LMFDB - Embedded newform 4001.2.a.a.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4001,2,Mod(1,4001)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4001, 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("4001.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4001 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4001.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:	$31.9481458487$
Analytic rank:	$1$
Dimension:	$149$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	4001.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.67250 q^{2} +0.814974 q^{3} +5.14227 q^{4} -1.39982 q^{5} -2.17802 q^{6} -2.73506 q^{7} -8.39771 q^{8} -2.33582 q^{9} +O(q^{10})$	\(q-2.67250 q^{2} +0.814974 q^{3} +5.14227 q^{4} -1.39982 q^{5} -2.17802 q^{6} -2.73506 q^{7} -8.39771 q^{8} -2.33582 q^{9} +3.74102 q^{10} +3.08147 q^{11} +4.19081 q^{12} -1.60727 q^{13} +7.30945 q^{14} -1.14082 q^{15} +12.1584 q^{16} +3.86902 q^{17} +6.24247 q^{18} +5.40098 q^{19} -7.19823 q^{20} -2.22900 q^{21} -8.23524 q^{22} +5.65129 q^{23} -6.84392 q^{24} -3.04051 q^{25} +4.29544 q^{26} -4.34855 q^{27} -14.0644 q^{28} -10.0434 q^{29} +3.04883 q^{30} -6.14553 q^{31} -15.6978 q^{32} +2.51132 q^{33} -10.3400 q^{34} +3.82858 q^{35} -12.0114 q^{36} +0.418846 q^{37} -14.4341 q^{38} -1.30989 q^{39} +11.7553 q^{40} +5.36339 q^{41} +5.95702 q^{42} +10.8191 q^{43} +15.8458 q^{44} +3.26972 q^{45} -15.1031 q^{46} -3.24446 q^{47} +9.90876 q^{48} +0.480552 q^{49} +8.12577 q^{50} +3.15315 q^{51} -8.26503 q^{52} +7.43909 q^{53} +11.6215 q^{54} -4.31350 q^{55} +22.9682 q^{56} +4.40166 q^{57} +26.8410 q^{58} -9.90302 q^{59} -5.86638 q^{60} -11.3451 q^{61} +16.4239 q^{62} +6.38860 q^{63} +17.6358 q^{64} +2.24989 q^{65} -6.71151 q^{66} +14.9613 q^{67} +19.8955 q^{68} +4.60566 q^{69} -10.2319 q^{70} +11.2842 q^{71} +19.6155 q^{72} -12.1402 q^{73} -1.11937 q^{74} -2.47794 q^{75} +27.7733 q^{76} -8.42801 q^{77} +3.50067 q^{78} +10.6986 q^{79} -17.0195 q^{80} +3.46349 q^{81} -14.3337 q^{82} +9.75746 q^{83} -11.4621 q^{84} -5.41592 q^{85} -28.9140 q^{86} -8.18512 q^{87} -25.8773 q^{88} +9.47888 q^{89} -8.73833 q^{90} +4.39599 q^{91} +29.0605 q^{92} -5.00845 q^{93} +8.67081 q^{94} -7.56038 q^{95} -12.7933 q^{96} -8.24216 q^{97} -1.28428 q^{98} -7.19776 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 149 q - 6 q^{2} - 28 q^{3} + 116 q^{4} - 19 q^{5} - 31 q^{6} - 47 q^{7} - 15 q^{8} + 115 q^{9}+O(q^{10}) $ 149 * q - 6 * q^2 - 28 * q^3 + 116 * q^4 - 19 * q^5 - 31 * q^6 - 47 * q^7 - 15 * q^8 + 115 * q^9	\( 149 q - 6 q^{2} - 28 q^{3} + 116 q^{4} - 19 q^{5} - 31 q^{6} - 47 q^{7} - 15 q^{8} + 115 q^{9} - 48 q^{10} - 31 q^{11} - 61 q^{12} - 54 q^{13} - 44 q^{14} - 65 q^{15} + 58 q^{16} - 26 q^{17} - 23 q^{18} - 86 q^{19} - 52 q^{20} - 30 q^{21} - 56 q^{22} - 63 q^{23} - 90 q^{24} + 92 q^{25} - 38 q^{26} - 103 q^{27} - 77 q^{28} - 51 q^{29} - 22 q^{30} - 256 q^{31} - 21 q^{32} - 36 q^{33} - 124 q^{34} - 50 q^{35} + 45 q^{36} - 42 q^{37} - 14 q^{38} - 119 q^{39} - 131 q^{40} - 55 q^{41} - 5 q^{42} - 55 q^{43} - 54 q^{44} - 68 q^{45} - 59 q^{46} - 82 q^{47} - 89 q^{48} + 30 q^{49} + 13 q^{50} - 83 q^{51} - 126 q^{52} - 23 q^{53} - 83 q^{54} - 244 q^{55} - 94 q^{56} - 14 q^{57} - 60 q^{58} - 93 q^{59} - 70 q^{60} - 139 q^{61} - 10 q^{62} - 120 q^{63} - 45 q^{64} - 37 q^{65} - 28 q^{66} - 110 q^{67} - 27 q^{68} - 79 q^{69} - 78 q^{70} - 123 q^{71} - 74 q^{73} - 25 q^{74} - 146 q^{75} - 192 q^{76} - q^{77} + 26 q^{78} - 273 q^{79} - 51 q^{80} + 41 q^{81} - 120 q^{82} - 27 q^{83} - 14 q^{84} - 71 q^{85} + 3 q^{86} - 98 q^{87} - 143 q^{88} - 70 q^{89} - 24 q^{90} - 256 q^{91} - 47 q^{92} + 16 q^{93} - 151 q^{94} - 83 q^{95} - 137 q^{96} - 108 q^{97} + 17 q^{98} - 131 q^{99}+O(q^{100}) \) 149 * q - 6 * q^2 - 28 * q^3 + 116 * q^4 - 19 * q^5 - 31 * q^6 - 47 * q^7 - 15 * q^8 + 115 * q^9 - 48 * q^10 - 31 * q^11 - 61 * q^12 - 54 * q^13 - 44 * q^14 - 65 * q^15 + 58 * q^16 - 26 * q^17 - 23 * q^18 - 86 * q^19 - 52 * q^20 - 30 * q^21 - 56 * q^22 - 63 * q^23 - 90 * q^24 + 92 * q^25 - 38 * q^26 - 103 * q^27 - 77 * q^28 - 51 * q^29 - 22 * q^30 - 256 * q^31 - 21 * q^32 - 36 * q^33 - 124 * q^34 - 50 * q^35 + 45 * q^36 - 42 * q^37 - 14 * q^38 - 119 * q^39 - 131 * q^40 - 55 * q^41 - 5 * q^42 - 55 * q^43 - 54 * q^44 - 68 * q^45 - 59 * q^46 - 82 * q^47 - 89 * q^48 + 30 * q^49 + 13 * q^50 - 83 * q^51 - 126 * q^52 - 23 * q^53 - 83 * q^54 - 244 * q^55 - 94 * q^56 - 14 * q^57 - 60 * q^58 - 93 * q^59 - 70 * q^60 - 139 * q^61 - 10 * q^62 - 120 * q^63 - 45 * q^64 - 37 * q^65 - 28 * q^66 - 110 * q^67 - 27 * q^68 - 79 * q^69 - 78 * q^70 - 123 * q^71 - 74 * q^73 - 25 * q^74 - 146 * q^75 - 192 * q^76 - q^77 + 26 * q^78 - 273 * q^79 - 51 * q^80 + 41 * q^81 - 120 * q^82 - 27 * q^83 - 14 * q^84 - 71 * q^85 + 3 * q^86 - 98 * q^87 - 143 * q^88 - 70 * q^89 - 24 * q^90 - 256 * q^91 - 47 * q^92 + 16 * q^93 - 151 * q^94 - 83 * q^95 - 137 * q^96 - 108 * q^97 + 17 * q^98 - 131 * 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 $

$2$	−2.67250	−1.88974	−0.944872	−	0.327440i	$-0.893814\pi$
$2$	−2.67250	−1.88974	−0.944872	+	0.327440i	$0.893814\pi$
$3$	0.814974	0.470526	0.235263	−	0.971932i	$-0.424405\pi$
$3$	0.814974	0.470526	0.235263	+	0.971932i	$0.424405\pi$
$4$	5.14227	2.57113
$5$	−1.39982	−0.626017	−0.313009	−	0.949750i	$-0.601337\pi$
$5$	−1.39982	−0.626017	−0.313009	+	0.949750i	$0.601337\pi$
$6$	−2.17802	−0.889173
$7$	−2.73506	−1.03376	−0.516878	−	0.856059i	$-0.672906\pi$
$7$	−2.73506	−1.03376	−0.516878	+	0.856059i	$0.672906\pi$
$8$	−8.39771	−2.96904
$9$	−2.33582	−0.778606
$10$	3.74102	1.18301
$11$	3.08147	0.929099	0.464550	−	0.885547i	$-0.346216\pi$
$11$	3.08147	0.929099	0.464550	+	0.885547i	$0.346216\pi$
$12$	4.19081	1.20978
$13$	−1.60727	−0.445777	−0.222889	−	0.974844i	$-0.571549\pi$
$13$	−1.60727	−0.445777	−0.222889	+	0.974844i	$0.571549\pi$
$14$	7.30945	1.95353
$15$	−1.14082	−0.294557
$16$	12.1584	3.03959
$17$	3.86902	0.938375	0.469188	−	0.883098i	$-0.344547\pi$
$17$	3.86902	0.938375	0.469188	+	0.883098i	$0.344547\pi$
$18$	6.24247	1.47137
$19$	5.40098	1.23907	0.619534	−	0.784969i	$-0.287321\pi$
$19$	5.40098	1.23907	0.619534	+	0.784969i	$0.287321\pi$
$20$	−7.19823	−1.60957
$21$	−2.22900	−0.486408
