LMFDB - Embedded newform 6014.2.a.e.1.6

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			1.6
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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.86116 q^{3} +1.00000 q^{4} -3.25735 q^{5} -1.86116 q^{6} -2.35478 q^{7} +1.00000 q^{8} +0.463919 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.86116 q^{3} +1.00000 q^{4} -3.25735 q^{5} -1.86116 q^{6} -2.35478 q^{7} +1.00000 q^{8} +0.463919 q^{9} -3.25735 q^{10} +4.08183 q^{11} -1.86116 q^{12} -5.56029 q^{13} -2.35478 q^{14} +6.06246 q^{15} +1.00000 q^{16} -1.83358 q^{17} +0.463919 q^{18} +3.58218 q^{19} -3.25735 q^{20} +4.38263 q^{21} +4.08183 q^{22} +4.99850 q^{23} -1.86116 q^{24} +5.61036 q^{25} -5.56029 q^{26} +4.72005 q^{27} -2.35478 q^{28} +0.324346 q^{29} +6.06246 q^{30} +1.00000 q^{31} +1.00000 q^{32} -7.59695 q^{33} -1.83358 q^{34} +7.67036 q^{35} +0.463919 q^{36} +9.87663 q^{37} +3.58218 q^{38} +10.3486 q^{39} -3.25735 q^{40} -0.175688 q^{41} +4.38263 q^{42} +2.08315 q^{43} +4.08183 q^{44} -1.51115 q^{45} +4.99850 q^{46} +10.0803 q^{47} -1.86116 q^{48} -1.45500 q^{49} +5.61036 q^{50} +3.41260 q^{51} -5.56029 q^{52} -7.85984 q^{53} +4.72005 q^{54} -13.2960 q^{55} -2.35478 q^{56} -6.66701 q^{57} +0.324346 q^{58} -3.88261 q^{59} +6.06246 q^{60} -9.78138 q^{61} +1.00000 q^{62} -1.09243 q^{63} +1.00000 q^{64} +18.1118 q^{65} -7.59695 q^{66} +10.6119 q^{67} -1.83358 q^{68} -9.30302 q^{69} +7.67036 q^{70} -6.00425 q^{71} +0.463919 q^{72} -1.96354 q^{73} +9.87663 q^{74} -10.4418 q^{75} +3.58218 q^{76} -9.61183 q^{77} +10.3486 q^{78} -1.70514 q^{79} -3.25735 q^{80} -10.1765 q^{81} -0.175688 q^{82} -4.54111 q^{83} +4.38263 q^{84} +5.97264 q^{85} +2.08315 q^{86} -0.603660 q^{87} +4.08183 q^{88} -14.0777 q^{89} -1.51115 q^{90} +13.0933 q^{91} +4.99850 q^{92} -1.86116 q^{93} +10.0803 q^{94} -11.6684 q^{95} -1.86116 q^{96} -1.00000 q^{97} -1.45500 q^{98} +1.89364 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−1.86116	−1.07454	−0.537271	−	0.843410i	$-0.680545\pi$
$3$	−1.86116	−1.07454	−0.537271	+	0.843410i	$0.680545\pi$
$4$	1.00000	0.500000
$5$	−3.25735	−1.45673	−0.728367	−	0.685188i	$-0.759720\pi$
$5$	−3.25735	−1.45673	−0.728367	+	0.685188i	$0.759720\pi$
$6$	−1.86116	−0.759816
$7$	−2.35478	−0.890024	−0.445012	−	0.895525i	$-0.646801\pi$
$7$	−2.35478	−0.890024	−0.445012	+	0.895525i	$0.646801\pi$
$8$	1.00000	0.353553
$9$	0.463919	0.154640
$10$	−3.25735	−1.03007
$11$	4.08183	1.23072	0.615360	−	0.788246i	$-0.289011\pi$
$11$	4.08183	1.23072	0.615360	+	0.788246i	$0.289011\pi$
$12$	−1.86116	−0.537271
$13$	−5.56029	−1.54215	−0.771073	−	0.636747i	$-0.780280\pi$
$13$	−5.56029	−1.54215	−0.771073	+	0.636747i	$0.780280\pi$
$14$	−2.35478	−0.629342
$15$	6.06246	1.56532
$16$	1.00000	0.250000
$17$	−1.83358	−0.444710	−0.222355	−	0.974966i	$-0.571374\pi$
$17$	−1.83358	−0.444710	−0.222355	+	0.974966i	$0.571374\pi$
$18$	0.463919	0.109347
$19$	3.58218	0.821808	0.410904	−	0.911679i	$-0.365213\pi$
$19$	3.58218	0.821808	0.410904	+	0.911679i	$0.365213\pi$
$20$	−3.25735	−0.728367
$21$	4.38263	0.956368
$22$	4.08183	0.870250
$23$	4.99850	1.04226	0.521130	−	0.853477i	$-0.325511\pi$
$23$	4.99850	1.04226	0.521130	+	0.853477i	$0.325511\pi$
$24$	−1.86116	−0.379908
$25$	5.61036	1.12207
$26$	−5.56029	−1.09046
$27$	4.72005	0.908375
$28$	−2.35478	−0.445012
$29$	0.324346	0.0602295	0.0301148	−	0.999546i	$-0.490413\pi$
$29$	0.324346	0.0602295	0.0301148	+	0.999546i	$0.490413\pi$
$30$	6.06246	1.10685
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	1.00000	0.176777
$33$	−7.59695	−1.32246
$34$	−1.83358	−0.314457
$35$	7.67036	1.29653
$36$	0.463919	0.0773199
$37$	9.87663	1.62371	0.811854	−	0.583861i	$-0.198459\pi$
$37$	9.87663	1.62371	0.811854	+	0.583861i	$0.198459\pi$
$38$	3.58218	0.581106
$39$	10.3486	1.65710
$40$	−3.25735	−0.515033
$41$	−0.175688	−0.0274378	−0.0137189	−	0.999906i	$-0.504367\pi$
$41$	−0.175688	−0.0274378	−0.0137189	+	0.999906i	$0.504367\pi$
$42$	4.38263	0.676254
$43$	2.08315	0.317677	0.158839	−	0.987305i	$-0.449225\pi$
$43$	2.08315	0.317677	0.158839	+	0.987305i	$0.449225\pi$
$44$	4.08183	0.615360
$45$	−1.51115	−0.225269
$46$	4.99850	0.736989
$47$	10.0803	1.47036	0.735180	−	0.677872i	$-0.237098\pi$
$47$	10.0803	1.47036	0.735180	+	0.677872i	$0.237098\pi$
$48$	−1.86116	−0.268635
$49$	−1.45500	−0.207857
$50$	5.61036	0.793425
$51$	3.41260	0.477859
$52$	−5.56029	−0.771073
$53$	−7.85984	−1.07963	−0.539816	−	0.841783i	$-0.681506\pi$
$53$	−7.85984	−1.07963	−0.539816	+	0.841783i	$0.681506\pi$
$54$	4.72005	0.642318
$55$	−13.2960	−1.79283
$56$	−2.35478	−0.314671
$57$	−6.66701	−0.883067
$58$	0.324346	0.0425887
$59$	−3.88261	−0.505472	−0.252736	−	0.967535i	$-0.581330\pi$
$59$	−3.88261	−0.505472	−0.252736	+	0.967535i	$0.581330\pi$
$60$	6.06246	0.782660
$61$	−9.78138	−1.25238	−0.626189	−	0.779672i	$-0.715386\pi$
$61$	−9.78138	−1.25238	−0.626189	+	0.779672i	$0.715386\pi$
$62$	1.00000	0.127000
$63$	−1.09243	−0.137633
$64$	1.00000	0.125000
$65$	18.1118	2.24650
$66$	−7.59695	−0.935120
$67$	10.6119	1.29645	0.648225	−	0.761449i	$-0.275512\pi$
$67$	10.6119	1.29645	0.648225	+	0.761449i	$0.275512\pi$
$68$	−1.83358	−0.222355
$69$	−9.30302	−1.11995
$70$	7.67036	0.916783
$71$	−6.00425	−0.712574	−0.356287	−	0.934377i	$-0.615957\pi$
$71$	−6.00425	−0.712574	−0.356287	+	0.934377i	$0.615957\pi$
$72$	0.463919	0.0546734
$73$	−1.96354	−0.229815	−0.114908	−	0.993376i	$-0.536657\pi$
$73$	−1.96354	−0.229815	−0.114908	+	0.993376i	$0.536657\pi$
$74$	9.87663	1.14813
$75$	−10.4418	−1.20571
$76$	3.58218	0.410904
$77$	−9.61183	−1.09537
