LMFDB - Embedded newform 462.2.j.h.421.2

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:	8.0.20164000000.8
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 6x^{6} + 76x^{4} + 781x^{2} + 5041 $ x^8 + 6x^6 + 76x^4 + 781*x^2 + 5041
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			421.2
Root			$2.50900 + 1.82290i$ of defining polynomial
Character	$\chi$	$=$	462.421
Dual form			462.2.j.h.169.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 - 0.587785i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(0.309017 - 0.951057i) q^{4} +(1.69998 + 1.23511i) q^{5} +(-0.809017 - 0.587785i) q^{6} +(-0.309017 + 0.951057i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(0.809017 - 0.587785i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(0.309017 - 0.951057i) q^{4} +(1.69998 + 1.23511i) q^{5} +(-0.809017 - 0.587785i) q^{6} +(-0.309017 + 0.951057i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(-0.809017 + 0.587785i) q^{9} +2.10130 q^{10} +(3.19998 - 0.871839i) q^{11} -1.00000 q^{12} +(4.47770 - 3.25324i) q^{13} +(0.309017 + 0.951057i) q^{14} +(0.649336 - 1.99845i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-1.50000 - 1.08981i) q^{17} +(-0.309017 + 0.951057i) q^{18} +(0.283278 + 0.871839i) q^{19} +(1.69998 - 1.23511i) q^{20} +1.00000 q^{21} +(2.07639 - 2.58624i) q^{22} -1.37084 q^{23} +(-0.809017 + 0.587785i) q^{24} +(-0.180638 - 0.555947i) q^{25} +(1.71033 - 5.26385i) q^{26} +(0.809017 + 0.587785i) q^{27} +(0.809017 + 0.587785i) q^{28} +(0.675075 - 2.07767i) q^{29} +(-0.649336 - 1.99845i) q^{30} +(-8.18668 + 5.94797i) q^{31} -1.00000 q^{32} +(-1.81802 - 2.77395i) q^{33} -1.85410 q^{34} +(-1.69998 + 1.23511i) q^{35} +(0.309017 + 0.951057i) q^{36} +(1.11460 - 3.43037i) q^{37} +(0.741631 + 0.538826i) q^{38} +(-4.47770 - 3.25324i) q^{39} +(0.649336 - 1.99845i) q^{40} +(3.45540 + 10.6346i) q^{41} +(0.809017 - 0.587785i) q^{42} -6.17346 q^{43} +(0.159681 - 3.31278i) q^{44} -2.10130 q^{45} +(-1.10903 + 0.805760i) q^{46} +(1.29311 + 3.97978i) q^{47} +(-0.309017 + 0.951057i) q^{48} +(-0.809017 - 0.587785i) q^{49} +(-0.472917 - 0.343594i) q^{50} +(-0.572949 + 1.76336i) q^{51} +(-1.71033 - 5.26385i) q^{52} +(5.76181 - 4.18620i) q^{53} +1.00000 q^{54} +(6.51674 + 2.47022i) q^{55} +1.00000 q^{56} +(0.741631 - 0.538826i) q^{57} +(-0.675075 - 2.07767i) q^{58} +(2.67508 - 8.23304i) q^{59} +(-1.69998 - 1.23511i) q^{60} +(4.11030 + 2.98631i) q^{61} +(-3.12703 + 9.62402i) q^{62} +(-0.309017 - 0.951057i) q^{63} +(-0.809017 + 0.587785i) q^{64} +11.6301 q^{65} +(-3.10130 - 1.17557i) q^{66} -9.55274 q^{67} +(-1.50000 + 1.08981i) q^{68} +(0.423613 + 1.30375i) q^{69} +(-0.649336 + 1.99845i) q^{70} +(-1.16390 - 0.845623i) q^{71} +(0.809017 + 0.587785i) q^{72} +(-4.05704 + 12.4863i) q^{73} +(-1.11460 - 3.43037i) q^{74} +(-0.472917 + 0.343594i) q^{75} +0.916706 q^{76} +(-0.159681 + 3.31278i) q^{77} -5.53474 q^{78} +(-14.3699 + 10.4404i) q^{79} +(-0.649336 - 1.99845i) q^{80} +(0.309017 - 0.951057i) q^{81} +(9.04635 + 6.57256i) q^{82} +(9.34636 + 6.79053i) q^{83} +(0.309017 - 0.951057i) q^{84} +(-1.20394 - 3.70533i) q^{85} +(-4.99444 + 3.62867i) q^{86} -2.18459 q^{87} +(-1.81802 - 2.77395i) q^{88} +3.87635 q^{89} +(-1.69998 + 1.23511i) q^{90} +(1.71033 + 5.26385i) q^{91} +(-0.423613 + 1.30375i) q^{92} +(8.18668 + 5.94797i) q^{93} +(3.38540 + 2.45964i) q^{94} +(-0.595250 + 1.83199i) q^{95} +(0.309017 + 0.951057i) q^{96} +(-4.62703 + 3.36174i) q^{97} -1.00000 q^{98} +(-2.07639 + 2.58624i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 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 - 2 * 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} - 2 q^{5} - 2 q^{6} + 2 q^{7} + 2 q^{8} - 2 q^{9} - 8 q^{10} + 10 q^{11} - 8 q^{12} + 10 q^{13} - 2 q^{14} + 2 q^{15} - 2 q^{16} - 12 q^{17} + 2 q^{18} + 2 q^{19} - 2 q^{20} + 8 q^{21} - 2 q^{24} - 4 q^{25} + 2 q^{27} + 2 q^{28} - 2 q^{29} - 2 q^{30} - 4 q^{31} - 8 q^{32} + 10 q^{33} + 12 q^{34} + 2 q^{35} - 2 q^{36} + 30 q^{37} - 2 q^{38} - 10 q^{39} + 2 q^{40} - 24 q^{41} + 2 q^{42} - 20 q^{43} + 8 q^{45} - 20 q^{46} - 6 q^{47} + 2 q^{48} - 2 q^{49} + 14 q^{50} - 18 q^{51} + 24 q^{53} + 8 q^{54} + 68 q^{55} + 8 q^{56} - 2 q^{57} + 2 q^{58} + 14 q^{59} + 2 q^{60} - 12 q^{61} + 4 q^{62} + 2 q^{63} - 2 q^{64} - 44 q^{65} - 12 q^{67} - 12 q^{68} + 20 q^{69} - 2 q^{70} + 4 q^{71} + 2 q^{72} - 34 q^{73} - 30 q^{74} + 14 q^{75} - 8 q^{76} - 20 q^{78} - 22 q^{79} - 2 q^{80} - 2 q^{81} - 6 q^{82} + 12 q^{83} - 2 q^{84} + 18 q^{85} - 30 q^{86} - 8 q^{87} + 10 q^{88} + 44 q^{89} + 2 q^{90} - 20 q^{92} + 4 q^{93} + 6 q^{94} - 44 q^{95} - 2 q^{96} - 8 q^{97} - 8 q^{98}+O(q^{100}) $ 8 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 - 2 * q^6 + 2 * q^7 + 2 * q^8 - 2 * q^9 - 8 * q^10 + 10 * q^11 - 8 * q^12 + 10 * q^13 - 2 * q^14 + 2 * q^15 - 2 * q^16 - 12 * q^17 + 2 * q^18 + 2 * q^19 - 2 * q^20 + 8 * q^21 - 2 * q^24 - 4 * q^25 + 2 * q^27 + 2 * q^28 - 2 * q^29 - 2 * q^30 - 4 * q^31 - 8 * q^32 + 10 * q^33 + 12 * q^34 + 2 * q^35 - 2 * q^36 + 30 * q^37 - 2 * q^38 - 10 * q^39 + 2 * q^40 - 24 * q^41 + 2 * q^42 - 20 * q^43 + 8 * q^45 - 20 * q^46 - 6 * q^47 + 2 * q^48 - 2 * q^49 + 14 * q^50 - 18 * q^51 + 24 * q^53 + 8 * q^54 + 68 * q^55 + 8 * q^56 - 2 * q^57 + 2 * q^58 + 14 * q^59 + 2 * q^60 - 12 * q^61 + 4 * q^62 + 2 * q^63 - 2 * q^64 - 44 * q^65 - 12 * q^67 - 12 * q^68 + 20 * q^69 - 2 * q^70 + 4 * q^71 + 2 * q^72 - 34 * q^73 - 30 * q^74 + 14 * q^75 - 8 * q^76 - 20 * q^78 - 22 * q^79 - 2 * q^80 - 2 * q^81 - 6 * q^82 + 12 * q^83 - 2 * q^84 + 18 * q^85 - 30 * q^86 - 8 * q^87 + 10 * q^88 + 44 * q^89 + 2 * q^90 - 20 * q^92 + 4 * q^93 + 6 * q^94 - 44 * q^95 - 2 * q^96 - 8 * q^97 - 8 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	0.809017	−	0.587785i	0.572061	−	0.415627i
$2$	0.809017	−	0.587785i	0.572061	−	0.415627i
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$4$	0.309017	−	0.951057i	0.154508	−	0.475528i
$5$	1.69998	+	1.23511i	0.760256	+	0.552358i	0.898989	−	0.437972i	$-0.144303\pi$
$5$	1.69998	+	1.23511i	0.760256	+	0.552358i	−0.138733	+	0.990330i	$0.544303\pi$
$6$	−0.809017	−	0.587785i	−0.330280	−	0.239962i
$7$	−0.309017	+	0.951057i	−0.116797	+	0.359466i
$7$	−0.309017	+	0.951057i	−0.116797	+	0.359466i
$8$	−0.309017	−	0.951057i	−0.109254	−	0.336249i
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$	2.10130			0.664488
$11$	3.19998	−	0.871839i	0.964831	−	0.262869i
$11$	3.19998	−	0.871839i	0.964831	−	0.262869i
$12$	−1.00000			−0.288675
$13$	4.47770	−	3.25324i	1.24189	−	0.902286i	0.244167	−	0.969733i	$-0.421485\pi$
$13$	4.47770	−	3.25324i	1.24189	−	0.902286i	0.997723	+	0.0674471i	$0.0214854\pi$
$14$	0.309017	+	0.951057i	0.0825883	+	0.254181i
$15$	0.649336	−	1.99845i	0.167658	−	0.515998i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	−1.50000	−	1.08981i	−0.363803	−	0.264319i	0.390833	−	0.920461i	$-0.372187\pi$
$17$	−1.50000	−	1.08981i	−0.363803	−	0.264319i	−0.754637	+	0.656143i	$0.772187\pi$
$18$	−0.309017	+	0.951057i	−0.0728360	+	0.224166i
$19$	0.283278	+	0.871839i	0.0649884	+	0.200014i	0.978278	−	0.207297i	$-0.0664666\pi$
$19$	0.283278	+	0.871839i	0.0649884	+	0.200014i	−0.913290	+	0.407311i	$0.866467\pi$
$20$	1.69998	−	1.23511i	0.380128	−	0.276179i
$21$	1.00000			0.218218
$22$	2.07639	−	2.58624i	0.442687	−	0.551387i
$23$	−1.37084			−0.285840			−0.142920	−	0.989734i	$-0.545649\pi$
$23$	−1.37084			−0.285840			−0.142920	+	0.989734i	$0.545649\pi$
$24$	−0.809017	+	0.587785i	−0.165140	+	0.119981i
$25$	−0.180638	−	0.555947i	−0.0361276	−	0.111189i
$26$	1.71033	−	5.26385i	0.335423	−	1.03233i
$27$	0.809017	+	0.587785i	0.155695	+	0.113119i
$28$	0.809017	+	0.587785i	0.152890	+	0.111081i
$29$	0.675075	−	2.07767i	0.125358	−	0.385813i	−0.868608	−	0.495500i	$-0.834985\pi$
$29$	0.675075	−	2.07767i	0.125358	−	0.385813i	0.993966	+	0.109687i	$0.0349848\pi$
$30$	−0.649336	−	1.99845i	−0.118552	−	0.364866i
$31$	−8.18668	+	5.94797i	−1.47037	+	1.06829i	−0.489866	+	0.871798i	$0.662954\pi$
$31$	−8.18668	+	5.94797i	−1.47037	+	1.06829i	−0.980506	+	0.196490i	$0.937046\pi$
$32$	−1.00000			−0.176777
$33$	−1.81802	−	2.77395i	−0.316476	−	0.482883i
$34$	−1.85410			−0.317976
$35$	−1.69998	+	1.23511i	−0.287350	+	0.208772i
$36$	0.309017	+	0.951057i	0.0515028	+	0.158509i
$37$	1.11460	−	3.43037i	0.183238	−	0.563950i	−0.816675	−	0.577098i	$-0.804185\pi$
$37$	1.11460	−	3.43037i	0.183238	−	0.563950i	0.999914	+	0.0131477i	$0.00418518\pi$
$38$	0.741631	+	0.538826i	0.120308	+	0.0874092i
$39$	−4.47770	−	3.25324i	−0.717006	−	0.520935i
$40$	0.649336	−	1.99845i	0.102669	−	0.315983i
$41$	3.45540	+	10.6346i	0.539642	+	1.66085i	0.733399	+	0.679799i	$0.237933\pi$
$41$	3.45540	+	10.6346i	0.539642	+	1.66085i	−0.193756	+	0.981050i	$0.562067\pi$
$42$	0.809017	−	0.587785i	0.124834	−	0.0906972i
$43$	−6.17346			−0.941444			−0.470722	−	0.882281i	$-0.656007\pi$
$43$	−6.17346			−0.941444			−0.470722	+	0.882281i	$0.656007\pi$
$44$	0.159681	−	3.31278i	0.0240728	−	0.499420i
$45$	−2.10130			−0.313243
$46$	−1.10903	+	0.805760i	−0.163518	+	0.118803i
$47$	1.29311	+	3.97978i	0.188619	+	0.580511i	0.999992	−	0.00401863i	$-0.00127917\pi$
$47$	1.29311	+	3.97978i	0.188619	+	0.580511i	−0.811373	+	0.584529i	$0.801279\pi$
$48$	−0.309017	+	0.951057i	−0.0446028	+	0.137273i
$49$	−0.809017	−	0.587785i	−0.115574	−	0.0839693i
$50$	−0.472917	−	0.343594i	−0.0668805	−	0.0485915i
$51$	−0.572949	+	1.76336i	−0.0802289	+	0.246919i
$52$	−1.71033	−	5.26385i	−0.237180	−	0.729965i
