LMFDB - Embedded newform 6023.2.a.d.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6023,2,Mod(1,6023)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6023, 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("6023.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6023 = 19 \cdot 317 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6023.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:	$48.0938971374$
Analytic rank:	$0$
Dimension:	$140$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	6023.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.62272 q^{2} +0.254820 q^{3} +4.87868 q^{4} +4.28261 q^{5} -0.668323 q^{6} +3.95531 q^{7} -7.54997 q^{8} -2.93507 q^{9} +O(q^{10})$	\(q-2.62272 q^{2} +0.254820 q^{3} +4.87868 q^{4} +4.28261 q^{5} -0.668323 q^{6} +3.95531 q^{7} -7.54997 q^{8} -2.93507 q^{9} -11.2321 q^{10} +2.57016 q^{11} +1.24319 q^{12} -0.526883 q^{13} -10.3737 q^{14} +1.09130 q^{15} +10.0441 q^{16} +5.93296 q^{17} +7.69787 q^{18} -1.00000 q^{19} +20.8935 q^{20} +1.00789 q^{21} -6.74081 q^{22} -2.15148 q^{23} -1.92389 q^{24} +13.3408 q^{25} +1.38187 q^{26} -1.51238 q^{27} +19.2967 q^{28} +9.56136 q^{29} -2.86217 q^{30} +0.940124 q^{31} -11.2430 q^{32} +0.654929 q^{33} -15.5605 q^{34} +16.9390 q^{35} -14.3192 q^{36} +9.43601 q^{37} +2.62272 q^{38} -0.134260 q^{39} -32.3336 q^{40} -2.20389 q^{41} -2.64342 q^{42} -3.20582 q^{43} +12.5390 q^{44} -12.5697 q^{45} +5.64275 q^{46} -1.93501 q^{47} +2.55945 q^{48} +8.64445 q^{49} -34.9891 q^{50} +1.51184 q^{51} -2.57049 q^{52} +0.870806 q^{53} +3.96654 q^{54} +11.0070 q^{55} -29.8624 q^{56} -0.254820 q^{57} -25.0768 q^{58} +3.70773 q^{59} +5.32408 q^{60} +2.42690 q^{61} -2.46569 q^{62} -11.6091 q^{63} +9.39909 q^{64} -2.25643 q^{65} -1.71770 q^{66} -6.55021 q^{67} +28.9450 q^{68} -0.548242 q^{69} -44.4264 q^{70} -9.90777 q^{71} +22.1597 q^{72} -2.02810 q^{73} -24.7480 q^{74} +3.39950 q^{75} -4.87868 q^{76} +10.1658 q^{77} +0.352128 q^{78} -13.9154 q^{79} +43.0151 q^{80} +8.41982 q^{81} +5.78019 q^{82} -2.81630 q^{83} +4.91718 q^{84} +25.4085 q^{85} +8.40799 q^{86} +2.43643 q^{87} -19.4046 q^{88} -4.23959 q^{89} +32.9670 q^{90} -2.08398 q^{91} -10.4964 q^{92} +0.239563 q^{93} +5.07500 q^{94} -4.28261 q^{95} -2.86495 q^{96} -2.47912 q^{97} -22.6720 q^{98} -7.54358 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 140 q + 4 q^{2} + 3 q^{3} + 162 q^{4} + 13 q^{5} + 12 q^{6} + 25 q^{7} + 12 q^{8} + 181 q^{9}+O(q^{10}) $ 140 * q + 4 * q^2 + 3 * q^3 + 162 * q^4 + 13 * q^5 + 12 * q^6 + 25 * q^7 + 12 * q^8 + 181 * q^9	\( 140 q + 4 q^{2} + 3 q^{3} + 162 q^{4} + 13 q^{5} + 12 q^{6} + 25 q^{7} + 12 q^{8} + 181 q^{9} + 8 q^{10} + 19 q^{11} + 17 q^{12} + 28 q^{13} + 5 q^{14} + 14 q^{15} + 202 q^{16} + 38 q^{17} + 26 q^{18} - 140 q^{19} + 36 q^{20} + 4 q^{21} + 53 q^{22} + 58 q^{23} + 47 q^{24} + 279 q^{25} + 29 q^{26} + 21 q^{27} + 69 q^{28} + 18 q^{29} + 50 q^{30} + 20 q^{31} + 13 q^{32} + 47 q^{33} + 6 q^{34} + 35 q^{35} + 230 q^{36} + 88 q^{37} - 4 q^{38} + 32 q^{39} + 32 q^{40} + 24 q^{41} + 75 q^{42} + 100 q^{43} + 63 q^{44} + 87 q^{45} + 23 q^{46} + 35 q^{47} + 46 q^{48} + 255 q^{49} + 11 q^{50} - 6 q^{51} + 47 q^{52} + 77 q^{53} + 16 q^{54} + 63 q^{55} + 21 q^{56} - 3 q^{57} + 165 q^{58} + 18 q^{59} + 28 q^{60} + 99 q^{61} + 34 q^{62} + 89 q^{63} + 298 q^{64} + 78 q^{65} - 3 q^{66} + 28 q^{67} + 93 q^{68} + 19 q^{69} + 16 q^{70} + q^{71} + 43 q^{72} + 201 q^{73} + 32 q^{74} + 22 q^{75} - 162 q^{76} + 86 q^{77} + 122 q^{78} + 58 q^{79} + 92 q^{80} + 288 q^{81} + 143 q^{82} + 57 q^{83} + q^{84} + 136 q^{85} - 6 q^{86} + 43 q^{87} + 198 q^{88} + 46 q^{89} + 30 q^{90} + 26 q^{91} + 129 q^{92} + 111 q^{93} + 44 q^{94} - 13 q^{95} + 32 q^{96} + 110 q^{97} - 34 q^{98} + 62 q^{99}+O(q^{100}) \) 140 * q + 4 * q^2 + 3 * q^3 + 162 * q^4 + 13 * q^5 + 12 * q^6 + 25 * q^7 + 12 * q^8 + 181 * q^9 + 8 * q^10 + 19 * q^11 + 17 * q^12 + 28 * q^13 + 5 * q^14 + 14 * q^15 + 202 * q^16 + 38 * q^17 + 26 * q^18 - 140 * q^19 + 36 * q^20 + 4 * q^21 + 53 * q^22 + 58 * q^23 + 47 * q^24 + 279 * q^25 + 29 * q^26 + 21 * q^27 + 69 * q^28 + 18 * q^29 + 50 * q^30 + 20 * q^31 + 13 * q^32 + 47 * q^33 + 6 * q^34 + 35 * q^35 + 230 * q^36 + 88 * q^37 - 4 * q^38 + 32 * q^39 + 32 * q^40 + 24 * q^41 + 75 * q^42 + 100 * q^43 + 63 * q^44 + 87 * q^45 + 23 * q^46 + 35 * q^47 + 46 * q^48 + 255 * q^49 + 11 * q^50 - 6 * q^51 + 47 * q^52 + 77 * q^53 + 16 * q^54 + 63 * q^55 + 21 * q^56 - 3 * q^57 + 165 * q^58 + 18 * q^59 + 28 * q^60 + 99 * q^61 + 34 * q^62 + 89 * q^63 + 298 * q^64 + 78 * q^65 - 3 * q^66 + 28 * q^67 + 93 * q^68 + 19 * q^69 + 16 * q^70 + q^71 + 43 * q^72 + 201 * q^73 + 32 * q^74 + 22 * q^75 - 162 * q^76 + 86 * q^77 + 122 * q^78 + 58 * q^79 + 92 * q^80 + 288 * q^81 + 143 * q^82 + 57 * q^83 + q^84 + 136 * q^85 - 6 * q^86 + 43 * q^87 + 198 * q^88 + 46 * q^89 + 30 * q^90 + 26 * q^91 + 129 * q^92 + 111 * q^93 + 44 * q^94 - 13 * q^95 + 32 * q^96 + 110 * q^97 - 34 * q^98 + 62 * 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 $

$2$	−2.62272	−1.85455	−0.927273	−	0.374387i	$-0.877853\pi$
$2$	−2.62272	−1.85455	−0.927273	+	0.374387i	$0.877853\pi$
$3$	0.254820	0.147121	0.0735603	−	0.997291i	$-0.476564\pi$
$3$	0.254820	0.147121	0.0735603	+	0.997291i	$0.476564\pi$
$4$	4.87868	2.43934
$5$	4.28261	1.91524	0.957621	−	0.288031i	$-0.0930008\pi$
$5$	4.28261	1.91524	0.957621	+	0.288031i	$0.0930008\pi$
$6$	−0.668323	−0.272842
$7$	3.95531	1.49497	0.747483	−	0.664281i	$-0.231262\pi$
$7$	3.95531	1.49497	0.747483	+	0.664281i	$0.231262\pi$
$8$	−7.54997	−2.66932
$9$	−2.93507	−0.978356
$10$	−11.2321	−3.55190
$11$	2.57016	0.774932	0.387466	−	0.921884i	$-0.373350\pi$
$11$	2.57016	0.774932	0.387466	+	0.921884i	$0.373350\pi$
$12$	1.24319	0.358877
$13$	−0.526883	−0.146131	−0.0730655	−	0.997327i	$-0.523278\pi$
$13$	−0.526883	−0.146131	−0.0730655	+	0.997327i	$0.523278\pi$
$14$	−10.3737	−2.77248
$15$	1.09130	0.281772
$16$	10.0441	2.51103
$17$	5.93296	1.43895	0.719477	−	0.694517i	$-0.244382\pi$
$17$	5.93296	1.43895	0.719477	+	0.694517i	$0.244382\pi$
$18$	7.69787	1.81440
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	20.8935	4.67192
$21$	1.00789	0.219940
$22$	−6.74081	−1.43715
$23$	−2.15148	−0.448616	−0.224308	−	0.974518i	$-0.572012\pi$