$78$	10.3486	1.17175
$79$	−1.70514	−0.191844	−0.0959218	−	0.995389i	$-0.530580\pi$
$79$	−1.70514	−0.191844	−0.0959218	+	0.995389i	$0.530580\pi$
$80$	−3.25735	−0.364183
$81$	−10.1765	−1.13073
$82$	−0.175688	−0.0194015
$83$	−4.54111	−0.498452	−0.249226	−	0.968445i	$-0.580176\pi$
$83$	−4.54111	−0.498452	−0.249226	+	0.968445i	$0.580176\pi$
$84$	4.38263	0.478184
$85$	5.97264	0.647823
$86$	2.08315	0.224632
$87$	−0.603660	−0.0647191
$88$	4.08183	0.435125
$89$	−14.0777	−1.49224	−0.746119	−	0.665813i	$-0.768085\pi$
$89$	−14.0777	−1.49224	−0.746119	+	0.665813i	$0.768085\pi$
$90$	−1.51115	−0.159289
$91$	13.0933	1.37255
$92$	4.99850	0.521130
$93$	−1.86116	−0.192993
$94$	10.0803	1.03970
$95$	−11.6684	−1.19716
$96$	−1.86116	−0.189954
$97$	−1.00000	−0.101535
$97$	−1.00000	−0.101535
$98$	−1.45500	−0.146977
$99$	1.89364	0.190318
$100$	5.61036	0.561036
$101$	−2.39280	−0.238093	−0.119046	−	0.992889i	$-0.537984\pi$
$101$	−2.39280	−0.238093	−0.119046	+	0.992889i	$0.537984\pi$
$102$	3.41260	0.337897
$103$	2.06090	0.203066	0.101533	−	0.994832i	$-0.467625\pi$
$103$	2.06090	0.203066	0.101533	+	0.994832i	$0.467625\pi$
$104$	−5.56029	−0.545231
$105$	−14.2758	−1.39317
$106$	−7.85984	−0.763415
$107$	−3.66593	−0.354399	−0.177199	−	0.984175i	$-0.556704\pi$
$107$	−3.66593	−0.354399	−0.177199	+	0.984175i	$0.556704\pi$
$108$	4.72005	0.454187
$109$	−17.3266	−1.65959	−0.829793	−	0.558071i	$-0.811542\pi$
$109$	−17.3266	−1.65959	−0.829793	+	0.558071i	$0.811542\pi$
$110$	−13.2960	−1.26772
$111$	−18.3820	−1.74474
$112$	−2.35478	−0.222506
$113$	−0.462772	−0.0435339	−0.0217670	−	0.999763i	$-0.506929\pi$
$113$	−0.462772	−0.0435339	−0.0217670	+	0.999763i	$0.506929\pi$
$114$	−6.66701	−0.624423
$115$	−16.2819	−1.51830
$116$	0.324346	0.0301148
$117$	−2.57952	−0.238477
$118$	−3.88261	−0.357423
$119$	4.31769	0.395802
$120$	6.06246	0.553424
$121$	5.66137	0.514670
$122$	−9.78138	−0.885564
$123$	0.326983	0.0294831
$124$	1.00000	0.0898027
$125$	−1.98815	−0.177826
$126$	−1.09243	−0.0973213
$127$	20.5395	1.82259	0.911293	−	0.411758i	$-0.135085\pi$
$127$	20.5395	1.82259	0.911293	+	0.411758i	$0.135085\pi$
$128$	1.00000	0.0883883
$129$	−3.87708	−0.341357
$130$	18.1118	1.58851
$131$	2.73272	0.238759	0.119379	−	0.992849i	$-0.461910\pi$
$131$	2.73272	0.238759	0.119379	+	0.992849i	$0.461910\pi$
$132$	−7.59695	−0.661230
$133$	−8.43525	−0.731429
$134$	10.6119	0.916728
$135$	−15.3749	−1.32326
$136$	−1.83358	−0.157229
$137$	18.9886	1.62231	0.811153	−	0.584834i	$-0.198840\pi$
$137$	18.9886	1.62231	0.811153	+	0.584834i	$0.198840\pi$
$138$	−9.30302	−0.791926
$139$	11.5489	0.979561	0.489780	−	0.871846i	$-0.337077\pi$
$139$	11.5489	0.979561	0.489780	+	0.871846i	$0.337077\pi$
$140$	7.67036	0.648264
$141$	−18.7610	−1.57996
$142$	−6.00425	−0.503866
$143$	−22.6962	−1.89795
$144$	0.463919	0.0386599
$145$	−1.05651	−0.0877384
$146$	−1.96354	−0.162504
$147$	2.70799	0.223351
$148$	9.87663	0.811854
$149$	12.4488	1.01985	0.509923	−	0.860220i	$-0.329674\pi$
$149$	12.4488	1.01985	0.509923	+	0.860220i	$0.329674\pi$
$150$	−10.4418	−0.852568
$151$	3.54271	0.288302	0.144151	−	0.989556i	$-0.453955\pi$
$151$	3.54271	0.288302	0.144151	+	0.989556i	$0.453955\pi$
$152$	3.58218	0.290553
$153$	−0.850636	−0.0687698
$154$	−9.61183	−0.774543
$155$	−3.25735	−0.261637
$156$	10.3486	0.828550
$157$	−6.99058	−0.557909	−0.278955	−	0.960304i	$-0.589988\pi$
$157$	−6.99058	−0.557909	−0.278955	+	0.960304i	$0.589988\pi$
$158$	−1.70514	−0.135654
$159$	14.6284	1.16011
$160$	−3.25735	−0.257516
$161$	−11.7704	−0.927637
$162$	−10.1765	−0.799544
$163$	0.0936218	0.00733302	0.00366651	−	0.999993i	$-0.498833\pi$
$163$	0.0936218	0.00733302	0.00366651	+	0.999993i	$0.498833\pi$
$164$	−0.175688	−0.0137189
$165$	24.7460	1.92647
$166$	−4.54111	−0.352459
$167$	−0.196748	−0.0152248	−0.00761240	−	0.999971i	$-0.502423\pi$
$167$	−0.196748	−0.0152248	−0.00761240	+	0.999971i	$0.502423\pi$
$168$	4.38263	0.338127
$169$	17.9168	1.37821
$170$	5.97264	0.458080
$171$	1.66184	0.127084
$172$	2.08315	0.158839
$173$	−18.0150	−1.36966	−0.684828	−	0.728705i	$-0.740123\pi$
$173$	−18.0150	−1.36966	−0.684828	+	0.728705i	$0.740123\pi$
$174$	−0.603660	−0.0457633
$175$	−13.2112	−0.998671
$176$	4.08183	0.307680
$177$	7.22615	0.543151
$178$	−14.0777	−1.05517
$179$	3.45246	0.258049	0.129024	−	0.991641i	$-0.458815\pi$
$179$	3.45246	0.258049	0.129024	+	0.991641i	$0.458815\pi$
$180$	−1.51115	−0.112634
$181$	−11.8626	−0.881744	−0.440872	−	0.897570i	$-0.645331\pi$
$181$	−11.8626	−0.881744	−0.440872	+	0.897570i	$0.645331\pi$
$182$	13.0933	0.970537
$183$	18.2047	1.34573
$184$	4.99850	0.368495
$185$	−32.1717	−2.36531
$186$	−1.86116	−0.136467
$187$	−7.48439	−0.547313
$188$	10.0803	0.735180
$189$	−11.1147	−0.808475
$190$	−11.6684	−0.846517
$191$	−4.99127	−0.361155	−0.180578	−	0.983561i	$-0.557797\pi$
$191$	−4.99127	−0.361155	−0.180578	+	0.983561i	$0.557797\pi$
$192$	−1.86116	−0.134318
$193$	−17.2266	−1.24000	−0.619999	−	0.784602i	$-0.712867\pi$
$193$	−17.2266	−1.24000	−0.619999	+	0.784602i	$0.712867\pi$
$194$	−1.00000	−0.0717958
$195$	−33.7090	−2.41395
$196$	−1.45500	−0.103929
$197$	−16.6638	−1.18724	−0.593622	−	0.804744i	$-0.702302\pi$
$197$	−16.6638	−1.18724	−0.593622	+	0.804744i	$0.702302\pi$
$198$	1.89364	0.134575
$199$	−10.4651	−0.741854	−0.370927	−	0.928662i	$-0.620960\pi$
$199$	−10.4651	−0.741854	−0.370927	+	0.928662i	$0.620960\pi$
$200$	5.61036	0.396712
$201$	−19.7504	−1.39309
$202$	−2.39280	−0.168357
$203$	−0.763764	−0.0536057
$204$	3.41260	0.238930
$205$	0.572277	0.0399696
$206$	2.06090	0.143589
$207$	2.31890	0.161175
