LMFDB - Embedded newform 462.2.i.f.67.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(67,462)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(462, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 0]))

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

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

chi := DirichletCharacter("462.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.i (of order $3$, degree $2$, 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:	$3.68908857338$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.1156923.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 12x^{4} - 19x^{3} + 27x^{2} - 18x + 4 $ x^6 - 3x^5 + 12x^4 - 19x^3 + 27x^2 - 18*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			67.3
Root			$0.500000 - 2.43956i$ of defining polynomial
Character	$\chi$	$=$	462.67
Dual form			462.2.i.f.331.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.60074 + 2.77256i) q^{5} +1.00000 q^{6} +(1.60074 + 2.10657i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.60074 + 2.77256i) q^{5} +1.00000 q^{6} +(1.60074 + 2.10657i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(1.60074 - 2.77256i) q^{10} +(-0.500000 + 0.866025i) q^{11} +(-0.500000 - 0.866025i) q^{12} -6.40294 q^{13} +(1.02398 - 2.43956i) q^{14} -3.20147 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-0.500000 + 0.866025i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(-0.576760 - 0.998977i) q^{19} -3.20147 q^{20} +(-2.62471 + 0.332992i) q^{21} +1.00000 q^{22} +(-0.976024 - 1.69052i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(-2.62471 + 4.54614i) q^{25} +(3.20147 + 5.54511i) q^{26} +1.00000 q^{27} +(-2.62471 + 0.332992i) q^{28} +7.24943 q^{29} +(1.60074 + 2.77256i) q^{30} +(-5.24943 + 9.09227i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-0.500000 - 0.866025i) q^{33} +1.00000 q^{34} +(-3.27823 + 7.81020i) q^{35} +1.00000 q^{36} +(-2.57676 - 4.46308i) q^{37} +(-0.576760 + 0.998977i) q^{38} +(3.20147 - 5.54511i) q^{39} +(1.60074 + 2.77256i) q^{40} +8.24943 q^{41} +(1.60074 + 2.10657i) q^{42} +5.15352 q^{43} +(-0.500000 - 0.866025i) q^{44} +(1.60074 - 2.77256i) q^{45} +(-0.976024 + 1.69052i) q^{46} +(3.02398 + 5.23768i) q^{47} +1.00000 q^{48} +(-1.87529 + 6.74413i) q^{49} +5.24943 q^{50} +(-0.500000 - 0.866025i) q^{51} +(3.20147 - 5.54511i) q^{52} +(3.20147 - 5.54511i) q^{53} +(-0.500000 - 0.866025i) q^{54} -3.20147 q^{55} +(1.60074 + 2.10657i) q^{56} +1.15352 q^{57} +(-3.62471 - 6.27819i) q^{58} +(-5.77823 + 10.0082i) q^{59} +(1.60074 - 2.77256i) q^{60} +(-4.85016 - 8.40073i) q^{61} +10.4989 q^{62} +(1.02398 - 2.43956i) q^{63} +1.00000 q^{64} +(-10.2494 - 17.7525i) q^{65} +(-0.500000 + 0.866025i) q^{66} +(-3.12471 + 5.41216i) q^{67} +(-0.500000 - 0.866025i) q^{68} +1.95205 q^{69} +(8.40294 - 1.06607i) q^{70} +5.24943 q^{71} +(-0.500000 - 0.866025i) q^{72} +(1.04795 - 1.81511i) q^{73} +(-2.57676 + 4.46308i) q^{74} +(-2.62471 - 4.54614i) q^{75} +1.15352 q^{76} +(-2.62471 + 0.332992i) q^{77} -6.40294 q^{78} +(2.80221 + 4.85357i) q^{79} +(1.60074 - 2.77256i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-4.12471 - 7.14421i) q^{82} +6.55646 q^{83} +(1.02398 - 2.43956i) q^{84} -3.20147 q^{85} +(-2.57676 - 4.46308i) q^{86} +(-3.62471 + 6.27819i) q^{87} +(-0.500000 + 0.866025i) q^{88} +(9.20147 + 15.9374i) q^{89} -3.20147 q^{90} +(-10.2494 - 13.4883i) q^{91} +1.95205 q^{92} +(-5.24943 - 9.09227i) q^{93} +(3.02398 - 5.23768i) q^{94} +(1.84648 - 3.19820i) q^{95} +(-0.500000 - 0.866025i) q^{96} -5.49885 q^{97} +(6.77823 - 1.74802i) q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{2} - 3 q^{3} - 3 q^{4} + 6 q^{6} + 6 q^{8} - 3 q^{9}+O(q^{10}) $ 6 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 + 6 * q^6 + 6 * q^8 - 3 * q^9	$ 6 q - 3 q^{2} - 3 q^{3} - 3 q^{4} + 6 q^{6} + 6 q^{8} - 3 q^{9} - 3 q^{11} - 3 q^{12} + 3 q^{14} - 3 q^{16} - 3 q^{17} - 3 q^{18} + 3 q^{19} - 3 q^{21} + 6 q^{22} - 9 q^{23} - 3 q^{24} - 3 q^{25} + 6 q^{27} - 3 q^{28} + 18 q^{29} - 6 q^{31} - 3 q^{32} - 3 q^{33} + 6 q^{34} + 6 q^{35} + 6 q^{36} - 9 q^{37} + 3 q^{38} + 24 q^{41} + 18 q^{43} - 3 q^{44} - 9 q^{46} + 15 q^{47} + 6 q^{48} - 24 q^{49} + 6 q^{50} - 3 q^{51} - 3 q^{54} - 6 q^{57} - 9 q^{58} - 9 q^{59} + 6 q^{61} + 12 q^{62} + 3 q^{63} + 6 q^{64} - 36 q^{65} - 3 q^{66} - 6 q^{67} - 3 q^{68} + 18 q^{69} + 12 q^{70} + 6 q^{71} - 3 q^{72} - 9 q^{74} - 3 q^{75} - 6 q^{76} - 3 q^{77} - 12 q^{79} - 3 q^{81} - 12 q^{82} - 12 q^{83} + 3 q^{84} - 9 q^{86} - 9 q^{87} - 3 q^{88} + 36 q^{89} - 36 q^{91} + 18 q^{92} - 6 q^{93} + 15 q^{94} + 24 q^{95} - 3 q^{96} + 18 q^{97} + 15 q^{98} + 6 q^{99}+O(q^{100}) $ 6 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 + 6 * q^6 + 6 * q^8 - 3 * q^9 - 3 * q^11 - 3 * q^12 + 3 * q^14 - 3 * q^16 - 3 * q^17 - 3 * q^18 + 3 * q^19 - 3 * q^21 + 6 * q^22 - 9 * q^23 - 3 * q^24 - 3 * q^25 + 6 * q^27 - 3 * q^28 + 18 * q^29 - 6 * q^31 - 3 * q^32 - 3 * q^33 + 6 * q^34 + 6 * q^35 + 6 * q^36 - 9 * q^37 + 3 * q^38 + 24 * q^41 + 18 * q^43 - 3 * q^44 - 9 * q^46 + 15 * q^47 + 6 * q^48 - 24 * q^49 + 6 * q^50 - 3 * q^51 - 3 * q^54 - 6 * q^57 - 9 * q^58 - 9 * q^59 + 6 * q^61 + 12 * q^62 + 3 * q^63 + 6 * q^64 - 36 * q^65 - 3 * q^66 - 6 * q^67 - 3 * q^68 + 18 * q^69 + 12 * q^70 + 6 * q^71 - 3 * q^72 - 9 * q^74 - 3 * q^75 - 6 * q^76 - 3 * q^77 - 12 * q^79 - 3 * q^81 - 12 * q^82 - 12 * q^83 + 3 * q^84 - 9 * q^86 - 9 * q^87 - 3 * q^88 + 36 * q^89 - 36 * q^91 + 18 * q^92 - 6 * q^93 + 15 * q^94 + 24 * q^95 - 3 * q^96 + 18 * q^97 + 15 * q^98 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	1.60074	+	2.77256i	0.715871	+	1.23992i	0.962623	+	0.270846i	$0.0873035\pi$
$5$	1.60074	+	2.77256i	0.715871	+	1.23992i	−0.246752	+	0.969079i	$0.579363\pi$
$6$	1.00000			0.408248
$7$	1.60074	+	2.10657i	0.605021	+	0.796209i
$7$	1.60074	+	2.10657i	0.605021	+	0.796209i
$8$	1.00000			0.353553
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	1.60074	−	2.77256i	0.506197	−	0.876759i
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$12$	−0.500000	−	0.866025i	−0.144338	−	0.250000i
$13$	−6.40294			−1.77586			−0.887929	−	0.459981i	$-0.847856\pi$
$13$	−6.40294			−1.77586			−0.887929	+	0.459981i	$0.847856\pi$
$14$	1.02398	−	2.43956i	0.273669	−	0.652001i
$15$	−3.20147			−0.826617
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−0.500000	+	0.866025i	−0.121268	+	0.210042i	−0.920268	−	0.391289i	$-0.872029\pi$
$17$	−0.500000	+	0.866025i	−0.121268	+	0.210042i	0.799000	+	0.601331i	$0.205363\pi$
$18$	−0.500000	+	0.866025i	−0.117851	+	0.204124i
$19$	−0.576760	−	0.998977i	−0.132318	−	0.229181i	0.792252	−	0.610194i	$-0.208909\pi$
$19$	−0.576760	−	0.998977i	−0.132318	−	0.229181i	−0.924570	+	0.381013i	$0.875575\pi$
$20$	−3.20147			−0.715871
$21$	−2.62471	+	0.332992i	−0.572759	+	0.0726649i
$22$	1.00000			0.213201
$23$	−0.976024	−	1.69052i	−0.203515	−	0.352498i	0.746144	−	0.665785i	$-0.231903\pi$
$23$	−0.976024	−	1.69052i	−0.203515	−	0.352498i	−0.949659	+	0.313287i	$0.898570\pi$
$24$	−0.500000	+	0.866025i	−0.102062	+	0.176777i
$25$	−2.62471	+	4.54614i	−0.524943	+	0.909227i
$26$	3.20147	+	5.54511i	0.627860	+	1.08749i
$27$	1.00000			0.192450
$28$	−2.62471	+	0.332992i	−0.496024	+	0.0629297i
$29$	7.24943			1.34618			0.673092	−	0.739559i	$-0.264966\pi$
$29$	7.24943			1.34618			0.673092	+	0.739559i	$0.264966\pi$
$30$	1.60074	+	2.77256i	0.292253	+	0.506197i
$31$	−5.24943	+	9.09227i	−0.942825	+	1.63302i	−0.182775	+	0.983155i	$0.558508\pi$
$31$	−5.24943	+	9.09227i	−0.942825	+	1.63302i	−0.760049	+	0.649865i	$0.774825\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	−0.500000	−	0.866025i	−0.0870388	−	0.150756i
$34$	1.00000			0.171499
$35$	−3.27823	+	7.81020i	−0.554122	+	1.32016i
$36$	1.00000			0.166667
$37$	−2.57676	−	4.46308i	−0.423617	−	0.733726i	0.572673	−	0.819784i	$-0.305906\pi$
$37$	−2.57676	−	4.46308i	−0.423617	−	0.733726i	−0.996290	+	0.0860579i	$0.972573\pi$
$38$	−0.576760	+	0.998977i	−0.0935628	+	0.162056i
$39$	3.20147	−	5.54511i	0.512646	−	0.887929i
$40$	1.60074	+	2.77256i	0.253099	+	0.438380i
$41$	8.24943			1.28834			0.644172	−	0.764881i	$-0.277202\pi$
$41$	8.24943			1.28834			0.644172	+	0.764881i	$0.277202\pi$
$42$	1.60074	+	2.10657i	0.246999	+	0.325051i
$43$	5.15352			0.785904			0.392952	−	0.919559i	$-0.371454\pi$
$43$	5.15352			0.785904			0.392952	+	0.919559i	$0.371454\pi$
$44$	−0.500000	−	0.866025i	−0.0753778	−	0.130558i
$45$	1.60074	−	2.77256i	0.238624	−	0.413308i
$46$	−0.976024	+	1.69052i	−0.143907	+	0.249254i
$47$	3.02398	+	5.23768i	0.441092	+	0.763994i	0.997771	−	0.0667337i	$-0.0212578\pi$
$47$	3.02398	+	5.23768i	0.441092	+	0.763994i	−0.556679	+	0.830728i	$0.687924\pi$
$48$	1.00000			0.144338
$49$	−1.87529	+	6.74413i	−0.267898	+	0.963447i
$50$	5.24943			0.742381
$51$	−0.500000	−	0.866025i	−0.0700140	−	0.121268i
$52$	3.20147	−	5.54511i	0.443964	−	0.768969i
$53$	3.20147	−	5.54511i	0.439756	−	0.761680i	−0.557914	−	0.829899i	$-0.688398\pi$
