LMFDB - Embedded newform 6001.2.a.c.1.8

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			1.8
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)

$f(q)$	$=$	$q-2.54984 q^{2} +3.38084 q^{3} +4.50169 q^{4} -1.07763 q^{5} -8.62059 q^{6} +1.13594 q^{7} -6.37892 q^{8} +8.43005 q^{9} +O(q^{10})$	\(q-2.54984 q^{2} +3.38084 q^{3} +4.50169 q^{4} -1.07763 q^{5} -8.62059 q^{6} +1.13594 q^{7} -6.37892 q^{8} +8.43005 q^{9} +2.74778 q^{10} -1.43464 q^{11} +15.2195 q^{12} -4.47634 q^{13} -2.89646 q^{14} -3.64328 q^{15} +7.26184 q^{16} -1.00000 q^{17} -21.4953 q^{18} -0.556760 q^{19} -4.85115 q^{20} +3.84042 q^{21} +3.65811 q^{22} -0.349457 q^{23} -21.5661 q^{24} -3.83872 q^{25} +11.4140 q^{26} +18.3581 q^{27} +5.11364 q^{28} +2.30924 q^{29} +9.28980 q^{30} +9.92024 q^{31} -5.75871 q^{32} -4.85028 q^{33} +2.54984 q^{34} -1.22412 q^{35} +37.9495 q^{36} -12.0180 q^{37} +1.41965 q^{38} -15.1338 q^{39} +6.87410 q^{40} +7.27393 q^{41} -9.79246 q^{42} -9.93059 q^{43} -6.45831 q^{44} -9.08446 q^{45} +0.891060 q^{46} +11.2886 q^{47} +24.5511 q^{48} -5.70965 q^{49} +9.78812 q^{50} -3.38084 q^{51} -20.1511 q^{52} +4.08070 q^{53} -46.8102 q^{54} +1.54601 q^{55} -7.24605 q^{56} -1.88231 q^{57} -5.88819 q^{58} +9.03418 q^{59} -16.4009 q^{60} +5.66397 q^{61} -25.2950 q^{62} +9.57601 q^{63} +0.160120 q^{64} +4.82383 q^{65} +12.3675 q^{66} +5.13364 q^{67} -4.50169 q^{68} -1.18146 q^{69} +3.12131 q^{70} +14.4112 q^{71} -53.7746 q^{72} +12.7036 q^{73} +30.6439 q^{74} -12.9781 q^{75} -2.50636 q^{76} -1.62966 q^{77} +38.5887 q^{78} +11.6038 q^{79} -7.82557 q^{80} +36.7756 q^{81} -18.5474 q^{82} -0.850452 q^{83} +17.2884 q^{84} +1.07763 q^{85} +25.3214 q^{86} +7.80715 q^{87} +9.15145 q^{88} -5.05516 q^{89} +23.1639 q^{90} -5.08484 q^{91} -1.57315 q^{92} +33.5387 q^{93} -28.7842 q^{94} +0.599980 q^{95} -19.4693 q^{96} +1.82769 q^{97} +14.5587 q^{98} -12.0941 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.54984	−1.80301	−0.901505	−	0.432769i	$-0.857537\pi$
$2$	−2.54984	−1.80301	−0.901505	+	0.432769i	$0.857537\pi$
$3$	3.38084	1.95193	0.975963	−	0.217936i	$-0.0699324\pi$
$3$	3.38084	1.95193	0.975963	+	0.217936i	$0.0699324\pi$
$4$	4.50169	2.25085
$5$	−1.07763	−0.481930	−0.240965	−	0.970534i	$-0.577464\pi$
$5$	−1.07763	−0.481930	−0.240965	+	0.970534i	$0.577464\pi$
$6$	−8.62059	−3.51934
$7$	1.13594	0.429344	0.214672	−	0.976686i	$-0.431132\pi$
$7$	1.13594	0.429344	0.214672	+	0.976686i	$0.431132\pi$
$8$	−6.37892	−2.25529
$9$	8.43005	2.81002
$10$	2.74778	0.868925
$11$	−1.43464	−0.432560	−0.216280	−	0.976331i	$-0.569392\pi$
$11$	−1.43464	−0.432560	−0.216280	+	0.976331i	$0.569392\pi$
$12$	15.2195	4.39348
$13$	−4.47634	−1.24151	−0.620757	−	0.784003i	$-0.713174\pi$
$13$	−4.47634	−1.24151	−0.620757	+	0.784003i	$0.713174\pi$
$14$	−2.89646	−0.774112
$15$	−3.64328	−0.940692
$16$	7.26184	1.81546
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−21.4953	−5.06649
$19$	−0.556760	−0.127730	−0.0638648	−	0.997959i	$-0.520343\pi$
$19$	−0.556760	−0.127730	−0.0638648	+	0.997959i	$0.520343\pi$
$20$	−4.85115	−1.08475
$21$	3.84042	0.838048
$22$	3.65811	0.779911
$23$	−0.349457	−0.0728669	−0.0364334	−	0.999336i	$-0.511600\pi$
$23$	−0.349457	−0.0728669	−0.0364334	+	0.999336i	$0.511600\pi$
$24$	−21.5661	−4.40215
$25$	−3.83872	−0.767743
$26$	11.4140	2.23846
$27$	18.3581	3.53302
$28$	5.11364	0.966387
$29$	2.30924	0.428815	0.214407	−	0.976744i	$-0.431218\pi$
$29$	2.30924	0.428815	0.214407	+	0.976744i	$0.431218\pi$
$30$	9.28980	1.69608
$31$	9.92024	1.78173	0.890864	−	0.454271i	$-0.150100\pi$
$31$	9.92024	1.78173	0.890864	+	0.454271i	$0.150100\pi$
$32$	−5.75871	−1.01801
$33$	−4.85028	−0.844326
$34$	2.54984	0.437294
$35$	−1.22412	−0.206914
$36$	37.9495	6.32491
$37$	−12.0180	−1.97574	−0.987871	−	0.155277i	$-0.950373\pi$
$37$	−12.0180	−1.97574	−0.987871	+	0.155277i	$0.950373\pi$
$38$	1.41965	0.230298
$39$	−15.1338	−2.42334
$40$	6.87410	1.08689
$41$	7.27393	1.13600	0.567999	−	0.823030i	$-0.307718\pi$
$41$	7.27393	1.13600	0.567999	+	0.823030i	$0.307718\pi$
$42$	−9.79246	−1.51101
$43$	−9.93059	−1.51440	−0.757200	−	0.653183i	$-0.773433\pi$
$43$	−9.93059	−1.51440	−0.757200	+	0.653183i	$0.773433\pi$
$44$	−6.45831	−0.973627
$45$	−9.08446	−1.35423
$46$	0.891060	0.131380
$47$	11.2886	1.64661	0.823306	−	0.567597i	$-0.192127\pi$
$47$	11.2886	1.64661	0.823306	+	0.567597i	$0.192127\pi$
$48$	24.5511	3.54364
$49$	−5.70965	−0.815664
$50$	9.78812	1.38425
$51$	−3.38084	−0.473412
$52$	−20.1511	−2.79445
$53$	4.08070	0.560528	0.280264	−	0.959923i	$-0.409578\pi$
$53$	4.08070	0.560528	0.280264	+	0.959923i	$0.409578\pi$
$54$	−46.8102	−6.37007
$55$	1.54601	0.208464
$56$	−7.24605	−0.968294
$57$	−1.88231	−0.249319
$58$	−5.88819	−0.773157
$59$	9.03418	1.17615	0.588075	−	0.808806i	$-0.299886\pi$
$59$	9.03418	1.17615	0.588075	+	0.808806i	$0.299886\pi$
$60$	−16.4009	−2.11735
$61$	5.66397	0.725197	0.362599	−	0.931945i	$-0.381890\pi$
$61$	5.66397	0.725197	0.362599	+	0.931945i	$0.381890\pi$
$62$	−25.2950	−3.21247
$63$	9.57601	1.20646
$64$	0.160120	0.0200150
$65$	4.82383	0.598322
$66$	12.3675	1.52233
$67$	5.13364	0.627174	0.313587	−	0.949560i	$-0.398469\pi$
$67$	5.13364	0.627174	0.313587	+	0.949560i	$0.398469\pi$
$68$	−4.50169	−0.545910
$69$	−1.18146	−0.142231
$70$	3.12131	0.373068
$71$	14.4112	1.71029	0.855146	−	0.518387i	$-0.173467\pi$
$71$	14.4112	1.71029	0.855146	+	0.518387i	$0.173467\pi$
$72$	−53.7746	−6.33739
$73$	12.7036	1.48684	0.743419	−	0.668826i	$-0.233203\pi$
$73$	12.7036	1.48684	0.743419	+	0.668826i	$0.233203\pi$
