LMFDB - Embedded newform 6014.2.a.k.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:	$0$
Dimension:	$37$
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)

$f(q)$	$=$	$q+1.00000 q^{2} -0.850163 q^{3} +1.00000 q^{4} +1.27366 q^{5} -0.850163 q^{6} -2.84006 q^{7} +1.00000 q^{8} -2.27722 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -0.850163 q^{3} +1.00000 q^{4} +1.27366 q^{5} -0.850163 q^{6} -2.84006 q^{7} +1.00000 q^{8} -2.27722 q^{9} +1.27366 q^{10} -0.285267 q^{11} -0.850163 q^{12} +3.11192 q^{13} -2.84006 q^{14} -1.08282 q^{15} +1.00000 q^{16} -2.75931 q^{17} -2.27722 q^{18} -8.04601 q^{19} +1.27366 q^{20} +2.41451 q^{21} -0.285267 q^{22} +3.29050 q^{23} -0.850163 q^{24} -3.37780 q^{25} +3.11192 q^{26} +4.48650 q^{27} -2.84006 q^{28} +4.20082 q^{29} -1.08282 q^{30} +1.00000 q^{31} +1.00000 q^{32} +0.242523 q^{33} -2.75931 q^{34} -3.61726 q^{35} -2.27722 q^{36} +6.43531 q^{37} -8.04601 q^{38} -2.64564 q^{39} +1.27366 q^{40} -9.08411 q^{41} +2.41451 q^{42} +10.5918 q^{43} -0.285267 q^{44} -2.90040 q^{45} +3.29050 q^{46} +13.2850 q^{47} -0.850163 q^{48} +1.06594 q^{49} -3.37780 q^{50} +2.34586 q^{51} +3.11192 q^{52} -3.71617 q^{53} +4.48650 q^{54} -0.363332 q^{55} -2.84006 q^{56} +6.84042 q^{57} +4.20082 q^{58} +0.587696 q^{59} -1.08282 q^{60} +9.07611 q^{61} +1.00000 q^{62} +6.46745 q^{63} +1.00000 q^{64} +3.96352 q^{65} +0.242523 q^{66} +9.18388 q^{67} -2.75931 q^{68} -2.79746 q^{69} -3.61726 q^{70} +2.53520 q^{71} -2.27722 q^{72} +8.18946 q^{73} +6.43531 q^{74} +2.87168 q^{75} -8.04601 q^{76} +0.810174 q^{77} -2.64564 q^{78} -9.33992 q^{79} +1.27366 q^{80} +3.01742 q^{81} -9.08411 q^{82} +7.37996 q^{83} +2.41451 q^{84} -3.51441 q^{85} +10.5918 q^{86} -3.57138 q^{87} -0.285267 q^{88} +5.72969 q^{89} -2.90040 q^{90} -8.83804 q^{91} +3.29050 q^{92} -0.850163 q^{93} +13.2850 q^{94} -10.2479 q^{95} -0.850163 q^{96} +1.00000 q^{97} +1.06594 q^{98} +0.649616 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 37 q + 37 q^{2} + 9 q^{3} + 37 q^{4} + 9 q^{5} + 9 q^{6} + 19 q^{7} + 37 q^{8} + 52 q^{9}+O(q^{10}) $ 37 * q + 37 * q^2 + 9 * q^3 + 37 * q^4 + 9 * q^5 + 9 * q^6 + 19 * q^7 + 37 * q^8 + 52 * q^9	\( 37 q + 37 q^{2} + 9 q^{3} + 37 q^{4} + 9 q^{5} + 9 q^{6} + 19 q^{7} + 37 q^{8} + 52 q^{9} + 9 q^{10} + 5 q^{11} + 9 q^{12} + 16 q^{13} + 19 q^{14} + 22 q^{15} + 37 q^{16} + 3 q^{17} + 52 q^{18} + 36 q^{19} + 9 q^{20} + 6 q^{21} + 5 q^{22} + 11 q^{23} + 9 q^{24} + 58 q^{25} + 16 q^{26} + 24 q^{27} + 19 q^{28} + 5 q^{29} + 22 q^{30} + 37 q^{31} + 37 q^{32} + q^{33} + 3 q^{34} + 28 q^{35} + 52 q^{36} + 21 q^{37} + 36 q^{38} + 38 q^{39} + 9 q^{40} + 21 q^{41} + 6 q^{42} + 14 q^{43} + 5 q^{44} + 55 q^{45} + 11 q^{46} + 59 q^{47} + 9 q^{48} + 82 q^{49} + 58 q^{50} + 46 q^{51} + 16 q^{52} + 8 q^{53} + 24 q^{54} + 25 q^{55} + 19 q^{56} + 5 q^{58} + 41 q^{59} + 22 q^{60} + 16 q^{61} + 37 q^{62} + 23 q^{63} + 37 q^{64} - 46 q^{65} + q^{66} + 45 q^{67} + 3 q^{68} + 68 q^{69} + 28 q^{70} + 55 q^{71} + 52 q^{72} + 29 q^{73} + 21 q^{74} - 12 q^{75} + 36 q^{76} + 30 q^{77} + 38 q^{78} + 25 q^{79} + 9 q^{80} + 73 q^{81} + 21 q^{82} + 70 q^{83} + 6 q^{84} - 21 q^{85} + 14 q^{86} + 37 q^{87} + 5 q^{88} + 55 q^{90} + 18 q^{91} + 11 q^{92} + 9 q^{93} + 59 q^{94} - 9 q^{95} + 9 q^{96} + 37 q^{97} + 82 q^{98} + 33 q^{99}+O(q^{100}) \) 37 * q + 37 * q^2 + 9 * q^3 + 37 * q^4 + 9 * q^5 + 9 * q^6 + 19 * q^7 + 37 * q^8 + 52 * q^9 + 9 * q^10 + 5 * q^11 + 9 * q^12 + 16 * q^13 + 19 * q^14 + 22 * q^15 + 37 * q^16 + 3 * q^17 + 52 * q^18 + 36 * q^19 + 9 * q^20 + 6 * q^21 + 5 * q^22 + 11 * q^23 + 9 * q^24 + 58 * q^25 + 16 * q^26 + 24 * q^27 + 19 * q^28 + 5 * q^29 + 22 * q^30 + 37 * q^31 + 37 * q^32 + q^33 + 3 * q^34 + 28 * q^35 + 52 * q^36 + 21 * q^37 + 36 * q^38 + 38 * q^39 + 9 * q^40 + 21 * q^41 + 6 * q^42 + 14 * q^43 + 5 * q^44 + 55 * q^45 + 11 * q^46 + 59 * q^47 + 9 * q^48 + 82 * q^49 + 58 * q^50 + 46 * q^51 + 16 * q^52 + 8 * q^53 + 24 * q^54 + 25 * q^55 + 19 * q^56 + 5 * q^58 + 41 * q^59 + 22 * q^60 + 16 * q^61 + 37 * q^62 + 23 * q^63 + 37 * q^64 - 46 * q^65 + q^66 + 45 * q^67 + 3 * q^68 + 68 * q^69 + 28 * q^70 + 55 * q^71 + 52 * q^72 + 29 * q^73 + 21 * q^74 - 12 * q^75 + 36 * q^76 + 30 * q^77 + 38 * q^78 + 25 * q^79 + 9 * q^80 + 73 * q^81 + 21 * q^82 + 70 * q^83 + 6 * q^84 - 21 * q^85 + 14 * q^86 + 37 * q^87 + 5 * q^88 + 55 * q^90 + 18 * q^91 + 11 * q^92 + 9 * q^93 + 59 * q^94 - 9 * q^95 + 9 * q^96 + 37 * q^97 + 82 * q^98 + 33 * 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
$3$	−0.850163	−0.490842	−0.245421	−	0.969417i	$-0.578926\pi$
$3$	−0.850163	−0.490842	−0.245421	+	0.969417i	$0.578926\pi$
$4$	1.00000	0.500000
$5$	1.27366	0.569597	0.284798	−	0.958587i	$-0.408073\pi$
$5$	1.27366	0.569597	0.284798	+	0.958587i	$0.408073\pi$
$6$	−0.850163	−0.347077
$7$	−2.84006	−1.07344	−0.536721	−	0.843760i	$-0.680337\pi$
$7$	−2.84006	−1.07344	−0.536721	+	0.843760i	$0.680337\pi$
$8$	1.00000	0.353553
$9$	−2.27722	−0.759075
$10$	1.27366	0.402766
$11$	−0.285267	−0.0860111	−0.0430056	−	0.999075i	$-0.513693\pi$
$11$	−0.285267	−0.0860111	−0.0430056	+	0.999075i	$0.513693\pi$
$12$	−0.850163	−0.245421
$13$	3.11192	0.863091	0.431545	−	0.902091i	$-0.357968\pi$
$13$	3.11192	0.863091	0.431545	+	0.902091i	$0.357968\pi$
$14$	−2.84006	−0.759038
$15$	−1.08282	−0.279582
$16$	1.00000	0.250000
$17$	−2.75931	−0.669230	−0.334615	−	0.942355i	$-0.608606\pi$
$17$	−2.75931	−0.669230	−0.334615	+	0.942355i	$0.608606\pi$
$18$	−2.27722	−0.536747
$19$	−8.04601	−1.84588	−0.922941	−	0.384941i	$-0.874222\pi$
$19$	−8.04601	−1.84588	−0.922941	+	0.384941i	$0.874222\pi$
$20$	1.27366	0.284798
$21$	2.41451	0.526890
$22$	−0.285267	−0.0608191
$23$	3.29050	0.686118	0.343059	−	0.939314i	$-0.388537\pi$
$23$	3.29050	0.686118	0.343059	+	0.939314i	$0.388537\pi$
$24$	−0.850163	−0.173539
$25$	−3.37780	−0.675559
$26$	3.11192	0.610297
$27$	4.48650	0.863427
$28$	−2.84006	−0.536721
$29$	4.20082	0.780072	0.390036	−	0.920800i	$-0.372463\pi$
$29$	4.20082	0.780072	0.390036	+	0.920800i	$0.372463\pi$
$30$	−1.08282	−0.197694
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	1.00000	0.176777
$33$	0.242523	0.0422178
$34$	−2.75931	−0.473217
