LMFDB - Embedded newform 6010.2.a.j.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6010,2,Mod(1,6010)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6010, 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("6010.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6010 = 2 \cdot 5 \cdot 601 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6010.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:	$47.9900916148$
Analytic rank:	$0$
Dimension:	$33$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Character	$\chi$	$=$	6010.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -0.635616 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.635616 q^{6} -1.32070 q^{7} +1.00000 q^{8} -2.59599 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -0.635616 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.635616 q^{6} -1.32070 q^{7} +1.00000 q^{8} -2.59599 q^{9} +1.00000 q^{10} -5.60507 q^{11} -0.635616 q^{12} -2.45315 q^{13} -1.32070 q^{14} -0.635616 q^{15} +1.00000 q^{16} +6.01284 q^{17} -2.59599 q^{18} -7.36781 q^{19} +1.00000 q^{20} +0.839458 q^{21} -5.60507 q^{22} +3.02733 q^{23} -0.635616 q^{24} +1.00000 q^{25} -2.45315 q^{26} +3.55690 q^{27} -1.32070 q^{28} +3.34027 q^{29} -0.635616 q^{30} +6.38765 q^{31} +1.00000 q^{32} +3.56267 q^{33} +6.01284 q^{34} -1.32070 q^{35} -2.59599 q^{36} +3.14616 q^{37} -7.36781 q^{38} +1.55926 q^{39} +1.00000 q^{40} -7.56744 q^{41} +0.839458 q^{42} +0.0321924 q^{43} -5.60507 q^{44} -2.59599 q^{45} +3.02733 q^{46} +9.23464 q^{47} -0.635616 q^{48} -5.25575 q^{49} +1.00000 q^{50} -3.82186 q^{51} -2.45315 q^{52} +0.477940 q^{53} +3.55690 q^{54} -5.60507 q^{55} -1.32070 q^{56} +4.68310 q^{57} +3.34027 q^{58} -2.63038 q^{59} -0.635616 q^{60} +10.4867 q^{61} +6.38765 q^{62} +3.42853 q^{63} +1.00000 q^{64} -2.45315 q^{65} +3.56267 q^{66} -0.0285912 q^{67} +6.01284 q^{68} -1.92422 q^{69} -1.32070 q^{70} +4.67795 q^{71} -2.59599 q^{72} +8.92092 q^{73} +3.14616 q^{74} -0.635616 q^{75} -7.36781 q^{76} +7.40262 q^{77} +1.55926 q^{78} +6.10555 q^{79} +1.00000 q^{80} +5.52716 q^{81} -7.56744 q^{82} +14.9213 q^{83} +0.839458 q^{84} +6.01284 q^{85} +0.0321924 q^{86} -2.12313 q^{87} -5.60507 q^{88} -11.7957 q^{89} -2.59599 q^{90} +3.23988 q^{91} +3.02733 q^{92} -4.06009 q^{93} +9.23464 q^{94} -7.36781 q^{95} -0.635616 q^{96} +13.3166 q^{97} -5.25575 q^{98} +14.5507 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 33 q + 33 q^{2} + 6 q^{3} + 33 q^{4} + 33 q^{5} + 6 q^{6} + 4 q^{7} + 33 q^{8} + 49 q^{9}+O(q^{10}) $ 33 * q + 33 * q^2 + 6 * q^3 + 33 * q^4 + 33 * q^5 + 6 * q^6 + 4 * q^7 + 33 * q^8 + 49 * q^9	\( 33 q + 33 q^{2} + 6 q^{3} + 33 q^{4} + 33 q^{5} + 6 q^{6} + 4 q^{7} + 33 q^{8} + 49 q^{9} + 33 q^{10} + 12 q^{11} + 6 q^{12} + 20 q^{13} + 4 q^{14} + 6 q^{15} + 33 q^{16} + 33 q^{17} + 49 q^{18} + 17 q^{19} + 33 q^{20} + 26 q^{21} + 12 q^{22} + 7 q^{23} + 6 q^{24} + 33 q^{25} + 20 q^{26} + 21 q^{27} + 4 q^{28} + 33 q^{29} + 6 q^{30} + 35 q^{31} + 33 q^{32} + 25 q^{33} + 33 q^{34} + 4 q^{35} + 49 q^{36} + 16 q^{37} + 17 q^{38} + 22 q^{39} + 33 q^{40} + 39 q^{41} + 26 q^{42} - 3 q^{43} + 12 q^{44} + 49 q^{45} + 7 q^{46} + 19 q^{47} + 6 q^{48} + 69 q^{49} + 33 q^{50} + 21 q^{51} + 20 q^{52} + 41 q^{53} + 21 q^{54} + 12 q^{55} + 4 q^{56} + 33 q^{58} + 18 q^{59} + 6 q^{60} + 30 q^{61} + 35 q^{62} - 15 q^{63} + 33 q^{64} + 20 q^{65} + 25 q^{66} - 9 q^{67} + 33 q^{68} + 23 q^{69} + 4 q^{70} + 36 q^{71} + 49 q^{72} + 35 q^{73} + 16 q^{74} + 6 q^{75} + 17 q^{76} + 26 q^{77} + 22 q^{78} + 32 q^{79} + 33 q^{80} + 53 q^{81} + 39 q^{82} + 24 q^{83} + 26 q^{84} + 33 q^{85} - 3 q^{86} + 12 q^{87} + 12 q^{88} + 40 q^{89} + 49 q^{90} + 5 q^{91} + 7 q^{92} + 18 q^{93} + 19 q^{94} + 17 q^{95} + 6 q^{96} + 39 q^{97} + 69 q^{98} + 3 q^{99}+O(q^{100}) \) 33 * q + 33 * q^2 + 6 * q^3 + 33 * q^4 + 33 * q^5 + 6 * q^6 + 4 * q^7 + 33 * q^8 + 49 * q^9 + 33 * q^10 + 12 * q^11 + 6 * q^12 + 20 * q^13 + 4 * q^14 + 6 * q^15 + 33 * q^16 + 33 * q^17 + 49 * q^18 + 17 * q^19 + 33 * q^20 + 26 * q^21 + 12 * q^22 + 7 * q^23 + 6 * q^24 + 33 * q^25 + 20 * q^26 + 21 * q^27 + 4 * q^28 + 33 * q^29 + 6 * q^30 + 35 * q^31 + 33 * q^32 + 25 * q^33 + 33 * q^34 + 4 * q^35 + 49 * q^36 + 16 * q^37 + 17 * q^38 + 22 * q^39 + 33 * q^40 + 39 * q^41 + 26 * q^42 - 3 * q^43 + 12 * q^44 + 49 * q^45 + 7 * q^46 + 19 * q^47 + 6 * q^48 + 69 * q^49 + 33 * q^50 + 21 * q^51 + 20 * q^52 + 41 * q^53 + 21 * q^54 + 12 * q^55 + 4 * q^56 + 33 * q^58 + 18 * q^59 + 6 * q^60 + 30 * q^61 + 35 * q^62 - 15 * q^63 + 33 * q^64 + 20 * q^65 + 25 * q^66 - 9 * q^67 + 33 * q^68 + 23 * q^69 + 4 * q^70 + 36 * q^71 + 49 * q^72 + 35 * q^73 + 16 * q^74 + 6 * q^75 + 17 * q^76 + 26 * q^77 + 22 * q^78 + 32 * q^79 + 33 * q^80 + 53 * q^81 + 39 * q^82 + 24 * q^83 + 26 * q^84 + 33 * q^85 - 3 * q^86 + 12 * q^87 + 12 * q^88 + 40 * q^89 + 49 * q^90 + 5 * q^91 + 7 * q^92 + 18 * q^93 + 19 * q^94 + 17 * q^95 + 6 * q^96 + 39 * q^97 + 69 * q^98 + 3 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−0.635616	−0.366973	−0.183486	−	0.983022i	$-0.558738\pi$
$3$	−0.635616	−0.366973	−0.183486	+	0.983022i	$0.558738\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−0.635616	−0.259489
$7$	−1.32070	−0.499178	−0.249589	−	0.968352i	$-0.580296\pi$
$7$	−1.32070	−0.499178	−0.249589	+	0.968352i	$0.580296\pi$
$8$	1.00000	0.353553
$9$	−2.59599	−0.865331
$10$	1.00000	0.316228
$11$	−5.60507	−1.68999	−0.844996	−	0.534772i	$-0.820397\pi$
$11$	−5.60507	−1.68999	−0.844996	+	0.534772i	$0.820397\pi$
$12$	−0.635616	−0.183486
$13$	−2.45315	−0.680382	−0.340191	−	0.940356i	$-0.610492\pi$
$13$	−2.45315	−0.680382	−0.340191	+	0.940356i	$0.610492\pi$
$14$	−1.32070	−0.352972
$15$	−0.635616	−0.164115
$16$	1.00000	0.250000
$17$	6.01284	1.45833	0.729164	−	0.684339i	$-0.239909\pi$
$17$	6.01284	1.45833	0.729164	+	0.684339i	$0.239909\pi$
$18$	−2.59599	−0.611881
$19$	−7.36781	−1.69029	−0.845146	−	0.534535i	$-0.820487\pi$
$19$	−7.36781	−1.69029	−0.845146	+	0.534535i	$0.820487\pi$
$20$	1.00000	0.223607
$21$	0.839458	0.183185
$22$	−5.60507	−1.19501
$23$	3.02733	0.631242	0.315621	−	0.948885i	$-0.397787\pi$
$23$	3.02733	0.631242	0.315621	+	0.948885i	$0.397787\pi$
$24$	−0.635616	−0.129745
$25$	1.00000	0.200000
$26$	−2.45315	−0.481103
$27$	3.55690	0.684526
$28$	−1.32070	−0.249589