$53$	5.76181	−	4.18620i	0.791445	−	0.575019i	−0.116947	−	0.993138i	$-0.537311\pi$
$53$	5.76181	−	4.18620i	0.791445	−	0.575019i	0.908392	+	0.418120i	$0.137311\pi$
$54$	1.00000			0.136083
$55$	6.51674	+	2.47022i	0.878717	+	0.333085i
$56$	1.00000			0.133631
$57$	0.741631	−	0.538826i	0.0982314	−	0.0713693i
$58$	−0.675075	−	2.07767i	−0.0886417	−	0.272811i
$59$	2.67508	−	8.23304i	0.348265	−	1.07185i	−0.611547	−	0.791208i	$-0.709453\pi$
$59$	2.67508	−	8.23304i	0.348265	−	1.07185i	0.959813	−	0.280642i	$-0.0905474\pi$
$60$	−1.69998	−	1.23511i	−0.219467	−	0.159452i
$61$	4.11030	+	2.98631i	0.526270	+	0.382357i	0.818960	−	0.573850i	$-0.194551\pi$
$61$	4.11030	+	2.98631i	0.526270	+	0.382357i	−0.292691	+	0.956207i	$0.594551\pi$
$62$	−3.12703	+	9.62402i	−0.397134	+	1.22225i
$63$	−0.309017	−	0.951057i	−0.0389325	−	0.119822i
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	11.6301			1.44254
$66$	−3.10130	−	1.17557i	−0.381743	−	0.144703i
$67$	−9.55274			−1.16705			−0.583527	−	0.812094i	$-0.698328\pi$
$67$	−9.55274			−1.16705			−0.583527	+	0.812094i	$0.698328\pi$
$68$	−1.50000	+	1.08981i	−0.181902	+	0.132159i
$69$	0.423613	+	1.30375i	0.0509970	+	0.156953i
$70$	−0.649336	+	1.99845i	−0.0776105	+	0.238861i
$71$	−1.16390	−	0.845623i	−0.138129	−	0.100357i	0.516575	−	0.856242i	$-0.327207\pi$
$71$	−1.16390	−	0.845623i	−0.138129	−	0.100357i	−0.654704	+	0.755885i	$0.727207\pi$
$72$	0.809017	+	0.587785i	0.0953436	+	0.0692712i
$73$	−4.05704	+	12.4863i	−0.474841	+	1.46141i	0.371332	+	0.928500i	$0.378901\pi$
$73$	−4.05704	+	12.4863i	−0.474841	+	1.46141i	−0.846172	+	0.532909i	$0.821099\pi$
$74$	−1.11460	−	3.43037i	−0.129569	−	0.398773i
$75$	−0.472917	+	0.343594i	−0.0546077	+	0.0396748i
$76$	0.916706			0.105153
$77$	−0.159681	+	3.31278i	−0.0181973	+	0.377526i
$78$	−5.53474			−0.626686
$79$	−14.3699	+	10.4404i	−1.61674	+	1.17463i	−0.784899	+	0.619624i	$0.787285\pi$
$79$	−14.3699	+	10.4404i	−1.61674	+	1.17463i	−0.831844	+	0.555009i	$0.812715\pi$
$80$	−0.649336	−	1.99845i	−0.0725980	−	0.223434i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	9.04635	+	6.57256i	0.999002	+	0.725817i
$83$	9.34636	+	6.79053i	1.02590	+	0.745358i	0.967483	−	0.252935i	$-0.0813958\pi$
$83$	9.34636	+	6.79053i	1.02590	+	0.745358i	0.0584134	+	0.998292i	$0.481396\pi$
$84$	0.309017	−	0.951057i	0.0337165	−	0.103769i
$85$	−1.20394	−	3.70533i	−0.130585	−	0.401900i
$86$	−4.99444	+	3.62867i	−0.538564	+	0.391290i
$87$	−2.18459			−0.234213
$88$	−1.81802	−	2.77395i	−0.193801	−	0.295704i
$89$	3.87635			0.410893			0.205446	−	0.978668i	$-0.434135\pi$
$89$	3.87635			0.410893			0.205446	+	0.978668i	$0.434135\pi$
$90$	−1.69998	+	1.23511i	−0.179194	+	0.130192i
$91$	1.71033	+	5.26385i	0.179291	+	0.551801i
$92$	−0.423613	+	1.30375i	−0.0441647	+	0.135925i
$93$	8.18668	+	5.94797i	0.848920	+	0.616776i
$94$	3.38540	+	2.45964i	0.349178	+	0.253692i
$95$	−0.595250	+	1.83199i	−0.0610714	+	0.187958i
$96$	0.309017	+	0.951057i	0.0315389	+	0.0970668i
$97$	−4.62703	+	3.36174i	−0.469804	+	0.341333i	−0.797365	−	0.603497i	$-0.793773\pi$
$97$	−4.62703	+	3.36174i	−0.469804	+	0.341333i	0.327561	+	0.944830i	$0.393773\pi$
$98$	−1.00000			−0.101015
$99$	−2.07639	+	2.58624i	−0.208685	+	0.259927i
$100$	−0.584557			−0.0584557
$101$	−4.80128	+	3.48833i	−0.477745	+	0.347102i	−0.800452	−	0.599397i	$-0.795407\pi$
$101$	−4.80128	+	3.48833i	−0.477745	+	0.347102i	0.322707	+	0.946499i	$0.395407\pi$
$102$	0.572949	+	1.76336i	0.0567304	+	0.174598i
$103$	1.25703	−	3.86873i	0.123858	−	0.381197i	−0.869833	−	0.493346i	$-0.835774\pi$
$103$	1.25703	−	3.86873i	0.123858	−	0.381197i	0.993691	+	0.112149i	$0.0357735\pi$
$104$	−4.47770	−	3.25324i	−0.439074	−	0.319006i
$105$	1.69998	+	1.23511i	0.165901	+	0.120534i
$106$	2.20081	−	6.77341i	0.213762	−	0.657892i
$107$	2.77933	+	8.55389i	0.268688	+	0.826935i	0.990821	+	0.135181i	$0.0431617\pi$
$107$	2.77933	+	8.55389i	0.268688	+	0.826935i	−0.722133	+	0.691754i	$0.756838\pi$
$108$	0.809017	−	0.587785i	0.0778477	−	0.0565597i
$109$	−11.3374			−1.08592			−0.542961	−	0.839758i	$-0.682697\pi$
$109$	−11.3374			−1.08592			−0.542961	+	0.839758i	$0.682697\pi$
$110$	6.72411	−	1.83199i	0.641119	−	0.174674i
$111$	−3.60691			−0.342353
$112$	0.809017	−	0.587785i	0.0764449	−	0.0555405i
$113$	0.263419	+	0.810719i	0.0247803	+	0.0762660i	0.962682	−	0.270635i	$-0.0872338\pi$
$113$	0.263419	+	0.810719i	0.0247803	+	0.0762660i	−0.937902	+	0.346902i	$0.887234\pi$
$114$	0.283278	−	0.871839i	0.0265314	−	0.0816552i
$115$	−2.33041	−	1.69314i	−0.217312	−	0.157886i
$116$	−1.76737	−	1.28407i	−0.164096	−	0.119223i
$117$	−1.71033	+	5.26385i	−0.158120	+	0.486643i
$118$	−2.67508	−	8.23304i	−0.246261	−	0.757912i
$119$	1.50000	−	1.08981i	0.137505	−	0.0999031i
$120$	−2.10130			−0.191821
$121$	9.47979	−	5.57974i	0.861799	−	0.507249i
$122$	5.08061			0.459976
$123$	9.04635	−	6.57256i	0.815682	−	0.592627i
$124$	3.12703	+	9.62402i	0.280816	+	0.864263i
$125$	3.62625	−	11.1605i	0.324342	−	0.998222i
$126$	−0.809017	−	0.587785i	−0.0720730	−	0.0523641i
$127$	−10.7429	−	7.80517i	−0.953278	−	0.692597i	−0.00169787	−	0.999999i	$-0.500540\pi$
$127$	−10.7429	−	7.80517i	−0.953278	−	0.692597i	−0.951580	+	0.307402i	$0.900540\pi$
$128$	−0.309017	+	0.951057i	−0.0273135	+	0.0840623i
$129$	1.90771	+	5.87131i	0.167964	+	0.516940i
$130$	9.40897	−	6.83602i	0.825221	−	0.599558i
$131$	−10.3347			−0.902945			−0.451472	−	0.892285i	$-0.649101\pi$
$131$	−10.3347			−0.902945			−0.451472	+	0.892285i	$0.649101\pi$
$132$	−3.19998	+	0.871839i	−0.278523	+	0.0758839i
$133$	−0.916706			−0.0794885
$134$	−7.72833	+	5.61496i	−0.667626	+	0.485059i
$135$	0.649336	+	1.99845i	0.0558859	+	0.171999i
$136$	−0.572949	+	1.76336i	−0.0491300	+	0.151207i
$137$	−11.1047	−	8.06806i	−0.948741	−	0.689301i	0.00176745	−	0.999998i	$-0.499437\pi$
$137$	−11.1047	−	8.06806i	−0.948741	−	0.689301i	−0.950509	+	0.310697i	$0.899437\pi$
$138$	1.10903	+	0.805760i	0.0944072	+	0.0685908i
$139$	−3.19998	+	9.84854i	−0.271419	+	0.835342i	0.718726	+	0.695294i	$0.244726\pi$
$139$	−3.19998	+	9.84854i	−0.271419	+	0.835342i	−0.990145	+	0.140048i	$0.955274\pi$
$140$	0.649336	+	1.99845i	0.0548789	+	0.168900i
$141$	3.38540	−	2.45964i	0.285102	−	0.207139i
$142$	−1.43866			−0.120730
$143$	11.4923	−	14.3141i	0.961031	−	1.19701i
$144$	1.00000			0.0833333
$145$	3.71377	−	2.69821i	0.308412	−	0.224074i
$146$	4.05704	+	12.4863i	0.335763	+	1.03337i
$147$	−0.309017	+	0.951057i	−0.0254873	+	0.0784418i
$148$	−2.91805	−	2.12009i	−0.239862	−	0.174270i
$149$	7.23607	+	5.25731i	0.592802	+	0.430696i	0.843317	−	0.537417i	$-0.180600\pi$
$149$	7.23607	+	5.25731i	0.592802	+	0.430696i	−0.250515	+	0.968113i	$0.580600\pi$
$150$	−0.180638	+	0.555947i	−0.0147490	+	0.0453929i
$151$	−5.54374	−	17.0619i	−0.451143	−	1.38848i	−0.875604	−	0.483030i	$-0.839536\pi$
$151$	−5.54374	−	17.0619i	−0.451143	−	1.38848i	0.424461	−	0.905446i	$-0.360464\pi$
$152$	0.741631	−	0.538826i	0.0601542	−	0.0437046i
$153$	1.85410			0.149895
$154$	1.81802	+	2.77395i	0.146500	+	0.223531i
$155$	−21.2636			−1.70794
$156$	−4.47770	+	3.25324i	−0.358503	+	0.260468i
$157$	−0.133111	−	0.409674i	−0.0106234	−	0.0326955i	0.945604	−	0.325319i	$-0.105472\pi$
$157$	−0.133111	−	0.409674i	−0.0106234	−	0.0326955i	−0.956228	+	0.292624i	$0.905472\pi$
$158$	−5.48882	+	16.8929i	−0.436667	+	1.34392i
$159$	−5.76181	−	4.18620i	−0.456941	−	0.331987i
$160$	−1.69998	−	1.23511i	−0.134396	−	0.0976441i
$161$	0.423613	−	1.30375i	0.0333854	−	0.102750i
$162$	−0.309017	−	0.951057i	−0.0242787	−	0.0747221i
$163$	14.5623	−	10.5801i	1.14061	−	0.828700i	0.153404	−	0.988164i	$-0.450976\pi$
$163$	14.5623	−	10.5801i	1.14061	−	0.828700i	0.987204	+	0.159463i	$0.0509764\pi$
$164$	11.1819			0.873160
$165$	0.335537	−	6.96113i	0.0261215	−	0.541923i
$166$	11.5527			0.896667
$167$	5.65060	−	4.10540i	0.437256	−	0.317685i	−0.347287	−	0.937759i	$-0.612897\pi$
$167$	5.65060	−	4.10540i	0.437256	−	0.317685i	0.784544	+	0.620073i	$0.212897\pi$
$168$	−0.309017	−	0.951057i	−0.0238412	−	0.0733756i
$169$	5.44900	−	16.7703i	0.419154	−	1.29002i
$170$	−3.15194	−	2.29002i	−0.241743	−	0.175637i
$171$	−0.741631	−	0.538826i	−0.0567139	−	0.0412051i
$172$	−1.90771	+	5.87131i	−0.145461	+	0.447683i
$173$	4.57260	+	14.0730i	0.347648	+	1.06995i	0.960151	+	0.279483i	$0.0901630\pi$
$173$	4.57260	+	14.0730i	0.347648	+	1.06995i	−0.612502	+	0.790469i	$0.709837\pi$
$174$	−1.76737	+	1.28407i	−0.133984	+	0.0973451i
$175$	0.584557			0.0441884
$176$	−3.10130	−	1.17557i	−0.233769	−	0.0886120i
$177$	−8.65673			−0.650679
$178$	3.13604	−	2.27846i	0.235056	−	0.170778i
$179$	4.58886	+	14.1230i	0.342987	+	1.05561i	0.962653	+	0.270740i	$0.0872684\pi$
$179$	4.58886	+	14.1230i	0.342987	+	1.05561i	−0.619665	+	0.784866i	$0.712732\pi$
$180$	−0.649336	+	1.99845i	−0.0483987	+	0.148956i
$181$	−8.14721	−	5.91930i	−0.605577	−	0.439978i	0.242277	−	0.970207i	$-0.422106\pi$
$181$	−8.14721	−	5.91930i	−0.605577	−	0.439978i	−0.847854	+	0.530229i	$0.822106\pi$
$182$	4.47770	+	3.25324i	0.331909	+	0.241146i
$183$	1.56999	−	4.83194i	0.116057	−	0.357188i
$184$	0.423613	+	1.30375i	0.0312292	+	0.0961135i
$185$	6.13169	−	4.45493i	0.450811	−	0.327533i
$186$	10.1193			0.741983
$187$	−5.75012	−	2.17963i	−0.420490	−	0.159390i
$188$	4.18459			0.305193
$189$	−0.809017	+	0.587785i	−0.0588473	+	0.0427551i
$190$	0.595250	+	1.83199i	0.0431840	+	0.132907i
$191$	1.72707	−	5.31537i	0.124966	−	0.384606i	−0.868929	−	0.494937i	$-0.835191\pi$
