LMFDB - Embedded newform 32.2.g.b.21.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [32,2,Mod(5,32)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(32, base_ring=CyclotomicField(8))

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

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

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

chi := DirichletCharacter("32.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 32 = 2^{5} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	32.g (of order $8$, degree $4$, 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:	$0.255521286468$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{8})$
Coefficient field:	8.0.18939904.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 14x^{6} - 28x^{5} + 43x^{4} - 44x^{3} + 30x^{2} - 12x + 2 $ x^8 - 4x^7 + 14x^6 - 28x^5 + 43x^4 - 44x^3 + 30x^2 - 12*x + 2
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			21.1
Root			$0.500000 + 0.0297061i$ of defining polynomial
Character	$\chi$	$=$	32.21
Dual form			32.2.g.b.29.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.40426 + 0.167452i) q^{2} +(1.27882 - 0.529706i) q^{3} +(1.94392 - 0.470294i) q^{4} +(-0.707107 + 1.70711i) q^{5} +(-1.70711 + 0.957989i) q^{6} +(-2.74912 - 2.74912i) q^{7} +(-2.65103 + 0.985930i) q^{8} +(-0.766519 + 0.766519i) q^{9} +(0.707107 - 2.51564i) q^{10} +(0.135390 + 0.0560803i) q^{11} +(2.23681 - 1.63113i) q^{12} +(1.18073 + 2.85054i) q^{13} +(4.32083 + 3.40014i) q^{14} +2.55765i q^{15} +(3.55765 - 1.82843i) q^{16} -6.44549i q^{17} +(0.948041 - 1.20475i) q^{18} +(0.805198 + 1.94392i) q^{19} +(-0.571717 + 3.65103i) q^{20} +(-4.97186 - 2.05941i) q^{21} +(-0.199514 - 0.0560803i) q^{22} +(0.749118 - 0.749118i) q^{23} +(-2.86794 + 2.66510i) q^{24} +(1.12132 + 1.12132i) q^{25} +(-2.13539 - 3.80520i) q^{26} +(-2.16333 + 5.22274i) q^{27} +(-6.63696 - 4.05117i) q^{28} +(4.32417 - 1.79113i) q^{29} +(-0.428283 - 3.59161i) q^{30} +1.17157 q^{31} +(-4.68971 + 3.16333i) q^{32} +0.202846 q^{33} +(1.07931 + 9.05117i) q^{34} +(6.63696 - 2.74912i) q^{35} +(-1.12956 + 1.85054i) q^{36} +(1.73172 - 4.18073i) q^{37} +(-1.45622 - 2.59495i) q^{38} +(3.01990 + 3.01990i) q^{39} +(0.191470 - 5.22274i) q^{40} +(-2.49824 + 2.49824i) q^{41} +(7.32666 + 2.05941i) q^{42} +(-6.10725 - 2.52971i) q^{43} +(0.289561 + 0.0453426i) q^{44} +(-0.766519 - 1.85054i) q^{45} +(-0.926518 + 1.17740i) q^{46} +2.66981i q^{47} +(3.58107 - 4.22274i) q^{48} +8.11529i q^{49} +(-1.76240 - 1.38686i) q^{50} +(-3.41421 - 8.24264i) q^{51} +(3.63584 + 4.98593i) q^{52} +(1.64769 + 0.682497i) q^{53} +(2.16333 - 7.69637i) q^{54} +(-0.191470 + 0.191470i) q^{55} +(9.99842 + 4.57754i) q^{56} +(2.05941 + 2.05941i) q^{57} +(-5.77235 + 3.23931i) q^{58} +(1.43744 - 3.47029i) q^{59} +(1.20285 + 4.97186i) q^{60} +(-3.46760 + 1.43633i) q^{61} +(-1.64520 + 0.196182i) q^{62} +4.21450 q^{63} +(6.05588 - 5.22746i) q^{64} -5.70108 q^{65} +(-0.284849 + 0.0339670i) q^{66} +(-14.0791 + 5.83176i) q^{67} +(-3.03127 - 12.5295i) q^{68} +(0.561177 - 1.35480i) q^{69} +(-8.85970 + 4.97186i) q^{70} +(-3.40950 - 3.40950i) q^{71} +(1.27633 - 2.78780i) q^{72} +(-0.442353 + 0.442353i) q^{73} +(-1.73172 + 6.16084i) q^{74} +(2.02794 + 0.840001i) q^{75} +(2.47945 + 3.40014i) q^{76} +(-0.218031 - 0.526374i) q^{77} +(-4.74642 - 3.73505i) q^{78} -7.07550i q^{79} +(0.605684 + 7.36618i) q^{80} +4.57283i q^{81} +(3.08985 - 3.92652i) q^{82} +(2.99862 + 7.23931i) q^{83} +(-10.6334 - 1.66510i) q^{84} +(11.0031 + 4.55765i) q^{85} +(8.99980 + 2.52971i) q^{86} +(4.58107 - 4.58107i) q^{87} +(-0.414214 - 0.0151854i) q^{88} +(-4.21803 - 4.21803i) q^{89} +(1.38627 + 2.47029i) q^{90} +(4.59050 - 11.0824i) q^{91} +(1.10392 - 1.80853i) q^{92} +(1.49824 - 0.620589i) q^{93} +(-0.447065 - 3.74912i) q^{94} -3.88784 q^{95} +(-4.32167 + 6.52951i) q^{96} +10.3267 q^{97} +(-1.35892 - 11.3960i) q^{98} +(-0.146766 + 0.0607923i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} - 4 q^{3} + 4 q^{4} - 8 q^{6} - 8 q^{7} - 4 q^{8} + 4 q^{11} + 12 q^{12} - 8 q^{13} + 12 q^{14} + 20 q^{18} + 4 q^{19} + 4 q^{20} + 4 q^{22} - 8 q^{23} - 8 q^{24} - 8 q^{25} - 20 q^{26} + 8 q^{27}+ \cdots + 28 q^{99}+O(q^{100}) $ 8 * q - 4 * q^2 - 4 * q^3 + 4 * q^4 - 8 * q^6 - 8 * q^7 - 4 * q^8 + 4 * q^11 + 12 * q^12 - 8 * q^13 + 12 * q^14 + 20 * q^18 + 4 * q^19 + 4 * q^20 + 4 * q^22 - 8 * q^23 - 8 * q^24 - 8 * q^25 - 20 * q^26 + 8 * q^27 - 16 * q^28 - 12 * q^30 + 32 * q^31 - 24 * q^32 - 16 * q^33 + 16 * q^35 - 40 * q^36 - 8 * q^37 + 8 * q^38 + 16 * q^39 + 16 * q^40 + 8 * q^41 + 8 * q^42 - 12 * q^43 + 20 * q^44 + 12 * q^46 + 48 * q^48 + 16 * q^50 - 16 * q^51 + 12 * q^52 + 8 * q^53 - 8 * q^54 - 16 * q^55 + 8 * q^56 + 16 * q^57 - 12 * q^58 - 20 * q^59 - 8 * q^60 + 24 * q^61 - 24 * q^62 - 40 * q^63 - 8 * q^64 - 28 * q^66 - 36 * q^67 + 16 * q^68 + 32 * q^69 - 8 * q^70 - 24 * q^71 + 12 * q^72 - 32 * q^73 + 8 * q^74 - 12 * q^75 - 20 * q^76 + 16 * q^77 + 28 * q^78 + 8 * q^80 - 20 * q^82 + 20 * q^83 + 8 * q^84 + 8 * q^85 + 4 * q^86 + 56 * q^87 + 8 * q^88 - 16 * q^89 + 28 * q^90 + 40 * q^91 - 16 * q^92 - 16 * q^93 - 24 * q^94 - 8 * q^95 - 16 * q^96 + 32 * q^97 - 24 * q^98 + 28 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/32\mathbb{Z}\right)^\times$.

$n$	$5$	$31$
$\chi(n)$	$e\left(\frac{5}{8}\right)$	$1$

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 $

$2$	−1.40426	+	0.167452i	−0.992965	+	0.118406i
$2$	−1.40426	+	0.167452i	−0.992965	+	0.118406i
$3$	1.27882	−	0.529706i	0.738329	−	0.305826i	0.0183595	−	0.999831i	$-0.494156\pi$
$3$	1.27882	−	0.529706i	0.738329	−	0.305826i	0.719970	+	0.694005i	$0.244156\pi$
$4$	1.94392	−	0.470294i	0.971960	−	0.235147i
$5$	−0.707107	+	1.70711i	−0.316228	+	0.763441i	0.683220	+	0.730213i	$0.260579\pi$
$5$	−0.707107	+	1.70711i	−0.316228	+	0.763441i	−0.999448	+	0.0332288i	$0.989421\pi$
$6$	−1.70711	+	0.957989i	−0.696923	+	0.391097i
$7$	−2.74912	−	2.74912i	−1.03907	−	1.03907i	−0.999205	−	0.0398636i	$-0.987308\pi$
$7$	−2.74912	−	2.74912i	−1.03907	−	1.03907i	−0.0398636	−	0.999205i	$-0.512692\pi$
$8$	−2.65103	+	0.985930i	−0.937279	+	0.348579i
$9$	−0.766519	+	0.766519i	−0.255506	+	0.255506i
$10$	0.707107	−	2.51564i	0.223607	−	0.795514i
$11$	0.135390	+	0.0560803i	0.0408216	+	0.0169089i	0.403001	−	0.915200i	$-0.367967\pi$
$11$	0.135390	+	0.0560803i	0.0408216	+	0.0169089i	−0.362179	+	0.932108i	$0.617967\pi$
$12$	2.23681	−	1.63113i	0.645712	−	0.470866i
$13$	1.18073	+	2.85054i	0.327476	+	0.790598i	0.998778	+	0.0494138i	$0.0157353\pi$
$13$	1.18073	+	2.85054i	0.327476	+	0.790598i	−0.671302	+	0.741184i	$0.734265\pi$
$14$	4.32083	+	3.40014i	1.15479	+	0.908727i
$15$			2.55765i			0.660382i
$16$	3.55765	−	1.82843i	0.889412	−	0.457107i
$17$		−	6.44549i		−	1.56326i	−0.623742	−	0.781630i	$-0.714389\pi$
$17$		−	6.44549i		−	1.56326i	0.623742	−	0.781630i	$-0.285611\pi$
$18$	0.948041	−	1.20475i	0.223455	−	0.283962i
$19$	0.805198	+	1.94392i	0.184725	+	0.445966i	0.988929	−	0.148387i	$-0.0474082\pi$
$19$	0.805198	+	1.94392i	0.184725	+	0.445966i	−0.804204	+	0.594353i	$0.797408\pi$
$20$	−0.571717	+	3.65103i	−0.127840	+	0.816394i
$21$	−4.97186	−	2.05941i	−1.08495	−	0.449401i
$22$	−0.199514	−	0.0560803i	−0.0425365	−	0.0119564i
$23$	0.749118	−	0.749118i	0.156202	−	0.156202i	−0.624679	−	0.780881i	$-0.714770\pi$
$23$	0.749118	−	0.749118i	0.156202	−	0.156202i	0.780881	+	0.624679i	$0.214770\pi$
$24$	−2.86794	+	2.66510i	−0.585416	+	0.544010i
$25$	1.12132	+	1.12132i	0.224264	+	0.224264i
$26$	−2.13539	−	3.80520i	−0.418784	−	0.746261i
$27$	−2.16333	+	5.22274i	−0.416333	+	1.00512i
$28$	−6.63696	−	4.05117i	−1.25427	−	0.765599i
$29$	4.32417	−	1.79113i	0.802978	−	0.332604i	0.0568292	−	0.998384i	$-0.481901\pi$
$29$	4.32417	−	1.79113i	0.802978	−	0.332604i	0.746148	+	0.665780i	$0.231901\pi$
$30$	−0.428283	−	3.59161i	−0.0781934	−	0.655736i
$31$	1.17157			0.210421			0.105210	−	0.994450i	$-0.466448\pi$
$31$	1.17157			0.210421			0.105210	+	0.994450i	$0.466448\pi$
$32$	−4.68971	+	3.16333i	−0.829031	+	0.559203i
$33$	0.202846			0.0353109
$34$	1.07931	+	9.05117i	0.185100	+	1.55226i
$35$	6.63696	−	2.74912i	1.12185	−	0.464686i
$36$	−1.12956	+	1.85054i	−0.188260	+	0.308423i
$37$	1.73172	−	4.18073i	0.284692	−	0.687308i	−0.715241	−	0.698878i	$-0.753683\pi$
$37$	1.73172	−	4.18073i	0.284692	−	0.687308i	0.999933	+	0.0115700i	$0.00368293\pi$
$38$	−1.45622	−	2.59495i	−0.236231	−	0.420956i
$39$	3.01990	+	3.01990i	0.483571	+	0.483571i
$40$	0.191470	−	5.22274i	0.0302741	−	0.825788i
$41$	−2.49824	+	2.49824i	−0.390159	+	0.390159i	−0.874744	−	0.484585i	$-0.838971\pi$
$41$	−2.49824	+	2.49824i	−0.390159	+	0.390159i	0.484585	+	0.874744i	$0.338971\pi$
$42$	7.32666	+	2.05941i	1.13053	+	0.317774i
$43$	−6.10725	−	2.52971i	−0.931347	−	0.385777i	−0.135158	−	0.990824i	$-0.543154\pi$
$43$	−6.10725	−	2.52971i	−0.931347	−	0.385777i	−0.796189	+	0.605048i	$0.793154\pi$
$44$	0.289561	+	0.0453426i	0.0436530	+	0.00683566i
$45$	−0.766519	−	1.85054i	−0.114266	−	0.275862i
$46$	−0.926518	+	1.17740i	−0.136608	+	0.173598i
$47$			2.66981i			0.389432i	0.980860	+	0.194716i	$0.0623784\pi$
$47$			2.66981i			0.389432i	−0.980860	+	0.194716i	$0.937622\pi$
$48$	3.58107	−	4.22274i	0.516884	−	0.609500i
$49$			8.11529i			1.15933i
$50$	−1.76240	−	1.38686i	−0.249241	−	0.196132i
$51$	−3.41421	−	8.24264i	−0.478086	−	1.15420i
$52$	3.63584	+	4.98593i	0.504200	+	0.691424i
$53$	1.64769	+	0.682497i	0.226328	+	0.0937482i	0.492966	−	0.870049i	$-0.335913\pi$
$53$	1.64769	+	0.682497i	0.226328	+	0.0937482i	−0.266638	+	0.963797i	$0.585913\pi$
$54$	2.16333	−	7.69637i	0.294392	−	1.04734i
$55$	−0.191470	+	0.191470i	−0.0258178	+	0.0258178i
