LMFDB - Embedded newform 4034.2.a.a.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4034,2,Mod(1,4034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4034, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("4034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4034 = 2 \cdot 2017 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4034.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:	$32.2116521754$
Analytic rank:	$1$
Dimension:	$33$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	4034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.73259 q^{3} +1.00000 q^{4} +3.77683 q^{5} -1.73259 q^{6} +0.621551 q^{7} +1.00000 q^{8} +0.00185264 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.73259 q^{3} +1.00000 q^{4} +3.77683 q^{5} -1.73259 q^{6} +0.621551 q^{7} +1.00000 q^{8} +0.00185264 q^{9} +3.77683 q^{10} -4.90919 q^{11} -1.73259 q^{12} -3.53636 q^{13} +0.621551 q^{14} -6.54368 q^{15} +1.00000 q^{16} -2.59436 q^{17} +0.00185264 q^{18} +5.60263 q^{19} +3.77683 q^{20} -1.07689 q^{21} -4.90919 q^{22} -3.80155 q^{23} -1.73259 q^{24} +9.26444 q^{25} -3.53636 q^{26} +5.19455 q^{27} +0.621551 q^{28} -9.57782 q^{29} -6.54368 q^{30} -4.66673 q^{31} +1.00000 q^{32} +8.50559 q^{33} -2.59436 q^{34} +2.34749 q^{35} +0.00185264 q^{36} -7.86970 q^{37} +5.60263 q^{38} +6.12704 q^{39} +3.77683 q^{40} -3.30469 q^{41} -1.07689 q^{42} +6.25439 q^{43} -4.90919 q^{44} +0.00699710 q^{45} -3.80155 q^{46} +3.02481 q^{47} -1.73259 q^{48} -6.61367 q^{49} +9.26444 q^{50} +4.49495 q^{51} -3.53636 q^{52} -7.54417 q^{53} +5.19455 q^{54} -18.5412 q^{55} +0.621551 q^{56} -9.70703 q^{57} -9.57782 q^{58} -5.00346 q^{59} -6.54368 q^{60} -10.5657 q^{61} -4.66673 q^{62} +0.00115151 q^{63} +1.00000 q^{64} -13.3562 q^{65} +8.50559 q^{66} -14.3564 q^{67} -2.59436 q^{68} +6.58651 q^{69} +2.34749 q^{70} +14.5392 q^{71} +0.00185264 q^{72} +10.1792 q^{73} -7.86970 q^{74} -16.0514 q^{75} +5.60263 q^{76} -3.05131 q^{77} +6.12704 q^{78} -3.02045 q^{79} +3.77683 q^{80} -9.00555 q^{81} -3.30469 q^{82} -9.48350 q^{83} -1.07689 q^{84} -9.79846 q^{85} +6.25439 q^{86} +16.5944 q^{87} -4.90919 q^{88} +11.2726 q^{89} +0.00699710 q^{90} -2.19803 q^{91} -3.80155 q^{92} +8.08550 q^{93} +3.02481 q^{94} +21.1602 q^{95} -1.73259 q^{96} +11.8726 q^{97} -6.61367 q^{98} -0.00909495 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 33 q + 33 q^{2} - 14 q^{3} + 33 q^{4} - 22 q^{5} - 14 q^{6} - 12 q^{7} + 33 q^{8} + 17 q^{9}+O(q^{10}) $ 33 * q + 33 * q^2 - 14 * q^3 + 33 * q^4 - 22 * q^5 - 14 * q^6 - 12 * q^7 + 33 * q^8 + 17 * q^9	\( 33 q + 33 q^{2} - 14 q^{3} + 33 q^{4} - 22 q^{5} - 14 q^{6} - 12 q^{7} + 33 q^{8} + 17 q^{9} - 22 q^{10} - 19 q^{11} - 14 q^{12} - 29 q^{13} - 12 q^{14} - 5 q^{15} + 33 q^{16} - 47 q^{17} + 17 q^{18} - 35 q^{19} - 22 q^{20} - 31 q^{21} - 19 q^{22} - 2 q^{23} - 14 q^{24} + 13 q^{25} - 29 q^{26} - 47 q^{27} - 12 q^{28} - 29 q^{29} - 5 q^{30} - 53 q^{31} + 33 q^{32} - 23 q^{33} - 47 q^{34} - 14 q^{35} + 17 q^{36} - 42 q^{37} - 35 q^{38} - 22 q^{40} - 42 q^{41} - 31 q^{42} - 26 q^{43} - 19 q^{44} - 55 q^{45} - 2 q^{46} - 14 q^{48} - 21 q^{49} + 13 q^{50} - 13 q^{51} - 29 q^{52} - 40 q^{53} - 47 q^{54} - 34 q^{55} - 12 q^{56} - 30 q^{57} - 29 q^{58} - 45 q^{59} - 5 q^{60} - 93 q^{61} - 53 q^{62} + 4 q^{63} + 33 q^{64} - 26 q^{65} - 23 q^{66} - 28 q^{67} - 47 q^{68} - 60 q^{69} - 14 q^{70} + 4 q^{71} + 17 q^{72} - 52 q^{73} - 42 q^{74} - 41 q^{75} - 35 q^{76} - 38 q^{77} - 38 q^{79} - 22 q^{80} + 25 q^{81} - 42 q^{82} - 42 q^{83} - 31 q^{84} - 21 q^{85} - 26 q^{86} + 12 q^{87} - 19 q^{88} - 58 q^{89} - 55 q^{90} - 79 q^{91} - 2 q^{92} + 25 q^{93} + 16 q^{95} - 14 q^{96} - 64 q^{97} - 21 q^{98} - 38 q^{99}+O(q^{100}) \) 33 * q + 33 * q^2 - 14 * q^3 + 33 * q^4 - 22 * q^5 - 14 * q^6 - 12 * q^7 + 33 * q^8 + 17 * q^9 - 22 * q^10 - 19 * q^11 - 14 * q^12 - 29 * q^13 - 12 * q^14 - 5 * q^15 + 33 * q^16 - 47 * q^17 + 17 * q^18 - 35 * q^19 - 22 * q^20 - 31 * q^21 - 19 * q^22 - 2 * q^23 - 14 * q^24 + 13 * q^25 - 29 * q^26 - 47 * q^27 - 12 * q^28 - 29 * q^29 - 5 * q^30 - 53 * q^31 + 33 * q^32 - 23 * q^33 - 47 * q^34 - 14 * q^35 + 17 * q^36 - 42 * q^37 - 35 * q^38 - 22 * q^40 - 42 * q^41 - 31 * q^42 - 26 * q^43 - 19 * q^44 - 55 * q^45 - 2 * q^46 - 14 * q^48 - 21 * q^49 + 13 * q^50 - 13 * q^51 - 29 * q^52 - 40 * q^53 - 47 * q^54 - 34 * q^55 - 12 * q^56 - 30 * q^57 - 29 * q^58 - 45 * q^59 - 5 * q^60 - 93 * q^61 - 53 * q^62 + 4 * q^63 + 33 * q^64 - 26 * q^65 - 23 * q^66 - 28 * q^67 - 47 * q^68 - 60 * q^69 - 14 * q^70 + 4 * q^71 + 17 * q^72 - 52 * q^73 - 42 * q^74 - 41 * q^75 - 35 * q^76 - 38 * q^77 - 38 * q^79 - 22 * q^80 + 25 * q^81 - 42 * q^82 - 42 * q^83 - 31 * q^84 - 21 * q^85 - 26 * q^86 + 12 * q^87 - 19 * q^88 - 58 * q^89 - 55 * q^90 - 79 * q^91 - 2 * q^92 + 25 * q^93 + 16 * q^95 - 14 * q^96 - 64 * q^97 - 21 * q^98 - 38 * 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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.73259	−1.00031	−0.500154	−	0.865936i	$-0.666723\pi$
$3$	−1.73259	−1.00031	−0.500154	+	0.865936i	$0.666723\pi$
$4$	1.00000	0.500000
$5$	3.77683	1.68905	0.844525	−	0.535516i	$-0.179883\pi$
$5$	3.77683	1.68905	0.844525	+	0.535516i	$0.179883\pi$
$6$	−1.73259	−0.707325
$7$	0.621551	0.234924	0.117462	−	0.993077i	$-0.462524\pi$
$7$	0.621551	0.234924	0.117462	+	0.993077i	$0.462524\pi$
$8$	1.00000	0.353553
$9$	0.00185264	0.000617546 0
$10$	3.77683	1.19434
$11$	−4.90919	−1.48018	−0.740088	−	0.672510i	$-0.765216\pi$
$11$	−4.90919	−1.48018	−0.740088	+	0.672510i	$0.765216\pi$
$12$	−1.73259	−0.500154
$13$	−3.53636	−0.980809	−0.490404	−	0.871495i	$-0.663151\pi$
$13$	−3.53636	−0.980809	−0.490404	+	0.871495i	$0.663151\pi$
$14$	0.621551	0.166117
$15$	−6.54368	−1.68957
$16$	1.00000	0.250000
$17$	−2.59436	−0.629225	−0.314612	−	0.949220i	$-0.601875\pi$
$17$	−2.59436	−0.629225	−0.314612	+	0.949220i	$0.601875\pi$
$18$	0.00185264	0.000436671 0
$19$	5.60263	1.28533	0.642665	−	0.766147i	$-0.277829\pi$
$19$	5.60263	1.28533	0.642665	+	0.766147i	$0.277829\pi$
$20$	3.77683	0.844525
$21$	−1.07689	−0.234997
$22$	−4.90919	−1.04664
$23$	−3.80155	−0.792677	−0.396339	−	0.918104i	$-0.629719\pi$
$23$	−3.80155	−0.792677	−0.396339	+	0.918104i	$0.629719\pi$
$24$	−1.73259	−0.353663
$25$	9.26444	1.85289
$26$	−3.53636	−0.693537
$27$	5.19455	0.999691