$74$	30.6439	3.56228
$75$	−12.9781	−1.49858
$76$	−2.50636	−0.287499
$77$	−1.62966	−0.185717
$78$	38.5887	4.36931
$79$	11.6038	1.30553	0.652767	−	0.757559i	$-0.273608\pi$
$79$	11.6038	1.30553	0.652767	+	0.757559i	$0.273608\pi$
$80$	−7.82557	−0.874925
$81$	36.7756	4.08617
$82$	−18.5474	−2.04821
$83$	−0.850452	−0.0933492	−0.0466746	−	0.998910i	$-0.514862\pi$
$83$	−0.850452	−0.0933492	−0.0466746	+	0.998910i	$0.514862\pi$
$84$	17.2884	1.88632
$85$	1.07763	0.116885
$86$	25.3214	2.73048
$87$	7.80715	0.837015
$88$	9.15145	0.975548
$89$	−5.05516	−0.535846	−0.267923	−	0.963440i	$-0.586337\pi$
$89$	−5.05516	−0.535846	−0.267923	+	0.963440i	$0.586337\pi$
$90$	23.1639	2.44169
$91$	−5.08484	−0.533036
$92$	−1.57315	−0.164012
$93$	33.5387	3.47780
$94$	−28.7842	−2.96886
$95$	0.599980	0.0615567
$96$	−19.4693	−1.98707
$97$	1.82769	0.185574	0.0927868	−	0.995686i	$-0.470422\pi$
$97$	1.82769	0.185574	0.0927868	+	0.995686i	$0.470422\pi$
$98$	14.5587	1.47065
$99$	−12.0941	−1.21550
$100$	−17.2807	−1.72807
$101$	1.60780	0.159982	0.0799911	−	0.996796i	$-0.474511\pi$
$101$	1.60780	0.159982	0.0799911	+	0.996796i	$0.474511\pi$
$102$	8.62059	0.853566
$103$	−9.18335	−0.904863	−0.452431	−	0.891799i	$-0.649443\pi$
$103$	−9.18335	−0.904863	−0.452431	+	0.891799i	$0.649443\pi$
$104$	28.5542	2.79997
$105$	−4.13854	−0.403880
$106$	−10.4051	−1.01064
$107$	−6.39113	−0.617854	−0.308927	−	0.951086i	$-0.599970\pi$
$107$	−6.39113	−0.617854	−0.308927	+	0.951086i	$0.599970\pi$
$108$	82.6425	7.95228
$109$	−0.0766268	−0.00733952	−0.00366976	−	0.999993i	$-0.501168\pi$
$109$	−0.0766268	−0.00733952	−0.00366976	+	0.999993i	$0.501168\pi$
$110$	−3.94208	−0.375862
$111$	−40.6308	−3.85650
$112$	8.24900	0.779457
$113$	9.79668	0.921594	0.460797	−	0.887506i	$-0.347564\pi$
$113$	9.79668	0.921594	0.460797	+	0.887506i	$0.347564\pi$
$114$	4.79960	0.449524
$115$	0.376585	0.0351167
$116$	10.3955	0.965196
$117$	−37.7358	−3.48867
$118$	−23.0357	−2.12061
$119$	−1.13594	−0.104131
$120$	23.2402	2.12153
$121$	−8.94181	−0.812892
$122$	−14.4422	−1.30754
$123$	24.5920	2.21738
$124$	44.6579	4.01039
$125$	9.52485	0.851929
$126$	−24.4173	−2.17527
$127$	0.523843	0.0464835	0.0232418	−	0.999730i	$-0.492601\pi$
$127$	0.523843	0.0464835	0.0232418	+	0.999730i	$0.492601\pi$
$128$	11.1091	0.981919
$129$	−33.5737	−2.95600
$130$	−12.3000	−1.07878
$131$	13.9428	1.21819	0.609093	−	0.793099i	$-0.291533\pi$
$131$	13.9428	1.21819	0.609093	+	0.793099i	$0.291533\pi$
$132$	−21.8345	−1.90045
$133$	−0.632445	−0.0548399
$134$	−13.0900	−1.13080
$135$	−19.7832	−1.70267
$136$	6.37892	0.546988
$137$	19.4223	1.65936	0.829678	−	0.558243i	$-0.188524\pi$
$137$	19.4223	1.65936	0.829678	+	0.558243i	$0.188524\pi$
$138$	3.01253	0.256443
$139$	0.413253	0.0350517	0.0175258	−	0.999846i	$-0.494421\pi$
$139$	0.413253	0.0350517	0.0175258	+	0.999846i	$0.494421\pi$
$140$	−5.51060	−0.465731
$141$	38.1649	3.21407
$142$	−36.7462	−3.08367
$143$	6.42194	0.537029
$144$	61.2177	5.10147
$145$	−2.48850	−0.206659
$146$	−32.3920	−2.68079
$147$	−19.3034	−1.59212
$148$	−54.1012	−4.44709
$149$	22.6854	1.85846	0.929232	−	0.369497i	$-0.120470\pi$
$149$	22.6854	1.85846	0.929232	+	0.369497i	$0.120470\pi$
$150$	33.0920	2.70195
$151$	16.1891	1.31745	0.658724	−	0.752385i	$-0.271096\pi$
$151$	16.1891	1.31745	0.658724	+	0.752385i	$0.271096\pi$
$152$	3.55153	0.288067
$153$	−8.43005	−0.681529
$154$	4.15538	0.334850
$155$	−10.6903	−0.858668
$156$	−68.1275	−5.45457
$157$	−4.18994	−0.334394	−0.167197	−	0.985924i	$-0.553472\pi$
$157$	−4.18994	−0.334394	−0.167197	+	0.985924i	$0.553472\pi$
$158$	−29.5880	−2.35389
$159$	13.7962	1.09411
$160$	6.20575	0.490608
$161$	−0.396962	−0.0312850
$162$	−93.7718	−7.36741
$163$	10.3756	0.812677	0.406338	−	0.913723i	$-0.366805\pi$
$163$	10.3756	0.812677	0.406338	+	0.913723i	$0.366805\pi$
$164$	32.7450	2.55695
$165$	5.22680	0.406906
$166$	2.16852	0.168310
$167$	−25.3306	−1.96014	−0.980069	−	0.198658i	$-0.936342\pi$
$167$	−25.3306	−1.96014	−0.980069	+	0.198658i	$0.936342\pi$
$168$	−24.4977	−1.89004
$169$	7.03761	0.541355
$170$	−2.74778	−0.210745
$171$	−4.69351	−0.358922
$172$	−44.7044	−3.40868
$173$	−21.3160	−1.62062	−0.810312	−	0.585999i	$-0.800702\pi$
$173$	−21.3160	−1.62062	−0.810312	+	0.585999i	$0.800702\pi$
$174$	−19.9070	−1.50915
$175$	−4.36054	−0.329626
$176$	−10.4181	−0.785296
$177$	30.5431	2.29576
$178$	12.8899	0.966135
$179$	−5.95303	−0.444951	−0.222475	−	0.974938i	$-0.571414\pi$
$179$	−5.95303	−0.444951	−0.222475	+	0.974938i	$0.571414\pi$
$180$	−40.8954	−3.04816
$181$	24.5511	1.82487	0.912434	−	0.409225i	$-0.134201\pi$
$181$	24.5511	1.82487	0.912434	+	0.409225i	$0.134201\pi$
$182$	12.9655	0.961070
$183$	19.1490	1.41553
$184$	2.22916	0.164336
$185$	12.9509	0.952169
$186$	−85.5183	−6.27051
$187$	1.43464	0.104911
$188$	50.8178	3.70627
$189$	20.8537	1.51688
$190$	−1.52986	−0.110987
$191$	16.1599	1.16929	0.584645	−	0.811290i	$-0.301234\pi$
$191$	16.1599	1.16929	0.584645	+	0.811290i	$0.301234\pi$
$192$	0.541338	0.0390677
$193$	−11.3641	−0.818009	−0.409004	−	0.912532i	$-0.634124\pi$
$193$	−11.3641	−0.818009	−0.409004	+	0.912532i	$0.634124\pi$
$194$	−4.66032	−0.334591
$195$	16.3086	1.16788
$196$	−25.7031	−1.83593
$197$	14.2686	1.01659	0.508297	−	0.861182i	$-0.330275\pi$
$197$	14.2686	1.01659	0.508297	+	0.861182i	$0.330275\pi$
$198$	30.8380	2.19156
$199$	13.0134	0.922498	0.461249	−	0.887271i	$-0.347402\pi$
$199$	13.0134	0.922498	0.461249	+	0.887271i	$0.347402\pi$
$200$	24.4869	1.73148
$201$	17.3560	1.22420
$202$	−4.09964	−0.288449
$203$	2.62315	0.184109
$204$	−15.2195	−1.06558