$22$	−8.23524	−1.75576
$23$	5.65129	1.17838	0.589188	−	0.807996i	$-0.299448\pi$
$23$	5.65129	1.17838	0.589188	+	0.807996i	$0.299448\pi$
$24$	−6.84392	−1.39701
$25$	−3.04051	−0.608102
$26$	4.29544	0.842405
$27$	−4.34855	−0.836880
$28$	−14.0644	−2.65792
$29$	−10.0434	−1.86501	−0.932507	−	0.361151i	$-0.882384\pi$
$29$	−10.0434	−1.86501	−0.932507	+	0.361151i	$0.882384\pi$
$30$	3.04883	0.556638
$31$	−6.14553	−1.10377	−0.551884	−	0.833921i	$-0.686091\pi$
$31$	−6.14553	−1.10377	−0.551884	+	0.833921i	$0.686091\pi$
$32$	−15.6978	−2.77501
$33$	2.51132	0.437165
$34$	−10.3400	−1.77329
$35$	3.82858	0.647149
$36$	−12.0114	−2.00190
$37$	0.418846	0.0688578	0.0344289	−	0.999407i	$-0.489039\pi$
$37$	0.418846	0.0688578	0.0344289	+	0.999407i	$0.489039\pi$
$38$	−14.4341	−2.34152
$39$	−1.30989	−0.209750
$40$	11.7553	1.85867
$41$	5.36339	0.837621	0.418810	−	0.908074i	$-0.362447\pi$
$41$	5.36339	0.837621	0.418810	+	0.908074i	$0.362447\pi$
$42$	5.95702	0.919188
$43$	10.8191	1.64989	0.824946	−	0.565211i	$-0.191205\pi$
$43$	10.8191	1.64989	0.824946	+	0.565211i	$0.191205\pi$
$44$	15.8458	2.38884
$45$	3.26972	0.487421
$46$	−15.1031	−2.22683
$47$	−3.24446	−0.473253	−0.236626	−	0.971601i	$-0.576042\pi$
$47$	−3.24446	−0.473253	−0.236626	+	0.971601i	$0.576042\pi$
$48$	9.90876	1.43021
$49$	0.480552	0.0686503
$50$	8.12577	1.14916
$51$	3.15315	0.441530
$52$	−8.26503	−1.14615
$53$	7.43909	1.02184	0.510919	−	0.859629i	$-0.329305\pi$
$53$	7.43909	1.02184	0.510919	+	0.859629i	$0.329305\pi$
$54$	11.6215	1.58149
$55$	−4.31350	−0.581632
$56$	22.9682	3.06926
$57$	4.40166	0.583014
$58$	26.8410	3.52440
$59$	−9.90302	−1.28926	−0.644632	−	0.764493i	$-0.722989\pi$
$59$	−9.90302	−1.28926	−0.644632	+	0.764493i	$0.722989\pi$
$60$	−5.86638	−0.757346
$61$	−11.3451	−1.45259	−0.726297	−	0.687381i	$-0.758760\pi$
$61$	−11.3451	−1.45259	−0.726297	+	0.687381i	$0.758760\pi$
$62$	16.4239	2.08584
$63$	6.38860	0.804888
$64$	17.6358	2.20447
$65$	2.24989	0.279064
$66$	−6.71151	−0.826130
$67$	14.9613	1.82781	0.913907	−	0.405924i	$-0.133050\pi$
$67$	14.9613	1.82781	0.913907	+	0.405924i	$0.133050\pi$
$68$	19.8955	2.41269
$69$	4.60566	0.554456
$70$	−10.2319	−1.22295
$71$	11.2842	1.33919	0.669596	−	0.742726i	$-0.266467\pi$
$71$	11.2842	1.33919	0.669596	+	0.742726i	$0.266467\pi$
$72$	19.6155	2.31171
$73$	−12.1402	−1.42091	−0.710453	−	0.703745i	$-0.751510\pi$
$73$	−12.1402	−1.42091	−0.710453	+	0.703745i	$0.751510\pi$
$74$	−1.11937	−0.130124
$75$	−2.47794	−0.286128
$76$	27.7733	3.18581
$77$	−8.42801	−0.960461
$78$	3.50067	0.396373
$79$	10.6986	1.20369	0.601843	−	0.798615i	$-0.294433\pi$
$79$	10.6986	1.20369	0.601843	+	0.798615i	$0.294433\pi$
$80$	−17.0195	−1.90284
$81$	3.46349	0.384832
$82$	−14.3337	−1.58289
$83$	9.75746	1.07102	0.535510	−	0.844529i	$-0.320119\pi$
$83$	9.75746	1.07102	0.535510	+	0.844529i	$0.320119\pi$
$84$	−11.4621	−1.25062
$85$	−5.41592	−0.587439
$86$	−28.9140	−3.11788
$87$	−8.18512	−0.877537
$88$	−25.8773	−2.75853
$89$	9.47888	1.00476	0.502380	−	0.864647i	$-0.332458\pi$
$89$	9.47888	1.00476	0.502380	+	0.864647i	$0.332458\pi$
$90$	−8.73833	−0.921100
$91$	4.39599	0.460825
$92$	29.0605	3.02976
$93$	−5.00845	−0.519352
$94$	8.67081	0.894326
$95$	−7.56038	−0.775679
$96$	−12.7933	−1.30571
$97$	−8.24216	−0.836864	−0.418432	−	0.908248i	$-0.637420\pi$
$97$	−8.24216	−0.836864	−0.418432	+	0.908248i	$0.637420\pi$
$98$	−1.28428	−0.129731
$99$	−7.19776	−0.723402
$100$	−15.6351	−1.56351
$101$	−13.9596	−1.38903	−0.694514	−	0.719479i	$-0.744381\pi$
$101$	−13.9596	−1.38903	−0.694514	+	0.719479i	$0.744381\pi$
$102$	−8.42681	−0.834378
$103$	−10.0563	−0.990872	−0.495436	−	0.868644i	$-0.664992\pi$
$103$	−10.0563	−0.990872	−0.495436	+	0.868644i	$0.664992\pi$
$104$	13.4974	1.32353
$105$	3.12020	0.304500
$106$	−19.8810	−1.93101
$107$	−1.82643	−0.176568	−0.0882839	−	0.996095i	$-0.528138\pi$
$107$	−1.82643	−0.176568	−0.0882839	+	0.996095i	$0.528138\pi$
$108$	−22.3614	−2.15173
$109$	−2.53044	−0.242372	−0.121186	−	0.992630i	$-0.538670\pi$
$109$	−2.53044	−0.242372	−0.121186	+	0.992630i	$0.538670\pi$
$110$	11.5278	1.09914
$111$	0.341349	0.0323994
$112$	−33.2539	−3.14219
$113$	5.87348	0.552530	0.276265	−	0.961081i	$-0.410903\pi$
$113$	5.87348	0.552530	0.276265	+	0.961081i	$0.410903\pi$
$114$	−11.7634	−1.10175
$115$	−7.91078	−0.737684
$116$	−51.6459	−4.79520
$117$	3.75430	0.347085
$118$	26.4658	2.43638
$119$	−10.5820	−0.970051
$120$	9.58024	0.874552
$121$	−1.50452	−0.136775
$122$	30.3199	2.74503
$123$	4.37102	0.394122
$124$	−31.6019	−2.83794
$125$	11.2552	1.00670
$126$	−17.0735	−1.52103
$127$	9.04963	0.803025	0.401513	−	0.915854i	$-0.368485\pi$
$127$	9.04963	0.803025	0.401513	+	0.915854i	$0.368485\pi$
$128$	−15.7359	−1.39087
$129$	8.81726	0.776317
$130$	−6.01283	−0.527360
$131$	18.4958	1.61598	0.807992	−	0.589194i	$-0.200555\pi$
$131$	18.4958	1.61598	0.807992	+	0.589194i	$0.200555\pi$
$132$	12.9139	1.12401
$133$	−14.7720	−1.28089
$134$	−39.9841	−3.45410
$135$	6.08718	0.523901
$136$	−32.4909	−2.78607
$137$	15.9199	1.36013	0.680067	−	0.733150i	$-0.261951\pi$
$137$	15.9199	1.36013	0.680067	+	0.733150i	$0.261951\pi$
$138$	−12.3086	−1.04778
$139$	−10.8203	−0.917767	−0.458883	−	0.888497i	$-0.651750\pi$
$139$	−10.8203	−0.917767	−0.458883	+	0.888497i	$0.651750\pi$
$140$	19.6876	1.66391
$141$	−2.64415	−0.222677
$142$	−30.1571	−2.53073
$143$	−4.95277	−0.414171
$144$	−28.3997	−2.36664
$145$	14.0589	1.16753
$146$	32.4448	2.68515
$147$	0.391637	0.0323017
$148$	2.15382	0.177043
$149$	−5.12393	−0.419769	−0.209884	−	0.977726i	$-0.567309\pi$
$149$	−5.12393	−0.419769	−0.209884	+	0.977726i	$0.567309\pi$
$150$	6.62229	0.540708
$151$	−10.1344	−0.824727	−0.412364	−	0.911019i	$-0.635297\pi$
$151$	−10.1344	−0.824727	−0.412364	+	0.911019i	$0.635297\pi$
$152$	−45.3558	−3.67884
$153$	−9.03732	−0.730624
$154$	22.5239	1.81503
$155$	8.60261	0.690979
$156$	−6.73578	−0.539294
$157$	−3.57337	−0.285186	−0.142593	−	0.989781i	$-0.545544\pi$
$157$	−3.57337	−0.285186	−0.142593	+	0.989781i	$0.545544\pi$
$158$	−28.5920	−2.27466
$159$	6.06267	0.480801
$160$	21.9741	1.73721
$161$	−15.4566	−1.21815
$162$	−9.25618	−0.727235
$163$	1.88960	0.148005	0.0740025	−	0.997258i	$-0.476423\pi$
$163$	1.88960	0.148005	0.0740025	+	0.997258i	$0.476423\pi$
$164$	27.5800	2.15363
