LMFDB - Embedded newform 4017.2.a.g.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4017,2,Mod(1,4017)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4017, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("4017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4017 = 3 \cdot 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4017.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:	$32.0759064919$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	4017.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.05828 q^{2} -1.00000 q^{3} -0.880046 q^{4} -0.912505 q^{5} -1.05828 q^{6} -3.63309 q^{7} -3.04789 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.05828 q^{2} -1.00000 q^{3} -0.880046 q^{4} -0.912505 q^{5} -1.05828 q^{6} -3.63309 q^{7} -3.04789 q^{8} +1.00000 q^{9} -0.965685 q^{10} -1.15222 q^{11} +0.880046 q^{12} -1.00000 q^{13} -3.84483 q^{14} +0.912505 q^{15} -1.46543 q^{16} -2.09451 q^{17} +1.05828 q^{18} -0.646012 q^{19} +0.803047 q^{20} +3.63309 q^{21} -1.21937 q^{22} -8.89813 q^{23} +3.04789 q^{24} -4.16733 q^{25} -1.05828 q^{26} -1.00000 q^{27} +3.19729 q^{28} +3.94970 q^{29} +0.965685 q^{30} -4.66229 q^{31} +4.54495 q^{32} +1.15222 q^{33} -2.21658 q^{34} +3.31522 q^{35} -0.880046 q^{36} -1.70522 q^{37} -0.683661 q^{38} +1.00000 q^{39} +2.78122 q^{40} -8.06085 q^{41} +3.84483 q^{42} +0.912813 q^{43} +1.01401 q^{44} -0.912505 q^{45} -9.41670 q^{46} +4.88621 q^{47} +1.46543 q^{48} +6.19937 q^{49} -4.41020 q^{50} +2.09451 q^{51} +0.880046 q^{52} -3.15100 q^{53} -1.05828 q^{54} +1.05140 q^{55} +11.0733 q^{56} +0.646012 q^{57} +4.17989 q^{58} +1.05612 q^{59} -0.803047 q^{60} -4.06408 q^{61} -4.93400 q^{62} -3.63309 q^{63} +7.74068 q^{64} +0.912505 q^{65} +1.21937 q^{66} +3.87694 q^{67} +1.84327 q^{68} +8.89813 q^{69} +3.50842 q^{70} +2.77471 q^{71} -3.04789 q^{72} -1.56883 q^{73} -1.80460 q^{74} +4.16733 q^{75} +0.568521 q^{76} +4.18612 q^{77} +1.05828 q^{78} +1.26952 q^{79} +1.33721 q^{80} +1.00000 q^{81} -8.53062 q^{82} +13.3649 q^{83} -3.19729 q^{84} +1.91125 q^{85} +0.966010 q^{86} -3.94970 q^{87} +3.51183 q^{88} -15.4734 q^{89} -0.965685 q^{90} +3.63309 q^{91} +7.83077 q^{92} +4.66229 q^{93} +5.17098 q^{94} +0.589489 q^{95} -4.54495 q^{96} +4.91041 q^{97} +6.56066 q^{98} -1.15222 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 3 q^{2} - 24 q^{3} + 25 q^{4} + 3 q^{5} - 3 q^{6} + 11 q^{7} + 6 q^{8} + 24 q^{9}+O(q^{10}) $ 24 * q + 3 * q^2 - 24 * q^3 + 25 * q^4 + 3 * q^5 - 3 * q^6 + 11 * q^7 + 6 * q^8 + 24 * q^9	\( 24 q + 3 q^{2} - 24 q^{3} + 25 q^{4} + 3 q^{5} - 3 q^{6} + 11 q^{7} + 6 q^{8} + 24 q^{9} - 2 q^{10} + 7 q^{11} - 25 q^{12} - 24 q^{13} + 8 q^{14} - 3 q^{15} + 23 q^{16} + 4 q^{17} + 3 q^{18} - 20 q^{19} + 8 q^{20} - 11 q^{21} + 5 q^{22} + 41 q^{23} - 6 q^{24} + 23 q^{25} - 3 q^{26} - 24 q^{27} + 16 q^{28} + 12 q^{29} + 2 q^{30} + 2 q^{31} + 25 q^{32} - 7 q^{33} - 11 q^{34} + 36 q^{35} + 25 q^{36} + 18 q^{37} + 10 q^{38} + 24 q^{39} + 14 q^{40} - 9 q^{41} - 8 q^{42} + 23 q^{43} + 41 q^{44} + 3 q^{45} + 7 q^{46} + 32 q^{47} - 23 q^{48} + 11 q^{49} + 26 q^{50} - 4 q^{51} - 25 q^{52} + 46 q^{53} - 3 q^{54} + 18 q^{55} + 26 q^{56} + 20 q^{57} + 37 q^{58} - 12 q^{59} - 8 q^{60} - q^{61} + 53 q^{62} + 11 q^{63} + 26 q^{64} - 3 q^{65} - 5 q^{66} + 8 q^{67} + 6 q^{68} - 41 q^{69} + 19 q^{70} + 20 q^{71} + 6 q^{72} + 12 q^{73} + 86 q^{74} - 23 q^{75} - 28 q^{76} + 23 q^{77} + 3 q^{78} + 27 q^{79} + 6 q^{80} + 24 q^{81} - 28 q^{82} + 33 q^{83} - 16 q^{84} - 13 q^{85} + 63 q^{86} - 12 q^{87} + 11 q^{88} - 2 q^{90} - 11 q^{91} + 79 q^{92} - 2 q^{93} - 12 q^{94} + 37 q^{95} - 25 q^{96} - 14 q^{97} + 20 q^{98} + 7 q^{99}+O(q^{100}) \) 24 * q + 3 * q^2 - 24 * q^3 + 25 * q^4 + 3 * q^5 - 3 * q^6 + 11 * q^7 + 6 * q^8 + 24 * q^9 - 2 * q^10 + 7 * q^11 - 25 * q^12 - 24 * q^13 + 8 * q^14 - 3 * q^15 + 23 * q^16 + 4 * q^17 + 3 * q^18 - 20 * q^19 + 8 * q^20 - 11 * q^21 + 5 * q^22 + 41 * q^23 - 6 * q^24 + 23 * q^25 - 3 * q^26 - 24 * q^27 + 16 * q^28 + 12 * q^29 + 2 * q^30 + 2 * q^31 + 25 * q^32 - 7 * q^33 - 11 * q^34 + 36 * q^35 + 25 * q^36 + 18 * q^37 + 10 * q^38 + 24 * q^39 + 14 * q^40 - 9 * q^41 - 8 * q^42 + 23 * q^43 + 41 * q^44 + 3 * q^45 + 7 * q^46 + 32 * q^47 - 23 * q^48 + 11 * q^49 + 26 * q^50 - 4 * q^51 - 25 * q^52 + 46 * q^53 - 3 * q^54 + 18 * q^55 + 26 * q^56 + 20 * q^57 + 37 * q^58 - 12 * q^59 - 8 * q^60 - q^61 + 53 * q^62 + 11 * q^63 + 26 * q^64 - 3 * q^65 - 5 * q^66 + 8 * q^67 + 6 * q^68 - 41 * q^69 + 19 * q^70 + 20 * q^71 + 6 * q^72 + 12 * q^73 + 86 * q^74 - 23 * q^75 - 28 * q^76 + 23 * q^77 + 3 * q^78 + 27 * q^79 + 6 * q^80 + 24 * q^81 - 28 * q^82 + 33 * q^83 - 16 * q^84 - 13 * q^85 + 63 * q^86 - 12 * q^87 + 11 * q^88 - 2 * q^90 - 11 * q^91 + 79 * q^92 - 2 * q^93 - 12 * q^94 + 37 * q^95 - 25 * q^96 - 14 * q^97 + 20 * q^98 + 7 * 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 $

$2$	1.05828	0.748316	0.374158	−	0.927365i	$-0.377932\pi$
$2$	1.05828	0.748316	0.374158	+	0.927365i	$0.377932\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−0.880046	−0.440023
$5$	−0.912505	−0.408085	−0.204042	−	0.978962i	$-0.565408\pi$
$5$	−0.912505	−0.408085	−0.204042	+	0.978962i	$0.565408\pi$
$6$	−1.05828	−0.432040
$7$	−3.63309	−1.37318	−0.686590	−	0.727045i	$-0.740893\pi$
$7$	−3.63309	−1.37318	−0.686590	+	0.727045i	$0.740893\pi$
$8$	−3.04789	−1.07759
$9$	1.00000	0.333333
$10$	−0.965685	−0.305376
$11$	−1.15222	−0.347407	−0.173703	−	0.984798i	$-0.555573\pi$
$11$	−1.15222	−0.347407	−0.173703	+	0.984798i	$0.555573\pi$
$12$	0.880046	0.254048
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−3.84483	−1.02757
$15$	0.912505	0.235608
$16$	−1.46543	−0.366356
$17$	−2.09451	−0.507994	−0.253997	−	0.967205i	$-0.581745\pi$
$17$	−2.09451	−0.507994	−0.253997	+	0.967205i	$0.581745\pi$
$18$	1.05828	0.249439
$19$	−0.646012	−0.148205	−0.0741027	−	0.997251i	$-0.523609\pi$
$19$	−0.646012	−0.148205	−0.0741027	+	0.997251i	$0.523609\pi$
$20$	0.803047	0.179567
$21$	3.63309	0.792806
$22$	−1.21937	−0.259970
$23$	−8.89813	−1.85539	−0.927694	−	0.373341i	$-0.878212\pi$
$23$	−8.89813	−1.85539	−0.927694	+	0.373341i	$0.878212\pi$
$24$	3.04789	0.622148
$25$	−4.16733	−0.833467
$26$	−1.05828	−0.207546
$27$	−1.00000	−0.192450
$28$	3.19729	0.604231