$205$	−7.83859	−0.547471
$206$	23.4161	1.63148
$207$	−2.94594	−0.204757
$208$	−32.5065	−2.25392
$209$	0.798751	0.0552507
$210$	10.5526	0.728201
$211$	−25.0533	−1.72474	−0.862369	−	0.506280i	$-0.831020\pi$
$211$	−25.0533	−1.72474	−0.862369	+	0.506280i	$0.831020\pi$
$212$	18.3701	1.26166
$213$	48.7218	3.33836
$214$	16.2964	1.11400
$215$	10.7015	0.729835
$216$	−117.105	−7.96797
$217$	11.2688	0.764974
$218$	0.195386	0.0132332
$219$	42.9486	2.90220
$220$	6.95966	0.469220
$221$	4.47634	0.301111
$222$	103.602	6.95331
$223$	3.03618	0.203318	0.101659	−	0.994819i	$-0.467585\pi$
$223$	3.03618	0.203318	0.101659	+	0.994819i	$0.467585\pi$
$224$	−6.54154	−0.437075
$225$	−32.3606	−2.15737
$226$	−24.9800	−1.66164
$227$	−5.51771	−0.366223	−0.183112	−	0.983092i	$-0.558617\pi$
$227$	−5.51771	−0.366223	−0.183112	+	0.983092i	$0.558617\pi$
$228$	−8.47360	−0.561178
$229$	−7.06509	−0.466874	−0.233437	−	0.972372i	$-0.574997\pi$
$229$	−7.06509	−0.466874	−0.233437	+	0.972372i	$0.574997\pi$
$230$	−0.960232	−0.0633158
$231$	−5.50962	−0.362506
$232$	−14.7304	−0.967100
$233$	18.6798	1.22375	0.611876	−	0.790954i	$-0.290415\pi$
$233$	18.6798	1.22375	0.611876	+	0.790954i	$0.290415\pi$
$234$	96.2202	6.29011
$235$	−12.1649	−0.793552
$236$	40.6691	2.64733
$237$	39.2307	2.54831
$238$	2.89646	0.187750
$239$	0.0929059	0.00600959	0.00300479	−	0.999995i	$-0.499044\pi$
$239$	0.0929059	0.00600959	0.00300479	+	0.999995i	$0.499044\pi$
$240$	−26.4569	−1.70779
$241$	24.9195	1.60521	0.802603	−	0.596514i	$-0.203448\pi$
$241$	24.9195	1.60521	0.802603	+	0.596514i	$0.203448\pi$
$242$	22.8002	1.46565
$243$	69.2578	4.44289
$244$	25.4975	1.63231
$245$	6.15288	0.393093
$246$	−62.7056	−3.99796
$247$	2.49225	0.158578
$248$	−63.2804	−4.01831
$249$	−2.87524	−0.182211
$250$	−24.2869	−1.53604
$251$	−4.41470	−0.278653	−0.139327	−	0.990246i	$-0.544494\pi$
$251$	−4.41470	−0.278653	−0.139327	+	0.990246i	$0.544494\pi$
$252$	43.1082	2.71556
$253$	0.501345	0.0315193
$254$	−1.33572	−0.0838103
$255$	3.64328	0.228151
$256$	−28.6468	−1.79042
$257$	18.4184	1.14891	0.574454	−	0.818537i	$-0.305214\pi$
$257$	18.4184	1.14891	0.574454	+	0.818537i	$0.305214\pi$
$258$	85.6076	5.32969
$259$	−13.6517	−0.848273
$260$	21.7154	1.34673
$261$	19.4670	1.20498
$262$	−35.5519	−2.19640
$263$	−26.2232	−1.61699	−0.808495	−	0.588503i	$-0.799717\pi$
$263$	−26.2232	−1.61699	−0.808495	+	0.588503i	$0.799717\pi$
$264$	30.9395	1.90420
$265$	−4.39748	−0.270135
$266$	1.61263	0.0988769
$267$	−17.0907	−1.04593
$268$	23.1100	1.41167
$269$	−7.89166	−0.481163	−0.240582	−	0.970629i	$-0.577338\pi$
$269$	−7.89166	−0.481163	−0.240582	+	0.970629i	$0.577338\pi$
$270$	50.4440	3.06993
$271$	−6.42596	−0.390349	−0.195175	−	0.980768i	$-0.562527\pi$
$271$	−6.42596	−0.390349	−0.195175	+	0.980768i	$0.562527\pi$
$272$	−7.26184	−0.440314
$273$	−17.1910	−1.04045
$274$	−49.5237	−2.99183
$275$	5.50718	0.332095
$276$	−5.31856	−0.320139
$277$	10.0682	0.604942	0.302471	−	0.953159i	$-0.402188\pi$
$277$	10.0682	0.604942	0.302471	+	0.953159i	$0.402188\pi$
$278$	−1.05373	−0.0631985
$279$	83.6281	5.00668
$280$	7.80855	0.466650
$281$	−14.4045	−0.859303	−0.429651	−	0.902995i	$-0.641364\pi$
$281$	−14.4045	−0.859303	−0.429651	+	0.902995i	$0.641364\pi$
$282$	−97.3145	−5.79499
$283$	−28.8436	−1.71457	−0.857286	−	0.514840i	$-0.827851\pi$
$283$	−28.8436	−1.71457	−0.857286	+	0.514840i	$0.827851\pi$
$284$	64.8747	3.84960
$285$	2.02844	0.120154
$286$	−16.3749	−0.968269
$287$	8.26273	0.487734
$288$	−48.5462	−2.86061
$289$	1.00000	0.0588235
$290$	6.34528	0.372608
$291$	6.17911	0.362226
$292$	57.1875	3.34664
$293$	−11.0205	−0.643822	−0.321911	−	0.946770i	$-0.604325\pi$
$293$	−11.0205	−0.643822	−0.321911	+	0.946770i	$0.604325\pi$
$294$	49.2205	2.87060
$295$	−9.73549	−0.566822
$296$	76.6616	4.45587
$297$	−26.3373	−1.52824
$298$	−57.8443	−3.35083
$299$	1.56429	0.0904652
$300$	−58.4233	−3.37307
$301$	−11.2805	−0.650199
$302$	−41.2796	−2.37537
$303$	5.43571	0.312273
$304$	−4.04310	−0.231888
$305$	−6.10366	−0.349494
$306$	21.4953	1.22880
$307$	24.2044	1.38142	0.690710	−	0.723132i	$-0.257298\pi$
$307$	24.2044	1.38142	0.690710	+	0.723132i	$0.257298\pi$
$308$	−7.33624	−0.418021
$309$	−31.0474	−1.76623
$310$	27.2586	1.54819
$311$	14.1964	0.805003	0.402501	−	0.915419i	$-0.368141\pi$
$311$	14.1964	0.805003	0.402501	+	0.915419i	$0.368141\pi$
$312$	96.5370	5.46533
$313$	−5.89753	−0.333348	−0.166674	−	0.986012i	$-0.553303\pi$
$313$	−5.89753	−0.333348	−0.166674	+	0.986012i	$0.553303\pi$
$314$	10.6837	0.602915
$315$	−10.3194	−0.581431
$316$	52.2369	2.93856
$317$	−24.3748	−1.36903	−0.684513	−	0.729001i	$-0.739985\pi$
$317$	−24.3748	−1.36903	−0.684513	+	0.729001i	$0.739985\pi$
$318$	−35.1781	−1.97269
$319$	−3.31293	−0.185488
$320$	−0.172550	−0.00964581
$321$	−21.6073	−1.20600
$322$	1.01219	0.0564071
$323$	0.556760	0.0309790
$324$	165.552	9.19734
$325$	17.1834	0.953164
$326$	−26.4560	−1.46526
$327$	−0.259063	−0.0143262
$328$	−46.3998	−2.56200
$329$	12.8232	0.706963
$330$	−13.3275	−0.733656
$331$	−4.21679	−0.231776	−0.115888	−	0.993262i	$-0.536971\pi$
$331$	−4.21679	−0.231776	−0.115888	+	0.993262i	$0.536971\pi$
$332$	−3.82847	−0.210115
$333$	−101.312	−5.55187
$334$	64.5889	3.53415
$335$	−5.53215	−0.302254
$336$	27.8885	1.52144
$337$	24.0154	1.30820	0.654102	−	0.756406i	$-0.273047\pi$
$337$	24.0154	1.30820	0.654102	+	0.756406i	$0.273047\pi$
$338$	−17.9448	−0.976068
$339$	33.1210	1.79888
$340$	4.85115	0.263091
$341$	−14.2320	−0.770705
$342$	11.9677	0.647140
$343$	−14.4374	−0.779544
$344$	63.3464	3.41541
