LMFDB - Embedded newform 4029.2.a.e.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4029,2,Mod(1,4029)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4029, 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("4029.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4029 = 3 \cdot 17 \cdot 79 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4029.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:	$32.1717269744$
Analytic rank:	$1$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 6 x^{17} - 10 x^{16} + 120 x^{15} - 56 x^{14} - 921 x^{13} + 1181 x^{12} + 3316 x^{11} + \cdots + 138 $ x^18 - 6x^17 - 10x^16 + 120x^15 - 56x^14 - 921x^13 + 1181x^12 + 3316x^11 - 6280x^10 - 5249x^9 + 15005x^8 + 1809x^7 - 16711x^6 + 2434x^5 + 8758x^4 - 1858x^3 - 1942x^2 + 318*x + 138
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Root			$-2.40783$ of defining polynomial
Character	$\chi$	$=$	4029.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.40783 q^{2} +1.00000 q^{3} +3.79762 q^{4} -0.151954 q^{5} +2.40783 q^{6} -4.33995 q^{7} +4.32836 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.40783 q^{2} +1.00000 q^{3} +3.79762 q^{4} -0.151954 q^{5} +2.40783 q^{6} -4.33995 q^{7} +4.32836 q^{8} +1.00000 q^{9} -0.365880 q^{10} -4.52014 q^{11} +3.79762 q^{12} -1.75564 q^{13} -10.4499 q^{14} -0.151954 q^{15} +2.82669 q^{16} +1.00000 q^{17} +2.40783 q^{18} -2.38203 q^{19} -0.577065 q^{20} -4.33995 q^{21} -10.8837 q^{22} -7.38452 q^{23} +4.32836 q^{24} -4.97691 q^{25} -4.22726 q^{26} +1.00000 q^{27} -16.4815 q^{28} +7.12054 q^{29} -0.365880 q^{30} -10.3924 q^{31} -1.85054 q^{32} -4.52014 q^{33} +2.40783 q^{34} +0.659475 q^{35} +3.79762 q^{36} -8.77196 q^{37} -5.73552 q^{38} -1.75564 q^{39} -0.657713 q^{40} +11.9057 q^{41} -10.4499 q^{42} +0.158288 q^{43} -17.1658 q^{44} -0.151954 q^{45} -17.7806 q^{46} +9.39878 q^{47} +2.82669 q^{48} +11.8352 q^{49} -11.9835 q^{50} +1.00000 q^{51} -6.66724 q^{52} +8.34880 q^{53} +2.40783 q^{54} +0.686856 q^{55} -18.7849 q^{56} -2.38203 q^{57} +17.1450 q^{58} -3.03303 q^{59} -0.577065 q^{60} +3.24816 q^{61} -25.0232 q^{62} -4.33995 q^{63} -10.1092 q^{64} +0.266777 q^{65} -10.8837 q^{66} +4.66531 q^{67} +3.79762 q^{68} -7.38452 q^{69} +1.58790 q^{70} +12.2005 q^{71} +4.32836 q^{72} +6.45751 q^{73} -21.1213 q^{74} -4.97691 q^{75} -9.04606 q^{76} +19.6172 q^{77} -4.22726 q^{78} -1.00000 q^{79} -0.429528 q^{80} +1.00000 q^{81} +28.6668 q^{82} -9.16300 q^{83} -16.4815 q^{84} -0.151954 q^{85} +0.381130 q^{86} +7.12054 q^{87} -19.5648 q^{88} +4.28387 q^{89} -0.365880 q^{90} +7.61938 q^{91} -28.0436 q^{92} -10.3924 q^{93} +22.6306 q^{94} +0.361961 q^{95} -1.85054 q^{96} -1.08395 q^{97} +28.4971 q^{98} -4.52014 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 6 q^{2} + 18 q^{3} + 20 q^{4} - 5 q^{5} - 6 q^{6} - 13 q^{7} - 12 q^{8} + 18 q^{9}+O(q^{10}) $ 18 * q - 6 * q^2 + 18 * q^3 + 20 * q^4 - 5 * q^5 - 6 * q^6 - 13 * q^7 - 12 * q^8 + 18 * q^9	\( 18 q - 6 q^{2} + 18 q^{3} + 20 q^{4} - 5 q^{5} - 6 q^{6} - 13 q^{7} - 12 q^{8} + 18 q^{9} - 15 q^{10} - 27 q^{11} + 20 q^{12} - 4 q^{13} - 5 q^{14} - 5 q^{15} + 16 q^{16} + 18 q^{17} - 6 q^{18} - 30 q^{19} - 16 q^{20} - 13 q^{21} + 13 q^{22} - 21 q^{23} - 12 q^{24} + 13 q^{25} - 20 q^{26} + 18 q^{27} - 33 q^{28} - 47 q^{29} - 15 q^{30} - 18 q^{31} - 45 q^{32} - 27 q^{33} - 6 q^{34} - 17 q^{35} + 20 q^{36} + q^{37} + 5 q^{38} - 4 q^{39} - 12 q^{40} - 18 q^{41} - 5 q^{42} - 39 q^{43} - 34 q^{44} - 5 q^{45} - 7 q^{46} + 16 q^{48} + 15 q^{49} - 23 q^{50} + 18 q^{51} + 5 q^{52} - 9 q^{53} - 6 q^{54} + q^{55} - 24 q^{56} - 30 q^{57} + 41 q^{58} - 42 q^{59} - 16 q^{60} - 43 q^{61} - 54 q^{62} - 13 q^{63} + 22 q^{64} - 25 q^{65} + 13 q^{66} + 20 q^{68} - 21 q^{69} + 17 q^{70} + 9 q^{71} - 12 q^{72} + 19 q^{73} - 30 q^{74} + 13 q^{75} - 17 q^{76} - 14 q^{77} - 20 q^{78} - 18 q^{79} + 36 q^{80} + 18 q^{81} - 3 q^{82} - 61 q^{83} - 33 q^{84} - 5 q^{85} - 24 q^{86} - 47 q^{87} - 25 q^{88} + 10 q^{89} - 15 q^{90} - 52 q^{91} - 74 q^{92} - 18 q^{93} + 31 q^{94} - 37 q^{95} - 45 q^{96} - 9 q^{97} + 27 q^{98} - 27 q^{99}+O(q^{100}) \) 18 * q - 6 * q^2 + 18 * q^3 + 20 * q^4 - 5 * q^5 - 6 * q^6 - 13 * q^7 - 12 * q^8 + 18 * q^9 - 15 * q^10 - 27 * q^11 + 20 * q^12 - 4 * q^13 - 5 * q^14 - 5 * q^15 + 16 * q^16 + 18 * q^17 - 6 * q^18 - 30 * q^19 - 16 * q^20 - 13 * q^21 + 13 * q^22 - 21 * q^23 - 12 * q^24 + 13 * q^25 - 20 * q^26 + 18 * q^27 - 33 * q^28 - 47 * q^29 - 15 * q^30 - 18 * q^31 - 45 * q^32 - 27 * q^33 - 6 * q^34 - 17 * q^35 + 20 * q^36 + q^37 + 5 * q^38 - 4 * q^39 - 12 * q^40 - 18 * q^41 - 5 * q^42 - 39 * q^43 - 34 * q^44 - 5 * q^45 - 7 * q^46 + 16 * q^48 + 15 * q^49 - 23 * q^50 + 18 * q^51 + 5 * q^52 - 9 * q^53 - 6 * q^54 + q^55 - 24 * q^56 - 30 * q^57 + 41 * q^58 - 42 * q^59 - 16 * q^60 - 43 * q^61 - 54 * q^62 - 13 * q^63 + 22 * q^64 - 25 * q^65 + 13 * q^66 + 20 * q^68 - 21 * q^69 + 17 * q^70 + 9 * q^71 - 12 * q^72 + 19 * q^73 - 30 * q^74 + 13 * q^75 - 17 * q^76 - 14 * q^77 - 20 * q^78 - 18 * q^79 + 36 * q^80 + 18 * q^81 - 3 * q^82 - 61 * q^83 - 33 * q^84 - 5 * q^85 - 24 * q^86 - 47 * q^87 - 25 * q^88 + 10 * q^89 - 15 * q^90 - 52 * q^91 - 74 * q^92 - 18 * q^93 + 31 * q^94 - 37 * q^95 - 45 * q^96 - 9 * q^97 + 27 * q^98 - 27 * 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 $

$2$	2.40783	1.70259	0.851295	−	0.524688i	$-0.175818\pi$
$2$	2.40783	1.70259	0.851295	+	0.524688i	$0.175818\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	3.79762	1.89881
$5$	−0.151954	−0.0679561	−0.0339780	−	0.999423i	$-0.510818\pi$
$5$	−0.151954	−0.0679561	−0.0339780	+	0.999423i	$0.510818\pi$
$6$	2.40783	0.982991
$7$	−4.33995	−1.64035	−0.820174	−	0.572114i	$-0.806124\pi$
$7$	−4.33995	−1.64035	−0.820174	+	0.572114i	$0.806124\pi$
$8$	4.32836	1.53031
$9$	1.00000	0.333333
$10$	−0.365880	−0.115701
$11$	−4.52014	−1.36287	−0.681437	−	0.731876i	$-0.738645\pi$
$11$	−4.52014	−1.36287	−0.681437	+	0.731876i	$0.738645\pi$
$12$	3.79762	1.09628
$13$	−1.75564	−0.486926	−0.243463	−	0.969910i	$-0.578283\pi$
$13$	−1.75564	−0.486926	−0.243463	+	0.969910i	$0.578283\pi$
$14$	−10.4499	−2.79284
$15$	−0.151954	−0.0392345
$16$	2.82669	0.706673
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	2.40783	0.567530
$19$	−2.38203	−0.546476	−0.273238	−	0.961946i	$-0.588095\pi$
