LMFDB - Embedded newform 6037.2.a.a.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6037,2,Mod(1,6037)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6037, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("6037.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6037 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6037.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:	$48.2056877002$
Analytic rank:	$1$
Dimension:	$243$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	6037.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.79471 q^{2} +3.05349 q^{3} +5.81042 q^{4} -2.55663 q^{5} -8.53363 q^{6} +4.45243 q^{7} -10.6490 q^{8} +6.32380 q^{9} +O(q^{10})$	\(q-2.79471 q^{2} +3.05349 q^{3} +5.81042 q^{4} -2.55663 q^{5} -8.53363 q^{6} +4.45243 q^{7} -10.6490 q^{8} +6.32380 q^{9} +7.14505 q^{10} -5.50709 q^{11} +17.7421 q^{12} -2.38269 q^{13} -12.4433 q^{14} -7.80664 q^{15} +18.1402 q^{16} +7.76504 q^{17} -17.6732 q^{18} -6.42314 q^{19} -14.8551 q^{20} +13.5954 q^{21} +15.3907 q^{22} -2.23674 q^{23} -32.5167 q^{24} +1.53636 q^{25} +6.65894 q^{26} +10.1492 q^{27} +25.8705 q^{28} -6.13576 q^{29} +21.8173 q^{30} +2.87212 q^{31} -29.3985 q^{32} -16.8158 q^{33} -21.7011 q^{34} -11.3832 q^{35} +36.7439 q^{36} +3.31673 q^{37} +17.9508 q^{38} -7.27553 q^{39} +27.2256 q^{40} -8.62516 q^{41} -37.9954 q^{42} -6.18188 q^{43} -31.9985 q^{44} -16.1676 q^{45} +6.25105 q^{46} +1.29486 q^{47} +55.3908 q^{48} +12.8241 q^{49} -4.29368 q^{50} +23.7105 q^{51} -13.8445 q^{52} +3.38940 q^{53} -28.3641 q^{54} +14.0796 q^{55} -47.4141 q^{56} -19.6130 q^{57} +17.1477 q^{58} +2.04515 q^{59} -45.3599 q^{60} -13.0614 q^{61} -8.02676 q^{62} +28.1563 q^{63} +45.8800 q^{64} +6.09166 q^{65} +46.9954 q^{66} -1.23788 q^{67} +45.1182 q^{68} -6.82987 q^{69} +31.8128 q^{70} -11.1513 q^{71} -67.3424 q^{72} -2.02579 q^{73} -9.26931 q^{74} +4.69126 q^{75} -37.3211 q^{76} -24.5199 q^{77} +20.3330 q^{78} -0.150445 q^{79} -46.3777 q^{80} +12.0190 q^{81} +24.1049 q^{82} +2.71466 q^{83} +78.9952 q^{84} -19.8523 q^{85} +17.2766 q^{86} -18.7355 q^{87} +58.6452 q^{88} -15.8644 q^{89} +45.1838 q^{90} -10.6088 q^{91} -12.9964 q^{92} +8.76999 q^{93} -3.61877 q^{94} +16.4216 q^{95} -89.7679 q^{96} -1.68753 q^{97} -35.8397 q^{98} -34.8257 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 243 q - 47 q^{2} - 31 q^{3} + 229 q^{4} - 40 q^{5} - 18 q^{6} - 42 q^{7} - 135 q^{8} + 214 q^{9}+O(q^{10}) $ 243 * q - 47 * q^2 - 31 * q^3 + 229 * q^4 - 40 * q^5 - 18 * q^6 - 42 * q^7 - 135 * q^8 + 214 * q^9	\( 243 q - 47 q^{2} - 31 q^{3} + 229 q^{4} - 40 q^{5} - 18 q^{6} - 42 q^{7} - 135 q^{8} + 214 q^{9} - 14 q^{10} - 112 q^{11} - 54 q^{12} - 45 q^{13} - 35 q^{14} - 56 q^{15} + 213 q^{16} - 71 q^{17} - 135 q^{18} - 69 q^{19} - 107 q^{20} - 36 q^{21} - 24 q^{22} - 162 q^{23} - 57 q^{24} + 203 q^{25} - 55 q^{26} - 115 q^{27} - 87 q^{28} - 76 q^{29} - 64 q^{30} - 35 q^{31} - 302 q^{32} - 77 q^{33} - 9 q^{34} - 264 q^{35} + 173 q^{36} - 61 q^{37} - 71 q^{38} - 123 q^{39} - 16 q^{40} - 74 q^{41} - 70 q^{42} - 178 q^{43} - 209 q^{44} - 107 q^{45} - 11 q^{46} - 191 q^{47} - 65 q^{48} + 211 q^{49} - 188 q^{50} - 175 q^{51} - 95 q^{52} - 122 q^{53} - 36 q^{54} - 47 q^{55} - 69 q^{56} - 103 q^{57} - 37 q^{58} - 212 q^{59} - 79 q^{60} - 14 q^{61} - 152 q^{62} - 203 q^{63} + 217 q^{64} - 159 q^{65} + 5 q^{66} - 202 q^{67} - 176 q^{68} - 34 q^{69} + 45 q^{70} - 170 q^{71} - 347 q^{72} - 57 q^{73} - 68 q^{74} - 124 q^{75} - 74 q^{76} - 166 q^{77} - 63 q^{78} - 48 q^{79} - 222 q^{80} + 159 q^{81} - 27 q^{82} - 434 q^{83} - 52 q^{84} - 57 q^{85} - 77 q^{86} - 184 q^{87} - 15 q^{88} - 62 q^{89} - 24 q^{90} - 81 q^{91} - 330 q^{92} - 164 q^{93} + 40 q^{94} - 182 q^{95} - 66 q^{96} - 21 q^{97} - 254 q^{98} - 306 q^{99}+O(q^{100}) \) 243 * q - 47 * q^2 - 31 * q^3 + 229 * q^4 - 40 * q^5 - 18 * q^6 - 42 * q^7 - 135 * q^8 + 214 * q^9 - 14 * q^10 - 112 * q^11 - 54 * q^12 - 45 * q^13 - 35 * q^14 - 56 * q^15 + 213 * q^16 - 71 * q^17 - 135 * q^18 - 69 * q^19 - 107 * q^20 - 36 * q^21 - 24 * q^22 - 162 * q^23 - 57 * q^24 + 203 * q^25 - 55 * q^26 - 115 * q^27 - 87 * q^28 - 76 * q^29 - 64 * q^30 - 35 * q^31 - 302 * q^32 - 77 * q^33 - 9 * q^34 - 264 * q^35 + 173 * q^36 - 61 * q^37 - 71 * q^38 - 123 * q^39 - 16 * q^40 - 74 * q^41 - 70 * q^42 - 178 * q^43 - 209 * q^44 - 107 * q^45 - 11 * q^46 - 191 * q^47 - 65 * q^48 + 211 * q^49 - 188 * q^50 - 175 * q^51 - 95 * q^52 - 122 * q^53 - 36 * q^54 - 47 * q^55 - 69 * q^56 - 103 * q^57 - 37 * q^58 - 212 * q^59 - 79 * q^60 - 14 * q^61 - 152 * q^62 - 203 * q^63 + 217 * q^64 - 159 * q^65 + 5 * q^66 - 202 * q^67 - 176 * q^68 - 34 * q^69 + 45 * q^70 - 170 * q^71 - 347 * q^72 - 57 * q^73 - 68 * q^74 - 124 * q^75 - 74 * q^76 - 166 * q^77 - 63 * q^78 - 48 * q^79 - 222 * q^80 + 159 * q^81 - 27 * q^82 - 434 * q^83 - 52 * q^84 - 57 * q^85 - 77 * q^86 - 184 * q^87 - 15 * q^88 - 62 * q^89 - 24 * q^90 - 81 * q^91 - 330 * q^92 - 164 * q^93 + 40 * q^94 - 182 * q^95 - 66 * q^96 - 21 * q^97 - 254 * q^98 - 306 * 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 $

$2$	−2.79471	−1.97616	−0.988080	−	0.153939i	$-0.950804\pi$
$2$	−2.79471	−1.97616	−0.988080	+	0.153939i	$0.950804\pi$
$3$	3.05349	1.76293	0.881466	−	0.472247i	$-0.156557\pi$
$3$	3.05349	1.76293	0.881466	+	0.472247i	$0.156557\pi$
$4$	5.81042	2.90521
$5$	−2.55663	−1.14336	−0.571680	−	0.820477i	$-0.693708\pi$
$5$	−2.55663	−1.14336	−0.571680	+	0.820477i	$0.693708\pi$
$6$	−8.53363	−3.48384
$7$	4.45243	1.68286	0.841430	−	0.540367i	$-0.181714\pi$
$7$	4.45243	1.68286	0.841430	+	0.540367i	$0.181714\pi$
$8$	−10.6490	−3.76500
$9$	6.32380	2.10793
$10$	7.14505	2.25946
$11$	−5.50709	−1.66045	−0.830225	−	0.557429i	$-0.811788\pi$
$11$	−5.50709	−1.66045	−0.830225	+	0.557429i	$0.811788\pi$
$12$	17.7421	5.12169
$13$	−2.38269	−0.660840	−0.330420	−	0.943834i	$-0.607190\pi$
$13$	−2.38269	−0.660840	−0.330420	+	0.943834i	$0.607190\pi$
$14$	−12.4433	−3.32560
$15$	−7.80664	−2.01567
$16$	18.1402	4.53504
$17$	7.76504	1.88330	0.941650	−	0.336595i	$-0.109275\pi$
$17$	7.76504	1.88330	0.941650	+	0.336595i	$0.109275\pi$
$18$	−17.6732	−4.16561
$19$	−6.42314	−1.47357	−0.736785	−	0.676128i	$-0.763657\pi$
$19$	−6.42314	−1.47357	−0.736785	+	0.676128i	$0.763657\pi$