$29$	3.94970	0.733441	0.366721	−	0.930331i	$-0.380480\pi$
$29$	3.94970	0.733441	0.366721	+	0.930331i	$0.380480\pi$
$30$	0.965685	0.176309
$31$	−4.66229	−0.837372	−0.418686	−	0.908131i	$-0.637509\pi$
$31$	−4.66229	−0.837372	−0.418686	+	0.908131i	$0.637509\pi$
$32$	4.54495	0.803442
$33$	1.15222	0.200575
$34$	−2.21658	−0.380140
$35$	3.31522	0.560374
$36$	−0.880046	−0.146674
$37$	−1.70522	−0.280337	−0.140168	−	0.990128i	$-0.544764\pi$
$37$	−1.70522	−0.280337	−0.140168	+	0.990128i	$0.544764\pi$
$38$	−0.683661	−0.110904
$39$	1.00000	0.160128
$40$	2.78122	0.439749
$41$	−8.06085	−1.25889	−0.629446	−	0.777044i	$-0.716718\pi$
$41$	−8.06085	−1.25889	−0.629446	+	0.777044i	$0.716718\pi$
$42$	3.84483	0.593269
$43$	0.912813	0.139203	0.0696013	−	0.997575i	$-0.477827\pi$
$43$	0.912813	0.139203	0.0696013	+	0.997575i	$0.477827\pi$
$44$	1.01401	0.152867
$45$	−0.912505	−0.136028
$46$	−9.41670	−1.38842
$47$	4.88621	0.712728	0.356364	−	0.934347i	$-0.384016\pi$
$47$	4.88621	0.712728	0.356364	+	0.934347i	$0.384016\pi$
$48$	1.46543	0.211516
$49$	6.19937	0.885625
$50$	−4.41020	−0.623697
$51$	2.09451	0.293291
$52$	0.880046	0.122040
$53$	−3.15100	−0.432823	−0.216411	−	0.976302i	$-0.569435\pi$
$53$	−3.15100	−0.432823	−0.216411	+	0.976302i	$0.569435\pi$
$54$	−1.05828	−0.144013
$55$	1.05140	0.141771
$56$	11.0733	1.47973
$57$	0.646012	0.0855664
$58$	4.17989	0.548846
$59$	1.05612	0.137495	0.0687474	−	0.997634i	$-0.478100\pi$
$59$	1.05612	0.137495	0.0687474	+	0.997634i	$0.478100\pi$
$60$	−0.803047	−0.103673
$61$	−4.06408	−0.520352	−0.260176	−	0.965561i	$-0.583781\pi$
$61$	−4.06408	−0.520352	−0.260176	+	0.965561i	$0.583781\pi$
$62$	−4.93400	−0.626619
$63$	−3.63309	−0.457727
$64$	7.74068	0.967585
$65$	0.912505	0.113182
$66$	1.21937	0.150094
$67$	3.87694	0.473644	0.236822	−	0.971553i	$-0.423894\pi$
$67$	3.87694	0.473644	0.236822	+	0.971553i	$0.423894\pi$
$68$	1.84327	0.223529
$69$	8.89813	1.07121
$70$	3.50842	0.419337
$71$	2.77471	0.329297	0.164649	−	0.986352i	$-0.447351\pi$
$71$	2.77471	0.329297	0.164649	+	0.986352i	$0.447351\pi$
$72$	−3.04789	−0.359197
$73$	−1.56883	−0.183617	−0.0918085	−	0.995777i	$-0.529265\pi$
$73$	−1.56883	−0.183617	−0.0918085	+	0.995777i	$0.529265\pi$
$74$	−1.80460	−0.209780
$75$	4.16733	0.481202
$76$	0.568521	0.0652138
$77$	4.18612	0.477052
$78$	1.05828	0.119826
$79$	1.26952	0.142832	0.0714159	−	0.997447i	$-0.477248\pi$
$79$	1.26952	0.142832	0.0714159	+	0.997447i	$0.477248\pi$
$80$	1.33721	0.149504
$81$	1.00000	0.111111
$82$	−8.53062	−0.942049
$83$	13.3649	1.46699	0.733495	−	0.679695i	$-0.237888\pi$
$83$	13.3649	1.46699	0.733495	+	0.679695i	$0.237888\pi$
$84$	−3.19729	−0.348853
$85$	1.91125	0.207305
$86$	0.966010	0.104168
$87$	−3.94970	−0.423453
$88$	3.51183	0.374363
$89$	−15.4734	−1.64018	−0.820090	−	0.572235i	$-0.806077\pi$
$89$	−15.4734	−1.64018	−0.820090	+	0.572235i	$0.806077\pi$
$90$	−0.965685	−0.101792
$91$	3.63309	0.380852
$92$	7.83077	0.816414
$93$	4.66229	0.483457
$94$	5.17098	0.533345
$95$	0.589489	0.0604803
$96$	−4.54495	−0.463867
$97$	4.91041	0.498577	0.249288	−	0.968429i	$-0.419803\pi$
$97$	4.91041	0.498577	0.249288	+	0.968429i	$0.419803\pi$
$98$	6.56066	0.662727
$99$	−1.15222	−0.115802
$100$	3.66745	0.366745
$101$	11.0928	1.10377	0.551887	−	0.833919i	$-0.313908\pi$
$101$	11.0928	1.10377	0.551887	+	0.833919i	$0.313908\pi$
$102$	2.21658	0.219474
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	3.04789	0.298870
$105$	−3.31522	−0.323532
$106$	−3.33463	−0.323888
$107$	15.3077	1.47985	0.739924	−	0.672691i	$-0.234862\pi$
$107$	15.3077	1.47985	0.739924	+	0.672691i	$0.234862\pi$
$108$	0.880046	0.0846825
$109$	5.50994	0.527756	0.263878	−	0.964556i	$-0.414998\pi$
$109$	5.50994	0.527756	0.263878	+	0.964556i	$0.414998\pi$
$110$	1.11268	0.106090
$111$	1.70522	0.161852
$112$	5.32403	0.503073
$113$	−9.38175	−0.882561	−0.441280	−	0.897369i	$-0.645476\pi$
$113$	−9.38175	−0.882561	−0.441280	+	0.897369i	$0.645476\pi$
$114$	0.683661	0.0640307
$115$	8.11959	0.757156
$116$	−3.47592	−0.322731
$117$	−1.00000	−0.0924500
$118$	1.11767	0.102890
$119$	7.60956	0.697568
$120$	−2.78122	−0.253889
$121$	−9.67239	−0.879309
$122$	−4.30093	−0.389388
$123$	8.06085	0.726822
$124$	4.10303	0.368463
$125$	8.36524	0.748210
$126$	−3.84483	−0.342524
$127$	14.9237	1.32427	0.662134	−	0.749385i	$-0.269651\pi$
$127$	14.9237	1.32427	0.662134	+	0.749385i	$0.269651\pi$
$128$	−0.898114	−0.0793828
$129$	−0.912813	−0.0803687
$130$	0.965685	0.0846962
$131$	−4.46081	−0.389743	−0.194871	−	0.980829i	$-0.562429\pi$
$131$	−4.46081	−0.389743	−0.194871	+	0.980829i	$0.562429\pi$
$132$	−1.01401	−0.0882578
$133$	2.34702	0.203513
$134$	4.10289	0.354435
$135$	0.912505	0.0785359
$136$	6.38385	0.547411
$137$	−11.3138	−0.966605	−0.483302	−	0.875454i	$-0.660563\pi$
$137$	−11.3138	−0.966605	−0.483302	+	0.875454i	$0.660563\pi$
$138$	9.41670	0.801603
$139$	6.61154	0.560784	0.280392	−	0.959886i	$-0.409536\pi$
$139$	6.61154	0.560784	0.280392	+	0.959886i	$0.409536\pi$
$140$	−2.91754	−0.246578
$141$	−4.88621	−0.411493
$142$	2.93641	0.246418
$143$	1.15222	0.0963533
$144$	−1.46543	−0.122119
$145$	−3.60412	−0.299306
$146$	−1.66025	−0.137404
$147$	−6.19937	−0.511316
$148$	1.50067	0.123355
$149$	−7.92785	−0.649475	−0.324737	−	0.945804i	$-0.605276\pi$
$149$	−7.92785	−0.649475	−0.324737	+	0.945804i	$0.605276\pi$
$150$	4.41020	0.360091
$151$	6.05700	0.492912	0.246456	−	0.969154i	$-0.420734\pi$
$151$	6.05700	0.492912	0.246456	+	0.969154i	$0.420734\pi$
$152$	1.96897	0.159705
$153$	−2.09451	−0.169331
$154$	4.43008	0.356986
$155$	4.25436	0.341719
$156$	−0.880046	−0.0704601
$157$	−19.9740	−1.59410	−0.797051	−	0.603912i	$-0.793608\pi$
$157$	−19.9740	−1.59410	−0.797051	+	0.603912i	$0.793608\pi$
$158$	1.34350	0.106883
$159$	3.15100	0.249890
$160$	−4.14729	−0.327872
$161$	32.3277	2.54778
$162$	1.05828	0.0831462
$163$	14.7633	1.15635	0.578176	−	0.815912i	$-0.303765\pi$
$163$	14.7633	1.15635	0.578176	+	0.815912i	$0.303765\pi$
$164$	7.09392	0.553942
$165$	−1.05140	−0.0818517
$166$	14.1438	1.09777
$167$	8.23190	0.637004	0.318502	−	0.947922i	$-0.396820\pi$
$167$	8.23190	0.637004	0.318502	+	0.947922i	$0.396820\pi$
$168$	−11.0733	−0.854322
$169$	1.00000	0.0769231
$170$	2.02264	0.155129
$171$	−0.646012	−0.0494018
$172$	−0.803318	−0.0612524
$173$	17.8449	1.35672	0.678362	−	0.734728i	$-0.262690\pi$
