LMFDB - Embedded newform 4019.2.a.a.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4019,2,Mod(1,4019)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4019, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4019.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4019 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4019.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$32.0918765724$
Analytic rank:	$1$
Dimension:	$149$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	4019.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.35135 q^{2} +2.82086 q^{3} +3.52886 q^{4} +0.184417 q^{5} -6.63284 q^{6} +2.16509 q^{7} -3.59489 q^{8} +4.95726 q^{9} +O(q^{10})$	\(q-2.35135 q^{2} +2.82086 q^{3} +3.52886 q^{4} +0.184417 q^{5} -6.63284 q^{6} +2.16509 q^{7} -3.59489 q^{8} +4.95726 q^{9} -0.433630 q^{10} +2.14046 q^{11} +9.95443 q^{12} -6.11089 q^{13} -5.09089 q^{14} +0.520215 q^{15} +1.39514 q^{16} -8.07735 q^{17} -11.6563 q^{18} -5.45101 q^{19} +0.650783 q^{20} +6.10742 q^{21} -5.03297 q^{22} -2.05115 q^{23} -10.1407 q^{24} -4.96599 q^{25} +14.3689 q^{26} +5.52116 q^{27} +7.64030 q^{28} +4.07824 q^{29} -1.22321 q^{30} +6.53252 q^{31} +3.90932 q^{32} +6.03794 q^{33} +18.9927 q^{34} +0.399280 q^{35} +17.4935 q^{36} +3.69488 q^{37} +12.8172 q^{38} -17.2380 q^{39} -0.662960 q^{40} -4.57700 q^{41} -14.3607 q^{42} -10.9333 q^{43} +7.55338 q^{44} +0.914204 q^{45} +4.82297 q^{46} -9.59260 q^{47} +3.93549 q^{48} -2.31239 q^{49} +11.6768 q^{50} -22.7851 q^{51} -21.5645 q^{52} -0.183631 q^{53} -12.9822 q^{54} +0.394737 q^{55} -7.78326 q^{56} -15.3765 q^{57} -9.58937 q^{58} -10.8462 q^{59} +1.83577 q^{60} -3.11089 q^{61} -15.3603 q^{62} +10.7329 q^{63} -11.9825 q^{64} -1.12695 q^{65} -14.1973 q^{66} +12.7351 q^{67} -28.5039 q^{68} -5.78600 q^{69} -0.938848 q^{70} +13.0782 q^{71} -17.8208 q^{72} +0.932173 q^{73} -8.68797 q^{74} -14.0084 q^{75} -19.2359 q^{76} +4.63428 q^{77} +40.5326 q^{78} -13.4589 q^{79} +0.257288 q^{80} +0.702642 q^{81} +10.7622 q^{82} +12.7780 q^{83} +21.5522 q^{84} -1.48960 q^{85} +25.7080 q^{86} +11.5041 q^{87} -7.69472 q^{88} -16.2812 q^{89} -2.14962 q^{90} -13.2306 q^{91} -7.23821 q^{92} +18.4273 q^{93} +22.5556 q^{94} -1.00526 q^{95} +11.0277 q^{96} -5.35851 q^{97} +5.43724 q^{98} +10.6108 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 149 q - 8 q^{2} - 12 q^{3} + 124 q^{4} - 36 q^{5} - 45 q^{6} - 32 q^{7} - 21 q^{8} + 115 q^{9}+O(q^{10}) $ 149 * q - 8 * q^2 - 12 * q^3 + 124 * q^4 - 36 * q^5 - 45 * q^6 - 32 * q^7 - 21 * q^8 + 115 * q^9	\( 149 q - 8 q^{2} - 12 q^{3} + 124 q^{4} - 36 q^{5} - 45 q^{6} - 32 q^{7} - 21 q^{8} + 115 q^{9} - 58 q^{10} - 33 q^{11} - 33 q^{12} - 107 q^{13} - 28 q^{14} - 24 q^{15} + 74 q^{16} - 39 q^{17} - 33 q^{18} - 93 q^{19} - 63 q^{20} - 113 q^{21} - 38 q^{22} - 11 q^{23} - 130 q^{24} + 85 q^{25} - 33 q^{26} - 30 q^{27} - 94 q^{28} - 85 q^{29} - 16 q^{30} - 129 q^{31} - 35 q^{32} - 64 q^{33} - 78 q^{34} - 27 q^{35} + 79 q^{36} - 135 q^{37} - 11 q^{38} - 73 q^{39} - 146 q^{40} - 101 q^{41} + 4 q^{42} - 55 q^{43} - 82 q^{44} - 168 q^{45} - 113 q^{46} - 40 q^{47} - 65 q^{48} + 27 q^{49} - 5 q^{50} - 49 q^{51} - 177 q^{52} - 32 q^{53} - 155 q^{54} - 128 q^{55} - 44 q^{56} - 47 q^{57} - 46 q^{58} - 53 q^{59} - 11 q^{60} - 347 q^{61} - 11 q^{62} - 73 q^{63} + q^{64} - 31 q^{65} - 37 q^{66} - 40 q^{67} - 80 q^{68} - 175 q^{69} - 61 q^{70} - 31 q^{71} - 68 q^{72} - 193 q^{73} - 33 q^{74} - 56 q^{75} - 248 q^{76} - 84 q^{77} + 40 q^{78} - 111 q^{79} - 54 q^{80} + 49 q^{81} - 74 q^{82} - 24 q^{83} - 159 q^{84} - 258 q^{85} - q^{86} - 66 q^{87} - 97 q^{88} - 76 q^{89} - 75 q^{90} - 134 q^{91} + 31 q^{92} - 97 q^{93} - 111 q^{94} - 14 q^{95} - 216 q^{96} - 140 q^{97} - 13 q^{98} - 116 q^{99}+O(q^{100}) \) 149 * q - 8 * q^2 - 12 * q^3 + 124 * q^4 - 36 * q^5 - 45 * q^6 - 32 * q^7 - 21 * q^8 + 115 * q^9 - 58 * q^10 - 33 * q^11 - 33 * q^12 - 107 * q^13 - 28 * q^14 - 24 * q^15 + 74 * q^16 - 39 * q^17 - 33 * q^18 - 93 * q^19 - 63 * q^20 - 113 * q^21 - 38 * q^22 - 11 * q^23 - 130 * q^24 + 85 * q^25 - 33 * q^26 - 30 * q^27 - 94 * q^28 - 85 * q^29 - 16 * q^30 - 129 * q^31 - 35 * q^32 - 64 * q^33 - 78 * q^34 - 27 * q^35 + 79 * q^36 - 135 * q^37 - 11 * q^38 - 73 * q^39 - 146 * q^40 - 101 * q^41 + 4 * q^42 - 55 * q^43 - 82 * q^44 - 168 * q^45 - 113 * q^46 - 40 * q^47 - 65 * q^48 + 27 * q^49 - 5 * q^50 - 49 * q^51 - 177 * q^52 - 32 * q^53 - 155 * q^54 - 128 * q^55 - 44 * q^56 - 47 * q^57 - 46 * q^58 - 53 * q^59 - 11 * q^60 - 347 * q^61 - 11 * q^62 - 73 * q^63 + q^64 - 31 * q^65 - 37 * q^66 - 40 * q^67 - 80 * q^68 - 175 * q^69 - 61 * q^70 - 31 * q^71 - 68 * q^72 - 193 * q^73 - 33 * q^74 - 56 * q^75 - 248 * q^76 - 84 * q^77 + 40 * q^78 - 111 * q^79 - 54 * q^80 + 49 * q^81 - 74 * q^82 - 24 * q^83 - 159 * q^84 - 258 * q^85 - q^86 - 66 * q^87 - 97 * q^88 - 76 * q^89 - 75 * q^90 - 134 * q^91 + 31 * q^92 - 97 * q^93 - 111 * q^94 - 14 * q^95 - 216 * q^96 - 140 * q^97 - 13 * q^98 - 116 * 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 $

$2$	−2.35135	−1.66266	−0.831329	−	0.555781i	$-0.812419\pi$
$2$	−2.35135	−1.66266	−0.831329	+	0.555781i	$0.812419\pi$
$3$	2.82086	1.62863	0.814313	−	0.580427i	$-0.197114\pi$
$3$	2.82086	1.62863	0.814313	+	0.580427i	$0.197114\pi$
$4$	3.52886	1.76443
$5$	0.184417	0.0824739	0.0412369	−	0.999149i	$-0.486870\pi$
$5$	0.184417	0.0824739	0.0412369	+	0.999149i	$0.486870\pi$
$6$	−6.63284	−2.70785
$7$	2.16509	0.818327	0.409163	−	0.912461i	$-0.365821\pi$
$7$	2.16509	0.818327	0.409163	+	0.912461i	$0.365821\pi$
$8$	−3.59489	−1.27099
$9$	4.95726	1.65242
$10$	−0.433630	−0.137126
$11$	2.14046	0.645372	0.322686	−	0.946506i	$-0.395414\pi$
$11$	2.14046	0.645372	0.322686	+	0.946506i	$0.395414\pi$
$12$	9.95443	2.87360
$13$	−6.11089	−1.69486	−0.847428	−	0.530910i	$-0.821850\pi$
$13$	−6.11089	−1.69486	−0.847428	+	0.530910i	$0.821850\pi$
$14$	−5.09089	−1.36060
$15$	0.520215	0.134319
$16$	1.39514	0.348785
$17$	−8.07735	−1.95905	−0.979523	−	0.201333i	$-0.935473\pi$
$17$	−8.07735	−1.95905	−0.979523	+	0.201333i	$0.935473\pi$
$18$	−11.6563	−2.74741
$19$	−5.45101	−1.25055	−0.625274	−	0.780406i	$-0.715013\pi$
$19$	−5.45101	−1.25055	−0.625274	+	0.780406i	$0.715013\pi$
$20$	0.650783	0.145519
$21$	6.10742	1.33275