$19$	−2.38203	−0.546476	−0.273238	+	0.961946i	$0.588095\pi$
$20$	−0.577065	−0.129036
$21$	−4.33995	−0.947056
$22$	−10.8837	−2.32042
$23$	−7.38452	−1.53978	−0.769889	−	0.638177i	$-0.779689\pi$
$23$	−7.38452	−1.53978	−0.769889	+	0.638177i	$0.779689\pi$
$24$	4.32836	0.883523
$25$	−4.97691	−0.995382
$26$	−4.22726	−0.829035
$27$	1.00000	0.192450
$28$	−16.4815	−3.11471
$29$	7.12054	1.32225	0.661125	−	0.750276i	$-0.270079\pi$
$29$	7.12054	1.32225	0.661125	+	0.750276i	$0.270079\pi$
$30$	−0.365880	−0.0668002
$31$	−10.3924	−1.86654	−0.933268	−	0.359180i	$-0.883057\pi$
$31$	−10.3924	−1.86654	−0.933268	+	0.359180i	$0.883057\pi$
$32$	−1.85054	−0.327133
$33$	−4.52014	−0.786856
$34$	2.40783	0.412939
$35$	0.659475	0.111472
$36$	3.79762	0.632937
$37$	−8.77196	−1.44210	−0.721051	−	0.692882i	$-0.756341\pi$
$37$	−8.77196	−1.44210	−0.721051	+	0.692882i	$0.756341\pi$
$38$	−5.73552	−0.930424
$39$	−1.75564	−0.281127
$40$	−0.657713	−0.103994
$41$	11.9057	1.85936	0.929679	−	0.368371i	$-0.120084\pi$
$41$	11.9057	1.85936	0.929679	+	0.368371i	$0.120084\pi$
$42$	−10.4499	−1.61245
$43$	0.158288	0.0241387	0.0120693	−	0.999927i	$-0.496158\pi$
$43$	0.158288	0.0241387	0.0120693	+	0.999927i	$0.496158\pi$
$44$	−17.1658	−2.58784
$45$	−0.151954	−0.0226520
$46$	−17.7806	−2.62161
$47$	9.39878	1.37095	0.685477	−	0.728095i	$-0.259594\pi$
$47$	9.39878	1.37095	0.685477	+	0.728095i	$0.259594\pi$
$48$	2.82669	0.407998
$49$	11.8352	1.69074
$50$	−11.9835	−1.69473
$51$	1.00000	0.140028
$52$	−6.66724	−0.924580
$53$	8.34880	1.14680	0.573398	−	0.819277i	$-0.305625\pi$
$53$	8.34880	1.14680	0.573398	+	0.819277i	$0.305625\pi$
$54$	2.40783	0.327664
$55$	0.686856	0.0926156
$56$	−18.7849	−2.51024
$57$	−2.38203	−0.315508
$58$	17.1450	2.25125
$59$	−3.03303	−0.394866	−0.197433	−	0.980316i	$-0.563261\pi$
$59$	−3.03303	−0.394866	−0.197433	+	0.980316i	$0.563261\pi$
$60$	−0.577065	−0.0744988
$61$	3.24816	0.415885	0.207942	−	0.978141i	$-0.433323\pi$
$61$	3.24816	0.415885	0.207942	+	0.978141i	$0.433323\pi$
$62$	−25.0232	−3.17795
$63$	−4.33995	−0.546783
$64$	−10.1092	−1.26365
$65$	0.266777	0.0330896
$66$	−10.8837	−1.33969
$67$	4.66531	0.569958	0.284979	−	0.958534i	$-0.408013\pi$
$67$	4.66531	0.569958	0.284979	+	0.958534i	$0.408013\pi$
$68$	3.79762	0.460529
$69$	−7.38452	−0.888992
$70$	1.58790	0.189790
$71$	12.2005	1.44794	0.723969	−	0.689833i	$-0.242316\pi$
$71$	12.2005	1.44794	0.723969	+	0.689833i	$0.242316\pi$
$72$	4.32836	0.510102
$73$	6.45751	0.755794	0.377897	−	0.925848i	$-0.376647\pi$
$73$	6.45751	0.755794	0.377897	+	0.925848i	$0.376647\pi$
$74$	−21.1213	−2.45531
$75$	−4.97691	−0.574684
$76$	−9.04606	−1.03765
$77$	19.6172	2.23559
$78$	−4.22726	−0.478643
$79$	−1.00000	−0.112509
$79$	−1.00000	−0.112509
$80$	−0.429528	−0.0480227
$81$	1.00000	0.111111
$82$	28.6668	3.16572
$83$	−9.16300	−1.00577	−0.502885	−	0.864353i	$-0.667728\pi$
$83$	−9.16300	−1.00577	−0.502885	+	0.864353i	$0.667728\pi$
$84$	−16.4815	−1.79828
$85$	−0.151954	−0.0164818
$86$	0.381130	0.0410983
$87$	7.12054	0.763402
$88$	−19.5648	−2.08562
$89$	4.28387	0.454089	0.227044	−	0.973884i	$-0.427094\pi$
$89$	4.28387	0.454089	0.227044	+	0.973884i	$0.427094\pi$
$90$	−0.365880	−0.0385671
$91$	7.61938	0.798728
$92$	−28.0436	−2.92375
$93$	−10.3924	−1.07765
$94$	22.6306	2.33417
$95$	0.361961	0.0371364
$96$	−1.85054	−0.188870
$97$	−1.08395	−0.110058	−0.0550291	−	0.998485i	$-0.517525\pi$
$97$	−1.08395	−0.110058	−0.0550291	+	0.998485i	$0.517525\pi$
$98$	28.4971	2.87864
$99$	−4.52014	−0.454292
$100$	−18.9004	−1.89004
$101$	7.11106	0.707577	0.353789	−	0.935325i	$-0.384893\pi$
$101$	7.11106	0.707577	0.353789	+	0.935325i	$0.384893\pi$
$102$	2.40783	0.238410
$103$	15.1293	1.49073	0.745366	−	0.666656i	$-0.232275\pi$
$103$	15.1293	1.49073	0.745366	+	0.666656i	$0.232275\pi$
$104$	−7.59903	−0.745146
$105$	0.659475	0.0643582
$106$	20.1024	1.95252
$107$	−18.5245	−1.79083	−0.895415	−	0.445232i	$-0.853121\pi$
$107$	−18.5245	−1.79083	−0.895415	+	0.445232i	$0.853121\pi$
$108$	3.79762	0.365426
$109$	5.49835	0.526646	0.263323	−	0.964708i	$-0.415181\pi$
$109$	5.49835	0.526646	0.263323	+	0.964708i	$0.415181\pi$
$110$	1.65383	0.157686
$111$	−8.77196	−0.832598
$112$	−12.2677	−1.15919
$113$	−14.7224	−1.38496	−0.692482	−	0.721435i	$-0.743483\pi$
$113$	−14.7224	−1.38496	−0.692482	+	0.721435i	$0.743483\pi$
$114$	−5.73552	−0.537181
$115$	1.12211	0.104637
$116$	27.0411	2.51070
$117$	−1.75564	−0.162309
$118$	−7.30300	−0.672295
$119$	−4.33995	−0.397843
$120$	−0.657713	−0.0600407
$121$	9.43171	0.857428
$122$	7.82101	0.708081
$123$	11.9057	1.07350
$124$	−39.4666	−3.54420
$125$	1.51604	0.135598
$126$	−10.4499	−0.930947
$127$	−5.59505	−0.496480	−0.248240	−	0.968699i	$-0.579852\pi$
$127$	−5.59505	−0.496480	−0.248240	+	0.968699i	$0.579852\pi$
$128$	−20.6400	−1.82434
$129$	0.158288	0.0139365
$130$	0.642351	0.0563380
$131$	−21.0989	−1.84342	−0.921711	−	0.387878i	$-0.873208\pi$
$131$	−21.0989	−1.84342	−0.921711	+	0.387878i	$0.873208\pi$
$132$	−17.1658	−1.49409
$133$	10.3379	0.896411
$134$	11.2332	0.970405
$135$	−0.151954	−0.0130782
$136$	4.32836	0.371154
$137$	4.71248	0.402614	0.201307	−	0.979528i	$-0.435481\pi$
$137$	4.71248	0.402614	0.201307	+	0.979528i	$0.435481\pi$
$138$	−17.7806	−1.51359
$139$	−10.8718	−0.922131	−0.461065	−	0.887366i	$-0.652533\pi$
$139$	−10.8718	−0.922131	−0.461065	+	0.887366i	$0.652533\pi$
$140$	2.50444	0.211664
$141$	9.39878	0.791520
$142$	29.3768	2.46524
$143$	7.93573	0.663619
$144$	2.82669	0.235558
$145$	−1.08200	−0.0898549
$146$	15.5486	1.28681
$147$	11.8352	0.976151
$148$	−33.3126	−2.73828
$149$	−14.1790	−1.16159	−0.580796	−	0.814049i	$-0.697259\pi$
$149$	−14.1790	−1.16159	−0.580796	+	0.814049i	$0.697259\pi$
$150$	−11.9835	−0.978451
$151$	−9.27349	−0.754666	−0.377333	−	0.926078i	$-0.623159\pi$
$151$	−9.27349	−0.754666	−0.377333	+	0.926078i	$0.623159\pi$
$152$	−10.3103	−0.836276
$153$	1.00000	0.0808452
$154$	47.2348	3.80629
$155$	1.57918	0.126843
$156$	−6.66724	−0.533807
$157$	−21.7457	−1.73549	−0.867747	−	0.497006i	$-0.834433\pi$
$157$	−21.7457	−1.73549	−0.867747	+	0.497006i	$0.834433\pi$
$158$	−2.40783	−0.191556
$159$	8.34880	0.662103
$160$	0.281198	0.0222307
$161$	32.0485	2.52577
$162$	2.40783	0.189177
$163$	−2.74398	−0.214925	−0.107463	−	0.994209i	$-0.534273\pi$