$28$	0.621551	0.117462
$29$	−9.57782	−1.77856	−0.889278	−	0.457367i	$-0.848793\pi$
$29$	−9.57782	−1.77856	−0.889278	+	0.457367i	$0.848793\pi$
$30$	−6.54368	−1.19471
$31$	−4.66673	−0.838169	−0.419084	−	0.907947i	$-0.637649\pi$
$31$	−4.66673	−0.838169	−0.419084	+	0.907947i	$0.637649\pi$
$32$	1.00000	0.176777
$33$	8.50559	1.48063
$34$	−2.59436	−0.444929
$35$	2.34749	0.396799
$36$	0.00185264	0.000308773 0
$37$	−7.86970	−1.29377	−0.646885	−	0.762587i	$-0.723929\pi$
$37$	−7.86970	−1.29377	−0.646885	+	0.762587i	$0.723929\pi$
$38$	5.60263	0.908866
$39$	6.12704	0.981112
$40$	3.77683	0.597169
$41$	−3.30469	−0.516106	−0.258053	−	0.966131i	$-0.583081\pi$
$41$	−3.30469	−0.516106	−0.258053	+	0.966131i	$0.583081\pi$
$42$	−1.07689	−0.166168
$43$	6.25439	0.953786	0.476893	−	0.878961i	$-0.341763\pi$
$43$	6.25439	0.953786	0.476893	+	0.878961i	$0.341763\pi$
$44$	−4.90919	−0.740088
$45$	0.00699710	0.00104307
$46$	−3.80155	−0.560508
$47$	3.02481	0.441214	0.220607	−	0.975363i	$-0.429196\pi$
$47$	3.02481	0.441214	0.220607	+	0.975363i	$0.429196\pi$
$48$	−1.73259	−0.250077
$49$	−6.61367	−0.944811
$50$	9.26444	1.31019
$51$	4.49495	0.629419
$52$	−3.53636	−0.490404
$53$	−7.54417	−1.03627	−0.518136	−	0.855298i	$-0.673374\pi$
$53$	−7.54417	−1.03627	−0.518136	+	0.855298i	$0.673374\pi$
$54$	5.19455	0.706888
$55$	−18.5412	−2.50009
$56$	0.621551	0.0830583
$57$	−9.70703	−1.28573
$58$	−9.57782	−1.25763
$59$	−5.00346	−0.651394	−0.325697	−	0.945474i	$-0.605599\pi$
$59$	−5.00346	−0.651394	−0.325697	+	0.945474i	$0.605599\pi$
$60$	−6.54368	−0.844786
$61$	−10.5657	−1.35280	−0.676401	−	0.736534i	$-0.736461\pi$
$61$	−10.5657	−1.35280	−0.676401	+	0.736534i	$0.736461\pi$
$62$	−4.66673	−0.592675
$63$	0.00115151	0.000145077 0
$64$	1.00000	0.125000
$65$	−13.3562	−1.65663
$66$	8.50559	1.04697
$67$	−14.3564	−1.75392	−0.876960	−	0.480564i	$-0.840432\pi$
$67$	−14.3564	−1.75392	−0.876960	+	0.480564i	$0.840432\pi$
$68$	−2.59436	−0.314612
$69$	6.58651	0.792922
$70$	2.34749	0.280579
$71$	14.5392	1.72548	0.862742	−	0.505644i	$-0.168745\pi$
$71$	14.5392	1.72548	0.862742	+	0.505644i	$0.168745\pi$
$72$	0.00185264	0.000218336 0
$73$	10.1792	1.19138	0.595692	−	0.803213i	$-0.296878\pi$
$73$	10.1792	1.19138	0.595692	+	0.803213i	$0.296878\pi$
$74$	−7.86970	−0.914834
$75$	−16.0514	−1.85346
$76$	5.60263	0.642665
$77$	−3.05131	−0.347729
$78$	6.12704	0.693751
$79$	−3.02045	−0.339828	−0.169914	−	0.985459i	$-0.554349\pi$
$79$	−3.02045	−0.339828	−0.169914	+	0.985459i	$0.554349\pi$
$80$	3.77683	0.422262
$81$	−9.00555	−1.00062
$82$	−3.30469	−0.364942
$83$	−9.48350	−1.04095	−0.520475	−	0.853877i	$-0.674245\pi$
$83$	−9.48350	−1.04095	−0.520475	+	0.853877i	$0.674245\pi$
$84$	−1.07689	−0.117498
$85$	−9.79846	−1.06279
$86$	6.25439	0.674429
$87$	16.5944	1.77911
$88$	−4.90919	−0.523321
$89$	11.2726	1.19490	0.597448	−	0.801908i	$-0.296181\pi$
$89$	11.2726	1.19490	0.597448	+	0.801908i	$0.296181\pi$
$90$	0.00699710	0.000737559 0
$91$	−2.19803	−0.230416
$92$	−3.80155	−0.396339
$93$	8.08550	0.838427
$94$	3.02481	0.311985
$95$	21.1602	2.17099
$96$	−1.73259	−0.176831
$97$	11.8726	1.20548	0.602739	−	0.797939i	$-0.294076\pi$
$97$	11.8726	1.20548	0.602739	+	0.797939i	$0.294076\pi$
$98$	−6.61367	−0.668082
$99$	−0.00909495	−0.000914077 0
$100$	9.26444	0.926444
$101$	14.9142	1.48402	0.742009	−	0.670390i	$-0.233873\pi$
$101$	14.9142	1.48402	0.742009	+	0.670390i	$0.233873\pi$
$102$	4.49495	0.445066
$103$	−10.8435	−1.06844	−0.534222	−	0.845344i	$-0.679395\pi$
$103$	−10.8435	−1.06844	−0.534222	+	0.845344i	$0.679395\pi$
$104$	−3.53636	−0.346768
$105$	−4.06723	−0.396921
$106$	−7.54417	−0.732754
$107$	14.7724	1.42810	0.714052	−	0.700093i	$-0.246858\pi$
$107$	14.7724	1.42810	0.714052	+	0.700093i	$0.246858\pi$
$108$	5.19455	0.499845
$109$	−2.39562	−0.229459	−0.114730	−	0.993397i	$-0.536600\pi$
$109$	−2.39562	−0.229459	−0.114730	+	0.993397i	$0.536600\pi$
$110$	−18.5412	−1.76783
$111$	13.6349	1.29417
$112$	0.621551	0.0587311
$113$	−0.865594	−0.0814282	−0.0407141	−	0.999171i	$-0.512963\pi$
$113$	−0.865594	−0.0814282	−0.0407141	+	0.999171i	$0.512963\pi$
$114$	−9.70703	−0.909147
$115$	−14.3578	−1.33887
$116$	−9.57782	−0.889278
$117$	−0.00655159	−0.000605695 0
$118$	−5.00346	−0.460605
$119$	−1.61253	−0.147820
$120$	−6.54368	−0.597354
$121$	13.1002	1.19092
$122$	−10.5657	−0.956575
$123$	5.72566	0.516265
$124$	−4.66673	−0.419084
$125$	16.1061	1.44057
$126$	0.00115151	0.000102585 0
$127$	−0.632403	−0.0561167	−0.0280583	−	0.999606i	$-0.508932\pi$
$127$	−0.632403	−0.0561167	−0.0280583	+	0.999606i	$0.508932\pi$
$128$	1.00000	0.0883883
$129$	−10.8363	−0.954081
$130$	−13.3562	−1.17142
$131$	17.5997	1.53769	0.768846	−	0.639434i	$-0.220831\pi$
$131$	17.5997	1.53769	0.768846	+	0.639434i	$0.220831\pi$
$132$	8.50559	0.740317
$133$	3.48232	0.301955
$134$	−14.3564	−1.24021
$135$	19.6189	1.68853
$136$	−2.59436	−0.222465
$137$	−21.1911	−1.81048	−0.905238	−	0.424906i	$-0.860307\pi$
$137$	−21.1911	−1.81048	−0.905238	+	0.424906i	$0.860307\pi$
$138$	6.58651	0.560681
$139$	−1.55184	−0.131625	−0.0658126	−	0.997832i	$-0.520964\pi$
$139$	−1.55184	−0.131625	−0.0658126	+	0.997832i	$0.520964\pi$
$140$	2.34749	0.198399
$141$	−5.24074	−0.441350
$142$	14.5392	1.22010
$143$	17.3606	1.45177
$144$	0.00185264	0.000154387 0
$145$	−36.1738	−3.00407
$146$	10.1792	0.842436
$147$	11.4588	0.945102
$148$	−7.86970	−0.646885
$149$	−13.0891	−1.07230	−0.536150	−	0.844123i	$-0.680122\pi$
$149$	−13.0891	−1.07230	−0.536150	+	0.844123i	$0.680122\pi$
$150$	−16.0514	−1.31059
$151$	−2.62847	−0.213902	−0.106951	−	0.994264i	$-0.534109\pi$
$151$	−2.62847	−0.213902	−0.106951	+	0.994264i	$0.534109\pi$
$152$	5.60263	0.454433
$153$	−0.00480641	−0.000388575 0
$154$	−3.05131	−0.245882
$155$	−17.6254	−1.41571
$156$	6.12704	0.490556
$157$	−5.27520	−0.421007	−0.210503	−	0.977593i	$-0.567510\pi$
$157$	−5.27520	−0.421007	−0.210503	+	0.977593i	$0.567510\pi$
$158$	−3.02045	−0.240294
$159$	13.0709	1.03659
$160$	3.77683	0.298585
$161$	−2.36286	−0.186219
$162$	−9.00555	−0.707543
$163$	5.44532	0.426510	0.213255	−	0.976997i	$-0.431593\pi$
$163$	5.44532	0.426510	0.213255	+	0.976997i	$0.431593\pi$
$164$	−3.30469	−0.258053
$165$	32.1242	2.50086
$166$	−9.48350	−0.736062
$167$	6.68002	0.516915	0.258458	−	0.966023i	$-0.416786\pi$
$167$	6.68002	0.516915	0.258458	+	0.966023i	$0.416786\pi$