$22$	−5.03297	−1.07303
$23$	−2.05115	−0.427693	−0.213847	−	0.976867i	$-0.568599\pi$
$23$	−2.05115	−0.427693	−0.213847	+	0.976867i	$0.568599\pi$
$24$	−10.1407	−2.06996
$25$	−4.96599	−0.993198
$26$	14.3689	2.81797
$27$	5.52116	1.06255
$28$	7.64030	1.44388
$29$	4.07824	0.757309	0.378655	−	0.925538i	$-0.376387\pi$
$29$	4.07824	0.757309	0.378655	+	0.925538i	$0.376387\pi$
$30$	−1.22321	−0.223327
$31$	6.53252	1.17328	0.586638	−	0.809849i	$-0.300451\pi$
$31$	6.53252	1.17328	0.586638	+	0.809849i	$0.300451\pi$
$32$	3.90932	0.691077
$33$	6.03794	1.05107
$34$	18.9927	3.25722
$35$	0.399280	0.0674906
$36$	17.4935	2.91558
$37$	3.69488	0.607435	0.303718	−	0.952762i	$-0.401772\pi$
$37$	3.69488	0.607435	0.303718	+	0.952762i	$0.401772\pi$
$38$	12.8172	2.07923
$39$	−17.2380	−2.76029
$40$	−0.662960	−0.104823
$41$	−4.57700	−0.714808	−0.357404	−	0.933950i	$-0.616338\pi$
$41$	−4.57700	−0.714808	−0.357404	+	0.933950i	$0.616338\pi$
$42$	−14.3607	−2.21590
$43$	−10.9333	−1.66731	−0.833654	−	0.552287i	$-0.813755\pi$
$43$	−10.9333	−1.66731	−0.833654	+	0.552287i	$0.813755\pi$
$44$	7.55338	1.13871
$45$	0.914204	0.136281
$46$	4.82297	0.711108
$47$	−9.59260	−1.39922	−0.699612	−	0.714523i	$-0.746644\pi$
$47$	−9.59260	−1.39922	−0.699612	+	0.714523i	$0.746644\pi$
$48$	3.93549	0.568040
$49$	−2.31239	−0.330341
$50$	11.6768	1.65135
$51$	−22.7851	−3.19055
$52$	−21.5645	−2.99046
$53$	−0.183631	−0.0252237	−0.0126118	−	0.999920i	$-0.504015\pi$
$53$	−0.183631	−0.0252237	−0.0126118	+	0.999920i	$0.504015\pi$
$54$	−12.9822	−1.76665
$55$	0.394737	0.0532264
$56$	−7.78326	−1.04008
$57$	−15.3765	−2.03667
$58$	−9.58937	−1.25915
$59$	−10.8462	−1.41205	−0.706027	−	0.708185i	$-0.749514\pi$
$59$	−10.8462	−1.41205	−0.706027	+	0.708185i	$0.749514\pi$
$60$	1.83577	0.236997
$61$	−3.11089	−0.398309	−0.199155	−	0.979968i	$-0.563820\pi$
$61$	−3.11089	−0.398309	−0.199155	+	0.979968i	$0.563820\pi$
$62$	−15.3603	−1.95076
$63$	10.7329	1.35222
$64$	−11.9825	−1.49781
$65$	−1.12695	−0.139781
$66$	−14.1973	−1.74757
$67$	12.7351	1.55584	0.777921	−	0.628362i	$-0.216274\pi$
$67$	12.7351	1.55584	0.777921	+	0.628362i	$0.216274\pi$
$68$	−28.5039	−3.45660
$69$	−5.78600	−0.696552
$70$	−0.938848	−0.112214
$71$	13.0782	1.55210	0.776048	−	0.630674i	$-0.217221\pi$
$71$	13.0782	1.55210	0.776048	+	0.630674i	$0.217221\pi$
$72$	−17.8208	−2.10020
$73$	0.932173	0.109103	0.0545513	−	0.998511i	$-0.482627\pi$
$73$	0.932173	0.109103	0.0545513	+	0.998511i	$0.482627\pi$
$74$	−8.68797	−1.00996
$75$	−14.0084	−1.61755
$76$	−19.2359	−2.20650
$77$	4.63428	0.528126
$78$	40.5326	4.58941
$79$	−13.4589	−1.51425	−0.757124	−	0.653271i	$-0.773396\pi$
$79$	−13.4589	−1.51425	−0.757124	+	0.653271i	$0.773396\pi$
$80$	0.257288	0.0287656
$81$	0.702642	0.0780714
$82$	10.7622	1.18848
$83$	12.7780	1.40257	0.701286	−	0.712880i	$-0.252610\pi$
$83$	12.7780	1.40257	0.701286	+	0.712880i	$0.252610\pi$
$84$	21.5522	2.35154
$85$	−1.48960	−0.161570
$86$	25.7080	2.77216
$87$	11.5041	1.23337
$88$	−7.69472	−0.820260
$89$	−16.2812	−1.72580	−0.862900	−	0.505374i	$-0.831355\pi$
$89$	−16.2812	−1.72580	−0.862900	+	0.505374i	$0.831355\pi$
$90$	−2.14962	−0.226589
$91$	−13.2306	−1.38695
$92$	−7.23821	−0.754635
$93$	18.4273	1.91083
$94$	22.5556	2.32643
$95$	−1.00526	−0.103137
$96$	11.0277	1.12550
$97$	−5.35851	−0.544074	−0.272037	−	0.962287i	$-0.587697\pi$
$97$	−5.35851	−0.544074	−0.272037	+	0.962287i	$0.587697\pi$
$98$	5.43724	0.549244
$99$	10.6108	1.06643
$100$	−17.5243	−1.75243
$101$	−10.0583	−1.00083	−0.500417	−	0.865784i	$-0.666820\pi$
$101$	−10.0583	−1.00083	−0.500417	+	0.865784i	$0.666820\pi$
$102$	53.5758	5.30479
$103$	5.14731	0.507180	0.253590	−	0.967312i	$-0.418389\pi$
$103$	5.14731	0.507180	0.253590	+	0.967312i	$0.418389\pi$
$104$	21.9680	2.15414
$105$	1.12631	0.109917
$106$	0.431782	0.0419384
$107$	10.3951	1.00493	0.502467	−	0.864597i	$-0.332426\pi$
$107$	10.3951	1.00493	0.502467	+	0.864597i	$0.332426\pi$
$108$	19.4834	1.87479
$109$	−7.80141	−0.747240	−0.373620	−	0.927582i	$-0.621884\pi$
$109$	−7.80141	−0.747240	−0.373620	+	0.927582i	$0.621884\pi$
$110$	−0.928167	−0.0884972
$111$	10.4228	0.989284
$112$	3.02060	0.285420
$113$	−8.32757	−0.783392	−0.391696	−	0.920095i	$-0.628111\pi$
$113$	−8.32757	−0.783392	−0.391696	+	0.920095i	$0.628111\pi$
$114$	36.1557	3.38629
$115$	−0.378267	−0.0352735
$116$	14.3915	1.33622
$117$	−30.2933	−2.80061
$118$	25.5032	2.34776
$119$	−17.4882	−1.60314
$120$	−1.87012	−0.170718
$121$	−6.41844	−0.583494
$122$	7.31481	0.662252
$123$	−12.9111	−1.16415
$124$	23.0524	2.07016
$125$	−1.83790	−0.164387
$126$	−25.2369	−2.24828
$127$	−10.0727	−0.893806	−0.446903	−	0.894582i	$-0.647473\pi$
$127$	−10.0727	−0.893806	−0.446903	+	0.894582i	$0.647473\pi$
$128$	20.3564	1.79927
$129$	−30.8413	−2.71542
$130$	2.64987	0.232409
$131$	3.01359	0.263299	0.131649	−	0.991296i	$-0.457973\pi$
$131$	3.01359	0.263299	0.131649	+	0.991296i	$0.457973\pi$
$132$	21.3070	1.85454
$133$	−11.8019	−1.02336
$134$	−29.9448	−2.58683
$135$	1.01820	0.0876324
$136$	29.0372	2.48992
$137$	21.8803	1.86936	0.934679	−	0.355493i	$-0.115687\pi$
$137$	21.8803	1.86936	0.934679	+	0.355493i	$0.115687\pi$
$138$	13.6049	1.15813
$139$	5.49133	0.465769	0.232884	−	0.972504i	$-0.425184\pi$
$139$	5.49133	0.465769	0.232884	+	0.972504i	$0.425184\pi$
$140$	1.40900	0.119082
$141$	−27.0594	−2.27881
$142$	−30.7514	−2.58060
$143$	−13.0801	−1.09381
$144$	6.91607	0.576339
$145$	0.752097	0.0624583
$146$	−2.19187	−0.181400
$147$	−6.52292	−0.538002
$148$	13.0387	1.07178
$149$	15.1288	1.23940	0.619702	−	0.784837i	$-0.287254\pi$
$149$	15.1288	1.23940	0.619702	+	0.784837i	$0.287254\pi$
$150$	32.9386	2.68943
$151$	−6.48324	−0.527599	−0.263799	−	0.964578i	$-0.584976\pi$
$151$	−6.48324	−0.527599	−0.263799	+	0.964578i	$0.584976\pi$
$152$	19.5958	1.58943
$153$	−40.0415	−3.23717
$154$	−10.8968	−0.878092
$155$	1.20471	0.0967646
$156$	−60.8304	−4.87033
$157$	13.2231	1.05532	0.527660	−	0.849456i	$-0.323069\pi$
$157$	13.2231	1.05532	0.527660	+	0.849456i	$0.323069\pi$
$158$	31.6467	2.51768
$159$	−0.517998	−0.0410799
$160$	0.720946	0.0569958
$161$	−4.44091	−0.349993
$162$	−1.65216	−0.129806
$163$	5.37763	0.421209	0.210604	−	0.977571i	$-0.432457\pi$
$163$	5.37763	0.421209	0.210604	+	0.977571i	$0.432457\pi$
$164$	−16.1516	−1.26123
$165$	1.11350	0.0866858
