LMFDB - Embedded newform 6013.2.a.f.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6013,2,Mod(1,6013)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6013, 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("6013.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6013 = 7 \cdot 859 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6013.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:	$48.0140467354$
Analytic rank:	$0$
Dimension:	$110$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	6013.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.57438 q^{2} +3.21457 q^{3} +4.62742 q^{4} -1.73819 q^{5} -8.27551 q^{6} -1.00000 q^{7} -6.76398 q^{8} +7.33344 q^{9} +O(q^{10})$	\(q-2.57438 q^{2} +3.21457 q^{3} +4.62742 q^{4} -1.73819 q^{5} -8.27551 q^{6} -1.00000 q^{7} -6.76398 q^{8} +7.33344 q^{9} +4.47476 q^{10} +4.02978 q^{11} +14.8752 q^{12} -2.56651 q^{13} +2.57438 q^{14} -5.58753 q^{15} +8.15820 q^{16} +1.98664 q^{17} -18.8791 q^{18} +6.36927 q^{19} -8.04335 q^{20} -3.21457 q^{21} -10.3742 q^{22} +4.85423 q^{23} -21.7433 q^{24} -1.97869 q^{25} +6.60717 q^{26} +13.9302 q^{27} -4.62742 q^{28} -8.33181 q^{29} +14.3844 q^{30} -0.290438 q^{31} -7.47433 q^{32} +12.9540 q^{33} -5.11437 q^{34} +1.73819 q^{35} +33.9350 q^{36} -2.24176 q^{37} -16.3969 q^{38} -8.25023 q^{39} +11.7571 q^{40} -11.7949 q^{41} +8.27551 q^{42} -2.66994 q^{43} +18.6475 q^{44} -12.7469 q^{45} -12.4966 q^{46} +9.56282 q^{47} +26.2251 q^{48} +1.00000 q^{49} +5.09390 q^{50} +6.38620 q^{51} -11.8763 q^{52} +7.84586 q^{53} -35.8615 q^{54} -7.00452 q^{55} +6.76398 q^{56} +20.4744 q^{57} +21.4492 q^{58} +15.1739 q^{59} -25.8559 q^{60} -7.31974 q^{61} +0.747697 q^{62} -7.33344 q^{63} +2.92536 q^{64} +4.46109 q^{65} -33.3485 q^{66} +10.8020 q^{67} +9.19304 q^{68} +15.6042 q^{69} -4.47476 q^{70} +2.84907 q^{71} -49.6033 q^{72} +4.71564 q^{73} +5.77113 q^{74} -6.36064 q^{75} +29.4733 q^{76} -4.02978 q^{77} +21.2392 q^{78} +12.1945 q^{79} -14.1805 q^{80} +22.7791 q^{81} +30.3645 q^{82} +9.88940 q^{83} -14.8752 q^{84} -3.45316 q^{85} +6.87342 q^{86} -26.7832 q^{87} -27.2573 q^{88} +4.98849 q^{89} +32.8154 q^{90} +2.56651 q^{91} +22.4626 q^{92} -0.933632 q^{93} -24.6183 q^{94} -11.0710 q^{95} -24.0268 q^{96} -3.46278 q^{97} -2.57438 q^{98} +29.5521 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 110 q + 16 q^{2} + 29 q^{3} + 118 q^{4} + 12 q^{6} - 110 q^{7} + 57 q^{8} + 127 q^{9}+O(q^{10}) $ 110 * q + 16 * q^2 + 29 * q^3 + 118 * q^4 + 12 * q^6 - 110 * q^7 + 57 * q^8 + 127 * q^9	\( 110 q + 16 q^{2} + 29 q^{3} + 118 q^{4} + 12 q^{6} - 110 q^{7} + 57 q^{8} + 127 q^{9} + 3 q^{10} + 52 q^{11} + 62 q^{12} - 9 q^{13} - 16 q^{14} + 39 q^{15} + 146 q^{16} + 11 q^{17} + 60 q^{18} + 14 q^{19} + 18 q^{20} - 29 q^{21} + 32 q^{22} + 73 q^{23} + 24 q^{24} + 132 q^{25} - 7 q^{26} + 116 q^{27} - 118 q^{28} + 35 q^{29} + 18 q^{30} + 36 q^{31} + 140 q^{32} + 42 q^{33} - 7 q^{34} + 180 q^{36} + 49 q^{37} + 45 q^{39} + 6 q^{40} - 14 q^{41} - 12 q^{42} + 58 q^{43} + 92 q^{44} + 17 q^{45} + 27 q^{46} + 87 q^{47} + 98 q^{48} + 110 q^{49} + 91 q^{50} + 42 q^{51} + 16 q^{52} + 95 q^{53} + 41 q^{54} + 8 q^{55} - 57 q^{56} + 61 q^{57} + 46 q^{58} + 114 q^{59} + 81 q^{60} - 47 q^{61} + 31 q^{62} - 127 q^{63} + 199 q^{64} + 62 q^{65} + 21 q^{66} + 95 q^{67} + 60 q^{68} - 39 q^{69} - 3 q^{70} + 131 q^{71} + 186 q^{72} + 31 q^{73} + 23 q^{74} + 121 q^{75} + 14 q^{76} - 52 q^{77} + 110 q^{78} + 9 q^{79} + 61 q^{80} + 194 q^{81} + 45 q^{82} + 73 q^{83} - 62 q^{84} + 59 q^{85} + 72 q^{86} + 64 q^{87} + 100 q^{88} - 17 q^{89} + 11 q^{90} + 9 q^{91} + 192 q^{92} + 85 q^{93} - 11 q^{94} + 108 q^{95} + 68 q^{96} + 32 q^{97} + 16 q^{98} + 160 q^{99}+O(q^{100}) \) 110 * q + 16 * q^2 + 29 * q^3 + 118 * q^4 + 12 * q^6 - 110 * q^7 + 57 * q^8 + 127 * q^9 + 3 * q^10 + 52 * q^11 + 62 * q^12 - 9 * q^13 - 16 * q^14 + 39 * q^15 + 146 * q^16 + 11 * q^17 + 60 * q^18 + 14 * q^19 + 18 * q^20 - 29 * q^21 + 32 * q^22 + 73 * q^23 + 24 * q^24 + 132 * q^25 - 7 * q^26 + 116 * q^27 - 118 * q^28 + 35 * q^29 + 18 * q^30 + 36 * q^31 + 140 * q^32 + 42 * q^33 - 7 * q^34 + 180 * q^36 + 49 * q^37 + 45 * q^39 + 6 * q^40 - 14 * q^41 - 12 * q^42 + 58 * q^43 + 92 * q^44 + 17 * q^45 + 27 * q^46 + 87 * q^47 + 98 * q^48 + 110 * q^49 + 91 * q^50 + 42 * q^51 + 16 * q^52 + 95 * q^53 + 41 * q^54 + 8 * q^55 - 57 * q^56 + 61 * q^57 + 46 * q^58 + 114 * q^59 + 81 * q^60 - 47 * q^61 + 31 * q^62 - 127 * q^63 + 199 * q^64 + 62 * q^65 + 21 * q^66 + 95 * q^67 + 60 * q^68 - 39 * q^69 - 3 * q^70 + 131 * q^71 + 186 * q^72 + 31 * q^73 + 23 * q^74 + 121 * q^75 + 14 * q^76 - 52 * q^77 + 110 * q^78 + 9 * q^79 + 61 * q^80 + 194 * q^81 + 45 * q^82 + 73 * q^83 - 62 * q^84 + 59 * q^85 + 72 * q^86 + 64 * q^87 + 100 * q^88 - 17 * q^89 + 11 * q^90 + 9 * q^91 + 192 * q^92 + 85 * q^93 - 11 * q^94 + 108 * q^95 + 68 * q^96 + 32 * q^97 + 16 * q^98 + 160 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.57438	−1.82036	−0.910180	−	0.414213i	$-0.864057\pi$
$2$	−2.57438	−1.82036	−0.910180	+	0.414213i	$0.864057\pi$
$3$	3.21457	1.85593	0.927966	−	0.372666i	$-0.121556\pi$
$3$	3.21457	1.85593	0.927966	+	0.372666i	$0.121556\pi$
$4$	4.62742	2.31371
$5$	−1.73819	−0.777343	−0.388671	−	0.921376i	$-0.627066\pi$
$5$	−1.73819	−0.777343	−0.388671	+	0.921376i	$0.627066\pi$
$6$	−8.27551	−3.37846
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−6.76398	−2.39143
$9$	7.33344	2.44448
$10$	4.47476	1.41504
$11$	4.02978	1.21502	0.607512	−	0.794311i	$-0.292168\pi$
$11$	4.02978	1.21502	0.607512	+	0.794311i	$0.292168\pi$
$12$	14.8752	4.29409
$13$	−2.56651	−0.711822	−0.355911	−	0.934520i	$-0.615829\pi$
$13$	−2.56651	−0.711822	−0.355911	+	0.934520i	$0.615829\pi$
$14$	2.57438	0.688032
$15$	−5.58753	−1.44269
$16$	8.15820	2.03955
$17$	1.98664	0.481832	0.240916	−	0.970546i	$-0.422552\pi$
$17$	1.98664	0.481832	0.240916	+	0.970546i	$0.422552\pi$
$18$	−18.8791	−4.44984
$19$	6.36927	1.46121	0.730605	−	0.682800i	$-0.239238\pi$
$19$	6.36927	1.46121	0.730605	+	0.682800i	$0.239238\pi$
$20$	−8.04335	−1.79855
$21$	−3.21457	−0.701476
$22$	−10.3742	−2.21178
$23$	4.85423	1.01218	0.506088	−	0.862482i	$-0.331091\pi$
$23$	4.85423	1.01218	0.506088	+	0.862482i	$0.331091\pi$
