LMFDB - Embedded newform 76.3.b.a.39.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,3,Mod(39,76)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("76.39");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	76.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:	$2.07085000914$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-19})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 4x^{2} - 5x + 25 $ x^4 - x^3 - 4x^2 - 5x + 25
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			39.2
Root			$2.13746 + 0.656712i$ of defining polynomial
Character	$\chi$	$=$	76.39
Dual form			76.3.b.a.39.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 - 1.73205i) q^{2} +1.31342i q^{3} +(-2.00000 + 3.46410i) q^{4} +6.54983 q^{5} +(2.27492 - 1.31342i) q^{6} -1.31342i q^{7} +8.00000 q^{8} +7.27492 q^{9} +O(q^{10})$	\(q+(-1.00000 - 1.73205i) q^{2} +1.31342i q^{3} +(-2.00000 + 3.46410i) q^{4} +6.54983 q^{5} +(2.27492 - 1.31342i) q^{6} -1.31342i q^{7} +8.00000 q^{8} +7.27492 q^{9} +(-6.54983 - 11.3446i) q^{10} -4.30136i q^{11} +(-4.54983 - 2.62685i) q^{12} +0.824752 q^{13} +(-2.27492 + 1.31342i) q^{14} +8.60271i q^{15} +(-8.00000 - 13.8564i) q^{16} +0.274917 q^{17} +(-7.27492 - 12.6005i) q^{18} +4.35890i q^{19} +(-13.0997 + 22.6893i) q^{20} +1.72508 q^{21} +(-7.45017 + 4.30136i) q^{22} +33.5578i q^{23} +10.5074i q^{24} +17.9003 q^{25} +(-0.824752 - 1.42851i) q^{26} +21.3759i q^{27} +(4.54983 + 2.62685i) q^{28} -33.3746 q^{29} +(14.9003 - 8.60271i) q^{30} -48.7276i q^{31} +(-16.0000 + 27.7128i) q^{32} +5.64950 q^{33} +(-0.274917 - 0.476171i) q^{34} -8.60271i q^{35} +(-14.5498 + 25.2011i) q^{36} -36.1993 q^{37} +(7.54983 - 4.35890i) q^{38} +1.08325i q^{39} +52.3987 q^{40} -68.7492 q^{41} +(-1.72508 - 2.98793i) q^{42} -55.6558i q^{43} +(14.9003 + 8.60271i) q^{44} +47.6495 q^{45} +(58.1238 - 33.5578i) q^{46} -24.1336i q^{47} +(18.1993 - 10.5074i) q^{48} +47.2749 q^{49} +(-17.9003 - 31.0043i) q^{50} +0.361083i q^{51} +(-1.64950 + 2.85702i) q^{52} +25.9244 q^{53} +(37.0241 - 21.3759i) q^{54} -28.1732i q^{55} -10.5074i q^{56} -5.72508 q^{57} +(33.3746 + 57.8065i) q^{58} +46.2317i q^{59} +(-29.8007 - 17.2054i) q^{60} -47.0997 q^{61} +(-84.3987 + 48.7276i) q^{62} -9.55505i q^{63} +64.0000 q^{64} +5.40199 q^{65} +(-5.64950 - 9.78523i) q^{66} +112.625i q^{67} +(-0.549834 + 0.952341i) q^{68} -44.0756 q^{69} +(-14.9003 + 8.60271i) q^{70} -70.4645i q^{71} +58.1993 q^{72} -58.0756 q^{73} +(36.1993 + 62.6991i) q^{74} +23.5107i q^{75} +(-15.0997 - 8.71780i) q^{76} -5.64950 q^{77} +(1.87624 - 1.08325i) q^{78} -113.478i q^{79} +(-52.3987 - 90.7572i) q^{80} +37.3987 q^{81} +(68.7492 + 119.077i) q^{82} +148.579i q^{83} +(-3.45017 + 5.97586i) q^{84} +1.80066 q^{85} +(-96.3987 + 55.6558i) q^{86} -43.8350i q^{87} -34.4108i q^{88} +57.8488 q^{89} +(-47.6495 - 82.5314i) q^{90} -1.08325i q^{91} +(-116.248 - 67.1155i) q^{92} +64.0000 q^{93} +(-41.8007 + 24.1336i) q^{94} +28.5501i q^{95} +(-36.3987 - 21.0148i) q^{96} -117.698 q^{97} +(-47.2749 - 81.8826i) q^{98} -31.2920i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} - 8 q^{4} - 4 q^{5} - 6 q^{6} + 32 q^{8} + 14 q^{9}+O(q^{10}) $ 4 * q - 4 * q^2 - 8 * q^4 - 4 * q^5 - 6 * q^6 + 32 * q^8 + 14 * q^9	$ 4 q - 4 q^{2} - 8 q^{4} - 4 q^{5} - 6 q^{6} + 32 q^{8} + 14 q^{9} + 4 q^{10} + 12 q^{12} - 42 q^{13} + 6 q^{14} - 32 q^{16} - 14 q^{17} - 14 q^{18} + 8 q^{20} + 22 q^{21} - 60 q^{22} + 132 q^{25} + 42 q^{26} - 12 q^{28} - 58 q^{29} + 120 q^{30} - 64 q^{32} - 68 q^{33} + 14 q^{34} - 28 q^{36} - 24 q^{37} - 32 q^{40} - 124 q^{41} - 22 q^{42} + 120 q^{44} + 100 q^{45} + 6 q^{46} - 48 q^{48} + 174 q^{49} - 132 q^{50} + 84 q^{52} - 2 q^{53} - 18 q^{54} - 38 q^{57} + 58 q^{58} - 240 q^{60} - 128 q^{61} - 96 q^{62} + 256 q^{64} + 384 q^{65} + 68 q^{66} + 28 q^{68} - 282 q^{69} - 120 q^{70} + 112 q^{72} - 338 q^{73} + 24 q^{74} + 68 q^{77} + 234 q^{78} + 32 q^{80} - 92 q^{81} + 124 q^{82} - 44 q^{84} + 128 q^{85} - 144 q^{86} + 20 q^{89} - 100 q^{90} - 12 q^{92} + 256 q^{93} - 288 q^{94} + 96 q^{96} - 48 q^{97} - 174 q^{98}+O(q^{100}) $ 4 * q - 4 * q^2 - 8 * q^4 - 4 * q^5 - 6 * q^6 + 32 * q^8 + 14 * q^9 + 4 * q^10 + 12 * q^12 - 42 * q^13 + 6 * q^14 - 32 * q^16 - 14 * q^17 - 14 * q^18 + 8 * q^20 + 22 * q^21 - 60 * q^22 + 132 * q^25 + 42 * q^26 - 12 * q^28 - 58 * q^29 + 120 * q^30 - 64 * q^32 - 68 * q^33 + 14 * q^34 - 28 * q^36 - 24 * q^37 - 32 * q^40 - 124 * q^41 - 22 * q^42 + 120 * q^44 + 100 * q^45 + 6 * q^46 - 48 * q^48 + 174 * q^49 - 132 * q^50 + 84 * q^52 - 2 * q^53 - 18 * q^54 - 38 * q^57 + 58 * q^58 - 240 * q^60 - 128 * q^61 - 96 * q^62 + 256 * q^64 + 384 * q^65 + 68 * q^66 + 28 * q^68 - 282 * q^69 - 120 * q^70 + 112 * q^72 - 338 * q^73 + 24 * q^74 + 68 * q^77 + 234 * q^78 + 32 * q^80 - 92 * q^81 + 124 * q^82 - 44 * q^84 + 128 * q^85 - 144 * q^86 + 20 * q^89 - 100 * q^90 - 12 * q^92 + 256 * q^93 - 288 * q^94 + 96 * q^96 - 48 * q^97 - 174 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$1$	$-1$

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 $

$2$	−1.00000	−	1.73205i	−0.500000	−	0.866025i
$2$	−1.00000	−	1.73205i	−0.500000	−	0.866025i
$3$			1.31342i			0.437808i	0.975746	+	0.218904i	$0.0702482\pi$
$3$			1.31342i			0.437808i	−0.975746	+	0.218904i	$0.929752\pi$
$4$	−2.00000	+	3.46410i	−0.500000	+	0.866025i
$5$	6.54983			1.30997			0.654983	−	0.755643i	$-0.272676\pi$
$5$	6.54983			1.30997			0.654983	+	0.755643i	$0.272676\pi$
$6$	2.27492	−	1.31342i	0.379153	−	0.218904i
$7$		−	1.31342i		−	0.187632i	−0.995590	−	0.0938160i	$-0.970093\pi$
$7$		−	1.31342i		−	0.187632i	0.995590	−	0.0938160i	$-0.0299065\pi$
$8$	8.00000			1.00000
$9$	7.27492			0.808324
$10$	−6.54983	−	11.3446i	−0.654983	−	1.13446i
$11$		−	4.30136i		−	0.391032i	−0.980700	−	0.195516i	$-0.937362\pi$
$11$		−	4.30136i		−	0.391032i	0.980700	−	0.195516i	$-0.0626382\pi$
$12$	−4.54983	−	2.62685i	−0.379153	−	0.218904i
$13$	0.824752			0.0634424			0.0317212	−	0.999497i	$-0.489901\pi$
$13$	0.824752			0.0634424			0.0317212	+	0.999497i	$0.489901\pi$
$14$	−2.27492	+	1.31342i	−0.162494	+	0.0938160i
$15$			8.60271i			0.573514i
$16$	−8.00000	−	13.8564i	−0.500000	−	0.866025i
$17$	0.274917			0.0161716			0.00808580	−	0.999967i	$-0.497426\pi$
$17$	0.274917			0.0161716			0.00808580	+	0.999967i	$0.497426\pi$
$18$	−7.27492	−	12.6005i	−0.404162	−	0.700029i
$19$			4.35890i			0.229416i
$19$			4.35890i			0.229416i
$20$	−13.0997	+	22.6893i	−0.654983	+	1.13446i
$21$	1.72508			0.0821468
$22$	−7.45017	+	4.30136i	−0.338644	+	0.195516i
$23$			33.5578i			1.45903i	0.683963	+	0.729517i	$0.260255\pi$
$23$			33.5578i			1.45903i	−0.683963	+	0.729517i	$0.739745\pi$
$24$			10.5074i			0.437808i
$25$	17.9003			0.716013
$26$	−0.824752	−	1.42851i	−0.0317212	−	0.0549428i
$27$			21.3759i			0.791699i
$28$	4.54983	+	2.62685i	0.162494	+	0.0938160i
$29$	−33.3746			−1.15085			−0.575424	−	0.817855i	$-0.695163\pi$
$29$	−33.3746			−1.15085			−0.575424	+	0.817855i	$0.695163\pi$
$30$	14.9003	−	8.60271i	0.496678	−	0.286757i
$31$		−	48.7276i		−	1.57186i	−0.618317	−	0.785929i	$-0.712185\pi$
$31$		−	48.7276i		−	1.57186i	0.618317	−	0.785929i	$-0.287815\pi$
$32$	−16.0000	+	27.7128i	−0.500000	+	0.866025i
$33$	5.64950			0.171197
$34$	−0.274917	−	0.476171i	−0.00808580	−	0.0140050i
$35$		−	8.60271i		−	0.245792i
$36$	−14.5498	+	25.2011i	−0.404162	+	0.700029i
$37$	−36.1993			−0.978360			−0.489180	−	0.872183i	$-0.662704\pi$
$37$	−36.1993			−0.978360			−0.489180	+	0.872183i	$0.662704\pi$
$38$	7.54983	−	4.35890i	0.198680	−	0.114708i
$39$			1.08325i			0.0277756i
$40$	52.3987			1.30997
$41$	−68.7492			−1.67681			−0.838405	−	0.545048i	$-0.816511\pi$
$41$	−68.7492			−1.67681			−0.838405	+	0.545048i	$0.816511\pi$
$42$	−1.72508	−	2.98793i	−0.0410734	−	0.0711412i
$43$		−	55.6558i		−	1.29432i	−0.762354	−	0.647160i	$-0.775956\pi$
$43$		−	55.6558i		−	1.29432i	0.762354	−	0.647160i	$-0.224044\pi$
$44$	14.9003	+	8.60271i	0.338644	+	0.195516i
$45$	47.6495			1.05888
$46$	58.1238	−	33.5578i	1.26356	−	0.729517i