$208$	−5.56029	−0.385537
$209$	14.6219	1.01142
$210$	−14.2758	−0.985122
$211$	19.4242	1.33722	0.668610	−	0.743613i	$-0.266890\pi$
$211$	19.4242	1.33722	0.668610	+	0.743613i	$0.266890\pi$
$212$	−7.85984	−0.539816
$213$	11.1749	0.765690
$214$	−3.66593	−0.250598
$215$	−6.78556	−0.462771
$216$	4.72005	0.321159
$217$	−2.35478	−0.159853
$218$	−17.3266	−1.17351
$219$	3.65447	0.246946
$220$	−13.2960	−0.896415
$221$	10.1953	0.685807
$222$	−18.3820	−1.23372
$223$	−8.56328	−0.573439	−0.286720	−	0.958015i	$-0.592565\pi$
$223$	−8.56328	−0.573439	−0.286720	+	0.958015i	$0.592565\pi$
$224$	−2.35478	−0.157335
$225$	2.60275	0.173517
$226$	−0.462772	−0.0307831
$227$	10.8494	0.720099	0.360049	−	0.932933i	$-0.382760\pi$
$227$	10.8494	0.720099	0.360049	+	0.932933i	$0.382760\pi$
$228$	−6.66701	−0.441534
$229$	6.31754	0.417475	0.208737	−	0.977972i	$-0.433065\pi$
$229$	6.31754	0.417475	0.208737	+	0.977972i	$0.433065\pi$
$230$	−16.2819	−1.07360
$231$	17.8892	1.17702
$232$	0.324346	0.0212944
$233$	−1.27294	−0.0833933	−0.0416967	−	0.999130i	$-0.513276\pi$
$233$	−1.27294	−0.0833933	−0.0416967	+	0.999130i	$0.513276\pi$
$234$	−2.57952	−0.168629
$235$	−32.8350	−2.14192
$236$	−3.88261	−0.252736
$237$	3.17355	0.206144
$238$	4.31769	0.279874
$239$	−13.5506	−0.876514	−0.438257	−	0.898850i	$-0.644404\pi$
$239$	−13.5506	−0.876514	−0.438257	+	0.898850i	$0.644404\pi$
$240$	6.06246	0.391330
$241$	−9.12517	−0.587804	−0.293902	−	0.955836i	$-0.594954\pi$
$241$	−9.12517	−0.587804	−0.293902	+	0.955836i	$0.594954\pi$
$242$	5.66137	0.363927
$243$	4.78001	0.306638
$244$	−9.78138	−0.626189
$245$	4.73946	0.302793
$246$	0.326983	0.0208477
$247$	−19.9179	−1.26735
$248$	1.00000	0.0635001
$249$	8.45174	0.535607
$250$	−1.98815	−0.125742
$251$	−16.7777	−1.05900	−0.529498	−	0.848311i	$-0.677620\pi$
$251$	−16.7777	−1.05900	−0.529498	+	0.848311i	$0.677620\pi$
$252$	−1.09243	−0.0688165
$253$	20.4031	1.28273
$254$	20.5395	1.28876
$255$	−11.1160	−0.696113
$256$	1.00000	0.0625000
$257$	−8.61319	−0.537276	−0.268638	−	0.963241i	$-0.586574\pi$
$257$	−8.61319	−0.537276	−0.268638	+	0.963241i	$0.586574\pi$
$258$	−3.87708	−0.241376
$259$	−23.2573	−1.44514
$260$	18.1118	1.12325
$261$	0.150470	0.00931388
$262$	2.73272	0.168828
$263$	−0.416467	−0.0256804	−0.0128402	−	0.999918i	$-0.504087\pi$
$263$	−0.416467	−0.0256804	−0.0128402	+	0.999918i	$0.504087\pi$
$264$	−7.59695	−0.467560
$265$	25.6023	1.57274
$266$	−8.43525	−0.517198
$267$	26.2009	1.60347
$268$	10.6119	0.648225
$269$	−5.94801	−0.362657	−0.181328	−	0.983423i	$-0.558040\pi$
$269$	−5.94801	−0.362657	−0.181328	+	0.983423i	$0.558040\pi$
$270$	−15.3749	−0.935686
$271$	1.82438	0.110823	0.0554116	−	0.998464i	$-0.482353\pi$
$271$	1.82438	0.110823	0.0554116	+	0.998464i	$0.482353\pi$
$272$	−1.83358	−0.111177
$273$	−24.3687	−1.47486
$274$	18.9886	1.14714
$275$	22.9006	1.38096
$276$	−9.30302	−0.559976
$277$	−31.3605	−1.88427	−0.942135	−	0.335234i	$-0.891185\pi$
$277$	−31.3605	−1.88427	−0.942135	+	0.335234i	$0.891185\pi$
$278$	11.5489	0.692654
$279$	0.463919	0.0277741
$280$	7.67036	0.458392
$281$	12.9428	0.772105	0.386053	−	0.922477i	$-0.373838\pi$
$281$	12.9428	0.772105	0.386053	+	0.922477i	$0.373838\pi$
$282$	−18.7610	−1.11720
$283$	21.1569	1.25764	0.628822	−	0.777549i	$-0.283537\pi$
$283$	21.1569	1.25764	0.628822	+	0.777549i	$0.283537\pi$
$284$	−6.00425	−0.356287
$285$	21.7168	1.28639
$286$	−22.6962	−1.34205
$287$	0.413706	0.0244203
$288$	0.463919	0.0273367
$289$	−13.6380	−0.802233
$290$	−1.05651	−0.0620404
$291$	1.86116	0.109103
$292$	−1.96354	−0.114908
$293$	5.41686	0.316456	0.158228	−	0.987403i	$-0.449422\pi$
$293$	5.41686	0.316456	0.158228	+	0.987403i	$0.449422\pi$
$294$	2.70799	0.157933
$295$	12.6470	0.736338
$296$	9.87663	0.574067
$297$	19.2665	1.11795
$298$	12.4488	0.721141
$299$	−27.7931	−1.60732
$300$	−10.4418	−0.602856
$301$	−4.90536	−0.282740
$302$	3.54271	0.203860
$303$	4.45339	0.255841
$304$	3.58218	0.205452
$305$	31.8614	1.82438
$306$	−0.850636	−0.0486276
$307$	−14.2493	−0.813249	−0.406625	−	0.913595i	$-0.633294\pi$
$307$	−14.2493	−0.813249	−0.406625	+	0.913595i	$0.633294\pi$
$308$	−9.61183	−0.547685
$309$	−3.83566	−0.218203
$310$	−3.25735	−0.185005
$311$	12.3211	0.698664	0.349332	−	0.936999i	$-0.386409\pi$
$311$	12.3211	0.698664	0.349332	+	0.936999i	$0.386409\pi$
$312$	10.3486	0.585873
$313$	−14.6274	−0.826788	−0.413394	−	0.910552i	$-0.635657\pi$
$313$	−14.6274	−0.826788	−0.413394	+	0.910552i	$0.635657\pi$
$314$	−6.99058	−0.394501
$315$	3.55843	0.200495
$316$	−1.70514	−0.0959218
$317$	2.26666	0.127308	0.0636542	−	0.997972i	$-0.479725\pi$
$317$	2.26666	0.127308	0.0636542	+	0.997972i	$0.479725\pi$
$318$	14.6284	0.820321
$319$	1.32393	0.0741256
$320$	−3.25735	−0.182092
$321$	6.82289	0.380816
$322$	−11.7704	−0.655938
$323$	−6.56823	−0.365466
$324$	−10.1765	−0.565363
$325$	−31.1952	−1.73040
$326$	0.0936218	0.00518523
$327$	32.2476	1.78330
$328$	−0.175688	−0.00970073
$329$	−23.7368	−1.30865
$330$	24.7460	1.36222
$331$	−25.5378	−1.40369	−0.701843	−	0.712332i	$-0.747639\pi$
$331$	−25.5378	−1.40369	−0.701843	+	0.712332i	$0.747639\pi$
$332$	−4.54111	−0.249226
$333$	4.58196	0.251090
$334$	−0.196748	−0.0107656
$335$	−34.5667	−1.88858
$336$	4.38263	0.239092
$337$	18.6741	1.01724	0.508622	−	0.860990i	$-0.330155\pi$
$337$	18.6741	1.01724	0.508622	+	0.860990i	$0.330155\pi$
$338$	17.9168	0.974545
$339$	0.861293	0.0467790
$340$	5.97264	0.323912
$341$	4.08183	0.221044
$342$	1.66184	0.0898621
$343$	19.9097	1.07502
$344$	2.08315	0.112316
$345$	30.3032	1.63147
$346$	−18.0150	−0.968493