$53$	3.20147	−	5.54511i	0.439756	−	0.761680i	0.997670	+	0.0682187i	$0.0217316\pi$
$54$	−0.500000	−	0.866025i	−0.0680414	−	0.117851i
$55$	−3.20147			−0.431686
$56$	1.60074	+	2.10657i	0.213907	+	0.281502i
$57$	1.15352			0.152787
$58$	−3.62471	−	6.27819i	−0.475948	−	0.824366i
$59$	−5.77823	+	10.0082i	−0.752262	+	1.30296i	0.194462	+	0.980910i	$0.437704\pi$
$59$	−5.77823	+	10.0082i	−0.752262	+	1.30296i	−0.946724	+	0.322046i	$0.895630\pi$
$60$	1.60074	−	2.77256i	0.206654	−	0.357935i
$61$	−4.85016	−	8.40073i	−0.621000	−	1.07560i	−0.989300	−	0.145896i	$-0.953394\pi$
$61$	−4.85016	−	8.40073i	−0.621000	−	1.07560i	0.368300	−	0.929707i	$-0.379940\pi$
$62$	10.4989			1.33336
$63$	1.02398	−	2.43956i	0.129009	−	0.307356i
$64$	1.00000			0.125000
$65$	−10.2494	−	17.7525i	−1.27128	−	2.20193i
$66$	−0.500000	+	0.866025i	−0.0615457	+	0.106600i
$67$	−3.12471	+	5.41216i	−0.381744	+	0.661201i	−0.991312	−	0.131534i	$-0.958010\pi$
$67$	−3.12471	+	5.41216i	−0.381744	+	0.661201i	0.609567	+	0.792734i	$0.291343\pi$
$68$	−0.500000	−	0.866025i	−0.0606339	−	0.105021i
$69$	1.95205			0.234999
$70$	8.40294	−	1.06607i	1.00434	−	0.127419i
$71$	5.24943			0.622992			0.311496	−	0.950247i	$-0.399170\pi$
$71$	5.24943			0.622992			0.311496	+	0.950247i	$0.399170\pi$
$72$	−0.500000	−	0.866025i	−0.0589256	−	0.102062i
$73$	1.04795	−	1.81511i	0.122654	−	0.212442i	−0.798160	−	0.602446i	$-0.794193\pi$
$73$	1.04795	−	1.81511i	0.122654	−	0.212442i	0.920813	+	0.390004i	$0.127526\pi$
$74$	−2.57676	+	4.46308i	−0.299542	+	0.518822i
$75$	−2.62471	−	4.54614i	−0.303076	−	0.524943i
$76$	1.15352			0.132318
$77$	−2.62471	+	0.332992i	−0.299114	+	0.0379480i
$78$	−6.40294			−0.724991
$79$	2.80221	+	4.85357i	0.315273	+	0.546069i	0.979496	−	0.201466i	$-0.0645706\pi$
$79$	2.80221	+	4.85357i	0.315273	+	0.546069i	−0.664222	+	0.747535i	$0.731237\pi$
$80$	1.60074	−	2.77256i	0.178968	−	0.309981i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−4.12471	−	7.14421i	−0.455498	−	0.788946i
$83$	6.55646			0.719665			0.359833	−	0.933017i	$-0.382834\pi$
$83$	6.55646			0.719665			0.359833	+	0.933017i	$0.382834\pi$
$84$	1.02398	−	2.43956i	0.111725	−	0.266178i
$85$	−3.20147			−0.347248
$86$	−2.57676	−	4.46308i	−0.277859	−	0.481266i
$87$	−3.62471	+	6.27819i	−0.388610	+	0.673092i
$88$	−0.500000	+	0.866025i	−0.0533002	+	0.0923186i
$89$	9.20147	+	15.9374i	0.975354	+	1.68936i	0.678761	+	0.734359i	$0.262517\pi$
$89$	9.20147	+	15.9374i	0.975354	+	1.68936i	0.296593	+	0.955004i	$0.404150\pi$
$90$	−3.20147			−0.337465
$91$	−10.2494	−	13.4883i	−1.07443	−	1.41395i
$92$	1.95205			0.203515
$93$	−5.24943	−	9.09227i	−0.544340	−	0.942825i
$94$	3.02398	−	5.23768i	0.311899	−	0.540226i
$95$	1.84648	−	3.19820i	0.189445	−	0.328128i
$96$	−0.500000	−	0.866025i	−0.0510310	−	0.0883883i
$97$	−5.49885			−0.558324			−0.279162	−	0.960244i	$-0.590057\pi$
$97$	−5.49885			−0.558324			−0.279162	+	0.960244i	$0.590057\pi$
$98$	6.77823	−	1.74802i	0.684705	−	0.176577i
$99$	1.00000			0.100504
$100$	−2.62471	−	4.54614i	−0.262471	−	0.454614i
$101$	9.97970	−	17.2854i	0.993018	−	1.71996i	0.394348	−	0.918961i	$-0.370971\pi$
$101$	9.97970	−	17.2854i	0.993018	−	1.71996i	0.598670	−	0.800996i	$-0.295696\pi$
$102$	−0.500000	+	0.866025i	−0.0495074	+	0.0857493i
$103$	−0.153520	−	0.265904i	−0.0151267	−	0.0262003i	0.858363	−	0.513043i	$-0.171482\pi$
$103$	−0.153520	−	0.265904i	−0.0151267	−	0.0262003i	−0.873490	+	0.486843i	$0.838149\pi$
$104$	−6.40294			−0.627860
$105$	−5.12471	−	6.74413i	−0.500121	−	0.658160i
$106$	−6.40294			−0.621909
$107$	4.52766	+	7.84213i	0.437705	+	0.758128i	0.997512	−	0.0704955i	$-0.0224580\pi$
$107$	4.52766	+	7.84213i	0.437705	+	0.758128i	−0.559807	+	0.828623i	$0.689125\pi$
$108$	−0.500000	+	0.866025i	−0.0481125	+	0.0833333i
$109$	4.85016	−	8.40073i	0.464561	−	0.804644i	−0.534620	−	0.845092i	$-0.679545\pi$
$109$	4.85016	−	8.40073i	0.464561	−	0.804644i	0.999182	+	0.0404487i	$0.0128787\pi$
$110$	1.60074	+	2.77256i	0.152624	+	0.264353i
$111$	5.15352			0.489150
$112$	1.02398	−	2.43956i	0.0967567	−	0.230517i
$113$	−12.4989			−1.17579			−0.587896	−	0.808936i	$-0.700044\pi$
$113$	−12.4989			−1.17579			−0.587896	+	0.808936i	$0.700044\pi$
$114$	−0.576760	−	0.998977i	−0.0540185	−	0.0935628i
$115$	3.12471	−	5.41216i	0.291381	−	0.504687i
$116$	−3.62471	+	6.27819i	−0.336546	+	0.582915i
$117$	3.20147	+	5.54511i	0.295976	+	0.512646i
$118$	11.5565			1.06386
$119$	−2.62471	+	0.332992i	−0.240607	+	0.0305254i
$120$	−3.20147			−0.292253
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$	−4.85016	+	8.40073i	−0.439113	+	0.760566i
$123$	−4.12471	+	7.14421i	−0.371913	+	0.644172i
$124$	−5.24943	−	9.09227i	−0.471412	−	0.816510i
$125$	−0.798528			−0.0714225
$126$	−2.62471	+	0.332992i	−0.233828	+	0.0296653i
$127$	8.35499			0.741386			0.370693	−	0.928756i	$-0.379120\pi$
$127$	8.35499			0.741386			0.370693	+	0.928756i	$0.379120\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	−2.57676	+	4.46308i	−0.226871	+	0.392952i
$130$	−10.2494	+	17.7525i	−0.898934	+	1.55700i
$131$	−7.65237	−	13.2543i	−0.668591	−	1.15803i	−0.978298	−	0.207201i	$-0.933565\pi$
$131$	−7.65237	−	13.2543i	−0.668591	−	1.15803i	0.309708	−	0.950832i	$-0.399769\pi$
$132$	1.00000			0.0870388
$133$	1.18118	−	2.81408i	0.102421	−	0.244012i
$134$	6.24943			0.539868
$135$	1.60074	+	2.77256i	0.137769	+	0.238624i
$136$	−0.500000	+	0.866025i	−0.0428746	+	0.0742611i
$137$	3.20147	−	5.54511i	0.273520	−	0.473751i	−0.696240	−	0.717809i	$-0.745145\pi$
$137$	3.20147	−	5.54511i	0.273520	−	0.473751i	0.969761	+	0.244058i	$0.0784786\pi$
$138$	−0.976024	−	1.69052i	−0.0830846	−	0.143907i
$139$	21.7483			1.84466			0.922332	−	0.386398i	$-0.126281\pi$
$139$	21.7483			1.84466			0.922332	+	0.386398i	$0.126281\pi$
$140$	−5.12471	−	6.74413i	−0.433117	−	0.569983i
$141$	−6.04795			−0.509330
$142$	−2.62471	−	4.54614i	−0.220261	−	0.381503i
$143$	3.20147	−	5.54511i	0.267721	−	0.463706i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	11.6044	+	20.0994i	0.963694	+	1.66917i
$146$	−2.09591			−0.173458
$147$	−4.90294	−	4.99611i	−0.404388	−	0.412072i
$148$	5.15352			0.423617
$149$	−3.42324	−	5.92923i	−0.280443	−	0.485741i	0.691051	−	0.722806i	$-0.257148\pi$
$149$	−3.42324	−	5.92923i	−0.280443	−	0.485741i	−0.971494	+	0.237065i	$0.923815\pi$
$150$	−2.62471	+	4.54614i	−0.214307	+	0.371190i
$151$	−7.42692	+	12.8638i	−0.604394	+	1.04684i	0.387753	+	0.921763i	$0.373251\pi$
$151$	−7.42692	+	12.8638i	−0.604394	+	1.04684i	−0.992147	+	0.125078i	$0.960082\pi$
$152$	−0.576760	−	0.998977i	−0.0467814	−	0.0810278i
$153$	1.00000			0.0808452
$154$	1.60074	+	2.10657i	0.128991	+	0.169752i
$155$	−33.6118			−2.69976
$156$	3.20147	+	5.54511i	0.256323	+	0.443964i
$157$	4.73028	−	8.19308i	0.377517	−	0.653879i	−0.613183	−	0.789941i	$-0.710111\pi$
$157$	4.73028	−	8.19308i	0.377517	−	0.653879i	0.990700	+	0.136062i	$0.0434445\pi$
$158$	2.80221	−	4.85357i	0.222932	−	0.386129i
$159$	3.20147	+	5.54511i	0.253893	+	0.439756i
$160$	−3.20147			−0.253099
$161$	1.99885	−	4.76214i	0.157531	−	0.375310i
$162$	1.00000			0.0785674
$163$	−6.52766	−	11.3062i	−0.511286	−	0.885573i	−0.999914	−	0.0130809i	$-0.995836\pi$
$163$	−6.52766	−	11.3062i	−0.511286	−	0.885573i	0.488629	−	0.872492i	$-0.337497\pi$
$164$	−4.12471	+	7.14421i	−0.322086	+	0.557869i
$165$	1.60074	−	2.77256i	0.124617	−	0.215843i
$166$	−3.27823	−	5.67806i	−0.254440	−	0.440703i
$167$	−6.70998			−0.519234			−0.259617	−	0.965712i	$-0.583596\pi$
$167$	−6.70998			−0.519234			−0.259617	+	0.965712i	$0.583596\pi$
$168$	−2.62471	+	0.332992i	−0.202501	+	0.0256909i
$169$	27.9977			2.15367
$170$	1.60074	+	2.77256i	0.122771	+	0.212645i
$171$	−0.576760	+	0.998977i	−0.0441059	+	0.0763937i
$172$	−2.57676	+	4.46308i	−0.196476	+	0.340307i
$173$	2.75057	+	4.76414i	0.209122	+	0.362211i	0.951438	−	0.307839i	$-0.0996060\pi$
$173$	2.75057	+	4.76414i	0.209122	+	0.362211i	−0.742316	+	0.670050i	$0.766273\pi$
$174$	7.24943			0.549578
$175$	−13.7782	+	1.74802i	−1.04154	+	0.132138i
$176$	1.00000			0.0753778
$177$	−5.77823	−	10.0082i	−0.434319	−	0.752262i
$178$	9.20147	−	15.9374i	0.689680	−	1.19456i
$179$	−0.826185	+	1.43099i	−0.0617520	+	0.106958i	−0.895249	−	0.445567i	$-0.853002\pi$
$179$	−0.826185	+	1.43099i	−0.0617520	+	0.106958i	0.833497	+	0.552525i	$0.186335\pi$
$180$	1.60074	+	2.77256i	0.119312	+	0.206654i
$181$	24.9018			1.85094			0.925468	−	0.378826i	$-0.123672\pi$
$181$	24.9018			1.85094			0.925468	+	0.378826i	$0.123672\pi$
$182$	−6.55646	+	15.6204i	−0.485997	+	1.15786i
$183$	9.70032			0.717068
$184$	−0.976024	−	1.69052i	−0.0719534	−	0.124627i
$185$	8.24943	−	14.2884i	0.606510	−	1.05051i
$186$	−5.24943	+	9.09227i	−0.384907	+	0.666678i
$187$	−0.500000	−	0.866025i	−0.0365636	−	0.0633300i
$188$	−6.04795			−0.441092
$189$	1.60074	+	2.10657i	0.116436	+	0.153231i
$190$	−3.69296			−0.267916
$191$	2.40294	+	4.16202i	0.173871	+	0.301153i	0.939770	−	0.341808i	$-0.111039\pi$