$173$	17.8449	1.35672	0.678362	+	0.734728i	$0.262690\pi$
$174$	−4.17989	−0.316876
$175$	15.1403	1.14450
$176$	1.68849	0.127275
$177$	−1.05612	−0.0793826
$178$	−16.3752	−1.22737
$179$	−8.56512	−0.640187	−0.320093	−	0.947386i	$-0.603714\pi$
$179$	−8.56512	−0.640187	−0.320093	+	0.947386i	$0.603714\pi$
$180$	0.803047	0.0598556
$181$	−18.6783	−1.38835	−0.694173	−	0.719808i	$-0.744230\pi$
$181$	−18.6783	−1.38835	−0.694173	+	0.719808i	$0.744230\pi$
$182$	3.84483	0.284997
$183$	4.06408	0.300426
$184$	27.1205	1.99935
$185$	1.55602	0.114401
$186$	4.93400	0.361779
$187$	2.41334	0.176481
$188$	−4.30009	−0.313617
$189$	3.63309	0.264269
$190$	0.623844	0.0452584
$191$	−14.2339	−1.02993	−0.514964	−	0.857212i	$-0.672195\pi$
$191$	−14.2339	−1.02993	−0.514964	+	0.857212i	$0.672195\pi$
$192$	−7.74068	−0.558635
$193$	18.3968	1.32423	0.662116	−	0.749401i	$-0.269658\pi$
$193$	18.3968	1.32423	0.662116	+	0.749401i	$0.269658\pi$
$194$	5.19658	0.373093
$195$	−0.912505	−0.0653459
$196$	−5.45573	−0.389695
$197$	−6.23250	−0.444047	−0.222024	−	0.975041i	$-0.571266\pi$
$197$	−6.23250	−0.444047	−0.222024	+	0.975041i	$0.571266\pi$
$198$	−1.21937	−0.0866567
$199$	12.6357	0.895719	0.447859	−	0.894104i	$-0.352186\pi$
$199$	12.6357	0.895719	0.447859	+	0.894104i	$0.352186\pi$
$200$	12.7016	0.898138
$201$	−3.87694	−0.273459
$202$	11.7393	0.825972
$203$	−14.3496	−1.00715
$204$	−1.84327	−0.129055
$205$	7.35556	0.513735
$206$	1.05828	0.0737338
$207$	−8.89813	−0.618463
$208$	1.46543	0.101609
$209$	0.744347	0.0514875
$210$	−3.50842	−0.242104
$211$	15.5477	1.07035	0.535175	−	0.844741i	$-0.320246\pi$
$211$	15.5477	1.07035	0.535175	+	0.844741i	$0.320246\pi$
$212$	2.77302	0.190452
$213$	−2.77471	−0.190120
$214$	16.1998	1.10739
$215$	−0.832946	−0.0568065
$216$	3.04789	0.207383
$217$	16.9385	1.14986
$218$	5.83105	0.394928
$219$	1.56883	0.106011
$220$	−0.925285	−0.0623827
$221$	2.09451	0.140892
$222$	1.80460	0.121117
$223$	1.85404	0.124156	0.0620778	−	0.998071i	$-0.480227\pi$
$223$	1.85404	0.124156	0.0620778	+	0.998071i	$0.480227\pi$
$224$	−16.5122	−1.10327
$225$	−4.16733	−0.277822
$226$	−9.92850	−0.660434
$227$	0.00619540	0.000411203 0	0.000205602	−	1.00000i	$-0.499935\pi$
$227$	0.00619540	0.000411203 0	0.000205602		1.00000i	$0.499935\pi$
$228$	−0.568521	−0.0376512
$229$	−20.8512	−1.37789	−0.688943	−	0.724815i	$-0.741925\pi$
$229$	−20.8512	−1.37789	−0.688943	+	0.724815i	$0.741925\pi$
$230$	8.59279	0.566592
$231$	−4.18612	−0.275426
$232$	−12.0383	−0.790351
$233$	−16.4976	−1.08080	−0.540398	−	0.841409i	$-0.681726\pi$
$233$	−16.4976	−1.08080	−0.540398	+	0.841409i	$0.681726\pi$
$234$	−1.05828	−0.0691818
$235$	−4.45870	−0.290853
$236$	−0.929432	−0.0605009
$237$	−1.26952	−0.0824639
$238$	8.05304	0.522001
$239$	−11.6051	−0.750669	−0.375335	−	0.926889i	$-0.622472\pi$
$239$	−11.6051	−0.750669	−0.375335	+	0.926889i	$0.622472\pi$
$240$	−1.33721	−0.0863164
$241$	−7.30272	−0.470409	−0.235205	−	0.971946i	$-0.575576\pi$
$241$	−7.30272	−0.470409	−0.235205	+	0.971946i	$0.575576\pi$
$242$	−10.2361	−0.658001
$243$	−1.00000	−0.0641500
$244$	3.57658	0.228967
$245$	−5.65696	−0.361410
$246$	8.53062	0.543892
$247$	0.646012	0.0411048
$248$	14.2102	0.902346
$249$	−13.3649	−0.846967
$250$	8.85275	0.559897
$251$	1.05425	0.0665437	0.0332719	−	0.999446i	$-0.489407\pi$
$251$	1.05425	0.0665437	0.0332719	+	0.999446i	$0.489407\pi$
$252$	3.19729	0.201410
$253$	10.2526	0.644575
$254$	15.7935	0.990971
$255$	−1.91125	−0.119687
$256$	−16.4318	−1.02699
$257$	1.32938	0.0829243	0.0414621	−	0.999140i	$-0.486798\pi$
$257$	1.32938	0.0829243	0.0414621	+	0.999140i	$0.486798\pi$
$258$	−0.966010	−0.0601412
$259$	6.19523	0.384953
$260$	−0.803047	−0.0498029
$261$	3.94970	0.244480
$262$	−4.72078	−0.291651
$263$	11.4127	0.703737	0.351869	−	0.936049i	$-0.385546\pi$
$263$	11.4127	0.703737	0.351869	+	0.936049i	$0.385546\pi$
$264$	−3.51183	−0.216138
$265$	2.87530	0.176628
$266$	2.48380	0.152292
$267$	15.4734	0.946958
$268$	−3.41189	−0.208414
$269$	25.9749	1.58371	0.791857	−	0.610706i	$-0.209114\pi$
$269$	25.9749	1.58371	0.791857	+	0.610706i	$0.209114\pi$
$270$	0.965685	0.0587697
$271$	−16.4799	−1.00108	−0.500542	−	0.865712i	$-0.666866\pi$
$271$	−16.4799	−1.00108	−0.500542	+	0.865712i	$0.666866\pi$
$272$	3.06935	0.186107
$273$	−3.63309	−0.219885
$274$	−11.9732	−0.723326
$275$	4.80168	0.289552
$276$	−7.83077	−0.471357
$277$	−4.87661	−0.293007	−0.146503	−	0.989210i	$-0.546802\pi$
$277$	−4.87661	−0.293007	−0.146503	+	0.989210i	$0.546802\pi$
$278$	6.99686	0.419644
$279$	−4.66229	−0.279124
$280$	−10.1044	−0.603855
$281$	−29.8226	−1.77907	−0.889533	−	0.456871i	$-0.848970\pi$
$281$	−29.8226	−1.77907	−0.889533	+	0.456871i	$0.848970\pi$
$282$	−5.17098	−0.307927
$283$	−8.51437	−0.506127	−0.253063	−	0.967450i	$-0.581438\pi$
$283$	−8.51437	−0.506127	−0.253063	+	0.967450i	$0.581438\pi$
$284$	−2.44187	−0.144898
$285$	−0.589489	−0.0349183
$286$	1.21937	0.0721027
$287$	29.2858	1.72869
$288$	4.54495	0.267814
$289$	−12.6130	−0.741942
$290$	−3.81417	−0.223976
$291$	−4.91041	−0.287853
$292$	1.38064	0.0807958
$293$	17.9383	1.04796	0.523982	−	0.851729i	$-0.324446\pi$
$293$	17.9383	1.04796	0.523982	+	0.851729i	$0.324446\pi$
$294$	−6.56066	−0.382626
$295$	−0.963713	−0.0561095
$296$	5.19733	0.302089
$297$	1.15222	0.0668585
$298$	−8.38987	−0.486012
$299$	8.89813	0.514592
$300$	−3.66745	−0.211740
$301$	−3.31633	−0.191150
$302$	6.40999	0.368854
$303$	−11.0928	−0.637264
$304$	0.946682	0.0542960
$305$	3.70850	0.212348
$306$	−2.21658	−0.126713
$307$	−13.1960	−0.753135	−0.376567	−	0.926389i	$-0.622896\pi$
$307$	−13.1960	−0.753135	−0.376567	+	0.926389i	$0.622896\pi$
$308$	−3.68398	−0.209914
$309$	−1.00000	−0.0568880
$310$	4.50230	0.255714
$311$	−11.8366	−0.671194	−0.335597	−	0.942006i	$-0.608938\pi$
$311$	−11.8366	−0.671194	−0.335597	+	0.942006i	$0.608938\pi$
$312$	−3.04789	−0.172553
$313$	−14.8906	−0.841666	−0.420833	−	0.907138i	$-0.638262\pi$
$313$	−14.8906	−0.841666	−0.420833	+	0.907138i	$0.638262\pi$
$314$	−21.1381	−1.19289
$315$	3.31522	0.186791
$316$	−1.11723	−0.0628493
$317$	14.5587	0.817699	0.408849	−	0.912602i	$-0.365930\pi$
$317$	14.5587	0.817699	0.408849	+	0.912602i	$0.365930\pi$
$318$	3.33463	0.186997
$319$	−4.55092	−0.254802
$320$	−7.06341	−0.394857