$166$	−30.0457	−2.33200
$167$	−0.771414	−0.0596938	−0.0298469	−	0.999554i	$-0.509502\pi$
$167$	−0.771414	−0.0596938	−0.0298469	+	0.999554i	$0.509502\pi$
$168$	−21.9555	−1.69390
$169$	24.3430	1.87254
$170$	3.50258	0.268636
$171$	−27.0221	−2.06643
$172$	−38.5820	−2.94185
$173$	24.4414	1.85825	0.929124	−	0.369769i	$-0.120563\pi$
$173$	24.4414	1.85825	0.929124	+	0.369769i	$0.120563\pi$
$174$	−27.0503	−2.05068
$175$	−10.7518	−0.812761
$176$	2.98624	0.225096
$177$	−30.5956	−2.29971
$178$	38.2828	2.86942
$179$	15.4842	1.15734	0.578671	−	0.815561i	$-0.303571\pi$
$179$	15.4842	1.15734	0.578671	+	0.815561i	$0.303571\pi$
$180$	3.22610	0.240459
$181$	−15.9905	−1.18856	−0.594281	−	0.804257i	$-0.702563\pi$
$181$	−15.9905	−1.18856	−0.594281	+	0.804257i	$0.702563\pi$
$182$	31.1099	2.30602
$183$	−8.77540	−0.648696
$184$	7.37365	0.543593
$185$	0.681400	0.0500975
$186$	−43.3292	−3.17705
$187$	−17.2892	−1.26431
$188$	−33.8509	−2.46883
$189$	11.9538	0.869511
$190$	2.36372	0.171482
$191$	11.3864	0.823892	0.411946	−	0.911208i	$-0.364849\pi$
$191$	11.3864	0.823892	0.411946	+	0.911208i	$0.364849\pi$
$192$	−33.8009	−2.43937
$193$	−8.73945	−0.629080	−0.314540	−	0.949244i	$-0.601850\pi$
$193$	−8.73945	−0.629080	−0.314540	+	0.949244i	$0.601850\pi$
$194$	12.5997	0.904609
$195$	−3.17898	−0.227651
$196$	−8.16009	−0.582864
$197$	16.4668	1.17321	0.586605	−	0.809873i	$-0.300464\pi$
$197$	16.4668	1.17321	0.586605	+	0.809873i	$0.300464\pi$
$198$	−24.9498	−1.77310
$199$	10.9570	0.776721	0.388360	−	0.921508i	$-0.373042\pi$
$199$	10.9570	0.776721	0.388360	+	0.921508i	$0.373042\pi$
$200$	17.8522	1.26234
$201$	35.9240	2.53388
$202$	23.6505	1.66405
$203$	8.82975	0.619727
$204$	−80.4054	−5.62951
$205$	−0.844078	−0.0589530
$206$	−12.1031	−0.843266
$207$	−10.1681	−0.706729
$208$	−8.52555	−0.591140
$209$	−11.6677	−0.807069
$210$	−2.64836	−0.182754
$211$	−16.5785	−1.14131	−0.570656	−	0.821189i	$-0.693311\pi$
$211$	−16.5785	−1.14131	−0.570656	+	0.821189i	$0.693311\pi$
$212$	−0.648009	−0.0445055
$213$	36.8918	2.52778
$214$	−24.4426	−1.67086
$215$	−2.01628	−0.137509
$216$	−19.8480	−1.35048
$217$	14.1435	0.960123
$218$	18.3439	1.24240
$219$	2.62953	0.177687
$220$	1.39297	0.0939142
$221$	49.3598	3.32030
$222$	−24.5076	−1.64484
$223$	1.50806	0.100987	0.0504937	−	0.998724i	$-0.483921\pi$
$223$	1.50806	0.100987	0.0504937	+	0.998724i	$0.483921\pi$
$224$	8.46403	0.565527
$225$	−24.6177	−1.64118
$226$	19.5811	1.30251
$227$	−2.11772	−0.140558	−0.0702790	−	0.997527i	$-0.522389\pi$
$227$	−2.11772	−0.140558	−0.0702790	+	0.997527i	$0.522389\pi$
$228$	−54.2617	−3.59357
$229$	−25.0577	−1.65586	−0.827929	−	0.560833i	$-0.810481\pi$
$229$	−25.0577	−1.65586	−0.827929	+	0.560833i	$0.810481\pi$
$230$	0.889438	0.0586478
$231$	13.0727	0.860119
$232$	−14.6608	−0.962530
$233$	23.5194	1.54081	0.770404	−	0.637555i	$-0.220054\pi$
$233$	23.5194	1.54081	0.770404	+	0.637555i	$0.220054\pi$
$234$	71.2302	4.65646
$235$	−1.76904	−0.115399
$236$	−38.2747	−2.49147
$237$	−37.9658	−2.46614
$238$	41.1209	2.66547
$239$	−16.0127	−1.03578	−0.517889	−	0.855448i	$-0.673282\pi$
$239$	−16.0127	−1.03578	−0.517889	+	0.855448i	$0.673282\pi$
$240$	0.725773	0.0468484
$241$	−12.4992	−0.805146	−0.402573	−	0.915388i	$-0.631884\pi$
$241$	−12.4992	−0.805146	−0.402573	+	0.915388i	$0.631884\pi$
$242$	15.0920	0.970151
$243$	−14.5814	−0.935398
$244$	−10.9779	−0.702789
$245$	−0.426444	−0.0272445
$246$	30.3585	1.93559
$247$	33.3105	2.11950
$248$	−23.4837	−1.49122
$249$	36.0451	2.28426
$250$	4.32155	0.273319
$251$	11.1560	0.704161	0.352080	−	0.935970i	$-0.385474\pi$
$251$	11.1560	0.704161	0.352080	+	0.935970i	$0.385474\pi$
$252$	37.8750	2.38590
$253$	−4.39039	−0.276022
$254$	23.6844	1.48609
$255$	−4.20196	−0.263137
$256$	−23.9001	−1.49376
$257$	11.9157	0.743281	0.371641	−	0.928377i	$-0.378795\pi$
$257$	11.9157	0.743281	0.371641	+	0.928377i	$0.378795\pi$
$258$	72.5187	4.51482
$259$	7.99975	0.497080
$260$	−3.97686	−0.246635
$261$	20.2169	1.25139
$262$	−7.08602	−0.437776
$263$	7.51677	0.463504	0.231752	−	0.972775i	$-0.425554\pi$
$263$	7.51677	0.463504	0.231752	+	0.972775i	$0.425554\pi$
$264$	−21.7057	−1.33590
$265$	−0.0338648	−0.00208030
$266$	27.7505	1.70149
$267$	−45.9269	−2.81068
$268$	44.9405	2.74518
$269$	−18.5227	−1.12935	−0.564676	−	0.825313i	$-0.690999\pi$
$269$	−18.5227	−1.12935	−0.564676	+	0.825313i	$0.690999\pi$
$270$	−2.39414	−0.145703
$271$	−19.7344	−1.19878	−0.599391	−	0.800457i	$-0.704590\pi$
$271$	−19.7344	−1.19878	−0.599391	+	0.800457i	$0.704590\pi$
$272$	−11.2690	−0.683285
$273$	−37.3218	−2.25882
$274$	−51.4483	−3.10810
$275$	−10.6295	−0.640983
$276$	−20.4180	−1.22902
$277$	26.5100	1.59283	0.796415	−	0.604750i	$-0.206727\pi$
$277$	26.5100	1.59283	0.796415	+	0.604750i	$0.206727\pi$
$278$	−12.9121	−0.774414
$279$	32.3834	1.93874
$280$	−1.43537	−0.0857796
$281$	0.276145	0.0164734	0.00823670	−	0.999966i	$-0.497378\pi$
$281$	0.276145	0.0164734	0.00823670	+	0.999966i	$0.497378\pi$
$282$	63.6262	3.78888
$283$	−12.8192	−0.762025	−0.381012	−	0.924570i	$-0.624424\pi$
$283$	−12.8192	−0.762025	−0.381012	+	0.924570i	$0.624424\pi$
$284$	46.1511	2.73857
$285$	−2.83570	−0.167972
$286$	30.7560	1.81864
$287$	−9.90963	−0.584947
$288$	19.3795	1.14195
$289$	48.2436	2.83786
$290$	−1.76845	−0.103847
$291$	−15.1156	−0.886093
$292$	3.28951	0.192504
$293$	−7.26241	−0.424275	−0.212137	−	0.977240i	$-0.568042\pi$
$293$	−7.26241	−0.424275	−0.212137	+	0.977240i	$0.568042\pi$
$294$	15.3377	0.894513
$295$	−2.00023	−0.116458
$296$	−13.2827	−0.772042
$297$	11.8178	0.685739
$298$	−35.5733	−2.06070
$299$	12.5343	0.724879
$300$	−49.4336	−2.85405
$301$	−23.6715	−1.36440
$302$	15.2444	0.877216
$303$	−28.3730	−1.62998
$304$	−7.60492	−0.436172
$305$	−0.573702	−0.0328501
$306$	94.1518	5.38230
$307$	7.83023	0.446895	0.223447	−	0.974716i	$-0.428269\pi$
$307$	7.83023	0.446895	0.223447	+	0.974716i	$0.428269\pi$
$308$	16.3537	0.931841
$309$	14.5198	0.826005
$310$	−2.83270	−0.160886
$311$	−3.63541	−0.206145	−0.103072	−	0.994674i	$-0.532867\pi$
$311$	−3.63541	−0.206145	−0.103072	+	0.994674i	$0.532867\pi$
$312$	61.9687	3.50829
$313$	22.1210	1.25035	0.625177	−	0.780483i	$-0.285027\pi$
$313$	22.1210	1.25035	0.625177	+	0.780483i	$0.285027\pi$
$314$	−31.0922	−1.75464
$315$	1.97933	0.111523
$316$	−47.4947	−2.67179
