LMFDB - Embedded newform 4017.2.a.l.1.8

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:	$32$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
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)

$f(q)$	$=$	$q-1.78664 q^{2} +1.00000 q^{3} +1.19208 q^{4} -1.81642 q^{5} -1.78664 q^{6} -4.42230 q^{7} +1.44346 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.78664 q^{2} +1.00000 q^{3} +1.19208 q^{4} -1.81642 q^{5} -1.78664 q^{6} -4.42230 q^{7} +1.44346 q^{8} +1.00000 q^{9} +3.24528 q^{10} +2.59918 q^{11} +1.19208 q^{12} -1.00000 q^{13} +7.90106 q^{14} -1.81642 q^{15} -4.96311 q^{16} -5.46728 q^{17} -1.78664 q^{18} -1.26902 q^{19} -2.16531 q^{20} -4.42230 q^{21} -4.64380 q^{22} +0.290604 q^{23} +1.44346 q^{24} -1.70063 q^{25} +1.78664 q^{26} +1.00000 q^{27} -5.27173 q^{28} -6.07278 q^{29} +3.24528 q^{30} -8.48304 q^{31} +5.98035 q^{32} +2.59918 q^{33} +9.76805 q^{34} +8.03274 q^{35} +1.19208 q^{36} +5.68870 q^{37} +2.26728 q^{38} -1.00000 q^{39} -2.62193 q^{40} -6.27485 q^{41} +7.90106 q^{42} +6.20194 q^{43} +3.09843 q^{44} -1.81642 q^{45} -0.519204 q^{46} +4.34627 q^{47} -4.96311 q^{48} +12.5568 q^{49} +3.03841 q^{50} -5.46728 q^{51} -1.19208 q^{52} +6.90863 q^{53} -1.78664 q^{54} -4.72120 q^{55} -6.38344 q^{56} -1.26902 q^{57} +10.8499 q^{58} -2.23980 q^{59} -2.16531 q^{60} +9.53707 q^{61} +15.1561 q^{62} -4.42230 q^{63} -0.758508 q^{64} +1.81642 q^{65} -4.64380 q^{66} -11.7505 q^{67} -6.51742 q^{68} +0.290604 q^{69} -14.3516 q^{70} -0.639653 q^{71} +1.44346 q^{72} -14.4100 q^{73} -10.1637 q^{74} -1.70063 q^{75} -1.51277 q^{76} -11.4944 q^{77} +1.78664 q^{78} +17.0632 q^{79} +9.01507 q^{80} +1.00000 q^{81} +11.2109 q^{82} -8.05185 q^{83} -5.27173 q^{84} +9.93085 q^{85} -11.0806 q^{86} -6.07278 q^{87} +3.75183 q^{88} -14.4519 q^{89} +3.24528 q^{90} +4.42230 q^{91} +0.346422 q^{92} -8.48304 q^{93} -7.76521 q^{94} +2.30507 q^{95} +5.98035 q^{96} +0.872842 q^{97} -22.4344 q^{98} +2.59918 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 5 q^{2} + 32 q^{3} + 45 q^{4} + q^{5} + 5 q^{6} + 11 q^{7} + 12 q^{8} + 32 q^{9}+O(q^{10}) $ 32 * q + 5 * q^2 + 32 * q^3 + 45 * q^4 + q^5 + 5 * q^6 + 11 * q^7 + 12 * q^8 + 32 * q^9	\( 32 q + 5 q^{2} + 32 q^{3} + 45 q^{4} + q^{5} + 5 q^{6} + 11 q^{7} + 12 q^{8} + 32 q^{9} + 16 q^{10} + 3 q^{11} + 45 q^{12} - 32 q^{13} + 12 q^{14} + q^{15} + 75 q^{16} + 10 q^{17} + 5 q^{18} + 4 q^{20} + 11 q^{21} + 27 q^{22} + 53 q^{23} + 12 q^{24} + 67 q^{25} - 5 q^{26} + 32 q^{27} + 32 q^{28} + 6 q^{29} + 16 q^{30} + 12 q^{31} + 19 q^{32} + 3 q^{33} + 25 q^{34} + 16 q^{35} + 45 q^{36} + 36 q^{37} + 8 q^{38} - 32 q^{39} + 36 q^{40} - 19 q^{41} + 12 q^{42} + 43 q^{43} - 23 q^{44} + q^{45} + 11 q^{46} + 30 q^{47} + 75 q^{48} + 75 q^{49} + 28 q^{50} + 10 q^{51} - 45 q^{52} + 22 q^{53} + 5 q^{54} + 58 q^{55} + 60 q^{56} + 33 q^{58} - 24 q^{59} + 4 q^{60} + 47 q^{61} - 25 q^{62} + 11 q^{63} + 146 q^{64} - q^{65} + 27 q^{66} + 34 q^{67} + 58 q^{68} + 53 q^{69} - 35 q^{70} + 18 q^{71} + 12 q^{72} - 2 q^{73} - 20 q^{74} + 67 q^{75} + 24 q^{76} + 39 q^{77} - 5 q^{78} + 39 q^{79} + 2 q^{80} + 32 q^{81} + 64 q^{82} + 17 q^{83} + 32 q^{84} + 35 q^{85} - 13 q^{86} + 6 q^{87} + 55 q^{88} - 48 q^{89} + 16 q^{90} - 11 q^{91} + 39 q^{92} + 12 q^{93} + 58 q^{94} + 59 q^{95} + 19 q^{96} + 42 q^{97} + 16 q^{98} + 3 q^{99}+O(q^{100}) \) 32 * q + 5 * q^2 + 32 * q^3 + 45 * q^4 + q^5 + 5 * q^6 + 11 * q^7 + 12 * q^8 + 32 * q^9 + 16 * q^10 + 3 * q^11 + 45 * q^12 - 32 * q^13 + 12 * q^14 + q^15 + 75 * q^16 + 10 * q^17 + 5 * q^18 + 4 * q^20 + 11 * q^21 + 27 * q^22 + 53 * q^23 + 12 * q^24 + 67 * q^25 - 5 * q^26 + 32 * q^27 + 32 * q^28 + 6 * q^29 + 16 * q^30 + 12 * q^31 + 19 * q^32 + 3 * q^33 + 25 * q^34 + 16 * q^35 + 45 * q^36 + 36 * q^37 + 8 * q^38 - 32 * q^39 + 36 * q^40 - 19 * q^41 + 12 * q^42 + 43 * q^43 - 23 * q^44 + q^45 + 11 * q^46 + 30 * q^47 + 75 * q^48 + 75 * q^49 + 28 * q^50 + 10 * q^51 - 45 * q^52 + 22 * q^53 + 5 * q^54 + 58 * q^55 + 60 * q^56 + 33 * q^58 - 24 * q^59 + 4 * q^60 + 47 * q^61 - 25 * q^62 + 11 * q^63 + 146 * q^64 - q^65 + 27 * q^66 + 34 * q^67 + 58 * q^68 + 53 * q^69 - 35 * q^70 + 18 * q^71 + 12 * q^72 - 2 * q^73 - 20 * q^74 + 67 * q^75 + 24 * q^76 + 39 * q^77 - 5 * q^78 + 39 * q^79 + 2 * q^80 + 32 * q^81 + 64 * q^82 + 17 * q^83 + 32 * q^84 + 35 * q^85 - 13 * q^86 + 6 * q^87 + 55 * q^88 - 48 * q^89 + 16 * q^90 - 11 * q^91 + 39 * q^92 + 12 * q^93 + 58 * q^94 + 59 * q^95 + 19 * q^96 + 42 * q^97 + 16 * q^98 + 3 * 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 $

$2$	−1.78664	−1.26334	−0.631672	−	0.775236i	$-0.717631\pi$
$2$	−1.78664	−1.26334	−0.631672	+	0.775236i	$0.717631\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.19208	0.596039
$5$	−1.81642	−0.812326	−0.406163	−	0.913801i	$-0.633134\pi$
$5$	−1.81642	−0.812326	−0.406163	+	0.913801i	$0.633134\pi$
$6$	−1.78664	−0.729392
$7$	−4.42230	−1.67147	−0.835737	−	0.549130i	$-0.814959\pi$
$7$	−4.42230	−1.67147	−0.835737	+	0.549130i	$0.814959\pi$
$8$	1.44346	0.510342
$9$	1.00000	0.333333
$10$	3.24528	1.02625
$11$	2.59918	0.783683	0.391842	−	0.920033i	$-0.371838\pi$
$11$	2.59918	0.783683	0.391842	+	0.920033i	$0.371838\pi$
$12$	1.19208	0.344123
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	7.90106	2.11165
$15$	−1.81642	−0.468997
$16$	−4.96311	−1.24078
$17$	−5.46728	−1.32601	−0.663005	−	0.748615i	$-0.730719\pi$
$17$	−5.46728	−1.32601	−0.663005	+	0.748615i	$0.730719\pi$
$18$	−1.78664	−0.421115
$19$	−1.26902	−0.291133	−0.145566	−	0.989348i	$-0.546500\pi$
$19$	−1.26902	−0.291133	−0.145566	+	0.989348i	$0.546500\pi$
$20$	−2.16531	−0.484178
$21$	−4.42230	−0.965026
$22$	−4.64380	−0.990062
$23$	0.290604	0.0605951	0.0302975	−	0.999541i	$-0.490355\pi$
$23$	0.290604	0.0605951	0.0302975	+	0.999541i	$0.490355\pi$
$24$	1.44346	0.294646
$25$	−1.70063	−0.340126
$26$	1.78664	0.350389
$27$	1.00000	0.192450
$28$	−5.27173	−0.996263
$29$	−6.07278	−1.12769	−0.563844	−	0.825882i	$-0.690678\pi$
$29$	−6.07278	−1.12769	−0.563844	+	0.825882i	$0.690678\pi$
$30$	3.24528	0.592504
$31$	−8.48304	−1.52360	−0.761799	−	0.647813i	$-0.775684\pi$
$31$	−8.48304	−1.52360	−0.761799	+	0.647813i	$0.775684\pi$
$32$	5.98035	1.05719
