LMFDB - Embedded newform 6001.2.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6001,2,Mod(1,6001)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6001, 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("6001.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6001 = 17 \cdot 353 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6001.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:	$47.9182262530$
Analytic rank:	$0$
Dimension:	$121$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	6001.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.80099 q^{2} +1.23587 q^{3} +5.84553 q^{4} -1.08657 q^{5} -3.46165 q^{6} -3.96716 q^{7} -10.7713 q^{8} -1.47263 q^{9} +O(q^{10})$	\(q-2.80099 q^{2} +1.23587 q^{3} +5.84553 q^{4} -1.08657 q^{5} -3.46165 q^{6} -3.96716 q^{7} -10.7713 q^{8} -1.47263 q^{9} +3.04347 q^{10} +3.26035 q^{11} +7.22431 q^{12} -3.69125 q^{13} +11.1120 q^{14} -1.34286 q^{15} +18.4792 q^{16} -1.00000 q^{17} +4.12481 q^{18} -1.13498 q^{19} -6.35159 q^{20} -4.90289 q^{21} -9.13221 q^{22} -8.02983 q^{23} -13.3119 q^{24} -3.81936 q^{25} +10.3391 q^{26} -5.52758 q^{27} -23.1902 q^{28} -1.02942 q^{29} +3.76133 q^{30} +0.676568 q^{31} -30.2174 q^{32} +4.02937 q^{33} +2.80099 q^{34} +4.31060 q^{35} -8.60829 q^{36} +3.19133 q^{37} +3.17907 q^{38} -4.56190 q^{39} +11.7038 q^{40} -4.64636 q^{41} +13.7329 q^{42} -11.1217 q^{43} +19.0585 q^{44} +1.60011 q^{45} +22.4915 q^{46} +0.0565963 q^{47} +22.8379 q^{48} +8.73835 q^{49} +10.6980 q^{50} -1.23587 q^{51} -21.5773 q^{52} +12.0838 q^{53} +15.4827 q^{54} -3.54261 q^{55} +42.7314 q^{56} -1.40269 q^{57} +2.88339 q^{58} +2.86987 q^{59} -7.84973 q^{60} -10.0966 q^{61} -1.89506 q^{62} +5.84215 q^{63} +47.6802 q^{64} +4.01081 q^{65} -11.2862 q^{66} +1.27948 q^{67} -5.84553 q^{68} -9.92382 q^{69} -12.0739 q^{70} +2.44454 q^{71} +15.8621 q^{72} -8.13747 q^{73} -8.93887 q^{74} -4.72023 q^{75} -6.63458 q^{76} -12.9343 q^{77} +12.7778 q^{78} -2.57775 q^{79} -20.0790 q^{80} -2.41349 q^{81} +13.0144 q^{82} -5.32068 q^{83} -28.6600 q^{84} +1.08657 q^{85} +31.1517 q^{86} -1.27223 q^{87} -35.1182 q^{88} -10.2723 q^{89} -4.48190 q^{90} +14.6438 q^{91} -46.9386 q^{92} +0.836149 q^{93} -0.158526 q^{94} +1.23324 q^{95} -37.3448 q^{96} -6.69182 q^{97} -24.4760 q^{98} -4.80129 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 121 q + 9 q^{2} + 13 q^{3} + 127 q^{4} + 21 q^{5} + 19 q^{6} - 13 q^{7} + 24 q^{8} + 134 q^{9}+O(q^{10}) $ 121 * q + 9 * q^2 + 13 * q^3 + 127 * q^4 + 21 * q^5 + 19 * q^6 - 13 * q^7 + 24 * q^8 + 134 * q^9	\( 121 q + 9 q^{2} + 13 q^{3} + 127 q^{4} + 21 q^{5} + 19 q^{6} - 13 q^{7} + 24 q^{8} + 134 q^{9} - q^{10} + 40 q^{11} + 41 q^{12} + 14 q^{13} + 32 q^{14} + 49 q^{15} + 135 q^{16} - 121 q^{17} + 28 q^{18} + 34 q^{19} + 64 q^{20} + 34 q^{21} - 18 q^{22} + 37 q^{23} + 54 q^{24} + 128 q^{25} + 91 q^{26} + 55 q^{27} - 28 q^{28} + 45 q^{29} + 30 q^{30} + 67 q^{31} + 47 q^{32} + 40 q^{33} - 9 q^{34} + 59 q^{35} + 138 q^{36} - 16 q^{37} + 30 q^{38} + 37 q^{39} + 14 q^{40} + 89 q^{41} + 33 q^{42} + 16 q^{43} + 90 q^{44} + 83 q^{45} - 9 q^{46} + 135 q^{47} + 96 q^{48} + 128 q^{49} + 71 q^{50} - 13 q^{51} + 47 q^{52} + 52 q^{53} + 90 q^{54} + 93 q^{55} + 69 q^{56} - 4 q^{57} + 5 q^{58} + 170 q^{59} + 78 q^{60} - 2 q^{61} + 46 q^{62} - 10 q^{63} + 182 q^{64} + 50 q^{65} + 68 q^{66} + 46 q^{67} - 127 q^{68} + 97 q^{69} + 46 q^{70} + 191 q^{71} + 57 q^{72} - 12 q^{73} + 68 q^{74} + 86 q^{75} + 108 q^{76} + 62 q^{77} - 10 q^{78} + 130 q^{80} + 149 q^{81} + 14 q^{82} + 83 q^{83} + 126 q^{84} - 21 q^{85} + 132 q^{86} + 50 q^{87} - 42 q^{88} + 144 q^{89} + 9 q^{90} + 13 q^{91} + 50 q^{92} + 43 q^{93} + 41 q^{94} + 82 q^{95} + 110 q^{96} - 3 q^{97} + 36 q^{98} + 89 q^{99}+O(q^{100}) \) 121 * q + 9 * q^2 + 13 * q^3 + 127 * q^4 + 21 * q^5 + 19 * q^6 - 13 * q^7 + 24 * q^8 + 134 * q^9 - q^10 + 40 * q^11 + 41 * q^12 + 14 * q^13 + 32 * q^14 + 49 * q^15 + 135 * q^16 - 121 * q^17 + 28 * q^18 + 34 * q^19 + 64 * q^20 + 34 * q^21 - 18 * q^22 + 37 * q^23 + 54 * q^24 + 128 * q^25 + 91 * q^26 + 55 * q^27 - 28 * q^28 + 45 * q^29 + 30 * q^30 + 67 * q^31 + 47 * q^32 + 40 * q^33 - 9 * q^34 + 59 * q^35 + 138 * q^36 - 16 * q^37 + 30 * q^38 + 37 * q^39 + 14 * q^40 + 89 * q^41 + 33 * q^42 + 16 * q^43 + 90 * q^44 + 83 * q^45 - 9 * q^46 + 135 * q^47 + 96 * q^48 + 128 * q^49 + 71 * q^50 - 13 * q^51 + 47 * q^52 + 52 * q^53 + 90 * q^54 + 93 * q^55 + 69 * q^56 - 4 * q^57 + 5 * q^58 + 170 * q^59 + 78 * q^60 - 2 * q^61 + 46 * q^62 - 10 * q^63 + 182 * q^64 + 50 * q^65 + 68 * q^66 + 46 * q^67 - 127 * q^68 + 97 * q^69 + 46 * q^70 + 191 * q^71 + 57 * q^72 - 12 * q^73 + 68 * q^74 + 86 * q^75 + 108 * q^76 + 62 * q^77 - 10 * q^78 + 130 * q^80 + 149 * q^81 + 14 * q^82 + 83 * q^83 + 126 * q^84 - 21 * q^85 + 132 * q^86 + 50 * q^87 - 42 * q^88 + 144 * q^89 + 9 * q^90 + 13 * q^91 + 50 * q^92 + 43 * q^93 + 41 * q^94 + 82 * q^95 + 110 * q^96 - 3 * q^97 + 36 * q^98 + 89 * 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 $

$2$	−2.80099	−1.98060	−0.990299	−	0.138955i	$-0.955626\pi$
$2$	−2.80099	−1.98060	−0.990299	+	0.138955i	$0.955626\pi$
$3$	1.23587	0.713529	0.356765	−	0.934194i	$-0.383880\pi$
$3$	1.23587	0.713529	0.356765	+	0.934194i	$0.383880\pi$
$4$	5.84553	2.92277
$5$	−1.08657	−0.485929	−0.242965	−	0.970035i	$-0.578120\pi$
$5$	−1.08657	−0.485929	−0.242965	+	0.970035i	$0.578120\pi$
$6$	−3.46165	−1.41321
$7$	−3.96716	−1.49945	−0.749723	−	0.661752i	$-0.769813\pi$
$7$	−3.96716	−1.49945	−0.749723	+	0.661752i	$0.769813\pi$
$8$	−10.7713	−3.80823
$9$	−1.47263	−0.490876
$10$	3.04347	0.962430
$11$	3.26035	0.983034	0.491517	−	0.870868i	$-0.336443\pi$
$11$	3.26035	0.983034	0.491517	+	0.870868i	$0.336443\pi$
$12$	7.22431	2.08548
$13$	−3.69125	−1.02377	−0.511884	−	0.859054i	$-0.671052\pi$
$13$	−3.69125	−1.02377	−0.511884	+	0.859054i	$0.671052\pi$
$14$	11.1120	2.96980
$15$	−1.34286	−0.346725
$16$	18.4792	4.61980
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	4.12481	0.972227
$19$	−1.13498	−0.260383	−0.130191	−	0.991489i	$-0.541559\pi$
$19$	−1.13498	−0.260383	−0.130191	+	0.991489i	$0.541559\pi$
$20$	−6.35159	−1.42026
$21$	−4.90289	−1.06990
$22$	−9.13221	−1.94699
$23$	−8.02983	−1.67434	−0.837168	−	0.546946i	$-0.815790\pi$
