LMFDB - Embedded newform 4009.2.a.c.1.68

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4009,2,Mod(1,4009)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4009, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4009.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4009 = 19 \cdot 211 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4009.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:	$32.0120261703$
Analytic rank:	$1$
Dimension:	$71$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.68
Character	$\chi$	$=$	4009.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.40972 q^{2} -1.84170 q^{3} +3.80675 q^{4} +0.346580 q^{5} -4.43798 q^{6} +0.765913 q^{7} +4.35377 q^{8} +0.391851 q^{9} +O(q^{10})$	\(q+2.40972 q^{2} -1.84170 q^{3} +3.80675 q^{4} +0.346580 q^{5} -4.43798 q^{6} +0.765913 q^{7} +4.35377 q^{8} +0.391851 q^{9} +0.835161 q^{10} -4.34092 q^{11} -7.01089 q^{12} -3.99798 q^{13} +1.84564 q^{14} -0.638296 q^{15} +2.87786 q^{16} +4.00500 q^{17} +0.944250 q^{18} +1.00000 q^{19} +1.31934 q^{20} -1.41058 q^{21} -10.4604 q^{22} +8.50028 q^{23} -8.01833 q^{24} -4.87988 q^{25} -9.63402 q^{26} +4.80342 q^{27} +2.91564 q^{28} -0.215301 q^{29} -1.53811 q^{30} -5.42448 q^{31} -1.77269 q^{32} +7.99467 q^{33} +9.65093 q^{34} +0.265450 q^{35} +1.49168 q^{36} -7.74449 q^{37} +2.40972 q^{38} +7.36308 q^{39} +1.50893 q^{40} -7.94696 q^{41} -3.39911 q^{42} +1.04427 q^{43} -16.5248 q^{44} +0.135808 q^{45} +20.4833 q^{46} -10.1550 q^{47} -5.30015 q^{48} -6.41338 q^{49} -11.7592 q^{50} -7.37600 q^{51} -15.2193 q^{52} +3.70504 q^{53} +11.5749 q^{54} -1.50448 q^{55} +3.33461 q^{56} -1.84170 q^{57} -0.518815 q^{58} -6.44227 q^{59} -2.42983 q^{60} +6.49860 q^{61} -13.0715 q^{62} +0.300124 q^{63} -10.0274 q^{64} -1.38562 q^{65} +19.2649 q^{66} -11.9106 q^{67} +15.2460 q^{68} -15.6550 q^{69} +0.639661 q^{70} -3.38178 q^{71} +1.70603 q^{72} -3.58137 q^{73} -18.6621 q^{74} +8.98727 q^{75} +3.80675 q^{76} -3.32477 q^{77} +17.7430 q^{78} +8.30176 q^{79} +0.997410 q^{80} -10.0220 q^{81} -19.1499 q^{82} -10.1950 q^{83} -5.36973 q^{84} +1.38805 q^{85} +2.51641 q^{86} +0.396519 q^{87} -18.8994 q^{88} -2.23579 q^{89} +0.327258 q^{90} -3.06211 q^{91} +32.3585 q^{92} +9.99025 q^{93} -24.4707 q^{94} +0.346580 q^{95} +3.26477 q^{96} -5.30892 q^{97} -15.4544 q^{98} -1.70099 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 71 q - 15 q^{2} - 8 q^{3} + 69 q^{4} - 18 q^{5} - 9 q^{6} - 19 q^{7} - 39 q^{8} + 63 q^{9}+O(q^{10}) $ 71 * q - 15 * q^2 - 8 * q^3 + 69 * q^4 - 18 * q^5 - 9 * q^6 - 19 * q^7 - 39 * q^8 + 63 * q^9	\( 71 q - 15 q^{2} - 8 q^{3} + 69 q^{4} - 18 q^{5} - 9 q^{6} - 19 q^{7} - 39 q^{8} + 63 q^{9} - 10 q^{10} - 52 q^{11} - 9 q^{12} - 15 q^{13} - 53 q^{14} - 33 q^{15} + 53 q^{16} - 10 q^{17} - 35 q^{18} + 71 q^{19} - 33 q^{20} - 38 q^{21} - 6 q^{22} - 65 q^{23} - 30 q^{24} + 51 q^{25} - 4 q^{26} - 23 q^{27} - 29 q^{28} - 97 q^{29} - 27 q^{30} - 53 q^{31} - 78 q^{32} - 17 q^{33} - 24 q^{34} - 38 q^{35} + 24 q^{36} - 33 q^{37} - 15 q^{38} - 86 q^{39} + 25 q^{40} - 69 q^{41} + 64 q^{42} - 10 q^{43} - 94 q^{44} - 34 q^{45} - 6 q^{46} - 37 q^{47} - q^{48} + 74 q^{49} - 41 q^{50} - 46 q^{51} - 30 q^{52} - 50 q^{53} - 17 q^{54} - 30 q^{55} - 116 q^{56} - 8 q^{57} + 11 q^{58} - 93 q^{59} - 56 q^{60} - 18 q^{61} - q^{62} - 84 q^{63} + 93 q^{64} - 78 q^{65} - 53 q^{66} - 5 q^{67} - 9 q^{68} - 69 q^{69} - 10 q^{70} - 221 q^{71} - 73 q^{72} - 34 q^{73} - 58 q^{74} - 70 q^{75} + 69 q^{76} - 2 q^{77} + 7 q^{78} - 68 q^{79} - 71 q^{80} + 39 q^{81} + 26 q^{82} - 45 q^{83} - 10 q^{84} - 44 q^{85} - 80 q^{86} - 7 q^{87} - 46 q^{88} - 143 q^{89} + 41 q^{90} - 30 q^{91} - 46 q^{92} + 32 q^{93} + 41 q^{94} - 18 q^{95} - 140 q^{96} - 18 q^{97} - 97 q^{98} - 142 q^{99}+O(q^{100}) \) 71 * q - 15 * q^2 - 8 * q^3 + 69 * q^4 - 18 * q^5 - 9 * q^6 - 19 * q^7 - 39 * q^8 + 63 * q^9 - 10 * q^10 - 52 * q^11 - 9 * q^12 - 15 * q^13 - 53 * q^14 - 33 * q^15 + 53 * q^16 - 10 * q^17 - 35 * q^18 + 71 * q^19 - 33 * q^20 - 38 * q^21 - 6 * q^22 - 65 * q^23 - 30 * q^24 + 51 * q^25 - 4 * q^26 - 23 * q^27 - 29 * q^28 - 97 * q^29 - 27 * q^30 - 53 * q^31 - 78 * q^32 - 17 * q^33 - 24 * q^34 - 38 * q^35 + 24 * q^36 - 33 * q^37 - 15 * q^38 - 86 * q^39 + 25 * q^40 - 69 * q^41 + 64 * q^42 - 10 * q^43 - 94 * q^44 - 34 * q^45 - 6 * q^46 - 37 * q^47 - q^48 + 74 * q^49 - 41 * q^50 - 46 * q^51 - 30 * q^52 - 50 * q^53 - 17 * q^54 - 30 * q^55 - 116 * q^56 - 8 * q^57 + 11 * q^58 - 93 * q^59 - 56 * q^60 - 18 * q^61 - q^62 - 84 * q^63 + 93 * q^64 - 78 * q^65 - 53 * q^66 - 5 * q^67 - 9 * q^68 - 69 * q^69 - 10 * q^70 - 221 * q^71 - 73 * q^72 - 34 * q^73 - 58 * q^74 - 70 * q^75 + 69 * q^76 - 2 * q^77 + 7 * q^78 - 68 * q^79 - 71 * q^80 + 39 * q^81 + 26 * q^82 - 45 * q^83 - 10 * q^84 - 44 * q^85 - 80 * q^86 - 7 * q^87 - 46 * q^88 - 143 * q^89 + 41 * q^90 - 30 * q^91 - 46 * q^92 + 32 * q^93 + 41 * q^94 - 18 * q^95 - 140 * q^96 - 18 * q^97 - 97 * q^98 - 142 * 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 $

$2$	2.40972	1.70393	0.851965	−	0.523599i	$-0.175411\pi$
$2$	2.40972	1.70393	0.851965	+	0.523599i	$0.175411\pi$
$3$	−1.84170	−1.06330	−0.531652	−	0.846963i	$-0.678429\pi$
$3$	−1.84170	−1.06330	−0.531652	+	0.846963i	$0.678429\pi$
$4$	3.80675	1.90338
$5$	0.346580	0.154995	0.0774976	−	0.996993i	$-0.475307\pi$
$5$	0.346580	0.154995	0.0774976	+	0.996993i	$0.475307\pi$
$6$	−4.43798	−1.81180
$7$	0.765913	0.289488	0.144744	−	0.989469i	$-0.453764\pi$
$7$	0.765913	0.289488	0.144744	+	0.989469i	$0.453764\pi$
$8$	4.35377	1.53929
$9$	0.391851	0.130617
$10$	0.835161	0.264101
$11$	−4.34092	−1.30884	−0.654419	−	0.756132i	$-0.727087\pi$
$11$	−4.34092	−1.30884	−0.654419	+	0.756132i	$0.727087\pi$
$12$	−7.01089	−2.02387
$13$	−3.99798	−1.10884	−0.554421	−	0.832237i	$-0.687060\pi$
$13$	−3.99798	−1.10884	−0.554421	+	0.832237i	$0.687060\pi$
$14$	1.84564	0.493267
$15$	−0.638296	−0.164807
$16$	2.87786	0.719466
$17$	4.00500	0.971355	0.485677	−	0.874138i	$-0.338573\pi$
$17$	4.00500	0.971355	0.485677	+	0.874138i	$0.338573\pi$
$18$	0.944250	0.222562
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	1.31934	0.295014
$21$	−1.41058	−0.307814
$22$	−10.4604	−2.23017
$23$	8.50028	1.77243	0.886216	−	0.463272i	$-0.153325\pi$
