LMFDB - Embedded newform 6023.2.a.b.1.29

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			1.29
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)

$f(q)$	$=$	$q-1.34833 q^{2} -1.65952 q^{3} -0.182003 q^{4} -3.09253 q^{5} +2.23758 q^{6} -0.433828 q^{7} +2.94206 q^{8} -0.246008 q^{9} +O(q^{10})$	\(q-1.34833 q^{2} -1.65952 q^{3} -0.182003 q^{4} -3.09253 q^{5} +2.23758 q^{6} -0.433828 q^{7} +2.94206 q^{8} -0.246008 q^{9} +4.16975 q^{10} -4.76055 q^{11} +0.302037 q^{12} -2.87706 q^{13} +0.584943 q^{14} +5.13210 q^{15} -3.60287 q^{16} +2.73377 q^{17} +0.331700 q^{18} -1.00000 q^{19} +0.562849 q^{20} +0.719944 q^{21} +6.41880 q^{22} -2.05161 q^{23} -4.88240 q^{24} +4.56374 q^{25} +3.87922 q^{26} +5.38680 q^{27} +0.0789579 q^{28} -3.23276 q^{29} -6.91977 q^{30} -9.53318 q^{31} -1.02626 q^{32} +7.90021 q^{33} -3.68603 q^{34} +1.34162 q^{35} +0.0447742 q^{36} +6.88791 q^{37} +1.34833 q^{38} +4.77452 q^{39} -9.09841 q^{40} -6.64270 q^{41} -0.970723 q^{42} -1.69885 q^{43} +0.866434 q^{44} +0.760787 q^{45} +2.76624 q^{46} +1.36739 q^{47} +5.97902 q^{48} -6.81179 q^{49} -6.15343 q^{50} -4.53674 q^{51} +0.523632 q^{52} +10.5365 q^{53} -7.26319 q^{54} +14.7221 q^{55} -1.27635 q^{56} +1.65952 q^{57} +4.35884 q^{58} -2.69263 q^{59} -0.934057 q^{60} -10.6844 q^{61} +12.8539 q^{62} +0.106725 q^{63} +8.58948 q^{64} +8.89738 q^{65} -10.6521 q^{66} +7.91188 q^{67} -0.497555 q^{68} +3.40467 q^{69} -1.80895 q^{70} +3.56771 q^{71} -0.723771 q^{72} +12.8960 q^{73} -9.28718 q^{74} -7.57359 q^{75} +0.182003 q^{76} +2.06526 q^{77} -6.43763 q^{78} +7.76881 q^{79} +11.1420 q^{80} -8.20146 q^{81} +8.95656 q^{82} +11.1224 q^{83} -0.131032 q^{84} -8.45428 q^{85} +2.29061 q^{86} +5.36482 q^{87} -14.0058 q^{88} +10.0618 q^{89} -1.02579 q^{90} +1.24815 q^{91} +0.373398 q^{92} +15.8205 q^{93} -1.84370 q^{94} +3.09253 q^{95} +1.70310 q^{96} -2.54702 q^{97} +9.18455 q^{98} +1.17113 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.34833	−0.953414	−0.476707	−	0.879062i	$-0.658170\pi$
$2$	−1.34833	−0.953414	−0.476707	+	0.879062i	$0.658170\pi$
$3$	−1.65952	−0.958122	−0.479061	−	0.877782i	$-0.659023\pi$
$3$	−1.65952	−0.958122	−0.479061	+	0.877782i	$0.659023\pi$
$4$	−0.182003	−0.0910015
$5$	−3.09253	−1.38302	−0.691511	−	0.722366i	$-0.743054\pi$
$5$	−3.09253	−1.38302	−0.691511	+	0.722366i	$0.743054\pi$
$6$	2.23758	0.913487
$7$	−0.433828	−0.163971	−0.0819857	−	0.996634i	$-0.526126\pi$
$7$	−0.433828	−0.163971	−0.0819857	+	0.996634i	$0.526126\pi$
$8$	2.94206	1.04018
$9$	−0.246008	−0.0820027
$10$	4.16975	1.31859
$11$	−4.76055	−1.43536	−0.717680	−	0.696373i	$-0.754796\pi$
$11$	−4.76055	−1.43536	−0.717680	+	0.696373i	$0.754796\pi$
$12$	0.302037	0.0871905
$13$	−2.87706	−0.797952	−0.398976	−	0.916961i	$-0.630634\pi$
$13$	−2.87706	−0.797952	−0.398976	+	0.916961i	$0.630634\pi$
$14$	0.584943	0.156333
$15$	5.13210	1.32510
$16$	−3.60287	−0.900717
$17$	2.73377	0.663038	0.331519	−	0.943449i	$-0.392439\pi$
$17$	2.73377	0.663038	0.331519	+	0.943449i	$0.392439\pi$
$18$	0.331700	0.0781825
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	0.562849	0.125857
$21$	0.719944	0.157105
$22$	6.41880	1.36849
$23$	−2.05161	−0.427789	−0.213895	−	0.976857i	$-0.568615\pi$
$23$	−2.05161	−0.427789	−0.213895	+	0.976857i	$0.568615\pi$
$24$	−4.88240	−0.996616
$25$	4.56374	0.912747
$26$	3.87922	0.760778
$27$	5.38680	1.03669
$28$	0.0789579	0.0149216
$29$	−3.23276	−0.600309	−0.300155	−	0.953891i	$-0.597038\pi$
$29$	−3.23276	−0.600309	−0.300155	+	0.953891i	$0.597038\pi$
$30$	−6.91977	−1.26337
$31$	−9.53318	−1.71221	−0.856105	−	0.516802i	$-0.827122\pi$
$31$	−9.53318	−1.71221	−0.856105	+	0.516802i	$0.827122\pi$
$32$	−1.02626	−0.181420
$33$	7.90021	1.37525
$34$	−3.68603	−0.632149
$35$	1.34162	0.226776
$36$	0.0447742	0.00746236
$37$	6.88791	1.13237	0.566183	−	0.824280i	$-0.308420\pi$
$37$	6.88791	1.13237	0.566183	+	0.824280i	$0.308420\pi$
$38$	1.34833	0.218728
$39$	4.77452	0.764535
$40$	−9.09841	−1.43859
$41$	−6.64270	−1.03742	−0.518708	−	0.854952i	$-0.673587\pi$
$41$	−6.64270	−1.03742	−0.518708	+	0.854952i	$0.673587\pi$
$42$	−0.970723	−0.149786
$43$	−1.69885	−0.259072	−0.129536	−	0.991575i	$-0.541349\pi$
$43$	−1.69885	−0.259072	−0.129536	+	0.991575i	$0.541349\pi$
$44$	0.866434	0.130620
$45$	0.760787	0.113411
$46$	2.76624	0.407860
$47$	1.36739	0.199455	0.0997273	−	0.995015i	$-0.468203\pi$
$47$	1.36739	0.199455	0.0997273	+	0.995015i	$0.468203\pi$
$48$	5.97902	0.862997
$49$	−6.81179	−0.973113
$50$	−6.15343	−0.870226
$51$	−4.53674	−0.635271
$52$	0.523632	0.0726148
$53$	10.5365	1.44729	0.723647	−	0.690170i	$-0.242464\pi$
$53$	10.5365	1.44729	0.723647	+	0.690170i	$0.242464\pi$
$54$	−7.26319	−0.988395
$55$	14.7221	1.98513
$56$	−1.27635	−0.170559
$57$	1.65952	0.219808
$58$	4.35884	0.572343
$59$	−2.69263	−0.350551	−0.175276	−	0.984519i	$-0.556082\pi$
$59$	−2.69263	−0.350551	−0.175276	+	0.984519i	$0.556082\pi$
$60$	−0.934057	−0.120586
$61$	−10.6844	−1.36799	−0.683997	−	0.729485i	$-0.739760\pi$
$61$	−10.6844	−1.36799	−0.683997	+	0.729485i	$0.739760\pi$
$62$	12.8539	1.63245
$63$	0.106725	0.0134461
$64$	8.58948	1.07369
$65$	8.89738	1.10358
$66$	−10.6521	−1.31118
$67$	7.91188	0.966590	0.483295	−	0.875458i	$-0.339440\pi$
$67$	7.91188	0.966590	0.483295	+	0.875458i	$0.339440\pi$
$68$	−0.497555	−0.0603374
$69$	3.40467	0.409874
$70$	−1.80895	−0.216211
$71$	3.56771	0.423409	0.211705	−	0.977334i	$-0.432098\pi$
$71$	3.56771	0.423409	0.211705	+	0.977334i	$0.432098\pi$
$72$	−0.723771	−0.0852972
$73$	12.8960	1.50937	0.754684	−	0.656088i	$-0.227790\pi$
$73$	12.8960	1.50937	0.754684	+	0.656088i	$0.227790\pi$
