LMFDB - Embedded newform 6013.2.a.d.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6013, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6013.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6013 = 7 \cdot 859 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6013.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$48.0140467354$
Analytic rank:	$1$
Dimension:	$104$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	6013.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.08457 q^{2} +2.65051 q^{3} +2.34543 q^{4} +3.08275 q^{5} -5.52518 q^{6} +1.00000 q^{7} -0.720080 q^{8} +4.02522 q^{9} +O(q^{10})$	\(q-2.08457 q^{2} +2.65051 q^{3} +2.34543 q^{4} +3.08275 q^{5} -5.52518 q^{6} +1.00000 q^{7} -0.720080 q^{8} +4.02522 q^{9} -6.42620 q^{10} -5.61700 q^{11} +6.21660 q^{12} +0.722869 q^{13} -2.08457 q^{14} +8.17086 q^{15} -3.18981 q^{16} -1.22877 q^{17} -8.39085 q^{18} -6.07460 q^{19} +7.23037 q^{20} +2.65051 q^{21} +11.7090 q^{22} -6.64138 q^{23} -1.90858 q^{24} +4.50332 q^{25} -1.50687 q^{26} +2.71735 q^{27} +2.34543 q^{28} -0.352878 q^{29} -17.0327 q^{30} -3.99616 q^{31} +8.08954 q^{32} -14.8879 q^{33} +2.56146 q^{34} +3.08275 q^{35} +9.44088 q^{36} -10.1035 q^{37} +12.6629 q^{38} +1.91597 q^{39} -2.21982 q^{40} -1.92668 q^{41} -5.52518 q^{42} -8.20979 q^{43} -13.1743 q^{44} +12.4087 q^{45} +13.8444 q^{46} +0.208543 q^{47} -8.45463 q^{48} +1.00000 q^{49} -9.38749 q^{50} -3.25687 q^{51} +1.69544 q^{52} +6.64348 q^{53} -5.66452 q^{54} -17.3158 q^{55} -0.720080 q^{56} -16.1008 q^{57} +0.735599 q^{58} -12.6872 q^{59} +19.1642 q^{60} +10.9831 q^{61} +8.33029 q^{62} +4.02522 q^{63} -10.4836 q^{64} +2.22842 q^{65} +31.0349 q^{66} +7.34317 q^{67} -2.88200 q^{68} -17.6031 q^{69} -6.42620 q^{70} +5.41250 q^{71} -2.89848 q^{72} +7.71966 q^{73} +21.0614 q^{74} +11.9361 q^{75} -14.2476 q^{76} -5.61700 q^{77} -3.99398 q^{78} -10.6843 q^{79} -9.83337 q^{80} -4.87327 q^{81} +4.01631 q^{82} +1.13591 q^{83} +6.21660 q^{84} -3.78798 q^{85} +17.1139 q^{86} -0.935308 q^{87} +4.04469 q^{88} -11.4936 q^{89} -25.8669 q^{90} +0.722869 q^{91} -15.5769 q^{92} -10.5919 q^{93} -0.434722 q^{94} -18.7264 q^{95} +21.4414 q^{96} +13.9964 q^{97} -2.08457 q^{98} -22.6096 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 104 q - 17 q^{2} - 34 q^{3} + 99 q^{4} - 46 q^{5} - 18 q^{6} + 104 q^{7} - 48 q^{8} + 98 q^{9}+O(q^{10}) $ 104 * q - 17 * q^2 - 34 * q^3 + 99 * q^4 - 46 * q^5 - 18 * q^6 + 104 * q^7 - 48 * q^8 + 98 * q^9	\( 104 q - 17 q^{2} - 34 q^{3} + 99 q^{4} - 46 q^{5} - 18 q^{6} + 104 q^{7} - 48 q^{8} + 98 q^{9} - 17 q^{10} - 46 q^{11} - 62 q^{12} - 37 q^{13} - 17 q^{14} - 17 q^{15} + 93 q^{16} - 75 q^{17} - 41 q^{18} - 40 q^{19} - 106 q^{20} - 34 q^{21} - 14 q^{22} - 57 q^{23} - 38 q^{24} + 102 q^{25} - 45 q^{26} - 121 q^{27} + 99 q^{28} - 29 q^{29} + 26 q^{30} - 42 q^{31} - 113 q^{32} - 42 q^{33} - 7 q^{34} - 46 q^{35} + 99 q^{36} - 31 q^{37} - 62 q^{38} - 9 q^{39} - 36 q^{40} - 106 q^{41} - 18 q^{42} - 29 q^{43} - 60 q^{44} - 121 q^{45} + 21 q^{46} - 141 q^{47} - 88 q^{48} + 104 q^{49} - 70 q^{50} - 2 q^{51} - 58 q^{52} - 70 q^{53} - 49 q^{54} - 14 q^{55} - 48 q^{56} - 11 q^{57} - 28 q^{58} - 202 q^{59} + 17 q^{60} - 79 q^{61} - 41 q^{62} + 98 q^{63} + 110 q^{64} - 34 q^{65} - 21 q^{66} - 57 q^{67} - 180 q^{68} - 99 q^{69} - 17 q^{70} - 109 q^{71} - 73 q^{72} - 46 q^{73} - 7 q^{74} - 146 q^{75} - 54 q^{76} - 46 q^{77} - 42 q^{78} - 12 q^{79} - 187 q^{80} + 100 q^{81} - 45 q^{82} - 156 q^{83} - 62 q^{84} - 13 q^{85} - 8 q^{86} - 76 q^{87} - 6 q^{88} - 140 q^{89} - 5 q^{90} - 37 q^{91} - 98 q^{92} - q^{93} - 17 q^{94} - 48 q^{95} - 12 q^{96} - 63 q^{97} - 17 q^{98} - 78 q^{99}+O(q^{100}) \) 104 * q - 17 * q^2 - 34 * q^3 + 99 * q^4 - 46 * q^5 - 18 * q^6 + 104 * q^7 - 48 * q^8 + 98 * q^9 - 17 * q^10 - 46 * q^11 - 62 * q^12 - 37 * q^13 - 17 * q^14 - 17 * q^15 + 93 * q^16 - 75 * q^17 - 41 * q^18 - 40 * q^19 - 106 * q^20 - 34 * q^21 - 14 * q^22 - 57 * q^23 - 38 * q^24 + 102 * q^25 - 45 * q^26 - 121 * q^27 + 99 * q^28 - 29 * q^29 + 26 * q^30 - 42 * q^31 - 113 * q^32 - 42 * q^33 - 7 * q^34 - 46 * q^35 + 99 * q^36 - 31 * q^37 - 62 * q^38 - 9 * q^39 - 36 * q^40 - 106 * q^41 - 18 * q^42 - 29 * q^43 - 60 * q^44 - 121 * q^45 + 21 * q^46 - 141 * q^47 - 88 * q^48 + 104 * q^49 - 70 * q^50 - 2 * q^51 - 58 * q^52 - 70 * q^53 - 49 * q^54 - 14 * q^55 - 48 * q^56 - 11 * q^57 - 28 * q^58 - 202 * q^59 + 17 * q^60 - 79 * q^61 - 41 * q^62 + 98 * q^63 + 110 * q^64 - 34 * q^65 - 21 * q^66 - 57 * q^67 - 180 * q^68 - 99 * q^69 - 17 * q^70 - 109 * q^71 - 73 * q^72 - 46 * q^73 - 7 * q^74 - 146 * q^75 - 54 * q^76 - 46 * q^77 - 42 * q^78 - 12 * q^79 - 187 * q^80 + 100 * q^81 - 45 * q^82 - 156 * q^83 - 62 * q^84 - 13 * q^85 - 8 * q^86 - 76 * q^87 - 6 * q^88 - 140 * q^89 - 5 * q^90 - 37 * q^91 - 98 * q^92 - q^93 - 17 * q^94 - 48 * q^95 - 12 * q^96 - 63 * q^97 - 17 * q^98 - 78 * 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 $

$2$	−2.08457	−1.47401	−0.737007	−	0.675885i	$-0.763762\pi$
$2$	−2.08457	−1.47401	−0.737007	+	0.675885i	$0.763762\pi$
$3$	2.65051	1.53027	0.765137	−	0.643867i	$-0.222671\pi$
$3$	2.65051	1.53027	0.765137	+	0.643867i	$0.222671\pi$
$4$	2.34543	1.17272
$5$	3.08275	1.37865	0.689323	−	0.724454i	$-0.257908\pi$
$5$	3.08275	1.37865	0.689323	+	0.724454i	$0.257908\pi$
$6$	−5.52518	−2.25565
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−0.720080	−0.254587
$9$	4.02522	1.34174
$10$	−6.42620	−2.03214
$11$	−5.61700	−1.69359	−0.846794	−	0.531920i	$-0.821471\pi$
$11$	−5.61700	−1.69359	−0.846794	+	0.531920i	$0.821471\pi$
$12$	6.21660	1.79458
$13$	0.722869	0.200488	0.100244	−	0.994963i	$-0.468038\pi$
$13$	0.722869	0.200488	0.100244	+	0.994963i	$0.468038\pi$
$14$	−2.08457	−0.557125
$15$	8.17086	2.10971
$16$	−3.18981	−0.797452
$17$	−1.22877	−0.298020	−0.149010	−	0.988836i	$-0.547609\pi$
$17$	−1.22877	−0.298020	−0.149010	+	0.988836i	$0.547609\pi$
$18$	−8.39085	−1.97774
$19$	−6.07460	−1.39361	−0.696804	−	0.717262i	$-0.745395\pi$
$19$	−6.07460	−1.39361	−0.696804	+	0.717262i	$0.745395\pi$
$20$	7.23037	1.61676
$21$	2.65051	0.578389
$22$	11.7090	2.49637
$23$	−6.64138	−1.38482	−0.692412	−	0.721502i	$-0.743452\pi$
$23$	−6.64138	−1.38482	−0.692412	+	0.721502i	$0.743452\pi$
