LMFDB - Embedded newform 4034.2.a.d.1.15

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:	$0$
Dimension:	$52$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.22639 q^{3} +1.00000 q^{4} -1.99280 q^{5} -1.22639 q^{6} -0.468701 q^{7} +1.00000 q^{8} -1.49597 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.22639 q^{3} +1.00000 q^{4} -1.99280 q^{5} -1.22639 q^{6} -0.468701 q^{7} +1.00000 q^{8} -1.49597 q^{9} -1.99280 q^{10} -3.45486 q^{11} -1.22639 q^{12} -1.26776 q^{13} -0.468701 q^{14} +2.44395 q^{15} +1.00000 q^{16} -2.46010 q^{17} -1.49597 q^{18} -5.31368 q^{19} -1.99280 q^{20} +0.574810 q^{21} -3.45486 q^{22} +5.20667 q^{23} -1.22639 q^{24} -1.02874 q^{25} -1.26776 q^{26} +5.51381 q^{27} -0.468701 q^{28} -7.19591 q^{29} +2.44395 q^{30} +2.21935 q^{31} +1.00000 q^{32} +4.23701 q^{33} -2.46010 q^{34} +0.934028 q^{35} -1.49597 q^{36} +2.86218 q^{37} -5.31368 q^{38} +1.55477 q^{39} -1.99280 q^{40} +1.05732 q^{41} +0.574810 q^{42} +9.41639 q^{43} -3.45486 q^{44} +2.98117 q^{45} +5.20667 q^{46} +10.8071 q^{47} -1.22639 q^{48} -6.78032 q^{49} -1.02874 q^{50} +3.01704 q^{51} -1.26776 q^{52} +13.2163 q^{53} +5.51381 q^{54} +6.88486 q^{55} -0.468701 q^{56} +6.51664 q^{57} -7.19591 q^{58} +9.17618 q^{59} +2.44395 q^{60} +11.1857 q^{61} +2.21935 q^{62} +0.701161 q^{63} +1.00000 q^{64} +2.52640 q^{65} +4.23701 q^{66} -14.5904 q^{67} -2.46010 q^{68} -6.38541 q^{69} +0.934028 q^{70} -9.48130 q^{71} -1.49597 q^{72} -8.28665 q^{73} +2.86218 q^{74} +1.26163 q^{75} -5.31368 q^{76} +1.61930 q^{77} +1.55477 q^{78} -7.53123 q^{79} -1.99280 q^{80} -2.27418 q^{81} +1.05732 q^{82} -12.5561 q^{83} +0.574810 q^{84} +4.90249 q^{85} +9.41639 q^{86} +8.82499 q^{87} -3.45486 q^{88} -11.0345 q^{89} +2.98117 q^{90} +0.594201 q^{91} +5.20667 q^{92} -2.72179 q^{93} +10.8071 q^{94} +10.5891 q^{95} -1.22639 q^{96} +1.02710 q^{97} -6.78032 q^{98} +5.16836 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q + 52 q^{2} + 16 q^{3} + 52 q^{4} + 24 q^{5} + 16 q^{6} + 12 q^{7} + 52 q^{8} + 70 q^{9}+O(q^{10}) $ 52 * q + 52 * q^2 + 16 * q^3 + 52 * q^4 + 24 * q^5 + 16 * q^6 + 12 * q^7 + 52 * q^8 + 70 * q^9	\( 52 q + 52 q^{2} + 16 q^{3} + 52 q^{4} + 24 q^{5} + 16 q^{6} + 12 q^{7} + 52 q^{8} + 70 q^{9} + 24 q^{10} + 19 q^{11} + 16 q^{12} + 27 q^{13} + 12 q^{14} + 5 q^{15} + 52 q^{16} + 43 q^{17} + 70 q^{18} + 35 q^{19} + 24 q^{20} + 29 q^{21} + 19 q^{22} + 2 q^{23} + 16 q^{24} + 88 q^{25} + 27 q^{26} + 49 q^{27} + 12 q^{28} + 31 q^{29} + 5 q^{30} + 59 q^{31} + 52 q^{32} + 45 q^{33} + 43 q^{34} + 18 q^{35} + 70 q^{36} + 60 q^{37} + 35 q^{38} + 6 q^{39} + 24 q^{40} + 56 q^{41} + 29 q^{42} + 34 q^{43} + 19 q^{44} + 61 q^{45} + 2 q^{46} - 4 q^{47} + 16 q^{48} + 102 q^{49} + 88 q^{50} + 23 q^{51} + 27 q^{52} + 30 q^{53} + 49 q^{54} + 24 q^{55} + 12 q^{56} + 32 q^{57} + 31 q^{58} + 27 q^{59} + 5 q^{60} + 107 q^{61} + 59 q^{62} - 4 q^{63} + 52 q^{64} + 46 q^{65} + 45 q^{66} + 22 q^{67} + 43 q^{68} + 36 q^{69} + 18 q^{70} + 8 q^{71} + 70 q^{72} + 66 q^{73} + 60 q^{74} + 53 q^{75} + 35 q^{76} + 26 q^{77} + 6 q^{78} + 50 q^{79} + 24 q^{80} + 108 q^{81} + 56 q^{82} + 52 q^{83} + 29 q^{84} + 19 q^{85} + 34 q^{86} - 32 q^{87} + 19 q^{88} + 62 q^{89} + 61 q^{90} + 69 q^{91} + 2 q^{92} + 21 q^{93} - 4 q^{94} - 44 q^{95} + 16 q^{96} + 82 q^{97} + 102 q^{98} + 16 q^{99}+O(q^{100}) \) 52 * q + 52 * q^2 + 16 * q^3 + 52 * q^4 + 24 * q^5 + 16 * q^6 + 12 * q^7 + 52 * q^8 + 70 * q^9 + 24 * q^10 + 19 * q^11 + 16 * q^12 + 27 * q^13 + 12 * q^14 + 5 * q^15 + 52 * q^16 + 43 * q^17 + 70 * q^18 + 35 * q^19 + 24 * q^20 + 29 * q^21 + 19 * q^22 + 2 * q^23 + 16 * q^24 + 88 * q^25 + 27 * q^26 + 49 * q^27 + 12 * q^28 + 31 * q^29 + 5 * q^30 + 59 * q^31 + 52 * q^32 + 45 * q^33 + 43 * q^34 + 18 * q^35 + 70 * q^36 + 60 * q^37 + 35 * q^38 + 6 * q^39 + 24 * q^40 + 56 * q^41 + 29 * q^42 + 34 * q^43 + 19 * q^44 + 61 * q^45 + 2 * q^46 - 4 * q^47 + 16 * q^48 + 102 * q^49 + 88 * q^50 + 23 * q^51 + 27 * q^52 + 30 * q^53 + 49 * q^54 + 24 * q^55 + 12 * q^56 + 32 * q^57 + 31 * q^58 + 27 * q^59 + 5 * q^60 + 107 * q^61 + 59 * q^62 - 4 * q^63 + 52 * q^64 + 46 * q^65 + 45 * q^66 + 22 * q^67 + 43 * q^68 + 36 * q^69 + 18 * q^70 + 8 * q^71 + 70 * q^72 + 66 * q^73 + 60 * q^74 + 53 * q^75 + 35 * q^76 + 26 * q^77 + 6 * q^78 + 50 * q^79 + 24 * q^80 + 108 * q^81 + 56 * q^82 + 52 * q^83 + 29 * q^84 + 19 * q^85 + 34 * q^86 - 32 * q^87 + 19 * q^88 + 62 * q^89 + 61 * q^90 + 69 * q^91 + 2 * q^92 + 21 * q^93 - 4 * q^94 - 44 * q^95 + 16 * q^96 + 82 * q^97 + 102 * q^98 + 16 * 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
$3$	−1.22639	−0.708057	−0.354028	−	0.935235i	$-0.615188\pi$
$3$	−1.22639	−0.708057	−0.354028	+	0.935235i	$0.615188\pi$
$4$	1.00000	0.500000
$5$	−1.99280	−0.891208	−0.445604	−	0.895230i	$-0.647011\pi$
$5$	−1.99280	−0.891208	−0.445604	+	0.895230i	$0.647011\pi$
$6$	−1.22639	−0.500672
$7$	−0.468701	−0.177152	−0.0885761	−	0.996069i	$-0.528232\pi$
$7$	−0.468701	−0.177152	−0.0885761	+	0.996069i	$0.528232\pi$
$8$	1.00000	0.353553
$9$	−1.49597	−0.498656
$10$	−1.99280	−0.630179
$11$	−3.45486	−1.04168	−0.520840	−	0.853654i	$-0.674381\pi$
$11$	−3.45486	−1.04168	−0.520840	+	0.853654i	$0.674381\pi$
$12$	−1.22639	−0.354028
$13$	−1.26776	−0.351614	−0.175807	−	0.984425i	$-0.556253\pi$
$13$	−1.26776	−0.351614	−0.175807	+	0.984425i	$0.556253\pi$
$14$	−0.468701	−0.125266
$15$	2.44395	0.631026
$16$	1.00000	0.250000
$17$	−2.46010	−0.596661	−0.298331	−	0.954463i	$-0.596430\pi$
$17$	−2.46010	−0.596661	−0.298331	+	0.954463i	$0.596430\pi$
$18$	−1.49597	−0.352603
$19$	−5.31368	−1.21904	−0.609521	−	0.792770i	$-0.708638\pi$
$19$	−5.31368	−1.21904	−0.609521	+	0.792770i	$0.708638\pi$
$20$	−1.99280	−0.445604
$21$	0.574810	0.125434
$22$	−3.45486	−0.736579
$23$	5.20667	1.08567	0.542833	−	0.839841i	$-0.317352\pi$
$23$	5.20667	1.08567	0.542833	+	0.839841i	$0.317352\pi$
$24$	−1.22639	−0.250336
$25$	−1.02874	−0.205748
$26$	−1.26776	−0.248629
$27$	5.51381	1.06113
$28$	−0.468701	−0.0885761
$29$	−7.19591	−1.33625	−0.668124	−	0.744050i	$-0.732902\pi$
$29$	−7.19591	−1.33625	−0.668124	+	0.744050i	$0.732902\pi$
$30$	2.44395	0.446203
$31$	2.21935	0.398607	0.199303	−	0.979938i	$-0.436132\pi$
$31$	2.21935	0.398607	0.199303	+	0.979938i	$0.436132\pi$