$163$	−2.74398	−0.214925	−0.107463	+	0.994209i	$0.534273\pi$
$164$	45.2133	3.53057
$165$	0.686856	0.0534717
$166$	−22.0629	−1.71241
$167$	0.399333	0.0309013	0.0154507	−	0.999881i	$-0.495082\pi$
$167$	0.399333	0.0309013	0.0154507	+	0.999881i	$0.495082\pi$
$168$	−18.7849	−1.44929
$169$	−9.91774	−0.762903
$170$	−0.365880	−0.0280617
$171$	−2.38203	−0.182159
$172$	0.601118	0.0458348
$173$	−6.19157	−0.470736	−0.235368	−	0.971906i	$-0.575630\pi$
$173$	−6.19157	−0.470736	−0.235368	+	0.971906i	$0.575630\pi$
$174$	17.1450	1.29976
$175$	21.5996	1.63277
$176$	−12.7770	−0.963106
$177$	−3.03303	−0.227976
$178$	10.3148	0.773127
$179$	−15.9676	−1.19347	−0.596736	−	0.802437i	$-0.703536\pi$
$179$	−15.9676	−1.19347	−0.596736	+	0.802437i	$0.703536\pi$
$180$	−0.577065	−0.0430119
$181$	−11.6744	−0.867751	−0.433876	−	0.900973i	$-0.642854\pi$
$181$	−11.6744	−0.867751	−0.433876	+	0.900973i	$0.642854\pi$
$182$	18.3461	1.35991
$183$	3.24816	0.240111
$184$	−31.9629	−2.35633
$185$	1.33294	0.0979996
$186$	−25.0232	−1.83479
$187$	−4.52014	−0.330546
$188$	35.6930	2.60318
$189$	−4.33995	−0.315685
$190$	0.871538	0.0632280
$191$	7.42146	0.536998	0.268499	−	0.963280i	$-0.413472\pi$
$191$	7.42146	0.536998	0.268499	+	0.963280i	$0.413472\pi$
$192$	−10.1092	−0.729566
$193$	−6.68968	−0.481534	−0.240767	−	0.970583i	$-0.577399\pi$
$193$	−6.68968	−0.481534	−0.240767	+	0.970583i	$0.577399\pi$
$194$	−2.60995	−0.187384
$195$	0.266777	0.0191043
$196$	44.9456	3.21040
$197$	3.13672	0.223482	0.111741	−	0.993737i	$-0.464357\pi$
$197$	3.13672	0.223482	0.111741	+	0.993737i	$0.464357\pi$
$198$	−10.8837	−0.773472
$199$	−20.2789	−1.43753	−0.718766	−	0.695252i	$-0.755293\pi$
$199$	−20.2789	−1.43753	−0.718766	+	0.695252i	$0.755293\pi$
$200$	−21.5419	−1.52324
$201$	4.66531	0.329065
$202$	17.1222	1.20471
$203$	−30.9028	−2.16895
$204$	3.79762	0.265887
$205$	−1.80912	−0.126355
$206$	36.4286	2.53810
$207$	−7.38452	−0.513260
$208$	−4.96264	−0.344097
$209$	10.7671	0.744778
$210$	1.58790	0.109576
$211$	−15.5992	−1.07390	−0.536948	−	0.843615i	$-0.680423\pi$
$211$	−15.5992	−1.07390	−0.536948	+	0.843615i	$0.680423\pi$
$212$	31.7056	2.17755
$213$	12.2005	0.835967
$214$	−44.6037	−3.04905
$215$	−0.0240526	−0.00164037
$216$	4.32836	0.294508
$217$	45.1027	3.06177
$218$	13.2391	0.896663
$219$	6.45751	0.436358
$220$	2.60842	0.175860
$221$	−1.75564	−0.118097
$222$	−21.1213	−1.41757
$223$	15.3667	1.02903	0.514516	−	0.857481i	$-0.327972\pi$
$223$	15.3667	1.02903	0.514516	+	0.857481i	$0.327972\pi$
$224$	8.03128	0.536612
$225$	−4.97691	−0.331794
$226$	−35.4489	−2.35803
$227$	11.9716	0.794584	0.397292	−	0.917692i	$-0.369950\pi$
$227$	11.9716	0.794584	0.397292	+	0.917692i	$0.369950\pi$
$228$	−9.04606	−0.599090
$229$	2.52381	0.166778	0.0833889	−	0.996517i	$-0.473426\pi$
$229$	2.52381	0.166778	0.0833889	+	0.996517i	$0.473426\pi$
$230$	2.70185	0.178154
$231$	19.6172	1.29072
$232$	30.8202	2.02345
$233$	7.91376	0.518448	0.259224	−	0.965817i	$-0.416533\pi$
$233$	7.91376	0.518448	0.259224	+	0.965817i	$0.416533\pi$
$234$	−4.22726	−0.276345
$235$	−1.42819	−0.0931646
$236$	−11.5183	−0.749777
$237$	−1.00000	−0.0649570
$238$	−10.4499	−0.677363
$239$	26.2797	1.69989	0.849946	−	0.526871i	$-0.176635\pi$
$239$	26.2797	1.69989	0.849946	+	0.526871i	$0.176635\pi$
$240$	−0.429528	−0.0277259
$241$	−7.55307	−0.486536	−0.243268	−	0.969959i	$-0.578219\pi$
$241$	−7.55307	−0.486536	−0.243268	+	0.969959i	$0.578219\pi$
$242$	22.7099	1.45985
$243$	1.00000	0.0641500
$244$	12.3353	0.789686
$245$	−1.79841	−0.114896
$246$	28.6668	1.82773
$247$	4.18198	0.266093
$248$	−44.9822	−2.85637
$249$	−9.16300	−0.580682
$250$	3.65035	0.230868
$251$	−0.414474	−0.0261614	−0.0130807	−	0.999914i	$-0.504164\pi$
$251$	−0.414474	−0.0261614	−0.0130807	+	0.999914i	$0.504164\pi$
$252$	−16.4815	−1.03824
$253$	33.3791	2.09853
$254$	−13.4719	−0.845302
$255$	−0.151954	−0.00951575
$256$	−29.4792	−1.84245
$257$	−1.80139	−0.112368	−0.0561839	−	0.998420i	$-0.517893\pi$
$257$	−1.80139	−0.112368	−0.0561839	+	0.998420i	$0.517893\pi$
$258$	0.381130	0.0237281
$259$	38.0699	2.36555
$260$	1.01312	0.0628308
$261$	7.12054	0.440750
$262$	−50.8025	−3.13859
$263$	2.42229	0.149365	0.0746824	−	0.997207i	$-0.476206\pi$
$263$	2.42229	0.149365	0.0746824	+	0.997207i	$0.476206\pi$
$264$	−19.5648	−1.20413
$265$	−1.26864	−0.0779317
$266$	24.8919	1.52622
$267$	4.28387	0.262168
$268$	17.7171	1.08224
$269$	−25.5784	−1.55954	−0.779771	−	0.626065i	$-0.784665\pi$
$269$	−25.5784	−1.55954	−0.779771	+	0.626065i	$0.784665\pi$
$270$	−0.365880	−0.0222667
$271$	−24.4811	−1.48712	−0.743562	−	0.668668i	$-0.766865\pi$
$271$	−24.4811	−1.48712	−0.743562	+	0.668668i	$0.766865\pi$
$272$	2.82669	0.171393
$273$	7.61938	0.461146
$274$	11.3468	0.685487
$275$	22.4964	1.35658
$276$	−28.0436	−1.68803
$277$	21.2521	1.27691	0.638456	−	0.769658i	$-0.279573\pi$
$277$	21.2521	1.27691	0.638456	+	0.769658i	$0.279573\pi$
$278$	−26.1773	−1.57001
$279$	−10.3924	−0.622179
$280$	2.85445	0.170586
$281$	1.77144	0.105675	0.0528375	−	0.998603i	$-0.483173\pi$
$281$	1.77144	0.105675	0.0528375	+	0.998603i	$0.483173\pi$
$282$	22.6306	1.34763
$283$	10.9800	0.652691	0.326345	−	0.945251i	$-0.394183\pi$
$283$	10.9800	0.652691	0.326345	+	0.945251i	$0.394183\pi$
$284$	46.3331	2.74936
$285$	0.361961	0.0214407
$286$	19.1078	1.12987
$287$	−51.6702	−3.05000
$288$	−1.85054	−0.109044
$289$	1.00000	0.0588235
$290$	−2.60526	−0.152986
$291$	−1.08395	−0.0635421
$292$	24.5232	1.43511
$293$	14.1476	0.826509	0.413254	−	0.910616i	$-0.364392\pi$
$293$	14.1476	0.826509	0.413254	+	0.910616i	$0.364392\pi$
$294$	28.4971	1.66198
$295$	0.460882	0.0268336
$296$	−37.9682	−2.20686
$297$	−4.52014	−0.262285
$298$	−34.1406	−1.97771
$299$	12.9645	0.749758
$300$	−18.9004	−1.09122
$301$	−0.686963	−0.0395959
$302$	−22.3290	−1.28489
$303$	7.11106	0.408520
$304$	−6.73327	−0.386180
$305$	−0.493573	−0.0282619
$306$	2.40783	0.137646
$307$	5.10899	0.291586	0.145793	−	0.989315i	$-0.453427\pi$
$307$	5.10899	0.291586	0.145793	+	0.989315i	$0.453427\pi$
$308$	74.4988	4.24496
$309$	15.1293	0.860674
$310$	3.80238	0.215961
$311$	−7.79621	−0.442083	−0.221041	−	0.975264i	$-0.570946\pi$
$311$	−7.79621	−0.442083	−0.221041	+	0.975264i	$0.570946\pi$
$312$	−7.59903	−0.430210
$313$	−21.3048	−1.20422	−0.602108	−	0.798415i	$-0.705672\pi$
$313$	−21.3048	−1.20422	−0.602108	+	0.798415i	$0.705672\pi$