$321$	−15.3077	−0.854390
$322$	34.2118	1.90655
$323$	1.35308	0.0752874
$324$	−0.880046	−0.0488915
$325$	4.16733	0.231162
$326$	15.6237	0.865317
$327$	−5.50994	−0.304700
$328$	24.5686	1.35657
$329$	−17.7521	−0.978703
$330$	−1.11268	−0.0612510
$331$	1.62408	0.0892673	0.0446337	−	0.999003i	$-0.485788\pi$
$331$	1.62408	0.0892673	0.0446337	+	0.999003i	$0.485788\pi$
$332$	−11.7617	−0.645509
$333$	−1.70522	−0.0934455
$334$	8.71165	0.476680
$335$	−3.53773	−0.193287
$336$	−5.32403	−0.290450
$337$	−4.58891	−0.249974	−0.124987	−	0.992158i	$-0.539889\pi$
$337$	−4.58891	−0.249974	−0.124987	+	0.992158i	$0.539889\pi$
$338$	1.05828	0.0575628
$339$	9.38175	0.509547
$340$	−1.68199	−0.0912188
$341$	5.37197	0.290909
$342$	−0.683661	−0.0369681
$343$	2.90876	0.157058
$344$	−2.78215	−0.150004
$345$	−8.11959	−0.437144
$346$	18.8849	1.01526
$347$	6.05498	0.325048	0.162524	−	0.986705i	$-0.448036\pi$
$347$	6.05498	0.325048	0.162524	+	0.986705i	$0.448036\pi$
$348$	3.47592	0.186329
$349$	−11.2034	−0.599705	−0.299853	−	0.953986i	$-0.596938\pi$
$349$	−11.2034	−0.599705	−0.299853	+	0.953986i	$0.596938\pi$
$350$	16.0227	0.856448
$351$	1.00000	0.0533761
$352$	−5.23678	−0.279121
$353$	18.2274	0.970145	0.485072	−	0.874474i	$-0.338793\pi$
$353$	18.2274	0.970145	0.485072	+	0.874474i	$0.338793\pi$
$354$	−1.11767	−0.0594033
$355$	−2.53193	−0.134381
$356$	13.6173	0.721717
$357$	−7.60956	−0.402741
$358$	−9.06428	−0.479062
$359$	−33.3969	−1.76262	−0.881310	−	0.472538i	$-0.843338\pi$
$359$	−33.3969	−1.76262	−0.881310	+	0.472538i	$0.843338\pi$
$360$	2.78122	0.146583
$361$	−18.5827	−0.978035
$362$	−19.7668	−1.03892
$363$	9.67239	0.507669
$364$	−3.19729	−0.167584
$365$	1.43156	0.0749313
$366$	4.30093	0.224813
$367$	−2.69579	−0.140719	−0.0703596	−	0.997522i	$-0.522415\pi$
$367$	−2.69579	−0.140719	−0.0703596	+	0.997522i	$0.522415\pi$
$368$	13.0395	0.679733
$369$	−8.06085	−0.419631
$370$	1.64671	0.0856082
$371$	11.4479	0.594344
$372$	−4.10303	−0.212732
$373$	29.4584	1.52530	0.762649	−	0.646813i	$-0.223898\pi$
$373$	29.4584	1.52530	0.762649	+	0.646813i	$0.223898\pi$
$374$	2.55398	0.132063
$375$	−8.36524	−0.431979
$376$	−14.8926	−0.768030
$377$	−3.94970	−0.203420
$378$	3.84483	0.197756
$379$	−27.9528	−1.43584	−0.717920	−	0.696126i	$-0.754906\pi$
$379$	−27.9528	−1.43584	−0.717920	+	0.696126i	$0.754906\pi$
$380$	−0.518778	−0.0266127
$381$	−14.9237	−0.764567
$382$	−15.0634	−0.770711
$383$	−5.24706	−0.268112	−0.134056	−	0.990974i	$-0.542800\pi$
$383$	−5.24706	−0.268112	−0.134056	+	0.990974i	$0.542800\pi$
$384$	0.898114	0.0458317
$385$	−3.81985	−0.194678
$386$	19.4690	0.990945
$387$	0.912813	0.0464009
$388$	−4.32139	−0.219385
$389$	−2.70325	−0.137060	−0.0685302	−	0.997649i	$-0.521831\pi$
$389$	−2.70325	−0.137060	−0.0685302	+	0.997649i	$0.521831\pi$
$390$	−0.965685	−0.0488993
$391$	18.6373	0.942526
$392$	−18.8950	−0.954342
$393$	4.46081	0.225018
$394$	−6.59572	−0.332288
$395$	−1.15844	−0.0582874
$396$	1.01401	0.0509557
$397$	−0.742341	−0.0372570	−0.0186285	−	0.999826i	$-0.505930\pi$
$397$	−0.742341	−0.0372570	−0.0186285	+	0.999826i	$0.505930\pi$
$398$	13.3721	0.670281
$399$	−2.34702	−0.117498
$400$	6.10692	0.305346
$401$	2.65955	0.132812	0.0664059	−	0.997793i	$-0.478847\pi$
$401$	2.65955	0.132812	0.0664059	+	0.997793i	$0.478847\pi$
$402$	−4.10289	−0.204633
$403$	4.66229	0.232245
$404$	−9.76218	−0.485686
$405$	−0.912505	−0.0453427
$406$	−15.1859	−0.753664
$407$	1.96479	0.0973908
$408$	−6.38385	−0.316048
$409$	15.2361	0.753379	0.376689	−	0.926340i	$-0.377062\pi$
$409$	15.2361	0.753379	0.376689	+	0.926340i	$0.377062\pi$
$410$	7.78424	0.384436
$411$	11.3138	0.558069
$412$	−0.880046	−0.0433568
$413$	−3.83697	−0.188805
$414$	−9.41670	−0.462806
$415$	−12.1955	−0.598656
$416$	−4.54495	−0.222835
$417$	−6.61154	−0.323769
$418$	0.787726	0.0385289
$419$	32.2369	1.57487	0.787437	−	0.616395i	$-0.211407\pi$
$419$	32.2369	1.57487	0.787437	+	0.616395i	$0.211407\pi$
$420$	2.91754	0.142362
$421$	−1.92093	−0.0936202	−0.0468101	−	0.998904i	$-0.514906\pi$
$421$	−1.92093	−0.0936202	−0.0468101	+	0.998904i	$0.514906\pi$
$422$	16.4538	0.800959
$423$	4.88621	0.237576
$424$	9.60390	0.466406
$425$	8.72854	0.423396
$426$	−2.93641	−0.142270
$427$	14.7652	0.714538
$428$	−13.4714	−0.651167
$429$	−1.15222	−0.0556296
$430$	−0.881489	−0.0425092
$431$	8.99846	0.433441	0.216720	−	0.976234i	$-0.430464\pi$
$431$	8.99846	0.433441	0.216720	+	0.976234i	$0.430464\pi$
$432$	1.46543	0.0705053
$433$	−14.4505	−0.694447	−0.347224	−	0.937782i	$-0.612876\pi$
$433$	−14.4505	−0.694447	−0.347224	+	0.937782i	$0.612876\pi$
$434$	17.9257	0.860461
$435$	3.60412	0.172805
$436$	−4.84900	−0.232225
$437$	5.74830	0.274978
$438$	1.66025	0.0793300
$439$	−4.41182	−0.210565	−0.105282	−	0.994442i	$-0.533575\pi$
$439$	−4.41182	−0.210565	−0.105282	+	0.994442i	$0.533575\pi$
$440$	−3.20457	−0.152772
$441$	6.19937	0.295208
$442$	2.21658	0.105432
$443$	14.7710	0.701792	0.350896	−	0.936414i	$-0.385877\pi$
$443$	14.7710	0.701792	0.350896	+	0.936414i	$0.385877\pi$
$444$	−1.50067	−0.0712188
$445$	14.1196	0.669332
$446$	1.96209	0.0929077
$447$	7.92785	0.374974
$448$	−28.1226	−1.32867
$449$	−25.5819	−1.20728	−0.603642	−	0.797256i	$-0.706284\pi$
$449$	−25.5819	−1.20728	−0.603642	+	0.797256i	$0.706284\pi$
$450$	−4.41020	−0.207899
$451$	9.28785	0.437348
$452$	8.25637	0.388347
$453$	−6.05700	−0.284583
$454$	0.00655646	0.000307710 0
$455$	−3.31522	−0.155420
$456$	−1.96897	−0.0922057
$457$	−18.8643	−0.882433	−0.441217	−	0.897401i	$-0.645453\pi$
$457$	−18.8643	−0.882433	−0.441217	+	0.897401i	$0.645453\pi$
$458$	−22.0664	−1.03109
$459$	2.09451	0.0977635
$460$	−7.14562	−0.333166
$461$	7.17280	0.334071	0.167035	−	0.985951i	$-0.446581\pi$
$461$	7.17280	0.334071	0.167035	+	0.985951i	$0.446581\pi$
$462$	−4.43008	−0.206106
$463$	−23.5859	−1.09613	−0.548066	−	0.836435i	$-0.684636\pi$
$463$	−23.5859	−1.09613	−0.548066	+	0.836435i	$0.684636\pi$
$464$	−5.78799	−0.268701
$465$	−4.25436	−0.197291
$466$	−17.4591	−0.808777
$467$	−33.7926	−1.56373	−0.781867	−	0.623445i	$-0.785733\pi$
$467$	−33.7926	−1.56373	−0.781867	+	0.623445i	$0.785733\pi$
$468$	0.880046	0.0406802
$469$	−14.0853	−0.650399
$470$	−4.71854	−0.217650
$471$	19.9740	0.920355
$472$	−3.21893	−0.148163
$473$	−1.05176	−0.0483599
$474$	−1.34350	−0.0617091