$47$		−	24.1336i		−	0.513481i	−0.966480	−	0.256741i	$-0.917351\pi$
$47$		−	24.1336i		−	0.513481i	0.966480	−	0.256741i	$-0.0826486\pi$
$48$	18.1993	−	10.5074i	0.379153	−	0.218904i
$49$	47.2749			0.964794
$50$	−17.9003	−	31.0043i	−0.358007	−	0.620086i
$51$			0.361083i			0.00708006i
$52$	−1.64950	+	2.85702i	−0.0317212	+	0.0549428i
$53$	25.9244			0.489140			0.244570	−	0.969632i	$-0.421353\pi$
$53$	25.9244			0.489140			0.244570	+	0.969632i	$0.421353\pi$
$54$	37.0241	−	21.3759i	0.685631	−	0.395849i
$55$		−	28.1732i		−	0.512239i
$56$		−	10.5074i		−	0.187632i
$57$	−5.72508			−0.100440
$58$	33.3746	+	57.8065i	0.575424	+	0.996663i
$59$			46.2317i			0.783587i	0.920053	+	0.391794i	$0.128145\pi$
$59$			46.2317i			0.783587i	−0.920053	+	0.391794i	$0.871855\pi$
$60$	−29.8007	−	17.2054i	−0.496678	−	0.286757i
$61$	−47.0997			−0.772126			−0.386063	−	0.922472i	$-0.626165\pi$
$61$	−47.0997			−0.772126			−0.386063	+	0.922472i	$0.626165\pi$
$62$	−84.3987	+	48.7276i	−1.36127	+	0.785929i
$63$		−	9.55505i		−	0.151667i
$64$	64.0000			1.00000
$65$	5.40199			0.0831075
$66$	−5.64950	−	9.78523i	−0.0855985	−	0.148261i
$67$			112.625i			1.68097i	0.541834	+	0.840485i	$0.317730\pi$
$67$			112.625i			1.68097i	−0.541834	+	0.840485i	$0.682270\pi$
$68$	−0.549834	+	0.952341i	−0.00808580	+	0.0140050i
$69$	−44.0756			−0.638777
$70$	−14.9003	+	8.60271i	−0.212862	+	0.122896i
$71$		−	70.4645i		−	0.992458i	−0.868192	−	0.496229i	$-0.834718\pi$
$71$		−	70.4645i		−	0.992458i	0.868192	−	0.496229i	$-0.165282\pi$
$72$	58.1993			0.808324
$73$	−58.0756			−0.795556			−0.397778	−	0.917482i	$-0.630219\pi$
$73$	−58.0756			−0.795556			−0.397778	+	0.917482i	$0.630219\pi$
$74$	36.1993	+	62.6991i	0.489180	+	0.847285i
$75$			23.5107i			0.313476i
$76$	−15.0997	−	8.71780i	−0.198680	−	0.114708i
$77$	−5.64950			−0.0733702
$78$	1.87624	−	1.08325i	0.0240544	−	0.0138878i
$79$		−	113.478i		−	1.43643i	−0.695820	−	0.718216i	$-0.744959\pi$
$79$		−	113.478i		−	1.43643i	0.695820	−	0.718216i	$-0.255041\pi$
$80$	−52.3987	−	90.7572i	−0.654983	−	1.13446i
$81$	37.3987			0.461712
$82$	68.7492	+	119.077i	0.838405	+	1.45216i
$83$			148.579i			1.79011i	0.445952	+	0.895057i	$0.352865\pi$
$83$			148.579i			1.79011i	−0.445952	+	0.895057i	$0.647135\pi$
$84$	−3.45017	+	5.97586i	−0.0410734	+	0.0711412i
$85$	1.80066			0.0211843
$86$	−96.3987	+	55.6558i	−1.12091	+	0.647160i
$87$		−	43.8350i		−	0.503850i
$88$		−	34.4108i		−	0.391032i
$89$	57.8488			0.649987			0.324993	−	0.945716i	$-0.394638\pi$
$89$	57.8488			0.649987			0.324993	+	0.945716i	$0.394638\pi$
$90$	−47.6495	−	82.5314i	−0.529439	−	0.917015i
$91$		−	1.08325i		−	0.0119038i
$92$	−116.248	−	67.1155i	−1.26356	−	0.729517i
$93$	64.0000			0.688172
$94$	−41.8007	+	24.1336i	−0.444688	+	0.256741i
$95$			28.5501i			0.300527i
$96$	−36.3987	−	21.0148i	−0.379153	−	0.218904i
$97$	−117.698			−1.21338			−0.606689	−	0.794939i	$-0.707503\pi$
$97$	−117.698			−1.21338			−0.606689	+	0.794939i	$0.707503\pi$
$98$	−47.2749	−	81.8826i	−0.482397	−	0.835536i
$99$		−	31.2920i		−	0.316081i
$100$	−35.8007	+	62.0086i	−0.358007	+	0.620086i
$101$	173.299			1.71583			0.857916	−	0.513790i	$-0.171759\pi$
$101$	173.299			1.71583			0.857916	+	0.513790i	$0.171759\pi$
$102$	0.625414	−	0.361083i	0.00613151	−	0.00354003i
$103$		−	1.18252i		−	0.0114807i	−0.999984	−	0.00574037i	$-0.998173\pi$
$103$		−	1.18252i		−	0.0114807i	0.999984	−	0.00574037i	$-0.00182723\pi$
$104$	6.59801			0.0634424
$105$	11.2990			0.107610
$106$	−25.9244	−	44.9024i	−0.244570	−	0.423608i
$107$			92.7928i			0.867222i	0.901100	+	0.433611i	$0.142761\pi$
$107$			92.7928i			0.867222i	−0.901100	+	0.433611i	$0.857239\pi$
$108$	−74.0482	−	42.7517i	−0.685631	−	0.395849i
$109$	−44.8248			−0.411236			−0.205618	−	0.978632i	$-0.565920\pi$
$109$	−44.8248			−0.411236			−0.205618	+	0.978632i	$0.565920\pi$
$110$	−48.7974	+	28.1732i	−0.443612	+	0.256120i
$111$		−	47.5451i		−	0.428334i
$112$	−18.1993	+	10.5074i	−0.162494	+	0.0938160i
$113$	65.6977			0.581395			0.290698	−	0.956815i	$-0.406113\pi$
$113$	65.6977			0.581395			0.290698	+	0.956815i	$0.406113\pi$
$114$	5.72508	+	9.91613i	0.0502200	+	0.0869836i
$115$			219.798i			1.91129i
$116$	66.7492	−	115.613i	0.575424	−	0.996663i
$117$	6.00000			0.0512821
$118$	80.0756	−	46.2317i	0.678607	−	0.391794i
$119$		−	0.361083i		−	0.00303431i
$120$			68.8217i			0.573514i
$121$	102.498			0.847094
$122$	47.0997	+	81.5790i	0.386063	+	0.668680i
$123$		−	90.2968i		−	0.734120i
$124$	168.797	+	97.4552i	1.36127	+	0.785929i
$125$	−46.5017			−0.372013
$126$	−16.5498	+	9.55505i	−0.131348	+	0.0758337i
$127$		−	93.9076i		−	0.739430i	−0.929145	−	0.369715i	$-0.879455\pi$
$127$		−	93.9076i		−	0.739430i	0.929145	−	0.369715i	$-0.120545\pi$
$128$	−64.0000	−	110.851i	−0.500000	−	0.866025i
$129$	73.0997			0.566664
$130$	−5.40199	−	9.35652i	−0.0415537	−	0.0719732i
$131$		−	9.81687i		−	0.0749379i	−0.999298	−	0.0374690i	$-0.988070\pi$
$131$		−	9.81687i		−	0.0749379i	0.999298	−	0.0374690i	$-0.0119295\pi$
$132$	−11.2990	+	19.5705i	−0.0855985	+	0.148261i
$133$	5.72508			0.0430457
$134$	195.072	−	112.625i	1.45576	−	0.840485i
$135$			140.008i			1.03710i
$136$	2.19934			0.0161716
$137$	63.9726			0.466953			0.233477	−	0.972362i	$-0.424990\pi$
$137$	63.9726			0.466953			0.233477	+	0.972362i	$0.424990\pi$
$138$	44.0756	+	76.3411i	0.319388	+	0.553197i
$139$		−	18.8799i		−	0.135827i	−0.997691	−	0.0679134i	$-0.978366\pi$
$139$		−	18.8799i		−	0.135827i	0.997691	−	0.0679134i	$-0.0216342\pi$
$140$	29.8007	+	17.2054i	0.212862	+	0.122896i
$141$	31.6977			0.224806
$142$	−122.048	+	70.4645i	−0.859494	+	0.496229i
$143$		−	3.54755i		−	0.0248080i
$144$	−58.1993	−	100.804i	−0.404162	−	0.700029i
$145$	−218.598			−1.50757
$146$	58.0756	+	100.590i	0.397778	+	0.688972i
$147$			62.0920i			0.422395i
$148$	72.3987	−	125.398i	0.489180	−	0.847285i
$149$	−78.9485			−0.529856			−0.264928	−	0.964268i	$-0.585348\pi$
$149$	−78.9485			−0.529856			−0.264928	+	0.964268i	$0.585348\pi$
$150$	40.7218	−	23.5107i	0.271478	−	0.156738i
$151$		−	192.744i		−	1.27645i	−0.769850	−	0.638225i	$-0.779669\pi$
$151$		−	192.744i		−	1.27645i	0.769850	−	0.638225i	$-0.220331\pi$
$152$			34.8712i			0.229416i
$153$	2.00000			0.0130719
$154$	5.64950	+	9.78523i	0.0366851	+	0.0635404i
$155$		−	319.158i		−	2.05908i
$156$	−3.75248	−	2.16650i	−0.0240544	−	0.0138878i
$157$	7.00331			0.0446071			0.0223035	−	0.999751i	$-0.492900\pi$
$157$	7.00331			0.0446071			0.0223035	+	0.999751i	$0.492900\pi$
$158$	−196.550	+	113.478i	−1.24399	+	0.718216i
$159$			34.0498i			0.214149i
$160$	−104.797	+	181.514i	−0.654983	+	1.13446i
$161$	44.0756			0.273761
$162$	−37.3987	−	64.7764i	−0.230856	−	0.399854i
$163$			12.6423i			0.0775598i	0.999248	+	0.0387799i	$0.0123471\pi$
$163$			12.6423i			0.0775598i	−0.999248	+	0.0387799i	$0.987653\pi$
$164$	137.498	−	238.154i	0.838405	−	1.45216i
$165$	37.0033			0.224262
$166$	257.347	−	148.579i	1.55028	−	0.895057i
$167$			112.296i			0.672429i	0.941786	+	0.336214i	$0.109147\pi$
$167$			112.296i			0.672429i	−0.941786	+	0.336214i	$0.890853\pi$
$168$	13.8007			0.0821468
$169$	−168.320			−0.995975
$170$	−1.80066	−	3.11884i	−0.0105921	−	0.0183461i
$171$			31.7106i			0.185442i
$172$	192.797	+	111.312i	1.12091	+	0.647160i
$173$	39.8970			0.230619			0.115309	−	0.993330i	$-0.463214\pi$
$173$	39.8970			0.230619			0.115309	+	0.993330i	$0.463214\pi$
$174$	−75.9244	+	43.8350i	−0.436347	+	0.251925i
$175$		−	23.5107i		−	0.134347i
$176$	−59.6013	+	34.4108i	−0.338644	+	0.195516i
$177$	−60.7218			−0.343061
$178$	−57.8488	−	100.197i	−0.324993	−	0.562905i
$179$		−	141.159i		−	0.788599i	−0.918982	−	0.394300i	$-0.870987\pi$
$179$		−	141.159i		−	0.788599i	0.918982	−	0.394300i	$-0.129013\pi$
$180$	−95.2990	+	165.063i	−0.529439	+	0.917015i
$181$	142.000			0.784530			0.392265	−	0.919852i	$-0.371692\pi$
$181$	142.000			0.784530			0.392265	+	0.919852i	$0.371692\pi$
$182$	−1.87624	+	1.08325i	−0.0103090	+	0.00595192i
$183$		−	61.8618i		−	0.338043i
$184$			268.462i			1.45903i
$185$	−237.100			−1.28162
$186$	−64.0000	−	110.851i	−0.344086	−	0.595974i