$24$	−21.7433	−4.43833
$25$	−1.97869	−0.395738
$26$	6.60717	1.29577
$27$	13.9302	2.68086
$28$	−4.62742	−0.874501
$29$	−8.33181	−1.54718	−0.773589	−	0.633687i	$-0.781541\pi$
$29$	−8.33181	−1.54718	−0.773589	+	0.633687i	$0.781541\pi$
$30$	14.3844	2.62622
$31$	−0.290438	−0.0521642	−0.0260821	−	0.999660i	$-0.508303\pi$
$31$	−0.290438	−0.0521642	−0.0260821	+	0.999660i	$0.508303\pi$
$32$	−7.47433	−1.32129
$33$	12.9540	2.25500
$34$	−5.11437	−0.877107
$35$	1.73819	0.293808
$36$	33.9350	5.65583
$37$	−2.24176	−0.368542	−0.184271	−	0.982875i	$-0.558992\pi$
$37$	−2.24176	−0.368542	−0.184271	+	0.982875i	$0.558992\pi$
$38$	−16.3969	−2.65993
$39$	−8.25023	−1.32109
$40$	11.7571	1.85896
$41$	−11.7949	−1.84205	−0.921027	−	0.389499i	$-0.872648\pi$
$41$	−11.7949	−1.84205	−0.921027	+	0.389499i	$0.872648\pi$
$42$	8.27551	1.27694
$43$	−2.66994	−0.407161	−0.203581	−	0.979058i	$-0.565258\pi$
$43$	−2.66994	−0.407161	−0.203581	+	0.979058i	$0.565258\pi$
$44$	18.6475	2.81121
$45$	−12.7469	−1.90020
$46$	−12.4966	−1.84253
$47$	9.56282	1.39488	0.697440	−	0.716643i	$-0.254322\pi$
$47$	9.56282	1.39488	0.697440	+	0.716643i	$0.254322\pi$
$48$	26.2251	3.78527
$49$	1.00000	0.142857
$50$	5.09390	0.720386
$51$	6.38620	0.894246
$52$	−11.8763	−1.64695
$53$	7.84586	1.07771	0.538856	−	0.842398i	$-0.318857\pi$
$53$	7.84586	1.07771	0.538856	+	0.842398i	$0.318857\pi$
$54$	−35.8615	−4.88013
$55$	−7.00452	−0.944490
$56$	6.76398	0.903875
$57$	20.4744	2.71191
$58$	21.4492	2.81642
$59$	15.1739	1.97547	0.987736	−	0.156135i	$-0.0499034\pi$
$59$	15.1739	1.97547	0.987736	+	0.156135i	$0.0499034\pi$
$60$	−25.8559	−3.33798
$61$	−7.31974	−0.937196	−0.468598	−	0.883411i	$-0.655241\pi$
$61$	−7.31974	−0.937196	−0.468598	+	0.883411i	$0.655241\pi$
$62$	0.747697	0.0949576
$63$	−7.33344	−0.923927
$64$	2.92536	0.365670
$65$	4.46109	0.553330
$66$	−33.3485	−4.10491
$67$	10.8020	1.31967	0.659834	−	0.751411i	$-0.270627\pi$
$67$	10.8020	1.31967	0.659834	+	0.751411i	$0.270627\pi$
$68$	9.19304	1.11482
$69$	15.6042	1.87853
$70$	−4.47476	−0.534836
$71$	2.84907	0.338122	0.169061	−	0.985606i	$-0.445927\pi$
$71$	2.84907	0.338122	0.169061	+	0.985606i	$0.445927\pi$
$72$	−49.6033	−5.84580
$73$	4.71564	0.551924	0.275962	−	0.961169i	$-0.411004\pi$
$73$	4.71564	0.551924	0.275962	+	0.961169i	$0.411004\pi$
$74$	5.77113	0.670880
$75$	−6.36064	−0.734463
$76$	29.4733	3.38082
$77$	−4.02978	−0.459236
$78$	21.2392	2.40487
$79$	12.1945	1.37198	0.685991	−	0.727610i	$-0.259369\pi$
$79$	12.1945	1.37198	0.685991	+	0.727610i	$0.259369\pi$
$80$	−14.1805	−1.58543
$81$	22.7791	2.53101
$82$	30.3645	3.35320
$83$	9.88940	1.08550	0.542751	−	0.839893i	$-0.317383\pi$
$83$	9.88940	1.08550	0.542751	+	0.839893i	$0.317383\pi$
$84$	−14.8752	−1.62301
$85$	−3.45316	−0.374548
$86$	6.87342	0.741180
$87$	−26.7832	−2.87146
$88$	−27.2573	−2.90564
$89$	4.98849	0.528778	0.264389	−	0.964416i	$-0.414830\pi$
$89$	4.98849	0.528778	0.264389	+	0.964416i	$0.414830\pi$
$90$	32.8154	3.45905
$91$	2.56651	0.269044
$92$	22.4626	2.34188
$93$	−0.933632	−0.0968132
$94$	−24.6183	−2.53919
$95$	−11.0710	−1.13586
$96$	−24.0268	−2.45222
$97$	−3.46278	−0.351593	−0.175796	−	0.984427i	$-0.556250\pi$
$97$	−3.46278	−0.351593	−0.175796	+	0.984427i	$0.556250\pi$
$98$	−2.57438	−0.260051
$99$	29.5521	2.97010
$100$	−9.15624	−0.915624
$101$	−15.6467	−1.55690	−0.778451	−	0.627705i	$-0.783994\pi$
$101$	−15.6467	−1.55690	−0.778451	+	0.627705i	$0.783994\pi$
$102$	−16.4405	−1.62785
$103$	−9.46942	−0.933050	−0.466525	−	0.884508i	$-0.654494\pi$
$103$	−9.46942	−0.933050	−0.466525	+	0.884508i	$0.654494\pi$
$104$	17.3598	1.70227
$105$	5.58753	0.545287
$106$	−20.1982	−1.96182
$107$	−12.2241	−1.18175	−0.590874	−	0.806764i	$-0.701217\pi$
$107$	−12.2241	−1.18175	−0.590874	+	0.806764i	$0.701217\pi$
$108$	64.4607	6.20274
$109$	16.0887	1.54102	0.770508	−	0.637431i	$-0.220003\pi$
$109$	16.0887	1.54102	0.770508	+	0.637431i	$0.220003\pi$
$110$	18.0323	1.71931
$111$	−7.20627	−0.683989
$112$	−8.15820	−0.770878
$113$	17.9465	1.68826	0.844130	−	0.536138i	$-0.180117\pi$
$113$	17.9465	1.68826	0.844130	+	0.536138i	$0.180117\pi$
$114$	−52.7090	−4.93665
$115$	−8.43758	−0.786808
$116$	−38.5548	−3.57973
$117$	−18.8214	−1.74004
$118$	−39.0633	−3.59607
$119$	−1.98664	−0.182115
$120$	37.7940	3.45010
$121$	5.23910	0.476282
$122$	18.8438	1.70603
$123$	−37.9155	−3.41873
$124$	−1.34398	−0.120693
$125$	12.1303	1.08497
$126$	18.8791	1.68188
$127$	−13.8644	−1.23027	−0.615135	−	0.788422i	$-0.710898\pi$
$127$	−13.8644	−1.23027	−0.615135	+	0.788422i	$0.710898\pi$
$128$	7.41769	0.655637
$129$	−8.58269	−0.755663
$130$	−11.4845	−1.00726
$131$	4.53883	0.396560	0.198280	−	0.980145i	$-0.436465\pi$
$131$	4.53883	0.396560	0.198280	+	0.980145i	$0.436465\pi$
$132$	59.9436	5.21742
$133$	−6.36927	−0.552286
$134$	−27.8083	−2.40227
$135$	−24.2133	−2.08395
$136$	−13.4376	−1.15227
$137$	−4.19823	−0.358679	−0.179339	−	0.983787i	$-0.557396\pi$
$137$	−4.19823	−0.358679	−0.179339	+	0.983787i	$0.557396\pi$
$138$	−40.1712	−3.41960
$139$	−0.00981907	−0.000832842 0	−0.000416421	−	1.00000i	$-0.500133\pi$
$139$	−0.00981907	−0.000832842 0	−0.000416421		1.00000i	$0.500133\pi$
$140$	8.04335	0.679787
$141$	30.7403	2.58880
$142$	−7.33457	−0.615504
$143$	−10.3425	−0.864881
$144$	59.8277	4.98564
$145$	14.4823	1.20269
$146$	−12.1398	−1.00470
$147$	3.21457	0.265133
$148$	−10.3736	−0.852701
$149$	7.74364	0.634384	0.317192	−	0.948361i	$-0.397260\pi$
$149$	7.74364	0.634384	0.317192	+	0.948361i	$0.397260\pi$
$150$	16.3747	1.33699
$151$	−10.7071	−0.871333	−0.435667	−	0.900108i	$-0.643487\pi$
$151$	−10.7071	−0.871333	−0.435667	+	0.900108i	$0.643487\pi$
$152$	−43.0816	−3.49438
$153$	14.5689	1.17783
$154$	10.3742	0.835974
$155$	0.504837	0.0405495
$156$	−38.1773	−3.05663
$157$	−1.93604	−0.154513	−0.0772566	−	0.997011i	$-0.524616\pi$
$157$	−1.93604	−0.154513	−0.0772566	+	0.997011i	$0.524616\pi$
$158$	−31.3931	−2.49750
$159$	25.2211	2.00016
$160$	12.9918	1.02709
$161$	−4.85423	−0.382567
$162$	−58.6420	−4.60735
$163$	−25.1469	−1.96966	−0.984829	−	0.173526i	$-0.944484\pi$
$163$	−25.1469	−1.96966	−0.984829	+	0.173526i	$0.944484\pi$
$164$	−54.5800	−4.26198
$165$	−22.5165	−1.75291
$166$	−25.4591	−1.97601