$74$	−9.28718	−1.07961
$75$	−7.57359	−0.874523
$76$	0.182003	0.0208772
$77$	2.06526	0.235358
$78$	−6.43763	−0.728918
$79$	7.76881	0.874060	0.437030	−	0.899447i	$-0.356030\pi$
$79$	7.76881	0.874060	0.437030	+	0.899447i	$0.356030\pi$
$80$	11.1420	1.24571
$81$	−8.20146	−0.911273
$82$	8.95656	0.989086
$83$	11.1224	1.22084	0.610422	−	0.792076i	$-0.291000\pi$
$83$	11.1224	1.22084	0.610422	+	0.792076i	$0.291000\pi$
$84$	−0.131032	−0.0142968
$85$	−8.45428	−0.916995
$86$	2.29061	0.247003
$87$	5.36482	0.575169
$88$	−14.0058	−1.49303
$89$	10.0618	1.06655	0.533275	−	0.845942i	$-0.320961\pi$
$89$	10.0618	1.06655	0.533275	+	0.845942i	$0.320961\pi$
$90$	−1.02579	−0.108128
$91$	1.24815	0.130841
$92$	0.373398	0.0389295
$93$	15.8205	1.64051
$94$	−1.84370	−0.190163
$95$	3.09253	0.317287
$96$	1.70310	0.173822
$97$	−2.54702	−0.258611	−0.129305	−	0.991605i	$-0.541275\pi$
$97$	−2.54702	−0.258611	−0.129305	+	0.991605i	$0.541275\pi$
$98$	9.18455	0.927780
$99$	1.17113	0.117703
$100$	−0.830613	−0.0830613
$101$	0.970683	0.0965866	0.0482933	−	0.998833i	$-0.484622\pi$
$101$	0.970683	0.0965866	0.0482933	+	0.998833i	$0.484622\pi$
$102$	6.11703	0.605676
$103$	18.3963	1.81264	0.906320	−	0.422592i	$-0.138880\pi$
$103$	18.3963	1.81264	0.906320	+	0.422592i	$0.138880\pi$
$104$	−8.46448	−0.830010
$105$	−2.22645	−0.217279
$106$	−14.2066	−1.37987
$107$	7.87631	0.761431	0.380716	−	0.924692i	$-0.375678\pi$
$107$	7.87631	0.761431	0.380716	+	0.924692i	$0.375678\pi$
$108$	−0.980414	−0.0943403
$109$	−15.2325	−1.45901	−0.729505	−	0.683976i	$-0.760249\pi$
$109$	−15.2325	−1.45901	−0.729505	+	0.683976i	$0.760249\pi$
$110$	−19.8503	−1.89265
$111$	−11.4306	−1.08494
$112$	1.56302	0.147692
$113$	−13.8370	−1.30168	−0.650839	−	0.759216i	$-0.725583\pi$
$113$	−13.8370	−1.30168	−0.650839	+	0.759216i	$0.725583\pi$
$114$	−2.23758	−0.209568
$115$	6.34465	0.591642
$116$	0.588373	0.0546290
$117$	0.707778	0.0654341
$118$	3.63056	0.334220
$119$	−1.18599	−0.108719
$120$	15.0990	1.37834
$121$	11.6628	1.06026
$122$	14.4061	1.30426
$123$	11.0237	0.993970
$124$	1.73507	0.155814
$125$	1.34916	0.120672
$126$	−0.143901	−0.0128197
$127$	−21.3591	−1.89531	−0.947655	−	0.319296i	$-0.896553\pi$
$127$	−21.3591	−1.89531	−0.947655	+	0.319296i	$0.896553\pi$
$128$	−9.52894	−0.842247
$129$	2.81926	0.248222
$130$	−11.9966	−1.05217
$131$	−4.12457	−0.360366	−0.180183	−	0.983633i	$-0.557669\pi$
$131$	−4.12457	−0.360366	−0.180183	+	0.983633i	$0.557669\pi$
$132$	−1.43786	−0.125150
$133$	0.433828	0.0376176
$134$	−10.6678	−0.921560
$135$	−16.6588	−1.43376
$136$	8.04294	0.689676
$137$	2.37270	0.202714	0.101357	−	0.994850i	$-0.467682\pi$
$137$	2.37270	0.202714	0.101357	+	0.994850i	$0.467682\pi$
$138$	−4.59062	−0.390780
$139$	8.90896	0.755648	0.377824	−	0.925877i	$-0.376672\pi$
$139$	8.90896	0.755648	0.377824	+	0.925877i	$0.376672\pi$
$140$	−0.244180	−0.0206369
$141$	−2.26921	−0.191102
$142$	−4.81046	−0.403685
$143$	13.6964	1.14535
$144$	0.886334	0.0738612
$145$	9.99742	0.830240
$146$	−17.3881	−1.43905
$147$	11.3043	0.932361
$148$	−1.25362	−0.103047
$149$	12.8362	1.05158	0.525792	−	0.850613i	$-0.323769\pi$
$149$	12.8362	1.05158	0.525792	+	0.850613i	$0.323769\pi$
$150$	10.2117	0.833783
$151$	−15.3706	−1.25084	−0.625422	−	0.780287i	$-0.715073\pi$
$151$	−15.3706	−1.25084	−0.625422	+	0.780287i	$0.715073\pi$
$152$	−2.94206	−0.238633
$153$	−0.672530	−0.0543708
$154$	−2.78465	−0.224394
$155$	29.4816	2.36802
$156$	−0.868976	−0.0695738
$157$	8.30805	0.663055	0.331527	−	0.943446i	$-0.392436\pi$
$157$	8.30805	0.663055	0.331527	+	0.943446i	$0.392436\pi$
$158$	−10.4749	−0.833341
$159$	−17.4854	−1.38668
$160$	3.17375	0.250907
$161$	0.890043	0.0701452
$162$	11.0583	0.868820
$163$	16.1258	1.26307	0.631535	−	0.775347i	$-0.282425\pi$
$163$	16.1258	1.26307	0.631535	+	0.775347i	$0.282425\pi$
$164$	1.20899	0.0944063
$165$	−24.4316	−1.90200
$166$	−14.9967	−1.16397
$167$	−3.99137	−0.308861	−0.154431	−	0.988004i	$-0.549354\pi$
$167$	−3.99137	−0.308861	−0.154431	+	0.988004i	$0.549354\pi$
$168$	2.11812	0.163417
$169$	−4.72255	−0.363273
$170$	11.3992	0.874276
$171$	0.246008	0.0188127
$172$	0.309195	0.0235759
$173$	21.8579	1.66183	0.830914	−	0.556401i	$-0.187818\pi$
$173$	21.8579	1.66183	0.830914	+	0.556401i	$0.187818\pi$
$174$	−7.23356	−0.548375
$175$	−1.97988	−0.149664
$176$	17.1516	1.29285
$177$	4.46847	0.335871
$178$	−13.5667	−1.01686
$179$	−3.10398	−0.232002	−0.116001	−	0.993249i	$-0.537008\pi$
$179$	−3.10398	−0.232002	−0.116001	+	0.993249i	$0.537008\pi$
$180$	−0.138465	−0.0103206
$181$	5.50220	0.408975	0.204488	−	0.978869i	$-0.434447\pi$
$181$	5.50220	0.408975	0.204488	+	0.978869i	$0.434447\pi$
$182$	−1.68291	−0.124746
$183$	17.7309	1.31070
$184$	−6.03595	−0.444976
$185$	−21.3011	−1.56609
$186$	−21.3312	−1.56408
$187$	−13.0143	−0.951698
$188$	−0.248869	−0.0181507
$189$	−2.33694	−0.169988
$190$	−4.16975	−0.302506
$191$	15.1151	1.09369	0.546846	−	0.837233i	$-0.315828\pi$
$191$	15.1151	1.09369	0.546846	+	0.837233i	$0.315828\pi$
$192$	−14.2544	−1.02872
$193$	8.57284	0.617086	0.308543	−	0.951210i	$-0.400159\pi$
$193$	8.57284	0.617086	0.308543	+	0.951210i	$0.400159\pi$
$194$	3.43423	0.246563
$195$	−14.7653	−1.05737
$196$	1.23977	0.0885547
$197$	−13.8392	−0.986000	−0.493000	−	0.870029i	$-0.664100\pi$
$197$	−13.8392	−0.986000	−0.493000	+	0.870029i	$0.664100\pi$
$198$	−1.57908	−0.112220
$199$	−7.53912	−0.534434	−0.267217	−	0.963636i	$-0.586104\pi$
$199$	−7.53912	−0.534434	−0.267217	+	0.963636i	$0.586104\pi$
$200$	13.4268	0.949418
$201$	−13.1299	−0.926111
$202$	−1.30880	−0.0920870
$203$	1.40246	0.0984336