$347$	−32.2348	−1.73046	−0.865228	−	0.501379i	$-0.832826\pi$
$347$	−32.2348	−1.73046	−0.865228	+	0.501379i	$0.832826\pi$
$348$	−0.603660	−0.0323596
$349$	13.4817	0.721658	0.360829	−	0.932632i	$-0.382494\pi$
$349$	13.4817	0.721658	0.360829	+	0.932632i	$0.382494\pi$
$350$	−13.2112	−0.706167
$351$	−26.2449	−1.40085
$352$	4.08183	0.217562
$353$	25.1009	1.33599	0.667993	−	0.744168i	$-0.267154\pi$
$353$	25.1009	1.33599	0.667993	+	0.744168i	$0.267154\pi$
$354$	7.22615	0.384066
$355$	19.5580	1.03803
$356$	−14.0777	−0.746119
$357$	−8.03592	−0.425306
$358$	3.45246	0.182468
$359$	−13.9248	−0.734924	−0.367462	−	0.930039i	$-0.619773\pi$
$359$	−13.9248	−0.734924	−0.367462	+	0.930039i	$0.619773\pi$
$360$	−1.51115	−0.0796446
$361$	−6.16800	−0.324631
$362$	−11.8626	−0.623487
$363$	−10.5367	−0.553034
$364$	13.0933	0.686273
$365$	6.39596	0.334780
$366$	18.2047	0.951576
$367$	−16.4702	−0.859738	−0.429869	−	0.902891i	$-0.641440\pi$
$367$	−16.4702	−0.859738	−0.429869	+	0.902891i	$0.641440\pi$
$368$	4.99850	0.260565
$369$	−0.0815049	−0.00424298
$370$	−32.1717	−1.67253
$371$	18.5082	0.960898
$372$	−1.86116	−0.0964967
$373$	−26.1160	−1.35223	−0.676117	−	0.736794i	$-0.736339\pi$
$373$	−26.1160	−1.35223	−0.676117	+	0.736794i	$0.736339\pi$
$374$	−7.48439	−0.387009
$375$	3.70028	0.191081
$376$	10.0803	0.519850
$377$	−1.80346	−0.0928827
$378$	−11.1147	−0.571678
$379$	−9.35864	−0.480721	−0.240360	−	0.970684i	$-0.577266\pi$
$379$	−9.35864	−0.480721	−0.240360	+	0.970684i	$0.577266\pi$
$380$	−11.6684	−0.598578
$381$	−38.2273	−1.95845
$382$	−4.99127	−0.255375
$383$	36.5369	1.86695	0.933474	−	0.358646i	$-0.116762\pi$
$383$	36.5369	1.86695	0.933474	+	0.358646i	$0.116762\pi$
$384$	−1.86116	−0.0949770
$385$	31.3091	1.59566
$386$	−17.2266	−0.876811
$387$	0.966413	0.0491255
$388$	−1.00000	−0.0507673
$389$	−19.6072	−0.994124	−0.497062	−	0.867715i	$-0.665588\pi$
$389$	−19.6072	−0.994124	−0.497062	+	0.867715i	$0.665588\pi$
$390$	−33.7090	−1.70692
$391$	−9.16518	−0.463503
$392$	−1.45500	−0.0734887
$393$	−5.08603	−0.256556
$394$	−16.6638	−0.839508
$395$	5.55426	0.279465
$396$	1.89364	0.0951591
$397$	32.5095	1.63161	0.815803	−	0.578330i	$-0.196295\pi$
$397$	32.5095	1.63161	0.815803	+	0.578330i	$0.196295\pi$
$398$	−10.4651	−0.524570
$399$	15.6994	0.785951
$400$	5.61036	0.280518
$401$	−16.0613	−0.802065	−0.401033	−	0.916064i	$-0.631349\pi$
$401$	−16.0613	−0.802065	−0.401033	+	0.916064i	$0.631349\pi$
$402$	−19.7504	−0.985062
$403$	−5.56029	−0.276978
$404$	−2.39280	−0.119046
$405$	33.1486	1.64717
$406$	−0.763764	−0.0379050
$407$	40.3147	1.99833
$408$	3.41260	0.168949
$409$	−16.9665	−0.838940	−0.419470	−	0.907769i	$-0.637784\pi$
$409$	−16.9665	−0.838940	−0.419470	+	0.907769i	$0.637784\pi$
$410$	0.572277	0.0282627
$411$	−35.3408	−1.74323
$412$	2.06090	0.101533
$413$	9.14269	0.449882
$414$	2.31890	0.113968
$415$	14.7920	0.726111
$416$	−5.56029	−0.272615
$417$	−21.4943	−1.05258
$418$	14.6219	0.715178
$419$	28.4488	1.38981	0.694907	−	0.719100i	$-0.255446\pi$
$419$	28.4488	1.38981	0.694907	+	0.719100i	$0.255446\pi$
$420$	−14.2758	−0.696586
$421$	−32.9563	−1.60619	−0.803097	−	0.595849i	$-0.796816\pi$
$421$	−32.9563	−1.60619	−0.803097	+	0.595849i	$0.796816\pi$
$422$	19.4242	0.945558
$423$	4.67643	0.227376
$424$	−7.85984	−0.381707
$425$	−10.2871	−0.498996
$426$	11.1749	0.541425
$427$	23.0330	1.11465
$428$	−3.66593	−0.177199
$429$	42.2412	2.03943
$430$	−6.78556	−0.327229
$431$	−21.1263	−1.01762	−0.508809	−	0.860879i	$-0.669914\pi$
$431$	−21.1263	−1.01762	−0.508809	+	0.860879i	$0.669914\pi$
$432$	4.72005	0.227094
$433$	13.9853	0.672092	0.336046	−	0.941846i	$-0.390910\pi$
$433$	13.9853	0.672092	0.336046	+	0.941846i	$0.390910\pi$
$434$	−2.35478	−0.113033
$435$	1.96633	0.0942785
$436$	−17.3266	−0.829793
$437$	17.9055	0.856538
$438$	3.65447	0.174617
$439$	0.331694	0.0158309	0.00791544	−	0.999969i	$-0.497480\pi$
$439$	0.331694	0.0158309	0.00791544	+	0.999969i	$0.497480\pi$
$440$	−13.2960	−0.633861
$441$	−0.675004	−0.0321430
$442$	10.1953	0.484939
$443$	−34.5498	−1.64151	−0.820754	−	0.571281i	$-0.806447\pi$
$443$	−34.5498	−1.64151	−0.820754	+	0.571281i	$0.806447\pi$
$444$	−18.3820	−0.872371
$445$	45.8562	2.17379
$446$	−8.56328	−0.405483
$447$	−23.1692	−1.09587
$448$	−2.35478	−0.111253
$449$	−12.8174	−0.604891	−0.302446	−	0.953167i	$-0.597803\pi$
$449$	−12.8174	−0.604891	−0.302446	+	0.953167i	$0.597803\pi$
$450$	2.60275	0.122695
$451$	−0.717128	−0.0337682
$452$	−0.462772	−0.0217670
$453$	−6.59355	−0.309792
$454$	10.8494	0.509187
$455$	−42.6494	−1.99943
$456$	−6.66701	−0.312211
$457$	15.3856	0.719707	0.359854	−	0.933009i	$-0.382827\pi$
$457$	15.3856	0.719707	0.359854	+	0.933009i	$0.382827\pi$
$458$	6.31754	0.295199
$459$	−8.65462	−0.403963
$460$	−16.2819	−0.759148
$461$	−16.4292	−0.765183	−0.382591	−	0.923918i	$-0.624968\pi$
$461$	−16.4292	−0.765183	−0.382591	+	0.923918i	$0.624968\pi$
$462$	17.8892	0.832279
$463$	−23.5694	−1.09536	−0.547682	−	0.836686i	$-0.684490\pi$
$463$	−23.5694	−1.09536	−0.547682	+	0.836686i	$0.684490\pi$
$464$	0.324346	0.0150574
$465$	6.06246	0.281140
$466$	−1.27294	−0.0589680
$467$	15.6825	0.725701	0.362851	−	0.931847i	$-0.381803\pi$
$467$	15.6825	0.725701	0.362851	+	0.931847i	$0.381803\pi$
$468$	−2.57952	−0.119239
$469$	−24.9887	−1.15387
$470$	−32.8350	−1.51457
$471$	13.0106	0.599497
$472$	−3.88261	−0.178711
$473$	8.50307	0.390972
$474$	3.17355	0.145766
$475$	20.0973	0.922128
$476$	4.31769	0.197901
$477$	−3.64633	−0.166954
$478$	−13.5506	−0.619789
$479$	−36.0388	−1.64666	−0.823328	−	0.567566i	$-0.807885\pi$
$479$	−36.0388	−1.64666	−0.823328	+	0.567566i	$0.807885\pi$