$35$	−3.61726	−0.611429
$36$	−2.27722	−0.379537
$37$	6.43531	1.05796	0.528979	−	0.848635i	$-0.322575\pi$
$37$	6.43531	1.05796	0.528979	+	0.848635i	$0.322575\pi$
$38$	−8.04601	−1.30524
$39$	−2.64564	−0.423641
$40$	1.27366	0.201383
$41$	−9.08411	−1.41870	−0.709350	−	0.704857i	$-0.751011\pi$
$41$	−9.08411	−1.41870	−0.709350	+	0.704857i	$0.751011\pi$
$42$	2.41451	0.372567
$43$	10.5918	1.61523	0.807614	−	0.589711i	$-0.200758\pi$
$43$	10.5918	1.61523	0.807614	+	0.589711i	$0.200758\pi$
$44$	−0.285267	−0.0430056
$45$	−2.90040	−0.432367
$46$	3.29050	0.485158
$47$	13.2850	1.93781	0.968906	−	0.247428i	$-0.0795854\pi$
$47$	13.2850	1.93781	0.968906	+	0.247428i	$0.0795854\pi$
$48$	−0.850163	−0.122710
$49$	1.06594	0.152277
$50$	−3.37780	−0.477693
$51$	2.34586	0.328486
$52$	3.11192	0.431545
$53$	−3.71617	−0.510455	−0.255228	−	0.966881i	$-0.582150\pi$
$53$	−3.71617	−0.510455	−0.255228	+	0.966881i	$0.582150\pi$
$54$	4.48650	0.610535
$55$	−0.363332	−0.0489917
$56$	−2.84006	−0.379519
$57$	6.84042	0.906036
$58$	4.20082	0.551594
$59$	0.587696	0.0765115	0.0382558	−	0.999268i	$-0.487820\pi$
$59$	0.587696	0.0765115	0.0382558	+	0.999268i	$0.487820\pi$
$60$	−1.08282	−0.139791
$61$	9.07611	1.16208	0.581038	−	0.813876i	$-0.302647\pi$
$61$	9.07611	1.16208	0.581038	+	0.813876i	$0.302647\pi$
$62$	1.00000	0.127000
$63$	6.46745	0.814822
$64$	1.00000	0.125000
$65$	3.96352	0.491614
$66$	0.242523	0.0298525
$67$	9.18388	1.12199	0.560995	−	0.827820i	$-0.310419\pi$
$67$	9.18388	1.12199	0.560995	+	0.827820i	$0.310419\pi$
$68$	−2.75931	−0.334615
$69$	−2.79746	−0.336775
$70$	−3.61726	−0.432346
$71$	2.53520	0.300873	0.150437	−	0.988620i	$-0.451932\pi$
$71$	2.53520	0.300873	0.150437	+	0.988620i	$0.451932\pi$
$72$	−2.27722	−0.268373
$73$	8.18946	0.958504	0.479252	−	0.877677i	$-0.340908\pi$
$73$	8.18946	0.958504	0.479252	+	0.877677i	$0.340908\pi$
$74$	6.43531	0.748089
$75$	2.87168	0.331593
$76$	−8.04601	−0.922941
$77$	0.810174	0.0923279
$78$	−2.64564	−0.299559
$79$	−9.33992	−1.05082	−0.525411	−	0.850848i	$-0.676089\pi$
$79$	−9.33992	−1.05082	−0.525411	+	0.850848i	$0.676089\pi$
$80$	1.27366	0.142399
$81$	3.01742	0.335269
$82$	−9.08411	−1.00317
$83$	7.37996	0.810056	0.405028	−	0.914304i	$-0.367262\pi$
$83$	7.37996	0.810056	0.405028	+	0.914304i	$0.367262\pi$
$84$	2.41451	0.263445
$85$	−3.51441	−0.381191
$86$	10.5918	1.14214
$87$	−3.57138	−0.382892
$88$	−0.285267	−0.0304095
$89$	5.72969	0.607346	0.303673	−	0.952776i	$-0.401787\pi$
$89$	5.72969	0.607346	0.303673	+	0.952776i	$0.401787\pi$
$90$	−2.90040	−0.305729
$91$	−8.83804	−0.926478
$92$	3.29050	0.343059
$93$	−0.850163	−0.0881577
$94$	13.2850	1.37024
$95$	−10.2479	−1.05141
$96$	−0.850163	−0.0867693
$97$	1.00000	0.101535
$97$	1.00000	0.101535
$98$	1.06594	0.107676
$99$	0.649616	0.0652889
$100$	−3.37780	−0.337780
$101$	−12.5142	−1.24521	−0.622605	−	0.782536i	$-0.713926\pi$
$101$	−12.5142	−1.24521	−0.622605	+	0.782536i	$0.713926\pi$
$102$	2.34586	0.232275
$103$	10.7196	1.05623	0.528114	−	0.849173i	$-0.322899\pi$
$103$	10.7196	1.05623	0.528114	+	0.849173i	$0.322899\pi$
$104$	3.11192	0.305149
$105$	3.07526	0.300115
$106$	−3.71617	−0.360946
$107$	2.56713	0.248174	0.124087	−	0.992271i	$-0.460400\pi$
$107$	2.56713	0.248174	0.124087	+	0.992271i	$0.460400\pi$
$108$	4.48650	0.431713
$109$	−11.0426	−1.05769	−0.528846	−	0.848718i	$-0.677375\pi$
$109$	−11.0426	−1.05769	−0.528846	+	0.848718i	$0.677375\pi$
$110$	−0.363332	−0.0346424
$111$	−5.47106	−0.519290
$112$	−2.84006	−0.268360
$113$	7.60187	0.715123	0.357562	−	0.933890i	$-0.383608\pi$
$113$	7.60187	0.715123	0.357562	+	0.933890i	$0.383608\pi$
$114$	6.84042	0.640664
$115$	4.19098	0.390811
$116$	4.20082	0.390036
$117$	−7.08654	−0.655150
$118$	0.587696	0.0541018
$119$	7.83659	0.718379
$120$	−1.08282	−0.0988471
$121$	−10.9186	−0.992602
$122$	9.07611	0.821712
$123$	7.72297	0.696357
$124$	1.00000	0.0898027
$125$	−10.6704	−0.954394
$126$	6.46745	0.576166
$127$	14.0991	1.25109	0.625546	−	0.780187i	$-0.284876\pi$
$127$	14.0991	1.25109	0.625546	+	0.780187i	$0.284876\pi$
$128$	1.00000	0.0883883
$129$	−9.00472	−0.792821
$130$	3.96352	0.347624
$131$	16.5052	1.44207	0.721035	−	0.692899i	$-0.243667\pi$
$131$	16.5052	1.44207	0.721035	+	0.692899i	$0.243667\pi$
$132$	0.242523	0.0211089
$133$	22.8512	1.98145
$134$	9.18388	0.793366
$135$	5.71426	0.491805
$136$	−2.75931	−0.236608
$137$	9.86751	0.843039	0.421519	−	0.906819i	$-0.361497\pi$
$137$	9.86751	0.843039	0.421519	+	0.906819i	$0.361497\pi$
$138$	−2.79746	−0.238136
$139$	−12.8397	−1.08905	−0.544524	−	0.838746i	$-0.683289\pi$
$139$	−12.8397	−1.08905	−0.544524	+	0.838746i	$0.683289\pi$
$140$	−3.61726	−0.305715
$141$	−11.2944	−0.951159
$142$	2.53520	0.212750
$143$	−0.887727	−0.0742354
$144$	−2.27722	−0.189769
$145$	5.35040	0.444327
$146$	8.18946	0.677765
$147$	−0.906223	−0.0747440
$148$	6.43531	0.528979
$149$	−15.3688	−1.25906	−0.629531	−	0.776976i	$-0.716753\pi$
$149$	−15.3688	−1.25906	−0.629531	+	0.776976i	$0.716753\pi$
$150$	2.87168	0.234471
$151$	13.5618	1.10364	0.551821	−	0.833962i	$-0.313933\pi$
$151$	13.5618	1.10364	0.551821	+	0.833962i	$0.313933\pi$
$152$	−8.04601	−0.652618
$153$	6.28356	0.507995
$154$	0.810174	0.0652857
$155$	1.27366	0.102303
$156$	−2.64564	−0.211820
$157$	8.44294	0.673820	0.336910	−	0.941537i	$-0.390618\pi$
$157$	8.44294	0.673820	0.336910	+	0.941537i	$0.390618\pi$
$158$	−9.33992	−0.743044
$159$	3.15935	0.250553
$160$	1.27366	0.100691
$161$	−9.34523	−0.736507
$162$	3.01742	0.237071
$163$	−15.4684	−1.21158	−0.605788	−	0.795626i	$-0.707142\pi$
$163$	−15.4684	−1.21158	−0.605788	+	0.795626i	$0.707142\pi$
$164$	−9.08411	−0.709350
$165$	0.308891	0.0240472
$166$	7.37996	0.572796
$167$	20.3354	1.57360	0.786800	−	0.617209i	$-0.211737\pi$
$167$	20.3354	1.57360	0.786800	+	0.617209i	$0.211737\pi$
$168$	2.41451	0.186284
$169$	−3.31596	−0.255074
$170$	−3.51441	−0.269543
$171$	18.3226	1.40116
$172$	10.5918	0.807614
$173$	−3.48192	−0.264725	−0.132363	−	0.991201i	$-0.542256\pi$
$173$	−3.48192	−0.264725	−0.132363	+	0.991201i	$0.542256\pi$
$174$	−3.57138	−0.270745
$175$	9.59314	0.725174
$176$	−0.285267	−0.0215028
$177$	−0.499637	−0.0375550
$178$	5.72969	0.429458
$179$	16.4069	1.22631	0.613153	−	0.789964i	$-0.289901\pi$