$187$		−	1.18252i		−	0.00632362i
$188$	83.6013	+	48.2672i	0.444688	+	0.256741i
$189$	28.0756			0.148548
$190$	49.4502	−	28.5501i	0.260264	−	0.150264i
$191$			315.416i			1.65139i	0.564115	+	0.825696i	$0.309217\pi$
$191$			315.416i			1.65139i	−0.564115	+	0.825696i	$0.690783\pi$
$192$			84.0591i			0.437808i
$193$	44.1993			0.229012			0.114506	−	0.993423i	$-0.463471\pi$
$193$	44.1993			0.229012			0.114506	+	0.993423i	$0.463471\pi$
$194$	117.698	+	203.858i	0.606689	+	1.05082i
$195$			7.09510i			0.0363851i
$196$	−94.5498	+	163.765i	−0.482397	+	0.835536i
$197$	−317.547			−1.61191			−0.805956	−	0.591976i	$-0.798348\pi$
$197$	−317.547			−1.61191			−0.805956	+	0.591976i	$0.798348\pi$
$198$	−54.1993	+	31.2920i	−0.273734	+	0.158040i
$199$		−	344.835i		−	1.73284i	−0.499317	−	0.866419i	$-0.666416\pi$
$199$		−	344.835i		−	1.73284i	0.499317	−	0.866419i	$-0.333584\pi$
$200$	143.203			0.716013
$201$	−147.924			−0.735942
$202$	−173.299	−	300.163i	−0.857916	−	1.48595i
$203$			43.8350i			0.215936i
$204$	−1.25083	−	0.722166i	−0.00613151	−	0.00354003i
$205$	−450.296			−2.19656
$206$	−2.04818	+	1.18252i	−0.00994262	+	0.00574037i
$207$			244.130i			1.17937i
$208$	−6.59801	−	11.4281i	−0.0317212	−	0.0549428i
$209$	18.7492			0.0897090
$210$	−11.2990	−	19.5705i	−0.0538048	−	0.0931926i
$211$			325.725i			1.54372i	0.635793	+	0.771860i	$0.280673\pi$
$211$			325.725i			1.54372i	−0.635793	+	0.771860i	$0.719327\pi$
$212$	−51.8488	+	89.8048i	−0.244570	+	0.423608i
$213$	92.5498			0.434506
$214$	160.722	−	92.7928i	0.751036	−	0.433611i
$215$		−	364.536i		−	1.69552i
$216$			171.007i			0.791699i
$217$	−64.0000			−0.294931
$218$	44.8248	+	77.6387i	0.205618	+	0.356141i
$219$		−	76.2779i		−	0.348301i
$220$	97.5947	+	56.3463i	0.443612	+	0.256120i
$221$	0.226738			0.00102597
$222$	−82.3505	+	47.5451i	−0.370948	+	0.214167i
$223$			300.246i			1.34640i	0.739463	+	0.673198i	$0.235080\pi$
$223$			300.246i			1.34640i	−0.739463	+	0.673198i	$0.764920\pi$
$224$	36.3987	+	21.0148i	0.162494	+	0.0938160i
$225$	130.223			0.578771
$226$	−65.6977	−	113.792i	−0.290698	−	0.503503i
$227$		−	177.376i		−	0.781390i	−0.920520	−	0.390695i	$-0.872235\pi$
$227$		−	177.376i		−	0.781390i	0.920520	−	0.390695i	$-0.127765\pi$
$228$	11.4502	−	19.8323i	0.0502200	−	0.0869836i
$229$	38.3987			0.167680			0.0838399	−	0.996479i	$-0.473282\pi$
$229$	38.3987			0.167680			0.0838399	+	0.996479i	$0.473282\pi$
$230$	380.701	−	219.798i	1.65522	−	0.955643i
$231$		−	7.42019i		−	0.0321221i
$232$	−266.997			−1.15085
$233$	374.399			1.60686			0.803431	−	0.595398i	$-0.203006\pi$
$233$	374.399			1.60686			0.803431	+	0.595398i	$0.203006\pi$
$234$	−6.00000	−	10.3923i	−0.0256410	−	0.0444116i
$235$		−	158.071i		−	0.672644i
$236$	−160.151	−	92.4633i	−0.678607	−	0.391794i
$237$	149.045			0.628881
$238$	−0.625414	+	0.361083i	−0.00262779	+	0.00151716i
$239$			17.3363i			0.0725369i	0.999342	+	0.0362685i	$0.0115471\pi$
$239$			17.3363i			0.0725369i	−0.999342	+	0.0362685i	$0.988453\pi$
$240$	119.203	−	68.8217i	0.496678	−	0.286757i
$241$	346.646			1.43837			0.719183	−	0.694821i	$-0.244516\pi$
$241$	346.646			1.43837			0.719183	+	0.694821i	$0.244516\pi$
$242$	−102.498	−	177.532i	−0.423547	−	0.733605i
$243$			241.503i			0.993840i
$244$	94.1993	−	163.158i	0.386063	−	0.668680i
$245$	309.643			1.26385
$246$	−156.399	+	90.2968i	−0.635767	+	0.367060i
$247$			3.59501i			0.0145547i
$248$		−	389.821i		−	1.57186i
$249$	−195.148			−0.783726
$250$	46.5017	+	80.5432i	0.186007	+	0.322173i
$251$			231.258i			0.921345i	0.887570	+	0.460672i	$0.152392\pi$
$251$			231.258i			0.921345i	−0.887570	+	0.460672i	$0.847608\pi$
$252$	33.0997	+	19.1101i	0.131348	+	0.0758337i
$253$	144.344			0.570529
$254$	−162.653	+	93.9076i	−0.640365	+	0.369715i
$255$			2.36503i			0.00927464i
$256$	−128.000	+	221.703i	−0.500000	+	0.866025i
$257$	169.849			0.660890			0.330445	−	0.943825i	$-0.392801\pi$
$257$	169.849			0.660890			0.330445	+	0.943825i	$0.392801\pi$
$258$	−73.0997	−	126.612i	−0.283332	−	0.490746i
$259$			47.5451i			0.183572i
$260$	−10.8040	+	18.7130i	−0.0415537	+	0.0719732i
$261$	−242.797			−0.930258
$262$	−17.0033	+	9.81687i	−0.0648981	+	0.0374690i
$263$		−	90.0666i		−	0.342459i	−0.985231	−	0.171229i	$-0.945226\pi$
$263$		−	90.0666i		−	0.342459i	0.985231	−	0.171229i	$-0.0547739\pi$
$264$	45.1960			0.171197
$265$	169.801			0.640757
$266$	−5.72508	−	9.91613i	−0.0215229	−	0.0372787i
$267$			75.9801i			0.284570i
$268$	−390.145	−	225.250i	−1.45576	−	0.840485i
$269$	435.993			1.62079			0.810397	−	0.585882i	$-0.199252\pi$
$269$	435.993			1.62079			0.810397	+	0.585882i	$0.199252\pi$
$270$	242.502	−	140.008i	0.898154	−	0.518550i
$271$		−	353.438i		−	1.30420i	−0.758134	−	0.652099i	$-0.773889\pi$
$271$		−	353.438i		−	1.30420i	0.758134	−	0.652099i	$-0.226111\pi$
$272$	−2.19934	−	3.80936i	−0.00808580	−	0.0140050i
$273$	1.42276			0.00521159
$274$	−63.9726	−	110.804i	−0.233477	−	0.404393i
$275$		−	76.9957i		−	0.279984i
$276$	88.1512	−	152.682i	0.319388	−	0.553197i
$277$	−227.045			−0.819657			−0.409828	−	0.912163i	$-0.634411\pi$
$277$	−227.045			−0.819657			−0.409828	+	0.912163i	$0.634411\pi$
$278$	−32.7010	+	18.8799i	−0.117629	+	0.0679134i
$279$		−	354.489i		−	1.27057i
$280$		−	68.8217i		−	0.245792i
$281$	114.646			0.407994			0.203997	−	0.978972i	$-0.434607\pi$
$281$	114.646			0.407994			0.203997	+	0.978972i	$0.434607\pi$
$282$	−31.6977	−	54.9020i	−0.112403	−	0.194688i
$283$		−	101.296i		−	0.357937i	−0.983855	−	0.178969i	$-0.942724\pi$
$283$		−	101.296i		−	0.357937i	0.983855	−	0.178969i	$-0.0572760\pi$
$284$	244.096	+	140.929i	0.859494	+	0.496229i
$285$	−37.4983			−0.131573
$286$	−6.14454	+	3.54755i	−0.0214844	+	0.0124040i
$287$			90.2968i			0.314623i
$288$	−116.399	+	201.608i	−0.404162	+	0.700029i
$289$	−288.924			−0.999738
$290$	218.598	+	378.623i	0.753786	+	1.30560i
$291$		−	154.587i		−	0.531227i
$292$	116.151	−	201.180i	0.397778	−	0.688972i
$293$	272.069			0.928563			0.464281	−	0.885688i	$-0.346313\pi$
$293$	272.069			0.928563			0.464281	+	0.885688i	$0.346313\pi$
$294$	107.547	−	62.0920i	0.365805	−	0.211197i
$295$			302.810i			1.02647i
$296$	−289.595			−0.978360
$297$	91.9452			0.309580
$298$	78.9485	+	136.743i	0.264928	+	0.458869i
$299$			27.6768i			0.0925646i
$300$	−81.4435	−	47.0215i	−0.271478	−	0.156738i
$301$	−73.0997			−0.242856
$302$	−333.842	+	192.744i	−1.10544	+	0.638225i
$303$			227.615i			0.751205i
$304$	60.3987	−	34.8712i	0.198680	−	0.114708i
$305$	−308.495			−1.01146
$306$	−2.00000	−	3.46410i	−0.00653595	−	0.0113206i
$307$			131.176i			0.427282i	0.976912	+	0.213641i	$0.0685322\pi$
$307$			131.176i			0.427282i	−0.976912	+	0.213641i	$0.931468\pi$
$308$	11.2990	−	19.5705i	0.0366851	−	0.0635404i
$309$	1.55315			0.00502636
$310$	−552.797	+	319.158i	−1.78322	+	1.02954i
$311$			486.423i			1.56406i	0.623240	+	0.782030i	$0.285816\pi$
$311$			486.423i			1.56406i	−0.623240	+	0.782030i	$0.714184\pi$
$312$			8.66599i			0.0277756i
$313$	308.027			0.984113			0.492057	−	0.870563i	$-0.336245\pi$
$313$	308.027			0.984113			0.492057	+	0.870563i	$0.336245\pi$
$314$	−7.00331	−	12.1301i	−0.0223035	−	0.0386309i
$315$		−	62.5840i		−	0.198679i
$316$	393.100	+	226.956i	1.24399	+	0.718216i
$317$	−219.918			−0.693747			−0.346873	−	0.937912i	$-0.612757\pi$
$317$	−219.918			−0.693747			−0.346873	+	0.937912i	$0.612757\pi$
$318$	58.9759	−	34.0498i	0.185459	−	0.107075i
$319$			143.556i			0.450019i
$320$	419.189			1.30997
$321$	−121.876			−0.379677
$322$	−44.0756	−	76.3411i	−0.136881	−	0.237084i
$323$			1.19834i			0.00371002i
$324$	−74.7974	+	129.553i	−0.230856	+	0.399854i
$325$	14.7633			0.0454256
$326$	21.8970	−	12.6423i	0.0671688	−	0.0387799i
$327$		−	58.8739i		−	0.180043i
$328$	−549.993			−1.67681
$329$	−31.6977			−0.0963455
$330$	−37.0033	−	64.0916i	−0.112131	−	0.194217i
$331$			107.110i			0.323594i	0.986824	+	0.161797i	$0.0517289\pi$
$331$			107.110i			0.323594i	−0.986824	+	0.161797i	$0.948271\pi$
$332$	−514.694	−	297.159i	−1.55028	−	0.895057i
$333$	−263.347			−0.790832
$334$	194.502	−	112.296i	0.582340	−	0.336214i
