LMFDB - Embedded newform 6014.2.a.e.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6014,2,Mod(1,6014)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6014, 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("6014.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6014 = 2 \cdot 31 \cdot 97 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6014.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:	$48.0220317756$
Analytic rank:	$1$
Dimension:	$21$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	6014.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.37186 q^{3} +1.00000 q^{4} -2.00517 q^{5} +1.37186 q^{6} +2.66469 q^{7} +1.00000 q^{8} -1.11799 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.37186 q^{3} +1.00000 q^{4} -2.00517 q^{5} +1.37186 q^{6} +2.66469 q^{7} +1.00000 q^{8} -1.11799 q^{9} -2.00517 q^{10} -4.40835 q^{11} +1.37186 q^{12} -0.130975 q^{13} +2.66469 q^{14} -2.75081 q^{15} +1.00000 q^{16} +0.338196 q^{17} -1.11799 q^{18} +0.171168 q^{19} -2.00517 q^{20} +3.65558 q^{21} -4.40835 q^{22} -0.132047 q^{23} +1.37186 q^{24} -0.979304 q^{25} -0.130975 q^{26} -5.64932 q^{27} +2.66469 q^{28} -1.40453 q^{29} -2.75081 q^{30} +1.00000 q^{31} +1.00000 q^{32} -6.04765 q^{33} +0.338196 q^{34} -5.34314 q^{35} -1.11799 q^{36} -10.6306 q^{37} +0.171168 q^{38} -0.179680 q^{39} -2.00517 q^{40} +6.03236 q^{41} +3.65558 q^{42} -9.78587 q^{43} -4.40835 q^{44} +2.24176 q^{45} -0.132047 q^{46} +0.129015 q^{47} +1.37186 q^{48} +0.100547 q^{49} -0.979304 q^{50} +0.463958 q^{51} -0.130975 q^{52} +5.39760 q^{53} -5.64932 q^{54} +8.83948 q^{55} +2.66469 q^{56} +0.234819 q^{57} -1.40453 q^{58} -1.58341 q^{59} -2.75081 q^{60} -9.37588 q^{61} +1.00000 q^{62} -2.97910 q^{63} +1.00000 q^{64} +0.262627 q^{65} -6.04765 q^{66} -10.1808 q^{67} +0.338196 q^{68} -0.181151 q^{69} -5.34314 q^{70} -2.79708 q^{71} -1.11799 q^{72} +13.2452 q^{73} -10.6306 q^{74} -1.34347 q^{75} +0.171168 q^{76} -11.7469 q^{77} -0.179680 q^{78} -8.45787 q^{79} -2.00517 q^{80} -4.39611 q^{81} +6.03236 q^{82} +11.1823 q^{83} +3.65558 q^{84} -0.678139 q^{85} -9.78587 q^{86} -1.92682 q^{87} -4.40835 q^{88} -4.76450 q^{89} +2.24176 q^{90} -0.349007 q^{91} -0.132047 q^{92} +1.37186 q^{93} +0.129015 q^{94} -0.343221 q^{95} +1.37186 q^{96} -1.00000 q^{97} +0.100547 q^{98} +4.92851 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21 q + 21 q^{2} - 10 q^{3} + 21 q^{4} - 10 q^{5} - 10 q^{6} - 11 q^{7} + 21 q^{8} + 7 q^{9}+O(q^{10}) $ 21 * q + 21 * q^2 - 10 * q^3 + 21 * q^4 - 10 * q^5 - 10 * q^6 - 11 * q^7 + 21 * q^8 + 7 * q^9	\( 21 q + 21 q^{2} - 10 q^{3} + 21 q^{4} - 10 q^{5} - 10 q^{6} - 11 q^{7} + 21 q^{8} + 7 q^{9} - 10 q^{10} - 12 q^{11} - 10 q^{12} - 14 q^{13} - 11 q^{14} + q^{15} + 21 q^{16} + 7 q^{18} - 27 q^{19} - 10 q^{20} - 6 q^{21} - 12 q^{22} - 4 q^{23} - 10 q^{24} + q^{25} - 14 q^{26} - 19 q^{27} - 11 q^{28} - 13 q^{29} + q^{30} + 21 q^{31} + 21 q^{32} - 20 q^{33} - 20 q^{35} + 7 q^{36} - 13 q^{37} - 27 q^{38} - 4 q^{39} - 10 q^{40} - 19 q^{41} - 6 q^{42} - 19 q^{43} - 12 q^{44} + 13 q^{45} - 4 q^{46} - 18 q^{47} - 10 q^{48} - 20 q^{49} + q^{50} - 33 q^{51} - 14 q^{52} - 15 q^{53} - 19 q^{54} - 26 q^{55} - 11 q^{56} + 9 q^{57} - 13 q^{58} - 32 q^{59} + q^{60} - 36 q^{61} + 21 q^{62} - 27 q^{63} + 21 q^{64} - 20 q^{65} - 20 q^{66} - 43 q^{67} - 11 q^{69} - 20 q^{70} - 31 q^{71} + 7 q^{72} - 11 q^{73} - 13 q^{74} - 22 q^{75} - 27 q^{76} + 12 q^{77} - 4 q^{78} - 31 q^{79} - 10 q^{80} - 39 q^{81} - 19 q^{82} - 26 q^{83} - 6 q^{84} - 12 q^{85} - 19 q^{86} + 19 q^{87} - 12 q^{88} - 14 q^{89} + 13 q^{90} - 30 q^{91} - 4 q^{92} - 10 q^{93} - 18 q^{94} - 40 q^{95} - 10 q^{96} - 21 q^{97} - 20 q^{98} - 17 q^{99}+O(q^{100}) \) 21 * q + 21 * q^2 - 10 * q^3 + 21 * q^4 - 10 * q^5 - 10 * q^6 - 11 * q^7 + 21 * q^8 + 7 * q^9 - 10 * q^10 - 12 * q^11 - 10 * q^12 - 14 * q^13 - 11 * q^14 + q^15 + 21 * q^16 + 7 * q^18 - 27 * q^19 - 10 * q^20 - 6 * q^21 - 12 * q^22 - 4 * q^23 - 10 * q^24 + q^25 - 14 * q^26 - 19 * q^27 - 11 * q^28 - 13 * q^29 + q^30 + 21 * q^31 + 21 * q^32 - 20 * q^33 - 20 * q^35 + 7 * q^36 - 13 * q^37 - 27 * q^38 - 4 * q^39 - 10 * q^40 - 19 * q^41 - 6 * q^42 - 19 * q^43 - 12 * q^44 + 13 * q^45 - 4 * q^46 - 18 * q^47 - 10 * q^48 - 20 * q^49 + q^50 - 33 * q^51 - 14 * q^52 - 15 * q^53 - 19 * q^54 - 26 * q^55 - 11 * q^56 + 9 * q^57 - 13 * q^58 - 32 * q^59 + q^60 - 36 * q^61 + 21 * q^62 - 27 * q^63 + 21 * q^64 - 20 * q^65 - 20 * q^66 - 43 * q^67 - 11 * q^69 - 20 * q^70 - 31 * q^71 + 7 * q^72 - 11 * q^73 - 13 * q^74 - 22 * q^75 - 27 * q^76 + 12 * q^77 - 4 * q^78 - 31 * q^79 - 10 * q^80 - 39 * q^81 - 19 * q^82 - 26 * q^83 - 6 * q^84 - 12 * q^85 - 19 * q^86 + 19 * q^87 - 12 * q^88 - 14 * q^89 + 13 * q^90 - 30 * q^91 - 4 * q^92 - 10 * q^93 - 18 * q^94 - 40 * q^95 - 10 * q^96 - 21 * q^97 - 20 * q^98 - 17 * 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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	1.37186	0.792045	0.396023	−	0.918241i	$-0.370390\pi$
$3$	1.37186	0.792045	0.396023	+	0.918241i	$0.370390\pi$
$4$	1.00000	0.500000
$5$	−2.00517	−0.896738	−0.448369	−	0.893849i	$-0.647995\pi$
$5$	−2.00517	−0.896738	−0.448369	+	0.893849i	$0.647995\pi$
$6$	1.37186	0.560061
$7$	2.66469	1.00716	0.503578	−	0.863950i	$-0.332017\pi$
$7$	2.66469	1.00716	0.503578	+	0.863950i	$0.332017\pi$
$8$	1.00000	0.353553
$9$	−1.11799	−0.372664
$10$	−2.00517	−0.634090
$11$	−4.40835	−1.32917	−0.664584	−	0.747214i	$-0.731391\pi$
$11$	−4.40835	−1.32917	−0.664584	+	0.747214i	$0.731391\pi$
$12$	1.37186	0.396023
$13$	−0.130975	−0.0363259	−0.0181630	−	0.999835i	$-0.505782\pi$
$13$	−0.130975	−0.0363259	−0.0181630	+	0.999835i	$0.505782\pi$
$14$	2.66469	0.712167
$15$	−2.75081	−0.710257
$16$	1.00000	0.250000
$17$	0.338196	0.0820245	0.0410122	−	0.999159i	$-0.486942\pi$
$17$	0.338196	0.0820245	0.0410122	+	0.999159i	$0.486942\pi$
$18$	−1.11799	−0.263514
$19$	0.171168	0.0392686	0.0196343	−	0.999807i	$-0.493750\pi$
$19$	0.171168	0.0392686	0.0196343	+	0.999807i	$0.493750\pi$
$20$	−2.00517	−0.448369
$21$	3.65558	0.797713
$22$	−4.40835	−0.939863
$23$	−0.132047	−0.0275338	−0.0137669	−	0.999905i	$-0.504382\pi$
$23$	−0.132047	−0.0275338	−0.0137669	+	0.999905i	$0.504382\pi$
$24$	1.37186	0.280030
$25$	−0.979304	−0.195861
$26$	−0.130975	−0.0256863
$27$	−5.64932	−1.08721
