LMFDB - Embedded newform 63.2.f.b.43.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [63,2,Mod(22,63)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(63, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("63.22");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	63.f (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:	$0.503057532734$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.309123.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 $ x^6 - 3x^5 + 10x^4 - 15x^3 + 19x^2 - 12*x + 3
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			43.3
Root			$0.500000 + 2.05195i$ of defining polynomial
Character	$\chi$	$=$	63.43
Dual form			63.2.f.b.22.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.23025 - 2.13086i) q^{2} +(-1.73025 + 0.0789082i) q^{3} +(-2.02704 - 3.51094i) q^{4} +(1.29679 + 2.24611i) q^{5} +(-1.96050 + 3.78400i) q^{6} +(0.500000 - 0.866025i) q^{7} -5.05408 q^{8} +(2.98755 - 0.273062i) q^{9} +O(q^{10})$	\(q+(1.23025 - 2.13086i) q^{2} +(-1.73025 + 0.0789082i) q^{3} +(-2.02704 - 3.51094i) q^{4} +(1.29679 + 2.24611i) q^{5} +(-1.96050 + 3.78400i) q^{6} +(0.500000 - 0.866025i) q^{7} -5.05408 q^{8} +(2.98755 - 0.273062i) q^{9} +6.38151 q^{10} +(-2.25729 + 3.90975i) q^{11} +(3.78434 + 5.91486i) q^{12} +(-0.500000 - 0.866025i) q^{13} +(-1.23025 - 2.13086i) q^{14} +(-2.42101 - 3.78400i) q^{15} +(-2.16372 + 3.74766i) q^{16} -0.945916 q^{17} +(3.09358 - 6.70198i) q^{18} -4.05408 q^{19} +(5.25729 - 9.10590i) q^{20} +(-0.796790 + 1.53790i) q^{21} +(5.55408 + 9.61996i) q^{22} +(0.136673 + 0.236725i) q^{23} +(8.74484 - 0.398809i) q^{24} +(-0.863327 + 1.49533i) q^{25} -2.46050 q^{26} +(-5.14766 + 0.708209i) q^{27} -4.05408 q^{28} +(-1.23025 + 2.13086i) q^{29} +(-11.0416 + 0.503554i) q^{30} +(-1.16372 - 2.01561i) q^{31} +(0.269748 + 0.467216i) q^{32} +(3.59718 - 6.94297i) q^{33} +(-1.16372 + 2.01561i) q^{34} +2.59358 q^{35} +(-7.01459 - 9.93559i) q^{36} +1.78074 q^{37} +(-4.98755 + 8.63868i) q^{38} +(0.933463 + 1.45899i) q^{39} +(-6.55408 - 11.3520i) q^{40} +(3.20321 + 5.54812i) q^{41} +(2.29679 + 3.58985i) q^{42} +(5.21780 - 9.03749i) q^{43} +18.3025 q^{44} +(4.48755 + 6.35624i) q^{45} +0.672570 q^{46} +(6.08113 - 10.5328i) q^{47} +(3.44805 - 6.65514i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(2.12422 + 3.67926i) q^{50} +(1.63667 - 0.0746406i) q^{51} +(-2.02704 + 3.51094i) q^{52} -6.27335 q^{53} +(-4.82383 + 11.8402i) q^{54} -11.7089 q^{55} +(-2.52704 + 4.37697i) q^{56} +(7.01459 - 0.319901i) q^{57} +(3.02704 + 5.24299i) q^{58} +(1.36333 + 2.36135i) q^{59} +(-8.37792 + 16.1704i) q^{60} +(1.13667 - 1.96878i) q^{61} -5.72665 q^{62} +(1.25729 - 2.72382i) q^{63} -7.32743 q^{64} +(1.29679 - 2.24611i) q^{65} +(-10.3691 - 16.2067i) q^{66} +(7.90856 + 13.6980i) q^{67} +(1.91741 + 3.32105i) q^{68} +(-0.255158 - 0.398809i) q^{69} +(3.19076 - 5.52655i) q^{70} +3.27335 q^{71} +(-15.0993 + 1.38008i) q^{72} -1.50739 q^{73} +(2.19076 - 3.79450i) q^{74} +(1.37578 - 2.65542i) q^{75} +(8.21780 + 14.2336i) q^{76} +(2.25729 + 3.90975i) q^{77} +(4.25729 - 0.194154i) q^{78} +(-7.35447 + 12.7383i) q^{79} -11.2235 q^{80} +(8.85087 - 1.63157i) q^{81} +15.7630 q^{82} +(0.472958 - 0.819187i) q^{83} +(7.01459 - 0.319901i) q^{84} +(-1.22665 - 2.12463i) q^{85} +(-12.8384 - 22.2368i) q^{86} +(1.96050 - 3.78400i) q^{87} +(11.4086 - 19.7602i) q^{88} -14.3566 q^{89} +(19.0651 - 1.74255i) q^{90} -1.00000 q^{91} +(0.554084 - 0.959702i) q^{92} +(2.17257 + 3.39569i) q^{93} +(-14.9626 - 25.9161i) q^{94} +(-5.25729 - 9.10590i) q^{95} +(-0.503599 - 0.787117i) q^{96} +(5.74484 - 9.95036i) q^{97} -2.46050 q^{98} +(-5.67617 + 12.2969i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + q^{2} - 4 q^{3} - 3 q^{4} + 5 q^{5} + q^{6} + 3 q^{7} - 12 q^{8} - 4 q^{9}+O(q^{10}) $ 6 * q + q^2 - 4 * q^3 - 3 * q^4 + 5 * q^5 + q^6 + 3 * q^7 - 12 * q^8 - 4 * q^9	\( 6 q + q^{2} - 4 q^{3} - 3 q^{4} + 5 q^{5} + q^{6} + 3 q^{7} - 12 q^{8} - 4 q^{9} + 2 q^{11} - 2 q^{12} - 3 q^{13} - q^{14} + 11 q^{15} - 3 q^{16} - 24 q^{17} + 13 q^{18} - 6 q^{19} + 16 q^{20} - 2 q^{21} + 15 q^{22} + 15 q^{24} - 6 q^{25} - 2 q^{26} - 7 q^{27} - 6 q^{28} - q^{29} - 26 q^{30} + 3 q^{31} + 8 q^{32} + 8 q^{33} + 3 q^{34} + 10 q^{35} - 11 q^{36} - 6 q^{37} - 8 q^{38} + 2 q^{39} - 21 q^{40} + 22 q^{41} + 11 q^{42} + 3 q^{43} + 46 q^{44} + 5 q^{45} + 24 q^{46} + 9 q^{47} - 14 q^{48} - 3 q^{49} - 10 q^{50} + 9 q^{51} - 3 q^{52} - 36 q^{53} - 17 q^{54} - 12 q^{55} - 6 q^{56} + 11 q^{57} + 9 q^{58} + 9 q^{59} - 20 q^{60} + 6 q^{61} - 36 q^{62} - 8 q^{63} - 24 q^{64} + 5 q^{65} - 2 q^{66} - 6 q^{68} - 39 q^{69} + 18 q^{71} - 24 q^{72} + 6 q^{73} - 6 q^{74} + 31 q^{75} + 21 q^{76} - 2 q^{77} + 10 q^{78} - 15 q^{79} + 22 q^{80} + 32 q^{81} + 18 q^{82} + 12 q^{83} + 11 q^{84} - 9 q^{85} - 34 q^{86} - q^{87} + 21 q^{88} - 4 q^{89} + 73 q^{90} - 6 q^{91} - 15 q^{92} + 33 q^{93} - 24 q^{94} - 16 q^{95} + 5 q^{96} - 3 q^{97} - 2 q^{98} - 46 q^{99}+O(q^{100}) \) 6 * q + q^2 - 4 * q^3 - 3 * q^4 + 5 * q^5 + q^6 + 3 * q^7 - 12 * q^8 - 4 * q^9 + 2 * q^11 - 2 * q^12 - 3 * q^13 - q^14 + 11 * q^15 - 3 * q^16 - 24 * q^17 + 13 * q^18 - 6 * q^19 + 16 * q^20 - 2 * q^21 + 15 * q^22 + 15 * q^24 - 6 * q^25 - 2 * q^26 - 7 * q^27 - 6 * q^28 - q^29 - 26 * q^30 + 3 * q^31 + 8 * q^32 + 8 * q^33 + 3 * q^34 + 10 * q^35 - 11 * q^36 - 6 * q^37 - 8 * q^38 + 2 * q^39 - 21 * q^40 + 22 * q^41 + 11 * q^42 + 3 * q^43 + 46 * q^44 + 5 * q^45 + 24 * q^46 + 9 * q^47 - 14 * q^48 - 3 * q^49 - 10 * q^50 + 9 * q^51 - 3 * q^52 - 36 * q^53 - 17 * q^54 - 12 * q^55 - 6 * q^56 + 11 * q^57 + 9 * q^58 + 9 * q^59 - 20 * q^60 + 6 * q^61 - 36 * q^62 - 8 * q^63 - 24 * q^64 + 5 * q^65 - 2 * q^66 - 6 * q^68 - 39 * q^69 + 18 * q^71 - 24 * q^72 + 6 * q^73 - 6 * q^74 + 31 * q^75 + 21 * q^76 - 2 * q^77 + 10 * q^78 - 15 * q^79 + 22 * q^80 + 32 * q^81 + 18 * q^82 + 12 * q^83 + 11 * q^84 - 9 * q^85 - 34 * q^86 - q^87 + 21 * q^88 - 4 * q^89 + 73 * q^90 - 6 * q^91 - 15 * q^92 + 33 * q^93 - 24 * q^94 - 16 * q^95 + 5 * q^96 - 3 * q^97 - 2 * q^98 - 46 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/63\mathbb{Z}\right)^\times$.

$n$	$10$	$29$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	1.23025	−	2.13086i	0.869920	−	1.50675i	0.00784213	−	0.999969i	$-0.497504\pi$
$2$	1.23025	−	2.13086i	0.869920	−	1.50675i	0.862078	−	0.506776i	$-0.169163\pi$
$3$	−1.73025	+	0.0789082i	−0.998962	+	0.0455577i
$3$	−1.73025	+	0.0789082i	−0.998962	+	0.0455577i
$4$	−2.02704	−	3.51094i	−1.01352	−	1.75547i
$5$	1.29679	+	2.24611i	0.579942	+	1.00449i	0.995485	+	0.0949156i	$0.0302581\pi$
$5$	1.29679	+	2.24611i	0.579942	+	1.00449i	−0.415543	+	0.909573i	$0.636409\pi$
$6$	−1.96050	+	3.78400i	−0.800373	+	1.54481i
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i
$8$	−5.05408			−1.78689
$9$	2.98755	−	0.273062i	0.995849	−	0.0910208i
$10$	6.38151			2.01801
$11$	−2.25729	+	3.90975i	−0.680600	+	1.17883i	0.294198	+	0.955744i	$0.404947\pi$
$11$	−2.25729	+	3.90975i	−0.680600	+	1.17883i	−0.974798	+	0.223089i	$0.928386\pi$
$12$	3.78434	+	5.91486i	1.09244	+	1.70747i
$13$	−0.500000	−	0.866025i	−0.138675	−	0.240192i	0.788320	−	0.615265i	$-0.210951\pi$
$13$	−0.500000	−	0.866025i	−0.138675	−	0.240192i	−0.926995	+	0.375073i	$0.877618\pi$
$14$	−1.23025	−	2.13086i	−0.328799	−	0.569496i
$15$	−2.42101	−	3.78400i	−0.625102	−	0.977025i
$16$	−2.16372	+	3.74766i	−0.540929	+	0.936916i
$17$	−0.945916			−0.229418			−0.114709	−	0.993399i	$-0.536594\pi$
$17$	−0.945916			−0.229418			−0.114709	+	0.993399i	$0.536594\pi$
$18$	3.09358	−	6.70198i	0.729164	−	1.57967i
$19$	−4.05408			−0.930071			−0.465035	−	0.885292i	$-0.653958\pi$
$19$	−4.05408			−0.930071			−0.465035	+	0.885292i	$0.653958\pi$
$20$	5.25729	−	9.10590i	1.17557	−	2.03614i
$21$	−0.796790	+	1.53790i	−0.173874	+	0.335597i
$22$	5.55408	+	9.61996i	1.18413	+	2.05098i
$23$	0.136673	+	0.236725i	0.0284983	+	0.0493605i	0.879923	−	0.475117i	$-0.157594\pi$
$23$	0.136673	+	0.236725i	0.0284983	+	0.0493605i	−0.851425	+	0.524477i	$0.824261\pi$
$24$	8.74484	−	0.398809i	1.78503	−	0.0814065i
$25$	−0.863327	+	1.49533i	−0.172665	+	0.299065i
$26$	−2.46050			−0.482545
$27$	−5.14766	+	0.708209i	−0.990668	+	0.136295i
$28$	−4.05408			−0.766150
$29$	−1.23025	+	2.13086i	−0.228452	+	0.395691i	−0.957350	−	0.288932i	$-0.906700\pi$
$29$	−1.23025	+	2.13086i	−0.228452	+	0.395691i	0.728897	+	0.684623i	$0.240033\pi$
$30$	−11.0416	+	0.503554i	−2.01592	+	0.0919360i
$31$	−1.16372	−	2.01561i	−0.209009	−	0.362015i	0.742393	−	0.669964i	$-0.233691\pi$
$31$	−1.16372	−	2.01561i	−0.209009	−	0.362015i	−0.951403	+	0.307949i	$0.900357\pi$
$32$	0.269748	+	0.467216i	0.0476851	+	0.0825930i
$33$	3.59718	−	6.94297i	0.626188	−	1.20862i
$34$	−1.16372	+	2.01561i	−0.199576	+	0.345675i
$35$	2.59358			0.438395
$36$	−7.01459	−	9.93559i	−1.16910	−	1.65593i
$37$	1.78074			0.292752			0.146376	−	0.989229i	$-0.453239\pi$
$37$	1.78074			0.292752			0.146376	+	0.989229i	$0.453239\pi$
$38$	−4.98755	+	8.63868i	−0.809087	+	1.40138i
$39$	0.933463	+	1.45899i	0.149474	+	0.233625i
$40$	−6.55408	−	11.3520i	−1.03629	−	1.79491i
$41$	3.20321	+	5.54812i	0.500257	+	0.866471i	1.00000		0.000297253i	$9.46187e-5\pi$
$41$	3.20321	+	5.54812i	0.500257	+	0.866471i	−0.499743	+	0.866174i	$0.666572\pi$
$42$	2.29679	+	3.58985i	0.354402	+	0.553926i
$43$	5.21780	−	9.03749i	0.795707	−	1.37820i	−0.126682	−	0.991943i	$-0.540433\pi$
$43$	5.21780	−	9.03749i	0.795707	−	1.37820i	0.922389	−	0.386262i	$-0.126234\pi$
$44$	18.3025			2.75921
$45$	4.48755	+	6.35624i	0.668964	+	0.947533i
