LMFDB - Embedded newform 6019.2.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6019,2,Mod(1,6019)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6019, 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("6019.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6019 = 13 \cdot 463 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6019.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:	$48.0619569766$
Analytic rank:	$1$
Dimension:	$108$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	6019.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.77848 q^{2} +2.29765 q^{3} +5.71995 q^{4} +2.18323 q^{5} -6.38396 q^{6} +0.752947 q^{7} -10.3358 q^{8} +2.27917 q^{9} +O(q^{10})$	\(q-2.77848 q^{2} +2.29765 q^{3} +5.71995 q^{4} +2.18323 q^{5} -6.38396 q^{6} +0.752947 q^{7} -10.3358 q^{8} +2.27917 q^{9} -6.06605 q^{10} -5.84116 q^{11} +13.1424 q^{12} -1.00000 q^{13} -2.09205 q^{14} +5.01628 q^{15} +17.2779 q^{16} +1.67477 q^{17} -6.33264 q^{18} -0.369876 q^{19} +12.4880 q^{20} +1.73000 q^{21} +16.2295 q^{22} +1.10881 q^{23} -23.7480 q^{24} -0.233522 q^{25} +2.77848 q^{26} -1.65620 q^{27} +4.30682 q^{28} +3.02051 q^{29} -13.9376 q^{30} -7.84456 q^{31} -27.3348 q^{32} -13.4209 q^{33} -4.65332 q^{34} +1.64385 q^{35} +13.0368 q^{36} +0.683881 q^{37} +1.02769 q^{38} -2.29765 q^{39} -22.5654 q^{40} +2.85496 q^{41} -4.80678 q^{42} +2.37080 q^{43} -33.4112 q^{44} +4.97595 q^{45} -3.08081 q^{46} -11.1830 q^{47} +39.6986 q^{48} -6.43307 q^{49} +0.648836 q^{50} +3.84803 q^{51} -5.71995 q^{52} -10.0200 q^{53} +4.60172 q^{54} -12.7526 q^{55} -7.78232 q^{56} -0.849843 q^{57} -8.39242 q^{58} -7.83855 q^{59} +28.6929 q^{60} +7.75538 q^{61} +21.7960 q^{62} +1.71610 q^{63} +41.3933 q^{64} -2.18323 q^{65} +37.2897 q^{66} +3.63717 q^{67} +9.57962 q^{68} +2.54766 q^{69} -4.56741 q^{70} +8.56799 q^{71} -23.5571 q^{72} -0.475662 q^{73} -1.90015 q^{74} -0.536551 q^{75} -2.11567 q^{76} -4.39808 q^{77} +6.38396 q^{78} +0.464395 q^{79} +37.7217 q^{80} -10.6429 q^{81} -7.93244 q^{82} +3.99696 q^{83} +9.89554 q^{84} +3.65641 q^{85} -6.58723 q^{86} +6.94006 q^{87} +60.3731 q^{88} -3.06289 q^{89} -13.8256 q^{90} -0.752947 q^{91} +6.34235 q^{92} -18.0240 q^{93} +31.0717 q^{94} -0.807522 q^{95} -62.8057 q^{96} +4.60043 q^{97} +17.8742 q^{98} -13.3130 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q - 11 q^{2} + q^{3} + 95 q^{4} - 40 q^{5} - 10 q^{6} - 8 q^{7} - 33 q^{8} + 79 q^{9}+O(q^{10}) $ 108 * q - 11 * q^2 + q^3 + 95 * q^4 - 40 * q^5 - 10 * q^6 - 8 * q^7 - 33 * q^8 + 79 * q^9	\( 108 q - 11 q^{2} + q^{3} + 95 q^{4} - 40 q^{5} - 10 q^{6} - 8 q^{7} - 33 q^{8} + 79 q^{9} - q^{10} - 45 q^{11} - 6 q^{12} - 108 q^{13} - 31 q^{14} - 39 q^{15} + 73 q^{16} + 21 q^{17} - 35 q^{18} - 19 q^{19} - 79 q^{20} - 72 q^{21} - 26 q^{23} - 23 q^{24} + 92 q^{25} + 11 q^{26} + 7 q^{27} - 21 q^{28} - 94 q^{29} - 24 q^{30} - 36 q^{31} - 77 q^{32} - 32 q^{33} - 58 q^{34} - 10 q^{35} + 17 q^{36} - 54 q^{37} - 12 q^{38} - q^{39} - 4 q^{40} - 68 q^{41} - 11 q^{42} - 32 q^{43} - 151 q^{44} - 121 q^{45} - 33 q^{46} - 51 q^{47} - 27 q^{48} + 72 q^{49} - 45 q^{50} - 24 q^{51} - 95 q^{52} - 81 q^{53} - 29 q^{54} + 4 q^{55} - 68 q^{56} - 45 q^{57} - 30 q^{58} - 94 q^{59} - 108 q^{60} - 39 q^{61} - 9 q^{62} - 52 q^{63} + 31 q^{64} + 40 q^{65} - 40 q^{66} - 47 q^{67} + 24 q^{68} - 60 q^{69} - 66 q^{70} - 86 q^{71} - 91 q^{72} - 51 q^{73} - 110 q^{74} - 7 q^{75} - 51 q^{76} - 96 q^{77} + 10 q^{78} - 18 q^{79} - 136 q^{80} - 24 q^{81} - 33 q^{82} - 77 q^{83} - 113 q^{84} - 95 q^{85} - 137 q^{86} + 23 q^{87} + 19 q^{88} - 112 q^{89} - 19 q^{90} + 8 q^{91} - 111 q^{92} - 124 q^{93} - 20 q^{94} - 73 q^{95} - 77 q^{96} - 41 q^{97} - 80 q^{98} - 154 q^{99}+O(q^{100}) \) 108 * q - 11 * q^2 + q^3 + 95 * q^4 - 40 * q^5 - 10 * q^6 - 8 * q^7 - 33 * q^8 + 79 * q^9 - q^10 - 45 * q^11 - 6 * q^12 - 108 * q^13 - 31 * q^14 - 39 * q^15 + 73 * q^16 + 21 * q^17 - 35 * q^18 - 19 * q^19 - 79 * q^20 - 72 * q^21 - 26 * q^23 - 23 * q^24 + 92 * q^25 + 11 * q^26 + 7 * q^27 - 21 * q^28 - 94 * q^29 - 24 * q^30 - 36 * q^31 - 77 * q^32 - 32 * q^33 - 58 * q^34 - 10 * q^35 + 17 * q^36 - 54 * q^37 - 12 * q^38 - q^39 - 4 * q^40 - 68 * q^41 - 11 * q^42 - 32 * q^43 - 151 * q^44 - 121 * q^45 - 33 * q^46 - 51 * q^47 - 27 * q^48 + 72 * q^49 - 45 * q^50 - 24 * q^51 - 95 * q^52 - 81 * q^53 - 29 * q^54 + 4 * q^55 - 68 * q^56 - 45 * q^57 - 30 * q^58 - 94 * q^59 - 108 * q^60 - 39 * q^61 - 9 * q^62 - 52 * q^63 + 31 * q^64 + 40 * q^65 - 40 * q^66 - 47 * q^67 + 24 * q^68 - 60 * q^69 - 66 * q^70 - 86 * q^71 - 91 * q^72 - 51 * q^73 - 110 * q^74 - 7 * q^75 - 51 * q^76 - 96 * q^77 + 10 * q^78 - 18 * q^79 - 136 * q^80 - 24 * q^81 - 33 * q^82 - 77 * q^83 - 113 * q^84 - 95 * q^85 - 137 * q^86 + 23 * q^87 + 19 * q^88 - 112 * q^89 - 19 * q^90 + 8 * q^91 - 111 * q^92 - 124 * q^93 - 20 * q^94 - 73 * q^95 - 77 * q^96 - 41 * q^97 - 80 * q^98 - 154 * 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 $

$2$	−2.77848	−1.96468	−0.982341	−	0.187099i	$-0.940091\pi$
$2$	−2.77848	−1.96468	−0.982341	+	0.187099i	$0.940091\pi$
$3$	2.29765	1.32655	0.663273	−	0.748377i	$-0.269167\pi$
$3$	2.29765	1.32655	0.663273	+	0.748377i	$0.269167\pi$
$4$	5.71995	2.85998
$5$	2.18323	0.976369	0.488184	−	0.872741i	$-0.337659\pi$
$5$	2.18323	0.976369	0.488184	+	0.872741i	$0.337659\pi$
$6$	−6.38396	−2.60624
$7$	0.752947	0.284587	0.142294	−	0.989825i	$-0.454552\pi$
$7$	0.752947	0.284587	0.142294	+	0.989825i	$0.454552\pi$
$8$	−10.3358	−3.65426
$9$	2.27917	0.759725
$10$	−6.06605	−1.91825
$11$	−5.84116	−1.76118	−0.880588	−	0.473882i	$-0.842852\pi$
$11$	−5.84116	−1.76118	−0.880588	+	0.473882i	$0.842852\pi$
$12$	13.1424	3.79389
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−2.09205	−0.559123
$15$	5.01628	1.29520
$16$	17.2779	4.31949
$17$	1.67477	0.406192	0.203096	−	0.979159i	$-0.434900\pi$
$17$	1.67477	0.406192	0.203096	+	0.979159i	$0.434900\pi$
$18$	−6.33264	−1.49262
$19$	−0.369876	−0.0848553	−0.0424276	−	0.999100i	$-0.513509\pi$
$19$	−0.369876	−0.0848553	−0.0424276	+	0.999100i	$0.513509\pi$
$20$	12.4880	2.79239
$21$	1.73000	0.377518
$22$	16.2295	3.46015
$23$	1.10881	0.231203	0.115602	−	0.993296i	$-0.463120\pi$
$23$	1.10881	0.231203	0.115602	+	0.993296i	$0.463120\pi$