$28$	2.66469	0.503578
$29$	−1.40453	−0.260814	−0.130407	−	0.991461i	$-0.541628\pi$
$29$	−1.40453	−0.260814	−0.130407	+	0.991461i	$0.541628\pi$
$30$	−2.75081	−0.502228
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	1.00000	0.176777
$33$	−6.04765	−1.05276
$34$	0.338196	0.0580001
$35$	−5.34314	−0.903155
$36$	−1.11799	−0.186332
$37$	−10.6306	−1.74766	−0.873829	−	0.486233i	$-0.838371\pi$
$37$	−10.6306	−1.74766	−0.873829	+	0.486233i	$0.838371\pi$
$38$	0.171168	0.0277671
$39$	−0.179680	−0.0287718
$40$	−2.00517	−0.317045
$41$	6.03236	0.942097	0.471048	−	0.882107i	$-0.343876\pi$
$41$	6.03236	0.942097	0.471048	+	0.882107i	$0.343876\pi$
$42$	3.65558	0.564069
$43$	−9.78587	−1.49233	−0.746166	−	0.665760i	$-0.768107\pi$
$43$	−9.78587	−1.49233	−0.746166	+	0.665760i	$0.768107\pi$
$44$	−4.40835	−0.664584
$45$	2.24176	0.334182
$46$	−0.132047	−0.0194693
$47$	0.129015	0.0188188	0.00940940	−	0.999956i	$-0.497005\pi$
$47$	0.129015	0.0188188	0.00940940	+	0.999956i	$0.497005\pi$
$48$	1.37186	0.198011
$49$	0.100547	0.0143639
$50$	−0.979304	−0.138494
$51$	0.463958	0.0649671
$52$	−0.130975	−0.0181630
$53$	5.39760	0.741417	0.370709	−	0.928749i	$-0.379115\pi$
$53$	5.39760	0.741417	0.370709	+	0.928749i	$0.379115\pi$
$54$	−5.64932	−0.768775
$55$	8.83948	1.19192
$56$	2.66469	0.356084
$57$	0.234819	0.0311025
$58$	−1.40453	−0.184423
$59$	−1.58341	−0.206143	−0.103071	−	0.994674i	$-0.532867\pi$
$59$	−1.58341	−0.206143	−0.103071	+	0.994674i	$0.532867\pi$
$60$	−2.75081	−0.355129
$61$	−9.37588	−1.20046	−0.600229	−	0.799828i	$-0.704924\pi$
$61$	−9.37588	−1.20046	−0.600229	+	0.799828i	$0.704924\pi$
$62$	1.00000	0.127000
$63$	−2.97910	−0.375331
$64$	1.00000	0.125000
$65$	0.262627	0.0325748
$66$	−6.04765	−0.744414
$67$	−10.1808	−1.24378	−0.621891	−	0.783104i	$-0.713635\pi$
$67$	−10.1808	−1.24378	−0.621891	+	0.783104i	$0.713635\pi$
$68$	0.338196	0.0410122
$69$	−0.181151	−0.0218080
$70$	−5.34314	−0.638627
$71$	−2.79708	−0.331953	−0.165976	−	0.986130i	$-0.553078\pi$
$71$	−2.79708	−0.331953	−0.165976	+	0.986130i	$0.553078\pi$
$72$	−1.11799	−0.131757
$73$	13.2452	1.55023	0.775117	−	0.631818i	$-0.217691\pi$
$73$	13.2452	1.55023	0.775117	+	0.631818i	$0.217691\pi$
$74$	−10.6306	−1.23578
$75$	−1.34347	−0.155131
$76$	0.171168	0.0196343
$77$	−11.7469	−1.33868
$78$	−0.179680	−0.0203447
$79$	−8.45787	−0.951585	−0.475792	−	0.879558i	$-0.657839\pi$
$79$	−8.45787	−0.951585	−0.475792	+	0.879558i	$0.657839\pi$
$80$	−2.00517	−0.224185
$81$	−4.39611	−0.488457
$82$	6.03236	0.666163
$83$	11.1823	1.22741	0.613707	−	0.789534i	$-0.289678\pi$
$83$	11.1823	1.22741	0.613707	+	0.789534i	$0.289678\pi$
$84$	3.65558	0.398857
$85$	−0.678139	−0.0735545
$86$	−9.78587	−1.05524
$87$	−1.92682	−0.206576
$88$	−4.40835	−0.469932
$89$	−4.76450	−0.505036	−0.252518	−	0.967592i	$-0.581259\pi$
$89$	−4.76450	−0.505036	−0.252518	+	0.967592i	$0.581259\pi$
$90$	2.24176	0.236303
$91$	−0.349007	−0.0365859
$92$	−0.132047	−0.0137669
$93$	1.37186	0.142256
$94$	0.129015	0.0133069
$95$	−0.343221	−0.0352137
$96$	1.37186	0.140015
$97$	−1.00000	−0.101535
$97$	−1.00000	−0.101535
$98$	0.100547	0.0101568
$99$	4.92851	0.495333
$100$	−0.979304	−0.0979304
$101$	6.76074	0.672719	0.336359	−	0.941734i	$-0.390804\pi$
$101$	6.76074	0.672719	0.336359	+	0.941734i	$0.390804\pi$
$102$	0.463958	0.0459387
$103$	11.5514	1.13819	0.569095	−	0.822272i	$-0.307294\pi$
$103$	11.5514	1.13819	0.569095	+	0.822272i	$0.307294\pi$
$104$	−0.130975	−0.0128431
$105$	−7.33005	−0.715340
$106$	5.39760	0.524261
$107$	−16.5174	−1.59679	−0.798397	−	0.602132i	$-0.794318\pi$
$107$	−16.5174	−1.59679	−0.798397	+	0.602132i	$0.794318\pi$
$108$	−5.64932	−0.543606
$109$	−4.39269	−0.420744	−0.210372	−	0.977621i	$-0.567467\pi$
$109$	−4.39269	−0.420744	−0.210372	+	0.977621i	$0.567467\pi$
$110$	8.83948	0.842811
$111$	−14.5837	−1.38422
$112$	2.66469	0.251789
$113$	2.34518	0.220616	0.110308	−	0.993897i	$-0.464816\pi$
$113$	2.34518	0.220616	0.110308	+	0.993897i	$0.464816\pi$
$114$	0.234819	0.0219928
$115$	0.264777	0.0246906
$116$	−1.40453	−0.130407
$117$	0.146429	0.0135374
$118$	−1.58341	−0.145765
$119$	0.901185	0.0826115
$120$	−2.75081	−0.251114
$121$	8.43355	0.766686
$122$	−9.37588	−0.848853
$123$	8.27557	0.746183
$124$	1.00000	0.0898027
$125$	11.9895	1.07237
$126$	−2.97910	−0.265399
$127$	8.40238	0.745591	0.372795	−	0.927914i	$-0.378399\pi$
$127$	8.40238	0.745591	0.372795	+	0.927914i	$0.378399\pi$
$128$	1.00000	0.0883883
$129$	−13.4249	−1.18199
$130$	0.262627	0.0230339
$131$	−10.0299	−0.876314	−0.438157	−	0.898898i	$-0.644369\pi$
$131$	−10.0299	−0.876314	−0.438157	+	0.898898i	$0.644369\pi$
$132$	−6.04765	−0.526380
$133$	0.456109	0.0395497
$134$	−10.1808	−0.879487
$135$	11.3278	0.974945
$136$	0.338196	0.0290000
$137$	−6.88000	−0.587798	−0.293899	−	0.955837i	$-0.594953\pi$
$137$	−6.88000	−0.587798	−0.293899	+	0.955837i	$0.594953\pi$
$138$	−0.181151	−0.0154206
$139$	−9.43778	−0.800502	−0.400251	−	0.916405i	$-0.631077\pi$
$139$	−9.43778	−0.800502	−0.400251	+	0.916405i	$0.631077\pi$
$140$	−5.34314	−0.451578
$141$	0.176991	0.0149053
$142$	−2.79708	−0.234726
$143$	0.577383	0.0482832
$144$	−1.11799	−0.0931661
$145$	2.81631	0.233882
$146$	13.2452	1.09618
$147$	0.137937	0.0113769
$148$	−10.6306	−0.873829
$149$	−9.44501	−0.773765	−0.386883	−	0.922129i	$-0.626448\pi$
$149$	−9.44501	−0.773765	−0.386883	+	0.922129i	$0.626448\pi$
$150$	−1.34347	−0.109694
$151$	6.34432	0.516294	0.258147	−	0.966106i	$-0.416888\pi$
$151$	6.34432	0.516294	0.258147	+	0.966106i	$0.416888\pi$
$152$	0.171168	0.0138836
$153$	−0.378100	−0.0305676
$154$	−11.7469	−0.946589
$155$	−2.00517	−0.161059
$156$	−0.179680	−0.0143859
$157$	−8.96688	−0.715635	−0.357818	−	0.933792i	$-0.616479\pi$
$157$	−8.96688	−0.715635	−0.357818	+	0.933792i	$0.616479\pi$
$158$	−8.45787	−0.672872
$159$	7.40476	0.587236
$160$	−2.00517	−0.158522
$161$	−0.351865	−0.0277308
$162$	−4.39611	−0.345391
$163$	−20.5899	−1.61272	−0.806362	−	0.591422i	$-0.798567\pi$
$163$	−20.5899	−1.61272	−0.806362	+	0.591422i	$0.798567\pi$
$164$	6.03236	0.471048
$165$	12.1266	0.944051
$166$	11.1823	0.867912
$167$	3.23851	0.250603	0.125302	−	0.992119i	$-0.460010\pi$
$167$	3.23851	0.250603	0.125302	+	0.992119i	$0.460010\pi$
$168$	3.65558	0.282034
$169$	−12.9828	−0.998680
$170$	−0.678139	−0.0520109
$171$	−0.191365	−0.0146340
$172$	−9.78587	−0.746166