$314$	−52.3598	−2.95483
$315$	0.659475	0.0371572
$316$	−3.79762	−0.213633
$317$	20.2665	1.13828	0.569140	−	0.822241i	$-0.307276\pi$
$317$	20.2665	1.13828	0.569140	+	0.822241i	$0.307276\pi$
$318$	20.1024	1.12729
$319$	−32.1859	−1.80206
$320$	1.53613	0.0858724
$321$	−18.5245	−1.03394
$322$	77.1671	4.30036
$323$	−2.38203	−0.132540
$324$	3.79762	0.210979
$325$	8.73764	0.484677
$326$	−6.60703	−0.365929
$327$	5.49835	0.304059
$328$	51.5322	2.84539
$329$	−40.7903	−2.24884
$330$	1.65383	0.0910403
$331$	21.7774	1.19700	0.598498	−	0.801125i	$-0.295765\pi$
$331$	21.7774	1.19700	0.598498	+	0.801125i	$0.295765\pi$
$332$	−34.7976	−1.90977
$333$	−8.77196	−0.480701
$334$	0.961525	0.0526123
$335$	−0.708914	−0.0387321
$336$	−12.2677	−0.669258
$337$	8.31558	0.452979	0.226489	−	0.974014i	$-0.427275\pi$
$337$	8.31558	0.452979	0.226489	+	0.974014i	$0.427275\pi$
$338$	−23.8802	−1.29891
$339$	−14.7224	−0.799610
$340$	−0.577065	−0.0312958
$341$	46.9753	2.54386
$342$	−5.73552	−0.310141
$343$	−20.9846	−1.13306
$344$	0.685128	0.0369396
$345$	1.12211	0.0604124
$346$	−14.9082	−0.801471
$347$	−10.3389	−0.555023	−0.277511	−	0.960722i	$-0.589510\pi$
$347$	−10.3389	−0.555023	−0.277511	+	0.960722i	$0.589510\pi$
$348$	27.0411	1.44956
$349$	14.3140	0.766212	0.383106	−	0.923704i	$-0.374854\pi$
$349$	14.3140	0.766212	0.383106	+	0.923704i	$0.374854\pi$
$350$	52.0080	2.77994
$351$	−1.75564	−0.0937089
$352$	8.36473	0.445841
$353$	−9.72900	−0.517822	−0.258911	−	0.965901i	$-0.583364\pi$
$353$	−9.72900	−0.517822	−0.258911	+	0.965901i	$0.583364\pi$
$354$	−7.30300	−0.388150
$355$	−1.85393	−0.0983962
$356$	16.2685	0.862229
$357$	−4.33995	−0.229695
$358$	−38.4471	−2.03199
$359$	−31.2316	−1.64834	−0.824169	−	0.566343i	$-0.808358\pi$
$359$	−31.2316	−1.64834	−0.824169	+	0.566343i	$0.808358\pi$
$360$	−0.657713	−0.0346645
$361$	−13.3259	−0.701364
$362$	−28.1099	−1.47742
$363$	9.43171	0.495036
$364$	28.9355	1.51663
$365$	−0.981247	−0.0513608
$366$	7.82101	0.408811
$367$	14.2351	0.743065	0.371533	−	0.928420i	$-0.378832\pi$
$367$	14.2351	0.743065	0.371533	+	0.928420i	$0.378832\pi$
$368$	−20.8738	−1.08812
$369$	11.9057	0.619786
$370$	3.20948	0.166853
$371$	−36.2334	−1.88114
$372$	−39.4666	−2.04625
$373$	23.5557	1.21967	0.609833	−	0.792530i	$-0.291237\pi$
$373$	23.5557	1.21967	0.609833	+	0.792530i	$0.291237\pi$
$374$	−10.8837	−0.562784
$375$	1.51604	0.0782877
$376$	40.6813	2.09798
$377$	−12.5011	−0.643838
$378$	−10.4499	−0.537482
$379$	−10.3850	−0.533439	−0.266720	−	0.963774i	$-0.585940\pi$
$379$	−10.3850	−0.533439	−0.266720	+	0.963774i	$0.585940\pi$
$380$	1.37459	0.0705149
$381$	−5.59505	−0.286643
$382$	17.8696	0.914288
$383$	18.1797	0.928941	0.464471	−	0.885588i	$-0.346245\pi$
$383$	18.1797	0.928941	0.464471	+	0.885588i	$0.346245\pi$
$384$	−20.6400	−1.05328
$385$	−2.98092	−0.151922
$386$	−16.1076	−0.819854
$387$	0.158288	0.00804623
$388$	−4.11642	−0.208980
$389$	−15.3436	−0.777950	−0.388975	−	0.921248i	$-0.627171\pi$
$389$	−15.3436	−0.777950	−0.388975	+	0.921248i	$0.627171\pi$
$390$	0.642351	0.0325267
$391$	−7.38452	−0.373451
$392$	51.2270	2.58736
$393$	−21.0989	−1.06430
$394$	7.55267	0.380498
$395$	0.151954	0.00764566
$396$	−17.1658	−0.862614
$397$	−5.99358	−0.300809	−0.150404	−	0.988625i	$-0.548058\pi$
$397$	−5.99358	−0.300809	−0.150404	+	0.988625i	$0.548058\pi$
$398$	−48.8280	−2.44753
$399$	10.3379	0.517543
$400$	−14.0682	−0.703409
$401$	0.0669525	0.00334345	0.00167172	−	0.999999i	$-0.499468\pi$
$401$	0.0669525	0.00334345	0.00167172	+	0.999999i	$0.499468\pi$
$402$	11.2332	0.560263
$403$	18.2453	0.908865
$404$	27.0051	1.34356
$405$	−0.151954	−0.00755067
$406$	−74.4086	−3.69283
$407$	39.6505	1.96540
$408$	4.32836	0.214286
$409$	−10.3500	−0.511776	−0.255888	−	0.966706i	$-0.582368\pi$
$409$	−10.3500	−0.511776	−0.255888	+	0.966706i	$0.582368\pi$
$410$	−4.35605	−0.215130
$411$	4.71248	0.232449
$412$	57.4552	2.83062
$413$	13.1632	0.647719
$414$	−17.7806	−0.873870
$415$	1.39236	0.0683482
$416$	3.24888	0.159290
$417$	−10.8718	−0.532393
$418$	25.9254	1.26805
$419$	−24.8740	−1.21518	−0.607588	−	0.794252i	$-0.707863\pi$
$419$	−24.8740	−1.21518	−0.607588	+	0.794252i	$0.707863\pi$
$420$	2.50444	0.122204
$421$	3.30639	0.161144	0.0805718	−	0.996749i	$-0.474325\pi$
$421$	3.30639	0.161144	0.0805718	+	0.996749i	$0.474325\pi$
$422$	−37.5602	−1.82840
$423$	9.39878	0.456984
$424$	36.1366	1.75495
$425$	−4.97691	−0.241416
$426$	29.3768	1.42331
$427$	−14.0969	−0.682196
$428$	−70.3490	−3.40045
$429$	7.93573	0.383141
$430$	−0.0579144	−0.00279288
$431$	−6.10745	−0.294185	−0.147093	−	0.989123i	$-0.546992\pi$
$431$	−6.10745	−0.294185	−0.147093	+	0.989123i	$0.546992\pi$
$432$	2.82669	0.135999
$433$	−28.3882	−1.36425	−0.682124	−	0.731236i	$-0.738944\pi$
$433$	−28.3882	−1.36425	−0.682124	+	0.731236i	$0.738944\pi$
$434$	108.599	5.21294
$435$	−1.08200	−0.0518778
$436$	20.8807	1.00000
$437$	17.5902	0.841452
$438$	15.5486	0.742938
$439$	23.7069	1.13147	0.565734	−	0.824588i	$-0.308593\pi$
$439$	23.7069	1.13147	0.565734	+	0.824588i	$0.308593\pi$
$440$	2.97296	0.141730
$441$	11.8352	0.563581
$442$	−4.22726	−0.201070
$443$	40.7013	1.93378	0.966889	−	0.255196i	$-0.0821399\pi$
$443$	40.7013	1.93378	0.966889	+	0.255196i	$0.0821399\pi$
$444$	−33.3126	−1.58095
$445$	−0.650952	−0.0308581
$446$	37.0004	1.75202
$447$	−14.1790	−0.670645
$448$	43.8733	2.07282
$449$	7.62124	0.359669	0.179834	−	0.983697i	$-0.442444\pi$
$449$	7.62124	0.359669	0.179834	+	0.983697i	$0.442444\pi$
$450$	−11.9835	−0.564909
$451$	−53.8155	−2.53407
$452$	−55.9100	−2.62979
$453$	−9.27349	−0.435707
$454$	28.8256	1.35285
$455$	−1.15780	−0.0542784
$456$	−10.3103	−0.482824
$457$	29.5250	1.38112	0.690560	−	0.723275i	$-0.257364\pi$
$457$	29.5250	1.38112	0.690560	+	0.723275i	$0.257364\pi$
$458$	6.07689	0.283954
$459$	1.00000	0.0466760
$460$	4.26135	0.198687
$461$	13.2856	0.618771	0.309386	−	0.950937i	$-0.399877\pi$
$461$	13.2856	0.618771	0.309386	+	0.950937i	$0.399877\pi$
$462$	47.2348	2.19756
$463$	17.8718	0.830571	0.415285	−	0.909691i	$-0.363682\pi$
$463$	17.8718	0.830571	0.415285	+	0.909691i	$0.363682\pi$
$464$	20.1276	0.934398
$465$	1.57918	0.0732326
$466$	19.0550	0.882704
$467$	−1.50477	−0.0696326	−0.0348163	−	0.999394i	$-0.511085\pi$
$467$	−1.50477	−0.0696326	−0.0348163	+	0.999394i	$0.511085\pi$
