LMFDB - Embedded newform 6019.2.a.e.1.8

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:	$0$
Dimension:	$130$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
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)

$f(q)$	$=$	$q-2.52101 q^{2} -1.65021 q^{3} +4.35552 q^{4} +2.33988 q^{5} +4.16020 q^{6} +4.41588 q^{7} -5.93829 q^{8} -0.276814 q^{9} +O(q^{10})$	\(q-2.52101 q^{2} -1.65021 q^{3} +4.35552 q^{4} +2.33988 q^{5} +4.16020 q^{6} +4.41588 q^{7} -5.93829 q^{8} -0.276814 q^{9} -5.89887 q^{10} -3.93477 q^{11} -7.18751 q^{12} +1.00000 q^{13} -11.1325 q^{14} -3.86129 q^{15} +6.25949 q^{16} +7.77488 q^{17} +0.697852 q^{18} -0.949298 q^{19} +10.1914 q^{20} -7.28712 q^{21} +9.91960 q^{22} +9.11744 q^{23} +9.79941 q^{24} +0.475040 q^{25} -2.52101 q^{26} +5.40742 q^{27} +19.2334 q^{28} -3.56487 q^{29} +9.73437 q^{30} -8.57783 q^{31} -3.90368 q^{32} +6.49318 q^{33} -19.6006 q^{34} +10.3326 q^{35} -1.20567 q^{36} -7.21947 q^{37} +2.39319 q^{38} -1.65021 q^{39} -13.8949 q^{40} -0.707939 q^{41} +18.3709 q^{42} +3.82303 q^{43} -17.1379 q^{44} -0.647711 q^{45} -22.9852 q^{46} -11.2957 q^{47} -10.3295 q^{48} +12.5000 q^{49} -1.19758 q^{50} -12.8302 q^{51} +4.35552 q^{52} +14.2983 q^{53} -13.6322 q^{54} -9.20688 q^{55} -26.2228 q^{56} +1.56654 q^{57} +8.98709 q^{58} -8.13736 q^{59} -16.8179 q^{60} +4.59769 q^{61} +21.6248 q^{62} -1.22238 q^{63} -2.67774 q^{64} +2.33988 q^{65} -16.3694 q^{66} -0.553144 q^{67} +33.8636 q^{68} -15.0457 q^{69} -26.0487 q^{70} -0.599521 q^{71} +1.64380 q^{72} +5.89199 q^{73} +18.2004 q^{74} -0.783914 q^{75} -4.13468 q^{76} -17.3755 q^{77} +4.16020 q^{78} +1.24972 q^{79} +14.6465 q^{80} -8.09293 q^{81} +1.78472 q^{82} +13.0085 q^{83} -31.7392 q^{84} +18.1923 q^{85} -9.63793 q^{86} +5.88278 q^{87} +23.3658 q^{88} +11.0310 q^{89} +1.63289 q^{90} +4.41588 q^{91} +39.7112 q^{92} +14.1552 q^{93} +28.4766 q^{94} -2.22124 q^{95} +6.44188 q^{96} +5.44077 q^{97} -31.5127 q^{98} +1.08920 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 130 q + 10 q^{2} + 11 q^{3} + 146 q^{4} + 40 q^{5} + 4 q^{6} + 8 q^{7} + 24 q^{8} + 181 q^{9}+O(q^{10}) $ 130 * q + 10 * q^2 + 11 * q^3 + 146 * q^4 + 40 * q^5 + 4 * q^6 + 8 * q^7 + 24 * q^8 + 181 * q^9	\( 130 q + 10 q^{2} + 11 q^{3} + 146 q^{4} + 40 q^{5} + 4 q^{6} + 8 q^{7} + 24 q^{8} + 181 q^{9} + 5 q^{10} + 43 q^{11} + 28 q^{12} + 130 q^{13} + 47 q^{14} + 29 q^{15} + 170 q^{16} + 85 q^{17} + 20 q^{18} + 3 q^{19} + 73 q^{20} + 62 q^{21} + 12 q^{22} + 62 q^{23} - 5 q^{24} + 178 q^{25} + 10 q^{26} + 35 q^{27} - q^{28} + 134 q^{29} + 24 q^{30} + 14 q^{31} + 48 q^{32} + 4 q^{33} + 4 q^{34} + 50 q^{35} + 244 q^{36} + 32 q^{37} + 76 q^{38} + 11 q^{39} - 6 q^{40} + 48 q^{41} + 9 q^{42} + 34 q^{43} + 123 q^{44} + 115 q^{45} + 5 q^{46} + 25 q^{47} + 35 q^{48} + 210 q^{49} + 24 q^{50} + 20 q^{51} + 146 q^{52} + 193 q^{53} - 39 q^{54} + 32 q^{55} + 122 q^{56} + 7 q^{57} - 4 q^{58} + 50 q^{59} + 42 q^{60} + 57 q^{61} + 51 q^{62} + 8 q^{63} + 172 q^{64} + 40 q^{65} - 4 q^{66} + 21 q^{67} + 132 q^{68} + 92 q^{69} - 46 q^{70} + 58 q^{71} - 26 q^{72} + 15 q^{73} + 120 q^{74} + 23 q^{75} - 65 q^{76} + 192 q^{77} + 4 q^{78} + 32 q^{79} + 66 q^{80} + 326 q^{81} + 11 q^{82} + 33 q^{83} + 5 q^{84} + 43 q^{85} + 105 q^{86} + 31 q^{87} - 17 q^{88} + 84 q^{89} - 73 q^{90} + 8 q^{91} + 161 q^{92} + 52 q^{93} + 4 q^{94} + 59 q^{95} - 77 q^{96} + 9 q^{97} - 61 q^{98} + 100 q^{99}+O(q^{100}) \) 130 * q + 10 * q^2 + 11 * q^3 + 146 * q^4 + 40 * q^5 + 4 * q^6 + 8 * q^7 + 24 * q^8 + 181 * q^9 + 5 * q^10 + 43 * q^11 + 28 * q^12 + 130 * q^13 + 47 * q^14 + 29 * q^15 + 170 * q^16 + 85 * q^17 + 20 * q^18 + 3 * q^19 + 73 * q^20 + 62 * q^21 + 12 * q^22 + 62 * q^23 - 5 * q^24 + 178 * q^25 + 10 * q^26 + 35 * q^27 - q^28 + 134 * q^29 + 24 * q^30 + 14 * q^31 + 48 * q^32 + 4 * q^33 + 4 * q^34 + 50 * q^35 + 244 * q^36 + 32 * q^37 + 76 * q^38 + 11 * q^39 - 6 * q^40 + 48 * q^41 + 9 * q^42 + 34 * q^43 + 123 * q^44 + 115 * q^45 + 5 * q^46 + 25 * q^47 + 35 * q^48 + 210 * q^49 + 24 * q^50 + 20 * q^51 + 146 * q^52 + 193 * q^53 - 39 * q^54 + 32 * q^55 + 122 * q^56 + 7 * q^57 - 4 * q^58 + 50 * q^59 + 42 * q^60 + 57 * q^61 + 51 * q^62 + 8 * q^63 + 172 * q^64 + 40 * q^65 - 4 * q^66 + 21 * q^67 + 132 * q^68 + 92 * q^69 - 46 * q^70 + 58 * q^71 - 26 * q^72 + 15 * q^73 + 120 * q^74 + 23 * q^75 - 65 * q^76 + 192 * q^77 + 4 * q^78 + 32 * q^79 + 66 * q^80 + 326 * q^81 + 11 * q^82 + 33 * q^83 + 5 * q^84 + 43 * q^85 + 105 * q^86 + 31 * q^87 - 17 * q^88 + 84 * q^89 - 73 * q^90 + 8 * q^91 + 161 * q^92 + 52 * q^93 + 4 * q^94 + 59 * q^95 - 77 * q^96 + 9 * q^97 - 61 * q^98 + 100 * 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 $

$2$	−2.52101	−1.78263	−0.891313	−	0.453388i	$-0.850215\pi$
$2$	−2.52101	−1.78263	−0.891313	+	0.453388i	$0.850215\pi$
$3$	−1.65021	−0.952748	−0.476374	−	0.879243i	$-0.658049\pi$
$3$	−1.65021	−0.952748	−0.476374	+	0.879243i	$0.658049\pi$
$4$	4.35552	2.17776
$5$	2.33988	1.04643	0.523213	−	0.852202i	$-0.324733\pi$
$5$	2.33988	1.04643	0.523213	+	0.852202i	$0.324733\pi$
$6$	4.16020	1.69839
$7$	4.41588	1.66905	0.834523	−	0.550973i	$-0.185743\pi$
$7$	4.41588	1.66905	0.834523	+	0.550973i	$0.185743\pi$
$8$	−5.93829	−2.09950
$9$	−0.276814	−0.0922713
$10$	−5.89887	−1.86539
$11$	−3.93477	−1.18638	−0.593188	−	0.805064i	$-0.702131\pi$
$11$	−3.93477	−1.18638	−0.593188	+	0.805064i	$0.702131\pi$
$12$	−7.18751	−2.07485
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−11.1325	−2.97529
$15$	−3.86129	−0.996981
$16$	6.25949	1.56487
$17$	7.77488	1.88569	0.942843	−	0.333238i	$-0.108141\pi$
$17$	7.77488	1.88569	0.942843	+	0.333238i	$0.108141\pi$
$18$	0.697852	0.164485
$19$	−0.949298	−0.217784	−0.108892	−	0.994054i	$-0.534730\pi$
$19$	−0.949298	−0.217784	−0.108892	+	0.994054i	$0.534730\pi$
$20$	10.1914	2.27886
$21$	−7.28712	−1.59018
$22$	9.91960	2.11487
$23$	9.11744	1.90112	0.950559	−	0.310545i	$-0.100511\pi$
$23$	9.11744	1.90112	0.950559	+	0.310545i	$0.100511\pi$
$24$	9.79941	2.00030
$25$	0.475040	0.0950079
$26$	−2.52101	−0.494412
$27$	5.40742	1.04066
$28$	19.2334	3.63478
$29$	−3.56487	−0.661980	−0.330990	−	0.943634i	$-0.607383\pi$
$29$	−3.56487	−0.661980	−0.330990	+	0.943634i	$0.607383\pi$
