LMFDB - Embedded newform 74.2.b.a.73.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [74,2,Mod(73,74)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(74, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1]))

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

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

chi := DirichletCharacter("74.73");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 74 = 2 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	74.b (of order $2$, degree $1$, minimal)

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:	no
Analytic conductor:	$0.590892974957$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{21})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 11x^{2} + 25 $ x^4 + 11*x^2 + 25
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			73.4
Root			$1.79129i$ of defining polynomial
Character	$\chi$	$=$	74.73
Dual form			74.2.b.a.73.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +1.79129 q^{3} -1.00000 q^{4} -0.791288i q^{5} +1.79129i q^{6} -2.00000 q^{7} -1.00000i q^{8} +0.208712 q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +1.79129 q^{3} -1.00000 q^{4} -0.791288i q^{5} +1.79129i q^{6} -2.00000 q^{7} -1.00000i q^{8} +0.208712 q^{9} +0.791288 q^{10} -0.791288 q^{11} -1.79129 q^{12} +3.79129i q^{13} -2.00000i q^{14} -1.41742i q^{15} +1.00000 q^{16} -7.58258i q^{17} +0.208712i q^{18} -1.58258i q^{19} +0.791288i q^{20} -3.58258 q^{21} -0.791288i q^{22} +3.79129i q^{23} -1.79129i q^{24} +4.37386 q^{25} -3.79129 q^{26} -5.00000 q^{27} +2.00000 q^{28} -3.79129i q^{29} +1.41742 q^{30} +8.37386i q^{31} +1.00000i q^{32} -1.41742 q^{33} +7.58258 q^{34} +1.58258i q^{35} -0.208712 q^{36} +(4.00000 + 4.58258i) q^{37} +1.58258 q^{38} +6.79129i q^{39} -0.791288 q^{40} +9.79129 q^{41} -3.58258i q^{42} +6.00000i q^{43} +0.791288 q^{44} -0.165151i q^{45} -3.79129 q^{46} -7.58258 q^{47} +1.79129 q^{48} -3.00000 q^{49} +4.37386i q^{50} -13.5826i q^{51} -3.79129i q^{52} -1.58258 q^{53} -5.00000i q^{54} +0.626136i q^{55} +2.00000i q^{56} -2.83485i q^{57} +3.79129 q^{58} -1.58258i q^{59} +1.41742i q^{60} -12.7913i q^{61} -8.37386 q^{62} -0.417424 q^{63} -1.00000 q^{64} +3.00000 q^{65} -1.41742i q^{66} +6.37386 q^{67} +7.58258i q^{68} +6.79129i q^{69} -1.58258 q^{70} -9.16515 q^{71} -0.208712i q^{72} -4.37386 q^{73} +(-4.58258 + 4.00000i) q^{74} +7.83485 q^{75} +1.58258i q^{76} +1.58258 q^{77} -6.79129 q^{78} -8.20871i q^{79} -0.791288i q^{80} -9.58258 q^{81} +9.79129i q^{82} +15.1652 q^{83} +3.58258 q^{84} -6.00000 q^{85} -6.00000 q^{86} -6.79129i q^{87} +0.791288i q^{88} -6.00000i q^{89} +0.165151 q^{90} -7.58258i q^{91} -3.79129i q^{92} +15.0000i q^{93} -7.58258i q^{94} -1.25227 q^{95} +1.79129i q^{96} +13.5826i q^{97} -3.00000i q^{98} -0.165151 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{3} - 4 q^{4} - 8 q^{7} + 10 q^{9}+O(q^{10}) $ 4 * q - 2 * q^3 - 4 * q^4 - 8 * q^7 + 10 * q^9	$ 4 q - 2 q^{3} - 4 q^{4} - 8 q^{7} + 10 q^{9} - 6 q^{10} + 6 q^{11} + 2 q^{12} + 4 q^{16} + 4 q^{21} - 10 q^{25} - 6 q^{26} - 20 q^{27} + 8 q^{28} + 24 q^{30} - 24 q^{33} + 12 q^{34} - 10 q^{36} + 16 q^{37} - 12 q^{38} + 6 q^{40} + 30 q^{41} - 6 q^{44} - 6 q^{46} - 12 q^{47} - 2 q^{48} - 12 q^{49} + 12 q^{53} + 6 q^{58} - 6 q^{62} - 20 q^{63} - 4 q^{64} + 12 q^{65} - 2 q^{67} + 12 q^{70} + 10 q^{73} + 68 q^{75} - 12 q^{77} - 18 q^{78} - 20 q^{81} + 24 q^{83} - 4 q^{84} - 24 q^{85} - 24 q^{86} - 36 q^{90} - 60 q^{95} + 36 q^{99}+O(q^{100}) $ 4 * q - 2 * q^3 - 4 * q^4 - 8 * q^7 + 10 * q^9 - 6 * q^10 + 6 * q^11 + 2 * q^12 + 4 * q^16 + 4 * q^21 - 10 * q^25 - 6 * q^26 - 20 * q^27 + 8 * q^28 + 24 * q^30 - 24 * q^33 + 12 * q^34 - 10 * q^36 + 16 * q^37 - 12 * q^38 + 6 * q^40 + 30 * q^41 - 6 * q^44 - 6 * q^46 - 12 * q^47 - 2 * q^48 - 12 * q^49 + 12 * q^53 + 6 * q^58 - 6 * q^62 - 20 * q^63 - 4 * q^64 + 12 * q^65 - 2 * q^67 + 12 * q^70 + 10 * q^73 + 68 * q^75 - 12 * q^77 - 18 * q^78 - 20 * q^81 + 24 * q^83 - 4 * q^84 - 24 * q^85 - 24 * q^86 - 36 * q^90 - 60 * q^95 + 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/74\mathbb{Z}\right)^\times$.

$n$	$39$
$\chi(n)$	$-1$

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	1.79129			1.03420			0.517100	−	0.855925i	$-0.327011\pi$
$3$	1.79129			1.03420			0.517100	+	0.855925i	$0.327011\pi$
$4$	−1.00000			−0.500000
$5$		−	0.791288i		−	0.353875i	−0.984222	−	0.176937i	$-0.943381\pi$
$5$		−	0.791288i		−	0.353875i	0.984222	−	0.176937i	$-0.0566190\pi$
$6$			1.79129i			0.731290i
$7$	−2.00000			−0.755929			−0.377964	−	0.925820i	$-0.623376\pi$
$7$	−2.00000			−0.755929			−0.377964	+	0.925820i	$0.623376\pi$
$8$		−	1.00000i		−	0.353553i
$9$	0.208712			0.0695707
$10$	0.791288			0.250227
$11$	−0.791288			−0.238582			−0.119291	−	0.992859i	$-0.538062\pi$
$11$	−0.791288			−0.238582			−0.119291	+	0.992859i	$0.538062\pi$
$12$	−1.79129			−0.517100
$13$			3.79129i			1.05151i	0.850635	+	0.525757i	$0.176218\pi$
$13$			3.79129i			1.05151i	−0.850635	+	0.525757i	$0.823782\pi$
$14$		−	2.00000i		−	0.534522i
$15$		−	1.41742i		−	0.365977i
$16$	1.00000			0.250000
$17$		−	7.58258i		−	1.83904i	−0.393038	−	0.919522i	$-0.628576\pi$
$17$		−	7.58258i		−	1.83904i	0.393038	−	0.919522i	$-0.371424\pi$
$18$			0.208712i			0.0491939i
$19$		−	1.58258i		−	0.363068i	−0.983385	−	0.181534i	$-0.941894\pi$
$19$		−	1.58258i		−	0.363068i	0.983385	−	0.181534i	$-0.0581062\pi$
$20$			0.791288i			0.176937i
$21$	−3.58258			−0.781782
$22$		−	0.791288i		−	0.168703i
$23$			3.79129i			0.790538i	0.918565	+	0.395269i	$0.129349\pi$
$23$			3.79129i			0.790538i	−0.918565	+	0.395269i	$0.870651\pi$
$24$		−	1.79129i		−	0.365645i
$25$	4.37386			0.874773
$26$	−3.79129			−0.743533
$27$	−5.00000			−0.962250
$28$	2.00000			0.377964
$29$		−	3.79129i		−	0.704024i	−0.935995	−	0.352012i	$-0.885498\pi$
$29$		−	3.79129i		−	0.704024i	0.935995	−	0.352012i	$-0.114502\pi$
$30$	1.41742			0.258785
$31$			8.37386i			1.50399i	0.659169	+	0.751995i	$0.270908\pi$
$31$			8.37386i			1.50399i	−0.659169	+	0.751995i	$0.729092\pi$
$32$			1.00000i			0.176777i
$33$	−1.41742			−0.246742
$34$	7.58258			1.30040
$35$			1.58258i			0.267504i
$36$	−0.208712			−0.0347854
$37$	4.00000	+	4.58258i	0.657596	+	0.753371i
$37$	4.00000	+	4.58258i	0.657596	+	0.753371i
$38$	1.58258			0.256728
$39$			6.79129i			1.08748i
$40$	−0.791288			−0.125114
$41$	9.79129			1.52914			0.764571	−	0.644539i	$-0.222951\pi$