$23$	−8.02983	−1.67434	−0.837168	+	0.546946i	$0.815790\pi$
$24$	−13.3119	−2.71728
$25$	−3.81936	−0.763873
$26$	10.3391	2.02767
$27$	−5.52758	−1.06378
$28$	−23.1902	−4.38253
$29$	−1.02942	−0.191158	−0.0955792	−	0.995422i	$-0.530470\pi$
$29$	−1.02942	−0.191158	−0.0955792	+	0.995422i	$0.530470\pi$
$30$	3.76133	0.686722
$31$	0.676568	0.121515	0.0607576	−	0.998153i	$-0.480648\pi$
$31$	0.676568	0.121515	0.0607576	+	0.998153i	$0.480648\pi$
$32$	−30.2174	−5.34173
$33$	4.02937	0.701424
$34$	2.80099	0.480365
$35$	4.31060	0.728624
$36$	−8.60829	−1.43471
$37$	3.19133	0.524651	0.262326	−	0.964979i	$-0.415511\pi$
$37$	3.19133	0.524651	0.262326	+	0.964979i	$0.415511\pi$
$38$	3.17907	0.515713
$39$	−4.56190	−0.730489
$40$	11.7038	1.85053
$41$	−4.64636	−0.725640	−0.362820	−	0.931859i	$-0.618186\pi$
$41$	−4.64636	−0.725640	−0.362820	+	0.931859i	$0.618186\pi$
$42$	13.7329	2.11904
$43$	−11.1217	−1.69604	−0.848021	−	0.529962i	$-0.822206\pi$
$43$	−11.1217	−1.69604	−0.848021	+	0.529962i	$0.822206\pi$
$44$	19.0585	2.87318
$45$	1.60011	0.238531
$46$	22.4915	3.31618
$47$	0.0565963	0.00825542	0.00412771	−	0.999991i	$-0.498686\pi$
$47$	0.0565963	0.00825542	0.00412771	+	0.999991i	$0.498686\pi$
$48$	22.8379	3.29636
$49$	8.73835	1.24834
$50$	10.6980	1.51292
$51$	−1.23587	−0.173056
$52$	−21.5773	−2.99224
$53$	12.0838	1.65984	0.829920	−	0.557883i	$-0.188386\pi$
$53$	12.0838	1.65984	0.829920	+	0.557883i	$0.188386\pi$
$54$	15.4827	2.10693
$55$	−3.54261	−0.477685
$56$	42.7314	5.71023
$57$	−1.40269	−0.185791
$58$	2.88339	0.378608
$59$	2.86987	0.373625	0.186813	−	0.982396i	$-0.440184\pi$
$59$	2.86987	0.373625	0.186813	+	0.982396i	$0.440184\pi$
$60$	−7.84973	−1.01340
$61$	−10.0966	−1.29273	−0.646366	−	0.763027i	$-0.723712\pi$
$61$	−10.0966	−1.29273	−0.646366	+	0.763027i	$0.723712\pi$
$62$	−1.89506	−0.240673
$63$	5.84215	0.736041
$64$	47.6802	5.96002
$65$	4.01081	0.497479
$66$	−11.2862	−1.38924
$67$	1.27948	0.156313	0.0781565	−	0.996941i	$-0.475097\pi$
$67$	1.27948	0.156313	0.0781565	+	0.996941i	$0.475097\pi$
$68$	−5.84553	−0.708875
$69$	−9.92382	−1.19469
$70$	−12.0739	−1.44311
$71$	2.44454	0.290113	0.145056	−	0.989423i	$-0.453664\pi$
$71$	2.44454	0.290113	0.145056	+	0.989423i	$0.453664\pi$
$72$	15.8621	1.86937
$73$	−8.13747	−0.952419	−0.476210	−	0.879332i	$-0.657990\pi$
$73$	−8.13747	−0.952419	−0.476210	+	0.879332i	$0.657990\pi$
$74$	−8.93887	−1.03912
$75$	−4.72023	−0.545046
$76$	−6.63458	−0.761038
$77$	−12.9343	−1.47401
$78$	12.7778	1.44681
$79$	−2.57775	−0.290019	−0.145010	−	0.989430i	$-0.546321\pi$
$79$	−2.57775	−0.290019	−0.145010	+	0.989430i	$0.546321\pi$
$80$	−20.0790	−2.24489
$81$	−2.41349	−0.268165
$82$	13.0144	1.43720
$83$	−5.32068	−0.584021	−0.292010	−	0.956415i	$-0.594324\pi$
$83$	−5.32068	−0.584021	−0.292010	+	0.956415i	$0.594324\pi$
$84$	−28.6600	−3.12706
$85$	1.08657	0.117855
$86$	31.1517	3.35918
$87$	−1.27223	−0.136397
$88$	−35.1182	−3.74362
$89$	−10.2723	−1.08886	−0.544431	−	0.838806i	$-0.683254\pi$
$89$	−10.2723	−1.08886	−0.544431	+	0.838806i	$0.683254\pi$
$90$	−4.48190	−0.472434
$91$	14.6438	1.53509
$92$	−46.9386	−4.89369
$93$	0.836149	0.0867046
$94$	−0.158526	−0.0163507
$95$	1.23324	0.126528
$96$	−37.3448	−3.81148
$97$	−6.69182	−0.679451	−0.339726	−	0.940525i	$-0.610334\pi$
$97$	−6.69182	−0.679451	−0.339726	+	0.940525i	$0.610334\pi$
$98$	−24.4760	−2.47245
$99$	−4.80129	−0.482547
$100$	−22.3262	−2.23262
$101$	12.0871	1.20271	0.601355	−	0.798982i	$-0.294628\pi$
$101$	12.0871	1.20271	0.601355	+	0.798982i	$0.294628\pi$
$102$	3.46165	0.342755
$103$	1.95644	0.192774	0.0963870	−	0.995344i	$-0.469271\pi$
$103$	1.95644	0.192774	0.0963870	+	0.995344i	$0.469271\pi$
$104$	39.7595	3.89874
$105$	5.32734	0.519895
$106$	−33.8466	−3.28747
$107$	−8.84782	−0.855351	−0.427675	−	0.903932i	$-0.640667\pi$
$107$	−8.84782	−0.855351	−0.427675	+	0.903932i	$0.640667\pi$
$108$	−32.3117	−3.10919
$109$	6.62183	0.634256	0.317128	−	0.948383i	$-0.397281\pi$
$109$	6.62183	0.634256	0.317128	+	0.948383i	$0.397281\pi$
$110$	9.92280	0.946102
$111$	3.94406	0.374354
$112$	−73.3099	−6.92713
$113$	0.102681	0.00965940	0.00482970	−	0.999988i	$-0.498463\pi$
$113$	0.102681	0.00965940	0.00482970	+	0.999988i	$0.498463\pi$
$114$	3.92892	0.367977
$115$	8.72498	0.813609
$116$	−6.01750	−0.558711
$117$	5.43584	0.502543
$118$	−8.03847	−0.740001
$119$	3.96716	0.363669
$120$	14.4643	1.32041
$121$	−0.370087	−0.0336443
$122$	28.2804	2.56038
$123$	−5.74230	−0.517766
$124$	3.95490	0.355160
$125$	9.58286	0.857117
$126$	−16.3638	−1.45780
$127$	1.11840	0.0992415	0.0496208	−	0.998768i	$-0.484199\pi$
$127$	1.11840	0.0992415	0.0496208	+	0.998768i	$0.484199\pi$
$128$	−73.1169	−6.46268
$129$	−13.7450	−1.21018
$130$	−11.2342	−0.985306
$131$	19.0842	1.66739	0.833696	−	0.552223i	$-0.186220\pi$
$131$	19.0842	1.66739	0.833696	+	0.552223i	$0.186220\pi$
$132$	23.5538	2.05010
$133$	4.50266	0.390430
$134$	−3.58380	−0.309593
$135$	6.00611	0.516924
$136$	10.7713	0.923631
$137$	5.17144	0.441826	0.220913	−	0.975294i	$-0.429096\pi$
$137$	5.17144	0.441826	0.220913	+	0.975294i	$0.429096\pi$
$138$	27.7965	2.36620
$139$	−3.93434	−0.333706	−0.166853	−	0.985982i	$-0.553361\pi$
$139$	−3.93434	−0.333706	−0.166853	+	0.985982i	$0.553361\pi$
$140$	25.1978	2.12960
$141$	0.0699457	0.00589049
$142$	−6.84711	−0.574597
$143$	−12.0348	−1.00640
$144$	−27.2130	−2.26775
$145$	1.11854	0.0928894
$146$	22.7930	1.88636
$147$	10.7995	0.890725
$148$	18.6550	1.53343
$149$	−19.0412	−1.55992	−0.779958	−	0.625832i	$-0.784760\pi$
$149$	−19.0412	−1.55992	−0.779958	+	0.625832i	$0.784760\pi$
$150$	13.2213	1.07952
$151$	3.93886	0.320540	0.160270	−	0.987073i	$-0.448764\pi$
$151$	3.93886	0.320540	0.160270	+	0.987073i	$0.448764\pi$
$152$	12.2252	0.991597
$153$	1.47263	0.119055
$154$	36.2289	2.91941
$155$	−0.735139	−0.0590478
$156$	−26.6668	−2.13505
$157$	−14.6388	−1.16831	−0.584153	−	0.811644i	$-0.698573\pi$
$157$	−14.6388	−1.16831	−0.584153	+	0.811644i	$0.698573\pi$
$158$	7.22024	0.574411
$159$	14.9340	1.18434
$160$	32.8334	2.59570
$161$	31.8556	2.51057
$162$	6.76015	0.531128
$163$	22.5537	1.76654	0.883270	−	0.468865i	$-0.155337\pi$
$163$	22.5537	1.76654	0.883270	+	0.468865i	$0.155337\pi$
$164$	−27.1605	−2.12088
$165$	−4.37820	−0.340842
$166$	14.9032	1.15671