$33$	2.59918	0.452460
$34$	9.76805	1.67521
$35$	8.03274	1.35778
$36$	1.19208	0.198680
$37$	5.68870	0.935217	0.467609	−	0.883936i	$-0.345116\pi$
$37$	5.68870	0.935217	0.467609	+	0.883936i	$0.345116\pi$
$38$	2.26728	0.367801
$39$	−1.00000	−0.160128
$40$	−2.62193	−0.414564
$41$	−6.27485	−0.979967	−0.489983	−	0.871732i	$-0.662997\pi$
$41$	−6.27485	−0.979967	−0.489983	+	0.871732i	$0.662997\pi$
$42$	7.90106	1.21916
$43$	6.20194	0.945786	0.472893	−	0.881120i	$-0.343210\pi$
$43$	6.20194	0.945786	0.472893	+	0.881120i	$0.343210\pi$
$44$	3.09843	0.467106
$45$	−1.81642	−0.270775
$46$	−0.519204	−0.0765524
$47$	4.34627	0.633968	0.316984	−	0.948431i	$-0.397330\pi$
$47$	4.34627	0.633968	0.316984	+	0.948431i	$0.397330\pi$
$48$	−4.96311	−0.716363
$49$	12.5568	1.79382
$50$	3.03841	0.429697
$51$	−5.46728	−0.765572
$52$	−1.19208	−0.165311
$53$	6.90863	0.948973	0.474487	−	0.880263i	$-0.342634\pi$
$53$	6.90863	0.948973	0.474487	+	0.880263i	$0.342634\pi$
$54$	−1.78664	−0.243131
$55$	−4.72120	−0.636606
$56$	−6.38344	−0.853023
$57$	−1.26902	−0.168086
$58$	10.8499	1.42466
$59$	−2.23980	−0.291597	−0.145798	−	0.989314i	$-0.546575\pi$
$59$	−2.23980	−0.291597	−0.145798	+	0.989314i	$0.546575\pi$
$60$	−2.16531	−0.279540
$61$	9.53707	1.22110	0.610548	−	0.791979i	$-0.290949\pi$
$61$	9.53707	1.22110	0.610548	+	0.791979i	$0.290949\pi$
$62$	15.1561	1.92483
$63$	−4.42230	−0.557158
$64$	−0.758508	−0.0948136
$65$	1.81642	0.225299
$66$	−4.64380	−0.571612
$67$	−11.7505	−1.43556	−0.717779	−	0.696271i	$-0.754841\pi$
$67$	−11.7505	−1.43556	−0.717779	+	0.696271i	$0.754841\pi$
$68$	−6.51742	−0.790353
$69$	0.290604	0.0349846
$70$	−14.3516	−1.71535
$71$	−0.639653	−0.0759128	−0.0379564	−	0.999279i	$-0.512085\pi$
$71$	−0.639653	−0.0759128	−0.0379564	+	0.999279i	$0.512085\pi$
$72$	1.44346	0.170114
$73$	−14.4100	−1.68656	−0.843279	−	0.537477i	$-0.819378\pi$
$73$	−14.4100	−1.68656	−0.843279	+	0.537477i	$0.819378\pi$
$74$	−10.1637	−1.18150
$75$	−1.70063	−0.196372
$76$	−1.51277	−0.173527
$77$	−11.4944	−1.30991
$78$	1.78664	0.202297
$79$	17.0632	1.91976	0.959880	−	0.280410i	$-0.0904705\pi$
$79$	17.0632	1.91976	0.959880	+	0.280410i	$0.0904705\pi$
$80$	9.01507	1.00792
$81$	1.00000	0.111111
$82$	11.2109	1.23804
$83$	−8.05185	−0.883806	−0.441903	−	0.897063i	$-0.645696\pi$
$83$	−8.05185	−0.883806	−0.441903	+	0.897063i	$0.645696\pi$
$84$	−5.27173	−0.575193
$85$	9.93085	1.07715
$86$	−11.0806	−1.19485
$87$	−6.07278	−0.651071
$88$	3.75183	0.399946
$89$	−14.4519	−1.53190	−0.765949	−	0.642902i	$-0.777730\pi$
$89$	−14.4519	−1.53190	−0.765949	+	0.642902i	$0.777730\pi$
$90$	3.24528	0.342083
$91$	4.42230	0.463583
$92$	0.346422	0.0361170
$93$	−8.48304	−0.879650
$94$	−7.76521	−0.800920
$95$	2.30507	0.236495
$96$	5.98035	0.610367
$97$	0.872842	0.0886237	0.0443119	−	0.999018i	$-0.485890\pi$
$97$	0.872842	0.0886237	0.0443119	+	0.999018i	$0.485890\pi$
$98$	−22.4344	−2.26622
$99$	2.59918	0.261228
$100$	−2.02729	−0.202729
$101$	−11.0407	−1.09859	−0.549293	−	0.835630i	$-0.685103\pi$
$101$	−11.0407	−1.09859	−0.549293	+	0.835630i	$0.685103\pi$
$102$	9.76805	0.967181
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	−1.44346	−0.141543
$105$	8.03274	0.783916
$106$	−12.3432	−1.19888
$107$	−20.2273	−1.95544	−0.977722	−	0.209905i	$-0.932684\pi$
$107$	−20.2273	−1.95544	−0.977722	+	0.209905i	$0.932684\pi$
$108$	1.19208	0.114708
$109$	−1.89462	−0.181472	−0.0907359	−	0.995875i	$-0.528922\pi$
$109$	−1.89462	−0.181472	−0.0907359	+	0.995875i	$0.528922\pi$
$110$	8.43508	0.804253
$111$	5.68870	0.539948
$112$	21.9484	2.07393
$113$	6.29495	0.592179	0.296089	−	0.955160i	$-0.404317\pi$
$113$	6.29495	0.592179	0.296089	+	0.955160i	$0.404317\pi$
$114$	2.26728	0.212350
$115$	−0.527857	−0.0492230
$116$	−7.23923	−0.672146
$117$	−1.00000	−0.0924500
$118$	4.00171	0.368387
$119$	24.1780	2.21639
$120$	−2.62193	−0.239349
$121$	−4.24425	−0.385841
$122$	−17.0393	−1.54267
$123$	−6.27485	−0.565784
$124$	−10.1124	−0.908124
$125$	12.1711	1.08862
$126$	7.90106	0.703882
$127$	2.29762	0.203881	0.101940	−	0.994790i	$-0.467495\pi$
$127$	2.29762	0.203881	0.101940	+	0.994790i	$0.467495\pi$
$128$	−10.6055	−0.937404
$129$	6.20194	0.546050
$130$	−3.24528	−0.284630
$131$	−19.1912	−1.67675	−0.838373	−	0.545097i	$-0.816493\pi$
$131$	−19.1912	−1.67675	−0.838373	+	0.545097i	$0.816493\pi$
$132$	3.09843	0.269684
$133$	5.61199	0.486621
$134$	20.9940	1.81360
$135$	−1.81642	−0.156332
$136$	−7.89182	−0.676718
$137$	22.4046	1.91416	0.957078	−	0.289831i	$-0.0935992\pi$
$137$	22.4046	1.91416	0.957078	+	0.289831i	$0.0935992\pi$
$138$	−0.519204	−0.0441976
$139$	−3.94775	−0.334844	−0.167422	−	0.985885i	$-0.553544\pi$
$139$	−3.94775	−0.334844	−0.167422	+	0.985885i	$0.553544\pi$
$140$	9.57566	0.809291
$141$	4.34627	0.366022
$142$	1.14283	0.0959041
$143$	−2.59918	−0.217355
$144$	−4.96311	−0.413592
$145$	11.0307	0.916050
$146$	25.7454	2.13070
$147$	12.5568	1.03566
$148$	6.78138	0.557426
$149$	12.7359	1.04337	0.521684	−	0.853139i	$-0.325304\pi$
$149$	12.7359	1.04337	0.521684	+	0.853139i	$0.325304\pi$
$150$	3.03841	0.248085
$151$	1.21645	0.0989936	0.0494968	−	0.998774i	$-0.484238\pi$
$151$	1.21645	0.0989936	0.0494968	+	0.998774i	$0.484238\pi$
$152$	−1.83178	−0.148577
$153$	−5.46728	−0.442003
$154$	20.5363	1.65486
$155$	15.4087	1.23766
$156$	−1.19208	−0.0954426
$157$	21.5060	1.71637	0.858185	−	0.513341i	$-0.171592\pi$
$157$	21.5060	1.71637	0.858185	+	0.513341i	$0.171592\pi$
$158$	−30.4858	−2.42532
$159$	6.90863	0.547890
$160$	−10.8628	−0.858780
$161$	−1.28514	−0.101283
$162$	−1.78664	−0.140372
$163$	18.7526	1.46882	0.734409	−	0.678708i	$-0.237460\pi$
$163$	18.7526	1.46882	0.734409	+	0.678708i	$0.237460\pi$
$164$	−7.48011	−0.584098
$165$	−4.72120	−0.367545
$166$	14.3858	1.11655
$167$	−20.2073	−1.56369	−0.781844	−	0.623474i	$-0.785721\pi$
$167$	−20.2073	−1.56369	−0.781844	+	0.623474i	$0.785721\pi$
$168$	−6.38344	−0.492493
$169$	1.00000	0.0769231
$170$	−17.7428	−1.36081
$171$	−1.26902	−0.0970443
$172$	7.39319	0.563725
$173$	12.6755	0.963698	0.481849	−	0.876254i	$-0.339965\pi$
$173$	12.6755	0.963698	0.481849	+	0.876254i	$0.339965\pi$
$174$	10.8499	0.822526
$175$	7.52071	0.568512
$176$	−12.9000	−0.972376