$56$	9.99842	+	4.57754i	1.33610	+	0.611700i
$57$	2.05941	+	2.05941i	0.272776	+	0.272776i
$58$	−5.77235	+	3.23931i	−0.757946	+	0.425342i
$59$	1.43744	−	3.47029i	0.187139	−	0.451794i	−0.802267	−	0.596965i	$-0.796373\pi$
$59$	1.43744	−	3.47029i	0.187139	−	0.451794i	0.989407	+	0.145171i	$0.0463732\pi$
$60$	1.20285	+	4.97186i	0.155287	+	0.641864i
$61$	−3.46760	+	1.43633i	−0.443981	+	0.183903i	−0.593462	−	0.804862i	$-0.702239\pi$
$61$	−3.46760	+	1.43633i	−0.443981	+	0.183903i	0.149482	+	0.988764i	$0.452239\pi$
$62$	−1.64520	+	0.196182i	−0.208940	+	0.0249152i
$63$	4.21450			0.530977
$64$	6.05588	−	5.22746i	0.756985	−	0.653432i
$65$	−5.70108			−0.707132
$66$	−0.284849	+	0.0339670i	−0.0350625	+	0.00418104i
$67$	−14.0791	+	5.83176i	−1.72004	+	0.712463i	−0.720212	+	0.693754i	$0.755956\pi$
$67$	−14.0791	+	5.83176i	−1.72004	+	0.712463i	−0.999825	+	0.0187090i	$0.994044\pi$
$68$	−3.03127	−	12.5295i	−0.367596	−	1.51943i
$69$	0.561177	−	1.35480i	0.0675578	−	0.163099i
$70$	−8.85970	+	4.97186i	−1.05894	+	0.594251i
$71$	−3.40950	−	3.40950i	−0.404633	−	0.404633i	0.475229	−	0.879862i	$-0.342365\pi$
$71$	−3.40950	−	3.40950i	−0.404633	−	0.404633i	−0.879862	+	0.475229i	$0.842365\pi$
$72$	1.27633	−	2.78780i	0.150417	−	0.328545i
$73$	−0.442353	+	0.442353i	−0.0517735	+	0.0517735i	−0.732520	−	0.680746i	$-0.761656\pi$
$73$	−0.442353	+	0.442353i	−0.0517735	+	0.0517735i	0.680746	+	0.732520i	$0.261656\pi$
$74$	−1.73172	+	6.16084i	−0.201308	+	0.716183i
$75$	2.02794	+	0.840001i	0.234166	+	0.0969949i
$76$	2.47945	+	3.40014i	0.284413	+	0.390023i
$77$	−0.218031	−	0.526374i	−0.0248470	−	0.0599859i
$78$	−4.74642	−	3.73505i	−0.537427	−	0.422911i
$79$		−	7.07550i		−	0.796056i	−0.917373	−	0.398028i	$-0.869695\pi$
$79$		−	7.07550i		−	0.796056i	0.917373	−	0.398028i	$-0.130305\pi$
$80$	0.605684	+	7.36618i	0.0677175	+	0.823564i
$81$			4.57283i			0.508093i
$82$	3.08985	−	3.92652i	0.341217	−	0.433611i
$83$	2.99862	+	7.23931i	0.329141	+	0.794617i	0.998656	+	0.0518190i	$0.0165019\pi$
$83$	2.99862	+	7.23931i	0.329141	+	0.794617i	−0.669515	+	0.742798i	$0.733498\pi$
$84$	−10.6334	−	1.66510i	−1.16020	−	0.181677i
$85$	11.0031	+	4.55765i	1.19346	+	0.494346i
$86$	8.99980	+	2.52971i	0.970474	+	0.272785i
$87$	4.58107	−	4.58107i	0.491143	−	0.491143i
$88$	−0.414214	−	0.0151854i	−0.0441553	−	0.00161877i
$89$	−4.21803	−	4.21803i	−0.447110	−	0.447110i	0.447282	−	0.894393i	$-0.352392\pi$
$89$	−4.21803	−	4.21803i	−0.447110	−	0.447110i	−0.894393	+	0.447282i	$0.852392\pi$
$90$	1.38627	+	2.47029i	0.146126	+	0.260392i
$91$	4.59050	−	11.0824i	0.481215	−	1.16176i
$92$	1.10392	−	1.80853i	0.115092	−	0.188552i
$93$	1.49824	−	0.620589i	0.155360	−	0.0643521i
$94$	−0.447065	−	3.74912i	−0.0461112	−	0.386692i
$95$	−3.88784			−0.398884
$96$	−4.32167	+	6.52951i	−0.441079	+	0.666415i
$97$	10.3267			1.04851			0.524257	−	0.851560i	$-0.324343\pi$
$97$	10.3267			1.04851			0.524257	+	0.851560i	$0.324343\pi$
$98$	−1.35892	−	11.3960i	−0.137272	−	1.15117i
$99$	−0.146766	+	0.0607923i	−0.0147505	+	0.00610986i
$100$	2.70711	+	1.65241i	0.270711	+	0.165241i
$101$	−4.31750	+	10.4234i	−0.429608	+	1.03716i	0.549805	+	0.835293i	$0.314702\pi$
$101$	−4.31750	+	10.4234i	−0.429608	+	1.03716i	−0.979412	+	0.201871i	$0.935298\pi$
$102$	6.17471	+	11.0031i	0.611387	+	1.08947i
$103$	13.3134	+	13.3134i	1.31181	+	1.31181i	0.920080	+	0.391732i	$0.128124\pi$
$103$	13.3134	+	13.3134i	1.31181	+	1.31181i	0.391732	+	0.920080i	$0.371876\pi$
$104$	−5.94059	−	6.39274i	−0.582523	−	0.626860i
$105$	7.03127	−	7.03127i	0.686182	−	0.686182i
$106$	−2.42809	−	0.682497i	−0.235836	−	0.0662900i
$107$	13.2507	+	5.48861i	1.28099	+	0.530604i	0.916288	−	0.400519i	$-0.131170\pi$
$107$	13.2507	+	5.48861i	1.28099	+	0.530604i	0.364704	+	0.931124i	$0.381170\pi$
$108$	−1.74912	+	11.1700i	−0.168309	+	1.07483i
$109$	−4.87515	−	11.7697i	−0.466955	−	1.12733i	−0.965486	−	0.260456i	$-0.916127\pi$
$109$	−4.87515	−	11.7697i	−0.466955	−	1.12733i	0.498531	−	0.866872i	$-0.333873\pi$
$110$	0.236813	−	0.300937i	0.0225792	−	0.0286932i
$111$		−	6.26372i		−	0.594526i
$112$	−14.8070	−	4.75383i	−1.39913	−	0.449195i
$113$		−	5.88118i		−	0.553254i	−0.960977	−	0.276627i	$-0.910783\pi$
$113$		−	5.88118i		−	0.553254i	0.960977	−	0.276627i	$-0.0892167\pi$
$114$	−3.23681	−	2.54711i	−0.303155	−	0.238558i
$115$	0.749118	+	1.80853i	0.0698556	+	0.168646i
$116$	7.56348	−	5.51544i	0.702251	−	0.512096i
$117$	−3.09005	−	1.27994i	−0.285675	−	0.118330i
$118$	−1.43744	+	5.11391i	−0.132327	+	0.470774i
$119$	−17.7194	+	17.7194i	−1.62433	+	1.62433i
$120$	−2.52166	−	6.78039i	−0.230195	−	0.618962i
$121$	−7.76299	−	7.76299i	−0.705726	−	0.705726i
$122$	4.62891	−	2.59764i	0.419082	−	0.235179i
$123$	−1.87147	+	4.51813i	−0.168745	+	0.407386i
$124$	2.27744	−	0.550984i	0.204520	−	0.0494798i
$125$	−11.2426	+	4.65685i	−1.00557	+	0.416522i
$126$	−5.91828	+	0.705727i	−0.527242	+	0.0628711i
$127$	−15.4022			−1.36672			−0.683360	−	0.730081i	$-0.739482\pi$
$127$	−15.4022			−1.36672			−0.683360	+	0.730081i	$0.739482\pi$
$128$	−7.62872	+	8.35480i	−0.674290	+	0.738467i
$129$	−9.15010			−0.805621
$130$	8.00583	−	0.954657i	0.702158	−	0.0837290i
$131$	−2.96382	+	1.22765i	−0.258950	+	0.107261i	−0.508382	−	0.861132i	$-0.669756\pi$
$131$	−2.96382	+	1.22765i	−0.258950	+	0.107261i	0.249432	+	0.968392i	$0.419756\pi$
$132$	0.394316	−	0.0953972i	0.0343208	−	0.00830326i
$133$	3.13048	−	7.55765i	0.271447	−	0.655331i
$134$	18.7943	−	10.5469i	1.62358	−	0.911114i
$135$	−7.38607	−	7.38607i	−0.635692	−	0.635692i
$136$	6.35480	+	17.0872i	0.544920	+	1.46521i
$137$	10.7757	−	10.7757i	0.920628	−	0.920628i	−0.0764454	−	0.997074i	$-0.524357\pi$
$137$	10.7757	−	10.7757i	0.920628	−	0.920628i	0.997074	+	0.0764454i	$0.0243571\pi$
$138$	−0.561177	+	1.99647i	−0.0477706	+	0.169951i
$139$	4.78372	+	1.98148i	0.405750	+	0.168067i	0.576218	−	0.817296i	$-0.304528\pi$
$139$	4.78372	+	1.98148i	0.405750	+	0.168067i	−0.170468	+	0.985363i	$0.554528\pi$
$140$	11.6088	−	8.46538i	0.981124	−	0.715456i
$141$	1.41421	+	3.41421i	0.119098	+	0.287529i
$142$	5.35877	+	4.21692i	0.449698	+	0.353876i
$143$			0.452150i			0.0378107i
$144$	−1.32548	+	4.12853i	−0.110457	+	0.344044i
$145$			8.64833i			0.718205i
$146$	0.547108	−	0.695253i	0.0452789	−	0.0575396i
$147$	4.29872	+	10.3780i	0.354553	+	0.855966i
$148$	1.40014	−	8.94142i	0.115091	−	0.734981i
$149$	4.32417	+	1.79113i	0.354250	+	0.146735i	0.552709	−	0.833374i	$-0.313594\pi$
$149$	4.32417	+	1.79113i	0.354250	+	0.146735i	−0.198460	+	0.980109i	$0.563594\pi$
$150$	−2.98843	−	0.840001i	−0.244004	−	0.0685858i
$151$	13.2344	−	13.2344i	1.07700	−	1.07700i	0.0802232	−	0.996777i	$-0.474437\pi$
$151$	13.2344	−	13.2344i	1.07700	−	1.07700i	0.996777	−	0.0802232i	$-0.0255633\pi$
$152$	−4.05117	−	4.35951i	−0.328593	−	0.353603i
$153$	4.94059	+	4.94059i	0.399423	+	0.399423i
$154$	0.394316	+	0.702659i	0.0317749	+	0.0566219i
$155$	−0.828427	+	2.00000i	−0.0665409	+	0.160644i
$156$	7.29068	+	4.45020i	0.583721	+	0.356301i
$157$	−15.9529	+	6.60790i	−1.27318	+	0.527368i	−0.913929	−	0.405874i	$-0.866967\pi$
$157$	−15.9529	+	6.60790i	−1.27318	+	0.527368i	−0.359249	+	0.933242i	$0.616967\pi$
$158$	1.18481	+	9.93588i	0.0942581	+	0.790456i
$159$	2.46863			0.195775
$160$	−2.08402	−	10.2426i	−0.164756	−	0.809752i
$161$	−4.11882			−0.324609
$162$	−0.765730	−	6.42147i	−0.0601614	−	0.504518i
$163$	10.6488	−	4.41088i	0.834079	−	0.345487i	0.0755629	−	0.997141i	$-0.475925\pi$
$163$	10.6488	−	4.41088i	0.834079	−	0.345487i	0.758516	+	0.651654i	$0.225925\pi$
$164$	−3.68146	+	6.03127i	−0.287474	+	0.470963i
$165$	−0.143434	+	0.346280i	−0.0111663	+	0.0269578i
$166$	−5.42309	−	9.66378i	−0.420914	−	0.750055i
$167$	−2.98677	−	2.98677i	−0.231123	−	0.231123i	0.582038	−	0.813161i	$-0.302255\pi$
$167$	−2.98677	−	2.98677i	−0.231123	−	0.231123i	−0.813161	+	0.582038i	$0.802255\pi$
$168$	15.2110	+	0.557647i	1.17355	+	0.0430234i
$169$	2.46094	−	2.46094i	0.189303	−	0.189303i
$170$	−16.2145	−	4.55765i	−1.24360	−	0.349556i
$171$	−2.10725	−	0.872852i	−0.161145	−	0.0667486i
$172$	−13.0617	−	2.04534i	−0.995946	−	0.155956i
$173$	7.85054	+	18.9529i	0.596866	+	1.44096i	0.876759	+	0.480930i	$0.159701\pi$
$173$	7.85054	+	18.9529i	0.596866	+	1.44096i	−0.279894	+	0.960031i	$0.590299\pi$
$174$	−5.66593	+	7.20015i	−0.429533	+	0.545842i
$175$		−	6.16528i		−	0.466052i
$176$	0.584208	−	0.0480365i	0.0440364	−	0.00362089i
$177$		−	5.19932i		−	0.390805i
$178$	6.62955	+	5.21692i	0.496906	+	0.391024i
$179$	−9.60549	−	23.1897i	−0.717948	−	1.73328i	−0.679113	−	0.734033i	$-0.737636\pi$
$179$	−9.60549	−	23.1897i	−0.717948	−	1.73328i	−0.0388344	−	0.999246i	$-0.512364\pi$
$180$	−2.36035	−	3.23681i	−0.175930	−	0.241258i
$181$	1.87868	+	0.778175i	0.139641	+	0.0578413i	0.451410	−	0.892317i	$-0.350921\pi$
$181$	1.87868	+	0.778175i	0.139641	+	0.0578413i	−0.311768	+	0.950158i	$0.600921\pi$
$182$	−4.59050	+	16.3314i	−0.340270	+	1.21056i
$183$	−3.67362	+	3.67362i	−0.271562	+	0.271562i
$184$	−1.24735	+	2.72451i	−0.0919561	+	0.200853i
$185$	5.91245	+	5.91245i	0.434692	+	0.434692i
$186$	−2.00000	+	1.12235i	−0.146647	+	0.0822950i
$187$	0.361465	−	0.872654i	0.0264329	−	0.0638148i
$188$	1.25559	+	5.18989i	0.0915736	+	0.378512i
$189$	20.3052	−	8.41068i	1.47699	−	0.611787i
$190$	5.45956	−	0.651026i	0.396078	−	0.0472304i
$191$	9.05902			0.655487			0.327744	−	0.944767i	$-0.393712\pi$
$191$	9.05902			0.655487			0.327744	+	0.944767i	$0.393712\pi$
$192$	4.97539	−	9.89283i	0.359068	−	0.713954i
$193$	6.24707			0.449674			0.224837	−	0.974396i	$-0.427815\pi$
$193$	6.24707			0.449674			0.224837	+	0.974396i	$0.427815\pi$
$194$	−14.5014	+	1.72922i	−1.04114	+	0.124151i
$195$	−7.29068	+	3.01990i	−0.522096	+	0.216259i