$167$	10.4710	0.810274	0.405137	−	0.914256i	$-0.367224\pi$
$167$	10.4710	0.810274	0.405137	+	0.914256i	$0.367224\pi$
$168$	52.8105	4.07442
$169$	0.625336	0.0481028
$170$	−3.04347	−0.233424
$171$	1.67141	0.127816
$172$	−65.0122	−4.95714
$173$	6.35909	0.483473	0.241736	−	0.970342i	$-0.422283\pi$
$173$	6.35909	0.483473	0.241736	+	0.970342i	$0.422283\pi$
$174$	3.56349	0.270148
$175$	15.1520	1.14539
$176$	60.2487	4.54142
$177$	3.54678	0.266593
$178$	28.7726	2.15660
$179$	−13.1115	−0.979998	−0.489999	−	0.871723i	$-0.663003\pi$
$179$	−13.1115	−0.979998	−0.489999	+	0.871723i	$0.663003\pi$
$180$	9.35352	0.697170
$181$	−17.6619	−1.31280	−0.656401	−	0.754412i	$-0.727922\pi$
$181$	−17.6619	−1.31280	−0.656401	+	0.754412i	$0.727922\pi$
$182$	−41.0171	−3.04039
$183$	−12.4780	−0.922403
$184$	86.4916	6.37625
$185$	−3.46760	−0.254943
$186$	−2.34204	−0.171727
$187$	−3.26035	−0.238421
$188$	0.330836	0.0241287
$189$	21.9288	1.59509
$190$	−3.45429	−0.250600
$191$	0.956853	0.0692355	0.0346177	−	0.999401i	$-0.488979\pi$
$191$	0.956853	0.0692355	0.0346177	+	0.999401i	$0.488979\pi$
$192$	58.9265	4.25265
$193$	−17.7873	−1.28036	−0.640179	−	0.768225i	$-0.721140\pi$
$193$	−17.7873	−1.28036	−0.640179	+	0.768225i	$0.721140\pi$
$194$	18.7437	1.34572
$195$	4.95683	0.354966
$196$	51.0803	3.64859
$197$	23.0438	1.64180	0.820902	−	0.571070i	$-0.193471\pi$
$197$	23.0438	1.64180	0.820902	+	0.571070i	$0.193471\pi$
$198$	13.4483	0.955732
$199$	−18.8993	−1.33974	−0.669868	−	0.742480i	$-0.733649\pi$
$199$	−18.8993	−1.33974	−0.669868	+	0.742480i	$0.733649\pi$
$200$	41.1395	2.90900
$201$	1.58127	0.111534
$202$	−33.8558	−2.38208
$203$	4.08387	0.286631
$204$	−7.22431	−0.505803
$205$	5.04860	0.352610
$206$	−5.47997	−0.381808
$207$	11.8249	0.821890
$208$	−68.2113	−4.72960
$209$	−3.70044	−0.255965
$210$	−14.9218	−1.02970
$211$	4.97360	0.342397	0.171198	−	0.985237i	$-0.445236\pi$
$211$	4.97360	0.342397	0.171198	+	0.985237i	$0.445236\pi$
$212$	70.6363	4.85132
$213$	3.02113	0.207004
$214$	24.7826	1.69411
$215$	12.0845	0.824157
$216$	59.5392	4.05113
$217$	−2.68405	−0.182205
$218$	−18.5477	−1.25621
$219$	−10.0569	−0.679579
$220$	−20.7084	−1.39616
$221$	3.69125	0.248300
$222$	−11.0473	−0.741445
$223$	−8.41244	−0.563339	−0.281669	−	0.959512i	$-0.590888\pi$
$223$	−8.41244	−0.563339	−0.281669	+	0.959512i	$0.590888\pi$
$224$	119.877	8.00964
$225$	5.62450	0.374967
$226$	−0.287608	−0.0191314
$227$	−9.93965	−0.659718	−0.329859	−	0.944030i	$-0.607001\pi$
$227$	−9.93965	−0.659718	−0.329859	+	0.944030i	$0.607001\pi$
$228$	−8.19947	−0.543023
$229$	−1.22137	−0.0807102	−0.0403551	−	0.999185i	$-0.512849\pi$
$229$	−1.22137	−0.0807102	−0.0403551	+	0.999185i	$0.512849\pi$
$230$	−24.4386	−1.61143
$231$	−15.9852	−1.05175
$232$	11.0882	0.727974
$233$	20.2392	1.32591	0.662956	−	0.748658i	$-0.269302\pi$
$233$	20.2392	1.32591	0.662956	+	0.748658i	$0.269302\pi$
$234$	−15.2257	−0.995336
$235$	−0.0614959	−0.00401155
$236$	16.7759	1.09202
$237$	−3.18576	−0.206937
$238$	−11.1120	−0.720282
$239$	22.2542	1.43951	0.719753	−	0.694230i	$-0.244255\pi$
$239$	22.2542	1.43951	0.719753	+	0.694230i	$0.244255\pi$
$240$	−24.8150	−1.60180
$241$	−0.938322	−0.0604427	−0.0302213	−	0.999543i	$-0.509621\pi$
$241$	−0.938322	−0.0604427	−0.0302213	+	0.999543i	$0.509621\pi$
$242$	1.03661	0.0666358
$243$	13.6000	0.872440
$244$	−59.0198	−3.77836
$245$	−9.49484	−0.606603
$246$	16.0841	1.02549
$247$	4.18950	0.266572
$248$	−7.28751	−0.462757
$249$	−6.57567	−0.416716
$250$	−26.8415	−1.69760
$251$	8.51475	0.537446	0.268723	−	0.963217i	$-0.413398\pi$
$251$	8.51475	0.537446	0.268723	+	0.963217i	$0.413398\pi$
$252$	34.1505	2.15128
$253$	−26.1801	−1.64593
$254$	−3.13261	−0.196558
$255$	1.34286	0.0840931
$256$	109.439	6.83994
$257$	16.5579	1.03286	0.516428	−	0.856331i	$-0.327261\pi$
$257$	16.5579	1.03286	0.516428	+	0.856331i	$0.327261\pi$
$258$	38.4995	2.39687
$259$	−12.6605	−0.786686
$260$	23.4453	1.45402
$261$	1.51595	0.0938350
$262$	−53.4546	−3.30243
$263$	7.99093	0.492742	0.246371	−	0.969176i	$-0.420762\pi$
$263$	7.99093	0.492742	0.246371	+	0.969176i	$0.420762\pi$
$264$	−43.4015	−2.67118
$265$	−13.1299	−0.806565
$266$	−12.6119	−0.773284
$267$	−12.6952	−0.776935
$268$	7.47922	0.456866
$269$	29.6434	1.80739	0.903695	−	0.428176i	$-0.140844\pi$
$269$	29.6434	1.80739	0.903695	+	0.428176i	$0.140844\pi$
$270$	−16.8230	−1.02382
$271$	9.51765	0.578156	0.289078	−	0.957306i	$-0.406651\pi$
$271$	9.51765	0.578156	0.289078	+	0.957306i	$0.406651\pi$
$272$	−18.4792	−1.12047
$273$	18.0978	1.09533
$274$	−14.4851	−0.875079
$275$	−12.4525	−0.750913
$276$	−58.0100	−3.49179
$277$	−5.15541	−0.309759	−0.154879	−	0.987933i	$-0.549499\pi$
$277$	−5.15541	−0.309759	−0.154879	+	0.987933i	$0.549499\pi$
$278$	11.0200	0.660938
$279$	−0.996332	−0.0596488
$280$	−46.4307	−2.77477
$281$	−30.7358	−1.83355	−0.916773	−	0.399408i	$-0.869216\pi$
$281$	−30.7358	−1.83355	−0.916773	+	0.399408i	$0.869216\pi$
$282$	−0.195917	−0.0116667
$283$	−23.3022	−1.38517	−0.692585	−	0.721336i	$-0.743528\pi$
$283$	−23.3022	−1.38517	−0.692585	+	0.721336i	$0.743528\pi$
$284$	14.2896	0.847932
$285$	1.52412	0.0902812
$286$	33.7093	1.99327
$287$	18.4329	1.08806
$288$	44.4990	2.62213
$289$	1.00000	0.0588235
$290$	−3.13301	−0.183977
$291$	−8.27021	−0.484808
$292$	−47.5679	−2.78370
$293$	−11.4146	−0.666850	−0.333425	−	0.942777i	$-0.608204\pi$
$293$	−11.4146	−0.666850	−0.333425	+	0.942777i	$0.608204\pi$
$294$	−30.2492	−1.76417
$295$	−3.11832	−0.181555
$296$	−34.3747	−1.99799
$297$	−18.0219	−1.04574
$298$	53.3342	3.08957
$299$	29.6401	1.71413
$300$	−27.5923	−1.59304
$301$	44.1215	2.54312
$302$	−11.0327	−0.634860
$303$	14.9381	0.858169
$304$	−20.9736	−1.20292
$305$	10.9706	0.628177
$306$	−4.12481	−0.235800
$307$	21.7898	1.24361	0.621805	−	0.783172i	$-0.286400\pi$
$307$	21.7898	1.24361	0.621805	+	0.783172i	$0.286400\pi$
$308$	−75.6081	−4.30817
$309$	2.41791	0.137550
$310$	2.05911	0.116950
$311$	−25.2616	−1.43245	−0.716226	−	0.697868i	$-0.754132\pi$
$311$	−25.2616	−1.43245	−0.716226	+	0.697868i	$0.754132\pi$
$312$	49.1376	2.78187
$313$	−5.65005	−0.319360	−0.159680	−	0.987169i	$-0.551046\pi$
$313$	−5.65005	−0.319360	−0.159680	+	0.987169i	$0.551046\pi$
$314$	41.0032	2.31394
$315$	−6.34791	−0.357664
$316$	−15.0683	−0.847658