$29$	3.34027	0.620272	0.310136	−	0.950692i	$-0.399625\pi$
$29$	3.34027	0.620272	0.310136	+	0.950692i	$0.399625\pi$
$30$	−0.635616	−0.116047
$31$	6.38765	1.14725	0.573627	−	0.819116i	$-0.305536\pi$
$31$	6.38765	1.14725	0.573627	+	0.819116i	$0.305536\pi$
$32$	1.00000	0.176777
$33$	3.56267	0.620181
$34$	6.01284	1.03119
$35$	−1.32070	−0.223239
$36$	−2.59599	−0.432665
$37$	3.14616	0.517225	0.258613	−	0.965981i	$-0.416735\pi$
$37$	3.14616	0.517225	0.258613	+	0.965981i	$0.416735\pi$
$38$	−7.36781	−1.19522
$39$	1.55926	0.249682
$40$	1.00000	0.158114
$41$	−7.56744	−1.18184	−0.590918	−	0.806732i	$-0.701234\pi$
$41$	−7.56744	−1.18184	−0.590918	+	0.806732i	$0.701234\pi$
$42$	0.839458	0.129531
$43$	0.0321924	0.00490929	0.00245465	−	0.999997i	$-0.499219\pi$
$43$	0.0321924	0.00490929	0.00245465	+	0.999997i	$0.499219\pi$
$44$	−5.60507	−0.844996
$45$	−2.59599	−0.386988
$46$	3.02733	0.446356
$47$	9.23464	1.34701	0.673506	−	0.739182i	$-0.264788\pi$
$47$	9.23464	1.34701	0.673506	+	0.739182i	$0.264788\pi$
$48$	−0.635616	−0.0917432
$49$	−5.25575	−0.750821
$50$	1.00000	0.141421
$51$	−3.82186	−0.535167
$52$	−2.45315	−0.340191
$53$	0.477940	0.0656501	0.0328250	−	0.999461i	$-0.489550\pi$
$53$	0.477940	0.0656501	0.0328250	+	0.999461i	$0.489550\pi$
$54$	3.55690	0.484033
$55$	−5.60507	−0.755788
$56$	−1.32070	−0.176486
$57$	4.68310	0.620292
$58$	3.34027	0.438599
$59$	−2.63038	−0.342446	−0.171223	−	0.985232i	$-0.554772\pi$
$59$	−2.63038	−0.342446	−0.171223	+	0.985232i	$0.554772\pi$
$60$	−0.635616	−0.0820576
$61$	10.4867	1.34269	0.671343	−	0.741147i	$-0.265718\pi$
$61$	10.4867	1.34269	0.671343	+	0.741147i	$0.265718\pi$
$62$	6.38765	0.811232
$63$	3.42853	0.431954
$64$	1.00000	0.125000
$65$	−2.45315	−0.304276
$66$	3.56267	0.438535
$67$	−0.0285912	−0.00349298	−0.00174649	−	0.999998i	$-0.500556\pi$
$67$	−0.0285912	−0.00349298	−0.00174649	+	0.999998i	$0.500556\pi$
$68$	6.01284	0.729164
$69$	−1.92422	−0.231649
$70$	−1.32070	−0.157854
$71$	4.67795	0.555171	0.277586	−	0.960701i	$-0.410466\pi$
$71$	4.67795	0.555171	0.277586	+	0.960701i	$0.410466\pi$
$72$	−2.59599	−0.305941
$73$	8.92092	1.04412	0.522058	−	0.852910i	$-0.325165\pi$
$73$	8.92092	1.04412	0.522058	+	0.852910i	$0.325165\pi$
$74$	3.14616	0.365734
$75$	−0.635616	−0.0733946
$76$	−7.36781	−0.845146
$77$	7.40262	0.843607
$78$	1.55926	0.176552
$79$	6.10555	0.686928	0.343464	−	0.939166i	$-0.388400\pi$
$79$	6.10555	0.686928	0.343464	+	0.939166i	$0.388400\pi$
$80$	1.00000	0.111803
$81$	5.52716	0.614128
$82$	−7.56744	−0.835684
$83$	14.9213	1.63783	0.818913	−	0.573917i	$-0.194577\pi$
$83$	14.9213	1.63783	0.818913	+	0.573917i	$0.194577\pi$
$84$	0.839458	0.0915924
$85$	6.01284	0.652184
$86$	0.0321924	0.00347139
$87$	−2.12313	−0.227623
$88$	−5.60507	−0.597503
$89$	−11.7957	−1.25034	−0.625172	−	0.780487i	$-0.714971\pi$
$89$	−11.7957	−1.25034	−0.625172	+	0.780487i	$0.714971\pi$
$90$	−2.59599	−0.273642
$91$	3.23988	0.339632
$92$	3.02733	0.315621
$93$	−4.06009	−0.421011
$94$	9.23464	0.952481
$95$	−7.36781	−0.755922
$96$	−0.635616	−0.0648723
$97$	13.3166	1.35210	0.676048	−	0.736857i	$-0.263691\pi$
$97$	13.3166	1.35210	0.676048	+	0.736857i	$0.263691\pi$
$98$	−5.25575	−0.530911
$99$	14.5507	1.46240
$100$	1.00000	0.100000
$101$	6.05888	0.602881	0.301440	−	0.953485i	$-0.402533\pi$
$101$	6.05888	0.602881	0.301440	+	0.953485i	$0.402533\pi$
$102$	−3.82186	−0.378420
$103$	−16.6764	−1.64317	−0.821586	−	0.570085i	$-0.806910\pi$
$103$	−16.6764	−1.64317	−0.821586	+	0.570085i	$0.806910\pi$
$104$	−2.45315	−0.240551
$105$	0.839458	0.0819228
$106$	0.477940	0.0464216
$107$	3.19172	0.308555	0.154278	−	0.988028i	$-0.450695\pi$
$107$	3.19172	0.308555	0.154278	+	0.988028i	$0.450695\pi$
$108$	3.55690	0.342263
$109$	17.0628	1.63432	0.817161	−	0.576410i	$-0.195547\pi$
$109$	17.0628	1.63432	0.817161	+	0.576410i	$0.195547\pi$
$110$	−5.60507	−0.534423
$111$	−1.99975	−0.189808
$112$	−1.32070	−0.124795
$113$	14.8463	1.39663	0.698313	−	0.715793i	$-0.253934\pi$
$113$	14.8463	1.39663	0.698313	+	0.715793i	$0.253934\pi$
$114$	4.68310	0.438612
$115$	3.02733	0.282300
$116$	3.34027	0.310136
$117$	6.36837	0.588756
$118$	−2.63038	−0.242146
$119$	−7.94117	−0.727966
$120$	−0.635616	−0.0580235
$121$	20.4168	1.85607
$122$	10.4867	0.949422
$123$	4.80999	0.433702
$124$	6.38765	0.573627
$125$	1.00000	0.0894427
$126$	3.42853	0.305438
$127$	8.82704	0.783273	0.391637	−	0.920120i	$-0.371909\pi$
$127$	8.82704	0.783273	0.391637	+	0.920120i	$0.371909\pi$
$128$	1.00000	0.0883883
$129$	−0.0204620	−0.00180158
$130$	−2.45315	−0.215156
$131$	−9.40907	−0.822074	−0.411037	−	0.911619i	$-0.634833\pi$
$131$	−9.40907	−0.822074	−0.411037	+	0.911619i	$0.634833\pi$
$132$	3.56267	0.310091
$133$	9.73068	0.843757
$134$	−0.0285912	−0.00246991
$135$	3.55690	0.306129
$136$	6.01284	0.515597
$137$	6.74484	0.576251	0.288125	−	0.957593i	$-0.406968\pi$
$137$	6.74484	0.576251	0.288125	+	0.957593i	$0.406968\pi$
$138$	−1.92422	−0.163800
$139$	11.5423	0.979006	0.489503	−	0.872002i	$-0.337178\pi$
$139$	11.5423	0.979006	0.489503	+	0.872002i	$0.337178\pi$
$140$	−1.32070	−0.111620
$141$	−5.86968	−0.494317
$142$	4.67795	0.392565
$143$	13.7501	1.14984
$144$	−2.59599	−0.216333
$145$	3.34027	0.277394
$146$	8.92092	0.738301
$147$	3.34064	0.275531
$148$	3.14616	0.258613
$149$	−21.7500	−1.78183	−0.890914	−	0.454172i	$-0.849935\pi$
$149$	−21.7500	−1.78183	−0.890914	+	0.454172i	$0.849935\pi$
$150$	−0.635616	−0.0518978
$151$	−23.2818	−1.89465	−0.947323	−	0.320280i	$-0.896223\pi$
$151$	−23.2818	−1.89465	−0.947323	+	0.320280i	$0.896223\pi$
$152$	−7.36781	−0.597609
$153$	−15.6093	−1.26194
$154$	7.40262	0.596520
$155$	6.38765	0.513068
$156$	1.55926	0.124841
$157$	5.37085	0.428641	0.214320	−	0.976763i	$-0.431246\pi$
$157$	5.37085	0.428641	0.214320	+	0.976763i	$0.431246\pi$
$158$	6.10555	0.485732
$159$	−0.303786	−0.0240918
$160$	1.00000	0.0790569
$161$	−3.99820	−0.315102
$162$	5.52716	0.434254
$163$	−0.140929	−0.0110384	−0.00551921	−	0.999985i	$-0.501757\pi$
$163$	−0.140929	−0.0110384	−0.00551921	+	0.999985i	$0.501757\pi$
$164$	−7.56744	−0.590918
$165$	3.56267	0.277354
$166$	14.9213	1.15812
$167$	−2.96973	−0.229805	−0.114902	−	0.993377i	$-0.536656\pi$
$167$	−2.96973	−0.229805	−0.114902	+	0.993377i	$0.536656\pi$
$168$	0.839458	0.0647656
$169$	−6.98204	−0.537080