$46$	0.672570			0.0991650
$47$	6.08113	−	10.5328i	0.887023	−	1.53637i	0.0436467	−	0.999047i	$-0.486102\pi$
$47$	6.08113	−	10.5328i	0.887023	−	1.53637i	0.843377	−	0.537323i	$-0.180564\pi$
$48$	3.44805	−	6.65514i	0.497683	−	0.960587i
$49$	−0.500000	−	0.866025i	−0.0714286	−	0.123718i
$50$	2.12422	+	3.67926i	0.300410	+	0.520326i
$51$	1.63667	−	0.0746406i	0.229180	−	0.0104518i
$52$	−2.02704	+	3.51094i	−0.281100	+	0.486880i
$53$	−6.27335			−0.861710			−0.430855	−	0.902421i	$-0.641788\pi$
$53$	−6.27335			−0.861710			−0.430855	+	0.902421i	$0.641788\pi$
$54$	−4.82383	+	11.8402i	−0.656440	+	1.61125i
$55$	−11.7089			−1.57883
$56$	−2.52704	+	4.37697i	−0.337690	+	0.584897i
$57$	7.01459	−	0.319901i	0.929105	−	0.0423719i
$58$	3.02704	+	5.24299i	0.397470	+	0.688438i
$59$	1.36333	+	2.36135i	0.177490	+	0.307422i	0.941020	−	0.338350i	$-0.109869\pi$
$59$	1.36333	+	2.36135i	0.177490	+	0.307422i	−0.763530	+	0.645772i	$0.776536\pi$
$60$	−8.37792	+	16.1704i	−1.08158	+	2.08758i
$61$	1.13667	−	1.96878i	0.145536	−	0.252076i	−0.784037	−	0.620714i	$-0.786843\pi$
$61$	1.13667	−	1.96878i	0.145536	−	0.252076i	0.929573	+	0.368639i	$0.120176\pi$
$62$	−5.72665			−0.727286
$63$	1.25729	−	2.72382i	0.158404	−	0.343169i
$64$	−7.32743			−0.915929
$65$	1.29679	−	2.24611i	0.160847	−	0.278595i
$66$	−10.3691	−	16.2067i	−1.27634	−	1.99491i
$67$	7.90856	+	13.6980i	0.966184	+	1.67348i	0.706400	+	0.707813i	$0.250318\pi$
$67$	7.90856	+	13.6980i	0.966184	+	1.67348i	0.259784	+	0.965667i	$0.416349\pi$
$68$	1.91741	+	3.32105i	0.232520	+	0.402737i
$69$	−0.255158	−	0.398809i	−0.0307175	−	0.0480110i
$70$	3.19076	−	5.52655i	0.381368	−	0.660550i
$71$	3.27335			0.388475			0.194237	−	0.980955i	$-0.437777\pi$
$71$	3.27335			0.388475			0.194237	+	0.980955i	$0.437777\pi$
$72$	−15.0993	+	1.38008i	−1.77947	+	0.162644i
$73$	−1.50739			−0.176427			−0.0882134	−	0.996102i	$-0.528116\pi$
$73$	−1.50739			−0.176427			−0.0882134	+	0.996102i	$0.528116\pi$
$74$	2.19076	−	3.79450i	0.254670	−	0.441102i
$75$	1.37578	−	2.65542i	0.158861	−	0.306621i
$76$	8.21780	+	14.2336i	0.942646	+	1.63271i
$77$	2.25729	+	3.90975i	0.257243	+	0.445557i
$78$	4.25729	−	0.194154i	0.482044	−	0.0219836i
$79$	−7.35447	+	12.7383i	−0.827443	+	1.43317i	0.0725952	+	0.997361i	$0.476872\pi$
$79$	−7.35447	+	12.7383i	−0.827443	+	1.43317i	−0.900038	+	0.435811i	$0.856461\pi$
$80$	−11.2235			−1.25483
$81$	8.85087	−	1.63157i	0.983430	−	0.181286i
$82$	15.7630			1.74074
$83$	0.472958	−	0.819187i	0.0519139	−	0.0899175i	−0.838901	−	0.544285i	$-0.816801\pi$
$83$	0.472958	−	0.819187i	0.0519139	−	0.0899175i	0.890815	+	0.454367i	$0.150135\pi$
$84$	7.01459	−	0.319901i	0.765354	−	0.0349040i
$85$	−1.22665	−	2.12463i	−0.133049	−	0.230448i
$86$	−12.8384	−	22.2368i	−1.38440	−	2.39786i
$87$	1.96050	−	3.78400i	0.210188	−	0.405688i
$88$	11.4086	−	19.7602i	1.21616	−	2.10644i
$89$	−14.3566			−1.52180			−0.760899	−	0.648871i	$-0.775242\pi$
$89$	−14.3566			−1.52180			−0.760899	+	0.648871i	$0.775242\pi$
$90$	19.0651	−	1.74255i	2.00964	−	0.183681i
$91$	−1.00000			−0.104828
$92$	0.554084	−	0.959702i	0.0577673	−	0.100056i
$93$	2.17257	+	3.39569i	0.225285	+	0.352117i
$94$	−14.9626	−	25.9161i	−1.54328	−	2.67304i
$95$	−5.25729	−	9.10590i	−0.539387	−	0.934246i
$96$	−0.503599	−	0.787117i	−0.0513983	−	0.0803348i
$97$	5.74484	−	9.95036i	0.583300	−	1.01031i	−0.411785	−	0.911281i	$-0.635094\pi$
$97$	5.74484	−	9.95036i	0.583300	−	1.01031i	0.995085	−	0.0990246i	$-0.0315722\pi$
$98$	−2.46050			−0.248549
$99$	−5.67617	+	12.2969i	−0.570476	+	1.23589i
$100$	7.00000			0.700000
$101$	1.83988	−	3.18677i	0.183075	−	0.317096i	−0.759851	−	0.650097i	$-0.774728\pi$
$101$	1.83988	−	3.18677i	0.183075	−	0.317096i	0.942926	+	0.333002i	$0.108061\pi$
$102$	1.85447	−	3.57935i	0.183620	−	0.354408i
$103$	4.86333	+	8.42353i	0.479198	+	0.829995i	0.999715	−	0.0238560i	$-0.00759431\pi$
$103$	4.86333	+	8.42353i	0.479198	+	0.829995i	−0.520518	+	0.853851i	$0.674261\pi$
$104$	2.52704	+	4.37697i	0.247797	+	0.429197i
$105$	−4.48755	+	0.204655i	−0.437940	+	0.0199723i
$106$	−7.71780	+	13.3676i	−0.749619	+	1.29838i
$107$	−1.37432			−0.132860			−0.0664301	−	0.997791i	$-0.521161\pi$
$107$	−1.37432			−0.132860			−0.0664301	+	0.997791i	$0.521161\pi$
$108$	12.9210	+	16.6376i	1.24332	+	1.60095i
$109$	−3.39922			−0.325587			−0.162793	−	0.986660i	$-0.552050\pi$
$109$	−3.39922			−0.325587			−0.162793	+	0.986660i	$0.552050\pi$
$110$	−14.4050	+	24.9501i	−1.37346	+	2.37890i
$111$	−3.08113	+	0.140515i	−0.292448	+	0.0133371i
$112$	2.16372	+	3.74766i	0.204452	+	0.354121i
$113$	−5.19436	−	8.99689i	−0.488644	−	0.846356i	0.511271	−	0.859420i	$-0.329175\pi$
$113$	−5.19436	−	8.99689i	−0.488644	−	0.846356i	−0.999915	+	0.0130636i	$0.995842\pi$
$114$	7.94805	−	15.3407i	0.744403	−	1.43678i
$115$	−0.354473	+	0.613964i	−0.0330547	+	0.0572525i
$116$	9.97509			0.926164
$117$	−1.73025	−	2.45076i	−0.159962	−	0.226573i
$118$	6.70895			0.617608
$119$	−0.472958	+	0.819187i	−0.0433560	+	0.0750948i
$120$	12.2360	+	19.1247i	1.11699	+	1.74584i
$121$	−4.69076	−	8.12463i	−0.426432	−	0.738603i
$122$	−2.79679	−	4.84418i	−0.253209	−	0.438572i
$123$	−5.98016	−	9.34689i	−0.539212	−	0.842781i
$124$	−4.71780	+	8.17147i	−0.423671	+	0.733820i
$125$	8.48968			0.759340
$126$	−4.25729	−	6.03011i	−0.379270	−	0.537205i
$127$	0.672570			0.0596809			0.0298405	−	0.999555i	$-0.490500\pi$
$127$	0.672570			0.0596809			0.0298405	+	0.999555i	$0.490500\pi$
$128$	−9.55408	+	16.5482i	−0.844470	+	1.46266i
$129$	−8.31498	+	16.0489i	−0.732093	+	1.41302i
$130$	−3.19076	−	5.52655i	−0.279848	−	0.484711i
$131$	−3.95691	−	6.85356i	−0.345717	−	0.598799i	0.639767	−	0.768569i	$-0.279031\pi$
$131$	−3.95691	−	6.85356i	−0.345717	−	0.598799i	−0.985484	+	0.169770i	$0.945697\pi$
$132$	−31.6680	+	1.44422i	−2.75634	+	0.125703i
$133$	−2.02704	+	3.51094i	−0.175767	+	0.304437i
$134$	38.9181			3.36201
$135$	−8.26615	−	10.6438i	−0.711437	−	0.916072i
$136$	4.78074			0.409945
$137$	1.83628	−	3.18054i	0.156884	−	0.271732i	−0.776859	−	0.629674i	$-0.783188\pi$
$137$	1.83628	−	3.18054i	0.156884	−	0.271732i	0.933744	+	0.357943i	$0.116522\pi$
$138$	−1.16372	+	0.0530713i	−0.0990620	+	0.00451773i
$139$	1.02704	+	1.77889i	0.0871126	+	0.150883i	0.906289	−	0.422658i	$-0.138903\pi$
$139$	1.02704	+	1.77889i	0.0871126	+	0.150883i	−0.819177	+	0.573541i	$0.805569\pi$
$140$	−5.25729	−	9.10590i	−0.444322	−	0.769589i
$141$	−9.69076	+	18.7043i	−0.816109	+	1.57519i
$142$	4.02704	−	6.97504i	0.337942	−	0.585332i
$143$	4.51459			0.377529
$144$	−5.44085	+	11.7872i	−0.453405	+	0.982263i
$145$	−6.38151			−0.529956
$146$	−1.85447	+	3.21204i	−0.153477	+	0.265830i
$147$	0.933463	+	1.45899i	0.0769907	+	0.120335i
$148$	−3.60963	−	6.25206i	−0.296710	−	0.513917i
$149$	6.77188	+	11.7292i	0.554774	+	0.960897i	0.997921	+	0.0644482i	$0.0205287\pi$
$149$	6.77188	+	11.7292i	0.554774	+	0.960897i	−0.443147	+	0.896449i	$0.646138\pi$
$150$	−3.96576	−	6.19843i	−0.323803	−	0.506099i
$151$	−4.96410	+	8.59808i	−0.403973	+	0.699702i	−0.994201	−	0.107535i	$-0.965704\pi$
$151$	−4.96410	+	8.59808i	−0.403973	+	0.699702i	0.590228	+	0.807236i	$0.299038\pi$
$152$	20.4897			1.66193
$153$	−2.82597	+	0.258294i	−0.228466	+	0.0208818i
$154$	11.1082			0.895122
$155$	3.01819	−	5.22765i	0.242427	−	0.419895i
$156$	3.23025	−	6.23476i	0.258627	−	0.499181i
$157$	−3.02704	−	5.24299i	−0.241584	−	0.418436i	0.719581	−	0.694408i	$-0.244334\pi$
$157$	−3.02704	−	5.24299i	−0.241584	−	0.418436i	−0.961166	+	0.275972i	$0.911000\pi$
$158$	18.0957	+	31.3427i	1.43962	+	2.49349i
$159$	10.8545	−	0.495019i	0.860816	−	0.0392575i
$160$	−0.699612	+	1.21176i	−0.0553092	+	0.0957983i
$161$	0.273346			0.0215427
$162$	7.41216	−	20.8672i	0.582354	−	1.63948i
$163$	17.8171			1.39554			0.697772	−	0.716320i	$-0.254175\pi$
$163$	17.8171			1.39554			0.697772	+	0.716320i	$0.254175\pi$
$164$	12.9861	−	22.4926i	1.01404	−	1.75637i
$165$	20.2594	−	0.923932i	1.57719	−	0.0719280i
$166$	−1.16372	−	2.01561i	−0.0903218	−	0.156442i
$167$	4.23385	+	7.33325i	0.327625	+	0.567464i	0.982040	−	0.188672i	$-0.0604183\pi$
$167$	4.23385	+	7.33325i	0.327625	+	0.567464i	−0.654415	+	0.756136i	$0.727085\pi$
$168$	4.02704	−	7.77266i	0.310693	−	0.599674i
$169$	6.00000	−	10.3923i	0.461538	−	0.799408i
$170$	−6.03638			−0.462969
$171$	−12.1118	+	1.10702i	−0.926210	+	0.0846558i
$172$	−42.3068			−3.22586
$173$	−8.67830	+	15.0313i	−0.659799	+	1.14281i	0.320868	+	0.947124i	$0.396025\pi$
$173$	−8.67830	+	15.0313i	−0.659799	+	1.14281i	−0.980667	+	0.195682i	$0.937308\pi$
$174$	−5.65126	−	8.83284i	−0.428421	−	0.669616i
$175$	0.863327	+	1.49533i	0.0652614	+	0.113036i
$176$	−9.76829	−	16.9192i	−0.736312	−	1.27533i
$177$	−2.54523	−	3.97816i	−0.191311	−	0.299017i
$178$	−17.6623	+	30.5919i	−1.32384	+	2.29296i
$179$	−11.3494			−0.848295			−0.424147	−	0.905593i	$-0.639426\pi$
$179$	−11.3494			−0.848295			−0.424147	+	0.905593i	$0.639426\pi$
$180$	13.2199	−	28.6399i	0.985356	−	2.13469i
$181$	21.8889			1.62699			0.813495	−	0.581572i	$-0.197562\pi$
$181$	21.8889			1.62699			0.813495	+	0.581572i	$0.197562\pi$
$182$	−1.23025	+	2.13086i	−0.0911924	+	0.157950i
$183$	−1.81138	+	3.49617i	−0.133901	+	0.258444i
$184$	−0.690757	−	1.19643i	−0.0509233	−	0.0882018i
$185$	2.30924	+	3.99973i	0.169779	+	0.294066i
$186$	9.90856	−	0.451880i	0.726531	−	0.0331335i
$187$	2.13521	−	3.69829i	0.156142	−	0.270446i
$188$	−49.3068			−3.59607
$189$	−1.96050	+	4.81211i	−0.142606	+	0.350030i
$190$	−25.8712			−1.87689
$191$	0.350874	−	0.607731i	0.0253883	−	0.0439739i	−0.853052	−	0.521826i	$-0.825251\pi$
