LMFDB - Embedded newform 6014.2.a.e.1.12

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			1.12
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)

$f(q)$	$=$	$q+1.00000 q^{2} -0.343301 q^{3} +1.00000 q^{4} +1.80151 q^{5} -0.343301 q^{6} +0.627271 q^{7} +1.00000 q^{8} -2.88214 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -0.343301 q^{3} +1.00000 q^{4} +1.80151 q^{5} -0.343301 q^{6} +0.627271 q^{7} +1.00000 q^{8} -2.88214 q^{9} +1.80151 q^{10} +0.780550 q^{11} -0.343301 q^{12} -4.94126 q^{13} +0.627271 q^{14} -0.618462 q^{15} +1.00000 q^{16} -4.50766 q^{17} -2.88214 q^{18} -1.06524 q^{19} +1.80151 q^{20} -0.215343 q^{21} +0.780550 q^{22} +3.16919 q^{23} -0.343301 q^{24} -1.75455 q^{25} -4.94126 q^{26} +2.01935 q^{27} +0.627271 q^{28} +3.69674 q^{29} -0.618462 q^{30} +1.00000 q^{31} +1.00000 q^{32} -0.267964 q^{33} -4.50766 q^{34} +1.13004 q^{35} -2.88214 q^{36} -2.77075 q^{37} -1.06524 q^{38} +1.69634 q^{39} +1.80151 q^{40} -4.35264 q^{41} -0.215343 q^{42} +2.93806 q^{43} +0.780550 q^{44} -5.19222 q^{45} +3.16919 q^{46} -4.43203 q^{47} -0.343301 q^{48} -6.60653 q^{49} -1.75455 q^{50} +1.54748 q^{51} -4.94126 q^{52} -6.07275 q^{53} +2.01935 q^{54} +1.40617 q^{55} +0.627271 q^{56} +0.365699 q^{57} +3.69674 q^{58} -4.26269 q^{59} -0.618462 q^{60} -13.0831 q^{61} +1.00000 q^{62} -1.80788 q^{63} +1.00000 q^{64} -8.90174 q^{65} -0.267964 q^{66} +6.12153 q^{67} -4.50766 q^{68} -1.08799 q^{69} +1.13004 q^{70} +4.34377 q^{71} -2.88214 q^{72} -0.606335 q^{73} -2.77075 q^{74} +0.602340 q^{75} -1.06524 q^{76} +0.489616 q^{77} +1.69634 q^{78} +14.0140 q^{79} +1.80151 q^{80} +7.95319 q^{81} -4.35264 q^{82} -7.84274 q^{83} -0.215343 q^{84} -8.12060 q^{85} +2.93806 q^{86} -1.26910 q^{87} +0.780550 q^{88} +3.24060 q^{89} -5.19222 q^{90} -3.09951 q^{91} +3.16919 q^{92} -0.343301 q^{93} -4.43203 q^{94} -1.91905 q^{95} -0.343301 q^{96} -1.00000 q^{97} -6.60653 q^{98} -2.24966 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−0.343301	−0.198205	−0.0991026	−	0.995077i	$-0.531597\pi$
$3$	−0.343301	−0.198205	−0.0991026	+	0.995077i	$0.531597\pi$
$4$	1.00000	0.500000
$5$	1.80151	0.805661	0.402830	−	0.915275i	$-0.368026\pi$
$5$	1.80151	0.805661	0.402830	+	0.915275i	$0.368026\pi$
$6$	−0.343301	−0.140152
$7$	0.627271	0.237086	0.118543	−	0.992949i	$-0.462178\pi$
$7$	0.627271	0.237086	0.118543	+	0.992949i	$0.462178\pi$
$8$	1.00000	0.353553
$9$	−2.88214	−0.960715
$10$	1.80151	0.569688
$11$	0.780550	0.235345	0.117672	−	0.993052i	$-0.462457\pi$
$11$	0.780550	0.235345	0.117672	+	0.993052i	$0.462457\pi$
$12$	−0.343301	−0.0991026
$13$	−4.94126	−1.37046	−0.685229	−	0.728327i	$-0.740298\pi$
$13$	−4.94126	−1.37046	−0.685229	+	0.728327i	$0.740298\pi$
$14$	0.627271	0.167645
$15$	−0.618462	−0.159686
$16$	1.00000	0.250000
$17$	−4.50766	−1.09327	−0.546634	−	0.837372i	$-0.684091\pi$
$17$	−4.50766	−1.09327	−0.546634	+	0.837372i	$0.684091\pi$
$18$	−2.88214	−0.679328
$19$	−1.06524	−0.244383	−0.122192	−	0.992507i	$-0.538992\pi$
$19$	−1.06524	−0.244383	−0.122192	+	0.992507i	$0.538992\pi$
$20$	1.80151	0.402830
$21$	−0.215343	−0.0469917
$22$	0.780550	0.166414
$23$	3.16919	0.660823	0.330411	−	0.943837i	$-0.392813\pi$
$23$	3.16919	0.660823	0.330411	+	0.943837i	$0.392813\pi$
$24$	−0.343301	−0.0700761
$25$	−1.75455	−0.350911
$26$	−4.94126	−0.969061
$27$	2.01935	0.388624
$28$	0.627271	0.118543
$29$	3.69674	0.686468	0.343234	−	0.939250i	$-0.388478\pi$
$29$	3.69674	0.686468	0.343234	+	0.939250i	$0.388478\pi$
$30$	−0.618462	−0.112915
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	1.00000	0.176777
$33$	−0.267964	−0.0466465
$34$	−4.50766	−0.773057
$35$	1.13004	0.191011
$36$	−2.88214	−0.480357
$37$	−2.77075	−0.455509	−0.227755	−	0.973719i	$-0.573138\pi$
$37$	−2.77075	−0.455509	−0.227755	+	0.973719i	$0.573138\pi$
$38$	−1.06524	−0.172805
$39$	1.69634	0.271632
$40$	1.80151	0.284844
$41$	−4.35264	−0.679768	−0.339884	−	0.940467i	$-0.610388\pi$
$41$	−4.35264	−0.679768	−0.339884	+	0.940467i	$0.610388\pi$
$42$	−0.215343	−0.0332281
$43$	2.93806	0.448050	0.224025	−	0.974583i	$-0.428080\pi$
$43$	2.93806	0.448050	0.224025	+	0.974583i	$0.428080\pi$
$44$	0.780550	0.117672
$45$	−5.19222	−0.774010
$46$	3.16919	0.467272
$47$	−4.43203	−0.646479	−0.323239	−	0.946317i	$-0.604772\pi$
$47$	−4.43203	−0.646479	−0.323239	+	0.946317i	$0.604772\pi$
$48$	−0.343301	−0.0495513
$49$	−6.60653	−0.943790
$50$	−1.75455	−0.248131
$51$	1.54748	0.216691
$52$	−4.94126	−0.685229
$53$	−6.07275	−0.834157	−0.417078	−	0.908871i	$-0.636946\pi$
$53$	−6.07275	−0.834157	−0.417078	+	0.908871i	$0.636946\pi$
$54$	2.01935	0.274799
$55$	1.40617	0.189608
$56$	0.627271	0.0838226
$57$	0.365699	0.0484380
$58$	3.69674	0.485406
$59$	−4.26269	−0.554955	−0.277478	−	0.960732i	$-0.589498\pi$
$59$	−4.26269	−0.554955	−0.277478	+	0.960732i	$0.589498\pi$
$60$	−0.618462	−0.0798431
$61$	−13.0831	−1.67512	−0.837560	−	0.546345i	$-0.816019\pi$
$61$	−13.0831	−1.67512	−0.837560	+	0.546345i	$0.816019\pi$
$62$	1.00000	0.127000
$63$	−1.80788	−0.227772
$64$	1.00000	0.125000
$65$	−8.90174	−1.10412
$66$	−0.267964	−0.0329841
$67$	6.12153	0.747864	0.373932	−	0.927456i	$-0.378009\pi$
$67$	6.12153	0.747864	0.373932	+	0.927456i	$0.378009\pi$
$68$	−4.50766	−0.546634
$69$	−1.08799	−0.130978
$70$	1.13004	0.135065
$71$	4.34377	0.515510	0.257755	−	0.966210i	$-0.417017\pi$
$71$	4.34377	0.515510	0.257755	+	0.966210i	$0.417017\pi$
$72$	−2.88214	−0.339664
$73$	−0.606335	−0.0709661	−0.0354831	−	0.999370i	$-0.511297\pi$
$73$	−0.606335	−0.0709661	−0.0354831	+	0.999370i	$0.511297\pi$
$74$	−2.77075	−0.322094
$75$	0.602340	0.0695523
$76$	−1.06524	−0.122192