$317$	15.4510	0.867814	0.433907	−	0.900958i	$-0.357135\pi$
$317$	15.4510	0.867814	0.433907	+	0.900958i	$0.357135\pi$
$318$	−41.8300	−2.34571
$319$	−3.35627	−0.187915
$320$	−51.8079	−2.89615
$321$	−10.9347	−0.610318
$322$	−89.2272	−4.97244
$323$	1.13498	0.0631521
$324$	−14.1081	−0.783785
$325$	14.0982	0.782029
$326$	−63.1726	−3.49880
$327$	8.18372	0.452561
$328$	50.0473	2.76340
$329$	−0.224527	−0.0123786
$330$	12.2633	0.675071
$331$	22.3967	1.23103	0.615517	−	0.788124i	$-0.288947\pi$
$331$	22.3967	1.23103	0.615517	+	0.788124i	$0.288947\pi$
$332$	−31.1022	−1.70696
$333$	−4.69964	−0.257538
$334$	−29.3293	−1.60483
$335$	−1.39024	−0.0759570
$336$	−90.6014	−4.94271
$337$	−5.27920	−0.287576	−0.143788	−	0.989609i	$-0.545928\pi$
$337$	−5.27920	−0.287576	−0.143788	+	0.989609i	$0.545928\pi$
$338$	−1.75156	−0.0952722
$339$	0.126900	0.00689227
$340$	6.35159	0.344463
$341$	2.20585	0.119453
$342$	−4.68159	−0.253151
$343$	−6.89632	−0.372366
$344$	119.795	6.45891
$345$	10.7829	0.580534
$346$	−17.8117	−0.957565
$347$	−11.8084	−0.633910	−0.316955	−	0.948441i	$-0.602660\pi$
$347$	−11.8084	−0.633910	−0.316955	+	0.948441i	$0.602660\pi$
$348$	−7.43685	−0.398657
$349$	28.7365	1.53823	0.769116	−	0.639110i	$-0.220697\pi$
$349$	28.7365	1.53823	0.769116	+	0.639110i	$0.220697\pi$
$350$	−42.4406	−2.26855
$351$	20.4037	1.08907
$352$	−98.5195	−5.25110
$353$	1.00000	0.0532246
$353$	1.00000	0.0532246
$354$	−9.93450	−0.528013
$355$	−2.65616	−0.140974
$356$	−60.0471	−3.18249
$357$	4.90289	0.259488
$358$	36.7251	1.94098
$359$	−21.0653	−1.11178	−0.555891	−	0.831255i	$-0.687623\pi$
$359$	−21.0653	−1.11178	−0.555891	+	0.831255i	$0.687623\pi$
$360$	−17.2353	−0.908380
$361$	−17.7118	−0.932201
$362$	49.4709	2.60013
$363$	−0.457379	−0.0240062
$364$	85.6007	4.48670
$365$	8.84194	0.462808
$366$	34.9508	1.82691
$367$	1.78964	0.0934183	0.0467091	−	0.998909i	$-0.485127\pi$
$367$	1.78964	0.0934183	0.0467091	+	0.998909i	$0.485127\pi$
$368$	−148.385	−7.73509
$369$	6.84236	0.356199
$370$	9.71272	0.504940
$371$	−47.9384	−2.48884
$372$	4.88774	0.253417
$373$	−20.2554	−1.04878	−0.524391	−	0.851477i	$-0.675707\pi$
$373$	−20.2554	−1.04878	−0.524391	+	0.851477i	$0.675707\pi$
$374$	9.13221	0.472216
$375$	11.8432	0.611579
$376$	−0.609616	−0.0314385
$377$	3.79984	0.195702
$378$	−61.4223	−3.15922
$379$	−19.1858	−0.985508	−0.492754	−	0.870169i	$-0.664010\pi$
$379$	−19.1858	−0.985508	−0.492754	+	0.870169i	$0.664010\pi$
$380$	7.20894	0.369811
$381$	1.38219	0.0708118
$382$	−2.68013	−0.137128
$383$	31.8381	1.62685	0.813426	−	0.581668i	$-0.197600\pi$
$383$	31.8381	1.62685	0.813426	+	0.581668i	$0.197600\pi$
$384$	−90.3629	−4.61131
$385$	14.0541	0.716263
$386$	49.8221	2.53588
$387$	16.3781	0.832546
$388$	−39.1172	−1.98588
$389$	0.0769479	0.00390141	0.00195071	−	0.999998i	$-0.499379\pi$
$389$	0.0769479	0.00390141	0.00195071	+	0.999998i	$0.499379\pi$
$390$	−13.8840	−0.703045
$391$	8.02983	0.406086
$392$	−94.1233	−4.75395
$393$	23.5856	1.18973
$394$	−64.5454	−3.25175
$395$	2.80090	0.140929
$396$	−28.0661	−1.41037
$397$	21.3845	1.07326	0.536628	−	0.843819i	$-0.319698\pi$
$397$	21.3845	1.07326	0.536628	+	0.843819i	$0.319698\pi$
$398$	52.9367	2.65348
$399$	5.56469	0.278583
$400$	−70.5787	−3.52894
$401$	−23.0251	−1.14982	−0.574909	−	0.818217i	$-0.694963\pi$
$401$	−23.0251	−1.14982	−0.574909	+	0.818217i	$0.694963\pi$
$402$	−4.42911	−0.220904
$403$	−2.49738	−0.124403
$404$	70.6554	3.51524
$405$	2.62243	0.130309
$406$	−11.4389	−0.567701
$407$	10.4049	0.515750
$408$	13.3119	0.659038
$409$	22.5260	1.11384	0.556918	−	0.830567i	$-0.311984\pi$
$409$	22.5260	1.11384	0.556918	+	0.830567i	$0.311984\pi$
$410$	−14.1411	−0.698378
$411$	6.39122	0.315256
$412$	11.4364	0.563433
$413$	−11.3852	−0.560231
$414$	−33.1215	−1.62783
$415$	5.78130	0.283793
$416$	111.540	5.46870
$417$	−4.86233	−0.238109
$418$	10.3649	0.506964
$419$	35.7560	1.74679	0.873397	−	0.487008i	$-0.161912\pi$
$419$	35.7560	1.74679	0.873397	+	0.487008i	$0.161912\pi$
$420$	31.1411	1.51953
$421$	1.86920	0.0910992	0.0455496	−	0.998962i	$-0.485496\pi$
$421$	1.86920	0.0910992	0.0455496	+	0.998962i	$0.485496\pi$
$422$	−13.9310	−0.678150
$423$	−0.0833453	−0.00405239
$424$	−130.158	−6.32104
$425$	3.81936	0.185266
$426$	−8.46214	−0.409992
$427$	40.0547	1.93838
$428$	−51.7202	−2.49999
$429$	−14.8734	−0.718096
$430$	−33.8486	−1.63232
$431$	−18.9943	−0.914923	−0.457461	−	0.889230i	$-0.651241\pi$
$431$	−18.9943	−0.914923	−0.457461	+	0.889230i	$0.651241\pi$
$432$	−102.145	−4.91447
$433$	14.0952	0.677372	0.338686	−	0.940900i	$-0.390018\pi$
$433$	14.0952	0.677372	0.338686	+	0.940900i	$0.390018\pi$
$434$	7.51800	0.360875
$435$	1.38237	0.0662793
$436$	38.7081	1.85378
$437$	9.11371	0.435968
$438$	28.1691	1.34597
$439$	−32.8500	−1.56784	−0.783922	−	0.620859i	$-0.786784\pi$
$439$	−32.8500	−1.56784	−0.783922	+	0.620859i	$0.786784\pi$
$440$	38.1584	1.81913
$441$	−12.8683	−0.612778
$442$	−10.3391	−0.491783
$443$	−27.0752	−1.28638	−0.643190	−	0.765707i	$-0.722389\pi$
$443$	−27.0752	−1.28638	−0.643190	+	0.765707i	$0.722389\pi$
$444$	23.0552	1.09415
$445$	11.1616	0.529110
$446$	23.5631	1.11575
$447$	−23.5324	−1.11305
$448$	−189.155	−8.93673
$449$	29.8543	1.40891	0.704456	−	0.709748i	$-0.251191\pi$
$449$	29.8543	1.40891	0.704456	+	0.709748i	$0.251191\pi$
$450$	−15.7542	−0.742658
$451$	−15.1488	−0.713329
$452$	0.600224	0.0282322
$453$	4.86791	0.228714
$454$	27.8408	1.30664
$455$	−15.9115	−0.745943
$456$	15.1088	0.707533
$457$	37.9777	1.77652	0.888262	−	0.459338i	$-0.151913\pi$
$457$	37.9777	1.77652	0.888262	+	0.459338i	$0.151913\pi$
$458$	3.42103	0.159854
$459$	5.52758	0.258005
$460$	51.0022	2.37799
$461$	34.3481	1.59975	0.799874	−	0.600167i	$-0.204899\pi$
$461$	34.3481	1.59975	0.799874	+	0.600167i	$0.204899\pi$
$462$	44.7742	2.08309
$463$	−2.70740	−0.125824	−0.0629119	−	0.998019i	$-0.520039\pi$
$463$	−2.70740	−0.125824	−0.0629119	+	0.998019i	$0.520039\pi$
$464$	−19.0228	−0.883113
$465$	−0.908535	−0.0421323
$466$	−56.6897	−2.62610
$467$	−20.2778	−0.938344	−0.469172	−	0.883107i	$-0.655447\pi$
$467$	−20.2778	−0.938344	−0.469172	+	0.883107i	$0.655447\pi$
$468$	31.7754	1.46882
$469$	−5.07589	−0.234383
$470$	0.172249	0.00794527
$471$	−18.0917	−0.833620
$472$	−30.9122	−1.42285