$204$	0.825700	0.0578106
$205$	20.5427	1.43477
$206$	−24.8043	−1.72820
$207$	0.504711	0.0350799
$208$	10.3657	0.718729
$209$	4.76055	0.329294
$210$	3.00199	0.207157
$211$	6.48569	0.446493	0.223247	−	0.974762i	$-0.428334\pi$
$211$	6.48569	0.446493	0.223247	+	0.974762i	$0.428334\pi$
$212$	−1.91767	−0.131706
$213$	−5.92067	−0.405678
$214$	−10.6199	−0.725959
$215$	5.25374	0.358302
$216$	15.8483	1.07834
$217$	4.13576	0.280754
$218$	20.5385	1.39104
$219$	−21.4012	−1.44616
$220$	−2.67947	−0.180650
$221$	−7.86522	−0.529072
$222$	15.4122	1.03440
$223$	−11.3211	−0.758119	−0.379060	−	0.925372i	$-0.623752\pi$
$223$	−11.3211	−0.758119	−0.379060	+	0.925372i	$0.623752\pi$
$224$	0.445222	0.0297476
$225$	−1.12272	−0.0748477
$226$	18.6569	1.24104
$227$	19.4995	1.29423	0.647113	−	0.762394i	$-0.275976\pi$
$227$	19.4995	1.29423	0.647113	+	0.762394i	$0.275976\pi$
$228$	−0.302037	−0.0200029
$229$	22.5780	1.49199	0.745997	−	0.665949i	$-0.231973\pi$
$229$	22.5780	1.49199	0.745997	+	0.665949i	$0.231973\pi$
$230$	−8.55469	−0.564079
$231$	−3.42733	−0.225502
$232$	−9.51100	−0.624427
$233$	10.4121	0.682121	0.341060	−	0.940041i	$-0.389214\pi$
$233$	10.4121	0.682121	0.341060	+	0.940041i	$0.389214\pi$
$234$	−0.954320	−0.0623858
$235$	−4.22870	−0.275850
$236$	0.490067	0.0319007
$237$	−12.8925	−0.837456
$238$	1.59910	0.103654
$239$	23.2096	1.50130	0.750651	−	0.660699i	$-0.229740\pi$
$239$	23.2096	1.50130	0.750651	+	0.660699i	$0.229740\pi$
$240$	−18.4903	−1.19354
$241$	−0.0762283	−0.00491030	−0.00245515	−	0.999997i	$-0.500781\pi$
$241$	−0.0762283	−0.00491030	−0.00245515	+	0.999997i	$0.500781\pi$
$242$	−15.7254	−1.01087
$243$	−2.54996	−0.163580
$244$	1.94459	0.124489
$245$	21.0657	1.34584
$246$	−14.8635	−0.947665
$247$	2.87706	0.183063
$248$	−28.0472	−1.78100
$249$	−18.4578	−1.16972
$250$	−1.81911	−0.115051
$251$	2.63706	0.166450	0.0832250	−	0.996531i	$-0.473478\pi$
$251$	2.63706	0.166450	0.0832250	+	0.996531i	$0.473478\pi$
$252$	−0.0194243	−0.00122361
$253$	9.76677	0.614032
$254$	28.7991	1.80702
$255$	14.0300	0.878593
$256$	−4.33080	−0.270675
$257$	−29.3091	−1.82825	−0.914126	−	0.405431i	$-0.867121\pi$
$257$	−29.3091	−1.82825	−0.914126	+	0.405431i	$0.867121\pi$
$258$	−3.80130	−0.236659
$259$	−2.98817	−0.185676
$260$	−1.61935	−0.100428
$261$	0.795286	0.0492270
$262$	5.56129	0.343578
$263$	16.8627	1.03980	0.519900	−	0.854227i	$-0.325969\pi$
$263$	16.8627	1.03980	0.519900	+	0.854227i	$0.325969\pi$
$264$	23.2429	1.43050
$265$	−32.5843	−2.00164
$266$	−0.584943	−0.0358652
$267$	−16.6977	−1.02188
$268$	−1.43998	−0.0879611
$269$	24.1318	1.47134	0.735672	−	0.677338i	$-0.236866\pi$
$269$	24.1318	1.47134	0.735672	+	0.677338i	$0.236866\pi$
$270$	22.4616	1.36697
$271$	28.5875	1.73657	0.868284	−	0.496067i	$-0.165223\pi$
$271$	28.5875	1.73657	0.868284	+	0.496067i	$0.165223\pi$
$272$	−9.84943	−0.597209
$273$	−2.07132	−0.125362
$274$	−3.19919	−0.193270
$275$	−21.7259	−1.31012
$276$	−0.619660	−0.0372992
$277$	21.4160	1.28676	0.643380	−	0.765547i	$-0.277531\pi$
$277$	21.4160	1.28676	0.643380	+	0.765547i	$0.277531\pi$
$278$	−12.0122	−0.720446
$279$	2.34524	0.140406
$280$	3.94714	0.235887
$281$	−12.6279	−0.753317	−0.376659	−	0.926352i	$-0.622927\pi$
$281$	−12.6279	−0.753317	−0.376659	+	0.926352i	$0.622927\pi$
$282$	3.05964	0.182199
$283$	−32.1189	−1.90927	−0.954635	−	0.297777i	$-0.903755\pi$
$283$	−32.1189	−1.90927	−0.954635	+	0.297777i	$0.903755\pi$
$284$	−0.649334	−0.0385309
$285$	−5.13210	−0.303999
$286$	−18.4672	−1.09199
$287$	2.88179	0.170106
$288$	0.252469	0.0148769
$289$	−9.52648	−0.560381
$290$	−13.4798	−0.791563
$291$	4.22682	0.247781
$292$	−2.34712	−0.137355
$293$	−27.9254	−1.63142	−0.815710	−	0.578461i	$-0.803653\pi$
$293$	−27.9254	−1.63142	−0.815710	+	0.578461i	$0.803653\pi$
$294$	−15.2419	−0.888926
$295$	8.32705	0.484820
$296$	20.2647	1.17786
$297$	−25.6441	−1.48802
$298$	−17.3075	−1.00259
$299$	5.90258	0.341355
$300$	1.37842	0.0795829
$301$	0.737007	0.0424804
$302$	20.7247	1.19257
$303$	−1.61086	−0.0925417
$304$	3.60287	0.206639
$305$	33.0417	1.89196
$306$	0.906794	0.0518379
$307$	−3.19306	−0.182238	−0.0911188	−	0.995840i	$-0.529044\pi$
$307$	−3.19306	−0.182238	−0.0911188	+	0.995840i	$0.529044\pi$
$308$	−0.375883	−0.0214179
$309$	−30.5289	−1.73673
$310$	−39.7510	−2.25771
$311$	9.82889	0.557345	0.278672	−	0.960386i	$-0.410106\pi$
$311$	9.82889	0.557345	0.278672	+	0.960386i	$0.410106\pi$
$312$	14.0469	0.795251
$313$	−9.48624	−0.536194	−0.268097	−	0.963392i	$-0.586395\pi$
$313$	−9.48624	−0.536194	−0.268097	+	0.963392i	$0.586395\pi$
$314$	−11.2020	−0.632166
$315$	−0.330050	−0.0185962
$316$	−1.41395	−0.0795407
$317$	−1.00000	−0.0561656
$317$	−1.00000	−0.0561656
$318$	23.5761	1.32208
$319$	15.3897	0.861660
$320$	−26.5632	−1.48493
$321$	−13.0709	−0.729544
$322$	−1.20007	−0.0668775
$323$	−2.73377	−0.152111
$324$	1.49269	0.0829272
$325$	−13.1301	−0.728328
$326$	−21.7429	−1.20423
$327$	25.2786	1.39791
$328$	−19.5432	−1.07909
$329$	−0.593213	−0.0327049
$330$	32.9419	1.81339
$331$	10.2924	0.565723	0.282861	−	0.959161i	$-0.408716\pi$
$331$	10.2924	0.565723	0.282861	+	0.959161i	$0.408716\pi$
$332$	−2.02431	−0.111099
$333$	−1.69448	−0.0928570
$334$	5.38169	0.294473
$335$	−24.4677	−1.33681
$336$	−2.59386	−0.141507
$337$	−27.5472	−1.50059	−0.750295	−	0.661103i	$-0.770089\pi$
$337$	−27.5472	−1.50059	−0.750295	+	0.661103i	$0.770089\pi$
$338$	6.36757	0.346350
$339$	22.9628	1.24717
$340$	1.53870	0.0834479
$341$	45.3832	2.45764
$342$	−0.331700	−0.0179363
$343$	5.99194	0.323534
$344$	−4.99812	−0.269480
$345$	−10.5290	−0.566865
$346$	−29.4717	−1.58441