$20$	−14.8551	−3.32170
$21$	13.5954	2.96677
$22$	15.3907	3.28131
$23$	−2.23674	−0.466393	−0.233196	−	0.972430i	$-0.574918\pi$
$23$	−2.23674	−0.466393	−0.233196	+	0.972430i	$0.574918\pi$
$24$	−32.5167	−6.63745
$25$	1.53636	0.307272
$26$	6.65894	1.30593
$27$	10.1492	1.95321
$28$	25.8705	4.88906
$29$	−6.13576	−1.13938	−0.569691	−	0.821859i	$-0.692937\pi$
$29$	−6.13576	−1.13938	−0.569691	+	0.821859i	$0.692937\pi$
$30$	21.8173	3.98328
$31$	2.87212	0.515848	0.257924	−	0.966165i	$-0.416962\pi$
$31$	2.87212	0.515848	0.257924	+	0.966165i	$0.416962\pi$
$32$	−29.3985	−5.19696
$33$	−16.8158	−2.92726
$34$	−21.7011	−3.72170
$35$	−11.3832	−1.92411
$36$	36.7439	6.12399
$37$	3.31673	0.545267	0.272634	−	0.962118i	$-0.412105\pi$
$37$	3.31673	0.545267	0.272634	+	0.962118i	$0.412105\pi$
$38$	17.9508	2.91201
$39$	−7.27553	−1.16502
$40$	27.2256	4.30475
$41$	−8.62516	−1.34702	−0.673512	−	0.739176i	$-0.735215\pi$
$41$	−8.62516	−1.34702	−0.673512	+	0.739176i	$0.735215\pi$
$42$	−37.9954	−5.86281
$43$	−6.18188	−0.942728	−0.471364	−	0.881939i	$-0.656238\pi$
$43$	−6.18188	−0.942728	−0.471364	+	0.881939i	$0.656238\pi$
$44$	−31.9985	−4.82396
$45$	−16.1676	−2.41013
$46$	6.25105	0.921667
$47$	1.29486	0.188875	0.0944375	−	0.995531i	$-0.469895\pi$
$47$	1.29486	0.188875	0.0944375	+	0.995531i	$0.469895\pi$
$48$	55.3908	7.99497
$49$	12.8241	1.83202
$50$	−4.29368	−0.607218
$51$	23.7105	3.32013
$52$	−13.8445	−1.91988
$53$	3.38940	0.465570	0.232785	−	0.972528i	$-0.425216\pi$
$53$	3.38940	0.465570	0.232785	+	0.972528i	$0.425216\pi$
$54$	−28.3641	−3.85986
$55$	14.0796	1.89849
$56$	−47.4141	−6.33597
$57$	−19.6130	−2.59780
$58$	17.1477	2.25160
$59$	2.04515	0.266256	0.133128	−	0.991099i	$-0.457498\pi$
$59$	2.04515	0.266256	0.133128	+	0.991099i	$0.457498\pi$
$60$	−45.3599	−5.85594
$61$	−13.0614	−1.67234	−0.836171	−	0.548469i	$-0.815211\pi$
$61$	−13.0614	−1.67234	−0.836171	+	0.548469i	$0.815211\pi$
$62$	−8.02676	−1.01940
$63$	28.1563	3.54735
$64$	45.8800	5.73500
$65$	6.09166	0.755578
$66$	46.9954	5.78474
$67$	−1.23788	−0.151231	−0.0756155	−	0.997137i	$-0.524092\pi$
$67$	−1.23788	−0.151231	−0.0756155	+	0.997137i	$0.524092\pi$
$68$	45.1182	5.47138
$69$	−6.82987	−0.822219
$70$	31.8128	3.80236
$71$	−11.1513	−1.32342	−0.661710	−	0.749760i	$-0.730169\pi$
$71$	−11.1513	−1.32342	−0.661710	+	0.749760i	$0.730169\pi$
$72$	−67.3424	−7.93637
$73$	−2.02579	−0.237101	−0.118550	−	0.992948i	$-0.537825\pi$
$73$	−2.02579	−0.237101	−0.118550	+	0.992948i	$0.537825\pi$
$74$	−9.26931	−1.07754
$75$	4.69126	0.541700
$76$	−37.3211	−4.28103
$77$	−24.5199	−2.79430
$78$	20.3330	2.30226
$79$	−0.150445	−0.0169264	−0.00846321	−	0.999964i	$-0.502694\pi$
$79$	−0.150445	−0.0169264	−0.00846321	+	0.999964i	$0.502694\pi$
$80$	−46.3777	−5.18518
$81$	12.0190	1.33545
$82$	24.1049	2.66194
$83$	2.71466	0.297972	0.148986	−	0.988839i	$-0.452399\pi$
$83$	2.71466	0.297972	0.148986	+	0.988839i	$0.452399\pi$
$84$	78.9952	8.61909
$85$	−19.8523	−2.15329
$86$	17.2766	1.86298
$87$	−18.7355	−2.00866
$88$	58.6452	6.25160
$89$	−15.8644	−1.68163	−0.840813	−	0.541326i	$-0.817922\pi$
$89$	−15.8644	−1.68163	−0.840813	+	0.541326i	$0.817922\pi$
$90$	45.1838	4.76280
$91$	−10.6088	−1.11210
$92$	−12.9964	−1.35497
$93$	8.76999	0.909406
$94$	−3.61877	−0.373247
$95$	16.4216	1.68482
$96$	−89.7679	−9.16190
$97$	−1.68753	−0.171343	−0.0856713	−	0.996323i	$-0.527303\pi$
$97$	−1.68753	−0.171343	−0.0856713	+	0.996323i	$0.527303\pi$
$98$	−35.8397	−3.62036
$99$	−34.8257	−3.50012
$100$	8.92689	0.892689
$101$	2.06284	0.205261	0.102630	−	0.994720i	$-0.467274\pi$
$101$	2.06284	0.205261	0.102630	+	0.994720i	$0.467274\pi$
$102$	−66.2640	−6.56111
$103$	4.10930	0.404902	0.202451	−	0.979292i	$-0.435109\pi$
$103$	4.10930	0.404902	0.202451	+	0.979292i	$0.435109\pi$
$104$	25.3734	2.48806
$105$	−34.7585	−3.39208
$106$	−9.47240	−0.920041
$107$	−1.47309	−0.142409	−0.0712043	−	0.997462i	$-0.522684\pi$
$107$	−1.47309	−0.142409	−0.0712043	+	0.997462i	$0.522684\pi$
$108$	58.9710	5.67449
$109$	−4.75663	−0.455603	−0.227801	−	0.973708i	$-0.573154\pi$
$109$	−4.75663	−0.455603	−0.227801	+	0.973708i	$0.573154\pi$
$110$	−39.3484	−3.75172
$111$	10.1276	0.961269
$112$	80.7677	7.63183
$113$	7.78307	0.732170	0.366085	−	0.930581i	$-0.380698\pi$
$113$	7.78307	0.732170	0.366085	+	0.930581i	$0.380698\pi$
$114$	54.8127	5.13368
$115$	5.71852	0.533255
$116$	−35.6514	−3.31015
$117$	−15.0677	−1.39301
$118$	−5.71562	−0.526165
$119$	34.5733	3.16933
$120$	83.1332	7.58899
$121$	19.3280	1.75709
$122$	36.5029	3.30482
$123$	−26.3368	−2.37471
$124$	16.6882	1.49865
$125$	8.85525	0.792038
$126$	−78.6887	−7.01014
$127$	5.90846	0.524291	0.262146	−	0.965028i	$-0.415570\pi$
$127$	5.90846	0.524291	0.262146	+	0.965028i	$0.415570\pi$
$128$	−69.4244	−6.13631
$129$	−18.8763	−1.66197
$130$	−17.0245	−1.49314
$131$	6.20641	0.542256	0.271128	−	0.962543i	$-0.412603\pi$
$131$	6.20641	0.542256	0.271128	+	0.962543i	$0.412603\pi$
$132$	−97.7071	−8.50431
$133$	−28.5986	−2.47981
$134$	3.45952	0.298857
$135$	−25.9477	−2.23322
$136$	−82.6902	−7.09063
$137$	16.7571	1.43165	0.715827	−	0.698277i	$-0.246050\pi$
$137$	16.7571	1.43165	0.715827	+	0.698277i	$0.246050\pi$
$138$	19.0875	1.62484
$139$	−7.42303	−0.629613	−0.314807	−	0.949156i	$-0.601940\pi$
$139$	−7.42303	−0.629613	−0.314807	+	0.949156i	$0.601940\pi$
$140$	−66.1413	−5.58996
$141$	3.95385	0.332974
$142$	31.1648	2.61529
$143$	13.1217	1.09729
$144$	114.715	9.55956
$145$	15.6869	1.30272
$146$	5.66150	0.468549
$147$	39.1583	3.22972
$148$	19.2716	1.58412
$149$	2.37313	0.194415	0.0972074	−	0.995264i	$-0.469009\pi$
$149$	2.37313	0.194415	0.0972074	+	0.995264i	$0.469009\pi$
$150$	−13.1107	−1.07049
$151$	−14.3736	−1.16971	−0.584853	−	0.811139i	$-0.698848\pi$
$151$	−14.3736	−1.16971	−0.584853	+	0.811139i	$0.698848\pi$
$152$	68.4002	5.54799
$153$	49.1045	3.96987
$154$	68.5261	5.52199
$155$	−7.34295	−0.589800
$156$	−42.2739	−3.38462
$157$	−19.2703	−1.53794	−0.768969	−	0.639286i	$-0.779230\pi$
$157$	−19.2703	−1.53794	−0.768969	+	0.639286i	$0.779230\pi$
$158$	0.420452	0.0334493
$159$	10.3495	0.820769
$160$	75.1610	5.94200
$161$	−9.95893	−0.784873
$162$	−33.5897	−2.63906
$163$	−6.33831	−0.496455	−0.248227	−	0.968702i	$-0.579848\pi$
$163$	−6.33831	−0.496455	−0.248227	+	0.968702i	$0.579848\pi$