$170$	6.01284	0.461164
$171$	19.1268	1.46266
$172$	0.0321924	0.00245465
$173$	−13.7074	−1.04215	−0.521076	−	0.853510i	$-0.674469\pi$
$173$	−13.7074	−1.04215	−0.521076	+	0.853510i	$0.674469\pi$
$174$	−2.12313	−0.160954
$175$	−1.32070	−0.0998356
$176$	−5.60507	−0.422498
$177$	1.67191	0.125668
$178$	−11.7957	−0.884126
$179$	7.41866	0.554497	0.277248	−	0.960798i	$-0.410577\pi$
$179$	7.41866	0.554497	0.277248	+	0.960798i	$0.410577\pi$
$180$	−2.59599	−0.193494
$181$	23.4746	1.74486	0.872428	−	0.488743i	$-0.162545\pi$
$181$	23.4746	1.74486	0.872428	+	0.488743i	$0.162545\pi$
$182$	3.23988	0.240156
$183$	−6.66552	−0.492729
$184$	3.02733	0.223178
$185$	3.14616	0.231310
$186$	−4.06009	−0.297700
$187$	−33.7024	−2.46456
$188$	9.23464	0.673506
$189$	−4.69760	−0.341700
$190$	−7.36781	−0.534517
$191$	−17.2485	−1.24805	−0.624027	−	0.781402i	$-0.714505\pi$
$191$	−17.2485	−1.24805	−0.624027	+	0.781402i	$0.714505\pi$
$192$	−0.635616	−0.0458716
$193$	3.38214	0.243452	0.121726	−	0.992564i	$-0.461157\pi$
$193$	3.38214	0.243452	0.121726	+	0.992564i	$0.461157\pi$
$194$	13.3166	0.956077
$195$	1.55926	0.111661
$196$	−5.25575	−0.375411
$197$	−24.3352	−1.73381	−0.866904	−	0.498475i	$-0.833894\pi$
$197$	−24.3352	−1.73381	−0.866904	+	0.498475i	$0.833894\pi$
$198$	14.5507	1.03407
$199$	−21.9937	−1.55909	−0.779547	−	0.626344i	$-0.784550\pi$
$199$	−21.9937	−1.55909	−0.779547	+	0.626344i	$0.784550\pi$
$200$	1.00000	0.0707107
$201$	0.0181730	0.00128183
$202$	6.05888	0.426301
$203$	−4.41150	−0.309626
$204$	−3.82186	−0.267584
$205$	−7.56744	−0.528533
$206$	−16.6764	−1.16190
$207$	−7.85893	−0.546233
$208$	−2.45315	−0.170096
$209$	41.2971	2.85658
$210$	0.839458	0.0579281
$211$	−11.7018	−0.805588	−0.402794	−	0.915291i	$-0.631961\pi$
$211$	−11.7018	−0.805588	−0.402794	+	0.915291i	$0.631961\pi$
$212$	0.477940	0.0328250
$213$	−2.97338	−0.203733
$214$	3.19172	0.218182
$215$	0.0321924	0.00219550
$216$	3.55690	0.242016
$217$	−8.43617	−0.572685
$218$	17.0628	1.15564
$219$	−5.67028	−0.383162
$220$	−5.60507	−0.377894
$221$	−14.7504	−0.992220
$222$	−1.99975	−0.134214
$223$	3.34384	0.223920	0.111960	−	0.993713i	$-0.464287\pi$
$223$	3.34384	0.223920	0.111960	+	0.993713i	$0.464287\pi$
$224$	−1.32070	−0.0882431
$225$	−2.59599	−0.173066
$226$	14.8463	0.987563
$227$	−15.9128	−1.05617	−0.528084	−	0.849192i	$-0.677089\pi$
$227$	−15.9128	−1.05617	−0.528084	+	0.849192i	$0.677089\pi$
$228$	4.68310	0.310146
$229$	5.78306	0.382155	0.191078	−	0.981575i	$-0.438802\pi$
$229$	5.78306	0.382155	0.191078	+	0.981575i	$0.438802\pi$
$230$	3.02733	0.199616
$231$	−4.70522	−0.309581
$232$	3.34027	0.219299
$233$	29.2502	1.91624	0.958122	−	0.286362i	$-0.0924459\pi$
$233$	29.2502	1.91624	0.958122	+	0.286362i	$0.0924459\pi$
$234$	6.36837	0.416313
$235$	9.23464	0.602402
$236$	−2.63038	−0.171223
$237$	−3.88078	−0.252084
$238$	−7.94117	−0.514749
$239$	−5.46265	−0.353350	−0.176675	−	0.984269i	$-0.556534\pi$
$239$	−5.46265	−0.353350	−0.176675	+	0.984269i	$0.556534\pi$
$240$	−0.635616	−0.0410288
$241$	14.8866	0.958933	0.479467	−	0.877560i	$-0.340830\pi$
$241$	14.8866	0.958933	0.479467	+	0.877560i	$0.340830\pi$
$242$	20.4168	1.31244
$243$	−14.1838	−0.909894
$244$	10.4867	0.671343
$245$	−5.25575	−0.335777
$246$	4.80999	0.306673
$247$	18.0744	1.15004
$248$	6.38765	0.405616
$249$	−9.48422	−0.601038
$250$	1.00000	0.0632456
$251$	−0.900501	−0.0568391	−0.0284196	−	0.999596i	$-0.509047\pi$
$251$	−0.900501	−0.0568391	−0.0284196	+	0.999596i	$0.509047\pi$
$252$	3.42853	0.215977
$253$	−16.9684	−1.06679
$254$	8.82704	0.553858
$255$	−3.82186	−0.239334
$256$	1.00000	0.0625000
$257$	25.4185	1.58556	0.792781	−	0.609506i	$-0.208632\pi$
$257$	25.4185	1.58556	0.792781	+	0.609506i	$0.208632\pi$
$258$	−0.0204620	−0.00127391
$259$	−4.15514	−0.258188
$260$	−2.45315	−0.152138
$261$	−8.67131	−0.536741
$262$	−9.40907	−0.581294
$263$	−1.46800	−0.0905208	−0.0452604	−	0.998975i	$-0.514412\pi$
$263$	−1.46800	−0.0905208	−0.0452604	+	0.998975i	$0.514412\pi$
$264$	3.56267	0.219267
$265$	0.477940	0.0293596
$266$	9.73068	0.596626
$267$	7.49754	0.458842
$268$	−0.0285912	−0.00174649
$269$	−16.3635	−0.997702	−0.498851	−	0.866688i	$-0.666244\pi$
$269$	−16.3635	−0.997702	−0.498851	+	0.866688i	$0.666244\pi$
$270$	3.55690	0.216466
$271$	−7.03533	−0.427366	−0.213683	−	0.976903i	$-0.568546\pi$
$271$	−7.03533	−0.427366	−0.213683	+	0.976903i	$0.568546\pi$
$272$	6.01284	0.364582
$273$	−2.05932	−0.124636
$274$	6.74484	0.407471
$275$	−5.60507	−0.337999
$276$	−1.92422	−0.115824
$277$	22.6805	1.36274	0.681371	−	0.731938i	$-0.261384\pi$
$277$	22.6805	1.36274	0.681371	+	0.731938i	$0.261384\pi$
$278$	11.5423	0.692262
$279$	−16.5823	−0.992755
$280$	−1.32070	−0.0789270
$281$	9.12455	0.544325	0.272162	−	0.962251i	$-0.412261\pi$
$281$	9.12455	0.544325	0.272162	+	0.962251i	$0.412261\pi$
$282$	−5.86968	−0.349535
$283$	5.12244	0.304497	0.152249	−	0.988342i	$-0.451349\pi$
$283$	5.12244	0.304497	0.152249	+	0.988342i	$0.451349\pi$
$284$	4.67795	0.277586
$285$	4.68310	0.277403
$286$	13.7501	0.813060
$287$	9.99433	0.589947
$288$	−2.59599	−0.152970
$289$	19.1543	1.12672
$290$	3.34027	0.196147
$291$	−8.46424	−0.496183
$292$	8.92092	0.522058
$293$	11.3338	0.662128	0.331064	−	0.943608i	$-0.392592\pi$
$293$	11.3338	0.662128	0.331064	+	0.943608i	$0.392592\pi$
$294$	3.34064	0.194830
$295$	−2.63038	−0.153147
$296$	3.14616	0.182867
$297$	−19.9367	−1.15684
$298$	−21.7500	−1.25994
$299$	−7.42651	−0.429486
$300$	−0.635616	−0.0366973
$301$	−0.0425165	−0.00245061
$302$	−23.2818	−1.33972
$303$	−3.85112	−0.221241
$304$	−7.36781	−0.422573
$305$	10.4867	0.600467
$306$	−15.6093	−0.892324
$307$	−4.27745	−0.244127	−0.122063	−	0.992522i	$-0.538951\pi$
$307$	−4.27745	−0.244127	−0.122063	+	0.992522i	$0.538951\pi$
$308$	7.40262	0.421804
$309$	10.5998	0.602999
$310$	6.38765	0.362794
$311$	2.75764	0.156372	0.0781858	−	0.996939i	$-0.475087\pi$
$311$	2.75764	0.156372	0.0781858	+	0.996939i	$0.475087\pi$
$312$	1.55926	0.0882758
$313$	28.7119	1.62289	0.811446	−	0.584427i	$-0.198681\pi$
$313$	28.7119	1.62289	0.811446	+	0.584427i	$0.198681\pi$
$314$	5.37085	0.303095
$315$	3.42853	0.193176
$316$	6.10555	0.343464
$317$	−26.5610	−1.49181	−0.745907	−	0.666050i	$-0.767984\pi$
$317$	−26.5610	−1.49181	−0.745907	+	0.666050i	$0.767984\pi$
$318$	−0.303786	−0.0170355