$317$	32.5474	1.82804	0.914022	−	0.405666i	$-0.132960\pi$
$317$	32.5474	1.82804	0.914022	+	0.405666i	$0.132960\pi$
$318$	1.21800	0.0683019
$319$	8.72930	0.488747
$320$	−2.20977	−0.123530
$321$	29.3232	1.63666
$322$	10.4422	0.581919
$323$	44.0297	2.44988
$324$	2.47953	0.137751
$325$	30.3466	1.68333
$326$	−12.6447	−0.700326
$327$	−22.0067	−1.21697
$328$	16.4538	0.908511
$329$	−20.7688	−1.14502
$330$	−2.61823	−0.144129
$331$	−28.0421	−1.54133	−0.770667	−	0.637238i	$-0.780077\pi$
$331$	−28.0421	−1.54133	−0.770667	+	0.637238i	$0.780077\pi$
$332$	45.0919	2.47474
$333$	18.3165	1.00374
$334$	1.81387	0.0992504
$335$	2.34858	0.128316
$336$	8.52070	0.464842
$337$	−5.49192	−0.299164	−0.149582	−	0.988749i	$-0.547793\pi$
$337$	−5.49192	−0.299164	−0.149582	+	0.988749i	$0.547793\pi$
$338$	−57.2390	−3.11339
$339$	−23.4909	−1.27585
$340$	−5.25660	−0.285079
$341$	13.9826	0.757200
$342$	63.5384	3.43576
$343$	−20.1622	−1.08865
$344$	39.3039	2.11913
$345$	−1.06704	−0.0574474
$346$	−57.4704	−3.08963
$347$	5.01514	0.269227	0.134613	−	0.990898i	$-0.457021\pi$
$347$	5.01514	0.269227	0.134613	+	0.990898i	$0.457021\pi$
$348$	40.5965	2.17620
$349$	−4.34936	−0.232816	−0.116408	−	0.993201i	$-0.537138\pi$
$349$	−4.34936	−0.232816	−0.116408	+	0.993201i	$0.537138\pi$
$350$	25.2813	1.35134
$351$	−33.7392	−1.80087
$352$	8.36774	0.446002
$353$	−22.2356	−1.18348	−0.591740	−	0.806129i	$-0.701559\pi$
$353$	−22.2356	−1.18348	−0.591740	+	0.806129i	$0.701559\pi$
$354$	71.9411	3.82363
$355$	2.41184	0.128007
$356$	−57.4540	−3.04506
$357$	−49.3318	−2.61091
$358$	−36.4088	−1.92426
$359$	−30.8385	−1.62759	−0.813797	−	0.581150i	$-0.802603\pi$
$359$	−30.8385	−1.62759	−0.813797	+	0.581150i	$0.802603\pi$
$360$	−3.28646	−0.173212
$361$	10.7135	0.563868
$362$	37.5992	1.97617
$363$	−18.1055	−0.950294
$364$	−46.6891	−2.44717
$365$	0.171909	0.00899812
$366$	20.6341	1.07856
$367$	2.43803	0.127264	0.0636322	−	0.997973i	$-0.479732\pi$
$367$	2.43803	0.127264	0.0636322	+	0.997973i	$0.479732\pi$
$368$	−2.86163	−0.149173
$369$	−22.6894	−1.18116
$370$	−1.60221	−0.0832950
$371$	−0.397578	−0.0206412
$372$	65.0275	3.37152
$373$	−8.13640	−0.421287	−0.210643	−	0.977563i	$-0.567556\pi$
$373$	−8.13640	−0.421287	−0.210643	+	0.977563i	$0.567556\pi$
$374$	40.6531	2.10212
$375$	−5.18446	−0.267724
$376$	34.4844	1.77839
$377$	−24.9217	−1.28353
$378$	−28.1076	−1.44570
$379$	−17.5951	−0.903801	−0.451901	−	0.892068i	$-0.649254\pi$
$379$	−17.5951	−0.903801	−0.451901	+	0.892068i	$0.649254\pi$
$380$	−3.54742	−0.181979
$381$	−28.4136	−1.45567
$382$	−26.7735	−1.36985
$383$	−33.7939	−1.72679	−0.863394	−	0.504530i	$-0.831666\pi$
$383$	−33.7939	−1.72679	−0.863394	+	0.504530i	$0.831666\pi$
$384$	57.4225	2.93033
$385$	0.854642	0.0435566
$386$	20.5495	1.04594
$387$	−54.1991	−2.75509
$388$	−18.9094	−0.959981
$389$	19.7774	1.00276	0.501378	−	0.865228i	$-0.332827\pi$
$389$	19.7774	1.00276	0.501378	+	0.865228i	$0.332827\pi$
$390$	7.47490	0.378507
$391$	16.5678	0.837871
$392$	8.31278	0.419859
$393$	8.50093	0.428815
$394$	−38.7192	−1.95065
$395$	−2.48206	−0.124886
$396$	37.4441	1.88164
$397$	−1.71241	−0.0859432	−0.0429716	−	0.999076i	$-0.513682\pi$
$397$	−1.71241	−0.0859432	−0.0429716	+	0.999076i	$0.513682\pi$
$398$	−25.7638	−1.29142
$399$	−33.2916	−1.66666
$400$	−6.92825	−0.346412
$401$	19.7037	0.983956	0.491978	−	0.870608i	$-0.336274\pi$
$401$	19.7037	0.983956	0.491978	+	0.870608i	$0.336274\pi$
$402$	−84.4700	−4.21298
$403$	−39.9195	−1.98853
$404$	−35.4942	−1.76590
$405$	0.129579	0.00643885
$406$	−20.7619	−1.03039
$407$	7.90874	0.392022
$408$	81.9100	4.05515
$409$	−9.77811	−0.483496	−0.241748	−	0.970339i	$-0.577721\pi$
$409$	−9.77811	−0.483496	−0.241748	+	0.970339i	$0.577721\pi$
$410$	1.98473	0.0980187
$411$	61.7212	3.04448
$412$	18.1641	0.894883
$413$	−23.4830	−1.15552
$414$	23.9087	1.17505
$415$	2.35649	0.115676
$416$	−23.8894	−1.17128
$417$	15.4903	0.758562
$418$	27.4348	1.34188
$419$	39.4393	1.92674	0.963368	−	0.268184i	$-0.0864235\pi$
$419$	39.4393	1.92674	0.963368	+	0.268184i	$0.0864235\pi$
$420$	3.97460	0.193941
$421$	32.7153	1.59444	0.797222	−	0.603686i	$-0.206302\pi$
$421$	32.7153	1.59444	0.797222	+	0.603686i	$0.206302\pi$
$422$	38.9819	1.89761
$423$	−47.5530	−2.31211
$424$	0.660135	0.0320590
$425$	40.1121	1.94572
$426$	−86.7456	−4.20284
$427$	−6.73536	−0.325947
$428$	36.6829	1.77313
$429$	−36.8972	−1.78141
$430$	4.74100	0.228631
$431$	2.28026	0.109836	0.0549181	−	0.998491i	$-0.482510\pi$
$431$	2.28026	0.109836	0.0549181	+	0.998491i	$0.482510\pi$
$432$	7.70278	0.370600
$433$	2.43900	0.117211	0.0586055	−	0.998281i	$-0.481335\pi$
$433$	2.43900	0.117211	0.0586055	+	0.998281i	$0.481335\pi$
$434$	−33.2564	−1.59636
$435$	2.12156	0.101721
$436$	−27.5301	−1.31845
$437$	11.1808	0.534851
$438$	−6.18296	−0.295433
$439$	30.2860	1.44547	0.722736	−	0.691125i	$-0.242884\pi$
$439$	30.2860	1.44547	0.722736	+	0.691125i	$0.242884\pi$
$440$	−1.41904	−0.0676500
$441$	−11.4631	−0.545862
$442$	−116.062	−5.52052
$443$	−10.7551	−0.510992	−0.255496	−	0.966810i	$-0.582239\pi$
$443$	−10.7551	−0.510992	−0.255496	+	0.966810i	$0.582239\pi$
$444$	36.7804	1.74552
$445$	−3.00253	−0.142334
$446$	−3.54599	−0.167907
$447$	42.6764	2.01852
$448$	−25.9431	−1.22570
$449$	3.36934	0.159009	0.0795045	−	0.996835i	$-0.474666\pi$
$449$	3.36934	0.159009	0.0795045	+	0.996835i	$0.474666\pi$
$450$	57.8849	2.72872
$451$	−9.79689	−0.461317
$452$	−29.3868	−1.38224
$453$	−18.2883	−0.859261
$454$	4.97951	0.233700
$455$	−2.43996	−0.114387
$456$	55.2770	2.58858
$457$	9.25144	0.432764	0.216382	−	0.976309i	$-0.430574\pi$
$457$	9.25144	0.432764	0.216382	+	0.976309i	$0.430574\pi$
$458$	58.9194	2.75312
$459$	−44.5963	−2.08158
$460$	−1.33485	−0.0622377
$461$	−2.35256	−0.109570	−0.0547849	−	0.998498i	$-0.517447\pi$
$461$	−2.35256	−0.109570	−0.0547849	+	0.998498i	$0.517447\pi$
$462$	−30.7385	−1.43008
$463$	−21.4209	−0.995515	−0.497758	−	0.867316i	$-0.665843\pi$
$463$	−21.4209	−0.995515	−0.497758	+	0.867316i	$0.665843\pi$
$464$	5.68971	0.264138
$465$	3.39832	0.157593
$466$	−55.3025	−2.56184
$467$	39.6469	1.83464	0.917319	−	0.398152i	$-0.130348\pi$
$467$	39.6469	1.83464	0.917319	+	0.398152i	$0.130348\pi$
$468$	−106.901	−4.94149
$469$	27.5727	1.27319
$470$	4.15964	0.191870
$471$	37.3006	1.71872