$345$	1.27317	0.0685453
$346$	54.3524	2.92200
$347$	−16.1341	−0.866124	−0.433062	−	0.901364i	$-0.642567\pi$
$347$	−16.1341	−0.866124	−0.433062	+	0.901364i	$0.642567\pi$
$348$	35.1454	1.88399
$349$	−23.8028	−1.27414	−0.637068	−	0.770808i	$-0.719853\pi$
$349$	−23.8028	−1.27414	−0.637068	+	0.770808i	$0.719853\pi$
$350$	11.1187	0.594319
$351$	−82.1771	−4.38629
$352$	8.26168	0.440349
$353$	1.00000	0.0532246
$353$	1.00000	0.0532246
$354$	−77.8800	−4.13928
$355$	−15.5299	−0.824241
$356$	−22.7568	−1.20611
$357$	−3.84042	−0.203256
$358$	15.1793	0.802250
$359$	−14.3514	−0.757437	−0.378719	−	0.925512i	$-0.623635\pi$
$359$	−14.3514	−0.757437	−0.378719	+	0.925512i	$0.623635\pi$
$360$	57.9490	3.05418
$361$	−18.6900	−0.983685
$362$	−62.6014	−3.29025
$363$	−30.2308	−1.58670
$364$	−22.8904	−1.19978
$365$	−13.6897	−0.716552
$366$	−48.8268	−2.55222
$367$	25.9382	1.35396	0.676981	−	0.736001i	$-0.263288\pi$
$367$	25.9382	1.35396	0.676981	+	0.736001i	$0.263288\pi$
$368$	−2.53770	−0.132287
$369$	61.3196	3.19217
$370$	−33.0228	−1.71677
$371$	4.63542	0.240659
$372$	150.981	7.82799
$373$	12.4184	0.643001	0.321501	−	0.946909i	$-0.395813\pi$
$373$	12.4184	0.643001	0.321501	+	0.946909i	$0.395813\pi$
$374$	−3.65811	−0.189156
$375$	32.2020	1.66290
$376$	−72.0091	−3.71358
$377$	−10.3369	−0.532379
$378$	−53.1735	−2.73495
$379$	17.2310	0.885095	0.442547	−	0.896745i	$-0.354075\pi$
$379$	17.2310	0.885095	0.442547	+	0.896745i	$0.354075\pi$
$380$	2.70093	0.138555
$381$	1.77103	0.0907324
$382$	−41.2052	−2.10824
$383$	−12.0591	−0.616189	−0.308094	−	0.951356i	$-0.599691\pi$
$383$	−12.0591	−0.616189	−0.308094	+	0.951356i	$0.599691\pi$
$384$	37.5582	1.91663
$385$	1.75617	0.0895027
$386$	28.9768	1.47488
$387$	−83.7153	−4.25549
$388$	8.22769	0.417698
$389$	−4.91462	−0.249181	−0.124590	−	0.992208i	$-0.539762\pi$
$389$	−4.91462	−0.249181	−0.124590	+	0.992208i	$0.539762\pi$
$390$	−41.5843	−2.10570
$391$	0.349457	0.0176728
$392$	36.4213	1.83956
$393$	47.1383	2.37781
$394$	−36.3826	−1.83293
$395$	−12.5046	−0.629176
$396$	−54.4438	−2.73591
$397$	9.53189	0.478392	0.239196	−	0.970971i	$-0.423116\pi$
$397$	9.53189	0.478392	0.239196	+	0.970971i	$0.423116\pi$
$398$	−33.1822	−1.66327
$399$	−2.13819	−0.107043
$400$	−27.8762	−1.39381
$401$	18.3279	0.915252	0.457626	−	0.889145i	$-0.348700\pi$
$401$	18.3279	0.915252	0.457626	+	0.889145i	$0.348700\pi$
$402$	−44.2550	−2.20724
$403$	−44.4064	−2.21204
$404$	7.23782	0.360095
$405$	−39.6304	−1.96925
$406$	−6.68862	−0.331950
$407$	17.2415	0.854628
$408$	21.5661	1.06768
$409$	−34.4085	−1.70139	−0.850696	−	0.525658i	$-0.823819\pi$
$409$	−34.4085	−1.70139	−0.850696	+	0.525658i	$0.823819\pi$
$410$	19.9872	0.987096
$411$	65.6634	3.23894
$412$	−41.3406	−2.03671
$413$	10.2623	0.504973
$414$	7.51168	0.369179
$415$	0.916471	0.0449878
$416$	25.7779	1.26387
$417$	1.39714	0.0684183
$418$	−2.03669	−0.0996176
$419$	−6.74820	−0.329671	−0.164835	−	0.986321i	$-0.552709\pi$
$419$	−6.74820	−0.329671	−0.164835	+	0.986321i	$0.552709\pi$
$420$	−18.6304	−0.909073
$421$	5.42894	0.264590	0.132295	−	0.991210i	$-0.457765\pi$
$421$	5.42894	0.264590	0.132295	+	0.991210i	$0.457765\pi$
$422$	63.8819	3.10972
$423$	95.1635	4.62701
$424$	−26.0305	−1.26415
$425$	3.83872	0.186205
$426$	−124.233	−6.01911
$427$	6.43392	0.311359
$428$	−28.7709	−1.39069
$429$	21.7115	1.04824
$430$	−27.2871	−1.31590
$431$	−40.4837	−1.95003	−0.975015	−	0.222138i	$-0.928696\pi$
$431$	−40.4837	−1.95003	−0.975015	+	0.222138i	$0.928696\pi$
$432$	133.314	6.41405
$433$	−19.4492	−0.934671	−0.467335	−	0.884080i	$-0.654786\pi$
$433$	−19.4492	−0.934671	−0.467335	+	0.884080i	$0.654786\pi$
$434$	−28.7336	−1.37926
$435$	−8.41321	−0.403382
$436$	−0.344950	−0.0165201
$437$	0.194564	0.00930725
$438$	−109.512	−5.23269
$439$	25.7306	1.22805	0.614027	−	0.789285i	$-0.289549\pi$
$439$	25.7306	1.22805	0.614027	+	0.789285i	$0.289549\pi$
$440$	−9.86186	−0.470146
$441$	−48.1326	−2.29203
$442$	−11.4140	−0.542906
$443$	−7.04263	−0.334605	−0.167303	−	0.985906i	$-0.553506\pi$
$443$	−7.04263	−0.334605	−0.167303	+	0.985906i	$0.553506\pi$
$444$	−182.907	−8.68039
$445$	5.44758	0.258240
$446$	−7.74178	−0.366584
$447$	76.6957	3.62758
$448$	0.181886	0.00859331
$449$	−10.2633	−0.484356	−0.242178	−	0.970232i	$-0.577862\pi$
$449$	−10.2633	−0.484356	−0.242178	+	0.970232i	$0.577862\pi$
$450$	82.5143	3.88976
$451$	−10.4355	−0.491387
$452$	44.1016	2.07437
$453$	54.7326	2.57156
$454$	14.0693	0.660304
$455$	5.47957	0.256886
$456$	12.0071	0.562285
$457$	−15.8985	−0.743700	−0.371850	−	0.928293i	$-0.621276\pi$
$457$	−15.8985	−0.743700	−0.371850	+	0.928293i	$0.621276\pi$
$458$	18.0149	0.841779
$459$	−18.3581	−0.856882
$460$	1.69527	0.0790423
$461$	−25.0549	−1.16692	−0.583461	−	0.812141i	$-0.698302\pi$
$461$	−25.0549	−1.16692	−0.583461	+	0.812141i	$0.698302\pi$
$462$	14.0487	0.653603
$463$	−1.18661	−0.0551466	−0.0275733	−	0.999620i	$-0.508778\pi$
$463$	−1.18661	−0.0551466	−0.0275733	+	0.999620i	$0.508778\pi$
$464$	16.7693	0.778496
$465$	−36.1422	−1.67606
$466$	−47.6304	−2.20644
$467$	−29.5484	−1.36734	−0.683668	−	0.729793i	$-0.739616\pi$
$467$	−29.5484	−1.36734	−0.683668	+	0.729793i	$0.739616\pi$
$468$	−169.875	−7.85246
$469$	5.83149	0.269273
$470$	31.0186	1.43078
$471$	−14.1655	−0.652712
$472$	−57.6283	−2.65256
$473$	14.2468	0.655070
$474$	−100.032	−4.59462
$475$	2.13724	0.0980635
$476$	−5.11364	−0.234383
$477$	34.4005	1.57509
$478$	−0.236895	−0.0108353
$479$	−10.8175	−0.494262	−0.247131	−	0.968982i	$-0.579488\pi$
$479$	−10.8175	−0.494262	−0.247131	+	0.968982i	$0.579488\pi$