$196$	3.81657	+	15.7755i	0.272612	+	1.12682i
$197$	−1.81298	+	4.37691i	−0.129169	+	0.311842i	−0.975212	−	0.221273i	$-0.928979\pi$
$197$	−1.81298	+	4.37691i	−0.129169	+	0.311842i	0.846043	+	0.533115i	$0.178979\pi$
$198$	0.195918	−	0.109945i	0.0139233	−	0.00781343i
$199$	6.14186	+	6.14186i	0.435385	+	0.435385i	0.890455	−	0.455071i	$-0.150386\pi$
$199$	6.14186	+	6.14186i	0.435385	+	0.435385i	−0.455071	+	0.890455i	$0.650386\pi$
$200$	−4.07819	−	1.86711i	−0.288372	−	0.132024i
$201$	−14.9156	+	14.9156i	−1.05206	+	1.05206i
$202$	4.31750	−	15.3602i	0.303778	−	1.08074i
$203$	−16.8117	−	6.96362i	−1.17995	−	0.488750i
$204$	−10.5134	−	14.4173i	−0.736087	−	1.00942i
$205$	−2.49824	−	6.03127i	−0.174484	−	0.421242i
$206$	−20.9249	−	16.4662i	−1.45791	−	1.14726i
$207$			1.14843i			0.0798211i
$208$	9.41264	+	7.98233i	0.652649	+	0.553475i
$209$			0.308343i			0.0213285i
$210$	−8.69637	+	11.0512i	−0.600106	+	0.762603i
$211$	5.21588	+	12.5923i	0.359076	+	0.866886i	0.995430	+	0.0954895i	$0.0304416\pi$
$211$	5.21588	+	12.5923i	0.359076	+	0.866886i	−0.636354	+	0.771397i	$0.719558\pi$
$212$	3.52396	+	0.551819i	0.242027	+	0.0378991i
$213$	−6.16619	−	2.55412i	−0.422500	−	0.175005i
$214$	−19.5265	−	5.48861i	−1.33481	−	0.375194i
$215$	8.63696	−	8.63696i	0.589036	−	0.589036i
$216$	0.585786	−	15.9785i	0.0398577	−	1.08720i
$217$	−3.22079	−	3.22079i	−0.218642	−	0.218642i
$218$	8.81685	+	15.7114i	0.597153	+	1.06411i
$219$	−0.331374	+	0.800008i	−0.0223922	+	0.0540595i
$220$	−0.282156	+	0.462250i	−0.0190229	+	0.0311649i
$221$	18.3731	−	7.61040i	1.23591	−	0.511931i
$222$	1.04887	+	8.79592i	0.0703957	+	0.590344i
$223$	−0.960579			−0.0643251			−0.0321626	−	0.999483i	$-0.510239\pi$
$223$	−0.960579			−0.0643251			−0.0321626	+	0.999483i	$0.510239\pi$
$224$	21.5889	+	4.19618i	1.44247	+	0.280369i
$225$	−1.71903			−0.114602
$226$	0.984815	+	8.25873i	0.0655089	+	0.549362i
$227$	14.1698	−	5.86932i	0.940482	−	0.389561i	0.140837	−	0.990033i	$-0.455021\pi$
$227$	14.1698	−	5.86932i	0.940482	−	0.389561i	0.799646	+	0.600472i	$0.205021\pi$
$228$	4.97186	+	3.03480i	0.329270	+	0.200985i
$229$	1.80408	−	4.35544i	0.119217	−	0.287816i	−0.852994	−	0.521920i	$-0.825216\pi$
$229$	1.80408	−	4.35544i	0.119217	−	0.287816i	0.972211	+	0.234105i	$0.0752159\pi$
$230$	−1.35480	−	2.41421i	−0.0893330	−	0.159189i
$231$	−0.557647	−	0.557647i	−0.0366905	−	0.0366905i
$232$	−9.69755	+	9.01166i	−0.636675	+	0.591644i
$233$	−16.7918	+	16.7918i	−1.10007	+	1.10007i	−0.105663	+	0.994402i	$0.533697\pi$
$233$	−16.7918	+	16.7918i	−1.10007	+	1.10007i	−0.994402	+	0.105663i	$0.966303\pi$
$234$	4.55357	+	1.27994i	0.297676	+	0.0836723i
$235$	−4.55765	−	1.88784i	−0.297308	−	0.123149i
$236$	1.16222	−	7.42199i	0.0756538	−	0.483131i
$237$	−3.74794	−	9.04832i	−0.243455	−	0.587751i
$238$	21.9156	−	27.8499i	1.42058	−	1.80524i
$239$			15.8414i			1.02469i	0.858779	+	0.512347i	$0.171224\pi$
$239$			15.8414i			1.02469i	−0.858779	+	0.512347i	$0.828776\pi$
$240$	4.67647	+	9.09921i	0.301865	+	0.587351i
$241$			0.313335i			0.0201837i	0.999949	+	0.0100918i	$0.00321239\pi$
$241$			0.313335i			0.0201837i	−0.999949	+	0.0100918i	$0.996788\pi$
$242$	12.2012	+	9.60136i	0.784324	+	0.617199i
$243$	−4.06774	−	9.82038i	−0.260945	−	0.629978i
$244$	−6.06524	+	4.42290i	−0.388287	+	0.283147i
$245$	−13.8537	−	5.73838i	−0.885079	−	0.366612i
$246$	1.87147	−	6.65804i	0.119321	−	0.424501i
$247$	−4.59050	+	4.59050i	−0.292086	+	0.292086i
$248$	−3.10587	+	1.15509i	−0.197223	+	0.0733482i
$249$	7.66941	+	7.66941i	0.486029	+	0.486029i
$250$	15.0078	−	8.42206i	0.949180	−	0.532658i
$251$	−3.55903	+	8.59225i	−0.224644	+	0.542338i	−0.995510	−	0.0946593i	$-0.969824\pi$
$251$	−3.55903	+	8.59225i	−0.224644	+	0.542338i	0.770866	+	0.636997i	$0.219824\pi$
$252$	8.19265	−	1.98205i	0.516089	−	0.124858i
$253$	0.143434	−	0.0594122i	0.00901760	−	0.00373521i
$254$	21.6287	−	2.57912i	1.35711	−	0.161829i
$255$	16.4853			1.03235
$256$	9.31371	−	13.0098i	0.582107	−	0.813112i
$257$	18.9043			1.17922			0.589609	−	0.807689i	$-0.299282\pi$
$257$	18.9043			1.17922			0.589609	+	0.807689i	$0.299282\pi$
$258$	12.8492	−	1.53220i	0.799954	−	0.0953907i
$259$	−16.2540	+	6.73263i	−1.00998	+	0.418346i
$260$	−11.0824	+	2.68118i	−0.687304	+	0.166280i
$261$	−1.94162	+	4.68749i	−0.120183	+	0.290148i
$262$	3.95641	−	2.22025i	0.244428	−	0.137167i
$263$	−16.6366	−	16.6366i	−1.02585	−	1.02585i	−0.999657	−	0.0261975i	$-0.991660\pi$
$263$	−16.6366	−	16.6366i	−1.02585	−	1.02585i	−0.0261975	−	0.999657i	$-0.508340\pi$
$264$	−0.537750	+	0.199992i	−0.0330962	+	0.0123087i
$265$	−2.33019	+	2.33019i	−0.143143	+	0.143143i
$266$	−3.13048	+	11.1371i	−0.191942	+	0.682862i
$267$	−7.62844	−	3.15980i	−0.466853	−	0.193377i
$268$	−24.6260	+	17.9578i	−1.50427	+	1.09695i
$269$	−5.01046	−	12.0963i	−0.305493	−	0.737525i	−0.999840	−	0.0178850i	$-0.994307\pi$
$269$	−5.01046	−	12.0963i	−0.305493	−	0.737525i	0.694347	−	0.719640i	$-0.255693\pi$
$270$	11.6088	+	9.13519i	0.706490	+	0.555950i
$271$			28.2141i			1.71388i	0.515412	+	0.856942i	$0.327639\pi$
$271$			28.2141i			1.71388i	−0.515412	+	0.856942i	$0.672361\pi$
$272$	−11.7851	−	22.9308i	−0.714577	−	1.39038i
$273$		−	16.6041i		−	1.00493i
$274$	−13.3275	+	16.9363i	−0.805144	+	1.02316i
$275$	0.0889314	+	0.214699i	0.00536277	+	0.0129469i
$276$	0.453728	−	2.89754i	0.0273112	−	0.174412i
$277$	−21.8246	−	9.04006i	−1.31132	−	0.543165i	−0.386047	−	0.922479i	$-0.626160\pi$
$277$	−21.8246	−	9.04006i	−1.31132	−	0.543165i	−0.925268	+	0.379314i	$0.876160\pi$
$278$	−7.04942	−	1.98148i	−0.422796	−	0.118841i
$279$	−0.898033	+	0.898033i	−0.0537638	+	0.0537638i
$280$	−14.8843	+	13.8316i	−0.889508	+	0.826594i
$281$	3.00666	+	3.00666i	0.179363	+	0.179363i	0.791078	−	0.611715i	$-0.209520\pi$
$281$	3.00666	+	3.00666i	0.179363	+	0.179363i	−0.611715	+	0.791078i	$0.709520\pi$
$282$	−2.55765	−	4.55765i	−0.152306	−	0.271404i
$283$	0.709521	−	1.71293i	0.0421766	−	0.101823i	−0.901387	−	0.433014i	$-0.857450\pi$
$283$	0.709521	−	1.71293i	0.0421766	−	0.101823i	0.943564	+	0.331190i	$0.107450\pi$
$284$	−8.23127	−	5.02433i	−0.488436	−	0.298139i
$285$	−4.97186	+	2.05941i	−0.294508	+	0.121989i
$286$	−0.0757135	−	0.634939i	−0.00447703	−	0.0375447i
$287$	13.7359			0.810804
$288$	1.16999	−	6.01950i	0.0689426	−	0.354703i
$289$	−24.5443			−1.44378
$290$	−1.44818	−	12.1445i	−0.0850401	−	0.713153i
$291$	13.2060	−	5.47010i	0.774148	−	0.320663i
$292$	−0.651862	+	1.06793i	−0.0381474	+	0.0624961i
$293$	10.5176	−	25.3917i	0.614444	−	1.48340i	−0.243627	−	0.969869i	$-0.578337\pi$
$293$	10.5176	−	25.3917i	0.614444	−	1.48340i	0.858071	−	0.513530i	$-0.171663\pi$
$294$	−7.77436	−	13.8537i	−0.453410	−	0.807963i
$295$	4.90774	+	4.90774i	0.285739	+	0.285739i
$296$	−0.468914	+	12.7906i	−0.0272551	+	0.743438i
$297$	−0.585786	+	0.585786i	−0.0339908	+	0.0339908i
$298$	−6.37220	−	1.79113i	−0.369132	−	0.103757i
$299$	3.01990	+	1.25088i	0.174645	+	0.0723404i
$300$	4.33720	+	0.679166i	0.250408	+	0.0392116i
$301$	9.83509	+	23.7440i	0.566885	+	1.36858i
$302$	−16.3685	+	20.8007i	−0.941900	+	1.19695i
$303$			15.6167i			0.897154i
$304$	6.41893	+	5.44353i	0.368151	+	0.312208i
$305$		−	6.93520i		−	0.397108i
$306$	−7.76521	−	6.11058i	−0.443907	−	0.349319i
$307$	5.80167	+	14.0065i	0.331119	+	0.799391i	0.998504	+	0.0546786i	$0.0174134\pi$
$307$	5.80167	+	14.0065i	0.331119	+	0.799391i	−0.667385	+	0.744713i	$0.732587\pi$
$308$	−0.671386	−	0.920690i	−0.0382558	−	0.0524612i
$309$	24.0777	+	9.97332i	1.36973	+	0.567363i
$310$	0.828427	−	2.94725i	0.0470515	−	0.167393i
$311$	7.15481	−	7.15481i	0.405712	−	0.405712i	−0.474528	−	0.880240i	$-0.657381\pi$
$311$	7.15481	−	7.15481i	0.405712	−	0.405712i	0.880240	+	0.474528i	$0.157381\pi$
$312$	−10.9832	−	5.02842i	−0.621803	−	0.284678i
$313$	−11.8512	−	11.8512i	−0.669868	−	0.669868i	0.287817	−	0.957685i	$-0.407070\pi$
$313$	−11.8512	−	11.8512i	−0.669868	−	0.669868i	−0.957685	+	0.287817i	$0.907070\pi$
$314$	21.2956	−	11.9506i	1.20178	−	0.674410i
$315$	−2.98010	+	7.19460i	−0.167910	+	0.405370i
$316$	−3.32756	−	13.7542i	−0.187190	−	0.773734i
$317$	18.9377	−	7.84425i	1.06365	−	0.440577i	0.218902	−	0.975747i	$-0.429752\pi$
$317$	18.9377	−	7.84425i	1.06365	−	0.440577i	0.844745	+	0.535170i	$0.179752\pi$
$318$	−3.46662	+	0.413378i	−0.194398	+	0.0231811i
$319$	0.685896			0.0384028
$320$	4.64167	+	14.0344i	0.259477	+	0.784547i
$321$	19.8526			1.10807
$322$	5.78392	−	0.689705i	0.322325	−	0.0384358i
$323$	12.5295	−	5.18989i	0.697160	−	0.288773i
$324$	2.15058	+	8.88922i	0.119476	+	0.493846i
$325$	−1.87239	+	4.52035i	−0.103861	+	0.250744i
$326$	−14.2151	+	7.97721i	−0.787304	+	0.441817i
$327$	−12.4689	−	12.4689i	−0.689533	−	0.689533i
$328$	4.15980	−	9.08597i	0.229687	−	0.501689i
$329$	7.33962	−	7.33962i	0.404646	−	0.404646i
$330$	0.143434	−	0.510287i	0.00789577	−	0.0280904i
$331$	9.91107	+	4.10530i	0.544762	+	0.225648i	0.638055	−	0.769991i	$-0.279739\pi$
$331$	9.91107	+	4.10530i	0.544762	+	0.225648i	−0.0932931	+	0.995639i	$0.529739\pi$
$332$	9.23368	+	12.6624i	0.506764	+	0.694940i
$333$	1.87722	+	4.53200i	0.102871	+	0.248352i
$334$	4.69435	+	3.69407i	0.256863	+	0.202131i
$335$		−	28.1582i		−	1.53845i
$336$	−21.4536	+	1.76402i	−1.17039	+	0.0962353i
$337$			3.23412i			0.176174i	0.996113	+	0.0880868i	$0.0280753\pi$
$337$			3.23412i			0.176174i	−0.996113	+	0.0880868i	$0.971925\pi$
$338$	−3.04372	+	3.86790i	−0.165556	+	0.210386i
$339$	−3.11529	−	7.52099i	−0.169200	−	0.408484i
$340$	23.5326	+	3.68499i	1.27624	+	0.199847i
$341$	0.158619	+	0.0657022i	0.00858971	+	0.00355797i
$342$	3.10530	+	0.872852i	0.167915	+	0.0471984i
$343$	3.06608	−	3.06608i	0.165553	−	0.165553i
$344$	18.6846	+	0.684993i	1.00741	+	0.0369324i