$472$	38.9909	1.79470
$473$	−23.4022	−1.07604
$474$	89.2710	4.10035
$475$	27.0697	1.24204
$476$	−61.7134	−2.82863
$477$	−0.910308	−0.0416801
$478$	37.6516	1.72214
$479$	4.94334	0.225867	0.112933	−	0.993603i	$-0.463975\pi$
$479$	4.94334	0.225867	0.112933	+	0.993603i	$0.463975\pi$
$480$	2.03369	0.0928248
$481$	−22.5790	−1.02952
$482$	29.3901	1.33868
$483$	−12.5272	−0.570007
$484$	−22.6498	−1.02954
$485$	−0.988201	−0.0448719
$486$	34.2861	1.55525
$487$	−12.4411	−0.563762	−0.281881	−	0.959449i	$-0.590958\pi$
$487$	−12.4411	−0.563762	−0.281881	+	0.959449i	$0.590958\pi$
$488$	11.1833	0.506246
$489$	15.1696	0.685991
$490$	1.00272	0.0452983
$491$	−39.1411	−1.76641	−0.883206	−	0.468984i	$-0.844620\pi$
$491$	−39.1411	−1.76641	−0.883206	+	0.468984i	$0.844620\pi$
$492$	−45.5615	−2.05407
$493$	−32.9413	−1.48360
$494$	−78.3248	−3.52400
$495$	1.95682	0.0879523
$496$	9.11378	0.409221
$497$	28.3155	1.27012
$498$	−84.7547	−3.79795
$499$	22.6165	1.01245	0.506227	−	0.862401i	$-0.331040\pi$
$499$	22.6165	1.01245	0.506227	+	0.862401i	$0.331040\pi$
$500$	−6.48569	−0.290049
$501$	−2.17605	−0.0972188
$502$	−26.2317	−1.17078
$503$	−28.0653	−1.25137	−0.625685	−	0.780076i	$-0.715180\pi$
$503$	−28.0653	−1.25137	−0.625685	+	0.780076i	$0.715180\pi$
$504$	−38.5837	−1.71865
$505$	−1.85492	−0.0825427
$506$	10.3234	0.458929
$507$	68.6682	3.04966
$508$	−35.5451	−1.57706
$509$	18.1486	0.804424	0.402212	−	0.915546i	$-0.368241\pi$
$509$	18.1486	0.804424	0.402212	+	0.915546i	$0.368241\pi$
$510$	9.88030	0.437507
$511$	2.01824	0.0892816
$512$	15.4848	0.684338
$513$	−30.0959	−1.32877
$514$	−28.0180	−1.23582
$515$	0.949253	0.0418291
$516$	−108.834	−4.79117
$517$	−20.5326	−0.903021
$518$	−18.8102	−0.826475
$519$	68.9459	3.02639
$520$	4.05128	0.177660
$521$	−19.1023	−0.836886	−0.418443	−	0.908243i	$-0.637424\pi$
$521$	−19.1023	−0.836886	−0.418443	+	0.908243i	$0.637424\pi$
$522$	−47.5370	−2.08064
$523$	−0.386880	−0.0169171	−0.00845854	−	0.999964i	$-0.502692\pi$
$523$	−0.386880	−0.0169171	−0.00845854	+	0.999964i	$0.502692\pi$
$524$	10.6345	0.464572
$525$	−30.3294	−1.32368
$526$	−17.6746	−0.770648
$527$	−52.7655	−2.29850
$528$	8.42376	0.366597
$529$	−18.7928	−0.817078
$530$	0.0796280	0.00345882
$531$	−53.7674	−2.33331
$532$	−41.6474	−1.80564
$533$	27.9696	1.21150
$534$	107.990	4.67320
$535$	1.91704	0.0828807
$536$	−45.7814	−1.97745
$537$	43.6788	1.88488
$538$	43.5535	1.87772
$539$	−4.94957	−0.213193
$540$	3.59307	0.154621
$541$	−1.91066	−0.0821457	−0.0410729	−	0.999156i	$-0.513078\pi$
$541$	−1.91066	−0.0821457	−0.0410729	+	0.999156i	$0.513078\pi$
$542$	46.4026	1.99316
$543$	−45.1069	−1.93572
$544$	−31.5770	−1.35385
$545$	−1.43871	−0.0616278
$546$	87.7567	3.75564
$547$	−5.16094	−0.220666	−0.110333	−	0.993895i	$-0.535192\pi$
$547$	−5.16094	−0.220666	−0.110333	+	0.993895i	$0.535192\pi$
$548$	77.2125	3.29835
$549$	−15.4215	−0.658174
$550$	24.9937	1.06573
$551$	−22.2305	−0.947051
$552$	20.8000	0.885308
$553$	−29.1398	−1.23915
$554$	−62.3343	−2.64833
$555$	1.92213	0.0815901
$556$	19.3781	0.821816
$557$	−6.20380	−0.262863	−0.131432	−	0.991325i	$-0.541957\pi$
$557$	−6.20380	−0.262863	−0.131432	+	0.991325i	$0.541957\pi$
$558$	−76.1448	−3.22347
$559$	66.8121	2.82585
$560$	0.557051	0.0235397
$561$	−48.7705	−2.05909
$562$	−0.649313	−0.0273896
$563$	−13.3562	−0.562895	−0.281447	−	0.959577i	$-0.590814\pi$
$563$	−13.3562	−0.562895	−0.281447	+	0.959577i	$0.590814\pi$
$564$	−95.4888	−4.02080
$565$	−1.53575	−0.0646094
$566$	30.1426	1.26699
$567$	1.52128	0.0638879
$568$	−47.0147	−1.97269
$569$	−15.9812	−0.669965	−0.334982	−	0.942224i	$-0.608730\pi$
$569$	−15.9812	−0.669965	−0.334982	+	0.942224i	$0.608730\pi$
$570$	6.66773	0.279280
$571$	0.281261	0.0117704	0.00588520	−	0.999983i	$-0.498127\pi$
$571$	0.281261	0.0117704	0.00588520	+	0.999983i	$0.498127\pi$
$572$	−46.1579	−1.92996
$573$	32.1195	1.34181
$574$	23.3010	0.972566
$575$	10.1860	0.424784
$576$	−59.4002	−2.47501
$577$	37.3232	1.55379	0.776893	−	0.629633i	$-0.216795\pi$
$577$	37.3232	1.55379	0.776893	+	0.629633i	$0.216795\pi$
$578$	−113.438	−4.71839
$579$	−24.6528	−1.02453
$580$	2.65405	0.110203
$581$	27.6656	1.14776
$582$	35.5421	1.47327
$583$	−0.393055	−0.0162787
$584$	−3.35106	−0.138668
$585$	−5.58660	−0.230978
$586$	17.0765	0.705424
$587$	5.02505	0.207406	0.103703	−	0.994608i	$-0.466931\pi$
$587$	5.02505	0.207406	0.103703	+	0.994608i	$0.466931\pi$
$588$	−23.0185	−0.949267
$589$	−35.6088	−1.46724
$590$	4.70324	0.193629
$591$	46.4505	1.91072
$592$	5.15488	0.211864
$593$	22.3274	0.916875	0.458437	−	0.888727i	$-0.348409\pi$
$593$	22.3274	0.916875	0.458437	+	0.888727i	$0.348409\pi$
$594$	−27.7878	−1.14015
$595$	−3.22512	−0.132217
$596$	53.3876	2.18684
$597$	30.9082	1.26499
$598$	−29.4726	−1.20523
$599$	21.3632	0.872875	0.436438	−	0.899735i	$-0.356240\pi$
$599$	21.3632	0.872875	0.436438	+	0.899735i	$0.356240\pi$
$600$	50.3586	2.05588
$601$	−19.4435	−0.793116	−0.396558	−	0.918010i	$-0.629795\pi$
$601$	−19.4435	−0.793116	−0.396558	+	0.918010i	$0.629795\pi$
$602$	55.6601	2.26854
$603$	63.1313	2.57091
$604$	−22.8785	−0.930911
$605$	−1.18367	−0.0481230
$606$	66.7149	2.71011
$607$	−30.0225	−1.21858	−0.609288	−	0.792949i	$-0.708545\pi$
$607$	−30.0225	−1.21858	−0.609288	+	0.792949i	$0.708545\pi$
$608$	−21.3097	−0.864224
$609$	24.9075	1.00930
$610$	1.34898	0.0546185
$611$	58.6193	2.37148
$612$	−141.301	−5.71175
$613$	−22.7560	−0.919106	−0.459553	−	0.888150i	$-0.651990\pi$
$613$	−22.7560	−0.919106	−0.459553	+	0.888150i	$0.651990\pi$
$614$	−18.4116	−0.743033
$615$	−2.38103	−0.0960123
$616$	−16.6598	−0.671241
$617$	−40.4622	−1.62895	−0.814474	−	0.580200i	$-0.802975\pi$
$617$	−40.4622	−1.62895	−0.814474	+	0.580200i	$0.802975\pi$
$618$	−34.1413	−1.37336
$619$	−20.4387	−0.821502	−0.410751	−	0.911748i	$-0.634733\pi$
$619$	−20.4387	−0.821502	−0.410751	+	0.911748i	$0.634733\pi$
$620$	4.25125	0.170734
$621$	−11.3247	−0.454444
$622$	8.54812	0.342748
$623$	−35.2502	−1.41227
$624$	−24.0494	−0.962746
$625$	24.4910	0.979640
$626$	−52.0143	−2.07891
$627$	−32.9128	−1.31441
$628$	46.6626	1.86204
$629$	−29.8449	−1.18999
$630$	−4.65411	−0.185424
$631$	22.4819	0.894990	0.447495	−	0.894286i	$-0.352316\pi$
$631$	22.4819	0.894990	0.447495	+	0.894286i	$0.352316\pi$
$632$	48.3834	1.92459
$633$	−46.7657	−1.85877
