LMFDB - Embedded newform 2738.2.a.h.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2738,2,Mod(1,2738)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2738, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("2738.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2738 = 2 \cdot 37^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2738.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:	$21.8630400734$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{21}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 5 $ x^2 - x - 5
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 74)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.79129$ of defining polynomial
Character	$\chi$	$=$	2738.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.79129 q^{3} +1.00000 q^{4} -0.791288 q^{5} +1.79129 q^{6} -2.00000 q^{7} -1.00000 q^{8} +0.208712 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.79129 q^{3} +1.00000 q^{4} -0.791288 q^{5} +1.79129 q^{6} -2.00000 q^{7} -1.00000 q^{8} +0.208712 q^{9} +0.791288 q^{10} +0.791288 q^{11} -1.79129 q^{12} +3.79129 q^{13} +2.00000 q^{14} +1.41742 q^{15} +1.00000 q^{16} -7.58258 q^{17} -0.208712 q^{18} -1.58258 q^{19} -0.791288 q^{20} +3.58258 q^{21} -0.791288 q^{22} +3.79129 q^{23} +1.79129 q^{24} -4.37386 q^{25} -3.79129 q^{26} +5.00000 q^{27} -2.00000 q^{28} +3.79129 q^{29} -1.41742 q^{30} -8.37386 q^{31} -1.00000 q^{32} -1.41742 q^{33} +7.58258 q^{34} +1.58258 q^{35} +0.208712 q^{36} +1.58258 q^{38} -6.79129 q^{39} +0.791288 q^{40} -9.79129 q^{41} -3.58258 q^{42} +6.00000 q^{43} +0.791288 q^{44} -0.165151 q^{45} -3.79129 q^{46} -7.58258 q^{47} -1.79129 q^{48} -3.00000 q^{49} +4.37386 q^{50} +13.5826 q^{51} +3.79129 q^{52} -1.58258 q^{53} -5.00000 q^{54} -0.626136 q^{55} +2.00000 q^{56} +2.83485 q^{57} -3.79129 q^{58} -1.58258 q^{59} +1.41742 q^{60} +12.7913 q^{61} +8.37386 q^{62} -0.417424 q^{63} +1.00000 q^{64} -3.00000 q^{65} +1.41742 q^{66} -6.37386 q^{67} -7.58258 q^{68} -6.79129 q^{69} -1.58258 q^{70} -9.16515 q^{71} -0.208712 q^{72} +4.37386 q^{73} +7.83485 q^{75} -1.58258 q^{76} -1.58258 q^{77} +6.79129 q^{78} -8.20871 q^{79} -0.791288 q^{80} -9.58258 q^{81} +9.79129 q^{82} +15.1652 q^{83} +3.58258 q^{84} +6.00000 q^{85} -6.00000 q^{86} -6.79129 q^{87} -0.791288 q^{88} +6.00000 q^{89} +0.165151 q^{90} -7.58258 q^{91} +3.79129 q^{92} +15.0000 q^{93} +7.58258 q^{94} +1.25227 q^{95} +1.79129 q^{96} +13.5826 q^{97} +3.00000 q^{98} +0.165151 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} + q^{3} + 2 q^{4} + 3 q^{5} - q^{6} - 4 q^{7} - 2 q^{8} + 5 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 + q^3 + 2 * q^4 + 3 * q^5 - q^6 - 4 * q^7 - 2 * q^8 + 5 * q^9	\( 2 q - 2 q^{2} + q^{3} + 2 q^{4} + 3 q^{5} - q^{6} - 4 q^{7} - 2 q^{8} + 5 q^{9} - 3 q^{10} - 3 q^{11} + q^{12} + 3 q^{13} + 4 q^{14} + 12 q^{15} + 2 q^{16} - 6 q^{17} - 5 q^{18} + 6 q^{19} + 3 q^{20} - 2 q^{21} + 3 q^{22} + 3 q^{23} - q^{24} + 5 q^{25} - 3 q^{26} + 10 q^{27} - 4 q^{28} + 3 q^{29} - 12 q^{30} - 3 q^{31} - 2 q^{32} - 12 q^{33} + 6 q^{34} - 6 q^{35} + 5 q^{36} - 6 q^{38} - 9 q^{39} - 3 q^{40} - 15 q^{41} + 2 q^{42} + 12 q^{43} - 3 q^{44} + 18 q^{45} - 3 q^{46} - 6 q^{47} + q^{48} - 6 q^{49} - 5 q^{50} + 18 q^{51} + 3 q^{52} + 6 q^{53} - 10 q^{54} - 15 q^{55} + 4 q^{56} + 24 q^{57} - 3 q^{58} + 6 q^{59} + 12 q^{60} + 21 q^{61} + 3 q^{62} - 10 q^{63} + 2 q^{64} - 6 q^{65} + 12 q^{66} + q^{67} - 6 q^{68} - 9 q^{69} + 6 q^{70} - 5 q^{72} - 5 q^{73} + 34 q^{75} + 6 q^{76} + 6 q^{77} + 9 q^{78} - 21 q^{79} + 3 q^{80} - 10 q^{81} + 15 q^{82} + 12 q^{83} - 2 q^{84} + 12 q^{85} - 12 q^{86} - 9 q^{87} + 3 q^{88} + 12 q^{89} - 18 q^{90} - 6 q^{91} + 3 q^{92} + 30 q^{93} + 6 q^{94} + 30 q^{95} - q^{96} + 18 q^{97} + 6 q^{98} - 18 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 + q^3 + 2 * q^4 + 3 * q^5 - q^6 - 4 * q^7 - 2 * q^8 + 5 * q^9 - 3 * q^10 - 3 * q^11 + q^12 + 3 * q^13 + 4 * q^14 + 12 * q^15 + 2 * q^16 - 6 * q^17 - 5 * q^18 + 6 * q^19 + 3 * q^20 - 2 * q^21 + 3 * q^22 + 3 * q^23 - q^24 + 5 * q^25 - 3 * q^26 + 10 * q^27 - 4 * q^28 + 3 * q^29 - 12 * q^30 - 3 * q^31 - 2 * q^32 - 12 * q^33 + 6 * q^34 - 6 * q^35 + 5 * q^36 - 6 * q^38 - 9 * q^39 - 3 * q^40 - 15 * q^41 + 2 * q^42 + 12 * q^43 - 3 * q^44 + 18 * q^45 - 3 * q^46 - 6 * q^47 + q^48 - 6 * q^49 - 5 * q^50 + 18 * q^51 + 3 * q^52 + 6 * q^53 - 10 * q^54 - 15 * q^55 + 4 * q^56 + 24 * q^57 - 3 * q^58 + 6 * q^59 + 12 * q^60 + 21 * q^61 + 3 * q^62 - 10 * q^63 + 2 * q^64 - 6 * q^65 + 12 * q^66 + q^67 - 6 * q^68 - 9 * q^69 + 6 * q^70 - 5 * q^72 - 5 * q^73 + 34 * q^75 + 6 * q^76 + 6 * q^77 + 9 * q^78 - 21 * q^79 + 3 * q^80 - 10 * q^81 + 15 * q^82 + 12 * q^83 - 2 * q^84 + 12 * q^85 - 12 * q^86 - 9 * q^87 + 3 * q^88 + 12 * q^89 - 18 * q^90 - 6 * q^91 + 3 * q^92 + 30 * q^93 + 6 * q^94 + 30 * q^95 - q^96 + 18 * q^97 + 6 * q^98 - 18 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.79129	−1.03420	−0.517100	−	0.855925i	$-0.672989\pi$
$3$	−1.79129	−1.03420	−0.517100	+	0.855925i	$0.672989\pi$
$4$	1.00000	0.500000
$5$	−0.791288	−0.353875	−0.176937	−	0.984222i	$-0.556619\pi$
$5$	−0.791288	−0.353875	−0.176937	+	0.984222i	$0.556619\pi$
$6$	1.79129	0.731290
$7$	−2.00000	−0.755929	−0.377964	−	0.925820i	$-0.623376\pi$
$7$	−2.00000	−0.755929	−0.377964	+	0.925820i	$0.623376\pi$
$8$	−1.00000	−0.353553
$9$	0.208712	0.0695707
$10$	0.791288	0.250227
$11$	0.791288	0.238582	0.119291	−	0.992859i	$-0.461938\pi$
$11$	0.791288	0.238582	0.119291	+	0.992859i	$0.461938\pi$
$12$	−1.79129	−0.517100
$13$	3.79129	1.05151	0.525757	−	0.850635i	$-0.323782\pi$
$13$	3.79129	1.05151	0.525757	+	0.850635i	$0.323782\pi$
$14$	2.00000	0.534522
$15$	1.41742	0.365977
$16$	1.00000	0.250000
$17$	−7.58258	−1.83904	−0.919522	−	0.393038i	$-0.871424\pi$
$17$	−7.58258	−1.83904	−0.919522	+	0.393038i	$0.871424\pi$
$18$	−0.208712	−0.0491939
$19$	−1.58258	−0.363068	−0.181534	−	0.983385i	$-0.558106\pi$
$19$	−1.58258	−0.363068	−0.181534	+	0.983385i	$0.558106\pi$
$20$	−0.791288	−0.176937
$21$	3.58258	0.781782
$22$	−0.791288	−0.168703
$23$	3.79129	0.790538	0.395269	−	0.918565i	$-0.370651\pi$
$23$	3.79129	0.790538	0.395269	+	0.918565i	$0.370651\pi$
$24$	1.79129	0.365645
$25$	−4.37386	−0.874773
$26$	−3.79129	−0.743533
$27$	5.00000	0.962250
$28$	−2.00000	−0.377964
$29$	3.79129	0.704024	0.352012	−	0.935995i	$-0.385498\pi$
