LMFDB - Embedded newform 462.2.j.e.379.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(169,462)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(462, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("462.169");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.j (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.68908857338$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.484000000.9
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + x^{6} + 16x^{4} + 66x^{2} + 121 $ x^8 + x^6 + 16x^4 + 66x^2 + 121
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			379.1
Root			$1.73855 + 1.26313i$ of defining polynomial
Character	$\chi$	$=$	462.379
Dual form			462.2.j.e.295.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.309017 + 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(0.0895849 - 0.275714i) q^{5} +(0.309017 - 0.951057i) q^{6} +(-0.809017 + 0.587785i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})$	\(q+(0.309017 + 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(0.0895849 - 0.275714i) q^{5} +(0.309017 - 0.951057i) q^{6} +(-0.809017 + 0.587785i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(0.309017 + 0.951057i) q^{9} +0.289903 q^{10} +(3.06668 + 1.26313i) q^{11} +1.00000 q^{12} +(1.16407 + 3.58263i) q^{13} +(-0.809017 - 0.587785i) q^{14} +(-0.234536 + 0.170401i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-2.03093 + 6.25055i) q^{17} +(-0.809017 + 0.587785i) q^{18} +(-0.879488 - 0.638985i) q^{19} +(0.0895849 + 0.275714i) q^{20} +1.00000 q^{21} +(-0.253650 + 3.30691i) q^{22} +1.94617 q^{23} +(0.309017 + 0.951057i) q^{24} +(3.97709 + 2.88953i) q^{25} +(-3.04756 + 2.21418i) q^{26} +(0.309017 - 0.951057i) q^{27} +(0.309017 - 0.951057i) q^{28} +(-5.54909 + 4.03165i) q^{29} +(-0.234536 - 0.170401i) q^{30} +(1.41195 + 4.34552i) q^{31} +1.00000 q^{32} +(-1.73855 - 2.82444i) q^{33} -6.57222 q^{34} +(0.0895849 + 0.275714i) q^{35} +(-0.809017 - 0.587785i) q^{36} +(4.00153 - 2.90728i) q^{37} +(0.335934 - 1.03390i) q^{38} +(1.16407 - 3.58263i) q^{39} +(-0.234536 + 0.170401i) q^{40} +(-9.36212 - 6.80198i) q^{41} +(0.309017 + 0.951057i) q^{42} +7.40866 q^{43} +(-3.22344 + 0.780656i) q^{44} +0.289903 q^{45} +(0.601398 + 1.85091i) q^{46} +(0.774080 + 0.562402i) q^{47} +(-0.809017 + 0.587785i) q^{48} +(0.309017 - 0.951057i) q^{49} +(-1.51911 + 4.67535i) q^{50} +(5.31704 - 3.86305i) q^{51} +(-3.04756 - 2.21418i) q^{52} +(0.608699 + 1.87338i) q^{53} +1.00000 q^{54} +(0.622990 - 0.732369i) q^{55} +1.00000 q^{56} +(0.335934 + 1.03390i) q^{57} +(-5.54909 - 4.03165i) q^{58} +(-5.17208 + 3.75774i) q^{59} +(0.0895849 - 0.275714i) q^{60} +(-0.537199 + 1.65333i) q^{61} +(-3.69652 + 2.68568i) q^{62} +(-0.809017 - 0.587785i) q^{63} +(0.309017 + 0.951057i) q^{64} +1.09206 q^{65} +(2.14896 - 2.52626i) q^{66} +6.92398 q^{67} +(-2.03093 - 6.25055i) q^{68} +(-1.57448 - 1.14393i) q^{69} +(-0.234536 + 0.170401i) q^{70} +(1.72877 - 5.32060i) q^{71} +(0.309017 - 0.951057i) q^{72} +(3.02312 - 2.19643i) q^{73} +(4.00153 + 2.90728i) q^{74} +(-1.51911 - 4.67535i) q^{75} +1.08711 q^{76} +(-3.22344 + 0.780656i) q^{77} +3.76700 q^{78} +(-3.26853 - 10.0595i) q^{79} +(-0.234536 - 0.170401i) q^{80} +(-0.809017 + 0.587785i) q^{81} +(3.57601 - 11.0058i) q^{82} +(4.87146 - 14.9928i) q^{83} +(-0.809017 + 0.587785i) q^{84} +(1.54142 + 1.11991i) q^{85} +(2.28940 + 7.04605i) q^{86} +6.85906 q^{87} +(-1.73855 - 2.82444i) q^{88} -11.8555 q^{89} +(0.0895849 + 0.275714i) q^{90} +(-3.04756 - 2.21418i) q^{91} +(-1.57448 + 1.14393i) q^{92} +(1.41195 - 4.34552i) q^{93} +(-0.295672 + 0.909986i) q^{94} +(-0.254966 + 0.185244i) q^{95} +(-0.809017 - 0.587785i) q^{96} +(-1.10140 - 3.38975i) q^{97} +1.00000 q^{98} +(-0.253650 + 3.30691i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} - 2 q^{3} - 2 q^{4} + 4 q^{5} - 2 q^{6} - 2 q^{7} - 2 q^{8} - 2 q^{9}+O(q^{10}) $ 8 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 + 4 * q^5 - 2 * q^6 - 2 * q^7 - 2 * q^8 - 2 * q^9	$ 8 q - 2 q^{2} - 2 q^{3} - 2 q^{4} + 4 q^{5} - 2 q^{6} - 2 q^{7} - 2 q^{8} - 2 q^{9} + 4 q^{10} + 8 q^{12} + 4 q^{13} - 2 q^{14} - 6 q^{15} - 2 q^{16} - 8 q^{17} - 2 q^{18} - 12 q^{19} + 4 q^{20} + 8 q^{21} - 4 q^{23} - 2 q^{24} + 4 q^{25} - 6 q^{26} - 2 q^{27} - 2 q^{28} - 4 q^{29} - 6 q^{30} - 14 q^{31} + 8 q^{32} + 12 q^{34} + 4 q^{35} - 2 q^{36} + 10 q^{37} + 8 q^{38} + 4 q^{39} - 6 q^{40} - 12 q^{41} - 2 q^{42} + 20 q^{43} + 4 q^{45} + 6 q^{46} + 28 q^{47} - 2 q^{48} - 2 q^{49} - 6 q^{50} + 2 q^{51} - 6 q^{52} + 2 q^{53} + 8 q^{54} + 4 q^{55} + 8 q^{56} + 8 q^{57} - 4 q^{58} + 4 q^{60} - 34 q^{61} + 6 q^{62} - 2 q^{63} - 2 q^{64} + 16 q^{65} - 24 q^{67} - 8 q^{68} - 4 q^{69} - 6 q^{70} - 2 q^{72} + 10 q^{74} - 6 q^{75} + 8 q^{76} + 4 q^{78} + 22 q^{79} - 6 q^{80} - 2 q^{81} - 2 q^{82} - 30 q^{83} - 2 q^{84} - 28 q^{85} + 36 q^{87} - 4 q^{89} + 4 q^{90} - 6 q^{91} - 4 q^{92} - 14 q^{93} - 22 q^{94} - 30 q^{95} - 2 q^{96} - 10 q^{97} + 8 q^{98}+O(q^{100}) $ 8 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 + 4 * q^5 - 2 * q^6 - 2 * q^7 - 2 * q^8 - 2 * q^9 + 4 * q^10 + 8 * q^12 + 4 * q^13 - 2 * q^14 - 6 * q^15 - 2 * q^16 - 8 * q^17 - 2 * q^18 - 12 * q^19 + 4 * q^20 + 8 * q^21 - 4 * q^23 - 2 * q^24 + 4 * q^25 - 6 * q^26 - 2 * q^27 - 2 * q^28 - 4 * q^29 - 6 * q^30 - 14 * q^31 + 8 * q^32 + 12 * q^34 + 4 * q^35 - 2 * q^36 + 10 * q^37 + 8 * q^38 + 4 * q^39 - 6 * q^40 - 12 * q^41 - 2 * q^42 + 20 * q^43 + 4 * q^45 + 6 * q^46 + 28 * q^47 - 2 * q^48 - 2 * q^49 - 6 * q^50 + 2 * q^51 - 6 * q^52 + 2 * q^53 + 8 * q^54 + 4 * q^55 + 8 * q^56 + 8 * q^57 - 4 * q^58 + 4 * q^60 - 34 * q^61 + 6 * q^62 - 2 * q^63 - 2 * q^64 + 16 * q^65 - 24 * q^67 - 8 * q^68 - 4 * q^69 - 6 * q^70 - 2 * q^72 + 10 * q^74 - 6 * q^75 + 8 * q^76 + 4 * q^78 + 22 * q^79 - 6 * q^80 - 2 * q^81 - 2 * q^82 - 30 * q^83 - 2 * q^84 - 28 * q^85 + 36 * q^87 - 4 * q^89 + 4 * q^90 - 6 * q^91 - 4 * q^92 - 14 * q^93 - 22 * q^94 - 30 * q^95 - 2 * q^96 - 10 * q^97 + 8 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{5}\right)$

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 $

$2$	0.309017	+	0.951057i	0.218508	+	0.672499i
$2$	0.309017	+	0.951057i	0.218508	+	0.672499i
$3$	−0.809017	−	0.587785i	−0.467086	−	0.339358i
$3$	−0.809017	−	0.587785i	−0.467086	−	0.339358i
$4$	−0.809017	+	0.587785i	−0.404508	+	0.293893i
$5$	0.0895849	−	0.275714i	0.0400636	−	0.123303i	−0.929024	−	0.370019i	$-0.879351\pi$
$5$	0.0895849	−	0.275714i	0.0400636	−	0.123303i	0.969088	+	0.246715i	$0.0793513\pi$
$6$	0.309017	−	0.951057i	0.126156	−	0.388267i
$7$	−0.809017	+	0.587785i	−0.305780	+	0.222162i
$7$	−0.809017	+	0.587785i	−0.305780	+	0.222162i
$8$	−0.809017	−	0.587785i	−0.286031	−	0.207813i
$9$	0.309017	+	0.951057i	0.103006	+	0.317019i
$10$	0.289903			0.0916754
$11$	3.06668	+	1.26313i	0.924638	+	0.380847i
$11$	3.06668	+	1.26313i	0.924638	+	0.380847i
$12$	1.00000			0.288675
$13$	1.16407	+	3.58263i	0.322854	+	0.993641i	0.972400	+	0.233320i	$0.0749588\pi$
$13$	1.16407	+	3.58263i	0.322854	+	0.993641i	−0.649546	+	0.760322i	$0.725041\pi$
$14$	−0.809017	−	0.587785i	−0.216219	−	0.157092i
$15$	−0.234536	+	0.170401i	−0.0605570	+	0.0439973i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	−2.03093	+	6.25055i	−0.492572	+	1.51598i	0.328134	+	0.944631i	$0.393580\pi$
$17$	−2.03093	+	6.25055i	−0.492572	+	1.51598i	−0.820706	+	0.571350i	$0.806420\pi$
$18$	−0.809017	+	0.587785i	−0.190687	+	0.138542i
$19$	−0.879488	−	0.638985i	−0.201768	−	0.146593i	0.482313	−	0.875999i	$-0.339797\pi$
$19$	−0.879488	−	0.638985i	−0.201768	−	0.146593i	−0.684081	+	0.729406i	$0.739797\pi$
$20$	0.0895849	+	0.275714i	0.0200318	+	0.0616515i
$21$	1.00000			0.218218
$22$	−0.253650	+	3.30691i	−0.0540785	+	0.705036i
$23$	1.94617			0.405803			0.202902	−	0.979199i	$-0.434963\pi$
$23$	1.94617			0.405803			0.202902	+	0.979199i	$0.434963\pi$
$24$	0.309017	+	0.951057i	0.0630778	+	0.194134i
$25$	3.97709	+	2.88953i	0.795418	+	0.577905i
$26$	−3.04756	+	2.21418i	−0.597676	+	0.434237i
$27$	0.309017	−	0.951057i	0.0594703	−	0.183031i
$28$	0.309017	−	0.951057i	0.0583987	−	0.179733i
$29$	−5.54909	+	4.03165i	−1.03044	+	0.748659i	−0.968397	−	0.249414i	$-0.919762\pi$
$29$	−5.54909	+	4.03165i	−1.03044	+	0.748659i	−0.0620441	+	0.998073i	$0.519762\pi$
$30$	−0.234536	−	0.170401i	−0.0428203	−	0.0311108i
$31$	1.41195	+	4.34552i	0.253593	+	0.780479i	0.994104	+	0.108435i	$0.0345838\pi$
$31$	1.41195	+	4.34552i	0.253593	+	0.780479i	−0.740510	+	0.672045i	$0.765416\pi$
$32$	1.00000			0.176777
$33$	−1.73855	−	2.82444i	−0.302642	−	0.491672i
$34$	−6.57222			−1.12713
$35$	0.0895849	+	0.275714i	0.0151426	+	0.0466042i
$36$	−0.809017	−	0.587785i	−0.134836	−	0.0979642i
$37$	4.00153	−	2.90728i	0.657848	−	0.477954i	−0.208088	−	0.978110i	$-0.566724\pi$
$37$	4.00153	−	2.90728i	0.657848	−	0.477954i	0.865935	+	0.500156i	$0.166724\pi$
$38$	0.335934	−	1.03390i	0.0544958	−	0.167721i
$39$	1.16407	−	3.58263i	0.186400	−	0.573679i
$40$	−0.234536	+	0.170401i	−0.0370835	+	0.0269427i
$41$	−9.36212	−	6.80198i	−1.46212	−	1.06229i	−0.982805	−	0.184646i	$-0.940886\pi$
$41$	−9.36212	−	6.80198i	−1.46212	−	1.06229i	−0.479313	−	0.877644i	$-0.659114\pi$
$42$	0.309017	+	0.951057i	0.0476824	+	0.146751i
$43$	7.40866			1.12981			0.564905	−	0.825156i	$-0.308913\pi$
$43$	7.40866			1.12981			0.564905	+	0.825156i	$0.308913\pi$
$44$	−3.22344	+	0.780656i	−0.485952	+	0.117688i
$45$	0.289903			0.0432162
$46$	0.601398	+	1.85091i	0.0886713	+	0.272902i
$47$	0.774080	+	0.562402i	0.112911	+	0.0820348i	0.642808	−	0.766027i	$-0.277769\pi$