$165$	−3.51539	−0.273673
$166$	−26.0768	−2.02396
$167$	2.17360	0.168198	0.0840992	−	0.996457i	$-0.473199\pi$
$167$	2.17360	0.168198	0.0840992	+	0.996457i	$0.473199\pi$
$168$	18.7185	1.44417
$169$	−10.4167	−0.801283
$170$	14.4741	1.11011
$171$	−12.6157	−0.964746
$172$	55.6345	4.24209
$173$	−7.83124	−0.595398	−0.297699	−	0.954660i	$-0.596219\pi$
$173$	−7.83124	−0.595398	−0.297699	+	0.954660i	$0.596219\pi$
$174$	21.8748	1.65832
$175$	8.31598	0.628629
$176$	37.4657	2.82408
$177$	−8.07071	−0.606631
$178$	−25.3323	−1.89874
$179$	−1.27803	−0.0955243	−0.0477622	−	0.998859i	$-0.515209\pi$
$179$	−1.27803	−0.0955243	−0.0477622	+	0.998859i	$0.515209\pi$
$180$	16.8138	1.25322
$181$	−16.9665	−1.26111	−0.630555	−	0.776145i	$-0.717173\pi$
$181$	−16.9665	−1.26111	−0.630555	+	0.776145i	$0.717173\pi$
$182$	−11.7483	−0.870841
$183$	−9.24599	−0.683483
$184$	−47.4579	−3.49865
$185$	−0.586308	−0.0431062
$186$	13.3851	0.981442
$187$	11.9223	0.871844
$188$	−16.6839	−1.21680
$189$	11.8936	0.865129
$190$	20.2051	1.46583
$191$	−26.6361	−1.92732	−0.963662	−	0.267126i	$-0.913926\pi$
$191$	−26.6361	−1.92732	−0.963662	+	0.267126i	$0.913926\pi$
$192$	14.3727	1.03726
$193$	−6.86648	−0.494260	−0.247130	−	0.968982i	$-0.579487\pi$
$193$	−6.86648	−0.494260	−0.247130	+	0.968982i	$0.579487\pi$
$194$	22.0272	1.58146
$195$	1.83360	0.131307
$196$	2.47113	0.176509
$197$	−10.6980	−0.762204	−0.381102	−	0.924533i	$-0.624455\pi$
$197$	−10.6980	−0.762204	−0.381102	+	0.924533i	$0.624455\pi$
$198$	19.2360	1.36704
$199$	−26.1463	−1.85346	−0.926731	−	0.375726i	$-0.877393\pi$
$199$	−26.1463	−1.85346	−0.926731	+	0.375726i	$0.877393\pi$
$200$	25.5333	1.80548
$201$	12.1931	0.860033
$202$	37.3070	2.62491
$203$	27.4693	1.92797
$204$	16.2143	1.13523
$205$	−7.50777	−0.524365
$206$	26.8754	1.87250
$207$	−13.2004	−0.917490
$208$	−19.5418	−1.35498
$209$	16.6430	1.15122
$210$	−8.33874	−0.575427
$211$	8.12464	0.559323	0.279662	−	0.960099i	$-0.409778\pi$
$211$	8.12464	0.559323	0.279662	+	0.960099i	$0.409778\pi$
$212$	38.2538	2.62728
$213$	9.19636	0.630124
$214$	4.88114	0.333668
$215$	−15.1447	−1.03286
$216$	36.5179	2.48473
$217$	16.8084	1.14103
$218$	6.76260	0.458021
$219$	−9.89397	−0.668573
$220$	−22.1812	−1.49545
$221$	−6.21857	−0.418306
$222$	−0.912255	−0.0612265
$223$	8.58420	0.574841	0.287420	−	0.957805i	$-0.407202\pi$
$223$	8.58420	0.574841	0.287420	+	0.957805i	$0.407202\pi$
$224$	42.9345	2.86868
$225$	7.10208	0.473472
$226$	−15.6969	−1.04414
$227$	6.14023	0.407541	0.203771	−	0.979019i	$-0.434680\pi$
$227$	6.14023	0.407541	0.203771	+	0.979019i	$0.434680\pi$
$228$	22.6345	1.49901
$229$	−8.01016	−0.529326	−0.264663	−	0.964341i	$-0.585261\pi$
$229$	−8.01016	−0.529326	−0.264663	+	0.964341i	$0.585261\pi$
$230$	21.1416	1.39403
$231$	−6.86862	−0.451922
$232$	84.3417	5.53730
$233$	−24.7640	−1.62235	−0.811173	−	0.584806i	$-0.801171\pi$
$233$	−24.7640	−1.62235	−0.811173	+	0.584806i	$0.801171\pi$
$234$	−10.0334	−0.655901
$235$	4.54165	0.296264
$236$	−50.9240	−3.31487
$237$	8.71907	0.566365
$238$	28.2804	1.83315
$239$	17.2842	1.11802	0.559012	−	0.829160i	$-0.311181\pi$
$239$	17.2842	1.11802	0.559012	+	0.829160i	$0.311181\pi$
$240$	−13.8705	−0.895334
$241$	5.53199	0.356347	0.178173	−	0.983999i	$-0.442981\pi$
$241$	5.53199	0.356347	0.178173	+	0.983999i	$0.442981\pi$
$242$	4.02084	0.258469
$243$	15.8683	1.01795
$244$	−58.3397	−3.73481
$245$	−0.672685	−0.0429763
$246$	−11.6816	−0.744790
$247$	−8.68084	−0.552349
$248$	51.6083	3.27713
$249$	7.95208	0.503943
$250$	−30.0797	−1.90241
$251$	1.42195	0.0897528	0.0448764	−	0.998993i	$-0.485711\pi$
$251$	1.42195	0.0897528	0.0448764	+	0.998993i	$0.485711\pi$
$252$	32.8519	2.06947
$253$	17.4143	1.09483
$254$	−24.1852	−1.51751
$255$	−4.41384	−0.276405
$256$	6.78277	0.423923
$257$	−23.8851	−1.48991	−0.744957	−	0.667113i	$-0.767530\pi$
$257$	−23.8851	−1.48991	−0.744957	+	0.667113i	$0.767530\pi$
$258$	−23.5642	−1.46704
$259$	−1.14557	−0.0711821
$260$	11.5695	0.717512
$261$	23.4596	1.45211
$262$	−49.4300	−3.05379
$263$	16.2088	0.999475	0.499738	−	0.866177i	$-0.333430\pi$
$263$	16.2088	0.999475	0.499738	+	0.866177i	$0.333430\pi$
$264$	−21.0894	−1.29796
$265$	−10.4134	−0.639688
$266$	39.4782	2.42056
$267$	7.72504	0.472765
$268$	76.9350	4.69955
$269$	−8.71535	−0.531384	−0.265692	−	0.964058i	$-0.585600\pi$
$269$	−8.71535	−0.531384	−0.265692	+	0.964058i	$0.585600\pi$
$270$	−16.2680	−0.990039
$271$	−24.0933	−1.46356	−0.731782	−	0.681538i	$-0.761311\pi$
$271$	−24.0933	−1.46356	−0.731782	+	0.681538i	$0.761311\pi$
$272$	47.0410	2.85228
$273$	3.58262	0.216830
$274$	−42.5461	−2.57030
$275$	−9.36925	−0.564987
$276$	23.6835	1.42558
$277$	−13.2080	−0.793591	−0.396796	−	0.917907i	$-0.629878\pi$
$277$	−13.2080	−0.793591	−0.396796	+	0.917907i	$0.629878\pi$
$278$	28.9173	1.73434
$279$	14.3548	0.859401
$280$	−32.1513	−1.92141
$281$	−6.77733	−0.404302	−0.202151	−	0.979354i	$-0.564793\pi$
$281$	−6.77733	−0.404302	−0.202151	+	0.979354i	$0.564793\pi$
$282$	7.06649	0.420803
$283$	0.528245	0.0314009	0.0157005	−	0.999877i	$-0.495002\pi$
$283$	0.528245	0.0314009	0.0157005	+	0.999877i	$0.495002\pi$
$284$	58.0265	3.44324
$285$	−6.16152	−0.364977
$286$	13.2363	0.782678
$287$	−14.6692	−0.865895
$288$	36.6673	2.16064
$289$	−2.03068	−0.119452
$290$	−37.5726	−2.20634
$291$	−6.71715	−0.393766
$292$	−62.4283	−3.65334
$293$	−5.62297	−0.328497	−0.164249	−	0.986419i	$-0.552520\pi$
$293$	−5.62297	−0.328497	−0.164249	+	0.986419i	$0.552520\pi$
$294$	−1.04665	−0.0610420
$295$	13.8624	0.807101
$296$	−3.51735	−0.204442
$297$	−13.4000	−0.777544
$298$	13.6937	0.793256
$299$	−9.08317	−0.525293
$300$	−12.7422	−0.735672
$301$	−29.5908	−1.70559
$302$	27.0842	1.55852
$303$	−11.3767	−0.653574
$304$	65.6670	3.76626
$305$	15.8811	0.909350
$306$	24.1523	1.38069
$307$	−20.3909	−1.16377	−0.581886	−	0.813270i	$-0.697685\pi$
$307$	−20.3909	−1.16377	−0.581886	+	0.813270i	$0.697685\pi$
$308$	−43.3391	−2.46947
$309$	−8.19559	−0.466231
$310$	−22.9905	−1.30577
$311$	10.5295	0.597071	0.298536	−	0.954398i	$-0.403502\pi$
$311$	10.5295	0.597071	0.298536	+	0.954398i	$0.403502\pi$
$312$	11.0000	0.622755
$313$	−19.4971	−1.10204	−0.551021	−	0.834491i	$-0.685762\pi$
$313$	−19.4971	−1.10204	−0.551021	+	0.834491i	$0.685762\pi$