$167$	−3.57232	−0.276434	−0.138217	−	0.990402i	$-0.544137\pi$
$167$	−3.57232	−0.276434	−0.138217	+	0.990402i	$0.544137\pi$
$168$	21.7433	1.67753
$169$	−6.41301	−0.493309
$170$	8.88975	0.681813
$171$	46.7087	3.57190
$172$	−12.3549	−0.942054
$173$	11.5546	0.878479	0.439239	−	0.898370i	$-0.355248\pi$
$173$	11.5546	0.878479	0.439239	+	0.898370i	$0.355248\pi$
$174$	68.9500	5.22709
$175$	1.97869	0.149575
$176$	32.8757	2.47810
$177$	48.7775	3.66634
$178$	−12.8422	−0.962567
$179$	8.32742	0.622420	0.311210	−	0.950341i	$-0.399266\pi$
$179$	8.32742	0.622420	0.311210	+	0.950341i	$0.399266\pi$
$180$	−58.9854	−4.39652
$181$	−6.81007	−0.506188	−0.253094	−	0.967442i	$-0.581448\pi$
$181$	−6.81007	−0.506188	−0.253094	+	0.967442i	$0.581448\pi$
$182$	−6.60717	−0.489756
$183$	−23.5298	−1.73937
$184$	−32.8339	−2.42055
$185$	3.89660	0.286484
$186$	2.40352	0.176235
$187$	8.00573	0.585437
$188$	44.2512	3.22735
$189$	−13.9302	−1.01327
$190$	28.5010	2.06768
$191$	−4.11712	−0.297904	−0.148952	−	0.988844i	$-0.547590\pi$
$191$	−4.11712	−0.297904	−0.148952	+	0.988844i	$0.547590\pi$
$192$	9.40377	0.678659
$193$	14.7359	1.06071	0.530357	−	0.847774i	$-0.322058\pi$
$193$	14.7359	1.06071	0.530357	+	0.847774i	$0.322058\pi$
$194$	8.91452	0.640025
$195$	14.3405	1.02694
$196$	4.62742	0.330530
$197$	−4.45529	−0.317426	−0.158713	−	0.987325i	$-0.550734\pi$
$197$	−4.45529	−0.317426	−0.158713	+	0.987325i	$0.550734\pi$
$198$	−76.0784	−5.40666
$199$	−8.62009	−0.611062	−0.305531	−	0.952182i	$-0.598834\pi$
$199$	−8.62009	−0.611062	−0.305531	+	0.952182i	$0.598834\pi$
$200$	13.3838	0.946380
$201$	34.7236	2.44921
$202$	40.2805	2.83412
$203$	8.33181	0.584779
$204$	29.5516	2.06903
$205$	20.5018	1.43191
$206$	24.3779	1.69849
$207$	35.5982	2.47425
$208$	−20.9381	−1.45180
$209$	25.6667	1.77540
$210$	−14.3844	−0.992620
$211$	−3.03237	−0.208757	−0.104378	−	0.994538i	$-0.533285\pi$
$211$	−3.03237	−0.208757	−0.104378	+	0.994538i	$0.533285\pi$
$212$	36.3061	2.49352
$213$	9.15852	0.627531
$214$	31.4695	2.15121
$215$	4.64086	0.316504
$216$	−94.2233	−6.41108
$217$	0.290438	0.0197162
$218$	−41.4183	−2.80520
$219$	15.1587	1.02433
$220$	−32.4129	−2.18528
$221$	−5.09874	−0.342979
$222$	18.5517	1.24511
$223$	−10.0886	−0.675582	−0.337791	−	0.941221i	$-0.609680\pi$
$223$	−10.0886	−0.675582	−0.337791	+	0.941221i	$0.609680\pi$
$224$	7.47433	0.499400
$225$	−14.5106	−0.967375
$226$	−46.2010	−3.07324
$227$	25.0032	1.65952	0.829761	−	0.558119i	$-0.188477\pi$
$227$	25.0032	1.65952	0.829761	+	0.558119i	$0.188477\pi$
$228$	94.7439	6.27457
$229$	−11.2235	−0.741671	−0.370836	−	0.928698i	$-0.620929\pi$
$229$	−11.2235	−0.741671	−0.370836	+	0.928698i	$0.620929\pi$
$230$	21.7215	1.43227
$231$	−12.9540	−0.852310
$232$	56.3562	3.69997
$233$	−13.3809	−0.876611	−0.438305	−	0.898826i	$-0.644421\pi$
$233$	−13.3809	−0.876611	−0.438305	+	0.898826i	$0.644421\pi$
$234$	48.4533	3.16749
$235$	−16.6220	−1.08430
$236$	70.2160	4.57067
$237$	39.1999	2.54631
$238$	5.11437	0.331515
$239$	21.3836	1.38319	0.691595	−	0.722286i	$-0.256908\pi$
$239$	21.3836	1.38319	0.691595	+	0.722286i	$0.256908\pi$
$240$	−45.5842	−2.94245
$241$	23.7088	1.52722	0.763609	−	0.645679i	$-0.223425\pi$
$241$	23.7088	1.52722	0.763609	+	0.645679i	$0.223425\pi$
$242$	−13.4874	−0.867005
$243$	31.4344	2.01652
$244$	−33.8715	−2.16840
$245$	−1.73819	−0.111049
$246$	97.6089	6.22331
$247$	−16.3468	−1.04012
$248$	1.96452	0.124747
$249$	31.7901	2.01462
$250$	−31.2280	−1.97503
$251$	−20.3373	−1.28368	−0.641840	−	0.766839i	$-0.721829\pi$
$251$	−20.3373	−1.28368	−0.641840	+	0.766839i	$0.721829\pi$
$252$	−33.9350	−2.13770
$253$	19.5615	1.22982
$254$	35.6923	2.23953
$255$	−11.1004	−0.695136
$256$	−24.9466	−1.55917
$257$	27.0592	1.68790	0.843952	−	0.536418i	$-0.180223\pi$
$257$	27.0592	1.68790	0.843952	+	0.536418i	$0.180223\pi$
$258$	22.0951	1.37558
$259$	2.24176	0.139296
$260$	20.6433	1.28025
$261$	−61.1009	−3.78205
$262$	−11.6847	−0.721881
$263$	27.7856	1.71333	0.856666	−	0.515872i	$-0.172532\pi$
$263$	27.7856	1.71333	0.856666	+	0.515872i	$0.172532\pi$
$264$	−87.6206	−5.39267
$265$	−13.6376	−0.837752
$266$	16.3969	1.00536
$267$	16.0358	0.981377
$268$	49.9852	3.05333
$269$	−19.6374	−1.19731	−0.598655	−	0.801007i	$-0.704298\pi$
$269$	−19.6374	−1.19731	−0.598655	+	0.801007i	$0.704298\pi$
$270$	62.3341	3.79353
$271$	17.1530	1.04197	0.520986	−	0.853565i	$-0.325564\pi$
$271$	17.1530	1.04197	0.520986	+	0.853565i	$0.325564\pi$
$272$	16.2074	0.982720
$273$	8.25023	0.499326
$274$	10.8078	0.652925
$275$	−7.97368	−0.480831
$276$	72.2074	4.34638
$277$	17.8168	1.07051	0.535255	−	0.844690i	$-0.320215\pi$
$277$	17.8168	1.07051	0.535255	+	0.844690i	$0.320215\pi$
$278$	0.0252780	0.00151607
$279$	−2.12991	−0.127514
$280$	−11.7571	−0.702621
$281$	−20.6083	−1.22939	−0.614694	−	0.788766i	$-0.710721\pi$
$281$	−20.6083	−1.22939	−0.614694	+	0.788766i	$0.710721\pi$
$282$	−79.1373	−4.71255
$283$	1.33393	0.0792937	0.0396468	−	0.999214i	$-0.487377\pi$
$283$	1.33393	0.0792937	0.0396468	+	0.999214i	$0.487377\pi$
$284$	13.1838	0.782317
$285$	−35.5885	−2.10808
$286$	26.6254	1.57439
$287$	11.7949	0.696231
$288$	−54.8126	−3.22986
$289$	−13.0533	−0.767838
$290$	−37.2829	−2.18933
$291$	−11.1314	−0.652532
$292$	21.8213	1.27699
$293$	20.2408	1.18248	0.591239	−	0.806496i	$-0.298639\pi$
$293$	20.2408	1.18248	0.591239	+	0.806496i	$0.298639\pi$
$294$	−8.27551	−0.482638
$295$	−26.3751	−1.53562
$296$	15.1632	0.881343
$297$	56.1354	3.25731
$298$	−19.9351	−1.15481
$299$	−12.4584	−0.720490
$300$	−29.4334	−1.69934
$301$	2.66994	0.153893
$302$	27.5642	1.58614
$303$	−50.2973	−2.88951
$304$	51.9618	2.98021
$305$	12.7231	0.728523
$306$	−37.5059	−2.14407
$307$	−25.9217	−1.47943	−0.739715	−	0.672920i	$-0.765040\pi$
$307$	−25.9217	−1.47943	−0.739715	+	0.672920i	$0.765040\pi$
$308$	−18.6475	−1.06254
$309$	−30.4401	−1.73168
$310$	−1.29964	−0.0738146
$311$	−24.1670	−1.37039	−0.685193	−	0.728361i	$-0.740282\pi$
$311$	−24.1670	−1.37039	−0.685193	+	0.728361i	$0.740282\pi$
$312$	55.8044	3.15930
$313$	23.9587	1.35422	0.677112	−	0.735880i	$-0.263231\pi$
$313$	23.9587	1.35422	0.677112	+	0.735880i	$0.263231\pi$
$314$	4.98411	0.281270
$315$	12.7469	0.718208
$316$	56.4289	3.17437
$317$	26.3271	1.47868	0.739338	−	0.673335i	$-0.235139\pi$