$177$	−2.23980	−0.168353
$178$	25.8203	1.93531
$179$	19.5083	1.45812	0.729060	−	0.684450i	$-0.239958\pi$
$179$	19.5083	1.45812	0.729060	+	0.684450i	$0.239958\pi$
$180$	−2.16531	−0.161393
$181$	8.37500	0.622509	0.311255	−	0.950327i	$-0.399251\pi$
$181$	8.37500	0.622509	0.311255	+	0.950327i	$0.399251\pi$
$182$	−7.90106	−0.585665
$183$	9.53707	0.705000
$184$	0.419476	0.0309242
$185$	−10.3331	−0.759701
$186$	15.1561	1.11130
$187$	−14.2105	−1.03917
$188$	5.18109	0.377870
$189$	−4.42230	−0.321675
$190$	−4.11832	−0.298774
$191$	−13.2689	−0.960107	−0.480053	−	0.877239i	$-0.659383\pi$
$191$	−13.2689	−0.960107	−0.480053	+	0.877239i	$0.659383\pi$
$192$	−0.758508	−0.0547406
$193$	20.4664	1.47320	0.736602	−	0.676326i	$-0.236429\pi$
$193$	20.4664	1.47320	0.736602	+	0.676326i	$0.236429\pi$
$194$	−1.55945	−0.111962
$195$	1.81642	0.130076
$196$	14.9686	1.06919
$197$	−8.39273	−0.597957	−0.298979	−	0.954260i	$-0.596646\pi$
$197$	−8.39273	−0.597957	−0.298979	+	0.954260i	$0.596646\pi$
$198$	−4.64380	−0.330021
$199$	17.0690	1.20999	0.604993	−	0.796231i	$-0.293176\pi$
$199$	17.0690	1.20999	0.604993	+	0.796231i	$0.293176\pi$
$200$	−2.45480	−0.173581
$201$	−11.7505	−0.828820
$202$	19.7257	1.38789
$203$	26.8557	1.88490
$204$	−6.51742	−0.456311
$205$	11.3977	0.796052
$206$	1.78664	0.124481
$207$	0.290604	0.0201984
$208$	4.96311	0.344129
$209$	−3.29841	−0.228156
$210$	−14.3516	−0.990355
$211$	23.3453	1.60715	0.803577	−	0.595201i	$-0.202928\pi$
$211$	23.3453	1.60715	0.803577	+	0.595201i	$0.202928\pi$
$212$	8.23562	0.565625
$213$	−0.639653	−0.0438283
$214$	36.1388	2.47040
$215$	−11.2653	−0.768287
$216$	1.44346	0.0982153
$217$	37.5146	2.54666
$218$	3.38500	0.229261
$219$	−14.4100	−0.973734
$220$	−5.62804	−0.379442
$221$	5.46728	0.367769
$222$	−10.1637	−0.682140
$223$	−19.2591	−1.28969	−0.644843	−	0.764315i	$-0.723077\pi$
$223$	−19.2591	−1.28969	−0.644843	+	0.764315i	$0.723077\pi$
$224$	−26.4469	−1.76706
$225$	−1.70063	−0.113375
$226$	−11.2468	−0.748126
$227$	25.5588	1.69639	0.848197	−	0.529680i	$-0.177688\pi$
$227$	25.5588	1.69639	0.848197	+	0.529680i	$0.177688\pi$
$228$	−1.51277	−0.100186
$229$	−17.1157	−1.13104	−0.565518	−	0.824736i	$-0.691324\pi$
$229$	−17.1157	−1.13104	−0.565518	+	0.824736i	$0.691324\pi$
$230$	0.943091	0.0621855
$231$	−11.4944	−0.756274
$232$	−8.76585	−0.575506
$233$	−5.44935	−0.356999	−0.178499	−	0.983940i	$-0.557124\pi$
$233$	−5.44935	−0.356999	−0.178499	+	0.983940i	$0.557124\pi$
$234$	1.78664	0.116796
$235$	−7.89463	−0.514989
$236$	−2.67001	−0.173803
$237$	17.0632	1.10837
$238$	−43.1973	−2.80006
$239$	12.7429	0.824272	0.412136	−	0.911122i	$-0.364783\pi$
$239$	12.7429	0.824272	0.412136	+	0.911122i	$0.364783\pi$
$240$	9.01507	0.581920
$241$	16.0145	1.03158	0.515792	−	0.856714i	$-0.327498\pi$
$241$	16.0145	1.03158	0.515792	+	0.856714i	$0.327498\pi$
$242$	7.58294	0.487450
$243$	1.00000	0.0641500
$244$	11.3689	0.727821
$245$	−22.8083	−1.45717
$246$	11.2109	0.714780
$247$	1.26902	0.0807457
$248$	−12.2450	−0.777556
$249$	−8.05185	−0.510266
$250$	−21.7454	−1.37530
$251$	8.32065	0.525195	0.262597	−	0.964905i	$-0.415421\pi$
$251$	8.32065	0.525195	0.262597	+	0.964905i	$0.415421\pi$
$252$	−5.27173	−0.332088
$253$	0.755332	0.0474873
$254$	−4.10502	−0.257572
$255$	9.93085	0.621894
$256$	20.4652	1.27908
$257$	−7.20626	−0.449514	−0.224757	−	0.974415i	$-0.572159\pi$
$257$	−7.20626	−0.449514	−0.224757	+	0.974415i	$0.572159\pi$
$258$	−11.0806	−0.689849
$259$	−25.1572	−1.56319
$260$	2.16531	0.134287
$261$	−6.07278	−0.375896
$262$	34.2878	2.11831
$263$	15.1598	0.934796	0.467398	−	0.884047i	$-0.345192\pi$
$263$	15.1598	0.934796	0.467398	+	0.884047i	$0.345192\pi$
$264$	3.75183	0.230909
$265$	−12.5489	−0.770876
$266$	−10.0266	−0.614770
$267$	−14.4519	−0.884442
$268$	−14.0076	−0.855648
$269$	−11.4237	−0.696513	−0.348256	−	0.937399i	$-0.613226\pi$
$269$	−11.4237	−0.696513	−0.348256	+	0.937399i	$0.613226\pi$
$270$	3.24528	0.197501
$271$	−9.68241	−0.588165	−0.294082	−	0.955780i	$-0.595014\pi$
$271$	−9.68241	−0.588165	−0.294082	+	0.955780i	$0.595014\pi$
$272$	27.1347	1.64528
$273$	4.42230	0.267650
$274$	−40.0290	−2.41824
$275$	−4.42025	−0.266551
$276$	0.346422	0.0208522
$277$	27.8062	1.67071	0.835355	−	0.549711i	$-0.185262\pi$
$277$	27.8062	1.67071	0.835355	+	0.549711i	$0.185262\pi$
$278$	7.05320	0.423023
$279$	−8.48304	−0.507866
$280$	11.5950	0.692933
$281$	−13.1124	−0.782223	−0.391111	−	0.920343i	$-0.627909\pi$
$281$	−13.1124	−0.782223	−0.391111	+	0.920343i	$0.627909\pi$
$282$	−7.76521	−0.462411
$283$	−1.22376	−0.0727450	−0.0363725	−	0.999338i	$-0.511580\pi$
$283$	−1.22376	−0.0727450	−0.0363725	+	0.999338i	$0.511580\pi$
$284$	−0.762516	−0.0452470
$285$	2.30507	0.136540
$286$	4.64380	0.274594
$287$	27.7493	1.63799
$288$	5.98035	0.352395
$289$	12.8911	0.758302
$290$	−19.7079	−1.15729
$291$	0.872842	0.0511669
$292$	−17.1778	−1.00525
$293$	−9.11658	−0.532596	−0.266298	−	0.963891i	$-0.585801\pi$
$293$	−9.11658	−0.532596	−0.266298	+	0.963891i	$0.585801\pi$
$294$	−22.4344	−1.30840
$295$	4.06840	0.236872
$296$	8.21144	0.477280
$297$	2.59918	0.150820
$298$	−22.7545	−1.31813
$299$	−0.290604	−0.0168060
$300$	−2.02729	−0.117045
$301$	−27.4268	−1.58086
$302$	−2.17336	−0.125063
$303$	−11.0407	−0.634269
$304$	6.29828	0.361231
$305$	−17.3233	−0.991929
$306$	9.76805	0.558402
$307$	−14.3576	−0.819431	−0.409716	−	0.912213i	$-0.634372\pi$
$307$	−14.3576	−0.819431	−0.409716	+	0.912213i	$0.634372\pi$
$308$	−13.7022	−0.780755
$309$	−1.00000	−0.0568880
$310$	−27.5298	−1.56359
$311$	−13.6795	−0.775691	−0.387846	−	0.921724i	$-0.626781\pi$
$311$	−13.6795	−0.775691	−0.387846	+	0.921724i	$0.626781\pi$
$312$	−1.44346	−0.0817201
$313$	33.1737	1.87509	0.937545	−	0.347864i	$-0.113093\pi$
$313$	33.1737	1.87509	0.937545	+	0.347864i	$0.113093\pi$
$314$	−38.4235	−2.16837
$315$	8.03274	0.452594
$316$	20.3407	1.14425
$317$	14.6628	0.823545	0.411772	−	0.911287i	$-0.364910\pi$
$317$	14.6628	0.823545	0.411772	+	0.911287i	$0.364910\pi$
$318$	−12.3432	−0.692174
$319$	−15.7843	−0.883750
$320$	1.37777	0.0770195
$321$	−20.2273	−1.12898
$322$	2.29608	0.127955
$323$	6.93808	0.386045
$324$	1.19208	0.0662265
$325$	1.70063	0.0943341
$326$	−33.5041	−1.85562