$29$	3.79129	0.704024	0.352012	+	0.935995i	$0.385498\pi$
$30$	−1.41742	−0.258785
$31$	−8.37386	−1.50399	−0.751995	−	0.659169i	$-0.770908\pi$
$31$	−8.37386	−1.50399	−0.751995	+	0.659169i	$0.770908\pi$
$32$	−1.00000	−0.176777
$33$	−1.41742	−0.246742
$34$	7.58258	1.30040
$35$	1.58258	0.267504
$36$	0.208712	0.0347854
$37$	0	0
$37$	0	0
$38$	1.58258	0.256728
$39$	−6.79129	−1.08748
$40$	0.791288	0.125114
$41$	−9.79129	−1.52914	−0.764571	−	0.644539i	$-0.777049\pi$
$41$	−9.79129	−1.52914	−0.764571	+	0.644539i	$0.777049\pi$
$42$	−3.58258	−0.552803
$43$	6.00000	0.914991	0.457496	−	0.889212i	$-0.348747\pi$
$43$	6.00000	0.914991	0.457496	+	0.889212i	$0.348747\pi$
$44$	0.791288	0.119291
$45$	−0.165151	−0.0246193
$46$	−3.79129	−0.558995
$47$	−7.58258	−1.10603	−0.553016	−	0.833171i	$-0.686523\pi$
$47$	−7.58258	−1.10603	−0.553016	+	0.833171i	$0.686523\pi$
$48$	−1.79129	−0.258550
$49$	−3.00000	−0.428571
$50$	4.37386	0.618558
$51$	13.5826	1.90194
$52$	3.79129	0.525757
$53$	−1.58258	−0.217383	−0.108692	−	0.994076i	$-0.534666\pi$
$53$	−1.58258	−0.217383	−0.108692	+	0.994076i	$0.534666\pi$
$54$	−5.00000	−0.680414
$55$	−0.626136	−0.0844282
$56$	2.00000	0.267261
$57$	2.83485	0.375485
$58$	−3.79129	−0.497820
$59$	−1.58258	−0.206034	−0.103017	−	0.994680i	$-0.532850\pi$
$59$	−1.58258	−0.206034	−0.103017	+	0.994680i	$0.532850\pi$
$60$	1.41742	0.182989
$61$	12.7913	1.63776	0.818878	−	0.573967i	$-0.194596\pi$
$61$	12.7913	1.63776	0.818878	+	0.573967i	$0.194596\pi$
$62$	8.37386	1.06348
$63$	−0.417424	−0.0525905
$64$	1.00000	0.125000
$65$	−3.00000	−0.372104
$66$	1.41742	0.174473
$67$	−6.37386	−0.778691	−0.389346	−	0.921092i	$-0.627299\pi$
$67$	−6.37386	−0.778691	−0.389346	+	0.921092i	$0.627299\pi$
$68$	−7.58258	−0.919522
$69$	−6.79129	−0.817575
$70$	−1.58258	−0.189154
$71$	−9.16515	−1.08770	−0.543852	−	0.839181i	$-0.683035\pi$
$71$	−9.16515	−1.08770	−0.543852	+	0.839181i	$0.683035\pi$
$72$	−0.208712	−0.0245970
$73$	4.37386	0.511922	0.255961	−	0.966687i	$-0.417608\pi$
$73$	4.37386	0.511922	0.255961	+	0.966687i	$0.417608\pi$
$74$	0	0
$75$	7.83485	0.904690
$76$	−1.58258	−0.181534
$77$	−1.58258	−0.180351
$78$	6.79129	0.768962
$79$	−8.20871	−0.923552	−0.461776	−	0.886997i	$-0.652788\pi$
$79$	−8.20871	−0.923552	−0.461776	+	0.886997i	$0.652788\pi$
$80$	−0.791288	−0.0884687
$81$	−9.58258	−1.06473
$82$	9.79129	1.08127
$83$	15.1652	1.66459	0.832296	−	0.554332i	$-0.187026\pi$
$83$	15.1652	1.66459	0.832296	+	0.554332i	$0.187026\pi$
$84$	3.58258	0.390891
$85$	6.00000	0.650791
$86$	−6.00000	−0.646997
$87$	−6.79129	−0.728102
$88$	−0.791288	−0.0843516
$89$	6.00000	0.635999	0.317999	−	0.948091i	$-0.396989\pi$
$89$	6.00000	0.635999	0.317999	+	0.948091i	$0.396989\pi$
$90$	0.165151	0.0174085
$91$	−7.58258	−0.794870
$92$	3.79129	0.395269
$93$	15.0000	1.55543
$94$	7.58258	0.782083
$95$	1.25227	0.128480
$96$	1.79129	0.182823
$97$	13.5826	1.37910	0.689551	−	0.724237i	$-0.257808\pi$
$97$	13.5826	1.37910	0.689551	+	0.724237i	$0.257808\pi$
$98$	3.00000	0.303046
$99$	0.165151	0.0165983
$100$	−4.37386	−0.437386
$101$	−7.58258	−0.754494	−0.377247	−	0.926113i	$-0.623129\pi$
$101$	−7.58258	−0.754494	−0.377247	+	0.926113i	$0.623129\pi$
$102$	−13.5826	−1.34488
$103$	6.79129	0.669165	0.334583	−	0.942366i	$-0.391405\pi$
$103$	6.79129	0.669165	0.334583	+	0.942366i	$0.391405\pi$
$104$	−3.79129	−0.371766
$105$	−2.83485	−0.276653
$106$	1.58258	0.153713
$107$	−5.37386	−0.519511	−0.259755	−	0.965674i	$-0.583642\pi$
$107$	−5.37386	−0.519511	−0.259755	+	0.965674i	$0.583642\pi$
$108$	5.00000	0.481125
$109$	−6.00000	−0.574696	−0.287348	−	0.957826i	$-0.592774\pi$
$109$	−6.00000	−0.574696	−0.287348	+	0.957826i	$0.592774\pi$
$110$	0.626136	0.0596998
$111$	0	0
$112$	−2.00000	−0.188982
$113$	−10.4174	−0.979989	−0.489994	−	0.871726i	$-0.663001\pi$
$113$	−10.4174	−0.979989	−0.489994	+	0.871726i	$0.663001\pi$
$114$	−2.83485	−0.265508
$115$	−3.00000	−0.279751
$116$	3.79129	0.352012
$117$	0.791288	0.0731546
$118$	1.58258	0.145688
$119$	15.1652	1.39019
$120$	−1.41742	−0.129393
$121$	−10.3739	−0.943079
$122$	−12.7913	−1.15807
$123$	17.5390	1.58144
$124$	−8.37386	−0.751995
$125$	7.41742	0.663435
$126$	0.417424	0.0371871
$127$	8.00000	0.709885	0.354943	−	0.934888i	$-0.384500\pi$
$127$	8.00000	0.709885	0.354943	+	0.934888i	$0.384500\pi$
$128$	−1.00000	−0.0883883
$129$	−10.7477	−0.946285
$130$	3.00000	0.263117
$131$	16.7477	1.46326	0.731628	−	0.681704i	$-0.238761\pi$
$131$	16.7477	1.46326	0.731628	+	0.681704i	$0.238761\pi$
$132$	−1.41742	−0.123371
$133$	3.16515	0.274453
$134$	6.37386	0.550618
$135$	−3.95644	−0.340516
$136$	7.58258	0.650201
$137$	−3.62614	−0.309802	−0.154901	−	0.987930i	$-0.549506\pi$
$137$	−3.62614	−0.309802	−0.154901	+	0.987930i	$0.549506\pi$
$138$	6.79129	0.578113
$139$	13.3739	1.13436	0.567178	−	0.823595i	$-0.308035\pi$
$139$	13.3739	1.13436	0.567178	+	0.823595i	$0.308035\pi$
$140$	1.58258	0.133752
$141$	13.5826	1.14386
$142$	9.16515	0.769122
$143$	3.00000	0.250873
$144$	0.208712	0.0173927
$145$	−3.00000	−0.249136
$146$	−4.37386	−0.361984
$147$	5.37386	0.443229
$148$	0	0
$149$	−4.41742	−0.361889	−0.180945	−	0.983493i	$-0.557916\pi$
$149$	−4.41742	−0.361889	−0.180945	+	0.983493i	$0.557916\pi$
$150$	−7.83485	−0.639713
$151$	14.7477	1.20015	0.600077	−	0.799943i	$-0.295137\pi$
$151$	14.7477	1.20015	0.600077	+	0.799943i	$0.295137\pi$
$152$	1.58258	0.128364
$153$	−1.58258	−0.127944
$154$	1.58258	0.127528
$155$	6.62614	0.532224
$156$	−6.79129	−0.543738
$157$	−2.00000	−0.159617	−0.0798087	−	0.996810i	$-0.525431\pi$
$157$	−2.00000	−0.159617	−0.0798087	+	0.996810i	$0.525431\pi$
$158$	8.20871	0.653050
$159$	2.83485	0.224818
$160$	0.791288	0.0625568
$161$	−7.58258	−0.597591
$162$	9.58258	0.752878
$163$	19.5826	1.53383	0.766913	−	0.641751i	$-0.221792\pi$
$163$	19.5826	1.53383	0.766913	+	0.641751i	$0.221792\pi$
$164$	−9.79129	−0.764571
$165$	1.12159	0.0873157
$166$	−15.1652	−1.17704
$167$	21.9564	1.69904	0.849520	−	0.527556i	$-0.176892\pi$
$167$	21.9564	1.69904	0.849520	+	0.527556i	$0.176892\pi$
$168$	−3.58258	−0.276402
$169$	1.37386	0.105682
$170$	−6.00000	−0.460179
$171$	−0.330303	−0.0252589
$172$	6.00000	0.457496
$173$	−15.1652	−1.15299	−0.576493	−	0.817102i	$-0.695579\pi$
$173$	−15.1652	−1.15299	−0.576493	+	0.817102i	$0.695579\pi$
$174$	6.79129	0.514846
$175$	8.74773	0.661266
