LMFDB - Embedded newform 4017.2.a.k.1.13

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			1.13
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)

$f(q)$	$=$	$q-0.628086 q^{2} +1.00000 q^{3} -1.60551 q^{4} -0.0316739 q^{5} -0.628086 q^{6} -0.526505 q^{7} +2.26457 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.628086 q^{2} +1.00000 q^{3} -1.60551 q^{4} -0.0316739 q^{5} -0.628086 q^{6} -0.526505 q^{7} +2.26457 q^{8} +1.00000 q^{9} +0.0198939 q^{10} -2.67351 q^{11} -1.60551 q^{12} +1.00000 q^{13} +0.330690 q^{14} -0.0316739 q^{15} +1.78867 q^{16} +2.49769 q^{17} -0.628086 q^{18} +5.54536 q^{19} +0.0508527 q^{20} -0.526505 q^{21} +1.67920 q^{22} -3.20955 q^{23} +2.26457 q^{24} -4.99900 q^{25} -0.628086 q^{26} +1.00000 q^{27} +0.845308 q^{28} +4.55942 q^{29} +0.0198939 q^{30} -3.85093 q^{31} -5.65258 q^{32} -2.67351 q^{33} -1.56877 q^{34} +0.0166764 q^{35} -1.60551 q^{36} +8.37022 q^{37} -3.48296 q^{38} +1.00000 q^{39} -0.0717276 q^{40} -3.01324 q^{41} +0.330690 q^{42} +5.35174 q^{43} +4.29235 q^{44} -0.0316739 q^{45} +2.01587 q^{46} -7.91283 q^{47} +1.78867 q^{48} -6.72279 q^{49} +3.13980 q^{50} +2.49769 q^{51} -1.60551 q^{52} +2.09930 q^{53} -0.628086 q^{54} +0.0846806 q^{55} -1.19231 q^{56} +5.54536 q^{57} -2.86370 q^{58} +6.00929 q^{59} +0.0508527 q^{60} -10.1843 q^{61} +2.41872 q^{62} -0.526505 q^{63} -0.0270468 q^{64} -0.0316739 q^{65} +1.67920 q^{66} -1.08092 q^{67} -4.01007 q^{68} -3.20955 q^{69} -0.0104742 q^{70} +1.42706 q^{71} +2.26457 q^{72} +4.44319 q^{73} -5.25721 q^{74} -4.99900 q^{75} -8.90312 q^{76} +1.40762 q^{77} -0.628086 q^{78} +14.8659 q^{79} -0.0566542 q^{80} +1.00000 q^{81} +1.89257 q^{82} +3.89608 q^{83} +0.845308 q^{84} -0.0791116 q^{85} -3.36135 q^{86} +4.55942 q^{87} -6.05436 q^{88} +9.34494 q^{89} +0.0198939 q^{90} -0.526505 q^{91} +5.15295 q^{92} -3.85093 q^{93} +4.96994 q^{94} -0.175643 q^{95} -5.65258 q^{96} -8.58297 q^{97} +4.22249 q^{98} -2.67351 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 5 q^{2} + 32 q^{3} + 41 q^{4} + 7 q^{5} + 5 q^{6} + 25 q^{7} + 12 q^{8} + 32 q^{9}+O(q^{10}) $ 32 * q + 5 * q^2 + 32 * q^3 + 41 * q^4 + 7 * q^5 + 5 * q^6 + 25 * q^7 + 12 * q^8 + 32 * q^9	\( 32 q + 5 q^{2} + 32 q^{3} + 41 q^{4} + 7 q^{5} + 5 q^{6} + 25 q^{7} + 12 q^{8} + 32 q^{9} + 2 q^{10} + 17 q^{11} + 41 q^{12} + 32 q^{13} - 10 q^{14} + 7 q^{15} + 51 q^{16} + 2 q^{17} + 5 q^{18} + 36 q^{19} - 2 q^{20} + 25 q^{21} - 3 q^{22} + 37 q^{23} + 12 q^{24} + 43 q^{25} + 5 q^{26} + 32 q^{27} + 54 q^{28} + 2 q^{29} + 2 q^{30} + 44 q^{31} + 19 q^{32} + 17 q^{33} + 27 q^{34} - 10 q^{35} + 41 q^{36} + 46 q^{37} - 6 q^{38} + 32 q^{39} - 6 q^{40} + 5 q^{41} - 10 q^{42} + 19 q^{43} + 37 q^{44} + 7 q^{45} + 23 q^{46} + 50 q^{47} + 51 q^{48} + 67 q^{49} - 4 q^{50} + 2 q^{51} + 41 q^{52} + 5 q^{54} + 18 q^{55} - 54 q^{56} + 36 q^{57} + 27 q^{58} + 26 q^{59} - 2 q^{60} + 23 q^{61} + 27 q^{62} + 25 q^{63} + 70 q^{64} + 7 q^{65} - 3 q^{66} + 30 q^{67} - 22 q^{68} + 37 q^{69} + 59 q^{70} + 34 q^{71} + 12 q^{72} + 54 q^{73} + 18 q^{74} + 43 q^{75} + 40 q^{76} - 5 q^{77} + 5 q^{78} + 35 q^{79} - 46 q^{80} + 32 q^{81} + 23 q^{83} + 54 q^{84} + 59 q^{85} - 5 q^{86} + 2 q^{87} - 13 q^{88} + 16 q^{89} + 2 q^{90} + 25 q^{91} + 101 q^{92} + 44 q^{93} - 16 q^{94} - q^{95} + 19 q^{96} + 44 q^{97} - 44 q^{98} + 17 q^{99}+O(q^{100}) \) 32 * q + 5 * q^2 + 32 * q^3 + 41 * q^4 + 7 * q^5 + 5 * q^6 + 25 * q^7 + 12 * q^8 + 32 * q^9 + 2 * q^10 + 17 * q^11 + 41 * q^12 + 32 * q^13 - 10 * q^14 + 7 * q^15 + 51 * q^16 + 2 * q^17 + 5 * q^18 + 36 * q^19 - 2 * q^20 + 25 * q^21 - 3 * q^22 + 37 * q^23 + 12 * q^24 + 43 * q^25 + 5 * q^26 + 32 * q^27 + 54 * q^28 + 2 * q^29 + 2 * q^30 + 44 * q^31 + 19 * q^32 + 17 * q^33 + 27 * q^34 - 10 * q^35 + 41 * q^36 + 46 * q^37 - 6 * q^38 + 32 * q^39 - 6 * q^40 + 5 * q^41 - 10 * q^42 + 19 * q^43 + 37 * q^44 + 7 * q^45 + 23 * q^46 + 50 * q^47 + 51 * q^48 + 67 * q^49 - 4 * q^50 + 2 * q^51 + 41 * q^52 + 5 * q^54 + 18 * q^55 - 54 * q^56 + 36 * q^57 + 27 * q^58 + 26 * q^59 - 2 * q^60 + 23 * q^61 + 27 * q^62 + 25 * q^63 + 70 * q^64 + 7 * q^65 - 3 * q^66 + 30 * q^67 - 22 * q^68 + 37 * q^69 + 59 * q^70 + 34 * q^71 + 12 * q^72 + 54 * q^73 + 18 * q^74 + 43 * q^75 + 40 * q^76 - 5 * q^77 + 5 * q^78 + 35 * q^79 - 46 * q^80 + 32 * q^81 + 23 * q^83 + 54 * q^84 + 59 * q^85 - 5 * q^86 + 2 * q^87 - 13 * q^88 + 16 * q^89 + 2 * q^90 + 25 * q^91 + 101 * q^92 + 44 * q^93 - 16 * q^94 - q^95 + 19 * q^96 + 44 * q^97 - 44 * q^98 + 17 * 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 $

$2$	−0.628086	−0.444124	−0.222062	−	0.975033i	$-0.571279\pi$
$2$	−0.628086	−0.444124	−0.222062	+	0.975033i	$0.571279\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.60551	−0.802754
$5$	−0.0316739	−0.0141650	−0.00708249	−	0.999975i	$-0.502254\pi$
$5$	−0.0316739	−0.0141650	−0.00708249	+	0.999975i	$0.502254\pi$
$6$	−0.628086	−0.256415
$7$	−0.526505	−0.199000	−0.0995001	−	0.995038i	$-0.531724\pi$
$7$	−0.526505	−0.199000	−0.0995001	+	0.995038i	$0.531724\pi$
$8$	2.26457	0.800646
$9$	1.00000	0.333333
$10$	0.0198939	0.00629100
$11$	−2.67351	−0.806095	−0.403047	−	0.915179i	$-0.632049\pi$
$11$	−2.67351	−0.806095	−0.403047	+	0.915179i	$0.632049\pi$
$12$	−1.60551	−0.463470
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	0.330690	0.0883806
$15$	−0.0316739	−0.00817816
$16$	1.78867	0.447169
$17$	2.49769	0.605780	0.302890	−	0.953026i	$-0.402049\pi$
$17$	2.49769	0.605780	0.302890	+	0.953026i	$0.402049\pi$
$18$	−0.628086	−0.148041
$19$	5.54536	1.27219	0.636096	−	0.771610i	$-0.280548\pi$
$19$	5.54536	1.27219	0.636096	+	0.771610i	$0.280548\pi$
$20$	0.0508527	0.0113710
$21$	−0.526505	−0.114893
$22$	1.67920	0.358006
$23$	−3.20955	−0.669237	−0.334618	−	0.942354i	$-0.608607\pi$
$23$	−3.20955	−0.669237	−0.334618	+	0.942354i	$0.608607\pi$
$24$	2.26457	0.462253
$25$	−4.99900	−0.999799
$26$	−0.628086	−0.123178
$27$	1.00000	0.192450
$28$	0.845308	0.159748
$29$	4.55942	0.846662	0.423331	−	0.905975i	$-0.360861\pi$
$29$	4.55942	0.846662	0.423331	+	0.905975i	$0.360861\pi$
$30$	0.0198939	0.00363211
$31$	−3.85093	−0.691648	−0.345824	−	0.938299i	$-0.612401\pi$
$31$	−3.85093	−0.691648	−0.345824	+	0.938299i	$0.612401\pi$
$32$	−5.65258	−0.999244
$33$	−2.67351	−0.465399
$34$	−1.56877	−0.269041
