423	−	0.995280i	$-0.469062\pi$
$947$	5.97264	0.194085	0.0970423	+	0.995280i	$0.469062\pi$
$948$	45.4466	1.47604
$949$	−8.35166	−0.271106
$950$	7.00570	0.227295
$951$	1.66546	0.0540062
$952$	5.46243	0.177038
$953$	−25.9103	−0.839317	−0.419658	−	0.907682i	$-0.637850\pi$
$953$	−25.9103	−0.839317	−0.419658	+	0.907682i	$0.637850\pi$
$954$	−3.93362	−0.127356
$955$	−56.7101	−1.83510
$956$	68.0005	2.19929
$957$	65.4812	2.11671
$958$	1.40537	0.0454053
$959$	7.87957	0.254445
$960$	60.8780	1.96483
$961$	55.7766	1.79924
$962$	−12.2498	−0.394949
$963$	2.22334	0.0716462
$964$	74.8247	2.40994
$965$	−25.6501	−0.825706
$966$	16.6620	0.536092
$967$	32.1479	1.03381	0.516904	−	0.856043i	$-0.327084\pi$
$967$	32.1479	1.03381	0.516904	+	0.856043i	$0.327084\pi$
$968$	−20.1669	−0.648189
$969$	4.76449	0.153057
$970$	22.3948	0.719053
$971$	−48.5836	−1.55912	−0.779561	−	0.626327i	$-0.784558\pi$
$971$	−48.5836	−1.55912	−0.779561	+	0.626327i	$0.784558\pi$
$972$	−6.72997	−0.215864
$973$	13.8856	0.445152
$974$	47.5578	1.52385
$975$	−7.98777	−0.255813
$976$	−1.02375	−0.0327694
$977$	−21.2550	−0.680009	−0.340004	−	0.940424i	$-0.610429\pi$
$977$	−21.2550	−0.680009	−0.340004	+	0.940424i	$0.610429\pi$
$978$	42.7908	1.36830
$979$	−30.2993	−0.968371
$980$	−49.2705	−1.57389
$981$	3.29601	0.105234
$982$	−31.3086	−0.999099
$983$	37.4467	1.19436	0.597181	−	0.802106i	$-0.296287\pi$
$983$	37.4467	1.19436	0.597181	+	0.802106i	$0.296287\pi$
$984$	13.3377	0.425190
$985$	−19.5035	−0.621434
$986$	53.4949	1.70363
$987$	−17.5290	−0.557954
$988$	−4.33314	−0.137855
$989$	47.4990	1.51038
$990$	6.62200	0.210461
$991$	48.0090	1.52506	0.762528	−	0.646956i	$-0.223958\pi$
$991$	48.0090	1.52506	0.762528	+	0.646956i	$0.223958\pi$
$992$	66.7113	2.11808
$993$	43.6275	1.38448
$994$	−2.86641	−0.0909172
$995$	12.6416	0.400765
$996$	22.0406	0.698383
$997$	−47.6187	−1.50810	−0.754050	−	0.656817i	$-0.771902\pi$
$997$	−47.6187	−1.50810	−0.754050	+	0.656817i	$0.771902\pi$
$998$	20.7110	0.655594
$999$	19.7479	0.624795

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6023.2.a.b.1.14	✓	99

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6023.2.a.b.1.14	✓	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)

\(f(q)\)	\(=\)	\(q-2.20648 q^{2} -1.66546 q^{3} +2.86855 q^{4} +2.85921 q^{5} +3.67480 q^{6} -0.996345 q^{7} -1.91643 q^{8} -0.226251 q^{9} +O(q^{10})\)	\(q-2.20648 q^{2} -1.66546 q^{3} +2.86855 q^{4} +2.85921 q^{5} +3.67480 q^{6} -0.996345 q^{7} -1.91643 q^{8} -0.226251 q^{9} -6.30878 q^{10} +4.63930 q^{11} -4.77745 q^{12} +1.51057 q^{13} +2.19841 q^{14} -4.76189 q^{15} -1.50853 q^{16} +2.86077 q^{17} +0.499218 q^{18} -1.00000 q^{19} +8.20177 q^{20} +1.65937 q^{21} -10.2365 q^{22} -4.55077 q^{23} +3.19174 q^{24} +3.17506 q^{25} -3.33304 q^{26} +5.37318 q^{27} -2.85806 q^{28} -8.47482 q^{29} +10.5070 q^{30} +9.31539 q^{31} +7.16140 q^{32} -7.72657 q^{33} -6.31222 q^{34} -2.84875 q^{35} -0.649012 q^{36} +3.67526 q^{37} +2.20648 q^{38} -2.51579 q^{39} -5.47948 q^{40} +4.17881 q^{41} -3.66136 q^{42} -10.4376 q^{43} +13.3081 q^{44} -0.646899 q^{45} +10.0412 q^{46} -10.5636 q^{47} +2.51239 q^{48} -6.00730 q^{49} -7.00570 q^{50} -4.76449 q^{51} +4.33314 q^{52} -7.87956 q^{53} -11.8558 q^{54} +13.2647 q^{55} +1.90943 q^{56} +1.66546 q^{57} +18.6995 q^{58} +4.45425 q^{59} -13.6597 q^{60} +0.678642 q^{61} -20.5542 q^{62} +0.225424 q^{63} -12.7844 q^{64} +4.31902 q^{65} +17.0485 q^{66} +10.1411 q^{67} +8.20625 q^{68} +7.57912 q^{69} +6.28572 q^{70} -1.30386 q^{71} +0.433595 q^{72} -5.52882 q^{73} -8.10939 q^{74} -5.28793 q^{75} -2.86855 q^{76} -4.62235 q^{77} +5.55103 q^{78} -9.51275 q^{79} -4.31319 q^{80} -8.27006 q^{81} -9.22046 q^{82} -4.61347 q^{83} +4.75998 q^{84} +8.17952 q^{85} +23.0303 q^{86} +14.1145 q^{87} -8.89092 q^{88} -6.53101 q^{89} +1.42737 q^{90} -1.50505 q^{91} -13.0541 q^{92} -15.5144 q^{93} +23.3085 q^{94} -2.85921 q^{95} -11.9270 q^{96} -3.54978 q^{97} +13.2550 q^{98} -1.04965 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 99 q - 4 q^{2} - 3 q^{3} + 80 q^{4} - 15 q^{5} - 12 q^{6} - 19 q^{7} - 12 q^{8} + 58 q^{9}+O(q^{10}) \) 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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