$191$	2.40294	+	4.16202i	0.173871	+	0.301153i	−0.765899	+	0.642961i	$0.777706\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$	−4.35499	+	7.54307i	−0.313479	+	0.542962i	−0.979113	−	0.203317i	$-0.934828\pi$
$193$	−4.35499	+	7.54307i	−0.313479	+	0.542962i	0.665634	+	0.746278i	$0.268161\pi$
$194$	2.74943	+	4.76214i	0.197397	+	0.341902i
$195$	20.4989			1.46795
$196$	−4.90294	−	4.99611i	−0.350210	−	0.356865i
$197$	0.654669			0.0466433			0.0233216	−	0.999728i	$-0.492576\pi$
$197$	0.654669			0.0466433			0.0233216	+	0.999728i	$0.492576\pi$
$198$	−0.500000	−	0.866025i	−0.0355335	−	0.0615457i
$199$	3.84648	−	6.66230i	0.272670	−	0.472278i	−0.696875	−	0.717193i	$-0.745427\pi$
$199$	3.84648	−	6.66230i	0.272670	−	0.472278i	0.969545	+	0.244915i	$0.0787600\pi$
$200$	−2.62471	+	4.54614i	−0.185595	+	0.321460i
$201$	−3.12471	−	5.41216i	−0.220400	−	0.381744i
$202$	−19.9594			−1.40434
$203$	11.6044	+	15.2714i	0.814470	+	1.07184i
$204$	1.00000			0.0700140
$205$	13.2052	+	22.8720i	0.922288	+	1.59745i
$206$	−0.153520	+	0.265904i	−0.0106962	+	0.0185264i
$207$	−0.976024	+	1.69052i	−0.0678383	+	0.117499i
$208$	3.20147	+	5.54511i	0.221982	+	0.384484i
$209$	1.15352			0.0797906
$210$	−3.27823	+	7.81020i	−0.226220	+	0.538955i
$211$	14.5948			1.00474			0.502372	−	0.864651i	$-0.332461\pi$
$211$	14.5948			1.00474			0.502372	+	0.864651i	$0.332461\pi$
$212$	3.20147	+	5.54511i	0.219878	+	0.380840i
$213$	−2.62471	+	4.54614i	−0.179842	+	0.311496i
$214$	4.52766	−	7.84213i	0.309504	−	0.536077i
$215$	8.24943	+	14.2884i	0.562606	+	0.974462i
$216$	1.00000			0.0680414
$217$	−27.5565	+	3.49604i	−1.87065	+	0.237326i
$218$	−9.70032			−0.656989
$219$	1.04795	+	1.81511i	0.0708141	+	0.122654i
$220$	1.60074	−	2.77256i	0.107922	−	0.186926i
$221$	3.20147	−	5.54511i	0.215354	−	0.373005i
$222$	−2.57676	−	4.46308i	−0.172941	−	0.299542i
$223$	−14.9018			−0.997898			−0.498949	−	0.866631i	$-0.666281\pi$
$223$	−14.9018			−0.997898			−0.498949	+	0.866631i	$0.666281\pi$
$224$	−2.62471	+	0.332992i	−0.175371	+	0.0222490i
$225$	5.24943			0.349962
$226$	6.24943	+	10.8243i	0.415706	+	0.720023i
$227$	0.124713	−	0.216009i	0.00827746	−	0.0143370i	−0.861857	−	0.507151i	$-0.830699\pi$
$227$	0.124713	−	0.216009i	0.00827746	−	0.0143370i	0.870134	+	0.492814i	$0.164032\pi$
$228$	−0.576760	+	0.998977i	−0.0381968	+	0.0661589i
$229$	2.04795	+	3.54716i	0.135333	+	0.234403i	0.925724	−	0.378199i	$-0.123456\pi$
$229$	2.04795	+	3.54716i	0.135333	+	0.234403i	−0.790392	+	0.612602i	$0.790123\pi$
$230$	−6.24943			−0.412075
$231$	1.02398	−	2.43956i	0.0673727	−	0.160512i
$232$	7.24943			0.475948
$233$	−5.65352	−	9.79218i	−0.370374	−	0.641507i	0.619249	−	0.785195i	$-0.287437\pi$
$233$	−5.65352	−	9.79218i	−0.370374	−	0.641507i	−0.989623	+	0.143688i	$0.954104\pi$
$234$	3.20147	−	5.54511i	0.209287	−	0.362495i
$235$	−9.68118	+	16.7683i	−0.631530	+	1.09384i
$236$	−5.77823	−	10.0082i	−0.376131	−	0.651478i
$237$	−5.60442			−0.364046
$238$	1.60074	+	2.10657i	0.103760	+	0.136549i
$239$	6.59476			0.426579			0.213290	−	0.976989i	$-0.431582\pi$
$239$	6.59476			0.426579			0.213290	+	0.976989i	$0.431582\pi$
$240$	1.60074	+	2.77256i	0.103327	+	0.178968i
$241$	−8.55646	+	14.8202i	−0.551170	+	0.954655i	0.447020	+	0.894524i	$0.352485\pi$
$241$	−8.55646	+	14.8202i	−0.551170	+	0.954655i	−0.998190	+	0.0601311i	$0.980848\pi$
$242$	−0.500000	+	0.866025i	−0.0321412	+	0.0556702i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	9.70032			0.621000
$245$	−21.7003	+	5.59623i	−1.38638	+	0.357530i
$246$	8.24943			0.525964
$247$	3.69296	+	6.39640i	0.234977	+	0.406993i
$248$	−5.24943	+	9.09227i	−0.333339	+	0.577360i
$249$	−3.27823	+	5.67806i	−0.207750	+	0.359833i
$250$	0.399264	+	0.691545i	0.0252517	+	0.0437372i
$251$	7.95941			0.502393			0.251197	−	0.967936i	$-0.419176\pi$
$251$	7.95941			0.502393			0.251197	+	0.967936i	$0.419176\pi$
$252$	1.60074	+	2.10657i	0.100837	+	0.132702i
$253$	1.95205			0.122724
$254$	−4.17750	−	7.23564i	−0.262119	−	0.454004i
$255$	1.60074	−	2.77256i	0.100242	−	0.173624i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	11.2015	+	19.4015i	0.698729	+	1.21023i	0.968907	+	0.247423i	$0.0795838\pi$
$257$	11.2015	+	19.4015i	0.698729	+	1.21023i	−0.270179	+	0.962810i	$0.587083\pi$
$258$	5.15352			0.320844
$259$	5.27708	−	12.5723i	0.327902	−	0.781207i
$260$	20.4989			1.27128
$261$	−3.62471	−	6.27819i	−0.224364	−	0.388610i
$262$	−7.65237	+	13.2543i	−0.472765	+	0.818853i
$263$	12.5085	−	21.6654i	0.771308	−	1.33594i	−0.165539	−	0.986203i	$-0.552936\pi$
$263$	12.5085	−	21.6654i	0.771308	−	1.33594i	0.936846	−	0.349741i	$-0.113730\pi$
$264$	−0.500000	−	0.866025i	−0.0307729	−	0.0533002i
$265$	20.4989			1.25923
$266$	−3.02766	+	0.384113i	−0.185638	+	0.0235515i
$267$	−18.4029			−1.12624
$268$	−3.12471	−	5.41216i	−0.190872	−	0.330600i
$269$	−4.05163	+	7.01764i	−0.247032	+	0.427873i	−0.962701	−	0.270567i	$-0.912789\pi$
$269$	−4.05163	+	7.01764i	−0.247032	+	0.427873i	0.715669	+	0.698440i	$0.246122\pi$
$270$	1.60074	−	2.77256i	0.0974177	−	0.168732i
$271$	2.40294	+	4.16202i	0.145968	+	0.252825i	0.929734	−	0.368232i	$-0.120037\pi$
$271$	2.40294	+	4.16202i	0.145968	+	0.252825i	−0.783765	+	0.621057i	$0.786704\pi$
$272$	1.00000			0.0606339
$273$	16.8059	−	2.13213i	1.01714	−	0.129042i
$274$	−6.40294			−0.386816
$275$	−2.62471	−	4.54614i	−0.158276	−	0.274142i
$276$	−0.976024	+	1.69052i	−0.0587497	+	0.101757i
$277$	5.60442	−	9.70714i	0.336737	−	0.583245i	−0.647080	−	0.762422i	$-0.724010\pi$
$277$	5.60442	−	9.70714i	0.336737	−	0.583245i	0.983817	+	0.179177i	$0.0573434\pi$
$278$	−10.8741	−	18.8346i	−0.652187	−	1.12962i
$279$	10.4989			0.628550
$280$	−3.27823	+	7.81020i	−0.195912	+	0.466749i
$281$	−17.4989			−1.04389			−0.521947	−	0.852978i	$-0.674794\pi$
$281$	−17.4989			−1.04389			−0.521947	+	0.852978i	$0.674794\pi$
$282$	3.02398	+	5.23768i	0.180075	+	0.311899i
$283$	−13.7003	+	23.7297i	−0.814400	+	1.41058i	0.0953585	+	0.995443i	$0.469600\pi$
$283$	−13.7003	+	23.7297i	−0.814400	+	1.41058i	−0.909758	+	0.415139i	$0.863733\pi$
$284$	−2.62471	+	4.54614i	−0.155748	+	0.269764i
$285$	1.84648	+	3.19820i	0.109376	+	0.189445i
$286$	−6.40294			−0.378614
$287$	13.2052	+	17.3780i	0.779476	+	1.02579i
$288$	1.00000			0.0589256
$289$	8.00000	+	13.8564i	0.470588	+	0.815083i
$290$	11.6044	−	20.0994i	0.681435	−	1.18028i
$291$	2.74943	−	4.76214i	0.161174	−	0.279162i
$292$	1.04795	+	1.81511i	0.0613268	+	0.106221i
$293$	−19.7483			−1.15371			−0.576853	−	0.816848i	$-0.695720\pi$
$293$	−19.7483			−1.15371			−0.576853	+	0.816848i	$0.695720\pi$
$294$	−1.87529	+	6.74413i	−0.109369	+	0.393326i
$295$	−36.9977			−2.15409
$296$	−2.57676	−	4.46308i	−0.149771	−	0.259411i
$297$	−0.500000	+	0.866025i	−0.0290129	+	0.0502519i
$298$	−3.42324	+	5.92923i	−0.198303	+	0.343471i
$299$	6.24943	+	10.8243i	0.361414	+	0.625987i
$300$	5.24943			0.303076
$301$	8.24943	+	10.8563i	0.475489	+	0.625744i
$302$	14.8538			0.854743
$303$	9.97970	+	17.2854i	0.573319	+	0.993018i
$304$	−0.576760	+	0.998977i	−0.0330794	+	0.0572953i
$305$	15.5277	−	26.8947i	0.889111	−	1.53999i
$306$	−0.500000	−	0.866025i	−0.0285831	−	0.0495074i
$307$	4.30704			0.245816			0.122908	−	0.992418i	$-0.460778\pi$
$307$	4.30704			0.245816			0.122908	+	0.992418i	$0.460778\pi$
$308$	1.02398	−	2.43956i	0.0583465	−	0.139007i
$309$	0.307039			0.0174668
$310$	16.8059	+	29.1087i	0.954510	+	1.65326i
$311$	7.37897	−	12.7807i	0.418423	−	0.724730i	−0.577358	−	0.816491i	$-0.695916\pi$
$311$	7.37897	−	12.7807i	0.418423	−	0.724730i	0.995781	+	0.0917613i	$0.0292497\pi$
$312$	3.20147	−	5.54511i	0.181248	−	0.313930i
$313$	−10.3753	−	17.9705i	−0.586446	−	1.01575i	−0.994693	−	0.102883i	$-0.967193\pi$
$313$	−10.3753	−	17.9705i	−0.586446	−	1.01575i	0.408248	−	0.912871i	$-0.366140\pi$
$314$	−9.46056			−0.533890
$315$	8.40294	−	1.06607i	0.473452	−	0.0600660i
$316$	−5.60442			−0.315273
$317$	−8.09959	−	14.0289i	−0.454918	−	0.787941i	0.543765	−	0.839237i	$-0.316998\pi$
$317$	−8.09959	−	14.0289i	−0.454918	−	0.787941i	−0.998683	+	0.0512960i	$0.983665\pi$
$318$	3.20147	−	5.54511i	0.179530	−	0.310954i
$319$	−3.62471	+	6.27819i	−0.202945	+	0.351511i
$320$	1.60074	+	2.77256i	0.0894839	+	0.154991i
$321$	−9.05531			−0.505418
$322$	−5.12356	+	0.650017i	−0.285525	+	0.0362240i
$323$	1.15352			0.0641835
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$	16.8059	−	29.1087i	0.932223	−	1.61466i
$326$	−6.52766	+	11.3062i	−0.361533	+	0.626194i
$327$	4.85016	+	8.40073i	0.268215	+	0.464561i
$328$	8.24943			0.455498
$329$	−6.19296	+	14.7544i	−0.341429	+	0.813435i
$330$	−3.20147			−0.176235
$331$	−10.6236	−	18.4006i	−0.583924	−	1.01139i	−0.995009	−	0.0997886i	$-0.968183\pi$
$331$	−10.6236	−	18.4006i	−0.583924	−	1.01139i	0.411085	−	0.911597i	$-0.365150\pi$
$332$	−3.27823	+	5.67806i	−0.179916	+	0.311624i
$333$	−2.57676	+	4.46308i	−0.141206	+	0.244575i
$334$	3.35499	+	5.81102i	0.183577	+	0.317965i
$335$	−20.0074			−1.09312
$336$	1.60074	+	2.10657i	0.0873273	+	0.114923i
$337$	−25.5159			−1.38994			−0.694969	−	0.719040i	$-0.744582\pi$
$337$	−25.5159			−1.38994			−0.694969	+	0.719040i	$0.744582\pi$