$47$	0.774080	+	0.562402i	0.112911	+	0.0820348i	−0.529897	+	0.848062i	$0.677769\pi$
$48$	−0.809017	+	0.587785i	−0.116772	+	0.0848395i
$49$	0.309017	−	0.951057i	0.0441453	−	0.135865i
$50$	−1.51911	+	4.67535i	−0.214835	+	0.661195i
$51$	5.31704	−	3.86305i	0.744534	−	0.540936i
$52$	−3.04756	−	2.21418i	−0.422621	−	0.307052i
$53$	0.608699	+	1.87338i	0.0836112	+	0.257329i	0.984119	−	0.177512i	$-0.0568047\pi$
$53$	0.608699	+	1.87338i	0.0836112	+	0.257329i	−0.900507	+	0.434841i	$0.856805\pi$
$54$	1.00000			0.136083
$55$	0.622990	−	0.732369i	0.0840040	−	0.0987526i
$56$	1.00000			0.133631
$57$	0.335934	+	1.03390i	0.0444956	+	0.136943i
$58$	−5.54909	−	4.03165i	−0.728632	−	0.529382i
$59$	−5.17208	+	3.75774i	−0.673348	+	0.489216i	−0.871144	−	0.491027i	$-0.836622\pi$
$59$	−5.17208	+	3.75774i	−0.673348	+	0.489216i	0.197796	+	0.980243i	$0.436622\pi$
$60$	0.0895849	−	0.275714i	0.0115654	−	0.0355945i
$61$	−0.537199	+	1.65333i	−0.0687813	+	0.211687i	−0.979539	−	0.201254i	$-0.935498\pi$
$61$	−0.537199	+	1.65333i	−0.0687813	+	0.211687i	0.910758	+	0.412941i	$0.135498\pi$
$62$	−3.69652	+	2.68568i	−0.469459	+	0.341082i
$63$	−0.809017	−	0.587785i	−0.101927	−	0.0740540i
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	1.09206			0.135454
$66$	2.14896	−	2.52626i	0.264519	−	0.310961i
$67$	6.92398			0.845898			0.422949	−	0.906153i	$-0.360995\pi$
$67$	6.92398			0.845898			0.422949	+	0.906153i	$0.360995\pi$
$68$	−2.03093	−	6.25055i	−0.246286	−	0.757991i
$69$	−1.57448	−	1.14393i	−0.189545	−	0.137713i
$70$	−0.234536	+	0.170401i	−0.0280325	+	0.0203668i
$71$	1.72877	−	5.32060i	0.205167	−	0.631439i	−0.794540	−	0.607212i	$-0.792288\pi$
$71$	1.72877	−	5.32060i	0.205167	−	0.631439i	0.999706	−	0.0242265i	$-0.00771227\pi$
$72$	0.309017	−	0.951057i	0.0364180	−	0.112083i
$73$	3.02312	−	2.19643i	0.353830	−	0.257072i	−0.396644	−	0.917972i	$-0.629825\pi$
$73$	3.02312	−	2.19643i	0.353830	−	0.257072i	0.750474	+	0.660900i	$0.229825\pi$
$74$	4.00153	+	2.90728i	0.465169	+	0.337965i
$75$	−1.51911	−	4.67535i	−0.175412	−	0.539863i
$76$	1.08711			0.124700
$77$	−3.22344	+	0.780656i	−0.367345	+	0.0889640i
$78$	3.76700			0.426528
$79$	−3.26853	−	10.0595i	−0.367738	−	1.13178i	−0.948249	−	0.317529i	$-0.897147\pi$
$79$	−3.26853	−	10.0595i	−0.367738	−	1.13178i	0.580511	−	0.814253i	$-0.302853\pi$
$80$	−0.234536	−	0.170401i	−0.0262220	−	0.0190514i
$81$	−0.809017	+	0.587785i	−0.0898908	+	0.0653095i
$82$	3.57601	−	11.0058i	0.394904	−	1.21539i
$83$	4.87146	−	14.9928i	0.534712	−	1.64567i	−0.209559	−	0.977796i	$-0.567203\pi$
$83$	4.87146	−	14.9928i	0.534712	−	1.64567i	0.744271	−	0.667878i	$-0.232797\pi$
$84$	−0.809017	+	0.587785i	−0.0882710	+	0.0641326i
$85$	1.54142	+	1.11991i	0.167191	+	0.121471i
$86$	2.28940	+	7.04605i	0.246872	+	0.759795i
$87$	6.85906			0.735368
$88$	−1.73855	−	2.82444i	−0.185330	−	0.301086i
$89$	−11.8555			−1.25668			−0.628342	−	0.777937i	$-0.716266\pi$
$89$	−11.8555			−1.25668			−0.628342	+	0.777937i	$0.716266\pi$
$90$	0.0895849	+	0.275714i	0.00944308	+	0.0290628i
$91$	−3.04756	−	2.21418i	−0.319471	−	0.232110i
$92$	−1.57448	+	1.14393i	−0.164151	+	0.119263i
$93$	1.41195	−	4.34552i	0.146412	−	0.450610i
$94$	−0.295672	+	0.909986i	−0.0304963	+	0.0938579i
$95$	−0.254966	+	0.185244i	−0.0261590	+	0.0190056i
$96$	−0.809017	−	0.587785i	−0.0825700	−	0.0599906i
$97$	−1.10140	−	3.38975i	−0.111830	−	0.344177i	0.879443	−	0.476005i	$-0.157916\pi$
$97$	−1.10140	−	3.38975i	−0.111830	−	0.344177i	−0.991273	+	0.131827i	$0.957916\pi$
$98$	1.00000			0.101015
$99$	−0.253650	+	3.30691i	−0.0254928	+	0.332357i
$100$	−4.91596			−0.491596
$101$	4.05938	+	12.4935i	0.403923	+	1.24315i	0.921791	+	0.387687i	$0.126726\pi$
$101$	4.05938	+	12.4935i	0.403923	+	1.24315i	−0.517868	+	0.855460i	$0.673274\pi$
$102$	5.31704	+	3.86305i	0.526465	+	0.382499i
$103$	14.5619	−	10.5799i	1.43483	−	1.04247i	0.445739	−	0.895163i	$-0.352941\pi$
$103$	14.5619	−	10.5799i	1.43483	−	1.04247i	0.989092	−	0.147302i	$-0.0470590\pi$
$104$	1.16407	−	3.58263i	0.114146	−	0.351305i
$105$	0.0895849	−	0.275714i	0.00874260	−	0.0269069i
$106$	−1.59359	+	1.15781i	−0.154784	+	0.112457i
$107$	−8.73359	−	6.34532i	−0.844308	−	0.613426i	0.0792627	−	0.996854i	$-0.474743\pi$
$107$	−8.73359	−	6.34532i	−0.844308	−	0.613426i	−0.923571	+	0.383428i	$0.874743\pi$
$108$	0.309017	+	0.951057i	0.0297352	+	0.0915155i
$109$	0.648243			0.0620904			0.0310452	−	0.999518i	$-0.490116\pi$
$109$	0.648243			0.0620904			0.0310452	+	0.999518i	$0.490116\pi$
$110$	0.889039	+	0.366184i	0.0847665	+	0.0349143i
$111$	−4.94617			−0.469469
$112$	0.309017	+	0.951057i	0.0291994	+	0.0898664i
$113$	10.4095	+	7.56292i	0.979240	+	0.711460i	0.957539	−	0.288305i	$-0.0930916\pi$
$113$	10.4095	+	7.56292i	0.979240	+	0.711460i	0.0217017	+	0.999764i	$0.493092\pi$
$114$	−0.879488	+	0.638985i	−0.0823716	+	0.0598465i
$115$	0.174347	−	0.536585i	0.0162579	−	0.0500368i
$116$	2.11957	−	6.52335i	0.196797	−	0.605678i
$117$	−3.04756	+	2.21418i	−0.281747	+	0.204701i
$118$	−5.17208	−	3.75774i	−0.476129	−	0.345928i
$119$	−2.03093	−	6.25055i	−0.186175	−	0.572987i
$120$	0.289903			0.0264644
$121$	7.80902	+	7.74721i	0.709911	+	0.704292i
$122$	−1.73841			−0.157388
$123$	3.57601	+	11.0058i	0.322438	+	0.992363i
$124$	−3.69652	−	2.68568i	−0.331958	−	0.241181i
$125$	2.32565	−	1.68969i	0.208013	−	0.151130i
$126$	0.309017	−	0.951057i	0.0275294	−	0.0847268i
$127$	−5.58426	+	17.1866i	−0.495523	+	1.52506i	0.320617	+	0.947209i	$0.396110\pi$
$127$	−5.58426	+	17.1866i	−0.495523	+	1.52506i	−0.816140	+	0.577854i	$0.803890\pi$
$128$	−0.809017	+	0.587785i	−0.0715077	+	0.0519534i
$129$	−5.99373	−	4.35470i	−0.527718	−	0.383410i
$130$	0.337466	+	1.03861i	0.0295977	+	0.0910924i
$131$	0.524801			0.0458521			0.0229260	−	0.999737i	$-0.492702\pi$
$131$	0.524801			0.0458521			0.0229260	+	0.999737i	$0.492702\pi$
$132$	3.06668	+	1.26313i	0.266920	+	0.109941i
$133$	1.08711			0.0942641
$134$	2.13963	+	6.58509i	0.184836	+	0.568865i
$135$	−0.234536	−	0.170401i	−0.0201857	−	0.0146658i
$136$	5.31704	−	3.86305i	0.455932	−	0.331254i
$137$	3.81200	−	11.7321i	0.325681	−	1.00234i	−0.645451	−	0.763801i	$-0.723331\pi$
$137$	3.81200	−	11.7321i	0.325681	−	1.00234i	0.971132	−	0.238541i	$-0.0766693\pi$
$138$	0.601398	−	1.85091i	0.0511944	−	0.157560i
$139$	13.2978	−	9.66141i	1.12790	−	0.819470i	0.142515	−	0.989793i	$-0.454481\pi$
$139$	13.2978	−	9.66141i	1.12790	−	0.819470i	0.985388	+	0.170323i	$0.0544810\pi$
$140$	−0.234536	−	0.170401i	−0.0198219	−	0.0144015i
$141$	−0.295672	−	0.909986i	−0.0249001	−	0.0766346i
$142$	5.59441			0.469472
$143$	−0.955500	+	12.4571i	−0.0799029	+	1.04172i
$144$	1.00000			0.0833333
$145$	0.614468	+	1.89114i	0.0510288	+	0.157051i
$146$	3.02312	+	2.19643i	0.250195	+	0.181778i
$147$	−0.809017	+	0.587785i	−0.0667266	+	0.0484797i
$148$	−1.52845	+	4.70408i	−0.125638	+	0.386673i
$149$	−6.40559	+	19.7144i	−0.524767	+	1.61507i	0.240010	+	0.970770i	$0.422849\pi$
$149$	−6.40559	+	19.7144i	−0.524767	+	1.61507i	−0.764777	+	0.644295i	$0.777151\pi$
$150$	3.97709	−	2.88953i	0.324728	−	0.235929i
$151$	−11.6736	−	8.48138i	−0.949985	−	0.690205i	0.000817995	−	1.00000i	$-0.499740\pi$
$151$	−11.6736	−	8.48138i	−0.949985	−	0.690205i	−0.950803	+	0.309795i	$0.899740\pi$
$152$	0.335934	+	1.03390i	0.0272479	+	0.0838604i
$153$	−6.57222			−0.531332
$154$	−1.73855	−	2.82444i	−0.140096	−	0.227600i
$155$	1.32461			0.106395
$156$	1.16407	+	3.58263i	0.0931998	+	0.286840i
$157$	−9.17421	−	6.66546i	−0.732182	−	0.531961i	0.158071	−	0.987428i	$-0.449473\pi$
$157$	−9.17421	−	6.66546i	−0.732182	−	0.531961i	−0.890253	+	0.455466i	$0.849473\pi$
$158$	8.55711	−	6.21711i	0.680767	−	0.494606i
$159$	0.608699	−	1.87338i	0.0482730	−	0.148569i
$160$	0.0895849	−	0.275714i	0.00708231	−	0.0217971i
$161$	−1.57448	+	1.14393i	−0.124086	+	0.0901541i
$162$	−0.809017	−	0.587785i	−0.0635624	−	0.0461808i
$163$	−4.69449	−	14.4482i	−0.367701	−	1.13167i	−0.948272	−	0.317458i	$-0.897171\pi$
$163$	−4.69449	−	14.4482i	−0.367701	−	1.13167i	0.580572	−	0.814209i	$-0.302829\pi$
$164$	11.5722			0.903638
$165$	−0.934485	+	0.226314i	−0.0727496	+	0.0176186i
$166$	15.7644			1.22355
$167$	3.28413	+	10.1075i	0.254134	+	0.782144i	0.993999	+	0.109389i	$0.0348893\pi$
$167$	3.28413	+	10.1075i	0.254134	+	0.782144i	−0.739865	+	0.672755i	$0.765111\pi$
$168$	−0.809017	−	0.587785i	−0.0624170	−	0.0453486i
$169$	−0.962934	+	0.699613i	−0.0740719	+	0.0538164i
$170$	−0.588772	+	1.81205i	−0.0451567	+	0.138978i
$171$	0.335934	−	1.03390i	0.0256896	−	0.0790643i
$172$	−5.99373	+	4.35470i	−0.457017	+	0.332043i
$173$	−14.1431	−	10.2755i	−1.07528	−	0.781234i	−0.0984235	−	0.995145i	$-0.531380\pi$
$173$	−14.1431	−	10.2755i	−1.07528	−	0.781234i	−0.976853	+	0.213910i	$0.931380\pi$
$174$	2.11957	+	6.52335i	0.160684	+	0.494534i
$175$	−4.91596			−0.371611
$176$	2.14896	−	2.52626i	0.161984	−	0.190424i
$177$	6.39305			0.480531
$178$	−3.66356	−	11.2753i	−0.274596	−	0.845119i
$179$	6.56705	+	4.77124i	0.490844	+	0.356619i	0.805509	−	0.592584i	$-0.201892\pi$
$179$	6.56705	+	4.77124i	0.490844	+	0.356619i	−0.314665	+	0.949203i	$0.601892\pi$
$180$	−0.234536	+	0.170401i	−0.0174813	+	0.0127009i
$181$	−1.97029	+	6.06394i	−0.146451	+	0.450729i	−0.997195	−	0.0748512i	$-0.976152\pi$
$181$	−1.97029	+	6.06394i	−0.146451	+	0.450729i	0.850744	+	0.525580i	$0.176152\pi$
$182$	1.16407	−	3.58263i	0.0862863	−	0.265562i
$183$	1.40641	−	1.02181i	0.103964	−	0.0755346i
$184$	−1.57448	−	1.14393i	−0.116072	−	0.0843314i
$185$	−0.443102	−	1.36373i	−0.0325775	−	0.100263i
$186$	4.56916			0.335027