$41$	9.79129			1.52914			0.764571	+	0.644539i	$0.222951\pi$
$42$		−	3.58258i		−	0.552803i
$43$			6.00000i			0.914991i	0.889212	+	0.457496i	$0.151253\pi$
$43$			6.00000i			0.914991i	−0.889212	+	0.457496i	$0.848747\pi$
$44$	0.791288			0.119291
$45$		−	0.165151i		−	0.0246193i
$46$	−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
$50$			4.37386i			0.618558i
$51$		−	13.5826i		−	1.90194i
$52$		−	3.79129i		−	0.525757i
$53$	−1.58258			−0.217383			−0.108692	−	0.994076i	$-0.534666\pi$
$53$	−1.58258			−0.217383			−0.108692	+	0.994076i	$0.534666\pi$
$54$		−	5.00000i		−	0.680414i
$55$			0.626136i			0.0844282i
$56$			2.00000i			0.267261i
$57$		−	2.83485i		−	0.375485i
$58$	3.79129			0.497820
$59$		−	1.58258i		−	0.206034i	−0.994680	−	0.103017i	$-0.967150\pi$
$59$		−	1.58258i		−	0.206034i	0.994680	−	0.103017i	$-0.0328496\pi$
$60$			1.41742i			0.182989i
$61$		−	12.7913i		−	1.63776i	−0.573967	−	0.818878i	$-0.694596\pi$
$61$		−	12.7913i		−	1.63776i	0.573967	−	0.818878i	$-0.305404\pi$
$62$	−8.37386			−1.06348
$63$	−0.417424			−0.0525905
$64$	−1.00000			−0.125000
$65$	3.00000			0.372104
$66$		−	1.41742i		−	0.174473i
$67$	6.37386			0.778691			0.389346	−	0.921092i	$-0.372701\pi$
$67$	6.37386			0.778691			0.389346	+	0.921092i	$0.372701\pi$
$68$			7.58258i			0.919522i
$69$			6.79129i			0.817575i
$70$	−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	$0.683035\pi$
$72$		−	0.208712i		−	0.0245970i
$73$	−4.37386			−0.511922			−0.255961	−	0.966687i	$-0.582392\pi$
$73$	−4.37386			−0.511922			−0.255961	+	0.966687i	$0.582392\pi$
$74$	−4.58258	+	4.00000i	−0.532714	+	0.464991i
$75$	7.83485			0.904690
$76$			1.58258i			0.181534i
$77$	1.58258			0.180351
$78$	−6.79129			−0.768962
$79$		−	8.20871i		−	0.923552i	−0.886997	−	0.461776i	$-0.847212\pi$
$79$		−	8.20871i		−	0.923552i	0.886997	−	0.461776i	$-0.152788\pi$
$80$		−	0.791288i		−	0.0884687i
$81$	−9.58258			−1.06473
$82$			9.79129i			1.08127i
$83$	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
$87$		−	6.79129i		−	0.728102i
$88$			0.791288i			0.0843516i
$89$		−	6.00000i		−	0.635999i	−0.948091	−	0.317999i	$-0.896989\pi$
$89$		−	6.00000i		−	0.635999i	0.948091	−	0.317999i	$-0.103011\pi$
$90$	0.165151			0.0174085
$91$		−	7.58258i		−	0.794870i
$92$		−	3.79129i		−	0.395269i
$93$			15.0000i			1.55543i
$94$		−	7.58258i		−	0.782083i
$95$	−1.25227			−0.128480
$96$			1.79129i			0.182823i
$97$			13.5826i			1.37910i	0.724237	+	0.689551i	$0.242192\pi$
$97$			13.5826i			1.37910i	−0.724237	+	0.689551i	$0.757808\pi$
$98$		−	3.00000i		−	0.303046i
$99$	−0.165151			−0.0165983
$100$	−4.37386			−0.437386
$101$	7.58258			0.754494			0.377247	−	0.926113i	$-0.376871\pi$
$101$	7.58258			0.754494			0.377247	+	0.926113i	$0.376871\pi$
$102$	13.5826			1.34488
$103$		−	6.79129i		−	0.669165i	−0.942366	−	0.334583i	$-0.891405\pi$
$103$		−	6.79129i		−	0.669165i	0.942366	−	0.334583i	$-0.108595\pi$
$104$	3.79129			0.371766
$105$			2.83485i			0.276653i
$106$		−	1.58258i		−	0.153713i
$107$	−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
$109$		−	6.00000i		−	0.574696i	−0.957826	−	0.287348i	$-0.907226\pi$
$109$		−	6.00000i		−	0.574696i	0.957826	−	0.287348i	$-0.0927736\pi$
$110$	−0.626136			−0.0596998
$111$	7.16515	+	8.20871i	0.680086	+	0.779136i
$112$	−2.00000			−0.188982
$113$			10.4174i			0.979989i	0.871726	+	0.489994i	$0.163001\pi$
$113$			10.4174i			0.979989i	−0.871726	+	0.489994i	$0.836999\pi$
$114$	2.83485			0.265508
$115$	3.00000			0.279751
$116$			3.79129i			0.352012i
$117$			0.791288i			0.0731546i
$118$	1.58258			0.145688
$119$			15.1652i			1.39019i
$120$	−1.41742			−0.129393
$121$	−10.3739			−0.943079
$122$	12.7913			1.15807
$123$	17.5390			1.58144
$124$		−	8.37386i		−	0.751995i
$125$		−	7.41742i		−	0.663435i
$126$		−	0.417424i		−	0.0371871i
$127$	8.00000			0.709885			0.354943	−	0.934888i	$-0.384500\pi$
$127$	8.00000			0.709885			0.354943	+	0.934888i	$0.384500\pi$
$128$		−	1.00000i		−	0.0883883i
$129$			10.7477i			0.946285i
$130$			3.00000i			0.263117i
$131$		−	16.7477i		−	1.46326i	−0.681704	−	0.731628i	$-0.738761\pi$
$131$		−	16.7477i		−	1.46326i	0.681704	−	0.731628i	$-0.261239\pi$
$132$	1.41742			0.123371
$133$			3.16515i			0.274453i
$134$			6.37386i			0.550618i
$135$			3.95644i			0.340516i
$136$	−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	$-0.691965\pi$
$139$	−13.3739			−1.13436			−0.567178	+	0.823595i	$0.691965\pi$
$140$		−	1.58258i		−	0.133752i
$141$	−13.5826			−1.14386
$142$		−	9.16515i		−	0.769122i
$143$		−	3.00000i		−	0.250873i
$144$	0.208712			0.0173927
$145$	−3.00000			−0.249136
$146$		−	4.37386i		−	0.361984i
$147$	−5.37386			−0.443229
$148$	−4.00000	−	4.58258i	−0.328798	−	0.376685i
$149$	−4.41742			−0.361889			−0.180945	−	0.983493i	$-0.557916\pi$
$149$	−4.41742			−0.361889			−0.180945	+	0.983493i	$0.557916\pi$
$150$			7.83485i			0.639713i
$151$	−14.7477			−1.20015			−0.600077	−	0.799943i	$-0.704863\pi$
$151$	−14.7477			−1.20015			−0.600077	+	0.799943i	$0.704863\pi$
$152$	−1.58258			−0.128364
$153$		−	1.58258i		−	0.127944i
$154$			1.58258i			0.127528i
$155$	6.62614			0.532224
$156$		−	6.79129i		−	0.543738i
$157$	−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
$161$		−	7.58258i		−	0.597591i
$162$		−	9.58258i		−	0.752878i
$163$		−	19.5826i		−	1.53383i	−0.641751	−	0.766913i	$-0.721792\pi$
$163$		−	19.5826i		−	1.53383i	0.641751	−	0.766913i	$-0.278208\pi$
$164$	−9.79129			−0.764571
$165$			1.12159i			0.0873157i
$166$			15.1652i			1.17704i
$167$			21.9564i			1.69904i	0.527556	+	0.849520i	$0.323108\pi$
$167$			21.9564i			1.69904i	−0.527556	+	0.849520i	$0.676892\pi$
$168$			3.58258i			0.276402i
$169$	−1.37386			−0.105682
$170$		−	6.00000i		−	0.460179i
$171$		−	0.330303i		−	0.0252589i
$172$		−	6.00000i		−	0.457496i
$173$	15.1652			1.15299			0.576493	−	0.817102i	$-0.304421\pi$
$173$	15.1652			1.15299			0.576493	+	0.817102i	$0.304421\pi$
$174$	6.79129			0.514846
$175$	−8.74773			−0.661266
$176$	−0.791288			−0.0596456
$177$		−	2.83485i		−	0.213080i
$178$	6.00000			0.449719
$179$		−	1.58258i		−	0.118287i	−0.998249	−	0.0591436i	$-0.981163\pi$
$179$		−	1.58258i		−	0.118287i	0.998249	−	0.0591436i	$-0.0188370\pi$
$180$			0.165151i			0.0123097i
$181$	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
$183$		−	22.9129i		−	1.69377i
$184$	3.79129			0.279497
$185$	3.62614	−	3.16515i	0.266599	−	0.232707i
$186$	−15.0000			−1.09985
$187$			6.00000i			0.438763i
$188$	7.58258			0.553016
$189$	10.0000			0.727393