$168$	−1.07689	−0.0830839
$169$	−0.494183	−0.0380141
$170$	−9.79846	−0.751507
$171$	0.0103796	0.000793751 0
$172$	6.25439	0.476893
$173$	−18.8548	−1.43350	−0.716752	−	0.697328i	$-0.754372\pi$
$173$	−18.8548	−1.43350	−0.716752	+	0.697328i	$0.754372\pi$
$174$	16.5944	1.25802
$175$	5.75833	0.435289
$176$	−4.90919	−0.370044
$177$	8.66891	0.651595
$178$	11.2726	0.844919
$179$	−4.53842	−0.339218	−0.169609	−	0.985511i	$-0.554250\pi$
$179$	−4.53842	−0.339218	−0.169609	+	0.985511i	$0.554250\pi$
$180$	0.00699710	0.000521533 0
$181$	−0.815070	−0.0605837	−0.0302919	−	0.999541i	$-0.509644\pi$
$181$	−0.815070	−0.0605837	−0.0302919	+	0.999541i	$0.509644\pi$
$182$	−2.19803	−0.162929
$183$	18.3060	1.35322
$184$	−3.80155	−0.280254
$185$	−29.7225	−2.18524
$186$	8.08550	0.592858
$187$	12.7362	0.931364
$188$	3.02481	0.220607
$189$	3.22868	0.234852
$190$	21.1602	1.53512
$191$	22.6936	1.64205	0.821025	−	0.570892i	$-0.193403\pi$
$191$	22.6936	1.64205	0.821025	+	0.570892i	$0.193403\pi$
$192$	−1.73259	−0.125039
$193$	−25.2255	−1.81577	−0.907886	−	0.419217i	$-0.862305\pi$
$193$	−25.2255	−1.81577	−0.907886	+	0.419217i	$0.862305\pi$
$194$	11.8726	0.852401
$195$	23.1408	1.65715
$196$	−6.61367	−0.472405
$197$	18.5006	1.31812	0.659058	−	0.752092i	$-0.270955\pi$
$197$	18.5006	1.31812	0.659058	+	0.752092i	$0.270955\pi$
$198$	−0.00909495	−0.000646350 0
$199$	−10.4840	−0.743191	−0.371596	−	0.928395i	$-0.621189\pi$
$199$	−10.4840	−0.743191	−0.371596	+	0.928395i	$0.621189\pi$
$200$	9.26444	0.655095
$201$	24.8738	1.75446
$202$	14.9142	1.04936
$203$	−5.95310	−0.417826
$204$	4.49495	0.314709
$205$	−12.4812	−0.871728
$206$	−10.8435	−0.755504
$207$	−0.00704289	−0.000489515 0
$208$	−3.53636	−0.245202
$209$	−27.5044	−1.90252
$210$	−4.06723	−0.280666
$211$	−23.3984	−1.61081	−0.805405	−	0.592726i	$-0.798052\pi$
$211$	−23.3984	−1.61081	−0.805405	+	0.592726i	$0.798052\pi$
$212$	−7.54417	−0.518136
$213$	−25.1904	−1.72602
$214$	14.7724	1.00982
$215$	23.6218	1.61099
$216$	5.19455	0.353444
$217$	−2.90061	−0.196906
$218$	−2.39562	−0.162252
$219$	−17.6363	−1.19175
$220$	−18.5412	−1.25005
$221$	9.17458	0.617149
$222$	13.6349	0.915116
$223$	−4.59552	−0.307739	−0.153870	−	0.988091i	$-0.549174\pi$
$223$	−4.59552	−0.307739	−0.153870	+	0.988091i	$0.549174\pi$
$224$	0.621551	0.0415291
$225$	0.0171637	0.00114424
$226$	−0.865594	−0.0575785
$227$	27.3416	1.81473	0.907364	−	0.420346i	$-0.138091\pi$
$227$	27.3416	1.81473	0.907364	+	0.420346i	$0.138091\pi$
$228$	−9.70703	−0.642864
$229$	13.5896	0.898024	0.449012	−	0.893526i	$-0.351776\pi$
$229$	13.5896	0.898024	0.449012	+	0.893526i	$0.351776\pi$
$230$	−14.3578	−0.946725
$231$	5.28666	0.347837
$232$	−9.57782	−0.628814
$233$	−19.3322	−1.26650	−0.633248	−	0.773949i	$-0.718279\pi$
$233$	−19.3322	−1.26650	−0.633248	+	0.773949i	$0.718279\pi$
$234$	−0.00655159	−0.000428291 0
$235$	11.4242	0.745232
$236$	−5.00346	−0.325697
$237$	5.23320	0.339933
$238$	−1.61253	−0.104525
$239$	−2.46101	−0.159190	−0.0795948	−	0.996827i	$-0.525363\pi$
$239$	−2.46101	−0.159190	−0.0795948	+	0.996827i	$0.525363\pi$
$240$	−6.54368	−0.422393
$241$	−11.7413	−0.756321	−0.378160	−	0.925740i	$-0.623443\pi$
$241$	−11.7413	−0.756321	−0.378160	+	0.925740i	$0.623443\pi$
$242$	13.1002	0.842110
$243$	0.0192532	0.00123509
$244$	−10.5657	−0.676401
$245$	−24.9787	−1.59583
$246$	5.72566	0.365055
$247$	−19.8129	−1.26066
$248$	−4.66673	−0.296337
$249$	16.4310	1.04127
$250$	16.1061	1.01864
$251$	−19.1216	−1.20695	−0.603473	−	0.797383i	$-0.706217\pi$
$251$	−19.1216	−1.20695	−0.603473	+	0.797383i	$0.706217\pi$
$252$	0.00115151	7.25383e−5 0
$253$	18.6625	1.17330
$254$	−0.632403	−0.0396805
$255$	16.9767	1.06312
$256$	1.00000	0.0625000
$257$	11.7111	0.730521	0.365261	−	0.930905i	$-0.380980\pi$
$257$	11.7111	0.730521	0.365261	+	0.930905i	$0.380980\pi$
$258$	−10.8363	−0.674637
$259$	−4.89142	−0.303938
$260$	−13.3562	−0.828317
$261$	−0.0177442	−0.00109834
$262$	17.5997	1.08731
$263$	−16.5775	−1.02221	−0.511107	−	0.859517i	$-0.670765\pi$
$263$	−16.5775	−1.02221	−0.511107	+	0.859517i	$0.670765\pi$
$264$	8.50559	0.523483
$265$	−28.4930	−1.75031
$266$	3.48232	0.213515
$267$	−19.5308	−1.19527
$268$	−14.3564	−0.876960
$269$	15.3069	0.933280	0.466640	−	0.884447i	$-0.345464\pi$
$269$	15.3069	0.933280	0.466640	+	0.884447i	$0.345464\pi$
$270$	19.6189	1.19397
$271$	24.9658	1.51657	0.758284	−	0.651925i	$-0.226038\pi$
$271$	24.9658	1.51657	0.758284	+	0.651925i	$0.226038\pi$
$272$	−2.59436	−0.157306
$273$	3.80827	0.230487
$274$	−21.1911	−1.28020
$275$	−45.4809	−2.74260
$276$	6.58651	0.396461
$277$	−13.9757	−0.839717	−0.419859	−	0.907589i	$-0.637920\pi$
$277$	−13.9757	−0.839717	−0.419859	+	0.907589i	$0.637920\pi$
$278$	−1.55184	−0.0930731
$279$	−0.00864575	−0.000517608 0
$280$	2.34749	0.140290
$281$	−21.0698	−1.25692	−0.628461	−	0.777841i	$-0.716315\pi$
$281$	−21.0698	−1.25692	−0.628461	+	0.777841i	$0.716315\pi$
$282$	−5.24074	−0.312082
$283$	21.3065	1.26654	0.633269	−	0.773932i	$-0.281713\pi$
$283$	21.3065	1.26654	0.633269	+	0.773932i	$0.281713\pi$
$284$	14.5392	0.862742
$285$	−36.6618	−2.17166
$286$	17.3606	1.02656
$287$	−2.05403	−0.121246
$288$	0.00185264	0.000109168 0
$289$	−10.2693	−0.604076
$290$	−36.1738	−2.12420
$291$	−20.5702	−1.20585
$292$	10.1792	0.595692
$293$	−2.38555	−0.139365	−0.0696826	−	0.997569i	$-0.522199\pi$
$293$	−2.38555	−0.139365	−0.0696826	+	0.997569i	$0.522199\pi$
$294$	11.4588	0.668288
$295$	−18.8972	−1.10024
$296$	−7.86970	−0.457417
$297$	−25.5010	−1.47972
$298$	−13.0891	−0.758231
$299$	13.4436	0.777465
$300$	−16.0514	−0.926730
$301$	3.88743	0.224068
$302$	−2.62847	−0.151251
$303$	−25.8401	−1.48448
$304$	5.60263	0.321333
$305$	−39.9049	−2.28495
$306$	−0.00480641	−0.000274764 0
$307$	−13.5514	−0.773421	−0.386711	−	0.922201i	$-0.626389\pi$
$307$	−13.5514	−0.773421	−0.386711	+	0.922201i	$0.626389\pi$
$308$	−3.05131	−0.173865
$309$	18.7873	1.06877
$310$	−17.6254	−1.00106
$311$	13.7149	0.777702	0.388851	−	0.921301i	$-0.372872\pi$
$311$	13.7149	0.777702	0.388851	+	0.921301i	$0.372872\pi$
$312$	6.12704	0.346875
$313$	35.0160	1.97922	0.989612	−	0.143764i	$-0.0459206\pi$
$313$	35.0160	1.97922	0.989612	+	0.143764i	$0.0459206\pi$
$314$	−5.27520	−0.297697
$315$	0.00434906	0.000245042 0
$316$	−3.02045	−0.169914
$317$	−5.40085	−0.303342	−0.151671	−	0.988431i	$-0.548465\pi$
