LMFDB - Embedded newform 4017.2.a.i.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4017,2,Mod(1,4017)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4017, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("4017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4017 = 3 \cdot 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4017.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:	$32.0759064919$
Analytic rank:	$1$
Dimension:	$25$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	4017.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.46693 q^{2} -1.00000 q^{3} +0.151895 q^{4} +0.636277 q^{5} -1.46693 q^{6} -0.403322 q^{7} -2.71105 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.46693 q^{2} -1.00000 q^{3} +0.151895 q^{4} +0.636277 q^{5} -1.46693 q^{6} -0.403322 q^{7} -2.71105 q^{8} +1.00000 q^{9} +0.933377 q^{10} -2.09764 q^{11} -0.151895 q^{12} -1.00000 q^{13} -0.591647 q^{14} -0.636277 q^{15} -4.28072 q^{16} +4.83658 q^{17} +1.46693 q^{18} +6.09893 q^{19} +0.0966476 q^{20} +0.403322 q^{21} -3.07710 q^{22} +5.96335 q^{23} +2.71105 q^{24} -4.59515 q^{25} -1.46693 q^{26} -1.00000 q^{27} -0.0612628 q^{28} -6.27177 q^{29} -0.933377 q^{30} -6.81119 q^{31} -0.857437 q^{32} +2.09764 q^{33} +7.09495 q^{34} -0.256625 q^{35} +0.151895 q^{36} -0.367471 q^{37} +8.94673 q^{38} +1.00000 q^{39} -1.72498 q^{40} +10.6748 q^{41} +0.591647 q^{42} -1.76138 q^{43} -0.318622 q^{44} +0.636277 q^{45} +8.74784 q^{46} -3.63775 q^{47} +4.28072 q^{48} -6.83733 q^{49} -6.74078 q^{50} -4.83658 q^{51} -0.151895 q^{52} +0.519483 q^{53} -1.46693 q^{54} -1.33468 q^{55} +1.09343 q^{56} -6.09893 q^{57} -9.20028 q^{58} -14.6887 q^{59} -0.0966476 q^{60} -12.3873 q^{61} -9.99156 q^{62} -0.403322 q^{63} +7.30363 q^{64} -0.636277 q^{65} +3.07710 q^{66} +3.66993 q^{67} +0.734655 q^{68} -5.96335 q^{69} -0.376452 q^{70} -9.78072 q^{71} -2.71105 q^{72} +0.651127 q^{73} -0.539056 q^{74} +4.59515 q^{75} +0.926400 q^{76} +0.846025 q^{77} +1.46693 q^{78} -10.4242 q^{79} -2.72372 q^{80} +1.00000 q^{81} +15.6592 q^{82} -2.86545 q^{83} +0.0612628 q^{84} +3.07741 q^{85} -2.58383 q^{86} +6.27177 q^{87} +5.68680 q^{88} -17.8464 q^{89} +0.933377 q^{90} +0.403322 q^{91} +0.905806 q^{92} +6.81119 q^{93} -5.33634 q^{94} +3.88061 q^{95} +0.857437 q^{96} +7.51287 q^{97} -10.0299 q^{98} -2.09764 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q - 2 q^{2} - 25 q^{3} + 28 q^{4} - 3 q^{5} + 2 q^{6} - 11 q^{7} - 15 q^{8} + 25 q^{9}+O(q^{10}) $ 25 * q - 2 * q^2 - 25 * q^3 + 28 * q^4 - 3 * q^5 + 2 * q^6 - 11 * q^7 - 15 * q^8 + 25 * q^9	\( 25 q - 2 q^{2} - 25 q^{3} + 28 q^{4} - 3 q^{5} + 2 q^{6} - 11 q^{7} - 15 q^{8} + 25 q^{9} + 2 q^{10} - q^{11} - 28 q^{12} - 25 q^{13} - 12 q^{14} + 3 q^{15} + 26 q^{16} - 10 q^{17} - 2 q^{18} + 22 q^{19} - 2 q^{20} + 11 q^{21} - 5 q^{22} - 49 q^{23} + 15 q^{24} + 22 q^{25} + 2 q^{26} - 25 q^{27} - 30 q^{28} - 22 q^{29} - 2 q^{30} + 8 q^{31} - 12 q^{32} + q^{33} - q^{34} - 2 q^{35} + 28 q^{36} - 26 q^{38} + 25 q^{39} - 22 q^{40} - 5 q^{41} + 12 q^{42} - 13 q^{43} - 25 q^{44} - 3 q^{45} + 13 q^{46} - 56 q^{47} - 26 q^{48} + 28 q^{49} - 31 q^{50} + 10 q^{51} - 28 q^{52} - 20 q^{53} + 2 q^{54} - 14 q^{55} - 22 q^{56} - 22 q^{57} - 21 q^{58} + 2 q^{59} + 2 q^{60} + 29 q^{61} - 39 q^{62} - 11 q^{63} + 21 q^{64} + 3 q^{65} + 5 q^{66} - 14 q^{67} - 60 q^{68} + 49 q^{69} - 31 q^{70} - 36 q^{71} - 15 q^{72} - 30 q^{73} - 64 q^{74} - 22 q^{75} + 38 q^{76} - 37 q^{77} - 2 q^{78} - 29 q^{79} + 25 q^{81} - 6 q^{82} - 17 q^{83} + 30 q^{84} + 3 q^{85} - 27 q^{86} + 22 q^{87} - 81 q^{88} - 38 q^{89} + 2 q^{90} + 11 q^{91} - 85 q^{92} - 8 q^{93} + 26 q^{94} - 71 q^{95} + 12 q^{96} + 19 q^{98} - q^{99}+O(q^{100}) \) 25 * q - 2 * q^2 - 25 * q^3 + 28 * q^4 - 3 * q^5 + 2 * q^6 - 11 * q^7 - 15 * q^8 + 25 * q^9 + 2 * q^10 - q^11 - 28 * q^12 - 25 * q^13 - 12 * q^14 + 3 * q^15 + 26 * q^16 - 10 * q^17 - 2 * q^18 + 22 * q^19 - 2 * q^20 + 11 * q^21 - 5 * q^22 - 49 * q^23 + 15 * q^24 + 22 * q^25 + 2 * q^26 - 25 * q^27 - 30 * q^28 - 22 * q^29 - 2 * q^30 + 8 * q^31 - 12 * q^32 + q^33 - q^34 - 2 * q^35 + 28 * q^36 - 26 * q^38 + 25 * q^39 - 22 * q^40 - 5 * q^41 + 12 * q^42 - 13 * q^43 - 25 * q^44 - 3 * q^45 + 13 * q^46 - 56 * q^47 - 26 * q^48 + 28 * q^49 - 31 * q^50 + 10 * q^51 - 28 * q^52 - 20 * q^53 + 2 * q^54 - 14 * q^55 - 22 * q^56 - 22 * q^57 - 21 * q^58 + 2 * q^59 + 2 * q^60 + 29 * q^61 - 39 * q^62 - 11 * q^63 + 21 * q^64 + 3 * q^65 + 5 * q^66 - 14 * q^67 - 60 * q^68 + 49 * q^69 - 31 * q^70 - 36 * q^71 - 15 * q^72 - 30 * q^73 - 64 * q^74 - 22 * q^75 + 38 * q^76 - 37 * q^77 - 2 * q^78 - 29 * q^79 + 25 * q^81 - 6 * q^82 - 17 * q^83 + 30 * q^84 + 3 * q^85 - 27 * q^86 + 22 * q^87 - 81 * q^88 - 38 * q^89 + 2 * q^90 + 11 * q^91 - 85 * q^92 - 8 * q^93 + 26 * q^94 - 71 * q^95 + 12 * q^96 + 19 * q^98 - q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.46693	1.03728	0.518640	−	0.854993i	$-0.326439\pi$
$2$	1.46693	1.03728	0.518640	+	0.854993i	$0.326439\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	0.151895	0.0759477
$5$	0.636277	0.284552	0.142276	−	0.989827i	$-0.454558\pi$
$5$	0.636277	0.284552	0.142276	+	0.989827i	$0.454558\pi$
$6$	−1.46693	−0.598873
$7$	−0.403322	−0.152442	−0.0762208	−	0.997091i	$-0.524285\pi$
$7$	−0.403322	−0.152442	−0.0762208	+	0.997091i	$0.524285\pi$
$8$	−2.71105	−0.958500
$9$	1.00000	0.333333
$10$	0.933377	0.295160
$11$	−2.09764	−0.632462	−0.316231	−	0.948682i	$-0.602418\pi$
$11$	−2.09764	−0.632462	−0.316231	+	0.948682i	$0.602418\pi$
$12$	−0.151895	−0.0438484
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−0.591647	−0.158124
$15$	−0.636277	−0.164286
$16$	−4.28072	−1.07018
$17$	4.83658	1.17304	0.586522	−	0.809934i	$-0.300497\pi$
$17$	4.83658	1.17304	0.586522	+	0.809934i	$0.300497\pi$
$18$	1.46693	0.345760
$19$	6.09893	1.39919	0.699596	−	0.714539i	$-0.253363\pi$
$19$	6.09893	1.39919	0.699596	+	0.714539i	$0.253363\pi$
$20$	0.0966476	0.0216111
$21$	0.403322	0.0880122
$22$	−3.07710	−0.656040
$23$	5.96335	1.24344	0.621722	−	0.783238i	$-0.286433\pi$
$23$	5.96335	1.24344	0.621722	+	0.783238i	$0.286433\pi$
$24$	2.71105	0.553390
$25$	−4.59515	−0.919030
$26$	−1.46693	−0.287689
$27$	−1.00000	−0.192450
$28$	−0.0612628	−0.0115776
$29$	−6.27177	−1.16464	−0.582319	−	0.812960i	$-0.697855\pi$