$190$		−	1.25227i		−	0.0908494i
$191$		−	8.37386i		−	0.605912i	−0.953005	−	0.302956i	$-0.902027\pi$
$191$		−	8.37386i		−	0.605912i	0.953005	−	0.302956i	$-0.0979734\pi$
$192$	−1.79129			−0.129275
$193$			18.3303i			1.31944i	0.751510	+	0.659722i	$0.229326\pi$
$193$			18.3303i			1.31944i	−0.751510	+	0.659722i	$0.770674\pi$
$194$	−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	$0.751019\pi$
$198$		−	0.165151i		−	0.0117368i
$199$			15.1652i			1.07503i	0.843254	+	0.537515i	$0.180637\pi$
$199$			15.1652i			1.07503i	−0.843254	+	0.537515i	$0.819363\pi$
$200$		−	4.37386i		−	0.309279i
$201$	11.4174			0.805323
$202$			7.58258i			0.533508i
$203$			7.58258i			0.532192i
$204$			13.5826i			0.950971i
$205$		−	7.74773i		−	0.541125i
$206$	6.79129			0.473171
$207$			0.791288i			0.0549983i
$208$			3.79129i			0.262879i
$209$			1.25227i			0.0866215i
$210$	−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
$214$		−	5.37386i		−	0.367350i
$215$	4.74773			0.323792
$216$			5.00000i			0.340207i
$217$		−	16.7477i		−	1.13691i
$218$	6.00000			0.406371
$219$	−7.83485			−0.529430
$220$		−	0.626136i		−	0.0422141i
$221$	28.7477			1.93378
$222$	−8.20871	+	7.16515i	−0.550933	+	0.480893i
$223$	14.0000			0.937509			0.468755	−	0.883328i	$-0.344703\pi$
$223$	14.0000			0.937509			0.468755	+	0.883328i	$0.344703\pi$
$224$		−	2.00000i		−	0.133631i
$225$	0.912878			0.0608586
$226$	−10.4174			−0.692957
$227$			25.9129i			1.71990i	0.510380	+	0.859949i	$0.329505\pi$
$227$			25.9129i			1.71990i	−0.510380	+	0.859949i	$0.670495\pi$
$228$			2.83485i			0.187742i
$229$	6.74773			0.445902			0.222951	−	0.974830i	$-0.428431\pi$
$229$	6.74773			0.445902			0.222951	+	0.974830i	$0.428431\pi$
$230$			3.00000i			0.197814i
$231$	2.83485			0.186519
$232$	−3.79129			−0.248910
$233$	−16.1216			−1.05616			−0.528080	−	0.849194i	$-0.677088\pi$
$233$	−16.1216			−1.05616			−0.528080	+	0.849194i	$0.677088\pi$
$234$	−0.791288			−0.0517281
$235$			6.00000i			0.391397i
$236$			1.58258i			0.103017i
$237$		−	14.7042i		−	0.955138i
$238$	−15.1652			−0.983011
$239$		−	2.04356i		−	0.132187i	−0.997813	−	0.0660935i	$-0.978946\pi$
$239$		−	2.04356i		−	0.132187i	0.997813	−	0.0660935i	$-0.0210536\pi$
$240$		−	1.41742i		−	0.0914943i
$241$		−	4.41742i		−	0.284551i	−0.989827	−	0.142276i	$-0.954558\pi$
$241$		−	4.41742i		−	0.284551i	0.989827	−	0.142276i	$-0.0454419\pi$
$242$		−	10.3739i		−	0.666857i
$243$	−2.16515			−0.138895
$244$			12.7913i			0.818878i
$245$			2.37386i			0.151661i
$246$			17.5390i			1.11825i
$247$	6.00000			0.381771
$248$	8.37386			0.531741
$249$	27.1652			1.72152
$250$	7.41742			0.469119
$251$		−	4.41742i		−	0.278825i	−0.990234	−	0.139413i	$-0.955479\pi$
$251$		−	4.41742i		−	0.278825i	0.990234	−	0.139413i	$-0.0445215\pi$
$252$	0.417424			0.0262953
$253$		−	3.00000i		−	0.188608i
$254$			8.00000i			0.501965i
$255$	−10.7477			−0.673049
$256$	1.00000			0.0625000
$257$			4.74773i			0.296155i	0.988976	+	0.148078i	$0.0473085\pi$
$257$			4.74773i			0.296155i	−0.988976	+	0.148078i	$0.952691\pi$
$258$	−10.7477			−0.669124
$259$	−8.00000	−	9.16515i	−0.497096	−	0.569495i
$260$	−3.00000			−0.186052
$261$		−	0.791288i		−	0.0489795i
$262$	16.7477			1.03468
$263$	−27.1652			−1.67507			−0.837537	−	0.546380i	$-0.816006\pi$
$263$	−27.1652			−1.67507			−0.837537	+	0.546380i	$0.816006\pi$
$264$			1.41742i			0.0872364i
$265$			1.25227i			0.0769265i
$266$	−3.16515			−0.194068
$267$		−	10.7477i		−	0.657750i
$268$	−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	$0.267064\pi$
$272$		−	7.58258i		−	0.459761i
$273$		−	13.5826i		−	0.822055i
$274$		−	3.62614i		−	0.219063i
$275$	−3.46099			−0.208705
$276$		−	6.79129i		−	0.408787i
$277$			9.62614i			0.578378i	0.957272	+	0.289189i	$0.0933857\pi$
$277$			9.62614i			0.578378i	−0.957272	+	0.289189i	$0.906614\pi$
$278$		−	13.3739i		−	0.802111i
$279$			1.74773i			0.104634i
$280$	1.58258			0.0945770
$281$		0			0		1.00000			$0$
$281$		0			0		−1.00000			$\pi$
$282$		−	13.5826i		−	0.808831i
$283$		−	24.0000i		−	1.42665i	−0.700832	−	0.713326i	$-0.747188\pi$
$283$		−	24.0000i		−	1.42665i	0.700832	−	0.713326i	$-0.252812\pi$
$284$	9.16515			0.543852
$285$	−2.24318			−0.132875
$286$	3.00000			0.177394
$287$	−19.5826			−1.15592
$288$			0.208712i			0.0122985i
$289$	−40.4955			−2.38209
$290$		−	3.00000i		−	0.176166i
$291$			24.3303i			1.42627i
$292$	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	$0.556077\pi$
$294$		−	5.37386i		−	0.313410i
$295$	−1.25227			−0.0729101
$296$	4.58258	−	4.00000i	0.266357	−	0.232495i
$297$	3.95644			0.229576
$298$		−	4.41742i		−	0.255895i
$299$	−14.3739			−0.831262
$300$	−7.83485			−0.452345
$301$		−	12.0000i		−	0.691669i
$302$		−	14.7477i		−	0.848636i
$303$	13.5826			0.780299
$304$		−	1.58258i		−	0.0907669i
$305$	−10.1216			−0.579561
$306$	1.58258			0.0904698
$307$	1.37386			0.0784105			0.0392053	−	0.999231i	$-0.487517\pi$
$307$	1.37386			0.0784105			0.0392053	+	0.999231i	$0.487517\pi$
$308$	−1.58258			−0.0901756
$309$		−	12.1652i		−	0.692051i
$310$			6.62614i			0.376339i
$311$			23.3739i			1.32541i	0.748880	+	0.662705i	$0.230592\pi$
$311$			23.3739i			1.32541i	−0.748880	+	0.662705i	$0.769408\pi$
$312$	6.79129			0.384481
$313$			14.8348i			0.838515i	0.907867	+	0.419258i	$0.137710\pi$
$313$			14.8348i			0.838515i	−0.907867	+	0.419258i	$0.862290\pi$
$314$		−	2.00000i		−	0.112867i
$315$			0.330303i			0.0186105i
$316$			8.20871i			0.461776i
$317$	−28.7477			−1.61463			−0.807317	−	0.590119i	$-0.799081\pi$
$317$	−28.7477			−1.61463			−0.807317	+	0.590119i	$0.799081\pi$
$318$		−	2.83485i		−	0.158970i
$319$			3.00000i			0.167968i
$320$			0.791288i			0.0442343i
$321$	−9.62614			−0.537279
$322$	7.58258			0.422560
$323$	−12.0000			−0.667698
$324$	9.58258			0.532365
$325$			16.5826i			0.919836i
$326$	19.5826			1.08458
$327$		−	10.7477i		−	0.594351i
$328$		−	9.79129i		−	0.540633i
$329$	15.1652			0.836082
$330$	−1.12159			−0.0617415
$331$			25.5826i			1.40615i	0.711118	+	0.703073i	$0.248189\pi$
$331$			25.5826i			1.40615i	−0.711118	+	0.703073i	$0.751811\pi$
$332$	−15.1652			−0.832296
$333$	0.834849	+	0.956439i	0.0457494	+	0.0524125i
$334$	−21.9564			−1.20140
$335$		−	5.04356i		−	0.275559i
$336$	−3.58258			−0.195446
$337$	33.1216			1.80425			0.902124	−	0.431477i	$-0.142007\pi$
$337$	33.1216			1.80425			0.902124	+	0.431477i	$0.142007\pi$
$338$		−	1.37386i		−	0.0747283i
$339$			18.6606i			1.01350i
$340$	6.00000			0.325396