$191$	0.350874	−	0.607731i	0.0253883	−	0.0439739i	0.878440	+	0.477852i	$0.158584\pi$
$192$	12.6783	−	0.578195i	0.914978	−	0.0417276i
$193$	−6.07227	−	10.5175i	−0.437092	−	0.757065i	0.560372	−	0.828241i	$-0.310658\pi$
$193$	−6.07227	−	10.5175i	−0.437092	−	0.757065i	−0.997464	+	0.0711760i	$0.977325\pi$
$194$	−14.1352	−	24.4829i	−1.01485	−	1.75777i
$195$	−2.06654	+	3.98866i	−0.147988	+	0.285634i
$196$	−2.02704	+	3.51094i	−0.144789	+	0.250781i
$197$	−16.4107			−1.16921			−0.584607	−	0.811317i	$-0.698751\pi$
$197$	−16.4107			−1.16921			−0.584607	+	0.811317i	$0.698751\pi$
$198$	19.2199	+	27.2235i	1.36590	+	1.93469i
$199$	22.7060			1.60959			0.804794	−	0.593555i	$-0.202276\pi$
$199$	22.7060			1.60959			0.804794	+	0.593555i	$0.202276\pi$
$200$	4.36333	−	7.55750i	0.308534	−	0.534396i
$201$	−14.7647	−	23.0770i	−1.04142	−	1.62773i
$202$	−4.52704	−	7.84107i	−0.318522	−	0.551696i
$203$	1.23025	+	2.13086i	0.0863468	+	0.149557i
$204$	−3.57966	−	5.59496i	−0.250627	−	0.391726i
$205$	−8.30778	+	14.3895i	−0.580241	+	1.00501i
$206$	23.9325			1.66745
$207$	0.472958	+	0.669906i	0.0328728	+	0.0465617i
$208$	4.32743			0.300053
$209$	9.15126	−	15.8505i	0.633006	−	1.09640i
$210$	−5.08472	+	9.81411i	−0.350879	+	0.677238i
$211$	−2.28074	−	3.95035i	−0.157012	−	0.271954i	0.776778	−	0.629775i	$-0.216853\pi$
$211$	−2.28074	−	3.95035i	−0.157012	−	0.271954i	−0.933790	+	0.357822i	$0.883520\pi$
$212$	12.7163	+	22.0253i	0.873362	+	1.51271i
$213$	−5.66372	+	0.258294i	−0.388071	+	0.0176980i
$214$	−1.69076	+	2.92848i	−0.115578	+	0.200187i
$215$	27.0656			1.84586
$216$	26.0167	−	3.57935i	1.77021	−	0.243544i
$217$	−2.32743			−0.157996
$218$	−4.18190	+	7.24327i	−0.283234	+	0.490576i
$219$	2.60817	−	0.118946i	0.176244	−	0.00803760i
$220$	23.7345	+	41.1094i	1.60018	+	2.77160i
$221$	0.472958	+	0.819187i	0.0318146	+	0.0551045i
$222$	−3.49115	+	6.73832i	−0.234310	+	0.452246i
$223$	−6.66225	+	11.5394i	−0.446137	+	0.772733i	−0.998131	−	0.0611159i	$-0.980534\pi$
$223$	−6.66225	+	11.5394i	−0.446137	+	0.772733i	0.551993	+	0.833849i	$0.313867\pi$
$224$	0.539495			0.0360465
$225$	−2.17091	+	4.70310i	−0.144727	+	0.313540i
$226$	−25.5615			−1.70032
$227$	−0.690757	+	1.19643i	−0.0458472	+	0.0794096i	−0.888038	−	0.459769i	$-0.847932\pi$
$227$	−0.690757	+	1.19643i	−0.0458472	+	0.0794096i	0.842191	+	0.539179i	$0.181265\pi$
$228$	−15.3420	−	23.9793i	−1.01605	−	1.58807i
$229$	8.98968	+	15.5706i	0.594055	+	1.02893i	0.993679	+	0.112254i	$0.0358072\pi$
$229$	8.98968	+	15.5706i	0.594055	+	1.02893i	−0.399625	+	0.916679i	$0.630859\pi$
$230$	0.872181	+	1.51066i	0.0575099	+	0.0996101i
$231$	−4.21420	−	6.58673i	−0.277274	−	0.433375i
$232$	6.21780	−	10.7695i	0.408219	−	0.707055i
$233$	−18.9823			−1.24357			−0.621786	−	0.783187i	$-0.713592\pi$
$233$	−18.9823			−1.24357			−0.621786	+	0.783187i	$0.713592\pi$
$234$	−7.35087	+	0.671871i	−0.480542	+	0.0439216i
$235$	31.5438			2.05769
$236$	5.52704	−	9.57312i	0.359780	−	0.623157i
$237$	11.7199	−	22.6208i	0.761292	−	1.46938i
$238$	1.16372	+	2.01561i	0.0754325	+	0.130653i
$239$	−2.44592	−	4.23645i	−0.158213	−	0.274033i	0.776011	−	0.630719i	$-0.217240\pi$
$239$	−2.44592	−	4.23645i	−0.158213	−	0.274033i	−0.934224	+	0.356686i	$0.883907\pi$
$240$	19.4195	−	0.885629i	1.25353	−	0.0571671i
$241$	13.0797	−	22.6546i	0.842535	−	1.45931i	−0.0452094	−	0.998978i	$-0.514396\pi$
$241$	13.0797	−	22.6546i	0.842535	−	1.45931i	0.887745	−	0.460336i	$-0.152271\pi$
$242$	−23.0833			−1.48385
$243$	−15.1855	+	3.52144i	−0.974150	+	0.225901i
$244$	−9.21634			−0.590016
$245$	1.29679	−	2.24611i	0.0828489	−	0.143498i
$246$	−27.2740	+	1.24383i	−1.73893	+	0.0793039i
$247$	2.02704	+	3.51094i	0.128978	+	0.223396i
$248$	5.88151	+	10.1871i	0.373477	+	0.646880i
$249$	−0.753696	+	1.45472i	−0.0477635	+	0.0921892i
$250$	10.4445	−	18.0903i	0.660565	−	1.14413i
$251$	18.4576			1.16503			0.582516	−	0.812819i	$-0.302068\pi$
$251$	18.4576			1.16503			0.582516	+	0.812819i	$0.302068\pi$
$252$	−12.1118	+	1.10702i	−0.762970	+	0.0697356i
$253$	−1.23405			−0.0775838
$254$	0.827430	−	1.43315i	0.0519176	−	0.0899239i
$255$	2.29007	+	3.57935i	0.143410	+	0.224147i
$256$	16.1804	+	28.0253i	1.01128	+	1.75158i
$257$	5.86693	+	10.1618i	0.365969	+	0.633876i	0.988931	−	0.148375i	$-0.0474044\pi$
$257$	5.86693	+	10.1618i	0.365969	+	0.633876i	−0.622962	+	0.782252i	$0.714071\pi$
$258$	23.9684	+	37.4622i	1.49221	+	2.33230i
$259$	0.890369	−	1.54216i	0.0553248	−	0.0958254i
$260$	−10.5146			−0.652087
$261$	−3.09358	+	6.70198i	−0.191488	+	0.414842i
$262$	−19.4720			−1.20298
$263$	3.76089	−	6.51406i	0.231907	−	0.401674i	−0.726463	−	0.687206i	$-0.758837\pi$
$263$	3.76089	−	6.51406i	0.231907	−	0.401674i	0.958369	+	0.285532i	$0.0921703\pi$
$264$	−18.1804	+	35.0904i	−1.11893	+	2.15966i
$265$	−8.13521	−	14.0906i	−0.499742	−	0.865579i
$266$	4.98755	+	8.63868i	0.305806	+	0.529672i
$267$	24.8406	−	1.13285i	1.52022	−	0.0693296i
$268$	32.0620	−	55.5329i	1.95850	−	3.39221i
$269$	−18.8348			−1.14838			−0.574190	−	0.818722i	$-0.694683\pi$
$269$	−18.8348			−1.14838			−0.574190	+	0.818722i	$0.694683\pi$
$270$	−32.8499	+	4.51945i	−1.99918	+	0.275045i
$271$	−23.9823			−1.45682			−0.728410	−	0.685141i	$-0.759740\pi$
$271$	−23.9823			−1.45682			−0.728410	+	0.685141i	$0.759740\pi$
$272$	2.04669	−	3.54498i	0.124099	−	0.214946i
$273$	1.73025	−	0.0789082i	0.104720	−	0.00477574i
$274$	−4.51819	−	7.82573i	−0.272954	−	0.472770i
$275$	−3.89757	−	6.75078i	−0.235032	−	0.407088i
$276$	−0.882977	+	1.70425i	−0.0531490	+	0.102584i
$277$	−3.58113	+	6.20269i	−0.215169	+	0.372684i	−0.953325	−	0.301947i	$-0.902364\pi$
$277$	−3.58113	+	6.20269i	−0.215169	+	0.372684i	0.738156	+	0.674630i	$0.235697\pi$
$278$	5.05408			0.303124
$279$	−4.02704	−	5.70397i	−0.241093	−	0.341488i
$280$	−13.1082			−0.783363
$281$	−7.44085	+	12.8879i	−0.443884	+	0.768830i	−0.997974	−	0.0636271i	$-0.979733\pi$
$281$	−7.44085	+	12.8879i	−0.443884	+	0.768830i	0.554090	+	0.832457i	$0.313067\pi$
$282$	27.9341	+	43.6606i	1.66345	+	2.59995i
$283$	−9.99854	−	17.3180i	−0.594351	−	1.02945i	−0.993638	−	0.112621i	$-0.964076\pi$
$283$	−9.99854	−	17.3180i	−0.594351	−	1.02945i	0.399287	−	0.916826i	$-0.369258\pi$
$284$	−6.63521	−	11.4925i	−0.393727	−	0.681956i
$285$	9.81498	+	15.3407i	0.581389	+	0.908703i
$286$	5.55408	−	9.61996i	0.328420	−	0.568840i
$287$	6.40642			0.378159
$288$	0.933463	+	1.32217i	0.0550048	+	0.0779098i
$289$	−16.1052			−0.947367
$290$	−7.85087	+	13.5981i	−0.461019	+	0.798509i
$291$	−9.15486	+	17.6699i	−0.536667	+	1.03583i
$292$	3.05555	+	5.29236i	0.178812	+	0.309712i
$293$	−7.53278	−	13.0472i	−0.440070	−	0.762223i	0.557625	−	0.830093i	$-0.311713\pi$
$293$	−7.53278	−	13.0472i	−0.440070	−	0.762223i	−0.997694	+	0.0678705i	$0.978380\pi$
$294$	4.25729	−	0.194154i	0.248290	−	0.0113233i
$295$	−3.53590	+	6.12435i	−0.205868	+	0.356574i
$296$	−9.00000			−0.523114
$297$	8.85087	−	21.7247i	0.513580	−	1.26060i
$298$	33.3245			1.93044
$299$	0.136673	−	0.236725i	0.00790401	−	0.0136901i
$300$	−12.1118	+	0.552358i	−0.699273	+	0.0318904i
$301$	−5.21780	−	9.03749i	−0.300749	−	0.520912i
$302$	12.2142	+	21.1556i	0.702848	+	1.21737i
$303$	−2.93200	+	5.65910i	−0.168439	+	0.325107i
$304$	8.77188	−	15.1933i	0.503102	−	0.871398i
$305$	5.89610			0.337610
$306$	−2.92627	+	6.33951i	−0.167283	+	0.362406i
$307$	−27.2704			−1.55641			−0.778203	−	0.628013i	$-0.783868\pi$
$307$	−27.2704			−1.55641			−0.778203	+	0.628013i	$0.783868\pi$
$308$	9.15126	−	15.8505i	0.521442	−	0.903163i
$309$	−9.07947	−	14.1911i	−0.516513	−	0.807302i
$310$	−7.42627	−	12.8627i	−0.421784	−	0.730551i
$311$	7.99115	+	13.8411i	0.453136	+	0.784855i	0.998579	−	0.0532931i	$-0.0169718\pi$
$311$	7.99115	+	13.8411i	0.453136	+	0.784855i	−0.545443	+	0.838148i	$0.683638\pi$
$312$	−4.71780	−	7.37385i	−0.267093	−	0.417462i
$313$	−5.79893	+	10.0440i	−0.327775	+	0.567722i	−0.982070	−	0.188517i	$-0.939632\pi$
$313$	−5.79893	+	10.0440i	−0.327775	+	0.567722i	0.654295	+	0.756239i	$0.272965\pi$
$314$	−14.8961			−0.840636
$315$	7.74844	−	0.708209i	0.436575	−	0.0399031i
$316$	59.6313			3.35452
$317$	1.00885	−	1.74739i	0.0566629	−	0.0981430i	−0.836303	−	0.548268i	$-0.815287\pi$
$317$	1.00885	−	1.74739i	0.0566629	−	0.0981430i	0.892965	+	0.450125i	$0.148621\pi$
$318$	12.2989	−	23.7384i	0.689690	−	1.33118i
$319$	−5.55408	−	9.61996i	−0.310969	−	0.538614i
$320$	−9.50214	−	16.4582i	−0.531186	−	0.920040i
$321$	2.37792	−	0.108445i	0.132722	−	0.00605281i
$322$	0.336285	−	0.582462i	0.0187404	−	0.0324594i
$323$	3.83482			0.213375
$324$	−23.6694	−	27.7676i	−1.31497	−	1.54265i
$325$	1.72665			0.0957775
$326$	21.9195	−	37.9658i	1.21401	−	2.10273i
$327$	5.88151	−	0.268227i	0.325249	−	0.0148330i
$328$	−16.1893	−	28.0407i	−0.893904	−	1.54829i
$329$	−6.08113	−	10.5328i	−0.335263	−	0.580693i
$330$	22.9554	−	44.3067i	1.26366	−	2.43900i
$331$	9.85447	−	17.0684i	0.541651	−	0.938167i	−0.457159	−	0.889385i	$-0.651133\pi$
$331$	9.85447	−	17.0684i	0.541651	−	0.938167i	0.998809	−	0.0487815i	$-0.0155338\pi$
$332$	−3.83482			−0.210463
$333$	5.32004	−	0.486253i	0.291536	−	0.0266465i
$334$	20.8348			1.14003
$335$	−20.5115	+	35.5269i	−1.12066	+	1.94104i
$336$	−4.03950	−	6.31367i	−0.220373	−	0.344439i
$337$	14.5256	+	25.1590i	0.791259	+	1.37050i	0.925188	+	0.379509i	$0.123907\pi$
$337$	14.5256	+	25.1590i	0.791259	+	1.37050i	−0.133929	+	0.990991i	$0.542759\pi$
$338$	−14.7630	−	25.5703i	−0.803003	−	1.39084i
$339$	9.69748	+	15.1570i	0.526695	+	0.823216i
$340$	−4.97296	+	8.61342i	−0.269697	+	0.467128i
$341$	10.5074			0.569007
$342$	−12.5416	+	27.1704i	−0.678174	+	1.46921i
$343$	−1.00000			−0.0539949