$164$	−50.1158	−3.91339
$165$	42.9919	3.34691
$166$	−7.58669	−0.588841
$167$	−2.49176	−0.192818	−0.0964090	−	0.995342i	$-0.530736\pi$
$167$	−2.49176	−0.192818	−0.0964090	+	0.995342i	$0.530736\pi$
$168$	−144.778	−11.1699
$169$	−7.32278	−0.563290
$170$	55.4816	4.25524
$171$	−40.6186	−3.10618
$172$	−35.9193	−2.73882
$173$	12.4683	0.947948	0.473974	−	0.880539i	$-0.342819\pi$
$173$	12.4683	0.947948	0.473974	+	0.880539i	$0.342819\pi$
$174$	52.3603	3.96943
$175$	6.84053	0.517095
$176$	−99.8994	−7.53020
$177$	6.24486	0.469392
$178$	44.3365	3.32316
$179$	−0.671599	−0.0501977	−0.0250988	−	0.999685i	$-0.507990\pi$
$179$	−0.671599	−0.0501977	−0.0250988	+	0.999685i	$0.507990\pi$
$180$	−93.9407	−7.00192
$181$	−16.9166	−1.25740	−0.628702	−	0.777647i	$-0.716413\pi$
$181$	−16.9166	−1.25740	−0.628702	+	0.777647i	$0.716413\pi$
$182$	29.6485	2.19769
$183$	−39.8829	−2.94823
$184$	23.8191	1.75597
$185$	−8.47965	−0.623436
$186$	−24.5096	−1.79713
$187$	−42.7628	−3.12712
$188$	7.52369	0.548722
$189$	45.1885	3.28698
$190$	−45.8936	−3.32947
$191$	3.42216	0.247619	0.123809	−	0.992306i	$-0.460489\pi$
$191$	3.42216	0.247619	0.123809	+	0.992306i	$0.460489\pi$
$192$	140.094	10.1104
$193$	8.25933	0.594519	0.297260	−	0.954797i	$-0.403927\pi$
$193$	8.25933	0.594519	0.297260	+	0.954797i	$0.403927\pi$
$194$	4.71616	0.338600
$195$	18.6008	1.33203
$196$	74.5135	5.32239
$197$	−12.0871	−0.861173	−0.430587	−	0.902549i	$-0.641693\pi$
$197$	−12.0871	−0.861173	−0.430587	+	0.902549i	$0.641693\pi$
$198$	97.3279	6.91679
$199$	−20.8324	−1.47677	−0.738385	−	0.674379i	$-0.764411\pi$
$199$	−20.8324	−1.47677	−0.738385	+	0.674379i	$0.764411\pi$
$200$	−16.3607	−1.15688
$201$	−3.77985	−0.266610
$202$	−5.76506	−0.405628
$203$	−27.3190	−1.91742
$204$	137.768	9.64568
$205$	22.0514	1.54013
$206$	−11.4843	−0.800151
$207$	−14.1447	−0.983124
$208$	−43.2224	−2.99694
$209$	35.3728	2.44679
$210$	97.1401	6.70330
$211$	−22.3795	−1.54067	−0.770335	−	0.637640i	$-0.779911\pi$
$211$	−22.3795	−1.54067	−0.770335	+	0.637640i	$0.779911\pi$
$212$	19.6939	1.35258
$213$	−34.0505	−2.33310
$214$	4.11685	0.281422
$215$	15.8048	1.07788
$216$	−108.079	−7.35384
$217$	12.7879	0.868100
$218$	13.2934	0.900344
$219$	−6.18573	−0.417993
$220$	81.8083	5.51552
$221$	−18.5017	−1.24456
$222$	−28.3037	−1.89962
$223$	21.8650	1.46419	0.732094	−	0.681203i	$-0.238543\pi$
$223$	21.8650	1.46419	0.732094	+	0.681203i	$0.238543\pi$
$224$	−130.895	−8.74576
$225$	9.71562	0.647708
$226$	−21.7514	−1.44688
$227$	4.04431	0.268430	0.134215	−	0.990952i	$-0.457149\pi$
$227$	4.04431	0.268430	0.134215	+	0.990952i	$0.457149\pi$
$228$	−113.960	−7.54717
$229$	−2.83235	−0.187167	−0.0935835	−	0.995611i	$-0.529832\pi$
$229$	−2.83235	−0.187167	−0.0935835	+	0.995611i	$0.529832\pi$
$230$	−15.9816	−1.05380
$231$	−74.8713	−4.92617
$232$	65.3400	4.28978
$233$	−20.6243	−1.35114	−0.675572	−	0.737294i	$-0.736103\pi$
$233$	−20.6243	−1.35114	−0.675572	+	0.737294i	$0.736103\pi$
$234$	42.1098	2.75280
$235$	−3.31048	−0.215952
$236$	11.8832	0.773531
$237$	−0.459383	−0.0298402
$238$	−96.6224	−6.26310
$239$	0.705067	0.0456070	0.0228035	−	0.999740i	$-0.492741\pi$
$239$	0.705067	0.0456070	0.0228035	+	0.999740i	$0.492741\pi$
$240$	−141.614	−9.14113
$241$	−23.7523	−1.53002	−0.765010	−	0.644019i	$-0.777266\pi$
$241$	−23.7523	−1.53002	−0.765010	+	0.644019i	$0.777266\pi$
$242$	−54.0162	−3.47230
$243$	6.25242	0.401093
$244$	−75.8923	−4.85851
$245$	−32.7865	−2.09465
$246$	73.6039	4.69282
$247$	15.3044	0.973794
$248$	−30.5853	−1.94217
$249$	8.28918	0.525305
$250$	−24.7479	−1.56519
$251$	−23.2618	−1.46827	−0.734135	−	0.679004i	$-0.762412\pi$
$251$	−23.2618	−1.46827	−0.734135	+	0.679004i	$0.762412\pi$
$252$	163.600	10.3058
$253$	12.3179	0.774421
$254$	−16.5125	−1.03608
$255$	−60.6189	−3.79610
$256$	102.261	6.39134
$257$	12.4533	0.776817	0.388408	−	0.921487i	$-0.373025\pi$
$257$	12.4533	0.776817	0.388408	+	0.921487i	$0.373025\pi$
$258$	52.7538	3.28431
$259$	14.7675	0.917608
$260$	35.3951	2.19511
$261$	−38.8013	−2.40174
$262$	−17.3451	−1.07159
$263$	4.38793	0.270571	0.135286	−	0.990807i	$-0.456805\pi$
$263$	4.38793	0.270571	0.135286	+	0.990807i	$0.456805\pi$
$264$	179.072	11.0211
$265$	−8.66545	−0.532314
$266$	79.9248	4.90050
$267$	−48.4418	−2.96459
$268$	−7.19260	−0.439358
$269$	−10.8489	−0.661470	−0.330735	−	0.943724i	$-0.607297\pi$
$269$	−10.8489	−0.661470	−0.330735	+	0.943724i	$0.607297\pi$
$270$	72.5164	4.41321
$271$	9.22021	0.560088	0.280044	−	0.959987i	$-0.409651\pi$
$271$	9.22021	0.560088	0.280044	+	0.959987i	$0.409651\pi$
$272$	140.859	8.54084
$273$	−32.3938	−1.96056
$274$	−46.8313	−2.82918
$275$	−8.46086	−0.510209
$276$	−39.6844	−2.38872
$277$	−17.6343	−1.05954	−0.529771	−	0.848141i	$-0.677722\pi$
$277$	−17.6343	−1.05954	−0.529771	+	0.848141i	$0.677722\pi$
$278$	20.7452	1.24422
$279$	18.1627	1.08737
$280$	121.220	7.24429
$281$	0.129372	0.00771771	0.00385885	−	0.999993i	$-0.498772\pi$
$281$	0.129372	0.00771771	0.00385885	+	0.999993i	$0.498772\pi$
$282$	−11.0499	−0.658010
$283$	−3.27027	−0.194397	−0.0971986	−	0.995265i	$-0.530988\pi$
$283$	−3.27027	−0.194397	−0.0971986	+	0.995265i	$0.530988\pi$
$284$	−64.7940	−3.84482
$285$	50.1432	2.97022
$286$	−36.6714	−2.16842
$287$	−38.4029	−2.26685
$288$	−185.910	−10.9548
$289$	43.2959	2.54682
$290$	−43.8403	−2.57439
$291$	−5.15285	−0.302065
$292$	−11.7707	−0.688828
$293$	16.2414	0.948833	0.474416	−	0.880301i	$-0.342659\pi$
$293$	16.2414	0.948833	0.474416	+	0.880301i	$0.342659\pi$
$294$	−109.436	−6.38245
$295$	−5.22870	−0.304427
$296$	−35.3200	−2.05293
$297$	−55.8924	−3.24321
$298$	−6.63223	−0.384195
$299$	5.32947	0.308211
$300$	27.2582	1.57375
$301$	−27.5244	−1.58648
$302$	40.1701	2.31153
$303$	6.29887	0.361861
$304$	−116.517	−6.68269
$305$	33.3932	1.91209
$306$	−137.233	−7.84510
$307$	28.4901	1.62602	0.813008	−	0.582252i	$-0.197828\pi$
$307$	28.4901	1.62602	0.813008	+	0.582252i	$0.197828\pi$
$308$	−142.471	−8.11804
$309$	12.5477	0.713815
$310$	20.5214	1.16554
$311$	2.56665	0.145541	0.0727707	−	0.997349i	$-0.476816\pi$
$311$	2.56665	0.145541	0.0727707	+	0.997349i	$0.476816\pi$
$312$	77.4774	4.38629
$313$	22.5687	1.27566	0.637829	−	0.770178i	$-0.279833\pi$
$313$	22.5687	1.27566	0.637829	+	0.770178i	$0.279833\pi$