$480$	6.06246	0.276712
$481$	−54.9169	−2.50399
$482$	−9.12517	−0.415640
$483$	21.9066	0.996784
$484$	5.66137	0.257335
$485$	3.25735	0.147909
$486$	4.78001	0.216826
$487$	28.1517	1.27568	0.637838	−	0.770170i	$-0.279829\pi$
$487$	28.1517	1.27568	0.637838	+	0.770170i	$0.279829\pi$
$488$	−9.78138	−0.442782
$489$	−0.174245	−0.00787964
$490$	4.73946	0.214107
$491$	−25.7283	−1.16110	−0.580551	−	0.814224i	$-0.697163\pi$
$491$	−25.7283	−1.16110	−0.580551	+	0.814224i	$0.697163\pi$
$492$	0.326983	0.0147415
$493$	−0.594716	−0.0267847
$494$	−19.9179	−0.896150
$495$	−6.16826	−0.277243
$496$	1.00000	0.0449013
$497$	14.1387	0.634208
$498$	8.45174	0.378731
$499$	11.0257	0.493578	0.246789	−	0.969069i	$-0.420624\pi$
$499$	11.0257	0.493578	0.246789	+	0.969069i	$0.420624\pi$
$500$	−1.98815	−0.0889130
$501$	0.366179	0.0163597
$502$	−16.7777	−0.748824
$503$	−32.7090	−1.45842	−0.729211	−	0.684289i	$-0.760113\pi$
$503$	−32.7090	−1.45842	−0.729211	+	0.684289i	$0.760113\pi$
$504$	−1.09243	−0.0486606
$505$	7.79421	0.346838
$506$	20.4031	0.907027
$507$	−33.3460	−1.48095
$508$	20.5395	0.911293
$509$	14.2701	0.632511	0.316255	−	0.948674i	$-0.397574\pi$
$509$	14.2701	0.632511	0.316255	+	0.948674i	$0.397574\pi$
$510$	−11.1160	−0.492226
$511$	4.62372	0.204541
$512$	1.00000	0.0441942
$513$	16.9081	0.746510
$514$	−8.61319	−0.379911
$515$	−6.71307	−0.295813
$516$	−3.87708	−0.170679
$517$	41.1460	1.80960
$518$	−23.2573	−1.02187
$519$	33.5288	1.47175
$520$	18.1118	0.794256
$521$	26.3527	1.15453	0.577266	−	0.816556i	$-0.304119\pi$
$521$	26.3527	1.15453	0.577266	+	0.816556i	$0.304119\pi$
$522$	0.150470	0.00658591
$523$	−28.3693	−1.24050	−0.620251	−	0.784403i	$-0.712969\pi$
$523$	−28.3693	−1.24050	−0.620251	+	0.784403i	$0.712969\pi$
$524$	2.73272	0.119379
$525$	24.5881	1.07311
$526$	−0.416467	−0.0181588
$527$	−1.83358	−0.0798722
$528$	−7.59695	−0.330615
$529$	1.98505	0.0863065
$530$	25.6023	1.11209
$531$	−1.80122	−0.0781661
$532$	−8.43525	−0.365714
$533$	0.976874	0.0423131
$534$	26.2009	1.13383
$535$	11.9412	0.516265
$536$	10.6119	0.458364
$537$	−6.42557	−0.277284
$538$	−5.94801	−0.256437
$539$	−5.93908	−0.255814
$540$	−15.3749	−0.661630
$541$	34.9470	1.50249	0.751245	−	0.660023i	$-0.229454\pi$
$541$	34.9470	1.50249	0.751245	+	0.660023i	$0.229454\pi$
$542$	1.82438	0.0783638
$543$	22.0783	0.947470
$544$	−1.83358	−0.0786143
$545$	56.4389	2.41758
$546$	−24.3687	−1.04288
$547$	33.6203	1.43750	0.718749	−	0.695269i	$-0.244715\pi$
$547$	33.6203	1.43750	0.718749	+	0.695269i	$0.244715\pi$
$548$	18.9886	0.811153
$549$	−4.53777	−0.193667
$550$	22.9006	0.976483
$551$	1.16186	0.0494971
$552$	−9.30302	−0.395963
$553$	4.01524	0.170745
$554$	−31.3605	−1.33238
$555$	59.8767	2.54162
$556$	11.5489	0.489780
$557$	−25.9757	−1.10063	−0.550313	−	0.834958i	$-0.685492\pi$
$557$	−25.9757	−1.10063	−0.550313	+	0.834958i	$0.685492\pi$
$558$	0.463919	0.0196393
$559$	−11.5829	−0.489905
$560$	7.67036	0.324132
$561$	13.9297	0.588110
$562$	12.9428	0.545961
$563$	33.8282	1.42569	0.712844	−	0.701323i	$-0.247407\pi$
$563$	33.8282	1.42569	0.712844	+	0.701323i	$0.247407\pi$
$564$	−18.7610	−0.789981
$565$	1.50741	0.0634173
$566$	21.1569	0.889289
$567$	23.9635	1.00637
$568$	−6.00425	−0.251933
$569$	20.2162	0.847506	0.423753	−	0.905778i	$-0.360712\pi$
$569$	20.2162	0.847506	0.423753	+	0.905778i	$0.360712\pi$
$570$	21.7168	0.909617
$571$	15.4107	0.644919	0.322459	−	0.946583i	$-0.395490\pi$
$571$	15.4107	0.644919	0.322459	+	0.946583i	$0.395490\pi$
$572$	−22.6962	−0.948974
$573$	9.28955	0.388076
$574$	0.413706	0.0172678
$575$	28.0434	1.16949
$576$	0.463919	0.0193300
$577$	4.93554	0.205469	0.102735	−	0.994709i	$-0.467241\pi$
$577$	4.93554	0.205469	0.102735	+	0.994709i	$0.467241\pi$
$578$	−13.6380	−0.567265
$579$	32.0615	1.33243
$580$	−1.05651	−0.0438692
$581$	10.6933	0.443634
$582$	1.86116	0.0771476
$583$	−32.0826	−1.32872
$584$	−1.96354	−0.0812520
$585$	8.40243	0.347398
$586$	5.41686	0.223768
$587$	−9.13707	−0.377127	−0.188564	−	0.982061i	$-0.560383\pi$
$587$	−9.13707	−0.377127	−0.188564	+	0.982061i	$0.560383\pi$
$588$	2.70799	0.111676
$589$	3.58218	0.147601
$590$	12.6470	0.520670
$591$	31.0139	1.27574
$592$	9.87663	0.405927
$593$	3.73267	0.153282	0.0766412	−	0.997059i	$-0.475580\pi$
$593$	3.73267	0.153282	0.0766412	+	0.997059i	$0.475580\pi$
$594$	19.2665	0.790513
$595$	−14.0643	−0.576578
$596$	12.4488	0.509923
$597$	19.4773	0.797153
$598$	−27.7931	−1.13655
$599$	14.8680	0.607491	0.303746	−	0.952753i	$-0.401763\pi$
$599$	14.8680	0.607491	0.303746	+	0.952753i	$0.401763\pi$
$600$	−10.4418	−0.426284
$601$	45.8850	1.87169	0.935844	−	0.352414i	$-0.114639\pi$
$601$	45.8850	1.87169	0.935844	+	0.352414i	$0.114639\pi$
$602$	−4.90536	−0.199928
$603$	4.92306	0.200483
$604$	3.54271	0.144151
$605$	−18.4411	−0.749737
$606$	4.45339	0.180907
$607$	−16.0041	−0.649585	−0.324793	−	0.945785i	$-0.605295\pi$
$607$	−16.0041	−0.649585	−0.324793	+	0.945785i	$0.605295\pi$
$608$	3.58218	0.145277
$609$	1.42149	0.0576016
$610$	31.8614	1.29003
$611$	−56.0492	−2.26751
$612$	−0.850636	−0.0343849
$613$	28.0270	1.13200	0.566000	−	0.824405i	$-0.308490\pi$
$613$	28.0270	1.13200	0.566000	+	0.824405i	$0.308490\pi$
$614$	−14.2493	−0.575054
$615$	−1.06510	−0.0429490
$616$	−9.61183	−0.387272
$617$	−19.2154	−0.773584	−0.386792	−	0.922167i	$-0.626417\pi$
$617$	−19.2154	−0.773584	−0.386792	+	0.922167i	$0.626417\pi$
$618$	−3.83566	−0.154293
$619$	3.33438	0.134020	0.0670101	−	0.997752i	$-0.478654\pi$
$619$	3.33438	0.134020	0.0670101	+	0.997752i	$0.478654\pi$
$620$	−3.25735	−0.130819
$621$	23.5932	0.946763