$30$	9.73437	1.77724
$31$	−8.57783	−1.54062	−0.770312	−	0.637667i	$-0.779899\pi$
$31$	−8.57783	−1.54062	−0.770312	+	0.637667i	$0.779899\pi$
$32$	−3.90368	−0.690080
$33$	6.49318	1.13032
$34$	−19.6006	−3.36147
$35$	10.3326	1.74653
$36$	−1.20567	−0.200944
$37$	−7.21947	−1.18687	−0.593437	−	0.804880i	$-0.702229\pi$
$37$	−7.21947	−1.18687	−0.593437	+	0.804880i	$0.702229\pi$
$38$	2.39319	0.388227
$39$	−1.65021	−0.264245
$40$	−13.8949	−2.19698
$41$	−0.707939	−0.110561	−0.0552807	−	0.998471i	$-0.517605\pi$
$41$	−0.707939	−0.110561	−0.0552807	+	0.998471i	$0.517605\pi$
$42$	18.3709	2.83470
$43$	3.82303	0.583007	0.291504	−	0.956570i	$-0.405844\pi$
$43$	3.82303	0.583007	0.291504	+	0.956570i	$0.405844\pi$
$44$	−17.1379	−2.58364
$45$	−0.647711	−0.0965551
$46$	−22.9852	−3.38898
$47$	−11.2957	−1.64765	−0.823823	−	0.566847i	$-0.808163\pi$
$47$	−11.2957	−1.64765	−0.823823	+	0.566847i	$0.808163\pi$
$48$	−10.3295	−1.49093
$49$	12.5000	1.78571
$50$	−1.19758	−0.169364
$51$	−12.8302	−1.79658
$52$	4.35552	0.604001
$53$	14.2983	1.96402	0.982012	−	0.188820i	$-0.0604662\pi$
$53$	14.2983	1.96402	0.982012	+	0.188820i	$0.0604662\pi$
$54$	−13.6322	−1.85511
$55$	−9.20688	−1.24146
$56$	−26.2228	−3.50417
$57$	1.56654	0.207493
$58$	8.98709	1.18006
$59$	−8.13736	−1.05939	−0.529697	−	0.848187i	$-0.677694\pi$
$59$	−8.13736	−1.05939	−0.529697	+	0.848187i	$0.677694\pi$
$60$	−16.8179	−2.17118
$61$	4.59769	0.588673	0.294337	−	0.955702i	$-0.404901\pi$
$61$	4.59769	0.588673	0.294337	+	0.955702i	$0.404901\pi$
$62$	21.6248	2.74636
$63$	−1.22238	−0.154005
$64$	−2.67774	−0.334717
$65$	2.33988	0.290226
$66$	−16.3694	−2.01493
$67$	−0.553144	−0.0675773	−0.0337886	−	0.999429i	$-0.510757\pi$
$67$	−0.553144	−0.0675773	−0.0337886	+	0.999429i	$0.510757\pi$
$68$	33.8636	4.10657
$69$	−15.0457	−1.81129
$70$	−26.0487	−3.11342
$71$	−0.599521	−0.0711501	−0.0355750	−	0.999367i	$-0.511326\pi$
$71$	−0.599521	−0.0711501	−0.0355750	+	0.999367i	$0.511326\pi$
$72$	1.64380	0.193724
$73$	5.89199	0.689605	0.344803	−	0.938675i	$-0.387946\pi$
$73$	5.89199	0.689605	0.344803	+	0.938675i	$0.387946\pi$
$74$	18.2004	2.11575
$75$	−0.783914	−0.0905186
$76$	−4.13468	−0.474281
$77$	−17.3755	−1.98012
$78$	4.16020	0.471050
$79$	1.24972	0.140605	0.0703023	−	0.997526i	$-0.477604\pi$
$79$	1.24972	0.140605	0.0703023	+	0.997526i	$0.477604\pi$
$80$	14.6465	1.63752
$81$	−8.09293	−0.899215
$82$	1.78472	0.197090
$83$	13.0085	1.42787	0.713934	−	0.700213i	$-0.246912\pi$
$83$	13.0085	1.42787	0.713934	+	0.700213i	$0.246912\pi$
$84$	−31.7392	−3.46303
$85$	18.1923	1.97323
$86$	−9.63793	−1.03928
$87$	5.88278	0.630700
$88$	23.3658	2.49080
$89$	11.0310	1.16928	0.584642	−	0.811291i	$-0.301235\pi$
$89$	11.0310	1.16928	0.584642	+	0.811291i	$0.301235\pi$
$90$	1.63289	0.172122
$91$	4.41588	0.462910
$92$	39.7112	4.14017
$93$	14.1552	1.46783
$94$	28.4766	2.93714
$95$	−2.22124	−0.227895
$96$	6.44188	0.657472
$97$	5.44077	0.552427	0.276213	−	0.961096i	$-0.410920\pi$
$97$	5.44077	0.552427	0.276213	+	0.961096i	$0.410920\pi$
$98$	−31.5127	−3.18326
$99$	1.08920	0.109468
$100$	2.06904	0.206904
$101$	10.5629	1.05105	0.525524	−	0.850779i	$-0.323869\pi$
$101$	10.5629	1.05105	0.525524	+	0.850779i	$0.323869\pi$
$102$	32.3451	3.20264
$103$	−3.68216	−0.362814	−0.181407	−	0.983408i	$-0.558065\pi$
$103$	−3.68216	−0.362814	−0.181407	+	0.983408i	$0.558065\pi$
$104$	−5.93829	−0.582297
$105$	−17.0510	−1.66401
$106$	−36.0462	−3.50112
$107$	2.16975	0.209758	0.104879	−	0.994485i	$-0.466554\pi$
$107$	2.16975	0.209758	0.104879	+	0.994485i	$0.466554\pi$
$108$	23.5521	2.26630
$109$	−4.16392	−0.398831	−0.199416	−	0.979915i	$-0.563904\pi$
$109$	−4.16392	−0.398831	−0.199416	+	0.979915i	$0.563904\pi$
$110$	23.2107	2.21305
$111$	11.9136	1.13079
$112$	27.6411	2.61184
$113$	−2.05267	−0.193099	−0.0965495	−	0.995328i	$-0.530781\pi$
$113$	−2.05267	−0.193099	−0.0965495	+	0.995328i	$0.530781\pi$
$114$	−3.94927	−0.369883
$115$	21.3337	1.98938
$116$	−15.5269	−1.44163
$117$	−0.276814	−0.0255914
$118$	20.5144	1.88850
$119$	34.3329	3.14730
$120$	22.9295	2.09316
$121$	4.48238	0.407489
$122$	−11.5908	−1.04939
$123$	1.16825	0.105337
$124$	−37.3609	−3.35511
$125$	−10.5879	−0.947007
$126$	3.08163	0.274533
$127$	5.53465	0.491120	0.245560	−	0.969381i	$-0.421028\pi$
$127$	5.53465	0.491120	0.245560	+	0.969381i	$0.421028\pi$
$128$	14.5580	1.28676
$129$	−6.30880	−0.555459
$130$	−5.89887	−0.517365
$131$	14.6304	1.27826	0.639132	−	0.769097i	$-0.279294\pi$
$131$	14.6304	1.27826	0.639132	+	0.769097i	$0.279294\pi$
$132$	28.2812	2.46156
$133$	−4.19199	−0.363491
$134$	1.39448	0.120465
$135$	12.6527	1.08897
$136$	−46.1695	−3.95900
$137$	−16.2986	−1.39248	−0.696240	−	0.717809i	$-0.745145\pi$
$137$	−16.2986	−1.39248	−0.696240	+	0.717809i	$0.745145\pi$
$138$	37.9304	3.22885
$139$	6.16064	0.522538	0.261269	−	0.965266i	$-0.415859\pi$
$139$	6.16064	0.522538	0.261269	+	0.965266i	$0.415859\pi$
$140$	45.0039	3.80353
$141$	18.6402	1.56979
$142$	1.51140	0.126834
$143$	−3.93477	−0.329042
$144$	−1.73271	−0.144393
$145$	−8.34137	−0.692713
$146$	−14.8538	−1.22931
$147$	−20.6276	−1.70134
$148$	−31.4445	−2.58472
$149$	13.5636	1.11117	0.555585	−	0.831460i	$-0.312494\pi$
$149$	13.5636	1.11117	0.555585	+	0.831460i	$0.312494\pi$
$150$	1.97626	0.161361
$151$	−3.67682	−0.299215	−0.149608	−	0.988745i	$-0.547801\pi$
$151$	−3.67682	−0.299215	−0.149608	+	0.988745i	$0.547801\pi$
$152$	5.63721	0.457238
$153$	−2.15219	−0.173995
$154$	43.8038	3.52981
$155$	−20.0711	−1.61215
$156$	−7.18751	−0.575461
$157$	−10.5469	−0.841735	−0.420868	−	0.907122i	$-0.638274\pi$
$157$	−10.5469	−0.841735	−0.420868	+	0.907122i	$0.638274\pi$
$158$	−3.15056	−0.250645
$159$	−23.5952	−1.87122
$160$	−9.13414	−0.722118
$161$	40.2615	3.17305
$162$	20.4024	1.60296
$163$	15.2448	1.19407	0.597033	−	0.802216i	$-0.296346\pi$
$163$	15.2448	1.19407	0.597033	+	0.802216i	$0.296346\pi$
$164$	−3.08344	−0.240776
$165$	15.1933	1.18279
$166$	−32.7946	−2.54535
$167$	−8.74286	−0.676543	−0.338271	−	0.941049i	$-0.609842\pi$
$167$	−8.74286	−0.676543	−0.338271	+	0.941049i	$0.609842\pi$
$168$	43.2730	3.33859
$169$	1.00000	0.0769231
$170$	−45.8630	−3.51753
$171$	0.262779	0.0200952
$172$	16.6513	1.26965