$191$	1.72707	−	5.31537i	0.124966	−	0.384606i	0.993895	+	0.110331i	$0.0351910\pi$
$192$	0.809017	+	0.587785i	0.0583858	+	0.0424197i
$193$	7.59221	+	5.51607i	0.546500	+	0.397055i	0.826493	−	0.562947i	$-0.190332\pi$
$193$	7.59221	+	5.51607i	0.546500	+	0.397055i	−0.279994	+	0.960002i	$0.590332\pi$
$194$	−1.76737	+	5.43941i	−0.126890	+	0.390527i
$195$	−3.59391	−	11.0609i	−0.257365	−	0.792088i
$196$	−0.809017	+	0.587785i	−0.0577869	+	0.0419847i
$197$	−19.0137			−1.35467			−0.677333	−	0.735676i	$-0.736864\pi$
$197$	−19.0137			−1.35467			−0.677333	+	0.735676i	$0.736864\pi$
$198$	−0.159681	+	3.31278i	−0.0113480	+	0.235429i
$199$	−13.2816			−0.941510			−0.470755	−	0.882264i	$-0.656018\pi$
$199$	−13.2816			−0.941510			−0.470755	+	0.882264i	$0.656018\pi$
$200$	−0.472917	+	0.343594i	−0.0334403	+	0.0242958i
$201$	2.95196	+	9.08520i	0.208215	+	0.640820i
$202$	−1.83393	+	5.64424i	−0.129035	+	0.397128i
$203$	1.76737	+	1.28407i	0.124045	+	0.0901240i
$204$	1.50000	+	1.08981i	0.105021	+	0.0763022i
$205$	−7.26081	+	22.3465i	−0.507117	+	1.56075i
$206$	−1.25703	−	3.86873i	−0.0875811	−	0.269547i
$207$	1.10903	−	0.805760i	0.0770831	−	0.0560042i
$208$	−5.53474			−0.383765
$209$	1.66659	+	2.54290i	0.115280	+	0.175896i
$210$	2.10130			0.145003
$211$	19.8656	−	14.4332i	1.36761	−	0.993624i	0.369687	−	0.929157i	$-0.379465\pi$
$211$	19.8656	−	14.4332i	1.36761	−	0.993624i	0.997920	−	0.0644676i	$-0.0205349\pi$
$212$	−2.20081	−	6.77341i	−0.151153	−	0.465200i
$213$	−0.444570	+	1.36825i	−0.0304614	+	0.0937507i
$214$	7.27637	+	5.28659i	0.497402	+	0.361384i
$215$	−10.4948	−	7.62491i	−0.715739	−	0.520015i
$216$	0.309017	−	0.951057i	0.0210259	−	0.0647112i
$217$	−3.12703	−	9.62402i	−0.212277	−	0.653321i
$218$	−9.17212	+	6.66394i	−0.621214	+	0.451339i
$219$	13.1289			0.887166
$220$	4.36310	−	5.43445i	0.294160	−	0.366390i
$221$	−10.2620			−0.690295
$222$	−2.91805	+	2.12009i	−0.195847	+	0.142291i
$223$	5.86227	+	18.0422i	0.392567	+	1.20820i	0.930840	+	0.365426i	$0.119077\pi$
$223$	5.86227	+	18.0422i	0.392567	+	1.20820i	−0.538274	+	0.842770i	$0.680923\pi$
$224$	0.309017	−	0.951057i	0.0206471	−	0.0635451i
$225$	0.472917	+	0.343594i	0.0315278	+	0.0229063i
$226$	0.689639	+	0.501052i	0.0458741	+	0.0333295i
$227$	7.40209	−	22.7813i	0.491294	−	1.51205i	−0.331359	−	0.943505i	$-0.607507\pi$
$227$	7.40209	−	22.7813i	0.491294	−	1.51205i	0.822653	−	0.568543i	$-0.192493\pi$
$228$	−0.283278	−	0.871839i	−0.0187605	−	0.0577390i
$229$	9.56443	−	6.94897i	0.632035	−	0.459201i	−0.225069	−	0.974343i	$-0.572261\pi$
$229$	9.56443	−	6.94897i	0.632035	−	0.459201i	0.857105	+	0.515142i	$0.172261\pi$
$230$	−2.88054			−0.189937
$231$	3.19998	−	0.871839i	0.210543	−	0.0573628i
$232$	−2.18459			−0.143425
$233$	14.7519	−	10.7179i	0.966429	−	0.702152i	0.0117939	−	0.999930i	$-0.496246\pi$
$233$	14.7519	−	10.7179i	0.966429	−	0.702152i	0.954635	+	0.297779i	$0.0962458\pi$
$234$	1.71033	+	5.26385i	0.111808	+	0.344109i
$235$	−2.71720	+	8.36270i	−0.177251	+	0.545522i
$236$	−7.00344	−	5.08830i	−0.455885	−	0.331220i
$237$	14.3699	+	10.4404i	0.933427	+	0.678175i
$238$	0.572949	−	1.76336i	0.0371388	−	0.114301i
$239$	−1.93766	−	5.96351i	−0.125337	−	0.385748i	0.868625	−	0.495470i	$-0.165004\pi$
$239$	−1.93766	−	5.96351i	−0.125337	−	0.385748i	−0.993962	+	0.109722i	$0.965004\pi$
$240$	−1.69998	+	1.23511i	−0.109733	+	0.0797260i
$241$	−16.3167			−1.05105			−0.525525	−	0.850778i	$-0.676131\pi$
$241$	−16.3167			−1.05105			−0.525525	+	0.850778i	$0.676131\pi$
$242$	4.38962	−	10.0862i	0.282176	−	0.648365i
$243$	−1.00000			−0.0641500
$244$	4.11030	−	2.98631i	0.263135	−	0.191179i
$245$	−0.649336	−	1.99845i	−0.0414846	−	0.127676i
$246$	3.45540	−	10.6346i	0.220308	−	0.678039i
$247$	4.10473	+	2.98226i	0.261178	+	0.189757i
$248$	8.18668	+	5.94797i	0.519855	+	0.377697i
$249$	3.56999	−	10.9873i	0.226239	−	0.696292i
$250$	−3.62625	−	11.1605i	−0.229344	−	0.705850i
$251$	−18.0657	+	13.1255i	−1.14030	+	0.828474i	−0.987161	−	0.159731i	$-0.948937\pi$
$251$	−18.0657	+	13.1255i	−1.14030	+	0.828474i	−0.153136	+	0.988205i	$0.548937\pi$
$252$	−1.00000			−0.0629941
$253$	−4.38667	+	1.19515i	−0.275787	+	0.0751386i
$254$	−13.2789			−0.833195
$255$	−3.15194	+	2.29002i	−0.197382	+	0.143407i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	6.42539	−	19.7753i	0.400805	−	1.23355i	−0.523543	−	0.851999i	$-0.675390\pi$
$257$	6.42539	−	19.7753i	0.400805	−	1.23355i	0.924348	−	0.381551i	$-0.124610\pi$
$258$	4.99444	+	3.62867i	0.310940	+	0.225911i
$259$	2.91805	+	2.12009i	0.181319	+	0.131736i
$260$	3.59391	−	11.0609i	0.222885	−	0.685968i
$261$	0.675075	+	2.07767i	0.0417861	+	0.128604i
$262$	−8.36093	+	6.07457i	−0.516540	+	0.375288i
$263$	0.337364			0.0208027			0.0104014	−	0.999946i	$-0.496689\pi$
$263$	0.337364			0.0208027			0.0104014	+	0.999946i	$0.496689\pi$
$264$	−2.07639	+	2.58624i	−0.127793	+	0.159172i
$265$	14.9654			0.919317
$266$	−0.741631	+	0.538826i	−0.0454723	+	0.0330376i
$267$	−1.19786	−	3.68663i	−0.0733078	−	0.225618i
$268$	−2.95196	+	9.08520i	−0.180320	+	0.554967i
$269$	−14.8928	−	10.8202i	−0.908030	−	0.659722i	0.0324861	−	0.999472i	$-0.489658\pi$
$269$	−14.8928	−	10.8202i	−0.908030	−	0.659722i	−0.940516	+	0.339750i	$0.889658\pi$
$270$	1.69998	+	1.23511i	0.103458	+	0.0751664i
$271$	−5.10312	+	15.7058i	−0.309993	+	0.954059i	0.667774	+	0.744364i	$0.267247\pi$
$271$	−5.10312	+	15.7058i	−0.309993	+	0.954059i	−0.977767	+	0.209695i	$0.932753\pi$
$272$	0.572949	+	1.76336i	0.0347401	+	0.106919i
$273$	4.47770	−	3.25324i	0.271003	−	0.196895i
$274$	−13.7262			−0.829230
$275$	−1.06274	−	1.62153i	−0.0640853	−	0.0977821i
$276$	1.37084			0.0825149
$277$	3.47431	−	2.52423i	0.208751	−	0.151667i	−0.478497	−	0.878089i	$-0.658818\pi$
$277$	3.47431	−	2.52423i	0.208751	−	0.151667i	0.687248	+	0.726422i	$0.258818\pi$
$278$	3.19998	+	9.84854i	0.191922	+	0.590676i
$279$	3.12703	−	9.62402i	0.187211	−	0.576175i
$280$	1.69998	+	1.23511i	0.101593	+	0.0738120i
$281$	22.0546	+	16.0236i	1.31567	+	0.955887i	0.999975	+	0.00702433i	$0.00223593\pi$
$281$	22.0546	+	16.0236i	1.31567	+	0.955887i	0.315690	+	0.948862i	$0.397764\pi$
$282$	1.29311	−	3.97978i	0.0770035	−	0.236993i
$283$	−5.23446	−	16.1100i	−0.311156	−	0.957640i	−0.977308	−	0.211824i	$-0.932060\pi$
$283$	−5.23446	−	16.1100i	−0.311156	−	0.957640i	0.666152	−	0.745816i	$-0.267940\pi$
$284$	−1.16390	+	0.845623i	−0.0690647	+	0.0501785i
$285$	1.92627			0.114102
$286$	0.883793	−	18.3354i	0.0522598	−	1.08419i
$287$	−11.1819			−0.660047
$288$	0.809017	−	0.587785i	0.0476718	−	0.0346356i
$289$	−4.19098	−	12.8985i	−0.246528	−	0.758736i
$290$	1.41853	−	4.36579i	0.0832991	−	0.256368i
$291$	4.62703	+	3.36174i	0.271242	+	0.197069i
$292$	10.6215	+	7.71695i	0.621575	+	0.451600i
$293$	1.64934	−	5.07613i	0.0963552	−	0.296551i	−0.891249	−	0.453514i	$-0.850170\pi$
$293$	1.64934	−	5.07613i	0.0963552	−	0.296551i	0.987605	+	0.156963i	$0.0501703\pi$
$294$	0.309017	+	0.951057i	0.0180222	+	0.0554667i
$295$	14.7163	−	10.6920i	0.856816	−	0.622513i
$296$	−3.60691			−0.209647
$297$	3.10130	+	1.17557i	0.179955	+	0.0682135i
$298$	8.94427			0.518128
$299$	−6.13821	+	4.45967i	−0.354982	+	0.257909i
$300$	0.180638	+	0.555947i	0.0104291	+	0.0320976i
$301$	1.90771	−	5.87131i	0.109958	−	0.338417i
$302$	−14.5137	−	10.5448i	−0.835170	−	0.606786i
$303$	4.80128	+	3.48833i	0.275826	+	0.200400i
$304$	0.283278	−	0.871839i	0.0162471	−	0.0500034i
$305$	3.29902	+	10.1533i	0.188901	+	0.581379i
$306$	1.50000	−	1.08981i	0.0857493	−	0.0623005i
$307$	10.4137			0.594342			0.297171	−	0.954824i	$-0.403957\pi$
$307$	10.4137			0.594342			0.297171	+	0.954824i	$0.403957\pi$
$308$	3.10130	+	1.17557i	0.176713	+	0.0669843i
$309$	−4.06782			−0.231410
$310$	−17.2026	+	12.4985i	−0.977044	+	0.709864i
$311$	−7.18012	−	22.0982i	−0.407148	−	1.25307i	−0.919089	−	0.394051i	$-0.871073\pi$
$311$	−7.18012	−	22.0982i	−0.407148	−	1.25307i	0.511941	−	0.859021i	$-0.328927\pi$
$312$	−1.71033	+	5.26385i	−0.0968283	+	0.298007i
$313$	11.1915	+	8.13108i	0.632579	+	0.459596i	0.857293	−	0.514829i	$-0.172145\pi$
$313$	11.1915	+	8.13108i	0.632579	+	0.459596i	−0.224714	+	0.974425i	$0.572145\pi$
$314$	−0.348489	−	0.253192i	−0.0196664	−	0.0142885i
$315$	0.649336	−	1.99845i	0.0365859	−	0.112600i
$316$	5.48882	+	16.8929i	0.308770	+	0.950298i
$317$	12.2631	−	8.90964i	0.688763	−	0.500415i	−0.187490	−	0.982266i	$-0.560035\pi$
$317$	12.2631	−	8.90964i	0.688763	−	0.500415i	0.876253	+	0.481851i	$0.160035\pi$
$318$	−7.12199			−0.399381
$319$	0.348837	−	7.23706i	0.0195311	−	0.405198i
$320$	−2.10130			−0.117466
$321$	7.27637	−	5.28659i	0.406127	−	0.295069i
$322$	−0.423613	−	1.30375i	−0.0236070	−	0.0726550i
$323$	0.525226	−	1.61648i	0.0292243	−	0.0899433i
$324$	−0.809017	−	0.587785i	−0.0449454	−	0.0326547i
$325$	−2.61747	−	1.90170i	−0.145191	−	0.105488i
$326$	5.56231	−	17.1190i	0.308068	−	0.948135i
$327$	3.50344	+	10.7825i	0.193741	+	0.596272i
$328$	9.04635	−	6.57256i	0.499501	−	0.362909i
$329$	−4.18459			−0.230704
$330$	−3.82019	−	5.82889i	−0.210295	−	0.320870i
$331$	3.28857			0.180756			0.0903782	−	0.995908i	$-0.471192\pi$
$331$	3.28857			0.180756			0.0903782	+	0.995908i	$0.471192\pi$
$332$	9.34636	−	6.79053i	0.512948	−	0.372679i
$333$	1.11460	+	3.43037i	0.0610795	+	0.187983i
$334$	2.15834	−	6.64268i	0.118099	−	0.363471i
$335$	−16.2395	−	11.7987i	−0.887259	−	0.644631i
$336$	−0.809017	−	0.587785i	−0.0441355	−	0.0320663i
$337$	−1.96526	+	6.04845i	−0.107055	+	0.329480i	−0.990207	−	0.139606i	$-0.955416\pi$