$622$	12.3211	0.494030
$623$	33.1500	1.32813
$624$	10.3486	0.414275
$625$	−21.5757	−0.863027
$626$	−14.6274	−0.584628
$627$	−27.2136	−1.08681
$628$	−6.99058	−0.278955
$629$	−18.1096	−0.722078
$630$	3.55843	0.141771
$631$	40.8216	1.62508	0.812541	−	0.582904i	$-0.198084\pi$
$631$	40.8216	1.62508	0.812541	+	0.582904i	$0.198084\pi$
$632$	−1.70514	−0.0678270
$633$	−36.1516	−1.43690
$634$	2.26666	0.0900206
$635$	−66.9045	−2.65502
$636$	14.6284	0.580055
$637$	8.09023	0.320547
$638$	1.32393	0.0524147
$639$	−2.78549	−0.110192
$640$	−3.25735	−0.128758
$641$	−11.3613	−0.448744	−0.224372	−	0.974504i	$-0.572033\pi$
$641$	−11.3613	−0.448744	−0.224372	+	0.974504i	$0.572033\pi$
$642$	6.82289	0.269278
$643$	−27.2478	−1.07455	−0.537274	−	0.843408i	$-0.680546\pi$
$643$	−27.2478	−1.07455	−0.537274	+	0.843408i	$0.680546\pi$
$644$	−11.7704	−0.463818
$645$	12.6290	0.497267
$646$	−6.56823	−0.258423
$647$	−25.0701	−0.985608	−0.492804	−	0.870140i	$-0.664028\pi$
$647$	−25.0701	−0.985608	−0.492804	+	0.870140i	$0.664028\pi$
$648$	−10.1765	−0.399772
$649$	−15.8482	−0.622094
$650$	−31.1952	−1.22358
$651$	4.38263	0.171769
$652$	0.0936218	0.00366651
$653$	23.0468	0.901889	0.450945	−	0.892552i	$-0.351087\pi$
$653$	23.0468	0.901889	0.450945	+	0.892552i	$0.351087\pi$
$654$	32.2476	1.26098
$655$	−8.90144	−0.347808
$656$	−0.175688	−0.00685945
$657$	−0.910926	−0.0355386
$658$	−23.7368	−0.925359
$659$	−14.5457	−0.566621	−0.283310	−	0.959028i	$-0.591433\pi$
$659$	−14.5457	−0.566621	−0.283310	+	0.959028i	$0.591433\pi$
$660$	24.7460	0.963235
$661$	−30.1712	−1.17352	−0.586761	−	0.809760i	$-0.699597\pi$
$661$	−30.1712	−1.17352	−0.586761	+	0.809760i	$0.699597\pi$
$662$	−25.5378	−0.992556
$663$	−18.9750	−0.736928
$664$	−4.54111	−0.176229
$665$	27.4766	1.06550
$666$	4.58196	0.177547
$667$	1.62124	0.0627748
$668$	−0.196748	−0.00761240
$669$	15.9376	0.616184
$670$	−34.5667	−1.33543
$671$	−39.9260	−1.54132
$672$	4.38263	0.169064
$673$	18.7529	0.722870	0.361435	−	0.932397i	$-0.382287\pi$
$673$	18.7529	0.722870	0.361435	+	0.932397i	$0.382287\pi$
$674$	18.6741	0.719300
$675$	26.4812	1.01926
$676$	17.9168	0.689107
$677$	−0.340297	−0.0130787	−0.00653934	−	0.999979i	$-0.502082\pi$
$677$	−0.340297	−0.0130787	−0.00653934	+	0.999979i	$0.502082\pi$
$678$	0.861293	0.0330778
$679$	2.35478	0.0903682
$680$	5.97264	0.229040
$681$	−20.1924	−0.773776
$682$	4.08183	0.156302
$683$	51.7316	1.97946	0.989728	−	0.142967i	$-0.0456641\pi$
$683$	51.7316	1.97946	0.989728	+	0.142967i	$0.0456641\pi$
$684$	1.66184	0.0635421
$685$	−61.8526	−2.36327
$686$	19.9097	0.760155
$687$	−11.7580	−0.448594
$688$	2.08315	0.0794193
$689$	43.7030	1.66495
$690$	30.3032	1.15362
$691$	−38.5440	−1.46628	−0.733142	−	0.680076i	$-0.761947\pi$
$691$	−38.5440	−1.46628	−0.733142	+	0.680076i	$0.761947\pi$
$692$	−18.0150	−0.684828
$693$	−4.45911	−0.169388
$694$	−32.2348	−1.22362
$695$	−37.6187	−1.42696
$696$	−0.603660	−0.0228817
$697$	0.322138	0.0122019
$698$	13.4817	0.510290
$699$	2.36915	0.0896096
$700$	−13.2112	−0.499335
$701$	−11.9998	−0.453225	−0.226613	−	0.973985i	$-0.572765\pi$
$701$	−11.9998	−0.453225	−0.226613	+	0.973985i	$0.572765\pi$
$702$	−26.2449	−0.990548
$703$	35.3798	1.33438
$704$	4.08183	0.153840
$705$	61.1113	2.30158
$706$	25.1009	0.944684
$707$	5.63453	0.211908
$708$	7.22615	0.271575
$709$	−47.4297	−1.78126	−0.890630	−	0.454729i	$-0.849736\pi$
$709$	−47.4297	−1.78126	−0.890630	+	0.454729i	$0.849736\pi$
$710$	19.5580	0.733998
$711$	−0.791049	−0.0296667
$712$	−14.0777	−0.527585
$713$	4.99850	0.187195
$714$	−8.03592	−0.300737
$715$	73.9295	2.76481
$716$	3.45246	0.129024
$717$	25.2198	0.941851
$718$	−13.9248	−0.519670
$719$	2.39080	0.0891618	0.0445809	−	0.999006i	$-0.485805\pi$
$719$	2.39080	0.0891618	0.0445809	+	0.999006i	$0.485805\pi$
$720$	−1.51115	−0.0563172
$721$	−4.85296	−0.180734
$722$	−6.16800	−0.229549
$723$	16.9834	0.631619
$724$	−11.8626	−0.440872
$725$	1.81970	0.0675818
$726$	−10.5367	−0.391054
$727$	18.8289	0.698327	0.349163	−	0.937062i	$-0.386466\pi$
$727$	18.8289	0.698327	0.349163	+	0.937062i	$0.386466\pi$
$728$	13.0933	0.485269
$729$	21.6332	0.801231
$730$	6.39596	0.236725
$731$	−3.81963	−0.141274
$732$	18.2047	0.672866
$733$	45.7067	1.68822	0.844108	−	0.536174i	$-0.180131\pi$
$733$	45.7067	1.68822	0.844108	+	0.536174i	$0.180131\pi$
$734$	−16.4702	−0.607927
$735$	−8.82089	−0.325364
$736$	4.99850	0.184247
$737$	43.3160	1.59556
$738$	−0.0815049	−0.00300024
$739$	−5.39942	−0.198621	−0.0993105	−	0.995056i	$-0.531664\pi$
$739$	−5.39942	−0.198621	−0.0993105	+	0.995056i	$0.531664\pi$
$740$	−32.1717	−1.18265
$741$	37.0705	1.36182
$742$	18.5082	0.679458
$743$	24.4827	0.898182	0.449091	−	0.893486i	$-0.351748\pi$
$743$	24.4827	0.898182	0.449091	+	0.893486i	$0.351748\pi$
$744$	−1.86116	−0.0682335
$745$	−40.5502	−1.48564
$746$	−26.1160	−0.956174
$747$	−2.10671	−0.0770805
$748$	−7.48439	−0.273656
$749$	8.63247	0.315424
$750$	3.70028	0.135115
$751$	−18.0084	−0.657134	−0.328567	−	0.944481i	$-0.606566\pi$
$751$	−18.0084	−0.657134	−0.328567	+	0.944481i	$0.606566\pi$
$752$	10.0803	0.367590
$753$	31.2259	1.13794
$754$	−1.80346	−0.0656780
$755$	−11.5399	−0.419979
$756$	−11.1147	−0.404238
$757$	−43.5445	−1.58265	−0.791327	−	0.611394i	$-0.790609\pi$
$757$	−43.5445	−1.58265	−0.791327	+	0.611394i	$0.790609\pi$
$758$	−9.35864	−0.339921
$759$	−37.9734	−1.37835
$760$	−11.6684	−0.423258
$761$	21.8079	0.790536	0.395268	−	0.918566i	$-0.370652\pi$
$761$	21.8079	0.790536	0.395268	+	0.918566i	$0.370652\pi$
$762$	−38.2273	−1.38483
$763$	40.8004	1.47707
$764$	−4.99127	−0.180578