$344$	−26.3712	+	45.6763i	−1.42184	+	2.46270i
$345$	0.564880	−	1.09028i	0.0304121	−	0.0586989i
$346$	21.3530	+	36.9845i	1.14794	+	1.98830i
$347$	−14.5416	−	25.1868i	−0.780636	−	1.35210i	−0.931572	−	0.363557i	$-0.881562\pi$
$347$	−14.5416	−	25.1868i	−0.780636	−	1.35210i	0.150936	−	0.988544i	$-0.451771\pi$
$348$	−17.2594	+	0.787117i	−0.925203	+	0.0421939i
$349$	−12.3815	+	21.4454i	−0.662767	+	1.14795i	0.317118	+	0.948386i	$0.397285\pi$
$349$	−12.3815	+	21.4454i	−0.662767	+	1.14795i	−0.979885	+	0.199561i	$0.936049\pi$
$350$	4.24844			0.227089
$351$	3.18716	+	4.10390i	0.170118	+	0.219050i
$352$	−2.43560			−0.129818
$353$	16.6513	−	28.8408i	0.886257	−	1.53504i	0.0419914	−	0.999118i	$-0.486630\pi$
$353$	16.6513	−	28.8408i	0.886257	−	1.53504i	0.844266	−	0.535925i	$-0.180037\pi$
$354$	−11.6082	+	0.529391i	−0.616967	+	0.0281368i
$355$	4.24484	+	7.35228i	0.225293	+	0.390219i
$356$	29.1015	+	50.4052i	1.54237	+	2.67147i
$357$	0.753696	−	1.45472i	0.0398898	−	0.0769920i
$358$	−13.9626	+	24.1840i	−0.737949	+	1.27816i
$359$	25.5366			1.34777			0.673884	−	0.738837i	$-0.264625\pi$
$359$	25.5366			1.34777			0.673884	+	0.738837i	$0.264625\pi$
$360$	−22.6804	−	32.1250i	−1.19536	−	1.69314i
$361$	−2.56440			−0.134968
$362$	26.9289	−	46.6422i	1.41535	−	2.45146i
$363$	8.75729	+	13.6875i	0.459639	+	0.718409i
$364$	2.02704	+	3.51094i	0.106246	+	0.184023i
$365$	−1.95477	−	3.38576i	−0.102317	−	0.177219i
$366$	5.22140	+	8.16097i	0.272927	+	0.426581i
$367$	−13.7252	+	23.7727i	−0.716449	+	1.24093i	0.245949	+	0.969283i	$0.420900\pi$
$367$	−13.7252	+	23.7727i	−0.716449	+	1.24093i	−0.962398	+	0.271644i	$0.912433\pi$
$368$	−1.18289			−0.0616622
$369$	11.0847	+	15.7006i	0.577048	+	0.817341i
$370$	11.3638			0.590776
$371$	−3.13667	+	5.43288i	−0.162848	+	0.282061i
$372$	7.51819	−	14.5110i	0.389800	−	0.752359i
$373$	−8.16372	−	14.1400i	−0.422701	−	0.732140i	0.573502	−	0.819204i	$-0.305585\pi$
$373$	−8.16372	−	14.1400i	−0.422701	−	0.732140i	−0.996203	+	0.0870646i	$0.972251\pi$
$374$	−5.25370	−	9.09967i	−0.271662	−	0.470533i
$375$	−14.6893	+	0.669906i	−0.758552	+	0.0345938i
$376$	−30.7345	+	53.2338i	−1.58501	+	2.74532i
$377$	2.46050			0.126722
$378$	7.84202	+	10.0977i	0.403350	+	0.519368i
$379$	12.0364			0.618267			0.309134	−	0.951019i	$-0.399961\pi$
$379$	12.0364			0.618267			0.309134	+	0.951019i	$0.399961\pi$
$380$	−21.3135	+	36.9161i	−1.09336	+	1.89376i
$381$	−1.16372	+	0.0530713i	−0.0596189	+	0.00271892i
$382$	−0.863327	−	1.49533i	−0.0441716	−	0.0765075i
$383$	6.21780	+	10.7695i	0.317715	+	0.550298i	0.980011	−	0.198944i	$-0.0637512\pi$
$383$	6.21780	+	10.7695i	0.317715	+	0.550298i	−0.662296	+	0.749242i	$0.730418\pi$
$384$	15.2252	−	29.3864i	0.776957	−	1.49962i
$385$	−5.85447	+	10.1402i	−0.298372	+	0.516795i
$386$	−29.8817			−1.52094
$387$	13.1206	−	28.4247i	0.666959	−	1.44491i
$388$	−46.5801			−2.36475
$389$	−10.3004	+	17.8408i	−0.522250	+	0.904564i	0.477414	+	0.878678i	$0.341574\pi$
$389$	−10.3004	+	17.8408i	−0.522250	+	0.904564i	−0.999665	+	0.0258860i	$0.991759\pi$
$390$	5.95691	+	9.31056i	0.301640	+	0.471458i
$391$	−0.129281	−	0.223922i	−0.00653803	−	0.0113242i
$392$	2.52704	+	4.37697i	0.127635	+	0.221070i
$393$	7.38725	+	11.5462i	0.372637	+	0.582427i
$394$	−20.1893	+	34.9689i	−1.01712	+	1.76171i
$395$	−38.1488			−1.91948
$396$	54.6797	−	4.99773i	2.74776	−	0.251145i
$397$	−23.6372			−1.18631			−0.593157	−	0.805087i	$-0.702119\pi$
$397$	−23.6372			−1.18631			−0.593157	+	0.805087i	$0.702119\pi$
$398$	27.9341	−	48.3833i	1.40021	−	2.42524i
$399$	3.23025	−	6.23476i	0.161715	−	0.312129i
$400$	−3.73599	−	6.47092i	−0.186799	−	0.323546i
$401$	1.28220	+	2.22084i	0.0640300	+	0.110903i	0.896263	−	0.443522i	$-0.146271\pi$
$401$	1.28220	+	2.22084i	0.0640300	+	0.110903i	−0.832233	+	0.554426i	$0.812938\pi$
$402$	−67.3381	+	3.07096i	−3.35852	+	0.153165i
$403$	−1.16372	+	2.01561i	−0.0579688	+	0.100405i
$404$	−14.9181			−0.742202
$405$	15.1424	+	17.7642i	0.752432	+	0.882710i
$406$	6.05408			0.300459
$407$	−4.01965	+	6.96224i	−0.199247	+	0.345105i
$408$	−8.27188	+	0.377240i	−0.409519	+	0.0186761i
$409$	17.1623	+	29.7259i	0.848619	+	1.46985i	0.882441	+	0.470423i	$0.155899\pi$
$409$	17.1623	+	29.7259i	0.848619	+	1.46985i	−0.0338223	+	0.999428i	$0.510768\pi$
$410$	20.4413	+	35.4054i	1.00953	+	1.74855i
$411$	−2.92627	+	5.64803i	−0.144342	+	0.278597i
$412$	19.7163	−	34.1497i	0.971354	−	1.68243i
$413$	2.72665			0.134170
$414$	2.00933	−	0.183653i	0.0987533	−	0.00902607i
$415$	2.45331			0.120428
$416$	0.269748	−	0.467216i	0.0132255	−	0.0229072i
$417$	−1.91741	−	2.99689i	−0.0938960	−	0.146758i
$418$	−22.5167	−	39.0001i	−1.10133	−	1.90756i
$419$	−2.02850	−	3.51347i	−0.0990989	−	0.171644i	0.812213	−	0.583361i	$-0.198263\pi$
$419$	−2.02850	−	3.51347i	−0.0990989	−	0.171644i	−0.911312	+	0.411717i	$0.864929\pi$
$420$	9.81498	+	15.3407i	0.478922	+	0.748548i
$421$	10.5344	−	18.2462i	0.513417	−	0.889264i	−0.486462	−	0.873702i	$-0.661713\pi$
$421$	10.5344	−	18.2462i	0.513417	−	0.889264i	0.999879	−	0.0155624i	$-0.00495387\pi$
$422$	−11.2235			−0.546353
$423$	15.2915	−	33.1278i	0.743500	−	1.61073i
$424$	31.7060			1.53978
$425$	0.816635	−	1.41445i	0.0396126	−	0.0686110i
$426$	−6.41741	+	12.3863i	−0.310925	+	0.600121i
$427$	−1.13667	−	1.96878i	−0.0550075	−	0.0952757i
$428$	2.78580	+	4.82515i	0.134657	+	0.233232i
$429$	−7.81138	+	0.356238i	−0.377137	+	0.0171993i
$430$	33.2975	−	57.6729i	1.60575	−	2.78123i
$431$	22.6185			1.08949			0.544747	−	0.838600i	$-0.316626\pi$
$431$	22.6185			1.08949			0.544747	+	0.838600i	$0.316626\pi$
$432$	8.48395	−	20.8241i	0.408184	−	1.00190i
$433$	2.41789			0.116196			0.0580982	−	0.998311i	$-0.481496\pi$
$433$	2.41789			0.116196			0.0580982	+	0.998311i	$0.481496\pi$
$434$	−2.86333	+	4.95943i	−0.137444	+	0.238060i
$435$	11.0416	−	0.503554i	0.529406	−	0.0241436i
$436$	6.89037	+	11.9345i	0.329989	+	0.571557i
$437$	−0.554084	−	0.959702i	−0.0265054	−	0.0459088i
$438$	2.95525	−	5.70397i	0.141207	−	0.272546i
$439$	11.7448	−	20.3427i	0.560551	−	0.970902i	−0.436898	−	0.899511i	$-0.643923\pi$
$439$	11.7448	−	20.3427i	0.560551	−	0.970902i	0.997448	−	0.0713911i	$-0.0227438\pi$
$440$	59.1780			2.82120
$441$	−1.73025	−	2.45076i	−0.0823930	−	0.116703i
$442$	2.32743			0.110705
$443$	6.70895	−	11.6202i	0.318752	−	0.552094i	−0.661476	−	0.749966i	$-0.730070\pi$
$443$	6.70895	−	11.6202i	0.318752	−	0.552094i	0.980228	+	0.197872i	$0.0634031\pi$
$444$	6.73891	+	10.5328i	0.319815	+	0.499866i
$445$	−18.6175	−	32.2465i	−0.882554	−	1.52863i
$446$	16.3925	+	28.3927i	0.776208	+	1.34443i
$447$	−12.6426	−	19.7602i	−0.597975	−	0.934625i
$448$	−3.66372	+	6.34574i	−0.173094	+	0.299808i
$449$	−9.16225			−0.432393			−0.216197	−	0.976350i	$-0.569365\pi$
$449$	−9.16225			−0.432393			−0.216197	+	0.976350i	$0.569365\pi$
$450$	7.35087	+	10.4119i	0.346524	+	0.490822i
$451$	−28.9224			−1.36190
$452$	−21.0584	+	36.4741i	−0.990502	+	1.71560i
$453$	7.91069	−	15.2686i	0.371677	−	0.717379i
$454$	1.69961	+	2.94381i	0.0797667	+	0.138160i
$455$	−1.29679	−	2.24611i	−0.0607944	−	0.105299i
$456$	−35.4523	+	1.61680i	−1.66021	+	0.0757138i
$457$	−4.40856	+	7.63584i	−0.206224	+	0.357190i	−0.950522	−	0.310658i	$-0.899451\pi$
$457$	−4.40856	+	7.63584i	−0.206224	+	0.357190i	0.744298	+	0.667847i	$0.232784\pi$
$458$	44.2383			2.06712
$459$	4.86926	−	0.669906i	0.227277	−	0.0312685i
$460$	2.87412			0.134007
$461$	2.82957	−	4.90095i	0.131786	−	0.228260i	−0.792579	−	0.609769i	$-0.791262\pi$
$461$	2.82957	−	4.90095i	0.131786	−	0.228260i	0.924365	+	0.381509i	$0.124595\pi$
$462$	−19.2199	+	0.876526i	−0.894192	+	0.0407797i
$463$	−7.86333	−	13.6197i	−0.365440	−	0.632960i	0.623407	−	0.781898i	$-0.285748\pi$
$463$	−7.86333	−	13.6197i	−0.365440	−	0.632960i	−0.988847	+	0.148937i	$0.952415\pi$
$464$	−5.32383	−	9.22115i	−0.247153	−	0.428081i
$465$	−4.80972	+	9.28332i	−0.223045	+	0.430504i
$466$	−23.3530	+	40.4486i	−1.08181	+	1.87375i
$467$	−21.9971			−1.01790			−0.508952	−	0.860795i	$-0.669967\pi$
$467$	−21.9971			−1.01790			−0.508952	+	0.860795i	$0.669967\pi$
$468$	−5.09718	+	11.0426i	−0.235617	+	0.510445i
$469$	15.8171			0.730366
$470$	38.8068	−	67.2153i	1.79002	−	3.10041i
$471$	5.65126	+	8.83284i	0.260396	+	0.406996i
$472$	−6.89037	−	11.9345i	−0.317155	−	0.549328i
$473$	23.5562	+	40.8006i	1.08312	+	1.87601i
$474$	−33.7834	−	52.8029i	−1.55172	−	2.42532i
$475$	3.50000	−	6.06218i	0.160591	−	0.278152i
$476$	3.83482			0.175769
$477$	−18.7419	+	1.71301i	−0.858133	+	0.0784336i
$478$	−12.0364			−0.550531
$479$	−12.4875	+	21.6291i	−0.570571	+	0.988257i	0.425937	+	0.904753i	$0.359945\pi$
$479$	−12.4875	+	21.6291i	−0.570571	+	0.988257i	−0.996507	+	0.0835043i	$0.973389\pi$
$480$	1.11489	−	2.15186i	0.0508874	−	0.0982186i
$481$	−0.890369	−	1.54216i	−0.0405973	−	0.0703166i
$482$	−32.1826	−	55.7419i	−1.46588	−	2.53897i
$483$	−0.472958	+	0.0215693i	−0.0215203	+	0.000981436i
$484$	−19.0167	+	32.9379i	−0.864397	+	1.49718i
$485$	29.7994			1.35312
$486$	−11.1783	+	36.6904i	−0.507058	+	1.66431i
$487$	−17.5979			−0.797435			−0.398717	−	0.917074i	$-0.630545\pi$
$487$	−17.5979			−0.797435			−0.398717	+	0.917074i	$0.630545\pi$
$488$	−5.74484	+	9.95036i	−0.260057	+	0.450432i
$489$	−30.8281	+	1.40592i	−1.39410	+	0.0635778i
$490$	−3.19076	−	5.52655i	−0.144144	−	0.249664i
$491$	−6.89757	−	11.9469i	−0.311283	−	0.539158i	0.667358	−	0.744737i	$-0.267425\pi$
$491$	−6.89757	−	11.9469i	−0.311283	−	0.539158i	−0.978640	+	0.205580i	$0.934092\pi$
$492$	−20.6944	+	39.9425i	−0.932974	+	1.80075i
$493$	1.16372	−	2.01561i	0.0524111	−	0.0907787i