$173$	−11.3593	−0.863628	−0.431814	−	0.901963i	$-0.642126\pi$
$173$	−11.3593	−0.863628	−0.431814	+	0.901963i	$0.642126\pi$
$174$	−1.92682	−0.146072
$175$	−2.60954	−0.197262
$176$	−4.40835	−0.332292
$177$	−2.17222	−0.163274
$178$	−4.76450	−0.357115
$179$	−2.60555	−0.194748	−0.0973741	−	0.995248i	$-0.531044\pi$
$179$	−2.60555	−0.194748	−0.0973741	+	0.995248i	$0.531044\pi$
$180$	2.24176	0.167091
$181$	−6.52241	−0.484807	−0.242403	−	0.970176i	$-0.577936\pi$
$181$	−6.52241	−0.484807	−0.242403	+	0.970176i	$0.577936\pi$
$182$	−0.349007	−0.0258701
$183$	−12.8624	−0.950818
$184$	−0.132047	−0.00973467
$185$	21.3161	1.56719
$186$	1.37186	0.100590
$187$	−1.49088	−0.109024
$188$	0.129015	0.00940940
$189$	−15.0537	−1.09499
$190$	−0.343221	−0.0248998
$191$	−6.94613	−0.502604	−0.251302	−	0.967909i	$-0.580859\pi$
$191$	−6.94613	−0.502604	−0.251302	+	0.967909i	$0.580859\pi$
$192$	1.37186	0.0990056
$193$	−10.0599	−0.724125	−0.362063	−	0.932154i	$-0.617927\pi$
$193$	−10.0599	−0.724125	−0.362063	+	0.932154i	$0.617927\pi$
$194$	−1.00000	−0.0717958
$195$	0.360288	0.0258007
$196$	0.100547	0.00718195
$197$	1.14485	0.0815673	0.0407836	−	0.999168i	$-0.487015\pi$
$197$	1.14485	0.0815673	0.0407836	+	0.999168i	$0.487015\pi$
$198$	4.92851	0.350254
$199$	9.31588	0.660385	0.330192	−	0.943914i	$-0.392886\pi$
$199$	9.31588	0.660385	0.330192	+	0.943914i	$0.392886\pi$
$200$	−0.979304	−0.0692472
$201$	−13.9667	−0.985132
$202$	6.76074	0.475684
$203$	−3.74262	−0.262681
$204$	0.463958	0.0324835
$205$	−12.0959	−0.844814
$206$	11.5514	0.804822
$207$	0.147628	0.0102609
$208$	−0.130975	−0.00908148
$209$	−0.754569	−0.0521946
$210$	−7.33005	−0.505822
$211$	−0.466418	−0.0321095	−0.0160548	−	0.999871i	$-0.505111\pi$
$211$	−0.466418	−0.0321095	−0.0160548	+	0.999871i	$0.505111\pi$
$212$	5.39760	0.370709
$213$	−3.83721	−0.262922
$214$	−16.5174	−1.12910
$215$	19.6223	1.33823
$216$	−5.64932	−0.384388
$217$	2.66469	0.180891
$218$	−4.39269	−0.297511
$219$	18.1706	1.22786
$220$	8.83948	0.595958
$221$	−0.0442951	−0.00297961
$222$	−14.5837	−0.978795
$223$	−11.9854	−0.802604	−0.401302	−	0.915946i	$-0.631442\pi$
$223$	−11.9854	−0.802604	−0.401302	+	0.915946i	$0.631442\pi$
$224$	2.66469	0.178042
$225$	1.09486	0.0729903
$226$	2.34518	0.155999
$227$	14.7614	0.979746	0.489873	−	0.871794i	$-0.337043\pi$
$227$	14.7614	0.979746	0.489873	+	0.871794i	$0.337043\pi$
$228$	0.234819	0.0155513
$229$	23.1774	1.53160	0.765802	−	0.643076i	$-0.222342\pi$
$229$	23.1774	1.53160	0.765802	+	0.643076i	$0.222342\pi$
$230$	0.264777	0.0174589
$231$	−16.1151	−1.06029
$232$	−1.40453	−0.0922117
$233$	−3.37356	−0.221010	−0.110505	−	0.993876i	$-0.535247\pi$
$233$	−3.37356	−0.221010	−0.110505	+	0.993876i	$0.535247\pi$
$234$	0.146429	0.00957237
$235$	−0.258697	−0.0168755
$236$	−1.58341	−0.103071
$237$	−11.6030	−0.753698
$238$	0.901185	0.0584151
$239$	19.5788	1.26645	0.633223	−	0.773970i	$-0.281732\pi$
$239$	19.5788	1.26645	0.633223	+	0.773970i	$0.281732\pi$
$240$	−2.75081	−0.177564
$241$	25.2278	1.62506	0.812531	−	0.582918i	$-0.198089\pi$
$241$	25.2278	1.62506	0.812531	+	0.582918i	$0.198089\pi$
$242$	8.43355	0.542129
$243$	10.9171	0.700332
$244$	−9.37588	−0.600229
$245$	−0.201614	−0.0128807
$246$	8.27557	0.527631
$247$	−0.0224187	−0.00142647
$248$	1.00000	0.0635001
$249$	15.3405	0.972167
$250$	11.9895	0.758283
$251$	17.4515	1.10153	0.550764	−	0.834661i	$-0.314336\pi$
$251$	17.4515	1.10153	0.550764	+	0.834661i	$0.314336\pi$
$252$	−2.97910	−0.187666
$253$	0.582111	0.0365970
$254$	8.40238	0.527212
$255$	−0.930313	−0.0582585
$256$	1.00000	0.0625000
$257$	−0.524699	−0.0327298	−0.0163649	−	0.999866i	$-0.505209\pi$
$257$	−0.524699	−0.0327298	−0.0163649	+	0.999866i	$0.505209\pi$
$258$	−13.4249	−0.835796
$259$	−28.3272	−1.76017
$260$	0.262627	0.0162874
$261$	1.57025	0.0971961
$262$	−10.0299	−0.619648
$263$	31.5198	1.94359	0.971797	−	0.235818i	$-0.0757770\pi$
$263$	31.5198	1.94359	0.971797	+	0.235818i	$0.0757770\pi$
$264$	−6.04765	−0.372207
$265$	−10.8231	−0.664857
$266$	0.456109	0.0279658
$267$	−6.53624	−0.400012
$268$	−10.1808	−0.621891
$269$	10.9713	0.668929	0.334464	−	0.942408i	$-0.391445\pi$
$269$	10.9713	0.668929	0.334464	+	0.942408i	$0.391445\pi$
$270$	11.3278	0.689390
$271$	−26.7582	−1.62544	−0.812722	−	0.582651i	$-0.802015\pi$
$271$	−26.7582	−1.62544	−0.812722	+	0.582651i	$0.802015\pi$
$272$	0.338196	0.0205061
$273$	−0.478789	−0.0289777
$274$	−6.88000	−0.415636
$275$	4.31711	0.260332
$276$	−0.181151	−0.0109040
$277$	25.5996	1.53813	0.769064	−	0.639171i	$-0.220723\pi$
$277$	25.5996	1.53813	0.769064	+	0.639171i	$0.220723\pi$
$278$	−9.43778	−0.566041
$279$	−1.11799	−0.0669325
$280$	−5.34314	−0.319314
$281$	5.74844	0.342923	0.171462	−	0.985191i	$-0.445151\pi$
$281$	5.74844	0.342923	0.171462	+	0.985191i	$0.445151\pi$
$282$	0.176991	0.0105397
$283$	0.810385	0.0481724	0.0240862	−	0.999710i	$-0.492332\pi$
$283$	0.810385	0.0481724	0.0240862	+	0.999710i	$0.492332\pi$
$284$	−2.79708	−0.165976
$285$	−0.470852	−0.0278908
$286$	0.577383	0.0341414
$287$	16.0743	0.948839
$288$	−1.11799	−0.0658784
$289$	−16.8856	−0.993272
$290$	2.81631	0.165379
$291$	−1.37186	−0.0804200
$292$	13.2452	0.775117
$293$	−3.65126	−0.213309	−0.106654	−	0.994296i	$-0.534014\pi$
$293$	−3.65126	−0.213309	−0.106654	+	0.994296i	$0.534014\pi$
$294$	0.137937	0.00804466
$295$	3.17501	0.184856
$296$	−10.6306	−0.617891
$297$	24.9042	1.44509
$298$	−9.44501	−0.547135
$299$	0.0172949	0.00100019
$300$	−1.34347	−0.0775653
$301$	−26.0763	−1.50301
$302$	6.34432	0.365075
$303$	9.27480	0.532824
$304$	0.171168	0.00981716
$305$	18.8002	1.07650
$306$	−0.378100	−0.0216146
$307$	1.65769	0.0946092	0.0473046	−	0.998881i	$-0.484937\pi$
$307$	1.65769	0.0946092	0.0473046	+	0.998881i	$0.484937\pi$
$308$	−11.7469	−0.669340
$309$	15.8469	0.901498
$310$	−2.00517	−0.113886
$311$	3.92423	0.222523	0.111261	−	0.993791i	$-0.464511\pi$
$311$	3.92423	0.222523	0.111261	+	0.993791i	$0.464511\pi$
$312$	−0.179680	−0.0101724
$313$	23.7350	1.34158	0.670791	−	0.741646i	$-0.265955\pi$
$313$	23.7350	1.34158	0.670791	+	0.741646i	$0.265955\pi$
$314$	−8.96688	−0.506030
$315$	5.97359	0.336574
$316$	−8.45787	−0.475792
$317$	−9.68588	−0.544013	−0.272007	−	0.962295i	$-0.587687\pi$
$317$	−9.68588	−0.544013	−0.272007	+	0.962295i	$0.587687\pi$
$318$	7.40476	0.415238
$319$	6.19164	0.346666
$320$	−2.00517	−0.112092