$335$			737.675i			2.20202i
$336$	−13.8007	−	23.9034i	−0.0410734	−	0.0711412i
$337$	425.849			1.26365			0.631823	−	0.775113i	$-0.282307\pi$
$337$	425.849			1.26365			0.631823	+	0.775113i	$0.282307\pi$
$338$	168.320	+	291.538i	0.497988	+	0.862540i
$339$			86.2889i			0.254540i
$340$	−3.60132	+	6.23768i	−0.0105921	+	0.0183461i
$341$	−209.595			−0.614647
$342$	54.9244	−	31.7106i	0.160598	−	0.0927211i
$343$		−	126.450i		−	0.368658i
$344$		−	445.246i		−	1.29432i
$345$	−288.688			−0.836776
$346$	−39.8970	−	69.1037i	−0.115309	−	0.199722i
$347$		−	633.427i		−	1.82544i	−0.408587	−	0.912719i	$-0.633978\pi$
$347$		−	633.427i		−	1.82544i	0.408587	−	0.912719i	$-0.366022\pi$
$348$	151.849	+	87.6700i	0.436347	+	0.251925i
$349$	−223.292			−0.639806			−0.319903	−	0.947450i	$-0.603650\pi$
$349$	−223.292			−0.639806			−0.319903	+	0.947450i	$0.603650\pi$
$350$	−40.7218	+	23.5107i	−0.116348	+	0.0671735i
$351$			17.6298i			0.0502273i
$352$	119.203	+	68.8217i	0.338644	+	0.195516i
$353$	122.323			0.346524			0.173262	−	0.984876i	$-0.444569\pi$
$353$	122.323			0.346524			0.173262	+	0.984876i	$0.444569\pi$
$354$	60.7218	+	105.173i	0.171530	+	0.297099i
$355$		−	461.531i		−	1.30009i
$356$	−115.698	+	200.394i	−0.324993	+	0.562905i
$357$	0.474255			0.00132845
$358$	−244.495	+	141.159i	−0.682947	+	0.394300i
$359$		−	535.214i		−	1.49085i	−0.666592	−	0.745423i	$-0.732247\pi$
$359$		−	535.214i		−	1.49085i	0.666592	−	0.745423i	$-0.267753\pi$
$360$	381.196			1.05888
$361$	−19.0000			−0.0526316
$362$	−142.000	−	245.951i	−0.392265	−	0.679423i
$363$			134.624i			0.370864i
$364$	3.75248	+	2.16650i	0.0103090	+	0.00595192i
$365$	−380.385			−1.04215
$366$	−107.148	+	61.8618i	−0.292754	+	0.169021i
$367$		−	100.177i		−	0.272962i	−0.990643	−	0.136481i	$-0.956421\pi$
$367$		−	100.177i		−	0.272962i	0.990643	−	0.136481i	$-0.0435792\pi$
$368$	464.990	−	268.462i	1.26356	−	0.729517i
$369$	−500.145			−1.35541
$370$	237.100	+	410.669i	0.640810	+	1.10992i
$371$		−	34.0498i		−	0.0917783i
$372$	−128.000	+	221.703i	−0.344086	+	0.595974i
$373$	191.767			0.514120			0.257060	−	0.966395i	$-0.417246\pi$
$373$	191.767			0.514120			0.257060	+	0.966395i	$0.417246\pi$
$374$	−2.04818	+	1.18252i	−0.00547641	+	0.00316181i
$375$		−	61.0764i		−	0.162870i
$376$		−	193.069i		−	0.513481i
$377$	−27.5257			−0.0730126
$378$	−28.0756	−	48.6283i	−0.0742740	−	0.128646i
$379$			108.292i			0.285731i	0.989742	+	0.142865i	$0.0456316\pi$
$379$			108.292i			0.285731i	−0.989742	+	0.142865i	$0.954368\pi$
$380$	−98.9003	−	57.1001i	−0.260264	−	0.150264i
$381$	123.341			0.323729
$382$	546.316	−	315.416i	1.43015	−	0.825696i
$383$			173.571i			0.453187i	0.973989	+	0.226593i	$0.0727588\pi$
$383$			173.571i			0.453187i	−0.973989	+	0.226593i	$0.927241\pi$
$384$	145.595	−	84.0591i	0.379153	−	0.218904i
$385$	−37.0033			−0.0961125
$386$	−44.1993	−	76.5555i	−0.114506	−	0.198330i
$387$		−	404.891i		−	1.04623i
$388$	235.395	−	407.717i	0.606689	−	1.05082i
$389$	−541.890			−1.39303			−0.696517	−	0.717540i	$-0.745268\pi$
$389$	−541.890			−1.39303			−0.696517	+	0.717540i	$0.745268\pi$
$390$	12.2891	−	7.09510i	0.0315104	−	0.0181926i
$391$			9.22561i			0.0235949i
$392$	378.199			0.964794
$393$	12.8937			0.0328084
$394$	317.547	+	550.007i	0.805956	+	1.39596i
$395$		−	743.263i		−	1.88168i
$396$	108.399	+	62.5840i	0.273734	+	0.158040i
$397$	443.444			1.11699			0.558493	−	0.829509i	$-0.311380\pi$
$397$	443.444			1.11699			0.558493	+	0.829509i	$0.311380\pi$
$398$	−597.272	+	344.835i	−1.50068	+	0.866419i
$399$			7.51946i			0.0188458i
$400$	−143.203	−	248.034i	−0.358007	−	0.620086i
$401$	−287.141			−0.716063			−0.358031	−	0.933710i	$-0.616552\pi$
$401$	−287.141			−0.716063			−0.358031	+	0.933710i	$0.616552\pi$
$402$	147.924	+	256.213i	0.367971	+	0.637345i
$403$		−	40.1882i		−	0.0997225i
$404$	−346.598	+	600.325i	−0.857916	+	1.48595i
$405$	244.955			0.604827
$406$	75.9244	−	43.8350i	0.187006	−	0.107968i
$407$			155.706i			0.382571i
$408$			2.88866i			0.00708006i
$409$	−258.248			−0.631412			−0.315706	−	0.948857i	$-0.602241\pi$
$409$	−258.248			−0.631412			−0.315706	+	0.948857i	$0.602241\pi$
$410$	450.296	+	779.935i	1.09828	+	1.90228i
$411$			84.0232i			0.204436i
$412$	4.09636	+	2.36503i	0.00994262	+	0.00574037i
$413$	60.7218			0.147026
$414$	422.846	−	244.130i	1.02137	−	0.589686i
$415$			973.171i			2.34499i
$416$	−13.1960	+	22.8562i	−0.0317212	+	0.0549428i
$417$	24.7974			0.0594661
$418$	−18.7492	−	32.4745i	−0.0448545	−	0.0776902i
$419$		−	421.176i		−	1.00519i	−0.864521	−	0.502597i	$-0.832378\pi$
$419$		−	421.176i		−	1.00519i	0.864521	−	0.502597i	$-0.167622\pi$
$420$	−22.5980	+	39.1409i	−0.0538048	+	0.0931926i
$421$	513.815			1.22046			0.610231	−	0.792223i	$-0.291076\pi$
$421$	513.815			1.22046			0.610231	+	0.792223i	$0.291076\pi$
$422$	564.172	−	325.725i	1.33690	−	0.771860i
$423$		−	175.570i		−	0.415059i
$424$	207.395			0.489140
$425$	4.92111			0.0115791
$426$	−92.5498	−	160.301i	−0.217253	−	0.376293i
$427$			61.8618i			0.144876i
$428$	−321.444	−	185.586i	−0.751036	−	0.433611i
$429$	4.65944			0.0108612
$430$	−631.395	+	364.536i	−1.46836	+	0.847759i
$431$			170.808i			0.396307i	0.980171	+	0.198154i	$0.0634945\pi$
$431$			170.808i			0.396307i	−0.980171	+	0.198154i	$0.936506\pi$
$432$	296.193	−	171.007i	0.685631	−	0.395849i
$433$	277.299			0.640413			0.320207	−	0.947348i	$-0.396248\pi$
$433$	277.299			0.640413			0.320207	+	0.947348i	$0.396248\pi$
$434$	64.0000	+	110.851i	0.147465	+	0.255418i
$435$		−	287.112i		−	0.660027i
$436$	89.6495	−	155.277i	0.205618	−	0.356141i
$437$	−146.275			−0.334725
$438$	−132.117	+	76.2779i	−0.301637	+	0.174150i
$439$			233.654i			0.532242i	0.963940	+	0.266121i	$0.0857421\pi$
$439$			233.654i			0.532242i	−0.963940	+	0.266121i	$0.914258\pi$
$440$		−	225.385i		−	0.512239i
$441$	343.921			0.779866
$442$	−0.226738	−	0.392722i	−0.000512983	−	0.000888512i
$443$		−	571.430i		−	1.28991i	−0.764221	−	0.644955i	$-0.776876\pi$
$443$		−	571.430i		−	1.28991i	0.764221	−	0.644955i	$-0.223124\pi$
$444$	164.701	+	95.0902i	0.370948	+	0.214167i
$445$	378.900			0.851461
$446$	520.042	−	300.246i	1.16601	−	0.673198i
$447$		−	103.693i		−	0.231975i
$448$		−	84.0591i		−	0.187632i
$449$	−230.990			−0.514454			−0.257227	−	0.966351i	$-0.582809\pi$
$449$	−230.990			−0.514454			−0.257227	+	0.966351i	$0.582809\pi$
$450$	−130.223	−	225.554i	−0.289385	−	0.501230i
$451$			295.715i			0.655686i
$452$	−131.395	+	227.583i	−0.290698	+	0.503503i
$453$	253.154			0.558840
$454$	−307.223	+	177.376i	−0.676704	+	0.390695i
$455$		−	7.09510i		−	0.0155936i
$456$	−45.8007			−0.100440
$457$	−412.275			−0.902133			−0.451067	−	0.892490i	$-0.648956\pi$
$457$	−412.275			−0.902133			−0.451067	+	0.892490i	$0.648956\pi$
$458$	−38.3987	−	66.5085i	−0.0838399	−	0.145215i
$459$			5.87659i			0.0128030i
$460$	−761.402	−	439.596i	−1.65522	−	0.955643i
$461$	−89.2575			−0.193617			−0.0968085	−	0.995303i	$-0.530863\pi$
$461$	−89.2575			−0.193617			−0.0968085	+	0.995303i	$0.530863\pi$
$462$	−12.8522	+	7.42019i	−0.0278185	+	0.0160610i
$463$		−	70.9565i		−	0.153254i	−0.997060	−	0.0766269i	$-0.975585\pi$
$463$		−	70.9565i		−	0.153254i	0.997060	−	0.0766269i	$-0.0244150\pi$
$464$	266.997	+	462.452i	0.575424	+	0.996663i
$465$	419.189			0.901483
$466$	−374.399	−	648.478i	−0.803431	−	1.39158i
$467$			592.508i			1.26875i	0.773024	+	0.634377i	$0.218743\pi$
$467$			592.508i			1.26875i	−0.773024	+	0.634377i	$0.781257\pi$
$468$	−12.0000	+	20.7846i	−0.0256410	+	0.0444116i
$469$	147.924			0.315404
$470$	−273.787	+	158.071i	−0.582526	+	0.336322i
$471$			9.19832i			0.0195293i
$472$			369.853i			0.783587i
$473$	−239.395			−0.506121
$474$	−149.045	−	258.153i	−0.314441	−	0.544627i
$475$			78.0257i			0.164265i
$476$	1.25083	+	0.722166i	0.00262779	+	0.00151716i
$477$	188.598			0.395384
$478$	30.0274	−	17.3363i	0.0628188	−	0.0362685i
$479$			697.257i			1.45565i	0.685762	+	0.727826i	$0.259469\pi$
$479$			697.257i			1.45565i	−0.685762	+	0.727826i	$0.740531\pi$
$480$	−238.405	−	137.643i	−0.496678	−	0.286757i