$341$		−	6.62614i		−	0.358825i
$342$	0.330303			0.0178607
$343$	20.0000			1.07990
$344$	6.00000			0.323498
$345$	5.37386			0.289319
$346$			15.1652i			0.815284i
$347$		−	7.58258i		−	0.407054i	−0.979069	−	0.203527i	$-0.934760\pi$
$347$		−	7.58258i		−	0.407054i	0.979069	−	0.203527i	$-0.0652405\pi$
$348$			6.79129i			0.364051i
$349$	10.0000			0.535288			0.267644	−	0.963518i	$-0.413755\pi$
$349$	10.0000			0.535288			0.267644	+	0.963518i	$0.413755\pi$
$350$		−	8.74773i		−	0.467586i
$351$		−	18.9564i		−	1.01182i
$352$		−	0.791288i		−	0.0421758i
$353$			1.58258i			0.0842320i	0.999113	+	0.0421160i	$0.0134099\pi$
$353$			1.58258i			0.0842320i	−0.999113	+	0.0421160i	$0.986590\pi$
$354$	2.83485			0.150671
$355$			7.25227i			0.384911i
$356$			6.00000i			0.317999i
$357$			27.1652i			1.43773i
$358$	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
$362$			8.74773i			0.459770i
$363$	−18.5826			−0.975332
$364$			7.58258i			0.397435i
$365$			3.46099i			0.181156i
$366$	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	$0.543773\pi$
$368$			3.79129i			0.197635i
$369$	2.04356			0.106384
$370$	3.16515	+	3.62614i	0.164548	+	0.188514i
$371$	3.16515			0.164326
$372$		−	15.0000i		−	0.777714i
$373$	−12.7477			−0.660052			−0.330026	−	0.943972i	$-0.607058\pi$
$373$	−12.7477			−0.660052			−0.330026	+	0.943972i	$0.607058\pi$
$374$	−6.00000			−0.310253
$375$		−	13.2867i		−	0.686124i
$376$			7.58258i			0.391041i
$377$	14.3739			0.740292
$378$			10.0000i			0.514344i
$379$	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
$383$			18.3303i			0.936635i	0.883560	+	0.468317i	$0.155140\pi$
$383$			18.3303i			0.936635i	−0.883560	+	0.468317i	$0.844860\pi$
$384$		−	1.79129i		−	0.0914113i
$385$		−	1.25227i		−	0.0638217i
$386$	−18.3303			−0.932988
$387$			1.25227i			0.0636566i
$388$		−	13.5826i		−	0.689551i
$389$		−	32.8693i		−	1.66654i	−0.552866	−	0.833270i	$-0.686466\pi$
$389$		−	32.8693i		−	1.66654i	0.552866	−	0.833270i	$-0.313534\pi$
$390$			5.37386i			0.272116i
$391$	28.7477			1.45384
$392$			3.00000i			0.151523i
$393$		−	30.0000i		−	1.51330i
$394$		−	19.9129i		−	1.00320i
$395$	−6.49545			−0.326822
$396$	0.165151			0.00829917
$397$	14.7477			0.740167			0.370084	−	0.928998i	$-0.379329\pi$
$397$	14.7477			0.740167			0.370084	+	0.928998i	$0.379329\pi$
$398$	−15.1652			−0.760160
$399$			5.66970i			0.283840i
$400$	4.37386			0.218693
$401$			16.7477i			0.836342i	0.908368	+	0.418171i	$0.137329\pi$
$401$			16.7477i			0.836342i	−0.908368	+	0.418171i	$0.862671\pi$
$402$			11.4174i			0.569449i
$403$	−31.7477			−1.58147
$404$	−7.58258			−0.377247
$405$			7.58258i			0.376781i
$406$	−7.58258			−0.376317
$407$	−3.16515	−	3.62614i	−0.156891	−	0.179741i
$408$	−13.5826			−0.672438
$409$		−	27.1652i		−	1.34323i	−0.740900	−	0.671615i	$-0.765601\pi$
$409$		−	27.1652i		−	1.34323i	0.740900	−	0.671615i	$-0.234399\pi$
$410$	7.74773			0.382633
$411$	−6.49545			−0.320397
$412$			6.79129i			0.334583i
$413$			3.16515i			0.155747i
$414$	−0.791288			−0.0388897
$415$		−	12.0000i		−	0.589057i
$416$	−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	$0.482818\pi$
$420$		−	2.83485i		−	0.138326i
$421$			18.9564i			0.923880i	0.886911	+	0.461940i	$0.152847\pi$
$421$			18.9564i			0.923880i	−0.886911	+	0.461940i	$0.847153\pi$
$422$			10.3739i			0.504992i
$423$	−1.58258			−0.0769475
$424$			1.58258i			0.0768567i
$425$		−	33.1652i		−	1.60875i
$426$		−	16.4174i		−	0.795427i
$427$			25.5826i			1.23803i
$428$	5.37386			0.259755
$429$		−	5.37386i		−	0.259453i
$430$			4.74773i			0.228956i
$431$			8.83485i			0.425560i	0.977100	+	0.212780i	$0.0682517\pi$
$431$			8.83485i			0.425560i	−0.977100	+	0.212780i	$0.931748\pi$
$432$	−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
$436$			6.00000i			0.287348i
$437$	6.00000			0.287019
$438$		−	7.83485i		−	0.374364i
$439$		−	12.6261i		−	0.602613i	−0.953527	−	0.301306i	$-0.902577\pi$
$439$		−	12.6261i		−	0.602613i	0.953527	−	0.301306i	$-0.0974227\pi$
$440$	0.626136			0.0298499
$441$	−0.626136			−0.0298160
$442$			28.7477i			1.36739i
$443$	27.9564			1.32825			0.664125	−	0.747621i	$-0.268804\pi$
$443$	27.9564			1.32825			0.664125	+	0.747621i	$0.268804\pi$
$444$	−7.16515	−	8.20871i	−0.340043	−	0.389568i
$445$	−4.74773			−0.225064
$446$			14.0000i			0.662919i
$447$	−7.91288			−0.374266
$448$	2.00000			0.0944911
$449$			2.83485i			0.133785i	0.997760	+	0.0668924i	$0.0213084\pi$
$449$			2.83485i			0.133785i	−0.997760	+	0.0668924i	$0.978692\pi$
$450$			0.912878i			0.0430335i
$451$	−7.74773			−0.364826
$452$		−	10.4174i		−	0.489994i
$453$	−26.4174			−1.24120
$454$	−25.9129			−1.21615
$455$	−6.00000			−0.281284
$456$	−2.83485			−0.132754
$457$			21.4955i			1.00551i	0.864428	+	0.502757i	$0.167681\pi$
$457$			21.4955i			1.00551i	−0.864428	+	0.502757i	$0.832319\pi$
$458$			6.74773i			0.315301i
$459$			37.9129i			1.76962i
$460$	−3.00000			−0.139876
$461$		−	12.3303i		−	0.574279i	−0.957889	−	0.287140i	$-0.907296\pi$
$461$		−	12.3303i		−	0.574279i	0.957889	−	0.287140i	$-0.0927044\pi$
$462$			2.83485i			0.131889i
$463$		−	29.7042i		−	1.38047i	−0.723585	−	0.690235i	$-0.757507\pi$
$463$		−	29.7042i		−	1.38047i	0.723585	−	0.690235i	$-0.242493\pi$
$464$		−	3.79129i		−	0.176006i
$465$	11.8693			0.550426
$466$		−	16.1216i		−	0.746818i
$467$		−	16.4174i		−	0.759708i	−0.925046	−	0.379854i	$-0.875974\pi$
$467$		−	16.4174i		−	0.759708i	0.925046	−	0.379854i	$-0.124026\pi$
$468$		−	0.791288i		−	0.0365773i
$469$	−12.7477			−0.588635
$470$	−6.00000			−0.276759
$471$	−3.58258			−0.165076
$472$	−1.58258			−0.0728440
$473$		−	4.74773i		−	0.218301i
$474$	14.7042			0.675385
$475$		−	6.92197i		−	0.317602i
$476$		−	15.1652i		−	0.695094i
$477$	−0.330303			−0.0151235
$478$	2.04356			0.0934703
$479$		−	3.79129i		−	0.173228i	−0.996242	−	0.0866142i	$-0.972395\pi$
$479$		−	3.79129i		−	0.173228i	0.996242	−	0.0866142i	$-0.0276047\pi$
$480$	1.41742			0.0646963
$481$	−17.3739	+	15.1652i	−0.792180	+	0.691471i
$482$	4.41742			0.201208
$483$		−	13.5826i		−	0.618029i
$484$	10.3739			0.471539
$485$	10.7477			0.488029
$486$		−	2.16515i		−	0.0982133i
$487$		−	36.6606i		−	1.66125i	−0.556832	−	0.830625i	$-0.687983\pi$
$487$		−	36.6606i		−	1.66125i	0.556832	−	0.830625i	$-0.312017\pi$
$488$	−12.7913			−0.579034
$489$		−	35.0780i		−	1.58628i
$490$	−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
$494$			6.00000i			0.269953i
$495$			0.130682i			0.00587373i
$496$			8.37386i			0.375998i