$23$	8.50028	1.77243	0.886216	+	0.463272i	$0.153325\pi$
$24$	−8.01833	−1.63673
$25$	−4.87988	−0.975976
$26$	−9.63402	−1.88939
$27$	4.80342	0.924419
$28$	2.91564	0.551005
$29$	−0.215301	−0.0399804	−0.0199902	−	0.999800i	$-0.506364\pi$
$29$	−0.215301	−0.0399804	−0.0199902	+	0.999800i	$0.506364\pi$
$30$	−1.53811	−0.280820
$31$	−5.42448	−0.974265	−0.487133	−	0.873328i	$-0.661957\pi$
$31$	−5.42448	−0.974265	−0.487133	+	0.873328i	$0.661957\pi$
$32$	−1.77269	−0.313371
$33$	7.99467	1.39169
$34$	9.65093	1.65512
$35$	0.265450	0.0448693
$36$	1.49168	0.248613
$37$	−7.74449	−1.27319	−0.636593	−	0.771200i	$-0.719657\pi$
$37$	−7.74449	−1.27319	−0.636593	+	0.771200i	$0.719657\pi$
$38$	2.40972	0.390908
$39$	7.36308	1.17904
$40$	1.50893	0.238583
$41$	−7.94696	−1.24111	−0.620553	−	0.784164i	$-0.713092\pi$
$41$	−7.94696	−1.24111	−0.620553	+	0.784164i	$0.713092\pi$
$42$	−3.39911	−0.524493
$43$	1.04427	0.159250	0.0796250	−	0.996825i	$-0.474628\pi$
$43$	1.04427	0.159250	0.0796250	+	0.996825i	$0.474628\pi$
$44$	−16.5248	−2.49121
$45$	0.135808	0.0202450
$46$	20.4833	3.02010
$47$	−10.1550	−1.48126	−0.740629	−	0.671914i	$-0.765472\pi$
$47$	−10.1550	−1.48126	−0.740629	+	0.671914i	$0.765472\pi$
$48$	−5.30015	−0.765011
$49$	−6.41338	−0.916197
$50$	−11.7592	−1.66300
$51$	−7.37600	−1.03285
$52$	−15.2193	−2.11054
$53$	3.70504	0.508927	0.254463	−	0.967082i	$-0.418101\pi$
$53$	3.70504	0.508927	0.254463	+	0.967082i	$0.418101\pi$
$54$	11.5749	1.57515
$55$	−1.50448	−0.202864
$56$	3.33461	0.445606
$57$	−1.84170	−0.243939
$58$	−0.518815	−0.0681238
$59$	−6.44227	−0.838712	−0.419356	−	0.907822i	$-0.637744\pi$
$59$	−6.44227	−0.838712	−0.419356	+	0.907822i	$0.637744\pi$
$60$	−2.42983	−0.313690
$61$	6.49860	0.832060	0.416030	−	0.909351i	$-0.363421\pi$
$61$	6.49860	0.832060	0.416030	+	0.909351i	$0.363421\pi$
$62$	−13.0715	−1.66008
$63$	0.300124	0.0378120
$64$	−10.0274	−1.25343
$65$	−1.38562	−0.171865
$66$	19.2649	2.37135
$67$	−11.9106	−1.45511	−0.727557	−	0.686047i	$-0.759344\pi$
$67$	−11.9106	−1.45511	−0.727557	+	0.686047i	$0.759344\pi$
$68$	15.2460	1.84885
$69$	−15.6550	−1.88464
$70$	0.639661	0.0764541
$71$	−3.38178	−0.401343	−0.200672	−	0.979659i	$-0.564312\pi$
$71$	−3.38178	−0.401343	−0.200672	+	0.979659i	$0.564312\pi$
$72$	1.70603	0.201057
$73$	−3.58137	−0.419167	−0.209584	−	0.977791i	$-0.567211\pi$
$73$	−3.58137	−0.419167	−0.209584	+	0.977791i	$0.567211\pi$
$74$	−18.6621	−2.16942
$75$	8.98727	1.03776
$76$	3.80675	0.436665
$77$	−3.32477	−0.378893
$78$	17.7430	2.00899
$79$	8.30176	0.934021	0.467011	−	0.884252i	$-0.345331\pi$
$79$	8.30176	0.934021	0.467011	+	0.884252i	$0.345331\pi$
$80$	0.997410	0.111514
$81$	−10.0220	−1.11356
$82$	−19.1499	−2.11476
$83$	−10.1950	−1.11905	−0.559526	−	0.828813i	$-0.689017\pi$
$83$	−10.1950	−1.11905	−0.559526	+	0.828813i	$0.689017\pi$
$84$	−5.36973	−0.585886
$85$	1.38805	0.150555
$86$	2.51641	0.271351
$87$	0.396519	0.0425113
$88$	−18.8994	−2.01468
$89$	−2.23579	−0.236993	−0.118496	−	0.992954i	$-0.537807\pi$
$89$	−2.23579	−0.236993	−0.118496	+	0.992954i	$0.537807\pi$
$90$	0.327258	0.0344961
$91$	−3.06211	−0.320996
$92$	32.3585	3.37361
$93$	9.99025	1.03594
$94$	−24.4707	−2.52396
$95$	0.346580	0.0355584
$96$	3.26477	0.333209
$97$	−5.30892	−0.539039	−0.269519	−	0.962995i	$-0.586865\pi$
$97$	−5.30892	−0.539039	−0.269519	+	0.962995i	$0.586865\pi$
$98$	−15.4544	−1.56113
$99$	−1.70099	−0.170956
$100$	−18.5765	−1.85765
$101$	13.5753	1.35079	0.675397	−	0.737454i	$-0.263972\pi$
$101$	13.5753	1.35079	0.675397	+	0.737454i	$0.263972\pi$
$102$	−17.7741	−1.75990
$103$	17.5707	1.73129	0.865647	−	0.500655i	$-0.166908\pi$
$103$	17.5707	1.73129	0.865647	+	0.500655i	$0.166908\pi$
$104$	−17.4063	−1.70683
$105$	−0.488879	−0.0477097
$106$	8.92812	0.867175
$107$	0.877689	0.0848494	0.0424247	−	0.999100i	$-0.486492\pi$
$107$	0.877689	0.0848494	0.0424247	+	0.999100i	$0.486492\pi$
$108$	18.2854	1.75952
$109$	8.92328	0.854695	0.427347	−	0.904087i	$-0.359448\pi$
$109$	8.92328	0.854695	0.427347	+	0.904087i	$0.359448\pi$
$110$	−3.62537	−0.345665
$111$	14.2630	1.35379
$112$	2.20419	0.208277
$113$	0.485072	0.0456318	0.0228159	−	0.999740i	$-0.492737\pi$
$113$	0.485072	0.0456318	0.0228159	+	0.999740i	$0.492737\pi$
$114$	−4.43798	−0.415655
$115$	2.94603	0.274719
$116$	−0.819598	−0.0760978
$117$	−1.56661	−0.144833
$118$	−15.5241	−1.42911
$119$	3.06748	0.281196
$120$	−2.77899	−0.253686
$121$	7.84361	0.713055
$122$	15.6598	1.41777
$123$	14.6359	1.31967
$124$	−20.6496	−1.85439
$125$	−3.42417	−0.306267
$126$	0.723214	0.0644290
$127$	−10.8148	−0.959655	−0.479827	−	0.877363i	$-0.659301\pi$
$127$	−10.8148	−0.959655	−0.479827	+	0.877363i	$0.659301\pi$
$128$	−20.6179	−1.82238
$129$	−1.92323	−0.169331
$130$	−3.33896	−0.292846
$131$	10.8877	0.951265	0.475632	−	0.879644i	$-0.342219\pi$
$131$	10.8877	0.951265	0.475632	+	0.879644i	$0.342219\pi$
$132$	30.4337	2.64892
$133$	0.765913	0.0664131
$134$	−28.7013	−2.47941
$135$	1.66477	0.143281
$136$	17.4368	1.49520
$137$	−17.3434	−1.48175	−0.740874	−	0.671643i	$-0.765589\pi$
$137$	−17.3434	−1.48175	−0.740874	+	0.671643i	$0.765589\pi$
$138$	−37.7241	−3.21129
$139$	1.10925	0.0940852	0.0470426	−	0.998893i	$-0.485020\pi$
$139$	1.10925	0.0940852	0.0470426	+	0.998893i	$0.485020\pi$
$140$	1.01050	0.0854031
$141$	18.7024	1.57503
$142$	−8.14914	−0.683861
$143$	17.3549	1.45129
$144$	1.12769	0.0939744
$145$	−0.0746190	−0.00619677
$146$	−8.63009	−0.714232
$147$	11.8115	0.974196
$148$	−29.4814	−2.42335
$149$	12.9935	1.06447	0.532236	−	0.846596i	$-0.321352\pi$
$149$	12.9935	1.06447	0.532236	+	0.846596i	$0.321352\pi$
$150$	21.6568	1.76827
$151$	−18.7620	−1.52683	−0.763414	−	0.645910i	$-0.776478\pi$
$151$	−18.7620	−1.52683	−0.763414	+	0.645910i	$0.776478\pi$
$152$	4.35377	0.353137
$153$	1.56936	0.126875
$154$	−8.01177	−0.645607
$155$	−1.88002	−0.151006
$156$	28.0294	2.24415
$157$	7.93812	0.633531	0.316766	−	0.948504i	$-0.397403\pi$
$157$	7.93812	0.633531	0.316766	+	0.948504i	$0.397403\pi$
$158$	20.0049	1.59151
$159$	−6.82357	−0.541144
$160$	−0.614380	−0.0485710
$161$	6.51048	0.513098
$162$	−24.1502	−1.89742
$163$	−17.4446	−1.36637	−0.683183	−	0.730247i	$-0.739405\pi$
$163$	−17.4446	−1.36637	−0.683183	+	0.730247i	$0.739405\pi$
$164$	−30.2521	−2.36229
$165$	2.77079	0.215706
$166$	−24.5672	−1.90679