$314$	9.54984	0.538928
$315$	−8.94287	−0.503874
$316$	55.0150	3.09483
$317$	5.58531	0.313702	0.156851	−	0.987622i	$-0.449866\pi$
$317$	5.58531	0.313702	0.156851	+	0.987622i	$0.449866\pi$
$318$	−16.2025	−0.908591
$319$	−30.9485	−1.73278
$320$	−24.6868	−1.38004
$321$	−1.48850	−0.0830797
$322$	41.3079	2.30200
$323$	20.8965	1.16271
$324$	17.8102	0.989455
$325$	4.88693	0.271078
$326$	−5.04996	−0.279692
$327$	−2.06224	−0.114042
$328$	−45.0402	−2.48693
$329$	8.87378	0.489227
$330$	9.39489	0.517172
$331$	−25.8929	−1.42320	−0.711602	−	0.702583i	$-0.752030\pi$
$331$	−25.8929	−1.42320	−0.711602	+	0.702583i	$0.752030\pi$
$332$	50.1755	2.75374
$333$	−0.978347	−0.0536131
$334$	−5.80896	−0.317852
$335$	−20.9431	−1.14424
$336$	−27.1010	−1.47848
$337$	−15.5680	−0.848045	−0.424022	−	0.905652i	$-0.639382\pi$
$337$	−15.5680	−0.848045	−0.424022	+	0.905652i	$0.639382\pi$
$338$	27.8386	1.51422
$339$	4.78673	0.259980
$340$	−27.8501	−1.51038
$341$	−18.9373	−1.02551
$342$	33.7155	1.82312
$343$	17.8311	0.962788
$344$	−90.8554	−4.89860
$345$	−6.44708	−0.347099
$346$	20.9290	1.12515
$347$	14.4485	0.775634	0.387817	−	0.921736i	$-0.373229\pi$
$347$	14.4485	0.775634	0.387817	+	0.921736i	$0.373229\pi$
$348$	−42.0901	−2.25627
$349$	−5.26534	−0.281847	−0.140924	−	0.990020i	$-0.545007\pi$
$349$	−5.26534	−0.281847	−0.140924	+	0.990020i	$0.545007\pi$
$350$	−22.2245	−1.18795
$351$	6.98931	0.373062
$352$	−48.3725	−2.57826
$353$	−21.5451	−1.14673	−0.573364	−	0.819301i	$-0.694362\pi$
$353$	−21.5451	−1.14673	−0.573364	+	0.819301i	$0.694362\pi$
$354$	21.5690	1.14638
$355$	−15.7959	−0.838357
$356$	48.7429	2.58337
$357$	−8.62406	−0.456434
$358$	3.41553	0.180517
$359$	31.9902	1.68838	0.844190	−	0.536045i	$-0.180082\pi$
$359$	31.9902	1.68838	0.844190	+	0.536045i	$0.180082\pi$
$360$	−27.4581	−1.44717
$361$	10.1705	0.535292
$362$	45.3430	2.38318
$363$	−1.22615	−0.0643560
$364$	22.6053	1.18484
$365$	16.9941	0.889512
$366$	24.7099	1.29161
$367$	−19.3220	−1.00860	−0.504300	−	0.863528i	$-0.668250\pi$
$367$	−19.3220	−1.00860	−0.504300	+	0.863528i	$0.668250\pi$
$368$	68.7105	3.58178
$369$	−12.5279	−0.652176
$370$	1.56691	0.0814597
$371$	−20.3464	−1.05633
$372$	−25.7548	−1.33532
$373$	32.8208	1.69940	0.849698	−	0.527269i	$-0.176784\pi$
$373$	32.8208	1.69940	0.849698	+	0.527269i	$0.176784\pi$
$374$	−31.8623	−1.64756
$375$	9.17274	0.473678
$376$	27.2460	1.40511
$377$	16.1425	0.831381
$378$	−31.7855	−1.63487
$379$	11.0556	0.567886	0.283943	−	0.958841i	$-0.408357\pi$
$379$	11.0556	0.567886	0.283943	+	0.958841i	$0.408357\pi$
$380$	−38.8775	−1.99437
$381$	7.37522	0.377844
$382$	71.1851	3.64215
$383$	23.5022	1.20091	0.600453	−	0.799660i	$-0.294987\pi$
$383$	23.5022	1.20091	0.600453	+	0.799660i	$0.294987\pi$
$384$	−12.8244	−0.654441
$385$	11.7977	0.601266
$386$	18.3507	0.934025
$387$	−25.2714	−1.28462
$388$	−42.3834	−2.15169
$389$	7.83178	0.397087	0.198544	−	0.980092i	$-0.436379\pi$
$389$	7.83178	0.397087	0.198544	+	0.980092i	$0.436379\pi$
$390$	−4.90030	−0.248137
$391$	21.8650	1.10576
$392$	−4.03554	−0.203825
$393$	15.0736	0.760362
$394$	28.5905	1.44037
$395$	−14.9761	−0.753528
$396$	−37.0128	−1.85996
$397$	−22.4242	−1.12544	−0.562719	−	0.826648i	$-0.690245\pi$
$397$	−22.4242	−1.12544	−0.562719	+	0.826648i	$0.690245\pi$
$398$	69.8760	3.50257
$399$	−12.0388	−0.602694
$400$	−36.9676	−1.84838
$401$	−26.7225	−1.33446	−0.667228	−	0.744853i	$-0.732519\pi$
$401$	−26.7225	−1.33446	−0.667228	+	0.744853i	$0.732519\pi$
$402$	−32.5860	−1.62524
$403$	9.87754	0.492035
$404$	−71.7838	−3.57138
$405$	−4.84825	−0.240912
$406$	−73.4118	−3.64337
$407$	1.29066	0.0639757
$408$	−26.4793	−1.31092
$409$	−21.5844	−1.06728	−0.533640	−	0.845712i	$-0.679176\pi$
$409$	−21.5844	−1.06728	−0.533640	+	0.845712i	$0.679176\pi$
$410$	20.0645	0.990916
$411$	12.9744	0.639978
$412$	−51.7119	−2.54766
$413$	27.0853	1.33278
$414$	35.2781	1.73382
$415$	−13.6587	−0.670478
$416$	25.2307	1.23704
$417$	−8.81828	−0.431833
$418$	−44.4783	−2.17551
$419$	−35.4501	−1.73185	−0.865926	−	0.500173i	$-0.833270\pi$
$419$	−35.4501	−1.73185	−0.865926	+	0.500173i	$0.833270\pi$
$420$	16.0449	0.782910
$421$	−18.0951	−0.881902	−0.440951	−	0.897531i	$-0.645359\pi$
$421$	−18.0951	−0.881902	−0.440951	+	0.897531i	$0.645359\pi$
$422$	−21.7131	−1.05698
$423$	7.57845	0.368477
$424$	−62.4713	−3.03388
$425$	−11.7638	−0.570628
$426$	−24.5773	−1.19077
$427$	31.0296	1.50163
$428$	−9.39200	−0.453979
$429$	−4.03638	−0.194878
$430$	40.4743	1.95184
$431$	−23.7635	−1.14465	−0.572324	−	0.820027i	$-0.693958\pi$
$431$	−23.7635	−1.14465	−0.572324	+	0.820027i	$0.693958\pi$
$432$	−52.8713	−2.54377
$433$	−16.2060	−0.778810	−0.389405	−	0.921067i	$-0.627319\pi$
$433$	−16.2060	−0.778810	−0.389405	+	0.921067i	$0.627319\pi$
$434$	−44.9204	−2.15625
$435$	11.4577	0.549354
$436$	−13.0122	−0.623171
$437$	30.5225	1.46009
$438$	26.4417	1.26343
$439$	9.68821	0.462393	0.231197	−	0.972907i	$-0.425736\pi$
$439$	9.68821	0.462393	0.231197	+	0.972907i	$0.425736\pi$
$440$	36.2235	1.72689
$441$	−1.12248	−0.0534515
$442$	16.6191	0.790492
$443$	−30.3713	−1.44298	−0.721492	−	0.692422i	$-0.756544\pi$
$443$	−30.3713	−1.44298	−0.721492	+	0.692422i	$0.756544\pi$
$444$	1.75531	0.0833031
$445$	−13.2687	−0.628997
$446$	−22.9413	−1.08630
$447$	−4.17587	−0.197512
$448$	−48.2349	−2.27888
$449$	−5.63754	−0.266052	−0.133026	−	0.991113i	$-0.542469\pi$
$449$	−5.63754	−0.266052	−0.133026	+	0.991113i	$0.542469\pi$
$450$	−18.9803	−0.894740
$451$	16.5271	0.778233
$452$	30.2030	1.42063
$453$	−8.25929	−0.388055
$454$	−16.4098	−0.770148
$455$	−6.15358	−0.288484
$456$	−36.9638	−1.73099
$457$	26.1881	1.22503	0.612514	−	0.790460i	$-0.290158\pi$
$457$	26.1881	1.22503	0.612514	+	0.790460i	$0.290158\pi$
$458$	21.4072	1.00029
$459$	−16.8246	−0.785307
$460$	−40.6793	−1.89668
$461$	−24.7729	−1.15379	−0.576895	−	0.816819i	$-0.695736\pi$
$461$	−24.7729	−1.15379	−0.576895	+	0.816819i	$0.695736\pi$
$462$	18.3564	0.854016
$463$	39.7578	1.84770	0.923851	−	0.382752i	$-0.125024\pi$
$463$	39.7578	1.84770	0.923851	+	0.382752i	$0.125024\pi$
$464$	−122.111	−5.66888
$465$	7.01091	0.325123
$466$	66.1820	3.06582
$467$	−20.5994	−0.953227	−0.476613	−	0.879113i	$-0.658136\pi$
$467$	−20.5994	−0.953227	−0.476613	+	0.879113i	$0.658136\pi$
$468$	19.3056	0.892401