$24$	−1.90858	−0.389588
$25$	4.50332	0.900664
$26$	−1.50687	−0.295522
$27$	2.71735	0.522955
$28$	2.34543	0.443245
$29$	−0.352878	−0.0655278	−0.0327639	−	0.999463i	$-0.510431\pi$
$29$	−0.352878	−0.0655278	−0.0327639	+	0.999463i	$0.510431\pi$
$30$	−17.0327	−3.10974
$31$	−3.99616	−0.717732	−0.358866	−	0.933389i	$-0.616837\pi$
$31$	−3.99616	−0.717732	−0.358866	+	0.933389i	$0.616837\pi$
$32$	8.08954	1.43004
$33$	−14.8879	−2.59166
$34$	2.56146	0.439286
$35$	3.08275	0.521079
$36$	9.44088	1.57348
$37$	−10.1035	−1.66100	−0.830499	−	0.557020i	$-0.811944\pi$
$37$	−10.1035	−1.66100	−0.830499	+	0.557020i	$0.811944\pi$
$38$	12.6629	2.05420
$39$	1.91597	0.306801
$40$	−2.21982	−0.350985
$41$	−1.92668	−0.300898	−0.150449	−	0.988618i	$-0.548072\pi$
$41$	−1.92668	−0.300898	−0.150449	+	0.988618i	$0.548072\pi$
$42$	−5.52518	−0.852554
$43$	−8.20979	−1.25198	−0.625991	−	0.779831i	$-0.715305\pi$
$43$	−8.20979	−1.25198	−0.625991	+	0.779831i	$0.715305\pi$
$44$	−13.1743	−1.98610
$45$	12.4087	1.84978
$46$	13.8444	2.04125
$47$	0.208543	0.0304191	0.0152095	−	0.999884i	$-0.495158\pi$
$47$	0.208543	0.0304191	0.0152095	+	0.999884i	$0.495158\pi$
$48$	−8.45463	−1.22032
$49$	1.00000	0.142857
$50$	−9.38749	−1.32759
$51$	−3.25687	−0.456053
$52$	1.69544	0.235115
$53$	6.64348	0.912552	0.456276	−	0.889838i	$-0.349183\pi$
$53$	6.64348	0.912552	0.456276	+	0.889838i	$0.349183\pi$
$54$	−5.66452	−0.770843
$55$	−17.3158	−2.33486
$56$	−0.720080	−0.0962248
$57$	−16.1008	−2.13260
$58$	0.735599	0.0965889
$59$	−12.6872	−1.65173	−0.825864	−	0.563870i	$-0.809312\pi$
$59$	−12.6872	−1.65173	−0.825864	+	0.563870i	$0.809312\pi$
$60$	19.1642	2.47409
$61$	10.9831	1.40625	0.703124	−	0.711068i	$-0.251788\pi$
$61$	10.9831	1.40625	0.703124	+	0.711068i	$0.251788\pi$
$62$	8.33029	1.05795
$63$	4.02522	0.507130
$64$	−10.4836	−1.31045
$65$	2.22842	0.276402
$66$	31.0349	3.82014
$67$	7.34317	0.897111	0.448556	−	0.893755i	$-0.351939\pi$
$67$	7.34317	0.897111	0.448556	+	0.893755i	$0.351939\pi$
$68$	−2.88200	−0.349493
$69$	−17.6031	−2.11916
$70$	−6.42620	−0.768078
$71$	5.41250	0.642346	0.321173	−	0.947021i	$-0.395923\pi$
$71$	5.41250	0.642346	0.321173	+	0.947021i	$0.395923\pi$
$72$	−2.89848	−0.341589
$73$	7.71966	0.903518	0.451759	−	0.892140i	$-0.350797\pi$
$73$	7.71966	0.903518	0.451759	+	0.892140i	$0.350797\pi$
$74$	21.0614	2.44833
$75$	11.9361	1.37826
$76$	−14.2476	−1.63431
$77$	−5.61700	−0.640116
$78$	−3.99398	−0.452229
$79$	−10.6843	−1.20208	−0.601041	−	0.799218i	$-0.705247\pi$
$79$	−10.6843	−1.20208	−0.601041	+	0.799218i	$0.705247\pi$
$80$	−9.83337	−1.09940
$81$	−4.87327	−0.541475
$82$	4.01631	0.443527
$83$	1.13591	0.124682	0.0623412	−	0.998055i	$-0.480143\pi$
$83$	1.13591	0.124682	0.0623412	+	0.998055i	$0.480143\pi$
$84$	6.21660	0.678287
$85$	−3.78798	−0.410864
$86$	17.1139	1.84544
$87$	−0.935308	−0.100276
$88$	4.04469	0.431165
$89$	−11.4936	−1.21832	−0.609158	−	0.793049i	$-0.708492\pi$
$89$	−11.4936	−1.21832	−0.609158	+	0.793049i	$0.708492\pi$
$90$	−25.8669	−2.72661
$91$	0.722869	0.0757773
$92$	−15.5769	−1.62401
$93$	−10.5919	−1.09833
$94$	−0.434722	−0.0448381
$95$	−18.7264	−1.92129
$96$	21.4414	2.18836
$97$	13.9964	1.42112	0.710559	−	0.703637i	$-0.248442\pi$
$97$	13.9964	1.42112	0.710559	+	0.703637i	$0.248442\pi$
$98$	−2.08457	−0.210573
$99$	−22.6096	−2.27235
$100$	10.5622	1.05622
$101$	−8.86333	−0.881934	−0.440967	−	0.897523i	$-0.645364\pi$
$101$	−8.86333	−0.881934	−0.440967	+	0.897523i	$0.645364\pi$
$102$	6.78917	0.672228
$103$	−4.50246	−0.443640	−0.221820	−	0.975088i	$-0.571200\pi$
$103$	−4.50246	−0.443640	−0.221820	+	0.975088i	$0.571200\pi$
$104$	−0.520524	−0.0510415
$105$	8.17086	0.797394
$106$	−13.8488	−1.34511
$107$	−13.1321	−1.26953	−0.634763	−	0.772707i	$-0.718902\pi$
$107$	−13.1321	−1.26953	−0.634763	+	0.772707i	$0.718902\pi$
$108$	6.37337	0.613278
$109$	12.8722	1.23293	0.616465	−	0.787382i	$-0.288564\pi$
$109$	12.8722	1.23293	0.616465	+	0.787382i	$0.288564\pi$
$110$	36.0960	3.44161
$111$	−26.7793	−2.54178
$112$	−3.18981	−0.301409
$113$	13.5855	1.27801	0.639006	−	0.769202i	$-0.279346\pi$
$113$	13.5855	1.27801	0.639006	+	0.769202i	$0.279346\pi$
$114$	33.5632	3.14349
$115$	−20.4737	−1.90918
$116$	−0.827652	−0.0768456
$117$	2.90971	0.269002
$118$	26.4473	2.43467
$119$	−1.22877	−0.112641
$120$	−5.88367	−0.537103
$121$	20.5507	1.86824
$122$	−22.8951	−2.07283
$123$	−5.10670	−0.460456
$124$	−9.37274	−0.841697
$125$	−1.53114	−0.136949
$126$	−8.39085	−0.747516
$127$	−2.65430	−0.235531	−0.117766	−	0.993041i	$-0.537573\pi$
$127$	−2.65430	−0.235531	−0.117766	+	0.993041i	$0.537573\pi$
$128$	5.67472	0.501579
$129$	−21.7601	−1.91587
$130$	−4.64530	−0.407420
$131$	5.69988	0.498001	0.249001	−	0.968503i	$-0.419898\pi$
$131$	5.69988	0.498001	0.249001	+	0.968503i	$0.419898\pi$
$132$	−34.9186	−3.03928
$133$	−6.07460	−0.526734
$134$	−15.3074	−1.32235
$135$	8.37691	0.720970
$136$	0.884813	0.0758721
$137$	−6.80055	−0.581010	−0.290505	−	0.956873i	$-0.593823\pi$
$137$	−6.80055	−0.581010	−0.290505	+	0.956873i	$0.593823\pi$
$138$	36.6948	3.12367
$139$	4.73114	0.401290	0.200645	−	0.979664i	$-0.435696\pi$
$139$	4.73114	0.401290	0.200645	+	0.979664i	$0.435696\pi$
$140$	7.23037	0.611078
$141$	0.552745	0.0465495
$142$	−11.2827	−0.946827
$143$	−4.06035	−0.339544
$144$	−12.8397	−1.06997
$145$	−1.08783	−0.0903396
$146$	−16.0922	−1.33180
$147$	2.65051	0.218611
$148$	−23.6970	−1.94788
$149$	−3.42269	−0.280398	−0.140199	−	0.990123i	$-0.544774\pi$
$149$	−3.42269	−0.280398	−0.140199	+	0.990123i	$0.544774\pi$
$150$	−24.8817	−2.03158
$151$	−7.53135	−0.612893	−0.306446	−	0.951888i	$-0.599140\pi$
$151$	−7.53135	−0.612893	−0.306446	+	0.951888i	$0.599140\pi$
$152$	4.37420	0.354794
$153$	−4.94606	−0.399866
$154$	11.7090	0.943540
$155$	−12.3192	−0.989499
$156$	4.49379	0.359791
$157$	−4.03322	−0.321886	−0.160943	−	0.986964i	$-0.551454\pi$
$157$	−4.03322	−0.321886	−0.160943	+	0.986964i	$0.551454\pi$
$158$	22.2723	1.77189
$159$	17.6086	1.39645
$160$	24.9380	1.97152
$161$	−6.64138	−0.523414
$162$	10.1587	0.798141
$163$	8.27624	0.648245	0.324123	−	0.946015i	$-0.394931\pi$
$163$	8.27624	0.648245	0.324123	+	0.946015i	$0.394931\pi$
$164$	−4.51891	−0.352868
$165$	−45.8957	−3.57297
$166$	−2.36789	−0.183784