$347$	2.37844	0.127682	0.0638408	−	0.997960i	$-0.479665\pi$
$347$	2.37844	0.127682	0.0638408	+	0.997960i	$0.479665\pi$
$348$	−0.976414	−0.0523413
$349$	−21.5142	−1.15163	−0.575815	−	0.817580i	$-0.695315\pi$
$349$	−21.5142	−1.15163	−0.575815	+	0.817580i	$0.695315\pi$
$350$	2.66953	0.142692
$351$	−15.4981	−0.827229
$352$	4.88558	0.260403
$353$	22.2548	1.18451	0.592253	−	0.805752i	$-0.298239\pi$
$353$	22.2548	1.18451	0.592253	+	0.805752i	$0.298239\pi$
$354$	−6.02498	−0.320224
$355$	−11.0333	−0.585584
$356$	−1.83128	−0.0970576
$357$	1.96816	0.104166
$358$	4.18519	0.221194
$359$	−35.1810	−1.85678	−0.928391	−	0.371605i	$-0.878807\pi$
$359$	−35.1810	−1.85678	−0.928391	+	0.371605i	$0.878807\pi$
$360$	2.23828	0.117968
$361$	1.00000	0.0526316
$362$	−7.41878	−0.389923
$363$	−19.3547	−1.01586
$364$	−0.227166	−0.0119067
$365$	−39.8814	−2.08749
$366$	−23.9071	−1.24964
$367$	−22.6826	−1.18402	−0.592011	−	0.805930i	$-0.701666\pi$
$367$	−22.6826	−1.18402	−0.592011	+	0.805930i	$0.701666\pi$
$368$	7.39167	0.385317
$369$	1.63416	0.0850708
$370$	28.7209	1.49313
$371$	−4.57101	−0.237315
$372$	−2.87937	−0.149288
$373$	−16.1173	−0.834524	−0.417262	−	0.908786i	$-0.637010\pi$
$373$	−16.1173	−0.834524	−0.417262	+	0.908786i	$0.637010\pi$
$374$	17.5475	0.907362
$375$	−2.23895	−0.115619
$376$	4.02295	0.207468
$377$	9.30084	0.479018
$378$	3.15097	0.162069
$379$	−19.6076	−1.00718	−0.503588	−	0.863944i	$-0.667987\pi$
$379$	−19.6076	−1.00718	−0.503588	+	0.863944i	$0.667987\pi$
$380$	−0.562849	−0.0288736
$381$	35.4457	1.81594
$382$	−20.3802	−1.04274
$383$	5.57576	0.284908	0.142454	−	0.989801i	$-0.454501\pi$
$383$	5.57576	0.284908	0.142454	+	0.989801i	$0.454501\pi$
$384$	15.8134	0.806975
$385$	−6.38687	−0.325505
$386$	−11.5590	−0.588339
$387$	0.417930	0.0212446
$388$	0.463565	0.0235340
$389$	13.9714	0.708377	0.354188	−	0.935174i	$-0.384757\pi$
$389$	13.9714	0.708377	0.354188	+	0.935174i	$0.384757\pi$
$390$	19.9086	1.00811
$391$	−5.60863	−0.283640
$392$	−20.0407	−1.01221
$393$	6.84479	0.345274
$394$	18.6598	0.940066
$395$	−24.0253	−1.20884
$396$	−0.213150	−0.0107112
$397$	−21.7927	−1.09374	−0.546872	−	0.837216i	$-0.684182\pi$
$397$	−21.7927	−1.09374	−0.546872	+	0.837216i	$0.684182\pi$
$398$	10.1652	0.509537
$399$	−0.719944	−0.0360423
$400$	−16.4425	−0.822127
$401$	4.67195	0.233306	0.116653	−	0.993173i	$-0.462783\pi$
$401$	4.67195	0.233306	0.116653	+	0.993173i	$0.462783\pi$
$402$	17.7034	0.882967
$403$	27.4275	1.36626
$404$	−0.176667	−0.00878952
$405$	25.3632	1.26031
$406$	−1.89098	−0.0938480
$407$	−32.7902	−1.62535
$408$	−13.3474	−0.660794
$409$	−25.8232	−1.27687	−0.638437	−	0.769674i	$-0.720419\pi$
$409$	−25.8232	−1.27687	−0.638437	+	0.769674i	$0.720419\pi$
$410$	−27.6984	−1.36793
$411$	−3.93754	−0.194224
$412$	−3.34818	−0.164953
$413$	1.16814	0.0574804
$414$	−0.680518	−0.0334456
$415$	−34.3964	−1.68845
$416$	2.95262	0.144764
$417$	−14.7846	−0.724003
$418$	−6.41880	−0.313954
$419$	−23.4088	−1.14359	−0.571797	−	0.820395i	$-0.693754\pi$
$419$	−23.4088	−1.14359	−0.571797	+	0.820395i	$0.693754\pi$
$420$	0.405220	0.0197727
$421$	−10.7720	−0.524996	−0.262498	−	0.964933i	$-0.584546\pi$
$421$	−10.7720	−0.524996	−0.262498	+	0.964933i	$0.584546\pi$
$422$	−8.74486	−0.425693
$423$	−0.336389	−0.0163558
$424$	30.9989	1.50544
$425$	12.4762	0.605186
$426$	7.98303	0.386779
$427$	4.63517	0.224312
$428$	−1.43351	−0.0692914
$429$	−22.7293	−1.09738
$430$	−7.08378	−0.341610
$431$	8.31639	0.400587	0.200293	−	0.979736i	$-0.435811\pi$
$431$	8.31639	0.400587	0.200293	+	0.979736i	$0.435811\pi$
$432$	−19.4079	−0.933765
$433$	−30.0119	−1.44228	−0.721139	−	0.692790i	$-0.756381\pi$
$433$	−30.0119	−1.44228	−0.721139	+	0.692790i	$0.756381\pi$
$434$	−5.57637	−0.267674
$435$	−16.5909	−0.795471
$436$	2.77236	0.132772
$437$	2.05161	0.0981416
$438$	28.8559	1.37879
$439$	3.52644	0.168308	0.0841540	−	0.996453i	$-0.473181\pi$
$439$	3.52644	0.168308	0.0841540	+	0.996453i	$0.473181\pi$
$440$	43.3135	2.06489
$441$	1.67576	0.0797979
$442$	10.6049	0.504425
$443$	3.66567	0.174161	0.0870806	−	0.996201i	$-0.472246\pi$
$443$	3.66567	0.174161	0.0870806	+	0.996201i	$0.472246\pi$
$444$	2.08040	0.0987315
$445$	−31.1165	−1.47506
$446$	15.2646	0.722801
$447$	−21.3019	−1.00754
$448$	−3.72636	−0.176054
$449$	−17.0339	−0.803881	−0.401941	−	0.915666i	$-0.631664\pi$
$449$	−17.0339	−0.803881	−0.401941	+	0.915666i	$0.631664\pi$
$450$	1.51379	0.0713609
$451$	31.6229	1.48906
$452$	2.51838	0.118455
$453$	25.5078	1.19846
$454$	−26.2917	−1.23393
$455$	−3.85993	−0.180956
$456$	4.88240	0.228639
$457$	41.2895	1.93144	0.965722	−	0.259580i	$-0.0835841\pi$
$457$	41.2895	1.93144	0.965722	+	0.259580i	$0.0835841\pi$
$458$	−30.4426	−1.42249
$459$	14.7263	0.687365
$460$	−1.15474	−0.0538403
$461$	−16.2921	−0.758800	−0.379400	−	0.925233i	$-0.623870\pi$
$461$	−16.2921	−0.758800	−0.379400	+	0.925233i	$0.623870\pi$
$462$	4.62118	0.214997
$463$	22.1063	1.02737	0.513685	−	0.857979i	$-0.328280\pi$
$463$	22.1063	1.02737	0.513685	+	0.857979i	$0.328280\pi$
$464$	11.6472	0.540709
$465$	−48.9253	−2.26885
$466$	−14.0390	−0.650343
$467$	25.8973	1.19839	0.599193	−	0.800604i	$-0.295488\pi$
$467$	25.8973	1.19839	0.599193	+	0.800604i	$0.295488\pi$
$468$	−0.128818	−0.00595460
$469$	−3.43239	−0.158493
$470$	5.70169	0.262999
$471$	−13.7873	−0.635287
$472$	−7.92190	−0.364635
$473$	8.08745	0.371861
$474$	17.3833	0.798442
$475$	−4.56374	−0.209399
$476$	0.215853	0.00989361
$477$	−2.59205	−0.118682
$478$	−31.2942	−1.43136
$479$	−32.8968	−1.50310	−0.751548	−	0.659679i	$-0.770692\pi$
$479$	−32.8968	−1.50310	−0.751548	+	0.659679i	$0.770692\pi$