$23$	−2.15148	−0.448616	−0.224308	+	0.974518i	$0.572012\pi$
$24$	−1.92389	−0.392712
$25$	13.3408	2.66815
$26$	1.38187	0.271007
$27$	−1.51238	−0.291057
$28$	19.2967	3.64673
$29$	9.56136	1.77550	0.887750	−	0.460325i	$-0.152267\pi$
$29$	9.56136	1.77550	0.887750	+	0.460325i	$0.152267\pi$
$30$	−2.86217	−0.522558
$31$	0.940124	0.168851	0.0844257	−	0.996430i	$-0.473094\pi$
$31$	0.940124	0.168851	0.0844257	+	0.996430i	$0.473094\pi$
$32$	−11.2430	−1.98751
$33$	0.654929	0.114008
$34$	−15.5605	−2.66860
$35$	16.9390	2.86322
$36$	−14.3192	−2.38654
$37$	9.43601	1.55127	0.775635	−	0.631181i	$-0.217430\pi$
$37$	9.43601	1.55127	0.775635	+	0.631181i	$0.217430\pi$
$38$	2.62272	0.425462
$39$	−0.134260	−0.0214989
$40$	−32.3336	−5.11239
$41$	−2.20389	−0.344190	−0.172095	−	0.985080i	$-0.555054\pi$
$41$	−2.20389	−0.344190	−0.172095	+	0.985080i	$0.555054\pi$
$42$	−2.64342	−0.407889
$43$	−3.20582	−0.488884	−0.244442	−	0.969664i	$-0.578605\pi$
$43$	−3.20582	−0.488884	−0.244442	+	0.969664i	$0.578605\pi$
$44$	12.5390	1.89032
$45$	−12.5697	−1.87379
$46$	5.64275	0.831978
$47$	−1.93501	−0.282250	−0.141125	−	0.989992i	$-0.545072\pi$
$47$	−1.93501	−0.282250	−0.141125	+	0.989992i	$0.545072\pi$
$48$	2.55945	0.369425
$49$	8.64445	1.23492
$50$	−34.9891	−4.94821
$51$	1.51184	0.211700
$52$	−2.57049	−0.356463
$53$	0.870806	0.119614	0.0598072	−	0.998210i	$-0.480951\pi$
$53$	0.870806	0.119614	0.0598072	+	0.998210i	$0.480951\pi$
$54$	3.96654	0.539778
$55$	11.0070	1.48418
$56$	−29.8624	−3.99054
$57$	−0.254820	−0.0337518
$58$	−25.0768	−3.29275
$59$	3.70773	0.482706	0.241353	−	0.970437i	$-0.422409\pi$
$59$	3.70773	0.482706	0.241353	+	0.970437i	$0.422409\pi$
$60$	5.32408	0.687336
$61$	2.42690	0.310733	0.155367	−	0.987857i	$-0.450344\pi$
$61$	2.42690	0.310733	0.155367	+	0.987857i	$0.450344\pi$
$62$	−2.46569	−0.313142
$63$	−11.6091	−1.46261
$64$	9.39909	1.17489
$65$	−2.25643	−0.279876
$66$	−1.71770	−0.211434
$67$	−6.55021	−0.800236	−0.400118	−	0.916464i	$-0.631031\pi$
$67$	−6.55021	−0.800236	−0.400118	+	0.916464i	$0.631031\pi$
$68$	28.9450	3.51009
$69$	−0.548242	−0.0660006
$70$	−44.4264	−5.30997
$71$	−9.90777	−1.17584	−0.587918	−	0.808921i	$-0.700052\pi$
$71$	−9.90777	−1.17584	−0.587918	+	0.808921i	$0.700052\pi$
$72$	22.1597	2.61154
$73$	−2.02810	−0.237371	−0.118685	−	0.992932i	$-0.537868\pi$
$73$	−2.02810	−0.237371	−0.118685	+	0.992932i	$0.537868\pi$
$74$	−24.7480	−2.87690
$75$	3.39950	0.392540
$76$	−4.87868	−0.559623
$77$	10.1658	1.15850
$78$	0.352128	0.0398706
$79$	−13.9154	−1.56561	−0.782803	−	0.622269i	$-0.786211\pi$
$79$	−13.9154	−1.56561	−0.782803	+	0.622269i	$0.786211\pi$
$80$	43.0151	4.80923
$81$	8.41982	0.935535
$82$	5.78019	0.638315
$83$	−2.81630	−0.309129	−0.154565	−	0.987983i	$-0.549397\pi$
$83$	−2.81630	−0.309129	−0.154565	+	0.987983i	$0.549397\pi$
$84$	4.91718	0.536509
$85$	25.4085	2.75594
$86$	8.40799	0.906657
$87$	2.43643	0.261213
$88$	−19.4046	−2.06854
$89$	−4.23959	−0.449395	−0.224698	−	0.974429i	$-0.572139\pi$
$89$	−4.23959	−0.449395	−0.224698	+	0.974429i	$0.572139\pi$
$90$	32.9670	3.47502
$91$	−2.08398	−0.218461
$92$	−10.4964	−1.09433
$93$	0.239563	0.0248415
$94$	5.07500	0.523446
$95$	−4.28261	−0.439387
$96$	−2.86495	−0.292403
$97$	−2.47912	−0.251717	−0.125858	−	0.992048i	$-0.540168\pi$
$97$	−2.47912	−0.251717	−0.125858	+	0.992048i	$0.540168\pi$
$98$	−22.6720	−2.29022
$99$	−7.54358	−0.758159
$100$	65.0852	6.50852
$101$	0.181456	0.0180555	0.00902777	−	0.999959i	$-0.497126\pi$
$101$	0.181456	0.0180555	0.00902777	+	0.999959i	$0.497126\pi$
$102$	−3.96513	−0.392607
$103$	13.0480	1.28566	0.642829	−	0.766010i	$-0.277761\pi$
$103$	13.0480	1.28566	0.642829	+	0.766010i	$0.277761\pi$
$104$	3.97795	0.390070
$105$	4.31641	0.421239
$106$	−2.28388	−0.221830
$107$	−19.7984	−1.91398	−0.956991	−	0.290116i	$-0.906306\pi$
$107$	−19.7984	−1.91398	−0.956991	+	0.290116i	$0.906306\pi$
$108$	−7.37839	−0.709986
$109$	14.5622	1.39480	0.697402	−	0.716680i	$-0.254339\pi$
$109$	14.5622	1.39480	0.697402	+	0.716680i	$0.254339\pi$
$110$	−28.8683	−2.75248
$111$	2.40449	0.228224
$112$	39.7276	3.75391
$113$	−17.7730	−1.67194	−0.835971	−	0.548773i	$-0.815095\pi$
$113$	−17.7730	−1.67194	−0.835971	+	0.548773i	$0.815095\pi$
$114$	0.668323	0.0625942
$115$	−9.21397	−0.859207
$116$	46.6468	4.33105
$117$	1.54644	0.142968
$118$	−9.72436	−0.895200
$119$	23.4667	2.15119
$120$	−8.23926	−0.752138
$121$	−4.39429	−0.399481
$122$	−6.36510	−0.576269
$123$	−0.561596	−0.0506374
$124$	4.58656	0.411885
$125$	35.7202	3.19491
$126$	30.4474	2.71247
$127$	9.83365	0.872595	0.436297	−	0.899802i	$-0.356290\pi$
$127$	9.83365	0.872595	0.436297	+	0.899802i	$0.356290\pi$
$128$	−2.16516	−0.191375
$129$	−0.816909	−0.0719248
$130$	5.91800	0.519043
$131$	8.06331	0.704495	0.352247	−	0.935907i	$-0.385418\pi$
$131$	8.06331	0.704495	0.352247	+	0.935907i	$0.385418\pi$
$132$	3.19518	0.278105
$133$	−3.95531	−0.342969
$134$	17.1794	1.48407
$135$	−6.47692	−0.557444
$136$	−44.7937	−3.84102
$137$	−1.53398	−0.131056	−0.0655282	−	0.997851i	$-0.520873\pi$
$137$	−1.53398	−0.131056	−0.0655282	+	0.997851i	$0.520873\pi$
$138$	1.43789	0.122401
$139$	18.8503	1.59886	0.799429	−	0.600761i	$-0.205136\pi$
$139$	18.8503	1.59886	0.799429	+	0.600761i	$0.205136\pi$
$140$	82.6401	6.98436
$141$	−0.493080	−0.0415249
$142$	25.9853	2.18064
$143$	−1.35417	−0.113242
$144$	−29.4802	−2.45668
$145$	40.9476	3.40051
$146$	5.31914	0.440215
$147$	2.20278	0.181682
$148$	46.0352	3.78407
$149$	2.59731	0.212780	0.106390	−	0.994324i	$-0.466071\pi$
$149$	2.59731	0.212780	0.106390	+	0.994324i	$0.466071\pi$
$150$	−8.91594	−0.727983
$151$	−5.41648	−0.440787	−0.220394	−	0.975411i	$-0.570734\pi$
$151$	−5.41648	−0.440787	−0.220394	+	0.975411i	$0.570734\pi$
$152$	7.54997	0.612383
$153$	−17.4136	−1.40781
$154$	−26.6620	−2.14848
$155$	4.02619	0.323391
$156$	−0.655013	−0.0524430
$157$	7.08613	0.565535	0.282767	−	0.959188i	$-0.408748\pi$
$157$	7.08613	0.565535	0.282767	+	0.959188i	$0.408748\pi$
$158$	36.4963	2.90349
$159$	0.221899	0.0175978
$160$	−48.1495	−3.80655
$161$	−8.50978	−0.670665
$162$	−22.0828	−1.73499
$163$	−18.1752	−1.42359	−0.711796	−	0.702386i	$-0.752118\pi$
$163$	−18.1752	−1.42359	−0.711796	+	0.702386i	$0.752118\pi$
$164$	−10.7521	−0.839595
$165$	2.80480	0.218354
$166$	7.38638	0.573294