$327$	−1.89462	−0.104773
$328$	−9.05752	−0.500118
$329$	−19.2205	−1.05966
$330$	8.43508	0.464336
$331$	30.4064	1.67129	0.835644	−	0.549272i	$-0.185095\pi$
$331$	30.4064	1.67129	0.835644	+	0.549272i	$0.185095\pi$
$332$	−9.59844	−0.526783
$333$	5.68870	0.311739
$334$	36.1032	1.97548
$335$	21.3439	1.16614
$336$	21.9484	1.19738
$337$	28.5710	1.55636	0.778180	−	0.628041i	$-0.216143\pi$
$337$	28.5710	1.55636	0.778180	+	0.628041i	$0.216143\pi$
$338$	−1.78664	−0.0971803
$339$	6.29495	0.341895
$340$	11.8384	0.642025
$341$	−22.0490	−1.19402
$342$	2.26728	0.122600
$343$	−24.5737	−1.32686
$344$	8.95228	0.482674
$345$	−0.527857	−0.0284189
$346$	−22.6465	−1.21748
$347$	16.0729	0.862839	0.431419	−	0.902151i	$-0.358013\pi$
$347$	16.0729	0.862839	0.431419	+	0.902151i	$0.358013\pi$
$348$	−7.23923	−0.388063
$349$	12.9546	0.693446	0.346723	−	0.937967i	$-0.387294\pi$
$349$	12.9546	0.693446	0.346723	+	0.937967i	$0.387294\pi$
$350$	−13.4368	−0.718227
$351$	−1.00000	−0.0533761
$352$	15.5440	0.828499
$353$	5.04857	0.268709	0.134354	−	0.990933i	$-0.457104\pi$
$353$	5.04857	0.268709	0.134354	+	0.990933i	$0.457104\pi$
$354$	4.00171	0.212688
$355$	1.16188	0.0616660
$356$	−17.2278	−0.913071
$357$	24.1780	1.27963
$358$	−34.8543	−1.84211
$359$	−0.126191	−0.00666012	−0.00333006	−	0.999994i	$-0.501060\pi$
$359$	−0.126191	−0.00666012	−0.00333006	+	0.999994i	$0.501060\pi$
$360$	−2.62193	−0.138188
$361$	−17.3896	−0.915242
$362$	−14.9631	−0.786443
$363$	−4.24425	−0.222765
$364$	5.27173	0.276314
$365$	26.1745	1.37003
$366$	−17.0393	−0.890658
$367$	−2.53272	−0.132207	−0.0661035	−	0.997813i	$-0.521057\pi$
$367$	−2.53272	−0.132207	−0.0661035	+	0.997813i	$0.521057\pi$
$368$	−1.44230	−0.0751849
$369$	−6.27485	−0.326656
$370$	18.4614	0.959764
$371$	−30.5521	−1.58618
$372$	−10.1124	−0.524306
$373$	28.3611	1.46848	0.734242	−	0.678888i	$-0.237538\pi$
$373$	28.3611	1.46848	0.734242	+	0.678888i	$0.237538\pi$
$374$	25.3889	1.31283
$375$	12.1711	0.628515
$376$	6.27368	0.323541
$377$	6.07278	0.312764
$378$	7.90106	0.406387
$379$	−7.41795	−0.381034	−0.190517	−	0.981684i	$-0.561016\pi$
$379$	−7.41795	−0.381034	−0.190517	+	0.981684i	$0.561016\pi$
$380$	2.74782	0.140960
$381$	2.29762	0.117711
$382$	23.7068	1.21295
$383$	0.224566	0.0114748	0.00573738	−	0.999984i	$-0.498174\pi$
$383$	0.224566	0.0114748	0.00573738	+	0.999984i	$0.498174\pi$
$384$	−10.6055	−0.541210
$385$	20.8786	1.06407
$386$	−36.5661	−1.86117
$387$	6.20194	0.315262
$388$	1.04050	0.0528232
$389$	16.6494	0.844159	0.422079	−	0.906559i	$-0.361300\pi$
$389$	16.6494	0.844159	0.422079	+	0.906559i	$0.361300\pi$
$390$	−3.24528	−0.164331
$391$	−1.58881	−0.0803497
$392$	18.1253	0.915464
$393$	−19.1912	−0.968070
$394$	14.9948	0.755426
$395$	−30.9939	−1.55947
$396$	3.09843	0.155702
$397$	36.0833	1.81097	0.905484	−	0.424381i	$-0.139508\pi$
$397$	36.0833	1.81097	0.905484	+	0.424381i	$0.139508\pi$
$398$	−30.4961	−1.52863
$399$	5.61199	0.280951
$400$	8.44041	0.422021
$401$	−15.3201	−0.765048	−0.382524	−	0.923946i	$-0.624945\pi$
$401$	−15.3201	−0.765048	−0.382524	+	0.923946i	$0.624945\pi$
$402$	20.9940	1.04708
$403$	8.48304	0.422570
$404$	−13.1613	−0.654800
$405$	−1.81642	−0.0902585
$406$	−47.9814	−2.38128
$407$	14.7860	0.732914
$408$	−7.89182	−0.390703
$409$	−36.0339	−1.78176	−0.890882	−	0.454235i	$-0.849913\pi$
$409$	−36.0339	−1.78176	−0.890882	+	0.454235i	$0.849913\pi$
$410$	−20.3636	−1.00569
$411$	22.4046	1.10514
$412$	−1.19208	−0.0587295
$413$	9.90506	0.487396
$414$	−0.519204	−0.0255175
$415$	14.6255	0.717939
$416$	−5.98035	−0.293211
$417$	−3.94775	−0.193322
$418$	5.89307	0.288240
$419$	21.6818	1.05923	0.529613	−	0.848239i	$-0.322337\pi$
$419$	21.6818	1.05923	0.529613	+	0.848239i	$0.322337\pi$
$420$	9.57566	0.467244
$421$	−17.3355	−0.844883	−0.422441	−	0.906390i	$-0.638827\pi$
$421$	−17.3355	−0.844883	−0.422441	+	0.906390i	$0.638827\pi$
$422$	−41.7095	−2.03039
$423$	4.34627	0.211323
$424$	9.97236	0.484301
$425$	9.29782	0.451011
$426$	1.14283	0.0553702
$427$	−42.1758	−2.04103
$428$	−24.1125	−1.16552
$429$	−2.59918	−0.125490
$430$	20.1270	0.970611
$431$	−21.6045	−1.04065	−0.520326	−	0.853968i	$-0.674190\pi$
$431$	−21.6045	−1.04065	−0.520326	+	0.853968i	$0.674190\pi$
$432$	−4.96311	−0.238788
$433$	−38.1651	−1.83410	−0.917050	−	0.398773i	$-0.869436\pi$
$433$	−38.1651	−1.83410	−0.917050	+	0.398773i	$0.869436\pi$
$434$	−67.0250	−3.21730
$435$	11.0307	0.528882
$436$	−2.25854	−0.108164
$437$	−0.368782	−0.0176412
$438$	25.7454	1.23016
$439$	9.45001	0.451024	0.225512	−	0.974240i	$-0.427594\pi$
$439$	9.45001	0.451024	0.225512	+	0.974240i	$0.427594\pi$
$440$	−6.81488	−0.324887
$441$	12.5568	0.597941
$442$	−9.76805	−0.464619
$443$	28.7744	1.36712	0.683558	−	0.729897i	$-0.260432\pi$
$443$	28.7744	1.36712	0.683558	+	0.729897i	$0.260432\pi$
$444$	6.78138	0.321830
$445$	26.2507	1.24440
$446$	34.4091	1.62932
$447$	12.7359	0.602389
$448$	3.35435	0.158478
$449$	−35.0393	−1.65361	−0.826803	−	0.562492i	$-0.809843\pi$
$449$	−35.0393	−1.65361	−0.826803	+	0.562492i	$0.809843\pi$
$450$	3.03841	0.143232
$451$	−16.3095	−0.767983
$452$	7.50407	0.352962
$453$	1.21645	0.0571540
$454$	−45.6643	−2.14313
$455$	−8.03274	−0.376581
$456$	−1.83178	−0.0857812
$457$	9.20948	0.430801	0.215401	−	0.976526i	$-0.430894\pi$
$457$	9.20948	0.430801	0.215401	+	0.976526i	$0.430894\pi$
$458$	30.5795	1.42889
$459$	−5.46728	−0.255191
$460$	−0.629247	−0.0293388
$461$	−6.61038	−0.307876	−0.153938	−	0.988080i	$-0.549196\pi$
$461$	−6.61038	−0.307876	−0.153938	+	0.988080i	$0.549196\pi$
$462$	20.5363	0.955435
$463$	−16.8452	−0.782864	−0.391432	−	0.920207i	$-0.628020\pi$
$463$	−16.8452	−0.782864	−0.391432	+	0.920207i	$0.628020\pi$
$464$	30.1399	1.39921
$465$	15.4087	0.714563
$466$	9.73601	0.451012
$467$	28.8570	1.33534	0.667672	−	0.744455i	$-0.267291\pi$
$467$	28.8570	1.33534	0.667672	+	0.744455i	$0.267291\pi$
$468$	−1.19208	−0.0551038
$469$	51.9645	2.39950
$470$	14.1049	0.650608
$471$	21.5060	0.990946
$472$	−3.23307	−0.148814
$473$	16.1200	0.741197
$474$	−30.4858	−1.40026
$475$	2.15813	0.0990220
$476$	28.8220	1.32105
$477$	6.90863	0.316324
$478$	−22.7670	−1.04134
$479$	29.1007	1.32964	0.664822	−	0.747002i	$-0.268507\pi$