$167$	−4.34000	−0.335839	−0.167920	−	0.985801i	$-0.553705\pi$
$167$	−4.34000	−0.335839	−0.167920	+	0.985801i	$0.553705\pi$
$168$	−1.90858	−0.147250
$169$	−12.4775	−0.959805
$170$	7.89632	0.605620
$171$	−24.4516	−1.86986
$172$	−19.2555	−1.46822
$173$	16.4857	1.25338	0.626692	−	0.779267i	$-0.284408\pi$
$173$	16.4857	1.25338	0.626692	+	0.779267i	$0.284408\pi$
$174$	1.94972	0.147808
$175$	4.50332	0.340419
$176$	17.9172	1.35056
$177$	−33.6275	−2.52760
$178$	23.9591	1.79581
$179$	11.5925	0.866467	0.433234	−	0.901282i	$-0.357373\pi$
$179$	11.5925	0.866467	0.433234	+	0.901282i	$0.357373\pi$
$180$	29.1038	2.16927
$181$	−22.2905	−1.65684	−0.828420	−	0.560107i	$-0.810760\pi$
$181$	−22.2905	−1.65684	−0.828420	+	0.560107i	$0.810760\pi$
$182$	−1.50687	−0.111697
$183$	29.1110	2.15194
$184$	4.78233	0.352558
$185$	−31.1464	−2.28993
$186$	22.0795	1.61895
$187$	6.90200	0.504724
$188$	0.489123	0.0356729
$189$	2.71735	0.197658
$190$	39.0366	2.83201
$191$	−1.73565	−0.125587	−0.0627935	−	0.998027i	$-0.520001\pi$
$191$	−1.73565	−0.125587	−0.0627935	+	0.998027i	$0.520001\pi$
$192$	−27.7869	−2.00535
$193$	−18.1299	−1.30502	−0.652510	−	0.757780i	$-0.726284\pi$
$193$	−18.1299	−1.30502	−0.652510	+	0.757780i	$0.726284\pi$
$194$	−29.1765	−2.09475
$195$	5.90646	0.422970
$196$	2.34543	0.167531
$197$	17.0793	1.21685	0.608424	−	0.793612i	$-0.291802\pi$
$197$	17.0793	1.21685	0.608424	+	0.793612i	$0.291802\pi$
$198$	47.1314	3.34948
$199$	6.76440	0.479516	0.239758	−	0.970833i	$-0.422932\pi$
$199$	6.76440	0.479516	0.239758	+	0.970833i	$0.422932\pi$
$200$	−3.24275	−0.229297
$201$	19.4632	1.37283
$202$	18.4762	1.29998
$203$	−0.352878	−0.0247672
$204$	−7.63877	−0.534821
$205$	−5.93948	−0.414831
$206$	9.38569	0.653932
$207$	−26.7330	−1.85807
$208$	−2.30581	−0.159879
$209$	34.1210	2.36020
$210$	−17.0327	−1.17537
$211$	2.22764	0.153357	0.0766787	−	0.997056i	$-0.475568\pi$
$211$	2.22764	0.153357	0.0766787	+	0.997056i	$0.475568\pi$
$212$	15.5818	1.07016
$213$	14.3459	0.982965
$214$	27.3747	1.87130
$215$	−25.3087	−1.72604
$216$	−1.95671	−0.133137
$217$	−3.99616	−0.271277
$218$	−26.8329	−1.81736
$219$	20.4611	1.38263
$220$	−40.6130	−2.73813
$221$	−0.888239	−0.0597494
$222$	55.8234	3.74662
$223$	−9.13350	−0.611625	−0.305812	−	0.952092i	$-0.598928\pi$
$223$	−9.13350	−0.611625	−0.305812	+	0.952092i	$0.598928\pi$
$224$	8.08954	0.540505
$225$	18.1268	1.20846
$226$	−28.3198	−1.88381
$227$	0.913789	0.0606503	0.0303251	−	0.999540i	$-0.490346\pi$
$227$	0.913789	0.0606503	0.0303251	+	0.999540i	$0.490346\pi$
$228$	−37.7633	−2.50094
$229$	11.0410	0.729609	0.364804	−	0.931084i	$-0.381136\pi$
$229$	11.0410	0.729609	0.364804	+	0.931084i	$0.381136\pi$
$230$	42.6789	2.81416
$231$	−14.8879	−0.979554
$232$	0.254101	0.0166825
$233$	2.73267	0.179023	0.0895116	−	0.995986i	$-0.471469\pi$
$233$	2.73267	0.179023	0.0895116	+	0.995986i	$0.471469\pi$
$234$	−6.06549	−0.396513
$235$	0.642884	0.0419371
$236$	−29.7569	−1.93701
$237$	−28.3190	−1.83951
$238$	2.56146	0.166035
$239$	5.69745	0.368537	0.184269	−	0.982876i	$-0.441008\pi$
$239$	5.69745	0.368537	0.184269	+	0.982876i	$0.441008\pi$
$240$	−26.0635	−1.68239
$241$	−4.79529	−0.308892	−0.154446	−	0.988001i	$-0.549359\pi$
$241$	−4.79529	−0.308892	−0.154446	+	0.988001i	$0.549359\pi$
$242$	−42.8393	−2.75382
$243$	−21.0687	−1.35156
$244$	25.7602	1.64913
$245$	3.08275	0.196949
$246$	10.6453	0.678718
$247$	−4.39114	−0.279401
$248$	2.87756	0.182725
$249$	3.01075	0.190798
$250$	3.19177	0.201865
$251$	−29.0416	−1.83309	−0.916546	−	0.399930i	$-0.869034\pi$
$251$	−29.0416	−1.83309	−0.916546	+	0.399930i	$0.869034\pi$
$252$	9.44088	0.594720
$253$	37.3046	2.34532
$254$	5.53308	0.347176
$255$	−10.0401	−0.628735
$256$	9.13785	0.571116
$257$	−14.0338	−0.875405	−0.437703	−	0.899120i	$-0.644208\pi$
$257$	−14.0338	−0.875405	−0.437703	+	0.899120i	$0.644208\pi$
$258$	45.3606	2.82403
$259$	−10.1035	−0.627798
$260$	5.22661	0.324141
$261$	−1.42041	−0.0879213
$262$	−11.8818	−0.734061
$263$	8.60147	0.530390	0.265195	−	0.964195i	$-0.414564\pi$
$263$	8.60147	0.530390	0.265195	+	0.964195i	$0.414564\pi$
$264$	10.7205	0.659801
$265$	20.4802	1.25809
$266$	12.6629	0.776414
$267$	−30.4638	−1.86436
$268$	17.2229	1.05206
$269$	−17.0549	−1.03985	−0.519927	−	0.854211i	$-0.674041\pi$
$269$	−17.0549	−1.03985	−0.519927	+	0.854211i	$0.674041\pi$
$270$	−17.4623	−1.06272
$271$	−12.5599	−0.762957	−0.381479	−	0.924378i	$-0.624585\pi$
$271$	−12.5599	−0.762957	−0.381479	+	0.924378i	$0.624585\pi$
$272$	3.91954	0.237657
$273$	1.91597	0.115960
$274$	14.1762	0.856417
$275$	−25.2951	−1.52535
$276$	−41.2868	−2.48518
$277$	22.7957	1.36966	0.684829	−	0.728704i	$-0.259877\pi$
$277$	22.7957	1.36966	0.684829	+	0.728704i	$0.259877\pi$
$278$	−9.86240	−0.591508
$279$	−16.0854	−0.963010
$280$	−2.21982	−0.132660
$281$	5.81141	0.346680	0.173340	−	0.984862i	$-0.444544\pi$
$281$	5.81141	0.346680	0.173340	+	0.984862i	$0.444544\pi$
$282$	−1.15224	−0.0686146
$283$	29.3827	1.74662	0.873309	−	0.487166i	$-0.161969\pi$
$283$	29.3827	1.74662	0.873309	+	0.487166i	$0.161969\pi$
$284$	12.6947	0.753290
$285$	−49.6347	−2.94010
$286$	8.46409	0.500492
$287$	−1.92668	−0.113729
$288$	32.5622	1.91874
$289$	−15.4901	−0.911184
$290$	2.26767	0.133162
$291$	37.0976	2.17470
$292$	18.1059	1.05957
$293$	1.13482	0.0662967	0.0331484	−	0.999450i	$-0.489447\pi$
$293$	1.13482	0.0662967	0.0331484	+	0.999450i	$0.489447\pi$
$294$	−5.52518	−0.322235
$295$	−39.1113	−2.27715
$296$	7.27530	0.422868
$297$	−15.2634	−0.885671
$298$	7.13484	0.413310
$299$	−4.80085	−0.277640
$300$	27.9953	1.61631
$301$	−8.20979	−0.473204
$302$	15.6996	0.903412
$303$	−23.4924	−1.34960
$304$	19.3768	1.11134
$305$	33.8582	1.93872
$306$	10.3104	0.589407
$307$	2.24731	0.128261	0.0641305	−	0.997942i	$-0.479573\pi$
$307$	2.24731	0.128261	0.0641305	+	0.997942i	$0.479573\pi$
$308$	−13.1743	−0.750675
$309$	−11.9338	−0.678891
$310$	25.6802	1.45853
$311$	25.9674	1.47247	0.736237	−	0.676724i	$-0.236601\pi$
$311$	25.9674	1.47247	0.736237	+	0.676724i	$0.236601\pi$
$312$	−1.37965	−0.0781076
$313$	32.1854	1.81923	0.909613	−	0.415456i	$-0.136378\pi$
$313$	32.1854	1.81923	0.909613	+	0.415456i	$0.136378\pi$
$314$	8.40754	0.474465
$315$	12.4087	0.699152
$316$	−25.0594	−1.40970
$317$	24.7598	1.39065	0.695326	−	0.718695i	$-0.255260\pi$