$173$	5.97699	0.454422	0.227211	−	0.973846i	$-0.427039\pi$
$173$	5.97699	0.454422	0.227211	+	0.973846i	$0.427039\pi$
$174$	−14.8306	−1.12430
$175$	2.09772	0.158573
$176$	−24.6296	−1.85653
$177$	13.4283	1.00934
$178$	−27.8093	−2.08440
$179$	16.8614	1.26028	0.630139	−	0.776482i	$-0.282998\pi$
$179$	16.8614	1.26028	0.630139	+	0.776482i	$0.282998\pi$
$180$	−2.82112	−0.210274
$181$	−0.0697767	−0.00518646	−0.00259323	−	0.999997i	$-0.500825\pi$
$181$	−0.0697767	−0.00518646	−0.00259323	+	0.999997i	$0.500825\pi$
$182$	−11.1325	−0.825196
$183$	−7.58714	−0.560857
$184$	−54.1420	−3.99140
$185$	−16.8927	−1.24198
$186$	−35.6855	−2.61659
$187$	−30.5923	−2.23713
$188$	−49.1986	−3.58817
$189$	23.8785	1.73691
$190$	5.59979	0.406251
$191$	15.9832	1.15650	0.578251	−	0.815859i	$-0.303736\pi$
$191$	15.9832	1.15650	0.578251	+	0.815859i	$0.303736\pi$
$192$	4.41883	0.318901
$193$	10.3949	0.748240	0.374120	−	0.927380i	$-0.377945\pi$
$193$	10.3949	0.748240	0.374120	+	0.927380i	$0.377945\pi$
$194$	−13.7163	−0.984771
$195$	−3.86129	−0.276513
$196$	54.4439	3.88885
$197$	21.5465	1.53512	0.767562	−	0.640975i	$-0.221470\pi$
$197$	21.5465	1.53512	0.767562	+	0.640975i	$0.221470\pi$
$198$	−2.74588	−0.195141
$199$	−3.80220	−0.269531	−0.134765	−	0.990878i	$-0.543028\pi$
$199$	−3.80220	−0.269531	−0.134765	+	0.990878i	$0.543028\pi$
$200$	−2.82092	−0.199469
$201$	0.912802	0.0643841
$202$	−26.6292	−1.87362
$203$	−15.7420	−1.10487
$204$	−55.8820	−3.91252
$205$	−1.65649	−0.115694
$206$	9.28278	0.646762
$207$	−2.52383	−0.175419
$208$	6.25949	0.434017
$209$	3.73527	0.258374
$210$	42.9858	2.96630
$211$	−18.6138	−1.28143	−0.640714	−	0.767780i	$-0.721362\pi$
$211$	−18.6138	−1.28143	−0.640714	+	0.767780i	$0.721362\pi$
$212$	62.2765	4.27717
$213$	0.989334	0.0677881
$214$	−5.46998	−0.373920
$215$	8.94544	0.610074
$216$	−32.1109	−2.18487
$217$	−37.8787	−2.57137
$218$	10.4973	0.710967
$219$	−9.72301	−0.657020
$220$	−40.1007	−2.70359
$221$	7.77488	0.522995
$222$	−30.0344	−2.01578
$223$	−26.1817	−1.75325	−0.876627	−	0.481171i	$-0.840212\pi$
$223$	−26.1817	−1.75325	−0.876627	+	0.481171i	$0.840212\pi$
$224$	−17.2382	−1.15177
$225$	−0.131497	−0.00876650
$226$	5.17481	0.344223
$227$	13.0199	0.864160	0.432080	−	0.901835i	$-0.357780\pi$
$227$	13.0199	0.864160	0.432080	+	0.901835i	$0.357780\pi$
$228$	6.82309	0.451870
$229$	1.72248	0.113825	0.0569125	−	0.998379i	$-0.481874\pi$
$229$	1.72248	0.113825	0.0569125	+	0.998379i	$0.481874\pi$
$230$	−53.7826	−3.54632
$231$	28.6731	1.88655
$232$	21.1692	1.38983
$233$	17.2863	1.13246	0.566230	−	0.824247i	$-0.308401\pi$
$233$	17.2863	1.13246	0.566230	+	0.824247i	$0.308401\pi$
$234$	0.697852	0.0456200
$235$	−26.4306	−1.72414
$236$	−35.4424	−2.30710
$237$	−2.06230	−0.133961
$238$	−86.5539	−5.61045
$239$	−9.26233	−0.599130	−0.299565	−	0.954076i	$-0.596842\pi$
$239$	−9.26233	−0.599130	−0.299565	+	0.954076i	$0.596842\pi$
$240$	−24.1697	−1.56015
$241$	−21.7411	−1.40047	−0.700234	−	0.713913i	$-0.746921\pi$
$241$	−21.7411	−1.40047	−0.700234	+	0.713913i	$0.746921\pi$
$242$	−11.3001	−0.726401
$243$	−2.86725	−0.183934
$244$	20.0253	1.28199
$245$	29.2485	1.86862
$246$	−2.94517	−0.187777
$247$	−0.949298	−0.0604024
$248$	50.9376	3.23454
$249$	−21.4667	−1.36040
$250$	26.6922	1.68816
$251$	−21.3120	−1.34520	−0.672602	−	0.740005i	$-0.734823\pi$
$251$	−21.3120	−1.34520	−0.672602	+	0.740005i	$0.734823\pi$
$252$	−5.32408	−0.335386
$253$	−35.8750	−2.25544
$254$	−13.9529	−0.875484
$255$	−30.0211	−1.87999
$256$	−31.3454	−1.95909
$257$	−8.26218	−0.515381	−0.257690	−	0.966228i	$-0.582961\pi$
$257$	−8.26218	−0.515381	−0.257690	+	0.966228i	$0.582961\pi$
$258$	15.9046	0.990176
$259$	−31.8803	−1.98095
$260$	10.1914	0.632043
$261$	0.986806	0.0610817
$262$	−36.8835	−2.27867
$263$	−1.68537	−0.103924	−0.0519621	−	0.998649i	$-0.516548\pi$
$263$	−1.68537	−0.103924	−0.0519621	+	0.998649i	$0.516548\pi$
$264$	−38.5584	−2.37311
$265$	33.4563	2.05521
$266$	10.5681	0.647969
$267$	−18.2035	−1.11403
$268$	−2.40923	−0.147167
$269$	5.32247	0.324517	0.162258	−	0.986748i	$-0.448122\pi$
$269$	5.32247	0.324517	0.162258	+	0.986748i	$0.448122\pi$
$270$	−31.8977	−1.94123
$271$	−12.9790	−0.788420	−0.394210	−	0.919020i	$-0.628982\pi$
$271$	−12.9790	−0.788420	−0.394210	+	0.919020i	$0.628982\pi$
$272$	48.6668	2.95086
$273$	−7.28712	−0.441037
$274$	41.0889	2.48227
$275$	−1.86917	−0.112715
$276$	−65.5317	−3.94454
$277$	3.25398	0.195513	0.0977563	−	0.995210i	$-0.468833\pi$
$277$	3.25398	0.195513	0.0977563	+	0.995210i	$0.468833\pi$
$278$	−15.5311	−0.931491
$279$	2.37446	0.142155
$280$	−61.3582	−3.66685
$281$	29.6050	1.76609	0.883044	−	0.469290i	$-0.155490\pi$
$281$	29.6050	1.76609	0.883044	+	0.469290i	$0.155490\pi$
$282$	−46.9923	−2.79835
$283$	28.5778	1.69878	0.849388	−	0.527769i	$-0.176971\pi$
$283$	28.5778	1.69878	0.849388	+	0.527769i	$0.176971\pi$
$284$	−2.61122	−0.154948
$285$	3.66551	0.217126
$286$	9.91960	0.586558
$287$	−3.12617	−0.184532
$288$	1.08059	0.0636745
$289$	43.4488	2.55581
$290$	21.0287	1.23485
$291$	−8.97841	−0.526324
$292$	25.6627	1.50179
$293$	−0.474736	−0.0277344	−0.0138672	−	0.999904i	$-0.504414\pi$
$293$	−0.474736	−0.0277344	−0.0138672	+	0.999904i	$0.504414\pi$
$294$	52.0025	3.03285
$295$	−19.0404	−1.10858
$296$	42.8713	2.49185
$297$	−21.2769	−1.23461
$298$	−34.1939	−1.98080
$299$	9.11744	0.527275
$300$	−3.41435	−0.197128
$301$	16.8821	0.973066
$302$	9.26931	0.533389
$303$	−17.4310	−1.00138
$304$	−5.94212	−0.340804
$305$	10.7580	0.616003
$306$	5.42571	0.310167
$307$	16.5796	0.946247	0.473123	−	0.880996i	$-0.343126\pi$
$307$	16.5796	0.946247	0.473123	+	0.880996i	$0.343126\pi$
$308$	−75.6791	−4.31221
$309$	6.07633	0.345670
$310$	50.5995	2.87386
$311$	7.72300	0.437931	0.218966	−	0.975733i	$-0.429732\pi$
$311$	7.72300	0.437931	0.218966	+	0.975733i	$0.429732\pi$
$312$	9.79941	0.554783
$313$	−27.6885	−1.56505	−0.782524	−	0.622621i	$-0.786068\pi$
$313$	−27.6885	−1.56505	−0.782524	+	0.622621i	$0.786068\pi$
$314$	26.5889	1.50050
$315$	−2.86021	−0.161155
$316$	5.44318	0.306203
$317$	5.85368	0.328775	0.164388	−	0.986396i	$-0.447435\pi$
$317$	5.85368	0.328775	0.164388	+	0.986396i	$0.447435\pi$
$318$	59.4838	3.33569
$319$	14.0269	0.785357