$187$	−14.1234	+	16.6031i	−1.03281	+	1.21414i
$188$	−0.956816			−0.0697830
$189$	0.309017	+	0.951057i	0.0224777	+	0.0691792i
$190$	−0.254966	−	0.185244i	−0.0184972	−	0.0134390i
$191$	16.2256	−	11.7886i	1.17404	−	0.852990i	0.182553	−	0.983196i	$-0.441564\pi$
$191$	16.2256	−	11.7886i	1.17404	−	0.852990i	0.991487	+	0.130206i	$0.0415638\pi$
$192$	0.309017	−	0.951057i	0.0223014	−	0.0686366i
$193$	−3.77575	+	11.6205i	−0.271784	+	0.836465i	0.718268	+	0.695766i	$0.244935\pi$
$193$	−3.77575	+	11.6205i	−0.271784	+	0.836465i	−0.990052	+	0.140699i	$0.955065\pi$
$194$	2.88350	−	2.09498i	0.207023	−	0.150411i
$195$	−0.883498	−	0.641899i	−0.0632686	−	0.0459673i
$196$	0.309017	+	0.951057i	0.0220726	+	0.0679326i
$197$	5.89334			0.419883			0.209941	−	0.977714i	$-0.432673\pi$
$197$	5.89334			0.419883			0.209941	+	0.977714i	$0.432673\pi$
$198$	−3.22344	+	0.780656i	−0.229080	+	0.0554788i
$199$	−8.43434			−0.597894			−0.298947	−	0.954270i	$-0.596635\pi$
$199$	−8.43434			−0.597894			−0.298947	+	0.954270i	$0.596635\pi$
$200$	−1.51911	−	4.67535i	−0.107418	−	0.330597i
$201$	−5.60161	−	4.06981i	−0.395107	−	0.287062i
$202$	−10.6276	+	7.72139i	−0.747754	+	0.543275i
$203$	2.11957	−	6.52335i	0.148764	−	0.457850i
$204$	−2.03093	+	6.25055i	−0.142193	+	0.437626i
$205$	−2.71411	+	1.97191i	−0.189561	+	0.137724i
$206$	14.5619	+	10.5799i	1.01458	+	0.737134i
$207$	0.601398	+	1.85091i	0.0418001	+	0.128647i
$208$	3.76700			0.261194
$209$	−1.88999	−	3.07047i	−0.130733	−	0.212389i
$210$	0.289903			0.0200052
$211$	8.25532	+	25.4072i	0.568319	+	1.74911i	0.657877	+	0.753125i	$0.271455\pi$
$211$	8.25532	+	25.4072i	0.568319	+	1.74911i	−0.0895576	+	0.995982i	$0.528545\pi$
$212$	−1.59359	−	1.15781i	−0.109449	−	0.0795190i
$213$	−4.52597	+	3.28831i	−0.310114	+	0.225311i
$214$	3.33593	−	10.2670i	0.228040	−	0.701834i
$215$	0.663704	−	2.04267i	0.0452642	−	0.139309i
$216$	−0.809017	+	0.587785i	−0.0550466	+	0.0399937i
$217$	−3.69652	−	2.68568i	−0.250936	−	0.182316i
$218$	0.200318	+	0.616515i	0.0135672	+	0.0417557i
$219$	−3.73679			−0.252509
$220$	−0.0735340	+	0.958683i	−0.00495766	+	0.0646344i
$221$	−24.7575			−1.66537
$222$	−1.52845	−	4.70408i	−0.102583	−	0.315717i
$223$	−17.1956	−	12.4933i	−1.15150	−	0.836614i	−0.162821	−	0.986656i	$-0.552059\pi$
$223$	−17.1956	−	12.4933i	−1.15150	−	0.836614i	−0.988680	+	0.150041i	$0.952059\pi$
$224$	−0.809017	+	0.587785i	−0.0540547	+	0.0392731i
$225$	−1.51911	+	4.67535i	−0.101274	+	0.311690i
$226$	−3.97606	+	12.2371i	−0.264484	+	0.813997i
$227$	−14.8070	+	10.7579i	−0.982773	+	0.714026i	−0.958327	−	0.285675i	$-0.907782\pi$
$227$	−14.8070	+	10.7579i	−0.982773	+	0.714026i	−0.0244465	+	0.999701i	$0.507782\pi$
$228$	−0.879488	−	0.638985i	−0.0582455	−	0.0423178i
$229$	2.91627	+	8.97535i	0.192712	+	0.593108i	0.999996	+	0.00294353i	$0.000936954\pi$
$229$	2.91627	+	8.97535i	0.192712	+	0.593108i	−0.807283	+	0.590164i	$0.799063\pi$
$230$	0.564199			0.0372022
$231$	3.06668	+	1.26313i	0.201773	+	0.0831077i
$232$	6.85906			0.450319
$233$	−3.27817	−	10.0892i	−0.214760	−	0.660964i	−0.999171	−	0.0407217i	$-0.987034\pi$
$233$	−3.27817	−	10.0892i	−0.214760	−	0.660964i	0.784410	−	0.620242i	$-0.212966\pi$
$234$	−3.04756	−	2.21418i	−0.199225	−	0.144746i
$235$	0.224408	−	0.163042i	0.0146388	−	0.0106357i
$236$	1.97556	−	6.08015i	0.128598	−	0.395784i
$237$	−3.26853	+	10.0595i	−0.212314	+	0.653434i
$238$	5.31704	−	3.86305i	0.344652	−	0.250405i
$239$	−5.61840	−	4.08201i	−0.363424	−	0.264043i	0.391055	−	0.920367i	$-0.372110\pi$
$239$	−5.61840	−	4.08201i	−0.363424	−	0.264043i	−0.754479	+	0.656324i	$0.772110\pi$
$240$	0.0895849	+	0.275714i	0.00578268	+	0.0177973i
$241$	2.97448			0.191603			0.0958016	−	0.995400i	$-0.469459\pi$
$241$	2.97448			0.191603			0.0958016	+	0.995400i	$0.469459\pi$
$242$	−4.95492	+	9.82084i	−0.318514	+	0.631307i
$243$	1.00000			0.0641500
$244$	−0.537199	−	1.65333i	−0.0343906	−	0.105844i
$245$	−0.234536	−	0.170401i	−0.0149840	−	0.0108865i
$246$	−9.36212	+	6.80198i	−0.596907	+	0.433678i
$247$	1.26546	−	3.89470i	0.0805195	−	0.247814i
$248$	1.41195	−	4.34552i	0.0896587	−	0.275941i
$249$	−12.7536	+	9.26606i	−0.808229	+	0.587213i
$250$	2.32565	+	1.68969i	0.147087	+	0.106865i
$251$	−3.13773	−	9.65695i	−0.198052	−	0.609541i	−0.999927	−	0.0120500i	$-0.996164\pi$
$251$	−3.13773	−	9.65695i	−0.198052	−	0.609541i	0.801875	−	0.597491i	$-0.203836\pi$
$252$	1.00000			0.0629941
$253$	5.96826	+	2.45825i	0.375221	+	0.154549i
$254$	−18.0710			−1.13388
$255$	−0.588772	−	1.81205i	−0.0368703	−	0.113475i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	6.24221	−	4.53523i	0.389378	−	0.282900i	−0.375822	−	0.926692i	$-0.622640\pi$
$257$	6.24221	−	4.53523i	0.389378	−	0.282900i	0.765201	+	0.643792i	$0.222640\pi$
$258$	2.28940	−	7.04605i	0.142532	−	0.438668i
$259$	−1.52845	+	4.70408i	−0.0949732	+	0.292297i
$260$	−0.883498	+	0.641899i	−0.0547922	+	0.0398089i
$261$	−5.54909	−	4.03165i	−0.343480	−	0.249553i
$262$	0.162172	+	0.499115i	0.0100190	+	0.0308354i
$263$	0.0736598			0.00454206			0.00227103	−	0.999997i	$-0.499277\pi$
$263$	0.0736598			0.00454206			0.00227103	+	0.999997i	$0.499277\pi$
$264$	−0.253650	+	3.30691i	−0.0156111	+	0.203526i
$265$	0.571048			0.0350792
$266$	0.335934	+	1.03390i	0.0205975	+	0.0633925i
$267$	9.59133	+	6.96851i	0.586980	+	0.426466i
$268$	−5.60161	+	4.06981i	−0.342173	+	0.248603i
$269$	−3.70351	+	11.3982i	−0.225807	+	0.694963i	0.772401	+	0.635135i	$0.219055\pi$
$269$	−3.70351	+	11.3982i	−0.225807	+	0.694963i	−0.998209	+	0.0598286i	$0.980945\pi$
$270$	0.0895849	−	0.275714i	0.00545197	−	0.0167794i
$271$	2.23973	−	1.62726i	0.136054	−	0.0988489i	−0.517677	−	0.855576i	$-0.673203\pi$
$271$	2.23973	−	1.62726i	0.136054	−	0.0988489i	0.653731	+	0.756727i	$0.273203\pi$
$272$	5.31704	+	3.86305i	0.322393	+	0.234232i
$273$	1.16407	+	3.58263i	0.0704524	+	0.216830i
$274$	12.3359			0.745238
$275$	8.54662	+	13.8848i	0.515380	+	0.837286i
$276$	1.94617			0.117145
$277$	4.69703	+	14.4560i	0.282217	+	0.868575i	0.987219	+	0.159369i	$0.0509461\pi$
$277$	4.69703	+	14.4560i	0.282217	+	0.868575i	−0.705002	+	0.709205i	$0.749054\pi$
$278$	13.2978	+	9.66141i	0.797548	+	0.579453i
$279$	−3.69652	+	2.68568i	−0.221305	+	0.160788i
$280$	0.0895849	−	0.275714i	0.00535372	−	0.0164771i
$281$	5.84125	−	17.9775i	0.348460	−	1.07245i	−0.611246	−	0.791441i	$-0.709331\pi$
$281$	5.84125	−	17.9775i	0.348460	−	1.07245i	0.959706	−	0.281008i	$-0.0906686\pi$
$282$	0.774080	−	0.562402i	0.0460958	−	0.0334906i
$283$	14.9570	+	10.8669i	0.889103	+	0.645971i	0.935644	−	0.352945i	$-0.114820\pi$
$283$	14.9570	+	10.8669i	0.889103	+	0.645971i	−0.0465408	+	0.998916i	$0.514820\pi$
$284$	1.72877	+	5.32060i	0.102583	+	0.315719i
$285$	0.315155			0.0186682
$286$	−12.1427	+	2.94073i	−0.718012	+	0.173889i
$287$	11.5722			0.683086
$288$	0.309017	+	0.951057i	0.0182090	+	0.0560415i
$289$	−21.1914	−	15.3965i	−1.24655	−	0.905675i
$290$	−1.60870	+	1.16879i	−0.0944661	+	0.0686336i
$291$	−1.10140	+	3.38975i	−0.0645651	+	0.198711i
$292$	−1.15473	+	3.55390i	−0.0675755	+	0.207976i
$293$	12.2376	−	8.89114i	0.714928	−	0.519426i	−0.169832	−	0.985473i	$-0.554322\pi$
$293$	12.2376	−	8.89114i	0.714928	−	0.519426i	0.884760	+	0.466047i	$0.154322\pi$
$294$	−0.809017	−	0.587785i	−0.0471828	−	0.0342803i
$295$	0.572721	+	1.76265i	0.0333451	+	0.102626i
$296$	−4.94617			−0.287490
$297$	2.14896	−	2.52626i	0.124695	−	0.146588i
$298$	−20.7289			−1.20079
$299$	2.26546	+	6.97238i	0.131015	+	0.403223i
$300$	3.97709	+	2.88953i	0.229618	+	0.166827i
$301$	−5.99373	+	4.35470i	−0.345473	+	0.251001i
$302$	4.45892	−	13.7232i	0.256582	−	0.789679i
$303$	4.05938	−	12.4935i	0.233205	−	0.717731i
$304$	−0.879488	+	0.638985i	−0.0504421	+	0.0366483i
$305$	0.407721	+	0.296227i	0.0233460	+	0.0169619i
$306$	−2.03093	−	6.25055i	−0.116100	−	0.357320i
$307$	23.5757			1.34554			0.672769	−	0.739853i	$-0.265105\pi$
$307$	23.5757			1.34554			0.672769	+	0.739853i	$0.265105\pi$
$308$	2.14896	−	2.52626i	0.122448	−	0.143947i
$309$	−17.9995			−1.02396
$310$	0.409328	+	1.25978i	0.0232482	+	0.0715507i
$311$	4.25788	+	3.09353i	0.241442	+	0.175418i	0.701925	−	0.712250i	$-0.252324\pi$
$311$	4.25788	+	3.09353i	0.241442	+	0.175418i	−0.460483	+	0.887668i	$0.652324\pi$
$312$	−3.04756	+	2.21418i	−0.172534	+	0.125353i
$313$	3.32813	−	10.2429i	0.188117	−	0.578965i	−0.811871	−	0.583837i	$-0.801551\pi$
$313$	3.32813	−	10.2429i	0.188117	−	0.578965i	0.999988	+	0.00487193i	$0.00155079\pi$
$314$	3.50424	−	10.7849i	0.197756	−	0.608629i
$315$	−0.234536	+	0.170401i	−0.0132146	+	0.00960099i
$316$	8.55711	+	6.21711i	0.481375	+	0.349740i
$317$	4.88896	+	15.0467i	0.274591	+	0.845105i	0.989327	+	0.145710i	$0.0465468\pi$
$317$	4.88896	+	15.0467i	0.274591	+	0.845105i	−0.714736	+	0.699394i	$0.753453\pi$
$318$	1.96979			0.110460
$319$	−22.1098	+	5.35456i	−1.23791	+	0.299798i
$320$	0.289903			0.0162061
$321$	3.33593	+	10.2670i	0.186194	+	0.573045i
$322$	−1.57448	−	1.14393i	−0.0877424	−	0.0637486i
$323$	5.78019	−	4.19955i	0.321618	−	0.233669i
$324$	0.309017	−	0.951057i	0.0171676	−	0.0528365i
$325$	−5.72250	+	17.6120i	−0.317427	+	0.976940i
$326$	12.2903	−	8.92945i	0.680699	−	0.494557i
$327$	−0.524439	−	0.381028i	−0.0290016	−	0.0210709i
$328$	3.57601	+	11.0058i	0.197452	+	0.607696i
$329$	−0.956816			−0.0527510
$330$	−0.504010	−	0.818813i	−0.0277448	−	0.0450742i
$331$	−11.7676			−0.646807			−0.323403	−	0.946261i	$-0.604827\pi$
$331$	−11.7676			−0.646807			−0.323403	+	0.946261i	$0.604827\pi$
$332$	4.87146	+	14.9928i	0.267356	+	0.822837i
$333$	4.00153	+	2.90728i	0.219283	+	0.159318i