$634$	−76.5304	−3.03941
$635$	−1.85758	−0.0737156
$636$	−1.82794	−0.0724827
$637$	14.1307	0.559881
$638$	−20.5257	−0.812618
$639$	64.8320	2.56471
$640$	3.75407	0.148393
$641$	−43.3672	−1.71290	−0.856452	−	0.516227i	$-0.827336\pi$
$641$	−43.3672	−1.71290	−0.856452	+	0.516227i	$0.827336\pi$
$642$	−68.9491	−2.72120
$643$	−6.01394	−0.237167	−0.118583	−	0.992944i	$-0.537835\pi$
$643$	−6.01394	−0.237167	−0.118583	+	0.992944i	$0.537835\pi$
$644$	−15.6714	−0.617538
$645$	−5.68766	−0.223951
$646$	−103.529	−4.07331
$647$	−21.4521	−0.843370	−0.421685	−	0.906742i	$-0.638561\pi$
$647$	−21.4521	−0.843370	−0.421685	+	0.906742i	$0.638561\pi$
$648$	−2.52592	−0.0992276
$649$	−23.2158	−0.911301
$650$	−71.3556	−2.79880
$651$	39.8969	1.56368
$652$	18.9769	0.743193
$653$	13.8956	0.543776	0.271888	−	0.962329i	$-0.412352\pi$
$653$	13.8956	0.543776	0.271888	+	0.962329i	$0.412352\pi$
$654$	51.7455	2.02341
$655$	0.555758	0.0217153
$656$	−6.38556	−0.249314
$657$	4.62102	0.180283
$658$	48.8349	1.90378
$659$	−29.3488	−1.14327	−0.571634	−	0.820509i	$-0.693690\pi$
$659$	−29.3488	−1.14327	−0.571634	+	0.820509i	$0.693690\pi$
$660$	3.92938	0.152951
$661$	8.46176	0.329124	0.164562	−	0.986367i	$-0.447379\pi$
$661$	8.46176	0.329124	0.164562	+	0.986367i	$0.447379\pi$
$662$	65.9369	2.56271
$663$	139.237	5.40753
$664$	−45.9357	−1.78265
$665$	−2.17648	−0.0844002
$666$	−43.0685	−1.66887
$667$	−8.36506	−0.323896
$668$	−2.72221	−0.105326
$669$	4.25404	0.164471
$670$	−5.52233	−0.213346
$671$	−6.65874	−0.257058
$672$	23.8759	0.921031
$673$	21.5032	0.828888	0.414444	−	0.910075i	$-0.363976\pi$
$673$	21.5032	0.828888	0.414444	+	0.910075i	$0.363976\pi$
$674$	12.9134	0.497407
$675$	−27.4180	−1.05532
$676$	85.9031	3.30396
$677$	37.1895	1.42931	0.714654	−	0.699478i	$-0.246584\pi$
$677$	37.1895	1.42931	0.714654	+	0.699478i	$0.246584\pi$
$678$	55.2354	2.12130
$679$	−11.6017	−0.445230
$680$	5.35496	0.205353
$681$	−5.97379	−0.228916
$682$	−32.8780	−1.25896
$683$	−46.4197	−1.77620	−0.888101	−	0.459648i	$-0.847976\pi$
$683$	−46.4197	−1.77620	−0.888101	+	0.459648i	$0.847976\pi$
$684$	−95.3571	−3.64607
$685$	4.03510	0.154173
$686$	47.4083	1.81006
$687$	−70.6842	−2.69677
$688$	−15.2534	−0.581532
$689$	1.12215	0.0427505
$690$	2.50898	0.0955153
$691$	−34.8012	−1.32390	−0.661950	−	0.749548i	$-0.730271\pi$
$691$	−34.8012	−1.32390	−0.661950	+	0.749548i	$0.730271\pi$
$692$	86.2504	3.27875
$693$	22.9733	0.872685
$694$	−11.7924	−0.447632
$695$	1.01270	0.0384137
$696$	−41.3561	−1.56760
$697$	36.9701	1.40034
$698$	10.2269	0.387093
$699$	66.3450	2.50940
$700$	−37.9417	−1.43406
$701$	−40.0998	−1.51455	−0.757274	−	0.653097i	$-0.773469\pi$
$701$	−40.0998	−1.51455	−0.757274	+	0.653097i	$0.773469\pi$
$702$	79.3328	2.99422
$703$	−20.1408	−0.759626
$704$	−25.6480	−0.966645
$705$	−4.99022	−0.187942
$706$	52.2836	1.96772
$707$	−21.7770	−0.819010
$708$	−107.968	−4.05768
$709$	−34.5804	−1.29869	−0.649347	−	0.760492i	$-0.724958\pi$
$709$	−34.5804	−1.29869	−0.649347	+	0.760492i	$0.724958\pi$
$710$	−5.67110	−0.212832
$711$	−66.7194	−2.50217
$712$	58.5291	2.19347
$713$	−13.3992	−0.501802
$714$	115.996	4.34106
$715$	−2.41220	−0.0902111
$716$	54.6416	2.04205
$717$	−45.1697	−1.68689
$718$	72.5122	2.70613
$719$	10.7042	0.399201	0.199600	−	0.979877i	$-0.436036\pi$
$719$	10.7042	0.399201	0.199600	+	0.979877i	$0.436036\pi$
$720$	1.27544	0.0475329
$721$	11.1444	0.415039
$722$	−25.1912	−0.937520
$723$	−35.2586	−1.31128
$724$	−56.4281	−2.09714
$725$	−20.2525	−0.752158
$726$	42.5725	1.58001
$727$	−16.8165	−0.623691	−0.311845	−	0.950133i	$-0.600947\pi$
$727$	−16.8165	−0.623691	−0.311845	+	0.950133i	$0.600947\pi$
$728$	47.5627	1.76279
$729$	−43.2401	−1.60148
$730$	−0.404218	−0.0149608
$731$	88.3119	3.26633
$732$	−30.9672	−1.14458
$733$	41.6626	1.53884	0.769421	−	0.638741i	$-0.220545\pi$
$733$	41.6626	1.53884	0.769421	+	0.638741i	$0.220545\pi$
$734$	−5.73268	−0.211597
$735$	−1.20294	−0.0443711
$736$	−8.01859	−0.295569
$737$	27.2590	1.00410
$738$	53.3508	1.96387
$739$	−28.4986	−1.04834	−0.524169	−	0.851614i	$-0.675624\pi$
$739$	−28.4986	−1.04834	−0.524169	+	0.851614i	$0.675624\pi$
$740$	2.40457	0.0883936
$741$	93.9644	3.45187
$742$	0.934847	0.0343193
$743$	−2.12511	−0.0779628	−0.0389814	−	0.999240i	$-0.512411\pi$
$743$	−2.12511	−0.0779628	−0.0389814	+	0.999240i	$0.512411\pi$
$744$	−66.2443	−2.42863
$745$	2.79002	0.102218
$746$	19.1316	0.700456
$747$	63.3440	2.31764
$748$	−61.0113	−2.23079
$749$	22.5063	0.822364
$750$	12.1905	0.445134
$751$	−6.11302	−0.223067	−0.111534	−	0.993761i	$-0.535576\pi$
$751$	−6.11302	−0.223067	−0.111534	+	0.993761i	$0.535576\pi$
$752$	−13.3830	−0.488028
$753$	31.4695	1.14681
$754$	58.5996	2.13407
$755$	−1.19562	−0.0435131
$756$	42.1833	1.53419
$757$	−37.7630	−1.37252	−0.686260	−	0.727357i	$-0.740749\pi$
$757$	−37.7630	−1.37252	−0.686260	+	0.727357i	$0.740749\pi$
$758$	41.3724	1.50271
$759$	−12.3847	−0.449536
$760$	3.61380	0.131086
$761$	21.4803	0.778662	0.389331	−	0.921098i	$-0.372706\pi$
$761$	21.4803	0.778662	0.389331	+	0.921098i	$0.372706\pi$
$762$	66.8105	2.42029
$763$	−16.8908	−0.611487
$764$	40.1811	1.45370
$765$	−7.38435	−0.266982
$766$	79.4614	2.87106
$767$	66.2799	2.39323
$768$	−67.4188	−2.43277
$769$	21.4662	0.774089	0.387045	−	0.922061i	$-0.373496\pi$
$769$	21.4662	0.774089	0.387045	+	0.922061i	$0.373496\pi$
$770$	−2.00956	−0.0724197
$771$	33.6126	1.21053
$772$	−30.8403	−1.10997
$773$	−41.2757	−1.48458	−0.742291	−	0.670078i	$-0.766261\pi$
$773$	−41.2757	−1.48458	−0.742291	+	0.670078i	$0.766261\pi$
$774$	127.441	4.58078
$775$	−32.4404	−1.16530
$776$	19.2633	0.691511
$777$	22.5662	0.809558
$778$	−46.5037	−1.66724
$779$	24.9493	0.893901
$780$	−11.2182	−0.401675
$781$	27.9933	1.00168
$782$	−38.9568	−1.39309
$783$	22.5166	0.804677
$784$	−3.22610	−0.115218
$785$	2.43857	0.0870364
$786$	−19.9887	−0.712973
$787$	25.6070	0.912790	0.456395	−	0.889777i	$-0.349140\pi$
$787$	25.6070	0.912790	0.456395	+	0.889777i	$0.349140\pi$
$788$	58.1090	2.07005
$789$	21.2038	0.754874
$790$	5.83620	0.207643
$791$	−18.0299	−0.641071
$792$	−38.1447	−1.35541
$793$	19.0103	0.675077
$794$	4.02647	0.142894
$795$	−0.0955278	−0.00338802
$796$	38.6657	1.37047
$797$	−19.0181	−0.673655	−0.336827	−	0.941566i	$-0.609354\pi$