$319$	−18.7224	−1.04826
$320$	1.00000	0.0559017
$321$	−2.02871	−0.113231
$322$	−3.99820	−0.222811
$323$	−44.3015	−2.46500
$324$	5.52716	0.307064
$325$	−2.45315	−0.136076
$326$	−0.140929	−0.00780535
$327$	−10.8454	−0.599752
$328$	−7.56744	−0.417842
$329$	−12.1962	−0.672399
$330$	3.56267	0.196119
$331$	32.4576	1.78403	0.892014	−	0.452007i	$-0.149292\pi$
$331$	32.4576	1.78403	0.892014	+	0.452007i	$0.149292\pi$
$332$	14.9213	0.818913
$333$	−8.16741	−0.447571
$334$	−2.96973	−0.162497
$335$	−0.0285912	−0.00156211
$336$	0.839458	0.0457962
$337$	31.5669	1.71956	0.859779	−	0.510666i	$-0.170601\pi$
$337$	31.5669	1.71956	0.859779	+	0.510666i	$0.170601\pi$
$338$	−6.98204	−0.379773
$339$	−9.43656	−0.512524
$340$	6.01284	0.326092
$341$	−35.8032	−1.93885
$342$	19.1268	1.03426
$343$	16.1862	0.873972
$344$	0.0321924	0.00173570
$345$	−1.92422	−0.103596
$346$	−13.7074	−0.736912
$347$	9.39202	0.504190	0.252095	−	0.967702i	$-0.418880\pi$
$347$	9.39202	0.504190	0.252095	+	0.967702i	$0.418880\pi$
$348$	−2.12313	−0.113812
$349$	−6.97816	−0.373532	−0.186766	−	0.982404i	$-0.559801\pi$
$349$	−6.97816	−0.373532	−0.186766	+	0.982404i	$0.559801\pi$
$350$	−1.32070	−0.0705944
$351$	−8.72562	−0.465739
$352$	−5.60507	−0.298751
$353$	−10.0759	−0.536285	−0.268142	−	0.963379i	$-0.586410\pi$
$353$	−10.0759	−0.536285	−0.268142	+	0.963379i	$0.586410\pi$
$354$	1.67191	0.0888610
$355$	4.67795	0.248280
$356$	−11.7957	−0.625172
$357$	5.04753	0.267144
$358$	7.41866	0.392089
$359$	27.3133	1.44154	0.720770	−	0.693175i	$-0.243789\pi$
$359$	27.3133	1.44154	0.720770	+	0.693175i	$0.243789\pi$
$360$	−2.59599	−0.136821
$361$	35.2847	1.85709
$362$	23.4746	1.23380
$363$	−12.9773	−0.681129
$364$	3.23988	0.169816
$365$	8.92092	0.466942
$366$	−6.66552	−0.348412
$367$	30.9747	1.61687	0.808434	−	0.588587i	$-0.200316\pi$
$367$	30.9747	1.61687	0.808434	+	0.588587i	$0.200316\pi$
$368$	3.02733	0.157811
$369$	19.6450	1.02268
$370$	3.14616	0.163561
$371$	−0.631215	−0.0327711
$372$	−4.06009	−0.210506
$373$	−31.2321	−1.61714	−0.808568	−	0.588403i	$-0.799757\pi$
$373$	−31.2321	−1.61714	−0.808568	+	0.588403i	$0.799757\pi$
$374$	−33.7024	−1.74271
$375$	−0.635616	−0.0328231
$376$	9.23464	0.476240
$377$	−8.19419	−0.422022
$378$	−4.69760	−0.241619
$379$	−23.0195	−1.18243	−0.591217	−	0.806512i	$-0.701352\pi$
$379$	−23.0195	−1.18243	−0.591217	+	0.806512i	$0.701352\pi$
$380$	−7.36781	−0.377961
$381$	−5.61061	−0.287440
$382$	−17.2485	−0.882508
$383$	8.09787	0.413782	0.206891	−	0.978364i	$-0.433666\pi$
$383$	8.09787	0.413782	0.206891	+	0.978364i	$0.433666\pi$
$384$	−0.635616	−0.0324361
$385$	7.40262	0.377273
$386$	3.38214	0.172147
$387$	−0.0835712	−0.00424816
$388$	13.3166	0.676048
$389$	27.1259	1.37534	0.687669	−	0.726025i	$-0.258634\pi$
$389$	27.1259	1.37534	0.687669	+	0.726025i	$0.258634\pi$
$390$	1.55926	0.0789563
$391$	18.2029	0.920559
$392$	−5.25575	−0.265455
$393$	5.98055	0.301679
$394$	−24.3352	−1.22599
$395$	6.10555	0.307204
$396$	14.5507	0.731201
$397$	−26.0918	−1.30951	−0.654754	−	0.755842i	$-0.727228\pi$
$397$	−26.0918	−1.30951	−0.654754	+	0.755842i	$0.727228\pi$
$398$	−21.9937	−1.10245
$399$	−6.18497	−0.309636
$400$	1.00000	0.0500000
$401$	13.5019	0.674254	0.337127	−	0.941459i	$-0.390545\pi$
$401$	13.5019	0.674254	0.337127	+	0.941459i	$0.390545\pi$
$402$	0.0181730	0.000906389 0
$403$	−15.6699	−0.780572
$404$	6.05888	0.301440
$405$	5.52716	0.274647
$406$	−4.41150	−0.218939
$407$	−17.6344	−0.874107
$408$	−3.82186	−0.189210
$409$	−26.1144	−1.29127	−0.645637	−	0.763645i	$-0.723408\pi$
$409$	−26.1144	−1.29127	−0.645637	+	0.763645i	$0.723408\pi$
$410$	−7.56744	−0.373729
$411$	−4.28713	−0.211468
$412$	−16.6764	−0.821586
$413$	3.47394	0.170942
$414$	−7.85893	−0.386245
$415$	14.9213	0.732458
$416$	−2.45315	−0.120276
$417$	−7.33648	−0.359269
$418$	41.2971	2.01991
$419$	−3.45902	−0.168984	−0.0844922	−	0.996424i	$-0.526927\pi$
$419$	−3.45902	−0.168984	−0.0844922	+	0.996424i	$0.526927\pi$
$420$	0.839458	0.0409614
$421$	−4.99974	−0.243673	−0.121836	−	0.992550i	$-0.538878\pi$
$421$	−4.99974	−0.243673	−0.121836	+	0.992550i	$0.538878\pi$
$422$	−11.7018	−0.569637
$423$	−23.9731	−1.16561
$424$	0.477940	0.0232108
$425$	6.01284	0.291666
$426$	−2.97338	−0.144061
$427$	−13.8498	−0.670239
$428$	3.19172	0.154278
$429$	−8.73978	−0.421960
$430$	0.0321924	0.00155245
$431$	26.2713	1.26544	0.632721	−	0.774379i	$-0.281938\pi$
$431$	26.2713	1.26544	0.632721	+	0.774379i	$0.281938\pi$
$432$	3.55690	0.171131
$433$	−24.8543	−1.19442	−0.597210	−	0.802085i	$-0.703724\pi$
$433$	−24.8543	−1.19442	−0.597210	+	0.802085i	$0.703724\pi$
$434$	−8.43617	−0.404949
$435$	−2.12313	−0.101796
$436$	17.0628	0.817161
$437$	−22.3048	−1.06698
$438$	−5.67028	−0.270936
$439$	18.4409	0.880138	0.440069	−	0.897964i	$-0.354954\pi$
$439$	18.4409	0.880138	0.440069	+	0.897964i	$0.354954\pi$
$440$	−5.60507	−0.267211
$441$	13.6439	0.649709
$442$	−14.7504	−0.701606
$443$	−23.2393	−1.10413	−0.552067	−	0.833800i	$-0.686161\pi$
$443$	−23.2393	−1.10413	−0.552067	+	0.833800i	$0.686161\pi$
$444$	−1.99975	−0.0949039
$445$	−11.7957	−0.559170
$446$	3.34384	0.158335
$447$	13.8246	0.653883
$448$	−1.32070	−0.0623973
$449$	−8.83317	−0.416863	−0.208432	−	0.978037i	$-0.566836\pi$
$449$	−8.83317	−0.416863	−0.208432	+	0.978037i	$0.566836\pi$
$450$	−2.59599	−0.122376
$451$	42.4161	1.99729
$452$	14.8463	0.698313
$453$	14.7983	0.695284
$454$	−15.9128	−0.746824
$455$	3.23988	0.151888
$456$	4.68310	0.219306
$457$	17.0179	0.796066	0.398033	−	0.917371i	$-0.369693\pi$
$457$	17.0179	0.796066	0.398033	+	0.917371i	$0.369693\pi$
$458$	5.78306	0.270225
$459$	21.3871	0.998264
$460$	3.02733	0.141150
$461$	−6.77129	−0.315371	−0.157685	−	0.987489i	$-0.550403\pi$
$461$	−6.77129	−0.315371	−0.157685	+	0.987489i	$0.550403\pi$
$462$	−4.70522	−0.218907
$463$	−32.6488	−1.51732	−0.758660	−	0.651487i	$-0.774146\pi$
$463$	−32.6488	−1.51732	−0.758660	+	0.651487i	$0.774146\pi$
$464$	3.34027	0.155068
$465$	−4.06009	−0.188282
$466$	29.2502	1.35499
$467$	−27.8998	−1.29105	−0.645524	−	0.763740i	$-0.723361\pi$
$467$	−27.8998	−1.29105	−0.645524	+	0.763740i	$0.723361\pi$
$468$	6.36837	0.294378
$469$	0.0377605	0.00174362
$470$	9.23464	0.425962
$471$	−3.41380	−0.157300
$472$	−2.63038	−0.121073
$473$	−0.180441	−0.00829667
$474$	−3.88078	−0.178250