$337$	−1.96526	+	6.04845i	−0.107055	+	0.329480i	0.883153	+	0.469086i	$0.155416\pi$
$338$	−5.44900	−	16.7703i	−0.296387	−	0.912185i
$339$	0.689639	−	0.501052i	0.0374560	−	0.0272134i
$340$	−3.89602			−0.211291
$341$	−21.0116	+	26.1709i	−1.13784	+	1.41723i
$342$	−0.916706			−0.0495698
$343$	0.809017	−	0.587785i	0.0436828	−	0.0317374i
$344$	1.90771	+	5.87131i	0.102857	+	0.316560i
$345$	−0.890136	+	2.73956i	−0.0479233	+	0.147493i
$346$	11.9712	+	8.69760i	0.643577	+	0.467586i
$347$	3.45835	+	2.51264i	0.185654	+	0.134886i	0.676730	−	0.736231i	$-0.263396\pi$
$347$	3.45835	+	2.51264i	0.185654	+	0.134886i	−0.491076	+	0.871117i	$0.663396\pi$
$348$	−0.675075	+	2.07767i	−0.0361878	+	0.111375i
$349$	9.28032	+	28.5619i	0.496764	+	1.52888i	0.814189	+	0.580600i	$0.197182\pi$
$349$	9.28032	+	28.5619i	0.496764	+	1.52888i	−0.317425	+	0.948283i	$0.602818\pi$
$350$	0.472917	−	0.343594i	0.0252785	−	0.0183659i
$351$	5.53474			0.295423
$352$	−3.19998	+	0.871839i	−0.170560	+	0.0464692i
$353$	−0.269545			−0.0143464			−0.00717321	−	0.999974i	$-0.502283\pi$
$353$	−0.269545			−0.0143464			−0.00717321	+	0.999974i	$0.502283\pi$
$354$	−7.00344	+	5.08830i	−0.372229	+	0.270440i
$355$	−0.934173	−	2.87509i	−0.0495808	−	0.152594i
$356$	1.19786	−	3.68663i	0.0634864	−	0.195391i
$357$	−1.50000	−	1.08981i	−0.0793884	−	0.0576791i
$358$	12.0138	+	8.72852i	0.634948	+	0.461317i
$359$	−1.31162	+	4.03676i	−0.0692249	+	0.213052i	−0.979684	−	0.200546i	$-0.935728\pi$
$359$	−1.31162	+	4.03676i	−0.0692249	+	0.213052i	0.910459	+	0.413599i	$0.135728\pi$
$360$	0.649336	+	1.99845i	0.0342230	+	0.105328i
$361$	14.6915	−	10.6740i	0.773235	−	0.561788i
$362$	−10.0705			−0.529294
$363$	−8.23607	−	7.29158i	−0.432281	−	0.382709i
$364$	5.53474			0.290099
$365$	−22.3189	+	16.2156i	−1.16822	+	0.848763i
$366$	−1.56999	−	4.83194i	−0.0820649	−	0.252570i
$367$	−3.70047	+	11.3889i	−0.193163	+	0.594494i	0.806830	+	0.590783i	$0.201181\pi$
$367$	−3.70047	+	11.3889i	−0.193163	+	0.594494i	−0.999993	+	0.00371067i	$0.998819\pi$
$368$	1.10903	+	0.805760i	0.0578124	+	0.0420031i
$369$	−9.04635	−	6.57256i	−0.470934	−	0.342154i
$370$	2.34210	−	7.20823i	0.121760	−	0.374738i
$371$	2.20081	+	6.77341i	0.114261	+	0.351658i
$372$	8.18668	−	5.94797i	0.424460	−	0.308388i
$373$	11.5537			0.598228			0.299114	−	0.954217i	$-0.403309\pi$
$373$	11.5537			0.598228			0.299114	+	0.954217i	$0.403309\pi$
$374$	−5.93310	+	1.61648i	−0.306793	+	0.0835861i
$375$	−11.7348			−0.605983
$376$	3.38540	−	2.45964i	0.174589	−	0.126846i
$377$	−3.73637	−	11.4994i	−0.192433	−	0.592247i
$378$	−0.309017	+	0.951057i	−0.0158941	+	0.0489171i
$379$	18.6782	+	13.5705i	0.959433	+	0.697069i	0.953019	−	0.302911i	$-0.0979584\pi$
$379$	18.6782	+	13.5705i	0.959433	+	0.697069i	0.00641393	+	0.999979i	$0.497958\pi$
$380$	1.55839	+	1.13223i	0.0799435	+	0.0580823i
$381$	−4.10342	+	12.6290i	−0.210225	+	0.647005i
$382$	−1.72707	−	5.31537i	−0.0883644	−	0.271958i
$383$	25.8275	−	18.7648i	1.31972	−	0.958835i	0.319788	−	0.947489i	$-0.396388\pi$
$383$	25.8275	−	18.7648i	1.31972	−	0.958835i	0.999936	−	0.0113462i	$-0.00361170\pi$
$384$	1.00000			0.0510310
$385$	−4.36310	+	5.43445i	−0.222364	+	0.276965i
$386$	9.38449			0.477658
$387$	4.99444	−	3.62867i	0.253882	−	0.184456i
$388$	1.76737	+	5.43941i	0.0897246	+	0.276144i
$389$	−7.44078	+	22.9004i	−0.377263	+	1.16110i	0.564677	+	0.825312i	$0.309001\pi$
$389$	−7.44078	+	22.9004i	−0.377263	+	1.16110i	−0.941939	+	0.335783i	$0.890999\pi$
$390$	−9.40897	−	6.83602i	−0.476442	−	0.346155i
$391$	2.05626	+	1.49396i	0.103990	+	0.0755528i
$392$	−0.309017	+	0.951057i	−0.0156077	+	0.0480356i
$393$	3.19359	+	9.82886i	0.161095	+	0.495800i
$394$	−15.3824	+	11.1759i	−0.774952	+	0.563036i
$395$	−37.3236			−1.87796
$396$	1.81802	+	2.77395i	0.0913588	+	0.139396i
$397$	4.69960			0.235866			0.117933	−	0.993022i	$-0.462373\pi$
$397$	4.69960			0.235866			0.117933	+	0.993022i	$0.462373\pi$
$398$	−10.7451	+	7.80675i	−0.538602	+	0.391317i
$399$	0.283278	+	0.871839i	0.0141816	+	0.0436466i
$400$	−0.180638	+	0.555947i	−0.00903190	+	0.0277973i
$401$	22.2519	+	16.1670i	1.11121	+	0.807341i	0.982854	−	0.184388i	$-0.0590302\pi$
$401$	22.2519	+	16.1670i	1.11121	+	0.807341i	0.128355	+	0.991728i	$0.459030\pi$
$402$	7.72833	+	5.61496i	0.385454	+	0.280049i
$403$	−17.3073	+	53.2665i	−0.862139	+	2.65339i
$404$	1.83393	+	5.64424i	0.0912412	+	0.280812i
$405$	1.69998	−	1.23511i	0.0844729	−	0.0613731i
$406$	2.18459			0.108419
$407$	0.575955	−	11.9489i	0.0285490	−	0.592284i
$408$	1.85410			0.0917917
$409$	15.2636	−	11.0897i	0.754738	−	0.548349i	−0.142554	−	0.989787i	$-0.545531\pi$
$409$	15.2636	−	11.0897i	0.754738	−	0.548349i	0.897292	+	0.441438i	$0.145531\pi$
$410$	7.26081	+	22.3465i	0.358586	+	1.10361i
$411$	−4.24163	+	13.0544i	−0.209224	+	0.643926i
$412$	−3.29093	−	2.39100i	−0.162133	−	0.117796i
$413$	7.00344	+	5.08830i	0.344617	+	0.250379i
$414$	0.423613	−	1.30375i	0.0208194	−	0.0640757i
$415$	7.50161	+	23.0876i	0.368240	+	1.13333i
$416$	−4.47770	+	3.25324i	−0.219537	+	0.159503i
$417$	10.3554			0.507104
$418$	2.84298	+	1.07765i	0.139055	+	0.0527097i
$419$	−36.1743			−1.76723			−0.883614	−	0.468216i	$-0.844897\pi$
$419$	−36.1743			−1.76723			−0.883614	+	0.468216i	$0.844897\pi$
$420$	1.69998	−	1.23511i	0.0829507	−	0.0602672i
$421$	−7.53982	−	23.2052i	−0.367468	−	1.13095i	−0.948421	−	0.317014i	$-0.897320\pi$
$421$	−7.53982	−	23.2052i	−0.367468	−	1.13095i	0.580953	−	0.813937i	$-0.302680\pi$
$422$	7.58800	−	23.3534i	0.369378	−	1.13683i
$423$	−3.38540	−	2.45964i	−0.164604	−	0.119592i
$424$	−5.76181	−	4.18620i	−0.279818	−	0.203300i
$425$	−0.334921	+	1.03078i	−0.0162461	+	0.0500003i
$426$	0.444570	+	1.36825i	0.0215395	+	0.0662917i
$427$	−4.11030	+	2.98631i	−0.198911	+	0.144517i
$428$	8.99409			0.434746
$429$	−17.1649	−	6.50648i	−0.828727	−	0.314136i
$430$	−12.9723			−0.625579
$431$	−13.2880	+	9.65428i	−0.640059	+	0.465030i	−0.859871	−	0.510512i	$-0.829456\pi$
$431$	−13.2880	+	9.65428i	−0.640059	+	0.465030i	0.219811	+	0.975542i	$0.429456\pi$
$432$	−0.309017	−	0.951057i	−0.0148676	−	0.0457577i
$433$	12.0477	−	37.0790i	0.578975	−	1.78190i	−0.0432504	−	0.999064i	$-0.513771\pi$
$433$	12.0477	−	37.0790i	0.578975	−	1.78190i	0.622226	−	0.782838i	$-0.286229\pi$
$434$	−8.18668	−	5.94797i	−0.392973	−	0.285512i
$435$	−3.71377	−	2.69821i	−0.178061	−	0.129369i
$436$	−3.50344	+	10.7825i	−0.167784	+	0.516387i
$437$	−0.388329	−	1.19515i	−0.0185763	−	0.0571719i
$438$	10.6215	−	7.71695i	0.507514	−	0.368730i
$439$	−26.1297			−1.24710			−0.623552	−	0.781782i	$-0.714311\pi$
$439$	−26.1297			−1.24710			−0.623552	+	0.781782i	$0.714311\pi$
$440$	0.335537	−	6.96113i	0.0159961	−	0.331859i
$441$	1.00000			0.0476190
$442$	−8.30211	+	6.03184i	−0.394891	+	0.286905i
$443$	−8.41214	−	25.8899i	−0.399673	−	1.23007i	−0.925262	−	0.379328i	$-0.876155\pi$
$443$	−8.41214	−	25.8899i	−0.399673	−	1.23007i	0.525589	−	0.850738i	$-0.323845\pi$
$444$	−1.11460	+	3.43037i	−0.0528964	+	0.162798i
$445$	6.58974	+	4.78772i	0.312384	+	0.226960i
$446$	15.3476	+	11.1507i	0.726731	+	0.528001i
$447$	2.76393	−	8.50651i	0.130729	−	0.402344i
$448$	−0.309017	−	0.951057i	−0.0145997	−	0.0449332i
$449$	−32.2059	+	23.3989i	−1.51989	+	1.10426i	−0.558346	+	0.829608i	$0.688564\pi$
$449$	−32.2059	+	23.3989i	−1.51989	+	1.10426i	−0.961543	+	0.274656i	$0.911436\pi$
$450$	0.584557			0.0275563
$451$	20.3289	+	31.0181i	0.957250	+	1.46058i
$452$	0.852441			0.0400954
$453$	−14.5137	+	10.5448i	−0.681913	+	0.495439i
$454$	−7.40209	−	22.7813i	−0.347397	−	1.06918i
$455$	−3.59391	+	11.0609i	−0.168485	+	0.518543i
$456$	−0.741631	−	0.538826i	−0.0347300	−	0.0252329i
$457$	−5.74168	−	4.17158i	−0.268585	−	0.195138i	0.445338	−	0.895362i	$-0.353083\pi$
$457$	−5.74168	−	4.17158i	−0.268585	−	0.195138i	−0.713923	+	0.700224i	$0.753083\pi$
$458$	3.65329	−	11.2437i	0.170707	−	0.525382i
$459$	−0.572949	−	1.76336i	−0.0267430	−	0.0823064i
$460$	−2.33041	+	1.69314i	−0.108656	+	0.0789430i
$461$	16.7003			0.777811			0.388905	−	0.921278i	$-0.372853\pi$
$461$	16.7003			0.777811			0.388905	+	0.921278i	$0.372853\pi$
$462$	2.07639	−	2.58624i	0.0966023	−	0.120323i
$463$	20.5373			0.954448			0.477224	−	0.878782i	$-0.341643\pi$
$463$	20.5373			0.954448			0.477224	+	0.878782i	$0.341643\pi$
$464$	−1.76737	+	1.28407i	−0.0820481	+	0.0596114i
$465$	6.57082	+	20.2229i	0.304715	+	0.937815i
$466$	5.63472	−	17.3419i	0.261023	−	0.803348i
$467$	−4.90771	−	3.56566i	−0.227102	−	0.164999i	0.468416	−	0.883508i	$-0.344825\pi$
$467$	−4.90771	−	3.56566i	−0.227102	−	0.164999i	−0.695518	+	0.718509i	$0.744825\pi$
$468$	4.47770	+	3.25324i	0.206982	+	0.150381i
$469$	2.95196	−	9.08520i	0.136309	−	0.419515i
$470$	2.71720	+	8.36270i	0.125335	+	0.385742i
$471$	−0.348489	+	0.253192i	−0.0160575	+	0.0116665i
$472$	−8.65673			−0.398458
$473$	−19.7550	+	5.38227i	−0.908335	+	0.247477i
$474$	17.7622			0.815845
$475$	0.433526	−	0.314975i	0.0198915	−	0.0144520i
$476$	−0.572949	−	1.76336i	−0.0262611	−	0.0808233i
$477$	−2.20081	+	6.77341i	−0.100768	+	0.310133i
$478$	−5.07287	−	3.68565i	−0.232028	−	0.168578i
$479$	33.1537	+	24.0876i	1.51483	+	1.10059i	0.963975	+	0.265991i	$0.0856993\pi$
$479$	33.1537	+	24.0876i	1.51483	+	1.10059i	0.550858	+	0.834599i	$0.314301\pi$
$480$	−0.649336	+	1.99845i	−0.0296380	+	0.0912164i
$481$	−6.16900	−	18.9862i	−0.281282	−	0.865697i
$482$	−13.2005	+	9.59070i	−0.601265	+	0.436844i
$483$	−1.37084			−0.0623754
$484$	−2.37723	−	10.7401i	−0.108056	−	0.488184i
$485$	−12.0180			−0.545709
$486$	−0.809017	+	0.587785i	−0.0366978	+	0.0266625i