$480$	20.9806	0.957630
$481$	53.7965	2.45291
$482$	−63.5408	−2.89420
$483$	−1.34206	−0.0610659
$484$	−40.2533	−1.82969
$485$	−1.96957	−0.0894335
$486$	−176.596	−8.01058
$487$	4.34113	0.196716	0.0983578	−	0.995151i	$-0.468641\pi$
$487$	4.34113	0.196716	0.0983578	+	0.995151i	$0.468641\pi$
$488$	−36.1300	−1.63553
$489$	35.0781	1.58628
$490$	−15.6889	−0.708750
$491$	−17.3251	−0.781871	−0.390935	−	0.920418i	$-0.627848\pi$
$491$	−17.3251	−0.781871	−0.390935	+	0.920418i	$0.627848\pi$
$492$	110.705	4.99099
$493$	−2.30924	−0.104003
$494$	−6.35484	−0.285918
$495$	13.0329	0.585787
$496$	72.0392	3.23466
$497$	16.3702	0.734304
$498$	7.33140	0.328528
$499$	0.0162864	0.000729077 0	0.000364539	−	1.00000i	$-0.499884\pi$
$499$	0.0162864	0.000729077 0	0.000364539		1.00000i	$0.499884\pi$
$500$	42.8779	1.91756
$501$	−85.6385	−3.82604
$502$	11.2568	0.502414
$503$	24.4086	1.08832	0.544162	−	0.838980i	$-0.316848\pi$
$503$	24.4086	1.08832	0.544162	+	0.838980i	$0.316848\pi$
$504$	−61.0846	−2.72092
$505$	−1.73261	−0.0771002
$506$	−1.27835	−0.0568296
$507$	23.7930	1.05668
$508$	2.35818	0.104627
$509$	−7.47953	−0.331524	−0.165762	−	0.986166i	$-0.553008\pi$
$509$	−7.47953	−0.331524	−0.165762	+	0.986166i	$0.553008\pi$
$510$	−9.28980	−0.411359
$511$	14.4304	0.638365
$512$	50.8265	2.24624
$513$	−10.2211	−0.451271
$514$	−46.9640	−2.07149
$515$	9.89624	0.436080
$516$	−151.138	−6.65349
$517$	−16.1951	−0.712259
$518$	34.8096	1.52945
$519$	−72.0658	−3.16334
$520$	−30.7708	−1.34939
$521$	−16.5885	−0.726756	−0.363378	−	0.931642i	$-0.618377\pi$
$521$	−16.5885	−0.726756	−0.363378	+	0.931642i	$0.618377\pi$
$522$	−49.6377	−2.17258
$523$	−28.3494	−1.23963	−0.619816	−	0.784747i	$-0.712793\pi$
$523$	−28.3494	−1.23963	−0.619816	+	0.784747i	$0.712793\pi$
$524$	62.7661	2.74195
$525$	−14.7423	−0.643406
$526$	66.8649	2.91545
$527$	−9.92024	−0.432132
$528$	−35.2220	−1.53284
$529$	−22.8779	−0.994690
$530$	11.2129	0.487056
$531$	76.1586	3.30500
$532$	−2.84707	−0.123436
$533$	−32.5606	−1.41036
$534$	43.5785	1.88582
$535$	6.88726	0.297762
$536$	−32.7470	−1.41446
$537$	−20.1262	−0.868511
$538$	20.1225	0.867542
$539$	8.19129	0.352824
$540$	−89.0579	−3.83244
$541$	2.60514	0.112004	0.0560018	−	0.998431i	$-0.482165\pi$
$541$	2.60514	0.112004	0.0560018	+	0.998431i	$0.482165\pi$
$542$	16.3852	0.703804
$543$	83.0032	3.56201
$544$	5.75871	0.246903
$545$	0.0825752	0.00353713
$546$	43.8344	1.87594
$547$	−7.10208	−0.303663	−0.151832	−	0.988406i	$-0.548517\pi$
$547$	−7.10208	−0.303663	−0.151832	+	0.988406i	$0.548517\pi$
$548$	87.4330	3.73495
$549$	47.7476	2.03782
$550$	−14.0424	−0.598771
$551$	−1.28569	−0.0547723
$552$	7.53642	0.320771
$553$	13.1812	0.560524
$554$	−25.6724	−1.09072
$555$	43.7849	1.85856
$556$	1.86034	0.0788959
$557$	37.8110	1.60210	0.801052	−	0.598595i	$-0.204274\pi$
$557$	37.8110	1.60210	0.801052	+	0.598595i	$0.204274\pi$
$558$	−213.238	−9.02710
$559$	44.4527	1.88015
$560$	−8.88935	−0.375644
$561$	4.85028	0.204779
$562$	36.7293	1.54933
$563$	−17.6344	−0.743203	−0.371602	−	0.928392i	$-0.621191\pi$
$563$	−17.6344	−0.743203	−0.371602	+	0.928392i	$0.621191\pi$
$564$	171.807	7.23437
$565$	−10.5572	−0.444144
$566$	73.5465	3.09139
$567$	41.7747	1.75437
$568$	−91.9277	−3.85720
$569$	35.9699	1.50793	0.753967	−	0.656912i	$-0.228138\pi$
$569$	35.9699	1.50793	0.753967	+	0.656912i	$0.228138\pi$
$570$	−5.17219	−0.216639
$571$	−42.1615	−1.76440	−0.882202	−	0.470871i	$-0.843940\pi$
$571$	−42.1615	−1.76440	−0.882202	+	0.470871i	$0.843940\pi$
$572$	28.9096	1.20877
$573$	54.6339	2.28237
$574$	−21.0687	−0.879389
$575$	1.34147	0.0559431
$576$	1.34982	0.0562424
$577$	−31.4429	−1.30898	−0.654492	−	0.756069i	$-0.727117\pi$
$577$	−31.4429	−1.30898	−0.654492	+	0.756069i	$0.727117\pi$
$578$	−2.54984	−0.106059
$579$	−38.4203	−1.59669
$580$	−11.2025	−0.465157
$581$	−0.966060	−0.0400789
$582$	−15.7558	−0.653097
$583$	−5.85434	−0.242462
$584$	−81.0349	−3.35325
$585$	40.6651	1.68130
$586$	28.1004	1.16082
$587$	−4.18387	−0.172687	−0.0863433	−	0.996265i	$-0.527518\pi$
$587$	−4.18387	−0.172687	−0.0863433	+	0.996265i	$0.527518\pi$
$588$	−86.8978	−3.58361
$589$	−5.52319	−0.227579
$590$	24.8240	1.02199
$591$	48.2398	1.98432
$592$	−87.2726	−3.58688
$593$	8.01001	0.328932	0.164466	−	0.986383i	$-0.447410\pi$
$593$	8.01001	0.328932	0.164466	+	0.986383i	$0.447410\pi$
$594$	67.1559	2.75544
$595$	1.22412	0.0501840
$596$	102.123	4.18311
$597$	43.9963	1.80065
$598$	−3.98869	−0.163110
$599$	2.68665	0.109774	0.0548868	−	0.998493i	$-0.482520\pi$
$599$	2.68665	0.109774	0.0548868	+	0.998493i	$0.482520\pi$
$600$	82.7860	3.37973
$601$	−39.5503	−1.61329	−0.806646	−	0.591035i	$-0.798719\pi$
$601$	−39.5503	−1.61329	−0.806646	+	0.591035i	$0.798719\pi$
$602$	28.7636	1.17232
$603$	43.2768	1.76237
$604$	72.8782	2.96537
$605$	9.63594	0.391757
$606$	−13.8602	−0.563032
$607$	18.8096	0.763460	0.381730	−	0.924274i	$-0.375328\pi$
$607$	18.8096	0.763460	0.381730	+	0.924274i	$0.375328\pi$
$608$	3.20622	0.130029
$609$	8.86844	0.359367
$610$	15.5634	0.630142
$611$	−50.5316	−2.04429
$612$	−37.9495	−1.53402
$613$	5.29573	0.213893	0.106946	−	0.994265i	$-0.465893\pi$
$613$	5.29573	0.213893	0.106946	+	0.994265i	$0.465893\pi$
$614$	−61.7174	−2.49071
$615$	−26.5010	−1.06862
$616$	10.3955	0.418846
$617$	29.7584	1.19803	0.599015	−	0.800738i	$-0.295559\pi$
$617$	29.7584	1.19803	0.599015	+	0.800738i	$0.295559\pi$
$618$	79.1660	3.18452
$619$	−0.817292	−0.0328498	−0.0164249	−	0.999865i	$-0.505228\pi$
$619$	−0.817292	−0.0328498	−0.0164249	+	0.999865i	$0.505228\pi$
$620$	−48.1246	−1.93273