$317$	26.3271	1.47868	0.739338	+	0.673335i	$0.235139\pi$
$318$	−64.9286	−3.64101
$319$	−33.5753	−1.87986
$320$	−5.08484	−0.284251
$321$	−39.2952	−2.19324
$322$	12.4966	0.696409
$323$	12.6535	0.704057
$324$	105.408	5.85603
$325$	5.07834	0.281695
$326$	64.7377	3.58549
$327$	51.7181	2.86002
$328$	79.7805	4.40514
$329$	−9.56282	−0.527215
$330$	57.9660	3.19092
$331$	14.7868	0.812756	0.406378	−	0.913705i	$-0.366792\pi$
$331$	14.7868	0.812756	0.406378	+	0.913705i	$0.366792\pi$
$332$	45.7624	2.51154
$333$	−16.4398	−0.900895
$334$	9.19649	0.503210
$335$	−18.7759	−1.02583
$336$	−26.2251	−1.43070
$337$	21.1554	1.15241	0.576205	−	0.817305i	$-0.304533\pi$
$337$	21.1554	1.15241	0.576205	+	0.817305i	$0.304533\pi$
$338$	16.5095	0.898000
$339$	57.6901	3.13330
$340$	−15.9793	−0.866597
$341$	−1.17040	−0.0633807
$342$	−120.246	−6.50215
$343$	−1.00000	−0.0539949
$344$	18.0594	0.973697
$345$	−27.1232	−1.46026
$346$	−29.7459	−1.59915
$347$	−13.7533	−0.738316	−0.369158	−	0.929367i	$-0.620354\pi$
$347$	−13.7533	−0.738316	−0.369158	+	0.929367i	$0.620354\pi$
$348$	−123.937	−6.64373
$349$	−5.75361	−0.307984	−0.153992	−	0.988072i	$-0.549213\pi$
$349$	−5.75361	−0.307984	−0.153992	+	0.988072i	$0.549213\pi$
$350$	−5.09390	−0.272280
$351$	−35.7519	−1.90830
$352$	−30.1199	−1.60540
$353$	25.1502	1.33861	0.669306	−	0.742987i	$-0.266592\pi$
$353$	25.1502	1.33861	0.669306	+	0.742987i	$0.266592\pi$
$354$	−125.572	−6.67406
$355$	−4.95222	−0.262837
$356$	23.0838	1.22344
$357$	−6.38620	−0.337993
$358$	−21.4379	−1.13303
$359$	−6.08361	−0.321080	−0.160540	−	0.987029i	$-0.551324\pi$
$359$	−6.08361	−0.321080	−0.160540	+	0.987029i	$0.551324\pi$
$360$	86.2200	4.54419
$361$	21.5676	1.13514
$362$	17.5317	0.921445
$363$	16.8414	0.883946
$364$	11.8763	0.622489
$365$	−8.19668	−0.429034
$366$	60.5746	3.16628
$367$	22.4821	1.17356	0.586779	−	0.809747i	$-0.300396\pi$
$367$	22.4821	1.17356	0.586779	+	0.809747i	$0.300396\pi$
$368$	39.6018	2.06439
$369$	−86.4973	−4.50287
$370$	−10.0313	−0.521504
$371$	−7.84586	−0.407337
$372$	−4.32031	−0.223998
$373$	−21.9133	−1.13463	−0.567315	−	0.823501i	$-0.692018\pi$
$373$	−21.9133	−1.13463	−0.567315	+	0.823501i	$0.692018\pi$
$374$	−20.6098	−1.06571
$375$	38.9937	2.01362
$376$	−64.6828	−3.33576
$377$	21.3837	1.10132
$378$	35.8615	1.84452
$379$	−9.00737	−0.462678	−0.231339	−	0.972873i	$-0.574311\pi$
$379$	−9.00737	−0.462678	−0.231339	+	0.972873i	$0.574311\pi$
$380$	−51.2302	−2.62806
$381$	−44.5681	−2.28330
$382$	10.5990	0.542293
$383$	−10.3994	−0.531383	−0.265692	−	0.964058i	$-0.585600\pi$
$383$	−10.3994	−0.531383	−0.265692	+	0.964058i	$0.585600\pi$
$384$	23.8447	1.21682
$385$	7.00452	0.356984
$386$	−37.9358	−1.93088
$387$	−19.5798	−0.995298
$388$	−16.0238	−0.813484
$389$	4.80683	0.243716	0.121858	−	0.992548i	$-0.461115\pi$
$389$	4.80683	0.243716	0.121858	+	0.992548i	$0.461115\pi$
$390$	−36.9178	−1.86941
$391$	9.64361	0.487699
$392$	−6.76398	−0.341633
$393$	14.5904	0.735987
$394$	11.4696	0.577830
$395$	−21.1963	−1.06650
$396$	136.750	6.87196
$397$	12.1338	0.608976	0.304488	−	0.952516i	$-0.401515\pi$
$397$	12.1338	0.608976	0.304488	+	0.952516i	$0.401515\pi$
$398$	22.1914	1.11235
$399$	−20.4744	−1.02500
$400$	−16.1426	−0.807128
$401$	−2.40562	−0.120131	−0.0600655	−	0.998194i	$-0.519131\pi$
$401$	−2.40562	−0.120131	−0.0600655	+	0.998194i	$0.519131\pi$
$402$	−89.3917	−4.45845
$403$	0.745413	0.0371316
$404$	−72.4038	−3.60222
$405$	−39.5944	−1.96746
$406$	−21.4492	−1.06451
$407$	−9.03377	−0.447788
$408$	−43.1961	−2.13853
$409$	−8.22190	−0.406547	−0.203273	−	0.979122i	$-0.565158\pi$
$409$	−8.22190	−0.406547	−0.203273	+	0.979122i	$0.565158\pi$
$410$	−52.7794	−2.60659
$411$	−13.4955	−0.665683
$412$	−43.8190	−2.15881
$413$	−15.1739	−0.746658
$414$	−91.6433	−4.50402
$415$	−17.1897	−0.843807
$416$	19.1830	0.940523
$417$	−0.0315641	−0.00154570
$418$	−66.0759	−3.23188
$419$	8.16819	0.399042	0.199521	−	0.979894i	$-0.436061\pi$
$419$	8.16819	0.399042	0.199521	+	0.979894i	$0.436061\pi$
$420$	25.8559	1.26164
$421$	34.1675	1.66522	0.832611	−	0.553859i	$-0.186845\pi$
$421$	34.1675	1.66522	0.832611	+	0.553859i	$0.186845\pi$
$422$	7.80647	0.380013
$423$	70.1284	3.40976
$424$	−53.0693	−2.57727
$425$	−3.93095	−0.190679
$426$	−23.5775	−1.14233
$427$	7.31974	0.354227
$428$	−56.5661	−2.73423
$429$	−33.2466	−1.60516
$430$	−11.9473	−0.576151
$431$	21.2300	1.02262	0.511308	−	0.859398i	$-0.329161\pi$
$431$	21.2300	1.02262	0.511308	+	0.859398i	$0.329161\pi$
$432$	113.645	5.46775
$433$	−10.3829	−0.498968	−0.249484	−	0.968379i	$-0.580261\pi$
$433$	−10.3829	−0.498968	−0.249484	+	0.968379i	$0.580261\pi$
$434$	−0.747697	−0.0358906
$435$	46.5543	2.23211
$436$	74.4491	3.56547
$437$	30.9179	1.47900
$438$	−39.0243	−1.86465
$439$	−12.9342	−0.617314	−0.308657	−	0.951173i	$-0.599879\pi$
$439$	−12.9342	−0.617314	−0.308657	+	0.951173i	$0.599879\pi$
$440$	47.3785	2.25868
$441$	7.33344	0.349212
$442$	13.1261	0.624345
$443$	−32.2797	−1.53366	−0.766828	−	0.641852i	$-0.778166\pi$
$443$	−32.2797	−1.53366	−0.766828	+	0.641852i	$0.778166\pi$
$444$	−33.3465	−1.58255
$445$	−8.67094	−0.411042
$446$	25.9718	1.22980
$447$	24.8924	1.17737
$448$	−2.92536	−0.138210
$449$	−16.9626	−0.800514	−0.400257	−	0.916403i	$-0.631079\pi$
$449$	−16.9626	−0.800514	−0.400257	+	0.916403i	$0.631079\pi$
$450$	37.3558	1.76097
$451$	−47.5308	−2.23814
$452$	83.0458	3.90615
$453$	−34.4188	−1.61713
$454$	−64.3677	−3.02093
$455$	−4.46109	−0.209139
$456$	−138.489	−6.48533
$457$	−19.7532	−0.924014	−0.462007	−	0.886876i	$-0.652870\pi$
$457$	−19.7532	−0.924014	−0.462007	+	0.886876i	$0.652870\pi$
$458$	28.8936	1.35011
$459$	27.6742	1.29172
$460$	−39.0442	−1.82045
$461$	−15.4484	−0.719502	−0.359751	−	0.933048i	$-0.617138\pi$
$461$	−15.4484	−0.719502	−0.359751	+	0.933048i	$0.617138\pi$
$462$	33.3485	1.55151
$463$	−1.16949	−0.0543509	−0.0271755	−	0.999631i	$-0.508651\pi$
$463$	−1.16949	−0.0543509	−0.0271755	+	0.999631i	$0.508651\pi$
$464$	−67.9726	−3.15555
$465$	1.62283	0.0752570
$466$	34.4474	1.59575
$467$	31.7000	1.46690	0.733451	−	0.679742i	$-0.237908\pi$
$467$	31.7000	1.46690	0.733451	+	0.679742i	$0.237908\pi$
$468$	−87.0945	−4.02594
$469$	−10.8020	−0.498788
$470$	42.7913	1.97382