$314$	53.8550	3.03921
$315$	−71.9851	−4.05590
$316$	−0.874151	−0.0491748
$317$	21.5161	1.20847	0.604234	−	0.796807i	$-0.293479\pi$
$317$	21.5161	1.20847	0.604234	+	0.796807i	$0.293479\pi$
$318$	−28.9239	−1.62197
$319$	33.7902	1.89189
$320$	−117.298	−6.55716
$321$	−4.49805	−0.251057
$322$	27.8323	1.55104
$323$	−49.8759	−2.77517
$324$	69.8356	3.87976
$325$	−3.66067	−0.203058
$326$	17.7138	0.981075
$327$	−14.5243	−0.803197
$328$	91.8497	5.07155
$329$	5.76528	0.317850
$330$	−120.150	−6.61404
$331$	−8.45250	−0.464591	−0.232296	−	0.972645i	$-0.574624\pi$
$331$	−8.45250	−0.464591	−0.232296	+	0.972645i	$0.574624\pi$
$332$	15.7733	0.865673
$333$	20.9743	1.14939
$334$	6.96375	0.381039
$335$	3.16480	0.172911
$336$	246.623	13.4544
$337$	11.7246	0.638677	0.319339	−	0.947641i	$-0.396539\pi$
$337$	11.7246	0.638677	0.319339	+	0.947641i	$0.396539\pi$
$338$	20.4651	1.11315
$339$	23.7655	1.29077
$340$	−115.350	−6.25576
$341$	−15.8170	−0.856540
$342$	113.517	6.13832
$343$	25.9314	1.40017
$344$	65.8310	3.54937
$345$	17.4614	0.940092
$346$	−34.8454	−1.87330
$347$	−25.5799	−1.37320	−0.686599	−	0.727036i	$-0.740897\pi$
$347$	−25.5799	−1.37320	−0.686599	+	0.727036i	$0.740897\pi$
$348$	−108.861	−5.83557
$349$	6.09544	0.326281	0.163141	−	0.986603i	$-0.447838\pi$
$349$	6.09544	0.326281	0.163141	+	0.986603i	$0.447838\pi$
$350$	−19.1173	−1.02186
$351$	−24.1824	−1.29076
$352$	161.900	8.62929
$353$	10.4896	0.558306	0.279153	−	0.960247i	$-0.409946\pi$
$353$	10.4896	0.558306	0.279153	+	0.960247i	$0.409946\pi$
$354$	−17.4526	−0.927594
$355$	28.5098	1.51315
$356$	−92.1790	−4.88548
$357$	105.569	5.58731
$358$	1.87693	0.0991986
$359$	−14.3166	−0.755599	−0.377799	−	0.925887i	$-0.623319\pi$
$359$	−14.3166	−0.755599	−0.377799	+	0.925887i	$0.623319\pi$
$360$	172.170	9.07413
$361$	22.2567	1.17141
$362$	47.2771	2.48483
$363$	59.0179	3.09763
$364$	−61.6414	−3.23089
$365$	5.17920	0.271092
$366$	111.461	5.82617
$367$	−23.5470	−1.22914	−0.614572	−	0.788861i	$-0.710671\pi$
$367$	−23.5470	−1.22914	−0.614572	+	0.788861i	$0.710671\pi$
$368$	−40.5748	−2.11511
$369$	−54.5438	−2.83944
$370$	23.6982	1.23201
$371$	15.0911	0.783489
$372$	50.9574	2.64202
$373$	10.9076	0.564772	0.282386	−	0.959301i	$-0.408874\pi$
$373$	10.9076	0.564772	0.282386	+	0.959301i	$0.408874\pi$
$374$	119.510	6.17970
$375$	27.0394	1.39631
$376$	−13.7890	−0.711115
$377$	14.6196	0.752950
$378$	−126.289	−6.49560
$379$	0.878344	0.0451175	0.0225588	−	0.999746i	$-0.492819\pi$
$379$	0.878344	0.0451175	0.0225588	+	0.999746i	$0.492819\pi$
$380$	95.4164	4.89476
$381$	18.0414	0.924290
$382$	−9.56395	−0.489334
$383$	−19.9978	−1.02184	−0.510919	−	0.859629i	$-0.670695\pi$
$383$	−19.9978	−1.02184	−0.510919	+	0.859629i	$0.670695\pi$
$384$	−211.987	−10.8179
$385$	62.6883	3.19489
$386$	−23.0824	−1.17487
$387$	−39.0929	−1.98721
$388$	−9.80525	−0.497786
$389$	−18.9838	−0.962515	−0.481258	−	0.876579i	$-0.659820\pi$
$389$	−18.9838	−0.962515	−0.481258	+	0.876579i	$0.659820\pi$
$390$	−51.9840	−2.63231
$391$	−17.3684	−0.878357
$392$	−136.564	−6.89755
$393$	18.9512	0.955962
$394$	33.7801	1.70182
$395$	0.384633	0.0193530
$396$	−202.352	−10.1686
$397$	−21.9326	−1.10077	−0.550383	−	0.834912i	$-0.685518\pi$
$397$	−21.9326	−1.10077	−0.550383	+	0.834912i	$0.685518\pi$
$398$	58.2206	2.91834
$399$	−87.3254	−4.37174
$400$	27.8698	1.39349
$401$	−2.40772	−0.120236	−0.0601179	−	0.998191i	$-0.519148\pi$
$401$	−2.40772	−0.120236	−0.0601179	+	0.998191i	$0.519148\pi$
$402$	10.5636	0.526864
$403$	−6.84338	−0.340893
$404$	11.9860	0.596325
$405$	−30.7282	−1.52690
$406$	76.3489	3.78913
$407$	−18.2655	−0.905388
$408$	−252.494	−12.5003
$409$	2.98964	0.147828	0.0739142	−	0.997265i	$-0.476451\pi$
$409$	2.98964	0.147828	0.0739142	+	0.997265i	$0.476451\pi$
$410$	−61.6272	−3.04355
$411$	51.1676	2.52391
$412$	23.8768	1.17632
$413$	9.10590	0.448072
$414$	39.5304	1.94281
$415$	−6.94038	−0.340690
$416$	70.0475	3.43436
$417$	−22.6661	−1.10997
$418$	−98.8568	−4.83524
$419$	−39.1411	−1.91217	−0.956083	−	0.293096i	$-0.905314\pi$
$419$	−39.1411	−1.91217	−0.956083	+	0.293096i	$0.905314\pi$
$420$	−201.962	−9.85472
$421$	37.8143	1.84296	0.921479	−	0.388428i	$-0.126982\pi$
$421$	37.8143	1.84296	0.921479	+	0.388428i	$0.126982\pi$
$422$	62.5443	3.04461
$423$	8.18844	0.398136
$424$	−36.0939	−1.75287
$425$	11.9299	0.578685
$426$	95.1614	4.61058
$427$	−58.1550	−2.81432
$428$	−8.55925	−0.413727
$429$	40.0670	1.93445
$430$	−44.1698	−2.13006
$431$	9.64942	0.464796	0.232398	−	0.972621i	$-0.425343\pi$
$431$	9.64942	0.464796	0.232398	+	0.972621i	$0.425343\pi$
$432$	184.108	8.85789
$433$	41.5005	1.99439	0.997193	−	0.0748680i	$-0.0238535\pi$
$433$	41.5005	1.99439	0.997193	+	0.0748680i	$0.0238535\pi$
$434$	−35.7385	−1.71551
$435$	47.8997	2.29662
$436$	−27.6380	−1.32362
$437$	14.3669	0.687262
$438$	17.2873	0.826021
$439$	32.1684	1.53531	0.767657	−	0.640860i	$-0.221422\pi$
$439$	32.1684	1.53531	0.767657	+	0.640860i	$0.221422\pi$
$440$	−149.934	−7.14782
$441$	81.0971	3.86177
$442$	51.7070	2.45945
$443$	34.4483	1.63669	0.818343	−	0.574730i	$-0.194893\pi$
$443$	34.4483	1.63669	0.818343	+	0.574730i	$0.194893\pi$
$444$	58.8456	2.79269
$445$	40.5595	1.92270
$446$	−61.1064	−2.89347
$447$	7.24634	0.342740
$448$	204.277	9.65119
$449$	−4.38231	−0.206814	−0.103407	−	0.994639i	$-0.532974\pi$
$449$	−4.38231	−0.206814	−0.103407	+	0.994639i	$0.532974\pi$
$450$	−27.1524	−1.27998
$451$	47.4995	2.23667
$452$	45.2229	2.12711
$453$	−43.8896	−2.06211
$454$	−11.3027	−0.530461
$455$	27.1227	1.27153
$456$	208.859	9.78074
$457$	−27.8641	−1.30343	−0.651714	−	0.758465i	$-0.725950\pi$
$457$	−27.8641	−1.30343	−0.651714	+	0.758465i	$0.725950\pi$
$458$	7.91561	0.369872
$459$	78.8088	3.67848
$460$	33.2270	1.54922
$461$	−3.75776	−0.175016	−0.0875081	−	0.996164i	$-0.527890\pi$
$461$	−3.75776	−0.175016	−0.0875081	+	0.996164i	$0.527890\pi$
$462$	209.244	9.73490
$463$	−5.55135	−0.257993	−0.128997	−	0.991645i	$-0.541176\pi$
$463$	−5.55135	−0.257993	−0.128997	+	0.991645i	$0.541176\pi$
$464$	−111.304	−5.16715
$465$	−22.4216	−1.03978
$466$	57.6390	2.67008
$467$	−1.56466	−0.0724040	−0.0362020	−	0.999344i	$-0.511526\pi$
$467$	−1.56466	−0.0724040	−0.0362020	+	0.999344i	$0.511526\pi$
$468$	−87.5495	−4.04698
$469$	−5.51157	−0.254501
$470$	9.25185	0.426756