$320$	−6.26559	−0.350257
$321$	−3.58055	−0.199847
$322$	−101.500	−5.65637
$323$	−7.38068	−0.410672
$324$	−35.2489	−1.95827
$325$	0.475040	0.0263505
$326$	−38.4324	−2.12858
$327$	6.87134	0.379986
$328$	4.20395	0.232124
$329$	−49.8804	−2.75000
$330$	−38.3025	−2.10848
$331$	−9.58640	−0.526916	−0.263458	−	0.964671i	$-0.584863\pi$
$331$	−9.58640	−0.526916	−0.263458	+	0.964671i	$0.584863\pi$
$332$	56.6587	3.10955
$333$	1.99845	0.109514
$334$	22.0409	1.20602
$335$	−1.29429	−0.0707146
$336$	−45.6136	−2.48843
$337$	−14.1003	−0.768093	−0.384047	−	0.923314i	$-0.625470\pi$
$337$	−14.1003	−0.768093	−0.384047	+	0.923314i	$0.625470\pi$
$338$	−2.52101	−0.137125
$339$	3.38733	0.183975
$340$	79.2368	4.29722
$341$	33.7517	1.82776
$342$	−0.662469	−0.0358222
$343$	24.2873	1.31139
$344$	−22.7023	−1.22403
$345$	−35.2051	−1.89538
$346$	−15.0681	−0.810065
$347$	26.1931	1.40612	0.703060	−	0.711131i	$-0.251817\pi$
$347$	26.1931	1.40612	0.703060	+	0.711131i	$0.251817\pi$
$348$	25.6225	1.37351
$349$	23.1656	1.24002	0.620012	−	0.784592i	$-0.287128\pi$
$349$	23.1656	1.24002	0.620012	+	0.784592i	$0.287128\pi$
$350$	−5.28838	−0.282676
$351$	5.40742	0.288627
$352$	15.3601	0.818694
$353$	−22.7238	−1.20947	−0.604733	−	0.796429i	$-0.706720\pi$
$353$	−22.7238	−1.20947	−0.604733	+	0.796429i	$0.706720\pi$
$354$	−33.8530	−1.79927
$355$	−1.40281	−0.0744533
$356$	48.0457	2.54642
$357$	−56.6565	−2.99858
$358$	−42.5078	−2.24660
$359$	−22.7107	−1.19862	−0.599312	−	0.800515i	$-0.704559\pi$
$359$	−22.7107	−1.19862	−0.599312	+	0.800515i	$0.704559\pi$
$360$	3.84630	0.202718
$361$	−18.0988	−0.952570
$362$	0.175908	0.00924553
$363$	−7.39686	−0.388234
$364$	19.2334	1.00811
$365$	13.7866	0.721621
$366$	19.1273	0.999800
$367$	35.0475	1.82947	0.914733	−	0.404059i	$-0.132401\pi$
$367$	35.0475	1.82947	0.914733	+	0.404059i	$0.132401\pi$
$368$	57.0705	2.97501
$369$	0.195967	0.0102016
$370$	42.5868	2.21398
$371$	63.1396	3.27805
$372$	61.6532	3.19657
$373$	−5.35565	−0.277305	−0.138653	−	0.990341i	$-0.544277\pi$
$373$	−5.35565	−0.277305	−0.138653	+	0.990341i	$0.544277\pi$
$374$	77.1237	3.98797
$375$	17.4722	0.902259
$376$	67.0771	3.45924
$377$	−3.56487	−0.183600
$378$	−60.1981	−3.09626
$379$	−7.95590	−0.408667	−0.204334	−	0.978901i	$-0.565503\pi$
$379$	−7.95590	−0.408667	−0.204334	+	0.978901i	$0.565503\pi$
$380$	−9.67466	−0.496300
$381$	−9.13332	−0.467914
$382$	−40.2938	−2.06161
$383$	19.7037	1.00681	0.503406	−	0.864050i	$-0.332080\pi$
$383$	19.7037	1.00681	0.503406	+	0.864050i	$0.332080\pi$
$384$	−24.0237	−1.22595
$385$	−40.6565	−2.07205
$386$	−26.2057	−1.33383
$387$	−1.05827	−0.0537948
$388$	23.6974	1.20305
$389$	−19.5424	−0.990837	−0.495419	−	0.868654i	$-0.664985\pi$
$389$	−19.5424	−0.990837	−0.495419	+	0.868654i	$0.664985\pi$
$390$	9.73437	0.492919
$391$	70.8870	3.58491
$392$	−74.2286	−3.74911
$393$	−24.1432	−1.21786
$394$	−54.3190	−2.73655
$395$	2.92420	0.147132
$396$	4.74402	0.238396
$397$	31.9525	1.60365	0.801826	−	0.597558i	$-0.203862\pi$
$397$	31.9525	1.60365	0.801826	+	0.597558i	$0.203862\pi$
$398$	9.58540	0.480472
$399$	6.91765	0.346316
$400$	2.97350	0.148675
$401$	−13.1950	−0.658927	−0.329463	−	0.944168i	$-0.606868\pi$
$401$	−13.1950	−0.658927	−0.329463	+	0.944168i	$0.606868\pi$
$402$	−2.30119	−0.114773
$403$	−8.57783	−0.427292
$404$	46.0069	2.28893
$405$	−18.9365	−0.940962
$406$	39.6859	1.96958
$407$	28.4069	1.40808
$408$	76.1893	3.77193
$409$	3.24808	0.160607	0.0803035	−	0.996770i	$-0.474411\pi$
$409$	3.24808	0.160607	0.0803035	+	0.996770i	$0.474411\pi$
$410$	4.17604	0.206240
$411$	26.8960	1.32668
$412$	−16.0377	−0.790121
$413$	−35.9336	−1.76818
$414$	6.36262	0.312706
$415$	30.4383	1.49416
$416$	−3.90368	−0.191394
$417$	−10.1663	−0.497847
$418$	−9.41666	−0.460584
$419$	−12.1104	−0.591630	−0.295815	−	0.955245i	$-0.595591\pi$
$419$	−12.1104	−0.591630	−0.295815	+	0.955245i	$0.595591\pi$
$420$	−74.2659	−3.62380
$421$	35.9925	1.75417	0.877085	−	0.480336i	$-0.159485\pi$
$421$	35.9925	1.75417	0.877085	+	0.480336i	$0.159485\pi$
$422$	46.9257	2.28431
$423$	3.12680	0.152030
$424$	−84.9075	−4.12347
$425$	3.69338	0.179155
$426$	−2.49413	−0.120841
$427$	20.3028	0.982523
$428$	9.45040	0.456802
$429$	6.49318	0.313494
$430$	−22.5516	−1.08753
$431$	−14.9812	−0.721621	−0.360810	−	0.932639i	$-0.617500\pi$
$431$	−14.9812	−0.721621	−0.360810	+	0.932639i	$0.617500\pi$
$432$	33.8477	1.62850
$433$	−16.5375	−0.794742	−0.397371	−	0.917658i	$-0.630077\pi$
$433$	−16.5375	−0.794742	−0.397371	+	0.917658i	$0.630077\pi$
$434$	95.4927	4.58380
$435$	13.7650	0.659981
$436$	−18.1360	−0.868558
$437$	−8.65517	−0.414033
$438$	24.5119	1.17122
$439$	−12.5919	−0.600978	−0.300489	−	0.953785i	$-0.597150\pi$
$439$	−12.5919	−0.600978	−0.300489	+	0.953785i	$0.597150\pi$
$440$	54.6731	2.60644
$441$	−3.46017	−0.164770
$442$	−19.6006	−0.932305
$443$	5.01044	0.238053	0.119027	−	0.992891i	$-0.462023\pi$
$443$	5.01044	0.238053	0.119027	+	0.992891i	$0.462023\pi$
$444$	51.8900	2.46259
$445$	25.8112	1.22357
$446$	66.0044	3.12540
$447$	−22.3827	−1.05866
$448$	−11.8246	−0.558659
$449$	29.1307	1.37476	0.687381	−	0.726297i	$-0.258760\pi$
$449$	29.1307	1.37476	0.687381	+	0.726297i	$0.258760\pi$
$450$	0.331507	0.0156274
$451$	2.78557	0.131167
$452$	−8.94044	−0.420523
$453$	6.06752	0.285077
$454$	−32.8233	−1.54048
$455$	10.3326	0.484401
$456$	−9.30257	−0.435633
$457$	−25.5122	−1.19341	−0.596705	−	0.802461i	$-0.703524\pi$
$457$	−25.5122	−1.19341	−0.596705	+	0.802461i	$0.703524\pi$
$458$	−4.34241	−0.202907
$459$	42.0421	1.96236
$460$	92.9193	4.33239
$461$	−10.4038	−0.484554	−0.242277	−	0.970207i	$-0.577894\pi$
$461$	−10.4038	−0.484554	−0.242277	+	0.970207i	$0.577894\pi$
$462$	−72.2853	−3.36302
$463$	−1.00000	−0.0464739
$463$	−1.00000	−0.0464739
$464$	−22.3143	−1.03591
$465$	33.1215	1.53597
$466$	−43.5789	−2.01875
$467$	−22.2929	−1.03159	−0.515795	−	0.856712i	$-0.672504\pi$
$467$	−22.2929	−1.03159	−0.515795	+	0.856712i	$0.672504\pi$
$468$	−1.20567	−0.0557320
$469$	−2.44262	−0.112790
$470$	66.6319	3.07350
$471$	17.4046	0.801962
$472$	48.3220	2.22420
$473$	−15.0427	−0.691666
$474$	5.19909	0.238802
$475$	−0.450954	−0.0206912
$476$	149.538	6.85405
$477$	−3.95797	−0.181223