$35$	0.0166764	0.00281883
$36$	−1.60551	−0.267585
$37$	8.37022	1.37606	0.688028	−	0.725685i	$-0.258477\pi$
$37$	8.37022	1.37606	0.688028	+	0.725685i	$0.258477\pi$
$38$	−3.48296	−0.565011
$39$	1.00000	0.160128
$40$	−0.0717276	−0.0113411
$41$	−3.01324	−0.470589	−0.235295	−	0.971924i	$-0.575606\pi$
$41$	−3.01324	−0.470589	−0.235295	+	0.971924i	$0.575606\pi$
$42$	0.330690	0.0510266
$43$	5.35174	0.816132	0.408066	−	0.912952i	$-0.366203\pi$
$43$	5.35174	0.816132	0.408066	+	0.912952i	$0.366203\pi$
$44$	4.29235	0.647096
$45$	−0.0316739	−0.00472166
$46$	2.01587	0.297224
$47$	−7.91283	−1.15420	−0.577102	−	0.816672i	$-0.695817\pi$
$47$	−7.91283	−1.15420	−0.577102	+	0.816672i	$0.695817\pi$
$48$	1.78867	0.258173
$49$	−6.72279	−0.960399
$50$	3.13980	0.444034
$51$	2.49769	0.349747
$52$	−1.60551	−0.222644
$53$	2.09930	0.288360	0.144180	−	0.989551i	$-0.453945\pi$
$53$	2.09930	0.288360	0.144180	+	0.989551i	$0.453945\pi$
$54$	−0.628086	−0.0854716
$55$	0.0846806	0.0114183
$56$	−1.19231	−0.159329
$57$	5.54536	0.734501
$58$	−2.86370	−0.376023
$59$	6.00929	0.782342	0.391171	−	0.920318i	$-0.372070\pi$
$59$	6.00929	0.782342	0.391171	+	0.920318i	$0.372070\pi$
$60$	0.0508527	0.00656505
$61$	−10.1843	−1.30397	−0.651985	−	0.758232i	$-0.726063\pi$
$61$	−10.1843	−1.30397	−0.651985	+	0.758232i	$0.726063\pi$
$62$	2.41872	0.307177
$63$	−0.526505	−0.0663334
$64$	−0.0270468	−0.00338085
$65$	−0.0316739	−0.00392866
$66$	1.67920	0.206695
$67$	−1.08092	−0.132056	−0.0660279	−	0.997818i	$-0.521033\pi$
$67$	−1.08092	−0.132056	−0.0660279	+	0.997818i	$0.521033\pi$
$68$	−4.01007	−0.486292
$69$	−3.20955	−0.386384
$70$	−0.0104742	−0.00125191
$71$	1.42706	0.169361	0.0846805	−	0.996408i	$-0.473013\pi$
$71$	1.42706	0.169361	0.0846805	+	0.996408i	$0.473013\pi$
$72$	2.26457	0.266882
$73$	4.44319	0.520035	0.260018	−	0.965604i	$-0.416272\pi$
$73$	4.44319	0.520035	0.260018	+	0.965604i	$0.416272\pi$
$74$	−5.25721	−0.611139
$75$	−4.99900	−0.577234
$76$	−8.90312	−1.02126
$77$	1.40762	0.160413
$78$	−0.628086	−0.0711167
$79$	14.8659	1.67255	0.836273	−	0.548313i	$-0.184730\pi$
$79$	14.8659	1.67255	0.836273	+	0.548313i	$0.184730\pi$
$80$	−0.0566542	−0.00633414
$81$	1.00000	0.111111
$82$	1.89257	0.209000
$83$	3.89608	0.427650	0.213825	−	0.976872i	$-0.431408\pi$
$83$	3.89608	0.427650	0.213825	+	0.976872i	$0.431408\pi$
$84$	0.845308	0.0922307
$85$	−0.0791116	−0.00858086
$86$	−3.36135	−0.362464
$87$	4.55942	0.488821
$88$	−6.05436	−0.645396
$89$	9.34494	0.990562	0.495281	−	0.868733i	$-0.335065\pi$
$89$	9.34494	0.990562	0.495281	+	0.868733i	$0.335065\pi$
$90$	0.0198939	0.00209700
$91$	−0.526505	−0.0551927
$92$	5.15295	0.537232
$93$	−3.85093	−0.399323
$94$	4.96994	0.512610
$95$	−0.175643	−0.0180206
$96$	−5.65258	−0.576914
$97$	−8.58297	−0.871469	−0.435734	−	0.900075i	$-0.643511\pi$
$97$	−8.58297	−0.871469	−0.435734	+	0.900075i	$0.643511\pi$
$98$	4.22249	0.426536
$99$	−2.67351	−0.268698
$100$	8.02593	0.802593
$101$	9.46244	0.941548	0.470774	−	0.882254i	$-0.343975\pi$
$101$	9.46244	0.941548	0.470774	+	0.882254i	$0.343975\pi$
$102$	−1.56877	−0.155331
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	2.26457	0.222059
$105$	0.0166764	0.00162745
$106$	−1.31854	−0.128068
$107$	−0.305241	−0.0295088	−0.0147544	−	0.999891i	$-0.504697\pi$
$107$	−0.305241	−0.0295088	−0.0147544	+	0.999891i	$0.504697\pi$
$108$	−1.60551	−0.154490
$109$	8.55910	0.819813	0.409907	−	0.912127i	$-0.365561\pi$
$109$	8.55910	0.819813	0.409907	+	0.912127i	$0.365561\pi$
$110$	−0.0531866	−0.00507115
$111$	8.37022	0.794466
$112$	−0.941746	−0.0889866
$113$	2.85165	0.268261	0.134130	−	0.990964i	$-0.457176\pi$
$113$	2.85165	0.268261	0.134130	+	0.990964i	$0.457176\pi$
$114$	−3.48296	−0.326209
$115$	0.101659	0.00947972
$116$	−7.32018	−0.679662
$117$	1.00000	0.0924500
$118$	−3.77435	−0.347457
$119$	−1.31505	−0.120550
$120$	−0.0717276	−0.00654781
$121$	−3.85232	−0.350211
$122$	6.39663	0.579123
$123$	−3.01324	−0.271695
$124$	6.18271	0.555224
$125$	0.316707	0.0283271
$126$	0.330690	0.0294602
$127$	16.9319	1.50246	0.751230	−	0.660041i	$-0.229461\pi$
$127$	16.9319	1.50246	0.751230	+	0.660041i	$0.229461\pi$
$128$	11.3221	1.00075
$129$	5.35174	0.471194
$130$	0.0198939	0.00174481
$131$	−4.61919	−0.403581	−0.201790	−	0.979429i	$-0.564676\pi$
$131$	−4.61919	−0.403581	−0.201790	+	0.979429i	$0.564676\pi$
$132$	4.29235	0.373601
$133$	−2.91966	−0.253167
$134$	0.678912	0.0586491
$135$	−0.0316739	−0.00272605
$136$	5.65620	0.485015
$137$	13.4637	1.15028	0.575140	−	0.818055i	$-0.304947\pi$
$137$	13.4637	1.15028	0.575140	+	0.818055i	$0.304947\pi$
$138$	2.01587	0.171602
$139$	10.5482	0.894685	0.447342	−	0.894363i	$-0.352371\pi$
$139$	10.5482	0.894685	0.447342	+	0.894363i	$0.352371\pi$
$140$	−0.0267742	−0.00226283
$141$	−7.91283	−0.666381
$142$	−0.896316	−0.0752172
$143$	−2.67351	−0.223571
$144$	1.78867	0.149056
$145$	−0.144414	−0.0119930
$146$	−2.79070	−0.230960
$147$	−6.72279	−0.554487
$148$	−13.4385	−1.10463
$149$	−1.71851	−0.140786	−0.0703928	−	0.997519i	$-0.522425\pi$
$149$	−1.71851	−0.140786	−0.0703928	+	0.997519i	$0.522425\pi$
$150$	3.13980	0.256363
$151$	10.1477	0.825812	0.412906	−	0.910774i	$-0.364514\pi$
$151$	10.1477	0.825812	0.412906	+	0.910774i	$0.364514\pi$
$152$	12.5578	1.01858
$153$	2.49769	0.201927
$154$	−0.884105	−0.0712432
$155$	0.121974	0.00979719
$156$	−1.60551	−0.128544
$157$	7.95179	0.634622	0.317311	−	0.948322i	$-0.397220\pi$
$157$	7.95179	0.634622	0.317311	+	0.948322i	$0.397220\pi$
$158$	−9.33707	−0.742817
$159$	2.09930	0.166485
$160$	0.179039	0.0141543
$161$	1.68984	0.133178
$162$	−0.628086	−0.0493471
$163$	22.7231	1.77981	0.889907	−	0.456143i	$-0.150769\pi$
$163$	22.7231	1.77981	0.889907	+	0.456143i	$0.150769\pi$
$164$	4.83779	0.377768
$165$	0.0846806	0.00659237
$166$	−2.44707	−0.189929
$167$	−22.2700	−1.72330	−0.861650	−	0.507503i	$-0.830569\pi$
$167$	−22.2700	−1.72330	−0.861650	+	0.507503i	$0.830569\pi$
$168$	−1.19231	−0.0919884
$169$	1.00000	0.0769231
$170$	0.0496889	0.00381096
$171$	5.54536	0.424064
$172$	−8.59226	−0.655154
$173$	−14.6403	−1.11308	−0.556542	−	0.830820i	$-0.687872\pi$
$173$	−14.6403	−1.11308	−0.556542	+	0.830820i	$0.687872\pi$
$174$	−2.86370	−0.217097
$175$	2.63200	0.198960
$176$	−4.78205	−0.360460
$177$	6.00929	0.451686
$178$	−5.86942	−0.439932