$167$	−7.72948	−0.598125	−0.299063	−	0.954233i	$-0.596674\pi$
$167$	−7.72948	−0.598125	−0.299063	+	0.954233i	$0.596674\pi$
$168$	−6.14135	−0.473815
$169$	2.98387	0.229529
$170$	3.34482	0.256536
$171$	0.391851	0.0299656
$172$	3.97529	0.303113
$173$	9.88449	0.751504	0.375752	−	0.926720i	$-0.377384\pi$
$173$	9.88449	0.751504	0.375752	+	0.926720i	$0.377384\pi$
$174$	0.955501	0.0724363
$175$	−3.73757	−0.282534
$176$	−12.4926	−0.941664
$177$	11.8647	0.891806
$178$	−5.38762	−0.403819
$179$	9.31381	0.696147	0.348073	−	0.937467i	$-0.386836\pi$
$179$	9.31381	0.696147	0.348073	+	0.937467i	$0.386836\pi$
$180$	0.516986	0.0385339
$181$	−5.94227	−0.441685	−0.220843	−	0.975309i	$-0.570881\pi$
$181$	−5.94227	−0.441685	−0.220843	+	0.975309i	$0.570881\pi$
$182$	−7.37883	−0.546955
$183$	−11.9685	−0.884733
$184$	37.0083	2.72829
$185$	−2.68409	−0.197338
$186$	24.0737	1.76517
$187$	−17.3854	−1.27135
$188$	−38.6575	−2.81939
$189$	3.67901	0.267608
$190$	0.835161	0.0605889
$191$	−4.81890	−0.348683	−0.174342	−	0.984685i	$-0.555780\pi$
$191$	−4.81890	−0.348683	−0.174342	+	0.984685i	$0.555780\pi$
$192$	18.4675	1.33278
$193$	−23.0059	−1.65600	−0.828001	−	0.560726i	$-0.810522\pi$
$193$	−23.0059	−1.65600	−0.828001	+	0.560726i	$0.810522\pi$
$194$	−12.7930	−0.918484
$195$	2.55190	0.182745
$196$	−24.4141	−1.74387
$197$	20.4120	1.45429	0.727147	−	0.686482i	$-0.240846\pi$
$197$	20.4120	1.45429	0.727147	+	0.686482i	$0.240846\pi$
$198$	−4.09892	−0.291297
$199$	−10.0141	−0.709883	−0.354942	−	0.934888i	$-0.615499\pi$
$199$	−10.0141	−0.709883	−0.354942	+	0.934888i	$0.615499\pi$
$200$	−21.2459	−1.50231
$201$	21.9358	1.54723
$202$	32.7127	2.30166
$203$	−0.164902	−0.0115738
$204$	−28.0786	−1.96589
$205$	−2.75426	−0.192366
$206$	42.3405	2.95000
$207$	3.33084	0.231509
$208$	−11.5057	−0.797773
$209$	−4.34092	−0.300268
$210$	−1.17806	−0.0812940
$211$	1.00000	0.0688428
$211$	1.00000	0.0688428
$212$	14.1042	0.968679
$213$	6.22822	0.426750
$214$	2.11499	0.144577
$215$	0.361924	0.0246830
$216$	20.9130	1.42295
$217$	−4.15468	−0.282038
$218$	21.5026	1.45634
$219$	6.59579	0.445702
$220$	−5.72717	−0.386126
$221$	−16.0119	−1.07708
$222$	34.3699	2.30675
$223$	21.4361	1.43547	0.717734	−	0.696318i	$-0.245179\pi$
$223$	21.4361	1.43547	0.717734	+	0.696318i	$0.245179\pi$
$224$	−1.35773	−0.0907172
$225$	−1.91218	−0.127479
$226$	1.16889	0.0777533
$227$	−0.0104538	−0.000693840 0	−0.000346920	−	1.00000i	$-0.500110\pi$
$227$	−0.0104538	−0.000693840 0	−0.000346920		1.00000i	$0.500110\pi$
$228$	−7.01089	−0.464307
$229$	11.7752	0.778128	0.389064	−	0.921211i	$-0.372799\pi$
$229$	11.7752	0.778128	0.389064	+	0.921211i	$0.372799\pi$
$230$	7.09911	0.468101
$231$	6.12322	0.402878
$232$	−0.937371	−0.0615414
$233$	6.26283	0.410292	0.205146	−	0.978731i	$-0.434233\pi$
$233$	6.26283	0.410292	0.205146	+	0.978731i	$0.434233\pi$
$234$	−3.77510	−0.246786
$235$	−3.51952	−0.229588
$236$	−24.5241	−1.59638
$237$	−15.2893	−0.993149
$238$	7.39177	0.479137
$239$	26.3947	1.70733	0.853666	−	0.520822i	$-0.174374\pi$
$239$	26.3947	1.70733	0.853666	+	0.520822i	$0.174374\pi$
$240$	−1.83693	−0.118573
$241$	5.33963	0.343956	0.171978	−	0.985101i	$-0.444984\pi$
$241$	5.33963	0.343956	0.171978	+	0.985101i	$0.444984\pi$
$242$	18.9009	1.21500
$243$	4.04724	0.259630
$244$	24.7386	1.58372
$245$	−2.22275	−0.142006
$246$	35.2684	2.24863
$247$	−3.99798	−0.254386
$248$	−23.6169	−1.49968
$249$	18.7762	1.18989
$250$	−8.25129	−0.521857
$251$	8.87052	0.559902	0.279951	−	0.960014i	$-0.409682\pi$
$251$	8.87052	0.559902	0.279951	+	0.960014i	$0.409682\pi$
$252$	1.14250	0.0719705
$253$	−36.8991	−2.31983
$254$	−26.0606	−1.63518
$255$	−2.55637	−0.160086
$256$	−29.6285	−1.85178
$257$	7.12486	0.444436	0.222218	−	0.974997i	$-0.428670\pi$
$257$	7.12486	0.444436	0.222218	+	0.974997i	$0.428670\pi$
$258$	−4.63446	−0.288529
$259$	−5.93161	−0.368572
$260$	−5.27472	−0.327124
$261$	−0.0843658	−0.00522211
$262$	26.2364	1.62089
$263$	−5.22198	−0.322001	−0.161000	−	0.986954i	$-0.551472\pi$
$263$	−5.22198	−0.322001	−0.161000	+	0.986954i	$0.551472\pi$
$264$	34.8069	2.14222
$265$	1.28409	0.0788812
$266$	1.84564	0.113163
$267$	4.11764	0.251996
$268$	−45.3408	−2.76963
$269$	4.51725	0.275422	0.137711	−	0.990472i	$-0.456025\pi$
$269$	4.51725	0.275422	0.137711	+	0.990472i	$0.456025\pi$
$270$	4.01163	0.244140
$271$	16.5608	1.00600	0.502999	−	0.864287i	$-0.332230\pi$
$271$	16.5608	1.00600	0.502999	+	0.864287i	$0.332230\pi$
$272$	11.5258	0.698856
$273$	5.63948	0.341317
$274$	−41.7928	−2.52480
$275$	21.1832	1.27739
$276$	−59.5945	−3.58717
$277$	14.2890	0.858542	0.429271	−	0.903176i	$-0.358770\pi$
$277$	14.2890	0.858542	0.429271	+	0.903176i	$0.358770\pi$
$278$	2.67298	0.160315
$279$	−2.12558	−0.127255
$280$	1.15571	0.0690668
$281$	−10.3800	−0.619217	−0.309608	−	0.950864i	$-0.600198\pi$
$281$	−10.3800	−0.619217	−0.309608	+	0.950864i	$0.600198\pi$
$282$	45.0676	2.68374
$283$	−21.4313	−1.27396	−0.636979	−	0.770881i	$-0.719816\pi$
$283$	−21.4313	−1.27396	−0.636979	+	0.770881i	$0.719816\pi$
$284$	−12.8736	−0.763908
$285$	−0.638296	−0.0378094
$286$	41.8205	2.47290
$287$	−6.08668	−0.359285
$288$	−0.694631	−0.0409315
$289$	−0.959994	−0.0564703
$290$	−0.179811	−0.0105589
$291$	9.77742	0.573162
$292$	−13.6334	−0.797833
$293$	−1.66455	−0.0972440	−0.0486220	−	0.998817i	$-0.515483\pi$
$293$	−1.66455	−0.0972440	−0.0486220	+	0.998817i	$0.515483\pi$
$294$	28.4624	1.65996
$295$	−2.23276	−0.129996
$296$	−33.7177	−1.95980
$297$	−20.8513	−1.20991
$298$	31.3108	1.81378
$299$	−33.9840	−1.96535
$300$	34.2123	1.97525
$301$	0.799822	0.0461010
$302$	−45.2111	−2.60161
$303$	−25.0016	−1.43631
$304$	2.87786	0.165057
$305$	2.25228	0.128965
$306$	3.78172	0.216187
$307$	−12.6319	−0.720938	−0.360469	−	0.932771i	$-0.617383\pi$
$307$	−12.6319	−0.720938	−0.360469	+	0.932771i	$0.617383\pi$
$308$	−12.6566	−0.721176
$309$	−32.3599	−1.84089
$310$	−4.53031	−0.257304
$311$	−24.6864	−1.39984	−0.699920	−	0.714221i	$-0.746781\pi$
$311$	−24.6864	−1.39984	−0.699920	+	0.714221i	$0.746781\pi$
$312$	32.0571	1.81488
$313$	22.6393	1.27965	0.639823	−	0.768522i	$-0.279007\pi$
$313$	22.6393	1.27965	0.639823	+	0.768522i	$0.279007\pi$
$314$	19.1287	1.07949
$315$	0.104017	0.00586068
$316$	31.6028	1.77779
$317$	22.5922	1.26890	0.634452	−	0.772962i	$-0.281226\pi$