$29$	−6.27177	−1.16464	−0.582319	+	0.812960i	$0.697855\pi$
$30$	−0.933377	−0.170411
$31$	−6.81119	−1.22333	−0.611663	−	0.791119i	$-0.709499\pi$
$31$	−6.81119	−1.22333	−0.611663	+	0.791119i	$0.709499\pi$
$32$	−0.857437	−0.151575
$33$	2.09764	0.365152
$34$	7.09495	1.21677
$35$	−0.256625	−0.0433775
$36$	0.151895	0.0253159
$37$	−0.367471	−0.0604119	−0.0302059	−	0.999544i	$-0.509616\pi$
$37$	−0.367471	−0.0604119	−0.0302059	+	0.999544i	$0.509616\pi$
$38$	8.94673	1.45135
$39$	1.00000	0.160128
$40$	−1.72498	−0.272743
$41$	10.6748	1.66712	0.833560	−	0.552429i	$-0.186299\pi$
$41$	10.6748	1.66712	0.833560	+	0.552429i	$0.186299\pi$
$42$	0.591647	0.0912932
$43$	−1.76138	−0.268608	−0.134304	−	0.990940i	$-0.542880\pi$
$43$	−1.76138	−0.268608	−0.134304	+	0.990940i	$0.542880\pi$
$44$	−0.318622	−0.0480341
$45$	0.636277	0.0948506
$46$	8.74784	1.28980
$47$	−3.63775	−0.530620	−0.265310	−	0.964163i	$-0.585474\pi$
$47$	−3.63775	−0.530620	−0.265310	+	0.964163i	$0.585474\pi$
$48$	4.28072	0.617869
$49$	−6.83733	−0.976762
$50$	−6.74078	−0.953291
$51$	−4.83658	−0.677257
$52$	−0.151895	−0.0210641
$53$	0.519483	0.0713565	0.0356783	−	0.999363i	$-0.488641\pi$
$53$	0.519483	0.0713565	0.0356783	+	0.999363i	$0.488641\pi$
$54$	−1.46693	−0.199624
$55$	−1.33468	−0.179968
$56$	1.09343	0.146115
$57$	−6.09893	−0.807823
$58$	−9.20028	−1.20806
$59$	−14.6887	−1.91230	−0.956152	−	0.292872i	$-0.905389\pi$
$59$	−14.6887	−1.91230	−0.956152	+	0.292872i	$0.905389\pi$
$60$	−0.0966476	−0.0124772
$61$	−12.3873	−1.58603	−0.793014	−	0.609203i	$-0.791489\pi$
$61$	−12.3873	−1.58603	−0.793014	+	0.609203i	$0.791489\pi$
$62$	−9.99156	−1.26893
$63$	−0.403322	−0.0508138
$64$	7.30363	0.912954
$65$	−0.636277	−0.0789205
$66$	3.07710	0.378765
$67$	3.66993	0.448354	0.224177	−	0.974548i	$-0.428031\pi$
$67$	3.66993	0.448354	0.224177	+	0.974548i	$0.428031\pi$
$68$	0.734655	0.0890900
$69$	−5.96335	−0.717903
$70$	−0.376452	−0.0449946
$71$	−9.78072	−1.16076	−0.580379	−	0.814347i	$-0.697096\pi$
$71$	−9.78072	−1.16076	−0.580379	+	0.814347i	$0.697096\pi$
$72$	−2.71105	−0.319500
$73$	0.651127	0.0762086	0.0381043	−	0.999274i	$-0.487868\pi$
$73$	0.651127	0.0762086	0.0381043	+	0.999274i	$0.487868\pi$
$74$	−0.539056	−0.0626639
$75$	4.59515	0.530602
$76$	0.926400	0.106265
$77$	0.846025	0.0964135
$78$	1.46693	0.166098
$79$	−10.4242	−1.17281	−0.586406	−	0.810017i	$-0.699458\pi$
$79$	−10.4242	−1.17281	−0.586406	+	0.810017i	$0.699458\pi$
$80$	−2.72372	−0.304522
$81$	1.00000	0.111111
$82$	15.6592	1.72927
$83$	−2.86545	−0.314524	−0.157262	−	0.987557i	$-0.550267\pi$
$83$	−2.86545	−0.314524	−0.157262	+	0.987557i	$0.550267\pi$
$84$	0.0612628	0.00668432
$85$	3.07741	0.333792
$86$	−2.58383	−0.278621
$87$	6.27177	0.672405
$88$	5.68680	0.606215
$89$	−17.8464	−1.89171	−0.945857	−	0.324583i	$-0.894776\pi$
$89$	−17.8464	−1.89171	−0.945857	+	0.324583i	$0.894776\pi$
$90$	0.933377	0.0983866
$91$	0.403322	0.0422797
$92$	0.905806	0.0944368
$93$	6.81119	0.706287
$94$	−5.33634	−0.550401
$95$	3.88061	0.398142
$96$	0.857437	0.0875118
$97$	7.51287	0.762817	0.381408	−	0.924407i	$-0.375439\pi$
$97$	7.51287	0.762817	0.381408	+	0.924407i	$0.375439\pi$
$98$	−10.0299	−1.01317
$99$	−2.09764	−0.210821
$100$	−0.697983	−0.0697983
$101$	−4.87100	−0.484683	−0.242341	−	0.970191i	$-0.577915\pi$
$101$	−4.87100	−0.484683	−0.242341	+	0.970191i	$0.577915\pi$
$102$	−7.09495	−0.702504
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	2.71105	0.265840
$105$	0.256625	0.0250440
$106$	0.762048	0.0740166
$107$	10.7312	1.03742	0.518712	−	0.854949i	$-0.326412\pi$
$107$	10.7312	1.03742	0.518712	+	0.854949i	$0.326412\pi$
$108$	−0.151895	−0.0146161
$109$	−2.24511	−0.215042	−0.107521	−	0.994203i	$-0.534291\pi$
$109$	−2.24511	−0.215042	−0.107521	+	0.994203i	$0.534291\pi$
$110$	−1.95789	−0.186677
$111$	0.367471	0.0348788
$112$	1.72651	0.163140
$113$	10.2841	0.967447	0.483724	−	0.875221i	$-0.339284\pi$
$113$	10.2841	0.967447	0.483724	+	0.875221i	$0.339284\pi$
$114$	−8.94673	−0.837938
$115$	3.79434	0.353824
$116$	−0.952654	−0.0884517
$117$	−1.00000	−0.0924500
$118$	−21.5473	−1.98359
$119$	−1.95070	−0.178821
$120$	1.72498	0.157468
$121$	−6.59991	−0.599991
$122$	−18.1713	−1.64515
$123$	−10.6748	−0.962512
$124$	−1.03459	−0.0929088
$125$	−6.10518	−0.546064
$126$	−0.591647	−0.0527081
$127$	0.0873014	0.00774675	0.00387337	−	0.999992i	$-0.498767\pi$
$127$	0.0873014	0.00774675	0.00387337	+	0.999992i	$0.498767\pi$
$128$	12.4288	1.09856
$129$	1.76138	0.155081
$130$	−0.933377	−0.0818626
$131$	−11.4165	−0.997464	−0.498732	−	0.866756i	$-0.666201\pi$
$131$	−11.4165	−0.997464	−0.498732	+	0.866756i	$0.666201\pi$
$132$	0.318622	0.0277325
$133$	−2.45984	−0.213295
$134$	5.38355	0.465068
$135$	−0.636277	−0.0547620
$136$	−13.1122	−1.12436
$137$	−13.7768	−1.17703	−0.588515	−	0.808486i	$-0.700287\pi$
$137$	−13.7768	−1.17703	−0.588515	+	0.808486i	$0.700287\pi$
$138$	−8.74784	−0.744666
$139$	−10.4336	−0.884968	−0.442484	−	0.896776i	$-0.645903\pi$
$139$	−10.4336	−0.884968	−0.442484	+	0.896776i	$0.645903\pi$
$140$	−0.0389802	−0.00329442
$141$	3.63775	0.306354
$142$	−14.3477	−1.20403
$143$	2.09764	0.175413
$144$	−4.28072	−0.356727
$145$	−3.99059	−0.331400
$146$	0.955160	0.0790496
$147$	6.83733	0.563934
$148$	−0.0558172	−0.00458814
$149$	11.8980	0.974721	0.487360	−	0.873201i	$-0.337960\pi$
$149$	11.8980	0.974721	0.487360	+	0.873201i	$0.337960\pi$
$150$	6.74078	0.550383
$151$	−12.9826	−1.05651	−0.528255	−	0.849086i	$-0.677153\pi$
$151$	−12.9826	−1.05651	−0.528255	+	0.849086i	$0.677153\pi$
$152$	−16.5345	−1.34112
$153$	4.83658	0.391014
$154$	1.24106	0.100008
$155$	−4.33380	−0.348100
$156$	0.151895	0.0121614
$157$	−9.78021	−0.780546	−0.390273	−	0.920699i	$-0.627619\pi$
$157$	−9.78021	−0.780546	−0.390273	+	0.920699i	$0.627619\pi$
$158$	−15.2916	−1.21653
$159$	−0.519483	−0.0411977
$160$	−0.545568	−0.0431309
$161$	−2.40515	−0.189553
$162$	1.46693	0.115253
$163$	16.0200	1.25478	0.627392	−	0.778703i	$-0.284122\pi$
$163$	16.0200	1.25478	0.627392	+	0.778703i	$0.284122\pi$
$164$	1.62145	0.126614
$165$	1.33468	0.103905
$166$	−4.20343	−0.326249
$167$	−22.1260	−1.71216	−0.856082	−	0.516840i	$-0.827108\pi$
$167$	−22.1260	−1.71216	−0.856082	+	0.516840i	$0.827108\pi$
$168$	−1.09343	−0.0843597
$169$	1.00000	0.0769231
$170$	4.51435	0.346235