$480$	−5.26689	−0.240400
$481$	−19.8169	−0.903573
$482$	0.102781	0.00468155
$483$	−1.47704	−0.0672077
$484$	−2.12267	−0.0964851
$485$	7.87674	0.357664
$486$	3.43819	0.155959
$487$	−12.0125	−0.544336	−0.272168	−	0.962250i	$-0.587741\pi$
$487$	−12.0125	−0.544336	−0.272168	+	0.962250i	$0.587741\pi$
$488$	−31.4341	−1.42295
$489$	−26.7610	−1.21018
$490$	−28.4035	−1.28314
$491$	−25.8633	−1.16720	−0.583598	−	0.812043i	$-0.698356\pi$
$491$	−25.8633	−1.16720	−0.583598	+	0.812043i	$0.698356\pi$
$492$	−2.00634	−0.0904527
$493$	−8.83765	−0.398028
$494$	−3.87922	−0.174535
$495$	−3.62176	−0.162786
$496$	34.3468	1.54222
$497$	−1.54777	−0.0694271
$498$	24.8873	1.11523
$499$	−23.0996	−1.03408	−0.517039	−	0.855962i	$-0.672966\pi$
$499$	−23.0996	−1.03408	−0.517039	+	0.855962i	$0.672966\pi$
$500$	−0.245551	−0.0109814
$501$	6.62374	0.295927
$502$	−3.55563	−0.158696
$503$	−13.3144	−0.593661	−0.296831	−	0.954930i	$-0.595930\pi$
$503$	−13.3144	−0.593661	−0.296831	+	0.954930i	$0.595930\pi$
$504$	0.313992	0.0139863
$505$	−3.00187	−0.133581
$506$	−13.1688	−0.585427
$507$	7.83715	0.348060
$508$	3.88741	0.172476
$509$	0.693672	0.0307465	0.0153732	−	0.999882i	$-0.495106\pi$
$509$	0.693672	0.0307465	0.0153732	+	0.999882i	$0.495106\pi$
$510$	−18.9171	−0.837663
$511$	−5.59466	−0.247493
$512$	24.8972	1.10031
$513$	−5.38680	−0.237833
$514$	39.5184	1.74308
$515$	−56.8911	−2.50692
$516$	−0.513114	−0.0225886
$517$	−6.50954	−0.286289
$518$	4.02904	0.177026
$519$	−36.2736	−1.59223
$520$	26.1766	1.14792
$521$	−5.72370	−0.250760	−0.125380	−	0.992109i	$-0.540015\pi$
$521$	−5.72370	−0.250760	−0.125380	+	0.992109i	$0.540015\pi$
$522$	−1.07231	−0.0469337
$523$	23.6975	1.03622	0.518110	−	0.855314i	$-0.326636\pi$
$523$	23.6975	1.03622	0.518110	+	0.855314i	$0.326636\pi$
$524$	0.750685	0.0327938
$525$	3.28563	0.143397
$526$	−22.7365	−0.991360
$527$	−26.0616	−1.13526
$528$	−28.4634	−1.23871
$529$	−18.7909	−0.816996
$530$	43.9344	1.90839
$531$	0.662410	0.0287461
$532$	−0.0789579	−0.00342326
$533$	19.1114	0.827807
$534$	22.5141	0.974280
$535$	−24.3577	−1.05308
$536$	23.2772	1.00542
$537$	5.15110	0.222286
$538$	−32.5377	−1.40280
$539$	32.4279	1.39677
$540$	3.03196	0.130475
$541$	−25.0206	−1.07572	−0.537859	−	0.843035i	$-0.680767\pi$
$541$	−25.0206	−1.07572	−0.537859	+	0.843035i	$0.680767\pi$
$542$	−38.5454	−1.65567
$543$	−9.13098	−0.391848
$544$	−2.80558	−0.120288
$545$	47.1070	2.01784
$546$	2.79282	0.119522
$547$	8.68374	0.371290	0.185645	−	0.982617i	$-0.440563\pi$
$547$	8.68374	0.371290	0.185645	+	0.982617i	$0.440563\pi$
$548$	−0.431839	−0.0184472
$549$	2.62844	0.112179
$550$	29.2937	1.24909
$551$	3.23276	0.137720
$552$	10.0168	0.426341
$553$	−3.37033	−0.143321
$554$	−28.8758	−1.22682
$555$	35.3494	1.50050
$556$	−1.62146	−0.0687651
$557$	28.6820	1.21530	0.607648	−	0.794206i	$-0.292113\pi$
$557$	28.6820	1.21530	0.607648	+	0.794206i	$0.292113\pi$
$558$	−3.16216	−0.133865
$559$	4.88768	0.206727
$560$	−4.83370	−0.204261
$561$	21.5974	0.911842
$562$	17.0266	0.718224
$563$	30.9577	1.30471	0.652357	−	0.757912i	$-0.273780\pi$
$563$	30.9577	1.30471	0.652357	+	0.757912i	$0.273780\pi$
$564$	0.413003	0.0173905
$565$	42.7914	1.80025
$566$	43.3069	1.82033
$567$	3.55802	0.149423
$568$	10.4964	0.440420
$569$	−13.4986	−0.565891	−0.282945	−	0.959136i	$-0.591312\pi$
$569$	−13.4986	−0.565891	−0.282945	+	0.959136i	$0.591312\pi$
$570$	6.91977	0.289837
$571$	−25.5125	−1.06766	−0.533832	−	0.845591i	$-0.679248\pi$
$571$	−25.5125	−1.06766	−0.533832	+	0.845591i	$0.679248\pi$
$572$	−2.49278	−0.104228
$573$	−25.0838	−1.04789
$574$	−3.88560	−0.162182
$575$	−9.36299	−0.390464
$576$	−2.11308	−0.0880450
$577$	−13.1442	−0.547200	−0.273600	−	0.961844i	$-0.588214\pi$
$577$	−13.1442	−0.547200	−0.273600	+	0.961844i	$0.588214\pi$
$578$	12.8448	0.534275
$579$	−14.2268	−0.591244
$580$	−1.81956	−0.0755531
$581$	−4.82521	−0.200184
$582$	−5.69915	−0.236238
$583$	−50.1594	−2.07739
$584$	37.9410	1.57001
$585$	−2.18883	−0.0904968
$586$	37.6527	1.55542
$587$	24.9088	1.02810	0.514049	−	0.857761i	$-0.328145\pi$
$587$	24.9088	1.02810	0.514049	+	0.857761i	$0.328145\pi$
$588$	−2.05741	−0.0848462
$589$	9.53318	0.392808
$590$	−11.2276	−0.462234
$591$	22.9663	0.944708
$592$	−24.8162	−1.01994
$593$	6.59266	0.270728	0.135364	−	0.990796i	$-0.456780\pi$
$593$	6.59266	0.270728	0.135364	+	0.990796i	$0.456780\pi$
$594$	34.5768	1.41870
$595$	3.66770	0.150361
$596$	−2.33623	−0.0956956
$597$	12.5113	0.512053
$598$	−7.95864	−0.325453
$599$	8.30139	0.339186	0.169593	−	0.985514i	$-0.445755\pi$
$599$	8.30139	0.339186	0.169593	+	0.985514i	$0.445755\pi$
$600$	−22.2820	−0.909658
$601$	41.7553	1.70323	0.851617	−	0.524165i	$-0.175623\pi$
$601$	41.7553	1.70323	0.851617	+	0.524165i	$0.175623\pi$
$602$	−0.993730	−0.0405014
$603$	−1.94638	−0.0792629
$604$	2.79750	0.113829
$605$	−36.0677	−1.46636
$606$	2.17198	0.0882306
$607$	−16.5074	−0.670014	−0.335007	−	0.942216i	$-0.608739\pi$
$607$	−16.5074	−0.670014	−0.335007	+	0.942216i	$0.608739\pi$
$608$	1.02626	0.0416205
$609$	−2.32741	−0.0943114
$610$	−44.5512	−1.80382
$611$	−3.93406	−0.159155
$612$	0.122402	0.00494783
$613$	24.0236	0.970305	0.485153	−	0.874430i	$-0.338764\pi$
$613$	24.0236	0.970305	0.485153	+	0.874430i	$0.338764\pi$
$614$	4.30530	0.173748
$615$	−34.0910	−1.37468
$616$	6.07612	0.244814
$617$	−2.87965	−0.115930	−0.0579651	−	0.998319i	$-0.518461\pi$
$617$	−2.87965	−0.115930	−0.0579651	+	0.998319i	$0.518461\pi$
$618$	41.1631	1.65582
$619$	−11.9672	−0.481001	−0.240501	−	0.970649i	$-0.577312\pi$
$619$	−11.9672	−0.481001	−0.240501	+	0.970649i	$0.577312\pi$