$468$	−6.66724	−0.308193
$469$	−20.2472	−0.934930
$470$	−3.43882	−0.158621
$471$	−21.7457	−1.00199
$472$	−13.1280	−0.604267
$473$	−0.715485	−0.0328980
$474$	−2.40783	−0.110595
$475$	11.8552	0.543952
$476$	−16.4815	−0.755429
$477$	8.34880	0.382265
$478$	63.2769	2.89422
$479$	−22.7167	−1.03795	−0.518976	−	0.854789i	$-0.673687\pi$
$479$	−22.7167	−1.03795	−0.518976	+	0.854789i	$0.673687\pi$
$480$	0.281198	0.0128349
$481$	15.4004	0.702197
$482$	−18.1865	−0.828371
$483$	32.0485	1.45826
$484$	35.8181	1.62809
$485$	0.164710	0.00747912
$486$	2.40783	0.109221
$487$	−16.8463	−0.763380	−0.381690	−	0.924290i	$-0.624658\pi$
$487$	−16.8463	−0.763380	−0.381690	+	0.924290i	$0.624658\pi$
$488$	14.0592	0.636431
$489$	−2.74398	−0.124087
$490$	−4.33026	−0.195621
$491$	9.92684	0.447992	0.223996	−	0.974590i	$-0.428090\pi$
$491$	9.92684	0.447992	0.223996	+	0.974590i	$0.428090\pi$
$492$	45.2133	2.03838
$493$	7.12054	0.320693
$494$	10.0695	0.453048
$495$	0.686856	0.0308719
$496$	−29.3762	−1.31903
$497$	−52.9498	−2.37512
$498$	−22.0629	−0.988663
$499$	−6.89244	−0.308548	−0.154274	−	0.988028i	$-0.549304\pi$
$499$	−6.89244	−0.308548	−0.154274	+	0.988028i	$0.549304\pi$
$500$	5.75733	0.257476
$501$	0.399333	0.0178409
$502$	−0.997981	−0.0445421
$503$	40.2706	1.79558	0.897788	−	0.440429i	$-0.145174\pi$
$503$	40.2706	1.79558	0.897788	+	0.440429i	$0.145174\pi$
$504$	−18.7849	−0.836745
$505$	−1.08056	−0.0480842
$506$	80.3710	3.57293
$507$	−9.91774	−0.440462
$508$	−21.2479	−0.942723
$509$	40.4304	1.79205	0.896023	−	0.444008i	$-0.146444\pi$
$509$	40.4304	1.79205	0.896023	+	0.444008i	$0.146444\pi$
$510$	−0.365880	−0.0162014
$511$	−28.0253	−1.23977
$512$	−29.7008	−1.31260
$513$	−2.38203	−0.105169
$514$	−4.33744	−0.191316
$515$	−2.29896	−0.101304
$516$	0.601118	0.0264628
$517$	−42.4839	−1.86844
$518$	91.6657	4.02756
$519$	−6.19157	−0.271780
$520$	1.15471	0.0506372
$521$	18.4965	0.810344	0.405172	−	0.914240i	$-0.367212\pi$
$521$	18.4965	0.810344	0.405172	+	0.914240i	$0.367212\pi$
$522$	17.1450	0.750417
$523$	12.5841	0.550263	0.275132	−	0.961407i	$-0.411279\pi$
$523$	12.5841	0.550263	0.275132	+	0.961407i	$0.411279\pi$
$524$	−80.1257	−3.50031
$525$	21.5996	0.942682
$526$	5.83245	0.254307
$527$	−10.3924	−0.452702
$528$	−12.7770	−0.556050
$529$	31.5311	1.37092
$530$	−3.05466	−0.132686
$531$	−3.03303	−0.131622
$532$	39.2595	1.70212
$533$	−20.9021	−0.905369
$534$	10.3148	0.446365
$535$	2.81488	0.121698
$536$	20.1931	0.872211
$537$	−15.9676	−0.689052
$538$	−61.5883	−2.65526
$539$	−53.4968	−2.30427
$540$	−0.577065	−0.0248329
$541$	−18.3771	−0.790092	−0.395046	−	0.918661i	$-0.629271\pi$
$541$	−18.3771	−0.790092	−0.395046	+	0.918661i	$0.629271\pi$
$542$	−58.9463	−2.53196
$543$	−11.6744	−0.500996
$544$	−1.85054	−0.0793414
$545$	−0.835498	−0.0357888
$546$	18.3461	0.785142
$547$	−12.5501	−0.536603	−0.268302	−	0.963335i	$-0.586462\pi$
$547$	−12.5501	−0.536603	−0.268302	+	0.963335i	$0.586462\pi$
$548$	17.8962	0.764488
$549$	3.24816	0.138628
$550$	54.1673	2.30970
$551$	−16.9614	−0.722578
$552$	−31.9629	−1.36043
$553$	4.33995	0.184554
$554$	51.1713	2.17406
$555$	1.33294	0.0565801
$556$	−41.2868	−1.75095
$557$	−20.7366	−0.878637	−0.439318	−	0.898331i	$-0.644780\pi$
$557$	−20.7366	−0.878637	−0.439318	+	0.898331i	$0.644780\pi$
$558$	−25.0232	−1.05932
$559$	−0.277896	−0.0117538
$560$	1.86413	0.0787740
$561$	−4.52014	−0.190841
$562$	4.26531	0.179921
$563$	−36.7156	−1.54738	−0.773689	−	0.633565i	$-0.781591\pi$
$563$	−36.7156	−1.54738	−0.773689	+	0.633565i	$0.781591\pi$
$564$	35.6930	1.50295
$565$	2.23713	0.0941168
$566$	26.4378	1.11126
$567$	−4.33995	−0.182261
$568$	52.8083	2.21579
$569$	−44.6064	−1.87000	−0.934998	−	0.354652i	$-0.884599\pi$
$569$	−44.6064	−1.87000	−0.934998	+	0.354652i	$0.884599\pi$
$570$	0.871538	0.0365047
$571$	10.7879	0.451458	0.225729	−	0.974190i	$-0.427524\pi$
$571$	10.7879	0.451458	0.225729	+	0.974190i	$0.427524\pi$
$572$	30.1369	1.26009
$573$	7.42146	0.310036
$574$	−124.413	−5.19289
$575$	36.7521	1.53267
$576$	−10.1092	−0.421215
$577$	−37.4809	−1.56035	−0.780175	−	0.625561i	$-0.784870\pi$
$577$	−37.4809	−1.56035	−0.780175	+	0.625561i	$0.784870\pi$
$578$	2.40783	0.100152
$579$	−6.68968	−0.278014
$580$	−4.10902	−0.170618
$581$	39.7670	1.64981
$582$	−2.60995	−0.108186
$583$	−37.7378	−1.56294
$584$	27.9504	1.15660
$585$	0.266777	0.0110299
$586$	34.0648	1.40721
$587$	−25.4342	−1.04978	−0.524891	−	0.851169i	$-0.675894\pi$
$587$	−25.4342	−1.04978	−0.524891	+	0.851169i	$0.675894\pi$
$588$	44.9456	1.85353
$589$	24.7551	1.02002
$590$	1.10972	0.0456866
$591$	3.13672	0.129027
$592$	−24.7956	−1.01909
$593$	−21.5914	−0.886653	−0.443326	−	0.896360i	$-0.646202\pi$
$593$	−21.5914	−0.886653	−0.443326	+	0.896360i	$0.646202\pi$
$594$	−10.8837	−0.446564
$595$	0.659475	0.0270358
$596$	−53.8466	−2.20564
$597$	−20.2789	−0.829959
$598$	31.2163	1.27653
$599$	43.7615	1.78804	0.894022	−	0.448022i	$-0.147872\pi$
$599$	43.7615	1.78804	0.894022	+	0.448022i	$0.147872\pi$
$600$	−21.5419	−0.879443
$601$	41.5009	1.69286	0.846428	−	0.532503i	$-0.178749\pi$
$601$	41.5009	1.69286	0.846428	+	0.532503i	$0.178749\pi$
$602$	−1.65409	−0.0674155
$603$	4.66531	0.189986
$604$	−35.2172	−1.43297
$605$	−1.43319	−0.0582674
$606$	17.1222	0.695541
$607$	4.86952	0.197648	0.0988239	−	0.995105i	$-0.468492\pi$
$607$	4.86952	0.197648	0.0988239	+	0.995105i	$0.468492\pi$
$608$	4.40806	0.178770
$609$	−30.9028	−1.25224
$610$	−1.18844	−0.0481184
$611$	−16.5008	−0.667553
$612$	3.79762	0.153510
$613$	31.4069	1.26851	0.634257	−	0.773122i	$-0.281306\pi$
$613$	31.4069	1.26851	0.634257	+	0.773122i	$0.281306\pi$
$614$	12.3016	0.496451
$615$	−1.80912	−0.0729509
$616$	84.9104	3.42114
$617$	−26.1190	−1.05151	−0.525756	−	0.850635i	$-0.676217\pi$
$617$	−26.1190	−1.05151	−0.525756	+	0.850635i	$0.676217\pi$
$618$	36.4286	1.46537
$619$	−31.1923	−1.25372	−0.626862	−	0.779130i	$-0.715661\pi$
$619$	−31.1923	−1.25372	−0.626862	+	0.779130i	$0.715661\pi$
$620$	5.99712	0.240850
$621$	−7.38452	−0.296331
$622$	−18.7719	−0.752685
$623$	−18.5918	−0.744864
$624$	−4.96264	−0.198665
$625$	24.6542	0.986167
$626$	−51.2981	−2.05029
$627$	10.7671	0.429998
$628$	−82.5819	−3.29538
$629$	−8.77196	−0.349761
$630$	1.58790	0.0632635
$631$	−6.37123	−0.253635	−0.126817	−	0.991926i	$-0.540476\pi$