$317$	−5.40085	−0.303342	−0.151671	+	0.988431i	$0.548465\pi$
$318$	13.0709	0.732981
$319$	47.0193	2.63258
$320$	3.77683	0.211131
$321$	−25.5945	−1.42854
$322$	−2.36286	−0.131677
$323$	−14.5352	−0.808762
$324$	−9.00555	−0.500309
$325$	−32.7624	−1.81733
$326$	5.44532	0.301588
$327$	4.15063	0.229530
$328$	−3.30469	−0.182471
$329$	1.88007	0.103652
$330$	32.1242	1.76838
$331$	8.59437	0.472389	0.236195	−	0.971706i	$-0.424100\pi$
$331$	8.59437	0.472389	0.236195	+	0.971706i	$0.424100\pi$
$332$	−9.48350	−0.520475
$333$	−0.0145797	−0.000798963 0
$334$	6.68002	0.365514
$335$	−54.2219	−2.96246
$336$	−1.07689	−0.0587492
$337$	3.09887	0.168806	0.0844032	−	0.996432i	$-0.473102\pi$
$337$	3.09887	0.168806	0.0844032	+	0.996432i	$0.473102\pi$
$338$	−0.494183	−0.0268800
$339$	1.49972	0.0814534
$340$	−9.79846	−0.531396
$341$	22.9098	1.24064
$342$	0.0103796	0.000561267 0
$343$	−8.46160	−0.456883
$344$	6.25439	0.337214
$345$	24.8761	1.33928
$346$	−18.8548	−1.01364
$347$	12.4036	0.665861	0.332930	−	0.942951i	$-0.391963\pi$
$347$	12.4036	0.665861	0.332930	+	0.942951i	$0.391963\pi$
$348$	16.5944	0.889553
$349$	−0.0554332	−0.00296727	−0.00148364	−	0.999999i	$-0.500472\pi$
$349$	−0.0554332	−0.00296727	−0.00148364	+	0.999999i	$0.500472\pi$
$350$	5.75833	0.307796
$351$	−18.3698	−0.980506
$352$	−4.90919	−0.261661
$353$	25.1781	1.34010	0.670048	−	0.742318i	$-0.266274\pi$
$353$	25.1781	1.34010	0.670048	+	0.742318i	$0.266274\pi$
$354$	8.66891	0.460748
$355$	54.9120	2.91443
$356$	11.2726	0.597448
$357$	2.79384	0.147866
$358$	−4.53842	−0.239863
$359$	−9.97920	−0.526682	−0.263341	−	0.964703i	$-0.584824\pi$
$359$	−9.97920	−0.526682	−0.263341	+	0.964703i	$0.584824\pi$
$360$	0.00699710	0.000368780 0
$361$	12.3894	0.652075
$362$	−0.815070	−0.0428392
$363$	−22.6971	−1.19129
$364$	−2.19803	−0.115208
$365$	38.4451	2.01231
$366$	18.3060	0.956871
$367$	−13.1325	−0.685509	−0.342754	−	0.939425i	$-0.611360\pi$
$367$	−13.1325	−0.685509	−0.342754	+	0.939425i	$0.611360\pi$
$368$	−3.80155	−0.198169
$369$	−0.00612239	−0.000318719 0
$370$	−29.7225	−1.54520
$371$	−4.68909	−0.243445
$372$	8.08550	0.419214
$373$	5.76800	0.298656	0.149328	−	0.988788i	$-0.452289\pi$
$373$	5.76800	0.298656	0.149328	+	0.988788i	$0.452289\pi$
$374$	12.7362	0.658574
$375$	−27.9052	−1.44102
$376$	3.02481	0.155993
$377$	33.8706	1.74442
$378$	3.22868	0.166065
$379$	−15.3569	−0.788832	−0.394416	−	0.918932i	$-0.629053\pi$
$379$	−15.3569	−0.788832	−0.394416	+	0.918932i	$0.629053\pi$
$380$	21.1602	1.08549
$381$	1.09569	0.0561340
$382$	22.6936	1.16110
$383$	26.4174	1.34986	0.674932	−	0.737880i	$-0.264173\pi$
$383$	26.4174	1.34986	0.674932	+	0.737880i	$0.264173\pi$
$384$	−1.73259	−0.0884156
$385$	−11.5243	−0.587332
$386$	−25.2255	−1.28394
$387$	0.0115871	0.000589007 0
$388$	11.8726	0.602739
$389$	−3.03008	−0.153631	−0.0768156	−	0.997045i	$-0.524475\pi$
$389$	−3.03008	−0.153631	−0.0768156	+	0.997045i	$0.524475\pi$
$390$	23.1408	1.17178
$391$	9.86258	0.498772
$392$	−6.61367	−0.334041
$393$	−30.4930	−1.53817
$394$	18.5006	0.932049
$395$	−11.4077	−0.573986
$396$	−0.00909495	−0.000457039 0
$397$	−9.12769	−0.458105	−0.229053	−	0.973414i	$-0.573563\pi$
$397$	−9.12769	−0.458105	−0.229053	+	0.973414i	$0.573563\pi$
$398$	−10.4840	−0.525515
$399$	−6.03342	−0.302049
$400$	9.26444	0.463222
$401$	−33.4946	−1.67264	−0.836321	−	0.548239i	$-0.815298\pi$
$401$	−33.4946	−1.67264	−0.836321	+	0.548239i	$0.815298\pi$
$402$	24.8738	1.24059
$403$	16.5032	0.822083
$404$	14.9142	0.742009
$405$	−34.0124	−1.69009
$406$	−5.95310	−0.295448
$407$	38.6338	1.91501
$408$	4.49495	0.222533
$409$	24.4021	1.20661	0.603304	−	0.797512i	$-0.293851\pi$
$409$	24.4021	1.20661	0.603304	+	0.797512i	$0.293851\pi$
$410$	−12.4812	−0.616405
$411$	36.7153	1.81103
$412$	−10.8435	−0.534222
$413$	−3.10990	−0.153028
$414$	−0.00704289	−0.000346139 0
$415$	−35.8176	−1.75822
$416$	−3.53636	−0.173384
$417$	2.68869	0.131666
$418$	−27.5044	−1.34528
$419$	−37.1260	−1.81373	−0.906863	−	0.421426i	$-0.861530\pi$
$419$	−37.1260	−1.81373	−0.906863	+	0.421426i	$0.861530\pi$
$420$	−4.06723	−0.198461
$421$	13.5621	0.660977	0.330489	−	0.943810i	$-0.392786\pi$
$421$	13.5621	0.660977	0.330489	+	0.943810i	$0.392786\pi$
$422$	−23.3984	−1.13901
$423$	0.00560388	0.000272470 0
$424$	−7.54417	−0.366377
$425$	−24.0353	−1.16588
$426$	−25.1904	−1.22048
$427$	−6.56714	−0.317806
$428$	14.7724	0.714052
$429$	−30.0788	−1.45222
$430$	23.6218	1.13914
$431$	9.34716	0.450237	0.225118	−	0.974331i	$-0.427723\pi$
$431$	9.34716	0.450237	0.225118	+	0.974331i	$0.427723\pi$
$432$	5.19455	0.249923
$433$	−17.1095	−0.822228	−0.411114	−	0.911584i	$-0.634860\pi$
$433$	−17.1095	−0.822228	−0.411114	+	0.911584i	$0.634860\pi$
$434$	−2.90061	−0.139234
$435$	62.6742	3.00500
$436$	−2.39562	−0.114730
$437$	−21.2986	−1.01885
$438$	−17.6363	−0.842696
$439$	16.5822	0.791428	0.395714	−	0.918374i	$-0.370497\pi$
$439$	16.5822	0.791428	0.395714	+	0.918374i	$0.370497\pi$
$440$	−18.5412	−0.883916
$441$	−0.0122527	−0.000583464 0
$442$	9.17458	0.436390
$443$	3.46718	0.164731	0.0823654	−	0.996602i	$-0.473753\pi$
$443$	3.46718	0.164731	0.0823654	+	0.996602i	$0.473753\pi$
$444$	13.6349	0.647085
$445$	42.5748	2.01824
$446$	−4.59552	−0.217604
$447$	22.6780	1.07263
$448$	0.621551	0.0293655
$449$	−22.4490	−1.05944	−0.529718	−	0.848174i	$-0.677702\pi$
$449$	−22.4490	−1.05944	−0.529718	+	0.848174i	$0.677702\pi$
$450$	0.0171637	0.000809103 0
$451$	16.2233	0.763928
$452$	−0.865594	−0.0407141
$453$	4.55405	0.213968
$454$	27.3416	1.28321
$455$	−8.30157	−0.389184
$456$	−9.70703	−0.454573
$457$	−21.8893	−1.02394	−0.511968	−	0.859004i	$-0.671084\pi$
$457$	−21.8893	−1.02394	−0.511968	+	0.859004i	$0.671084\pi$
$458$	13.5896	0.634999
$459$	−13.4765	−0.629030
$460$	−14.3578	−0.669436
$461$	−4.12669	−0.192199	−0.0960996	−	0.995372i	$-0.530637\pi$
$461$	−4.12669	−0.192199	−0.0960996	+	0.995372i	$0.530637\pi$
$462$	5.28666	0.245958
$463$	−2.12230	−0.0986318	−0.0493159	−	0.998783i	$-0.515704\pi$
$463$	−2.12230	−0.0986318	−0.0493159	+	0.998783i	$0.515704\pi$
$464$	−9.57782	−0.444639
$465$	30.5376	1.41615
$466$	−19.3322	−0.895548
$467$	−2.27060	−0.105071	−0.0525353	−	0.998619i	$-0.516730\pi$
$467$	−2.27060	−0.105071	−0.0525353	+	0.998619i	$0.516730\pi$
$468$	−0.00655159	−0.000302847 0
$469$	−8.92327	−0.412038
$470$	11.4242	0.526959