$765$	2.77082	0.100179
$766$	36.5369	1.32013
$767$	21.5884	0.779512
$768$	−1.86116	−0.0671589
$769$	−24.1262	−0.870013	−0.435006	−	0.900427i	$-0.643254\pi$
$769$	−24.1262	−0.870013	−0.435006	+	0.900427i	$0.643254\pi$
$770$	31.3091	1.12830
$771$	16.0305	0.577325
$772$	−17.2266	−0.619999
$773$	27.5118	0.989530	0.494765	−	0.869027i	$-0.335254\pi$
$773$	27.5118	0.989530	0.494765	+	0.869027i	$0.335254\pi$
$774$	0.966413	0.0347370
$775$	5.61036	0.201530
$776$	−1.00000	−0.0358979
$777$	43.2856	1.55286
$778$	−19.6072	−0.702952
$779$	−0.629345	−0.0225486
$780$	−33.7090	−1.20698
$781$	−24.5084	−0.876978
$782$	−9.16518	−0.327746
$783$	1.53093	0.0547110
$784$	−1.45500	−0.0519644
$785$	22.7708	0.812725
$786$	−5.08603	−0.181413
$787$	30.0429	1.07092	0.535458	−	0.844562i	$-0.320139\pi$
$787$	30.0429	1.07092	0.535458	+	0.844562i	$0.320139\pi$
$788$	−16.6638	−0.593622
$789$	0.775112	0.0275947
$790$	5.55426	0.197612
$791$	1.08973	0.0387462
$792$	1.89364	0.0672876
$793$	54.3873	1.93135
$794$	32.5095	1.15372
$795$	−47.6500	−1.68997
$796$	−10.4651	−0.370927
$797$	−25.6694	−0.909257	−0.454628	−	0.890681i	$-0.650228\pi$
$797$	−25.6694	−0.909257	−0.454628	+	0.890681i	$0.650228\pi$
$798$	15.6994	0.555751
$799$	−18.4830	−0.653883
$800$	5.61036	0.198356
$801$	−6.53093	−0.230759
$802$	−16.0613	−0.567146
$803$	−8.01486	−0.282838
$804$	−19.7504	−0.696544
$805$	38.3403	1.35132
$806$	−5.56029	−0.195853
$807$	11.0702	0.389690
$808$	−2.39280	−0.0841786
$809$	25.4349	0.894243	0.447121	−	0.894473i	$-0.352449\pi$
$809$	25.4349	0.894243	0.447121	+	0.894473i	$0.352449\pi$
$810$	33.1486	1.16472
$811$	−29.0224	−1.01911	−0.509557	−	0.860437i	$-0.670191\pi$
$811$	−29.0224	−1.01911	−0.509557	+	0.860437i	$0.670191\pi$
$812$	−0.763764	−0.0268029
$813$	−3.39546	−0.119084
$814$	40.3147	1.41303
$815$	−0.304959	−0.0106823
$816$	3.41260	0.119465
$817$	7.46221	0.261070
$818$	−16.9665	−0.593220
$819$	6.07422	0.212250
$820$	0.572277	0.0199848
$821$	25.9477	0.905580	0.452790	−	0.891617i	$-0.350429\pi$
$821$	25.9477	0.905580	0.452790	+	0.891617i	$0.350429\pi$
$822$	−35.3408	−1.23265
$823$	32.7006	1.13987	0.569936	−	0.821689i	$-0.306968\pi$
$823$	32.7006	1.13987	0.569936	+	0.821689i	$0.306968\pi$
$824$	2.06090	0.0717947
$825$	−42.6216	−1.48389
$826$	9.14269	0.318115
$827$	27.5551	0.958183	0.479092	−	0.877765i	$-0.340966\pi$
$827$	27.5551	0.958183	0.479092	+	0.877765i	$0.340966\pi$
$828$	2.31890	0.0805874
$829$	−41.9878	−1.45830	−0.729149	−	0.684355i	$-0.760084\pi$
$829$	−41.9878	−1.45830	−0.729149	+	0.684355i	$0.760084\pi$
$830$	14.7920	0.513438
$831$	58.3669	2.02473
$832$	−5.56029	−0.192768
$833$	2.66787	0.0924362
$834$	−21.4943	−0.744286
$835$	0.640877	0.0221785
$836$	14.6219	0.505708
$837$	4.72005	0.163149
$838$	28.4488	0.982746
$839$	0.602578	0.0208033	0.0104017	−	0.999946i	$-0.496689\pi$
$839$	0.602578	0.0208033	0.0104017	+	0.999946i	$0.496689\pi$
$840$	−14.2758	−0.492561
$841$	−28.8948	−0.996372
$842$	−32.9563	−1.13575
$843$	−24.0887	−0.829659
$844$	19.4242	0.668610
$845$	−58.3613	−2.00769
$846$	4.67643	0.160779
$847$	−13.3313	−0.458069
$848$	−7.85984	−0.269908
$849$	−39.3763	−1.35139
$850$	−10.2871	−0.352844
$851$	49.3684	1.69233
$852$	11.1749	0.382845
$853$	7.75484	0.265521	0.132760	−	0.991148i	$-0.457616\pi$
$853$	7.75484	0.265521	0.132760	+	0.991148i	$0.457616\pi$
$854$	23.0330	0.788173
$855$	−5.41321	−0.185128
$856$	−3.66593	−0.125299
$857$	8.44005	0.288307	0.144153	−	0.989555i	$-0.453954\pi$
$857$	8.44005	0.288307	0.144153	+	0.989555i	$0.453954\pi$
$858$	42.2412	1.44209
$859$	−18.1690	−0.619918	−0.309959	−	0.950750i	$-0.600315\pi$
$859$	−18.1690	−0.619918	−0.309959	+	0.950750i	$0.600315\pi$
$860$	−6.78556	−0.231386
$861$	−0.769974	−0.0262406
$862$	−21.1263	−0.719565
$863$	9.92120	0.337722	0.168861	−	0.985640i	$-0.445991\pi$
$863$	9.92120	0.337722	0.168861	+	0.985640i	$0.445991\pi$
$864$	4.72005	0.160579
$865$	58.6813	1.99522
$866$	13.9853	0.475241
$867$	25.3824	0.862033
$868$	−2.35478	−0.0799265
$869$	−6.96011	−0.236106
$870$	1.96633	0.0666650
$871$	−59.0052	−1.99931
$872$	−17.3266	−0.586753
$873$	−0.463919	−0.0157013
$874$	17.9055	0.605664
$875$	4.68167	0.158269
$876$	3.65447	0.123473
$877$	−41.0717	−1.38689	−0.693446	−	0.720509i	$-0.743908\pi$
$877$	−41.0717	−1.38689	−0.693446	+	0.720509i	$0.743908\pi$
$878$	0.331694	0.0111941
$879$	−10.0816	−0.340045
$880$	−13.2960	−0.448207
$881$	52.5961	1.77201	0.886005	−	0.463677i	$-0.153470\pi$
$881$	52.5961	1.77201	0.886005	+	0.463677i	$0.153470\pi$
$882$	−0.675004	−0.0227286
$883$	−39.3059	−1.32275	−0.661375	−	0.750056i	$-0.730027\pi$
$883$	−39.3059	−1.32275	−0.661375	+	0.750056i	$0.730027\pi$
$884$	10.1953	0.342904
$885$	−23.5381	−0.791226
$886$	−34.5498	−1.16072
$887$	−0.907328	−0.0304651	−0.0152326	−	0.999884i	$-0.504849\pi$
$887$	−0.907328	−0.0304651	−0.0152326	+	0.999884i	$0.504849\pi$
$888$	−18.3820	−0.616859
$889$	−48.3661	−1.62215
$890$	45.8562	1.53710
$891$	−41.5389	−1.39161
$892$	−8.56328	−0.286720
$893$	36.1093	1.20835
$894$	−23.1692	−0.774896
$895$	−11.2459	−0.375908
$896$	−2.35478	−0.0786677
$897$	51.7275	1.72713
$898$	−12.8174	−0.427723
$899$	0.324346	0.0108175
$900$	2.60275	0.0867585
$901$	14.4117	0.480123
$902$	−0.717128	−0.0238777
$903$	9.12967	0.303816
$904$	−0.462772	−0.0153916
$905$	38.6408	1.28447
$906$	−6.59355	−0.219056
$907$	−43.6149	−1.44821	−0.724104	−	0.689691i	$-0.757746\pi$
$907$	−43.6149	−1.44821	−0.724104	+	0.689691i	$0.757746\pi$
$908$	10.8494	0.360049
$909$	−1.11007	−0.0368186
$910$	−42.6494	−1.41381
$911$	−10.5511	−0.349575	−0.174788	−	0.984606i	$-0.555924\pi$