$24$	−23.7480	−4.84755
$25$	−0.233522	−0.0467044
$26$	2.77848	0.544905
$27$	−1.65620	−0.318736
$28$	4.30682	0.813912
$29$	3.02051	0.560894	0.280447	−	0.959869i	$-0.409517\pi$
$29$	3.02051	0.560894	0.280447	+	0.959869i	$0.409517\pi$
$30$	−13.9376	−2.54465
$31$	−7.84456	−1.40892	−0.704462	−	0.709741i	$-0.748812\pi$
$31$	−7.84456	−1.40892	−0.704462	+	0.709741i	$0.748812\pi$
$32$	−27.3348	−4.83216
$33$	−13.4209	−2.33628
$34$	−4.65332	−0.798038
$35$	1.64385	0.277862
$36$	13.0368	2.17279
$37$	0.683881	0.112429	0.0562146	−	0.998419i	$-0.482097\pi$
$37$	0.683881	0.112429	0.0562146	+	0.998419i	$0.482097\pi$
$38$	1.02769	0.166714
$39$	−2.29765	−0.367918
$40$	−22.5654	−3.56791
$41$	2.85496	0.445869	0.222935	−	0.974833i	$-0.428436\pi$
$41$	2.85496	0.445869	0.222935	+	0.974833i	$0.428436\pi$
$42$	−4.80678	−0.741703
$43$	2.37080	0.361544	0.180772	−	0.983525i	$-0.442140\pi$
$43$	2.37080	0.361544	0.180772	+	0.983525i	$0.442140\pi$
$44$	−33.4112	−5.03692
$45$	4.97595	0.741771
$46$	−3.08081	−0.454241
$47$	−11.1830	−1.63120	−0.815602	−	0.578613i	$-0.803594\pi$
$47$	−11.1830	−1.63120	−0.815602	+	0.578613i	$0.803594\pi$
$48$	39.6986	5.73000
$49$	−6.43307	−0.919010
$50$	0.648836	0.0917593
$51$	3.84803	0.538833
$52$	−5.71995	−0.793215
$53$	−10.0200	−1.37635	−0.688174	−	0.725545i	$-0.741588\pi$
$53$	−10.0200	−1.37635	−0.688174	+	0.725545i	$0.741588\pi$
$54$	4.60172	0.626215
$55$	−12.7526	−1.71956
$56$	−7.78232	−1.03996
$57$	−0.849843	−0.112564
$58$	−8.39242	−1.10198
$59$	−7.83855	−1.02049	−0.510246	−	0.860028i	$-0.670446\pi$
$59$	−7.83855	−1.02049	−0.510246	+	0.860028i	$0.670446\pi$
$60$	28.6929	3.70424
$61$	7.75538	0.992974	0.496487	−	0.868044i	$-0.334623\pi$
$61$	7.75538	0.992974	0.496487	+	0.868044i	$0.334623\pi$
$62$	21.7960	2.76809
$63$	1.71610	0.216208
$64$	41.3933	5.17416
$65$	−2.18323	−0.270796
$66$	37.2897	4.59005
$67$	3.63717	0.444351	0.222176	−	0.975007i	$-0.428684\pi$
$67$	3.63717	0.444351	0.222176	+	0.975007i	$0.428684\pi$
$68$	9.57962	1.16170
$69$	2.54766	0.306702
$70$	−4.56741	−0.545910
$71$	8.56799	1.01683	0.508417	−	0.861111i	$-0.330231\pi$
$71$	8.56799	1.01683	0.508417	+	0.861111i	$0.330231\pi$
$72$	−23.5571	−2.77623
$73$	−0.475662	−0.0556720	−0.0278360	−	0.999613i	$-0.508862\pi$
$73$	−0.475662	−0.0556720	−0.0278360	+	0.999613i	$0.508862\pi$
$74$	−1.90015	−0.220888
$75$	−0.536551	−0.0619555
$76$	−2.11567	−0.242684
$77$	−4.39808	−0.501208
$78$	6.38396	0.722841
$79$	0.464395	0.0522486	0.0261243	−	0.999659i	$-0.491683\pi$
$79$	0.464395	0.0522486	0.0261243	+	0.999659i	$0.491683\pi$
$80$	37.7217	4.21741
$81$	−10.6429	−1.18254
$82$	−7.93244	−0.875992
$83$	3.99696	0.438723	0.219362	−	0.975644i	$-0.429603\pi$
$83$	3.99696	0.438723	0.219362	+	0.975644i	$0.429603\pi$
$84$	9.89554	1.07969
$85$	3.65641	0.396593
$86$	−6.58723	−0.710319
$87$	6.94006	0.744052
$88$	60.3731	6.43580
$89$	−3.06289	−0.324666	−0.162333	−	0.986736i	$-0.551902\pi$
$89$	−3.06289	−0.324666	−0.162333	+	0.986736i	$0.551902\pi$
$90$	−13.8256	−1.45735
$91$	−0.752947	−0.0789303
$92$	6.34235	0.661235
$93$	−18.0240	−1.86900
$94$	31.0717	3.20480
$95$	−0.807522	−0.0828500
$96$	−62.8057	−6.41008
$97$	4.60043	0.467103	0.233551	−	0.972344i	$-0.424965\pi$
$97$	4.60043	0.467103	0.233551	+	0.972344i	$0.424965\pi$
$98$	17.8742	1.80556
$99$	−13.3130	−1.33801
$100$	−1.33573	−0.133573
$101$	−11.0352	−1.09804	−0.549020	−	0.835809i	$-0.684999\pi$
$101$	−11.0352	−1.09804	−0.549020	+	0.835809i	$0.684999\pi$
$102$	−10.6917	−1.05863
$103$	−6.49925	−0.640390	−0.320195	−	0.947352i	$-0.603748\pi$
$103$	−6.49925	−0.640390	−0.320195	+	0.947352i	$0.603748\pi$
$104$	10.3358	1.01351
$105$	3.77699	0.368597
$106$	27.8403	2.70409
$107$	−14.1368	−1.36665	−0.683327	−	0.730113i	$-0.739468\pi$
$107$	−14.1368	−1.36665	−0.683327	+	0.730113i	$0.739468\pi$
$108$	−9.47339	−0.911577
$109$	−12.9703	−1.24233	−0.621163	−	0.783682i	$-0.713339\pi$
$109$	−12.9703	−1.24233	−0.621163	+	0.783682i	$0.713339\pi$
$110$	35.4328	3.37838
$111$	1.57132	0.149143
$112$	13.0094	1.22927
$113$	8.18100	0.769604	0.384802	−	0.922999i	$-0.374270\pi$
$113$	8.18100	0.769604	0.384802	+	0.922999i	$0.374270\pi$
$114$	2.36127	0.221153
$115$	2.42079	0.225740
$116$	17.2772	1.60414
$117$	−2.27917	−0.210710
$118$	21.7793	2.00494
$119$	1.26101	0.115597
$120$	−51.8473	−4.73299
$121$	23.1192	2.10174
$122$	−21.5482	−1.95088
$123$	6.55968	0.591466
$124$	−44.8705	−4.02949
$125$	−11.4260	−1.02197
$126$	−4.76814	−0.424780
$127$	17.9154	1.58973	0.794867	−	0.606784i	$-0.207541\pi$
$127$	17.9154	1.58973	0.794867	+	0.606784i	$0.207541\pi$
$128$	−60.3409	−5.33343
$129$	5.44726	0.479605
$130$	6.06605	0.532028
$131$	4.88211	0.426552	0.213276	−	0.976992i	$-0.431587\pi$
$131$	4.88211	0.426552	0.213276	+	0.976992i	$0.431587\pi$
$132$	−76.7670	−6.68171
$133$	−0.278497	−0.0241487
$134$	−10.1058	−0.873009
$135$	−3.61586	−0.311204
$136$	−17.3101	−1.48433
$137$	−15.1486	−1.29423	−0.647114	−	0.762393i	$-0.724024\pi$
$137$	−15.1486	−1.29423	−0.647114	+	0.762393i	$0.724024\pi$
$138$	−7.07861	−0.602571
$139$	7.46948	0.633553	0.316777	−	0.948500i	$-0.397399\pi$
$139$	7.46948	0.633553	0.316777	+	0.948500i	$0.397399\pi$
$140$	9.40276	0.794678
$141$	−25.6945	−2.16387
$142$	−23.8060	−1.99775
$143$	5.84116	0.488462
$144$	39.3795	3.28162
$145$	6.59445	0.547639
$146$	1.32162	0.109378
$147$	−14.7809	−1.21911
$148$	3.91176	0.321545
$149$	−13.1913	−1.08068	−0.540338	−	0.841448i	$-0.681704\pi$
$149$	−13.1913	−1.08068	−0.540338	+	0.841448i	$0.681704\pi$
$150$	1.49080	0.121723
$151$	19.7800	1.60967	0.804837	−	0.593496i	$-0.202253\pi$
$151$	19.7800	1.60967	0.804837	+	0.593496i	$0.202253\pi$
$152$	3.82296	0.310083
$153$	3.81710	0.308594
$154$	12.2200	0.984714
$155$	−17.1264	−1.37563
$156$	−13.1424	−1.05224
$157$	−4.82393	−0.384992	−0.192496	−	0.981298i	$-0.561658\pi$
$157$	−4.82393	−0.384992	−0.192496	+	0.981298i	$0.561658\pi$
$158$	−1.29031	−0.102652
$159$	−23.0223	−1.82579
$160$	−59.6781	−4.71797
$161$	0.834876	0.0657974
$162$	29.5710	2.32332
$163$	−5.72813	−0.448662	−0.224331	−	0.974513i	$-0.572020\pi$
$163$	−5.72813	−0.448662	−0.224331	+	0.974513i	$0.572020\pi$
$164$	16.3302	1.27518
$165$	−29.3009	−2.28107
$166$	−11.1055	−0.861952
$167$	−1.03747	−0.0802822	−0.0401411	−	0.999194i	$-0.512781\pi$