$334$	−8.59797	+	6.24679i	−0.470460	+	0.341809i
$335$	0.620284	−	1.90904i	0.0338897	−	0.104302i
$336$	0.309017	−	0.951057i	0.0168583	−	0.0518844i
$337$	19.6444	−	14.2725i	1.07010	−	0.777474i	0.0941703	−	0.995556i	$-0.469980\pi$
$337$	19.6444	−	14.2725i	1.07010	−	0.777474i	0.975930	+	0.218082i	$0.0699802\pi$
$338$	−0.962934	−	0.699613i	−0.0523767	−	0.0380539i
$339$	−3.97606	−	12.2371i	−0.215950	−	0.664626i
$340$	−1.90531			−0.103330
$341$	−1.15897	+	15.1098i	−0.0627617	+	0.818241i
$342$	1.08711			0.0587840
$343$	0.309017	+	0.951057i	0.0166853	+	0.0513522i
$344$	−5.99373	−	4.35470i	−0.323160	−	0.234790i
$345$	−0.456447	+	0.331628i	−0.0245743	+	0.0178542i
$346$	5.40217	−	16.6262i	0.290422	−	0.893828i
$347$	3.14509	−	9.67960i	0.168837	−	0.519628i	−0.830461	−	0.557077i	$-0.811923\pi$
$347$	3.14509	−	9.67960i	0.168837	−	0.519628i	0.999299	+	0.0374484i	$0.0119230\pi$
$348$	−5.54909	+	4.03165i	−0.297463	+	0.216119i
$349$	27.5396	+	20.0087i	1.47416	+	1.07104i	0.979381	+	0.202024i	$0.0647517\pi$
$349$	27.5396	+	20.0087i	1.47416	+	1.07104i	0.494781	+	0.869018i	$0.335248\pi$
$350$	−1.51911	−	4.67535i	−0.0812001	−	0.249908i
$351$	3.76700			0.201067
$352$	3.06668	+	1.26313i	0.163454	+	0.0673249i
$353$	14.8999			0.793041			0.396521	−	0.918026i	$-0.370218\pi$
$353$	14.8999			0.793041			0.396521	+	0.918026i	$0.370218\pi$
$354$	1.97556	+	6.08015i	0.105000	+	0.323156i
$355$	−1.31209	−	0.953291i	−0.0696386	−	0.0505954i
$356$	9.59133	−	6.96851i	0.508340	−	0.369330i
$357$	−2.03093	+	6.25055i	−0.107488	+	0.330814i
$358$	−2.50839	+	7.72003i	−0.132572	+	0.408016i
$359$	24.9850	−	18.1526i	1.31866	−	0.958060i	0.318708	−	0.947853i	$-0.396751\pi$
$359$	24.9850	−	18.1526i	1.31866	−	0.958060i	0.999948	−	0.0102068i	$-0.00324899\pi$
$360$	−0.234536	−	0.170401i	−0.0123612	−	0.00898090i
$361$	−5.50613	−	16.9461i	−0.289796	−	0.891901i
$362$	−6.37600			−0.335115
$363$	−1.76393	−	10.8576i	−0.0925824	−	0.569879i
$364$	3.76700			0.197444
$365$	−0.334760	−	1.03028i	−0.0175221	−	0.0539276i
$366$	1.40641	+	1.02181i	0.0735140	+	0.0534110i
$367$	16.7867	−	12.1962i	0.876258	−	0.636639i	−0.0560006	−	0.998431i	$-0.517835\pi$
$367$	16.7867	−	12.1962i	0.876258	−	0.636639i	0.932259	+	0.361792i	$0.117835\pi$
$368$	0.601398	−	1.85091i	0.0313500	−	0.0964855i
$369$	3.57601	−	11.0058i	0.186160	−	0.572941i
$370$	1.16006	−	0.842830i	0.0603084	−	0.0438166i
$371$	−1.59359	−	1.15781i	−0.0827353	−	0.0601107i
$372$	1.41195	+	4.34552i	0.0732060	+	0.225305i
$373$	12.1945			0.631407			0.315703	−	0.948858i	$-0.397760\pi$
$373$	12.1945			0.631407			0.315703	+	0.948858i	$0.397760\pi$
$374$	−20.1549	−	8.30155i	−1.04218	−	0.429263i
$375$	−2.87467			−0.148447
$376$	−0.295672	−	0.909986i	−0.0152481	−	0.0469289i
$377$	−20.9034	−	15.1872i	−1.07658	−	0.782182i
$378$	−0.809017	+	0.587785i	−0.0416113	+	0.0302324i
$379$	−6.97556	+	21.4686i	−0.358310	+	1.10277i	0.595755	+	0.803167i	$0.296853\pi$
$379$	−6.97556	+	21.4686i	−0.358310	+	1.10277i	−0.954065	+	0.299600i	$0.903147\pi$
$380$	0.0973884	−	0.299731i	0.00499592	−	0.0153759i
$381$	14.6198	−	10.6219i	0.748994	−	0.544176i
$382$	16.2256	+	11.7886i	0.830172	+	0.603155i
$383$	−1.20938	−	3.72208i	−0.0617964	−	0.190190i	0.915392	−	0.402563i	$-0.131881\pi$
$383$	−1.20938	−	3.72208i	−0.0617964	−	0.190190i	−0.977189	+	0.212374i	$0.931881\pi$
$384$	1.00000			0.0510310
$385$	−0.0735340	+	0.958683i	−0.00374764	+	0.0488590i
$386$	−12.2186			−0.621909
$387$	2.28940	+	7.04605i	0.116377	+	0.358171i
$388$	2.88350	+	2.09498i	0.146387	+	0.106357i
$389$	15.6148	−	11.3448i	0.791703	−	0.575206i	−0.116765	−	0.993160i	$-0.537253\pi$
$389$	15.6148	−	11.3448i	0.791703	−	0.575206i	0.908468	+	0.417954i	$0.137253\pi$
$390$	0.337466	−	1.03861i	0.0170883	−	0.0525922i
$391$	−3.95252	+	12.1646i	−0.199887	+	0.615190i
$392$	−0.809017	+	0.587785i	−0.0408615	+	0.0296876i
$393$	−0.424573	−	0.308470i	−0.0214169	−	0.0155603i
$394$	1.82114	+	5.60489i	0.0917477	+	0.282371i
$395$	−3.06635			−0.154285
$396$	−1.73855	−	2.82444i	−0.0873652	−	0.141933i
$397$	2.30597			0.115733			0.0578666	−	0.998324i	$-0.481570\pi$
$397$	2.30597			0.115733			0.0578666	+	0.998324i	$0.481570\pi$
$398$	−2.60635	−	8.02153i	−0.130645	−	0.402083i
$399$	−0.879488	−	0.638985i	−0.0440295	−	0.0319893i
$400$	3.97709	−	2.88953i	0.198855	−	0.144476i
$401$	6.72250	−	20.6897i	0.335705	−	1.03319i	−0.630668	−	0.776053i	$-0.717219\pi$
$401$	6.72250	−	20.6897i	0.335705	−	1.03319i	0.966374	−	0.257142i	$-0.0827809\pi$
$402$	2.13963	−	6.58509i	0.106715	−	0.328435i
$403$	−13.9248	+	10.1170i	−0.693643	+	0.503961i
$404$	−10.6276	−	7.72139i	−0.528742	−	0.384154i
$405$	0.0895849	+	0.275714i	0.00445151	+	0.0137003i
$406$	6.85906			0.340409
$407$	15.9437	−	3.86125i	0.790299	−	0.191395i
$408$	−6.57222			−0.325373
$409$	6.10171	+	18.7791i	0.301710	+	0.928568i	0.980884	+	0.194591i	$0.0623380\pi$
$409$	6.10171	+	18.7791i	0.301710	+	0.928568i	−0.679174	+	0.733977i	$0.737662\pi$
$410$	−2.71411	−	1.97191i	−0.134040	−	0.0973859i
$411$	−9.97994	+	7.25085i	−0.492274	+	0.357658i
$412$	−5.56216	+	17.1186i	−0.274028	+	0.843372i
$413$	1.97556	−	6.08015i	0.0972110	−	0.299185i
$414$	−1.57448	+	1.14393i	−0.0773815	+	0.0562209i
$415$	−3.69732	−	2.68626i	−0.181494	−	0.131863i
$416$	1.16407	+	3.58263i	0.0570730	+	0.175653i
$417$	−16.4370			−0.804922
$418$	2.33615	−	2.74631i	0.114265	−	0.134326i
$419$	3.65057			0.178342			0.0891709	−	0.996016i	$-0.471578\pi$
$419$	3.65057			0.178342			0.0891709	+	0.996016i	$0.471578\pi$
$420$	0.0895849	+	0.275714i	0.00437130	+	0.0134535i
$421$	−22.9310	−	16.6604i	−1.11759	−	0.811977i	−0.133749	−	0.991015i	$-0.542702\pi$
$421$	−22.9310	−	16.6604i	−1.11759	−	0.811977i	−0.983842	+	0.179038i	$0.942702\pi$
$422$	−21.6127	+	15.7025i	−1.05209	+	0.764388i
$423$	−0.295672	+	0.909986i	−0.0143761	+	0.0442450i
$424$	0.608699	−	1.87338i	0.0295610	−	0.0909795i
$425$	−26.1383	+	18.9906i	−1.26789	+	0.921179i
$426$	−4.52597	−	3.28831i	−0.219284	−	0.159319i
$427$	−0.537199	−	1.65333i	−0.0259969	−	0.0800102i
$428$	10.7953			0.521811
$429$	8.09513	−	9.51639i	0.390836	−	0.459456i
$430$	2.14779			0.103576
$431$	−10.2996	−	31.6989i	−0.496114	−	1.52688i	−0.815214	−	0.579160i	$-0.803381\pi$
$431$	−10.2996	−	31.6989i	−0.496114	−	1.52688i	0.319100	−	0.947721i	$-0.396619\pi$
$432$	−0.809017	−	0.587785i	−0.0389238	−	0.0282798i
$433$	28.7626	−	20.8972i	1.38224	−	1.00426i	0.385575	−	0.922676i	$-0.374003\pi$
$433$	28.7626	−	20.8972i	1.38224	−	1.00426i	0.996667	−	0.0815812i	$-0.0259970\pi$
$434$	1.41195	−	4.34552i	0.0677756	−	0.208592i
$435$	0.614468	−	1.89114i	0.0294615	−	0.0906732i
$436$	−0.524439	+	0.381028i	−0.0251161	+	0.0182479i
$437$	−1.71163	−	1.24357i	−0.0818783	−	0.0594881i
$438$	−1.15473	−	3.55390i	−0.0551752	−	0.169812i
$439$	−31.6885			−1.51241			−0.756205	−	0.654335i	$-0.772949\pi$
$439$	−31.6885			−1.51241			−0.756205	+	0.654335i	$0.772949\pi$
$440$	−0.934485	+	0.226314i	−0.0445498	+	0.0107891i
$441$	1.00000			0.0476190
$442$	−7.65049	−	23.5458i	−0.363897	−	1.11996i
$443$	21.7879	+	15.8298i	1.03517	+	0.752097i	0.969337	−	0.245734i	$-0.0790289\pi$
$443$	21.7879	+	15.8298i	1.03517	+	0.752097i	0.0658350	+	0.997831i	$0.479029\pi$
$444$	4.00153	−	2.90728i	0.189904	−	0.137974i
$445$	−1.06208	+	3.26874i	−0.0503473	+	0.154953i
$446$	6.56813	−	20.2146i	0.311010	−	0.957190i
$447$	16.7701	−	12.1842i	0.793197	−	0.576291i
$448$	−0.809017	−	0.587785i	−0.0382225	−	0.0277702i
$449$	−7.62931	−	23.4806i	−0.360049	−	1.10812i	−0.953023	−	0.302896i	$-0.902046\pi$
$449$	−7.62931	−	23.4806i	−0.360049	−	1.10812i	0.592974	−	0.805221i	$-0.297954\pi$
$450$	−4.91596			−0.231740
$451$	−20.1188	−	32.6850i	−0.947359	−	1.53908i
$452$	−12.8668			−0.605204
$453$	4.45892	+	13.7232i	0.209499	+	0.644770i
$454$	−14.8070	−	10.7579i	−0.694926	−	0.504893i
$455$	−0.883498	+	0.641899i	−0.0414190	+	0.0300927i
$456$	0.335934	−	1.03390i	0.0157316	−	0.0484168i
$457$	3.86518	−	11.8958i	0.180806	−	0.556463i	−0.819045	−	0.573729i	$-0.805496\pi$
$457$	3.86518	−	11.8958i	0.180806	−	0.556463i	0.999851	+	0.0172662i	$0.00549628\pi$
$458$	−7.63489	+	5.54707i	−0.356755	+	0.259198i
$459$	5.31704	+	3.86305i	0.248178	+	0.180312i
$460$	0.174347	+	0.536585i	0.00812897	+	0.0250184i
$461$	−0.552378			−0.0257268			−0.0128634	−	0.999917i	$-0.504095\pi$
$461$	−0.552378			−0.0257268			−0.0128634	+	0.999917i	$0.504095\pi$
$462$	−0.253650	+	3.30691i	−0.0118009	+	0.153851i
$463$	−8.98990			−0.417796			−0.208898	−	0.977937i	$-0.566988\pi$
$463$	−8.98990			−0.417796			−0.208898	+	0.977937i	$0.566988\pi$
$464$	2.11957	+	6.52335i	0.0983984	+	0.302839i
$465$	−1.07163	−	0.778587i	−0.0496958	−	0.0361061i
$466$	8.58237	−	6.23545i	0.397570	−	0.288852i
$467$	−1.38941	+	4.27616i	−0.0642941	+	0.197877i	−0.978043	−	0.208402i	$-0.933174\pi$
$467$	−1.38941	+	4.27616i	−0.0642941	+	0.197877i	0.913749	+	0.406279i	$0.133174\pi$
$468$	1.16407	−	3.58263i	0.0538089	−	0.165607i
$469$	−5.60161	+	4.06981i	−0.258658	+	0.187926i
$470$	0.224408	+	0.163042i	0.0103512	+	0.00752057i
$471$	3.50424	+	10.7849i	0.161467	+	0.496944i
$472$	6.39305			0.294264
$473$	22.7200	+	9.35808i	1.04466	+	0.430285i
$474$	−10.5772			−0.485826
$475$	−1.65144	−	5.08261i	−0.0757732	−	0.233206i
$476$	5.31704	+	3.86305i	0.243706	+	0.177063i
$477$	−1.59359	+	1.15781i	−0.0729657	+	0.0530127i
$478$	2.14604	−	6.60483i	0.0981575	−	0.302098i
$479$	0.185752	−	0.571687i	0.00848724	−	0.0261210i	−0.946723	−	0.322048i	$-0.895629\pi$
$479$	0.185752	−	0.571687i	0.00848724	−	0.0261210i	0.955210	+	0.295927i	$0.0956286\pi$
$480$	−0.234536	+	0.170401i	−0.0107051	+	0.00777769i