$179$	−2.01252	−0.150423	−0.0752115	−	0.997168i	$-0.523963\pi$
$179$	−2.01252	−0.150423	−0.0752115	+	0.997168i	$0.523963\pi$
$180$	0.0508527	0.00379033
$181$	1.12101	0.0833242	0.0416621	−	0.999132i	$-0.486735\pi$
$181$	1.12101	0.0833242	0.0416621	+	0.999132i	$0.486735\pi$
$182$	0.330690	0.0245124
$183$	−10.1843	−0.752847
$184$	−7.26823	−0.535821
$185$	−0.265117	−0.0194918
$186$	2.41872	0.177349
$187$	−6.67762	−0.488316
$188$	12.7041	0.926543
$189$	−0.526505	−0.0382976
$190$	0.110319	0.00800337
$191$	17.8629	1.29251	0.646256	−	0.763120i	$-0.276334\pi$
$191$	17.8629	1.29251	0.646256	+	0.763120i	$0.276334\pi$
$192$	−0.0270468	−0.00195193
$193$	−9.87771	−0.711013	−0.355506	−	0.934674i	$-0.615692\pi$
$193$	−9.87771	−0.711013	−0.355506	+	0.934674i	$0.615692\pi$
$194$	5.39084	0.387040
$195$	−0.0316739	−0.00226821
$196$	10.7935	0.770964
$197$	23.6649	1.68605	0.843026	−	0.537872i	$-0.180772\pi$
$197$	23.6649	1.68605	0.843026	+	0.537872i	$0.180772\pi$
$198$	1.67920	0.119335
$199$	−17.8649	−1.26641	−0.633203	−	0.773986i	$-0.718260\pi$
$199$	−17.8649	−1.26641	−0.633203	+	0.773986i	$0.718260\pi$
$200$	−11.3206	−0.800485
$201$	−1.08092	−0.0762424
$202$	−5.94322	−0.418164
$203$	−2.40055	−0.168486
$204$	−4.01007	−0.280761
$205$	0.0954410	0.00666589
$206$	−0.628086	−0.0437608
$207$	−3.20955	−0.223079
$208$	1.78867	0.124022
$209$	−14.8256	−1.02551
$210$	−0.0104742	−0.000722791 0
$211$	24.5957	1.69324	0.846620	−	0.532198i	$-0.178634\pi$
$211$	24.5957	1.69324	0.846620	+	0.532198i	$0.178634\pi$
$212$	−3.37044	−0.231483
$213$	1.42706	0.0977806
$214$	0.191718	0.0131055
$215$	−0.169510	−0.0115605
$216$	2.26457	0.154084
$217$	2.02754	0.137638
$218$	−5.37585	−0.364098
$219$	4.44319	0.300243
$220$	−0.135955	−0.00916611
$221$	2.49769	0.168013
$222$	−5.25721	−0.352841
$223$	13.6027	0.910902	0.455451	−	0.890261i	$-0.349478\pi$
$223$	13.6027	0.910902	0.455451	+	0.890261i	$0.349478\pi$
$224$	2.97611	0.198850
$225$	−4.99900	−0.333266
$226$	−1.79108	−0.119141
$227$	−1.90953	−0.126740	−0.0633701	−	0.997990i	$-0.520185\pi$
$227$	−1.90953	−0.126740	−0.0633701	+	0.997990i	$0.520185\pi$
$228$	−8.90312	−0.589624
$229$	6.40016	0.422934	0.211467	−	0.977385i	$-0.432176\pi$
$229$	6.40016	0.422934	0.211467	+	0.977385i	$0.432176\pi$
$230$	−0.0638504	−0.00421017
$231$	1.40762	0.0926145
$232$	10.3251	0.677876
$233$	−14.3162	−0.937884	−0.468942	−	0.883229i	$-0.655365\pi$
$233$	−14.3162	−0.937884	−0.468942	+	0.883229i	$0.655365\pi$
$234$	−0.628086	−0.0410592
$235$	0.250630	0.0163493
$236$	−9.64796	−0.628029
$237$	14.8659	0.965645
$238$	0.825963	0.0535392
$239$	18.1506	1.17407	0.587033	−	0.809563i	$-0.300296\pi$
$239$	18.1506	1.17407	0.587033	+	0.809563i	$0.300296\pi$
$240$	−0.0566542	−0.00365702
$241$	4.90040	0.315662	0.157831	−	0.987466i	$-0.449550\pi$
$241$	4.90040	0.315662	0.157831	+	0.987466i	$0.449550\pi$
$242$	2.41959	0.155537
$243$	1.00000	0.0641500
$244$	16.3510	1.04677
$245$	0.212937	0.0136040
$246$	1.89257	0.120666
$247$	5.54536	0.352843
$248$	−8.72070	−0.553765
$249$	3.89608	0.246904
$250$	−0.198919	−0.0125807
$251$	11.7755	0.743262	0.371631	−	0.928381i	$-0.378799\pi$
$251$	11.7755	0.743262	0.371631	+	0.928381i	$0.378799\pi$
$252$	0.845308	0.0532494
$253$	8.58077	0.539468
$254$	−10.6347	−0.667278
$255$	−0.0791116	−0.00495416
$256$	−7.05718	−0.441074
$257$	−28.1350	−1.75502	−0.877508	−	0.479563i	$-0.840795\pi$
$257$	−28.1350	−1.75502	−0.877508	+	0.479563i	$0.840795\pi$
$258$	−3.36135	−0.209268
$259$	−4.40696	−0.273835
$260$	0.0508527	0.00315375
$261$	4.55942	0.282221
$262$	2.90125	0.179240
$263$	22.9278	1.41379	0.706894	−	0.707319i	$-0.250096\pi$
$263$	22.9278	1.41379	0.706894	+	0.707319i	$0.250096\pi$
$264$	−6.05436	−0.372620
$265$	−0.0664928	−0.00408462
$266$	1.83380	0.112437
$267$	9.34494	0.571901
$268$	1.73543	0.106008
$269$	−22.4849	−1.37093	−0.685463	−	0.728108i	$-0.740400\pi$
$269$	−22.4849	−1.37093	−0.685463	+	0.728108i	$0.740400\pi$
$270$	0.0198939	0.00121070
$271$	1.07014	0.0650063	0.0325031	−	0.999472i	$-0.489652\pi$
$271$	1.07014	0.0650063	0.0325031	+	0.999472i	$0.489652\pi$
$272$	4.46756	0.270886
$273$	−0.526505	−0.0318655
$274$	−8.45635	−0.510867
$275$	13.3649	0.805933
$276$	5.15295	0.310171
$277$	−6.23190	−0.374438	−0.187219	−	0.982318i	$-0.559947\pi$
$277$	−6.23190	−0.374438	−0.187219	+	0.982318i	$0.559947\pi$
$278$	−6.62516	−0.397351
$279$	−3.85093	−0.230549
$280$	0.0377649	0.00225689
$281$	8.18261	0.488134	0.244067	−	0.969758i	$-0.421518\pi$
$281$	8.18261	0.488134	0.244067	+	0.969758i	$0.421518\pi$
$282$	4.96994	0.295955
$283$	30.3972	1.80693	0.903463	−	0.428666i	$-0.141016\pi$
$283$	30.3972	1.80693	0.903463	+	0.428666i	$0.141016\pi$
$284$	−2.29116	−0.135955
$285$	−0.175643	−0.0104042
$286$	1.67920	0.0992929
$287$	1.58649	0.0936473
$288$	−5.65258	−0.333081
$289$	−10.7615	−0.633031
$290$	0.0907046	0.00532636
$291$	−8.58297	−0.503143
$292$	−7.13357	−0.417461
$293$	27.8612	1.62767	0.813835	−	0.581095i	$-0.197376\pi$
$293$	27.8612	1.62767	0.813835	+	0.581095i	$0.197376\pi$
$294$	4.22249	0.246261
$295$	−0.190337	−0.0110819
$296$	18.9549	1.10173
$297$	−2.67351	−0.155133
$298$	1.07937	0.0625262
$299$	−3.20955	−0.185613
$300$	8.02593	0.463377
$301$	−2.81772	−0.162410
$302$	−6.37365	−0.366762
$303$	9.46244	0.543603
$304$	9.91884	0.568885
$305$	0.322577	0.0184707
$306$	−1.56877	−0.0896804
$307$	9.27413	0.529303	0.264651	−	0.964344i	$-0.414743\pi$
$307$	9.27413	0.529303	0.264651	+	0.964344i	$0.414743\pi$
$308$	−2.25994	−0.128772
$309$	1.00000	0.0568880
$310$	−0.0766101	−0.00435116
$311$	−9.39760	−0.532889	−0.266444	−	0.963850i	$-0.585849\pi$
$311$	−9.39760	−0.532889	−0.266444	+	0.963850i	$0.585849\pi$
$312$	2.26457	0.128206
$313$	22.5832	1.27648	0.638238	−	0.769839i	$-0.279664\pi$
$313$	22.5832	1.27648	0.638238	+	0.769839i	$0.279664\pi$
$314$	−4.99440	−0.281851
$315$	0.0166764	0.000939611 0
$316$	−23.8674	−1.34264
$317$	29.4545	1.65433	0.827166	−	0.561958i	$-0.189952\pi$
$317$	29.4545	1.65433	0.827166	+	0.561958i	$0.189952\pi$
$318$	−1.31854	−0.0739399
$319$	−12.1897	−0.682490
$320$	0.000856676 0	4.78896e−5 0
$321$	−0.305241	−0.0170369
$322$	−1.06136	−0.0591476
$323$	13.8506	0.770669
$324$	−1.60551	−0.0891949
$325$	−4.99900	−0.277294
$326$	−14.2721	−0.790457
$327$	8.55910	0.473320
$328$	−6.82369	−0.376775