$494$	9.97509			0.448801
$495$	−34.9810	+	3.19727i	−1.57228	+	0.143707i
$496$	10.0718			0.452237
$497$	1.63667	−	2.83480i	0.0734148	−	0.127158i
$498$	2.17257	+	3.39569i	0.0973552	+	0.152165i
$499$	−6.54377	−	11.3341i	−0.292939	−	0.507386i	0.681564	−	0.731758i	$-0.261300\pi$
$499$	−6.54377	−	11.3341i	−0.292939	−	0.507386i	−0.974503	+	0.224373i	$0.927967\pi$
$500$	−17.2089	−	29.8068i	−0.769607	−	1.33300i
$501$	−7.90428	−	12.3543i	−0.353137	−	0.551949i
$502$	22.7075	−	39.3305i	1.01348	−	1.75541i
$503$	−22.3068			−0.994611			−0.497305	−	0.867576i	$-0.665677\pi$
$503$	−22.3068			−0.994611			−0.497305	+	0.867576i	$0.665677\pi$
$504$	−6.35447	+	13.7664i	−0.283051	+	0.613206i
$505$	9.54377			0.424692
$506$	−1.51819	+	2.62958i	−0.0674917	+	0.116899i
$507$	−9.56148	+	18.4548i	−0.424640	+	0.819605i
$508$	−1.36333	−	2.36135i	−0.0604879	−	0.104768i
$509$	7.94659	+	13.7639i	0.352226	+	0.610074i	0.986639	−	0.162920i	$-0.0520914\pi$
$509$	7.94659	+	13.7639i	0.352226	+	0.610074i	−0.634413	+	0.772994i	$0.718758\pi$
$510$	10.4445	−	0.476320i	0.462488	−	0.0210918i
$511$	−0.753696	+	1.30544i	−0.0333415	+	0.0577492i
$512$	41.4078			1.82998
$513$	20.8691	−	2.87114i	0.921392	−	0.126764i
$514$	28.8712			1.27345
$515$	−12.6134	+	21.8471i	−0.555814	+	0.962698i
$516$	73.2014	−	3.33836i	3.22251	−	0.146963i
$517$	27.4538	+	47.5514i	1.20742	+	2.09131i
$518$	−2.19076	−	3.79450i	−0.0962563	−	0.166721i
$519$	13.8296	−	26.6927i	0.607051	−	1.17168i
$520$	−6.55408	+	11.3520i	−0.287416	+	0.497818i
$521$	4.41789			0.193551			0.0967756	−	0.995306i	$-0.469147\pi$
$521$	4.41789			0.193551			0.0967756	+	0.995306i	$0.469147\pi$
$522$	10.4751	+	14.8371i	0.458482	+	0.649403i
$523$	25.2733			1.10513			0.552563	−	0.833471i	$-0.313650\pi$
$523$	25.2733			1.10513			0.552563	+	0.833471i	$0.313650\pi$
$524$	−16.0416	+	27.7849i	−0.700782	+	1.21379i
$525$	−1.61177	−	2.51917i	−0.0703433	−	0.109946i
$526$	−9.25370	−	16.0279i	−0.403480	−	0.698848i
$527$	1.10078	+	1.90660i	0.0479506	+	0.0830528i
$528$	18.2367	+	28.5036i	0.793649	+	1.24046i
$529$	11.4626	−	19.8539i	0.498376	−	0.863212i
$530$	−40.0335			−1.73894
$531$	4.71780	+	6.68238i	0.204735	+	0.289990i
$532$	16.4356			0.712574
$533$	3.20321	−	5.54812i	0.138746	−	0.240316i
$534$	28.1462	−	54.3254i	1.21801	−	2.35089i
$535$	−1.78220	−	3.08686i	−0.0770513	−	0.133457i
$536$	−39.9705	−	69.2310i	−1.72646	−	2.99032i
$537$	19.6373	−	0.895562i	0.847414	−	0.0386464i
$538$	−23.1716	+	40.1344i	−0.998998	+	1.73032i
$539$	4.51459			0.194457
$540$	−20.6139	+	50.5974i	−0.887081	+	2.17736i
$541$	−3.43852			−0.147834			−0.0739168	−	0.997264i	$-0.523550\pi$
$541$	−3.43852			−0.147834			−0.0739168	+	0.997264i	$0.523550\pi$
$542$	−29.5043	+	51.1029i	−1.26732	+	2.19506i
$543$	−37.8733	+	1.72722i	−1.62530	+	0.0741219i
$544$	−0.255158	−	0.441947i	−0.0109398	−	0.0189483i
$545$	−4.40808	−	7.63501i	−0.188821	−	0.327048i
$546$	1.96050	−	3.78400i	0.0839019	−	0.161940i
$547$	3.46410	−	6.00000i	0.148114	−	0.256542i	−0.782416	−	0.622756i	$-0.786013\pi$
$547$	3.46410	−	6.00000i	0.148114	−	0.256542i	0.930531	+	0.366214i	$0.119346\pi$
$548$	−14.8889			−0.636023
$549$	2.85827	−	6.19219i	0.121988	−	0.264276i
$550$	−19.1800			−0.817836
$551$	4.98755	−	8.63868i	0.212477	−	0.368020i
$552$	1.28959	+	2.01561i	0.0548887	+	0.0857902i
$553$	7.35447	+	12.7383i	0.312744	+	0.541688i
$554$	8.81138	+	15.2618i	0.374360	+	0.648410i
$555$	−4.31118	−	6.73832i	−0.183000	−	0.286026i
$556$	4.16372	−	7.21177i	0.176581	−	0.305847i
$557$	33.5835			1.42298			0.711488	−	0.702698i	$-0.248021\pi$
$557$	33.5835			1.42298			0.711488	+	0.702698i	$0.248021\pi$
$558$	−17.1086	+	1.56373i	−0.724267	+	0.0661981i
$559$	−10.4356			−0.441379
$560$	−5.61177	+	9.71987i	−0.237140	+	0.410739i
$561$	−3.40263	+	6.56747i	−0.143659	+	0.277279i
$562$	18.3083	+	31.7108i	0.772287	+	1.33764i
$563$	−21.2396	−	36.7880i	−0.895142	−	1.55043i	−0.833629	−	0.552325i	$-0.813741\pi$
$563$	−21.2396	−	36.7880i	−0.895142	−	1.55043i	−0.0615128	−	0.998106i	$-0.519593\pi$
$564$	85.3132	−	3.89071i	3.59233	−	0.163829i
$565$	13.4720	−	23.3341i	0.566770	−	0.981675i
$566$	−49.2029			−2.06815
$567$	3.01245	−	8.48087i	0.126511	−	0.356163i
$568$	−16.5438			−0.694161
$569$	−5.20175	+	9.00969i	−0.218069	+	0.377706i	−0.954217	−	0.299114i	$-0.903309\pi$
$569$	−5.20175	+	9.00969i	−0.218069	+	0.377706i	0.736149	+	0.676820i	$0.236642\pi$
$570$	44.7637	−	2.04145i	1.87495	−	0.0855070i
$571$	−8.92480	−	15.4582i	−0.373491	−	0.646906i	0.616609	−	0.787270i	$-0.288506\pi$
$571$	−8.92480	−	15.4582i	−0.373491	−	0.646906i	−0.990100	+	0.140364i	$0.955173\pi$
$572$	−9.15126	−	15.8505i	−0.382633	−	0.662741i
$573$	−0.559145	+	1.07922i	−0.0233586	+	0.0450849i
$574$	7.88151	−	13.6512i	0.328968	−	0.569789i
$575$	−0.471974			−0.0196827
$576$	−21.8910	+	2.00085i	−0.912127	+	0.0833686i
$577$	11.9430			0.497193			0.248597	−	0.968607i	$-0.420031\pi$
$577$	11.9430			0.497193			0.248597	+	0.968607i	$0.420031\pi$
$578$	−19.8135	+	34.3180i	−0.824134	+	1.42744i
$579$	11.3365	+	17.7187i	0.471128	+	0.736366i
$580$	12.9356	+	22.4051i	0.537122	+	0.930322i
$581$	−0.472958	−	0.819187i	−0.0196216	−	0.0339856i
$582$	26.3894	+	41.2462i	1.09388	+	1.70971i
$583$	14.1608	−	24.5272i	0.586480	−	1.01581i
$584$	7.61849			0.315255
$585$	3.26089	−	7.06445i	0.134821	−	0.292079i
$586$	−37.0689			−1.53130
$587$	−11.9299	+	20.6631i	−0.492398	+	0.852859i	−0.999962	−	0.00875568i	$-0.997213\pi$
$587$	−11.9299	+	20.6631i	−0.492398	+	0.852859i	0.507563	+	0.861614i	$0.330546\pi$
$588$	3.23025	−	6.23476i	0.133213	−	0.257117i
$589$	4.71780	+	8.17147i	0.194394	+	0.336699i
$590$	8.70009	+	15.0690i	0.358177	+	0.620381i
$591$	28.3946	−	1.29494i	1.16800	−	0.0532667i
$592$	−3.85301	+	6.67361i	−0.158358	+	0.274284i
$593$	19.5801			0.804060			0.402030	−	0.915626i	$-0.368305\pi$
$593$	19.5801			0.804060			0.402030	+	0.915626i	$0.368305\pi$
$594$	−35.4035	−	45.5868i	−1.45262	−	1.87045i
$595$	−2.45331			−0.100576
$596$	27.4538	−	47.5514i	1.12455	−	1.94778i
$597$	−39.2871	+	1.79169i	−1.60792	+	0.0733291i
$598$	−0.336285	−	0.582462i	−0.0137517	−	0.0238187i
$599$	−9.27335	−	16.0619i	−0.378899	−	0.656272i	0.612004	−	0.790855i	$-0.290364\pi$
$599$	−9.27335	−	16.0619i	−0.378899	−	0.656272i	−0.990902	+	0.134583i	$0.957030\pi$
$600$	−6.95331	+	13.4207i	−0.283868	+	0.547897i
$601$	9.09931	−	15.7605i	0.371169	−	0.642883i	−0.618577	−	0.785724i	$-0.712290\pi$
$601$	9.09931	−	15.7605i	0.371169	−	0.642883i	0.989746	+	0.142841i	$0.0456238\pi$
$602$	−25.6768			−1.04651
$603$	27.3676	+	38.7640i	1.11449	+	1.57859i
$604$	40.2498			1.63774
$605$	12.1659	−	21.0719i	0.494612	−	0.856693i
$606$	8.45165	+	13.2098i	0.343325	+	0.536612i
$607$	11.1549	+	19.3208i	0.452762	+	0.784206i	0.998556	−	0.0537125i	$-0.0171055\pi$
$607$	11.1549	+	19.3208i	0.452762	+	0.784206i	−0.545795	+	0.837919i	$0.683772\pi$
$608$	−1.09358	−	1.89413i	−0.0443505	−	0.0768173i
$609$	−2.29679	−	3.58985i	−0.0930706	−	0.145468i
$610$	7.25370	−	12.5638i	0.293694	−	0.508692i
$611$	−12.1623			−0.492032
$612$	6.63521	+	9.39823i	0.268212	+	0.379901i
$613$	10.2370			0.413467			0.206734	−	0.978397i	$-0.433717\pi$
$613$	10.2370			0.413467			0.206734	+	0.978397i	$0.433717\pi$
$614$	−33.5495	+	58.1094i	−1.35395	+	2.34511i
$615$	13.2391	−	25.5530i	0.533852	−	1.03040i
$616$	−11.4086	−	19.7602i	−0.459664	−	0.796161i
$617$	5.66372	+	9.80984i	0.228013	+	0.394929i	0.957219	−	0.289364i	$-0.0934439\pi$
$617$	5.66372	+	9.80984i	0.228013	+	0.394929i	−0.729206	+	0.684294i	$0.760111\pi$
$618$	−41.4092	+	1.88847i	−1.66572	+	0.0759654i
$619$	−4.31663	+	7.47663i	−0.173500	+	0.300511i	−0.939641	−	0.342161i	$-0.888841\pi$
$619$	−4.31663	+	7.47663i	−0.173500	+	0.300511i	0.766141	+	0.642672i	$0.222174\pi$
$620$	−24.4720			−0.982818
$621$	−0.871198	−	1.12179i	−0.0349600	−	0.0450157i
$622$	39.3245			1.57677
$623$	−7.17830	+	12.4332i	−0.287593	+	0.498125i
$624$	−7.48755	+	0.341470i	−0.299742	+	0.0136697i
$625$	15.3260	+	26.5454i	0.613039	+	1.06181i
$626$	14.2683	+	24.7134i	0.570275	+	0.987746i
$627$	−14.5833	+	28.1474i	−0.582399	+	1.12410i
$628$	−12.2719	+	21.2555i	−0.489701	+	0.848188i
$629$	−1.68443			−0.0671626
$630$	8.02344	−	17.3821i	0.319662	−	0.692520i
$631$	−14.8535			−0.591308			−0.295654	−	0.955295i	$-0.595538\pi$
$631$	−14.8535			−0.591308			−0.295654	+	0.955295i	$0.595538\pi$
$632$	37.1701	−	64.3805i	1.47855	−	2.56092i
$633$	4.25797	+	6.65514i	0.169239	+	0.264518i
$634$	−2.48229	−	4.29945i	−0.0985844	−	0.170753i
$635$	0.872181	+	1.51066i	0.0346115	+	0.0599488i
$636$	−23.7405	−	37.1060i	−0.941370	−	1.47135i
$637$	−0.500000	+	0.866025i	−0.0198107	+	0.0343132i
$638$	−27.3317			−1.08207
$639$	9.77928	−	0.893828i	0.386862	−	0.0353593i
$640$	−49.5586			−1.95897
$641$	17.0797	−	29.5828i	0.674606	−	1.16845i	−0.301978	−	0.953315i	$-0.597647\pi$
$641$	17.0797	−	29.5828i	0.674606	−	1.16845i	0.976584	−	0.215137i	$-0.0690199\pi$
$642$	2.69436	−	5.20042i	0.106338	−	0.205244i
$643$	5.41741	+	9.38323i	0.213642	+	0.370039i	0.952852	−	0.303437i	$-0.0981341\pi$
$643$	5.41741	+	9.38323i	0.213642	+	0.370039i	−0.739210	+	0.673475i	$0.764801\pi$
$644$	−0.554084	−	0.959702i	−0.0218340	−	0.0378176i
$645$	−46.8302	+	2.13570i	−1.84394	+	0.0840929i
$646$	4.71780	−	8.17147i	0.185619	−	0.321502i
$647$	32.9692			1.29615			0.648077	−	0.761575i	$-0.275573\pi$
$647$	32.9692			1.29615			0.648077	+	0.761575i	$0.275573\pi$
$648$	−44.7331	+	8.24611i	−1.75728	+	0.323938i
$649$	−12.3097			−0.483199
$650$	2.12422	−	3.67926i	0.0833188	−	0.144312i
$651$	4.02704	−	0.183653i	0.157832	−	0.00719795i