$481$	−29.8555			−0.0620696
$482$	−346.646	−	600.409i	−0.719183	−	1.24566i
$483$			57.8899i			0.119855i
$484$	−204.997	+	355.065i	−0.423547	+	0.733605i
$485$	−770.900			−1.58949
$486$	418.296	−	241.503i	0.860691	−	0.496920i
$487$		−	241.869i		−	0.496650i	−0.968677	−	0.248325i	$-0.920120\pi$
$487$		−	241.869i		−	0.496650i	0.968677	−	0.248325i	$-0.0798801\pi$
$488$	−376.797			−0.772126
$489$	−16.6046			−0.0339563
$490$	−309.643	−	536.317i	−0.631924	−	1.09452i
$491$		−	195.601i		−	0.398373i	−0.979962	−	0.199186i	$-0.936170\pi$
$491$		−	195.601i		−	0.398373i	0.979962	−	0.199186i	$-0.0638299\pi$
$492$	312.797	+	180.594i	0.635767	+	0.367060i
$493$	−9.17525			−0.0186111
$494$	6.22674	−	3.59501i	0.0126047	−	0.00727735i
$495$		−	204.957i		−	0.414055i
$496$	−675.189	+	389.821i	−1.36127	+	0.785929i
$497$	−92.5498			−0.186217
$498$	195.148	+	338.006i	0.391863	+	0.678727i
$499$			237.233i			0.475418i	0.971336	+	0.237709i	$0.0763964\pi$
$499$			237.233i			0.475418i	−0.971336	+	0.237709i	$0.923604\pi$
$500$	93.0033	−	161.086i	0.186007	−	0.322173i
$501$	−147.492			−0.294395
$502$	400.550	−	231.258i	0.797908	−	0.460672i
$503$			162.472i			0.323006i	0.986872	+	0.161503i	$0.0516341\pi$
$503$			162.472i			0.323006i	−0.986872	+	0.161503i	$0.948366\pi$
$504$		−	76.4404i		−	0.151667i
$505$	1135.08			2.24768
$506$	−144.344	−	250.011i	−0.285265	−	0.494093i
$507$		−	221.075i		−	0.436046i
$508$	325.306	+	187.815i	0.640365	+	0.369715i
$509$	55.7043			0.109439			0.0547194	−	0.998502i	$-0.482574\pi$
$509$	55.7043			0.109439			0.0547194	+	0.998502i	$0.482574\pi$
$510$	4.09636	−	2.36503i	0.00803207	−	0.00463732i
$511$			76.2779i			0.149272i
$512$	512.000			1.00000
$513$	−93.1752			−0.181628
$514$	−169.849	−	294.187i	−0.330445	−	0.572348i
$515$		−	7.74529i		−	0.0150394i
$516$	−146.199	+	253.225i	−0.283332	+	0.490746i
$517$	−103.807			−0.200788
$518$	82.3505	−	47.5451i	0.158978	−	0.0917859i
$519$			52.4017i			0.100967i
$520$	43.2159			0.0831075
$521$	−15.4435			−0.0296421			−0.0148211	−	0.999890i	$-0.504718\pi$
$521$	−15.4435			−0.0296421			−0.0148211	+	0.999890i	$0.504718\pi$
$522$	242.797	+	420.537i	0.465129	+	0.805627i
$523$		−	388.246i		−	0.742343i	−0.928564	−	0.371172i	$-0.878956\pi$
$523$		−	388.246i		−	0.742343i	0.928564	−	0.371172i	$-0.121044\pi$
$524$	34.0066	+	19.6337i	0.0648981	+	0.0374690i
$525$	30.8796			0.0588182
$526$	−156.000	+	90.0666i	−0.296578	+	0.171229i
$527$		−	13.3961i		−	0.0254195i
$528$	−45.1960	−	78.2818i	−0.0855985	−	0.148261i
$529$	−597.124			−1.12878
$530$	−169.801	−	294.103i	−0.320379	−	0.554912i
$531$			336.331i			0.633393i
$532$	−11.4502	+	19.8323i	−0.0215229	+	0.0372787i
$533$	−56.7010			−0.106381
$534$	131.601	−	75.9801i	0.246444	−	0.142285i
$535$			607.777i			1.13603i
$536$			901.000i			1.68097i
$537$	185.402			0.345255
$538$	−435.993	−	755.163i	−0.810397	−	1.40365i
$539$		−	203.346i		−	0.377266i
$540$	−485.003	−	280.017i	−0.898154	−	0.518550i
$541$	630.894			1.16616			0.583081	−	0.812414i	$-0.301847\pi$
$541$	630.894			1.16616			0.583081	+	0.812414i	$0.301847\pi$
$542$	−612.172	+	353.438i	−1.12947	+	0.652099i
$543$			186.506i			0.343474i
$544$	−4.39868	+	7.61873i	−0.00808580	+	0.0140050i
$545$	−293.595			−0.538706
$546$	−1.42276	−	2.46430i	−0.00260580	−	0.00451337i
$547$			746.969i			1.36557i	0.730618	+	0.682787i	$0.239232\pi$
$547$			746.969i			1.36557i	−0.730618	+	0.682787i	$0.760768\pi$
$548$	−127.945	+	221.608i	−0.233477	+	0.404393i
$549$	−342.646			−0.624128
$550$	−133.360	+	76.9957i	−0.242474	+	0.139992i
$551$		−	145.476i		−	0.264023i
$552$	−352.605			−0.638777
$553$	−149.045			−0.269521
$554$	227.045	+	393.253i	0.409828	+	0.709843i
$555$		−	311.412i		−	0.561103i
$556$	65.4020	+	37.7599i	0.117629	+	0.0679134i
$557$	320.145			0.574766			0.287383	−	0.957816i	$-0.407215\pi$
$557$	320.145			0.574766			0.287383	+	0.957816i	$0.407215\pi$
$558$	−613.993	+	354.489i	−1.10035	+	0.635285i
$559$		−	45.9022i		−	0.0821149i
$560$	−119.203	+	68.8217i	−0.212862	+	0.122896i
$561$	1.55315			0.00276853
$562$	−114.646	−	198.573i	−0.203997	−	0.353333i
$563$			532.885i			0.946509i	0.880926	+	0.473255i	$0.156921\pi$
$563$			532.885i			0.946509i	−0.880926	+	0.473255i	$0.843079\pi$
$564$	−63.3954	+	109.804i	−0.112403	+	0.194688i
$565$	430.309			0.761609
$566$	−175.450	+	101.296i	−0.309983	+	0.178969i
$567$		−	49.1203i		−	0.0866320i
$568$		−	563.716i		−	0.992458i
$569$	−212.749			−0.373900			−0.186950	−	0.982369i	$-0.559860\pi$
$569$	−212.749			−0.373900			−0.186950	+	0.982369i	$0.559860\pi$
$570$	37.4983	+	64.9490i	0.0657866	+	0.113946i
$571$		−	544.439i		−	0.953484i	−0.879043	−	0.476742i	$-0.841818\pi$
$571$		−	544.439i		−	0.953484i	0.879043	−	0.476742i	$-0.158182\pi$
$572$	12.2891	+	7.09510i	0.0214844	+	0.0124040i
$573$	−414.275			−0.722993
$574$	156.399	−	90.2968i	0.272472	−	0.157312i
$575$			600.695i			1.04469i
$576$	465.595			0.808324
$577$	1094.65			1.89715			0.948573	−	0.316557i	$-0.102527\pi$
$577$	1094.65			1.89715			0.948573	+	0.316557i	$0.102527\pi$
$578$	288.924	+	500.432i	0.499869	+	0.865799i
$579$			58.0525i			0.100263i
$580$	437.196	−	757.246i	0.753786	−	1.30560i
$581$	195.148			0.335883
$582$	−267.752	+	154.587i	−0.460056	+	0.265613i
$583$		−	111.510i		−	0.191270i
$584$	−464.605			−0.795556
$585$	39.2990			0.0671778
$586$	−272.069	−	471.237i	−0.464281	−	0.804159i
$587$			334.292i			0.569492i	0.958603	+	0.284746i	$0.0919092\pi$
$587$			334.292i			0.569492i	−0.958603	+	0.284746i	$0.908091\pi$
$588$	−215.093	−	124.184i	−0.365805	−	0.211197i
$589$	212.399			0.360609
$590$	524.482	−	302.810i	0.888952	−	0.513237i
$591$		−	417.073i		−	0.705708i
$592$	289.595	+	501.593i	0.489180	+	0.847285i
$593$	834.385			1.40706			0.703529	−	0.710667i	$-0.251607\pi$
$593$	834.385			1.40706			0.703529	+	0.710667i	$0.251607\pi$
$594$	−91.9452	−	159.254i	−0.154790	−	0.268104i
$595$		−	2.36503i		−	0.00397485i
$596$	157.897	−	273.486i	0.264928	−	0.458869i
$597$	452.914			0.758651
$598$	47.9377	−	27.6768i	0.0801633	−	0.0462823i
$599$		−	619.602i		−	1.03439i	−0.855866	−	0.517197i	$-0.826975\pi$
$599$		−	619.602i		−	1.03439i	0.855866	−	0.517197i	$-0.173025\pi$
$600$			188.086i			0.313476i
$601$	245.450			0.408403			0.204201	−	0.978929i	$-0.434540\pi$
$601$	245.450			0.408403			0.204201	+	0.978929i	$0.434540\pi$
$602$	73.0997	+	126.612i	0.121428	+	0.210320i
$603$			819.338i			1.35877i
$604$	667.684	+	385.488i	1.10544	+	0.638225i
$605$	671.347			1.10966
$606$	394.241	−	227.615i	0.650563	−	0.375602i
$607$		−	827.250i		−	1.36285i	−0.731888	−	0.681425i	$-0.761361\pi$
$607$		−	827.250i		−	1.36285i	0.731888	−	0.681425i	$-0.238639\pi$
$608$	−120.797	−	69.7424i	−0.198680	−	0.114708i
$609$	−57.5739			−0.0945385
$610$	308.495	+	534.329i	0.505730	+	0.875949i
$611$		−	19.9042i		−	0.0325765i
$612$	−4.00000	+	6.92820i	−0.00653595	+	0.0113206i
$613$	−909.093			−1.48302			−0.741511	−	0.670940i	$-0.765891\pi$
$613$	−909.093			−1.48302			−0.741511	+	0.670940i	$0.765891\pi$
$614$	227.203	−	131.176i	0.370037	−	0.213641i
$615$		−	591.429i		−	0.961674i
$616$	−45.1960			−0.0733702
$617$	−809.382			−1.31180			−0.655901	−	0.754847i	$-0.727711\pi$
$617$	−809.382			−1.31180			−0.655901	+	0.754847i	$0.727711\pi$
$618$	−1.55315	−	2.69013i	−0.00251318	−	0.00435296i
$619$		−	484.085i		−	0.782044i	−0.920381	−	0.391022i	$-0.872122\pi$
$619$		−	484.085i		−	0.782044i	0.920381	−	0.391022i	$-0.127878\pi$
$620$	1105.59	+	638.315i	1.78322	+	1.02954i
$621$	−717.326			−1.15511
$622$	842.509	−	486.423i	1.35452	−	0.782030i
$623$		−	75.9801i		−	0.121958i
$624$	15.0099	−	8.66599i	0.0240544	−	0.0138878i
$625$	−752.086			−1.20334
$626$	−308.027	−	533.519i	−0.492057	−	0.852267i
$627$			24.6256i			0.0392753i
$628$	−14.0066	+	24.2602i	−0.0223035	+	0.0386309i
$629$	−9.95182			−0.0158217
$630$	−108.399	+	62.5840i	−0.172061	+	0.0993397i
$631$		−	427.350i		−	0.677259i	−0.940920	−	0.338630i	$-0.890037\pi$
$631$		−	427.350i		−	0.677259i	0.940920	−	0.338630i	$-0.109963\pi$
$632$		−	907.825i		−	1.43643i
$633$	−427.815			−0.675853