$479$	29.1007	1.32964	0.664822	+	0.747002i	$0.268507\pi$
$480$	−10.8628	−0.495817
$481$	−5.68870	−0.259383
$482$	−28.6121	−1.30325
$483$	−1.28514	−0.0584758
$484$	−5.05947	−0.229976
$485$	−1.58545	−0.0719914
$486$	−1.78664	−0.0810436
$487$	−0.636241	−0.0288309	−0.0144154	−	0.999896i	$-0.504589\pi$
$487$	−0.636241	−0.0288309	−0.0144154	+	0.999896i	$0.504589\pi$
$488$	13.7664	0.623177
$489$	18.7526	0.848022
$490$	40.7502	1.84091
$491$	35.3781	1.59659	0.798296	−	0.602265i	$-0.205735\pi$
$491$	35.3781	1.59659	0.798296	+	0.602265i	$0.205735\pi$
$492$	−7.48011	−0.337229
$493$	33.2016	1.49532
$494$	−2.26728	−0.102010
$495$	−4.72120	−0.212202
$496$	42.1022	1.89045
$497$	2.82874	0.126886
$498$	14.3858	0.644641
$499$	−20.2402	−0.906077	−0.453038	−	0.891491i	$-0.649660\pi$
$499$	−20.2402	−0.906077	−0.453038	+	0.891491i	$0.649660\pi$
$500$	14.5089	0.648860
$501$	−20.2073	−0.902796
$502$	−14.8660	−0.663502
$503$	5.72166	0.255116	0.127558	−	0.991831i	$-0.459286\pi$
$503$	5.72166	0.255116	0.127558	+	0.991831i	$0.459286\pi$
$504$	−6.38344	−0.284341
$505$	20.0544	0.892410
$506$	−1.34951	−0.0599929
$507$	1.00000	0.0444116
$508$	2.73894	0.121521
$509$	23.0196	1.02033	0.510164	−	0.860077i	$-0.329585\pi$
$509$	23.0196	1.02033	0.510164	+	0.860077i	$0.329585\pi$
$510$	−17.7428	−0.785666
$511$	63.7252	2.81904
$512$	−15.3530	−0.678511
$513$	−1.26902	−0.0560286
$514$	12.8750	0.567891
$515$	1.81642	0.0800409
$516$	7.39319	0.325467
$517$	11.2967	0.496830
$518$	44.9468	1.97485
$519$	12.6755	0.556392
$520$	2.62193	0.114979
$521$	−38.1312	−1.67056	−0.835279	−	0.549827i	$-0.814694\pi$
$521$	−38.1312	−1.67056	−0.835279	+	0.549827i	$0.814694\pi$
$522$	10.8499	0.474886
$523$	11.1176	0.486140	0.243070	−	0.970009i	$-0.421846\pi$
$523$	11.1176	0.486140	0.243070	+	0.970009i	$0.421846\pi$
$524$	−22.8775	−0.999406
$525$	7.52071	0.328231
$526$	−27.0852	−1.18097
$527$	46.3791	2.02031
$528$	−12.9000	−0.561401
$529$	−22.9155	−0.996328
$530$	22.4204	0.973882
$531$	−2.23980	−0.0971989
$532$	6.68993	0.290045
$533$	6.27485	0.271794
$534$	25.8203	1.11735
$535$	36.7411	1.58846
$536$	−16.9615	−0.732625
$537$	19.5083	0.841845
$538$	20.4100	0.879936
$539$	32.6373	1.40579
$540$	−2.16531	−0.0931801
$541$	42.0820	1.80925	0.904623	−	0.426213i	$-0.140153\pi$
$541$	42.0820	1.80925	0.904623	+	0.426213i	$0.140153\pi$
$542$	17.2990	0.743055
$543$	8.37500	0.359406
$544$	−32.6962	−1.40184
$545$	3.44142	0.147414
$546$	−7.90106	−0.338134
$547$	−29.6838	−1.26919	−0.634594	−	0.772846i	$-0.718833\pi$
$547$	−29.6838	−1.26919	−0.634594	+	0.772846i	$0.718833\pi$
$548$	26.7080	1.14091
$549$	9.53707	0.407032
$550$	7.89739	0.336746
$551$	7.70648	0.328307
$552$	0.419476	0.0178541
$553$	−75.4587	−3.20883
$554$	−49.6796	−2.11068
$555$	−10.3331	−0.438614
$556$	−4.70602	−0.199580
$557$	22.7811	0.965266	0.482633	−	0.875823i	$-0.339681\pi$
$557$	22.7811	0.965266	0.482633	+	0.875823i	$0.339681\pi$
$558$	15.1561	0.641610
$559$	−6.20194	−0.262314
$560$	−39.8674	−1.68470
$561$	−14.2105	−0.599966
$562$	23.4272	0.988217
$563$	6.19944	0.261275	0.130638	−	0.991430i	$-0.458298\pi$
$563$	6.19944	0.261275	0.130638	+	0.991430i	$0.458298\pi$
$564$	5.18109	0.218163
$565$	−11.4342	−0.481042
$566$	2.18642	0.0919020
$567$	−4.42230	−0.185719
$568$	−0.923317	−0.0387415
$569$	−29.7565	−1.24746	−0.623728	−	0.781642i	$-0.714383\pi$
$569$	−29.7565	−1.24746	−0.623728	+	0.781642i	$0.714383\pi$
$570$	−4.11832	−0.172498
$571$	−2.21861	−0.0928460	−0.0464230	−	0.998922i	$-0.514782\pi$
$571$	−2.21861	−0.0928460	−0.0464230	+	0.998922i	$0.514782\pi$
$572$	−3.09843	−0.129552
$573$	−13.2689	−0.554318
$574$	−49.5779	−2.06934
$575$	−0.494210	−0.0206100
$576$	−0.758508	−0.0316045
$577$	7.05113	0.293542	0.146771	−	0.989170i	$-0.453112\pi$
$577$	7.05113	0.293542	0.146771	+	0.989170i	$0.453112\pi$
$578$	−23.0318	−0.957996
$579$	20.4664	0.850555
$580$	13.1495	0.546001
$581$	35.6077	1.47726
$582$	−1.55945	−0.0646414
$583$	17.9568	0.743694
$584$	−20.8003	−0.860721
$585$	1.81642	0.0750996
$586$	16.2880	0.672852
$587$	17.7424	0.732307	0.366154	−	0.930554i	$-0.380675\pi$
$587$	17.7424	0.732307	0.366154	+	0.930554i	$0.380675\pi$
$588$	14.9686	0.617297
$589$	10.7651	0.443570
$590$	−7.26877	−0.299250
$591$	−8.39273	−0.345231
$592$	−28.2336	−1.16040
$593$	−3.31156	−0.135990	−0.0679948	−	0.997686i	$-0.521660\pi$
$593$	−3.31156	−0.135990	−0.0679948	+	0.997686i	$0.521660\pi$
$594$	−4.64380	−0.190537
$595$	−43.9172	−1.80043
$596$	15.1822	0.621888
$597$	17.0690	0.698586
$598$	0.519204	0.0212318
$599$	−24.4463	−0.998850	−0.499425	−	0.866357i	$-0.666455\pi$
$599$	−24.4463	−0.998850	−0.499425	+	0.866357i	$0.666455\pi$
$600$	−2.45480	−0.100217
$601$	−31.8276	−1.29827	−0.649136	−	0.760672i	$-0.724870\pi$
$601$	−31.8276	−1.29827	−0.649136	+	0.760672i	$0.724870\pi$
$602$	49.0019	1.99717
$603$	−11.7505	−0.478519
$604$	1.45011	0.0590041
$605$	7.70932	0.313429
$606$	19.7257	0.801300
$607$	−20.0049	−0.811975	−0.405987	−	0.913879i	$-0.633072\pi$
$607$	−20.0049	−0.811975	−0.405987	+	0.913879i	$0.633072\pi$
$608$	−7.58917	−0.307782
$609$	26.8557	1.08825
$610$	30.9505	1.25315
$611$	−4.34627	−0.175831
$612$	−6.51742	−0.263451
$613$	−2.31053	−0.0933213	−0.0466606	−	0.998911i	$-0.514858\pi$
$613$	−2.31053	−0.0933213	−0.0466606	+	0.998911i	$0.514858\pi$
$614$	25.6518	1.03522
$615$	11.3977	0.459601
$616$	−16.5917	−0.668500
$617$	−47.3313	−1.90549	−0.952744	−	0.303774i	$-0.901753\pi$
$617$	−47.3313	−1.90549	−0.952744	+	0.303774i	$0.901753\pi$
$618$	1.78664	0.0718691
$619$	30.3286	1.21901	0.609504	−	0.792783i	$-0.291369\pi$
$619$	30.3286	1.21901	0.609504	+	0.792783i	$0.291369\pi$
$620$	18.3684	0.737693
$621$	0.290604	0.0116615
$622$	24.4403	0.979965
$623$	63.9107	2.56053
$624$	4.96311	0.198683
$625$	−13.6047	−0.544188
$626$	−59.2695	−2.36888
$627$	−3.29841	−0.131726
$628$	25.6369	1.02302
$629$	−31.1017	−1.24011
$630$	−14.3516	−0.571782
$631$	23.7315	0.944736	0.472368	−	0.881402i	$-0.343399\pi$
$631$	23.7315	0.944736	0.472368	+	0.881402i	$0.343399\pi$
$632$	24.6301	0.979734
$633$	23.3453	0.927890
$634$	−26.1971	−1.04042
$635$	−4.17344	−0.165618
$636$	8.23562	0.326564
$637$	−12.5568	−0.497517
$638$	28.2008	1.11648