$631$	−6.37123	−0.253635	−0.126817	+	0.991926i	$0.540476\pi$
$632$	−4.32836	−0.172173
$633$	−15.5992	−0.620014
$634$	48.7982	1.93802
$635$	0.850193	0.0337389
$636$	31.7056	1.25721
$637$	−20.7783	−0.823267
$638$	−77.4979	−3.06817
$639$	12.2005	0.482646
$640$	3.13634	0.123975
$641$	−14.4331	−0.570072	−0.285036	−	0.958517i	$-0.592006\pi$
$641$	−14.4331	−0.570072	−0.285036	+	0.958517i	$0.592006\pi$
$642$	−44.6037	−1.76037
$643$	39.0090	1.53837	0.769183	−	0.639029i	$-0.220663\pi$
$643$	39.0090	1.53837	0.769183	+	0.639029i	$0.220663\pi$
$644$	121.708	4.79597
$645$	−0.0240526	−0.000947069 0
$646$	−5.73552	−0.225661
$647$	−13.3064	−0.523129	−0.261564	−	0.965186i	$-0.584238\pi$
$647$	−13.3064	−0.523129	−0.261564	+	0.965186i	$0.584238\pi$
$648$	4.32836	0.170034
$649$	13.7097	0.538154
$650$	21.0387	0.825206
$651$	45.1027	1.76771
$652$	−10.4206	−0.408102
$653$	−20.1716	−0.789374	−0.394687	−	0.918816i	$-0.629147\pi$
$653$	−20.1716	−0.789374	−0.394687	+	0.918816i	$0.629147\pi$
$654$	13.2391	0.517688
$655$	3.20607	0.125272
$656$	33.6537	1.31396
$657$	6.45751	0.251931
$658$	−98.2159	−3.82885
$659$	−21.1452	−0.823699	−0.411850	−	0.911252i	$-0.635117\pi$
$659$	−21.1452	−0.823699	−0.411850	+	0.911252i	$0.635117\pi$
$660$	2.60842	0.101533
$661$	−4.48074	−0.174281	−0.0871404	−	0.996196i	$-0.527773\pi$
$661$	−4.48074	−0.174281	−0.0871404	+	0.996196i	$0.527773\pi$
$662$	52.4362	2.03799
$663$	−1.75564	−0.0681833
$664$	−39.6608	−1.53914
$665$	−1.57089	−0.0609166
$666$	−21.1213	−0.818436
$667$	−52.5817	−2.03597
$668$	1.51652	0.0586758
$669$	15.3667	0.594112
$670$	−1.70694	−0.0659449
$671$	−14.6822	−0.566799
$672$	8.03128	0.309813
$673$	−14.2279	−0.548445	−0.274223	−	0.961666i	$-0.588421\pi$
$673$	−14.2279	−0.548445	−0.274223	+	0.961666i	$0.588421\pi$
$674$	20.0225	0.771237
$675$	−4.97691	−0.191561
$676$	−37.6638	−1.44861
$677$	10.2841	0.395251	0.197626	−	0.980278i	$-0.436677\pi$
$677$	10.2841	0.395251	0.197626	+	0.980278i	$0.436677\pi$
$678$	−35.4489	−1.36141
$679$	4.70428	0.180534
$680$	−0.657713	−0.0252222
$681$	11.9716	0.458753
$682$	113.108	4.33114
$683$	−31.7041	−1.21312	−0.606562	−	0.795036i	$-0.707452\pi$
$683$	−31.7041	−1.21312	−0.606562	+	0.795036i	$0.707452\pi$
$684$	−9.04606	−0.345885
$685$	−0.716082	−0.0273601
$686$	−50.5272	−1.92914
$687$	2.52381	0.0962892
$688$	0.447431	0.0170582
$689$	−14.6575	−0.558404
$690$	2.70185	0.102858
$691$	30.9763	1.17839	0.589197	−	0.807989i	$-0.299444\pi$
$691$	30.9763	1.17839	0.589197	+	0.807989i	$0.299444\pi$
$692$	−23.5132	−0.893839
$693$	19.6172	0.745197
$694$	−24.8943	−0.944976
$695$	1.65201	0.0626644
$696$	30.8202	1.16824
$697$	11.9057	0.450961
$698$	34.4657	1.30454
$699$	7.91376	0.299326
$700$	82.0270	3.10033
$701$	−7.11076	−0.268570	−0.134285	−	0.990943i	$-0.542874\pi$
$701$	−7.11076	−0.268570	−0.134285	+	0.990943i	$0.542874\pi$
$702$	−4.22726	−0.159548
$703$	20.8951	0.788074
$704$	45.6949	1.72219
$705$	−1.42819	−0.0537886
$706$	−23.4257	−0.881639
$707$	−30.8617	−1.16067
$708$	−11.5183	−0.432884
$709$	0.291372	0.0109427	0.00547135	−	0.999985i	$-0.498258\pi$
$709$	0.291372	0.0109427	0.00547135	+	0.999985i	$0.498258\pi$
$710$	−4.46393	−0.167528
$711$	−1.00000	−0.0375029
$712$	18.5421	0.694895
$713$	76.7432	2.87405
$714$	−10.4499	−0.391076
$715$	−1.20587	−0.0450969
$716$	−60.6388	−2.26618
$717$	26.2797	0.981433
$718$	−75.2001	−2.80644
$719$	16.9154	0.630837	0.315418	−	0.948953i	$-0.397855\pi$
$719$	16.9154	0.630837	0.315418	+	0.948953i	$0.397855\pi$
$720$	−0.429528	−0.0160076
$721$	−65.6603	−2.44532
$722$	−32.0865	−1.19413
$723$	−7.55307	−0.280902
$724$	−44.3349	−1.64770
$725$	−35.4383	−1.31614
$726$	22.7099	0.842844
$727$	−0.318045	−0.0117956	−0.00589782	−	0.999983i	$-0.501877\pi$
$727$	−0.318045	−0.0117956	−0.00589782	+	0.999983i	$0.501877\pi$
$728$	32.9794	1.22230
$729$	1.00000	0.0370370
$730$	−2.36267	−0.0874464
$731$	0.158288	0.00585449
$732$	12.3353	0.455926
$733$	−12.0064	−0.443465	−0.221733	−	0.975107i	$-0.571171\pi$
$733$	−12.0064	−0.443465	−0.221733	+	0.975107i	$0.571171\pi$
$734$	34.2756	1.26513
$735$	−1.79841	−0.0663354
$736$	13.6654	0.503713
$737$	−21.0879	−0.776782
$738$	28.6668	1.05524
$739$	−42.2325	−1.55355	−0.776774	−	0.629779i	$-0.783145\pi$
$739$	−42.2325	−1.55355	−0.776774	+	0.629779i	$0.783145\pi$
$740$	5.06200	0.186083
$741$	4.18198	0.153629
$742$	−87.2437	−3.20282
$743$	−8.13526	−0.298454	−0.149227	−	0.988803i	$-0.547678\pi$
$743$	−8.13526	−0.298454	−0.149227	+	0.988803i	$0.547678\pi$
$744$	−44.9822	−1.64913
$745$	2.15457	0.0789372
$746$	56.7179	2.07659
$747$	−9.16300	−0.335257
$748$	−17.1658	−0.627644
$749$	80.3954	2.93759
$750$	3.65035	0.133292
$751$	0.687285	0.0250794	0.0125397	−	0.999921i	$-0.496008\pi$
$751$	0.687285	0.0250794	0.0125397	+	0.999921i	$0.496008\pi$
$752$	26.5674	0.968815
$753$	−0.414474	−0.0151043
$754$	−30.1004	−1.09619
$755$	1.40915	0.0512842
$756$	−16.4815	−0.599427
$757$	−2.41360	−0.0877239	−0.0438619	−	0.999038i	$-0.513966\pi$
$757$	−2.41360	−0.0877239	−0.0438619	+	0.999038i	$0.513966\pi$
$758$	−25.0051	−0.908228
$759$	33.3791	1.21158
$760$	1.56670	0.0568300
$761$	21.9144	0.794396	0.397198	−	0.917733i	$-0.369983\pi$
$761$	21.9144	0.794396	0.397198	+	0.917733i	$0.369983\pi$
$762$	−13.4719	−0.488036
$763$	−23.8626	−0.863884
$764$	28.1839	1.01966
$765$	−0.151954	−0.00549392
$766$	43.7736	1.58161
$767$	5.32489	0.192271
$768$	−29.4792	−1.06374
$769$	−43.6963	−1.57573	−0.787864	−	0.615849i	$-0.788813\pi$
$769$	−43.6963	−1.57573	−0.787864	+	0.615849i	$0.788813\pi$
$770$	−7.17754	−0.258661
$771$	−1.80139	−0.0648756
$772$	−25.4049	−0.914342
$773$	−1.04580	−0.0376148	−0.0188074	−	0.999823i	$-0.505987\pi$
$773$	−1.04580	−0.0376148	−0.0188074	+	0.999823i	$0.505987\pi$
$774$	0.381130	0.0136994
$775$	51.7222	1.85792
$776$	−4.69171	−0.168423
$777$	38.0699	1.36575
$778$	−36.9446	−1.32453
$779$	−28.3598	−1.01609
$780$	1.01312	0.0362754
$781$	−55.1482	−1.97336
$782$	−17.7806	−0.635834
$783$	7.12054	0.254467
$784$	33.4545	1.19480
$785$	3.30435	0.117937
$786$	−50.8025	−1.81207
$787$	12.7612	0.454886	0.227443	−	0.973791i	$-0.426963\pi$
$787$	12.7612	0.454886	0.227443	+	0.973791i	$0.426963\pi$
$788$	11.9121	0.424350
$789$	2.42229	0.0862358
$790$	0.365880	0.0130174
$791$	63.8945	2.27183
$792$	−19.5648	−0.695205
$793$	−5.70259	−0.202505
$794$	−14.4315	−0.512154