$32$	1.00000	0.176777
$33$	4.23701	0.737569
$34$	−2.46010	−0.421903
$35$	0.934028	0.157880
$36$	−1.49597	−0.249328
$37$	2.86218	0.470539	0.235269	−	0.971930i	$-0.424403\pi$
$37$	2.86218	0.470539	0.235269	+	0.971930i	$0.424403\pi$
$38$	−5.31368	−0.861993
$39$	1.55477	0.248963
$40$	−1.99280	−0.315090
$41$	1.05732	0.165125	0.0825624	−	0.996586i	$-0.473690\pi$
$41$	1.05732	0.165125	0.0825624	+	0.996586i	$0.473690\pi$
$42$	0.574810	0.0886951
$43$	9.41639	1.43599	0.717993	−	0.696050i	$-0.245061\pi$
$43$	9.41639	1.43599	0.717993	+	0.696050i	$0.245061\pi$
$44$	−3.45486	−0.520840
$45$	2.98117	0.444406
$46$	5.20667	0.767682
$47$	10.8071	1.57637	0.788187	−	0.615436i	$-0.211020\pi$
$47$	10.8071	1.57637	0.788187	+	0.615436i	$0.211020\pi$
$48$	−1.22639	−0.177014
$49$	−6.78032	−0.968617
$50$	−1.02874	−0.145486
$51$	3.01704	0.422470
$52$	−1.26776	−0.175807
$53$	13.2163	1.81540	0.907699	−	0.419621i	$-0.137837\pi$
$53$	13.2163	1.81540	0.907699	+	0.419621i	$0.137837\pi$
$54$	5.51381	0.750334
$55$	6.88486	0.928354
$56$	−0.468701	−0.0626328
$57$	6.51664	0.863151
$58$	−7.19591	−0.944870
$59$	9.17618	1.19464	0.597319	−	0.802004i	$-0.296233\pi$
$59$	9.17618	1.19464	0.597319	+	0.802004i	$0.296233\pi$
$60$	2.44395	0.315513
$61$	11.1857	1.43219	0.716094	−	0.698004i	$-0.245928\pi$
$61$	11.1857	1.43219	0.716094	+	0.698004i	$0.245928\pi$
$62$	2.21935	0.281858
$63$	0.701161	0.0883380
$64$	1.00000	0.125000
$65$	2.52640	0.313362
$66$	4.23701	0.521540
$67$	−14.5904	−1.78250	−0.891251	−	0.453510i	$-0.850172\pi$
$67$	−14.5904	−1.78250	−0.891251	+	0.453510i	$0.850172\pi$
$68$	−2.46010	−0.298331
$69$	−6.38541	−0.768713
$70$	0.934028	0.111638
$71$	−9.48130	−1.12522	−0.562612	−	0.826721i	$-0.690203\pi$
$71$	−9.48130	−1.12522	−0.562612	+	0.826721i	$0.690203\pi$
$72$	−1.49597	−0.176301
$73$	−8.28665	−0.969879	−0.484940	−	0.874548i	$-0.661158\pi$
$73$	−8.28665	−0.969879	−0.484940	+	0.874548i	$0.661158\pi$
$74$	2.86218	0.332721
$75$	1.26163	0.145681
$76$	−5.31368	−0.609521
$77$	1.61930	0.184536
$78$	1.55477	0.176043
$79$	−7.53123	−0.847330	−0.423665	−	0.905819i	$-0.639257\pi$
$79$	−7.53123	−0.847330	−0.423665	+	0.905819i	$0.639257\pi$
$80$	−1.99280	−0.222802
$81$	−2.27418	−0.252686
$82$	1.05732	0.116761
$83$	−12.5561	−1.37821	−0.689104	−	0.724662i	$-0.741996\pi$
$83$	−12.5561	−1.37821	−0.689104	+	0.724662i	$0.741996\pi$
$84$	0.574810	0.0627169
$85$	4.90249	0.531750
$86$	9.41639	1.01540
$87$	8.82499	0.946139
$88$	−3.45486	−0.368290
$89$	−11.0345	−1.16965	−0.584827	−	0.811158i	$-0.698838\pi$
$89$	−11.0345	−1.16965	−0.584827	+	0.811158i	$0.698838\pi$
$90$	2.98117	0.314243
$91$	0.594201	0.0622892
$92$	5.20667	0.542833
$93$	−2.72179	−0.282236
$94$	10.8071	1.11466
$95$	10.5891	1.08642
$96$	−1.22639	−0.125168
$97$	1.02710	0.104286	0.0521431	−	0.998640i	$-0.483395\pi$
$97$	1.02710	0.104286	0.0521431	+	0.998640i	$0.483395\pi$
$98$	−6.78032	−0.684916
$99$	5.16836	0.519440
$100$	−1.02874	−0.102874
$101$	5.56064	0.553305	0.276652	−	0.960970i	$-0.410775\pi$
$101$	5.56064	0.553305	0.276652	+	0.960970i	$0.410775\pi$
$102$	3.01704	0.298731
$103$	17.3209	1.70668	0.853341	−	0.521354i	$-0.174573\pi$
$103$	17.3209	1.70668	0.853341	+	0.521354i	$0.174573\pi$
$104$	−1.26776	−0.124314
$105$	−1.14548	−0.111788
$106$	13.2163	1.28368
$107$	4.27354	0.413139	0.206570	−	0.978432i	$-0.433770\pi$
$107$	4.27354	0.413139	0.206570	+	0.978432i	$0.433770\pi$
$108$	5.51381	0.530567
$109$	9.01216	0.863209	0.431604	−	0.902063i	$-0.357948\pi$
$109$	9.01216	0.863209	0.431604	+	0.902063i	$0.357948\pi$
$110$	6.88486	0.656446
$111$	−3.51014	−0.333168
$112$	−0.468701	−0.0442881
$113$	1.97136	0.185450	0.0927252	−	0.995692i	$-0.470442\pi$
$113$	1.97136	0.185450	0.0927252	+	0.995692i	$0.470442\pi$
$114$	6.51664	0.610340
$115$	−10.3759	−0.967555
$116$	−7.19591	−0.668124
$117$	1.89653	0.175335
$118$	9.17618	0.844736
$119$	1.15305	0.105700
$120$	2.44395	0.223101
$121$	0.936076	0.0850978
$122$	11.1857	1.01271
$123$	−1.29668	−0.116918
$124$	2.21935	0.199303
$125$	12.0141	1.07457
$126$	0.701161	0.0624644
$127$	18.0401	1.60080	0.800402	−	0.599464i	$-0.204620\pi$
$127$	18.0401	1.60080	0.800402	+	0.599464i	$0.204620\pi$
$128$	1.00000	0.0883883
$129$	−11.5482	−1.01676
$130$	2.52640	0.221580
$131$	−10.7284	−0.937346	−0.468673	−	0.883372i	$-0.655268\pi$
$131$	−10.7284	−0.937346	−0.468673	+	0.883372i	$0.655268\pi$
$132$	4.23701	0.368784
$133$	2.49053	0.215956
$134$	−14.5904	−1.26042
$135$	−10.9879	−0.945691
$136$	−2.46010	−0.210952
$137$	−0.261550	−0.0223458	−0.0111729	−	0.999938i	$-0.503557\pi$
$137$	−0.261550	−0.0223458	−0.0111729	+	0.999938i	$0.503557\pi$
$138$	−6.38541	−0.543562
$139$	20.8819	1.77118	0.885591	−	0.464466i	$-0.153754\pi$
$139$	20.8819	1.77118	0.885591	+	0.464466i	$0.153754\pi$
$140$	0.934028	0.0789398
$141$	−13.2537	−1.11616
$142$	−9.48130	−0.795653
$143$	4.37995	0.366270
$144$	−1.49597	−0.124664
$145$	14.3400	1.19087
$146$	−8.28665	−0.685808
$147$	8.31532	0.685836
$148$	2.86218	0.235269
$149$	5.09400	0.417317	0.208658	−	0.977989i	$-0.433090\pi$
$149$	5.09400	0.417317	0.208658	+	0.977989i	$0.433090\pi$
$150$	1.26163	0.103012
$151$	−12.1959	−0.992489	−0.496244	−	0.868183i	$-0.665288\pi$
$151$	−12.1959	−0.992489	−0.496244	+	0.868183i	$0.665288\pi$
$152$	−5.31368	−0.430996
$153$	3.68023	0.297529
$154$	1.61930	0.130487
$155$	−4.42272	−0.355242
$156$	1.55477	0.124481
$157$	22.6683	1.80913	0.904564	−	0.426337i	$-0.140196\pi$
$157$	22.6683	1.80913	0.904564	+	0.426337i	$0.140196\pi$
$158$	−7.53123	−0.599153
$159$	−16.2083	−1.28540
$160$	−1.99280	−0.157545
$161$	−2.44037	−0.192328
$162$	−2.27418	−0.178676
$163$	3.49835	0.274012	0.137006	−	0.990570i	$-0.456252\pi$
$163$	3.49835	0.274012	0.137006	+	0.990570i	$0.456252\pi$
$164$	1.05732	0.0825624
$165$	−8.44352	−0.657327
$166$	−12.5561	−0.974541
$167$	1.11061	0.0859412	0.0429706	−	0.999076i	$-0.486318\pi$
$167$	1.11061	0.0859412	0.0429706	+	0.999076i	$0.486318\pi$
$168$	0.574810	0.0443475
$169$	−11.3928	−0.876367
$170$	4.90249	0.376004
$171$	7.94909	0.607882
$172$	9.41639	0.717993
$173$	−4.81367	−0.365977	−0.182988	−	0.983115i	$-0.558577\pi$
$173$	−4.81367	−0.365977	−0.182988	+	0.983115i	$0.558577\pi$
$174$	8.82499	0.669021