$797$	−19.0181	−0.673655	−0.336827	+	0.941566i	$0.609354\pi$
$798$	78.2803	2.77109
$799$	77.4828	2.74114
$800$	−19.4136	−0.686376
$801$	−80.7100	−2.85175
$802$	−46.3304	−1.63598
$803$	1.99528	0.0704118
$804$	126.771	4.47086
$805$	−0.818981	−0.0288653
$806$	93.8649	3.30625
$807$	−52.2501	−1.83929
$808$	36.1584	1.27205
$809$	3.47798	0.122279	0.0611397	−	0.998129i	$-0.480526\pi$
$809$	3.47798	0.122279	0.0611397	+	0.998129i	$0.480526\pi$
$810$	−0.304687	−0.0107056
$811$	21.2105	0.744801	0.372400	−	0.928072i	$-0.378535\pi$
$811$	21.2105	0.744801	0.372400	+	0.928072i	$0.378535\pi$
$812$	31.1590	1.09346
$813$	−55.6681	−1.95237
$814$	−18.5962	−0.651798
$815$	0.991728	0.0347387
$816$	−31.7884	−1.11282
$817$	59.5974	2.08505
$818$	22.9918	0.803889
$819$	−65.5877	−2.29182
$820$	−2.97864	−0.104018
$821$	−18.0545	−0.630106	−0.315053	−	0.949074i	$-0.602022\pi$
$821$	−18.0545	−0.630106	−0.315053	+	0.949074i	$0.602022\pi$
$822$	−145.128	−5.06193
$823$	−46.8043	−1.63150	−0.815748	−	0.578408i	$-0.803674\pi$
$823$	−46.8043	−1.63150	−0.815748	+	0.578408i	$0.803674\pi$
$824$	−18.5040	−0.644618
$825$	−29.9843	−1.04392
$826$	55.2168	1.92124
$827$	−10.2734	−0.357242	−0.178621	−	0.983918i	$-0.557164\pi$
$827$	−10.2734	−0.357242	−0.178621	+	0.983918i	$0.557164\pi$
$828$	−35.8817	−1.24697
$829$	−47.7764	−1.65934	−0.829672	−	0.558251i	$-0.811472\pi$
$829$	−47.7764	−1.65934	−0.829672	+	0.558251i	$0.811472\pi$
$830$	−5.54094	−0.192329
$831$	74.7810	2.59412
$832$	73.2236	2.53857
$833$	18.6780	0.647153
$834$	−36.4231	−1.26123
$835$	−0.142262	−0.00492318
$836$	−41.1735	−1.42402
$837$	36.0671	1.24666
$838$	−92.7357	−3.20350
$839$	−43.5597	−1.50385	−0.751924	−	0.659250i	$-0.770874\pi$
$839$	−43.5597	−1.50385	−0.751924	+	0.659250i	$0.770874\pi$
$840$	−4.04897	−0.139703
$841$	−12.3680	−0.426482
$842$	−76.9251	−2.65102
$843$	0.778966	0.0268290
$844$	−58.5033	−2.01377
$845$	4.48927	0.154436
$846$	111.814	3.84424
$847$	−13.8965	−0.477489
$848$	−0.256191	−0.00879764
$849$	−36.1613	−1.24105
$850$	−94.3176	−3.23507
$851$	−7.57874	−0.259796
$852$	130.186	4.46010
$853$	−4.66110	−0.159593	−0.0797964	−	0.996811i	$-0.525427\pi$
$853$	−4.66110	−0.159593	−0.0797964	+	0.996811i	$0.525427\pi$
$854$	15.8372	0.541939
$855$	−4.98333	−0.170426
$856$	−37.3693	−1.27726
$857$	−14.5987	−0.498683	−0.249341	−	0.968416i	$-0.580214\pi$
$857$	−14.5987	−0.498683	−0.249341	+	0.968416i	$0.580214\pi$
$858$	86.7583	2.96188
$859$	−2.53408	−0.0864615	−0.0432308	−	0.999065i	$-0.513765\pi$
$859$	−2.53408	−0.0864615	−0.0432308	+	0.999065i	$0.513765\pi$
$860$	−7.11519	−0.242626
$861$	−27.9537	−0.952659
$862$	−5.36169	−0.182620
$863$	−42.4353	−1.44451	−0.722257	−	0.691625i	$-0.756895\pi$
$863$	−42.4353	−1.44451	−0.722257	+	0.691625i	$0.756895\pi$
$864$	21.5840	0.734302
$865$	4.50742	0.153257
$866$	−5.73495	−0.194882
$867$	136.089	4.62181
$868$	49.9104	1.69407
$869$	−28.8083	−0.977255
$870$	−4.98854	−0.169127
$871$	−77.8230	−2.63693
$872$	28.0452	0.949732
$873$	−26.5635	−0.899039
$874$	−26.2900	−0.889274
$875$	−3.97922	−0.134522
$876$	9.27925	0.313517
$877$	29.4687	0.995087	0.497543	−	0.867439i	$-0.334236\pi$
$877$	29.4687	0.995087	0.497543	+	0.867439i	$0.334236\pi$
$878$	−71.2130	−2.40332
$879$	−20.4863	−0.690984
$880$	0.550714	0.0185646
$881$	33.7924	1.13850	0.569248	−	0.822166i	$-0.307234\pi$
$881$	33.7924	1.13850	0.569248	+	0.822166i	$0.307234\pi$
$882$	26.9538	0.907582
$883$	51.6999	1.73984	0.869920	−	0.493193i	$-0.164170\pi$
$883$	51.6999	1.73984	0.869920	+	0.493193i	$0.164170\pi$
$884$	174.184	5.85844
$885$	−5.64236	−0.189666
$886$	25.2891	0.849604
$887$	−27.5511	−0.925074	−0.462537	−	0.886600i	$-0.653061\pi$
$887$	−27.5511	−0.925074	−0.462537	+	0.886600i	$0.653061\pi$
$888$	−37.4687	−1.25737
$889$	−21.8083	−0.731425
$890$	7.06000	0.236652
$891$	1.50398	0.0503851
$892$	5.32174	0.178185
$893$	52.2893	1.74980
$894$	−100.347	−3.35611
$895$	2.85555	0.0954506
$896$	44.0734	1.47239
$897$	35.3576	1.18056
$898$	−7.92251	−0.264378
$899$	26.6412	0.888533
$900$	−86.8725	−2.89575
$901$	1.48325	0.0494144
$902$	23.0359	0.767013
$903$	−66.7741	−2.22210
$904$	29.9367	0.995680
$905$	−2.94892	−0.0980253
$906$	43.0023	1.42866
$907$	27.8263	0.923958	0.461979	−	0.886891i	$-0.347140\pi$
$907$	27.8263	0.923958	0.461979	+	0.886891i	$0.347140\pi$
$908$	−7.47314	−0.248005
$909$	−49.8614	−1.65380
$910$	5.73720	0.190186
$911$	−11.7801	−0.390293	−0.195146	−	0.980774i	$-0.562518\pi$
$911$	−11.7801	−0.390293	−0.195146	+	0.980774i	$0.562518\pi$
$912$	−21.4524	−0.710361
$913$	27.3508	0.905181
$914$	−21.7534	−0.719539
$915$	−1.61834	−0.0535005
$916$	−88.4251	−2.92165
$917$	6.52470	0.215465
$918$	104.862	3.46095
$919$	52.6174	1.73569	0.867843	−	0.496838i	$-0.165506\pi$
$919$	52.6174	1.73569	0.867843	+	0.496838i	$0.165506\pi$
$920$	1.35983	0.0448322
$921$	22.0880	0.727824
$922$	5.53170	0.182177
$923$	−79.9194	−2.63058
$924$	46.1317	1.51762
$925$	−18.3488	−0.603303
$926$	50.3682	1.65520
$927$	25.5166	0.838074
$928$	15.9431	0.523359
$929$	−49.0208	−1.60832	−0.804160	−	0.594413i	$-0.797384\pi$
$929$	−49.0208	−1.60832	−0.804160	+	0.594413i	$0.797384\pi$
$930$	−7.99065	−0.262024
$931$	12.6048	0.413107
$932$	82.9968	2.71865
$933$	−10.2550	−0.335733
$934$	−93.2238	−3.05038
$935$	−3.18843	−0.104273
$936$	108.901	3.55954
$937$	−0.266454	−0.00870469	−0.00435234	−	0.999991i	$-0.501385\pi$
$937$	−0.266454	−0.00870469	−0.00435234	+	0.999991i	$0.501385\pi$
$938$	−64.8331	−2.11688
$939$	62.4003	2.03636
$940$	−6.24270	−0.203614
$941$	20.3030	0.661858	0.330929	−	0.943656i	$-0.392638\pi$
$941$	20.3030	0.661858	0.330929	+	0.943656i	$0.392638\pi$
$942$	−87.7069	−2.85764
$943$	9.38810	0.305719
$944$	−15.1320	−0.492503
$945$	2.20449	0.0717120
$946$	55.0269	1.78908
$947$	41.7017	1.35512	0.677562	−	0.735466i	$-0.263037\pi$
$947$	41.7017	1.35512	0.677562	+	0.735466i	$0.263037\pi$
$948$	−133.976	−4.35134
$949$	−5.69641	−0.184913
$950$	−63.6503	−2.06509
$951$	91.8117	2.97720
$952$	62.8682	2.03757
$953$	30.7871	0.997291	0.498646	−	0.866806i	$-0.333831\pi$
$953$	30.7871	0.997291	0.498646	+	0.866806i	$0.333831\pi$
$954$	2.14046	0.0692998
$955$	2.09985	0.0679495
$956$	−56.5067	−1.82756
$957$	24.6241	0.795985
$958$	−11.6235	−0.375539
$959$	47.3728	1.52975
$960$	−6.23347	−0.201184
$961$	11.6739	0.376576
$962$	53.0913	1.71173