$478$	23.3505	1.06803
$479$	−30.0710	−1.37398	−0.686988	−	0.726668i	$-0.741068\pi$
$479$	−30.0710	−1.37398	−0.686988	+	0.726668i	$0.741068\pi$
$480$	15.0732	0.687996
$481$	−7.21947	−0.329180
$482$	54.8097	2.49651
$483$	−66.4399	−3.02312
$484$	19.5231	0.887412
$485$	12.7308	0.578074
$486$	7.22838	0.327886
$487$	21.1327	0.957614	0.478807	−	0.877920i	$-0.341069\pi$
$487$	21.1327	0.957614	0.478807	+	0.877920i	$0.341069\pi$
$488$	−27.3024	−1.23592
$489$	−25.1571	−1.13764
$490$	−73.7359	−3.33105
$491$	−25.8953	−1.16864	−0.584318	−	0.811525i	$-0.698638\pi$
$491$	−25.8953	−1.16864	−0.584318	+	0.811525i	$0.698638\pi$
$492$	5.08831	0.229399
$493$	−27.7165	−1.24829
$494$	2.39319	0.107675
$495$	2.54859	0.114551
$496$	−53.6928	−2.41088
$497$	−2.64741	−0.118753
$498$	54.1179	2.42508
$499$	−43.5093	−1.94774	−0.973872	−	0.227096i	$-0.927077\pi$
$499$	−43.5093	−1.94774	−0.973872	+	0.227096i	$0.927077\pi$
$500$	−46.1156	−2.06235
$501$	14.4275	0.644575
$502$	53.7279	2.39800
$503$	−0.953282	−0.0425048	−0.0212524	−	0.999774i	$-0.506765\pi$
$503$	−0.953282	−0.0425048	−0.0212524	+	0.999774i	$0.506765\pi$
$504$	7.25883	0.323334
$505$	24.7159	1.09984
$506$	90.4414	4.02061
$507$	−1.65021	−0.0732883
$508$	24.1062	1.06954
$509$	1.36340	0.0604317	0.0302159	−	0.999543i	$-0.490381\pi$
$509$	1.36340	0.0604317	0.0302159	+	0.999543i	$0.490381\pi$
$510$	75.6835	3.35132
$511$	26.0183	1.15098
$512$	49.9063	2.20557
$513$	−5.13326	−0.226639
$514$	20.8291	0.918731
$515$	−8.61581	−0.379658
$516$	−27.4781	−1.20966
$517$	44.4459	1.95473
$518$	80.3708	3.53129
$519$	−9.86328	−0.432950
$520$	−13.8949	−0.609331
$521$	−8.26592	−0.362136	−0.181068	−	0.983471i	$-0.557955\pi$
$521$	−8.26592	−0.362136	−0.181068	+	0.983471i	$0.557955\pi$
$522$	−2.48775	−0.108886
$523$	26.8931	1.17596	0.587978	−	0.808877i	$-0.299924\pi$
$523$	26.8931	1.17596	0.587978	+	0.808877i	$0.299924\pi$
$524$	63.7230	2.78375
$525$	−3.46167	−0.151080
$526$	4.24884	0.185258
$527$	−66.6916	−2.90513
$528$	40.6440	1.76880
$529$	60.1277	2.61425
$530$	−84.3439	−3.66366
$531$	2.25253	0.0977516
$532$	−18.2583	−0.791596
$533$	−0.707939	−0.0306642
$534$	45.8912	1.98591
$535$	5.07697	0.219496
$536$	3.28473	0.141879
$537$	−27.8248	−1.20073
$538$	−13.4180	−0.578492
$539$	−49.1846	−2.11853
$540$	55.1091	2.37152
$541$	−14.4611	−0.621730	−0.310865	−	0.950454i	$-0.600619\pi$
$541$	−14.4611	−0.621730	−0.310865	+	0.950454i	$0.600619\pi$
$542$	32.7203	1.40546
$543$	0.115146	0.00494139
$544$	−30.3507	−1.30127
$545$	−9.74308	−0.417348
$546$	18.3709	0.786204
$547$	17.8783	0.764421	0.382210	−	0.924075i	$-0.375163\pi$
$547$	17.8783	0.764421	0.382210	+	0.924075i	$0.375163\pi$
$548$	−70.9886	−3.03248
$549$	−1.27270	−0.0543176
$550$	4.71220	0.200929
$551$	3.38413	0.144169
$552$	89.3456	3.80280
$553$	5.51862	0.234675
$554$	−8.20333	−0.348526
$555$	27.8765	1.18329
$556$	26.8327	1.13796
$557$	31.7623	1.34581	0.672906	−	0.739728i	$-0.265046\pi$
$557$	31.7623	1.34581	0.672906	+	0.739728i	$0.265046\pi$
$558$	−5.98605	−0.253410
$559$	3.82303	0.161697
$560$	64.6770	2.73310
$561$	50.4837	2.13142
$562$	−74.6347	−3.14828
$563$	−5.58389	−0.235333	−0.117666	−	0.993053i	$-0.537541\pi$
$563$	−5.58389	−0.235333	−0.117666	+	0.993053i	$0.537541\pi$
$564$	81.1879	3.41863
$565$	−4.80300	−0.202064
$566$	−72.0452	−3.02828
$567$	−35.7374	−1.50083
$568$	3.56013	0.149380
$569$	15.2608	0.639768	0.319884	−	0.947457i	$-0.396356\pi$
$569$	15.2608	0.639768	0.319884	+	0.947457i	$0.396356\pi$
$570$	−9.24082	−0.387055
$571$	−35.5432	−1.48744	−0.743719	−	0.668492i	$-0.766940\pi$
$571$	−35.5432	−1.48744	−0.743719	+	0.668492i	$0.766940\pi$
$572$	−17.1379	−0.716573
$573$	−26.3756	−1.10185
$574$	7.88113	0.328952
$575$	4.33114	0.180621
$576$	0.741235	0.0308848
$577$	38.4644	1.60129	0.800647	−	0.599137i	$-0.204489\pi$
$577$	38.4644	1.60129	0.800647	+	0.599137i	$0.204489\pi$
$578$	−109.535	−4.55606
$579$	−17.1537	−0.712885
$580$	−36.3310	−1.50856
$581$	57.4439	2.38318
$582$	22.6347	0.938239
$583$	−56.2605	−2.33007
$584$	−34.9884	−1.44783
$585$	−0.647711	−0.0267796
$586$	1.19682	0.0494400
$587$	−11.3030	−0.466525	−0.233262	−	0.972414i	$-0.574940\pi$
$587$	−11.3030	−0.466525	−0.233262	+	0.972414i	$0.574940\pi$
$588$	−89.8438	−3.70510
$589$	8.14292	0.335523
$590$	48.0012	1.97618
$591$	−35.5562	−1.46259
$592$	−45.1902	−1.85731
$593$	5.89166	0.241941	0.120971	−	0.992656i	$-0.461399\pi$
$593$	5.89166	0.241941	0.120971	+	0.992656i	$0.461399\pi$
$594$	53.6395	2.20086
$595$	80.3350	3.29341
$596$	59.0763	2.41986
$597$	6.27442	0.256795
$598$	−22.9852	−0.939935
$599$	−41.1177	−1.68002	−0.840011	−	0.542570i	$-0.817451\pi$
$599$	−41.1177	−1.68002	−0.840011	+	0.542570i	$0.817451\pi$
$600$	4.65511	0.190044
$601$	−7.96799	−0.325021	−0.162511	−	0.986707i	$-0.551959\pi$
$601$	−7.96799	−0.325021	−0.162511	+	0.986707i	$0.551959\pi$
$602$	−42.5599	−1.73461
$603$	0.153118	0.00623544
$604$	−16.0144	−0.651618
$605$	10.4882	0.426407
$606$	43.9437	1.78509
$607$	−6.53004	−0.265046	−0.132523	−	0.991180i	$-0.542308\pi$
$607$	−6.53004	−0.265046	−0.132523	+	0.991180i	$0.542308\pi$
$608$	3.70576	0.150288
$609$	25.9776	1.05267
$610$	−27.1212	−1.09810
$611$	−11.2957	−0.456975
$612$	−9.37392	−0.378918
$613$	17.4493	0.704772	0.352386	−	0.935855i	$-0.385370\pi$
$613$	17.4493	0.704772	0.352386	+	0.935855i	$0.385370\pi$
$614$	−41.7974	−1.68680
$615$	2.73356	0.110228
$616$	103.180	4.15726
$617$	−38.2311	−1.53913	−0.769563	−	0.638571i	$-0.779526\pi$
$617$	−38.2311	−1.53913	−0.769563	+	0.638571i	$0.779526\pi$
$618$	−15.3185	−0.616201
$619$	21.9934	0.883988	0.441994	−	0.897018i	$-0.354271\pi$
$619$	21.9934	0.883988	0.441994	+	0.897018i	$0.354271\pi$
$620$	−87.4200	−3.51087
$621$	49.3019	1.97842
$622$	−19.4698	−0.780668
$623$	48.7116	1.95159
$624$	−10.3295	−0.413509
$625$	−27.1495	−1.08598
$626$	69.8032	2.78990
$627$	−6.16396	−0.246165
$628$	−45.9372	−1.83310
$629$	−56.1305	−2.23807
$630$	7.21064	0.287279
$631$	2.66626	0.106142	0.0530711	−	0.998591i	$-0.483099\pi$
$631$	2.66626	0.106142	0.0530711	+	0.998591i	$0.483099\pi$
$632$	−7.42120	−0.295200
$633$	30.7167	1.22088
$634$	−14.7572	−0.586083
$635$	12.9504	0.513921
$636$	−102.769	−4.07506
$637$	12.5000	0.495268