$77$	0.489616	0.0557969
$78$	1.69634	0.192073
$79$	14.0140	1.57669	0.788347	−	0.615231i	$-0.210937\pi$
$79$	14.0140	1.57669	0.788347	+	0.615231i	$0.210937\pi$
$80$	1.80151	0.201415
$81$	7.95319	0.883687
$82$	−4.35264	−0.480668
$83$	−7.84274	−0.860852	−0.430426	−	0.902626i	$-0.641637\pi$
$83$	−7.84274	−0.860852	−0.430426	+	0.902626i	$0.641637\pi$
$84$	−0.215343	−0.0234958
$85$	−8.12060	−0.880803
$86$	2.93806	0.316819
$87$	−1.26910	−0.136061
$88$	0.780550	0.0832069
$89$	3.24060	0.343503	0.171752	−	0.985140i	$-0.445057\pi$
$89$	3.24060	0.343503	0.171752	+	0.985140i	$0.445057\pi$
$90$	−5.19222	−0.547308
$91$	−3.09951	−0.324917
$92$	3.16919	0.330411
$93$	−0.343301	−0.0355987
$94$	−4.43203	−0.457129
$95$	−1.91905	−0.196890
$96$	−0.343301	−0.0350381
$97$	−1.00000	−0.101535
$97$	−1.00000	−0.101535
$98$	−6.60653	−0.667360
$99$	−2.24966	−0.226099
$100$	−1.75455	−0.175455
$101$	−17.1323	−1.70473	−0.852365	−	0.522947i	$-0.824833\pi$
$101$	−17.1323	−1.70473	−0.852365	+	0.522947i	$0.824833\pi$
$102$	1.54748	0.153224
$103$	−17.5590	−1.73014	−0.865072	−	0.501647i	$-0.832728\pi$
$103$	−17.5590	−1.73014	−0.865072	+	0.501647i	$0.832728\pi$
$104$	−4.94126	−0.484530
$105$	−0.387943	−0.0378594
$106$	−6.07275	−0.589838
$107$	−1.11796	−0.108077	−0.0540385	−	0.998539i	$-0.517209\pi$
$107$	−1.11796	−0.108077	−0.0540385	+	0.998539i	$0.517209\pi$
$108$	2.01935	0.194312
$109$	−6.68998	−0.640783	−0.320392	−	0.947285i	$-0.603815\pi$
$109$	−6.68998	−0.640783	−0.320392	+	0.947285i	$0.603815\pi$
$110$	1.40617	0.134073
$111$	0.951204	0.0902843
$112$	0.627271	0.0592715
$113$	0.425846	0.0400602	0.0200301	−	0.999799i	$-0.493624\pi$
$113$	0.425846	0.0400602	0.0200301	+	0.999799i	$0.493624\pi$
$114$	0.365699	0.0342509
$115$	5.70934	0.532399
$116$	3.69674	0.343234
$117$	14.2414	1.31662
$118$	−4.26269	−0.392412
$119$	−2.82752	−0.259198
$120$	−0.618462	−0.0564576
$121$	−10.3907	−0.944613
$122$	−13.0831	−1.18449
$123$	1.49427	0.134733
$124$	1.00000	0.0898027
$125$	−12.1684	−1.08838
$126$	−1.80788	−0.161059
$127$	−12.8685	−1.14190	−0.570949	−	0.820985i	$-0.693425\pi$
$127$	−12.8685	−1.14190	−0.570949	+	0.820985i	$0.693425\pi$
$128$	1.00000	0.0883883
$129$	−1.00864	−0.0888058
$130$	−8.90174	−0.780734
$131$	−6.25371	−0.546389	−0.273195	−	0.961959i	$-0.588080\pi$
$131$	−6.25371	−0.546389	−0.273195	+	0.961959i	$0.588080\pi$
$132$	−0.267964	−0.0233233
$133$	−0.668195	−0.0579399
$134$	6.12153	0.528820
$135$	3.63788	0.313099
$136$	−4.50766	−0.386528
$137$	−7.18183	−0.613585	−0.306793	−	0.951776i	$-0.599256\pi$
$137$	−7.18183	−0.613585	−0.306793	+	0.951776i	$0.599256\pi$
$138$	−1.08799	−0.0926158
$139$	−12.4214	−1.05357	−0.526784	−	0.849999i	$-0.676602\pi$
$139$	−12.4214	−1.05357	−0.526784	+	0.849999i	$0.676602\pi$
$140$	1.13004	0.0955055
$141$	1.52152	0.128135
$142$	4.34377	0.364521
$143$	−3.85690	−0.322530
$144$	−2.88214	−0.240179
$145$	6.65973	0.553060
$146$	−0.606335	−0.0501806
$147$	2.26803	0.187064
$148$	−2.77075	−0.227755
$149$	11.3325	0.928398	0.464199	−	0.885731i	$-0.346342\pi$
$149$	11.3325	0.928398	0.464199	+	0.885731i	$0.346342\pi$
$150$	0.602340	0.0491809
$151$	12.9979	1.05776	0.528878	−	0.848698i	$-0.322613\pi$
$151$	12.9979	1.05776	0.528878	+	0.848698i	$0.322613\pi$
$152$	−1.06524	−0.0864026
$153$	12.9917	1.05032
$154$	0.489616	0.0394544
$155$	1.80151	0.144701
$156$	1.69634	0.135816
$157$	24.4706	1.95297	0.976484	−	0.215589i	$-0.0691670\pi$
$157$	24.4706	1.95297	0.976484	+	0.215589i	$0.0691670\pi$
$158$	14.0140	1.11489
$159$	2.08478	0.165334
$160$	1.80151	0.142422
$161$	1.98794	0.156672
$162$	7.95319	0.624861
$163$	8.22866	0.644519	0.322259	−	0.946651i	$-0.395558\pi$
$163$	8.22866	0.644519	0.322259	+	0.946651i	$0.395558\pi$
$164$	−4.35264	−0.339884
$165$	−0.482740	−0.0375813
$166$	−7.84274	−0.608714
$167$	1.70877	0.132228	0.0661141	−	0.997812i	$-0.478940\pi$
$167$	1.70877	0.132228	0.0661141	+	0.997812i	$0.478940\pi$
$168$	−0.215343	−0.0166141
$169$	11.4160	0.878157
$170$	−8.12060	−0.622822
$171$	3.07018	0.234783
$172$	2.93806	0.224025
$173$	−19.7283	−1.49992	−0.749958	−	0.661486i	$-0.769926\pi$
$173$	−19.7283	−1.49992	−0.749958	+	0.661486i	$0.769926\pi$
$174$	−1.26910	−0.0962100
$175$	−1.10058	−0.0831960
$176$	0.780550	0.0588362
$177$	1.46339	0.109995
$178$	3.24060	0.242893
$179$	−16.4568	−1.23004	−0.615019	−	0.788512i	$-0.710852\pi$
$179$	−16.4568	−1.23004	−0.615019	+	0.788512i	$0.710852\pi$
$180$	−5.19222	−0.387005
$181$	0.903363	0.0671465	0.0335732	−	0.999436i	$-0.489311\pi$
$181$	0.903363	0.0671465	0.0335732	+	0.999436i	$0.489311\pi$
$182$	−3.09951	−0.229751
$183$	4.49145	0.332017
$184$	3.16919	0.233636
$185$	−4.99155	−0.366986
$186$	−0.343301	−0.0251721
$187$	−3.51845	−0.257295
$188$	−4.43203	−0.323239
$189$	1.26668	0.0921373
$190$	−1.91905	−0.139222
$191$	4.61963	0.334264	0.167132	−	0.985934i	$-0.446549\pi$
$191$	4.61963	0.334264	0.167132	+	0.985934i	$0.446549\pi$
$192$	−0.343301	−0.0247756
$193$	7.57967	0.545597	0.272798	−	0.962071i	$-0.412051\pi$
$193$	7.57967	0.545597	0.272798	+	0.962071i	$0.412051\pi$
$194$	−1.00000	−0.0717958
$195$	3.05598	0.218843
$196$	−6.60653	−0.471895
$197$	17.6123	1.25482	0.627411	−	0.778688i	$-0.284115\pi$
$197$	17.6123	1.25482	0.627411	+	0.778688i	$0.284115\pi$
$198$	−2.24966	−0.159876
$199$	−12.7299	−0.902400	−0.451200	−	0.892423i	$-0.649004\pi$
$199$	−12.7299	−0.902400	−0.451200	+	0.892423i	$0.649004\pi$
$200$	−1.75455	−0.124066
$201$	−2.10153	−0.148230
$202$	−17.1323	−1.20543
$203$	2.31886	0.162752
$204$	1.54748	0.108346
$205$	−7.84133	−0.547662
$206$	−17.5590	−1.22340
$207$	−9.13407	−0.634862
$208$	−4.94126	−0.342615