$317$	22.5922	1.26890	0.634452	+	0.772962i	$0.281226\pi$
$318$	−16.4429	−0.922072
$319$	0.934605	0.0523278
$320$	−3.47530	−0.194275
$321$	−1.61644	−0.0902208
$322$	15.6884	0.874283
$323$	4.00500	0.222844
$324$	−38.1513	−2.11952
$325$	19.5097	1.08220
$326$	−42.0366	−2.32819
$327$	−16.4340	−0.908801
$328$	−34.5992	−1.91042
$329$	−7.77784	−0.428806
$330$	6.67683	0.367548
$331$	0.469771	0.0258210	0.0129105	−	0.999917i	$-0.495890\pi$
$331$	0.469771	0.0258210	0.0129105	+	0.999917i	$0.495890\pi$
$332$	−38.8100	−2.12998
$333$	−3.03468	−0.166300
$334$	−18.6259	−1.01916
$335$	−4.12798	−0.225536
$336$	−4.05946	−0.221462
$337$	1.10419	0.0601489	0.0300745	−	0.999548i	$-0.490426\pi$
$337$	1.10419	0.0601489	0.0300745	+	0.999548i	$0.490426\pi$
$338$	7.19030	0.391101
$339$	−0.893357	−0.0485205
$340$	5.28397	0.286564
$341$	23.5472	1.27515
$342$	0.944250	0.0510592
$343$	−10.2735	−0.554716
$344$	4.54652	0.245132
$345$	−5.42569	−0.292110
$346$	23.8189	1.28051
$347$	6.80329	0.365220	0.182610	−	0.983185i	$-0.441545\pi$
$347$	6.80329	0.365220	0.182610	+	0.983185i	$0.441545\pi$
$348$	1.50945	0.0809151
$349$	16.1192	0.862839	0.431420	−	0.902151i	$-0.358013\pi$
$349$	16.1192	0.862839	0.431420	+	0.902151i	$0.358013\pi$
$350$	−9.00649	−0.481417
$351$	−19.2040	−1.02503
$352$	7.69513	0.410152
$353$	−6.89285	−0.366870	−0.183435	−	0.983032i	$-0.558722\pi$
$353$	−6.89285	−0.366870	−0.183435	+	0.983032i	$0.558722\pi$
$354$	28.5906	1.51957
$355$	−1.17206	−0.0622063
$356$	−8.51109	−0.451087
$357$	−5.64937	−0.298997
$358$	22.4437	1.18619
$359$	13.6807	0.722038	0.361019	−	0.932558i	$-0.382429\pi$
$359$	13.6807	0.722038	0.361019	+	0.932558i	$0.382429\pi$
$360$	0.591275	0.0311629
$361$	1.00000	0.0526316
$362$	−14.3192	−0.752601
$363$	−14.4456	−0.758195
$364$	−11.6567	−0.610977
$365$	−1.24123	−0.0649689
$366$	−28.8406	−1.50752
$367$	−10.6981	−0.558438	−0.279219	−	0.960227i	$-0.590076\pi$
$367$	−10.6981	−0.558438	−0.279219	+	0.960227i	$0.590076\pi$
$368$	24.4627	1.27520
$369$	−3.11402	−0.162109
$370$	−6.46790	−0.336250
$371$	2.83774	0.147328
$372$	38.0304	1.97179
$373$	−38.0379	−1.96953	−0.984764	−	0.173895i	$-0.944365\pi$
$373$	−38.0379	−1.96953	−0.984764	+	0.173895i	$0.944365\pi$
$374$	−41.8939	−2.16628
$375$	6.30629	0.325655
$376$	−44.2125	−2.28009
$377$	0.860770	0.0443319
$378$	8.86538	0.455986
$379$	−10.9818	−0.564097	−0.282048	−	0.959400i	$-0.591014\pi$
$379$	−10.9818	−0.564097	−0.282048	+	0.959400i	$0.591014\pi$
$380$	1.31934	0.0676809
$381$	19.9175	1.02041
$382$	−11.6122	−0.594131
$383$	−24.8926	−1.27195	−0.635976	−	0.771709i	$-0.719402\pi$
$383$	−24.8926	−1.27195	−0.635976	+	0.771709i	$0.719402\pi$
$384$	37.9719	1.93775
$385$	−1.15230	−0.0587266
$386$	−55.4378	−2.82171
$387$	0.409199	0.0208007
$388$	−20.2097	−1.02599
$389$	3.60401	0.182730	0.0913652	−	0.995817i	$-0.470877\pi$
$389$	3.60401	0.182730	0.0913652	+	0.995817i	$0.470877\pi$
$390$	6.14935	0.311385
$391$	34.0436	1.72166
$392$	−27.9224	−1.41029
$393$	−20.0519	−1.01148
$394$	49.1872	2.47801
$395$	2.87722	0.144769
$396$	−6.47526	−0.325394
$397$	29.0857	1.45977	0.729884	−	0.683571i	$-0.239574\pi$
$397$	29.0857	1.45977	0.729884	+	0.683571i	$0.239574\pi$
$398$	−24.1313	−1.20959
$399$	−1.41058	−0.0706174
$400$	−14.0436	−0.702182
$401$	−22.7392	−1.13554	−0.567770	−	0.823187i	$-0.692194\pi$
$401$	−22.7392	−1.13554	−0.567770	+	0.823187i	$0.692194\pi$
$402$	52.8591	2.63637
$403$	21.6870	1.08031
$404$	51.6779	2.57107
$405$	−3.47343	−0.172596
$406$	−0.397368	−0.0197210
$407$	33.6182	1.66639
$408$	−32.1134	−1.58985
$409$	19.6457	0.971418	0.485709	−	0.874121i	$-0.338561\pi$
$409$	19.6457	0.971418	0.485709	+	0.874121i	$0.338561\pi$
$410$	−6.63699	−0.327777
$411$	31.9414	1.57555
$412$	66.8874	3.29530
$413$	−4.93422	−0.242797
$414$	8.02640	0.394476
$415$	−3.53340	−0.173448
$416$	7.08720	0.347479
$417$	−2.04290	−0.100041
$418$	−10.4604	−0.511635
$419$	−5.38155	−0.262906	−0.131453	−	0.991322i	$-0.541964\pi$
$419$	−5.38155	−0.262906	−0.131453	+	0.991322i	$0.541964\pi$
$420$	−1.86104	−0.0908096
$421$	16.0428	0.781877	0.390938	−	0.920417i	$-0.372151\pi$
$421$	16.0428	0.781877	0.390938	+	0.920417i	$0.372151\pi$
$422$	2.40972	0.117303
$423$	−3.97924	−0.193477
$424$	16.1309	0.783386
$425$	−19.5439	−0.948019
$426$	15.0083	0.727152
$427$	4.97736	0.240871
$428$	3.34115	0.161500
$429$	−31.9625	−1.54317
$430$	0.872136	0.0420581
$431$	−13.5289	−0.651663	−0.325832	−	0.945428i	$-0.605644\pi$
$431$	−13.5289	−0.651663	−0.325832	+	0.945428i	$0.605644\pi$
$432$	13.8236	0.665088
$433$	18.7964	0.903297	0.451648	−	0.892196i	$-0.350836\pi$
$433$	18.7964	0.903297	0.451648	+	0.892196i	$0.350836\pi$
$434$	−10.0116	−0.480573
$435$	0.137426	0.00658906
$436$	33.9687	1.62681
$437$	8.50028	0.406624
$438$	15.8940	0.759446
$439$	17.8539	0.852118	0.426059	−	0.904695i	$-0.359902\pi$
$439$	17.8539	0.852118	0.426059	+	0.904695i	$0.359902\pi$
$440$	−6.55015	−0.312266
$441$	−2.51309	−0.119671
$442$	−38.5842	−1.83527
$443$	28.1658	1.33820	0.669098	−	0.743174i	$-0.266681\pi$
$443$	28.1658	1.33820	0.669098	+	0.743174i	$0.266681\pi$
$444$	54.2958	2.57676
$445$	−0.774879	−0.0367328
$446$	51.6550	2.44594
$447$	−23.9301	−1.13186
$448$	−7.68014	−0.362852
$449$	−10.6178	−0.501087	−0.250543	−	0.968105i	$-0.580609\pi$
$449$	−10.6178	−0.501087	−0.250543	+	0.968105i	$0.580609\pi$
$450$	−4.60783	−0.217215
$451$	34.4971	1.62441
$452$	1.84655	0.0868544
$453$	34.5539	1.62348
$454$	−0.0251906	−0.00118225
$455$	−1.06127	−0.0497529
$456$	−8.01833	−0.375493
$457$	−30.3287	−1.41872	−0.709360	−	0.704847i	$-0.751016\pi$
$457$	−30.3287	−1.41872	−0.709360	+	0.704847i	$0.751016\pi$
$458$	28.3750	1.32588
$459$	19.2377	0.897939
$460$	11.2148	0.522893
$461$	32.9191	1.53319	0.766597	−	0.642129i	$-0.221949\pi$
$461$	32.9191	1.53319	0.766597	+	0.642129i	$0.221949\pi$
$462$	14.7553	0.686477
$463$	−26.7936	−1.24521	−0.622603	−	0.782538i	$-0.713925\pi$
$463$	−26.7936	−1.24521	−0.622603	+	0.782538i	$0.713925\pi$
$464$	−0.619607	−0.0287645
$465$	3.46242	0.160566
$466$	15.0917	0.699109
$467$	12.8370	0.594023	0.297012	−	0.954874i	$-0.404010\pi$
$467$	12.8370	0.594023	0.297012	+	0.954874i	$0.404010\pi$
$468$	−5.96371	−0.275672
$469$	−9.12251	−0.421238
$470$	−8.48105	−0.391202
$471$	−14.6196	−0.673637
$472$	−28.0482	−1.29102
$473$	−4.53311	−0.208432