$911$	−10.5511	−0.349575	−0.174788	+	0.984606i	$0.555924\pi$
$912$	−6.66701	−0.220767
$913$	−18.5361	−0.613454
$914$	15.3856	0.508910
$915$	−59.2992	−1.96037
$916$	6.31754	0.208737
$917$	−6.43496	−0.212501
$918$	−8.65462	−0.285645
$919$	37.0020	1.22058	0.610292	−	0.792177i	$-0.291052\pi$
$919$	37.0020	1.22058	0.610292	+	0.792177i	$0.291052\pi$
$920$	−16.2819	−0.536798
$921$	26.5202	0.873870
$922$	−16.4292	−0.541066
$923$	33.3854	1.09889
$924$	17.8892	0.588510
$925$	55.4114	1.82192
$926$	−23.5694	−0.774540
$927$	0.956090	0.0314021
$928$	0.324346	0.0106472
$929$	−1.89921	−0.0623110	−0.0311555	−	0.999515i	$-0.509919\pi$
$929$	−1.89921	−0.0623110	−0.0311555	+	0.999515i	$0.509919\pi$
$930$	6.06246	0.198796
$931$	−5.21208	−0.170819
$932$	−1.27294	−0.0416967
$933$	−22.9315	−0.750743
$934$	15.6825	0.513148
$935$	24.3793	0.797289
$936$	−2.57952	−0.0843144
$937$	−39.7714	−1.29927	−0.649637	−	0.760245i	$-0.725079\pi$
$937$	−39.7714	−1.29927	−0.649637	+	0.760245i	$0.725079\pi$
$938$	−24.9887	−0.815910
$939$	27.2239	0.888419
$940$	−32.8350	−1.07096
$941$	−21.3805	−0.696983	−0.348491	−	0.937312i	$-0.613306\pi$
$941$	−21.3805	−0.696983	−0.348491	+	0.937312i	$0.613306\pi$
$942$	13.0106	0.423908
$943$	−0.878176	−0.0285973
$944$	−3.88261	−0.126368
$945$	36.2045	1.17773
$946$	8.50307	0.276459
$947$	25.6445	0.833334	0.416667	−	0.909059i	$-0.363198\pi$
$947$	25.6445	0.833334	0.416667	+	0.909059i	$0.363198\pi$
$948$	3.17355	0.103072
$949$	10.9179	0.354409
$950$	20.0973	0.652043
$951$	−4.21862	−0.136798
$952$	4.31769	0.139937
$953$	17.6029	0.570214	0.285107	−	0.958496i	$-0.407971\pi$
$953$	17.6029	0.570214	0.285107	+	0.958496i	$0.407971\pi$
$954$	−3.64633	−0.118054
$955$	16.2583	0.526107
$956$	−13.5506	−0.438257
$957$	−2.46404	−0.0796511
$958$	−36.0388	−1.16436
$959$	−44.7140	−1.44389
$960$	6.06246	0.195665
$961$	1.00000	0.0322581
$962$	−54.9169	−1.77059
$963$	−1.70070	−0.0548042
$964$	−9.12517	−0.293902
$965$	56.1132	1.80635
$966$	21.9066	0.704833
$967$	−42.0234	−1.35138	−0.675690	−	0.737185i	$-0.736154\pi$
$967$	−42.0234	−1.35138	−0.675690	+	0.737185i	$0.736154\pi$
$968$	5.66137	0.181963
$969$	12.2245	0.392708
$970$	3.25735	0.104587
$971$	−46.4837	−1.49173	−0.745867	−	0.666095i	$-0.767964\pi$
$971$	−46.4837	−1.49173	−0.745867	+	0.666095i	$0.767964\pi$
$972$	4.78001	0.153319
$973$	−27.1950	−0.871832
$974$	28.1517	0.902039
$975$	58.0593	1.85939
$976$	−9.78138	−0.313094
$977$	11.9395	0.381979	0.190990	−	0.981592i	$-0.438830\pi$
$977$	11.9395	0.381979	0.190990	+	0.981592i	$0.438830\pi$
$978$	−0.174245	−0.00557175
$979$	−57.4630	−1.83652
$980$	4.73946	0.151396
$981$	−8.03814	−0.256638
$982$	−25.7283	−0.821023
$983$	−39.0202	−1.24455	−0.622275	−	0.782798i	$-0.713792\pi$
$983$	−39.0202	−1.24455	−0.622275	+	0.782798i	$0.713792\pi$
$984$	0.326983	0.0104238
$985$	54.2797	1.72950
$986$	−0.594716	−0.0189396
$987$	44.1781	1.40620
$988$	−19.9179	−0.633674
$989$	10.4126	0.331102
$990$	−6.16826	−0.196040
$991$	34.8823	1.10807	0.554036	−	0.832493i	$-0.313087\pi$
$991$	34.8823	1.10807	0.554036	+	0.832493i	$0.313087\pi$
$992$	1.00000	0.0317500
$993$	47.5300	1.50832
$994$	14.1387	0.448452
$995$	34.0887	1.08068
$996$	8.45174	0.267804
$997$	−21.2754	−0.673800	−0.336900	−	0.941540i	$-0.609378\pi$
$997$	−21.2754	−0.673800	−0.336900	+	0.941540i	$0.609378\pi$
$998$	11.0257	0.349013
$999$	46.6182	1.47493

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6014.2.a.e.1.6	✓	21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6014.2.a.e.1.6	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.86116 q^{3} +1.00000 q^{4} -3.25735 q^{5} -1.86116 q^{6} -2.35478 q^{7} +1.00000 q^{8} +0.463919 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.86116 q^{3} +1.00000 q^{4} -3.25735 q^{5} -1.86116 q^{6} -2.35478 q^{7} +1.00000 q^{8} +0.463919 q^{9} -3.25735 q^{10} +4.08183 q^{11} -1.86116 q^{12} -5.56029 q^{13} -2.35478 q^{14} +6.06246 q^{15} +1.00000 q^{16} -1.83358 q^{17} +0.463919 q^{18} +3.58218 q^{19} -3.25735 q^{20} +4.38263 q^{21} +4.08183 q^{22} +4.99850 q^{23} -1.86116 q^{24} +5.61036 q^{25} -5.56029 q^{26} +4.72005 q^{27} -2.35478 q^{28} +0.324346 q^{29} +6.06246 q^{30} +1.00000 q^{31} +1.00000 q^{32} -7.59695 q^{33} -1.83358 q^{34} +7.67036 q^{35} +0.463919 q^{36} +9.87663 q^{37} +3.58218 q^{38} +10.3486 q^{39} -3.25735 q^{40} -0.175688 q^{41} +4.38263 q^{42} +2.08315 q^{43} +4.08183 q^{44} -1.51115 q^{45} +4.99850 q^{46} +10.0803 q^{47} -1.86116 q^{48} -1.45500 q^{49} +5.61036 q^{50} +3.41260 q^{51} -5.56029 q^{52} -7.85984 q^{53} +4.72005 q^{54} -13.2960 q^{55} -2.35478 q^{56} -6.66701 q^{57} +0.324346 q^{58} -3.88261 q^{59} +6.06246 q^{60} -9.78138 q^{61} +1.00000 q^{62} -1.09243 q^{63} +1.00000 q^{64} +18.1118 q^{65} -7.59695 q^{66} +10.6119 q^{67} -1.83358 q^{68} -9.30302 q^{69} +7.67036 q^{70} -6.00425 q^{71} +0.463919 q^{72} -1.96354 q^{73} +9.87663 q^{74} -10.4418 q^{75} +3.58218 q^{76} -9.61183 q^{77} +10.3486 q^{78} -1.70514 q^{79} -3.25735 q^{80} -10.1765 q^{81} -0.175688 q^{82} -4.54111 q^{83} +4.38263 q^{84} +5.97264 q^{85} +2.08315 q^{86} -0.603660 q^{87} +4.08183 q^{88} -14.0777 q^{89} -1.51115 q^{90} +13.0933 q^{91} +4.99850 q^{92} -1.86116 q^{93} +10.0803 q^{94} -11.6684 q^{95} -1.86116 q^{96} -1.00000 q^{97} -1.45500 q^{98} +1.89364 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 21 q^{2} - 10 q^{3} + 21 q^{4} - 10 q^{5} - 10 q^{6} - 11 q^{7} + 21 q^{8} + 7 q^{9}+O(q^{10}) \) 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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