$345$	1.91598	+	1.91598i	0.103153	+	0.103153i
$346$	−14.1979	−	25.3003i	−0.763286	−	1.36015i
$347$	−9.82705	+	23.7246i	−0.527544	+	1.27360i	0.405584	+	0.914058i	$0.367068\pi$
$347$	−9.82705	+	23.7246i	−0.527544	+	1.27360i	−0.933128	+	0.359545i	$0.882932\pi$
$348$	6.75079	−	11.0597i	0.361880	−	0.592862i
$349$	−12.5762	+	5.20925i	−0.673190	+	0.278845i	−0.692977	−	0.720960i	$-0.743701\pi$
$349$	−12.5762	+	5.20925i	−0.673190	+	0.278845i	0.0197868	+	0.999804i	$0.493701\pi$
$350$	1.03239	+	8.65769i	0.0551835	+	0.462773i
$351$	−17.4420			−0.930983
$352$	−0.812340	+	0.165283i	−0.0432978	+	0.00880961i
$353$	−8.67371			−0.461655			−0.230828	−	0.972995i	$-0.574143\pi$
$353$	−8.67371			−0.461655			−0.230828	+	0.972995i	$0.574143\pi$
$354$	0.870636	+	7.30122i	0.0462738	+	0.388055i
$355$	8.23127	−	3.40950i	0.436870	−	0.180958i
$356$	−10.1832	−	6.21580i	−0.539710	−	0.329437i
$357$	−13.2739	+	32.0461i	−0.702530	+	1.69606i
$358$	17.3718	+	30.9560i	0.918129	+	1.63608i
$359$	13.6307	+	13.6307i	0.719399	+	0.719399i	0.968482	−	0.249083i	$-0.0801292\pi$
$359$	13.6307	+	13.6307i	0.719399	+	0.719399i	−0.249083	+	0.968482i	$0.580129\pi$
$360$	3.85657	+	4.15010i	0.203259	+	0.218729i
$361$	10.3045	−	10.3045i	0.542345	−	0.542345i
$362$	−2.76847	−	0.778175i	−0.145508	−	0.0408999i
$363$	−14.0396	−	5.81539i	−0.736888	−	0.305229i
$364$	3.71155	−	23.7023i	0.194538	−	1.24234i
$365$	−0.442353	−	1.06793i	−0.0231538	−	0.0558982i
$366$	4.54358	−	5.77389i	0.237497	−	0.301806i
$367$		−	28.9800i		−	1.51274i	−0.654142	−	0.756371i	$-0.726970\pi$
$367$		−	28.9800i		−	1.51274i	0.654142	−	0.756371i	$-0.273030\pi$
$368$	1.29539	−	4.03480i	0.0675268	−	0.210329i
$369$		−	3.82989i		−	0.199376i
$370$	−9.29270	−	7.31259i	−0.483104	−	0.380164i
$371$	−2.65344	−	6.40597i	−0.137760	−	0.332581i
$372$	2.62059	−	1.91099i	0.135871	−	0.0990800i
$373$	−5.56367	−	2.30455i	−0.288076	−	0.119325i	0.233966	−	0.972245i	$-0.424830\pi$
$373$	−5.56367	−	2.30455i	−0.288076	−	0.119325i	−0.522042	+	0.852920i	$0.674830\pi$
$374$	−0.361465	+	1.28597i	−0.0186909	+	0.0664957i
$375$	−11.9106	+	11.9106i	−0.615060	+	0.615060i
$376$	−2.63224	−	7.07773i	−0.135748	−	0.365006i
$377$	10.2114	+	10.2114i	0.525912	+	0.525912i
$378$	−27.1055	+	15.2110i	−1.39416	+	0.782368i
$379$	8.55274	−	20.6481i	0.439325	−	1.06062i	−0.536858	−	0.843673i	$-0.680389\pi$
$379$	8.55274	−	20.6481i	0.439325	−	1.06062i	0.976183	−	0.216951i	$-0.0696111\pi$
$380$	−7.55765	+	1.82843i	−0.387699	+	0.0937963i
$381$	−19.6966	+	8.15862i	−1.00909	+	0.417979i
$382$	−12.7213	+	1.51695i	−0.650876	+	0.0776139i
$383$	−30.5667			−1.56188			−0.780942	−	0.624603i	$-0.785261\pi$
$383$	−30.5667			−1.56188			−0.780942	+	0.624603i	$0.785261\pi$
$384$	−5.33019	+	14.7253i	−0.272005	+	0.751447i
$385$	1.05275			0.0536530
$386$	−8.77254	+	1.04608i	−0.446511	+	0.0532443i
$387$	6.62039	−	2.74226i	0.336533	−	0.139397i
$388$	20.0742	−	4.85657i	1.01911	−	0.246555i
$389$	−7.06634	+	17.0597i	−0.358278	+	0.864959i	0.637265	+	0.770645i	$0.280066\pi$
$389$	−7.06634	+	17.0597i	−0.358278	+	0.864959i	−0.995543	+	0.0943139i	$0.969934\pi$
$390$	9.73235	−	5.46157i	0.492817	−	0.276558i
$391$	−4.82843	−	4.82843i	−0.244184	−	0.244184i
$392$	−8.00112	−	21.5139i	−0.404117	−	1.08661i
$393$	−3.13990	+	3.13990i	−0.158387	+	0.158387i
$394$	1.81298	−	6.44993i	0.0913365	−	0.324943i
$395$	12.0786	+	5.00313i	0.607742	+	0.251735i
$396$	−0.256710	+	0.187198i	−0.0129002	+	0.00940707i
$397$	7.15759	+	17.2799i	0.359229	+	0.867255i	0.995409	+	0.0957146i	$0.0305136\pi$
$397$	7.15759	+	17.2799i	0.359229	+	0.867255i	−0.636180	+	0.771541i	$0.719486\pi$
$398$	−9.65326	−	7.59633i	−0.483874	−	0.380769i
$399$		−	11.3231i		−	0.566866i
$400$	6.03951	+	1.93901i	0.301976	+	0.0969505i
$401$			11.0004i			0.549332i	0.961540	+	0.274666i	$0.0885674\pi$
$401$			11.0004i			0.549332i	−0.961540	+	0.274666i	$0.911433\pi$
$402$	18.4478	−	23.4431i	0.920092	−	1.16923i
$403$	1.38331	+	3.33962i	0.0689078	+	0.166358i
$404$	−3.49083	+	22.2927i	−0.173675	+	1.10910i
$405$	−7.80631	−	3.23348i	−0.387899	−	0.160673i
$406$	24.7741	+	6.96362i	1.22952	+	0.345599i
$407$	0.468914	−	0.468914i	0.0232432	−	0.0232432i
$408$	17.1778	+	18.4853i	0.850430	+	0.915158i
$409$	−1.15862	−	1.15862i	−0.0572900	−	0.0572900i	0.677881	−	0.735171i	$-0.262898\pi$
$409$	−1.15862	−	1.15862i	−0.0572900	−	0.0572900i	−0.735171	+	0.677881i	$0.762898\pi$
$410$	4.51813	+	8.05117i	0.223135	+	0.397619i
$411$	8.07225	−	19.4881i	0.398175	−	0.961279i
$412$	32.1415	+	19.6190i	1.58350	+	0.966559i
$413$	−13.4919	+	5.58855i	−0.663895	+	0.274994i
$414$	−0.192306	−	1.61269i	−0.00945133	−	0.0792596i
$415$	−14.4786			−0.710727
$416$	−14.5545	−	9.63315i	−0.713593	−	0.472304i
$417$	7.16714			0.350976
$418$	−0.0516326	−	0.432995i	−0.00252543	−	0.0211785i
$419$	−32.0362	+	13.2698i	−1.56507	+	0.648273i	−0.985961	−	0.166978i	$-0.946599\pi$
$419$	−32.0362	+	13.2698i	−1.56507	+	0.648273i	−0.579108	+	0.815251i	$0.696599\pi$
$420$	10.3615	−	16.9750i	0.505588	−	0.828295i
$421$	9.34602	−	22.5633i	0.455497	−	1.09967i	−0.514705	−	0.857368i	$-0.672098\pi$
$421$	9.34602	−	22.5633i	0.455497	−	1.09967i	0.970202	−	0.242299i	$-0.0779016\pi$
$422$	−9.43308	−	16.8094i	−0.459195	−	0.818271i
$423$	−2.04646	−	2.04646i	−0.0995022	−	0.0995022i
$424$	−5.04098	−	0.184807i	−0.244811	−	0.00897500i
$425$	7.22746	−	7.22746i	0.350583	−	0.350583i
$426$	9.08665	+	2.55412i	0.440250	+	0.123747i
$427$	13.4815	+	5.58421i	0.652414	+	0.270239i
$428$	28.3395	+	4.43771i	1.36984	+	0.214505i
$429$	0.239507	+	0.578221i	0.0115635	+	0.0279168i
$430$	−10.6823	+	13.5749i	−0.515146	+	0.654637i
$431$			4.47586i			0.215594i	0.994173	+	0.107797i	$0.0343797\pi$
$431$			4.47586i			0.215594i	−0.994173	+	0.107797i	$0.965620\pi$
$432$	1.85304	+	22.5362i	0.0891543	+	1.08427i
$433$			1.44196i			0.0692960i	0.999400	+	0.0346480i	$0.0110310\pi$
$433$			1.44196i			0.0692960i	−0.999400	+	0.0346480i	$0.988969\pi$
$434$	5.06217	+	3.98352i	0.242992	+	0.191215i
$435$	4.58107	+	11.0597i	0.219646	+	0.530272i
$436$	−15.0121	−	20.5865i	−0.718949	−	0.985915i
$437$	2.05941	+	0.853036i	0.0985150	+	0.0408063i
$438$	0.331374	−	1.17891i	0.0158337	−	0.0563306i
$439$	0.854615	−	0.854615i	0.0407885	−	0.0407885i	−0.686418	−	0.727207i	$-0.740818\pi$
$439$	0.854615	−	0.854615i	0.0407885	−	0.0407885i	0.727207	+	0.686418i	$0.240818\pi$
$440$	0.318816	−	0.696369i	0.0151990	−	0.0331981i
$441$	−6.22053	−	6.22053i	−0.296216	−	0.296216i
$442$	−24.5264	+	13.7636i	−1.16660	+	0.654669i
$443$	4.68913	−	11.3206i	0.222787	−	0.537857i	−0.772479	−	0.635040i	$-0.780983\pi$
$443$	4.68913	−	11.3206i	0.222787	−	0.537857i	0.995266	+	0.0971838i	$0.0309835\pi$
$444$	−2.94579	−	12.1762i	−0.139801	−	0.577855i
$445$	10.1832	−	4.21803i	0.482731	−	0.199954i
$446$	1.34891	−	0.160851i	0.0638726	−	0.00761651i
$447$	6.47862			0.306428
$448$	−31.0192	−	2.27744i	−1.46552	−	0.107599i
$449$	−24.5573			−1.15893			−0.579464	−	0.814998i	$-0.696738\pi$
$449$	−24.5573			−1.15893			−0.579464	+	0.814998i	$0.696738\pi$
$450$	2.41397	−	0.287854i	0.113796	−	0.0135696i
$451$	−0.478338	+	0.198134i	−0.0225240	+	0.00932976i
$452$	−2.76588	−	11.4325i	−0.130096	−	0.537741i
$453$	9.91412	−	23.9348i	0.465806	−	1.12456i
$454$	−18.9153	+	10.6148i	−0.887740	+	0.498179i
$455$	15.6729	+	15.6729i	0.734759	+	0.734759i
$456$	−7.48999	−	3.42912i	−0.350751	−	0.160583i
$457$	14.1684	−	14.1684i	0.662771	−	0.662771i	−0.293262	−	0.956032i	$-0.594741\pi$
$457$	14.1684	−	14.1684i	0.662771	−	0.662771i	0.956032	+	0.293262i	$0.0947407\pi$
$458$	−1.80408	+	6.41829i	−0.0842992	+	0.299907i
$459$	33.6631	+	13.9437i	1.57126	+	0.650837i
$460$	2.30676	+	3.16333i	0.107553	+	0.147491i
$461$	−11.7965	−	28.4793i	−0.549417	−	1.32641i	−0.917913	−	0.396782i	$-0.870127\pi$
$461$	−11.7965	−	28.4793i	−0.549417	−	1.32641i	0.368496	−	0.929630i	$-0.379873\pi$
$462$	0.876464	+	0.689705i	0.0407768	+	0.0320880i
$463$			14.8190i			0.688697i	0.938842	+	0.344349i	$0.111900\pi$
$463$			14.8190i			0.688697i	−0.938842	+	0.344349i	$0.888100\pi$
$464$	12.1089	−	14.2786i	0.562142	−	0.662869i
$465$			2.99647i			0.138958i
$466$	20.7683	−	26.3919i	0.962072	−	1.22258i
$467$	5.43521	+	13.1218i	0.251512	+	0.607203i	0.998326	−	0.0578293i	$-0.0184179\pi$
$467$	5.43521	+	13.1218i	0.251512	+	0.607203i	−0.746815	+	0.665032i	$0.768418\pi$
$468$	−6.60875	−	1.03487i	−0.305490	−	0.0478368i
$469$	54.7373	+	22.6729i	2.52753	+	1.04694i
$470$	6.71627	+	1.88784i	0.309798	+	0.0870795i
$471$	−16.9007	+	16.9007i	−0.778742	+	0.778742i
$472$	−0.389231	+	10.6171i	−0.0179158	+	0.488690i
$473$	−0.684993	−	0.684993i	−0.0314960	−	0.0314960i
$474$	6.77825	+	12.0786i	0.311335	+	0.554790i
$475$	−1.27687	+	3.08264i	−0.0585869	+	0.141441i
$476$	−26.1118	+	42.7784i	−1.19683	+	1.96075i
$477$	−1.78614	+	0.739842i	−0.0817816	+	0.0338750i
$478$	−2.65267	−	22.2455i	−0.121330	−	1.01749i
$479$	32.3727			1.47915			0.739574	−	0.673076i	$-0.235027\pi$
$479$	32.3727			1.47915			0.739574	+	0.673076i	$0.235027\pi$
$480$	−8.09069	−	11.9946i	−0.369288	−	0.547477i
$481$	13.9620			0.636614
$482$	−0.0524685	−	0.440005i	−0.00238988	−	0.0200417i
$483$	−5.26725	+	2.18177i	−0.239668	+	0.0992738i
$484$	−18.7415	−	11.4397i	−0.851887	−	0.519988i
$485$	−7.30205	+	17.6287i	−0.331569	+	0.800479i
$486$	7.35662	+	13.1093i	0.333703	+	0.594649i
$487$	−1.89478	−	1.89478i	−0.0858608	−	0.0858608i	0.662872	−	0.748733i	$-0.269337\pi$
$487$	−1.89478	−	1.89478i	−0.0858608	−	0.0858608i	−0.748733	+	0.662872i	$0.769337\pi$
$488$	7.77658	−	7.22655i	0.352029	−	0.327131i
$489$	11.2815	−	11.2815i	0.510166	−	0.510166i
$490$	20.4151	+	5.73838i	0.922262	+	0.259234i