$474$	−36.8430	−1.69226
$475$	−4.87988	−0.223904
$476$	11.6771	0.535221
$477$	1.45182	0.0664744
$478$	63.6038	2.90917
$479$	1.46343	0.0668657	0.0334328	−	0.999441i	$-0.489356\pi$
$479$	1.46343	0.0668657	0.0334328	+	0.999441i	$0.489356\pi$
$480$	1.13150	0.0516458
$481$	30.9623	1.41176
$482$	12.8670	0.586077
$483$	−11.9903	−0.545579
$484$	29.8587	1.35721
$485$	−1.83996	−0.0835485
$486$	9.75271	0.442392
$487$	−32.7396	−1.48357	−0.741787	−	0.670636i	$-0.766021\pi$
$487$	−32.7396	−1.48357	−0.741787	+	0.670636i	$0.766021\pi$
$488$	28.2934	1.28078
$489$	32.1277	1.45286
$490$	−5.35620	−0.241969
$491$	−18.0251	−0.813460	−0.406730	−	0.913548i	$-0.633331\pi$
$491$	−18.0251	−0.813460	−0.406730	+	0.913548i	$0.633331\pi$
$492$	55.7152	2.51184
$493$	−0.862280	−0.0388351
$494$	−9.63402	−0.433455
$495$	−0.589530	−0.0264974
$496$	−15.6109	−0.700950
$497$	−2.59015	−0.116184
$498$	45.2454	2.02749
$499$	−4.75257	−0.212754	−0.106377	−	0.994326i	$-0.533925\pi$
$499$	−4.75257	−0.212754	−0.106377	+	0.994326i	$0.533925\pi$
$500$	−13.0350	−0.582941
$501$	14.2354	0.635989
$502$	21.3755	0.954034
$503$	−10.1737	−0.453622	−0.226811	−	0.973939i	$-0.572830\pi$
$503$	−10.1737	−0.453622	−0.226811	+	0.973939i	$0.572830\pi$
$504$	1.30667	0.0582037
$505$	4.70493	0.209367
$506$	−88.9165	−3.95282
$507$	−5.49539	−0.244059
$508$	−41.1691	−1.82658
$509$	3.19916	0.141800	0.0709001	−	0.997483i	$-0.477413\pi$
$509$	3.19916	0.141800	0.0709001	+	0.997483i	$0.477413\pi$
$510$	−6.16014	−0.272776
$511$	−2.74302	−0.121344
$512$	−30.1607	−1.33293
$513$	4.80342	0.212076
$514$	17.1689	0.757289
$515$	6.08966	0.268342
$516$	−7.32128	−0.322301
$517$	44.0820	1.93873
$518$	−14.2935	−0.628021
$519$	−18.2042	−0.799078
$520$	−6.03268	−0.264550
$521$	17.0284	0.746030	0.373015	−	0.927825i	$-0.378324\pi$
$521$	17.0284	0.746030	0.373015	+	0.927825i	$0.378324\pi$
$522$	−0.203298	−0.00889812
$523$	0.923721	0.0403915	0.0201957	−	0.999796i	$-0.493571\pi$
$523$	0.923721	0.0403915	0.0201957	+	0.999796i	$0.493571\pi$
$524$	41.4469	1.81061
$525$	6.88347	0.300419
$526$	−12.5835	−0.548667
$527$	−21.7250	−0.946357
$528$	23.0076	1.00128
$529$	49.2548	2.14151
$530$	3.09431	0.134408
$531$	−2.52441	−0.109550
$532$	2.91564	0.126409
$533$	31.7718	1.37619
$534$	9.92237	0.429383
$535$	0.304189	0.0131513
$536$	−51.8561	−2.23984
$537$	−17.1532	−0.740216
$538$	10.8853	0.469300
$539$	27.8400	1.19915
$540$	6.33737	0.272717
$541$	40.2717	1.73141	0.865707	−	0.500550i	$-0.166869\pi$
$541$	40.2717	1.73141	0.865707	+	0.500550i	$0.166869\pi$
$542$	39.9069	1.71415
$543$	10.9439	0.469646
$544$	−7.09963	−0.304394
$545$	3.09263	0.132474
$546$	13.5896	0.581580
$547$	10.0612	0.430184	0.215092	−	0.976594i	$-0.430995\pi$
$547$	10.0612	0.430184	0.215092	+	0.976594i	$0.430995\pi$
$548$	−66.0221	−2.82033
$549$	2.54648	0.108681
$550$	51.0456	2.17659
$551$	−0.215301	−0.00917213
$552$	−68.1581	−2.90100
$553$	6.35843	0.270388
$554$	34.4325	1.46290
$555$	4.94327	0.209830
$556$	4.22264	0.179080
$557$	−0.514164	−0.0217858	−0.0108929	−	0.999941i	$-0.503467\pi$
$557$	−0.514164	−0.0217858	−0.0108929	+	0.999941i	$0.503467\pi$
$558$	−5.12207	−0.216834
$559$	−4.17498	−0.176583
$560$	0.763930	0.0322819
$561$	32.0186	1.35183
$562$	−25.0128	−1.05510
$563$	−24.4935	−1.03228	−0.516139	−	0.856505i	$-0.672631\pi$
$563$	−24.4935	−1.03228	−0.516139	+	0.856505i	$0.672631\pi$
$564$	71.1955	2.99787
$565$	0.168116	0.00707271
$566$	−51.6434	−2.17074
$567$	−7.67599	−0.322361
$568$	−14.7235	−0.617784
$569$	−4.28487	−0.179631	−0.0898156	−	0.995958i	$-0.528628\pi$
$569$	−4.28487	−0.179631	−0.0898156	+	0.995958i	$0.528628\pi$
$570$	−1.53811	−0.0644245
$571$	−8.17136	−0.341961	−0.170980	−	0.985274i	$-0.554693\pi$
$571$	−8.17136	−0.341961	−0.170980	+	0.985274i	$0.554693\pi$
$572$	66.0660	2.76236
$573$	8.87495	0.370756
$574$	−14.6672	−0.612197
$575$	−41.4804	−1.72985
$576$	−3.92925	−0.163719
$577$	2.45865	0.102355	0.0511775	−	0.998690i	$-0.483703\pi$
$577$	2.45865	0.102355	0.0511775	+	0.998690i	$0.483703\pi$
$578$	−2.31332	−0.0962214
$579$	42.3699	1.76083
$580$	−0.284056	−0.0117948
$581$	−7.80852	−0.323952
$582$	23.5608	0.976628
$583$	−16.0833	−0.666102
$584$	−15.5924	−0.645220
$585$	−0.542956	−0.0224485
$586$	−4.01110	−0.165697
$587$	1.90797	0.0787502	0.0393751	−	0.999224i	$-0.487463\pi$
$587$	1.90797	0.0787502	0.0393751	+	0.999224i	$0.487463\pi$
$588$	44.9635	1.85426
$589$	−5.42448	−0.223512
$590$	−5.38033	−0.221505
$591$	−37.5927	−1.54636
$592$	−22.2876	−0.916014
$593$	23.6238	0.970114	0.485057	−	0.874482i	$-0.338799\pi$
$593$	23.6238	0.970114	0.485057	+	0.874482i	$0.338799\pi$
$594$	−50.2458	−2.06161
$595$	1.06313	0.0435840
$596$	49.4631	2.02609
$597$	18.4430	0.754822
$598$	−81.8919	−3.34881
$599$	−36.8865	−1.50714	−0.753570	−	0.657368i	$-0.771670\pi$
$599$	−36.8865	−1.50714	−0.753570	+	0.657368i	$0.771670\pi$
$600$	39.1285	1.59741
$601$	−6.53738	−0.266665	−0.133333	−	0.991071i	$-0.542568\pi$
$601$	−6.53738	−0.266665	−0.133333	+	0.991071i	$0.542568\pi$
$602$	1.92735	0.0785529
$603$	−4.66719	−0.190062
$604$	−71.4222	−2.90613
$605$	2.71844	0.110520
$606$	−60.2469	−2.44736
$607$	10.6188	0.431003	0.215501	−	0.976504i	$-0.430861\pi$
$607$	10.6188	0.431003	0.215501	+	0.976504i	$0.430861\pi$
$608$	−1.77269	−0.0718922
$609$	0.303700	0.0123065
$610$	5.42737	0.219748
$611$	40.5995	1.64248
$612$	5.97417	0.241491
$613$	−4.94454	−0.199708	−0.0998540	−	0.995002i	$-0.531838\pi$
$613$	−4.94454	−0.199708	−0.0998540	+	0.995002i	$0.531838\pi$
$614$	−30.4392	−1.22843
$615$	5.07251	0.204543
$616$	−14.4753	−0.583226
$617$	28.6749	1.15441	0.577205	−	0.816599i	$-0.304143\pi$
$617$	28.6749	1.15441	0.577205	+	0.816599i	$0.304143\pi$
$618$	−77.9784	−3.13675
$619$	−32.3355	−1.29968	−0.649838	−	0.760073i	$-0.725163\pi$
$619$	−32.3355	−1.29968	−0.649838	+	0.760073i	$0.725163\pi$
$620$	−7.15676	−0.287422
$621$	40.8305	1.63847
$622$	−59.4874	−2.38523
$623$	−1.71242	−0.0686066
$624$	21.1899	0.848276
$625$	23.2127	0.928507
$626$	54.5543	2.18043
$627$	7.99467	0.319276
$628$	30.2185	1.20585
$629$	−31.0167	−1.23672
$630$	0.250652	0.00998620
$631$	−4.14020	−0.164819	−0.0824094	−	0.996599i	$-0.526262\pi$
$631$	−4.14020	−0.164819	−0.0824094	+	0.996599i	$0.526262\pi$
$632$	36.1440	1.43773
$633$	−1.84170	−0.0732009