$338$	−13.9989	−	24.2467i	−0.761437	−	1.31885i
$339$	6.24943	−	10.8243i	0.339422	−	0.587896i
$340$	1.60074	−	2.77256i	0.0868121	−	0.150363i
$341$	−5.24943	−	9.09227i	−0.284272	−	0.492374i
$342$	1.15352			0.0623752
$343$	−17.2088	+	6.84515i	−0.929190	+	0.369603i
$344$	5.15352			0.277859
$345$	3.12471	+	5.41216i	0.168229	+	0.291381i
$346$	2.75057	−	4.76414i	0.147872	−	0.256122i
$347$	−1.52766	+	2.64598i	−0.0820089	+	0.142044i	−0.904113	−	0.427294i	$-0.859467\pi$
$347$	−1.52766	+	2.64598i	−0.0820089	+	0.142044i	0.822104	+	0.569338i	$0.192800\pi$
$348$	−3.62471	−	6.27819i	−0.194305	−	0.336546i
$349$	−4.00736			−0.214509			−0.107255	−	0.994232i	$-0.534206\pi$
$349$	−4.00736			−0.214509			−0.107255	+	0.994232i	$0.534206\pi$
$350$	8.40294	+	11.0583i	0.449156	+	0.591090i
$351$	−6.40294			−0.341764
$352$	−0.500000	−	0.866025i	−0.0266501	−	0.0461593i
$353$	0.549103	−	0.951073i	0.0292258	−	0.0506205i	−0.851043	−	0.525097i	$-0.824029\pi$
$353$	0.549103	−	0.951073i	0.0292258	−	0.0506205i	0.880268	+	0.474476i	$0.157362\pi$
$354$	−5.77823	+	10.0082i	−0.307110	+	0.531929i
$355$	8.40294	+	14.5543i	0.445982	+	0.772463i
$356$	−18.4029			−0.975354
$357$	1.02398	−	2.43956i	0.0541946	−	0.129115i
$358$	1.65237			0.0873305
$359$	−7.80589	−	13.5202i	−0.411979	−	0.713569i	0.583127	−	0.812381i	$-0.301829\pi$
$359$	−7.80589	−	13.5202i	−0.411979	−	0.713569i	−0.995106	+	0.0988123i	$0.968496\pi$
$360$	1.60074	−	2.77256i	0.0843662	−	0.146127i
$361$	8.83470	−	15.3021i	0.464984	−	0.805376i
$362$	−12.4509	−	21.5656i	−0.654405	−	1.13346i
$363$	1.00000			0.0524864
$364$	16.8059	−	2.13213i	0.880868	−	0.111754i
$365$	6.70998			0.351217
$366$	−4.85016	−	8.40073i	−0.253522	−	0.439113i
$367$	−0.395583	+	0.685170i	−0.0206493	+	0.0357656i	−0.876165	−	0.482011i	$-0.839907\pi$
$367$	−0.395583	+	0.685170i	−0.0206493	+	0.0357656i	0.855516	+	0.517776i	$0.173240\pi$
$368$	−0.976024	+	1.69052i	−0.0508787	+	0.0881246i
$369$	−4.12471	−	7.14421i	−0.214724	−	0.371913i
$370$	−16.4989			−0.857734
$371$	16.8059	−	2.13213i	0.872518	−	0.110695i
$372$	10.4989			0.544340
$373$	−7.95573	−	13.7797i	−0.411932	−	0.713487i	0.583169	−	0.812351i	$-0.301813\pi$
$373$	−7.95573	−	13.7797i	−0.411932	−	0.713487i	−0.995101	+	0.0988637i	$0.968479\pi$
$374$	−0.500000	+	0.866025i	−0.0258544	+	0.0447811i
$375$	0.399264	−	0.691545i	0.0206179	−	0.0357112i
$376$	3.02398	+	5.23768i	0.155950	+	0.270113i
$377$	−46.4177			−2.39063
$378$	1.02398	−	2.43956i	0.0526677	−	0.125478i
$379$	−17.0553			−0.876073			−0.438036	−	0.898957i	$-0.644326\pi$
$379$	−17.0553			−0.876073			−0.438036	+	0.898957i	$0.644326\pi$
$380$	1.84648	+	3.19820i	0.0947224	+	0.164064i
$381$	−4.17750	+	7.23564i	−0.214020	+	0.370693i
$382$	2.40294	−	4.16202i	0.122945	−	0.212948i
$383$	−6.72062	−	11.6405i	−0.343408	−	0.594799i	0.641656	−	0.766993i	$-0.278248\pi$
$383$	−6.72062	−	11.6405i	−0.343408	−	0.594799i	−0.985063	+	0.172194i	$0.944915\pi$
$384$	1.00000			0.0510310
$385$	−5.12471	−	6.74413i	−0.261180	−	0.343713i
$386$	8.70998			0.443327
$387$	−2.57676	−	4.46308i	−0.130984	−	0.226871i
$388$	2.74943	−	4.76214i	0.139581	−	0.241761i
$389$	3.60074	−	6.23666i	0.182565	−	0.316211i	−0.760189	−	0.649702i	$-0.774893\pi$
$389$	3.60074	−	6.23666i	0.182565	−	0.316211i	0.942753	+	0.333491i	$0.108227\pi$
$390$	−10.2494	−	17.7525i	−0.519000	−	0.898934i
$391$	1.95205			0.0987193
$392$	−1.87529	+	6.74413i	−0.0947163	+	0.340630i
$393$	15.3047			0.772022
$394$	−0.327335	−	0.566960i	−0.0164909	−	0.0285630i
$395$	−8.97119	+	15.5386i	−0.451390	+	0.781830i
$396$	−0.500000	+	0.866025i	−0.0251259	+	0.0435194i
$397$	−6.47119	−	11.2084i	−0.324780	−	0.562535i	0.656688	−	0.754162i	$-0.271957\pi$
$397$	−6.47119	−	11.2084i	−0.324780	−	0.562535i	−0.981468	+	0.191627i	$0.938624\pi$
$398$	−7.69296			−0.385613
$399$	1.84648	+	2.42997i	0.0924396	+	0.121651i
$400$	5.24943			0.262471
$401$	8.45090	+	14.6374i	0.422018	+	0.730956i	0.996137	−	0.0878158i	$-0.0279887\pi$
$401$	8.45090	+	14.6374i	0.422018	+	0.730956i	−0.574119	+	0.818772i	$0.694655\pi$
$402$	−3.12471	+	5.41216i	−0.155846	+	0.269934i
$403$	33.6118	−	58.2173i	1.67432	−	2.90001i
$404$	9.97970	+	17.2854i	0.496509	+	0.859979i
$405$	−3.20147			−0.159082
$406$	7.42324	−	17.6854i	0.368409	−	0.877713i
$407$	5.15352			0.255450
$408$	−0.500000	−	0.866025i	−0.0247537	−	0.0428746i
$409$	18.5468	−	32.1240i	0.917080	−	1.58843i	0.113254	−	0.993566i	$-0.463873\pi$
$409$	18.5468	−	32.1240i	0.917080	−	1.58843i	0.803827	−	0.594864i	$-0.202794\pi$
$410$	13.2052	−	22.8720i	0.652156	−	1.12957i
$411$	3.20147	+	5.54511i	0.157917	+	0.273520i
$412$	0.307039			0.0151267
$413$	−30.3324	+	3.84821i	−1.49256	+	0.189358i
$414$	1.95205			0.0959379
$415$	10.4952	+	18.1782i	0.515188	+	0.892331i
$416$	3.20147	−	5.54511i	0.156965	−	0.271872i
$417$	−10.8741	+	18.8346i	−0.532509	+	0.922332i
$418$	−0.576760	−	0.998977i	−0.0282102	−	0.0488616i
$419$	22.4583			1.09716			0.548579	−	0.836099i	$-0.315169\pi$
$419$	22.4583			1.09716			0.548579	+	0.836099i	$0.315169\pi$
$420$	8.40294	−	1.06607i	0.410022	−	0.0520187i
$421$	−23.3453			−1.13778			−0.568891	−	0.822413i	$-0.692627\pi$
$421$	−23.3453			−1.13778			−0.568891	+	0.822413i	$0.692627\pi$
$422$	−7.29738	−	12.6394i	−0.355231	−	0.615278i
$423$	3.02398	−	5.23768i	0.147031	−	0.254665i
$424$	3.20147	−	5.54511i	0.155477	−	0.269294i
$425$	−2.62471	−	4.54614i	−0.127317	−	0.220520i
$426$	5.24943			0.254335
$427$	9.93290	−	23.6646i	0.480687	−	1.14521i
$428$	−9.05531			−0.437705
$429$	3.20147	+	5.54511i	0.154569	+	0.267721i
$430$	8.24943	−	14.2884i	0.397823	−	0.689049i
$431$	−15.9115	+	27.5595i	−0.766428	+	1.32749i	0.173060	+	0.984911i	$0.444634\pi$
$431$	−15.9115	+	27.5595i	−0.766428	+	1.32749i	−0.939488	+	0.342581i	$0.888699\pi$
$432$	−0.500000	−	0.866025i	−0.0240563	−	0.0416667i
$433$	30.3047			1.45635			0.728176	−	0.685390i	$-0.240368\pi$
$433$	30.3047			1.45635			0.728176	+	0.685390i	$0.240368\pi$
$434$	16.8059	+	22.1166i	0.806709	+	1.06163i
$435$	−23.2088			−1.11278
$436$	4.85016	+	8.40073i	0.232281	+	0.402322i
$437$	−1.12586	+	1.95005i	−0.0538573	+	0.0932836i
$438$	1.04795	−	1.81511i	0.0500731	−	0.0867292i
$439$	5.33102	+	9.23359i	0.254435	+	0.440695i	0.964742	−	0.263197i	$-0.0847770\pi$
$439$	5.33102	+	9.23359i	0.254435	+	0.440695i	−0.710307	+	0.703892i	$0.751444\pi$
$440$	−3.20147			−0.152624
$441$	6.77823	−	1.74802i	0.322773	−	0.0832390i
$442$	−6.40294			−0.304557
$443$	18.0277	+	31.2248i	0.856520	+	1.48354i	0.875228	+	0.483711i	$0.160711\pi$
$443$	18.0277	+	31.2248i	0.856520	+	1.48354i	−0.0187080	+	0.999825i	$0.505955\pi$
$444$	−2.57676	+	4.46308i	−0.122288	+	0.211808i
$445$	−29.4583	+	51.0232i	−1.39646	+	2.41873i
$446$	7.45090	+	12.9053i	0.352810	+	0.611085i
$447$	6.84648			0.323827
$448$	1.60074	+	2.10657i	0.0756277	+	0.0995262i
$449$	23.4006			1.10434			0.552172	−	0.833730i	$-0.313799\pi$
$449$	23.4006			1.10434			0.552172	+	0.833730i	$0.313799\pi$
$450$	−2.62471	−	4.54614i	−0.123730	−	0.214307i
$451$	−4.12471	+	7.14421i	−0.194225	+	0.336408i
$452$	6.24943	−	10.8243i	0.293948	−	0.509133i
$453$	−7.42692	−	12.8638i	−0.348947	−	0.604394i
$454$	−0.249425			−0.0117061
$455$	20.9903	−	50.0083i	0.984042	−	2.34442i
$456$	1.15352			0.0540185
$457$	9.30704	+	16.1203i	0.435365	+	0.754074i	0.997325	−	0.0730899i	$-0.0232860\pi$
$457$	9.30704	+	16.1203i	0.435365	+	0.754074i	−0.561960	+	0.827164i	$0.689953\pi$
$458$	2.04795	−	3.54716i	0.0956945	−	0.165748i
$459$	−0.500000	+	0.866025i	−0.0233380	+	0.0404226i
$460$	3.12471	+	5.41216i	0.145690	+	0.252343i
$461$	−31.4412			−1.46436			−0.732182	−	0.681109i	$-0.761498\pi$
$461$	−31.4412			−1.46436			−0.732182	+	0.681109i	$0.761498\pi$
$462$	−2.62471	+	0.332992i	−0.122113	+	0.0154922i
$463$	−22.0959			−1.02688			−0.513442	−	0.858124i	$-0.671630\pi$
$463$	−22.0959			−1.02688			−0.513442	+	0.858124i	$0.671630\pi$
$464$	−3.62471	−	6.27819i	−0.168273	−	0.291457i
$465$	16.8059	−	29.1087i	0.779354	−	1.34988i
$466$	−5.65352	+	9.79218i	−0.261894	+	0.453614i
$467$	−10.5288	−	18.2364i	−0.487215	−	0.843881i	0.512677	−	0.858582i	$-0.328654\pi$
$467$	−10.5288	−	18.2364i	−0.487215	−	0.843881i	−0.999892	+	0.0147004i	$0.995321\pi$
$468$	−6.40294			−0.295976
$469$	−16.4029	+	2.08101i	−0.757418	+	0.0960922i
$470$	19.3624			0.893119
$471$	4.73028	+	8.19308i	0.217960	+	0.377517i
$472$	−5.77823	+	10.0082i	−0.265965	+	0.460664i
$473$	−2.57676	+	4.46308i	−0.118480	+	0.205213i
$474$	2.80221	+	4.85357i	0.128710	+	0.222932i
$475$	6.05531			0.277837
$476$	1.02398	−	2.43956i	0.0469339	−	0.111817i
$477$	−6.40294			−0.293171
$478$	−3.29738	−	5.71123i	−0.150819	−	0.261225i
$479$	10.6044	−	18.3674i	0.484528	−	0.839227i	−0.515314	−	0.857002i	$-0.672325\pi$
$479$	10.6044	−	18.3674i	0.484528	−	0.839227i	0.999842	+	0.0177741i	$0.00565797\pi$
$480$	1.60074	−	2.77256i	0.0730633	−	0.126549i
$481$	16.4989	+	28.5768i	0.752283	+	1.30299i
$482$	17.1129			0.779473
$483$	3.12471	+	4.11213i	0.142179	+	0.187108i
$484$	1.00000			0.0454545
$485$	−8.80221	−	15.2459i	−0.399688	−	0.692279i