$321$	−22.6595	−1.26473
$322$	−0.351865	−0.0196087
$323$	0.0578883	0.00322099
$324$	−4.39611	−0.244228
$325$	0.128264	0.00711482
$326$	−20.5899	−1.14037
$327$	−6.02617	−0.333248
$328$	6.03236	0.333081
$329$	0.343785	0.0189535
$330$	12.1266	0.667545
$331$	−25.6042	−1.40733	−0.703667	−	0.710530i	$-0.748455\pi$
$331$	−25.6042	−1.40733	−0.703667	+	0.710530i	$0.748455\pi$
$332$	11.1823	0.613707
$333$	11.8849	0.651290
$334$	3.23851	0.177203
$335$	20.4142	1.11535
$336$	3.65558	0.199428
$337$	7.05789	0.384468	0.192234	−	0.981349i	$-0.438427\pi$
$337$	7.05789	0.384468	0.192234	+	0.981349i	$0.438427\pi$
$338$	−12.9828	−0.706174
$339$	3.21727	0.174738
$340$	−0.678139	−0.0367772
$341$	−4.40835	−0.238726
$342$	−0.191365	−0.0103478
$343$	−18.3849	−0.992690
$344$	−9.78587	−0.527619
$345$	0.363238	0.0195561
$346$	−11.3593	−0.610677
$347$	−20.4096	−1.09565	−0.547823	−	0.836595i	$-0.684543\pi$
$347$	−20.4096	−1.09565	−0.547823	+	0.836595i	$0.684543\pi$
$348$	−1.92682	−0.103288
$349$	−25.1337	−1.34538	−0.672688	−	0.739926i	$-0.734860\pi$
$349$	−25.1337	−1.34538	−0.672688	+	0.739926i	$0.734860\pi$
$350$	−2.60954	−0.139486
$351$	0.739919	0.0394940
$352$	−4.40835	−0.234966
$353$	−19.8265	−1.05526	−0.527628	−	0.849475i	$-0.676919\pi$
$353$	−19.8265	−1.05526	−0.527628	+	0.849475i	$0.676919\pi$
$354$	−2.17222	−0.115452
$355$	5.60862	0.297675
$356$	−4.76450	−0.252518
$357$	1.23630	0.0654320
$358$	−2.60555	−0.137708
$359$	17.3486	0.915626	0.457813	−	0.889049i	$-0.348633\pi$
$359$	17.3486	0.915626	0.457813	+	0.889049i	$0.348633\pi$
$360$	2.24176	0.118151
$361$	−18.9707	−0.998458
$362$	−6.52241	−0.342810
$363$	11.5697	0.607250
$364$	−0.349007	−0.0182929
$365$	−26.5588	−1.39015
$366$	−12.8624	−0.672330
$367$	3.60621	0.188243	0.0941213	−	0.995561i	$-0.469996\pi$
$367$	3.60621	0.188243	0.0941213	+	0.995561i	$0.469996\pi$
$368$	−0.132047	−0.00688345
$369$	−6.74414	−0.351086
$370$	21.3161	1.10817
$371$	14.3829	0.746723
$372$	1.37186	0.0711278
$373$	3.35276	0.173599	0.0867996	−	0.996226i	$-0.472336\pi$
$373$	3.35276	0.173599	0.0867996	+	0.996226i	$0.472336\pi$
$374$	−1.49088	−0.0770918
$375$	16.4480	0.849369
$376$	0.129015	0.00665345
$377$	0.183958	0.00947431
$378$	−15.0537	−0.774277
$379$	33.4394	1.71767	0.858834	−	0.512255i	$-0.171190\pi$
$379$	33.4394	1.71767	0.858834	+	0.512255i	$0.171190\pi$
$380$	−0.343221	−0.0176068
$381$	11.5269	0.590542
$382$	−6.94613	−0.355395
$383$	0.171973	0.00878742	0.00439371	−	0.999990i	$-0.498601\pi$
$383$	0.171973	0.00878742	0.00439371	+	0.999990i	$0.498601\pi$
$384$	1.37186	0.0700076
$385$	23.5544	1.20044
$386$	−10.0599	−0.512034
$387$	10.9405	0.556139
$388$	−1.00000	−0.0507673
$389$	−23.7746	−1.20542	−0.602710	−	0.797960i	$-0.705912\pi$
$389$	−23.7746	−1.20542	−0.602710	+	0.797960i	$0.705912\pi$
$390$	0.360288	0.0182439
$391$	−0.0446579	−0.00225844
$392$	0.100547	0.00507841
$393$	−13.7596	−0.694080
$394$	1.14485	0.0576768
$395$	16.9594	0.853322
$396$	4.92851	0.247667
$397$	9.99761	0.501766	0.250883	−	0.968017i	$-0.419279\pi$
$397$	9.99761	0.501766	0.250883	+	0.968017i	$0.419279\pi$
$398$	9.31588	0.466963
$399$	0.625719	0.0313251
$400$	−0.979304	−0.0489652
$401$	2.76037	0.137846	0.0689230	−	0.997622i	$-0.478044\pi$
$401$	2.76037	0.137846	0.0689230	+	0.997622i	$0.478044\pi$
$402$	−13.9667	−0.696593
$403$	−0.130975	−0.00652432
$404$	6.76074	0.336359
$405$	8.81494	0.438018
$406$	−3.74262	−0.185743
$407$	46.8634	2.32293
$408$	0.463958	0.0229693
$409$	−12.7086	−0.628398	−0.314199	−	0.949357i	$-0.601736\pi$
$409$	−12.7086	−0.628398	−0.314199	+	0.949357i	$0.601736\pi$
$410$	−12.0959	−0.597374
$411$	−9.43841	−0.465562
$412$	11.5514	0.569095
$413$	−4.21930	−0.207618
$414$	0.147628	0.00725553
$415$	−22.4223	−1.10067
$416$	−0.130975	−0.00642157
$417$	−12.9473	−0.634034
$418$	−0.754569	−0.0369072
$419$	−3.89020	−0.190049	−0.0950243	−	0.995475i	$-0.530293\pi$
$419$	−3.89020	−0.190049	−0.0950243	+	0.995475i	$0.530293\pi$
$420$	−7.33005	−0.357670
$421$	−11.2415	−0.547879	−0.273939	−	0.961747i	$-0.588327\pi$
$421$	−11.2415	−0.547879	−0.273939	+	0.961747i	$0.588327\pi$
$422$	−0.466418	−0.0227049
$423$	−0.144238	−0.00701310
$424$	5.39760	0.262131
$425$	−0.331196	−0.0160654
$426$	−3.83721	−0.185914
$427$	−24.9838	−1.20905
$428$	−16.5174	−0.798397
$429$	0.792090	0.0382425
$430$	19.6223	0.946272
$431$	−4.32190	−0.208178	−0.104089	−	0.994568i	$-0.533193\pi$
$431$	−4.32190	−0.208178	−0.104089	+	0.994568i	$0.533193\pi$
$432$	−5.64932	−0.271803
$433$	23.2078	1.11530	0.557648	−	0.830078i	$-0.311704\pi$
$433$	23.2078	1.11530	0.557648	+	0.830078i	$0.311704\pi$
$434$	2.66469	0.127909
$435$	3.86359	0.185245
$436$	−4.39269	−0.210372
$437$	−0.0226023	−0.00108121
$438$	18.1706	0.868225
$439$	−2.00561	−0.0957226	−0.0478613	−	0.998854i	$-0.515241\pi$
$439$	−2.00561	−0.0957226	−0.0478613	+	0.998854i	$0.515241\pi$
$440$	8.83948	0.421406
$441$	−0.112411	−0.00535292
$442$	−0.0442951	−0.00210690
$443$	13.9910	0.664733	0.332366	−	0.943150i	$-0.392153\pi$
$443$	13.9910	0.664733	0.332366	+	0.943150i	$0.392153\pi$
$444$	−14.5837	−0.692112
$445$	9.55363	0.452885
$446$	−11.9854	−0.567527
$447$	−12.9573	−0.612857
$448$	2.66469	0.125895
$449$	39.4298	1.86081	0.930403	−	0.366537i	$-0.119457\pi$
$449$	39.4298	1.86081	0.930403	+	0.366537i	$0.119457\pi$
$450$	1.09486	0.0516120
$451$	−26.5928	−1.25220
$452$	2.34518	0.110308
$453$	8.70354	0.408928
$454$	14.7614	0.692785
$455$	0.699817	0.0328079
$456$	0.234819	0.0109964
$457$	−23.2908	−1.08950	−0.544748	−	0.838600i	$-0.683375\pi$
$457$	−23.2908	−1.08950	−0.544748	+	0.838600i	$0.683375\pi$
$458$	23.1774	1.08301
$459$	−1.91058	−0.0891780
$460$	0.264777	0.0123453
$461$	−1.04340	−0.0485960	−0.0242980	−	0.999705i	$-0.507735\pi$
$461$	−1.04340	−0.0485960	−0.0242980	+	0.999705i	$0.507735\pi$
$462$	−16.1151	−0.749742
$463$	−14.3873	−0.668636	−0.334318	−	0.942460i	$-0.608506\pi$
$463$	−14.3873	−0.668636	−0.334318	+	0.942460i	$0.608506\pi$
$464$	−1.40453	−0.0652035
$465$	−2.75081	−0.127566
$466$	−3.37356	−0.156277
$467$	29.1085	1.34698	0.673490	−	0.739196i	$-0.264794\pi$
$467$	29.1085	1.34698	0.673490	+	0.739196i	$0.264794\pi$
$468$	0.146429	0.00676869
$469$	−27.1286	−1.25268
$470$	−0.258697	−0.0119328
$471$	−12.3013	−0.566815
$472$	−1.58341	−0.0728825
$473$	43.1395	1.98356
$474$	−11.6030	−0.532945
$475$	−0.167626	−0.00769119