$209$	−0.831475	−0.0575143
$210$	−0.387943	−0.0267706
$211$	11.4597	0.788921	0.394461	−	0.918913i	$-0.370931\pi$
$211$	11.4597	0.788921	0.394461	+	0.918913i	$0.370931\pi$
$212$	−6.07275	−0.417078
$213$	−1.49122	−0.102177
$214$	−1.11796	−0.0764220
$215$	5.29295	0.360976
$216$	2.01935	0.137399
$217$	0.627271	0.0425819
$218$	−6.68998	−0.453102
$219$	0.208156	0.0140659
$220$	1.40617	0.0948040
$221$	22.2735	1.49828
$222$	0.951204	0.0638406
$223$	12.0508	0.806979	0.403490	−	0.914984i	$-0.367797\pi$
$223$	12.0508	0.806979	0.403490	+	0.914984i	$0.367797\pi$
$224$	0.627271	0.0419113
$225$	5.05687	0.337125
$226$	0.425846	0.0283268
$227$	15.9998	1.06194	0.530972	−	0.847389i	$-0.321827\pi$
$227$	15.9998	1.06194	0.530972	+	0.847389i	$0.321827\pi$
$228$	0.365699	0.0242190
$229$	21.0694	1.39230	0.696152	−	0.717894i	$-0.254894\pi$
$229$	21.0694	1.39230	0.696152	+	0.717894i	$0.254894\pi$
$230$	5.70934	0.376463
$231$	−0.168086	−0.0110592
$232$	3.69674	0.242703
$233$	22.1777	1.45291	0.726453	−	0.687216i	$-0.241167\pi$
$233$	22.1777	1.45291	0.726453	+	0.687216i	$0.241167\pi$
$234$	14.2414	0.930991
$235$	−7.98437	−0.520843
$236$	−4.26269	−0.277478
$237$	−4.81101	−0.312509
$238$	−2.82752	−0.183281
$239$	−15.9167	−1.02956	−0.514782	−	0.857321i	$-0.672127\pi$
$239$	−15.9167	−1.02956	−0.514782	+	0.857321i	$0.672127\pi$
$240$	−0.618462	−0.0399215
$241$	4.35656	0.280631	0.140315	−	0.990107i	$-0.455188\pi$
$241$	4.35656	0.280631	0.140315	+	0.990107i	$0.455188\pi$
$242$	−10.3907	−0.667942
$243$	−8.78839	−0.563775
$244$	−13.0831	−0.837560
$245$	−11.9017	−0.760375
$246$	1.49427	0.0952709
$247$	5.26364	0.334917
$248$	1.00000	0.0635001
$249$	2.69242	0.170625
$250$	−12.1684	−0.769598
$251$	14.7879	0.933401	0.466701	−	0.884415i	$-0.345443\pi$
$251$	14.7879	0.933401	0.466701	+	0.884415i	$0.345443\pi$
$252$	−1.80788	−0.113886
$253$	2.47371	0.155521
$254$	−12.8685	−0.807444
$255$	2.78781	0.174580
$256$	1.00000	0.0625000
$257$	−14.6545	−0.914122	−0.457061	−	0.889435i	$-0.651098\pi$
$257$	−14.6545	−0.914122	−0.457061	+	0.889435i	$0.651098\pi$
$258$	−1.00864	−0.0627952
$259$	−1.73801	−0.107995
$260$	−8.90174	−0.552062
$261$	−10.6545	−0.659500
$262$	−6.25371	−0.386355
$263$	21.9742	1.35499	0.677493	−	0.735529i	$-0.263066\pi$
$263$	21.9742	1.35499	0.677493	+	0.735529i	$0.263066\pi$
$264$	−0.267964	−0.0164920
$265$	−10.9401	−0.672047
$266$	−0.668195	−0.0409697
$267$	−1.11250	−0.0680841
$268$	6.12153	0.373932
$269$	13.1278	0.800419	0.400209	−	0.916424i	$-0.368937\pi$
$269$	13.1278	0.800419	0.400209	+	0.916424i	$0.368937\pi$
$270$	3.63788	0.221394
$271$	16.5999	1.00837	0.504185	−	0.863596i	$-0.331793\pi$
$271$	16.5999	1.00837	0.504185	+	0.863596i	$0.331793\pi$
$272$	−4.50766	−0.273317
$273$	1.06406	0.0644001
$274$	−7.18183	−0.433870
$275$	−1.36952	−0.0825849
$276$	−1.08799	−0.0654892
$277$	11.9732	0.719402	0.359701	−	0.933068i	$-0.382879\pi$
$277$	11.9732	0.719402	0.359701	+	0.933068i	$0.382879\pi$
$278$	−12.4214	−0.744985
$279$	−2.88214	−0.172549
$280$	1.13004	0.0675326
$281$	−21.9702	−1.31063	−0.655316	−	0.755354i	$-0.727465\pi$
$281$	−21.9702	−1.31063	−0.655316	+	0.755354i	$0.727465\pi$
$282$	1.52152	0.0906054
$283$	−10.6582	−0.633566	−0.316783	−	0.948498i	$-0.602603\pi$
$283$	−10.6582	−0.633566	−0.316783	+	0.948498i	$0.602603\pi$
$284$	4.34377	0.257755
$285$	0.658812	0.0390246
$286$	−3.85690	−0.228063
$287$	−2.73028	−0.161163
$288$	−2.88214	−0.169832
$289$	3.31897	0.195233
$290$	6.65973	0.391073
$291$	0.343301	0.0201247
$292$	−0.606335	−0.0354831
$293$	−19.4025	−1.13351	−0.566753	−	0.823888i	$-0.691800\pi$
$293$	−19.4025	−1.13351	−0.566753	+	0.823888i	$0.691800\pi$
$294$	2.26803	0.132274
$295$	−7.67929	−0.447106
$296$	−2.77075	−0.161047
$297$	1.57620	0.0914606
$298$	11.3325	0.656477
$299$	−15.6598	−0.905630
$300$	0.602340	0.0347761
$301$	1.84296	0.106226
$302$	12.9979	0.747946
$303$	5.88155	0.337886
$304$	−1.06524	−0.0610958
$305$	−23.5694	−1.34958
$306$	12.9917	0.742687
$307$	−5.75789	−0.328620	−0.164310	−	0.986409i	$-0.552540\pi$
$307$	−5.75789	−0.328620	−0.164310	+	0.986409i	$0.552540\pi$
$308$	0.489616	0.0278985
$309$	6.02805	0.342924
$310$	1.80151	0.102319
$311$	−14.7182	−0.834594	−0.417297	−	0.908770i	$-0.637022\pi$
$311$	−14.7182	−0.834594	−0.417297	+	0.908770i	$0.637022\pi$
$312$	1.69634	0.0960364
$313$	8.72635	0.493243	0.246621	−	0.969112i	$-0.420680\pi$
$313$	8.72635	0.493243	0.246621	+	0.969112i	$0.420680\pi$
$314$	24.4706	1.38096
$315$	−3.25693	−0.183507
$316$	14.0140	0.788347
$317$	−5.24694	−0.294697	−0.147349	−	0.989085i	$-0.547074\pi$
$317$	−5.24694	−0.294697	−0.147349	+	0.989085i	$0.547074\pi$
$318$	2.08478	0.116909
$319$	2.88549	0.161557
$320$	1.80151	0.100708
$321$	0.383797	0.0214214
$322$	1.98794	0.110784
$323$	4.80175	0.267176
$324$	7.95319	0.441844
$325$	8.66970	0.480908
$326$	8.22866	0.455743
$327$	2.29668	0.127007
$328$	−4.35264	−0.240334
$329$	−2.78008	−0.153271
$330$	−0.482740	−0.0265740
$331$	−1.26032	−0.0692733	−0.0346366	−	0.999400i	$-0.511027\pi$
$331$	−1.26032	−0.0692733	−0.0346366	+	0.999400i	$0.511027\pi$
$332$	−7.84274	−0.430426
$333$	7.98571	0.437614
$334$	1.70877	0.0934995
$335$	11.0280	0.602525
$336$	−0.215343	−0.0117479
$337$	−2.39800	−0.130627	−0.0653137	−	0.997865i	$-0.520805\pi$
$337$	−2.39800	−0.130627	−0.0653137	+	0.997865i	$0.520805\pi$
$338$	11.4160	0.620951
$339$	−0.146193	−0.00794014
$340$	−8.12060	−0.440401
$341$	0.780550	0.0422692
$342$	3.07018	0.166016
$343$	−8.53498	−0.460845
$344$	2.93806	0.158410
$345$	−1.96003	−0.105524
$346$	−19.7283	−1.06060
$347$	17.0421	0.914866	0.457433	−	0.889244i	$-0.348769\pi$