$471$	−58.8417	−2.71128
$472$	−21.7789	−1.00246
$473$	34.0441	1.56535
$474$	1.28384	0.0589689
$475$	−9.86825	−0.452786
$476$	200.885	9.20757
$477$	21.4339	0.981390
$478$	−1.97046	−0.0901268
$479$	36.1354	1.65107	0.825535	−	0.564351i	$-0.190874\pi$
$479$	36.1354	1.65107	0.825535	+	0.564351i	$0.190874\pi$
$480$	229.503	10.4753
$481$	−7.90275	−0.360334
$482$	66.3808	3.02356
$483$	−30.4095	−1.38368
$484$	112.304	5.10472
$485$	4.31439	0.195906
$486$	−17.4737	−0.792624
$487$	−1.05771	−0.0479296	−0.0239648	−	0.999713i	$-0.507629\pi$
$487$	−1.05771	−0.0479296	−0.0239648	+	0.999713i	$0.507629\pi$
$488$	139.091	6.29637
$489$	−19.3540	−0.875217
$490$	91.6289	4.13937
$491$	18.7381	0.845638	0.422819	−	0.906214i	$-0.361041\pi$
$491$	18.7381	0.845638	0.422819	+	0.906214i	$0.361041\pi$
$492$	−153.028	−6.89904
$493$	−47.6445	−2.14580
$494$	−42.7713	−1.92437
$495$	89.0365	4.00189
$496$	52.1007	2.33939
$497$	−49.6505	−2.22713
$498$	−23.1659	−1.03809
$499$	−13.6193	−0.609682	−0.304841	−	0.952403i	$-0.598603\pi$
$499$	−13.6193	−0.609682	−0.304841	+	0.952403i	$0.598603\pi$
$500$	51.4527	2.30104
$501$	−7.60856	−0.339925
$502$	65.0100	2.90154
$503$	32.7412	1.45986	0.729930	−	0.683522i	$-0.239553\pi$
$503$	32.7412	1.45986	0.729930	+	0.683522i	$0.239553\pi$
$504$	−299.837	−13.3558
$505$	−5.27393	−0.234687
$506$	−34.4251	−1.53038
$507$	−22.3600	−0.993043
$508$	34.3306	1.52318
$509$	7.80498	0.345950	0.172975	−	0.984926i	$-0.444662\pi$
$509$	7.80498	0.345950	0.172975	+	0.984926i	$0.444662\pi$
$510$	169.412	7.50171
$511$	−9.01968	−0.399007
$512$	−146.942	−6.49400
$513$	−65.1896	−2.87819
$514$	−34.8035	−1.53511
$515$	−10.5060	−0.462948
$516$	−109.679	−4.82836
$517$	−7.13092	−0.313617
$518$	−41.2709	−1.81334
$519$	38.0719	1.67117
$520$	−64.8704	−2.84475
$521$	−14.7997	−0.648387	−0.324193	−	0.945991i	$-0.605093\pi$
$521$	−14.7997	−0.648387	−0.324193	+	0.945991i	$0.605093\pi$
$522$	108.439	4.74623
$523$	−2.47310	−0.108141	−0.0540706	−	0.998537i	$-0.517220\pi$
$523$	−2.47310	−0.108141	−0.0540706	+	0.998537i	$0.517220\pi$
$524$	36.0619	1.57537
$525$	20.8875	0.911604
$526$	−12.2630	−0.534693
$527$	22.3021	0.971496
$528$	−305.042	−13.2752
$529$	−17.9970	−0.782478
$530$	24.2174	1.05194
$531$	12.9331	0.561251
$532$	−166.170	−7.20437
$533$	20.5511	0.890168
$534$	135.381	5.85851
$535$	3.76614	0.162824
$536$	13.1822	0.569385
$537$	−2.05072	−0.0884951
$538$	30.3196	1.30717
$539$	−70.6235	−3.04197
$540$	−150.767	−6.48798
$541$	19.9374	0.857174	0.428587	−	0.903501i	$-0.359012\pi$
$541$	19.9374	0.857174	0.428587	+	0.903501i	$0.359012\pi$
$542$	−25.7678	−1.10682
$543$	−51.6547	−2.21672
$544$	−228.280	−9.78744
$545$	12.1609	0.520918
$546$	90.5313	3.87438
$547$	43.3836	1.85495	0.927474	−	0.373888i	$-0.121976\pi$
$547$	43.3836	1.85495	0.927474	+	0.373888i	$0.121976\pi$
$548$	97.3658	4.15926
$549$	−82.5977	−3.52518
$550$	23.6457	1.00826
$551$	39.4109	1.67896
$552$	72.7315	3.09566
$553$	−0.669847	−0.0284848
$554$	49.2828	2.09382
$555$	−25.8925	−1.09908
$556$	−43.1309	−1.82916
$557$	−10.1887	−0.431710	−0.215855	−	0.976425i	$-0.569254\pi$
$557$	−10.1887	−0.431710	−0.215855	+	0.976425i	$0.569254\pi$
$558$	−50.7596	−2.14882
$559$	14.7295	0.622992
$560$	−206.493	−8.72593
$561$	−130.576	−5.51291
$562$	−0.361559	−0.0152514
$563$	−10.1584	−0.428125	−0.214063	−	0.976820i	$-0.568670\pi$
$563$	−10.1584	−0.428125	−0.214063	+	0.976820i	$0.568670\pi$
$564$	22.9735	0.967360
$565$	−19.8984	−0.837133
$566$	9.13946	0.384160
$567$	53.5138	2.24737
$568$	118.751	4.98268
$569$	−4.71026	−0.197464	−0.0987322	−	0.995114i	$-0.531479\pi$
$569$	−4.71026	−0.197464	−0.0987322	+	0.995114i	$0.531479\pi$
$570$	−140.136	−5.86964
$571$	−20.8126	−0.870979	−0.435489	−	0.900194i	$-0.643425\pi$
$571$	−20.8126	−0.870979	−0.435489	+	0.900194i	$0.643425\pi$
$572$	76.2426	3.18786
$573$	10.4495	0.436535
$574$	107.325	4.47966
$575$	−3.43644	−0.143309
$576$	290.136	12.0890
$577$	17.6467	0.734640	0.367320	−	0.930095i	$-0.380275\pi$
$577$	17.6467	0.734640	0.367320	+	0.930095i	$0.380275\pi$
$578$	−121.000	−5.03292
$579$	25.2198	1.04810
$580$	91.1474	3.78469
$581$	12.0868	0.501446
$582$	14.4007	0.596930
$583$	−18.6657	−0.773056
$584$	21.5727	0.892685
$585$	38.5225	1.59271
$586$	−45.3900	−1.87505
$587$	−33.9244	−1.40021	−0.700105	−	0.714040i	$-0.746863\pi$
$587$	−33.9244	−1.40021	−0.700105	+	0.714040i	$0.746863\pi$
$588$	227.526	9.38302
$589$	−18.4480	−0.760138
$590$	14.6127	0.601597
$591$	−36.9080	−1.51819
$592$	60.1660	2.47281
$593$	−21.0921	−0.866150	−0.433075	−	0.901358i	$-0.642572\pi$
$593$	−21.0921	−0.866150	−0.433075	+	0.901358i	$0.642572\pi$
$594$	156.203	6.40910
$595$	−88.3911	−3.62368
$596$	13.7889	0.564816
$597$	−63.6116	−2.60345
$598$	−14.8943	−0.609074
$599$	5.52094	0.225580	0.112790	−	0.993619i	$-0.464021\pi$
$599$	5.52094	0.225580	0.112790	+	0.993619i	$0.464021\pi$
$600$	−49.9574	−2.03950
$601$	−12.5474	−0.511819	−0.255909	−	0.966701i	$-0.582375\pi$
$601$	−12.5474	−0.511819	−0.255909	+	0.966701i	$0.582375\pi$
$602$	76.9227	3.13514
$603$	−7.82810	−0.318785
$604$	−83.5166	−3.39824
$605$	−49.4146	−2.00899
$606$	−17.6035	−0.715095
$607$	−18.2380	−0.740256	−0.370128	−	0.928981i	$-0.620686\pi$
$607$	−18.2380	−0.740256	−0.370128	+	0.928981i	$0.620686\pi$
$608$	188.830	7.65809
$609$	−83.4184	−3.38029
$610$	−93.3244	−3.77859
$611$	−3.08526	−0.124816
$612$	285.318	11.5333
$613$	35.4235	1.43074	0.715371	−	0.698745i	$-0.246258\pi$
$613$	35.4235	1.43074	0.715371	+	0.698745i	$0.246258\pi$
$614$	−79.6217	−3.21327
$615$	67.3336	2.71515
$616$	261.113	10.5206
$617$	38.4560	1.54818	0.774091	−	0.633074i	$-0.218207\pi$
$617$	38.4560	1.54818	0.774091	+	0.633074i	$0.218207\pi$
$618$	−35.0673	−1.41061
$619$	1.29268	0.0519570	0.0259785	−	0.999663i	$-0.491730\pi$
$619$	1.29268	0.0519570	0.0259785	+	0.999663i	$0.491730\pi$
$620$	−42.6657	−1.71349
$621$	−22.7011	−0.910963
$622$	−7.17305	−0.287613
$623$	−70.6352	−2.82994
$624$	−131.979	−5.28340
$625$	−30.3214	−1.21286
$626$	−63.0730	−2.52090
$627$	108.010	4.31352
$628$	−111.969	−4.46804
$629$	25.7545	1.02690
$630$	201.178	8.01512
$631$	−18.6172	−0.741138	−0.370569	−	0.928805i	$-0.620837\pi$
$631$	−18.6172	−0.741138	−0.370569	+	0.928805i	$0.620837\pi$
$632$	1.60210	0.0637281
$633$	−68.3356	−2.71610