$171$	6.09893	0.466397
$172$	−0.267546	−0.0204002
$173$	6.94631	0.528118	0.264059	−	0.964507i	$-0.414939\pi$
$173$	6.94631	0.528118	0.264059	+	0.964507i	$0.414939\pi$
$174$	9.20028	0.697471
$175$	1.85333	0.140098
$176$	8.97941	0.676848
$177$	14.6887	1.10407
$178$	−26.1795	−1.96224
$179$	−8.38920	−0.627038	−0.313519	−	0.949582i	$-0.601508\pi$
$179$	−8.38920	−0.627038	−0.313519	+	0.949582i	$0.601508\pi$
$180$	0.0966476	0.00720369
$181$	23.7290	1.76376	0.881881	−	0.471472i	$-0.156277\pi$
$181$	23.7290	1.76376	0.881881	+	0.471472i	$0.156277\pi$
$182$	0.591647	0.0438558
$183$	12.3873	0.915694
$184$	−16.1669	−1.19184
$185$	−0.233813	−0.0171903
$186$	9.99156	0.732617
$187$	−10.1454	−0.741906
$188$	−0.552557	−0.0402994
$189$	0.403322	0.0293374
$190$	5.69260	0.412985
$191$	3.54811	0.256732	0.128366	−	0.991727i	$-0.459027\pi$
$191$	3.54811	0.256732	0.128366	+	0.991727i	$0.459027\pi$
$192$	−7.30363	−0.527094
$193$	−2.16040	−0.155509	−0.0777546	−	0.996973i	$-0.524775\pi$
$193$	−2.16040	−0.155509	−0.0777546	+	0.996973i	$0.524775\pi$
$194$	11.0209	0.791254
$195$	0.636277	0.0455648
$196$	−1.03856	−0.0741828
$197$	11.7304	0.835756	0.417878	−	0.908503i	$-0.362774\pi$
$197$	11.7304	0.835756	0.417878	+	0.908503i	$0.362774\pi$
$198$	−3.07710	−0.218680
$199$	14.8164	1.05030	0.525152	−	0.851008i	$-0.324008\pi$
$199$	14.8164	1.05030	0.525152	+	0.851008i	$0.324008\pi$
$200$	12.4577	0.880891
$201$	−3.66993	−0.258857
$202$	−7.14544	−0.502751
$203$	2.52955	0.177539
$204$	−0.734655	−0.0514361
$205$	6.79212	0.474382
$206$	−1.46693	−0.102206
$207$	5.96335	0.414482
$208$	4.28072	0.296814
$209$	−12.7934	−0.884936
$210$	0.376452	0.0259776
$211$	14.6531	1.00876	0.504381	−	0.863481i	$-0.331721\pi$
$211$	14.6531	1.00876	0.504381	+	0.863481i	$0.331721\pi$
$212$	0.0789072	0.00541937
$213$	9.78072	0.670164
$214$	15.7420	1.07610
$215$	−1.12073	−0.0764329
$216$	2.71105	0.184463
$217$	2.74710	0.186486
$218$	−3.29342	−0.223059
$219$	−0.651127	−0.0439991
$220$	−0.202732	−0.0136682
$221$	−4.83658	−0.325344
$222$	0.539056	0.0361790
$223$	2.87501	0.192525	0.0962623	−	0.995356i	$-0.469311\pi$
$223$	2.87501	0.192525	0.0962623	+	0.995356i	$0.469311\pi$
$224$	0.345824	0.0231063
$225$	−4.59515	−0.306343
$226$	15.0861	1.00351
$227$	19.0960	1.26745	0.633725	−	0.773559i	$-0.281525\pi$
$227$	19.0960	1.26745	0.633725	+	0.773559i	$0.281525\pi$
$228$	−0.926400	−0.0613524
$229$	−13.8819	−0.917343	−0.458672	−	0.888606i	$-0.651675\pi$
$229$	−13.8819	−0.917343	−0.458672	+	0.888606i	$0.651675\pi$
$230$	5.56605	0.367015
$231$	−0.846025	−0.0556644
$232$	17.0031	1.11631
$233$	21.4163	1.40303	0.701514	−	0.712656i	$-0.252508\pi$
$233$	21.4163	1.40303	0.701514	+	0.712656i	$0.252508\pi$
$234$	−1.46693	−0.0958965
$235$	−2.31462	−0.150989
$236$	−2.23114	−0.145235
$237$	10.4242	0.677124
$238$	−2.86155	−0.185487
$239$	−29.6022	−1.91480	−0.957402	−	0.288757i	$-0.906758\pi$
$239$	−29.6022	−1.91480	−0.957402	+	0.288757i	$0.906758\pi$
$240$	2.72372	0.175816
$241$	−7.16493	−0.461534	−0.230767	−	0.973009i	$-0.574123\pi$
$241$	−7.16493	−0.461534	−0.230767	+	0.973009i	$0.574123\pi$
$242$	−9.68163	−0.622359
$243$	−1.00000	−0.0641500
$244$	−1.88157	−0.120455
$245$	−4.35044	−0.277939
$246$	−15.6592	−0.998394
$247$	−6.09893	−0.388066
$248$	18.4655	1.17256
$249$	2.86545	0.181591
$250$	−8.95589	−0.566420
$251$	11.2472	0.709917	0.354959	−	0.934882i	$-0.384495\pi$
$251$	11.2472	0.709917	0.354959	+	0.934882i	$0.384495\pi$
$252$	−0.0612628	−0.00385920
$253$	−12.5090	−0.786432
$254$	0.128065	0.00803554
$255$	−3.07741	−0.192715
$256$	3.62500	0.226562
$257$	−20.0648	−1.25161	−0.625803	−	0.779981i	$-0.715228\pi$
$257$	−20.0648	−1.25161	−0.625803	+	0.779981i	$0.715228\pi$
$258$	2.58383	0.160862
$259$	0.148209	0.00920928
$260$	−0.0966476	−0.00599383
$261$	−6.27177	−0.388213
$262$	−16.7472	−1.03465
$263$	−23.2705	−1.43492	−0.717461	−	0.696599i	$-0.754696\pi$
$263$	−23.2705	−1.43492	−0.717461	+	0.696599i	$0.754696\pi$
$264$	−5.68680	−0.349998
$265$	0.330535	0.0203046
$266$	−3.60842	−0.221246
$267$	17.8464	1.09218
$268$	0.557446	0.0340515
$269$	9.54807	0.582156	0.291078	−	0.956699i	$-0.405986\pi$
$269$	9.54807	0.582156	0.291078	+	0.956699i	$0.405986\pi$
$270$	−0.933377	−0.0568035
$271$	−0.418090	−0.0253971	−0.0126986	−	0.999919i	$-0.504042\pi$
$271$	−0.418090	−0.0253971	−0.0126986	+	0.999919i	$0.504042\pi$
$272$	−20.7040	−1.25537
$273$	−0.403322	−0.0244102
$274$	−20.2096	−1.22091
$275$	9.63897	0.581252
$276$	−0.905806	−0.0545231
$277$	−15.1969	−0.913094	−0.456547	−	0.889699i	$-0.650914\pi$
$277$	−15.1969	−0.913094	−0.456547	+	0.889699i	$0.650914\pi$
$278$	−15.3054	−0.917959
$279$	−6.81119	−0.407775
$280$	0.695722	0.0415774
$281$	31.0827	1.85424	0.927119	−	0.374768i	$-0.122278\pi$
$281$	31.0827	1.85424	0.927119	+	0.374768i	$0.122278\pi$
$282$	5.33634	0.317774
$283$	−23.4143	−1.39183	−0.695917	−	0.718122i	$-0.745002\pi$
$283$	−23.4143	−1.39183	−0.695917	+	0.718122i	$0.745002\pi$
$284$	−1.48565	−0.0881569
$285$	−3.88061	−0.229868
$286$	3.07710	0.181953
$287$	−4.30538	−0.254138
$288$	−0.857437	−0.0505250
$289$	6.39252	0.376030
$290$	−5.85393	−0.343754
$291$	−7.51287	−0.440412
$292$	0.0989032	0.00578787
$293$	11.9327	0.697113	0.348557	−	0.937288i	$-0.386672\pi$
$293$	11.9327	0.697113	0.348557	+	0.937288i	$0.386672\pi$
$294$	10.0299	0.584956
$295$	−9.34607	−0.544149
$296$	0.996231	0.0579048
$297$	2.09764	0.121717
$298$	17.4536	1.01106
$299$	−5.96335	−0.344870
$300$	0.697983	0.0402980
$301$	0.710404	0.0409470
$302$	−19.0446	−1.09589
$303$	4.87100	0.279832
$304$	−26.1078	−1.49739
$305$	−7.88174	−0.451307
$306$	7.09495	0.405591
$307$	−9.52052	−0.543365	−0.271682	−	0.962387i	$-0.587580\pi$
$307$	−9.52052	−0.543365	−0.271682	+	0.962387i	$0.587580\pi$
$308$	0.128507	0.00732239
$309$	1.00000	0.0568880
$310$	−6.35741	−0.361076
$311$	−9.91011	−0.561951	−0.280975	−	0.959715i	$-0.590658\pi$
$311$	−9.91011	−0.561951	−0.280975	+	0.959715i	$0.590658\pi$
$312$	−2.71105	−0.153483
$313$	−11.9062	−0.672980	−0.336490	−	0.941687i	$-0.609240\pi$
$313$	−11.9062	−0.672980	−0.336490	+	0.941687i	$0.609240\pi$
$314$	−14.3469	−0.809644
$315$	−0.256625	−0.0144592
$316$	−1.58339	−0.0890725
$317$	−21.8328	−1.22625	−0.613125	−	0.789986i	$-0.710088\pi$
$317$	−21.8328	−1.22625	−0.613125	+	0.789986i	$0.710088\pi$