$175$	0.482170	0.0364486
$176$	−3.45486	−0.260420
$177$	−11.2536	−0.845871
$178$	−11.0345	−0.827071
$179$	−0.366851	−0.0274198	−0.0137099	−	0.999906i	$-0.504364\pi$
$179$	−0.366851	−0.0274198	−0.0137099	+	0.999906i	$0.504364\pi$
$180$	2.98117	0.222203
$181$	16.7553	1.24541	0.622706	−	0.782456i	$-0.286033\pi$
$181$	16.7553	1.24541	0.622706	+	0.782456i	$0.286033\pi$
$182$	0.594201	0.0440451
$183$	−13.7181	−1.01407
$184$	5.20667	0.383841
$185$	−5.70375	−0.419348
$186$	−2.72179	−0.199571
$187$	8.49930	0.621530
$188$	10.8071	0.788187
$189$	−2.58433	−0.187982
$190$	10.5891	0.768215
$191$	14.6870	1.06271	0.531357	−	0.847148i	$-0.321682\pi$
$191$	14.6870	1.06271	0.531357	+	0.847148i	$0.321682\pi$
$192$	−1.22639	−0.0885071
$193$	−1.48909	−0.107187	−0.0535935	−	0.998563i	$-0.517068\pi$
$193$	−1.48909	−0.107187	−0.0535935	+	0.998563i	$0.517068\pi$
$194$	1.02710	0.0737415
$195$	−3.09835	−0.221878
$196$	−6.78032	−0.484309
$197$	11.1774	0.796358	0.398179	−	0.917308i	$-0.369642\pi$
$197$	11.1774	0.796358	0.398179	+	0.917308i	$0.369642\pi$
$198$	5.16836	0.367300
$199$	−5.08108	−0.360188	−0.180094	−	0.983649i	$-0.557640\pi$
$199$	−5.08108	−0.360188	−0.180094	+	0.983649i	$0.557640\pi$
$200$	−1.02874	−0.0727428
$201$	17.8935	1.26211
$202$	5.56064	0.391245
$203$	3.37273	0.236719
$204$	3.01704	0.211235
$205$	−2.10702	−0.147161
$206$	17.3209	1.20681
$207$	−7.78902	−0.541374
$208$	−1.26776	−0.0879035
$209$	18.3580	1.26985
$210$	−1.14548	−0.0790458
$211$	16.1157	1.10945	0.554727	−	0.832033i	$-0.312823\pi$
$211$	16.1157	1.10945	0.554727	+	0.832033i	$0.312823\pi$
$212$	13.2163	0.907699
$213$	11.6278	0.796722
$214$	4.27354	0.292133
$215$	−18.7650	−1.27976
$216$	5.51381	0.375167
$217$	−1.04021	−0.0706141
$218$	9.01216	0.610381
$219$	10.1627	0.686729
$220$	6.88486	0.464177
$221$	3.11882	0.209795
$222$	−3.51014	−0.235585
$223$	−14.0246	−0.939158	−0.469579	−	0.882890i	$-0.655594\pi$
$223$	−14.0246	−0.939158	−0.469579	+	0.882890i	$0.655594\pi$
$224$	−0.468701	−0.0313164
$225$	1.53896	0.102597
$226$	1.97136	0.131133
$227$	−11.6235	−0.771478	−0.385739	−	0.922608i	$-0.626054\pi$
$227$	−11.6235	−0.771478	−0.385739	+	0.922608i	$0.626054\pi$
$228$	6.51664	0.431575
$229$	−7.63220	−0.504350	−0.252175	−	0.967682i	$-0.581146\pi$
$229$	−7.63220	−0.504350	−0.252175	+	0.967682i	$0.581146\pi$
$230$	−10.3759	−0.684165
$231$	−1.98589	−0.130662
$232$	−7.19591	−0.472435
$233$	3.48540	0.228336	0.114168	−	0.993461i	$-0.463580\pi$
$233$	3.48540	0.228336	0.114168	+	0.993461i	$0.463580\pi$
$234$	1.89653	0.123980
$235$	−21.5364	−1.40488
$236$	9.17618	0.597319
$237$	9.23623	0.599957
$238$	1.15305	0.0747411
$239$	−20.7109	−1.33967	−0.669837	−	0.742508i	$-0.733636\pi$
$239$	−20.7109	−1.33967	−0.669837	+	0.742508i	$0.733636\pi$
$240$	2.44395	0.157756
$241$	−2.17768	−0.140276	−0.0701382	−	0.997537i	$-0.522344\pi$
$241$	−2.17768	−0.140276	−0.0701382	+	0.997537i	$0.522344\pi$
$242$	0.936076	0.0601732
$243$	−13.7524	−0.882217
$244$	11.1857	0.716094
$245$	13.5118	0.863240
$246$	−1.29668	−0.0826733
$247$	6.73649	0.428632
$248$	2.21935	0.140929
$249$	15.3986	0.975850
$250$	12.0141	0.759837
$251$	−26.2146	−1.65465	−0.827324	−	0.561724i	$-0.810138\pi$
$251$	−26.2146	−1.65465	−0.827324	+	0.561724i	$0.810138\pi$
$252$	0.701161	0.0441690
$253$	−17.9883	−1.13092
$254$	18.0401	1.13194
$255$	−6.01236	−0.376509
$256$	1.00000	0.0625000
$257$	10.8492	0.676754	0.338377	−	0.941011i	$-0.390122\pi$
$257$	10.8492	0.676754	0.338377	+	0.941011i	$0.390122\pi$
$258$	−11.5482	−0.718958
$259$	−1.34150	−0.0833570
$260$	2.52640	0.156681
$261$	10.7649	0.666328
$262$	−10.7284	−0.662804
$263$	−11.5792	−0.714003	−0.357001	−	0.934104i	$-0.616201\pi$
$263$	−11.5792	−0.714003	−0.357001	+	0.934104i	$0.616201\pi$
$264$	4.23701	0.260770
$265$	−26.3375	−1.61790
$266$	2.49053	0.152704
$267$	13.5326	0.828182
$268$	−14.5904	−0.891251
$269$	−7.95732	−0.485166	−0.242583	−	0.970131i	$-0.577995\pi$
$269$	−7.95732	−0.485166	−0.242583	+	0.970131i	$0.577995\pi$
$270$	−10.9879	−0.668704
$271$	15.3230	0.930806	0.465403	−	0.885099i	$-0.345909\pi$
$271$	15.3230	0.930806	0.465403	+	0.885099i	$0.345909\pi$
$272$	−2.46010	−0.149165
$273$	−0.728723	−0.0441043
$274$	−0.261550	−0.0158008
$275$	3.55415	0.214323
$276$	−6.38541	−0.384357
$277$	23.9857	1.44116	0.720581	−	0.693371i	$-0.243875\pi$
$277$	23.9857	1.44116	0.720581	+	0.693371i	$0.243875\pi$
$278$	20.8819	1.25241
$279$	−3.32007	−0.198768
$280$	0.934028	0.0558188
$281$	−0.496586	−0.0296238	−0.0148119	−	0.999890i	$-0.504715\pi$
$281$	−0.496586	−0.0296238	−0.0148119	+	0.999890i	$0.504715\pi$
$282$	−13.2537	−0.789245
$283$	18.5242	1.10115	0.550575	−	0.834786i	$-0.314408\pi$
$283$	18.5242	1.10115	0.550575	+	0.834786i	$0.314408\pi$
$284$	−9.48130	−0.562612
$285$	−12.9864	−0.769247
$286$	4.37995	0.258992
$287$	−0.495564	−0.0292522
$288$	−1.49597	−0.0881507
$289$	−10.9479	−0.643995
$290$	14.3400	0.842076
$291$	−1.25962	−0.0738405
$292$	−8.28665	−0.484940
$293$	9.03198	0.527654	0.263827	−	0.964570i	$-0.415015\pi$
$293$	9.03198	0.527654	0.263827	+	0.964570i	$0.415015\pi$
$294$	8.31532	0.484959
$295$	−18.2863	−1.06467
$296$	2.86218	0.166361
$297$	−19.0495	−1.10536
$298$	5.09400	0.295088
$299$	−6.60083	−0.381736
$300$	1.26163	0.0728405
$301$	−4.41347	−0.254388
$302$	−12.1959	−0.701796
$303$	−6.81952	−0.391771
$304$	−5.31368	−0.304760
$305$	−22.2910	−1.27638
$306$	3.68023	0.210385
$307$	18.3884	1.04948	0.524741	−	0.851262i	$-0.324162\pi$
$307$	18.3884	1.04948	0.524741	+	0.851262i	$0.324162\pi$
$308$	1.61930	0.0922680
$309$	−21.2422	−1.20843
$310$	−4.42272	−0.251194
$311$	−0.472049	−0.0267674	−0.0133837	−	0.999910i	$-0.504260\pi$
$311$	−0.472049	−0.0267674	−0.0133837	+	0.999910i	$0.504260\pi$
$312$	1.55477	0.0880216
$313$	26.2113	1.48155	0.740775	−	0.671753i	$-0.234459\pi$
$313$	26.2113	1.48155	0.740775	+	0.671753i	$0.234459\pi$
$314$	22.6683	1.27925
$315$	−1.39728	−0.0787276
$316$	−7.53123	−0.423665
$317$	15.1408	0.850391	0.425195	−	0.905102i	$-0.360205\pi$
$317$	15.1408	0.850391	0.425195	+	0.905102i	$0.360205\pi$
$318$	−16.2083	−0.908918
$319$	24.8609	1.39194
$320$	−1.99280	−0.111401
$321$	−5.24103	−0.292526
$322$	−2.44037	−0.135997
$323$	13.0722	0.727355
$324$	−2.27418	−0.126343
$325$	1.30420	0.0723438