$347$	17.0421	0.914866	0.457433	+	0.889244i	$0.348769\pi$
$348$	−1.26910	−0.0680307
$349$	7.02701	0.376147	0.188074	−	0.982155i	$-0.439776\pi$
$349$	7.02701	0.376147	0.188074	+	0.982155i	$0.439776\pi$
$350$	−1.10058	−0.0588284
$351$	−9.97812	−0.532593
$352$	0.780550	0.0416035
$353$	−20.3390	−1.08254	−0.541268	−	0.840850i	$-0.682056\pi$
$353$	−20.3390	−1.08254	−0.541268	+	0.840850i	$0.682056\pi$
$354$	1.46339	0.0777782
$355$	7.82535	0.415327
$356$	3.24060	0.171752
$357$	0.970692	0.0513745
$358$	−16.4568	−0.869768
$359$	−23.5095	−1.24079	−0.620393	−	0.784291i	$-0.713027\pi$
$359$	−23.5095	−1.24079	−0.620393	+	0.784291i	$0.713027\pi$
$360$	−5.19222	−0.273654
$361$	−17.8653	−0.940277
$362$	0.903363	0.0474797
$363$	3.56716	0.187227
$364$	−3.09951	−0.162458
$365$	−1.09232	−0.0571746
$366$	4.49145	0.234772
$367$	−35.6659	−1.86174	−0.930872	−	0.365344i	$-0.880951\pi$
$367$	−35.6659	−1.86174	−0.930872	+	0.365344i	$0.880951\pi$
$368$	3.16919	0.165206
$369$	12.5449	0.653063
$370$	−4.99155	−0.259498
$371$	−3.80926	−0.197767
$372$	−0.343301	−0.0177994
$373$	21.2511	1.10034	0.550171	−	0.835052i	$-0.314563\pi$
$373$	21.2511	1.10034	0.550171	+	0.835052i	$0.314563\pi$
$374$	−3.51845	−0.181935
$375$	4.17743	0.215722
$376$	−4.43203	−0.228565
$377$	−18.2666	−0.940776
$378$	1.26668	0.0651509
$379$	−29.6023	−1.52057	−0.760283	−	0.649592i	$-0.774940\pi$
$379$	−29.6023	−1.52057	−0.760283	+	0.649592i	$0.774940\pi$
$380$	−1.91905	−0.0984450
$381$	4.41779	0.226330
$382$	4.61963	0.236361
$383$	0.224249	0.0114586	0.00572929	−	0.999984i	$-0.498176\pi$
$383$	0.224249	0.0114586	0.00572929	+	0.999984i	$0.498176\pi$
$384$	−0.343301	−0.0175190
$385$	0.882050	0.0449534
$386$	7.57967	0.385795
$387$	−8.46791	−0.430448
$388$	−1.00000	−0.0507673
$389$	−26.8457	−1.36113	−0.680566	−	0.732687i	$-0.738266\pi$
$389$	−26.8457	−1.36113	−0.680566	+	0.732687i	$0.738266\pi$
$390$	3.05598	0.154746
$391$	−14.2856	−0.722456
$392$	−6.60653	−0.333680
$393$	2.14691	0.108297
$394$	17.6123	0.887293
$395$	25.2463	1.27028
$396$	−2.24966	−0.113050
$397$	−2.54046	−0.127502	−0.0637510	−	0.997966i	$-0.520306\pi$
$397$	−2.54046	−0.127502	−0.0637510	+	0.997966i	$0.520306\pi$
$398$	−12.7299	−0.638093
$399$	0.229392	0.0114840
$400$	−1.75455	−0.0877276
$401$	−18.9267	−0.945155	−0.472578	−	0.881289i	$-0.656676\pi$
$401$	−18.9267	−0.945155	−0.472578	+	0.881289i	$0.656676\pi$
$402$	−2.10153	−0.104815
$403$	−4.94126	−0.246142
$404$	−17.1323	−0.852365
$405$	14.3278	0.711952
$406$	2.31886	0.115083
$407$	−2.16271	−0.107202
$408$	1.54748	0.0766119
$409$	17.7698	0.878660	0.439330	−	0.898326i	$-0.355216\pi$
$409$	17.7698	0.878660	0.439330	+	0.898326i	$0.355216\pi$
$410$	−7.84133	−0.387256
$411$	2.46553	0.121616
$412$	−17.5590	−0.865072
$413$	−2.67386	−0.131572
$414$	−9.13407	−0.448915
$415$	−14.1288	−0.693555
$416$	−4.94126	−0.242265
$417$	4.26428	0.208823
$418$	−0.831475	−0.0406688
$419$	−7.07029	−0.345406	−0.172703	−	0.984974i	$-0.555250\pi$
$419$	−7.07029	−0.345406	−0.172703	+	0.984974i	$0.555250\pi$
$420$	−0.387943	−0.0189297
$421$	−14.1775	−0.690971	−0.345485	−	0.938424i	$-0.612286\pi$
$421$	−14.1775	−0.690971	−0.345485	+	0.938424i	$0.612286\pi$
$422$	11.4597	0.557852
$423$	12.7738	0.621082
$424$	−6.07275	−0.294919
$425$	7.90892	0.383639
$426$	−1.49122	−0.0722499
$427$	−8.20665	−0.397147
$428$	−1.11796	−0.0540385
$429$	1.32408	0.0639272
$430$	5.29295	0.255249
$431$	−5.77351	−0.278100	−0.139050	−	0.990285i	$-0.544405\pi$
$431$	−5.77351	−0.278100	−0.139050	+	0.990285i	$0.544405\pi$
$432$	2.01935	0.0971560
$433$	−7.92177	−0.380696	−0.190348	−	0.981717i	$-0.560962\pi$
$433$	−7.92177	−0.380696	−0.190348	+	0.981717i	$0.560962\pi$
$434$	0.627271	0.0301100
$435$	−2.28629	−0.109619
$436$	−6.68998	−0.320392
$437$	−3.37596	−0.161494
$438$	0.208156	0.00994606
$439$	6.23872	0.297758	0.148879	−	0.988855i	$-0.452434\pi$
$439$	6.23872	0.297758	0.148879	+	0.988855i	$0.452434\pi$
$440$	1.40617	0.0670366
$441$	19.0410	0.906713
$442$	22.2735	1.05944
$443$	26.4763	1.25792	0.628962	−	0.777436i	$-0.283480\pi$
$443$	26.4763	1.25792	0.628962	+	0.777436i	$0.283480\pi$
$444$	0.951204	0.0451421
$445$	5.83798	0.276747
$446$	12.0508	0.570620
$447$	−3.89048	−0.184013
$448$	0.627271	0.0296357
$449$	30.8636	1.45654	0.728272	−	0.685288i	$-0.240324\pi$
$449$	30.8636	1.45654	0.728272	+	0.685288i	$0.240324\pi$
$450$	5.05687	0.238383
$451$	−3.39745	−0.159980
$452$	0.425846	0.0200301
$453$	−4.46221	−0.209653
$454$	15.9998	0.750908
$455$	−5.58380	−0.261773
$456$	0.365699	0.0171254
$457$	−33.8271	−1.58236	−0.791182	−	0.611580i	$-0.790534\pi$
$457$	−33.8271	−1.58236	−0.791182	+	0.611580i	$0.790534\pi$
$458$	21.0694	0.984508
$459$	−9.10253	−0.424870
$460$	5.70934	0.266199
$461$	13.6292	0.634777	0.317388	−	0.948296i	$-0.397194\pi$
$461$	13.6292	0.634777	0.317388	+	0.948296i	$0.397194\pi$
$462$	−0.168086	−0.00782006
$463$	−3.80898	−0.177018	−0.0885091	−	0.996075i	$-0.528210\pi$
$463$	−3.80898	−0.177018	−0.0885091	+	0.996075i	$0.528210\pi$
$464$	3.69674	0.171617
$465$	−0.618462	−0.0286805
$466$	22.1777	1.02736
$467$	9.36719	0.433462	0.216731	−	0.976231i	$-0.430461\pi$
$467$	9.36719	0.433462	0.216731	+	0.976231i	$0.430461\pi$
$468$	14.2414	0.658310
$469$	3.83986	0.177308
$470$	−7.98437	−0.368291
$471$	−8.40080	−0.387088
$472$	−4.26269	−0.196206
$473$	2.29330	0.105446
$474$	−4.81101	−0.220977
$475$	1.86902	0.0857567
$476$	−2.82752	−0.129599
$477$	17.5025	0.801387
$478$	−15.9167	−0.728012
$479$	33.8912	1.54853	0.774264	−	0.632863i	$-0.218120\pi$
$479$	33.8912	1.54853	0.774264	+	0.632863i	$0.218120\pi$
$480$	−0.618462	−0.0282288