$652$	−36.1160	−	62.5548i	−1.41441	−	2.44984i
$653$	1.96557	+	3.40446i	0.0769185	+	0.133227i	0.901919	−	0.431905i	$-0.142159\pi$
$653$	1.96557	+	3.40446i	0.0769185	+	0.133227i	−0.825000	+	0.565132i	$0.808825\pi$
$654$	6.66419	−	12.8627i	0.260591	−	0.502970i
$655$	10.2626	−	17.7753i	0.400991	−	0.694537i
$656$	−27.7233			−1.08241
$657$	−4.50340	+	0.411612i	−0.175695	+	0.0160585i
$658$	−29.9253			−1.16661
$659$	−8.40856	+	14.5640i	−0.327551	+	0.567335i	−0.982025	−	0.188749i	$-0.939557\pi$
$659$	−8.40856	+	14.5640i	−0.327551	+	0.567335i	0.654474	+	0.756084i	$0.272890\pi$
$660$	−44.3106	−	69.2568i	−1.72479	−	2.69582i
$661$	8.51080	+	14.7411i	0.331032	+	0.573364i	0.982714	−	0.185128i	$-0.0592700\pi$
$661$	8.51080	+	14.7411i	0.331032	+	0.573364i	−0.651683	+	0.758492i	$0.725937\pi$
$662$	−24.2470	−	41.9970i	−0.942386	−	1.63226i
$663$	−0.882977	−	1.38008i	−0.0342920	−	0.0535979i
$664$	−2.39037	+	4.14024i	−0.0927643	+	0.160672i
$665$	−10.5146			−0.407738
$666$	5.50885	−	11.9345i	0.213464	−	0.462451i
$667$	−0.672570			−0.0260420
$668$	17.1644	−	29.7296i	0.664110	−	1.15027i
$669$	10.6168	−	20.4917i	0.410470	−	0.792255i
$670$	50.4686	+	87.4141i	1.94977	+	3.37710i
$671$	5.13161	+	8.88821i	0.198104	+	0.343126i
$672$	−0.933463	+	0.0425706i	−0.0360091	+	0.00164220i
$673$	−14.3727	+	24.8942i	−0.554025	+	0.959600i	0.443953	+	0.896050i	$0.353576\pi$
$673$	−14.3727	+	24.8942i	−0.554025	+	0.959600i	−0.997979	+	0.0635501i	$0.979758\pi$
$674$	71.4805			2.75333
$675$	3.38511	−	8.30885i	0.130293	−	0.319808i
$676$	−48.6490			−1.87112
$677$	3.01819	−	5.22765i	0.115998	−	0.200915i	−0.802180	−	0.597082i	$-0.796327\pi$
$677$	3.01819	−	5.22765i	0.115998	−	0.200915i	0.918178	+	0.396167i	$0.129660\pi$
$678$	44.2278	−	2.01701i	1.69856	−	0.0774628i
$679$	−5.74484	−	9.95036i	−0.220467	−	0.381860i
$680$	6.19961	+	10.7380i	0.237744	+	0.411785i
$681$	1.10078	−	2.12463i	0.0421818	−	0.0814159i
$682$	12.9267	−	22.3898i	0.494991	−	0.857349i
$683$	20.5113			0.784842			0.392421	−	0.919786i	$-0.371638\pi$
$683$	20.5113			0.784842			0.392421	+	0.919786i	$0.371638\pi$
$684$	28.4377	+	40.2797i	1.08734	+	1.54013i
$685$	9.52510			0.363935
$686$	−1.23025	+	2.13086i	−0.0469713	+	0.0813566i
$687$	−16.7831	−	26.2317i	−0.640314	−	1.00080i
$688$	22.5797	+	39.1091i	0.860842	+	1.49102i
$689$	3.13667	+	5.43288i	0.119498	+	0.206976i
$690$	−1.62830	−	2.54500i	−0.0619882	−	0.0968867i
$691$	7.50146	−	12.9929i	0.285369	−	0.494274i	−0.687330	−	0.726346i	$-0.741217\pi$
$691$	7.50146	−	12.9929i	0.285369	−	0.494274i	0.972699	+	0.232072i	$0.0745505\pi$
$692$	70.3652			2.67488
$693$	7.81138	+	11.0642i	0.296730	+	0.420293i
$694$	−71.5595			−2.71636
$695$	−2.66372	+	4.61369i	−0.101040	+	0.175007i
$696$	−9.90856	+	19.1247i	−0.375583	+	0.724919i
$697$	−3.02997	−	5.24806i	−0.114768	−	0.198784i
$698$	30.4648	+	52.7665i	1.15311	+	1.99724i
$699$	32.8442	−	1.49786i	1.24228	−	0.0566542i
$700$	3.50000	−	6.06218i	0.132288	−	0.229129i
$701$	38.5113			1.45455			0.727275	−	0.686346i	$-0.240786\pi$
$701$	38.5113			1.45455			0.727275	+	0.686346i	$0.240786\pi$
$702$	12.6659	−	1.74255i	0.478042	−	0.0657684i
$703$	−7.21926			−0.272280
$704$	16.5402	−	28.6484i	0.623381	−	1.07973i
$705$	−54.5787	+	2.48906i	−2.05555	+	0.0937435i
$706$	−40.9705	−	70.9630i	−1.54195	−	2.67073i
$707$	−1.83988	−	3.18677i	−0.0691959	−	0.119851i
$708$	−8.80778	+	17.0000i	−0.331017	+	0.638901i
$709$	−3.82004	+	6.61650i	−0.143465	+	0.248488i	−0.928799	−	0.370584i	$-0.879158\pi$
$709$	−3.82004	+	6.61650i	−0.143465	+	0.248488i	0.785334	+	0.619072i	$0.212491\pi$
$710$	20.8889			0.783947
$711$	−18.4935	+	40.0646i	−0.693560	+	1.50254i
$712$	72.5595			2.71928
$713$	0.318097	−	0.550960i	0.0119128	−	0.0206336i
$714$	−2.17257	−	3.39569i	−0.0813064	−	0.127081i
$715$	5.85447	+	10.1402i	0.218945	+	0.379224i
$716$	23.0057	+	39.8471i	0.859765	+	1.48916i
$717$	4.56634	+	7.13713i	0.170533	+	0.266541i
$718$	31.4164	−	54.4148i	1.17245	−	2.03074i
$719$	−30.0364			−1.12017			−0.560084	−	0.828436i	$-0.689231\pi$
$719$	−30.0364			−1.12017			−0.560084	+	0.828436i	$0.689231\pi$
$720$	−33.5308	+	3.06472i	−1.24962	+	0.114216i
$721$	9.72665			0.362240
$722$	−3.15486	+	5.46438i	−0.117412	+	0.203363i
$723$	−20.8435	+	40.2303i	−0.775177	+	1.49618i
$724$	−44.3697	−	76.8506i	−1.64899	−	2.85613i
$725$	−2.12422	−	3.67926i	−0.0788916	−	0.136644i
$726$	39.9399	−	1.82146i	1.48231	−	0.0676007i
$727$	−1.72812	+	2.99319i	−0.0640923	+	0.111011i	−0.896291	−	0.443466i	$-0.853749\pi$
$727$	−1.72812	+	2.99319i	−0.0640923	+	0.111011i	0.832199	+	0.554478i	$0.187082\pi$
$728$	5.05408			0.187317
$729$	25.9969	−	7.29124i	0.962847	−	0.270046i
$730$	−9.61944			−0.356032
$731$	−4.93560	+	8.54871i	−0.182550	+	0.316185i
$732$	15.9466	−	0.727245i	0.589403	−	0.0268797i
$733$	−19.2630	−	33.3645i	−0.711496	−	1.23235i	−0.964295	−	0.264829i	$-0.914685\pi$
$733$	−19.2630	−	33.3645i	−0.711496	−	1.23235i	0.252799	−	0.967519i	$-0.418649\pi$
$734$	33.7709	+	58.4929i	1.24651	+	2.15901i
$735$	−2.06654	+	3.98866i	−0.0762254	+	0.147124i
$736$	−0.0737345	+	0.127712i	−0.00271789	+	0.00470752i
$737$	−71.4078			−2.63034
$738$	47.0928	−	4.30429i	1.73351	−	0.158443i
$739$	45.1239			1.65991			0.829955	−	0.557830i	$-0.188366\pi$
$739$	45.1239			1.65991			0.829955	+	0.557830i	$0.188366\pi$
$740$	9.36186	−	16.2152i	0.344149	−	0.596084i
$741$	−3.78434	−	5.91486i	−0.139021	−	0.217288i
$742$	7.71780	+	13.3676i	0.283329	+	0.490741i
$743$	−4.74338	−	8.21577i	−0.174018	−	0.301407i	0.765803	−	0.643075i	$-0.222342\pi$
$743$	−4.74338	−	8.21577i	−0.174018	−	0.301407i	−0.939821	+	0.341668i	$0.889008\pi$
$744$	−10.9803	−	17.1621i	−0.402559	−	0.629194i
$745$	−17.5634	+	30.4207i	−0.643474	+	1.11453i
$746$	−40.1737			−1.47086
$747$	1.18929	−	2.57651i	0.0435140	−	0.0942695i
$748$	−17.3126			−0.633013
$749$	−0.687159	+	1.19019i	−0.0251082	+	0.0434887i
$750$	−16.6441	+	32.1250i	−0.607755	+	1.17304i
$751$	4.91595	+	8.51467i	0.179386	+	0.310705i	0.941670	−	0.336537i	$-0.109256\pi$
$751$	4.91595	+	8.51467i	0.179386	+	0.310705i	−0.762285	+	0.647242i	$0.775922\pi$
$752$	26.3157	+	45.5800i	0.959633	+	1.66213i
$753$	−31.9363	+	1.45646i	−1.16382	+	0.0530762i
$754$	3.02704	−	5.24299i	0.110238	−	0.190938i
$755$	−25.7496			−0.937124
$756$	20.8691	−	2.87114i	0.759000	−	0.104422i
$757$	−41.8171			−1.51987			−0.759934	−	0.650000i	$-0.774769\pi$
$757$	−41.8171			−1.51987			−0.759934	+	0.650000i	$0.774769\pi$
$758$	14.8078	−	25.6478i	0.537843	−	0.931571i
$759$	2.13521	−	0.0973764i	0.0775032	−	0.00353454i
$760$	26.5708	+	46.0220i	0.963825	+	1.66939i
$761$	−11.4897	−	19.9007i	−0.416501	−	0.721400i	0.579084	−	0.815268i	$-0.303410\pi$
$761$	−11.4897	−	19.9007i	−0.416501	−	0.721400i	−0.995585	+	0.0938675i	$0.970077\pi$
$762$	−1.31858	+	2.54500i	−0.0477670	+	0.0921958i
$763$	−1.69961	+	2.94381i	−0.0615301	+	0.106573i
$764$	−2.84494			−0.102926
$765$	−4.24484	−	6.01247i	−0.153473	−	0.217381i
$766$	30.5979			1.10555
$767$	1.36333	−	2.36135i	0.0492269	−	0.0852635i
$768$	−30.2077	−	47.2142i	−1.09003	−	1.70369i
$769$	−3.04329	−	5.27113i	−0.109744	−	0.190082i	0.805923	−	0.592021i	$-0.201670\pi$
$769$	−3.04329	−	5.27113i	−0.109744	−	0.190082i	−0.915666	+	0.401939i	$0.868336\pi$
$770$	14.4050	+	24.9501i	0.519119	+	0.899140i
$771$	−10.9531	−	17.1196i	−0.394467	−	0.616546i
$772$	−24.6175	+	42.6388i	−0.886003	+	1.53460i
$773$	−41.8214			−1.50421			−0.752105	−	0.659043i	$-0.770962\pi$
$773$	−41.8214			−1.50421			−0.752105	+	0.659043i	$0.770962\pi$
$774$	−44.4274	−	62.9278i	−1.59691	−	2.26189i
$775$	4.01867			0.144355
$776$	−29.0349	+	50.2899i	−1.04229	+	1.80530i
$777$	−1.41887	+	2.73859i	−0.0509018	+	0.0982464i
$778$	25.3442	+	43.8974i	0.908632	+	1.57380i
$779$	−12.9861	−	22.4926i	−0.465275	−	0.805880i
$780$	18.1929	−	0.829688i	0.651410	−	0.0297076i
$781$	−7.38891	+	12.7980i	−0.264396	+	0.457947i
$782$	−0.636194			−0.0227503
$783$	4.82383	−	11.8402i	0.172390	−	0.423135i
$784$	4.32743			0.154551
$785$	7.85087	−	13.5981i	0.280210	−	0.485337i
$786$	33.6914	−	1.53650i	1.20173	−	0.0548051i
$787$	−16.1460	−	27.9657i	−0.575543	−	0.996870i	−0.995982	−	0.0895491i	$-0.971457\pi$
$787$	−16.1460	−	27.9657i	−0.575543	−	0.996870i	0.420439	−	0.907321i	$-0.361876\pi$
$788$	33.2652	+	57.6170i	1.18502	+	2.05252i
$789$	−5.99328	+	11.5677i	−0.213366	+	0.411822i
$790$	−46.9327	+	81.2898i	−1.66979	+	2.89216i
$791$	−10.3887			−0.369380
$792$	28.6878	−	62.1498i	1.01938	−	2.20840i
$793$	−2.27335			−0.0807289
$794$	−29.0797	+	50.3675i	−1.03200	+	1.78747i
$795$	15.1878	+	23.7384i	0.538657	+	0.841913i
$796$	−46.0261	−	79.7195i	−1.63135	−	2.82558i
$797$	−23.2829	−	40.3271i	−0.824722	−	1.42846i	−0.902132	−	0.431461i	$-0.857998\pi$
$797$	−23.2829	−	40.3271i	−0.824722	−	1.42846i	0.0774101	−	0.996999i	$-0.475335\pi$
$798$	−9.31138	−	14.5535i	−0.329619	−	0.515190i
$799$	−5.75223	+	9.96316i	−0.203499	+	0.352471i
$800$	−0.931521			−0.0329343
$801$	−42.8910	+	3.92025i	−1.51548	+	0.138515i
$802$	6.30972			0.222804
$803$	3.40263	−	5.89352i	0.120076	−	0.207978i
$804$	−51.0933	+	98.6159i	−1.80192	+	3.47792i
$805$	0.354473	+	0.613964i	0.0124935	+	0.0216394i
$806$	2.86333	+	4.95943i	0.100856	+	0.174688i
$807$	32.5890	−	1.48622i	1.14719	−	0.0523175i
$808$	−9.29893	+	16.1062i	−0.327135	+	0.566615i
$809$	−10.8023			−0.379790			−0.189895	−	0.981804i	$-0.560815\pi$
$809$	−10.8023			−0.379790			−0.189895	+	0.981804i	$0.560815\pi$
$810$	56.4820	−	10.4119i	1.98457	−	0.365837i
$811$	5.58307			0.196048			0.0980240	−	0.995184i	$-0.468748\pi$
$811$	5.58307			0.196048			0.0980240	+	0.995184i	$0.468748\pi$