$167$	−20.2646	−1.56812	−0.784062	−	0.620683i	$-0.786856\pi$
$167$	−20.2646	−1.56812	−0.784062	+	0.620683i	$0.786856\pi$
$168$	−7.60956	−0.587090
$169$	−12.7224	−0.978646
$170$	−66.6396	−5.11102
$171$	2.93507	0.224450
$172$	−15.6402	−1.19255
$173$	20.3192	1.54484	0.772420	−	0.635112i	$-0.219046\pi$
$173$	20.3192	1.54484	0.772420	+	0.635112i	$0.219046\pi$
$174$	−6.39008	−0.484431
$175$	52.7668	3.98879
$176$	25.8150	1.94588
$177$	0.944806	0.0710160
$178$	11.1193	0.833424
$179$	−0.500689	−0.0374233	−0.0187116	−	0.999825i	$-0.505956\pi$
$179$	−0.500689	−0.0374233	−0.0187116	+	0.999825i	$0.505956\pi$
$180$	−61.3237	−4.57080
$181$	−14.1449	−1.05138	−0.525690	−	0.850676i	$-0.676193\pi$
$181$	−14.1449	−1.05138	−0.525690	+	0.850676i	$0.676193\pi$
$182$	5.46571	0.405145
$183$	0.618425	0.0457153
$184$	16.2436	1.19750
$185$	40.4108	2.97106
$186$	−0.628307	−0.0460697
$187$	15.2486	1.11509
$188$	−9.44029	−0.688504
$189$	−5.98191	−0.435120
$190$	11.2321	0.814862
$191$	−7.47030	−0.540532	−0.270266	−	0.962786i	$-0.587112\pi$
$191$	−7.47030	−0.540532	−0.270266	+	0.962786i	$0.587112\pi$
$192$	2.39508	0.172850
$193$	0.163979	0.0118035	0.00590173	−	0.999983i	$-0.498121\pi$
$193$	0.163979	0.0118035	0.00590173	+	0.999983i	$0.498121\pi$
$194$	6.50205	0.466820
$195$	−0.574985	−0.0411756
$196$	42.1735	3.01239
$197$	−25.2935	−1.80208	−0.901042	−	0.433731i	$-0.857197\pi$
$197$	−25.2935	−1.80208	−0.901042	+	0.433731i	$0.857197\pi$
$198$	19.7847	1.40604
$199$	6.23257	0.441815	0.220907	−	0.975295i	$-0.429098\pi$
$199$	6.23257	0.441815	0.220907	+	0.975295i	$0.429098\pi$
$200$	−100.722	−7.12214
$201$	−1.66913	−0.117731
$202$	−0.475909	−0.0334848
$203$	37.8181	2.65431
$204$	7.37577	0.516407
$205$	−9.43840	−0.659206
$206$	−34.2213	−2.38431
$207$	6.31475	0.438906
$208$	−5.29208	−0.366940
$209$	−2.57016	−0.177782
$210$	−11.3208	−0.781206
$211$	6.31696	0.434878	0.217439	−	0.976074i	$-0.430230\pi$
$211$	6.31696	0.434878	0.217439	+	0.976074i	$0.430230\pi$
$212$	4.24838	0.291780
$213$	−2.52470	−0.172990
$214$	51.9257	3.54957
$215$	−13.7293	−0.936330
$216$	11.4184	0.776923
$217$	3.71848	0.252427
$218$	−38.1926	−2.58673
$219$	−0.516800	−0.0349221
$220$	53.6995	3.62042
$221$	−3.12597	−0.210276
$222$	−6.30631	−0.423252
$223$	25.6725	1.71916	0.859580	−	0.511002i	$-0.170726\pi$
$223$	25.6725	1.71916	0.859580	+	0.511002i	$0.170726\pi$
$224$	−44.4696	−2.97125
$225$	−39.1560	−2.61040
$226$	46.6137	3.10069
$227$	−24.4741	−1.62440	−0.812200	−	0.583379i	$-0.801730\pi$
$227$	−24.4741	−1.62440	−0.812200	+	0.583379i	$0.801730\pi$
$228$	−1.24319	−0.0823320
$229$	12.7185	0.840461	0.420230	−	0.907417i	$-0.361949\pi$
$229$	12.7185	0.840461	0.420230	+	0.907417i	$0.361949\pi$
$230$	24.1657	1.59344
$231$	2.59044	0.170439
$232$	−72.1880	−4.73938
$233$	4.90719	0.321481	0.160740	−	0.986997i	$-0.448612\pi$
$233$	4.90719	0.321481	0.160740	+	0.986997i	$0.448612\pi$
$234$	−4.05587	−0.265141
$235$	−8.28690	−0.540578
$236$	18.0888	1.17748
$237$	−3.54593	−0.230333
$238$	−61.5466	−3.98947
$239$	−19.1360	−1.23781	−0.618903	−	0.785468i	$-0.712422\pi$
$239$	−19.1360	−1.23781	−0.618903	+	0.785468i	$0.712422\pi$
$240$	10.9611	0.707538
$241$	−13.3094	−0.857336	−0.428668	−	0.903462i	$-0.641017\pi$
$241$	−13.3094	−0.857336	−0.428668	+	0.903462i	$0.641017\pi$
$242$	11.5250	0.740855
$243$	6.68267	0.428693
$244$	11.8401	0.757983
$245$	37.0208	2.36517
$246$	1.47291	0.0939093
$247$	0.526883	0.0335247
$248$	−7.09791	−0.450718
$249$	−0.717651	−0.0454793
$250$	−93.6842	−5.92511
$251$	16.2150	1.02348	0.511739	−	0.859141i	$-0.329001\pi$
$251$	16.2150	1.02348	0.511739	+	0.859141i	$0.329001\pi$
$252$	−56.6370	−3.56779
$253$	−5.52966	−0.347646
$254$	−25.7909	−1.61827
$255$	6.47462	0.405456
$256$	−13.1196	−0.819973
$257$	2.14436	0.133761	0.0668807	−	0.997761i	$-0.478695\pi$
$257$	2.14436	0.133761	0.0668807	+	0.997761i	$0.478695\pi$
$258$	2.14253	0.133388
$259$	37.3223	2.31910
$260$	−11.0084	−0.682713
$261$	−28.0632	−1.73707
$262$	−21.1478	−1.30652
$263$	6.09909	0.376086	0.188043	−	0.982161i	$-0.439786\pi$
$263$	6.09909	0.376086	0.188043	+	0.982161i	$0.439786\pi$
$264$	−4.94469	−0.304325
$265$	3.72932	0.229091
$266$	10.3737	0.636051
$267$	−1.08033	−0.0661153
$268$	−31.9564	−1.95205
$269$	0.977693	0.0596110	0.0298055	−	0.999556i	$-0.490511\pi$
$269$	0.977693	0.0596110	0.0298055	+	0.999556i	$0.490511\pi$
$270$	16.9872	1.03381
$271$	−28.0938	−1.70658	−0.853288	−	0.521440i	$-0.825395\pi$
$271$	−28.0938	−1.70658	−0.853288	+	0.521440i	$0.825395\pi$
$272$	59.5914	3.61326
$273$	−0.531041	−0.0321401
$274$	4.02319	0.243050
$275$	34.2879	2.06764
$276$	−2.67470	−0.160998
$277$	−9.94416	−0.597487	−0.298743	−	0.954333i	$-0.596567\pi$
$277$	−9.94416	−0.597487	−0.298743	+	0.954333i	$0.596567\pi$
$278$	−49.4390	−2.96515
$279$	−2.75933	−0.165197
$280$	−127.889	−7.64284
$281$	−31.2422	−1.86375	−0.931875	−	0.362779i	$-0.881828\pi$
$281$	−31.2422	−1.86375	−0.931875	+	0.362779i	$0.881828\pi$
$282$	1.29321	0.0770097
$283$	−3.04668	−0.181106	−0.0905531	−	0.995892i	$-0.528863\pi$
$283$	−3.04668	−0.181106	−0.0905531	+	0.995892i	$0.528863\pi$
$284$	−48.3368	−2.86826
$285$	−1.09130	−0.0646428
$286$	3.55162	0.210012
$287$	−8.71706	−0.514552
$288$	32.9990	1.94449
$289$	18.2000	1.07059
$290$	−107.394	−6.30641
$291$	−0.631730	−0.0370327
$292$	−9.89443	−0.579028
$293$	5.31385	0.310438	0.155219	−	0.987880i	$-0.450392\pi$
$293$	5.31385	0.310438	0.155219	+	0.987880i	$0.450392\pi$
$294$	−5.77729	−0.336938
$295$	15.8788	0.924498
$296$	−71.2416	−4.14083
$297$	−3.88704	−0.225549
$298$	−6.81202	−0.394610
$299$	1.13358	0.0655566
$300$	16.5850	0.957538
$301$	−12.6800	−0.730864
$302$	14.2059	0.817460
$303$	0.0462387	0.00265634
$304$	−10.0441	−0.576070
$305$	10.3935	0.595129
$306$	45.6711	2.61084
$307$	7.89383	0.450524	0.225262	−	0.974298i	$-0.427676\pi$
$307$	7.89383	0.450524	0.225262	+	0.974298i	$0.427676\pi$
$308$	49.5955	2.82596
$309$	3.32490	0.189147
$310$	−10.5596	−0.599743
$311$	−21.1712	−1.20051	−0.600255	−	0.799809i	$-0.704934\pi$
$311$	−21.1712	−1.20051	−0.600255	+	0.799809i	$0.704934\pi$
$312$	1.01366	0.0573873
$313$	24.8729	1.40590	0.702950	−	0.711239i	$-0.251866\pi$
$313$	24.8729	1.40590	0.702950	+	0.711239i	$0.251866\pi$
$314$	−18.5850	−1.04881
$315$	−49.7172	−2.80125