$176$	0.791288	0.0596456
$177$	2.83485	0.213080
$178$	−6.00000	−0.449719
$179$	1.58258	0.118287	0.0591436	−	0.998249i	$-0.481163\pi$
$179$	1.58258	0.118287	0.0591436	+	0.998249i	$0.481163\pi$
$180$	−0.165151	−0.0123097
$181$	8.74773	0.650213	0.325107	−	0.945677i	$-0.394600\pi$
$181$	8.74773	0.650213	0.325107	+	0.945677i	$0.394600\pi$
$182$	7.58258	0.562058
$183$	−22.9129	−1.69377
$184$	−3.79129	−0.279497
$185$	0	0
$186$	−15.0000	−1.09985
$187$	−6.00000	−0.438763
$188$	−7.58258	−0.553016
$189$	−10.0000	−0.727393
$190$	−1.25227	−0.0908494
$191$	−8.37386	−0.605912	−0.302956	−	0.953005i	$-0.597973\pi$
$191$	−8.37386	−0.605912	−0.302956	+	0.953005i	$0.597973\pi$
$192$	−1.79129	−0.129275
$193$	18.3303	1.31944	0.659722	−	0.751510i	$-0.270674\pi$
$193$	18.3303	1.31944	0.659722	+	0.751510i	$0.270674\pi$
$194$	−13.5826	−0.975172
$195$	5.37386	0.384830
$196$	−3.00000	−0.214286
$197$	−19.9129	−1.41873	−0.709367	−	0.704839i	$-0.751019\pi$
$197$	−19.9129	−1.41873	−0.709367	+	0.704839i	$0.751019\pi$
$198$	−0.165151	−0.0117368
$199$	−15.1652	−1.07503	−0.537515	−	0.843254i	$-0.680637\pi$
$199$	−15.1652	−1.07503	−0.537515	+	0.843254i	$0.680637\pi$
$200$	4.37386	0.309279
$201$	11.4174	0.805323
$202$	7.58258	0.533508
$203$	−7.58258	−0.532192
$204$	13.5826	0.950971
$205$	7.74773	0.541125
$206$	−6.79129	−0.473171
$207$	0.791288	0.0549983
$208$	3.79129	0.262879
$209$	−1.25227	−0.0866215
$210$	2.83485	0.195623
$211$	10.3739	0.714166	0.357083	−	0.934073i	$-0.383771\pi$
$211$	10.3739	0.714166	0.357083	+	0.934073i	$0.383771\pi$
$212$	−1.58258	−0.108692
$213$	16.4174	1.12490
$214$	5.37386	0.367350
$215$	−4.74773	−0.323792
$216$	−5.00000	−0.340207
$217$	16.7477	1.13691
$218$	6.00000	0.406371
$219$	−7.83485	−0.529430
$220$	−0.626136	−0.0422141
$221$	−28.7477	−1.93378
$222$	0	0
$223$	14.0000	0.937509	0.468755	−	0.883328i	$-0.344703\pi$
$223$	14.0000	0.937509	0.468755	+	0.883328i	$0.344703\pi$
$224$	2.00000	0.133631
$225$	−0.912878	−0.0608586
$226$	10.4174	0.692957
$227$	25.9129	1.71990	0.859949	−	0.510380i	$-0.170495\pi$
$227$	25.9129	1.71990	0.859949	+	0.510380i	$0.170495\pi$
$228$	2.83485	0.187742
$229$	6.74773	0.445902	0.222951	−	0.974830i	$-0.428431\pi$
$229$	6.74773	0.445902	0.222951	+	0.974830i	$0.428431\pi$
$230$	3.00000	0.197814
$231$	2.83485	0.186519
$232$	−3.79129	−0.248910
$233$	16.1216	1.05616	0.528080	−	0.849194i	$-0.322912\pi$
$233$	16.1216	1.05616	0.528080	+	0.849194i	$0.322912\pi$
$234$	−0.791288	−0.0517281
$235$	6.00000	0.391397
$236$	−1.58258	−0.103017
$237$	14.7042	0.955138
$238$	−15.1652	−0.983011
$239$	−2.04356	−0.132187	−0.0660935	−	0.997813i	$-0.521054\pi$
$239$	−2.04356	−0.132187	−0.0660935	+	0.997813i	$0.521054\pi$
$240$	1.41742	0.0914943
$241$	−4.41742	−0.284551	−0.142276	−	0.989827i	$-0.545442\pi$
$241$	−4.41742	−0.284551	−0.142276	+	0.989827i	$0.545442\pi$
$242$	10.3739	0.666857
$243$	2.16515	0.138895
$244$	12.7913	0.818878
$245$	2.37386	0.151661
$246$	−17.5390	−1.11825
$247$	−6.00000	−0.381771
$248$	8.37386	0.531741
$249$	−27.1652	−1.72152
$250$	−7.41742	−0.469119
$251$	4.41742	0.278825	0.139413	−	0.990234i	$-0.455479\pi$
$251$	4.41742	0.278825	0.139413	+	0.990234i	$0.455479\pi$
$252$	−0.417424	−0.0262953
$253$	3.00000	0.188608
$254$	−8.00000	−0.501965
$255$	−10.7477	−0.673049
$256$	1.00000	0.0625000
$257$	4.74773	0.296155	0.148078	−	0.988976i	$-0.452691\pi$
$257$	4.74773	0.296155	0.148078	+	0.988976i	$0.452691\pi$
$258$	10.7477	0.669124
$259$	0	0
$260$	−3.00000	−0.186052
$261$	0.791288	0.0489795
$262$	−16.7477	−1.03468
$263$	27.1652	1.67507	0.837537	−	0.546380i	$-0.183994\pi$
$263$	27.1652	1.67507	0.837537	+	0.546380i	$0.183994\pi$
$264$	1.41742	0.0872364
$265$	1.25227	0.0769265
$266$	−3.16515	−0.194068
$267$	−10.7477	−0.657750
$268$	−6.37386	−0.389346
$269$	16.7477	1.02113	0.510563	−	0.859840i	$-0.329437\pi$
$269$	16.7477	1.02113	0.510563	+	0.859840i	$0.329437\pi$
$270$	3.95644	0.240781
$271$	22.0000	1.33640	0.668202	−	0.743980i	$-0.267064\pi$
$271$	22.0000	1.33640	0.668202	+	0.743980i	$0.267064\pi$
$272$	−7.58258	−0.459761
$273$	13.5826	0.822055
$274$	3.62614	0.219063
$275$	−3.46099	−0.208705
$276$	−6.79129	−0.408787
$277$	−9.62614	−0.578378	−0.289189	−	0.957272i	$-0.593386\pi$
$277$	−9.62614	−0.578378	−0.289189	+	0.957272i	$0.593386\pi$
$278$	−13.3739	−0.802111
$279$	−1.74773	−0.104634
$280$	−1.58258	−0.0945770
$281$	0	0		−	1.00000i	$-0.5\pi$
$281$	0	0			1.00000i	$0.5\pi$
$282$	−13.5826	−0.808831
$283$	24.0000	1.42665	0.713326	−	0.700832i	$-0.247188\pi$
$283$	24.0000	1.42665	0.713326	+	0.700832i	$0.247188\pi$
$284$	−9.16515	−0.543852
$285$	−2.24318	−0.132875
$286$	−3.00000	−0.177394
$287$	19.5826	1.15592
$288$	−0.208712	−0.0122985
$289$	40.4955	2.38209
$290$	3.00000	0.176166
$291$	−24.3303	−1.42627
$292$	4.37386	0.255961
$293$	−6.00000	−0.350524	−0.175262	−	0.984522i	$-0.556077\pi$
$293$	−6.00000	−0.350524	−0.175262	+	0.984522i	$0.556077\pi$
$294$	−5.37386	−0.313410
$295$	1.25227	0.0729101
$296$	0	0
$297$	3.95644	0.229576
$298$	4.41742	0.255895
$299$	14.3739	0.831262
$300$	7.83485	0.452345
$301$	−12.0000	−0.691669
$302$	−14.7477	−0.848636
$303$	13.5826	0.780299
$304$	−1.58258	−0.0907669
$305$	−10.1216	−0.579561
$306$	1.58258	0.0904698
$307$	−1.37386	−0.0784105	−0.0392053	−	0.999231i	$-0.512483\pi$
$307$	−1.37386	−0.0784105	−0.0392053	+	0.999231i	$0.512483\pi$
$308$	−1.58258	−0.0901756
$309$	−12.1652	−0.692051
$310$	−6.62614	−0.376339
$311$	−23.3739	−1.32541	−0.662705	−	0.748880i	$-0.730592\pi$
$311$	−23.3739	−1.32541	−0.662705	+	0.748880i	$0.730592\pi$
$312$	6.79129	0.384481
$313$	14.8348	0.838515	0.419258	−	0.907867i	$-0.362290\pi$
$313$	14.8348	0.838515	0.419258	+	0.907867i	$0.362290\pi$
$314$	2.00000	0.112867
$315$	0.330303	0.0186105
$316$	−8.20871	−0.461776
$317$	28.7477	1.61463	0.807317	−	0.590119i	$-0.200919\pi$
$317$	28.7477	1.61463	0.807317	+	0.590119i	$0.200919\pi$
$318$	−2.83485	−0.158970
$319$	3.00000	0.167968
$320$	−0.791288	−0.0442343
$321$	9.62614	0.537279
$322$	7.58258	0.422560
$323$	12.0000	0.667698
$324$	−9.58258	−0.532365
$325$	−16.5826	−0.919836
$326$	−19.5826	−1.08458
$327$	10.7477	0.594351
$328$	9.79129	0.540633
$329$	15.1652	0.836082
$330$	−1.12159	−0.0617415
$331$	25.5826	1.40615	0.703073	−	0.711118i	$-0.251811\pi$
$331$	25.5826	1.40615	0.703073	+	0.711118i	$0.251811\pi$
$332$	15.1652	0.832296
$333$	0	0