$487$	0.181151	+	0.557527i	0.00820876	+	0.0252640i	0.955077	−	0.296358i	$-0.0957721\pi$
$487$	0.181151	+	0.557527i	0.00820876	+	0.0252640i	−0.946868	+	0.321622i	$0.895772\pi$
$488$	1.56999	−	4.83194i	0.0710703	−	0.218732i
$489$	−14.5623	−	10.5801i	−0.658530	−	0.478450i
$490$	−1.69998	−	1.23511i	−0.0767974	−	0.0557966i
$491$	0.151194	−	0.465326i	0.00682327	−	0.0209999i	−0.947587	−	0.319498i	$-0.896486\pi$
$491$	0.151194	−	0.465326i	0.00682327	−	0.0209999i	0.954410	+	0.298498i	$0.0964857\pi$
$492$	−3.45540	−	10.6346i	−0.155781	−	0.479446i
$493$	−3.27688	+	2.38080i	−0.147583	+	0.107226i
$494$	5.07373			0.228278
$495$	−6.72411	+	1.83199i	−0.302226	+	0.0823419i
$496$	10.1193			0.454370
$497$	1.16390	−	0.845623i	0.0522080	−	0.0379314i
$498$	−3.56999	−	10.9873i	−0.159975	−	0.492353i
$499$	−4.95918	+	15.2628i	−0.222004	+	0.683257i	0.776578	+	0.630021i	$0.216954\pi$
$499$	−4.95918	+	15.2628i	−0.222004	+	0.683257i	−0.998582	+	0.0532361i	$0.983046\pi$
$500$	−9.49366	−	6.89755i	−0.424569	−	0.308468i
$501$	−5.65060	−	4.10540i	−0.252450	−	0.183416i
$502$	−6.90048	+	21.2375i	−0.307984	+	0.947876i
$503$	8.64114	+	26.5947i	0.385289	+	1.18580i	0.936270	+	0.351280i	$0.114254\pi$
$503$	8.64114	+	26.5947i	0.385289	+	1.18580i	−0.550981	+	0.834518i	$0.685746\pi$
$504$	−0.809017	+	0.587785i	−0.0360365	+	0.0261820i
$505$	−12.4706			−0.554933
$506$	−2.84640	+	3.54532i	−0.126538	+	0.157609i
$507$	−17.6333			−0.783124
$508$	−10.7429	+	7.80517i	−0.476639	+	0.346298i
$509$	−1.87159	−	5.76016i	−0.0829568	−	0.255315i	0.900972	−	0.433878i	$-0.142855\pi$
$509$	−1.87159	−	5.76016i	−0.0829568	−	0.255315i	−0.983928	+	0.178563i	$0.942855\pi$
$510$	−1.20394	+	3.70533i	−0.0533111	+	0.164075i
$511$	−10.6215	−	7.71695i	−0.469866	−	0.341378i
$512$	0.809017	+	0.587785i	0.0357538	+	0.0259767i
$513$	−0.283278	+	0.871839i	−0.0125070	+	0.0384926i
$514$	−6.42539	−	19.7753i	−0.283412	−	0.872252i
$515$	6.91523	−	5.02421i	0.304721	−	0.221393i
$516$	6.17346			0.271772
$517$	7.60766	+	11.6079i	0.334584	+	0.510513i
$518$	3.60691			0.158478
$519$	11.9712	−	8.69760i	0.525478	−	0.381782i
$520$	−3.59391	−	11.0609i	−0.157603	−	0.485053i
$521$	−0.590170	+	1.81636i	−0.0258558	+	0.0795760i	−0.963152	−	0.268958i	$-0.913321\pi$
$521$	−0.590170	+	1.81636i	−0.0258558	+	0.0795760i	0.937296	+	0.348534i	$0.113321\pi$
$522$	1.76737	+	1.28407i	0.0773557	+	0.0562022i
$523$	−11.9235	−	8.66295i	−0.521380	−	0.378804i	0.295744	−	0.955267i	$-0.404433\pi$
$523$	−11.9235	−	8.66295i	−0.521380	−	0.378804i	−0.817123	+	0.576463i	$0.804433\pi$
$524$	−3.19359	+	9.82886i	−0.139513	+	0.429376i
$525$	−0.180638	−	0.555947i	−0.00788369	−	0.0242635i
$526$	0.272933	−	0.198297i	0.0119004	−	0.00864617i
$527$	18.7622			0.817295
$528$	−0.159681	+	3.31278i	−0.00694922	+	0.144170i
$529$	−21.1208			−0.918296
$530$	12.1073	−	8.79644i	0.525906	−	0.382093i
$531$	2.67508	+	8.23304i	0.116088	+	0.357283i
$532$	−0.283278	+	0.871839i	−0.0122816	+	0.0377990i
$533$	50.0692	+	36.3774i	2.16874	+	1.57568i
$534$	−3.13604	−	2.27846i	−0.135710	−	0.0985987i
$535$	−5.84019	+	17.9742i	−0.252493	+	0.777094i
$536$	2.95196	+	9.08520i	0.127505	+	0.392421i
$537$	12.0138	−	8.72852i	0.518433	−	0.376664i
$538$	−18.4085			−0.793647
$539$	−3.10130	−	1.17557i	−0.133582	−	0.0506354i
$540$	2.10130			0.0904254
$541$	−25.9996	+	18.8898i	−1.11781	+	0.812137i	−0.983876	−	0.178853i	$-0.942761\pi$
$541$	−25.9996	+	18.8898i	−1.11781	+	0.812137i	−0.133935	+	0.990990i	$0.542761\pi$
$542$	5.10312	+	15.7058i	0.219198	+	0.674622i
$543$	−3.11196	+	9.57762i	−0.133547	+	0.411015i
$544$	1.50000	+	1.08981i	0.0643120	+	0.0467254i
$545$	−19.2733	−	14.0029i	−0.825579	−	0.599818i
$546$	1.71033	−	5.26385i	0.0731953	−	0.225272i
$547$	7.11455	+	21.8963i	0.304196	+	0.936219i	0.979976	+	0.199116i	$0.0638069\pi$
$547$	7.11455	+	21.8963i	0.304196	+	0.936219i	−0.675780	+	0.737103i	$0.736193\pi$
$548$	−11.1047	+	8.06806i	−0.474371	+	0.344650i
$549$	−5.08061			−0.216835
$550$	−1.81288	−	0.687188i	−0.0773016	−	0.0293018i
$551$	2.00263			0.0853148
$552$	1.10903	−	0.805760i	0.0472036	−	0.0342954i
$553$	−5.48882	−	16.8929i	−0.233409	−	0.718358i
$554$	1.32707	−	4.08430i	0.0563817	−	0.173525i
$555$	−6.13169	−	4.45493i	−0.260276	−	0.189101i
$556$	8.37767	+	6.08673i	0.355292	+	0.258135i
$557$	−10.5475	+	32.4620i	−0.446913	+	1.37546i	0.433459	+	0.901173i	$0.357293\pi$
$557$	−10.5475	+	32.4620i	−0.446913	+	1.37546i	−0.880372	+	0.474284i	$0.842707\pi$
$558$	−3.12703	−	9.62402i	−0.132378	−	0.407417i
$559$	−27.6429	+	20.0838i	−1.16917	+	0.849452i
$560$	2.10130			0.0887959
$561$	−0.296065	+	6.14223i	−0.0124999	+	0.259325i
$562$	27.2609			1.14993
$563$	26.8898	−	19.5366i	1.13327	−	0.823367i	0.147101	−	0.989121i	$-0.453006\pi$
$563$	26.8898	−	19.5366i	1.13327	−	0.823367i	0.986167	+	0.165754i	$0.0530058\pi$
$564$	−1.29311	−	3.97978i	−0.0544497	−	0.167579i
$565$	−0.553520	+	1.70356i	−0.0232868	+	0.0716693i
$566$	−13.7040	−	9.95653i	−0.576021	−	0.418504i
$567$	0.809017	+	0.587785i	0.0339755	+	0.0246847i
$568$	−0.444570	+	1.36825i	−0.0186537	+	0.0574103i
$569$	−4.85520	−	14.9428i	−0.203541	−	0.626433i	−0.999770	−	0.0214389i	$-0.993175\pi$
$569$	−4.85520	−	14.9428i	−0.203541	−	0.626433i	0.796230	−	0.604995i	$-0.206825\pi$
$570$	1.55839	−	1.13223i	0.0652736	−	0.0474240i
$571$	42.4136			1.77495			0.887476	−	0.460854i	$-0.152457\pi$
$571$	42.4136			1.77495			0.887476	+	0.460854i	$0.152457\pi$
$572$	−10.0623	−	15.3531i	−0.420724	−	0.641946i
$573$	−5.58891			−0.233480
$574$	−9.04635	+	6.57256i	−0.377587	+	0.274333i
$575$	0.247626	+	0.762114i	0.0103267	+	0.0317824i
$576$	0.309017	−	0.951057i	0.0128757	−	0.0396274i
$577$	−9.32836	−	6.77745i	−0.388345	−	0.282149i	0.376432	−	0.926444i	$-0.377151\pi$
$577$	−9.32836	−	6.77745i	−0.388345	−	0.282149i	−0.764777	+	0.644295i	$0.777151\pi$
$578$	−10.9721	−	7.97172i	−0.456381	−	0.331580i
$579$	2.89997	−	8.92518i	0.120519	−	0.370918i
$580$	−1.41853	−	4.36579i	−0.0589014	−	0.181280i
$581$	−9.34636	+	6.79053i	−0.387753	+	0.281719i
$582$	5.71933			0.237074
$583$	14.7880	−	18.4191i	0.612456	−	0.762843i
$584$	13.1289			0.543276
$585$	−9.40897	+	6.83602i	−0.389013	+	0.282634i
$586$	−1.64934	−	5.07613i	−0.0681334	−	0.209693i
$587$	2.42587	−	7.46607i	0.100126	−	0.308158i	−0.888429	−	0.459013i	$-0.848203\pi$
$587$	2.42587	−	7.46607i	0.100126	−	0.308158i	0.988556	+	0.150856i	$0.0482030\pi$
$588$	0.809017	+	0.587785i	0.0333633	+	0.0242399i
$589$	−7.50478	−	5.45254i	−0.309229	−	0.224668i
$590$	5.62112	−	17.3000i	0.231418	−	0.712231i
$591$	5.87554	+	18.0831i	0.241687	+	0.743838i
$592$	−2.91805	+	2.12009i	−0.119931	+	0.0871351i
$593$	15.9182			0.653682			0.326841	−	0.945079i	$-0.394016\pi$
$593$	15.9182			0.653682			0.326841	+	0.945079i	$0.394016\pi$
$594$	3.19998	−	0.871839i	0.131297	−	0.0357720i
$595$	3.89602			0.159721
$596$	7.23607	−	5.25731i	0.296401	−	0.215348i
$597$	4.10425	+	12.6316i	0.167976	+	0.516976i
$598$	−2.34459	+	7.21590i	−0.0958773	+	0.295080i
$599$	5.54769	+	4.03063i	0.226673	+	0.164687i	0.695325	−	0.718695i	$-0.255260\pi$
$599$	5.54769	+	4.03063i	0.226673	+	0.164687i	−0.468653	+	0.883383i	$0.655260\pi$
$600$	0.472917	+	0.343594i	0.0193067	+	0.0140272i
$601$	1.03079	−	3.17244i	0.0420467	−	0.129407i	−0.927830	−	0.373004i	$-0.878328\pi$
$601$	1.03079	−	3.17244i	0.0420467	−	0.129407i	0.969876	+	0.243598i	$0.0783277\pi$
$602$	−1.90771	−	5.87131i	−0.0777523	−	0.239297i
$603$	7.72833	−	5.61496i	0.314722	−	0.228659i
$604$	−17.9399			−0.729965
$605$	23.0071	+	2.22312i	0.935371	+	0.0903826i
$606$	5.93471			0.241081
$607$	13.4146	−	9.74626i	0.544481	−	0.395589i	−0.281265	−	0.959630i	$-0.590754\pi$
$607$	13.4146	−	9.74626i	0.544481	−	0.395589i	0.825747	+	0.564041i	$0.190754\pi$
$608$	−0.283278	−	0.871839i	−0.0114884	−	0.0353578i
$609$	0.675075	−	2.07767i	0.0273554	−	0.0841914i
$610$	8.63695	+	6.27511i	0.349700	+	0.254072i
$611$	18.7373	+	13.6135i	0.758031	+	0.550742i
$612$	0.572949	−	1.76336i	0.0231601	−	0.0712794i
$613$	−7.49887	−	23.0792i	−0.302877	−	0.932158i	−0.980461	−	0.196713i	$-0.936973\pi$
$613$	−7.49887	−	23.0792i	−0.302877	−	0.932158i	0.677585	−	0.735445i	$-0.263027\pi$
$614$	8.42488	−	6.12103i	0.340000	−	0.247025i
$615$	23.4965			0.947469
$616$	3.19998	−	0.871839i	0.128931	−	0.0351274i
$617$	29.3743			1.18257			0.591283	−	0.806464i	$-0.298622\pi$
$617$	29.3743			1.18257			0.591283	+	0.806464i	$0.298622\pi$
$618$	−3.29093	+	2.39100i	−0.132381	+	0.0961803i
$619$	−6.61965	−	20.3732i	−0.266066	−	0.818867i	−0.991446	−	0.130518i	$-0.958336\pi$
$619$	−6.61965	−	20.3732i	−0.266066	−	0.818867i	0.725380	−	0.688349i	$-0.241664\pi$
$620$	−6.57082	+	20.2229i	−0.263891	+	0.812172i
$621$	−1.10903	−	0.805760i	−0.0445040	−	0.0323340i
$622$	−18.7978	−	13.6574i	−0.753724	−	0.547612i
$623$	−1.19786	+	3.68663i	−0.0479912	+	0.147702i
$624$	1.71033	+	5.26385i	0.0684679	+	0.210723i
$625$	17.5844	−	12.7758i	0.703376	−	0.511032i
$626$	13.8334			0.552894
$627$	1.90344	−	2.37082i	0.0760159	−	0.0946814i
$628$	−0.430756			−0.0171890
$629$	−5.41036	+	3.93086i	−0.215725	+	0.156734i
$630$	−0.649336	−	1.99845i	−0.0258702	−	0.0796202i
$631$	−3.29786	+	10.1498i	−0.131286	+	0.404056i	−0.994994	−	0.0999364i	$-0.968136\pi$
$631$	−3.29786	+	10.1498i	−0.131286	+	0.404056i	0.863708	+	0.503992i	$0.168136\pi$
$632$	14.3699	+	10.4404i	0.571605	+	0.415295i
$633$	−19.8656	−	14.4332i	−0.789588	−	0.573669i
$634$	4.68408	−	14.4161i	0.186028	−	0.572537i
$635$	−8.62250	−	26.5373i	−0.342173	−	1.05310i