$471$	9.13974	0.421137
$472$	−5.00346	−0.230303
$473$	−30.7040	−1.41177
$474$	5.23320	0.240369
$475$	51.9052	2.38157
$476$	−1.61253	−0.0739101
$477$	−0.0139766	−0.000639945 0
$478$	−2.46101	−0.112564
$479$	−18.8788	−0.862596	−0.431298	−	0.902209i	$-0.641944\pi$
$479$	−18.8788	−0.862596	−0.431298	+	0.902209i	$0.641944\pi$
$480$	−6.54368	−0.298677
$481$	27.8301	1.26894
$482$	−11.7413	−0.534800
$483$	4.09385	0.186277
$484$	13.1002	0.595461
$485$	44.8407	2.03611
$486$	0.0192532	0.000873342 0
$487$	37.6391	1.70559	0.852795	−	0.522246i	$-0.174906\pi$
$487$	37.6391	1.70559	0.852795	+	0.522246i	$0.174906\pi$
$488$	−10.5657	−0.478288
$489$	−9.43448	−0.426642
$490$	−24.9787	−1.12842
$491$	23.2332	1.04850	0.524249	−	0.851565i	$-0.324346\pi$
$491$	23.2332	1.04850	0.524249	+	0.851565i	$0.324346\pi$
$492$	5.72566	0.258133
$493$	24.8483	1.11911
$494$	−19.8129	−0.891424
$495$	−0.0343501	−0.00154392
$496$	−4.66673	−0.209542
$497$	9.03685	0.405358
$498$	16.4310	0.736290
$499$	7.47317	0.334545	0.167272	−	0.985911i	$-0.446504\pi$
$499$	7.47317	0.334545	0.167272	+	0.985911i	$0.446504\pi$
$500$	16.1061	0.720286
$501$	−11.5737	−0.517075
$502$	−19.1216	−0.853440
$503$	−10.2569	−0.457333	−0.228666	−	0.973505i	$-0.573436\pi$
$503$	−10.2569	−0.457333	−0.228666	+	0.973505i	$0.573436\pi$
$504$	0.00115151	5.12923e−5 0
$505$	56.3284	2.50658
$506$	18.6625	0.829650
$507$	0.856215	0.0380258
$508$	−0.632403	−0.0280583
$509$	33.5677	1.48786	0.743932	−	0.668256i	$-0.232959\pi$
$509$	33.5677	1.48786	0.743932	+	0.668256i	$0.232959\pi$
$510$	16.9767	0.751739
$511$	6.32689	0.279885
$512$	1.00000	0.0441942
$513$	29.1031	1.28493
$514$	11.7111	0.516556
$515$	−40.9541	−1.80465
$516$	−10.8363	−0.477040
$517$	−14.8494	−0.653074
$518$	−4.89142	−0.214917
$519$	32.6675	1.43395
$520$	−13.3562	−0.585709
$521$	14.8697	0.651455	0.325727	−	0.945464i	$-0.394391\pi$
$521$	14.8697	0.651455	0.325727	+	0.945464i	$0.394391\pi$
$522$	−0.0177442	−0.000776644 0
$523$	−33.7603	−1.47623	−0.738117	−	0.674673i	$-0.764285\pi$
$523$	−33.7603	−1.47623	−0.738117	+	0.674673i	$0.764285\pi$
$524$	17.5997	0.768846
$525$	−9.97679	−0.435423
$526$	−16.5775	−0.722815
$527$	12.1072	0.527396
$528$	8.50559	0.370158
$529$	−8.54824	−0.371662
$530$	−28.4930	−1.23766
$531$	−0.00926959	−0.000402266 0
$532$	3.48232	0.150978
$533$	11.6866	0.506201
$534$	−19.5308	−0.845180
$535$	55.7929	2.41214
$536$	−14.3564	−0.620104
$537$	7.86320	0.339322
$538$	15.3069	0.659929
$539$	32.4678	1.39849
$540$	19.6189	0.844264
$541$	−34.1029	−1.46620	−0.733100	−	0.680121i	$-0.761927\pi$
$541$	−34.1029	−1.46620	−0.733100	+	0.680121i	$0.761927\pi$
$542$	24.9658	1.07237
$543$	1.41218	0.0606024
$544$	−2.59436	−0.111232
$545$	−9.04787	−0.387568
$546$	3.80827	0.162979
$547$	6.69417	0.286222	0.143111	−	0.989707i	$-0.454289\pi$
$547$	6.69417	0.286222	0.143111	+	0.989707i	$0.454289\pi$
$548$	−21.1911	−0.905238
$549$	−0.0195745	−0.000835417 0
$550$	−45.4809	−1.93931
$551$	−53.6609	−2.28603
$552$	6.58651	0.280340
$553$	−1.87737	−0.0798338
$554$	−13.9757	−0.593770
$555$	51.4968	2.18592
$556$	−1.55184	−0.0658126
$557$	18.8539	0.798867	0.399433	−	0.916762i	$-0.369207\pi$
$557$	18.8539	0.798867	0.399433	+	0.916762i	$0.369207\pi$
$558$	−0.00864575	−0.000366004 0
$559$	−22.1178	−0.935482
$560$	2.34749	0.0991997
$561$	−22.0666	−0.931651
$562$	−21.0698	−0.888778
$563$	−25.8700	−1.09029	−0.545146	−	0.838341i	$-0.683526\pi$
$563$	−25.8700	−1.09029	−0.545146	+	0.838341i	$0.683526\pi$
$564$	−5.24074	−0.220675
$565$	−3.26920	−0.137536
$566$	21.3065	0.895577
$567$	−5.59741	−0.235069
$568$	14.5392	0.610051
$569$	−23.4750	−0.984125	−0.492062	−	0.870560i	$-0.663757\pi$
$569$	−23.4750	−0.984125	−0.492062	+	0.870560i	$0.663757\pi$
$570$	−36.6618	−1.53559
$571$	15.0806	0.631104	0.315552	−	0.948908i	$-0.397810\pi$
$571$	15.0806	0.631104	0.315552	+	0.948908i	$0.397810\pi$
$572$	17.3606	0.725885
$573$	−39.3186	−1.64256
$574$	−2.05403	−0.0857337
$575$	−35.2192	−1.46874
$576$	0.00185264	7.71933e−5 0
$577$	21.0327	0.875603	0.437802	−	0.899072i	$-0.355757\pi$
$577$	21.0327	0.875603	0.437802	+	0.899072i	$0.355757\pi$
$578$	−10.2693	−0.427146
$579$	43.7054	1.81633
$580$	−36.1738	−1.50203
$581$	−5.89448	−0.244544
$582$	−20.5702	−0.852664
$583$	37.0358	1.53386
$584$	10.1792	0.421218
$585$	−0.0247442	−0.00102305
$586$	−2.38555	−0.0985461
$587$	35.5494	1.46728	0.733640	−	0.679538i	$-0.237820\pi$
$587$	35.5494	1.46728	0.733640	+	0.679538i	$0.237820\pi$
$588$	11.4588	0.472551
$589$	−26.1459	−1.07732
$590$	−18.8972	−0.777985
$591$	−32.0539	−1.31852
$592$	−7.86970	−0.323443
$593$	−6.49658	−0.266783	−0.133391	−	0.991063i	$-0.542587\pi$
$593$	−6.49658	−0.266783	−0.133391	+	0.991063i	$0.542587\pi$
$594$	−25.5010	−1.04632
$595$	−6.09024	−0.249676
$596$	−13.0891	−0.536150
$597$	18.1644	0.743421
$598$	13.4436	0.549751
$599$	33.7615	1.37946	0.689729	−	0.724067i	$-0.257730\pi$
$599$	33.7615	1.37946	0.689729	+	0.724067i	$0.257730\pi$
$600$	−16.0514	−0.655297
$601$	−30.7641	−1.25489	−0.627447	−	0.778660i	$-0.715900\pi$
$601$	−30.7641	−1.25489	−0.627447	+	0.778660i	$0.715900\pi$
$602$	3.88743	0.158440
$603$	−0.0265973	−0.00108313
$604$	−2.62847	−0.106951
$605$	49.4770	2.01153
$606$	−25.8401	−1.04968
$607$	0.834643	0.0338771	0.0169386	−	0.999857i	$-0.494608\pi$
$607$	0.834643	0.0338771	0.0169386	+	0.999857i	$0.494608\pi$
$608$	5.60263	0.227216
$609$	10.3143	0.417955
$610$	−39.9049	−1.61570
$611$	−10.6968	−0.432746
$612$	−0.00480641	−0.000194288 0
$613$	1.10651	0.0446915	0.0223457	−	0.999750i	$-0.492887\pi$
$613$	1.10651	0.0446915	0.0223457	+	0.999750i	$0.492887\pi$
$614$	−13.5514	−0.546891
$615$	21.6248	0.871997
$616$	−3.05131	−0.122941
$617$	15.2320	0.613217	0.306608	−	0.951836i	$-0.400806\pi$
$617$	15.2320	0.613217	0.306608	+	0.951836i	$0.400806\pi$
$618$	18.7873	0.755737
$619$	−43.4313	−1.74565	−0.872825	−	0.488033i	$-0.837714\pi$
$619$	−43.4313	−1.74565	−0.872825	+	0.488033i	$0.837714\pi$
$620$	−17.6254	−0.707854
$621$	−19.7473	−0.792433
$622$	13.7149	0.549918
$623$	7.00652	0.280710
$624$	6.12704	0.245278
$625$	14.5077	0.580308
$626$	35.0160	1.39952
$627$	47.6537	1.90310
$628$	−5.27520	−0.210503
$629$	20.4168	0.814072
$630$	0.00434906	0.000173271 0
$631$	−13.8953	−0.553164	−0.276582	−	0.960990i	$-0.589202\pi$
$631$	−13.8953	−0.553164	−0.276582	+	0.960990i	$0.589202\pi$