$634$	54.4409	2.16212
$635$	−3.74818	−0.148742
$636$	−25.9756	−1.03000
$637$	25.6406	1.01592
$638$	2.25214	0.0891630
$639$	−1.32515	−0.0524222
$640$	−7.14575	−0.282461
$641$	−21.1796	−0.836545	−0.418272	−	0.908322i	$-0.637364\pi$
$641$	−21.1796	−0.836545	−0.418272	+	0.908322i	$0.637364\pi$
$642$	−3.89516	−0.153730
$643$	−32.5705	−1.28445	−0.642227	−	0.766515i	$-0.721989\pi$
$643$	−32.5705	−1.28445	−0.642227	+	0.766515i	$0.721989\pi$
$644$	24.7838	0.976618
$645$	−0.666555	−0.0262456
$646$	9.65093	0.379711
$647$	−17.7336	−0.697180	−0.348590	−	0.937275i	$-0.613340\pi$
$647$	−17.7336	−0.697180	−0.348590	+	0.937275i	$0.613340\pi$
$648$	−43.6335	−1.71409
$649$	27.9654	1.09774
$650$	47.0129	1.84400
$651$	7.65167	0.299892
$652$	−66.4073	−2.60071
$653$	17.5156	0.685438	0.342719	−	0.939438i	$-0.388652\pi$
$653$	17.5156	0.685438	0.342719	+	0.939438i	$0.388652\pi$
$654$	−39.6013	−1.54853
$655$	3.77347	0.147442
$656$	−22.8703	−0.892934
$657$	−1.40336	−0.0547503
$658$	−18.7424	−0.730656
$659$	1.44478	0.0562805	0.0281402	−	0.999604i	$-0.491042\pi$
$659$	1.44478	0.0562805	0.0281402	+	0.999604i	$0.491042\pi$
$660$	10.5477	0.410569
$661$	37.1527	1.44507	0.722536	−	0.691333i	$-0.242976\pi$
$661$	37.1527	1.44507	0.722536	+	0.691333i	$0.242976\pi$
$662$	1.13202	0.0439971
$663$	29.4891	1.14526
$664$	−44.3869	−1.72255
$665$	0.265450	0.0102937
$666$	−7.31274	−0.283363
$667$	−1.83012	−0.0708625
$668$	−29.4242	−1.13846
$669$	−39.4788	−1.52634
$670$	−9.94729	−0.384297
$671$	−28.2099	−1.08903
$672$	2.50053	0.0964600
$673$	12.5167	0.482482	0.241241	−	0.970465i	$-0.422445\pi$
$673$	12.5167	0.482482	0.241241	+	0.970465i	$0.422445\pi$
$674$	2.66078	0.102490
$675$	−23.4401	−0.902211
$676$	11.3589	0.436879
$677$	22.7006	0.872457	0.436228	−	0.899836i	$-0.356314\pi$
$677$	22.7006	0.872457	0.436228	+	0.899836i	$0.356314\pi$
$678$	−2.15274	−0.0826755
$679$	−4.06617	−0.156045
$680$	6.04326	0.231748
$681$	0.0192527	0.000737763 0
$682$	56.7423	2.17277
$683$	8.45849	0.323655	0.161828	−	0.986819i	$-0.448261\pi$
$683$	8.45849	0.323655	0.161828	+	0.986819i	$0.448261\pi$
$684$	1.49168	0.0570358
$685$	−6.01088	−0.229664
$686$	−24.7562	−0.945197
$687$	−21.6864	−0.827387
$688$	3.00527	0.114575
$689$	−14.8127	−0.564319
$690$	−13.0744	−0.497734
$691$	18.7026	0.711480	0.355740	−	0.934585i	$-0.384229\pi$
$691$	18.7026	0.711480	0.355740	+	0.934585i	$0.384229\pi$
$692$	37.6278	1.43040
$693$	−1.30281	−0.0494898
$694$	16.3940	0.622309
$695$	0.384443	0.0145828
$696$	1.72635	0.0654373
$697$	−31.8275	−1.20555
$698$	38.8427	1.47022
$699$	−11.5342	−0.436265
$700$	−14.2280	−0.537768
$701$	−0.816525	−0.0308397	−0.0154199	−	0.999881i	$-0.504908\pi$
$701$	−0.816525	−0.0308397	−0.0154199	+	0.999881i	$0.504908\pi$
$702$	−46.2763	−1.74659
$703$	−7.74449	−0.292089
$704$	43.5283	1.64053
$705$	6.48189	0.244122
$706$	−16.6099	−0.625120
$707$	10.3975	0.391039
$708$	45.1660	1.69744
$709$	−38.6609	−1.45194	−0.725970	−	0.687727i	$-0.758609\pi$
$709$	−38.6609	−1.45194	−0.725970	+	0.687727i	$0.758609\pi$
$710$	−2.82433	−0.105995
$711$	3.25305	0.121999
$712$	−9.73410	−0.364801
$713$	−46.1096	−1.72682
$714$	−13.6134	−0.509469
$715$	6.01487	0.224944
$716$	35.4554	1.32503
$717$	−48.6111	−1.81541
$718$	32.9666	1.23030
$719$	−31.9845	−1.19282	−0.596411	−	0.802679i	$-0.703407\pi$
$719$	−31.9845	−1.19282	−0.596411	+	0.802679i	$0.703407\pi$
$720$	0.390836	0.0145656
$721$	13.4576	0.501189
$722$	2.40972	0.0896805
$723$	−9.83399	−0.365730
$724$	−22.6208	−0.840694
$725$	1.05064	0.0390199
$726$	−34.8098	−1.29191
$727$	18.1927	0.674731	0.337366	−	0.941374i	$-0.390464\pi$
$727$	18.1927	0.674731	0.337366	+	0.941374i	$0.390464\pi$
$728$	−13.3317	−0.494106
$729$	22.6122	0.837490
$730$	−2.99102	−0.110703
$731$	4.18231	0.154688
$732$	−45.5609	−1.68398
$733$	8.05732	0.297604	0.148802	−	0.988867i	$-0.452458\pi$
$733$	8.05732	0.297604	0.148802	+	0.988867i	$0.452458\pi$
$734$	−25.7795	−0.951539
$735$	4.09363	0.150996
$736$	−15.0684	−0.555429
$737$	51.7031	1.90451
$738$	−7.50392	−0.276223
$739$	−14.6694	−0.539621	−0.269811	−	0.962913i	$-0.586961\pi$
$739$	−14.6694	−0.539621	−0.269811	+	0.962913i	$0.586961\pi$
$740$	−10.2177	−0.375608
$741$	7.36308	0.270489
$742$	6.83816	0.251037
$743$	46.8276	1.71794	0.858969	−	0.512027i	$-0.171105\pi$
$743$	46.8276	1.71794	0.858969	+	0.512027i	$0.171105\pi$
$744$	43.4952	1.59461
$745$	4.50330	0.164988
$746$	−91.6607	−3.35594
$747$	−3.99494	−0.146167
$748$	−66.1819	−2.41985
$749$	0.672234	0.0245629
$750$	15.1964	0.554894
$751$	−38.3632	−1.39989	−0.699946	−	0.714196i	$-0.746792\pi$
$751$	−38.3632	−1.39989	−0.699946	+	0.714196i	$0.746792\pi$
$752$	−29.2247	−1.06571
$753$	−16.3368	−0.595347
$754$	2.07422	0.0755385
$755$	−6.50252	−0.236651
$756$	14.0051	0.509359
$757$	−9.49953	−0.345266	−0.172633	−	0.984986i	$-0.555227\pi$
$757$	−9.49953	−0.345266	−0.172633	+	0.984986i	$0.555227\pi$
$758$	−26.4630	−0.961181
$759$	67.9569	2.46668
$760$	1.50893	0.0547346
$761$	21.5811	0.782316	0.391158	−	0.920324i	$-0.372075\pi$
$761$	21.5811	0.782316	0.391158	+	0.920324i	$0.372075\pi$
$762$	47.9957	1.73870
$763$	6.83446	0.247424
$764$	−18.3443	−0.663675
$765$	0.543909	0.0196651
$766$	−59.9842	−2.16732
$767$	25.7561	0.929998
$768$	54.5668	1.96901
$769$	−22.3562	−0.806184	−0.403092	−	0.915159i	$-0.632065\pi$
$769$	−22.3562	−0.806184	−0.403092	+	0.915159i	$0.632065\pi$
$770$	−2.77672	−0.100066
$771$	−13.1218	−0.472571
$772$	−87.5779	−3.15200
$773$	−51.3991	−1.84870	−0.924349	−	0.381548i	$-0.875391\pi$
$773$	−51.3991	−1.84870	−0.924349	+	0.381548i	$0.875391\pi$
$774$	0.986055	0.0354430
$775$	26.4708	0.950860
$776$	−23.1138	−0.829737
$777$	10.9242	0.391905
$778$	8.68465	0.311360
$779$	−7.94696	−0.284729
$780$	9.71444	0.347833
$781$	14.6800	0.525293
$782$	82.0356	2.93359
$783$	−1.03418	−0.0369586
$784$	−18.4568	−0.659172
$785$	2.75120	0.0981944
$786$	−48.3195	−1.72350
$787$	25.4105	0.905786	0.452893	−	0.891565i	$-0.350392\pi$
$787$	25.4105	0.905786	0.452893	+	0.891565i	$0.350392\pi$
$788$	77.7034	2.76807
$789$	9.61730	0.342385
$790$	6.93331	0.246676
$791$	0.371523	0.0132099
$792$	−7.40573	−0.263151
$793$	−25.9813	−0.922622
$794$	70.0883	2.48734
$795$	−2.36491	−0.0838748
$796$	−38.1213	−1.35118
$797$	−40.7299	−1.44273	−0.721364	−	0.692556i	$-0.756484\pi$