$795$	−1.26864	−0.0449939
$796$	−77.0115	−2.72960
$797$	−21.0045	−0.744018	−0.372009	−	0.928229i	$-0.621331\pi$
$797$	−21.0045	−0.744018	−0.372009	+	0.928229i	$0.621331\pi$
$798$	24.8919	0.881164
$799$	9.39878	0.332505
$800$	9.20999	0.325622
$801$	4.28387	0.151363
$802$	0.161210	0.00569252
$803$	−29.1889	−1.03005
$804$	17.7171	0.624833
$805$	−4.86991	−0.171642
$806$	43.9316	1.54742
$807$	−25.5784	−0.900402
$808$	30.7792	1.08281
$809$	45.7764	1.60941	0.804706	−	0.593674i	$-0.202323\pi$
$809$	45.7764	1.60941	0.804706	+	0.593674i	$0.202323\pi$
$810$	−0.365880	−0.0128557
$811$	17.0285	0.597952	0.298976	−	0.954261i	$-0.403355\pi$
$811$	17.0285	0.597952	0.298976	+	0.954261i	$0.403355\pi$
$812$	−117.357	−4.11843
$813$	−24.4811	−0.858591
$814$	95.4716	3.34628
$815$	0.416960	0.0146055
$816$	2.82669	0.0989540
$817$	−0.377047	−0.0131912
$818$	−24.9211	−0.871345
$819$	7.61938	0.266243
$820$	−6.87037	−0.239924
$821$	41.8254	1.45972	0.729858	−	0.683599i	$-0.239586\pi$
$821$	41.8254	1.45972	0.729858	+	0.683599i	$0.239586\pi$
$822$	11.3468	0.395766
$823$	26.1918	0.912988	0.456494	−	0.889726i	$-0.349105\pi$
$823$	26.1918	0.912988	0.456494	+	0.889726i	$0.349105\pi$
$824$	65.4849	2.28128
$825$	22.4964	0.783222
$826$	31.6947	1.10280
$827$	37.5846	1.30694	0.653472	−	0.756950i	$-0.273312\pi$
$827$	37.5846	1.30694	0.653472	+	0.756950i	$0.273312\pi$
$828$	−28.0436	−0.974583
$829$	−10.3705	−0.360183	−0.180091	−	0.983650i	$-0.557639\pi$
$829$	−10.3705	−0.360183	−0.180091	+	0.983650i	$0.557639\pi$
$830$	3.35256	0.116369
$831$	21.2521	0.737226
$832$	17.7480	0.615302
$833$	11.8352	0.410066
$834$	−26.1773	−0.906446
$835$	−0.0606804	−0.00209993
$836$	40.8895	1.41419
$837$	−10.3924	−0.359215
$838$	−59.8923	−2.06895
$839$	29.2401	1.00948	0.504741	−	0.863271i	$-0.331588\pi$
$839$	29.2401	1.00948	0.504741	+	0.863271i	$0.331588\pi$
$840$	2.85445	0.0984877
$841$	21.7020	0.748346
$842$	7.96121	0.274361
$843$	1.77144	0.0610115
$844$	−59.2400	−2.03913
$845$	1.50704	0.0518439
$846$	22.6306	0.778057
$847$	−40.9332	−1.40648
$848$	23.5995	0.810409
$849$	10.9800	0.376831
$850$	−11.9835	−0.411032
$851$	64.7767	2.22052
$852$	46.3331	1.58734
$853$	7.43773	0.254663	0.127332	−	0.991860i	$-0.459359\pi$
$853$	7.43773	0.254663	0.127332	+	0.991860i	$0.459359\pi$
$854$	−33.9428	−1.16150
$855$	0.361961	0.0123788
$856$	−80.1807	−2.74052
$857$	−3.89692	−0.133116	−0.0665582	−	0.997783i	$-0.521202\pi$
$857$	−3.89692	−0.133116	−0.0665582	+	0.997783i	$0.521202\pi$
$858$	19.1078	0.652331
$859$	−14.1101	−0.481431	−0.240716	−	0.970596i	$-0.577382\pi$
$859$	−14.1101	−0.481431	−0.240716	+	0.970596i	$0.577382\pi$
$860$	−0.0913426	−0.00311476
$861$	−51.6702	−1.76092
$862$	−14.7057	−0.500877
$863$	−22.7184	−0.773343	−0.386672	−	0.922217i	$-0.626375\pi$
$863$	−22.7184	−0.773343	−0.386672	+	0.922217i	$0.626375\pi$
$864$	−1.85054	−0.0629568
$865$	0.940836	0.0319894
$866$	−68.3537	−2.32275
$867$	1.00000	0.0339618
$868$	171.283	5.81373
$869$	4.52014	0.153335
$870$	−2.60526	−0.0883266
$871$	−8.19058	−0.277527
$872$	23.7988	0.805930
$873$	−1.08395	−0.0366860
$874$	42.3541	1.43265
$875$	−6.57952	−0.222429
$876$	24.5232	0.828561
$877$	−5.65038	−0.190800	−0.0953999	−	0.995439i	$-0.530413\pi$
$877$	−5.65038	−0.190800	−0.0953999	+	0.995439i	$0.530413\pi$
$878$	57.0821	1.92643
$879$	14.1476	0.477185
$880$	1.94153	0.0654489
$881$	−43.8473	−1.47725	−0.738627	−	0.674114i	$-0.764526\pi$
$881$	−43.8473	−1.47725	−0.738627	+	0.674114i	$0.764526\pi$
$882$	28.4971	0.959547
$883$	36.1839	1.21768	0.608842	−	0.793291i	$-0.291634\pi$
$883$	36.1839	1.21768	0.608842	+	0.793291i	$0.291634\pi$
$884$	−6.66724	−0.224244
$885$	0.460882	0.0154924
$886$	98.0017	3.29243
$887$	16.3070	0.547534	0.273767	−	0.961796i	$-0.411730\pi$
$887$	16.3070	0.547534	0.273767	+	0.961796i	$0.411730\pi$
$888$	−37.9682	−1.27413
$889$	24.2823	0.814401
$890$	−1.56738	−0.0525387
$891$	−4.52014	−0.151431
$892$	58.3570	1.95394
$893$	−22.3882	−0.749193
$894$	−34.1406	−1.14183
$895$	2.42634	0.0811037
$896$	89.5767	2.99255
$897$	12.9645	0.432873
$898$	18.3506	0.612368
$899$	−73.9997	−2.46803
$900$	−18.9004	−0.630014
$901$	8.34880	0.278139
$902$	−129.578	−4.31448
$903$	−0.686963	−0.0228607
$904$	−63.7238	−2.11942
$905$	1.77398	0.0589690
$906$	−22.3290	−0.741830
$907$	−29.1358	−0.967437	−0.483718	−	0.875224i	$-0.660714\pi$
$907$	−29.1358	−0.967437	−0.483718	+	0.875224i	$0.660714\pi$
$908$	45.4637	1.50877
$909$	7.11106	0.235859
$910$	−2.78778	−0.0924139
$911$	−16.2787	−0.539338	−0.269669	−	0.962953i	$-0.586914\pi$
$911$	−16.2787	−0.539338	−0.269669	+	0.962953i	$0.586914\pi$
$912$	−6.73327	−0.222961
$913$	41.4181	1.37074
$914$	71.0910	2.35148
$915$	−0.493573	−0.0163170
$916$	9.58446	0.316680
$917$	91.5683	3.02385
$918$	2.40783	0.0794701
$919$	43.4182	1.43224	0.716118	−	0.697980i	$-0.245917\pi$
$919$	43.4182	1.43224	0.716118	+	0.697980i	$0.245917\pi$
$920$	4.85690	0.160127
$921$	5.10899	0.168347
$922$	31.9893	1.05351
$923$	−21.4197	−0.705038
$924$	74.4988	2.45083
$925$	43.6573	1.43544
$926$	43.0321	1.41412
$927$	15.1293	0.496910
$928$	−13.1769	−0.432552
$929$	−56.1792	−1.84318	−0.921591	−	0.388163i	$-0.873110\pi$
$929$	−56.1792	−1.84318	−0.921591	+	0.388163i	$0.873110\pi$
$930$	3.80238	0.124685
$931$	−28.1919	−0.923951
$932$	30.0535	0.984434
$933$	−7.79621	−0.255236
$934$	−3.62323	−0.118556
$935$	0.686856	0.0224626
$936$	−7.59903	−0.248382
$937$	−3.34745	−0.109356	−0.0546782	−	0.998504i	$-0.517413\pi$
$937$	−3.34745	−0.109356	−0.0546782	+	0.998504i	$0.517413\pi$
$938$	−48.7518	−1.59180
$939$	−21.3048	−0.695254
$940$	−5.42371	−0.176902
$941$	−36.8811	−1.20229	−0.601145	−	0.799140i	$-0.705288\pi$
$941$	−36.8811	−1.20229	−0.601145	+	0.799140i	$0.705288\pi$
$942$	−52.3598	−1.70597
$943$	−87.9179	−2.86300
$944$	−8.57343	−0.279041
$945$	0.659475	0.0214527
$946$	−1.72276	−0.0560118
$947$	29.6257	0.962706	0.481353	−	0.876527i	$-0.340146\pi$
$947$	29.6257	0.962706	0.481353	+	0.876527i	$0.340146\pi$
$948$	−3.79762	−0.123341
$949$	−11.3370	−0.368016
$950$	28.5452	0.926128
$951$	20.2665	0.657186
$952$	−18.7849	−0.608822
$953$	12.4910	0.404624	0.202312	−	0.979321i	$-0.435154\pi$
$953$	12.4910	0.404624	0.202312	+	0.979321i	$0.435154\pi$
$954$	20.1024	0.650841
$955$	−1.12772	−0.0364923
$956$	99.8003	3.22777