$632$	−3.02045	−0.120147
$633$	40.5396	1.61131
$634$	−5.40085	−0.214495
$635$	−2.38848	−0.0947839
$636$	13.0709	0.518296
$637$	23.3883	0.926679
$638$	47.0193	1.86151
$639$	0.0269359	0.00106557
$640$	3.77683	0.149292
$641$	42.0089	1.65925	0.829625	−	0.558320i	$-0.188554\pi$
$641$	42.0089	1.65925	0.829625	+	0.558320i	$0.188554\pi$
$642$	−25.5945	−1.01013
$643$	−31.4562	−1.24051	−0.620255	−	0.784400i	$-0.712971\pi$
$643$	−31.4562	−1.24051	−0.620255	+	0.784400i	$0.712971\pi$
$644$	−2.36286	−0.0931096
$645$	−40.9268	−1.61149
$646$	−14.5352	−0.571881
$647$	27.7208	1.08982	0.544908	−	0.838496i	$-0.316564\pi$
$647$	27.7208	1.08982	0.544908	+	0.838496i	$0.316564\pi$
$648$	−9.00555	−0.353772
$649$	24.5629	0.964179
$650$	−32.7624	−1.28505
$651$	5.02555	0.196967
$652$	5.44532	0.213255
$653$	−6.91434	−0.270579	−0.135289	−	0.990806i	$-0.543196\pi$
$653$	−6.91434	−0.270579	−0.135289	+	0.990806i	$0.543196\pi$
$654$	4.15063	0.162302
$655$	66.4710	2.59724
$656$	−3.30469	−0.129026
$657$	0.0188584	0.000735735 0
$658$	1.88007	0.0732929
$659$	−28.5785	−1.11326	−0.556630	−	0.830760i	$-0.687906\pi$
$659$	−28.5785	−1.11326	−0.556630	+	0.830760i	$0.687906\pi$
$660$	32.1242	1.25043
$661$	−40.6031	−1.57928	−0.789638	−	0.613573i	$-0.789732\pi$
$661$	−40.6031	−1.57928	−0.789638	+	0.613573i	$0.789732\pi$
$662$	8.59437	0.334030
$663$	−15.8957	−0.617340
$664$	−9.48350	−0.368031
$665$	13.1521	0.510018
$666$	−0.0145797	−0.000564952 0
$667$	36.4105	1.40982
$668$	6.68002	0.258458
$669$	7.96214	0.307834
$670$	−54.2219	−2.09477
$671$	51.8691	2.00239
$672$	−1.07689	−0.0415420
$673$	4.07153	0.156946	0.0784729	−	0.996916i	$-0.474996\pi$
$673$	4.07153	0.156946	0.0784729	+	0.996916i	$0.474996\pi$
$674$	3.09887	0.119364
$675$	48.1246	1.85232
$676$	−0.494183	−0.0190071
$677$	−40.1448	−1.54289	−0.771446	−	0.636295i	$-0.780466\pi$
$677$	−40.1448	−1.54289	−0.771446	+	0.636295i	$0.780466\pi$
$678$	1.49972	0.0575962
$679$	7.37941	0.283196
$680$	−9.79846	−0.375754
$681$	−47.3717	−1.81529
$682$	22.9098	0.877263
$683$	7.04570	0.269596	0.134798	−	0.990873i	$-0.456961\pi$
$683$	7.04570	0.269596	0.134798	+	0.990873i	$0.456961\pi$
$684$	0.0103796	0.000396875 0
$685$	−80.0351	−3.05798
$686$	−8.46160	−0.323065
$687$	−23.5451	−0.898302
$688$	6.25439	0.238447
$689$	26.6789	1.01638
$690$	24.8761	0.947017
$691$	−3.88409	−0.147758	−0.0738788	−	0.997267i	$-0.523538\pi$
$691$	−3.88409	−0.147758	−0.0738788	+	0.997267i	$0.523538\pi$
$692$	−18.8548	−0.716752
$693$	−0.00565298	−0.000214739 0
$694$	12.4036	0.470835
$695$	−5.86103	−0.222322
$696$	16.5944	0.629009
$697$	8.57355	0.324746
$698$	−0.0554332	−0.00209818
$699$	33.4947	1.26689
$700$	5.75833	0.217644
$701$	20.4366	0.771879	0.385939	−	0.922524i	$-0.373877\pi$
$701$	20.4366	0.771879	0.385939	+	0.922524i	$0.373877\pi$
$702$	−18.3698	−0.693322
$703$	−44.0910	−1.66292
$704$	−4.90919	−0.185022
$705$	−19.7934	−0.745462
$706$	25.1781	0.947591
$707$	9.26993	0.348632
$708$	8.66891	0.325798
$709$	14.1727	0.532268	0.266134	−	0.963936i	$-0.414254\pi$
$709$	14.1727	0.532268	0.266134	+	0.963936i	$0.414254\pi$
$710$	54.9120	2.06081
$711$	−0.00559581	−0.000209859 0
$712$	11.2726	0.422460
$713$	17.7408	0.664397
$714$	2.79384	0.104557
$715$	65.5682	2.45211
$716$	−4.53842	−0.169609
$717$	4.26391	0.159239
$718$	−9.97920	−0.372420
$719$	18.8891	0.704444	0.352222	−	0.935916i	$-0.385426\pi$
$719$	18.8891	0.704444	0.352222	+	0.935916i	$0.385426\pi$
$720$	0.00699710	0.000260767 0
$721$	−6.73980	−0.251003
$722$	12.3894	0.461086
$723$	20.3427	0.756554
$724$	−0.815070	−0.0302919
$725$	−88.7332	−3.29547
$726$	−22.6971	−0.842370
$727$	12.7517	0.472933	0.236467	−	0.971640i	$-0.424011\pi$
$727$	12.7517	0.472933	0.236467	+	0.971640i	$0.424011\pi$
$728$	−2.19803	−0.0814643
$729$	26.9833	0.999382
$730$	38.4451	1.42292
$731$	−16.2261	−0.600146
$732$	18.3060	0.676610
$733$	21.8668	0.807669	0.403834	−	0.914832i	$-0.367677\pi$
$733$	21.8668	0.807669	0.403834	+	0.914832i	$0.367677\pi$
$734$	−13.1325	−0.484728
$735$	43.2778	1.59632
$736$	−3.80155	−0.140127
$737$	70.4785	2.59611
$738$	−0.00612239	−0.000225368 0
$739$	10.4322	0.383755	0.191877	−	0.981419i	$-0.438542\pi$
$739$	10.4322	0.383755	0.191877	+	0.981419i	$0.438542\pi$
$740$	−29.7225	−1.09262
$741$	34.3275	1.26105
$742$	−4.68909	−0.172142
$743$	−20.0029	−0.733834	−0.366917	−	0.930254i	$-0.619587\pi$
$743$	−20.0029	−0.733834	−0.366917	+	0.930254i	$0.619587\pi$
$744$	8.08550	0.296429
$745$	−49.4353	−1.81117
$746$	5.76800	0.211182
$747$	−0.0175695	−0.000642834 0
$748$	12.7362	0.465682
$749$	9.18181	0.335496
$750$	−27.9052	−1.01895
$751$	−45.4446	−1.65830	−0.829149	−	0.559027i	$-0.811175\pi$
$751$	−45.4446	−1.65830	−0.829149	+	0.559027i	$0.811175\pi$
$752$	3.02481	0.110303
$753$	33.1298	1.20732
$754$	33.8706	1.23349
$755$	−9.92728	−0.361291
$756$	3.22868	0.117426
$757$	34.6114	1.25797	0.628986	−	0.777417i	$-0.283470\pi$
$757$	34.6114	1.25797	0.628986	+	0.777417i	$0.283470\pi$
$758$	−15.3569	−0.557789
$759$	−32.3344	−1.17366
$760$	21.1602	0.767560
$761$	−21.4182	−0.776408	−0.388204	−	0.921573i	$-0.626904\pi$
$761$	−21.4182	−0.776408	−0.388204	+	0.921573i	$0.626904\pi$
$762$	1.09569	0.0396927
$763$	−1.48900	−0.0539056
$764$	22.6936	0.821025
$765$	−0.0181530	−0.000656323 0
$766$	26.4174	0.954498
$767$	17.6940	0.638893
$768$	−1.73259	−0.0625193
$769$	28.0138	1.01020	0.505102	−	0.863060i	$-0.331455\pi$
$769$	28.0138	1.01020	0.505102	+	0.863060i	$0.331455\pi$
$770$	−11.5243	−0.415307
$771$	−20.2906	−0.730747
$772$	−25.2255	−0.907886
$773$	6.91305	0.248645	0.124323	−	0.992242i	$-0.460324\pi$
$773$	6.91305	0.248645	0.124323	+	0.992242i	$0.460324\pi$
$774$	0.0115871	0.000416491 0
$775$	−43.2346	−1.55303
$776$	11.8726	0.426200
$777$	8.47480	0.304032
$778$	−3.03008	−0.108634
$779$	−18.5149	−0.663366
$780$	23.1408	0.828573
$781$	−71.3756	−2.55402
$782$	9.86258	0.352685
$783$	−49.7524	−1.77801
$784$	−6.61367	−0.236203
$785$	−19.9235	−0.711101
$786$	−30.4930	−1.08765
$787$	−20.7761	−0.740586	−0.370293	−	0.928915i	$-0.620743\pi$
$787$	−20.7761	−0.740586	−0.370293	+	0.928915i	$0.620743\pi$
$788$	18.5006	0.659058
$789$	28.7220	1.02253
$790$	−11.4077	−0.405869
$791$	−0.538011	−0.0191295
$792$	−0.00909495	−0.000323175 0
$793$	37.3641	1.32684
$794$	−9.12769	−0.323929
$795$	49.3666	1.75085
$796$	−10.4840	−0.371596