$486$	−0.500000	+	0.866025i	−0.0226805	+	0.0392837i
$487$	19.3550	−	33.5238i	0.877058	−	1.51911i	0.0225047	−	0.999747i	$-0.492836\pi$
$487$	19.3550	−	33.5238i	0.877058	−	1.51911i	0.854554	−	0.519363i	$-0.173831\pi$
$488$	−4.85016	−	8.40073i	−0.219556	−	0.380283i
$489$	13.0553			0.590382
$490$	15.6966	+	15.9949i	0.709102	+	0.722577i
$491$	19.1705			0.865154			0.432577	−	0.901597i	$-0.357604\pi$
$491$	19.1705			0.865154			0.432577	+	0.901597i	$0.357604\pi$
$492$	−4.12471	−	7.14421i	−0.185956	−	0.322086i
$493$	−3.62471	+	6.27819i	−0.163249	+	0.282755i
$494$	3.69296	−	6.39640i	0.166154	−	0.287787i
$495$	1.60074	+	2.77256i	0.0719477	+	0.124617i
$496$	10.4989			0.471412
$497$	8.40294	+	11.0583i	0.376924	+	0.496032i
$498$	6.55646			0.293802
$499$	13.9594	+	24.1784i	0.624909	+	1.08237i	0.988558	+	0.150838i	$0.0481973\pi$
$499$	13.9594	+	24.1784i	0.624909	+	1.08237i	−0.363649	+	0.931536i	$0.618469\pi$
$500$	0.399264	−	0.691545i	0.0178556	−	0.0309268i
$501$	3.35499	−	5.81102i	0.149890	−	0.259617i
$502$	−3.97970	−	6.89305i	−0.177623	−	0.307652i
$503$	−8.70998			−0.388359			−0.194179	−	0.980966i	$-0.562204\pi$
$503$	−8.70998			−0.388359			−0.194179	+	0.980966i	$0.562204\pi$
$504$	1.02398	−	2.43956i	0.0456115	−	0.108667i
$505$	63.8995			2.84349
$506$	−0.976024	−	1.69052i	−0.0433895	−	0.0751529i
$507$	−13.9989	+	24.2467i	−0.621711	+	1.07683i
$508$	−4.17750	+	7.23564i	−0.185346	+	0.321029i
$509$	0.894433	+	1.54920i	0.0396451	+	0.0686673i	0.885167	−	0.465273i	$-0.154044\pi$
$509$	0.894433	+	1.54920i	0.0396451	+	0.0686673i	−0.845522	+	0.533941i	$0.820711\pi$
$510$	−3.20147			−0.141764
$511$	5.50115	−	0.697921i	0.243357	−	0.0308742i
$512$	1.00000			0.0441942
$513$	−0.576760	−	0.998977i	−0.0254646	−	0.0441059i
$514$	11.2015	−	19.4015i	0.494076	−	0.855764i
$515$	0.491489	−	0.851283i	0.0216576	−	0.0375120i
$516$	−2.57676	−	4.46308i	−0.113436	−	0.196476i
$517$	−6.04795			−0.265989
$518$	−13.5265	+	1.71608i	−0.594321	+	0.0754004i
$519$	−5.50115			−0.241474
$520$	−10.2494	−	17.7525i	−0.449467	−	0.778500i
$521$	−11.8059	+	20.4484i	−0.517225	+	0.895861i	0.482574	+	0.875855i	$0.339702\pi$
$521$	−11.8059	+	20.4484i	−0.517225	+	0.895861i	−0.999800	+	0.0200057i	$0.993632\pi$
$522$	−3.62471	+	6.27819i	−0.158649	+	0.274789i
$523$	−21.7003	−	37.5861i	−0.948889	−	1.64352i	−0.747771	−	0.663957i	$-0.768876\pi$
$523$	−21.7003	−	37.5861i	−0.948889	−	1.64352i	−0.201118	−	0.979567i	$-0.564457\pi$
$524$	15.3047			0.668591
$525$	5.37529	−	12.8063i	0.234597	−	0.558913i
$526$	−25.0170			−1.09079
$527$	−5.24943	−	9.09227i	−0.228669	−	0.396066i
$528$	−0.500000	+	0.866025i	−0.0217597	+	0.0376889i
$529$	9.59476	−	16.6186i	0.417163	−	0.722548i
$530$	−10.2494	−	17.7525i	−0.445207	−	0.771120i
$531$	11.5565			0.501508
$532$	1.84648	+	2.42997i	0.0800551	+	0.105353i
$533$	−52.8206			−2.28791
$534$	9.20147	+	15.9374i	0.398187	+	0.689680i
$535$	−14.4952	+	25.1064i	−0.626681	+	1.08544i
$536$	−3.12471	+	5.41216i	−0.134967	+	0.233770i
$537$	−0.826185	−	1.43099i	−0.0356525	−	0.0617520i
$538$	8.10327			0.349357
$539$	−4.90294	−	4.99611i	−0.211185	−	0.215198i
$540$	−3.20147			−0.137769
$541$	−8.49517	−	14.7141i	−0.365236	−	0.632607i	0.623578	−	0.781761i	$-0.285678\pi$
$541$	−8.49517	−	14.7141i	−0.365236	−	0.632607i	−0.988814	+	0.149154i	$0.952345\pi$
$542$	2.40294	−	4.16202i	0.103215	−	0.178774i
$543$	−12.4509	+	21.5656i	−0.534319	+	0.925468i
$544$	−0.500000	−	0.866025i	−0.0214373	−	0.0371305i
$545$	31.0553			1.33026
$546$	−10.2494	−	13.4883i	−0.438635	−	0.577244i
$547$	−1.34533			−0.0575222			−0.0287611	−	0.999586i	$-0.509156\pi$
$547$	−1.34533			−0.0575222			−0.0287611	+	0.999586i	$0.509156\pi$
$548$	3.20147	+	5.54511i	0.136760	+	0.236875i
$549$	−4.85016	+	8.40073i	−0.207000	+	0.358534i
$550$	−2.62471	+	4.54614i	−0.111918	+	0.193848i
$551$	−4.18118	−	7.24201i	−0.178124	−	0.308520i
$552$	1.95205			0.0830846
$553$	−5.73879	+	13.6723i	−0.244038	+	0.581407i
$554$	−11.2088			−0.476218
$555$	8.24943	+	14.2884i	0.350169	+	0.606510i
$556$	−10.8741	+	18.8346i	−0.461166	+	0.798763i
$557$	8.32733	−	14.4234i	0.352840	−	0.611138i	−0.633905	−	0.773411i	$-0.718549\pi$
$557$	8.32733	−	14.4234i	0.352840	−	0.611138i	0.986746	+	0.162273i	$0.0518825\pi$
$558$	−5.24943	−	9.09227i	−0.222226	−	0.384907i
$559$	−32.9977			−1.39565
$560$	8.40294	−	1.06607i	0.355089	−	0.0450495i
$561$	1.00000			0.0422200
$562$	8.74943	+	15.1544i	0.369072	+	0.639252i
$563$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$563$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$564$	3.02398	−	5.23768i	0.127332	−	0.220546i
$565$	−20.0074	−	34.6538i	−0.841716	−	1.45789i
$566$	27.4006			1.15174
$567$	−2.62471	+	0.332992i	−0.110228	+	0.0139844i
$568$	5.24943			0.220261
$569$	5.27708	+	9.14017i	0.221227	+	0.383176i	0.955181	−	0.296023i	$-0.0956606\pi$
$569$	5.27708	+	9.14017i	0.221227	+	0.383176i	−0.733954	+	0.679199i	$0.762327\pi$
$570$	1.84648	−	3.19820i	0.0773406	−	0.133958i
$571$	−2.37529	+	4.11412i	−0.0994027	+	0.172171i	−0.911438	−	0.411438i	$-0.865027\pi$
$571$	−2.37529	+	4.11412i	−0.0994027	+	0.172171i	0.812035	+	0.583609i	$0.198360\pi$
$572$	3.20147	+	5.54511i	0.133860	+	0.231853i
$573$	−4.80589			−0.200769
$574$	8.44722	−	20.1250i	0.352580	−	0.840001i
$575$	10.2471			0.427335
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	−18.7771	+	32.5229i	−0.781700	+	1.35394i	0.149250	+	0.988799i	$0.452314\pi$
$577$	−18.7771	+	32.5229i	−0.781700	+	1.35394i	−0.930951	+	0.365145i	$0.881019\pi$
$578$	8.00000	−	13.8564i	0.332756	−	0.576351i
$579$	−4.35499	−	7.54307i	−0.180987	−	0.313479i
$580$	−23.2088			−0.963694
$581$	10.4952	+	13.8117i	0.435413	+	0.573004i
$582$	−5.49885			−0.227935
$583$	3.20147	+	5.54511i	0.132591	+	0.229655i
$584$	1.04795	−	1.81511i	0.0433646	−	0.0751097i
$585$	−10.2494	+	17.7525i	−0.423762	+	0.733977i
$586$	9.87414	+	17.1025i	0.407897	+	0.706498i
$587$	−17.0982			−0.705718			−0.352859	−	0.935676i	$-0.614791\pi$
$587$	−17.0982			−0.705718			−0.352859	+	0.935676i	$0.614791\pi$
$588$	6.77823	−	1.74802i	0.279530	−	0.0720871i
$589$	12.1106			0.499010
$590$	18.4989	+	32.0409i	0.761586	+	1.31910i
$591$	−0.327335	+	0.566960i	−0.0134647	+	0.0233216i
$592$	−2.57676	+	4.46308i	−0.105904	+	0.183431i
$593$	16.1236	+	27.9268i	0.662115	+	1.14682i	0.980059	+	0.198708i	$0.0636745\pi$
$593$	16.1236	+	27.9268i	0.662115	+	1.14682i	−0.317943	+	0.948110i	$0.602992\pi$
$594$	1.00000			0.0410305
$595$	−5.12471	−	6.74413i	−0.210093	−	0.276482i
$596$	6.84648			0.280443
$597$	3.84648	+	6.66230i	0.157426	+	0.272670i
$598$	6.24943	−	10.8243i	0.255558	−	0.442639i
$599$	−1.69664	+	2.93867i	−0.0693229	+	0.120071i	−0.898603	−	0.438762i	$-0.855417\pi$
$599$	−1.69664	+	2.93867i	−0.0693229	+	0.120071i	0.829281	+	0.558833i	$0.188751\pi$
$600$	−2.62471	−	4.54614i	−0.107153	−	0.185595i
$601$	30.4989			1.24407			0.622037	−	0.782988i	$-0.286305\pi$
$601$	30.4989			1.24407			0.622037	+	0.782988i	$0.286305\pi$
$602$	5.27708	−	12.5723i	0.215078	−	0.512410i
$603$	6.24943			0.254496
$604$	−7.42692	−	12.8638i	−0.302197	−	0.523421i
$605$	1.60074	−	2.77256i	0.0650792	−	0.112720i
$606$	9.97970	−	17.2854i	0.405398	−	0.702170i
$607$	−6.49517	−	11.2500i	−0.263631	−	0.456622i	0.703573	−	0.710623i	$-0.251587\pi$
$607$	−6.49517	−	11.2500i	−0.263631	−	0.456622i	−0.967204	+	0.254001i	$0.918253\pi$
$608$	1.15352			0.0467814
$609$	−19.0277	+	2.41400i	−0.771040	+	0.0978204i
$610$	−31.0553			−1.25739
$611$	−19.3624	−	33.5366i	−0.783317	−	1.35674i
$612$	−0.500000	+	0.866025i	−0.0202113	+	0.0350070i
$613$	−10.0996	+	17.4930i	−0.407918	+	0.706535i	−0.994656	−	0.103241i	$-0.967079\pi$
$613$	−10.0996	+	17.4930i	−0.407918	+	0.706535i	0.586738	+	0.809777i	$0.300412\pi$
$614$	−2.15352	−	3.73001i	−0.0869090	−	0.150531i
$615$	−26.4103			−1.06497
$616$	−2.62471	+	0.332992i	−0.105753	+	0.0134166i
$617$	17.0936			0.688163			0.344081	−	0.938940i	$-0.388190\pi$
$617$	17.0936			0.688163			0.344081	+	0.938940i	$0.388190\pi$
$618$	−0.153520	−	0.265904i	−0.00617546	−	0.0106962i
$619$	−20.8347	+	36.0868i	−0.837417	+	1.45045i	0.0546300	+	0.998507i	$0.482602\pi$
$619$	−20.8347	+	36.0868i	−0.837417	+	1.45045i	−0.892047	+	0.451942i	$0.850731\pi$
$620$	16.8059	−	29.1087i	0.674941	−	1.16903i
$621$	−0.976024	−	1.69052i	−0.0391665	−	0.0678383i
$622$	−14.7579			−0.591739
$623$	−18.8442	+	44.8952i	−0.754976	+	1.79869i
$624$	−6.40294			−0.256323
$625$	11.8453	+	20.5167i	0.473813	+	0.820669i
$626$	−10.3753	+	17.9705i	−0.414680	+	0.718247i
$627$	−0.576760	+	0.998977i	−0.0230336	+	0.0398953i
$628$	4.73028	+	8.19308i	0.188759	+	0.326940i
$629$	5.15352			0.205484
$630$	−5.12471	−	6.74413i	−0.204173	−	0.268693i
$631$	−23.8995			−0.951424			−0.475712	−	0.879601i	$-0.657810\pi$
$631$	−23.8995			−0.951424			−0.475712	+	0.879601i	$0.657810\pi$
$632$	2.80221	+	4.85357i	0.111466	+	0.193065i
$633$	−7.29738	+	12.6394i	−0.290045	+	0.502372i
$634$	−8.09959	+	14.0289i	−0.321676	+	0.557159i
$635$	13.3741	+	23.1647i	0.530736	+	0.919263i