$634$	219.918	+	380.909i	0.346873	+	0.600803i
$635$		−	615.080i		−	0.968629i
$636$	−117.952	−	68.0995i	−0.185459	−	0.107075i
$637$	38.9901			0.0612089
$638$	248.646	−	143.556i	0.389728	−	0.225009i
$639$		−	512.624i		−	0.802228i
$640$	−419.189	−	726.057i	−0.654983	−	1.13446i
$641$	−120.804			−0.188462			−0.0942309	−	0.995550i	$-0.530039\pi$
$641$	−120.804			−0.188462			−0.0942309	+	0.995550i	$0.530039\pi$
$642$	121.876	+	211.096i	0.189838	+	0.328810i
$643$		−	220.163i		−	0.342400i	−0.985236	−	0.171200i	$-0.945236\pi$
$643$		−	220.163i		−	0.342400i	0.985236	−	0.171200i	$-0.0547644\pi$
$644$	−88.1512	+	152.682i	−0.136881	+	0.237084i
$645$	478.791			0.742311
$646$	2.07558	−	1.19834i	0.00321297	−	0.00185501i
$647$			143.362i			0.221579i	0.993844	+	0.110790i	$0.0353380\pi$
$647$			143.362i			0.221579i	−0.993844	+	0.110790i	$0.964662\pi$
$648$	299.189			0.461712
$649$	198.859			0.306408
$650$	−14.7633	−	25.5708i	−0.0227128	−	0.0393397i
$651$		−	84.0591i		−	0.129123i
$652$	−43.7940	−	25.2845i	−0.0671688	−	0.0387799i
$653$	−494.042			−0.756572			−0.378286	−	0.925689i	$-0.623486\pi$
$653$	−494.042			−0.756572			−0.378286	+	0.925689i	$0.623486\pi$
$654$	−101.973	+	58.8739i	−0.155921	+	0.0900213i
$655$		−	64.2988i		−	0.0981662i
$656$	549.993	+	952.616i	0.838405	+	1.45216i
$657$	−422.495			−0.643067
$658$	31.6977	+	54.9020i	0.0481728	+	0.0834377i
$659$			1213.13i			1.84087i	0.390901	+	0.920433i	$0.372164\pi$
$659$			1213.13i			1.84087i	−0.390901	+	0.920433i	$0.627836\pi$
$660$	−74.0066	+	128.183i	−0.112131	+	0.194217i
$661$	−761.718			−1.15237			−0.576186	−	0.817318i	$-0.695460\pi$
$661$	−761.718			−1.15237			−0.576186	+	0.817318i	$0.695460\pi$
$662$	185.519	−	107.110i	0.280240	−	0.161797i
$663$			0.297804i			0.000449176i
$664$			1188.64i			1.79011i
$665$	37.4983			0.0563885
$666$	263.347	+	456.131i	0.395416	+	0.684881i
$667$		−	1119.98i		−	1.67913i
$668$	−389.003	−	224.591i	−0.582340	−	0.336214i
$669$	−394.350			−0.589463
$670$	1277.69	−	737.675i	1.90700	−	1.10101i
$671$			202.592i			0.301926i
$672$	−27.6013	+	47.8069i	−0.0410734	+	0.0711412i
$673$	−825.836			−1.22710			−0.613548	−	0.789657i	$-0.710258\pi$
$673$	−825.836			−1.22710			−0.613548	+	0.789657i	$0.710258\pi$
$674$	−425.849	−	737.592i	−0.631823	−	1.09435i
$675$			382.635i			0.566867i
$676$	336.640	−	583.077i	0.497988	−	0.862540i
$677$	303.767			0.448695			0.224348	−	0.974509i	$-0.427975\pi$
$677$	303.767			0.448695			0.224348	+	0.974509i	$0.427975\pi$
$678$	149.457	−	86.2889i	0.220438	−	0.127270i
$679$			154.587i			0.227669i
$680$	14.4053			0.0211843
$681$	232.969			0.342099
$682$	209.595	+	363.029i	0.307324	+	0.532300i
$683$			314.197i			0.460026i	0.973188	+	0.230013i	$0.0738768\pi$
$683$			314.197i			0.460026i	−0.973188	+	0.230013i	$0.926123\pi$
$684$	−109.849	−	63.4213i	−0.160598	−	0.0927211i
$685$	419.010			0.611693
$686$	−219.017	+	126.450i	−0.319267	+	0.184329i
$687$			50.4337i			0.0734116i
$688$	−771.189	+	445.246i	−1.12091	+	0.647160i
$689$	21.3812			0.0310322
$690$	288.688	+	500.022i	0.418388	+	0.724669i
$691$			731.469i			1.05857i	0.848445	+	0.529283i	$0.177539\pi$
$691$			731.469i			1.05857i	−0.848445	+	0.529283i	$0.822461\pi$
$692$	−79.7940	+	138.207i	−0.115309	+	0.199722i
$693$	−41.0997			−0.0593069
$694$	−1097.13	+	633.427i	−1.58088	+	0.912719i
$695$		−	123.660i		−	0.177929i
$696$		−	350.680i		−	0.503850i
$697$	−18.9003			−0.0271167
$698$	223.292	+	386.754i	0.319903	+	0.554088i
$699$			491.744i			0.703497i
$700$	81.4435	+	47.0215i	0.116348	+	0.0671735i
$701$	103.952			0.148291			0.0741454	−	0.997247i	$-0.476377\pi$
$701$	103.952			0.148291			0.0741454	+	0.997247i	$0.476377\pi$
$702$	30.5357	−	17.6298i	0.0434981	−	0.0251137i
$703$		−	157.789i		−	0.224451i
$704$		−	275.287i		−	0.391032i
$705$	207.615			0.294489
$706$	−122.323	−	211.870i	−0.173262	−	0.300099i
$707$		−	227.615i		−	0.321945i
$708$	121.444	−	210.346i	0.171530	−	0.297099i
$709$	−899.086			−1.26810			−0.634052	−	0.773290i	$-0.718610\pi$
$709$	−899.086			−1.26810			−0.634052	+	0.773290i	$0.718610\pi$
$710$	−799.395	+	461.531i	−1.12591	+	0.650044i
$711$		−	825.544i		−	1.16110i
$712$	462.791			0.649987
$713$	1635.19			2.29339
$714$	−0.474255	−	0.821434i	−0.000664223	−	0.00115047i
$715$		−	23.2359i		−	0.0324977i
$716$	488.990	+	282.319i	0.682947	+	0.394300i
$717$	−22.7700			−0.0317573
$718$	−927.017	+	535.214i	−1.29111	+	0.745423i
$719$		−	601.472i		−	0.836539i	−0.908323	−	0.418270i	$-0.862637\pi$
$719$		−	601.472i		−	0.836539i	0.908323	−	0.418270i	$-0.137363\pi$
$720$	−381.196	−	660.251i	−0.529439	−	0.917015i
$721$	−1.55315			−0.00215415
$722$	19.0000	+	32.9090i	0.0263158	+	0.0455803i
$723$			455.293i			0.629728i
$724$	−284.000	+	491.902i	−0.392265	+	0.679423i
$725$	−597.416			−0.824022
$726$	233.175	−	134.624i	0.321178	−	0.185432i
$727$			863.895i			1.18830i	0.804354	+	0.594151i	$0.202512\pi$
$727$			863.895i			1.18830i	−0.804354	+	0.594151i	$0.797488\pi$
$728$		−	8.66599i		−	0.0119038i
$729$	19.3921			0.0266009
$730$	380.385	+	658.847i	0.521076	+	0.902530i
$731$		−	15.3007i		−	0.0209312i
$732$	214.296	+	123.724i	0.292754	+	0.169021i
$733$	−979.238			−1.33593			−0.667966	−	0.744192i	$-0.732835\pi$
$733$	−979.238			−1.33593			−0.667966	+	0.744192i	$0.732835\pi$
$734$	−173.512	+	100.177i	−0.236392	+	0.136481i
$735$			406.692i			0.553323i
$736$	−929.980	−	536.924i	−1.26356	−	0.729517i
$737$	484.440			0.657314
$738$	500.145	+	866.276i	0.677703	+	1.17382i
$739$			944.578i			1.27818i	0.769130	+	0.639092i	$0.220690\pi$
$739$			944.578i			1.27818i	−0.769130	+	0.639092i	$0.779310\pi$
$740$	474.199	−	821.337i	0.640810	−	1.10992i
$741$	−4.72177			−0.00637216
$742$	−58.9759	+	34.0498i	−0.0794824	+	0.0458892i
$743$		−	443.278i		−	0.596606i	−0.954471	−	0.298303i	$-0.903579\pi$
$743$		−	443.278i		−	0.596606i	0.954471	−	0.298303i	$-0.0964206\pi$
$744$	512.000			0.688172
$745$	−517.100			−0.694094
$746$	−191.767	−	332.150i	−0.257060	−	0.445241i
$747$			1080.90i			1.44699i
$748$	4.09636	+	2.36503i	0.00547641	+	0.00316181i
$749$	121.876			0.162719
$750$	−105.787	+	61.0764i	−0.141050	+	0.0814352i
$751$			42.6165i			0.0567463i	0.999597	+	0.0283732i	$0.00903267\pi$
$751$			42.6165i			0.0567463i	−0.999597	+	0.0283732i	$0.990967\pi$
$752$	−334.405	+	193.069i	−0.444688	+	0.256741i
$753$	−303.739			−0.403372
$754$	27.5257	+	47.6760i	0.0365063	+	0.0632308i
$755$		−	1262.44i		−	1.67211i
$756$	−56.1512	+	97.2567i	−0.0742740	+	0.128646i
$757$	−166.000			−0.219287			−0.109643	−	0.993971i	$-0.534971\pi$
$757$	−166.000			−0.219287			−0.109643	+	0.993971i	$0.534971\pi$
$758$	187.567	−	108.292i	0.247450	−	0.142865i
$759$			189.585i			0.249782i
$760$			228.401i			0.300527i
$761$	−1009.71			−1.32681			−0.663407	−	0.748259i	$-0.730890\pi$
$761$	−1009.71			−1.32681			−0.663407	+	0.748259i	$0.730890\pi$
$762$	−123.341	−	213.632i	−0.161864	−	0.280357i
$763$			58.8739i			0.0771611i
$764$	−1092.63	−	630.832i	−1.43015	−	0.825696i
$765$	13.0997			0.0171238
$766$	300.633	−	173.571i	0.392471	−	0.226593i
$767$			38.1296i			0.0497127i
$768$	−291.189	−	168.118i	−0.379153	−	0.218904i
$769$	157.512			0.204828			0.102414	−	0.994742i	$-0.467343\pi$
$769$	157.512			0.204828			0.102414	+	0.994742i	$0.467343\pi$
$770$	37.0033	+	64.0916i	0.0480562	+	0.0832359i
$771$			223.084i			0.289343i
$772$	−88.3987	+	153.111i	−0.114506	+	0.198330i
$773$	1048.26			1.35610			0.678048	−	0.735018i	$-0.262826\pi$
$773$	1048.26			1.35610			0.678048	+	0.735018i	$0.262826\pi$
$774$	−701.292	+	404.891i	−0.906063	+	0.523115i
$775$		−	872.240i		−	1.12547i
$776$	−941.581			−1.21338
$777$	−62.4469			−0.0803692
$778$	541.890	+	938.582i	0.696517	+	1.20640i
$779$		−	299.671i		−	0.384686i
$780$	−24.5781	−	14.1902i	−0.0315104	−	0.0181926i
$781$	−303.093			−0.388083
$782$	15.9792	−	9.22561i	0.0204338	−	0.0117975i
$783$		−	713.411i		−	0.911125i
$784$	−378.199	−	655.060i	−0.482397	−	0.835536i
$785$	45.8705			0.0584338
$786$	−12.8937	−	22.3326i	−0.0164042	−	0.0284129i