$797$	−20.4994	−0.726125	−0.363062	−	0.931765i	$-0.618269\pi$
$797$	−20.4994	−0.726125	−0.363062	+	0.931765i	$0.618269\pi$
$798$	−6.03342	−0.213581
$799$	−7.84744	−0.277623
$800$	9.26444	0.327548
$801$	0.0208841	0.000737903 0
$802$	−33.4946	−1.18274
$803$	−49.9716	−1.76346
$804$	24.8738	0.877230
$805$	−8.92411	−0.314533
$806$	16.5032	0.581301
$807$	−26.5206	−0.933568
$808$	14.9142	0.524679
$809$	20.4663	0.719557	0.359779	−	0.933038i	$-0.382852\pi$
$809$	20.4663	0.719557	0.359779	+	0.933038i	$0.382852\pi$
$810$	−34.0124	−1.19508
$811$	1.02643	0.0360427	0.0180214	−	0.999838i	$-0.494263\pi$
$811$	1.02643	0.0360427	0.0180214	+	0.999838i	$0.494263\pi$
$812$	−5.95310	−0.208913
$813$	−43.2555	−1.51704
$814$	38.6338	1.35412
$815$	20.5660	0.720397
$816$	4.49495	0.157355
$817$	35.0410	1.22593
$818$	24.4021	0.853200
$819$	−0.00407215	−0.000142292 0
$820$	−12.4812	−0.435864
$821$	9.71180	0.338944	0.169472	−	0.985535i	$-0.445794\pi$
$821$	9.71180	0.338944	0.169472	+	0.985535i	$0.445794\pi$
$822$	36.7153	1.28059
$823$	42.3147	1.47500	0.737499	−	0.675348i	$-0.236006\pi$
$823$	42.3147	1.47500	0.737499	+	0.675348i	$0.236006\pi$
$824$	−10.8435	−0.377752
$825$	78.7996	2.74345
$826$	−3.10990	−0.108207
$827$	2.38718	0.0830104	0.0415052	−	0.999138i	$-0.486785\pi$
$827$	2.38718	0.0830104	0.0415052	+	0.999138i	$0.486785\pi$
$828$	−0.00704289	−0.000244757 0
$829$	−11.6753	−0.405499	−0.202750	−	0.979231i	$-0.564988\pi$
$829$	−11.6753	−0.405499	−0.202750	+	0.979231i	$0.564988\pi$
$830$	−35.8176	−1.24325
$831$	24.2141	0.839977
$832$	−3.53636	−0.122601
$833$	17.1582	0.594498
$834$	2.68869	0.0931019
$835$	25.2293	0.873096
$836$	−27.5044	−0.951258
$837$	−24.2415	−0.837910
$838$	−37.1260	−1.28250
$839$	−49.0254	−1.69254	−0.846272	−	0.532751i	$-0.821158\pi$
$839$	−49.0254	−1.69254	−0.846272	+	0.532751i	$0.821158\pi$
$840$	−4.06723	−0.140333
$841$	62.7346	2.16326
$842$	13.5621	0.467382
$843$	36.5053	1.25731
$844$	−23.3984	−0.805405
$845$	−1.86645	−0.0642077
$846$	0.00560388	0.000192665 0
$847$	8.14242	0.279777
$848$	−7.54417	−0.259068
$849$	−36.9153	−1.26693
$850$	−24.0353	−0.824404
$851$	29.9170	1.02554
$852$	−25.1904	−0.863008
$853$	11.0020	0.376700	0.188350	−	0.982102i	$-0.439686\pi$
$853$	11.0020	0.376700	0.188350	+	0.982102i	$0.439686\pi$
$854$	−6.56714	−0.224723
$855$	0.0392021	0.00134068
$856$	14.7724	0.504911
$857$	48.2961	1.64976	0.824882	−	0.565305i	$-0.191241\pi$
$857$	48.2961	1.64976	0.824882	+	0.565305i	$0.191241\pi$
$858$	−30.0788	−1.02687
$859$	−34.5108	−1.17749	−0.588746	−	0.808318i	$-0.700378\pi$
$859$	−34.5108	−1.17749	−0.588746	+	0.808318i	$0.700378\pi$
$860$	23.6218	0.805496
$861$	3.55879	0.121283
$862$	9.34716	0.318366
$863$	49.8336	1.69635	0.848177	−	0.529713i	$-0.177700\pi$
$863$	49.8336	1.69635	0.848177	+	0.529713i	$0.177700\pi$
$864$	5.19455	0.176722
$865$	−71.2114	−2.42126
$866$	−17.1095	−0.581403
$867$	17.7924	0.604263
$868$	−2.90061	−0.0984531
$869$	14.8280	0.503005
$870$	62.6742	2.12485
$871$	50.7695	1.72026
$872$	−2.39562	−0.0811261
$873$	0.0219956	0.000744438 0
$874$	−21.2986	−0.720438
$875$	10.0108	0.338425
$876$	−17.6363	−0.595876
$877$	13.0465	0.440550	0.220275	−	0.975438i	$-0.429305\pi$
$877$	13.0465	0.440550	0.220275	+	0.975438i	$0.429305\pi$
$878$	16.5822	0.559624
$879$	4.13317	0.139408
$880$	−18.5412	−0.625023
$881$	−38.4371	−1.29498	−0.647490	−	0.762074i	$-0.724181\pi$
$881$	−38.4371	−1.29498	−0.647490	+	0.762074i	$0.724181\pi$
$882$	−0.0122527	−0.000412571 0
$883$	53.6981	1.80708	0.903542	−	0.428500i	$-0.140958\pi$
$883$	53.6981	1.80708	0.903542	+	0.428500i	$0.140958\pi$
$884$	9.17458	0.308575
$885$	32.7410	1.10058
$886$	3.46718	0.116482
$887$	−3.15780	−0.106029	−0.0530143	−	0.998594i	$-0.516883\pi$
$887$	−3.15780	−0.106029	−0.0530143	+	0.998594i	$0.516883\pi$
$888$	13.6349	0.457558
$889$	−0.393071	−0.0131832
$890$	42.5748	1.42711
$891$	44.2100	1.48109
$892$	−4.59552	−0.153870
$893$	16.9469	0.567106
$894$	22.6780	0.758465
$895$	−17.1408	−0.572955
$896$	0.621551	0.0207646
$897$	−23.2922	−0.777705
$898$	−22.4490	−0.749134
$899$	44.6970	1.49073
$900$	0.0171637	0.000572122 0
$901$	19.5723	0.652047
$902$	16.2233	0.540178
$903$	−6.73530	−0.224137
$904$	−0.865594	−0.0287892
$905$	−3.07838	−0.102329
$906$	4.55405	0.151298
$907$	42.4982	1.41113	0.705565	−	0.708645i	$-0.250693\pi$
$907$	42.4982	1.41113	0.705565	+	0.708645i	$0.250693\pi$
$908$	27.3416	0.907364
$909$	0.0276306	0.000916449 0
$910$	−8.30157	−0.275194
$911$	11.7771	0.390192	0.195096	−	0.980784i	$-0.437498\pi$
$911$	11.7771	0.390192	0.195096	+	0.980784i	$0.437498\pi$
$912$	−9.70703	−0.321432
$913$	46.5563	1.54079
$914$	−21.8893	−0.724033
$915$	69.1387	2.28565
$916$	13.5896	0.449012
$917$	10.9391	0.361241
$918$	−13.4765	−0.444792
$919$	38.4144	1.26718	0.633588	−	0.773671i	$-0.281582\pi$
$919$	38.4144	1.26718	0.633588	+	0.773671i	$0.281582\pi$
$920$	−14.3578	−0.473363
$921$	23.4790	0.773660
$922$	−4.12669	−0.135905
$923$	−51.4157	−1.69237
$924$	5.28666	0.173918
$925$	−72.9084	−2.39721
$926$	−2.12230	−0.0697432
$927$	−0.0200891	−0.000659813 0
$928$	−9.57782	−0.314407
$929$	20.4523	0.671017	0.335509	−	0.942037i	$-0.391092\pi$
$929$	20.4523	0.671017	0.335509	+	0.942037i	$0.391092\pi$
$930$	30.5376	1.00137
$931$	−37.0539	−1.21439
$932$	−19.3322	−0.633248
$933$	−23.7623	−0.777942
$934$	−2.27060	−0.0742962
$935$	48.1025	1.57312
$936$	−0.00655159	−0.000214145 0
$937$	0.419647	0.0137093	0.00685464	−	0.999977i	$-0.497818\pi$
$937$	0.419647	0.0137093	0.00685464	+	0.999977i	$0.497818\pi$
$938$	−8.92327	−0.291355
$939$	−60.6683	−1.97984
$940$	11.4242	0.372616
$941$	13.3075	0.433813	0.216907	−	0.976192i	$-0.430403\pi$
$941$	13.3075	0.433813	0.216907	+	0.976192i	$0.430403\pi$
$942$	9.13974	0.297789
$943$	12.5629	0.409105
$944$	−5.00346	−0.162849
$945$	12.1942	0.396676
$946$	−30.7040	−0.998274
$947$	5.40132	0.175519	0.0877597	−	0.996142i	$-0.472029\pi$
$947$	5.40132	0.175519	0.0877597	+	0.996142i	$0.472029\pi$
$948$	5.23320	0.169966
$949$	−35.9973	−1.16852
$950$	51.9052	1.68403
$951$	9.35743	0.303435
$952$	−1.61253	−0.0522623
$953$	−18.4431	−0.597430	−0.298715	−	0.954342i	$-0.596558\pi$
$953$	−18.4431	−0.597430	−0.298715	+	0.954342i	$0.596558\pi$
$954$	−0.0139766	−0.000452510 0
$955$	85.7098	2.77350
$956$	−2.46101	−0.0795948
$957$	−81.4650	−2.63339
$958$	−18.8788	−0.609948