$481$	15.0737	+	10.9517i	0.687304	+	0.499355i
$482$	0.919165	+	2.82890i	0.0418668	+	0.128853i
$483$	1.94617			0.0885536
$484$	−10.8713	−	1.67760i	−0.494151	−	0.0762545i
$485$	−1.03327			−0.0469185
$486$	0.309017	+	0.951057i	0.0140173	+	0.0431408i
$487$	19.0020	+	13.8057i	0.861062	+	0.625598i	0.928174	−	0.372147i	$-0.121378\pi$
$487$	19.0020	+	13.8057i	0.861062	+	0.625598i	−0.0671116	+	0.997745i	$0.521378\pi$
$488$	1.40641	−	1.02181i	0.0636650	−	0.0462553i
$489$	−4.69449	+	14.4482i	−0.212292	+	0.653368i
$490$	0.0895849	−	0.275714i	0.00404704	−	0.0124555i
$491$	10.0773	−	7.32161i	0.454783	−	0.330420i	−0.336698	−	0.941613i	$-0.609310\pi$
$491$	10.0773	−	7.32161i	0.454783	−	0.330420i	0.791481	+	0.611193i	$0.209310\pi$
$492$	−9.36212	−	6.80198i	−0.422077	−	0.306657i
$493$	−13.9302	−	42.8729i	−0.627387	−	1.93090i
$494$	4.09513			0.184248
$495$	0.889039	+	0.366184i	0.0399593	+	0.0164588i
$496$	4.56916			0.205161
$497$	1.72877	+	5.32060i	0.0775458	+	0.238661i
$498$	−12.7536	−	9.26606i	−0.571504	−	0.415222i
$499$	18.1840	−	13.2114i	0.814027	−	0.591425i	−0.100969	−	0.994890i	$-0.532194\pi$
$499$	18.1840	−	13.2114i	0.814027	−	0.591425i	0.914995	+	0.403465i	$0.132194\pi$
$500$	−0.888320	+	2.73397i	−0.0397269	+	0.122267i
$501$	3.28413	−	10.1075i	0.146724	−	0.451571i
$502$	8.21469	−	5.96832i	0.366640	−	0.266379i
$503$	1.39413	+	1.01289i	0.0621611	+	0.0451627i	0.618432	−	0.785838i	$-0.287768\pi$
$503$	1.39413	+	1.01289i	0.0621611	+	0.0451627i	−0.556271	+	0.831001i	$0.687768\pi$
$504$	0.309017	+	0.951057i	0.0137647	+	0.0423634i
$505$	3.80829			0.169467
$506$	−0.493646	+	6.43579i	−0.0219452	+	0.286106i
$507$	1.19025			0.0528610
$508$	−5.58426	−	17.1866i	−0.247761	−	0.762531i
$509$	12.5421	+	9.11237i	0.555919	+	0.403899i	0.829963	−	0.557818i	$-0.188361\pi$
$509$	12.5421	+	9.11237i	0.555919	+	0.403899i	−0.274044	+	0.961717i	$0.588361\pi$
$510$	1.54142	−	1.11991i	0.0682554	−	0.0495905i
$511$	−1.15473	+	3.55390i	−0.0510823	+	0.157215i
$512$	0.309017	−	0.951057i	0.0136568	−	0.0420312i
$513$	−0.879488	+	0.638985i	−0.0388303	+	0.0282119i
$514$	6.24221	+	4.53523i	0.275332	+	0.200040i
$515$	−1.61249	−	4.96273i	−0.0710547	−	0.218684i
$516$	7.40866			0.326148
$517$	1.66347	+	2.70247i	0.0731592	+	0.118854i
$518$	−4.94617			−0.217322
$519$	5.40217	+	16.6262i	0.237129	+	0.729808i
$520$	−0.883498	−	0.641899i	−0.0387439	−	0.0281491i
$521$	−18.6723	+	13.5662i	−0.818049	+	0.594348i	−0.916153	−	0.400829i	$-0.868722\pi$
$521$	−18.6723	+	13.5662i	−0.818049	+	0.594348i	0.0981038	+	0.995176i	$0.468722\pi$
$522$	2.11957	−	6.52335i	0.0927709	−	0.285519i
$523$	3.37823	−	10.3971i	0.147720	−	0.454635i	−0.849631	−	0.527378i	$-0.823175\pi$
$523$	3.37823	−	10.3971i	0.147720	−	0.454635i	0.997351	+	0.0727431i	$0.0231753\pi$
$524$	−0.424573	+	0.308470i	−0.0185476	+	0.0134756i
$525$	3.97709	+	2.88953i	0.173575	+	0.126109i
$526$	0.0227621	+	0.0700547i	0.000992477	+	0.00305453i
$527$	−30.0295			−1.30810
$528$	−3.22344	+	0.780656i	−0.140282	+	0.0339737i
$529$	−19.2124			−0.835324
$530$	0.176464	+	0.543099i	0.00766509	+	0.0235907i
$531$	−5.17208	−	3.75774i	−0.224449	−	0.163072i
$532$	−0.879488	+	0.638985i	−0.0381306	+	0.0277035i
$533$	13.4708	−	41.4589i	0.583486	−	1.79579i
$534$	−3.66356	+	11.2753i	−0.158538	+	0.487929i
$535$	−2.53189	+	1.83953i	−0.109463	+	0.0795297i
$536$	−5.60161	−	4.06981i	−0.241953	−	0.175789i
$537$	−2.50839	−	7.72003i	−0.108245	−	0.333144i
$538$	−11.9848			−0.516702
$539$	2.14896	−	2.52626i	0.0925623	−	0.108814i
$540$	0.289903			0.0124754
$541$	−4.75549	−	14.6359i	−0.204455	−	0.629247i	−0.999735	−	0.0230052i	$-0.992677\pi$
$541$	−4.75549	−	14.6359i	−0.204455	−	0.629247i	0.795281	−	0.606241i	$-0.207323\pi$
$542$	2.23973	+	1.62726i	0.0962046	+	0.0698967i
$543$	5.15830	−	3.74772i	0.221364	−	0.160830i
$544$	−2.03093	+	6.25055i	−0.0870753	+	0.267990i
$545$	0.0580728	−	0.178730i	0.00248756	−	0.00765594i
$546$	−3.04756	+	2.21418i	−0.130424	+	0.0947583i
$547$	−34.3757	−	24.9754i	−1.46980	−	1.06787i	−0.980672	−	0.195657i	$-0.937316\pi$
$547$	−34.3757	−	24.9754i	−1.46980	−	1.06787i	−0.489125	−	0.872214i	$-0.662684\pi$
$548$	3.81200	+	11.7321i	0.162840	+	0.501171i
$549$	−1.73841			−0.0741936
$550$	−10.5642	+	12.4190i	−0.450459	+	0.529546i
$551$	7.45653			0.317659
$552$	0.601398	+	1.85091i	0.0255972	+	0.0787801i
$553$	8.55711	+	6.21711i	0.363885	+	0.264378i
$554$	−12.2970	+	8.93428i	−0.522448	+	0.379581i
$555$	−0.443102	+	1.36373i	−0.0188086	+	0.0578870i
$556$	−5.07930	+	15.6325i	−0.215410	+	0.662965i
$557$	−23.3751	+	16.9830i	−0.990435	+	0.719593i	−0.960016	−	0.279944i	$-0.909684\pi$
$557$	−23.3751	+	16.9830i	−0.990435	+	0.719593i	−0.0304191	+	0.999537i	$0.509684\pi$
$558$	−3.69652	−	2.68568i	−0.156486	−	0.113694i
$559$	8.62416	+	26.5424i	0.364763	+	1.12263i
$560$	0.289903			0.0122506
$561$	21.1852	−	5.13064i	0.894438	−	0.216616i
$562$	18.9027			0.797361
$563$	11.9270	+	36.7075i	0.502663	+	1.54704i	0.804665	+	0.593730i	$0.202345\pi$
$563$	11.9270	+	36.7075i	0.502663	+	1.54704i	−0.302002	+	0.953307i	$0.597655\pi$
$564$	0.774080	+	0.562402i	0.0325947	+	0.0236814i
$565$	3.01774	−	2.19251i	0.126957	−	0.0922397i
$566$	−5.71308	+	17.5830i	−0.240139	+	0.739071i
$567$	0.309017	−	0.951057i	0.0129775	−	0.0399406i
$568$	−4.52597	+	3.28831i	−0.189906	+	0.137974i
$569$	13.6847	+	9.94252i	0.573692	+	0.416812i	0.836445	−	0.548051i	$-0.184630\pi$
$569$	13.6847	+	9.94252i	0.573692	+	0.416812i	−0.262752	+	0.964863i	$0.584630\pi$
$570$	0.0973884	+	0.299731i	0.00407915	+	0.0125543i
$571$	−9.29649			−0.389046			−0.194523	−	0.980898i	$-0.562316\pi$
$571$	−9.29649			−0.389046			−0.194523	+	0.980898i	$0.562316\pi$
$572$	−6.54909	−	10.6396i	−0.273831	−	0.444866i
$573$	−20.0559			−0.837847
$574$	3.57601	+	11.0058i	0.149260	+	0.459375i
$575$	7.74008	+	5.62350i	0.322784	+	0.234516i
$576$	−0.809017	+	0.587785i	−0.0337090	+	0.0244911i
$577$	9.85964	−	30.3448i	0.410462	−	1.26327i	−0.505785	−	0.862659i	$-0.668797\pi$
$577$	9.85964	−	30.3448i	0.410462	−	1.26327i	0.916247	−	0.400613i	$-0.131203\pi$
$578$	8.09441	−	24.9120i	0.336683	−	1.03620i
$579$	9.88503	−	7.18189i	0.410808	−	0.298469i
$580$	−1.60870	−	1.16879i	−0.0667976	−	0.0485313i
$581$	4.87146	+	14.9928i	0.202102	+	0.622006i
$582$	−3.56420			−0.147741
$583$	−0.499638	+	6.51392i	−0.0206929	+	0.269779i
$584$	−3.73679			−0.154629
$585$	0.337466	+	1.03861i	0.0139525	+	0.0429414i
$586$	12.2376	+	8.89114i	0.505531	+	0.367289i
$587$	−8.11612	+	5.89671i	−0.334988	+	0.243383i	−0.742544	−	0.669797i	$-0.766381\pi$
$587$	−8.11612	+	5.89671i	−0.334988	+	0.243383i	0.407556	+	0.913180i	$0.366381\pi$
$588$	0.309017	−	0.951057i	0.0127436	−	0.0392209i
$589$	1.53494	−	4.72405i	0.0632460	−	0.194651i
$590$	−1.49940	+	1.08938i	−0.0617294	+	0.0448491i
$591$	−4.76781	−	3.46402i	−0.196121	−	0.142491i
$592$	−1.52845	−	4.70408i	−0.0628189	−	0.193337i
$593$	19.6355			0.806334			0.403167	−	0.915126i	$-0.367909\pi$
$593$	19.6355			0.806334			0.403167	+	0.915126i	$0.367909\pi$
$594$	3.06668	+	1.26313i	0.125827	+	0.0518268i
$595$	−1.90531			−0.0781099
$596$	−6.40559	−	19.7144i	−0.262383	−	0.807533i
$597$	6.82352	+	4.95758i	0.279268	+	0.202900i
$598$	−5.93106	+	4.30917i	−0.242539	+	0.176215i
$599$	−9.04333	+	27.8325i	−0.369500	+	1.13720i	0.577614	+	0.816310i	$0.303984\pi$
$599$	−9.04333	+	27.8325i	−0.369500	+	1.13720i	−0.947115	+	0.320895i	$0.896016\pi$
$600$	−1.51911	+	4.67535i	−0.0620176	+	0.190870i
$601$	23.6428	−	17.1775i	0.964411	−	0.700686i	0.0102401	−	0.999948i	$-0.496740\pi$
$601$	23.6428	−	17.1775i	0.964411	−	0.700686i	0.954171	+	0.299262i	$0.0967404\pi$
$602$	−5.99373	−	4.35470i	−0.244286	−	0.177484i
$603$	2.13963	+	6.58509i	0.0871323	+	0.268166i
$604$	14.4294			0.587123
$605$	2.83559	−	1.45902i	0.115283	−	0.0593177i
$606$	13.1364			0.533630
$607$	−0.0959903	−	0.295428i	−0.00389612	−	0.0119910i	0.949090	−	0.315006i	$-0.102007\pi$
$607$	−0.0959903	−	0.295428i	−0.00389612	−	0.0119910i	−0.952986	+	0.303015i	$0.902007\pi$
$608$	−0.879488	−	0.638985i	−0.0356679	−	0.0259143i
$609$	−5.54909	+	4.03165i	−0.224861	+	0.163371i
$610$	−0.155736	+	0.479305i	−0.00630555	+	0.0194065i
$611$	−1.11380	+	3.42791i	−0.0450594	+	0.138678i
$612$	5.31704	−	3.86305i	0.214928	−	0.156155i
$613$	37.6130	+	27.3274i	1.51917	+	1.10374i	0.961895	+	0.273420i	$0.0881549\pi$
$613$	37.6130	+	27.3274i	1.51917	+	1.10374i	0.557280	+	0.830325i	$0.311845\pi$
$614$	7.28530	+	22.4218i	0.294011	+	0.904872i
$615$	3.35482			0.135279
$616$	3.06668	+	1.26313i	0.123560	+	0.0508929i
$617$	−19.7582			−0.795437			−0.397718	−	0.917508i	$-0.630198\pi$
$617$	−19.7582			−0.795437			−0.397718	+	0.917508i	$0.630198\pi$
$618$	−5.56216	−	17.1186i	−0.223743	−	0.688610i
$619$	−20.4471	−	14.8557i	−0.821838	−	0.597100i	0.0954002	−	0.995439i	$-0.469587\pi$
$619$	−20.4471	−	14.8557i	−0.821838	−	0.597100i	−0.917238	+	0.398339i	$0.869587\pi$
$620$	−1.07163	+	0.778587i	−0.0430378	+	0.0312688i
$621$	0.601398	−	1.85091i	0.0241333	−	0.0742746i
$622$	−1.62636	+	5.00543i	−0.0652113	+	0.200700i
$623$	9.59133	−	6.96851i	0.384269	−	0.279187i
$624$	−3.04756	−	2.21418i	−0.122000	−	0.0886383i
$625$	7.33804	+	22.5842i	0.293522	+	0.903367i
$626$	10.7701			0.430458
$627$	−0.275745	+	3.59497i	−0.0110122	+	0.143569i
$628$	11.3400			0.452513
$629$	10.0453	+	30.9163i	0.400532	+	1.23271i
$630$	−0.234536	−	0.170401i	−0.00934415	−	0.00678893i
$631$	−31.7621	+	23.0765i	−1.26443	+	0.918661i	−0.998966	−	0.0454598i	$-0.985525\pi$
$631$	−31.7621	+	23.0765i	−1.26443	+	0.918661i	−0.265463	+	0.964121i	$0.585525\pi$