$787$		−	146.774i		−	0.186498i	−0.995643	−	0.0932491i	$-0.970275\pi$
$787$		−	146.774i		−	0.186498i	0.995643	−	0.0932491i	$-0.0297253\pi$
$788$	635.093	−	1100.01i	0.805956	−	1.39596i
$789$	118.296			0.149931
$790$	−1287.37	+	743.263i	−1.62958	+	0.940839i
$791$		−	86.2889i		−	0.109088i
$792$		−	250.336i		−	0.316081i
$793$	−38.8455			−0.0489855
$794$	−443.444	−	768.067i	−0.558493	−	0.967338i
$795$			223.020i			0.280529i
$796$	1194.54	+	689.670i	1.50068	+	0.866419i
$797$	523.217			0.656483			0.328241	−	0.944594i	$-0.393544\pi$
$797$	523.217			0.656483			0.328241	+	0.944594i	$0.393544\pi$
$798$	13.0241	−	7.51946i	0.0163209	−	0.00942288i
$799$		−	6.63475i		−	0.00830382i
$800$	−286.405	+	496.069i	−0.358007	+	0.620086i
$801$	420.846			0.525400
$802$	287.141	+	497.343i	0.358031	+	0.620129i
$803$			249.804i			0.311088i
$804$	295.849	−	512.425i	0.367971	−	0.637345i
$805$	288.688			0.358618
$806$	−69.6079	+	40.1882i	−0.0863622	+	0.0498612i
$807$			572.644i			0.709596i
$808$	1386.39			1.71583
$809$	487.821			0.602993			0.301497	−	0.953467i	$-0.402514\pi$
$809$	487.821			0.602993			0.301497	+	0.953467i	$0.402514\pi$
$810$	−244.955	−	424.275i	−0.302414	−	0.523796i
$811$		−	362.501i		−	0.446980i	−0.974706	−	0.223490i	$-0.928255\pi$
$811$		−	362.501i		−	0.446980i	0.974706	−	0.223490i	$-0.0717450\pi$
$812$	−151.849	−	87.6700i	−0.187006	−	0.107968i
$813$	464.213			0.570988
$814$	269.691	−	155.706i	0.331316	−	0.191285i
$815$			82.8046i			0.101601i
$816$	5.00331	−	2.88866i	0.00613151	−	0.00354003i
$817$	242.598			0.296938
$818$	258.248	+	447.298i	0.315706	+	0.546819i
$819$		−	7.88054i		−	0.00962215i
$820$	900.591	−	1559.87i	1.09828	−	1.90228i
$821$	1260.35			1.53514			0.767570	−	0.640965i	$-0.221466\pi$
$821$	1260.35			1.53514			0.767570	+	0.640965i	$0.221466\pi$
$822$	145.532	−	84.0232i	0.177047	−	0.102218i
$823$			436.179i			0.529987i	0.964250	+	0.264993i	$0.0853698\pi$
$823$			436.179i			0.529987i	−0.964250	+	0.264993i	$0.914630\pi$
$824$		−	9.46013i		−	0.0114807i
$825$	101.128			0.122579
$826$	−60.7218	−	105.173i	−0.0735130	−	0.127328i
$827$			51.0250i			0.0616989i	0.999524	+	0.0308495i	$0.00982125\pi$
$827$			51.0250i			0.0616989i	−0.999524	+	0.0308495i	$0.990179\pi$
$828$	−845.691	−	488.260i	−1.02137	−	0.589686i
$829$	−153.416			−0.185062			−0.0925308	−	0.995710i	$-0.529496\pi$
$829$	−153.416			−0.185062			−0.0925308	+	0.995710i	$0.529496\pi$
$830$	1685.58	−	973.171i	2.03082	−	1.17250i
$831$		−	298.206i		−	0.358852i
$832$	52.7841			0.0634424
$833$	12.9967			0.0156023
$834$	−24.7974	−	42.9503i	−0.0297330	−	0.0514991i
$835$			735.517i			0.880859i
$836$	−37.4983	+	64.9490i	−0.0448545	+	0.0776902i
$837$	1041.59			1.24444
$838$	−729.498	+	421.176i	−0.870523	+	0.502597i
$839$		−	687.106i		−	0.818959i	−0.912319	−	0.409479i	$-0.865710\pi$
$839$		−	687.106i		−	0.818959i	0.912319	−	0.409479i	$-0.134290\pi$
$840$	90.3921			0.107610
$841$	272.863			0.324451
$842$	−513.815	−	889.953i	−0.610231	−	1.05695i
$843$			150.579i			0.178623i
$844$	−1128.34	−	651.450i	−1.33690	−	0.771860i
$845$	−1102.47			−1.30469
$846$	−304.096	+	175.570i	−0.359452	+	0.207530i
$847$		−	134.624i		−	0.158942i
$848$	−207.395	−	359.219i	−0.244570	−	0.423608i
$849$	133.045			0.156708
$850$	−4.92111	−	8.52361i	−0.00578954	−	0.0100278i
$851$		−	1214.77i		−	1.42746i
$852$	−185.100	+	320.602i	−0.217253	+	0.376293i
$853$	1116.89			1.30936			0.654682	−	0.755905i	$-0.272803\pi$
$853$	1116.89			1.30936			0.654682	+	0.755905i	$0.272803\pi$
$854$	107.148	−	61.8618i	0.125466	−	0.0724378i
$855$			207.699i			0.242923i
$856$			742.342i			0.867222i
$857$	1526.94			1.78172			0.890861	−	0.454277i	$-0.150102\pi$
$857$	1526.94			1.78172			0.890861	+	0.454277i	$0.150102\pi$
$858$	−4.65944	−	8.07038i	−0.00543058	−	0.00940604i
$859$			487.641i			0.567685i	0.958871	+	0.283842i	$0.0916093\pi$
$859$			487.641i			0.567685i	−0.958871	+	0.283842i	$0.908391\pi$
$860$	1262.79	+	729.073i	1.46836	+	0.847759i
$861$	−118.598			−0.137744
$862$	295.849	−	170.808i	0.343212	−	0.198154i
$863$			1657.13i			1.92019i	0.279669	+	0.960097i	$0.409775\pi$
$863$			1657.13i			1.92019i	−0.279669	+	0.960097i	$0.590225\pi$
$864$	−592.385	−	342.014i	−0.685631	−	0.395849i
$865$	261.319			0.302103
$866$	−277.299	−	480.296i	−0.320207	−	0.554614i
$867$		−	379.480i		−	0.437694i
$868$	128.000	−	221.703i	0.147465	−	0.255418i
$869$	−488.110			−0.561691
$870$	−497.292	+	287.112i	−0.571600	+	0.330014i
$871$			92.8877i			0.106645i
$872$	−358.598			−0.411236
$873$	−856.241			−0.980803
$874$	146.275	+	253.356i	0.167363	+	0.289881i
$875$			61.0764i			0.0698016i
$876$	264.234	+	152.556i	0.301637	+	0.174150i
$877$	−349.429			−0.398437			−0.199219	−	0.979955i	$-0.563840\pi$
$877$	−349.429			−0.398437			−0.199219	+	0.979955i	$0.563840\pi$
$878$	404.701	−	233.654i	0.460935	−	0.266121i
$879$			357.342i			0.406532i
$880$	−390.379	+	225.385i	−0.443612	+	0.256120i
$881$	−101.890			−0.115653			−0.0578266	−	0.998327i	$-0.518417\pi$
$881$	−101.890			−0.115653			−0.0578266	+	0.998327i	$0.518417\pi$
$882$	−343.921	−	595.689i	−0.389933	−	0.675384i
$883$			1012.41i			1.14655i	0.819362	+	0.573277i	$0.194328\pi$
$883$			1012.41i			1.14655i	−0.819362	+	0.573277i	$0.805672\pi$
$884$	−0.453477	+	0.785445i	−0.000512983	+	0.000888512i
$885$	−397.718			−0.449398
$886$	−989.746	+	571.430i	−1.11709	+	0.644955i
$887$			984.067i			1.10943i	0.832040	+	0.554716i	$0.187173\pi$
$887$			984.067i			1.10943i	−0.832040	+	0.554716i	$0.812827\pi$
$888$		−	380.361i		−	0.428334i
$889$	−123.341			−0.138741
$890$	−378.900	−	656.275i	−0.425731	−	0.737387i
$891$		−	160.865i		−	0.180544i
$892$	−1040.08	−	600.492i	−1.16601	−	0.673198i
$893$	105.196			0.117801
$894$	−179.601	+	103.693i	−0.200896	+	0.115988i
$895$		−	924.570i		−	1.03304i
$896$	−145.595	+	84.0591i	−0.162494	+	0.0938160i
$897$	−36.3514			−0.0405255
$898$	230.990	+	400.087i	0.257227	+	0.445531i
$899$			1626.26i			1.80897i
$900$	−260.447	+	451.107i	−0.289385	+	0.501230i
$901$	7.12707			0.00791018
$902$	512.193	−	295.715i	0.567841	−	0.327843i
$903$		−	96.0109i		−	0.106324i
$904$	525.581			0.581395
$905$	930.076			1.02771
$906$	−253.154	−	438.476i	−0.279420	−	0.483970i
$907$		−	1497.68i		−	1.65124i	−0.564223	−	0.825622i	$-0.690824\pi$
$907$		−	1497.68i		−	1.65124i	0.564223	−	0.825622i	$-0.309176\pi$
$908$	614.447	+	354.751i	0.676704	+	0.390695i
$909$	1260.74			1.38695
$910$	−12.2891	+	7.09510i	−0.0135045	+	0.00779681i
$911$		−	550.384i		−	0.604153i	−0.953284	−	0.302077i	$-0.902320\pi$
$911$		−	550.384i		−	0.604153i	0.953284	−	0.302077i	$-0.0976798\pi$
$912$	45.8007	+	79.3291i	0.0502200	+	0.0869836i
$913$	639.093			0.699992
$914$	412.275	+	714.081i	0.451067	+	0.781270i
$915$		−	405.185i		−	0.442825i
$916$	−76.7974	+	133.017i	−0.0838399	+	0.145215i
$917$	−12.8937			−0.0140608
$918$	10.1786	−	5.87659i	0.0110878	−	0.00640152i
$919$			706.483i			0.768751i	0.923177	+	0.384376i	$0.125583\pi$
$919$			706.483i			0.768751i	−0.923177	+	0.384376i	$0.874417\pi$
$920$			1758.38i			1.91129i
$921$	−172.289			−0.187067
$922$	89.2575	+	154.598i	0.0968085	+	0.167677i
$923$		−	58.1158i		−	0.0629640i
$924$	25.7043	+	14.8404i	0.0278185	+	0.0160610i
$925$	−647.980			−0.700519
$926$	−122.900	+	70.9565i	−0.132722	+	0.0766269i
$927$		−	8.60271i		−	0.00928016i
$928$	533.993	−	924.904i	0.575424	−	0.996663i
$929$	145.609			0.156737			0.0783686	−	0.996924i	$-0.475029\pi$
$929$	145.609			0.156737			0.0783686	+	0.996924i	$0.475029\pi$
$930$	−419.189	−	726.057i	−0.450741	−	0.780707i
$931$			206.067i			0.221339i
$932$	−748.797	+	1296.96i	−0.803431	+	1.39158i
$933$	−638.880			−0.684758
$934$	1026.25	−	592.508i	1.09877	−	0.634377i
$935$		−	7.74529i		−	0.00828373i
$936$	48.0000			0.0512821
$937$	−909.953			−0.971134			−0.485567	−	0.874199i	$-0.661387\pi$
$937$	−909.953			−0.971134			−0.485567	+	0.874199i	$0.661387\pi$
$938$	−147.924	−	256.213i	−0.157702	−	0.273148i
$939$			404.571i			0.430853i
$940$	547.575	+	316.142i	0.582526	+	0.336322i
$941$	−248.963			−0.264572			−0.132286	−	0.991212i	$-0.542232\pi$