$469$	−40.9200	−1.88951
$470$	−12.1376	−0.559864
$471$	−2.91220	−0.134187
$472$	83.1627	3.82787
$473$	33.3387	1.53291
$474$	−23.3017	−1.07028
$475$	−16.4217	−0.753480
$476$	−54.4155	−2.49413
$477$	−17.3764	−0.795608
$478$	−46.1921	−2.11278
$479$	−19.4182	−0.887242	−0.443621	−	0.896215i	$-0.646306\pi$
$479$	−19.4182	−0.887242	−0.443621	+	0.896215i	$0.646306\pi$
$480$	17.9083	0.817400
$481$	−0.673200	−0.0306953
$482$	−14.7843	−0.673404
$483$	−12.5968	−0.573172
$484$	−7.73665	−0.351666
$485$	11.5375	0.523892
$486$	−42.4081	−1.92367
$487$	−21.7670	−0.986357	−0.493178	−	0.869928i	$-0.664165\pi$
$487$	−21.7670	−0.986357	−0.493178	+	0.869928i	$0.664165\pi$
$488$	95.2731	4.31281
$489$	1.53998	0.0696402
$490$	1.79775	0.0812141
$491$	23.0208	1.03891	0.519456	−	0.854497i	$-0.326135\pi$
$491$	23.0208	1.03891	0.519456	+	0.854497i	$0.326135\pi$
$492$	22.4770	1.01334
$493$	−38.8582	−1.75008
$494$	23.1996	1.04380
$495$	10.0755	0.452862
$496$	−74.7196	−3.35501
$497$	−30.8630	−1.38440
$498$	−21.2520	−0.952323
$499$	7.62155	0.341187	0.170594	−	0.985341i	$-0.445431\pi$
$499$	7.62155	0.341187	0.170594	+	0.985341i	$0.445431\pi$
$500$	57.8775	2.58836
$501$	1.77143	0.0791417
$502$	−3.80017	−0.169610
$503$	−1.35981	−0.0606308	−0.0303154	−	0.999540i	$-0.509651\pi$
$503$	−1.35981	−0.0606308	−0.0303154	+	0.999540i	$0.509651\pi$
$504$	−53.6496	−2.38974
$505$	19.5408	0.869556
$506$	−46.5398	−2.06895
$507$	−8.48932	−0.377024
$508$	46.5356	2.06468
$509$	−32.0122	−1.41891	−0.709457	−	0.704749i	$-0.751060\pi$
$509$	−32.0122	−1.41891	−0.709457	+	0.704749i	$0.751060\pi$
$510$	11.7960	0.522335
$511$	33.2042	1.46887
$512$	13.3449	0.589766
$513$	−23.4864	−1.03695
$514$	63.8330	2.81555
$515$	14.0769	0.620303
$516$	45.3407	1.99601
$517$	−9.99770	−0.439699
$518$	3.06153	0.134516
$519$	−6.38226	−0.280150
$520$	−18.8939	−0.828553
$521$	7.61548	0.333640	0.166820	−	0.985987i	$-0.446650\pi$
$521$	7.61548	0.333640	0.166820	+	0.985987i	$0.446650\pi$
$522$	−62.6957	−2.74412
$523$	−7.09924	−0.310428	−0.155214	−	0.987881i	$-0.549607\pi$
$523$	−7.09924	−0.310428	−0.155214	+	0.987881i	$0.549607\pi$
$524$	95.1102	4.15491
$525$	6.77731	0.295786
$526$	−43.3180	−1.88875
$527$	−23.7772	−1.03575
$528$	30.5336	1.32880
$529$	8.93713	0.388571
$530$	27.8297	1.20885
$531$	23.1316	1.00383
$532$	−75.9615	−3.29335
$533$	−8.62043	−0.373392
$534$	−20.6452	−0.893405
$535$	2.55667	0.110535
$536$	−125.641	−5.42685
$537$	−1.04156	−0.0449466
$538$	23.2918	1.00418
$539$	1.48081	0.0637829
$540$	31.3019	1.34702
$541$	30.0629	1.29251	0.646253	−	0.763123i	$-0.276335\pi$
$541$	30.0629	1.29251	0.646253	+	0.763123i	$0.276335\pi$
$542$	64.3894	2.76576
$543$	−13.8273	−0.593385
$544$	−60.7352	−2.60400
$545$	3.54215	0.151729
$546$	−9.57455	−0.409753
$547$	−30.7503	−1.31479	−0.657394	−	0.753547i	$-0.728341\pi$
$547$	−30.7503	−1.31479	−0.657394	+	0.753547i	$0.728341\pi$
$548$	81.8646	3.49708
$549$	26.5001	1.13100
$550$	25.0393	1.06768
$551$	−54.2442	−2.31088
$552$	−38.6770	−1.64620
$553$	−29.2613	−1.24432
$554$	35.2984	1.49968
$555$	−0.477826	−0.0202826
$556$	−55.6409	−2.35970
$557$	−34.7689	−1.47320	−0.736602	−	0.676327i	$-0.763571\pi$
$557$	−34.7689	−1.47320	−0.736602	+	0.676327i	$0.763571\pi$
$558$	−38.3633	−1.62405
$559$	−17.3892	−0.735485
$560$	46.5493	1.96707
$561$	9.71636	0.410225
$562$	18.1124	0.764026
$563$	−26.6360	−1.12257	−0.561286	−	0.827622i	$-0.689693\pi$
$563$	−26.6360	−1.12257	−0.561286	+	0.827622i	$0.689693\pi$
$564$	−13.5969	−0.572533
$565$	−8.22179	−0.345893
$566$	−1.41174	−0.0593397
$567$	−9.47285	−0.397822
$568$	−94.7617	−3.97611
$569$	39.3686	1.65042	0.825209	−	0.564827i	$-0.191057\pi$
$569$	39.3686	1.65042	0.825209	+	0.564827i	$0.191057\pi$
$570$	16.4667	0.689713
$571$	10.7543	0.450055	0.225028	−	0.974352i	$-0.427753\pi$
$571$	10.7543	0.450055	0.225028	+	0.974352i	$0.427753\pi$
$572$	−25.4685	−1.06489
$573$	−21.7078	−0.906855
$574$	39.2034	1.63632
$575$	−17.1828	−0.716573
$576$	−41.1939	−1.71641
$577$	10.1968	0.424499	0.212249	−	0.977216i	$-0.431921\pi$
$577$	10.1968	0.424499	0.212249	+	0.977216i	$0.431921\pi$
$578$	5.42700	0.225733
$579$	−5.59601	−0.232562
$580$	72.2948	3.00188
$581$	−26.6872	−1.10717
$582$	17.9516	0.744117
$583$	22.9234	0.949388
$584$	101.950	4.21873
$585$	−5.25533	−0.217281
$586$	15.0274	0.620776
$587$	−31.4264	−1.29711	−0.648554	−	0.761169i	$-0.724626\pi$
$587$	−31.4264	−1.29711	−0.648554	+	0.761169i	$0.724626\pi$
$588$	2.01390	0.0830520
$589$	−33.1918	−1.36765
$590$	−37.0473	−1.52521
$591$	−8.71863	−0.358636
$592$	5.09248	0.209300
$593$	27.0279	1.10990	0.554952	−	0.831883i	$-0.312737\pi$
$593$	27.0279	1.10990	0.554952	+	0.831883i	$0.312737\pi$
$594$	35.8114	1.46936
$595$	14.8129	0.607269
$596$	−26.3486	−1.07928
$597$	−21.3086	−0.872101
$598$	24.2748	0.992670
$599$	1.96662	0.0803538	0.0401769	−	0.999193i	$-0.487208\pi$
$599$	1.96662	0.0803538	0.0401769	+	0.999193i	$0.487208\pi$
$600$	20.8090	0.849524
$601$	5.40812	0.220602	0.110301	−	0.993898i	$-0.464819\pi$
$601$	5.40812	0.220602	0.110301	+	0.993898i	$0.464819\pi$
$602$	79.0815	3.22312
$603$	−34.9469	−1.42315
$604$	−52.1139	−2.12048
$605$	2.10606	0.0856234
$606$	30.4042	1.23509
$607$	−4.24776	−0.172411	−0.0862057	−	0.996277i	$-0.527474\pi$
$607$	−4.24776	−0.172411	−0.0862057	+	0.996277i	$0.527474\pi$
$608$	−84.7836	−3.43843
$609$	22.3868	0.907159
$610$	−42.4423	−1.71844
$611$	5.21473	0.210965
$612$	−46.4723	−1.87853
$613$	16.1635	0.652839	0.326419	−	0.945225i	$-0.394158\pi$
$613$	16.1635	0.652839	0.326419	+	0.945225i	$0.394158\pi$
$614$	54.4948	2.19923
$615$	−6.11864	−0.246727
$616$	70.7760	2.85165
$617$	−21.4142	−0.862103	−0.431052	−	0.902327i	$-0.641857\pi$
$617$	−21.4142	−0.862103	−0.431052	+	0.902327i	$0.641857\pi$
$618$	21.9027	0.881057
$619$	42.9190	1.72506	0.862530	−	0.506006i	$-0.168879\pi$
$619$	42.9190	1.72506	0.862530	+	0.506006i	$0.168879\pi$
$620$	44.2369	1.77660
$621$	−24.5750	−0.986159
$622$	−28.1400	−1.12831
$623$	−25.9253	−1.03868
$624$	−15.9261	−0.637553
$625$	−0.552741	−0.0221096
$626$	52.1061	2.08258
$627$	13.5636	0.541678
$628$	−18.3752	−0.733251
$629$	1.62052	0.0646145
$630$	23.8998	0.952193
$631$	8.42804	0.335515	0.167758	−	0.985828i	$-0.446347\pi$
$631$	8.42804	0.335515	0.167758	+	0.985828i	$0.446347\pi$