$638$	−35.3621	−1.40000
$639$	0.165956	0.00656511
$640$	34.0639	1.34650
$641$	20.0506	0.791949	0.395975	−	0.918261i	$-0.370407\pi$
$641$	20.0506	0.791949	0.395975	+	0.918261i	$0.370407\pi$
$642$	9.02661	0.356252
$643$	15.3071	0.603654	0.301827	−	0.953363i	$-0.402404\pi$
$643$	15.3071	0.603654	0.301827	+	0.953363i	$0.402404\pi$
$644$	175.360	6.91014
$645$	−14.7618	−0.581247
$646$	18.6068	0.732075
$647$	−38.3570	−1.50797	−0.753985	−	0.656891i	$-0.771871\pi$
$647$	−38.3570	−1.50797	−0.753985	+	0.656891i	$0.771871\pi$
$648$	48.0582	1.88790
$649$	32.0186	1.25684
$650$	−1.19758	−0.0469730
$651$	62.5077	2.44987
$652$	66.3991	2.60039
$653$	46.6542	1.82572	0.912861	−	0.408271i	$-0.133868\pi$
$653$	46.6542	1.82572	0.912861	+	0.408271i	$0.133868\pi$
$654$	−17.3227	−0.677373
$655$	34.2334	1.33761
$656$	−4.43133	−0.173014
$657$	−1.63098	−0.0636308
$658$	125.749	4.90222
$659$	22.1643	0.863398	0.431699	−	0.902018i	$-0.357914\pi$
$659$	22.1643	0.863398	0.431699	+	0.902018i	$0.357914\pi$
$660$	66.1745	2.57584
$661$	−12.7218	−0.494819	−0.247409	−	0.968911i	$-0.579579\pi$
$661$	−12.7218	−0.494819	−0.247409	+	0.968911i	$0.579579\pi$
$662$	24.1675	0.939295
$663$	−12.8302	−0.498283
$664$	−77.2482	−2.99781
$665$	−9.80875	−0.380367
$666$	−5.03812	−0.195223
$667$	−32.5025	−1.25850
$668$	−38.0797	−1.47335
$669$	43.2052	1.67041
$670$	3.26292	0.126058
$671$	−18.0908	−0.698388
$672$	28.4466	1.09735
$673$	0.310620	0.0119735	0.00598677	−	0.999982i	$-0.498094\pi$
$673$	0.310620	0.0119735	0.00598677	+	0.999982i	$0.498094\pi$
$674$	35.5471	1.36922
$675$	2.56874	0.0988709
$676$	4.35552	0.167520
$677$	42.2529	1.62391	0.811955	−	0.583720i	$-0.198403\pi$
$677$	42.2529	1.62391	0.811955	+	0.583720i	$0.198403\pi$
$678$	−8.53952	−0.327958
$679$	24.0258	0.922026
$680$	−108.031	−4.14280
$681$	−21.4855	−0.823327
$682$	−85.0887	−3.25821
$683$	−5.12201	−0.195988	−0.0979942	−	0.995187i	$-0.531243\pi$
$683$	−5.12201	−0.195988	−0.0979942	+	0.995187i	$0.531243\pi$
$684$	1.14454	0.0437625
$685$	−38.1367	−1.45713
$686$	−61.2287	−2.33772
$687$	−2.84246	−0.108447
$688$	23.9302	0.912332
$689$	14.2983	0.544722
$690$	88.7525	3.37875
$691$	28.1253	1.06994	0.534969	−	0.844872i	$-0.320323\pi$
$691$	28.1253	1.06994	0.534969	+	0.844872i	$0.320323\pi$
$692$	26.0329	0.989622
$693$	4.80976	0.182708
$694$	−66.0332	−2.50659
$695$	14.4151	0.546798
$696$	−34.9337	−1.32416
$697$	−5.50414	−0.208484
$698$	−58.4007	−2.21050
$699$	−28.5259	−1.07895
$700$	9.13664	0.345333
$701$	25.4219	0.960170	0.480085	−	0.877222i	$-0.340606\pi$
$701$	25.4219	0.960170	0.480085	+	0.877222i	$0.340606\pi$
$702$	−13.6322	−0.514514
$703$	6.85343	0.258482
$704$	10.5363	0.397101
$705$	43.6159	1.64267
$706$	57.2870	2.15602
$707$	46.6445	1.75425
$708$	58.4873	2.19809
$709$	−4.12306	−0.154845	−0.0774224	−	0.996998i	$-0.524669\pi$
$709$	−4.12306	−0.154845	−0.0774224	+	0.996998i	$0.524669\pi$
$710$	3.53650	0.132722
$711$	−0.345940	−0.0129738
$712$	−65.5053	−2.45492
$713$	−78.2078	−2.92891
$714$	142.832	5.34535
$715$	−9.20688	−0.344318
$716$	73.4400	2.74458
$717$	15.2848	0.570820
$718$	57.2540	2.13670
$719$	43.6742	1.62877	0.814387	−	0.580322i	$-0.197073\pi$
$719$	43.6742	1.62877	0.814387	+	0.580322i	$0.197073\pi$
$720$	−4.05434	−0.151096
$721$	−16.2600	−0.605553
$722$	45.6274	1.69808
$723$	35.8774	1.33429
$724$	−0.303914	−0.0112949
$725$	−1.69345	−0.0628933
$726$	18.6476	0.692077
$727$	−11.2301	−0.416502	−0.208251	−	0.978075i	$-0.566777\pi$
$727$	−11.2301	−0.416502	−0.208251	+	0.978075i	$0.566777\pi$
$728$	−26.2228	−0.971881
$729$	29.0104	1.07446
$730$	−34.7561	−1.28638
$731$	29.7236	1.09937
$732$	−33.0459	−1.22141
$733$	−34.1188	−1.26021	−0.630104	−	0.776511i	$-0.716988\pi$
$733$	−34.1188	−1.26021	−0.630104	+	0.776511i	$0.716988\pi$
$734$	−88.3553	−3.26125
$735$	−48.2661	−1.78032
$736$	−35.5916	−1.31192
$737$	2.17649	0.0801721
$738$	−0.494036	−0.0181857
$739$	−37.1967	−1.36830	−0.684151	−	0.729340i	$-0.739827\pi$
$739$	−37.1967	−1.36830	−0.684151	+	0.729340i	$0.739827\pi$
$740$	−73.5764	−2.70472
$741$	1.56654	0.0575483
$742$	−159.176	−5.84353
$743$	41.2394	1.51293	0.756464	−	0.654035i	$-0.226925\pi$
$743$	41.2394	1.51293	0.756464	+	0.654035i	$0.226925\pi$
$744$	−84.0577	−3.08171
$745$	31.7371	1.16276
$746$	13.5017	0.494331
$747$	−3.60093	−0.131751
$748$	−133.245	−4.87193
$749$	9.58137	0.350096
$750$	−44.0476	−1.60839
$751$	−7.34499	−0.268023	−0.134011	−	0.990980i	$-0.542786\pi$
$751$	−7.34499	−0.268023	−0.134011	+	0.990980i	$0.542786\pi$
$752$	−70.7053	−2.57836
$753$	35.1693	1.28164
$754$	8.98709	0.327291
$755$	−8.60332	−0.313107
$756$	104.003	3.78257
$757$	21.4438	0.779388	0.389694	−	0.920944i	$-0.372581\pi$
$757$	21.4438	0.779388	0.389694	+	0.920944i	$0.372581\pi$
$758$	20.0569	0.728501
$759$	59.2012	2.14887
$760$	13.1904	0.478466
$761$	14.9904	0.543402	0.271701	−	0.962382i	$-0.412414\pi$
$761$	14.9904	0.543402	0.271701	+	0.962382i	$0.412414\pi$
$762$	23.0252	0.834116
$763$	−18.3874	−0.665668
$764$	69.6149	2.51858
$765$	−5.03588	−0.182073
$766$	−49.6734	−1.79477
$767$	−8.13736	−0.293823
$768$	51.7264	1.86652
$769$	−29.9909	−1.08150	−0.540750	−	0.841183i	$-0.681860\pi$
$769$	−29.9909	−1.08150	−0.540750	+	0.841183i	$0.681860\pi$
$770$	102.496	3.69368
$771$	13.6343	0.491028
$772$	45.2751	1.62949
$773$	−16.1603	−0.581245	−0.290622	−	0.956838i	$-0.593862\pi$
$773$	−16.1603	−0.581245	−0.290622	+	0.956838i	$0.593862\pi$
$774$	2.66791	0.0958961
$775$	−4.07481	−0.146371
$776$	−32.3089	−1.15982
$777$	52.6092	1.88734
$778$	49.2666	1.76629
$779$	0.672045	0.0240785
$780$	−16.8179	−0.602178
$781$	2.35897	0.0844107
$782$	−178.707	−6.39056
$783$	−19.2768	−0.688896
$784$	78.2436	2.79441
$785$	−24.6785	−0.880814
$786$	60.8654	2.17100
$787$	−6.77099	−0.241360	−0.120680	−	0.992691i	$-0.538507\pi$
$787$	−6.77099	−0.241360	−0.120680	+	0.992691i	$0.538507\pi$
$788$	93.8461	3.34313
$789$	2.78121	0.0990136
$790$	−7.37194	−0.262282
$791$	−9.06435	−0.322291
$792$	−6.46797	−0.229829
$793$	4.59769	0.163269
$794$	−80.5528	−2.85871
$795$	−55.2099	−1.95809
$796$	−16.5605	−0.586972
$797$	54.6415	1.93550	0.967751	−	0.251907i	$-0.0810576\pi$
$797$	54.6415	1.93550	0.967751	+	0.251907i	$0.0810576\pi$