$179$	16.4069	1.22631	0.613153	+	0.789964i	$0.289901\pi$
$180$	−2.90040	−0.216183
$181$	21.5576	1.60236	0.801180	−	0.598423i	$-0.204206\pi$
$181$	21.5576	1.60236	0.801180	+	0.598423i	$0.204206\pi$
$182$	−8.83804	−0.655119
$183$	−7.71617	−0.570395
$184$	3.29050	0.242579
$185$	8.19638	0.602610
$186$	−0.850163	−0.0623369
$187$	0.787138	0.0575612
$188$	13.2850	0.968906
$189$	−12.7419	−0.926838
$190$	−10.2479	−0.743458
$191$	−10.6923	−0.773665	−0.386832	−	0.922150i	$-0.626431\pi$
$191$	−10.6923	−0.773665	−0.386832	+	0.922150i	$0.626431\pi$
$192$	−0.850163	−0.0613552
$193$	−2.34312	−0.168661	−0.0843306	−	0.996438i	$-0.526875\pi$
$193$	−2.34312	−0.168661	−0.0843306	+	0.996438i	$0.526875\pi$
$194$	1.00000	0.0717958
$195$	−3.36964	−0.241305
$196$	1.06594	0.0761386
$197$	5.50225	0.392019	0.196010	−	0.980602i	$-0.437202\pi$
$197$	5.50225	0.392019	0.196010	+	0.980602i	$0.437202\pi$
$198$	0.649616	0.0461662
$199$	−11.4306	−0.810294	−0.405147	−	0.914252i	$-0.632780\pi$
$199$	−11.4306	−0.810294	−0.405147	+	0.914252i	$0.632780\pi$
$200$	−3.37780	−0.238846
$201$	−7.80779	−0.550719
$202$	−12.5142	−0.880497
$203$	−11.9306	−0.837362
$204$	2.34586	0.164243
$205$	−11.5700	−0.808087
$206$	10.7196	0.746867
$207$	−7.49321	−0.520814
$208$	3.11192	0.215773
$209$	2.29526	0.158766
$210$	3.07526	0.212213
$211$	−16.3799	−1.12764	−0.563818	−	0.825899i	$-0.690668\pi$
$211$	−16.3799	−1.12764	−0.563818	+	0.825899i	$0.690668\pi$
$212$	−3.71617	−0.255228
$213$	−2.15534	−0.147681
$214$	2.56713	0.175485
$215$	13.4903	0.920029
$216$	4.48650	0.305268
$217$	−2.84006	−0.192796
$218$	−11.0426	−0.747901
$219$	−6.96237	−0.470474
$220$	−0.363332	−0.0244958
$221$	−8.58673	−0.577606
$222$	−5.47106	−0.367193
$223$	−8.46130	−0.566611	−0.283305	−	0.959030i	$-0.591431\pi$
$223$	−8.46130	−0.566611	−0.283305	+	0.959030i	$0.591431\pi$
$224$	−2.84006	−0.189759
$225$	7.69200	0.512800
$226$	7.60187	0.505669
$227$	20.5570	1.36441	0.682207	−	0.731159i	$-0.261020\pi$
$227$	20.5570	1.36441	0.682207	+	0.731159i	$0.261020\pi$
$228$	6.84042	0.453018
$229$	−12.1734	−0.804440	−0.402220	−	0.915543i	$-0.631761\pi$
$229$	−12.1734	−0.804440	−0.402220	+	0.915543i	$0.631761\pi$
$230$	4.19098	0.276345
$231$	−0.688780	−0.0453184
$232$	4.20082	0.275797
$233$	11.5419	0.756136	0.378068	−	0.925778i	$-0.376588\pi$
$233$	11.5419	0.756136	0.378068	+	0.925778i	$0.376588\pi$
$234$	−7.08654	−0.463261
$235$	16.9205	1.10377
$236$	0.587696	0.0382558
$237$	7.94045	0.515788
$238$	7.83659	0.507971
$239$	18.3786	1.18881	0.594405	−	0.804166i	$-0.297388\pi$
$239$	18.3786	1.18881	0.594405	+	0.804166i	$0.297388\pi$
$240$	−1.08282	−0.0698955
$241$	13.9035	0.895606	0.447803	−	0.894132i	$-0.352207\pi$
$241$	13.9035	0.895606	0.447803	+	0.894132i	$0.352207\pi$
$242$	−10.9186	−0.701876
$243$	−16.0248	−1.02799
$244$	9.07611	0.581038
$245$	1.35764	0.0867366
$246$	7.72297	0.492399
$247$	−25.0385	−1.59316
$248$	1.00000	0.0635001
$249$	−6.27417	−0.397609
$250$	−10.6704	−0.674858
$251$	19.6297	1.23901	0.619507	−	0.784991i	$-0.287332\pi$
$251$	19.6297	1.23901	0.619507	+	0.784991i	$0.287332\pi$
$252$	6.46745	0.407411
$253$	−0.938671	−0.0590138
$254$	14.0991	0.884656
$255$	2.98782	0.187105
$256$	1.00000	0.0625000
$257$	−11.7029	−0.730005	−0.365002	−	0.931007i	$-0.618932\pi$
$257$	−11.7029	−0.730005	−0.365002	+	0.931007i	$0.618932\pi$
$258$	−9.00472	−0.560609
$259$	−18.2767	−1.13566
$260$	3.96352	0.245807
$261$	−9.56620	−0.592133
$262$	16.5052	1.01970
$263$	−21.2053	−1.30757	−0.653787	−	0.756679i	$-0.726821\pi$
$263$	−21.2053	−1.30757	−0.653787	+	0.756679i	$0.726821\pi$
$264$	0.242523	0.0149263
$265$	−4.73313	−0.290754
$266$	22.8512	1.40109
$267$	−4.87117	−0.298111
$268$	9.18388	0.560995
$269$	14.4723	0.882394	0.441197	−	0.897410i	$-0.354554\pi$
$269$	14.4723	0.882394	0.441197	+	0.897410i	$0.354554\pi$
$270$	5.71426	0.347759
$271$	−4.09012	−0.248457	−0.124229	−	0.992254i	$-0.539646\pi$
$271$	−4.09012	−0.248457	−0.124229	+	0.992254i	$0.539646\pi$
$272$	−2.75931	−0.167307
$273$	7.51377	0.454754
$274$	9.86751	0.596118
$275$	0.963573	0.0581056
$276$	−2.79746	−0.168388
$277$	−10.3926	−0.624430	−0.312215	−	0.950012i	$-0.601071\pi$
$277$	−10.3926	−0.624430	−0.312215	+	0.950012i	$0.601071\pi$
$278$	−12.8397	−0.770073
$279$	−2.27722	−0.136334
$280$	−3.61726	−0.216173
$281$	−2.03581	−0.121447	−0.0607233	−	0.998155i	$-0.519341\pi$
$281$	−2.03581	−0.121447	−0.0607233	+	0.998155i	$0.519341\pi$
$282$	−11.2944	−0.672571
$283$	16.0274	0.952731	0.476365	−	0.879247i	$-0.341954\pi$
$283$	16.0274	0.952731	0.476365	+	0.879247i	$0.341954\pi$
$284$	2.53520	0.150437
$285$	8.71235	0.516075
$286$	−0.887727	−0.0524924
$287$	25.7994	1.52289
$288$	−2.27722	−0.134187
$289$	−9.38624	−0.552131
$290$	5.35040	0.314186
$291$	−0.850163	−0.0498374
$292$	8.18946	0.479252
$293$	3.11891	0.182209	0.0911044	−	0.995841i	$-0.470960\pi$
$293$	3.11891	0.182209	0.0911044	+	0.995841i	$0.470960\pi$
$294$	−0.906223	−0.0528520
$295$	0.748524	0.0435807
$296$	6.43531	0.374045
$297$	−1.27985	−0.0742643
$298$	−15.3688	−0.890291
$299$	10.2398	0.592182
$300$	2.87168	0.165796
$301$	−30.0812	−1.73385
$302$	13.5618	0.780393
$303$	10.6391	0.611201
$304$	−8.04601	−0.461471
$305$	11.5599	0.661915
$306$	6.28356	0.359207
$307$	32.6011	1.86065	0.930323	−	0.366742i	$-0.119527\pi$
$307$	32.6011	1.86065	0.930323	+	0.366742i	$0.119527\pi$
$308$	0.810174	0.0461640
$309$	−9.11336	−0.518441
$310$	1.27366	0.0723389
$311$	27.2724	1.54647	0.773237	−	0.634117i	$-0.218636\pi$
$311$	27.2724	1.54647	0.773237	+	0.634117i	$0.218636\pi$
$312$	−2.64564	−0.149780
$313$	−18.0179	−1.01843	−0.509216	−	0.860639i	$-0.670065\pi$
$313$	−18.0179	−1.01843	−0.509216	+	0.860639i	$0.670065\pi$
$314$	8.44294	0.476463
$315$	8.23732	0.464120
$316$	−9.33992	−0.525411
$317$	−29.4486	−1.65400	−0.827000	−	0.562202i	$-0.809954\pi$
$317$	−29.4486	−1.65400	−0.827000	+	0.562202i	$0.809954\pi$
$318$	3.15935	0.177168
$319$	−1.19835	−0.0670949
$320$	1.27366	0.0711996
$321$	−2.18248	−0.121814
$322$	−9.34523	−0.520789
$323$	22.2014	1.23532
$324$	3.01742	0.167634
$325$	−10.5114	−0.583069
$326$	−15.4684	−0.856714
$327$	9.38803	0.519159
$328$	−9.08411	−0.501586