$318$	−0.762048	−0.0427335
$319$	13.1559	0.736590
$320$	4.64714	0.259783
$321$	−10.7312	−0.598957
$322$	−3.52820	−0.196619
$323$	29.4980	1.64131
$324$	0.151895	0.00843864
$325$	4.59515	0.254893
$326$	23.5003	1.30156
$327$	2.24511	0.124155
$328$	−28.9398	−1.59793
$329$	1.46719	0.0808885
$330$	1.95789	0.107778
$331$	24.4613	1.34451	0.672256	−	0.740319i	$-0.265325\pi$
$331$	24.4613	1.34451	0.672256	+	0.740319i	$0.265325\pi$
$332$	−0.435249	−0.0238874
$333$	−0.367471	−0.0201373
$334$	−32.4574	−1.77599
$335$	2.33510	0.127580
$336$	−1.72651	−0.0941888
$337$	6.22429	0.339059	0.169529	−	0.985525i	$-0.445775\pi$
$337$	6.22429	0.339059	0.169529	+	0.985525i	$0.445775\pi$
$338$	1.46693	0.0797907
$339$	−10.2841	−0.558556
$340$	0.467444	0.0253507
$341$	14.2874	0.773707
$342$	8.94673	0.483784
$343$	5.58091	0.301341
$344$	4.77519	0.257461
$345$	−3.79434	−0.204281
$346$	10.1898	0.547806
$347$	−13.8473	−0.743360	−0.371680	−	0.928361i	$-0.621218\pi$
$347$	−13.8473	−0.743360	−0.371680	+	0.928361i	$0.621218\pi$
$348$	0.952654	0.0510676
$349$	29.1476	1.56024	0.780118	−	0.625633i	$-0.215159\pi$
$349$	29.1476	1.56024	0.780118	+	0.625633i	$0.215159\pi$
$350$	2.71871	0.145321
$351$	1.00000	0.0533761
$352$	1.79859	0.0958654
$353$	24.3485	1.29594	0.647970	−	0.761666i	$-0.275618\pi$
$353$	24.3485	1.29594	0.647970	+	0.761666i	$0.275618\pi$
$354$	21.5473	1.14523
$355$	−6.22325	−0.330296
$356$	−2.71079	−0.143671
$357$	1.95070	0.103242
$358$	−12.3064	−0.650414
$359$	0.392251	0.0207022	0.0103511	−	0.999946i	$-0.496705\pi$
$359$	0.392251	0.0207022	0.0103511	+	0.999946i	$0.496705\pi$
$360$	−1.72498	−0.0909143
$361$	18.1970	0.957736
$362$	34.8089	1.82951
$363$	6.59991	0.346405
$364$	0.0612628	0.00321105
$365$	0.414297	0.0216853
$366$	18.1713	0.949830
$367$	−22.8252	−1.19146	−0.595732	−	0.803183i	$-0.703138\pi$
$367$	−22.8252	−1.19146	−0.595732	+	0.803183i	$0.703138\pi$
$368$	−25.5274	−1.33071
$369$	10.6748	0.555707
$370$	−0.342989	−0.0178311
$371$	−0.209519	−0.0108777
$372$	1.03459	0.0536409
$373$	−12.7563	−0.660494	−0.330247	−	0.943895i	$-0.607132\pi$
$373$	−12.7563	−0.660494	−0.330247	+	0.943895i	$0.607132\pi$
$374$	−14.8826	−0.769563
$375$	6.10518	0.315270
$376$	9.86211	0.508599
$377$	6.27177	0.323013
$378$	0.591647	0.0304311
$379$	0.134929	0.00693083	0.00346542	−	0.999994i	$-0.498897\pi$
$379$	0.134929	0.00693083	0.00346542	+	0.999994i	$0.498897\pi$
$380$	0.589447	0.0302380
$381$	−0.0873014	−0.00447259
$382$	5.20484	0.266303
$383$	−35.1617	−1.79668	−0.898340	−	0.439300i	$-0.855227\pi$
$383$	−35.1617	−1.79668	−0.898340	+	0.439300i	$0.855227\pi$
$384$	−12.4288	−0.634256
$385$	0.538307	0.0274346
$386$	−3.16917	−0.161306
$387$	−1.76138	−0.0895360
$388$	1.14117	0.0579342
$389$	−32.6883	−1.65736	−0.828680	−	0.559722i	$-0.810908\pi$
$389$	−32.6883	−1.65736	−0.828680	+	0.559722i	$0.810908\pi$
$390$	0.933377	0.0472634
$391$	28.8422	1.45861
$392$	18.5363	0.936226
$393$	11.4165	0.575886
$394$	17.2077	0.866912
$395$	−6.63267	−0.333726
$396$	−0.318622	−0.0160114
$397$	2.14069	0.107438	0.0537191	−	0.998556i	$-0.482892\pi$
$397$	2.14069	0.107438	0.0537191	+	0.998556i	$0.482892\pi$
$398$	21.7346	1.08946
$399$	2.45984	0.123146
$400$	19.6705	0.983527
$401$	0.391058	0.0195285	0.00976426	−	0.999952i	$-0.496892\pi$
$401$	0.391058	0.0195285	0.00976426	+	0.999952i	$0.496892\pi$
$402$	−5.38355	−0.268507
$403$	6.81119	0.339289
$404$	−0.739883	−0.0368106
$405$	0.636277	0.0316169
$406$	3.71068	0.184158
$407$	0.770822	0.0382082
$408$	13.1122	0.649151
$409$	−32.5136	−1.60770	−0.803848	−	0.594834i	$-0.797218\pi$
$409$	−32.5136	−1.60770	−0.803848	+	0.594834i	$0.797218\pi$
$410$	9.96359	0.492067
$411$	13.7768	0.679558
$412$	−0.151895	−0.00748335
$413$	5.92427	0.291514
$414$	8.74784	0.429933
$415$	−1.82322	−0.0894984
$416$	0.857437	0.0420393
$417$	10.4336	0.510937
$418$	−18.7670	−0.917925
$419$	23.0670	1.12690	0.563448	−	0.826152i	$-0.309475\pi$
$419$	23.0670	1.12690	0.563448	+	0.826152i	$0.309475\pi$
$420$	0.0389802	0.00190204
$421$	19.1651	0.934050	0.467025	−	0.884244i	$-0.345326\pi$
$421$	19.1651	0.934050	0.467025	+	0.884244i	$0.345326\pi$
$422$	21.4951	1.04637
$423$	−3.63775	−0.176873
$424$	−1.40834	−0.0683952
$425$	−22.2248	−1.07806
$426$	14.3477	0.695147
$427$	4.99607	0.241777
$428$	1.63002	0.0787900
$429$	−2.09764	−0.101275
$430$	−1.64403	−0.0792822
$431$	−20.2577	−0.975781	−0.487891	−	0.872905i	$-0.662234\pi$
$431$	−20.2577	−0.975781	−0.487891	+	0.872905i	$0.662234\pi$
$432$	4.28072	0.205956
$433$	1.97636	0.0949776	0.0474888	−	0.998872i	$-0.484878\pi$
$433$	1.97636	0.0949776	0.0474888	+	0.998872i	$0.484878\pi$
$434$	4.02982	0.193438
$435$	3.99059	0.191334
$436$	−0.341022	−0.0163320
$437$	36.3701	1.73982
$438$	−0.955160	−0.0456393
$439$	8.47228	0.404360	0.202180	−	0.979348i	$-0.435197\pi$
$439$	8.47228	0.404360	0.202180	+	0.979348i	$0.435197\pi$
$440$	3.61838	0.172500
$441$	−6.83733	−0.325587
$442$	−7.09495	−0.337472
$443$	17.7822	0.844857	0.422428	−	0.906396i	$-0.361178\pi$
$443$	17.7822	0.844857	0.422428	+	0.906396i	$0.361178\pi$
$444$	0.0558172	0.00264897
$445$	−11.3553	−0.538291
$446$	4.21744	0.199702
$447$	−11.8980	−0.562755
$448$	−2.94572	−0.139172
$449$	−38.8863	−1.83516	−0.917580	−	0.397552i	$-0.869860\pi$
$449$	−38.8863	−1.83516	−0.917580	+	0.397552i	$0.869860\pi$
$450$	−6.74078	−0.317764
$451$	−22.3918	−1.05439
$452$	1.56211	0.0734754
$453$	12.9826	0.609976
$454$	28.0126	1.31470
$455$	0.256625	0.0120308
$456$	16.5345	0.774299
$457$	17.6647	0.826319	0.413159	−	0.910659i	$-0.364425\pi$
$457$	17.6647	0.826319	0.413159	+	0.910659i	$0.364425\pi$
$458$	−20.3639	−0.951541
$459$	−4.83658	−0.225752
$460$	0.576344	0.0268722
$461$	−23.3792	−1.08888	−0.544439	−	0.838800i	$-0.683258\pi$
$461$	−23.3792	−1.08888	−0.544439	+	0.838800i	$0.683258\pi$
$462$	−1.24106	−0.0577395
$463$	24.9025	1.15732	0.578659	−	0.815570i	$-0.303576\pi$
$463$	24.9025	1.15732	0.578659	+	0.815570i	$0.303576\pi$
$464$	26.8477	1.24637
$465$	4.33380	0.200975
$466$	31.4163	1.45533
$467$	6.24182	0.288837	0.144418	−	0.989517i	$-0.453869\pi$
$467$	6.24182	0.288837	0.144418	+	0.989517i	$0.453869\pi$
$468$	−0.151895	−0.00702137
$469$	−1.48017	−0.0683478
$470$	−3.39539	−0.156618
$471$	9.78021	0.450648
$472$	39.8217	1.83294
$473$	3.69474	0.169884