$475$	2.69215	0.123524
$476$	−6.69677	−0.306946
$477$	−3.15100	−0.144274
$478$	−12.2814	−0.561738
$479$	−19.2375	−0.878983	−0.439491	−	0.898247i	$-0.644841\pi$
$479$	−19.2375	−0.878983	−0.439491	+	0.898247i	$0.644841\pi$
$480$	4.14729	0.189297
$481$	1.70522	0.0777514
$482$	−7.72831	−0.352015
$483$	−32.3277	−1.47096
$484$	8.51216	0.386916
$485$	−4.48077	−0.203461
$486$	−1.05828	−0.0480045
$487$	24.5015	1.11027	0.555134	−	0.831761i	$-0.312667\pi$
$487$	24.5015	1.11027	0.555134	+	0.831761i	$0.312667\pi$
$488$	12.3869	0.560728
$489$	−14.7633	−0.667620
$490$	−5.98664	−0.270449
$491$	28.8003	1.29974	0.649870	−	0.760046i	$-0.274823\pi$
$491$	28.8003	1.29974	0.649870	+	0.760046i	$0.274823\pi$
$492$	−7.09392	−0.319819
$493$	−8.27270	−0.372584
$494$	0.683661	0.0307593
$495$	1.05140	0.0472571
$496$	6.83224	0.306777
$497$	−10.0808	−0.452184
$498$	−14.1438	−0.633799
$499$	−5.77561	−0.258552	−0.129276	−	0.991609i	$-0.541265\pi$
$499$	−5.77561	−0.258552	−0.129276	+	0.991609i	$0.541265\pi$
$500$	−7.36180	−0.329230
$501$	−8.23190	−0.367774
$502$	1.11569	0.0497957
$503$	27.8274	1.24076	0.620381	−	0.784301i	$-0.286978\pi$
$503$	27.8274	1.24076	0.620381	+	0.784301i	$0.286978\pi$
$504$	11.0733	0.493243
$505$	−10.1222	−0.450433
$506$	10.8501	0.482345
$507$	−1.00000	−0.0444116
$508$	−13.1336	−0.582709
$509$	−5.90413	−0.261696	−0.130848	−	0.991402i	$-0.541770\pi$
$509$	−5.90413	−0.261696	−0.130848	+	0.991402i	$0.541770\pi$
$510$	−2.02264	−0.0895640
$511$	5.69969	0.252139
$512$	−15.5932	−0.689129
$513$	0.646012	0.0285221
$514$	1.40685	0.0620536
$515$	−0.912505	−0.0402098
$516$	0.803318	0.0353641
$517$	−5.62998	−0.247606
$518$	6.55628	0.288066
$519$	−17.8449	−0.783305
$520$	−2.78122	−0.121964
$521$	2.91277	0.127611	0.0638053	−	0.997962i	$-0.479676\pi$
$521$	2.91277	0.127611	0.0638053	+	0.997962i	$0.479676\pi$
$522$	4.17989	0.182949
$523$	−19.4860	−0.852063	−0.426032	−	0.904708i	$-0.640089\pi$
$523$	−19.4860	−0.852063	−0.426032	+	0.904708i	$0.640089\pi$
$524$	3.92572	0.171496
$525$	−15.1403	−0.660778
$526$	12.0778	0.526618
$527$	9.76523	0.425380
$528$	−1.68849	−0.0734821
$529$	56.1767	2.44247
$530$	3.04287	0.132174
$531$	1.05612	0.0458316
$532$	−2.06549	−0.0895503
$533$	8.06085	0.349154
$534$	16.3752	0.708624
$535$	−13.9683	−0.603903
$536$	−11.8165	−0.510395
$537$	8.56512	0.369612
$538$	27.4886	1.18512
$539$	−7.14303	−0.307672
$540$	−0.803047	−0.0345576
$541$	13.7847	0.592652	0.296326	−	0.955087i	$-0.404238\pi$
$541$	13.7847	0.592652	0.296326	+	0.955087i	$0.404238\pi$
$542$	−17.4404	−0.749128
$543$	18.6783	0.801562
$544$	−9.51947	−0.408144
$545$	−5.02784	−0.215369
$546$	−3.84483	−0.164543
$547$	41.0007	1.75306	0.876531	−	0.481345i	$-0.159851\pi$
$547$	41.0007	1.75306	0.876531	+	0.481345i	$0.159851\pi$
$548$	9.95668	0.425328
$549$	−4.06408	−0.173451
$550$	5.08151	0.216676
$551$	−2.55156	−0.108700
$552$	−27.1205	−1.15433
$553$	−4.61227	−0.196134
$554$	−5.16081	−0.219262
$555$	−1.55602	−0.0660495
$556$	−5.81847	−0.246758
$557$	36.6413	1.55254	0.776271	−	0.630400i	$-0.217109\pi$
$557$	36.6413	1.55254	0.776271	+	0.630400i	$0.217109\pi$
$558$	−4.93400	−0.208873
$559$	−0.912813	−0.0386079
$560$	−4.85820	−0.205297
$561$	−2.41334	−0.101891
$562$	−31.5606	−1.33130
$563$	30.7776	1.29712	0.648562	−	0.761162i	$-0.275371\pi$
$563$	30.7776	1.29712	0.648562	+	0.761162i	$0.275371\pi$
$564$	4.30009	0.181067
$565$	8.56090	0.360160
$566$	−9.01057	−0.378743
$567$	−3.63309	−0.152576
$568$	−8.45700	−0.354848
$569$	−23.4563	−0.983340	−0.491670	−	0.870782i	$-0.663613\pi$
$569$	−23.4563	−0.983340	−0.491670	+	0.870782i	$0.663613\pi$
$570$	−0.623844	−0.0261299
$571$	−12.9784	−0.543127	−0.271564	−	0.962421i	$-0.587541\pi$
$571$	−12.9784	−0.543127	−0.271564	+	0.962421i	$0.587541\pi$
$572$	−1.01401	−0.0423977
$573$	14.2339	0.594629
$574$	30.9925	1.29360
$575$	37.0815	1.54640
$576$	7.74068	0.322528
$577$	−21.5678	−0.897880	−0.448940	−	0.893562i	$-0.648198\pi$
$577$	−21.5678	−0.897880	−0.448940	+	0.893562i	$0.648198\pi$
$578$	−13.3481	−0.555207
$579$	−18.3968	−0.764546
$580$	3.17180	0.131702
$581$	−48.5560	−2.01444
$582$	−5.19658	−0.215405
$583$	3.63063	0.150366
$584$	4.78161	0.197864
$585$	0.912505	0.0377274
$586$	18.9837	0.784208
$587$	−26.5715	−1.09672	−0.548362	−	0.836241i	$-0.684748\pi$
$587$	−26.5715	−1.09672	−0.548362	+	0.836241i	$0.684748\pi$
$588$	5.45573	0.224991
$589$	3.01189	0.124103
$590$	−1.01988	−0.0419876
$591$	6.23250	0.256371
$592$	2.49887	0.102703
$593$	2.89906	0.119050	0.0595250	−	0.998227i	$-0.481041\pi$
$593$	2.89906	0.119050	0.0595250	+	0.998227i	$0.481041\pi$
$594$	1.21937	0.0500313
$595$	−6.94377	−0.284667
$596$	6.97688	0.285784
$597$	−12.6357	−0.517144
$598$	9.41670	0.385078
$599$	31.1460	1.27259	0.636295	−	0.771446i	$-0.280466\pi$
$599$	31.1460	1.27259	0.636295	+	0.771446i	$0.280466\pi$
$600$	−12.7016	−0.518540
$601$	34.4732	1.40619	0.703095	−	0.711096i	$-0.251801\pi$
$601$	34.4732	1.40619	0.703095	+	0.711096i	$0.251801\pi$
$602$	−3.50961	−0.143041
$603$	3.87694	0.157881
$604$	−5.33044	−0.216893
$605$	8.82611	0.358832
$606$	−11.7393	−0.476875
$607$	6.91780	0.280785	0.140393	−	0.990096i	$-0.455164\pi$
$607$	6.91780	0.280785	0.140393	+	0.990096i	$0.455164\pi$
$608$	−2.93610	−0.119074
$609$	14.3496	0.581477
$610$	3.92462	0.158903
$611$	−4.88621	−0.197675
$612$	1.84327	0.0745097
$613$	−22.7641	−0.919432	−0.459716	−	0.888066i	$-0.652049\pi$
$613$	−22.7641	−0.919432	−0.459716	+	0.888066i	$0.652049\pi$
$614$	−13.9650	−0.563583
$615$	−7.35556	−0.296605
$616$	−12.7588	−0.514068
$617$	23.5136	0.946623	0.473312	−	0.880895i	$-0.343058\pi$
$617$	23.5136	0.946623	0.473312	+	0.880895i	$0.343058\pi$
$618$	−1.05828	−0.0425702
$619$	−28.0906	−1.12906	−0.564529	−	0.825413i	$-0.690942\pi$
$619$	−28.0906	−1.12906	−0.564529	+	0.825413i	$0.690942\pi$
$620$	−3.74404	−0.150364
$621$	8.89813	0.357070
$622$	−12.5265	−0.502265
$623$	56.2164	2.25226
$624$	−1.46543	−0.0586640
$625$	13.2033	0.528134
$626$	−15.7584	−0.629832
$627$	−0.744347	−0.0297263
$628$	17.5781	0.701442
$629$	3.57161	0.142409
$630$	3.50842	0.139779
$631$	−37.4438	−1.49062	−0.745308	−	0.666721i	$-0.767697\pi$
$631$	−37.4438	−1.49062	−0.745308	+	0.666721i	$0.767697\pi$
$632$	−3.86935	−0.153914
$633$	−15.5477	−0.617966
$634$	15.4072	0.611897
$635$	−13.6180	−0.540414