$634$	−60.1315	−2.38813
$635$	−15.1057	−0.599453
$636$	60.1350	2.38451
$637$	−30.5559	−1.21067
$638$	−94.4339	−3.73867
$639$	−70.5188	−2.78968
$640$	177.493	7.01601
$641$	30.8513	1.21855	0.609276	−	0.792958i	$-0.291460\pi$
$641$	30.8513	1.21855	0.609276	+	0.792958i	$0.291460\pi$
$642$	12.5708	0.496129
$643$	36.7154	1.44792	0.723958	−	0.689844i	$-0.242321\pi$
$643$	36.7154	1.44792	0.723958	+	0.689844i	$0.242321\pi$
$644$	−57.8656	−2.28022
$645$	48.2597	1.90022
$646$	139.389	5.48418
$647$	−45.7503	−1.79863	−0.899315	−	0.437301i	$-0.855935\pi$
$647$	−45.7503	−1.79863	−0.899315	+	0.437301i	$0.855935\pi$
$648$	−127.991	−5.02796
$649$	−11.2628	−0.442105
$650$	10.2305	0.401274
$651$	39.0478	1.53040
$652$	−36.8283	−1.44231
$653$	−6.46236	−0.252892	−0.126446	−	0.991974i	$-0.540357\pi$
$653$	−6.46236	−0.252892	−0.126446	+	0.991974i	$0.540357\pi$
$654$	40.5913	1.58725
$655$	−15.8675	−0.619994
$656$	−156.462	−6.10881
$657$	−12.8107	−0.499793
$658$	−16.1123	−0.628123
$659$	22.2984	0.868623	0.434312	−	0.900763i	$-0.356992\pi$
$659$	22.2984	0.868623	0.434312	+	0.900763i	$0.356992\pi$
$660$	249.801	9.72349
$661$	18.3372	0.713233	0.356616	−	0.934251i	$-0.383930\pi$
$661$	18.3372	0.713233	0.356616	+	0.934251i	$0.383930\pi$
$662$	23.6223	0.918107
$663$	−56.4948	−2.19407
$664$	−28.9085	−1.12187
$665$	73.1160	2.83532
$666$	−58.6172	−2.27137
$667$	13.7241	0.531400
$668$	−14.4782	−0.560177
$669$	66.7645	2.58127
$670$	−8.84471	−0.341701
$671$	71.9303	2.77684
$672$	−399.685	−15.4182
$673$	−28.9269	−1.11505	−0.557524	−	0.830161i	$-0.688249\pi$
$673$	−28.9269	−1.11505	−0.557524	+	0.830161i	$0.688249\pi$
$674$	−32.7668	−1.26213
$675$	15.5928	0.600167
$676$	−42.5484	−1.63648
$677$	19.6307	0.754470	0.377235	−	0.926118i	$-0.376875\pi$
$677$	19.6307	0.754470	0.377235	+	0.926118i	$0.376875\pi$
$678$	−66.4178	−2.55076
$679$	−7.51360	−0.288345
$680$	211.408	8.10714
$681$	12.3492	0.473224
$682$	44.2040	1.69266
$683$	−39.4635	−1.51003	−0.755015	−	0.655708i	$-0.772370\pi$
$683$	−39.4635	−1.51003	−0.755015	+	0.655708i	$0.772370\pi$
$684$	−236.011	−9.02412
$685$	−42.8417	−1.63690
$686$	−72.4709	−2.76695
$687$	−8.64855	−0.329963
$688$	−112.140	−4.27531
$689$	−8.07590	−0.307667
$690$	−48.7997	−1.85777
$691$	−23.3292	−0.887484	−0.443742	−	0.896155i	$-0.646349\pi$
$691$	−23.3292	−0.887484	−0.443742	+	0.896155i	$0.646349\pi$
$692$	72.4462	2.75399
$693$	−155.059	−5.89020
$694$	71.4884	2.71366
$695$	18.9779	0.719875
$696$	199.515	7.56259
$697$	−66.9747	−2.53685
$698$	−17.0350	−0.644784
$699$	−62.9761	−2.38198
$700$	39.7463	1.50227
$701$	−16.2150	−0.612434	−0.306217	−	0.951962i	$-0.599063\pi$
$701$	−16.2150	−0.612434	−0.306217	+	0.951962i	$0.599063\pi$
$702$	67.5828	2.55075
$703$	−21.3038	−0.803489
$704$	−252.665	−9.52267
$705$	−10.1085	−0.380709
$706$	−29.3155	−1.10330
$707$	9.18466	0.345425
$708$	36.2853	1.36368
$709$	14.0878	0.529080	0.264540	−	0.964375i	$-0.414780\pi$
$709$	14.0878	0.529080	0.264540	+	0.964375i	$0.414780\pi$
$710$	−79.6769	−2.99022
$711$	−0.951386	−0.0356798
$712$	168.941	6.33132
$713$	−6.42419	−0.240588
$714$	−295.036	−11.0414
$715$	−33.5473	−1.25460
$716$	−3.90227	−0.145835
$717$	2.15292	0.0804021
$718$	40.0107	1.49318
$719$	40.1690	1.49805	0.749025	−	0.662541i	$-0.230522\pi$
$719$	40.1690	1.49805	0.749025	+	0.662541i	$0.230522\pi$
$720$	−293.283	−10.9300
$721$	18.2964	0.681393
$722$	−62.2011	−2.31489
$723$	−72.5274	−2.69732
$724$	−98.2928	−3.65302
$725$	−9.42674	−0.350100
$726$	−164.938	−6.12142
$727$	−20.7617	−0.770007	−0.385004	−	0.922915i	$-0.625800\pi$
$727$	−20.7617	−0.770007	−0.385004	+	0.922915i	$0.625800\pi$
$728$	112.973	4.18706
$729$	−16.9654	−0.628347
$730$	−14.4744	−0.535720
$731$	−48.0025	−1.77544
$732$	−231.736	−8.56522
$733$	18.9271	0.699087	0.349543	−	0.936920i	$-0.386337\pi$
$733$	18.9271	0.699087	0.349543	+	0.936920i	$0.386337\pi$
$734$	65.8072	2.42899
$735$	−100.113	−3.69273
$736$	65.7568	2.42383
$737$	6.81711	0.251111
$738$	152.434	5.61118
$739$	−38.3730	−1.41157	−0.705786	−	0.708425i	$-0.749406\pi$
$739$	−38.3730	−1.41157	−0.705786	+	0.708425i	$0.749406\pi$
$740$	−49.2704	−1.81121
$741$	46.7317	1.71673
$742$	−42.1752	−1.54830
$743$	−26.5464	−0.973895	−0.486947	−	0.873431i	$-0.661890\pi$
$743$	−26.5464	−0.973895	−0.486947	+	0.873431i	$0.661890\pi$
$744$	−93.3920	−3.42392
$745$	−6.06723	−0.222286
$746$	−30.4835	−1.11608
$747$	17.1669	0.628106
$748$	−248.470	−9.08495
$749$	−6.55881	−0.239654
$750$	−75.5674	−2.75933
$751$	9.33238	0.340543	0.170272	−	0.985397i	$-0.445535\pi$
$751$	9.33238	0.340543	0.170272	+	0.985397i	$0.445535\pi$
$752$	23.4890	0.856556
$753$	−71.0295	−2.58846
$754$	−40.8577	−1.48795
$755$	36.7479	1.33739
$756$	262.564	9.54937
$757$	−26.6078	−0.967077	−0.483538	−	0.875323i	$-0.660649\pi$
$757$	−26.6078	−0.967077	−0.483538	+	0.875323i	$0.660649\pi$
$758$	−2.45472	−0.0891595
$759$	37.6127	1.36525
$760$	−174.874	−6.34335
$761$	−32.6303	−1.18285	−0.591424	−	0.806360i	$-0.701434\pi$
$761$	−32.6303	−1.18285	−0.591424	+	0.806360i	$0.701434\pi$
$762$	−50.4206	−1.82655
$763$	−21.1786	−0.766715
$764$	19.8842	0.719385
$765$	−125.542	−4.53899
$766$	55.8881	2.01932
$767$	−4.87297	−0.175953
$768$	312.254	11.2675
$769$	−25.1282	−0.906146	−0.453073	−	0.891473i	$-0.649672\pi$
$769$	−25.1282	−0.906146	−0.453073	+	0.891473i	$0.649672\pi$
$770$	−175.196	−6.31362
$771$	38.0261	1.36948
$772$	47.9902	1.72720
$773$	−20.6135	−0.741416	−0.370708	−	0.928749i	$-0.620885\pi$
$773$	−20.6135	−0.741416	−0.370708	+	0.928749i	$0.620885\pi$
$774$	109.254	3.92704
$775$	4.41261	0.158506
$776$	17.9706	0.645105
$777$	45.0924	1.61768
$778$	53.0542	1.90208
$779$	55.4006	1.98493
$780$	108.079	3.86984
$781$	61.4114	2.19747
$782$	48.5397	1.73577
$783$	−62.2730	−2.22546
$784$	232.631	8.30827
$785$	49.2671	1.75842
$786$	−52.9632	−1.88913
$787$	28.7944	1.02641	0.513205	−	0.858266i	$-0.328458\pi$
$787$	28.7944	1.02641	0.513205	+	0.858266i	$0.328458\pi$
$788$	−70.2314	−2.50189
$789$	13.3985	0.476999
$790$	−1.07494	−0.0382446
$791$	34.6536	1.23214
$792$	370.860	13.1779
$793$	31.1213	1.10515
$794$	61.2953	2.17529
$795$	−26.4599	−0.938434
$796$	−121.045	−4.29033
$797$	35.4892	1.25709	0.628546	−	0.777773i	$-0.283651\pi$
$797$	35.4892	1.25709	0.628546	+	0.777773i	$0.283651\pi$