$474$	15.2916	0.702366
$475$	−28.0255	−1.28590
$476$	−0.296303	−0.0135810
$477$	0.519483	0.0237855
$478$	−43.4244	−1.98619
$479$	−30.6484	−1.40036	−0.700181	−	0.713965i	$-0.746897\pi$
$479$	−30.6484	−1.40036	−0.700181	+	0.713965i	$0.746897\pi$
$480$	0.545568	0.0249016
$481$	0.367471	0.0167552
$482$	−10.5105	−0.478739
$483$	2.40515	0.109438
$484$	−1.00250	−0.0455680
$485$	4.78027	0.217061
$486$	−1.46693	−0.0665415
$487$	0.635900	0.0288154	0.0144077	−	0.999896i	$-0.495414\pi$
$487$	0.635900	0.0288154	0.0144077	+	0.999896i	$0.495414\pi$
$488$	33.5825	1.52021
$489$	−16.0200	−0.724450
$490$	−6.38181	−0.288301
$491$	−2.52494	−0.113949	−0.0569746	−	0.998376i	$-0.518145\pi$
$491$	−2.52494	−0.113949	−0.0569746	+	0.998376i	$0.518145\pi$
$492$	−1.62145	−0.0731006
$493$	−30.3339	−1.36617
$494$	−8.94673	−0.402533
$495$	−1.33468	−0.0599894
$496$	29.1568	1.30918
$497$	3.94478	0.176948
$498$	4.20343	0.188360
$499$	−13.4040	−0.600043	−0.300022	−	0.953932i	$-0.596994\pi$
$499$	−13.4040	−0.600043	−0.300022	+	0.953932i	$0.596994\pi$
$500$	−0.927349	−0.0414723
$501$	22.1260	0.988519
$502$	16.4989	0.736382
$503$	21.2150	0.945929	0.472965	−	0.881081i	$-0.343184\pi$
$503$	21.2150	0.945929	0.472965	+	0.881081i	$0.343184\pi$
$504$	1.09343	0.0487051
$505$	−3.09931	−0.137917
$506$	−18.3498	−0.815749
$507$	−1.00000	−0.0444116
$508$	0.0132607	0.000588348 0
$509$	36.0661	1.59860	0.799301	−	0.600931i	$-0.205203\pi$
$509$	36.0661	1.59860	0.799301	+	0.600931i	$0.205203\pi$
$510$	−4.51435	−0.199899
$511$	−0.262614	−0.0116174
$512$	−19.5400	−0.863555
$513$	−6.09893	−0.269274
$514$	−29.4337	−1.29826
$515$	−0.636277	−0.0280377
$516$	0.267546	0.0117780
$517$	7.63069	0.335597
$518$	0.217413	0.00955259
$519$	−6.94631	−0.304909
$520$	1.72498	0.0756453
$521$	29.7408	1.30297	0.651485	−	0.758661i	$-0.274146\pi$
$521$	29.7408	1.30297	0.651485	+	0.758661i	$0.274146\pi$
$522$	−9.20028	−0.402685
$523$	−14.9856	−0.655275	−0.327638	−	0.944803i	$-0.606253\pi$
$523$	−14.9856	−0.655275	−0.327638	+	0.944803i	$0.606253\pi$
$524$	−1.73411	−0.0757551
$525$	−1.85333	−0.0808858
$526$	−34.1363	−1.48841
$527$	−32.9429	−1.43501
$528$	−8.97941	−0.390779
$529$	12.5616	0.546155
$530$	0.484874	0.0210616
$531$	−14.6887	−0.637434
$532$	−0.373638	−0.0161993
$533$	−10.6748	−0.462376
$534$	26.1795	1.13290
$535$	6.82801	0.295201
$536$	−9.94937	−0.429747
$537$	8.38920	0.362021
$538$	14.0064	0.603858
$539$	14.3423	0.617765
$540$	−0.0966476	−0.00415905
$541$	18.2535	0.784780	0.392390	−	0.919799i	$-0.371648\pi$
$541$	18.2535	0.784780	0.392390	+	0.919799i	$0.371648\pi$
$542$	−0.613310	−0.0263439
$543$	−23.7290	−1.01831
$544$	−4.14706	−0.177804
$545$	−1.42851	−0.0611907
$546$	−0.591647	−0.0253202
$547$	24.6410	1.05357	0.526786	−	0.849998i	$-0.323397\pi$
$547$	24.6410	1.05357	0.526786	+	0.849998i	$0.323397\pi$
$548$	−2.09263	−0.0893927
$549$	−12.3873	−0.528676
$550$	14.1397	0.602920
$551$	−38.2511	−1.62955
$552$	16.1669	0.688110
$553$	4.20431	0.178785
$554$	−22.2929	−0.947133
$555$	0.233813	0.00992483
$556$	−1.58482	−0.0672113
$557$	32.0074	1.35620	0.678100	−	0.734970i	$-0.262804\pi$
$557$	32.0074	1.35620	0.678100	+	0.734970i	$0.262804\pi$
$558$	−9.99156	−0.422977
$559$	1.76138	0.0744985
$560$	1.09854	0.0464217
$561$	10.1454	0.428339
$562$	45.5962	1.92336
$563$	−26.1466	−1.10195	−0.550974	−	0.834522i	$-0.685744\pi$
$563$	−26.1466	−1.10195	−0.550974	+	0.834522i	$0.685744\pi$
$564$	0.552557	0.0232669
$565$	6.54354	0.275289
$566$	−34.3472	−1.44372
$567$	−0.403322	−0.0169379
$568$	26.5160	1.11259
$569$	12.3171	0.516359	0.258180	−	0.966097i	$-0.416877\pi$
$569$	12.3171	0.516359	0.258180	+	0.966097i	$0.416877\pi$
$570$	−5.69260	−0.238437
$571$	16.6039	0.694852	0.347426	−	0.937707i	$-0.387056\pi$
$571$	16.6039	0.694852	0.347426	+	0.937707i	$0.387056\pi$
$572$	0.318622	0.0133223
$573$	−3.54811	−0.148224
$574$	−6.31570	−0.263612
$575$	−27.4025	−1.14276
$576$	7.30363	0.304318
$577$	29.0851	1.21083	0.605414	−	0.795911i	$-0.293008\pi$
$577$	29.0851	1.21083	0.605414	+	0.795911i	$0.293008\pi$
$578$	9.37740	0.390048
$579$	2.16040	0.0897833
$580$	−0.606152	−0.0251691
$581$	1.15570	0.0479465
$582$	−11.0209	−0.456831
$583$	−1.08969	−0.0451303
$584$	−1.76524	−0.0730459
$585$	−0.636277	−0.0263068
$586$	17.5044	0.723101
$587$	−5.55221	−0.229164	−0.114582	−	0.993414i	$-0.536553\pi$
$587$	−5.55221	−0.229164	−0.114582	+	0.993414i	$0.536553\pi$
$588$	1.03856	0.0428295
$589$	−41.5410	−1.71167
$590$	−13.7101	−0.564435
$591$	−11.7304	−0.482524
$592$	1.57304	0.0646515
$593$	17.8289	0.732145	0.366073	−	0.930586i	$-0.380702\pi$
$593$	17.8289	0.732145	0.366073	+	0.930586i	$0.380702\pi$
$594$	3.07710	0.126255
$595$	−1.24119	−0.0508837
$596$	1.80725	0.0740278
$597$	−14.8164	−0.606393
$598$	−8.74784	−0.357726
$599$	−12.2860	−0.501990	−0.250995	−	0.967988i	$-0.580758\pi$
$599$	−12.2860	−0.501990	−0.250995	+	0.967988i	$0.580758\pi$
$600$	−12.4577	−0.508582
$601$	18.4036	0.750698	0.375349	−	0.926884i	$-0.377523\pi$
$601$	18.4036	0.750698	0.375349	+	0.926884i	$0.377523\pi$
$602$	1.04212	0.0424735
$603$	3.66993	0.149451
$604$	−1.97200	−0.0802395
$605$	−4.19937	−0.170729
$606$	7.14544	0.290264
$607$	17.4953	0.710112	0.355056	−	0.934845i	$-0.384462\pi$
$607$	17.4953	0.710112	0.355056	+	0.934845i	$0.384462\pi$
$608$	−5.22945	−0.212082
$609$	−2.52955	−0.102502
$610$	−11.5620	−0.468131
$611$	3.63775	0.147168
$612$	0.734655	0.0296967
$613$	16.5046	0.666613	0.333306	−	0.942819i	$-0.391836\pi$
$613$	16.5046	0.666613	0.333306	+	0.942819i	$0.391836\pi$
$614$	−13.9660	−0.563621
$615$	−6.79212	−0.273885
$616$	−2.29361	−0.0924124
$617$	40.6992	1.63849	0.819245	−	0.573444i	$-0.194393\pi$
$617$	40.6992	1.63849	0.819245	+	0.573444i	$0.194393\pi$
$618$	1.46693	0.0590087
$619$	5.35707	0.215319	0.107659	−	0.994188i	$-0.465664\pi$
$619$	5.35707	0.215319	0.107659	+	0.994188i	$0.465664\pi$
$620$	−0.658285	−0.0264374
$621$	−5.96335	−0.239301
$622$	−14.5375	−0.582899
$623$	7.19785	0.288376
$624$	−4.28072	−0.171366
$625$	19.0912	0.763647
$626$	−17.4656	−0.698068
$627$	12.7934	0.510918
$628$	−1.48557	−0.0592807
$629$	−1.77730	−0.0708657
$630$	−0.376452	−0.0149982
$631$	2.22182	0.0884494	0.0442247	−	0.999022i	$-0.485918\pi$
$631$	2.22182	0.0884494	0.0442247	+	0.999022i	$0.485918\pi$
$632$	28.2605	1.12414