$639$	−0.639653	−0.0253043
$640$	19.2640	0.761478
$641$	34.8096	1.37490	0.687448	−	0.726234i	$-0.258731\pi$
$641$	34.8096	1.37490	0.687448	+	0.726234i	$0.258731\pi$
$642$	36.1388	1.42629
$643$	−12.3746	−0.488005	−0.244003	−	0.969775i	$-0.578461\pi$
$643$	−12.3746	−0.488005	−0.244003	+	0.969775i	$0.578461\pi$
$644$	−1.53198	−0.0603687
$645$	−11.2653	−0.443571
$646$	−12.3958	−0.487708
$647$	−6.07802	−0.238952	−0.119476	−	0.992837i	$-0.538121\pi$
$647$	−6.07802	−0.238952	−0.119476	+	0.992837i	$0.538121\pi$
$648$	1.44346	0.0567047
$649$	−5.82164	−0.228519
$650$	−3.03841	−0.119176
$651$	37.5146	1.47031
$652$	22.3546	0.875472
$653$	28.5933	1.11894	0.559471	−	0.828850i	$-0.311004\pi$
$653$	28.5933	1.11894	0.559471	+	0.828850i	$0.311004\pi$
$654$	3.38500	0.132364
$655$	34.8593	1.36206
$656$	31.1427	1.21592
$657$	−14.4100	−0.562186
$658$	34.3401	1.33872
$659$	−35.3208	−1.37590	−0.687952	−	0.725756i	$-0.741490\pi$
$659$	−35.3208	−1.37590	−0.687952	+	0.725756i	$0.741490\pi$
$660$	−5.62804	−0.219071
$661$	−16.9232	−0.658237	−0.329118	−	0.944289i	$-0.606751\pi$
$661$	−16.9232	−0.658237	−0.329118	+	0.944289i	$0.606751\pi$
$662$	−54.3253	−2.11141
$663$	5.46728	0.212331
$664$	−11.6226	−0.451043
$665$	−10.1937	−0.395295
$666$	−10.1637	−0.393834
$667$	−1.76477	−0.0683323
$668$	−24.0887	−0.932019
$669$	−19.2591	−0.744601
$670$	−38.1338	−1.47324
$671$	24.7886	0.956953
$672$	−26.4469	−1.02021
$673$	−40.4798	−1.56038	−0.780190	−	0.625542i	$-0.784878\pi$
$673$	−40.4798	−1.56038	−0.780190	+	0.625542i	$0.784878\pi$
$674$	−51.0460	−1.96622
$675$	−1.70063	−0.0654573
$676$	1.19208	0.0458491
$677$	−49.8123	−1.91444	−0.957220	−	0.289360i	$-0.906558\pi$
$677$	−49.8123	−1.91444	−0.957220	+	0.289360i	$0.906558\pi$
$678$	−11.2468	−0.431931
$679$	−3.85997	−0.148132
$680$	14.3348	0.549716
$681$	25.5588	0.979414
$682$	39.3935	1.50846
$683$	−42.5830	−1.62939	−0.814697	−	0.579886i	$-0.803097\pi$
$683$	−42.5830	−1.62939	−0.814697	+	0.579886i	$0.803097\pi$
$684$	−1.51277	−0.0578422
$685$	−40.6961	−1.55492
$686$	43.9044	1.67628
$687$	−17.1157	−0.653004
$688$	−30.7809	−1.17351
$689$	−6.90863	−0.263198
$690$	0.943091	0.0359028
$691$	19.9786	0.760023	0.380011	−	0.924982i	$-0.375920\pi$
$691$	19.9786	0.760023	0.380011	+	0.924982i	$0.375920\pi$
$692$	15.1102	0.574402
$693$	−11.4944	−0.436635
$694$	−28.7165	−1.09006
$695$	7.17075	0.272002
$696$	−8.76585	−0.332269
$697$	34.3063	1.29945
$698$	−23.1453	−0.876062
$699$	−5.44935	−0.206113
$700$	8.96527	0.338855
$701$	−16.2950	−0.615455	−0.307728	−	0.951474i	$-0.599569\pi$
$701$	−16.2950	−0.615455	−0.307728	+	0.951474i	$0.599569\pi$
$702$	1.78664	0.0674323
$703$	−7.21907	−0.272272
$704$	−1.97150	−0.0743038
$705$	−7.89463	−0.297329
$706$	−9.01998	−0.339471
$707$	48.8251	1.83626
$708$	−2.67001	−0.100345
$709$	−1.84906	−0.0694430	−0.0347215	−	0.999397i	$-0.511054\pi$
$709$	−1.84906	−0.0694430	−0.0347215	+	0.999397i	$0.511054\pi$
$710$	−2.07585	−0.0779054
$711$	17.0632	0.639920
$712$	−20.8608	−0.781792
$713$	−2.46520	−0.0923226
$714$	−43.1973	−1.61662
$715$	4.72120	0.176563
$716$	23.2554	0.869096
$717$	12.7429	0.475894
$718$	0.225458	0.00841403
$719$	−5.90234	−0.220120	−0.110060	−	0.993925i	$-0.535104\pi$
$719$	−5.90234	−0.220120	−0.110060	+	0.993925i	$0.535104\pi$
$720$	9.01507	0.335972
$721$	4.42230	0.164695
$722$	31.0689	1.15627
$723$	16.0145	0.595585
$724$	9.98366	0.371040
$725$	10.3276	0.383556
$726$	7.58294	0.281429
$727$	26.1329	0.969215	0.484607	−	0.874732i	$-0.338962\pi$
$727$	26.1329	0.969215	0.484607	+	0.874732i	$0.338962\pi$
$728$	6.38344	0.236586
$729$	1.00000	0.0370370
$730$	−46.7643	−1.73083
$731$	−33.9077	−1.25412
$732$	11.3689	0.420208
$733$	−19.2482	−0.710948	−0.355474	−	0.934686i	$-0.615680\pi$
$733$	−19.2482	−0.710948	−0.355474	+	0.934686i	$0.615680\pi$
$734$	4.52506	0.167023
$735$	−22.8083	−0.841298
$736$	1.73791	0.0640603
$737$	−30.5418	−1.12502
$738$	11.2109	0.412678
$739$	48.7402	1.79294	0.896469	−	0.443106i	$-0.146124\pi$
$739$	48.7402	1.79294	0.896469	+	0.443106i	$0.146124\pi$
$740$	−12.3178	−0.452812
$741$	1.26902	0.0466186
$742$	54.5855	2.00390
$743$	−25.2845	−0.927600	−0.463800	−	0.885940i	$-0.653514\pi$
$743$	−25.2845	−0.927600	−0.463800	+	0.885940i	$0.653514\pi$
$744$	−12.2450	−0.448922
$745$	−23.1338	−0.847556
$746$	−50.6711	−1.85520
$747$	−8.05185	−0.294602
$748$	−16.9400	−0.619387
$749$	89.4511	3.26847
$750$	−21.7454	−0.794031
$751$	−43.7103	−1.59501	−0.797506	−	0.603311i	$-0.793848\pi$
$751$	−43.7103	−1.59501	−0.797506	+	0.603311i	$0.793848\pi$
$752$	−21.5710	−0.786613
$753$	8.32065	0.303221
$754$	−10.8499	−0.395129
$755$	−2.20959	−0.0804151
$756$	−5.27173	−0.191731
$757$	−32.3665	−1.17638	−0.588191	−	0.808722i	$-0.700160\pi$
$757$	−32.3665	−1.17638	−0.588191	+	0.808722i	$0.700160\pi$
$758$	13.2532	0.481378
$759$	0.755332	0.0274168
$760$	3.32728	0.120693
$761$	−30.8963	−1.11999	−0.559995	−	0.828496i	$-0.689197\pi$
$761$	−30.8963	−1.11999	−0.559995	+	0.828496i	$0.689197\pi$
$762$	−4.10502	−0.148709
$763$	8.37859	0.303325
$764$	−15.8176	−0.572261
$765$	9.93085	0.359051
$766$	−0.401218	−0.0144966
$767$	2.23980	0.0808744
$768$	20.4652	0.738476
$769$	−1.08930	−0.0392813	−0.0196407	−	0.999807i	$-0.506252\pi$
$769$	−1.08930	−0.0392813	−0.0196407	+	0.999807i	$0.506252\pi$
$770$	−37.3025	−1.34429
$771$	−7.20626	−0.259527
$772$	24.3976	0.878088
$773$	−9.90492	−0.356255	−0.178128	−	0.984007i	$-0.557004\pi$
$773$	−9.90492	−0.356255	−0.178128	+	0.984007i	$0.557004\pi$
$774$	−11.0806	−0.398285
$775$	14.4265	0.518216
$776$	1.25992	0.0452284
$777$	−25.1572	−0.902509
$778$	−29.7465	−1.06646
$779$	7.96290	0.285301
$780$	2.16531	0.0775305
$781$	−1.66257	−0.0594916
$782$	2.83863	0.101509
$783$	−6.07278	−0.217024
$784$	−62.3206	−2.22573
$785$	−39.0639	−1.39425
$786$	34.2878	1.22301
$787$	13.8894	0.495104	0.247552	−	0.968875i	$-0.420374\pi$
$787$	13.8894	0.495104	0.247552	+	0.968875i	$0.420374\pi$
$788$	−10.0048	−0.356406
$789$	15.1598	0.539705
$790$	55.3749	1.97015
$791$	−27.8382	−0.989811
$792$	3.75183	0.133315
$793$	−9.53707	−0.338671
$794$	−64.4678	−2.28788
$795$	−12.5489	−0.445065
$796$	20.3475	0.721199
$797$	43.5581	1.54291	0.771454	−	0.636285i	$-0.219530\pi$