$798$	−17.4395	−0.617352
$799$	−87.8227	−3.10694
$800$	−1.85440	−0.0655630
$801$	−3.05353	−0.107891
$802$	33.2648	1.17462
$803$	−23.1836	−0.818131
$804$	3.97572	0.140213
$805$	94.2071	3.32036
$806$	21.6248	0.761702
$807$	−8.78318	−0.309183
$808$	−62.7255	−2.20668
$809$	−16.3796	−0.575876	−0.287938	−	0.957649i	$-0.592970\pi$
$809$	−16.3796	−0.575876	−0.287938	+	0.957649i	$0.592970\pi$
$810$	47.7392	1.67738
$811$	21.0427	0.738908	0.369454	−	0.929249i	$-0.379545\pi$
$811$	21.0427	0.738908	0.369454	+	0.929249i	$0.379545\pi$
$812$	−68.5647	−2.40615
$813$	21.4181	0.751166
$814$	−71.6143	−2.51008
$815$	35.6711	1.24950
$816$	−80.3103	−2.81142
$817$	−3.62920	−0.126970
$818$	−8.18845	−0.286302
$819$	−1.22238	−0.0427133
$820$	−7.21487	−0.251954
$821$	8.18375	0.285615	0.142807	−	0.989751i	$-0.454387\pi$
$821$	8.18375	0.285615	0.142807	+	0.989751i	$0.454387\pi$
$822$	−67.8052	−2.36498
$823$	−42.5386	−1.48280	−0.741401	−	0.671062i	$-0.765838\pi$
$823$	−42.5386	−1.48280	−0.741401	+	0.671062i	$0.765838\pi$
$824$	21.8657	0.761729
$825$	3.08452	0.107389
$826$	90.5891	3.15200
$827$	0.900449	0.0313117	0.0156558	−	0.999877i	$-0.495016\pi$
$827$	0.900449	0.0313117	0.0156558	+	0.999877i	$0.495016\pi$
$828$	−10.9926	−0.382019
$829$	−24.6231	−0.855197	−0.427599	−	0.903969i	$-0.640640\pi$
$829$	−24.6231	−0.855197	−0.427599	+	0.903969i	$0.640640\pi$
$830$	−76.7354	−2.66353
$831$	−5.36974	−0.186274
$832$	−2.67774	−0.0928339
$833$	97.1860	3.36729
$834$	25.6295	0.887476
$835$	−20.4572	−0.707952
$836$	16.2690	0.562675
$837$	−46.3840	−1.60326
$838$	30.5304	1.05465
$839$	−17.9265	−0.618891	−0.309445	−	0.950917i	$-0.600143\pi$
$839$	−17.9265	−0.618891	−0.309445	+	0.950917i	$0.600143\pi$
$840$	101.254	3.49359
$841$	−16.2917	−0.561783
$842$	−90.7377	−3.12703
$843$	−48.8545	−1.68264
$844$	−81.0728	−2.79064
$845$	2.33988	0.0804943
$846$	−7.88272	−0.271013
$847$	19.7936	0.680118
$848$	89.5001	3.07345
$849$	−47.1594	−1.61851
$850$	−9.31106	−0.319367
$851$	−65.8231	−2.25639
$852$	4.30906	0.147626
$853$	16.7509	0.573539	0.286770	−	0.958000i	$-0.407419\pi$
$853$	16.7509	0.573539	0.286770	+	0.958000i	$0.407419\pi$
$854$	−51.1837	−1.75147
$855$	0.614871	0.0210281
$856$	−12.8846	−0.440388
$857$	−2.50965	−0.0857280	−0.0428640	−	0.999081i	$-0.513648\pi$
$857$	−2.50965	−0.0857280	−0.0428640	+	0.999081i	$0.513648\pi$
$858$	−16.3694	−0.558842
$859$	15.6477	0.533893	0.266946	−	0.963711i	$-0.413985\pi$
$859$	15.6477	0.533893	0.266946	+	0.963711i	$0.413985\pi$
$860$	38.9620	1.32859
$861$	5.15883	0.175813
$862$	37.7679	1.28638
$863$	8.99803	0.306297	0.153148	−	0.988203i	$-0.451059\pi$
$863$	8.99803	0.306297	0.153148	+	0.988203i	$0.451059\pi$
$864$	−21.1089	−0.718138
$865$	13.9854	0.475519
$866$	41.6913	1.41673
$867$	−71.6995	−2.43504
$868$	−164.981	−5.59982
$869$	−4.91736	−0.166810
$870$	−34.7018	−1.17650
$871$	−0.553144	−0.0187426
$872$	24.7266	0.837347
$873$	−1.50608	−0.0509731
$874$	21.8198	0.738066
$875$	−46.7547	−1.58060
$876$	−42.3487	−1.43083
$877$	53.9637	1.82222	0.911112	−	0.412159i	$-0.135225\pi$
$877$	53.9637	1.82222	0.911112	+	0.412159i	$0.135225\pi$
$878$	31.7444	1.07132
$879$	0.783413	0.0264239
$880$	−57.6304	−1.94272
$881$	−21.3544	−0.719448	−0.359724	−	0.933059i	$-0.617129\pi$
$881$	−21.3544	−0.719448	−0.359724	+	0.933059i	$0.617129\pi$
$882$	8.72314	0.293724
$883$	−1.32767	−0.0446798	−0.0223399	−	0.999750i	$-0.507112\pi$
$883$	−1.32767	−0.0446798	−0.0223399	+	0.999750i	$0.507112\pi$
$884$	33.8636	1.13896
$885$	31.4207	1.05620
$886$	−12.6314	−0.424360
$887$	46.4009	1.55799	0.778995	−	0.627030i	$-0.215730\pi$
$887$	46.4009	1.55799	0.778995	+	0.627030i	$0.215730\pi$
$888$	−70.7466	−2.37410
$889$	24.4403	0.819702
$890$	−65.0705	−2.18117
$891$	31.8438	1.06681
$892$	−114.035	−3.81816
$893$	10.7230	0.358831
$894$	56.4271	1.88720
$895$	39.4536	1.31879
$896$	64.2863	2.14765
$897$	−15.0457	−0.502360
$898$	−73.4389	−2.45069
$899$	30.5789	1.01986
$900$	−0.572739	−0.0190913
$901$	111.168	3.70353
$902$	−7.02247	−0.233823
$903$	−27.8589	−0.927087
$904$	12.1894	0.405412
$905$	−0.163269	−0.00542725
$906$	−15.2963	−0.508185
$907$	13.9630	0.463632	0.231816	−	0.972760i	$-0.425533\pi$
$907$	13.9630	0.463632	0.231816	+	0.972760i	$0.425533\pi$
$908$	56.7083	1.88193
$909$	−2.92395	−0.0969815
$910$	−26.0487	−0.863506
$911$	−28.6352	−0.948727	−0.474363	−	0.880329i	$-0.657322\pi$
$911$	−28.6352	−0.948727	−0.474363	+	0.880329i	$0.657322\pi$
$912$	9.80573	0.324700
$913$	−51.1854	−1.69399
$914$	64.3166	2.12741
$915$	−17.7530	−0.586896
$916$	7.50231	0.247883
$917$	64.6061	2.13348
$918$	−105.989	−3.49815
$919$	23.2432	0.766723	0.383362	−	0.923598i	$-0.374766\pi$
$919$	23.2432	0.766723	0.383362	+	0.923598i	$0.374766\pi$
$920$	−126.686	−4.17671
$921$	−27.3598	−0.901535
$922$	26.2282	0.863779
$923$	−0.599521	−0.0197335
$924$	124.886	4.10845
$925$	−3.42953	−0.112762
$926$	2.52101	0.0828457
$927$	1.01927	0.0334773
$928$	13.9161	0.456819
$929$	13.2379	0.434321	0.217160	−	0.976136i	$-0.430321\pi$
$929$	13.2379	0.434321	0.217160	+	0.976136i	$0.430321\pi$
$930$	−83.4997	−2.73806
$931$	−11.8662	−0.388900
$932$	75.2905	2.46622
$933$	−12.7446	−0.417238
$934$	56.2006	1.83894
$935$	−71.5824	−2.34099
$936$	1.64380	0.0537293
$937$	56.6394	1.85033	0.925164	−	0.379569i	$-0.123928\pi$
$937$	56.6394	1.85033	0.925164	+	0.379569i	$0.123928\pi$
$938$	6.15787	0.201062
$939$	45.6918	1.49110
$940$	−115.119	−3.75476
$941$	−6.00049	−0.195610	−0.0978051	−	0.995206i	$-0.531182\pi$
$941$	−6.00049	−0.195610	−0.0978051	+	0.995206i	$0.531182\pi$
$942$	−43.8773	−1.42960
$943$	−6.45459	−0.210190
$944$	−50.9357	−1.65782
$945$	55.8729	1.81755
$946$	37.9230	1.23298
$947$	6.07248	0.197329	0.0986645	−	0.995121i	$-0.468543\pi$
$947$	6.07248	0.197329	0.0986645	+	0.995121i	$0.468543\pi$
$948$	−8.98238	−0.291734
$949$	5.89199	0.191262
$950$	1.13686	0.0368847
$951$	−9.65978	−0.313240
$952$	−203.879	−6.60776
$953$	−3.08608	−0.0999678	−0.0499839	−	0.998750i	$-0.515917\pi$
$953$	−3.08608	−0.0999678	−0.0499839	+	0.998750i	$0.515917\pi$
$954$	9.97810	0.323053
$955$	37.3987	1.21019
$956$	−40.3422	−1.30476
$957$	−23.1474	−0.748248
$958$	75.8093	2.44929
$959$	−71.9724	−2.32411
$960$	10.3395	0.333707