$326$	3.49835	0.193756
$327$	−11.0524	−0.611201
$328$	1.05732	0.0583805
$329$	−5.06528	−0.279258
$330$	−8.44352	−0.464801
$331$	−27.5801	−1.51594	−0.757970	−	0.652290i	$-0.773809\pi$
$331$	−27.5801	−1.51594	−0.757970	+	0.652290i	$0.773809\pi$
$332$	−12.5561	−0.689104
$333$	−4.28172	−0.234637
$334$	1.11061	0.0607696
$335$	29.0758	1.58858
$336$	0.574810	0.0313584
$337$	16.0622	0.874962	0.437481	−	0.899228i	$-0.355871\pi$
$337$	16.0622	0.874962	0.437481	+	0.899228i	$0.355871\pi$
$338$	−11.3928	−0.619685
$339$	−2.41766	−0.131309
$340$	4.90249	0.265875
$341$	−7.66755	−0.415221
$342$	7.94909	0.429838
$343$	6.45885	0.348745
$344$	9.41639	0.507698
$345$	12.7249	0.685084
$346$	−4.81367	−0.258785
$347$	−2.01697	−0.108277	−0.0541383	−	0.998533i	$-0.517241\pi$
$347$	−2.01697	−0.108277	−0.0541383	+	0.998533i	$0.517241\pi$
$348$	8.82499	0.473069
$349$	17.0248	0.911317	0.455658	−	0.890155i	$-0.349404\pi$
$349$	17.0248	0.911317	0.455658	+	0.890155i	$0.349404\pi$
$350$	0.482170	0.0257731
$351$	−6.99020	−0.373109
$352$	−3.45486	−0.184145
$353$	27.5866	1.46829	0.734143	−	0.678995i	$-0.237584\pi$
$353$	27.5866	1.46829	0.734143	+	0.678995i	$0.237584\pi$
$354$	−11.2536	−0.598121
$355$	18.8944	1.00281
$356$	−11.0345	−0.584827
$357$	−1.41409	−0.0748415
$358$	−0.366851	−0.0193887
$359$	−33.2045	−1.75247	−0.876233	−	0.481888i	$-0.839951\pi$
$359$	−33.2045	−1.75247	−0.876233	+	0.481888i	$0.839951\pi$
$360$	2.98117	0.157121
$361$	9.23520	0.486063
$362$	16.7553	0.880640
$363$	−1.14799	−0.0602540
$364$	0.594201	0.0311446
$365$	16.5137	0.864364
$366$	−13.7181	−0.717056
$367$	−2.21268	−0.115501	−0.0577505	−	0.998331i	$-0.518393\pi$
$367$	−2.21268	−0.115501	−0.0577505	+	0.998331i	$0.518393\pi$
$368$	5.20667	0.271417
$369$	−1.58171	−0.0823405
$370$	−5.70375	−0.296524
$371$	−6.19449	−0.321602
$372$	−2.72179	−0.141118
$373$	0.285462	0.0147807	0.00739034	−	0.999973i	$-0.497648\pi$
$373$	0.285462	0.0147807	0.00739034	+	0.999973i	$0.497648\pi$
$374$	8.49930	0.439488
$375$	−14.7340	−0.760858
$376$	10.8071	0.557332
$377$	9.12271	0.469844
$378$	−2.58433	−0.132923
$379$	14.7529	0.757804	0.378902	−	0.925437i	$-0.376302\pi$
$379$	14.7529	0.757804	0.378902	+	0.925437i	$0.376302\pi$
$380$	10.5891	0.543210
$381$	−22.1242	−1.13346
$382$	14.6870	0.751453
$383$	5.84673	0.298754	0.149377	−	0.988780i	$-0.452273\pi$
$383$	5.84673	0.298754	0.149377	+	0.988780i	$0.452273\pi$
$384$	−1.22639	−0.0625839
$385$	−3.22694	−0.164460
$386$	−1.48909	−0.0757926
$387$	−14.0866	−0.716063
$388$	1.02710	0.0521431
$389$	−22.9421	−1.16321	−0.581606	−	0.813471i	$-0.697575\pi$
$389$	−22.9421	−1.16321	−0.581606	+	0.813471i	$0.697575\pi$
$390$	−3.09835	−0.156891
$391$	−12.8089	−0.647775
$392$	−6.78032	−0.342458
$393$	13.1572	0.663694
$394$	11.1774	0.563110
$395$	15.0083	0.755147
$396$	5.16836	0.259720
$397$	−27.6353	−1.38698	−0.693489	−	0.720467i	$-0.743927\pi$
$397$	−27.6353	−1.38698	−0.693489	+	0.720467i	$0.743927\pi$
$398$	−5.08108	−0.254691
$399$	−3.05436	−0.152909
$400$	−1.02874	−0.0514369
$401$	−23.4743	−1.17225	−0.586125	−	0.810221i	$-0.699347\pi$
$401$	−23.4743	−1.17225	−0.586125	+	0.810221i	$0.699347\pi$
$402$	17.8935	0.892448
$403$	−2.81361	−0.140156
$404$	5.56064	0.276652
$405$	4.53199	0.225196
$406$	3.37273	0.167386
$407$	−9.88843	−0.490151
$408$	3.01704	0.149366
$409$	−19.5672	−0.967538	−0.483769	−	0.875196i	$-0.660733\pi$
$409$	−19.5672	−0.967538	−0.483769	+	0.875196i	$0.660733\pi$
$410$	−2.10702	−0.104058
$411$	0.320763	0.0158221
$412$	17.3209	0.853341
$413$	−4.30088	−0.211633
$414$	−7.78902	−0.382809
$415$	25.0218	1.22827
$416$	−1.26776	−0.0621572
$417$	−25.6094	−1.25410
$418$	18.3580	0.897921
$419$	−37.7940	−1.84636	−0.923179	−	0.384370i	$-0.874419\pi$
$419$	−37.7940	−1.84636	−0.923179	+	0.384370i	$0.874419\pi$
$420$	−1.14548	−0.0558938
$421$	5.94735	0.289856	0.144928	−	0.989442i	$-0.453705\pi$
$421$	5.94735	0.289856	0.144928	+	0.989442i	$0.453705\pi$
$422$	16.1157	0.784502
$423$	−16.1670	−0.786068
$424$	13.2163	0.641840
$425$	2.53080	0.122762
$426$	11.6278	0.563367
$427$	−5.24277	−0.253715
$428$	4.27354	0.206570
$429$	−5.37152	−0.259340
$430$	−18.7650	−0.904929
$431$	−18.5632	−0.894157	−0.447078	−	0.894495i	$-0.647535\pi$
$431$	−18.5632	−0.894157	−0.447078	+	0.894495i	$0.647535\pi$
$432$	5.51381	0.265283
$433$	29.0746	1.39724	0.698618	−	0.715495i	$-0.253799\pi$
$433$	29.0746	1.39724	0.698618	+	0.715495i	$0.253799\pi$
$434$	−1.04021	−0.0499317
$435$	−17.5865	−0.843207
$436$	9.01216	0.431604
$437$	−27.6666	−1.32347
$438$	10.1627	0.485591
$439$	12.4853	0.595890	0.297945	−	0.954583i	$-0.403699\pi$
$439$	12.4853	0.595890	0.297945	+	0.954583i	$0.403699\pi$
$440$	6.88486	0.328223
$441$	10.1431	0.483007
$442$	3.11882	0.148347
$443$	10.6334	0.505210	0.252605	−	0.967570i	$-0.418713\pi$
$443$	10.6334	0.505210	0.252605	+	0.967570i	$0.418713\pi$
$444$	−3.51014	−0.166584
$445$	21.9896	1.04241
$446$	−14.0246	−0.664085
$447$	−6.24723	−0.295484
$448$	−0.468701	−0.0221440
$449$	−13.8383	−0.653068	−0.326534	−	0.945186i	$-0.605881\pi$
$449$	−13.8383	−0.653068	−0.326534	+	0.945186i	$0.605881\pi$
$450$	1.53896	0.0725472
$451$	−3.65288	−0.172007
$452$	1.97136	0.0927252
$453$	14.9569	0.702738
$454$	−11.6235	−0.545517
$455$	−1.18413	−0.0555127
$456$	6.51664	0.305170
$457$	−19.8523	−0.928652	−0.464326	−	0.885664i	$-0.653703\pi$
$457$	−19.8523	−0.928652	−0.464326	+	0.885664i	$0.653703\pi$
$458$	−7.63220	−0.356629
$459$	−13.5645	−0.633137
$460$	−10.3759	−0.483778
$461$	28.4002	1.32273	0.661366	−	0.750064i	$-0.269977\pi$
$461$	28.4002	1.32273	0.661366	+	0.750064i	$0.269977\pi$
$462$	−1.98589	−0.0923919
$463$	10.2596	0.476806	0.238403	−	0.971166i	$-0.423376\pi$
$463$	10.2596	0.476806	0.238403	+	0.971166i	$0.423376\pi$
$464$	−7.19591	−0.334062
$465$	5.42398	0.251531
$466$	3.48540	0.161458
$467$	36.2596	1.67789	0.838947	−	0.544214i	$-0.183172\pi$
$467$	36.2596	1.67789	0.838947	+	0.544214i	$0.183172\pi$
$468$	1.89653	0.0876673
$469$	6.83853	0.315774
$470$	−21.5364	−0.993398
$471$	−27.8002	−1.28097
$472$	9.17618	0.422368
$473$	−32.5323	−1.49584
$474$	9.23623	0.424234
$475$	5.46639	0.250815
$476$	1.15305	0.0528499
$477$	−19.7712	−0.905259
$478$	−20.7109	−0.947293