$167$	−1.03747	−0.0802822	−0.0401411	+	0.999194i	$0.512781\pi$
$168$	−17.8810	−1.37955
$169$	1.00000	0.0769231
$170$	−10.1593	−0.779180
$171$	−0.843011	−0.0644667
$172$	13.5609	1.03401
$173$	−18.5954	−1.41378	−0.706892	−	0.707322i	$-0.749903\pi$
$173$	−18.5954	−1.41378	−0.706892	+	0.707322i	$0.749903\pi$
$174$	−19.2828	−1.46183
$175$	−0.175830	−0.0132915
$176$	−100.923	−7.60738
$177$	−18.0102	−1.35373
$178$	8.51019	0.637866
$179$	−12.0081	−0.897529	−0.448765	−	0.893650i	$-0.648136\pi$
$179$	−12.0081	−0.897529	−0.448765	+	0.893650i	$0.648136\pi$
$180$	28.4622	2.12145
$181$	−17.7919	−1.32246	−0.661229	−	0.750184i	$-0.729965\pi$
$181$	−17.7919	−1.32246	−0.661229	+	0.750184i	$0.729965\pi$
$182$	2.09205	0.155073
$183$	17.8191	1.31723
$184$	−11.4605	−0.844877
$185$	1.49307	0.109772
$186$	50.0794	3.67200
$187$	−9.78262	−0.715376
$188$	−63.9661	−4.66521
$189$	−1.24703	−0.0907082
$190$	2.24368	0.162774
$191$	−24.5105	−1.77352	−0.886759	−	0.462232i	$-0.847049\pi$
$191$	−24.5105	−1.77352	−0.886759	+	0.462232i	$0.847049\pi$
$192$	95.1072	6.86377
$193$	5.65542	0.407086	0.203543	−	0.979066i	$-0.434754\pi$
$193$	5.65542	0.407086	0.203543	+	0.979066i	$0.434754\pi$
$194$	−12.7822	−0.917708
$195$	−5.01628	−0.359223
$196$	−36.7969	−2.62835
$197$	1.04159	0.0742100	0.0371050	−	0.999311i	$-0.488186\pi$
$197$	1.04159	0.0742100	0.0371050	+	0.999311i	$0.488186\pi$
$198$	36.9900	2.62876
$199$	11.2989	0.800958	0.400479	−	0.916306i	$-0.368844\pi$
$199$	11.2989	0.800958	0.400479	+	0.916306i	$0.368844\pi$
$200$	2.41364	0.170670
$201$	8.35693	0.589452
$202$	30.6610	2.15730
$203$	2.27428	0.159623
$204$	22.0106	1.54105
$205$	6.23302	0.435333
$206$	18.0580	1.25816
$207$	2.52717	0.175651
$208$	−17.2779	−1.19801
$209$	2.16050	0.149445
$210$	−10.4943	−0.724175
$211$	17.4147	1.19888	0.599439	−	0.800421i	$-0.295391\pi$
$211$	17.4147	1.19888	0.599439	+	0.800421i	$0.295391\pi$
$212$	−57.3137	−3.93632
$213$	19.6862	1.34888
$214$	39.2787	2.68504
$215$	5.17600	0.353000
$216$	17.1182	1.16474
$217$	−5.90653	−0.400962
$218$	36.0376	2.44078
$219$	−1.09290	−0.0738515
$220$	−72.9441	−4.91789
$221$	−1.67477	−0.112657
$222$	−4.36587	−0.293018
$223$	25.2593	1.69149	0.845743	−	0.533590i	$-0.179157\pi$
$223$	25.2593	1.69149	0.845743	+	0.533590i	$0.179157\pi$
$224$	−20.5816	−1.37517
$225$	−0.532237	−0.0354825
$226$	−22.7308	−1.51203
$227$	−8.14202	−0.540405	−0.270202	−	0.962804i	$-0.587091\pi$
$227$	−8.14202	−0.540405	−0.270202	+	0.962804i	$0.587091\pi$
$228$	−4.86106	−0.321932
$229$	−7.54801	−0.498786	−0.249393	−	0.968402i	$-0.580231\pi$
$229$	−7.54801	−0.498786	−0.249393	+	0.968402i	$0.580231\pi$
$230$	−6.72611	−0.443506
$231$	−10.1052	−0.664876
$232$	−31.2194	−2.04965
$233$	23.2242	1.52147	0.760735	−	0.649062i	$-0.224839\pi$
$233$	23.2242	1.52147	0.760735	+	0.649062i	$0.224839\pi$
$234$	6.33264	0.413978
$235$	−24.4150	−1.59266
$236$	−44.8361	−2.91858
$237$	1.06702	0.0693101
$238$	−3.50370	−0.227111
$239$	19.0857	1.23455	0.617275	−	0.786747i	$-0.288237\pi$
$239$	19.0857	1.23455	0.617275	+	0.786747i	$0.288237\pi$
$240$	86.6710	5.59459
$241$	−23.8277	−1.53487	−0.767437	−	0.641124i	$-0.778468\pi$
$241$	−23.8277	−1.53487	−0.767437	+	0.641124i	$0.778468\pi$
$242$	−64.2361	−4.12925
$243$	−19.4850	−1.24996
$244$	44.3604	2.83988
$245$	−14.0449	−0.897293
$246$	−18.2259	−1.16204
$247$	0.369876	0.0235346
$248$	81.0799	5.14858
$249$	9.18360	0.581987
$250$	31.7468	2.00784
$251$	7.76343	0.490023	0.245012	−	0.969520i	$-0.421208\pi$
$251$	7.76343	0.490023	0.245012	+	0.969520i	$0.421208\pi$
$252$	9.81599	0.618349
$253$	−6.47675	−0.407190
$254$	−49.7776	−3.12332
$255$	8.40113	0.526099
$256$	84.8694	5.30434
$257$	−27.8611	−1.73793	−0.868964	−	0.494875i	$-0.835214\pi$
$257$	−27.8611	−1.73793	−0.868964	+	0.494875i	$0.835214\pi$
$258$	−15.1351	−0.942271
$259$	0.514926	0.0319959
$260$	−12.4880	−0.774470
$261$	6.88426	0.426125
$262$	−13.5648	−0.838039
$263$	−13.3677	−0.824289	−0.412145	−	0.911118i	$-0.635220\pi$
$263$	−13.3677	−0.824289	−0.412145	+	0.911118i	$0.635220\pi$
$264$	138.716	8.53738
$265$	−21.8759	−1.34382
$266$	0.773797	0.0474445
$267$	−7.03745	−0.430685
$268$	20.8044	1.27083
$269$	23.4729	1.43117	0.715583	−	0.698527i	$-0.246161\pi$
$269$	23.4729	1.43117	0.715583	+	0.698527i	$0.246161\pi$
$270$	10.0466	0.611417
$271$	−5.38154	−0.326906	−0.163453	−	0.986551i	$-0.552263\pi$
$271$	−5.38154	−0.326906	−0.163453	+	0.986551i	$0.552263\pi$
$272$	28.9366	1.75454
$273$	−1.73000	−0.104705
$274$	42.0900	2.54275
$275$	1.36404	0.0822547
$276$	14.5725	0.877159
$277$	−12.8583	−0.772583	−0.386291	−	0.922377i	$-0.626244\pi$
$277$	−12.8583	−0.772583	−0.386291	+	0.922377i	$0.626244\pi$
$278$	−20.7538	−1.24473
$279$	−17.8791	−1.07039
$280$	−16.9906	−1.01538
$281$	−25.7588	−1.53664	−0.768320	−	0.640065i	$-0.778907\pi$
$281$	−25.7588	−1.53664	−0.768320	+	0.640065i	$0.778907\pi$
$282$	71.3917	4.25131
$283$	−24.4401	−1.45281	−0.726407	−	0.687265i	$-0.758811\pi$
$283$	−24.4401	−1.45281	−0.726407	+	0.687265i	$0.758811\pi$
$284$	49.0085	2.90812
$285$	−1.85540	−0.109904
$286$	−16.2295	−0.959673
$287$	2.14963	0.126889
$288$	−62.3008	−3.67111
$289$	−14.1951	−0.835008
$290$	−18.3226	−1.07594
$291$	10.5702	0.619633
$292$	−2.72076	−0.159221
$293$	−13.1590	−0.768758	−0.384379	−	0.923175i	$-0.625584\pi$
$293$	−13.1590	−0.768758	−0.384379	+	0.923175i	$0.625584\pi$
$294$	41.0685	2.39516
$295$	−17.1133	−0.996377
$296$	−7.06846	−0.410846
$297$	9.67414	0.561350
$298$	36.6519	2.12318
$299$	−1.10881	−0.0641242
$300$	−3.06904	−0.177191
$301$	1.78509	0.102891
$302$	−54.9583	−3.16250
$303$	−25.3549	−1.45660
$304$	−6.39069	−0.366531
$305$	16.9317	0.969509
$306$	−10.6057	−0.606290
$307$	27.2775	1.55681	0.778405	−	0.627762i	$-0.216029\pi$
$307$	27.2775	1.55681	0.778405	+	0.627762i	$0.216029\pi$
$308$	−25.1568	−1.43344
$309$	−14.9330	−0.849507
$310$	47.5855	2.70267
$311$	1.32941	0.0753838	0.0376919	−	0.999289i	$-0.487999\pi$
$311$	1.32941	0.0753838	0.0376919	+	0.999289i	$0.487999\pi$
$312$	23.7480	1.34447
$313$	−3.53001	−0.199528	−0.0997640	−	0.995011i	$-0.531809\pi$
$313$	−3.53001	−0.199528	−0.0997640	+	0.995011i	$0.531809\pi$
$314$	13.4032	0.756386
$315$	3.74663	0.211099
$316$	2.65632	0.149430