$797$	43.5581	1.54291	0.771454	+	0.636285i	$0.219530\pi$
$798$	−10.0266	−0.354938
$799$	−23.7622	−0.840648
$800$	−10.1704	−0.359577
$801$	−14.4519	−0.510633
$802$	27.3714	0.966519
$803$	−37.4541	−1.32173
$804$	−14.0076	−0.494009
$805$	2.33435	0.0822749
$806$	−15.1561	−0.533852
$807$	−11.4237	−0.402132
$808$	−15.9368	−0.560655
$809$	−27.7558	−0.975842	−0.487921	−	0.872888i	$-0.662245\pi$
$809$	−27.7558	−0.975842	−0.487921	+	0.872888i	$0.662245\pi$
$810$	3.24528	0.114028
$811$	−44.2040	−1.55221	−0.776106	−	0.630602i	$-0.782808\pi$
$811$	−44.2040	−1.55221	−0.776106	+	0.630602i	$0.782808\pi$
$812$	32.0141	1.12347
$813$	−9.68241	−0.339577
$814$	−26.4172	−0.925923
$815$	−34.0625	−1.19316
$816$	27.1347	0.949904
$817$	−7.87037	−0.275350
$818$	64.3796	2.25098
$819$	4.42230	0.154528
$820$	13.5870	0.474478
$821$	2.74884	0.0959352	0.0479676	−	0.998849i	$-0.484726\pi$
$821$	2.74884	0.0959352	0.0479676	+	0.998849i	$0.484726\pi$
$822$	−40.0290	−1.39617
$823$	20.9599	0.730617	0.365309	−	0.930886i	$-0.380963\pi$
$823$	20.9599	0.730617	0.365309	+	0.930886i	$0.380963\pi$
$824$	−1.44346	−0.0502855
$825$	−4.42025	−0.153893
$826$	−17.6968	−0.615749
$827$	34.9563	1.21555	0.607775	−	0.794109i	$-0.292062\pi$
$827$	34.9563	1.21555	0.607775	+	0.794109i	$0.292062\pi$
$828$	0.346422	0.0120390
$829$	18.8130	0.653403	0.326702	−	0.945128i	$-0.394063\pi$
$829$	18.8130	0.653403	0.326702	+	0.945128i	$0.394063\pi$
$830$	−26.1305	−0.907004
$831$	27.8062	0.964585
$832$	0.758508	0.0262965
$833$	−68.6513	−2.37863
$834$	7.05320	0.244232
$835$	36.7049	1.27023
$836$	−3.93196	−0.135990
$837$	−8.48304	−0.293217
$838$	−38.7376	−1.33817
$839$	11.2164	0.387233	0.193616	−	0.981077i	$-0.437978\pi$
$839$	11.2164	0.387233	0.193616	+	0.981077i	$0.437978\pi$
$840$	11.5950	0.400065
$841$	7.87869	0.271679
$842$	30.9723	1.06738
$843$	−13.1124	−0.451617
$844$	27.8294	0.957926
$845$	−1.81642	−0.0624866
$846$	−7.76521	−0.266973
$847$	18.7694	0.644923
$848$	−34.2883	−1.17746
$849$	−1.22376	−0.0419994
$850$	−16.6119	−0.569782
$851$	1.65316	0.0566695
$852$	−0.762516	−0.0261234
$853$	−32.2909	−1.10562	−0.552810	−	0.833307i	$-0.686445\pi$
$853$	−32.2909	−1.10562	−0.552810	+	0.833307i	$0.686445\pi$
$854$	75.3529	2.57852
$855$	2.30507	0.0788316
$856$	−29.1973	−0.997945
$857$	4.16872	0.142401	0.0712004	−	0.997462i	$-0.477317\pi$
$857$	4.16872	0.142401	0.0712004	+	0.997462i	$0.477317\pi$
$858$	4.64380	0.158537
$859$	−25.6046	−0.873618	−0.436809	−	0.899554i	$-0.643891\pi$
$859$	−25.6046	−0.873618	−0.436809	+	0.899554i	$0.643891\pi$
$860$	−13.4291	−0.457929
$861$	27.7493	0.945693
$862$	38.5994	1.31470
$863$	36.4957	1.24233	0.621164	−	0.783681i	$-0.286660\pi$
$863$	36.4957	1.24233	0.621164	+	0.783681i	$0.286660\pi$
$864$	5.98035	0.203456
$865$	−23.0239	−0.782837
$866$	68.1873	2.31710
$867$	12.8911	0.437806
$868$	44.7203	1.51791
$869$	44.3504	1.50448
$870$	−19.7079	−0.668160
$871$	11.7505	0.398152
$872$	−2.73482	−0.0926126
$873$	0.872842	0.0295412
$874$	0.658880	0.0222869
$875$	−53.8245	−1.81960
$876$	−17.1778	−0.580384
$877$	−17.8168	−0.601631	−0.300815	−	0.953682i	$-0.597259\pi$
$877$	−17.8168	−0.601631	−0.300815	+	0.953682i	$0.597259\pi$
$878$	−16.8838	−0.569799
$879$	−9.11658	−0.307495
$880$	23.4318	0.789886
$881$	41.1360	1.38591	0.692954	−	0.720981i	$-0.256309\pi$
$881$	41.1360	1.38591	0.692954	+	0.720981i	$0.256309\pi$
$882$	−22.4344	−0.755406
$883$	39.2960	1.32242	0.661209	−	0.750202i	$-0.270044\pi$
$883$	39.2960	1.32242	0.661209	+	0.750202i	$0.270044\pi$
$884$	6.51742	0.219205
$885$	4.06840	0.136758
$886$	−51.4095	−1.72714
$887$	2.31222	0.0776368	0.0388184	−	0.999246i	$-0.487641\pi$
$887$	2.31222	0.0776368	0.0388184	+	0.999246i	$0.487641\pi$
$888$	8.21144	0.275558
$889$	−10.1608	−0.340782
$890$	−46.9004	−1.57211
$891$	2.59918	0.0870759
$892$	−22.9584	−0.768703
$893$	−5.51549	−0.184569
$894$	−22.7545	−0.761025
$895$	−35.4352	−1.18447
$896$	46.9008	1.56685
$897$	−0.290604	−0.00970298
$898$	62.6025	2.08907
$899$	51.5157	1.71814
$900$	−2.02729	−0.0675762
$901$	−37.7714	−1.25835
$902$	29.1391	0.970227
$903$	−27.4268	−0.912708
$904$	9.08653	0.302214
$905$	−15.2125	−0.505680
$906$	−2.17336	−0.0722052
$907$	−30.8833	−1.02546	−0.512732	−	0.858549i	$-0.671367\pi$
$907$	−30.8833	−1.02546	−0.512732	+	0.858549i	$0.671367\pi$
$908$	30.4680	1.01112
$909$	−11.0407	−0.366195
$910$	14.3516	0.475751
$911$	16.3436	0.541486	0.270743	−	0.962652i	$-0.412731\pi$
$911$	16.3436	0.541486	0.270743	+	0.962652i	$0.412731\pi$
$912$	6.29828	0.208557
$913$	−20.9282	−0.692624
$914$	−16.4540	−0.544250
$915$	−17.3233	−0.572690
$916$	−20.4032	−0.674142
$917$	84.8695	2.80264
$918$	9.76805	0.322394
$919$	26.7948	0.883880	0.441940	−	0.897044i	$-0.354290\pi$
$919$	26.7948	0.883880	0.441940	+	0.897044i	$0.354290\pi$
$920$	−0.761944	−0.0251205
$921$	−14.3576	−0.473099
$922$	11.8104	0.388954
$923$	0.639653	0.0210544
$924$	−13.7022	−0.450769
$925$	−9.67439	−0.318092
$926$	30.0963	0.989026
$927$	−1.00000	−0.0328443
$928$	−36.3174	−1.19218
$929$	−8.09324	−0.265530	−0.132765	−	0.991148i	$-0.542386\pi$
$929$	−8.09324	−0.265530	−0.132765	+	0.991148i	$0.542386\pi$
$930$	−27.5298	−0.902739
$931$	−15.9348	−0.522241
$932$	−6.49605	−0.212785
$933$	−13.6795	−0.447845
$934$	−51.5571	−1.68700
$935$	25.8121	0.844146
$936$	−1.44346	−0.0471811
$937$	43.3836	1.41728	0.708640	−	0.705570i	$-0.249309\pi$
$937$	43.3836	1.41728	0.708640	+	0.705570i	$0.249309\pi$
$938$	−92.8418	−3.03139
$939$	33.1737	1.08258
$940$	−9.41101	−0.306953
$941$	−12.4458	−0.405723	−0.202861	−	0.979207i	$-0.565024\pi$
$941$	−12.4458	−0.405723	−0.202861	+	0.979207i	$0.565024\pi$
$942$	−38.4235	−1.25191
$943$	−1.82349	−0.0593812
$944$	11.1164	0.361806
$945$	8.03274	0.261305
$946$	−28.8006	−0.936387
$947$	27.3826	0.889815	0.444907	−	0.895577i	$-0.353237\pi$
$947$	27.3826	0.889815	0.444907	+	0.895577i	$0.353237\pi$
$948$	20.3407	0.660634
$949$	14.4100	0.467767
$950$	−3.85580	−0.125099
$951$	14.6628	0.475474
$952$	34.9000	1.13112
$953$	−52.1427	−1.68907	−0.844534	−	0.535501i	$-0.820123\pi$
$953$	−52.1427	−1.68907	−0.844534	+	0.535501i	$0.820123\pi$
$954$	−12.3432	−0.399627
$955$	24.1019	0.779920
$956$	15.1906	0.491298