$636$	−6.40294			−0.253893
$637$	12.0074	−	43.1823i	0.475749	−	1.71094i
$638$	7.24943			0.287007
$639$	−2.62471	−	4.54614i	−0.103832	−	0.179842i
$640$	1.60074	−	2.77256i	0.0632747	−	0.109595i
$641$	7.15352	−	12.3903i	0.282547	−	0.489386i	−0.689464	−	0.724320i	$-0.742154\pi$
$641$	7.15352	−	12.3903i	0.282547	−	0.489386i	0.972011	+	0.234934i	$0.0754873\pi$
$642$	4.52766	+	7.84213i	0.178692	+	0.309504i
$643$	−35.4966			−1.39985			−0.699924	−	0.714218i	$-0.746783\pi$
$643$	−35.4966			−1.39985			−0.699924	+	0.714218i	$0.746783\pi$
$644$	3.12471	+	4.11213i	0.123131	+	0.162041i
$645$	−16.4989			−0.649642
$646$	−0.576760	−	0.998977i	−0.0226923	−	0.0393042i
$647$	−11.9078	+	20.6249i	−0.468143	+	0.810847i	−0.999337	−	0.0364027i	$-0.988410\pi$
$647$	−11.9078	+	20.6249i	−0.468143	+	0.810847i	0.531194	+	0.847250i	$0.321743\pi$
$648$	−0.500000	+	0.866025i	−0.0196419	+	0.0340207i
$649$	−5.77823	−	10.0082i	−0.226815	−	0.392856i
$650$	−33.6118			−1.31836
$651$	10.7506	−	25.6126i	0.421348	−	1.00384i
$652$	13.0553			0.511286
$653$	6.89811	+	11.9479i	0.269944	+	0.467557i	0.968847	−	0.247660i	$-0.0796615\pi$
$653$	6.89811	+	11.9479i	0.269944	+	0.467557i	−0.698903	+	0.715216i	$0.746328\pi$
$654$	4.85016	−	8.40073i	0.189656	−	0.328494i
$655$	24.4989	−	42.4333i	0.957249	−	1.65800i
$656$	−4.12471	−	7.14421i	−0.161043	−	0.278935i
$657$	−2.09591			−0.0817691
$658$	15.8741	−	2.01392i	0.618838	−	0.0785109i
$659$	18.9447			0.737980			0.368990	−	0.929433i	$-0.379704\pi$
$659$	18.9447			0.737980			0.368990	+	0.929433i	$0.379704\pi$
$660$	1.60074	+	2.77256i	0.0623086	+	0.107922i
$661$	−1.97970	+	3.42895i	−0.0770016	+	0.133371i	−0.901955	−	0.431830i	$-0.857868\pi$
$661$	−1.97970	+	3.42895i	−0.0770016	+	0.133371i	0.824953	+	0.565201i	$0.191201\pi$
$662$	−10.6236	+	18.4006i	−0.412896	+	0.715158i
$663$	3.20147	+	5.54511i	0.124335	+	0.215354i
$664$	6.55646			0.254440
$665$	9.69296	−	1.22973i	0.375877	−	0.0476868i
$666$	5.15352			0.199695
$667$	−7.07561	−	12.2553i	−0.273969	−	0.474528i
$668$	3.35499	−	5.81102i	0.129809	−	0.224835i
$669$	7.45090	−	12.9053i	0.288068	−	0.498949i
$670$	10.0037	+	17.3269i	0.386476	+	0.669396i
$671$	9.70032			0.374477
$672$	1.02398	−	2.43956i	0.0395007	−	0.0941082i
$673$	−8.69066			−0.335000			−0.167500	−	0.985872i	$-0.553569\pi$
$673$	−8.69066			−0.335000			−0.167500	+	0.985872i	$0.553569\pi$
$674$	12.7579	+	22.0974i	0.491417	+	0.851160i
$675$	−2.62471	+	4.54614i	−0.101025	+	0.174981i
$676$	−13.9989	+	24.2467i	−0.538417	+	0.932566i
$677$	15.7303	+	27.2456i	0.604564	+	1.04714i	0.992120	+	0.125289i	$0.0399859\pi$
$677$	15.7303	+	27.2456i	0.604564	+	1.04714i	−0.387557	+	0.921846i	$0.626681\pi$
$678$	−12.4989			−0.480015
$679$	−8.80221	−	11.5837i	−0.337798	−	0.444542i
$680$	−3.20147			−0.122771
$681$	0.124713	+	0.216009i	0.00477900	+	0.00827746i
$682$	−5.24943	+	9.09227i	−0.201011	+	0.348161i
$683$	−12.3730	+	21.4306i	−0.473439	+	0.820021i	−0.999538	−	0.0304028i	$-0.990321\pi$
$683$	−12.3730	+	21.4306i	−0.473439	+	0.820021i	0.526098	+	0.850424i	$0.323654\pi$
$684$	−0.576760	−	0.998977i	−0.0220530	−	0.0381968i
$685$	20.4989			0.783221
$686$	14.5325	+	11.4807i	0.554853	+	0.438336i
$687$	−4.09591			−0.156269
$688$	−2.57676	−	4.46308i	−0.0982380	−	0.170153i
$689$	−20.4989	+	35.5051i	−0.780944	+	1.35263i
$690$	3.12471	−	5.41216i	0.118956	−	0.206037i
$691$	−12.7771	−	22.1306i	−0.486063	−	0.841886i	0.513809	−	0.857905i	$-0.328234\pi$
$691$	−12.7771	−	22.1306i	−0.486063	−	0.841886i	−0.999872	+	0.0160188i	$0.994901\pi$
$692$	−5.50115			−0.209122
$693$	1.60074	+	2.10657i	0.0608069	+	0.0800220i
$694$	3.05531			0.115978
$695$	34.8133	+	60.2983i	1.32054	+	2.28725i
$696$	−3.62471	+	6.27819i	−0.137394	+	0.237974i
$697$	−4.12471	+	7.14421i	−0.156235	+	0.270606i
$698$	2.00368	+	3.47048i	0.0758404	+	0.131359i
$699$	11.3070			0.427671
$700$	5.37529	−	12.8063i	0.203167	−	0.484033i
$701$	−14.1512			−0.534484			−0.267242	−	0.963629i	$-0.586112\pi$
$701$	−14.1512			−0.534484			−0.267242	+	0.963629i	$0.586112\pi$
$702$	3.20147	+	5.54511i	0.120832	+	0.209287i
$703$	−2.97234	+	5.14825i	−0.112104	+	0.194170i
$704$	−0.500000	+	0.866025i	−0.0188445	+	0.0326396i
$705$	−9.68118	−	16.7683i	−0.364614	−	0.631530i
$706$	−1.09821			−0.0413315
$707$	52.3877	−	6.64633i	1.97024	−	0.249961i
$708$	11.5565			0.434319
$709$	5.37529	+	9.31027i	0.201873	+	0.349655i	0.949132	−	0.314879i	$-0.101964\pi$
$709$	5.37529	+	9.31027i	0.201873	+	0.349655i	−0.747259	+	0.664533i	$0.768630\pi$
$710$	8.40294	−	14.5543i	0.315357	−	0.546214i
$711$	2.80221	−	4.85357i	0.105091	−	0.182023i
$712$	9.20147	+	15.9374i	0.344840	+	0.597280i
$713$	20.4943			0.767516
$714$	−2.62471	+	0.332992i	−0.0982274	+	0.0124619i
$715$	20.4989			0.766614
$716$	−0.826185	−	1.43099i	−0.0308760	−	0.0534788i
$717$	−3.29738	+	5.71123i	−0.123143	+	0.213290i
$718$	−7.80589	+	13.5202i	−0.291313	+	0.504569i
$719$	−1.37897	−	2.38844i	−0.0514268	−	0.0890739i	0.839166	−	0.543875i	$-0.183044\pi$
$719$	−1.37897	−	2.38844i	−0.0514268	−	0.0890739i	−0.890593	+	0.454801i	$0.849710\pi$
$720$	−3.20147			−0.119312
$721$	0.314401	−	0.749041i	0.0117089	−	0.0278958i
$722$	−17.6694			−0.657587
$723$	−8.55646	−	14.8202i	−0.318218	−	0.551170i
$724$	−12.4509	+	21.5656i	−0.462734	+	0.801479i
$725$	−19.0277	+	32.9569i	−0.706669	+	1.22399i
$726$	−0.500000	−	0.866025i	−0.0185567	−	0.0321412i
$727$	14.6141			0.542006			0.271003	−	0.962578i	$-0.412645\pi$
$727$	14.6141			0.542006			0.271003	+	0.962578i	$0.412645\pi$
$728$	−10.2494	−	13.4883i	−0.379869	−	0.499908i
$729$	1.00000			0.0370370
$730$	−3.35499	−	5.81102i	−0.124174	−	0.215075i
$731$	−2.57676	+	4.46308i	−0.0953049	+	0.165073i
$732$	−4.85016	+	8.40073i	−0.179267	+	0.310500i
$733$	−3.55278	−	6.15360i	−0.131225	−	0.227288i	0.792924	−	0.609321i	$-0.208558\pi$
$733$	−3.55278	−	6.15360i	−0.131225	−	0.227288i	−0.924149	+	0.382032i	$0.875224\pi$
$734$	0.791166			0.0292025
$735$	6.00368	−	21.5911i	0.221449	−	0.796401i
$736$	1.95205			0.0719534
$737$	−3.12471	−	5.41216i	−0.115100	−	0.199360i
$738$	−4.12471	+	7.14421i	−0.151833	+	0.262982i
$739$	20.7483	−	35.9371i	0.763238	−	1.32197i	−0.177936	−	0.984042i	$-0.556942\pi$
$739$	20.7483	−	35.9371i	0.763238	−	1.32197i	0.941173	−	0.337924i	$-0.109725\pi$
$740$	8.24943	+	14.2884i	0.303255	+	0.525253i
$741$	−7.38592			−0.271329
$742$	−10.2494	−	13.4883i	−0.376268	−	0.495170i
$743$	−31.9041			−1.17045			−0.585224	−	0.810872i	$-0.698993\pi$
$743$	−31.9041			−1.17045			−0.585224	+	0.810872i	$0.698993\pi$
$744$	−5.24943	−	9.09227i	−0.192453	−	0.333339i
$745$	10.9594	−	18.9823i	0.401522	−	0.695456i
$746$	−7.95573	+	13.7797i	−0.291280	+	0.504512i
$747$	−3.27823	−	5.67806i	−0.119944	−	0.207750i
$748$	1.00000			0.0365636
$749$	−9.27243	+	22.0910i	−0.338807	+	0.807188i
$750$	−0.798528			−0.0291581
$751$	−6.75794	−	11.7051i	−0.246601	−	0.427125i	0.715980	−	0.698121i	$-0.245980\pi$
$751$	−6.75794	−	11.7051i	−0.246601	−	0.427125i	−0.962580	+	0.270996i	$0.912647\pi$
$752$	3.02398	−	5.23768i	0.110273	−	0.190999i
$753$	−3.97970	+	6.89305i	−0.145028	+	0.251197i
$754$	23.2088	+	40.1989i	0.845216	+	1.46396i
$755$	−47.5542			−1.73067
$756$	−2.62471	+	0.332992i	−0.0954599	+	0.0121108i
$757$	−18.5542			−0.674363			−0.337181	−	0.941440i	$-0.609474\pi$
$757$	−18.5542			−0.674363			−0.337181	+	0.941440i	$0.609474\pi$
$758$	8.52766	+	14.7703i	0.309738	+	0.536483i
$759$	−0.976024	+	1.69052i	−0.0354274	+	0.0613621i
$760$	1.84648	−	3.19820i	0.0669789	−	0.116011i
$761$	−7.87529	−	13.6404i	−0.285479	−	0.494464i	0.687246	−	0.726425i	$-0.258819\pi$
$761$	−7.87529	−	13.6404i	−0.285479	−	0.494464i	−0.972725	+	0.231960i	$0.925486\pi$
$762$	8.35499			0.302669
$763$	25.4606	−	3.23013i	0.921734	−	0.116939i
$764$	−4.80589			−0.173871
$765$	1.60074	+	2.77256i	0.0578747	+	0.100242i
$766$	−6.72062	+	11.6405i	−0.242826	+	0.420587i
$767$	36.9977	−	64.0819i	1.33591	−	2.31386i
$768$	−0.500000	−	0.866025i	−0.0180422	−	0.0312500i
$769$	41.2854			1.48879			0.744395	−	0.667739i	$-0.232738\pi$
$769$	41.2854			1.48879			0.744395	+	0.667739i	$0.232738\pi$
$770$	−3.27823	+	7.81020i	−0.118139	+	0.281460i
$771$	−22.4029			−0.806822
$772$	−4.35499	−	7.54307i	−0.156740	−	0.271481i
$773$	−2.45458	+	4.25145i	−0.0882850	+	0.152914i	−0.906786	−	0.421591i	$-0.861472\pi$
$773$	−2.45458	+	4.25145i	−0.0882850	+	0.152914i	0.818501	+	0.574505i	$0.194805\pi$
$774$	−2.57676	+	4.46308i	−0.0926197	+	0.160422i
$775$	−27.5565	−	47.7292i	−0.989857	−	1.71448i
$776$	−5.49885			−0.197397
$777$	8.24943	+	10.8563i	0.295946	+	0.389466i
$778$	−7.20147			−0.258185
$779$	−4.75794	−	8.24099i	−0.170471	−	0.295264i
$780$	−10.2494	+	17.7525i	−0.366988	+	0.635642i
$781$	−2.62471	+	4.54614i	−0.0939196	+	0.162674i
$782$	−0.976024	−	1.69052i	−0.0349025	−	0.0604530i
$783$	7.24943			0.259073
$784$	6.77823	−	1.74802i	0.242080	−	0.0624292i
$785$	30.2877			1.08101
$786$	−7.65237	−	13.2543i	−0.272951	−	0.472765i
$787$	−0.384949	+	0.666751i	−0.0137219	+	0.0237671i	−0.872805	−	0.488069i	$-0.837701\pi$