$632$	−89.8436	−3.57379
$633$	6.62137	0.263176
$634$	−14.9267	−0.592817
$635$	−12.6678	−0.502708
$636$	31.1758	1.23620
$637$	−0.772378	−0.0306027
$638$	82.7099	3.27452
$639$	−26.3579	−1.04270
$640$	22.0274	0.870710
$641$	38.3992	1.51668	0.758338	−	0.651862i	$-0.226012\pi$
$641$	38.3992	1.51668	0.758338	+	0.651862i	$0.226012\pi$
$642$	3.97801	0.156999
$643$	38.6710	1.52504	0.762518	−	0.646967i	$-0.223963\pi$
$643$	38.6710	1.52504	0.762518	+	0.646967i	$0.223963\pi$
$644$	−79.4821	−3.13203
$645$	−12.3426	−0.485988
$646$	−55.8459	−2.19723
$647$	32.9150	1.29402	0.647011	−	0.762481i	$-0.276019\pi$
$647$	32.9150	1.29402	0.647011	+	0.762481i	$0.276019\pi$
$648$	−29.0854	−1.14258
$649$	−30.5159	−1.19785
$650$	−13.0603	−0.512268
$651$	13.6984	0.536883
$652$	9.71684	0.380541
$653$	2.97848	0.116557	0.0582784	−	0.998300i	$-0.481439\pi$
$653$	2.97848	0.116557	0.0582784	+	0.998300i	$0.481439\pi$
$654$	5.51134	0.215511
$655$	−25.8907	−1.01163
$656$	65.2100	2.54602
$657$	28.3573	1.10633
$658$	−23.7152	−0.924515
$659$	−31.1988	−1.21533	−0.607667	−	0.794192i	$-0.707895\pi$
$659$	−31.1988	−1.21533	−0.607667	+	0.794192i	$0.707895\pi$
$660$	−18.0771	−0.703649
$661$	−14.1174	−0.549104	−0.274552	−	0.961572i	$-0.588529\pi$
$661$	−14.1174	−0.549104	−0.274552	+	0.961572i	$0.588529\pi$
$662$	69.1989	2.68949
$663$	−5.06798	−0.196824
$664$	−81.9404	−3.17990
$665$	20.6781	0.801862
$666$	2.61463	0.101315
$667$	−56.7583	−2.19769
$668$	11.1772	0.432460
$669$	6.99591	0.270477
$670$	55.9704	2.16233
$671$	−34.9597	−1.34960
$672$	34.9905	1.34979
$673$	−11.9925	−0.462275	−0.231138	−	0.972921i	$-0.574245\pi$
$673$	−11.9925	−0.462275	−0.231138	+	0.972921i	$0.574245\pi$
$674$	41.6056	1.60259
$675$	13.2218	0.508908
$676$	−53.5653	−2.06020
$677$	−26.2364	−1.00835	−0.504173	−	0.863603i	$-0.668203\pi$
$677$	−26.2364	−1.00835	−0.504173	+	0.863603i	$0.668203\pi$
$678$	−12.7925	−0.491295
$679$	22.5428	0.865113
$680$	45.4814	1.74413
$681$	5.00413	0.191759
$682$	50.6099	1.93795
$683$	19.9565	0.763616	0.381808	−	0.924242i	$-0.375302\pi$
$683$	19.9565	0.763616	0.381808	+	0.924242i	$0.375302\pi$
$684$	−64.8732	−2.48049
$685$	−22.2850	−0.851467
$686$	−47.6536	−1.81942
$687$	−6.52807	−0.249062
$688$	131.542	5.01500
$689$	−11.9566	−0.455512
$690$	17.2298	0.655929
$691$	47.1340	1.79306	0.896531	−	0.442980i	$-0.146079\pi$
$691$	47.1340	1.79306	0.896531	+	0.442980i	$0.146079\pi$
$692$	−40.2703	−1.53085
$693$	19.6863	0.747821
$694$	−38.6135	−1.46575
$695$	15.1465	0.574538
$696$	68.7363	2.60544
$697$	20.7511	0.786002
$698$	14.0716	0.532619
$699$	−20.1821	−0.763356
$700$	42.7630	1.61629
$701$	−35.7950	−1.35196	−0.675979	−	0.736921i	$-0.736279\pi$
$701$	−35.7950	−1.35196	−0.675979	+	0.736921i	$0.736279\pi$
$702$	−18.6790	−0.704992
$703$	2.26218	0.0853196
$704$	54.3441	2.04817
$705$	3.70133	0.139400
$706$	57.5793	2.16702
$707$	38.1802	1.43592
$708$	−41.5017	−1.55973
$709$	−6.09651	−0.228959	−0.114480	−	0.993426i	$-0.536520\pi$
$709$	−6.09651	−0.228959	−0.114480	+	0.993426i	$0.536520\pi$
$710$	42.2145	1.58428
$711$	−24.9899	−0.937196
$712$	−79.6009	−2.98317
$713$	−34.7302	−1.30066
$714$	23.0478	0.862543
$715$	6.93297	0.259279
$716$	−6.57196	−0.245606
$717$	14.0862	0.526059
$718$	−85.4939	−3.19060
$719$	−37.3567	−1.39317	−0.696585	−	0.717475i	$-0.745298\pi$
$719$	−37.3567	−1.39317	−0.696585	+	0.717475i	$0.745298\pi$
$720$	39.7544	1.48156
$721$	27.5045	1.02432
$722$	−27.1808	−1.01156
$723$	4.50843	0.167670
$724$	−87.2463	−3.24248
$725$	30.5371	1.13412
$726$	3.27688	0.121616
$727$	−5.73655	−0.212757	−0.106378	−	0.994326i	$-0.533925\pi$
$727$	−5.73655	−0.212757	−0.106378	+	0.994326i	$0.533925\pi$
$728$	−36.9162	−1.36821
$729$	2.54180	0.0941408
$730$	−45.4168	−1.68095
$731$	41.8592	1.54822
$732$	−47.5453	−1.75733
$733$	−13.0735	−0.482879	−0.241440	−	0.970416i	$-0.577620\pi$
$733$	−13.0735	−0.482879	−0.241440	+	0.970416i	$0.577620\pi$
$734$	51.6381	1.90600
$735$	−0.548221	−0.0202214
$736$	−88.7131	−3.27001
$737$	46.1028	1.69822
$738$	33.4808	1.23245
$739$	−18.4746	−0.679597	−0.339799	−	0.940498i	$-0.610359\pi$
$739$	−18.4746	−0.679597	−0.339799	+	0.940498i	$0.610359\pi$
$740$	−3.01495	−0.110832
$741$	−7.07466	−0.259894
$742$	54.3757	1.99619
$743$	5.71288	0.209585	0.104793	−	0.994494i	$-0.466582\pi$
$743$	5.71288	0.209585	0.104793	+	0.994494i	$0.466582\pi$
$744$	42.0595	1.54198
$745$	7.17257	0.262783
$746$	−87.7137	−3.21143
$747$	−22.7917	−0.833903
$748$	61.3076	2.24163
$749$	4.99540	0.182528
$750$	−24.5142	−0.895131
$751$	−27.9926	−1.02146	−0.510732	−	0.859740i	$-0.670626\pi$
$751$	−27.9926	−1.02146	−0.510732	+	0.859740i	$0.670626\pi$
$752$	−39.4473	−1.43849
$753$	1.15885	0.0422310
$754$	−43.1409	−1.57110
$755$	14.1863	0.516294
$756$	61.1598	2.22436
$757$	38.4170	1.39629	0.698144	−	0.715957i	$-0.254009\pi$
$757$	38.4170	1.39629	0.698144	+	0.715957i	$0.254009\pi$
$758$	−29.5460	−1.07316
$759$	14.1922	0.515145
$760$	63.4899	2.30302
$761$	33.0121	1.19669	0.598344	−	0.801239i	$-0.295826\pi$
$761$	33.0121	1.19669	0.598344	+	0.801239i	$0.295826\pi$
$762$	−19.7103	−0.714028
$763$	6.92090	0.250553
$764$	−136.970	−4.95540
$765$	12.6506	0.457384
$766$	−62.8097	−2.26941
$767$	15.9169	0.574724
$768$	5.52779	0.199467
$769$	19.2603	0.694546	0.347273	−	0.937764i	$-0.387108\pi$
$769$	19.2603	0.694546	0.347273	+	0.937764i	$0.387108\pi$
$770$	−31.5293	−1.13624
$771$	−19.4658	−0.701042
$772$	−35.3093	−1.27081
$773$	12.7195	0.457490	0.228745	−	0.973486i	$-0.426538\pi$
$773$	12.7195	0.457490	0.228745	+	0.973486i	$0.426538\pi$
$774$	67.5378	2.42759
$775$	18.6855	0.671204
$776$	69.2153	2.48468
$777$	−0.933609	−0.0334930
$778$	−20.9305	−0.750393
$779$	28.9675	1.03787
$780$	9.42887	0.337608
$781$	34.7721	1.24424
$782$	−58.4342	−2.08960
$783$	43.6743	1.56079
$784$	5.84273	0.208669
$785$	5.00206	0.178531
$786$	−40.2842	−1.43689
$787$	−49.3069	−1.75760	−0.878800	−	0.477190i	$-0.841655\pi$
$787$	−49.3069	−1.75760	−0.878800	+	0.477190i	$0.841655\pi$
$788$	−55.0122	−1.95973
$789$	13.2097	0.470279
$790$	40.0236	1.42397
$791$	−16.0643	−0.571181
$792$	60.4447	2.14781
$793$	18.2347	0.647534
$794$	59.9287	2.12679
$795$	−8.48663	−0.300990
$796$	−134.451	−4.76550
$797$	14.6368	0.518461	0.259231	−	0.965815i	$-0.416531\pi$