$471$	−6.22354	−0.286766
$472$	−102.636	−4.72420
$473$	−10.7592	−0.494710
$474$	−100.915	−4.63519
$475$	−12.6028	−0.578257
$476$	−9.19304	−0.421362
$477$	57.5372	2.63445
$478$	−55.0495	−2.51790
$479$	4.07584	0.186230	0.0931150	−	0.995655i	$-0.470318\pi$
$479$	4.07584	0.186230	0.0931150	+	0.995655i	$0.470318\pi$
$480$	41.7631	1.90622
$481$	5.75349	0.262337
$482$	−61.0354	−2.78009
$483$	−15.6042	−0.710018
$484$	24.2435	1.10198
$485$	6.01898	0.273308
$486$	−80.9241	−3.67079
$487$	−10.2957	−0.466542	−0.233271	−	0.972412i	$-0.574943\pi$
$487$	−10.2957	−0.466542	−0.233271	+	0.972412i	$0.574943\pi$
$488$	49.5106	2.24124
$489$	−80.8365	−3.65555
$490$	4.47476	0.202149
$491$	36.6057	1.65199	0.825996	−	0.563676i	$-0.190613\pi$
$491$	36.6057	1.65199	0.825996	+	0.563676i	$0.190613\pi$
$492$	−175.451	−7.90995
$493$	−16.5523	−0.745480
$494$	42.0829	1.89340
$495$	−51.3673	−2.30879
$496$	−2.36945	−0.106392
$497$	−2.84907	−0.127798
$498$	−81.8398	−3.66733
$499$	26.4408	1.18365	0.591827	−	0.806065i	$-0.298407\pi$
$499$	26.4408	1.18365	0.591827	+	0.806065i	$0.298407\pi$
$500$	56.1320	2.51030
$501$	−11.4834	−0.513043
$502$	52.3559	2.33676
$503$	17.1986	0.766849	0.383425	−	0.923572i	$-0.374745\pi$
$503$	17.1986	0.766849	0.383425	+	0.923572i	$0.374745\pi$
$504$	49.6033	2.20951
$505$	27.1969	1.21025
$506$	−50.3586	−2.23871
$507$	−20.6151	−0.915547
$508$	−64.1566	−2.84649
$509$	25.1454	1.11455	0.557275	−	0.830328i	$-0.311847\pi$
$509$	25.1454	1.11455	0.557275	+	0.830328i	$0.311847\pi$
$510$	28.5767	1.26540
$511$	−4.71564	−0.208608
$512$	49.3867	2.18261
$513$	88.7249	3.91730
$514$	−69.6605	−3.07259
$515$	16.4597	0.725300
$516$	−39.7157	−1.74839
$517$	38.5360	1.69481
$518$	−5.77113	−0.253569
$519$	37.1430	1.63040
$520$	−30.1747	−1.32325
$521$	−7.14126	−0.312864	−0.156432	−	0.987689i	$-0.549999\pi$
$521$	−7.14126	−0.312864	−0.156432	+	0.987689i	$0.549999\pi$
$522$	157.297	6.88469
$523$	−26.3146	−1.15066	−0.575330	−	0.817922i	$-0.695126\pi$
$523$	−26.3146	−1.15066	−0.575330	+	0.817922i	$0.695126\pi$
$524$	21.0031	0.917525
$525$	6.36064	0.277601
$526$	−71.5306	−3.11888
$527$	−0.576996	−0.0251344
$528$	105.681	4.59919
$529$	0.563525	0.0245011
$530$	35.1084	1.52501
$531$	111.277	4.82900
$532$	−29.4733	−1.27783
$533$	30.2718	1.31122
$534$	−41.2823	−1.78646
$535$	21.2478	0.918624
$536$	−73.0642	−3.15589
$537$	26.7690	1.15517
$538$	50.5540	2.17954
$539$	4.02978	0.173575
$540$	−112.045	−4.82165
$541$	−15.6580	−0.673190	−0.336595	−	0.941649i	$-0.609275\pi$
$541$	−15.6580	−0.673190	−0.336595	+	0.941649i	$0.609275\pi$
$542$	−44.1584	−1.89676
$543$	−21.8914	−0.939451
$544$	−14.8488	−0.636638
$545$	−27.9652	−1.19790
$546$	−21.2392	−0.908954
$547$	7.39515	0.316194	0.158097	−	0.987424i	$-0.449464\pi$
$547$	7.39515	0.316194	0.158097	+	0.987424i	$0.449464\pi$
$548$	−19.4270	−0.829879
$549$	−53.6789	−2.29096
$550$	20.5273	0.875286
$551$	−53.0676	−2.26075
$552$	−105.547	−4.49237
$553$	−12.1945	−0.518561
$554$	−45.8673	−1.94872
$555$	12.5259	0.531694
$556$	−0.0454370	−0.00192696
$557$	6.64247	0.281451	0.140725	−	0.990049i	$-0.455057\pi$
$557$	6.64247	0.281451	0.140725	+	0.990049i	$0.455057\pi$
$558$	5.48320	0.232122
$559$	6.85242	0.289827
$560$	14.1805	0.599236
$561$	25.7349	1.08653
$562$	53.0536	2.23793
$563$	3.29393	0.138822	0.0694112	−	0.997588i	$-0.477888\pi$
$563$	3.29393	0.138822	0.0694112	+	0.997588i	$0.477888\pi$
$564$	142.249	5.98974
$565$	−31.1944	−1.31236
$566$	−3.43403	−0.144343
$567$	−22.7791	−0.956631
$568$	−19.2710	−0.808595
$569$	40.5381	1.69945	0.849723	−	0.527229i	$-0.176769\pi$
$569$	40.5381	1.69945	0.849723	+	0.527229i	$0.176769\pi$
$570$	91.6183	3.83747
$571$	42.2323	1.76737	0.883684	−	0.468084i	$-0.155056\pi$
$571$	42.2323	1.76737	0.883684	+	0.468084i	$0.155056\pi$
$572$	−47.8590	−2.00109
$573$	−13.2348	−0.552890
$574$	−30.3645	−1.26739
$575$	−9.60502	−0.400557
$576$	21.4530	0.893874
$577$	46.6106	1.94043	0.970213	−	0.242253i	$-0.0778865\pi$
$577$	46.6106	1.94043	0.970213	+	0.242253i	$0.0778865\pi$
$578$	33.6040	1.39774
$579$	47.3696	1.96861
$580$	67.0157	2.78267
$581$	−9.88940	−0.410281
$582$	28.6563	1.18784
$583$	31.6171	1.30945
$584$	−31.8965	−1.31989
$585$	32.7152	1.35261
$586$	−52.1074	−2.15254
$587$	−13.3958	−0.552902	−0.276451	−	0.961028i	$-0.589158\pi$
$587$	−13.3958	−0.552902	−0.276451	+	0.961028i	$0.589158\pi$
$588$	14.8752	0.613442
$589$	−1.84988	−0.0762229
$590$	67.8995	2.79538
$591$	−14.3218	−0.589121
$592$	−18.2887	−0.751661
$593$	−24.0198	−0.986377	−0.493188	−	0.869923i	$-0.664169\pi$
$593$	−24.0198	−0.986377	−0.493188	+	0.869923i	$0.664169\pi$
$594$	−144.514	−5.92947
$595$	3.45316	0.141566
$596$	35.8331	1.46778
$597$	−27.7099	−1.13409
$598$	32.0727	1.31155
$599$	6.46174	0.264020	0.132010	−	0.991248i	$-0.457857\pi$
$599$	6.46174	0.264020	0.132010	+	0.991248i	$0.457857\pi$
$600$	43.0232	1.75642
$601$	−7.34487	−0.299604	−0.149802	−	0.988716i	$-0.547864\pi$
$601$	−7.34487	−0.299604	−0.149802	+	0.988716i	$0.547864\pi$
$602$	−6.87342	−0.280140
$603$	79.2155	3.22590
$604$	−49.5464	−2.01601
$605$	−9.10656	−0.370234
$606$	129.484	5.25994
$607$	45.8516	1.86106	0.930530	−	0.366216i	$-0.119347\pi$
$607$	45.8516	1.86106	0.930530	+	0.366216i	$0.119347\pi$
$608$	−47.6061	−1.93068
$609$	26.7832	1.08531
$610$	−32.7541	−1.32617
$611$	−24.5431	−0.992908
$612$	67.4166	2.72516
$613$	25.0875	1.01328	0.506638	−	0.862159i	$-0.330888\pi$
$613$	25.0875	1.01328	0.506638	+	0.862159i	$0.330888\pi$
$614$	66.7323	2.69310
$615$	65.9044	2.65752
$616$	27.2573	1.09823
$617$	16.4850	0.663659	0.331830	−	0.943339i	$-0.392334\pi$
$617$	16.4850	0.663659	0.331830	+	0.943339i	$0.392334\pi$
$618$	78.3643	3.15228
$619$	−25.5837	−1.02829	−0.514147	−	0.857702i	$-0.671891\pi$
$619$	−25.5837	−1.02829	−0.514147	+	0.857702i	$0.671891\pi$
$620$	2.33609	0.0938198
$621$	67.6201	2.71350
$622$	62.2151	2.49460
$623$	−4.98849	−0.199859
$624$	−67.3070	−2.69444
$625$	−11.1913	−0.447653
$626$	−61.6787	−2.46518
$627$	82.5074	3.29503
$628$	−8.95890	−0.357499
$629$	−4.45357	−0.177575
$630$	−32.8154	−1.30740
$631$	−43.6750	−1.73867	−0.869337	−	0.494219i	$-0.835454\pi$
$631$	−43.6750	−1.73867	−0.869337	+	0.494219i	$0.835454\pi$
$632$	−82.4831	−3.28100
$633$	−9.74776	−0.387439