$798$	244.049	8.63926
$799$	10.0547	0.355708
$800$	−45.1666	−1.59688
$801$	−100.323	−3.54475
$802$	6.72888	0.237605
$803$	11.1562	0.393694
$804$	−21.9625	−0.774559
$805$	25.4613	0.897393
$806$	19.1253	0.673660
$807$	−33.1270	−1.16613
$808$	−21.9673	−0.772807
$809$	−27.6455	−0.971965	−0.485982	−	0.873969i	$-0.661538\pi$
$809$	−27.6455	−0.971965	−0.485982	+	0.873969i	$0.661538\pi$
$810$	85.8765	3.01739
$811$	33.5460	1.17796	0.588980	−	0.808147i	$-0.299530\pi$
$811$	33.5460	1.17796	0.588980	+	0.808147i	$0.299530\pi$
$812$	−158.735	−5.57051
$813$	28.1538	0.987397
$814$	51.0469	1.78919
$815$	16.2047	0.567627
$816$	430.112	15.0569
$817$	39.7071	1.38917
$818$	−8.35519	−0.292133
$819$	−67.0877	−2.34423
$820$	128.128	4.47441
$821$	−9.61130	−0.335437	−0.167718	−	0.985835i	$-0.553640\pi$
$821$	−9.61130	−0.335437	−0.167718	+	0.985835i	$0.553640\pi$
$822$	−142.999	−4.98765
$823$	−6.70644	−0.233772	−0.116886	−	0.993145i	$-0.537291\pi$
$823$	−6.70644	−0.233772	−0.116886	+	0.993145i	$0.537291\pi$
$824$	−43.7601	−1.52446
$825$	−25.8352	−0.899465
$826$	−25.4484	−0.885463
$827$	−36.3590	−1.26432	−0.632162	−	0.774836i	$-0.717832\pi$
$827$	−36.3590	−1.26432	−0.632162	+	0.774836i	$0.717832\pi$
$828$	−82.1867	−2.85618
$829$	5.75956	0.200038	0.100019	−	0.994986i	$-0.468110\pi$
$829$	5.75956	0.200038	0.100019	+	0.994986i	$0.468110\pi$
$830$	19.3964	0.673258
$831$	−53.8461	−1.86790
$832$	−109.318	−3.78992
$833$	99.5798	3.45023
$834$	63.3454	2.19347
$835$	6.37050	0.220460
$836$	205.531	7.10843
$837$	29.1497	1.00756
$838$	109.388	3.77875
$839$	30.6372	1.05771	0.528856	−	0.848711i	$-0.322621\pi$
$839$	30.6372	1.05771	0.528856	+	0.848711i	$0.322621\pi$
$840$	370.145	12.7712
$841$	8.64761	0.298193
$842$	−105.680	−3.64198
$843$	0.395037	0.0136058
$844$	−130.034	−4.47597
$845$	18.7216	0.644044
$846$	−22.8844	−0.786780
$847$	86.0566	2.95694
$848$	61.4843	2.11138
$849$	−9.98573	−0.342709
$850$	−33.3406	−1.14357
$851$	−7.41867	−0.254309
$852$	−197.848	−6.77815
$853$	−20.2603	−0.693699	−0.346849	−	0.937921i	$-0.612748\pi$
$853$	−20.2603	−0.693699	−0.346849	+	0.937921i	$0.612748\pi$
$854$	162.526	5.56154
$855$	103.847	3.55149
$856$	15.6869	0.536169
$857$	7.19830	0.245889	0.122945	−	0.992414i	$-0.460766\pi$
$857$	7.19830	0.245889	0.122945	+	0.992414i	$0.460766\pi$
$858$	−111.976	−3.82279
$859$	−32.0364	−1.09307	−0.546534	−	0.837437i	$-0.684053\pi$
$859$	−32.0364	−1.09307	−0.546534	+	0.837437i	$0.684053\pi$
$860$	91.8324	3.13146
$861$	−117.263	−3.99631
$862$	−26.9674	−0.918512
$863$	53.9679	1.83709	0.918544	−	0.395318i	$-0.129366\pi$
$863$	53.9679	1.83709	0.918544	+	0.395318i	$0.129366\pi$
$864$	−298.370	−10.1508
$865$	−31.8769	−1.08385
$866$	−115.982	−3.94123
$867$	132.203	4.48986
$868$	74.3032	2.52201
$869$	0.828516	0.0281055
$870$	−133.866	−4.53848
$871$	2.94949	0.0999395
$872$	50.6535	1.71535
$873$	−10.6716	−0.361179
$874$	−40.1514	−1.35814
$875$	39.4274	1.33289
$876$	−35.9417	−1.21436
$877$	16.1246	0.544487	0.272244	−	0.962228i	$-0.412234\pi$
$877$	16.1246	0.544487	0.272244	+	0.962228i	$0.412234\pi$
$878$	−89.9015	−3.03403
$879$	49.5929	1.67273
$880$	255.406	8.60973
$881$	−44.9900	−1.51575	−0.757876	−	0.652399i	$-0.773763\pi$
$881$	−44.9900	−1.51575	−0.757876	+	0.652399i	$0.773763\pi$
$882$	−226.643	−7.63147
$883$	38.8742	1.30822	0.654110	−	0.756400i	$-0.273043\pi$
$883$	38.8742	1.30822	0.654110	+	0.756400i	$0.273043\pi$
$884$	−107.503	−3.61571
$885$	−15.9658	−0.536684
$886$	−96.2730	−3.23436
$887$	−51.5319	−1.73027	−0.865137	−	0.501536i	$-0.832768\pi$
$887$	−51.5319	−1.73027	−0.865137	+	0.501536i	$0.832768\pi$
$888$	−107.849	−3.61918
$889$	26.3070	0.882308
$890$	−113.352	−3.79957
$891$	−66.1898	−2.21744
$892$	127.045	4.25378
$893$	−8.31708	−0.278320
$894$	−20.2514	−0.677310
$895$	1.71703	0.0573940
$896$	−309.107	−10.3265
$897$	16.2735	0.543355
$898$	12.2473	0.408698
$899$	−17.6227	−0.587749
$900$	56.4519	1.88173
$901$	26.3188	0.876808
$902$	−132.748	−4.42001
$903$	−84.0454	−2.79685
$904$	−82.8822	−2.75662
$905$	43.2496	1.43766
$906$	122.659	4.07507
$907$	−10.1566	−0.337246	−0.168623	−	0.985681i	$-0.553932\pi$
$907$	−10.1566	−0.337246	−0.168623	+	0.985681i	$0.553932\pi$
$908$	23.4991	0.779846
$909$	13.0450	0.432676
$910$	−75.8002	−2.51275
$911$	24.0203	0.795827	0.397913	−	0.917423i	$-0.369734\pi$
$911$	24.0203	0.795827	0.397913	+	0.917423i	$0.369734\pi$
$912$	−355.783	−11.7811
$913$	−14.9499	−0.494768
$914$	77.8721	2.57578
$915$	101.966	3.37088
$916$	−16.4572	−0.543760
$917$	27.6336	0.912541
$918$	−220.248	−7.26927
$919$	−50.0150	−1.64984	−0.824921	−	0.565249i	$-0.808780\pi$
$919$	−50.0150	−1.64984	−0.824921	+	0.565249i	$0.808780\pi$
$920$	−60.8967	−2.00771
$921$	86.9943	2.86656
$922$	10.5018	0.345860
$923$	26.5702	0.874569
$924$	−435.034	−14.3116
$925$	5.09569	0.167545
$926$	15.5144	0.509836
$927$	25.9864	0.853505
$928$	180.382	5.92133
$929$	17.5934	0.577222	0.288611	−	0.957446i	$-0.406807\pi$
$929$	17.5934	0.577222	0.288611	+	0.957446i	$0.406807\pi$
$930$	62.6620	2.05477
$931$	−82.3711	−2.69960
$932$	−119.836	−3.92536
$933$	7.83724	0.256580
$934$	4.37279	0.143082
$935$	109.329	3.57543
$936$	160.456	5.24467
$937$	−33.1198	−1.08198	−0.540988	−	0.841030i	$-0.681950\pi$
$937$	−33.1198	−1.08198	−0.540988	+	0.841030i	$0.681950\pi$
$938$	15.4033	0.502934
$939$	68.9132	2.24890
$940$	−19.2353	−0.627386
$941$	−3.30061	−0.107597	−0.0537984	−	0.998552i	$-0.517133\pi$
$941$	−3.30061	−0.107597	−0.0537984	+	0.998552i	$0.517133\pi$
$942$	164.446	5.35793
$943$	19.2923	0.628242
$944$	37.0994	1.20748
$945$	−115.530	−3.75820
$946$	−95.1436	−3.09339
$947$	−24.6007	−0.799415	−0.399708	−	0.916643i	$-0.630888\pi$
$947$	−24.6007	−0.799415	−0.399708	+	0.916643i	$0.630888\pi$
$948$	−2.66921	−0.0866920
$949$	4.82684	0.156686
$950$	27.5789	0.894778
$951$	65.6993	2.13045
$952$	−368.172	−11.9325
$953$	−17.3137	−0.560846	−0.280423	−	0.959876i	$-0.590475\pi$
$953$	−17.3137	−0.560846	−0.280423	+	0.959876i	$0.590475\pi$
$954$	−59.9016	−1.93939
$955$	−8.74920	−0.283117
$956$	4.09674	0.132498
$957$	103.178	3.33527
$958$	−100.988	−3.26278
$959$	74.6097	2.40927
$960$	−358.169	−11.5598
$961$	−22.7509	−0.733901
$962$	22.0859	0.712078
$963$	−9.31550	−0.300188
$964$	−138.011	−4.44503