$963$	51.5313	1.66057
$964$	−44.1080	−1.42062
$965$	−1.61171	−0.0518826
$966$	29.4559	0.947727
$967$	−4.40997	−0.141815	−0.0709075	−	0.997483i	$-0.522590\pi$
$967$	−4.40997	−0.141815	−0.0709075	+	0.997483i	$0.522590\pi$
$968$	23.0736	0.741613
$969$	124.202	3.98993
$970$	2.32361	0.0746066
$971$	3.62171	0.116226	0.0581132	−	0.998310i	$-0.481492\pi$
$971$	3.62171	0.116226	0.0581132	+	0.998310i	$0.481492\pi$
$972$	−51.4558	−1.65045
$973$	11.8892	0.381151
$974$	29.2535	0.937344
$975$	85.6036	2.74151
$976$	−4.34013	−0.138924
$977$	46.3347	1.48238	0.741189	−	0.671296i	$-0.234262\pi$
$977$	46.3347	1.48238	0.741189	+	0.671296i	$0.234262\pi$
$978$	−35.6690	−1.14057
$979$	−34.8492	−1.11378
$980$	−1.50486	−0.0480710
$981$	−38.6736	−1.23475
$982$	92.0345	2.93694
$983$	16.4105	0.523413	0.261706	−	0.965148i	$-0.415715\pi$
$983$	16.4105	0.523413	0.261706	+	0.965148i	$0.415715\pi$
$984$	46.4140	1.47962
$985$	3.03676	0.0967592
$986$	77.4567	2.46673
$987$	−58.5860	−1.86481
$988$	117.548	3.73971
$989$	22.4257	0.713097
$990$	−4.60116	−0.146235
$991$	−10.4882	−0.333170	−0.166585	−	0.986027i	$-0.553274\pi$
$991$	−10.4882	−0.333170	−0.166585	+	0.986027i	$0.553274\pi$
$992$	25.5377	0.810824
$993$	−79.1029	−2.51025
$994$	−66.5796	−2.11178
$995$	2.02066	0.0640592
$996$	127.198	4.03042
$997$	−13.1879	−0.417665	−0.208832	−	0.977951i	$-0.566966\pi$
$997$	−13.1879	−0.417665	−0.208832	+	0.977951i	$0.566966\pi$
$998$	−53.1794	−1.68336
$999$	20.4000	0.645428

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4019.2.a.a.1.16	✓	149

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4019.2.a.a.1.16	✓	149	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 4019 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4019.a (trivial)

\(f(q)\)	\(=\)	\(q-2.35135 q^{2} +2.82086 q^{3} +3.52886 q^{4} +0.184417 q^{5} -6.63284 q^{6} +2.16509 q^{7} -3.59489 q^{8} +4.95726 q^{9} +O(q^{10})\)	\(q-2.35135 q^{2} +2.82086 q^{3} +3.52886 q^{4} +0.184417 q^{5} -6.63284 q^{6} +2.16509 q^{7} -3.59489 q^{8} +4.95726 q^{9} -0.433630 q^{10} +2.14046 q^{11} +9.95443 q^{12} -6.11089 q^{13} -5.09089 q^{14} +0.520215 q^{15} +1.39514 q^{16} -8.07735 q^{17} -11.6563 q^{18} -5.45101 q^{19} +0.650783 q^{20} +6.10742 q^{21} -5.03297 q^{22} -2.05115 q^{23} -10.1407 q^{24} -4.96599 q^{25} +14.3689 q^{26} +5.52116 q^{27} +7.64030 q^{28} +4.07824 q^{29} -1.22321 q^{30} +6.53252 q^{31} +3.90932 q^{32} +6.03794 q^{33} +18.9927 q^{34} +0.399280 q^{35} +17.4935 q^{36} +3.69488 q^{37} +12.8172 q^{38} -17.2380 q^{39} -0.662960 q^{40} -4.57700 q^{41} -14.3607 q^{42} -10.9333 q^{43} +7.55338 q^{44} +0.914204 q^{45} +4.82297 q^{46} -9.59260 q^{47} +3.93549 q^{48} -2.31239 q^{49} +11.6768 q^{50} -22.7851 q^{51} -21.5645 q^{52} -0.183631 q^{53} -12.9822 q^{54} +0.394737 q^{55} -7.78326 q^{56} -15.3765 q^{57} -9.58937 q^{58} -10.8462 q^{59} +1.83577 q^{60} -3.11089 q^{61} -15.3603 q^{62} +10.7329 q^{63} -11.9825 q^{64} -1.12695 q^{65} -14.1973 q^{66} +12.7351 q^{67} -28.5039 q^{68} -5.78600 q^{69} -0.938848 q^{70} +13.0782 q^{71} -17.8208 q^{72} +0.932173 q^{73} -8.68797 q^{74} -14.0084 q^{75} -19.2359 q^{76} +4.63428 q^{77} +40.5326 q^{78} -13.4589 q^{79} +0.257288 q^{80} +0.702642 q^{81} +10.7622 q^{82} +12.7780 q^{83} +21.5522 q^{84} -1.48960 q^{85} +25.7080 q^{86} +11.5041 q^{87} -7.69472 q^{88} -16.2812 q^{89} -2.14962 q^{90} -13.2306 q^{91} -7.23821 q^{92} +18.4273 q^{93} +22.5556 q^{94} -1.00526 q^{95} +11.0277 q^{96} -5.35851 q^{97} +5.43724 q^{98} +10.6108 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 149 q - 8 q^{2} - 12 q^{3} + 124 q^{4} - 36 q^{5} - 45 q^{6} - 32 q^{7} - 21 q^{8} + 115 q^{9}+O(q^{10}) \) 149 * q - 8 * q^2 - 12 * q^3 + 124 * q^4 - 36 * q^5 - 45 * q^6 - 32 * q^7 - 21 * q^8 + 115 * q^9	\( 149 q - 8 q^{2} - 12 q^{3} + 124 q^{4} - 36 q^{5} - 45 q^{6} - 32 q^{7} - 21 q^{8} + 115 q^{9} - 58 q^{10} - 33 q^{11} - 33 q^{12} - 107 q^{13} - 28 q^{14} - 24 q^{15} + 74 q^{16} - 39 q^{17} - 33 q^{18} - 93 q^{19} - 63 q^{20} - 113 q^{21} - 38 q^{22} - 11 q^{23} - 130 q^{24} + 85 q^{25} - 33 q^{26} - 30 q^{27} - 94 q^{28} - 85 q^{29} - 16 q^{30} - 129 q^{31} - 35 q^{32} - 64 q^{33} - 78 q^{34} - 27 q^{35} + 79 q^{36} - 135 q^{37} - 11 q^{38} - 73 q^{39} - 146 q^{40} - 101 q^{41} + 4 q^{42} - 55 q^{43} - 82 q^{44} - 168 q^{45} - 113 q^{46} - 40 q^{47} - 65 q^{48} + 27 q^{49} - 5 q^{50} - 49 q^{51} - 177 q^{52} - 32 q^{53} - 155 q^{54} - 128 q^{55} - 44 q^{56} - 47 q^{57} - 46 q^{58} - 53 q^{59} - 11 q^{60} - 347 q^{61} - 11 q^{62} - 73 q^{63} + q^{64} - 31 q^{65} - 37 q^{66} - 40 q^{67} - 80 q^{68} - 175 q^{69} - 61 q^{70} - 31 q^{71} - 68 q^{72} - 193 q^{73} - 33 q^{74} - 56 q^{75} - 248 q^{76} - 84 q^{77} + 40 q^{78} - 111 q^{79} - 54 q^{80} + 49 q^{81} - 74 q^{82} - 24 q^{83} - 159 q^{84} - 258 q^{85} - q^{86} - 66 q^{87} - 97 q^{88} - 76 q^{89} - 75 q^{90} - 134 q^{91} + 31 q^{92} - 97 q^{93} - 111 q^{94} - 14 q^{95} - 216 q^{96} - 140 q^{97} - 13 q^{98} - 116 q^{99}+O(q^{100}) \) 149 * q - 8 * q^2 - 12 * q^3 + 124 * q^4 - 36 * q^5 - 45 * q^6 - 32 * q^7 - 21 * q^8 + 115 * q^9 - 58 * q^10 - 33 * q^11 - 33 * q^12 - 107 * q^13 - 28 * q^14 - 24 * q^15 + 74 * q^16 - 39 * q^17 - 33 * q^18 - 93 * q^19 - 63 * q^20 - 113 * q^21 - 38 * q^22 - 11 * q^23 - 130 * q^24 + 85 * q^25 - 33 * q^26 - 30 * q^27 - 94 * q^28 - 85 * q^29 - 16 * q^30 - 129 * q^31 - 35 * q^32 - 64 * q^33 - 78 * q^34 - 27 * q^35 + 79 * q^36 - 135 * q^37 - 11 * q^38 - 73 * q^39 - 146 * q^40 - 101 * q^41 + 4 * q^42 - 55 * q^43 - 82 * q^44 - 168 * q^45 - 113 * q^46 - 40 * q^47 - 65 * q^48 + 27 * q^49 - 5 * q^50 - 49 * q^51 - 177 * q^52 - 32 * q^53 - 155 * q^54 - 128 * q^55 - 44 * q^56 - 47 * q^57 - 46 * q^58 - 53 * q^59 - 11 * q^60 - 347 * q^61 - 11 * q^62 - 73 * q^63 + q^64 - 31 * q^65 - 37 * q^66 - 40 * q^67 - 80 * q^68 - 175 * q^69 - 61 * q^70 - 31 * q^71 - 68 * q^72 - 193 * q^73 - 33 * q^74 - 56 * q^75 - 248 * q^76 - 84 * q^77 + 40 * q^78 - 111 * q^79 - 54 * q^80 + 49 * q^81 - 74 * q^82 - 24 * q^83 - 159 * q^84 - 258 * q^85 - q^86 - 66 * q^87 - 97 * q^88 - 76 * q^89 - 75 * q^90 - 134 * q^91 + 31 * q^92 - 97 * q^93 - 111 * q^94 - 14 * q^95 - 216 * q^96 - 140 * q^97 - 13 * q^98 - 116 * q^99

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