$634$	−67.7758	−2.69172
$635$	24.0990	0.956341
$636$	116.709	4.62779
$637$	−2.56651	−0.101689
$638$	86.4356	3.42202
$639$	20.8935	0.826533
$640$	−12.8934	−0.509655
$641$	16.1327	0.637204	0.318602	−	0.947889i	$-0.396787\pi$
$641$	16.1327	0.637204	0.318602	+	0.947889i	$0.396787\pi$
$642$	101.161	3.99250
$643$	6.86320	0.270658	0.135329	−	0.990801i	$-0.456791\pi$
$643$	6.86320	0.270658	0.135329	+	0.990801i	$0.456791\pi$
$644$	−22.4626	−0.885149
$645$	14.9184	0.587409
$646$	−32.5748	−1.28164
$647$	17.0386	0.669857	0.334929	−	0.942243i	$-0.391288\pi$
$647$	17.0386	0.669857	0.334929	+	0.942243i	$0.391288\pi$
$648$	−154.077	−6.05273
$649$	61.1474	2.40024
$650$	−13.0736	−0.512787
$651$	0.933632	0.0365919
$652$	−116.365	−4.55722
$653$	26.4272	1.03418	0.517088	−	0.855932i	$-0.327016\pi$
$653$	26.4272	1.03418	0.517088	+	0.855932i	$0.327016\pi$
$654$	−133.142	−5.20627
$655$	−7.88936	−0.308263
$656$	−96.2252	−3.75696
$657$	34.5819	1.34917
$658$	24.6183	0.959722
$659$	−10.3240	−0.402167	−0.201083	−	0.979574i	$-0.564446\pi$
$659$	−10.3240	−0.402167	−0.201083	+	0.979574i	$0.564446\pi$
$660$	−104.193	−4.05572
$661$	−1.87049	−0.0727536	−0.0363768	−	0.999338i	$-0.511582\pi$
$661$	−1.87049	−0.0727536	−0.0363768	+	0.999338i	$0.511582\pi$
$662$	−38.0668	−1.47951
$663$	−16.3903	−0.636545
$664$	−66.8917	−2.59590
$665$	11.0710	0.429315
$666$	42.3222	1.63995
$667$	−40.4445	−1.56602
$668$	−16.5306	−0.639589
$669$	−32.4305	−1.25383
$670$	48.3362	1.86739
$671$	−29.4969	−1.13872
$672$	24.0268	0.926852
$673$	−25.0636	−0.966129	−0.483065	−	0.875585i	$-0.660476\pi$
$673$	−25.0636	−0.966129	−0.483065	+	0.875585i	$0.660476\pi$
$674$	−54.4621	−2.09780
$675$	−27.5635	−1.06092
$676$	−29.6757	−1.14137
$677$	−14.1442	−0.543605	−0.271803	−	0.962353i	$-0.587620\pi$
$677$	−14.1442	−0.543605	−0.271803	+	0.962353i	$0.587620\pi$
$678$	−148.516	−5.70373
$679$	3.46278	0.132889
$680$	23.3571	0.895706
$681$	80.3745	3.07996
$682$	3.01305	0.115376
$683$	−3.72990	−0.142721	−0.0713603	−	0.997451i	$-0.522734\pi$
$683$	−3.72990	−0.142721	−0.0713603	+	0.997451i	$0.522734\pi$
$684$	216.141	8.26435
$685$	7.29732	0.278816
$686$	2.57438	0.0982902
$687$	−36.0788	−1.37649
$688$	−21.7819	−0.830426
$689$	−20.1365	−0.767140
$690$	69.8253	2.65820
$691$	27.1548	1.03302	0.516509	−	0.856282i	$-0.327231\pi$
$691$	27.1548	1.03302	0.516509	+	0.856282i	$0.327231\pi$
$692$	53.4680	2.03255
$693$	−29.5521	−1.12259
$694$	35.4062	1.34400
$695$	0.0170674	0.000647404 0
$696$	181.161	6.86689
$697$	−23.4323	−0.887560
$698$	14.8120	0.560641
$699$	−43.0137	−1.62693
$700$	9.15624	0.346073
$701$	2.05984	0.0777992	0.0388996	−	0.999243i	$-0.487615\pi$
$701$	2.05984	0.0777992	0.0388996	+	0.999243i	$0.487615\pi$
$702$	92.0389	3.47379
$703$	−14.2783	−0.538518
$704$	11.7885	0.444298
$705$	−53.4326	−2.01239
$706$	−64.7462	−2.43676
$707$	15.6467	0.588454
$708$	225.714	8.48285
$709$	10.7220	0.402674	0.201337	−	0.979522i	$-0.435471\pi$
$709$	10.7220	0.402674	0.201337	+	0.979522i	$0.435471\pi$
$710$	12.7489	0.478457
$711$	89.4273	3.35379
$712$	−33.7420	−1.26454
$713$	−1.40985	−0.0527994
$714$	16.4405	0.615270
$715$	17.9772	0.672309
$716$	38.5345	1.44010
$717$	68.7390	2.56711
$718$	15.6615	0.584482
$719$	−15.1931	−0.566606	−0.283303	−	0.959030i	$-0.591430\pi$
$719$	−15.1931	−0.566606	−0.283303	+	0.959030i	$0.591430\pi$
$720$	−103.992	−3.87555
$721$	9.46942	0.352660
$722$	−55.5231	−2.06636
$723$	76.2136	2.83441
$724$	−31.5131	−1.17117
$725$	16.4861	0.612278
$726$	−43.3562	−1.60910
$727$	24.1428	0.895409	0.447704	−	0.894182i	$-0.352242\pi$
$727$	24.1428	0.895409	0.447704	+	0.894182i	$0.352242\pi$
$728$	−17.3598	−0.643399
$729$	32.7109	1.21151
$730$	21.1014	0.780996
$731$	−5.30421	−0.196183
$732$	−108.882	−4.02441
$733$	10.5626	0.390139	0.195069	−	0.980789i	$-0.437507\pi$
$733$	10.5626	0.390139	0.195069	+	0.980789i	$0.437507\pi$
$734$	−57.8775	−2.13630
$735$	−5.58753	−0.206099
$736$	−36.2821	−1.33738
$737$	43.5294	1.60343
$738$	222.677	8.19684
$739$	−38.8031	−1.42740	−0.713698	−	0.700454i	$-0.752981\pi$
$739$	−38.8031	−1.42740	−0.713698	+	0.700454i	$0.752981\pi$
$740$	18.0312	0.662841
$741$	−52.5479	−1.93040
$742$	20.1982	0.741500
$743$	−4.78975	−0.175719	−0.0878595	−	0.996133i	$-0.528003\pi$
$743$	−4.78975	−0.175719	−0.0878595	+	0.996133i	$0.528003\pi$
$744$	6.31507	0.231522
$745$	−13.4599	−0.493133
$746$	56.4132	2.06543
$747$	72.5234	2.65349
$748$	37.0459	1.35453
$749$	12.2241	0.446659
$750$	−100.384	−3.66552
$751$	−6.84933	−0.249936	−0.124968	−	0.992161i	$-0.539883\pi$
$751$	−6.84933	−0.249936	−0.124968	+	0.992161i	$0.539883\pi$
$752$	78.0154	2.84493
$753$	−65.3757	−2.38242
$754$	−55.0497	−2.00479
$755$	18.6110	0.677324
$756$	−64.4607	−2.34441
$757$	27.2575	0.990692	0.495346	−	0.868696i	$-0.335041\pi$
$757$	27.2575	0.990692	0.495346	+	0.868696i	$0.335041\pi$
$758$	23.1884	0.842240
$759$	62.8816	2.28246
$760$	74.8841	2.71633
$761$	3.56958	0.129397	0.0646986	−	0.997905i	$-0.479391\pi$
$761$	3.56958	0.129397	0.0646986	+	0.997905i	$0.479391\pi$
$762$	114.735	4.15642
$763$	−16.0887	−0.582449
$764$	−19.0517	−0.689265
$765$	−25.3236	−0.915576
$766$	26.7719	0.967309
$767$	−38.9440	−1.40618
$768$	−80.1927	−2.89370
$769$	−18.5652	−0.669477	−0.334738	−	0.942311i	$-0.608648\pi$
$769$	−18.5652	−0.669477	−0.334738	+	0.942311i	$0.608648\pi$
$770$	−18.0323	−0.649839
$771$	86.9835	3.13263
$772$	68.1893	2.45419
$773$	−18.5090	−0.665722	−0.332861	−	0.942976i	$-0.608014\pi$
$773$	−18.5090	−0.665722	−0.332861	+	0.942976i	$0.608014\pi$
$774$	50.4059	1.81180
$775$	0.574687	0.0206434
$776$	23.4222	0.840809
$777$	7.20627	0.258524
$778$	−12.3746	−0.443651
$779$	−75.1249	−2.69163
$780$	66.3594	2.37605
$781$	11.4811	0.410826
$782$	−24.8263	−0.887787
$783$	−116.063	−4.14777
$784$	8.15820	0.291364
$785$	3.36521	0.120110
$786$	−37.5612	−1.33976
$787$	−19.1723	−0.683418	−0.341709	−	0.939806i	$-0.611006\pi$
$787$	−19.1723	−0.683418	−0.341709	+	0.939806i	$0.611006\pi$
$788$	−20.6165	−0.734432
$789$	89.3186	3.17983
$790$	54.5673	1.94142
$791$	−17.9465	−0.638102
$792$	−199.890	−7.10279
$793$	18.7862	0.667117
$794$	−31.2369	−1.10856
$795$	−43.8390	−1.55481
$796$	−39.8888	−1.41382
$797$	−33.0380	−1.17027	−0.585134	−	0.810937i	$-0.698958\pi$