$317$	19.2276	1.07993	0.539963	−	0.841688i	$-0.318438\pi$
$317$	19.2276	1.07993	0.539963	+	0.841688i	$0.318438\pi$
$318$	63.9671	3.58710
$319$	−17.6433	−0.987833
$320$	90.3710	5.05189
$321$	−32.4813	−1.81293
$322$	−2.31969	−0.129271
$323$	−0.619458	−0.0344675
$324$	−60.8768	−3.38204
$325$	0.233522	0.0129535
$326$	15.9155	0.881478
$327$	−29.8011	−1.64800
$328$	−29.5083	−1.62932
$329$	−8.42018	−0.464220
$330$	81.4120	4.48158
$331$	−19.2891	−1.06023	−0.530113	−	0.847927i	$-0.677851\pi$
$331$	−19.2891	−1.06023	−0.530113	+	0.847927i	$0.677851\pi$
$332$	22.8624	1.25474
$333$	1.55868	0.0854153
$334$	2.88260	0.157729
$335$	7.94077	0.433851
$336$	29.8909	1.63068
$337$	7.98183	0.434798	0.217399	−	0.976083i	$-0.430243\pi$
$337$	7.98183	0.434798	0.217399	+	0.976083i	$0.430243\pi$
$338$	−2.77848	−0.151129
$339$	18.7970	1.02092
$340$	20.9145	1.13425
$341$	45.8213	2.48136
$342$	2.34229	0.126656
$343$	−10.1144	−0.546126
$344$	−24.5042	−1.32118
$345$	5.56211	0.299454
$346$	51.6670	2.77764
$347$	2.46082	0.132104	0.0660520	−	0.997816i	$-0.478960\pi$
$347$	2.46082	0.132104	0.0660520	+	0.997816i	$0.478960\pi$
$348$	39.6968	2.12797
$349$	−10.7772	−0.576891	−0.288445	−	0.957496i	$-0.593138\pi$
$349$	−10.7772	−0.576891	−0.288445	+	0.957496i	$0.593138\pi$
$350$	0.488539	0.0261135
$351$	1.65620	0.0884015
$352$	159.667	8.51028
$353$	−20.4374	−1.08777	−0.543886	−	0.839159i	$-0.683048\pi$
$353$	−20.4374	−1.08777	−0.543886	+	0.839159i	$0.683048\pi$
$354$	50.0410	2.65965
$355$	18.7059	0.992804
$356$	−17.5196	−0.928537
$357$	2.89736	0.153345
$358$	33.3643	1.76336
$359$	25.2735	1.33388	0.666941	−	0.745110i	$-0.267603\pi$
$359$	25.2735	1.33388	0.666941	+	0.745110i	$0.267603\pi$
$360$	−51.4305	−2.71063
$361$	−18.8632	−0.992800
$362$	49.4343	2.59821
$363$	53.1196	2.78806
$364$	−4.30682	−0.225739
$365$	−1.03848	−0.0543564
$366$	−49.5100	−2.58793
$367$	−5.29893	−0.276602	−0.138301	−	0.990390i	$-0.544164\pi$
$367$	−5.29893	−0.276602	−0.138301	+	0.990390i	$0.544164\pi$
$368$	19.1580	0.998679
$369$	6.50695	0.338738
$370$	−4.14846	−0.215668
$371$	−7.54450	−0.391691
$372$	−103.097	−5.34530
$373$	38.0431	1.96980	0.984900	−	0.173126i	$-0.0553869\pi$
$373$	38.0431	1.96980	0.984900	+	0.173126i	$0.0553869\pi$
$374$	27.1808	1.40549
$375$	−26.2528	−1.35569
$376$	115.585	5.96085
$377$	−3.02051	−0.155564
$378$	3.46485	0.178213
$379$	11.6631	0.599096	0.299548	−	0.954081i	$-0.403164\pi$
$379$	11.6631	0.599096	0.299548	+	0.954081i	$0.403164\pi$
$380$	−4.61899	−0.236949
$381$	41.1632	2.10886
$382$	68.1019	3.48440
$383$	24.9019	1.27243	0.636213	−	0.771513i	$-0.280500\pi$
$383$	24.9019	1.27243	0.636213	+	0.771513i	$0.280500\pi$
$384$	−138.642	−7.07504
$385$	−9.60201	−0.489364
$386$	−15.7135	−0.799795
$387$	5.40347	0.274674
$388$	26.3142	1.33590
$389$	29.0129	1.47101	0.735506	−	0.677518i	$-0.236944\pi$
$389$	29.0129	1.47101	0.735506	+	0.677518i	$0.236944\pi$
$390$	13.9376	0.705760
$391$	1.85701	0.0939129
$392$	66.4910	3.35830
$393$	11.2174	0.565841
$394$	−2.89403	−0.145799
$395$	1.01388	0.0510139
$396$	−76.1499	−3.82667
$397$	−27.4298	−1.37666	−0.688332	−	0.725396i	$-0.741657\pi$
$397$	−27.4298	−1.37666	−0.688332	+	0.725396i	$0.741657\pi$
$398$	−31.3938	−1.57363
$399$	−0.639886	−0.0320344
$400$	−4.03478	−0.201739
$401$	25.5091	1.27386	0.636931	−	0.770921i	$-0.280204\pi$
$401$	25.5091	1.27386	0.636931	+	0.770921i	$0.280204\pi$
$402$	−23.2196	−1.15809
$403$	7.84456	0.390765
$404$	−63.1206	−3.14037
$405$	−23.2358	−1.15460
$406$	−6.31904	−0.313609
$407$	−3.99466	−0.198008
$408$	−39.7726	−1.96904
$409$	−19.3315	−0.955883	−0.477941	−	0.878392i	$-0.658617\pi$
$409$	−19.3315	−0.955883	−0.477941	+	0.878392i	$0.658617\pi$
$410$	−17.3183	−0.855291
$411$	−34.8060	−1.71685
$412$	−37.1754	−1.83150
$413$	−5.90201	−0.290419
$414$	−7.02171	−0.345098
$415$	8.72627	0.428356
$416$	27.3348	1.34020
$417$	17.1622	0.840438
$418$	−6.00291	−0.293612
$419$	4.99707	0.244123	0.122061	−	0.992523i	$-0.461050\pi$
$419$	4.99707	0.244123	0.122061	+	0.992523i	$0.461050\pi$
$420$	21.6042	1.05418
$421$	−22.9226	−1.11718	−0.558590	−	0.829444i	$-0.688657\pi$
$421$	−22.9226	−1.11718	−0.558590	+	0.829444i	$0.688657\pi$
$422$	−48.3864	−2.35541
$423$	−25.4879	−1.23927
$424$	103.565	5.02954
$425$	−0.391096	−0.0189710
$426$	−54.6977	−2.65011
$427$	5.83939	0.282588
$428$	−80.8617	−3.90860
$429$	13.4209	0.647968
$430$	−14.3814	−0.693533
$431$	−15.3888	−0.741251	−0.370626	−	0.928782i	$-0.620857\pi$
$431$	−15.3888	−0.741251	−0.370626	+	0.928782i	$0.620857\pi$
$432$	−28.6158	−1.37678
$433$	−3.49976	−0.168188	−0.0840938	−	0.996458i	$-0.526800\pi$
$433$	−3.49976	−0.168188	−0.0840938	+	0.996458i	$0.526800\pi$
$434$	16.4112	0.787762
$435$	15.1517	0.726469
$436$	−74.1893	−3.55302
$437$	−0.410122	−0.0196188
$438$	3.03661	0.145095
$439$	16.7090	0.797479	0.398739	−	0.917064i	$-0.369448\pi$
$439$	16.7090	0.797479	0.398739	+	0.917064i	$0.369448\pi$
$440$	131.808	6.28371
$441$	−14.6621	−0.698195
$442$	4.65332	0.221336
$443$	−6.74554	−0.320490	−0.160245	−	0.987077i	$-0.551228\pi$
$443$	−6.74554	−0.320490	−0.160245	+	0.987077i	$0.551228\pi$
$444$	8.98785	0.426544
$445$	−6.68699	−0.316994
$446$	−70.1824	−3.32323
$447$	−30.3090	−1.43357
$448$	31.1670	1.47250
$449$	7.19925	0.339753	0.169877	−	0.985465i	$-0.445663\pi$
$449$	7.19925	0.339753	0.169877	+	0.985465i	$0.445663\pi$
$450$	1.47881	0.0697118
$451$	−16.6763	−0.785255
$452$	46.7949	2.20105
$453$	45.4474	2.13531
$454$	22.6224	1.06172
$455$	−1.64385	−0.0770650
$456$	8.78382	0.411340
$457$	18.8183	0.880281	0.440140	−	0.897929i	$-0.354929\pi$
$457$	18.8183	0.880281	0.440140	+	0.897929i	$0.354929\pi$
$458$	20.9720	0.979957
$459$	−2.77376	−0.129468
$460$	13.8468	0.645610
$461$	−29.2948	−1.36440	−0.682198	−	0.731168i	$-0.738976\pi$
$461$	−29.2948	−1.36440	−0.682198	+	0.731168i	$0.738976\pi$
$462$	28.0772	1.30627
$463$	−1.00000	−0.0464739
$463$	−1.00000	−0.0464739
$464$	52.1882	2.42277
$465$	−39.3505	−1.82484
$466$	−64.5281	−2.98921
$467$	28.2975	1.30945	0.654726	−	0.755867i	$-0.272784\pi$
$467$	28.2975	1.30945	0.654726	+	0.755867i	$0.272784\pi$
$468$	−13.0368	−0.602625
$469$	2.73860	0.126457
$470$	67.8365	3.12906
$471$	−11.0837	−0.510709
$472$	81.0178	3.72915
$473$	−13.8482	−0.636743
$474$	−2.96468	−0.136172