$636$	−5.76181	+	4.18620i	−0.228471	+	0.165994i
$637$	−5.53474			−0.219294
$638$	−3.97162	−	6.05995i	−0.157238	−	0.239916i
$639$	1.43866			0.0569125
$640$	−1.69998	+	1.23511i	−0.0671978	+	0.0488220i
$641$	−10.1600	−	31.2693i	−0.401296	−	1.23506i	−0.923949	−	0.382516i	$-0.875058\pi$
$641$	−10.1600	−	31.2693i	−0.401296	−	1.23506i	0.522653	−	0.852545i	$-0.324942\pi$
$642$	2.77933	−	8.55389i	0.109691	−	0.337595i
$643$	26.6857	+	19.3883i	1.05238	+	0.764601i	0.972664	−	0.232216i	$-0.0745978\pi$
$643$	26.6857	+	19.3883i	1.05238	+	0.764601i	0.0797188	+	0.996817i	$0.474598\pi$
$644$	−1.10903	−	0.805760i	−0.0437020	−	0.0317514i
$645$	−4.00865	+	12.3374i	−0.157841	+	0.485783i
$646$	−0.525226	−	1.61648i	−0.0206647	−	0.0635995i
$647$	29.7392	−	21.6068i	1.16917	−	0.849451i	0.178260	−	0.983983i	$-0.442953\pi$
$647$	29.7392	−	21.6068i	1.16917	−	0.849451i	0.990909	+	0.134533i	$0.0429533\pi$
$648$	−1.00000			−0.0392837
$649$	1.38231	−	28.6778i	0.0542606	−	1.12570i
$650$	−3.23537			−0.126902
$651$	−8.18668	+	5.94797i	−0.320861	+	0.233119i
$652$	−5.56231	−	17.1190i	−0.217837	−	0.670432i
$653$	4.95231	−	15.2416i	0.193799	−	0.596451i	−0.806190	−	0.591657i	$-0.798474\pi$
$653$	4.95231	−	15.2416i	0.193799	−	0.596451i	0.999989	−	0.00479421i	$-0.00152605\pi$
$654$	9.17212	+	6.66394i	0.358658	+	0.260580i
$655$	−17.5688	−	12.7645i	−0.686469	−	0.498749i
$656$	3.45540	−	10.6346i	0.134911	−	0.415212i
$657$	−4.05704	−	12.4863i	−0.158280	−	0.487137i
$658$	−3.38540	+	2.45964i	−0.131977	+	0.0958867i
$659$	15.0609			0.586691			0.293346	−	0.956006i	$-0.405231\pi$
$659$	15.0609			0.586691			0.293346	+	0.956006i	$0.405231\pi$
$660$	−6.51674	−	2.47022i	−0.253664	−	0.0961532i
$661$	21.9475			0.853659			0.426829	−	0.904332i	$-0.359631\pi$
$661$	21.9475			0.853659			0.426829	+	0.904332i	$0.359631\pi$
$662$	2.66051	−	1.93297i	0.103404	−	0.0751272i
$663$	3.17112	+	9.75972i	0.123156	+	0.379036i
$664$	3.56999	−	10.9873i	0.138543	−	0.426390i
$665$	−1.55839	−	1.13223i	−0.0604316	−	0.0439061i
$666$	2.91805	+	2.12009i	0.113072	+	0.0821517i
$667$	−0.925420	+	2.84815i	−0.0358324	+	0.110281i
$668$	−2.15834	−	6.64268i	−0.0835086	−	0.257013i
$669$	15.3476	−	11.1507i	0.593374	−	0.431111i
$670$	−20.0731			−0.775493
$671$	15.7565	+	5.97261i	0.608271	+	0.230570i
$672$	−1.00000			−0.0385758
$673$	−11.8430	+	8.60443i	−0.456513	+	0.331676i	−0.792162	−	0.610311i	$-0.791044\pi$
$673$	−11.8430	+	8.60443i	−0.456513	+	0.331676i	0.335649	+	0.941987i	$0.391044\pi$
$674$	1.96526	+	6.04845i	0.0756990	+	0.232978i
$675$	0.180638	−	0.555947i	0.00695276	−	0.0213984i
$676$	−14.2657	−	10.3646i	−0.548680	−	0.398639i
$677$	−21.1692	−	15.3803i	−0.813599	−	0.591114i	0.101273	−	0.994859i	$-0.467709\pi$
$677$	−21.1692	−	15.3803i	−0.813599	−	0.591114i	−0.914872	+	0.403744i	$0.867709\pi$
$678$	0.263419	−	0.810719i	0.0101165	−	0.0311355i
$679$	−1.76737	−	5.43941i	−0.0678254	−	0.208745i
$680$	−3.15194	+	2.29002i	−0.120872	+	0.0878183i
$681$	−23.9537			−0.917907
$682$	−1.61586	+	33.5230i	−0.0618744	+	1.28366i
$683$	1.96071			0.0750246			0.0375123	−	0.999296i	$-0.488057\pi$
$683$	1.96071			0.0750246			0.0375123	+	0.999296i	$0.488057\pi$
$684$	−0.741631	+	0.538826i	−0.0283570	+	0.0206025i
$685$	−8.91292	−	27.4311i	−0.340545	−	1.04809i
$686$	0.309017	−	0.951057i	0.0117983	−	0.0363115i
$687$	−9.56443	−	6.94897i	−0.364906	−	0.265120i
$688$	4.99444	+	3.62867i	0.190411	+	0.138342i
$689$	12.1809	−	37.4891i	0.464057	−	1.42822i
$690$	0.890136	+	2.73956i	0.0338869	+	0.104293i
$691$	2.15960	−	1.56904i	0.0821551	−	0.0596891i	−0.545950	−	0.837818i	$-0.683831\pi$
$691$	2.15960	−	1.56904i	0.0821551	−	0.0596891i	0.628105	+	0.778129i	$0.283831\pi$
$692$	14.7972			0.562507
$693$	−1.81802	−	2.77395i	−0.0690608	−	0.105374i
$694$	4.27476			0.162268
$695$	−17.6040	+	12.7900i	−0.667756	+	0.485153i
$696$	0.675075	+	2.07767i	0.0255887	+	0.0787538i
$697$	6.40666	−	19.7177i	0.242670	−	0.746860i
$698$	24.2962	+	17.6522i	0.919625	+	0.668146i
$699$	−14.7519	−	10.7179i	−0.557968	−	0.405387i
$700$	0.180638	−	0.555947i	0.00682748	−	0.0210128i
$701$	7.75624	+	23.8713i	0.292949	+	0.901605i	0.983903	+	0.178706i	$0.0571910\pi$
$701$	7.75624	+	23.8713i	0.292949	+	0.901605i	−0.690953	+	0.722899i	$0.742809\pi$
$702$	4.47770	−	3.25324i	0.169000	−	0.122786i
$703$	3.30647			0.124706
$704$	−2.07639	+	2.58624i	−0.0782568	+	0.0974724i
$705$	8.79306			0.331166
$706$	−0.218066	+	0.158435i	−0.00820704	+	0.00596276i
$707$	−1.83393	−	5.64424i	−0.0689719	−	0.212274i
$708$	−2.67508	+	8.23304i	−0.100535	+	0.309416i
$709$	−35.3841	−	25.7081i	−1.32888	−	0.965487i	−0.999775	−	0.0211925i	$-0.993254\pi$
$709$	−35.3841	−	25.7081i	−1.32888	−	0.965487i	−0.329103	−	0.944294i	$-0.606746\pi$
$710$	−2.44570	−	1.77690i	−0.0917854	−	0.0666860i
$711$	5.48882	−	16.8929i	0.205847	−	0.633532i
$712$	−1.19786	−	3.68663i	−0.0448917	−	0.138162i
$713$	11.2226	−	8.15372i	0.420291	−	0.305359i
$714$	−1.85410			−0.0693880
$715$	37.2162	−	10.1396i	1.39181	−	0.379200i
$716$	14.8499			0.554965
$717$	−5.07287	+	3.68565i	−0.189450	+	0.137643i
$718$	1.31162	+	4.03676i	0.0489494	+	0.150651i
$719$	−7.55199	+	23.2426i	−0.281642	+	0.866804i	0.705743	+	0.708468i	$0.250613\pi$
$719$	−7.55199	+	23.2426i	−0.281642	+	0.866804i	−0.987385	+	0.158337i	$0.949387\pi$
$720$	1.69998	+	1.23511i	0.0633547	+	0.0460299i
$721$	3.29093	+	2.39100i	0.122561	+	0.0890456i
$722$	5.61164	−	17.2709i	0.208844	−	0.642755i
$723$	5.04213	+	15.5181i	0.187519	+	0.577124i
$724$	−8.14721	+	5.91930i	−0.302789	+	0.219989i
$725$	−1.27702			−0.0474272
$726$	−10.9490	−	1.05798i	−0.406356	−	0.0392651i
$727$	−10.9451			−0.405933			−0.202966	−	0.979186i	$-0.565058\pi$
$727$	−10.9451			−0.405933			−0.202966	+	0.979186i	$0.565058\pi$
$728$	4.47770	−	3.25324i	0.165955	−	0.120573i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	−8.52504	+	26.2374i	−0.315526	+	0.971089i
$731$	9.26020	+	6.72793i	0.342501	+	0.248841i
$732$	−4.11030	−	2.98631i	−0.151921	−	0.110377i
$733$	7.19112	−	22.1320i	0.265610	−	0.817463i	−0.725942	−	0.687756i	$-0.758596\pi$
$733$	7.19112	−	22.1320i	0.265610	−	0.817463i	0.991552	−	0.129708i	$-0.0414039\pi$
$734$	3.70047	+	11.3889i	0.136587	+	0.420371i
$735$	−1.69998	+	1.23511i	−0.0627048	+	0.0455577i
$736$	1.37084			0.0505298
$737$	−30.5686	+	8.32846i	−1.12601	+	0.306783i
$738$	−11.1819			−0.411611
$739$	37.9202	−	27.5506i	1.39492	−	1.01347i	0.399611	−	0.916685i	$-0.369145\pi$
$739$	37.9202	−	27.5506i	1.39492	−	1.01347i	0.995306	−	0.0967819i	$-0.0308549\pi$
$740$	−2.34210	−	7.20823i	−0.0860971	−	0.264980i
$741$	1.56787	−	4.82540i	0.0575971	−	0.177266i
$742$	5.76181	+	4.18620i	0.211523	+	0.153680i
$743$	36.4613	+	26.4907i	1.33763	+	0.971848i	0.999527	+	0.0307409i	$0.00978667\pi$
$743$	36.4613	+	26.4907i	1.33763	+	0.971848i	0.338107	+	0.941108i	$0.390213\pi$
$744$	3.12703	−	9.62402i	0.114643	−	0.352834i
$745$	5.80784	+	17.8747i	0.212783	+	0.654878i
$746$	9.34714	−	6.79110i	0.342223	−	0.248640i
$747$	−11.5527			−0.422693
$748$	−3.84983	+	4.79515i	−0.140764	+	0.175328i
$749$	−8.99409			−0.328637
$750$	−9.49366	+	6.89755i	−0.346659	+	0.251863i
$751$	−13.0175	−	40.0639i	−0.475017	−	1.46195i	−0.845935	−	0.533286i	$-0.820957\pi$
$751$	−13.0175	−	40.0639i	−0.475017	−	1.46195i	0.370918	−	0.928665i	$-0.379043\pi$
$752$	1.29311	−	3.97978i	0.0471548	−	0.145128i
$753$	18.0657	+	13.1255i	0.658350	+	0.478320i
$754$	−9.78193	−	7.10699i	−0.356237	−	0.258821i
$755$	11.6490	−	35.8521i	0.423952	−	1.30479i
$756$	0.309017	+	0.951057i	0.0112388	+	0.0345896i
$757$	−33.8613	+	24.6017i	−1.23071	+	0.894164i	−0.996943	−	0.0781286i	$-0.975106\pi$
$757$	−33.8613	+	24.6017i	−1.23071	+	0.894164i	−0.233768	+	0.972292i	$0.575106\pi$
$758$	23.0875			0.838575
$759$	2.49221	+	3.80265i	0.0904616	+	0.138027i
$760$	1.92627			0.0698732
$761$	20.6884	−	15.0310i	0.749953	−	0.544873i	−0.145859	−	0.989305i	$-0.546595\pi$
$761$	20.6884	−	15.0310i	0.749953	−	0.544873i	0.895812	+	0.444433i	$0.146595\pi$
$762$	4.10342	+	12.6290i	0.148651	+	0.457501i
$763$	3.50344	−	10.7825i	0.126833	−	0.390352i
$764$	−4.52152	−	3.28508i	−0.163583	−	0.118850i
$765$	3.15194	+	2.29002i	0.113959	+	0.0827959i
$766$	9.86523	−	30.3620i	0.356445	−	1.09703i
$767$	−14.8058	−	45.5677i	−0.534608	−	1.64535i
$768$	0.809017	−	0.587785i	0.0291929	−	0.0212099i
$769$	−8.94577			−0.322593			−0.161296	−	0.986906i	$-0.551568\pi$
$769$	−8.94577			−0.322593			−0.161296	+	0.986906i	$0.551568\pi$
$770$	−0.335537	+	6.96113i	−0.0120919	+	0.250862i
$771$	−20.7930			−0.748842
$772$	7.59221	−	5.51607i	0.273250	−	0.198528i
$773$	14.6439	+	45.0692i	0.526704	+	1.62103i	0.760922	+	0.648843i	$0.224747\pi$
$773$	14.6439	+	45.0692i	0.526704	+	1.62103i	−0.234219	+	0.972184i	$0.575253\pi$
$774$	1.90771	−	5.87131i	0.0685710	−	0.211040i
$775$	4.78558	+	3.47693i	0.171903	+	0.124895i
$776$	4.62703	+	3.36174i	0.166101	+	0.120679i
$777$	1.11460	−	3.43037i	0.0399859	−	0.123064i
$778$	7.44078	+	22.9004i	0.266765	+	0.821018i
$779$	−8.29284	+	6.02510i	−0.297122	+	0.215872i
$780$	−11.6301			−0.416425
$781$	−4.46171	−	1.69125i	−0.159652	−	0.0605175i
$782$	2.54168			0.0908902
$783$	1.76737	−	1.28407i	0.0631607	−	0.0458889i
$784$	0.309017	+	0.951057i	0.0110363	+	0.0339663i
$785$	0.279706	−	0.860845i	0.00998312	−	0.0307249i
$786$	8.36093	+	6.07457i	0.298224	+	0.216673i
$787$	14.6096	+	10.6145i	0.520775	+	0.378365i	0.816896	−	0.576785i	$-0.195693\pi$
$787$	14.6096	+	10.6145i	0.520775	+	0.378365i	−0.296121	+	0.955150i	$0.595693\pi$