$797$	−33.0380	−1.17027	−0.585134	+	0.810937i	$0.698958\pi$
$798$	52.7090	1.86588
$799$	18.9979	0.672098
$800$	14.7894	0.522884
$801$	36.5828	1.29259
$802$	6.19298	0.218682
$803$	19.0030	0.670600
$804$	160.681	5.66678
$805$	8.43758	0.297385
$806$	−1.91897	−0.0675930
$807$	−63.1256	−2.22213
$808$	105.834	3.72322
$809$	0.142773	0.00501963	0.00250981	−	0.999997i	$-0.499201\pi$
$809$	0.142773	0.00501963	0.00250981	+	0.999997i	$0.499201\pi$
$810$	101.931	3.58149
$811$	−54.5389	−1.91512	−0.957560	−	0.288236i	$-0.906931\pi$
$811$	−54.5389	−1.91512	−0.957560	+	0.288236i	$0.906931\pi$
$812$	38.5548	1.35301
$813$	55.1395	1.93383
$814$	23.2563	0.815135
$815$	43.7101	1.53110
$816$	52.0999	1.82386
$817$	−17.0055	−0.594948
$818$	21.1663	0.740062
$819$	18.8214	0.657672
$820$	94.8705	3.31302
$821$	−35.8303	−1.25049	−0.625244	−	0.780429i	$-0.715000\pi$
$821$	−35.8303	−1.25049	−0.625244	+	0.780429i	$0.715000\pi$
$822$	34.7425	1.21178
$823$	54.3333	1.89394	0.946970	−	0.321321i	$-0.104127\pi$
$823$	54.3333	1.89394	0.946970	+	0.321321i	$0.104127\pi$
$824$	64.0510	2.23132
$825$	−25.6319	−0.892390
$826$	39.0633	1.35919
$827$	38.1785	1.32760	0.663798	−	0.747912i	$-0.268943\pi$
$827$	38.1785	1.32760	0.663798	+	0.747912i	$0.268943\pi$
$828$	164.728	5.72469
$829$	−13.0930	−0.454737	−0.227369	−	0.973809i	$-0.573012\pi$
$829$	−13.0930	−0.454737	−0.227369	+	0.973809i	$0.573012\pi$
$830$	44.2527	1.53603
$831$	57.2735	1.98679
$832$	−7.50797	−0.260292
$833$	1.98664	0.0688331
$834$	0.0812578	0.00281373
$835$	6.20937	0.214884
$836$	118.771	4.10778
$837$	−4.04584	−0.139845
$838$	−21.0280	−0.726401
$839$	6.71849	0.231948	0.115974	−	0.993252i	$-0.463001\pi$
$839$	6.71849	0.231948	0.115974	+	0.993252i	$0.463001\pi$
$840$	−37.7940	−1.30402
$841$	40.4191	1.39376
$842$	−87.9600	−3.03130
$843$	−66.2468	−2.28166
$844$	−14.0321	−0.483004
$845$	11.1470	0.383470
$846$	−180.537	−6.20699
$847$	−5.23910	−0.180018
$848$	64.0082	2.19805
$849$	4.28800	0.147164
$850$	10.1198	0.347105
$851$	−10.8820	−0.373030
$852$	42.3803	1.45193
$853$	−19.9778	−0.684027	−0.342014	−	0.939695i	$-0.611109\pi$
$853$	−19.9778	−0.684027	−0.342014	+	0.939695i	$0.611109\pi$
$854$	−18.8438	−0.644821
$855$	−81.1886	−2.77659
$856$	82.6836	2.82607
$857$	−6.86311	−0.234439	−0.117220	−	0.993106i	$-0.537398\pi$
$857$	−6.86311	−0.234439	−0.117220	+	0.993106i	$0.537398\pi$
$858$	85.5893	2.92197
$859$	1.00000	0.0341196
$859$	1.00000	0.0341196
$860$	21.4752	0.732299
$861$	37.9155	1.29216
$862$	−54.6542	−1.86153
$863$	−45.9028	−1.56255	−0.781275	−	0.624187i	$-0.785430\pi$
$863$	−45.9028	−1.56255	−0.781275	+	0.624187i	$0.785430\pi$
$864$	−104.119	−3.54219
$865$	−20.0841	−0.682879
$866$	26.7294	0.908302
$867$	−41.9606	−1.42506
$868$	1.34398	0.0456176
$869$	49.1409	1.66699
$870$	−119.848	−4.06324
$871$	−27.7233	−0.939370
$872$	−108.824	−3.68523
$873$	−25.3941	−0.859461
$874$	−79.5943	−2.69232
$875$	−12.1303	−0.410079
$876$	70.1459	2.37001
$877$	−52.2626	−1.76478	−0.882392	−	0.470515i	$-0.844068\pi$
$877$	−52.2626	−1.76478	−0.882392	+	0.470515i	$0.844068\pi$
$878$	33.2974	1.12373
$879$	65.0654	2.19460
$880$	−57.1443	−1.92633
$881$	−46.6212	−1.57071	−0.785354	−	0.619047i	$-0.787519\pi$
$881$	−46.6212	−1.57071	−0.785354	+	0.619047i	$0.787519\pi$
$882$	−18.8791	−0.635691
$883$	2.54720	0.0857202	0.0428601	−	0.999081i	$-0.486353\pi$
$883$	2.54720	0.0857202	0.0428601	+	0.999081i	$0.486353\pi$
$884$	−23.5940	−0.793553
$885$	−84.7846	−2.85000
$886$	83.1003	2.79181
$887$	−30.6847	−1.03029	−0.515145	−	0.857103i	$-0.672262\pi$
$887$	−30.6847	−1.03029	−0.515145	+	0.857103i	$0.672262\pi$
$888$	48.7431	1.63571
$889$	13.8644	0.464998
$890$	22.3223	0.748245
$891$	91.7946	3.07523
$892$	−46.6842	−1.56310
$893$	60.9082	2.03821
$894$	−64.0826	−2.14324
$895$	−14.4746	−0.483834
$896$	−7.41769	−0.247807
$897$	−40.0485	−1.33718
$898$	43.6681	1.45722
$899$	2.41987	0.0807073
$900$	−67.1468	−2.23823
$901$	15.5869	0.519276
$902$	122.362	4.07422
$903$	8.58269	0.285614
$904$	−121.389	−4.03735
$905$	11.8372	0.393482
$906$	88.6069	2.94377
$907$	0.449395	0.0149219	0.00746095	−	0.999972i	$-0.497625\pi$
$907$	0.449395	0.0149219	0.00746095	+	0.999972i	$0.497625\pi$
$908$	115.700	3.83965
$909$	−114.744	−3.80582
$910$	11.4845	0.380708
$911$	36.1793	1.19867	0.599336	−	0.800498i	$-0.295431\pi$
$911$	36.1793	1.19867	0.599336	+	0.800498i	$0.295431\pi$
$912$	167.035	5.53107
$913$	39.8521	1.31891
$914$	50.8521	1.68204
$915$	40.8993	1.35209
$916$	−51.9360	−1.71601
$917$	−4.53883	−0.149885
$918$	−71.2439	−2.35140
$919$	10.2567	0.338337	0.169169	−	0.985587i	$-0.445892\pi$
$919$	10.2567	0.338337	0.169169	+	0.985587i	$0.445892\pi$
$920$	57.0716	1.88160
$921$	−83.3271	−2.74572
$922$	39.7699	1.30975
$923$	−7.31216	−0.240683
$924$	−59.9436	−1.97200
$925$	4.43574	0.145846
$926$	3.01071	0.0989382
$927$	−69.4435	−2.28082
$928$	62.2748	2.04427
$929$	−41.5506	−1.36323	−0.681615	−	0.731711i	$-0.738722\pi$
$929$	−41.5506	−1.36323	−0.681615	+	0.731711i	$0.738722\pi$
$930$	−4.17778	−0.136995
$931$	6.36927	0.208744
$932$	−61.9190	−2.02822
$933$	−77.6866	−2.54334
$934$	−81.6079	−2.67029
$935$	−13.9155	−0.455085
$936$	127.307	4.16117
$937$	−49.8880	−1.62977	−0.814885	−	0.579623i	$-0.803200\pi$
$937$	−49.8880	−1.62977	−0.814885	+	0.579623i	$0.803200\pi$
$938$	27.8083	0.907973
$939$	77.0168	2.51335
$940$	−76.9171	−2.50876
$941$	−10.8724	−0.354430	−0.177215	−	0.984172i	$-0.556709\pi$
$941$	−10.8724	−0.354430	−0.177215	+	0.984172i	$0.556709\pi$
$942$	16.0218	0.522017
$943$	−57.2551	−1.86448
$944$	123.792	4.02907
$945$	24.2133	0.787658
$946$	27.6984	0.900551
$947$	−0.343977	−0.0111777	−0.00558887	−	0.999984i	$-0.501779\pi$
$947$	−0.343977	−0.0111777	−0.00558887	+	0.999984i	$0.501779\pi$
$948$	181.394	5.89142
$949$	−12.1027	−0.392872
$950$	32.4444	1.05264
$951$	84.6302	2.74432
$952$	13.4376	0.435516
$953$	−1.41572	−0.0458597	−0.0229299	−	0.999737i	$-0.507299\pi$
$953$	−1.41572	−0.0458597	−0.0229299	+	0.999737i	$0.507299\pi$
$954$	−148.123	−4.79564
$955$	7.15634	0.231574
$956$	98.9510	3.20030
$957$	−107.930	−3.48889
$958$	−10.4928	−0.339006
$959$	4.19823	0.135568
$960$	−16.3455	−0.527550
$961$	−30.9156	−0.997279
$962$	−14.8117	−0.477547