$475$	0.0863740	0.00396311
$476$	7.21294	0.330605
$477$	−22.8373	−1.04565
$478$	−53.0292	−2.42550
$479$	13.4334	0.613788	0.306894	−	0.951744i	$-0.400710\pi$
$479$	13.4334	0.613788	0.306894	+	0.951744i	$0.400710\pi$
$480$	−137.119	−6.25860
$481$	−0.683881	−0.0311823
$482$	66.2047	3.01554
$483$	1.91825	0.0872833
$484$	132.240	6.01093
$485$	10.0438	0.456064
$486$	54.1386	2.45578
$487$	20.5958	0.933284	0.466642	−	0.884446i	$-0.345464\pi$
$487$	20.5958	0.933284	0.466642	+	0.884446i	$0.345464\pi$
$488$	−80.1581	−3.62859
$489$	−13.1612	−0.595171
$490$	39.0233	1.76289
$491$	25.4077	1.14664	0.573318	−	0.819333i	$-0.305656\pi$
$491$	25.4077	1.14664	0.573318	+	0.819333i	$0.305656\pi$
$492$	37.5211	1.69158
$493$	5.05866	0.227831
$494$	−1.02769	−0.0462380
$495$	−29.0653	−1.30639
$496$	−135.538	−6.08583
$497$	6.45124	0.289378
$498$	−25.5164	−1.14342
$499$	16.8433	0.754011	0.377006	−	0.926211i	$-0.376954\pi$
$499$	16.8433	0.754011	0.377006	+	0.926211i	$0.376954\pi$
$500$	−65.3560	−2.92281
$501$	−2.38375	−0.106498
$502$	−21.5705	−0.962740
$503$	11.6568	0.519753	0.259877	−	0.965642i	$-0.416318\pi$
$503$	11.6568	0.519753	0.259877	+	0.965642i	$0.416318\pi$
$504$	−17.7373	−0.790080
$505$	−24.0922	−1.07209
$506$	17.9955	0.799998
$507$	2.29765	0.102042
$508$	102.475	4.54660
$509$	3.11707	0.138162	0.0690809	−	0.997611i	$-0.477993\pi$
$509$	3.11707	0.138162	0.0690809	+	0.997611i	$0.477993\pi$
$510$	−23.3424	−1.03362
$511$	−0.358148	−0.0158435
$512$	−115.126	−5.08790
$513$	0.612588	0.0270464
$514$	77.4116	3.41448
$515$	−14.1893	−0.625257
$516$	31.1581	1.37166
$517$	65.3215	2.87284
$518$	−1.43071	−0.0628618
$519$	−42.7257	−1.87545
$520$	22.5654	0.989559
$521$	−31.3387	−1.37297	−0.686487	−	0.727142i	$-0.740848\pi$
$521$	−31.3387	−1.37297	−0.686487	+	0.727142i	$0.740848\pi$
$522$	−19.1278	−0.837201
$523$	−12.0780	−0.528135	−0.264068	−	0.964504i	$-0.585064\pi$
$523$	−12.0780	−0.528135	−0.264068	+	0.964504i	$0.585064\pi$
$524$	27.9254	1.21993
$525$	−0.403994	−0.0176317
$526$	37.1420	1.61947
$527$	−13.1379	−0.572294
$528$	−231.886	−10.0915
$529$	−21.7705	−0.946545
$530$	60.7816	2.64019
$531$	−17.8654	−0.775294
$532$	−1.59299	−0.0690647
$533$	−2.85496	−0.123662
$534$	19.5534	0.846159
$535$	−30.8638	−1.33436
$536$	−37.5931	−1.62378
$537$	−27.5904	−1.19061
$538$	−65.2189	−2.81179
$539$	37.5766	1.61854
$540$	−20.6826	−0.890036
$541$	18.2619	0.785140	0.392570	−	0.919722i	$-0.371586\pi$
$541$	18.2619	0.785140	0.392570	+	0.919722i	$0.371586\pi$
$542$	14.9525	0.642265
$543$	−40.8794	−1.75430
$544$	−45.7796	−1.96278
$545$	−28.3170	−1.21297
$546$	4.80678	0.205711
$547$	−17.9515	−0.767550	−0.383775	−	0.923427i	$-0.625376\pi$
$547$	−17.9515	−0.767550	−0.383775	+	0.923427i	$0.625376\pi$
$548$	−86.6490	−3.70146
$549$	17.6759	0.754387
$550$	−3.78996	−0.161604
$551$	−1.11721	−0.0475948
$552$	−26.3321	−1.12077
$553$	0.349665	0.0148693
$554$	35.7266	1.51788
$555$	3.43054	0.145618
$556$	42.7251	1.81195
$557$	−11.5189	−0.488072	−0.244036	−	0.969766i	$-0.578471\pi$
$557$	−11.5189	−0.488072	−0.244036	+	0.969766i	$0.578471\pi$
$558$	49.6768	2.10299
$559$	−2.37080	−0.100274
$560$	28.4024	1.20022
$561$	−22.4770	−0.948979
$562$	71.5703	3.01901
$563$	21.1227	0.890216	0.445108	−	0.895477i	$-0.353165\pi$
$563$	21.1227	0.890216	0.445108	+	0.895477i	$0.353165\pi$
$564$	−146.971	−6.18861
$565$	17.8610	0.751417
$566$	67.9064	2.85432
$567$	−8.01353	−0.336536
$568$	−88.5571	−3.71577
$569$	−11.8745	−0.497807	−0.248903	−	0.968528i	$-0.580070\pi$
$569$	−11.8745	−0.497807	−0.248903	+	0.968528i	$0.580070\pi$
$570$	5.15519	0.215927
$571$	−31.4473	−1.31603	−0.658015	−	0.753005i	$-0.728604\pi$
$571$	−31.4473	−1.31603	−0.658015	+	0.753005i	$0.728604\pi$
$572$	33.4112	1.39699
$573$	−56.3164	−2.35265
$574$	−5.97271	−0.249296
$575$	−0.258932	−0.0107982
$576$	94.3426	3.93094
$577$	18.3040	0.762007	0.381003	−	0.924574i	$-0.375579\pi$
$577$	18.3040	0.762007	0.381003	+	0.924574i	$0.375579\pi$
$578$	39.4409	1.64053
$579$	12.9942	0.540018
$580$	37.7199	1.56624
$581$	3.00950	0.124855
$582$	−29.3690	−1.21738
$583$	58.5282	2.42399
$584$	4.91635	0.203440
$585$	−4.97595	−0.205730
$586$	36.5621	1.51036
$587$	−3.80743	−0.157149	−0.0785747	−	0.996908i	$-0.525037\pi$
$587$	−3.80743	−0.157149	−0.0785747	+	0.996908i	$0.525037\pi$
$588$	−84.5461	−3.48662
$589$	2.90151	0.119555
$590$	47.5491	1.95756
$591$	2.39320	0.0984429
$592$	11.8161	0.485637
$593$	1.16574	0.0478711	0.0239355	−	0.999714i	$-0.492380\pi$
$593$	1.16574	0.0478711	0.0239355	+	0.999714i	$0.492380\pi$
$594$	−26.8794	−1.10288
$595$	2.75308	0.112865
$596$	−75.4538	−3.09071
$597$	25.9609	1.06251
$598$	3.08081	0.125984
$599$	23.4851	0.959575	0.479787	−	0.877385i	$-0.340714\pi$
$599$	23.4851	0.959575	0.479787	+	0.877385i	$0.340714\pi$
$600$	5.54569	0.226402
$601$	−11.7693	−0.480080	−0.240040	−	0.970763i	$-0.577161\pi$
$601$	−11.7693	−0.480080	−0.240040	+	0.970763i	$0.577161\pi$
$602$	−4.95983	−0.202148
$603$	8.28975	0.337585
$604$	113.141	4.60363
$605$	50.4744	2.05207
$606$	70.4480	2.86176
$607$	−41.7676	−1.69529	−0.847647	−	0.530561i	$-0.821981\pi$
$607$	−41.7676	−1.69529	−0.847647	+	0.530561i	$0.821981\pi$
$608$	10.1105	0.410034
$609$	5.22549	0.211748
$610$	−47.0445	−1.90478
$611$	11.1830	0.452415
$612$	21.8336	0.882572
$613$	−9.81613	−0.396470	−0.198235	−	0.980155i	$-0.563521\pi$
$613$	−9.81613	−0.396470	−0.198235	+	0.980155i	$0.563521\pi$
$614$	−75.7901	−3.05864
$615$	14.3213	0.577489
$616$	45.4578	1.83155
$617$	−35.2518	−1.41918	−0.709592	−	0.704612i	$-0.751121\pi$
$617$	−35.2518	−1.41918	−0.709592	+	0.704612i	$0.751121\pi$
$618$	41.4910	1.66901
$619$	−16.5190	−0.663953	−0.331976	−	0.943288i	$-0.607715\pi$
$619$	−16.5190	−0.663953	−0.331976	+	0.943288i	$0.607715\pi$
$620$	−97.9625	−3.93427
$621$	−1.83641	−0.0736928
$622$	−3.69373	−0.148105
$623$	−2.30620	−0.0923958
$624$	−39.6986	−1.58922
$625$	−23.7779	−0.951114
$626$	9.80806	0.392009
$627$	4.96407	0.198246
$628$	−27.5927	−1.10107
$629$	1.14534	0.0456679
$630$	−10.4099	−0.414742
$631$	49.4754	1.96958	0.984792	−	0.173737i	$-0.0555843\pi$
$631$	49.4754	1.96958	0.984792	+	0.173737i	$0.0555843\pi$
$632$	−4.79990	−0.190930
$633$	40.0128	1.59037
$634$	−53.4234	−2.12171
$635$	39.1134	1.55217
$636$	−131.687	−5.22172