$334$	−21.9564	−1.20140
$335$	5.04356	0.275559
$336$	3.58258	0.195446
$337$	−33.1216	−1.80425	−0.902124	−	0.431477i	$-0.857993\pi$
$337$	−33.1216	−1.80425	−0.902124	+	0.431477i	$0.857993\pi$
$338$	−1.37386	−0.0747283
$339$	18.6606	1.01350
$340$	6.00000	0.325396
$341$	−6.62614	−0.358825
$342$	0.330303	0.0178607
$343$	20.0000	1.07990
$344$	−6.00000	−0.323498
$345$	5.37386	0.289319
$346$	15.1652	0.815284
$347$	7.58258	0.407054	0.203527	−	0.979069i	$-0.434760\pi$
$347$	7.58258	0.407054	0.203527	+	0.979069i	$0.434760\pi$
$348$	−6.79129	−0.364051
$349$	10.0000	0.535288	0.267644	−	0.963518i	$-0.413755\pi$
$349$	10.0000	0.535288	0.267644	+	0.963518i	$0.413755\pi$
$350$	−8.74773	−0.467586
$351$	18.9564	1.01182
$352$	−0.791288	−0.0421758
$353$	−1.58258	−0.0842320	−0.0421160	−	0.999113i	$-0.513410\pi$
$353$	−1.58258	−0.0842320	−0.0421160	+	0.999113i	$0.513410\pi$
$354$	−2.83485	−0.150671
$355$	7.25227	0.384911
$356$	6.00000	0.317999
$357$	−27.1652	−1.43773
$358$	−1.58258	−0.0836417
$359$	−8.83485	−0.466285	−0.233143	−	0.972443i	$-0.574901\pi$
$359$	−8.83485	−0.466285	−0.233143	+	0.972443i	$0.574901\pi$
$360$	0.165151	0.00870424
$361$	−16.4955	−0.868182
$362$	−8.74773	−0.459770
$363$	18.5826	0.975332
$364$	−7.58258	−0.397435
$365$	−3.46099	−0.181156
$366$	22.9129	1.19768
$367$	−5.25227	−0.274166	−0.137083	−	0.990560i	$-0.543773\pi$
$367$	−5.25227	−0.274166	−0.137083	+	0.990560i	$0.543773\pi$
$368$	3.79129	0.197635
$369$	−2.04356	−0.106384
$370$	0	0
$371$	3.16515	0.164326
$372$	15.0000	0.777714
$373$	12.7477	0.660052	0.330026	−	0.943972i	$-0.392942\pi$
$373$	12.7477	0.660052	0.330026	+	0.943972i	$0.392942\pi$
$374$	6.00000	0.310253
$375$	−13.2867	−0.686124
$376$	7.58258	0.391041
$377$	14.3739	0.740292
$378$	10.0000	0.514344
$379$	20.1216	1.03358	0.516788	−	0.856113i	$-0.327127\pi$
$379$	20.1216	1.03358	0.516788	+	0.856113i	$0.327127\pi$
$380$	1.25227	0.0642402
$381$	−14.3303	−0.734164
$382$	8.37386	0.428444
$383$	18.3303	0.936635	0.468317	−	0.883560i	$-0.344860\pi$
$383$	18.3303	0.936635	0.468317	+	0.883560i	$0.344860\pi$
$384$	1.79129	0.0914113
$385$	1.25227	0.0638217
$386$	−18.3303	−0.932988
$387$	1.25227	0.0636566
$388$	13.5826	0.689551
$389$	−32.8693	−1.66654	−0.833270	−	0.552866i	$-0.813534\pi$
$389$	−32.8693	−1.66654	−0.833270	+	0.552866i	$0.813534\pi$
$390$	−5.37386	−0.272116
$391$	−28.7477	−1.45384
$392$	3.00000	0.151523
$393$	−30.0000	−1.51330
$394$	19.9129	1.00320
$395$	6.49545	0.326822
$396$	0.165151	0.00829917
$397$	−14.7477	−0.740167	−0.370084	−	0.928998i	$-0.620671\pi$
$397$	−14.7477	−0.740167	−0.370084	+	0.928998i	$0.620671\pi$
$398$	15.1652	0.760160
$399$	−5.66970	−0.283840
$400$	−4.37386	−0.218693
$401$	−16.7477	−0.836342	−0.418171	−	0.908368i	$-0.637329\pi$
$401$	−16.7477	−0.836342	−0.418171	+	0.908368i	$0.637329\pi$
$402$	−11.4174	−0.569449
$403$	−31.7477	−1.58147
$404$	−7.58258	−0.377247
$405$	7.58258	0.376781
$406$	7.58258	0.376317
$407$	0	0
$408$	−13.5826	−0.672438
$409$	27.1652	1.34323	0.671615	−	0.740900i	$-0.265601\pi$
$409$	27.1652	1.34323	0.671615	+	0.740900i	$0.265601\pi$
$410$	−7.74773	−0.382633
$411$	6.49545	0.320397
$412$	6.79129	0.334583
$413$	3.16515	0.155747
$414$	−0.791288	−0.0388897
$415$	−12.0000	−0.589057
$416$	−3.79129	−0.185883
$417$	−23.9564	−1.17315
$418$	1.25227	0.0612507
$419$	2.20871	0.107903	0.0539513	−	0.998544i	$-0.482818\pi$
$419$	2.20871	0.107903	0.0539513	+	0.998544i	$0.482818\pi$
$420$	−2.83485	−0.138326
$421$	−18.9564	−0.923880	−0.461940	−	0.886911i	$-0.652847\pi$
$421$	−18.9564	−0.923880	−0.461940	+	0.886911i	$0.652847\pi$
$422$	−10.3739	−0.504992
$423$	−1.58258	−0.0769475
$424$	1.58258	0.0768567
$425$	33.1652	1.60875
$426$	−16.4174	−0.795427
$427$	−25.5826	−1.23803
$428$	−5.37386	−0.259755
$429$	−5.37386	−0.259453
$430$	4.74773	0.228956
$431$	−8.83485	−0.425560	−0.212780	−	0.977100i	$-0.568252\pi$
$431$	−8.83485	−0.425560	−0.212780	+	0.977100i	$0.568252\pi$
$432$	5.00000	0.240563
$433$	10.6261	0.510660	0.255330	−	0.966854i	$-0.417816\pi$
$433$	10.6261	0.510660	0.255330	+	0.966854i	$0.417816\pi$
$434$	−16.7477	−0.803917
$435$	5.37386	0.257657
$436$	−6.00000	−0.287348
$437$	−6.00000	−0.287019
$438$	7.83485	0.374364
$439$	12.6261	0.602613	0.301306	−	0.953527i	$-0.402577\pi$
$439$	12.6261	0.602613	0.301306	+	0.953527i	$0.402577\pi$
$440$	0.626136	0.0298499
$441$	−0.626136	−0.0298160
$442$	28.7477	1.36739
$443$	−27.9564	−1.32825	−0.664125	−	0.747621i	$-0.731196\pi$
$443$	−27.9564	−1.32825	−0.664125	+	0.747621i	$0.731196\pi$
$444$	0	0
$445$	−4.74773	−0.225064
$446$	−14.0000	−0.662919
$447$	7.91288	0.374266
$448$	−2.00000	−0.0944911
$449$	2.83485	0.133785	0.0668924	−	0.997760i	$-0.478692\pi$
$449$	2.83485	0.133785	0.0668924	+	0.997760i	$0.478692\pi$
$450$	0.912878	0.0430335
$451$	−7.74773	−0.364826
$452$	−10.4174	−0.489994
$453$	−26.4174	−1.24120
$454$	−25.9129	−1.21615
$455$	6.00000	0.281284
$456$	−2.83485	−0.132754
$457$	21.4955	1.00551	0.502757	−	0.864428i	$-0.332319\pi$
$457$	21.4955	1.00551	0.502757	+	0.864428i	$0.332319\pi$
$458$	−6.74773	−0.315301
$459$	−37.9129	−1.76962
$460$	−3.00000	−0.139876
$461$	−12.3303	−0.574279	−0.287140	−	0.957889i	$-0.592704\pi$
$461$	−12.3303	−0.574279	−0.287140	+	0.957889i	$0.592704\pi$
$462$	−2.83485	−0.131889
$463$	−29.7042	−1.38047	−0.690235	−	0.723585i	$-0.742493\pi$
$463$	−29.7042	−1.38047	−0.690235	+	0.723585i	$0.742493\pi$
$464$	3.79129	0.176006
$465$	−11.8693	−0.550426
$466$	−16.1216	−0.746818
$467$	−16.4174	−0.759708	−0.379854	−	0.925046i	$-0.624026\pi$
$467$	−16.4174	−0.759708	−0.379854	+	0.925046i	$0.624026\pi$
$468$	0.791288	0.0365773
$469$	12.7477	0.588635
$470$	−6.00000	−0.276759
$471$	3.58258	0.165076
$472$	1.58258	0.0728440
$473$	4.74773	0.218301
$474$	−14.7042	−0.675385
$475$	6.92197	0.317602
$476$	15.1652	0.695094
$477$	−0.330303	−0.0151235
$478$	2.04356	0.0934703
$479$	−3.79129	−0.173228	−0.0866142	−	0.996242i	$-0.527605\pi$
$479$	−3.79129	−0.173228	−0.0866142	+	0.996242i	$0.527605\pi$
$480$	−1.41742	−0.0646963
$481$	0	0
$482$	4.41742	0.201208
$483$	13.5826	0.618029
$484$	−10.3739	−0.471539
$485$	−10.7477	−0.488029
$486$	−2.16515	−0.0982133
$487$	−36.6606	−1.66125	−0.830625	−	0.556832i	$-0.812017\pi$
$487$	−36.6606	−1.66125	−0.830625	+	0.556832i	$0.812017\pi$
$488$	−12.7913	−0.579034
$489$	−35.0780	−1.58628
$490$	−2.37386	−0.107240