$497$	18.3303			0.822226
$498$			27.1652i			1.21730i
$499$			10.7477i			0.481134i	0.970632	+	0.240567i	$0.0773334\pi$
$499$			10.7477i			0.481134i	−0.970632	+	0.240567i	$0.922667\pi$
$500$			7.41742i			0.331717i
$501$			39.3303i			1.75715i
$502$	4.41742			0.197159
$503$		−	15.6261i		−	0.696735i	−0.937358	−	0.348367i	$-0.886736\pi$
$503$		−	15.6261i		−	0.696735i	0.937358	−	0.348367i	$-0.113264\pi$
$504$			0.417424i			0.0185936i
$505$		−	6.00000i		−	0.266996i
$506$	3.00000			0.133366
$507$	−2.46099			−0.109296
$508$	−8.00000			−0.354943
$509$	4.41742			0.195799			0.0978994	−	0.995196i	$-0.468788\pi$
$509$	4.41742			0.195799			0.0978994	+	0.995196i	$0.468788\pi$
$510$		−	10.7477i		−	0.475917i
$511$	8.74773			0.386977
$512$			1.00000i			0.0441942i
$513$			7.91288i			0.349362i
$514$	−4.74773			−0.209413
$515$	−5.37386			−0.236801
$516$		−	10.7477i		−	0.473142i
$517$	6.00000			0.263880
$518$	9.16515	−	8.00000i	0.402694	−	0.351500i
$519$	27.1652			1.19242
$520$		−	3.00000i		−	0.131559i
$521$	−9.16515			−0.401533			−0.200766	−	0.979639i	$-0.564343\pi$
$521$	−9.16515			−0.401533			−0.200766	+	0.979639i	$0.564343\pi$
$522$	0.791288			0.0346337
$523$		−	15.1652i		−	0.663126i	−0.943433	−	0.331563i	$-0.892424\pi$
$523$		−	15.1652i		−	0.663126i	0.943433	−	0.331563i	$-0.107576\pi$
$524$			16.7477i			0.731628i
$525$	−15.6697			−0.683882
$526$		−	27.1652i		−	1.18446i
$527$	63.4955			2.76591
$528$	−1.41742			−0.0616855
$529$	8.62614			0.375049
$530$	−1.25227			−0.0543953
$531$		−	0.330303i		−	0.0143339i
$532$		−	3.16515i		−	0.137227i
$533$			37.1216i			1.60791i
$534$	10.7477			0.465100
$535$			4.25227i			0.183842i
$536$		−	6.37386i		−	0.275309i
$537$		−	2.83485i		−	0.122333i
$538$			16.7477i			0.722046i
$539$	2.37386			0.102250
$540$		−	3.95644i		−	0.170258i
$541$			12.7913i			0.549940i	0.961453	+	0.274970i	$0.0886680\pi$
$541$			12.7913i			0.549940i	−0.961453	+	0.274970i	$0.911332\pi$
$542$			22.0000i			0.944981i
$543$	15.6697			0.672451
$544$	7.58258			0.325100
$545$	−4.74773			−0.203370
$546$	13.5826			0.581281
$547$			25.9129i			1.10795i	0.832532	+	0.553977i	$0.186891\pi$
$547$			25.9129i			1.10795i	−0.832532	+	0.553977i	$0.813109\pi$
$548$	3.62614			0.154901
$549$		−	2.66970i		−	0.113940i
$550$		−	3.46099i		−	0.147577i
$551$	−6.00000			−0.255609
$552$	6.79129			0.289056
$553$			16.4174i			0.698140i
$554$	−9.62614			−0.408975
$555$	6.49545	−	5.66970i	0.275717	−	0.240665i
$556$	13.3739			0.567178
$557$			8.70417i			0.368807i	0.982851	+	0.184404i	$0.0590354\pi$
$557$			8.70417i			0.368807i	−0.982851	+	0.184404i	$0.940965\pi$
$558$	−1.74773			−0.0739872
$559$	−22.7477			−0.962126
$560$			1.58258i			0.0668760i
$561$			10.7477i			0.453769i
$562$		0			0
$563$		−	10.7477i		−	0.452963i	−0.974016	−	0.226481i	$-0.927278\pi$
$563$		−	10.7477i		−	0.452963i	0.974016	−	0.226481i	$-0.0727222\pi$
$564$	13.5826			0.571930
$565$	8.24318			0.346793
$566$	24.0000			1.00880
$567$	19.1652			0.804861
$568$			9.16515i			0.384561i
$569$			45.1652i			1.89342i	0.322085	+	0.946711i	$0.395616\pi$
$569$			45.1652i			1.89342i	−0.322085	+	0.946711i	$0.604384\pi$
$570$		−	2.24318i		−	0.0939565i
$571$	−14.6261			−0.612085			−0.306042	−	0.952018i	$-0.599005\pi$
$571$	−14.6261			−0.612085			−0.306042	+	0.952018i	$0.599005\pi$
$572$			3.00000i			0.125436i
$573$		−	15.0000i		−	0.626634i
$574$		−	19.5826i		−	0.817361i
$575$			16.5826i			0.691541i
$576$	−0.208712			−0.00869634
$577$			13.5826i			0.565450i	0.959201	+	0.282725i	$0.0912384\pi$
$577$			13.5826i			0.565450i	−0.959201	+	0.282725i	$0.908762\pi$
$578$		−	40.4955i		−	1.68439i
$579$			32.8348i			1.36457i
$580$	3.00000			0.124568
$581$	−30.3303			−1.25831
$582$	−24.3303			−1.00852
$583$	1.25227			0.0518638
$584$			4.37386i			0.180992i
$585$	0.626136			0.0258876
$586$		−	6.00000i		−	0.247858i
$587$		−	19.9129i		−	0.821892i	−0.911660	−	0.410946i	$-0.865198\pi$
$587$		−	19.9129i		−	0.821892i	0.911660	−	0.410946i	$-0.134802\pi$
$588$	5.37386			0.221614
$589$	13.2523			0.546050
$590$		−	1.25227i		−	0.0515553i
$591$	−35.6697			−1.46726
$592$	4.00000	+	4.58258i	0.164399	+	0.188343i
$593$	−18.7913			−0.771666			−0.385833	−	0.922569i	$-0.626086\pi$
$593$	−18.7913			−0.771666			−0.385833	+	0.922569i	$0.626086\pi$
$594$			3.95644i			0.162335i
$595$	12.0000			0.491952
$596$	4.41742			0.180945
$597$			27.1652i			1.11180i
$598$		−	14.3739i		−	0.587791i
$599$	8.83485			0.360982			0.180491	−	0.983577i	$-0.442231\pi$
$599$	8.83485			0.360982			0.180491	+	0.983577i	$0.442231\pi$
$600$		−	7.83485i		−	0.319856i
$601$	−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
$605$			8.20871i			0.333732i
$606$			13.5826i			0.551754i
$607$		−	26.5390i		−	1.07719i	−0.842566	−	0.538593i	$-0.818956\pi$
$607$		−	26.5390i		−	1.07719i	0.842566	−	0.538593i	$-0.181044\pi$
$608$	1.58258			0.0641819
$609$			13.5826i			0.550394i
$610$		−	10.1216i		−	0.409811i
$611$		−	28.7477i		−	1.16301i
$612$			1.58258i			0.0639718i
$613$	−49.4955			−1.99910			−0.999551	−	0.0299539i	$-0.990464\pi$
$613$	−49.4955			−1.99910			−0.999551	+	0.0299539i	$0.990464\pi$
$614$			1.37386i			0.0554446i
$615$		−	13.8784i		−	0.559631i
$616$		−	1.58258i		−	0.0637638i
$617$	−23.0436			−0.927699			−0.463849	−	0.885914i	$-0.653532\pi$
$617$	−23.0436			−0.927699			−0.463849	+	0.885914i	$0.653532\pi$
$618$	12.1652			0.489354
$619$	−35.1216			−1.41166			−0.705828	−	0.708383i	$-0.749425\pi$
$619$	−35.1216			−1.41166			−0.705828	+	0.708383i	$0.749425\pi$
$620$	−6.62614			−0.266112
$621$		−	18.9564i		−	0.760696i
$622$	−23.3739			−0.937207
$623$			12.0000i			0.480770i
$624$			6.79129i			0.271869i
$625$	16.0000			0.640000
$626$	−14.8348			−0.592920
$627$			2.24318i			0.0895840i
$628$	2.00000			0.0798087
$629$	34.7477	−	30.3303i	1.38548	−	1.20935i
$630$	−0.330303			−0.0131596
$631$		−	18.9564i		−	0.754644i	−0.926082	−	0.377322i	$-0.876845\pi$
$631$		−	18.9564i		−	0.754644i	0.926082	−	0.377322i	$-0.123155\pi$
$632$	−8.20871			−0.326525
$633$	18.5826			0.738591
$634$		−	28.7477i		−	1.14172i
$635$		−	6.33030i		−	0.251210i
$636$	2.83485			0.112409
$637$		−	11.3739i		−	0.450649i
$638$	−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	$0.521774\pi$
$642$		−	9.62614i		−	0.379913i
$643$			39.4955i			1.55755i	0.627304	+	0.778774i	$0.284158\pi$
$643$			39.4955i			1.55755i	−0.627304	+	0.778774i	$0.715842\pi$
$644$			7.58258i			0.298795i
$645$	8.50455			0.334866
$646$		−	12.0000i		−	0.472134i