$787$	−0.384949	+	0.666751i	−0.0137219	+	0.0237671i	0.859083	+	0.511836i	$0.171035\pi$
$788$	−0.327335	+	0.566960i	−0.0116608	+	0.0201971i
$789$	12.5085	+	21.6654i	0.445315	+	0.771308i
$790$	17.9424			0.638361
$791$	−20.0074	−	26.3297i	−0.711380	−	0.936177i
$792$	1.00000			0.0355335
$793$	31.0553	+	53.7894i	1.10281	+	1.91012i
$794$	−6.47119	+	11.2084i	−0.229654	+	0.397772i
$795$	−10.2494	+	17.7525i	−0.363510	+	0.629617i
$796$	3.84648	+	6.66230i	0.136335	+	0.236139i
$797$	28.9092			1.02401			0.512007	−	0.858981i	$-0.328902\pi$
$797$	28.9092			1.02401			0.512007	+	0.858981i	$0.328902\pi$
$798$	1.18118	−	2.81408i	0.0418132	−	0.0996175i
$799$	−6.04795			−0.213961
$800$	−2.62471	−	4.54614i	−0.0927976	−	0.160730i
$801$	9.20147	−	15.9374i	0.325118	−	0.563121i
$802$	8.45090	−	14.6374i	0.298412	−	0.516864i
$803$	1.04795	+	1.81511i	0.0369815	+	0.0640538i
$804$	6.24943			0.220400
$805$	16.4029	−	2.08101i	0.578128	−	0.0733460i
$806$	−67.2236			−2.36785
$807$	−4.05163	−	7.01764i	−0.142624	−	0.247032i
$808$	9.97970	−	17.2854i	0.351085	−	0.608097i
$809$	10.1247	−	17.5365i	0.355966	−	0.616551i	−0.631317	−	0.775525i	$-0.717485\pi$
$809$	10.1247	−	17.5365i	0.355966	−	0.616551i	0.987283	+	0.158974i	$0.0508186\pi$
$810$	1.60074	+	2.77256i	0.0562441	+	0.0974177i
$811$	−48.4989			−1.70302			−0.851512	−	0.524334i	$-0.824314\pi$
$811$	−48.4989			−1.70302			−0.851512	+	0.524334i	$0.824314\pi$
$812$	−19.0277	+	2.41400i	−0.667740	+	0.0847149i
$813$	−4.80589			−0.168550
$814$	−2.57676	−	4.46308i	−0.0903154	−	0.156431i
$815$	20.8981	−	36.1966i	0.732029	−	1.26791i
$816$	−0.500000	+	0.866025i	−0.0175035	+	0.0303170i
$817$	−2.97234	−	5.14825i	−0.103989	−	0.180114i
$818$	−37.0936			−1.29695
$819$	−6.55646	+	15.6204i	−0.229101	+	0.545821i
$820$	−26.4103			−0.922288
$821$	−15.6524	−	27.1107i	−0.546271	−	0.946170i	−0.998526	−	0.0542809i	$-0.982713\pi$
$821$	−15.6524	−	27.1107i	−0.546271	−	0.946170i	0.452254	−	0.891889i	$-0.350620\pi$
$822$	3.20147	−	5.54511i	0.111664	−	0.193408i
$823$	−0.143858	+	0.249170i	−0.00501459	+	0.00868552i	−0.868522	−	0.495651i	$-0.834930\pi$
$823$	−0.143858	+	0.249170i	−0.00501459	+	0.00868552i	0.863507	+	0.504336i	$0.168263\pi$
$824$	−0.153520	−	0.265904i	−0.00534811	−	0.00926319i
$825$	5.24943			0.182762
$826$	18.4989	+	24.3445i	0.643657	+	0.847054i
$827$	37.2471			1.29521			0.647605	−	0.761976i	$-0.275771\pi$
$827$	37.2471			1.29521			0.647605	+	0.761976i	$0.275771\pi$
$828$	−0.976024	−	1.69052i	−0.0339192	−	0.0587497i
$829$	−24.5768	+	42.5682i	−0.853586	+	1.47845i	0.0243643	+	0.999703i	$0.492244\pi$
$829$	−24.5768	+	42.5682i	−0.853586	+	1.47845i	−0.877950	+	0.478751i	$0.841090\pi$
$830$	10.4952	−	18.1782i	0.364293	−	0.630973i
$831$	5.60442	+	9.70714i	0.194415	+	0.336737i
$832$	−6.40294			−0.221982
$833$	−4.90294	−	4.99611i	−0.169877	−	0.173105i
$834$	21.7483			0.753081
$835$	−10.7409	−	18.6038i	−0.371705	−	0.643811i
$836$	−0.576760	+	0.998977i	−0.0199477	+	0.0345503i
$837$	−5.24943	+	9.09227i	−0.181447	+	0.314275i
$838$	−11.2291	−	19.4494i	−0.387904	−	0.671869i
$839$	−2.81785			−0.0972830			−0.0486415	−	0.998816i	$-0.515489\pi$
$839$	−2.81785			−0.0972830			−0.0486415	+	0.998816i	$0.515489\pi$
$840$	−5.12471	−	6.74413i	−0.176819	−	0.232695i
$841$	23.5542			0.812213
$842$	11.6727	+	20.2176i	0.402267	+	0.696746i
$843$	8.74943	−	15.1544i	0.301346	−	0.521947i
$844$	−7.29738	+	12.6394i	−0.251186	+	0.435067i
$845$	44.8169	+	77.6252i	1.54175	+	2.67039i
$846$	−6.04795			−0.207933
$847$	1.02398	−	2.43956i	0.0351842	−	0.0838244i
$848$	−6.40294			−0.219878
$849$	−13.7003	−	23.7297i	−0.470194	−	0.814400i
$850$	−2.62471	+	4.54614i	−0.0900269	+	0.155931i
$851$	−5.02996	+	8.71214i	−0.172425	+	0.298648i
$852$	−2.62471	−	4.54614i	−0.0899212	−	0.155748i
$853$	2.39558			0.0820232			0.0410116	−	0.999159i	$-0.486942\pi$
$853$	2.39558			0.0820232			0.0410116	+	0.999159i	$0.486942\pi$
$854$	−25.4606	+	3.23013i	−0.871242	+	0.110533i
$855$	−3.69296			−0.126297
$856$	4.52766	+	7.84213i	0.154752	+	0.268039i
$857$	−0.404094	+	0.699912i	−0.0138036	+	0.0239085i	−0.872845	−	0.487998i	$-0.837727\pi$
$857$	−0.404094	+	0.699912i	−0.0138036	+	0.0239085i	0.859041	+	0.511907i	$0.171061\pi$
$858$	3.20147	−	5.54511i	0.109296	−	0.189307i
$859$	−3.27823	−	5.67806i	−0.111852	−	0.193733i	0.804665	−	0.593729i	$-0.202345\pi$
$859$	−3.27823	−	5.67806i	−0.111852	−	0.193733i	−0.916517	+	0.399996i	$0.869012\pi$
$860$	−16.4989			−0.562606
$861$	−21.6524	+	2.74700i	−0.737911	+	0.0936174i
$862$	31.8229			1.08389
$863$	10.3034	+	17.8459i	0.350730	+	0.607483i	0.986378	−	0.164497i	$-0.0526000\pi$
$863$	10.3034	+	17.8459i	0.350730	+	0.607483i	−0.635647	+	0.771980i	$0.719267\pi$
$864$	−0.500000	+	0.866025i	−0.0170103	+	0.0294628i
$865$	−8.80589	+	15.2522i	−0.299409	+	0.518592i
$866$	−15.1524	−	26.2447i	−0.514898	−	0.891830i
$867$	−16.0000			−0.543388
$868$	10.7506	−	25.6126i	0.364898	−	0.869349i
$869$	−5.60442			−0.190117
$870$	11.6044	+	20.0994i	0.393427	+	0.681435i
$871$	20.0074	−	34.6538i	0.677924	−	1.17420i
$872$	4.85016	−	8.40073i	0.164247	−	0.284484i
$873$	2.74943	+	4.76214i	0.0930539	+	0.161174i
$874$	2.25172			0.0761657
$875$	−1.27823	−	1.68216i	−0.0432121	−	0.0568672i
$876$	−2.09591			−0.0708141
$877$	−13.3011	−	23.0381i	−0.449145	−	0.777942i	0.549186	−	0.835700i	$-0.314938\pi$
$877$	−13.3011	−	23.0381i	−0.449145	−	0.777942i	−0.998331	+	0.0577586i	$0.981605\pi$
$878$	5.33102	−	9.23359i	0.179913	−	0.311619i
$879$	9.87414	−	17.1025i	0.333046	−	0.576853i
$880$	1.60074	+	2.77256i	0.0539608	+	0.0934629i
$881$	−8.49885			−0.286334			−0.143167	−	0.989699i	$-0.545729\pi$
$881$	−8.49885			−0.286334			−0.143167	+	0.989699i	$0.545729\pi$
$882$	−4.90294	−	4.99611i	−0.165091	−	0.168228i
$883$	46.2448			1.55626			0.778131	−	0.628102i	$-0.216168\pi$
$883$	46.2448			1.55626			0.778131	+	0.628102i	$0.216168\pi$
$884$	3.20147	+	5.54511i	0.107677	+	0.186502i
$885$	18.4989	−	32.0409i	0.621832	−	1.07704i
$886$	18.0277	−	31.2248i	0.605651	−	1.04902i
$887$	−9.14386	−	15.8376i	−0.307021	−	0.531775i	0.670688	−	0.741739i	$-0.265999\pi$
$887$	−9.14386	−	15.8376i	−0.307021	−	0.531775i	−0.977709	+	0.209964i	$0.932665\pi$
$888$	5.15352			0.172941
$889$	13.3741	+	17.6004i	0.448554	+	0.590298i
$890$	58.9165			1.97489
$891$	−0.500000	−	0.866025i	−0.0167506	−	0.0290129i
$892$	7.45090	−	12.9053i	0.249474	−	0.432103i
$893$	3.48822	−	6.04177i	0.116729	−	0.202180i
$894$	−3.42324	−	5.92923i	−0.114490	−	0.198303i
$895$	−5.29002			−0.176826
$896$	1.02398	−	2.43956i	0.0342087	−	0.0815001i
$897$	−12.4989			−0.417324
$898$	−11.7003	−	20.2656i	−0.390445	−	0.676270i
$899$	−38.0553	+	65.9137i	−1.26922	+	2.19835i
$900$	−2.62471	+	4.54614i	−0.0874904	+	0.151538i
$901$	3.20147	+	5.54511i	0.106657	+	0.184734i
$902$	8.24943			0.274676
$903$	−13.5265	+	1.71608i	−0.450134	+	0.0571077i
$904$	−12.4989			−0.415706
$905$	39.8612	+	69.0416i	1.32503	+	2.29502i
$906$	−7.42692	+	12.8638i	−0.246743	+	0.427371i
$907$	15.8347	−	27.4265i	0.525782	−	0.910682i	−0.473766	−	0.880651i	$-0.657106\pi$
$907$	15.8347	−	27.4265i	0.525782	−	0.910682i	0.999549	−	0.0300314i	$-0.00956074\pi$
$908$	0.124713	+	0.216009i	0.00413873	+	0.00716849i
$909$	−19.9594			−0.662012
$910$	−53.8036	+	6.82596i	−1.78357	+	0.226278i
$911$	58.7727			1.94723			0.973613	−	0.228207i	$-0.0732864\pi$
$911$	58.7727			1.94723			0.973613	+	0.228207i	$0.0732864\pi$
$912$	−0.576760	−	0.998977i	−0.0190984	−	0.0330794i
$913$	−3.27823	+	5.67806i	−0.108494	+	0.187917i
$914$	9.30704	−	16.1203i	0.307849	−	0.533211i
$915$	15.5277	+	26.8947i	0.513329	+	0.889111i
$916$	−4.09591			−0.135333
$917$	15.6717	−	37.3369i	0.517525	−	1.23297i
$918$	1.00000			0.0330049
$919$	16.4845	+	28.5521i	0.543775	+	0.941845i	0.998683	+	0.0513070i	$0.0163387\pi$
$919$	16.4845	+	28.5521i	0.543775	+	0.941845i	−0.454908	+	0.890538i	$0.650328\pi$
$920$	3.12471	−	5.41216i	0.103019	−	0.178434i
$921$	−2.15352	+	3.73001i	−0.0709609	+	0.122908i
$922$	15.7206	+	27.2289i	0.517731	+	0.896736i
$923$	−33.6118			−1.10635
$924$	1.60074	+	2.10657i	0.0526604	+	0.0693011i
$925$	27.0530			0.889498
$926$	11.0480	+	19.1356i	0.363058	+	0.628835i
$927$	−0.153520	+	0.265904i	−0.00504224	+	0.00873342i
$928$	−3.62471	+	6.27819i	−0.118987	+	0.206092i
$929$	−20.9497	−	36.2860i	−0.687339	−	1.19051i	−0.972696	−	0.232085i	$-0.925445\pi$
$929$	−20.9497	−	36.2860i	−0.687339	−	1.19051i	0.285357	−	0.958421i	$-0.407888\pi$
$930$	−33.6118			−1.10217
$931$	7.81882	−	2.01637i	0.256252	−	0.0660840i
$932$	11.3070			0.370374
$933$	7.37897	+	12.7807i	0.241577	+	0.418423i
$934$	−10.5288	+	18.2364i	−0.344513	+	0.596714i
$935$	1.60074	−	2.77256i	0.0523497	−	0.0906723i
$936$	3.20147	+	5.54511i	0.104643	+	0.181248i
$937$	−33.4966			−1.09428			−0.547142	−	0.837040i	$-0.684284\pi$
$937$	−33.4966			−1.09428			−0.547142	+	0.837040i	$0.684284\pi$
$938$	10.0037	+	13.1649i	0.326632	+	0.429848i
$939$	20.7506			0.677169
$940$	−9.68118	−	16.7683i	−0.315765	−	0.546921i