$473$	−36.2607	−1.66727
$474$	8.92327	0.409859
$475$	4.33491	0.198899
$476$	23.1902	1.06292
$477$	−17.7949	−0.814775
$478$	−62.3338	−2.85108
$479$	−8.19879	−0.374612	−0.187306	−	0.982302i	$-0.559976\pi$
$479$	−8.19879	−0.374612	−0.187306	+	0.982302i	$0.559976\pi$
$480$	40.5777	1.85211
$481$	−11.7800	−0.537122
$482$	2.62823	0.119713
$483$	39.3694	1.79137
$484$	−2.16336	−0.0983344
$485$	7.27113	0.330165
$486$	−38.0934	−1.72795
$487$	−29.0037	−1.31428	−0.657141	−	0.753768i	$-0.728234\pi$
$487$	−29.0037	−1.31428	−0.657141	+	0.753768i	$0.728234\pi$
$488$	108.753	4.92302
$489$	27.8734	1.26048
$490$	26.5949	1.20144
$491$	4.05750	0.183112	0.0915562	−	0.995800i	$-0.470816\pi$
$491$	4.05750	0.183112	0.0915562	+	0.995800i	$0.470816\pi$
$492$	−33.5668	−1.51331
$493$	1.02942	0.0463627
$494$	−11.7348	−0.527971
$495$	5.21694	0.234484
$496$	12.5024	0.561375
$497$	−9.69786	−0.435009
$498$	18.4184	0.825346
$499$	13.3239	0.596459	0.298229	−	0.954494i	$-0.403604\pi$
$499$	13.3239	0.596459	0.298229	+	0.954494i	$0.403604\pi$
$500$	56.0169	2.50515
$501$	12.9408	0.578154
$502$	−23.8497	−1.06446
$503$	−13.1590	−0.586730	−0.293365	−	0.956001i	$-0.594775\pi$
$503$	−13.1590	−0.586730	−0.293365	+	0.956001i	$0.594775\pi$
$504$	−62.9275	−2.80301
$505$	−13.1335	−0.584432
$506$	73.3301	3.25992
$507$	0.772834	0.0343227
$508$	6.53762	0.290060
$509$	14.3806	0.637409	0.318705	−	0.947854i	$-0.396752\pi$
$509$	14.3806	0.637409	0.318705	+	0.947854i	$0.396752\pi$
$510$	−3.76133	−0.166555
$511$	32.2827	1.42810
$512$	−160.304	−7.08449
$513$	6.27371	0.276991
$514$	−46.3786	−2.04567
$515$	−2.12581	−0.0936745
$516$	−80.3466	−3.53706
$517$	0.184524	0.00811536
$518$	35.4619	1.55811
$519$	7.85900	0.344972
$520$	−43.2016	−1.89451
$521$	−5.04879	−0.221191	−0.110596	−	0.993865i	$-0.535276\pi$
$521$	−5.04879	−0.221191	−0.110596	+	0.993865i	$0.535276\pi$
$522$	−4.24616	−0.185849
$523$	−28.4338	−1.24333	−0.621663	−	0.783285i	$-0.713542\pi$
$523$	−28.4338	−1.24333	−0.621663	+	0.783285i	$0.713542\pi$
$524$	111.557	4.87340
$525$	18.7259	0.817266
$526$	−22.3825	−0.975923
$527$	−0.676568	−0.0294717
$528$	74.4595	3.24044
$529$	41.4782	1.80340
$530$	36.7767	1.59748
$531$	−4.22625	−0.183404
$532$	26.3204	1.14113
$533$	17.1509	0.742888
$534$	35.5592	1.53880
$535$	9.61378	0.415640
$536$	−13.7816	−0.595275
$537$	−16.2041	−0.699258
$538$	−83.0308	−3.57971
$539$	28.4901	1.22716
$540$	35.1089	1.51085
$541$	4.69287	0.201762	0.100881	−	0.994898i	$-0.467834\pi$
$541$	4.69287	0.201762	0.100881	+	0.994898i	$0.467834\pi$
$542$	−26.6588	−1.14509
$543$	−21.8279	−0.936723
$544$	30.2174	1.29556
$545$	−7.19509	−0.308204
$546$	−50.6917	−2.16941
$547$	−16.9444	−0.724489	−0.362245	−	0.932083i	$-0.617990\pi$
$547$	−16.9444	−0.724489	−0.362245	+	0.932083i	$0.617990\pi$
$548$	30.2298	1.29135
$549$	14.8685	0.634571
$550$	34.8792	1.48726
$551$	1.16837	0.0497743
$552$	106.892	4.54964
$553$	10.2263	0.434868
$554$	14.4402	0.613507
$555$	−4.28551	−0.181910
$556$	−22.9983	−0.975345
$557$	7.03238	0.297971	0.148986	−	0.988839i	$-0.452399\pi$
$557$	7.03238	0.297971	0.148986	+	0.988839i	$0.452399\pi$
$558$	2.79071	0.118140
$559$	41.0530	1.73636
$560$	79.6564	3.36610
$561$	−4.02937	−0.170120
$562$	86.0907	3.63152
$563$	−28.4864	−1.20056	−0.600279	−	0.799791i	$-0.704944\pi$
$563$	−28.4864	−1.20056	−0.600279	+	0.799791i	$0.704944\pi$
$564$	0.408870	0.0172165
$565$	−0.111570	−0.00469379
$566$	65.2691	2.74346
$567$	9.57469	0.402099
$568$	−26.3308	−1.10482
$569$	−2.21738	−0.0929572	−0.0464786	−	0.998919i	$-0.514800\pi$
$569$	−2.21738	−0.0929572	−0.0464786	+	0.998919i	$0.514800\pi$
$570$	−4.26905	−0.178811
$571$	4.28813	0.179453	0.0897263	−	0.995966i	$-0.471401\pi$
$571$	4.28813	0.179453	0.0897263	+	0.995966i	$0.471401\pi$
$572$	−70.3498	−2.94147
$573$	1.18255	0.0494015
$574$	−51.6302	−2.15500
$575$	30.6688	1.27898
$576$	−70.2151	−2.92563
$577$	29.1152	1.21208	0.606040	−	0.795434i	$-0.292757\pi$
$577$	29.1152	1.21208	0.606040	+	0.795434i	$0.292757\pi$
$578$	−2.80099	−0.116506
$579$	−21.9828	−0.913574
$580$	6.53844	0.271494
$581$	21.1080	0.875707
$582$	23.1648	0.960210
$583$	39.3975	1.63168
$584$	87.6511	3.62703
$585$	−5.90642	−0.244201
$586$	31.9722	1.32076
$587$	23.8311	0.983615	0.491808	−	0.870704i	$-0.336336\pi$
$587$	23.8311	0.983615	0.491808	+	0.870704i	$0.336336\pi$
$588$	63.1286	2.60338
$589$	−0.767892	−0.0316404
$590$	8.73437	0.359588
$591$	28.4791	1.17147
$592$	58.9732	2.42378
$593$	−17.4421	−0.716260	−0.358130	−	0.933672i	$-0.616586\pi$
$593$	−17.4421	−0.716260	−0.358130	+	0.933672i	$0.616586\pi$
$594$	50.4791	2.07118
$595$	−4.31060	−0.176717
$596$	−111.306	−4.55927
$597$	−23.3571	−0.955941
$598$	−83.0216	−3.39501
$599$	−29.5360	−1.20681	−0.603405	−	0.797435i	$-0.706190\pi$
$599$	−29.5360	−1.20681	−0.603405	+	0.797435i	$0.706190\pi$
$600$	50.8430	2.07566
$601$	−25.8366	−1.05390	−0.526949	−	0.849897i	$-0.676664\pi$
$601$	−25.8366	−1.05390	−0.526949	+	0.849897i	$0.676664\pi$
$602$	−123.584	−5.03690
$603$	−1.88419	−0.0767302
$604$	23.0247	0.936862
$605$	0.402126	0.0163487
$606$	−41.8413	−1.69969
$607$	12.6508	0.513480	0.256740	−	0.966480i	$-0.417352\pi$
$607$	12.6508	0.513480	0.256740	+	0.966480i	$0.417352\pi$
$608$	34.2962	1.39090
$609$	5.04713	0.204520
$610$	−30.7286	−1.24417
$611$	−0.208911	−0.00845165
$612$	8.60829	0.347969
$613$	41.0528	1.65811	0.829054	−	0.559168i	$-0.188879\pi$
$613$	41.0528	1.65811	0.829054	+	0.559168i	$0.188879\pi$
$614$	−61.0330	−2.46309
$615$	6.23942	0.251598
$616$	139.320	5.61335
$617$	16.5051	0.664468	0.332234	−	0.943197i	$-0.392198\pi$
$617$	16.5051	0.664468	0.332234	+	0.943197i	$0.392198\pi$
$618$	−6.77253	−0.272431
$619$	−1.84972	−0.0743464	−0.0371732	−	0.999309i	$-0.511835\pi$
$619$	−1.84972	−0.0743464	−0.0371732	+	0.999309i	$0.511835\pi$
$620$	−4.29728	−0.172583
$621$	44.3855	1.78113
$622$	70.7574	2.83711
$623$	40.7519	1.63269
$624$	−84.3003	−3.37471
$625$	8.68436	0.347374
$626$	15.8257	0.632523
$627$	−4.57327	−0.182639
$628$	−85.5717	−3.41468
$629$	−3.19133	−0.127247
$630$	17.7804	0.708388
$631$	−44.3479	−1.76546	−0.882732	−	0.469877i	$-0.844298\pi$
$631$	−44.3479	−1.76546	−0.882732	+	0.469877i	$0.844298\pi$
$632$	27.7657	1.10446
$633$	6.14672	0.244310
$634$	−43.2780	−1.71879