$647$		−	17.7042i		−	0.696023i	−0.937490	−	0.348011i	$-0.886857\pi$
$647$		−	17.7042i		−	0.696023i	0.937490	−	0.348011i	$-0.113143\pi$
$648$			9.58258i			0.376439i
$649$			1.25227i			0.0491560i
$650$	−16.5826			−0.650422
$651$		−	30.0000i		−	1.17579i
$652$			19.5826i			0.766913i
$653$		−	0.626136i		−	0.0245026i	−0.999925	−	0.0122513i	$-0.996100\pi$
$653$		−	0.626136i		−	0.0245026i	0.999925	−	0.0122513i	$-0.00389981\pi$
$654$	10.7477			0.420269
$655$	−13.2523			−0.517809
$656$	9.79129			0.382286
$657$	−0.912878			−0.0356148
$658$			15.1652i			0.591199i
$659$	11.0436			0.430196			0.215098	−	0.976592i	$-0.430993\pi$
$659$	11.0436			0.430196			0.215098	+	0.976592i	$0.430993\pi$
$660$		−	1.12159i		−	0.0436579i
$661$		−	32.2087i		−	1.25277i	−0.779512	−	0.626387i	$-0.784533\pi$
$661$		−	32.2087i		−	1.25277i	0.779512	−	0.626387i	$-0.215467\pi$
$662$	−25.5826			−0.994295
$663$	51.4955			1.99992
$664$		−	15.1652i		−	0.588522i
$665$	2.50455			0.0971221
$666$	−0.956439	+	0.834849i	−0.0370613	+	0.0323497i
$667$	14.3739			0.556558
$668$		−	21.9564i		−	0.849520i
$669$	25.0780			0.969573
$670$	5.04356			0.194850
$671$			10.1216i			0.390740i
$672$		−	3.58258i		−	0.138201i
$673$	−36.1216			−1.39238			−0.696192	−	0.717855i	$-0.745124\pi$
$673$	−36.1216			−1.39238			−0.696192	+	0.717855i	$0.745124\pi$
$674$			33.1216i			1.27580i
$675$	−21.8693			−0.841750
$676$	1.37386			0.0528409
$677$	9.16515			0.352245			0.176123	−	0.984368i	$-0.443644\pi$
$677$	9.16515			0.352245			0.176123	+	0.984368i	$0.443644\pi$
$678$	−18.6606			−0.716656
$679$		−	27.1652i		−	1.04250i
$680$			6.00000i			0.230089i
$681$			46.4174i			1.77872i
$682$	6.62614			0.253728
$683$			31.5826i			1.20847i	0.796805	+	0.604237i	$0.206522\pi$
$683$			31.5826i			1.20847i	−0.796805	+	0.604237i	$0.793478\pi$
$684$			0.330303i			0.0126294i
$685$			2.86932i			0.109631i
$686$			20.0000i			0.763604i
$687$	12.0871			0.461152
$688$			6.00000i			0.228748i
$689$		−	6.00000i		−	0.228582i
$690$			5.37386i			0.204579i
$691$	25.4955			0.969893			0.484946	−	0.874544i	$-0.338839\pi$
$691$	25.4955			0.969893			0.484946	+	0.874544i	$0.338839\pi$
$692$	−15.1652			−0.576493
$693$	0.330303			0.0125472
$694$	7.58258			0.287831
$695$			10.5826i			0.401420i
$696$	−6.79129			−0.257423
$697$		−	74.2432i		−	2.81216i
$698$			10.0000i			0.378506i
$699$	−28.8784			−1.09228
$700$	8.74773			0.330633
$701$		−	3.95644i		−	0.149433i	−0.997205	−	0.0747163i	$-0.976195\pi$
$701$		−	3.95644i		−	0.149433i	0.997205	−	0.0747163i	$-0.0238051\pi$
$702$	18.9564			0.715465
$703$	7.25227	−	6.33030i	0.273525	−	0.238752i
$704$	0.791288			0.0298228
$705$			10.7477i			0.404783i
$706$	−1.58258			−0.0595610
$707$	−15.1652			−0.570344
$708$			2.83485i			0.106540i
$709$		−	23.2087i		−	0.871621i	−0.900038	−	0.435811i	$-0.856462\pi$
$709$		−	23.2087i		−	0.871621i	0.900038	−	0.435811i	$-0.143538\pi$
$710$	−7.25227			−0.272173
$711$		−	1.71326i		−	0.0642522i
$712$	−6.00000			−0.224860
$713$	−31.7477			−1.18896
$714$	−27.1652			−1.01663
$715$	−2.37386			−0.0887775
$716$			1.58258i			0.0591436i
$717$		−	3.66061i		−	0.136708i
$718$		−	8.83485i		−	0.329714i
$719$	−21.1652			−0.789327			−0.394663	−	0.918826i	$-0.629139\pi$
$719$	−21.1652			−0.789327			−0.394663	+	0.918826i	$0.629139\pi$
$720$		−	0.165151i		−	0.00615483i
$721$			13.5826i			0.505842i
$722$			16.4955i			0.613897i
$723$		−	7.91288i		−	0.294283i
$724$	−8.74773			−0.325107
$725$		−	16.5826i		−	0.615861i
$726$		−	18.5826i		−	0.689664i
$727$			13.1216i			0.486653i	0.969944	+	0.243326i	$0.0782386\pi$
$727$			13.1216i			0.486653i	−0.969944	+	0.243326i	$0.921761\pi$
$728$	−7.58258			−0.281029
$729$	24.8693			0.921086
$730$	−3.46099			−0.128097
$731$	45.4955			1.68271
$732$			22.9129i			0.846884i
$733$	47.4955			1.75428			0.877142	−	0.480231i	$-0.159447\pi$
$733$	47.4955			1.75428			0.877142	+	0.480231i	$0.159447\pi$
$734$		−	5.25227i		−	0.193865i
$735$			4.25227i			0.156847i
$736$	−3.79129			−0.139749
$737$	−5.04356			−0.185782
$738$			2.04356i			0.0752245i
$739$	−35.1216			−1.29197			−0.645984	−	0.763351i	$-0.723553\pi$
$739$	−35.1216			−1.29197			−0.645984	+	0.763351i	$0.723553\pi$
$740$	−3.62614	+	3.16515i	−0.133299	+	0.116353i
$741$	10.7477			0.394828
$742$			3.16515i			0.116196i
$743$	15.1652			0.556355			0.278178	−	0.960530i	$-0.410270\pi$
$743$	15.1652			0.556355			0.278178	+	0.960530i	$0.410270\pi$
$744$	15.0000			0.549927
$745$			3.49545i			0.128064i
$746$		−	12.7477i		−	0.466727i
$747$	3.16515			0.115807
$748$		−	6.00000i		−	0.219382i
$749$	10.7477			0.392713
$750$	13.2867			0.485163
$751$	−41.4955			−1.51419			−0.757095	−	0.653304i	$-0.773382\pi$
$751$	−41.4955			−1.51419			−0.757095	+	0.653304i	$0.773382\pi$
$752$	−7.58258			−0.276508
$753$		−	7.91288i		−	0.288361i
$754$			14.3739i			0.523465i
$755$			11.6697i			0.424704i
$756$	−10.0000			−0.363696
$757$			35.2087i			1.27968i	0.768507	+	0.639841i	$0.221000\pi$
$757$			35.2087i			1.27968i	−0.768507	+	0.639841i	$0.779000\pi$
$758$			20.1216i			0.730849i
$759$		−	5.37386i		−	0.195059i
$760$			1.25227i			0.0454247i
$761$	14.2087			0.515065			0.257533	−	0.966270i	$-0.417090\pi$
$761$	14.2087			0.515065			0.257533	+	0.966270i	$0.417090\pi$
$762$			14.3303i			0.519132i
$763$			12.0000i			0.434429i
$764$			8.37386i			0.302956i
$765$	−1.25227			−0.0452760
$766$	−18.3303			−0.662301
$767$	6.00000			0.216647
$768$	1.79129			0.0646375
$769$			11.6697i			0.420820i	0.977613	+	0.210410i	$0.0674799\pi$
$769$			11.6697i			0.420820i	−0.977613	+	0.210410i	$0.932520\pi$
$770$	1.25227			0.0451288
$771$			8.50455i			0.306284i
$772$		−	18.3303i		−	0.659722i
$773$	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
$775$			36.6261i			1.31565i
$776$	13.5826			0.487586
$777$	−14.3303	−	16.4174i	−0.514097	−	0.588972i
$778$	32.8693			1.17842
$779$		−	15.4955i		−	0.555182i
$780$	−5.37386			−0.192415
$781$	7.25227			0.259507
$782$			28.7477i			1.02802i
$783$			18.9564i			0.677448i
$784$	−3.00000			−0.107143
$785$			1.58258i			0.0564845i
$786$	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
$790$		−	6.49545i		−	0.231098i
$791$		−	20.8348i		−	0.740802i
$792$			0.165151i			0.00586840i
$793$	48.4955			1.72212
$794$			14.7477i			0.523377i
$795$			2.24318i			0.0795574i
$796$		−	15.1652i		−	0.537515i
$797$		−	35.3739i		−	1.25301i	−0.779419	−	0.626503i	$-0.784486\pi$
$797$		−	35.3739i		−	1.25301i	0.779419	−	0.626503i	$-0.215514\pi$