$329$	4.16614	0.229687
$330$	−0.0531866	−0.00292783
$331$	−29.0257	−1.59540	−0.797698	−	0.603057i	$-0.793949\pi$
$331$	−29.0257	−1.59540	−0.797698	+	0.603057i	$0.793949\pi$
$332$	−6.25519	−0.343298
$333$	8.37022	0.458685
$334$	13.9874	0.765358
$335$	0.0342370	0.00187057
$336$	−0.941746	−0.0513764
$337$	35.4643	1.93186	0.965932	−	0.258796i	$-0.0833256\pi$
$337$	35.4643	1.93186	0.965932	+	0.258796i	$0.0833256\pi$
$338$	−0.628086	−0.0341634
$339$	2.85165	0.154881
$340$	0.127014	0.00688832
$341$	10.2955	0.557534
$342$	−3.48296	−0.188337
$343$	7.22512	0.390120
$344$	12.1194	0.653433
$345$	0.101659	0.00547312
$346$	9.19538	0.494347
$347$	−25.8638	−1.38844	−0.694222	−	0.719761i	$-0.744251\pi$
$347$	−25.8638	−1.38844	−0.694222	+	0.719761i	$0.744251\pi$
$348$	−7.32018	−0.392403
$349$	5.94542	0.318251	0.159126	−	0.987258i	$-0.449133\pi$
$349$	5.94542	0.318251	0.159126	+	0.987258i	$0.449133\pi$
$350$	−1.65312	−0.0883629
$351$	1.00000	0.0533761
$352$	15.1122	0.805485
$353$	−31.6029	−1.68205	−0.841026	−	0.540995i	$-0.818048\pi$
$353$	−31.6029	−1.68205	−0.841026	+	0.540995i	$0.818048\pi$
$354$	−3.77435	−0.200604
$355$	−0.0452005	−0.00239900
$356$	−15.0034	−0.795178
$357$	−1.31505	−0.0695997
$358$	1.26404	0.0668064
$359$	4.59211	0.242362	0.121181	−	0.992630i	$-0.461332\pi$
$359$	4.59211	0.242362	0.121181	+	0.992630i	$0.461332\pi$
$360$	−0.0717276	−0.00378038
$361$	11.7510	0.618474
$362$	−0.704092	−0.0370063
$363$	−3.85232	−0.202194
$364$	0.845308	0.0443062
$365$	−0.140733	−0.00736629
$366$	6.39663	0.334357
$367$	14.7822	0.771624	0.385812	−	0.922577i	$-0.373921\pi$
$367$	14.7822	0.771624	0.385812	+	0.922577i	$0.373921\pi$
$368$	−5.74083	−0.299262
$369$	−3.01324	−0.156863
$370$	0.166516	0.00865677
$371$	−1.10529	−0.0573838
$372$	6.18271	0.320559
$373$	10.5565	0.546595	0.273298	−	0.961929i	$-0.411886\pi$
$373$	10.5565	0.546595	0.273298	+	0.961929i	$0.411886\pi$
$374$	4.19412	0.216873
$375$	0.316707	0.0163547
$376$	−17.9191	−0.924109
$377$	4.55942	0.234822
$378$	0.330690	0.0170089
$379$	35.2081	1.80852	0.904260	−	0.426983i	$-0.140424\pi$
$379$	35.2081	1.80852	0.904260	+	0.426983i	$0.140424\pi$
$380$	0.281996	0.0144661
$381$	16.9319	0.867445
$382$	−11.2194	−0.574035
$383$	−26.9146	−1.37527	−0.687635	−	0.726056i	$-0.741351\pi$
$383$	−26.9146	−1.37527	−0.687635	+	0.726056i	$0.741351\pi$
$384$	11.3221	0.577781
$385$	−0.0445847	−0.00227225
$386$	6.20405	0.315778
$387$	5.35174	0.272044
$388$	13.7800	0.699575
$389$	−32.8918	−1.66768	−0.833840	−	0.552005i	$-0.813863\pi$
$389$	−32.8918	−1.66768	−0.833840	+	0.552005i	$0.813863\pi$
$390$	0.0198939	0.00100737
$391$	−8.01646	−0.405410
$392$	−15.2242	−0.768939
$393$	−4.61919	−0.233007
$394$	−14.8636	−0.748816
$395$	−0.470861	−0.0236916
$396$	4.29235	0.215699
$397$	−4.98382	−0.250131	−0.125065	−	0.992148i	$-0.539914\pi$
$397$	−4.98382	−0.250131	−0.125065	+	0.992148i	$0.539914\pi$
$398$	11.2207	0.562441
$399$	−2.91966	−0.146166
$400$	−8.94158	−0.447079
$401$	−15.6191	−0.779979	−0.389990	−	0.920819i	$-0.627521\pi$
$401$	−15.6191	−0.779979	−0.389990	+	0.920819i	$0.627521\pi$
$402$	0.678912	0.0338611
$403$	−3.85093	−0.191829
$404$	−15.1920	−0.755832
$405$	−0.0316739	−0.00157389
$406$	1.50775	0.0748286
$407$	−22.3779	−1.10923
$408$	5.65620	0.280023
$409$	−16.5072	−0.816229	−0.408115	−	0.912931i	$-0.633814\pi$
$409$	−16.5072	−0.816229	−0.408115	+	0.912931i	$0.633814\pi$
$410$	−0.0599451	−0.00296048
$411$	13.4637	0.664115
$412$	−1.60551	−0.0790977
$413$	−3.16392	−0.155686
$414$	2.01587	0.0990746
$415$	−0.123404	−0.00605766
$416$	−5.65258	−0.277140
$417$	10.5482	0.516547
$418$	9.31175	0.455452
$419$	29.0261	1.41802	0.709009	−	0.705200i	$-0.249143\pi$
$419$	29.0261	1.41802	0.709009	+	0.705200i	$0.249143\pi$
$420$	−0.0267742	−0.00130645
$421$	6.29299	0.306702	0.153351	−	0.988172i	$-0.450994\pi$
$421$	6.29299	0.306702	0.153351	+	0.988172i	$0.450994\pi$
$422$	−15.4482	−0.752008
$423$	−7.91283	−0.384735
$424$	4.75400	0.230875
$425$	−12.4860	−0.605658
$426$	−0.896316	−0.0434267
$427$	5.36210	0.259490
$428$	0.490067	0.0236883
$429$	−2.67351	−0.129079
$430$	0.106467	0.00513429
$431$	10.7371	0.517188	0.258594	−	0.965986i	$-0.416741\pi$
$431$	10.7371	0.517188	0.258594	+	0.965986i	$0.416741\pi$
$432$	1.78867	0.0860576
$433$	−19.7589	−0.949551	−0.474776	−	0.880107i	$-0.657471\pi$
$433$	−19.7589	−0.949551	−0.474776	+	0.880107i	$0.657471\pi$
$434$	−1.27347	−0.0611283
$435$	−0.144414	−0.00692414
$436$	−13.7417	−0.658109
$437$	−17.7981	−0.851398
$438$	−2.79070	−0.133345
$439$	36.4922	1.74168	0.870838	−	0.491569i	$-0.163577\pi$
$439$	36.4922	1.74168	0.870838	+	0.491569i	$0.163577\pi$
$440$	0.191765	0.00914203
$441$	−6.72279	−0.320133
$442$	−1.56877	−0.0746186
$443$	−35.9110	−1.70618	−0.853091	−	0.521762i	$-0.825275\pi$
$443$	−35.9110	−1.70618	−0.853091	+	0.521762i	$0.825275\pi$
$444$	−13.4385	−0.637761
$445$	−0.295990	−0.0140313
$446$	−8.54364	−0.404553
$447$	−1.71851	−0.0812826
$448$	0.0142403	0.000672789 0
$449$	−10.1772	−0.480289	−0.240145	−	0.970737i	$-0.577195\pi$
$449$	−10.1772	−0.480289	−0.240145	+	0.970737i	$0.577195\pi$
$450$	3.13980	0.148011
$451$	8.05595	0.379340
$452$	−4.57835	−0.215348
$453$	10.1477	0.476783
$454$	1.19935	0.0562883
$455$	0.0166764	0.000781804 0
$456$	12.5578	0.588075
$457$	36.3269	1.69930	0.849649	−	0.527348i	$-0.176814\pi$
$457$	36.3269	1.69930	0.849649	+	0.527348i	$0.176814\pi$
$458$	−4.01985	−0.187835
$459$	2.49769	0.116582
$460$	−0.163214	−0.00760989
$461$	21.3868	0.996083	0.498042	−	0.867153i	$-0.334053\pi$
$461$	21.3868	0.996083	0.498042	+	0.867153i	$0.334053\pi$
$462$	−0.884105	−0.0411323
$463$	−25.0919	−1.16612	−0.583060	−	0.812429i	$-0.698145\pi$
$463$	−25.0919	−1.16612	−0.583060	+	0.812429i	$0.698145\pi$
$464$	8.15531	0.378601
$465$	0.121974	0.00565641
$466$	8.99179	0.416536
$467$	−18.1911	−0.841783	−0.420892	−	0.907111i	$-0.638283\pi$
$467$	−18.1911	−0.841783	−0.420892	+	0.907111i	$0.638283\pi$
$468$	−1.60551	−0.0742147
$469$	0.569111	0.0262791
$470$	−0.157417	−0.00726111
$471$	7.95179	0.366399
$472$	13.6084	0.626379
$473$	−14.3079	−0.657880
$474$	−9.33707	−0.428866
$475$	−27.7212	−1.27194
$476$	2.11132	0.0967722
$477$	2.09930	0.0961201
$478$	−11.4001	−0.521430
$479$	−32.5646	−1.48791	−0.743956	−	0.668228i	$-0.767053\pi$