$632$	−3.26853	+	10.0595i	−0.130015	+	0.400145i
$633$	8.25532	−	25.4072i	0.328119	−	1.00985i
$634$	−12.7995	+	9.29935i	−0.508331	+	0.369324i
$635$	4.23832	+	3.07932i	0.168193	+	0.122199i
$636$	0.608699	+	1.87338i	0.0241365	+	0.0742845i
$637$	3.76700			0.149254
$638$	−11.9248	−	19.3730i	−0.472107	−	0.766984i
$639$	5.59441			0.221311
$640$	0.0895849	+	0.275714i	0.00354116	+	0.0108986i
$641$	15.4188	+	11.2024i	0.609006	+	0.442469i	0.849064	−	0.528290i	$-0.177166\pi$
$641$	15.4188	+	11.2024i	0.609006	+	0.442469i	−0.240058	+	0.970759i	$0.577166\pi$
$642$	−8.73359	+	6.34532i	−0.344687	+	0.250430i
$643$	−2.43764	+	7.50229i	−0.0961313	+	0.295862i	−0.987547	−	0.157325i	$-0.949713\pi$
$643$	−2.43764	+	7.50229i	−0.0961313	+	0.295862i	0.891416	+	0.453187i	$0.149713\pi$
$644$	0.601398	−	1.85091i	0.0236984	−	0.0729362i
$645$	−1.73760	+	1.26244i	−0.0684179	+	0.0497085i
$646$	5.78019	+	4.19955i	0.227418	+	0.165229i
$647$	−0.583682	−	1.79639i	−0.0229469	−	0.0706233i	0.938927	−	0.344116i	$-0.111821\pi$
$647$	−0.583682	−	1.79639i	−0.0229469	−	0.0706233i	−0.961874	+	0.273492i	$0.911821\pi$
$648$	1.00000			0.0392837
$649$	−20.6076	+	4.99077i	−0.808920	+	0.195905i
$650$	−18.5184			−0.726351
$651$	1.41195	+	4.34552i	0.0553386	+	0.170315i
$652$	12.2903	+	8.92945i	0.481327	+	0.349704i
$653$	−17.9021	+	13.0066i	−0.700563	+	0.508989i	−0.880116	−	0.474759i	$-0.842535\pi$
$653$	−17.9021	+	13.0066i	−0.700563	+	0.508989i	0.179552	+	0.983748i	$0.442535\pi$
$654$	0.200318	−	0.616515i	0.00783305	−	0.0241077i
$655$	0.0470143	−	0.144695i	0.00183700	−	0.00565370i
$656$	−9.36212	+	6.80198i	−0.365529	+	0.265573i
$657$	3.02312	+	2.19643i	0.117943	+	0.0856908i
$658$	−0.295672	−	0.909986i	−0.0115265	−	0.0354749i
$659$	−13.8856			−0.540905			−0.270452	−	0.962733i	$-0.587173\pi$
$659$	−13.8856			−0.540905			−0.270452	+	0.962733i	$0.587173\pi$
$660$	0.622990	−	0.732369i	0.0242499	−	0.0285074i
$661$	24.0051			0.933691			0.466845	−	0.884339i	$-0.345390\pi$
$661$	24.0051			0.933691			0.466845	+	0.884339i	$0.345390\pi$
$662$	−3.63639	−	11.1917i	−0.141332	−	0.434977i
$663$	20.0292	+	14.5521i	0.777872	+	0.565157i
$664$	−12.7536	+	9.26606i	−0.494937	+	0.359593i
$665$	0.0973884	−	0.299731i	0.00377656	−	0.0116231i
$666$	−1.52845	+	4.70408i	−0.0592262	+	0.182279i
$667$	−10.7995	+	7.84626i	−0.418157	+	0.303808i
$668$	−8.59797	−	6.24679i	−0.332666	−	0.241696i
$669$	6.56813	+	20.2146i	0.253938	+	0.781542i
$670$	2.00728			0.0775480
$671$	−3.73578	+	4.39167i	−0.144218	+	0.169539i
$672$	1.00000			0.0385758
$673$	−7.97374	−	24.5407i	−0.307365	−	0.945973i	−0.978784	−	0.204895i	$-0.934315\pi$
$673$	−7.97374	−	24.5407i	−0.307365	−	0.945973i	0.671419	−	0.741078i	$-0.265685\pi$
$674$	19.6444	+	14.2725i	0.756675	+	0.549757i
$675$	3.97709	−	2.88953i	0.153078	−	0.111218i
$676$	0.367808	−	1.13200i	0.0141465	−	0.0435384i
$677$	−12.4186	+	38.2204i	−0.477284	+	1.46893i	0.365568	+	0.930785i	$0.380875\pi$
$677$	−12.4186	+	38.2204i	−0.477284	+	1.46893i	−0.842852	+	0.538145i	$0.819125\pi$
$678$	10.4095	−	7.56292i	0.399773	−	0.290452i
$679$	2.88350	+	2.09498i	0.110658	+	0.0803981i
$680$	−0.588772	−	1.81205i	−0.0225784	−	0.0694891i
$681$	18.3024			0.701350
$682$	−14.7284	+	3.56694i	−0.563980	+	0.136585i
$683$	0.759879			0.0290760			0.0145380	−	0.999894i	$-0.495372\pi$
$683$	0.759879			0.0290760			0.0145380	+	0.999894i	$0.495372\pi$
$684$	0.335934	+	1.03390i	0.0128448	+	0.0395322i
$685$	−2.89321	−	2.10204i	−0.110544	−	0.0803149i
$686$	−0.809017	+	0.587785i	−0.0308884	+	0.0224417i
$687$	2.91627	−	8.97535i	0.111263	−	0.342431i
$688$	2.28940	−	7.04605i	0.0872826	−	0.268628i
$689$	−6.00306	+	4.36148i	−0.228698	+	0.166159i
$690$	−0.456447	−	0.331628i	−0.0173766	−	0.0126249i
$691$	−6.72302	−	20.6913i	−0.255756	−	0.787135i	−0.993680	−	0.112252i	$-0.964194\pi$
$691$	−6.72302	−	20.6913i	−0.255756	−	0.787135i	0.737924	−	0.674884i	$-0.235806\pi$
$692$	17.4818			0.664558
$693$	−1.73855	−	2.82444i	−0.0660419	−	0.107292i
$694$	10.1777			0.386341
$695$	−1.47251	−	4.53190i	−0.0558553	−	0.171905i
$696$	−5.54909	−	4.03165i	−0.210338	−	0.152819i
$697$	61.5299	−	44.7041i	2.33061	−	1.69329i
$698$	−10.5192	+	32.3748i	−0.398157	+	1.22540i
$699$	−3.27817	+	10.0892i	−0.123992	+	0.381608i
$700$	3.97709	−	2.88953i	0.150320	−	0.109214i
$701$	−24.4699	−	17.7784i	−0.924214	−	0.671481i	0.0203554	−	0.999793i	$-0.493520\pi$
$701$	−24.4699	−	17.7784i	−0.924214	−	0.671481i	−0.944569	+	0.328312i	$0.893520\pi$
$702$	1.16407	+	3.58263i	0.0439348	+	0.135217i
$703$	−5.37701			−0.202798
$704$	−0.253650	+	3.30691i	−0.00955981	+	0.124634i
$705$	−0.277384			−0.0104469
$706$	4.60432	+	14.1706i	0.173286	+	0.533319i
$707$	−10.6276	−	7.72139i	−0.399691	−	0.290393i
$708$	−5.17208	+	3.75774i	−0.194379	+	0.141225i
$709$	−11.4154	+	35.1329i	−0.428713	+	1.31944i	0.470681	+	0.882304i	$0.344008\pi$
$709$	−11.4154	+	35.1329i	−0.428713	+	1.31944i	−0.899394	+	0.437140i	$0.855992\pi$
$710$	0.501175	−	1.54246i	0.0188088	−	0.0578874i
$711$	8.55711	−	6.21711i	0.320917	−	0.233160i
$712$	9.59133	+	6.96851i	0.359450	+	0.261156i
$713$	2.74788	+	8.45711i	0.102909	+	0.316721i
$714$	−6.57222			−0.245959
$715$	3.34900	+	1.37942i	0.125246	+	0.0515872i
$716$	−8.11732			−0.303358
$717$	2.14604	+	6.60483i	0.0801453	+	0.246662i
$718$	24.9850	+	18.1526i	0.932431	+	0.677451i
$719$	17.0069	−	12.3563i	0.634252	−	0.460811i	−0.223619	−	0.974677i	$-0.571787\pi$
$719$	17.0069	−	12.3563i	0.634252	−	0.460811i	0.857871	+	0.513866i	$0.171787\pi$
$720$	0.0895849	−	0.275714i	0.00333863	−	0.0102753i
$721$	−5.56216	+	17.1186i	−0.207146	+	0.637529i
$722$	14.4152	−	10.4733i	0.536479	−	0.389775i
$723$	−2.40641	−	1.74836i	−0.0894952	−	0.0650221i
$724$	−1.97029	−	6.06394i	−0.0732254	−	0.225365i
$725$	−33.7188			−1.25229
$726$	9.78115	−	5.03280i	0.363013	−	0.186785i
$727$	0.807855			0.0299617			0.0149808	−	0.999888i	$-0.495231\pi$
$727$	0.807855			0.0299617			0.0149808	+	0.999888i	$0.495231\pi$
$728$	1.16407	+	3.58263i	0.0431431	+	0.132781i
$729$	−0.809017	−	0.587785i	−0.0299636	−	0.0217698i
$730$	0.876413	−	0.636751i	0.0324375	−	0.0235672i
$731$	−15.0464	+	46.3082i	−0.556513	+	1.71277i
$732$	−0.537199	+	1.65333i	−0.0198554	+	0.0611088i
$733$	−29.6775	+	21.5620i	−1.09616	+	0.796409i	−0.980429	−	0.196871i	$-0.936922\pi$
$733$	−29.6775	+	21.5620i	−1.09616	+	0.796409i	−0.115734	+	0.993280i	$0.536922\pi$
$734$	16.7867	+	12.1962i	0.619608	+	0.450172i
$735$	0.0895849	+	0.275714i	0.00330439	+	0.0101699i
$736$	1.94617			0.0717366
$737$	21.2336	+	8.74587i	0.782150	+	0.322158i
$738$	11.5722			0.425979
$739$	−11.6386	−	35.8199i	−0.428133	−	1.31766i	−0.899962	−	0.435967i	$-0.856406\pi$
$739$	−11.6386	−	35.8199i	−0.428133	−	1.31766i	0.471830	−	0.881690i	$-0.343594\pi$
$740$	1.16006	+	0.842830i	0.0426445	+	0.0309830i
$741$	−3.31303	+	2.40705i	−0.121707	+	0.0884254i
$742$	0.608699	−	1.87338i	0.0223460	−	0.0687740i
$743$	−9.41807	+	28.9858i	−0.345516	+	1.06339i	0.615792	+	0.787909i	$0.288836\pi$
$743$	−9.41807	+	28.9858i	−0.345516	+	1.06339i	−0.961307	+	0.275479i	$0.911164\pi$
$744$	−3.69652	+	2.68568i	−0.135521	+	0.0984619i
$745$	4.86169	+	3.53222i	0.178119	+	0.129411i
$746$	3.76830	+	11.5976i	0.137967	+	0.424620i
$747$	15.7644			0.576788
$748$	1.66705	−	21.7337i	0.0609532	−	0.794664i
$749$	10.7953			0.394452
$750$	−0.888320	−	2.73397i	−0.0324369	−	0.0998304i
$751$	−11.9177	−	8.65872i	−0.434883	−	0.315961i	0.348715	−	0.937229i	$-0.386618\pi$
$751$	−11.9177	−	8.65872i	−0.434883	−	0.315961i	−0.783598	+	0.621268i	$0.786618\pi$
$752$	0.774080	−	0.562402i	0.0282278	−	0.0205087i
$753$	−3.13773	+	9.65695i	−0.114345	+	0.351919i
$754$	7.98439	−	24.5734i	0.290774	−	0.894912i
$755$	−3.38422	+	2.45878i	−0.123164	+	0.0894841i
$756$	−0.809017	−	0.587785i	−0.0294237	−	0.0213775i
$757$	−8.95572	−	27.5629i	−0.325501	−	1.00179i	−0.971214	−	0.238209i	$-0.923440\pi$
$757$	−8.95572	−	27.5629i	−0.325501	−	1.00179i	0.645713	−	0.763580i	$-0.276560\pi$
$758$	−22.5734			−0.819902
$759$	−3.38350	−	5.49683i	−0.122813	−	0.199522i
$760$	0.315155			0.0114319
$761$	0.874665	+	2.69194i	0.0317066	+	0.0975828i	0.965657	−	0.259819i	$-0.0836628\pi$
$761$	0.874665	+	2.69194i	0.0317066	+	0.0975828i	−0.933951	+	0.357401i	$0.883663\pi$
$762$	14.6198	+	10.6219i	0.529619	+	0.384791i
$763$	−0.524439	+	0.381028i	−0.0189860	+	0.0137941i
$764$	−6.19761	+	19.0743i	−0.224222	+	0.690084i
$765$	−0.588772	+	1.81205i	−0.0212871	+	0.0655149i
$766$	3.16619	−	2.30037i	0.114399	−	0.0831159i
$767$	−19.4832	−	14.1554i	−0.703498	−	0.511121i
$768$	0.309017	+	0.951057i	0.0111507	+	0.0343183i
$769$	−31.7769			−1.14590			−0.572952	−	0.819589i	$-0.694202\pi$
$769$	−31.7769			−1.14590			−0.572952	+	0.819589i	$0.694202\pi$
$770$	−0.934485	+	0.226314i	−0.0336765	+	0.00815581i
$771$	−7.71579			−0.277877
$772$	−3.77575	−	11.6205i	−0.135892	−	0.418233i
$773$	1.88764	+	1.37145i	0.0678937	+	0.0493277i	0.621214	−	0.783641i	$-0.286640\pi$
$773$	1.88764	+	1.37145i	0.0678937	+	0.0493277i	−0.553321	+	0.832968i	$0.686640\pi$
$774$	−5.99373	+	4.35470i	−0.215440	+	0.156526i
$775$	−6.94107	+	21.3624i	−0.249331	+	0.767360i
$776$	−1.10140	+	3.38975i	−0.0395379	+	0.121685i
$777$	4.00153	−	2.90728i	0.143554	−	0.104298i
$778$	15.6148	+	11.3448i	0.559819	+	0.406732i
$779$	3.88751	+	11.9645i	0.139284	+	0.428673i
$780$	1.09206			0.0391021
$781$	12.0222	−	14.1329i	0.430187	−	0.505715i
$782$	−12.7906			−0.457392
$783$	2.11957	+	6.52335i	0.0757471	+	0.233126i
$784$	−0.809017	−	0.587785i	−0.0288935	−	0.0209923i
$785$	−2.65963	+	1.93234i	−0.0949263	+	0.0689680i