$316$	−67.8888	−3.81904
$317$	1.00000	0.0561656
$317$	1.00000	0.0561656
$318$	−0.581980	−0.0326358
$319$	24.5742	1.37589
$320$	40.2527	2.25019
$321$	−5.04503	−0.281586
$322$	22.3188	1.24378
$323$	−5.93296	−0.330119
$324$	41.0776	2.28209
$325$	−7.02902	−0.389900
$326$	47.6685	2.64012
$327$	3.71074	0.205204
$328$	16.6393	0.918751
$329$	−7.65356	−0.421955
$330$	−7.35623	−0.404947
$331$	3.42152	0.188064	0.0940320	−	0.995569i	$-0.470024\pi$
$331$	3.42152	0.188064	0.0940320	+	0.995569i	$0.470024\pi$
$332$	−13.7398	−0.754070
$333$	−27.6953	−1.51769
$334$	53.1485	2.90816
$335$	−28.0520	−1.53264
$336$	10.1234	0.552277
$337$	−9.36771	−0.510292	−0.255146	−	0.966903i	$-0.582123\pi$
$337$	−9.36771	−0.510292	−0.255146	+	0.966903i	$0.582123\pi$
$338$	33.3673	1.81494
$339$	−4.52892	−0.245977
$340$	123.960	6.72268
$341$	2.41627	0.130848
$342$	−7.69787	−0.416253
$343$	6.50431	0.351199
$344$	24.2039	1.30499
$345$	−2.34791	−0.126407
$346$	−53.2916	−2.86498
$347$	20.3700	1.09352	0.546758	−	0.837290i	$-0.315862\pi$
$347$	20.3700	1.09352	0.546758	+	0.837290i	$0.315862\pi$
$348$	11.8866	0.637186
$349$	25.0002	1.33823	0.669114	−	0.743160i	$-0.266674\pi$
$349$	25.0002	1.33823	0.669114	+	0.743160i	$0.266674\pi$
$350$	−138.393	−7.39740
$351$	0.796845	0.0425324
$352$	−28.8964	−1.54018
$353$	−14.3143	−0.761872	−0.380936	−	0.924601i	$-0.624398\pi$
$353$	−14.3143	−0.761872	−0.380936	+	0.924601i	$0.624398\pi$
$354$	−2.47796	−0.131702
$355$	−42.4311	−2.25201
$356$	−20.6836	−1.09623
$357$	5.97978	0.316484
$358$	1.31317	0.0694032
$359$	−19.0516	−1.00551	−0.502753	−	0.864430i	$-0.667679\pi$
$359$	−19.0516	−1.00551	−0.502753	+	0.864430i	$0.667679\pi$
$360$	94.9012	5.00173
$361$	1.00000	0.0526316
$362$	37.0981	1.94983
$363$	−1.11975	−0.0587719
$364$	−10.1671	−0.532900
$365$	−8.68555	−0.454623
$366$	−1.62196	−0.0847810
$367$	−16.4832	−0.860414	−0.430207	−	0.902730i	$-0.641559\pi$
$367$	−16.4832	−0.860414	−0.430207	+	0.902730i	$0.641559\pi$
$368$	−21.6098	−1.12649
$369$	6.46856	0.336740
$370$	−105.986	−5.50996
$371$	3.44431	0.178819
$372$	1.16875	0.0605968
$373$	12.6337	0.654149	0.327075	−	0.944999i	$-0.393937\pi$
$373$	12.6337	0.654149	0.327075	+	0.944999i	$0.393937\pi$
$374$	−39.9929	−2.06799
$375$	9.10224	0.470038
$376$	14.6093	0.753416
$377$	−5.03772	−0.259456
$378$	15.6889	0.806950
$379$	−14.7128	−0.755746	−0.377873	−	0.925857i	$-0.623344\pi$
$379$	−14.7128	−0.755746	−0.377873	+	0.925857i	$0.623344\pi$
$380$	−20.8935	−1.07181
$381$	2.50581	0.128377
$382$	19.5925	1.00244
$383$	17.2541	0.881645	0.440823	−	0.897594i	$-0.354687\pi$
$383$	17.2541	0.881645	0.440823	+	0.897594i	$0.354687\pi$
$384$	−0.551727	−0.0281552
$385$	43.5360	2.21880
$386$	−0.430072	−0.0218901
$387$	9.40931	0.478302
$388$	−12.0948	−0.614022
$389$	−16.7595	−0.849740	−0.424870	−	0.905254i	$-0.639680\pi$
$389$	−16.7595	−0.849740	−0.424870	+	0.905254i	$0.639680\pi$
$390$	1.50803	0.0763619
$391$	−12.7647	−0.645537
$392$	−65.2653	−3.29640
$393$	2.05470	0.103646
$394$	66.3378	3.34205
$395$	−59.5943	−2.99852
$396$	−36.8027	−1.84941
$397$	14.4342	0.724431	0.362216	−	0.932094i	$-0.382020\pi$
$397$	14.4342	0.724431	0.362216	+	0.932094i	$0.382020\pi$
$398$	−16.3463	−0.819366
$399$	−1.00789	−0.0504577
$400$	133.996	6.69981
$401$	−20.5285	−1.02515	−0.512573	−	0.858644i	$-0.671308\pi$
$401$	−20.5285	−1.02515	−0.512573	+	0.858644i	$0.671308\pi$
$402$	4.37766	0.218338
$403$	−0.495335	−0.0246744
$404$	0.885265	0.0440436
$405$	36.0588	1.79178
$406$	−99.1865	−4.92254
$407$	24.2520	1.20213
$408$	−11.4143	−0.565094
$409$	−1.86793	−0.0923630	−0.0461815	−	0.998933i	$-0.514705\pi$
$409$	−1.86793	−0.0923630	−0.0461815	+	0.998933i	$0.514705\pi$
$410$	24.7543	1.22253
$411$	−0.390888	−0.0192811
$412$	63.6570	3.13615
$413$	14.6652	0.721628
$414$	−16.5618	−0.813970
$415$	−12.0611	−0.592057
$416$	5.92376	0.290436
$417$	4.80343	0.235225
$418$	6.74081	0.329704
$419$	22.6339	1.10574	0.552870	−	0.833267i	$-0.313533\pi$
$419$	22.6339	1.10574	0.552870	+	0.833267i	$0.313533\pi$
$420$	21.0584	1.02754
$421$	21.4748	1.04662	0.523309	−	0.852143i	$-0.324697\pi$
$421$	21.4748	1.04662	0.523309	+	0.852143i	$0.324697\pi$
$422$	−16.5676	−0.806500
$423$	5.67939	0.276141
$424$	−6.57456	−0.319289
$425$	79.1501	3.83935
$426$	6.62159	0.320817
$427$	9.59915	0.464535
$428$	−96.5900	−4.66885
$429$	−0.345071	−0.0166602
$430$	36.0081	1.73647
$431$	−28.4680	−1.37125	−0.685627	−	0.727953i	$-0.740472\pi$
$431$	−28.4680	−1.37125	−0.685627	+	0.727953i	$0.740472\pi$
$432$	−15.1905	−0.730853
$433$	2.96727	0.142598	0.0712989	−	0.997455i	$-0.477286\pi$
$433$	2.96727	0.142598	0.0712989	+	0.997455i	$0.477286\pi$
$434$	−9.75254	−0.468137
$435$	10.4343	0.500286
$436$	71.0442	3.40240
$437$	2.15148	0.102919
$438$	1.35542	0.0647647
$439$	14.5213	0.693065	0.346533	−	0.938038i	$-0.387359\pi$
$439$	14.5213	0.693065	0.346533	+	0.938038i	$0.387359\pi$
$440$	−83.1024	−3.96175
$441$	−25.3720	−1.20819
$442$	8.19856	0.389966
$443$	20.2101	0.960209	0.480104	−	0.877211i	$-0.340599\pi$
$443$	20.2101	0.960209	0.480104	+	0.877211i	$0.340599\pi$
$444$	11.7307	0.556715
$445$	−18.1565	−0.860701
$446$	−67.3319	−3.18826
$447$	0.661847	0.0313043
$448$	37.1763	1.75641
$449$	−40.0663	−1.89085	−0.945424	−	0.325844i	$-0.894352\pi$
$449$	−40.0663	−1.89085	−0.945424	+	0.325844i	$0.894352\pi$
$450$	102.695	4.84111
$451$	−5.66434	−0.266723
$452$	−86.7087	−4.07843
$453$	−1.38023	−0.0648489
$454$	64.1887	3.01252
$455$	−8.92489	−0.418405
$456$	1.92389	0.0900942
$457$	35.6857	1.66931	0.834654	−	0.550774i	$-0.185667\pi$
$457$	35.6857	1.66931	0.834654	+	0.550774i	$0.185667\pi$
$458$	−33.3570	−1.55867
$459$	−8.97286	−0.418817
$460$	−44.9520	−2.09590
$461$	4.52694	0.210841	0.105420	−	0.994428i	$-0.466381\pi$
$461$	4.52694	0.210841	0.105420	+	0.994428i	$0.466381\pi$
$462$	−6.79402	−0.316086
$463$	28.7426	1.33578	0.667890	−	0.744260i	$-0.267198\pi$
$463$	28.7426	1.33578	0.667890	+	0.744260i	$0.267198\pi$
$464$	96.0356	4.45834
$465$	1.02595	0.0475775
$466$	−12.8702	−0.596201
$467$	5.62693	0.260383	0.130192	−	0.991489i	$-0.458441\pi$
$467$	5.62693	0.260383	0.130192	+	0.991489i	$0.458441\pi$
$468$	7.54456	0.348747
$469$	−25.9081	−1.19632
$470$	21.7342	1.00253
$471$	1.80569	0.0832018
$472$	−27.9933	−1.28849