$475$	−7.36781	−0.338059
$476$	−7.94117	−0.363983
$477$	−1.24073	−0.0568090
$478$	−5.46265	−0.249856
$479$	31.7647	1.45136	0.725682	−	0.688030i	$-0.241524\pi$
$479$	31.7647	1.45136	0.725682	+	0.688030i	$0.241524\pi$
$480$	−0.635616	−0.0290118
$481$	−7.71801	−0.351911
$482$	14.8866	0.678068
$483$	2.54132	0.115634
$484$	20.4168	0.928037
$485$	13.3166	0.604676
$486$	−14.1838	−0.643392
$487$	−29.9605	−1.35764	−0.678819	−	0.734306i	$-0.737508\pi$
$487$	−29.9605	−1.35764	−0.678819	+	0.734306i	$0.737508\pi$
$488$	10.4867	0.474711
$489$	0.0895768	0.00405080
$490$	−5.25575	−0.237431
$491$	29.4434	1.32876	0.664381	−	0.747394i	$-0.268695\pi$
$491$	29.4434	1.32876	0.664381	+	0.747394i	$0.268695\pi$
$492$	4.80999	0.216851
$493$	20.0845	0.904561
$494$	18.0744	0.813204
$495$	14.5507	0.654006
$496$	6.38765	0.286814
$497$	−6.17818	−0.277129
$498$	−9.48422	−0.424998
$499$	20.6441	0.924155	0.462077	−	0.886840i	$-0.347104\pi$
$499$	20.6441	0.924155	0.462077	+	0.886840i	$0.347104\pi$
$500$	1.00000	0.0447214
$501$	1.88761	0.0843322
$502$	−0.900501	−0.0401913
$503$	12.5877	0.561256	0.280628	−	0.959817i	$-0.409457\pi$
$503$	12.5877	0.561256	0.280628	+	0.959817i	$0.409457\pi$
$504$	3.42853	0.152719
$505$	6.05888	0.269616
$506$	−16.9684	−0.754338
$507$	4.43790	0.197094
$508$	8.82704	0.391637
$509$	27.4067	1.21478	0.607390	−	0.794404i	$-0.292217\pi$
$509$	27.4067	1.21478	0.607390	+	0.794404i	$0.292217\pi$
$510$	−3.82186	−0.169235
$511$	−11.7819	−0.521199
$512$	1.00000	0.0441942
$513$	−26.2066	−1.15705
$514$	25.4185	1.12116
$515$	−16.6764	−0.734849
$516$	−0.0204620	−0.000900789 0
$517$	−51.7608	−2.27644
$518$	−4.15514	−0.182566
$519$	8.71261	0.382441
$520$	−2.45315	−0.107578
$521$	−4.84078	−0.212079	−0.106039	−	0.994362i	$-0.533817\pi$
$521$	−4.84078	−0.212079	−0.106039	+	0.994362i	$0.533817\pi$
$522$	−8.67131	−0.379533
$523$	−33.9763	−1.48568	−0.742840	−	0.669469i	$-0.766522\pi$
$523$	−33.9763	−1.48568	−0.742840	+	0.669469i	$0.766522\pi$
$524$	−9.40907	−0.411037
$525$	0.839458	0.0366370
$526$	−1.46800	−0.0640078
$527$	38.4079	1.67307
$528$	3.56267	0.155045
$529$	−13.8353	−0.601533
$530$	0.477940	0.0207604
$531$	6.82844	0.296329
$532$	9.73068	0.421879
$533$	18.5641	0.804100
$534$	7.49754	0.324450
$535$	3.19172	0.137990
$536$	−0.0285912	−0.00123495
$537$	−4.71542	−0.203485
$538$	−16.3635	−0.705482
$539$	29.4588	1.26888
$540$	3.55690	0.153065
$541$	−5.37855	−0.231242	−0.115621	−	0.993293i	$-0.536886\pi$
$541$	−5.37855	−0.231242	−0.115621	+	0.993293i	$0.536886\pi$
$542$	−7.03533	−0.302193
$543$	−14.9208	−0.640315
$544$	6.01284	0.257798
$545$	17.0628	0.730891
$546$	−2.05932	−0.0881307
$547$	36.5371	1.56221	0.781107	−	0.624397i	$-0.214655\pi$
$547$	36.5371	1.56221	0.781107	+	0.624397i	$0.214655\pi$
$548$	6.74484	0.288125
$549$	−27.2234	−1.16187
$550$	−5.60507	−0.239001
$551$	−24.6105	−1.04844
$552$	−1.92422	−0.0819002
$553$	−8.06361	−0.342900
$554$	22.6805	0.963604
$555$	−1.99975	−0.0848846
$556$	11.5423	0.489503
$557$	29.4531	1.24797	0.623983	−	0.781438i	$-0.285513\pi$
$557$	29.4531	1.24797	0.623983	+	0.781438i	$0.285513\pi$
$558$	−16.5823	−0.701984
$559$	−0.0789728	−0.00334020
$560$	−1.32070	−0.0558098
$561$	21.4218	0.904428
$562$	9.12455	0.384896
$563$	−1.86470	−0.0785879	−0.0392939	−	0.999228i	$-0.512511\pi$
$563$	−1.86470	−0.0785879	−0.0392939	+	0.999228i	$0.512511\pi$
$564$	−5.86968	−0.247158
$565$	14.8463	0.624590
$566$	5.12244	0.215312
$567$	−7.29972	−0.306559
$568$	4.67795	0.196283
$569$	40.6458	1.70396	0.851979	−	0.523575i	$-0.175402\pi$
$569$	40.6458	1.70396	0.851979	+	0.523575i	$0.175402\pi$
$570$	4.68310	0.196153
$571$	−12.3154	−0.515381	−0.257691	−	0.966227i	$-0.582962\pi$
$571$	−12.3154	−0.515381	−0.257691	+	0.966227i	$0.582962\pi$
$572$	13.7501	0.574920
$573$	10.9634	0.458002
$574$	9.99433	0.417155
$575$	3.02733	0.126248
$576$	−2.59599	−0.108166
$577$	16.5034	0.687045	0.343522	−	0.939145i	$-0.388380\pi$
$577$	16.5034	0.687045	0.343522	+	0.939145i	$0.388380\pi$
$578$	19.1543	0.796713
$579$	−2.14974	−0.0893403
$580$	3.34027	0.138697
$581$	−19.7066	−0.817567
$582$	−8.46424	−0.350854
$583$	−2.67889	−0.110948
$584$	8.92092	0.369150
$585$	6.36837	0.263300
$586$	11.3338	0.468195
$587$	−9.24344	−0.381518	−0.190759	−	0.981637i	$-0.561095\pi$
$587$	−9.24344	−0.381518	−0.190759	+	0.981637i	$0.561095\pi$
$588$	3.34064	0.137766
$589$	−47.0630	−1.93920
$590$	−2.63038	−0.108291
$591$	15.4678	0.636261
$592$	3.14616	0.129306
$593$	−23.0779	−0.947695	−0.473847	−	0.880607i	$-0.657135\pi$
$593$	−23.0779	−0.947695	−0.473847	+	0.880607i	$0.657135\pi$
$594$	−19.9367	−0.818012
$595$	−7.94117	−0.325556
$596$	−21.7500	−0.890914
$597$	13.9796	0.572145
$598$	−7.42651	−0.303692
$599$	23.7408	0.970023	0.485011	−	0.874508i	$-0.338815\pi$
$599$	23.7408	0.970023	0.485011	+	0.874508i	$0.338815\pi$
$600$	−0.635616	−0.0259489
$601$	1.00000	0.0407909
$601$	1.00000	0.0407909
$602$	−0.0425165	−0.00173284
$603$	0.0742226	0.00302258
$604$	−23.2818	−0.947323
$605$	20.4168	0.830062
$606$	−3.85112	−0.156441
$607$	−3.84566	−0.156090	−0.0780452	−	0.996950i	$-0.524868\pi$
$607$	−3.84566	−0.156090	−0.0780452	+	0.996950i	$0.524868\pi$
$608$	−7.36781	−0.298804
$609$	2.80402	0.113624
$610$	10.4867	0.424594
$611$	−22.6540	−0.916482
$612$	−15.6093	−0.630968
$613$	5.14465	0.207790	0.103895	−	0.994588i	$-0.466869\pi$
$613$	5.14465	0.207790	0.103895	+	0.994588i	$0.466869\pi$
$614$	−4.27745	−0.172624
$615$	4.80999	0.193957
$616$	7.40262	0.298260
$617$	21.2122	0.853973	0.426986	−	0.904258i	$-0.359575\pi$
$617$	21.2122	0.853973	0.426986	+	0.904258i	$0.359575\pi$
$618$	10.5998	0.426385
$619$	13.1452	0.528352	0.264176	−	0.964475i	$-0.414900\pi$
$619$	13.1452	0.528352	0.264176	+	0.964475i	$0.414900\pi$
$620$	6.38765	0.256534
$621$	10.7679	0.432102
$622$	2.75764	0.110571
$623$	15.5786	0.624144
$624$	1.55926	0.0624204
$625$	1.00000	0.0400000
$626$	28.7119	1.14756
$627$	−26.2491	−1.04829
$628$	5.37085	0.214320
$629$	18.9174	0.754285
$630$	3.42853	0.136596
$631$	9.87599	0.393157	0.196579	−	0.980488i	$-0.437017\pi$
$631$	9.87599	0.393157	0.196579	+	0.980488i	$0.437017\pi$
$632$	6.10555	0.242866
$633$	7.43788	0.295629
$634$	−26.5610	−1.05487
$635$	8.82704	0.350291
$636$	−0.303786	−0.0120459
$637$	12.8932	0.510845
$638$	−18.7224	−0.741228