$637$	6.43307	0.254888
$638$	49.0215	1.94078
$639$	19.5279	0.772513
$640$	−131.738	−5.20740
$641$	−6.82915	−0.269735	−0.134868	−	0.990864i	$-0.543061\pi$
$641$	−6.82915	−0.269735	−0.134868	+	0.990864i	$0.543061\pi$
$642$	90.2486	3.56183
$643$	−13.1536	−0.518727	−0.259363	−	0.965780i	$-0.583513\pi$
$643$	−13.1536	−0.518727	−0.259363	+	0.965780i	$0.583513\pi$
$644$	4.77545	0.188179
$645$	11.8926	0.468271
$646$	1.72115	0.0677178
$647$	12.8153	0.503820	0.251910	−	0.967751i	$-0.418941\pi$
$647$	12.8153	0.503820	0.251910	+	0.967751i	$0.418941\pi$
$648$	110.003	4.32132
$649$	45.7862	1.79727
$650$	−0.648836	−0.0254494
$651$	−13.5711	−0.531894
$652$	−32.7646	−1.28316
$653$	−5.82415	−0.227917	−0.113958	−	0.993486i	$-0.536353\pi$
$653$	−5.82415	−0.227917	−0.113958	+	0.993486i	$0.536353\pi$
$654$	82.8017	3.23780
$655$	10.6588	0.416472
$656$	49.3278	1.92593
$657$	−1.08412	−0.0422954
$658$	23.3953	0.912044
$659$	−28.4595	−1.10863	−0.554313	−	0.832308i	$-0.687019\pi$
$659$	−28.4595	−1.10863	−0.554313	+	0.832308i	$0.687019\pi$
$660$	−167.600	−6.52381
$661$	26.3632	1.02541	0.512705	−	0.858565i	$-0.328643\pi$
$661$	26.3632	1.02541	0.512705	+	0.858565i	$0.328643\pi$
$662$	53.5944	2.08301
$663$	−3.84803	−0.149445
$664$	−41.3118	−1.60321
$665$	−0.608021	−0.0235780
$666$	−4.33077	−0.167814
$667$	3.34917	0.129681
$668$	−5.93431	−0.229605
$669$	58.0369	2.24384
$670$	−22.0633	−0.852378
$671$	−45.3004	−1.74880
$672$	−47.2893	−1.82423
$673$	32.4688	1.25158	0.625791	−	0.779991i	$-0.284776\pi$
$673$	32.4688	1.25158	0.625791	+	0.779991i	$0.284776\pi$
$674$	−22.1774	−0.854240
$675$	0.386759	0.0148864
$676$	5.71995	0.219998
$677$	2.01286	0.0773605	0.0386802	−	0.999252i	$-0.487685\pi$
$677$	2.01286	0.0773605	0.0386802	+	0.999252i	$0.487685\pi$
$678$	−52.2272	−2.00577
$679$	3.46388	0.132931
$680$	−37.7920	−1.44926
$681$	−18.7075	−0.716872
$682$	−127.314	−4.87509
$683$	−0.612667	−0.0234430	−0.0117215	−	0.999931i	$-0.503731\pi$
$683$	−0.612667	−0.0234430	−0.0117215	+	0.999931i	$0.503731\pi$
$684$	−4.82198	−0.184373
$685$	−33.0727	−1.26364
$686$	28.1026	1.07296
$687$	−17.3426	−0.661663
$688$	40.9626	1.56168
$689$	10.0200	0.381730
$690$	−15.4542	−0.588332
$691$	20.9842	0.798277	0.399138	−	0.916891i	$-0.369309\pi$
$691$	20.9842	0.798277	0.399138	+	0.916891i	$0.369309\pi$
$692$	−106.365	−4.04339
$693$	−10.0240	−0.380780
$694$	−6.83735	−0.259542
$695$	16.3076	0.618582
$696$	−71.7311	−2.71896
$697$	4.78141	0.181109
$698$	29.9443	1.13341
$699$	53.3611	2.01830
$700$	−1.00574	−0.0380133
$701$	−30.7394	−1.16101	−0.580505	−	0.814257i	$-0.697145\pi$
$701$	−30.7394	−1.16101	−0.580505	+	0.814257i	$0.697145\pi$
$702$	−4.60172	−0.173681
$703$	−0.252951	−0.00954022
$704$	−241.785	−9.11262
$705$	−56.0969	−2.11273
$706$	56.7849	2.13713
$707$	−8.30888	−0.312488
$708$	−103.018	−3.87164
$709$	−41.2906	−1.55070	−0.775350	−	0.631531i	$-0.782427\pi$
$709$	−41.2906	−1.55070	−0.775350	+	0.631531i	$0.782427\pi$
$710$	−51.9739	−1.95054
$711$	1.05844	0.0396945
$712$	31.6575	1.18642
$713$	−8.69814	−0.325748
$714$	−8.05027	−0.301274
$715$	12.7526	0.476919
$716$	−68.6859	−2.56691
$717$	43.8521	1.63769
$718$	−70.2218	−2.62066
$719$	−17.3516	−0.647105	−0.323553	−	0.946210i	$-0.604877\pi$
$719$	−17.3516	−0.647105	−0.323553	+	0.946210i	$0.604877\pi$
$720$	85.9743	3.20407
$721$	−4.89359	−0.182247
$722$	52.4110	1.95054
$723$	−54.7475	−2.03608
$724$	−101.769	−3.78220
$725$	−0.705355	−0.0261962
$726$	−147.592	−5.47765
$727$	3.67125	0.136159	0.0680796	−	0.997680i	$-0.478313\pi$
$727$	3.67125	0.136159	0.0680796	+	0.997680i	$0.478313\pi$
$728$	7.78232	0.288432
$729$	−12.8409	−0.475589
$730$	2.88539	0.106793
$731$	3.97056	0.146856
$732$	101.924	3.76724
$733$	26.5535	0.980775	0.490387	−	0.871505i	$-0.336855\pi$
$733$	26.5535	0.980775	0.490387	+	0.871505i	$0.336855\pi$
$734$	14.7230	0.543435
$735$	−32.2701	−1.19030
$736$	−30.3091	−1.11721
$737$	−21.2453	−0.782581
$738$	−18.0794	−0.665513
$739$	17.8837	0.657861	0.328930	−	0.944354i	$-0.393312\pi$
$739$	17.8837	0.657861	0.328930	+	0.944354i	$0.393312\pi$
$740$	8.54027	0.313947
$741$	0.849843	0.0312198
$742$	20.9622	0.769548
$743$	17.5483	0.643784	0.321892	−	0.946776i	$-0.395681\pi$
$743$	17.5483	0.643784	0.321892	+	0.946776i	$0.395681\pi$
$744$	186.293	6.82983
$745$	−28.7997	−1.05514
$746$	−105.702	−3.87003
$747$	9.10977	0.333309
$748$	−55.9561	−2.04596
$749$	−10.6442	−0.388932
$750$	72.9429	2.66350
$751$	28.6922	1.04699	0.523497	−	0.852028i	$-0.324627\pi$
$751$	28.6922	1.04699	0.523497	+	0.852028i	$0.324627\pi$
$752$	−193.219	−7.04596
$753$	17.8376	0.650038
$754$	8.39242	0.305634
$755$	43.1842	1.57163
$756$	−7.13296	−0.259423
$757$	37.4151	1.35988	0.679938	−	0.733269i	$-0.262007\pi$
$757$	37.4151	1.35988	0.679938	+	0.733269i	$0.262007\pi$
$758$	−32.4058	−1.17703
$759$	−14.8813	−0.540156
$760$	8.34640	0.302756
$761$	−1.84781	−0.0669829	−0.0334915	−	0.999439i	$-0.510663\pi$
$761$	−1.84781	−0.0669829	−0.0334915	+	0.999439i	$0.510663\pi$
$762$	−114.371	−4.14323
$763$	−9.76591	−0.353550
$764$	−140.199	−5.07222
$765$	8.33359	0.301302
$766$	−69.1894	−2.49991
$767$	7.83855	0.283034
$768$	195.000	7.03645
$769$	2.01045	0.0724988	0.0362494	−	0.999343i	$-0.488459\pi$
$769$	2.01045	0.0724988	0.0362494	+	0.999343i	$0.488459\pi$
$770$	26.6790	0.961444
$771$	−64.0150	−2.30544
$772$	32.3487	1.16426
$773$	−7.34161	−0.264059	−0.132030	−	0.991246i	$-0.542149\pi$
$773$	−7.34161	−0.264059	−0.132030	+	0.991246i	$0.542149\pi$
$774$	−15.0134	−0.539647
$775$	1.83188	0.0658029
$776$	−47.5492	−1.70692
$777$	1.18312	0.0424441
$778$	−80.6118	−2.89007
$779$	−1.05598	−0.0378344
$780$	−28.6929	−1.02737
$781$	−50.0470	−1.79082
$782$	−5.15966	−0.184509
$783$	−5.00257	−0.178777
$784$	−111.150	−3.96965
$785$	−10.5317	−0.375894
$786$	−31.1672	−1.11170
$787$	44.3513	1.58095	0.790477	−	0.612491i	$-0.209833\pi$
$787$	44.3513	1.58095	0.790477	+	0.612491i	$0.209833\pi$
$788$	5.95782	0.212239
$789$	−30.7143	−1.09346
$790$	−2.81705	−0.100226
$791$	6.15986	0.219019
$792$	137.601	4.88944
$793$	−7.75538	−0.275402
$794$	76.2132	2.70471
$795$	−50.2630	−1.78264
$796$	64.6291	2.29072
$797$	42.5152	1.50596	0.752982	−	0.658041i	$-0.228615\pi$
$797$	42.5152	1.50596	0.752982	+	0.658041i	$0.228615\pi$