$481$	13.6910	0.624257
$482$	4.35656	0.198436
$483$	−0.682463	−0.0310532
$484$	−10.3907	−0.472306
$485$	−1.80151	−0.0818025
$486$	−8.78839	−0.398649
$487$	29.7099	1.34629	0.673143	−	0.739513i	$-0.264944\pi$
$487$	29.7099	1.34629	0.673143	+	0.739513i	$0.264944\pi$
$488$	−13.0831	−0.592244
$489$	−2.82491	−0.127747
$490$	−11.9017	−0.537666
$491$	−33.7853	−1.52471	−0.762355	−	0.647159i	$-0.775957\pi$
$491$	−33.7853	−1.52471	−0.762355	+	0.647159i	$0.775957\pi$
$492$	1.49427	0.0673667
$493$	−16.6636	−0.750493
$494$	5.26364	0.236822
$495$	−4.05279	−0.182159
$496$	1.00000	0.0449013
$497$	2.72472	0.122220
$498$	2.69242	0.120650
$499$	29.3656	1.31459	0.657293	−	0.753635i	$-0.271701\pi$
$499$	29.3656	1.31459	0.657293	+	0.753635i	$0.271701\pi$
$500$	−12.1684	−0.544188
$501$	−0.586622	−0.0262083
$502$	14.7879	0.660015
$503$	39.4337	1.75826	0.879132	−	0.476579i	$-0.158123\pi$
$503$	39.4337	1.75826	0.879132	+	0.476579i	$0.158123\pi$
$504$	−1.80788	−0.0805296
$505$	−30.8641	−1.37343
$506$	2.47371	0.109970
$507$	−3.91914	−0.174055
$508$	−12.8685	−0.570949
$509$	−6.12783	−0.271611	−0.135806	−	0.990736i	$-0.543362\pi$
$509$	−6.12783	−0.271611	−0.135806	+	0.990736i	$0.543362\pi$
$510$	2.78781	0.123446
$511$	−0.380336	−0.0168251
$512$	1.00000	0.0441942
$513$	−2.15110	−0.0949732
$514$	−14.6545	−0.646382
$515$	−31.6328	−1.39391
$516$	−1.00864	−0.0444029
$517$	−3.45942	−0.152145
$518$	−1.73801	−0.0763639
$519$	6.77276	0.297291
$520$	−8.90174	−0.390367
$521$	−0.195247	−0.00855392	−0.00427696	−	0.999991i	$-0.501361\pi$
$521$	−0.195247	−0.00855392	−0.00427696	+	0.999991i	$0.501361\pi$
$522$	−10.6545	−0.466337
$523$	−27.0136	−1.18122	−0.590610	−	0.806957i	$-0.701113\pi$
$523$	−27.0136	−1.18122	−0.590610	+	0.806957i	$0.701113\pi$
$524$	−6.25371	−0.273195
$525$	0.377830	0.0164899
$526$	21.9742	0.958120
$527$	−4.50766	−0.196357
$528$	−0.267964	−0.0116616
$529$	−12.9562	−0.563313
$530$	−10.9401	−0.475209
$531$	12.2857	0.533153
$532$	−0.668195	−0.0289699
$533$	21.5075	0.931593
$534$	−1.11250	−0.0481427
$535$	−2.01402	−0.0870735
$536$	6.12153	0.264410
$537$	5.64964	0.243800
$538$	13.1278	0.565982
$539$	−5.15673	−0.222116
$540$	3.63788	0.156550
$541$	19.7982	0.851189	0.425595	−	0.904914i	$-0.360065\pi$
$541$	19.7982	0.851189	0.425595	+	0.904914i	$0.360065\pi$
$542$	16.5999	0.713025
$543$	−0.310126	−0.0133088
$544$	−4.50766	−0.193264
$545$	−12.0521	−0.516254
$546$	1.06406	0.0455378
$547$	−21.1350	−0.903668	−0.451834	−	0.892102i	$-0.649230\pi$
$547$	−21.1350	−0.903668	−0.451834	+	0.892102i	$0.649230\pi$
$548$	−7.18183	−0.306793
$549$	37.7074	1.60931
$550$	−1.36952	−0.0583964
$551$	−3.93793	−0.167761
$552$	−1.08799	−0.0463079
$553$	8.79054	0.373812
$554$	11.9732	0.508694
$555$	1.71361	0.0727385
$556$	−12.4214	−0.526784
$557$	7.39783	0.313456	0.156728	−	0.987642i	$-0.449905\pi$
$557$	7.39783	0.313456	0.156728	+	0.987642i	$0.449905\pi$
$558$	−2.88214	−0.122011
$559$	−14.5177	−0.614034
$560$	1.13004	0.0477527
$561$	1.20789	0.0509971
$562$	−21.9702	−0.926757
$563$	−32.3140	−1.36187	−0.680937	−	0.732342i	$-0.738427\pi$
$563$	−32.3140	−1.36187	−0.680937	+	0.732342i	$0.738427\pi$
$564$	1.52152	0.0640677
$565$	0.767166	0.0322749
$566$	−10.6582	−0.447999
$567$	4.98880	0.209510
$568$	4.34377	0.182260
$569$	22.7470	0.953603	0.476801	−	0.879011i	$-0.341796\pi$
$569$	22.7470	0.953603	0.476801	+	0.879011i	$0.341796\pi$
$570$	0.658812	0.0275946
$571$	−11.7726	−0.492668	−0.246334	−	0.969185i	$-0.579226\pi$
$571$	−11.7726	−0.492668	−0.246334	+	0.969185i	$0.579226\pi$
$572$	−3.85690	−0.161265
$573$	−1.58592	−0.0662529
$574$	−2.73028	−0.113960
$575$	−5.56052	−0.231890
$576$	−2.88214	−0.120089
$577$	−21.6743	−0.902311	−0.451155	−	0.892445i	$-0.648988\pi$
$577$	−21.6743	−0.902311	−0.451155	+	0.892445i	$0.648988\pi$
$578$	3.31897	0.138051
$579$	−2.60211	−0.108140
$580$	6.65973	0.276530
$581$	−4.91952	−0.204096
$582$	0.343301	0.0142303
$583$	−4.74009	−0.196314
$584$	−0.606335	−0.0250903
$585$	25.6561	1.06075
$586$	−19.4025	−0.801509
$587$	31.5061	1.30039	0.650197	−	0.759765i	$-0.274686\pi$
$587$	31.5061	1.30039	0.650197	+	0.759765i	$0.274686\pi$
$588$	2.26803	0.0935321
$589$	−1.06524	−0.0438925
$590$	−7.67929	−0.316151
$591$	−6.04632	−0.248712
$592$	−2.77075	−0.113877
$593$	−9.28815	−0.381419	−0.190709	−	0.981647i	$-0.561079\pi$
$593$	−9.28815	−0.381419	−0.190709	+	0.981647i	$0.561079\pi$
$594$	1.57620	0.0646724
$595$	−5.09381	−0.208826
$596$	11.3325	0.464199
$597$	4.37020	0.178860
$598$	−15.6598	−0.640377
$599$	−9.51171	−0.388638	−0.194319	−	0.980938i	$-0.562250\pi$
$599$	−9.51171	−0.388638	−0.194319	+	0.980938i	$0.562250\pi$
$600$	0.602340	0.0245904
$601$	−24.2629	−0.989703	−0.494851	−	0.868978i	$-0.664778\pi$
$601$	−24.2629	−0.989703	−0.494851	+	0.868978i	$0.664778\pi$
$602$	1.84296	0.0751134
$603$	−17.6431	−0.718484
$604$	12.9979	0.528878
$605$	−18.7191	−0.761038
$606$	5.88155	0.238922
$607$	8.66505	0.351704	0.175852	−	0.984417i	$-0.443732\pi$
$607$	8.66505	0.351704	0.175852	+	0.984417i	$0.443732\pi$
$608$	−1.06524	−0.0432013
$609$	−0.796067	−0.0322583
$610$	−23.5694	−0.954296
$611$	21.8998	0.885972
$612$	12.9917	0.525159
$613$	32.6081	1.31703	0.658515	−	0.752568i	$-0.271185\pi$
$613$	32.6081	1.31703	0.658515	+	0.752568i	$0.271185\pi$
$614$	−5.75789	−0.232370
$615$	2.69194	0.108549
$616$	0.489616	0.0197272
$617$	17.6667	0.711235	0.355618	−	0.934632i	$-0.384271\pi$
$617$	17.6667	0.711235	0.355618	+	0.934632i	$0.384271\pi$
$618$	6.02805	0.242484
$619$	30.3808	1.22111	0.610554	−	0.791974i	$-0.290947\pi$
$619$	30.3808	1.22111	0.610554	+	0.791974i	$0.290947\pi$
$620$	1.80151	0.0723505