$329$	−37.7301	−2.08013
$330$	0.308891	0.0170039
$331$	−2.62073	−0.144048	−0.0720242	−	0.997403i	$-0.522946\pi$
$331$	−2.62073	−0.144048	−0.0720242	+	0.997403i	$0.522946\pi$
$332$	7.37996	0.405028
$333$	−14.6546	−0.803069
$334$	20.3354	1.11270
$335$	11.6971	0.639082
$336$	2.41451	0.131722
$337$	14.5175	0.790818	0.395409	−	0.918505i	$-0.370603\pi$
$337$	14.5175	0.790818	0.395409	+	0.918505i	$0.370603\pi$
$338$	−3.31596	−0.180365
$339$	−6.46282	−0.351012
$340$	−3.51441	−0.190596
$341$	−0.285267	−0.0154481
$342$	18.3226	0.990771
$343$	16.8531	0.909981
$344$	10.5918	0.571069
$345$	−3.56301	−0.191826
$346$	−3.48192	−0.187189
$347$	29.7149	1.59518	0.797591	−	0.603199i	$-0.206107\pi$
$347$	29.7149	1.59518	0.797591	+	0.603199i	$0.206107\pi$
$348$	−3.57138	−0.191446
$349$	−0.756445	−0.0404916	−0.0202458	−	0.999795i	$-0.506445\pi$
$349$	−0.756445	−0.0404916	−0.0202458	+	0.999795i	$0.506445\pi$
$350$	9.59314	0.512775
$351$	13.9616	0.745216
$352$	−0.285267	−0.0152048
$353$	−12.9138	−0.687334	−0.343667	−	0.939092i	$-0.611669\pi$
$353$	−12.9138	−0.687334	−0.343667	+	0.939092i	$0.611669\pi$
$354$	−0.499637	−0.0265554
$355$	3.22898	0.171377
$356$	5.72969	0.303673
$357$	−6.66238	−0.352610
$358$	16.4069	0.867129
$359$	4.88032	0.257574	0.128787	−	0.991672i	$-0.458892\pi$
$359$	4.88032	0.257574	0.128787	+	0.991672i	$0.458892\pi$
$360$	−2.90040	−0.152865
$361$	45.7383	2.40728
$362$	21.5576	1.13304
$363$	9.28260	0.487210
$364$	−8.83804	−0.463239
$365$	10.4306	0.545961
$366$	−7.71617	−0.403330
$367$	17.2135	0.898539	0.449270	−	0.893396i	$-0.351684\pi$
$367$	17.2135	0.898539	0.449270	+	0.893396i	$0.351684\pi$
$368$	3.29050	0.171529
$369$	20.6866	1.07690
$370$	8.19638	0.426109
$371$	10.5541	0.547944
$372$	−0.850163	−0.0440789
$373$	−36.9785	−1.91467	−0.957337	−	0.288975i	$-0.906686\pi$
$373$	−36.9785	−1.91467	−0.957337	+	0.288975i	$0.906686\pi$
$374$	0.787138	0.0407019
$375$	9.07161	0.468456
$376$	13.2850	0.685120
$377$	13.0726	0.673273
$378$	−12.7419	−0.655374
$379$	1.44901	0.0744308	0.0372154	−	0.999307i	$-0.488151\pi$
$379$	1.44901	0.0744308	0.0372154	+	0.999307i	$0.488151\pi$
$380$	−10.2479	−0.525704
$381$	−11.9865	−0.614088
$382$	−10.6923	−0.547064
$383$	−23.3116	−1.19117	−0.595583	−	0.803293i	$-0.703079\pi$
$383$	−23.3116	−1.19117	−0.595583	+	0.803293i	$0.703079\pi$
$384$	−0.850163	−0.0433847
$385$	1.03188	0.0525897
$386$	−2.34312	−0.119261
$387$	−24.1198	−1.22608
$388$	1.00000	0.0507673
$389$	1.58552	0.0803889	0.0401945	−	0.999192i	$-0.487202\pi$
$389$	1.58552	0.0803889	0.0401945	+	0.999192i	$0.487202\pi$
$390$	−3.36964	−0.170628
$391$	−9.07951	−0.459170
$392$	1.06594	0.0538381
$393$	−14.0321	−0.707828
$394$	5.50225	0.277200
$395$	−11.8959	−0.598546
$396$	0.649616	0.0326444
$397$	−25.7466	−1.29218	−0.646091	−	0.763260i	$-0.723597\pi$
$397$	−25.7466	−1.29218	−0.646091	+	0.763260i	$0.723597\pi$
$398$	−11.4306	−0.572965
$399$	−19.4272	−0.972576
$400$	−3.37780	−0.168890
$401$	33.6513	1.68047	0.840233	−	0.542226i	$-0.182418\pi$
$401$	33.6513	1.68047	0.840233	+	0.542226i	$0.182418\pi$
$402$	−7.80779	−0.389417
$403$	3.11192	0.155016
$404$	−12.5142	−0.622605
$405$	3.84316	0.190968
$406$	−11.9306	−0.592104
$407$	−1.83578	−0.0909962
$408$	2.34586	0.116137
$409$	−3.76337	−0.186087	−0.0930434	−	0.995662i	$-0.529660\pi$
$409$	−3.76337	−0.186087	−0.0930434	+	0.995662i	$0.529660\pi$
$410$	−11.5700	−0.571404
$411$	−8.38899	−0.413798
$412$	10.7196	0.528114
$413$	−1.66909	−0.0821307
$414$	−7.49321	−0.368271
$415$	9.39955	0.461406
$416$	3.11192	0.152574
$417$	10.9158	0.534550
$418$	2.29526	0.112265
$419$	−32.6854	−1.59679	−0.798394	−	0.602136i	$-0.794317\pi$
$419$	−32.6854	−1.59679	−0.798394	+	0.602136i	$0.794317\pi$
$420$	3.07526	0.150057
$421$	31.0940	1.51543	0.757714	−	0.652587i	$-0.226316\pi$
$421$	31.0940	1.51543	0.757714	+	0.652587i	$0.226316\pi$
$422$	−16.3799	−0.797359
$423$	−30.2529	−1.47094
$424$	−3.71617	−0.180473
$425$	9.32037	0.452104
$426$	−2.15534	−0.104426
$427$	−25.7767	−1.24742
$428$	2.56713	0.124087
$429$	0.754712	0.0364378
$430$	13.4903	0.650559
$431$	−35.6430	−1.71686	−0.858431	−	0.512930i	$-0.828560\pi$
$431$	−35.6430	−1.71686	−0.858431	+	0.512930i	$0.828560\pi$
$432$	4.48650	0.215857
$433$	14.5015	0.696895	0.348448	−	0.937328i	$-0.386709\pi$
$433$	14.5015	0.696895	0.348448	+	0.937328i	$0.386709\pi$
$434$	−2.84006	−0.136327
$435$	−4.54871	−0.218094
$436$	−11.0426	−0.528846
$437$	−26.4754	−1.26649
$438$	−6.96237	−0.332675
$439$	21.2910	1.01617	0.508083	−	0.861308i	$-0.330354\pi$
$439$	21.2910	1.01617	0.508083	+	0.861308i	$0.330354\pi$
$440$	−0.363332	−0.0173212
$441$	−2.42738	−0.115590
$442$	−8.58673	−0.408429
$443$	3.39711	0.161402	0.0807008	−	0.996738i	$-0.474284\pi$
$443$	3.39711	0.161402	0.0807008	+	0.996738i	$0.474284\pi$
$444$	−5.47106	−0.259645
$445$	7.29766	0.345942
$446$	−8.46130	−0.400654
$447$	13.0660	0.617999
$448$	−2.84006	−0.134180
$449$	29.3897	1.38698	0.693492	−	0.720465i	$-0.256071\pi$
$449$	29.3897	1.38698	0.693492	+	0.720465i	$0.256071\pi$
$450$	7.69200	0.362604
$451$	2.59139	0.122024
$452$	7.60187	0.357562
$453$	−11.5297	−0.541714
$454$	20.5570	0.964787
$455$	−11.2566	−0.527719
$456$	6.84042	0.320332
$457$	37.5311	1.75563	0.877816	−	0.478997i	$-0.159000\pi$
$457$	37.5311	1.75563	0.877816	+	0.478997i	$0.159000\pi$
$458$	−12.1734	−0.568825
$459$	−12.3796	−0.577831
$460$	4.19098	0.195405
$461$	−39.3023	−1.83049	−0.915246	−	0.402896i	$-0.868003\pi$
$461$	−39.3023	−1.83049	−0.915246	+	0.402896i	$0.868003\pi$
$462$	−0.688780	−0.0320449
$463$	18.0626	0.839438	0.419719	−	0.907654i	$-0.362129\pi$
$463$	18.0626	0.839438	0.419719	+	0.907654i	$0.362129\pi$
$464$	4.20082	0.195018
$465$	−1.08282	−0.0502144
$466$	11.5419	0.534669
$467$	13.2091	0.611242	0.305621	−	0.952153i	$-0.401136\pi$
$467$	13.2091	0.611242	0.305621	+	0.952153i	$0.401136\pi$
$468$	−7.08654	−0.327575
$469$	−26.0828	−1.20439
$470$	16.9205	0.780485
$471$	−7.17787	−0.330739
$472$	0.587696	0.0270509
$473$	−3.02148	−0.138928
$474$	7.94045	0.364717
$475$	27.1778	1.24700
$476$	7.83659	0.359190
$477$	8.46255	0.387474
$478$	18.3786	0.840616
$479$	−0.506016	−0.0231205	−0.0115602	−	0.999933i	$-0.503680\pi$