$491$	−18.2886	−	7.57539i	−0.825354	−	0.341873i	−0.0702922	−	0.997526i	$-0.522393\pi$
$491$	−18.2886	−	7.57539i	−0.825354	−	0.341873i	−0.755062	+	0.655654i	$0.772393\pi$
$492$	−1.51314	+	9.66303i	−0.0682176	+	0.435643i
$493$	−11.5447	−	27.8714i	−0.519947	−	1.25526i
$494$	5.67759	−	7.21496i	0.255447	−	0.324617i
$495$		−	0.293531i		−	0.0131932i
$496$	4.16804	−	2.14214i	0.187151	−	0.0961847i
$497$			18.7462i			0.840884i
$498$	−12.0541	−	9.48563i	−0.540159	−	0.425061i
$499$	−9.54921	−	23.0538i	−0.427481	−	1.03203i	−0.980083	−	0.198586i	$-0.936365\pi$
$499$	−9.54921	−	23.0538i	−0.427481	−	1.03203i	0.552602	−	0.833445i	$-0.313635\pi$
$500$	−19.6647	+	14.3399i	−0.879432	+	0.641300i
$501$	−5.40166	−	2.23744i	−0.241328	−	0.0999614i
$502$	3.55903	−	12.6618i	0.158847	−	0.565122i
$503$	22.6436	−	22.6436i	1.00963	−	1.00963i	0.00967595	−	0.999953i	$-0.496920\pi$
$503$	22.6436	−	22.6436i	1.00963	−	1.00963i	0.999953	−	0.00967595i	$-0.00308000\pi$
$504$	−11.1728	+	4.15521i	−0.497674	+	0.185088i
$505$	−14.7409	−	14.7409i	−0.655960	−	0.655960i
$506$	−0.191470	+	0.107449i	−0.00851189	+	0.00477668i
$507$	1.84353	−	4.45068i	0.0818741	−	0.197661i
$508$	−29.9406	+	7.24354i	−1.32840	+	0.321380i
$509$	−21.3715	+	8.85238i	−0.947276	+	0.392375i	−0.802206	−	0.597047i	$-0.796341\pi$
$509$	−21.3715	+	8.85238i	−0.947276	+	0.392375i	−0.145070	+	0.989421i	$0.546341\pi$
$510$	−23.1497	+	2.76049i	−1.02509	+	0.122237i
$511$	2.43216			0.107592
$512$	−10.9004	+	19.8288i	−0.481734	+	0.876317i
$513$	−11.8945			−0.525155
$514$	−26.5466	+	3.16556i	−1.17092	+	0.139627i
$515$	−32.1415	+	13.3134i	−1.41632	+	0.586660i
$516$	−17.7871	+	4.30324i	−0.783031	+	0.189439i
$517$	−0.149724	+	0.361465i	−0.00658484	+	0.0158972i
$518$	21.6976	−	12.1762i	0.953336	−	0.534990i
$519$	20.0789	+	20.0789i	0.881366	+	0.881366i
$520$	15.1137	−	5.62087i	0.662780	−	0.246491i
$521$	−9.76588	+	9.76588i	−0.427851	+	0.427851i	−0.887896	−	0.460045i	$-0.847833\pi$
$521$	−9.76588	+	9.76588i	−0.427851	+	0.427851i	0.460045	+	0.887896i	$0.347833\pi$
$522$	1.94162	−	6.90761i	0.0849825	−	0.302338i
$523$	−16.9370	−	7.01552i	−0.740601	−	0.306767i	−0.0197010	−	0.999806i	$-0.506271\pi$
$523$	−16.9370	−	7.01552i	−0.740601	−	0.306767i	−0.720900	+	0.693039i	$0.756271\pi$
$524$	−5.18406	+	3.78032i	−0.226467	+	0.165144i
$525$	−3.26579	−	7.88431i	−0.142531	−	0.344099i
$526$	26.1480	+	20.5763i	1.14011	+	0.897170i
$527$		−	7.55136i		−	0.328942i
$528$	0.721654	−	0.370889i	0.0314060	−	0.0161409i
$529$			21.8776i			0.951202i
$530$	2.88201	−	3.66240i	0.125187	−	0.159085i
$531$	1.55822	+	3.76187i	0.0676209	+	0.163251i
$532$	2.53109	−	16.1637i	0.109737	−	0.700785i
$533$	−10.0711	−	4.17157i	−0.436226	−	0.180691i
$534$	11.2415	+	3.15980i	0.486465	+	0.136738i
$535$	−18.7393	+	18.7393i	−0.810170	+	0.810170i
$536$	31.5744	−	29.3412i	1.36381	−	1.26735i
$537$	−24.5674	−	24.5674i	−1.06016	−	1.06016i
$538$	9.06156	+	16.1474i	0.390672	+	0.696165i
$539$	−0.455108	+	1.09873i	−0.0196029	+	0.0473256i
$540$	−17.8316	−	10.8843i	−0.767348	−	0.468386i
$541$	14.2214	−	5.89071i	0.611427	−	0.253261i	−0.0554115	−	0.998464i	$-0.517647\pi$
$541$	14.2214	−	5.89071i	0.611427	−	0.253261i	0.666839	+	0.745202i	$0.267647\pi$
$542$	−4.72451	−	39.6201i	−0.202935	−	1.70183i
$543$	2.81470			0.120791
$544$	20.3892	+	30.2274i	0.874180	+	1.29599i
$545$	23.5393			1.00831
$546$	2.78039	+	23.3166i	0.118990	+	0.997857i
$547$	−9.67342	+	4.00686i	−0.413606	+	0.171321i	−0.579776	−	0.814776i	$-0.696860\pi$
$547$	−9.67342	+	4.00686i	−0.413606	+	0.171321i	0.166170	+	0.986097i	$0.446860\pi$
$548$	15.8793	−	26.0148i	0.678331	−	1.11130i
$549$	1.55701	−	3.75895i	0.0664515	−	0.160428i
$550$	−0.160835	−	0.286603i	−0.00685803	−	0.0122208i
$551$	6.96362	+	6.96362i	0.296660	+	0.296660i
$552$	−0.151955	+	4.14490i	−0.00646765	+	0.176418i
$553$	−19.4514	+	19.4514i	−0.827157	+	0.827157i
$554$	32.1613	+	9.04006i	1.36640	+	0.384075i
$555$	10.6928	+	4.42912i	0.453886	+	0.188006i
$556$	10.2311	+	1.60209i	0.433893	+	0.0679437i
$557$	−3.08965	−	7.45908i	−0.130913	−	0.316051i	0.844808	−	0.535070i	$-0.179715\pi$
$557$	−3.08965	−	7.45908i	−0.130913	−	0.316051i	−0.975721	+	0.219018i	$0.929715\pi$
$558$	1.11070	−	1.41145i	0.0470196	−	0.0597516i
$559$		−	20.3959i		−	0.862653i
$560$	18.5854	−	21.9156i	0.785376	−	0.926102i
$561$		−	1.30744i		−	0.0552002i
$562$	−4.72562	−	3.71868i	−0.199338	−	0.156863i
$563$	10.1815	+	24.5802i	0.429097	+	1.03593i	0.979574	+	0.201082i	$0.0644457\pi$
$563$	10.1815	+	24.5802i	0.429097	+	1.03593i	−0.550477	+	0.834850i	$0.685554\pi$
$564$	4.35480	+	5.97186i	0.183370	+	0.251461i
$565$	10.0398	+	4.15862i	0.422377	+	0.174954i
$566$	−0.709521	+	2.52422i	−0.0298234	+	0.106101i
$567$	12.5713	−	12.5713i	0.527943	−	0.527943i
$568$	12.4002	+	5.67715i	0.520301	+	0.238208i
$569$	8.12862	+	8.12862i	0.340770	+	0.340770i	0.856657	−	0.515887i	$-0.172538\pi$
$569$	8.12862	+	8.12862i	0.340770	+	0.340770i	−0.515887	+	0.856657i	$0.672538\pi$
$570$	6.63696	−	3.72451i	0.277992	−	0.156002i
$571$	−7.40930	+	17.8876i	−0.310070	+	0.748574i	0.689632	+	0.724160i	$0.257772\pi$
$571$	−7.40930	+	17.8876i	−0.310070	+	0.748574i	−0.999702	+	0.0244147i	$0.992228\pi$
$572$	0.212644	+	0.878944i	0.00889107	+	0.0367505i
$573$	11.5849	−	4.79862i	0.483965	−	0.200465i
$574$	−19.2888	+	2.30010i	−0.805100	+	0.0960044i
$575$	1.68000			0.0700609
$576$	−0.635005	+	8.64889i	−0.0264585	+	0.360371i
$577$	−11.9134			−0.495959			−0.247980	−	0.968765i	$-0.579767\pi$
$577$	−11.9134			−0.495959			−0.247980	+	0.968765i	$0.579767\pi$
$578$	34.4667	−	4.10999i	1.43363	−	0.170953i
$579$	7.98890	−	3.30911i	0.332008	−	0.137522i
$580$	4.06726	+	16.8117i	0.168884	+	0.698066i
$581$	11.6582	−	28.1453i	0.483662	−	1.16766i
$582$	−17.6287	+	9.89283i	−0.730734	+	0.410071i
$583$	0.184807	+	0.184807i	0.00765391	+	0.00765391i
$584$	0.736560	−	1.60882i	0.0304791	−	0.0665734i
$585$	4.36999	−	4.36999i	0.180677	−	0.180677i
$586$	−10.5176	+	37.4179i	−0.434478	+	1.54572i
$587$	−23.6011	−	9.77588i	−0.974120	−	0.403494i	−0.161876	−	0.986811i	$-0.551754\pi$
$587$	−23.6011	−	9.77588i	−0.974120	−	0.403494i	−0.812244	+	0.583318i	$0.801754\pi$
$588$	13.2371	+	18.1524i	0.545889	+	0.748592i
$589$	0.943348	+	2.27744i	0.0388700	+	0.0938404i
$590$	−7.71357	−	6.06995i	−0.317563	−	0.249896i
$591$			6.55765i			0.269746i
$592$	−1.48333	−	18.0399i	−0.0609645	−	0.741435i
$593$			12.5549i			0.515567i	0.966203	+	0.257784i	$0.0829922\pi$
$593$			12.5549i			0.515567i	−0.966203	+	0.257784i	$0.917008\pi$
$594$	0.724508	−	0.920690i	0.0297269	−	0.0377764i
$595$	−17.7194	−	42.7784i	−0.726425	−	1.75374i
$596$	9.24819	+	1.44818i	0.378821	+	0.0593198i
$597$	11.1077	+	4.60097i	0.454609	+	0.188305i
$598$	−4.45020	−	1.25088i	−0.181982	−	0.0511524i
$599$	−6.66010	+	6.66010i	−0.272124	+	0.272124i	−0.829955	−	0.557830i	$-0.811634\pi$
$599$	−6.66010	+	6.66010i	−0.272124	+	0.272124i	0.557830	+	0.829955i	$0.311634\pi$
$600$	−6.20431	−	0.227455i	−0.253290	−	0.00928582i
$601$	27.4318	+	27.4318i	1.11896	+	1.11896i	0.991894	+	0.127071i	$0.0405577\pi$
$601$	27.4318	+	27.4318i	1.11896	+	1.11896i	0.127071	+	0.991894i	$0.459442\pi$
$602$	−17.7871	−	31.6960i	−0.724946	−	1.29183i
$603$	6.32175	−	15.2621i	0.257442	−	0.621519i
$604$	19.5026	−	31.9507i	0.793548	−	1.30005i
$605$	18.7415	−	7.76299i	0.761951	−	0.315610i
$606$	−2.61504	−	21.9299i	−0.106229	−	0.890843i
$607$	−20.3361			−0.825416			−0.412708	−	0.910863i	$-0.635417\pi$
$607$	−20.3361			−0.825416			−0.412708	+	0.910863i	$0.635417\pi$
$608$	−9.92540	−	6.56930i	−0.402528	−	0.266420i
$609$	−25.1878			−1.02066
$610$	1.16131	+	9.73886i	0.0470202	+	0.394315i
$611$	−7.61040	+	3.15233i	−0.307884	+	0.127530i
$612$	11.9276	+	7.28058i	0.482146	+	0.294300i
$613$	−13.3277	+	32.1759i	−0.538301	+	1.29957i	0.387608	+	0.921824i	$0.373301\pi$
$613$	−13.3277	+	32.1759i	−0.538301	+	1.29957i	−0.925908	+	0.377748i	$0.876699\pi$
$614$	−10.4925	−	18.6973i	−0.423442	−	0.754561i
$615$	−6.38960	−	6.38960i	−0.257654	−	0.257654i
$616$	1.09698	+	1.18047i	0.0441984	+	0.0475624i
$617$	−11.3168	+	11.3168i	−0.455599	+	0.455599i	−0.897208	−	0.441609i	$-0.854408\pi$
$617$	−11.3168	+	11.3168i	−0.455599	+	0.455599i	0.441609	+	0.897208i	$0.354408\pi$
$618$	−35.4816	−	9.97332i	−1.42728	−	0.401186i
$619$	−0.224799	−	0.0931149i	−0.00903545	−	0.00374260i	0.378161	−	0.925740i	$-0.376557\pi$
$619$	−0.224799	−	0.0931149i	−0.00903545	−	0.00374260i	−0.387197	+	0.921997i	$0.626557\pi$
$620$	−0.669808	+	4.27744i	−0.0269001	+	0.171786i
$621$	2.29186	+	5.53304i	0.0919691	+	0.222033i
$622$	−8.84916	+	11.2453i	−0.354819	+	0.450897i
$623$			23.1917i			0.929157i
$624$	16.2654	+	5.22207i	0.651137	+	0.209050i
$625$		−	14.5563i		−	0.582254i
$626$	18.6267	+	14.6577i	0.744473	+	0.585839i
$627$	0.163331	+	0.394316i	0.00652282	+	0.0157475i
$628$	−27.9035	+	20.3478i	−1.11347	+	0.811964i
$629$	−26.9469	−	11.1618i	−1.07444	−	0.445048i
$630$	2.98010	−	10.6022i	0.118730	−	0.422400i
$631$	1.15481	−	1.15481i	0.0459722	−	0.0459722i	−0.683747	−	0.729719i	$-0.739651\pi$
$631$	1.15481	−	1.15481i	0.0459722	−	0.0459722i	0.729719	+	0.683747i	$0.239651\pi$
$632$	6.97595	+	18.7573i	0.277488	+	0.746127i
$633$	13.3404	+	13.3404i	0.530233	+	0.530233i
$634$	−25.2800	+	14.1866i	−1.00400	+	0.563420i
$635$	10.8910	−	26.2931i	0.432195	−	1.04341i
$636$	4.79883	−	1.16098i	0.190286	−	0.0460360i
$637$	−23.1330	+	9.58199i	−0.916562	+	0.379652i
$638$	−0.963179	+	0.114855i	−0.0381326	+	0.00454714i
$639$	5.22690			0.206773
$640$	−8.86822	−	18.9308i	−0.350547	−	0.748304i
$641$	−14.1953			−0.560679			−0.280339	−	0.959901i	$-0.590447\pi$
$641$	−14.1953			−0.560679			−0.280339	+	0.959901i	$0.590447\pi$