$476$	0.901185	0.0413057
$477$	−6.03448	−0.276300
$478$	19.5788	0.895512
$479$	12.9428	0.591370	0.295685	−	0.955285i	$-0.404452\pi$
$479$	12.9428	0.591370	0.295685	+	0.955285i	$0.404452\pi$
$480$	−2.75081	−0.125557
$481$	1.39234	0.0634853
$482$	25.2278	1.14909
$483$	−0.482710	−0.0219641
$484$	8.43355	0.383343
$485$	2.00517	0.0910500
$486$	10.9171	0.495210
$487$	−0.884103	−0.0400625	−0.0200313	−	0.999799i	$-0.506377\pi$
$487$	−0.884103	−0.0400625	−0.0200313	+	0.999799i	$0.506377\pi$
$488$	−9.37588	−0.424426
$489$	−28.2465	−1.27735
$490$	−0.201614	−0.00910800
$491$	−25.4472	−1.14842	−0.574208	−	0.818709i	$-0.694690\pi$
$491$	−25.4472	−1.14842	−0.574208	+	0.818709i	$0.694690\pi$
$492$	8.27557	0.373092
$493$	−0.475005	−0.0213931
$494$	−0.0224187	−0.00100867
$495$	−9.88248	−0.444184
$496$	1.00000	0.0449013
$497$	−7.45335	−0.334328
$498$	15.3405	0.687426
$499$	−18.3925	−0.823360	−0.411680	−	0.911328i	$-0.635058\pi$
$499$	−18.3925	−0.823360	−0.411680	+	0.911328i	$0.635058\pi$
$500$	11.9895	0.536187
$501$	4.44278	0.198489
$502$	17.4515	0.778898
$503$	19.9744	0.890613	0.445307	−	0.895378i	$-0.353095\pi$
$503$	19.9744	0.890613	0.445307	+	0.895378i	$0.353095\pi$
$504$	−2.97910	−0.132700
$505$	−13.5564	−0.603252
$506$	0.582111	0.0258780
$507$	−17.8107	−0.791000
$508$	8.40238	0.372795
$509$	14.5208	0.643622	0.321811	−	0.946804i	$-0.395708\pi$
$509$	14.5208	0.643622	0.321811	+	0.946804i	$0.395708\pi$
$510$	−0.930313	−0.0411950
$511$	35.2943	1.56133
$512$	1.00000	0.0441942
$513$	−0.966983	−0.0426934
$514$	−0.524699	−0.0231435
$515$	−23.1624	−1.02066
$516$	−13.4249	−0.590997
$517$	−0.568744	−0.0250133
$518$	−28.3272	−1.24462
$519$	−15.5833	−0.684033
$520$	0.262627	0.0115169
$521$	−24.7165	−1.08285	−0.541426	−	0.840749i	$-0.682115\pi$
$521$	−24.7165	−1.08285	−0.541426	+	0.840749i	$0.682115\pi$
$522$	1.57025	0.0687280
$523$	−6.23235	−0.272522	−0.136261	−	0.990673i	$-0.543509\pi$
$523$	−6.23235	−0.272522	−0.136261	+	0.990673i	$0.543509\pi$
$524$	−10.0299	−0.438157
$525$	−3.57992	−0.156241
$526$	31.5198	1.37433
$527$	0.338196	0.0147320
$528$	−6.04765	−0.263190
$529$	−22.9826	−0.999242
$530$	−10.8231	−0.470125
$531$	1.77024	0.0768221
$532$	0.456109	0.0197748
$533$	−0.790088	−0.0342225
$534$	−6.53624	−0.282851
$535$	33.1201	1.43191
$536$	−10.1808	−0.439743
$537$	−3.57446	−0.154249
$538$	10.9713	0.473004
$539$	−0.443248	−0.0190920
$540$	11.3278	0.487472
$541$	19.2891	0.829304	0.414652	−	0.909980i	$-0.363903\pi$
$541$	19.2891	0.829304	0.414652	+	0.909980i	$0.363903\pi$
$542$	−26.7582	−1.14936
$543$	−8.94784	−0.383989
$544$	0.338196	0.0145000
$545$	8.80809	0.377297
$546$	−0.478789	−0.0204903
$547$	2.83703	0.121302	0.0606512	−	0.998159i	$-0.480682\pi$
$547$	2.83703	0.121302	0.0606512	+	0.998159i	$0.480682\pi$
$548$	−6.88000	−0.293899
$549$	10.4822	0.447368
$550$	4.31711	0.184082
$551$	−0.240410	−0.0102418
$552$	−0.181151	−0.00771030
$553$	−22.5376	−0.958395
$554$	25.5996	1.08762
$555$	29.2428	1.24129
$556$	−9.43778	−0.400251
$557$	−15.0323	−0.636939	−0.318470	−	0.947933i	$-0.603169\pi$
$557$	−15.0323	−0.636939	−0.318470	+	0.947933i	$0.603169\pi$
$558$	−1.11799	−0.0473284
$559$	1.28170	0.0542103
$560$	−5.34314	−0.225789
$561$	−2.04529	−0.0863521
$562$	5.74844	0.242483
$563$	−36.9230	−1.55612	−0.778059	−	0.628192i	$-0.783795\pi$
$563$	−36.9230	−1.55612	−0.778059	+	0.628192i	$0.783795\pi$
$564$	0.176991	0.00745267
$565$	−4.70248	−0.197835
$566$	0.810385	0.0340630
$567$	−11.7143	−0.491952
$568$	−2.79708	−0.117363
$569$	14.9952	0.628633	0.314316	−	0.949318i	$-0.398225\pi$
$569$	14.9952	0.628633	0.314316	+	0.949318i	$0.398225\pi$
$570$	−0.470852	−0.0197218
$571$	23.2942	0.974832	0.487416	−	0.873170i	$-0.337940\pi$
$571$	23.2942	0.974832	0.487416	+	0.873170i	$0.337940\pi$
$572$	0.577383	0.0241416
$573$	−9.52913	−0.398085
$574$	16.0743	0.670930
$575$	0.129315	0.00539279
$576$	−1.11799	−0.0465831
$577$	4.83724	0.201377	0.100688	−	0.994918i	$-0.467895\pi$
$577$	4.83724	0.201377	0.100688	+	0.994918i	$0.467895\pi$
$578$	−16.8856	−0.702349
$579$	−13.8008	−0.573540
$580$	2.81631	0.116941
$581$	29.7972	1.23620
$582$	−1.37186	−0.0568655
$583$	−23.7945	−0.985468
$584$	13.2452	0.548090
$585$	−0.293615	−0.0121395
$586$	−3.65126	−0.150832
$587$	31.3158	1.29254	0.646270	−	0.763109i	$-0.276328\pi$
$587$	31.3158	1.29254	0.646270	+	0.763109i	$0.276328\pi$
$588$	0.137937	0.00568843
$589$	0.171168	0.00705286
$590$	3.17501	0.130713
$591$	1.57058	0.0646050
$592$	−10.6306	−0.436915
$593$	−9.41584	−0.386662	−0.193331	−	0.981134i	$-0.561929\pi$
$593$	−9.41584	−0.386662	−0.193331	+	0.981134i	$0.561929\pi$
$594$	24.9042	1.02183
$595$	−1.80703	−0.0740809
$596$	−9.44501	−0.386883
$597$	12.7801	0.523055
$598$	0.0172949	0.000707241 0
$599$	−17.7423	−0.724931	−0.362465	−	0.931997i	$-0.618065\pi$
$599$	−17.7423	−0.724931	−0.362465	+	0.931997i	$0.618065\pi$
$600$	−1.34347	−0.0548469
$601$	−0.926347	−0.0377865	−0.0188932	−	0.999822i	$-0.506014\pi$
$601$	−0.926347	−0.0377865	−0.0188932	+	0.999822i	$0.506014\pi$
$602$	−26.0763	−1.06279
$603$	11.3821	0.463513
$604$	6.34432	0.258147
$605$	−16.9107	−0.687517
$606$	9.27480	0.376763
$607$	−11.1853	−0.453996	−0.226998	−	0.973895i	$-0.572891\pi$
$607$	−11.1853	−0.453996	−0.226998	+	0.973895i	$0.572891\pi$
$608$	0.171168	0.00694178
$609$	−5.13436	−0.208055
$610$	18.8002	0.761199
$611$	−0.0168978	−0.000683610 0
$612$	−0.378100	−0.0152838
$613$	−3.52051	−0.142192	−0.0710961	−	0.997469i	$-0.522650\pi$
$613$	−3.52051	−0.142192	−0.0710961	+	0.997469i	$0.522650\pi$
$614$	1.65769	0.0668988
$615$	−16.5939	−0.669131
$616$	−11.7469	−0.473295
$617$	3.41769	0.137591	0.0687954	−	0.997631i	$-0.478084\pi$
$617$	3.41769	0.137591	0.0687954	+	0.997631i	$0.478084\pi$
$618$	15.8469	0.637455
$619$	40.7614	1.63834	0.819169	−	0.573553i	$-0.194435\pi$
$619$	40.7614	1.63834	0.819169	+	0.573553i	$0.194435\pi$
$620$	−2.00517	−0.0805295
$621$	0.745978	0.0299351
$622$	3.92423	0.157347
$623$	−12.6959	−0.508651
$624$	−0.179680	−0.00719294
$625$	−19.1444	−0.765778
$626$	23.7350	0.948642
$627$	−1.03516	−0.0413405
$628$	−8.96688	−0.357818
$629$	−3.59522	−0.143351
$630$	5.97359	0.237994
$631$	46.7914	1.86274	0.931368	−	0.364080i	$-0.118617\pi$
$631$	46.7914	1.86274	0.931368	+	0.364080i	$0.118617\pi$
$632$	−8.45787	−0.336436
$633$	−0.639861	−0.0254322
$634$	−9.68588	−0.384675