$798$	1.77791	0.0629374
$799$	−18.7289	−0.662582
$800$	6.38328	0.225683
$801$	−6.98087	−0.246657
$802$	−70.8764	−2.50273
$803$	2.77842	0.0980482
$804$	47.8012	1.68582
$805$	1.82272	0.0642426
$806$	−21.7960	−0.767730
$807$	53.9323	1.89851
$808$	114.057	4.01252
$809$	−3.11472	−0.109508	−0.0547539	−	0.998500i	$-0.517437\pi$
$809$	−3.11472	−0.109508	−0.0547539	+	0.998500i	$0.517437\pi$
$810$	64.5603	2.26842
$811$	−15.3377	−0.538580	−0.269290	−	0.963059i	$-0.586789\pi$
$811$	−15.3377	−0.538580	−0.269290	+	0.963059i	$0.586789\pi$
$812$	13.0088	0.456519
$813$	−12.3649	−0.433655
$814$	11.0991	0.389022
$815$	−12.5058	−0.438059
$816$	66.4861	2.32748
$817$	−0.876902	−0.0306789
$818$	53.7123	1.87801
$819$	−1.71610	−0.0599653
$820$	35.6526	1.24504
$821$	−27.0450	−0.943875	−0.471938	−	0.881632i	$-0.656445\pi$
$821$	−27.0450	−0.943875	−0.471938	+	0.881632i	$0.656445\pi$
$822$	96.7078	3.37307
$823$	−7.79780	−0.271814	−0.135907	−	0.990722i	$-0.543395\pi$
$823$	−7.79780	−0.271814	−0.135907	+	0.990722i	$0.543395\pi$
$824$	67.1751	2.34015
$825$	3.13408	0.109115
$826$	16.3986	0.570581
$827$	−9.93355	−0.345424	−0.172712	−	0.984972i	$-0.555253\pi$
$827$	−9.93355	−0.345424	−0.172712	+	0.984972i	$0.555253\pi$
$828$	14.4553	0.502357
$829$	55.9754	1.94410	0.972052	−	0.234764i	$-0.0754317\pi$
$829$	55.9754	1.94410	0.972052	+	0.234764i	$0.0754317\pi$
$830$	−24.2458	−0.841583
$831$	−29.5439	−1.02487
$832$	−41.3933	−1.43506
$833$	−10.7739	−0.373295
$834$	−47.6849	−1.65119
$835$	−2.26504	−0.0783850
$836$	12.3580	0.427409
$837$	12.9922	0.449075
$838$	−13.8843	−0.479624
$839$	36.8493	1.27218	0.636090	−	0.771615i	$-0.280551\pi$
$839$	36.8493	1.27218	0.636090	+	0.771615i	$0.280551\pi$
$840$	−39.0383	−1.34695
$841$	−19.8765	−0.685398
$842$	63.6900	2.19490
$843$	−59.1846	−2.03842
$844$	99.6112	3.42876
$845$	2.18323	0.0751053
$846$	70.8178	2.43476
$847$	17.4075	0.598129
$848$	−173.124	−5.94512
$849$	−56.1547	−1.92723
$850$	1.08665	0.0372719
$851$	0.758295	0.0259940
$852$	112.604	3.85775
$853$	−20.5407	−0.703300	−0.351650	−	0.936132i	$-0.614379\pi$
$853$	−20.5407	−0.703300	−0.351650	+	0.936132i	$0.614379\pi$
$854$	−16.2246	−0.555195
$855$	−1.84048	−0.0629432
$856$	146.115	4.99411
$857$	21.4551	0.732892	0.366446	−	0.930439i	$-0.380574\pi$
$857$	21.4551	0.732892	0.366446	+	0.930439i	$0.380574\pi$
$858$	−37.2897	−1.27305
$859$	−38.8471	−1.32545	−0.662723	−	0.748864i	$-0.730599\pi$
$859$	−38.8471	−1.32545	−0.662723	+	0.748864i	$0.730599\pi$
$860$	29.6065	1.00957
$861$	4.93909	0.168324
$862$	42.7574	1.45632
$863$	0.562745	0.0191560	0.00957802	−	0.999954i	$-0.496951\pi$
$863$	0.562745	0.0191560	0.00957802	+	0.999954i	$0.496951\pi$
$864$	45.2719	1.54018
$865$	−40.5980	−1.38037
$866$	9.72401	0.330435
$867$	−32.6154	−1.10768
$868$	−33.7851	−1.14674
$869$	−2.71261	−0.0920189
$870$	−42.0987	−1.42728
$871$	−3.63717	−0.123241
$872$	134.058	4.53978
$873$	10.4852	0.354870
$874$	1.13952	0.0385447
$875$	−8.60314	−0.290839
$876$	−6.25135	−0.211214
$877$	−0.774064	−0.0261383	−0.0130691	−	0.999915i	$-0.504160\pi$
$877$	−0.774064	−0.0261383	−0.0130691	+	0.999915i	$0.504160\pi$
$878$	−46.4257	−1.56679
$879$	−30.2347	−1.01979
$880$	−220.338	−7.42760
$881$	30.8052	1.03785	0.518927	−	0.854819i	$-0.326332\pi$
$881$	30.8052	1.03785	0.518927	+	0.854819i	$0.326332\pi$
$882$	40.7383	1.37173
$883$	46.5200	1.56552	0.782761	−	0.622322i	$-0.213811\pi$
$883$	46.5200	1.56552	0.782761	+	0.622322i	$0.213811\pi$
$884$	−9.57962	−0.322198
$885$	−39.3204	−1.32174
$886$	18.7423	0.629661
$887$	18.3353	0.615640	0.307820	−	0.951445i	$-0.400401\pi$
$887$	18.3353	0.615640	0.307820	+	0.951445i	$0.400401\pi$
$888$	−16.2408	−0.545006
$889$	13.4893	0.452418
$890$	18.5797	0.622792
$891$	62.1668	2.08267
$892$	144.482	4.83761
$893$	4.13631	0.138416
$894$	84.2130	2.81650
$895$	−26.2165	−0.876320
$896$	−45.4335	−1.51783
$897$	−2.54766	−0.0850637
$898$	−20.0030	−0.667507
$899$	−23.6945	−0.790257
$900$	−3.04437	−0.101479
$901$	−16.7812	−0.559062
$902$	46.3347	1.54278
$903$	4.10150	0.136489
$904$	−84.5573	−2.81233
$905$	−38.8437	−1.29121
$906$	−126.275	−4.19520
$907$	−2.37725	−0.0789354	−0.0394677	−	0.999221i	$-0.512566\pi$
$907$	−2.37725	−0.0789354	−0.0394677	+	0.999221i	$0.512566\pi$
$908$	−46.5720	−1.54555
$909$	−25.1510	−0.834208
$910$	4.56741	0.151408
$911$	−27.5129	−0.911542	−0.455771	−	0.890097i	$-0.650636\pi$
$911$	−27.5129	−0.911542	−0.455771	+	0.890097i	$0.650636\pi$
$912$	−14.6835	−0.486221
$913$	−23.3469	−0.772669
$914$	−52.2862	−1.72947
$915$	38.9031	1.28610
$916$	−43.1742	−1.42652
$917$	3.67597	0.121391
$918$	7.70684	0.254364
$919$	−59.6427	−1.96743	−0.983715	−	0.179733i	$-0.942477\pi$
$919$	−59.6427	−1.96743	−0.983715	+	0.179733i	$0.942477\pi$
$920$	−25.0208	−0.824911
$921$	62.6741	2.06518
$922$	81.3950	2.68060
$923$	−8.56799	−0.282019
$924$	−57.8015	−1.90153
$925$	−0.159701	−0.00525094
$926$	2.77848	0.0913065
$927$	−14.8129	−0.486520
$928$	−82.5650	−2.71033
$929$	−14.4760	−0.474943	−0.237472	−	0.971394i	$-0.576319\pi$
$929$	−14.4760	−0.474943	−0.237472	+	0.971394i	$0.576319\pi$
$930$	109.335	3.58522
$931$	2.37944	0.0779829
$932$	132.842	4.35137
$933$	3.05451	0.100000
$934$	−78.6240	−2.57266
$935$	−21.3577	−0.698471
$936$	23.5571	0.769989
$937$	−11.3662	−0.371317	−0.185659	−	0.982614i	$-0.559442\pi$
$937$	−11.3662	−0.371317	−0.185659	+	0.982614i	$0.559442\pi$
$938$	−7.60914	−0.248447
$939$	−8.11071	−0.264683
$940$	−139.652	−4.55496
$941$	−16.0302	−0.522568	−0.261284	−	0.965262i	$-0.584146\pi$
$941$	−16.0302	−0.522568	−0.261284	+	0.965262i	$0.584146\pi$
$942$	30.7958	1.00338
$943$	3.16561	0.103086
$944$	−135.434	−4.40800
$945$	−2.72255	−0.0885646
$946$	38.4771	1.25100
$947$	−36.0414	−1.17119	−0.585594	−	0.810604i	$-0.699139\pi$
$947$	−36.0414	−1.17119	−0.585594	+	0.810604i	$0.699139\pi$
$948$	6.10328	0.198225
$949$	0.475662	0.0154406
$950$	−0.239989	−0.00778626
$951$	44.1781	1.43257
$952$	−13.0336	−0.422422
$953$	−24.7339	−0.801211	−0.400606	−	0.916251i	$-0.631200\pi$
$953$	−24.7339	−0.801211	−0.400606	+	0.916251i	$0.631200\pi$
$954$	63.4529	2.05436
$955$	−53.5120	−1.73161
$956$	109.169	3.53078
$957$	−40.5380	−1.31041
$958$	−37.3245	−1.20590
$959$	−11.4061	−0.368321
$960$	207.640	6.70157
$961$	30.5371	0.985068