$621$	6.39971	0.256811
$622$	−14.7182	−0.590147
$623$	2.03273	0.0814398
$624$	1.69634	0.0679080
$625$	−13.1488	−0.525951
$626$	8.72635	0.348775
$627$	0.285447	0.0113996
$628$	24.4706	0.976484
$629$	12.4896	0.497993
$630$	−3.25693	−0.129759
$631$	41.7231	1.66097	0.830484	−	0.557042i	$-0.188064\pi$
$631$	41.7231	1.66097	0.830484	+	0.557042i	$0.188064\pi$
$632$	14.0140	0.557445
$633$	−3.93415	−0.156368
$634$	−5.24694	−0.208382
$635$	−23.1828	−0.919983
$636$	2.08478	0.0826671
$637$	32.6446	1.29343
$638$	2.88549	0.114238
$639$	−12.5194	−0.495259
$640$	1.80151	0.0712110
$641$	19.3389	0.763841	0.381920	−	0.924195i	$-0.375263\pi$
$641$	19.3389	0.763841	0.381920	+	0.924195i	$0.375263\pi$
$642$	0.383797	0.0151472
$643$	4.28992	0.169178	0.0845889	−	0.996416i	$-0.473042\pi$
$643$	4.28992	0.169178	0.0845889	+	0.996416i	$0.473042\pi$
$644$	1.98794	0.0783359
$645$	−1.81708	−0.0715474
$646$	4.80175	0.188922
$647$	−35.7955	−1.40727	−0.703633	−	0.710564i	$-0.748440\pi$
$647$	−35.7955	−1.40727	−0.703633	+	0.710564i	$0.748440\pi$
$648$	7.95319	0.312431
$649$	−3.32724	−0.130606
$650$	8.66970	0.340054
$651$	−0.215343	−0.00843995
$652$	8.22866	0.322259
$653$	15.9074	0.622505	0.311252	−	0.950327i	$-0.399252\pi$
$653$	15.9074	0.622505	0.311252	+	0.950327i	$0.399252\pi$
$654$	2.29668	0.0898072
$655$	−11.2661	−0.440204
$656$	−4.35264	−0.169942
$657$	1.74754	0.0681782
$658$	−2.78008	−0.108379
$659$	30.2888	1.17988	0.589942	−	0.807446i	$-0.299151\pi$
$659$	30.2888	1.17988	0.589942	+	0.807446i	$0.299151\pi$
$660$	−0.482740	−0.0187906
$661$	33.3237	1.29614	0.648070	−	0.761580i	$-0.275576\pi$
$661$	33.3237	1.29614	0.648070	+	0.761580i	$0.275576\pi$
$662$	−1.26032	−0.0489836
$663$	−7.64652	−0.296966
$664$	−7.84274	−0.304357
$665$	−1.20376	−0.0466799
$666$	7.98571	0.309440
$667$	11.7157	0.453634
$668$	1.70877	0.0661141
$669$	−4.13705	−0.159947
$670$	11.0280	0.426049
$671$	−10.2120	−0.394231
$672$	−0.215343	−0.00830703
$673$	16.1653	0.623127	0.311563	−	0.950225i	$-0.399147\pi$
$673$	16.1653	0.623127	0.311563	+	0.950225i	$0.399147\pi$
$674$	−2.39800	−0.0923675
$675$	−3.54305	−0.136372
$676$	11.4160	0.439078
$677$	5.42236	0.208398	0.104199	−	0.994556i	$-0.466772\pi$
$677$	5.42236	0.208398	0.104199	+	0.994556i	$0.466772\pi$
$678$	−0.146193	−0.00561452
$679$	−0.627271	−0.0240724
$680$	−8.12060	−0.311411
$681$	−5.49275	−0.210483
$682$	0.780550	0.0298888
$683$	−9.36679	−0.358410	−0.179205	−	0.983812i	$-0.557353\pi$
$683$	−9.36679	−0.358410	−0.179205	+	0.983812i	$0.557353\pi$
$684$	3.07018	0.117391
$685$	−12.9382	−0.494342
$686$	−8.53498	−0.325867
$687$	−7.23315	−0.275962
$688$	2.93806	0.112012
$689$	30.0070	1.14318
$690$	−1.96003	−0.0746169
$691$	−41.8494	−1.59203	−0.796013	−	0.605279i	$-0.793061\pi$
$691$	−41.8494	−1.59203	−0.796013	+	0.605279i	$0.793061\pi$
$692$	−19.7283	−0.749958
$693$	−1.41114	−0.0536049
$694$	17.0421	0.646908
$695$	−22.3773	−0.848818
$696$	−1.26910	−0.0481050
$697$	19.6202	0.743168
$698$	7.02701	0.265976
$699$	−7.61362	−0.287974
$700$	−1.10058	−0.0415980
$701$	−28.7055	−1.08419	−0.542096	−	0.840317i	$-0.682369\pi$
$701$	−28.7055	−1.08419	−0.542096	+	0.840317i	$0.682369\pi$
$702$	−9.97812	−0.376600
$703$	2.95153	0.111319
$704$	0.780550	0.0294181
$705$	2.74104	0.103234
$706$	−20.3390	−0.765469
$707$	−10.7466	−0.404168
$708$	1.46339	0.0549975
$709$	14.9580	0.561761	0.280880	−	0.959743i	$-0.409374\pi$
$709$	14.9580	0.561761	0.280880	+	0.959743i	$0.409374\pi$
$710$	7.82535	0.293680
$711$	−40.3902	−1.51475
$712$	3.24060	0.121447
$713$	3.16919	0.118687
$714$	0.970692	0.0363272
$715$	−6.94825	−0.259850
$716$	−16.4568	−0.615019
$717$	5.46422	0.204065
$718$	−23.5095	−0.877369
$719$	−32.3685	−1.20714	−0.603571	−	0.797309i	$-0.706256\pi$
$719$	−32.3685	−1.20714	−0.603571	+	0.797309i	$0.706256\pi$
$720$	−5.19222	−0.193503
$721$	−11.0143	−0.410193
$722$	−17.8653	−0.664876
$723$	−1.49561	−0.0556225
$724$	0.903363	0.0335732
$725$	−6.48613	−0.240889
$726$	3.56716	0.132390
$727$	31.8725	1.18209	0.591043	−	0.806640i	$-0.298716\pi$
$727$	31.8725	1.18209	0.591043	+	0.806640i	$0.298716\pi$
$728$	−3.09951	−0.114875
$729$	−20.8425	−0.771944
$730$	−1.09232	−0.0404286
$731$	−13.2438	−0.489838
$732$	4.49145	0.166009
$733$	−11.8009	−0.435877	−0.217938	−	0.975963i	$-0.569933\pi$
$733$	−11.8009	−0.435877	−0.217938	+	0.975963i	$0.569933\pi$
$734$	−35.6659	−1.31645
$735$	4.08589	0.150710
$736$	3.16919	0.116818
$737$	4.77816	0.176006
$738$	12.5449	0.461785
$739$	19.9685	0.734553	0.367276	−	0.930112i	$-0.380290\pi$
$739$	19.9685	0.734553	0.367276	+	0.930112i	$0.380290\pi$
$740$	−4.99155	−0.183493
$741$	−1.80701	−0.0663823
$742$	−3.80926	−0.139842
$743$	−19.0792	−0.699947	−0.349974	−	0.936760i	$-0.613809\pi$
$743$	−19.0792	−0.699947	−0.349974	+	0.936760i	$0.613809\pi$
$744$	−0.343301	−0.0125860
$745$	20.4157	0.747974
$746$	21.2511	0.778059
$747$	22.6039	0.827033
$748$	−3.51845	−0.128647
$749$	−0.701262	−0.0256236
$750$	4.17743	0.152538
$751$	−20.0118	−0.730240	−0.365120	−	0.930960i	$-0.618972\pi$
$751$	−20.0118	−0.730240	−0.365120	+	0.930960i	$0.618972\pi$
$752$	−4.43203	−0.161620
$753$	−5.07669	−0.185005
$754$	−18.2666	−0.665229
$755$	23.4159	0.852193
$756$	1.26668	0.0460686
$757$	−1.87777	−0.0682488	−0.0341244	−	0.999418i	$-0.510864\pi$
$757$	−1.87777	−0.0682488	−0.0341244	+	0.999418i	$0.510864\pi$
$758$	−29.6023	−1.07520
$759$	−0.849230	−0.0308251
$760$	−1.91905	−0.0696112
$761$	−0.525081	−0.0190342	−0.00951708	−	0.999955i	$-0.503029\pi$
$761$	−0.525081	−0.0190342	−0.00951708	+	0.999955i	$0.503029\pi$
$762$	4.41779	0.160040
$763$	−4.19642	−0.151921
$764$	4.61963	0.167132