$797$	−40.7299	−1.44273	−0.721364	+	0.692556i	$0.756484\pi$
$798$	−3.39911	−0.120327
$799$	−40.6707	−1.43883
$800$	8.65054	0.305843
$801$	−0.876095	−0.0309553
$802$	−54.7950	−1.93488
$803$	15.5464	0.548622
$804$	83.5041	2.94496
$805$	2.25640	0.0795277
$806$	52.2595	1.84076
$807$	−8.31942	−0.292857
$808$	59.1038	2.07926
$809$	−10.7414	−0.377646	−0.188823	−	0.982011i	$-0.560467\pi$
$809$	−10.7414	−0.377646	−0.188823	+	0.982011i	$0.560467\pi$
$810$	−8.36999	−0.294091
$811$	42.0285	1.47582	0.737910	−	0.674899i	$-0.235813\pi$
$811$	42.0285	1.47582	0.737910	+	0.674899i	$0.235813\pi$
$812$	−0.627741	−0.0220294
$813$	−30.5000	−1.06968
$814$	81.0105	2.83942
$815$	−6.04595	−0.211780
$816$	−21.2271	−0.743097
$817$	1.04427	0.0365345
$818$	47.3407	1.65523
$819$	−1.19989	−0.0419275
$820$	−10.4848	−0.366144
$821$	−48.2201	−1.68289	−0.841446	−	0.540341i	$-0.818295\pi$
$821$	−48.2201	−1.68289	−0.841446	+	0.540341i	$0.818295\pi$
$822$	76.9697	2.68463
$823$	34.8349	1.21427	0.607134	−	0.794599i	$-0.292319\pi$
$823$	34.8349	1.21427	0.607134	+	0.794599i	$0.292319\pi$
$824$	76.4988	2.66496
$825$	−39.0130	−1.35826
$826$	−11.8901	−0.413709
$827$	30.6958	1.06740	0.533698	−	0.845675i	$-0.320802\pi$
$827$	30.6958	1.06740	0.533698	+	0.845675i	$0.320802\pi$
$828$	12.6797	0.440650
$829$	31.7392	1.10235	0.551175	−	0.834390i	$-0.314180\pi$
$829$	31.7392	1.10235	0.551175	+	0.834390i	$0.314180\pi$
$830$	−8.51450	−0.295543
$831$	−26.3160	−0.912892
$832$	40.0895	1.38985
$833$	−25.6856	−0.889952
$834$	−4.92282	−0.170463
$835$	−2.67888	−0.0927066
$836$	−16.5248	−0.571523
$837$	−26.0561	−0.900629
$838$	−12.9680	−0.447974
$839$	−43.6145	−1.50574	−0.752870	−	0.658170i	$-0.771331\pi$
$839$	−43.6145	−1.50574	−0.752870	+	0.658170i	$0.771331\pi$
$840$	−2.12847	−0.0734391
$841$	−28.9536	−0.998402
$842$	38.6586	1.33226
$843$	19.1168	0.658416
$844$	3.80675	0.131034
$845$	1.03415	0.0355759
$846$	−9.58885	−0.329672
$847$	6.00753	0.206421
$848$	10.6626	0.366155
$849$	39.4700	1.35461
$850$	−47.0954	−1.61536
$851$	−65.8304	−2.25664
$852$	23.7093	0.812266
$853$	23.0521	0.789288	0.394644	−	0.918834i	$-0.370868\pi$
$853$	23.0521	0.789288	0.394644	+	0.918834i	$0.370868\pi$
$854$	11.9941	0.410428
$855$	0.135808	0.00464452
$856$	3.82126	0.130608
$857$	−31.8294	−1.08727	−0.543636	−	0.839321i	$-0.682953\pi$
$857$	−31.8294	−1.08727	−0.543636	+	0.839321i	$0.682953\pi$
$858$	−77.0208	−2.62945
$859$	−12.1874	−0.415827	−0.207914	−	0.978147i	$-0.566667\pi$
$859$	−12.1874	−0.415827	−0.207914	+	0.978147i	$0.566667\pi$
$860$	1.37776	0.0469811
$861$	11.2098	0.382030
$862$	−32.6008	−1.11039
$863$	−43.9647	−1.49658	−0.748288	−	0.663374i	$-0.769124\pi$
$863$	−43.9647	−1.49658	−0.748288	+	0.663374i	$0.769124\pi$
$864$	−8.51500	−0.289686
$865$	3.42577	0.116480
$866$	45.2940	1.53915
$867$	1.76802	0.0600451
$868$	−15.8158	−0.536825
$869$	−36.0373	−1.22248
$870$	0.331158	0.0112273
$871$	47.6185	1.61349
$872$	38.8499	1.31562
$873$	−2.08030	−0.0704075
$874$	20.4833	0.692858
$875$	−2.62262	−0.0886606
$876$	25.1086	0.848340
$877$	−17.3253	−0.585033	−0.292517	−	0.956260i	$-0.594493\pi$
$877$	−17.3253	−0.585033	−0.292517	+	0.956260i	$0.594493\pi$
$878$	43.0228	1.45195
$879$	3.06560	0.103400
$880$	−4.32968	−0.145953
$881$	−2.32214	−0.0782349	−0.0391174	−	0.999235i	$-0.512455\pi$
$881$	−2.32214	−0.0782349	−0.0391174	+	0.999235i	$0.512455\pi$
$882$	−6.05583	−0.203911
$883$	−33.4081	−1.12427	−0.562135	−	0.827045i	$-0.690020\pi$
$883$	−33.4081	−1.12427	−0.562135	+	0.827045i	$0.690020\pi$
$884$	−60.9534	−2.05008
$885$	4.11207	0.138226
$886$	67.8717	2.28019
$887$	21.2442	0.713311	0.356656	−	0.934236i	$-0.383917\pi$
$887$	21.2442	0.713311	0.356656	+	0.934236i	$0.383917\pi$
$888$	62.0979	2.08387
$889$	−8.28317	−0.277809
$890$	−1.86724	−0.0625901
$891$	43.5047	1.45746
$892$	81.6020	2.73224
$893$	−10.1550	−0.339824
$894$	−57.6650	−1.92860
$895$	3.22798	0.107899
$896$	−15.7915	−0.527558
$897$	62.5882	2.08976
$898$	−25.5860	−0.853817
$899$	1.16790	0.0389515
$900$	−7.27922	−0.242641
$901$	14.8387	0.494348
$902$	83.1284	2.76787
$903$	−1.47303	−0.0490194
$904$	2.11189	0.0702405
$905$	−2.05947	−0.0684592
$906$	83.2652	2.76630
$907$	−21.8268	−0.724748	−0.362374	−	0.932033i	$-0.618034\pi$
$907$	−21.8268	−0.724748	−0.362374	+	0.932033i	$0.618034\pi$
$908$	−0.0397949	−0.00132064
$909$	5.31950	0.176437
$910$	−2.55735	−0.0847755
$911$	59.2783	1.96398	0.981988	−	0.188942i	$-0.0605060\pi$
$911$	59.2783	1.96398	0.981988	+	0.188942i	$0.0605060\pi$
$912$	−5.30015	−0.175506
$913$	44.2559	1.46466
$914$	−73.0838	−2.41740
$915$	−4.14803	−0.137129
$916$	44.8253	1.48107
$917$	8.33905	0.275380
$918$	46.3575	1.53002
$919$	30.2002	0.996212	0.498106	−	0.867116i	$-0.334029\pi$
$919$	30.2002	0.996212	0.498106	+	0.867116i	$0.334029\pi$
$920$	12.8263	0.422872
$921$	23.2641	0.766577
$922$	79.3257	2.61245
$923$	13.5203	0.445026
$924$	23.3096	0.766829
$925$	37.7922	1.24260
$926$	−64.5651	−2.12174
$927$	6.88509	0.226136
$928$	0.381663	0.0125287
$929$	−28.5481	−0.936632	−0.468316	−	0.883561i	$-0.655139\pi$
$929$	−28.5481	−0.936632	−0.468316	+	0.883561i	$0.655139\pi$
$930$	8.34347	0.273593
$931$	−6.41338	−0.210190
$932$	23.8411	0.780940
$933$	45.4650	1.48846
$934$	30.9335	1.01217
$935$	−6.02543	−0.197053
$936$	−6.82067	−0.222941
$937$	12.7389	0.416161	0.208080	−	0.978112i	$-0.433278\pi$
$937$	12.7389	0.416161	0.208080	+	0.978112i	$0.433278\pi$
$938$	−21.9827	−0.717760
$939$	−41.6947	−1.36065
$940$	−13.3979	−0.436992
$941$	6.13156	0.199883	0.0999416	−	0.994993i	$-0.468134\pi$
$941$	6.13156	0.199883	0.0999416	+	0.994993i	$0.468134\pi$
$942$	−35.2292	−1.14783
$943$	−67.5514	−2.19978
$944$	−18.5400	−0.603424
$945$	1.27507	0.0414780
$946$	−10.9235	−0.355154
$947$	−41.5705	−1.35086	−0.675429	−	0.737425i	$-0.736042\pi$
$947$	−41.5705	−1.35086	−0.675429	+	0.737425i	$0.736042\pi$
$948$	−58.2027	−1.89034
$949$	14.3182	0.464790
$950$	−11.7592	−0.381517
$951$	−41.6080	−1.34923
$952$	13.3551	0.432842
$953$	−12.8430	−0.416025	−0.208012	−	0.978126i	$-0.566699\pi$
$953$	−12.8430	−0.416025	−0.208012	+	0.978126i	$0.566699\pi$
$954$	3.49849	0.113268
$955$	−1.67013	−0.0540442
$956$	100.478	3.24969
$957$	−1.72126	−0.0556404
$958$	3.52645	0.113934
$959$	−13.2836	−0.428949
$960$	6.40046	0.206574
$961$	−1.57504	−0.0508077