$786$	0.162172	−	0.499115i	0.00578450	−	0.0178029i
$787$	9.26473	−	28.5139i	0.330252	−	1.01641i	−0.638762	−	0.769405i	$-0.720553\pi$
$787$	9.26473	−	28.5139i	0.330252	−	1.01641i	0.969014	−	0.247007i	$-0.0794470\pi$
$788$	−4.76781	+	3.46402i	−0.169846	+	0.123400i
$789$	−0.0595921	−	0.0432962i	−0.00212153	−	0.00154138i
$790$	−0.947556	−	2.91628i	−0.0337125	−	0.103756i
$791$	−12.8668			−0.457491
$792$	2.14896	−	2.52626i	0.0763600	−	0.0897666i
$793$	−6.54859			−0.232547
$794$	0.712583	+	2.19310i	0.0252886	+	0.0778304i
$795$	−0.461988	−	0.335654i	−0.0163850	−	0.0119044i
$796$	6.82352	−	4.95758i	0.241853	−	0.175717i
$797$	−13.0251	+	40.0871i	−0.461373	+	1.41996i	0.402115	+	0.915589i	$0.368275\pi$
$797$	−13.0251	+	40.0871i	−0.461373	+	1.41996i	−0.863488	+	0.504370i	$0.831725\pi$
$798$	0.335934	−	1.03390i	0.0118920	−	0.0365997i
$799$	−5.08742	+	3.69623i	−0.179980	+	0.130763i
$800$	3.97709	+	2.88953i	0.140611	+	0.102160i
$801$	−3.66356	−	11.2753i	−0.129446	−	0.398393i
$802$	21.7545			0.768176
$803$	12.0453	−	2.91714i	0.425070	−	0.102944i
$804$	6.92398			0.244190
$805$	0.174347	+	0.536585i	0.00614493	+	0.0189121i
$806$	−13.9248	−	10.1170i	−0.490480	−	0.356354i
$807$	9.69593	−	7.04450i	0.341313	−	0.247978i
$808$	4.05938	−	12.4935i	0.142808	−	0.439519i
$809$	15.5916	−	47.9859i	0.548170	−	1.68709i	−0.165161	−	0.986267i	$-0.552815\pi$
$809$	15.5916	−	47.9859i	0.548170	−	1.68709i	0.713331	−	0.700827i	$-0.247185\pi$
$810$	−0.234536	+	0.170401i	−0.00824077	+	0.00598727i
$811$	3.91758	+	2.84629i	0.137565	+	0.0999468i	0.654440	−	0.756114i	$-0.272905\pi$
$811$	3.91758	+	2.84629i	0.137565	+	0.0999468i	−0.516875	+	0.856061i	$0.672905\pi$
$812$	2.11957	+	6.52335i	0.0743822	+	0.228925i
$813$	−2.76846			−0.0970940
$814$	8.59914	+	13.9701i	0.301400	+	0.489653i
$815$	−4.40412			−0.154269
$816$	−2.03093	−	6.25055i	−0.0710967	−	0.218813i
$817$	−6.51582	−	4.73402i	−0.227960	−	0.165622i
$818$	−15.9745	+	11.6061i	−0.558535	+	0.405799i
$819$	1.16407	−	3.58263i	0.0406757	−	0.125187i
$820$	1.03670	−	3.19062i	0.0362030	−	0.111421i
$821$	−8.45440	+	6.14248i	−0.295061	+	0.214374i	−0.725460	−	0.688265i	$-0.758373\pi$
$821$	−8.45440	+	6.14248i	−0.295061	+	0.214374i	0.430399	+	0.902639i	$0.358373\pi$
$822$	−9.97994	−	7.25085i	−0.348090	−	0.252902i
$823$	3.49598	+	10.7595i	0.121862	+	0.375054i	0.993316	−	0.115424i	$-0.0368225\pi$
$823$	3.49598	+	10.7595i	0.121862	+	0.375054i	−0.871454	+	0.490477i	$0.836823\pi$
$824$	−17.9995			−0.627044
$825$	1.24693	−	16.2566i	0.0434127	−	0.565983i
$826$	6.39305			0.222443
$827$	−1.03260	−	3.17802i	−0.0359070	−	0.110510i	0.931497	−	0.363750i	$-0.118504\pi$
$827$	−1.03260	−	3.17802i	−0.0359070	−	0.110510i	−0.967404	+	0.253240i	$0.918504\pi$
$828$	−1.57448	−	1.14393i	−0.0547170	−	0.0397542i
$829$	−14.3604	+	10.4335i	−0.498759	+	0.362370i	−0.808543	−	0.588437i	$-0.799743\pi$
$829$	−14.3604	+	10.4335i	−0.498759	+	0.362370i	0.309784	+	0.950807i	$0.399743\pi$
$830$	1.41225	−	4.34646i	0.0490199	−	0.150868i
$831$	4.69703	−	14.4560i	0.162938	−	0.501472i
$832$	−3.04756	+	2.21418i	−0.105655	+	0.0767630i
$833$	5.31704	+	3.86305i	0.184224	+	0.133847i
$834$	−5.07930	−	15.6325i	−0.175882	−	0.541309i
$835$	3.08100			0.106622
$836$	3.33381	+	1.37315i	0.115302	+	0.0474915i
$837$	4.56916			0.157933
$838$	1.12809	+	3.47190i	0.0389691	+	0.119935i
$839$	−21.5400	−	15.6497i	−0.743643	−	0.540288i	0.150207	−	0.988655i	$-0.452006\pi$
$839$	−21.5400	−	15.6497i	−0.743643	−	0.540288i	−0.893850	+	0.448366i	$0.852006\pi$
$840$	−0.234536	+	0.170401i	−0.00809228	+	0.00587938i
$841$	5.57673	−	17.1634i	0.192301	−	0.591842i
$842$	8.75888	−	26.9571i	0.301851	−	0.929002i
$843$	−15.2926	+	11.1107i	−0.526705	+	0.382673i
$844$	−21.6127	−	15.7025i	−0.743940	−	0.540504i
$845$	0.106629	+	0.328169i	0.00366814	+	0.0112894i
$846$	−0.956816			−0.0328960
$847$	−10.8713	−	1.67760i	−0.373543	−	0.0576430i
$848$	1.96979			0.0676429
$849$	−5.71308	−	17.5830i	−0.196072	−	0.603449i
$850$	−26.1383	−	18.9906i	−0.896537	−	0.651372i
$851$	7.78764	−	5.65805i	0.266957	−	0.193956i
$852$	1.72877	−	5.32060i	0.0592266	−	0.182281i
$853$	−6.35762	+	19.5667i	−0.217681	+	0.669952i	0.781272	+	0.624191i	$0.214571\pi$
$853$	−6.35762	+	19.5667i	−0.217681	+	0.669952i	−0.998952	+	0.0457611i	$0.985429\pi$
$854$	1.40641	−	1.02181i	0.0481262	−	0.0349657i
$855$	−0.254966	−	0.185244i	−0.00871966	−	0.00633520i
$856$	3.33593	+	10.2670i	0.114020	+	0.350917i
$857$	−30.2889			−1.03465			−0.517324	−	0.855790i	$-0.673072\pi$
$857$	−30.2889			−1.03465			−0.517324	+	0.855790i	$0.673072\pi$
$858$	11.5522	+	4.75820i	0.394384	+	0.162442i
$859$	37.8187			1.29036			0.645180	−	0.764031i	$-0.276783\pi$
$859$	37.8187			1.29036			0.645180	+	0.764031i	$0.276783\pi$
$860$	0.663704	+	2.04267i	0.0226321	+	0.0696545i
$861$	−9.36212	−	6.80198i	−0.319060	−	0.231811i
$862$	26.9647	−	19.5910i	0.918420	−	0.667271i
$863$	−8.33928	+	25.6657i	−0.283872	+	0.873669i	0.702862	+	0.711326i	$0.251905\pi$
$863$	−8.33928	+	25.6657i	−0.283872	+	0.873669i	−0.986734	+	0.162343i	$0.948095\pi$
$864$	0.309017	−	0.951057i	0.0105130	−	0.0323556i
$865$	−4.10011	+	2.97891i	−0.139408	+	0.101286i
$866$	28.7626	+	20.8972i	0.977393	+	0.710117i
$867$	8.09441	+	24.9120i	0.274900	+	0.846057i
$868$	4.56916			0.155087
$869$	2.68291	−	34.9778i	0.0910113	−	1.18654i
$870$	1.98846			0.0674152
$871$	8.05996	+	24.8060i	0.273101	+	0.840520i
$872$	−0.524439	−	0.381028i	−0.0177598	−	0.0129032i
$873$	2.88350	−	2.09498i	0.0975916	−	0.0709045i
$874$	0.653784	−	2.01214i	0.0221146	−	0.0680617i
$875$	−0.888320	+	2.73397i	−0.0300307	+	0.0924250i
$876$	3.02312	−	2.19643i	0.102142	−	0.0742104i
$877$	26.2724	+	19.0880i	0.887156	+	0.644557i	0.935135	−	0.354292i	$-0.115278\pi$
$877$	26.2724	+	19.0880i	0.887156	+	0.644557i	−0.0479789	+	0.998848i	$0.515278\pi$
$878$	−9.79229	−	30.1376i	−0.330474	−	1.01709i
$879$	−15.1265			−0.510204
$880$	−0.504010	−	0.818813i	−0.0169902	−	0.0276022i
$881$	−21.6151			−0.728232			−0.364116	−	0.931354i	$-0.618629\pi$
$881$	−21.6151			−0.728232			−0.364116	+	0.931354i	$0.618629\pi$
$882$	0.309017	+	0.951057i	0.0104051	+	0.0320237i
$883$	−26.7541	−	19.4380i	−0.900346	−	0.654140i	0.0382087	−	0.999270i	$-0.487835\pi$
$883$	−26.7541	−	19.4380i	−0.900346	−	0.654140i	−0.938555	+	0.345130i	$0.887835\pi$
$884$	20.0292	−	14.5521i	0.673657	−	0.489440i
$885$	0.572721	−	1.76265i	0.0192518	−	0.0592510i
$886$	−8.32222	+	25.6132i	−0.279590	+	0.860491i
$887$	−6.75685	+	4.90914i	−0.226873	+	0.164833i	−0.695415	−	0.718608i	$-0.744779\pi$
$887$	−6.75685	+	4.90914i	−0.226873	+	0.164833i	0.468542	+	0.883441i	$0.344779\pi$
$888$	4.00153	+	2.90728i	0.134283	+	0.0975620i
$889$	−5.58426	−	17.1866i	−0.187290	−	0.576420i
$890$	−3.43696			−0.115207
$891$	−3.22344	+	0.780656i	−0.107989	+	0.0261530i
$892$	21.2549			0.711667
$893$	−0.321427	−	0.989252i	−0.0107562	−	0.0331040i
$894$	16.7701	+	12.1842i	0.560875	+	0.407499i
$895$	1.90381	−	1.38320i	0.0636372	−	0.0462351i
$896$	0.309017	−	0.951057i	0.0103235	−	0.0317726i
$897$	2.26546	−	6.97238i	0.0756416	−	0.232801i
$898$	19.9738	−	14.5118i	0.666534	−	0.484265i
$899$	−25.3547	−	18.4212i	−0.845626	−	0.614383i
$900$	−1.51911	−	4.67535i	−0.0506371	−	0.155845i
$901$	−12.9459			−0.431290
$902$	24.8682	−	29.2344i	0.828022	−	0.973398i
$903$	7.40866			0.246545
$904$	−3.97606	−	12.2371i	−0.132242	−	0.406999i
$905$	1.49541	+	1.08648i	0.0497090	+	0.0361157i
$906$	−11.6736	+	8.48138i	−0.387830	+	0.281775i
$907$	−5.99025	+	18.4361i	−0.198903	+	0.612161i	0.801006	+	0.598657i	$0.204299\pi$
$907$	−5.99025	+	18.4361i	−0.198903	+	0.612161i	−0.999909	+	0.0135040i	$0.995701\pi$
$908$	5.65576	−	17.4066i	0.187693	−	0.577660i
$909$	−10.6276	+	7.72139i	−0.352495	+	0.256102i
$910$	−0.883498	−	0.641899i	−0.0292877	−	0.0212787i
$911$	6.02642	+	18.5474i	0.199664	+	0.614503i	0.999890	+	0.0148051i	$0.00471278\pi$
$911$	6.02642	+	18.5474i	0.199664	+	0.614503i	−0.800226	+	0.599698i	$0.795287\pi$
$912$	1.08711			0.0359977
$913$	33.8770	−	39.8248i	1.12117	−	1.31801i
$914$	12.5080			0.413728
$915$	−0.155736	−	0.479305i	−0.00514846	−	0.0158453i
$916$	−7.63489	−	5.54707i	−0.252264	−	0.183280i
$917$	−0.424573	+	0.308470i	−0.0140206	+	0.0101866i
$918$	−2.03093	+	6.25055i	−0.0670306	+	0.206299i
$919$	−15.3874	+	47.3575i	−0.507583	+	1.56218i	0.288800	+	0.957389i	$0.406744\pi$
$919$	−15.3874	+	47.3575i	−0.507583	+	1.56218i	−0.796384	+	0.604792i	$0.793256\pi$
$920$	−0.456447	+	0.331628i	−0.0150486	+	0.0109334i
$921$	−19.0732	−	13.8575i	−0.628482	−	0.456619i
$922$	−0.170694	−	0.525343i	−0.00562152	−	0.0173012i
$923$	21.0741			0.693663
$924$	−3.22344	+	0.780656i	−0.106043	+	0.0256817i
$925$	24.3151			0.799477
$926$	−2.77803	−	8.54990i	−0.0912918	−	0.280967i
$927$	14.5619	+	10.5799i	0.478277	+	0.347488i
$928$	−5.54909	+	4.03165i	−0.182158	+	0.132346i
$929$	11.9915	−	36.9061i	0.393429	−	1.21085i	−0.536749	−	0.843742i	$-0.680348\pi$
$929$	11.9915	−	36.9061i	0.393429	−	1.21085i	0.930178	−	0.367109i	$-0.119652\pi$
$930$	0.409328	−	1.25978i	0.0134224	−	0.0413098i
$931$	−0.879488	+	0.638985i	−0.0288241	+	0.0209419i
$932$	8.58237	+	6.23545i	0.281125	+	0.204249i
$933$	−1.62636	−	5.00543i	−0.0532448	−	0.163871i
$934$	−4.49622			−0.147121
$935$	3.31246	+	5.38142i	0.108329	+	0.175991i
$936$	3.76700			0.123128
$937$	2.09125	+	6.43621i	0.0683182	+	0.210262i	0.979387	−	0.201992i	$-0.0647416\pi$
$937$	2.09125	+	6.43621i	0.0683182	+	0.210262i	−0.911069	+	0.412254i	$0.864742\pi$
$938$	−5.60161	−	4.06981i	−0.182899	−	0.132884i
$939$	−8.71316	+	6.33048i	−0.284343	+	0.206587i