$788$	−5.87554	+	18.0831i	−0.209308	+	0.644182i
$789$	−0.104251	−	0.320852i	−0.00371144	−	0.0114226i
$790$	−30.1955	+	21.9383i	−1.07431	+	0.780529i
$791$	−0.852441			−0.0303093
$792$	3.10130	+	1.17557i	0.110200	+	0.0417721i
$793$	28.1198			0.998564
$794$	3.80206	−	2.76236i	0.134930	−	0.0980324i
$795$	−4.62456	−	14.2329i	−0.164016	−	0.504790i
$796$	−4.10425	+	12.6316i	−0.145471	+	0.447715i
$797$	8.84841	+	6.42874i	0.313427	+	0.227718i	0.733365	−	0.679835i	$-0.237948\pi$
$797$	8.84841	+	6.42874i	0.313427	+	0.227718i	−0.419939	+	0.907552i	$0.637948\pi$
$798$	0.741631	+	0.538826i	0.0262534	+	0.0190742i
$799$	2.39756	−	7.37892i	0.0848194	−	0.261047i
$800$	0.180638	+	0.555947i	0.00638652	+	0.0196557i
$801$	−3.13604	+	2.27846i	−0.110806	+	0.0805055i
$802$	27.5049			0.971232
$803$	−2.09643	+	43.4930i	−0.0739814	+	1.53484i
$804$	9.55274			0.336899
$805$	2.33041	−	1.69314i	0.0821360	−	0.0596753i
$806$	17.3073	+	53.2665i	0.609625	+	1.87623i
$807$	−5.68854	+	17.5075i	−0.200246	+	0.616294i
$808$	4.80128	+	3.48833i	0.168908	+	0.122719i
$809$	−2.54987	−	1.85259i	−0.0896486	−	0.0651335i	0.542058	−	0.840341i	$-0.317645\pi$
$809$	−2.54987	−	1.85259i	−0.0896486	−	0.0651335i	−0.631707	+	0.775208i	$0.717645\pi$
$810$	0.649336	−	1.99845i	0.0228153	−	0.0702184i
$811$	−6.60359	−	20.3237i	−0.231883	−	0.713663i	−0.997520	−	0.0703896i	$-0.977576\pi$
$811$	−6.60359	−	20.3237i	−0.231883	−	0.713663i	0.765636	−	0.643274i	$-0.222424\pi$
$812$	1.76737	−	1.28407i	0.0620225	−	0.0450620i
$813$	16.5141			0.579173
$814$	−6.55742	−	10.0054i	−0.229838	−	0.350689i
$815$	37.8233			1.32489
$816$	1.50000	−	1.08981i	0.0525105	−	0.0381511i
$817$	−1.74880	−	5.38227i	−0.0611829	−	0.188302i
$818$	5.83019	−	17.9435i	0.203848	−	0.627379i
$819$	−4.47770	−	3.25324i	−0.156463	−	0.113677i
$820$	19.0091	+	13.8109i	0.663825	+	0.482297i
$821$	2.16199	−	6.65392i	0.0754540	−	0.232223i	−0.906215	−	0.422817i	$-0.861041\pi$
$821$	2.16199	−	6.65392i	0.0754540	−	0.232223i	0.981669	+	0.190594i	$0.0610413\pi$
$822$	4.24163	+	13.0544i	0.147944	+	0.455324i
$823$	8.72924	−	6.34217i	0.304282	−	0.221074i	−0.425157	−	0.905120i	$-0.639781\pi$
$823$	8.72924	−	6.34217i	0.304282	−	0.221074i	0.729439	+	0.684046i	$0.239781\pi$
$824$	−4.06782			−0.141709
$825$	−1.21377	+	1.51180i	−0.0422579	+	0.0526342i
$826$	8.65673			0.301206
$827$	1.63330	−	1.18666i	0.0567953	−	0.0412642i	−0.559025	−	0.829151i	$-0.688825\pi$
$827$	1.63330	−	1.18666i	0.0567953	−	0.0412642i	0.615821	+	0.787886i	$0.288825\pi$
$828$	−0.423613	−	1.30375i	−0.0147216	−	0.0453083i
$829$	−8.86123	+	27.2720i	−0.307763	+	0.947197i	0.670869	+	0.741576i	$0.265921\pi$
$829$	−8.86123	+	27.2720i	−0.307763	+	0.947197i	−0.978632	+	0.205621i	$0.934079\pi$
$830$	19.6395	+	14.2689i	0.681696	+	0.495281i
$831$	−3.47431	−	2.52423i	−0.120523	−	0.0875647i
$832$	−1.71033	+	5.26385i	−0.0592950	+	0.182491i
$833$	0.572949	+	1.76336i	0.0198515	+	0.0610967i
$834$	8.37767	−	6.08673i	0.290095	−	0.210766i
$835$	14.6766			0.507903
$836$	2.93344	−	0.799220i	0.101455	−	0.0276416i
$837$	−10.1193			−0.349774
$838$	−29.2656	+	21.2627i	−1.01096	+	0.734508i
$839$	1.46211	+	4.49991i	0.0504776	+	0.155354i	0.973118	−	0.230308i	$-0.0739732\pi$
$839$	1.46211	+	4.49991i	0.0504776	+	0.155354i	−0.922640	+	0.385662i	$0.873973\pi$
$840$	0.649336	−	1.99845i	0.0224042	−	0.0689531i
$841$	19.6005	+	14.2406i	0.675880	+	0.491055i
$842$	−19.7395	−	14.3416i	−0.680268	−	0.494244i
$843$	8.42410	−	25.9267i	0.290141	−	0.892963i
$844$	−7.58800	−	23.3534i	−0.261190	−	0.803859i
$845$	29.9764	−	21.7791i	1.03122	−	0.749225i
$846$	−4.18459			−0.143869
$847$	2.37723	+	10.7401i	0.0816827	+	0.369033i
$848$	−7.12199			−0.244570
$849$	−13.7040	+	9.95653i	−0.470320	+	0.341707i
$850$	0.334921	+	1.03078i	0.0114877	+	0.0353555i
$851$	−1.52793	+	4.70249i	−0.0523769	+	0.161199i
$852$	1.16390	+	0.845623i	0.0398745	+	0.0289706i
$853$	−4.10398	−	2.98172i	−0.140518	−	0.102092i	0.515306	−	0.857006i	$-0.327678\pi$
$853$	−4.10398	−	2.98172i	−0.140518	−	0.102092i	−0.655823	+	0.754914i	$0.727678\pi$
$854$	−1.56999	+	4.83194i	−0.0537241	+	0.165346i
$855$	−0.595250	−	1.83199i	−0.0203571	−	0.0626528i
$856$	7.27637	−	5.28659i	0.248701	−	0.180692i
$857$	−53.0300			−1.81147			−0.905736	−	0.423843i	$-0.860681\pi$
$857$	−53.0300			−1.81147			−0.905736	+	0.423843i	$0.860681\pi$
$858$	−17.7111	+	4.82540i	−0.604646	+	0.164737i
$859$	−23.4919			−0.801532			−0.400766	−	0.916180i	$-0.631256\pi$
$859$	−23.4919			−0.801532			−0.400766	+	0.916180i	$0.631256\pi$
$860$	−10.4948	+	7.62491i	−0.357869	+	0.260007i
$861$	3.45540	+	10.6346i	0.117760	+	0.362427i
$862$	−5.07556	+	15.6210i	−0.172874	+	0.532052i
$863$	−13.6201	−	9.89560i	−0.463635	−	0.336850i	0.331321	−	0.943518i	$-0.392506\pi$
$863$	−13.6201	−	9.89560i	−0.463635	−	0.336850i	−0.794955	+	0.606668i	$0.792506\pi$
$864$	−0.809017	−	0.587785i	−0.0275233	−	0.0199969i
$865$	−9.60839	+	29.5716i	−0.326695	+	1.00546i
$866$	−12.0477	−	37.0790i	−0.409397	−	1.26000i
$867$	−10.9721	+	7.97172i	−0.372633	+	0.270734i
$868$	−10.1193			−0.343471
$869$	−36.8812	+	45.9373i	−1.25111	+	1.55831i
$870$	−4.59047			−0.155631
$871$	−42.7743	+	31.0773i	−1.44935	+	1.05302i
$872$	3.50344	+	10.7825i	0.118641	+	0.365141i
$873$	1.76737	−	5.43941i	0.0598164	−	0.184096i
$874$	−1.01666	−	0.738645i	−0.0343890	−	0.0249850i
$875$	9.49366	+	6.89755i	0.320944	+	0.233180i
$876$	4.05704	−	12.4863i	0.137075	−	0.421873i
$877$	−9.26622	−	28.5185i	−0.312898	−	0.963001i	−0.976611	−	0.215014i	$-0.931020\pi$
$877$	−9.26622	−	28.5185i	−0.312898	−	0.963001i	0.663713	−	0.747987i	$-0.268980\pi$
$878$	−21.1394	+	15.3587i	−0.713420	+	0.518330i
$879$	−5.33736			−0.180025
$880$	−3.82019	−	5.82889i	−0.128779	−	0.196492i
$881$	−10.8375			−0.365125			−0.182562	−	0.983194i	$-0.558439\pi$
$881$	−10.8375			−0.365125			−0.182562	+	0.983194i	$0.558439\pi$
$882$	0.809017	−	0.587785i	0.0272410	−	0.0197918i
$883$	−15.6368	−	48.1253i	−0.526222	−	1.61954i	−0.761887	−	0.647710i	$-0.775727\pi$
$883$	−15.6368	−	48.1253i	−0.526222	−	1.61954i	0.235665	−	0.971834i	$-0.424273\pi$
$884$	−3.17112	+	9.75972i	−0.106656	+	0.328255i
$885$	−14.7163	−	10.6920i	−0.494683	−	0.359408i
$886$	−22.0233	−	16.0008i	−0.739886	−	0.537559i
$887$	3.02459	−	9.30873i	0.101556	−	0.312557i	−0.887351	−	0.461095i	$-0.847457\pi$
$887$	3.02459	−	9.30873i	0.101556	−	0.312557i	0.988907	+	0.148538i	$0.0474568\pi$
$888$	1.11460	+	3.43037i	0.0374034	+	0.115116i
$889$	10.7429	−	7.80517i	0.360305	−	0.261777i
$890$	8.14536			0.273033
$891$	0.159681	−	3.31278i	0.00534951	−	0.110982i
$892$	18.9707			0.635186
$893$	−3.10342	+	2.25477i	−0.103852	+	0.0754529i
$894$	−2.76393	−	8.50651i	−0.0924397	−	0.284500i
$895$	−9.64254	+	29.6767i	−0.322315	+	0.991983i
$896$	−0.809017	−	0.587785i	−0.0270274	−	0.0196365i
$897$	6.13821	+	4.45967i	0.204949	+	0.148904i
$898$	−12.3015	+	37.8603i	−0.410508	+	1.26341i
$899$	6.83129	+	21.0245i	0.227836	+	0.701208i
$900$	0.472917	−	0.343594i	0.0157639	−	0.0114531i
$901$	−13.2049			−0.439919
$902$	34.6784	+	13.1451i	1.15466	+	0.437684i
$903$	−6.17346			−0.205440
$904$	0.689639	−	0.501052i	0.0229370	−	0.0166647i
$905$	−6.53914	−	20.1254i	−0.217368	−	0.668991i
$906$	−5.54374	+	17.0619i	−0.184178	+	0.566843i
$907$	47.8300	+	34.7505i	1.58817	+	1.15387i	0.906494	+	0.422219i	$0.138749\pi$
$907$	47.8300	+	34.7505i	1.58817	+	1.15387i	0.681676	+	0.731654i	$0.261251\pi$
$908$	−19.3789	−	14.0796i	−0.643112	−	0.467248i
$909$	1.83393	−	5.64424i	0.0608275	−	0.187208i
$910$	3.59391	+	11.0609i	0.119137	+	0.366665i
$911$	−40.5330	+	29.4490i	−1.34292	+	0.975688i	−0.343588	+	0.939121i	$0.611642\pi$
$911$	−40.5330	+	29.4490i	−1.34292	+	0.975688i	−0.999331	+	0.0365669i	$0.988358\pi$
$912$	−0.916706			−0.0303552
$913$	35.8285	+	13.5811i	1.18575	+	0.449468i
$914$	−7.09711			−0.234751
$915$	8.63695	−	6.27511i	0.285529	−	0.207449i
$916$	−3.65329	−	11.2437i	−0.120708	−	0.371501i
$917$	3.19359	−	9.82886i	0.105462	−	0.324578i
$918$	−1.50000	−	1.08981i	−0.0495074	−	0.0359692i
$919$	−26.6030	−	19.3282i	−0.877551	−	0.637578i	0.0550517	−	0.998484i	$-0.482468\pi$
$919$	−26.6030	−	19.3282i	−0.877551	−	0.637578i	−0.932602	+	0.360906i	$0.882468\pi$
$920$	−0.890136	+	2.73956i	−0.0293469	+	0.0903205i
$921$	−3.21802	−	9.90404i	−0.106037	−	0.326349i
$922$	13.5108	−	9.81619i	0.444955	−	0.323279i
$923$	−7.96260			−0.262092
$924$	0.159681	−	3.31278i	0.00525312	−	0.108982i
$925$	−2.10844			−0.0693252
$926$	16.6150	−	12.0715i	0.546003	−	0.396694i
$927$	1.25703	+	3.86873i	0.0412861	+	0.127066i
$928$	−0.675075	+	2.07767i	−0.0221604	+	0.0682028i
$929$	−31.6023	−	22.9604i	−1.03684	−	0.753306i	−0.0671710	−	0.997741i	$-0.521397\pi$
$929$	−31.6023	−	22.9604i	−1.03684	−	0.753306i	−0.969666	+	0.244436i	$0.921397\pi$
$930$	17.2026	+	12.4985i	0.564097	+	0.409840i
$931$	0.283278	−	0.871839i	0.00928405	−	0.0285734i
$932$	−5.63472	−	17.3419i	−0.184571	−	0.568053i
$933$	−18.7978	+	13.6574i	−0.615413	+	0.447123i
$934$	−6.06626			−0.198494
$935$	−7.08303	−	10.8074i	−0.231640	−	0.353439i
$936$	5.53474			0.180909
$937$	−9.45053	+	6.86622i	−0.308735	+	0.224309i	−0.731354	−	0.681998i	$-0.761111\pi$
$937$	−9.45053	+	6.86622i	−0.308735	+	0.224309i	0.422618	+	0.906308i	$0.361111\pi$
$938$	−2.95196	−	9.08520i	−0.0963849	−	0.296642i
$939$	4.27476	−	13.1564i	0.139502	−	0.429341i
$940$	7.11373	+	5.16843i	0.232024	+	0.168576i
$941$	−36.1559	−	26.2688i	−1.17865	−	0.856339i	−0.186630	−	0.982430i	$-0.559757\pi$