$633$	−14.6531	−0.582409
$634$	−32.0272	−1.27196
$635$	0.0555479	0.00220435
$636$	−0.0789072	−0.00312887
$637$	6.83733	0.270905
$638$	19.2989	0.764049
$639$	−9.78072	−0.386919
$640$	7.90818	0.312598
$641$	1.36973	0.0541012	0.0270506	−	0.999634i	$-0.491388\pi$
$641$	1.36973	0.0541012	0.0270506	+	0.999634i	$0.491388\pi$
$642$	−15.7420	−0.621285
$643$	−26.5725	−1.04792	−0.523958	−	0.851744i	$-0.675545\pi$
$643$	−26.5725	−1.04792	−0.523958	+	0.851744i	$0.675545\pi$
$644$	−0.365332	−0.0143961
$645$	1.12073	0.0441286
$646$	43.2716	1.70250
$647$	−27.4990	−1.08110	−0.540548	−	0.841313i	$-0.681783\pi$
$647$	−27.4990	−1.08110	−0.540548	+	0.841313i	$0.681783\pi$
$648$	−2.71105	−0.106500
$649$	30.8116	1.20946
$650$	6.74078	0.264395
$651$	−2.74710	−0.107668
$652$	2.43337	0.0952980
$653$	−40.7612	−1.59511	−0.797554	−	0.603248i	$-0.793873\pi$
$653$	−40.7612	−1.59511	−0.797554	+	0.603248i	$0.793873\pi$
$654$	3.29342	0.128783
$655$	−7.26405	−0.283830
$656$	−45.6957	−1.78412
$657$	0.651127	0.0254029
$658$	2.15226	0.0839040
$659$	15.3045	0.596178	0.298089	−	0.954538i	$-0.403651\pi$
$659$	15.3045	0.596178	0.298089	+	0.954538i	$0.403651\pi$
$660$	0.202732	0.00789133
$661$	47.8447	1.86094	0.930471	−	0.366365i	$-0.119398\pi$
$661$	47.8447	1.86094	0.930471	+	0.366365i	$0.119398\pi$
$662$	35.8830	1.39463
$663$	4.83658	0.187837
$664$	7.76837	0.301471
$665$	−1.56514	−0.0606934
$666$	−0.539056	−0.0208880
$667$	−37.4008	−1.44816
$668$	−3.36085	−0.130035
$669$	−2.87501	−0.111154
$670$	3.42543	0.132336
$671$	25.9840	1.00310
$672$	−0.345824	−0.0133404
$673$	−14.8842	−0.573745	−0.286872	−	0.957969i	$-0.592616\pi$
$673$	−14.8842	−0.573745	−0.286872	+	0.957969i	$0.592616\pi$
$674$	9.13063	0.351699
$675$	4.59515	0.176867
$676$	0.151895	0.00584213
$677$	32.7411	1.25834	0.629171	−	0.777267i	$-0.283395\pi$
$677$	32.7411	1.25834	0.629171	+	0.777267i	$0.283395\pi$
$678$	−15.0861	−0.579378
$679$	−3.03011	−0.116285
$680$	−8.34299	−0.319939
$681$	−19.0960	−0.731762
$682$	20.9587	0.802550
$683$	−12.9023	−0.493693	−0.246847	−	0.969055i	$-0.579394\pi$
$683$	−12.9023	−0.493693	−0.246847	+	0.969055i	$0.579394\pi$
$684$	0.926400	0.0354218
$685$	−8.76585	−0.334926
$686$	8.18682	0.312574
$687$	13.8819	0.529628
$688$	7.53997	0.287459
$689$	−0.519483	−0.0197907
$690$	−5.56605	−0.211896
$691$	22.7570	0.865718	0.432859	−	0.901462i	$-0.357505\pi$
$691$	22.7570	0.865718	0.432859	+	0.901462i	$0.357505\pi$
$692$	1.05511	0.0401094
$693$	0.846025	0.0321378
$694$	−20.3130	−0.771072
$695$	−6.63867	−0.251819
$696$	−17.0031	−0.644500
$697$	51.6294	1.95560
$698$	42.7576	1.61840
$699$	−21.4163	−0.810038
$700$	0.281512	0.0106402
$701$	−25.2564	−0.953922	−0.476961	−	0.878924i	$-0.658262\pi$
$701$	−25.2564	−0.953922	−0.476961	+	0.878924i	$0.658262\pi$
$702$	1.46693	0.0553659
$703$	−2.24118	−0.0845277
$704$	−15.3204	−0.577409
$705$	2.31462	0.0871735
$706$	35.7176	1.34425
$707$	1.96458	0.0738858
$708$	2.23114	0.0838515
$709$	13.6575	0.512917	0.256458	−	0.966555i	$-0.417444\pi$
$709$	13.6575	0.512917	0.256458	+	0.966555i	$0.417444\pi$
$710$	−9.12910	−0.342609
$711$	−10.4242	−0.390938
$712$	48.3824	1.81321
$713$	−40.6175	−1.52114
$714$	2.86155	0.107091
$715$	1.33468	0.0499142
$716$	−1.27428	−0.0476221
$717$	29.6022	1.10551
$718$	0.575407	0.0214740
$719$	13.0732	0.487548	0.243774	−	0.969832i	$-0.421614\pi$
$719$	13.0732	0.487548	0.243774	+	0.969832i	$0.421614\pi$
$720$	−2.72372	−0.101507
$721$	0.403322	0.0150205
$722$	26.6938	0.993440
$723$	7.16493	0.266467
$724$	3.60433	0.133954
$725$	28.8197	1.07034
$726$	9.68163	0.359319
$727$	39.1014	1.45019	0.725096	−	0.688648i	$-0.241795\pi$
$727$	39.1014	1.45019	0.725096	+	0.688648i	$0.241795\pi$
$728$	−1.09343	−0.0405251
$729$	1.00000	0.0370370
$730$	0.607746	0.0224937
$731$	−8.51906	−0.315089
$732$	1.88157	0.0695449
$733$	31.7995	1.17454	0.587271	−	0.809390i	$-0.300202\pi$
$733$	31.7995	1.17454	0.587271	+	0.809390i	$0.300202\pi$
$734$	−33.4830	−1.23588
$735$	4.35044	0.160468
$736$	−5.11320	−0.188475
$737$	−7.69820	−0.283567
$738$	15.6592	0.576423
$739$	31.7433	1.16770	0.583849	−	0.811862i	$-0.301546\pi$
$739$	31.7433	1.16770	0.583849	+	0.811862i	$0.301546\pi$
$740$	−0.0355152	−0.00130556
$741$	6.09893	0.224050
$742$	−0.307351	−0.0112832
$743$	−15.5880	−0.571870	−0.285935	−	0.958249i	$-0.592304\pi$
$743$	−15.5880	−0.571870	−0.285935	+	0.958249i	$0.592304\pi$
$744$	−18.4655	−0.676976
$745$	7.57042	0.277359
$746$	−18.7126	−0.685117
$747$	−2.86545	−0.104841
$748$	−1.54104	−0.0563460
$749$	−4.32813	−0.158146
$750$	8.95589	0.327023
$751$	−31.8304	−1.16151	−0.580754	−	0.814079i	$-0.697242\pi$
$751$	−31.8304	−1.16151	−0.580754	+	0.814079i	$0.697242\pi$
$752$	15.5722	0.567859
$753$	−11.2472	−0.409871
$754$	9.20028	0.335054
$755$	−8.26053	−0.300632
$756$	0.0612628	0.00222811
$757$	−8.33972	−0.303112	−0.151556	−	0.988449i	$-0.548428\pi$
$757$	−8.33972	−0.303112	−0.151556	+	0.988449i	$0.548428\pi$
$758$	0.197932	0.00718921
$759$	12.5090	0.454047
$760$	−10.5205	−0.381620
$761$	13.3227	0.482947	0.241473	−	0.970407i	$-0.422369\pi$
$761$	13.3227	0.482947	0.241473	+	0.970407i	$0.422369\pi$
$762$	−0.128065	−0.00463932
$763$	0.905502	0.0327814
$764$	0.538942	0.0194982
$765$	3.07741	0.111264
$766$	−51.5799	−1.86366
$767$	14.6887	0.530378
$768$	−3.62500	−0.130806
$769$	30.5896	1.10309	0.551545	−	0.834145i	$-0.314039\pi$
$769$	30.5896	1.10309	0.551545	+	0.834145i	$0.314039\pi$
$770$	0.789660	0.0284574
$771$	20.0648	0.722615
$772$	−0.328155	−0.0118106
$773$	−8.35149	−0.300382	−0.150191	−	0.988657i	$-0.547989\pi$
$773$	−8.35149	−0.300382	−0.150191	+	0.988657i	$0.547989\pi$
$774$	−2.58383	−0.0928738
$775$	31.2984	1.12427
$776$	−20.3678	−0.731160
$777$	−0.148209	−0.00531698
$778$	−47.9515	−1.71915
$779$	65.1048	2.33262
$780$	0.0966476	0.00346054
$781$	20.5164	0.734136
$782$	42.3097	1.51299
$783$	6.27177	0.224135
$784$	29.2687	1.04531
$785$	−6.22293	−0.222106
$786$	16.7472	0.597354
$787$	−40.2952	−1.43637	−0.718184	−	0.695853i	$-0.755026\pi$
$787$	−40.2952	−1.43637	−0.718184	+	0.695853i	$0.755026\pi$
$788$	1.78179	0.0634738
$789$	23.2705	0.828453
$790$	−9.72969	−0.346167
$791$	−4.14781	−0.147479
$792$	5.68680	0.202072
$793$	12.3873	0.439885
$794$	3.14025	0.111443
$795$	−0.330535	−0.0117229
$796$	2.25054	0.0797682