$639$	−12.1439	−0.480407
$640$	1.00000	0.0395285
$641$	−4.24122	−0.167518	−0.0837590	−	0.996486i	$-0.526693\pi$
$641$	−4.24122	−0.167518	−0.0837590	+	0.996486i	$0.526693\pi$
$642$	−2.02871	−0.0800667
$643$	22.0829	0.870864	0.435432	−	0.900222i	$-0.356596\pi$
$643$	22.0829	0.870864	0.435432	+	0.900222i	$0.356596\pi$
$644$	−3.99820	−0.157551
$645$	−0.0204620	−0.000805690 0
$646$	−44.3015	−1.74302
$647$	12.7979	0.503138	0.251569	−	0.967839i	$-0.419053\pi$
$647$	12.7979	0.503138	0.251569	+	0.967839i	$0.419053\pi$
$648$	5.52716	0.217127
$649$	14.7435	0.578731
$650$	−2.45315	−0.0962205
$651$	5.36216	0.210160
$652$	−0.140929	−0.00551921
$653$	−2.69860	−0.105604	−0.0528022	−	0.998605i	$-0.516815\pi$
$653$	−2.69860	−0.105604	−0.0528022	+	0.998605i	$0.516815\pi$
$654$	−10.8454	−0.424089
$655$	−9.40907	−0.367643
$656$	−7.56744	−0.295459
$657$	−23.1587	−0.903505
$658$	−12.1962	−0.475458
$659$	−5.29788	−0.206376	−0.103188	−	0.994662i	$-0.532904\pi$
$659$	−5.29788	−0.206376	−0.103188	+	0.994662i	$0.532904\pi$
$660$	3.56267	0.138677
$661$	−6.48755	−0.252337	−0.126168	−	0.992009i	$-0.540268\pi$
$661$	−6.48755	−0.252337	−0.126168	+	0.992009i	$0.540268\pi$
$662$	32.4576	1.26150
$663$	9.37560	0.364118
$664$	14.9213	0.579059
$665$	9.73068	0.377340
$666$	−8.16741	−0.316481
$667$	10.1121	0.391542
$668$	−2.96973	−0.114902
$669$	−2.12540	−0.0821726
$670$	−0.0285912	−0.00110458
$671$	−58.7787	−2.26913
$672$	0.839458	0.0323828
$673$	−7.62580	−0.293953	−0.146976	−	0.989140i	$-0.546954\pi$
$673$	−7.62580	−0.293953	−0.146976	+	0.989140i	$0.546954\pi$
$674$	31.5669	1.21591
$675$	3.55690	0.136905
$676$	−6.98204	−0.268540
$677$	14.0310	0.539256	0.269628	−	0.962965i	$-0.413099\pi$
$677$	14.0310	0.539256	0.269628	+	0.962965i	$0.413099\pi$
$678$	−9.43656	−0.362409
$679$	−17.5873	−0.674937
$680$	6.01284	0.230582
$681$	10.1144	0.387585
$682$	−35.8032	−1.37098
$683$	14.6844	0.561885	0.280942	−	0.959725i	$-0.409353\pi$
$683$	14.6844	0.561885	0.280942	+	0.959725i	$0.409353\pi$
$684$	19.1268	0.731331
$685$	6.74484	0.257707
$686$	16.1862	0.617991
$687$	−3.67580	−0.140241
$688$	0.0321924	0.00122732
$689$	−1.17246	−0.0446671
$690$	−1.92422	−0.0732538
$691$	−7.20448	−0.274071	−0.137036	−	0.990566i	$-0.543757\pi$
$691$	−7.20448	−0.274071	−0.137036	+	0.990566i	$0.543757\pi$
$692$	−13.7074	−0.521076
$693$	−19.2172	−0.729999
$694$	9.39202	0.356516
$695$	11.5423	0.437825
$696$	−2.12313	−0.0804769
$697$	−45.5018	−1.72350
$698$	−6.97816	−0.264127
$699$	−18.5919	−0.703209
$700$	−1.32070	−0.0499178
$701$	−45.4477	−1.71653	−0.858267	−	0.513203i	$-0.828459\pi$
$701$	−45.4477	−1.71653	−0.858267	+	0.513203i	$0.828459\pi$
$702$	−8.72562	−0.329327
$703$	−23.1803	−0.874262
$704$	−5.60507	−0.211249
$705$	−5.86968	−0.221065
$706$	−10.0759	−0.379211
$707$	−8.00196	−0.300945
$708$	1.67191	0.0628342
$709$	17.3914	0.653148	0.326574	−	0.945172i	$-0.394106\pi$
$709$	17.3914	0.653148	0.326574	+	0.945172i	$0.394106\pi$
$710$	4.67795	0.175561
$711$	−15.8500	−0.594420
$712$	−11.7957	−0.442063
$713$	19.3375	0.724196
$714$	5.04753	0.188899
$715$	13.7501	0.514224
$716$	7.41866	0.277248
$717$	3.47215	0.129670
$718$	27.3133	1.01932
$719$	−2.40229	−0.0895904	−0.0447952	−	0.998996i	$-0.514264\pi$
$719$	−2.40229	−0.0895904	−0.0447952	+	0.998996i	$0.514264\pi$
$720$	−2.59599	−0.0967469
$721$	22.0245	0.820235
$722$	35.2847	1.31316
$723$	−9.46219	−0.351903
$724$	23.4746	0.872428
$725$	3.34027	0.124054
$726$	−12.9773	−0.481631
$727$	−21.0234	−0.779716	−0.389858	−	0.920875i	$-0.627476\pi$
$727$	−21.0234	−0.779716	−0.389858	+	0.920875i	$0.627476\pi$
$728$	3.23988	0.120078
$729$	−7.56599	−0.280222
$730$	8.92092	0.330178
$731$	0.193568	0.00715936
$732$	−6.66552	−0.246365
$733$	−34.0632	−1.25815	−0.629076	−	0.777344i	$-0.716567\pi$
$733$	−34.0632	−1.25815	−0.629076	+	0.777344i	$0.716567\pi$
$734$	30.9747	1.14330
$735$	3.34064	0.123221
$736$	3.02733	0.111589
$737$	0.160256	0.00590310
$738$	19.6450	0.723143
$739$	0.437132	0.0160801	0.00804007	−	0.999968i	$-0.497441\pi$
$739$	0.437132	0.0160801	0.00804007	+	0.999968i	$0.497441\pi$
$740$	3.14616	0.115655
$741$	−11.4884	−0.422035
$742$	−0.631215	−0.0231726
$743$	−25.8981	−0.950108	−0.475054	−	0.879957i	$-0.657571\pi$
$743$	−25.8981	−0.950108	−0.475054	+	0.879957i	$0.657571\pi$
$744$	−4.06009	−0.148850
$745$	−21.7500	−0.796858
$746$	−31.2321	−1.14349
$747$	−38.7356	−1.41726
$748$	−33.7024	−1.23228
$749$	−4.21531	−0.154024
$750$	−0.635616	−0.0232094
$751$	24.9961	0.912119	0.456060	−	0.889949i	$-0.349260\pi$
$751$	24.9961	0.912119	0.456060	+	0.889949i	$0.349260\pi$
$752$	9.23464	0.336753
$753$	0.572373	0.0208584
$754$	−8.19419	−0.298415
$755$	−23.2818	−0.847311
$756$	−4.69760	−0.170850
$757$	7.85790	0.285600	0.142800	−	0.989752i	$-0.454389\pi$
$757$	7.85790	0.285600	0.142800	+	0.989752i	$0.454389\pi$
$758$	−23.0195	−0.836107
$759$	10.7854	0.391485
$760$	−7.36781	−0.267259
$761$	−21.5365	−0.780699	−0.390350	−	0.920667i	$-0.627646\pi$
$761$	−21.5365	−0.780699	−0.390350	+	0.920667i	$0.627646\pi$
$762$	−5.61061	−0.203251
$763$	−22.5349	−0.815818
$764$	−17.2485	−0.624027
$765$	−15.6093	−0.564355
$766$	8.09787	0.292588
$767$	6.45272	0.232994
$768$	−0.635616	−0.0229358
$769$	−23.1077	−0.833284	−0.416642	−	0.909071i	$-0.636793\pi$
$769$	−23.1077	−0.833284	−0.416642	+	0.909071i	$0.636793\pi$
$770$	7.40262	0.266772
$771$	−16.1564	−0.581858
$772$	3.38214	0.121726
$773$	27.5141	0.989614	0.494807	−	0.869003i	$-0.335239\pi$
$773$	27.5141	0.989614	0.494807	+	0.869003i	$0.335239\pi$
$774$	−0.0835712	−0.00300391
$775$	6.38765	0.229451
$776$	13.3166	0.478038
$777$	2.64107	0.0947479
$778$	27.1259	0.972510
$779$	55.7555	1.99765
$780$	1.55926	0.0558305
$781$	−26.2203	−0.938235
$782$	18.2029	0.650933
$783$	11.8810	0.424592
$784$	−5.25575	−0.187705
$785$	5.37085	0.191694
$786$	5.98055	0.213319
$787$	−46.3285	−1.65143	−0.825715	−	0.564087i	$-0.809228\pi$
$787$	−46.3285	−1.65143	−0.825715	+	0.564087i	$0.809228\pi$
$788$	−24.3352	−0.866904
$789$	0.933084	0.0332187
$790$	6.10555	0.217226
$791$	−19.6076	−0.697165
$792$	14.5507	0.517037
$793$	−25.7255	−0.913539
$794$	−26.0918	−0.925962
$795$	−0.303786	−0.0107742
$796$	−21.9937	−0.779547
$797$	23.0771	0.817432	0.408716	−	0.912662i	$-0.365977\pi$
$797$	23.0771	0.817432	0.408716	+	0.912662i	$0.365977\pi$