$491$	5.37386	0.242519	0.121260	−	0.992621i	$-0.461307\pi$
$491$	5.37386	0.242519	0.121260	+	0.992621i	$0.461307\pi$
$492$	17.5390	0.790720
$493$	−28.7477	−1.29473
$494$	6.00000	0.269953
$495$	−0.130682	−0.00587373
$496$	−8.37386	−0.375998
$497$	18.3303	0.822226
$498$	27.1652	1.21730
$499$	−10.7477	−0.481134	−0.240567	−	0.970632i	$-0.577333\pi$
$499$	−10.7477	−0.481134	−0.240567	+	0.970632i	$0.577333\pi$
$500$	7.41742	0.331717
$501$	−39.3303	−1.75715
$502$	−4.41742	−0.197159
$503$	−15.6261	−0.696735	−0.348367	−	0.937358i	$-0.613264\pi$
$503$	−15.6261	−0.696735	−0.348367	+	0.937358i	$0.613264\pi$
$504$	0.417424	0.0185936
$505$	6.00000	0.266996
$506$	−3.00000	−0.133366
$507$	−2.46099	−0.109296
$508$	8.00000	0.354943
$509$	−4.41742	−0.195799	−0.0978994	−	0.995196i	$-0.531212\pi$
$509$	−4.41742	−0.195799	−0.0978994	+	0.995196i	$0.531212\pi$
$510$	10.7477	0.475917
$511$	−8.74773	−0.386977
$512$	−1.00000	−0.0441942
$513$	−7.91288	−0.349362
$514$	−4.74773	−0.209413
$515$	−5.37386	−0.236801
$516$	−10.7477	−0.473142
$517$	−6.00000	−0.263880
$518$	0	0
$519$	27.1652	1.19242
$520$	3.00000	0.131559
$521$	9.16515	0.401533	0.200766	−	0.979639i	$-0.435657\pi$
$521$	9.16515	0.401533	0.200766	+	0.979639i	$0.435657\pi$
$522$	−0.791288	−0.0346337
$523$	−15.1652	−0.663126	−0.331563	−	0.943433i	$-0.607576\pi$
$523$	−15.1652	−0.663126	−0.331563	+	0.943433i	$0.607576\pi$
$524$	16.7477	0.731628
$525$	−15.6697	−0.683882
$526$	−27.1652	−1.18446
$527$	63.4955	2.76591
$528$	−1.41742	−0.0616855
$529$	−8.62614	−0.375049
$530$	−1.25227	−0.0543953
$531$	−0.330303	−0.0143339
$532$	3.16515	0.137227
$533$	−37.1216	−1.60791
$534$	10.7477	0.465100
$535$	4.25227	0.183842
$536$	6.37386	0.275309
$537$	−2.83485	−0.122333
$538$	−16.7477	−0.722046
$539$	−2.37386	−0.102250
$540$	−3.95644	−0.170258
$541$	12.7913	0.549940	0.274970	−	0.961453i	$-0.411332\pi$
$541$	12.7913	0.549940	0.274970	+	0.961453i	$0.411332\pi$
$542$	−22.0000	−0.944981
$543$	−15.6697	−0.672451
$544$	7.58258	0.325100
$545$	4.74773	0.203370
$546$	−13.5826	−0.581281
$547$	−25.9129	−1.10795	−0.553977	−	0.832532i	$-0.686891\pi$
$547$	−25.9129	−1.10795	−0.553977	+	0.832532i	$0.686891\pi$
$548$	−3.62614	−0.154901
$549$	2.66970	0.113940
$550$	3.46099	0.147577
$551$	−6.00000	−0.255609
$552$	6.79129	0.289056
$553$	16.4174	0.698140
$554$	9.62614	0.408975
$555$	0	0
$556$	13.3739	0.567178
$557$	−8.70417	−0.368807	−0.184404	−	0.982851i	$-0.559035\pi$
$557$	−8.70417	−0.368807	−0.184404	+	0.982851i	$0.559035\pi$
$558$	1.74773	0.0739872
$559$	22.7477	0.962126
$560$	1.58258	0.0668760
$561$	10.7477	0.453769
$562$	0	0
$563$	−10.7477	−0.452963	−0.226481	−	0.974016i	$-0.572722\pi$
$563$	−10.7477	−0.452963	−0.226481	+	0.974016i	$0.572722\pi$
$564$	13.5826	0.571930
$565$	8.24318	0.346793
$566$	−24.0000	−1.00880
$567$	19.1652	0.804861
$568$	9.16515	0.384561
$569$	−45.1652	−1.89342	−0.946711	−	0.322085i	$-0.895616\pi$
$569$	−45.1652	−1.89342	−0.946711	+	0.322085i	$0.895616\pi$
$570$	2.24318	0.0939565
$571$	−14.6261	−0.612085	−0.306042	−	0.952018i	$-0.599005\pi$
$571$	−14.6261	−0.612085	−0.306042	+	0.952018i	$0.599005\pi$
$572$	3.00000	0.125436
$573$	15.0000	0.626634
$574$	−19.5826	−0.817361
$575$	−16.5826	−0.691541
$576$	0.208712	0.00869634
$577$	13.5826	0.565450	0.282725	−	0.959201i	$-0.408762\pi$
$577$	13.5826	0.565450	0.282725	+	0.959201i	$0.408762\pi$
$578$	−40.4955	−1.68439
$579$	−32.8348	−1.36457
$580$	−3.00000	−0.124568
$581$	−30.3303	−1.25831
$582$	24.3303	1.00852
$583$	−1.25227	−0.0518638
$584$	−4.37386	−0.180992
$585$	−0.626136	−0.0258876
$586$	6.00000	0.247858
$587$	19.9129	0.821892	0.410946	−	0.911660i	$-0.365198\pi$
$587$	19.9129	0.821892	0.410946	+	0.911660i	$0.365198\pi$
$588$	5.37386	0.221614
$589$	13.2523	0.546050
$590$	−1.25227	−0.0515553
$591$	35.6697	1.46726
$592$	0	0
$593$	−18.7913	−0.771666	−0.385833	−	0.922569i	$-0.626086\pi$
$593$	−18.7913	−0.771666	−0.385833	+	0.922569i	$0.626086\pi$
$594$	−3.95644	−0.162335
$595$	−12.0000	−0.491952
$596$	−4.41742	−0.180945
$597$	27.1652	1.11180
$598$	−14.3739	−0.587791
$599$	8.83485	0.360982	0.180491	−	0.983577i	$-0.442231\pi$
$599$	8.83485	0.360982	0.180491	+	0.983577i	$0.442231\pi$
$600$	−7.83485	−0.319856
$601$	−33.1216	−1.35106	−0.675529	−	0.737333i	$-0.736085\pi$
$601$	−33.1216	−1.35106	−0.675529	+	0.737333i	$0.736085\pi$
$602$	12.0000	0.489083
$603$	−1.33030	−0.0541741
$604$	14.7477	0.600077
$605$	8.20871	0.333732
$606$	−13.5826	−0.551754
$607$	26.5390	1.07719	0.538593	−	0.842566i	$-0.318956\pi$
$607$	26.5390	1.07719	0.538593	+	0.842566i	$0.318956\pi$
$608$	1.58258	0.0641819
$609$	13.5826	0.550394
$610$	10.1216	0.409811
$611$	−28.7477	−1.16301
$612$	−1.58258	−0.0639718
$613$	49.4955	1.99910	0.999551	−	0.0299539i	$-0.00953603\pi$
$613$	49.4955	1.99910	0.999551	+	0.0299539i	$0.00953603\pi$
$614$	1.37386	0.0554446
$615$	−13.8784	−0.559631
$616$	1.58258	0.0637638
$617$	23.0436	0.927699	0.463849	−	0.885914i	$-0.346468\pi$
$617$	23.0436	0.927699	0.463849	+	0.885914i	$0.346468\pi$
$618$	12.1652	0.489354
$619$	35.1216	1.41166	0.705828	−	0.708383i	$-0.250575\pi$
$619$	35.1216	1.41166	0.705828	+	0.708383i	$0.250575\pi$
$620$	6.62614	0.266112
$621$	18.9564	0.760696
$622$	23.3739	0.937207
$623$	−12.0000	−0.480770
$624$	−6.79129	−0.271869
$625$	16.0000	0.640000
$626$	−14.8348	−0.592920
$627$	2.24318	0.0895840
$628$	−2.00000	−0.0798087
$629$	0	0
$630$	−0.330303	−0.0131596
$631$	18.9564	0.754644	0.377322	−	0.926082i	$-0.376845\pi$
$631$	18.9564	0.754644	0.377322	+	0.926082i	$0.376845\pi$
$632$	8.20871	0.326525
$633$	−18.5826	−0.738591
$634$	−28.7477	−1.14172
$635$	−6.33030	−0.251210
$636$	2.83485	0.112409
$637$	−11.3739	−0.450649
$638$	−3.00000	−0.118771
$639$	−1.91288	−0.0756723
$640$	0.791288	0.0312784
$641$	−3.46099	−0.136701	−0.0683503	−	0.997661i	$-0.521774\pi$
$641$	−3.46099	−0.136701	−0.0683503	+	0.997661i	$0.521774\pi$
$642$	−9.62614	−0.379913
$643$	−39.4955	−1.55755	−0.778774	−	0.627304i	$-0.784158\pi$
$643$	−39.4955	−1.55755	−0.778774	+	0.627304i	$0.784158\pi$
$644$	−7.58258	−0.298795
$645$	8.50455	0.334866
$646$	−12.0000	−0.472134
$647$	17.7042	0.696023	0.348011	−	0.937490i	$-0.386857\pi$
$647$	17.7042	0.696023	0.348011	+	0.937490i	$0.386857\pi$
$648$	9.58258	0.376439
$649$	−1.25227	−0.0491560
$650$	16.5826	0.650422
$651$	−30.0000	−1.17579
$652$	19.5826	0.766913