$798$	−5.66970			−0.200705
$799$			57.4955i			2.03404i
$800$			4.37386i			0.154639i
$801$		−	1.25227i		−	0.0442469i
$802$	−16.7477			−0.591383
$803$	3.46099			0.122136
$804$	−11.4174			−0.402662
$805$	−6.00000			−0.211472
$806$		−	31.7477i		−	1.11827i
$807$	30.0000			1.05605
$808$		−	7.58258i		−	0.266754i
$809$			53.0780i			1.86612i	0.359715	+	0.933062i	$0.382874\pi$
$809$			53.0780i			1.86612i	−0.359715	+	0.933062i	$0.617126\pi$
$810$	−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	$0.613429\pi$
$812$		−	7.58258i		−	0.266096i
$813$	39.4083			1.38211
$814$	3.62614	−	3.16515i	0.127096	−	0.110938i
$815$	−15.4955			−0.542782
$816$		−	13.5826i		−	0.475485i
$817$	9.49545			0.332204
$818$	27.1652			0.949807
$819$		−	1.58258i		−	0.0552997i
$820$			7.74773i			0.270562i
$821$	3.16515			0.110465			0.0552323	−	0.998474i	$-0.482410\pi$
$821$	3.16515			0.110465			0.0552323	+	0.998474i	$0.482410\pi$
$822$		−	6.49545i		−	0.226555i
$823$	−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
$827$		−	33.1652i		−	1.15327i	−0.817004	−	0.576633i	$-0.804366\pi$
$827$		−	33.1652i		−	1.15327i	0.817004	−	0.576633i	$-0.195634\pi$
$828$		−	0.791288i		−	0.0274992i
$829$		−	17.0436i		−	0.591947i	−0.955196	−	0.295974i	$-0.904356\pi$
$829$		−	17.0436i		−	0.591947i	0.955196	−	0.295974i	$-0.0956441\pi$
$830$	12.0000			0.416526
$831$			17.2432i			0.598159i
$832$		−	3.79129i		−	0.131439i
$833$			22.7477i			0.788162i
$834$		−	23.9564i		−	0.829544i
$835$	17.3739			0.601247
$836$		−	1.25227i		−	0.0433108i
$837$		−	41.8693i		−	1.44722i
$838$			2.20871i			0.0762987i
$839$	3.49545			0.120676			0.0603382	−	0.998178i	$-0.480782\pi$
$839$	3.49545			0.120676			0.0603382	+	0.998178i	$0.480782\pi$
$840$	2.83485			0.0978116
$841$	14.6261			0.504350
$842$	−18.9564			−0.653282
$843$		0			0
$844$	−10.3739			−0.357083
$845$			1.08712i			0.0373981i
$846$		−	1.58258i		−	0.0544101i
$847$	20.7477			0.712900
$848$	−1.58258			−0.0543459
$849$		−	42.9909i		−	1.47544i
$850$	33.1652			1.13756
$851$	−17.3739	+	15.1652i	−0.595568	+	0.519855i
$852$	16.4174			0.562452
$853$		−	44.7042i		−	1.53064i	−0.643649	−	0.765321i	$-0.722580\pi$
$853$		−	44.7042i		−	1.53064i	0.643649	−	0.765321i	$-0.277420\pi$
$854$	−25.5826			−0.875418
$855$	−0.261365			−0.00893848
$856$			5.37386i			0.183675i
$857$		−	33.1652i		−	1.13290i	−0.824096	−	0.566450i	$-0.808316\pi$
$857$		−	33.1652i		−	1.13290i	0.824096	−	0.566450i	$-0.191684\pi$
$858$	5.37386			0.183461
$859$			18.6606i			0.636692i	0.947975	+	0.318346i	$0.103127\pi$
$859$			18.6606i			0.636692i	−0.947975	+	0.318346i	$0.896873\pi$
$860$	−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	$0.606266\pi$
$864$		−	5.00000i		−	0.170103i
$865$		−	12.0000i		−	0.408012i
$866$			10.6261i			0.361091i
$867$	−72.5390			−2.46355
$868$			16.7477i			0.568455i
$869$			6.49545i			0.220343i
$870$		−	5.37386i		−	0.182191i
$871$			24.1652i			0.818805i
$872$	−6.00000			−0.203186
$873$			2.83485i			0.0959451i
$874$			6.00000i			0.202953i
$875$			14.8348i			0.501509i
$876$	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
$880$			0.626136i			0.0211071i
$881$	−13.1216			−0.442078			−0.221039	−	0.975265i	$-0.570945\pi$
$881$	−13.1216			−0.442078			−0.221039	+	0.975265i	$0.570945\pi$
$882$		−	0.626136i		−	0.0210831i
$883$		−	31.9129i		−	1.07395i	−0.843597	−	0.536977i	$-0.819566\pi$
$883$		−	31.9129i		−	1.07395i	0.843597	−	0.536977i	$-0.180434\pi$
$884$	−28.7477			−0.966891
$885$	−2.24318			−0.0754037
$886$			27.9564i			0.939215i
$887$	−57.8258			−1.94160			−0.970799	−	0.239893i	$-0.922888\pi$
$887$	−57.8258			−1.94160			−0.970799	+	0.239893i	$0.922888\pi$
$888$	8.20871	−	7.16515i	0.275466	−	0.240447i
$889$	−16.0000			−0.536623
$890$		−	4.74773i		−	0.159144i
$891$	7.58258			0.254026
$892$	−14.0000			−0.468755
$893$			12.0000i			0.401565i
$894$		−	7.91288i		−	0.264646i
$895$	−1.25227			−0.0418589
$896$			2.00000i			0.0668153i
$897$	−25.7477			−0.859692
$898$	−2.83485			−0.0946001
$899$	31.7477			1.05885
$900$	−0.912878			−0.0304293
$901$			12.0000i			0.399778i
$902$		−	7.74773i		−	0.257971i
$903$		−	21.4955i		−	0.715324i
$904$	10.4174			0.346478
$905$		−	6.92197i		−	0.230094i
$906$		−	26.4174i		−	0.877660i
$907$			30.3303i			1.00710i	0.863966	+	0.503551i	$0.167973\pi$
$907$			30.3303i			1.00710i	−0.863966	+	0.503551i	$0.832027\pi$
$908$		−	25.9129i		−	0.859949i
$909$	1.58258			0.0524907
$910$		−	6.00000i		−	0.198898i
$911$		−	17.6697i		−	0.585423i	−0.956201	−	0.292712i	$-0.905442\pi$
$911$		−	17.6697i		−	0.585423i	0.956201	−	0.292712i	$-0.0945576\pi$
$912$		−	2.83485i		−	0.0938712i
$913$	−12.0000			−0.397142
$914$	−21.4955			−0.711006
$915$	−18.1307			−0.599382
$916$	−6.74773			−0.222951
$917$			33.4955i			1.10612i
$918$	−37.9129			−1.25131
$919$		−	36.0000i		−	1.18753i	−0.804638	−	0.593765i	$-0.797641\pi$
$919$		−	36.0000i		−	1.18753i	0.804638	−	0.593765i	$-0.202359\pi$
$920$		−	3.00000i		−	0.0989071i
$921$	2.46099			0.0810922
$922$	12.3303			0.406077
$923$		−	34.7477i		−	1.14374i
$924$	−2.83485			−0.0932597
$925$	17.4955	+	20.0436i	0.575247	+	0.659028i
$926$	29.7042			0.976139
$927$		−	1.41742i		−	0.0465543i
$928$	3.79129			0.124455
$929$	8.37386			0.274738			0.137369	−	0.990520i	$-0.456135\pi$
$929$	8.37386			0.274738			0.137369	+	0.990520i	$0.456135\pi$
$930$			11.8693i			0.389210i
$931$			4.74773i			0.155600i
$932$	16.1216			0.528080
$933$			41.8693i			1.37074i
$934$	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	$0.307111\pi$
$938$		−	12.7477i		−	0.416228i
$939$			26.5735i			0.867193i
$940$		−	6.00000i		−	0.195698i
$941$	−21.4955			−0.700732			−0.350366	−	0.936613i	$-0.613943\pi$
$941$	−21.4955			−0.700732			−0.350366	+	0.936613i	$0.613943\pi$
$942$		−	3.58258i		−	0.116727i
$943$			37.1216i			1.20885i
$944$		−	1.58258i		−	0.0515085i
$945$		−	7.91288i		−	0.257406i
$946$	4.74773			0.154362
$947$			1.25227i			0.0406934i	0.999793	+	0.0203467i	$0.00647700\pi$
$947$			1.25227i			0.0406934i	−0.999793	+	0.0203467i	$0.993523\pi$
$948$			14.7042i			0.477569i
$949$		−	16.5826i		−	0.538293i
$950$	6.92197			0.224578
$951$	−51.4955			−1.66985
$952$	15.1652			0.491505
$953$	31.4519			1.01883			0.509413	−	0.860522i	$-0.329862\pi$
$953$	31.4519			1.01883			0.509413	+	0.860522i	$0.329862\pi$
$954$		−	0.330303i		−	0.0106939i
$955$	−6.62614			−0.214417
$956$			2.04356i			0.0660935i
$957$			5.37386i			0.173712i
$958$	3.79129			0.122491