$479$	−0.506016	−0.0231205	−0.0115602	+	0.999933i	$0.503680\pi$
$480$	−1.08282	−0.0494236
$481$	20.0262	0.913114
$482$	13.9035	0.633289
$483$	7.94496	0.361508
$484$	−10.9186	−0.496301
$485$	1.27366	0.0578338
$486$	−16.0248	−0.726899
$487$	−42.5298	−1.92721	−0.963604	−	0.267335i	$-0.913857\pi$
$487$	−42.5298	−1.92721	−0.963604	+	0.267335i	$0.913857\pi$
$488$	9.07611	0.410856
$489$	13.1506	0.594692
$490$	1.35764	0.0613321
$491$	−30.0260	−1.35506	−0.677528	−	0.735497i	$-0.736949\pi$
$491$	−30.0260	−1.35506	−0.677528	+	0.735497i	$0.736949\pi$
$492$	7.72297	0.348178
$493$	−11.5913	−0.522047
$494$	−25.0385	−1.12654
$495$	0.827388	0.0371883
$496$	1.00000	0.0449013
$497$	−7.20013	−0.322970
$498$	−6.27417	−0.281152
$499$	−16.9131	−0.757133	−0.378566	−	0.925574i	$-0.623583\pi$
$499$	−16.9131	−0.757133	−0.378566	+	0.925574i	$0.623583\pi$
$500$	−10.6704	−0.477197
$501$	−17.2884	−0.772388
$502$	19.6297	0.876116
$503$	−14.4736	−0.645348	−0.322674	−	0.946510i	$-0.604582\pi$
$503$	−14.4736	−0.645348	−0.322674	+	0.946510i	$0.604582\pi$
$504$	6.46745	0.288083
$505$	−15.9388	−0.709268
$506$	−0.938671	−0.0417290
$507$	2.81911	0.125201
$508$	14.0991	0.625546
$509$	4.35434	0.193003	0.0965015	−	0.995333i	$-0.469235\pi$
$509$	4.35434	0.193003	0.0965015	+	0.995333i	$0.469235\pi$
$510$	2.98782	0.132303
$511$	−23.2586	−1.02890
$512$	1.00000	0.0441942
$513$	−36.0984	−1.59378
$514$	−11.7029	−0.516191
$515$	13.6530	0.601625
$516$	−9.00472	−0.396411
$517$	−3.78976	−0.166673
$518$	−18.2767	−0.803030
$519$	2.96019	0.129938
$520$	3.96352	0.173812
$521$	34.9842	1.53269	0.766344	−	0.642431i	$-0.222074\pi$
$521$	34.9842	1.53269	0.766344	+	0.642431i	$0.222074\pi$
$522$	−9.56620	−0.418701
$523$	−41.1249	−1.79827	−0.899133	−	0.437676i	$-0.855802\pi$
$523$	−41.1249	−1.79827	−0.899133	+	0.437676i	$0.855802\pi$
$524$	16.5052	0.721035
$525$	−8.15573	−0.355945
$526$	−21.2053	−0.924594
$527$	−2.75931	−0.120197
$528$	0.242523	0.0105545
$529$	−12.1726	−0.529243
$530$	−4.73313	−0.205594
$531$	−1.33832	−0.0580780
$532$	22.8512	0.990723
$533$	−28.2690	−1.22447
$534$	−4.87117	−0.210796
$535$	3.26965	0.141359
$536$	9.18388	0.396683
$537$	−13.9485	−0.601922
$538$	14.4723	0.623947
$539$	−0.304077	−0.0130975
$540$	5.71426	0.245903
$541$	−7.35820	−0.316354	−0.158177	−	0.987411i	$-0.550562\pi$
$541$	−7.35820	−0.316354	−0.158177	+	0.987411i	$0.550562\pi$
$542$	−4.09012	−0.175686
$543$	−18.3274	−0.786505
$544$	−2.75931	−0.118304
$545$	−14.0645	−0.602458
$546$	7.51377	0.321560
$547$	37.2969	1.59470	0.797349	−	0.603518i	$-0.206235\pi$
$547$	37.2969	1.59470	0.797349	+	0.603518i	$0.206235\pi$
$548$	9.86751	0.421519
$549$	−20.6683	−0.882103
$550$	0.963573	0.0410869
$551$	−33.7998	−1.43992
$552$	−2.79746	−0.119068
$553$	26.5259	1.12800
$554$	−10.3926	−0.441538
$555$	−6.96825	−0.295786
$556$	−12.8397	−0.544524
$557$	32.6944	1.38531	0.692653	−	0.721271i	$-0.256442\pi$
$557$	32.6944	1.38531	0.692653	+	0.721271i	$0.256442\pi$
$558$	−2.27722	−0.0964026
$559$	32.9607	1.39409
$560$	−3.61726	−0.152857
$561$	−0.669195	−0.0282534
$562$	−2.03581	−0.0858757
$563$	−24.6301	−1.03804	−0.519018	−	0.854763i	$-0.673702\pi$
$563$	−24.6301	−1.03804	−0.519018	+	0.854763i	$0.673702\pi$
$564$	−11.2944	−0.475579
$565$	9.68217	0.407332
$566$	16.0274	0.673682
$567$	−8.56965	−0.359892
$568$	2.53520	0.106375
$569$	−28.1264	−1.17912	−0.589560	−	0.807725i	$-0.700699\pi$
$569$	−28.1264	−1.17912	−0.589560	+	0.807725i	$0.700699\pi$
$570$	8.71235	0.364920
$571$	22.8348	0.955609	0.477804	−	0.878466i	$-0.341433\pi$
$571$	22.8348	0.955609	0.477804	+	0.878466i	$0.341433\pi$
$572$	−0.887727	−0.0371177
$573$	9.09016	0.379747
$574$	25.7994	1.07685
$575$	−11.1147	−0.463513
$576$	−2.27722	−0.0948843
$577$	21.4463	0.892820	0.446410	−	0.894828i	$-0.352702\pi$
$577$	21.4463	0.892820	0.446410	+	0.894828i	$0.352702\pi$
$578$	−9.38624	−0.390416
$579$	1.99203	0.0827859
$580$	5.35040	0.222163
$581$	−20.9595	−0.869548
$582$	−0.850163	−0.0352404
$583$	1.06010	0.0439048
$584$	8.18946	0.338882
$585$	−9.02582	−0.373172
$586$	3.11891	0.128841
$587$	9.27252	0.382718	0.191359	−	0.981520i	$-0.438711\pi$
$587$	9.27252	0.382718	0.191359	+	0.981520i	$0.438711\pi$
$588$	−0.906223	−0.0373720
$589$	−8.04601	−0.331530
$590$	0.748524	0.0308162
$591$	−4.67781	−0.192419
$592$	6.43531	0.264490
$593$	6.98137	0.286691	0.143345	−	0.989673i	$-0.454214\pi$
$593$	6.98137	0.286691	0.143345	+	0.989673i	$0.454214\pi$
$594$	−1.27985	−0.0525128
$595$	9.98113	0.409187
$596$	−15.3688	−0.629531
$597$	9.71787	0.397726
$598$	10.2398	0.418736
$599$	27.0469	1.10511	0.552554	−	0.833477i	$-0.313653\pi$
$599$	27.0469	1.10511	0.552554	+	0.833477i	$0.313653\pi$
$600$	2.87168	0.117236
$601$	−27.8244	−1.13498	−0.567490	−	0.823380i	$-0.692086\pi$
$601$	−27.8244	−1.13498	−0.567490	+	0.823380i	$0.692086\pi$
$602$	−30.0812	−1.22602
$603$	−20.9137	−0.851673
$604$	13.5618	0.551821
$605$	−13.9066	−0.565383
$606$	10.6391	0.432184
$607$	−28.0783	−1.13966	−0.569832	−	0.821762i	$-0.692992\pi$
$607$	−28.0783	−1.13966	−0.569832	+	0.821762i	$0.692992\pi$
$608$	−8.04601	−0.326309
$609$	10.1429	0.411012
$610$	11.5599	0.468045
$611$	41.3418	1.67251
$612$	6.28356	0.253998
$613$	3.44904	0.139305	0.0696526	−	0.997571i	$-0.477811\pi$
$613$	3.44904	0.139305	0.0696526	+	0.997571i	$0.477811\pi$
$614$	32.6011	1.31567
$615$	9.83642	0.396643
$616$	0.810174	0.0326429
$617$	−31.8916	−1.28391	−0.641954	−	0.766743i	$-0.721876\pi$
$617$	−31.8916	−1.28391	−0.641954	+	0.766743i	$0.721876\pi$
$618$	−9.11336	−0.366593
$619$	6.77441	0.272286	0.136143	−	0.990689i	$-0.456529\pi$
$619$	6.77441	0.272286	0.136143	+	0.990689i	$0.456529\pi$
$620$	1.27366	0.0511513
$621$	14.7628	0.592412
$622$	27.2724	1.09352
$623$	−16.2727	−0.651951
$624$	−2.64564	−0.105910
$625$	3.29849	0.131940
$626$	−18.0179	−0.720140
$627$	−1.95134	−0.0779292
$628$	8.44294	0.336910
$629$	−17.7570	−0.708017
$630$	8.23732	0.328183
$631$	8.05732	0.320757	0.160378	−	0.987056i	$-0.448729\pi$
$631$	8.05732	0.320757	0.160378	+	0.987056i	$0.448729\pi$
$632$	−9.33992	−0.371522
$633$	13.9255	0.553491
$634$	−29.4486	−1.16955
$635$	17.9574	0.712618
$636$	3.15935	0.125276
$637$	3.31712	0.131429
$638$	−1.19835	−0.0474432