$798$	−6.18497	−0.218946
$799$	55.5265	1.96438
$800$	1.00000	0.0353553
$801$	30.6216	1.08196
$802$	13.5019	0.476770
$803$	−50.0024	−1.76455
$804$	0.0181730	0.000640914 0
$805$	−3.99820	−0.140918
$806$	−15.6699	−0.551947
$807$	10.4009	0.366130
$808$	6.05888	0.213150
$809$	16.5988	0.583583	0.291791	−	0.956482i	$-0.405749\pi$
$809$	16.5988	0.583583	0.291791	+	0.956482i	$0.405749\pi$
$810$	5.52716	0.194204
$811$	−7.51222	−0.263790	−0.131895	−	0.991264i	$-0.542106\pi$
$811$	−7.51222	−0.263790	−0.131895	+	0.991264i	$0.542106\pi$
$812$	−4.41150	−0.154813
$813$	4.47176	0.156832
$814$	−17.6344	−0.618087
$815$	−0.140929	−0.00493653
$816$	−3.82186	−0.133792
$817$	−0.237188	−0.00829814
$818$	−26.1144	−0.913068
$819$	−8.41071	−0.293894
$820$	−7.56744	−0.264267
$821$	40.1748	1.40211	0.701055	−	0.713107i	$-0.252713\pi$
$821$	40.1748	1.40211	0.701055	+	0.713107i	$0.252713\pi$
$822$	−4.28713	−0.149531
$823$	−19.0732	−0.664850	−0.332425	−	0.943130i	$-0.607867\pi$
$823$	−19.0732	−0.664850	−0.332425	+	0.943130i	$0.607867\pi$
$824$	−16.6764	−0.580949
$825$	3.56267	0.124036
$826$	3.47394	0.120874
$827$	24.5363	0.853210	0.426605	−	0.904438i	$-0.359709\pi$
$827$	24.5363	0.853210	0.426605	+	0.904438i	$0.359709\pi$
$828$	−7.85893	−0.273117
$829$	−5.79713	−0.201343	−0.100671	−	0.994920i	$-0.532099\pi$
$829$	−5.79713	−0.201343	−0.100671	+	0.994920i	$0.532099\pi$
$830$	14.9213	0.517926
$831$	−14.4161	−0.500089
$832$	−2.45315	−0.0850478
$833$	−31.6020	−1.09494
$834$	−7.33648	−0.254041
$835$	−2.96973	−0.102772
$836$	41.2971	1.42829
$837$	22.7202	0.785326
$838$	−3.45902	−0.119490
$839$	20.6192	0.711854	0.355927	−	0.934514i	$-0.384165\pi$
$839$	20.6192	0.711854	0.355927	+	0.934514i	$0.384165\pi$
$840$	0.839458	0.0289641
$841$	−17.8426	−0.615262
$842$	−4.99974	−0.172303
$843$	−5.79971	−0.199753
$844$	−11.7018	−0.402794
$845$	−6.98204	−0.240190
$846$	−23.9731	−0.824211
$847$	−26.9645	−0.926512
$848$	0.477940	0.0164125
$849$	−3.25590	−0.111742
$850$	6.01284	0.206239
$851$	9.52447	0.326495
$852$	−2.97338	−0.101866
$853$	−25.6299	−0.877551	−0.438775	−	0.898597i	$-0.644588\pi$
$853$	−25.6299	−0.877551	−0.438775	+	0.898597i	$0.644588\pi$
$854$	−13.8498	−0.473931
$855$	19.1268	0.654122
$856$	3.19172	0.109091
$857$	−25.2947	−0.864050	−0.432025	−	0.901862i	$-0.642201\pi$
$857$	−25.2947	−0.864050	−0.432025	+	0.901862i	$0.642201\pi$
$858$	−8.73978	−0.298371
$859$	21.8036	0.743928	0.371964	−	0.928247i	$-0.378684\pi$
$859$	21.8036	0.743928	0.371964	+	0.928247i	$0.378684\pi$
$860$	0.0321924	0.00109775
$861$	−6.35255	−0.216494
$862$	26.2713	0.894803
$863$	−19.8692	−0.676356	−0.338178	−	0.941082i	$-0.609811\pi$
$863$	−19.8692	−0.676356	−0.338178	+	0.941082i	$0.609811\pi$
$864$	3.55690	0.121008
$865$	−13.7074	−0.466064
$866$	−24.8543	−0.844583
$867$	−12.1748	−0.413476
$868$	−8.43617	−0.286342
$869$	−34.2220	−1.16090
$870$	−2.12313	−0.0719807
$871$	0.0701387	0.00237656
$872$	17.0628	0.577820
$873$	−34.5698	−1.17001
$874$	−22.3048	−0.754472
$875$	−1.32070	−0.0446478
$876$	−5.67028	−0.191581
$877$	31.0482	1.04842	0.524212	−	0.851588i	$-0.324360\pi$
$877$	31.0482	1.04842	0.524212	+	0.851588i	$0.324360\pi$
$878$	18.4409	0.622352
$879$	−7.20394	−0.242983
$880$	−5.60507	−0.188947
$881$	10.7176	0.361086	0.180543	−	0.983567i	$-0.442215\pi$
$881$	10.7176	0.361086	0.180543	+	0.983567i	$0.442215\pi$
$882$	13.6439	0.459413
$883$	−3.42195	−0.115158	−0.0575789	−	0.998341i	$-0.518338\pi$
$883$	−3.42195	−0.115158	−0.0575789	+	0.998341i	$0.518338\pi$
$884$	−14.7504	−0.496110
$885$	1.67191	0.0562006
$886$	−23.2393	−0.780741
$887$	29.2681	0.982725	0.491363	−	0.870955i	$-0.336499\pi$
$887$	29.2681	0.982725	0.491363	+	0.870955i	$0.336499\pi$
$888$	−1.99975	−0.0671072
$889$	−11.6579	−0.390993
$890$	−11.7957	−0.395393
$891$	−30.9801	−1.03787
$892$	3.34384	0.111960
$893$	−68.0391	−2.27684
$894$	13.8246	0.462365
$895$	7.41866	0.247979
$896$	−1.32070	−0.0441215
$897$	4.72040	0.157610
$898$	−8.83317	−0.294767
$899$	21.3364	0.711610
$900$	−2.59599	−0.0865331
$901$	2.87378	0.0957394
$902$	42.4161	1.41230
$903$	0.0270242	0.000899308 0
$904$	14.8463	0.493782
$905$	23.4746	0.780323
$906$	14.7983	0.491640
$907$	46.8880	1.55689	0.778445	−	0.627713i	$-0.216009\pi$
$907$	46.8880	1.55689	0.778445	+	0.627713i	$0.216009\pi$
$908$	−15.9128	−0.528084
$909$	−15.7288	−0.521691
$910$	3.23988	0.107401
$911$	−27.6932	−0.917516	−0.458758	−	0.888561i	$-0.651705\pi$
$911$	−27.6932	−0.917516	−0.458758	+	0.888561i	$0.651705\pi$
$912$	4.68310	0.155073
$913$	−83.6350	−2.76792
$914$	17.0179	0.562903
$915$	−6.66552	−0.220355
$916$	5.78306	0.191078
$917$	12.4266	0.410361
$918$	21.3871	0.705879
$919$	−24.2819	−0.800987	−0.400494	−	0.916300i	$-0.631161\pi$
$919$	−24.2819	−0.800987	−0.400494	+	0.916300i	$0.631161\pi$
$920$	3.02733	0.0998082
$921$	2.71881	0.0895880
$922$	−6.77129	−0.223001
$923$	−11.4757	−0.377728
$924$	−4.70522	−0.154791
$925$	3.14616	0.103445
$926$	−32.6488	−1.07291
$927$	43.2917	1.42189
$928$	3.34027	0.109650
$929$	42.3298	1.38880	0.694398	−	0.719591i	$-0.255671\pi$
$929$	42.3298	1.38880	0.694398	+	0.719591i	$0.255671\pi$
$930$	−4.06009	−0.133136
$931$	38.7234	1.26911
$932$	29.2502	0.958122
$933$	−1.75280	−0.0573841
$934$	−27.8998	−0.912909
$935$	−33.7024	−1.10219
$936$	6.36837	0.208157
$937$	35.6975	1.16619	0.583093	−	0.812406i	$-0.301842\pi$
$937$	35.6975	1.16619	0.583093	+	0.812406i	$0.301842\pi$
$938$	0.0377605	0.00123292
$939$	−18.2497	−0.595558
$940$	9.23464	0.301201
$941$	40.9159	1.33382	0.666910	−	0.745138i	$-0.267616\pi$
$941$	40.9159	1.33382	0.666910	+	0.745138i	$0.267616\pi$
$942$	−3.41380	−0.111228
$943$	−22.9092	−0.746025
$944$	−2.63038	−0.0856115
$945$	−4.69760	−0.152813
$946$	−0.180441	−0.00586663
$947$	2.57274	0.0836027	0.0418014	−	0.999126i	$-0.486690\pi$
$947$	2.57274	0.0836027	0.0418014	+	0.999126i	$0.486690\pi$
$948$	−3.88078	−0.126042
$949$	−21.8844	−0.710397
$950$	−7.36781	−0.239043
$951$	16.8826	0.547455
$952$	−7.94117	−0.257375
$953$	3.37006	0.109167	0.0545834	−	0.998509i	$-0.482617\pi$
$953$	3.37006	0.109167	0.0545834	+	0.998509i	$0.482617\pi$
$954$	−1.24073	−0.0401700
$955$	−17.2485	−0.558147
$956$	−5.46265	−0.176675
$957$	11.9003	0.384681
$958$	31.7647	1.02627
$959$	−8.90792	−0.287652
$960$	−0.635616	−0.0205144
$961$	9.80201	0.316194