$940$	−0.0857163	+	0.263808i	−0.00279576	+	0.00860445i
$941$	10.3571	−	31.8758i	0.337631	−	1.03912i	−0.627781	−	0.778390i	$-0.716036\pi$
$941$	10.3571	−	31.8758i	0.337631	−	1.03912i	0.965412	−	0.260731i	$-0.0839635\pi$
$942$	−9.17421	+	6.66546i	−0.298912	+	0.217172i
$943$	−18.2202	−	13.2378i	−0.593332	−	0.431081i
$944$	1.97556	+	6.08015i	0.0642990	+	0.197892i
$945$	0.289903			0.00943054
$946$	−1.87921	+	24.4998i	−0.0610983	+	0.796556i
$947$	−20.5900			−0.669085			−0.334542	−	0.942381i	$-0.608582\pi$
$947$	−20.5900			−0.669085			−0.334542	+	0.942381i	$0.608582\pi$
$948$	−3.26853	−	10.0595i	−0.106157	−	0.326717i
$949$	11.3881	+	8.27393i	0.369673	+	0.268583i
$950$	4.32352	−	3.14122i	0.140274	−	0.101915i
$951$	4.88896	−	15.0467i	0.158535	−	0.487921i
$952$	−2.03093	+	6.25055i	−0.0658227	+	0.202582i
$953$	20.8654	−	15.1596i	0.675896	−	0.491067i	−0.196098	−	0.980584i	$-0.562827\pi$
$953$	20.8654	−	15.1596i	0.675896	−	0.491067i	0.871994	+	0.489517i	$0.162827\pi$
$954$	−1.59359	−	1.15781i	−0.0515945	−	0.0374856i
$955$	−1.79671	−	5.52969i	−0.0581400	−	0.178937i
$956$	6.94473			0.224609
$957$	21.0345	+	8.66387i	0.679949	+	0.280063i
$958$	0.601107			0.0194209
$959$	3.81200	+	11.7321i	0.123096	+	0.378850i
$960$	−0.234536	−	0.170401i	−0.00756963	−	0.00549966i
$961$	8.18953	−	5.95004i	0.264179	−	0.191937i
$962$	−5.75766	+	17.7203i	−0.185634	+	0.571324i
$963$	3.33593	−	10.2670i	0.107499	−	0.330848i
$964$	−2.40641	+	1.74836i	−0.0775051	+	0.0563108i
$965$	2.86570	+	2.08205i	0.0922501	+	0.0670236i
$966$	0.601398	+	1.85091i	0.0193497	+	0.0595521i
$967$	−33.7292			−1.08466			−0.542329	−	0.840166i	$-0.682457\pi$
$967$	−33.7292			−1.08466			−0.542329	+	0.840166i	$0.682457\pi$
$968$	−1.76393	−	10.8576i	−0.0566949	−	0.348978i
$969$	−7.14470			−0.229521
$970$	−0.319299	−	0.982700i	−0.0102521	−	0.0315526i
$971$	9.87064	+	7.17144i	0.316764	+	0.230143i	0.734793	−	0.678291i	$-0.237279\pi$
$971$	9.87064	+	7.17144i	0.316764	+	0.230143i	−0.418029	+	0.908433i	$0.637279\pi$
$972$	−0.809017	+	0.587785i	−0.0259492	+	0.0188532i
$973$	−5.07930	+	15.6325i	−0.162835	+	0.501155i
$974$	−7.25811	+	22.3382i	−0.232565	+	0.715761i
$975$	14.9817	−	10.8848i	0.479798	−	0.348594i
$976$	1.40641	+	1.02181i	0.0450179	+	0.0327074i
$977$	−10.7477	−	33.0779i	−0.343849	−	1.05826i	−0.962197	−	0.272353i	$-0.912198\pi$
$977$	−10.7477	−	33.0779i	−0.343849	−	1.05826i	0.618349	−	0.785904i	$-0.287802\pi$
$978$	−15.1917			−0.485777
$979$	−36.3571	−	14.9751i	−1.16198	−	0.478605i
$980$	0.289903			0.00926061
$981$	0.200318	+	0.616515i	0.00639566	+	0.0196838i
$982$	10.0773	+	7.32161i	0.321580	+	0.233642i
$983$	−36.6636	+	26.6376i	−1.16939	+	0.849609i	−0.990935	−	0.134340i	$-0.957108\pi$
$983$	−36.6636	+	26.6376i	−1.16939	+	0.849609i	−0.178451	+	0.983949i	$0.557108\pi$
$984$	3.57601	−	11.0058i	0.113999	−	0.350853i
$985$	0.527954	−	1.62488i	0.0168220	−	0.0517728i
$986$	36.4699	−	26.4969i	1.16144	−	0.843833i
$987$	0.774080	+	0.562402i	0.0246392	+	0.0179015i
$988$	1.26546	+	3.89470i	0.0402598	+	0.123907i
$989$	14.4185			0.458481
$990$	−0.0735340	+	0.958683i	−0.00233706	+	0.0304690i
$991$	−0.115806			−0.00367871			−0.00183936	−	0.999998i	$-0.500585\pi$
$991$	−0.115806			−0.00367871			−0.00183936	+	0.999998i	$0.500585\pi$
$992$	1.41195	+	4.34552i	0.0448293	+	0.137971i
$993$	9.52020	+	6.91683i	0.302114	+	0.219499i
$994$	−4.52597	+	3.28831i	−0.143555	+	0.104299i
$995$	−0.755590	+	2.32547i	−0.0239538	+	0.0737222i
$996$	4.87146	−	14.9928i	0.154358	−	0.475065i
$997$	−22.0595	+	16.0271i	−0.698630	+	0.507584i	−0.879486	−	0.475925i	$-0.842113\pi$
$997$	−22.0595	+	16.0271i	−0.698630	+	0.507584i	0.180856	+	0.983510i	$0.442113\pi$
$998$	18.1840	+	13.2114i	0.575604	+	0.418201i
$999$	−1.52845	−	4.70408i	−0.0483580	−	0.148831i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.j.e.379.1	yes	8
11.3	even	5		5082.2.a.cf.1.2		4
11.8	odd	10		5082.2.a.ca.1.2		4
11.9	even	5	inner	462.2.j.e.295.1	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.j.e.295.1	✓	8	11.9	even	5	inner
462.2.j.e.379.1	yes	8	1.1	even	1	trivial
5082.2.a.ca.1.2		4	11.8	odd	10
5082.2.a.cf.1.2		4	11.3	even	5

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.j (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.309017 + 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(0.0895849 - 0.275714i) q^{5} +(0.309017 - 0.951057i) q^{6} +(-0.809017 + 0.587785i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})\)	\(q+(0.309017 + 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(0.0895849 - 0.275714i) q^{5} +(0.309017 - 0.951057i) q^{6} +(-0.809017 + 0.587785i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(0.309017 + 0.951057i) q^{9} +0.289903 q^{10} +(3.06668 + 1.26313i) q^{11} +1.00000 q^{12} +(1.16407 + 3.58263i) q^{13} +(-0.809017 - 0.587785i) q^{14} +(-0.234536 + 0.170401i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-2.03093 + 6.25055i) q^{17} +(-0.809017 + 0.587785i) q^{18} +(-0.879488 - 0.638985i) q^{19} +(0.0895849 + 0.275714i) q^{20} +1.00000 q^{21} +(-0.253650 + 3.30691i) q^{22} +1.94617 q^{23} +(0.309017 + 0.951057i) q^{24} +(3.97709 + 2.88953i) q^{25} +(-3.04756 + 2.21418i) q^{26} +(0.309017 - 0.951057i) q^{27} +(0.309017 - 0.951057i) q^{28} +(-5.54909 + 4.03165i) q^{29} +(-0.234536 - 0.170401i) q^{30} +(1.41195 + 4.34552i) q^{31} +1.00000 q^{32} +(-1.73855 - 2.82444i) q^{33} -6.57222 q^{34} +(0.0895849 + 0.275714i) q^{35} +(-0.809017 - 0.587785i) q^{36} +(4.00153 - 2.90728i) q^{37} +(0.335934 - 1.03390i) q^{38} +(1.16407 - 3.58263i) q^{39} +(-0.234536 + 0.170401i) q^{40} +(-9.36212 - 6.80198i) q^{41} +(0.309017 + 0.951057i) q^{42} +7.40866 q^{43} +(-3.22344 + 0.780656i) q^{44} +0.289903 q^{45} +(0.601398 + 1.85091i) q^{46} +(0.774080 + 0.562402i) q^{47} +(-0.809017 + 0.587785i) q^{48} +(0.309017 - 0.951057i) q^{49} +(-1.51911 + 4.67535i) q^{50} +(5.31704 - 3.86305i) q^{51} +(-3.04756 - 2.21418i) q^{52} +(0.608699 + 1.87338i) q^{53} +1.00000 q^{54} +(0.622990 - 0.732369i) q^{55} +1.00000 q^{56} +(0.335934 + 1.03390i) q^{57} +(-5.54909 - 4.03165i) q^{58} +(-5.17208 + 3.75774i) q^{59} +(0.0895849 - 0.275714i) q^{60} +(-0.537199 + 1.65333i) q^{61} +(-3.69652 + 2.68568i) q^{62} +(-0.809017 - 0.587785i) q^{63} +(0.309017 + 0.951057i) q^{64} +1.09206 q^{65} +(2.14896 - 2.52626i) q^{66} +6.92398 q^{67} +(-2.03093 - 6.25055i) q^{68} +(-1.57448 - 1.14393i) q^{69} +(-0.234536 + 0.170401i) q^{70} +(1.72877 - 5.32060i) q^{71} +(0.309017 - 0.951057i) q^{72} +(3.02312 - 2.19643i) q^{73} +(4.00153 + 2.90728i) q^{74} +(-1.51911 - 4.67535i) q^{75} +1.08711 q^{76} +(-3.22344 + 0.780656i) q^{77} +3.76700 q^{78} +(-3.26853 - 10.0595i) q^{79} +(-0.234536 - 0.170401i) q^{80} +(-0.809017 + 0.587785i) q^{81} +(3.57601 - 11.0058i) q^{82} +(4.87146 - 14.9928i) q^{83} +(-0.809017 + 0.587785i) q^{84} +(1.54142 + 1.11991i) q^{85} +(2.28940 + 7.04605i) q^{86} +6.85906 q^{87} +(-1.73855 - 2.82444i) q^{88} -11.8555 q^{89} +(0.0895849 + 0.275714i) q^{90} +(-3.04756 - 2.21418i) q^{91} +(-1.57448 + 1.14393i) q^{92} +(1.41195 - 4.34552i) q^{93} +(-0.295672 + 0.909986i) q^{94} +(-0.254966 + 0.185244i) q^{95} +(-0.809017 - 0.587785i) q^{96} +(-1.10140 - 3.38975i) q^{97} +1.00000 q^{98} +(-0.253650 + 3.30691i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} - 2 q^{3} - 2 q^{4} + 4 q^{5} - 2 q^{6} - 2 q^{7} - 2 q^{8} - 2 q^{9}+O(q^{10}) \) 8 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 + 4 * q^5 - 2 * q^6 - 2 * q^7 - 2 * q^8 - 2 * q^9	\( 8 q - 2 q^{2} - 2 q^{3} - 2 q^{4} + 4 q^{5} - 2 q^{6} - 2 q^{7} - 2 q^{8} - 2 q^{9} + 4 q^{10} + 8 q^{12} + 4 q^{13} - 2 q^{14} - 6 q^{15} - 2 q^{16} - 8 q^{17} - 2 q^{18} - 12 q^{19} + 4 q^{20} + 8 q^{21} - 4 q^{23} - 2 q^{24} + 4 q^{25} - 6 q^{26} - 2 q^{27} - 2 q^{28} - 4 q^{29} - 6 q^{30} - 14 q^{31} + 8 q^{32} + 12 q^{34} + 4 q^{35} - 2 q^{36} + 10 q^{37} + 8 q^{38} + 4 q^{39} - 6 q^{40} - 12 q^{41} - 2 q^{42} + 20 q^{43} + 4 q^{45} + 6 q^{46} + 28 q^{47} - 2 q^{48} - 2 q^{49} - 6 q^{50} + 2 q^{51} - 6 q^{52} + 2 q^{53} + 8 q^{54} + 4 q^{55} + 8 q^{56} + 8 q^{57} - 4 q^{58} + 4 q^{60} - 34 q^{61} + 6 q^{62} - 2 q^{63} - 2 q^{64} + 16 q^{65} - 24 q^{67} - 8 q^{68} - 4 q^{69} - 6 q^{70} - 2 q^{72} + 10 q^{74} - 6 q^{75} + 8 q^{76} + 4 q^{78} + 22 q^{79} - 6 q^{80} - 2 q^{81} - 2 q^{82} - 30 q^{83} - 2 q^{84} - 28 q^{85} + 36 q^{87} - 4 q^{89} + 4 q^{90} - 6 q^{91} - 4 q^{92} - 14 q^{93} - 22 q^{94} - 30 q^{95} - 2 q^{96} - 10 q^{97} + 8 q^{98}+O(q^{100}) \) 8 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 + 4 * q^5 - 2 * q^6 - 2 * q^7 - 2 * q^8 - 2 * q^9 + 4 * q^10 + 8 * q^12 + 4 * q^13 - 2 * q^14 - 6 * q^15 - 2 * q^16 - 8 * q^17 - 2 * q^18 - 12 * q^19 + 4 * q^20 + 8 * q^21 - 4 * q^23 - 2 * q^24 + 4 * q^25 - 6 * q^26 - 2 * q^27 - 2 * q^28 - 4 * q^29 - 6 * q^30 - 14 * q^31 + 8 * q^32 + 12 * q^34 + 4 * q^35 - 2 * q^36 + 10 * q^37 + 8 * q^38 + 4 * q^39 - 6 * q^40 - 12 * q^41 - 2 * q^42 + 20 * q^43 + 4 * q^45 + 6 * q^46 + 28 * q^47 - 2 * q^48 - 2 * q^49 - 6 * q^50 + 2 * q^51 - 6 * q^52 + 2 * q^53 + 8 * q^54 + 4 * q^55 + 8 * q^56 + 8 * q^57 - 4 * q^58 + 4 * q^60 - 34 * q^61 + 6 * q^62 - 2 * q^63 - 2 * q^64 + 16 * q^65 - 24 * q^67 - 8 * q^68 - 4 * q^69 - 6 * q^70 - 2 * q^72 + 10 * q^74 - 6 * q^75 + 8 * q^76 + 4 * q^78 + 22 * q^79 - 6 * q^80 - 2 * q^81 - 2 * q^82 - 30 * q^83 - 2 * q^84 - 28 * q^85 + 36 * q^87 - 4 * q^89 + 4 * q^90 - 6 * q^91 - 4 * q^92 - 14 * q^93 - 22 * q^94 - 30 * q^95 - 2 * q^96 - 10 * q^97 + 8 * q^98

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