$962$	1.90015	0.0612633
$963$	−32.2202	−1.03828
$964$	−136.293	−4.38970
$965$	12.3471	0.397466
$966$	−5.32982	−0.171484
$967$	32.6388	1.04959	0.524797	−	0.851227i	$-0.324141\pi$
$967$	32.6388	1.04959	0.524797	+	0.851227i	$0.324141\pi$
$968$	−238.955	−7.68031
$969$	−1.42329	−0.0457228
$970$	−27.9064	−0.896022
$971$	−5.66265	−0.181723	−0.0908616	−	0.995864i	$-0.528962\pi$
$971$	−5.66265	−0.181723	−0.0908616	+	0.995864i	$0.528962\pi$
$972$	−111.453	−3.57486
$973$	5.62412	0.180301
$974$	−57.2250	−1.83361
$975$	0.536551	0.0171834
$976$	133.997	4.28914
$977$	2.31925	0.0741993	0.0370996	−	0.999312i	$-0.488188\pi$
$977$	2.31925	0.0741993	0.0370996	+	0.999312i	$0.488188\pi$
$978$	36.5682	1.16932
$979$	17.8909	0.571794
$980$	−80.3359	−2.56624
$981$	−29.5615	−0.943826
$982$	−70.5949	−2.25277
$983$	34.6904	1.10645	0.553226	−	0.833031i	$-0.313397\pi$
$983$	34.6904	1.10645	0.553226	+	0.833031i	$0.313397\pi$
$984$	−67.7996	−2.16137
$985$	2.27402	0.0724563
$986$	−14.0554	−0.447615
$987$	−19.3466	−0.615809
$988$	2.11567	0.0673084
$989$	2.62877	0.0835901
$990$	80.7575	2.56664
$991$	−13.3713	−0.424753	−0.212376	−	0.977188i	$-0.568120\pi$
$991$	−13.3713	−0.424753	−0.212376	+	0.977188i	$0.568120\pi$
$992$	214.429	6.80814
$993$	−44.3196	−1.40644
$994$	−17.9246	−0.568535
$995$	24.6680	0.782030
$996$	52.5297	1.66447
$997$	37.2498	1.17971	0.589857	−	0.807508i	$-0.299184\pi$
$997$	37.2498	1.17971	0.589857	+	0.807508i	$0.299184\pi$
$998$	−46.7989	−1.48139
$999$	−1.13264	−0.0358353

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6019.2.a.c.1.1	✓	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6019.2.a.c.1.1	✓	108	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:	\( N \)	\(=\)	\( 6019 = 13 \cdot 463 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6019.a (trivial)

\(f(q)\)	\(=\)	\(q-2.77848 q^{2} +2.29765 q^{3} +5.71995 q^{4} +2.18323 q^{5} -6.38396 q^{6} +0.752947 q^{7} -10.3358 q^{8} +2.27917 q^{9} +O(q^{10})\)	\(q-2.77848 q^{2} +2.29765 q^{3} +5.71995 q^{4} +2.18323 q^{5} -6.38396 q^{6} +0.752947 q^{7} -10.3358 q^{8} +2.27917 q^{9} -6.06605 q^{10} -5.84116 q^{11} +13.1424 q^{12} -1.00000 q^{13} -2.09205 q^{14} +5.01628 q^{15} +17.2779 q^{16} +1.67477 q^{17} -6.33264 q^{18} -0.369876 q^{19} +12.4880 q^{20} +1.73000 q^{21} +16.2295 q^{22} +1.10881 q^{23} -23.7480 q^{24} -0.233522 q^{25} +2.77848 q^{26} -1.65620 q^{27} +4.30682 q^{28} +3.02051 q^{29} -13.9376 q^{30} -7.84456 q^{31} -27.3348 q^{32} -13.4209 q^{33} -4.65332 q^{34} +1.64385 q^{35} +13.0368 q^{36} +0.683881 q^{37} +1.02769 q^{38} -2.29765 q^{39} -22.5654 q^{40} +2.85496 q^{41} -4.80678 q^{42} +2.37080 q^{43} -33.4112 q^{44} +4.97595 q^{45} -3.08081 q^{46} -11.1830 q^{47} +39.6986 q^{48} -6.43307 q^{49} +0.648836 q^{50} +3.84803 q^{51} -5.71995 q^{52} -10.0200 q^{53} +4.60172 q^{54} -12.7526 q^{55} -7.78232 q^{56} -0.849843 q^{57} -8.39242 q^{58} -7.83855 q^{59} +28.6929 q^{60} +7.75538 q^{61} +21.7960 q^{62} +1.71610 q^{63} +41.3933 q^{64} -2.18323 q^{65} +37.2897 q^{66} +3.63717 q^{67} +9.57962 q^{68} +2.54766 q^{69} -4.56741 q^{70} +8.56799 q^{71} -23.5571 q^{72} -0.475662 q^{73} -1.90015 q^{74} -0.536551 q^{75} -2.11567 q^{76} -4.39808 q^{77} +6.38396 q^{78} +0.464395 q^{79} +37.7217 q^{80} -10.6429 q^{81} -7.93244 q^{82} +3.99696 q^{83} +9.89554 q^{84} +3.65641 q^{85} -6.58723 q^{86} +6.94006 q^{87} +60.3731 q^{88} -3.06289 q^{89} -13.8256 q^{90} -0.752947 q^{91} +6.34235 q^{92} -18.0240 q^{93} +31.0717 q^{94} -0.807522 q^{95} -62.8057 q^{96} +4.60043 q^{97} +17.8742 q^{98} -13.3130 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q - 11 q^{2} + q^{3} + 95 q^{4} - 40 q^{5} - 10 q^{6} - 8 q^{7} - 33 q^{8} + 79 q^{9}+O(q^{10}) \) 108 * q - 11 * q^2 + q^3 + 95 * q^4 - 40 * q^5 - 10 * q^6 - 8 * q^7 - 33 * q^8 + 79 * q^9	\( 108 q - 11 q^{2} + q^{3} + 95 q^{4} - 40 q^{5} - 10 q^{6} - 8 q^{7} - 33 q^{8} + 79 q^{9} - q^{10} - 45 q^{11} - 6 q^{12} - 108 q^{13} - 31 q^{14} - 39 q^{15} + 73 q^{16} + 21 q^{17} - 35 q^{18} - 19 q^{19} - 79 q^{20} - 72 q^{21} - 26 q^{23} - 23 q^{24} + 92 q^{25} + 11 q^{26} + 7 q^{27} - 21 q^{28} - 94 q^{29} - 24 q^{30} - 36 q^{31} - 77 q^{32} - 32 q^{33} - 58 q^{34} - 10 q^{35} + 17 q^{36} - 54 q^{37} - 12 q^{38} - q^{39} - 4 q^{40} - 68 q^{41} - 11 q^{42} - 32 q^{43} - 151 q^{44} - 121 q^{45} - 33 q^{46} - 51 q^{47} - 27 q^{48} + 72 q^{49} - 45 q^{50} - 24 q^{51} - 95 q^{52} - 81 q^{53} - 29 q^{54} + 4 q^{55} - 68 q^{56} - 45 q^{57} - 30 q^{58} - 94 q^{59} - 108 q^{60} - 39 q^{61} - 9 q^{62} - 52 q^{63} + 31 q^{64} + 40 q^{65} - 40 q^{66} - 47 q^{67} + 24 q^{68} - 60 q^{69} - 66 q^{70} - 86 q^{71} - 91 q^{72} - 51 q^{73} - 110 q^{74} - 7 q^{75} - 51 q^{76} - 96 q^{77} + 10 q^{78} - 18 q^{79} - 136 q^{80} - 24 q^{81} - 33 q^{82} - 77 q^{83} - 113 q^{84} - 95 q^{85} - 137 q^{86} + 23 q^{87} + 19 q^{88} - 112 q^{89} - 19 q^{90} + 8 q^{91} - 111 q^{92} - 124 q^{93} - 20 q^{94} - 73 q^{95} - 77 q^{96} - 41 q^{97} - 80 q^{98} - 154 q^{99}+O(q^{100}) \) 108 * q - 11 * q^2 + q^3 + 95 * q^4 - 40 * q^5 - 10 * q^6 - 8 * q^7 - 33 * q^8 + 79 * q^9 - q^10 - 45 * q^11 - 6 * q^12 - 108 * q^13 - 31 * q^14 - 39 * q^15 + 73 * q^16 + 21 * q^17 - 35 * q^18 - 19 * q^19 - 79 * q^20 - 72 * q^21 - 26 * q^23 - 23 * q^24 + 92 * q^25 + 11 * q^26 + 7 * q^27 - 21 * q^28 - 94 * q^29 - 24 * q^30 - 36 * q^31 - 77 * q^32 - 32 * q^33 - 58 * q^34 - 10 * q^35 + 17 * q^36 - 54 * q^37 - 12 * q^38 - q^39 - 4 * q^40 - 68 * q^41 - 11 * q^42 - 32 * q^43 - 151 * q^44 - 121 * q^45 - 33 * q^46 - 51 * q^47 - 27 * q^48 + 72 * q^49 - 45 * q^50 - 24 * q^51 - 95 * q^52 - 81 * q^53 - 29 * q^54 + 4 * q^55 - 68 * q^56 - 45 * q^57 - 30 * q^58 - 94 * q^59 - 108 * q^60 - 39 * q^61 - 9 * q^62 - 52 * q^63 + 31 * q^64 + 40 * q^65 - 40 * q^66 - 47 * q^67 + 24 * q^68 - 60 * q^69 - 66 * q^70 - 86 * q^71 - 91 * q^72 - 51 * q^73 - 110 * q^74 - 7 * q^75 - 51 * q^76 - 96 * q^77 + 10 * q^78 - 18 * q^79 - 136 * q^80 - 24 * q^81 - 33 * q^82 - 77 * q^83 - 113 * q^84 - 95 * q^85 - 137 * q^86 + 23 * q^87 + 19 * q^88 - 112 * q^89 - 19 * q^90 + 8 * q^91 - 111 * q^92 - 124 * q^93 - 20 * q^94 - 73 * q^95 - 77 * q^96 - 41 * q^97 - 80 * q^98 - 154 * q^99

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