$479$	−32.5646	−1.48791	−0.743956	+	0.668228i	$0.767053\pi$
$480$	0.179039	0.00817197
$481$	8.37022	0.381649
$482$	−3.07787	−0.140193
$483$	1.68984	0.0768904
$484$	6.18493	0.281133
$485$	0.271856	0.0123443
$486$	−0.628086	−0.0284905
$487$	−6.30825	−0.285854	−0.142927	−	0.989733i	$-0.545651\pi$
$487$	−6.30825	−0.285854	−0.142927	+	0.989733i	$0.545651\pi$
$488$	−23.0631	−1.04402
$489$	22.7231	1.02758
$490$	−0.133743	−0.00604187
$491$	5.90173	0.266342	0.133171	−	0.991093i	$-0.457484\pi$
$491$	5.90173	0.266342	0.133171	+	0.991093i	$0.457484\pi$
$492$	4.83779	0.218104
$493$	11.3880	0.512891
$494$	−3.48296	−0.156706
$495$	0.0846806	0.00380611
$496$	−6.88807	−0.309283
$497$	−0.751354	−0.0337029
$498$	−2.44707	−0.109656
$499$	11.4193	0.511199	0.255599	−	0.966783i	$-0.417727\pi$
$499$	11.4193	0.511199	0.255599	+	0.966783i	$0.417727\pi$
$500$	−0.508476	−0.0227397
$501$	−22.2700	−0.994948
$502$	−7.39601	−0.330100
$503$	−31.1228	−1.38770	−0.693848	−	0.720121i	$-0.744086\pi$
$503$	−31.1228	−1.38770	−0.693848	+	0.720121i	$0.744086\pi$
$504$	−1.19231	−0.0531095
$505$	−0.299712	−0.0133370
$506$	−5.38946	−0.239591
$507$	1.00000	0.0444116
$508$	−27.1842	−1.20611
$509$	19.2461	0.853070	0.426535	−	0.904471i	$-0.359734\pi$
$509$	19.2461	0.853070	0.426535	+	0.904471i	$0.359734\pi$
$510$	0.0496889	0.00220026
$511$	−2.33936	−0.103487
$512$	−18.2118	−0.804854
$513$	5.54536	0.244834
$514$	17.6712	0.779444
$515$	−0.0316739	−0.00139572
$516$	−8.59226	−0.378253
$517$	21.1551	0.930399
$518$	2.76795	0.121617
$519$	−14.6403	−0.642639
$520$	−0.0717276	−0.00314546
$521$	−13.6066	−0.596116	−0.298058	−	0.954548i	$-0.596339\pi$
$521$	−13.6066	−0.596116	−0.298058	+	0.954548i	$0.596339\pi$
$522$	−2.86370	−0.125341
$523$	26.6109	1.16361	0.581806	−	0.813327i	$-0.302346\pi$
$523$	26.6109	1.16361	0.581806	+	0.813327i	$0.302346\pi$
$524$	7.41615	0.323976
$525$	2.63200	0.114870
$526$	−14.4006	−0.627897
$527$	−9.61846	−0.418987
$528$	−4.78205	−0.208112
$529$	−12.6988	−0.552122
$530$	0.0417632	0.00181408
$531$	6.00929	0.260781
$532$	4.68754	0.203230
$533$	−3.01324	−0.130518
$534$	−5.86942	−0.253995
$535$	0.00966817	0.000417991 0
$536$	−2.44782	−0.105730
$537$	−2.01252	−0.0868467
$538$	14.1224	0.608860
$539$	17.9735	0.774173
$540$	0.0508527	0.00218835
$541$	36.7295	1.57912	0.789562	−	0.613670i	$-0.210308\pi$
$541$	36.7295	1.57912	0.789562	+	0.613670i	$0.210308\pi$
$542$	−0.672138	−0.0288708
$543$	1.12101	0.0481073
$544$	−14.1184	−0.605322
$545$	−0.271100	−0.0116126
$546$	0.330690	0.0141522
$547$	20.3279	0.869159	0.434580	−	0.900633i	$-0.356897\pi$
$547$	20.3279	0.869159	0.434580	+	0.900633i	$0.356897\pi$
$548$	−21.6161	−0.923393
$549$	−10.1843	−0.434656
$550$	−8.39430	−0.357934
$551$	25.2836	1.07712
$552$	−7.26823	−0.309357
$553$	−7.82698	−0.332837
$554$	3.91417	0.166297
$555$	−0.265117	−0.0112536
$556$	−16.9352	−0.718212
$557$	−0.533416	−0.0226016	−0.0113008	−	0.999936i	$-0.503597\pi$
$557$	−0.533416	−0.0226016	−0.0113008	+	0.999936i	$0.503597\pi$
$558$	2.41872	0.102392
$559$	5.35174	0.226354
$560$	0.0298287	0.00126049
$561$	−6.67762	−0.281929
$562$	−5.13938	−0.216792
$563$	1.08768	0.0458400	0.0229200	−	0.999737i	$-0.492704\pi$
$563$	1.08768	0.0458400	0.0229200	+	0.999737i	$0.492704\pi$
$564$	12.7041	0.534940
$565$	−0.0903229	−0.00379991
$566$	−19.0920	−0.802498
$567$	−0.526505	−0.0221111
$568$	3.23168	0.135598
$569$	−37.9208	−1.58972	−0.794862	−	0.606791i	$-0.792457\pi$
$569$	−37.9208	−1.58972	−0.794862	+	0.606791i	$0.792457\pi$
$570$	0.110319	0.00462075
$571$	29.2688	1.22486	0.612430	−	0.790524i	$-0.290192\pi$
$571$	29.2688	1.22486	0.612430	+	0.790524i	$0.290192\pi$
$572$	4.29235	0.179472
$573$	17.8629	0.746233
$574$	−0.996449	−0.0415910
$575$	16.0445	0.669102
$576$	−0.0270468	−0.00112695
$577$	−37.3989	−1.55694	−0.778469	−	0.627683i	$-0.784003\pi$
$577$	−37.3989	−1.55694	−0.778469	+	0.627683i	$0.784003\pi$
$578$	6.75916	0.281144
$579$	−9.87771	−0.410503
$580$	0.231858	0.00962740
$581$	−2.05130	−0.0851024
$582$	5.39084	0.223458
$583$	−5.61250	−0.232446
$584$	10.0619	0.416364
$585$	−0.0316739	−0.00130955
$586$	−17.4992	−0.722887
$587$	25.6062	1.05688	0.528441	−	0.848970i	$-0.322777\pi$
$587$	25.6062	1.05688	0.528441	+	0.848970i	$0.322777\pi$
$588$	10.7935	0.445116
$589$	−21.3548	−0.879910
$590$	0.119548	0.00492172
$591$	23.6649	0.973443
$592$	14.9716	0.615329
$593$	−34.1420	−1.40204	−0.701022	−	0.713139i	$-0.747273\pi$
$593$	−34.1420	−1.40204	−0.701022	+	0.713139i	$0.747273\pi$
$594$	1.67920	0.0688982
$595$	0.0416527	0.00170759
$596$	2.75908	0.113016
$597$	−17.8649	−0.731160
$598$	2.01587	0.0824350
$599$	−6.64645	−0.271567	−0.135783	−	0.990739i	$-0.543355\pi$
$599$	−6.64645	−0.271567	−0.135783	+	0.990739i	$0.543355\pi$
$600$	−11.3206	−0.462160
$601$	0.282100	0.0115071	0.00575355	−	0.999983i	$-0.498169\pi$
$601$	0.282100	0.0115071	0.00575355	+	0.999983i	$0.498169\pi$
$602$	1.76977	0.0721303
$603$	−1.08092	−0.0440186
$604$	−16.2923	−0.662924
$605$	0.122018	0.00496073
$606$	−5.94322	−0.241427
$607$	−13.8535	−0.562298	−0.281149	−	0.959664i	$-0.590715\pi$
$607$	−13.8535	−0.562298	−0.281149	+	0.959664i	$0.590715\pi$
$608$	−31.3456	−1.27123
$609$	−2.40055	−0.0972754
$610$	−0.202606	−0.00820327
$611$	−7.91283	−0.320119
$612$	−4.01007	−0.162097
$613$	−34.2748	−1.38435	−0.692174	−	0.721731i	$-0.743347\pi$
$613$	−34.2748	−1.38435	−0.692174	+	0.721731i	$0.743347\pi$
$614$	−5.82495	−0.235076
$615$	0.0954410	0.00384855
$616$	3.18765	0.128434
$617$	14.0270	0.564705	0.282353	−	0.959311i	$-0.408885\pi$
$617$	14.0270	0.564705	0.282353	+	0.959311i	$0.408885\pi$
$618$	−0.628086	−0.0252653
$619$	−28.9557	−1.16383	−0.581913	−	0.813251i	$-0.697696\pi$
$619$	−28.9557	−1.16383	−0.581913	+	0.813251i	$0.697696\pi$
$620$	−0.195830	−0.00786473
$621$	−3.20955	−0.128795
$622$	5.90250	0.236669
$623$	−4.92016	−0.197122
$624$	1.78867	0.0716043
$625$	24.9850	0.999398
$626$	−14.1842	−0.566913
$627$	−14.8256	−0.592077
$628$	−12.7667	−0.509445
$629$	20.9062	0.833586
$630$	−0.0104742	−0.000417304 0
$631$	−12.0483	−0.479636	−0.239818	−	0.970818i	$-0.577088\pi$
$631$	−12.0483	−0.479636	−0.239818	+	0.970818i	$0.577088\pi$
$632$	33.6649	1.33912
$633$	24.5957	0.977592
$634$	−18.5000	−0.734728
$635$	−0.536297	−0.0212823
$636$	−3.37044	−0.133647
$637$	−6.72279	−0.266367