$797$	−3.53793	−0.125320	−0.0626599	−	0.998035i	$-0.519958\pi$
$797$	−3.53793	−0.125320	−0.0626599	+	0.998035i	$0.519958\pi$
$798$	3.60842	0.127737
$799$	−17.5943	−0.622440
$800$	3.94005	0.139302
$801$	−17.8464	−0.630572
$802$	0.573657	0.0202565
$803$	−1.36583	−0.0481991
$804$	−0.557446	−0.0196596
$805$	−1.53034	−0.0539375
$806$	9.99156	0.351938
$807$	−9.54807	−0.336108
$808$	13.2055	0.464568
$809$	−33.3937	−1.17406	−0.587029	−	0.809566i	$-0.699703\pi$
$809$	−33.3937	−1.17406	−0.587029	+	0.809566i	$0.699703\pi$
$810$	0.933377	0.0327955
$811$	−20.1242	−0.706655	−0.353328	−	0.935500i	$-0.614950\pi$
$811$	−20.1242	−0.706655	−0.353328	+	0.935500i	$0.614950\pi$
$812$	0.384227	0.0134837
$813$	0.418090	0.0146630
$814$	1.13074	0.0396326
$815$	10.1932	0.357051
$816$	20.7040	0.724786
$817$	−10.7425	−0.375834
$818$	−47.6954	−1.66763
$819$	0.403322	0.0140932
$820$	1.03169	0.0360282
$821$	14.4373	0.503866	0.251933	−	0.967745i	$-0.418934\pi$
$821$	14.4373	0.503866	0.251933	+	0.967745i	$0.418934\pi$
$822$	20.2096	0.704892
$823$	−43.2396	−1.50724	−0.753620	−	0.657311i	$-0.771694\pi$
$823$	−43.2396	−1.50724	−0.753620	+	0.657311i	$0.771694\pi$
$824$	2.71105	0.0944438
$825$	−9.63897	−0.335586
$826$	8.69052	0.302382
$827$	−25.7953	−0.896991	−0.448495	−	0.893785i	$-0.648040\pi$
$827$	−25.7953	−0.896991	−0.448495	+	0.893785i	$0.648040\pi$
$828$	0.905806	0.0314789
$829$	28.2029	0.979527	0.489763	−	0.871855i	$-0.337083\pi$
$829$	28.2029	0.979527	0.489763	+	0.871855i	$0.337083\pi$
$830$	−2.67455	−0.0928348
$831$	15.1969	0.527175
$832$	−7.30363	−0.253208
$833$	−33.0693	−1.14578
$834$	15.3054	0.529984
$835$	−14.0783	−0.487200
$836$	−1.94325	−0.0672089
$837$	6.81119	0.235429
$838$	33.8377	1.16891
$839$	−22.1794	−0.765718	−0.382859	−	0.923807i	$-0.625060\pi$
$839$	−22.1794	−0.765718	−0.382859	+	0.923807i	$0.625060\pi$
$840$	−0.695722	−0.0240047
$841$	10.3351	0.356384
$842$	28.1139	0.968870
$843$	−31.0827	−1.07054
$844$	2.22574	0.0766131
$845$	0.636277	0.0218886
$846$	−5.33634	−0.183467
$847$	2.66189	0.0914636
$848$	−2.22376	−0.0763643
$849$	23.4143	0.803576
$850$	−32.6023	−1.11825
$851$	−2.19136	−0.0751188
$852$	1.48565	0.0508974
$853$	28.5080	0.976095	0.488047	−	0.872817i	$-0.337709\pi$
$853$	28.5080	0.976095	0.488047	+	0.872817i	$0.337709\pi$
$854$	7.32890	0.250790
$855$	3.88061	0.132714
$856$	−29.0928	−0.994370
$857$	−40.1630	−1.37194	−0.685970	−	0.727630i	$-0.740622\pi$
$857$	−40.1630	−1.37194	−0.685970	+	0.727630i	$0.740622\pi$
$858$	−3.07710	−0.105050
$859$	24.4809	0.835278	0.417639	−	0.908613i	$-0.362858\pi$
$859$	24.4809	0.835278	0.417639	+	0.908613i	$0.362858\pi$
$860$	−0.170233	−0.00580491
$861$	4.30538	0.146727
$862$	−29.7168	−1.01216
$863$	1.13722	0.0387114	0.0193557	−	0.999813i	$-0.493838\pi$
$863$	1.13722	0.0387114	0.0193557	+	0.999813i	$0.493838\pi$
$864$	0.857437	0.0291706
$865$	4.41978	0.150277
$866$	2.89918	0.0985183
$867$	−6.39252	−0.217101
$868$	0.417273	0.0141632
$869$	21.8662	0.741760
$870$	5.85393	0.198467
$871$	−3.66993	−0.124351
$872$	6.08659	0.206118
$873$	7.51287	0.254272
$874$	53.3525	1.80468
$875$	2.46235	0.0832428
$876$	−0.0989032	−0.00334163
$877$	−40.4550	−1.36607	−0.683033	−	0.730387i	$-0.739340\pi$
$877$	−40.4550	−1.36607	−0.683033	+	0.730387i	$0.739340\pi$
$878$	12.4283	0.419434
$879$	−11.9327	−0.402479
$880$	5.71339	0.192598
$881$	47.4177	1.59754	0.798771	−	0.601636i	$-0.205484\pi$
$881$	47.4177	1.59754	0.798771	+	0.601636i	$0.205484\pi$
$882$	−10.0299	−0.337725
$883$	37.7172	1.26928	0.634642	−	0.772806i	$-0.281147\pi$
$883$	37.7172	1.26928	0.634642	+	0.772806i	$0.281147\pi$
$884$	−0.734655	−0.0247091
$885$	9.34607	0.314165
$886$	26.0853	0.876352
$887$	32.6274	1.09552	0.547761	−	0.836635i	$-0.315480\pi$
$887$	32.6274	1.09552	0.547761	+	0.836635i	$0.315480\pi$
$888$	−0.996231	−0.0334313
$889$	−0.0352106	−0.00118093
$890$	−16.6574	−0.558358
$891$	−2.09764	−0.0702736
$892$	0.436700	0.0146218
$893$	−22.1864	−0.742439
$894$	−17.4536	−0.583734
$895$	−5.33786	−0.178425
$896$	−5.01282	−0.167467
$897$	5.96335	0.199111
$898$	−57.0437	−1.90357
$899$	42.7182	1.42473
$900$	−0.697983	−0.0232661
$901$	2.51252	0.0837043
$902$	−32.8474	−1.09370
$903$	−0.710404	−0.0236408
$904$	−27.8807	−0.927298
$905$	15.0982	0.501882
$906$	19.0446	0.632715
$907$	−18.2395	−0.605632	−0.302816	−	0.953049i	$-0.597927\pi$
$907$	−18.2395	−0.605632	−0.302816	+	0.953049i	$0.597927\pi$
$908$	2.90060	0.0962599
$909$	−4.87100	−0.161561
$910$	0.376452	0.0124793
$911$	6.70123	0.222022	0.111011	−	0.993819i	$-0.464591\pi$
$911$	6.70123	0.222022	0.111011	+	0.993819i	$0.464591\pi$
$912$	26.1078	0.864516
$913$	6.01069	0.198925
$914$	25.9129	0.857123
$915$	7.88174	0.260562
$916$	−2.10860	−0.0696701
$917$	4.60453	0.152055
$918$	−7.09495	−0.234168
$919$	−0.446721	−0.0147360	−0.00736798	−	0.999973i	$-0.502345\pi$
$919$	−0.446721	−0.0147360	−0.00736798	+	0.999973i	$0.502345\pi$
$920$	−10.2866	−0.339141
$921$	9.52052	0.313712
$922$	−34.2958	−1.12947
$923$	9.78072	0.321936
$924$	−0.128507	−0.00422758
$925$	1.68858	0.0555203
$926$	36.5303	1.20046
$927$	−1.00000	−0.0328443
$928$	5.37765	0.176530
$929$	−5.27760	−0.173152	−0.0865762	−	0.996245i	$-0.527593\pi$
$929$	−5.27760	−0.173152	−0.0865762	+	0.996245i	$0.527593\pi$
$930$	6.35741	0.208468
$931$	−41.7004	−1.36668
$932$	3.25304	0.106557
$933$	9.91011	0.324442
$934$	9.15633	0.299604
$935$	−6.45529	−0.211111
$936$	2.71105	0.0886134
$937$	7.30840	0.238755	0.119377	−	0.992849i	$-0.461910\pi$
$937$	7.30840	0.238755	0.119377	+	0.992849i	$0.461910\pi$
$938$	−2.17131	−0.0708957
$939$	11.9062	0.388545
$940$	−0.351580	−0.0114673
$941$	43.5181	1.41865	0.709324	−	0.704883i	$-0.249000\pi$
$941$	43.5181	1.41865	0.709324	+	0.704883i	$0.249000\pi$
$942$	14.3469	0.467448
$943$	63.6574	2.07297
$944$	62.8781	2.04651
$945$	0.256625	0.00834801
$946$	5.41994	0.176218
$947$	−46.6206	−1.51496	−0.757482	−	0.652856i	$-0.773571\pi$
$947$	−46.6206	−1.51496	−0.757482	+	0.652856i	$0.773571\pi$
$948$	1.58339	0.0514260
$949$	−0.651127	−0.0211365
$950$	−41.1116	−1.33384
$951$	21.8328	0.707976
$952$	5.28844	0.171399
$953$	16.1879	0.524378	0.262189	−	0.965017i	$-0.415556\pi$
$953$	16.1879	0.524378	0.262189	+	0.965017i	$0.415556\pi$
$954$	0.762048	0.0246722
$955$	2.25758	0.0730536
$956$	−4.49643	−0.145425
$957$	−13.1559	−0.425271