$639$	−5.77323	−0.228385
$640$	1.27366	0.0503457
$641$	30.6290	1.20977	0.604887	−	0.796312i	$-0.293218\pi$
$641$	30.6290	1.20977	0.604887	+	0.796312i	$0.293218\pi$
$642$	−2.18248	−0.0861355
$643$	40.1183	1.58211	0.791057	−	0.611743i	$-0.209531\pi$
$643$	40.1183	1.58211	0.791057	+	0.611743i	$0.209531\pi$
$644$	−9.34523	−0.368254
$645$	−11.4689	−0.451589
$646$	22.2014	0.873503
$647$	29.0665	1.14272	0.571361	−	0.820699i	$-0.306416\pi$
$647$	29.0665	1.14272	0.571361	+	0.820699i	$0.306416\pi$
$648$	3.01742	0.118535
$649$	−0.167650	−0.00658084
$650$	−10.5114	−0.412292
$651$	2.41451	0.0946322
$652$	−15.4684	−0.605788
$653$	38.2366	1.49631	0.748157	−	0.663522i	$-0.230939\pi$
$653$	38.2366	1.49631	0.748157	+	0.663522i	$0.230939\pi$
$654$	9.38803	0.367101
$655$	21.0220	0.821399
$656$	−9.08411	−0.354675
$657$	−18.6492	−0.727576
$658$	−37.7301	−1.47087
$659$	−10.1919	−0.397020	−0.198510	−	0.980099i	$-0.563610\pi$
$659$	−10.1919	−0.397020	−0.198510	+	0.980099i	$0.563610\pi$
$660$	0.308891	0.0120236
$661$	35.9134	1.39687	0.698434	−	0.715674i	$-0.253880\pi$
$661$	35.9134	1.39687	0.698434	+	0.715674i	$0.253880\pi$
$662$	−2.62073	−0.101858
$663$	7.30012	0.283513
$664$	7.37996	0.286398
$665$	29.1046	1.12863
$666$	−14.6546	−0.567856
$667$	13.8228	0.535221
$668$	20.3354	0.786800
$669$	7.19348	0.278116
$670$	11.6971	0.451899
$671$	−2.58911	−0.0999515
$672$	2.41451	0.0931418
$673$	28.3480	1.09274	0.546368	−	0.837545i	$-0.316010\pi$
$673$	28.3480	1.09274	0.546368	+	0.837545i	$0.316010\pi$
$674$	14.5175	0.559193
$675$	−15.1545	−0.583296
$676$	−3.31596	−0.127537
$677$	11.0272	0.423811	0.211905	−	0.977290i	$-0.432033\pi$
$677$	11.0272	0.423811	0.211905	+	0.977290i	$0.432033\pi$
$678$	−6.46282	−0.248203
$679$	−2.84006	−0.108991
$680$	−3.51441	−0.134771
$681$	−17.4768	−0.669712
$682$	−0.285267	−0.0109234
$683$	−31.4967	−1.20519	−0.602594	−	0.798048i	$-0.705866\pi$
$683$	−31.4967	−1.20519	−0.602594	+	0.798048i	$0.705866\pi$
$684$	18.3226	0.700581
$685$	12.5678	0.480192
$686$	16.8531	0.643454
$687$	10.3494	0.394853
$688$	10.5918	0.403807
$689$	−11.5644	−0.440569
$690$	−3.56301	−0.135641
$691$	−45.6022	−1.73479	−0.867395	−	0.497620i	$-0.834207\pi$
$691$	−45.6022	−1.73479	−0.867395	+	0.497620i	$0.834207\pi$
$692$	−3.48192	−0.132363
$693$	−1.84495	−0.0700838
$694$	29.7149	1.12796
$695$	−16.3534	−0.620318
$696$	−3.57138	−0.135373
$697$	25.0658	0.949436
$698$	−0.756445	−0.0286319
$699$	−9.81251	−0.371143
$700$	9.59314	0.362587
$701$	−34.2653	−1.29418	−0.647091	−	0.762413i	$-0.724015\pi$
$701$	−34.2653	−1.29418	−0.647091	+	0.762413i	$0.724015\pi$
$702$	13.9616	0.526947
$703$	−51.7786	−1.95287
$704$	−0.285267	−0.0107514
$705$	−14.3852	−0.541777
$706$	−12.9138	−0.486019
$707$	35.5411	1.33666
$708$	−0.499637	−0.0187775
$709$	19.1970	0.720958	0.360479	−	0.932767i	$-0.382613\pi$
$709$	19.1970	0.720958	0.360479	+	0.932767i	$0.382613\pi$
$710$	3.22898	0.121182
$711$	21.2691	0.797653
$712$	5.72969	0.214729
$713$	3.29050	0.123230
$714$	−6.66238	−0.249333
$715$	−1.13066	−0.0422843
$716$	16.4069	0.613153
$717$	−15.6248	−0.583518
$718$	4.88032	0.182132
$719$	38.2711	1.42727	0.713635	−	0.700518i	$-0.247048\pi$
$719$	38.2711	1.42727	0.713635	+	0.700518i	$0.247048\pi$
$720$	−2.90040	−0.108092
$721$	−30.4442	−1.13380
$722$	45.7383	1.70220
$723$	−11.8203	−0.439600
$724$	21.5576	0.801180
$725$	−14.1895	−0.526985
$726$	9.28260	0.344510
$727$	−34.4427	−1.27741	−0.638704	−	0.769453i	$-0.720529\pi$
$727$	−34.4427	−1.27741	−0.638704	+	0.769453i	$0.720529\pi$
$728$	−8.83804	−0.327559
$729$	4.57142	0.169312
$730$	10.4306	0.386053
$731$	−29.2259	−1.08096
$732$	−7.71617	−0.285198
$733$	−28.1809	−1.04088	−0.520442	−	0.853897i	$-0.674233\pi$
$733$	−28.1809	−1.04088	−0.520442	+	0.853897i	$0.674233\pi$
$734$	17.2135	0.635363
$735$	−1.15422	−0.0425739
$736$	3.29050	0.121290
$737$	−2.61985	−0.0965036
$738$	20.6866	0.761482
$739$	29.0710	1.06939	0.534697	−	0.845044i	$-0.320426\pi$
$739$	29.0710	1.06939	0.534697	+	0.845044i	$0.320426\pi$
$740$	8.19638	0.301305
$741$	21.2868	0.781991
$742$	10.5541	0.387455
$743$	7.49570	0.274991	0.137495	−	0.990502i	$-0.456095\pi$
$743$	7.49570	0.274991	0.137495	+	0.990502i	$0.456095\pi$
$744$	−0.850163	−0.0311685
$745$	−19.5746	−0.717157
$746$	−36.9785	−1.35388
$747$	−16.8058	−0.614893
$748$	0.787138	0.0287806
$749$	−7.29080	−0.266400
$750$	9.07161	0.331248
$751$	−15.6254	−0.570178	−0.285089	−	0.958501i	$-0.592023\pi$
$751$	−15.6254	−0.570178	−0.285089	+	0.958501i	$0.592023\pi$
$752$	13.2850	0.484453
$753$	−16.6884	−0.608160
$754$	13.0726	0.476076
$755$	17.2731	0.628632
$756$	−12.7419	−0.463419
$757$	32.1655	1.16907	0.584537	−	0.811367i	$-0.301276\pi$
$757$	32.1655	1.16907	0.584537	+	0.811367i	$0.301276\pi$
$758$	1.44901	0.0526305
$759$	0.798023	0.0289664
$760$	−10.2479	−0.371729
$761$	18.3620	0.665622	0.332811	−	0.942994i	$-0.392003\pi$
$761$	18.3620	0.665622	0.332811	+	0.942994i	$0.392003\pi$
$762$	−11.9865	−0.434226
$763$	31.3617	1.13537
$764$	−10.6923	−0.386832
$765$	8.00310	0.289353
$766$	−23.3116	−0.842282
$767$	1.82886	0.0660364
$768$	−0.850163	−0.0306776
$769$	12.9552	0.467177	0.233589	−	0.972336i	$-0.424953\pi$
$769$	12.9552	0.467177	0.233589	+	0.972336i	$0.424953\pi$
$770$	1.03188	0.0371865
$771$	9.94934	0.358317
$772$	−2.34312	−0.0843306
$773$	−0.273436	−0.00983480	−0.00491740	−	0.999988i	$-0.501565\pi$
$773$	−0.273436	−0.00983480	−0.00491740	+	0.999988i	$0.501565\pi$
$774$	−24.1198	−0.866969
$775$	−3.37780	−0.121334
$776$	1.00000	0.0358979
$777$	15.5381	0.557427
$778$	1.58552	0.0568436
$779$	73.0909	2.61875
$780$	−3.36964	−0.120652
$781$	−0.723209	−0.0258785
$782$	−9.07951	−0.324682
$783$	18.8470	0.673535
$784$	1.06594	0.0380693
$785$	10.7534	0.383806
$786$	−14.0321	−0.500510
$787$	−51.8696	−1.84895	−0.924476	−	0.381239i	$-0.875497\pi$
$787$	−51.8696	−1.84895	−0.924476	+	0.381239i	$0.875497\pi$
$788$	5.50225	0.196010
$789$	18.0279	0.641811
$790$	−11.8959	−0.423236
$791$	−21.5898	−0.767643
$792$	0.649616	0.0230831
$793$	28.2441	1.00298
$794$	−25.7466	−0.913711
$795$	4.02393	0.142714
$796$	−11.4306	−0.405147
$797$	−17.3411	−0.614252	−0.307126	−	0.951669i	$-0.599367\pi$
$797$	−17.3411	−0.614252	−0.307126	+	0.951669i	$0.599367\pi$