$317$	24.7598	1.39065	0.695326	+	0.718695i	$0.255260\pi$
$318$	−36.7064	−2.05839
$319$	1.98212	0.110977
$320$	−32.3183	−1.80665
$321$	−34.8068	−1.94272
$322$	13.8444	0.771520
$323$	7.46428	0.415324
$324$	−11.4299	−0.634996
$325$	3.25531	0.180572
$326$	−17.2524	−0.955522
$327$	34.1178	1.88672
$328$	1.38737	0.0766046
$329$	0.208543	0.0114973
$330$	95.6728	5.26661
$331$	11.3695	0.624923	0.312462	−	0.949930i	$-0.398846\pi$
$331$	11.3695	0.624923	0.312462	+	0.949930i	$0.398846\pi$
$332$	2.66420	0.146217
$333$	−40.6686	−2.22863
$334$	9.04703	0.495031
$335$	22.6371	1.23680
$336$	−8.45463	−0.461238
$337$	29.1644	1.58869	0.794344	−	0.607468i	$-0.207815\pi$
$337$	29.1644	1.58869	0.794344	+	0.607468i	$0.207815\pi$
$338$	26.0101	1.41477
$339$	36.0084	1.95571
$340$	−8.88446	−0.481828
$341$	22.4464	1.21554
$342$	50.9710	2.75620
$343$	1.00000	0.0539949
$344$	5.91171	0.318738
$345$	−54.2658	−2.92157
$346$	−34.3656	−1.84751
$347$	−32.9597	−1.76937	−0.884683	−	0.466192i	$-0.845626\pi$
$347$	−32.9597	−1.76937	−0.884683	+	0.466192i	$0.845626\pi$
$348$	−2.19370	−0.117595
$349$	2.25635	0.120780	0.0603900	−	0.998175i	$-0.480766\pi$
$349$	2.25635	0.120780	0.0603900	+	0.998175i	$0.480766\pi$
$350$	−9.38749	−0.501782
$351$	1.96429	0.104846
$352$	−45.4389	−2.42190
$353$	−10.4470	−0.556040	−0.278020	−	0.960575i	$-0.589678\pi$
$353$	−10.4470	−0.556040	−0.278020	+	0.960575i	$0.589678\pi$
$354$	70.0988	3.72571
$355$	16.6854	0.885567
$356$	−26.9574	−1.42874
$357$	−3.25687	−0.172372
$358$	−24.1655	−1.27718
$359$	−10.5527	−0.556952	−0.278476	−	0.960443i	$-0.589829\pi$
$359$	−10.5527	−0.556952	−0.278476	+	0.960443i	$0.589829\pi$
$360$	−8.93528	−0.470930
$361$	17.9007	0.942143
$362$	46.4661	2.44221
$363$	54.4698	2.85892
$364$	1.69544	0.0888653
$365$	23.7977	1.24563
$366$	−60.6838	−3.17199
$367$	25.0102	1.30552	0.652760	−	0.757565i	$-0.273611\pi$
$367$	25.0102	1.30552	0.652760	+	0.757565i	$0.273611\pi$
$368$	21.1847	1.10433
$369$	−7.75533	−0.403726
$370$	64.9268	3.37538
$371$	6.64348	0.344912
$372$	−24.8426	−1.28803
$373$	5.19202	0.268832	0.134416	−	0.990925i	$-0.457084\pi$
$373$	5.19202	0.268832	0.134416	+	0.990925i	$0.457084\pi$
$374$	−14.3877	−0.743970
$375$	−4.05830	−0.209570
$376$	−0.150167	−0.00774429
$377$	−0.255085	−0.0131375
$378$	−5.66452	−0.291351
$379$	26.7577	1.37445	0.687226	−	0.726443i	$-0.258828\pi$
$379$	26.7577	1.37445	0.687226	+	0.726443i	$0.258828\pi$
$380$	−43.9216	−2.25313
$381$	−7.03526	−0.360427
$382$	3.61808	0.185117
$383$	−33.4494	−1.70919	−0.854593	−	0.519298i	$-0.826193\pi$
$383$	−33.4494	−1.70919	−0.854593	+	0.519298i	$0.826193\pi$
$384$	15.0409	0.767554
$385$	−17.3158	−0.882494
$386$	37.7931	1.92362
$387$	−33.0462	−1.67983
$388$	32.8276	1.66657
$389$	24.3790	1.23606	0.618032	−	0.786153i	$-0.287930\pi$
$389$	24.3790	1.23606	0.618032	+	0.786153i	$0.287930\pi$
$390$	−12.3124	−0.623464
$391$	8.16073	0.412706
$392$	−0.720080	−0.0363695
$393$	15.1076	0.762079
$394$	−35.6030	−1.79365
$395$	−32.9371	−1.65724
$396$	−53.0294	−2.66483
$397$	−10.7147	−0.537754	−0.268877	−	0.963175i	$-0.586652\pi$
$397$	−10.7147	−0.537754	−0.268877	+	0.963175i	$0.586652\pi$
$398$	−14.1009	−0.706813
$399$	−16.1008	−0.806048
$400$	−14.3647	−0.718236
$401$	−21.5001	−1.07366	−0.536832	−	0.843689i	$-0.680379\pi$
$401$	−21.5001	−1.07366	−0.536832	+	0.843689i	$0.680379\pi$
$402$	−40.5723	−2.02356
$403$	−2.88870	−0.143897
$404$	−20.7883	−1.03426
$405$	−15.0231	−0.746502
$406$	0.735599	0.0365072
$407$	56.7511	2.81305
$408$	2.34521	0.116105
$409$	32.8455	1.62411	0.812053	−	0.583584i	$-0.198350\pi$
$409$	32.8455	1.62411	0.812053	+	0.583584i	$0.198350\pi$
$410$	12.3813	0.611467
$411$	−18.0249	−0.889105
$412$	−10.5602	−0.520264
$413$	−12.6872	−0.624294
$414$	55.7269	2.73883
$415$	3.50173	0.171893
$416$	5.84768	0.286706
$417$	12.5400	0.614084
$418$	−71.1276	−3.47897
$419$	−21.1073	−1.03116	−0.515580	−	0.856841i	$-0.672424\pi$
$419$	−21.1073	−1.03116	−0.515580	+	0.856841i	$0.672424\pi$
$420$	19.1642	0.935117
$421$	−35.5189	−1.73109	−0.865543	−	0.500834i	$-0.833027\pi$
$421$	−35.5189	−1.73109	−0.865543	+	0.500834i	$0.833027\pi$
$422$	−4.64368	−0.226051
$423$	0.839429	0.0408144
$424$	−4.78384	−0.232324
$425$	−5.53354	−0.268416
$426$	−29.9051	−1.44890
$427$	10.9831	0.531511
$428$	−30.8004	−1.48879
$429$	−10.7620	−0.519595
$430$	52.7577	2.54420
$431$	−12.2795	−0.591484	−0.295742	−	0.955268i	$-0.595567\pi$
$431$	−12.2795	−0.591484	−0.295742	+	0.955268i	$0.595567\pi$
$432$	−8.66784	−0.417032
$433$	34.5349	1.65964	0.829821	−	0.558029i	$-0.188442\pi$
$433$	34.5349	1.65964	0.829821	+	0.558029i	$0.188442\pi$
$434$	8.33029	0.399867
$435$	−2.88332	−0.138244
$436$	30.1908	1.44588
$437$	40.3437	1.92990
$438$	−42.6525	−2.03802
$439$	−10.8085	−0.515861	−0.257931	−	0.966163i	$-0.583041\pi$
$439$	−10.8085	−0.515861	−0.257931	+	0.966163i	$0.583041\pi$
$440$	12.4687	0.594424
$441$	4.02522	0.191677
$442$	1.85160	0.0880715
$443$	23.2560	1.10493	0.552464	−	0.833537i	$-0.313688\pi$
$443$	23.2560	1.10493	0.552464	+	0.833537i	$0.313688\pi$
$444$	−62.8091	−2.98079
$445$	−35.4317	−1.67963
$446$	19.0394	0.901543
$447$	−9.07189	−0.429086
$448$	−10.4836	−0.495304
$449$	0.476868	0.0225048	0.0112524	−	0.999937i	$-0.496418\pi$
$449$	0.476868	0.0225048	0.0112524	+	0.999937i	$0.496418\pi$
$450$	−37.7867	−1.78128
$451$	10.8222	0.509597
$452$	31.8638	1.49875
$453$	−19.9619	−0.937894
$454$	−1.90486	−0.0893994
$455$	2.22842	0.104470
$456$	11.5939	0.542933
$457$	15.5884	0.729195	0.364597	−	0.931165i	$-0.381207\pi$
$457$	15.5884	0.729195	0.364597	+	0.931165i	$0.381207\pi$
$458$	−23.0157	−1.07545
$459$	−3.33900	−0.155851
$460$	−48.0197	−2.23893
$461$	13.5211	0.629742	0.314871	−	0.949134i	$-0.398039\pi$
$461$	13.5211	0.629742	0.314871	+	0.949134i	$0.398039\pi$
$462$	31.0349	1.44388
$463$	6.80847	0.316416	0.158208	−	0.987406i	$-0.449428\pi$
$463$	6.80847	0.316416	0.158208	+	0.987406i	$0.449428\pi$
$464$	1.12561	0.0522553
$465$	−32.6521	−1.51420
$466$	−5.69644	−0.263883
$467$	−5.78344	−0.267626	−0.133813	−	0.991007i	$-0.542722\pi$
$467$	−5.78344	−0.267626	−0.133813	+	0.991007i	$0.542722\pi$
$468$	6.82452	0.315464
$469$	7.34317	0.339076
$470$	−1.34014	−0.0618159
$471$	−10.6901	−0.492574
$472$	9.13577	0.420508