$473$	−8.23947	−0.378851
$474$	9.30000	0.427163
$475$	−13.3408	−0.612116
$476$	114.486	5.24747
$477$	−2.55587	−0.117025
$478$	50.1884	2.29557
$479$	31.7674	1.45149	0.725744	−	0.687965i	$-0.241496\pi$
$479$	31.7674	1.45149	0.725744	+	0.687965i	$0.241496\pi$
$480$	−12.2695	−0.560023
$481$	−4.97167	−0.226689
$482$	34.9070	1.58997
$483$	−2.16847	−0.0986686
$484$	−21.4383	−0.974469
$485$	−10.6171	−0.482098
$486$	−17.5268	−0.795031
$487$	7.62204	0.345387	0.172694	−	0.984976i	$-0.444753\pi$
$487$	7.62204	0.345387	0.172694	+	0.984976i	$0.444753\pi$
$488$	−18.3231	−0.829446
$489$	−4.63141	−0.209440
$490$	−97.0954	−4.38632
$491$	−29.6050	−1.33606	−0.668028	−	0.744136i	$-0.732861\pi$
$491$	−29.6050	−1.33606	−0.668028	+	0.744136i	$0.732861\pi$
$492$	−2.73984	−0.123522
$493$	56.7272	2.55486
$494$	−1.38187	−0.0621732
$495$	−32.3062	−1.45206
$496$	9.44273	0.423991
$497$	−39.1883	−1.75783
$498$	1.88220	0.0843434
$499$	−18.2721	−0.817971	−0.408985	−	0.912541i	$-0.634117\pi$
$499$	−18.2721	−0.817971	−0.408985	+	0.912541i	$0.634117\pi$
$500$	174.267	7.79347
$501$	−5.16384	−0.230703
$502$	−42.5273	−1.89809
$503$	11.4345	0.509841	0.254920	−	0.966962i	$-0.417951\pi$
$503$	11.4345	0.509841	0.254920	+	0.966962i	$0.417951\pi$
$504$	87.6483	3.90416
$505$	0.777105	0.0345807
$506$	14.5028	0.644726
$507$	−3.24193	−0.143979
$508$	47.9752	2.12855
$509$	−5.53035	−0.245129	−0.122564	−	0.992461i	$-0.539112\pi$
$509$	−5.53035	−0.245129	−0.122564	+	0.992461i	$0.539112\pi$
$510$	−16.9811	−0.751937
$511$	−8.02175	−0.354861
$512$	38.7393	1.71205
$513$	1.51238	0.0667730
$514$	−5.62406	−0.248066
$515$	55.8795	2.46234
$516$	−3.98544	−0.175449
$517$	−4.97328	−0.218725
$518$	−97.8861	−4.30087
$519$	5.17775	0.227278
$520$	17.0360	0.747078
$521$	32.2994	1.41506	0.707530	−	0.706683i	$-0.249809\pi$
$521$	32.2994	1.41506	0.707530	+	0.706683i	$0.249809\pi$
$522$	73.6021	3.22148
$523$	11.3019	0.494198	0.247099	−	0.968990i	$-0.420523\pi$
$523$	11.3019	0.494198	0.247099	+	0.968990i	$0.420523\pi$
$524$	39.3383	1.71850
$525$	13.4461	0.586834
$526$	−15.9962	−0.697469
$527$	5.57772	0.242969
$528$	6.57819	0.286279
$529$	−18.3711	−0.798744
$530$	−9.78099	−0.424859
$531$	−10.8824	−0.472258
$532$	−19.2967	−0.836616
$533$	1.16119	0.0502968
$534$	2.83342	0.122614
$535$	−84.7888	−3.66574
$536$	49.4539	2.13608
$537$	−0.127586	−0.00550574
$538$	−2.56422	−0.110551
$539$	22.2176	0.956980
$540$	−31.5988	−1.35980
$541$	−24.8667	−1.06910	−0.534552	−	0.845136i	$-0.679519\pi$
$541$	−24.8667	−1.06910	−0.534552	+	0.845136i	$0.679519\pi$
$542$	73.6822	3.16492
$543$	−3.60440	−0.154680
$544$	−66.7044	−2.85993
$545$	62.3642	2.67139
$546$	1.39277	0.0596052
$547$	−23.5622	−1.00745	−0.503724	−	0.863865i	$-0.668037\pi$
$547$	−23.5622	−1.00745	−0.503724	+	0.863865i	$0.668037\pi$
$548$	−7.48377	−0.319691
$549$	−7.12312	−0.304008
$550$	−89.9275	−3.83452
$551$	−9.56136	−0.407328
$552$	4.13921	0.176177
$553$	−55.0397	−2.34053
$554$	26.0808	1.10807
$555$	10.2975	0.437104
$556$	91.9643	3.90015
$557$	25.5367	1.08203	0.541013	−	0.841015i	$-0.318041\pi$
$557$	25.5367	1.08203	0.541013	+	0.841015i	$0.318041\pi$
$558$	7.23695	0.306365
$559$	1.68909	0.0714410
$560$	170.138	7.18964
$561$	3.88566	0.164053
$562$	81.9395	3.45641
$563$	43.6799	1.84089	0.920444	−	0.390873i	$-0.127827\pi$
$563$	43.6799	1.84089	0.920444	+	0.390873i	$0.127827\pi$
$564$	−2.40558	−0.101293
$565$	−76.1148	−3.20218
$566$	7.99059	0.335870
$567$	33.3030	1.39859
$568$	74.8033	3.13868
$569$	−5.94697	−0.249310	−0.124655	−	0.992200i	$-0.539782\pi$
$569$	−5.94697	−0.249310	−0.124655	+	0.992200i	$0.539782\pi$
$570$	2.86217	0.119883
$571$	−28.7752	−1.20421	−0.602103	−	0.798418i	$-0.705670\pi$
$571$	−28.7752	−1.20421	−0.602103	+	0.798418i	$0.705670\pi$
$572$	−6.60657	−0.276234
$573$	−1.90359	−0.0795234
$574$	22.8624	0.954259
$575$	−28.7024	−1.19697
$576$	−27.5870	−1.14946
$577$	33.8247	1.40814	0.704071	−	0.710130i	$-0.251364\pi$
$577$	33.8247	1.40814	0.704071	+	0.710130i	$0.251364\pi$
$578$	−47.7335	−1.98545
$579$	0.0417852	0.00173653
$580$	199.770	8.29500
$581$	−11.1393	−0.462137
$582$	1.65685	0.0686788
$583$	2.23811	0.0926930
$584$	15.3121	0.633618
$585$	6.62278	0.273818
$586$	−13.9367	−0.575722
$587$	−1.96768	−0.0812149	−0.0406075	−	0.999175i	$-0.512929\pi$
$587$	−1.96768	−0.0812149	−0.0406075	+	0.999175i	$0.512929\pi$
$588$	10.7467	0.443185
$589$	−0.940124	−0.0387371
$590$	−41.6456	−1.71452
$591$	−6.44529	−0.265124
$592$	94.7765	3.89529
$593$	−10.6281	−0.436444	−0.218222	−	0.975899i	$-0.570026\pi$
$593$	−10.6281	−0.436444	−0.218222	+	0.975899i	$0.570026\pi$
$594$	10.1946	0.418291
$595$	100.499	4.12004
$596$	12.6714	0.519042
$597$	1.58818	0.0650001
$598$	−2.97307	−0.121578
$599$	−16.7642	−0.684966	−0.342483	−	0.939524i	$-0.611268\pi$
$599$	−16.7642	−0.684966	−0.342483	+	0.939524i	$0.611268\pi$
$600$	−25.6661	−1.04781
$601$	−16.3163	−0.665557	−0.332779	−	0.943005i	$-0.607986\pi$
$601$	−16.3163	−0.665557	−0.332779	+	0.943005i	$0.607986\pi$
$602$	33.2562	1.35542
$603$	19.2253	0.782915
$604$	−26.4253	−1.07523
$605$	−18.8190	−0.765102
$606$	−0.121271	−0.00492631
$607$	9.00352	0.365441	0.182721	−	0.983165i	$-0.441510\pi$
$607$	9.00352	0.365441	0.182721	+	0.983165i	$0.441510\pi$
$608$	11.2430	0.455965
$609$	9.63683	0.390504
$610$	−27.2592	−1.10369
$611$	1.01952	0.0412455
$612$	−84.9554	−3.43412
$613$	39.2627	1.58581	0.792903	−	0.609348i	$-0.208569\pi$
$613$	39.2627	1.58581	0.792903	+	0.609348i	$0.208569\pi$
$614$	−20.7033	−0.835518
$615$	−2.40510	−0.0969828
$616$	−76.7512	−3.09239
$617$	−25.3343	−1.01992	−0.509959	−	0.860198i	$-0.670340\pi$
$617$	−25.3343	−1.01992	−0.509959	+	0.860198i	$0.670340\pi$
$618$	−8.72028	−0.350781
$619$	13.9437	0.560446	0.280223	−	0.959935i	$-0.409592\pi$
$619$	13.9437	0.560446	0.280223	+	0.959935i	$0.409592\pi$
$620$	19.6425	0.788860
$621$	3.25385	0.130573
$622$	55.5262	2.22640
$623$	−16.7689	−0.671831
$624$	−1.34853	−0.0539844
$625$	86.2720	3.45088
$626$	−65.2348	−2.60731
$627$	−0.654929	−0.0261553
$628$	34.5709	1.37953
$629$	55.9834	2.23221
$630$	130.394	5.19504
$631$	29.1180	1.15917	0.579585	−	0.814912i	$-0.303215\pi$
$631$	29.1180	1.15917	0.579585	+	0.814912i	$0.303215\pi$
$632$	105.061	4.17910
$633$	1.60969	0.0639795
$634$	−2.62272	−0.104162
$635$	42.1137	1.67123