$963$	−89.6448	−2.88876
$964$	109.711	3.53354
$965$	−25.6138	−0.824538
$966$	40.1712	1.29249
$967$	−15.8503	−0.509712	−0.254856	−	0.966979i	$-0.582028\pi$
$967$	−15.8503	−0.509712	−0.254856	+	0.966979i	$0.582028\pi$
$968$	−35.4372	−1.13899
$969$	40.6754	1.30668
$970$	−15.4951	−0.497519
$971$	−0.799978	−0.0256725	−0.0128363	−	0.999918i	$-0.504086\pi$
$971$	−0.799978	−0.0256725	−0.0128363	+	0.999918i	$0.504086\pi$
$972$	145.460	4.66565
$973$	0.00981907	0.000314785 0
$974$	26.5050	0.849275
$975$	16.3247	0.522807
$976$	−59.7159	−1.91146
$977$	20.6951	0.662094	0.331047	−	0.943614i	$-0.392598\pi$
$977$	20.6951	0.662094	0.331047	+	0.943614i	$0.392598\pi$
$978$	208.104	6.65442
$979$	20.1025	0.642478
$980$	−8.04335	−0.256935
$981$	117.985	3.76698
$982$	−94.2369	−3.00722
$983$	−0.270605	−0.00863097	−0.00431549	−	0.999991i	$-0.501374\pi$
$983$	−0.270605	−0.00863097	−0.00431549	+	0.999991i	$0.501374\pi$
$984$	256.460	8.17564
$985$	7.74414	0.246749
$986$	42.6120	1.35704
$987$	−30.7403	−0.978476
$988$	−75.6436	−2.40654
$989$	−12.9605	−0.412119
$990$	132.239	4.20283
$991$	−7.80368	−0.247892	−0.123946	−	0.992289i	$-0.539555\pi$
$991$	−7.80368	−0.247892	−0.123946	+	0.992289i	$0.539555\pi$
$992$	2.17083	0.0689239
$993$	47.5332	1.50842
$994$	7.33457	0.232639
$995$	14.9834	0.475004
$996$	147.106	4.66125
$997$	−30.5919	−0.968856	−0.484428	−	0.874831i	$-0.660972\pi$
$997$	−30.5919	−0.968856	−0.484428	+	0.874831i	$0.660972\pi$
$998$	−68.0687	−2.15468
$999$	−31.2280	−0.988010

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6013.2.a.f.1.6	✓	110

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6013.2.a.f.1.6	✓	110	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:	\( N \)	\(=\)	\( 6013 = 7 \cdot 859 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6013.a (trivial)

\(f(q)\)	\(=\)	\(q-2.57438 q^{2} +3.21457 q^{3} +4.62742 q^{4} -1.73819 q^{5} -8.27551 q^{6} -1.00000 q^{7} -6.76398 q^{8} +7.33344 q^{9} +O(q^{10})\)	\(q-2.57438 q^{2} +3.21457 q^{3} +4.62742 q^{4} -1.73819 q^{5} -8.27551 q^{6} -1.00000 q^{7} -6.76398 q^{8} +7.33344 q^{9} +4.47476 q^{10} +4.02978 q^{11} +14.8752 q^{12} -2.56651 q^{13} +2.57438 q^{14} -5.58753 q^{15} +8.15820 q^{16} +1.98664 q^{17} -18.8791 q^{18} +6.36927 q^{19} -8.04335 q^{20} -3.21457 q^{21} -10.3742 q^{22} +4.85423 q^{23} -21.7433 q^{24} -1.97869 q^{25} +6.60717 q^{26} +13.9302 q^{27} -4.62742 q^{28} -8.33181 q^{29} +14.3844 q^{30} -0.290438 q^{31} -7.47433 q^{32} +12.9540 q^{33} -5.11437 q^{34} +1.73819 q^{35} +33.9350 q^{36} -2.24176 q^{37} -16.3969 q^{38} -8.25023 q^{39} +11.7571 q^{40} -11.7949 q^{41} +8.27551 q^{42} -2.66994 q^{43} +18.6475 q^{44} -12.7469 q^{45} -12.4966 q^{46} +9.56282 q^{47} +26.2251 q^{48} +1.00000 q^{49} +5.09390 q^{50} +6.38620 q^{51} -11.8763 q^{52} +7.84586 q^{53} -35.8615 q^{54} -7.00452 q^{55} +6.76398 q^{56} +20.4744 q^{57} +21.4492 q^{58} +15.1739 q^{59} -25.8559 q^{60} -7.31974 q^{61} +0.747697 q^{62} -7.33344 q^{63} +2.92536 q^{64} +4.46109 q^{65} -33.3485 q^{66} +10.8020 q^{67} +9.19304 q^{68} +15.6042 q^{69} -4.47476 q^{70} +2.84907 q^{71} -49.6033 q^{72} +4.71564 q^{73} +5.77113 q^{74} -6.36064 q^{75} +29.4733 q^{76} -4.02978 q^{77} +21.2392 q^{78} +12.1945 q^{79} -14.1805 q^{80} +22.7791 q^{81} +30.3645 q^{82} +9.88940 q^{83} -14.8752 q^{84} -3.45316 q^{85} +6.87342 q^{86} -26.7832 q^{87} -27.2573 q^{88} +4.98849 q^{89} +32.8154 q^{90} +2.56651 q^{91} +22.4626 q^{92} -0.933632 q^{93} -24.6183 q^{94} -11.0710 q^{95} -24.0268 q^{96} -3.46278 q^{97} -2.57438 q^{98} +29.5521 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 110 q + 16 q^{2} + 29 q^{3} + 118 q^{4} + 12 q^{6} - 110 q^{7} + 57 q^{8} + 127 q^{9}+O(q^{10}) \) 110 * q + 16 * q^2 + 29 * q^3 + 118 * q^4 + 12 * q^6 - 110 * q^7 + 57 * q^8 + 127 * q^9	\( 110 q + 16 q^{2} + 29 q^{3} + 118 q^{4} + 12 q^{6} - 110 q^{7} + 57 q^{8} + 127 q^{9} + 3 q^{10} + 52 q^{11} + 62 q^{12} - 9 q^{13} - 16 q^{14} + 39 q^{15} + 146 q^{16} + 11 q^{17} + 60 q^{18} + 14 q^{19} + 18 q^{20} - 29 q^{21} + 32 q^{22} + 73 q^{23} + 24 q^{24} + 132 q^{25} - 7 q^{26} + 116 q^{27} - 118 q^{28} + 35 q^{29} + 18 q^{30} + 36 q^{31} + 140 q^{32} + 42 q^{33} - 7 q^{34} + 180 q^{36} + 49 q^{37} + 45 q^{39} + 6 q^{40} - 14 q^{41} - 12 q^{42} + 58 q^{43} + 92 q^{44} + 17 q^{45} + 27 q^{46} + 87 q^{47} + 98 q^{48} + 110 q^{49} + 91 q^{50} + 42 q^{51} + 16 q^{52} + 95 q^{53} + 41 q^{54} + 8 q^{55} - 57 q^{56} + 61 q^{57} + 46 q^{58} + 114 q^{59} + 81 q^{60} - 47 q^{61} + 31 q^{62} - 127 q^{63} + 199 q^{64} + 62 q^{65} + 21 q^{66} + 95 q^{67} + 60 q^{68} - 39 q^{69} - 3 q^{70} + 131 q^{71} + 186 q^{72} + 31 q^{73} + 23 q^{74} + 121 q^{75} + 14 q^{76} - 52 q^{77} + 110 q^{78} + 9 q^{79} + 61 q^{80} + 194 q^{81} + 45 q^{82} + 73 q^{83} - 62 q^{84} + 59 q^{85} + 72 q^{86} + 64 q^{87} + 100 q^{88} - 17 q^{89} + 11 q^{90} + 9 q^{91} + 192 q^{92} + 85 q^{93} - 11 q^{94} + 108 q^{95} + 68 q^{96} + 32 q^{97} + 16 q^{98} + 160 q^{99}+O(q^{100}) \) 110 * q + 16 * q^2 + 29 * q^3 + 118 * q^4 + 12 * q^6 - 110 * q^7 + 57 * q^8 + 127 * q^9 + 3 * q^10 + 52 * q^11 + 62 * q^12 - 9 * q^13 - 16 * q^14 + 39 * q^15 + 146 * q^16 + 11 * q^17 + 60 * q^18 + 14 * q^19 + 18 * q^20 - 29 * q^21 + 32 * q^22 + 73 * q^23 + 24 * q^24 + 132 * q^25 - 7 * q^26 + 116 * q^27 - 118 * q^28 + 35 * q^29 + 18 * q^30 + 36 * q^31 + 140 * q^32 + 42 * q^33 - 7 * q^34 + 180 * q^36 + 49 * q^37 + 45 * q^39 + 6 * q^40 - 14 * q^41 - 12 * q^42 + 58 * q^43 + 92 * q^44 + 17 * q^45 + 27 * q^46 + 87 * q^47 + 98 * q^48 + 110 * q^49 + 91 * q^50 + 42 * q^51 + 16 * q^52 + 95 * q^53 + 41 * q^54 + 8 * q^55 - 57 * q^56 + 61 * q^57 + 46 * q^58 + 114 * q^59 + 81 * q^60 - 47 * q^61 + 31 * q^62 - 127 * q^63 + 199 * q^64 + 62 * q^65 + 21 * q^66 + 95 * q^67 + 60 * q^68 - 39 * q^69 - 3 * q^70 + 131 * q^71 + 186 * q^72 + 31 * q^73 + 23 * q^74 + 121 * q^75 + 14 * q^76 - 52 * q^77 + 110 * q^78 + 9 * q^79 + 61 * q^80 + 194 * q^81 + 45 * q^82 + 73 * q^83 - 62 * q^84 + 59 * q^85 + 72 * q^86 + 64 * q^87 + 100 * q^88 - 17 * q^89 + 11 * q^90 + 9 * q^91 + 192 * q^92 + 85 * q^93 - 11 * q^94 + 108 * q^95 + 68 * q^96 + 32 * q^97 + 16 * q^98 + 160 * q^99

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