$621$	−6.41537	−0.257440
$622$	−36.1985	−1.45143
$623$	−5.74234	−0.230062
$624$	−109.899	−4.39948
$625$	8.92934	0.357174
$626$	15.0378	0.601030
$627$	2.70044	0.107845
$628$	−18.8618	−0.752668
$629$	12.0180	0.479188
$630$	26.3128	1.04833
$631$	0.376980	0.0150073	0.00750367	−	0.999972i	$-0.497611\pi$
$631$	0.376980	0.0150073	0.00750367	+	0.999972i	$0.497611\pi$
$632$	−74.0199	−2.94436
$633$	−84.7010	−3.36656
$634$	62.1519	2.46837
$635$	−0.564508	−0.0224018
$636$	62.1062	2.46267
$637$	25.5583	1.01266
$638$	8.44744	0.334437
$639$	121.487	4.80595
$640$	−11.9715	−0.473216
$641$	−26.1472	−1.03275	−0.516376	−	0.856362i	$-0.672719\pi$
$641$	−26.1472	−1.03275	−0.516376	+	0.856362i	$0.672719\pi$
$642$	55.0953	2.17444
$643$	23.4894	0.926333	0.463167	−	0.886271i	$-0.346713\pi$
$643$	23.4894	0.926333	0.463167	+	0.886271i	$0.346713\pi$
$644$	−1.78700	−0.0704176
$645$	36.1799	1.42458
$646$	−1.41965	−0.0558554
$647$	−13.4017	−0.526875	−0.263437	−	0.964677i	$-0.584856\pi$
$647$	−13.4017	−0.526875	−0.263437	+	0.964677i	$0.584856\pi$
$648$	−234.588	−9.21549
$649$	−12.9608	−0.508756
$650$	−43.8149	−1.71856
$651$	38.0979	1.49317
$652$	46.7076	1.82921
$653$	−7.39124	−0.289242	−0.144621	−	0.989487i	$-0.546196\pi$
$653$	−7.39124	−0.289242	−0.144621	+	0.989487i	$0.546196\pi$
$654$	0.660569	0.0258303
$655$	−15.0251	−0.587081
$656$	52.8221	2.06236
$657$	107.092	4.17804
$658$	−32.6970	−1.27466
$659$	41.0968	1.60091	0.800453	−	0.599396i	$-0.204593\pi$
$659$	41.0968	1.60091	0.800453	+	0.599396i	$0.204593\pi$
$660$	23.5294	0.915883
$661$	−14.1222	−0.549292	−0.274646	−	0.961545i	$-0.588561\pi$
$661$	−14.1222	−0.549292	−0.274646	+	0.961545i	$0.588561\pi$
$662$	10.7521	0.417894
$663$	15.1338	0.587747
$664$	5.42496	0.210529
$665$	0.681540	0.0264290
$666$	258.330	10.0101
$667$	−0.806980	−0.0312464
$668$	−114.030	−4.41197
$669$	10.2648	0.396861
$670$	14.1061	0.544967
$671$	−8.12576	−0.313692
$672$	−22.1159	−0.853138
$673$	5.83810	0.225042	0.112521	−	0.993649i	$-0.464107\pi$
$673$	5.83810	0.225042	0.112521	+	0.993649i	$0.464107\pi$
$674$	−61.2355	−2.35870
$675$	−70.4715	−2.71245
$676$	31.6812	1.21851
$677$	32.8958	1.26429	0.632144	−	0.774851i	$-0.282175\pi$
$677$	32.8958	1.26429	0.632144	+	0.774851i	$0.282175\pi$
$678$	−84.4532	−3.24340
$679$	2.07614	0.0796750
$680$	−6.87410	−0.263610
$681$	−18.6545	−0.714840
$682$	36.2893	1.38959
$683$	−22.2552	−0.851571	−0.425785	−	0.904824i	$-0.640002\pi$
$683$	−22.2552	−0.851571	−0.425785	+	0.904824i	$0.640002\pi$
$684$	−21.1288	−0.807878
$685$	−20.9300	−0.799693
$686$	36.8130	1.40553
$687$	−23.8859	−0.911304
$688$	−72.1143	−2.74933
$689$	−18.2666	−0.695902
$690$	−3.24639	−0.123588
$691$	27.8313	1.05875	0.529377	−	0.848387i	$-0.322426\pi$
$691$	27.8313	1.05875	0.529377	+	0.848387i	$0.322426\pi$
$692$	−95.9580	−3.64777
$693$	−13.7381	−0.521868
$694$	41.1394	1.56163
$695$	−0.445333	−0.0168925
$696$	−49.8012	−1.88771
$697$	−7.27393	−0.275520
$698$	60.6934	2.29728
$699$	63.1532	2.38867
$700$	−19.6298	−0.741938
$701$	−45.7262	−1.72705	−0.863526	−	0.504303i	$-0.831749\pi$
$701$	−45.7262	−1.72705	−0.863526	+	0.504303i	$0.831749\pi$
$702$	209.538	7.90852
$703$	6.69113	0.252361
$704$	−0.229714	−0.00865768
$705$	−41.1276	−1.54895
$706$	−2.54984	−0.0959645
$707$	1.82636	0.0686874
$708$	137.496	5.16740
$709$	52.8360	1.98430	0.992149	−	0.125065i	$-0.0399139\pi$
$709$	52.8360	1.98430	0.992149	+	0.125065i	$0.0399139\pi$
$710$	39.5988	1.48612
$711$	97.8210	3.66857
$712$	32.2464	1.20849
$713$	−3.46670	−0.129829
$714$	9.79246	0.366474
$715$	−6.92046	−0.258811
$716$	−26.7987	−1.00152
$717$	0.314100	0.0117303
$718$	36.5938	1.36567
$719$	31.0017	1.15617	0.578085	−	0.815977i	$-0.303800\pi$
$719$	31.0017	1.15617	0.578085	+	0.815977i	$0.303800\pi$
$720$	−65.9699	−2.45855
$721$	−10.4317	−0.388497
$722$	47.6566	1.77359
$723$	84.2487	3.13324
$724$	110.521	4.10749
$725$	−8.86451	−0.329220
$726$	77.0837	2.86084
$727$	−43.6723	−1.61971	−0.809857	−	0.586627i	$-0.800455\pi$
$727$	−43.6723	−1.61971	−0.809857	+	0.586627i	$0.800455\pi$
$728$	32.4358	1.20215
$729$	123.823	4.58602
$730$	34.9066	1.29195
$731$	9.93059	0.367296
$732$	86.2027	3.18614
$733$	−10.3876	−0.383675	−0.191838	−	0.981427i	$-0.561445\pi$
$733$	−10.3876	−0.383675	−0.191838	+	0.981427i	$0.561445\pi$
$734$	−66.1382	−2.44121
$735$	20.8019	0.767288
$736$	2.01242	0.0741789
$737$	−7.36492	−0.271290
$738$	−156.355	−5.75551
$739$	−12.3130	−0.452940	−0.226470	−	0.974018i	$-0.572718\pi$
$739$	−12.3130	−0.452940	−0.226470	+	0.974018i	$0.572718\pi$
$740$	58.3010	2.14319
$741$	8.42588	0.309532
$742$	−11.8196	−0.433911
$743$	−20.4676	−0.750883	−0.375441	−	0.926846i	$-0.622509\pi$
$743$	−20.4676	−0.750883	−0.375441	+	0.926846i	$0.622509\pi$
$744$	−213.940	−7.84344
$745$	−24.4465	−0.895649
$746$	−31.6650	−1.15934
$747$	−7.16935	−0.262313
$748$	6.45831	0.236139
$749$	−7.25992	−0.265272
$750$	−82.1099	−2.99823
$751$	41.2790	1.50629	0.753146	−	0.657853i	$-0.228535\pi$
$751$	41.2790	1.50629	0.753146	+	0.657853i	$0.228535\pi$
$752$	81.9761	2.98936
$753$	−14.9254	−0.543910
$754$	26.3575	0.959885
$755$	−17.4458	−0.634918
$756$	93.8767	3.41426
$757$	2.78480	0.101215	0.0506077	−	0.998719i	$-0.483884\pi$
$757$	2.78480	0.101215	0.0506077	+	0.998719i	$0.483884\pi$
$758$	−43.9362	−1.59583
$759$	1.69497	0.0615234
$760$	−3.82723	−0.138828
$761$	−5.94133	−0.215373	−0.107686	−	0.994185i	$-0.534344\pi$
$761$	−5.94133	−0.215373	−0.107686	+	0.994185i	$0.534344\pi$
$762$	−4.51584	−0.163592
$763$	−0.0870433	−0.00315118
$764$	72.7469	2.63189