$642$	−27.8784	+	3.32436i	−1.10027	+	0.131202i
$643$	33.9334	−	14.0557i	1.33820	−	0.554302i	0.405219	−	0.914219i	$-0.367195\pi$
$643$	33.9334	−	14.0557i	1.33820	−	0.554302i	0.932984	+	0.359917i	$0.117195\pi$
$644$	−8.00666	+	1.93706i	−0.315507	+	0.0763308i
$645$	6.47010	−	15.6202i	0.254760	−	0.615045i
$646$	−16.7257	+	9.38607i	−0.658063	+	0.369290i
$647$	8.73969	+	8.73969i	0.343593	+	0.343593i	0.857716	−	0.514123i	$-0.171883\pi$
$647$	8.73969	+	8.73969i	0.343593	+	0.343593i	−0.514123	+	0.857716i	$0.671883\pi$
$648$	−4.50849	−	12.1227i	−0.177110	−	0.476225i
$649$	0.389231	−	0.389231i	0.0152786	−	0.0152786i
$650$	1.87239	−	6.66130i	0.0734412	−	0.261278i
$651$	−5.82490	−	2.41275i	−0.228296	−	0.0945632i
$652$	18.6260	−	13.5825i	0.729451	−	0.531931i
$653$	16.1182	+	38.9127i	0.630753	+	1.52277i	0.838679	+	0.544627i	$0.183329\pi$
$653$	16.1182	+	38.9127i	0.630753	+	1.52277i	−0.207926	+	0.978145i	$0.566671\pi$
$654$	19.5976	+	15.4217i	0.766327	+	0.603037i
$655$		−	5.92763i		−	0.231612i
$656$	−4.32000	+	13.4557i	−0.168668	+	0.525356i
$657$		−	0.678143i		−	0.0264569i
$658$	−9.07773	+	11.5358i	−0.353887	+	0.449712i
$659$	−8.93958	−	21.5821i	−0.348237	−	0.840718i	−0.996828	−	0.0795812i	$-0.974642\pi$
$659$	−8.93958	−	21.5821i	−0.348237	−	0.840718i	0.648592	−	0.761136i	$-0.275358\pi$
$660$	−0.115970	+	0.740596i	−0.00451414	+	0.0288277i
$661$	−22.0088	−	9.11633i	−0.856042	−	0.354584i	−0.0888835	−	0.996042i	$-0.528330\pi$
$661$	−22.0088	−	9.11633i	−0.856042	−	0.354584i	−0.767158	+	0.641458i	$0.778330\pi$
$662$	−14.6052	−	4.10530i	−0.567647	−	0.159557i
$663$	19.4647	−	19.4647i	0.755947	−	0.755947i
$664$	−15.0869	−	16.2352i	−0.585484	−	0.630047i
$665$	10.6881	+	10.6881i	0.414468	+	0.414468i
$666$	−3.39500	−	6.04979i	−0.131554	−	0.234425i
$667$	1.89754	−	4.58107i	0.0734732	−	0.177380i
$668$	−7.21069	−	4.40138i	−0.278990	−	0.170294i
$669$	−1.22841	+	0.508825i	−0.0474931	+	0.0196723i
$670$	4.71515	+	39.5416i	0.182162	+	1.52763i
$671$	−0.550028			−0.0212336
$672$	29.8312	−	6.06961i	1.15076	−	0.234140i
$673$	45.0980			1.73840			0.869200	−	0.494460i	$-0.164634\pi$
$673$	45.0980			1.73840			0.869200	+	0.494460i	$0.164634\pi$
$674$	−0.541560	−	4.54156i	−0.0208601	−	0.174934i
$675$	−8.28216	+	3.43058i	−0.318780	+	0.132043i
$676$	3.62650	−	5.94123i	0.139481	−	0.228509i
$677$	13.6058	−	32.8474i	0.522915	−	1.26243i	−0.413170	−	0.910654i	$-0.635579\pi$
$677$	13.6058	−	32.8474i	0.522915	−	1.26243i	0.936085	−	0.351774i	$-0.114421\pi$
$678$	5.63410	+	10.0398i	0.216376	+	0.385576i
$679$	−28.3892	−	28.3892i	−1.08948	−	1.08948i
$680$	−33.6631	−	1.23412i	−1.29092	−	0.0473263i
$681$	15.0117	−	15.0117i	0.575248	−	0.575248i
$682$	−0.233745	−	0.0657022i	−0.00895057	−	0.00251587i
$683$	18.8141	+	7.79305i	0.719901	+	0.298193i	0.712395	−	0.701779i	$-0.247611\pi$
$683$	18.8141	+	7.79305i	0.719901	+	0.298193i	0.00750651	+	0.999972i	$0.497611\pi$
$684$	−4.50682	−	0.705727i	−0.172323	−	0.0269841i
$685$	10.7757	+	26.0148i	0.411718	+	0.993974i
$686$	−3.79216	+	4.81900i	−0.144785	+	0.183990i
$687$		−	6.52547i		−	0.248962i
$688$	−26.3528	+	2.16686i	−1.00469	+	0.0826108i
$689$			5.50267i			0.209635i
$690$	−3.01138	−	2.36971i	−0.114641	−	0.0902132i
$691$	12.6322	+	30.4967i	0.480550	+	1.16015i	0.959348	+	0.282226i	$0.0910726\pi$
$691$	12.6322	+	30.4967i	0.480550	+	1.16015i	−0.478798	+	0.877925i	$0.658927\pi$
$692$	24.1742	+	33.1508i	0.918967	+	1.26020i
$693$	0.570601	+	0.236351i	0.0216753	+	0.00897822i
$694$	9.82705	−	34.9612i	0.373030	−	1.32711i
$695$	−6.76521	+	6.76521i	−0.256619	+	0.256619i
$696$	−7.62793	+	16.6612i	−0.289136	+	0.631540i
$697$	16.1023	+	16.1023i	0.609920	+	0.609920i
$698$	16.7881	−	9.42108i	0.635437	−	0.356593i
$699$	−12.5790	+	30.3684i	−0.475782	+	1.14864i
$700$	−2.89949	−	11.9848i	−0.109591	−	0.452983i
$701$	0.915341	−	0.379146i	0.0345719	−	0.0143202i	−0.365330	−	0.930878i	$-0.619044\pi$
$701$	0.915341	−	0.379146i	0.0345719	−	0.0143202i	0.399902	+	0.916558i	$0.369044\pi$
$702$	24.4931	−	2.92069i	0.924434	−	0.110234i
$703$	9.52138			0.359106
$704$	1.11306	−	0.368129i	0.0419501	−	0.0138744i
$705$	−6.82843			−0.257173
$706$	12.1802	−	1.45243i	0.458407	−	0.0546629i
$707$	40.5244	−	16.7858i	1.52408	−	0.631293i
$708$	−2.44521	−	10.1071i	−0.0918965	−	0.379846i
$709$	−18.9677	+	45.7920i	−0.712346	+	1.71975i	−0.0182911	+	0.999833i	$0.505823\pi$
$709$	−18.9677	+	45.7920i	−0.712346	+	1.71975i	−0.694055	+	0.719922i	$0.744177\pi$
$710$	−10.9879	+	6.16619i	−0.412370	+	0.231413i
$711$	5.42350	+	5.42350i	0.203397	+	0.203397i
$712$	15.3408	+	7.02343i	0.574921	+	0.263214i
$713$	0.877646	−	0.877646i	0.0328681	−	0.0328681i
$714$	13.2739	−	47.2239i	0.496764	−	1.76731i
$715$	−0.771869	−	0.319719i	−0.0288663	−	0.0119568i
$716$	−29.5783	−	40.5615i	−1.10539	−	1.51585i
$717$	8.39128	+	20.2583i	0.313378	+	0.756561i
$718$	−21.4235	−	16.8586i	−0.799520	−	0.629157i
$719$		−	12.7931i		−	0.477102i	−0.971130	−	0.238551i	$-0.923328\pi$
$719$		−	12.7931i		−	0.477102i	0.971130	−	0.238551i	$-0.0766724\pi$
$720$	−6.11058	−	5.18205i	−0.227728	−	0.193123i
$721$		−	73.2004i		−	2.72612i
$722$	−12.7448	+	16.1958i	−0.474312	+	0.602746i
$723$	0.165975	+	0.400700i	0.00617269	+	0.0149022i
$724$	4.01797	+	0.629177i	0.149327	+	0.0233832i
$725$	6.85720	+	2.84035i	0.254670	+	0.105488i
$726$	20.6891	+	5.81539i	0.767845	+	0.215829i
$727$	−0.466154	+	0.466154i	−0.0172887	+	0.0172887i	−0.715698	−	0.698410i	$-0.753891\pi$
$727$	−0.466154	+	0.466154i	−0.0172887	+	0.0172887i	0.698410	+	0.715698i	$0.253891\pi$
$728$	−1.24301	+	33.9058i	−0.0460692	+	1.25663i
$729$	−20.1043	−	20.1043i	−0.744603	−	0.744603i
$730$	0.800008	+	1.42559i	0.0296096	+	0.0527634i
$731$	−16.3052	+	39.3642i	−0.603069	+	1.45594i
$732$	−5.41354	+	8.86890i	−0.200090	+	0.327804i
$733$	34.0271	−	14.0945i	1.25682	−	0.520591i	0.347887	−	0.937536i	$-0.386899\pi$
$733$	34.0271	−	14.0945i	1.25682	−	0.520591i	0.908932	+	0.416945i	$0.136899\pi$
$734$	4.85276	+	40.6956i	0.179119	+	1.50210i
$735$	−20.7561			−0.765599
$736$	−1.14343	+	5.88285i	−0.0421475	+	0.216845i
$737$	−2.23322			−0.0822616
$738$	0.641323	+	5.37818i	0.0236074	+	0.197974i
$739$	8.25825	−	3.42068i	0.303785	−	0.125832i	−0.225584	−	0.974224i	$-0.572429\pi$
$739$	8.25825	−	3.42068i	0.303785	−	0.125832i	0.529368	+	0.848392i	$0.322429\pi$
$740$	14.2739	+	8.71274i	0.524720	+	0.320287i
$741$	−3.43882	+	8.30205i	−0.126328	+	0.304984i
$742$	4.79883	+	8.55136i	0.176170	+	0.313930i
$743$	−32.4060	−	32.4060i	−1.18886	−	1.18886i	−0.977383	−	0.211477i	$-0.932173\pi$
$743$	−32.4060	−	32.4060i	−1.18886	−	1.18886i	−0.211477	−	0.977383i	$-0.567827\pi$
$744$	−3.36000	+	3.12235i	−0.123184	+	0.114471i
$745$	−6.11529	+	6.11529i	−0.224047	+	0.224047i
$746$	8.19877	+	2.30455i	0.300178	+	0.0843755i
$747$	−7.84757	−	3.25057i	−0.287127	−	0.118932i
$748$	0.292255	−	1.86636i	0.0106859	−	0.0682410i
$749$	−21.3388	−	51.5165i	−0.779704	−	1.88237i
$750$	14.7312	−	18.7201i	0.537906	−	0.683561i
$751$			21.5108i			0.784939i	0.919765	+	0.392470i	$0.128379\pi$
$751$			21.5108i			0.784939i	−0.919765	+	0.392470i	$0.871621\pi$
$752$	4.88155	+	9.49824i	0.178012	+	0.346365i
$753$			12.8732i			0.469126i
$754$	−16.0494	−	12.6296i	−0.584484	−	0.459941i
$755$	13.2344	+	31.9507i	0.481649	+	1.16280i
$756$	35.5162	−	25.8991i	1.29171	−	0.941941i
$757$	−17.3649	−	7.19276i	−0.631137	−	0.261425i	0.0440993	−	0.999027i	$-0.485958\pi$
$757$	−17.3649	−	7.19276i	−0.631137	−	0.261425i	−0.675236	+	0.737602i	$0.735958\pi$
$758$	−8.55274	+	30.4276i	−0.310649	+	1.10518i
$759$	0.151955	−	0.151955i	0.00551563	−	0.00551563i
$760$	10.3068	−	3.83314i	0.373866	−	0.139043i
$761$	−37.8574	−	37.8574i	−1.37233	−	1.37233i	−0.856977	−	0.515354i	$-0.827660\pi$
$761$	−37.8574	−	37.8574i	−1.37233	−	1.37233i	−0.515354	−	0.856977i	$-0.672340\pi$
$762$	26.2931	−	14.7551i	0.952500	−	0.534521i
$763$	−18.9538	+	45.7585i	−0.686174	+	1.65657i
$764$	17.6100	−	4.26040i	0.637107	−	0.154136i
$765$	−11.9276	+	4.94059i	−0.431245	+	0.178627i
$766$	42.9237	−	5.11845i	1.55090	−	0.184937i
$767$	11.5894			0.418471
$768$	5.01922	−	21.5708i	0.181116	−	0.778368i
$769$	3.07370			0.110840			0.0554201	−	0.998463i	$-0.482350\pi$
$769$	3.07370			0.110840			0.0554201	+	0.998463i	$0.482350\pi$
$770$	−1.47834	+	0.176285i	−0.0532756	+	0.00635286i
$771$	24.1753	−	10.0137i	0.870651	−	0.360635i
$772$	12.1438	−	2.93796i	0.437065	−	0.105740i
$773$	−6.55831	+	15.8332i	−0.235886	+	0.569479i	−0.996850	−	0.0793155i	$-0.974727\pi$
$773$	−6.55831	+	15.8332i	−0.235886	+	0.569479i	0.760964	+	0.648795i	$0.224727\pi$
$774$	−8.83759	+	4.95945i	−0.317660	+	0.178264i
$775$	1.31371	+	1.31371i	0.0471898	+	0.0471898i
$776$	−27.3763	+	10.1814i	−0.982750	+	0.365490i
$777$	−17.2197	+	17.2197i	−0.617753	+	0.617753i
$778$	7.06634	−	25.1395i	0.253341	−	0.901296i
$779$	−6.86794	−	2.84479i	−0.246070	−	0.101925i
$780$	−12.7523	+	9.29920i	−0.456604	+	0.332965i
$781$	−0.270406	−	0.652818i	−0.00967589	−	0.0233597i
$782$	7.58892	+	5.97186i	0.271379	+	0.213553i
$783$			26.4588i			0.945561i
$784$	14.8382	+	28.8714i	0.529937	+	1.03112i
$785$		−	31.9058i		−	1.13877i
$786$	3.88347	−	4.93504i	0.138519	−	0.176027i
$787$	−6.77706	−	16.3613i	−0.241576	−	0.583216i	0.755864	−	0.654729i	$-0.227217\pi$
$787$	−6.77706	−	16.3613i	−0.241576	−	0.583216i	−0.997440	+	0.0715129i	$0.977217\pi$
$788$	−1.46585	+	9.36100i	−0.0522186	+	0.333472i
$789$	−30.0877	−	12.4627i	−1.07115	−	0.443685i
$790$	−17.7994	−	5.00313i	−0.633274	−	0.178004i
$791$	−16.1680	+	16.1680i	−0.574869	+	0.574869i
$792$	0.329142	−	0.305863i	0.0116956	−	0.0108684i
$793$	−8.18862	−	8.18862i	−0.290786	−	0.290786i
$794$	−12.9447	−	23.0671i	−0.459390	−	0.818619i