$797$	14.6368	0.518461	0.259231	+	0.965815i	$0.416531\pi$
$798$	32.1737	1.13894
$799$	−12.5529	−0.444088
$800$	47.7294	1.68749
$801$	−22.1409	−0.782311
$802$	71.4158	2.52178
$803$	−37.4098	−1.32016
$804$	62.7000	2.21126
$805$	21.6365	0.762585
$806$	−26.3977	−0.929821
$807$	−7.10278	−0.250030
$808$	117.228	4.12408
$809$	3.28684	0.115559	0.0577795	−	0.998329i	$-0.481598\pi$
$809$	3.28684	0.115559	0.0577795	+	0.998329i	$0.481598\pi$
$810$	12.9570	0.455262
$811$	41.2914	1.44994	0.724968	−	0.688782i	$-0.241854\pi$
$811$	41.2914	1.44994	0.724968	+	0.688782i	$0.241854\pi$
$812$	141.255	4.95706
$813$	−19.6354	−0.688645
$814$	−3.44930	−0.120898
$815$	−2.64510	−0.0926537
$816$	38.3372	1.34207
$817$	58.4335	2.04433
$818$	57.6844	2.01689
$819$	−10.2682	−0.358801
$820$	−38.6069	−1.34821
$821$	43.1307	1.50527	0.752636	−	0.658437i	$-0.228782\pi$
$821$	43.1307	1.50527	0.752636	+	0.658437i	$0.228782\pi$
$822$	−34.6740	−1.20939
$823$	−17.0074	−0.592841	−0.296420	−	0.955058i	$-0.595793\pi$
$823$	−17.0074	−0.592841	−0.296420	+	0.955058i	$0.595793\pi$
$824$	84.4495	2.94194
$825$	−7.63570	−0.265841
$826$	−72.3856	−2.51862
$827$	31.5512	1.09714	0.548571	−	0.836104i	$-0.315172\pi$
$827$	31.5512	1.09714	0.548571	+	0.836104i	$0.315172\pi$
$828$	−67.8799	−2.35899
$829$	18.2996	0.635571	0.317786	−	0.948163i	$-0.397061\pi$
$829$	18.2996	0.635571	0.317786	+	0.948163i	$0.397061\pi$
$830$	36.5028	1.26703
$831$	−10.7642	−0.373405
$832$	−28.3455	−0.982703
$833$	1.85926	0.0644197
$834$	23.5669	0.816054
$835$	−3.04265	−0.105295
$836$	85.5825	2.95993
$837$	26.7241	0.923722
$838$	94.7405	3.27276
$839$	−11.2384	−0.387992	−0.193996	−	0.981002i	$-0.562145\pi$
$839$	−11.2384	−0.387992	−0.193996	+	0.981002i	$0.562145\pi$
$840$	−26.2025	−0.904073
$841$	71.8701	2.47828
$842$	48.3592	1.66657
$843$	−5.52335	−0.190234
$844$	41.7791	1.43809
$845$	14.5814	0.501617
$846$	−20.2534	−0.696327
$847$	4.11496	0.141392
$848$	90.4472	3.10597
$849$	0.430506	0.0147749
$850$	31.4388	1.07834
$851$	2.36702	0.0811404
$852$	47.2901	1.62013
$853$	41.6341	1.42553	0.712763	−	0.701405i	$-0.247444\pi$
$853$	41.6341	1.42553	0.712763	+	0.701405i	$0.247444\pi$
$854$	−82.9267	−2.83769
$855$	17.6597	0.603948
$856$	15.3378	0.524237
$857$	−33.9530	−1.15981	−0.579906	−	0.814683i	$-0.696911\pi$
$857$	−33.9530	−1.15981	−0.579906	+	0.814683i	$0.696911\pi$
$858$	10.7872	0.368270
$859$	−51.4915	−1.75687	−0.878434	−	0.477865i	$-0.841411\pi$
$859$	−51.4915	−1.75687	−0.878434	+	0.477865i	$0.841411\pi$
$860$	−77.8782	−2.65562
$861$	−11.9550	−0.407426
$862$	63.5081	2.16309
$863$	35.4538	1.20686	0.603430	−	0.797416i	$-0.293800\pi$
$863$	35.4538	1.20686	0.603430	+	0.797416i	$0.293800\pi$
$864$	68.2629	2.32235
$865$	10.9623	0.372730
$866$	43.3105	1.47175
$867$	−1.65495	−0.0562051
$868$	86.4332	2.93373
$869$	32.9674	1.11834
$870$	−30.6207	−1.03814
$871$	−24.0469	−0.814798
$872$	21.2499	0.719612
$873$	19.2522	0.651587
$874$	−81.5714	−2.75920
$875$	−30.7838	−1.04068
$876$	−50.8774	−1.71899
$877$	−44.4134	−1.49973	−0.749867	−	0.661589i	$-0.769882\pi$
$877$	−44.4134	−1.49973	−0.749867	+	0.661589i	$0.769882\pi$
$878$	−25.8918	−0.873805
$879$	−4.58258	−0.154566
$880$	−52.4451	−1.76792
$881$	25.4638	0.857898	0.428949	−	0.903329i	$-0.358884\pi$
$881$	25.4638	0.857898	0.428949	+	0.903329i	$0.358884\pi$
$882$	2.99983	0.101010
$883$	35.2764	1.18714	0.593572	−	0.804781i	$-0.297717\pi$
$883$	35.2764	1.18714	0.593572	+	0.804781i	$0.297717\pi$
$884$	−31.9776	−1.07552
$885$	11.2975	0.379762
$886$	81.1674	2.72687
$887$	28.4444	0.955070	0.477535	−	0.878613i	$-0.341530\pi$
$887$	28.4444	0.955070	0.477535	+	0.878613i	$0.341530\pi$
$888$	−2.86655	−0.0961950
$889$	−24.7513	−0.830131
$890$	35.4606	1.18864
$891$	10.6727	0.357547
$892$	44.1423	1.47799
$893$	−17.5232	−0.586392
$894$	11.1600	0.373247
$895$	1.78901	0.0597999
$896$	43.0387	1.43782
$897$	−7.40255	−0.247164
$898$	15.0663	0.502770
$899$	61.7220	2.05855
$900$	36.5208	1.21736
$901$	28.7820	0.958867
$902$	−44.1688	−1.47066
$903$	−24.1157	−0.802522
$904$	−49.3238	−1.64048
$905$	23.7500	0.789477
$906$	22.0730	0.733325
$907$	−37.8707	−1.25747	−0.628737	−	0.777618i	$-0.716428\pi$
$907$	−37.8707	−1.25747	−0.628737	+	0.777618i	$0.716428\pi$
$908$	31.5747	1.04784
$909$	32.6070	1.08151
$910$	16.4455	0.545162
$911$	−49.3327	−1.63447	−0.817233	−	0.576307i	$-0.804493\pi$
$911$	−49.3327	−1.63447	−0.817233	+	0.576307i	$0.804493\pi$
$912$	53.5170	1.77212
$913$	30.0674	0.995085
$914$	−69.9877	−2.31499
$915$	12.9427	0.427872
$916$	−41.1904	−1.36097
$917$	−50.5870	−1.67053
$918$	44.9639	1.48403
$919$	4.98447	0.164422	0.0822112	−	0.996615i	$-0.473802\pi$
$919$	4.98447	0.164422	0.0822112	+	0.996615i	$0.473802\pi$
$920$	66.4325	2.19021
$921$	−16.6181	−0.547585
$922$	66.2056	2.18037
$923$	−18.1368	−0.596981
$924$	−35.3202	−1.16195
$925$	−1.27351	−0.0418726
$926$	−106.253	−3.49168
$927$	23.4896	0.771499
$928$	157.660	5.17544
$929$	−11.1717	−0.366531	−0.183266	−	0.983063i	$-0.558667\pi$
$929$	−11.1717	−0.366531	−0.183266	+	0.983063i	$0.558667\pi$
$930$	−18.7367	−0.614400
$931$	2.59545	0.0850624
$932$	−127.343	−4.17127
$933$	8.58125	0.280937
$934$	55.0519	1.80135
$935$	−16.6890	−0.545789
$936$	−31.5275	−1.03051
$937$	0.558114	0.0182328	0.00911640	−	0.999958i	$-0.497098\pi$
$937$	0.558114	0.0182328	0.00911640	+	0.999958i	$0.497098\pi$
$938$	109.359	3.57069
$939$	−15.8897	−0.518539
$940$	23.3544	0.761735
$941$	−52.6141	−1.71517	−0.857586	−	0.514341i	$-0.828037\pi$
$941$	−52.6141	−1.71517	−0.857586	+	0.514341i	$0.828037\pi$
$942$	7.78287	0.253580
$943$	30.3101	0.987032
$944$	−120.405	−3.91883
$945$	−16.6488	−0.541586
$946$	−89.0977	−2.89682
$947$	−36.5310	−1.18710	−0.593549	−	0.804798i	$-0.702274\pi$
$947$	−36.5310	−1.18710	−0.593549	+	0.804798i	$0.702274\pi$
$948$	44.8358	1.45620
$949$	19.5127	0.633408
$950$	43.8871	1.42389
$951$	4.55188	0.147605
$952$	88.8646	2.88012
$953$	−18.4959	−0.599140	−0.299570	−	0.954074i	$-0.596843\pi$
$953$	−18.4959	−0.599140	−0.299570	+	0.954074i	$0.596843\pi$
$954$	46.4383	1.50350
$955$	37.2857	1.20654
$956$	88.8800	2.87459
$957$	−25.2222	−0.815319
$958$	51.8953	1.67666
$959$	−43.5420	−1.40604
$960$	−20.1191	−0.649343
$961$	6.76748	0.218306
$962$	1.79913	0.0580062