$620$	−5.36575	−0.215494
$621$	−11.0516	−0.443485
$622$	−13.2526	−0.531381
$623$	−4.36509	−0.174884
$624$	−17.2020	−0.688630
$625$	−26.9910	−1.07964
$626$	12.7906	0.511215
$627$	−7.90021	−0.315504
$628$	−1.51209	−0.0603389
$629$	18.8300	0.750801
$630$	0.445017	0.0177299
$631$	−27.7602	−1.10512	−0.552559	−	0.833474i	$-0.686349\pi$
$631$	−27.7602	−1.10512	−0.552559	+	0.833474i	$0.686349\pi$
$632$	22.8563	0.909176
$633$	−10.7631	−0.427795
$634$	1.34833	0.0535491
$635$	66.0535	2.62125
$636$	3.18240	0.126190
$637$	19.5979	0.776497
$638$	−20.7505	−0.821519
$639$	−0.877685	−0.0347207
$640$	29.4685	1.16485
$641$	4.51282	0.178246	0.0891228	−	0.996021i	$-0.471594\pi$
$641$	4.51282	0.178246	0.0891228	+	0.996021i	$0.471594\pi$
$642$	17.6238	0.695558
$643$	6.99626	0.275905	0.137953	−	0.990439i	$-0.455948\pi$
$643$	6.99626	0.275905	0.137953	+	0.990439i	$0.455948\pi$
$644$	−0.161990	−0.00638332
$645$	−8.71866	−0.343297
$646$	3.68603	0.145025
$647$	7.56894	0.297566	0.148783	−	0.988870i	$-0.452464\pi$
$647$	7.56894	0.297566	0.148783	+	0.988870i	$0.452464\pi$
$648$	−24.1292	−0.947884
$649$	12.8184	0.503167
$650$	17.7038	0.694398
$651$	−6.86336	−0.268996
$652$	−2.93494	−0.114941
$653$	−28.9696	−1.13367	−0.566835	−	0.823831i	$-0.691832\pi$
$653$	−28.9696	−1.13367	−0.566835	+	0.823831i	$0.691832\pi$
$654$	−34.0839	−1.33279
$655$	12.7554	0.498393
$656$	23.9328	0.934418
$657$	−3.17253	−0.123772
$658$	0.799847	0.0311813
$659$	6.58159	0.256383	0.128191	−	0.991749i	$-0.459083\pi$
$659$	6.58159	0.256383	0.128191	+	0.991749i	$0.459083\pi$
$660$	4.44663	0.173085
$661$	13.3830	0.520538	0.260269	−	0.965536i	$-0.416189\pi$
$661$	13.3830	0.520538	0.260269	+	0.965536i	$0.416189\pi$
$662$	−13.8776	−0.539368
$663$	13.0525	0.506915
$664$	32.7229	1.26989
$665$	−1.34162	−0.0520260
$666$	2.28472	0.0885311
$667$	6.63236	0.256806
$668$	0.726441	0.0281068
$669$	18.7876	0.726370
$670$	32.9906	1.27454
$671$	50.8635	1.96356
$672$	−0.738853	−0.0285019
$673$	22.7228	0.875899	0.437949	−	0.899000i	$-0.355705\pi$
$673$	22.7228	0.875899	0.437949	+	0.899000i	$0.355705\pi$
$674$	37.1427	1.43068
$675$	24.5839	0.946236
$676$	0.859519	0.0330584
$677$	36.0205	1.38438	0.692191	−	0.721715i	$-0.256646\pi$
$677$	36.0205	1.38438	0.692191	+	0.721715i	$0.256646\pi$
$678$	−30.9614	−1.18907
$679$	1.10497	0.0424048
$680$	−24.8730	−0.953836
$681$	−32.3597	−1.24003
$682$	−61.1916	−2.34315
$683$	0.547146	0.0209359	0.0104680	−	0.999945i	$-0.496668\pi$
$683$	0.547146	0.0209359	0.0104680	+	0.999945i	$0.496668\pi$
$684$	−0.0447742	−0.00171198
$685$	−7.33765	−0.280357
$686$	−8.07912	−0.308462
$687$	−37.4685	−1.42951
$688$	6.12073	0.233351
$689$	−30.3140	−1.15487
$690$	14.1966	0.540457
$691$	−30.4179	−1.15715	−0.578576	−	0.815628i	$-0.696391\pi$
$691$	−30.4179	−1.15715	−0.578576	+	0.815628i	$0.696391\pi$
$692$	−3.97821	−0.151229
$693$	−0.508070	−0.0193000
$694$	−3.20693	−0.121733
$695$	−27.5512	−1.04508
$696$	15.7836	0.598278
$697$	−18.1596	−0.687845
$698$	29.0083	1.09798
$699$	−17.2791	−0.653555
$700$	0.360343	0.0136197
$701$	3.45675	0.130560	0.0652799	−	0.997867i	$-0.479206\pi$
$701$	3.45675	0.130560	0.0652799	+	0.997867i	$0.479206\pi$
$702$	20.8966	0.788691
$703$	−6.88791	−0.259782
$704$	−40.8907	−1.54113
$705$	7.01759	0.264298
$706$	−30.0069	−1.12932
$707$	−0.421109	−0.0158374
$708$	−0.813275	−0.0305647
$709$	−30.6033	−1.14933	−0.574666	−	0.818388i	$-0.694868\pi$
$709$	−30.6033	−1.14933	−0.574666	+	0.818388i	$0.694868\pi$
$710$	14.8765	0.558304
$711$	−1.91119	−0.0716752
$712$	29.6025	1.10940
$713$	19.5583	0.732465
$714$	−2.65374	−0.0993136
$715$	−42.3564	−1.58404
$716$	0.564933	0.0211125
$717$	−38.5166	−1.43843
$718$	47.4356	1.77028
$719$	8.83534	0.329502	0.164751	−	0.986335i	$-0.447318\pi$
$719$	8.83534	0.329502	0.164751	+	0.986335i	$0.447318\pi$
$720$	−2.74102	−0.102152
$721$	−7.98082	−0.297221
$722$	−1.34833	−0.0501797
$723$	0.126502	0.00470466
$724$	−1.00142	−0.0372173
$725$	−14.7535	−0.547931
$726$	26.0965	0.968532
$727$	−13.3040	−0.493416	−0.246708	−	0.969090i	$-0.579349\pi$
$727$	−13.3040	−0.493416	−0.246708	+	0.969090i	$0.579349\pi$
$728$	3.67212	0.136098
$729$	28.8361	1.06800
$730$	53.7733	1.99024
$731$	−4.64427	−0.171774
$732$	−3.22707	−0.119276
$733$	3.59565	0.132808	0.0664042	−	0.997793i	$-0.478847\pi$
$733$	3.59565	0.132808	0.0664042	+	0.997793i	$0.478847\pi$
$734$	30.5837	1.12886
$735$	−34.9588	−1.28948
$736$	2.10549	0.0776094
$737$	−37.6649	−1.38740
$738$	−2.20338	−0.0811077
$739$	−14.7205	−0.541504	−0.270752	−	0.962649i	$-0.587272\pi$
$739$	−14.7205	−0.541504	−0.270752	+	0.962649i	$0.587272\pi$
$740$	3.87686	0.142516
$741$	−4.77452	−0.175396
$742$	6.16323	0.226259
$743$	52.5582	1.92817	0.964087	−	0.265588i	$-0.0855662\pi$
$743$	52.5582	1.92817	0.964087	+	0.265588i	$0.0855662\pi$
$744$	46.5448	1.70642
$745$	−39.6963	−1.45436
$746$	21.7315	0.795647
$747$	−2.73620	−0.100112
$748$	2.36864	0.0866059
$749$	−3.41696	−0.124853
$750$	3.01885	0.110233
$751$	13.9357	0.508520	0.254260	−	0.967136i	$-0.418168\pi$
$751$	13.9357	0.508520	0.254260	+	0.967136i	$0.418168\pi$
$752$	−4.92653	−0.179652
$753$	−4.37625	−0.159479
$754$	−12.5406	−0.456702
$755$	47.5341	1.72994
$756$	0.425331	0.0154691
$757$	−2.53163	−0.0920136	−0.0460068	−	0.998941i	$-0.514650\pi$
$757$	−2.53163	−0.0920136	−0.0460068	+	0.998941i	$0.514650\pi$
$758$	26.4376	0.960256
$759$	−16.2081	−0.588317
$760$	9.09841	0.330034
$761$	12.7092	0.460707	0.230353	−	0.973107i	$-0.426012\pi$
$761$	12.7092	0.460707	0.230353	+	0.973107i	$0.426012\pi$
$762$	−47.7925	−1.73134
$763$	6.60828	0.239236
$764$	−2.75099	−0.0995275