$636$	1.08257	0.0429269
$637$	−4.55461	−0.180460
$638$	−64.4514	−2.55165
$639$	29.0800	1.15039
$640$	−9.27253	−0.366529
$641$	5.54522	0.219023	0.109512	−	0.993986i	$-0.465071\pi$
$641$	5.54522	0.219023	0.109512	+	0.993986i	$0.465071\pi$
$642$	13.2317	0.522215
$643$	−9.78157	−0.385747	−0.192874	−	0.981224i	$-0.561781\pi$
$643$	−9.78157	−0.385747	−0.192874	+	0.981224i	$0.561781\pi$
$644$	−41.5165	−1.63598
$645$	−3.49850	−0.137753
$646$	15.5605	0.612220
$647$	−35.6397	−1.40114	−0.700570	−	0.713584i	$-0.747071\pi$
$647$	−35.6397	−1.40114	−0.700570	+	0.713584i	$0.747071\pi$
$648$	−63.5694	−2.49724
$649$	9.52946	0.374064
$650$	18.4352	0.723086
$651$	0.947544	0.0371372
$652$	−88.6709	−3.47262
$653$	−39.9271	−1.56247	−0.781234	−	0.624238i	$-0.785409\pi$
$653$	−39.9271	−1.56247	−0.781234	+	0.624238i	$0.785409\pi$
$654$	−9.73225	−0.380561
$655$	34.5320	1.34928
$656$	−22.1361	−0.864271
$657$	5.95260	0.232233
$658$	20.0732	0.782534
$659$	−5.09845	−0.198607	−0.0993037	−	0.995057i	$-0.531662\pi$
$659$	−5.09845	−0.198607	−0.0993037	+	0.995057i	$0.531662\pi$
$660$	13.6837	0.532639
$661$	47.9315	1.86432	0.932160	−	0.362046i	$-0.117922\pi$
$661$	47.9315	1.86432	0.932160	+	0.362046i	$0.117922\pi$
$662$	−8.97371	−0.348773
$663$	−0.796562	−0.0309359
$664$	21.2630	0.825164
$665$	−16.9390	−0.656868
$666$	72.6372	2.81463
$667$	−20.5711	−0.796517
$668$	−98.8645	−3.82518
$669$	6.54188	0.252924
$670$	73.5726	2.84236
$671$	6.23753	0.240797
$672$	−11.3318	−0.437132
$673$	12.2407	0.471846	0.235923	−	0.971772i	$-0.424189\pi$
$673$	12.2407	0.471846	0.235923	+	0.971772i	$0.424189\pi$
$674$	24.5689	0.946359
$675$	−20.1762	−0.776584
$676$	−62.0684	−2.38725
$677$	−45.4160	−1.74548	−0.872739	−	0.488187i	$-0.837658\pi$
$677$	−45.4160	−1.74548	−0.872739	+	0.488187i	$0.837658\pi$
$678$	11.8781	0.456176
$679$	−9.80568	−0.376308
$680$	−191.834	−7.35649
$681$	−6.23649	−0.238983
$682$	−6.33720	−0.242664
$683$	−17.5569	−0.671796	−0.335898	−	0.941898i	$-0.609040\pi$
$683$	−17.5569	−0.671796	−0.335898	+	0.941898i	$0.609040\pi$
$684$	14.3192	0.547510
$685$	−6.56942	−0.251005
$686$	−17.0590	−0.651315
$687$	3.24093	0.123649
$688$	−32.1997	−1.22760
$689$	−0.458813	−0.0174794
$690$	6.15791	0.234428
$691$	−27.4230	−1.04322	−0.521610	−	0.853184i	$-0.674668\pi$
$691$	−27.4230	−1.04322	−0.521610	+	0.853184i	$0.674668\pi$
$692$	99.1308	3.76839
$693$	−29.8372	−1.13342
$694$	−53.4248	−2.02798
$695$	80.7283	3.06220
$696$	−18.3950	−0.697260
$697$	−13.0756	−0.495273
$698$	−65.5685	−2.48181
$699$	1.25045	0.0472965
$700$	257.432	9.73002
$701$	41.4515	1.56560	0.782801	−	0.622272i	$-0.213790\pi$
$701$	41.4515	1.56560	0.782801	+	0.622272i	$0.213790\pi$
$702$	−2.08990	−0.0788783
$703$	−9.43601	−0.355886
$704$	24.1572	0.910457
$705$	−2.11167	−0.0795301
$706$	37.5424	1.41293
$707$	0.717714	0.0269924
$708$	4.60940	0.173232
$709$	33.7211	1.26642	0.633210	−	0.773980i	$-0.281737\pi$
$709$	33.7211	1.26642	0.633210	+	0.773980i	$0.281737\pi$
$710$	111.285	4.17645
$711$	40.8427	1.53172
$712$	32.0088	1.19958
$713$	−2.02266	−0.0757493
$714$	−15.6833	−0.586933
$715$	−5.79939	−0.216885
$716$	−2.44270	−0.0912881
$717$	−4.87624	−0.182107
$718$	49.9671	1.86476
$719$	−8.32561	−0.310493	−0.155246	−	0.987876i	$-0.549617\pi$
$719$	−8.32561	−0.310493	−0.155246	+	0.987876i	$0.549617\pi$
$720$	−126.252	−4.70514
$721$	51.6088	1.92201
$722$	−2.62272	−0.0976076
$723$	−3.39152	−0.126132
$724$	−69.0082	−2.56467
$725$	127.556	4.73730
$726$	2.93681	0.108995
$727$	−40.7870	−1.51271	−0.756353	−	0.654164i	$-0.773021\pi$
$727$	−40.7870	−1.51271	−0.756353	+	0.654164i	$0.773021\pi$
$728$	15.7340	0.583141
$729$	−23.5566	−0.872465
$730$	22.7798	0.843118
$731$	−19.0200	−0.703481
$732$	3.01709	0.111515
$733$	−47.0779	−1.73886	−0.869430	−	0.494056i	$-0.835514\pi$
$733$	−47.0779	−1.73886	−0.869430	+	0.494056i	$0.835514\pi$
$734$	43.2308	1.59568
$735$	9.43366	0.347966
$736$	24.1892	0.891626
$737$	−16.8351	−0.620128
$738$	−16.9652	−0.624499
$739$	1.07298	0.0394701	0.0197351	−	0.999805i	$-0.493718\pi$
$739$	1.07298	0.0394701	0.0197351	+	0.999805i	$0.493718\pi$
$740$	197.151	7.24742
$741$	0.134260	0.00493218
$742$	−9.03346	−0.331629
$743$	−4.35695	−0.159841	−0.0799205	−	0.996801i	$-0.525467\pi$
$743$	−4.35695	−0.159841	−0.0799205	+	0.996801i	$0.525467\pi$
$744$	−1.80869	−0.0663099
$745$	11.1233	0.407525
$746$	−33.1347	−1.21315
$747$	8.26603	0.302438
$748$	74.3932	2.72008
$749$	−78.3087	−2.86134
$750$	−23.8727	−0.871706
$751$	1.25377	0.0457505	0.0228753	−	0.999738i	$-0.492718\pi$
$751$	1.25377	0.0457505	0.0228753	+	0.999738i	$0.492718\pi$
$752$	−19.4355	−0.708740
$753$	4.13190	0.150575
$754$	13.2125	0.481172
$755$	−23.1967	−0.844214
$756$	−29.1838	−1.06140
$757$	12.9169	0.469473	0.234736	−	0.972059i	$-0.424577\pi$
$757$	12.9169	0.469473	0.234736	+	0.972059i	$0.424577\pi$
$758$	38.5876	1.40157
$759$	−1.40907	−0.0511460
$760$	32.3336	1.17286
$761$	23.3567	0.846681	0.423341	−	0.905971i	$-0.360857\pi$
$761$	23.3567	0.846681	0.423341	+	0.905971i	$0.360857\pi$
$762$	−6.57205	−0.238080
$763$	57.5979	2.08518
$764$	−36.4452	−1.31854
$765$	−74.5758	−2.69629
$766$	−45.2528	−1.63505
$767$	−1.95354	−0.0705383
$768$	−3.34313	−0.120635
$769$	−46.3516	−1.67148	−0.835741	−	0.549124i	$-0.814962\pi$
$769$	−46.3516	−1.67148	−0.835741	+	0.549124i	$0.814962\pi$
$770$	−114.183	−4.11487
$771$	0.546426	0.0196791
$772$	0.800001	0.0287927
$773$	−33.7809	−1.21501	−0.607507	−	0.794314i	$-0.707830\pi$
$773$	−33.7809	−1.21501	−0.607507	+	0.794314i	$0.707830\pi$
$774$	−24.6780	−0.887032
$775$	12.5420	0.450521
$776$	18.7173	0.671911
$777$	9.51049	0.341187
$778$	43.9555	1.57588
$779$	2.20389	0.0789625
$780$	−2.80517	−0.100441
$781$	−25.4645	−0.911192
$782$	33.4782	1.19718
$783$	−14.4604	−0.516772
$784$	86.8260	3.10093
$785$	30.3471	1.08314
$786$	−5.38890	−0.192216
$787$	34.3413	1.22414	0.612068	−	0.790805i	$-0.290338\pi$
$787$	34.3413	1.22414	0.612068	+	0.790805i	$0.290338\pi$
$788$	−123.399	−4.39589
$789$	1.55417	0.0553300
$790$	156.299	5.56088
$791$	−70.2977	−2.49950
$792$	56.9538	2.02377
$793$	−1.27869	−0.0454077
$794$	−37.8569	−1.34349
$795$	0.950308	0.0337039
$796$	30.4067	1.07774
$797$	−9.46524	−0.335276	−0.167638	−	0.985849i	$-0.553614\pi$
$797$	−9.46524	−0.335276	−0.167638	+	0.985849i	$0.553614\pi$