$638$	7.65615	0.303110
$639$	1.42706	0.0564537
$640$	−0.358616	−0.0141755
$641$	31.6164	1.24877	0.624387	−	0.781115i	$-0.285349\pi$
$641$	31.6164	1.24877	0.624387	+	0.781115i	$0.285349\pi$
$642$	0.191718	0.00756649
$643$	43.6911	1.72301	0.861504	−	0.507751i	$-0.169523\pi$
$643$	43.6911	1.72301	0.861504	+	0.507751i	$0.169523\pi$
$644$	−2.71305	−0.106909
$645$	−0.169510	−0.00667446
$646$	−8.69937	−0.342272
$647$	16.6644	0.655145	0.327573	−	0.944826i	$-0.393769\pi$
$647$	16.6644	0.655145	0.327573	+	0.944826i	$0.393769\pi$
$648$	2.26457	0.0889606
$649$	−16.0659	−0.630642
$650$	3.13980	0.123153
$651$	2.02754	0.0794654
$652$	−36.4822	−1.42875
$653$	2.48312	0.0971721	0.0485860	−	0.998819i	$-0.484528\pi$
$653$	2.48312	0.0971721	0.0485860	+	0.998819i	$0.484528\pi$
$654$	−5.37585	−0.210212
$655$	0.146308	0.00571671
$656$	−5.38971	−0.210433
$657$	4.44319	0.173345
$658$	−2.61669	−0.102009
$659$	8.12780	0.316614	0.158307	−	0.987390i	$-0.449396\pi$
$659$	8.12780	0.316614	0.158307	+	0.987390i	$0.449396\pi$
$660$	−0.135955	−0.00529205
$661$	41.8956	1.62955	0.814775	−	0.579777i	$-0.196860\pi$
$661$	41.8956	1.62955	0.814775	+	0.579777i	$0.196860\pi$
$662$	18.2306	0.708553
$663$	2.49769	0.0970024
$664$	8.82293	0.342396
$665$	0.0924769	0.00358610
$666$	−5.25721	−0.203713
$667$	−14.6337	−0.566617
$668$	35.7546	1.38339
$669$	13.6027	0.525910
$670$	−0.0215038	−0.000830763 0
$671$	27.2279	1.05112
$672$	2.97611	0.114806
$673$	−26.6556	−1.02750	−0.513749	−	0.857941i	$-0.671744\pi$
$673$	−26.6556	−1.02750	−0.513749	+	0.857941i	$0.671744\pi$
$674$	−22.2746	−0.857986
$675$	−4.99900	−0.192411
$676$	−1.60551	−0.0617503
$677$	34.0693	1.30939	0.654695	−	0.755893i	$-0.272797\pi$
$677$	34.0693	1.30939	0.654695	+	0.755893i	$0.272797\pi$
$678$	−1.79108	−0.0687861
$679$	4.51898	0.173422
$680$	−0.179154	−0.00687023
$681$	−1.90953	−0.0731735
$682$	−6.46647	−0.247614
$683$	−9.87068	−0.377691	−0.188846	−	0.982007i	$-0.560475\pi$
$683$	−9.87068	−0.377691	−0.188846	+	0.982007i	$0.560475\pi$
$684$	−8.90312	−0.340419
$685$	−0.426447	−0.0162937
$686$	−4.53799	−0.173261
$687$	6.40016	0.244181
$688$	9.57251	0.364949
$689$	2.09930	0.0799768
$690$	−0.0638504	−0.00243074
$691$	6.12356	0.232951	0.116476	−	0.993194i	$-0.462840\pi$
$691$	6.12356	0.232951	0.116476	+	0.993194i	$0.462840\pi$
$692$	23.5052	0.893533
$693$	1.40762	0.0534710
$694$	16.2447	0.616641
$695$	−0.334102	−0.0126732
$696$	10.3251	0.391372
$697$	−7.52616	−0.285074
$698$	−3.73424	−0.141343
$699$	−14.3162	−0.541488
$700$	−4.22569	−0.159716
$701$	41.7006	1.57501	0.787506	−	0.616307i	$-0.211372\pi$
$701$	41.7006	1.57501	0.787506	+	0.616307i	$0.211372\pi$
$702$	−0.628086	−0.0237056
$703$	46.4159	1.75061
$704$	0.0723099	0.00272528
$705$	0.250630	0.00943927
$706$	19.8493	0.747039
$707$	−4.98202	−0.187368
$708$	−9.64796	−0.362593
$709$	2.13495	0.0801799	0.0400900	−	0.999196i	$-0.487236\pi$
$709$	2.13495	0.0801799	0.0400900	+	0.999196i	$0.487236\pi$
$710$	0.0283898	0.00106545
$711$	14.8659	0.557516
$712$	21.1623	0.793089
$713$	12.3598	0.462876
$714$	0.825963	0.0309109
$715$	0.0846806	0.00316687
$716$	3.23112	0.120753
$717$	18.1506	0.677847
$718$	−2.88424	−0.107639
$719$	−41.1877	−1.53604	−0.768022	−	0.640424i	$-0.778759\pi$
$719$	−41.1877	−1.53604	−0.768022	+	0.640424i	$0.778759\pi$
$720$	−0.0566542	−0.00211138
$721$	−0.526505	−0.0196081
$722$	−7.38064	−0.274679
$723$	4.90040	0.182248
$724$	−1.79980	−0.0668889
$725$	−22.7925	−0.846492
$726$	2.41959	0.0897993
$727$	−15.5736	−0.577594	−0.288797	−	0.957390i	$-0.593255\pi$
$727$	−15.5736	−0.577594	−0.288797	+	0.957390i	$0.593255\pi$
$728$	−1.19231	−0.0441898
$729$	1.00000	0.0370370
$730$	0.0883923	0.00327155
$731$	13.3670	0.494396
$732$	16.3510	0.604351
$733$	17.6015	0.650125	0.325063	−	0.945692i	$-0.394615\pi$
$733$	17.6015	0.650125	0.325063	+	0.945692i	$0.394615\pi$
$734$	−9.28448	−0.342697
$735$	0.212937	0.00785429
$736$	18.1422	0.668730
$737$	2.88986	0.106449
$738$	1.89257	0.0696666
$739$	49.5165	1.82149	0.910747	−	0.412965i	$-0.135507\pi$
$739$	49.5165	1.82149	0.910747	+	0.412965i	$0.135507\pi$
$740$	0.425648	0.0156471
$741$	5.54536	0.203714
$742$	0.694216	0.0254855
$743$	−24.5637	−0.901155	−0.450577	−	0.892737i	$-0.648782\pi$
$743$	−24.5637	−0.901155	−0.450577	+	0.892737i	$0.648782\pi$
$744$	−8.72070	−0.319717
$745$	0.0544318	0.00199423
$746$	−6.63039	−0.242756
$747$	3.89608	0.142550
$748$	10.7210	0.391998
$749$	0.160711	0.00587225
$750$	−0.198919	−0.00726350
$751$	−28.1071	−1.02564	−0.512821	−	0.858495i	$-0.671400\pi$
$751$	−28.1071	−1.02564	−0.512821	+	0.858495i	$0.671400\pi$
$752$	−14.1535	−0.516124
$753$	11.7755	0.429122
$754$	−2.86370	−0.104290
$755$	−0.321418	−0.0116976
$756$	0.845308	0.0307436
$757$	−38.7682	−1.40905	−0.704527	−	0.709677i	$-0.748841\pi$
$757$	−38.7682	−1.40905	−0.704527	+	0.709677i	$0.748841\pi$
$758$	−22.1137	−0.803206
$759$	8.58077	0.311462
$760$	−0.397755	−0.0144281
$761$	−32.9025	−1.19272	−0.596358	−	0.802719i	$-0.703386\pi$
$761$	−32.9025	−1.19272	−0.596358	+	0.802719i	$0.703386\pi$
$762$	−10.6347	−0.385253
$763$	−4.50641	−0.163143
$764$	−28.6790	−1.03757
$765$	−0.0791116	−0.00286029
$766$	16.9047	0.610790
$767$	6.00929	0.216983
$768$	−7.05718	−0.254654
$769$	−16.2220	−0.584979	−0.292489	−	0.956269i	$-0.594484\pi$
$769$	−16.2220	−0.584979	−0.292489	+	0.956269i	$0.594484\pi$
$770$	0.0280030	0.00100916
$771$	−28.1350	−1.01326
$772$	15.8587	0.570769
$773$	9.64140	0.346777	0.173388	−	0.984854i	$-0.444528\pi$
$773$	9.64140	0.346777	0.173388	+	0.984854i	$0.444528\pi$
$774$	−3.36135	−0.120821
$775$	19.2508	0.691510
$776$	−19.4367	−0.697738
$777$	−4.40696	−0.158099
$778$	20.6589	0.740656
$779$	−16.7095	−0.598680
$780$	0.0508527	0.00182082
$781$	−3.81527	−0.136521
$782$	5.03502	0.180052
$783$	4.55942	0.162940
$784$	−12.0249	−0.429460
$785$	−0.251864	−0.00898941
$786$	2.90125	0.103484
$787$	18.0949	0.645014	0.322507	−	0.946567i	$-0.395474\pi$
$787$	18.0949	0.645014	0.322507	+	0.946567i	$0.395474\pi$
$788$	−37.9942	−1.35349
$789$	22.9278	0.816251
$790$	0.295741	0.0105220
$791$	−1.50141	−0.0533840
$792$	−6.05436	−0.215132
$793$	−10.1843	−0.361656
$794$	3.13027	0.111089
$795$	−0.0664928	−0.00235826
$796$	28.6822	1.01661
$797$	−20.4252	−0.723497	−0.361749	−	0.932276i	$-0.617820\pi$