$473$	46.1144	2.12034
$474$	59.0329	2.71147
$475$	−27.3559	−1.25517
$476$	−2.88200	−0.132096
$477$	26.7414	1.22441
$478$	−11.8767	−0.543229
$479$	−6.37358	−0.291216	−0.145608	−	0.989342i	$-0.546514\pi$
$479$	−6.37358	−0.291216	−0.145608	+	0.989342i	$0.546514\pi$
$480$	66.0985	3.01697
$481$	−7.30347	−0.333010
$482$	9.99612	0.455311
$483$	−17.6031	−0.800968
$484$	48.2002	2.19092
$485$	43.1473	1.95922
$486$	43.9193	1.99222
$487$	−13.3727	−0.605973	−0.302987	−	0.952995i	$-0.597984\pi$
$487$	−13.3727	−0.605973	−0.302987	+	0.952995i	$0.597984\pi$
$488$	−7.90874	−0.358012
$489$	21.9363	0.991993
$490$	−6.42620	−0.290306
$491$	20.2391	0.913379	0.456690	−	0.889626i	$-0.349035\pi$
$491$	20.2391	0.913379	0.456690	+	0.889626i	$0.349035\pi$
$492$	−11.9774	−0.539984
$493$	0.433606	0.0195286
$494$	9.15363	0.411841
$495$	−69.6998	−3.13277
$496$	12.7470	0.572357
$497$	5.41250	0.242784
$498$	−6.27612	−0.281239
$499$	−18.9392	−0.847835	−0.423917	−	0.905701i	$-0.639345\pi$
$499$	−18.9392	−0.847835	−0.423917	+	0.905701i	$0.639345\pi$
$500$	−3.59118	−0.160603
$501$	−11.5032	−0.513926
$502$	60.5393	2.70200
$503$	−11.0708	−0.493623	−0.246811	−	0.969064i	$-0.579383\pi$
$503$	−11.0708	−0.493623	−0.246811	+	0.969064i	$0.579383\pi$
$504$	−2.89848	−0.129109
$505$	−27.3234	−1.21587
$506$	−77.7642	−3.45704
$507$	−33.0717	−1.46876
$508$	−6.22548	−0.276211
$509$	−7.17506	−0.318029	−0.159014	−	0.987276i	$-0.550832\pi$
$509$	−7.17506	−0.318029	−0.159014	+	0.987276i	$0.550832\pi$
$510$	20.9293	0.926765
$511$	7.71966	0.341498
$512$	−30.3979	−1.34341
$513$	−16.5068	−0.728794
$514$	29.2545	1.29036
$515$	−13.8799	−0.611623
$516$	−51.0370	−2.24678
$517$	−1.17138	−0.0515174
$518$	21.0614	0.925383
$519$	43.6956	1.91802
$520$	−1.60464	−0.0703682
$521$	−1.63040	−0.0714291	−0.0357145	−	0.999362i	$-0.511371\pi$
$521$	−1.63040	−0.0714291	−0.0357145	+	0.999362i	$0.511371\pi$
$522$	2.96095	0.129597
$523$	24.1933	1.05790	0.528950	−	0.848653i	$-0.322586\pi$
$523$	24.1933	1.05790	0.528950	+	0.848653i	$0.322586\pi$
$524$	13.3687	0.584014
$525$	11.9361	0.520934
$526$	−17.9304	−0.781802
$527$	4.91036	0.213899
$528$	47.4896	2.06672
$529$	21.1080	0.917739
$530$	−42.6923	−1.85444
$531$	−51.0686	−2.21619
$532$	−14.2476	−0.617710
$533$	−1.39274	−0.0603263
$534$	63.5040	2.74809
$535$	−40.4829	−1.75023
$536$	−5.28767	−0.228393
$537$	30.7262	1.32593
$538$	35.5521	1.53276
$539$	−5.61700	−0.241941
$540$	19.6475	0.845493
$541$	−31.0386	−1.33445	−0.667227	−	0.744854i	$-0.732519\pi$
$541$	−31.0386	−1.33445	−0.667227	+	0.744854i	$0.732519\pi$
$542$	26.1819	1.12461
$543$	−59.0813	−2.53542
$544$	−9.94018	−0.426182
$545$	39.6816	1.69977
$546$	−3.99398	−0.170927
$547$	22.3141	0.954082	0.477041	−	0.878881i	$-0.341709\pi$
$547$	22.3141	0.954082	0.477041	+	0.878881i	$0.341709\pi$
$548$	−15.9502	−0.681360
$549$	44.2095	1.88682
$550$	52.7295	2.24839
$551$	2.14359	0.0913201
$552$	12.6756	0.539511
$553$	−10.6843	−0.454344
$554$	−47.5191	−2.01890
$555$	−82.5539	−3.50422
$556$	11.0966	0.470600
$557$	−7.51116	−0.318258	−0.159129	−	0.987258i	$-0.550869\pi$
$557$	−7.51116	−0.318258	−0.159129	+	0.987258i	$0.550869\pi$
$558$	33.5312	1.41949
$559$	−5.93460	−0.251007
$560$	−9.83337	−0.415536
$561$	18.2938	0.772366
$562$	−12.1143	−0.511011
$563$	−1.01163	−0.0426353	−0.0213176	−	0.999773i	$-0.506786\pi$
$563$	−1.01163	−0.0426353	−0.0213176	+	0.999773i	$0.506786\pi$
$564$	1.29643	0.0545894
$565$	41.8805	1.76193
$566$	−61.2502	−2.57454
$567$	−4.87327	−0.204658
$568$	−3.89744	−0.163533
$569$	4.03837	0.169297	0.0846486	−	0.996411i	$-0.473023\pi$
$569$	4.03837	0.169297	0.0846486	+	0.996411i	$0.473023\pi$
$570$	103.467	4.33375
$571$	17.5472	0.734326	0.367163	−	0.930157i	$-0.380329\pi$
$571$	17.5472	0.734326	0.367163	+	0.930157i	$0.380329\pi$
$572$	−9.52329	−0.398189
$573$	−4.60036	−0.192183
$574$	4.01631	0.167638
$575$	−29.9083	−1.24726
$576$	−42.1988	−1.75828
$577$	−42.6617	−1.77603	−0.888014	−	0.459816i	$-0.847915\pi$
$577$	−42.6617	−1.77603	−0.888014	+	0.459816i	$0.847915\pi$
$578$	32.2903	1.34310
$579$	−48.0536	−1.99704
$580$	−2.55144	−0.105943
$581$	1.13591	0.0471255
$582$	−77.3326	−3.20554
$583$	−37.3164	−1.54549
$584$	−5.55877	−0.230024
$585$	8.96988	0.370859
$586$	−2.36561	−0.0977223
$587$	−4.66801	−0.192669	−0.0963347	−	0.995349i	$-0.530712\pi$
$587$	−4.66801	−0.192669	−0.0963347	+	0.995349i	$0.530712\pi$
$588$	6.21660	0.256368
$589$	24.2751	1.00024
$590$	81.5302	3.35655
$591$	45.2689	1.86211
$592$	32.2281	1.32457
$593$	30.7826	1.26409	0.632046	−	0.774931i	$-0.282216\pi$
$593$	30.7826	1.26409	0.632046	+	0.774931i	$0.282216\pi$
$594$	31.8176	1.30549
$595$	−3.78798	−0.155292
$596$	−8.02769	−0.328827
$597$	17.9291	0.733790
$598$	10.0077	0.409246
$599$	−27.5742	−1.12665	−0.563325	−	0.826236i	$-0.690478\pi$
$599$	−27.5742	−1.12665	−0.563325	+	0.826236i	$0.690478\pi$
$600$	−8.59496	−0.350888
$601$	1.80916	0.0737970	0.0368985	−	0.999319i	$-0.488252\pi$
$601$	1.80916	0.0737970	0.0368985	+	0.999319i	$0.488252\pi$
$602$	17.1139	0.697510
$603$	29.5579	1.20369
$604$	−17.6643	−0.718750
$605$	63.3525	2.57564
$606$	48.9715	1.98933
$607$	−23.4115	−0.950244	−0.475122	−	0.879920i	$-0.657596\pi$
$607$	−23.4115	−0.950244	−0.475122	+	0.879920i	$0.657596\pi$
$608$	−49.1407	−1.99292
$609$	−0.935308	−0.0379006
$610$	−70.5799	−2.85769
$611$	0.150749	0.00609865
$612$	−11.6007	−0.468929
$613$	13.9999	0.565449	0.282724	−	0.959201i	$-0.408762\pi$
$613$	13.9999	0.565449	0.282724	+	0.959201i	$0.408762\pi$
$614$	−4.68468	−0.189058
$615$	−15.7427	−0.634806
$616$	4.04469	0.162965
$617$	24.8500	1.00042	0.500211	−	0.865904i	$-0.333256\pi$
$617$	24.8500	1.00042	0.500211	+	0.865904i	$0.333256\pi$
$618$	24.8769	1.00069
$619$	9.78358	0.393235	0.196618	−	0.980480i	$-0.437004\pi$
$619$	9.78358	0.393235	0.196618	+	0.980480i	$0.437004\pi$
$620$	−28.8938	−1.16040
$621$	−18.0470	−0.724201
$622$	−54.1308	−2.17045
$623$	−11.4936	−0.460480
$624$	−6.11159	−0.244659
$625$	−27.2367	−1.08947
$626$	−67.0927	−2.68157
$627$	90.4381	3.61175
$628$	−9.45966	−0.377481
$629$	12.4148	0.495011
$630$	−25.8669	−1.03056
$631$	7.23651	0.288081	0.144041	−	0.989572i	$-0.453990\pi$
$631$	7.23651	0.288081	0.144041	+	0.989572i	$0.453990\pi$
$632$	7.69358	0.306034
$633$	5.90440	0.234679