$479$	19.3438	0.883842	0.441921	−	0.897054i	$-0.354297\pi$
$479$	19.3438	0.883842	0.441921	+	0.897054i	$0.354297\pi$
$480$	2.44395	0.111551
$481$	−3.62856	−0.165448
$482$	−2.17768	−0.0991904
$483$	2.99285	0.136179
$484$	0.936076	0.0425489
$485$	−2.04681	−0.0929407
$486$	−13.7524	−0.623822
$487$	−10.6202	−0.481248	−0.240624	−	0.970618i	$-0.577352\pi$
$487$	−10.6202	−0.481248	−0.240624	+	0.970618i	$0.577352\pi$
$488$	11.1857	0.506355
$489$	−4.29034	−0.194016
$490$	13.5118	0.610403
$491$	26.9304	1.21535	0.607676	−	0.794185i	$-0.292102\pi$
$491$	26.9304	1.21535	0.607676	+	0.794185i	$0.292102\pi$
$492$	−1.29668	−0.0584589
$493$	17.7026	0.797287
$494$	6.73649	0.303089
$495$	−10.2995	−0.462929
$496$	2.21935	0.0996517
$497$	4.44389	0.199336
$498$	15.3986	0.690030
$499$	8.48031	0.379631	0.189815	−	0.981820i	$-0.439211\pi$
$499$	8.48031	0.379631	0.189815	+	0.981820i	$0.439211\pi$
$500$	12.0141	0.537286
$501$	−1.36204	−0.0608513
$502$	−26.2146	−1.17001
$503$	−28.6508	−1.27748	−0.638739	−	0.769424i	$-0.720544\pi$
$503$	−28.6508	−1.27748	−0.638739	+	0.769424i	$0.720544\pi$
$504$	0.701161	0.0312322
$505$	−11.0813	−0.493110
$506$	−17.9883	−0.799679
$507$	13.9720	0.620518
$508$	18.0401	0.800402
$509$	41.4837	1.83873	0.919366	−	0.393404i	$-0.128703\pi$
$509$	41.4837	1.83873	0.919366	+	0.393404i	$0.128703\pi$
$510$	−6.01236	−0.266232
$511$	3.88396	0.171816
$512$	1.00000	0.0441942
$513$	−29.2986	−1.29357
$514$	10.8492	0.478537
$515$	−34.5172	−1.52101
$516$	−11.5482	−0.508380
$517$	−37.3369	−1.64208
$518$	−1.34150	−0.0589423
$519$	5.90344	0.259132
$520$	2.52640	0.110790
$521$	−21.7332	−0.952149	−0.476075	−	0.879405i	$-0.657941\pi$
$521$	−21.7332	−0.952149	−0.476075	+	0.879405i	$0.657941\pi$
$522$	10.7649	0.471165
$523$	42.3559	1.85210	0.926048	−	0.377406i	$-0.123184\pi$
$523$	42.3559	1.85210	0.926048	+	0.377406i	$0.123184\pi$
$524$	−10.7284	−0.468673
$525$	−0.591329	−0.0258077
$526$	−11.5792	−0.504876
$527$	−5.45982	−0.237833
$528$	4.23701	0.184392
$529$	4.10945	0.178672
$530$	−26.3375	−1.14403
$531$	−13.7273	−0.595713
$532$	2.49053	0.107978
$533$	−1.34043	−0.0580603
$534$	13.5326	0.585613
$535$	−8.51633	−0.368193
$536$	−14.5904	−0.630210
$537$	0.449903	0.0194147
$538$	−7.95732	−0.343064
$539$	23.4251	1.00899
$540$	−10.9879	−0.472845
$541$	14.9391	0.642282	0.321141	−	0.947031i	$-0.395934\pi$
$541$	14.9391	0.642282	0.321141	+	0.947031i	$0.395934\pi$
$542$	15.3230	0.658179
$543$	−20.5486	−0.881823
$544$	−2.46010	−0.105476
$545$	−17.9595	−0.769299
$546$	−0.728723	−0.0311864
$547$	−23.8414	−1.01938	−0.509692	−	0.860357i	$-0.670241\pi$
$547$	−23.8414	−1.01938	−0.509692	+	0.860357i	$0.670241\pi$
$548$	−0.261550	−0.0111729
$549$	−16.7335	−0.714169
$550$	3.55415	0.151549
$551$	38.2368	1.62894
$552$	−6.38541	−0.271781
$553$	3.52989	0.150106
$554$	23.9857	1.01906
$555$	6.99502	0.296922
$556$	20.8819	0.885591
$557$	−25.4238	−1.07724	−0.538621	−	0.842548i	$-0.681055\pi$
$557$	−25.4238	−1.07724	−0.538621	+	0.842548i	$0.681055\pi$
$558$	−3.32007	−0.140550
$559$	−11.9378	−0.504913
$560$	0.934028	0.0394699
$561$	−10.4235	−0.440079
$562$	−0.496586	−0.0209472
$563$	−31.7593	−1.33849	−0.669247	−	0.743040i	$-0.733383\pi$
$563$	−31.7593	−1.33849	−0.669247	+	0.743040i	$0.733383\pi$
$564$	−13.2537	−0.558081
$565$	−3.92854	−0.165275
$566$	18.5242	0.778631
$567$	1.06591	0.0447639
$568$	−9.48130	−0.397826
$569$	1.91690	0.0803607	0.0401803	−	0.999192i	$-0.487207\pi$
$569$	1.91690	0.0803607	0.0401803	+	0.999192i	$0.487207\pi$
$570$	−12.9864	−0.543940
$571$	43.9925	1.84103	0.920514	−	0.390709i	$-0.127770\pi$
$571$	43.9925	1.84103	0.920514	+	0.390709i	$0.127770\pi$
$572$	4.37995	0.183135
$573$	−18.0120	−0.752462
$574$	−0.495564	−0.0206845
$575$	−5.35630	−0.223373
$576$	−1.49597	−0.0623320
$577$	−40.7671	−1.69716	−0.848578	−	0.529070i	$-0.822541\pi$
$577$	−40.7671	−1.69716	−0.848578	+	0.529070i	$0.822541\pi$
$578$	−10.9479	−0.455373
$579$	1.82620	0.0758944
$580$	14.3400	0.595437
$581$	5.88504	0.244153
$582$	−1.25962	−0.0522131
$583$	−45.6605	−1.89106
$584$	−8.28665	−0.342904
$585$	−3.77942	−0.156260
$586$	9.03198	0.373107
$587$	−34.9801	−1.44378	−0.721891	−	0.692007i	$-0.756727\pi$
$587$	−34.9801	−1.44378	−0.721891	+	0.692007i	$0.756727\pi$
$588$	8.31532	0.342918
$589$	−11.7929	−0.485918
$590$	−18.2863	−0.752836
$591$	−13.7079	−0.563867
$592$	2.86218	0.117635
$593$	−12.4676	−0.511983	−0.255992	−	0.966679i	$-0.582402\pi$
$593$	−12.4676	−0.511983	−0.255992	+	0.966679i	$0.582402\pi$
$594$	−19.0495	−0.781609
$595$	−2.29780	−0.0942006
$596$	5.09400	0.208658
$597$	6.23138	0.255033
$598$	−6.60083	−0.269928
$599$	0.735309	0.0300439	0.0150220	−	0.999887i	$-0.495218\pi$
$599$	0.735309	0.0300439	0.0150220	+	0.999887i	$0.495218\pi$
$600$	1.26163	0.0515060
$601$	37.9668	1.54870	0.774350	−	0.632758i	$-0.218077\pi$
$601$	37.9668	1.54870	0.774350	+	0.632758i	$0.218077\pi$
$602$	−4.41347	−0.179880
$603$	21.8268	0.888855
$604$	−12.1959	−0.496244
$605$	−1.86541	−0.0758399
$606$	−6.81952	−0.277024
$607$	−6.91276	−0.280580	−0.140290	−	0.990110i	$-0.544804\pi$
$607$	−6.91276	−0.280580	−0.140290	+	0.990110i	$0.544804\pi$
$608$	−5.31368	−0.215498
$609$	−4.13628	−0.167611
$610$	−22.2910	−0.902535
$611$	−13.7008	−0.554275
$612$	3.68023	0.148764
$613$	42.0624	1.69888	0.849441	−	0.527683i	$-0.176939\pi$
$613$	42.0624	1.69888	0.849441	+	0.527683i	$0.176939\pi$
$614$	18.3884	0.742096
$615$	2.58403	0.104198
$616$	1.61930	0.0652433
$617$	−38.5018	−1.55003	−0.775013	−	0.631946i	$-0.782257\pi$
$617$	−38.5018	−1.55003	−0.775013	+	0.631946i	$0.782257\pi$
$618$	−21.2422	−0.854487
$619$	21.7947	0.876003	0.438001	−	0.898974i	$-0.355686\pi$
$619$	21.7947	0.876003	0.438001	+	0.898974i	$0.355686\pi$
$620$	−4.42272	−0.177621
$621$	28.7086	1.15204
$622$	−0.472049	−0.0189274
$623$	5.17188	0.207207
$624$	1.55477	0.0622407
$625$	−18.7980	−0.751920
$626$	26.2113	1.04761
$627$	−22.5141	−0.899127
$628$	22.6683	0.904564
$629$	−7.04123	−0.280752
$630$	−1.39728	−0.0556688
$631$	−27.9156	−1.11130	−0.555651	−	0.831416i	$-0.687531\pi$
$631$	−27.9156	−1.11130	−0.555651	+	0.831416i	$0.687531\pi$
$632$	−7.53123	−0.299576
$633$	−19.7642	−0.785556
$634$	15.1408	0.601317
$635$	−35.9504	−1.42665
$636$	−16.2083	−0.642702
$637$	8.59584	0.340580