$958$	−44.9592	−1.45257
$959$	5.55648	0.179428
$960$	−4.64714	−0.149986
$961$	15.3923	0.496525
$962$	0.539056	0.0173799
$963$	10.7312	0.345808
$964$	−1.08832	−0.0350524
$965$	−1.37462	−0.0442504
$966$	3.52820	0.113518
$967$	18.5456	0.596388	0.298194	−	0.954505i	$-0.403616\pi$
$967$	18.5456	0.596388	0.298194	+	0.954505i	$0.403616\pi$
$968$	17.8927	0.575092
$969$	−29.4980	−0.947612
$970$	7.01234	0.225153
$971$	−58.9509	−1.89182	−0.945912	−	0.324425i	$-0.894829\pi$
$971$	−58.9509	−1.89182	−0.945912	+	0.324425i	$0.894829\pi$
$972$	−0.151895	−0.00487205
$973$	4.20811	0.134906
$974$	0.932823	0.0298896
$975$	−4.59515	−0.147163
$976$	53.0264	1.69733
$977$	−2.37584	−0.0760098	−0.0380049	−	0.999278i	$-0.512100\pi$
$977$	−2.37584	−0.0760098	−0.0380049	+	0.999278i	$0.512100\pi$
$978$	−23.5003	−0.751457
$979$	37.4353	1.19644
$980$	−0.660812	−0.0211089
$981$	−2.24511	−0.0716807
$982$	−3.70393	−0.118197
$983$	−22.4227	−0.715174	−0.357587	−	0.933880i	$-0.616400\pi$
$983$	−22.4227	−0.715174	−0.357587	+	0.933880i	$0.616400\pi$
$984$	28.9398	0.922568
$985$	7.46378	0.237816
$986$	−44.4979	−1.41710
$987$	−1.46719	−0.0467010
$988$	−0.926400	−0.0294727
$989$	−10.5037	−0.333999
$990$	−1.95789	−0.0622258
$991$	49.1265	1.56056	0.780278	−	0.625433i	$-0.215078\pi$
$991$	49.1265	1.56056	0.780278	+	0.625433i	$0.215078\pi$
$992$	5.84017	0.185425
$993$	−24.4613	−0.776254
$994$	5.78674	0.183544
$995$	9.42731	0.298866
$996$	0.435249	0.0137914
$997$	−30.1588	−0.955139	−0.477569	−	0.878594i	$-0.658482\pi$
$997$	−30.1588	−0.955139	−0.477569	+	0.878594i	$0.658482\pi$
$998$	−19.6627	−0.622412
$999$	0.367471	0.0116263

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4017.2.a.i.1.20	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4017.2.a.i.1.20	✓	25	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:	\( N \)	\(=\)	\( 4017 = 3 \cdot 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4017.a (trivial)

\(f(q)\)	\(=\)	\(q+1.46693 q^{2} -1.00000 q^{3} +0.151895 q^{4} +0.636277 q^{5} -1.46693 q^{6} -0.403322 q^{7} -2.71105 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.46693 q^{2} -1.00000 q^{3} +0.151895 q^{4} +0.636277 q^{5} -1.46693 q^{6} -0.403322 q^{7} -2.71105 q^{8} +1.00000 q^{9} +0.933377 q^{10} -2.09764 q^{11} -0.151895 q^{12} -1.00000 q^{13} -0.591647 q^{14} -0.636277 q^{15} -4.28072 q^{16} +4.83658 q^{17} +1.46693 q^{18} +6.09893 q^{19} +0.0966476 q^{20} +0.403322 q^{21} -3.07710 q^{22} +5.96335 q^{23} +2.71105 q^{24} -4.59515 q^{25} -1.46693 q^{26} -1.00000 q^{27} -0.0612628 q^{28} -6.27177 q^{29} -0.933377 q^{30} -6.81119 q^{31} -0.857437 q^{32} +2.09764 q^{33} +7.09495 q^{34} -0.256625 q^{35} +0.151895 q^{36} -0.367471 q^{37} +8.94673 q^{38} +1.00000 q^{39} -1.72498 q^{40} +10.6748 q^{41} +0.591647 q^{42} -1.76138 q^{43} -0.318622 q^{44} +0.636277 q^{45} +8.74784 q^{46} -3.63775 q^{47} +4.28072 q^{48} -6.83733 q^{49} -6.74078 q^{50} -4.83658 q^{51} -0.151895 q^{52} +0.519483 q^{53} -1.46693 q^{54} -1.33468 q^{55} +1.09343 q^{56} -6.09893 q^{57} -9.20028 q^{58} -14.6887 q^{59} -0.0966476 q^{60} -12.3873 q^{61} -9.99156 q^{62} -0.403322 q^{63} +7.30363 q^{64} -0.636277 q^{65} +3.07710 q^{66} +3.66993 q^{67} +0.734655 q^{68} -5.96335 q^{69} -0.376452 q^{70} -9.78072 q^{71} -2.71105 q^{72} +0.651127 q^{73} -0.539056 q^{74} +4.59515 q^{75} +0.926400 q^{76} +0.846025 q^{77} +1.46693 q^{78} -10.4242 q^{79} -2.72372 q^{80} +1.00000 q^{81} +15.6592 q^{82} -2.86545 q^{83} +0.0612628 q^{84} +3.07741 q^{85} -2.58383 q^{86} +6.27177 q^{87} +5.68680 q^{88} -17.8464 q^{89} +0.933377 q^{90} +0.403322 q^{91} +0.905806 q^{92} +6.81119 q^{93} -5.33634 q^{94} +3.88061 q^{95} +0.857437 q^{96} +7.51287 q^{97} -10.0299 q^{98} -2.09764 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q - 2 q^{2} - 25 q^{3} + 28 q^{4} - 3 q^{5} + 2 q^{6} - 11 q^{7} - 15 q^{8} + 25 q^{9}+O(q^{10}) \) 25 * q - 2 * q^2 - 25 * q^3 + 28 * q^4 - 3 * q^5 + 2 * q^6 - 11 * q^7 - 15 * q^8 + 25 * q^9	\( 25 q - 2 q^{2} - 25 q^{3} + 28 q^{4} - 3 q^{5} + 2 q^{6} - 11 q^{7} - 15 q^{8} + 25 q^{9} + 2 q^{10} - q^{11} - 28 q^{12} - 25 q^{13} - 12 q^{14} + 3 q^{15} + 26 q^{16} - 10 q^{17} - 2 q^{18} + 22 q^{19} - 2 q^{20} + 11 q^{21} - 5 q^{22} - 49 q^{23} + 15 q^{24} + 22 q^{25} + 2 q^{26} - 25 q^{27} - 30 q^{28} - 22 q^{29} - 2 q^{30} + 8 q^{31} - 12 q^{32} + q^{33} - q^{34} - 2 q^{35} + 28 q^{36} - 26 q^{38} + 25 q^{39} - 22 q^{40} - 5 q^{41} + 12 q^{42} - 13 q^{43} - 25 q^{44} - 3 q^{45} + 13 q^{46} - 56 q^{47} - 26 q^{48} + 28 q^{49} - 31 q^{50} + 10 q^{51} - 28 q^{52} - 20 q^{53} + 2 q^{54} - 14 q^{55} - 22 q^{56} - 22 q^{57} - 21 q^{58} + 2 q^{59} + 2 q^{60} + 29 q^{61} - 39 q^{62} - 11 q^{63} + 21 q^{64} + 3 q^{65} + 5 q^{66} - 14 q^{67} - 60 q^{68} + 49 q^{69} - 31 q^{70} - 36 q^{71} - 15 q^{72} - 30 q^{73} - 64 q^{74} - 22 q^{75} + 38 q^{76} - 37 q^{77} - 2 q^{78} - 29 q^{79} + 25 q^{81} - 6 q^{82} - 17 q^{83} + 30 q^{84} + 3 q^{85} - 27 q^{86} + 22 q^{87} - 81 q^{88} - 38 q^{89} + 2 q^{90} + 11 q^{91} - 85 q^{92} - 8 q^{93} + 26 q^{94} - 71 q^{95} + 12 q^{96} + 19 q^{98} - q^{99}+O(q^{100}) \) 25 * q - 2 * q^2 - 25 * q^3 + 28 * q^4 - 3 * q^5 + 2 * q^6 - 11 * q^7 - 15 * q^8 + 25 * q^9 + 2 * q^10 - q^11 - 28 * q^12 - 25 * q^13 - 12 * q^14 + 3 * q^15 + 26 * q^16 - 10 * q^17 - 2 * q^18 + 22 * q^19 - 2 * q^20 + 11 * q^21 - 5 * q^22 - 49 * q^23 + 15 * q^24 + 22 * q^25 + 2 * q^26 - 25 * q^27 - 30 * q^28 - 22 * q^29 - 2 * q^30 + 8 * q^31 - 12 * q^32 + q^33 - q^34 - 2 * q^35 + 28 * q^36 - 26 * q^38 + 25 * q^39 - 22 * q^40 - 5 * q^41 + 12 * q^42 - 13 * q^43 - 25 * q^44 - 3 * q^45 + 13 * q^46 - 56 * q^47 - 26 * q^48 + 28 * q^49 - 31 * q^50 + 10 * q^51 - 28 * q^52 - 20 * q^53 + 2 * q^54 - 14 * q^55 - 22 * q^56 - 22 * q^57 - 21 * q^58 + 2 * q^59 + 2 * q^60 + 29 * q^61 - 39 * q^62 - 11 * q^63 + 21 * q^64 + 3 * q^65 + 5 * q^66 - 14 * q^67 - 60 * q^68 + 49 * q^69 - 31 * q^70 - 36 * q^71 - 15 * q^72 - 30 * q^73 - 64 * q^74 - 22 * q^75 + 38 * q^76 - 37 * q^77 - 2 * q^78 - 29 * q^79 + 25 * q^81 - 6 * q^82 - 17 * q^83 + 30 * q^84 + 3 * q^85 - 27 * q^86 + 22 * q^87 - 81 * q^88 - 38 * q^89 + 2 * q^90 + 11 * q^91 - 85 * q^92 - 8 * q^93 + 26 * q^94 - 71 * q^95 + 12 * q^96 + 19 * q^98 - q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more