$812$	4.98755	−	8.63868i	0.175029	−	0.303158i
$813$	41.4954	−	1.89240i	1.45531	−	0.0663694i
$814$	9.89037	+	17.1306i	0.346657	+	0.600428i
$815$	23.1050	+	40.0191i	0.809335	+	1.40181i
$816$	−3.26157	+	6.29520i	−0.114178	+	0.220376i
$817$	−21.1534	+	36.6388i	−0.740064	+	1.28183i
$818$	84.4556			2.95292
$819$	−2.98755	+	0.273062i	−0.104393	+	0.00954157i
$820$	67.3609			2.35234
$821$	15.8940	−	27.5292i	0.554703	−	0.960774i	−0.443223	−	0.896411i	$-0.646165\pi$
$821$	15.8940	−	27.5292i	0.554703	−	0.960774i	0.997927	−	0.0643630i	$-0.0205016\pi$
$822$	8.43512	+	13.1840i	0.294209	+	0.459844i
$823$	18.0000	+	31.1769i	0.627441	+	1.08676i	0.988063	+	0.154047i	$0.0492308\pi$
$823$	18.0000	+	31.1769i	0.627441	+	1.08676i	−0.360623	+	0.932712i	$0.617436\pi$
$824$	−24.5797	−	42.5732i	−0.856273	−	1.48311i
$825$	7.27647	+	11.3730i	0.253334	+	0.395957i
$826$	3.35447	−	5.81012i	0.116717	−	0.202160i
$827$	15.9224			0.553675			0.276837	−	0.960917i	$-0.410714\pi$
$827$	15.9224			0.553675			0.276837	+	0.960917i	$0.410714\pi$
$828$	1.39329	−	3.01845i	0.0484203	−	0.104899i
$829$	35.4720			1.23199			0.615996	−	0.787749i	$-0.288754\pi$
$829$	35.4720			1.23199			0.615996	+	0.787749i	$0.288754\pi$
$830$	3.01819	−	5.22765i	0.104763	−	0.181455i
$831$	5.70681	−	11.0148i	0.197967	−	0.382099i
$832$	3.66372	+	6.34574i	0.127016	+	0.219999i
$833$	0.472958	+	0.819187i	0.0163870	+	0.0283832i
$834$	−8.74484	+	0.398809i	−0.302809	+	0.0138096i
$835$	−10.9808	+	19.0194i	−0.380007	+	0.658192i
$836$	−74.2000			−2.56626
$837$	7.41789	+	9.55155i	0.256400	+	0.330150i
$838$	−9.98229			−0.344833
$839$	27.3391	−	47.3527i	0.943850	−	1.63480i	0.185814	−	0.982585i	$-0.440508\pi$
$839$	27.3391	−	47.3527i	0.943850	−	1.63480i	0.758037	−	0.652212i	$-0.226159\pi$
$840$	22.6804	−	1.03434i	0.782550	−	0.0356882i
$841$	11.4730	+	19.8717i	0.395619	+	0.685233i
$842$	−25.9200	−	44.8948i	−0.893263	−	1.54718i
$843$	11.8576	−	22.8865i	0.408397	−	0.788254i
$844$	−9.24630	+	16.0151i	−0.318271	+	0.551261i
$845$	31.1230			1.07066
$846$	−51.7783	−	73.3397i	−1.78017	−	2.52147i
$847$	−9.38151			−0.322353
$848$	13.5737	−	23.5104i	0.466124	−	0.807350i
$849$	18.6665	+	29.1755i	0.640633	+	1.00130i
$850$	−2.00933	−	3.48027i	−0.0689196	−	0.119372i
$851$	0.243379	+	0.421545i	0.00834292	+	0.0144504i
$852$	12.3874	+	19.3614i	0.424387	+	0.663310i
$853$	1.09884	−	1.90324i	0.0376234	−	0.0651656i	−0.846601	−	0.532229i	$-0.821355\pi$
$853$	1.09884	−	1.90324i	0.0376234	−	0.0651656i	0.884224	+	0.467063i	$0.154688\pi$
$854$	−5.59358			−0.191408
$855$	−18.1929	−	25.7687i	−0.622184	−	0.881272i
$856$	6.94592			0.237407
$857$	7.88823	−	13.6628i	0.269457	−	0.466713i	−0.699265	−	0.714863i	$-0.746489\pi$
$857$	7.88823	−	13.6628i	0.269457	−	0.466713i	0.968722	+	0.248150i	$0.0798225\pi$
$858$	−8.85087	+	17.0832i	−0.302164	+	0.583211i
$859$	−2.78813	−	4.82918i	−0.0951298	−	0.164770i	0.814533	−	0.580117i	$-0.196993\pi$
$859$	−2.78813	−	4.82918i	−0.0951298	−	0.164770i	−0.909663	+	0.415348i	$0.863660\pi$
$860$	−54.8630	−	95.0255i	−1.87081	−	3.24034i
$861$	−11.0847	+	0.505519i	−0.377766	+	0.0172281i
$862$	27.8264	−	48.1968i	0.947773	−	1.64159i
$863$	23.1268			0.787247			0.393623	−	0.919272i	$-0.371221\pi$
$863$	23.1268			0.787247			0.393623	+	0.919272i	$0.371221\pi$
$864$	−1.71946	−	2.21404i	−0.0584971	−	0.0753230i
$865$	−45.0157			−1.53058
$866$	2.97462	−	5.15218i	0.101082	−	0.175078i
$867$	27.8661	−	1.27084i	0.946384	−	0.0431599i
$868$	4.71780	+	8.17147i	0.160133	+	0.277358i
$869$	−33.2024	−	57.5083i	−1.12631	−	1.95083i
$870$	12.5110	−	24.1477i	0.424162	−	0.818683i
$871$	7.90856	−	13.6980i	0.267971	−	0.464140i
$872$	17.1800			0.581787
$873$	14.4459	−	31.2959i	0.488920	−	1.05920i
$874$	−2.72665			−0.0922304
$875$	4.24484	−	7.35228i	0.143502	−	0.248552i
$876$	−5.70448	−	8.91601i	−0.192736	−	0.301244i
$877$	−1.96264	−	3.39939i	−0.0662737	−	0.114789i	0.830985	−	0.556295i	$-0.187778\pi$
$877$	−1.96264	−	3.39939i	−0.0662737	−	0.114789i	−0.897258	+	0.441506i	$0.854444\pi$
$878$	−28.8982	−	50.0532i	−0.975268	−	1.68921i
$879$	14.0631	+	21.9805i	0.474338	+	0.741383i
$880$	25.3348	−	43.8812i	0.854037	−	1.47923i
$881$	27.1986			0.916345			0.458173	−	0.888863i	$-0.348504\pi$
$881$	27.1986			0.916345			0.458173	+	0.888863i	$0.348504\pi$
$882$	−7.35087	+	0.671871i	−0.247517	+	0.0226231i
$883$	8.21341			0.276403			0.138202	−	0.990404i	$-0.455868\pi$
$883$	8.21341			0.276403			0.138202	+	0.990404i	$0.455868\pi$
$884$	1.91741	−	3.32105i	0.0644895	−	0.111699i
$885$	5.63473	−	10.8757i	0.189409	−	0.365582i
$886$	−16.5074	−	28.5916i	−0.554577	−	0.960555i
$887$	3.24057	+	5.61283i	0.108808	+	0.188460i	0.915287	−	0.402801i	$-0.131963\pi$
$887$	3.24057	+	5.61283i	0.108808	+	0.188460i	−0.806480	+	0.591262i	$0.798630\pi$
$888$	15.5723	−	0.710174i	0.522571	−	0.0238319i
$889$	0.336285	−	0.582462i	0.0112786	−	0.0195352i
$890$	−91.6169			−3.07101
$891$	−13.6000	+	38.2876i	−0.455617	+	1.28268i
$892$	54.0187			1.80868
$893$	−24.6534	+	42.7009i	−0.824995	+	1.42893i
$894$	−57.6598	+	2.62958i	−1.92843	+	0.0879463i
$895$	−14.7178	−	25.4920i	−0.491962	−	0.852103i
$896$	9.55408	+	16.5482i	0.319180	+	0.552835i
$897$	−0.217799	+	0.420378i	−0.00727211	+	0.0140360i
$898$	−11.2719	+	19.5235i	−0.376148	+	0.651507i
$899$	5.72665			0.190995
$900$	20.9128	−	1.91144i	0.697094	−	0.0637146i
$901$	5.93406			0.197692
$902$	−35.5818	+	61.6295i	−1.18474	+	2.05204i
$903$	9.74124	+	15.2254i	0.324168	+	0.506670i
$904$	26.2527	+	45.4710i	0.873152	+	1.51234i
$905$	28.3853	+	49.1648i	0.943560	+	1.63429i
$906$	−22.8030	−	35.6408i	−0.757579	−	1.18408i
$907$	−5.06440	+	8.77180i	−0.168161	+	0.291263i	−0.937773	−	0.347248i	$-0.887116\pi$
$907$	−5.06440	+	8.77180i	−0.168161	+	0.291263i	0.769613	+	0.638511i	$0.220449\pi$
$908$	5.60078			0.185868
$909$	4.62655	−	10.0230i	0.153453	−	0.332443i
$910$	−6.38151			−0.211545
$911$	−22.9612	+	39.7699i	−0.760738	+	1.31764i	0.181733	+	0.983348i	$0.441829\pi$
$911$	−22.9612	+	39.7699i	−0.760738	+	1.31764i	−0.942471	+	0.334289i	$0.891504\pi$
$912$	−13.9787	+	26.9805i	−0.462881	+	0.893414i
$913$	2.13521	+	3.69829i	0.0706652	+	0.122396i
$914$	10.8473	+	18.7880i	0.358796	+	0.621453i
$915$	−10.2017	+	0.465251i	−0.337259	+	0.0153807i
$916$	36.4449	−	63.1245i	1.20417	−	2.08569i
$917$	−7.91381			−0.261337
$918$	4.56294	−	11.1999i	0.150599	−	0.369650i
$919$	−4.92432			−0.162438			−0.0812192	−	0.996696i	$-0.525881\pi$
$919$	−4.92432			−0.162438			−0.0812192	+	0.996696i	$0.525881\pi$
$920$	1.79153	−	3.10303i	0.0590651	−	0.102304i
$921$	47.1847	−	2.15186i	1.55479	−	0.0709062i
$922$	−6.96216	−	12.0588i	−0.229287	−	0.397136i
$923$	−1.63667	−	2.83480i	−0.0538718	−	0.0933086i
$924$	−14.5833	+	28.1474i	−0.479754	+	0.925981i
$925$	−1.53736	+	2.66278i	−0.0505481	+	0.0875518i
$926$	−38.6955			−1.27161
$927$	16.8296	+	23.8377i	0.552755	+	0.782933i
$928$	−1.32743			−0.0435750
$929$	−0.00379324	+	0.00657009i	−0.000124452	+	0.000215558i	−0.866088	−	0.499892i	$-0.833373\pi$
$929$	−0.00379324	+	0.00657009i	−0.000124452	+	0.000215558i	0.865963	+	0.500108i	$0.166706\pi$
$930$	13.8643	+	21.6697i	0.454628	+	0.710577i
$931$	2.02704	+	3.51094i	0.0664336	+	0.115066i
$932$	38.4779	+	66.6457i	1.26039	+	2.18305i
$933$	−14.9189	−	23.3180i	−0.488422	−	0.763396i
$934$	−27.0620	+	46.8727i	−0.885494	+	1.53372i
$935$	11.0757			0.362213
$936$	8.74484	+	12.3863i	0.285834	+	0.404860i
$937$	21.1623			0.691341			0.345670	−	0.938356i	$-0.387652\pi$
$937$	21.1623			0.691341			0.345670	+	0.938356i	$0.387652\pi$
$938$	19.4590	−	33.7040i	0.635360	−	1.10048i
$939$	9.24105	−	17.8363i	0.301570	−	0.582066i
$940$	−63.9405	−	110.748i	−2.08551	−	3.61221i
$941$	−2.27908	−	3.94748i	−0.0742959	−	0.128684i	0.826484	−	0.562960i	$-0.190338\pi$
$941$	−2.27908	−	3.94748i	−0.0742959	−	0.128684i	−0.900780	+	0.434276i	$0.857004\pi$
$942$	25.7740	−	1.17543i	0.839763	−	0.0382974i
$943$	−0.875585	+	1.51656i	−0.0285130	+	0.0493859i
$944$	−11.7994			−0.384038
$945$	−13.3509	+	1.83680i	−0.434304	+	0.0597510i
$946$	115.920			3.76890
$947$	−6.86760	+	11.8950i	−0.223167	+	0.386537i	−0.955768	−	0.294122i	$-0.904973\pi$
$947$	−6.86760	+	11.8950i	−0.223167	+	0.386537i	0.732601	+	0.680658i	$0.238306\pi$
$948$	−103.177	+	4.70540i	−3.35104	+	0.152824i
$949$	0.753696	+	1.30544i	0.0244660	+	0.0423764i
$950$	−8.61177	−	14.9160i	−0.279403	−	0.483940i
$951$	−1.60769	+	3.10303i	−0.0521329	+	0.100623i
$952$	2.39037	−	4.14024i	0.0774723	−	0.134186i
$953$	8.80699			0.285286			0.142643	−	0.989774i	$-0.454440\pi$
$953$	8.80699			0.285286			0.142643	+	0.989774i	$0.454440\pi$
$954$	−19.4071	+	42.0438i	−0.628328	+	1.36122i
$955$	1.82004			0.0588951
$956$	−9.91595	+	17.1749i	−0.320705	+	0.555477i
$957$	10.3691	+	16.2067i	0.335184	+	0.523888i
$958$	30.7257	+	53.2184i	0.992701	+	1.71941i
$959$	−1.83628	−	3.18054i	−0.0592967	−	0.102705i
$960$	17.7398	+	27.7270i	0.572549	+	0.894886i
$961$	12.7915	−	22.1556i	0.412630	−	0.714696i
$962$	−4.38151			−0.141266
$963$	−4.10584	+	0.375274i	−0.132309	+	0.0120930i
$964$	−106.052			−3.41571
$965$	15.7489	−	27.2779i	0.506976	−	0.878108i
$966$	−0.535897	+	1.03434i	−0.0172422	+	0.0332794i
$967$	−19.1642	−	33.1934i	−0.616279	−	1.06743i	−0.990159	−	0.139949i	$-0.955306\pi$
$967$	−19.1642	−	33.1934i	−0.616279	−	1.06743i	0.373880	−	0.927477i	$-0.378027\pi$
$968$	23.7075	+	41.0626i	0.761987	+	1.31980i
$969$	−6.63521	+	0.302599i	−0.213154	+	0.00972088i
$970$	36.6608	−	63.4984i	1.17711	−	2.03881i
$971$	−31.0187			−0.995436			−0.497718	−	0.867339i	$-0.665829\pi$