$635$	−16.8482	−0.668600
$636$	7.40476	0.293618
$637$	−0.0131692	−0.000521782 0
$638$	6.19164	0.245130
$639$	3.12712	0.123707
$640$	−2.00517	−0.0792612
$641$	−17.2045	−0.679538	−0.339769	−	0.940509i	$-0.610349\pi$
$641$	−17.2045	−0.679538	−0.339769	+	0.940509i	$0.610349\pi$
$642$	−22.6595	−0.894301
$643$	−9.91892	−0.391164	−0.195582	−	0.980687i	$-0.562660\pi$
$643$	−9.91892	−0.391164	−0.195582	+	0.980687i	$0.562660\pi$
$644$	−0.351865	−0.0138654
$645$	26.9191	1.05994
$646$	0.0578883	0.00227758
$647$	−4.85975	−0.191056	−0.0955282	−	0.995427i	$-0.530454\pi$
$647$	−4.85975	−0.191056	−0.0955282	+	0.995427i	$0.530454\pi$
$648$	−4.39611	−0.172696
$649$	6.98024	0.273998
$650$	0.128264	0.00503094
$651$	3.65558	0.143274
$652$	−20.5899	−0.806362
$653$	−12.0534	−0.471685	−0.235842	−	0.971791i	$-0.575785\pi$
$653$	−12.0534	−0.471685	−0.235842	+	0.971791i	$0.575785\pi$
$654$	−6.02617	−0.235642
$655$	20.1116	0.785824
$656$	6.03236	0.235524
$657$	−14.8080	−0.577717
$658$	0.343785	0.0134021
$659$	48.0217	1.87066	0.935331	−	0.353774i	$-0.115102\pi$
$659$	48.0217	1.87066	0.935331	+	0.353774i	$0.115102\pi$
$660$	12.1266	0.472025
$661$	−32.8454	−1.27754	−0.638769	−	0.769398i	$-0.720556\pi$
$661$	−32.8454	−1.27754	−0.638769	+	0.769398i	$0.720556\pi$
$662$	−25.6042	−0.995136
$663$	−0.0607668	−0.00235999
$664$	11.1823	0.433956
$665$	−0.914575	−0.0354657
$666$	11.8849	0.460532
$667$	0.185464	0.00718120
$668$	3.23851	0.125302
$669$	−16.4424	−0.635698
$670$	20.4142	0.788669
$671$	41.3322	1.59561
$672$	3.65558	0.141017
$673$	−41.3975	−1.59576	−0.797878	−	0.602819i	$-0.794044\pi$
$673$	−41.3975	−1.59576	−0.797878	+	0.602819i	$0.794044\pi$
$674$	7.05789	0.271860
$675$	5.53240	0.212942
$676$	−12.9828	−0.499340
$677$	28.3009	1.08769	0.543846	−	0.839185i	$-0.316968\pi$
$677$	28.3009	1.08769	0.543846	+	0.839185i	$0.316968\pi$
$678$	3.21727	0.123558
$679$	−2.66469	−0.102261
$680$	−0.678139	−0.0260054
$681$	20.2506	0.776003
$682$	−4.40835	−0.168804
$683$	1.22202	0.0467594	0.0233797	−	0.999727i	$-0.492557\pi$
$683$	1.22202	0.0467594	0.0233797	+	0.999727i	$0.492557\pi$
$684$	−0.191365	−0.00731701
$685$	13.7955	0.527101
$686$	−18.3849	−0.701938
$687$	31.7962	1.21310
$688$	−9.78587	−0.373083
$689$	−0.706950	−0.0269326
$690$	0.363238	0.0138282
$691$	−24.3393	−0.925910	−0.462955	−	0.886382i	$-0.653211\pi$
$691$	−24.3393	−0.925910	−0.462955	+	0.886382i	$0.653211\pi$
$692$	−11.3593	−0.431814
$693$	13.1329	0.498878
$694$	−20.4096	−0.774738
$695$	18.9243	0.717841
$696$	−1.92682	−0.0730358
$697$	2.04012	0.0772750
$698$	−25.1337	−0.951325
$699$	−4.62807	−0.175050
$700$	−2.60954	−0.0986312
$701$	1.32124	0.0499027	0.0249513	−	0.999689i	$-0.492057\pi$
$701$	1.32124	0.0499027	0.0249513	+	0.999689i	$0.492057\pi$
$702$	0.739919	0.0279265
$703$	−1.81962	−0.0686282
$704$	−4.40835	−0.166146
$705$	−0.354897	−0.0133662
$706$	−19.8265	−0.746179
$707$	18.0152	0.677533
$708$	−2.17222	−0.0816372
$709$	−19.4493	−0.730432	−0.365216	−	0.930923i	$-0.619005\pi$
$709$	−19.4493	−0.730432	−0.365216	+	0.930923i	$0.619005\pi$
$710$	5.60862	0.210488
$711$	9.45584	0.354622
$712$	−4.76450	−0.178557
$713$	−0.132047	−0.00494522
$714$	1.23630	0.0462674
$715$	−1.15775	−0.0432974
$716$	−2.60555	−0.0973741
$717$	26.8594	1.00308
$718$	17.3486	0.647445
$719$	14.0855	0.525299	0.262649	−	0.964891i	$-0.415404\pi$
$719$	14.0855	0.525299	0.262649	+	0.964891i	$0.415404\pi$
$720$	2.24176	0.0835456
$721$	30.7808	1.14634
$722$	−18.9707	−0.706016
$723$	34.6090	1.28712
$724$	−6.52241	−0.242403
$725$	1.37546	0.0510832
$726$	11.5697	0.429391
$727$	−19.3326	−0.717007	−0.358503	−	0.933528i	$-0.616713\pi$
$727$	−19.3326	−0.717007	−0.358503	+	0.933528i	$0.616713\pi$
$728$	−0.349007	−0.0129351
$729$	28.1651	1.04315
$730$	−26.5588	−0.982987
$731$	−3.30954	−0.122408
$732$	−12.8624	−0.475409
$733$	−7.45075	−0.275200	−0.137600	−	0.990488i	$-0.543939\pi$
$733$	−7.45075	−0.275200	−0.137600	+	0.990488i	$0.543939\pi$
$734$	3.60621	0.133108
$735$	−0.276587	−0.0102021
$736$	−0.132047	−0.00486733
$737$	44.8805	1.65319
$738$	−6.74414	−0.248255
$739$	11.5621	0.425318	0.212659	−	0.977126i	$-0.431788\pi$
$739$	11.5621	0.425318	0.212659	+	0.977126i	$0.431788\pi$
$740$	21.3161	0.783596
$741$	−0.0307554	−0.00112983
$742$	14.3829	0.528013
$743$	45.2595	1.66041	0.830205	−	0.557458i	$-0.188223\pi$
$743$	45.2595	1.66041	0.830205	+	0.557458i	$0.188223\pi$
$744$	1.37186	0.0502949
$745$	18.9388	0.693865
$746$	3.35276	0.122753
$747$	−12.5017	−0.457413
$748$	−1.49088	−0.0545121
$749$	−44.0136	−1.60822
$750$	16.4480	0.600594
$751$	−0.109036	−0.00397877	−0.00198938	−	0.999998i	$-0.500633\pi$
$751$	−0.109036	−0.00397877	−0.00198938	+	0.999998i	$0.500633\pi$
$752$	0.129015	0.00470470
$753$	23.9410	0.872460
$754$	0.183958	0.00669935
$755$	−12.7214	−0.462980
$756$	−15.0537	−0.547496
$757$	25.3946	0.922982	0.461491	−	0.887145i	$-0.347315\pi$
$757$	25.3946	0.922982	0.461491	+	0.887145i	$0.347315\pi$
$758$	33.4394	1.21457
$759$	0.798577	0.0289865
$760$	−0.343221	−0.0124499
$761$	37.1860	1.34799	0.673995	−	0.738736i	$-0.264577\pi$
$761$	37.1860	1.34799	0.673995	+	0.738736i	$0.264577\pi$
$762$	11.5269	0.417576
$763$	−11.7051	−0.423755
$764$	−6.94613	−0.251302
$765$	0.758155	0.0274111
$766$	0.171973	0.00621365
$767$	0.207387	0.00748832
$768$	1.37186	0.0495028
$769$	−7.99642	−0.288358	−0.144179	−	0.989552i	$-0.546054\pi$
$769$	−7.99642	−0.288358	−0.144179	+	0.989552i	$0.546054\pi$
$770$	23.5544	0.848843
$771$	−0.719815	−0.0259235
$772$	−10.0599	−0.362063
$773$	−10.9300	−0.393126	−0.196563	−	0.980491i	$-0.562978\pi$
$773$	−10.9300	−0.393126	−0.196563	+	0.980491i	$0.562978\pi$
$774$	10.9405	0.393250
$775$	−0.979304	−0.0351776
$776$	−1.00000	−0.0358979
$777$	−38.8610	−1.39413
$778$	−23.7746	−0.852361
$779$	1.03255	0.0369949
$780$	0.360288	0.0129004
$781$	12.3305	0.441221
$782$	−0.0446579	−0.00159696
$783$	7.93462	0.283560
$784$	0.100547	0.00359098
$785$	17.9801	0.641737
$786$	−13.7596	−0.490789
$787$	37.5770	1.33947	0.669737	−	0.742598i	$-0.266407\pi$
$787$	37.5770	1.33947	0.669737	+	0.742598i	$0.266407\pi$
$788$	1.14485	0.0407836
$789$	43.2408	1.53941
$790$	16.9594	0.603390
$791$	6.24917	0.222195
$792$	4.92851	0.175127
$793$	1.22801	0.0436078
$794$	9.99761	0.354802
$795$	−14.8478	−0.526597
$796$	9.31588	0.330192