$963$	4.26621	0.137477
$964$	28.4470	0.916215
$965$	9.61182	0.309415
$966$	33.6649	1.08315
$967$	41.5322	1.33558	0.667792	−	0.744348i	$-0.267239\pi$
$967$	41.5322	1.33558	0.667792	+	0.744348i	$0.267239\pi$
$968$	12.6345	0.406090
$969$	17.0301	0.547086
$970$	−30.8340	−0.990021
$971$	−15.7745	−0.506227	−0.253113	−	0.967437i	$-0.581455\pi$
$971$	−15.7745	−0.506227	−0.253113	+	0.967437i	$0.581455\pi$
$972$	81.5991	2.61729
$973$	29.5942	0.948746
$974$	58.1723	1.86396
$975$	3.98272	0.127549
$976$	−137.938	−4.41529
$977$	−41.9019	−1.34056	−0.670280	−	0.742109i	$-0.733826\pi$
$977$	−41.9019	−1.34056	−0.670280	+	0.742109i	$0.733826\pi$
$978$	−4.11559	−0.131602
$979$	29.2089	0.933521
$980$	−3.45912	−0.110498
$981$	5.91064	0.188712
$982$	−61.5230	−1.96328
$983$	−47.4092	−1.51212	−0.756059	−	0.654503i	$-0.772878\pi$
$983$	−47.4092	−1.51212	−0.756059	+	0.654503i	$0.772878\pi$
$984$	−36.7066	−1.17016
$985$	14.9753	0.477153
$986$	103.849	3.30721
$987$	7.23190	0.230194
$988$	−44.6392	−1.42016
$989$	61.1417	1.94419
$990$	−26.9269	−0.855794
$991$	−29.1683	−0.926561	−0.463281	−	0.886212i	$-0.653328\pi$
$991$	−29.1683	−0.926561	−0.463281	+	0.886212i	$0.653328\pi$
$992$	96.4714	3.06297
$993$	−21.1021	−0.669654
$994$	82.4815	2.61616
$995$	36.6000	1.16030
$996$	40.8917	1.29570
$997$	−27.6623	−0.876073	−0.438036	−	0.898957i	$-0.644326\pi$
$997$	−27.6623	−0.876073	−0.438036	+	0.898957i	$0.644326\pi$
$998$	−20.3686	−0.644757
$999$	−1.82137	−0.0576257

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4001.2.a.a.1.3	✓	149

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4001.2.a.a.1.3	✓	149	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:	\( N \)	\(=\)	\( 4001 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4001.a (trivial)

\(f(q)\)	\(=\)	\(q-2.67250 q^{2} +0.814974 q^{3} +5.14227 q^{4} -1.39982 q^{5} -2.17802 q^{6} -2.73506 q^{7} -8.39771 q^{8} -2.33582 q^{9} +O(q^{10})\)	\(q-2.67250 q^{2} +0.814974 q^{3} +5.14227 q^{4} -1.39982 q^{5} -2.17802 q^{6} -2.73506 q^{7} -8.39771 q^{8} -2.33582 q^{9} +3.74102 q^{10} +3.08147 q^{11} +4.19081 q^{12} -1.60727 q^{13} +7.30945 q^{14} -1.14082 q^{15} +12.1584 q^{16} +3.86902 q^{17} +6.24247 q^{18} +5.40098 q^{19} -7.19823 q^{20} -2.22900 q^{21} -8.23524 q^{22} +5.65129 q^{23} -6.84392 q^{24} -3.04051 q^{25} +4.29544 q^{26} -4.34855 q^{27} -14.0644 q^{28} -10.0434 q^{29} +3.04883 q^{30} -6.14553 q^{31} -15.6978 q^{32} +2.51132 q^{33} -10.3400 q^{34} +3.82858 q^{35} -12.0114 q^{36} +0.418846 q^{37} -14.4341 q^{38} -1.30989 q^{39} +11.7553 q^{40} +5.36339 q^{41} +5.95702 q^{42} +10.8191 q^{43} +15.8458 q^{44} +3.26972 q^{45} -15.1031 q^{46} -3.24446 q^{47} +9.90876 q^{48} +0.480552 q^{49} +8.12577 q^{50} +3.15315 q^{51} -8.26503 q^{52} +7.43909 q^{53} +11.6215 q^{54} -4.31350 q^{55} +22.9682 q^{56} +4.40166 q^{57} +26.8410 q^{58} -9.90302 q^{59} -5.86638 q^{60} -11.3451 q^{61} +16.4239 q^{62} +6.38860 q^{63} +17.6358 q^{64} +2.24989 q^{65} -6.71151 q^{66} +14.9613 q^{67} +19.8955 q^{68} +4.60566 q^{69} -10.2319 q^{70} +11.2842 q^{71} +19.6155 q^{72} -12.1402 q^{73} -1.11937 q^{74} -2.47794 q^{75} +27.7733 q^{76} -8.42801 q^{77} +3.50067 q^{78} +10.6986 q^{79} -17.0195 q^{80} +3.46349 q^{81} -14.3337 q^{82} +9.75746 q^{83} -11.4621 q^{84} -5.41592 q^{85} -28.9140 q^{86} -8.18512 q^{87} -25.8773 q^{88} +9.47888 q^{89} -8.73833 q^{90} +4.39599 q^{91} +29.0605 q^{92} -5.00845 q^{93} +8.67081 q^{94} -7.56038 q^{95} -12.7933 q^{96} -8.24216 q^{97} -1.28428 q^{98} -7.19776 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 149 q - 6 q^{2} - 28 q^{3} + 116 q^{4} - 19 q^{5} - 31 q^{6} - 47 q^{7} - 15 q^{8} + 115 q^{9}+O(q^{10}) \) 149 * q - 6 * q^2 - 28 * q^3 + 116 * q^4 - 19 * q^5 - 31 * q^6 - 47 * q^7 - 15 * q^8 + 115 * q^9	\( 149 q - 6 q^{2} - 28 q^{3} + 116 q^{4} - 19 q^{5} - 31 q^{6} - 47 q^{7} - 15 q^{8} + 115 q^{9} - 48 q^{10} - 31 q^{11} - 61 q^{12} - 54 q^{13} - 44 q^{14} - 65 q^{15} + 58 q^{16} - 26 q^{17} - 23 q^{18} - 86 q^{19} - 52 q^{20} - 30 q^{21} - 56 q^{22} - 63 q^{23} - 90 q^{24} + 92 q^{25} - 38 q^{26} - 103 q^{27} - 77 q^{28} - 51 q^{29} - 22 q^{30} - 256 q^{31} - 21 q^{32} - 36 q^{33} - 124 q^{34} - 50 q^{35} + 45 q^{36} - 42 q^{37} - 14 q^{38} - 119 q^{39} - 131 q^{40} - 55 q^{41} - 5 q^{42} - 55 q^{43} - 54 q^{44} - 68 q^{45} - 59 q^{46} - 82 q^{47} - 89 q^{48} + 30 q^{49} + 13 q^{50} - 83 q^{51} - 126 q^{52} - 23 q^{53} - 83 q^{54} - 244 q^{55} - 94 q^{56} - 14 q^{57} - 60 q^{58} - 93 q^{59} - 70 q^{60} - 139 q^{61} - 10 q^{62} - 120 q^{63} - 45 q^{64} - 37 q^{65} - 28 q^{66} - 110 q^{67} - 27 q^{68} - 79 q^{69} - 78 q^{70} - 123 q^{71} - 74 q^{73} - 25 q^{74} - 146 q^{75} - 192 q^{76} - q^{77} + 26 q^{78} - 273 q^{79} - 51 q^{80} + 41 q^{81} - 120 q^{82} - 27 q^{83} - 14 q^{84} - 71 q^{85} + 3 q^{86} - 98 q^{87} - 143 q^{88} - 70 q^{89} - 24 q^{90} - 256 q^{91} - 47 q^{92} + 16 q^{93} - 151 q^{94} - 83 q^{95} - 137 q^{96} - 108 q^{97} + 17 q^{98} - 131 q^{99}+O(q^{100}) \) 149 * q - 6 * q^2 - 28 * q^3 + 116 * q^4 - 19 * q^5 - 31 * q^6 - 47 * q^7 - 15 * q^8 + 115 * q^9 - 48 * q^10 - 31 * q^11 - 61 * q^12 - 54 * q^13 - 44 * q^14 - 65 * q^15 + 58 * q^16 - 26 * q^17 - 23 * q^18 - 86 * q^19 - 52 * q^20 - 30 * q^21 - 56 * q^22 - 63 * q^23 - 90 * q^24 + 92 * q^25 - 38 * q^26 - 103 * q^27 - 77 * q^28 - 51 * q^29 - 22 * q^30 - 256 * q^31 - 21 * q^32 - 36 * q^33 - 124 * q^34 - 50 * q^35 + 45 * q^36 - 42 * q^37 - 14 * q^38 - 119 * q^39 - 131 * q^40 - 55 * q^41 - 5 * q^42 - 55 * q^43 - 54 * q^44 - 68 * q^45 - 59 * q^46 - 82 * q^47 - 89 * q^48 + 30 * q^49 + 13 * q^50 - 83 * q^51 - 126 * q^52 - 23 * q^53 - 83 * q^54 - 244 * q^55 - 94 * q^56 - 14 * q^57 - 60 * q^58 - 93 * q^59 - 70 * q^60 - 139 * q^61 - 10 * q^62 - 120 * q^63 - 45 * q^64 - 37 * q^65 - 28 * q^66 - 110 * q^67 - 27 * q^68 - 79 * q^69 - 78 * q^70 - 123 * q^71 - 74 * q^73 - 25 * q^74 - 146 * q^75 - 192 * q^76 - q^77 + 26 * q^78 - 273 * q^79 - 51 * q^80 + 41 * q^81 - 120 * q^82 - 27 * q^83 - 14 * q^84 - 71 * q^85 + 3 * q^86 - 98 * q^87 - 143 * q^88 - 70 * q^89 - 24 * q^90 - 256 * q^91 - 47 * q^92 + 16 * q^93 - 151 * q^94 - 83 * q^95 - 137 * q^96 - 108 * q^97 + 17 * q^98 - 131 * q^99

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