$765$	2.07982	0.0751960
$766$	−7.51797	−0.271635
$767$	7.74686	0.279723
$768$	7.18703	0.259340
$769$	6.68342	0.241010	0.120505	−	0.992713i	$-0.461549\pi$
$769$	6.68342	0.241010	0.120505	+	0.992713i	$0.461549\pi$
$770$	8.61162	0.310341
$771$	48.6389	1.75169
$772$	−1.56028	−0.0561558
$773$	−25.4886	−0.916762	−0.458381	−	0.888756i	$-0.651571\pi$
$773$	−25.4886	−0.916762	−0.458381	+	0.888756i	$0.651571\pi$
$774$	−0.563508	−0.0202549
$775$	−43.5069	−1.56282
$776$	−7.49349	−0.269001
$777$	4.95891	0.177900
$778$	−18.8380	−0.675376
$779$	6.64270	0.237999
$780$	2.68733	0.0962220
$781$	−16.9843	−0.607745
$782$	7.56229	0.270427
$783$	−17.4143	−0.622335
$784$	24.5420	0.876500
$785$	−25.6929	−0.917018
$786$	−9.22905	−0.329189
$787$	38.6297	1.37700	0.688500	−	0.725237i	$-0.258270\pi$
$787$	38.6297	1.37700	0.688500	+	0.725237i	$0.258270\pi$
$788$	2.51877	0.0897274
$789$	−27.9839	−0.996255
$790$	32.3940	1.15253
$791$	6.00288	0.213438
$792$	3.44555	0.122432
$793$	30.7395	1.09159
$794$	29.3838	1.04279
$795$	54.0742	1.91781
$796$	1.37214	0.0486342
$797$	46.1738	1.63556	0.817780	−	0.575532i	$-0.195205\pi$
$797$	46.1738	1.63556	0.817780	+	0.575532i	$0.195205\pi$
$798$	0.970723	0.0343632
$799$	3.73814	0.132246
$800$	−4.68360	−0.165590
$801$	−2.47529	−0.0874599
$802$	−6.29933	−0.222437
$803$	−61.3923	−2.16649
$804$	2.38968	0.0842774
$805$	−2.75248	−0.0970123
$806$	−36.9813	−1.30261
$807$	−40.0472	−1.40973
$808$	2.85581	0.100467
$809$	20.6937	0.727553	0.363777	−	0.931486i	$-0.381487\pi$
$809$	20.6937	0.727553	0.363777	+	0.931486i	$0.381487\pi$
$810$	−34.1981	−1.20160
$811$	45.6867	1.60428	0.802138	−	0.597139i	$-0.203696\pi$
$811$	45.6867	1.60428	0.802138	+	0.597139i	$0.203696\pi$
$812$	−0.255252	−0.00895760
$813$	−47.4414	−1.66384
$814$	44.2121	1.54963
$815$	−49.8695	−1.74685
$816$	16.3453	0.572199
$817$	1.69885	0.0594352
$818$	34.8182	1.21739
$819$	−0.307054	−0.0107293
$820$	−3.73884	−0.130566
$821$	−1.72967	−0.0603659	−0.0301830	−	0.999544i	$-0.509609\pi$
$821$	−1.72967	−0.0603659	−0.0301830	+	0.999544i	$0.509609\pi$
$822$	5.30910	0.185176
$823$	−7.25859	−0.253019	−0.126509	−	0.991965i	$-0.540377\pi$
$823$	−7.25859	−0.253019	−0.126509	+	0.991965i	$0.540377\pi$
$824$	54.1230	1.88547
$825$	36.0545	1.25526
$826$	−1.57504	−0.0548026
$827$	10.0440	0.349265	0.174633	−	0.984634i	$-0.444126\pi$
$827$	10.0440	0.349265	0.174633	+	0.984634i	$0.444126\pi$
$828$	−0.0918589	−0.00319232
$829$	44.4981	1.54548	0.772741	−	0.634721i	$-0.218885\pi$
$829$	44.4981	1.54548	0.772741	+	0.634721i	$0.218885\pi$
$830$	46.3777	1.60980
$831$	−35.5401	−1.23287
$832$	−24.7124	−0.856749
$833$	−18.6219	−0.645211
$834$	19.9345	0.690275
$835$	12.3434	0.427162
$836$	−0.866434	−0.0299663
$837$	−51.3534	−1.77503
$838$	31.5628	1.09032
$839$	−13.4466	−0.464227	−0.232114	−	0.972689i	$-0.574564\pi$
$839$	−13.4466	−0.464227	−0.232114	+	0.972689i	$0.574564\pi$
$840$	−6.55035	−0.226008
$841$	−18.5492	−0.639629
$842$	14.5242	0.500538
$843$	20.9562	0.721770
$844$	−1.18041	−0.0406315
$845$	14.6046	0.502415
$846$	0.453564	0.0155939
$847$	−5.05967	−0.173852
$848$	−37.9615	−1.30360
$849$	53.3018	1.82931
$850$	−16.8221	−0.576993
$851$	−14.1313	−0.484414
$852$	1.07758	0.0369173
$853$	30.9755	1.06058	0.530291	−	0.847816i	$-0.322083\pi$
$853$	30.9755	1.06058	0.530291	+	0.847816i	$0.322083\pi$
$854$	−6.24975	−0.213862
$855$	−0.760787	−0.0260184
$856$	23.1726	0.792023
$857$	−48.0890	−1.64269	−0.821345	−	0.570432i	$-0.806776\pi$
$857$	−48.0890	−1.64269	−0.821345	+	0.570432i	$0.806776\pi$
$858$	30.6467	1.04626
$859$	17.7949	0.607155	0.303577	−	0.952807i	$-0.401819\pi$
$859$	17.7949	0.607155	0.303577	+	0.952807i	$0.401819\pi$
$860$	−0.956195	−0.0326060
$861$	−4.78237	−0.162983
$862$	−11.2133	−0.381925
$863$	−37.3502	−1.27142	−0.635708	−	0.771929i	$-0.719292\pi$
$863$	−37.3502	−1.27142	−0.635708	+	0.771929i	$0.719292\pi$
$864$	−5.52828	−0.188076
$865$	−67.5963	−2.29834
$866$	40.4659	1.37509
$867$	15.8093	0.536913
$868$	−0.752720	−0.0255490
$869$	−36.9838	−1.25459
$870$	22.3700	0.758414
$871$	−22.7629	−0.771292
$872$	−44.8150	−1.51763
$873$	0.626587	0.0212068
$874$	−2.76624	−0.0935696
$875$	−0.585303	−0.0197868
$876$	3.89508	0.131603
$877$	52.5135	1.77325	0.886627	−	0.462485i	$-0.153042\pi$
$877$	52.5135	1.77325	0.886627	+	0.462485i	$0.153042\pi$
$878$	−4.75482	−0.160467
$879$	46.3426	1.56310
$880$	−53.0419	−1.78804
$881$	35.5538	1.19784	0.598919	−	0.800809i	$-0.295597\pi$
$881$	35.5538	1.19784	0.598919	+	0.800809i	$0.295597\pi$
$882$	−2.25947	−0.0760804
$883$	−45.0667	−1.51661	−0.758307	−	0.651898i	$-0.773973\pi$
$883$	−45.0667	−1.51661	−0.758307	+	0.651898i	$0.773973\pi$
$884$	1.43149	0.0481463
$885$	−13.8189	−0.464516
$886$	−4.94253	−0.166048
$887$	4.29796	0.144311	0.0721557	−	0.997393i	$-0.477012\pi$
$887$	4.29796	0.144311	0.0721557	+	0.997393i	$0.477012\pi$
$888$	−33.6295	−1.12853
$889$	9.26615	0.310777
$890$	41.9553	1.40634
$891$	39.0434	1.30800
$892$	2.06048	0.0689899
$893$	−1.36739	−0.0457580
$894$	28.7220	0.960607
$895$	9.59914	0.320864
$896$	4.13392	0.138104
$897$	−9.79543	−0.327060
$898$	22.9674	0.766432
$899$	30.8185	1.02786
$900$	0.204337	0.00681125
$901$	28.8043	0.959611
$902$	−42.6381	−1.41969
$903$	−1.22308	−0.0407014
$904$	−40.7094	−1.35397
$905$	−17.0157	−0.565621
$906$	−34.3929	−1.14263
$907$	−41.4784	−1.37727	−0.688634	−	0.725109i	$-0.741790\pi$
$907$	−41.4784	−1.37727	−0.688634	+	0.725109i	$0.741790\pi$
$908$	−3.54896	−0.117776
$909$	−0.238796	−0.00792036
$910$	5.20446	0.172526
$911$	17.4731	0.578909	0.289454	−	0.957192i	$-0.406526\pi$