$765$	23.4047	0.846200
$766$	0.224249	0.00810244
$767$	21.0631	0.760543
$768$	−0.343301	−0.0123878
$769$	37.1784	1.34069	0.670344	−	0.742051i	$-0.266147\pi$
$769$	37.1784	1.34069	0.670344	+	0.742051i	$0.266147\pi$
$770$	0.882050	0.0317869
$771$	5.03091	0.181184
$772$	7.57967	0.272798
$773$	2.17743	0.0783165	0.0391583	−	0.999233i	$-0.487532\pi$
$773$	2.17743	0.0783165	0.0391583	+	0.999233i	$0.487532\pi$
$774$	−8.46791	−0.304373
$775$	−1.75455	−0.0630254
$776$	−1.00000	−0.0358979
$777$	0.596662	0.0214051
$778$	−26.8457	−0.962465
$779$	4.63661	0.166124
$780$	3.05598	0.109422
$781$	3.39053	0.121323
$782$	−14.2856	−0.510853
$783$	7.46501	0.266778
$784$	−6.60653	−0.235948
$785$	44.0841	1.57343
$786$	2.14691	0.0765777
$787$	41.2602	1.47077	0.735383	−	0.677651i	$-0.237002\pi$
$787$	41.2602	1.47077	0.735383	+	0.677651i	$0.237002\pi$
$788$	17.6123	0.627411
$789$	−7.54377	−0.268565
$790$	25.2463	0.898224
$791$	0.267120	0.00949771
$792$	−2.24966	−0.0799381
$793$	64.6470	2.29568
$794$	−2.54046	−0.0901576
$795$	3.75577	0.133203
$796$	−12.7299	−0.451200
$797$	16.1596	0.572401	0.286200	−	0.958170i	$-0.407608\pi$
$797$	16.1596	0.572401	0.286200	+	0.958170i	$0.407608\pi$
$798$	0.229392	0.00812040
$799$	19.9781	0.706774
$800$	−1.75455	−0.0620328
$801$	−9.33988	−0.330008
$802$	−18.9267	−0.668326
$803$	−0.473275	−0.0167015
$804$	−2.10153	−0.0741152
$805$	3.58130	0.126224
$806$	−4.94126	−0.174048
$807$	−4.50681	−0.158647
$808$	−17.1323	−0.602713
$809$	46.5936	1.63814	0.819072	−	0.573691i	$-0.194489\pi$
$809$	46.5936	1.63814	0.819072	+	0.573691i	$0.194489\pi$
$810$	14.3278	0.503426
$811$	−22.7482	−0.798798	−0.399399	−	0.916777i	$-0.630781\pi$
$811$	−22.7482	−0.798798	−0.399399	+	0.916777i	$0.630781\pi$
$812$	2.31886	0.0813760
$813$	−5.69875	−0.199864
$814$	−2.16271	−0.0758031
$815$	14.8240	0.519263
$816$	1.54748	0.0541728
$817$	−3.12975	−0.109496
$818$	17.7698	0.621307
$819$	8.93322	0.312152
$820$	−7.84133	−0.273831
$821$	−0.579141	−0.0202122	−0.0101061	−	0.999949i	$-0.503217\pi$
$821$	−0.579141	−0.0202122	−0.0101061	+	0.999949i	$0.503217\pi$
$822$	2.46553	0.0859953
$823$	24.2335	0.844727	0.422364	−	0.906426i	$-0.361201\pi$
$823$	24.2335	0.844727	0.422364	+	0.906426i	$0.361201\pi$
$824$	−17.5590	−0.611698
$825$	0.470157	0.0163688
$826$	−2.67386	−0.0930355
$827$	−30.1327	−1.04782	−0.523909	−	0.851774i	$-0.675527\pi$
$827$	−30.1327	−1.04782	−0.523909	+	0.851774i	$0.675527\pi$
$828$	−9.13407	−0.317431
$829$	−23.5721	−0.818694	−0.409347	−	0.912379i	$-0.634244\pi$
$829$	−23.5721	−0.818694	−0.409347	+	0.912379i	$0.634244\pi$
$830$	−14.1288	−0.490417
$831$	−4.11043	−0.142589
$832$	−4.94126	−0.171307
$833$	29.7800	1.03182
$834$	4.26428	0.147660
$835$	3.07836	0.106531
$836$	−0.831475	−0.0287572
$837$	2.01935	0.0697989
$838$	−7.07029	−0.244239
$839$	−3.62917	−0.125293	−0.0626464	−	0.998036i	$-0.519954\pi$
$839$	−3.62917	−0.125293	−0.0626464	+	0.998036i	$0.519954\pi$
$840$	−0.387943	−0.0133853
$841$	−15.3341	−0.528762
$842$	−14.1775	−0.488590
$843$	7.54240	0.259774
$844$	11.4597	0.394461
$845$	20.5661	0.707497
$846$	12.7738	0.439171
$847$	−6.51781	−0.223954
$848$	−6.07275	−0.208539
$849$	3.65899	0.125576
$850$	7.90892	0.271274
$851$	−8.78106	−0.301011
$852$	−1.49122	−0.0510884
$853$	−14.8414	−0.508159	−0.254080	−	0.967183i	$-0.581772\pi$
$853$	−14.8414	−0.508159	−0.254080	+	0.967183i	$0.581772\pi$
$854$	−8.20665	−0.280826
$855$	5.53097	0.189155
$856$	−1.11796	−0.0382110
$857$	−22.6028	−0.772097	−0.386048	−	0.922479i	$-0.626160\pi$
$857$	−22.6028	−0.772097	−0.386048	+	0.922479i	$0.626160\pi$
$858$	1.32408	0.0452033
$859$	−14.9470	−0.509984	−0.254992	−	0.966943i	$-0.582073\pi$
$859$	−14.9470	−0.509984	−0.254992	+	0.966943i	$0.582073\pi$
$860$	5.29295	0.180488
$861$	0.937309	0.0319434
$862$	−5.77351	−0.196647
$863$	25.7435	0.876320	0.438160	−	0.898897i	$-0.355630\pi$
$863$	25.7435	0.876320	0.438160	+	0.898897i	$0.355630\pi$
$864$	2.01935	0.0686996
$865$	−35.5408	−1.20842
$866$	−7.92177	−0.269193
$867$	−1.13941	−0.0386963
$868$	0.627271	0.0212910
$869$	10.9386	0.371066
$870$	−2.28629	−0.0775126
$871$	−30.2481	−1.02492
$872$	−6.68998	−0.226551
$873$	2.88214	0.0975458
$874$	−3.37596	−0.114194
$875$	−7.63289	−0.258039
$876$	0.208156	0.00703293
$877$	19.5177	0.659067	0.329533	−	0.944144i	$-0.393109\pi$
$877$	19.5177	0.659067	0.329533	+	0.944144i	$0.393109\pi$
$878$	6.23872	0.210547
$879$	6.66090	0.224667
$880$	1.40617	0.0474020
$881$	−47.5837	−1.60313	−0.801567	−	0.597905i	$-0.796000\pi$
$881$	−47.5837	−1.60313	−0.801567	+	0.597905i	$0.796000\pi$
$882$	19.0410	0.641143
$883$	−35.1461	−1.18276	−0.591381	−	0.806393i	$-0.701417\pi$
$883$	−35.1461	−1.18276	−0.591381	+	0.806393i	$0.701417\pi$
$884$	22.2735	0.749139
$885$	2.63631	0.0886186
$886$	26.4763	0.889487
$887$	6.26862	0.210480	0.105240	−	0.994447i	$-0.466439\pi$
$887$	6.26862	0.210480	0.105240	+	0.994447i	$0.466439\pi$
$888$	0.951204	0.0319203
$889$	−8.07206	−0.270728
$890$	5.83798	0.195690
$891$	6.20786	0.207971
$892$	12.0508	0.403490
$893$	4.72119	0.157989
$894$	−3.89048	−0.130117
$895$	−29.6471	−0.990993
$896$	0.627271	0.0209556
$897$	5.37603	0.179501
$898$	30.8636	1.02993
$899$	3.69674	0.123293
$900$	5.05687	0.168562
$901$	27.3739	0.911956
$902$	−3.39745	−0.113123
$903$	−0.632690	−0.0210546
$904$	0.425846	0.0141634
$905$	1.62742	0.0540973
$906$	−4.46221	−0.148247
$907$	−27.9319	−0.927462	−0.463731	−	0.885976i	$-0.653490\pi$
$907$	−27.9319	−0.927462	−0.463731	+	0.885976i	$0.653490\pi$
$908$	15.9998	0.530972
$909$	49.3778	1.63776
$910$	−5.58380	−0.185101
$911$	−47.8023	−1.58376	−0.791881	−	0.610675i	$-0.790898\pi$