$798$	2.64342	0.0935762
$799$	−11.4803	−0.406145
$800$	−149.991	−5.30297
$801$	12.4435	0.439668
$802$	53.8406	1.90118
$803$	−5.21253	−0.183946
$804$	−8.14313	−0.287186
$805$	−36.4441	−1.28449
$806$	1.29913	0.0457598
$807$	0.249136	0.00877000
$808$	−1.36999	−0.0481960
$809$	−43.1593	−1.51740	−0.758700	−	0.651440i	$-0.774165\pi$
$809$	−43.1593	−1.51740	−0.758700	+	0.651440i	$0.774165\pi$
$810$	−94.5722	−3.32293
$811$	−33.1813	−1.16515	−0.582577	−	0.812776i	$-0.697956\pi$
$811$	−33.1813	−1.16515	−0.582577	+	0.812776i	$0.697956\pi$
$812$	184.502	6.47476
$813$	−7.15887	−0.251072
$814$	−63.6064	−2.22940
$815$	−77.8373	−2.72652
$816$	15.1851	0.531585
$817$	3.20582	0.112158
$818$	4.89905	0.171291
$819$	6.11663	0.213732
$820$	−46.0469	−1.60803
$821$	−52.5830	−1.83516	−0.917579	−	0.397554i	$-0.869859\pi$
$821$	−52.5830	−1.83516	−0.917579	+	0.397554i	$0.869859\pi$
$822$	1.02519	0.0357577
$823$	−37.5904	−1.31032	−0.655160	−	0.755490i	$-0.727399\pi$
$823$	−37.5904	−1.31032	−0.655160	+	0.755490i	$0.727399\pi$
$824$	−98.5120	−3.43183
$825$	8.73724	0.304192
$826$	−38.4628	−1.33829
$827$	31.6821	1.10169	0.550847	−	0.834606i	$-0.314305\pi$
$827$	31.6821	1.10169	0.550847	+	0.834606i	$0.314305\pi$
$828$	30.8076	1.07064
$829$	−24.4868	−0.850463	−0.425231	−	0.905085i	$-0.639807\pi$
$829$	−24.4868	−0.850463	−0.425231	+	0.905085i	$0.639807\pi$
$830$	31.6330	1.09800
$831$	−2.53398	−0.0879026
$832$	−4.95222	−0.171687
$833$	51.2872	1.77699
$834$	−12.5981	−0.436235
$835$	−86.7855	−3.00334
$836$	−12.5390	−0.433669
$837$	−1.42182	−0.0491453
$838$	−59.3625	−2.05065
$839$	48.5788	1.67713	0.838563	−	0.544805i	$-0.183396\pi$
$839$	48.5788	1.67713	0.838563	+	0.544805i	$0.183396\pi$
$840$	−32.5888	−1.12442
$841$	62.4197	2.15240
$842$	−56.3225	−1.94100
$843$	−7.96114	−0.274196
$844$	30.8184	1.06081
$845$	−54.4851	−1.87434
$846$	−14.8955	−0.512116
$847$	−17.3808	−0.597210
$848$	8.74649	0.300356
$849$	−0.776355	−0.0266444
$850$	−207.589	−7.12024
$851$	−20.3014	−0.695924
$852$	−12.3172	−0.421980
$853$	−52.2309	−1.78835	−0.894175	−	0.447717i	$-0.852237\pi$
$853$	−52.2309	−1.78835	−0.894175	+	0.447717i	$0.852237\pi$
$854$	−25.1759	−0.861502
$855$	12.5697	0.429876
$856$	149.477	5.10903
$857$	−15.2863	−0.522171	−0.261085	−	0.965316i	$-0.584080\pi$
$857$	−15.2863	−0.522171	−0.261085	+	0.965316i	$0.584080\pi$
$858$	0.905025	0.0308970
$859$	−17.9031	−0.610845	−0.305422	−	0.952217i	$-0.598798\pi$
$859$	−17.9031	−0.610845	−0.305422	+	0.952217i	$0.598798\pi$
$860$	−66.9808	−2.28403
$861$	−2.22128	−0.0757011
$862$	74.6636	2.54305
$863$	51.6565	1.75841	0.879205	−	0.476444i	$-0.158075\pi$
$863$	51.6565	1.75841	0.879205	+	0.476444i	$0.158075\pi$
$864$	17.0037	0.578477
$865$	87.0192	2.95874
$866$	−7.78232	−0.264454
$867$	4.63773	0.157505
$868$	18.1413	0.615754
$869$	−35.7648	−1.21324
$870$	−27.3662	−0.927802
$871$	3.45119	0.116939
$872$	−109.944	−3.72318
$873$	7.27638	0.246268
$874$	−5.64275	−0.190869
$875$	141.284	4.77629
$876$	−2.52130	−0.0851869
$877$	30.5016	1.02997	0.514984	−	0.857200i	$-0.327798\pi$
$877$	30.5016	1.02997	0.514984	+	0.857200i	$0.327798\pi$
$878$	−38.0854	−1.28532
$879$	1.35408	0.0456719
$880$	110.556	3.72683
$881$	−22.7846	−0.767634	−0.383817	−	0.923409i	$-0.625391\pi$
$881$	−22.7846	−0.767634	−0.383817	+	0.923409i	$0.625391\pi$
$882$	66.5438	2.24065
$883$	−30.2618	−1.01839	−0.509195	−	0.860651i	$-0.670057\pi$
$883$	−30.2618	−1.01839	−0.509195	+	0.860651i	$0.670057\pi$
$884$	−15.2506	−0.512933
$885$	4.04624	0.136013
$886$	−53.0054	−1.78075
$887$	49.8366	1.67335	0.836675	−	0.547699i	$-0.184496\pi$
$887$	49.8366	1.67335	0.836675	+	0.547699i	$0.184496\pi$
$888$	−18.1538	−0.609202
$889$	38.8951	1.30450
$890$	47.6195	1.59621
$891$	21.6403	0.724976
$892$	125.248	4.19361
$893$	1.93501	0.0647527
$894$	−1.73584	−0.0580552
$895$	−2.14426	−0.0716747
$896$	−8.56387	−0.286099
$897$	0.288859	0.00964473
$898$	105.083	3.50666
$899$	8.98887	0.299796
$900$	−191.030	−6.36765
$901$	5.16646	0.172120
$902$	14.8560	0.494651
$903$	−3.23113	−0.107525
$904$	134.186	4.46295
$905$	−60.5769	−2.01365
$906$	3.61996	0.120265
$907$	45.3653	1.50633	0.753165	−	0.657832i	$-0.228526\pi$
$907$	45.3653	1.50633	0.753165	+	0.657832i	$0.228526\pi$
$908$	−119.401	−3.96246
$909$	−0.532585	−0.0176647
$910$	23.4075	0.775951
$911$	−54.2571	−1.79762	−0.898808	−	0.438342i	$-0.855566\pi$
$911$	−54.2571	−1.79762	−0.898808	+	0.438342i	$0.855566\pi$
$912$	−2.55945	−0.0847518
$913$	−7.23834	−0.239554
$914$	−93.5938	−3.09581
$915$	2.64847	0.0875558
$916$	62.0493	2.05017
$917$	31.8929	1.05320
$918$	23.5333	0.776716
$919$	−45.8285	−1.51174	−0.755871	−	0.654721i	$-0.772786\pi$
$919$	−45.8285	−1.51174	−0.755871	+	0.654721i	$0.772786\pi$
$920$	69.5652	2.29350
$921$	2.01151	0.0662814
$922$	−11.8729	−0.391013
$923$	5.22023	0.171826
$924$	12.6379	0.415758
$925$	125.884	4.13902
$926$	−75.3838	−2.47727
$927$	−38.2967	−1.25783
$928$	−107.499	−3.52882
$929$	43.9587	1.44224	0.721119	−	0.692811i	$-0.243628\pi$
$929$	43.9587	1.44224	0.721119	+	0.692811i	$0.243628\pi$
$930$	−2.69079	−0.0882346
$931$	−8.64445	−0.283310
$932$	23.9406	0.784201
$933$	−5.39486	−0.176620
$934$	−14.7579	−0.482892
$935$	65.3040	2.13567
$936$	−11.6755	−0.381627
$937$	−29.6841	−0.969737	−0.484868	−	0.874587i	$-0.661132\pi$
$937$	−29.6841	−0.969737	−0.484868	+	0.874587i	$0.661132\pi$
$938$	67.9497	2.21864
$939$	6.33812	0.206837
$940$	−40.4291	−1.31865
$941$	7.79156	0.253997	0.126999	−	0.991903i	$-0.459466\pi$
$941$	7.79156	0.253997	0.126999	+	0.991903i	$0.459466\pi$
$942$	−4.73583	−0.154302
$943$	4.74163	0.154409
$944$	37.2410	1.21209
$945$	−25.6182	−0.833360
$946$	21.6099	0.702597
$947$	27.5558	0.895443	0.447721	−	0.894173i	$-0.352236\pi$
$947$	27.5558	0.895443	0.447721	+	0.894173i	$0.352236\pi$
$948$	−17.2995	−0.561860
$949$	1.06857	0.0346872
$950$	34.9891	1.13520
$951$	0.254820	0.00826312
$952$	−177.173	−5.74220
$953$	−21.9978	−0.712578	−0.356289	−	0.934376i	$-0.615958\pi$
$953$	−21.9978	−0.712578	−0.356289	+	0.934376i	$0.615958\pi$
$954$	6.70335	0.217029
$955$	−31.9924	−1.03525
$956$	−93.3584	−3.01943
$957$	6.26201	0.202422
$958$	−83.3170	−2.69185
$959$	−6.06734	−0.195925
$960$	10.2572	0.331050
$961$	−30.1162	−0.971489
$962$	13.0393	0.420404