$636$	−2.77302	−0.109958
$637$	−6.19937	−0.245628
$638$	−4.81614	−0.190673
$639$	2.77471	0.109766
$640$	0.819534	0.0323949
$641$	34.9305	1.37967	0.689836	−	0.723966i	$-0.257683\pi$
$641$	34.9305	1.37967	0.689836	+	0.723966i	$0.257683\pi$
$642$	−16.1998	−0.639354
$643$	35.9677	1.41843	0.709214	−	0.704993i	$-0.249050\pi$
$643$	35.9677	1.41843	0.709214	+	0.704993i	$0.249050\pi$
$644$	−28.4499	−1.12108
$645$	0.832946	0.0327972
$646$	1.43194	0.0563388
$647$	49.3445	1.93993	0.969967	−	0.243237i	$-0.0782092\pi$
$647$	49.3445	1.93993	0.969967	+	0.243237i	$0.0782092\pi$
$648$	−3.04789	−0.119732
$649$	−1.21688	−0.0477666
$650$	4.41020	0.172982
$651$	−16.9385	−0.663874
$652$	−12.9924	−0.508822
$653$	16.8876	0.660864	0.330432	−	0.943830i	$-0.392806\pi$
$653$	16.8876	0.660864	0.330432	+	0.943830i	$0.392806\pi$
$654$	−5.83105	−0.228012
$655$	4.07051	0.159048
$656$	11.8126	0.461203
$657$	−1.56883	−0.0612057
$658$	−18.7866	−0.732379
$659$	−29.5954	−1.15287	−0.576437	−	0.817142i	$-0.695557\pi$
$659$	−29.5954	−1.15287	−0.576437	+	0.817142i	$0.695557\pi$
$660$	0.925285	0.0360167
$661$	−26.7152	−1.03910	−0.519550	−	0.854440i	$-0.673901\pi$
$661$	−26.7152	−1.03910	−0.519550	+	0.854440i	$0.673901\pi$
$662$	1.71873	0.0668002
$663$	−2.09451	−0.0813442
$664$	−40.7348	−1.58082
$665$	−2.14167	−0.0830504
$666$	−1.80460	−0.0699268
$667$	−35.1450	−1.36082
$668$	−7.24446	−0.280296
$669$	−1.85404	−0.0716813
$670$	−3.74391	−0.144640
$671$	4.68271	0.180774
$672$	16.5122	0.636974
$673$	15.7330	0.606461	0.303230	−	0.952917i	$-0.401935\pi$
$673$	15.7330	0.606461	0.303230	+	0.952917i	$0.401935\pi$
$674$	−4.85634	−0.187059
$675$	4.16733	0.160401
$676$	−0.880046	−0.0338479
$677$	−0.416439	−0.0160051	−0.00800253	−	0.999968i	$-0.502547\pi$
$677$	−0.416439	−0.0160051	−0.00800253	+	0.999968i	$0.502547\pi$
$678$	9.92850	0.381302
$679$	−17.8400	−0.684636
$680$	−5.82530	−0.223390
$681$	−0.00619540	−0.000237408 0
$682$	5.68504	0.217692
$683$	14.8619	0.568675	0.284337	−	0.958724i	$-0.408226\pi$
$683$	14.8619	0.568675	0.284337	+	0.958724i	$0.408226\pi$
$684$	0.568521	0.0217379
$685$	10.3239	0.394457
$686$	3.07828	0.117529
$687$	20.8512	0.795523
$688$	−1.33766	−0.0509978
$689$	3.15100	0.120043
$690$	−8.59279	−0.327122
$691$	−30.7192	−1.16862	−0.584308	−	0.811532i	$-0.698634\pi$
$691$	−30.7192	−1.16862	−0.584308	+	0.811532i	$0.698634\pi$
$692$	−15.7044	−0.596990
$693$	4.18612	0.159017
$694$	6.40786	0.243239
$695$	−6.03307	−0.228847
$696$	12.0383	0.456309
$697$	16.8835	0.639510
$698$	−11.8563	−0.448769
$699$	16.4976	0.623998
$700$	−13.3242	−0.503607
$701$	36.6486	1.38420	0.692098	−	0.721803i	$-0.256686\pi$
$701$	36.6486	1.38420	0.692098	+	0.721803i	$0.256686\pi$
$702$	1.05828	0.0399422
$703$	1.10159	0.0415474
$704$	−8.91895	−0.336146
$705$	4.45870	0.167924
$706$	19.2896	0.725975
$707$	−40.3012	−1.51568
$708$	0.929432	0.0349302
$709$	−9.79318	−0.367791	−0.183895	−	0.982946i	$-0.558871\pi$
$709$	−9.79318	−0.367791	−0.183895	+	0.982946i	$0.558871\pi$
$710$	−2.67949	−0.100560
$711$	1.26952	0.0476106
$712$	47.1613	1.76744
$713$	41.4857	1.55365
$714$	−8.05304	−0.301377
$715$	−1.05140	−0.0393203
$716$	7.53770	0.281697
$717$	11.6051	0.433399
$718$	−35.3432	−1.31900
$719$	10.8265	0.403760	0.201880	−	0.979410i	$-0.435295\pi$
$719$	10.8265	0.403760	0.201880	+	0.979410i	$0.435295\pi$
$720$	1.33721	0.0498348
$721$	−3.63309	−0.135303
$722$	−19.6656	−0.731879
$723$	7.30272	0.271591
$724$	16.4378	0.610904
$725$	−16.4597	−0.611299
$726$	10.2361	0.379897
$727$	−27.5127	−1.02039	−0.510194	−	0.860059i	$-0.670426\pi$
$727$	−27.5127	−1.02039	−0.510194	+	0.860059i	$0.670426\pi$
$728$	−11.0733	−0.410403
$729$	1.00000	0.0370370
$730$	1.51499	0.0560723
$731$	−1.91190	−0.0707141
$732$	−3.57658	−0.132194
$733$	3.65073	0.134843	0.0674215	−	0.997725i	$-0.478523\pi$
$733$	3.65073	0.134843	0.0674215	+	0.997725i	$0.478523\pi$
$734$	−2.85290	−0.105302
$735$	5.65696	0.208660
$736$	−40.4416	−1.49070
$737$	−4.46708	−0.164547
$738$	−8.53062	−0.314016
$739$	−22.1767	−0.815783	−0.407892	−	0.913030i	$-0.633736\pi$
$739$	−22.1767	−0.815783	−0.407892	+	0.913030i	$0.633736\pi$
$740$	−1.36937	−0.0503391
$741$	−0.646012	−0.0237318
$742$	12.1150	0.444757
$743$	−32.5742	−1.19503	−0.597515	−	0.801858i	$-0.703845\pi$
$743$	−32.5742	−1.19503	−0.597515	+	0.801858i	$0.703845\pi$
$744$	−14.2102	−0.520969
$745$	7.23420	0.265041
$746$	31.1752	1.14140
$747$	13.3649	0.488996
$748$	−2.12385	−0.0776555
$749$	−55.6142	−2.03210
$750$	−8.85275	−0.323257
$751$	20.8635	0.761321	0.380660	−	0.924715i	$-0.375697\pi$
$751$	20.8635	0.761321	0.380660	+	0.924715i	$0.375697\pi$
$752$	−7.16038	−0.261112
$753$	−1.05425	−0.0384190
$754$	−4.17989	−0.152222
$755$	−5.52704	−0.201150
$756$	−3.19729	−0.116284
$757$	8.93766	0.324845	0.162422	−	0.986721i	$-0.448069\pi$
$757$	8.93766	0.324845	0.162422	+	0.986721i	$0.448069\pi$
$758$	−29.5819	−1.07446
$759$	−10.2526	−0.372145
$760$	−1.79670	−0.0651731
$761$	−51.8674	−1.88019	−0.940096	−	0.340910i	$-0.889265\pi$
$761$	−51.8674	−1.88019	−0.940096	+	0.340910i	$0.889265\pi$
$762$	−15.7935	−0.572138
$763$	−20.0181	−0.724704
$764$	12.5265	0.453192
$765$	1.91125	0.0691015
$766$	−5.55285	−0.200633
$767$	−1.05612	−0.0381342
$768$	16.4318	0.592932
$769$	−13.1951	−0.475826	−0.237913	−	0.971286i	$-0.576463\pi$
$769$	−13.1951	−0.475826	−0.237913	+	0.971286i	$0.576463\pi$
$770$	−4.04247	−0.145680
$771$	−1.32938	−0.0478764
$772$	−16.1901	−0.582693
$773$	1.09411	0.0393524	0.0196762	−	0.999806i	$-0.493736\pi$
$773$	1.09411	0.0393524	0.0196762	+	0.999806i	$0.493736\pi$
$774$	0.966010	0.0347225
$775$	19.4293	0.697922
$776$	−14.9664	−0.537262
$777$	−6.19523	−0.222253
$778$	−2.86079	−0.102564
$779$	5.20740	0.186575
$780$	0.803047	0.0287537
$781$	−3.19707	−0.114400
$782$	19.7234	0.705308
$783$	−3.94970	−0.141151
$784$	−9.08472	−0.324454
$785$	18.2264	0.650529
$786$	4.72078	0.168385
$787$	47.3597	1.68819	0.844096	−	0.536193i	$-0.180138\pi$
$787$	47.3597	1.68819	0.844096	+	0.536193i	$0.180138\pi$
$788$	5.48489	0.195391
$789$	−11.4127	−0.406303
$790$	−1.22595	−0.0436174
$791$	34.0848	1.21192
$792$	3.51183	0.124788
$793$	4.06408	0.144320
$794$	−0.785604	−0.0278800
$795$	−2.87530	−0.101976
$796$	−11.1200	−0.394137
$797$	−32.5906	−1.15442	−0.577209	−	0.816596i	$-0.695858\pi$