$941$	−36.1559	−	26.2688i	−1.17865	−	0.856339i	−0.992019	+	0.126091i	$0.959757\pi$
$942$	−0.133111	+	0.409674i	−0.00433699	+	0.0133479i
$943$	−4.73680	−	14.5784i	−0.154251	−	0.474737i
$944$	−7.00344	+	5.08830i	−0.227942	+	0.165610i
$945$	−2.10130			−0.0683551
$946$	−12.8185	+	15.9660i	−0.416765	+	0.519101i
$947$	−16.2970			−0.529582			−0.264791	−	0.964306i	$-0.585303\pi$
$947$	−16.2970			−0.529582			−0.264791	+	0.964306i	$0.585303\pi$
$948$	14.3699	−	10.4404i	0.466714	−	0.339087i
$949$	22.4547	+	69.1084i	0.728909	+	2.24335i
$950$	0.165592	−	0.509640i	0.00537251	−	0.0165349i
$951$	−12.2631	−	8.90964i	−0.397657	−	0.288915i
$952$	−1.50000	−	1.08981i	−0.0486153	−	0.0353211i
$953$	1.52918	−	4.70632i	0.0495349	−	0.152453i	−0.923229	−	0.384249i	$-0.874460\pi$
$953$	1.52918	−	4.70632i	0.0495349	−	0.152453i	0.972764	+	0.231796i	$0.0744603\pi$
$954$	2.20081	+	6.77341i	0.0712540	+	0.219297i
$955$	9.50105	−	6.90292i	0.307447	−	0.223373i
$956$	−6.27041			−0.202800
$957$	−6.99065	+	1.90461i	−0.225976	+	0.0615673i
$958$	40.9803			1.32401
$959$	11.1047	−	8.06806i	0.358591	−	0.260531i
$960$	0.649336	+	1.99845i	0.0209572	+	0.0644997i
$961$	22.0639	−	67.9056i	0.711738	−	2.19050i
$962$	−16.1506	−	11.7341i	−0.520718	−	0.378324i
$963$	−7.27637	−	5.28659i	−0.234478	−	0.170358i
$964$	−5.04213	+	15.5181i	−0.162396	+	0.499804i
$965$	6.09369	+	18.7544i	0.196163	+	0.603727i
$966$	−1.10903	+	0.805760i	−0.0356826	+	0.0259249i
$967$	5.26257			0.169233			0.0846164	−	0.996414i	$-0.473034\pi$
$967$	5.26257			0.169233			0.0846164	+	0.996414i	$0.473034\pi$
$968$	−8.23607	−	7.29158i	−0.264717	−	0.234360i
$969$	−1.69967			−0.0546012
$970$	−9.72277	+	7.06400i	−0.312179	+	0.226812i
$971$	−3.72167	−	11.4541i	−0.119434	−	0.367580i	0.873412	−	0.486982i	$-0.161902\pi$
$971$	−3.72167	−	11.4541i	−0.119434	−	0.367580i	−0.992846	+	0.119402i	$0.961902\pi$
$972$	−0.309017	+	0.951057i	−0.00991172	+	0.0305052i
$973$	−8.37767	−	6.08673i	−0.268576	−	0.195132i
$974$	0.474261	+	0.344571i	0.0151963	+	0.0110408i
$975$	−0.999785	+	3.07702i	−0.0320187	+	0.0985435i
$976$	−1.56999	−	4.83194i	−0.0502543	−	0.154667i
$977$	39.6224	−	28.7874i	1.26763	−	0.920990i	0.268528	−	0.963272i	$-0.413463\pi$
$977$	39.6224	−	28.7874i	1.26763	−	0.920990i	0.999106	+	0.0422817i	$0.0134627\pi$
$978$	−18.0000			−0.575577
$979$	12.4043	−	3.37956i	0.396442	−	0.108011i
$980$	−2.10130			−0.0671234
$981$	9.17212	−	6.66394i	0.292843	−	0.212763i
$982$	−0.151194	−	0.465326i	−0.00482478	−	0.0148492i
$983$	−0.497075	+	1.52984i	−0.0158542	+	0.0487943i	−0.958671	−	0.284518i	$-0.908166\pi$
$983$	−0.497075	+	1.52984i	−0.0158542	+	0.0487943i	0.942816	+	0.333312i	$0.108166\pi$
$984$	−9.04635	−	6.57256i	−0.288387	−	0.209525i
$985$	−32.3229	−	23.4840i	−1.02989	−	0.748261i
$986$	−1.25166	+	3.85221i	−0.0398609	+	0.122679i
$987$	1.29311	+	3.97978i	0.0411601	+	0.126678i
$988$	4.10473	−	2.98226i	0.130589	−	0.0948784i
$989$	8.46283			0.269102
$990$	−4.36310	+	5.43445i	−0.138669	+	0.172718i
$991$	39.9054			1.26764			0.633819	−	0.773482i	$-0.281487\pi$
$991$	39.9054			1.26764			0.633819	+	0.773482i	$0.281487\pi$
$992$	8.18668	−	5.94797i	0.259927	−	0.188848i
$993$	−1.01623	−	3.12762i	−0.0322489	−	0.0992520i
$994$	0.444570	−	1.36825i	0.0141009	−	0.0433981i
$995$	−22.5786	−	16.4043i	−0.715789	−	0.520051i
$996$	−9.34636	−	6.79053i	−0.296151	−	0.215166i
$997$	−7.08192	+	21.7959i	−0.224287	+	0.690283i	0.774077	+	0.633092i	$0.218214\pi$
$997$	−7.08192	+	21.7959i	−0.224287	+	0.690283i	−0.998363	+	0.0571913i	$0.981786\pi$
$998$	4.95918	+	15.2628i	0.156980	+	0.483135i
$999$	2.91805	−	2.12009i	0.0923230	−	0.0670766i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.j.h.421.2	yes	8
11.2	odd	10		5082.2.a.cd.1.1		4
11.4	even	5	inner	462.2.j.h.169.2	✓	8
11.9	even	5		5082.2.a.by.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.j.h.169.2	✓	8	11.4	even	5	inner
462.2.j.h.421.2	yes	8	1.1	even	1	trivial
5082.2.a.by.1.1		4	11.9	even	5
5082.2.a.cd.1.1		4	11.2	odd	10

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)

\(f(q)\)	\(=\)	\(q+(0.809017 - 0.587785i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(0.309017 - 0.951057i) q^{4} +(1.69998 + 1.23511i) q^{5} +(-0.809017 - 0.587785i) q^{6} +(-0.309017 + 0.951057i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(0.809017 - 0.587785i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(0.309017 - 0.951057i) q^{4} +(1.69998 + 1.23511i) q^{5} +(-0.809017 - 0.587785i) q^{6} +(-0.309017 + 0.951057i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(-0.809017 + 0.587785i) q^{9} +2.10130 q^{10} +(3.19998 - 0.871839i) q^{11} -1.00000 q^{12} +(4.47770 - 3.25324i) q^{13} +(0.309017 + 0.951057i) q^{14} +(0.649336 - 1.99845i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-1.50000 - 1.08981i) q^{17} +(-0.309017 + 0.951057i) q^{18} +(0.283278 + 0.871839i) q^{19} +(1.69998 - 1.23511i) q^{20} +1.00000 q^{21} +(2.07639 - 2.58624i) q^{22} -1.37084 q^{23} +(-0.809017 + 0.587785i) q^{24} +(-0.180638 - 0.555947i) q^{25} +(1.71033 - 5.26385i) q^{26} +(0.809017 + 0.587785i) q^{27} +(0.809017 + 0.587785i) q^{28} +(0.675075 - 2.07767i) q^{29} +(-0.649336 - 1.99845i) q^{30} +(-8.18668 + 5.94797i) q^{31} -1.00000 q^{32} +(-1.81802 - 2.77395i) q^{33} -1.85410 q^{34} +(-1.69998 + 1.23511i) q^{35} +(0.309017 + 0.951057i) q^{36} +(1.11460 - 3.43037i) q^{37} +(0.741631 + 0.538826i) q^{38} +(-4.47770 - 3.25324i) q^{39} +(0.649336 - 1.99845i) q^{40} +(3.45540 + 10.6346i) q^{41} +(0.809017 - 0.587785i) q^{42} -6.17346 q^{43} +(0.159681 - 3.31278i) q^{44} -2.10130 q^{45} +(-1.10903 + 0.805760i) q^{46} +(1.29311 + 3.97978i) q^{47} +(-0.309017 + 0.951057i) q^{48} +(-0.809017 - 0.587785i) q^{49} +(-0.472917 - 0.343594i) q^{50} +(-0.572949 + 1.76336i) q^{51} +(-1.71033 - 5.26385i) q^{52} +(5.76181 - 4.18620i) q^{53} +1.00000 q^{54} +(6.51674 + 2.47022i) q^{55} +1.00000 q^{56} +(0.741631 - 0.538826i) q^{57} +(-0.675075 - 2.07767i) q^{58} +(2.67508 - 8.23304i) q^{59} +(-1.69998 - 1.23511i) q^{60} +(4.11030 + 2.98631i) q^{61} +(-3.12703 + 9.62402i) q^{62} +(-0.309017 - 0.951057i) q^{63} +(-0.809017 + 0.587785i) q^{64} +11.6301 q^{65} +(-3.10130 - 1.17557i) q^{66} -9.55274 q^{67} +(-1.50000 + 1.08981i) q^{68} +(0.423613 + 1.30375i) q^{69} +(-0.649336 + 1.99845i) q^{70} +(-1.16390 - 0.845623i) q^{71} +(0.809017 + 0.587785i) q^{72} +(-4.05704 + 12.4863i) q^{73} +(-1.11460 - 3.43037i) q^{74} +(-0.472917 + 0.343594i) q^{75} +0.916706 q^{76} +(-0.159681 + 3.31278i) q^{77} -5.53474 q^{78} +(-14.3699 + 10.4404i) q^{79} +(-0.649336 - 1.99845i) q^{80} +(0.309017 - 0.951057i) q^{81} +(9.04635 + 6.57256i) q^{82} +(9.34636 + 6.79053i) q^{83} +(0.309017 - 0.951057i) q^{84} +(-1.20394 - 3.70533i) q^{85} +(-4.99444 + 3.62867i) q^{86} -2.18459 q^{87} +(-1.81802 - 2.77395i) q^{88} +3.87635 q^{89} +(-1.69998 + 1.23511i) q^{90} +(1.71033 + 5.26385i) q^{91} +(-0.423613 + 1.30375i) q^{92} +(8.18668 + 5.94797i) q^{93} +(3.38540 + 2.45964i) q^{94} +(-0.595250 + 1.83199i) q^{95} +(0.309017 + 0.951057i) q^{96} +(-4.62703 + 3.36174i) q^{97} -1.00000 q^{98} +(-2.07639 + 2.58624i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} - 2 q^{6} + 2 q^{7} + 2 q^{8} - 2 q^{9}+O(q^{10}) \) 8 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 - 2 * q^6 + 2 * q^7 + 2 * q^8 - 2 * q^9	\( 8 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} - 2 q^{6} + 2 q^{7} + 2 q^{8} - 2 q^{9} - 8 q^{10} + 10 q^{11} - 8 q^{12} + 10 q^{13} - 2 q^{14} + 2 q^{15} - 2 q^{16} - 12 q^{17} + 2 q^{18} + 2 q^{19} - 2 q^{20} + 8 q^{21} - 2 q^{24} - 4 q^{25} + 2 q^{27} + 2 q^{28} - 2 q^{29} - 2 q^{30} - 4 q^{31} - 8 q^{32} + 10 q^{33} + 12 q^{34} + 2 q^{35} - 2 q^{36} + 30 q^{37} - 2 q^{38} - 10 q^{39} + 2 q^{40} - 24 q^{41} + 2 q^{42} - 20 q^{43} + 8 q^{45} - 20 q^{46} - 6 q^{47} + 2 q^{48} - 2 q^{49} + 14 q^{50} - 18 q^{51} + 24 q^{53} + 8 q^{54} + 68 q^{55} + 8 q^{56} - 2 q^{57} + 2 q^{58} + 14 q^{59} + 2 q^{60} - 12 q^{61} + 4 q^{62} + 2 q^{63} - 2 q^{64} - 44 q^{65} - 12 q^{67} - 12 q^{68} + 20 q^{69} - 2 q^{70} + 4 q^{71} + 2 q^{72} - 34 q^{73} - 30 q^{74} + 14 q^{75} - 8 q^{76} - 20 q^{78} - 22 q^{79} - 2 q^{80} - 2 q^{81} - 6 q^{82} + 12 q^{83} - 2 q^{84} + 18 q^{85} - 30 q^{86} - 8 q^{87} + 10 q^{88} + 44 q^{89} + 2 q^{90} - 20 q^{92} + 4 q^{93} + 6 q^{94} - 44 q^{95} - 2 q^{96} - 8 q^{97} - 8 q^{98}+O(q^{100}) \) 8 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 - 2 * q^6 + 2 * q^7 + 2 * q^8 - 2 * q^9 - 8 * q^10 + 10 * q^11 - 8 * q^12 + 10 * q^13 - 2 * q^14 + 2 * q^15 - 2 * q^16 - 12 * q^17 + 2 * q^18 + 2 * q^19 - 2 * q^20 + 8 * q^21 - 2 * q^24 - 4 * q^25 + 2 * q^27 + 2 * q^28 - 2 * q^29 - 2 * q^30 - 4 * q^31 - 8 * q^32 + 10 * q^33 + 12 * q^34 + 2 * q^35 - 2 * q^36 + 30 * q^37 - 2 * q^38 - 10 * q^39 + 2 * q^40 - 24 * q^41 + 2 * q^42 - 20 * q^43 + 8 * q^45 - 20 * q^46 - 6 * q^47 + 2 * q^48 - 2 * q^49 + 14 * q^50 - 18 * q^51 + 24 * q^53 + 8 * q^54 + 68 * q^55 + 8 * q^56 - 2 * q^57 + 2 * q^58 + 14 * q^59 + 2 * q^60 - 12 * q^61 + 4 * q^62 + 2 * q^63 - 2 * q^64 - 44 * q^65 - 12 * q^67 - 12 * q^68 + 20 * q^69 - 2 * q^70 + 4 * q^71 + 2 * q^72 - 34 * q^73 - 30 * q^74 + 14 * q^75 - 8 * q^76 - 20 * q^78 - 22 * q^79 - 2 * q^80 - 2 * q^81 - 6 * q^82 + 12 * q^83 - 2 * q^84 + 18 * q^85 - 30 * q^86 - 8 * q^87 + 10 * q^88 + 44 * q^89 + 2 * q^90 - 20 * q^92 + 4 * q^93 + 6 * q^94 - 44 * q^95 - 2 * q^96 - 8 * q^97 - 8 * q^98

Introduction

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