$961$	42.5792	1.37352
$962$	18.2004	0.586804
$963$	−0.600618	−0.0193546
$964$	−94.6938	−3.04988
$965$	24.3228	0.782978
$966$	167.496	5.38909
$967$	24.8001	0.797517	0.398759	−	0.917056i	$-0.369441\pi$
$967$	24.8001	0.797517	0.398759	+	0.917056i	$0.369441\pi$
$968$	−26.6177	−0.855524
$969$	12.1797	0.391267
$970$	−32.0944	−1.03049
$971$	−20.6640	−0.663138	−0.331569	−	0.943431i	$-0.607578\pi$
$971$	−20.6640	−0.663138	−0.331569	+	0.943431i	$0.607578\pi$
$972$	−12.4884	−0.400564
$973$	27.2046	0.872140
$974$	−53.2758	−1.70707
$975$	−0.783914	−0.0251053
$976$	28.7792	0.921199
$977$	27.7777	0.888687	0.444344	−	0.895856i	$-0.353437\pi$
$977$	27.7777	0.888687	0.444344	+	0.895856i	$0.353437\pi$
$978$	63.4215	2.02800
$979$	−43.4044	−1.38721
$980$	127.392	4.06940
$981$	1.15263	0.0368007
$982$	65.2823	2.08324
$983$	62.5271	1.99430	0.997152	−	0.0754152i	$-0.0240282\pi$
$983$	62.5271	1.99430	0.997152	+	0.0754152i	$0.0240282\pi$
$984$	−6.93738	−0.221156
$985$	50.4162	1.60639
$986$	69.8736	2.22523
$987$	82.3131	2.62005
$988$	−4.13468	−0.131542
$989$	34.8563	1.10837
$990$	−6.42504	−0.204201
$991$	7.15027	0.227136	0.113568	−	0.993530i	$-0.463772\pi$
$991$	7.15027	0.227136	0.113568	+	0.993530i	$0.463772\pi$
$992$	33.4851	1.06315
$993$	15.8196	0.502019
$994$	6.67417	0.211692
$995$	−8.89669	−0.282044
$996$	−93.4986	−2.96262
$997$	18.4804	0.585281	0.292640	−	0.956223i	$-0.405466\pi$
$997$	18.4804	0.585281	0.292640	+	0.956223i	$0.405466\pi$
$998$	109.688	3.47210
$999$	−39.0387	−1.23513

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6019.2.a.e.1.8	✓	130

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6019.2.a.e.1.8	✓	130	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)

\(f(q)\)	\(=\)	\(q-2.52101 q^{2} -1.65021 q^{3} +4.35552 q^{4} +2.33988 q^{5} +4.16020 q^{6} +4.41588 q^{7} -5.93829 q^{8} -0.276814 q^{9} +O(q^{10})\)	\(q-2.52101 q^{2} -1.65021 q^{3} +4.35552 q^{4} +2.33988 q^{5} +4.16020 q^{6} +4.41588 q^{7} -5.93829 q^{8} -0.276814 q^{9} -5.89887 q^{10} -3.93477 q^{11} -7.18751 q^{12} +1.00000 q^{13} -11.1325 q^{14} -3.86129 q^{15} +6.25949 q^{16} +7.77488 q^{17} +0.697852 q^{18} -0.949298 q^{19} +10.1914 q^{20} -7.28712 q^{21} +9.91960 q^{22} +9.11744 q^{23} +9.79941 q^{24} +0.475040 q^{25} -2.52101 q^{26} +5.40742 q^{27} +19.2334 q^{28} -3.56487 q^{29} +9.73437 q^{30} -8.57783 q^{31} -3.90368 q^{32} +6.49318 q^{33} -19.6006 q^{34} +10.3326 q^{35} -1.20567 q^{36} -7.21947 q^{37} +2.39319 q^{38} -1.65021 q^{39} -13.8949 q^{40} -0.707939 q^{41} +18.3709 q^{42} +3.82303 q^{43} -17.1379 q^{44} -0.647711 q^{45} -22.9852 q^{46} -11.2957 q^{47} -10.3295 q^{48} +12.5000 q^{49} -1.19758 q^{50} -12.8302 q^{51} +4.35552 q^{52} +14.2983 q^{53} -13.6322 q^{54} -9.20688 q^{55} -26.2228 q^{56} +1.56654 q^{57} +8.98709 q^{58} -8.13736 q^{59} -16.8179 q^{60} +4.59769 q^{61} +21.6248 q^{62} -1.22238 q^{63} -2.67774 q^{64} +2.33988 q^{65} -16.3694 q^{66} -0.553144 q^{67} +33.8636 q^{68} -15.0457 q^{69} -26.0487 q^{70} -0.599521 q^{71} +1.64380 q^{72} +5.89199 q^{73} +18.2004 q^{74} -0.783914 q^{75} -4.13468 q^{76} -17.3755 q^{77} +4.16020 q^{78} +1.24972 q^{79} +14.6465 q^{80} -8.09293 q^{81} +1.78472 q^{82} +13.0085 q^{83} -31.7392 q^{84} +18.1923 q^{85} -9.63793 q^{86} +5.88278 q^{87} +23.3658 q^{88} +11.0310 q^{89} +1.63289 q^{90} +4.41588 q^{91} +39.7112 q^{92} +14.1552 q^{93} +28.4766 q^{94} -2.22124 q^{95} +6.44188 q^{96} +5.44077 q^{97} -31.5127 q^{98} +1.08920 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 130 q + 10 q^{2} + 11 q^{3} + 146 q^{4} + 40 q^{5} + 4 q^{6} + 8 q^{7} + 24 q^{8} + 181 q^{9}+O(q^{10}) \) 130 * q + 10 * q^2 + 11 * q^3 + 146 * q^4 + 40 * q^5 + 4 * q^6 + 8 * q^7 + 24 * q^8 + 181 * q^9	\( 130 q + 10 q^{2} + 11 q^{3} + 146 q^{4} + 40 q^{5} + 4 q^{6} + 8 q^{7} + 24 q^{8} + 181 q^{9} + 5 q^{10} + 43 q^{11} + 28 q^{12} + 130 q^{13} + 47 q^{14} + 29 q^{15} + 170 q^{16} + 85 q^{17} + 20 q^{18} + 3 q^{19} + 73 q^{20} + 62 q^{21} + 12 q^{22} + 62 q^{23} - 5 q^{24} + 178 q^{25} + 10 q^{26} + 35 q^{27} - q^{28} + 134 q^{29} + 24 q^{30} + 14 q^{31} + 48 q^{32} + 4 q^{33} + 4 q^{34} + 50 q^{35} + 244 q^{36} + 32 q^{37} + 76 q^{38} + 11 q^{39} - 6 q^{40} + 48 q^{41} + 9 q^{42} + 34 q^{43} + 123 q^{44} + 115 q^{45} + 5 q^{46} + 25 q^{47} + 35 q^{48} + 210 q^{49} + 24 q^{50} + 20 q^{51} + 146 q^{52} + 193 q^{53} - 39 q^{54} + 32 q^{55} + 122 q^{56} + 7 q^{57} - 4 q^{58} + 50 q^{59} + 42 q^{60} + 57 q^{61} + 51 q^{62} + 8 q^{63} + 172 q^{64} + 40 q^{65} - 4 q^{66} + 21 q^{67} + 132 q^{68} + 92 q^{69} - 46 q^{70} + 58 q^{71} - 26 q^{72} + 15 q^{73} + 120 q^{74} + 23 q^{75} - 65 q^{76} + 192 q^{77} + 4 q^{78} + 32 q^{79} + 66 q^{80} + 326 q^{81} + 11 q^{82} + 33 q^{83} + 5 q^{84} + 43 q^{85} + 105 q^{86} + 31 q^{87} - 17 q^{88} + 84 q^{89} - 73 q^{90} + 8 q^{91} + 161 q^{92} + 52 q^{93} + 4 q^{94} + 59 q^{95} - 77 q^{96} + 9 q^{97} - 61 q^{98} + 100 q^{99}+O(q^{100}) \) 130 * q + 10 * q^2 + 11 * q^3 + 146 * q^4 + 40 * q^5 + 4 * q^6 + 8 * q^7 + 24 * q^8 + 181 * q^9 + 5 * q^10 + 43 * q^11 + 28 * q^12 + 130 * q^13 + 47 * q^14 + 29 * q^15 + 170 * q^16 + 85 * q^17 + 20 * q^18 + 3 * q^19 + 73 * q^20 + 62 * q^21 + 12 * q^22 + 62 * q^23 - 5 * q^24 + 178 * q^25 + 10 * q^26 + 35 * q^27 - q^28 + 134 * q^29 + 24 * q^30 + 14 * q^31 + 48 * q^32 + 4 * q^33 + 4 * q^34 + 50 * q^35 + 244 * q^36 + 32 * q^37 + 76 * q^38 + 11 * q^39 - 6 * q^40 + 48 * q^41 + 9 * q^42 + 34 * q^43 + 123 * q^44 + 115 * q^45 + 5 * q^46 + 25 * q^47 + 35 * q^48 + 210 * q^49 + 24 * q^50 + 20 * q^51 + 146 * q^52 + 193 * q^53 - 39 * q^54 + 32 * q^55 + 122 * q^56 + 7 * q^57 - 4 * q^58 + 50 * q^59 + 42 * q^60 + 57 * q^61 + 51 * q^62 + 8 * q^63 + 172 * q^64 + 40 * q^65 - 4 * q^66 + 21 * q^67 + 132 * q^68 + 92 * q^69 - 46 * q^70 + 58 * q^71 - 26 * q^72 + 15 * q^73 + 120 * q^74 + 23 * q^75 - 65 * q^76 + 192 * q^77 + 4 * q^78 + 32 * q^79 + 66 * q^80 + 326 * q^81 + 11 * q^82 + 33 * q^83 + 5 * q^84 + 43 * q^85 + 105 * q^86 + 31 * q^87 - 17 * q^88 + 84 * q^89 - 73 * q^90 + 8 * q^91 + 161 * q^92 + 52 * q^93 + 4 * q^94 + 59 * q^95 - 77 * q^96 + 9 * q^97 - 61 * q^98 + 100 * q^99

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