$634$	−51.6136	−2.04984
$635$	−8.18253	−0.324714
$636$	41.2999	1.63765
$637$	0.722869	0.0286411
$638$	−4.13186	−0.163582
$639$	21.7865	0.861861
$640$	17.4937	0.691500
$641$	−42.4232	−1.67562	−0.837808	−	0.545966i	$-0.816163\pi$
$641$	−42.4232	−1.67562	−0.837808	+	0.545966i	$0.816163\pi$
$642$	72.5571	2.86360
$643$	−9.31864	−0.367491	−0.183746	−	0.982974i	$-0.558822\pi$
$643$	−9.31864	−0.367491	−0.183746	+	0.982974i	$0.558822\pi$
$644$	−15.5769	−0.613817
$645$	−67.0810	−2.64131
$646$	−15.5598	−0.612193
$647$	37.4901	1.47389	0.736944	−	0.675954i	$-0.236268\pi$
$647$	37.4901	1.47389	0.736944	+	0.675954i	$0.236268\pi$
$648$	3.50915	0.137852
$649$	71.2638	2.79735
$650$	−6.78592	−0.266166
$651$	−10.5919	−0.415129
$652$	19.4114	0.760208
$653$	−10.1529	−0.397314	−0.198657	−	0.980069i	$-0.563658\pi$
$653$	−10.1529	−0.397314	−0.198657	+	0.980069i	$0.563658\pi$
$654$	−71.1211	−2.78105
$655$	17.5713	0.686567
$656$	6.14576	0.239951
$657$	31.0733	1.21229
$658$	−0.434722	−0.0169472
$659$	−13.9753	−0.544402	−0.272201	−	0.962240i	$-0.587752\pi$
$659$	−13.9753	−0.544402	−0.272201	+	0.962240i	$0.587752\pi$
$660$	−107.645	−4.19009
$661$	−37.1833	−1.44626	−0.723132	−	0.690710i	$-0.757298\pi$
$661$	−37.1833	−1.44626	−0.723132	+	0.690710i	$0.757298\pi$
$662$	−23.7005	−0.921146
$663$	−2.35429	−0.0914330
$664$	−0.817947	−0.0317425
$665$	−18.7264	−0.726180
$666$	84.7766	3.28503
$667$	2.34360	0.0907445
$668$	−10.1792	−0.393844
$669$	−24.2085	−0.935953
$670$	−47.1887	−1.82306
$671$	−61.6923	−2.38160
$672$	21.4414	0.827121
$673$	−2.48096	−0.0956338	−0.0478169	−	0.998856i	$-0.515226\pi$
$673$	−2.48096	−0.0956338	−0.0478169	+	0.998856i	$0.515226\pi$
$674$	−60.7953	−2.34175
$675$	12.2371	0.471007
$676$	−29.2651	−1.12558
$677$	−3.38167	−0.129968	−0.0649840	−	0.997886i	$-0.520700\pi$
$677$	−3.38167	−0.129968	−0.0649840	+	0.997886i	$0.520700\pi$
$678$	−75.0621	−2.88274
$679$	13.9964	0.537132
$680$	2.72765	0.104601
$681$	2.42201	0.0928116
$682$	−46.7912	−1.79173
$683$	23.6991	0.906822	0.453411	−	0.891302i	$-0.350207\pi$
$683$	23.6991	0.906822	0.453411	+	0.891302i	$0.350207\pi$
$684$	−57.3495	−2.19281
$685$	−20.9644	−0.801007
$686$	−2.08457	−0.0795893
$687$	29.2643	1.11650
$688$	26.1877	0.998395
$689$	4.80236	0.182956
$690$	113.121	4.30644
$691$	14.4805	0.550864	0.275432	−	0.961321i	$-0.411179\pi$
$691$	14.4805	0.550864	0.275432	+	0.961321i	$0.411179\pi$
$692$	38.6661	1.46987
$693$	−22.6096	−0.858869
$694$	68.7067	2.60807
$695$	14.5849	0.553237
$696$	0.673497	0.0255288
$697$	2.36745	0.0896736
$698$	−4.70353	−0.178031
$699$	7.24298	0.273955
$700$	10.5622	0.399215
$701$	−40.5712	−1.53235	−0.766176	−	0.642631i	$-0.777843\pi$
$701$	−40.5712	−1.53235	−0.766176	+	0.642631i	$0.777843\pi$
$702$	−4.09470	−0.154545
$703$	61.3744	2.31478
$704$	58.8864	2.21936
$705$	1.70397	0.0641753
$706$	21.7776	0.819610
$707$	−8.86333	−0.333340
$708$	−78.8710	−2.96415
$709$	11.6053	0.435848	0.217924	−	0.975966i	$-0.430072\pi$
$709$	11.6053	0.435848	0.217924	+	0.975966i	$0.430072\pi$
$710$	−34.7818	−1.30534
$711$	−43.0068	−1.61288
$712$	8.27629	0.310167
$713$	26.5401	0.993933
$714$	6.78917	0.254078
$715$	−12.5170	−0.468111
$716$	27.1895	1.01612
$717$	15.1012	0.563963
$718$	21.9979	0.820955
$719$	−27.4890	−1.02517	−0.512583	−	0.858638i	$-0.671311\pi$
$719$	−27.4890	−1.02517	−0.512583	+	0.858638i	$0.671311\pi$
$720$	−39.5815	−1.47511
$721$	−4.50246	−0.167680
$722$	−37.3153	−1.38873
$723$	−12.7100	−0.472689
$724$	−52.2809	−1.94300
$725$	−1.58912	−0.0590185
$726$	−113.546	−4.21409
$727$	−35.5877	−1.31988	−0.659938	−	0.751320i	$-0.729418\pi$
$727$	−35.5877	−1.31988	−0.659938	+	0.751320i	$0.729418\pi$
$728$	−0.520524	−0.0192919
$729$	−41.2231	−1.52678
$730$	−49.6081	−1.83608
$731$	10.0879	0.373116
$732$	68.2778	2.52362
$733$	18.4849	0.682756	0.341378	−	0.939926i	$-0.389106\pi$
$733$	18.4849	0.682756	0.341378	+	0.939926i	$0.389106\pi$
$734$	−52.1355	−1.92436
$735$	8.17086	0.301387
$736$	−53.7258	−1.98036
$737$	−41.2466	−1.51934
$738$	16.1665	0.595098
$739$	28.3980	1.04464	0.522318	−	0.852751i	$-0.325067\pi$
$739$	28.3980	1.04464	0.522318	+	0.852751i	$0.325067\pi$
$740$	−73.0518	−2.68544
$741$	−11.6388	−0.427561
$742$	−13.8488	−0.508405
$743$	−31.4772	−1.15479	−0.577394	−	0.816466i	$-0.695930\pi$
$743$	−31.4772	−1.15479	−0.577394	+	0.816466i	$0.695930\pi$
$744$	7.62701	0.279620
$745$	−10.5513	−0.386569
$746$	−10.8231	−0.396263
$747$	4.57229	0.167291
$748$	16.1882	0.591898
$749$	−13.1321	−0.479836
$750$	8.45981	0.308909
$751$	−29.0073	−1.05849	−0.529245	−	0.848469i	$-0.677525\pi$
$751$	−29.0073	−1.05849	−0.529245	+	0.848469i	$0.677525\pi$
$752$	−0.665211	−0.0242577
$753$	−76.9752	−2.80513
$754$	0.531742	0.0193649
$755$	−23.2172	−0.844962
$756$	6.37337	0.231797
$757$	10.7882	0.392105	0.196053	−	0.980593i	$-0.437188\pi$
$757$	10.7882	0.392105	0.196053	+	0.980593i	$0.437188\pi$
$758$	−55.7784	−2.02596
$759$	98.8764	3.58899
$760$	13.4845	0.489136
$761$	−39.6849	−1.43858	−0.719288	−	0.694712i	$-0.755532\pi$
$761$	−39.6849	−1.43858	−0.719288	+	0.694712i	$0.755532\pi$
$762$	14.6655	0.531275
$763$	12.8722	0.466004
$764$	−4.07085	−0.147278
$765$	−15.2475	−0.551273
$766$	69.7277	2.51936
$767$	−9.17115	−0.331151
$768$	24.2200	0.873963
$769$	−43.0573	−1.55268	−0.776342	−	0.630312i	$-0.782927\pi$
$769$	−43.0573	−1.55268	−0.776342	+	0.630312i	$0.782927\pi$
$770$	36.0960	1.30081
$771$	−37.1968	−1.33961
$772$	−42.5225	−1.53042
$773$	−12.2911	−0.442080	−0.221040	−	0.975265i	$-0.570945\pi$
$773$	−12.2911	−0.442080	−0.221040	+	0.975265i	$0.570945\pi$
$774$	68.8871	2.47610
$775$	−17.9960	−0.646436
$776$	−10.0785	−0.361798
$777$	−26.7793	−0.960703
$778$	−50.8198	−1.82198
$779$	11.7038	0.419333
$780$	13.8532	0.496024
$781$	−30.4020	−1.08787
$782$	−17.0116	−0.608334
$783$	−0.958895	−0.0342681
$784$	−3.18981	−0.113922
$785$	−12.4334	−0.443767
$786$	−31.4929	−1.12331
$787$	−10.0763	−0.359180	−0.179590	−	0.983742i	$-0.557477\pi$
$787$	−10.0763	−0.359180	−0.179590	+	0.983742i	$0.557477\pi$
$788$	40.0583	1.42702
$789$	22.7983	0.811642
$790$	68.6597	2.44280
$791$	13.5855	0.483043
$792$	16.2808	0.578512
$793$	7.93937	0.281935
$794$	22.3355	0.792656
$795$	54.2829	1.92522
$796$	15.8654	0.562336
$797$	1.32176	0.0468191	0.0234095	−	0.999726i	$-0.492548\pi$