$797$	−32.5906	−1.15442	−0.577209	+	0.816596i	$0.695858\pi$
$798$	−2.48380	−0.0879257
$799$	−10.2342	−0.362061
$800$	−18.9403	−0.669642
$801$	−15.4734	−0.546727
$802$	2.81455	0.0993851
$803$	1.80763	0.0637898
$804$	3.41189	0.120328
$805$	−29.4992	−1.03971
$806$	4.93400	0.173793
$807$	−25.9749	−0.914358
$808$	−33.8096	−1.18942
$809$	−1.17356	−0.0412601	−0.0206301	−	0.999787i	$-0.506567\pi$
$809$	−1.17356	−0.0412601	−0.0206301	+	0.999787i	$0.506567\pi$
$810$	−0.965685	−0.0339307
$811$	−24.8317	−0.871959	−0.435980	−	0.899957i	$-0.643598\pi$
$811$	−24.8317	−0.871959	−0.435980	+	0.899957i	$0.643598\pi$
$812$	12.6283	0.443168
$813$	16.4799	0.577976
$814$	2.07929	0.0728791
$815$	−13.4716	−0.471890
$816$	−3.06935	−0.107449
$817$	−0.589688	−0.0206306
$818$	16.1241	0.563765
$819$	3.63309	0.126951
$820$	−6.47324	−0.226055
$821$	49.4197	1.72476	0.862380	−	0.506261i	$-0.168973\pi$
$821$	49.4197	1.72476	0.862380	+	0.506261i	$0.168973\pi$
$822$	11.9732	0.417612
$823$	−44.0564	−1.53571	−0.767854	−	0.640625i	$-0.778675\pi$
$823$	−44.0564	−1.53571	−0.767854	+	0.640625i	$0.778675\pi$
$824$	−3.04789	−0.106178
$825$	−4.80168	−0.167173
$826$	−4.06059	−0.141286
$827$	−4.83406	−0.168097	−0.0840484	−	0.996462i	$-0.526785\pi$
$827$	−4.83406	−0.168097	−0.0840484	+	0.996462i	$0.526785\pi$
$828$	7.83077	0.272138
$829$	12.7858	0.444071	0.222035	−	0.975039i	$-0.428730\pi$
$829$	12.7858	0.444071	0.222035	+	0.975039i	$0.428730\pi$
$830$	−12.9063	−0.447984
$831$	4.87661	0.169168
$832$	−7.74068	−0.268360
$833$	−12.9847	−0.449892
$834$	−6.99686	−0.242281
$835$	−7.51165	−0.259951
$836$	−0.655059	−0.0226557
$837$	4.66229	0.161152
$838$	34.1156	1.17850
$839$	−18.6518	−0.643932	−0.321966	−	0.946751i	$-0.604344\pi$
$839$	−18.6518	−0.643932	−0.321966	+	0.946751i	$0.604344\pi$
$840$	10.1044	0.348636
$841$	−13.3998	−0.462064
$842$	−2.03287	−0.0700575
$843$	29.8226	1.02714
$844$	−13.6827	−0.470978
$845$	−0.912505	−0.0313911
$846$	5.17098	0.177782
$847$	35.1407	1.20745
$848$	4.61755	0.158567
$849$	8.51437	0.292212
$850$	9.23722	0.316834
$851$	15.1733	0.520133
$852$	2.44187	0.0836571
$853$	−43.9046	−1.50326	−0.751632	−	0.659582i	$-0.770733\pi$
$853$	−43.9046	−1.50326	−0.751632	+	0.659582i	$0.770733\pi$
$854$	15.6257	0.534700
$855$	0.589489	0.0201601
$856$	−46.6561	−1.59467
$857$	18.5751	0.634515	0.317257	−	0.948339i	$-0.397238\pi$
$857$	18.5751	0.634515	0.317257	+	0.948339i	$0.397238\pi$
$858$	−1.21937	−0.0416285
$859$	−55.1525	−1.88178	−0.940890	−	0.338712i	$-0.890009\pi$
$859$	−55.1525	−1.88178	−0.940890	+	0.338712i	$0.890009\pi$
$860$	0.733032	0.0249962
$861$	−29.2858	−0.998058
$862$	9.52288	0.324351
$863$	11.8656	0.403911	0.201955	−	0.979395i	$-0.435270\pi$
$863$	11.8656	0.403911	0.201955	+	0.979395i	$0.435270\pi$
$864$	−4.54495	−0.154622
$865$	−16.2836	−0.553658
$866$	−15.2927	−0.519666
$867$	12.6130	0.428360
$868$	−14.9067	−0.505966
$869$	−1.46276	−0.0496207
$870$	3.81417	0.129312
$871$	−3.87694	−0.131365
$872$	−16.7937	−0.568706
$873$	4.91041	0.166192
$874$	6.08330	0.205771
$875$	−30.3917	−1.02743
$876$	−1.38064	−0.0466475
$877$	−13.7934	−0.465771	−0.232886	−	0.972504i	$-0.574817\pi$
$877$	−13.7934	−0.465771	−0.232886	+	0.972504i	$0.574817\pi$
$878$	−4.66893	−0.157569
$879$	−17.9383	−0.605042
$880$	−1.54076	−0.0519388
$881$	35.0062	1.17939	0.589694	−	0.807627i	$-0.299248\pi$
$881$	35.0062	1.17939	0.589694	+	0.807627i	$0.299248\pi$
$882$	6.56066	0.220909
$883$	7.56853	0.254701	0.127351	−	0.991858i	$-0.459353\pi$
$883$	7.56853	0.254701	0.127351	+	0.991858i	$0.459353\pi$
$884$	−1.84327	−0.0619958
$885$	0.963713	0.0323948
$886$	15.6318	0.525162
$887$	−38.7055	−1.29960	−0.649801	−	0.760104i	$-0.725148\pi$
$887$	−38.7055	−1.29960	−0.649801	+	0.760104i	$0.725148\pi$
$888$	−5.19733	−0.174411
$889$	−54.2194	−1.81846
$890$	14.9424	0.500872
$891$	−1.15222	−0.0386007
$892$	−1.63164	−0.0546314
$893$	−3.15655	−0.105630
$894$	8.38987	0.280599
$895$	7.81571	0.261250
$896$	3.26293	0.109007
$897$	−8.89813	−0.297100
$898$	−27.0727	−0.903429
$899$	−18.4147	−0.614163
$900$	3.66745	0.122248
$901$	6.59980	0.219871
$902$	9.82913	0.327274
$903$	3.31633	0.110361
$904$	28.5946	0.951041
$905$	17.0440	0.566563
$906$	−6.40999	−0.212958
$907$	−36.4509	−1.21033	−0.605167	−	0.796099i	$-0.706894\pi$
$907$	−36.4509	−1.21033	−0.605167	+	0.796099i	$0.706894\pi$
$908$	−0.00545224	−0.000180939 0
$909$	11.0928	0.367925
$910$	−3.50842	−0.116303
$911$	−18.2314	−0.604032	−0.302016	−	0.953303i	$-0.597660\pi$
$911$	−18.2314	−0.604032	−0.302016	+	0.953303i	$0.597660\pi$
$912$	−0.946682	−0.0313478
$913$	−15.3993	−0.509642
$914$	−19.9636	−0.660339
$915$	−3.70850	−0.122599
$916$	18.3500	0.606302
$917$	16.2065	0.535187
$918$	2.21658	0.0731580
$919$	20.6215	0.680239	0.340120	−	0.940382i	$-0.389532\pi$
$919$	20.6215	0.680239	0.340120	+	0.940382i	$0.389532\pi$
$920$	−24.7476	−0.815905
$921$	13.1960	0.434822
$922$	7.59082	0.249990
$923$	−2.77471	−0.0913306
$924$	3.68398	0.121194
$925$	7.10623	0.233651
$926$	−24.9605	−0.820253
$927$	1.00000	0.0328443
$928$	17.9512	0.589278
$929$	28.0681	0.920884	0.460442	−	0.887690i	$-0.347691\pi$
$929$	28.0681	0.920884	0.460442	+	0.887690i	$0.347691\pi$
$930$	−4.50230	−0.147636
$931$	−4.00487	−0.131254
$932$	14.5187	0.475575
$933$	11.8366	0.387514
$934$	−35.7620	−1.17017
$935$	−2.20218	−0.0720190
$936$	3.04789	0.0996234
$937$	−37.8188	−1.23549	−0.617743	−	0.786380i	$-0.711953\pi$
$937$	−37.8188	−1.23549	−0.617743	+	0.786380i	$0.711953\pi$
$938$	−14.9062	−0.486704
$939$	14.8906	0.485936
$940$	3.92386	0.127982
$941$	21.1615	0.689846	0.344923	−	0.938631i	$-0.387905\pi$
$941$	21.1615	0.689846	0.344923	+	0.938631i	$0.387905\pi$
$942$	21.1381	0.688717
$943$	71.7265	2.33574
$944$	−1.54766	−0.0503721
$945$	−3.31522	−0.107844
$946$	−1.11305	−0.0361885
$947$	29.6597	0.963811	0.481905	−	0.876223i	$-0.339945\pi$
$947$	29.6597	0.963811	0.481905	+	0.876223i	$0.339945\pi$
$948$	1.11723	0.0362860
$949$	1.56883	0.0509262
$950$	2.84904	0.0924351
$951$	−14.5587	−0.472099
$952$	−23.1931	−0.751693
$953$	−11.5483	−0.374086	−0.187043	−	0.982352i	$-0.559890\pi$
$953$	−11.5483	−0.374086	−0.187043	+	0.982352i	$0.559890\pi$
$954$	−3.33463	−0.107963
$955$	12.9885	0.420298
$956$	10.2130	0.330312
$957$	4.55092	0.147110
$958$	−20.3586	−0.657757