$795$	−1.74559	+	4.21422i	−0.0619096	+	0.149463i
$796$	14.8278	+	9.05080i	0.525556	+	0.320797i
$797$	−32.4476	+	13.4402i	−1.14935	+	0.476077i	−0.874316	−	0.485356i	$-0.838690\pi$
$797$	−32.4476	+	13.4402i	−1.14935	+	0.476077i	−0.275036	+	0.961434i	$0.588690\pi$
$798$	1.89608	+	15.9007i	0.0671205	+	0.562878i
$799$	17.2082			0.608783
$800$	−8.80577	−	1.71155i	−0.311331	−	0.0605126i
$801$	6.46640			0.228479
$802$	−1.84203	−	15.4474i	−0.0650445	−	0.545468i
$803$	−0.0846974	+	0.0350828i	−0.00298891	+	0.00123805i
$804$	−21.9800	+	36.0094i	−0.775174	+	1.26995i
$805$	2.91245	−	7.03127i	0.102650	−	0.247820i
$806$	−2.50176	−	4.45807i	−0.0881209	−	0.157029i
$807$	−12.8150	−	12.8150i	−0.451109	−	0.451109i
$808$	1.16909	−	31.8894i	0.0411285	−	1.12187i
$809$	11.2704	−	11.2704i	0.396246	−	0.396246i	−0.480661	−	0.876907i	$-0.659603\pi$
$809$	11.2704	−	11.2704i	0.396246	−	0.396246i	0.876907	+	0.480661i	$0.159603\pi$
$810$	11.5036	+	3.23348i	0.404195	+	0.113613i
$811$	−16.3328	−	6.76529i	−0.573524	−	0.237561i	0.0770206	−	0.997029i	$-0.475459\pi$
$811$	−16.3328	−	6.76529i	−0.573524	−	0.237561i	−0.650545	+	0.759468i	$0.725459\pi$
$812$	−35.9555	−	5.63029i	−1.26179	−	0.197585i
$813$	14.9452	+	36.0809i	0.524150	+	1.26541i
$814$	−0.579959	+	0.737000i	−0.0203275	+	0.0258318i
$815$			21.2976i			0.746023i
$816$	−27.2176	−	23.0818i	−0.952808	−	0.808023i
$817$		−	13.9089i		−	0.486611i
$818$	1.82102	+	1.43300i	0.0636705	+	0.0501035i
$819$	4.97620	+	12.0136i	0.173882	+	0.419789i
$820$	−7.69284	−	10.5494i	−0.268646	−	0.368401i
$821$	29.5124	+	12.2244i	1.02999	+	0.426636i	0.832709	−	0.553711i	$-0.186789\pi$
$821$	29.5124	+	12.2244i	1.02999	+	0.426636i	0.197281	+	0.980347i	$0.436789\pi$
$822$	−8.07225	+	28.7182i	−0.281552	+	1.00166i
$823$	1.00381	−	1.00381i	0.0349906	−	0.0349906i	−0.689395	−	0.724386i	$-0.742124\pi$
$823$	1.00381	−	1.00381i	0.0349906	−	0.0349906i	0.724386	+	0.689395i	$0.242124\pi$
$824$	−48.4204	−	22.1681i	−1.68680	−	0.772264i
$825$	0.227455	+	0.227455i	0.00791898	+	0.00791898i
$826$	18.0105	−	10.1071i	0.626664	−	0.351669i
$827$	15.7060	−	37.9176i	0.546151	−	1.31852i	−0.374170	−	0.927360i	$-0.622072\pi$
$827$	15.7060	−	37.9176i	0.546151	−	1.31852i	0.920321	−	0.391165i	$-0.127928\pi$
$828$	0.540098	+	2.23245i	0.0187697	+	0.0775829i
$829$	31.9806	−	13.2468i	1.11073	−	0.460081i	0.249543	−	0.968364i	$-0.419720\pi$
$829$	31.9806	−	13.2468i	1.11073	−	0.460081i	0.861190	+	0.508283i	$0.169720\pi$
$830$	20.3318	−	2.42447i	0.705728	−	0.0841547i
$831$	−32.6984			−1.13430
$832$	22.0515	+	11.0903i	0.764496	+	0.384487i
$833$	52.3070			1.81233
$834$	−10.0646	+	1.20015i	−0.348507	+	0.0415579i
$835$	7.21069	−	2.98677i	0.249536	−	0.103361i
$836$	0.145012	+	0.599394i	0.00501534	+	0.0207305i
$837$	−2.53450	+	6.11882i	−0.0876051	+	0.211498i
$838$	42.7652	−	23.9989i	1.47730	−	0.829027i
$839$	3.42599	+	3.42599i	0.118278	+	0.118278i	0.763768	−	0.645490i	$-0.223347\pi$
$839$	3.42599	+	3.42599i	0.118278	+	0.118278i	−0.645490	+	0.763768i	$0.723347\pi$
$840$	−11.7077	+	25.5724i	−0.403956	+	0.882333i
$841$	−5.01582	+	5.01582i	−0.172959	+	0.172959i
$842$	−9.34602	+	33.2498i	−0.322085	+	1.14586i
$843$	5.43764	+	2.25234i	0.187282	+	0.0775749i
$844$	16.0613	+	22.0253i	0.552853	+	0.758143i
$845$	2.46094	+	5.94123i	0.0846588	+	0.204384i
$846$	3.21645	+	2.53109i	0.110584	+	0.0870205i
$847$			42.6827i			1.46660i
$848$	7.10981	−	0.584604i	0.244152	−	0.0200754i
$849$		−	2.56638i		−	0.0880779i
$850$	−8.93901	+	11.3595i	−0.306606	+	0.389628i
$851$	−1.83460	−	4.42912i	−0.0628893	−	0.151828i
$852$	−13.1878	−	2.06508i	−0.451805	−	0.0707485i
$853$	−33.4739	−	13.8653i	−1.14612	−	0.474740i	−0.272892	−	0.962045i	$-0.587980\pi$
$853$	−33.4739	−	13.8653i	−1.14612	−	0.474740i	−0.873232	+	0.487305i	$0.837980\pi$
$854$	−19.8666	−	5.58421i	−0.679823	−	0.191088i
$855$	2.98010	−	2.98010i	0.101917	−	0.101917i
$856$	−40.5393	−	1.48621i	−1.38560	−	0.0507975i
$857$	19.6667	+	19.6667i	0.671800	+	0.671800i	0.958131	−	0.286331i	$-0.0924356\pi$
$857$	19.6667	+	19.6667i	0.671800	+	0.671800i	−0.286331	+	0.958131i	$0.592436\pi$
$858$	−0.433155	−	0.771869i	−0.0147877	−	0.0263512i
$859$	15.0121	−	36.2424i	0.512207	−	1.23658i	−0.430390	−	0.902643i	$-0.641624\pi$
$859$	15.0121	−	36.2424i	0.512207	−	1.23658i	0.942597	−	0.333933i	$-0.108376\pi$
$860$	12.7276	−	20.8515i	0.434009	−	0.711029i
$861$	17.5658	−	7.27598i	0.598640	−	0.247965i
$862$	−0.749491	−	6.28529i	−0.0255278	−	0.214078i
$863$	28.3727			0.965819			0.482909	−	0.875670i	$-0.339580\pi$
$863$	28.3727			0.965819			0.482909	+	0.875670i	$0.339580\pi$
$864$	−6.37588	−	31.3365i	−0.216912	−	1.06609i
$865$	−37.9058			−1.28883
$866$	−0.241459	−	2.02489i	−0.00820510	−	0.0688085i
$867$	−31.3878	+	13.0013i	−1.06599	+	0.441546i
$868$	−7.77568	−	4.74624i	−0.263924	−	0.161098i
$869$	0.396796	−	0.957951i	0.0134604	−	0.0324963i
$870$	−8.28501	−	14.7636i	−0.280888	−	0.500534i
$871$	−33.2473	−	33.2473i	−1.12654	−	1.12654i
$872$	24.5282	+	26.3951i	0.830630	+	0.893851i
$873$	−7.91558	+	7.91558i	−0.267902	+	0.267902i
$874$	−3.03480	−	0.853036i	−0.102654	−	0.0288544i
$875$	43.7096	+	18.1051i	1.47765	+	0.612064i
$876$	−0.267926	+	1.71099i	−0.00905238	+	0.0578092i
$877$	−10.1396	−	24.4793i	−0.342391	−	0.826606i	−0.997473	−	0.0710476i	$-0.977366\pi$
$877$	−10.1396	−	24.4793i	−0.342391	−	0.826606i	0.655082	−	0.755558i	$-0.272634\pi$
$878$	−1.05700	+	1.34321i	−0.0356720	+	0.0453312i
$879$		−	38.0427i		−	1.28315i
$880$	−0.331094	+	1.03127i	−0.0111612	+	0.0347642i
$881$			9.35846i			0.315295i	0.987495	+	0.157647i	$0.0503909\pi$
$881$			9.35846i			0.315295i	−0.987495	+	0.157647i	$0.949609\pi$
$882$	9.77691	+	7.69363i	0.329206	+	0.259058i
$883$	7.09207	+	17.1218i	0.238667	+	0.576193i	0.997145	−	0.0755050i	$-0.0240569\pi$
$883$	7.09207	+	17.1218i	0.238667	+	0.576193i	−0.758478	+	0.651698i	$0.774057\pi$
$884$	32.1367	−	23.4348i	1.08088	−	0.788196i
$885$	8.87579	+	3.67647i	0.298356	+	0.123583i
$886$	−4.68913	+	16.6823i	−0.157535	+	0.560452i
$887$	30.8931	−	30.8931i	1.03729	−	1.03729i	0.0380100	−	0.999277i	$-0.487898\pi$
$887$	30.8931	−	30.8931i	1.03729	−	1.03729i	0.999277	−	0.0380100i	$-0.0121019\pi$
$888$	6.17559	+	16.6053i	0.207239	+	0.557237i
$889$	42.3424	+	42.3424i	1.42012	+	1.42012i
$890$	−13.5936	+	7.62844i	−0.455660	+	0.255706i
$891$	−0.256446	+	0.619115i	−0.00859126	+	0.0207411i
$892$	−1.86729	+	0.451754i	−0.0625214	+	0.0151259i
$893$	−5.18989	+	2.14972i	−0.173673	+	0.0719378i
$894$	−9.09770	+	1.08486i	−0.304272	+	0.0362831i
$895$	46.3794			1.55029
$896$	43.9406	−	1.99610i	1.46795	−	0.0666849i
$897$	4.52452			0.151069
$898$	34.4849	−	4.11216i	1.15078	−	0.137225i
$899$	5.06608	−	2.09844i	0.168963	−	0.0699868i
$900$	−3.34165	+	0.808448i	−0.111388	+	0.0269483i
$901$	4.39903	−	10.6202i	0.146553	−	0.353810i
$902$	0.638535	−	0.358331i	0.0212609	−	0.0119311i
$903$	25.1547	+	25.1547i	0.837096	+	0.837096i
$904$	5.79843	+	15.5912i	0.192853	+	0.518554i
$905$	−2.65685	+	2.65685i	−0.0883168	+	0.0883168i
$906$	−9.91412	+	35.2709i	−0.329375	+	1.17180i
$907$	12.6479	+	5.23891i	0.419965	+	0.173955i	0.582651	−	0.812723i	$-0.302016\pi$
$907$	12.6479	+	5.23891i	0.419965	+	0.173955i	−0.162686	+	0.986678i	$0.552016\pi$
$908$	24.7846	−	18.0735i	0.822507	−	0.599789i
$909$	−4.68027	−	11.2992i	−0.155235	−	0.374770i
$910$	−24.6334	−	19.3845i	−0.816590	−	0.642590i
$911$		−	35.3498i		−	1.17119i	−0.810604	−	0.585595i	$-0.800861\pi$
$911$		−	35.3498i		−	1.17119i	0.810604	−	0.585595i	$-0.199139\pi$
$912$	11.0921	+	3.56118i	0.367298	+	0.117922i
$913$			1.14829i			0.0380030i
$914$	−17.5237	+	22.2687i	−0.579632	+	0.736584i
$915$	−3.67362	−	8.86890i	−0.121446	−	0.293197i
$916$	1.45865	−	9.31507i	0.0481953	−	0.307779i
$917$	11.5228	+	4.77292i	0.380518	+	0.157616i
$918$	−49.6068	−	13.9437i	−1.63727	−	0.460211i
$919$	−30.0652	+	30.0652i	−0.991759	+	0.991759i	−0.999966	−	0.00820720i	$-0.997388\pi$
$919$	−30.0652	+	30.0652i	−0.991759	+	0.991759i	0.00820720	+	0.999966i	$0.497388\pi$
$920$	−3.76901	−	4.05588i	−0.124261	−	0.133718i
$921$	14.8386	+	14.8386i	0.488949	+	0.488949i
$922$	21.3343	+	38.0171i	0.702608	+	1.25203i
$923$	5.69321	−	13.7446i	0.187394	−	0.452410i
$924$	−1.34628	−	0.821763i	−0.0442893	−	0.0270340i
$925$	6.62975	−	2.74613i	0.217985	−	0.0902923i
$926$	−2.48147	−	20.8098i	−0.0815462	−	0.683853i
$927$	−20.4100			−0.670352
$928$	−14.6131	+	22.0786i	−0.479700	+	0.724767i
$929$	7.62858			0.250286			0.125143	−	0.992139i	$-0.460061\pi$
$929$	7.62858			0.250286			0.125143	+	0.992139i	$0.460061\pi$
$930$	−0.501765	−	4.20784i	−0.0164535	−	0.137980i
$931$	−15.7755	+	6.53442i	−0.517020	+	0.214157i
$932$	−24.7448	+	40.5389i	−0.810542	+	1.32790i
$933$	5.35979	−	12.9397i	0.175472	−	0.423626i
$934$	−9.82974	−	17.5163i	−0.321639	−	0.573151i
$935$	1.23412	+	1.23412i	0.0403600	+	0.0403600i
$936$	9.45373	+	0.346582i	0.309005	+	0.0113284i
$937$	−21.2074	+	21.2074i	−0.692817	+	0.692817i	−0.962851	−	0.270034i	$-0.912965\pi$
$937$	−21.2074	+	21.2074i	−0.692817	+	0.692817i	0.270034	+	0.962851i	$0.412965\pi$
$938$	−80.6623	−	22.6729i	−2.63372	−	0.740298i
$939$	−21.4332	−	8.87793i	−0.699446	−	0.289720i
$940$	−9.74754	−	1.52637i	−0.317930	−	0.0497848i
$941$	13.0249	+	31.4448i	0.424599	+	1.02507i	0.980974	+	0.194141i	$0.0621918\pi$
$941$	13.0249	+	31.4448i	0.424599	+	1.02507i	−0.556375	+	0.830931i	$0.687808\pi$
$942$	20.9030	−	26.5631i	0.681056	−	0.865472i
$943$			3.74294i			0.121887i
$944$	−1.23127	−	14.9743i	−0.0400743	−	0.487373i
$945$			40.6104i			1.32106i
$946$	1.07662	+	0.847209i	0.0350038	+	0.0275451i
$947$	−18.6229	−	44.9596i	−0.605162	−	1.46099i	−0.868205	−	0.496206i	$-0.834726\pi$