$635$	−1.21522	−0.0482244
$636$	87.2973	3.46156
$637$	−32.2555	−1.27801
$638$	9.40087	0.372184
$639$	−3.59989	−0.142409
$640$	79.4466	3.14040
$641$	21.3463	0.843127	0.421564	−	0.906799i	$-0.361481\pi$
$641$	21.3463	0.843127	0.421564	+	0.906799i	$0.361481\pi$
$642$	30.6281	1.20879
$643$	18.7513	0.739480	0.369740	−	0.929135i	$-0.379447\pi$
$643$	18.7513	0.739480	0.369740	+	0.929135i	$0.379447\pi$
$644$	186.213	7.33782
$645$	14.9349	0.588060
$646$	−3.17907	−0.125079
$647$	31.0739	1.22164	0.610820	−	0.791769i	$-0.290840\pi$
$647$	31.0739	1.22164	0.610820	+	0.791769i	$0.290840\pi$
$648$	25.9964	1.02123
$649$	9.35679	0.367286
$650$	−39.4890	−1.54888
$651$	−3.31714	−0.130009
$652$	131.838	5.16318
$653$	−14.1762	−0.554758	−0.277379	−	0.960761i	$-0.589466\pi$
$653$	−14.1762	−0.554758	−0.277379	+	0.960761i	$0.589466\pi$
$654$	−22.9225	−0.896340
$655$	−20.7363	−0.810235
$656$	−85.8610	−3.35231
$657$	11.9835	0.467519
$658$	0.628896	0.0245169
$659$	32.9123	1.28208	0.641040	−	0.767507i	$-0.278503\pi$
$659$	32.9123	1.28208	0.641040	+	0.767507i	$0.278503\pi$
$660$	−25.5929	−0.996203
$661$	5.63159	0.219043	0.109522	−	0.993984i	$-0.465068\pi$
$661$	5.63159	0.219043	0.109522	+	0.993984i	$0.465068\pi$
$662$	−62.7328	−2.43818
$663$	4.56190	0.177170
$664$	57.3106	2.22408
$665$	−4.89245	−0.189721
$666$	13.1636	0.510080
$667$	8.26606	0.320063
$668$	61.2088	2.36824
$669$	−10.3967	−0.401959
$670$	3.89405	0.150440
$671$	−32.9184	−1.27080
$672$	148.153	5.71511
$673$	−24.7137	−0.952644	−0.476322	−	0.879271i	$-0.658030\pi$
$673$	−24.7137	−0.952644	−0.476322	+	0.879271i	$0.658030\pi$
$674$	14.7870	0.569572
$675$	21.1118	0.812595
$676$	3.65542	0.140593
$677$	15.5169	0.596363	0.298181	−	0.954509i	$-0.403620\pi$
$677$	15.5169	0.596363	0.298181	+	0.954509i	$0.403620\pi$
$678$	−0.355446	−0.0136508
$679$	26.5475	1.01880
$680$	−11.7038	−0.448819
$681$	−12.2841	−0.470728
$682$	−6.17856	−0.236589
$683$	15.1324	0.579027	0.289513	−	0.957174i	$-0.406507\pi$
$683$	15.1324	0.579027	0.289513	+	0.957174i	$0.406507\pi$
$684$	9.77026	0.373575
$685$	−5.61914	−0.214696
$686$	19.3165	0.737508
$687$	−1.50945	−0.0575891
$688$	−205.520	−7.83537
$689$	−44.6044	−1.69929
$690$	−30.2029	−1.14980
$691$	−10.8510	−0.412793	−0.206397	−	0.978468i	$-0.566174\pi$
$691$	−10.8510	−0.412793	−0.206397	+	0.978468i	$0.566174\pi$
$692$	37.1723	1.41308
$693$	19.0475	0.723553
$694$	33.0753	1.25552
$695$	4.27494	0.162158
$696$	13.7035	0.519431
$697$	4.64636	0.175994
$698$	−80.4907	−3.04662
$699$	25.0130	0.946078
$700$	88.5716	3.34769
$701$	8.62413	0.325729	0.162864	−	0.986648i	$-0.447927\pi$
$701$	8.62413	0.325729	0.162864	+	0.986648i	$0.447927\pi$
$702$	−57.1505	−2.15701
$703$	−3.62210	−0.136610
$704$	155.454	5.85891
$705$	−0.0760009	−0.00286236
$706$	−2.80099	−0.105417
$707$	−47.9514	−1.80340
$708$	20.7328	0.779188
$709$	−28.0778	−1.05448	−0.527242	−	0.849715i	$-0.676774\pi$
$709$	−28.0778	−1.05448	−0.527242	+	0.849715i	$0.676774\pi$
$710$	7.43988	0.279214
$711$	3.79606	0.142363
$712$	110.646	4.14663
$713$	−5.43272	−0.203457
$714$	−13.7329	−0.513942
$715$	13.0767	0.489039
$716$	−76.6436	−2.86431
$717$	27.5033	1.02713
$718$	59.0035	2.20199
$719$	48.9331	1.82490	0.912448	−	0.409193i	$-0.134190\pi$
$719$	48.9331	1.82490	0.912448	+	0.409193i	$0.134190\pi$
$720$	29.5688	1.10196
$721$	−7.76152	−0.289054
$722$	49.6106	1.84631
$723$	−1.15964	−0.0431276
$724$	−103.243	−3.83701
$725$	3.93173	0.146021
$726$	1.28111	0.0475466
$727$	44.7439	1.65946	0.829729	−	0.558166i	$-0.188495\pi$
$727$	44.7439	1.65946	0.829729	+	0.558166i	$0.188495\pi$
$728$	−157.732	−5.84595
$729$	24.0483	0.890677
$730$	−24.7662	−0.916637
$731$	11.1217	0.411351
$732$	−72.9408	−2.69597
$733$	31.9111	1.17866	0.589332	−	0.807891i	$-0.299391\pi$
$733$	31.9111	1.17866	0.589332	+	0.807891i	$0.299391\pi$
$734$	−5.01275	−0.185024
$735$	−11.7344	−0.432829
$736$	242.641	8.94385
$737$	4.17155	0.153661
$738$	−19.1654	−0.705487
$739$	−53.8269	−1.98005	−0.990026	−	0.140882i	$-0.955006\pi$
$739$	−53.8269	−1.98005	−0.990026	+	0.140882i	$0.955006\pi$
$740$	−20.2700	−0.745140
$741$	5.17768	0.190207
$742$	134.275	4.92939
$743$	−29.1941	−1.07103	−0.535513	−	0.844527i	$-0.679882\pi$
$743$	−29.1941	−1.07103	−0.535513	+	0.844527i	$0.679882\pi$
$744$	−9.00641	−0.330191
$745$	20.6896	0.758009
$746$	56.7350	2.07722
$747$	7.83538	0.286681
$748$	−19.0585	−0.696848
$749$	35.1007	1.28255
$750$	−33.1726	−1.21129
$751$	−45.2612	−1.65161	−0.825803	−	0.563959i	$-0.809278\pi$
$751$	−45.2612	−1.65161	−0.825803	+	0.563959i	$0.809278\pi$
$752$	1.04585	0.0381384
$753$	10.5231	0.383484
$754$	−10.6433	−0.387607
$755$	−4.27985	−0.155760
$756$	128.186	4.66206
$757$	16.0545	0.583512	0.291756	−	0.956493i	$-0.405761\pi$
$757$	16.0545	0.583512	0.291756	+	0.956493i	$0.405761\pi$
$758$	53.7392	1.95190
$759$	−32.3552	−1.17442
$760$	−13.2836	−0.481846
$761$	18.2604	0.661940	0.330970	−	0.943641i	$-0.392624\pi$
$761$	18.2604	0.661940	0.330970	+	0.943641i	$0.392624\pi$
$762$	−3.87150	−0.140250
$763$	−26.2699	−0.951033
$764$	5.59332	0.202359
$765$	−1.60011	−0.0578522
$766$	−89.1782	−3.22214
$767$	−10.5934	−0.382506
$768$	135.252	4.88050
$769$	−8.51815	−0.307172	−0.153586	−	0.988135i	$-0.549082\pi$
$769$	−8.51815	−0.307172	−0.153586	+	0.988135i	$0.549082\pi$
$770$	−39.3653	−1.41863
$771$	20.4634	0.736973
$772$	−103.976	−3.74219
$773$	−37.7900	−1.35921	−0.679606	−	0.733577i	$-0.737849\pi$
$773$	−37.7900	−1.35921	−0.679606	+	0.733577i	$0.737849\pi$
$774$	−45.8749	−1.64894
$775$	−2.58406	−0.0928221
$776$	72.0795	2.58750
$777$	−15.6467	−0.561323
$778$	−0.215530	−0.00772713
$779$	5.27354	0.188944
$780$	28.9753	1.03748
$781$	7.97005	0.285191
$782$	−22.4915	−0.804293
$783$	5.69020	0.203351
$784$	161.478	5.76706
$785$	15.9061	0.567714
$786$	−66.0629	−2.35638
$787$	1.00198	0.0357168	0.0178584	−	0.999841i	$-0.494315\pi$
$787$	1.00198	0.0357168	0.0178584	+	0.999841i	$0.494315\pi$
$788$	134.703	4.79861
$789$	9.87574	0.351586
$790$	−7.84530	−0.279123
$791$	−0.407351	−0.0144837
$792$	51.7161	1.83765
$793$	37.2690	1.32346
$794$	−59.8976	−2.12569
$795$	−16.2269	−0.575508
$796$	−110.476	−3.91573
$797$	−10.0509	−0.356021	−0.178010	−	0.984029i	$-0.556966\pi$
$797$	−10.0509	−0.356021	−0.178010	+	0.984029i	$0.556966\pi$