$797$	1.78852	0.0633525	0.0316763	−	0.999498i	$-0.489915\pi$
$797$	1.78852	0.0633525	0.0316763	+	0.999498i	$0.489915\pi$
$798$	0.625719	0.0221502
$799$	0.0436324	0.00154360
$800$	−0.979304	−0.0346236
$801$	5.32668	0.188209
$802$	2.76037	0.0974719
$803$	−58.3895	−2.06052
$804$	−13.9667	−0.492566
$805$	0.705548	0.0248673
$806$	−0.130975	−0.00461339
$807$	15.0510	0.529822
$808$	6.76074	0.237842
$809$	−26.9800	−0.948566	−0.474283	−	0.880372i	$-0.657293\pi$
$809$	−26.9800	−0.948566	−0.474283	+	0.880372i	$0.657293\pi$
$810$	8.81494	0.309725
$811$	−31.0374	−1.08987	−0.544935	−	0.838478i	$-0.683446\pi$
$811$	−31.0374	−1.08987	−0.544935	+	0.838478i	$0.683446\pi$
$812$	−3.74262	−0.131340
$813$	−36.7086	−1.28743
$814$	46.8634	1.64256
$815$	41.2862	1.44619
$816$	0.463958	0.0162418
$817$	−1.67503	−0.0586018
$818$	−12.7086	−0.444345
$819$	0.390187	0.0136343
$820$	−12.0959	−0.422407
$821$	19.3435	0.675094	0.337547	−	0.941309i	$-0.390403\pi$
$821$	19.3435	0.675094	0.337547	+	0.941309i	$0.390403\pi$
$822$	−9.43841	−0.329202
$823$	−14.1784	−0.494227	−0.247114	−	0.968987i	$-0.579482\pi$
$823$	−14.1784	−0.494227	−0.247114	+	0.968987i	$0.579482\pi$
$824$	11.5514	0.402411
$825$	5.92249	0.206195
$826$	−4.21930	−0.146808
$827$	32.0539	1.11462	0.557311	−	0.830304i	$-0.311833\pi$
$827$	32.0539	1.11462	0.557311	+	0.830304i	$0.311833\pi$
$828$	0.147628	0.00513043
$829$	−27.1643	−0.943454	−0.471727	−	0.881745i	$-0.656369\pi$
$829$	−27.1643	−0.943454	−0.471727	+	0.881745i	$0.656369\pi$
$830$	−22.4223	−0.778290
$831$	35.1191	1.21827
$832$	−0.130975	−0.00454074
$833$	0.0340047	0.00117819
$834$	−12.9473	−0.448330
$835$	−6.49375	−0.224725
$836$	−0.754569	−0.0260973
$837$	−5.64932	−0.195269
$838$	−3.89020	−0.134385
$839$	0.0207653	0.000716898 0	0.000358449	−	1.00000i	$-0.499886\pi$
$839$	0.0207653	0.000716898 0	0.000358449		1.00000i	$0.499886\pi$
$840$	−7.33005	−0.252911
$841$	−27.0273	−0.931976
$842$	−11.2415	−0.387409
$843$	7.88607	0.271611
$844$	−0.466418	−0.0160548
$845$	26.0328	0.895555
$846$	−0.144238	−0.00495901
$847$	22.4728	0.772173
$848$	5.39760	0.185354
$849$	1.11174	0.0381547
$850$	−0.331196	−0.0113599
$851$	1.40374	0.0481197
$852$	−3.83721	−0.131461
$853$	41.1199	1.40792	0.703959	−	0.710241i	$-0.251414\pi$
$853$	41.1199	1.40792	0.703959	+	0.710241i	$0.251414\pi$
$854$	−24.9838	−0.854927
$855$	0.383718	0.0131229
$856$	−16.5174	−0.564552
$857$	−28.1912	−0.962993	−0.481497	−	0.876448i	$-0.659907\pi$
$857$	−28.1912	−0.962993	−0.481497	+	0.876448i	$0.659907\pi$
$858$	0.792090	0.0270415
$859$	−18.8649	−0.643662	−0.321831	−	0.946797i	$-0.604298\pi$
$859$	−18.8649	−0.643662	−0.321831	+	0.946797i	$0.604298\pi$
$860$	19.6223	0.669115
$861$	22.0518	0.751523
$862$	−4.32190	−0.147204
$863$	−37.0256	−1.26036	−0.630182	−	0.776447i	$-0.717020\pi$
$863$	−37.0256	−1.26036	−0.630182	+	0.776447i	$0.717020\pi$
$864$	−5.64932	−0.192194
$865$	22.7772	0.774448
$866$	23.2078	0.788633
$867$	−23.1648	−0.786716
$868$	2.66469	0.0904453
$869$	37.2853	1.26482
$870$	3.86359	0.130988
$871$	1.33343	0.0451815
$872$	−4.39269	−0.148755
$873$	1.11799	0.0378383
$874$	−0.0226023	−0.000764534 0
$875$	31.9483	1.08005
$876$	18.1706	0.613928
$877$	−13.5774	−0.458475	−0.229238	−	0.973370i	$-0.573623\pi$
$877$	−13.5774	−0.458475	−0.229238	+	0.973370i	$0.573623\pi$
$878$	−2.00561	−0.0676861
$879$	−5.00903	−0.168950
$880$	8.83948	0.297979
$881$	35.0538	1.18099	0.590497	−	0.807040i	$-0.298932\pi$
$881$	35.0538	1.18099	0.590497	+	0.807040i	$0.298932\pi$
$882$	−0.112411	−0.00378508
$883$	37.6235	1.26613	0.633065	−	0.774098i	$-0.281796\pi$
$883$	37.6235	1.26613	0.633065	+	0.774098i	$0.281796\pi$
$884$	−0.0442951	−0.00148981
$885$	4.35567	0.146414
$886$	13.9910	0.470037
$887$	−20.6672	−0.693935	−0.346968	−	0.937877i	$-0.612789\pi$
$887$	−20.6672	−0.693935	−0.346968	+	0.937877i	$0.612789\pi$
$888$	−14.5837	−0.489397
$889$	22.3897	0.750927
$890$	9.55363	0.320238
$891$	19.3796	0.649241
$892$	−11.9854	−0.401302
$893$	0.0220833	0.000738989 0
$894$	−12.9573	−0.433355
$895$	5.22457	0.174638
$896$	2.66469	0.0890209
$897$	0.0237262	0.000792196 0
$898$	39.4298	1.31579
$899$	−1.40453	−0.0468436
$900$	1.09486	0.0364952
$901$	1.82544	0.0608144
$902$	−26.5928	−0.885442
$903$	−35.7731	−1.19045
$904$	2.34518	0.0779995
$905$	13.0785	0.434745
$906$	8.70354	0.289156
$907$	13.4768	0.447490	0.223745	−	0.974648i	$-0.428172\pi$
$907$	13.4768	0.447490	0.223745	+	0.974648i	$0.428172\pi$
$908$	14.7614	0.489873
$909$	−7.55846	−0.250698
$910$	0.699817	0.0231987
$911$	−13.6517	−0.452302	−0.226151	−	0.974092i	$-0.572614\pi$
$911$	−13.6517	−0.452302	−0.226151	+	0.974092i	$0.572614\pi$
$912$	0.234819	0.00777564
$913$	−49.2953	−1.63144
$914$	−23.2908	−0.770390
$915$	25.7913	0.852634
$916$	23.1774	0.765802
$917$	−26.7265	−0.882585
$918$	−1.91058	−0.0630584
$919$	2.03289	0.0670588	0.0335294	−	0.999438i	$-0.489325\pi$
$919$	2.03289	0.0670588	0.0335294	+	0.999438i	$0.489325\pi$
$920$	0.264777	0.00872945
$921$	2.27412	0.0749347
$922$	−1.04340	−0.0343625
$923$	0.366348	0.0120585
$924$	−16.1151	−0.530147
$925$	10.4106	0.342298
$926$	−14.3873	−0.472797
$927$	−12.9144	−0.424163
$928$	−1.40453	−0.0461058
$929$	49.2076	1.61445	0.807225	−	0.590244i	$-0.200968\pi$
$929$	49.2076	1.61445	0.807225	+	0.590244i	$0.200968\pi$
$930$	−2.75081	−0.0902027
$931$	0.0172105	0.000564051 0
$932$	−3.37356	−0.110505
$933$	5.38350	0.176248
$934$	29.1085	0.952459
$935$	2.98947	0.0977662
$936$	0.146429	0.00478618
$937$	−9.73856	−0.318145	−0.159072	−	0.987267i	$-0.550850\pi$
$937$	−9.73856	−0.318145	−0.159072	+	0.987267i	$0.550850\pi$
$938$	−27.1286	−0.885781
$939$	32.5612	1.06259
$940$	−0.258697	−0.00843777
$941$	−26.5313	−0.864896	−0.432448	−	0.901659i	$-0.642350\pi$
$941$	−26.5313	−0.864896	−0.432448	+	0.901659i	$0.642350\pi$
$942$	−12.3013	−0.400799
$943$	−0.796558	−0.0259395
$944$	−1.58341	−0.0515357
$945$	30.1851	0.981922
$946$	43.1395	1.40259
$947$	−16.9373	−0.550389	−0.275195	−	0.961389i	$-0.588742\pi$
$947$	−16.9373	−0.550389	−0.275195	+	0.961389i	$0.588742\pi$
$948$	−11.6030	−0.376849
$949$	−1.73479	−0.0563136
$950$	−0.167626	−0.00543849
$951$	−13.2877	−0.430883
$952$	0.901185	0.0292076
$953$	−50.2168	−1.62668	−0.813341	−	0.581787i	$-0.802354\pi$
$953$	−50.2168	−1.62668	−0.813341	+	0.581787i	$0.802354\pi$
$954$	−6.03448	−0.195373
$955$	13.9281	0.450704