$959$	41.1042	1.32732
$960$	7.06341	0.227971
$961$	−9.26306	−0.298808
$962$	1.80460	0.0581826
$963$	15.3077	0.493282
$964$	6.42673	0.206991
$965$	−16.7872	−0.540399
$966$	−34.2118	−1.10075
$967$	52.3562	1.68366	0.841831	−	0.539741i	$-0.181478\pi$
$967$	52.3562	1.68366	0.841831	+	0.539741i	$0.181478\pi$
$968$	29.4804	0.947536
$969$	−1.35308	−0.0434672
$970$	−4.74191	−0.152253
$971$	−13.0417	−0.418527	−0.209264	−	0.977859i	$-0.567107\pi$
$971$	−13.0417	−0.418527	−0.209264	+	0.977859i	$0.567107\pi$
$972$	0.880046	0.0282275
$973$	−24.0204	−0.770057
$974$	25.9294	0.830831
$975$	−4.16733	−0.133462
$976$	5.95561	0.190634
$977$	−35.6600	−1.14087	−0.570433	−	0.821344i	$-0.693225\pi$
$977$	−35.6600	−1.14087	−0.570433	+	0.821344i	$0.693225\pi$
$978$	−15.6237	−0.499591
$979$	17.8288	0.569809
$980$	4.97839	0.159029
$981$	5.50994	0.175919
$982$	30.4787	0.972616
$983$	42.1476	1.34430	0.672150	−	0.740415i	$-0.265371\pi$
$983$	42.1476	1.34430	0.672150	+	0.740415i	$0.265371\pi$
$984$	−24.5686	−0.783218
$985$	5.68719	0.181209
$986$	−8.75483	−0.278810
$987$	17.7521	0.565055
$988$	−0.568521	−0.0180870
$989$	−8.12233	−0.258275
$990$	1.11268	0.0353633
$991$	8.97040	0.284954	0.142477	−	0.989798i	$-0.454493\pi$
$991$	8.97040	0.284954	0.142477	+	0.989798i	$0.454493\pi$
$992$	−21.1899	−0.672780
$993$	−1.62408	−0.0515385
$994$	−10.6683	−0.338377
$995$	−11.5301	−0.365529
$996$	11.7617	0.372685
$997$	1.39992	0.0443358	0.0221679	−	0.999754i	$-0.492943\pi$
$997$	1.39992	0.0443358	0.0221679	+	0.999754i	$0.492943\pi$
$998$	−6.11220	−0.193478
$999$	1.70522	0.0539508

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4017.2.a.g.1.16	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4017.2.a.g.1.16	✓	24	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:	\( N \)	\(=\)	\( 4017 = 3 \cdot 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4017.a (trivial)

\(f(q)\)	\(=\)	\(q+1.05828 q^{2} -1.00000 q^{3} -0.880046 q^{4} -0.912505 q^{5} -1.05828 q^{6} -3.63309 q^{7} -3.04789 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.05828 q^{2} -1.00000 q^{3} -0.880046 q^{4} -0.912505 q^{5} -1.05828 q^{6} -3.63309 q^{7} -3.04789 q^{8} +1.00000 q^{9} -0.965685 q^{10} -1.15222 q^{11} +0.880046 q^{12} -1.00000 q^{13} -3.84483 q^{14} +0.912505 q^{15} -1.46543 q^{16} -2.09451 q^{17} +1.05828 q^{18} -0.646012 q^{19} +0.803047 q^{20} +3.63309 q^{21} -1.21937 q^{22} -8.89813 q^{23} +3.04789 q^{24} -4.16733 q^{25} -1.05828 q^{26} -1.00000 q^{27} +3.19729 q^{28} +3.94970 q^{29} +0.965685 q^{30} -4.66229 q^{31} +4.54495 q^{32} +1.15222 q^{33} -2.21658 q^{34} +3.31522 q^{35} -0.880046 q^{36} -1.70522 q^{37} -0.683661 q^{38} +1.00000 q^{39} +2.78122 q^{40} -8.06085 q^{41} +3.84483 q^{42} +0.912813 q^{43} +1.01401 q^{44} -0.912505 q^{45} -9.41670 q^{46} +4.88621 q^{47} +1.46543 q^{48} +6.19937 q^{49} -4.41020 q^{50} +2.09451 q^{51} +0.880046 q^{52} -3.15100 q^{53} -1.05828 q^{54} +1.05140 q^{55} +11.0733 q^{56} +0.646012 q^{57} +4.17989 q^{58} +1.05612 q^{59} -0.803047 q^{60} -4.06408 q^{61} -4.93400 q^{62} -3.63309 q^{63} +7.74068 q^{64} +0.912505 q^{65} +1.21937 q^{66} +3.87694 q^{67} +1.84327 q^{68} +8.89813 q^{69} +3.50842 q^{70} +2.77471 q^{71} -3.04789 q^{72} -1.56883 q^{73} -1.80460 q^{74} +4.16733 q^{75} +0.568521 q^{76} +4.18612 q^{77} +1.05828 q^{78} +1.26952 q^{79} +1.33721 q^{80} +1.00000 q^{81} -8.53062 q^{82} +13.3649 q^{83} -3.19729 q^{84} +1.91125 q^{85} +0.966010 q^{86} -3.94970 q^{87} +3.51183 q^{88} -15.4734 q^{89} -0.965685 q^{90} +3.63309 q^{91} +7.83077 q^{92} +4.66229 q^{93} +5.17098 q^{94} +0.589489 q^{95} -4.54495 q^{96} +4.91041 q^{97} +6.56066 q^{98} -1.15222 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 3 q^{2} - 24 q^{3} + 25 q^{4} + 3 q^{5} - 3 q^{6} + 11 q^{7} + 6 q^{8} + 24 q^{9}+O(q^{10}) \) 24 * q + 3 * q^2 - 24 * q^3 + 25 * q^4 + 3 * q^5 - 3 * q^6 + 11 * q^7 + 6 * q^8 + 24 * q^9	\( 24 q + 3 q^{2} - 24 q^{3} + 25 q^{4} + 3 q^{5} - 3 q^{6} + 11 q^{7} + 6 q^{8} + 24 q^{9} - 2 q^{10} + 7 q^{11} - 25 q^{12} - 24 q^{13} + 8 q^{14} - 3 q^{15} + 23 q^{16} + 4 q^{17} + 3 q^{18} - 20 q^{19} + 8 q^{20} - 11 q^{21} + 5 q^{22} + 41 q^{23} - 6 q^{24} + 23 q^{25} - 3 q^{26} - 24 q^{27} + 16 q^{28} + 12 q^{29} + 2 q^{30} + 2 q^{31} + 25 q^{32} - 7 q^{33} - 11 q^{34} + 36 q^{35} + 25 q^{36} + 18 q^{37} + 10 q^{38} + 24 q^{39} + 14 q^{40} - 9 q^{41} - 8 q^{42} + 23 q^{43} + 41 q^{44} + 3 q^{45} + 7 q^{46} + 32 q^{47} - 23 q^{48} + 11 q^{49} + 26 q^{50} - 4 q^{51} - 25 q^{52} + 46 q^{53} - 3 q^{54} + 18 q^{55} + 26 q^{56} + 20 q^{57} + 37 q^{58} - 12 q^{59} - 8 q^{60} - q^{61} + 53 q^{62} + 11 q^{63} + 26 q^{64} - 3 q^{65} - 5 q^{66} + 8 q^{67} + 6 q^{68} - 41 q^{69} + 19 q^{70} + 20 q^{71} + 6 q^{72} + 12 q^{73} + 86 q^{74} - 23 q^{75} - 28 q^{76} + 23 q^{77} + 3 q^{78} + 27 q^{79} + 6 q^{80} + 24 q^{81} - 28 q^{82} + 33 q^{83} - 16 q^{84} - 13 q^{85} + 63 q^{86} - 12 q^{87} + 11 q^{88} - 2 q^{90} - 11 q^{91} + 79 q^{92} - 2 q^{93} - 12 q^{94} + 37 q^{95} - 25 q^{96} - 14 q^{97} + 20 q^{98} + 7 q^{99}+O(q^{100}) \) 24 * q + 3 * q^2 - 24 * q^3 + 25 * q^4 + 3 * q^5 - 3 * q^6 + 11 * q^7 + 6 * q^8 + 24 * q^9 - 2 * q^10 + 7 * q^11 - 25 * q^12 - 24 * q^13 + 8 * q^14 - 3 * q^15 + 23 * q^16 + 4 * q^17 + 3 * q^18 - 20 * q^19 + 8 * q^20 - 11 * q^21 + 5 * q^22 + 41 * q^23 - 6 * q^24 + 23 * q^25 - 3 * q^26 - 24 * q^27 + 16 * q^28 + 12 * q^29 + 2 * q^30 + 2 * q^31 + 25 * q^32 - 7 * q^33 - 11 * q^34 + 36 * q^35 + 25 * q^36 + 18 * q^37 + 10 * q^38 + 24 * q^39 + 14 * q^40 - 9 * q^41 - 8 * q^42 + 23 * q^43 + 41 * q^44 + 3 * q^45 + 7 * q^46 + 32 * q^47 - 23 * q^48 + 11 * q^49 + 26 * q^50 - 4 * q^51 - 25 * q^52 + 46 * q^53 - 3 * q^54 + 18 * q^55 + 26 * q^56 + 20 * q^57 + 37 * q^58 - 12 * q^59 - 8 * q^60 - q^61 + 53 * q^62 + 11 * q^63 + 26 * q^64 - 3 * q^65 - 5 * q^66 + 8 * q^67 + 6 * q^68 - 41 * q^69 + 19 * q^70 + 20 * q^71 + 6 * q^72 + 12 * q^73 + 86 * q^74 - 23 * q^75 - 28 * q^76 + 23 * q^77 + 3 * q^78 + 27 * q^79 + 6 * q^80 + 24 * q^81 - 28 * q^82 + 33 * q^83 - 16 * q^84 - 13 * q^85 + 63 * q^86 - 12 * q^87 + 11 * q^88 - 2 * q^90 - 11 * q^91 + 79 * q^92 - 2 * q^93 - 12 * q^94 + 37 * q^95 - 25 * q^96 - 14 * q^97 + 20 * q^98 + 7 * q^99

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