$798$	−15.5866	−0.551761
$799$	−0.0565963	−0.00200223
$800$	115.411	4.08040
$801$	15.1273	0.534496
$802$	64.4930	2.27733
$803$	−26.5310	−0.936260
$804$	9.24334	0.325987
$805$	−34.6134	−1.21996
$806$	6.99513	0.246393
$807$	36.6354	1.28963
$808$	−130.193	−4.58019
$809$	15.7934	0.555266	0.277633	−	0.960687i	$-0.410450\pi$
$809$	15.7934	0.555266	0.277633	+	0.960687i	$0.410450\pi$
$810$	−7.34538	−0.258091
$811$	21.0943	0.740722	0.370361	−	0.928888i	$-0.379234\pi$
$811$	21.0943	0.740722	0.370361	+	0.928888i	$0.379234\pi$
$812$	23.8724	0.837757
$813$	11.7626	0.412531
$814$	−29.1439	−1.02149
$815$	−24.5062	−0.858414
$816$	−22.8379	−0.799485
$817$	12.6229	0.441620
$818$	−63.0949	−2.20606
$819$	−21.5648	−0.753536
$820$	29.5118	1.03060
$821$	−31.4289	−1.09688	−0.548438	−	0.836191i	$-0.684777\pi$
$821$	−31.4289	−1.09688	−0.548438	+	0.836191i	$0.684777\pi$
$822$	−17.9017	−0.624395
$823$	−47.6686	−1.66162	−0.830812	−	0.556553i	$-0.812123\pi$
$823$	−47.6686	−1.66162	−0.830812	+	0.556553i	$0.812123\pi$
$824$	−21.0734	−0.734127
$825$	−15.3896	−0.535798
$826$	31.8899	1.10959
$827$	46.3213	1.61075	0.805374	−	0.592767i	$-0.201964\pi$
$827$	46.3213	1.61075	0.805374	+	0.592767i	$0.201964\pi$
$828$	69.1231	2.40219
$829$	−47.5185	−1.65038	−0.825192	−	0.564852i	$-0.808933\pi$
$829$	−47.5185	−1.65038	−0.825192	+	0.564852i	$0.808933\pi$
$830$	−16.1933	−0.562079
$831$	−6.37141	−0.221022
$832$	−176.000	−6.10169
$833$	−8.73835	−0.302766
$834$	13.6193	0.471598
$835$	−11.3775	−0.393736
$836$	−21.6311	−0.748126
$837$	−3.73978	−0.129266
$838$	−100.152	−3.45970
$839$	3.89713	0.134544	0.0672719	−	0.997735i	$-0.478570\pi$
$839$	3.89713	0.134544	0.0672719	+	0.997735i	$0.478570\pi$
$840$	−57.3823	−1.97988
$841$	−27.9403	−0.963458
$842$	−5.23560	−0.180431
$843$	−37.9855	−1.30829
$844$	29.0733	1.00075
$845$	−0.679472	−0.0233745
$846$	0.233449	0.00802615
$847$	1.46819	0.0504478
$848$	223.299	7.66812
$849$	−28.7984	−0.988359
$850$	−10.6980	−0.366938
$851$	−25.6258	−0.878442
$852$	17.6601	0.605025
$853$	28.0799	0.961436	0.480718	−	0.876875i	$-0.340376\pi$
$853$	28.0799	0.961436	0.480718	+	0.876875i	$0.340376\pi$
$854$	−112.193	−3.83915
$855$	−1.81610	−0.0621093
$856$	95.3024	3.25737
$857$	−44.6206	−1.52421	−0.762106	−	0.647452i	$-0.775834\pi$
$857$	−44.6206	−1.52421	−0.762106	+	0.647452i	$0.775834\pi$
$858$	41.6603	1.42226
$859$	7.51593	0.256440	0.128220	−	0.991746i	$-0.459074\pi$
$859$	7.51593	0.256440	0.128220	+	0.991746i	$0.459074\pi$
$860$	70.6404	2.40882
$861$	22.7806	0.776361
$862$	53.2028	1.81209
$863$	30.4739	1.03734	0.518672	−	0.854973i	$-0.326427\pi$
$863$	30.4739	1.03734	0.518672	+	0.854973i	$0.326427\pi$
$864$	167.029	5.68245
$865$	−6.90960	−0.234934
$866$	−39.4805	−1.34160
$867$	1.23587	0.0419723
$868$	−15.6897	−0.532543
$869$	−8.40437	−0.285099
$870$	−3.87199	−0.131273
$871$	−4.72287	−0.160028
$872$	−71.3257	−2.41539
$873$	9.85455	0.333526
$874$	−25.5274	−0.863477
$875$	−38.0167	−1.28520
$876$	−58.7877	−1.98625
$877$	13.7662	0.464851	0.232425	−	0.972614i	$-0.425334\pi$
$877$	13.7662	0.464851	0.232425	+	0.972614i	$0.425334\pi$
$878$	92.0124	3.10527
$879$	−14.1070	−0.475817
$880$	−65.4645	−2.20681
$881$	−45.8523	−1.54480	−0.772402	−	0.635134i	$-0.780945\pi$
$881$	−45.8523	−1.54480	−0.772402	+	0.635134i	$0.780945\pi$
$882$	36.0440	1.21367
$883$	−28.7748	−0.968348	−0.484174	−	0.874972i	$-0.660880\pi$
$883$	−28.7748	−0.968348	−0.484174	+	0.874972i	$0.660880\pi$
$884$	21.5773	0.725724
$885$	−3.85383	−0.129545
$886$	75.8372	2.54780
$887$	35.1629	1.18066	0.590328	−	0.807164i	$-0.298999\pi$
$887$	35.1629	1.18066	0.590328	+	0.807164i	$0.298999\pi$
$888$	−42.4827	−1.42562
$889$	−4.43685	−0.148807
$890$	−31.2635	−1.04795
$891$	−7.86883	−0.263616
$892$	−49.1752	−1.64651
$893$	−0.0642358	−0.00214957
$894$	65.9141	2.20450
$895$	14.2466	0.476210
$896$	290.066	9.69043
$897$	36.6313	1.22308
$898$	−83.6215	−2.79049
$899$	−0.696472	−0.0232286
$900$	32.8782	1.09594
$901$	−12.0838	−0.402570
$902$	42.4316	1.41282
$903$	54.5285	1.81459
$904$	−1.10601	−0.0367852
$905$	19.1910	0.637929
$906$	−13.6350	−0.452991
$907$	−2.38274	−0.0791177	−0.0395588	−	0.999217i	$-0.512595\pi$
$907$	−2.38274	−0.0791177	−0.0395588	+	0.999217i	$0.512595\pi$
$908$	−58.1026	−1.92820
$909$	−17.7998	−0.590381
$910$	44.5679	1.47741
$911$	−12.2639	−0.406322	−0.203161	−	0.979145i	$-0.565122\pi$
$911$	−12.2639	−0.406322	−0.203161	+	0.979145i	$0.565122\pi$
$912$	−25.9206	−0.858316
$913$	−17.3473	−0.574112
$914$	−106.375	−3.51858
$915$	13.5583	0.448223
$916$	−7.13954	−0.235897
$917$	−75.7100	−2.50016
$918$	−15.4827	−0.511005
$919$	−35.2020	−1.16121	−0.580604	−	0.814186i	$-0.697183\pi$
$919$	−35.2020	−1.16121	−0.580604	+	0.814186i	$0.697183\pi$
$920$	−93.9793	−3.09841
$921$	26.9294	0.887353
$922$	−96.2085	−3.16846
$923$	−9.02339	−0.297009
$924$	−93.4418	−3.07401
$925$	−12.1888	−0.400767
$926$	7.58341	0.249206
$927$	−2.88111	−0.0946280
$928$	31.1064	1.02112
$929$	5.72804	0.187931	0.0939654	−	0.995575i	$-0.470046\pi$
$929$	5.72804	0.187931	0.0939654	+	0.995575i	$0.470046\pi$
$930$	2.54480	0.0834472
$931$	−9.91787	−0.325045
$932$	118.309	3.87533
$933$	−31.2200	−1.02210
$934$	56.7978	1.85848
$935$	3.54261	0.115856
$936$	−58.5510	−1.91380
$937$	−36.6452	−1.19715	−0.598573	−	0.801068i	$-0.704265\pi$
$937$	−36.6452	−1.19715	−0.598573	+	0.801068i	$0.704265\pi$
$938$	14.2175	0.464218
$939$	−6.98272	−0.227873
$940$	−0.359476	−0.0117248
$941$	−51.6842	−1.68486	−0.842429	−	0.538808i	$-0.818875\pi$
$941$	−51.6842	−1.68486	−0.842429	+	0.538808i	$0.818875\pi$
$942$	50.6745	1.65107
$943$	37.3095	1.21496
$944$	53.0329	1.72607
$945$	−23.8272	−0.775099
$946$	101.566	3.30219
$947$	39.9617	1.29858	0.649290	−	0.760541i	$-0.275066\pi$
$947$	39.9617	1.29858	0.649290	+	0.760541i	$0.275066\pi$
$948$	−18.6225	−0.604829
$949$	30.0375	0.975057
$950$	−12.1420	−0.393939
$951$	19.0954	0.619211
$952$	−42.7314	−1.38493
$953$	−27.2901	−0.884013	−0.442007	−	0.897012i	$-0.645733\pi$
$953$	−27.2901	−0.884013	−0.442007	+	0.897012i	$0.645733\pi$
$954$	49.8434	1.61374
$955$	−1.03969	−0.0336435
$956$	130.088	4.20734
$957$	−4.14791	−0.134083
$958$	22.9647	0.741956
$959$	−20.5159	−0.662494
$960$	−64.0278	−2.06649
$961$	−30.5423	−0.985234
$962$	32.9956	1.06382