$765$	9.08446	0.328449
$766$	30.7487	1.11099
$767$	−40.4401	−1.46021
$768$	−96.8501	−3.49478
$769$	−11.7947	−0.425327	−0.212663	−	0.977126i	$-0.568214\pi$
$769$	−11.7947	−0.425327	−0.212663	+	0.977126i	$0.568214\pi$
$770$	−4.47796	−0.161374
$771$	62.2696	2.24258
$772$	−51.1579	−1.84121
$773$	12.6198	0.453901	0.226950	−	0.973906i	$-0.427124\pi$
$773$	12.6198	0.453901	0.226950	+	0.973906i	$0.427124\pi$
$774$	213.461	7.67269
$775$	−38.0810	−1.36791
$776$	−11.6587	−0.418522
$777$	−46.1540	−1.65577
$778$	12.5315	0.449276
$779$	−4.04983	−0.145100
$780$	73.4162	2.62872
$781$	−20.6749	−0.739805
$782$	−0.891060	−0.0318643
$783$	42.3932	1.51501
$784$	−41.4625	−1.48080
$785$	4.51520	0.161154
$786$	−120.195	−4.28722
$787$	2.75357	0.0981541	0.0490771	−	0.998795i	$-0.484372\pi$
$787$	2.75357	0.0981541	0.0490771	+	0.998795i	$0.484372\pi$
$788$	64.2328	2.28820
$789$	−88.6562	−3.15624
$790$	31.8848	1.13441
$791$	11.1284	0.395681
$792$	77.1472	2.74131
$793$	−25.3539	−0.900342
$794$	−24.3048	−0.862545
$795$	−14.8672	−0.527284
$796$	58.5824	2.07640
$797$	−24.6047	−0.871542	−0.435771	−	0.900058i	$-0.643524\pi$
$797$	−24.6047	−0.871542	−0.435771	+	0.900058i	$0.643524\pi$
$798$	5.45205	0.193000
$799$	−11.2886	−0.399362
$800$	22.1061	0.781568
$801$	−42.6152	−1.50573
$802$	−46.7332	−1.65021
$803$	−18.2250	−0.643147
$804$	78.1313	2.75548
$805$	0.427777	0.0150772
$806$	113.229	3.98833
$807$	−26.6804	−0.939195
$808$	−10.2560	−0.360806
$809$	−33.0277	−1.16119	−0.580596	−	0.814192i	$-0.697180\pi$
$809$	−33.0277	−1.16119	−0.580596	+	0.814192i	$0.697180\pi$
$810$	101.051	3.55058
$811$	−11.4173	−0.400916	−0.200458	−	0.979702i	$-0.564243\pi$
$811$	−11.4173	−0.400916	−0.200458	+	0.979702i	$0.564243\pi$
$812$	11.8086	0.414401
$813$	−21.7251	−0.761933
$814$	−43.9630	−1.54090
$815$	−11.1810	−0.391653
$816$	−24.5511	−0.859460
$817$	5.52896	0.193434
$818$	87.7363	3.06763
$819$	−42.8655	−1.49784
$820$	−35.2869	−1.23227
$821$	49.6231	1.73186	0.865930	−	0.500165i	$-0.166727\pi$
$821$	49.6231	1.73186	0.865930	+	0.500165i	$0.166727\pi$
$822$	−167.431	−5.83984
$823$	47.9532	1.67154	0.835771	−	0.549078i	$-0.185021\pi$
$823$	47.9532	1.67154	0.835771	+	0.549078i	$0.185021\pi$
$824$	58.5798	2.04073
$825$	18.6189	0.648226
$826$	−26.1672	−0.910472
$827$	3.57327	0.124255	0.0621273	−	0.998068i	$-0.480212\pi$
$827$	3.57327	0.124255	0.0621273	+	0.998068i	$0.480212\pi$
$828$	−13.2617	−0.460876
$829$	0.345885	0.0120131	0.00600654	−	0.999982i	$-0.498088\pi$
$829$	0.345885	0.0120131	0.00600654	+	0.999982i	$0.498088\pi$
$830$	−2.33686	−0.0811134
$831$	34.0391	1.18080
$832$	−0.716750	−0.0248488
$833$	5.70965	0.197827
$834$	−3.56249	−0.123359
$835$	27.2969	0.944649
$836$	3.59573	0.124361
$837$	182.117	6.29487
$838$	17.2068	0.594400
$839$	43.0511	1.48629	0.743144	−	0.669132i	$-0.233334\pi$
$839$	43.0511	1.48629	0.743144	+	0.669132i	$0.233334\pi$
$840$	26.3994	0.910867
$841$	−23.6674	−0.816118
$842$	−13.8429	−0.477059
$843$	−48.6994	−1.67730
$844$	−112.782	−3.88212
$845$	−7.58393	−0.260895
$846$	−242.652	−8.34254
$847$	−10.1573	−0.349010
$848$	29.6334	1.01762
$849$	−97.5153	−3.34672
$850$	−9.78812	−0.335730
$851$	4.19977	0.143966
$852$	219.331	7.51414
$853$	−38.7903	−1.32815	−0.664077	−	0.747664i	$-0.731175\pi$
$853$	−38.7903	−1.32815	−0.664077	+	0.747664i	$0.731175\pi$
$854$	−16.4055	−0.561384
$855$	5.05786	0.172975
$856$	40.7685	1.39344
$857$	18.1196	0.618955	0.309477	−	0.950907i	$-0.399846\pi$
$857$	18.1196	0.618955	0.309477	+	0.950907i	$0.399846\pi$
$858$	−55.3609	−1.88999
$859$	1.64469	0.0561161	0.0280581	−	0.999606i	$-0.491068\pi$
$859$	1.64469	0.0561161	0.0280581	+	0.999606i	$0.491068\pi$
$860$	48.1748	1.64275
$861$	27.9349	0.952020
$862$	103.227	3.51592
$863$	−20.5623	−0.699949	−0.349975	−	0.936759i	$-0.613810\pi$
$863$	−20.5623	−0.699949	−0.349975	+	0.936759i	$0.613810\pi$
$864$	−105.719	−3.59663
$865$	22.9707	0.781027
$866$	49.5925	1.68522
$867$	3.38084	0.114819
$868$	50.7285	1.72184
$869$	−16.6473	−0.564722
$870$	21.4523	0.727303
$871$	−22.9799	−0.778644
$872$	0.488796	0.0165527
$873$	15.4075	0.521465
$874$	−0.496107	−0.0167811
$875$	10.8196	0.365771
$876$	193.341	6.53240
$877$	50.9724	1.72121	0.860607	−	0.509270i	$-0.170084\pi$
$877$	50.9724	1.72121	0.860607	+	0.509270i	$0.170084\pi$
$878$	−65.6089	−2.21419
$879$	−37.2583	−1.25669
$880$	11.2269	0.378458
$881$	−7.46227	−0.251410	−0.125705	−	0.992068i	$-0.540119\pi$
$881$	−7.46227	−0.251410	−0.125705	+	0.992068i	$0.540119\pi$
$882$	122.730	4.13255
$883$	27.5788	0.928099	0.464050	−	0.885809i	$-0.346396\pi$
$883$	27.5788	0.928099	0.464050	+	0.885809i	$0.346396\pi$
$884$	20.1511	0.677755
$885$	−32.9141	−1.10640
$886$	17.9576	0.603297
$887$	−48.6565	−1.63372	−0.816862	−	0.576833i	$-0.804288\pi$
$887$	−48.6565	−1.63372	−0.816862	+	0.576833i	$0.804288\pi$
$888$	259.180	8.69752
$889$	0.595053	0.0199574
$890$	−13.8905	−0.465610
$891$	−52.7597	−1.76752
$892$	13.6679	0.457637
$893$	−6.28505	−0.210321
$894$	−195.562	−6.54057
$895$	6.41516	0.214435
$896$	12.6193	0.421581
$897$	5.28860	0.176581
$898$	26.1698	0.873299
$899$	22.9082	0.764031
$900$	−145.677	−4.85591
$901$	−4.08070	−0.135948
$902$	26.6088	0.885976
$903$	−38.1376	−1.26914
$904$	−62.4922	−2.07846
$905$	−26.4569	−0.879458
$906$	−139.559	−4.63655
$907$	−14.4959	−0.481330	−0.240665	−	0.970608i	$-0.577365\pi$
$907$	−14.4959	−0.481330	−0.240665	+	0.970608i	$0.577365\pi$
$908$	−24.8390	−0.824311
$909$	13.5538	0.449552
$910$	−13.9720	−0.463168
$911$	−19.8284	−0.656945	−0.328473	−	0.944513i	$-0.606534\pi$