$638$	24.8609	0.984252
$639$	14.1837	0.561099
$640$	−1.99280	−0.0787724
$641$	−0.211616	−0.00835835	−0.00417917	−	0.999991i	$-0.501330\pi$
$641$	−0.211616	−0.00835835	−0.00417917	+	0.999991i	$0.501330\pi$
$642$	−5.24103	−0.206847
$643$	−36.7885	−1.45080	−0.725398	−	0.688330i	$-0.758344\pi$
$643$	−36.7885	−1.45080	−0.725398	+	0.688330i	$0.758344\pi$
$644$	−2.44037	−0.0961641
$645$	23.0132	0.906145
$646$	13.0722	0.514318
$647$	25.0198	0.983631	0.491815	−	0.870700i	$-0.336334\pi$
$647$	25.0198	0.983631	0.491815	+	0.870700i	$0.336334\pi$
$648$	−2.27418	−0.0893381
$649$	−31.7024	−1.24443
$650$	1.30420	0.0511548
$651$	1.27570	0.0499988
$652$	3.49835	0.137006
$653$	−0.663535	−0.0259661	−0.0129831	−	0.999916i	$-0.504133\pi$
$653$	−0.663535	−0.0259661	−0.0129831	+	0.999916i	$0.504133\pi$
$654$	−11.0524	−0.432184
$655$	21.3796	0.835371
$656$	1.05732	0.0412812
$657$	12.3966	0.483636
$658$	−5.06528	−0.197465
$659$	−20.3893	−0.794254	−0.397127	−	0.917764i	$-0.629993\pi$
$659$	−20.3893	−0.794254	−0.397127	+	0.917764i	$0.629993\pi$
$660$	−8.44352	−0.328664
$661$	25.3599	0.986386	0.493193	−	0.869920i	$-0.335830\pi$
$661$	25.3599	0.986386	0.493193	+	0.869920i	$0.335830\pi$
$662$	−27.5801	−1.07193
$663$	−3.82489	−0.148546
$664$	−12.5561	−0.487270
$665$	−4.96313	−0.192462
$666$	−4.28172	−0.165913
$667$	−37.4668	−1.45072
$668$	1.11061	0.0429706
$669$	17.1997	0.664977
$670$	29.0758	1.12330
$671$	−38.6452	−1.49188
$672$	0.574810	0.0221738
$673$	22.6291	0.872288	0.436144	−	0.899877i	$-0.356344\pi$
$673$	22.6291	0.872288	0.436144	+	0.899877i	$0.356344\pi$
$674$	16.0622	0.618692
$675$	−5.67227	−0.218326
$676$	−11.3928	−0.438184
$677$	38.5144	1.48023	0.740114	−	0.672481i	$-0.234772\pi$
$677$	38.5144	1.48023	0.740114	+	0.672481i	$0.234772\pi$
$678$	−2.41766	−0.0928498
$679$	−0.481402	−0.0184745
$680$	4.90249	0.188002
$681$	14.2549	0.546250
$682$	−7.66755	−0.293606
$683$	−29.6764	−1.13554	−0.567768	−	0.823189i	$-0.692193\pi$
$683$	−29.6764	−1.13554	−0.567768	+	0.823189i	$0.692193\pi$
$684$	7.94909	0.303941
$685$	0.521218	0.0199147
$686$	6.45885	0.246600
$687$	9.36005	0.357108
$688$	9.41639	0.358997
$689$	−16.7551	−0.638320
$690$	12.7249	0.484427
$691$	17.2758	0.657204	0.328602	−	0.944469i	$-0.393423\pi$
$691$	17.2758	0.657204	0.328602	+	0.944469i	$0.393423\pi$
$692$	−4.81367	−0.182988
$693$	−2.42242	−0.0920200
$694$	−2.01697	−0.0765631
$695$	−41.6136	−1.57849
$696$	8.82499	0.334511
$697$	−2.60110	−0.0985236
$698$	17.0248	0.644398
$699$	−4.27446	−0.161675
$700$	0.482170	0.0182243
$701$	7.14664	0.269925	0.134962	−	0.990851i	$-0.456909\pi$
$701$	7.14664	0.269925	0.134962	+	0.990851i	$0.456909\pi$
$702$	−6.99020	−0.263828
$703$	−15.2087	−0.573607
$704$	−3.45486	−0.130210
$705$	26.4120	0.994732
$706$	27.5866	1.03823
$707$	−2.60628	−0.0980191
$708$	−11.2536	−0.422935
$709$	3.34637	0.125676	0.0628378	−	0.998024i	$-0.479985\pi$
$709$	3.34637	0.125676	0.0628378	+	0.998024i	$0.479985\pi$
$710$	18.8944	0.709093
$711$	11.2665	0.422526
$712$	−11.0345	−0.413535
$713$	11.5554	0.432754
$714$	−1.41409	−0.0529209
$715$	−8.72837	−0.326423
$716$	−0.366851	−0.0137099
$717$	25.3996	0.948565
$718$	−33.2045	−1.23918
$719$	30.2300	1.12739	0.563693	−	0.825984i	$-0.309380\pi$
$719$	30.2300	1.12739	0.563693	+	0.825984i	$0.309380\pi$
$720$	2.98117	0.111102
$721$	−8.11833	−0.302342
$722$	9.23520	0.343699
$723$	2.67068	0.0993236
$724$	16.7553	0.622706
$725$	7.40271	0.274930
$726$	−1.14799	−0.0426060
$727$	−24.9277	−0.924515	−0.462258	−	0.886746i	$-0.652960\pi$
$727$	−24.9277	−0.924515	−0.462258	+	0.886746i	$0.652960\pi$
$728$	0.594201	0.0220226
$729$	23.6883	0.877346
$730$	16.5137	0.611198
$731$	−23.1652	−0.856798
$732$	−13.7181	−0.507035
$733$	−34.7321	−1.28286	−0.641430	−	0.767182i	$-0.721658\pi$
$733$	−34.7321	−1.28286	−0.641430	+	0.767182i	$0.721658\pi$
$734$	−2.21268	−0.0816715
$735$	−16.5708	−0.611222
$736$	5.20667	0.191921
$737$	50.4079	1.85680
$738$	−1.58171	−0.0582235
$739$	32.8629	1.20888	0.604441	−	0.796650i	$-0.293396\pi$
$739$	32.8629	1.20888	0.604441	+	0.796650i	$0.293396\pi$
$740$	−5.70375	−0.209674
$741$	−8.26156	−0.303496
$742$	−6.19449	−0.227407
$743$	−19.9724	−0.732717	−0.366358	−	0.930474i	$-0.619396\pi$
$743$	−19.9724	−0.732717	−0.366358	+	0.930474i	$0.619396\pi$
$744$	−2.72179	−0.0997856
$745$	−10.1513	−0.371916
$746$	0.285462	0.0104515
$747$	18.7835	0.687252
$748$	8.49930	0.310765
$749$	−2.00301	−0.0731885
$750$	−14.7340	−0.538008
$751$	38.3818	1.40057	0.700286	−	0.713862i	$-0.253056\pi$
$751$	38.3818	1.40057	0.700286	+	0.713862i	$0.253056\pi$
$752$	10.8071	0.394093
$753$	32.1493	1.17158
$754$	9.12271	0.332230
$755$	24.3040	0.884514
$756$	−2.58433	−0.0939910
$757$	4.98078	0.181030	0.0905148	−	0.995895i	$-0.471149\pi$
$757$	4.98078	0.181030	0.0905148	+	0.995895i	$0.471149\pi$
$758$	14.7529	0.535849
$759$	22.0607	0.800753
$760$	10.5891	0.384108
$761$	29.1946	1.05830	0.529152	−	0.848527i	$-0.322510\pi$
$761$	29.1946	1.05830	0.529152	+	0.848527i	$0.322510\pi$
$762$	−22.1242	−0.801477
$763$	−4.22401	−0.152919
$764$	14.6870	0.531357
$765$	−7.33397	−0.265160
$766$	5.84673	0.211251
$767$	−11.6332	−0.420051
$768$	−1.22639	−0.0442535
$769$	−23.1290	−0.834052	−0.417026	−	0.908895i	$-0.636928\pi$
$769$	−23.1290	−0.834052	−0.417026	+	0.908895i	$0.636928\pi$
$770$	−3.22694	−0.116291
$771$	−13.3053	−0.479180
$772$	−1.48909	−0.0535935
$773$	−5.18341	−0.186434	−0.0932171	−	0.995646i	$-0.529715\pi$
$773$	−5.18341	−0.186434	−0.0932171	+	0.995646i	$0.529715\pi$
$774$	−14.0866	−0.506333
$775$	−2.28313	−0.0820124
$776$	1.02710	0.0368707
$777$	1.64521	0.0590215
$778$	−22.9421	−0.822514
$779$	−5.61823	−0.201294
$780$	−3.09835	−0.110939
$781$	32.7566	1.17212
$782$	−12.8089	−0.458046
$783$	−39.6769	−1.41794
$784$	−6.78032	−0.242154
$785$	−45.1735	−1.61231
$786$	13.1572	0.469303
$787$	−38.5988	−1.37590	−0.687949	−	0.725759i	$-0.741489\pi$
$787$	−38.5988	−1.37590	−0.687949	+	0.725759i	$0.741489\pi$
$788$	11.1774	0.398179
$789$	14.2006	0.505554
$790$	15.0083	0.533970
$791$	−0.923980	−0.0328530
$792$	5.16836	0.183650
$793$	−14.1809	−0.503577
$794$	−27.6353	−0.980742
$795$	32.3000	1.14556
$796$	−5.08108	−0.180094
$797$	−17.2442	−0.610820	−0.305410	−	0.952221i	$-0.598793\pi$