$941$	22.8741	−	39.6192i	0.745676	−	1.29155i	−0.204203	−	0.978929i	$-0.565460\pi$
$941$	22.8741	−	39.6192i	0.745676	−	1.29155i	0.949878	−	0.312619i	$-0.101206\pi$
$942$	4.73028	−	8.19308i	0.154121	−	0.266945i
$943$	−8.05163	−	13.9458i	−0.262197	−	0.454139i
$944$	11.5565			0.376131
$945$	−3.27823	+	7.81020i	−0.106641	+	0.254066i
$946$	5.15352			0.167555
$947$	22.5265	+	39.0171i	0.732013	+	1.26788i	0.956021	+	0.293297i	$0.0947524\pi$
$947$	22.5265	+	39.0171i	0.732013	+	1.26788i	−0.224008	+	0.974587i	$0.571914\pi$
$948$	2.80221	−	4.85357i	0.0910115	−	0.157637i
$949$	−6.70998	+	11.6220i	−0.217815	+	0.377267i
$950$	−3.02766	−	5.24406i	−0.0982302	−	0.170140i
$951$	16.1992			0.525294
$952$	−2.62471	+	0.332992i	−0.0850674	+	0.0107923i
$953$	37.1705			1.20407			0.602036	−	0.798469i	$-0.294356\pi$
$953$	37.1705			1.20407			0.602036	+	0.798469i	$0.294356\pi$
$954$	3.20147	+	5.54511i	0.103651	+	0.179530i
$955$	−7.69296	+	13.3246i	−0.248938	+	0.431174i
$956$	−3.29738	+	5.71123i	−0.106645	+	0.184714i
$957$	−3.62471	−	6.27819i	−0.117170	−	0.202945i
$958$	−21.2088			−0.685226
$959$	16.8059	−	2.13213i	0.542690	−	0.0688501i
$960$	−3.20147			−0.103327
$961$	−39.6129	−	68.6116i	−1.27784	−	2.21328i
$962$	16.4989	−	28.5768i	0.531944	−	0.921355i
$963$	4.52766	−	7.84213i	0.145902	−	0.252709i
$964$	−8.55646	−	14.8202i	−0.275585	−	0.477327i
$965$	−27.8848			−0.897643
$966$	1.99885	−	4.76214i	0.0643120	−	0.153219i
$967$	42.7579			1.37500			0.687501	−	0.726183i	$-0.258708\pi$
$967$	42.7579			1.37500			0.687501	+	0.726183i	$0.258708\pi$
$968$	−0.500000	−	0.866025i	−0.0160706	−	0.0278351i
$969$	−0.576760	+	0.998977i	−0.0185282	+	0.0320918i
$970$	−8.80221	+	15.2459i	−0.282622	+	0.489515i
$971$	−0.345331	−	0.598130i	−0.0110822	−	0.0191949i	0.860431	−	0.509567i	$-0.170194\pi$
$971$	−0.345331	−	0.598130i	−0.0110822	−	0.0191949i	−0.871513	+	0.490372i	$0.836861\pi$
$972$	1.00000			0.0320750
$973$	34.8133	+	45.8143i	1.11606	+	1.46874i
$974$	−38.7100			−1.24035
$975$	16.8059	+	29.1087i	0.538219	+	0.932223i
$976$	−4.85016	+	8.40073i	−0.155250	+	0.268901i
$977$	16.5948	−	28.7430i	0.530913	−	0.919569i	−0.468436	−	0.883497i	$-0.655182\pi$
$977$	16.5948	−	28.7430i	0.530913	−	0.919569i	0.999349	−	0.0360713i	$-0.0114843\pi$
$978$	−6.52766	−	11.3062i	−0.208731	−	0.361533i
$979$	−18.4029			−0.588161
$980$	6.00368	−	21.5911i	0.191781	−	0.689704i
$981$	−9.70032			−0.309707
$982$	−9.58527	−	16.6022i	−0.305878	−	0.529797i
$983$	21.3310	−	36.9464i	0.680354	−	1.17841i	−0.294519	−	0.955646i	$-0.595159\pi$
$983$	21.3310	−	36.9464i	0.680354	−	1.17841i	0.974873	−	0.222762i	$-0.0715072\pi$
$984$	−4.12471	+	7.14421i	−0.131491	+	0.227749i
$985$	1.04795	+	1.81511i	0.0333906	+	0.0578341i
$986$	7.24943			0.230869
$987$	−9.68118	−	12.7404i	−0.308155	−	0.405533i
$988$	−7.38592			−0.234977
$989$	−5.02996	−	8.71214i	−0.159943	−	0.277030i
$990$	1.60074	−	2.77256i	0.0508747	−	0.0881176i
$991$	12.0074	−	20.7974i	0.381426	−	0.660650i	−0.609840	−	0.792525i	$-0.708766\pi$
$991$	12.0074	−	20.7974i	0.381426	−	0.660650i	0.991266	+	0.131875i	$0.0420996\pi$
$992$	−5.24943	−	9.09227i	−0.166669	−	0.288680i
$993$	21.2471			0.674257
$994$	5.37529	−	12.8063i	0.170494	−	0.406191i
$995$	24.6288			0.780785
$996$	−3.27823	−	5.67806i	−0.103875	−	0.179916i
$997$	−16.7985	+	29.0959i	−0.532015	+	0.921477i	0.467287	+	0.884106i	$0.345232\pi$
$997$	−16.7985	+	29.0959i	−0.532015	+	0.921477i	−0.999301	+	0.0373707i	$0.988102\pi$
$998$	13.9594	−	24.1784i	0.441877	−	0.765354i
$999$	−2.57676	−	4.46308i	−0.0815251	−	0.141206i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.i.f.67.3	✓	6
3.2	odd	2		1386.2.k.w.991.1		6
7.2	even	3	inner	462.2.i.f.331.3	yes	6
7.3	odd	6		3234.2.a.bg.1.3		3
7.4	even	3		3234.2.a.bi.1.1		3
21.2	odd	6		1386.2.k.w.793.1		6
21.11	odd	6		9702.2.a.dt.1.3		3
21.17	even	6		9702.2.a.du.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.i.f.67.3	✓	6	1.1	even	1	trivial
462.2.i.f.331.3	yes	6	7.2	even	3	inner
1386.2.k.w.793.1		6	21.2	odd	6
1386.2.k.w.991.1		6	3.2	odd	2
3234.2.a.bg.1.3		3	7.3	odd	6
3234.2.a.bi.1.1		3	7.4	even	3
9702.2.a.dt.1.3		3	21.11	odd	6
9702.2.a.du.1.1		3	21.17	even	6

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:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	462.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.60074 + 2.77256i) q^{5} +1.00000 q^{6} +(1.60074 + 2.10657i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.60074 + 2.77256i) q^{5} +1.00000 q^{6} +(1.60074 + 2.10657i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(1.60074 - 2.77256i) q^{10} +(-0.500000 + 0.866025i) q^{11} +(-0.500000 - 0.866025i) q^{12} -6.40294 q^{13} +(1.02398 - 2.43956i) q^{14} -3.20147 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-0.500000 + 0.866025i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(-0.576760 - 0.998977i) q^{19} -3.20147 q^{20} +(-2.62471 + 0.332992i) q^{21} +1.00000 q^{22} +(-0.976024 - 1.69052i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(-2.62471 + 4.54614i) q^{25} +(3.20147 + 5.54511i) q^{26} +1.00000 q^{27} +(-2.62471 + 0.332992i) q^{28} +7.24943 q^{29} +(1.60074 + 2.77256i) q^{30} +(-5.24943 + 9.09227i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-0.500000 - 0.866025i) q^{33} +1.00000 q^{34} +(-3.27823 + 7.81020i) q^{35} +1.00000 q^{36} +(-2.57676 - 4.46308i) q^{37} +(-0.576760 + 0.998977i) q^{38} +(3.20147 - 5.54511i) q^{39} +(1.60074 + 2.77256i) q^{40} +8.24943 q^{41} +(1.60074 + 2.10657i) q^{42} +5.15352 q^{43} +(-0.500000 - 0.866025i) q^{44} +(1.60074 - 2.77256i) q^{45} +(-0.976024 + 1.69052i) q^{46} +(3.02398 + 5.23768i) q^{47} +1.00000 q^{48} +(-1.87529 + 6.74413i) q^{49} +5.24943 q^{50} +(-0.500000 - 0.866025i) q^{51} +(3.20147 - 5.54511i) q^{52} +(3.20147 - 5.54511i) q^{53} +(-0.500000 - 0.866025i) q^{54} -3.20147 q^{55} +(1.60074 + 2.10657i) q^{56} +1.15352 q^{57} +(-3.62471 - 6.27819i) q^{58} +(-5.77823 + 10.0082i) q^{59} +(1.60074 - 2.77256i) q^{60} +(-4.85016 - 8.40073i) q^{61} +10.4989 q^{62} +(1.02398 - 2.43956i) q^{63} +1.00000 q^{64} +(-10.2494 - 17.7525i) q^{65} +(-0.500000 + 0.866025i) q^{66} +(-3.12471 + 5.41216i) q^{67} +(-0.500000 - 0.866025i) q^{68} +1.95205 q^{69} +(8.40294 - 1.06607i) q^{70} +5.24943 q^{71} +(-0.500000 - 0.866025i) q^{72} +(1.04795 - 1.81511i) q^{73} +(-2.57676 + 4.46308i) q^{74} +(-2.62471 - 4.54614i) q^{75} +1.15352 q^{76} +(-2.62471 + 0.332992i) q^{77} -6.40294 q^{78} +(2.80221 + 4.85357i) q^{79} +(1.60074 - 2.77256i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-4.12471 - 7.14421i) q^{82} +6.55646 q^{83} +(1.02398 - 2.43956i) q^{84} -3.20147 q^{85} +(-2.57676 - 4.46308i) q^{86} +(-3.62471 + 6.27819i) q^{87} +(-0.500000 + 0.866025i) q^{88} +(9.20147 + 15.9374i) q^{89} -3.20147 q^{90} +(-10.2494 - 13.4883i) q^{91} +1.95205 q^{92} +(-5.24943 - 9.09227i) q^{93} +(3.02398 - 5.23768i) q^{94} +(1.84648 - 3.19820i) q^{95} +(-0.500000 - 0.866025i) q^{96} -5.49885 q^{97} +(6.77823 - 1.74802i) q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} - 3 q^{3} - 3 q^{4} + 6 q^{6} + 6 q^{8} - 3 q^{9}+O(q^{10}) \) 6 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 + 6 * q^6 + 6 * q^8 - 3 * q^9	\( 6 q - 3 q^{2} - 3 q^{3} - 3 q^{4} + 6 q^{6} + 6 q^{8} - 3 q^{9} - 3 q^{11} - 3 q^{12} + 3 q^{14} - 3 q^{16} - 3 q^{17} - 3 q^{18} + 3 q^{19} - 3 q^{21} + 6 q^{22} - 9 q^{23} - 3 q^{24} - 3 q^{25} + 6 q^{27} - 3 q^{28} + 18 q^{29} - 6 q^{31} - 3 q^{32} - 3 q^{33} + 6 q^{34} + 6 q^{35} + 6 q^{36} - 9 q^{37} + 3 q^{38} + 24 q^{41} + 18 q^{43} - 3 q^{44} - 9 q^{46} + 15 q^{47} + 6 q^{48} - 24 q^{49} + 6 q^{50} - 3 q^{51} - 3 q^{54} - 6 q^{57} - 9 q^{58} - 9 q^{59} + 6 q^{61} + 12 q^{62} + 3 q^{63} + 6 q^{64} - 36 q^{65} - 3 q^{66} - 6 q^{67} - 3 q^{68} + 18 q^{69} + 12 q^{70} + 6 q^{71} - 3 q^{72} - 9 q^{74} - 3 q^{75} - 6 q^{76} - 3 q^{77} - 12 q^{79} - 3 q^{81} - 12 q^{82} - 12 q^{83} + 3 q^{84} - 9 q^{86} - 9 q^{87} - 3 q^{88} + 36 q^{89} - 36 q^{91} + 18 q^{92} - 6 q^{93} + 15 q^{94} + 24 q^{95} - 3 q^{96} + 18 q^{97} + 15 q^{98} + 6 q^{99}+O(q^{100}) \) 6 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 + 6 * q^6 + 6 * q^8 - 3 * q^9 - 3 * q^11 - 3 * q^12 + 3 * q^14 - 3 * q^16 - 3 * q^17 - 3 * q^18 + 3 * q^19 - 3 * q^21 + 6 * q^22 - 9 * q^23 - 3 * q^24 - 3 * q^25 + 6 * q^27 - 3 * q^28 + 18 * q^29 - 6 * q^31 - 3 * q^32 - 3 * q^33 + 6 * q^34 + 6 * q^35 + 6 * q^36 - 9 * q^37 + 3 * q^38 + 24 * q^41 + 18 * q^43 - 3 * q^44 - 9 * q^46 + 15 * q^47 + 6 * q^48 - 24 * q^49 + 6 * q^50 - 3 * q^51 - 3 * q^54 - 6 * q^57 - 9 * q^58 - 9 * q^59 + 6 * q^61 + 12 * q^62 + 3 * q^63 + 6 * q^64 - 36 * q^65 - 3 * q^66 - 6 * q^67 - 3 * q^68 + 18 * q^69 + 12 * q^70 + 6 * q^71 - 3 * q^72 - 9 * q^74 - 3 * q^75 - 6 * q^76 - 3 * q^77 - 12 * q^79 - 3 * q^81 - 12 * q^82 - 12 * q^83 + 3 * q^84 - 9 * q^86 - 9 * q^87 - 3 * q^88 + 36 * q^89 - 36 * q^91 + 18 * q^92 - 6 * q^93 + 15 * q^94 + 24 * q^95 - 3 * q^96 + 18 * q^97 + 15 * q^98 + 6 * q^99

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