$957$	−15.7843	−0.510233
$958$	−51.9924	−1.67980
$959$	−99.0800	−3.19946
$960$	1.37777	0.0444672
$961$	40.9620	1.32135
$962$	10.1637	0.327689
$963$	−20.2273	−0.651814
$964$	19.0905	0.614864
$965$	−37.1755	−1.19672
$966$	2.29608	0.0738751
$967$	−50.7214	−1.63109	−0.815546	−	0.578693i	$-0.803563\pi$
$967$	−50.7214	−1.63109	−0.815546	+	0.578693i	$0.803563\pi$
$968$	−6.12642	−0.196911
$969$	6.93808	0.222883
$970$	2.83262	0.0909499
$971$	−4.51299	−0.144829	−0.0724143	−	0.997375i	$-0.523070\pi$
$971$	−4.51299	−0.144829	−0.0724143	+	0.997375i	$0.523070\pi$
$972$	1.19208	0.0382359
$973$	17.4581	0.559682
$974$	1.13673	0.0364233
$975$	1.70063	0.0544638
$976$	−47.3335	−1.51511
$977$	6.04137	0.193281	0.0966403	−	0.995319i	$-0.469190\pi$
$977$	6.04137	0.193281	0.0966403	+	0.995319i	$0.469190\pi$
$978$	−33.5041	−1.07134
$979$	−37.5631	−1.20052
$980$	−27.1893	−0.868530
$981$	−1.89462	−0.0604906
$982$	−63.2079	−2.01705
$983$	7.75890	0.247470	0.123735	−	0.992315i	$-0.460513\pi$
$983$	7.75890	0.247470	0.123735	+	0.992315i	$0.460513\pi$
$984$	−9.05752	−0.288743
$985$	15.2447	0.485736
$986$	−59.3192	−1.88911
$987$	−19.2205	−0.611796
$988$	1.51277	0.0481276
$989$	1.80231	0.0573100
$990$	8.43508	0.268084
$991$	−26.1093	−0.829390	−0.414695	−	0.909960i	$-0.636112\pi$
$991$	−26.1093	−0.829390	−0.414695	+	0.909960i	$0.636112\pi$
$992$	−50.7315	−1.61073
$993$	30.4064	0.964918
$994$	−5.05394	−0.160301
$995$	−31.0043	−0.982904
$996$	−9.59844	−0.304138
$997$	3.92326	0.124251	0.0621254	−	0.998068i	$-0.480212\pi$
$997$	3.92326	0.124251	0.0621254	+	0.998068i	$0.480212\pi$
$998$	36.1620	1.14469
$999$	5.68870	0.179983

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4017.2.a.l.1.8	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4017.2.a.l.1.8	✓	32	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)

\(f(q)\)	\(=\)	\(q-1.78664 q^{2} +1.00000 q^{3} +1.19208 q^{4} -1.81642 q^{5} -1.78664 q^{6} -4.42230 q^{7} +1.44346 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.78664 q^{2} +1.00000 q^{3} +1.19208 q^{4} -1.81642 q^{5} -1.78664 q^{6} -4.42230 q^{7} +1.44346 q^{8} +1.00000 q^{9} +3.24528 q^{10} +2.59918 q^{11} +1.19208 q^{12} -1.00000 q^{13} +7.90106 q^{14} -1.81642 q^{15} -4.96311 q^{16} -5.46728 q^{17} -1.78664 q^{18} -1.26902 q^{19} -2.16531 q^{20} -4.42230 q^{21} -4.64380 q^{22} +0.290604 q^{23} +1.44346 q^{24} -1.70063 q^{25} +1.78664 q^{26} +1.00000 q^{27} -5.27173 q^{28} -6.07278 q^{29} +3.24528 q^{30} -8.48304 q^{31} +5.98035 q^{32} +2.59918 q^{33} +9.76805 q^{34} +8.03274 q^{35} +1.19208 q^{36} +5.68870 q^{37} +2.26728 q^{38} -1.00000 q^{39} -2.62193 q^{40} -6.27485 q^{41} +7.90106 q^{42} +6.20194 q^{43} +3.09843 q^{44} -1.81642 q^{45} -0.519204 q^{46} +4.34627 q^{47} -4.96311 q^{48} +12.5568 q^{49} +3.03841 q^{50} -5.46728 q^{51} -1.19208 q^{52} +6.90863 q^{53} -1.78664 q^{54} -4.72120 q^{55} -6.38344 q^{56} -1.26902 q^{57} +10.8499 q^{58} -2.23980 q^{59} -2.16531 q^{60} +9.53707 q^{61} +15.1561 q^{62} -4.42230 q^{63} -0.758508 q^{64} +1.81642 q^{65} -4.64380 q^{66} -11.7505 q^{67} -6.51742 q^{68} +0.290604 q^{69} -14.3516 q^{70} -0.639653 q^{71} +1.44346 q^{72} -14.4100 q^{73} -10.1637 q^{74} -1.70063 q^{75} -1.51277 q^{76} -11.4944 q^{77} +1.78664 q^{78} +17.0632 q^{79} +9.01507 q^{80} +1.00000 q^{81} +11.2109 q^{82} -8.05185 q^{83} -5.27173 q^{84} +9.93085 q^{85} -11.0806 q^{86} -6.07278 q^{87} +3.75183 q^{88} -14.4519 q^{89} +3.24528 q^{90} +4.42230 q^{91} +0.346422 q^{92} -8.48304 q^{93} -7.76521 q^{94} +2.30507 q^{95} +5.98035 q^{96} +0.872842 q^{97} -22.4344 q^{98} +2.59918 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 5 q^{2} + 32 q^{3} + 45 q^{4} + q^{5} + 5 q^{6} + 11 q^{7} + 12 q^{8} + 32 q^{9}+O(q^{10}) \) 32 * q + 5 * q^2 + 32 * q^3 + 45 * q^4 + q^5 + 5 * q^6 + 11 * q^7 + 12 * q^8 + 32 * q^9	\( 32 q + 5 q^{2} + 32 q^{3} + 45 q^{4} + q^{5} + 5 q^{6} + 11 q^{7} + 12 q^{8} + 32 q^{9} + 16 q^{10} + 3 q^{11} + 45 q^{12} - 32 q^{13} + 12 q^{14} + q^{15} + 75 q^{16} + 10 q^{17} + 5 q^{18} + 4 q^{20} + 11 q^{21} + 27 q^{22} + 53 q^{23} + 12 q^{24} + 67 q^{25} - 5 q^{26} + 32 q^{27} + 32 q^{28} + 6 q^{29} + 16 q^{30} + 12 q^{31} + 19 q^{32} + 3 q^{33} + 25 q^{34} + 16 q^{35} + 45 q^{36} + 36 q^{37} + 8 q^{38} - 32 q^{39} + 36 q^{40} - 19 q^{41} + 12 q^{42} + 43 q^{43} - 23 q^{44} + q^{45} + 11 q^{46} + 30 q^{47} + 75 q^{48} + 75 q^{49} + 28 q^{50} + 10 q^{51} - 45 q^{52} + 22 q^{53} + 5 q^{54} + 58 q^{55} + 60 q^{56} + 33 q^{58} - 24 q^{59} + 4 q^{60} + 47 q^{61} - 25 q^{62} + 11 q^{63} + 146 q^{64} - q^{65} + 27 q^{66} + 34 q^{67} + 58 q^{68} + 53 q^{69} - 35 q^{70} + 18 q^{71} + 12 q^{72} - 2 q^{73} - 20 q^{74} + 67 q^{75} + 24 q^{76} + 39 q^{77} - 5 q^{78} + 39 q^{79} + 2 q^{80} + 32 q^{81} + 64 q^{82} + 17 q^{83} + 32 q^{84} + 35 q^{85} - 13 q^{86} + 6 q^{87} + 55 q^{88} - 48 q^{89} + 16 q^{90} - 11 q^{91} + 39 q^{92} + 12 q^{93} + 58 q^{94} + 59 q^{95} + 19 q^{96} + 42 q^{97} + 16 q^{98} + 3 q^{99}+O(q^{100}) \) 32 * q + 5 * q^2 + 32 * q^3 + 45 * q^4 + q^5 + 5 * q^6 + 11 * q^7 + 12 * q^8 + 32 * q^9 + 16 * q^10 + 3 * q^11 + 45 * q^12 - 32 * q^13 + 12 * q^14 + q^15 + 75 * q^16 + 10 * q^17 + 5 * q^18 + 4 * q^20 + 11 * q^21 + 27 * q^22 + 53 * q^23 + 12 * q^24 + 67 * q^25 - 5 * q^26 + 32 * q^27 + 32 * q^28 + 6 * q^29 + 16 * q^30 + 12 * q^31 + 19 * q^32 + 3 * q^33 + 25 * q^34 + 16 * q^35 + 45 * q^36 + 36 * q^37 + 8 * q^38 - 32 * q^39 + 36 * q^40 - 19 * q^41 + 12 * q^42 + 43 * q^43 - 23 * q^44 + q^45 + 11 * q^46 + 30 * q^47 + 75 * q^48 + 75 * q^49 + 28 * q^50 + 10 * q^51 - 45 * q^52 + 22 * q^53 + 5 * q^54 + 58 * q^55 + 60 * q^56 + 33 * q^58 - 24 * q^59 + 4 * q^60 + 47 * q^61 - 25 * q^62 + 11 * q^63 + 146 * q^64 - q^65 + 27 * q^66 + 34 * q^67 + 58 * q^68 + 53 * q^69 - 35 * q^70 + 18 * q^71 + 12 * q^72 - 2 * q^73 - 20 * q^74 + 67 * q^75 + 24 * q^76 + 39 * q^77 - 5 * q^78 + 39 * q^79 + 2 * q^80 + 32 * q^81 + 64 * q^82 + 17 * q^83 + 32 * q^84 + 35 * q^85 - 13 * q^86 + 6 * q^87 + 55 * q^88 - 48 * q^89 + 16 * q^90 - 11 * q^91 + 39 * q^92 + 12 * q^93 + 58 * q^94 + 59 * q^95 + 19 * q^96 + 42 * q^97 + 16 * q^98 + 3 * q^99

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