$957$	−32.1859	−1.04042
$958$	−54.6978	−1.76721
$959$	−20.4519	−0.660427
$960$	1.53613	0.0495785
$961$	77.0028	2.48396
$962$	37.0814	1.19555
$963$	−18.5245	−0.596943
$964$	−28.6837	−0.923840
$965$	1.01653	0.0327231
$966$	77.1671	2.48281
$967$	−23.3470	−0.750789	−0.375395	−	0.926865i	$-0.622493\pi$
$967$	−23.3470	−0.750789	−0.375395	+	0.926865i	$0.622493\pi$
$968$	40.8238	1.31213
$969$	−2.38203	−0.0765219
$970$	0.396594	0.0127339
$971$	−29.9290	−0.960468	−0.480234	−	0.877141i	$-0.659448\pi$
$971$	−29.9290	−0.960468	−0.480234	+	0.877141i	$0.659448\pi$
$972$	3.79762	0.121809
$973$	47.1830	1.51262
$974$	−40.5630	−1.29972
$975$	8.73764	0.279829
$976$	9.18155	0.293894
$977$	12.6785	0.405620	0.202810	−	0.979218i	$-0.434993\pi$
$977$	12.6785	0.405620	0.202810	+	0.979218i	$0.434993\pi$
$978$	−6.60703	−0.211269
$979$	−19.3637	−0.618866
$980$	−6.82969	−0.218166
$981$	5.49835	0.175549
$982$	23.9021	0.762747
$983$	−30.8456	−0.983822	−0.491911	−	0.870646i	$-0.663701\pi$
$983$	−30.8456	−0.983822	−0.491911	+	0.870646i	$0.663701\pi$
$984$	51.5322	1.64279
$985$	−0.476638	−0.0151870
$986$	17.1450	0.546008
$987$	−40.7903	−1.29837
$988$	15.8816	0.505261
$989$	−1.16888	−0.0371683
$990$	1.65383	0.0525621
$991$	2.04285	0.0648932	0.0324466	−	0.999473i	$-0.489670\pi$
$991$	2.04285	0.0648932	0.0324466	+	0.999473i	$0.489670\pi$
$992$	19.2317	0.610606
$993$	21.7774	0.691085
$994$	−127.494	−4.04386
$995$	3.08146	0.0976890
$996$	−34.7976	−1.10260
$997$	10.2710	0.325285	0.162642	−	0.986685i	$-0.447998\pi$
$997$	10.2710	0.325285	0.162642	+	0.986685i	$0.447998\pi$
$998$	−16.5958	−0.525331
$999$	−8.77196	−0.277533

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4029.2.a.e.1.18	✓	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4029.2.a.e.1.18	✓	18	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:	\( N \)	\(=\)	\( 4029 = 3 \cdot 17 \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4029.a (trivial)

\(f(q)\)	\(=\)	\(q+2.40783 q^{2} +1.00000 q^{3} +3.79762 q^{4} -0.151954 q^{5} +2.40783 q^{6} -4.33995 q^{7} +4.32836 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.40783 q^{2} +1.00000 q^{3} +3.79762 q^{4} -0.151954 q^{5} +2.40783 q^{6} -4.33995 q^{7} +4.32836 q^{8} +1.00000 q^{9} -0.365880 q^{10} -4.52014 q^{11} +3.79762 q^{12} -1.75564 q^{13} -10.4499 q^{14} -0.151954 q^{15} +2.82669 q^{16} +1.00000 q^{17} +2.40783 q^{18} -2.38203 q^{19} -0.577065 q^{20} -4.33995 q^{21} -10.8837 q^{22} -7.38452 q^{23} +4.32836 q^{24} -4.97691 q^{25} -4.22726 q^{26} +1.00000 q^{27} -16.4815 q^{28} +7.12054 q^{29} -0.365880 q^{30} -10.3924 q^{31} -1.85054 q^{32} -4.52014 q^{33} +2.40783 q^{34} +0.659475 q^{35} +3.79762 q^{36} -8.77196 q^{37} -5.73552 q^{38} -1.75564 q^{39} -0.657713 q^{40} +11.9057 q^{41} -10.4499 q^{42} +0.158288 q^{43} -17.1658 q^{44} -0.151954 q^{45} -17.7806 q^{46} +9.39878 q^{47} +2.82669 q^{48} +11.8352 q^{49} -11.9835 q^{50} +1.00000 q^{51} -6.66724 q^{52} +8.34880 q^{53} +2.40783 q^{54} +0.686856 q^{55} -18.7849 q^{56} -2.38203 q^{57} +17.1450 q^{58} -3.03303 q^{59} -0.577065 q^{60} +3.24816 q^{61} -25.0232 q^{62} -4.33995 q^{63} -10.1092 q^{64} +0.266777 q^{65} -10.8837 q^{66} +4.66531 q^{67} +3.79762 q^{68} -7.38452 q^{69} +1.58790 q^{70} +12.2005 q^{71} +4.32836 q^{72} +6.45751 q^{73} -21.1213 q^{74} -4.97691 q^{75} -9.04606 q^{76} +19.6172 q^{77} -4.22726 q^{78} -1.00000 q^{79} -0.429528 q^{80} +1.00000 q^{81} +28.6668 q^{82} -9.16300 q^{83} -16.4815 q^{84} -0.151954 q^{85} +0.381130 q^{86} +7.12054 q^{87} -19.5648 q^{88} +4.28387 q^{89} -0.365880 q^{90} +7.61938 q^{91} -28.0436 q^{92} -10.3924 q^{93} +22.6306 q^{94} +0.361961 q^{95} -1.85054 q^{96} -1.08395 q^{97} +28.4971 q^{98} -4.52014 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 6 q^{2} + 18 q^{3} + 20 q^{4} - 5 q^{5} - 6 q^{6} - 13 q^{7} - 12 q^{8} + 18 q^{9}+O(q^{10}) \) 18 * q - 6 * q^2 + 18 * q^3 + 20 * q^4 - 5 * q^5 - 6 * q^6 - 13 * q^7 - 12 * q^8 + 18 * q^9	\( 18 q - 6 q^{2} + 18 q^{3} + 20 q^{4} - 5 q^{5} - 6 q^{6} - 13 q^{7} - 12 q^{8} + 18 q^{9} - 15 q^{10} - 27 q^{11} + 20 q^{12} - 4 q^{13} - 5 q^{14} - 5 q^{15} + 16 q^{16} + 18 q^{17} - 6 q^{18} - 30 q^{19} - 16 q^{20} - 13 q^{21} + 13 q^{22} - 21 q^{23} - 12 q^{24} + 13 q^{25} - 20 q^{26} + 18 q^{27} - 33 q^{28} - 47 q^{29} - 15 q^{30} - 18 q^{31} - 45 q^{32} - 27 q^{33} - 6 q^{34} - 17 q^{35} + 20 q^{36} + q^{37} + 5 q^{38} - 4 q^{39} - 12 q^{40} - 18 q^{41} - 5 q^{42} - 39 q^{43} - 34 q^{44} - 5 q^{45} - 7 q^{46} + 16 q^{48} + 15 q^{49} - 23 q^{50} + 18 q^{51} + 5 q^{52} - 9 q^{53} - 6 q^{54} + q^{55} - 24 q^{56} - 30 q^{57} + 41 q^{58} - 42 q^{59} - 16 q^{60} - 43 q^{61} - 54 q^{62} - 13 q^{63} + 22 q^{64} - 25 q^{65} + 13 q^{66} + 20 q^{68} - 21 q^{69} + 17 q^{70} + 9 q^{71} - 12 q^{72} + 19 q^{73} - 30 q^{74} + 13 q^{75} - 17 q^{76} - 14 q^{77} - 20 q^{78} - 18 q^{79} + 36 q^{80} + 18 q^{81} - 3 q^{82} - 61 q^{83} - 33 q^{84} - 5 q^{85} - 24 q^{86} - 47 q^{87} - 25 q^{88} + 10 q^{89} - 15 q^{90} - 52 q^{91} - 74 q^{92} - 18 q^{93} + 31 q^{94} - 37 q^{95} - 45 q^{96} - 9 q^{97} + 27 q^{98} - 27 q^{99}+O(q^{100}) \) 18 * q - 6 * q^2 + 18 * q^3 + 20 * q^4 - 5 * q^5 - 6 * q^6 - 13 * q^7 - 12 * q^8 + 18 * q^9 - 15 * q^10 - 27 * q^11 + 20 * q^12 - 4 * q^13 - 5 * q^14 - 5 * q^15 + 16 * q^16 + 18 * q^17 - 6 * q^18 - 30 * q^19 - 16 * q^20 - 13 * q^21 + 13 * q^22 - 21 * q^23 - 12 * q^24 + 13 * q^25 - 20 * q^26 + 18 * q^27 - 33 * q^28 - 47 * q^29 - 15 * q^30 - 18 * q^31 - 45 * q^32 - 27 * q^33 - 6 * q^34 - 17 * q^35 + 20 * q^36 + q^37 + 5 * q^38 - 4 * q^39 - 12 * q^40 - 18 * q^41 - 5 * q^42 - 39 * q^43 - 34 * q^44 - 5 * q^45 - 7 * q^46 + 16 * q^48 + 15 * q^49 - 23 * q^50 + 18 * q^51 + 5 * q^52 - 9 * q^53 - 6 * q^54 + q^55 - 24 * q^56 - 30 * q^57 + 41 * q^58 - 42 * q^59 - 16 * q^60 - 43 * q^61 - 54 * q^62 - 13 * q^63 + 22 * q^64 - 25 * q^65 + 13 * q^66 + 20 * q^68 - 21 * q^69 + 17 * q^70 + 9 * q^71 - 12 * q^72 + 19 * q^73 - 30 * q^74 + 13 * q^75 - 17 * q^76 - 14 * q^77 - 20 * q^78 - 18 * q^79 + 36 * q^80 + 18 * q^81 - 3 * q^82 - 61 * q^83 - 33 * q^84 - 5 * q^85 - 24 * q^86 - 47 * q^87 - 25 * q^88 + 10 * q^89 - 15 * q^90 - 52 * q^91 - 74 * q^92 - 18 * q^93 + 31 * q^94 - 37 * q^95 - 45 * q^96 - 9 * q^97 + 27 * q^98 - 27 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more