$797$	−17.2442	−0.610820	−0.305410	+	0.952221i	$0.598793\pi$
$798$	−3.05436	−0.108123
$799$	−26.5864	−0.940561
$800$	−1.02874	−0.0363714
$801$	16.5073	0.583255
$802$	−23.4743	−0.828906
$803$	28.6292	1.01030
$804$	17.8935	0.631056
$805$	4.86318	0.171405
$806$	−2.81361	−0.0991051
$807$	9.75877	0.343525
$808$	5.56064	0.195623
$809$	−39.6251	−1.39314	−0.696571	−	0.717488i	$-0.745292\pi$
$809$	−39.6251	−1.39314	−0.696571	+	0.717488i	$0.745292\pi$
$810$	4.53199	0.159238
$811$	−15.3270	−0.538202	−0.269101	−	0.963112i	$-0.586727\pi$
$811$	−15.3270	−0.538202	−0.269101	+	0.963112i	$0.586727\pi$
$812$	3.37273	0.118360
$813$	−18.7920	−0.659063
$814$	−9.88843	−0.346589
$815$	−6.97152	−0.244202
$816$	3.01704	0.105617
$817$	−50.0357	−1.75053
$818$	−19.5672	−0.684153
$819$	−0.888906	−0.0310609
$820$	−2.10702	−0.0735803
$821$	−31.4855	−1.09885	−0.549425	−	0.835543i	$-0.685153\pi$
$821$	−31.4855	−1.09885	−0.549425	+	0.835543i	$0.685153\pi$
$822$	0.320763	0.0111879
$823$	50.9733	1.77682	0.888409	−	0.459052i	$-0.151811\pi$
$823$	50.9733	1.77682	0.888409	+	0.459052i	$0.151811\pi$
$824$	17.3209	0.603403
$825$	−4.35877	−0.151753
$826$	−4.30088	−0.149647
$827$	−14.6151	−0.508218	−0.254109	−	0.967176i	$-0.581782\pi$
$827$	−14.6151	−0.508218	−0.254109	+	0.967176i	$0.581782\pi$
$828$	−7.78902	−0.270687
$829$	35.5328	1.23411	0.617053	−	0.786922i	$-0.288326\pi$
$829$	35.5328	1.23411	0.617053	+	0.786922i	$0.288326\pi$
$830$	25.0218	0.868519
$831$	−29.4158	−1.02042
$832$	−1.26776	−0.0439518
$833$	16.6802	0.577936
$834$	−25.6094	−0.886781
$835$	−2.21322	−0.0765916
$836$	18.3580	0.634926
$837$	12.2371	0.422975
$838$	−37.7940	−1.30557
$839$	48.5533	1.67625	0.838124	−	0.545480i	$-0.183653\pi$
$839$	48.5533	1.67625	0.838124	+	0.545480i	$0.183653\pi$
$840$	−1.14548	−0.0395229
$841$	22.7812	0.785557
$842$	5.94735	0.204959
$843$	0.609008	0.0209753
$844$	16.1157	0.554727
$845$	22.7036	0.781026
$846$	−16.1670	−0.555834
$847$	−0.438739	−0.0150753
$848$	13.2163	0.453850
$849$	−22.7179	−0.779677
$850$	2.53080	0.0868056
$851$	14.9024	0.510848
$852$	11.6278	0.398361
$853$	25.2425	0.864288	0.432144	−	0.901805i	$-0.357757\pi$
$853$	25.2425	0.864288	0.432144	+	0.901805i	$0.357757\pi$
$854$	−5.24277	−0.179404
$855$	−15.8410	−0.541750
$856$	4.27354	0.146067
$857$	34.5179	1.17911	0.589554	−	0.807729i	$-0.299303\pi$
$857$	34.5179	1.17911	0.589554	+	0.807729i	$0.299303\pi$
$858$	−5.37152	−0.183381
$859$	−17.7314	−0.604989	−0.302495	−	0.953151i	$-0.597819\pi$
$859$	−17.7314	−0.604989	−0.302495	+	0.953151i	$0.597819\pi$
$860$	−18.7650	−0.639882
$861$	0.607755	0.0207122
$862$	−18.5632	−0.632264
$863$	24.6702	0.839785	0.419892	−	0.907574i	$-0.362068\pi$
$863$	24.6702	0.839785	0.419892	+	0.907574i	$0.362068\pi$
$864$	5.51381	0.187584
$865$	9.59270	0.326162
$866$	29.0746	0.987995
$867$	13.4264	0.455985
$868$	−1.04021	−0.0353070
$869$	26.0194	0.882647
$870$	−17.5865	−0.596237
$871$	18.4972	0.626753
$872$	9.01216	0.305190
$873$	−1.53651	−0.0520029
$874$	−27.6666	−0.935837
$875$	−5.63101	−0.190363
$876$	10.1627	0.343365
$877$	11.8329	0.399567	0.199784	−	0.979840i	$-0.435976\pi$
$877$	11.8329	0.399567	0.199784	+	0.979840i	$0.435976\pi$
$878$	12.4853	0.421358
$879$	−11.0767	−0.373609
$880$	6.88486	0.232089
$881$	5.19631	0.175068	0.0875340	−	0.996162i	$-0.472101\pi$
$881$	5.19631	0.175068	0.0875340	+	0.996162i	$0.472101\pi$
$882$	10.1431	0.341537
$883$	41.1552	1.38498	0.692492	−	0.721426i	$-0.256513\pi$
$883$	41.1552	1.38498	0.692492	+	0.721426i	$0.256513\pi$
$884$	3.11882	0.104897
$885$	22.4262	0.753847
$886$	10.6334	0.357237
$887$	49.2283	1.65293	0.826463	−	0.562992i	$-0.190350\pi$
$887$	49.2283	1.65293	0.826463	+	0.562992i	$0.190350\pi$
$888$	−3.51014	−0.117793
$889$	−8.45543	−0.283586
$890$	21.9896	0.737092
$891$	7.85697	0.263218
$892$	−14.0246	−0.469579
$893$	−57.4253	−1.92166
$894$	−6.24723	−0.208939
$895$	0.731062	0.0244367
$896$	−0.468701	−0.0156582
$897$	8.09519	0.270290
$898$	−13.8383	−0.461789
$899$	−15.9702	−0.532637
$900$	1.53896	0.0512986
$901$	−32.5134	−1.08318
$902$	−3.65288	−0.121628
$903$	5.41264	0.180121
$904$	1.97136	0.0655666
$905$	−33.3900	−1.10992
$906$	14.9569	0.496911
$907$	−31.0853	−1.03217	−0.516085	−	0.856538i	$-0.672611\pi$
$907$	−31.0853	−1.03217	−0.516085	+	0.856538i	$0.672611\pi$
$908$	−11.6235	−0.385739
$909$	−8.31854	−0.275909
$910$	−1.18413	−0.0392534
$911$	−55.7799	−1.84807	−0.924035	−	0.382309i	$-0.875129\pi$
$911$	−55.7799	−1.84807	−0.924035	+	0.382309i	$0.875129\pi$
$912$	6.51664	0.215788
$913$	43.3795	1.43565
$914$	−19.8523	−0.656656
$915$	27.3374	0.903747
$916$	−7.63220	−0.252175
$917$	5.02842	0.166053
$918$	−13.5645	−0.447696
$919$	22.9204	0.756073	0.378037	−	0.925791i	$-0.376599\pi$
$919$	22.9204	0.756073	0.378037	+	0.925791i	$0.376599\pi$
$920$	−10.3759	−0.342082
$921$	−22.5514	−0.743093
$922$	28.4002	0.935312
$923$	12.0200	0.395644
$924$	−1.98589	−0.0653309
$925$	−2.94443	−0.0968123
$926$	10.2596	0.337153
$927$	−25.9115	−0.851047
$928$	−7.19591	−0.236217
$929$	13.5354	0.444084	0.222042	−	0.975037i	$-0.428728\pi$
$929$	13.5354	0.444084	0.222042	+	0.975037i	$0.428728\pi$
$930$	5.42398	0.177859
$931$	36.0285	1.18078
$932$	3.48540	0.114168
$933$	0.578916	0.0189529
$934$	36.2596	1.18645
$935$	−16.9374	−0.553913
$936$	1.89653	0.0619901
$937$	−16.2354	−0.530389	−0.265194	−	0.964195i	$-0.585436\pi$
$937$	−16.2354	−0.530389	−0.265194	+	0.964195i	$0.585436\pi$
$938$	6.83853	0.223286
$939$	−32.1453	−1.04902
$940$	−21.5364	−0.702438
$941$	57.8556	1.88604	0.943020	−	0.332737i	$-0.107972\pi$
$941$	57.8556	1.88604	0.943020	+	0.332737i	$0.107972\pi$
$942$	−27.8002	−0.905779
$943$	5.50509	0.179271
$944$	9.17618	0.298659
$945$	5.15005	0.167531
$946$	−32.5323	−1.05772
$947$	7.41463	0.240943	0.120472	−	0.992717i	$-0.461559\pi$
$947$	7.41463	0.240943	0.120472	+	0.992717i	$0.461559\pi$
$948$	9.23623	0.299979
$949$	10.5055	0.341023
$950$	5.46639	0.177353
$951$	−18.5685	−0.602125
$952$	1.15305	0.0373705
$953$	28.1055	0.910426	0.455213	−	0.890382i	$-0.349563\pi$
$953$	28.1055	0.910426	0.455213	+	0.890382i	$0.349563\pi$
$954$	−19.7712	−0.640115
$955$	−29.2683	−0.947100
$956$	−20.7109	−0.669837
$957$	−30.4891	−0.985574
$958$	19.3438	0.624970
$959$	0.122589	0.00395860