$797$	−20.4252	−0.723497	−0.361749	+	0.932276i	$0.617820\pi$
$798$	1.83380	0.0649157
$799$	−19.7638	−0.699194
$800$	28.2572	0.999043
$801$	9.34494	0.330187
$802$	9.81012	0.346407
$803$	−11.8789	−0.419198
$804$	1.73543	0.0612039
$805$	−0.0535238	−0.00188647
$806$	2.41872	0.0851957
$807$	−22.4849	−0.791504
$808$	21.4283	0.753847
$809$	−4.08156	−0.143500	−0.0717501	−	0.997423i	$-0.522858\pi$
$809$	−4.08156	−0.143500	−0.0717501	+	0.997423i	$0.522858\pi$
$810$	0.0198939	0.000699000 0
$811$	22.1613	0.778189	0.389094	−	0.921198i	$-0.372788\pi$
$811$	22.1613	0.778189	0.389094	+	0.921198i	$0.372788\pi$
$812$	3.85411	0.135253
$813$	1.07014	0.0375314
$814$	14.0552	0.492636
$815$	−0.719730	−0.0252110
$816$	4.46756	0.156396
$817$	29.6773	1.03828
$818$	10.3679	0.362507
$819$	−0.526505	−0.0183976
$820$	−0.153231	−0.00535107
$821$	38.2383	1.33453	0.667263	−	0.744822i	$-0.267466\pi$
$821$	38.2383	1.33453	0.667263	+	0.744822i	$0.267466\pi$
$822$	−8.45635	−0.294949
$823$	−36.5919	−1.27551	−0.637756	−	0.770238i	$-0.720137\pi$
$823$	−36.5919	−1.27551	−0.637756	+	0.770238i	$0.720137\pi$
$824$	2.26457	0.0788900
$825$	13.3649	0.465306
$826$	1.98721	0.0691439
$827$	2.01376	0.0700253	0.0350126	−	0.999387i	$-0.488853\pi$
$827$	2.01376	0.0700253	0.0350126	+	0.999387i	$0.488853\pi$
$828$	5.15295	0.179077
$829$	−38.5077	−1.33743	−0.668715	−	0.743519i	$-0.733155\pi$
$829$	−38.5077	−1.33743	−0.668715	+	0.743519i	$0.733155\pi$
$830$	0.0775082	0.00269035
$831$	−6.23190	−0.216182
$832$	−0.0270468	−0.000937678 0
$833$	−16.7915	−0.581790
$834$	−6.62516	−0.229411
$835$	0.705375	0.0244105
$836$	23.8026	0.823231
$837$	−3.85093	−0.133108
$838$	−18.2309	−0.629775
$839$	−12.7086	−0.438749	−0.219375	−	0.975641i	$-0.570402\pi$
$839$	−12.7086	−0.438749	−0.219375	+	0.975641i	$0.570402\pi$
$840$	0.0377649	0.00130301
$841$	−8.21173	−0.283163
$842$	−3.95254	−0.136213
$843$	8.18261	0.281824
$844$	−39.4886	−1.35926
$845$	−0.0316739	−0.00108961
$846$	4.96994	0.170870
$847$	2.02826	0.0696920
$848$	3.75496	0.128946
$849$	30.3972	1.04323
$850$	7.84225	0.268987
$851$	−26.8646	−0.920906
$852$	−2.29116	−0.0784938
$853$	20.7509	0.710496	0.355248	−	0.934772i	$-0.384396\pi$
$853$	20.7509	0.710496	0.355248	+	0.934772i	$0.384396\pi$
$854$	−3.36786	−0.115246
$855$	−0.175643	−0.00600686
$856$	−0.691239	−0.0236261
$857$	13.5928	0.464322	0.232161	−	0.972677i	$-0.425420\pi$
$857$	13.5928	0.464322	0.232161	+	0.972677i	$0.425420\pi$
$858$	1.67920	0.0573268
$859$	−11.0145	−0.375810	−0.187905	−	0.982187i	$-0.560170\pi$
$859$	−11.0145	−0.375810	−0.187905	+	0.982187i	$0.560170\pi$
$860$	0.272150	0.00928024
$861$	1.58649	0.0540673
$862$	−6.74382	−0.229695
$863$	−5.89679	−0.200729	−0.100365	−	0.994951i	$-0.532001\pi$
$863$	−5.89679	−0.200729	−0.100365	+	0.994951i	$0.532001\pi$
$864$	−5.65258	−0.192305
$865$	0.463716	0.0157668
$866$	12.4103	0.421718
$867$	−10.7615	−0.365481
$868$	−3.25523	−0.110490
$869$	−39.7443	−1.34823
$870$	0.0907046	0.00307517
$871$	−1.08092	−0.0366257
$872$	19.3827	0.656380
$873$	−8.58297	−0.290490
$874$	11.1787	0.378126
$875$	−0.166748	−0.00563710
$876$	−7.13357	−0.241021
$877$	−23.1738	−0.782522	−0.391261	−	0.920280i	$-0.627961\pi$
$877$	−23.1738	−0.782522	−0.391261	+	0.920280i	$0.627961\pi$
$878$	−22.9202	−0.773520
$879$	27.8612	0.939736
$880$	0.151466	0.00510592
$881$	−15.3550	−0.517323	−0.258661	−	0.965968i	$-0.583281\pi$
$881$	−15.3550	−0.517323	−0.258661	+	0.965968i	$0.583281\pi$
$882$	4.22249	0.142179
$883$	−53.3905	−1.79673	−0.898366	−	0.439247i	$-0.855245\pi$
$883$	−53.3905	−1.79673	−0.898366	+	0.439247i	$0.855245\pi$
$884$	−4.01007	−0.134873
$885$	−0.190337	−0.00639812
$886$	22.5552	0.757756
$887$	−19.8680	−0.667103	−0.333552	−	0.942732i	$-0.608247\pi$
$887$	−19.8680	−0.667103	−0.333552	+	0.942732i	$0.608247\pi$
$888$	18.9549	0.636086
$889$	−8.91470	−0.298990
$890$	0.185907	0.00623163
$891$	−2.67351	−0.0895661
$892$	−21.8392	−0.731231
$893$	−43.8795	−1.46837
$894$	1.07937	0.0360995
$895$	0.0637444	0.00213074
$896$	−5.96116	−0.199148
$897$	−3.20955	−0.107164
$898$	6.39212	0.213308
$899$	−17.5580	−0.585592
$900$	8.02593	0.267531
$901$	5.24340	0.174683
$902$	−5.05982	−0.168474
$903$	−2.81772	−0.0937677
$904$	6.45776	0.214782
$905$	−0.0355068	−0.00118029
$906$	−6.37365	−0.211750
$907$	−40.4630	−1.34355	−0.671776	−	0.740754i	$-0.734468\pi$
$907$	−40.4630	−1.34355	−0.671776	+	0.740754i	$0.734468\pi$
$908$	3.06577	0.101741
$909$	9.46244	0.313849
$910$	−0.0104742	−0.000347218 0
$911$	−1.39501	−0.0462187	−0.0231094	−	0.999733i	$-0.507357\pi$
$911$	−1.39501	−0.0462187	−0.0231094	+	0.999733i	$0.507357\pi$
$912$	9.91884	0.328446
$913$	−10.4162	−0.344727
$914$	−22.8164	−0.754699
$915$	0.322577	0.0106641
$916$	−10.2755	−0.339512
$917$	2.43203	0.0803126
$918$	−1.56877	−0.0517770
$919$	50.3658	1.66141	0.830707	−	0.556710i	$-0.187937\pi$
$919$	50.3658	1.66141	0.830707	+	0.556710i	$0.187937\pi$
$920$	0.230213	0.00758990
$921$	9.27413	0.305593
$922$	−13.4327	−0.442384
$923$	1.42706	0.0469723
$924$	−2.25994	−0.0743467
$925$	−41.8427	−1.37578
$926$	15.7599	0.517901
$927$	1.00000	0.0328443
$928$	−25.7724	−0.846022
$929$	−35.0028	−1.14841	−0.574203	−	0.818713i	$-0.694688\pi$
$929$	−35.0028	−1.14841	−0.574203	+	0.818713i	$0.694688\pi$
$930$	−0.0766101	−0.00251214
$931$	−37.2803	−1.22181
$932$	22.9847	0.752890
$933$	−9.39760	−0.307664
$934$	11.4256	0.373856
$935$	0.211506	0.00691699
$936$	2.26457	0.0740197
$937$	−29.5795	−0.966322	−0.483161	−	0.875532i	$-0.660511\pi$
$937$	−29.5795	−0.966322	−0.483161	+	0.875532i	$0.660511\pi$
$938$	−0.357450	−0.0116712
$939$	22.5832	0.736973
$940$	−0.402389	−0.0131245
$941$	14.5577	0.474568	0.237284	−	0.971440i	$-0.423743\pi$
$941$	14.5577	0.474568	0.237284	+	0.971440i	$0.423743\pi$
$942$	−4.99440	−0.162726
$943$	9.67114	0.314936
$944$	10.7487	0.349839
$945$	0.0166764	0.000542485 0
$946$	8.98662	0.292180
$947$	−46.2814	−1.50394	−0.751972	−	0.659195i	$-0.770897\pi$
$947$	−46.2814	−1.50394	−0.751972	+	0.659195i	$0.770897\pi$
$948$	−23.8674	−0.775176
$949$	4.44319	0.144232
$950$	17.4113	0.564897
$951$	29.4545	0.955129
$952$	−2.97802	−0.0965180
$953$	−53.7595	−1.74144	−0.870721	−	0.491778i	$-0.836347\pi$
$953$	−53.7595	−1.74144	−0.870721	+	0.491778i	$0.836347\pi$
$954$	−1.31854	−0.0426892
$955$	−0.565787	−0.0183084