$911$	−19.8284	−0.656945	−0.328473	+	0.944513i	$0.606534\pi$
$912$	−13.6691	−0.452628
$913$	1.22009	0.0403792
$914$	40.5386	1.34090
$915$	−20.6355	−0.682187
$916$	−31.8049	−1.05086
$917$	15.8381	0.523021
$918$	46.8102	1.54497
$919$	32.8332	1.08307	0.541534	−	0.840679i	$-0.317844\pi$
$919$	32.8332	1.08307	0.541534	+	0.840679i	$0.317844\pi$
$920$	−2.40220	−0.0791983
$921$	81.8312	2.69643
$922$	63.8860	2.10397
$923$	−64.5093	−2.12335
$924$	−24.8026	−0.815946
$925$	46.1336	1.51686
$926$	3.02567	0.0994298
$927$	−77.4161	−2.54268
$928$	−13.2982	−0.436536
$929$	8.69212	0.285179	0.142590	−	0.989782i	$-0.454457\pi$
$929$	8.69212	0.285179	0.142590	+	0.989782i	$0.454457\pi$
$930$	92.1570	3.02195
$931$	3.17890	0.104184
$932$	84.0905	2.75448
$933$	47.9956	1.57131
$934$	75.3437	2.46532
$935$	−1.54601	−0.0505599
$936$	240.713	7.86796
$937$	13.1730	0.430344	0.215172	−	0.976576i	$-0.430969\pi$
$937$	13.1730	0.430344	0.215172	+	0.976576i	$0.430969\pi$
$938$	−14.8694	−0.485502
$939$	−19.9386	−0.650671
$940$	−54.7627	−1.78616
$941$	47.3169	1.54249	0.771243	−	0.636541i	$-0.219635\pi$
$941$	47.3169	1.54249	0.771243	+	0.636541i	$0.219635\pi$
$942$	36.1198	1.17685
$943$	−2.54193	−0.0827765
$944$	65.6048	2.13525
$945$	−22.4725	−0.731030
$946$	−36.3271	−1.18110
$947$	42.5757	1.38352	0.691762	−	0.722126i	$-0.256835\pi$
$947$	42.5757	1.38352	0.691762	+	0.722126i	$0.256835\pi$
$948$	176.604	5.73585
$949$	−56.8654	−1.84593
$950$	−5.44964	−0.176810
$951$	−82.4072	−2.67224
$952$	7.24605	0.234846
$953$	34.5511	1.11922	0.559609	−	0.828757i	$-0.310951\pi$
$953$	34.5511	1.11922	0.559609	+	0.828757i	$0.310951\pi$
$954$	−87.7159	−2.83991
$955$	−17.4144	−0.563515
$956$	0.418234	0.0135266
$957$	−11.2005	−0.362059
$958$	27.5828	0.891160
$959$	22.0625	0.712434
$960$	−0.583362	−0.0188279
$961$	67.4111	2.17455
$962$	−137.173	−4.42262
$963$	−53.8775	−1.73618
$964$	112.180	3.61307
$965$	12.2463	0.394223
$966$	3.42204	0.110102
$967$	5.11285	0.164418	0.0822091	−	0.996615i	$-0.473802\pi$
$967$	5.11285	0.164418	0.0822091	+	0.996615i	$0.473802\pi$
$968$	57.0390	1.83330
$969$	1.88231	0.0604687
$970$	5.02209	0.161250
$971$	4.12140	0.132262	0.0661310	−	0.997811i	$-0.478934\pi$
$971$	4.12140	0.132262	0.0661310	+	0.997811i	$0.478934\pi$
$972$	311.777	10.0003
$973$	0.469430	0.0150492
$974$	−11.0692	−0.354680
$975$	58.0942	1.86050
$976$	41.1309	1.31657
$977$	−54.3139	−1.73766	−0.868829	−	0.495113i	$-0.835127\pi$
$977$	−54.3139	−1.73766	−0.868829	+	0.495113i	$0.835127\pi$
$978$	−89.4435	−2.86009
$979$	7.25233	0.231786
$980$	27.6983	0.884791
$981$	−0.645968	−0.0206242
$982$	44.1763	1.40972
$983$	3.85760	0.123038	0.0615192	−	0.998106i	$-0.480405\pi$
$983$	3.85760	0.123038	0.0615192	+	0.998106i	$0.480405\pi$
$984$	−156.870	−5.00083
$985$	−15.3762	−0.489928
$986$	5.88819	0.187518
$987$	43.3530	1.37994
$988$	11.2193	0.356934
$989$	3.47032	0.110350
$990$	−33.2319	−1.05618
$991$	19.4247	0.617045	0.308523	−	0.951217i	$-0.400165\pi$
$991$	19.4247	0.617045	0.308523	+	0.951217i	$0.400165\pi$
$992$	−57.1278	−1.81381
$993$	−14.2563	−0.452409
$994$	−41.7414	−1.32396
$995$	−14.0236	−0.444579
$996$	−12.9434	−0.410128
$997$	51.7412	1.63866	0.819331	−	0.573321i	$-0.194345\pi$
$997$	51.7412	1.63866	0.819331	+	0.573321i	$0.194345\pi$
$998$	−0.0415276	−0.00131453
$999$	−220.627	−6.98033

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6001.2.a.c.1.8	✓	121

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6001.2.a.c.1.8	✓	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)

\(f(q)\)	\(=\)	\(q-2.54984 q^{2} +3.38084 q^{3} +4.50169 q^{4} -1.07763 q^{5} -8.62059 q^{6} +1.13594 q^{7} -6.37892 q^{8} +8.43005 q^{9} +O(q^{10})\)	\(q-2.54984 q^{2} +3.38084 q^{3} +4.50169 q^{4} -1.07763 q^{5} -8.62059 q^{6} +1.13594 q^{7} -6.37892 q^{8} +8.43005 q^{9} +2.74778 q^{10} -1.43464 q^{11} +15.2195 q^{12} -4.47634 q^{13} -2.89646 q^{14} -3.64328 q^{15} +7.26184 q^{16} -1.00000 q^{17} -21.4953 q^{18} -0.556760 q^{19} -4.85115 q^{20} +3.84042 q^{21} +3.65811 q^{22} -0.349457 q^{23} -21.5661 q^{24} -3.83872 q^{25} +11.4140 q^{26} +18.3581 q^{27} +5.11364 q^{28} +2.30924 q^{29} +9.28980 q^{30} +9.92024 q^{31} -5.75871 q^{32} -4.85028 q^{33} +2.54984 q^{34} -1.22412 q^{35} +37.9495 q^{36} -12.0180 q^{37} +1.41965 q^{38} -15.1338 q^{39} +6.87410 q^{40} +7.27393 q^{41} -9.79246 q^{42} -9.93059 q^{43} -6.45831 q^{44} -9.08446 q^{45} +0.891060 q^{46} +11.2886 q^{47} +24.5511 q^{48} -5.70965 q^{49} +9.78812 q^{50} -3.38084 q^{51} -20.1511 q^{52} +4.08070 q^{53} -46.8102 q^{54} +1.54601 q^{55} -7.24605 q^{56} -1.88231 q^{57} -5.88819 q^{58} +9.03418 q^{59} -16.4009 q^{60} +5.66397 q^{61} -25.2950 q^{62} +9.57601 q^{63} +0.160120 q^{64} +4.82383 q^{65} +12.3675 q^{66} +5.13364 q^{67} -4.50169 q^{68} -1.18146 q^{69} +3.12131 q^{70} +14.4112 q^{71} -53.7746 q^{72} +12.7036 q^{73} +30.6439 q^{74} -12.9781 q^{75} -2.50636 q^{76} -1.62966 q^{77} +38.5887 q^{78} +11.6038 q^{79} -7.82557 q^{80} +36.7756 q^{81} -18.5474 q^{82} -0.850452 q^{83} +17.2884 q^{84} +1.07763 q^{85} +25.3214 q^{86} +7.80715 q^{87} +9.15145 q^{88} -5.05516 q^{89} +23.1639 q^{90} -5.08484 q^{91} -1.57315 q^{92} +33.5387 q^{93} -28.7842 q^{94} +0.599980 q^{95} -19.4693 q^{96} +1.82769 q^{97} +14.5587 q^{98} -12.0941 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 121 q + 9 q^{2} + 13 q^{3} + 127 q^{4} + 21 q^{5} + 19 q^{6} - 13 q^{7} + 24 q^{8} + 134 q^{9}+O(q^{10}) \) 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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