$653$	0.626136	0.0245026	0.0122513	−	0.999925i	$-0.496100\pi$
$653$	0.626136	0.0245026	0.0122513	+	0.999925i	$0.496100\pi$
$654$	−10.7477	−0.420269
$655$	−13.2523	−0.517809
$656$	−9.79129	−0.382286
$657$	0.912878	0.0356148
$658$	−15.1652	−0.591199
$659$	−11.0436	−0.430196	−0.215098	−	0.976592i	$-0.569007\pi$
$659$	−11.0436	−0.430196	−0.215098	+	0.976592i	$0.569007\pi$
$660$	1.12159	0.0436579
$661$	32.2087	1.25277	0.626387	−	0.779512i	$-0.284533\pi$
$661$	32.2087	1.25277	0.626387	+	0.779512i	$0.284533\pi$
$662$	−25.5826	−0.994295
$663$	51.4955	1.99992
$664$	−15.1652	−0.588522
$665$	−2.50455	−0.0971221
$666$	0	0
$667$	14.3739	0.556558
$668$	21.9564	0.849520
$669$	−25.0780	−0.969573
$670$	−5.04356	−0.194850
$671$	10.1216	0.390740
$672$	−3.58258	−0.138201
$673$	−36.1216	−1.39238	−0.696192	−	0.717855i	$-0.745124\pi$
$673$	−36.1216	−1.39238	−0.696192	+	0.717855i	$0.745124\pi$
$674$	33.1216	1.27580
$675$	−21.8693	−0.841750
$676$	1.37386	0.0528409
$677$	−9.16515	−0.352245	−0.176123	−	0.984368i	$-0.556356\pi$
$677$	−9.16515	−0.352245	−0.176123	+	0.984368i	$0.556356\pi$
$678$	−18.6606	−0.716656
$679$	−27.1652	−1.04250
$680$	−6.00000	−0.230089
$681$	−46.4174	−1.77872
$682$	6.62614	0.253728
$683$	31.5826	1.20847	0.604237	−	0.796805i	$-0.293478\pi$
$683$	31.5826	1.20847	0.604237	+	0.796805i	$0.293478\pi$
$684$	−0.330303	−0.0126294
$685$	2.86932	0.109631
$686$	−20.0000	−0.763604
$687$	−12.0871	−0.461152
$688$	6.00000	0.228748
$689$	−6.00000	−0.228582
$690$	−5.37386	−0.204579
$691$	−25.4955	−0.969893	−0.484946	−	0.874544i	$-0.661161\pi$
$691$	−25.4955	−0.969893	−0.484946	+	0.874544i	$0.661161\pi$
$692$	−15.1652	−0.576493
$693$	−0.330303	−0.0125472
$694$	−7.58258	−0.287831
$695$	−10.5826	−0.401420
$696$	6.79129	0.257423
$697$	74.2432	2.81216
$698$	−10.0000	−0.378506
$699$	−28.8784	−1.09228
$700$	8.74773	0.330633
$701$	−3.95644	−0.149433	−0.0747163	−	0.997205i	$-0.523805\pi$
$701$	−3.95644	−0.149433	−0.0747163	+	0.997205i	$0.523805\pi$
$702$	−18.9564	−0.715465
$703$	0	0
$704$	0.791288	0.0298228
$705$	−10.7477	−0.404783
$706$	1.58258	0.0595610
$707$	15.1652	0.570344
$708$	2.83485	0.106540
$709$	−23.2087	−0.871621	−0.435811	−	0.900038i	$-0.643538\pi$
$709$	−23.2087	−0.871621	−0.435811	+	0.900038i	$0.643538\pi$
$710$	−7.25227	−0.272173
$711$	−1.71326	−0.0642522
$712$	−6.00000	−0.224860
$713$	−31.7477	−1.18896
$714$	27.1652	1.01663
$715$	−2.37386	−0.0887775
$716$	1.58258	0.0591436
$717$	3.66061	0.136708
$718$	8.83485	0.329714
$719$	−21.1652	−0.789327	−0.394663	−	0.918826i	$-0.629139\pi$
$719$	−21.1652	−0.789327	−0.394663	+	0.918826i	$0.629139\pi$
$720$	−0.165151	−0.00615483
$721$	−13.5826	−0.505842
$722$	16.4955	0.613897
$723$	7.91288	0.294283
$724$	8.74773	0.325107
$725$	−16.5826	−0.615861
$726$	−18.5826	−0.689664
$727$	−13.1216	−0.486653	−0.243326	−	0.969944i	$-0.578239\pi$
$727$	−13.1216	−0.486653	−0.243326	+	0.969944i	$0.578239\pi$
$728$	7.58258	0.281029
$729$	24.8693	0.921086
$730$	3.46099	0.128097
$731$	−45.4955	−1.68271
$732$	−22.9129	−0.846884
$733$	−47.4955	−1.75428	−0.877142	−	0.480231i	$-0.840553\pi$
$733$	−47.4955	−1.75428	−0.877142	+	0.480231i	$0.840553\pi$
$734$	5.25227	0.193865
$735$	−4.25227	−0.156847
$736$	−3.79129	−0.139749
$737$	−5.04356	−0.185782
$738$	2.04356	0.0752245
$739$	35.1216	1.29197	0.645984	−	0.763351i	$-0.276447\pi$
$739$	35.1216	1.29197	0.645984	+	0.763351i	$0.276447\pi$
$740$	0	0
$741$	10.7477	0.394828
$742$	−3.16515	−0.116196
$743$	−15.1652	−0.556355	−0.278178	−	0.960530i	$-0.589730\pi$
$743$	−15.1652	−0.556355	−0.278178	+	0.960530i	$0.589730\pi$
$744$	−15.0000	−0.549927
$745$	3.49545	0.128064
$746$	−12.7477	−0.466727
$747$	3.16515	0.115807
$748$	−6.00000	−0.219382
$749$	10.7477	0.392713
$750$	13.2867	0.485163
$751$	41.4955	1.51419	0.757095	−	0.653304i	$-0.226618\pi$
$751$	41.4955	1.51419	0.757095	+	0.653304i	$0.226618\pi$
$752$	−7.58258	−0.276508
$753$	−7.91288	−0.288361
$754$	−14.3739	−0.523465
$755$	−11.6697	−0.424704
$756$	−10.0000	−0.363696
$757$	35.2087	1.27968	0.639841	−	0.768507i	$-0.279000\pi$
$757$	35.2087	1.27968	0.639841	+	0.768507i	$0.279000\pi$
$758$	−20.1216	−0.730849
$759$	−5.37386	−0.195059
$760$	−1.25227	−0.0454247
$761$	−14.2087	−0.515065	−0.257533	−	0.966270i	$-0.582910\pi$
$761$	−14.2087	−0.515065	−0.257533	+	0.966270i	$0.582910\pi$
$762$	14.3303	0.519132
$763$	12.0000	0.434429
$764$	−8.37386	−0.302956
$765$	1.25227	0.0452760
$766$	−18.3303	−0.662301
$767$	−6.00000	−0.216647
$768$	−1.79129	−0.0646375
$769$	−11.6697	−0.420820	−0.210410	−	0.977613i	$-0.567480\pi$
$769$	−11.6697	−0.420820	−0.210410	+	0.977613i	$0.567480\pi$
$770$	−1.25227	−0.0451288
$771$	−8.50455	−0.306284
$772$	18.3303	0.659722
$773$	31.9129	1.14783	0.573913	−	0.818916i	$-0.305425\pi$
$773$	31.9129	1.14783	0.573913	+	0.818916i	$0.305425\pi$
$774$	−1.25227	−0.0450120
$775$	36.6261	1.31565
$776$	−13.5826	−0.487586
$777$	0	0
$778$	32.8693	1.17842
$779$	15.4955	0.555182
$780$	5.37386	0.192415
$781$	−7.25227	−0.259507
$782$	28.7477	1.02802
$783$	18.9564	0.677448
$784$	−3.00000	−0.107143
$785$	1.58258	0.0564845
$786$	30.0000	1.07006
$787$	8.00000	0.285169	0.142585	−	0.989783i	$-0.454459\pi$
$787$	8.00000	0.285169	0.142585	+	0.989783i	$0.454459\pi$
$788$	−19.9129	−0.709367
$789$	−48.6606	−1.73236
$790$	−6.49545	−0.231098
$791$	20.8348	0.740802
$792$	−0.165151	−0.00586840
$793$	48.4955	1.72212
$794$	14.7477	0.523377
$795$	−2.24318	−0.0795574
$796$	−15.1652	−0.537515
$797$	35.3739	1.25301	0.626503	−	0.779419i	$-0.284486\pi$
$797$	35.3739	1.25301	0.626503	+	0.779419i	$0.284486\pi$
$798$	5.66970	0.200705
$799$	57.4955	2.03404
$800$	4.37386	0.154639
$801$	1.25227	0.0442469
$802$	16.7477	0.591383
$803$	3.46099	0.122136
$804$	11.4174	0.402662
$805$	6.00000	0.211472
$806$	31.7477	1.11827
$807$	−30.0000	−1.05605
$808$	7.58258	0.266754
$809$	−53.0780	−1.86612	−0.933062	−	0.359715i	$-0.882874\pi$
$809$	−53.0780	−1.86612	−0.933062	+	0.359715i	$0.882874\pi$
$810$	−7.58258	−0.266425
$811$	−19.8693	−0.697706	−0.348853	−	0.937177i	$-0.613429\pi$
$811$	−19.8693	−0.697706	−0.348853	+	0.937177i	$0.613429\pi$
$812$	−7.58258	−0.266096
$813$	−39.4083	−1.38211
$814$	0	0
$815$	−15.4955	−0.542782
$816$	13.5826	0.475485
$817$	−9.49545	−0.332204
$818$	−27.1652	−0.949807
$819$	−1.58258	−0.0552997
$820$	7.74773	0.270562
$821$	3.16515	0.110465	0.0552323	−	0.998474i	$-0.482410\pi$