$798$	−19.4272	−0.687715
$799$	−36.6573	−1.29684
$800$	−3.37780	−0.119423
$801$	−13.0478	−0.461021
$802$	33.6513	1.18827
$803$	−2.33618	−0.0824420
$804$	−7.80779	−0.275359
$805$	−11.9026	−0.419512
$806$	3.11192	0.109613
$807$	−12.3038	−0.433116
$808$	−12.5142	−0.440248
$809$	19.4449	0.683645	0.341823	−	0.939765i	$-0.388956\pi$
$809$	19.4449	0.683645	0.341823	+	0.939765i	$0.388956\pi$
$810$	3.84316	0.135035
$811$	10.0190	0.351814	0.175907	−	0.984407i	$-0.443714\pi$
$811$	10.0190	0.351814	0.175907	+	0.984407i	$0.443714\pi$
$812$	−11.9306	−0.418681
$813$	3.47727	0.121953
$814$	−1.83578	−0.0643440
$815$	−19.7014	−0.690110
$816$	2.34586	0.0821214
$817$	−85.2214	−2.98152
$818$	−3.76337	−0.131583
$819$	20.1262	0.703266
$820$	−11.5700	−0.404043
$821$	−0.135351	−0.00472378	−0.00236189	−	0.999997i	$-0.500752\pi$
$821$	−0.135351	−0.00472378	−0.00236189	+	0.999997i	$0.500752\pi$
$822$	−8.38899	−0.292600
$823$	−3.21163	−0.111950	−0.0559751	−	0.998432i	$-0.517827\pi$
$823$	−3.21163	−0.111950	−0.0559751	+	0.998432i	$0.517827\pi$
$824$	10.7196	0.373433
$825$	−0.819193	−0.0285207
$826$	−1.66909	−0.0580752
$827$	−37.7420	−1.31242	−0.656209	−	0.754579i	$-0.727841\pi$
$827$	−37.7420	−1.31242	−0.656209	+	0.754579i	$0.727841\pi$
$828$	−7.49321	−0.260407
$829$	−32.8920	−1.14239	−0.571193	−	0.820816i	$-0.693519\pi$
$829$	−32.8920	−1.14239	−0.571193	+	0.820816i	$0.693519\pi$
$830$	9.39955	0.326263
$831$	8.83538	0.306496
$832$	3.11192	0.107886
$833$	−2.94125	−0.101908
$834$	10.9158	0.377984
$835$	25.9003	0.896317
$836$	2.29526	0.0793832
$837$	4.48650	0.155076
$838$	−32.6854	−1.12910
$839$	33.9577	1.17235	0.586174	−	0.810185i	$-0.300633\pi$
$839$	33.9577	1.17235	0.586174	+	0.810185i	$0.300633\pi$
$840$	3.07526	0.106107
$841$	−11.3531	−0.391488
$842$	31.0940	1.07157
$843$	1.73077	0.0596110
$844$	−16.3799	−0.563818
$845$	−4.22340	−0.145289
$846$	−30.2529	−1.04011
$847$	31.0095	1.06550
$848$	−3.71617	−0.127614
$849$	−13.6259	−0.467640
$850$	9.32037	0.319686
$851$	21.1754	0.725884
$852$	−2.15534	−0.0738406
$853$	22.1523	0.758481	0.379240	−	0.925298i	$-0.376185\pi$
$853$	22.1523	0.758481	0.379240	+	0.925298i	$0.376185\pi$
$854$	−25.7767	−0.882060
$855$	23.3367	0.798098
$856$	2.56713	0.0877427
$857$	10.1009	0.345040	0.172520	−	0.985006i	$-0.444809\pi$
$857$	10.1009	0.345040	0.172520	+	0.985006i	$0.444809\pi$
$858$	0.754712	0.0257654
$859$	−19.3831	−0.661343	−0.330672	−	0.943746i	$-0.607275\pi$
$859$	−19.3831	−0.661343	−0.330672	+	0.943746i	$0.607275\pi$
$860$	13.4903	0.460015
$861$	−21.9337	−0.747498
$862$	−35.6430	−1.21400
$863$	−35.1763	−1.19742	−0.598708	−	0.800967i	$-0.704319\pi$
$863$	−35.1763	−1.19742	−0.598708	+	0.800967i	$0.704319\pi$
$864$	4.48650	0.152634
$865$	−4.43477	−0.150787
$866$	14.5015	0.492779
$867$	7.97983	0.271009
$868$	−2.84006	−0.0963979
$869$	2.66437	0.0903825
$870$	−4.54871	−0.154216
$871$	28.5795	0.968379
$872$	−11.0426	−0.373951
$873$	−2.27722	−0.0770723
$874$	−26.4754	−0.895545
$875$	30.3047	1.02449
$876$	−6.96237	−0.235237
$877$	3.73461	0.126109	0.0630544	−	0.998010i	$-0.479916\pi$
$877$	3.73461	0.126109	0.0630544	+	0.998010i	$0.479916\pi$
$878$	21.2910	0.718537
$879$	−2.65158	−0.0894357
$880$	−0.363332	−0.0122479
$881$	−23.9288	−0.806183	−0.403092	−	0.915160i	$-0.632064\pi$
$881$	−23.9288	−0.806183	−0.403092	+	0.915160i	$0.632064\pi$
$882$	−2.42738	−0.0817343
$883$	16.9983	0.572038	0.286019	−	0.958224i	$-0.407668\pi$
$883$	16.9983	0.572038	0.286019	+	0.958224i	$0.407668\pi$
$884$	−8.58673	−0.288803
$885$	−0.636367	−0.0213912
$886$	3.39711	0.114128
$887$	48.4195	1.62577	0.812884	−	0.582425i	$-0.197896\pi$
$887$	48.4195	1.62577	0.812884	+	0.582425i	$0.197896\pi$
$888$	−5.47106	−0.183597
$889$	−40.0423	−1.34297
$890$	7.29766	0.244618
$891$	−0.860769	−0.0288368
$892$	−8.46130	−0.283305
$893$	−106.891	−3.57697
$894$	13.0660	0.436992
$895$	20.8967	0.698500
$896$	−2.84006	−0.0948797
$897$	−8.70548	−0.290667
$898$	29.3897	0.980745
$899$	4.20082	0.140105
$900$	7.69200	0.256400
$901$	10.2541	0.341612
$902$	2.59139	0.0862840
$903$	25.5739	0.851047
$904$	7.60187	0.252834
$905$	27.4569	0.912699
$906$	−11.5297	−0.383049
$907$	0.967487	0.0321249	0.0160624	−	0.999871i	$-0.494887\pi$
$907$	0.967487	0.0321249	0.0160624	+	0.999871i	$0.494887\pi$
$908$	20.5570	0.682207
$909$	28.4977	0.945208
$910$	−11.2566	−0.373154
$911$	−13.3176	−0.441232	−0.220616	−	0.975361i	$-0.570807\pi$
$911$	−13.3176	−0.441232	−0.220616	+	0.975361i	$0.570807\pi$
$912$	6.84042	0.226509
$913$	−2.10526	−0.0696739
$914$	37.5311	1.24142
$915$	−9.82775	−0.324895
$916$	−12.1734	−0.402220
$917$	−46.8759	−1.54798
$918$	−12.3796	−0.408588
$919$	−0.338784	−0.0111754	−0.00558772	−	0.999984i	$-0.501779\pi$
$919$	−0.338784	−0.0111754	−0.00558772	+	0.999984i	$0.501779\pi$
$920$	4.19098	0.138172
$921$	−27.7163	−0.913282
$922$	−39.3023	−1.29435
$923$	7.88935	0.259681
$924$	−0.688780	−0.0226592
$925$	−21.7372	−0.714713
$926$	18.0626	0.593573
$927$	−24.4108	−0.801756
$928$	4.20082	0.137899
$929$	15.3261	0.502832	0.251416	−	0.967879i	$-0.419104\pi$
$929$	15.3261	0.502832	0.251416	+	0.967879i	$0.419104\pi$
$930$	−1.08282	−0.0355069
$931$	−8.57657	−0.281086
$932$	11.5419	0.378068
$933$	−23.1859	−0.759074
$934$	13.2091	0.432214
$935$	1.00254	0.0327867
$936$	−7.08654	−0.231631
$937$	−13.8535	−0.452576	−0.226288	−	0.974060i	$-0.572659\pi$
$937$	−13.8535	−0.452576	−0.226288	+	0.974060i	$0.572659\pi$
$938$	−26.0828	−0.851632
$939$	15.3181	0.499889
$940$	16.9205	0.551886
$941$	−38.2839	−1.24802	−0.624010	−	0.781417i	$-0.714497\pi$
$941$	−38.2839	−1.24802	−0.624010	+	0.781417i	$0.714497\pi$
$942$	−7.17787	−0.233868
$943$	−29.8913	−0.973395
$944$	0.587696	0.0191279
$945$	−16.2288	−0.527924
$946$	−3.02148	−0.0982367
$947$	−18.8340	−0.612024	−0.306012	−	0.952028i	$-0.598995\pi$
$947$	−18.8340	−0.612024	−0.306012	+	0.952028i	$0.598995\pi$
$948$	7.94045	0.257894
$949$	25.4849	0.827276
$950$	27.1778	0.881764
$951$	25.0361	0.811852
$952$	7.83659	0.253985
$953$	−51.2170	−1.65908	−0.829540	−	0.558447i	$-0.811397\pi$
$953$	−51.2170	−1.65908	−0.829540	+	0.558447i	$0.811397\pi$
$954$	8.46255	0.273985
$955$	−13.6183	−0.440677