$911$	−47.8023	−1.58376	−0.791881	+	0.610675i	$0.790898\pi$
$912$	0.365699	0.0121095
$913$	−6.12165	−0.202597
$914$	−33.8271	−1.11890
$915$	8.09140	0.267493
$916$	21.0694	0.696152
$917$	−3.92277	−0.129541
$918$	−9.10253	−0.300428
$919$	−37.1219	−1.22454	−0.612270	−	0.790649i	$-0.709743\pi$
$919$	−37.1219	−1.22454	−0.612270	+	0.790649i	$0.709743\pi$
$920$	5.70934	0.188231
$921$	1.97669	0.0651342
$922$	13.6292	0.448855
$923$	−21.4637	−0.706486
$924$	−0.168086	−0.00552962
$925$	4.86143	0.159843
$926$	−3.80898	−0.125171
$927$	50.6077	1.66218
$928$	3.69674	0.121352
$929$	−13.1095	−0.430109	−0.215055	−	0.976602i	$-0.568993\pi$
$929$	−13.1095	−0.430109	−0.215055	+	0.976602i	$0.568993\pi$
$930$	−0.618462	−0.0202802
$931$	7.03756	0.230647
$932$	22.1777	0.726453
$933$	5.05279	0.165421
$934$	9.36719	0.306504
$935$	−6.33854	−0.207292
$936$	14.2414	0.465495
$937$	19.0780	0.623251	0.311625	−	0.950205i	$-0.399127\pi$
$937$	19.0780	0.623251	0.311625	+	0.950205i	$0.399127\pi$
$938$	3.83986	0.125376
$939$	−2.99577	−0.0977632
$940$	−7.98437	−0.260421
$941$	39.1109	1.27498	0.637489	−	0.770459i	$-0.279973\pi$
$941$	39.1109	1.27498	0.637489	+	0.770459i	$0.279973\pi$
$942$	−8.40080	−0.273713
$943$	−13.7943	−0.449206
$944$	−4.26269	−0.138739
$945$	2.28194	0.0742314
$946$	2.29330	0.0745617
$947$	31.7887	1.03299	0.516497	−	0.856289i	$-0.327236\pi$
$947$	31.7887	1.03299	0.516497	+	0.856289i	$0.327236\pi$
$948$	−4.81101	−0.156254
$949$	2.99606	0.0972561
$950$	1.86902	0.0606391
$951$	1.80128	0.0584105
$952$	−2.82752	−0.0916405
$953$	45.5181	1.47447	0.737237	−	0.675634i	$-0.236130\pi$
$953$	45.5181	1.47447	0.737237	+	0.675634i	$0.236130\pi$
$954$	17.5025	0.566666
$955$	8.32232	0.269304
$956$	−15.9167	−0.514782
$957$	−0.990594	−0.0320214
$958$	33.8912	1.09497
$959$	−4.50495	−0.145472
$960$	−0.618462	−0.0199608
$961$	1.00000	0.0322581
$962$	13.6910	0.441416
$963$	3.22212	0.103831
$964$	4.35656	0.140315
$965$	13.6549	0.439566
$966$	−0.682463	−0.0219579
$967$	−24.3686	−0.783641	−0.391821	−	0.920042i	$-0.628155\pi$
$967$	−24.3686	−0.783641	−0.391821	+	0.920042i	$0.628155\pi$
$968$	−10.3907	−0.333971
$969$	−1.64845	−0.0529557
$970$	−1.80151	−0.0578431
$971$	21.9476	0.704332	0.352166	−	0.935938i	$-0.385445\pi$
$971$	21.9476	0.704332	0.352166	+	0.935938i	$0.385445\pi$
$972$	−8.78839	−0.281888
$973$	−7.79157	−0.249786
$974$	29.7099	0.951968
$975$	−2.97632	−0.0953185
$976$	−13.0831	−0.418780
$977$	−28.4075	−0.908838	−0.454419	−	0.890788i	$-0.650153\pi$
$977$	−28.4075	−0.908838	−0.454419	+	0.890788i	$0.650153\pi$
$978$	−2.82491	−0.0903307
$979$	2.52945	0.0808416
$980$	−11.9017	−0.380187
$981$	19.2815	0.615610
$982$	−33.7853	−1.07813
$983$	53.2496	1.69840	0.849199	−	0.528074i	$-0.177085\pi$
$983$	53.2496	1.69840	0.849199	+	0.528074i	$0.177085\pi$
$984$	1.49427	0.0476355
$985$	31.7287	1.01096
$986$	−16.6636	−0.530679
$987$	0.954407	0.0303791
$988$	5.26364	0.167459
$989$	9.31128	0.296082
$990$	−4.05279	−0.128806
$991$	−15.4993	−0.492350	−0.246175	−	0.969225i	$-0.579174\pi$
$991$	−15.4993	−0.492350	−0.246175	+	0.969225i	$0.579174\pi$
$992$	1.00000	0.0317500
$993$	0.432669	0.0137303
$994$	2.72472	0.0864228
$995$	−22.9331	−0.727029
$996$	2.69242	0.0853127
$997$	39.0251	1.23594	0.617968	−	0.786203i	$-0.287956\pi$
$997$	39.0251	1.23594	0.617968	+	0.786203i	$0.287956\pi$
$998$	29.3656	0.929553
$999$	−5.59512	−0.177022

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6014.2.a.e.1.12	✓	21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6014.2.a.e.1.12	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -0.343301 q^{3} +1.00000 q^{4} +1.80151 q^{5} -0.343301 q^{6} +0.627271 q^{7} +1.00000 q^{8} -2.88214 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -0.343301 q^{3} +1.00000 q^{4} +1.80151 q^{5} -0.343301 q^{6} +0.627271 q^{7} +1.00000 q^{8} -2.88214 q^{9} +1.80151 q^{10} +0.780550 q^{11} -0.343301 q^{12} -4.94126 q^{13} +0.627271 q^{14} -0.618462 q^{15} +1.00000 q^{16} -4.50766 q^{17} -2.88214 q^{18} -1.06524 q^{19} +1.80151 q^{20} -0.215343 q^{21} +0.780550 q^{22} +3.16919 q^{23} -0.343301 q^{24} -1.75455 q^{25} -4.94126 q^{26} +2.01935 q^{27} +0.627271 q^{28} +3.69674 q^{29} -0.618462 q^{30} +1.00000 q^{31} +1.00000 q^{32} -0.267964 q^{33} -4.50766 q^{34} +1.13004 q^{35} -2.88214 q^{36} -2.77075 q^{37} -1.06524 q^{38} +1.69634 q^{39} +1.80151 q^{40} -4.35264 q^{41} -0.215343 q^{42} +2.93806 q^{43} +0.780550 q^{44} -5.19222 q^{45} +3.16919 q^{46} -4.43203 q^{47} -0.343301 q^{48} -6.60653 q^{49} -1.75455 q^{50} +1.54748 q^{51} -4.94126 q^{52} -6.07275 q^{53} +2.01935 q^{54} +1.40617 q^{55} +0.627271 q^{56} +0.365699 q^{57} +3.69674 q^{58} -4.26269 q^{59} -0.618462 q^{60} -13.0831 q^{61} +1.00000 q^{62} -1.80788 q^{63} +1.00000 q^{64} -8.90174 q^{65} -0.267964 q^{66} +6.12153 q^{67} -4.50766 q^{68} -1.08799 q^{69} +1.13004 q^{70} +4.34377 q^{71} -2.88214 q^{72} -0.606335 q^{73} -2.77075 q^{74} +0.602340 q^{75} -1.06524 q^{76} +0.489616 q^{77} +1.69634 q^{78} +14.0140 q^{79} +1.80151 q^{80} +7.95319 q^{81} -4.35264 q^{82} -7.84274 q^{83} -0.215343 q^{84} -8.12060 q^{85} +2.93806 q^{86} -1.26910 q^{87} +0.780550 q^{88} +3.24060 q^{89} -5.19222 q^{90} -3.09951 q^{91} +3.16919 q^{92} -0.343301 q^{93} -4.43203 q^{94} -1.91905 q^{95} -0.343301 q^{96} -1.00000 q^{97} -6.60653 q^{98} -2.24966 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 21 q^{2} - 10 q^{3} + 21 q^{4} - 10 q^{5} - 10 q^{6} - 11 q^{7} + 21 q^{8} + 7 q^{9}+O(q^{10}) \) 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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