$797$	1.32176	0.0468191	0.0234095	+	0.999726i	$0.492548\pi$
$798$	33.5632	1.18813
$799$	−0.256251	−0.00906550
$800$	36.4298	1.28799
$801$	−46.2641	−1.63466
$802$	44.8184	1.58259
$803$	−43.3613	−1.53019
$804$	45.6496	1.60994
$805$	−20.4737	−0.721603
$806$	6.02170	0.212106
$807$	−45.2041	−1.59126
$808$	6.38231	0.224529
$809$	−15.8799	−0.558307	−0.279154	−	0.960246i	$-0.590054\pi$
$809$	−15.8799	−0.558307	−0.279154	+	0.960246i	$0.590054\pi$
$810$	31.3166	1.10035
$811$	7.14988	0.251066	0.125533	−	0.992089i	$-0.459936\pi$
$811$	7.14988	0.251066	0.125533	+	0.992089i	$0.459936\pi$
$812$	−0.827652	−0.0290449
$813$	−33.2901	−1.16753
$814$	−118.302	−4.14647
$815$	25.5135	0.893700
$816$	10.3888	0.363680
$817$	49.8712	1.74477
$818$	−68.4688	−2.39395
$819$	2.90971	0.101673
$820$	−13.9307	−0.486480
$821$	−8.64615	−0.301753	−0.150876	−	0.988553i	$-0.548210\pi$
$821$	−8.64615	−0.301753	−0.150876	+	0.988553i	$0.548210\pi$
$822$	37.5742	1.31055
$823$	−44.8529	−1.56347	−0.781737	−	0.623608i	$-0.785666\pi$
$823$	−44.8529	−1.56347	−0.781737	+	0.623608i	$0.785666\pi$
$824$	3.24213	0.112945
$825$	−67.0451	−2.33421
$826$	26.4473	0.920218
$827$	30.7827	1.07042	0.535209	−	0.844720i	$-0.320233\pi$
$827$	30.7827	1.07042	0.535209	+	0.844720i	$0.320233\pi$
$828$	−62.7005	−2.17899
$829$	−17.6866	−0.614281	−0.307140	−	0.951664i	$-0.599372\pi$
$829$	−17.6866	−0.614281	−0.307140	+	0.951664i	$0.599372\pi$
$830$	−7.29959	−0.253373
$831$	60.4202	2.09595
$832$	−7.57827	−0.262729
$833$	−1.22877	−0.0425743
$834$	−26.1404	−0.905169
$835$	−13.3791	−0.463003
$836$	80.0285	2.76784
$837$	−10.8590	−0.375342
$838$	43.9997	1.51994
$839$	−12.1794	−0.420479	−0.210240	−	0.977650i	$-0.567424\pi$
$839$	−12.1794	−0.420479	−0.210240	+	0.977650i	$0.567424\pi$
$840$	−5.88367	−0.203006
$841$	−28.8755	−0.995706
$842$	74.0417	2.55165
$843$	15.4032	0.530515
$844$	5.22479	0.179845
$845$	−38.4648	−1.32323
$846$	−1.74985	−0.0601611
$847$	20.5507	0.706129
$848$	−21.1914	−0.727717
$849$	77.8791	2.67281
$850$	11.5351	0.395649
$851$	67.1009	2.30019
$852$	33.6474	1.15274
$853$	18.1192	0.620390	0.310195	−	0.950673i	$-0.399606\pi$
$853$	18.1192	0.620390	0.310195	+	0.950673i	$0.399606\pi$
$854$	−22.8951	−0.783455
$855$	−75.3780	−2.57787
$856$	9.45615	0.323205
$857$	5.79054	0.197801	0.0989005	−	0.995097i	$-0.468467\pi$
$857$	5.79054	0.197801	0.0989005	+	0.995097i	$0.468467\pi$
$858$	22.4342	0.765890
$859$	1.00000	0.0341196
$859$	1.00000	0.0341196
$860$	−59.3598	−2.02415
$861$	−5.10670	−0.174036
$862$	25.5975	0.871855
$863$	−15.3837	−0.523669	−0.261834	−	0.965113i	$-0.584327\pi$
$863$	−15.3837	−0.523669	−0.261834	+	0.965113i	$0.584327\pi$
$864$	21.9821	0.747848
$865$	50.8212	1.72797
$866$	−71.9905	−2.44634
$867$	−41.0568	−1.39436
$868$	−9.37274	−0.318131
$869$	60.0139	2.03583
$870$	6.01048	0.203774
$871$	5.30815	0.179860
$872$	−9.26899	−0.313888
$873$	56.3385	1.90677
$874$	−84.0993	−2.84470
$875$	−1.53114	−0.0517619
$876$	47.9900	1.62143
$877$	−13.5572	−0.457794	−0.228897	−	0.973451i	$-0.573512\pi$
$877$	−13.5572	−0.457794	−0.228897	+	0.973451i	$0.573512\pi$
$878$	22.5311	0.760386
$879$	3.00785	0.101452
$880$	55.2340	1.86194
$881$	−54.6738	−1.84201	−0.921004	−	0.389554i	$-0.872629\pi$
$881$	−54.6738	−1.84201	−0.921004	+	0.389554i	$0.872629\pi$
$882$	−8.39085	−0.282535
$883$	−35.3660	−1.19016	−0.595081	−	0.803666i	$-0.702880\pi$
$883$	−35.3660	−1.19016	−0.595081	+	0.803666i	$0.702880\pi$
$884$	−2.08331	−0.0700692
$885$	−103.665	−3.48466
$886$	−48.4788	−1.62868
$887$	−4.44096	−0.149113	−0.0745564	−	0.997217i	$-0.523754\pi$
$887$	−4.44096	−0.149113	−0.0745564	+	0.997217i	$0.523754\pi$
$888$	19.2833	0.647104
$889$	−2.65430	−0.0890224
$890$	73.8600	2.47579
$891$	27.3732	0.917035
$892$	−21.4220	−0.717262
$893$	−1.26681	−0.0423922
$894$	18.9110	0.632478
$895$	35.7369	1.19455
$896$	5.67472	0.189579
$897$	−12.7247	−0.424866
$898$	−0.994065	−0.0331724
$899$	1.41016	0.0470314
$900$	42.5153	1.41718
$901$	−8.16330	−0.271959
$902$	−22.5596	−0.751153
$903$	−21.7601	−0.724132
$904$	−9.78262	−0.325365
$905$	−68.7160	−2.28420
$906$	41.6121	1.38247
$907$	18.4563	0.612831	0.306415	−	0.951898i	$-0.400870\pi$
$907$	18.4563	0.612831	0.306415	+	0.951898i	$0.400870\pi$
$908$	2.14323	0.0711256
$909$	−35.6768	−1.18333
$910$	−4.64530	−0.153990
$911$	−50.0783	−1.65917	−0.829584	−	0.558382i	$-0.811422\pi$
$911$	−50.0783	−1.65917	−0.829584	+	0.558382i	$0.811422\pi$
$912$	51.3585	1.70065
$913$	−6.38041	−0.211161
$914$	−32.4951	−1.07484
$915$	89.7417	2.96677
$916$	25.8959	0.855624
$917$	5.69988	0.188227
$918$	6.96038	0.229727
$919$	4.12329	0.136015	0.0680074	−	0.997685i	$-0.478336\pi$
$919$	4.12329	0.136015	0.0680074	+	0.997685i	$0.478336\pi$
$920$	14.7427	0.486053
$921$	5.95654	0.196275
$922$	−28.1858	−0.928249
$923$	3.91253	0.128783
$924$	−34.9186	−1.14874
$925$	−45.4991	−1.49600
$926$	−14.1927	−0.466402
$927$	−18.1234	−0.595249
$928$	−2.85462	−0.0937076
$929$	−42.9802	−1.41013	−0.705067	−	0.709140i	$-0.749083\pi$
$929$	−42.9802	−1.41013	−0.705067	+	0.709140i	$0.749083\pi$
$930$	68.0656	2.23196
$931$	−6.07460	−0.199087
$932$	6.40930	0.209943
$933$	68.8268	2.25329
$934$	12.0560	0.394484
$935$	21.2771	0.695835
$936$	−2.09522	−0.0684845
$937$	34.7055	1.13378	0.566889	−	0.823794i	$-0.308147\pi$
$937$	34.7055	1.13378	0.566889	+	0.823794i	$0.308147\pi$
$938$	−15.3074	−0.499803
$939$	85.3078	2.78392
$940$	1.50784	0.0491803
$941$	−39.8762	−1.29993	−0.649963	−	0.759966i	$-0.725216\pi$
$941$	−39.8762	−1.29993	−0.649963	+	0.759966i	$0.725216\pi$
$942$	22.2843	0.726061
$943$	12.7959	0.416690
$944$	40.4696	1.31717
$945$	8.37691	0.272501
$946$	−96.1286	−3.12541
$947$	−34.9148	−1.13458	−0.567289	−	0.823519i	$-0.692008\pi$
$947$	−34.9148	−1.13458	−0.567289	+	0.823519i	$0.692008\pi$
$948$	−66.4203	−2.15723
$949$	5.58030	0.181144
$950$	57.0252	1.85014
$951$	65.6263	2.12808
$952$	0.884813	0.0286769
$953$	2.69044	0.0871519	0.0435760	−	0.999050i	$-0.486125\pi$
$953$	2.69044	0.0871519	0.0435760	+	0.999050i	$0.486125\pi$
$954$	−55.7444	−1.80479
$955$	−5.35056	−0.173140
$956$	13.3630	0.432190
$957$	5.25362	0.169826
$958$	13.2862	0.429257
$959$	−6.80055	−0.219601
$960$	−85.6600	−2.76466
$961$	−15.0307	−0.484860
$962$	15.2246	0.490861