$971$	−31.0187			−0.995436			−0.497718	+	0.867339i	$0.665829\pi$
$972$	43.1452	+	46.1773i	1.38388	+	1.48114i
$973$	2.05408			0.0658509
$974$	−21.6498	+	37.4986i	−0.693704	+	1.20153i
$975$	−2.98755	+	0.136247i	−0.0956781	+	0.00436340i
$976$	4.91887	+	8.51974i	0.157449	+	0.272710i
$977$	26.3712	+	45.6763i	0.843689	+	1.46131i	0.886755	+	0.462241i	$0.152954\pi$
$977$	26.3712	+	45.6763i	0.843689	+	1.46131i	−0.0430652	+	0.999072i	$0.513712\pi$
$978$	−34.9305	+	67.4200i	−1.11696	+	2.15585i
$979$	32.4071	−	56.1307i	1.03574	−	1.79395i
$980$	−10.5146			−0.335876
$981$	−10.1553	+	0.928200i	−0.324235	+	0.0296351i
$982$	−33.9430			−1.08316
$983$	9.15146	−	15.8508i	0.291886	−	0.505562i	−0.682370	−	0.731007i	$-0.739050\pi$
$983$	9.15146	−	15.8508i	0.291886	−	0.505562i	0.974256	+	0.225446i	$0.0723838\pi$
$984$	30.2242	+	47.2400i	0.963513	+	1.50596i
$985$	−21.2812	−	36.8601i	−0.678076	−	1.17446i
$986$	−2.86333	−	4.95943i	−0.0911869	−	0.157940i
$987$	11.3530	+	17.7446i	0.361370	+	0.564816i
$988$	8.21780	−	14.2336i	0.261443	−	0.452833i
$989$	2.85253			0.0907052
$990$	−36.2226	+	78.4731i	−1.15123	+	2.49404i
$991$	−12.6008			−0.400277			−0.200138	−	0.979768i	$-0.564139\pi$
$991$	−12.6008			−0.400277			−0.200138	+	0.979768i	$0.564139\pi$
$992$	0.627819	−	1.08741i	0.0199333	−	0.0345254i
$993$	−15.7039	+	30.3103i	−0.498348	+	0.961869i
$994$	−4.02704	−	6.97504i	−0.127730	−	0.221235i
$995$	29.4449	+	51.0001i	0.933467	+	1.61681i
$996$	6.63521	−	0.302599i	0.210245	−	0.00958822i
$997$	−5.87120	+	10.1692i	−0.185943	+	0.322062i	−0.943894	−	0.330249i	$-0.892867\pi$
$997$	−5.87120	+	10.1692i	−0.185943	+	0.322062i	0.757951	+	0.652311i	$0.226201\pi$
$998$	−32.2019			−1.01933
$999$	−9.16664	+	1.26113i	−0.290020	+	0.0399005i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.2.f.b.43.3	yes	6
3.2	odd	2		189.2.f.a.127.1		6
4.3	odd	2		1008.2.r.k.673.3		6
7.2	even	3		441.2.h.c.214.1		6
7.3	odd	6		441.2.g.d.79.3		6
7.4	even	3		441.2.g.e.79.3		6
7.5	odd	6		441.2.h.b.214.1		6
7.6	odd	2		441.2.f.d.295.3		6
9.2	odd	6		567.2.a.g.1.3		3
9.4	even	3	inner	63.2.f.b.22.3	✓	6
9.5	odd	6		189.2.f.a.64.1		6
9.7	even	3		567.2.a.d.1.1		3
12.11	even	2		3024.2.r.g.2017.2		6
21.2	odd	6		1323.2.h.d.802.3		6
21.5	even	6		1323.2.h.e.802.3		6
21.11	odd	6		1323.2.g.c.667.1		6
21.17	even	6		1323.2.g.b.667.1		6
21.20	even	2		1323.2.f.c.883.1		6
36.7	odd	6		9072.2.a.bq.1.2		3
36.11	even	6		9072.2.a.cd.1.2		3
36.23	even	6		3024.2.r.g.1009.2		6
36.31	odd	6		1008.2.r.k.337.3		6
63.4	even	3		441.2.h.c.373.1		6
63.5	even	6		1323.2.g.b.361.1		6
63.13	odd	6		441.2.f.d.148.3		6
63.20	even	6		3969.2.a.p.1.3		3
63.23	odd	6		1323.2.g.c.361.1		6
63.31	odd	6		441.2.h.b.373.1		6
63.32	odd	6		1323.2.h.d.226.3		6
63.34	odd	6		3969.2.a.m.1.1		3
63.40	odd	6		441.2.g.d.67.3		6
63.41	even	6		1323.2.f.c.442.1		6
63.58	even	3		441.2.g.e.67.3		6
63.59	even	6		1323.2.h.e.226.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.f.b.22.3	✓	6	9.4	even	3	inner
63.2.f.b.43.3	yes	6	1.1	even	1	trivial
189.2.f.a.64.1		6	9.5	odd	6
189.2.f.a.127.1		6	3.2	odd	2
441.2.f.d.148.3		6	63.13	odd	6
441.2.f.d.295.3		6	7.6	odd	2
441.2.g.d.67.3		6	63.40	odd	6
441.2.g.d.79.3		6	7.3	odd	6
441.2.g.e.67.3		6	63.58	even	3
441.2.g.e.79.3		6	7.4	even	3
441.2.h.b.214.1		6	7.5	odd	6
441.2.h.b.373.1		6	63.31	odd	6
441.2.h.c.214.1		6	7.2	even	3
441.2.h.c.373.1		6	63.4	even	3
567.2.a.d.1.1		3	9.7	even	3
567.2.a.g.1.3		3	9.2	odd	6
1008.2.r.k.337.3		6	36.31	odd	6
1008.2.r.k.673.3		6	4.3	odd	2
1323.2.f.c.442.1		6	63.41	even	6
1323.2.f.c.883.1		6	21.20	even	2
1323.2.g.b.361.1		6	63.5	even	6
1323.2.g.b.667.1		6	21.17	even	6
1323.2.g.c.361.1		6	63.23	odd	6
1323.2.g.c.667.1		6	21.11	odd	6
1323.2.h.d.226.3		6	63.32	odd	6
1323.2.h.d.802.3		6	21.2	odd	6
1323.2.h.e.226.3		6	63.59	even	6
1323.2.h.e.802.3		6	21.5	even	6
3024.2.r.g.1009.2		6	36.23	even	6
3024.2.r.g.2017.2		6	12.11	even	2
3969.2.a.m.1.1		3	63.34	odd	6
3969.2.a.p.1.3		3	63.20	even	6
9072.2.a.bq.1.2		3	36.7	odd	6
9072.2.a.cd.1.2		3	36.11	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:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	63.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.23025 - 2.13086i) q^{2} +(-1.73025 + 0.0789082i) q^{3} +(-2.02704 - 3.51094i) q^{4} +(1.29679 + 2.24611i) q^{5} +(-1.96050 + 3.78400i) q^{6} +(0.500000 - 0.866025i) q^{7} -5.05408 q^{8} +(2.98755 - 0.273062i) q^{9} +O(q^{10})\)	\(q+(1.23025 - 2.13086i) q^{2} +(-1.73025 + 0.0789082i) q^{3} +(-2.02704 - 3.51094i) q^{4} +(1.29679 + 2.24611i) q^{5} +(-1.96050 + 3.78400i) q^{6} +(0.500000 - 0.866025i) q^{7} -5.05408 q^{8} +(2.98755 - 0.273062i) q^{9} +6.38151 q^{10} +(-2.25729 + 3.90975i) q^{11} +(3.78434 + 5.91486i) q^{12} +(-0.500000 - 0.866025i) q^{13} +(-1.23025 - 2.13086i) q^{14} +(-2.42101 - 3.78400i) q^{15} +(-2.16372 + 3.74766i) q^{16} -0.945916 q^{17} +(3.09358 - 6.70198i) q^{18} -4.05408 q^{19} +(5.25729 - 9.10590i) q^{20} +(-0.796790 + 1.53790i) q^{21} +(5.55408 + 9.61996i) q^{22} +(0.136673 + 0.236725i) q^{23} +(8.74484 - 0.398809i) q^{24} +(-0.863327 + 1.49533i) q^{25} -2.46050 q^{26} +(-5.14766 + 0.708209i) q^{27} -4.05408 q^{28} +(-1.23025 + 2.13086i) q^{29} +(-11.0416 + 0.503554i) q^{30} +(-1.16372 - 2.01561i) q^{31} +(0.269748 + 0.467216i) q^{32} +(3.59718 - 6.94297i) q^{33} +(-1.16372 + 2.01561i) q^{34} +2.59358 q^{35} +(-7.01459 - 9.93559i) q^{36} +1.78074 q^{37} +(-4.98755 + 8.63868i) q^{38} +(0.933463 + 1.45899i) q^{39} +(-6.55408 - 11.3520i) q^{40} +(3.20321 + 5.54812i) q^{41} +(2.29679 + 3.58985i) q^{42} +(5.21780 - 9.03749i) q^{43} +18.3025 q^{44} +(4.48755 + 6.35624i) q^{45} +0.672570 q^{46} +(6.08113 - 10.5328i) q^{47} +(3.44805 - 6.65514i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(2.12422 + 3.67926i) q^{50} +(1.63667 - 0.0746406i) q^{51} +(-2.02704 + 3.51094i) q^{52} -6.27335 q^{53} +(-4.82383 + 11.8402i) q^{54} -11.7089 q^{55} +(-2.52704 + 4.37697i) q^{56} +(7.01459 - 0.319901i) q^{57} +(3.02704 + 5.24299i) q^{58} +(1.36333 + 2.36135i) q^{59} +(-8.37792 + 16.1704i) q^{60} +(1.13667 - 1.96878i) q^{61} -5.72665 q^{62} +(1.25729 - 2.72382i) q^{63} -7.32743 q^{64} +(1.29679 - 2.24611i) q^{65} +(-10.3691 - 16.2067i) q^{66} +(7.90856 + 13.6980i) q^{67} +(1.91741 + 3.32105i) q^{68} +(-0.255158 - 0.398809i) q^{69} +(3.19076 - 5.52655i) q^{70} +3.27335 q^{71} +(-15.0993 + 1.38008i) q^{72} -1.50739 q^{73} +(2.19076 - 3.79450i) q^{74} +(1.37578 - 2.65542i) q^{75} +(8.21780 + 14.2336i) q^{76} +(2.25729 + 3.90975i) q^{77} +(4.25729 - 0.194154i) q^{78} +(-7.35447 + 12.7383i) q^{79} -11.2235 q^{80} +(8.85087 - 1.63157i) q^{81} +15.7630 q^{82} +(0.472958 - 0.819187i) q^{83} +(7.01459 - 0.319901i) q^{84} +(-1.22665 - 2.12463i) q^{85} +(-12.8384 - 22.2368i) q^{86} +(1.96050 - 3.78400i) q^{87} +(11.4086 - 19.7602i) q^{88} -14.3566 q^{89} +(19.0651 - 1.74255i) q^{90} -1.00000 q^{91} +(0.554084 - 0.959702i) q^{92} +(2.17257 + 3.39569i) q^{93} +(-14.9626 - 25.9161i) q^{94} +(-5.25729 - 9.10590i) q^{95} +(-0.503599 - 0.787117i) q^{96} +(5.74484 - 9.95036i) q^{97} -2.46050 q^{98} +(-5.67617 + 12.2969i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + q^{2} - 4 q^{3} - 3 q^{4} + 5 q^{5} + q^{6} + 3 q^{7} - 12 q^{8} - 4 q^{9}+O(q^{10}) \) 6 * q + q^2 - 4 * q^3 - 3 * q^4 + 5 * q^5 + q^6 + 3 * q^7 - 12 * q^8 - 4 * q^9	\( 6 q + q^{2} - 4 q^{3} - 3 q^{4} + 5 q^{5} + q^{6} + 3 q^{7} - 12 q^{8} - 4 q^{9} + 2 q^{11} - 2 q^{12} - 3 q^{13} - q^{14} + 11 q^{15} - 3 q^{16} - 24 q^{17} + 13 q^{18} - 6 q^{19} + 16 q^{20} - 2 q^{21} + 15 q^{22} + 15 q^{24} - 6 q^{25} - 2 q^{26} - 7 q^{27} - 6 q^{28} - q^{29} - 26 q^{30} + 3 q^{31} + 8 q^{32} + 8 q^{33} + 3 q^{34} + 10 q^{35} - 11 q^{36} - 6 q^{37} - 8 q^{38} + 2 q^{39} - 21 q^{40} + 22 q^{41} + 11 q^{42} + 3 q^{43} + 46 q^{44} + 5 q^{45} + 24 q^{46} + 9 q^{47} - 14 q^{48} - 3 q^{49} - 10 q^{50} + 9 q^{51} - 3 q^{52} - 36 q^{53} - 17 q^{54} - 12 q^{55} - 6 q^{56} + 11 q^{57} + 9 q^{58} + 9 q^{59} - 20 q^{60} + 6 q^{61} - 36 q^{62} - 8 q^{63} - 24 q^{64} + 5 q^{65} - 2 q^{66} - 6 q^{68} - 39 q^{69} + 18 q^{71} - 24 q^{72} + 6 q^{73} - 6 q^{74} + 31 q^{75} + 21 q^{76} - 2 q^{77} + 10 q^{78} - 15 q^{79} + 22 q^{80} + 32 q^{81} + 18 q^{82} + 12 q^{83} + 11 q^{84} - 9 q^{85} - 34 q^{86} - q^{87} + 21 q^{88} - 4 q^{89} + 73 q^{90} - 6 q^{91} - 15 q^{92} + 33 q^{93} - 24 q^{94} - 16 q^{95} + 5 q^{96} - 3 q^{97} - 2 q^{98} - 46 q^{99}+O(q^{100}) \) 6 * q + q^2 - 4 * q^3 - 3 * q^4 + 5 * q^5 + q^6 + 3 * q^7 - 12 * q^8 - 4 * q^9 + 2 * q^11 - 2 * q^12 - 3 * q^13 - q^14 + 11 * q^15 - 3 * q^16 - 24 * q^17 + 13 * q^18 - 6 * q^19 + 16 * q^20 - 2 * q^21 + 15 * q^22 + 15 * q^24 - 6 * q^25 - 2 * q^26 - 7 * q^27 - 6 * q^28 - q^29 - 26 * q^30 + 3 * q^31 + 8 * q^32 + 8 * q^33 + 3 * q^34 + 10 * q^35 - 11 * q^36 - 6 * q^37 - 8 * q^38 + 2 * q^39 - 21 * q^40 + 22 * q^41 + 11 * q^42 + 3 * q^43 + 46 * q^44 + 5 * q^45 + 24 * q^46 + 9 * q^47 - 14 * q^48 - 3 * q^49 - 10 * q^50 + 9 * q^51 - 3 * q^52 - 36 * q^53 - 17 * q^54 - 12 * q^55 - 6 * q^56 + 11 * q^57 + 9 * q^58 + 9 * q^59 - 20 * q^60 + 6 * q^61 - 36 * q^62 - 8 * q^63 - 24 * q^64 + 5 * q^65 - 2 * q^66 - 6 * q^68 - 39 * q^69 + 18 * q^71 - 24 * q^72 + 6 * q^73 - 6 * q^74 + 31 * q^75 + 21 * q^76 - 2 * q^77 + 10 * q^78 - 15 * q^79 + 22 * q^80 + 32 * q^81 + 18 * q^82 + 12 * q^83 + 11 * q^84 - 9 * q^85 - 34 * q^86 - q^87 + 21 * q^88 - 4 * q^89 + 73 * q^90 - 6 * q^91 - 15 * q^92 + 33 * q^93 - 24 * q^94 - 16 * q^95 + 5 * q^96 - 3 * q^97 - 2 * q^98 - 46 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more