$963$	58.1096	1.87256
$964$	−64.9325	−2.09133
$965$	0.702258	0.0226065
$966$	5.68729	0.182985
$967$	14.8909	0.478858	0.239429	−	0.970914i	$-0.423040\pi$
$967$	14.8909	0.478858	0.239429	+	0.970914i	$0.423040\pi$
$968$	33.1767	1.06634
$969$	−1.51184	−0.0485672
$970$	27.8457	0.894073
$971$	32.9726	1.05814	0.529070	−	0.848578i	$-0.322541\pi$
$971$	32.9726	1.05814	0.529070	+	0.848578i	$0.322541\pi$
$972$	32.6026	1.04573
$973$	74.5585	2.39024
$974$	−19.9905	−0.640537
$975$	−1.79114	−0.0573623
$976$	24.3761	0.780261
$977$	22.9459	0.734106	0.367053	−	0.930200i	$-0.380367\pi$
$977$	22.9459	0.734106	0.367053	+	0.930200i	$0.380367\pi$
$978$	12.1469	0.388415
$979$	−10.8964	−0.348251
$980$	180.613	5.76946
$981$	−42.7410	−1.36461
$982$	77.6458	2.47778
$983$	−13.8960	−0.443214	−0.221607	−	0.975136i	$-0.571130\pi$
$983$	−13.8960	−0.443214	−0.221607	+	0.975136i	$0.571130\pi$
$984$	4.24003	0.135167
$985$	−108.322	−3.45143
$986$	−148.780	−4.73811
$987$	−1.95028	−0.0620782
$988$	2.57049	0.0817782
$989$	6.89728	0.219321
$990$	84.7303	2.69291
$991$	61.5215	1.95429	0.977147	−	0.212564i	$-0.0681815\pi$
$991$	61.5215	1.95429	0.977147	+	0.212564i	$0.0681815\pi$
$992$	−10.5698	−0.335593
$993$	0.871874	0.0276681
$994$	102.780	3.25998
$995$	26.6917	0.846182
$996$	−3.50119	−0.110939
$997$	−8.83965	−0.279955	−0.139977	−	0.990155i	$-0.544703\pi$
$997$	−8.83965	−0.279955	−0.139977	+	0.990155i	$0.544703\pi$
$998$	47.9226	1.51696
$999$	−14.2708	−0.451508

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6023.2.a.d.1.7	✓	140

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6023.2.a.d.1.7	✓	140	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:	\( N \)	\(=\)	\( 6023 = 19 \cdot 317 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6023.a (trivial)

\(f(q)\)	\(=\)	\(q-2.62272 q^{2} +0.254820 q^{3} +4.87868 q^{4} +4.28261 q^{5} -0.668323 q^{6} +3.95531 q^{7} -7.54997 q^{8} -2.93507 q^{9} +O(q^{10})\)	\(q-2.62272 q^{2} +0.254820 q^{3} +4.87868 q^{4} +4.28261 q^{5} -0.668323 q^{6} +3.95531 q^{7} -7.54997 q^{8} -2.93507 q^{9} -11.2321 q^{10} +2.57016 q^{11} +1.24319 q^{12} -0.526883 q^{13} -10.3737 q^{14} +1.09130 q^{15} +10.0441 q^{16} +5.93296 q^{17} +7.69787 q^{18} -1.00000 q^{19} +20.8935 q^{20} +1.00789 q^{21} -6.74081 q^{22} -2.15148 q^{23} -1.92389 q^{24} +13.3408 q^{25} +1.38187 q^{26} -1.51238 q^{27} +19.2967 q^{28} +9.56136 q^{29} -2.86217 q^{30} +0.940124 q^{31} -11.2430 q^{32} +0.654929 q^{33} -15.5605 q^{34} +16.9390 q^{35} -14.3192 q^{36} +9.43601 q^{37} +2.62272 q^{38} -0.134260 q^{39} -32.3336 q^{40} -2.20389 q^{41} -2.64342 q^{42} -3.20582 q^{43} +12.5390 q^{44} -12.5697 q^{45} +5.64275 q^{46} -1.93501 q^{47} +2.55945 q^{48} +8.64445 q^{49} -34.9891 q^{50} +1.51184 q^{51} -2.57049 q^{52} +0.870806 q^{53} +3.96654 q^{54} +11.0070 q^{55} -29.8624 q^{56} -0.254820 q^{57} -25.0768 q^{58} +3.70773 q^{59} +5.32408 q^{60} +2.42690 q^{61} -2.46569 q^{62} -11.6091 q^{63} +9.39909 q^{64} -2.25643 q^{65} -1.71770 q^{66} -6.55021 q^{67} +28.9450 q^{68} -0.548242 q^{69} -44.4264 q^{70} -9.90777 q^{71} +22.1597 q^{72} -2.02810 q^{73} -24.7480 q^{74} +3.39950 q^{75} -4.87868 q^{76} +10.1658 q^{77} +0.352128 q^{78} -13.9154 q^{79} +43.0151 q^{80} +8.41982 q^{81} +5.78019 q^{82} -2.81630 q^{83} +4.91718 q^{84} +25.4085 q^{85} +8.40799 q^{86} +2.43643 q^{87} -19.4046 q^{88} -4.23959 q^{89} +32.9670 q^{90} -2.08398 q^{91} -10.4964 q^{92} +0.239563 q^{93} +5.07500 q^{94} -4.28261 q^{95} -2.86495 q^{96} -2.47912 q^{97} -22.6720 q^{98} -7.54358 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 140 q + 4 q^{2} + 3 q^{3} + 162 q^{4} + 13 q^{5} + 12 q^{6} + 25 q^{7} + 12 q^{8} + 181 q^{9}+O(q^{10}) \) 140 * q + 4 * q^2 + 3 * q^3 + 162 * q^4 + 13 * q^5 + 12 * q^6 + 25 * q^7 + 12 * q^8 + 181 * q^9	\( 140 q + 4 q^{2} + 3 q^{3} + 162 q^{4} + 13 q^{5} + 12 q^{6} + 25 q^{7} + 12 q^{8} + 181 q^{9} + 8 q^{10} + 19 q^{11} + 17 q^{12} + 28 q^{13} + 5 q^{14} + 14 q^{15} + 202 q^{16} + 38 q^{17} + 26 q^{18} - 140 q^{19} + 36 q^{20} + 4 q^{21} + 53 q^{22} + 58 q^{23} + 47 q^{24} + 279 q^{25} + 29 q^{26} + 21 q^{27} + 69 q^{28} + 18 q^{29} + 50 q^{30} + 20 q^{31} + 13 q^{32} + 47 q^{33} + 6 q^{34} + 35 q^{35} + 230 q^{36} + 88 q^{37} - 4 q^{38} + 32 q^{39} + 32 q^{40} + 24 q^{41} + 75 q^{42} + 100 q^{43} + 63 q^{44} + 87 q^{45} + 23 q^{46} + 35 q^{47} + 46 q^{48} + 255 q^{49} + 11 q^{50} - 6 q^{51} + 47 q^{52} + 77 q^{53} + 16 q^{54} + 63 q^{55} + 21 q^{56} - 3 q^{57} + 165 q^{58} + 18 q^{59} + 28 q^{60} + 99 q^{61} + 34 q^{62} + 89 q^{63} + 298 q^{64} + 78 q^{65} - 3 q^{66} + 28 q^{67} + 93 q^{68} + 19 q^{69} + 16 q^{70} + q^{71} + 43 q^{72} + 201 q^{73} + 32 q^{74} + 22 q^{75} - 162 q^{76} + 86 q^{77} + 122 q^{78} + 58 q^{79} + 92 q^{80} + 288 q^{81} + 143 q^{82} + 57 q^{83} + q^{84} + 136 q^{85} - 6 q^{86} + 43 q^{87} + 198 q^{88} + 46 q^{89} + 30 q^{90} + 26 q^{91} + 129 q^{92} + 111 q^{93} + 44 q^{94} - 13 q^{95} + 32 q^{96} + 110 q^{97} - 34 q^{98} + 62 q^{99}+O(q^{100}) \) 140 * q + 4 * q^2 + 3 * q^3 + 162 * q^4 + 13 * q^5 + 12 * q^6 + 25 * q^7 + 12 * q^8 + 181 * q^9 + 8 * q^10 + 19 * q^11 + 17 * q^12 + 28 * q^13 + 5 * q^14 + 14 * q^15 + 202 * q^16 + 38 * q^17 + 26 * q^18 - 140 * q^19 + 36 * q^20 + 4 * q^21 + 53 * q^22 + 58 * q^23 + 47 * q^24 + 279 * q^25 + 29 * q^26 + 21 * q^27 + 69 * q^28 + 18 * q^29 + 50 * q^30 + 20 * q^31 + 13 * q^32 + 47 * q^33 + 6 * q^34 + 35 * q^35 + 230 * q^36 + 88 * q^37 - 4 * q^38 + 32 * q^39 + 32 * q^40 + 24 * q^41 + 75 * q^42 + 100 * q^43 + 63 * q^44 + 87 * q^45 + 23 * q^46 + 35 * q^47 + 46 * q^48 + 255 * q^49 + 11 * q^50 - 6 * q^51 + 47 * q^52 + 77 * q^53 + 16 * q^54 + 63 * q^55 + 21 * q^56 - 3 * q^57 + 165 * q^58 + 18 * q^59 + 28 * q^60 + 99 * q^61 + 34 * q^62 + 89 * q^63 + 298 * q^64 + 78 * q^65 - 3 * q^66 + 28 * q^67 + 93 * q^68 + 19 * q^69 + 16 * q^70 + q^71 + 43 * q^72 + 201 * q^73 + 32 * q^74 + 22 * q^75 - 162 * q^76 + 86 * q^77 + 122 * q^78 + 58 * q^79 + 92 * q^80 + 288 * q^81 + 143 * q^82 + 57 * q^83 + q^84 + 136 * q^85 - 6 * q^86 + 43 * q^87 + 198 * q^88 + 46 * q^89 + 30 * q^90 + 26 * q^91 + 129 * q^92 + 111 * q^93 + 44 * q^94 - 13 * q^95 + 32 * q^96 + 110 * q^97 - 34 * q^98 + 62 * q^99

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