$962$	−7.71801	−0.248839
$963$	−8.28568	−0.267002
$964$	14.8866	0.479467
$965$	3.38214	0.108875
$966$	2.54132	0.0817656
$967$	13.6082	0.437611	0.218805	−	0.975769i	$-0.429784\pi$
$967$	13.6082	0.437611	0.218805	+	0.975769i	$0.429784\pi$
$968$	20.4168	0.656222
$969$	28.1587	0.904589
$970$	13.3166	0.427570
$971$	−27.2377	−0.874101	−0.437050	−	0.899437i	$-0.643977\pi$
$971$	−27.2377	−0.874101	−0.437050	+	0.899437i	$0.643977\pi$
$972$	−14.1838	−0.454947
$973$	−15.2439	−0.488699
$974$	−29.9605	−0.959995
$975$	1.55926	0.0499364
$976$	10.4867	0.335671
$977$	−46.7936	−1.49706	−0.748531	−	0.663100i	$-0.769240\pi$
$977$	−46.7936	−1.49706	−0.748531	+	0.663100i	$0.769240\pi$
$978$	0.0895768	0.00286435
$979$	66.1158	2.11307
$980$	−5.25575	−0.167889
$981$	−44.2950	−1.41423
$982$	29.4434	0.939576
$983$	28.0847	0.895763	0.447881	−	0.894093i	$-0.352179\pi$
$983$	28.0847	0.895763	0.447881	+	0.894093i	$0.352179\pi$
$984$	4.80999	0.153337
$985$	−24.3352	−0.775383
$986$	20.0845	0.639621
$987$	7.75210	0.246752
$988$	18.0744	0.575022
$989$	0.0974570	0.00309895
$990$	14.5507	0.462452
$991$	35.1536	1.11669	0.558345	−	0.829609i	$-0.311437\pi$
$991$	35.1536	1.11669	0.558345	+	0.829609i	$0.311437\pi$
$992$	6.38765	0.202808
$993$	−20.6305	−0.654690
$994$	−6.17818	−0.195960
$995$	−21.9937	−0.697248
$996$	−9.48422	−0.300519
$997$	−13.6030	−0.430813	−0.215406	−	0.976524i	$-0.569108\pi$
$997$	−13.6030	−0.430813	−0.215406	+	0.976524i	$0.569108\pi$
$998$	20.6441	0.653476
$999$	11.1906	0.354054

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6010.2.a.j.1.13	✓	33

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6010.2.a.j.1.13	✓	33	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:	\( N \)	\(=\)	\( 6010 = 2 \cdot 5 \cdot 601 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6010.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -0.635616 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.635616 q^{6} -1.32070 q^{7} +1.00000 q^{8} -2.59599 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -0.635616 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.635616 q^{6} -1.32070 q^{7} +1.00000 q^{8} -2.59599 q^{9} +1.00000 q^{10} -5.60507 q^{11} -0.635616 q^{12} -2.45315 q^{13} -1.32070 q^{14} -0.635616 q^{15} +1.00000 q^{16} +6.01284 q^{17} -2.59599 q^{18} -7.36781 q^{19} +1.00000 q^{20} +0.839458 q^{21} -5.60507 q^{22} +3.02733 q^{23} -0.635616 q^{24} +1.00000 q^{25} -2.45315 q^{26} +3.55690 q^{27} -1.32070 q^{28} +3.34027 q^{29} -0.635616 q^{30} +6.38765 q^{31} +1.00000 q^{32} +3.56267 q^{33} +6.01284 q^{34} -1.32070 q^{35} -2.59599 q^{36} +3.14616 q^{37} -7.36781 q^{38} +1.55926 q^{39} +1.00000 q^{40} -7.56744 q^{41} +0.839458 q^{42} +0.0321924 q^{43} -5.60507 q^{44} -2.59599 q^{45} +3.02733 q^{46} +9.23464 q^{47} -0.635616 q^{48} -5.25575 q^{49} +1.00000 q^{50} -3.82186 q^{51} -2.45315 q^{52} +0.477940 q^{53} +3.55690 q^{54} -5.60507 q^{55} -1.32070 q^{56} +4.68310 q^{57} +3.34027 q^{58} -2.63038 q^{59} -0.635616 q^{60} +10.4867 q^{61} +6.38765 q^{62} +3.42853 q^{63} +1.00000 q^{64} -2.45315 q^{65} +3.56267 q^{66} -0.0285912 q^{67} +6.01284 q^{68} -1.92422 q^{69} -1.32070 q^{70} +4.67795 q^{71} -2.59599 q^{72} +8.92092 q^{73} +3.14616 q^{74} -0.635616 q^{75} -7.36781 q^{76} +7.40262 q^{77} +1.55926 q^{78} +6.10555 q^{79} +1.00000 q^{80} +5.52716 q^{81} -7.56744 q^{82} +14.9213 q^{83} +0.839458 q^{84} +6.01284 q^{85} +0.0321924 q^{86} -2.12313 q^{87} -5.60507 q^{88} -11.7957 q^{89} -2.59599 q^{90} +3.23988 q^{91} +3.02733 q^{92} -4.06009 q^{93} +9.23464 q^{94} -7.36781 q^{95} -0.635616 q^{96} +13.3166 q^{97} -5.25575 q^{98} +14.5507 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 33 q + 33 q^{2} + 6 q^{3} + 33 q^{4} + 33 q^{5} + 6 q^{6} + 4 q^{7} + 33 q^{8} + 49 q^{9}+O(q^{10}) \) 33 * q + 33 * q^2 + 6 * q^3 + 33 * q^4 + 33 * q^5 + 6 * q^6 + 4 * q^7 + 33 * q^8 + 49 * q^9	\( 33 q + 33 q^{2} + 6 q^{3} + 33 q^{4} + 33 q^{5} + 6 q^{6} + 4 q^{7} + 33 q^{8} + 49 q^{9} + 33 q^{10} + 12 q^{11} + 6 q^{12} + 20 q^{13} + 4 q^{14} + 6 q^{15} + 33 q^{16} + 33 q^{17} + 49 q^{18} + 17 q^{19} + 33 q^{20} + 26 q^{21} + 12 q^{22} + 7 q^{23} + 6 q^{24} + 33 q^{25} + 20 q^{26} + 21 q^{27} + 4 q^{28} + 33 q^{29} + 6 q^{30} + 35 q^{31} + 33 q^{32} + 25 q^{33} + 33 q^{34} + 4 q^{35} + 49 q^{36} + 16 q^{37} + 17 q^{38} + 22 q^{39} + 33 q^{40} + 39 q^{41} + 26 q^{42} - 3 q^{43} + 12 q^{44} + 49 q^{45} + 7 q^{46} + 19 q^{47} + 6 q^{48} + 69 q^{49} + 33 q^{50} + 21 q^{51} + 20 q^{52} + 41 q^{53} + 21 q^{54} + 12 q^{55} + 4 q^{56} + 33 q^{58} + 18 q^{59} + 6 q^{60} + 30 q^{61} + 35 q^{62} - 15 q^{63} + 33 q^{64} + 20 q^{65} + 25 q^{66} - 9 q^{67} + 33 q^{68} + 23 q^{69} + 4 q^{70} + 36 q^{71} + 49 q^{72} + 35 q^{73} + 16 q^{74} + 6 q^{75} + 17 q^{76} + 26 q^{77} + 22 q^{78} + 32 q^{79} + 33 q^{80} + 53 q^{81} + 39 q^{82} + 24 q^{83} + 26 q^{84} + 33 q^{85} - 3 q^{86} + 12 q^{87} + 12 q^{88} + 40 q^{89} + 49 q^{90} + 5 q^{91} + 7 q^{92} + 18 q^{93} + 19 q^{94} + 17 q^{95} + 6 q^{96} + 39 q^{97} + 69 q^{98} + 3 q^{99}+O(q^{100}) \) 33 * q + 33 * q^2 + 6 * q^3 + 33 * q^4 + 33 * q^5 + 6 * q^6 + 4 * q^7 + 33 * q^8 + 49 * q^9 + 33 * q^10 + 12 * q^11 + 6 * q^12 + 20 * q^13 + 4 * q^14 + 6 * q^15 + 33 * q^16 + 33 * q^17 + 49 * q^18 + 17 * q^19 + 33 * q^20 + 26 * q^21 + 12 * q^22 + 7 * q^23 + 6 * q^24 + 33 * q^25 + 20 * q^26 + 21 * q^27 + 4 * q^28 + 33 * q^29 + 6 * q^30 + 35 * q^31 + 33 * q^32 + 25 * q^33 + 33 * q^34 + 4 * q^35 + 49 * q^36 + 16 * q^37 + 17 * q^38 + 22 * q^39 + 33 * q^40 + 39 * q^41 + 26 * q^42 - 3 * q^43 + 12 * q^44 + 49 * q^45 + 7 * q^46 + 19 * q^47 + 6 * q^48 + 69 * q^49 + 33 * q^50 + 21 * q^51 + 20 * q^52 + 41 * q^53 + 21 * q^54 + 12 * q^55 + 4 * q^56 + 33 * q^58 + 18 * q^59 + 6 * q^60 + 30 * q^61 + 35 * q^62 - 15 * q^63 + 33 * q^64 + 20 * q^65 + 25 * q^66 - 9 * q^67 + 33 * q^68 + 23 * q^69 + 4 * q^70 + 36 * q^71 + 49 * q^72 + 35 * q^73 + 16 * q^74 + 6 * q^75 + 17 * q^76 + 26 * q^77 + 22 * q^78 + 32 * q^79 + 33 * q^80 + 53 * q^81 + 39 * q^82 + 24 * q^83 + 26 * q^84 + 33 * q^85 - 3 * q^86 + 12 * q^87 + 12 * q^88 + 40 * q^89 + 49 * q^90 + 5 * q^91 + 7 * q^92 + 18 * q^93 + 19 * q^94 + 17 * q^95 + 6 * q^96 + 39 * q^97 + 69 * q^98 + 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more