$947$	−18.6229	−	44.9596i	−0.605162	−	1.46099i	0.263043	−	0.964784i	$-0.415274\pi$
$948$	−11.5411	−	15.8266i	−0.374836	−	0.514023i
$949$	−1.78324	−	0.738644i	−0.0578866	−	0.0239774i
$950$	1.27687	−	4.54266i	0.0414272	−	0.147383i
$951$	20.0628	−	20.0628i	0.650582	−	0.650582i
$952$	29.5045	−	64.4447i	0.956246	−	2.08866i
$953$	−33.7784	−	33.7784i	−1.09419	−	1.09419i	−0.995076	−	0.0991142i	$-0.968399\pi$
$953$	−33.7784	−	33.7784i	−1.09419	−	1.09419i	−0.0991142	−	0.995076i	$-0.531601\pi$
$954$	2.38432	−	1.33803i	0.0771952	−	0.0433202i
$955$	−6.40569	+	15.4647i	−0.207283	+	0.500426i
$956$	7.45010	+	30.7944i	0.240954	+	0.995961i
$957$	0.877140	−	0.363323i	0.0283539	−	0.0117446i
$958$	−45.4599	+	5.42088i	−1.46874	+	0.175141i
$959$	−59.2472			−1.91319
$960$	13.3700	+	15.4888i	0.431514	+	0.499899i
$961$	−29.6274			−0.955723
$962$	−19.6064	+	2.33797i	−0.632136	+	0.0753792i
$963$	−14.3640	+	5.94977i	−0.462874	+	0.191729i
$964$	0.147359	+	0.609098i	0.00474613	+	0.0196177i
$965$	−4.41735	+	10.6644i	−0.142199	+	0.343300i
$966$	7.03127	−	3.94579i	0.226228	−	0.126954i
$967$	19.3234	+	19.3234i	0.621399	+	0.621399i	0.945889	−	0.324490i	$-0.105193\pi$
$967$	19.3234	+	19.3234i	0.621399	+	0.621399i	−0.324490	+	0.945889i	$0.605193\pi$
$968$	28.2337	+	12.9261i	0.907464	+	0.415461i
$969$	13.2739	−	13.2739i	0.426420	−	0.426420i
$970$	7.30205	−	25.9781i	0.234455	−	0.834107i
$971$	−52.9160	−	21.9185i	−1.69816	−	0.703399i	−0.698234	−	0.715869i	$-0.746031\pi$
$971$	−52.9160	−	21.9185i	−1.69816	−	0.703399i	−0.999922	+	0.0124699i	$0.996031\pi$
$972$	−12.5258	−	17.1770i	−0.401766	−	0.550953i
$973$	−7.70369	−	18.5983i	−0.246969	−	0.596236i
$974$	2.97806	+	2.34349i	0.0954233	+	0.0750903i
$975$			6.77254i			0.216895i
$976$	−9.71028	+	11.4502i	−0.310818	+	0.366512i
$977$			12.2792i			0.392848i	0.980519	+	0.196424i	$0.0629329\pi$
$977$			12.2792i			0.392848i	−0.980519	+	0.196424i	$0.937067\pi$
$978$	−13.9531	+	17.7313i	−0.446170	+	0.566984i
$979$	−0.334530	−	0.807628i	−0.0106916	−	0.0258119i
$980$	−29.6292	−	4.63965i	−0.946469	−	0.148208i
$981$	12.7586	+	5.28477i	0.407349	+	0.168730i
$982$	26.9506	+	7.57539i	0.860028	+	0.241741i
$983$	−14.1052	+	14.1052i	−0.449887	+	0.449887i	−0.895317	−	0.445430i	$-0.853051\pi$
$983$	−14.1052	+	14.1052i	−0.449887	+	0.449887i	0.445430	+	0.895317i	$0.353051\pi$
$984$	0.506757	−	13.8228i	0.0161548	−	0.440656i
$985$	−6.18989	−	6.18989i	−0.197226	−	0.197226i
$986$	20.8789	+	37.2056i	0.664920	+	1.18487i
$987$	5.49824	−	13.2739i	0.175011	−	0.422513i
$988$	−6.76468	+	11.0824i	−0.215213	+	0.352579i
$989$	−6.47010	+	2.68000i	−0.205737	+	0.0852191i
$990$	0.0491524	+	0.412196i	0.00156217	+	0.0131004i
$991$	39.8015			1.26434			0.632169	−	0.774831i	$-0.282165\pi$
$991$	39.8015			1.26434			0.632169	+	0.774831i	$0.282165\pi$
$992$	−5.49433	+	3.70607i	−0.174445	+	0.117668i
$993$	14.8491			0.471222
$994$	−3.13910	−	26.3247i	−0.0995661	−	0.834968i
$995$	−14.8278	+	6.14186i	−0.470071	+	0.194710i
$996$	18.5156	+	11.3018i	0.586689	+	0.358113i
$997$	2.57111	−	6.20720i	0.0814278	−	0.196584i	−0.877922	−	0.478803i	$-0.841071\pi$
$997$	2.57111	−	6.20720i	0.0814278	−	0.196584i	0.959350	+	0.282219i	$0.0910706\pi$
$998$	17.2700	+	30.7746i	0.546673	+	0.974154i
$999$	18.0886	+	18.0886i	0.572299	+	0.572299i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	32.2.g.b.21.1	✓	8
3.2	odd	2		288.2.v.b.181.2		8
4.3	odd	2		128.2.g.b.49.1		8
5.2	odd	4		800.2.ba.c.149.1		8
5.3	odd	4		800.2.ba.d.149.2		8
5.4	even	2		800.2.y.b.501.2		8
8.3	odd	2		256.2.g.c.97.2		8
8.5	even	2		256.2.g.d.97.1		8
12.11	even	2		1152.2.v.b.433.2		8
16.3	odd	4		512.2.g.f.449.1		8
16.5	even	4		512.2.g.e.449.1		8
16.11	odd	4		512.2.g.g.449.2		8
16.13	even	4		512.2.g.h.449.2		8
32.3	odd	8		128.2.g.b.81.1		8
32.5	even	8		512.2.g.e.65.1		8
32.11	odd	8		512.2.g.f.65.1		8
32.13	even	8		256.2.g.d.161.1		8
32.19	odd	8		256.2.g.c.161.2		8
32.21	even	8		512.2.g.h.65.2		8
32.27	odd	8		512.2.g.g.65.2		8
32.29	even	8	inner	32.2.g.b.29.1	yes	8
64.3	odd	16		4096.2.a.q.1.6		8
64.29	even	16		4096.2.a.k.1.6		8
64.35	odd	16		4096.2.a.q.1.3		8
64.61	even	16		4096.2.a.k.1.3		8
96.29	odd	8		288.2.v.b.253.2		8
96.35	even	8		1152.2.v.b.721.2		8
160.29	even	8		800.2.y.b.701.2		8
160.93	odd	8		800.2.ba.c.349.1		8
160.157	odd	8		800.2.ba.d.349.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.2.g.b.21.1	✓	8	1.1	even	1	trivial
32.2.g.b.29.1	yes	8	32.29	even	8	inner
128.2.g.b.49.1		8	4.3	odd	2
128.2.g.b.81.1		8	32.3	odd	8
256.2.g.c.97.2		8	8.3	odd	2
256.2.g.c.161.2		8	32.19	odd	8
256.2.g.d.97.1		8	8.5	even	2
256.2.g.d.161.1		8	32.13	even	8
288.2.v.b.181.2		8	3.2	odd	2
288.2.v.b.253.2		8	96.29	odd	8
512.2.g.e.65.1		8	32.5	even	8
512.2.g.e.449.1		8	16.5	even	4
512.2.g.f.65.1		8	32.11	odd	8
512.2.g.f.449.1		8	16.3	odd	4
512.2.g.g.65.2		8	32.27	odd	8
512.2.g.g.449.2		8	16.11	odd	4
512.2.g.h.65.2		8	32.21	even	8
512.2.g.h.449.2		8	16.13	even	4
800.2.y.b.501.2		8	5.4	even	2
800.2.y.b.701.2		8	160.29	even	8
800.2.ba.c.149.1		8	5.2	odd	4
800.2.ba.c.349.1		8	160.93	odd	8
800.2.ba.d.149.2		8	5.3	odd	4
800.2.ba.d.349.2		8	160.157	odd	8
1152.2.v.b.433.2		8	12.11	even	2
1152.2.v.b.721.2		8	96.35	even	8
4096.2.a.k.1.3		8	64.61	even	16
4096.2.a.k.1.6		8	64.29	even	16
4096.2.a.q.1.3		8	64.35	odd	16
4096.2.a.q.1.6		8	64.3	odd	16

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:	\( N \)	\(=\)	\( 32 = 2^{5} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	32.g (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40426 + 0.167452i) q^{2} +(1.27882 - 0.529706i) q^{3} +(1.94392 - 0.470294i) q^{4} +(-0.707107 + 1.70711i) q^{5} +(-1.70711 + 0.957989i) q^{6} +(-2.74912 - 2.74912i) q^{7} +(-2.65103 + 0.985930i) q^{8} +(-0.766519 + 0.766519i) q^{9} +(0.707107 - 2.51564i) q^{10} +(0.135390 + 0.0560803i) q^{11} +(2.23681 - 1.63113i) q^{12} +(1.18073 + 2.85054i) q^{13} +(4.32083 + 3.40014i) q^{14} +2.55765i q^{15} +(3.55765 - 1.82843i) q^{16} -6.44549i q^{17} +(0.948041 - 1.20475i) q^{18} +(0.805198 + 1.94392i) q^{19} +(-0.571717 + 3.65103i) q^{20} +(-4.97186 - 2.05941i) q^{21} +(-0.199514 - 0.0560803i) q^{22} +(0.749118 - 0.749118i) q^{23} +(-2.86794 + 2.66510i) q^{24} +(1.12132 + 1.12132i) q^{25} +(-2.13539 - 3.80520i) q^{26} +(-2.16333 + 5.22274i) q^{27} +(-6.63696 - 4.05117i) q^{28} +(4.32417 - 1.79113i) q^{29} +(-0.428283 - 3.59161i) q^{30} +1.17157 q^{31} +(-4.68971 + 3.16333i) q^{32} +0.202846 q^{33} +(1.07931 + 9.05117i) q^{34} +(6.63696 - 2.74912i) q^{35} +(-1.12956 + 1.85054i) q^{36} +(1.73172 - 4.18073i) q^{37} +(-1.45622 - 2.59495i) q^{38} +(3.01990 + 3.01990i) q^{39} +(0.191470 - 5.22274i) q^{40} +(-2.49824 + 2.49824i) q^{41} +(7.32666 + 2.05941i) q^{42} +(-6.10725 - 2.52971i) q^{43} +(0.289561 + 0.0453426i) q^{44} +(-0.766519 - 1.85054i) q^{45} +(-0.926518 + 1.17740i) q^{46} +2.66981i q^{47} +(3.58107 - 4.22274i) q^{48} +8.11529i q^{49} +(-1.76240 - 1.38686i) q^{50} +(-3.41421 - 8.24264i) q^{51} +(3.63584 + 4.98593i) q^{52} +(1.64769 + 0.682497i) q^{53} +(2.16333 - 7.69637i) q^{54} +(-0.191470 + 0.191470i) q^{55} +(9.99842 + 4.57754i) q^{56} +(2.05941 + 2.05941i) q^{57} +(-5.77235 + 3.23931i) q^{58} +(1.43744 - 3.47029i) q^{59} +(1.20285 + 4.97186i) q^{60} +(-3.46760 + 1.43633i) q^{61} +(-1.64520 + 0.196182i) q^{62} +4.21450 q^{63} +(6.05588 - 5.22746i) q^{64} -5.70108 q^{65} +(-0.284849 + 0.0339670i) q^{66} +(-14.0791 + 5.83176i) q^{67} +(-3.03127 - 12.5295i) q^{68} +(0.561177 - 1.35480i) q^{69} +(-8.85970 + 4.97186i) q^{70} +(-3.40950 - 3.40950i) q^{71} +(1.27633 - 2.78780i) q^{72} +(-0.442353 + 0.442353i) q^{73} +(-1.73172 + 6.16084i) q^{74} +(2.02794 + 0.840001i) q^{75} +(2.47945 + 3.40014i) q^{76} +(-0.218031 - 0.526374i) q^{77} +(-4.74642 - 3.73505i) q^{78} -7.07550i q^{79} +(0.605684 + 7.36618i) q^{80} +4.57283i q^{81} +(3.08985 - 3.92652i) q^{82} +(2.99862 + 7.23931i) q^{83} +(-10.6334 - 1.66510i) q^{84} +(11.0031 + 4.55765i) q^{85} +(8.99980 + 2.52971i) q^{86} +(4.58107 - 4.58107i) q^{87} +(-0.414214 - 0.0151854i) q^{88} +(-4.21803 - 4.21803i) q^{89} +(1.38627 + 2.47029i) q^{90} +(4.59050 - 11.0824i) q^{91} +(1.10392 - 1.80853i) q^{92} +(1.49824 - 0.620589i) q^{93} +(-0.447065 - 3.74912i) q^{94} -3.88784 q^{95} +(-4.32167 + 6.52951i) q^{96} +10.3267 q^{97} +(-1.35892 - 11.3960i) q^{98} +(-0.146766 + 0.0607923i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} - 4 q^{3} + 4 q^{4} - 8 q^{6} - 8 q^{7} - 4 q^{8} + 4 q^{11} + 12 q^{12} - 8 q^{13} + 12 q^{14} + 20 q^{18} + 4 q^{19} + 4 q^{20} + 4 q^{22} - 8 q^{23} - 8 q^{24} - 8 q^{25} - 20 q^{26} + 8 q^{27}+ \cdots + 28 q^{99}+O(q^{100}) \) 8 * q - 4 * q^2 - 4 * q^3 + 4 * q^4 - 8 * q^6 - 8 * q^7 - 4 * q^8 + 4 * q^11 + 12 * q^12 - 8 * q^13 + 12 * q^14 + 20 * q^18 + 4 * q^19 + 4 * q^20 + 4 * q^22 - 8 * q^23 - 8 * q^24 - 8 * q^25 - 20 * q^26 + 8 * q^27 - 16 * q^28 - 12 * q^30 + 32 * q^31 - 24 * q^32 - 16 * q^33 + 16 * q^35 - 40 * q^36 - 8 * q^37 + 8 * q^38 + 16 * q^39 + 16 * q^40 + 8 * q^41 + 8 * q^42 - 12 * q^43 + 20 * q^44 + 12 * q^46 + 48 * q^48 + 16 * q^50 - 16 * q^51 + 12 * q^52 + 8 * q^53 - 8 * q^54 - 16 * q^55 + 8 * q^56 + 16 * q^57 - 12 * q^58 - 20 * q^59 - 8 * q^60 + 24 * q^61 - 24 * q^62 - 40 * q^63 - 8 * q^64 - 28 * q^66 - 36 * q^67 + 16 * q^68 + 32 * q^69 - 8 * q^70 - 24 * q^71 + 12 * q^72 - 32 * q^73 + 8 * q^74 - 12 * q^75 - 20 * q^76 + 16 * q^77 + 28 * q^78 + 8 * q^80 - 20 * q^82 + 20 * q^83 + 8 * q^84 + 8 * q^85 + 4 * q^86 + 56 * q^87 + 8 * q^88 - 16 * q^89 + 28 * q^90 + 40 * q^91 - 16 * q^92 - 16 * q^93 - 24 * q^94 - 8 * q^95 - 16 * q^96 + 32 * q^97 - 24 * q^98 + 28 * q^99

Introduction

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