$959$	−13.1713	−0.425325
$960$	−6.54368	−0.211196
$961$	−9.22167	−0.297473
$962$	27.8301	0.897277
$963$	0.0273679	0.000881920 0
$964$	−11.7413	−0.378160
$965$	−95.2725	−3.06693
$966$	4.09385	0.131717
$967$	9.12307	0.293378	0.146689	−	0.989183i	$-0.453138\pi$
$967$	9.12307	0.293378	0.146689	+	0.989183i	$0.453138\pi$
$968$	13.1002	0.421055
$969$	25.1835	0.809011
$970$	44.8407	1.43975
$971$	35.6150	1.14294	0.571470	−	0.820623i	$-0.306373\pi$
$971$	35.6150	1.14294	0.571470	+	0.820623i	$0.306373\pi$
$972$	0.0192532	0.000617546 0
$973$	−0.964547	−0.0309220
$974$	37.6391	1.20603
$975$	56.7636	1.81789
$976$	−10.5657	−0.338200
$977$	29.8122	0.953777	0.476888	−	0.878964i	$-0.341765\pi$
$977$	29.8122	0.953777	0.476888	+	0.878964i	$0.341765\pi$
$978$	−9.43448	−0.301681
$979$	−55.3395	−1.76866
$980$	−24.9787	−0.797916
$981$	−0.00443823	−0.000141702 0
$982$	23.2332	0.741400
$983$	−38.0320	−1.21303	−0.606516	−	0.795071i	$-0.707433\pi$
$983$	−38.0320	−1.21303	−0.606516	+	0.795071i	$0.707433\pi$
$984$	5.72566	0.182527
$985$	69.8738	2.22636
$986$	24.8483	0.791331
$987$	−3.25739	−0.103684
$988$	−19.8129	−0.630332
$989$	−23.7764	−0.756045
$990$	−0.0343501	−0.00109172
$991$	−8.82535	−0.280346	−0.140173	−	0.990127i	$-0.544766\pi$
$991$	−8.82535	−0.280346	−0.140173	+	0.990127i	$0.544766\pi$
$992$	−4.66673	−0.148169
$993$	−14.8905	−0.472535
$994$	9.03685	0.286631
$995$	−39.5963	−1.25529
$996$	16.4310	0.520635
$997$	14.3728	0.455192	0.227596	−	0.973756i	$-0.426913\pi$
$997$	14.3728	0.455192	0.227596	+	0.973756i	$0.426913\pi$
$998$	7.47317	0.236559
$999$	−40.8795	−1.29337

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4034.2.a.a.1.10	✓	33

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4034.2.a.a.1.10	✓	33	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:	\( N \)	\(=\)	\( 4034 = 2 \cdot 2017 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4034.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.73259 q^{3} +1.00000 q^{4} +3.77683 q^{5} -1.73259 q^{6} +0.621551 q^{7} +1.00000 q^{8} +0.00185264 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.73259 q^{3} +1.00000 q^{4} +3.77683 q^{5} -1.73259 q^{6} +0.621551 q^{7} +1.00000 q^{8} +0.00185264 q^{9} +3.77683 q^{10} -4.90919 q^{11} -1.73259 q^{12} -3.53636 q^{13} +0.621551 q^{14} -6.54368 q^{15} +1.00000 q^{16} -2.59436 q^{17} +0.00185264 q^{18} +5.60263 q^{19} +3.77683 q^{20} -1.07689 q^{21} -4.90919 q^{22} -3.80155 q^{23} -1.73259 q^{24} +9.26444 q^{25} -3.53636 q^{26} +5.19455 q^{27} +0.621551 q^{28} -9.57782 q^{29} -6.54368 q^{30} -4.66673 q^{31} +1.00000 q^{32} +8.50559 q^{33} -2.59436 q^{34} +2.34749 q^{35} +0.00185264 q^{36} -7.86970 q^{37} +5.60263 q^{38} +6.12704 q^{39} +3.77683 q^{40} -3.30469 q^{41} -1.07689 q^{42} +6.25439 q^{43} -4.90919 q^{44} +0.00699710 q^{45} -3.80155 q^{46} +3.02481 q^{47} -1.73259 q^{48} -6.61367 q^{49} +9.26444 q^{50} +4.49495 q^{51} -3.53636 q^{52} -7.54417 q^{53} +5.19455 q^{54} -18.5412 q^{55} +0.621551 q^{56} -9.70703 q^{57} -9.57782 q^{58} -5.00346 q^{59} -6.54368 q^{60} -10.5657 q^{61} -4.66673 q^{62} +0.00115151 q^{63} +1.00000 q^{64} -13.3562 q^{65} +8.50559 q^{66} -14.3564 q^{67} -2.59436 q^{68} +6.58651 q^{69} +2.34749 q^{70} +14.5392 q^{71} +0.00185264 q^{72} +10.1792 q^{73} -7.86970 q^{74} -16.0514 q^{75} +5.60263 q^{76} -3.05131 q^{77} +6.12704 q^{78} -3.02045 q^{79} +3.77683 q^{80} -9.00555 q^{81} -3.30469 q^{82} -9.48350 q^{83} -1.07689 q^{84} -9.79846 q^{85} +6.25439 q^{86} +16.5944 q^{87} -4.90919 q^{88} +11.2726 q^{89} +0.00699710 q^{90} -2.19803 q^{91} -3.80155 q^{92} +8.08550 q^{93} +3.02481 q^{94} +21.1602 q^{95} -1.73259 q^{96} +11.8726 q^{97} -6.61367 q^{98} -0.00909495 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 33 q + 33 q^{2} - 14 q^{3} + 33 q^{4} - 22 q^{5} - 14 q^{6} - 12 q^{7} + 33 q^{8} + 17 q^{9}+O(q^{10}) \) 33 * q + 33 * q^2 - 14 * q^3 + 33 * q^4 - 22 * q^5 - 14 * q^6 - 12 * q^7 + 33 * q^8 + 17 * q^9	\( 33 q + 33 q^{2} - 14 q^{3} + 33 q^{4} - 22 q^{5} - 14 q^{6} - 12 q^{7} + 33 q^{8} + 17 q^{9} - 22 q^{10} - 19 q^{11} - 14 q^{12} - 29 q^{13} - 12 q^{14} - 5 q^{15} + 33 q^{16} - 47 q^{17} + 17 q^{18} - 35 q^{19} - 22 q^{20} - 31 q^{21} - 19 q^{22} - 2 q^{23} - 14 q^{24} + 13 q^{25} - 29 q^{26} - 47 q^{27} - 12 q^{28} - 29 q^{29} - 5 q^{30} - 53 q^{31} + 33 q^{32} - 23 q^{33} - 47 q^{34} - 14 q^{35} + 17 q^{36} - 42 q^{37} - 35 q^{38} - 22 q^{40} - 42 q^{41} - 31 q^{42} - 26 q^{43} - 19 q^{44} - 55 q^{45} - 2 q^{46} - 14 q^{48} - 21 q^{49} + 13 q^{50} - 13 q^{51} - 29 q^{52} - 40 q^{53} - 47 q^{54} - 34 q^{55} - 12 q^{56} - 30 q^{57} - 29 q^{58} - 45 q^{59} - 5 q^{60} - 93 q^{61} - 53 q^{62} + 4 q^{63} + 33 q^{64} - 26 q^{65} - 23 q^{66} - 28 q^{67} - 47 q^{68} - 60 q^{69} - 14 q^{70} + 4 q^{71} + 17 q^{72} - 52 q^{73} - 42 q^{74} - 41 q^{75} - 35 q^{76} - 38 q^{77} - 38 q^{79} - 22 q^{80} + 25 q^{81} - 42 q^{82} - 42 q^{83} - 31 q^{84} - 21 q^{85} - 26 q^{86} + 12 q^{87} - 19 q^{88} - 58 q^{89} - 55 q^{90} - 79 q^{91} - 2 q^{92} + 25 q^{93} + 16 q^{95} - 14 q^{96} - 64 q^{97} - 21 q^{98} - 38 q^{99}+O(q^{100}) \) 33 * q + 33 * q^2 - 14 * q^3 + 33 * q^4 - 22 * q^5 - 14 * q^6 - 12 * q^7 + 33 * q^8 + 17 * q^9 - 22 * q^10 - 19 * q^11 - 14 * q^12 - 29 * q^13 - 12 * q^14 - 5 * q^15 + 33 * q^16 - 47 * q^17 + 17 * q^18 - 35 * q^19 - 22 * q^20 - 31 * q^21 - 19 * q^22 - 2 * q^23 - 14 * q^24 + 13 * q^25 - 29 * q^26 - 47 * q^27 - 12 * q^28 - 29 * q^29 - 5 * q^30 - 53 * q^31 + 33 * q^32 - 23 * q^33 - 47 * q^34 - 14 * q^35 + 17 * q^36 - 42 * q^37 - 35 * q^38 - 22 * q^40 - 42 * q^41 - 31 * q^42 - 26 * q^43 - 19 * q^44 - 55 * q^45 - 2 * q^46 - 14 * q^48 - 21 * q^49 + 13 * q^50 - 13 * q^51 - 29 * q^52 - 40 * q^53 - 47 * q^54 - 34 * q^55 - 12 * q^56 - 30 * q^57 - 29 * q^58 - 45 * q^59 - 5 * q^60 - 93 * q^61 - 53 * q^62 + 4 * q^63 + 33 * q^64 - 26 * q^65 - 23 * q^66 - 28 * q^67 - 47 * q^68 - 60 * q^69 - 14 * q^70 + 4 * q^71 + 17 * q^72 - 52 * q^73 - 42 * q^74 - 41 * q^75 - 35 * q^76 - 38 * q^77 - 38 * q^79 - 22 * q^80 + 25 * q^81 - 42 * q^82 - 42 * q^83 - 31 * q^84 - 21 * q^85 - 26 * q^86 + 12 * q^87 - 19 * q^88 - 58 * q^89 - 55 * q^90 - 79 * q^91 - 2 * q^92 + 25 * q^93 + 16 * q^95 - 14 * q^96 - 64 * q^97 - 21 * q^98 - 38 * q^99

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