$960$	2.44395	0.0788782
$961$	−26.0745	−0.841113
$962$	−3.62856	−0.116990
$963$	−6.39308	−0.206014
$964$	−2.17768	−0.0701382
$965$	2.96746	0.0955259
$966$	2.99285	0.0962933
$967$	−54.4429	−1.75077	−0.875383	−	0.483430i	$-0.839391\pi$
$967$	−54.4429	−1.75077	−0.875383	+	0.483430i	$0.839391\pi$
$968$	0.936076	0.0300866
$969$	−16.0316	−0.515009
$970$	−2.04681	−0.0657190
$971$	−26.5135	−0.850860	−0.425430	−	0.904991i	$-0.639877\pi$
$971$	−26.5135	−0.850860	−0.425430	+	0.904991i	$0.639877\pi$
$972$	−13.7524	−0.441108
$973$	−9.78738	−0.313769
$974$	−10.6202	−0.340293
$975$	−1.59945	−0.0512235
$976$	11.1857	0.358047
$977$	55.0904	1.76250	0.881250	−	0.472651i	$-0.156703\pi$
$977$	55.0904	1.76250	0.881250	+	0.472651i	$0.156703\pi$
$978$	−4.29034	−0.137190
$979$	38.1227	1.21841
$980$	13.5118	0.431620
$981$	−13.4819	−0.430444
$982$	26.9304	0.859384
$983$	−15.8480	−0.505472	−0.252736	−	0.967535i	$-0.581330\pi$
$983$	−15.8480	−0.505472	−0.252736	+	0.967535i	$0.581330\pi$
$984$	−1.29668	−0.0413367
$985$	−22.2744	−0.709721
$986$	17.7026	0.563767
$987$	6.21201	0.197730
$988$	6.73649	0.214316
$989$	49.0281	1.55900
$990$	−10.2995	−0.327340
$991$	−0.00674818	−0.000214363 0	−0.000107182	−	1.00000i	$-0.500034\pi$
$991$	−0.00674818	−0.000214363 0	−0.000107182		1.00000i	$0.500034\pi$
$992$	2.21935	0.0704644
$993$	33.8240	1.07337
$994$	4.44389	0.140952
$995$	10.1256	0.321002
$996$	15.3986	0.487925
$997$	−42.5804	−1.34854	−0.674268	−	0.738487i	$-0.735541\pi$
$997$	−42.5804	−1.34854	−0.674268	+	0.738487i	$0.735541\pi$
$998$	8.48031	0.268439
$999$	15.7815	0.499304

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4034.2.a.d.1.15	✓	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4034.2.a.d.1.15	✓	52	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.22639 q^{3} +1.00000 q^{4} -1.99280 q^{5} -1.22639 q^{6} -0.468701 q^{7} +1.00000 q^{8} -1.49597 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.22639 q^{3} +1.00000 q^{4} -1.99280 q^{5} -1.22639 q^{6} -0.468701 q^{7} +1.00000 q^{8} -1.49597 q^{9} -1.99280 q^{10} -3.45486 q^{11} -1.22639 q^{12} -1.26776 q^{13} -0.468701 q^{14} +2.44395 q^{15} +1.00000 q^{16} -2.46010 q^{17} -1.49597 q^{18} -5.31368 q^{19} -1.99280 q^{20} +0.574810 q^{21} -3.45486 q^{22} +5.20667 q^{23} -1.22639 q^{24} -1.02874 q^{25} -1.26776 q^{26} +5.51381 q^{27} -0.468701 q^{28} -7.19591 q^{29} +2.44395 q^{30} +2.21935 q^{31} +1.00000 q^{32} +4.23701 q^{33} -2.46010 q^{34} +0.934028 q^{35} -1.49597 q^{36} +2.86218 q^{37} -5.31368 q^{38} +1.55477 q^{39} -1.99280 q^{40} +1.05732 q^{41} +0.574810 q^{42} +9.41639 q^{43} -3.45486 q^{44} +2.98117 q^{45} +5.20667 q^{46} +10.8071 q^{47} -1.22639 q^{48} -6.78032 q^{49} -1.02874 q^{50} +3.01704 q^{51} -1.26776 q^{52} +13.2163 q^{53} +5.51381 q^{54} +6.88486 q^{55} -0.468701 q^{56} +6.51664 q^{57} -7.19591 q^{58} +9.17618 q^{59} +2.44395 q^{60} +11.1857 q^{61} +2.21935 q^{62} +0.701161 q^{63} +1.00000 q^{64} +2.52640 q^{65} +4.23701 q^{66} -14.5904 q^{67} -2.46010 q^{68} -6.38541 q^{69} +0.934028 q^{70} -9.48130 q^{71} -1.49597 q^{72} -8.28665 q^{73} +2.86218 q^{74} +1.26163 q^{75} -5.31368 q^{76} +1.61930 q^{77} +1.55477 q^{78} -7.53123 q^{79} -1.99280 q^{80} -2.27418 q^{81} +1.05732 q^{82} -12.5561 q^{83} +0.574810 q^{84} +4.90249 q^{85} +9.41639 q^{86} +8.82499 q^{87} -3.45486 q^{88} -11.0345 q^{89} +2.98117 q^{90} +0.594201 q^{91} +5.20667 q^{92} -2.72179 q^{93} +10.8071 q^{94} +10.5891 q^{95} -1.22639 q^{96} +1.02710 q^{97} -6.78032 q^{98} +5.16836 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q + 52 q^{2} + 16 q^{3} + 52 q^{4} + 24 q^{5} + 16 q^{6} + 12 q^{7} + 52 q^{8} + 70 q^{9}+O(q^{10}) \) 52 * q + 52 * q^2 + 16 * q^3 + 52 * q^4 + 24 * q^5 + 16 * q^6 + 12 * q^7 + 52 * q^8 + 70 * q^9	\( 52 q + 52 q^{2} + 16 q^{3} + 52 q^{4} + 24 q^{5} + 16 q^{6} + 12 q^{7} + 52 q^{8} + 70 q^{9} + 24 q^{10} + 19 q^{11} + 16 q^{12} + 27 q^{13} + 12 q^{14} + 5 q^{15} + 52 q^{16} + 43 q^{17} + 70 q^{18} + 35 q^{19} + 24 q^{20} + 29 q^{21} + 19 q^{22} + 2 q^{23} + 16 q^{24} + 88 q^{25} + 27 q^{26} + 49 q^{27} + 12 q^{28} + 31 q^{29} + 5 q^{30} + 59 q^{31} + 52 q^{32} + 45 q^{33} + 43 q^{34} + 18 q^{35} + 70 q^{36} + 60 q^{37} + 35 q^{38} + 6 q^{39} + 24 q^{40} + 56 q^{41} + 29 q^{42} + 34 q^{43} + 19 q^{44} + 61 q^{45} + 2 q^{46} - 4 q^{47} + 16 q^{48} + 102 q^{49} + 88 q^{50} + 23 q^{51} + 27 q^{52} + 30 q^{53} + 49 q^{54} + 24 q^{55} + 12 q^{56} + 32 q^{57} + 31 q^{58} + 27 q^{59} + 5 q^{60} + 107 q^{61} + 59 q^{62} - 4 q^{63} + 52 q^{64} + 46 q^{65} + 45 q^{66} + 22 q^{67} + 43 q^{68} + 36 q^{69} + 18 q^{70} + 8 q^{71} + 70 q^{72} + 66 q^{73} + 60 q^{74} + 53 q^{75} + 35 q^{76} + 26 q^{77} + 6 q^{78} + 50 q^{79} + 24 q^{80} + 108 q^{81} + 56 q^{82} + 52 q^{83} + 29 q^{84} + 19 q^{85} + 34 q^{86} - 32 q^{87} + 19 q^{88} + 62 q^{89} + 61 q^{90} + 69 q^{91} + 2 q^{92} + 21 q^{93} - 4 q^{94} - 44 q^{95} + 16 q^{96} + 82 q^{97} + 102 q^{98} + 16 q^{99}+O(q^{100}) \) 52 * q + 52 * q^2 + 16 * q^3 + 52 * q^4 + 24 * q^5 + 16 * q^6 + 12 * q^7 + 52 * q^8 + 70 * q^9 + 24 * q^10 + 19 * q^11 + 16 * q^12 + 27 * q^13 + 12 * q^14 + 5 * q^15 + 52 * q^16 + 43 * q^17 + 70 * q^18 + 35 * q^19 + 24 * q^20 + 29 * q^21 + 19 * q^22 + 2 * q^23 + 16 * q^24 + 88 * q^25 + 27 * q^26 + 49 * q^27 + 12 * q^28 + 31 * q^29 + 5 * q^30 + 59 * q^31 + 52 * q^32 + 45 * q^33 + 43 * q^34 + 18 * q^35 + 70 * q^36 + 60 * q^37 + 35 * q^38 + 6 * q^39 + 24 * q^40 + 56 * q^41 + 29 * q^42 + 34 * q^43 + 19 * q^44 + 61 * q^45 + 2 * q^46 - 4 * q^47 + 16 * q^48 + 102 * q^49 + 88 * q^50 + 23 * q^51 + 27 * q^52 + 30 * q^53 + 49 * q^54 + 24 * q^55 + 12 * q^56 + 32 * q^57 + 31 * q^58 + 27 * q^59 + 5 * q^60 + 107 * q^61 + 59 * q^62 - 4 * q^63 + 52 * q^64 + 46 * q^65 + 45 * q^66 + 22 * q^67 + 43 * q^68 + 36 * q^69 + 18 * q^70 + 8 * q^71 + 70 * q^72 + 66 * q^73 + 60 * q^74 + 53 * q^75 + 35 * q^76 + 26 * q^77 + 6 * q^78 + 50 * q^79 + 24 * q^80 + 108 * q^81 + 56 * q^82 + 52 * q^83 + 29 * q^84 + 19 * q^85 + 34 * q^86 - 32 * q^87 + 19 * q^88 + 62 * q^89 + 61 * q^90 + 69 * q^91 + 2 * q^92 + 21 * q^93 - 4 * q^94 - 44 * q^95 + 16 * q^96 + 82 * q^97 + 102 * q^98 + 16 * q^99

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