$959$	7.25227			0.234188
$960$			1.41742i			0.0457472i
$961$	−39.1216			−1.26199
$962$	−15.1652	−	17.3739i	−0.488944	−	0.560156i
$963$	−1.12159			−0.0361428
$964$			4.41742i			0.142276i
$965$	14.5045			0.466918
$966$	13.5826			0.437012
$967$			21.9564i			0.706071i	0.935610	+	0.353036i	$0.114851\pi$
$967$			21.9564i			0.706071i	−0.935610	+	0.353036i	$0.885149\pi$
$968$			10.3739i			0.333429i
$969$	−21.4955			−0.690533
$970$			10.7477i			0.345089i
$971$	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
$975$			29.7042i			0.951295i
$976$		−	12.7913i		−	0.409439i
$977$		−	41.0780i		−	1.31420i	−0.753802	−	0.657101i	$-0.771782\pi$
$977$		−	41.0780i		−	1.31420i	0.753802	−	0.657101i	$-0.228218\pi$
$978$	35.0780			1.12167
$979$			4.74773i			0.151738i
$980$		−	2.37386i		−	0.0758303i
$981$		−	1.25227i		−	0.0399820i
$982$			5.37386i			0.171487i
$983$	−18.3303			−0.584646			−0.292323	−	0.956320i	$-0.594428\pi$
$983$	−18.3303			−0.584646			−0.292323	+	0.956320i	$0.594428\pi$
$984$		−	17.5390i		−	0.559123i
$985$			15.7568i			0.502054i
$986$		−	28.7477i		−	0.915514i
$987$	27.1652			0.864676
$988$	−6.00000			−0.190885
$989$	−22.7477			−0.723336
$990$	−0.130682			−0.00415336
$991$		−	18.9564i		−	0.602171i	−0.953597	−	0.301086i	$-0.902651\pi$
$991$		−	18.9564i		−	0.602171i	0.953597	−	0.301086i	$-0.0973490\pi$
$992$	−8.37386			−0.265870
$993$			45.8258i			1.45424i
$994$			18.3303i			0.581402i
$995$	12.0000			0.380426
$996$	−27.1652			−0.860761
$997$			18.0000i			0.570066i	0.958518	+	0.285033i	$0.0920045\pi$
$997$			18.0000i			0.570066i	−0.958518	+	0.285033i	$0.907995\pi$
$998$	−10.7477			−0.340213
$999$	−20.0000	−	22.9129i	−0.632772	−	0.724931i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	74.2.b.a.73.4	yes	4
3.2	odd	2		666.2.c.b.73.2		4
4.3	odd	2		592.2.g.c.369.1		4
5.2	odd	4		1850.2.c.g.1849.2		4
5.3	odd	4		1850.2.c.h.1849.3		4
5.4	even	2		1850.2.d.e.1701.1		4
8.3	odd	2		2368.2.g.h.961.4		4
8.5	even	2		2368.2.g.j.961.2		4
12.11	even	2		5328.2.h.m.2737.3		4
37.6	odd	4		2738.2.a.k.1.1		2
37.31	odd	4		2738.2.a.h.1.1		2
37.36	even	2	inner	74.2.b.a.73.2	✓	4
111.110	odd	2		666.2.c.b.73.3		4
148.147	odd	2		592.2.g.c.369.2		4
185.73	odd	4		1850.2.c.g.1849.3		4
185.147	odd	4		1850.2.c.h.1849.2		4
185.184	even	2		1850.2.d.e.1701.3		4
296.147	odd	2		2368.2.g.h.961.3		4
296.221	even	2		2368.2.g.j.961.1		4
444.443	even	2		5328.2.h.m.2737.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.2.b.a.73.2	✓	4	37.36	even	2	inner
74.2.b.a.73.4	yes	4	1.1	even	1	trivial
592.2.g.c.369.1		4	4.3	odd	2
592.2.g.c.369.2		4	148.147	odd	2
666.2.c.b.73.2		4	3.2	odd	2
666.2.c.b.73.3		4	111.110	odd	2
1850.2.c.g.1849.2		4	5.2	odd	4
1850.2.c.g.1849.3		4	185.73	odd	4
1850.2.c.h.1849.2		4	185.147	odd	4
1850.2.c.h.1849.3		4	5.3	odd	4
1850.2.d.e.1701.1		4	5.4	even	2
1850.2.d.e.1701.3		4	185.184	even	2
2368.2.g.h.961.3		4	296.147	odd	2
2368.2.g.h.961.4		4	8.3	odd	2
2368.2.g.j.961.1		4	296.221	even	2
2368.2.g.j.961.2		4	8.5	even	2
2738.2.a.h.1.1		2	37.31	odd	4
2738.2.a.k.1.1		2	37.6	odd	4
5328.2.h.m.2737.2		4	444.443	even	2
5328.2.h.m.2737.3		4	12.11	even	2

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:	\( N \)	\(=\)	\( 74 = 2 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	74.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +1.79129 q^{3} -1.00000 q^{4} -0.791288i q^{5} +1.79129i q^{6} -2.00000 q^{7} -1.00000i q^{8} +0.208712 q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +1.79129 q^{3} -1.00000 q^{4} -0.791288i q^{5} +1.79129i q^{6} -2.00000 q^{7} -1.00000i q^{8} +0.208712 q^{9} +0.791288 q^{10} -0.791288 q^{11} -1.79129 q^{12} +3.79129i q^{13} -2.00000i q^{14} -1.41742i q^{15} +1.00000 q^{16} -7.58258i q^{17} +0.208712i q^{18} -1.58258i q^{19} +0.791288i q^{20} -3.58258 q^{21} -0.791288i q^{22} +3.79129i q^{23} -1.79129i q^{24} +4.37386 q^{25} -3.79129 q^{26} -5.00000 q^{27} +2.00000 q^{28} -3.79129i q^{29} +1.41742 q^{30} +8.37386i q^{31} +1.00000i q^{32} -1.41742 q^{33} +7.58258 q^{34} +1.58258i q^{35} -0.208712 q^{36} +(4.00000 + 4.58258i) q^{37} +1.58258 q^{38} +6.79129i q^{39} -0.791288 q^{40} +9.79129 q^{41} -3.58258i q^{42} +6.00000i q^{43} +0.791288 q^{44} -0.165151i q^{45} -3.79129 q^{46} -7.58258 q^{47} +1.79129 q^{48} -3.00000 q^{49} +4.37386i q^{50} -13.5826i q^{51} -3.79129i q^{52} -1.58258 q^{53} -5.00000i q^{54} +0.626136i q^{55} +2.00000i q^{56} -2.83485i q^{57} +3.79129 q^{58} -1.58258i q^{59} +1.41742i q^{60} -12.7913i q^{61} -8.37386 q^{62} -0.417424 q^{63} -1.00000 q^{64} +3.00000 q^{65} -1.41742i q^{66} +6.37386 q^{67} +7.58258i q^{68} +6.79129i q^{69} -1.58258 q^{70} -9.16515 q^{71} -0.208712i q^{72} -4.37386 q^{73} +(-4.58258 + 4.00000i) q^{74} +7.83485 q^{75} +1.58258i q^{76} +1.58258 q^{77} -6.79129 q^{78} -8.20871i q^{79} -0.791288i q^{80} -9.58258 q^{81} +9.79129i q^{82} +15.1652 q^{83} +3.58258 q^{84} -6.00000 q^{85} -6.00000 q^{86} -6.79129i q^{87} +0.791288i q^{88} -6.00000i q^{89} +0.165151 q^{90} -7.58258i q^{91} -3.79129i q^{92} +15.0000i q^{93} -7.58258i q^{94} -1.25227 q^{95} +1.79129i q^{96} +13.5826i q^{97} -3.00000i q^{98} -0.165151 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{3} - 4 q^{4} - 8 q^{7} + 10 q^{9}+O(q^{10}) \) 4 * q - 2 * q^3 - 4 * q^4 - 8 * q^7 + 10 * q^9	\( 4 q - 2 q^{3} - 4 q^{4} - 8 q^{7} + 10 q^{9} - 6 q^{10} + 6 q^{11} + 2 q^{12} + 4 q^{16} + 4 q^{21} - 10 q^{25} - 6 q^{26} - 20 q^{27} + 8 q^{28} + 24 q^{30} - 24 q^{33} + 12 q^{34} - 10 q^{36} + 16 q^{37} - 12 q^{38} + 6 q^{40} + 30 q^{41} - 6 q^{44} - 6 q^{46} - 12 q^{47} - 2 q^{48} - 12 q^{49} + 12 q^{53} + 6 q^{58} - 6 q^{62} - 20 q^{63} - 4 q^{64} + 12 q^{65} - 2 q^{67} + 12 q^{70} + 10 q^{73} + 68 q^{75} - 12 q^{77} - 18 q^{78} - 20 q^{81} + 24 q^{83} - 4 q^{84} - 24 q^{85} - 24 q^{86} - 36 q^{90} - 60 q^{95} + 36 q^{99}+O(q^{100}) \) 4 * q - 2 * q^3 - 4 * q^4 - 8 * q^7 + 10 * q^9 - 6 * q^10 + 6 * q^11 + 2 * q^12 + 4 * q^16 + 4 * q^21 - 10 * q^25 - 6 * q^26 - 20 * q^27 + 8 * q^28 + 24 * q^30 - 24 * q^33 + 12 * q^34 - 10 * q^36 + 16 * q^37 - 12 * q^38 + 6 * q^40 + 30 * q^41 - 6 * q^44 - 6 * q^46 - 12 * q^47 - 2 * q^48 - 12 * q^49 + 12 * q^53 + 6 * q^58 - 6 * q^62 - 20 * q^63 - 4 * q^64 + 12 * q^65 - 2 * q^67 + 12 * q^70 + 10 * q^73 + 68 * q^75 - 12 * q^77 - 18 * q^78 - 20 * q^81 + 24 * q^83 - 4 * q^84 - 24 * q^85 - 24 * q^86 - 36 * q^90 - 60 * q^95 + 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more