$965$	−21.1160	−0.679750
$966$	84.9858	2.73437
$967$	−18.4608	−0.593660	−0.296830	−	0.954930i	$-0.595929\pi$
$967$	−18.4608	−0.593660	−0.296830	+	0.954930i	$0.595929\pi$
$968$	−205.825	−6.61546
$969$	−152.296	−4.89244
$970$	−12.0575	−0.387142
$971$	−23.5635	−0.756189	−0.378094	−	0.925767i	$-0.623421\pi$
$971$	−23.5635	−0.756189	−0.378094	+	0.925767i	$0.623421\pi$
$972$	36.3292	1.16526
$973$	−33.0505	−1.05955
$974$	2.95601	0.0947167
$975$	−11.1778	−0.357977
$976$	−236.936	−7.58414
$977$	−36.6062	−1.17113	−0.585567	−	0.810624i	$-0.699128\pi$
$977$	−36.6062	−1.17113	−0.585567	+	0.810624i	$0.699128\pi$
$978$	54.0888	1.72957
$979$	87.3667	2.79225
$980$	−190.503	−6.08541
$981$	−30.0800	−0.960380
$982$	−52.3676	−1.67112
$983$	55.6772	1.77583	0.887914	−	0.460009i	$-0.152154\pi$
$983$	55.6772	1.77583	0.887914	+	0.460009i	$0.152154\pi$
$984$	280.462	8.94080
$985$	30.9024	0.984631
$986$	133.153	4.24044
$987$	17.6042	0.560348
$988$	88.9248	2.82908
$989$	13.8273	0.439681
$990$	−248.831	−7.90838
$991$	8.48001	0.269377	0.134688	−	0.990888i	$-0.456997\pi$
$991$	8.48001	0.269377	0.134688	+	0.990888i	$0.456997\pi$
$992$	−84.4360	−2.68084
$993$	−25.8096	−0.819043
$994$	138.759	4.40117
$995$	53.2608	1.68848
$996$	48.1636	1.52612
$997$	25.6503	0.812352	0.406176	−	0.913795i	$-0.366862\pi$
$997$	25.6503	0.812352	0.406176	+	0.913795i	$0.366862\pi$
$998$	38.0620	1.20483
$999$	33.6621	1.06502

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6037.2.a.a.1.4	✓	243

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6037.2.a.a.1.4	✓	243	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:	\( N \)	\(=\)	\( 6037 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6037.a (trivial)

\(f(q)\)	\(=\)	\(q-2.79471 q^{2} +3.05349 q^{3} +5.81042 q^{4} -2.55663 q^{5} -8.53363 q^{6} +4.45243 q^{7} -10.6490 q^{8} +6.32380 q^{9} +O(q^{10})\)	\(q-2.79471 q^{2} +3.05349 q^{3} +5.81042 q^{4} -2.55663 q^{5} -8.53363 q^{6} +4.45243 q^{7} -10.6490 q^{8} +6.32380 q^{9} +7.14505 q^{10} -5.50709 q^{11} +17.7421 q^{12} -2.38269 q^{13} -12.4433 q^{14} -7.80664 q^{15} +18.1402 q^{16} +7.76504 q^{17} -17.6732 q^{18} -6.42314 q^{19} -14.8551 q^{20} +13.5954 q^{21} +15.3907 q^{22} -2.23674 q^{23} -32.5167 q^{24} +1.53636 q^{25} +6.65894 q^{26} +10.1492 q^{27} +25.8705 q^{28} -6.13576 q^{29} +21.8173 q^{30} +2.87212 q^{31} -29.3985 q^{32} -16.8158 q^{33} -21.7011 q^{34} -11.3832 q^{35} +36.7439 q^{36} +3.31673 q^{37} +17.9508 q^{38} -7.27553 q^{39} +27.2256 q^{40} -8.62516 q^{41} -37.9954 q^{42} -6.18188 q^{43} -31.9985 q^{44} -16.1676 q^{45} +6.25105 q^{46} +1.29486 q^{47} +55.3908 q^{48} +12.8241 q^{49} -4.29368 q^{50} +23.7105 q^{51} -13.8445 q^{52} +3.38940 q^{53} -28.3641 q^{54} +14.0796 q^{55} -47.4141 q^{56} -19.6130 q^{57} +17.1477 q^{58} +2.04515 q^{59} -45.3599 q^{60} -13.0614 q^{61} -8.02676 q^{62} +28.1563 q^{63} +45.8800 q^{64} +6.09166 q^{65} +46.9954 q^{66} -1.23788 q^{67} +45.1182 q^{68} -6.82987 q^{69} +31.8128 q^{70} -11.1513 q^{71} -67.3424 q^{72} -2.02579 q^{73} -9.26931 q^{74} +4.69126 q^{75} -37.3211 q^{76} -24.5199 q^{77} +20.3330 q^{78} -0.150445 q^{79} -46.3777 q^{80} +12.0190 q^{81} +24.1049 q^{82} +2.71466 q^{83} +78.9952 q^{84} -19.8523 q^{85} +17.2766 q^{86} -18.7355 q^{87} +58.6452 q^{88} -15.8644 q^{89} +45.1838 q^{90} -10.6088 q^{91} -12.9964 q^{92} +8.76999 q^{93} -3.61877 q^{94} +16.4216 q^{95} -89.7679 q^{96} -1.68753 q^{97} -35.8397 q^{98} -34.8257 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 243 q - 47 q^{2} - 31 q^{3} + 229 q^{4} - 40 q^{5} - 18 q^{6} - 42 q^{7} - 135 q^{8} + 214 q^{9}+O(q^{10}) \) 243 * q - 47 * q^2 - 31 * q^3 + 229 * q^4 - 40 * q^5 - 18 * q^6 - 42 * q^7 - 135 * q^8 + 214 * q^9	\( 243 q - 47 q^{2} - 31 q^{3} + 229 q^{4} - 40 q^{5} - 18 q^{6} - 42 q^{7} - 135 q^{8} + 214 q^{9} - 14 q^{10} - 112 q^{11} - 54 q^{12} - 45 q^{13} - 35 q^{14} - 56 q^{15} + 213 q^{16} - 71 q^{17} - 135 q^{18} - 69 q^{19} - 107 q^{20} - 36 q^{21} - 24 q^{22} - 162 q^{23} - 57 q^{24} + 203 q^{25} - 55 q^{26} - 115 q^{27} - 87 q^{28} - 76 q^{29} - 64 q^{30} - 35 q^{31} - 302 q^{32} - 77 q^{33} - 9 q^{34} - 264 q^{35} + 173 q^{36} - 61 q^{37} - 71 q^{38} - 123 q^{39} - 16 q^{40} - 74 q^{41} - 70 q^{42} - 178 q^{43} - 209 q^{44} - 107 q^{45} - 11 q^{46} - 191 q^{47} - 65 q^{48} + 211 q^{49} - 188 q^{50} - 175 q^{51} - 95 q^{52} - 122 q^{53} - 36 q^{54} - 47 q^{55} - 69 q^{56} - 103 q^{57} - 37 q^{58} - 212 q^{59} - 79 q^{60} - 14 q^{61} - 152 q^{62} - 203 q^{63} + 217 q^{64} - 159 q^{65} + 5 q^{66} - 202 q^{67} - 176 q^{68} - 34 q^{69} + 45 q^{70} - 170 q^{71} - 347 q^{72} - 57 q^{73} - 68 q^{74} - 124 q^{75} - 74 q^{76} - 166 q^{77} - 63 q^{78} - 48 q^{79} - 222 q^{80} + 159 q^{81} - 27 q^{82} - 434 q^{83} - 52 q^{84} - 57 q^{85} - 77 q^{86} - 184 q^{87} - 15 q^{88} - 62 q^{89} - 24 q^{90} - 81 q^{91} - 330 q^{92} - 164 q^{93} + 40 q^{94} - 182 q^{95} - 66 q^{96} - 21 q^{97} - 254 q^{98} - 306 q^{99}+O(q^{100}) \) 243 * q - 47 * q^2 - 31 * q^3 + 229 * q^4 - 40 * q^5 - 18 * q^6 - 42 * q^7 - 135 * q^8 + 214 * q^9 - 14 * q^10 - 112 * q^11 - 54 * q^12 - 45 * q^13 - 35 * q^14 - 56 * q^15 + 213 * q^16 - 71 * q^17 - 135 * q^18 - 69 * q^19 - 107 * q^20 - 36 * q^21 - 24 * q^22 - 162 * q^23 - 57 * q^24 + 203 * q^25 - 55 * q^26 - 115 * q^27 - 87 * q^28 - 76 * q^29 - 64 * q^30 - 35 * q^31 - 302 * q^32 - 77 * q^33 - 9 * q^34 - 264 * q^35 + 173 * q^36 - 61 * q^37 - 71 * q^38 - 123 * q^39 - 16 * q^40 - 74 * q^41 - 70 * q^42 - 178 * q^43 - 209 * q^44 - 107 * q^45 - 11 * q^46 - 191 * q^47 - 65 * q^48 + 211 * q^49 - 188 * q^50 - 175 * q^51 - 95 * q^52 - 122 * q^53 - 36 * q^54 - 47 * q^55 - 69 * q^56 - 103 * q^57 - 37 * q^58 - 212 * q^59 - 79 * q^60 - 14 * q^61 - 152 * q^62 - 203 * q^63 + 217 * q^64 - 159 * q^65 + 5 * q^66 - 202 * q^67 - 176 * q^68 - 34 * q^69 + 45 * q^70 - 170 * q^71 - 347 * q^72 - 57 * q^73 - 68 * q^74 - 124 * q^75 - 74 * q^76 - 166 * q^77 - 63 * q^78 - 48 * q^79 - 222 * q^80 + 159 * q^81 - 27 * q^82 - 434 * q^83 - 52 * q^84 - 57 * q^85 - 77 * q^86 - 184 * q^87 - 15 * q^88 - 62 * q^89 - 24 * q^90 - 81 * q^91 - 330 * q^92 - 164 * q^93 + 40 * q^94 - 182 * q^95 - 66 * q^96 - 21 * q^97 - 254 * q^98 - 306 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more