$963$	−52.8595	−1.70337
$964$	−11.2470	−0.362242
$965$	−55.8899	−1.79916
$966$	36.6948	1.18064
$967$	−50.3684	−1.61974	−0.809870	−	0.586609i	$-0.800462\pi$
$967$	−50.3684	−1.61974	−0.809870	+	0.586609i	$0.800462\pi$
$968$	−14.7981	−0.475630
$969$	19.7842	0.635559
$970$	−89.9436	−2.88792
$971$	−47.3251	−1.51873	−0.759367	−	0.650662i	$-0.774491\pi$
$971$	−47.3251	−1.51873	−0.759367	+	0.650662i	$0.774491\pi$
$972$	−49.4153	−1.58500
$973$	4.73114	0.151674
$974$	27.8762	0.893213
$975$	8.62824	0.276325
$976$	−35.0341	−1.12141
$977$	−42.9185	−1.37308	−0.686542	−	0.727090i	$-0.740872\pi$
$977$	−42.9185	−1.37308	−0.686542	+	0.727090i	$0.740872\pi$
$978$	−45.7277	−1.46221
$979$	64.5593	2.06333
$980$	7.23037	0.230966
$981$	51.8133	1.65427
$982$	−42.1899	−1.34633
$983$	34.2399	1.09208	0.546041	−	0.837758i	$-0.316134\pi$
$983$	34.2399	1.09208	0.546041	+	0.837758i	$0.316134\pi$
$984$	3.67724	0.117226
$985$	52.6511	1.67760
$986$	−0.903882	−0.0287855
$987$	0.552745	0.0175941
$988$	−10.2991	−0.327659
$989$	54.5244	1.73377
$990$	145.294	4.61775
$991$	10.1436	0.322221	0.161111	−	0.986936i	$-0.448492\pi$
$991$	10.1436	0.322221	0.161111	+	0.986936i	$0.448492\pi$
$992$	−32.3271	−1.02639
$993$	30.1350	0.956304
$994$	−11.2827	−0.357867
$995$	20.8529	0.661082
$996$	7.06151	0.223752
$997$	−16.1572	−0.511703	−0.255851	−	0.966716i	$-0.582356\pi$
$997$	−16.1572	−0.511703	−0.255851	+	0.966716i	$0.582356\pi$
$998$	39.4801	1.24972
$999$	−27.4547	−0.868627

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6013.2.a.d.1.20	✓	104

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6013.2.a.d.1.20	✓	104	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 6013 = 7 \cdot 859 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6013.a (trivial)

\(f(q)\)	\(=\)	\(q-2.08457 q^{2} +2.65051 q^{3} +2.34543 q^{4} +3.08275 q^{5} -5.52518 q^{6} +1.00000 q^{7} -0.720080 q^{8} +4.02522 q^{9} +O(q^{10})\)	\(q-2.08457 q^{2} +2.65051 q^{3} +2.34543 q^{4} +3.08275 q^{5} -5.52518 q^{6} +1.00000 q^{7} -0.720080 q^{8} +4.02522 q^{9} -6.42620 q^{10} -5.61700 q^{11} +6.21660 q^{12} +0.722869 q^{13} -2.08457 q^{14} +8.17086 q^{15} -3.18981 q^{16} -1.22877 q^{17} -8.39085 q^{18} -6.07460 q^{19} +7.23037 q^{20} +2.65051 q^{21} +11.7090 q^{22} -6.64138 q^{23} -1.90858 q^{24} +4.50332 q^{25} -1.50687 q^{26} +2.71735 q^{27} +2.34543 q^{28} -0.352878 q^{29} -17.0327 q^{30} -3.99616 q^{31} +8.08954 q^{32} -14.8879 q^{33} +2.56146 q^{34} +3.08275 q^{35} +9.44088 q^{36} -10.1035 q^{37} +12.6629 q^{38} +1.91597 q^{39} -2.21982 q^{40} -1.92668 q^{41} -5.52518 q^{42} -8.20979 q^{43} -13.1743 q^{44} +12.4087 q^{45} +13.8444 q^{46} +0.208543 q^{47} -8.45463 q^{48} +1.00000 q^{49} -9.38749 q^{50} -3.25687 q^{51} +1.69544 q^{52} +6.64348 q^{53} -5.66452 q^{54} -17.3158 q^{55} -0.720080 q^{56} -16.1008 q^{57} +0.735599 q^{58} -12.6872 q^{59} +19.1642 q^{60} +10.9831 q^{61} +8.33029 q^{62} +4.02522 q^{63} -10.4836 q^{64} +2.22842 q^{65} +31.0349 q^{66} +7.34317 q^{67} -2.88200 q^{68} -17.6031 q^{69} -6.42620 q^{70} +5.41250 q^{71} -2.89848 q^{72} +7.71966 q^{73} +21.0614 q^{74} +11.9361 q^{75} -14.2476 q^{76} -5.61700 q^{77} -3.99398 q^{78} -10.6843 q^{79} -9.83337 q^{80} -4.87327 q^{81} +4.01631 q^{82} +1.13591 q^{83} +6.21660 q^{84} -3.78798 q^{85} +17.1139 q^{86} -0.935308 q^{87} +4.04469 q^{88} -11.4936 q^{89} -25.8669 q^{90} +0.722869 q^{91} -15.5769 q^{92} -10.5919 q^{93} -0.434722 q^{94} -18.7264 q^{95} +21.4414 q^{96} +13.9964 q^{97} -2.08457 q^{98} -22.6096 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 104 q - 17 q^{2} - 34 q^{3} + 99 q^{4} - 46 q^{5} - 18 q^{6} + 104 q^{7} - 48 q^{8} + 98 q^{9}+O(q^{10}) \) 104 * q - 17 * q^2 - 34 * q^3 + 99 * q^4 - 46 * q^5 - 18 * q^6 + 104 * q^7 - 48 * q^8 + 98 * q^9	\( 104 q - 17 q^{2} - 34 q^{3} + 99 q^{4} - 46 q^{5} - 18 q^{6} + 104 q^{7} - 48 q^{8} + 98 q^{9} - 17 q^{10} - 46 q^{11} - 62 q^{12} - 37 q^{13} - 17 q^{14} - 17 q^{15} + 93 q^{16} - 75 q^{17} - 41 q^{18} - 40 q^{19} - 106 q^{20} - 34 q^{21} - 14 q^{22} - 57 q^{23} - 38 q^{24} + 102 q^{25} - 45 q^{26} - 121 q^{27} + 99 q^{28} - 29 q^{29} + 26 q^{30} - 42 q^{31} - 113 q^{32} - 42 q^{33} - 7 q^{34} - 46 q^{35} + 99 q^{36} - 31 q^{37} - 62 q^{38} - 9 q^{39} - 36 q^{40} - 106 q^{41} - 18 q^{42} - 29 q^{43} - 60 q^{44} - 121 q^{45} + 21 q^{46} - 141 q^{47} - 88 q^{48} + 104 q^{49} - 70 q^{50} - 2 q^{51} - 58 q^{52} - 70 q^{53} - 49 q^{54} - 14 q^{55} - 48 q^{56} - 11 q^{57} - 28 q^{58} - 202 q^{59} + 17 q^{60} - 79 q^{61} - 41 q^{62} + 98 q^{63} + 110 q^{64} - 34 q^{65} - 21 q^{66} - 57 q^{67} - 180 q^{68} - 99 q^{69} - 17 q^{70} - 109 q^{71} - 73 q^{72} - 46 q^{73} - 7 q^{74} - 146 q^{75} - 54 q^{76} - 46 q^{77} - 42 q^{78} - 12 q^{79} - 187 q^{80} + 100 q^{81} - 45 q^{82} - 156 q^{83} - 62 q^{84} - 13 q^{85} - 8 q^{86} - 76 q^{87} - 6 q^{88} - 140 q^{89} - 5 q^{90} - 37 q^{91} - 98 q^{92} - q^{93} - 17 q^{94} - 48 q^{95} - 12 q^{96} - 63 q^{97} - 17 q^{98} - 78 q^{99}+O(q^{100}) \) 104 * q - 17 * q^2 - 34 * q^3 + 99 * q^4 - 46 * q^5 - 18 * q^6 + 104 * q^7 - 48 * q^8 + 98 * q^9 - 17 * q^10 - 46 * q^11 - 62 * q^12 - 37 * q^13 - 17 * q^14 - 17 * q^15 + 93 * q^16 - 75 * q^17 - 41 * q^18 - 40 * q^19 - 106 * q^20 - 34 * q^21 - 14 * q^22 - 57 * q^23 - 38 * q^24 + 102 * q^25 - 45 * q^26 - 121 * q^27 + 99 * q^28 - 29 * q^29 + 26 * q^30 - 42 * q^31 - 113 * q^32 - 42 * q^33 - 7 * q^34 - 46 * q^35 + 99 * q^36 - 31 * q^37 - 62 * q^38 - 9 * q^39 - 36 * q^40 - 106 * q^41 - 18 * q^42 - 29 * q^43 - 60 * q^44 - 121 * q^45 + 21 * q^46 - 141 * q^47 - 88 * q^48 + 104 * q^49 - 70 * q^50 - 2 * q^51 - 58 * q^52 - 70 * q^53 - 49 * q^54 - 14 * q^55 - 48 * q^56 - 11 * q^57 - 28 * q^58 - 202 * q^59 + 17 * q^60 - 79 * q^61 - 41 * q^62 + 98 * q^63 + 110 * q^64 - 34 * q^65 - 21 * q^66 - 57 * q^67 - 180 * q^68 - 99 * q^69 - 17 * q^70 - 109 * q^71 - 73 * q^72 - 46 * q^73 - 7 * q^74 - 146 * q^75 - 54 * q^76 - 46 * q^77 - 42 * q^78 - 12 * q^79 - 187 * q^80 + 100 * q^81 - 45 * q^82 - 156 * q^83 - 62 * q^84 - 13 * q^85 - 8 * q^86 - 76 * q^87 - 6 * q^88 - 140 * q^89 - 5 * q^90 - 37 * q^91 - 98 * q^92 - q^93 - 17 * q^94 - 48 * q^95 - 12 * q^96 - 63 * q^97 - 17 * q^98 - 78 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more