$963$	13.0295	0.419871
$964$	−5.48499	−0.176660
$965$	19.3272	0.622164
$966$	−110.273	−3.54798
$967$	−48.1494	−1.54838	−0.774189	−	0.632954i	$-0.781842\pi$
$967$	−48.1494	−1.54838	−0.774189	+	0.632954i	$0.781842\pi$
$968$	3.98632	0.128125
$969$	1.40269	0.0450609
$970$	−20.3664	−0.653924
$971$	31.3319	1.00549	0.502744	−	0.864435i	$-0.332324\pi$
$971$	31.3319	1.00549	0.502744	+	0.864435i	$0.332324\pi$
$972$	79.4992	2.54994
$973$	15.6081	0.500374
$974$	81.2389	2.60306
$975$	17.4236	0.558001
$976$	−186.576	−5.97216
$977$	−45.2133	−1.44650	−0.723252	−	0.690585i	$-0.757353\pi$
$977$	−45.2133	−1.44650	−0.723252	+	0.690585i	$0.757353\pi$
$978$	−78.0730	−2.49650
$979$	−33.4913	−1.07039
$980$	−55.5024	−1.77296
$981$	−9.75149	−0.311341
$982$	−11.3650	−0.362672
$983$	6.05395	0.193091	0.0965455	−	0.995329i	$-0.469221\pi$
$983$	6.05395	0.193091	0.0965455	+	0.995329i	$0.469221\pi$
$984$	61.8520	1.97177
$985$	−25.0387	−0.797800
$986$	−2.88339	−0.0918259
$987$	−0.277486	−0.00883246
$988$	24.4899	0.779127
$989$	89.3053	2.83974
$990$	−14.6126	−0.464418
$991$	19.9578	0.633981	0.316991	−	0.948429i	$-0.397328\pi$
$991$	19.9578	0.633981	0.316991	+	0.948429i	$0.397328\pi$
$992$	−20.4441	−0.649101
$993$	27.6794	0.878378
$994$	27.1636	0.861577
$995$	20.5354	0.651017
$996$	−38.4383	−1.21796
$997$	51.4394	1.62910	0.814551	−	0.580092i	$-0.196984\pi$
$997$	51.4394	1.62910	0.814551	+	0.580092i	$0.196984\pi$
$998$	−37.3200	−1.18134
$999$	−17.6403	−0.558115

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6001.2.a.c.1.1	✓	121

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6001.2.a.c.1.1	✓	121	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:	\( N \)	\(=\)	\( 6001 = 17 \cdot 353 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6001.a (trivial)

\(f(q)\)	\(=\)	\(q-2.80099 q^{2} +1.23587 q^{3} +5.84553 q^{4} -1.08657 q^{5} -3.46165 q^{6} -3.96716 q^{7} -10.7713 q^{8} -1.47263 q^{9} +O(q^{10})\)	\(q-2.80099 q^{2} +1.23587 q^{3} +5.84553 q^{4} -1.08657 q^{5} -3.46165 q^{6} -3.96716 q^{7} -10.7713 q^{8} -1.47263 q^{9} +3.04347 q^{10} +3.26035 q^{11} +7.22431 q^{12} -3.69125 q^{13} +11.1120 q^{14} -1.34286 q^{15} +18.4792 q^{16} -1.00000 q^{17} +4.12481 q^{18} -1.13498 q^{19} -6.35159 q^{20} -4.90289 q^{21} -9.13221 q^{22} -8.02983 q^{23} -13.3119 q^{24} -3.81936 q^{25} +10.3391 q^{26} -5.52758 q^{27} -23.1902 q^{28} -1.02942 q^{29} +3.76133 q^{30} +0.676568 q^{31} -30.2174 q^{32} +4.02937 q^{33} +2.80099 q^{34} +4.31060 q^{35} -8.60829 q^{36} +3.19133 q^{37} +3.17907 q^{38} -4.56190 q^{39} +11.7038 q^{40} -4.64636 q^{41} +13.7329 q^{42} -11.1217 q^{43} +19.0585 q^{44} +1.60011 q^{45} +22.4915 q^{46} +0.0565963 q^{47} +22.8379 q^{48} +8.73835 q^{49} +10.6980 q^{50} -1.23587 q^{51} -21.5773 q^{52} +12.0838 q^{53} +15.4827 q^{54} -3.54261 q^{55} +42.7314 q^{56} -1.40269 q^{57} +2.88339 q^{58} +2.86987 q^{59} -7.84973 q^{60} -10.0966 q^{61} -1.89506 q^{62} +5.84215 q^{63} +47.6802 q^{64} +4.01081 q^{65} -11.2862 q^{66} +1.27948 q^{67} -5.84553 q^{68} -9.92382 q^{69} -12.0739 q^{70} +2.44454 q^{71} +15.8621 q^{72} -8.13747 q^{73} -8.93887 q^{74} -4.72023 q^{75} -6.63458 q^{76} -12.9343 q^{77} +12.7778 q^{78} -2.57775 q^{79} -20.0790 q^{80} -2.41349 q^{81} +13.0144 q^{82} -5.32068 q^{83} -28.6600 q^{84} +1.08657 q^{85} +31.1517 q^{86} -1.27223 q^{87} -35.1182 q^{88} -10.2723 q^{89} -4.48190 q^{90} +14.6438 q^{91} -46.9386 q^{92} +0.836149 q^{93} -0.158526 q^{94} +1.23324 q^{95} -37.3448 q^{96} -6.69182 q^{97} -24.4760 q^{98} -4.80129 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 121 q + 9 q^{2} + 13 q^{3} + 127 q^{4} + 21 q^{5} + 19 q^{6} - 13 q^{7} + 24 q^{8} + 134 q^{9}+O(q^{10}) \) 121 * q + 9 * q^2 + 13 * q^3 + 127 * q^4 + 21 * q^5 + 19 * q^6 - 13 * q^7 + 24 * q^8 + 134 * q^9	\( 121 q + 9 q^{2} + 13 q^{3} + 127 q^{4} + 21 q^{5} + 19 q^{6} - 13 q^{7} + 24 q^{8} + 134 q^{9} - q^{10} + 40 q^{11} + 41 q^{12} + 14 q^{13} + 32 q^{14} + 49 q^{15} + 135 q^{16} - 121 q^{17} + 28 q^{18} + 34 q^{19} + 64 q^{20} + 34 q^{21} - 18 q^{22} + 37 q^{23} + 54 q^{24} + 128 q^{25} + 91 q^{26} + 55 q^{27} - 28 q^{28} + 45 q^{29} + 30 q^{30} + 67 q^{31} + 47 q^{32} + 40 q^{33} - 9 q^{34} + 59 q^{35} + 138 q^{36} - 16 q^{37} + 30 q^{38} + 37 q^{39} + 14 q^{40} + 89 q^{41} + 33 q^{42} + 16 q^{43} + 90 q^{44} + 83 q^{45} - 9 q^{46} + 135 q^{47} + 96 q^{48} + 128 q^{49} + 71 q^{50} - 13 q^{51} + 47 q^{52} + 52 q^{53} + 90 q^{54} + 93 q^{55} + 69 q^{56} - 4 q^{57} + 5 q^{58} + 170 q^{59} + 78 q^{60} - 2 q^{61} + 46 q^{62} - 10 q^{63} + 182 q^{64} + 50 q^{65} + 68 q^{66} + 46 q^{67} - 127 q^{68} + 97 q^{69} + 46 q^{70} + 191 q^{71} + 57 q^{72} - 12 q^{73} + 68 q^{74} + 86 q^{75} + 108 q^{76} + 62 q^{77} - 10 q^{78} + 130 q^{80} + 149 q^{81} + 14 q^{82} + 83 q^{83} + 126 q^{84} - 21 q^{85} + 132 q^{86} + 50 q^{87} - 42 q^{88} + 144 q^{89} + 9 q^{90} + 13 q^{91} + 50 q^{92} + 43 q^{93} + 41 q^{94} + 82 q^{95} + 110 q^{96} - 3 q^{97} + 36 q^{98} + 89 q^{99}+O(q^{100}) \) 121 * q + 9 * q^2 + 13 * q^3 + 127 * q^4 + 21 * q^5 + 19 * q^6 - 13 * q^7 + 24 * q^8 + 134 * q^9 - q^10 + 40 * q^11 + 41 * q^12 + 14 * q^13 + 32 * q^14 + 49 * q^15 + 135 * q^16 - 121 * q^17 + 28 * q^18 + 34 * q^19 + 64 * q^20 + 34 * q^21 - 18 * q^22 + 37 * q^23 + 54 * q^24 + 128 * q^25 + 91 * q^26 + 55 * q^27 - 28 * q^28 + 45 * q^29 + 30 * q^30 + 67 * q^31 + 47 * q^32 + 40 * q^33 - 9 * q^34 + 59 * q^35 + 138 * q^36 - 16 * q^37 + 30 * q^38 + 37 * q^39 + 14 * q^40 + 89 * q^41 + 33 * q^42 + 16 * q^43 + 90 * q^44 + 83 * q^45 - 9 * q^46 + 135 * q^47 + 96 * q^48 + 128 * q^49 + 71 * q^50 - 13 * q^51 + 47 * q^52 + 52 * q^53 + 90 * q^54 + 93 * q^55 + 69 * q^56 - 4 * q^57 + 5 * q^58 + 170 * q^59 + 78 * q^60 - 2 * q^61 + 46 * q^62 - 10 * q^63 + 182 * q^64 + 50 * q^65 + 68 * q^66 + 46 * q^67 - 127 * q^68 + 97 * q^69 + 46 * q^70 + 191 * q^71 + 57 * q^72 - 12 * q^73 + 68 * q^74 + 86 * q^75 + 108 * q^76 + 62 * q^77 - 10 * q^78 + 130 * q^80 + 149 * q^81 + 14 * q^82 + 83 * q^83 + 126 * q^84 - 21 * q^85 + 132 * q^86 + 50 * q^87 - 42 * q^88 + 144 * q^89 + 9 * q^90 + 13 * q^91 + 50 * q^92 + 43 * q^93 + 41 * q^94 + 82 * q^95 + 110 * q^96 - 3 * q^97 + 36 * q^98 + 89 * q^99

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