$821$	3.16515	0.110465	0.0552323	+	0.998474i	$0.482410\pi$
$822$	−6.49545	−0.226555
$823$	−16.0000	−0.557725	−0.278862	−	0.960331i	$-0.589957\pi$
$823$	−16.0000	−0.557725	−0.278862	+	0.960331i	$0.589957\pi$
$824$	−6.79129	−0.236586
$825$	6.19962	0.215843
$826$	−3.16515	−0.110130
$827$	−33.1652	−1.15327	−0.576633	−	0.817004i	$-0.695634\pi$
$827$	−33.1652	−1.15327	−0.576633	+	0.817004i	$0.695634\pi$
$828$	0.791288	0.0274992
$829$	17.0436	0.591947	0.295974	−	0.955196i	$-0.404356\pi$
$829$	17.0436	0.591947	0.295974	+	0.955196i	$0.404356\pi$
$830$	12.0000	0.416526
$831$	17.2432	0.598159
$832$	3.79129	0.131439
$833$	22.7477	0.788162
$834$	23.9564	0.829544
$835$	−17.3739	−0.601247
$836$	−1.25227	−0.0433108
$837$	−41.8693	−1.44722
$838$	−2.20871	−0.0762987
$839$	−3.49545	−0.120676	−0.0603382	−	0.998178i	$-0.519218\pi$
$839$	−3.49545	−0.120676	−0.0603382	+	0.998178i	$0.519218\pi$
$840$	2.83485	0.0978116
$841$	−14.6261	−0.504350
$842$	18.9564	0.653282
$843$	0	0
$844$	10.3739	0.357083
$845$	−1.08712	−0.0373981
$846$	1.58258	0.0544101
$847$	20.7477	0.712900
$848$	−1.58258	−0.0543459
$849$	−42.9909	−1.47544
$850$	−33.1652	−1.13756
$851$	0	0
$852$	16.4174	0.562452
$853$	44.7042	1.53064	0.765321	−	0.643649i	$-0.222580\pi$
$853$	44.7042	1.53064	0.765321	+	0.643649i	$0.222580\pi$
$854$	25.5826	0.875418
$855$	0.261365	0.00893848
$856$	5.37386	0.183675
$857$	−33.1652	−1.13290	−0.566450	−	0.824096i	$-0.691684\pi$
$857$	−33.1652	−1.13290	−0.566450	+	0.824096i	$0.691684\pi$
$858$	5.37386	0.183461
$859$	18.6606	0.636692	0.318346	−	0.947975i	$-0.396873\pi$
$859$	18.6606	0.636692	0.318346	+	0.947975i	$0.396873\pi$
$860$	−4.74773	−0.161896
$861$	−35.0780	−1.19546
$862$	8.83485	0.300916
$863$	−19.2523	−0.655355	−0.327677	−	0.944790i	$-0.606266\pi$
$863$	−19.2523	−0.655355	−0.327677	+	0.944790i	$0.606266\pi$
$864$	−5.00000	−0.170103
$865$	12.0000	0.408012
$866$	−10.6261	−0.361091
$867$	−72.5390	−2.46355
$868$	16.7477	0.568455
$869$	−6.49545	−0.220343
$870$	−5.37386	−0.182191
$871$	−24.1652	−0.818805
$872$	6.00000	0.203186
$873$	2.83485	0.0959451
$874$	6.00000	0.202953
$875$	−14.8348	−0.501509
$876$	−7.83485	−0.264715
$877$	11.2523	0.379962	0.189981	−	0.981788i	$-0.439157\pi$
$877$	11.2523	0.379962	0.189981	+	0.981788i	$0.439157\pi$
$878$	−12.6261	−0.426111
$879$	10.7477	0.362512
$880$	−0.626136	−0.0211071
$881$	13.1216	0.442078	0.221039	−	0.975265i	$-0.429055\pi$
$881$	13.1216	0.442078	0.221039	+	0.975265i	$0.429055\pi$
$882$	0.626136	0.0210831
$883$	31.9129	1.07395	0.536977	−	0.843597i	$-0.319566\pi$
$883$	31.9129	1.07395	0.536977	+	0.843597i	$0.319566\pi$
$884$	−28.7477	−0.966891
$885$	−2.24318	−0.0754037
$886$	27.9564	0.939215
$887$	57.8258	1.94160	0.970799	−	0.239893i	$-0.0771122\pi$
$887$	57.8258	1.94160	0.970799	+	0.239893i	$0.0771122\pi$
$888$	0	0
$889$	−16.0000	−0.536623
$890$	4.74773	0.159144
$891$	−7.58258	−0.254026
$892$	14.0000	0.468755
$893$	12.0000	0.401565
$894$	−7.91288	−0.264646
$895$	−1.25227	−0.0418589
$896$	2.00000	0.0668153
$897$	−25.7477	−0.859692
$898$	−2.83485	−0.0946001
$899$	−31.7477	−1.05885
$900$	−0.912878	−0.0304293
$901$	12.0000	0.399778
$902$	7.74773	0.257971
$903$	21.4955	0.715324
$904$	10.4174	0.346478
$905$	−6.92197	−0.230094
$906$	26.4174	0.877660
$907$	30.3303	1.00710	0.503551	−	0.863966i	$-0.332027\pi$
$907$	30.3303	1.00710	0.503551	+	0.863966i	$0.332027\pi$
$908$	25.9129	0.859949
$909$	−1.58258	−0.0524907
$910$	−6.00000	−0.198898
$911$	−17.6697	−0.585423	−0.292712	−	0.956201i	$-0.594558\pi$
$911$	−17.6697	−0.585423	−0.292712	+	0.956201i	$0.594558\pi$
$912$	2.83485	0.0938712
$913$	12.0000	0.397142
$914$	−21.4955	−0.711006
$915$	18.1307	0.599382
$916$	6.74773	0.222951
$917$	−33.4955	−1.10612
$918$	37.9129	1.25131
$919$	36.0000	1.18753	0.593765	−	0.804638i	$-0.297641\pi$
$919$	36.0000	1.18753	0.593765	+	0.804638i	$0.297641\pi$
$920$	3.00000	0.0989071
$921$	2.46099	0.0810922
$922$	12.3303	0.406077
$923$	−34.7477	−1.14374
$924$	2.83485	0.0932597
$925$	0	0
$926$	29.7042	0.976139
$927$	1.41742	0.0465543
$928$	−3.79129	−0.124455
$929$	−8.37386	−0.274738	−0.137369	−	0.990520i	$-0.543865\pi$
$929$	−8.37386	−0.274738	−0.137369	+	0.990520i	$0.543865\pi$
$930$	11.8693	0.389210
$931$	4.74773	0.155600
$932$	16.1216	0.528080
$933$	41.8693	1.37074
$934$	16.4174	0.537195
$935$	4.74773	0.155267
$936$	−0.791288	−0.0258641
$937$	34.8693	1.13913	0.569565	−	0.821946i	$-0.307111\pi$
$937$	34.8693	1.13913	0.569565	+	0.821946i	$0.307111\pi$
$938$	−12.7477	−0.416228
$939$	−26.5735	−0.867193
$940$	6.00000	0.195698
$941$	−21.4955	−0.700732	−0.350366	−	0.936613i	$-0.613943\pi$
$941$	−21.4955	−0.700732	−0.350366	+	0.936613i	$0.613943\pi$
$942$	−3.58258	−0.116727
$943$	−37.1216	−1.20885
$944$	−1.58258	−0.0515085
$945$	7.91288	0.257406
$946$	−4.74773	−0.154362
$947$	1.25227	0.0406934	0.0203467	−	0.999793i	$-0.493523\pi$
$947$	1.25227	0.0406934	0.0203467	+	0.999793i	$0.493523\pi$
$948$	14.7042	0.477569
$949$	16.5826	0.538293
$950$	−6.92197	−0.224578
$951$	−51.4955	−1.66985
$952$	−15.1652	−0.491505
$953$	−31.4519	−1.01883	−0.509413	−	0.860522i	$-0.670138\pi$
$953$	−31.4519	−1.01883	−0.509413	+	0.860522i	$0.670138\pi$
$954$	0.330303	0.0106939
$955$	6.62614	0.214417
$956$	−2.04356	−0.0660935
$957$	−5.37386	−0.173712
$958$	3.79129	0.122491
$959$	7.25227	0.234188
$960$	1.41742	0.0457472
$961$	39.1216	1.26199
$962$	0	0
$963$	−1.12159	−0.0361428
$964$	−4.41742	−0.142276
$965$	−14.5045	−0.466918
$966$	−13.5826	−0.437012
$967$	21.9564	0.706071	0.353036	−	0.935610i	$-0.385149\pi$
$967$	21.9564	0.706071	0.353036	+	0.935610i	$0.385149\pi$
$968$	10.3739	0.333429
$969$	−21.4955	−0.690533
$970$	10.7477	0.345089
$971$	50.3739	1.61657	0.808287	−	0.588789i	$-0.200395\pi$
$971$	50.3739	1.61657	0.808287	+	0.588789i	$0.200395\pi$
$972$	2.16515	0.0694473
$973$	−26.7477	−0.857493
$974$	36.6606	1.17468
$975$	29.7042	0.951295
$976$	12.7913	0.409439
$977$	41.0780	1.31420	0.657101	−	0.753802i	$-0.271782\pi$
$977$	41.0780	1.31420	0.657101	+	0.753802i	$0.271782\pi$
$978$	35.0780	1.12167
$979$	4.74773	0.151738
$980$	2.37386	0.0758303
$981$	−1.25227	−0.0399820
$982$	−5.37386	−0.171487
$983$	18.3303	0.584646	0.292323	−	0.956320i	$-0.405572\pi$
$983$	18.3303	0.584646	0.292323	+	0.956320i	$0.405572\pi$
$984$	−17.5390	−0.559123
$985$	15.7568	0.502054