$956$	19.5788	0.633223
$957$	8.49408	0.274575
$958$	12.9428	0.418162
$959$	−18.3330	−0.592004
$960$	−2.75081	−0.0887821
$961$	1.00000	0.0322581
$962$	1.39234	0.0448909
$963$	18.4663	0.595068
$964$	25.2278	0.812531
$965$	20.1717	0.649351
$966$	−0.482710	−0.0155309
$967$	−41.7104	−1.34132	−0.670658	−	0.741767i	$-0.733988\pi$
$967$	−41.7104	−1.34132	−0.670658	+	0.741767i	$0.733988\pi$
$968$	8.43355	0.271065
$969$	0.0794148	0.00255117
$970$	2.00517	0.0643820
$971$	50.5650	1.62271	0.811354	−	0.584555i	$-0.198731\pi$
$971$	50.5650	1.62271	0.811354	+	0.584555i	$0.198731\pi$
$972$	10.9171	0.350166
$973$	−25.1487	−0.806231
$974$	−0.884103	−0.0283285
$975$	0.175961	0.00563526
$976$	−9.37588	−0.300115
$977$	10.5940	0.338933	0.169466	−	0.985536i	$-0.445796\pi$
$977$	10.5940	0.338933	0.169466	+	0.985536i	$0.445796\pi$
$978$	−28.2465	−0.903223
$979$	21.0036	0.671278
$980$	−0.201614	−0.00644033
$981$	4.91100	0.156796
$982$	−25.4472	−0.812053
$983$	23.5480	0.751064	0.375532	−	0.926809i	$-0.377460\pi$
$983$	23.5480	0.751064	0.375532	+	0.926809i	$0.377460\pi$
$984$	8.27557	0.263816
$985$	−2.29562	−0.0731445
$986$	−0.475005	−0.0151272
$987$	0.471626	0.0150120
$988$	−0.0224187	−0.000713235 0
$989$	1.29220	0.0410895
$990$	−9.88248	−0.314086
$991$	39.2230	1.24596	0.622981	−	0.782237i	$-0.285922\pi$
$991$	39.2230	1.24596	0.622981	+	0.782237i	$0.285922\pi$
$992$	1.00000	0.0317500
$993$	−35.1255	−1.11467
$994$	−7.45335	−0.236406
$995$	−18.6799	−0.592192
$996$	15.3405	0.486083
$997$	26.9698	0.854144	0.427072	−	0.904218i	$-0.359545\pi$
$997$	26.9698	0.854144	0.427072	+	0.904218i	$0.359545\pi$
$998$	−18.3925	−0.582204
$999$	60.0556	1.90008

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6014.2.a.e.1.16	✓	21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6014.2.a.e.1.16	✓	21	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:	\( N \)	\(=\)	\( 6014 = 2 \cdot 31 \cdot 97 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6014.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.37186 q^{3} +1.00000 q^{4} -2.00517 q^{5} +1.37186 q^{6} +2.66469 q^{7} +1.00000 q^{8} -1.11799 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.37186 q^{3} +1.00000 q^{4} -2.00517 q^{5} +1.37186 q^{6} +2.66469 q^{7} +1.00000 q^{8} -1.11799 q^{9} -2.00517 q^{10} -4.40835 q^{11} +1.37186 q^{12} -0.130975 q^{13} +2.66469 q^{14} -2.75081 q^{15} +1.00000 q^{16} +0.338196 q^{17} -1.11799 q^{18} +0.171168 q^{19} -2.00517 q^{20} +3.65558 q^{21} -4.40835 q^{22} -0.132047 q^{23} +1.37186 q^{24} -0.979304 q^{25} -0.130975 q^{26} -5.64932 q^{27} +2.66469 q^{28} -1.40453 q^{29} -2.75081 q^{30} +1.00000 q^{31} +1.00000 q^{32} -6.04765 q^{33} +0.338196 q^{34} -5.34314 q^{35} -1.11799 q^{36} -10.6306 q^{37} +0.171168 q^{38} -0.179680 q^{39} -2.00517 q^{40} +6.03236 q^{41} +3.65558 q^{42} -9.78587 q^{43} -4.40835 q^{44} +2.24176 q^{45} -0.132047 q^{46} +0.129015 q^{47} +1.37186 q^{48} +0.100547 q^{49} -0.979304 q^{50} +0.463958 q^{51} -0.130975 q^{52} +5.39760 q^{53} -5.64932 q^{54} +8.83948 q^{55} +2.66469 q^{56} +0.234819 q^{57} -1.40453 q^{58} -1.58341 q^{59} -2.75081 q^{60} -9.37588 q^{61} +1.00000 q^{62} -2.97910 q^{63} +1.00000 q^{64} +0.262627 q^{65} -6.04765 q^{66} -10.1808 q^{67} +0.338196 q^{68} -0.181151 q^{69} -5.34314 q^{70} -2.79708 q^{71} -1.11799 q^{72} +13.2452 q^{73} -10.6306 q^{74} -1.34347 q^{75} +0.171168 q^{76} -11.7469 q^{77} -0.179680 q^{78} -8.45787 q^{79} -2.00517 q^{80} -4.39611 q^{81} +6.03236 q^{82} +11.1823 q^{83} +3.65558 q^{84} -0.678139 q^{85} -9.78587 q^{86} -1.92682 q^{87} -4.40835 q^{88} -4.76450 q^{89} +2.24176 q^{90} -0.349007 q^{91} -0.132047 q^{92} +1.37186 q^{93} +0.129015 q^{94} -0.343221 q^{95} +1.37186 q^{96} -1.00000 q^{97} +0.100547 q^{98} +4.92851 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 21 q^{2} - 10 q^{3} + 21 q^{4} - 10 q^{5} - 10 q^{6} - 11 q^{7} + 21 q^{8} + 7 q^{9}+O(q^{10}) \) 21 * q + 21 * q^2 - 10 * q^3 + 21 * q^4 - 10 * q^5 - 10 * q^6 - 11 * q^7 + 21 * q^8 + 7 * q^9	\( 21 q + 21 q^{2} - 10 q^{3} + 21 q^{4} - 10 q^{5} - 10 q^{6} - 11 q^{7} + 21 q^{8} + 7 q^{9} - 10 q^{10} - 12 q^{11} - 10 q^{12} - 14 q^{13} - 11 q^{14} + q^{15} + 21 q^{16} + 7 q^{18} - 27 q^{19} - 10 q^{20} - 6 q^{21} - 12 q^{22} - 4 q^{23} - 10 q^{24} + q^{25} - 14 q^{26} - 19 q^{27} - 11 q^{28} - 13 q^{29} + q^{30} + 21 q^{31} + 21 q^{32} - 20 q^{33} - 20 q^{35} + 7 q^{36} - 13 q^{37} - 27 q^{38} - 4 q^{39} - 10 q^{40} - 19 q^{41} - 6 q^{42} - 19 q^{43} - 12 q^{44} + 13 q^{45} - 4 q^{46} - 18 q^{47} - 10 q^{48} - 20 q^{49} + q^{50} - 33 q^{51} - 14 q^{52} - 15 q^{53} - 19 q^{54} - 26 q^{55} - 11 q^{56} + 9 q^{57} - 13 q^{58} - 32 q^{59} + q^{60} - 36 q^{61} + 21 q^{62} - 27 q^{63} + 21 q^{64} - 20 q^{65} - 20 q^{66} - 43 q^{67} - 11 q^{69} - 20 q^{70} - 31 q^{71} + 7 q^{72} - 11 q^{73} - 13 q^{74} - 22 q^{75} - 27 q^{76} + 12 q^{77} - 4 q^{78} - 31 q^{79} - 10 q^{80} - 39 q^{81} - 19 q^{82} - 26 q^{83} - 6 q^{84} - 12 q^{85} - 19 q^{86} + 19 q^{87} - 12 q^{88} - 14 q^{89} + 13 q^{90} - 30 q^{91} - 4 q^{92} - 10 q^{93} - 18 q^{94} - 40 q^{95} - 10 q^{96} - 21 q^{97} - 20 q^{98} - 17 q^{99}+O(q^{100}) \) 21 * q + 21 * q^2 - 10 * q^3 + 21 * q^4 - 10 * q^5 - 10 * q^6 - 11 * q^7 + 21 * q^8 + 7 * q^9 - 10 * q^10 - 12 * q^11 - 10 * q^12 - 14 * q^13 - 11 * q^14 + q^15 + 21 * q^16 + 7 * q^18 - 27 * q^19 - 10 * q^20 - 6 * q^21 - 12 * q^22 - 4 * q^23 - 10 * q^24 + q^25 - 14 * q^26 - 19 * q^27 - 11 * q^28 - 13 * q^29 + q^30 + 21 * q^31 + 21 * q^32 - 20 * q^33 - 20 * q^35 + 7 * q^36 - 13 * q^37 - 27 * q^38 - 4 * q^39 - 10 * q^40 - 19 * q^41 - 6 * q^42 - 19 * q^43 - 12 * q^44 + 13 * q^45 - 4 * q^46 - 18 * q^47 - 10 * q^48 - 20 * q^49 + q^50 - 33 * q^51 - 14 * q^52 - 15 * q^53 - 19 * q^54 - 26 * q^55 - 11 * q^56 + 9 * q^57 - 13 * q^58 - 32 * q^59 + q^60 - 36 * q^61 + 21 * q^62 - 27 * q^63 + 21 * q^64 - 20 * q^65 - 20 * q^66 - 43 * q^67 - 11 * q^69 - 20 * q^70 - 31 * q^71 + 7 * q^72 - 11 * q^73 - 13 * q^74 - 22 * q^75 - 27 * q^76 + 12 * q^77 - 4 * q^78 - 31 * q^79 - 10 * q^80 - 39 * q^81 - 19 * q^82 - 26 * q^83 - 6 * q^84 - 12 * q^85 - 19 * q^86 + 19 * q^87 - 12 * q^88 - 14 * q^89 + 13 * q^90 - 30 * q^91 - 4 * q^92 - 10 * q^93 - 18 * q^94 - 40 * q^95 - 10 * q^96 - 21 * q^97 - 20 * q^98 - 17 * q^99

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