$911$	17.4731	0.578909	0.289454	+	0.957192i	$0.406526\pi$
$912$	−5.97902	−0.197985
$913$	−52.9488	−1.75235
$914$	−55.6720	−1.84147
$915$	−54.8332	−1.81273
$916$	−4.10926	−0.135774
$917$	1.78935	0.0590897
$918$	−19.8559	−0.655343
$919$	0.379096	0.0125052	0.00625262	−	0.999980i	$-0.498010\pi$
$919$	0.379096	0.0125052	0.00625262	+	0.999980i	$0.498010\pi$
$920$	18.6664	0.615412
$921$	5.29893	0.174606
$922$	21.9672	0.723450
$923$	−10.2645	−0.337860
$924$	0.623784	0.0205210
$925$	31.4346	1.03356
$926$	−29.8067	−0.979508
$927$	−4.52563	−0.148641
$928$	3.31767	0.108908
$929$	39.5203	1.29662	0.648310	−	0.761377i	$-0.275476\pi$
$929$	39.5203	1.29662	0.648310	+	0.761377i	$0.275476\pi$
$930$	65.9674	2.16316
$931$	6.81179	0.223248
$932$	−1.89504	−0.0620740
$933$	−16.3112	−0.534004
$934$	−34.9182	−1.14256
$935$	40.2470	1.31622
$936$	2.08233	0.0680630
$937$	−6.22659	−0.203414	−0.101707	−	0.994814i	$-0.532430\pi$
$937$	−6.22659	−0.203414	−0.101707	+	0.994814i	$0.532430\pi$
$938$	4.62800	0.151110
$939$	15.7426	0.513739
$940$	0.769636	0.0251027
$941$	8.55323	0.278827	0.139414	−	0.990234i	$-0.455478\pi$
$941$	8.55323	0.278827	0.139414	+	0.990234i	$0.455478\pi$
$942$	18.5899	0.605692
$943$	13.6282	0.443795
$944$	9.70121	0.315748
$945$	7.22707	0.235096
$946$	−10.9046	−0.354538
$947$	51.8189	1.68389	0.841944	−	0.539565i	$-0.181411\pi$
$947$	51.8189	1.68389	0.841944	+	0.539565i	$0.181411\pi$
$948$	2.34647	0.0762097
$949$	−37.1026	−1.20440
$950$	6.15343	0.199644
$951$	1.65952	0.0538135
$952$	−3.48925	−0.113087
$953$	−16.4772	−0.533748	−0.266874	−	0.963731i	$-0.585991\pi$
$953$	−16.4772	−0.533748	−0.266874	+	0.963731i	$0.585991\pi$
$954$	3.49495	0.113153
$955$	−46.7439	−1.51260
$956$	−4.22421	−0.136621
$957$	−25.5395	−0.825575
$958$	44.3558	1.43307
$959$	−1.02934	−0.0332393
$960$	44.0821	1.42274
$961$	59.8816	1.93166
$962$	26.7197	0.861479
$963$	−1.93763	−0.0624394
$964$	0.0138738	0.000446844 0
$965$	−26.5118	−0.853443
$966$	1.99154	0.0640768
$967$	43.0345	1.38390	0.691949	−	0.721947i	$-0.256752\pi$
$967$	43.0345	1.38390	0.691949	+	0.721947i	$0.256752\pi$
$968$	34.3128	1.10286
$969$	4.53674	0.145741
$970$	−10.6204	−0.341002
$971$	−20.3635	−0.653497	−0.326749	−	0.945111i	$-0.605953\pi$
$971$	−20.3635	−0.653497	−0.326749	+	0.945111i	$0.605953\pi$
$972$	0.464100	0.0148860
$973$	−3.86495	−0.123905
$974$	16.1968	0.518978
$975$	21.7896	0.697827
$976$	38.4944	1.23217
$977$	−8.89442	−0.284558	−0.142279	−	0.989827i	$-0.545443\pi$
$977$	−8.89442	−0.284558	−0.142279	+	0.989827i	$0.545443\pi$
$978$	36.0827	1.15380
$979$	−47.8998	−1.53088
$980$	−3.83401	−0.122473
$981$	3.74732	0.119643
$982$	34.8723	1.11282
$983$	−26.9945	−0.860991	−0.430495	−	0.902593i	$-0.641661\pi$
$983$	−26.9945	−0.860991	−0.430495	+	0.902593i	$0.641661\pi$
$984$	32.4323	1.03390
$985$	42.7980	1.36366
$986$	11.9161	0.379485
$987$	0.984446	0.0313352
$988$	−0.523632	−0.0166590
$989$	3.48537	0.110828
$990$	4.88334	0.155203
$991$	14.3260	0.455079	0.227540	−	0.973769i	$-0.426932\pi$
$991$	14.3260	0.455079	0.227540	+	0.973769i	$0.426932\pi$
$992$	9.78357	0.310629
$993$	−17.0804	−0.542031
$994$	2.08691	0.0661927
$995$	23.3149	0.739133
$996$	3.35938	0.106446
$997$	27.8707	0.882673	0.441337	−	0.897342i	$-0.354504\pi$
$997$	27.8707	0.882673	0.441337	+	0.897342i	$0.354504\pi$
$998$	31.1459	0.985905
$999$	37.1038	1.17391

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6023.2.a.b.1.29	✓	99

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6023.2.a.b.1.29	✓	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)

\(f(q)\)	\(=\)	\(q-1.34833 q^{2} -1.65952 q^{3} -0.182003 q^{4} -3.09253 q^{5} +2.23758 q^{6} -0.433828 q^{7} +2.94206 q^{8} -0.246008 q^{9} +O(q^{10})\)	\(q-1.34833 q^{2} -1.65952 q^{3} -0.182003 q^{4} -3.09253 q^{5} +2.23758 q^{6} -0.433828 q^{7} +2.94206 q^{8} -0.246008 q^{9} +4.16975 q^{10} -4.76055 q^{11} +0.302037 q^{12} -2.87706 q^{13} +0.584943 q^{14} +5.13210 q^{15} -3.60287 q^{16} +2.73377 q^{17} +0.331700 q^{18} -1.00000 q^{19} +0.562849 q^{20} +0.719944 q^{21} +6.41880 q^{22} -2.05161 q^{23} -4.88240 q^{24} +4.56374 q^{25} +3.87922 q^{26} +5.38680 q^{27} +0.0789579 q^{28} -3.23276 q^{29} -6.91977 q^{30} -9.53318 q^{31} -1.02626 q^{32} +7.90021 q^{33} -3.68603 q^{34} +1.34162 q^{35} +0.0447742 q^{36} +6.88791 q^{37} +1.34833 q^{38} +4.77452 q^{39} -9.09841 q^{40} -6.64270 q^{41} -0.970723 q^{42} -1.69885 q^{43} +0.866434 q^{44} +0.760787 q^{45} +2.76624 q^{46} +1.36739 q^{47} +5.97902 q^{48} -6.81179 q^{49} -6.15343 q^{50} -4.53674 q^{51} +0.523632 q^{52} +10.5365 q^{53} -7.26319 q^{54} +14.7221 q^{55} -1.27635 q^{56} +1.65952 q^{57} +4.35884 q^{58} -2.69263 q^{59} -0.934057 q^{60} -10.6844 q^{61} +12.8539 q^{62} +0.106725 q^{63} +8.58948 q^{64} +8.89738 q^{65} -10.6521 q^{66} +7.91188 q^{67} -0.497555 q^{68} +3.40467 q^{69} -1.80895 q^{70} +3.56771 q^{71} -0.723771 q^{72} +12.8960 q^{73} -9.28718 q^{74} -7.57359 q^{75} +0.182003 q^{76} +2.06526 q^{77} -6.43763 q^{78} +7.76881 q^{79} +11.1420 q^{80} -8.20146 q^{81} +8.95656 q^{82} +11.1224 q^{83} -0.131032 q^{84} -8.45428 q^{85} +2.29061 q^{86} +5.36482 q^{87} -14.0058 q^{88} +10.0618 q^{89} -1.02579 q^{90} +1.24815 q^{91} +0.373398 q^{92} +15.8205 q^{93} -1.84370 q^{94} +3.09253 q^{95} +1.70310 q^{96} -2.54702 q^{97} +9.18455 q^{98} +1.17113 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 99 q - 4 q^{2} - 3 q^{3} + 80 q^{4} - 15 q^{5} - 12 q^{6} - 19 q^{7} - 12 q^{8} + 58 q^{9}+O(q^{10}) \) 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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