$986$	28.7477	0.915514
$987$	−27.1652	−0.864676
$988$	−6.00000	−0.190885
$989$	22.7477	0.723336
$990$	0.130682	0.00415336
$991$	18.9564	0.602171	0.301086	−	0.953597i	$-0.402651\pi$
$991$	18.9564	0.602171	0.301086	+	0.953597i	$0.402651\pi$
$992$	8.37386	0.265870
$993$	−45.8258	−1.45424
$994$	−18.3303	−0.581402
$995$	12.0000	0.380426
$996$	−27.1652	−0.860761
$997$	18.0000	0.570066	0.285033	−	0.958518i	$-0.407995\pi$
$997$	18.0000	0.570066	0.285033	+	0.958518i	$0.407995\pi$
$998$	10.7477	0.340213
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2738.2.a.h.1.1		2
37.6	odd	4		74.2.b.a.73.4	yes	4
37.31	odd	4		74.2.b.a.73.2	✓	4
37.36	even	2		2738.2.a.k.1.1		2
111.68	even	4		666.2.c.b.73.3		4
111.80	even	4		666.2.c.b.73.2		4
148.31	even	4		592.2.g.c.369.2		4
148.43	even	4		592.2.g.c.369.1		4
185.43	even	4		1850.2.c.h.1849.3		4
185.68	even	4		1850.2.c.g.1849.3		4
185.117	even	4		1850.2.c.g.1849.2		4
185.142	even	4		1850.2.c.h.1849.2		4
185.154	odd	4		1850.2.d.e.1701.1		4
185.179	odd	4		1850.2.d.e.1701.3		4
296.43	even	4		2368.2.g.h.961.4		4
296.117	odd	4		2368.2.g.j.961.2		4
296.179	even	4		2368.2.g.h.961.3		4
296.253	odd	4		2368.2.g.j.961.1		4
444.179	odd	4		5328.2.h.m.2737.2		4
444.191	odd	4		5328.2.h.m.2737.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.2.b.a.73.2	✓	4	37.31	odd	4
74.2.b.a.73.4	yes	4	37.6	odd	4
592.2.g.c.369.1		4	148.43	even	4
592.2.g.c.369.2		4	148.31	even	4
666.2.c.b.73.2		4	111.80	even	4
666.2.c.b.73.3		4	111.68	even	4
1850.2.c.g.1849.2		4	185.117	even	4
1850.2.c.g.1849.3		4	185.68	even	4
1850.2.c.h.1849.2		4	185.142	even	4
1850.2.c.h.1849.3		4	185.43	even	4
1850.2.d.e.1701.1		4	185.154	odd	4
1850.2.d.e.1701.3		4	185.179	odd	4
2368.2.g.h.961.3		4	296.179	even	4
2368.2.g.h.961.4		4	296.43	even	4
2368.2.g.j.961.1		4	296.253	odd	4
2368.2.g.j.961.2		4	296.117	odd	4
2738.2.a.h.1.1		2	1.1	even	1	trivial
2738.2.a.k.1.1		2	37.36	even	2
5328.2.h.m.2737.2		4	444.179	odd	4
5328.2.h.m.2737.3		4	444.191	odd	4

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:	\( N \)	\(=\)	\( 2738 = 2 \cdot 37^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2738.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.79129 q^{3} +1.00000 q^{4} -0.791288 q^{5} +1.79129 q^{6} -2.00000 q^{7} -1.00000 q^{8} +0.208712 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.79129 q^{3} +1.00000 q^{4} -0.791288 q^{5} +1.79129 q^{6} -2.00000 q^{7} -1.00000 q^{8} +0.208712 q^{9} +0.791288 q^{10} +0.791288 q^{11} -1.79129 q^{12} +3.79129 q^{13} +2.00000 q^{14} +1.41742 q^{15} +1.00000 q^{16} -7.58258 q^{17} -0.208712 q^{18} -1.58258 q^{19} -0.791288 q^{20} +3.58258 q^{21} -0.791288 q^{22} +3.79129 q^{23} +1.79129 q^{24} -4.37386 q^{25} -3.79129 q^{26} +5.00000 q^{27} -2.00000 q^{28} +3.79129 q^{29} -1.41742 q^{30} -8.37386 q^{31} -1.00000 q^{32} -1.41742 q^{33} +7.58258 q^{34} +1.58258 q^{35} +0.208712 q^{36} +1.58258 q^{38} -6.79129 q^{39} +0.791288 q^{40} -9.79129 q^{41} -3.58258 q^{42} +6.00000 q^{43} +0.791288 q^{44} -0.165151 q^{45} -3.79129 q^{46} -7.58258 q^{47} -1.79129 q^{48} -3.00000 q^{49} +4.37386 q^{50} +13.5826 q^{51} +3.79129 q^{52} -1.58258 q^{53} -5.00000 q^{54} -0.626136 q^{55} +2.00000 q^{56} +2.83485 q^{57} -3.79129 q^{58} -1.58258 q^{59} +1.41742 q^{60} +12.7913 q^{61} +8.37386 q^{62} -0.417424 q^{63} +1.00000 q^{64} -3.00000 q^{65} +1.41742 q^{66} -6.37386 q^{67} -7.58258 q^{68} -6.79129 q^{69} -1.58258 q^{70} -9.16515 q^{71} -0.208712 q^{72} +4.37386 q^{73} +7.83485 q^{75} -1.58258 q^{76} -1.58258 q^{77} +6.79129 q^{78} -8.20871 q^{79} -0.791288 q^{80} -9.58258 q^{81} +9.79129 q^{82} +15.1652 q^{83} +3.58258 q^{84} +6.00000 q^{85} -6.00000 q^{86} -6.79129 q^{87} -0.791288 q^{88} +6.00000 q^{89} +0.165151 q^{90} -7.58258 q^{91} +3.79129 q^{92} +15.0000 q^{93} +7.58258 q^{94} +1.25227 q^{95} +1.79129 q^{96} +13.5826 q^{97} +3.00000 q^{98} +0.165151 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + q^{3} + 2 q^{4} + 3 q^{5} - q^{6} - 4 q^{7} - 2 q^{8} + 5 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 + q^3 + 2 * q^4 + 3 * q^5 - q^6 - 4 * q^7 - 2 * q^8 + 5 * q^9	\( 2 q - 2 q^{2} + q^{3} + 2 q^{4} + 3 q^{5} - q^{6} - 4 q^{7} - 2 q^{8} + 5 q^{9} - 3 q^{10} - 3 q^{11} + q^{12} + 3 q^{13} + 4 q^{14} + 12 q^{15} + 2 q^{16} - 6 q^{17} - 5 q^{18} + 6 q^{19} + 3 q^{20} - 2 q^{21} + 3 q^{22} + 3 q^{23} - q^{24} + 5 q^{25} - 3 q^{26} + 10 q^{27} - 4 q^{28} + 3 q^{29} - 12 q^{30} - 3 q^{31} - 2 q^{32} - 12 q^{33} + 6 q^{34} - 6 q^{35} + 5 q^{36} - 6 q^{38} - 9 q^{39} - 3 q^{40} - 15 q^{41} + 2 q^{42} + 12 q^{43} - 3 q^{44} + 18 q^{45} - 3 q^{46} - 6 q^{47} + q^{48} - 6 q^{49} - 5 q^{50} + 18 q^{51} + 3 q^{52} + 6 q^{53} - 10 q^{54} - 15 q^{55} + 4 q^{56} + 24 q^{57} - 3 q^{58} + 6 q^{59} + 12 q^{60} + 21 q^{61} + 3 q^{62} - 10 q^{63} + 2 q^{64} - 6 q^{65} + 12 q^{66} + q^{67} - 6 q^{68} - 9 q^{69} + 6 q^{70} - 5 q^{72} - 5 q^{73} + 34 q^{75} + 6 q^{76} + 6 q^{77} + 9 q^{78} - 21 q^{79} + 3 q^{80} - 10 q^{81} + 15 q^{82} + 12 q^{83} - 2 q^{84} + 12 q^{85} - 12 q^{86} - 9 q^{87} + 3 q^{88} + 12 q^{89} - 18 q^{90} - 6 q^{91} + 3 q^{92} + 30 q^{93} + 6 q^{94} + 30 q^{95} - q^{96} + 18 q^{97} + 6 q^{98} - 18 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 + q^3 + 2 * q^4 + 3 * q^5 - q^6 - 4 * q^7 - 2 * q^8 + 5 * q^9 - 3 * q^10 - 3 * q^11 + q^12 + 3 * q^13 + 4 * q^14 + 12 * q^15 + 2 * q^16 - 6 * q^17 - 5 * q^18 + 6 * q^19 + 3 * q^20 - 2 * q^21 + 3 * q^22 + 3 * q^23 - q^24 + 5 * q^25 - 3 * q^26 + 10 * q^27 - 4 * q^28 + 3 * q^29 - 12 * q^30 - 3 * q^31 - 2 * q^32 - 12 * q^33 + 6 * q^34 - 6 * q^35 + 5 * q^36 - 6 * q^38 - 9 * q^39 - 3 * q^40 - 15 * q^41 + 2 * q^42 + 12 * q^43 - 3 * q^44 + 18 * q^45 - 3 * q^46 - 6 * q^47 + q^48 - 6 * q^49 - 5 * q^50 + 18 * q^51 + 3 * q^52 + 6 * q^53 - 10 * q^54 - 15 * q^55 + 4 * q^56 + 24 * q^57 - 3 * q^58 + 6 * q^59 + 12 * q^60 + 21 * q^61 + 3 * q^62 - 10 * q^63 + 2 * q^64 - 6 * q^65 + 12 * q^66 + q^67 - 6 * q^68 - 9 * q^69 + 6 * q^70 - 5 * q^72 - 5 * q^73 + 34 * q^75 + 6 * q^76 + 6 * q^77 + 9 * q^78 - 21 * q^79 + 3 * q^80 - 10 * q^81 + 15 * q^82 + 12 * q^83 - 2 * q^84 + 12 * q^85 - 12 * q^86 - 9 * q^87 + 3 * q^88 + 12 * q^89 - 18 * q^90 - 6 * q^91 + 3 * q^92 + 30 * q^93 + 6 * q^94 + 30 * q^95 - q^96 + 18 * q^97 + 6 * q^98 - 18 * q^99

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