$956$	18.3786	0.594405
$957$	1.01879	0.0329330
$958$	−0.506016	−0.0163486
$959$	−28.0243	−0.904953
$960$	−1.08282	−0.0349477
$961$	1.00000	0.0322581
$962$	20.0262	0.645669
$963$	−5.84593	−0.188382
$964$	13.9035	0.447803
$965$	−2.98433	−0.0960689
$966$	7.94496	0.255625
$967$	17.5219	0.563467	0.281733	−	0.959493i	$-0.409091\pi$
$967$	17.5219	0.563467	0.281733	+	0.959493i	$0.409091\pi$
$968$	−10.9186	−0.350938
$969$	−18.8748	−0.606346
$970$	1.27366	0.0408947
$971$	6.16075	0.197708	0.0988540	−	0.995102i	$-0.468482\pi$
$971$	6.16075	0.197708	0.0988540	+	0.995102i	$0.468482\pi$
$972$	−16.0248	−0.513995
$973$	36.4654	1.16903
$974$	−42.5298	−1.36274
$975$	8.93642	0.286195
$976$	9.07611	0.290519
$977$	29.6219	0.947688	0.473844	−	0.880609i	$-0.342866\pi$
$977$	29.6219	0.947688	0.473844	+	0.880609i	$0.342866\pi$
$978$	13.1506	0.420511
$979$	−1.63449	−0.0522385
$980$	1.35764	0.0433683
$981$	25.1465	0.802867
$982$	−30.0260	−0.958169
$983$	49.7424	1.58654	0.793268	−	0.608873i	$-0.208378\pi$
$983$	49.7424	1.58654	0.793268	+	0.608873i	$0.208378\pi$
$984$	7.72297	0.246199
$985$	7.00799	0.223293
$986$	−11.5913	−0.369143
$987$	32.0767	1.02101
$988$	−25.0385	−0.796582
$989$	34.8522	1.10824
$990$	0.827388	0.0262961
$991$	−45.2152	−1.43631	−0.718154	−	0.695884i	$-0.755013\pi$
$991$	−45.2152	−1.43631	−0.718154	+	0.695884i	$0.755013\pi$
$992$	1.00000	0.0317500
$993$	2.22805	0.0707049
$994$	−7.20013	−0.228374
$995$	−14.5587	−0.461541
$996$	−6.27417	−0.198805
$997$	43.5076	1.37790	0.688949	−	0.724809i	$-0.258072\pi$
$997$	43.5076	1.37790	0.688949	+	0.724809i	$0.258072\pi$
$998$	−16.9131	−0.535374
$999$	28.8720	0.913469

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6014.2.a.k.1.12	✓	37

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6014.2.a.k.1.12	✓	37	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -0.850163 q^{3} +1.00000 q^{4} +1.27366 q^{5} -0.850163 q^{6} -2.84006 q^{7} +1.00000 q^{8} -2.27722 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -0.850163 q^{3} +1.00000 q^{4} +1.27366 q^{5} -0.850163 q^{6} -2.84006 q^{7} +1.00000 q^{8} -2.27722 q^{9} +1.27366 q^{10} -0.285267 q^{11} -0.850163 q^{12} +3.11192 q^{13} -2.84006 q^{14} -1.08282 q^{15} +1.00000 q^{16} -2.75931 q^{17} -2.27722 q^{18} -8.04601 q^{19} +1.27366 q^{20} +2.41451 q^{21} -0.285267 q^{22} +3.29050 q^{23} -0.850163 q^{24} -3.37780 q^{25} +3.11192 q^{26} +4.48650 q^{27} -2.84006 q^{28} +4.20082 q^{29} -1.08282 q^{30} +1.00000 q^{31} +1.00000 q^{32} +0.242523 q^{33} -2.75931 q^{34} -3.61726 q^{35} -2.27722 q^{36} +6.43531 q^{37} -8.04601 q^{38} -2.64564 q^{39} +1.27366 q^{40} -9.08411 q^{41} +2.41451 q^{42} +10.5918 q^{43} -0.285267 q^{44} -2.90040 q^{45} +3.29050 q^{46} +13.2850 q^{47} -0.850163 q^{48} +1.06594 q^{49} -3.37780 q^{50} +2.34586 q^{51} +3.11192 q^{52} -3.71617 q^{53} +4.48650 q^{54} -0.363332 q^{55} -2.84006 q^{56} +6.84042 q^{57} +4.20082 q^{58} +0.587696 q^{59} -1.08282 q^{60} +9.07611 q^{61} +1.00000 q^{62} +6.46745 q^{63} +1.00000 q^{64} +3.96352 q^{65} +0.242523 q^{66} +9.18388 q^{67} -2.75931 q^{68} -2.79746 q^{69} -3.61726 q^{70} +2.53520 q^{71} -2.27722 q^{72} +8.18946 q^{73} +6.43531 q^{74} +2.87168 q^{75} -8.04601 q^{76} +0.810174 q^{77} -2.64564 q^{78} -9.33992 q^{79} +1.27366 q^{80} +3.01742 q^{81} -9.08411 q^{82} +7.37996 q^{83} +2.41451 q^{84} -3.51441 q^{85} +10.5918 q^{86} -3.57138 q^{87} -0.285267 q^{88} +5.72969 q^{89} -2.90040 q^{90} -8.83804 q^{91} +3.29050 q^{92} -0.850163 q^{93} +13.2850 q^{94} -10.2479 q^{95} -0.850163 q^{96} +1.00000 q^{97} +1.06594 q^{98} +0.649616 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 37 q + 37 q^{2} + 9 q^{3} + 37 q^{4} + 9 q^{5} + 9 q^{6} + 19 q^{7} + 37 q^{8} + 52 q^{9}+O(q^{10}) \) 37 * q + 37 * q^2 + 9 * q^3 + 37 * q^4 + 9 * q^5 + 9 * q^6 + 19 * q^7 + 37 * q^8 + 52 * q^9	\( 37 q + 37 q^{2} + 9 q^{3} + 37 q^{4} + 9 q^{5} + 9 q^{6} + 19 q^{7} + 37 q^{8} + 52 q^{9} + 9 q^{10} + 5 q^{11} + 9 q^{12} + 16 q^{13} + 19 q^{14} + 22 q^{15} + 37 q^{16} + 3 q^{17} + 52 q^{18} + 36 q^{19} + 9 q^{20} + 6 q^{21} + 5 q^{22} + 11 q^{23} + 9 q^{24} + 58 q^{25} + 16 q^{26} + 24 q^{27} + 19 q^{28} + 5 q^{29} + 22 q^{30} + 37 q^{31} + 37 q^{32} + q^{33} + 3 q^{34} + 28 q^{35} + 52 q^{36} + 21 q^{37} + 36 q^{38} + 38 q^{39} + 9 q^{40} + 21 q^{41} + 6 q^{42} + 14 q^{43} + 5 q^{44} + 55 q^{45} + 11 q^{46} + 59 q^{47} + 9 q^{48} + 82 q^{49} + 58 q^{50} + 46 q^{51} + 16 q^{52} + 8 q^{53} + 24 q^{54} + 25 q^{55} + 19 q^{56} + 5 q^{58} + 41 q^{59} + 22 q^{60} + 16 q^{61} + 37 q^{62} + 23 q^{63} + 37 q^{64} - 46 q^{65} + q^{66} + 45 q^{67} + 3 q^{68} + 68 q^{69} + 28 q^{70} + 55 q^{71} + 52 q^{72} + 29 q^{73} + 21 q^{74} - 12 q^{75} + 36 q^{76} + 30 q^{77} + 38 q^{78} + 25 q^{79} + 9 q^{80} + 73 q^{81} + 21 q^{82} + 70 q^{83} + 6 q^{84} - 21 q^{85} + 14 q^{86} + 37 q^{87} + 5 q^{88} + 55 q^{90} + 18 q^{91} + 11 q^{92} + 9 q^{93} + 59 q^{94} - 9 q^{95} + 9 q^{96} + 37 q^{97} + 82 q^{98} + 33 q^{99}+O(q^{100}) \) 37 * q + 37 * q^2 + 9 * q^3 + 37 * q^4 + 9 * q^5 + 9 * q^6 + 19 * q^7 + 37 * q^8 + 52 * q^9 + 9 * q^10 + 5 * q^11 + 9 * q^12 + 16 * q^13 + 19 * q^14 + 22 * q^15 + 37 * q^16 + 3 * q^17 + 52 * q^18 + 36 * q^19 + 9 * q^20 + 6 * q^21 + 5 * q^22 + 11 * q^23 + 9 * q^24 + 58 * q^25 + 16 * q^26 + 24 * q^27 + 19 * q^28 + 5 * q^29 + 22 * q^30 + 37 * q^31 + 37 * q^32 + q^33 + 3 * q^34 + 28 * q^35 + 52 * q^36 + 21 * q^37 + 36 * q^38 + 38 * q^39 + 9 * q^40 + 21 * q^41 + 6 * q^42 + 14 * q^43 + 5 * q^44 + 55 * q^45 + 11 * q^46 + 59 * q^47 + 9 * q^48 + 82 * q^49 + 58 * q^50 + 46 * q^51 + 16 * q^52 + 8 * q^53 + 24 * q^54 + 25 * q^55 + 19 * q^56 + 5 * q^58 + 41 * q^59 + 22 * q^60 + 16 * q^61 + 37 * q^62 + 23 * q^63 + 37 * q^64 - 46 * q^65 + q^66 + 45 * q^67 + 3 * q^68 + 68 * q^69 + 28 * q^70 + 55 * q^71 + 52 * q^72 + 29 * q^73 + 21 * q^74 - 12 * q^75 + 36 * q^76 + 30 * q^77 + 38 * q^78 + 25 * q^79 + 9 * q^80 + 73 * q^81 + 21 * q^82 + 70 * q^83 + 6 * q^84 - 21 * q^85 + 14 * q^86 + 37 * q^87 + 5 * q^88 + 55 * q^90 + 18 * q^91 + 11 * q^92 + 9 * q^93 + 59 * q^94 - 9 * q^95 + 9 * q^96 + 37 * q^97 + 82 * q^98 + 33 * q^99

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