$962$	74.6106	2.40554
$963$	0.343923	0.0110828
$964$	20.3267	0.654678
$965$	−7.97339	−0.256673
$966$	−28.8934	−0.929629
$967$	−1.65359	−0.0531758	−0.0265879	−	0.999646i	$-0.508464\pi$
$967$	−1.65359	−0.0531758	−0.0265879	+	0.999646i	$0.508464\pi$
$968$	34.1493	1.09760
$969$	−7.37600	−0.236951
$970$	−4.43380	−0.142361
$971$	−51.8386	−1.66358	−0.831790	−	0.555090i	$-0.812684\pi$
$971$	−51.8386	−1.66358	−0.831790	+	0.555090i	$0.812684\pi$
$972$	15.4068	0.494174
$973$	0.849588	0.0272366
$974$	−78.8933	−2.52791
$975$	−35.9310	−1.15071
$976$	18.7021	0.598639
$977$	−27.8391	−0.890651	−0.445326	−	0.895369i	$-0.646912\pi$
$977$	−27.8391	−0.890651	−0.445326	+	0.895369i	$0.646912\pi$
$978$	77.4187	2.47558
$979$	9.70538	0.310185
$980$	−8.46145	−0.270291
$981$	3.49659	0.111638
$982$	−43.4354	−1.38608
$983$	56.0034	1.78623	0.893116	−	0.449827i	$-0.148514\pi$
$983$	56.0034	1.78623	0.893116	+	0.449827i	$0.148514\pi$
$984$	63.7213	2.03136
$985$	7.07439	0.225409
$986$	−2.07785	−0.0661724
$987$	14.3244	0.455952
$988$	−15.2193	−0.484192
$989$	8.87661	0.282260
$990$	−1.42060	−0.0451497
$991$	5.18465	0.164696	0.0823479	−	0.996604i	$-0.473758\pi$
$991$	5.18465	0.164696	0.0823479	+	0.996604i	$0.473758\pi$
$992$	9.61594	0.305306
$993$	−0.865177	−0.0274555
$994$	−6.24154	−0.197970
$995$	−3.47070	−0.110029
$996$	71.4763	2.26481
$997$	59.1471	1.87321	0.936604	−	0.350390i	$-0.113951\pi$
$997$	59.1471	1.87321	0.936604	+	0.350390i	$0.113951\pi$
$998$	−11.4524	−0.362518
$999$	−37.2001	−1.17696

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4009.2.a.c.1.68	✓	71

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4009.2.a.c.1.68	✓	71	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:	\( N \)	\(=\)	\( 4009 = 19 \cdot 211 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4009.a (trivial)

\(f(q)\)	\(=\)	\(q+2.40972 q^{2} -1.84170 q^{3} +3.80675 q^{4} +0.346580 q^{5} -4.43798 q^{6} +0.765913 q^{7} +4.35377 q^{8} +0.391851 q^{9} +O(q^{10})\)	\(q+2.40972 q^{2} -1.84170 q^{3} +3.80675 q^{4} +0.346580 q^{5} -4.43798 q^{6} +0.765913 q^{7} +4.35377 q^{8} +0.391851 q^{9} +0.835161 q^{10} -4.34092 q^{11} -7.01089 q^{12} -3.99798 q^{13} +1.84564 q^{14} -0.638296 q^{15} +2.87786 q^{16} +4.00500 q^{17} +0.944250 q^{18} +1.00000 q^{19} +1.31934 q^{20} -1.41058 q^{21} -10.4604 q^{22} +8.50028 q^{23} -8.01833 q^{24} -4.87988 q^{25} -9.63402 q^{26} +4.80342 q^{27} +2.91564 q^{28} -0.215301 q^{29} -1.53811 q^{30} -5.42448 q^{31} -1.77269 q^{32} +7.99467 q^{33} +9.65093 q^{34} +0.265450 q^{35} +1.49168 q^{36} -7.74449 q^{37} +2.40972 q^{38} +7.36308 q^{39} +1.50893 q^{40} -7.94696 q^{41} -3.39911 q^{42} +1.04427 q^{43} -16.5248 q^{44} +0.135808 q^{45} +20.4833 q^{46} -10.1550 q^{47} -5.30015 q^{48} -6.41338 q^{49} -11.7592 q^{50} -7.37600 q^{51} -15.2193 q^{52} +3.70504 q^{53} +11.5749 q^{54} -1.50448 q^{55} +3.33461 q^{56} -1.84170 q^{57} -0.518815 q^{58} -6.44227 q^{59} -2.42983 q^{60} +6.49860 q^{61} -13.0715 q^{62} +0.300124 q^{63} -10.0274 q^{64} -1.38562 q^{65} +19.2649 q^{66} -11.9106 q^{67} +15.2460 q^{68} -15.6550 q^{69} +0.639661 q^{70} -3.38178 q^{71} +1.70603 q^{72} -3.58137 q^{73} -18.6621 q^{74} +8.98727 q^{75} +3.80675 q^{76} -3.32477 q^{77} +17.7430 q^{78} +8.30176 q^{79} +0.997410 q^{80} -10.0220 q^{81} -19.1499 q^{82} -10.1950 q^{83} -5.36973 q^{84} +1.38805 q^{85} +2.51641 q^{86} +0.396519 q^{87} -18.8994 q^{88} -2.23579 q^{89} +0.327258 q^{90} -3.06211 q^{91} +32.3585 q^{92} +9.99025 q^{93} -24.4707 q^{94} +0.346580 q^{95} +3.26477 q^{96} -5.30892 q^{97} -15.4544 q^{98} -1.70099 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 71 q - 15 q^{2} - 8 q^{3} + 69 q^{4} - 18 q^{5} - 9 q^{6} - 19 q^{7} - 39 q^{8} + 63 q^{9}+O(q^{10}) \) 71 * q - 15 * q^2 - 8 * q^3 + 69 * q^4 - 18 * q^5 - 9 * q^6 - 19 * q^7 - 39 * q^8 + 63 * q^9	\( 71 q - 15 q^{2} - 8 q^{3} + 69 q^{4} - 18 q^{5} - 9 q^{6} - 19 q^{7} - 39 q^{8} + 63 q^{9} - 10 q^{10} - 52 q^{11} - 9 q^{12} - 15 q^{13} - 53 q^{14} - 33 q^{15} + 53 q^{16} - 10 q^{17} - 35 q^{18} + 71 q^{19} - 33 q^{20} - 38 q^{21} - 6 q^{22} - 65 q^{23} - 30 q^{24} + 51 q^{25} - 4 q^{26} - 23 q^{27} - 29 q^{28} - 97 q^{29} - 27 q^{30} - 53 q^{31} - 78 q^{32} - 17 q^{33} - 24 q^{34} - 38 q^{35} + 24 q^{36} - 33 q^{37} - 15 q^{38} - 86 q^{39} + 25 q^{40} - 69 q^{41} + 64 q^{42} - 10 q^{43} - 94 q^{44} - 34 q^{45} - 6 q^{46} - 37 q^{47} - q^{48} + 74 q^{49} - 41 q^{50} - 46 q^{51} - 30 q^{52} - 50 q^{53} - 17 q^{54} - 30 q^{55} - 116 q^{56} - 8 q^{57} + 11 q^{58} - 93 q^{59} - 56 q^{60} - 18 q^{61} - q^{62} - 84 q^{63} + 93 q^{64} - 78 q^{65} - 53 q^{66} - 5 q^{67} - 9 q^{68} - 69 q^{69} - 10 q^{70} - 221 q^{71} - 73 q^{72} - 34 q^{73} - 58 q^{74} - 70 q^{75} + 69 q^{76} - 2 q^{77} + 7 q^{78} - 68 q^{79} - 71 q^{80} + 39 q^{81} + 26 q^{82} - 45 q^{83} - 10 q^{84} - 44 q^{85} - 80 q^{86} - 7 q^{87} - 46 q^{88} - 143 q^{89} + 41 q^{90} - 30 q^{91} - 46 q^{92} + 32 q^{93} + 41 q^{94} - 18 q^{95} - 140 q^{96} - 18 q^{97} - 97 q^{98} - 142 q^{99}+O(q^{100}) \) 71 * q - 15 * q^2 - 8 * q^3 + 69 * q^4 - 18 * q^5 - 9 * q^6 - 19 * q^7 - 39 * q^8 + 63 * q^9 - 10 * q^10 - 52 * q^11 - 9 * q^12 - 15 * q^13 - 53 * q^14 - 33 * q^15 + 53 * q^16 - 10 * q^17 - 35 * q^18 + 71 * q^19 - 33 * q^20 - 38 * q^21 - 6 * q^22 - 65 * q^23 - 30 * q^24 + 51 * q^25 - 4 * q^26 - 23 * q^27 - 29 * q^28 - 97 * q^29 - 27 * q^30 - 53 * q^31 - 78 * q^32 - 17 * q^33 - 24 * q^34 - 38 * q^35 + 24 * q^36 - 33 * q^37 - 15 * q^38 - 86 * q^39 + 25 * q^40 - 69 * q^41 + 64 * q^42 - 10 * q^43 - 94 * q^44 - 34 * q^45 - 6 * q^46 - 37 * q^47 - q^48 + 74 * q^49 - 41 * q^50 - 46 * q^51 - 30 * q^52 - 50 * q^53 - 17 * q^54 - 30 * q^55 - 116 * q^56 - 8 * q^57 + 11 * q^58 - 93 * q^59 - 56 * q^60 - 18 * q^61 - q^62 - 84 * q^63 + 93 * q^64 - 78 * q^65 - 53 * q^66 - 5 * q^67 - 9 * q^68 - 69 * q^69 - 10 * q^70 - 221 * q^71 - 73 * q^72 - 34 * q^73 - 58 * q^74 - 70 * q^75 + 69 * q^76 - 2 * q^77 + 7 * q^78 - 68 * q^79 - 71 * q^80 + 39 * q^81 + 26 * q^82 - 45 * q^83 - 10 * q^84 - 44 * q^85 - 80 * q^86 - 7 * q^87 - 46 * q^88 - 143 * q^89 + 41 * q^90 - 30 * q^91 - 46 * q^92 + 32 * q^93 + 41 * q^94 - 18 * q^95 - 140 * q^96 - 18 * q^97 - 97 * q^98 - 142 * q^99

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