$956$	−29.1410	−0.942486
$957$	−12.1897	−0.394036
$958$	20.4533	0.660817
$959$	−7.08870	−0.228906
$960$	0.000856676 0	2.76491e−5 0
$961$	−16.1703	−0.521623
$962$	−5.25721	−0.169499
$963$	−0.305241	−0.00983626
$964$	−7.86763	−0.253399
$965$	0.312865	0.0100715
$966$	−1.06136	−0.0341489
$967$	39.1897	1.26026	0.630128	−	0.776491i	$-0.283002\pi$
$967$	39.1897	1.26026	0.630128	+	0.776491i	$0.283002\pi$
$968$	−8.72384	−0.280395
$969$	13.8506	0.444946
$970$	−0.170749	−0.00548241
$971$	34.7627	1.11559	0.557793	−	0.829980i	$-0.311648\pi$
$971$	34.7627	1.11559	0.557793	+	0.829980i	$0.311648\pi$
$972$	−1.60551	−0.0514967
$973$	−5.55367	−0.178042
$974$	3.96212	0.126954
$975$	−4.99900	−0.160096
$976$	−18.2164	−0.583094
$977$	−12.1811	−0.389709	−0.194854	−	0.980832i	$-0.562423\pi$
$977$	−12.1811	−0.389709	−0.194854	+	0.980832i	$0.562423\pi$
$978$	−14.2721	−0.456371
$979$	−24.9838	−0.798487
$980$	−0.341872	−0.0109207
$981$	8.55910	0.273271
$982$	−3.70679	−0.118289
$983$	54.4147	1.73556	0.867779	−	0.496950i	$-0.165547\pi$
$983$	54.4147	1.73556	0.867779	+	0.496950i	$0.165547\pi$
$984$	−6.82369	−0.217531
$985$	−0.749558	−0.0238829
$986$	−7.15265	−0.227787
$987$	4.16614	0.132610
$988$	−8.90312	−0.283246
$989$	−17.1766	−0.546185
$990$	−0.0531866	−0.00169038
$991$	58.3535	1.85366	0.926831	−	0.375480i	$-0.122522\pi$
$991$	58.3535	1.85366	0.926831	+	0.375480i	$0.122522\pi$
$992$	21.7677	0.691125
$993$	−29.0257	−0.921103
$994$	0.471915	0.0149682
$995$	0.565849	0.0179386
$996$	−6.25519	−0.198203
$997$	−32.7929	−1.03856	−0.519280	−	0.854604i	$-0.673800\pi$
$997$	−32.7929	−1.03856	−0.519280	+	0.854604i	$0.673800\pi$
$998$	−7.17231	−0.227035
$999$	8.37022	0.264822

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4017.2.a.k.1.13	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4017.2.a.k.1.13	✓	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)

\(f(q)\)	\(=\)	\(q-0.628086 q^{2} +1.00000 q^{3} -1.60551 q^{4} -0.0316739 q^{5} -0.628086 q^{6} -0.526505 q^{7} +2.26457 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.628086 q^{2} +1.00000 q^{3} -1.60551 q^{4} -0.0316739 q^{5} -0.628086 q^{6} -0.526505 q^{7} +2.26457 q^{8} +1.00000 q^{9} +0.0198939 q^{10} -2.67351 q^{11} -1.60551 q^{12} +1.00000 q^{13} +0.330690 q^{14} -0.0316739 q^{15} +1.78867 q^{16} +2.49769 q^{17} -0.628086 q^{18} +5.54536 q^{19} +0.0508527 q^{20} -0.526505 q^{21} +1.67920 q^{22} -3.20955 q^{23} +2.26457 q^{24} -4.99900 q^{25} -0.628086 q^{26} +1.00000 q^{27} +0.845308 q^{28} +4.55942 q^{29} +0.0198939 q^{30} -3.85093 q^{31} -5.65258 q^{32} -2.67351 q^{33} -1.56877 q^{34} +0.0166764 q^{35} -1.60551 q^{36} +8.37022 q^{37} -3.48296 q^{38} +1.00000 q^{39} -0.0717276 q^{40} -3.01324 q^{41} +0.330690 q^{42} +5.35174 q^{43} +4.29235 q^{44} -0.0316739 q^{45} +2.01587 q^{46} -7.91283 q^{47} +1.78867 q^{48} -6.72279 q^{49} +3.13980 q^{50} +2.49769 q^{51} -1.60551 q^{52} +2.09930 q^{53} -0.628086 q^{54} +0.0846806 q^{55} -1.19231 q^{56} +5.54536 q^{57} -2.86370 q^{58} +6.00929 q^{59} +0.0508527 q^{60} -10.1843 q^{61} +2.41872 q^{62} -0.526505 q^{63} -0.0270468 q^{64} -0.0316739 q^{65} +1.67920 q^{66} -1.08092 q^{67} -4.01007 q^{68} -3.20955 q^{69} -0.0104742 q^{70} +1.42706 q^{71} +2.26457 q^{72} +4.44319 q^{73} -5.25721 q^{74} -4.99900 q^{75} -8.90312 q^{76} +1.40762 q^{77} -0.628086 q^{78} +14.8659 q^{79} -0.0566542 q^{80} +1.00000 q^{81} +1.89257 q^{82} +3.89608 q^{83} +0.845308 q^{84} -0.0791116 q^{85} -3.36135 q^{86} +4.55942 q^{87} -6.05436 q^{88} +9.34494 q^{89} +0.0198939 q^{90} -0.526505 q^{91} +5.15295 q^{92} -3.85093 q^{93} +4.96994 q^{94} -0.175643 q^{95} -5.65258 q^{96} -8.58297 q^{97} +4.22249 q^{98} -2.67351 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 5 q^{2} + 32 q^{3} + 41 q^{4} + 7 q^{5} + 5 q^{6} + 25 q^{7} + 12 q^{8} + 32 q^{9}+O(q^{10}) \) 32 * q + 5 * q^2 + 32 * q^3 + 41 * q^4 + 7 * q^5 + 5 * q^6 + 25 * q^7 + 12 * q^8 + 32 * q^9	\( 32 q + 5 q^{2} + 32 q^{3} + 41 q^{4} + 7 q^{5} + 5 q^{6} + 25 q^{7} + 12 q^{8} + 32 q^{9} + 2 q^{10} + 17 q^{11} + 41 q^{12} + 32 q^{13} - 10 q^{14} + 7 q^{15} + 51 q^{16} + 2 q^{17} + 5 q^{18} + 36 q^{19} - 2 q^{20} + 25 q^{21} - 3 q^{22} + 37 q^{23} + 12 q^{24} + 43 q^{25} + 5 q^{26} + 32 q^{27} + 54 q^{28} + 2 q^{29} + 2 q^{30} + 44 q^{31} + 19 q^{32} + 17 q^{33} + 27 q^{34} - 10 q^{35} + 41 q^{36} + 46 q^{37} - 6 q^{38} + 32 q^{39} - 6 q^{40} + 5 q^{41} - 10 q^{42} + 19 q^{43} + 37 q^{44} + 7 q^{45} + 23 q^{46} + 50 q^{47} + 51 q^{48} + 67 q^{49} - 4 q^{50} + 2 q^{51} + 41 q^{52} + 5 q^{54} + 18 q^{55} - 54 q^{56} + 36 q^{57} + 27 q^{58} + 26 q^{59} - 2 q^{60} + 23 q^{61} + 27 q^{62} + 25 q^{63} + 70 q^{64} + 7 q^{65} - 3 q^{66} + 30 q^{67} - 22 q^{68} + 37 q^{69} + 59 q^{70} + 34 q^{71} + 12 q^{72} + 54 q^{73} + 18 q^{74} + 43 q^{75} + 40 q^{76} - 5 q^{77} + 5 q^{78} + 35 q^{79} - 46 q^{80} + 32 q^{81} + 23 q^{83} + 54 q^{84} + 59 q^{85} - 5 q^{86} + 2 q^{87} - 13 q^{88} + 16 q^{89} + 2 q^{90} + 25 q^{91} + 101 q^{92} + 44 q^{93} - 16 q^{94} - q^{95} + 19 q^{96} + 44 q^{97} - 44 q^{98} + 17 q^{99}+O(q^{100}) \) 32 * q + 5 * q^2 + 32 * q^3 + 41 * q^4 + 7 * q^5 + 5 * q^6 + 25 * q^7 + 12 * q^8 + 32 * q^9 + 2 * q^10 + 17 * q^11 + 41 * q^12 + 32 * q^13 - 10 * q^14 + 7 * q^15 + 51 * q^16 + 2 * q^17 + 5 * q^18 + 36 * q^19 - 2 * q^20 + 25 * q^21 - 3 * q^22 + 37 * q^23 + 12 * q^24 + 43 * q^25 + 5 * q^26 + 32 * q^27 + 54 * q^28 + 2 * q^29 + 2 * q^30 + 44 * q^31 + 19 * q^32 + 17 * q^33 + 27 * q^34 - 10 * q^35 + 41 * q^36 + 46 * q^37 - 6 * q^38 + 32 * q^39 - 6 * q^40 + 5 * q^41 - 10 * q^42 + 19 * q^43 + 37 * q^44 + 7 * q^45 + 23 * q^46 + 50 * q^47 + 51 * q^48 + 67 * q^49 - 4 * q^50 + 2 * q^51 + 41 * q^52 + 5 * q^54 + 18 * q^55 - 54 * q^56 + 36 * q^57 + 27 * q^58 + 26 * q^59 - 2 * q^60 + 23 * q^61 + 27 * q^62 + 25 * q^63 + 70 * q^64 + 7 * q^65 - 3 * q^66 + 30 * q^67 - 22 * q^68 + 37 * q^69 + 59 * q^70 + 34 * q^71 + 12 * q^72 + 54 * q^73 + 18 * q^74 + 43 * q^75 + 40 * q^76 - 5 * q^77 + 5 * q^78 + 35 * q^79 - 46 * q^80 + 32 * q^81 + 23 * q^83 + 54 * q^84 + 59 * q^85 - 5 * q^86 + 2 * q^87 - 13 * q^88 + 16 * q^89 + 2 * q^90 + 25 * q^91 + 101 * q^92 + 44 * q^93 - 16 * q^94 - q^95 + 19 * q^96 + 44 * q^97 - 44 * q^98 + 17 * q^99

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