$941$	−248.963			−0.264572			−0.132286	+	0.991212i	$0.542232\pi$
$942$	15.9320	−	9.19832i	0.0169129	−	0.00976467i
$943$		−	2307.07i		−	2.44652i
$944$	640.605	−	369.853i	0.678607	−	0.391794i
$945$	183.890			0.194593
$946$	239.395	+	414.645i	0.253061	+	0.438314i
$947$		−	1304.57i		−	1.37759i	−0.724958	−	0.688793i	$-0.758141\pi$
$947$		−	1304.57i		−	1.37759i	0.724958	−	0.688793i	$-0.241859\pi$
$948$	−298.090	+	516.307i	−0.314441	+	0.544627i
$949$	−47.8979			−0.0504720
$950$	135.145	−	78.0257i	0.142257	−	0.0821324i
$951$		−	288.845i		−	0.303728i
$952$		−	2.88866i		−	0.00303431i
$953$	−710.605			−0.745650			−0.372825	−	0.927902i	$-0.621611\pi$
$953$	−710.605			−0.745650			−0.372825	+	0.927902i	$0.621611\pi$
$954$	−188.598	−	326.661i	−0.197692	−	0.342412i
$955$			2065.92i			2.16327i
$956$	−60.0548	−	34.6727i	−0.0628188	−	0.0362685i
$957$	−188.550			−0.197022
$958$	1207.68	−	697.257i	1.26063	−	0.727826i
$959$		−	84.0232i		−	0.0876154i
$960$			550.573i			0.573514i
$961$	−1413.38			−1.47074
$962$	29.8555	+	51.7112i	0.0310348	+	0.0537538i
$963$			675.060i			0.700997i
$964$	−693.292	+	1200.82i	−0.719183	+	1.24566i
$965$	289.498			0.299998
$966$	100.268	−	57.8899i	0.103797	−	0.0599275i
$967$		−	692.924i		−	0.716571i	−0.933612	−	0.358285i	$-0.883361\pi$
$967$		−	692.924i		−	0.716571i	0.933612	−	0.358285i	$-0.116639\pi$
$968$	819.987			0.847094
$969$	−1.57392			−0.00162428
$970$	770.900	+	1335.24i	0.794743	+	1.37653i
$971$			1042.10i			1.07322i	0.843831	+	0.536610i	$0.180295\pi$
$971$			1042.10i			1.07322i	−0.843831	+	0.536610i	$0.819705\pi$
$972$	−836.591	−	483.006i	−0.860691	−	0.496920i
$973$	−24.7974			−0.0254855
$974$	−418.929	+	241.869i	−0.430112	+	0.248325i
$975$			19.3905i			0.0198877i
$976$	376.797	+	652.632i	0.386063	+	0.668680i
$977$	−1488.13			−1.52316			−0.761582	−	0.648069i	$-0.775577\pi$
$977$	−1488.13			−1.52316			−0.761582	+	0.648069i	$0.775577\pi$
$978$	16.6046	+	28.7601i	0.0169782	+	0.0294070i
$979$		−	248.828i		−	0.254166i
$980$	−619.286	+	1072.63i	−0.631924	+	1.09452i
$981$	−326.096			−0.332412
$982$	−338.791	+	195.601i	−0.345001	+	0.199186i
$983$		−	988.210i		−	1.00530i	−0.864490	−	0.502650i	$-0.832358\pi$
$983$		−	988.210i		−	1.00530i	0.864490	−	0.502650i	$-0.167642\pi$
$984$		−	722.375i		−	0.734120i
$985$	−2079.88			−2.11155
$986$	9.17525	+	15.8920i	0.00930553	+	0.0161176i
$987$		−	41.6325i		−	0.0421808i
$988$	−12.4535	−	7.19002i	−0.0126047	−	0.00727735i
$989$	1867.68			1.88846
$990$	−354.997	+	204.957i	−0.358583	+	0.207028i
$991$			692.694i			0.698985i	0.936939	+	0.349492i	$0.113646\pi$
$991$			692.694i			0.698985i	−0.936939	+	0.349492i	$0.886354\pi$
$992$	1350.38	+	779.642i	1.36127	+	0.785929i
$993$	−140.680			−0.141672
$994$	92.5498	+	160.301i	0.0931085	+	0.161269i
$995$		−	2258.61i		−	2.26996i
$996$	390.296	−	676.012i	0.391863	−	0.678727i
$997$	−1405.22			−1.40945			−0.704723	−	0.709483i	$-0.748929\pi$
$997$	−1405.22			−1.40945			−0.704723	+	0.709483i	$0.748929\pi$
$998$	410.900	−	237.233i	0.411724	−	0.237709i
$999$		−	773.792i		−	0.774567i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.3.b.a.39.2	✓	4
3.2	odd	2		684.3.g.a.343.3		4
4.3	odd	2	inner	76.3.b.a.39.3	yes	4
8.3	odd	2		1216.3.d.a.191.3		4
8.5	even	2		1216.3.d.a.191.2		4
12.11	even	2		684.3.g.a.343.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.3.b.a.39.2	✓	4	1.1	even	1	trivial
76.3.b.a.39.3	yes	4	4.3	odd	2	inner
684.3.g.a.343.1		4	12.11	even	2
684.3.g.a.343.3		4	3.2	odd	2
1216.3.d.a.191.2		4	8.5	even	2
1216.3.d.a.191.3		4	8.3	odd	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:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	76.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.73205i) q^{2} +1.31342i q^{3} +(-2.00000 + 3.46410i) q^{4} +6.54983 q^{5} +(2.27492 - 1.31342i) q^{6} -1.31342i q^{7} +8.00000 q^{8} +7.27492 q^{9} +O(q^{10})\)	\(q+(-1.00000 - 1.73205i) q^{2} +1.31342i q^{3} +(-2.00000 + 3.46410i) q^{4} +6.54983 q^{5} +(2.27492 - 1.31342i) q^{6} -1.31342i q^{7} +8.00000 q^{8} +7.27492 q^{9} +(-6.54983 - 11.3446i) q^{10} -4.30136i q^{11} +(-4.54983 - 2.62685i) q^{12} +0.824752 q^{13} +(-2.27492 + 1.31342i) q^{14} +8.60271i q^{15} +(-8.00000 - 13.8564i) q^{16} +0.274917 q^{17} +(-7.27492 - 12.6005i) q^{18} +4.35890i q^{19} +(-13.0997 + 22.6893i) q^{20} +1.72508 q^{21} +(-7.45017 + 4.30136i) q^{22} +33.5578i q^{23} +10.5074i q^{24} +17.9003 q^{25} +(-0.824752 - 1.42851i) q^{26} +21.3759i q^{27} +(4.54983 + 2.62685i) q^{28} -33.3746 q^{29} +(14.9003 - 8.60271i) q^{30} -48.7276i q^{31} +(-16.0000 + 27.7128i) q^{32} +5.64950 q^{33} +(-0.274917 - 0.476171i) q^{34} -8.60271i q^{35} +(-14.5498 + 25.2011i) q^{36} -36.1993 q^{37} +(7.54983 - 4.35890i) q^{38} +1.08325i q^{39} +52.3987 q^{40} -68.7492 q^{41} +(-1.72508 - 2.98793i) q^{42} -55.6558i q^{43} +(14.9003 + 8.60271i) q^{44} +47.6495 q^{45} +(58.1238 - 33.5578i) q^{46} -24.1336i q^{47} +(18.1993 - 10.5074i) q^{48} +47.2749 q^{49} +(-17.9003 - 31.0043i) q^{50} +0.361083i q^{51} +(-1.64950 + 2.85702i) q^{52} +25.9244 q^{53} +(37.0241 - 21.3759i) q^{54} -28.1732i q^{55} -10.5074i q^{56} -5.72508 q^{57} +(33.3746 + 57.8065i) q^{58} +46.2317i q^{59} +(-29.8007 - 17.2054i) q^{60} -47.0997 q^{61} +(-84.3987 + 48.7276i) q^{62} -9.55505i q^{63} +64.0000 q^{64} +5.40199 q^{65} +(-5.64950 - 9.78523i) q^{66} +112.625i q^{67} +(-0.549834 + 0.952341i) q^{68} -44.0756 q^{69} +(-14.9003 + 8.60271i) q^{70} -70.4645i q^{71} +58.1993 q^{72} -58.0756 q^{73} +(36.1993 + 62.6991i) q^{74} +23.5107i q^{75} +(-15.0997 - 8.71780i) q^{76} -5.64950 q^{77} +(1.87624 - 1.08325i) q^{78} -113.478i q^{79} +(-52.3987 - 90.7572i) q^{80} +37.3987 q^{81} +(68.7492 + 119.077i) q^{82} +148.579i q^{83} +(-3.45017 + 5.97586i) q^{84} +1.80066 q^{85} +(-96.3987 + 55.6558i) q^{86} -43.8350i q^{87} -34.4108i q^{88} +57.8488 q^{89} +(-47.6495 - 82.5314i) q^{90} -1.08325i q^{91} +(-116.248 - 67.1155i) q^{92} +64.0000 q^{93} +(-41.8007 + 24.1336i) q^{94} +28.5501i q^{95} +(-36.3987 - 21.0148i) q^{96} -117.698 q^{97} +(-47.2749 - 81.8826i) q^{98} -31.2920i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} - 8 q^{4} - 4 q^{5} - 6 q^{6} + 32 q^{8} + 14 q^{9}+O(q^{10}) \) 4 * q - 4 * q^2 - 8 * q^4 - 4 * q^5 - 6 * q^6 + 32 * q^8 + 14 * q^9	\( 4 q - 4 q^{2} - 8 q^{4} - 4 q^{5} - 6 q^{6} + 32 q^{8} + 14 q^{9} + 4 q^{10} + 12 q^{12} - 42 q^{13} + 6 q^{14} - 32 q^{16} - 14 q^{17} - 14 q^{18} + 8 q^{20} + 22 q^{21} - 60 q^{22} + 132 q^{25} + 42 q^{26} - 12 q^{28} - 58 q^{29} + 120 q^{30} - 64 q^{32} - 68 q^{33} + 14 q^{34} - 28 q^{36} - 24 q^{37} - 32 q^{40} - 124 q^{41} - 22 q^{42} + 120 q^{44} + 100 q^{45} + 6 q^{46} - 48 q^{48} + 174 q^{49} - 132 q^{50} + 84 q^{52} - 2 q^{53} - 18 q^{54} - 38 q^{57} + 58 q^{58} - 240 q^{60} - 128 q^{61} - 96 q^{62} + 256 q^{64} + 384 q^{65} + 68 q^{66} + 28 q^{68} - 282 q^{69} - 120 q^{70} + 112 q^{72} - 338 q^{73} + 24 q^{74} + 68 q^{77} + 234 q^{78} + 32 q^{80} - 92 q^{81} + 124 q^{82} - 44 q^{84} + 128 q^{85} - 144 q^{86} + 20 q^{89} - 100 q^{90} - 12 q^{92} + 256 q^{93} - 288 q^{94} + 96 q^{96} - 48 q^{97} - 174 q^{98}+O(q^{100}) \) 4 * q - 4 * q^2 - 8 * q^4 - 4 * q^5 - 6 * q^6 + 32 * q^8 + 14 * q^9 + 4 * q^10 + 12 * q^12 - 42 * q^13 + 6 * q^14 - 32 * q^16 - 14 * q^17 - 14 * q^18 + 8 * q^20 + 22 * q^21 - 60 * q^22 + 132 * q^25 + 42 * q^26 - 12 * q^28 - 58 * q^29 + 120 * q^30 - 64 * q^32 - 68 * q^33 + 14 * q^34 - 28 * q^36 - 24 * q^37 - 32 * q^40 - 124 * q^41 - 22 * q^42 + 120 * q^44 + 100 * q^45 + 6 * q^46 - 48 * q^48 + 174 * q^49 - 132 * q^50 + 84 * q^52 - 2 * q^53 - 18 * q^54 - 38 * q^57 + 58 * q^58 - 240 * q^60 - 128 * q^61 - 96 * q^62 + 256 * q^64 + 384 * q^65 + 68 * q^66 + 28 * q^68 - 282 * q^69 - 120 * q^70 + 112 * q^72 - 338 * q^73 + 24 * q^74 + 68 * q^77 + 234 * q^78 + 32 * q^80 - 92 * q^81 + 124 * q^82 - 44 * q^84 + 128 * q^85 - 144 * q^86 + 20 * q^89 - 100 * q^90 - 12 * q^92 + 256 * q^93 - 288 * q^94 + 96 * q^96 - 48 * q^97 - 174 * q^98

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